text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
Badge Will Call
Retail Summits
Show Info & Policies
Reserve Hotel Rooms
Register for Badges
2019 Badge Receipts
Top 100 Dealer Awards
NAMM Russia
2020 Summer NAMM
Global Report
NAMM Standards
NAMM Young Professionals
Playback Blog
Join NAMM
NAMM U
Music History Project Podcast
Music Research
SupportMusic Coalition on Coalitions
Music Advocacy Fly-In
Chris Climer
Chris Climer wanted to play the piano and organ when he was 16 years old. He did not have the money to purchase an instrument so he made an arrangement to work in a music store in Arkansas to earn the money to make the payments –and he has been in the industry ever since! He learned to deliver...
Music Retail, Deceased, Pianos, Arkansas, Texas, Baldwin Piano Company, PTG, Piano Technicians
Jim Coffin
Jim Coffin was instantly recognized at any given trade show or industry meeting as the energetic advocate for music and music making. Jim's career as a music director and educator includes authoring several important method tools including the popular "Performing Percussionist." The book has been...
Deceased, Music Education, Percussion, Drums, PAS, Music Advocacy, Artist Relations
Buddy Collette
Buddy Collette changed music in more than one way. As a noted reed man, he played jazz along some of the greatest players in history including his boyhood friend, Charlie Mingus. Buddy was instrumental in the birth of the Los Angeles jazz scene. Beginning in the late 1940s, Buddy set out to break...
Jazz, Los Angeles CA, Saxophones, Band and Orchestra, Flutes, AFM, Clarinets, Deceased, Civil Rights, Charles Mingus
Bill Collings
Bill Collings' passion for guitars may have started on his father's workbench when as a boy he tinkered with woods and making things. His father's background in engineering was also an influence and before too long Bill made up his mind that he wanted to build guitars. Unlike many luthiers, Bill...
Luthiers, Music Manufacturing, Deceased, Guitars, Texas
John Connolly established the Connolly Music Company (originally Connolly & Co., Inc.) back in 1970. Best known for distributing such brands as Thomastik-Infeld and König & Meyer, the company remains a family owned enterprise, with John's son, Jake, now at the helm. In 1954 John was hired...
Classical Guitar Strings, The Beatles, Music Manufacturing, Music Wholesale-Distribution, New York State, String Instruments, Instrument Strings, Hofner Bass, Deceased
Dick Contino
Dick Contino had a series of hit recordings and popular television appearances in the 1950s playing his trusty accordion. By the end of that decade, he was hired by M. H. Berlin at Chicago Musical Instruments (CMI) to introduce a string of innovative products. It was Dick who first introduced the...
Accordions, CMI, Television, Deceased
Jack Cookerly
Jack Cookerly was an accordionist who was among the first to connect the instrument to the technology behind the electronic keyboard. He was chief engineer at Lowrey Organs and designed a number of unique and important advancements for the electronic organ. The resulting efforts can be found in the...
Organs, Lowrey Organs, Songwriter, Music Manufacturing, Product Engineers, Deceased, Lowrey MX1
David Cooper recalled, with a warm smile, when his father took him to his first NAMM Show. The Cooper Piano and Organ Store in Georgia began in 1905; therefore, David did not just grow up in the business--his life was always involved in music. The store enjoyed great success over the years due to...
Georgia, Music Retail, Pianos, Organs, Deceased, NAMM Board of Directors-Interviewed
Larry Coryell enjoyed a long career as a jazz guitarist. In addition to touring and recording on his own, Larry worked with some of the greatest names in jazz. Over the years he developed his own method of playing, and wrote a series of teaching books and DVDs. His educational publications have...
Jazz, Guitars, Deceased, Music Publishing, Method Book Author
Robert C. Cosgrove
Robert C. Cosgrove was hired by the Baldwin Piano Company following World War II and later worked his way up to vice president. He witnessed the re-building of the production line, which during the war was used to assemble wooden gliders. Bob also took part in what he described as a historic...
AMC, Baldwin Piano Company, Music Manufacturing, Pianos, Deceased, Centenarians, Henry Z. Steinway
Antitrust Compliance
Bands@NAMM
General Show Info & Policies
Other NAMM Websites
NAMM Foundation
Museum of Making Music
TEC Awards
The NAMM Store
© NAMM 2020 All rights reserved. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,402 |
<?php
namespace SilverStripe\Omnipay\Admin;
use SilverStripe\Omnipay\GatewayInfo;
use SilverStripe\Control\Controller;
use SilverStripe\Control\Director;
use SilverStripe\Dev\DebugView;
/**
* Development tools for payments
*
* @package payment
*/
class PaymentDevelopmentAdmin extends Controller
{
public function index()
{
$renderer = DebugView::create();
$renderer->renderHeader();
$renderer->renderInfo("Installed Omnipay Payment Gateways", Director::absoluteBaseURL());
$types = $this->PaymentTypes();
echo "<table style=\"font-size:12px;\" border=1 cellspacing=0>
<thead>
<tr>
<td>Short Name</td>
<td>Full name</td>
<td>Purchase</td>
<td>Authorize</td>
<td>CompleteAuthorize</td>
<td>Capture</td>
<td>Complete Purchase</td>
<td>Refund</td>
<td>Void</td>
<td>Create Card</td>
<td>Delete Card</td>
<td>Update Card</td>
<td>Accept Notification</td>
</tr>
</thead>
<tbody>";
foreach ($types as $gateway) {
echo "<tr>".
"<td>".$gateway->getShortName()."</td>".
"<td>".$gateway->getName()."</td>".
"<td>yes</td>". //purchase is always supported
"<td>".($gateway->supportsAuthorize() ? "yes" : "")."</td>".
"<td>".($gateway->supportsCompleteAuthorize() ? "yes" : "")."</td>".
"<td>".($gateway->supportsCapture() ? "yes" : "")."</td>".
"<td>".($gateway->supportsCompletePurchase() ? "yes" : "")."</td>".
"<td>".($gateway->supportsRefund() ? "yes" : "")."</td>".
"<td>".($gateway->supportsVoid() ? "yes" : "")."</td>".
"<td>".($gateway->supportsCreateCard() ? "yes" : "")."</td>".
"<td>".($gateway->supportsDeleteCard() ? "yes" : "")."</td>".
"<td>".($gateway->supportsUpdateCard() ? "yes" : "")."</td>".
"<td>".($gateway->supportsAcceptNotification() ? "yes" : "")."</td>".
"</tr>";
if ($this->request->getVar('defaults')) {
echo "<tr><td colspan=\"11\">";
var_dump($gateway->getDefaultParameters());
echo "</td></tr>";
}
}
echo "</tbody></table>";
$renderer->renderFooter();
}
/**
* Get all available payment types
*/
private function PaymentTypes()
{
$factory = new \Omnipay\Common\GatewayFactory;
// since the omnipay gateway factory only returns gateways from the composer.json extra data,
// we should merge it with user-defined gateways from Payment.allowed_gateways
$gateways = array_unique(array_merge(
$factory->find(),
array_keys(GatewayInfo::getSupportedGateways(false))
));
$supportedGateways = array();
array_walk($gateways, function ($name, $index) use (&$supportedGateways, &$factory) {
try {
$instance = $factory->create($name);
$supportedGateways[$name] = $instance;
} catch (\Exception $e) {
}
});
return $supportedGateways;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,898 |
{"url":"https:\/\/lingpipe-blog.com\/2009\/02\/16\/rennie-shih-teevan-and-karger-2003-tackling-poor-assumptions-naive-bayes-text-classifiers\/","text":"## Rennie, Shih, Teevan, and Karger (2003) Tackling the Poor Assumptions of Naive Bayes Text\u00a0Classifiers\n\nIt turns out Nigam et al. weren\u2019t the only ones fiddling with naive Bayes. I just finished:\n\nRennie et al. introduce four distinct modifications to Naive Bayes:\n\n1. log term frequency normalization, to cope with overdispersion,\n2. length normalization, to dampen inter-term correlation,\n3. inverse doc frequency normalization, to cope with noise from common features, and\n4. complementation, to cope with low-count bias.\n\n### Log Term Frequency (TF)\n\nWord counts tend to be overdispersed relative to what is predicted by a multinomial. Simply put, two or three occurrences of a word in a document are much more common than predicted by multinomials. Ken Church called this \u201cburstiness\u201d. The two principled ways to address this are (1) mixture models, including the gamma\/Poisson [negative binomial], the Dirichlet\/multinomial, and zero-inflated models, and (2) latent topic models, where the latent topics model correlations among terms.\n\nRennie et al. motivate log word frequency transforms on the basis that modeling log counts with a multinomial is overdispersed compared to standard multinomial models of linear counts.\n\nRather than training on raw document counts, as in standard naive Bayes, the count vectors count(w,d) of words in documents are first transformed based on term frequency (TF) and inverse document frequency (IDF):\n\n$\\mbox{\\rm tfIdf}(w,d) = \\mbox{\\rm tf}(w,d) \\ \\mbox{\\rm idf}(w,d)$\n\nwhere\n\n$\\mbox{\\rm tf}(w,d) = \\log (\\mbox{\\rm count}(w,d) + 1)$\n\nand where count(w,d) is the count of word w in document d.\n\n### Inverse Document Frequency (IDF)\n\nTo help eliminate noise caused by common words (defined as those that show up in many documents), word counts are next scaled by inverse document frequency:\n\n$\\mbox{\\rm idf}(w) = \\log \\frac{\\mbox{\\rm numDocs}}{\\mbox{\\rm numDocs}(w)}$\n\nwhere numDocs is the total number of documents and numDocs(w) is the total number of documents containing word w.\n\n### Length Normalization (L2)\n\nLength normalization dampens the correlations among words in documents. It also scales probabilities for different lengths, which is not important for Rennie et al.\u2019s first-best classifiers.\nTo L2 (Euclidean) length normalize, they divide the vector of TF\/IDF counts by its length:\n\n$\\mbox{\\rm l2TfIdf}(w,d) = \\frac{\\mbox{\\rm tfIdf}(w,d)}{||\\mbox{\\rm tfIdf}(d)||_2}$\n\nwhere the L2 (Euclidean) length of the term vector for document d is defined by:\n\n$||\\mbox{tfIdf}(d)||_2 = \\sqrt{\\sum_w \\mbox{tfIdf}(w,d)^2}$\n\nI\u2019ve been doing classification like this ever since I started doing classification, which is why the result so far looks like LingPipe\u2019s classify.TfIdfClassifierTrainer.\n\n### Complementation\n\nWhat I\u2019d never seen done is complementation. Complementation is introduced to deal with the bias seen with imbalanced training data. What\u2019s really nifty is their comparison to one-versus-all formulations of linear classifiers. I\u2019ll talk about both of these issues in a future blog post.\n\nInstead of training a category based on its own counts and then taking the most likely category, Rennie et al. train a category based on all other category counts, then take the lowest scoring category.\n\n$\\mbox{compL2TfIdf}(w,c) = \\sum_{c' \\neq c} \\mbox{l2TfIdf}(w,c')$\n\nThat is, we count all the instances (after all the TF\/IDF and length norms) of the word in categories other than c. Finally, the discrete distribution underlying category c is defined as:\n\n$p(w|c) \\propto \\log \\frac{\\mbox{compL2TfIdf(w,c)}}{\\sum_w' \\mbox{compL2TfIdf(w',c)}}$\n\n### Classification\n\nThe output is a set of weights that can be used as the basis of a regular old linear classifier (with intercept feature of the category probabilities). As such, this looks like search-engine TF\/IDF computations for information retrieval (see my post TF\/IDF, Scaling and Symmetry for gory details), for which there are typically no normalizations applied to the queries. It\u2019s possible to roll most of the norms into the training, so this is no big deal, and the final length normalization doesn\u2019t affect first-best answers.\n\n### First-Best, Conditional Probabilities and EM\n\nRecall that (Nigam, McCallum and Mitchell 2003) (L1) length-normalized the documents being classified, to fit better semi-supervised models with expectation maximization (EM). Although this has no effect on first-best classification, it does change the category probability estimates, and thus affects expectations, and hence EM. Ironically, Rennie et al. list not being able to run EM as a drawback to their ad-hoc normalizations. As Nigam et al. showed, you really only need the conditional estimates for computing the E step, and these may be computed with Rennie et al.\u2019s modifications as well as with Nigam et al.\u2019s. Then the M step can be any old model fitting, including Rennie et al.\u2019s.\n\n### 6 Responses to \u201cRennie, Shih, Teevan, and Karger (2003) Tackling the Poor Assumptions of Naive Bayes Text\u00a0Classifiers\u201d\n\n1. Mathieu Says:\n\nThe equation for compL2TfIdf seems to be wrong. I think it should be:\n\ncompL2TfIdf(w, c) = \\sum_{d: c\u2019 \\neq c} l2TfIdf(w,d)\n\n\u2022 lingpipe Says:\n\nI don\u2019t understand where your $d$ came from \u2014 it\u2019s not bound in the condition $c' \\neq c$.\n\n2. Mathieu Says:\n\nSo, to elaborate why I think there\u2019s something wrong: in compL2TfIdf, you\u2019re using l2TfIdf(w,c\u2019) but according to the definition of l2TfIdf you wrote above, the second variable should be a document, not a class.\n\nThe equation I wrote reads: sum of all documents d whose class c\u2019 is different from c. To make it more explicit, you may want to use y_d (the class of d) instead of c\u2019. See Table 4 in Rennie et al.\u2019s paper.\n\n\u2022 lingpipe Says:\n\nThanks! Table 4 (page 7) of their paper has the full definition, and the one in the blog text above is wrong. If we let $\\mbox{cat}(d)$ be the category of document $d$, that\u2019d be\n\n$\\mbox{compL2TfIdf}(w,c) = \\sum_{d \\, : \\, \\mbox{\\tiny cat}(d) \\neq c} \\mbox{l2TfIdf}(w,d)$\n\nI think there\u2019s a remaining inconsistency with their general prior (smoothing) term $\\alpha_i$ and normalization; just read their defs!\n\n3. rrenaud Says:\n\nAll of the equations aren\u2019t rendered here.\n\n(And it might be useful to me, as a practitioner, arguing with a coworker about normalizing for document length with naive bayes models).\n\n\u2022 Bob Carpenter Says:\n\nOK \u2014 I fixed them. Luckily I put in alt text for this. I used to be using a LaTeX rendering service, but it\u2019s no longer in business so the early LaTeX links are dead. Now WordPress supports LaTeX directly.","date":"2016-09-30 18:32:56","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\": 13, \"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\": 0.7423000931739807, \"perplexity\": 2347.1730192295095}, \"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-2016-40\/segments\/1474738662321.90\/warc\/CC-MAIN-20160924173742-00290-ip-10-143-35-109.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/openstudy.com\/updates\/510585c1e4b03186c3f9b9ce","text":"## anonymous 3 years ago Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. Find the volume of this solid. y^2=4x x=y I don't know how to start!\n\n1. cwrw238\n\nthe diagram looks something like this\n\n2. anonymous\n\nAlways begin with a drawing, to see what is going on:\n\n3. cwrw238\n\n|dw:1359323354480:dw|\n\n4. cwrw238\n\nvery rough of course!!!!\n\n5. anonymous\n\n@cwrw238: Geogebra is your friend ;)\n\n6. anonymous\n\n@Aenn88: do you know the Shell method?\n\n7. cwrw238\n\ngeogebra? i must try that\n\n8. anonymous\n\nusing cylindrical shells? i somewhat understand it in watching videos but I have a hard time applying it to another problem. i will use geogebra in the future! :)\n\n9. anonymous\n\n@ZeHanz\n\n10. anonymous\n\nSee geogebra.org. First , remember if y\u00b2=4x then y=\u221a(4x). Here r is x, and h is the length of the vertical difference of the two graphs: Cylindrical shells:$\\int\\limits_{0}^{4}2\\pi r hdr=\\int\\limits_{0}^{4}2\\pi x(\\sqrt{4x}-x)dx$\n\n11. anonymous\n\nok that makes sense..thank you","date":"2016-05-29 00:13:16","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\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6491477489471436, \"perplexity\": 1634.423251631769}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-22\/segments\/1464049278244.7\/warc\/CC-MAIN-20160524002118-00196-ip-10-185-217-139.ec2.internal.warc.gz\"}"} | null | null |
ACCEPTED
#### According to
Index Fungorum
#### Published in
Sb. nár. Mus. Praze 40B(3-4): 161 (1985)
#### Original name
Helotium mirabile Velen.
### Remarks
null | {
"redpajama_set_name": "RedPajamaGithub"
} | 251 |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!-- NewPage -->
<html lang="de">
<head>
<!-- Generated by javadoc (1.8.0_20) on Thu Jul 23 10:45:47 CEST 2015 -->
<title>AFXWorkbench</title>
<meta name="date" content="2015-07-23">
<link rel="stylesheet" type="text/css" href="../../../../stylesheet.css" title="Style">
<script type="text/javascript" src="../../../../script.js"></script>
</head>
<body>
<script type="text/javascript"><!--
try {
if (location.href.indexOf('is-external=true') == -1) {
parent.document.title="AFXWorkbench";
}
}
catch(err) {
}
//-->
var methods = {"i0":10,"i1":10,"i2":10,"i3":10,"i4":10,"i5":10,"i6":10,"i7":10,"i8":10,"i9":10,"i10":10,"i11":10,"i12":10};
var tabs = {65535:["t0","All Methods"],2:["t2","Instance Methods"],8:["t4","Concrete Methods"]};
var altColor = "altColor";
var rowColor = "rowColor";
var tableTab = "tableTab";
var activeTableTab = "activeTableTab";
</script>
<noscript>
<div>JavaScript is disabled on your browser.</div>
</noscript>
<!-- ========= START OF TOP NAVBAR ======= -->
<div class="topNav"><a name="navbar.top">
<!-- -->
</a>
<div class="skipNav"><a href="#skip.navbar.top" title="Skip navigation links">Skip navigation links</a></div>
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<ul class="navList" title="Navigation">
<li><a href="../../../../overview-summary.html">Overview</a></li>
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<li><a href="package-tree.html">Tree</a></li>
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<li><a href="../../../../index-files/index-1.html">Index</a></li>
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</div>
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<li><a href="../../../../index.html?org/jacpfx/rcp/workbench/AFXWorkbench.html" target="_top">Frames</a></li>
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<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li><a href="#constructor.summary">Constr</a> | </li>
<li><a href="#method.summary">Method</a></li>
</ul>
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<li>Detail: </li>
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<!-- ======== START OF CLASS DATA ======== -->
<div class="header">
<div class="subTitle">org.jacpfx.rcp.workbench</div>
<h2 title="Class AFXWorkbench" class="title">Class AFXWorkbench</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li>java.lang.Object</li>
<li>
<ul class="inheritance">
<li>org.jacpfx.rcp.workbench.AFXWorkbench</li>
</ul>
</li>
</ul>
<div class="description">
<ul class="blockList">
<li class="blockList">
<dl>
<dt>All Implemented Interfaces:</dt>
<dd>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>>, org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></dd>
</dl>
<dl>
<dt>Direct Known Subclasses:</dt>
<dd><a href="../../../../org/jacpfx/rcp/workbench/EmbeddedFXWorkbench.html" title="class in org.jacpfx.rcp.workbench">EmbeddedFXWorkbench</a></dd>
</dl>
<hr>
<br>
<pre>public abstract class <span class="typeNameLabel">AFXWorkbench</span>
extends java.lang.Object
implements org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>, org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></pre>
<div class="block">represents the basic JavaFX workbench instance; handles perspective and
component;</div>
<dl>
<dt><span class="simpleTagLabel">Author:</span></dt>
<dd>Andy Moncsek, Patrick Symmangk</dd>
</dl>
</li>
</ul>
</div>
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<ul class="blockList">
<li class="blockList">
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<caption><span>Constructors</span><span class="tabEnd"> </span></caption>
<tr>
<th class="colOne" scope="col">Constructor and Description</th>
</tr>
<tr class="altColor">
<td class="colOne"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#AFXWorkbench--">AFXWorkbench</a></span>()</code> </td>
</tr>
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</li>
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<h3>Method Summary</h3>
<table class="memberSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span id="t0" class="activeTableTab"><span>All Methods</span><span class="tabEnd"> </span></span><span id="t2" class="tableTab"><span><a href="javascript:show(2);">Instance Methods</a></span><span class="tabEnd"> </span></span><span id="t4" class="tableTab"><span><a href="javascript:show(8);">Concrete Methods</a></span><span class="tabEnd"> </span></span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr id="i0" class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#addComponent-org.jacpfx.api.component.Perspective-">addComponent</a></span>(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</code>
<div class="block">Add a component, this does not fully register the component.</div>
</td>
</tr>
<tr id="i1" class="rowColor">
<td class="colFirst"><code><a href="../../../../org/jacpfx/rcp/workbench/FXWorkbench.html" title="interface in org.jacpfx.rcp.workbench">FXWorkbench</a></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#getComponentHandle--">getComponentHandle</a></span>()</code>
<div class="block">Returns the component handle class, this is the users implementation of the component.</div>
</td>
</tr>
<tr id="i2" class="altColor">
<td class="colFirst"><code>org.jacpfx.api.handler.ComponentHandler<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#getComponentHandler--">getComponentHandler</a></span>()</code>
<div class="block">Returns component handler to handle initialization and reassignment of
subcomponents.</div>
</td>
</tr>
<tr id="i3" class="rowColor">
<td class="colFirst"><code>org.jacpfx.api.context.JacpContext</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#getContext--">getContext</a></span>()</code>
<div class="block">Returns the component context object.</div>
</td>
</tr>
<tr id="i4" class="altColor">
<td class="colFirst"><code>java.util.List<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#getPerspectives--">getPerspectives</a></span>()</code>
<div class="block">Get perspective in workbench.</div>
</td>
</tr>
<tr id="i5" class="rowColor">
<td class="colFirst"><code>protected <a href="../../../../org/jacpfx/rcp/components/workbench/WorkbenchDecorator.html" title="interface in org.jacpfx.rcp.components.workbench">WorkbenchDecorator</a></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#getWorkbenchDecorator--">getWorkbenchDecorator</a></span>()</code> </td>
</tr>
<tr id="i6" class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#init-org.jacpfx.api.launcher.Launcher-java.lang.Object-">init</a></span>(org.jacpfx.api.launcher.Launcher<?> launcher,
java.lang.Object root)</code>
<div class="block">Initialization sequence returns basic container to handle perspective.</div>
</td>
</tr>
<tr id="i7" class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#initComponents-org.jacpfx.api.message.Message-">initComponents</a></span>(org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object> action)</code>
<div class="block">Handles initialization of subcomponents.</div>
</td>
</tr>
<tr id="i8" class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#registerComponent-org.jacpfx.api.component.Perspective-">registerComponent</a></span>(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</code>
<div class="block">Register the component at the listener.</div>
</td>
</tr>
<tr id="i9" class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#removeAllCompnents--">removeAllCompnents</a></span>()</code>
<div class="block">Remove all component when perspective is shut down.</div>
</td>
</tr>
<tr id="i10" class="altColor">
<td class="colFirst"><code><X extends org.jacpfx.api.component.Injectable><br>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#setComponentHandle-X-">setComponentHandle</a></span>(X handle)</code>
<div class="block">Set the component handle class.</div>
</td>
</tr>
<tr id="i11" class="rowColor">
<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#setWorkbenchDecorator-org.jacpfx.rcp.components.workbench.WorkbenchDecorator-">setWorkbenchDecorator</a></span>(<a href="../../../../org/jacpfx/rcp/components/workbench/WorkbenchDecorator.html" title="interface in org.jacpfx.rcp.components.workbench">WorkbenchDecorator</a> workbenchDecorator)</code> </td>
</tr>
<tr id="i12" class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../org/jacpfx/rcp/workbench/AFXWorkbench.html#unregisterComponent-org.jacpfx.api.component.Perspective-">unregisterComponent</a></span>(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</code>
<div class="block">Unregister component from current perspective.</div>
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<h3>Methods inherited from class java.lang.Object</h3>
<code>clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</code></li>
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<pre>public AFXWorkbench()</pre>
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<h4>init</h4>
<pre>public void init(org.jacpfx.api.launcher.Launcher<?> launcher,
java.lang.Object root)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.workbench.Base</code></span></div>
<div class="block">Initialization sequence returns basic container to handle perspective.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>init</code> in interface <code>org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></code></dd>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>launcher</code> - for di container</dd>
</dl>
</li>
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<pre>public final void initComponents(org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object> action)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Handles initialization of subcomponents.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>initComponents</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
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<pre>public final void registerComponent(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Register the component at the listener.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>registerComponent</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
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<pre>public final void addComponent(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Add a component, this does not fully register the component.
If you want to add a newly created component use registerComponent instead.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>addComponent</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
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<pre>public final void unregisterComponent(org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object> perspective)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Unregister component from current perspective.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>unregisterComponent</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
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<pre>public final void removeAllCompnents()</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Remove all component when perspective is shut down.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>removeAllCompnents</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
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<pre>public org.jacpfx.api.handler.ComponentHandler<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>> getComponentHandler()</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.component.RootComponent</code></span></div>
<div class="block">Returns component handler to handle initialization and reassignment of
subcomponents.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>getComponentHandler</code> in interface <code>org.jacpfx.api.component.RootComponent<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>,org.jacpfx.api.message.Message<javafx.event.Event,java.lang.Object>></code></dd>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>the component handler</dd>
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<h4>getPerspectives</h4>
<pre>public final java.util.List<org.jacpfx.api.component.Perspective<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object>> getPerspectives()</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.workbench.Base</code></span></div>
<div class="block">Get perspective in workbench.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>getPerspectives</code> in interface <code>org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></code></dd>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>a list of all perspective</dd>
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<pre>public org.jacpfx.api.context.JacpContext getContext()</pre>
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<div class="block">Returns the component context object.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>getContext</code> in interface <code>org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></code></dd>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>the context object.</dd>
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<h4>getComponentHandle</h4>
<pre>public <a href="../../../../org/jacpfx/rcp/workbench/FXWorkbench.html" title="interface in org.jacpfx.rcp.workbench">FXWorkbench</a> getComponentHandle()</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.workbench.Base</code></span></div>
<div class="block">Returns the component handle class, this is the users implementation of the component.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>getComponentHandle</code> in interface <code>org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></code></dd>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>ComponentHandle, the component handle.</dd>
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</li>
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<pre>public <X extends org.jacpfx.api.component.Injectable> void setComponentHandle(X handle)</pre>
<div class="block"><span class="descfrmTypeLabel">Description copied from interface: <code>org.jacpfx.api.workbench.Base</code></span></div>
<div class="block">Set the component handle class. This is the users implementation of the component.</div>
<dl>
<dt><span class="overrideSpecifyLabel">Specified by:</span></dt>
<dd><code>setComponentHandle</code> in interface <code>org.jacpfx.api.workbench.Base<javafx.scene.Node,javafx.event.EventHandler<javafx.event.Event>,javafx.event.Event,java.lang.Object></code></dd>
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<pre>protected <a href="../../../../org/jacpfx/rcp/components/workbench/WorkbenchDecorator.html" title="interface in org.jacpfx.rcp.components.workbench">WorkbenchDecorator</a> getWorkbenchDecorator()</pre>
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<pre>protected void setWorkbenchDecorator(<a href="../../../../org/jacpfx/rcp/components/workbench/WorkbenchDecorator.html" title="interface in org.jacpfx.rcp.components.workbench">WorkbenchDecorator</a> workbenchDecorator)</pre>
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,872 |
ADVANCE PRAISE FOR MADE TO BREAK
"D. Foy's writing is so rich, so saturated in both life and literature, that one is tempted to strain for comparison, to find whatever madcap equivalencies ("It's X meets Y!") might begin to describe it accurately. Yet its whorl and grain, the fantastical strangeness of Foy's sentences and the astonishing accuracy of his perception, amounts to something I can only call new. _Made to Break_ is that rare thing: a truly original, and ferociously necessary, book."
—MATTHEW SPECKTOR
" _Made to Break_ is a fearless exploration of fragility—the fragility of friendship, the fragility of romance, the fragility of human life—but the book itself, trussed by D. Foy's lavishly constructed sentences and astute psychological observations, is built to last. Think: Céline. Think: Burroughs. Think: Denis Johnson. Or better yet, think: D. Foy, poet laureate-elect of that marginal America filled with junkies and drunks, where death is omnipresent, and the refuge of an open diner on a stormy night is the closest one gets to the American Dream."
—ADAM WILSON
"While reading _Made to Break_ I just couldn't believe it was the author's first novel. The characters are deadly, troubled, vibrant, and their world is suffused with evil—not the manufactured evil of a Hollywood horror movie, but the carefully paced malevolence of a world doomed to swallow its inhabitants, consuming their shallow, fucked up memories in a swell of amoral darkness. D. Foy is not just a writer. He's the kind of archangel Stanley Kubrick would have built wings for. Don't just read this book. Revel in it. I swear you won't be able to stop."
—SAMUEL SATTIN
* * *
**TWO DOLLAR RADIO** is a family-run outfit founded in 2005 with the mission to reaffirm the cultural and artistic spirit of the publishing industry.
We aim to do this by presenting bold works of literary merit, each book, individually and collectively, providing a sonic progression that we believe to be too loud to ignore.
* * *
Copyright © 2014 by D. Foy
All rights reserved
ISBN: 978-1-937512-17-0
Library of Congress Control Number: 2014930484
**Author photograph:** Snorri Sturluson
**Cover photographs:** (background) David Falconer, Photographer/Environmental
Protection Agency, 1973; (overlay) NASA/CXC/CfA/S.Wolk et al.
You can see a short interview with D. Foy here: **https://vimeo.com/70723153**
Typeset in Garamond, the best font ever.
_No portion of this book may be copied or reproduced, with the exception of quotes used in critical essays and reviews, without the written permission of the publisher_.
_This is a work of fiction. All names, characters, places, and incidents are products of the author's lively imagination. Any resemblance to real events or persons, living or dead, is entirely coincidental_.
www.TwoDollarRadio.com
twodollar@TwoDollarRadio.com
For Jeanine
MADE TO BREAK TABLE OF CONTENTS
Chapter I
Chapter II
Chapter III
Chapter IV
In no sense sober, we barbershopped together and never heard the discords in our music or saw ourselves as dirty, cheap, or silly.
— William H. Gass
_I never said_ , This is nothing more than words on water, _but something inside me knew it the same, like the world won't count what isn't there. I saw everything, but nothing made me see. I heard everything, but nothing made me hear. I knew nothing of how things begin or end, I was just an animal. Then I walked through a door in the hand of a woman who knew I'd fallen but didn't care. In so many words she'd said_ , I'm with you today—isn't that what matters? _There in the midst of laughter and warmth, an unveiling had begun. All I'd known in the days before was a lie. I myself was a liar and a lie..._
CHRISTMAS EVE WORD GOT OUT LUCILLE HAD been taken by the real world, of corporate jobs and big-big coin. Christmas Day the scene was on. As for that affair, the only thing I know for sure is some time close to three or four we laid into a mound of dope. But now the New Year was two days off, and what had been a mound of dope was just a dirty mirror...
Locked into four-by at eighty-plus, we were headed for Tahoe, and Dinky's family cabin. The radio was playing some power-pop group, Ring Finger, I think it was.
_I gave it all up for you_ ,
_and I'm happy today_ ,
_yeah my sky is blue today!_
_It's true little baby_ ,
_we're a thing called us_ ,
_all shiny and new—_
_the brand new me_
_and super new you!_
Of course by the time we hit Bridal Veil Falls, the tank was dry, and we were stuck. Hickory nudged me as she pointed to the sign.
"Romantic," I said.
"Nice," Dinky said.
And then we were trekking through rain, to some joint up the road he thought had fuel. An hour and a half got us four blistered feet and a defunct inn that looked like a Swiss chalet. When finally a man brought us gas, we headed down the mountain for more. A pack of tourists had crowded the inn the second time round, waiting for some guy to fix their flat. Basil dropped drawer and stuck his ass to the window while Lucille assaulted the horn. "Idiots!" we shouted...
Truth was the cabin in lights through a swirl of ice and rain. We'd nothing to do but get to the door, but the stairs slipped me up, and I collapsed, and lost my bottle, too... The stars were dead. The night was rage. The earth was sick with danger. Someone moaned, and from the blue I understood: time is a leech... And then a butcher jumped my head, a squat little man with an Abe Lincoln beard and collection of filthy knives. And then when I heard the breaking glass, the butcher turned and vanished...
Basil had smashed a window with his hatchet after Dinky confessed he'd lost his key. Now the giant appeared at the door with an arm swept out in phony cheer. I remembered once a girl called him handsome.
" _Entrez-vous_ ," he said.
"You smell that?" I said about the stink.
"Whoo-wee!" said Lucille.
"I smoke," Basil said. "I can't smell dick."
"I can assure you," Hickory said. "This is not the smell of dick."
We headed to the kitchen for glasses and ice, the scent growing stronger, a compound more like mildew and vanilla.
"Oh goody," Basil said.
There was nothing in the fridge but the little bags of glop people use for wounds.
My hand knocked Basil's hat to the floor, the porkpie his grandfather gave him a decade back. The doof had been wearing it all this time, every day but Christmas.
"If it's not one thing," I said, "it's your mother."
Dinky flipped the light. "Christ on a crutch," he said.
On the floor, in a bamboo cage with pits and dung, lay a lovebird dead as wood.
"Now _that_ ," Basil said, tapping the cage with his boot, "is some weird-ass shit."
Hickory looked at Dinky. "You're not going to tell me this was yours, I hope."
"We've never seen the thing."
"Maybe," I said, "it was your grandpa's."
"Granddad hates animals. He wouldn't let Dad have a fish."
Lucille had been picking at her lip so long her mouth looked like a steak. "I had a bird once," she said. "When we lived in Carolina."
"That's very nice, Lucille," Dinky said. "Thank you for sharing that with us."
She ignored this and shuffled closer. "It was a finch. Then one day I came home from school, and she was gone."
"It flew away?" Hickory said.
"Her name was Zoë," Lucille said, and put a hand to her face. The stink was really nuts. "My father said if he had to hear that racket for one more day, he'd be forced to use his gun."
"You ever hear a finch?" I said. "Not loud at all. Finches are about the nicest bird around."
"He hated cleaning its cage, is what I think."
I left the kitchen as Hickory told Basil to dump the bird. He complained at first, but then a door slammed and slammed again, and there they were, Dinky and Basil, huffing at their smokes.
Lucille had laid out a dog-eared copy of _Fear and Loathing_ next to a stack of discs. She jabbed the On button, then Play—out came "Bela Lugosi's Dead."
"So who's going to get the ice?"
I told her she had two legs.
"Excuse me?"
She was always making people repeat themselves. It gave her notions of power.
"Turn that down," I said. She waited a second before turning it down. "I said you've got two legs."
"You ought to know. You've been staring at them long enough."
"Check the TV," Dinky said. "We want to see if they're still saying it's going to flood."
"It's the day before New Year's Eve," Basil said, as if the weather played to dates.
Dinky ran through the channels till he reached a woman with hair like GI Joe's. On the screen beside her flashed bombed-out streets and men at guns, perched on inexorable tanks. Another face appeared, a weeping crone, trailed by a man with a shapka and fatigues. The anchorwoman sat with considered reserve. Her voice was a tool for faith. _Operation Joint Endeavor_ , she said, _appears to have reached a point of..._
Dinky squealed like he'd won a prize. "That's Atherton," he said. "From _our_ company!" He knelt by the tube and gestured toward some pimply kid in a truck. "Jesus, that's our whole frigging company!"
"So much for your fifteen minutes, huh, Dink?" I said.
"You know I can't drink my whiskey without ice," Lucille said.
"Snow's good," Basil said. "Use snow."
"We're going to draw straws," Lucille said. "The two with the shortest get to make a run."
Dinky shook a bottle. "But we don't need no ice. We need _bourbon_. And as we can all see, we have _mas_ bourbon."
" _No mas_ no _more, pinche_ ," Lucille said, and squeezed Dinky's ass.
We cut the straw from a broom in the kitchen. Then Basil took the longest, Hickory the next, Lucille after that.
"Welly, welly, welly, welly, welly, welly, well," Basil said.
"Sorry," Hickory said.
Dinky looked like he might cry. "Why's it always me that's getting the shaft?"
"Cause you're feeble," Lucille said. "And jinxed."
" _Hatchet Lady_ ," Basil said, classic. "So mean."
"Just remember whose cabin you're in," Dinky said. "We're here for a week."
I punched Basil's arm. "Hey, asshole. You get rid of the bird?"
THE ROAD WAS RUNNY AND BLACK, AND WHEN the lights hit the trees they looked like creeping skin. A DJ yammered about our noses and what Jack Frost had done.
"So whose idea was it," Dinky said. But instead of taking his bait, like usual, I waited. He said, "We know you're familiar with the word _moronic_ , Andrew. We won't talk about how we spent the last nine months in a place so cold your pee breaks on the ground. We'll save that for our golden years. You know what we need?"
I stared at him. He didn't want an answer. He'd ask you a goddamned question just to answer himself.
"What we need," he said, "is _Hawaii_. What we need is _Guam_. Girls in grass skirts and pigs with apples in their traps. Mai tais is what we need, AJ." And the gloopy bastard never drove with his hands at ten and two, either. One of them flapped about as he talked while the other hung across the wheel like an old rubber chicken. "How," he said, "are we ever supposed to get Hickory on her back when all she can think about is misery?"
I fiddled with the radio. I pulled down the visor to hate my face in the mirror. "You take a look in the mirror these days?"
"You know we don't like mirrors."
"Look at you. Look at your head. _Especially_ your head. You were planning to get laid with that thing?"
Dinky started coughing so bad he stopped in the road. "We did fine in Germany," he said. Then he saw my retard's face and hit the gas. "You know, with the chicks."
"The _chick_ , you mean. I saw her picture. She looked like a fat albino parrot. Not to mention she's a professional thief. Not to mention she gave you the clap."
"Fortunately for us, Uncle Sam takes care of his boys."
I studied the water on the window as it turned to pearls and marveled at the creatures in their snowbound lairs. I thought about my grandmother, how she answered the phone to say she'd been raped, or lost her child, or found a bag of stones. She hobbled from my flat one day, and when I asked her purpose, she said, _Home_.
"This thing in four-by?" I said.
"What do we think?"
"We think we should get the lead out."
The road had just two lanes. Trees flashed by, now sparkling, now black, a strobic land of bugaboos dreamed and real. We saw no cars, no people, not even the twinkle of lights on another unnamed road. The Cruiser heaved with empty cans and cigarette butts, a single dirty sock. And roasted peanuts and peanut shells, Basil had tossed them everywhere, the dashboard, the seats, one was in my hair. It stunk of laundry hampers, and ragamuffin carnivals, sculleries from days of yore...
My old toad once brought me to a creek bottom full of sycamore and oak. Everything shone in hues of green, lancets of sun pushing through the shadows. An odor of struggle suffused the air. It was the odor of springtime, of birth. High overhead a worry of jays had attacked a nest of fledglings. When my toad climbed a stone to piss the creek, I made my way to the tree. Shells lay about, and in fact a fledgling too, blue as tainted meat and with its tiny quaking eyes utterly pathetic. I took stock. Gone as God my old toad was, wandered off, not a soul could tell. I trusted in his return, however, if only to grill me, that much no doubt I'd learned. At my feet the fledgling sawed away with its little grey beak, gasping and sawing with a relentlessness only its mortality in the offing could afford. Christ but what I would've given to flee that place, what meager breath as witness to this struggle I myself could draw, the creature's eyes watching mine, or rather not watching mine, not watching anything likely. To think otherwise had been absurd. They were like drops of shuddering ink, those eyes, so tiny, goddamn it, so sad, so full of such terrible, newborn horror that to call them eyes at all was somehow blasphemous. And the eyes of birds have never been the same. _Answer me!_ they seemed to say. _Answer!_ But I had no answer. And anyhow, _I_? Not even the nobility of silence was sufficient to that demand. Nothing was sufficient. I poked at the creature with a twig, and then with my toe I flipped it over, and then with my heel I crushed it...
"The army say anything to you about that bark of yours?" I said.
"The army doesn't say anything unless you get your arm blown off."
"You could pay down the debt yourself, you know. If you'd just get serious."
"How much more serious can we get than clearing mines from a war zone in the middle of hellish winter?"
"Pass the bar, Dinky. Do the law."
"There's no need to torture us, you know."
"I'm all gold," I said, and took another slug. "If nothing else you got the name for it."
"Now, class," Dinky said with the nasally voice he assumed to mock himself. "Why is it we think Stuyvesant Wainwright the Fourth has failed the bar six times?" He raised his eyebrows and spoke in singsong cadence. " _Because he didn't learn anything in school but how to do lots and lots of drugs and drink lots and lots of booze_. Let that," he said, "be a lesson in how to fail."
"And get sick," I said.
For an instant through the trees the casinos glimmered down the strip. The dealers hung tight in those mad shops, I knew how, working the gamblers to their rings. Where was Hickory—her eyes, her mouth, the voice that purred from it?
"The army," said Dinky, raising his arm strongman-like. " _That_ takes youth."
He turned at me to grin. Which is why I thought he might not've seen the mudslide on the road, though in truth he had, because all at once his eyes popped out, and we went lurching this way and that until we broke into a spin that closed on a bank of stones.
I woke up to a land of dark. Neither Dinky nor I said a word. We just sat there in the cold, and all that giant black seemed to've swallowed up the world. Where were all the lovely people? Where were all the vermin, and where were all the stars?
When finally I got the nerve to look at my friend, he was pinned in his seat by the wheel. It wasn't until I'd begun to think maybe he was knocked out, maybe even dead, that he wriggled free. Out in the night, he looked like one of those freaks you see on _Ripley's Believe It or Not!_ , the one abducted by Martians. He stood there for a minute, then staggered off and fell in the mud.
"It used to be when I coughed I heard bees in my head. Now all I hear is fire."
"Write a poem about it sometime," I said, and scanned the road.
"AJ... AJ..." And then, "Please."
"We're buddies," I told him. "Remember?"
Mud rushed down the mountain. The rain was an opaque sheet. I held Dinky's head and waited.
"Get me that bourbon, would you?"
And then we heard an engine, a song for all we cared, followed by lights through the dark and, again, after something like an epoch, a truck round the bend.
"You see that, buddy?" I said, waving my arms. "That's your guardian angel. We'll be home in a minute."
BASIL HAD NO BALLS TO JUMP LUCILLE TILL THE stretch last summer at San Quintín. Dinky had passed out that night, though it wouldn't have mattered. Sooner or later she'd have left him as she did. Nearly five whole years they'd stuck it out—a goodish while in the buddy world, an eon or two for her. It was midnight on the beach, the moon was making hay. I'd stuffed my pockets with silver dollars and fireworks, and packets of musty Chiclets. The fine grey sand was dancing everywhere, across the dunes and slick opalescence where the water meets the shore. When at last I spied them in a hollow of grass, Lucille was bouncing like the bluest blue-movie girl the boys have ever seen. Doubtless neither had meant to hurt our friend. What were they, anyhow, but two sad dolts caught up in the malice of affairs? Lucille wasn't as mean back then, either, not like she'd come to be. She was free from the fear of her corporate future, if in fact that's what it had been. Nor did Basil ever hold ills, nothing genuine at least. He was a single child. He only knew to take what he saw. I never expected more. Still, they should've known better than to play with the clan. We'd pledged allegiance to it like a flag: _Buddies forever_ , we'd promised, and we were solemn. But today things were different. I knew it. Dinky knew it, too. We all did. And now to prove it he was sprawled in a storm with his bottle, waiting for the guy that had just rolled up to save us.
First thing I noticed was the monkey—dead—dangling from the mirror on a string of beads. It could've been a fetus of hair, this thing, with pebbles for eyes and corn for teeth. The man that had hung it sat motionless behind the wheel, clad in weathered denim. He had sunken cheeks and hollow eyes and a silver beard to boot. I scratched my ear—his eyes traced my hand. I drummed my fingers—his eyes traced my hand. Klaus Kinski came to mind, as Herzog's Nosferatu, and grunions filled my head, beneath a heavy moon. We were alone.
"That little flake," said the man as he nodded to the monkey, "is called José." He sucked a tooth and gestured to a crucifix he himself must have painted red. "Ronald, though, he's not so bad as Fortinbras or him." Tattooed across the fingers of one hand was the word BEND, across the other, GIVE. A cigarette twitched in the webbing there. Empties fouled the dash.
"We hit a bear," I said.
Why I did I couldn't say. We'd had an accident. What difference how? Maybe I feared any less a case for invading the old man's turf—and sure as shit I had such a feeling, like I'd missed some glaring portent of doom, I didn't know—would send him on a rampage. Or maybe it was just his creepy gaze.
"Who's that?" he said. Dinky was still in the mud.
"He's sick."
"I see, I see, so that's who he is."
"Listen, mister, we need a ride bad."
"You need something bad," said the man. In slow order he tapped the Christ, the monkey, and the yellow dog beside him. "What do you fellows think R-E this crisis?" I stood waiting while he sucked his teeth some more and spit. "Throw him in," he said with a jerk of his thumb to the rear.
"He's _sick_ ," I said.
"You hear that, Fortinbras?" he said to the dog.
I found no change in the geeze's tone, but Fortinbras dropped from the window and appeared in the bed behind him. A spate of dolls in varied dismemberment lay about the beast, some missing heads, others arms or legs. The man shot me a look part fishy, part fatherly, his eyes running off two ways at once.
"You going to lay one, boy, or get off the pot?"
I wanted to be naked, to lie naked beneath a tender sun. I wanted the smell of a clean bright day, and heat, tart and dry. I wanted a heat that lasted, endless sand, visions of dazzle and grain. Why wouldn't his eyes release me?... _Lanterns, vultures, many things in hell... I made up my mind to take the life of the old man, and thus rid myself of the eye forever... Madmen know nothing..._
I got Dinky in the cab. The man took my hand. It was smooth and hard and cold as outer space.
"The name is Super."
"Andrew," I said. "That's Dinky."
"Pleased to rub truth with you boys."
"We could use a doctor now, I think."
Super gripped his wheel. "You do what you've done, you'll get what you've got. Catch our drift?"
Dinky drew himself up to look at this strange man. "We hate doctors," he said.
"Then which way you going?" I said.
"The only way that's good," Super said, "and that's the way we come."
"That _is_ good," Dinky said with a smile. "Because we sure do hate a doctor."
BIRDFEED AND BULLETS, THE WEEPING BARK OF A million pines...
A freezer's scent of the clinic and the morgue...
The gleam of a roadside can...
The road wound on, the road kept winding, and sound was a cat's rough tongue...
Super's face was constant motion—that silver beard, those leathery cheeks, tiny eyes that flitted and bounced...
He ranted and sang and whispered and howled, and he did it all with ease...
We'd been forsaken, more or less, adrift with the phantoms that were the old man's words, loosed, it seemed, with each wave of his troubling hand...
At some point he set in about the doings in our cabin, inexplicable, he said, slippery, he said, though never exactly what...
I saw the lovebird, its gaping beak and eyes, I smelled ice cream and road kill and blood...
That familiar longing had returned, for my noons of summer, counting minnows in a jar and naming each breeze. What had happened to those days?
A meerschaum appeared in Super's hand and then from the glove a bag of gnarly weed, but Dinky went on drooling. Super crammed the stuff in the pipe and with a nail snicked the match he'd somehow managed to keep...
He chortled and smiled, puffed and drove, happy is as happy can...
I took the pipe, he the bottle...
The road was thick with water and mud and stones from the crumbling earth. At every pothole my friend yipped like a dog asleep till at last he jerked to with eyes that could've been eggs. When Super gave him the pipe, I thought he'd start coughing, but instead his face melted with the smoke from his lips.
"I was going to ask where we were," he said, "but now I don't even care. Onward, Benson!"
"We are no man's slave," Super said, and jerked his thumb aft, referring, I supposed, to the bed of broken dolls. "If you care to differ, interrogate the rest."
"I'm an army man, mister whatever-your-name-is," Dinky said.
"The name, boy, is Super."
"The way I said, Super," said Dinky, and drew himself up, "I'm an _army_ man. And the only thing I'm good for is knowing what makes the grass grow green." He pointed at Super. "You know what makes the grass grow green?" he said. "Bright red blood."
"See what you know after you've been wearing that grass for a hat a few years."
"He's not always like this," I said.
Super let out a noise, maybe a chuckle, maybe not. "Oh, but you know he is," he said. "He's the marathon man. Catch our drift?"
"I am man!" Dinky shouted. "Hear me roar!"
In the distance a light appeared, I hadn't seen it off to the west as we came in—who lived out there? I thought, there's a light out there attached to nothing, it looked, a lonesome bulb in the trees—but then soon enough, like everything else, the question fell away, and when I looked up, we had reached our cabin.
The man turned his body and head in tandem. His mouth was an earwig, his eyes gleaming coins. "We'll be sorry to see you go."
"You don't have to go," Dinky said. "This is _our_ place." Super fixed his gaze on my pal and said no more. "But we've got booze," Dinky said.
"We're a free man, boys, and wish you alike."
It must've been a good ten minutes we stood in the rain while Dinky worked to bring Super in, but the man evaded my friend until he had no choice but to turn away.
"There's nothing you can take from me," said Super when Dinky announced he'd take his leave, "but my life, but my life, but my life. Fortinbras!" he shouted at his dog. "It's time to make the soldiers shoot!"
Fortinbras appeared in the cab with his nose out the window, and the truck sputtered on. The last thing I saw was a sticker on the bumper. _I Have a Dream!_
WE STOOD IN THE RAIN, WATCHING BASIL through the window, berserk with his cherished knife. The freak never left without it, plus some rope and his grandfather's stupid hatchet, what, with the sack that held them, he called his _man-bag_. Every so often he'd mellow some, long enough to hypnotize whatever conjured fool had been dumb enough to block him. Then he spun off into the kicking, punching, and cutting he thought his moment of glory, the killing time. Well, the boob was dancing, and who could tell him otherwise?
Soundgarden was the band they'd picked to beat the ghosts. Hickory of course was what my eyes wanted, but they got Lucille—goddamn—snapping her fingers as she twirled. When finally Hickory did float up, Dinky fairly groaned. She was too lovely for her own good, it was true, and I was a fool in the rain.
"She's so beautiful," Dinky said.
"Lucy?" I said. "She's all right."
"Look at her," Dinky said. "She moves like... smoke."
"I don't know about you, but I am freezing."
Dinky wiped his nose. It could've been rotten fruit. "Basil won't be happy about his truck," he said. "He won't be happy at all."
My pal didn't look so hot. In fact my pal looked downright fucked. "Basil," I said, "can gargle my nut sack. Let's go call you a doctor."
"Who do we think we are, always telling us what to do?"
"We think we're the guy who's smarter than the moron we're taking care of."
"Where's our bottle?"
"Milk's all gone, Dink," I said. "Diapers, too, in case you're wondering."
My friend glared like I'd stuck him with a shiv. "Have you ever chased a pig with a spear, AJ, then realized there was no pig?"
"What?" I said.
"Exactly," he said, and walked up the stairs.
SOMEONE HAD SET OUT THE CASE OF OLD CROW we'd brought, and the liter of Safeway coca-cola, all in a row with five new glasses. The rest lay spread across the table—CDs, lighters, bottle caps, shades, smoke packs empty and full, a half-munched bag of Chips Ahoy and a full one of Doritos, gum wrappers, peanut shells, matches, gum. Basil still had the knife, but now he had a bottle, too, stuck in his hole, what else. I thought he'd drain the thing for sure, but somehow he found the grace to pull up short and squirt an arc of whiskey through his teeth. Maybe fifteen bottles and cans lay about him, Lucky Lager, this round, with rebuses in their caps.
Hickory pointed at us the way children point at people who are fat. "They're here," she said.
Lucille ran outside, looking, I guessed, for the ice we'd never got.
"Some rabbits ran across the road," I said, and listened to the phone hum like a seashell at my ear.
"Where's my truck?" Basil said, moving in.
He did this sort of thing a lot, most recently to some pencil-necked kid at Radio Shack. At first the kid had given Basil hell for a mike cord he wanted to return. By the time we left, he'd freaked the kid so bad he had both his cord and a gift card worth ten bucks.
"We had an accident," Dinky said.
"An accident," Hickory said.
"This phone's shit the bed," I told them. "Is there another?"
Lucille, wet once again, had balled herself up in a chair by the hearth. Poor girl. The world wouldn't reckon like she'd been told.
"You blockheads," she said with tears in her eyes. "You're all a pack of blockheads." Dinky's nose was crusty with blood and snot. Anyone else would've been horrified just to see him. But these people, they didn't say a word. "All I wanted," Lucille said, "was a bag of ice."
Part of me had a craving to smack Lucille. Instead I knelt down before her. "Pretty often," I said, "it's hard to tell the difference between what hurts and what doesn't."
"I'm a sellout," she said. "A crappy, lousy sellout."
"I don't know about all that," Basil said. "I mean, you're just doing what you got to do."
"What would you know about it?"
"I work."
"At staying drunk you do. At schmoozing you do."
"Lucy," I said.
"You're wasting your time, AJ," Basil said. "Nothing you can do when she gets like this."
Lucille took up the _National Enquirer_ at her feet and began to shred it. "How would you like to go around calling yourself, AJH vanden Heuvel, failed painter? AJH vanden Heuvel, CreditCom's newest Junior Project Analyst?"
"No one said you can't still do your thing," I said.
"Oh, joy. Yes, I'll give china-painting lessons Sunday afternoons. That'll do it."
I put a hand on her leg. "Have a beer," I said.
"I _know_ what I am," she said. "It's just that I can't seem to help myself."
"People only think they know what they are."
"Yeah, well, I may not know all that, but what I think I know is that I'm a bitch."
"You hear that?" Basil said. "Mark that shit down."
"What I want to know," Lucille said, "is how life ever got to be so lovely and sweet."
The dead bird, its horrible stink, I couldn't get away...
I looked over my shoulder, and what should I see but two eyes staring from this poster, a cowgirl circa '75, with her fringed suede vest and denim blouse round the tits of the poster girl she was. She'd perked herself up against a pair of skis to smile toward the bedroom her smile let you know you'd soon be in... And now a shade's old song gamboled through my head, a poem I'd written way, way back, the worst... _a thousand wintry heaves ache beneath the sky... stop the whisper, recall the spring... when your shadow nears my blood, i sleep..._
"He needs a doctor," I said.
"Is he sick?" Lucille said.
"Is he sick."
"Are you sick, Dinky?" said Hickory. She'd got down beside him now and was stroking his arm.
"Look at him," I said. "I mean, Christ, you know?"
Basil drained a beer and flung the can. "Let's everybody look at poor Dinky." He wrinkled up his face and extended his hands like an impresario weary of his freak. "You'd think he's miserable. But the thing is, he likes it when crap goes sour."
"Are you actually putting _effort_ into being such a dick?" Hickory said.
"All this attention he gets?" Basil said. "He's as happy as white on rice."
The tube meantime had been feeding us steady ruin—houses mired in water and mud; trees on roads; children clutching elders; stern-faced men, spent-faced men, some with slickers, others dusters, hauling sandbags and chattel; stranded vehicles and collapsing bridges; creatures mad with terror...
"AJ, baby," Basil said. "Bosom buddy. _Please_. Where the hell's my truck?"
"There was this rabbit," I said. "A guy gave us a ride."
"And who, pray tell, might that be?" Hickory said.
I told them about Super and his monkey. I told them about Fortinbras, and the little red Christ, and the truck of mangled dolls. Dinky stood up and shouted. He said how nervous we'd got when Super claimed to read our thoughts, how the geeze had ranted on about eagles and atomizers, the reversal of poles and the rest. Hickory asked if he was a shrink.
"He gave us drugs," Dinky said.
That got them frisky, all right.
"I'll tell you guys what," Basil said. "Maybe—and I mean just _maybe_ —if you two morons get me really fucking baked, I'll forget you wrecked my truck."
I hadn't thought to query the old man whether he kept a stash for times he ran across dorks in the rain at night. That's what I said.
"So what was his name, then?" said Lucille.
"This you're not going to believe."
"Like I didn't already stop believing anything you say ten years back."
"He said it was Stuyvesant Something Something. Yeah. But he told us to call him Super."
Lucille said, "Next you'll be telling us he put a gun to your head and banged you in the heiny."
"Banged them in the ear, more like it," Basil said. "Knocked what was left of their rocks clean out."
Hickory said, "But wouldn't it be a marvel if he and Dinky were blood?"
Basil was pacing. "What are we going to do about my truck?" He poked Dinky's arm. "Cause in case you guys didn't know, good old shit for brains here was right for once in his life. The weatherman says it's going to flood like hell."
"Limo Wreck" became "The Day I Tried to Live." We gaped speechless at the phone till Hickory's sigh confirmed the real.
"We're stuck," she said.
Basil took up his knife. For a long time he gave us his back, running a thumb down the blade, but then he spun round and flung the thing at a pile of wood.
"You two morons are so lucky," he said after his knife had clattered to the floor. "I should skin you both, right here and now."
"You're lucky Granddad isn't here to skin _you_ ," Dinky said. "Granddad wouldn't like the way you're treating his place."
Lucille's face looked suddenly very stupid, like some girl about to get killed in a flick. "Did you hear that?" she said. No one said a word. "It was a voice," she said. "Like some horrible singing."
"You might remember, kids," Basil said, "there's something out there called a storm?"
"Sometimes, _squeeze_ ," Lucille said, "I think about what a bummer it is I'm not a man. I'd fuck you so hard you'd never—"
Subtle though it was, the sound repeated, just as Lucille had said, like some horrible singing. She went to the window—followed by me and Hickory and Basil with his hatchet—and moved from it to the next.
"Maybe it was a bear," she said after we'd covered the place for nothing.
Again Basil turned on her. "That's about as retarded as when you didn't know what a belly button is." This was true. At a lobster joint north of Ensenada, Lucille had downed a pitcher of booze and claimed belly buttons the stuff of shots at birth.
"Bears hibernate, Lucille," Dinky said.
"Yeah, well," Lucille said, grimacing at Basil, "at least I don't have a dick that hooks off thirty degrees right." She brushed a lock of hair from her face. "Fucking banana dick."
Now this was something not even I had ever heard. In all the time I'd known Basil, he'd never mentioned a faulty unit. "You're kidding," I said.
We all turned to the giant and watched his face screw up. He began to stutter, but that didn't work either, so he poured himself a drink.
"Anyway," he said, "there's nothing out there."
"There's nothing out there _now_ ," Hickory said.
"Who's your closest neighbor?" I said.
"We don't have neighbors," Dinky said. "We've got fences."
"Turn out the lights," I said.
"Fuck you," Basil said.
"So we can see what's out there."
Again we peered out the window, looking for shapes, a car, a ghost, whatever, but found the same old rain and trees in the same old howling night, the same uncanny sense of possibilities imminent.
"The wind can do some batty shit," Basil said, and raised his glass in a toast. "Here's to Buddy Time."
Hickory stood close against me, jungle sweet, the smell of her strong, cucumber and vanilla. Her hand covered mine, she smiled, my hand was in hers, my hand was in her hand. I wanted to eat her teeth, then. I wanted to climb inside her, tired and full, and fall into precious sleep.
"Days like this," she said, "they say _damn the water and burn the wine_."
"Sounds to us," Dinky said, "a bit like that _seize the day_ crap everyone's been spouting."
Lucille picked up _Fear and Loathing_. "'We had two bags of grass,' she said, reading from the cover, 'seventy-five pellets of mescaline, five sheets of high-powered blotter acid, a salt shaker half-full of cocaine and a whole galaxy of multicolored uppers, downers, screamers, laughers and also a quart of tequila, a quart of rum, a case of Budweiser, a pint of raw ether, and two dozen amyls.' Is that cool or what?" she said, and tossed the book down.
"Everyone knows Hunter S is our hero," Dinky said. "His work with the Hell's Angels was nothing short of revolutionary."
"Now that," Basil said, "I'll give you."
"They even put a contract out on him for it. Who's that Indian fellow, Rushdie or whoever the heck?" Dinky turned away to cough. "Excuse us," he said, wiping his mouth with an arm. "The guy the Ayatollah wants offed? An _ant. A_ literary microbe squirming in the shadow of the god." He shuffled over and held out the book like the Bible itself. "'He who makes a beast of himself,' he said, quoting from the epigraph, 'gets rid of the pain of being a man.'" He took a moment to stare us down. "Hunter S," he said, "showed us all who we really are."
"I got to give it to you one more time, Dink," Basil said, slapping him on the back. "You poor fuckless fart."
"Hey you guys," Hickory said. "Guess what?"
"What?" Basil said.
"Lick my butt!" Hickory said, and burst out laughing. She was whacking on her knee like some old gal from Arkansas. "No, but seriously. Anybody here ever play Truth or Dare?"
"We won't play," Dinky said, "but we'll sure watch." He beamed at Hickory and made an effort to grin. "We _like_ to watch."
Hickory led Lucille to the center of the room and plopped down on the floor. "Come along now, Basil darling," she said. "We're dying to know your secrets."
Basil scratched his balls. "I like a good dare every now and then. Keeps me on my toes."
"Bring the hooch," I said, "and whatever else."
"Perchance we could change the music?" Hickory said. "And that abominable machine as well," she said, indicating the TV. "Please."
"'4th of July,'" Basil said, "is one of the great all-timers."
"Try the Jelly Roll Morton."
Some talk went round how the old master thought a Haitian witch had cursed him. Dinky, back on the couch, said that in the end Jelly Roll had taken to acting like Howard Hughes.
"The guy never ventured out," he said. "And nobody cursed him, either. He'd simply trapped himself in his own little cage of fear. At least that's our view. For what it's worth."
"Break out the Jelly Roll, _squeeze_!"
"Damn it, woman," Basil said. "How many times do I have to tell you not to call me that in public?"
Lucille squinted. "This is public?"
WE'D MET HICKORY AT A PARTY IN THE CITY. TO get inside, you had to take an ancient lift, the kind with a platform behind a metal door that wouldn't budge without a couple of trolls to heave on some old chain. They even had a bellhop, in a red-velvet monkey suit and pillbox hat with a strap. For eyebrows the kid had little steel barbells, five or six per side, and for teeth real fangs, straight-up Lestat. And if that weren't enough, he was running Maori-style ink on his chin, and every patch of his face but that was goofy with shiny dust.
Before us lay a massive room, probably two- or three-hundred yards long and half as wide, chockful with every type of gork in the book. Guys with bunless chaps ran around the place smacking each other with crops. Chicks, too, more than half of them decked out like Catwoman, scampered about with nipple clamps and whips and chains, wreaking all manner of hell. There were go-go dancers in bubbles and cages, Rastafaris, homeboys, deathrockers and mods, rockabilly kids, swingers and punks, not to mention your basic Haight Street hipsters. Jumbotrons swayed from the ceilings flashing clever retromercials, and thrift-store TVs lined the walls fuzzy with chickens in the slaughterhouse and Japanimation and big-time sex acts, the whole of it swamped in banks of chemical fog. Some heavy-duty industrial house provided the coup de grâce for this late-night get down, pumping so hard you could feel it from the marrow in your bones to the depths of your aching nards. The four of us snagged some drinks and split, the two traitors one way, Dinky and I the next.
We stumbled on our girl in some sort of cave, everyone but her stupid with dope. In her tight corduroys and glittering boots, she sat among thirty or forty crackpot fiends sucking fingers, faces, toes, whatever their mouths could hold. But what stung most was the guy beside her, an image to the T of my old toad in a picture I'd seen when he was a Hare Krishna. He had fierce blue eyes and a queue from his head, all the way down his back. He was even wearing bamboo thongs. Soon, however, he slipped off, and I forgot him and was glad. Jerks by the droves kept trying to get their paws on Hickory, but she sat among them cool as a queen, there, as she'd said, "to take in all the footage." We never asked her name, and she never said. It was Dinky laid the moniker down. "You look like a Hickory girl if ever we've seen one," he told her, to which she said, "Hickory dickory dock, the mouse ran up the clock." All the while her face lay before us unreadable as Chinese kanji. I remember staring at her for a preposterously long time, asking myself just who in hell this willow was, with the ovate eyes and strong white teeth, and me like a doofus trying to smile.
So I'd known what I wanted before the game had begun. The problem was, having so much to want, I had to choose.
"What's your name?" I said. "Your _real_ name."
No one but Dinky would've expected that. Neither Basil nor Lucille had ever known Hickory wasn't Hickory. The day we introduced her, it was _Hickory, meet Basil and Lucille_. Their faces didn't quite know what to do.
"I've always wondered," Hickory said, "why none of you have asked."
"It can't be more fucked up than Hickory," Basil said.
"Elmira Pugsley?" Hickory said.
"It's different," Lucille said. "That's for sure."
"It's after my granny. But since the point here's to be totally honest—and I'm a totally honest gal—the full name's Elmira Beatrice Pugsley."
Basil clicked his tongue. "Poor, _poor_ girl," he said.
"No wonder you go around letting everyone call you Hickory," Lucille said.
Dinky burbled from the couch. "We don't think that's very nice, now do we?"
"Who asked you to wake up, hey moron?" Basil said.
"The middle name," Hickory went on, "that was my father's doing. They were farmer hippies."
"You," I said, "come from _hippies_?"
Hickory smiled. "I spent the first ten years of my life on a commune up in Oregon. We had beehives and everything. Organic bees. Organic everything."
"Poor, poor girl," Basil said.
Hickory put her chin in her palm and looked us over. When she stopped at me I knew what she wanted, but then she passed to Basil. "You, tough guy. Which will it be?"
"Toss a mop on the floor," I said at Basil's show of squirming. "See which way it flops."
Even as I said this it struck me just how much we didn't care what Basil did. We knew—or at least I knew, or thought I knew—that either way he turned wouldn't change a thing. How could he choose when he had no choice, the difference between a Truth or Dare having collapsed beneath their emptiness? For Basil, to be honest meant to be daring. And however strangely, however sadly, daring was as close as Basil ever got to truth. The notions had become two mirrors reflecting only themselves.
"Goddamn it," Basil said. " _Shit_. Truth."
"Oh dear yes, quite lovely indeed," Hickory said in this high-society debutante voice. "Now. What's the most shameful thing you've ever done—sexually, I mean?" Basil looked blank, so Hickory said, "Of course I mean shameful in the traditional sense, the sub _urban_ sense."
"I can tell you _that_ ," Lucille said. "It happened only last week, when he greased me up like a Thanksgiving turkey and tried to—"
"I already heard that story," I said. Lucille turned with gaping eyes. "He told me _every_ thing," I said.
"Everything?" she said.
Basil cleared his throat. "When I was a kid," he said, "I had a stuffed monkey."
"How old are we talking?" Hickory said.
"Twelve or thirteen, I guess. My dad had given it to me before he took off. Anyways, it had this hole in its crotch. It started out little, but kept getting bigger." Basil had been slouching forward as he talked. Now he planted his hands on the floor, as if the telling were over.
"What kind of story is that?" I said.
Basil's face was flushing now. "There's more," he said.
"Come, come," Hickory said.
"One day I was in the closet."
"Yes?"
"With the monkey."
"Yes?"
"And I was looking at pornos, you know, and, I don't know, there it was." Here Basil paused with great melodrama, worse than a creep on the tube.
"Out with it!" I shouted.
"So I fucked it."
"Really?" Lucille said, her face lit up.
"That's not all," Basil said.
"There's more," I said. "There's always more with this guy."
"See, when I finished, I wanted to hide the bastard, but I couldn't think of any place where my ma wouldn't find it. There was also another lady and her kid living with us in this house. You can see why I had to destroy the facts. So I got out a big old garbage bag, one of those super heavy-duty Glad bags, and stuffed the monkey in there. Then I jumped on my moped and drove out to the mall. They had all those dumpsters in the alley behind the Mervyns there. Thing is, I didn't just chuck it in there. I _buried_ it. Dug through old tampons and shit, and chicken bones and diapers and soup cans, all that repugnant shit, and crammed that little fucker down at the very, very bottom, and then I covered it all back up."
"You _interred_ it," Hickory said. "As in a mausoleum." Now she circled our faces with a look that said _I'm going to tell you all what this really means_. "Some people would say that was very symbolic."
"Not this again," Lucille said.
"I fucked a stuffed monkey," Basil said. "Big deal."
"First of all," Hickory said, "it wasn't just any old monkey. It was the monkey your _father_ gave you before he _abandoned_ you. That's why you killed the monkey. You _fucked_ it, as you say. And then, because you couldn't live with the guilt, you buried it someplace where no one would ever find it."
"You," Basil said, "are a goddamned fruit loop."
"Check out the science," Hickory said.
"Ha!" Lucille said.
"Seriously," Hickory said. "I'm not surprised in the least. It was a very normal thing to do for a boy that age. Especially in our culture. He just did it in an abnormal way."
Dinky rolled up on an elbow and scratched his chest. "You know what Hermann Goering said about our culture? He said, 'When I hear anyone speak of culture, I reach for my revolver.'"
" _You're_ the one belongs in the loony bin," I told Basil. He had a big whitehead on his nose I'd just noticed. "I'll bet you even crammed that thing full of mayonnaise before you did it."
"It's all right, baby," Lucille said, rubbing his back. "I still love you."
"We think we'll be going upstairs now," Dinky said. "We're going to lie down for a while." He stood there in his Cal Bears rugby shirt and Joe Boxer boxers with their bologna-sandwich appliqués. Then he sniffled and wiped his nose and started away, dragging his feet like they were a couple of sleds. "We don't suppose any of you would care to tuck us in?"
"I'd love to oblige," Lucille said, "but I know how you get when a bed's nearby."
"Not that I'd worry so much about that," Basil said. His face was waxy now, a veneer of cosmopolite ugly. "He ain't exactly what I'd call, you know, at the height of his form these days."
Dinky picked his nose. Then, his face a model of serenity, he extended his arm and with a simple motion of thumb and finger flicked the booger onto Basil's hat. "At least our dick is straight," he said, looking at Lucille.
"That thing better not have landed on me," Basil said. "I'll cut that straight dick off. Go ahead," he said, "go to sleep. But beware."
"I knew a guy," I said, "who woke up one morning and went to take a pee, and when he pulled his dick out, guess what color it was?"
"You guys are so sick," Hickory said. "I'm trapped in a shack with a grade-A bunch of sickos."
"Black," I said. "As your crappy gaping pupils, I'm talking."
"In fact, to call you nothing but sickos is a kindness you scarcely deserve."
"Turns out," I said, "the guy had got so blotto he didn't even know his frat buddy'd taken the thing out in the middle of the night and colored it with a Magic Marker, one of those big-ass felt-tipped Magic Markers with the refillable cartridges even."
"I find a booger on me," Basil said, "I'll cut his dick off."
"Come on, Dinky," Hickory said. "You go lie down, and I'll make you some tea."
Dinky left. We could hear him shuffling up the stairs and across the floor above. No one said anything to Basil about the booger on his hat. We just poured more drinks.
"Sometimes," Basil said, "I think, _Man, that guy's got no spine at all_."
"Character," Lucille said. "He's got no character."
"No, I mean _spine_. Character'd be what you are. And you're only what you are when the lights go down."
"The guy's been a year in Bosnia," I said. "Sleeping in two feet of mud. Eating Ball Park Franks and Twinkies and shit."
"We all know he didn't go over there because he's a patriot."
"If you were into ninety grand of debt," I said, "and didn't have a way to pay it off, you'd've joined the army, too."
"Dinky joined the army because it's not the _real world_. Like everything else he does. To keep from doing anything _real_ , I mean. Like a real job. Like a career."
Hickory snorted. "What, and you call driving around HelLA a couple hours a day a career? You call that a _job_ even, chucking papers on the curb?"
"He wouldn't even do that," I said, "if he didn't feel so guilty for a life's worth of mooching off his sugar units."
"Bitch," said Basil. "I'm a professional musician."
"You're a record company's bagboy."
"I'm the mother fucking mover and shaker who's going to make your ass pay, is what I am. And guess what else? It's only a matter of time."
"You're thirty-five years old, Basil. You know as well as those record people do the kiddies won't be lining up to see your teeth fall out. Not to mention you could stop kicking everybody out of your band all the time."
"So I'll be fat and bald and toothless, but at least I'll be up there. Sure as hell beats chasing pubes for a living."
"That's not _even_ cool."
"You want to be cool, be cool."
"Look, you boobs," Lucille said, "are we still playing or what?"
There was that briefest moment of doubt where Basil and I considered exchanging our knives for guns or throwing the knives away. But really the doubt was feigned. We knew what would happen. The kill was just a dream. The sight of blood was enough. We were only after the blood. This of course was a perversion cultivated over time, like a taste for taboo food, monkey brain or mice. The satisfaction of knowing we'd wounded one another was more than sufficient. In fact, it had become for us a fix of sorts, why our hate for one another always equaled our need. Basil and I were Siamese twins parted only in flesh.
"Hell yes, we are," he said, "and it's still my turn."
"Your turn?" Hickory said.
"To ask."
Lucille tossed back a shot. "Well ask away then," she said. "Ask away the doo-da day."
BASIL WASN'T GOING TO ASK LUCILLE ANYTHING worth her breath. He already thought he knew everything she had to say, a presumption which, so far as I could tell, was nowhere near the facts. And whereas it was true that before she'd become his woman he wouldn't have thought twice about crushing her at every meal, now that she was his, he'd save his curiosity for the pillow talk to come.
I was absolutely positive, for instance, he didn't know a thing about the times my ex-wife and I found the cupboards full of empty cereal boxes those three months Lucille had crashed our sofa. And if not cereal boxes, it was milk cartons at the back of the fridge, dry, or garbage cans stuffed with candy bar wrappers and foils from TV dinners. An entire roast would've vanished in the night, or a pot of spaghetti we'd just made, or a half-gallon of ice cream, all manner of food all of the time. Basil didn't know, either, how those very mornings, I'd enter the bathroom to the odor of Lysol and vomit.
And neither would Basil ask why Lucille had slept with each of the three Gladden brothers that crazy summer of '87, when after munching three grams of shrooms and a hit of blotter our friend Moo-Moo stumbled through a skylight and broke his legs; when our dealer Tony the Tongue invited four girls to the House of Men for a session of free love only to fake an epilepsy fit after two of the vixens tried to pork him with their strap-ons; when in front of the Grand Lake Theater a herd of cops arrested me and Dinky and Basil for having bombed a woman with a fire extinguisher just because she looked, as Basil claimed, like Barney Rubble with tits: while she went ape shit and chased us howling, we burned rubber through a KFC lot full of cops gathered for an ad lib feast. They caught us with three fat blunts, a bottle of wine, and a BB gun, fully loaded.
But Lucille. First she'd taken Bobby, then Benjamin, then Brad. Not one of these brothers knew the rest were boofing her, too. Because with the mornings, with the rising of suns and fungus-eyed friends—whichever friends happened to've been in whatever house she and the brother-at-hand had done their boofing in—Lucille would appear all by her lonesome in the crumpled state she'd adopted as style. Back then, the girl wore nothing but Birkenstock sandals and macramé anklets, cutoff Levi's or OshKosh overalls smeared with the paint of her artistic dabblings—an imitative blend of Arthur Dove and Marsden Hartley with a hint of Homer's seascapes—them and her Grateful Dead tees, tie-dyed, of course. When the weather was bad, she'd wear some Tijuana poncho and often even a blanket round her neck, like some queen-of-People's-Park swaddled in mangy ermine. And this was on top of her feeble attempt at sprouting a noggin full of dreads. The day would begin like habit, bong hits all around, the morning's wine in homemade mugs. Whichever Gladden brother she'd been with had already slipped through the woodwork like the creeping ferret he was, so that when all was said and done, that, as they say, was that.
Later, after these affairs had caved, we began to crush Lucille with gossip. And though for the next few years shadows kept the details grey, the matter cohered vaguely nonetheless. That's how these things work: one morning, said Misha, who'd got the scoop from Lisa, who'd pinched it from her boy Sam, whom Bobby himself had told, Bobby bragged about the compliments his lovers all gave his beautiful cock, which, according to Lisa-by-way-of-Karen-by-way-of-Lucille, was hardly the case; as for Brad—Lucille's last of the brothers—he had caught the clap (someone else had slipped between him and Ben); and Ben had a girl in the east who'd found out about his slick business, then told another friend, who, of course—because, again, that's the way these things go down—was a friend of mine.
And where I was concerned, what could Basil ask he didn't already know? How many diseases I'd got by the time I hit twenty, or had I shoplifted as a kid or tinkered with sex? The closest it came to that was kissing my cousin when I was five, beneath a blanket on Christmas Eve. Though my dear old toad had no doubt caught us, he was kind enough to wait till morning, dressed like a Hare Krishna elf, to beat me with his paddle.
Nor would Basil ask why I'd called last year at four a.m. to say something was amiss with his granny. She'd just suffered a lapse in health he and his mom went nutty for, some sort of brain hemorrhage I knew nothing of. At the time I considered my little call a motiveless joke spawned by a five-day binge during which I'd consumed three eight balls, seven quarts of bourbon, five cases of sucky beer, and nineteen or twenty packs of smokes—and that's forgetting my jaunt through Berkeley's midnight streets in nothing but a beanie with a propeller on top, ranting about Ezekiel's wheels gleaming of beryl and the predictions of Nostradamus.
But later, in the clarity of my regret, I saw the canker in the bloom. Basil had "fired" me (that was the expression he used once he started talking smack) from what he obviously had considered "his" band. In a dull autumn noon veined with dull autumn smog, we sat over a mound of pad thai and confessed our interests had suffered a rift. He felt, or so he said, I could do better elsewhere. Get out on my own maybe, he'd been stifling my creativity and such, he said. But even in the midst of these shams we both knew he was wonking through his bullshit tulips, making a farce of protecting my ego while disguising the rage of his own.
That he knew I knew he knew I knew all this made it the more obscene. His head had grown bigger even than Dinky's, which wasn't to say my own had shrunk. I'd risen from the glop of my tyro swamp, having begun my apprenticeship in music just five years back. Now a producer chose my song from a group of twenty-plus that Basil and I'd mostly co-written, claiming it the stuff of hits. But that didn't justify anyone calling me greedy, not like they could Basil. The cat couldn't share a stinking thing—not money, not women, not smokes, not booze, not cars, not drugs, not _nada_. Why the hell would he share the title Creative Genius—whatever that meant: more groupie sex? a solo name-drop in the _Chronicle_ 's Pink Section or _BAM_ magazine?—even though he'd already taken all but the glamor-light itself with his singing and playing both? People by then were comparing him to stars like Paul Westerberg and Chris Cornell and Sting. Did that matter? Not a stewed red penny. A shadow's shadow threatened the kid. The shadow itself nigh on crushed him. And the thing that made the shadow, when it came too near, it might as well have been King Kong. We sat there stabbing at our shrimps, hoping the waiter would bring us the check so we could go get drunker than we were.
And the more I thought, the more seeds of deviance I scraped up. In our high school days, Basil's grandparents left each year for a three-month tour to Europe or wherever, leaving us to our bashes at their mansion in the hills. It was during their last trip, before his grandpa died, that I got plastered on Rainier Ale. I was sixteen years old, shorter and skinnier than I am today, a gawky, graceless runt, for sure, in size five-and-a-half waffle stompers and a Gor-Tex parka stuffed with paraphernalia and drugs, and long, greasy hair, and zits the size of gumballs. Between my having left the party and gained the john, I'd become so drunk that when finally I began to hurl I lost control and shit my pants. And this was no ordinary shitting, either, nothing like a few solid logs you could scrape into the bowl and have done. We were talking about a sloppy, repulsive mess, full of chilidogs and Funyuns and Hostess Apple Pie, to say nothing of all that brew, an honest-to-god shitting if ever a shitting was. Really, I should've been proud of that dump, but I was a twerp. It made the Montezuma's Revenge in some tripper's shorts look like a painting by Renoir, green and yellow and slimy as it was, running down my legs and the pants at my ankles and even in my boots. To make matters worse—if that were possible—a very special girl had come that night, a little vixen with whom I fancied myself in love. For months I'd been chasing her eye, going so far as to write her a poem she wasted no time laughing at with her friends on the quad. Had I merely barfed, I'd've been okay. But I had to go and crap my pants, and that no one could pardon. So there I stood moaning and crying and retching in the shower, and when I called Basil to ask for a pair of trunks, what did he do but burst out cackling. Because that was the kind of guy Basil was. He made buffoonery of your heroics and heroics of your buffoonery. If you told a joke, he made it your inexcusable flaw. You had a flaw, he turned it to a nasty joke. After laughing till he cried, my dear buddy rushed out to the PA for his band. "Hey, everybody!" he yelled at the mike. "Guess what? AJ just crapped his pants!"
Another time, high on mesc, Basil lit some kid's hair on fire just because it looked, as Basil said, _like it would burn real good_. Another time yet he turned me in to the dean after the dean had caught us smoking dope in the bushes behind the portables. I'd run down the hill and got away clean while Basil and the other tard with us stayed put like the dean had said. Basil never knew I was the one who'd slashed his tires the night he fell asleep in his van after banging some girl he'd dragged from The Ivy Room. Basil never found out, either, how I'd filled the lock to his apartment with glue. He was living in a rat hole near West Oakland, whose landlord hated to answer his phone. Wearing his clothes for the days it took Basil to get inside pounded him with jock itch.
The one person Basil could demand a real Truth or Dare from was Hickory, the only one he hadn't known for more than half his life. I listened to the howling rain while Jelly Roll Morton bopped on the ivories and Lucille tore open some Mexican candy bar I'd never seen, with a load of marshmallow and other shit that looked like blood. I thought how when it rained my old toad would tell me the undertaker's wife was coming to take me away. He and moms had so many ways of expressing their love. _Every time you sigh_ , moms used to say, _you lose a drop of blood, and that just keeps bringing you closer to death_. Then she'd sigh, and I would scream, _O Mama, Mama, Mama!_ while she and my toad fell back laughing. I thought about all the creatures in this wintry world, out where the rocks lay cold and the mud ran thick and the trees and wind and clouds sputtered and racked and rolled, and Basil sat there before me with his impudence and his flaws and his knowledge of and persistence in them. He took great pleasure in these traits. They somehow gave him the sense he'd become indispensable to the people on whom he committed his tiny crimes, the way delusions become vital to the hypochondriac. His face was always glistening with that petty smirk of self-awareness. Even in his antagonism he'd become precious to those he knew—big, goofy, confident, fashionable, dear, droll Basil, the helpmeet fright wig, twentieth-century portrait of Juvenalian adage—two things only the people anxiously desire: bread and circuses. God, how I hated that I loved him. And then there was Hickory lounging in the smoke with her ink-black hair and creamy throat while upstairs Dinky wheezed among his dreams.
"I should ask her," Basil said, as I had guessed, sneering Hickory's way. The booger was still lodged in his hat. "But I won't. You, doofus," he said to me, "Truth or Dare. And don't give us another one of your boring-ass stories we've all heard a jillion times."
Across the room our bottles sang their nitwit song. I'd talked to them in the past, my bottles, and held them close. "Sweet, sweet booze," I'd say, "please don't ever leave me." I crawled to the table and stuck one in my mouth.
"Truth," I said.
"We want to hear more about your fucked up family."
"Yeah," Lucille said. "Tell us more about your Hare Krishna dad."
I smiled my smile of the hero, the general at his table of defeat, surrendering up his troops.
"I ever tell you my old toad was a paperboy?"
"Every kid was a paperboy," Lucille said.
"I mean when he was forty-two."
I told them how after he'd quit the Hare Krishna's, no place would hire him, no place real. He still had that bald head with the queue down his back. Who was going to hire a guy that looked like soap-on-a-rope? He delivered those worthless inserts with the advertisements in them, I explained, the ones with the Round Table Pizza coupons and Thrifty's discount ads and such.
But what I did not tell them was how my whole life it seemed I had to watch my ass, waiting for that fuck to sneak up and holler: _Andrew Jackson!_
What I did not tell them was how he would jump, and I'd run, and bit by bit the time would pass until he caught me with his paddle.
What I did not tell them was how from the shadows my mother would always laugh. _Yes_ , she'd say, _yes..._
And for absolutely positively certain what I did not tell them was every time he saw me my grandfather said how he and dear ma had spoiled my mother past sense. They may've had to scratch it out, but that never kept them from giving her love. He gave her love sure, he'd say, especially him, more than she could use. Their lives, he said, were each other. On their wedding day, when they and theirs and all theirs too came dusting through the gates to the fields trying to swallow up the house for the last hundred years, the place was a vision or mirage. They spat from barrels and slapped on legs and pebbled the hens and drank from a bottomless jug. And the goods, he said, did they ever have them: black-eyed peas, corn bread and greens, pickled peaches, and okra, and ham. Greasy fingers ran through tri-tip and pone, gravy and spuds and coleslaw, too, and laughing mouths scarfed cookies and apple pie. If the men weren't eating or drinking in tens, and the women weren't doing the same, it's because they were together. They hooted into that Texas night, he said, and no one cried unless for good. In the morning, for their honeymoon, they chugged on down to Austin. He spoke about those times like they'd just passed, my grandfather did, their five wild nights in the honkytonks and jukes and once a hall with its giant band, the champagne swilling and they screwing like bugs wherever they could—on the hay-riddled planks of the '29 Ford, in the alleys with the tramps and garbage and toms, but mostly in their eight-bit bed—all this before returning to the dust of the fields and the everyday sun. Lucky for grandy she couldn't make more after whelping out moms, my grandfather said. _She all but dried up, like a row of set alfalfa_. Of course the coot presumed he'd done what he could to make sure moms knew he loved her. He never could see how once she'd grown to bleed she didn't want him anymore, he said, why she went away. And the day he himself went away, I drove off with my old toad and moms to gather what he'd left of grandy in Lamesa. Not so, however, the day my own toad croaked. The first thing I did was strip an ambulance clean and smash it all to bits. It was only later someone told me I'd done every crumb of dope I stole before they'd fed my toad to the grave, how everything stunk of ether and mints. _Red rover, red rover, send happiness over_ —that's what the voices said. And then it was them on the street, plotting my destruction, bearded women, first, then barkers and trolls, then geeks and elves and clowns would come to lay me siege. Robitussin low balls and speed-jacked marys made my fare. Sometimes I drank water, sometimes I even slept. We buddies went to jerks with names we didn't know and watched films whose stories were an endless blur. And sometimes, like now, we journeyed on trips whose ends we'd never guess...
For a long while no one said a word. That stood to sense. The only thing we knew was how to keep on boozing. And my dear friends, I trusted, wouldn't—couldn't—ever feel the emptiness of that, leastwise not how I did. We couldn't go forever. Sooner or later we'd have to lie down in darkness. Without the speed that had kept us hopping, I saw no other way. Any time now we'd collapse around the secrets of ourselves, the ones we knew and the ones we didn't.
I was tired of believing a shroud could mute the sense that some dimly feared disaster might beset me in the night. Let it come. It couldn't be more terrifying than sleep, with its dreams realer than our lives. The party was ending, that was sure. We'd torn our gifts open to find boxes inside boxes inside boxes, and nothing in the last. Good riddance, holidays— _sayonara_.
"I forgot Dinky's tea," Hickory said at last, and glided toward the kitchen. "I'll just make him a cup of tea."
"What're you going to make it with, pine cones?"
Basil was right. Everything we had was on the table.
"Think I'll go see what's up with army boy myself," I said.
"Check the phone while you're at it," Basil said. "Maybe it's working now."
But when still nothing but fuzz dribbled from the thing, Basil flung his hatchet at the stack of wood and cracked his knuckles like he did when he was tight, a tic I'd grown to hate across the years, not for its sound but what it foretold: my bosom pal was about to become a bigger asshole yet.
"Next thing you know," he said, "we'll be eating each other for breakfast like the losers in the Donner Party." He dug his fingers into Lucille's ass and lurched at her with fangs. "My oh my how these buttocks are sweet," he said. "Fingergoddamnedlickinggood they are, oh my, oh my."
"That's not funny," Hickory said.
"This isn't funny?"
"What you said. It wasn't funny."
"But her ass does taste good." Basil held a hand over Lucille's butt. "See for yourself."
"It's just not funny, talking about our predicament that way. Even as a joke."
I was surprised at Basil's little fun. He had his man-bag with its hatchet and knife and rope for good reason, or for reason good for him. Territory past any town's limit was territory rife with _Deliverance_ -type freaks and fools gone native, full of conspiracy theories and tales of a world destroyed—with fruitcakes, essentially, like Super. Every time we hit Baja, much less the Berkeley Hills, Basil would forage through the mess in his truck to make sure he had his kit. It didn't matter the fun we made. He'd just tell us to thank him when we're old, for our necks from the noose that day back when. And the Donner Party especially. I don't know how many times he'd spun yarns about it, like tales from the crypt, bemoaning, at bottom, their fates as fodder for themselves. The notion he'd end his days in someone else's stomach was for him the doomsday to beat all doom ever. The man couldn't see three frames of a zombie flick without breaking into hives. Watching him blow his top was always a gas. Every now and then, just to flip his wig the way I knew it would, I'd break out the drumstick from a turkey or chicken and cackle like hell while the fantods rocked him. If he was joking about the Donner Party now, it meant one thing: he was scared.
"I'm sorry," Basil said. "It just seemed like a good time to throw caution to the wind."
Hickory gave him two numb eyes, then went to the CD player and dropped in _Murder Ballads_ , by Nick Cave and his Seeds. A ghost-cold bass sauntered from the speakers, and then that guitar's staccato chook, the piano leaping at every fourth while the reverb spread like a stain...
_So he walked through the rain_ ,
_and he walked through the mud_
_till he came to a place called The Bucket of Blood—_
_Stagger Lee!_
I'D JUST SCANNED AN AD FOR A DILDO INSIDE Dinky's latest trash, _Pink Champagne Bitch_ , when a turmoil of voices called me back.
"I'm telling you," Lucille shouted, "someone's out there!"
Dinky must have heard it, too. He lurched up hideous and swollen and said, "That's our book... Turn out the lights... No..." Then he cocked an ear to the door. "Who invited her?"
"I came in to check on you," I said.
"In the dream I was having..." I waited for him to go on about this dream but his words were dribble.
"In the dream you were having what?"
Dinky covered his face with the sheet and coughed. "Maybe we could ask those chuckleheads to put a lid on it. Do you think we could do that, Andrew?"
From the wall above him a clown gazed out with that comically lugubrious expression old people somehow feel compelled to adorn the faces of clowns in art. Dinky's great-goddamned-grandmother, or someone like her, had probably slapped it up.
"Even if I wanted to," he said, and looked away, "I couldn't." I watched him fumble with his pants. He looked like a child, with a child's confessional eyes. "Hickory, I mean," he said, though I'd known what he meant. His lips were trembling. He was speaking of himself as _I_. "I only wanted someone to hold," he said. I realized then the clown was staring at me, too, or so it seemed. I hated clowns more than anything, to say nothing of paintings of clowns. And now Dinky had to go and lay a guilt trip out. "About getting her on her back. You know I didn't mean it... Right?" His hands came up as if with a toxic globe. "Look at me," he said. I tried to look out the window but only saw myself. "How can a guy get any sleep with that?"
We heard Basil say, "Turn out the lights," and then Hickory something about a lamp. Meanwhile Lucille had begun to chant: "O my God O my God O my God."
The sounds were undeniable, clunky and deep at first, like a hammer on a hollow box, scratchy and thin the next. By the time we reached them, Hickory, Basil, and Lucille were at the window again, with just their eyes above the sill.
"Watch it, you guys," Lucille said. "Someone's out there."
"No one's out there," Basil said.
Dinky slid down the jamb and turned into a ball. "Is that why we're all on our hands and knees?"
"There," Lucille said, and pointed. "Did you see that?"
For just this once I wished she'd been lying, but she had seen what she'd seen. A shadow moved through the rain, then faded into mist. Then the sounds began again, leisurely nearly, steady, like a bridge troll, or maybe a giant, crunching on his bones.
"Who do you think it is?" I whispered.
On a talk show on the tube three enormous women argued round a little man while the singer from his box moaned about a girl with hair full of ribbons and gloves on her hands.
"You're out of your mind," Basil said. "I didn't see dick."
"Someone _is_ out there," I said.
"Then that's it," Basil said, and strode to the door with his hatchet. "I go out there and holler, and no one answers, I don't care if it's the Queen of fucking England, when I see him, he's as dead as fuck. What's the matter, baldy?" he said when Dinky wouldn't budge. "Afraid of the big bad wolf?"
"The guy can hardly walk," I said.
"He's good enough to get out of bed, he's good enough to kick some ass."
"Blood," Dinky mumbled. "Bright red blood."
"Don't do it," Hickory said.
Lucille began to wail, something I couldn't get.
Basil glared. "You coming or not?"
We went into that fist of night, hunched against the rain, scared as hell, too, speaking for myself. Something was out there, in the wallows beneath the deck perchance, lurking and munching, and we were stoned and drunk and tired, to say nothing of critically blind. I looked to Hickory above me, her hand on Dinky's arm. The best my friend could do was prop himself up to watch. By the way she cradled him, I could tell it was all for show. She wanted him to think she thought he needed checking. The rain had soaked me through again, now. I felt dirty and soft and stupid as could be.
Basil moved crabwise down the stairs, brandishing the hatchet. "Whoever you are," he said, "you'd better stop fucking around, cause we mean business."
Once upon a time I'd fancied myself that bearded miser's secret spy for truth— _once upon a time_. Because now we were stuck in a game. Anything could happen, anything at all.
"After we go around," I said, "you stick to the wall, and I'll slip over by the trees. That way, whoever it is, if he's got a gun, he can't get both of us at once."
"Where's my knife?"
The water ran down our faces, over the brim of Basil's hat, his face a glistening shade. I could see his hatchet. I could see his shiny teeth.
"There's this," I said, and showed him my Swiss Army pocketknife.
"You _little_ fuck," he said.
I stepped toward the trees, trying to keep my footing in the mud. Basil crept along the wall until a thick, hollow _cloonk_ sounded through the pitch, and then a muffled _humph_. He had plunged to the ground and by the time I reached him was rocking to and fro.
"Son of a bitch of a stone slammed me in the balls, man."
Again we heard the sounds, this time from inside the cabin. My brain was reeling, with gutter rags and dirty socks, and broken teeth, and fingers, and brooms.
"He's in the basement," I said.
"I heard the bastard."
I tried to take his hatchet. "Maybe you should give me that."
"The hell you will."
My buddies at the window couldn't see us or anything else. They couldn't hear a thing, either—nothing but wind and rain. All they could do was wait, afraid for the sound of a shot, the screams of some twit getting killed. I squinted hard at the trees as their skin crept round their Etch A Sketch limbs, searching endlessly it seemed for the lamest of signs, until just as I was ready to quit a shape emerged from the wall at my right, about twenty feet off, and like a phantom set our way.
"There he is!" I said.
Basil leapt growling to his feet and drove toward the shape, its movements clipped, as if by a wound. The shape came on, a man now, I knew, who might not've seen us even, lurching as he was to some alien poise. But just as Basil fell on him, the man feinted one way and dodged the next. The hatchet made an arc of whaleback-blue, then dropped wide of the man, and the man leapt forward and spun and with a boot sent Basil down. Then both fell from sight but as quickly emerged, then fell back again. I heard a crack, and then a grunt, and then, as though by bitter poets, a cry of hurt and rage. To know what was what or who who was hard, but soon the man rose in deep silhouette, the hatchet aimed at Basil's neck, his face the print of terror.
I rushed in now, my little knife lost, and took the man by his wrist. Straddling Basil, still pinned, he swiveled round to meet me. Those pale eyes—that silver beard and earwig mouth—the hand with the hatchet bony and wet—the tattoos on the fingers—
" _You_ ," I said.
"No, no," Super said. "Not me." He still had my friend by the throat. Basil tried to speak, but couldn't so much as squeal. "You ain't no bard," Super told him. "Rest a while, now."
"It was you in the basement," I said.
" _We_ weren't nowhere near the basement."
"You would've killed him."
The old man snorted. "This little squirrel? Heh. We were just scratching his mortality some. Catch our drift?"
I looked at the hatchet. I looked at Basil. I looked at the hatchet, and then again at this spooky man. And then once more I saw the rain, veiling with its ceaselessness stage and play alike, and knew I was just a groundling.
"I don't suppose you have any more of that stuff," I said, hoping Super would know my intent.
With two fingers he picked a blob of mud from his face and studied it like he might a gem. Then he balled up the blob and squashed it. Next to him, as if he'd been there always, sat Fortinbras the dog.
"Laddie," the old man said, "your telephone has gone kapooey."
"What?" I said.
"But fear not, fear not. The man we used to be just did a bit of surgery. The wires are fine, we think."
"Who is this guy?" Basil said, and I just about laughed. With his blackface of mud he looked a wretched minstrel.
"The one we told you about."
"This crusty boob?"
Super stood quietly by, a quasi-grin working beneath his beard. He'd just topped Basil at his own game, _mano a mano_. But worse than that, he'd shamed him. Looks made Super the grizzled old man half Basil's size. And yet here he was carrying on like the matter had been less than a drill in humor. He could've been the high school jock laying a yo-yo on a freshman nerd.
" _Naw_ ," Super said. "Don't say it's so."
"You want to cut my throat, dickwad, get on with it. Otherwise, blow me."
"Tell us, Laertes. Just how is it you expect to get our cousin down the mountain?"
"You have any idea what he's talking about?" Basil asked.
I shook my head.
"Stuyvesant Wainwright the Fourth, of course. We come to see that old black clown doesn't carry him off."
"Let's get out of this rain," I said.
"Not till you officiate some manners-making, you won't." I looked at the old man. "Your cohort," he said. "We don't know him from Hill."
Goddamn. Crazy as it was, the geeze wanted introductions. "Super," I said, "meet Basil. Basil, Super."
Super extended a hand. "Pleased to rub truth with you, son."
"Basil. My name is Basil."
The old man scratched his beard. "If we can recollect better than piss in a pot, memory says the name ain't never the thing. Fools of nature's all we are, to the last of us."
Basil turned to me, defeated. "I'm really cold," he said, almost whispering. "And this guy makes me feel like a mollusk. You mind if I kind of just, you know, go inside?"
I ASKED SUPER IN, BUT HE LEANED AGAINST A boulder and pulled off a boot.
"Something," he said, "is itching at us."
Where a foot and five toes should've been was a chunk of salmon-colored plastic. He peered into the boot, tapped its sole, turned it down, and shook it.
"Ha!" he shouted. "Someone needs to ring them bells!"
It was hard to believe, but before my eyes, on the old man's palm, lay a little stone. He examined it, grinning, then looked up like I were a man imprisoned.
"Take this," he said, hand held out, "and we will set you free."
"Don't you ever get cold?"
"We wanted to make sure you got help for Stuyvey. Some investigation after we dropped off you and him revealed that a sore impossibility, hence our return. We are good with wires."
Again I made away but the old man wouldn't budge. A pallor had crept over him now, a rich air of sadness.
"Not that we'd recommend such activity beyond the pure necessities," he said, and turned toward the light someone in the cabin had just switched on, "given our mission's success and your telephone does now work."
Dinky and Hickory were gazing down from one window, Lucille from another.
"So how'd you know about that thing anyhow?" I said, indicating the little stone.
"Ever hear that old saw," he said, "'All the world's in a grain of sand?'"
"If I did, I don't remember."
Super tossed the stone and donned his boot. The last thing he wanted, it seemed, was to go inside. I recalled his truck's open windows, his refusal of Dinky's invite. Finally he stood and called his dog Fortinbras, then cleared his throat for speech.
"After the doctors pitched them boys in the Cong the better half of our two legs," he said, "—hold on now, let us ponder... that was back in March of '68, we believe, Tet offensive is when the foul deed done been done—well, like we said, after they snatched it off the way they did and throwed it to the dogs what with only a scratch, we didn't have any more sense where it had been than a germ has brains. But later we got to feeling these itches down there, and other pains and whatnots. Our ghost foot, they called it. We can feel, all right."
After that, what I really had to say couldn't be said. I was just too tired.
"You're welcome to come inside," I said. "But whatever you do, I've got to go."
"Well you go on and go, then, though again we must decline. We only hope you and yours got enough of that blister-your-sister up there to last the night or more. In case nobody told you, there's a bastard of a flood in progress as we speak. The spirits are truly calling."
A CIRCUS-MUSIC AIR SEEPED THROUGH THE WALLS, a voice croaking on about whispers and dances and the lie that was home. It was the mongoloid glee of pots and pans, and marimbas, and accordions, and guitars that wouldn't tune. And like the song, all inside was doorway huddlings and splashing wine, the mirth, it's true, of fantastic ends. The world had changed between now and then, but the cabin had not, nor the humans in it. How is it the strangest people we know are nearly always ourselves?
My boys and girls were at it again, none of them eager, of course, to know how we'd fared. The two girls and Dinky sat round Basil sprawled on the floor with a bottle in his fist.
Lucille was making a pile from the mud she'd pinched off her man. She paused when I walked in, more, it seemed, from the disturbance I'd created than anything else.
Dinky had propped himself on an elbow to motion at his drink. No doubt he'd struck the pose merely to impress. In all our years, our lasting pride was standing off the Comedown.
The Comedown—ah—what's got to be the nearest drunks can get to Old Scratch's terror when Sir Nothing cast him out—far from your mother's kisses and the SweeTarts bought on Sunday with the coins from Saturday's chores after waffles and bacon and eggs—crushed in that void, totally confounded: Jim Carroll's lovely at the corner of Seamen and Dripp, who every Friday night bangs this jerk or that to rise come _mañana_ with a frog in her throat and Ding Dongs and beer and rubs on the floor: the tone arm's bouncing in "Angie's" last groove, the stench is sick as a cheeseburger's ghost, the light through the blinds are the fires of hell, and _nothing_ —nothing like a blot—of true love is lost in the depths of her hair. Still, and for all that, you'd never find us giving in to the thing, admitting our defeat, not ever. The Comedown could gouge our eyes and break our teeth, stab us and choke us and carve its name in our heads, but we'd only scream for more. It didn't matter that we'd slipped down its throat, our hands gone utterly wild. Fuck that beast! It could swallow us whole! And whenever we did find ourselves in that dark fix, really and truly—and we did, we did—you'd not once hear us say it. Someone came along to ask our thoughts, they'd get the old two thumbs. Serve up that grime. Serve up the shit entire. We'd be there sure with bibs besides, slurping it down to the drop.
Something good and mean had Dinky all right, if not the Comedown then some other such piece of woe. Anyone could see it. He gazed out emptily now, frogish and huge. A person could've slapped his face with a skunk or crammed his ass full of melon, he wouldn't have squawked a peep. His face didn't lie. It was a fallen house, in whose halls slunk that oaf, Remembrance.
"You're back," he said, struggling to his hands and knees. He couldn't decide to stay put or stand, or even what to say. "Welcome once again, old pal... to our little... fold."
And then Hickory rose to greet me, the shag fell away, goofy and light she floated my way, petals in her hair and from her eyes, though still I was numb, still my head was a bucket of sand, that floating blossom, dancing girl, she came my way to pour herself out and smother me gold, it was only for me to cry the word, her with her voice, her with her lips and eyes, for now I was home, made limber and fine, another time yet I'd been brought clear, I could smell her now, she drove me bent, hallelujah, lord, praise be the stars, for man, oh man, this I knew, I was most certainly fucked...
"Look at you," she said. "Your face..."
They were gawking at me, then, all of them, the mannequin, too, staring me down with its empty eyes. Then clarity took me, and I snatched up the mannequin to kiss it again and again. And then I tucked it in my arm and with my free hand high went forth.
"My friends!" I said. "My friends!" I grabbed a bottle and poured five shots. "I'd like to propose a toast!"
"Come again?" Lucille said.
"A toast, my dear. In fact, a toast to you. In honor of your promotion." I raised my glass. The spirit of the underground man had crept into my head, through the porch of my sleeping ear. "Let us all drink," I shouted, "to the success of Lucille Bonnery. May she live long and prosper in her new status as Queen of the Corporate Raiders!"
Dinky found the strength to burble "Hear! Hear!" while Basil sat up with "I'll drink to that—hell, I'll drink to anything!" They emptied their glasses with a single draught, Hickory and Lucille, too. "A toast!" they said, and drank.
I choked down my shot and began to convulse...
When at last I came to from an apparent fit of speaking in tongues, Basil was standing above me, rubbing his eyes. He looked hideous and comical, encrusted with mud, it and that hat perched on his head like some ugly bird from the sea.
"Maybe you guys've got the skinny from the inside," he said, "but I haven't understood half the crap this whacko said."
"So your question is...?" Lucille said.
" _Hatchet Lady!_ " Hickory said.
"Nice," Dinky said.
On the mantle, between a badly carved falcon and some frou-frou matches, stood a little doll from Mexico, huaraches, serape, sombrero, all. When you pulled the sombrero off its head, a giant boner sprang from its pants, only some wise guy had wedged a twig beneath the thing's sombrero to keep the boner boned.
I held up the mannequin like some ventriloquist's dummy. "This is not a prison," it said. "Because if it is, what the heck is the world?"
Dinky coughed. "Well put, mannequin," he said.
"You, my fat-headed friend," said Basil as he whirled on Dinky with more savagery than he seemed able, "had better watch it."
Dinky fell into another fit, his worst so far. Super had returned to fix the phone, I remembered. That's what he'd been doing in the basement, working on the wires for the phone. If the phone worked, we could call for help, we could bring in a winch for Basil's truck. And if the roads hadn't been washed away like They were saying they might, we could run our friend to the doc's and throw a celebration. And if the phone didn't work, well, Super had got here somehow. If he was here, so was his truck.
Fancy ideas, and probable, too, had the phone not been made worthless for good. From the other room, the news warned folks trapped in the storm to remain inside with patience. Mr and Mrs Jones would love this, I thought, free of the flood in their cozy dens. They'd hunker round the tube with their top-shelf booze and gourmet ale to point and exclaim, taken for a time from gluing their models or paging through zines or waking from another nap.
Dinky was hacking so bad my friends couldn't help but see. They gathered round him now, outrageous. They wouldn't admit it, not yet, but the sons of bitches were scared. Dinky looked worse than he had in the rain. "What's wrong, what's wrong?" Hickory said, and cried.
Pretty soon they got him on the couch, and pretty soon again he set into the lines from some old poem while making gestures no one could stop. "Dinky's sick," he said. "He must die—Lord, have mercy on us!" Then he'd cough or burble or whimper or sometimes even laugh. And then the tedium would repeat.
"That's not funny, Dink," Basil kept saying. "That's not funny."
"It's no joke," I said.
"Really?" Lucille said. "Maybe you could tell me what you're doing with that mannequin then."
"Not right now," Basil told her. "Just don't."
"Well," Lucille said, "then maybe _you'll_ let me know when I've got your permission, O Lord of Lords."
"I'm serious, Lucille."
I dropped the mannequin and kicked it. "Now you're serious. It takes Stuyvesant getting like this for you to get serious."
"That supposed to mean something?"
"Unbelievable," I said.
"What, like you've been telling me something?" Basil said. He flung his hand toward Dinky. "I mean, look at the bastard."
Hickory's face had become a mask, not so much of sadness or despair, though these were plain, too, in a tired sort of way, but more of simple disgust. "Someone get me a towel," she said. "And another pillow."
We heard Lucille in the kitchen rifling through cupboards and drawers. From another room a door skreeked open, and Lucille returned with a rag and icky pillow.
"The situation's evident," I said. "But if we stay here much longer we might not be able to leave."
"Anyone can see he's sick, _dork_ ," Basil said. "A fucking bat in a goddamned fucking cave could see that."
" _Dinky's sick, he must die—Lord, have mercy on us!_ "
Hickory took the rag from the bowl and passed it over Dinky's head. She caressed him with easy words.
"Anyone," I said, "could've seen the guy was sick a-way back when, _squeeze_. But no one here gave a goddamn till the shit was in their face."
"Who cares?" Lucille said. "The point is we give a damn now. At least I do." She looked like she'd just been indicted for some heinous crime. Her eyes leapt from face to face. "I _do_ care," she said.
"Not enough," I said, "to've ever been straight with him. Not when you had the chance."
"I know you're not talking about what I think you're talking about."
"Just how many were there before the Gladden brothers, Lucy? How many after?"
"That's not fair, AJ."
"Or what about telling us all why you didn't care for Dinky enough to confess the fun you were having that summer he was away? Or any other time you couldn't shrug off your seven-month itch."
I was getting to her all right. She was crumbling. "That's not fair," she said.
"You think he doesn't know all about your games?"
" _You_ don't know the half of it, you bastard," she said. "I had my reasons."
"You did," I said. "And I know the hole they crawled out of."
"That's not fair. It's not fair."
"It's a little hard to cry wolf when you're one of them."
"None of that stuff had anything to do with how I feel about Dinky. How would you know what he means to me?"
"I wouldn't, Lucy. That's my point. I can't see you give a stinking straw for the son of a bitch."
"You bastard."
I ignored her and went on. "Is that what you told Basil last summer, fucking him under that Mexican moon? I know how you are, Lucy. Hang the cost! _Shit_. You care so much for Dinky you just sent him into a hurricane for a bag of ice."
Basil rose. "I should cave your skull in right fucking now."
My hands flipped up to frame my face with a set of waggling fingers. Somewhere in my heart I'd hoped to look like Munch's screaming man. "I'm sooooo fwightened," I said. And then I snarled. "You cock head. If you had anything in your skull to make it worthwhile, I'd have done you a lifetime back."
Basil stood there in his suit of mud. He still had that blackface, and the hat besides, perched on his head like an ugly bird.
"I'm your _boss_ ," he said. "Remember that? In fact, now that I think about it, I'm your _former_ boss."
"I never worked for you."
"I suppose I'm not the one who's been signing your checks these last eight years then."
"You jerk. Everyone here knows your grandma owns the buildings. That she got from your grandpa no less. All of which makes you nothing but a trust-fund piece of crap with insurance and fancy clothes."
My friend was fazed, I could see, but that didn't keep him from shooting back. "It's a hell of a lot better than being a talent-lacking toilet-scrubber," he said.
" _Dinky's sick, he must die—Lord, have mercy on us!_ "
Hickory had stayed by Dinky throughout, hand-in-hand, passing the rag along his brow. Now she turned our way with liquid eyes.
"Please, you guys," she said. "Stop."
" _Dinky's sick, he must die—_ "
"Shut up!" Basil said.
"Dinky," Lucille said, "we're going to get you out of here."
"After Pac Bell comes in to fix the phone we might," I said.
" _Dinky's sick, he must—_ "
"Dinky," Lucille said.
" _He must die—Lord, have mercy on us_!"
"He doesn't even know what he's saying anymore," Hickory said.
"Maybe Super's still around," I said.
"What?" said Lucille.
" _Fuck_ that guy," said Basil.
"No," I said. "I mean, if he's around, so's his truck. He had to get here somehow, didn't he?"
" _If_ we can find him," Hickory said.
"Maybe we can. Me and Basil, I mean. At least we can try."
"The hell _I_ am. After what he did to me?"
"What _he_ did to _you_?" said Lucille. "I thought you said he was just some old nut."
"But you don't know. The guy's a freak, as in for real. It's like he's the actual _devil_ or something."
"That doesn't mean he won't help us," I said.
"I'm not going anywhere."
Another fit had settled over Dinky, the coughing again, the same spewing again of blood and phlegm. I smoothed his blanket and dabbed his mouth. Hickory told me to kill my smoke, so I got up and took about fourteen slugs of bourbon. Then I went into the storm, hollering out for some wild old man, with his wasted monkey and bed of dolls and dog standing quietly by. An emptiness had opened up inside me. The night was wet and black and empty and cold, and I was scared, more so than I'd ever been. Maybe this is _it_ , I thought, maybe this is where I'll see the face no one but the dead have ever seen. But maybe I won't be dead, just almost-dead, just passed out kind of in a forest of mud, curled up like some little bald worm in the mud.
THERE ARE TIMES YOU SEE THE ROT YOU'VE always been. My days were a trail of liquor-store bumblings and sunrise guilt, and every penny I'd earned these years had come to rest in a dirty glass. I'd ceased caring for others, and definitely for myself. The only things that mattered were booze and books. Scrubbing toilets—the very ones I'd puked into so many times—that was what I knew. The hurly burly of solitude that took me come each day's midnight had stripped any cool I might still have owned a long time back. Night after night, in the chill of an empty school, my ambitions fell away like leaves from boughs in autumn. And wandering those halls, moving from bin to toilet to bin, the few kind trophies of memory that did remain floated by as evil nymphs—evil because angelic, angelic because there in the corridors of my past those trophies were safe from deeper ruin. And like angels they were accessible in only the cruelest of ways. What was the good in having something you could never hold?
Dozing behind the desks in that collegiate gloom, the times of my youth would tiptoe up with a sort of wary glee, now days of drowsing in my grandfather's swing, now lightning in a field. Grape juice popsicles melted in my hand, beneath the shade of a swaying oak. My young mother would come to play in the wading pool. And rustling leaves, and tinkling ice, and the buzzing of bees, and pie...
And now? Now I was a shrunken head...
In the cabin some jazzy swing had commenced. Any other day it would've been a finger-snapping bop for Lucky Strikes and gimlets and velvet gowns on creamy skin, spiffed up wingtips and watches on fobs, dipping your darling with her mouth full of giggles and hot white teeth—Bobby Darin crooning for the sharks and the billowing blood. But that was not the case tonight. Tonight was a heckler in the dark.
I remembered in the midst of my shouting the light I'd seen through the trees when after the wreck Super brought us home. Dinky had said he had no neighbors, but if that were true, what was behind the light? A couple hundred yards down the road, I met another that spliced away, made just of dirt albeit. At first I couldn't see zilch, much less a would-be light. The wind roaring as it was, the water coming down as it was, not from the sky at the moment, but from the trees, with needles and leaves and dirt, and the groaning of the trees and rush off the mountain of water still in sheets, it was all I could do to keep from turning back. It seemed to me the notion of a boob to walk up that road alone—surely I'd deserve whatever I got. Who knew what I'd find, if not Super or a neighbor then may chance a pissed off lion, as scared as I was scared and hungry as hell besides. And what if I did find a man, but that man was no neighbor or even a neighborly man, but the kind Basil had always feared, the freak in the plastic suit, with six fingers and toes and a penis on his chin, wielding a flamethrower and Sawzall both? Not good, not good, any way you sliced it, not a bit of it was good. On the other hand, who the frick cared what I found? If I did nothing, chances we all croaked up here on the mountain wouldn't be so slim. Certainly Dinky wasn't going to mend. The guy needed a doctor, pronto. Not to mention if I ran off now, down the line I'd have to live with myself, a prospect at its best unspeakably vile. Getting killed was preferable to such a fate, honestly. I hoofed it up the road therefore on a bit less than faith, my adrenalin pumping as I stumbled along. And then I saw it, like before, a single light shining faintly through the trees. So it was actually there. So I had not been totally tripping. And lights meant power, and power, human beings. My eyes swelled bigger, then, I was ready for the worst, though just what I'd do when the worst came down, the best could never say. The road wound toward the light, but dwindled soon to a shabby trail leading higher up the mountain than the light had had me guess. Oh well. I'd gone this far, and now I had to see it through. The trail wended on, this way and that, until abruptly it debouched onto a tiny glade crepuscular with the light of a bulb on a wire through trees about twenty feet up. In the middle of the glade was a grimy tent, that was all, shaking in the wind. I cast about, struggling to discern a figure or shape, something squirming hogtied in a bag near the edge of the glade, I didn't care, I only wanted the what-was-what, even if that what was drastic. But I saw nothing but the rickety tent—not a clothesline, not a fire pit, not a chair or box or ice chest or stove, just a rickety, grimy tent. It simply didn't make sense, this scene. What was the source of this odd light's power? And who needed light to sleep in a tent, since pretty plainly nothing else was happening here? And why even a tent, in this of all wicked places? The last thing I wanted was to look inside, but knew I couldn't do other. That no doubt would be the test. The tent could even have been booby trapped, I thought. The freak with his bear-hide cowl and dick-chin and bones could be lurking anywhere, really, patiently waiting me out, itsy bitsy fly that I'd then be. And that was all it would take, my stepping into the creepy glade, whereon the fiend could drill an arrow through my neck or maybe just wait snaggletoothed and grinning till I stepped in the jaws of the trap he'd camo'd at the front of the tent, then rush up to hack out the pieces of me he'd forthwith set to slobbering on while writhing in eldritch pain and eldritch horror I lay by watching, pathetic. A few minutes of this whimsy later, having been struck that I could stand there forever conjuring the scene of my demise, I set toward the tent, listening through the wrack for some atypical sound, however teensy, however bright, anything to presage if only by an instant my impending harm, pressing on through the aura the hammer of my heart had generated round me, turned by now half-puke/half-stone, my legs prehistoric sarcophagi. My vision had contracted into the space of the tent itself, buffered all around by a band of quivering mist. And the closer I drew, the farther away the tent seemed to get, until in the space of a step the distance vanished, and there I stood before the tent. It seemed almost a being itself, the tent, its canvas in the wind like the skin of a creature from the sea or the north, a leviathan, suddenly, hunkered in the mud, I could easily have believed. Somehow I'd taken the zipper in hand, itself already half undone, and slid it till the entrance material had crumpled at my feet. And yet when I leaned into the tent, expecting who knows what to materialize before me—a stack of corpses, a cache of grub, magazines of ammo, maybe, tent-top high—what should I find but... nothing. The tent was as empty as a dead man's mind, not a scrap to be found, nothing so much as a wayward battery or dented cup, nor candy bar wrapper nor length of string nor nubbins of some candle. And it was then I saw the nature of terror, because it was then the nature of my predicament, like a toxic cloud, swallowed me utterly up. Terror, I realized, had nothing to do with time and space but with the absence of them, and with the incomprehensibility of that absence. There before that rotting little tent empty in the night in the glade in the forest in the heart of a pulsing storm, the emptiness of my life, and of my aloneness in it, usurped my thoughts with cruelty I couldn't fathom. A cipher just the moment before, the tent was now clothed in the powers of a totem, implausibly vicious, and I was numb head to toe, not a single atom free. I turned away in my deadness and broke through the night, blind, numb, thoughtless, empty, dead, Frodo in his fog of malice having donned that hideous Ring. I don't know how long I ran, but only that I ran till the earth resolved to steal my feet. My face had hit the mud at the base of the trail. I'd tripped on a branch, and lay in the mud, now, gasping for breath as once again the rain came down. When finally I rolled over and planted my hand, instead of the sense of slimy mud, the crinkle of cellophane brought me to. And what should that cellophane be part of, I saw, but an empty pack of smokes, Pall Malls, no doubt, goddamn. I dropped the thing and ran up the road shouting once more for Super. I shouted and cried, but come the fork at the road to the cabin, I'd seen nothing, Super most of all. What was the use. There was no use. Nothing mattered. Uselessness ruled. The numbness had left me. _I_ had returned, my body in woe, the wet and the cold and the bitterness of my presence in their midst. I put my hands in my pockets and chin on my chest and stumbled toward the cabin.
It wasn't long before, unbelievably, he reappeared, that weird old man, hobbling up from a path to the lake, Fortinbras at his heel. My heart at first leapt with fright—after all I'd been through, my expectations lapsed, I no more thought I'd see him again than a witch. But there he came, lurching along with his earwig mouth, and I knew it would help little to speak of the tent and certainly of where he'd been. Super hadn't been merely _out there_ , but _out there and everywhere else_. He _liked_ it out there. _Out there_ was where the bastard _lived_.
"We hadn't planned on leaving you down and friendless, young Horatio," he said, "if that's what brings you through this rage."
"Dinky needs help, right now," I said, shivering, "but the phone's still dead."
"You know like we know that the closest you are to another phone is a generous league. You seen the distance between here and the next abode."
I put a hand on his shoulder. Like his hands, it felt hard as ivory, and cold. Even out here I could smell him—cigarettes, marijuana, blood. "But what about your place?" I said, desperate, knowing as I spoke the vanity of my words. "Don't you live somewhere here nearby? Don't you have a phone?"
"Your phone, boy, was fixed and fixed. If it don't work, nobody's does." He may as well have handed me a rock. "Where's Laertes?" he said. "We'll be needing his size for the expedition we have in mind."
"He's a little scared of you," I said.
"And yet what with our wheels knee high in mud, we require a beast of his mass."
Super's company back to the cabin was welcomer to me than his presence was to Basil at it.
"Is he kidding?" he said when I told him Super wanted his help.
The old man stood just outside, smoking and sucking his teeth. "Come with us, now, Laertes," he said, and leaned in and pointed at Dinky. "Any little fuzznuts can see what our good cousin's worth. And as for young Horatio here, even if he does have a furious heart, well, he's just a bit too scrawny."
"If you think for even two seconds I'm going out there," Basil said, "into _that_ , with _you_ no less, you're one hell of a lot crazier than I thought."
Hickory squared herself to Basil. She whispered. "Dinky is sick, Basil. Do you understand?"
"I know it."
"So then pull on your boots and all that and help the man get help."
"How do I know he's not going to slice my throat once he's got me hunched over out there in Shitholeville?"
"You should be ashamed of yourself."
"If he was going to mess you up," I said, "he'd have already done it."
"That's a joke," Lucille said.
"Andrew's right," Hickory said. "Why else would he be here?"
"Oh Laeeeeee-er-teeeees," Super said, sounding like Bugs-Freaking-Bunny taunting Elmer Fudd. Basil said nothing and glared. Super waved his pipe. "We've got a little something for the road, if you catch our drift."
He'd poked my friend where he was soft. Basil knew about Super's drugs. That's a thing he'd never forget.
"And this is no ordinary bud we're talking about," I said. "You get some of what he's got and you'll be riding a freaking dragon."
Basil looked at me and Super and then at Super's pipe. Then he pulled his porkpie down and said, "What's a little more rain?"
DINKY'S HEAD ALONE DIDN'T WEIGH TWO-FORTY. And he wasn't fat, either, just thick as a Nordic killer. And something else that confounded the world, myself included, was his skin, tan all year and, like a doll's, seamless. It was his skin, I figured, that kept folks from seeing what a speed buster he'd been those years at Hastings, when the professor would call him out to say, for instance, whether a man who'd signed a contract with another man and then stabbed that man with a pencil could be held liable, given he'd met his contractual obligation— _Mr Wainwright, will you please explain?_ —and Dinky, insomniacal, garbed rain or shine in rugby shirt and Bermuda shorts, would totter from his seat to hold forth like a limey MP. But just as the class thought itself with a kook, Dinky would somehow manage to conjure the magic words. "And finally, sir," he said that time I accompanied him, "since the injury in question has nothing to do with said contract, it should rightly be considered a circumstance actionable in tort. Thus, by virtue of precedent, that being Tabucchi vs. Collins, 1976, the answer to your question must be indisputably affirmative." And that was him. He'd huff and he'd puff like some crook on the lamb, but unless he wanted you to see it, what you saw was a man turned gold from days on a lounge in the sun, impeccable coif and skin.
Well, he was huffing and puffing now, only his hair was gone and his skin like a plum in dirt. He was so far out, in fact, it took us all to drag him to his room. We got him in the bed with his snot rags and porns, and when the gang withdrew, Basil grumbling about the dope Super'd best give him, Dinky and I were left with no one for comfort but the clown on the wall, chained to its horrible stasis.
Super as it happens never did give Basil the pipe. Fiend that he was, the old man tormented my pal, dangling the pipe before him like some thingamajig of beckoning. He knew full well Basil couldn't resist trying to snatch it. The two slogged along for what Basil later described as "a shitload of time," up the road opposite their aim, until at last they wound about headed toward the 50, by which time Basil had been reduced to beggary, and then to outright theft. Predictably, he said, he waited till Super lost himself in a rant on the treachery of winter before lunging at his pocket. Super, however, unlike Basil, wasn't born at night or a fool. In short order, he slammed my friend against a tree and stuck a cutter to his throat while Fortinbras locked fangs on his ankle. Basil just stood there—what else?—helpless before the pictures in his mind, he said, though in the end they surrendered to a single image—Gomer Pyle's face, grinning like the village dolt. _Surprise! Surprise! Surprise!_
For a long time I didn't know a thing about this tale. Had Basil not called me a few months later, after I'd moved away and rented a shack by the river in Portland, I wouldn't have known anything but what he'd told me the first time round, all of which, as it turns out, was a lie. But he did tell me, and, for what it was worth at the time, given our fix, I believed him.
The way he put it, Super slammed him against that tree strictly to air the knowledge he'd got these years wandering the vasty planet. There Basil stood, looking into Super's eyes, knowing that for the second time in his life he was crippled. Oddly, Basil said, he almost enjoyed that sensation of helplessness, the compulsion, he said, actually to submit. I said _You're joking_ and he said _No_ and I said _So then now you're addicted to crack?_ and he said _I'm telling you, it just happened_ , and that was that, he went on to lay it down.
No one had witnessed his fall, he said, but Super and his dog. And if no one had seen it, how could they use it against him—at some later date, he meant, to fuck with him at the Roxy for instance or maybe the Coconut Teaszer, as he hooked into some under-aged nubile with bocci-ball tits and the ass of a little boy? He found it damn near relaxing to let Super rant on with his deep, rumbling voice. It sounded like music, almost, cozily uncertain, uncertainly familiar. Whenever I tried to butt in, Basil got all Zen and proceeded with the sappy, parson-like tongue he invoked most times for dramalogues. What with Super's voice, he said, and the rain thrumming down and the wind through the trees, the moment made him think of some New Age soundtrack these sandal-wearing meat-haters use to fall asleep when they traipse into town. He even went so far as to confess he couldn't tell whether he loved the old man or hated him. He wavered between wishing he could stay there forever, he said, cradled in Super's zany wisdom, or hoping someone might come along with a pistol to pop a cap in the old man's ass.
It grieved him to his heart, Super said, that the powers had ever made human beings, and worse, that he'd been born unto them. He praised the storm if only that it might blot from the earth not just him and Basil but all humankind, people together with animals and creeping things and creatures of the air. The earth was corrupt, he said, the earth was filled with violence.
But each time Basil tried to leaven Super's weight, he gave him a taste of the cutter, and a squirt of fetid breath would escape his teeth, and his eyes would roll up, and he'd set again to ranting.
He swore about certain pods of anguish, of how soon, on a bed of niggardly hearts and jealous bones, beaks sewn shut with thread and the toes of babes hacked off with shears, those pods would blossom into flowers of spleen, and the colossus of venality humanity had become would shudder and by crappers crumble in that swarm. Super was mad. The moon had come too near, he said. The eagle should never have landed. And the man on the moon was a whoreson goon and all the world his toilet. Basil looked skyward, and by godfrey there it hung, the moon, peering through the clouds like the eye of a giant owl. Even as they spoke, Super told him, they were bound by a Gordian knot and that, _ecce signum_ , here be the storm that corresponded to the storm in the eye of another storm yet, turning on itself and turning on its turn.
"We're just varlets in a void," Super said, Basil said. "The stratosphere was a lovely basket before the likes of you and me and the man we used to be come along with our fubbings and shoggings and horses from the same bleeding opera evening after absurd evening. Don't you know, boy? Don't you know?"
Basil stayed pressed to the tree, silent and amazed, feeling he should know, feeling he _did_ know, but for all his trying couldn't say. And even if he could've said it, he wouldn't have. Because he wanted the old man to say it for him. At that moment, Basil felt as if Super's words somehow possessed the amplitude of prophecy. He could've said _Orangejuice_ or _Snot_ or _Duran Duran_ and Basil would've found some meaning. The geeze had been trying to teach him something, but Basil, insolent and ingrate, had been unwilling to learn. Again he tried opening himself to the old man's hoodoo but felt he was nothing to him but a trinket with which he could entertain himself until ennui sent him forth once more to search. When finally Super had resumed his speech, it seemed to Basil the sun should've risen and the storm passed. But not a minute had passed, much less an hour. The old man's fingers loosened, the cutter fell away. Basil could scarcely blink or breathe, the old man had been squeezing him so. A protracted shiver ran through him as he gazed into Super's face, and then an icy numbness. The old man grinned. The grin became a chortle and the chortle a laugh, an obscenely sinister sound that seemed from the throat of a ghoul. And yet again Super dangled his fancy pipe. "You can't always get what you want, boy," he said. "Just what you need." Then he turned up the road, Fortinbras at his heel.
Basil felt ultimate disappointment. Super had lied. More heinous still, he'd stolen his lie from a song by one of Basil's most idolized bands, those five timeless beings who with sheer cheek and scorn for so-called bourgeoisie protocol had achieved a stature very near to that of God and second only to Iggy Pop, who was himself God (after all, Basil had said on numerous occasions, no one but God could survive on peanuts and bloody marys and bihourly main bangers of the jeweler's little kid, and then hit the road to put on the show Iggy put on night after night, and any dork foolish enough to say otherwise must be summarily flogged). And not only had Super lied—he'd had audacity enough to fob the notion off as his. Now the words would be forever leashed to his condescending growl. Not to mention, again, they were a lie. Basil had always got what he wanted, for as long as he could remember. And yet, he thought, if that were so, why was he standing alone in the dark in a storm?
_You can't always get what you want_.
He'd wanted to shout after Super, to tell him how full of shit he was, that he didn't, as Dinky'd always said, know his ass from fat meat. But Basil only stood there, absurd, swathed with the mud the old man had given him a rolling in. He peered through the gloom, hoping some face from his past might appear, cheesy and smiling, to reassure him—Potsie Weber or Mr Rogers or the Charmin Man—but nothing of the sort. Super had gone for good.
_You can't always get what you want_.
But goddamn it, maybe Super hadn't lied. When Basil looked at his life, he had to confess that nothing he really wanted had fallen his way. He'd wanted, for instance, to be a rock star since that day in '75, when he'd gone to see KISS at the Cow Palace (in the middle of "Rock and Roll All Nite" Paul Stanley had skittered across the stage with his famous mouth and eye, straight toward the hirsute but awestruck teenager, and flung his monogrammed pick right at him; after all these years Basil still carried the thing; he loved it so much, he always bragged, he intended someday to bestow it on his eldest child as a principal family heirloom), and yet They hadn't deemed him worthy. His grandparents by then had of course already given him more money than he could spend, but not a dollar in the pile had lured Fame his way, the old pimp, nor the love and attention he'd thought Fame would bear.
But more than the rest, Basil longed for a father, or for the return of the father he'd had. Come Basil's seventh b-day the swindler told the boy's mother he needed to run an errand. On his way back, he promised, he'd nab some Otter Pops and Fritos for the imminent bash. Instead the villain bailed—caught a number 15 AC Transit to the Fruitvale BART, a train to Civic Center Frisco, a jitney to SFO, and thence a plane to Puerto Vallarta, where he rendezvoused with a recently immigrated Hungarian secretary from the accounts department of Kilpatrick Baking Company, Oakland, California, a woman whom only three months earlier he'd bought a new nose, two grand. The mula for this he'd conned from another mark yet, a senior citizen named Mrs Annabelle Lovejoy, exstripper, porn-star, and erstwhile mentor to Bettie Page—yes, _the_ Bettie Page—who, Mrs Lovejoy, had been making regular monthly deposits of 500 smackaroonies into Basil's father's account, under the presumption, as the tale gets told, that he in turn would soon begin work on a private ranch in southern Nevada, a discreet, albeit fully indulgent, men's club. And once bolted, Basil's father never returned. Nor did he so much as call, nor even send a card. His mother learned of his father's whereabouts four years later, by happenstance, from a grocery clerk at Lucky's whose husband knew a bookie Basil's father was up to his neck in debt to. He'd left his Hungarian nosejob for the daughter of a snake-charming preacher from the Church of the Redemption of the Lost Apostles, Woodland, CA. Yes, he'd got religion now, and in the biggest way. Holy-rolling via cable from his own late-night soap box (much like the infamous Dr Scott), he and his sermons (authorized of course not only by the good Lord Himself but as well by a PhD from Dr Ronald Hassler's Night School for the Ecclesiastical Faithful, Soledad, CA, just a block down the street from the prison) could now be seen and heard in more than fifty-five municipalities throughout the Great Central Valley. Not until Super had appeared, Basil said, had he admitted how very much he'd missed his father, and yearned for his father, and for his father's love. He'd wanted his father's love for as long as he could remember, really, badly enough that ultimately that wanting had parleyed to a hurt only a bottle or bud or rock could ease. They, however, hadn't seen fit to grant him this, either, this revenant daddy.
Basil found himself shortly crying out, and more than once at that, but for answer got only the wind and rain and the creaking of trees in the wind and rain. To the west he could see the void that was the lake, black as the hole of his hurt. Lights winked at its edges, a perforated thread which for now was all that stood twixt the town and its destruction.
Basil began to shiver. At first he managed to contain his fear, but as it all continued to mingle and grow, his loneliness and guilt and disconsolation, so too did its outward display. Something had been taken from him, that much he knew, and yet precisely what he couldn't explain. Or perhaps he was simply lost. He knew only that with the ferocity of some malevolent germ the sense he'd been living a protracted mistake was devouring what little of him remained. And then he wept into oblivion.
When he came to, he said, he was so cold that should someone so much as tap him, his body would shatter like an effigy of ice. But the longer he waited, the more deeply he'd be lost. He didn't have his hatchet. He didn't have even a knife.
And so visions of catastrophe rollicked through his mind. Any minute now a tour-bus jammed with cultic octogenarians might descend on him, strayed from the path to some Lawn Bowling Tournament for Abused Geriatrics. They'd have painted faces and doctor's smocks, wooden dentures and powdered wigs. They'd sport bifocaled pince-nez, diapers by the ream, and with their embroidery needles tipped in poison they'd set to work on his flesh as though a hopelessly imperfect doily. Or maybe something worse, a heretofore undiscovered tiger perchance, the last of its kind pouncing from the dark with nuclear fangs. Or maybe a swarm of winter-loving bugs, clawing through the earth to feed on his brain. But worst of all, he fantasized, much worse, he said—and here, at this possibility, Basil felt what he only later realized was the essence of panic, of real human terror—a colony of Lilliputian Deadheads might emerge from the boroughs of patchouli they'd fashioned in the trees about him, roaring about in a murder of Lilliputian schoolbuses, each painted in patterns of red, white, and blue, replete with toupéed death-heads, all of the groupies with their nasty feet and rastafied haberdashery, macraméd roach clips, earthenware bongs, Moosewood Cookbooks and astrology charts, organic cottonwear, dreadlocks, Greenpeace and tarot cards, too, and the diminutive women with their hairy legs and bushes, and the men with their John Muir beards, they'd all truss him up and cram his gullet with Ben and Jerry's Cherry Garcia while around him, from the multitude of Lilliputian tweeders and woofers they'd have installed on the roofs of their Lilliputian busses, the anthemic "Truckin'" would blare, each and every one of these fiends, man, woman, and Muckluckian brat, flailing about in terpsichorean frenzy, The Wiggly-Womp Dance of the Dead. Basil wanted to run but his feet had sunk to the ankles in sludge. Sad but true, the bastard was stuck.
Directly after our conversation that early April afternoon, I walked into the sun to contemplate whether Basil had found any pleasure in his despair. Because now and then, I've heard it said, it's in despair we find our deepest joy, and more so yet when we see the hopelessness of our state. But who's to say? None of us really knows that much.
That night in the rain nearly four days had passed since Basil had slept. The meth was at best a ghost in his veins, and he'd been heavily drinking. Going underground was not an option. He may've been wretched, but he wasn't a mouse. And yet neither was he any longer the man he'd been, if ever he was that man. He didn't know who he was anymore, or what. He knew only that once upon a time he'd scoffed at the delay of action, because delay implied thought and thought, in short, was for pussies. And this for Basil was so. He'd never measured the cost of his deeds—what might happen should he bash this nose or snap that arm, say, or ingest this drug, or bang that drunken lass. Never once had he agonized before probable litigation, damage to the brain, unwieldy prophylactics. All these things Basil would do in a flash, especially if the man was blocking his yen, or the drug could bring him up or down, or the lass was there for the taking. Because Basil too had adopted The Cry of Twentieth-Century Solipsism, come straight from the mouth of his sometime-significant other. _Hang the cost!_ he'd shout, and leap into the fray. Never once, in truth, had Basil considered even the _notion_ of consequences, not, at least, insofar as that thinking concerned the philosophies of action and reaction, how in his moments of resolution he, Basil, functioned merely as a catalyst for the further realization of as-yet suppressed events.
And so he was trapped in this limbo of grey. He could stay where he was, he thought, and maybe, though more probably, die—a not unattractive notion on the chance we buddies viewed his death as martyrdom—or chase after Super, or return to the cabin to plan new modes of breaking away. But the deeper his reflection, the greater his fear. He couldn't free his feet, much less reach them to touch. He'd grown too stiff, for that matter, even to touch his knees. That was when the panic engulfed him, he said, that was when he fell. So brightly excruciating was his pain that at first he thought it rapture, though it wasn't, of course, or anything distantly like it. Pain pure and simple had struck him, such terribly horrifically appalling pain that the cry he let out could as easily have been heard as rhapsody than ecumenical howl. He pulled his dogs clear of both boots and mud and curled up like a question mark in tears, wanting nothing then but oblivion, or some place instead with quiet and warmth, and a beautiful girl, and booze...
_BOOZE. BOURBON TEA. GIRLS..._
The girls had gone to make bourbon tea, and Basil had left with Super. The door swung open, the door clunked shut. All lay in silence, they were gone.
But then I heard voices, and then a frisky tune, both jovial and odd, bopping to lyrics odder still.
_When my baby makes love to me_ , the woman sang, _it's murder_.
Dinky lay on the bed, mumbling against this scene, which by now had become a cinema of useless torture. Nor could I shake free of his mantra. Like evil vines, it had grown purchase in my head: _Dinky's sick, he must die—Lard, have mercy on us!_
The man didn't even seem real anymore. Or maybe he was realer than I could take. I held his hand. I stroked his head. His face felt clammy and hot. Above us, the clown looked content as a louse on a kid, staring with that sinister smile, its carnation, withered and doomed, the fucking thing. To hear the timpani of his heart I lay my head on Dinky's chest, but in my ears sang scratching claws. If in that moment a single word could've peeled away all the pretense and falsity behind which our lives had till then squirmed, I would've said that word, and said that word, and said that word again.
_When my baby makes love to me, it's murder_.
The night itself had become a lamentation, the dawn, trudging our way, its unshed tear. I wanted so badly to make up for all I'd done and been. But first I had to make myself, whoever that was, happy, whole, something. How I was to accomplish that, though, redeem myself, when that redemption hinged on so many needs, some impossible giving away of self, only doom could say. When my life amounted to a spoil of fits and starts? When I myself was a fake, if that, endlessly tangled in my web of fear?
I dropped into a chair and let it fade...
Down a slope of brush I tumbled, into a wasted canyon. A host of women rose from the banks of some dead river, their hair, like queens', in chignons pierced by sticks. They had elongated waists and statuary thighs, and their faces were veiled as in some ritualized state of mourning. Bangles and bands and bracelets of steel adorned their arms and wrists. I'd never seen something at once so beautiful and inert, postures, it seemed, intended as much to seduce as repel. I was negotiated through these idols like some apathetic hero, never touching them or land. I didn't speak to them, either, nor did I hear them speak. They were cold, these women, queer, and yet somehow I knew they'd gathered to keep me safe. And then a mouth opened up, the canyon was ending, and I hovered at the breach while a woman's voice sounded in my ear, just a word: _Keys_... I was vomited toward a lifeless plain. Among the rubble of some great alluvial fan I lay until with horror I saw that what had looked from above to be a knoll of rock and wood was in truth a mound of bones. I began to laugh. And when my laughter was exhausted, I fell into a swoon...
I rose to a world of verdure and flesh, maidens in a spring. A breeze caressed me. Birds in shadow sang. I was the voyeur in hiding. I smelled the smell of imminent love. They were angels to the last, each with Hickory's eyes, Hickory's nose, Hickory's mouth of red. But soon the green had melted, and I was made a blur. Murder was a sweet and death the moon. Knowledge entered: I had been so blessed...
_Gesundheit!_
Dinky had been sneezing. He lay propped against the wall, Hickory beside him with a mug of steam across whose side were the words, _Don't Worry, Be Happy!_ She must've just come in. On the stool to my side sat a mug of my own. My eyes I kept nearly closed.
"The sleep's done you good," Hickory said.
She'd gathered her hair in a bun and stuck it through with a pen. The tattoo of a skeleton key on the back of her neck whispered in my ear. _I don't know where the lock is now. Do you?_ Her face was graceful, quietly sad. It darkened for a time, then the corner of her mouth lifted to a faint encouraging smile.
"Drink this," she said.
"What time is it?" Dinky said, and spat into a rag.
"You know I don't own a watch."
"I want to see how long till sunrise."
Hickory shook her head. "The sun will rise, Dinky. You know that." She dabbed at his nose with a tissue. "Drink this."
"It's all bees now," Dinky said.
Hickory paused, as though digging deep for a clever word. She looked sheepish. "The I'll-be-damned kind or the I'll-be-a-son-of-a-guns?"
"In my head I mean."
"Drink."
"I mean it's not fires any more. Just bees."
Hickory drew back the curtain. She leaned into the window till steam fanned out before her. "Pretty soon," she said, "Basil and that old man will be back with the truck."
"I want to ask you a favor."
Her smile was pretense now for sure. And her voice sounded weaker, the skin on her face was tight. Anyone could see she'd grown thin on all the faking.
"Just so long," she said, "as it doesn't involve taking off my clothes."
"Your name. Hickory, I mean. It's not you."
"Someone here's forgetting that someone else made it up."
"I mean, I was wondering, you know, if you'd mind if maybe I called you by your real name."
"I don't care what you call me. You know that, too."
"Mira then. How about I call you Mira."
"Anything you want, Dinky."
After a time my pal sipped from his mug and said, "I saw you dancing. Tonight, when Super brought us back." Hickory smiled. "I told Andrew you moved like smoke."
"Maybe we can go some time," she said. "The five of us together, when we get out of here?"
"Maybe."
"Dinky."
"Leave me alone now. Can you do that for me?"
"You know that's not what you want."
"I'm really, really tired," said Dinky, crying now.
"No, Dinky," she said, "I won't."
THE MUG BESIDE ME SMELLED OF WHISKEY AND something else, some kind of flower, it seemed. White string dangled from its side. Hickory, I figured, had got resourceful. I cleared my throat.
"I made you some tea, too," Hickory said.
"It tastes like ca-ca," Dinky said, so strange, his face still wet with tears.
"That," Hickory said, "was supposed to be a surprise."
I forced a yawn and then a smile, and took the teabag from my mug. On the end of the string was something like a bandage. "What the hell?"
Hickory's mouth was a tight blue heart. "It's my secret brew."
"Jesus," Dinky said.
"If you really want to know," Hickory said, "it comes from a jam jar."
"A jam jar."
"Like the thing that keeps what you put on your toast?"
I looked again at the so-called teabag. "No toast I've ever had."
"Yeah?"
I studied the thing. The image of a jam jar with a big fly's wings bumped through my head. Then I remembered it, that scene from a few years back, with Lucille.
"Is this what I think it is?"
"You can think it's whatever you want, but it came from a jam jar."
"We've been everywhere there is to go," Dinky said, "and everywhere we've been that's called a tampon."
Hickory meanwhile had kept her mouth tight in that little heart. Now she narrowed her eyes.
"Like I said, _it's from a jam jar_."
So far as I knew, no one had told Hickory the infamous story of Roper and Lucille. She must've just heard it, from Lucille herself, I guessed, probably while they were brewing this toxic grog.
I'd just come in from a long night of raves south of Market. My pal Bruno and I had hooked up with a pal of his, a shrimp of a cat named Andre. The kid was black as a raven, with a hoop through his septum and bleach his fro—a stripe front to back—and an Angel Flight suit, white, propped by a polyester shirt of midnight black, and gold enough round his neck to've drained Fort Knox. He was the slickest dealer I'd ever met.
But before that even, Bruno and I had dropped a few tabs of X and hit the floor to mix it with the ladies. Three spicy Filipinas caught us gawking and slithered over post-haste, wriggles and tits and laughter. We zoomed in on two and left the third to share till someone else appeared. This went on for who-knows-how-long, ten or fifteen, or forty-five or fifty. What I can say for sure is how once Bruno's chick began to outdo mine, I weaseled my way between them. And by God if it wasn't five minutes more that the girl had grown eight arms, a hand on my chest, a hand in my hair, another on my Jean Jeudi.
"Your cock," she said, "I want it so bad in my mouth."
So that's how it was going to play. I'd give the she-devil what she wanted, all right, but first she needed some good old-fashioned romance. We went on with the dancing and kissing, the girl chanting in my ear the whole damned time, great godly filthy things, working herself up, I could see, into a frenzy. It was only after I'd run my hands across her rack a few hundred times that it struck me things were out of joint. Where, for crying out loud, was all the T&A? And then like a nightmare born I realized this goon had no more cleavage than the side of a train. In a panic I ran my fingers through her hair—a freaking wig, no doubt, coarse as a mop. Still, I had to be sure, and the only way to accomplish that was to stroll through the sanctum sanctorum. The X by then had me like a blight. Half of me didn't give a flying rat's ass what this thing was—part man, part woman, a little bit of beast—the other half swam with horror and rage. I spent a few minutes working up my nerve while whatever it was tried to swab my ear clean with its fruity tongue.
"Oh, sugar," it whispered, "I'm so wet down there, so wet for you."
At last my hand found its way into the drop zone, but—aarrrggghhh!—there in the cleft of a tight little buttocks lay a package bigger than my own. It was true, for sunshine's sake, I'd been played like a Mississippi catfish! My furious little fiend had herself a furious little appetite, yes indeed, and time was moving on. For the tiniest instant, I thought, _Hell, maybe I should just go along with this little snowqueen_. After everything else I'd done to get in this spot, it seemed I deserved whatever came my way. And if that weren't a death blow, I looked around to find me ditched by Bruno. I was on the verge of losing my bird when from out of the crowd stepped Alex, my friend from down-unda, purveyor of smart drugs extraordinaire.
"Drinks are on me," I told my little he-she as I rattled my glass of ice.
"Don't go!" it said. "Cammy don't want nothing but you!"
"Worry not, my sweet," I said, sounding like some dickweed Marlow, and bolted.
"You've got to help me," I told Alex.
"Easy now, mate, easy."
The bastard was sporting a boutonniere, of all things, a carnation garishly red. He adjusted this now with stoned aplomb and stepped back to take me in. Between the X and my terror, my peepers had gone Marty Feldman. From every little cranny nodules of color grotesquely pulsed, and the odor of booze, goddamn, the joint was packed with the stuff to the gills, manhattans and martinis and margaritas and woo woos, and wallbangers and grey hounds and midoris and macs—booze and more booze wherever I turned—and the gut-deep bass and calliope of synths, no horn or string could shape such sound, like the syncopated wailings of alien babies and alien dogs, and the cigarettes and cigars, the perfume and dope and hair spray and mints jostled with the stench of so many wet wool coats—well, stab me in my eyes, the works made me zany, I was itches and sweat, a guy built to spill, no shit, and Alex had not a hint or clue. From a fancy silver case dense with glyptics and birds he selected a smoke and tapped it out and lit it. Then he sat there inhaling the thing like a man who loves cheese, very sauve, very dramatic, his watery eyes aglimmer through the fuzz.
"What's the problem, mate?" he said.
"I am in deep doo-doo, man, as in up to my neck."
"You said that."
"I mean _serious_." It took everything I had to keep from looking at Cammy the Man. "This thing," I said. "It's after me."
Alex puffed out a line of smoke-rings and surveyed the room. "I see a lot of blokes doing their best to snare a little piece running round here. Where's these things?"
"It's not a thing, Alex. It's a ghoul."
"Now it's a ghoul."
"No," I said. "Not a ghoul. A dude." Alex kept up with the fancy inhalations and watery stare. "In drag," I said.
"Now we're getting somewhere." This was all so extremely amusing to him, just another whacked-out night in the city.
"Wait a minute," I said. "Don't look now." Cammy had been staring at me, licking her filthy hungry chops as she wriggled and spun. "The tiny thing with the black wig," I said. "With the halter top with sequins?"
"You've got to be kidding," Alex said, his eyes grown noticeably wetter. "If that's a bloke, I am Sherilyn Fenn."
By now my horror had all but caved to anger. I was near ready to slap this guy. "I'm telling you, man," I practically wheezed.
Alex laid his hand on my shoulder and drew me near. "AJ," he said. "What are you on?"
"Nothing," I said, and studied my feet.
"Nothing, eh? How come nothing's never got my orbs looking like a set of mum's best chiner saucers then?"
"Just a little X is all," I said. "Hardly any."
"A bit of the X, he says." At this point the room was whirling. Alex narrowed his eyes. The guy reminded me of James Bond, early Connery even, say from _Dr. No_. "Here's what I'd do if I were you," he said, patronizing as hell. "Go right back over to that little honey and tell her you're in love. Then take her back home and give her a shank on the kitchen table." He put his hands on my shoulders and turned me round. "Look at her," he said. "She's a bloody beauty, mate. Forget you're tripping and step to it."
"That bloody beauty, as you call it," I said, snatching him up by the collar, "has got a cock the size of your kangaroo-spanking arm." Malapropos, _really_ , Cammy now decided to shimmy her way over. "Are you going to help me out," I said, "or what?"
"Sure, mate," Alex said, baffled. "Sure."
"I don't care what you say just so long as you say it."
Cammy rubbed my ass. "When you come back, sugar?" she said. "I miss you."
"Cammy. I want you to meet my good friend, Alex."
"He handsome, too," she said.
"Hello, love," Alex said in that exceptionally Aussie way of his. He extended his fancy case but Cammy waved him off. "Listen," Alex said. "Do you think I could keep your beau for just another minute or two? We've been discussing a bit of business here, and we're just about concluded."
"I'm sorry," I said to Cammy. "I almost forgot about that drink."
"No drink," she said. "Just dance." She licked her filthy chops and took my hands, pulling me toward the floor. "Come dance me, sugar. Come."
"Just give me two shakes of the old lamb's tail," I said.
Cammy must've been as high as the rest, else she would've seen me for the fool I was. Her face assumed a corny pout. "You make me so sad," she said.
"I promise you, love," said Alex. "I'll have your chap back in a New York minute." He put his hand on my shoulder and headed toward the bar. "We'll just be right over here," he said, and smiled yellowly. We eased away at a steady pace until Cammy had returned to the floor. Then we broke into a trot.
"The least you could do," Alex said, seeing I'd already forgotten him in my rush toward the exit, "is offer the bloke who saved your arse a drink."
I handed him a fiver. "I don't want to take any chances," I said.
And now the coat check girl was giving me grief. It turns out I'd lost the ticket for my leather.
"Last time I gave a coat back without a ticket," she said, "I nearly got canned."
She had a web of tribal-style ink creeping from beneath the collar of her vintage coat, some Channel cut with a damask print. She worried her hands on the counter before her, smoothing out a piece of invisible cloth.
If I hung around too long, Alex's slippery doings might go to waste. My little fiend could materialize anytime now, _slurp, slurp_.
"Maybe I could tell you what it looks like," I said. The girl paged through a magazine. "I can tell you what's in it," I said. "Whatever you want." She kept up with this dumb act until pretty soon a sleek Cleopatra-type gal approached. Of course she had _her_ ticket. The check girl disappeared behind a rack and returned a minute later with a leopard fur coat. "Don't you remember me giving it to you?" I said.
"You give me a ticket," she said, "I get your jacket. _Capiche_?"
If the word _capiche_ was bad enough from the mouth of a guy, it was ten times worse from the mouth of some poseur of a girl making six bucks an hour. "But what," I said, "if I never find my ticket?"
The girl shrugged. "What if?"
I wanted my coat, but out even more. Cammy hadn't surfaced. I gave the room a final sweep, then checked my pockets. Turns out the fiver I'd slapped on Alex was the last of its kind. All told, I had some matches with a phone-sex girl, a smattering of lint balls, and $2.50 in change, pennies included. That at least would get me a pack of smokes. If nothing else I could hunker down against some warehouse to wait for the return of Bruno and Co.
Gillian the Peachy Puff girl appeared like a nicotine angel. She laid a hand across my wrist as I began to count my change.
"Stop it, AJ," she said. "Before I get embarrassed." I always did like her cutesy hat and those creamy thighs jacked up on stilettos. She handed me a pack of Camel Lights. "It'll be our little secret," she said, and I could've married the girl on the spot.
"I'll tell you all about it over coffee someday," I said.
Her smile hadn't budged. "If it's anything like the rest of your stories, I'll be getting off cheap."
"It's better," I said.
"You watch out," she said.
Sweet, sweet girl! She pecked me on the cheek and wobbled through the crowd. I tore out a smoke and clottered past a couple of bouncers, a gang of jeans-and-leather tough boys, two dykes creaming uglies in the photo booth. Some girl I'd dumped because of her shit-for-breath squealed my way, but I rolled through, faker of oblivion. The doorway was there, the night cheered me on.
Cattycorner from me a Dashiell Hammett lamp sprayed its glow onto the cab beneath it, a Luxor it looked like through rain, beige and purple as it was. Cars and bikes lined both sides of the street, north to south, and yet for the life of me, I couldn't spot a single crummy soul. No way I was going to stand around waiting for Cammy to show her darling face. Fifteen minutes: if Bruno hadn't appeared by then, I'd split like a banana.
The rain came down in mantles. The street looked like a mirror or pool. A line of traffic signals, steadily diminishing, cycled through their colors until far away, ten or twelve blocks, they merged into that familiar anonymity of concrete, wire, and fog. I took a breath and stepped out from my niche. The storm came down, thick with the odors not just of rain on concrete and paint and metal and wood, but of rain on scum, as well, breaking through that crust of dog-day vomit, and piss and poop and oil. A garbage truck drew into a phalanx of dumpsters with its tusk-like prongs. Out near the bay a klaxon lowed. At first it felt good, the cool and the wet. For one slippery moment I seemed to've been blessed with clarity. The world was truly gorgeous! The world had become a special place! But soon I was shivering, and I saw the streets for what they'd been, rows of cars like great sleepy turtles, pigeons huddled along the warehouse sills, all hyper-graffiti and brick. The billboards over the highway, eerie with faces beaming at banks and cars. The strands of mist about them. The endlessly strobing lights.
A white stretch limo inched toward the club. When finally it stopped before me, the last tinted window in a row of tinted windows began to disappear, until Bruno with his chill-blue eyes gazed dopily out.
"Me and Andre," he said, nervously it seemed, for his loss of words at my new look, or for ditching me, I couldn't tell, "were saying how you'd probably busted a nut or two by now."
"Wouldn't you and Andre like to know."
Andre was kicking it regal as a Space Age potentate. A ginormous mirror lay across his lap, covered with a mound of wings. "Hop in, brother," he said, "and spill your woes."
We rolled on down to another club, monotonous and droll. We did this three more times before I had Andre's driver leave me at my flat on Clinton Park. The rain had ceased, the sun plodding up the East Bay clouds.
At that time I was living with Lucille and a dude named Roper, George, that is, a fattish plucker of banjoes who worked in the mailroom for a stock-broking firm up on California Street. First thing he did each night when he got home in his thrift-store suit was change it for his tie-dye and spin some Dead or other such crap, Crosby, Stills, Nash & Young, or Joplin, or maybe even Dylan's whiney ass. But always it was LPs, and that's because Roper, aspiring Luddite that he was, had long ago made a point to boycott advancing tech, CDs, too, no doubt. Lover of bongs packed with green and steins full of lukewarm Guinness, he was, more or less, a grody son of a bitch.
I crept up the stairs and squatted on the throne to empty out my day's worth of living. A rueful song slippery with clarinets and trumpets had seeped in by way of the neighbors. It made me think of _La Dolce Vita_ , that scene where Marcello and his old man are sitting drunk with Paparazzo, watching a carpet of balloons follow the clown once he nods their way. The only thing I wanted now was exceeding dreams. But just as I was masking the proof of my deed with a squirt of the trusty freshener, I heard a low giggle, and then a voice in turn. Thinking these to've hatched from the street, I slithered nearer that way and heard them again, a crazy mix of childish giggle and executioner snarl. They, whoever, were in Lucille's room. I stepped softly now, lest the floorboards creak. This guy, whoever, made it _El Numero Cinco_ for the girl in two days under a fortnight. I placed my ear to the door.
"Mommy wants Daddy to lick her jam jar," Lucille said. The man's voice grumbled something I couldn't get. "Come on, Daddy," she said, her words both vampy and firm, "lick my jam jar."
"Not this jam jar," said the man.
_Holy holey_ , I thought, _it's Roper!_ Now I'd never cared what Lucille banged, but this surpassed all bounds. It wasn't so much her shanking eight million dudes that did me in—I'd coped with that plenty—but of her shanking Roper in particular, in secret, no less, after she'd sworn to the world till her face ran blue he was so grotesque she wouldn't kiss him with a taze. The image of Roper's hairy ass jiggling round Lucille, a-pumping and a-groaning like the porker he was, well, it about drove me to the edge.
With my ear to the door, I couldn't help but see the painting Lucille had hung on the wall beside it. A naked woman lay on a plain, her neck inhumanly bent. And though her face held enough of grief, its grimace revealed some pleasure, too, a thin, canine joy. But it was her eyes that conveyed the bulk of this sense. They'd rolled up in Spartan bliss, half angel, half wolf. Her face, still scarier, showed Lucille's twenty years down the line, the younger in the old, defeated and sad, and the once-full breasts like moribund flowers, and the bulge of stomach, and the veins in the pit behind the knee, and the clefts of her pappy ankles. Roper's voice grumbled on, louder than before.
"Damn it, Lucy, let go of my head."
"Just one tiny lick," Lucille said.
Blankets rustled, springs groaned. "I'll do all kinds of shit," Roper said as Lucille giggled, "but that's not one of them."
"Since when was a big man like you afraid of a little blood?"
"I'm telling you," Roper said. "I don't lick jam jars while the jam's still in them."
Of course the next day I told Basil what I'd heard.
" _Lick my jam jar, Daddy?_ " he said. "Are you serious?"
"I just about cried," I said.
When I told Dinky about the incident he took the Blow-Pop from his mouth and whistled. This was before his head had swelled up like a snake-bit horse, back when he still had hair. "Isn't she the rambunctious little harlot," he said.
That night we went to The Trophy Room. Dinky and Basil and I, and two chicks named Tina and Jimmy Sue, had set up camp near the pool table, waiting for Lucille to return with drinks.
"I don't believe you," Jimmy Sue said to Basil. "I know Lucy, and, unfortunately, I know Roper, too. She just wouldn't do it."
"Talk to Mr Jackson," Basil said. "He was there."
"I don't care if you heard it from J. Edgar Hoover. There's no way it's true."
I cast a look round the bunch. "If I told you the shit I know about our friend Miss Bonnery, you'd run to the clinic for a shot in the ass and a couple of cartons of bug juice."
Basil laughed so hard he coughed up his drink, right there on the table. Tina did her damnedest to freak me with her stink eye.
"Wait till Lucy hears this," she said. "She'll claw your fucking eyeballs out."
"She is the Hatchet Lady," Dinky said.
Jimmy Sue tapped the table. "First of all," she said, "Roper looks like Deputy Dog. Second of all, he's a fat greasy pig with a case of dandruff and breath like rotten chicken. I mean, the guy still wears tie-dye."
"That's true," I said, "every bit. But still."
"Still nothing," Tina said.
"I heard what I heard."
"You're disgusting," Jimmy Sue said.
"You think I like it? Cause I don't. I don't like it a bit. In fact, the shit's already a ghost." I expected one of the girls to come back with some lip, but they only sat there huffing on their smokes. "Listen," I said. "Once I had to take a crap in a public restroom, right? I've never done it before in my life, because next to a hippie, public toilets are about the filthiest, most repugnant things I know. And after you hear this little tale, you'll see why. The commode in question happened to be down at the Kabuki. It's Dan Aykroyd and Bill Murray in _Ghostbusters_ , fucking up the monster that looks like the Pillsbury Doughboy on PCP. But I have to pinch a loaf so bad I can't sit still. I do my best to stay, the flick is awesome, only to scurry from the scene like a clam. So there I am, doing my thing, praising the gods and their minions for not making me shit the bed—you can ask Basil the details there—when by the TP hanger I see a hole in the wall. And I'm not talking about some pinhole here. This thing was big as a can. But of course that's not all, because inside this hole, like a picture in a goddamned frame, is a little pink cock with a little pink hand just whacking away, going at it like there's no tomorrow."
"Ahhhhhhhhhhhhh!!!"
Anytime I ever told this story I got the standard communal howl. The table was absolutely cringing.
"That's right," I said. "How do you think I felt?"
"I would've kicked that guy's ass so bad," Basil said.
"And why is that, _mon frère_?" I said.
"Are you kidding? My space, man, my mind. The little shit, he invaded you. That's how he was getting off. Thinking about you watching him through that hole."
" _Exactly_ ," I said. "And now I've got this disgusting image in my head. That I'll never, _ever_ be rid of. And every time I see a public restroom, that's what I'll see—a little pink hand jerking away at a pink little ugly cock."
"That's all very splendid," Tina said. "But what's it got to do with you lying about Roper and Lucy?"
"From now on," I said, "I have to think about Roper with his head between Lucy's legs, trying to get away from her kooch. And every time I want some jelly on my toast, I'm going to hear Lucy's voice saying, _Lick my jam jar, Daddy, lick my jam jar_. Now if you think that's sick, so be it. All I know is I wish I hadn't been there to hear it."
"I would've kicked his faggot ass so, so bad," Basil said.
"The masturbation thing I get," said Jimmy Sue. "That you couldn't help. But this other thing, it's your own fault."
"What's a lad to do," Dinky said, "when he's living with such a rowdy minx?"
"Keep away from her door when he hears noise behind it," Tina said.
"Like you wouldn't've done the same," Basil said.
"Bellissima!" Jimmy Sue said, and kissed her fingers. Lucille had returned with our tray of margaritas.
"You," I said to Lucille, "are a doll."
"Wait a minute," Basil said, and paused very dramatically, a strained pinch to his face, studying Lucille's wares. "Where is it?"
"Where's what?" she said.
" _You_ know."
"No," she said, "I don't."
"The jam jar," said my friend The Prick, taking us into uncharted lands. "You forgot the jam jar!"
Lucille would've dropped the tray had she not already placed it—her eyes had expanded like yawning mouths.
"Pardon me?" she said, Hatchet Lady on her way.
"He's asking," Dinky interrupted, "why you didn't bring the _jam jar_."
"You guys," Tina said. "Don't."
"Yeah," Basil said. "Cause Daddy wants to lick it."
A Rocky-Horror-Picture-Show-Type goobus at the next table over was busy doing magic tricks for his Rocky-Horror-Picture-Show-Type goobus friends, the three of them slouched in their booth with their dyed black hair and big black coats and tight black pants tucked into black Doc Martins and patent leather Beatle boots. They were all glopped up with lipstick and mascara, and Goobus #1, Lord Fascination, had a pink toy dinosaur, Barney, from what I could tell.
"How much do we owe you for the drinks?" I said.
Lucille's eyes were burning. "I thought they were on you," she hissed.
"Did I say that?"
"That must mean you get to lick the jam jar!" Good old Basil. He'd seen my ploy to change the tune and was having not a jot.
"What is this crap, anyway?" Lucille said, playing dumb to the end.
"Come, come, Lucille," Dinky said. "The time for charades has long passed. Andrew Jackson, your roommate, we might remind you, heard the goings-on between you and blubber boy last night."
"Pardon?"
"When was it you forgot how to speak English?" Basil said.
"I heard him, all right. I don't think I understood him."
"Don't even worry about it, Lucy," Tina said. She held up a glass. "Who had salt?"
"Right here," Jimmy Sue said.
"Me, too," I said.
"All right, you bastards. Out with it."
Jimmy Sue stirred her drink and licked a blob of salt from the rim. She wasn't looking at Lucille. "AJ said he heard you with Roper last night."
"But we didn't believe him," Tina said.
"You've got to be kidding. You're kidding, right?"
"Only a miserable twerp like AJ would make up a story like that," said Jimmy Sue.
"It's no big deal really," I said. "Just surprised me is all."
Lucille stood back, her eyes hopelessly, frantically shifting. "You little runt," she said. "You puny little runt."
"Look at him," Jimmy Sue said, pointing my way. "He's shit faced."
"Take it back. Tell them it's a lie."
Tina glared at me. "He's so full of shit." She held up her glass. "Forget about it, Lucy."
"I won't forget about it. What exactly did you tell them?"
"Mommy," Dinky said in his best hot-to-trot vixen's voice, "wants Daddy to lick her jam jar. Please, Daddy, lick it."
" _Maaaaa-mmmyyyy!_ " said Basil with his hands out before him like a baby at the breast.
Lucille flicked her smoke into my eye, and then, to The Clash's "Stand By Me," dove across the table screaming, "Liar! liar! liar!"
We fell into a wall hung with ribbons and trophies and pictures of athletes retired. The drinks went flying, in my hair and down my pants—Lucille even took a chunk from my face with her nails. I could see The Rocky-Horror-Picture-Show-Type goobs blurry behind the rest, with their capes and sneers, mumbling stuff like, "She's nothing at all like Pam Grier," and "Violence is so mundane." But Jimmy Sue and Tina got the biggest kick of all. Jimmy Sue's distaste for me I could understand. On a date a few months back, we'd quibbled over sushi at Ibisu, bickered to death the secret of great art, and snarled through choosing the show we'd hit, my pick Monkey Rhythm and The Plimsouls, hers The Misfits and a Sex Pistols wannabe act. When later she announced with a toss of her bob that _Even Cowgirls Get the Blues_ was the twentieth century's greatest book, I had to take her home. Tina, on the other hand, unless I could be blamed for having brought her into the Buddy mix way back when, six or seven months before the night in question, and whom I'd recently given a book of Diane Arbus photos for her b-day, hadn't so much as dandruff to put me down. I could hear the two of them cheering Lucille on as she pummeled away. "Fuck him up!" Jimmy Sue cried. "Yeah, Lucy," Tina shouted, "get him!"
In the end some mondo bastard with a vest full of patches dragged us to the street. Next to the Kodak booth on the corner, an ancient bum was hollering at passersby. His old Schwinn bike, a masterpiece, really, had a banana seat and two-foot sissy bar, and ape hangers, too, with long-tasseled grips. The guy was bedecked in leather, head to foot, and sported a helmet from Germany strapped with vintage goggles.
"Now don't spaz out over there," he shouted when he saw us. "If you can't dance, don't start off with the funky chicken!"
The night may have gone sour, but that hadn't kept the gang from stepping out to the tune of _Hatchet Lady!_ and _Oh Mommy, Mommy!_ and _Daddy still wants to lick the jam jar!_ The Trophy Room's neon bathed the street in sad pink light. I thought of Lucille's painting, the woman collapsed in her fruitless world. Her head hung low, Lucille was a spooky premonition.
"For whatever it's worth," I said, "I'm sorry."
Her eyes were mascara ruined by tears. "You didn't have to tell them that."
"I'm really sorry." I tried to put my arm around her, but she shrugged me off and turned away. "Look," I said. "I'll tell them I was lying."
"All you know is little and mean."
"I'll make it up," I said. "Just tell me what to do, and I will."
"Go to hell."
And with that she ran up the Haight, past the bowling alley, past the Mickey D's, and melted into shadows in the park.
"You may think you got over good," Tina said, up in my face for added effect, "but Karma's going to get you."
"You know what you guys are?" Basil said to the girls. "A couple a type-1 morons. Now that," he said with a slap to my back, "was some kind of joke."
"I told you not to tell her."
"It was a joke," Basil said, and slipped a lemon-drop in his mouth. "Forget about it."
The old leather dude was still yammering at the passersby. "I ask you," he shouted at one woman, "if Death Valley is below LA or to the west of LA, and you don't know. You don't know anything. You're just Mrs Motor Mouth. And you're a messy housekeeper, too!" Then he saw me gaping and said, "You want to know a secret, pal?"
"What's that?"
"Dead men are heavier than Sunday afternoons."
"Yeah?"
"Them and wedding vows."
Dinky, gazing up through the gridlock of muni-wires, still hadn't said a word.
"Tell him, Dink," Basil said.
"Tell him what?"
"That she'll get over it."
"We must always remember old Tom's wondrous words of wisdom," Dinky said, smiling. " _There's nothing wrong with her a hundred dollars won't fix_."
AUGUST IN THE CAPAY VALLEY IS STRAIGHT-UP death. What water doesn't touch, the sun destroys, the nut trees droop under coats of dust, and the hillsides big with jim brush and sage fret with the shadows of buzzards, and hiding sparrows, and mice. And yet, even so, from a ruin of drought you can walk into corn so dense it might be a wall of scrumptious hair. With dusk the heat resolves—if only faintly, the sky's on you still—until at last night emerges and sleep becomes something you think could be real. That's the rattler's hour, then, time of the skunk, time of the owl, some Achemon sphinx with wings of blood-stained eyes.
For the month since I returned from Portland I've been trucking crops most days and nights to outfits down in Sacto and the Bay, Oaktown mostly, and the veggie quarter south of Frisco. I live in a trailer on cinderblocks, now, with one pair of boots, a pair of cutoffs and two of socks, and an old wool sweater nabbed from Sally-Alley. And save the nip here and there I take with Thomas the Tattooed Whiskey Man, I've quit with the drinking and smoking both. As for the folks who roust me some nights, when the bongos beat and the jug goes round the flames, well, they say I talk in my sleep about a girl by the name of Avey.
It's hard to believe I lived that other life. Not that this one's all that different. I've got nothing to my name but the letters it's made of, them and my rags and the copy of _Fear and Loathing_ I stashed in my ruck the day Super got us to the lake. A host of black birds ten thousand strong will rise from a field like a cloud from myth, and it's no more to me than dishes in my sink. I hit the peak of a rise on the road to look down windrows gold as my mother's gold ring, wider and farther than I can tell, and if I don't feel bewildered, it's because I'm numb.
Any boob with sense can see me for what I am. I could care less. Yet when I think on that night, up at Dinky's cabin, waiting for Super to return while Lucille told Hickory I was Satan in the guise of a drunk, how I'd always wanted Lucille for myself but couldn't, not, she said, because I never tried but because she wouldn't have me, how her scorn made me do things no human should have done to a person they called friend, how if Hickory knew what was good she'd get as far from me as her legs could go—when I think of that night from here in the endless quiet heat, I feel I've drunk a bucket of blood. Where Lucille got that stuff, I will never know. Not a snatch of it was true, not the parts that mattered. And besides, what difference did it make, so long as she never tried to load Hickory up with poison? That's how it went: I woke from a nap with a tampon in my tea and her saying she'd found it in some jam.
"It sure does look like one to me," I said. Dinky had sunk back into his pillow. Hickory was glaring. "What exactly did Lucy say?"
She dipped her rag in the basin and sponged Dinky's brow. "You could've told me you were just about anything," she said, "and I'd have believed you."
I'd hoped she'd ask me to explain, or even not to explain, that whatever had happened happened and nothing she or I could do would change it, that even if we could it wouldn't matter, because none of it had happened between us. I wanted her to trust in the promise of the man I was trying to give her. But she dropped her rag and left.
Dinky was snoring. A faint glow had crept into the room. Through the window I watched the swaying trees...
One of the girls had slapped in another disc, I couldn't quite make it out, a wheezing melody, country-like, the lyrics scarcely patchy... _learn how to steer... spill my beer..._ Hickory and Lucille were talking—"come back"—"fucking nightmare"—"just those Doritos"... I slipped toward the landing and cocked my head.
"What if they can't get the truck?" Lucille said.
"They'll get it."
"That old man scares me." One glass clinked on another. Something plastic bounced on the table, a lighter or a cup. The couch springs creaked, then the wooden rocker.
"Dinky," Hickory said, "told me you two used to have a thing."
"You think we should be worried about him?"
The music played on... _I don't like riding on the passenger side..._
"I am a little curious, though," Hickory said. "Why'd you leave him?"
"You ever meet someone who'll never say what it is they want? I mean, even when they know it?"
"He says you left him drunk in a fireworks shop. Down in some dirty town in Baja."
"He says that about every woman he's ever had. But really Dinky left himself."
"You and Basil are... Well. You guys can be pretty harsh."
"Buddy Time," Lucille said. "I know, I know. It's hard to understand, especially if you haven't been in it long."
The gnome at my feet was irking me to hell. Everywhere I turned found me challenged by some scrap of carnival, mannequins and clowns and gnomes. You had to wonder what the Wainwrights were about, this family full of tightlipped babbitts who thought they were cool every time they stuck some doll with a boner on their mantle.
"It's funny, you know," Lucille said, "how sometimes things just happen."
"I'm tired of things just happening," Hickory said.
"How things can happen and you don't understand them till after it's too late?"
"And that's if you're lucky."
"It's like when I had that shitty temp job out in Walnut Creek that time," Lucille said. "Ten or so years back, I guess, the summer before I got out of State. I'd taken on this temp job down at Blue Boss Insurance, to make up for what my parents wouldn't cover. Opening mail and photocopying and stuff. There were four of us there, me and this girl named Chiffon-Latrese, and two other bimbos from Antioch. About every three or four days, this guy'd call on the phone. He was a quiet kind of guy. He didn't have any business with the company, that's not why he was calling. He just wanted to hear a woman's voice, he said. It didn't take long to figure out he wanted more than that. Really he was calling to hear our voices while he beat off. He never said that's what he was doing. I just knew it. You could hear him over the line doing his thing, it was kind of loud, and he'd breathe real hard, you know. The thing is, he never said anything nasty to me or anyone else. Two of the girls, the bimbos, they wouldn't talk to him. He'd call and they'd hang up. Only Chiffon-Latrese would talk to him. And me. We felt sorry for him, I guess. Every time I answered it seems like I'd end up talking to him until he was through. You get tired of reading magazines, you know? Chiffon-Latrese, though, she was like me. A temp. Which means after about a month or so she got shipped off to some other shitty hole. Some days the guy would call up and ask me to tell him about my sisters. Some days it was the other women in the office he wanted to know about, what they were doing, that sort of thing. I could always hear him, too, going at it, I mean. But after a couple of weeks he started getting weirder. He asked me to call him names. 'What kind of names,' I said. 'Dirty names,' he said. 'Insult me.' So first I told him he's a good-for-nothing jerk and an asswipe besides, and what did he do but groan and ask for more. I called him a dirty bastard prick and he groans again and starts in with the heavy breathing. I called him a fucking douchebag fuck. I called him a cocksucking piece of dickweed. I called him everything he'd ever read in the _Penthouse_ forum, and then some. I was probably getting off on it all more than he was. It was sort of out of hand, I guess, when I really think about it. It had got to the point where I was practically screaming at the top of my lungs when his voice kind of shuddered, and he hung up. The two bimbos were staring at me. It made me think how creepy I must've been. I mean, I was enjoying all of that, you know? It wasn't for about a week or so that the guy called me back. But you know what he does? The first thing he does is ask how big my feet are. I told him I was a tall girl. My feet are bigger than most girls' feet, I said, but they fit my body. He said what size. Ten, I told him, they're size ten. But they fit my body. And then he hung up. Three days later he calls again to say he's been dreaming about me every night, says he's dreaming about my feet. He's been having sex with my feet, he says. I ask what he means by with my feet and he says he's been sticking his dick between my toes after I go to sleep, but that's okay, because that was how we'd planned it. Meaning, in his dream I'd told him the whole thing was cool with me but just to wait till I'd passed out. He asked me if that's okay, that he's been dreaming about me, and I tell him sure, that's okay, why should I care what you do at night. The next time he called, another two or three days'd gone by. He asks if I think he's a pervert. Well look what you've been doing, I say. So I am a pervert, he says. Sure, I say, yeah. But that's okay. It's not like you're stalking me or anything. But I'm a pervert, he says. Everybody's got their thing, I say. And he says, Yes, but I'm a pervert. Then he hung up, and I never heard from him again."
"People do things," Hickory said.
"But you know what?" Lucille said. "I didn't think there was anything wrong with it. I mean, if you really want to know, I thought there was something wrong with _me_. I kept taking his calls. It's like I actually enjoyed talking to him. And when he stopped calling, I missed him. I even got depressed, you know? Every day I'm answering the phone hoping it's my quiet little pervert. One day, after a couple of weeks, I pick up and there's a guy on the end who sounds exactly like my man. I was so obsessed with the whole thing, I'd brainwashed myself into thinking it had to be him. And so in this disgustingly breathy voice I said, _I've missed you, baby_ , and the guy says, _Who is this?_ Turns out it was just some schmuck calling about his reimbursement. That's when it hit me. _You're_ the one who's pathetic, Lucille. You. Fucking pathetic."
The girls were quiet then. I went back to Dinky. His breathing was still bad, and he was sweating and gibbering again, this freaky thing after that. The wreck must've busted him up inside, the way he carried on. Sure, he was sick before we'd got here, but not like that. Or maybe he'd always been sick but just never said. Or maybe he'd never said because he wanted us to see for ourselves, to say something, maybe, as if we cared, to console or advise him—it was there before our eyes, wasn't it, plain as a bomb going off?—or maybe just to ignore it altogether, anything so long as it wasn't this elephant-in-the-living-room type scene we all made light of in that lily-livered way of ours, when things got too heavy for anything else. He wanted something pure, I imagine, something he could count on.
I sat down beside him, wondering what I could do to make it go away. Spittle had pooled at the corners of his mouth. I wrung out the cloth from the basin and placed it on his brow. Once again he began to weep. I looked away, out toward the advancing dawn, and watched a list of stillicides trickle from the eaves...
_A sphere of glass filled with plastic snow. A withered hand clutching the sphere until it slipped and shattered on the marble floor. Rosebuds across a carpet, yellow, white, and red..._
Downstairs I paused in the landing this side of the door, and peered around the corner. Hickory lay on the couch, fooling with a Rubik's Cube. Lucille had propped herself up by a bourbon at the table to doodle on a napkin.
"It's pretty bad, huh?" Lucille said.
"You saw him yourself," Hickory said.
"But you don't know him like I do. I've seen him this way a hundred times."
"Still."
Lucille slapped the pen down and gulped at her drink. "Maybe the phone'll start working."
"Maybe," Hickory said.
"He shouldn't have let himself get that way."
"Maybe we should try and grab some sleep."
"He'll be fine."
"I could use some of that." I went to the table and poured myself a shot. The girls wore faces so thick they could've been spirits from an ancient play. At a low, nearly subliminal volume, Black Francis with his half-scream/half-croon kept repeating his line. _It is time, it is time, it is time for stormy weather_. "Is that some kind of joke?" I said, and killed the sound.
"Ode," Lucille said.
"What?"
"It's supposed to be ironic," Hickory said.
"You're just pissed," Lucille said, "because of that time Black Francis said he wanted to cut your ponytail off."
This was true. We'd gone to Smarts, this trendy LA hole you could spot a handful of stars in any given day. One night we found Uma Thurman, Johnny Depp, and Ethan Hawke playing pool together, drunk as goons in a depot. The night in question we'd run across Black Francis—AKA Frank Black, AKA Charlie Thompson—hiding in a corner, scowling with his porcine eyes. I had a ponytail then, like Lucille said. What Lucille did not say was how I'd whipped it into Charlie's face and told him I had to take a shit.
"Black Francis," I said, "is a pudgy glob of snot with a tude."
"You," Lucille said, "were just too much of a puss to say anything to him. Basil would've kicked his ass."
"Basil would've eaten his ass clean out if he'd thought it would get him somewhere."
"He'll kick _your_ ass the second he gets back and I tell him about all the smack you're talking."
"He can eat my ass, too. Just like you. Eat my ass."
"Maybe you children could save it?" Hickory said.
"Don't look at me," Lucille said.
"She sure as hell isn't going to look at me," I said.
Hickory started toward the stairs. "I'm going to lie down."
Lucille and I sat there twiddling, furious in our ineptitude.
"We're pretty sorry, all right," I said.
"All I want is to get the hell out of this dump."
"Whatever I've done to get on your bad side, I'm sorry."
"Payback's a bitch, ain't it?"
"Have it your way. But remember. You've got to deal with it till we're gone."
"You've got nothing, AJ. No life, nothing. If I thought otherwise, I'd say you make me sick."
I shuffled across the room like a freshly spanked child and stopped before a penny on the carpet. Old Abe's face in copper profile must've done something to me, because from out of nowhere, like some cat in a game show from Mars, I was swirling in a vortex of happenstance and quirk: Lincoln was elected president in 1860, Kennedy in 1960. Both were slain on Fridays, in the presence of their wives, both were shot in their imperial skulls. John Wilkes Booth was hatched in 1839, Lee Harvey Oswald in 1939. Lincoln had a gofer named Kennedy, Kennedy one named Lincoln... Yes, yes—and the hip bone's connected to the leg bone. One bygone Christmas, before the looney tunes had stepped up to conk her, my grandmother gave me a two dollar bill, a Pet Rock, and a book of disco dance steps, including the Bionic Boogie, the Weekend Two-Step, and Le Freak. Last year, on Christmas Day, in a drunken tango down Waller Street with a girl named Date, I fell to the walk before a makeshift sign of bamboo and cardboard, its words scrawled with a paintbrush in the hand of a child: On December 24th THIS DATE PALM WAS STOLEN BY A SHORT WHITE MALE WITH SHOULDER LENGTH BROWN HAIR MERRY X-MAS DIRT BALL! And Lucille Ball's all-time favorite show was M*A*S*H, and Amos Alonzo Stagg, AKA The Masher, invented the football dummy in 1889. Scat of the opossum, a beast that plays dumb when scared, is called werderobe, scat of the otter, spraints. The Yokut Indians used dust of spraints mixed with a liquor derived from the coffee bush to rid minds possessed by an odious spirit from the lands of thunder song and rattles. And while Jelly Roll Morton died believing he'd been cursed by a voodoo witch, Hippocrates ushered medicine from the realm of muddled superstition. Love is superstition, superstition, danger. Danger is an owl in the night.
SPC Stuyvesant Wainwright, IV
B Co 16th En Br
Operation Joint Endeavor
APO AE 09789
5 Feb 96
Dear Andrew Jackson Harerama vanden Heuvel
How are you my night-owlish friend? I've not heard any news from you since before you took on that job at State. Write to me and tell me what your plans are for the future.
I got a Christmas card from Jacquelyn and she said you weren't seeing each other anymore. But that was two months ago. I'm sure things may have changed by now. I wrote Basil about him breaking up too and said we could be 3 bachelor amigos when we get back. But I'm sure your situations will have changed by then.
Life here in Bosnia is usually boring but occasionally dangerous. The first American just died yesterday—the papers/news media are filled with speculation as to how. Military intelligence has informed us that he went out to take a shit (right off the road). He was squatting down and saw something in the ground. He took his Leatherman pocket pliers and poked at it. The medics found half his leatherman embedded in his brain! Lovely, huh?
Yesterday I spent all night day burning shit. 9-1/2 hours to burn 1/2 barrel of shit and piss. It is a smelly, shitty detail but somebody has to do it. Ha ha. We pour diesel into the 1/2 barrel (which sits below the bench in the 3-seater latrine) and stir it up. Then we light it and stir it constantly. Sounds like fun, huh? I can't wait for a job with a desk, buddy!
Buddies forever,
Stuyvesant
It was all too horribly true...
I had no money, I had no power, Lord of the Latrines I was, Prince of the Pubes, credentials alone to have got me elected President of the Cult of the Fool. How does such a man break out like wild dogs, much less like a parakeet? How does such a man give his ghosts the bodies they've lost, much less make them bleed?
Next to the bath, the cabin had two upper rooms. Dinky was unchanged, mumbling his flow of applesauce and bile. I groped my way into the second room, fixed on purging myself and the girl in it of the germs that kept us low.
_Tweet, tweet, tweet, my darling, tweet, tweet, tweet!_
_And the moments, dear, look how fast, look how lithe and fleet!_
MOST NIGHTS I LAY ON MY COT PICKING PETALS off imaginary daisies and conjure visions of those hours with Avey May Jones, of how as she melted to my words it struck me she'd grant my wish at last and give both body and words to me in return, if not forever then for what was left of that one sad night. All my life I'd dreamed of finding her. For all those days and all those years she'd been the knot of my dreams, my honeyed lump of winter mud, my mud song, simple, warm. I wanted to get stuck in her, all right. I wanted to stay that way forever...
I told her what had happened the time I came home to find Roper and Lucille. I told her what had happened at the Trophy Room, too, when Dinky and Basil had opened their can of fucked-up worms and set high the bar of mutilation. Then I told her the story of my wicked worthless life, of everything I'd thought I knew myself to be, who I was and where I'd been, and where I'd wanted to go and be. Had I tried to present myself as anything more than pitifully pitiful, she'd probably have abandoned me on the spot. However foolish I'd been till then, I was smart enough in those few moments to know my limits. The only thing worse than denying you're pitiful is to act it while you are.
"Nothing I told you tonight was the truth," she said. I'd just finished up my tale of squalor and abuse. "About myself, I mean. When we were playing Truth or Dare."
"Not even your name?"
"Naming something is the fastest way I know to screw it up."
"I don't think I believe that."
"Name a thing, you strangle it."
"You must've had a reason."
"I grew up in a dusty little town with a state mental hospital and a Boss Hogg-type cattle baron. My dad worked for the county fixing potholes and signs."
"Bet your mom dug that."
"Dead people don't dig anything I'm aware of."
"Before that, I mean, if there was a before."
"I never knew one way or another how she felt about anything. And what I do remember isn't much fun."
"I guess that's the problem, huh? How much we need our memories, but hate ourselves for the needing and having both?"
Hickory went to the bureau with Dinky's family photos. When she turned back, I knew she was going to spin a yarn.
"We lived at the outskirts of town. Out by the hills. There weren't many houses there. Just a couple of adobe bungalows and a big metal barn they used for storing hay. Daddy did side work for the guy who owned it. He was an old guy with a bunch of cars Daddy fixed on weekends. Anyhow, one day when I was six or seven the school had a bomb threat. Somebody called up and said they were going to kill every kid in town, and they sent us home. I'd gone in through the back, by the garage, to scrounge around the kitchen for something to eat. But just as I was turning on the TV I heard voices from the back of the house. Most days Mom was never home, she had a part-time job some place, I don't know what or where, so at first the voices scared me.
"I snuck around the corner. You know how you get when you're a kid and something breaks down your notions of the way things are? No one had ever been in the house during the day except for my mom. But this was a man's voice. I didn't know whose it was. I just knew it wasn't Daddy's. The man was laughing. Not loud. Soft, but different than Daddy's kind of soft. The hallway was dark. Up and down the walls we had these family photos, all the usual thieves. Most were people I'd never met, old men and women with eyes like eyes in daguerreotypes. I'd seen them all so many times it'd got to where I didn't notice them any more. But that day all I could do was stand beneath them, watching them watch me with those eyes.
"I can't remember how long I stood there while the man kept laughing. It never got louder or softer. Every once in a while the woman said something I couldn't understand. It didn't sound like my mom, though, though I knew it was her. I must've done something, maybe scraped the wall, because my dog Blinky-Doo started barking, and then he came trotting round the corner. That's when the man stopped laughing. 'Is someone here?' he said, and my mom said, 'Hello?' but I didn't answer.
"Next thing I heard was a mumble of whispers and scratchy sounds. Blinky-Doo was licking my face. Then I looked up, and my mom was there with messy hair and her face all smeared, wearing an open robe. The man I'd remembered seeing before, at some store in town or just on the street. He had hair all over his belly and chest. His shirt was unbuttoned, and he had a mustache, that much I remember, too. I thought he was going to say something, but he just looked at me till after a while he left.
"'They made me come home early,' I told my mom. 'You little sneak,' she said. 'I wasn't,' I said. My mom's eyes, I realized, were glued to my dress. It was hot and wet, and so was the carpet. 'If you don't tell your daddy what you saw today,' she said, 'I won't tell him what you just did.'"
"I hate people," I said. "Sometimes I do."
"I never did tell him."
"If I ask you something," I said, "will you tell me?"
"Depends."
"What did they call you, your mom and dad?"
"The name on my birth certificate says Avey May Jones. But the day I was born, when I was still in the hospital, the nurse who brought me out to Daddy said, _She's the sweetest little mud patty I've ever seen_ , and Daddy said, _Hello, Mud. I'm your daddy_. From then on out it's been Mud."
"She said that? That's like, I don't know, like stuff from fairytales and film."
"Like stuff that happens in little towns with insane asylums and slaughterhouses."
"She really said that?"
"I can only guess it's because Daddy's half-black. His mother was the only black woman in Ft Smith married to a white man. That's how they came out here. Nobody could stand it, her practically being made into a whitey."
"My name is Mud," I said. "I like that."
"You like it?"
"Like is not the word."
We were on the bed. She was holding my hand, without fear or pretense, as if really and truly it was something she'd wanted as much as I. Her breath smelled like bourbon and ginger and peach and smoke, the soul of an antique dream. I could see the smallest hairs above her lip. A vein ran along her jaw, just below her ear, in her evening-colored skin, the faintest pulsing blue.
"What?" I said.
I know it couldn't have really been that way, but that's the way I imagined it, or thought I'd imagined it, because I thought I imagined she kissed me. Her breath smelled of mountains, then, and of butterfly dust, and of the feathers of quiet birds. The sound of her heart came up through her mouth, I could taste it, too, the sound of her heart, a morsel of chocolate, laughing. She took my face in her hands, she held my face as though at any moment it might explode. Her hair fell across my face, and she closed her eyes, and I felt it again, the first time since forever, brand-spanking-new. That goddamned girl—that's what she did—she made it all feel so shiny and new.
We didn't know it then, or maybe we did, fuck it, but we were only using each other, hiding in each other the fates of our broken selves, all those years of hope and dread. _Call-notes of dark sobbing_ , sang Rilke. And that's what it was, that love, impossible to swallow...
I ran my hands along her neck, her shoulders and smallish breasts. A tattoo circled her navel, a sun with rays of purple and black, and I made a circle over that. There was only the wind and rain...
The clock on the stand said 4:32, Wednesday, December 31st, New Year's Eve: the beginning of an end, the end of a beginning, more than ninety hours since any of us had known a wink of sleep.
Avey and I were silent with our new misunderstanding, which was all we could ever have been...
The smell of us was strong in that mountain air, my breath on her neck, dying...
My having made this girl had only put us further apart. A pinhead of black had crept into my bowels, but then the sandman came, and I was taken with a sigh...
THE SUN HAD RISEN BY THE TIME THAT TREE slammed through the cabin, but neither Avey nor I had heard it. I thought of disbelieving Basil's claim to've slept through those tornadoes in Kansas, after the funeral of a chain-smoking cousin.
"Everybody was in the same room," he said. "Six or seven of my great uncles and aunts and fifty thousand cousins."
"Baloney," I said.
"Try staying up for five days of drinking and snorting," he said, "before topping it off with a funeral. See how fast you come to."
We were hanging at the Mallard, waiting to play pool. Down the bar Dinky and some other boobs were deep in a game of liar's dice. Basil took an ice cube and bopped it off our friend's titanic head.
"Hey, O'Connor," Dinky shouted to the bartender.
"Now what?" O'Connor said, cramming his brush into a glass.
"We thought we'd agreed to 86 that blowhard next time he started up with his shenanigans."
Basil leaned over the bar to better yell at Dinky. "Just making sure that sack of concrete you call a head was still hard enough for me to knock around at pool, Dink. Serious," he said, back at me. "I was eight sheets to the wind."
"But that didn't keep you from making a good show for the familia, I'll bet."
"Three tornadoes in a row—blam, blam, blam—one right after the next."
"So how is it then you're still around to tell the tale?"
"Hit every house but ours, cross my heart. Motherfucking Godzilla could've smashed through the walls, having it out with Mothra, and I wouldn't've heard dick."
It wasn't until an incoherent rant had broken through my dreams, like a siren in the distance, that I suspected something wrong. Avey nuzzled into me, the smell of her restful, kind, and mumbled that Lucille ought to shut it. The world was suspended in haze—the rose-patterned linen, the vase on the floor, the print of a goat on a craggy spire, gazing toward a stretch of valleys and arêtes. I wanted to stay in that haze, for a while at least, and in the shelter of Avey's hair, but the storm raged about us, and the voice went on.
"Get down here, you guys," Lucille was shouting. "Hurry!"
Avey shuffled along beside me, drowsy at the rail. Then we saw the carnage, and snapped sober in a beat. Half the front of the cabin had collapsed into the living room, crushed by a giant pine.
Lucille looked as we'd left her, a drink in this hand, a smoke in that.
"Murphy's Law," Avey said.
"What?" Lucille said.
"Whatever can go wrong," I said, "will."
The tree hadn't crushed the living room alone, but most of the deck, besides. Good thing for us old Granddad Wainwright had had the wits to hire craftsmen, not the jerks you see today, wobbling round some rafter fifty-feet up, guzzling a frosty as they slice off their ruined hands. None of that, though, meant we could stay.
"I guess they haven't made it back," I said.
"I only wanted to have a good time before my life was over," Lucille said, crying. "Nothing big or fancy, you know?"
"Put on your jacket."
"What?" she said.
Avey made her way to a pile of clothes near the hearth and picked out Lucille's jacket.
"Come here," I said.
"What?" Lucille said, rooted to the spot with her washed-out face. I stepped through the wreckage and hugged her as she cried like you do when you don't know who you are.
"I'm sorry," she said. "I'm sorry. Can't we just, I don't know... _go_?"
"Let's get your jacket on," I said. "We'll get your jacket on and fix a little something up for your belly."
"Promise me you'll get us out of here."
"Put your jacket on."
"Promise me, AJ."
"If Basil and Super get here soon," Avey said, "we stand a chance of hitting Berkeley in time to sing 'Auld Lang Syne.'"
"Did either of you happen to bring an umbrella?" I said.
"By the door," Lucille said.
"I'm going out."
"Maybe we should check on Dink," Lucille said.
"Let him sleep," I said. "You two head upstairs and kick it till I'm back."
North and south the road lay slick with mud, worse in the light of day than I'd imagined it last night. With Lucille's absurd umbrella, semé with smiley faces—yellow, naturally—I went the way of Basil and that freak of a man, hoping round the bend to meet some crew, but found just more desolation. Long minutes passed before a figure appeared at the end of the road, who, it didn't matter: I wanted news from the world, that was all. But the harder I looked, the greater it seemed the figure to be more beast than man, Sasquatch meets the Scarecrow. It was only after I'd decided to take cover that a man called out, and I knew that it was Basil.
"Where's Super?" I said.
My pal sat down with dangling arms, his feet, both bare, a mass of sores. "That old fucking fuck," he said. "He tried to take a razor to my ass."
Basil unhurt that I could see left me unsure what to say. "So then you never made it to his wheels."
"I said I needed to rest. But you know what he does? He starts in with one of those psycho rants. When I told him to cut the crap, dude came up with a razor. And that dog of his. Turned into frigging Cujo."
"He was helping us. He needed your help with the truck."
Basil picked a twig from his foot. He was virtually in tears. "A hundred times I tried to tell you."
"Are you all right?"
"Sure, AJ," he said, "I'm fine. In just a second here I'm going to jump up and sing in all this rain."
"You must've really pissed him off."
"Attacked him with a hatchet's all."
"Dude, he took you down and laughed. The man's a vet for Christ sake."
"He's a psychopath is what he is, AJ."
"I don't know."
"Go ahead then, tit. Believe what you want. All I know is he and his beast came at me like gangbusters."
"And then he let you skate."
"The old caveman combo."
"Let's just hope he comes back."
"He does, it won't be to bring us flowers."
"He liked us, Baze. He did me and Dinky, at least."
"Goddamn it. Goddamn it, goddamn it, goddamn it."
"Think you can make it to the cabin?"
"I am so very fucking done, AJ, you don't even know."
I got Basil to his feet and his arm round my neck. "I forgot to tell you."
"Don't even mess with me, okay?"
"A tree kind of smashed up the cabin."
"Goddamn it. Godfuckingdamn it."
We limped up the road. Minutes passed before we spoke.
"You're a good guy," Basil said.
"I try."
Before the spectacle of the cabin, Basil's face went rubbery and helpless and gleeful and sour, none of it for long. A face of horror took him, then, and then again he began to weep.
"You guys polish off the hooch?" he managed to say.
"We got some hooch, I think."
"Because I want them to find us like a jar full of top drawer fucking pickles."
"The old man's coming back, you know. He said he was coming back."
My friend was shaking now, too, nearly uncontrollably, his feet might've been stuffed through an old-school grinder. He gazed up at the cabin and shook his head.
"Looks like Godzilla came through here," he said.
"It's true," I said. "Him and Mothra both."
IT OCCURRED TO ME AS WE MOUNTED THE STAIRS that Dinky wouldn't have to engineer a story for his grandfather about the window Basil smashed. The birdcage was there, caging a bird that was dead. I scooped the cage up with Lucille's umbrella and tossed them in the mud.
Inside, with no lights or music to make a cheery fiction, everything was cloaked in grey—dripping water, trembling prints, shadows and slime and shit.
"So now the power's cut, too, I take it," Basil said.
"Yup."
"Where is everybody?"
"Last I checked the girls were upstairs in bed."
"I just want to go home."
"We need a plan."
"But we can't go home. Because we are fucking stuck."
"I say we take what we can carry and go."
"Like a pack of tittysucking rats."
"I'm serious, dude."
"Denial ain't a river in Egypt, Jackson." He looked at me now with gravity I'd never seen. For the first time in his life he was trying to be real. "You smell me, or what?"
I sat on the bench and lit a smoke and handed it to Basil, then lit one for myself.
"I wish to God I couldn't," I said.
"And I wish to God you could understand me for once. You know that?"
"No, I don't. I've got no idea what you mean."
"Of course you don't. You never do, and never have. You've never understood a thing about me."
"We get ourselves out of here in one piece," I said, and grinned, "I promise we can go to counseling. How's that sound?"
"I love you, too," Basil said. "So, _so_ much."
Lucky for us he'd remembered to bring his suitcase in before Dinky and I wrecked his Cruiser. We stripped our clothes and argued over who'd wear what. Basil pointed at my shriveled up dong and asked how I'd gotten a shroom to grow in my crotch. I called him a rich boy. I called him a monkey-fucking banana dick. Then I put on one of his dress shirts, with the French cuffs and polka dots, and a red velvet vest over that, and lo and behold, I looked like a numbskull in the hand-me-downs of his brother the mime. Basil went to see about the girls.
In its way the earth had gone quiet, the solemn trees, the heaving sky. Veils of rain continued to fall, the lake was hidden, there was only mud, only trees and sky. But soon a woman cried out, and soon another began to scream, Lucille louder than Avey at first, though presently they were wailing as one, cries with pain enough to rend the hardest man, ah, exactly what we needed. Hardly had I thought to investigate than Basil stood beside me again, his face as long and blue as ever a face could be.
He lifted me off the ground and squeezed till I lost my breath. I could feel him shaking, his whole body in tremors, ambushed by a life of hurt. It was only some years later, or so it seemed, that he gave in, his voice a boom in my ear, nothing comprehensible. Shaking and sobbing, he just held me tight.
"He's dead, AJ. I went in to see him... He was just _dead_."
Basil said that, and his face dropped away like a coin off a cliff. I fell dizzy with pictures of catheters and cotton and chromium rails, and screens above flowers and sirens, too, host after host, and widowers and widows, the injustice of their eyes, and needles, and hoses, and smocks, and tubes...
A hand lay on my brow, cool as a spring, I could smell Avey's breath and hair. We lay on the bed we'd slept in, a cheap coverlet scratching at my jaw. An old chiffonier stood across the room with its small brass tub of imitation flowers. Next to it was a smattering of novels from the World's Best Reading and a painting of Jesus in a dime store frame. Lucille was perched on a cedar chest, her arms around her knees. Basil sat beside me, with a smoke.
"Are you okay?" Avey ran her fingers through my hair, they were light and soft.
"Where is he?"
"Sssshhhh."
I looked into her eyes. I nuzzled in her hair. "I'm okay. I'm fine."
Basil went to Lucille, he held Lucille's hand. They were silent.
"Where is he?"
"In there," Lucille said.
For a moment the room seemed crooked, everything floaty with mist. Then it cleared, and I was on my feet, steady as could be by Avey, her hand on my leg.
There was a door.
I went in. By the bed I got down. I got down on my knees. But I did not look. Not at him, his face. I couldn't. For a long time I sat that way...
His face. Not his face...
No can. Maybe never, maybe not never, not knowing when, maybe never...
Laid there, he, it, he, a cold stiff thing, stretched out like a dummy, CPR, a hand, not like his face had been, not jaundiced, not sweaty and pained, hands of a workman never done work, no not. And fingers, thick, blunt at the tips, where thick hard nails were growing still, no, not growing, not life, never again, not, no, no pulseless mush but veins, and blue cording, and thickish veins, ah, heavy, ah, like ugly crappy wire. Little blond hairs not vanished, no not, no not, and thousands of hole-dots, and lines connect dots, not color in, no not, no not, no not, design, no design, no not, never, nothing, no, where wrinkles there, and cold, so cold, hand in hand, so cold, so cold, no not, not, not, not think meat, not think friend, not friend, not think, no not, no nothing there, nothing, no, not, no, no, no, no, not, no not, no not not, not, not. And you will look, now, yes, you will look. At him. At not him, at not it but him, but Dinky, look at him, no, look at him, yes, you, now, yes, because, because, because. And there, yes, and there now, and there. And it's okay, you are there, you are fine, it's okay, it is okay, everything's okay, it is...
Peaceful is not the word. Dinky's face was not peaceful. That, I thought, was the big untruth, this business of peace suffusing the dead. But though it looked nothing at all like peace, my friend's lifeless face, neither did it look sad, nor helpless, nor anguished, nor anything of the sort. Content, perhaps. Or perhaps _nothing_ is more like it. More like it, yes, Dinky had a face of nothing, a face no longer burdened, with worry, with fear, with anything to speak of, desire, anger, rage—that was all.
I wiped my mouth. I wiped my eyes. My fingers shook, and my hand. But then I made that hand touch him, his face, his mouth, his eyes, everything he'd been, my damp hand on his dead face, which wasn't cold but cool. And that was all. It rested there, I let it, my hand on his brow, and then I began to sob, and everything left me, all my thoughts and all my words swallowed up by that good cry. You son of a bitch, you, you beautiful mother fucker, you, who couldn't stand another day. I pulled the sheet to his chin and made it straight. I shouldn't thank you, I thought, but I can't help it. Thank you, Dinky, thank you, Stuyvesant Wainwright, IV. And then I pulled the sheet over his face and smoothed it again, and then I said, _Thank you, again_ , I said, _thank you_... _Yes_ , I said, _thanks_ , I said, _you old bastard, thanks_.
THE WAY WE LOVE THE DEAD'S GOT NOTHING TO do with how we love the living.
I'd be hauling down some road with a mackerel sky against the dawn, watching crows in the fields or egrets in rice, and like fear it would hit me I couldn't go home expecting his voice on the line whenever I called, rambling about the game he'd just bought or the stripper he'd had that photo-op with, with the massive tits she let him squash his face into while the cameras ticked and flashed. Or before that, before I'd moved to these podunk lands, when I was still a sofa-surfer, tripping place-to-place with my bag of books, I'd be hanging at the Strada or Milano, watching the students and the freaks, the little rich daddy's girls, the hard-nosed punks shouting for coin enough to make them puke, the date-rape jug heads and beret-wearing doofs with their euro smokes and foreign mags, and it would hit me, uncanny as hell, the friend I thought I'd known like the day, different every time, saying or doing what I couldn't recall him saying or doing while he was yet alive.
The only thing sure I could say about Dinky was he'd taken off for that whorehouse in the sky—that and how every time I thought of him, I was loving him. But the Dinky of my eulogies had no part in the Dinky I had known. The Dinky of my eulogies was the Dinky of my grief, the Dinky of my heart gone soft. He was never the kid I'd witnessed barfing off a terrace, the kid with a bag of speed grumbling about the law, who cringed at the thought of his father, wanting nothing more than to satisfy the man, at whatever cost to his own small needs. The sob stories he used to spew had lapsed into murk the moment he had himself. And even if he did resemble that, it wasn't his fault. Always he floated before me as the angel done wrong. He'd lost his way among the dangers of this shithole world, then found himself in a haunted house. The cards had turned up cold. The cookie had crumbled on another guy's plate, the milk was forever spilling. The only way he could get what mattered most—a simple embrace, just acceptance, just love—was to die. Well, now he'd got his wish. I can't speak for his family, but I can for us buddies: Dinky died, and we were sorry, and we loved the son of a bitch now like we never had while he was here to take it.
From time to time I'd think on this, late at night, in the grip of my insomnia. The cicadas would whir. The great horned owls, six syllables to the hoot, would softly, repeatedly call. In the heat of a furnace-like noon, dreaming at the wheel, I'd think about it then, as well, and I'd hate us all in our cock-eyed ways.
Maybe it's wrong to love the dead. Maybe that kind of love is nothing but the product of our selfish wants, unguent of grief, salve of messy guilt. But what are the options? Should I have committed myself to a life with the monks for not doing right by my friend? Flopped myself down on an old prie-dieu and waited for the Word? It's not as though I'd intended this, this morbid, useless love. It's not as though I'd needed Dinky dead before I could give him his deserts. Now and again, though, when the trick's all said and done, you find yourself left with nothing to say but _That's the way it is_. You can talk a lot of dirt in this world, everyone knows, but you can never say the way we love the dead's got thing one to do with how we love the living.
THE LITTLE GNOME WAS GLEAMING ITS HORRIBLE joy when I stepped into the hall. I kicked its face and watched it blow down the stairs in a dust of plaster and paint...
Some human outside was whistling, "Blue Moon," the reason far beyond. But out on the deck I understood: Super had returned with Fortinbras the dog. And yet something wasn't right. Super, Fortinbras, Fortinbras, Super: nothing but a weird old man like rags on a stick—him and his henchman, and through the trees the mist on the lake.
"You got the truck?" I said.
Super had seen our disaster—he must have—and yet he was smiling. Here was a man who'd part for confusion every time. Here was a man who loved what was toppled, broken, spinning, and cracked, the man with the hands of ink and bone, the man with the monkey, the impervious match. O give me a plain where the wild things grow, give me a spread of broken dolls, O give me a national anthem.
"It's as clear to us as a mountain spring that you smell this business with a dead man's nose."
"You think that's cute?" I said.
"All right, all right, soothe yourself, now. Our wheels we do have."
"That's good, Super, cause Stuyvesant is dead."
For the briefest of instants the old man assumed a pose so brittle it seemed impossible to contain. He might've been seized by some grotesque rash of meaning, a thing with talons and fangs, whose sole purpose was to hurl us through the void. He pulled out a watch and wound it so long I thought surely it would break. But then he stopped and looked into my eyes and let fall the watch to crush with his heel.
"Come on in," I said. "As a favor to Dinky."
The mannequin lay in a twist of stuff and tree. Bits of glass dully spangled, spears of wood harshly jutted, the mobile clinked, the curtains flapped, the cabin creaked and groaned. The rain had ceased for a time. Beads of grey plopped and plopped, from a dangling wire, a frond of fir, that stupid-ass Mexican boner-doll.
The old man's eyes traveled the room with a helplessness he hadn't yet revealed. It wasn't the cabin's state that had got him, I thought, so much as what it stood for. The place could've gone up like Sodom and Gomorrah, as long as Dinky didn't watch. But Dinky had watched, and now, leastwise for Super, he'd become a pillar of salt. The geeze held my shoulder. His face drew near, so close his beard touched my chin, and hovered there infused with the grief in an old seal's eye, perhaps, or the wisdom of a puppy. I began to weep again.
"We know this concern," he said. "We've been where there is to be and seen what there is to see."
The tears were coming so hard it was difficult to stay with Super's words.
"Like we said, the world's gone flat. Days'll come and go and leave you shy of a whit of sun—of that you can be sure. But so long as you're living you ain't broke. No matter what you do, you can only go so low. You bend, you give, you give some more and then you bend again. And just when you think you've got to where you can't go no more, you find yourself giving another pinch of sand, bending another inch. And then you twist back up and start from the get. You might want to, boy, trust him, old Super knows, but you couldn't break if you tried. You're too tiny."
The old man stepped off with a face of good and held me till I laughed.
"What are we going to do?"
"We'll take care of the Wainwright boy."
I'd forgotten about Avey and the others. I thought of what Basil had said, that he'd wanted the old man dead.
"I'd better go let them know you're here."
"You do that. And when you're finished, we'll be waiting."
The crew had by now fully zonked. I shut the door and whispered. No one stirred. I kneeled at Avey's side, I stroked her hair, I gazed into her sleeping face. She murmured. Then I kissed her, and she murmured like before.
"Super's back," I said. "Wake up."
"I don't want to," she said.
I kissed her face. I kissed her eyes, her mouth, her nose. "All we've got to do is make it to the truck." When she stirred again, Basil jerked to with screwy eyes.
"Calm yourself," I said.
"Where you been?"
"Listen. You do something stupid, you could really botch it up."
"He's back?"
"Yes."
Basil tried to stand, but couldn't. "Son of a bitching mother fucking shit!" he said as he collapsed.
I felt for him, a little. The guy couldn't make any more trouble for Super now than he could for the pope. Of course this commotion had pressed our beauties to another go at life.
"What's wrong?" Lucille said.
"His feet are all messed up."
"That's why you woke us?"
"The old man," Basil said. "He's back."
"With the truck I hope."
"Yup," I said.
Lucille jumped. "What are we waiting for?"
"Super's going to help us with Dinky. Okay?"
"You just make sure," Basil said, taking up his bottle, "that that fiend ain't pulling a fast one."
Super appeared at the door. He looked at the girls and said, "Hello, butterflies."
"Don't take this personally," Lucille said, "but I thought you had a truck."
"It's up the road," I said.
"That," Basil said, "is where he and his beast are going to chop us into suey."
"Now, now, Laertes," Super said, and extended a bony hand, "we were hoping there'd be no armored sentiments here."
"My sentiments're armored all right. I don't feel a thing."
"Come on," I said. "Shake his hand."
"I don't want to shake his hand."
I couldn't believe it. The lunk was positively sulking. "Basil. The man is helping us."
"You can stay here if you want to, lover," Lucille said. "You want to stay here?"
"I'm like an elephant. I never forget." Basil sat there blinking. His head was swaying, a balloon on a string. We watched him. "What the hell," he said, and gave his hand. "If it'll make you tits all happy."
"You're a good boy, Laertes. Fortinbras said so on the hump. We're sorry you had to learn that way."
"Was he really that much trouble?" Lucille said.
"We never did know the meaning of that word."
"I only meant," Lucille said, "he didn't mean any harm." In her voice I heard desperation. The time had long passed for rudeness with the geeze who for some crazy reason had kept on coming back. "We just want to go home."
"The sooner we get to the wheels, the sooner you'll not be here."
" _So_ ," Avey said.
No one had to probe her gist. Her gaze had wandered toward Dinky's room. Basil hit the bottle. Lucille picked her lip.
"We take it that's where you're weeping for the Wainwright boy," Super said.
"How is it you plan to get him out of here?" Basil said.
"We can help," Lucille said. She looked at Avey.
"You two help Basil," I said. "We'll get Dinky."
"What," Basil said, "you think he somehow lost a hundred and fifty pounds?"
"I can carry my half," I said, "if he can carry his."
"We can carry him and his coffin if needs be," Super said.
"AJ," Basil said as he drew near. "You really think the old man's square?"
"He takes us into town, I don't care what the fuck he is."
Basil looked out through the ruins, his features hardening. "Right," he said.
_Pink Champagne Bitch_ lay by Dinky, next to some bottles and a tray full of butts. A wad of bubblegum stuck to the nightstand. A pair of socks poked from under the bed. There was a wet and stinking pea coat, two shitty sneakers, a bag stuffed with underwear and shirts and a worthless belt. And shaving cream, and toothpaste, and lotion, and a pack half-empty of Camel Lights, and those stinking awful clowns.
When Super pulled down Dinky's blanket, I expected eyes like pinballs staring through the cold. But someone had come in and put a ski cap over his face, which I removed and placed on my head. And his face _was_ cold, and his eyes _were_ pinballs, blind as pinball chrome. Maybe that was good. Who could say what Dinky saw on the other side? Maybe little nymphs with paper wings, or hobgoblins and beetles and fire and heath, and the flesh of sinners peeling from bones. And anyway, who the hell really cared? I only knew what he wouldn't be seeing, what he'd never dream again. Not the tsunamis of December or the tippy-tip toes of a gorgeous ballerina. He'd never once, not ever again, see a hatchling from its egg, a leaf on a breeze, chocolate on a shelf in the sun. Women would fight with their men in tenemental gloam, and trout would flop on the fishmonger's board. And masons would trowel, and strippers dance, and bankers bank, but Dinky, he wouldn't know it, because, turning to dirt like a rabbit in the woods, he wasn't any more now than the dream of the dreamer dreaming. If only it were easy as saying, _Arrivederci, pal, and good luck. I'll toss one back when there's land in sight_. Goddamn, but one thing's sure—there's not a stitch of glory in death.
"How far did you say it was to the truck?"
"It ain't. You take his feet and we'll get his head."
I didn't think it right we cart Dinky off like a sack of dirt. We had to wrap him up first, at least. That's what I told Super, and he agreed. I took down the blanket and rolled him. He was heavy as a block of steel. And all along his backside, ankles to groin, his skin had mottled up in a swirl of purples and blues. It looked as if he'd been lying for weeks in a pool of wine. The flesh beneath the hair on his legs was cool. I could've been holding a chunk of moldy pipe.
"That'll happen to the best of them," Super said, gesturing at the color.
"What is it?"
"Everything that made him a man."
Super mashed the last of his smoke into the palm of his hand and stuck the butt in his pocket. He got down on his knees and laid a hand on Dinky's brow. My friend's face lay motionless and dull as that of some first-man staring from a wall of ice. When Super rose, two buffalo nickels lay on Dinky's eyes.
"Every man is turned to destruction. And sooner or later every man hears, in his distracted globe, that old voice calling out, _Return, ye children of men, return_."
I remember stumbling over the mannequin and falling to the couch, Dinky's toe an inch away. I remember the crow through the trees, and the sprig in its beak. I remember Basil and Lucille in Super's truck, too weary to care for the monkey on its beads...
We laid Dinky lengthwise, down on the bed of broken dolls. Super hobbled to the cabin, returned with blankets and bags. He kicked his tires, bound with chains, then got behind the wheel. Avey wrapped me in her arm, she took my hand, she kissed me on the cheek. I'd forgotten how good that could be, just a kiss. It was raining again, and somehow I felt free.
IF THERE'S ONE THING I HATE MORE THAN clowns, it's riding in the back of a truck. The last time I'd done that was twenty years past, in Texas, through fields of cotton in the sun, me and my terrier Biscuit watching the dust go swirl, the astonishing skies, the rows of green on either side, fanning to the ends of vision.
Distance will confuse. You were there, and then you weren't. In the moment of sense you make about the difference between the space of then and now, it's all changed, _now_ has been snatched away, it's like everything else, an act of colossal dupery, _now_ is _then_ and _then_ a silly idea. There was sense, and there was nonsense, and neither had had any mercy. You think you saw a bird on a post, but the road paid out, and the bird disappeared. There you were trying to puzzle up what little it had shown while sorting through the whim of recent _thens_ —what could have been a snake in the road or coil of twine, a man in the shade with a flashlight or hammer or gun—the creature with eyes like topaz, the way they followed you and your dog, wary but detached, its head revolving as you sped by. Then the head shrank, the eyes ebbed to phlegm, to murk, till flatness too had eaten them up, and, again, before you could sort out the mess, it was all just a spot on a line, distressingly significant, distressingly empty, a place holder of sorts for what amounted to yet another of your ideas of the way things are, some hole of wonder in which you could ponder the worth of your mind—did reality need it, did your ego need it, was the thing you'd seen still there once you couldn't see it, did such a matter matter, really, because after all, the way things are has nothing to do with how we think.
A cur bounded up from the ditch, and Biscuit, having flung herself at it, tumbled away in a flurry of dust and hair. It took some time for this to make sense, too. I couldn't say what had happened, even after I'd turned to beat on the cab. My uncle drained his Coors and nudged my toad. He swung to the shoulder and placed his hat and slid from the door and wiped his pants. I shouted what happened, I cried, and back with my dog, I got in the dirt and slobbered on her hair.
"My head's just about as empty as that can there," my uncle said, "but I can tell you now. There ain't but one way to handle a thing like this."
A breeze swept through the fields. The cotton groaned. I never saw him come or go, and yet my uncle stood above me with his gun, his mouth a penciled line. Then my old toad took the gun and ordered me away.
"Leave her," he said, his baldness felloed with light.
"Please, Dad."
"I said leave her."
The shot sounded off before I'd even made the truck. I turned to see my toad with the rifle on his shoulder while behind him my uncle tossed Biscuit in the ditch.
We drove up the road and turned onto another that led to cotton-nowhere. There was a shack with cardboard on the windows and a line strung out with threadbare clothes. An old Studebaker sat by a pump, stuffed full of papers and bottles and gizmos gone bad. Dirty children peered from the door. A man in huaraches and mismatched socks stepped through the kids and spoke to my uncle in Spanish, my uncle replying in pidgin, interrupting his words here and there to spit while waving his hands like his man was a fool. At last he nodded the way we'd come, and the man nodded back. I heard the words _muerto_ and _perro_ and _well number four_. Then a woman appeared in an oversized tee with a peace sign of red, white, and blue. The man called out to her, then made into the cotton. " _A dónde va?_ " said the woman, but the man only raised a hand.
The machinery of hub-bubs and what-nots had started up again, the truck paid out more road. I settled back to silence, never once considering how elemental fear is to the sacred. And Biscuit was there, and then she wasn't. And the sky was blue, and the land was green.
Back home, my uncle gave me a Tootsie Pop, its wrapper with a kid in a headdress shooting an arrow from his bow. When I asked my uncle why he'd killed my dog, he snorted and scratched his nose. "Everthing runs on a leash," he said. "Most especially dogs."
"You don't know anything about dogs."
He tossed back a shot of red eye. "Oh yes I do," he said.
On the farm now, Thomas the Tattooed Whiskey Man is the only guy I really know. In just a few weeks, I told him everything that had happened those days in Tahoe, about me and Avey, and Dinky and Super and Basil and Lucille, everything and the rest. At the part where I'd forgotten the day Biscuit died until I found myself trapped with a dog, a dead man, and a beautiful girl, all in the back of a madman's truck, how my old toad and uncle had shot Biscuit dead without a blink of guilt then tried to buy me off with candy, he said, "And you wonder why I live here on this farm."
We'd been swimming the river in our birthday suits when two of the boss's kids ran off with our threads. They took every stitch, the bananas, and how so full of glee they were. I was about to end the story, lying on the pebbly beach, but mid-sentence Thomas cut me off. He could see how parched I was, he said, which I took to mean he'd decided to show me the still he kept out in the tamarisk, which he then did. We had mason jars to drink the corn, and the kids had left the pouch of smoke. I listened to the water back an angry crow.
"It's quiet here," Thomas said.
"So?"
"So I can hear the noise when it's not."
"That is special, I suppose."
"If it weren't for the quiet, Johnny, there wouldn't be any noise."
That's what they call me here—Johnny. First day I arrived, I had to toil through the rigmarole of how funny it must sound, of how, sure, it was ridiculous and sad as a name could be, but yes, my name was John Henry Doe. They all liked that, and laughed for a beat, but when they tried to break me, I wouldn't say, and couldn't have if I wanted. I'd got too far stuck in my story. The Doe had cut away and John had grown legs. Now it was plain old Johnny.
"How much of this stuff you keep on hand?" I said to Thomas.
"Did you hear what I said?"
"I heard you." I finished rolling his smoke and stood up to leave for another dip, but Thomas held me back.
"All things," he said, "shine brightest in the shadow of what they're not."
"Tell it to the river," I said, and left.
SUPER HAD REACHED THE 50. WE HOVE ON OUT, and in it we were, the midst of cars, an actual line of actual cars, with actual people clutching and banging and shaking actual wheels. This road, too, had been wrecked, though not so badly as up the hill—maintenance crews had cleared the worst. A couple geriatrics in a late model Ford hunkered over the dash behind us, old gramps looking fragile as love, his kisser slack with focus. Horns honked, people screamed, a sheriff flapped his arms. Buildings appeared either side. Through the trees the lake with its little piers and boats swelled against the shore. We passed a shopping center with a supermarket and liquor store and hair salon, a row of commercial atrocities, Dayton's Floors, Fruity's Superior Nails. Farther down, a swampy meadow appeared and then more buildings yet—Douglas County Administrative Offices, the Sheriff and Justice Court. Some hokey chapel floated past, up on a hillock, the kind of hole where you slap on a tux before marriage to a song by Elvis.
We hove on. A golf course swam by, the polders flooded out, the lake out past it again. Then came the casinos, looming like teeth, Caesar's here, Horizon there, and Bill's and Harvey's and Harrah's. People were still rushing in and out with coin buckets for the slots. By their faces, they could've been on Dagobah and never known, some bright with fever, others in its wake so grim. That the world was breaking to pieces didn't mean poodly lark.
But we hove on. Nevada became California. Past pizza joints and past motels we chugged and choked, past tourist traps and pharmacies and jewelers and boutiques, here a grocer, there a cleaner, here a seller of knives and guns. A McDonald's sailed by, then a diner, then a bodega for cigarettes and gas. The world flowed away in a psychedelic stream of greens and greys, a volte-face of perception. We came to a stretch of cars like monsters drowned, submerged in water to their roofs. Steam drifted from them, exhaust through the water, on one a family—mommy and daddy and their whey-faced runts—heavy with hopelessness and wear. Later, three children cried in a boat, pushed by a man in slickers, the water to his thighs.
At the river, the bridge poured out like a floating road. Trucks in water wheels-high made giant wakes, their beds crammed with chattel and children and pets. Engines coughed and rain thrummed and ceased and thrummed again. Near the Long's Drugs, the parking lot had flooded to the storefront itself. Government vehicles loaded with sandbags moved to and fro, but we didn't stop, but hove on through. Finally a red and white billboard pointed the way to Barton Memorial Hospital. We turned down a road with a trailer park and tenements, and suddenly we were there.
The hospital reminded me of some resort-asylum for rich drunks and addicts. A porte-cochère with a river-rock facade and clear-pine trim presided over the roundabout. On either side the bureaucrats had planted boxy lawns studded with ornamental plums and jeffrey pines, and flowerbeds full of bark.
Super stepped from the truck and mumbled to his dog, then Basil hobbled out, _sans_ Lucille.
"Now here's a rumbling bellyful," the old man said, raking at his beard. "Here's lunatics and rage."
Basil squinted. He ran a hand across his face and hawked out a loogie. He was beat to shit. "I still can't tell," he said, and his voice sounded worse than he looked, "if this guy's the devil or a nine-to-five fool." He stooped for the lighter he'd dropped. "I'm dying here."
"Most times it's the fool's the prophet," Super said, and tickled Basil's chin.
"Show me the profit here, and I'll cut off my right hand." Basil was turning in a slow circle, now, his arms spread wide.
"Maybe," Avey said, "you should wait for us to bring you a wheelchair."
"Ha," Basil said.
"They'll bandage up your dogs," I said. "They might even help you walk."
Super dropped the tailgate and took up Dinky's feet. A portly man with a goose down parka and pipe in his mouth glanced our way, a paper at his bald spot. It seemed he'd keep on, but then he fixed on our friend with the dolls. "Hope that's not what I think it is," he said, and stopped to light the pipe.
"Beat it, yuppie," Basil said.
"Let's get, Horatio."
"Basil's right, Super," Avey said. "It's probably not the best idea to go traipsing in there with a... with Dinky like he is."
"That's true," I said.
"Oh will you now."
Avey locked eyes with Super. "This is no time for screwing around," she said, somehow effectively. For once the old man was silent.
"Let's just go in there and see what they want," Basil said.
"They'll call the cops on us, I bet," I said, thinking as I did how much Basil hated humans in a uniform, but most especially cops.
"They'll take one look at Dinky and know it was an accident."
"It's no use standing here guessing," I said.
Basil raised an arm that I slid under, Avey did, too, and off we went.
The triage windows were jammed. Before one sat a father with his teenage son, his ankle in a cast of rags. Around the other, an entire family had clustered, all of them jabbering one atop the other in a blur of non-Mexican Spanish. The place stunk of armpits, blood, carpet cleaner, dust. Everywhere people were roiling in fits, and those who weren't looked on the verge. When finally the kid with the ankle got up, I slid into the seat before some bleeding woman and told her it was life and death.
"But you can't do that," she said. She dropped her rotten tissue on the counter and tapped at the window to the nurse behind it. "Tell him he can't do that," she said.
"You can't do that," said the nurse. She was young and appallingly thin, with close-set eyes and enormous specs.
"I'm a hemophiliac," said the woman. "You just can't do that."
I leaned into the speaker and told the nurse, "My friend is dead."
"This is very important, miss," the hemophiliac said. "Would you please tell him he just can't do that?"
"Where is this friend?" said the nurse, whose name by her tag was "Wendy."
"In the back of our truck."
"And you're sure he's deceased."
"Listen, miss," Basil said, "no disrespect intended, but we're in no mood for snazzy gags. You got a stretcher or something we can haul him in on?"
Wendy shot Basil a smile meant to wither.
"He's got problems, too," I said.
"What's wrong with him."
"His feet." I pointed at Basil's feet. "What's your procedure for taking in, you know, for taking in corpses?"
Wendy saw that we weren't joking. She slid her pen into the board with the sign-in list. The hemophiliac had started harping again, but Wendy stifled her with a hand. "We'll have some nurses come out with a gurney," she told me, her voice gone mellow. "They'll have to admit the body through the ambulance bay."
"Here's my number," I said, "and this is his license. How long you think they'll be?"
"I'll be right back," she said.
Rockets would sigh that night, high over this somber town. They'd explode in the clouds and mingle the rain of that outcry with the rain that had been and would be, and though that show might gesture toward elegance, even toward a grotesque munificence, it would never quite make the grade. How is it we think that to achieve ourselves we must stand on the backs of notions? Let's bring the stars down to earth. Let's cut down a tree to hang the stars on. Let's maim our blunders with time, and with whispers and gifts and cheap perfume. In the crowd we'll savor the taste of false vitality and pretend we're not ourselves, not even people, but only an image of the sights around. Orgy of the whir, orgy of the hum, in these we'll search for the things we'd been told we could hope to be. Behind the smile on that man, the gaze of that girl—there's but an effigy, the shimmer of so many days pushed through—ching-a-ling-ching, rattle-bang-boom: shriek, laugh, cry, groan. There on the streets, in the swarming casinos, we'd watch the past slide off and wait for the bells to toll a new year. Who knows what it means to police their days? This night we'd need to shrink the field, lower the boom, raise high the lanterns, red and green and gold. And the meager light we'd thought we made for ourselves would be little more than the twilight we thought we knew. The rockets would care for the rest. They'd explode, and we would sigh, and the faces around us, whatever they might be, would give comfort, if only by their numbers. Because tomorrow would be new, a brand new month and year. Let the night take our money and our pain. Yes, and yes. Calendar on...
Later, smiling at Basil and Lucille as they danced among the crowds, the old man would say, "It's survival of the slickest, boy, and that's something even the blind can see." And then he'd turn away, his face a puzzle, mumbling about maltworms and knaves, and vanish in the people, Fortinbras at his heel. I thought of Joubert's notion of the nest in the mind of the bird. All over the world, this very moment even, creatures were busy building homes—nests and hives and caves and dens and tunnels and lairs and dams, and hobo jungles and tenement slums, and birdhouses, and dovecotes, and dumps—everywhere, everywhere, a place for each and all. That's why we could play tonight, and that's why we could pray tomorrow. You want your moments, you need a place to make them, the way you need that place to remember and regret. We'd need roofs over our heads when it was said and done, and pillows beneath them, else how could we trick ourselves for even a moment with the platitudes that help to make us real? I'm as good as gold, and you're an angel in disguise, and the devil may care, though not, perhaps, until tomorrow, so hey, run with the money while you can, baby, run, you're a nine days' wonder... God is not just one. Our clichés tell us so every minute.
Wendy never returned. How could I hope to know what would be? I took Avey's hand, and we turned to face the crowd. A series of watercolors lined the walls, made by kids. Most scenes were happy families, father on the left, the tallest, followed by mom and the children by height, with a dog at the end: Daddy, Mommy, Stephanie, Abbie, Socks. There was a drawing too of a gold-haired woman with a jagged smile and flat blue eyes. That was it—no father, no children, no dog. Beneath her, in lopsided scrawl, was the single word, MOM. And mom was crying, and her tears were blood. Barry Manilow muzak piped through the speakers, just below the general din, "Copacabana," it seemed, though I didn't know for sure. Next to a TV running a soap sat a hundred gallon aquarium, filled, like the room its people, with all manner of fish. I watched them bump through a maze of shipwrecks and logs, endlessly gaping, until an old coot hobbled by, stinking of baby food and bad cologne, and a little girl maybe four years old let out a howl only children can make, packed with the world's own pain and sin. At that, her mother jerked her wrist and quick as light snatched the slipper from her foot and rapped the child's head. And then a woman was at my ear, with braces on her teeth and Mary Hartman braids.
"He's outside," Avey told her.
"In the parking lot?" said the woman's colleague. Stocky like a miner, she had a mullet with gelled spikes on top and a stringy mane down her back—the kind of do middle-aged lesbians have been rocking for a decade or so.
"In our truck," said Basil. He'd limped over once he realized the women had come for us. "You guys're going to take him?"
The stocky woman clasped her hands at her waist and wore a face reminiscent of certain preschool teachers, deceptively bemused, falsely sympathetic. "Do you know what happened?" she said.
"We had an accident," I said.
"An accident," said the tall gal. Now she was the sweet one. No crappy faces or half-baked pity. She was for real.
"We had a wreck last night."
"Up on the mountain," Basil said.
"And then what," said the stocky one, crossing her arms.
"They went out for some ice," Avey said, "and got into a wreck. When we woke up this morning he'd... you know." She started for the door. "You'll probably want to see for yourselves."
"You got something to carry him in on?" Basil said.
The stocky woman twirled the tail at her shoulder. "I'm going to pack it over my shoulder," she said.
"Pardon?" Basil said.
"I'm exceptionally well conditioned," the woman said.
"Come on, Karen," said the tall one with a big metal smile. She was a peach, this gal, for real. I guessed she had a houseful of animals, not cats, but dogs. "Eden," said her tag.
Basil had already made it to the first set of sliding doors. "When you're finished, maybe you could take care of him, too," I said. "I know you're busy and all."
"What's your name?"
It occurred to me that in my polka dot shirt and muddy boots I was still dressed like a clown. "He's in pretty bad shape, you know."
"Maybe we should have a look at you first," Eden said.
With her gurney on wheels, Nurse Karen marched out and fell in beside us. Super had enfolded Lucille with an arm to mumble his wisdom as she cried, and she had let him do it. The tailgate was open still, Dinky exposed to all who cared. Once again it began to rain.
"What're you doing?" Lucille said, her face wide with horror. Nurse Karen had hopped up and crouched near Dinky's head.
"Now, now," said the old man.
"Mind if we take it with the blanket?"
" _It?_ " Lucille said.
Super peeled off from Lucille to face Nurse Karen. "You'll excuse our saying so, misses, but we'll have to ask you to disembark the wheels till we've given the boy his due."
"Looks like a three-phase operation," Nurse Karen said to Eden. "Slide it down—"
"Step off the wheels, misses," Super said, "if you please."
Nurse Karen's face hardened. "As you can see, sir, we're much too busy for formalities. Just take up the feet," she said to Eden, "and slide it down far enough for us to make the turn."
"That's it?" Lucille said. "You're just going to haul him away?"
"Maybe you could give us a minute?" I said to Eden.
"Karen?" she said.
Nurse Karen bounced from the truck and began to pace.
"It's raining," Eden said to me. "So..."
"Thanks," said Avey.
Super drew off the blanket... Birds were in the trees... I smelled ice cream, I smelled rain... In the distance I heard laughter, but knew it wouldn't count—no one counts laughter, because laughter disappears... I was just an animal, words on the lake... Then a bird flew, and the rest flew after, and Basil limped up and took Dinky's feet and pulled his shoulders to the gate, where Super spun him even to it—our old pal Dinky, he was dead.
I hadn't seen the geeze take his nickels from Dinky's eyes, but somehow he had, only to lay them down again and step back cap in hand.
"It is clear, friends," he said, his voice grown solemn, "that before us lies a perturbed spirit without a finger on his lips to smother grief. It's our job to send him off with nary a whisper at his ears, though he be alone. Blood or no blood, you were his brothers and sisters. And so you loved the boy as we did. You don't have to croak for us to see how forty thousand brigands couldn't add to our sum, not with all their stolen love. For ourselves, we'd eat a crocodile if it meant he'd be delivered, ready to bend and give and move through the world with a smile. And we know you'd do it, too. Give this boy his due, friends, then cut the line with hearts full of thanks and cheer."
Some gawkers had massed about twenty feet off. Lucille was shuddering, she was crying so hard. She took Dinky's hand and kissed and pressed it to her cheek. Then she lurched into the truck.
"What the fuck're you staring at?" Basil said to the gawkers. It wasn't until he'd started toward them that they began to part. A woman walked by, shielding her daughter's eyes.
"But what is it, Mommy?" the child said.
"That's right," Basil said. "Scram!"
"Finished?" said Nurse Karen.
I touched Dinky's hand. A crust of blood had grown along the top of one of his nails. Avey held me. Her face was swollen.
"Take him," she said.
"Wait," Basil said. He brought out a guitar pick—Paul Stanley's, I knew—and tucked it into Dinky's shirt. "Rock and roll, buddy," he said. "We'll catch you on the rebound."
And that was it. No police, no questions, no forms. Nurse Karen and Eden just put our pal on the gurney and whisked him through the doors. Poof! He was there, and then he wasn't. Disgusting. Tremendous. Done.
Super's dolls covered the bed of his truck, plastic eyes rolling, plastic hair clinging to horrible plastic heads. No sign of sun, no sign of shit but _mucho_ rain and _mucho_ mud. A wind rose up and drove the trees...
Times like this the whole blasted planet creaks on its hinges, waiting for you to give, the way it knows you will, if you're ordinary... Your life's just residue. You're the sloughing-offs of so many sloughing-offs you couldn't say which was which or what went where and when. You can't see between the main or remains anymore, the remains or the remainder's residue. All you know is flux and everflux, the monstrous process—in the big sense, the really big sense—of eating and shitting and eating and shitting and eating... For a single hideous moment, there in the slippery rain, surrounded by the only people I'd ever truly known and who for that reason were strangers, I saw the ruin of distinctions. The weight of Dinky's absence became the weight of Dinky's presence. His death had become his life, his laughter my memory of it, my memory the laughing world's. Beauty and terror, the sacred and the feared—these had lost their color...
"You want me to get in the back a while?" Basil said, his eyes gone crooked the way they did when he grew tired.
"Might as well take care of your feet while we're here," I said.
"Yeah," Avey said. "You wait much longer, and they might have to amputate."
"Go on, boy," said the geeze. "That old gal with the tracks in her mouth'll take good care."
Basil limped to his girl, who hadn't seemed so much as to blink. "You okay?" He took her hand, but she didn't twitch. "I'll be back in a flash with a Coke on ice," he said, "just the way you like it."
IT WASN'T TILL LATER, AS WE LAY IN OUR MOTEL, that Avey said why she told Lucille what she told her while Basil fixed his feet.
"I'm never going to see those people again," Avey said from her pillow.
"How do you figure?"
"You think this is the first time I've hit a snag?"
"How aren't you going to see them?"
"You won't either."
"Avey," I said. "They're all I've got."
She ran a finger down my chest. She kissed me there, she kissed my mouth. " _Were_ , baby," she said, "and _had_." I considered the stains on the ceiling, adjusting to her words. "You know it's over," she said. "I saw it coming a week after I met you guys, and I'm slow."
"That still doesn't say why you had to tell her all that."
"It made her feel better."
"But it's just a name."
"A name is not a name is not a name. And it sure as hell isn't _me_."
I waited for her to continue, but she rolled to her back and took my hand and smiled.
"That's fucked up," I said.
"Yeah?"
"Look. I know you're restless. What I don't get is, why me?"
"A long time ago," she said, "just after I'd run away from home the first time, I bought a fifty-cent box of chow mein down on 42nd street, in New York. I ate it all, and when I finished, I ate the fortune cookie, too. You want to know what the fortune said?"
"Fortune's are for weaklings," I said.
"It said, _Discontent is the first step in the progress of a man or a nation_."
I didn't have to tell her the idea was worth regard. But neither did I want to say something too glib or hifalutin.
"Traveling cures these things," she said. "I'm on the road. My secrets are my steps."
"Sounds like a fancy way to say you're just a liar."
"Let's go to sleep."
"If it's the way you say it is, then why didn't you tell her your name was Mud?"
Avey put two fingers on my lips. "I've never told anybody that," she said. "Not even you."
There must've been more to Avey's telling Lucille her real name than she'd admit. Our friend had died, the woman was filled with grief. Lucille wouldn't've cared if Avey had said her name was Trash.
It was hard at first. Lucille's silence, it seemed, was a forest through which she couldn't find her way. We asked how she felt, for nothing. We asked was she tired, the same. We asked what she wanted now we were free, but still she said not a word. I flicked the monkey so it bumped and spun.
"The old man calls this thing José," I said. "As if at any minute it might want to rhumba."
Lucille was listening now. Her eyes had kicked the blur. She even almost laughed, I thought.
"I notice you haven't called me Elmira," Avey said.
"I like Hickory better."
"What if I told you Elmira's no more my name than Hickory?"
"I'd say that was a good thing."
"What if I told you it's Avey?"
"You want to be called Avey, I'll call you Avey. You want the other, I'll call you that. Just tell me what you want."
"I want for you to be happy."
"Basil wants to get his truck," said Lucille.
The old man had remained quiet in the drizzle. "What about him?" Avey said.
"He needs us right now," I said.
"Somebody needs somebody," Lucille said.
"The man is back in town!"
And so he was: Basil Badalamente, musician, doofus, drunk, asshole-cum-friend, friend-cum-foe, and foe-champ, all in the sense of huge, of extraordinaire, of bigger than life itself. Yes, yes, yes, Basil was big, Basil was huge, as huge as ever and maybe huger, but that didn't mean he wasn't a fake. Fakes was what we were, really, every last one of us, and fakery was our game, especially times like these. There's no such thing, after all, as the Comedown, so long as we never called it. Ergo, with fakery and lies, this had become routine. _I am not ugly, but stoked. I am not wounded, but charmed. I am not hurt, but pissed. And I will laugh at it all—ha! ha!—and keep on laughing—ha! ha! ha!—down to the putrid dregs_. Basil, undisputed King of the Fakes, now threw down his cane and proffered a Coke on ice.
"Am I good, baby," he said, "or am I _good_?"
I took the soda. "Mighty white of you, friend."
"How are you?" Lucille said.
He looked like a hairy scab. But to see his twinkling eyes and mouthful of teeth, you'd think he thought himself a hawk. "On top of the world," he said. "On top of the freaking world!"
"Hey, Super," Avey said, tugging at the old man's sleeve. "You ready?"
"Our name's Steady," Super said.
"We thought we'd pick up some clothes," I told Basil, "then hit a motel and place to eat. Then you can see about the Cruiser."
"That okay with you, geeze?" Basil said to Super.
"So long as Horatio here lives to tell the tale, we can run the race." And at that, Fortinbras the dog appeared in the bed behind his master.
"We're not getting back there again," I said.
Lucille sat up to protest, but Avey cut her off. "And we shant be drawing straws."
"It's only just down the way," Basil said.
I offered Lucille the Coke. Little by little her face grew soft. "I'm sorry," she said at last.
We didn't say a word. There was no word to say. Her sorrow, I saw, was more than she herself could say. Her face was the saying, and the wet of her eye. I thought of infants and of hatchlings, and of the trillions of creatures searching through this world, those in this land of wintry muck and those out there, beneath the sun, away at the world's ends. Lucille was in her hair shirt. Times like this you don't say dook. What you do is breathe.
Super drew the door and stepped aside. "Well sure you are," he said. "Sorrow's _always_ better than laughter." Avey got out, then Lucille, the old man tapped his chest and grinned. "It's by sadness the heart's made good."
"If only this were another day," Lucille said.
"Oh, but you're wrong, young misses. This here day's better than the rest, by far."
"Not to change the subject or anything," Avey said, "but do you know where these guys can get a change of clothes for cheap?"
Super said he did, and sure enough, at the 89 and 50, it was: a Millers Outpost, like a beacon from the mist. With the $52.38 in my pocket, the bills completely soaked, I bought some 501s, a cheap blue flannel and long sleeve tee, and was left with some change till I could tap my nest egg, 262 lousy bucks. Basil got identical stuff, fifty sizes larger, and a pair of Reeboks, size 17, for the bindings on his feet.
"You wouldn't happen to have a paper I could buy?" I said to the kid who helped us. He was a white boy, skinny as Fred Astaire, with a baseball cap and little bald head and giant shirt across which, in skate-punk graffiti, read the word _THINK!_
"Don't be crazy, man." He took a paper from under the reg and tossed it on the counter. "Y'all can _have_ it."
"Slap me some skin," I said, and held out my hand.
The kid eyed my hand like it might become a snake. "You a weird-ass."
"Slap me some skin," I said.
Basil was waiting. The kid ran his hand across mine, way too fast, and our business was complete. "You a weird-ass dude," he said. "I check you out."
I opened the paper. LAKE MAROONED BY TORRENTIAL RAIN, said the headline. Basil leaned over my shoulder:
_With rushing floodwaters undermining U.S. Highway 50 in numerous locations, the main route from Sacramento to South Lake Tahoe will remain closed indefinitely... Rain and melting snow have filled rivers and caused dangerous mudslides throughout the Tahoe Basin, where more than 2,000 US West customers were without phone service... About 7,300 Northern California customers were without power yesterday, while about13,000 Washington households were without power, down from a peak of 250,000..._
"I wasn't going anywhere, anyway," Basil said. "You going anywhere?"
"I'm just a weird-ass, Basil. You know?"
He pinched one of his little ears, and it struck me he didn't have his hat. He'd slept and showered and shit with the thing for the better part of ten forsaken years, and now, someway, it was lost.
"Speaking for myself," he said, "I'm one famished son of a bitch."
"We need a room," I said.
"Mark my words. We'll be sleeping in the old man's crate."
On top of the flooding, it was New Year's Eve, a not-so-small fact that happened to've slipped my mind. Super rolled to the 50 again and headed for Nevada. The world was still a sad-sack place, its folks a sad-sack lot. Every roach trap along the way had someone sleeping in a closet. Maybe he was right, Basil, and we were doomed to a night in the basement of a church, eating macaroons and Jello with bluehairs and bums and other sundry dopes.
Through this spot and that we made our way, past the unlucky bastards we'd seen the journey in, the roofs of their cars nearly swallowed. A grown man sat on one, a big old dude with a Grizzly Adams beard and shearling vest. From a distance it seemed he was talking to himself, or maybe even singing, but closer it grew plain the bear was sobbing like a kitten. He just stood there on display, right in the open, pouring out his guts.
"Pity," Super said, "never cries in the streets. But wisdom. Every day it's howling on the roads, and not a varlet hears it."
Was he a cream puff, this man? We thought not, though, again, he was no insensitive beast... The song about the man who couldn't cry until he'd been taken to the place for the insensitive and insane. Who after that not only cried, but cried every time it rained. Who once it had rained for forty days and forty nights died on the forty-first day—he just dehydrated and died...
And it was true, I thought: he was there, and then he wasn't...
We hove on, getting the brush at every joint—stuck in and shut out, all at once. I picked up the paper. "'Fed by a week of pounding rain and melting snow,'" I read, "'Lake Tahoe rose to its highest level in modern times Tuesday, rising six inches in a day to surpass the lake's legal storage capacity—'"
"Needles in your brain, Horatio, is all that is."
"Says here it's a twelve hour drive just to Sacramento."
"We got a friend," Super said. "Up yonder."
"What friend is that," Avey said.
"Fear not, butterfly. She will feed you."
Around the bend the lake rolled into view once more, turbulent, vast, and blue, roiling with whitecaps, and scarves of mist, and not a single squawking gull, nothing from a painting on a doctor's wall, just apathy, brutal, just eternity, cruel. A flooded shopping center drifted past, and then a golf course, flooded, too. Then more concerns, the Mickey D's again, the crowded Shell's, that diner packed with refugees and locals and archangels and creeps. And then we were parked before the Thunder Chief Motel, a drowsy looking joint with dripping eaves and needles on the porch. But just like the rest, this one had its blinking sign: NO VACANCY.
"I know you can read," I told the old man.
"We've got a friend."
"By the looks of it," Avey said, "he's doing a good business."
The old man wriggled in his seat. I looked at his fingers on the wheel: BEND and GIVE.
"What's the deal?" Basil said.
"The old man says he's got a friend in there," Avey said.
"The implication," I said, "is he can somehow squeeze us in."
"I'll hold my breath," Basil said.
Inside, I rang the bell. To the left hung a pic of two of the scariest entities I had ever seen. The woman reminded me of something from Poe, risen from ancestral vaults. She had a forehead like a boxing glove, her eyes bulged over a steak-knife nose above a scratch for lips, and her beehive do was purple. Next to her, and much taller, stood her giant of a freak, Herman Munster's brother, his iron hair in a bowl-cut and skin like the rinds on nasty cheese. At least the office was warm. It smelled of TV dinners and mentholated smoke. I rang the bell again.
"Be right with you," said a voice from behind a half-drawn door.
I had my arm around Avey. She looked at me and smiled. I wanted to be alone with her, in the warmth of a room with chocolate and toast, beneath some grandma's quilt. We'd murmur to each other, we'd sleep, I'd rest in the belly of her sighs. I wanted to say, _I love you_ , but mumbled, "Take your time."
The guy through the door was the monster in the pic, the selfsame bizzaro of a guy. He was not, however, clad in a tux, but bicycling shorts and a pale green tee that said MARINE WORLD, AFRICA USA. He was barefoot. Most of his toenails were black. Best of all, he was an inch or two taller than Basil, pushing seven feet.
"What can we do for you kids?" he said, and placed a dish of olives on the counter.
It took me a second to find my voice. "Hows about telling us you accidentally switched on your NO VACANCY sign?"
"Since Moses got the tablets," said the man, "I been sitting in this office. That's a long time, you know." I picked up a postcard featuring a Fabio-type lunk in a g-string, smoldering with his pinched blue eyes and ridiculous bulge. It said FABULOUS LAKE TAHOE. "And in all that time," the man said, "I haven't seen anything like what we've got going on here." Now that he'd moved closer, the sacks beneath eyes took on a whole new meaning. "I ask you," he said, "would either one of you kids go out in this if you did not absolutely have to?"
"So you did make a mistake with the sign," Avey said.
The man smacked his lips. "Nincompoops I think the world is spawning these days," he said. "If you ask me, that's what I'd say. This genius of a couple, it turns out, decided they were going to try to make it home tonight. Only fifteen minutes ago they conceived of this exploit."
"You're kidding," I said.
The man crammed a handful of olives in his mouth. "Do I look like the kind who kids?"
"Depends on what the-kind-who-kids looks like," I said.
The man took a step back from the counter and held out his arms. "The father of our country?" he said, smacking on his olives. "He's a big fat nothing next to me."
"How much," Avey said.
"Maybe I'm wrong, I don't know. But I think you'll agree that $59.95, plus tax, is a precious good deal."
"We'll take it."
"Just the two of you?"
"We've got three more outside."
"Not to be slippery, but that will make it $89.95." From behind a pair of thrift store specs, he took up a pencil and licked its tip. "Two king-sizes ought to keep you, I think."
"You know an old man named Super?" Avey said.
"That I cannot say."
"He says he knows you."
"Lots of people say they know me when I don't know them from Jehoshaphat."
"He's right outside." I pointed out the window, but go figure, Super had disappeared. "Well," I said, "he was a minute ago."
"He couldn't've gone far," said the man. He slid his check-in book my way. "Now if one of you gentle people would be so kind as to share your intimates." He snuck another peep outside. "You may think I'm plotzing, but my eyes, they tell me there's a little monkey out there, dangling in that truck, I swear."
"Plotzing you are not," Avey said.
The man shook his head. "Then I wasn't plotzing."
I asked Basil to cover the tab till we could reach a bank.
"You got dough in the bank?" he said. I looked at him. A wad of bills appeared in his hand. "Here."
The room was typical, a tube on the wall, plastic drinking cups and cheap white towels, the Hallmark photo of two owls in a hole in a tree. Lucille wanted to get in bed but Basil wouldn't let her. He needed her to get his truck. Triple A told us such conditions would usually keep us waiting two or three hours, but it just so happened a man was nearby. Fifteen minutes later, our buddies were gone.
Not until the door had shut behind them and the hush came down did I comprehend: this was the real world, this normality, we were safe again in the real world now, Avey and I were alone.
Her eyes were black, her skin a lake of shadows and cream. A thick green light had fallen on her, full of swirling motes. Her mouth, her lips, her teeth—she was all too terribly edible, so deceptive, so pure.
I imagined her finger along my teeth and over my tongue, and then another finger and another until soon her hand had eased down my throat, and then her arm, too, and other hand and arm, and her face, and head, and on, till she was all inside. I touched her mouth. Her eyelids drooped.
"So pretty," I said.
She blushed. "Really?"
I plucked her nose and stuck my thumb between my fingers. "Really."
Avey kissed me again, and we laughed.
"I like you, AJ," she said.
"I like you, Mud."
It was unbelievably quiet. Everything lay quiet, everything still. The room was a cave under water and all that was in it a merking's things, silent as the depths, lovely and green, a silence only the gifted could know, the gifted and the drowned. Avey sat on my lap.
"I feel so greasy," she said.
I put my face in her neck, her hair. We rocked to and fro. Such stillness, such quiet, what a world...
And the rain kept raining, down the mountains, into rivers and lakes...
"Speaking of which," she said at last, "did you know there was some greasy spoon down the way?"
"I saw it."
"Let's walk down there."
"What about Super?"
"You really like that old guy, don't you."
"He's the kind of guy who scares you while he makes you laugh. But I feel sorry for him. I don't know why."
"He's a lonely man."
"His truck's outside."
"Come on."
"I don't want to be anything like him," I said. Avey shook her head. "But then again, I want to be exactly like him." Avey smiled. "You miss Dinky?"
"I started missing Dinky the day we met."
"It's like he's on vacation," I said. "Like he left on a train."
"Come on."
I took her hand. "I like you, Mud."
Again she smiled. "I can see that, AJ. I like you, too."
A DARK-SKINNED MAN WITH KRIS KRINGLE EYES and big gold teeth met us at the door and took our name.
"Is cold out there," he said, "and warm in here. We take good care of you."
Here was a place full of people who might never have known they were trapped in a storm. Families of all sorts had jammed the room to the gunnels. Maple syrup and waffles, hash browns and crepes, and pork chops and ketchup and muffins and toast, and burgers, too, and corned beef and sauerkraut on rye, and hot chocolate and tea, and onions and root beer and coffee and milk, and French toast, and raspberry jam. Smells swirled round us thick with the hum of satisfied speech, a great single body of glistening eyes and munching mouths, the clatter and clink of spoons in cups and forks on plates, and the steamy hiss of fryer and grill, and the banter of waitresses, children, cooks. An infant sat in her mother's lap, feeding from a bottle. The mother herself was engaged in talk with a boy in a mask, waving a plastic gun, another, I guessed, of her many. The boy had asked about the difference between bacon and ham, whereon she took the baby's foot and jiggled its toes. "This little piggy," she said, "went to the market. This little piggy stayed home..." The boy tore off his mask and squealed. "Oink, oink!" he shouted. "Oink!" Two girls maybe seven or eight were playing a game of patty cakes. An old woman sat with her old man holding hands in silence, not for nothing to say, I could see, but for the glow that was The Real. Red and green crepe bunting festooned the place. Lights twinkled, music purred.
A woman approached. She was pregnant and wore her hair in a braid, tied up top with a bow of white taffeta. Around her neck on a silver chain hung a silver ball that tinkled as she moved. She was tall and thin, and her eyes gleamed with such joy, I had never seen. I recognized the song, by Captain & Tennille— _I will! I will! I will!_
"Hello, hello," the woman said. I wanted to call her Old Lady Pear, but she wasn't old, but like a pear. "I sure do hope you two are ready to eat, because we're ready to serve you. Ready spaghetti!"
"I am no lie, eh?" said the man with gold teeth as the woman led us off.
"What's your name?" Avey said.
"My name," said the woman, and pinched the chain above her silver ball, "is Robin. Did I sprinkle magic dust on you yet?"
"I don't think we've had the pleasure," I said.
"Never say never," she said, and giggled. She leaned first to Avey's side of the booth and then to mine and shook the ball so it tinkled. "All of us girls have them," she said. "I was the first. Now every girl gets one on her birthday. We're all fairy sisters!"
"You're lucky," Avey said.
"You don't know the _half_ of it," Robin said. She stood back and gleamed. "You two look like you could use a good strong cup of motor starter!"
"Is she cool or what?" Avey said when Robin had left.
"Straight from a book," I said.
Robin came back with coffee and filled our cups. It was so hot and black and the steam so thick I almost didn't want to drink it. Nothing, it seemed, had been so inviting for years.
"I've told you my name," said Robin, "but you haven't told me yours."
"I'm Avey. That's AJ."
"Well, Avey and AJ, would you mind if I make a suggestion?"
"I don't know..." Avey said, drawing out the words.
" _Swiss Boysenberry Crepes_."
"You like those, do you?"
"Like them?" Robin wore heavy blue eye shadow that glistened when she blinked. "Goodness, AJ. I could eat those until they came out my ears!"
"Well what are you waiting for?" I said. "This guy's starving."
Robin's smile never left. Avey touched her arm. "Don't take it personally, but I'm kind of in the mood for eggs."
"I do love eggs," said Robin as her hand described a circle round her belly. "They make me think of how fast my little one here's gone from being a little teensy egg to _this_."
"When're you due?" I said.
"Make me a promise?" Robin said.
"Depends."
Robin giggled. "Think of me on Ground Hog Day!" she said, somehow able to laugh and talk at once.
"That's it?" I said. "The big day?"
"The big day. Pop!" Robin poked her belly. "Now about those eggs," she said. "We can make them any way you like, scrambled hard or soft, soft boiled, hard boiled, poached, sunnyside-up, over easy, over hard, what's your pleasure, Avey? Speak now or I'll have to come again!"
"Scrambled," Avey said, "with cheese. And toast and hash browns and jelly. And orange juice, too. Doesn't orange juice sound divine?" she said.
"Orange juice sounds just lovely," I said.
"I can't believe how perfect you two are," Robin said. "It makes me all warm and mushy inside just to see you. How long have you been married?"
"We're not," Avey said.
"Well you should be," Robin said. She spun round on her pediatric shoes and shouted. "Yoo- _hoo_ , Ma- _ri_ -a!" A curvy girl with kinky hair and tiny teeth pattered to the table. "Do they or do they not look like the _per_ fect couple?"
Robin hadn't lied about the silver balls. Maria pulled one from her blouse and shook it. "It's your destiny," she said.
"See?" Robin said.
"You're a regular gypsy," I said.
"I'm good, I'm bad," Robin said, "though I might be a little ugly."
" _No_ ," Avey said.
"Yes!" One of the cooks called Robin's name, and she jumped. "Goodness. They'll have my head on a platter before I know it. I've got to get your order filled."
The place was really bustling, the air enough to swoon. Waitresses worked their way through the aisles, each with a silver ball on a silver chain. Two construction-type guys sat hunkered over plates full of biscuits and gravy and pancakes and butter and bacon, all good things for hungry working men. Young and upcoming professionals decked out in Calvin Klein shades and Gucci skiwear clambered round tables loaded with grub, grandmas and grandpas, as well, gnawing on bones and sucking down fries, their grandsons and -daughters righteously porking along. Here was the ontology of oneness in a world gone mad, the music of chaos and bliss, some bright and risen band of lovelies playing for our ears only. Or maybe it was the way things had been and would always be, plain as a mountain, jeering at my stupor with good-natured amplitude until finally, like a man who'd been anesthetized, like it knew would be, I came round. The fragrance of so many meals, and the gorgeous din, the coffee in my mouth, hot with sugar and cream, these were a euphony all their own. Since I could remember, this was the first time my body had keened with a sense the world calls delight. My head swam loud with textures, tastes, colors, sound. On every wall hung pictures of the famous who'd graced the joint, a regular Vegas pantheon. There was Crystal Gayle in a white lace dress, and The Oak Ridge Boys with pompadours and smiles, the Denvers, too, John and Bob, and Wayne Newton, and Sammy Davis Jr, and Three Dog Night. The cheese factor was as high as the spirits. Hosannas from the sky couldn't have sweetened the pot.
"Avey," I said. She didn't answer. She only looked. "I don't know," I said. "It's like this place fills me with a huge sense of, I don't know, well-being, I guess."
"That is _so_ weird," Avey said like a high school bimbo, though I loved her for it anyway, "because that's exactly how I feel, too."
"It's a Brady Bunch thing," I said.
"I wish I could live here."
"Me, too," I said. "With you."
"Really?"
"Really."
"Me, I mean, with you."
Steam like genies swarmed from our plates when Robin set them down, boysenberries oozed across my crepes, cheese over Avey's eggs, them and mounds of butter. A smorgasbord of syrup magically appeared—strawberry, raspberry, blueberry, maple—the whole goddamned works. And though I'd never asked, Robin had brought me a giant glass of milk. If Avey's face was a picture of mine, we must have looked the King and Queen of Earth.
"Say, Robin."
"Yes, dear?"
"You wouldn't by any chance know a silver-haired man called Super?"
"Super Duper? Supercalifragilisticexpialidocious?"
"Yeah, yeah," I said. "You know him?"
"Can't say I do."
"You've heard of him then," Avey said.
"Nope."
"Then how'd you know his name?"
"Silly! Everyone is super-duper to me!"
Avey and I laid into our meals. For a solid five minutes we didn't say a word. Finally I looked up. Avey was staring with a smile.
"What?" I said, looking at my shirt to see if I'd drooled. "Do I have a bat in the cave or what?"
"Can't a girl just smile?"
I took Avey's hands. I leaned across the table and kissed her. "Marry me," I said. "Today. Right now."
"AJ."
"Marry me. We can go into Nevada and get hitched today. It's no secret the way I feel about you. Besides, you heard what that woman said."
"That they're fairies?"
"That it's in the stars, you. Marry me."
Avey took a sip of water. She leaned into her seat. " _AaaaaaJaaaaay_."
"AJ nothing. Let's do it."
My girl was smiling, the way humans do when the world turns strange, my girl was stirring her eggs. I waited, watching her smile stay and stay, until she put her hands on the table and brought her face to mine.
"Let's do it," she said.
I ran to the man with golden teeth and hollered for our check. "Snap, snap, Mr Wonderful," I said. " _We_ are getting married!"
"I no tell you a lie, eh? We take care of you."
"You're beautiful, my friend," I said, and meant it.
And then Robin appeared. "What's the matter," she said, "are the alien's coming?"
"We, Robin, are getting married."
"Well, can you feature that?"
I grabbed her face and gave it a giant kiss. "You are a freaking angel."
Robin waggled her silver ball. "The more you give, the better it is," she said. "Empty your cup!"
From the phone booth outside we called a cab, and the next thing we knew, we were at the County Clerk's applying for a license to get hitched. Avey and I both were as amazed by how well the world seemed to work, given the mayhem it had been cast into, as we had been by the mayhem at its peak. Last night, we were trapped in a cabin on a mountain that snatched up the life of our friend and set us fearing for our own. Today, our friend was gone, and we were eating crepes and eggs in a diner full of merrymaking fools, and rushing off to marriage. You never know what's coming for you, I said to Avey. And what's coming for you, Avey said, is always what's best, even if you don't know it. That was good enough for me, then: she was holding my hand. I told the preacher who answered the number off our list we needed someone to make quick work of two desperate lovers.
"Chomping at the old bit are you?" the reverend said as though he were hard of hearing.
"Right now," I said. "Can you do it?"
"Think you can hold the old horses for about an hour?"
"What time is it?" I said.
"Noon, of course," he said. "Listen. The old wife's got leftover turkey and stuffing on the table as we speak."
"Where're you located?"
"I'll tell you what, son. We aren't going anywheres today, what with this infernal weather. If you can be here by one, we'll be pleased as punch to do you right."
Good thing we'd hit the Wells Fargo inside Raley's before heading to the diner. I'd left just two bucks in my account, the balance a fire in my pocket. To hell with Super, to hell with Basil and Lucille. We didn't need them. The cab would cost plenty, that much we knew, but I didn't care and neither did my girl.
Our driver was a tiny guy, smaller than me, a hundred pounds, if that. He looked a lot like the rat from _Reservoir Dogs_ , actually, the one with the scrawny van dyke and yellowy teeth played by Steve Buscemi, an impression that sealed when he crammed a thumb against a nostril and honked some junk from the other. A scarcely concealed agitation entered his voice when we told him our destination.
"Lucky for you it's slow today," he said. "I don't normally go nowhere past Elk Point."
No doubt his attitude changed after I said there'd be an extra twenty in the deal if he'd shut his mouth and drive. For about fifteen minutes everything was peachy, me and my mud-paddy necking away like a couple of teenaged horn dogs. But there's always something, and the car began to shudder.
"What the hell?" I said.
"Didn't nobody tell me the gas gauge was busted."
"Look," I said. "We're on our way to get married."
"So what do you want, a toaster?"
"Maybe you could get on the horn," Avey said, "and call somebody. Think you can do that?"
The twerp picked up his radio and turned a couple of knobs. "For your sake I'll pretend I didn't hear nothing." He rolled down the window and waved his hand at the world. "I don't hear nothing but the cars passing by."
When we pulled up at the reverend's nearly an hour on, an old man and woman were in their garage, between two cars.
"Are you Reverend Rumsey?" I said.
A short man with a handlebar mustache and thinning hair, he wore a black wool blazer and collarless shirt played up by a diamond in gold, the size of a Canadian dime. "Friends call me Rev-Up," he said, and noted the plates on his car. REV UP, it said, opposite the other, JMP 4 JOY. "Just like that," the man said, "only with a hyphen."
"You were going to conduct a service for us."
"You know what time it is, son?"
"We had a blowout on the way up." I gestured toward the ratman. "Our cab."
"One-thirty," said Rev-Up. "Or thereabouts."
Avey flashed her best sad frown. "You said you weren't going out today."
"I said I wasn't going out for _work_. Me and the old gal got thirsty."
"So you're not going to marry us."
"Did I say that?" Rev-Up stepped to the door of the car his wife had got in and said, "Looks like they're here, Dale."
The place was warm and bright and smelled of potpourri and burning wood and mincemeat pie and spuds.
"Now I'm not criticizing you," Rev-Up said, "but why in the heck did you kids choose today of all days to tie the old knot?"
Avey slapped her legs. "It's another one of those real-long-stories deals," she said.
"We know all about _those_ ," said Dale. Her rhinestone brooch, in the shape of a cross, twinkled in the lights from the Xmas tree. "If only we had a nickel for every time we've heard that line—"
"—we'd be gazillionaires," said Rev-Up. He was twisting the tips of his stache. Funny I hadn't noticed, but his fingers were those of a woman, long and slender and tapered at the ends, with longish nails, too, that looked like they'd been shellacked. He was the type of guy, I saw, who studied his stamps in panties he nabbed from his wife. He finished with his twiddling and took a pipe from beside a red glass bowl of candy. "Any particular angle," he asked, "you want to the service?"
"I've never gone in for too much Bible pounding," I said. "No offense."
"None taken," Rev-Up said. He drew at his pipe and twiddled his stache. "Hows about some good old-fashioned spirituals then?"
"What do you think?" I said to Avey.
"With them," said Rev-Up, "it's about the Great Spirit and such-like."
All this talk was making me nervous. It didn't matter to me what the man said, so long as it was legal.
"Personally," Rev-Up said, "for my money, I'd go with old Heyzoose Himself. The New Testament, straight down the line. But that's just me, of course."
"The other stuff sounded good to me," said Avey.
Rev-Up looked to see I was with her. "Then the other stuff it shall be. Any time you two're ready."
Avey didn't have a veil. Dale offered a rhinestone tiara, but Avey took my snowcap, the one I'd got from Dinky, and garnished it with toilet paper, green. And there we were, hand-in-hand to Rev-Up's voice, sonorous and warm. "It is," I heard him say, "an important moment when two people, who at one time were strangers to one another, are drawn together by an irresistible force, so that, henceforth, their lives will not be divided by space or by time..." And later a bit of Kahlil Gibran snuck into the picture, something about singing and dancing in the midst of being alone. "The strings of a lute," Rev-Up intoned, "though they quiver with the same music, are alone. And you will stand together, yet not too near together, for the pillars of the temple stand apart, and the oak and the cypress grow not in each other's shadow... You are performing an act of complete and utter faith..." And then my head went south, a misty curtain draping from the wings. Rev-Up was asking for the symbols of our commitment. It took a minute to find the rings we'd got from the gumball machine at the diner. Our man was dismayed when he saw them, but discretely forged ahead. "These rings are a symbol in this your wedding ceremony and in your marriage of two things. First, they are made of a material that does not tarnish, and this symbolizes your love for one another remaining forever pure and untarnished. Second, they are made in a complete circle, having no beginning and no end. This, too, symbolizes your love for one another, remaining forever."
A minute later found me saying, "With this ring I thee wed. Let it ever be to us a symbol of our eternal love," and a minute later yet Rev-Up said, "By the authority vested in me by my church and by the state of Nevada, I now pronounce you husband and wife. You may kiss each other!"
And then Avey was on my back. Snow had somehow appeared, or maybe it had been there always, I don't know, but we were piggybacking through the stuff, and falling in the stuff, and laughing and kissing and laughing. Just across the way an old pair of Czechs had set up a store that sold us cheap champagne. The ratman told us we were nuts, and we laughingly agreed.
BACK AT THE MOTEL, WE FOUND SUPER IN HIS truck with his Pall Mall, Fortinbras as ever by his side.
"We have the curious suspicion something heterodoxical's in the air."
"Super," I said, "meet Avey vanden Heuvel, my new wife."
"Well, well," Super said. "Isn't that a thrifty board you've set."
"I don't catch your drift."
"What's to catch? There's not a fool this side of the pass that can't see the funeral-baked meats'll do fine for the marital feast. If that's not thrift, we don't know it." The old man clapped me on the shoulder and said his heart was glad. Then, with a stiff but passionate dip of his head, he took Avey's hand and kissed it. "Reap while you can, butterfly," he said. "Reap while you can."
In our room, alone at last, we dallied in love till solitude took us, followed by dreamless sleep. We woke to the sounds of laughter. The room now was black, I didn't know where I was. Something brushed my cheek, a strand of hair, I thought, that made me think of a man I'd known, who when he saw hair on a motel bed thought it from a Turk. It's true how rooms like these harbor what's left of others, bits of tawdry fact crying out from time—the illegible guest books and marked-up scriptures in the Gideons by the bed, a forgotten pair of panties beneath the mattress and burns on the stand, the solitary clip of nail that scrapes your feet and conjures to mind this day or that long past. Once, as a child, my family had stayed at the only motel in town. Death Valley was the place, or maybe some dump near the waste that is Needles. It was hot and dry and dark, with a skyful of stars I remember as sad. The clerk that night had stepped out for a smoke and seen me by the fence round the pool, staring at the water. _Don't go getting any far out ideas_ , he'd said, _about sticking your tootsies in that, my friend. But it's so hot_ , I said. _You don't figure that fence ain't there for nothing, do you?_ he said. I asked what he meant, and he knelt in the rocks and told of the boy who'd drowned last year, a boy, in fact, about my age. His parents had put him to bed and gone to eat, then come back to a TV lost in fuzz. It wasn't till morning, after they'd phoned the police and firemen and county sheriff too that the man himself found the kid, floating in the pool by a little dead mouse. All my life I'd remember that story. And more than once I'd find myself thinking of the lights in the pool, the boy above, luminescent, void, bobbing with the ripples of the cruising snake...
Avey stirred at my side, I rose to the surface, I knew where I was, on solid ground at last.
"Open up, you fools," Basil shouted.
I went to the door in a blanket. Lucille had a cocktail, a bourbon and coke on a pile of ice, and was smiling like a little girl.
"What have we here?" Basil said.
"Some hanky panky no doubt," Lucille said.
"We got married," Avey said.
"That's just about the most stupidest thing I ever heard," Basil said.
"This calls for a celebration!" Lucille said.
"We don't want a celebration," Avey said, and hid beneath the sheets.
"But it's New Year's Eve," Basil said.
"And it's still my party," Lucille said. "Besides, that's what Dinky would've wanted."
Basil flipped the lights. " _Get on uppa!_ " he sang, doing his best James Brown.
"Basil won 600 bucks at the table," Lucille said.
"What about the Cruiser?" Avey said.
"It's totaled," Lucille said.
"We'll rent a car tomorrow," Basil said.
"We're going to tear this place up," Lucille said, and emptied a bag on the bureau, bourbon and cokes and magazines and smokes and beer. "It took us a while to get things right," she said, "but now we're back on track." She spun round to Basil. "Turn on some music, squeeze."
"Ah baby, for Pete's sake, when're you going to stop that?"
"Squeeze got a boom box," Lucille said.
"Magnavox," Basil said. "A hundred and sixty-nine bones at K-Mart." He flipped a switch and out came "Let Me Drown." "So you really did it?" he said. Avey held up her hand. "What's that?"
"My wedding ring of course."
"You got a problem with it?" I said.
"It's from a box of Cracker Jacks."
"Gumball machine," I said. "Twenty-five cents."
"When are you going to pop the question to me, honey-buns?" said Lucille.
"See what you went and did?" Basil said.
"You know Chris Rock," Avey said.
"Do I know Chris Rock," Basil said. "Of course I know Chris Rock. I know everything."
"Then you've heard his routine about the old man in the club."
"I haven't," Lucille said.
"'You don't get married,' he says, 'pretty soon you'll find yourself a single man, too old for the club. Not really old, just a little bit too old to be in the club.'"
"He's already too old to be in the club," I said.
"Fix yourself a drink," Basil said. "For some crazy reason, I'm in a decent mood."
We took turns in the shower, slamming cocktails as we went. None of what had happened had happened at all, it seemed. No one mentioned Dinky. Everyone was happy. It was like we were truly friends.
As for the rest of the world, it too may as well have forgotten the storm with all its havoc. Up on the strip, from state line to Caesar's, the 50 was jammed with boobs galore.
Oily women with giant hair and turquoise jewels squealed at their men. His hand trembling with uncertainty or hope, a one-legged man spooned sugar on a napkin. When a cocktail girl with tits so big they had to've cost ten grand apiece asked the man his pleasure, he stuck a fifty in her cleavage and said, "Hows about twenty with you?" Blackjack dealers dealt their cards and waited for deliverance. A bald man flung his toupee at a man with too much hair while a tubby guy in spandex on a circular stage crooned "Tiny Bubbles" so well Don Ho would've liked to see him dead. Everywhere we went, obscenity and artifice swam in the general eye. Voices sang out, grunts were heard, the smell of money and booze and costly steaks oozed from every door.
Basil paid a bag lady dripping with mud five crazy dollars for a photo of our bunch. Super appeared and disappeared, we could never say why or how. A woman at least three hundred pounds hit the jackpot on a dollar machine, then burst into a fit of laughter. When her money spilled from the pan, she dropped to the floor and rolled among the coins. The night raged on. Hostesses in corsets handed drinks to any who asked, the world was overjoyed. I clung to Avey and she to me, we were hugging and kissing and laughing and shouting and tripping and stumbling and shouting. And then we heard a drunk cry out midnight was on its way.
We found ourselves in the street, on the state line outside Harrah's. All around people had joined hands and begun to rally in a single line, twisting and turning as the countdown neared. I tried to keep up but tripped in the gutter, a strange hand before me, and five behind it. I hadn't yet reached my feet when, dimly at first, a voice rolled through the crowd. Only after it had swelled to a roar did I know it was the voice of the crowd itself, a unified chant, counting down from ten.
I stood up. Faces had turned to the sky. When the roar descended to the number zero, rockets went sighing to the heavens and exploded all around. That was it, then, midnight, no longer New Year's Eve, not yet New Year's Day. Everyone was kissing everyone, you couldn't have stopped them if you tried. A thousand laughing faces, every single face, had melded into one. We spun in circles, Avey and I, round and round, until the dizziness took us, and we fell into the crowd. Goddamn, it was a celebration.
Gratitude
I have so many people in my life who've done so much for me in so many ways, I hardly know where to begin to thank you all. If you're not here, but know you should be, I hope you won't be too hard: it's my oversight entirely.
Jeanine, Jeanine, Jeanine, without whom this book wouldn't be.
Bharati, who supported me when I didn't deserve support and gave me the best advice a writer could have, what kept me going all those times I wanted to stop: I've never forgotten, Bharati, I am so grateful.
Clark, man of wisdom and grace.
Hillary, who knows why.
Tony, through thick and thin.
Andy, who's always had my back.
James, absurd hustler, artiste supreme, bad motherfucker, my man.
Eric, who saw what no one else had seen, then walked his talk the way we've all come to appreciate (and expect).
Eliza, powerhouse extraordinaire.
And, in no special order, for reasons big and small (you all know why, too):
Augustus Rose, Nami Mun, Jennifer Deitz, Nick Petrulakis, Bridget Hoida, Jenn Stroud Rossman, John Beckman, Snorri Sturluson, Sean Madigan Hoen, Neil Wiltshire, Brendan Burke, Stephen Stralka, Jack Hicks, Brett Beutel, Butch O'Brien, TT O'Brien, Janis Finwall, Todd O'Brien, Christopher O'Brien, Tim O'Brien, Mary DeMartinis, Lauren O'Brien, Christian Kiefer, Xander Cameron, David Gutowski, Gabrielle Gantz, Jason Diamond, Karolina Waclawiak, Jeff Jackson, Joshua Mohr, Anne-Marie Kinney, Grace Krilanovich, Barbara Browning, Don DeLillo, Emily Gould, Matthew Specktor, Gabino Iglesias, Luke Goebel, Richard Nash, Terese Svoboda, Adam Wilson, Jocelyn Tobias, Samuel Sattin, Mike Young, Cari Luna, Robbie Egan, Mark Cugini, Gregory Henry, Adam Robinson, Benjamin Dreyer, Scott McClanahan, Laura van den Berg, Halimah Marcus, Deborah Hay, Hilary Clark, Eric Palmerlee, Andrea Johnston, Molly Poerstel, Ros Warby, Sher Doriff, Luke Degnan, Oona Patrick, Stephen Corey, Mindy Wilson, Germán Sierra, Cal Morgan, Kyle Minor, Stephen Dunn, Brian Bouldrey, Nicole Elizabeth, Lauren Cerand, Molly Gaudry, Renee Zuckerbrot, Chris Parris-Lamb, Andrea Coates, Michael J Seidlinger, Oren Moverman, Brian Bennett, Victor Giganti, Eddie Evanisko, Michele Durning, Douglas Durning, Carole Doughty, Joseph Fuqua, Ben Austin, Anneke Hansen, Daniel Scott, David Duhr, Deborah Lohse, Eddy Rathke, Erika Anderson, Penina Roth, Graham Storey, Major West, Leslie O'Neill, Gregg Holtgrewe, Julian Barnett, Daniel Sullivan, Julie Mayo, Melissa Maino, Ron Tanner, Ryan Johnston, Jason Ross, Sean H. Doyle, Susie DeFord, Tamara Ober, Virginia Konchan, Will Jones, Michael Harris, Scott Cheshire, Alice Peck, Jason Russo, Virginia Hatt, Kashana Cauley, Christine Onorati, Emily Pullen, Jenn Northington, Mark Snyder, WORD Books, Monica Westin, Aaron Garson, Caitlin Elizabeth Harper, Elvis Alves, Donald Ray Pollock, Joseph Salvatore, Jean-Pierre Karwacki, Deb Cameron, Adam Pieroni, Jennifer Pieroni, Minna Proctor, Renée Ashley, David Daniel, Jeff Johnson, Jen Loy, Kaya Oakes, Jennifer McCulloch, Kymba Bartley, Boris Hauf, Litó Walkey, Martin Nachbar, Zoë Knights, Austin Wilson, Brooks Sterritt, Julia Fierro...
| {
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Maciste (Macistus, ) és un dels personatges de ficció recurrents més antics del cinema, creats per Gabriele d'Annunzio i Giovanni Pastrone. Es tracta d'una figura heroica al llarg de la història del cinema d'Itàlia des de la dècada de 1910 fins a la dècada de 1960.
Generalment es representa com una emulació d'Hèrcules, utilitzant la seva immensa força per aconseguir fites heroiques que els homes ordinaris no poden fer. Molts de les pel·lícules italianes de la dècada del 1950 amb Maciste van ser reanomenades en altres països, amb noms més locals més populars com Hèrcules, Goliat o Samsó.
Nom
Hi ha diverses referències al nom en literarura. El nom de Maciste apareix en una frase a la Geografia d'Estrabó (Llibre 8, Capítol 3, Secció 21), en què es descriu: - "I al mig es troba el temple dels Macistianos Heracles, i el riu Acidon". L'epítet Μακίστιος (Makistios, latinitzat com Macistius) és generalment un adjectiu referit a un poble anomenat Μάκιστος (Makistos) a la província de Triphylia a Elis.
En el primer volum del Dizionario universale archeologico-artistico-technologico[https://"> (1858), Macistius es dona entre diversos epítets d'Hèrcules (Ercole). Al segon volum del mateix diccionari (1864), aquest nom apareix en italià com a "Maciste", definit com "uno dei soprannomi d'Ercole" ("un dels sobrenoms d'Hèrcules").
Segons el "Diccionari de la mitologia grega i romana" de William Smith, Macistus (Μάκιστος) era "un cognom d'Heracles, que tenia un temple als voltants de la ciutat de Macistus a Trifília" . Makistos va ser també el tercer fill d'Athamas i Nephele, segons la mitologia grega.
En el projecte original de la pel·lícula de 1914 Cabiria del director Giovanni Pastrone, el nom del forçut heroi havia estat Ercole. En el guió revisat, l'escriptor Gabriele d'Annunzio va donar al personatge el nom Maciste, que va comprendre un sinònim erudit d'Hèrcules.
Escriptors posteriors que van utilitzar el personatge, generalment, no han considerat l'etimologia original, i van construir una etimologia popular basada en la semblança superficial del nom amb la paraula italiana "macigno" "pedra gran"; en les primeres pel·lícules dels anys seixanta, Maciste li diu a un altre personatge de la pel·lícula que el seu nom significa "nascut de la roca", i en una pel·lícula posterior, Maciste es mostra en una escena que apareix des d'una paret de roca sòlida en una cova, de forma màgica
Cabiria
Maciste va debutar el 1914 a la pel·lícula muda italiana clàssica Cabiria. Cabiria va ser una història sobre un esclau anomenat Maciste (interpretat per Bartolomeo Pagano) que va participar en el rescat d'una princesa romana anomenada Cabiria (interpretada per Lidia Quaranta) d'un malvat monarca cartaginès que tramava sacrificar-la al cruel déu Moloch. La pel·lícula era una llunyana referència a "Salammbo", una novel·la històrica de Gustave Flaubert, amb una trama i guió de Gabriele D'Annunzio.
El debut de Maciste va marcar el to de les seves posteriors aventures. Incloent-hi la mateixa Cabiria, hi ha hagut almenys 52 pel·lícules amb Maciste, 27 de les quals són pel·lícules mudes pre-1927 protagonitzades per Bartolomeo Pagano i les altres 25 són una sèrie de pel·lícules sonores / color produïdes a principis dels anys seixanta. Les trames típiques impliquen governants tirans que practiquen vils rituals màgics o culte al déu del mal. Normalment, la jove dama, enamorada, corre al costat del malvat governant. Maciste, que posseeix força sobrehumana, ha de rescatar-la. Sovint hi ha un rei legítim que vol enderrocar el malvat usurpador, així com una escena de dansa del ventre i també una reina malvada que té desitjos carnals sobre l'heroi. Aquestes pel·lícules es van establir en geografies com Mongòlia, Perú, Egipte i l'Imperi Romà.
Filmografia
Cabiria (1914) de Giovanni Pastrone
Maciste (1914)
Maciste alpino (1916) di Giovanni Pastrone
Maciste atleta (1918) di Giovanni Pastrone
Maciste e il nipote d'America (1923)
Maciste imperatore (1924)
Maciste all'inferno (1925)
Maciste contro lo sceicco (1925)
Maciste nella gabbia dei leoni (1926)
Maciste nella Valle dei Re (1960) de Carlo Campogalliani
Maciste nella terra dei ciclopi (1961) d'Antonio Leonviola
Totò contro Maciste (1961) de Fernando Cerchio
Maciste contro lo sceicco (1961) de Domenico Paolella
Maciste contro Ercole nella valle dei guai (1961) de Mario Mattoli
Maciste l'uomo piu' forte del mondo (1961) d'Antonio Leonviola
Il trionfo di Maciste (1961) de Tanio Boccia
Maciste contro il vampiro (1961) de Sergio Corbucci
Maciste contro i mostri (1962) de Guido Malatesta
Zorro contro Maciste (1963) de Umberto Lenzi
Maciste l'eroe piu' grande del mondo (1963) de Michele Lupo
Maciste alla corte dello Zar (1964) de Tanio Boccia
Ercole, Sansone, Maciste e Ursus gli invincibili (1964) de Giorgio Capitani
Maciste contro i mongoli (1964) de Domenico Paolella
Maciste nelle miniere di re Salomone (1964) de Piero Regnoli
Maciste nell'inferno di Gengis Khan (1964) de Domenico Paolella
Maciste e la regina di Samar (1964) de Giacomo Gentilomo
Maciste gladiatore di Sparta (1965) de Mario Caiano
Referències
Personatges de cinema
Personatges de la mitologia grega | {
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from unittest import TestCase
from gitsync.config import Config
__author__ = 'wenqiushi'
class TestConfig(TestCase):
def test_config_immutability(self):
config = Config()
expected = config.view_path_mapping()
expected["new_key"] = "new_value"
self.assertTrue("new_key" in expected)
self.assertFalse("new_key" in config.view_path_mapping())
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,631 |
Aurora police arrest man during peaceful protest
Steve Zalusky
Updated 7/3/2020 11:51 PM
A man was arrested during a peaceful protest Friday evening after he ignored a number of requests to stop blocking the street, Aurora police said Friday night.
Jose Garcia, 30, was charged with obstructing an officer and improper walking on the roadway.
Police said that just before 7:45 p.m., about 20 people began marching from a protest at downtown Aurora's Millennium Plaza eastward on East Galena Boulevard.
Police said the protesters were blocking traffic and that drivers were attempting to drive around the group and turn against traffic, creating unsafe conditions. A police sergeant ordered the crowd to disperse and told the protesters that they could march on sidewalks, police said.
According to police, all but Garcia obeyed the order. He refused additional orders to leave the street and shouted expletives at officers before he was arrested, police said.
"It is the policy of the Aurora Police Department to support and promote the exercise of individual rights, to fulfill its responsibility to uphold the law, to provide for the safety of public assembly participants as well as members of the public," police said in a statement Friday night. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,881 |
Q: $_POST is empty even though I can see the $_POST data in firebug post, html, and response tabs So I'm grabbing the state of a jquery date picker and a dropdown select menu and trying to send those two variables to another php file using AJAX.
var_dump($_POST);
results in this on the webpage:
array(0) {
}
BUT, when I look at the Net panel in Firebug, I can see the POST and GET urls and it shows the Post, Response, and HTML all showing the variables that I sent to the PHP file, but when dumping, it shows nothing on the page.
I've been looking through other similar issues on SO that has led me to changing the php.ini file to increase the post size and to updating my ajax call to use json objects and then parse through it on the php side.
Currently I'm just trying to get passing a string to work, and my code looks like this:
AJAX:
$("#submit_button").click(function() {
// get date if selected
var selected_date = $("#datepicker").datepicker("getDate");
// get show id if selected
var selected_dj = $("#show-list").val();
// put the variables into a json object
var json = {demo : 'this is just a simple json object'};
// convert to json
var post_data = JSON.stringify(json);
// now put in variable for posting
var post_array = {json : post_data};
$.ajax({
type: "POST",
url: template_dir + "/get-show-logs.php",
data: post_array,
success: function(){
alert("Query Submitted");
},
error: function(xhr, ajaxOptions, thrownError){
alert(xhr.status);
alert(thrownError);
}
});
// clear div to make room for new query
$("#archived-posts-container").empty();
// now load with data
$("#archived-posts-container").load(template_dir + "/get-show-logs.php #get_logs");
});
Now this is the php that's running from the .load() call, and where I'm trying to access the $_POST variables:
get-show-logs.PHP:
<div id="get_logs">
<?php
if(isset($_POST["json"])){
$json = stripslashes($_POST["json"]);
$output = json_decode($json);
echo "im here";
var_dump($output);
// Now you can access your php object like so
// $output[0]->variable-name
}
var_dump(getRealPOST());
function getRealPOST() {
$pairs = explode("&", file_get_contents("php://input"));
$vars = array();
foreach ($pairs as $pair) {
$nv = explode("=", $pair);
$name = urldecode($nv[0]);
$value = urldecode($nv[1]);
$vars[$name] = $value;
}
return $vars;
}
?>
</div>
You can see that I'm trying just accessing the $_POST variable, and the isset check isn't passing, (the page isn't echoing "im here"), and then I'm also trying parsing through the input myself, and that is also empty.
the output on the page looks like this:
array(1){[""]=>string(0)""}
BUT, once again, the Firebug Net panel shows the following under the Response tab:
<div id="get_logs">
im hereobject(stdClass)#1 (1) {
["demo"]=>
string(33) "this is just a simple json object"
}
array(1) {
["json"]=>
string(44) "{"demo":"this is just a simple json object"}"
}
</div>
I'm not sure what could be causing the issue, the Firebug can see it, but the php file sees an empty array.
Now I'm very new at using ajax and $_POST and such, so if you read anything that you're not 100% sure about, don't assume that I know anything about it! Speak up! haha.
Also, I'm doing this with MAMP on Localhost, so I'm not sure if that leads to any issues.
Thanks for the help in advance!
A: You aren't using the response in your AJAX call currently. See this example which will output the returned response to the console.
$.ajax({
type: "POST",
url: template_dir + "/get-show-logs.php",
data: post_array,
success: function(response){
console.log(response);
},
error: function(xhr, ajaxOptions, thrownError){
alert(xhr.status);
alert(thrownError);
}
});
Success
Type: Function( Anything data, String textStatus, jqXHR jqXHR )
A function to be called if the request succeeds. The function gets passed three arguments: The data returned from the server, formatted according to the dataType parameter or the dataFilter callback function, if specified; a string describing the status; and the jqXHR (in jQuery 1.4.x, XMLHttpRequest) object.
-http://api.jquery.com/jquery.ajax/
Also this might be a good page to read more about jQuery and AJAX, https://learn.jquery.com/ajax/jquery-ajax-methods/.
| {
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} | 9,954 |
{"url":"https:\/\/questions.examside.com\/past-years\/jee\/jee-main\/mathematics\/trigonometric-functions-and-equations","text":"JEE Main\nMathematics\nTrigonometric Functions & Equations\nPrevious Years Questions\n\nIf $$\\tan 15^\\circ + {1 \\over {\\tan 75^\\circ }} + {1 \\over {\\tan 105^\\circ }} + \\tan 195^\\circ = 2a$$, then the value of $$\\left( {a + {1 \\over a}} ... The set of all values of$$\\lambda$$for which the equation$${\\cos ^2}2x - 2{\\sin ^4}x - 2{\\cos ^2}x = \\lambda $$has a real solution$$x$$, is... Let$$f(\\theta ) = 3\\left( {{{\\sin }^4}\\left( {{{3\\pi } \\over 2} - \\theta } \\right) + {{\\sin }^4}(3\\pi + \\theta )} \\right) - 2(1 - {\\sin ^2}2\\theta )...\nThe number of elements in the set $$S=\\left\\{x \\in \\mathbb{R}: 2 \\cos \\left(\\frac{x^{2}+x}{6}\\right)=4^{x}+4^{-x}\\right\\}$$ is :\nLet $$S=\\left\\{\\theta \\in\\left(0, \\frac{\\pi}{2}\\right): \\sum\\limits_{m=1}^{9} \\sec \\left(\\theta+(m-1) \\frac{\\pi}{6}\\right) \\sec \\left(\\theta+\\frac{m \\... Let$$S=\\left\\{\\theta \\in[0,2 \\pi]: 8^{2 \\sin ^{2} \\theta}+8^{2 \\cos ^{2} \\theta}=16\\right\\} .$$Then$$n(s) + \\sum\\limits_{\\theta \\in S}^{} {\\left( ...\n$$2 \\sin \\left(\\frac{\\pi}{22}\\right) \\sin \\left(\\frac{3 \\pi}{22}\\right) \\sin \\left(\\frac{5 \\pi}{22}\\right) \\sin \\left(\\frac{7 \\pi}{22}\\right) \\sin \\le... The number of solutions of$$|\\cos x|=\\sin x$$, such that$$-4 \\pi \\leq x \\leq 4 \\pi$$is : If cot$$\\alpha$$= 1 and sec$$\\beta$$=$$ - {5 \\over 3}$$, where$$\\pi ...\nLet for some real numbers $$\\alpha$$ and $$\\beta$$, $$a = \\alpha - i\\beta$$. If the system of equations $$4ix + (1 + i)y = 0$$ and $$8\\left( {\\cos {...$$\\alpha = \\sin 36^\\circ $$is a root of which of the following equation? The value of$$\\cos \\left( {{{2\\pi } \\over 7}} \\right) + \\cos \\left( {{{4\\pi } \\over 7}} \\right) + \\cos \\left( {{{6\\pi } \\over 7}} \\right)$$is equal ...$$16\\sin (20^\\circ )\\sin (40^\\circ )\\sin (80^\\circ )$$is equal to : The value of 2sin (12$$^\\circ$$)$$-$$sin (72$$^\\circ$$) is : The number of solutions of the equation$$\\cos \\left( {x + {\\pi \\over 3}} \\right)\\cos \\left( {{\\pi \\over 3} - x} \\right) = {1 \\over 4}{\\cos ^2}2x$$,... Let$$S = \\left\\{ {\\theta \\in [ - \\pi ,\\pi ] - \\left\\{ { \\pm \\,\\,{\\pi \\over 2}} \\right\\}:\\sin \\theta \\tan \\theta + \\tan \\theta = \\sin 2\\theta } \\r...\nIf n is the number of solutions of the equation $$2\\cos x\\left( {4\\sin \\left( {{\\pi \\over 4} + x} \\right)\\sin \\left( {{\\pi \\over 4} - x} \\right) - 1... The number of solutions of the equation$${32^{{{\\tan }^2}x}} + {32^{{{\\sec }^2}x}} = 81,\\,0 \\le x \\le {\\pi \\over 4}$$is : The distance of the point (1,$$-$$2, 3) from the plane x$$-$$y + z = 5 measured parallel to a line, whose direction ratios are 2, 3,$$-$$6 is : The value of$$2\\sin \\left( {{\\pi \\over 8}} \\right)\\sin \\left( {{{2\\pi } \\over 8}} \\right)\\sin \\left( {{{3\\pi } \\over 8}} \\right)\\sin \\left( {{{5\\pi ...\nThe sum of solutions of the equation $${{\\cos x} \\over {1 + \\sin x}} = \\left| {\\tan 2x} \\right|$$, $$x \\in \\left( { - {\\pi \\over 2},{\\pi \\over 2}} \\... If$$\\tan \\left( {{\\pi \\over 9}} \\right),x,\\tan \\left( {{{7\\pi } \\over {18}}} \\right)$$are in arithmetic progression and$$\\tan \\left( {{\\pi \\over ...\nIf $$\\sin \\theta + \\cos \\theta = {1 \\over 2}$$, then 16(sin(2$$\\theta$$) + cos(4$$\\theta$$) + sin(6$$\\theta$$)) is equal to :\nThe value of $$\\cot {\\pi \\over {24}}$$ is :\nThe sum of all values of x in [0, 2$$\\pi$$], for which sin x + sin 2x + sin 3x + sin 4x = 0, is equal to :\nIf 15sin4$$\\alpha$$ + 10cos4$$\\alpha$$ = 6, for some $$\\alpha$$$$\\in$$R, then the value of 27sec6$$\\alpha$$ + 8cosec6$$\\alpha$$ is equal to :...\nThe number of solutions of the equation x + 2tanx = $${\\pi \\over 2}$$ in the interval [0, 2$$\\pi$$] is :\nThe number of roots of the equation, (81)sin2x + (81)cos2x = 30 in the interval [ 0, $$\\pi$$ ] is equal to :...\nIf for x $$\\in$$ $$\\left( {0,{\\pi \\over 2}} \\right)$$, log10sinx + log10cosx = $$-$$1 and log10(sinx + cosx) = $${1 \\over 2}$$(log10 n $$-$$ 1), n &g...\nIf 0 < x, y < $$\\pi$$ and cosx + cosy $$-$$ cos(x + y) = $${3 \\over 2}$$, then sinx + cosy is equal to :\nAll possible values of $$\\theta$$ $$\\in$$ [0, 2$$\\pi$$] for which sin 2$$\\theta$$ + tan 2$$\\theta$$ > 0 lie in :\nIf $${e^{\\left( {{{\\cos }^2}x + {{\\cos }^4}x + {{\\cos }^6}x + ...\\infty } \\right){{\\log }_e}2}}$$ satisfies the equation t2 - 9t + 8 = 0, then the val...\nIf L = sin2$$\\left( {{\\pi \\over {16}}} \\right)$$ - sin2$$\\left( {{\\pi \\over {8}}} \\right)$$ and M = cos2$$\\left( {{\\pi \\over {16}}} \\right)$$ - sin...\nIf the equation cos4 $$\\theta$$ + sin4 $$\\theta$$ + $$\\lambda$$ = 0 has real solutions for $$\\theta$$, then $$\\lambda$$ lies in the interval :...\nIf $$x = \\sum\\limits_{n = 0}^\\infty {{{\\left( { - 1} \\right)}^n}{{\\tan }^{2n}}\\theta }$$ and $$y = \\sum\\limits_{n = 0}^\\infty {{{\\cos }^{2n}}\\thet... The value of$${\\cos ^3}\\left( {{\\pi \\over 8}} \\right){\\cos}\\left( {{3\\pi \\over 8}} \\right)$$+$${\\sin ^3}\\left( {{\\pi \\over 8}} \\right){\\si...\nIf [x] denotes the greatest integer $$\\le$$ x, then the system of linear equations [sin $$\\theta$$]x + [\u2013cos$$\\theta$$]y = 0, [cot$$\\theta$$]x + ...\nLet S be the set of all $$\\alpha$$ $$\\in$$ R such that the equation, cos2x + $$\\alpha$$sinx = 2$$\\alpha$$\u2013 7 has a solution. Then S is equal to :\nThe number of solutions of the equation 1 + sin4 x = cos23x, $$x \\in \\left[ { - {{5\\pi } \\over 2},{{5\\pi } \\over 2}} \\right]$$ is :...\nThe equation y = sinx sin (x + 2) \u2013 sin2 (x + 1) represents a straight line lying in :\nThe value of sin 10\u00ba sin30\u00ba sin50\u00ba sin70\u00ba is :-\nLet S = {$$\\theta$$ $$\\in$$ [\u20132$$\\pi$$, 2$$\\pi$$] : 2cos2$$\\theta$$ + 3sin$$\\theta$$ = 0}. Then the sum of the elements of S is\nThe value of cos210\u00b0 \u2013 cos10\u00b0cos50\u00b0 + cos250\u00b0 is\nIf cos($$\\alpha$$ + $$\\beta$$) = 3\/5 ,sin ( $$\\alpha$$ - $$\\beta$$) = 5\/13 and 0 < $$\\alpha , \\beta$$ < $$\\pi \\over 4$$, then tan(2$$\\alpha ... The maximum value of 3cos$$\\theta $$+ 5sin$$\\left( {\\theta - {\\pi \\over 6}} \\right)$$for any real value of$$\\theta $$is : The value of$$\\cos {\\pi \\over {{2^2}}}.\\cos {\\pi \\over {{2^3}}}\\,.....\\cos {\\pi \\over {{2^{10}}}}.\\sin {\\pi \\over {{2^{10}}}}$$is - The sum of all values of$$\\theta \\in \\left( {0,{\\pi \\over 2}} \\right)$$satisfying sin2 2$$\\theta $$+ cos4 2$$\\theta $$=$${3 \\over 4}$$... If 0$$ \\le $$x <$${\\pi \\over 2}$$, then the number of values of x for which sin x$$-$$sin 2x + sin 3x = 0, is : For any$$\\theta \\in \\left( {{\\pi \\over 4},{\\pi \\over 2}} \\right)$$, the expression$$3{(\\cos \\theta - \\sin \\theta )^4} + 6{(\\sin \\theta + ...\nIf sum of all the solutions of the equation $$8\\cos x.\\left( {\\cos \\left( {{\\pi \\over 6} + x} \\right).\\cos \\left( {{\\pi \\over 6} - x} \\right) - {1 \\... PQR is a triangular park with PQ = PR = 200 m. A T.V. tower stands at the mid-point of QR. If the angles of elevation of the top of the tower at P, Q ... The number of solutions of sin3x = cos 2x, in the interval$$\\left( {{\\pi \\over 2},\\pi } \\right)$$is : Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that AP = 2AB. If$$\\angl...\nIf $$5\\left( {{{\\tan }^2}x - {{\\cos }^2}x} \\right) = 2\\cos 2x + 9$$, then the value of $$\\cos 4x$$ is\nLet f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :\nThe number of x $$\\in$$ [0, \u00a0 2$$\\pi$$ ] for which $$\\left| {\\sqrt {2{{\\sin }^4}x + 18{{\\cos }^2}x} - \\sqrt {2{{\\cos }^4}x + 18{{\\sin }^2}x... If m and M are the minimum and the maximum values of 4 +$${1 \\over 2}$$sin2 2x$$-$$2cos4 x, x$$ \\in $$R, then M$$-$$m is equal to :... If$$0 \\le x < 2\\pi $$, then the number of real values of$$x$$, which satisfy the equation$$\\,\\cos x + \\cos 2x + \\cos 3x + \\cos 4x = 0$$is: Let$$fk\\left( x \\right) = {1 \\over k}\\left( {{{\\sin }^k}x + {{\\cos }^k}x} \\right)$$where$$x \\in R$$and$$k \\ge \\,.$$Then$${f_4}\\left( x \\right) ...\nThe expression $${{\\tan {\\rm A}} \\over {1 - \\cot {\\rm A}}} + {{\\cot {\\rm A}} \\over {1 - \\tan {\\rm A}}}$$ can be written as:\n$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \\bot CD.$$ If $$\\angle ADB = \\theta ,\\,BC = p$$ and $$CD = q,$$ then AB is e...\nIn a $$\\Delta PQR,{\\mkern 1mu} {\\mkern 1mu} {\\mkern 1mu}$$ If $$3{\\mkern 1mu} \\sin {\\mkern 1mu} P + 4{\\mkern 1mu} \\cos {\\mkern 1mu} Q = 6$$ and $$4... If$$A = {\\sin ^2}x + {\\cos ^4}x,$$then for all real$$x$$: Let$$\\cos \\left( {\\alpha + \\beta } \\right) = {4 \\over 5}$$and$$\\sin \\,\\,\\,\\left( {\\alpha - \\beta } \\right) = {5 \\over {13}},$$where$$0 \\le \\alp...\nLet A and B denote the statements A: $$\\cos \\alpha + \\cos \\beta + \\cos \\gamma = 0$$ B: $$\\sin \\alpha + \\sin \\beta + \\sin \\gamma = 0$$ If $$\\cos... If$$0 < x < \\pi $$and$$\\cos x + \\sin x = {1 \\over 2},$$then$$\\tan x$$is The number of values of$$x$$in the interval$$\\left[ {0,3\\pi } \\right]\\,$$satisfying the equation$$2{\\sin ^2}x + 5\\sin x - 3 = 0$$is Let$$\\alpha ,\\,\\beta $$be such that$$\\pi < \\alpha - \\beta < 3\\pi $$. If$$sin{\\mkern 1mu} \\alpha + \\sin \\beta = - {{21} \\over {65}}$$a... If$$u = \\sqrt {{a^2}{{\\cos }^2}\\theta + {b^2}{{\\sin }^2}\\theta } + \\sqrt {{a^2}{{\\sin }^2}\\theta + {b^2}{{\\cos }^2}\\theta } $$then the differen... A line makes the same angle$$\\theta $$, with each of the$$x$$and$$z$$axis. If the angle$$\\beta \\,$$, which it makes with y-axis, is such that... The period of$${\\sin ^2}\\theta $$is The number of solution of$$\\tan \\,x + \\sec \\,x = 2\\cos \\,x$$in$$\\left[ {0,\\,2\\,\\pi } \\right]$$is Which one is not periodic ## Numerical If m and n respectively are the numbers of positive and negative values of$$\\theta$$in the interval$$[-\\pi,\\pi]$$that satisfy the equation$$\\cos ...\nLet $$\\mathrm{S = \\{ \\theta \\in [0,2\\pi ):\\tan (\\pi \\cos \\theta ) + \\tan (\\pi \\sin \\theta ) = 0\\}}$$. Then $$\\sum\\limits_{\\theta \\in S} {{{\\sin }^2}... Let$$S=\\left\\{\\theta \\in(0,2 \\pi): 7 \\cos ^{2} \\theta-3 \\sin ^{2} \\theta-2 \\cos ^{2} 2 \\theta=2\\right\\}$$. Then, the sum of roots of all the equation... Let$$S=\\left[-\\pi, \\frac{\\pi}{2}\\right)-\\left\\{-\\frac{\\pi}{2},-\\frac{\\pi}{4},-\\frac{3 \\pi}{4}, \\frac{\\pi}{4}\\right\\}$$. Then the number of elements i... If the sum of solutions of the system of equations$$2 \\sin ^{2} \\theta-\\cos 2 \\theta=0$$and$$2 \\cos ^{2} \\theta+3 \\sin \\theta=0$$in the interval ... Let$${S_1} = \\{ x \\in [0,12\\pi ]:{\\sin ^5}x + {\\cos ^5}x = 1\\} $$and$${S_2} = \\{ x \\in [0,8\\pi ]:{\\sin ^7}x + {\\cos ^7}x = 1\\} $$Then$$n({S_1}) -...\nThe number of solutions of the equation $$\\sin x = {\\cos ^2}x$$ in the interval (0, 10) is _________.\nThe number of elements in the set $$S = \\{ \\theta \\in [ - 4\\pi ,4\\pi ]:3{\\cos ^2}2\\theta + 6\\cos 2\\theta - 10{\\cos ^2}\\theta + 5 = 0\\}$$ is _____...\nThe number of solutions of the equation $$2\\theta - {\\cos ^2}\\theta + \\sqrt 2 = 0$$ in R is equal to ___________.\nIf $${\\sin ^2}(10^\\circ )\\sin (20^\\circ )\\sin (40^\\circ )\\sin (50^\\circ )\\sin (70^\\circ ) = \\alpha - {1 \\over {16}}\\sin (10^\\circ )$$, then $$16 + {\\... The number of values of x in the interval$$\\left( {{\\pi \\over 4},{{7\\pi } \\over 4}} \\right)$$for which$$14\\cos e{c^2}x - 2{\\sin ^2}x = 21 - 4{\\cos...\nLet S be the sum of all solutions (in radians) of the equation $${\\sin ^4}\\theta + {\\cos ^4}\\theta - \\sin \\theta \\cos \\theta = 0$$ in [0, 4$$\\pi$$]...\nThe probability distribution of random variable X is given by : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-sty...\nLet z1 and z2 be two complex numbers such that $$\\arg ({z_1} - {z_2}) = {\\pi \\over 4}$$ and z1, z2 satisfy the equation | z $$-$$ 3 | = Re(z). Then t...\nLet S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A $$\\subseteq$$ S : A $$\\ne$$ $$\\phi$$ and the sum of all the elements of...\nThe number of solutions of the equation $$|\\cot x| = \\cot x + {1 \\over {\\sin x}}$$ in the interval [ 0, 2$$\\pi$$ ] is\nIf $$\\sqrt 3 ({\\cos ^2}x) = (\\sqrt 3 - 1)\\cos x + 1$$, the number of solutions of the given equation when $$x \\in \\left[ {0,{\\pi \\over 2}} \\right]$$...\nThe number of integral values of 'k' for which the equation $$3\\sin x + 4\\cos x = k + 1$$ has a solution, k$$\\in$$R is ___________.\nIf $${{\\sqrt 2 \\sin \\alpha } \\over {\\sqrt {1 + \\cos 2\\alpha } }} = {1 \\over 7}$$ and \\sqrt {{{1 - \\cos 2\\beta } \\over 2}} = {1 \\over {\\sqrt {10} }}...\nEXAM MAP\nJoint Entrance Examination","date":"2023-03-20 21:42:55","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\": 0.9999915361404419, \"perplexity\": 2997.9657893155195}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296943562.70\/warc\/CC-MAIN-20230320211022-20230321001022-00558.warc.gz\"}"} | null | null |
How To Be Sick
More About How To Live Well
How To Wake Up
Psychology Today Blog
More Praise for How To Wake Up
"In a fresh and articulate voice, truly grounded in authenticity, Toni Bernhard interprets ancient wisdom for our modern times."—Sylvia Boorstein, author of It's Easier Than You Think
"A beautiful, wise, and practical book presenting the Buddha's teaching for our contemporary world."
—Gil Fronsdal, author of The Dhammapada: A New Translation of the Buddhist Classic
"Toni Bernhard brings new depths of understanding and new possibilities of freedom in this wonderfully clear guide to engaging all the joys and sorrows of our experience with awareness, grace, and wisdom." —Joseph Goldstein, author of A Heart Full of Peace
"In How to Wake Up, Toni Bernhard invites us into the conversation of Buddhism. I can't think of a better way to begin the journey. As always, Bernhard's writing is lucid, direct, elegant and absolutely authentic. This is a book for all of us." —Alida Brill, author of Dancing at the River's Edge
"Do you want to live differently? From the author of How to Be Sick comes a book on how to be well. A careful, lucid and loving interpretation of the medicine first given by Buddha, the great physician, as a universal antidote for our ills: waking up. Follow these simple directions and bring yourself back to life." —Karen Maezen Miller, author of Hand Wash Cold
"Casually open this book to any page, and there are teachings and practices always right there. Read it through, and emerge with a whole set of teachings leading to awakening. Like her last book, How to Wake Up is highly personal, very readable, and filled with wisdom."—Mary Grace Orr, teacher, Spirit Rock Meditation Center and Founding teacher of Insight Santa Cruz
"Separateness, isolation, and competition have guided western civilization to a precipice. But beyond the thinnest of veils lies another reality, in which we are infinite, united, and one. This realm is our birthright; it does not have to be invented or manufactured, only realized. This luminous book shows how." —Larry Dossey, M.D., author of One Mind
"Toni Bernhard brings an elegant simplicity to a deep and nuanced exploration of this very human project of waking up right now, in this very moment. Highly recommended for those new to the path as well as those who are already deeply immersed." —Mu Soeng, author of The Heart of the Universe
"Toni writes with clarity and insight that makes ancient Buddhist teachings accessible to our modern lives. I am honored to recommend this book to anyone looking to live a deeper and more engaging life."
–Danea Horn, author of Chronic Resilience: 10 Sanity-Saving Strategies for Women Coping with the Stress of Illness
"No one ever said life would be easy, but Toni Bernhard finds a path through the difficulties and points the way to freedom, thereby enabling each of us to embrace our circumstances rather than be swallowed up by them. This is a vital guide for every journey to finding our true home." —Ed and Deb Shapiro, authors of Be the Change
"Toni Bernhard offers all-purpose advice as good as your grandmother gave you, and just as straightforward and heartfelt." —Barry Boyce, editor-in-chief of Mindful magazine and mindful.org
"In the times of confusion, sorrow, and pain that are part of every human life, we long for a map to show us the way to a greater peace, compassion and freedom. In How To Wake Up, Toni Bernhard offers just such a map; clear, concise and accessible to anyone wishing to cultivate a path of greater awareness and understanding."—Christina Feldman, author of Compassion: Listening to the Cries of the World
"Bernhard advises us to not wallow, but to wake up and embrace our life no matter the circumstance. She shows us how to gain peace of mind in a time of storm; how to be content in times of calamity. A must-read for all."—Melody T. McCloud, M.D., author of First Do No Harm...In Your Relationships.
"To the lay reader, the foreign sounding names and practices of Buddhism might at first seem to be esoteric and unreachable. In How to Wake Up, Toni Bernhard takes loving hold of them, one by one, and places them gently in the reader's lap. This book is accessible, useful, and filled with her personal insight and wisdom gained from her own challenging experiences with illness and sorrow. It has been a path that has led her to a place of contentment, a place to which she now leads her readers." —Joy H. Selak, author of You Don't Look Sick! Living Well with Invisible Chronic Illness
"In How to Wake Up, Toni Bernhard deftly presents deep, profound teachings in an amazingly simple, accessible way. It's like taking a powerful healing medicine that goes down like a delicious milkshake. Bravo!" —James Baraz, author of Awakening Joy
"In How To Wake Up, Toni Bernhard guides us to fully engage our lives as they are, rather than how we wish they could be. Like a wise, compassionate friend who is as imperfect as we are, Toni shares lessons learned from her own difficult experiences and Buddhist sources in a way that is accessible, supportive, and encouraging. How to Wake up is guide that will help us with everyday frustrations and disappointments as well as with the pain of sickness, old age, death, and separation. This is a book for everyone, and everyone should read this book." —Lizabeth Roemer, co-author of The Mindful Way Through Anxiety
"Toni Bernhard's beautiful book is a new invitation to investigate the Buddha's teachings in the laboratories of our own lives. How to Wake Up will be greatly appreciated by readers new to the Buddhist path, as well as by seasoned practitioners." —Sharon Salzberg, author of Real Happiness
Toni Bernhard has a stunning talent for telling stories and offering insights. How to Wake Up gives us tools for navigating our way through the joys and challenges of an ordinary human life. I am deeply grateful for this book. It sits at my bedside where I can reach out for it again and again, offering me soul food and practical guidance for the journey. —Oriah Mountain Dreamer, author of The Invitation
This wonderful book is written from the heart and out of the depths of the author's own practice. Toni Bernhard has away of articulating the Buddha's profound understanding of the nature of the human condition in such a way that truly brings it into the contemporary world and makes it relevant for everyone. This could only be achieved by someone who is both rooted in a theoretical knowledge of the teachings and who has actually grappled with life's dilemmas and put the teachings into practice. —Dr. John Peacock, University of Oxford Mindfulness Centre | {
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{"url":"https:\/\/brilliant.org\/problems\/inspired-by-problem-3-imo-1973\/","text":"# Inspired by problem 3, IMO 1973\n\nCalculus Level 5\n\n$\\large x^4+ a x^3 + x^2 + b x+1=0$Let $$A$$ be the set of points $$(a,b)$$ for which the above equation has no real root. Area of $$A$$ can be expressed as$\\frac{p\\sqrt{q}}{r}+ s \\ \\tanh ^{-1} \\left( \\sqrt{\\frac{t}{u}} \\right)$Find the value of $$p+q+r+s+t+u$$.\n\nDetails and Assumptions:\n\n\u2022 $$a$$, $$b$$ are real numbers.\n\u2022 $$p$$, $$q$$, $$r$$, $$s$$, $$t$$ and $$u$$ are positive integers, $$q$$ is square free and $$\\gcd(p, r)=\\gcd(t, u)=1$$.\n\u00d7","date":"2017-01-22 12:21:30","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\": 0.8200767040252686, \"perplexity\": 224.36694399672956}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-04\/segments\/1484560281424.85\/warc\/CC-MAIN-20170116095121-00181-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
I often receive interesting pictures taken by my friend during her voyages. Recently, I've received these painted doors, which charmed me. It crossed my mind to open my blog with them. I believe that somewhere, there is a small bridge between their so diverse stories and the unknown stories of the interiors towards they could open to.
But it would be nice to imagine the story behind these doors…from before…the story that would belong to this superb island too and to the people leaving in it. | {
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Q: Updating the time of a Date subject Is there a way in which I can update say the time of a Subject within my service?
I am thinking of abstracting the following function into a service:
date: Date;
setTime(hours: number, mins: number, secs: number): void {
this.date.setHours(hours);
this.date.setMinutes(mins);
this.date.setSeconds(secs);
}
service example
date: Subject<Date>;
constructor() {
this.date = new Subject();
}
setDate(hrs: number, mins: number, secs: number): Observable<Date> {
const tempDate = this.date;
// tempDate.set - Cannot do .setXXX here since it is a Subject and not a Date
this.date.next
}
stackblitz
A: You could just create a new date, that copies the date part of the current date, and uses time parameters. and then push the tempDate to the subject.
something like this:
setDate(hrs: number, mins: number, secs: number): Observable<Date> {
let tempDate = this.date.getValue(); //gets the value of the subject, not the actual subject
tempDate.setHours(hours);
tempDate.setMinutes(mins);
tempDate.setSeconds(secs);
this.date.next(tempDate);
}
| {
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{"url":"https:\/\/www.scijournal.org\/articles\/absolute-value-symbol-in-latex","text":"How to create an absolute value symbol in LaTeX?\n\n# How to create an absolute value symbol in LaTeX?\n\nThis post may contain affiliate links that allow us to earn a commission at no expense to you. Learn more\n\nThis article aims to show you a simple way to create an absolute value symbol in LaTeX.\n\nBy definition, the absolute value or modulus is the non-negative value of x without regard to its sign. But if you need to insert it in your LaTeX documents, today you will learn how to do it.\n\n## Absolute Value Symbol\n\nThe most common way to represent the absolute value symbol is using two vertical lines on each side of the expression. For example\n\nThere are many commands of ways to insert the absolute value, but in this article, we will focus on the most common ways to write the symbol.\n\n## Absolute Value \\mid\n\nThe first option is using the command \\mid, it generates a vertical line where you type it, therefore you will need two \\mid commands for the absolute value, it requires math mode enabled. For example\n\n\\begin{document}\n\nAbsolute using $\\backslash$mid $\\mid x+y \\mid$\n\n\\end{document}\n\nThe \\mid command has bigger blank spaces on the argument of the absolute value, this is my go-to option to write inline equations.\n\n## Absolute Value Lines\n\nThe second option is using the key \u201c|\u201d, your keyboard has it but you can also write it by typing alt + 124. It goes to each side of the argument of the absolute value, and it requires the math mode. As you can see absolute value symbol is not an actual command but rather just a key.\n\nFor example,\n\n\\begin{document}\n\nAbsolute value using \u201c$|$\u201d $|x+z|$\n\n\\end{document}\n\n## Absolute Value Vertical Commands\n\nYou can also use two commands to create the vertical lines on each side, for the left side you use the command \\lvert, and for the right side \\rvert, both commands require importing the amsmath package. For example\n\n\\documentclass{article}\n\n\\usepackage{amsmath}\n\n\\begin{document}\n\nAbsolute value using $\\backslash$lvert and $\\backslash$rvert\n\n$$\\lvert y + 3 \\rvert$$\n\n\\end{document}\n\n\\lvert stands for left vertical, and \\rvert for right vertical. As you can see these commands don\u2019t have a lot of blank space for the argument of the absolute value.\n\n## Resizable Value Symbol\n\nTo this point we have only used inline equation, but what about including integrals or summation, you can use all of the options above, for example\n\n\\documentclass{article}\n\n\\usepackage{amsmath}\n\n\\begin{document}\n\n$$|\\int x^2 dx|$$\n\n$$\\mid \\sum_{i=0}^{\\infty} \\dfrac{x_{i}}{x^2 + 4} \\mid$$\n\n$$\\lvert \\dfrac{x^3+x^2+x+6}{x-9} \\rvert$$\n\n\\end{document}\n\nAs you can see, the vertical bars on each side of the expressions do not have the same height as the argument. To solve this you have to use two commands \\left and \\right, just before inserting the vertical bars, let\u2019s recreate the example above but using these two new commands,\n\n\\documentclass{article}\n\n\\usepackage{amsmath}\n\n\\begin{document}\n\n$$\\left | \\int x^2 dx \\right |$$\n\n$$\\left \\lvert \\dfrac{x^3+x^2+x+6}{x-9} \\right \\rvert$$\n\n\\end{document}\n\nYou may be probably noticing that the \\mid command is missing, and that\u2019s because the \\left and \\right commands don\u2019t work with the \\mid command.\n\nNow you have it, all the knowledge you may need to correctly write the absolute value symbols in different ways in your LaTeX document, remember you can always look at the documentation of the packages (amsmath).\n\nI hope this tutorial was helpful in guiding you in LaTeX, and as always keep writing in LaTeX.","date":"2022-08-16 07:21:40","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\": 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\": 0.9424082636833191, \"perplexity\": 618.549489283981}, \"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-2022-33\/segments\/1659882572221.38\/warc\/CC-MAIN-20220816060335-20220816090335-00043.warc.gz\"}"} | null | null |
Ericsson R380 var den första smarttelefonen från Ericsson Mobile Communications och lanserades år 2000. Den använde GSM-nätet och baserades på operativsystemet Symbian. Den var Ericssons första mobiltelefon med en pekskärm. Den monokroma skärmen täcktes delvis av en lucka, där knappsatsen fanns. Med R380 kunde användare koppla upp sig mot internet med hjälp av tekniken WAP.
R380 | {
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Since before they could talk, they knew. The fearlessness of a pre-schooler's heart that knows no endings.
BY VANESSA ABLE
CORA IS SQUATTING on the living room floor surrounded by a storm of paper, tape, ribbon, pens and a card. She is preparing a birthday gift for her best friend Morgan, who is turning five. It is a Teen Titans costume she had me order more than a month ago.
'Mama, what shall I write in his card?' she asks me.
'How about, Happy Birthday?'
She pauses, then starts scrawling. When I walk past her and try to look over her shoulder, she hunches protectively over her work. When she's done, she hands me the card and instructs me not to read it.
I open it a tiny amount as I slip it into the envelope and I can see it doesn't say Happy Birthday at all. It says I love you so much.
Morgan and Cora were 18 months old when they first met at a toddler's gym. It was not an age of great communication between peers, but after some weeks, Morgan's nanny told to me that he had been singing songs about Cora at home. He had noticed her, and he liked her. She liked him too, and I took her frenzied repetition of his name after we left the gym as an expression of her desire to see him again. We started hanging back in the park after class and soon they broke the firewall of parallel play by sharing blueberries and cheese chunks.
Gym graduated to art class, soccer class and then they started at the same preschool. Cora was enrolled full-time and Morgan came every other day. On the dark mornings of his absence, she faced her abandonment alone: when it was time for me to leave, she stuck on like a little crab, her fingers digging into my legs as she tried to climb me. But on Morgan Days, as they came to be known, she peeled right off. Leaving the house in the morning was a cinch: she stood still as I dressed her, ate her cereal with focus and even brushed her own teeth. Once at school, instead of holding on to me, she picked up her nerve and placed herself next to Morgan among a pile of wooden blocks or at the coloring table.
It was a while before I took their relationship seriously. I had become wise to the fact that in early childhood, everything changes. Food preferences, toilet habits, sleeping patterns, mood swings, favorite toys; fast flux was the new normal, and I was a keen student of this commendable lightness of being. Cora's affection for Morgan was the first thing that started to outlast every other phase. I began to sit up.
Who was this kid? What did she see in him? Was this actually a thing? The sweet little boy with blue eyes, freckles and long, curly hair suddenly took on a whole new and fascinating aspect. I started to eye him across the room: Stay on the right side of her, pal.
I realized very quickly that Morgan was a great kid, and their pairing worked. Ages two and three were a heady time; in the grip of emotional disarray, she was easily triggered. There were moments when my husband and I despaired: 'She'll be a difficult woman,' he prophesized grimly. I wanted to serve up her defense, but all I had were received truisms – she's, you know, spirited. Better a fighter than a victim?
It rang hollow because at times it was hard to be enthused by her random exactitudes and the associated shifting rage. Being locked in a debate with her over what constituted a healthy daily dose of sugar, the right temperature of soup or how many minutes to bedtime, meant doing battle with the harshest, most defiant of opponents.
In the light of this, her connection with Morgan made sense. Calm, measured, less prone to outbursts; he accommodated her in a way that other kids didn't. If she wanted something he had, he'd usually just give it to her. And when she could not bring herself to return the gesture, he seemed to understand. In the rocky world of emerging egos and proprietary battles, Morgan was an island of calm and acceptance for Cora. He didn't punish her for her outbursts; he ran with them, without tripping into the pit of being pushed around. I began to admire him. And his patience paid off as change endured and Cora emerged from the tunnel of her tempestuous threes into the less volatile territory of calmer fours.
This is love that is unselfconscious, that pops up like daisies springing from the lawn. It doesn't need to be taught or chaperoned because it hasn't yet learned how precarious self-conscious living and loving can actually be.
'We'd like to be able to foster their friendship,' their teacher told me from across a long desk during a parent-teacher meeting. 'It's great that they get on so well. But –'
'But?' I leant in. 'Do you think there's a problem?'
'Not a problem. But we are encouraging Cora to also be independent. We say, it's great to do things with your friend, but also wonderful to do them alone, no?'
'I suppose.' I was compelled to defend them. 'It seems so natural, though, don't you think? I mean, isn't it amazing how kids so young can be so in touch?'
The teacher smiled sadly and nodded the same way she did with the kids. 'Yes. I suppose it's a question of self-sufficiency—'
'Are you going to separate them?'
'No. Not yet. Now we just help them to also be with other children. And to make decisions on their own. It is more healthy like that, no?'
I decide to steel her. I tell Cora she and Morgan might not be in the same classroom next year. We are in the car stopped at a light and I am watching her face in the rearview. She whines and I continue to explain that they mix up the classes anyway, and that it's good to play with other kids too. It's all I want to say. Already I feel like a double agent, acting on behalf of an authority I disagree with. And besides, it's just one tough truth piled on another much more sinister secret that I can't bring myself to mention at all: Morgan's family is planning to move to New Zealand next year or the year after. Whichever way I turn, I can't get away from the fact that there is rupture on the horizon. Still, everything changes, I remind myself; Kindergarten is a whole other world. The beauty of how they live is that they have no real concept—and so, no fear—of endings.
I was watching them once at a birthday party in a large, crowded sports center. They were following a line walking next to one another and holding hands when Cora suddenly became anxious. Morgan was trying to appease her, but she was shaking her head and had tears in her eyes. At that moment, he stopped talking and he put his hand gently on her waist. They kept walking like this, his arm protectively around her as she leaned into him.
I can see the foundations of their emotional marrow being laid with every tender encounter. This is love that is unselfconscious, that pops up like daisies springing from the lawn. It doesn't need to be taught or chaperoned because it hasn't yet learned how precarious self-conscious living and loving can actually be.
Now when Cora gets to school, she leaves her bag in the cubby outside her classroom, sits down to yank off her shoes and put on her slippers, then heads inside. If she's feeling inclined, I'll get a kiss. Otherwise, she raises her hand in a gesture of dismissal and goes in search of Morgan. As soon as they spot one another, they lock into orbit and launch into urgent updates. They take each other in, check out each other's clothes, shoes, stuffies. They make faces at one another. Morgan tells Cora her dress is beautiful, she tells him that his t-shirt is cool then they head off into an activity together.
At the end of the day, I shuffle through the wood chips of the playground and start the unwelcome process of extraction. Hanging from the climbing frame, or engaged in a classified exchange – can they have just five more minutes? Some days I creep in so she doesn't see me; I practice pushing her out to sea for an imagined minute to see whether she'll float. I watch her and see that she's assured and confident; a self-contained player in a huddle of five-year-olds whispering conspiratorially or giving voice to some ebullient element within themselves. She loves, and can love, independent of me. There's relief in that.
'Who do you love?'
'I love you and Daddy of course. But I love Morgan more than both of you.'
I feign offence.
'You love Morgan more than your parents?'
'Of course. Morgan's my champion.'
'Your champion?' I ask, 'What does that mean?'
She shrugs. 'He told me,' she assures me. 'Morgan says, he's my champion. And I'm his champion too.'
They don't see me behind the tree as they round the edge of the playground together. They are animated, engaged and joyful. Cora is making some kind of joke, gesturing widely with her arms and pulling a face while Morgan laughs. Then they both sprint for a few seconds until she finally spots me and acts out a show of injustice and disappointment. She stomps over in my direction, while Morgan turns the other way and takes an interest in the sand pit. As we walk towards the gate, she stops and pulls my sleeve.
'There's something really important I have to go and tell Morgan.'
She bolts over to him, whispers something in his ear then puts her arms around him so tightly that he has trouble reciprocating. She goes to leave, then stops and turns one more time. This time she kisses him on the lips. He's not at all surprised. As she runs away from him and back to me, he returns to his digging.
Vanessa Able
Vanessa Able is the founder and editor of The Dewdrop.
Tagged Children, Courage, fearlessness, innocence, loss, love
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3 thoughts on "Champions"
Vesna Able says:
Champions is a true champion story. Interesting, detailed, almost romantic but happy at the same time, showing how early human beings begin to learn & feel love. So proud that those two girls are mine: Cora as the main heroine & Vanessa as her devoted mother who keeps a watchful eye on her adorable daughter!
Vanessa Able says:
Mum!! 🙂 xx
Deanna Adams says:
Smiles for miles;]]]]]]]]]]]]]]]]]]]]] My eyes are teary and my heart is happy. You've captured their love story beautifully. | {
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En histología, el plexo de Meissner, también llamado plexo submucoso, es una de las porciones el sistema nervioso entérico. El sistema nervioso entérico está constituido por un conjunto de neuronas y fibras nerviosas que se ubican en la pared del tubo digestivo y puede dividirse en dos componentes principales, el plexo de Auerbach o mientérico y el plexo de Meissner o submucoso.
Historia
Debe su nombre al médico alemán Georg Meissner que realizó diversos estudios sobre el mismo. El plexo de Meissner no debe confundirse con los corpúsculos de Meissner situados en la piel con los que no guarda ninguna relación.
Descripción
El plexo de Meissner se encuentra situado en la capa submucosa de la pared del tubo digestivo. Su desarrollo es más importante en el intestino delgado y el intestino grueso, en el esófago es casi inexistente y en el estómago escaso. Está formado por un grupo de neuronas interconectadas, incluyendo motoneuronas, interneuronas y neuronas sensitivas. Algunas de ellas inervan las células secretoras que están situadas en la mucosa del intestino, controlando el proceso de secreción.
Referencias
Aparato digestivo | {
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Marshall University Sports History Display at the Hall of Fame Cafe
The Marshall Hall of Fame Café is restaurant and museum dedicated to the sports history of Marshall University. It stands as a memorial to the players, coaches, and fans who died in the tragic plane crash on November 14, 1970. The Hall of Fame Café serves as a museum to all Marshall University sports teams spanning the athletic history of the university. The artifacts and memorabilia are kept well preserved here for the generations to come and for then people of Huntington, West Virginia to learn and admire.
this picture is of the room dedicated to the We are Marshall movie.
The outside of the cafe
The Marshall Hall of Fame Café opened in August 2001. It is a restaurant dedicated to showing the highlights and memories of Marshall University sports. To the right inside of the restaurant's entrance, is a display that contains different props from the movie We Are Marshall, which was released in 2006.
The front left side of the restaurant includes an original painted mural by the artist Tim Decker, and the restaurant as a whole depicts the history of different Marshall sports teams and icons through the university's history, spanning from 1837 to 2001. Some significant moments included within the mural are the Hightower pass from the football game against WVU, the 1947 Men's National Basketball Championship, and the first win for the 1971 Marshall University football team, a victory against Xavier, which was the university's first win following the loss of football players and community members in the 1970 plane crash.
Continuing through the restaurant, people will find glass cases that are filled with signed memorabilia from different Marshall players. There are pictures of Randy Moss, Chad Pennington, and Byron Leftwich, among other stars from the school's history. On the floor of the restaurant is the "Walk of Fame," which is made of tiles showing the names of all the Marshall All-Americans in various sports.
The Marshall Hall of Fame Café is a museum that honors all Marshall players and teams throughout the years. The back wall is lined with newspaper articles and photos dedicated to the Marshall 1970 plane crash victims. This is a really important part of the Marshall University and Huntington community because the plane crash is a strong memory in the hearts of all Marshall Alumni, students, and residents of Huntington.
The museum displays are free to the public.
Accessed November 14, 2016. www.mhofc.com.
The Integration of Marshall University Athletics
Marshall Hall of Fame Cafe Facebook
857 3rd Avenue
Huntington , West Virginia 25701
Restaurant/Museum Display: Sunday-Thursday 11am-10pm Saturday 11am-11pm
This entry has been edited 10 times.
Created by Jon Decker on June 20th 2014, 7:10:44 pm.
Last updated by Alexa Antill (Preservation Alliance of West Virginia) on November 14th 2016, 3:36:40 pm.
Marshall University Plane Crash Memorial Trail
Marshall University was forever changed on November 14, 1970 when Southern Airways Flight 932 crashed and killed all 75 people on board, including many members and fans of the Marshall Thundering Herd football team. This tour takes you to many of the memorials and monuments honoring the victims of the darkest chapter in Marshall's history.
Downtown Huntington Walking Tour
This tour of downtown Huntington begins at the statue of Colis P. Huntington and proceeds to some of the city's historic buildings, theaters, churches, monuments, and markers. The tour includes a number of "time capsule" entries that allow you to experience civil rights demonstrations, bootlegging, and buildings and monuments that have been lost to time. After a stop at the Convention and Visitor's Bureau, the tour continues to the Riverfront Park, an art gallery, and medical history museum. The tour concludes at the Marshall Hall of Fame Cafe, where you can enjoy exhibits related to the history of Marshall sports and well-earned refreshments.
Discover U.S. 60: The Midland Trail
Originating first as a buffalo trail adopted by Native Americans for east-west tavel, today the Midland Trail remains an important route of travel across West Virginia. | {
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**HarperCollins Publishers**
Westerhill Road
Bishopbriggs
Glasgow
G64 2QT
Great Britain
First Edition 2006
© HarperCollins Publishers 2006
EPUB Edition © July 2011 ISBN-13 978-0-00-744457-1
ISBN-10 0-00-723156-3
Collins® and Bank of English® are registered trademarks of HarperCollins Publishers Limited
www.collins.co.uk
A catalogue record for this book is available from the British Library
Typeset by Davidson Pre-Press, Glasgow
Printed in Italy by Rotolito Lombarda SpA
**Acknowledgements**
We would like to thank those authors and publishers who kindly gave permission for copyright material to be used in the Collins Word Web. We would also like to thank Times Newspapers Ltd for providing valuable data.
All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on screen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins.
Entered words that we have reason to believe constitute trademarks have been designated as such.However,neither the presence nor absence of such designation should be regarded as affecting the legal status of any trademark.
PUBLISHING DIRECTOR
Lorna Knight
EDITORIAL DIRECTOR
Michela Clari
MANAGING EDITOR
Maree Airlie
PROJECT CO-ORDINATOR
Gaëlle Amiot-Cadey
CONTRIBUTORS
José Martín Galera
Val McNulty
Julie Muleba
Victoria Romero Cerro
William Collins' dream of knowledge for all began with the publication of his first book in 1819. A self-educated mill worker, he not only enriched millions of lives, but also founded a flourishing publishing house. Today, staying true to this spirit, Collins books are packed with inspiration, innovation, and practical expertise. They place you at the centre of a world of possibility and give you exactly what you need to explore it.
Language is the key to this exploration, and at the heart of Collins Dictionaries is language as it is really used. New words, phrases, and meanings spring up every day, and all of them are captured and analysed by the Collins Word Web. Constantly updated, and with over 2.5 billion entries, this living language resource is unique to our dictionaries.
Words are tools for life. And a Collins Dictionary makes them work for you.
**Collins. Do more.**
# contents
air travel
---
animals
bikes
birds
body
calendar
camping
careers
cars
clothes
colours
computing and IT
countries and nationalities
countryside
describing people
education
environment
family
farm
fish and insects
food and drink
free time
fruit
furniture and appliances
geographical names
greetings and everyday phrases
health
hotel
house – general
house – particular
information and services
law
materials
music
numbers and quantities
personal items
plants and gardens
seaside and boats
shopping
sports
theatre and cinema
time
tools
town
trains
trees
vegetables
vehicles
the weather
youth hostelling
supplementary vocabulary
articles and pronouns
conjunctions
adjectives
adverbs and prepositions
nouns
verbs
English index
# how to use this book
_Collins Easy Learning Spanish Words_ is designed for both young and adult learners. Whether you are starting to learn Spanish for the first time, revising for school exams or simply want to brush up on your Spanish, _Collins Easy Learning Spanish Words_ offers you the information you require in a clear and accessible format.
This book is divided into 50 topics, arranged in alphabetical order. This thematic approach enables you to learn related words and phrases together, so that you can become confident in using particular vocabulary in context.
Vocabulary within each topic is divided into nouns and useful phrases which are aimed at helping you to express yourself in idiomatic Spanish. Vocabulary within each topic is graded to help you prioritize your learning. Essential words include the basic words you will need to be able to communicate effectively, important words help expand your knowledge, and useful words provide additional vocabulary which will enable you to express yourself more fully.
Nouns are grouped by gender: masculine ("el") nouns are given on the left-hand page, and feminine ("la") nouns on the right-hand page, enabling you to memorize words according to their gender. In addition, all feminine forms of adjectives are shown, as are irregular plurals.
At the end of the book you will find a list of supplementary vocabulary, grouped according to part of speech – adjective, verb, noun and so on. This is vocabulary which you will come across in many everyday situations.
Finally, there is an English index which lists all the essential and important nouns given under the topic headings for quick reference.
_Collins Easy Learning Spanish Words_ helps you to consolidate your language learning. Together with the other titles in the _Easy Learning_ range you can be sure that you have all the help you need when learning Spanish at your fingertips.
# abbreviations
**ABBREVIATIONS**
---
_adj_ | adjective
_adv_ | adverb
_algn_ | alguien
_conj_ | conjunction
_f_ | feminine
_inv_ | invariable
_LAm_ | word used in Latin America
_m_ | masculine
_m+f_ | masculine and feminine form
_Mex_ | word used in Mexico
_n_ | noun
_pl_ | plural
_prep_ | preposition
_sb_ | somebody
_sing_ | singular
_Sp_ | word used in Spain
_sth_ | something
The swung dash ~ is used to indicate the basic elements of the compound and appropriate endings are then added.
**PLURALS AND GENDER**
In Spanish, if a noun ends in a vowel it generally takes –s in the plural (casa > casas). If it ends in a consonant (including y) it generally takes –es in the plural (reloj > relojes). If it doesn't follow these rules, then the plural will be given in the text.
Although most masculine nouns take "el" and most feminine nouns take "la", you will find a few nouns grouped under feminine words which take "el" (el agua water; el arca chest; el aula classroom) because they are actually feminine.
# air travel
**ESSENTIAL WORDS** _(masculine)_
---
| el | **aeropuerto** | airport
| el | **agente de viajes** | travel agent
| el | **alquiler de coches** | car hire
| el | **avión** ( _pl_ aviones) | plane
| el | **billete** ( _Sp_ ), el **boleto** ( _LAm_ ) | ticket
| el | **bolso** | bag
| el | **carnet** ( _or_ carné) **de identidad** | ID card
| | ( _pl_ carnets _or_ carnés ~ ~)
| el | **enlace** | connection
| el | **equipaje** | luggage
| el | **equipaje de mano** | hand luggage
| el | **horario** | timetable
| el | **número** | number
| el | **oficial de aduanas** | customs officer
| el | **pasajero** | passenger
| el | **pasaporte** | passport
| el | **(precio del) billete** ( _Sp_ ) _or_ **boleto** ( _LAm_ ) | fare
| el | **retraso** | delay
| los | **servicios** | toilets
| el | **taxi** | taxi
| el | **turista** | tourist
| el | **viaje** | trip
| el | **viajero** | traveller
**USEFUL PHRASES**
viajar en avión to travel by plane
un billete ( _Sp_ ) _or_ boleto ( _LAm_ ) de ida a single ticket
un billete ( _Sp_ ) _or_ boleto ( _LAm_ ) de ida y vuelta, un boleto redondo ( _Mex)_ a return ticket
reservar un billete ( _Sp_ ) _or_ boleto ( _LAm_ ) de avión to book a plane ticket
"por avión" "by airmail"
facturar el equipaje to check in one's luggage
perdí el enlace I missed my connection
el avión ha despegado/ha aterrizado the plane has taken off/has landed
el panel de llegadas/salidas the arrivals/departures board
el vuelo número 776 procedente de Madrid/con destino Madrid flight number 776 from Madrid/to Madrid
**ESSENTIAL WORDS** _(feminine)_
---
| la | **aduana** | customs
| la | **agente de viajes** | travel agent
| la | **cancelación** ( _pl_ cancelaciones) | cancellation
| la | **duty free** | duty-free (shop)
| la | **entrada** | entrance
| la | **información** ( _pl_ informaciones) | information desk; information
| la | **llegada** | arrival
| la | **maleta** | bag; suitcase
| la | **oficial de aduanas** | customs officer
| la | **pasajera** | passenger
| la | **puerta de embarque** | departure gate
| la | **reserva** | reservation
| la | **salida** | departure; exit
| la | **salida de emergencia** | emergency exit
| la | **tarifa** | fare
| la | **tarjeta de embarque** | boarding card
| la | **turista** | tourist
| la | **viajera** | traveller
**USEFUL PHRASES**
recoger el equipaje to collect one's luggage
"recogida de equipajes" "baggage reclaim"
pasar por la aduana to go through customs
tengo algo que declarar I have something to declare
no tengo nada que declarar I have nothing to declare
registrar el equipaje to search the luggage
**IMPORTANT WORDS** _(masculine)_
---
| el | **accidente de avión** | plane crash
| el | **billete electrónico** | e-ticket
| el | **carrito** | trolley
| el | **cinturón de seguridad** | seat belt
| | ( _pl_ cinturones ~ ~) |
| el | **helicóptero** | helicopter
| el | **mapa** | map
| el | **mareo** ( **en avión** ) | airsickness
| el | **piloto** | pilot
| el | **reloj** | clock
| el | **vuelo** | flight
**USEFUL WORDS** _(masculine)_
| el | **asiento** | seat
| el | **aterrizaje** | landing
| el | **auxiliar de vuelo** | steward; flight attendant
| el | **cambiador para bebés** | mother and baby room
| el | **control de seguridad** | security check
| el | **controlador aéreo** | air-traffic controller
| los | **derechos de aduana** | customs duty
| el | **despegue** | take-off
| el | **detector de metales** | metal detector
| el | **embarque** | boarding
| el | **horario** | timetable
| el | **jumbo** | jumbo jet
| los | **mandos** | controls
| el | **paracaídas** ( _pl inv_ ) | parachute
| el | **radar** | radar
| el | **reactor** | jet plane/engine
| el | **satélite** | satellite terminal
| el | **veraneante** | holiday-maker
**USEFUL PHRASES**
a bordo on board; "prohibido fumar" "no smoking"
"abróchense el cinturón de seguridad" "fasten your seat belts"
estamos sobrevolando Londres we are flying over London
me estoy mareando I am feeling sick; secuestrar un avión to hijack a plane
**IMPORTANT WORDS** _(feminine)_
---
| la | **duración** ( _pl_ duraciones) | length; duration
| la | **escalera mecánica** | escalator
| la | **piloto** | pilot
| la | **sala de embarque** | departure lounge
| la | **velocidad** | speed
**USEFUL WORDS** _(feminine)_
| el | **ala** ( _pl f_ las alas) | wing
| la | **altitud** | altitude
| la | **altura** | height
| la | **auxiliar de vuelo** | air hostess; flight attendant
| la | **barrera del sonido** | sound barrier
| la | **bolsa de aire** | air pocket
| la | **caja negra** | black box
| la | **cinta transportadora** | carousel
| la | **controladora aérea** | air-traffic controller
| la | **escala** | stopover
| la | **etiqueta** | label
| la | **hélice** | propeller
| la | **línea aérea** | airline
| la | **pista (de aterrizaje)** | runway
| la | **terminal** | terminal
| la | **tienda libre de impuestos** | duty-free shop
| la | **torre de control** | control tower
| la | **tripulación** ( _pl_ tripulaciones) | crew
| la | **turbulencia** | turbulence
| la | **ventanilla** | window
| la | **veraneante** | holiday-maker
**USEFUL PHRASES**
"pasajeros del vuelo AB251 con destino Madrid embarquen por la puerta 51" "flight AB251 to Madrid now boarding at gate 51"
hicimos escala en Nueva York we stopped over in New York
un aterrizaje forzoso _or_ de emergencia an emergency landing
un aterrizaje violento a crash landing
cigarrillos libres de impuestos duty-free cigarettes
#
animals
**ESSENTIAL WORDS** _(masculine)_
---
| el | **animal** | animal
| el | **buey** ( _pl_ ~es) | ox
| el | **caballo** | horse
| el | **cachorro** | puppy
| el | **cerdo** | pig
| el | **conejo** | rabbit
| el | **cordero** | lamb
| el | **elefante** | elephant
| el | **gato** | cat
| el | **gatito** | kitten
| el | **hámster** ( _pl_ ~s) | hamster
| el | **león** ( _pl_ leones) | lion
| el | **pájaro** | bird
| el | **perro** | dog
| el | **perrito** | puppy
| el | **pelaje** | fur, coat
| el | **pelo** | coat, hair
| el | **pescado** | fish
| el | **pez** ( _pl_ peces) | fish
| el | **potro** | foal
| el | **ratón** ( _pl_ ratones) | mouse
| el | **ternero** | calf
| el | **tigre** | tiger
| el | **zoo** ( _pl_ ~s) | zoo
| el | **zoológico** | zoo
**USEFUL PHRASES**
me gustan los gatos, odio las serpientes, prefiero los ratones I like cats, I hate snakes, I prefer mice
tenemos 12 animales en casa we have 12 pets in our house
no tenemos animales en casa we have no pets in our house
los animales salvajes wild animals
los animales domésticos _or_ las mascotas pets
el ganado livestock
meter un animal en una jaula to put an animal in a cage
liberar un animal to set an animal free
**ESSENTIAL WORDS** _(feminine)_
---
| el | **ave** ( _pl f_ las aves) | bird
| la | **gata** | cat _(female)_
| la | **oveja** | ewe
| la | **perra** | dog _(female)_
| la | **tortuga** | tortoise
| la | **vaca** | cow
**IMPORTANT WORDS** __(feminine)__
| la | **cola** | tail
| la | **jaula** | cage
**USEFUL PHRASES**
el perro ladra the dog barks; gruñe it growls
el gato maulla the cat miaows; ronronea it purrs
me gusta la equitación _or_ montar a caballo I like horse-riding
a caballo on horseback
"cuidado con el perro" "beware of the dog"
"no se admiten perros" "no dogs allowed"
"¡quieto!" ( _to dog_ ) "down!"
los derechos de los animales animal rights
**USEFUL WORDS** __(masculine)__
---
| el | **asno** | donkey
| el | **burro** | donkey
| el | **camello** | camel
| el | **canguro** | kangaroo
| el | **caparazón** ( _pl_ caparazones) | shell ( _of tortoise_ )
| el | **casco** | hoof
| el | **cerdo** | pig
| el | **ciervo** | stag
| el | **cocodrilo** | crocodile
| el | **colmillo** | tusk
| el | **conejillo de Indias** | guinea pig
| el | **cuerno** | horn
| el | **erizo** | hedgehog
| el | **hipopótamo** | hippopotamus
| el | **hocico** | snout
| el | **lobo** | wolf
| el | **macho cabrío** | billy goat
| el | **mono** | monkey
| el | **mulo** | mule
| el | **murciélago** | bat
| el | **oso** | bear
| el | **oso polar** | polar bear
| el | **pavo** | turkey
| el | **pony** ( _pl_ ~s) | pony
| el | **rinoceronte** | rhinoceros
| el | **sapo** | toad
| el | **tiburón** ( _pl_ tiburones) | shark
| el | **topo** | mole
| el | **toro** | bull
| el | **zorro** | fox
**USEFUL WORDS** __(feminine)__
---
| la | **ardilla** | squirrel
| el | **asta** ( _pl f_ las astas) | antler
| la | **ballena** | whale
| la | **boca** | mouth
| la | **bolsa** | pouch ( _of kangaroo_ )
| la | **cabra** | (nanny) goat
| la | **crin** | mane
| la | **culebra** | (grass) snake
| la | **foca** | seal
| la | **garra** | claw
| la | **jirafa** | giraffe
| la | **joroba** | hump ( _of camel_ )
| la | **leona** | lioness
| la | **liebre** | hare
| la | **melena** | mane
| la | **mula** | mule
| la | **pajarería** | pet shop
| la | **pata** | paw
| la | **pezuña** | hoof
| la | **piel** | fur; hide ( _of cow, elephant etc_ )
| la | **rana** | frog
| las | **rayas** | stripes ( _of zebra_ )
| la | **serpiente** | snake
| la | **tienda de animales** | pet shop
| la | **tigresa** | tigress
| la | **trampa** | trap
| la | **trompa** | trunk ( _of elephant_ )
| la | **yegua** | mare
| la | **zebra** | zebra
#
bikes
**ESSENTIAL WORDS** __(masculine)__
---
| el | **casco** | helmet
| el | **ciclismo** | cycling
| el | **ciclista** | cyclist
| el | **faro** | lamp
| el | **freno** | brake
| el | **neumático** | tyre
**IMPORTANT WORDS** __(masculine)__
| el | **pinchazo** | puncture
**USEFUL WORDS** __(masculine)__
| el | **ascenso** | climb
| el | **candado** | padlock
| el | **carril bici** | cycle lane
| el | **descarrilamiento** | derailleur
| el | **descenso** | descent
| el | **eje** | hub
| el | **guardabarros** ( _pl inv_ ) ( _Sp_ ) | mudguard
| el | **kit de reparación de pinchazos** | puncture repair kit
| | ( _pl_ ~s ~ ~ ~ ~) |
| el | **manillar** | handlebars
| el | **pedal** | pedal
| el | **portaequipajes** ( _pl inv_ ) | carrier
| el | **radio** | spoke
| el | **reflector** | reflector
| el | **sillín** ( _pl_ sillines) | saddle
| el | **timbre** | bell
**USEFUL PHRASES**
ir en bici(cleta) to go by bike, to cycle
vine en bici(cleta) I came by bike
viajar to travel
a toda velocidad at full speed
cambiar de marchas to change gears
pararse to stop
frenar bruscamente to brake suddenly
**ESSENTIAL WORDS** __(feminine)__
---
| la | **bici** | bike
| la | **bicicleta** | bicycle
| la | **bicicleta de montaña** | mountain bike
| la | **vuelta ciclista a España** | Tour of Spain
**IMPORTANT WORDS** __(feminine)__
| la | **rueda** | wheel
| la | **velocidad** | speed; gear
**USEFUL WORDS** __(feminine)__
| la | **alforja** | pannier
| la | **barra** | crossbar
| la | **bomba** | pump
| la | **cadena** | chain
| la | **cuesta** | slope
| la | **cumbre** | top ( _of hill_ )
| la | **dínamo** | dynamo
| la | **luz delantera** ( _pl_ luces ~s) | front light
| la | **pendiente** | slope
| la | **salpicadera** _( _Mex_ )_ | mudguard
| la | **subida** | climb
| la | **válvula** | valve
**USEFUL PHRASES**
dar una vuelta _or_ pasear en bici(cleta) to go for a bike ride
tener un pinchazo _or_ una rueda pinchada to have a puncture
arreglar un pinchazo to mend a puncture
la rueda delantera/trasera the front/back wheel
inflar las ruedas to blow up the tyres
brillante, reluciente shiny
oxidado(a) rusty
fluorescente fluorescent
#
birds
**ESSENTIAL WORDS** __(masculine)__
---
| el | **cielo** | sky
| el | **gallo** | cock
| el | **ganso** | goose
| el | **loro** | parrot
| el | **pájaro** | bird
| el | **pato** | duck
| el | **pavo** | turkey
| el | **periquito** | budgie
**USEFUL WORDS** __(masculine)__
| el | **avestruz** ( _pl_ avestruces) | ostrich
| el | **búho** | owl
| el | **buitre** | vulture
| el | **canario** | canary
| el | **chochín** ( _pl_ chochines) | wren
| el | **cisne** | swan
| el | **cuervo** | raven; crow
| el | **cuco** | cuckoo
| el | **estornino** | starling
| el | **faisán** ( _pl_ faisanes) | pheasant
| el | **gorrión** ( _pl_ gorriones) | sparrow
| el | **halcón** ( _pl_ halcones) | falcon
| el | **herrerillo** | bluetit
| el | **huevo** | egg
| el | **martín pescador** | kingfisher
| | ( _pl_ martines ~es) |
| el | **mirlo** | blackbird
| el | **nido** | nest
| el | **pájaro carpintero** | woodpecker
| el | **pavo real** | peacock
| el | **petirrojo** | robin
| el | **pico** | beak
| el | **pingüino** | penguin
| el | **ruiseñor** | nightingale
| el | **tordo** | thrush
| el | **urogallo** | grouse
**ESSENTIAL WORDS** __(feminine)__
---
| la | **gallina** | hen
**USEFUL WORDS** __(feminine)__
| el | **águila** ( _pl f_ las águilas) | eagle
| el | **ala** ( _pl f_ las alas) | wing
| la | **alondra** | lark
| el | **ave** ( _pl f_ las aves) | bird
| el | **ave de rapiña** ( _pl f_ las ~s ~ ~) | bird of prey
| el | **ave rapaz** ( _pl f_ las ~s rapaces) | bird of prey
| la | **cigüeña** | stork
| la | **codorniz** ( _pl_ codornices) | quail
| la | **gaviota** | seagull
| la | **golondrina** | swallow
| la | **grajilla** | jackdaw
| la | **jaula** | cage
| la | **paloma** | pigeon; dove
| la | **perdiz** ( _pl_ perdices) | partridge
| la | **pluma** | feather
| la | **urraca** | magpie
**USEFUL PHRASES**
volar to fly
emprender vuelo to fly away
construir un nido to build a nest
silbar to whistle
cantar to sing
la gente los mete en jaulas people put them in cages
hibernar to hibernate
poner un huevo to lay an egg
un ave migratoria a migratory bird
#
body
**ESSENTIAL WORDS** __(masculine)__
---
| el | **brazo** | arm
| el | **cabello** | hair
| el | **corazón** ( _pl_ corazones) | heart
| el | **cuerpo** | body
| el | **dedo** | finger
| el | **diente** | tooth
| el | **estómago** | stomach
| el | **ojo** | eye
| el | **pelo** | hair
| el | **pie** | foot
| el | **rostro** | face
**IMPORTANT WORDS** __(masculine)__
| el | **cuello** | neck
| el | **hombro** | shoulder
| el | **pecho** | chest; bust
| el | **pulgar** | thumb
| el | **tobillo** | ankle
**USEFUL PHRASES**
de pie standing
sentado(a) sitting
tumbado(a) lying
**ESSENTIAL WORDS** __(feminine)__
---
| la | **boca** | mouth
| la | **cabeza** | head
| la | **espalda** | back
| la | **garganta** | throat
| la | **mano** | hand
| la | **nariz** ( _pl_ narices) | nose
| la | **oreja** | ear
| la | **pierna** | leg
| la | **rodilla** | knee
**IMPORTANT WORDS** __(feminine)__
| la | **barbilla** | chin
| la | **cara** | face
| la | **ceja** | eyebrow
| la | **frente** | forehead
| la | **lengua** | tongue
| la | **mejilla** | cheek
| la | **piel** | skin
| la | **sangre** | blood
| la | **voz** ( _pl_ voces) | voice
**USEFUL PHRASES**
grande big
alto(a) tall
pequeño(a) small
bajo(a) short
gordo(a) fat
flaco(a) skinny
delgado(a) slim
bonito(a) pretty
feo(a) ugly
**USEFUL WORDS** __(masculine)__
---
| el | **cerebro** | brain
| el | **codo** | elbow
| el | **cutis** ( _pl inv_ ) | skin, complexion
| el | **dedo del pie** | toe
| el | **dedo índice** | forefinger
| el | **dedo gordo** | the big toe
| los | **dedos del pie** | toes
| el | **esqueleto** | skeleton
| el | **gesto** | gesture
| el | **hígado** | liver
| el | **hueso** | bone
| el | **labio** | lip
| el | **músculo** | muscle
| el | **muslo** | thigh
| el | **párpado** | eyelid
| el | **pulmón** ( _pl_ pulmones) | lung
| el | **puño** | fist
| el | **rasgo** | feature
| el | **riñón** ( _pl_ riñones) | kidney
| el | **seno** | breast
| el | **talle** | waist
| el | **talón** ( _pl_ talones) | heel
| el | **trasero** | bottom
**USEFUL PHRASES**
sonarse (la nariz) to blow one's nose
cortarse las uñas to cut one's nails
cortarse el pelo to have one's hair cut
encogerse de hombros to shrug one's shoulders
asentir/decir que sí con la cabeza to nod one's head
negar/decir que no con la cabeza to shake one's head
ver to see; oir to hear; sentir to feel
oler to smell; tocar to touch; probar to taste
estrechar la mano a alguien to shake hands with somebody
saludar a alguien con la mano to wave at somebody
señalar algo to point at something
**USEFUL WORDS** __(feminine)__
---
| la | **arteria** | artery
| la | **cadera** | hip
| la | **carne** | flesh
| la | **columna (vertebral)** | spine
| la | **costilla** | rib
| la | **facción** ( _pl_ facciones) | feature
| la | **mandíbula** | jaw
| la | **muñeca** | wrist
| la | **nuca** | nape of the neck
| la | **pantorrilla** | calf ( _of leg_ )
| la | **pestaña** | eyelash
| la | **planta del pie** | sole of the foot
| la | **pupila** | pupil ( _of the eye_ )
| la | **sien** | temple ( _of head_ )
| la | **talla** | size
| la | **tez** ( _pl_ teces) | complexion
| la | **uña** | nail
| la | **vena** | vein
**USEFUL PHRASES**
contorno de caderas hip measurement
cintura waist measurement
contorno de pecho chest measurement
sordo(a) deaf
ciego(a) blind
mudo(a) mute
discapacitado(a) disabled
disminuido(a) psíquico(a) person with learning difficulties
él es más alto que tú he is taller than you
ella ha crecido mucho she has grown a lot
estoy demasiado gordo(a) _or_ tengo sobrepeso I am overweight
ella ha engordado/adelgazado she has put on/lost weight
ella mide 1,47 metros she is 1.47 metres tall
él pesa 40 kilos he weighs 40 kilos
#
calendar
**SEASONS**
---
| la | **primavera** | spring
| el | **verano** | summer
| el | **otoño** | autumn
| el | **invierno** | winter
**MONTHS**
---
**enero** | January | **julio** | July
**febrero** | February | **agosto** | August
**marzo** | March | **septiembre** | September
**abril** | April | **octubre** | October
**mayo** | May | **noviembre** | November
**junio** | June | **diciembre** | December
**Days of the Week**
---
**lunes** | Monday
**martes** | Tuesday
**miércoles** | Wednesday
**jueves** | Thursday
**viernes** | Friday
**sábado** | Saturday
**domingo** | Sunday
**USEFUL PHRASES**
en primavera/verano/otoño/invierno in spring/summer/autumn/winter
en mayo in May
el 10 de julio de 2006 on 10 July 2006
es 3 de diciembre it's 3rd December
los sábados voy a la piscina on Saturdays I go to the swimming pool
el sábado fui a la piscina on Saturday I went to the swimming pool
el próximo sábado/el sábado pasado next/last Saturday
el sábado anterior/siguiente the previous/following Saturday
**Calendar**
---
| el | **calendario** | calendar
| el | **día** | day
| los | **días de la semana** | days of the week
| el | **día festivo** | public holiday
| la | **estación** ( _pl_ estaciones) | season
| el | **mes** | month
| la | **semana** | week
**USEFUL PHRASES**
el día de los (Santos) Inocentes April Fools' Day ( _celebrated on 28 December in Spain_ )
la broma del día de los (Santos) Inocentes April fool's trick
el primero de mayo May Day
el día de la Hispanidad Columbus Day ( _Spain's national day, celebrated on 12 October_ )
el himno nacional de España Spain's national anthem
el día D D-Day
el día de San Valentín St Valentine's Day
el día de Todos los Santos All Saints' Day
la Semana Santa Easter
el Domingo de Resurrección _or_ Pascua Easter Sunday
el Lunes de Pascua Easter Monday
el Miércoles de Ceniza Ash Wednesday
el Viernes Santo Good Friday
la Cuaresma Lent
la Pascua judía Passover
el Ramadán Ramadan
el Hanukkah Hanukkah _or_ Hanukah
el Divali _or_ el Festival de la Luz Divali _or_ Diwali
el Adviento Advent
la Nochebuena Christmas Eve
la Navidad Christmas
en Navidad at Christmas
el día de Navidad Christmas Day
la Nochevieja New Year's Eve
el día de Año Nuevo New Year's Day
la cena _or_ fiesta de Fin de Año New Year's Eve dinner _or_ party
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aniversario de boda** | wedding anniversary
| el | **cumpleaños** ( _pl inv_ ) | birthday
| el | **(día del) santo** | saint's day
| el | **divorcio** | divorce
| el | **matrimonio** | marriage
| el | **regalo** | present
**IMPORTANT WORDS** __(masculine)__
| el | **compromiso** | engagement
| el | **festival** | festival
| los | **fuegos artificiales** | fireworks; firework display
| el | **nacimiento** | birth
| el | **parque de atracciones** | fun fair
**USEFUL WORDS** __(masculine)__
| el | **bautismo** | christening
| el | **cementerio** | cemetery
| el | **entierro** | funeral
| el | **festival folclórico** | folk festival
| el | **testigo** | witness
| el | **regalo de Navidad** | Christmas present
**USEFUL PHRASES**
celebrar el cumpleaños to celebrate one's birthday
mi hermana nació en 1995 my sister was born in 1995
ella acaba de cumplir 17 años she's just turned 17
él me dio este regalo he gave me this present
¡te lo regalo! I'm giving it to you!
gracias thank you
divorciarse to get divorced
casarse to get married
comprometerse (con algn) to get engaged (to sb)
mi padre murió hace dos años my father died two years ago
enterrar to bury
**ESSENTIAL WORDS** __(feminine)__
---
| la | **boda** | wedding
| la | **cita** | appointment, date
| la | **fecha** | date
| la | **fiesta** | festival; fair; party
**IMPORTANT WORDS** __(feminine)__
| las | **fiestas** | festivities
| la | **feria** | fair
| la | **muerte** | death
| la | **hoguera** | bonfire
**USEFUL WORDS** __(feminine)__
| la | **ceremonia** | ceremony
| la | **dama de honor** | bridesmaid
| la | **invitación de boda** | wedding invitation
| | ( _pl_ invitaciones ~ ~) |
| la | **jubilación** ( _pl_ jubilaciones) | retirement
| la | **luna de miel** | honeymoon
| la | **procesión** ( _pl_ procesiones) | procession; march
| la | **tarjeta de felicitación** | greetings card
| la | **testigo** | witness
**USEFUL PHRASES**
bodas de plata/oro/diamante silver/golden/diamond wedding anniversary
desear a algn (un) Feliz Año to wish sb a happy New Year
dar _or_ hacer una fiesta to have a party
invitar a los amigos to invite one's friends
elegir un regalo to choose a gift
¡Feliz navidad! _or_ ¡Felices Pascuas! Happy Christmas!
¡Feliz cumpleaños! happy birthday!
(con) nuestros mejores deseos best wishes
#
camping
**ESSENTIAL WORDS** __(masculine)__
---
| los | **aseos** | toilets
| los | **baños** ( _LAm)_ | washrooms; toilets
| el | **bote** | tin, can
| el | **camping** ( _pl_ ~s) | camping; campsite
| el | **campista** | camper
| el | **cerillo** ( _LAm)_ | match
| el | **cubo de la basura** | dustbin
| el | **cuchillo** | knife
| el | **depósito de butano** | butane store
| el | **emplazamiento** | pitch, site
| el | **espejo** | mirror
| el | **gas** | gas
| el | **guarda** | warden
| el | **lavabo** | washbasin
| el | **plato** | plate
| los | **servicios** ( _Sp)_ | washrooms; toilets
| el | **suplemento** | extra charge
| el | **tenedor** | fork
| el | **trailer** ( _pl_ ~s) ( _LAm)_ | trailer
| el | **vehículo** | vehicle
**IMPORTANT WORDS** __(masculine)__
| el | **abrelatas** ( _pl inv_ ) | tin-opener
| el | **colchón inflable** ( _pl_ colchones ~s) | airbed
| el | **detergente** | washing powder
| el | **enchufe** | socket
| el | **hornillo** | stove
| el | **sacacorchos** ( _pl inv_ ) | corkscrew
| el | **saco de dormir** | sleeping bag
**USEFUL PHRASES**
ir de _or_ hacer camping to go camping
acampar to camp
bien equipado(a) well equipped
hacer una hoguera to make a fire
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua (no) potable** ( _f)_ | (non-)drinking water
| la | **alberca** ( _Mex)_ | swimming pool
| la | **caja** | box
| la | **cama plegable** | camp bed
| la | **campista** | camper
| la | **caravana** | caravan; motorhome
| la | **carpa** ( _LAm_ ) | tent
| la | **cerilla** | match
| la | **comida enlatada** | tinned food
| la | **cuchara** | spoon
| la | **ducha** | shower
| la | **hoguera de campamento** | campfire
| la | **lata** | tin, can
| la | **lavadora** | washing machine
| la | **linterna** | torch
| la | **mesa** | table
| la | **navaja** | penknife
| la | **noche** | night
| la | **piscina** ( _Sp_ ) | swimming pool
| la | **sala** | room; hall
| la | **tienda (de campaña)** ( _Sp_ ) | tent
| la | **tumbona** | deckchair
**IMPORTANT WORDS** __(feminine)__
| la | **barbacoa** | barbecue
| la | **colada** | washing
| las | **instalaciones sanitarias** | washing facilities
| la | **lavandería** | launderette
| la | **mochila** | rucksack
| las | **normas** | rules
| la | **sala de juegos** | games room
| la | **sombra** | shade; shadow
| la | **toma de corriente** | socket
**USEFUL PHRASES**
montar una tienda to pitch a tent
asar unas salchichas (a la parrilla) to grill some sausages
#
careers
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aeromozo** ( _LAm)_ | steward; flight attendant
| el | **agricultor** | farmer
| el | **auxiliar de vuelo** ( _Sp)_ | steward; flight attendant
| el | **banco** | bank
| el | **bombero** | fireman
| el | **cajero** | check-out assistant
| el | **cartero** | postman
| el | **diseñador de páginas web** | web designer
| el | **electricista** | electrician
| el | **empleado** | employee
| el | **empresario** | employer
| el | **enfermero** | nurse
| el | **farmacéutico** | chemist
| el | **informático** | computer programmer
| el | **jefe** | boss
| el | **maquinista** | engineer; train driver
| el | **mecánico** | mechanic
| el | **médico** | doctor
| el | **minero** | miner
| el | **oficio** | trade
| el | **orientador profesional** | careers adviser
| el | **policía** | policeman
| el | **profesor** | teacher
| el | **propietario de un taller** | garage owner
| | **(mecánico** _or_ **de reparaciones)** |
| el | **redactor** | editor
| el | **soldado** | soldier
| el | **sueldo** | wages
| el | **taxista** | taxi driver
| el | **trabajo** | job; work
| el | **vendedor** | sales assistant, shop assistant
**USEFUL PHRASES**
interesante/poco interesante interesting/not very interesting
él es cartero he is a postman; él/ella es médico he/she is a doctor
trabajar to work
hacerse, volverse to become
**ESSENTIAL WORDS** __(feminine)__
---
| la | **aeromoza** ( _LAm)_ | stewardess; flight attendant
| la | **agricultora** | farmer
| la | **ambición** ( _pl_ ambiciones) | ambition
| la | **auxiliar de vuelo** | stewardess; flight attendant
| la | **cajera** | check-out assistant
| la | **cartera** | postwoman
| la | **consejera profesional** | careers adviser
| la | **empleada** | employee
| la | **enfermera** | nurse
| la | **estrella** ( _m+f_ ) | star
| la | **fábrica** | factory
| la | **informática** | computer programmer
| la | **jefa** | boss
| la | **jubilación** ( _pl_ jubilaciones) | retirement
| la | **mecanógrafa** | typist
| la | **médico** | doctor
| la | **oficina** | office
| la | **profesión** ( _pl_ profesiones) | profession
| la | **profesora** | teacher
| la | **recepcionista** | receptionist
| la | **redactora** | editor
| la | **secretaria** | secretary
| la | **vendedora** | sales assistant, shop assistant
| la | **vida** | life
| la | **vida laboral** | working life
**USEFUL PHRASES**
trabajar para ganarse la vida to work for one's living
mi ambición es ser juez(a) it is my ambition to be a judge
¿en qué trabajas? what do you do (for a living)?
solicitar un trabajo to apply for a job
**IMPORTANT WORDS** __(masculine)__
---
| el | **aprendizaje** | apprenticeship
| el | **asalariado** | wage-earner
| el | **aumento** | rise
| el | **autor** | author
| el | **bombero** | fireman
| el | **colega** | colleague
| el | **comerciante** | shopkeeper
| el | **contrato** | contract
| el | **conserje** | caretaker
| el | **decorador** | decorator
| el | **desempleado** | unemployed person
| el | **desempleo** | unemployment
| el | **empleo** | job; situation
| el | **fontanero** ( _Sp_ ) | plumber
| el | **futuro** | future
| el | **gerente** | manager
| el | **hombre de negocios** | businessman
| el | **INEM** | employment organization;
| | | institute of employment
| el | **interino** | temp
| el | **jefe** | boss
| el | **mercado laboral** | job market
| el | **negocio** _or_ los **negocios** | business
| el | **óptico** | optician
| el | **peluquero** | hairdresser
| el | **piloto** | pilot
| el | **pintor** | painter
| el | **plomero** ( _Mex_ ) | plumber
| el | **presidente** | president; chairperson
| el | **sindicato** | trade union
| el | **trabajador** | worker
| el | **trabajo** | job
**USEFUL PHRASES**
estar desempleado(a) _or_ en paro to be unemployed
despedir a algn to make sb redundant
contrato indefinido/temporal/a término fijo permanent/temporary/ fixed term contract
**IMPORTANT WORDS** __(feminine)__
---
| la | **acomodadora** | usher
| la | **agencia de trabajo temporal** | temping agency
| la | **asalariada** | wage-earner
| la | **biblioteca** | library
| la | **carrera** | career
| la | **carta adjunta** | covering letter
| la | **cocinera** | cook
| la | **colega** | colleague
| la | **conserje** | caretaker
| la | **entrevista (de trabajo)** | (job) interview
| la | **gerente** | manager
| la | **huelga** | strike
| la | **interina** | temp
| la | **limpiadora** | cleaner
| la | **mujer de negocios** | businesswoman
| la | **oficina de empleo** | job centre
| la | **peluquera** | hairdresser
| la | **pintora** | painter
| la | **política** | politics
| la | **presidenta** | president; chairperson
| la | **solicitud** | application
| la | **trabajadora** | worker
**USEFUL PHRASES**
"demandas de empleo" "situations wanted"
"ofertas de empleo" "situations vacant"
estar en/pertenercer a un sindicato to be in a union
ganar 150 libras a la semana to earn £150 a week
una subida _or_ un aumento de sueldo a pay rise
ponerse _or_ declararse en huelga to go on strike
estar en huelga to be on strike
trabajar jornada completa/media jornada to work full-time/part-time
trabajar horas extra(s) to work overtime
reducción de la jornada laboral reduction in working hours
**USEFUL WORDS** __(masculine)__
---
| el | **abogado** | lawyer
| el | **agente comercial** | sales rep
| el | **albañil** | mason
| el | **arquitecto** | architect
| el | **artista** | artist
| el | **carpintero** | joiner
| el | **cirujano** | surgeon
| el | **contable** ( _Sp_ ), el **contador** ( _LAm_ ) | accountant
| el | **cosmonauta** | cosmonaut
| el | **cura** | priest
| el | **curso de formación** | training course
| el | **diputado** | MP
| el | **diseñador** | fashion designer
| el | **ejecutivo** | executive
| el | **escritor** | writer
| el | **fotógrafo** | photographer
| el | **funcionario** | civil servant
| el | **horario** | schedule
| el | **ingeniero** | engineer
| el | **intérprete** | interpreter
| el | **investigador** | researcher
| el | **juez** ( _pl_ jueces) | judge
| el | **marinero** | sailor
| el | **modelo** | model ( _person_ )
| el | **monitor de actividades** | activity leader
| el | **negocio** | business
| el | **notario** | notary
| el | **paro** | unemployment benefit
| el | **periodista** | journalist
| el | **(período de) trabajo en prácticas** | work placement
| el | **personal** | staff
| el | **político** | politician
| el | **director ejecutivo** | managing director
| el | **procurador** | solicitor
| el | **representante** | rep; sales rep
| el | **sacerdote** | priest
| el | **traductor** | translator
| el | **veterinario** | vet
| el | **viticultor** | wine grower
**USEFUL WORDS** __(feminine)__
---
| la | **abogada** | lawyer
| la | **administración** | administration
| | ( _pl_ administraciones) |
| el | **ama de casa** ( _pl f_ amas ~ ~) | housewife
| la | **monitora de actividades** | activity leader
| la | **artista** | artist
| la | **compañía** | company
| la | **contable** ( _Sp_ ), la **contadora** ( _LAm_ ) | accountant
| la | **empresa** | company
| la | **formación** | training
| la | **funcionaria** | civil servant
| la | **huelga de celo** | work-to-rule; go-slow
| la | **indemnización por desempleo** | redundancy payment
| la | **intérprete** | interpreter
| la | **jueza** | judge
| la | **locutora** | announcer
| la | **modelo** | model ( _person_ )
| la | **modista** | dressmaker
| la | **monja** | nun
| la | **orientación profesional** | careers guidance
| la | **periodista** | journalist
| la | **policía** | policewoman
| la | **religiosa** | nun
| la | **representante** | rep; sales rep
| la | **taquimecanógrafa** | shorthand typist
| la | **traductora** | translator
**USEFUL PHRASES**
el trabajo temporal seasonal work
un empleo temporal/permanente a temporary/permanent job
un trabajo a tiempo parcial ( _Sp_ ) _or_ a medio tiempo ( _LAm_ ) a part-time job
ser contratado(a) to be taken on; ser despedido(a) to be dismissed
despedir _or_ echar a algn to give sb the sack
buscar trabajo to look for work
hacer un curso de formación profesional to go on a training course
fichar al entrar a/al salir de trabajar to clock in/out
trabajar en horario flexible to work flexitime
#
cars
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aceite** | oil
| el | **agente de policía** | policeman
| el | **aparcamiento** ( _Sp_ ) | car park
| el | **atasco** | traffic jam
| el | **autoestop** | hitch-hiking
| el | **autoestopista** | hitch-hiker
| el | **automóvil** | car
| el | **aventón** ( _Mex_ ) | hitch-hiking
| el | **callejero** | street map
| el | **camión** ( _pl_ camiones) | lorry, truck
| el | **carnet** _or_ **carné de conducir** | driving licence
| | ( _Sp_ ) ( _pl_ ~s _or_ ~s ~ ~) |
| el | **carro** ( _LAm_ ) | car
| el | **chófer** | driver; chauffeur
| el | **ciclista** | cyclist
| el | **coche** ( _Sp_ ) | car
| el | **conductor** | driver
| el | **cruce** | crossroads
| el | **diesel** | diesel
| el | **estacionamiento** ( _LAm_ ) | car park
| los | **faros** | headlights
| el | **freno** | brake
| el | **garaje** | garage
| el | **gasoil** | diesel ( _oil_ )
| el | **kilómetro** | kilometre
| el | **litro** | litre
| el | **mapa de carreteras** | road map
| el | **mecánico** | mechanic
| el | **neumático** | tyre
| el | **número** | number
| el | **parking** ( _pl_ ~s) | car park
| el | **peaje** | toll
| el | **peatón** ( _pl_ peatones) | pedestrian
| el | **radar** | speed camera
| el | **semáforo** | traffic lights
| el | **trailer** ( _pl_ ~s) ( _LAm_ ) | caravan
| el | **viaje** | journey
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua** ( _f_ ) | water
| la | **autoestopista** | hitch-hiker
| la | **autopista** | motorway
| la | **autopista de peaje** | toll motorway
| la | **caravana** ( _Sp_ ) | caravan
| la | **carretera** | road
| la | **carretera nacional** | main road
| la | **chófer** | driver; chauffeur
| la | **ciclista** | cyclist
| la | **cochera** | garage
| la | **conductora** | driver
| la | **desviación** ( _pl_ desviaciones) | diversion
| la | **dirección** ( _pl_ direcciones) | direction
| la | **dirección asistida** ( _pl_ direcciones ~s) | power steering
| la | **distancia** | distance
| la | **estación de servicio** | petrol station
| | ( _pl_ estaciones ~ ~) |
| la | **gasolina** | petrol
| la | **gasolina sin plomo** | unleaded petrol
| la | **libreta de manejar** ( _Mex_ ) | driving licence
| la | **matrícula** ( _Sp_ ), la **placa** ( _LAm_ ) | (car) registration document
| la | **policía** | police
| la | **póliza de seguros** | insurance certificate
**USEFUL PHRASES**
frenar bruscamente to brake suddenly
100 kilómetros por hora 100 kilometres an hour
¿tienes carné ( _or_ carnet) de conducir? do you have a driving licence?
vamos a dar una vuelta (en coche) we're going for a drive (in the car)
¡lleno, por favor!, ¡llénelo, por favor! fill her up please!
tomar la carretera a/hacia Córdoba take the road to Córdoba
es un viaje de tres horas it's a 3-hour journey
¡buen viaje! have a good journey!
¡vámonos!, ¡en marcha! let's go!
de camino vimos... on the way we saw...
adelantar a un coche to overtake a car
**IMPORTANT WORDS** __(masculine)__
---
| el | **accidente (de carretera)** | (road) accident
| el | **aparcamiento** | parking
| el | **atasco** | traffic jam
| el | **camionero** | lorry driver
| el | **choque** | collision
| el | **cinturón de seguridad** | seat belt
| | ( _pl_ cinturones ~ ~) |
| el | **claxon** ( _pl_ cláxones _or_ ~s) | horn
| el | **código de la circulación** | highway code
| el | **daño** | damage
| el | **embrague** | clutch
| el | **encargado de una gasolinera** | petrol pump attendant
| el | **faro** | headlight
| el | **maletero** ( _Sp_ ) | boot
| el | **motociclista** | motorcyclist
| el | **motor** | engine
| el | **motorista** | motorist
| los | **papeles (del coche)** | official papers
| el | **pinchazo** | puncture
| el | **pito** | horn
| el | **salpicadero** | dashboard
| el | **seguro** | insurance
| el | **surtidor (de gasolina)** | petrol pump
| el | **tráfico** | traffïc
| el | **túnel de lavado de coches** | car wash
**USEFUL PHRASES**
primero enciendes _or_ pones el motor en marcha first you switch on the engine
el motor arranca _or_ se pone en marcha the engine starts up
el coche se pone en marcha the car moves off
estamos circulando we're driving along
acelerar to accelerate; continuar to continue
reducir _or_ aminorar la velocidad _or_ la marcha to slow down
detenerse to stop; aparcar (el coche) to park (the car)
apagar el motor to switch off the engine
parar con el semáforo en rojo to stop at the red light
**IMPORTANT WORDS** __(feminine)__
---
| la | **autoescuela** ( _Sp_ ) | driving school
| la | **avería** | breakdown
| la | **batería** | battery
| la | **cajuela** ( _Mex_ ) | boot
| la | **calle de sentido único** | one-way street
| la | **carrocería** | body work
| la | **colisión** ( _pl_ **colisiones)** | collision
| la | **documentación (del coche)** | official papers
| la | **esculela de conductores** ( _LAm_ ) | driving school
| | _or_ **de manejo** ( _Mex_ ) |
| la | **frontera** | border
| la | **glorieta** | roundabout
| la | **grúa** | breakdown van
| la | **ITV (inspección técnica** | MOT test
| | **de vehículos)** ( _Sp_ ) |
| la | **marca** | make ( _of car_ )
| la | **motociclista** | motorcyclist
| la | **motorista** | motorist
| la | **pieza de repuesto** | spare part
| la | **póliza de seguros** | insurance policy
| la | **prioridad** | right of way
| la | **prueba del alcohol** | Breathalyser® test
| la | **puerta** | ( _car_ ) door
| la | **rotonda** | roundabout
| la | **rueda** | tyre
| la | **rueda de repuesto** | spare tyre
| la | **velocidad** | speed; gear
| la | **zona azul** | restricted parking zone
**USEFUL PHRASES**
ha habido un accidente there's been an accident
hubo seis heridos en el accidente six people were injured in the accident
¿puedo ver la documentación _or_ los papeles del coche, por favor? may I see your papers please?
pinchar, tener un pinchazo to have a puncture; arreglar to fix
averiarse _or_ tener una avería to break down
me he quedado sin gasolina I've run out of petrol
**USEFUL WORDS** __(masculine)__
---
| el | **acelerador** | accelerator
| el | **arcén** ( _pl_ arcenes) | hard shoulder
| el | **autolavado** | car-wash
| el | **botón de arranque** ( _pl_ botones ~ ~) | starter
| el | **capó** | bonnet
| el | **carburador** | carburettor
| el | **carril** | lane
| el | **catalizador** | catalytic converter
| el | **conductor novel** | learner driver
| el | **consumo de gasolina** | petrol consumption
| el | **cuentakilómetros** ( _pl inv_ ) | speedometer
| el | **desvío** | detour
| el | **guardia de tráfico** | traffic warden
| el | **herido** | casualty
| el | **intermitente** | indicator
| el | **lavacoches** ( _pl inv_ ) | car-wash
| el | **límite de velocidad** | speed limit
| el | **limpiaparabrisas** ( _pl inv_ ) | windscreen wiper
| el | **parabrisas** ( _pl inv_ ) | windscreen
| el | **parachoques** ( _pl inv_ ) | bumper
| el | **parquímetro** | parking meter
| el | **pedal** | pedal
| el | **policía motorizado** | motorcycle policeman
| el | **profesor de autoescuela** | driving instructor
| el | **remolque** | trailer
| el | **retrovisor** | rear-view mirror
| el | **(sistema de navegación) GPS** | satellite navigation system
| el | **volante** | steering wheel
**USEFUL PHRASES**
en la hora punta at rush hour
le pusieron una multa de 100 euros he got a 100-euro fine
¿está asegurado? are you insured?
no olviden ponerse los cinturones de seguridad don't forget to put on your seat belts
en la frontera at the border
hacer autoestop to hitch-hike
**USEFUL WORDS** __(feminine)__
---
| el | **área de descanso** ( _pl f_ las áreas ~ ~) | lay-by
| el | **área de servicio** ( _pl f_ las áreas ~ ~) | service area
| la | **baca** | roof rack
| la | **caja de cambios** | gearbox
| la | **carretera de circunvalación** | ring road
| la | **clase de conducir** | driving lesson
| la | **curva** | bend
| la | **estación de servicio** | filling station
| | ( _pl_ estaciones ~ ~) |
| la | **gasolinera** | filling station
| la | **guardia de tráfico** | traffic warden
| la | **infracción de tráfico** | traffic offence
| | ( _pl_ infracciones ~ ~) |
| la | **matrícula** | number plate
| la | **mediana** | central reservation
| la | **multa** | fine
| la | **parada de emergencia** | emergency stop
| la | **presión** | pressure
| la | **señal de tráfico** | road sign
| la | **vía** | way, road; lane ( _on road_ )
| la | **vía de acceso** | slip road
| la | **víctima** ( _m+f_ ) | casualty
| la | **zona urbanizada** | built-up area
**USEFUL PHRASES**
la rueda delantera/trasera the front/back wheel
tenemos que desviarnos we have to make a detour
una multa por exceso de velocidad a fine for speeding
contratar a un conductor to book a driver
"ceda el paso a la derecha" "give way to the right"
"circule por la derecha" "keep to the right"
"prohibido el paso" "no entry"
"prohibido aparcar" "no parking"
"obras" "roadworks"
#
clothes
**ESSENTIAL WORDS** __(masculine)__
---
| el | **abrigo** | overcoat; coat
| el | **anorak** ( _pl inv or_ ~s) | anorak
| el | **bañador** | swimming trunks; swimsuit
| el | **bolso** | bag
| el | **botón** ( _pl_ botones) | button
| el | **calcetín** ( _pl_ calcetines) | sock
| los | **calzoncillos** | pants; boxer shorts
| los | **calzones** ( _LAm_ ) | knickers
| el | **camisón** ( _pl_ camisones) | nightdress
| el | **chubasquero** | raincoat
| el | **cuello** | collar
| el | **jersey** ( _pl_ ~s) | jumper
| el | **número (de pie)** | (shoe) size
| el | **pantalón** ( _pl_ pantalones) | trousers
| los | **(pantalones) vaqueros** | jeans
| el | **pañuelo** | handkerchief
| el | **paraguas** ( _pl inv_ ) | umbrella
| el | **pijama** | pyjamas
| el | **sombrero** | hat
| el | **talle** | waist
| el | **traje** | suit ( _for man_ ); costume
| el | **traje de chaqueta** | suit
| el | **vestido** | dress
| el | **zapato** | shoe
**IMPORTANT WORDS** __(masculine)__
| el | **bolsillo** | pocket
| el | **bolso** | handbag
| el | **cinturón** ( _pl_ cinturones) | belt
| el | **guante** | glove
| el | **impermeable** | raincoat
| los | **pantalones cortos** | shorts
| el | **uniforme** | uniform
**ESSENTIAL WORDS** __(feminine)__
---
| la | **braga (del bikini)** | bikini bottoms
| las | **bragas** ( _Sp_ ) | pants; knickers
| la | **camisa** | shirt
| la | **camiseta** | T-shirt
| la | **capucha** | hood
| la | **chaqueta** | jacket
| la | **corbata** | tie
| la | **falda** | skirt
| las | **medias** | tights
| la | **moda** | fashion
| la | **parka** | parka
| la | **ropa** | clothes
| la | **ropa interior** | underwear
| la | **sandalia** | sandal
| la | **talla** | size
**IMPORTANT WORDS** __(feminine)__
| la | **americana** | jacket ( _for man_ )
| la | **blusa** | blouse
| la | **bota** | boot
| las | **prendas de vestir** | clothes
| la | **zapatilla** | slipper
**USEFUL PHRASES**
por la mañana me visto in the morning I get dressed
por la tarde me desvisto in the evening I get undressed
cuando llego a casa del colegio me cambio when I get home from school I get changed
llevar, llevar puesto to wear
ponerse to put on
eso es muy elegante that's very smart
(eso) te queda bien that suits you
¿qué talla tienes ( _or_ tiene)? what size do you take?
¿qué número de pie tienes ( _or_ tiene)? what shoe size do you take?
tengo un 38 (de pie), calzo un 38 I take size 38 in shoes
**USEFUL WORDS** __(masculine)__
---
| los | **accesorios** | accessories
| el | **bastón** ( _pl_ bastones) | walking stick
| el | **bolso bandolera** ( _pl_ ~s ~) | shoulder bag
| el | **cárdigan** ( _pl_ ~s) | cardigan
| el | **chaleco** | vest; waistcoat
| el | **chándal** ( _pl_ ~s) | tracksuit
| los | **cordones** | (shoe)laces
| el | **delantal** | apron
| el | **desfile de moda** | fashion show
| el | **foulard** ( _pl_ ~s) | scarf
| el | **lazo** | ribbon
| el | **mono** | overalls
| el | **ojal** | buttonhole
| los | **pantis** | tights
| el | **pañuelo** | scarf
| el | **peto** | overalls; dungarees
| el | **polar** | fleece
| el | **polo** | polo shirt
| el | **probador** | fitting room
| el | **sujetador** | bra
| el | **traje de chaqueta** | suit ( _for woman_ )
| el | **traje de etiqueta** | evening dress ( _for man_ )
| el | **traje de noche** | evening dress ( _for woman_ )
| el | **traje pantalón** ( _pl_ ~s ~) | trouser suit
| los | **tirantes** | braces
| el | **vestido de novia** | wedding dress
| los | **zapatos de tacón** | high heels
| los | **zapatos de tacón de aguja** | stiletto heels
**USEFUL WORDS** __(feminine)__
---
| la | **alpargata** | espadrille
| la | **alta costura** | haute couture
| la | **bandolera** | shoulder bag
| la | **bata** | dressing gown
| las | **bermudas** | Bermuda shorts
| la | **boina** | beret
| la | **bufanda** | scarf
| la | **camiseta con capucha** | hooded top
| la | **camiseta sin mangas** | tank top
| las | **chanclas** | flip flops
| la | **cinta** | ribbon
| la | **colada** | washing
| la | **combinación** ( _pl_ combinaciones) | underskirt
| la | **cremallera** | zip
| la(s) | **enagua(s)** | underskirt
| la | **falda pantalón** ( _pl_ ~s ~) | culottes
| la | **gorra** | cap
| la | **limpieza en seco** | dry-cleaning
| la | **manga** | sleeve
| las | **medias** | stockings
| la | **pajarita** | bow tie
| la | **rebeca** | cardigan
| la | **ropa blanca** | washing
| la | **sudadera** | sweatshirt
| las | **zapatillas de deporte** | trainers
**USEFUL PHRASES**
largo(a) long; corto(a) short
un vestido de manga corta/larga a short-sleeved/long-sleeved dress
estrecho(a), ajustado(a) tight
amplio(a), suelto(a) loose
una falda ajustada _or_ ceñida a tight skirt
a rayas, de rayas striped; a cuadros, de cuadros checked; de lunares spotted
ropa de sport, ropa informal casual clothes
con vestido de noche in evening dress
a la moda, de moda fashionable; moderno(a) trendy
pasado(a) de moda, anticuado(a) old-fashioned
#
colours
**amarillo(a)** | yellow
---|---
**azul** | blue
**azul celeste** | sky blue
**azul claro** | pale blue
**azul marino** | navy blue
**azul oscuro** | dark blue
**azul real** | royal blue
**beige,** **beis** | beige
**blanco(a)** | white
**burdeos** ( _pl inv_ ) | maroon
**crudo(a)** | natural
**dorado(a)** | golden
**granate** | maroon
**gris** | grey
**malva** | mauve
**marrón** ( _pl_ marrones) | brown
**morado(a)** | purple
**naranja** | orange
**negro(a)** | black
**rojo(a)** | red
**rojo fuerte** _or_ **intenso** | bright red
**rosa** | pink
**turquesa** | turquoise
**verde** | green
**violeta** | violet
**USEFUL PHRASES**
el color colour
¿de qué color tienes ( _or_ tiene) los ojos/el pelo? what colour are your eyes/ is your hair?
el azul te sienta bien blue suits you; the blue one suits you
pintar algo de azul to paint sth blue
los zapatos azules blue shoes
los zapatos azul claro light blue shoes
(ella) tiene los ojos verdes she has green eyes
cambiar de color to change colour
la Casa Blanca the White House
un (hombre) blanco a white man
una (mujer) blanca a white woman
un (hombre) negro a black man
una (mujer) negra a black woman
blanco como la nieve as white as snow
Blancanieves Snow White
Caperucita Roja Little Red Riding Hood
ponerse colorado(a) _or_ rojo(a) to turn red
sonrojarse de vergüenza to blush with shame
blanco(a) como el papel as white as a sheet
muy moreno(a), muy bronceado(a) as brown as a berry
(él) estaba cubierto de cardenales he was black and blue
un ojo morado a black eye
un filete muy poco hecho a very rare steak, an underdone steak
# computing and IT
**ESSENTIAL WORDS** __(masculine)__
---
| el | **ordenador (personal)** | (personal) computer
| el | **programa** | program
| el | **programador** | programmer
| el | **ratón** ( _pl_ ratones) | mouse
**USEFUL WORDS** __(masculine)__
| el | **cartucho de tinta** | ink cartridge
| el | **CD-ROM** ( _pl inv_ ) | CD-ROM
| el | **corrector ortográfico** | spellchecker
| el | **correo electrónico** | email
| el | **cursor** | cursor
| los | **datos** | data
| el | **disco duro** | hard disk
| el | **disquete** | floppy disk
| el | **documento** | document
| el | **fichero** | file
| el | **icono** | icon
| el | **internauta** | internet user
| el | **Internet** | internet
| el | **juego de ordenador** | computer game
| el | **mail** ( _pl_ ~s) | email
| el | **menú** | menu
| el | **módem** ( _pl_ ~s) | modem
| el | **monitor** | monitor
| el | **navegador** | browser
| el | **ordenador portátil** | laptop
| el | **paquete de programas** | software package
| el | **pirata informático** | hacker
| el | **procesador de textos** | wordprocessor
| el | **servidor** | server
| el | **sitio web** | website
| el | **software** ( _pl inv_ ) | software
| el | **soporte (físico)** | hardware
| el | **teclado** | keyboard
| el | **virus** ( _pl inv_ ) | virus
| el | **Web** ( _pl_ ~s) | Web
| el | **wifi** | wifi
**ESSENTIAL WORDS** __(feminine)__
---
| la | **impresora** | printer
| la | **informática** | computer science; computer
| | | studies
**USEFUL WORDS** __(feminine)__
| la | **aplicación** ( _pl_ aplicaciones) | program
| la | **banda ancha** | broadband
| la | **base de datos** | database
| la | **computadora (personal)** ( _LAm_ ) | (personal) computer
| la | **copia de seguridad** | back-up
| la | **copia impresa** | print-out
| la | **dirección de correo (electrónico)** | e-mail address
| | ( _pl_ direcciones ~ ~ (~)) |
| la | **función** ( _pl_ funciones) | function
| la | **grabadora de DVD** | DVD writer
| la | **hoja de cálculo** | spreadsheet
| la | **interfaz** ( _pl_ interfaces) | interface
| la | **internauta** | internet user
| la | **Internet** | Internet
| la | **llave USB** | USB key
| la | **memoria** | memory
| la | **memoria RAM** | RAM, random-access memory
| la | **memoria ROM** | ROM, read-only Memory
| la | **página de inicio** | home page
| la | **pantalla** | screen
| la | **papelera de reciclaje** | recycle bin
| la | **red** | network
| la | **unidad de disco** | disk drive
| la | **ventana** | window
| la | **Web** ( _pl_ ~s) | Web
| la | **webcam** ( _pl_ ~s) | webcam
**USEFUL PHRASES**
copiar to copy; eliminar, suprimir to delete; formatear to format
descargar un archivo to download a file
guardar to save; imprimir to print; teclear to key
navegar por Internet to surf the internet
#
countries and nationalities
**COUNTRIES**
---
**ESSENTIAL WORDS** __(masculine)__
| | **Canadá** | Canada
| | **EE.UU.** | USA
| | **Estados Unidos** | United States
| | **país** | country
| | **Países Bajos** | Netherlands
| | **Reino Unido** | United Kingdom
**USEFUL WORDS** __(masculine)__
| | **Brasil** | Brazil
| | **Ecuador** | Ecuador
| | **El Salvador** | El Salvador
| | **Japón** | Japan
| | **Marruecos** | Morocco
| | **México** | Mexico
| | **Pakistán** | Pakistan
| | **Panamá** | Panama
| | **Paraguay** | Paraguay
| | **Perú** | Peru
| | **Tercer Mundo** | Third World
| | **Túnez** | Tunisia
| | **Uruguay** | Uruguay
**USEFUL PHRASES**
mi país de origen my native country
la capital de España the capital of Spain
¿de qué país eres ( _or_ es)? what country do you come from?
soy de (los) Estados Unidos/de Canadá I come from the United States/ from Canada
nací en Escocia I was born in Scotland
me voy a los Países Bajos I'm going to the Netherlands
acabo de regresar de (los) Estados Unidos I have just come back from the United States
los países en (vías de) desarrollo the developing countries
países de habla hispana Spanish-speaking countries
**ESSENTIAL WORDS** __(feminine)__
---
| | **América** | America
| | **América del Sur** | South America
| | **Alemania** | Germany
| | **Bélgica** | Belgium
| | **Escocia** | Scotland
| | **España** | Spain
| | **Europa** | Europe
| | **Francia** | France
| | **Gran Bretaña** | Great Britain
| | **Holanda** | Holland
| | **Inglaterra** | England
| | **Irlanda (del Norte)** | (Northern) Ireland
| | **Italia** | Italy
| | **(el País de) Gales** | Wales
| | **Sudamérica** | South America
| | **Suiza** | Switzerland
| | **USA** | USA
**USEFUL WORDS** __(feminine)__
| | **África** | Africa
| | **Argelia** | Algeria
| | **Asia** | Asia
| | **Bolivia** | Bolivia
| | **Colombia** | Colombia
| | **Costa Rica** | Costa Rica
| | **Cuba** | Cuba
| | **Francia** | France
| | **Grecia** | Greece
| | **Guatemala** | Guatemala
| la | **India** | India
| | **Nicaragua** | Nicaragua
| la | **República Dominicana** | the Dominican Republic
| la | **Unión Europea, UE** | the European Union, the EU
| | **Venezuela** | Venezuela
**NATIONALITIES**
---
**ESSENTIAL WORDS** __(masculine)__
| un | **alemán** ( _pl_ alemanes) | a German
| un | **americano** | an American
| un | **belga** | a Belgian
| un | **británico** | a Briton
| un | **canadiense** | a Canadian
| un | **escocés** ( _pl_ escoceses) | a Scot
| un | **español** | a Spaniard
| un | **europeo** | a European
| un | **francés** ( _pl_ franceses) | a Frenchman
| un | **galés** ( _pl_ galeses) | a Welshman
| un | **holandés** ( _pl_ holandeses) | a Dutchman
| un | **inglés** ( _pl_ ingleses) | an Englishman
| un | **irlandés** ( _pl_ irlandeses) | an Irishman
| un | **italiano** | an Italian
| un | **pakistaní** ( _pl_ ~es _or_ ~s) | a Pakistani
| un | **suizo** | a Swiss (man _or_ boy)
**USEFUL PHRASES**
(él) es irlandés he is Irish
(ella) es irlandesa she is Irish
la campiña irlandesa the Irish countryside
una ciudad irlandesa an Irish town
**ESSENTIAL WORDS** __(feminine)__
---
| una | **alemana** | a German
| una | **americana** | an American
| una | **belga** | a Belgian
| una | **británica** | a Briton, a British woman _or_ girl
| una | **canadiense** | a Canadian
| una | **escocesa** | a Scot
| una | **española** | a Spaniard
| una | **europea** | a European
| una | **francesa** | a Frenchwoman, a French girl
| una | **galesa** | a Welshwoman, a Welsh girl
| una | **holandesa** | a Dutchwoman, a Dutch girl
| una | **inglesa** | an Englishwoman, an English
| | | girl
| una | **irlandesa** | an Irishwoman, an Irish girl
| una | **italiana** | an Italian
| una | **pakistaní** ( _pl_ ~es _or_ ~s) | a Pakistani
| una | **suiza** | a Swiss girl _or_ woman
**USEFUL PHRASES**
soy escocés – hablo inglés I am Scottish – I speak English
soy escocesa I am Scottish
un(a) extranjero(a) a foreigner
en el extranjero abroad
la nacionalidad nationality
**USEFUL WORDS** __(masculine)__
---
| un | **africano** | an African
| un | **antillano** | a West Indian
| un | **árabe** | an Arab
| un | **argelino** | an Algerian
| un | **argentino** | an Argentinian
| un | **boliviano** | a Bolivian
| un | **brasileño** | a Brazilian
| un | **chileno** | a Chilean
| un | **chino** | a Chinese
| un | **colombiano** | a Colombian
| un | **costarricense ** | a Costa Rican
| un | **cubano** | a Cuban
| un | **dominicano** | a Dominican
| un | **ecuatoriano** | an Ecuadorean
| un | **griego** | a Greek
| un | **guatemalteco** | a Guatemalan
| un | **indio** | an Indian
| un | **japonés** ( _pl_ japoneses) | a Japanese
| un | **marroquí** ( _pl_ ~es _or_ ~s) | a Moroccan
| un | **mexicano** | a Mexican
| un | **nicaragüense** | a Nicaraguan
| un | **panameño** | a Panamanian
| un | **paraguayo** | a Paraguayan
| un | **peruano** | a Peruvian
| un | **ruso** | a Russian
| un | **salvadoreño** | a Salvadorian
| un | **tunecino** | a Tunisian
| un | **turco** | a Turk
| un | **uruguayo** | a Uruguayan
| un | **venezolano** | a Venezuelan
**USEFUL WORDS** __(feminine)__
---
| una | **africana** | an African
| una | **antillana** | a West Indian
| una | **árabe** | an Arab
| una | **argelina** | an Algerian
| una | **argentina** | an Argentinian
| una | **boliviana** | a Bolivian
| una | **brasileña** | a Brazilian
| una | **chilena** | a Chilean
| una | **china** | a Chinese
| una | **colombiana** | a Colombian
| una | **costarricense** | a Costa Rican
| una | **cubana** | a Cuban
| una | **dominicana** | a Dominican
| una | **ecuatoriana** | an Ecuadorean
| una | **griega** | a Greek
| una | **guatemalteca** | a Guatemalan
| una | **india** | an Indian
| una | **japonesa** | a Japanese
| una | **marroquí** ( _pl_ ~es _or_ ~s) | a Moroccan
| una | **mexicana** | a Mexican
| una | **nicaragüense** | a Nicaraguan
| una | **panameña** | a Panamanian
| una | **paraguaya** | a Paraguayan
| una | **peruana** | a Peruvian
| una | **rusa** | a Russian
| una | **salvadoreña** | a Salvadorian
| una | **tunecina** | a Tunisian
| una | **turca** | a Turk
| una | **uruguaya** | a Uruguayan
| una | **venezolana** | a Venezuelan
#
countryside
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aire** | air
| el | **albergue juvenil** | youth hostel
| el | **árbol** | tree
| el | **arroyo** | stream
| el | **bastón** ( _pl_ bastones) | walking stick
| el | **bosque** | wood; forest
| el | **camino** | way
| el | **campesino** | countryman; farmer
| el | **campo** | country; countryside
| el | **castillo** | castle
| el | **cazador** | hunter
| el | **granjero** | farmer
| el | **mercado** | market
| el | **paisaje** | scenery
| el | **paseo** | walk
| el | **picnic** ( _pl inv or_ ~s) | picnic
| el | **prado** | field
| el | **pueblo** | village
| el | **puente** | bridge
| el | **río** | river
| el | **ruido** | noise
| el | **sendero** | path; track
| el | **terreno** | soil; ground
| el | **turista** | tourist
| el | **valle** | valley
**USEFUL PHRASES**
al aire libre in the open air
sé el camino al pueblo I know the way to the village
salir en bicicleta to go cycling
los vecinos _or_ los habitantes de la zona the locals
fuimos de picnic we went for a picnic
**ESSENTIAL WORDS** __(feminine)__
---
| la | **barrera** | gate; fence
| la | **camioneta** ( _Sp_ ) | van
| la | **campesina** | countrywoman; farmer
| la | **carretera** | road
| la | **cazadora** | hunter
| la | **excursión** ( _pl_ excursiones) | hike
| la | **granja** | farm, farmhouse
| la | **granjera** | farmer
| la | **montaña** | mountain
| la | **piedra** | stone; rock
| la | **región** ( _pl_ regiones) | district
| la | **tierra** | land; earth; soil; ground
| la | **torre** | tower
| la | **turista** | tourist
| la | **vagoneta** ( _Mex_ ) | van
| la | **valla** | fence
**USEFUL PHRASES**
en el campo in the country
ir (de excursión) al campo to go into the country
vivir en el campo/en la ciudad to live in the country/in town
cultivar la tierra to cultivate the land
**IMPORTANT WORDS** __(masculine)__
---
| el | **agricultor** ( _Sp_ ) | farmer
| el | **guardia civil** | civil guard ( _person_ )
| el | **lago** | lake
| el | **mesón** ( _pl_ mesones) | inn
| el | **polvo** | dust
| el | **ranchero** ( _Mex_ ) | farmer
**USEFUL WORDS** __(masculine)__
| los | **anteojos de larga vista** ( _LAm_ ) | binoculars
| el | **arbusto** | bush
| el | **barro** | mud
| el | **brezo** | heather
| el | **charco** | puddle
| el | **estanque** | pond
| el | **guijarro** | pebble
| el | **heno** | hay
| el | **matorral** | bush
| el | **molino (de viento)** | (wind)mill
| el | **palo** | stick
| el | **pantano** | marsh
| el | **páramo** | moor
| el | **poste telegráfico** | telegraph pole
| el | **prado** | meadow
| los | **prismáticos** ( _Sp_ ) | binoculars
| el | **seto** | hedge
| el | **trigo** | corn; wheat
**USEFUL PHRASES**
agrícola agricultural
apacible, tranquilo(a) peaceful
en la cima de la colina at the top of the hill
caer en una trampa to fall into a trap
**IMPORTANT WORDS** __(feminine)__
---
| la | **agricultora** ( _Sp_ ) | farmer
| la | **agricultura** | agriculture
| la | **calzada** | road surface
| la | **catiusca, katiuska** | (wellington) boot
| la | **cima** | top ( _of hill_ )
| la | **colina** | hill
| la | **gente del campo** | country people
| la | **guardia civil** | civil guard ( _person_ )
| la | **Guardia Civil** | Civil Guard
| la | **hoja** | leaf
| la | **posada** | inn
| la | **propiedad** | property; estate
| la | **ranchera** ( _Mex_ ) | farmer
| la | **tranquilidad** | peace
**USEFUL WORDS** __(feminine)__
| la | **aldea** | hamlet
| la | **bota de goma** | (wellington) boot
| la | **cantera** | quarry
| la | **cascada** | waterfall
| la | **caverna** | cave
| la | **caza** | hunting; shooting
| la | **cosecha** | crop; harvest
| la | **fuente** | spring; source
| la | **furgoneta** | van
| la | **llanura** | plain
| la | **orilla** | bank ( _of river_ )
| las | **ruinas** | ruins
| la | **señal** | signpost
| la | **trampa** | trap
| la | **vendimia** | grape harvest
| la | **zanja** | ditch
**USEFUL PHRASES**
perderse to lose one's way
recoger la cosecha to bring in the harvest
vendimiar, hacer la vendimia to harvest the grapes
#
describing people
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aspecto** | appearance
| el | **bigote** | moustache
| el | **cabello** | hair
| el | **color** | colour
| los | **ojos** | eyes
| el | **talle** | waist
**USEFUL PHRASES**
alegre cheerful
alto(a) tall
amable nice
antiguo(a) old
asqueroso(a) disgusting
bajo(a) short
barbudo(a), con barba bearded, with a beard
bonito(a) pretty
bueno(a) kind
calvo(a) bald
delgado(a) skinny
desagradable unpleasant
dinámico(a) dynamic
divertido(a), entretenido(a) amusing, entertaining
educado(a) polite
esbelto(a) slim
estupendo(a) great
feliz ( _pl_ felices) happy
feo(a) ugly
gordo(a) fat
gracioso(a) funny
grosero(a) rude
guapo handsome; guapa beautiful
horrible hideous
infeliz ( _pl_ infelices), desgraciado(a) unhappy, unfortunate
inquieto(a) agitated
inteligente intelligent
**ESSENTIAL WORDS** __(feminine)__
---
| la | **barba** | beard
| la | **edad** | age
| la | **estatura** | height; size
| las | **gafas** | glasses
| la | **identidad** | ID
| la | **lágrima** | tear
| la | **persona** | person
| la | **talla** | size; height
**USEFUL PHRASES**
joven ( _pl_ jóvenes) young
largo(a) long
malo(a) naughty
mono(a) cute
nervioso(a), tenso(a) nervous, tense
optimista/pesimista optimistic/pessimistic
pequeño(a) small, little
que se porta bien well-behaved
serio(a) serious
tímido(a) shy
tonto(a) stupid
tranquilo(a) calm
viejo(a) old
(ella) parece triste she looks sad
(él) estaba llorando he was crying
(él) sonreía he was smiling
(él) tenía lágrimas en los ojos he had tears in his eyes
un hombre de estatura mediana a man of average height
mido 1 metro 70 _or_ uno setenta _or_ 1,70 I am 1 metre 70 tall
¿de qué color son tus ( _or_ sus) ojos/es tu ( _or_ su) pelo? what colour are your eyes/is your hair?
tengo el pelo rubio I have fair hair
tengo los ojos azules/verdes I have blue/green eyes
pelo moreno _or_ castaño dark _or_ brown hair
pelo castaño light brown hair; pelo rizado curly hair; pelirrojo(a) red-haired
pelo negro/canoso black/grey hair
pelo teñido dyed hair
**IMPORTANT WORDS** __(masculine)__
---
| el | **carácter** ( _pl_ caracteres) | character; nature
| el | **grano** | spot
| el | **humor** | mood
**USEFUL WORDS** __(masculine)__
| el | **cerquillo** ( _LAm_ ) | fringe
| el | **defecto** | fault
| el | **fleco** ( _Mex_ ), el **flequillo** ( _Sp_ ) | fringe
| el | **gesto** | gesture
| el | **gigante** | giant
| los | **hoyuelos** | dimples
| el | **lunar** | mole, beauty spot
| el | **parecido** | resemblance
| el | **peso** | weight
| el | **rizo** | curl
**USEFUL PHRASES**
(él) tiene buen carácter he is good-tempered
(él) tiene mal genio _or_ carácter he is bad-tempered
tener la tez pálida _or_ muy blanca to have a pale complexion
llevar gafas/lentes de contacto _or_ lentillas to wear glasses/contact lenses
**IMPORTANT WORDS** __(feminine)__
---
| la | **belleza** | beauty
| la | **calidad** | (good) quality
| la | **costumbre** | habit
| la | **curiosidad** | curiosity
| la | **expresión** ( _pl_ expresiones) | expression
| la | **fealdad** | ugliness
| las | **lentillas** | contact lenses
| la | **mirada** | look
| la | **sonrisa** | smile
| la | **tez** ( _pl_ teces) | complexion
| la | **voz** ( _pl_ voces) | voice
**USEFUL WORDS** __(feminine)__
| las | **arrugas** | wrinkles
| la | **cicatriz** ( _pl_ cicatrices) | scar
| la | **dentadura (postiza)** | false teeth
| las | **pecas** | freckles
| la | **permanente** | perm
| la | **timidez** | shyness
**USEFUL PHRASES**
siempre estoy de buen humor I am always in a good mood
(él) está de mal humor he is in a bad mood
(él) se enfadó he got angry
(ella) se parece a su madre she looks like her mother
(él) se muerde las uñas he bites his nails
#
education
**ESSENTIAL WORDS** __(masculine)__
---
| el | **alemán** | German
| el | **alfabeto** | alphabet
| el | **alumno** | pupil; schoolboy
| el | **amigo** | pal
| el | **aprendizaje** | apprenticeship
| el | **club** ( _pl_ ~s _or_ ~es) | club
| el | **colegio** | school
| el | **colegio de secundaria** | secondary school
| el | **comedor** | dining hall
| el | **comienzo del curso** | beginning of term
| el | **compañero de clase** | school friend
| el | **concierto** | concert
| el | **cuaderno** | notebook; exercise book
| los | **deberes** | homework
| el | **día** | day
| el | **dibujo** | drawing
| el | **director** | headmaster
| el | **dormitorio** | dormitory
| el | **error** | mistake
| el | **escolar** | schoolboy
| el | **español** | Spanish
| el | **estudiante** | student
| el | **estudio (de)** | study (of)
| los | **estudios** | studies
| el | **examen** ( _pl_ exámenes) | exam
| el | **examen de prueba** | mock exam
| | ( _pl_ exámenes ~ ~) |
| el | **experimento** | experiment
| el | **fallo** | mistake
| el | **francés** | French
| el | **gimnasio** | gym
| el | **grupo** | group
| el | **horario** | timetable
| el | **IES (Instituto de** | comprehensive school
| | **Enseñanza Secundaria)** |
| el | **inglés** | English
| el | **instituto** | secondary school
| el | **intercambio** | exchange
| el | **italiano** | Italian
**ESSENTIAL WORDS** __(feminine)__
---
| la | **alberca** ( _Mex_ ) | swimming pool
| la | **alumna** | pupil; schoolgirl
| la | **amiga** | pal
| el | **aula** ( _pl f_ las aulas) | classroom
| la | **biología** | biology
| la | **cafetería** | canteen
| las | **ciencias** | science
| la | **clase** | class; year; classroom
| las | **clases** | lessons
| las | **clases prácticas** | practical class
| la | **compañera de clase** | school friend
| la | **directora** | headmistress
| la | **educación física** | PE
| la | **electrónica** | electronics
| la | **enseñanza** | education; teaching
| la | **escolar** | schoolgirl
| la | **escuela** | school
| la | **escuela de primaria** | primary school
| la | **escuela infantil** | nursery school
| la | **estudiante** | student
| la | **excursión** ( _pl_ excursiones) | trip; outing
| la | **exposición** ( _pl_ exposiciones) | presentation
| la | **física** | physics
| la | **frase** | sentence
| la | **geografía** | geography
| la | **gimnasia** | gym
| la | **goma (de borrar)** | rubber
| la | **grabadora** | tape recorder
| la | **guardería** | nursery school
| la | **historia** | history; story
| la | **informática** | computer studies
| la | **lección** ( _pl_ lecciones) | lesson
| la | **lectura** | reading
| las | **lenguas (modernas)** | (modern) languages
| la | **maestra de primaria** | primary schoolteacher
| | _or_ **de infantil** |
| las | **matemáticas** | mathematics
| la | **materia (escolar)** | (school) subject
**ESSENTIAL WORDS** __(masculine continued)__
| el | **laboratorio** | laboratory
| el | **lápiz** ( _pl_ lápices) | pencil
| el | **libro** | book
| el | **maestro de primaria** | primary schoolteacher
| | _or_ **de infantil** |
| el | **mapa** | map
| el | **ordenador** | computer
| el | **premio** | prize
| el | **profesor** | teacher
| el | **progreso** | progress
| el | **recreo** | break; playtime
| el | **resultado** | result
| el | **semestre** | semester
| el | **trabajo** | work
| los | **trabajos manuales** | handicrafts
**USEFUL PHRASES**
trabajar to work
aprender to learn
estudiar to study
¿cuánto tiempo llevas ( _or_ lleva) aprendiendo español? how long have you been learning Spanish?
aprenderse algo de memoria to learn sth off by heart
tengo deberes/tareas todos los días _or_ a diario I have homework every day
mi hermana pequeña va a primaria/al colegio – yo voy a secundaria _or_ al instituto my little sister goes to primary school – I go to secondary school
enseñar español to teach Spanish
el/la profesor(a) de alemán the German teacher
he mejorado en matemáticas I have made progress in maths
hacer un examen to sit an exam
aprobar un examen to pass an exam
suspender un examen to fail an exam
sacar un aprobado to get a pass mark
**ESSENTIAL WORDS** __(feminine continued)__
---
| las | **mates** | maths
| la | **música** | music
| la | **natación** | swimming
| la | **nota** | mark
| la | **palabra** | word
| la | **piscina** | swimming pool
| la | **pizarra** | blackboard
| la | **pregunta** | question
| la | **profesora** | teacher
| la | **química** | chemistry
| la | **respuesta** | answer
| la | **sala de profesores** | staffroom
| la | **tarea** | homework; task
| la | **universidad** | university
| las | **vacaciones** | holidays
| las | **vacaciones de verano** | summer holidays
**USEFUL PHRASES**
fácil easy; difícil difficult
interesante interesting
aburrido(a) boring
leer to read; escribir to write
escuchar to listen (to)
mirar to look at, watch
repetir to repeat
responder to reply
hablar to speak
es la primera _or_ mejor de la clase she is top of the class
es la última _or_ peor de la clase she is bottom of the class
entrar en clase to go into the classroom
cometer un error _or_ fallo to make a mistake
corregir to correct
cometí un error gramatical I made a grammatical error
he sacado buena nota I got a good mark
¡responde a la pregunta! answer the question!
¡levantad la mano! put your hand up!
**IMPORTANT WORDS** __(masculine)__
---
| el | **bachillerato** , el **bachiller** | higher school-leaving course/
| | | certificate
| el | **certificado** | certificate
| el | **colegio concertado** | grant-aided school
| el | **colegio privado** | private school
| el | **colegio público** | state school
| el | **despacho** | office
| el | **día libre** | day off
| el | **diploma** | diploma
| el | **estuche** | pencil case
| el | **examen escrito** ( _pl_ exámenes ~s) | written exam
| el | **examen oral** ( _pl_ exámenes ~es) | oral exam
| el | **expediente** | file
| el | **papel** | paper
| el | **pasillo** | corridor
| el | **patio (de recreo)** | playground
**USEFUL PHRASES**
mi amigo se está preparando la selectividad my friend is sitting his university entrance exam
repasar (la lección) to revise
repasaré otra vez la lección mañana I'll go over the lesson again tomorrow
**IMPORTANT WORDS** __(feminine)__
---
| la | **ausencia** | absence
| la | **carpeta** | folder; file
| la | **conferencia** | lecture
| las | **normas** | rules
| las | **notas** | report
| la | **oposición** ( _pl_ oposiciones) | competitive exam
| la | **regla** | rule; ruler
| la | **selectividad** ( _Sp_ ) | entrance examination
| la | **traducción** ( _pl_ traducciones) | translation
| la | **versión** ( _pl_ versiones) | translation
| | | ( _from foreign language to English_ )
**USEFUL PHRASES**
en segundo de primaria in year two
en primero de ESO in year seven
en segundo de ESO in year eight
en tercero de ESO in year nine
en cuarto de ESO in year ten
en primero de bachillerato in year eleven
presente present
ausente absent
castigar a un(a) alumno(a) to punish a pupil
el/la profesor(a) los castigó sin recreo the teacher kept them in at break time
¡silencio!, ¡callaos! be quiet!
**USEFUL WORDS** __(masculine)__
---
| el | **bedel** | janitor
| el | **bloc** ( _pl_ ~s) | jotter
| el | **boli, bolígrafo** | Biro®
| el | **borrador** | rough copy
| el | **cálculo** | sum
| el | **castigo** | detention; punishment
| el | **comportamiento** | behaviour
| el | **corrector (líquido)** | correction fluid
| el | **diccionario** | dictionary
| el | **ejercicio** | exercise
| el | **examinador** | examiner
| el | **griego** | Greek
| el | **jefe de estudios** | director of studies
| el | **inspector** | school inspector
| el | **internado** | boarding school
| el | **interno** | boarder
| el | **latín** | Latin
| el | **libro de texto** | textbook
| el | **maletín** ( _pl_ maletines) | briefcase
| el | **parte (de faltas** _or_ **ausencias)** | absence sheet
| el | **parvulario** | nursery school
| el | **profesor consejero** | form tutor
| el | **pupitre** | desk
| el | **rotulador** | felt-tip pen
| el | **sacapuntas** ( _pl inv_ ) | pencil sharpener
| el | **test** ( _pl_ ~s) | test
| el | **trabajo** | essay; class exam
| el | **trimestre** | term
| el | **vestuario** | cloakroom
| el | **vocabulario** | vocabulary
**USEFUL WORDS** __(feminine)__
---
| el | **álgebra** ( _f_ ) | algebra
| la | **aritmética** | arithmetic
| la | **bedel** | janitor
| la | **calculadora** | calculator
| la | **caligrafía** | handwriting
| la | **carpintería** | woodwork
| la | **cartera** | satchel; schoolbag; briefcase
| las | **ciencias del medio ambiente** | natural science
| las | **ciencias naturales** | natural history
| la | **enseñanza religiosa** | religious instruction
| la | **entrega de premios** | prize-giving
| la | **ESO (Educación Secundaria** | compulsory secondary
| | **Obligatoria)** ( _Sp_ ) | education
| la | **facultad** | faculty
| la | **fila** | row ( _of seats etc_ )
| la | **FP (formación profesional)** ( _Sp_ ) | technical college
| la | **geometría** | geometry
| la | **gramática** | grammar
| la | **inspectora** | school inspector
| la | **interna** | boarder
| la | **mancha** | blot
| la | **nota media** | pass mark; average mark
| la | **ortografía** | spelling
| la | **pizarra (electrónica)** | interactive whiteboard
| | **interactiva** |
| la | **poesía** | poetry; poem
| la | **prueba** | test
| las | **TIC (tecnologías de la** | ICT
| | **información y la comunicación)** |
| la | **tinta** | ink
| la | **tiza** | chalk
| la | **traducción inversa** | prose translation
| | ( _pl_ traducciones ~s)
#
environment
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aerogenerador** | wind turbine
| el | **agujero** | hole
| el | **aire** | air
| los | **animales** | animals
| los | **árboles** | trees
| el | **bosque** | wood
| el | **coche** | car
| el | **diesel** | diesel
| el | **ecologista** | environmentalist
| el | **gas** | gas
| los | **gases de escape** | exhaust fumes
| el | **gasoil** | diesel
| los | **habitantes** | inhabitants
| el | **mapa** | map
| el | **mar** | sea
| el | **medio ambiente** | environment
| el | **mundo** | world
| el | **país** | country
| el | **pescado** | fish
| el | **tiempo** | weather; time
| los | **Verdes** | the Greens
| el | **vidrio** | glass
**IMPORTANT WORDS** __(masculine)__
| el | **acontecimiento** | event
| el | **aluminio** | aluminium
| el | **calor** | heat
| el | **clima** | climate
| el | **contaminante** | pollutant
| el | **daño** | damage
| el | **detergente** | detergent; washing powder
| el | **futuro** | future
| el | **gobierno** | government
| el | **impuesto** | tax
| el | **lago** | lake
| el | **parque eólico** | windfarm
| el | **planeta** | planet
| el | **río** | river
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua** ( _f_ ) | water
| las | **botellas** | bottles
| la | **contaminación** | pollution
| la | **costa** | coast
| la | **cuestión** ( _pl_ cuestiones) | question
| la | **ecología** | ecology
| la | **especie** | species
| la | **fábrica** | factory
| la | **flor** | flower
| la | **fruta** | fruit
| la | **gasolina** | petrol
| la | **isla** | island
| la | **lluvia** | rain
| la | **montaña** | mountain
| la | **planta** | plant
| la | **playa** | beach
| la | **región** ( _pl_ regiones) | region; area
| la | **temperatura** | temperature
| la | **tierra** | earth
| la(s) | **verdura(s)** | vegetables
**IMPORTANT WORDS** __(feminine)__
| la | **central nuclear** | nuclear plant
| la | **crisis** ( _pl inv_ ) | crisis
| la | **legumbre** | vegetable
| la | **selva** | forest; jungle
| la | **solución** ( _pl_ soluciones) | solution
| la | **zona** | zone
**USEFUL WORDS** __(masculine)__
---
| el | **aerosol** | aerosol
| los | **alimentos orgánicos** | organic food
| el | **calentamiento global** | global warming
| el | **canal** | canal
| el | **catalizador** | catalytic converter
| el | **CFC (clorofluorocarbono)** | CFC
| los | **científicos** | scientists
| el | **combustible** | fuel
| el | **continente** | continent
| el | **desarrollo sostenible** | sustainable development
| el | **desierto** | desert
| el | **ecosistema** | ecosystem
| el | **fertilizante** | (artificial) fertilizer
| el | **investigador** | researcher
| el | **océano** | ocean
| el | **OGM (organismo** | GMO
| | **genéticamente modificado)** |
| el | **producto** | product
| los | **productos químicos** | chemicals
| el | **reciclado,** el **reciclaje** | recycling
| los | **residuos nucleares/** | nuclear/industrial waste
| | **industriales** |
| el | **universo** | universe
| el | **vertedero** | dumping ground
**USEFUL PHRASES**
(él) es muy respetuoso con el medio ambiente he's very environmentally-minded
un producto ecológico an eco-friendly product
en el futuro in the future
destruir to destroy
contaminar to contaminate; to pollute
prohibir to ban
salvar to save
reciclar to recycle
verde green
**USEFUL WORDS** __(feminine)__
---
| las | **aguas residuales** | sewage
| la | **capa de ozono** | ozone layer
| la | **catástrofe** | disaster
| la | **contaminación acústica** | noise pollution
| la | **energía eólica** | wind power
| la | **energía nuclear** | nuclear power
| la | **energía renovable** | renewable energy
| la | **lluvia ácida** | acid rain
| la | **luna** | moon
| la | **marea negra** | oil slick
| la | **población** ( _pl_ poblaciones) | population
| la | **selva tropical** | tropical rainforest
**USEFUL PHRASES**
biodegradable biodegradable
nocivo(a) _or_ dañino(a) para el medio ambiente harmful to the environment
orgánico(a), biológico(a), ecológico(a) organic
gasolina sin plomo unleaded petrol
(las) especies en peligro de extinción endangered species
#
family
**ESSENTIAL WORDS** __(masculine)__
---
| el | **abuelo** | grandfather
| los | **abuelos** | grandparents
| los | **adultos** | adults
| el | **apellido** | surname
| el | **apellido de soltera** | maiden name
| el | **bebé** | baby
| la | **edad** | age
| el | **hermano** | brother
| el | **hijo** | son
| el | **hombre** | man
| el | **joven** ( _pl_ jóvenes) | youth, young man
| los | **jóvenes** | young people
| el | **marido** | husband
| el | **niño** | child, boy
| el | **nombre** | name
| el | **nombre (de pila)** | first _or_ Christian name
| el | **novio** | fiancé
| el | **padre** | father
| los | **padres** | parents
| el | **papá** | daddy
| el | **pariente** | relative
| el | **primo** | cousin
| el | **prometido** | fiancé
| el | **tío** | uncle
**USEFUL PHRASES**
¿qué edad tiene ( _or_ tienes)?, ¿cuántos años tiene ( _or_ tienes)? how old are you?
tengo 15 años – él tiene 40 años I'm 15 – he is 40
¿cómo se llama ( _or_ te llamas)? what is your name?
me llamo Daniela my name is Daniela
él se llama Paco his name is Paco
prometido(a) engaged
casado(a) married
divorciado(a) divorced
separado(a) separated
casarse con algn to marry sb
casarse to get married; divorciarse to get divorced
**ESSENTIAL WORDS** __(feminine)__
---
| la | **abuela** | grandmother
| la | **familia** | family
| la | **gente** | people
| la | **hermana** | sister
| la | **hija** | daughter; girl
| la | **joven** ( _pl_ jóvenes) | youth
| la | **madre** | mother
| la | **mamá** | mummy
| los | **mayores** | grown-ups
| la | **mujer** | woman; wife
| la | **niña** | child, girl
| la | **novia** | fiancée
| la | **persona** | person
| la | **prima** | cousin
| la | **prometida** | fiancée
| la | **señora** | lady
| la | **tía** | aunt
**USEFUL PHRASES**
más joven/mayor que yo younger/older than me
¿tiene ( _or_ tienes) hermanos? do you have any brothers or sisters?
tengo un hermano y una hermana I have one brother and one sister
no tengo hermanos I don't have any brothers or sisters
soy hijo(a) único(a) I am an only child
toda la familia the whole family
crecer to grow
envejecer, hacerse viejo(a) to get old
me llevo bien con mis padres I get on well with my parents
mi madre trabaja my mother works
**IMPORTANT WORDS** __(masculine)__
---
| el | **adolescente** | teenager
| el | **esposo** | husband
| el | **nieto** | grandson
| los | **nietos** | grandchildren
| el | **padrastro** | stepfather
| el | **sobrino** | nephew
| el | **soltero** | bachelor
| el | **subsidio familiar (por hijos)** | child benefit
| el | **suegro** | father-in-law
| el | **vecino** | neighbour
| el | **viudo** | widower
**USEFUL WORDS** __(masculine)__
| el | **ahijado** | godson
| el | **anciano** | old man
| el | **apodo** | nickname
| el | **chaval,** el **chico** | kid
| el | **cuñado** | brother-in-law
| los | **gemelos** | identical twins
| el | **hermanastro** | stepbrother
| el | **hijastro** | stepson
| el | **huérfano** | orphan
| el | **jubilado** | pensioner
| el | **marido** | bridegroom
| los | **mellizos** | twins
| el | **mote** | nickname
| el | **padrino** | godfather
| los | **recién casados** | newlyweds
| los | **trillizos** | triplets
| el | **viejo** | old man
| el | **yerno** | son-in-law
**USEFUL PHRASES**
nacer to be born; vivir to live; morir to die nací en 1990 I was born in 1990
mi abuela murió _or_ está muerta my grandmother is dead
ella murió en 1995 she died in 1995
**IMPORTANT WORDS** __(feminine)__
---
| la | **adolescente** | teenager
| la | **au pair** ( _pl inv_ ) | au pair girl
| la | **esposa** | wife
| la | **madrastra** | stepmother
| la | **nieta** | granddaughter
| la | **sobrina** | niece
| la | **soltera** | single woman
| la | **suegra** | mother-in-law
| la | **vecina** | neighbour
| la | **viuda** | widow
**USEFUL WORDS** __(feminine)__
| la | **ahijada** | goddaughter
| el | **ama de casa** ( _pl f_ las amas ~ ~) | housewife
| la | **anciana** | old woman
| la | **chavala,** la **chica** | kid
| la | **cuñada** | sister-in-law
| las | **gemelas** | identical twins
| la | **hermanastra** | stepsister
| la | **hijastra** | stepdaughter
| la | **huérfana** | orphan
| la | **jubilada** | pensioner
| la | **madrina** | godmother
| las | **mellizas** | twins, twin sisters
| la | **niñera** | nanny
| la | **novia** | bride
| la | **nuera** | daughter-in-law
| la | **pareja** | couple
| la | **vejez** | old age
| la | **vieja** | old woman
**USEFUL PHRASES**
él/ella es soltero(a) he/she is single
él es viudo he is a widower; ella es viuda she is a widow
soy el/la más joven I am the youngest; soy el/la mayor I am the eldest
mi hermana mayor my older sister
# farm
**ESSENTIAL WORDS** __(masculine)__
---
| el | **agricultor** ( _Sp_ ) | farmer
| el | **animal** | animal
| el | **bosque** | forest
| el | **buey** | ox
| el | **caballo** | horse
| el | **cabrito** | kid
| el | **campo** | field; country
| el | **cerdo** | pig
| el | **chivo** | kid
| el | **gato** | cat
| el | **granjero** | farmer
| el | **invernadero** | greenhouse
| el | **pato** | duck
| el | **pavo** | turkey
| el | **perro** | dog
| el | **perro pastor** ( _pl_ ~s ~) | sheepdog
| el | **pollo** | chicken
| el | **pueblo** | village
| el | **ranchero** ( _Mex_ ) | farmer
| el | **ternero** | calf
**IMPORTANT WORDS** __(masculine)__
| el | **campesino** | countryman
| el | **cordero** | lamb
| el | **gallo** | cock
| el | **tractor** | tractor
**USEFUL PHRASES**
un trigal, un maizal a cornfield
la agricultura ecológica organic farming
los pollos de granja free range chickens
los huevos de corral free range eggs
cuidar los animales to look after the animals
recolectar to harvest
recoger la cosecha to bring in the harvest/crops
**ESSENTIAL WORDS** __(feminine)__
---
| la | **agricultora** ( _Sp_ ) | farmer
| la | **camioneta** ( _Sp_ ) | van
| la | **cerda** | sow
| la | **finca** | farm
| la | **gallina** | hen
| la | **granja** | farm; farmhouse
| la | **granjera** | farmer; farmer's wife
| la | **oveja** | sheep; ewe
| la | **puerta** | gate
| la | **ranchera** ( _Mex_ ) | farmer
| la | **tierra** | earth; ground
| la | **vaca** | cow
| la | **vagoneta** ( _Mex_ ) | van
| la | **valla** | fence
| la | **verja** | gate
| la | **yegua** | mare
**IMPORTANT WORDS** __(feminine)__
| la | **campesina** | countrywoman
| la | **colina** | hill
**USEFUL PHRASES**
vivir en el campo to live in the country
trabajar en una granja to work on a farm
recolectar el heno to make hay
**USEFUL WORDS** __(masculine)__
---
| el | **abono** | manure; fertilizer
| el | **almiar** | haystack
| el | **arado** | plough
| el | **barro** | mud
| el | **burro** | donkey
| el | **carnero** | ram
| el | **centeno** | rye
| el | **cerdo** | pig
| el | **cereal** | cereal, crop
| el | **cobertizo** | shed
| el | **corral** | farmyard
| el | **espantapájaros** ( _pl inv_ ) | scarecrow
| el | **establo** | cow shed, byre
| el | **estanque** | pond
| el | **estiércol** | manure
| el | **gallinero** | henhouse
| el | **ganado** | cattle
| el | **ganso** | goose
| el | **granero** | barn
| el | **grano** | grain, seed
| el | **heno** | hay
| el | **maíz** ( _pl_ maices) | maize
| el | **molino (de viento)** | (wind)mill
| el | **paisaje** | landscape
| el | **pajar** | loft
| el | **páramo** | moor, heath
| el | **pastor** | shepherd
| el | **pollito** | chick
| el | **potro** | foal
| el | **pozo** | well
| el | **prado** | meadow
| el | **rebaño** | ( _sheep_ ) flock; ( _cattle_ ) herd
| el | **suelo** | ground, earth
| el | **surco** | furrow
| el | **toro** | bull
| el | **trigo** | corn; wheat
**USEFUL WORDS** __(feminine)__
---
| la | **avena** | oats
| la | **cabra** | goat
| la | **cabritilla** | kid
| la | **carretilla** | cart
| la | **casita (con el tejado de paja)** | (thatched) cottage
| la | **cebada** | barley
| la | **cosecha** | crop
| la | **cosechadora** | combine harvester
| la | **cuadra** | stable
| la | **escalera** | ladder
| la | **ganadería** | cattle farm
| la | **lana** | wool
| la | **lonja** | market
| la | **paja** | straw
| la | **pocilga** | pigsty
| la | **recolección** ( _pl_ recolecciones) | harvest
| la | **uva** | grapes
| la | **vendimia** | grape harvest, grape picking
| la | **viña** | vine
| la | **zanja** | ditch
#
fish and insects
**ESSENTIAL WORDS** __(masculine)__
---
| el | **marisco** | seafood
| el | **pez** ( _pl_ peces) | fish
| el | **pez de colores** ( _pl_ peces ~ ~) | goldfish
**IMPORTANT WORDS** __(masculine)__
| el | **cangrejo** | crab
| el | **insecto** | insect
**USEFUL WORDS** __(masculine)__
| el | **acuario** | aquarium
| el | **arenque** | herring
| el | **atún** ( _pl_ atunes) | tuna
| el | **avispón** ( _pl_ avispones) | hornet
| el | **bacalao** | cod
| el | **calamar** | squid
| el | **camarón** ( _pl_ camarones) | shrimp
| el | **cangrejo de río** | crayfish
| el | **chinche** | bug
| el | **eglefino** | haddock
| el | **grillo** | cricket
| el | **gusano** | worm
| el | **gusano de seda** | silkworm
| los | **langostinos** | scampi
| el | **lenguado** | sole
| el | **lucio** | pike
| el | **mejillón** ( _pl_ mejillones) | mussel
| el | **mosquito** | mosquito
| el | **pulpo** | octopus
| el | **renacuajo** | tadpole
| el | **salmón** ( _pl_ salmones) | salmon
| el | **saltamontes** ( _pl inv_ ) | grasshopper
| el | **tiburón** ( _pl_ tiburones) | shark
**USEFUL PHRASES**
nadar to swim
volar to fly
vamos a ir a pescar we're going fishing
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua** ( _f_ ) | water
**IMPORTANT WORDS** __(feminine)__
| la | **mosca** | fly
| la | **sardina** | sardine
| la | **trucha** | trout
**USEFUL WORDS** __(feminine)__
| la | **abeja** | bee
| el | **ala** ( _pl f_ las alas) | wing
| la | **anguila** | eel
| la | **araña** | spider
| la | **avispa** | wasp
| la | **cigala** | crayfish
| la | **cigarra** | cicada
| la | **cucaracha** | cockroach
| la | **hormiga** | ant
| la | **langosta** | lobster
| la | **libélula** | dragonfly
| la | **mariposa** | butterfly
| la | **mariquita** | ladybird
| la | **medusa** | jellyfish
| la | **mosquilla** | midge
| la | **mosquita** | midge
| la | **oruga** | caterpillar
| la | **ostra** | oyster
| la | **pescadilla** | whiting
| la | **polilla** | moth
| la | **pulga** | flea
| la | **rana** | frog
**USEFUL PHRASES**
una picadura de avispa a wasp sting
una tela de araña a spider's web
#
food and drink
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aceite** | oil
| el | **agua mineral** | (mineral) water
| el | **alcohol** | alcohol
| el | **almuerzo** | lunch
| el | **aperitivo** | aperitif
| el | **arroz** | rice
| el | **asado** | roast
| el | **autoservicio** | self-service restaurant
| el | **azúcar** | sugar
| el | **bar** | bar
| el | **bistec** ( _pl inv or_ ~s) | steak
| el | **bol** | bowl
| el | **bote** | tin, can
| el | **café** | coffee; café
| el | **café con leche** | coffee with milk
| el | **café con más leche** | milky coffee
| el | **camarero** ( _Sp_ ) | waiter
| los | **caramelos** | sweets
| el | **cerdo** | pork
| los | **cereales** | cereal
| el | **chocolate (caliente)** | (hot) chocolate
| el | **cocinero** | cook
| el | **consomé** | soup
| el | **croissant** _or_ el **cruasán** | croissant
| | ( _pl_ cruasanes) |
| el | **cuarto** | quarter ( _bottle/litre etc_ )
| el | **cuenco** | bowl
| el | **cuchillo** | knife
| el | **desayuno** | breakfast
| el | **dueño** | owner
| los | **entrantes** | hors d'œuvres, starters
| el | **entrecot** ( _pl inv or_ ~s) | (entrecôte) steak
| el | **filete** | steak
| el | **helado** | ice cream
| el | **huevo** | egg
| el | **huevo duro** _or_ **cocido** | hard-boiled egg
| el | **huevo pasado por agua** | soft-boiled egg
| el | **jamón** ( _pl_ jamones) | ham
**ESSENTIAL WORDS** __(feminine)__
---
| la | **aceituna** | olive
| la | **baguette** ( _pl inv or_ ~s) | French loaf
| la | **bandeja** | tray
| la | **bebida** | drink
| la | **botella** | bottle
| la | **caja** | box
| la | **carne** | meat
| la | **carne de vaca** | beef
| la | **carta** | menu
| la | **cena** | dinner
| la | **cerveza** | beer
| la | **Coca-Cola ®** ( _pl_ ~s) | Coke®
| la | **comida** | lunch; meal
| la | **comida precocinada** | ready-made meal
| | _or_ **preparada** |
| las | **conservas** | canned food
| la | **cuchara** | spoon
| la | **cuenta** | bill
| la | **ensalada** | salad
| la | **ensalada mixta** | mixed salad
| la | **fruta** | fruit
| el | **hambre** ( _f_ ) | hunger
| la | **hamburguesa** | hamburger
| la | **lata** | tin, can
| la | **leche** | milk
| la | **limonada** | lemonade
| la | **loncha (de)** | slice (of)
| la | **mantequilla** | butter
| la | **mermelada** | jam
| la | **mermelada (de cítricos)** | marmalade
| la | **mesa** | table
| la | **pastelería** | pastry; cake shop
| las | **patatas fritas** | chips; crisps
| la | **pescadería** | fish shop
| la | **pieza de fruta** | piece of fruit
| la | **repostería** | pastry; cake shop
| la | **sal** | salt
| la | **salchicha** | sausage
**ESSENTIAL WORDS** __(masculine continued)__
---
| el | **marisco** | seafood
| el | **menú del día** | fixed-price menu
| el | **mesero** ( _LAm_ ) | waiter
| el | **pan** | bread
| el | **paté** | pâté
| el | **pescado** | fish
| el | **picnic** ( _pl inv_ _or_ ~s) | picnic
| el | **platillo** | saucer
| el | **plato** | plate; dish; course
| el | **plato del día** | today's special
| el | **pollo (asado)** | (roast) chicken
| el | **postre** | dessert
| el | **primero,** el **primer plato** | first course, starter
| el | **queso** | cheese
| el | **quiche** ( _pl inv_ ) | quiche
| el | **restaurante** | restaurant
| el | **salami,** el **salchichón** | salami
| | ( _pl_ salchichones) |
| el | **sándwich** ( _pl_ ~s _or_ ~es) | sandwich
| el | **self-service** ( _pl inv_ ) | self-service restaurant
| el | **servicio** | service
| el | **té** | tea
| el | **tenedor** | fork
| el | **vaso** | glass
| el | **vinagre** | vinegar
| el | **vino** | wine
| el | **yogur(t)** | yoghurt
| el | **zumo de fruta** | fruit juice
**USEFUL PHRASES**
cocinar to cook; comer to eat
beber to drink; tragar to swallow
mi plato favorito my favourite dish
¿qué vas ( _or_ va) a beber? what are you having to drink?
está bueno _or_ rico it's nice
estar hambriento, tener hambre to be hungry
estar sediendo, tener sed to be thirsty
**ESSENTIAL WORDS** __(feminine continued)__
---
| la | **sed** ( _pl inv_ ) | thirst
| la | **sidra** | cider
| la | **sopa** | soup
| la | **tarta** | cake
| la | **taza** | cup
| la | **ternera** | veal
| la | **tortilla francesa** | omelette
| la | **tortita** | pancake
| la | **tostada** | toast
| la | **vajilla** | dishes
| las | **verduras** | vegetables
**IMPORTANT WORDS** __(feminine)__
| la | **cafetería** | cafeteria
| la | **camarera** | waitress
| la | **carne asada** _or_ **a la parrilla** | grilled meat
| la | **cerveza de barril** | draught beer
| la | **chef** ( _pl inv_ _or_ ~s) | chef
| la | **chuleta de cerdo** | pork chop
| la | **cucharilla** | teaspoon
| la | **cucharita (de postre)** | dessertspoon
| la | **cuchara de servir** | tablespoon
| la | **garrafa** | carafe
| la | **harina** | flour
| la | **jarra** | jug
| la | **mayonesa** | mayonnaise
| la | **mostaza** | mustard
| la | **nata** | cream
| las | **patatas fritas (de bolsa)** | crisps
| la | **pimienta** | pepper
| la | **pizza** | pizza
| la | **propina** | tip
| la | **receta** | recipe
| la | **selección** ( _pl_ selecciones) | choice
| la | **tarta** | tart
| la | **tetera** | teapot
| la | **vainilla** | vanilla
**IMPORTANT WORDS** __(masculine)__
---
| el | **ajo** | garlic
| el | **almíbar** | syrup
| el | **aperitivo** | snack
| el | **camarero** | waiter
| los | **caracoles** | snails
| el | **carrito** | trolley
| el | **chef** ( _pl inv_ _or_ ~s) | chef
| el | **cocinero jefe** | chef
| el | **conejo** | rabbit
| el | **cordero** | lamb; mutton
| el | **cubierto** | cover charge; place setting
| el | **gusto** | taste
| el | **olor** | smell
| el | **precio con todo incluido** | inclusive price
| el | **precio fijo** | set price
| el | **refresco concentrado** | cordial
| el | **restaurante** | restaurant
| el | **sabor** | flavour
| el | **suplemento** | extra charge
| el | **tentempié** | snack
**USEFUL WORDS** __(masculine)__
| el | **abrelatas** ( _pl inv_ ) | tin opener
| el | **aperitivo** | snack
| el | **beicon** | bacon
| el | **biscote** | Melba toast
| el | **bollito** | roll
| el | **bollo** | bun
| el | **cacao** | cocoa
| el | **champán** ( _pl_ champanes) | champagne
| el | **coñac** ( _pl inv_ ) | brandy
| el | **corcho** | cork
| el | **cubito (de hielo)** | ice cube
| el | **estofado** | stew
| el | **foie gras** ( _pl inv_ ) | liver pâté
| el | **hígado** | liver
| el | **ketchup** ( _pl inv_ ) | ketchup
| el | **mantel** | tablecloth
**USEFUL WORDS** __(feminine)__
---
| las | **aves** | poultry
| la | **carta de vinos** | wine list
| la | **caza** | game
| la | **chuleta** | chop
| la | **clara** | shandy
| la | **comida** | food
| la | **gelatina** | jelly
| la | **infusión** ( _pl_ infusiones) | herbal tea
| la | **jarra** | jug
| la | **margarina** | margarine
| la | **miel** | honey
| la | **miga** | crumb
| la | **nata montada** | whipped cream
| las | **natillas** | custard
| la | **pajita** | straw
| la | **pasta** | pasta
| la | **rebanada** | piece of bread and butter
| la | **salsa** | sauce
| la | **salsa de jugo de carne** | gravy
| la | **servilleta** | napkin
| la | **tisana** | herbal tea
| las | **tripas** | tripe
| la | **tostada** | slice of toast
| la | **vinagreta** | vinaigrette dressing
**USEFUL PHRASES**
fregar los platos to do the dishes
cuando volvemos del colegio merendamos we have a snack when we come back from school
desayunar _,_ tomar el desayuno to have breakfast
delicioso(a) delicious; repugnante disgusting
¡que aproveche! enjoy your meal!; ¡salud! cheers!
¡la cuenta, por favor! the bill please!
"servicio (no) incluido" "service (not) included"
comer fuera to eat out
invitar a algn a comer to invite sb to lunch
tomar algo de beber _,_ beber algo to have drinks
**USEFUL WORDS** __(masculine continued)__
---
| los | **mejillones** | mussels
| el | **panecillo** | roll
| el | **paté de carne** | potted meat
| el | **paté de hígado** | liver pâté
| el | **paté de oca** | goose pâté
| el | **puré de patatas** | mashed potatoes
| los | **riñones** | kidneys
| el | **rosbif** ( _pl inv_ _or_ ~s) | roast beef
| el | **sacacorchos** ( _pl inv_ ) | corkscrew
| el | **tapón** ( _pl_ tapones) | cork
| el | **termo** | flask
| el | **torrezno** | diced bacon
| el | **whisky, whiskey** ( _pl_ ~s) | whisky
| el | **zumo natural de limón** | freshly-squeezed lemon juice
**USEFUL PHRASES**
poner la mesa to set the table; quitar la mesa to clear the table
comer, almorzar to have lunch
cenar to have dinner
probar algo to taste sth
¡eso huele bien! that smells good!
vino blanco/rosado/tinto white/rosé/red wine
un filete poco hecho/en su punto/bien hecho a rare/medium/ well-done steak
un sándwich (tostado) de jamón y queso a ham and cheese toastie
**SMOKING**
---
| el | **cenicero** | ashtray
| la | **cerilla** | match
| el | **cigarrillo** | cigarette
| el | **cigarro** | cigar
| el | **estanco** | tobacconist's
| el | **mechero** | lighter
| la | **pipa** | pipe
| el | **tabaco** | tobacco
**USEFUL PHRASES**
una caja de cerillas a box of matches
¿tienes ( _or_ tiene) fuego? do you have a light?
encender un cigarrillo to light up
"prohibido fumar" "no smoking"
no fumo I don't smoke
he dejado de fumar, he dejado el tabaco I've stopped smoking
fumar es perjudicial para tí _or_ la salud smoking is very bad for you
#
free time
**ESSENTIAL WORDS** __(masculine)__
---
| el | **ajedrez** | chess
| el | **amigo por correspondencia** | pen friend
| el | **baile** | dance
| el | **billete** ( _Sp_ ) | ticket
| el | **boleto** ( _LAm_ ) | ticket
| el | **cantante** | singer
| el | **canto** | singing
| el | **CD** ( _pl inv or_ ~s) | CD
| el | **cine** | cinema
| el | **club** ( _pl_ ~s _or_ ~es) | club
| el | **concierto** | concert
| los | **deportes** | sports
| el | **dinero de bolsillo** | pocket money
| el | **disco** | record
| el | **DVD** ( _pl inv or_ ~s) | DVD
| el | **espectáculo** | show
| el | **fin de semana** | weekend
| el | **folleto** | leaflet
| el | **futbolín** ( _pl_ futbolines) | table football
| el | **hobby** ( _pl_ hobbies) | hobby
| el | **Internet** | internet
| el | **juego** | game
| el | **lector de CD/DVD/MP3** | CD/DVD/MP3 player
| el | **miembro** | member
| el | **museo** | museum; art gallery
| el | **paseo** | walk
| el | **periódico** | newspaper
| el | **programa** | programme
| el | **teatro** | theatre
| el | **(teléfono) móvil** ( _Sp_ ) _or_ | mobile (phone)
| | **celular** ( _LAm_ ) |
| el | **tiempo libre** | free time
| el | **videojuego** | video game
| el | **walkman ®** ( _pl_ ~s) | personal stereo
**ESSENTIAL WORDS** __(feminine)__
---
| la | **afición** ( _pl_ aficiones) | hobby
| la | **amiga por correspondencia** | pen friend
| la | **cadena de televisión** | TV channel
| la | **cámara (de fotos)** | camera
| la | **canción** ( _pl_ canciones) | song
| la | **cantante** | singer
| las | **cartas** | cards
| la | **disco(teca)** | disco
| la | **diversión** ( _pl_ diversiones) | entertainment
| la | **estrella (de cine)** ( _m+f_ ) | (film) star
| la | **excursión** ( _pl_ excursiones) | trip; outing; hike
| la | **fiesta** | party
| la | **foto** | photo
| la | **historieta** | comic strip
| la | **lectura** | reading
| la | **música (pop/clásica)** | (pop/classical) music
| las | **noticias** | news
| la | **novela** | novel
| la | **novela policíaca** _or_ **policiaca** | detective novel
| la | **película** | film
| la | **pista de patinaje** | skating rink
| la | **prensa** | the press
| la | **publicidad** | publicity
| la | **radio** | radio
| la | **revista** | magazine
| la | **tele(visión)** ( _pl_ teles, televisiones) | television, TV
| la | **videoconsola** | games console
**USEFUL PHRASES**
salgo con mis amigos I go out with my friends
leo el periódico I read the newspaper
veo la televisión I watch television
juego al fútbol/al tenis/a las cartas I play football/tennis/cards
hacer bricolaje to do DIY
hacer de canguro to baby-sit
hacer zapping to channel-hop
ir de discoteca _or_ marcha ( _Sp_ ) to go clubbing
**IMPORTANT WORDS** __(masculine)__
---
| el | **anuncio** | notice; poster
| los | **anuncios por palabras** | adverts; small ads
| el | **carrete** | film ( _for camera_ )
| el | **compact disc** ( _pl_ ~ ~s) | compact disc, CD
| el | **concurso** | competition
| los | **dibujos animados** | cartoon
| el | **juguete** | toy
| el | **mensaje de texto** | text message
| el | **noticiero** ( _LAm_ ) | news
| el | **novio** | boyfriend
| el | **ordenador (personal)** ( _Sp_ ) | personal computer
| los | **pasatiempos** | leisure activities
| el | **PC** ( _pl inv_ ) | PC
| el | **programa** | programme
| el | **punto** | knitting
| el | **SMS** ( _pl inv_ ) | text message
| el | **telediario** ( _Sp_ ) | news
| el | **vídeo** ( _Sp_ ) **,** el **video** ( _LAm_ ) | video recorder
| el | **website** | website
**USEFUL WORDS** __(masculine)__
| el | **aficionado** | fan
| el | **blog** | blog
| el | **campamento de verano** | holiday camp
| el | **chat** | chat; chatroom
| el | **club nocturno** ( _pl_ ~s _or_ ~es ~s) | night club
| el | **coro** | choir
| el | **crucigrama** | crossword puzzle(s)
| el | **explorador** | scout
| el | **juego de mesa** | board game
| el | **monopatín** ( _pl_ monopatines) | skateboard
| el | **videoclub** ( _pl_ ~s _or_ ~es) | video shop
**USEFUL PHRASES**
emocionante exciting
aburrido(a) boring
divertido(a) funny
**IMPORTANT WORDS** __(feminine)__
---
| la | **cámara digital** | digital camera
| la | **casa de la juventud** | youth club
| la | **cinta** | tape
| la | **cinta de vídeo** | video cassette
| la | **colección** ( _pl_ colecciones) | collection
| la | **computadora (personal)** ( _LAm_ ) | personal computer
| la | **exposición** ( _pl_ exposiciones) | exhibition
| la | **filmadora** ( _LAm_ ) | camcorder
| la | **grabadora de CD/DVD** | CD/DVD writer
| la | **noche** | evening
| la | **novia** | girlfriend
| la | **pintura** | painting
| la | **reunión** ( _pl_ reuniones) | meeting
| la | **serie** | serial
| la | **tarde** | evening
| la | **telenovela** | soap (opera)
| la | **videocámara** ( _Sp_ ) | camcorder
**USEFUL WORDS** __(feminine)__
| la | **aficionada** | fan
| la | **diapositiva** | slide
| la | **exploradora** | (girl) guide, girl scout
| la | **fotografía** | photograph; photography
| la | **lista de éxitos** | charts
**USEFUL PHRASES**
no está mal it's not bad
bastante bien quite good
bailar to dance
hacer fotos to take photos
estoy aburrido(a) I'm bored
quedamos los viernes we meet on Fridays
estoy ahorrando para comprarme un DVD I'm saving up to buy a DVD
me gustaría dar la vuelta al mundo I'd like to go round the world
#
fruit
**ESSENTIAL WORDS** __(masculine)__
---
| el | **albaricoque** | apricot
| el | **limón** ( _pl_ limones) | lemon
| el | **melocotón** ( _pl_ melocotones) | peach
| el | **plátano** | banana
| el | **pomelo** | grapefruit
| el | **tomate** | tomato
**IMPORTANT WORDS** __(masculine)__
| el | **árbol frutal** | fruit tree
| el | **melón** ( _pl_ melones) | melon
**USEFUL WORDS** __(masculine)__
| el | **aguacate** | avocado
| el | **anacardo** | cashew nut
| el | **arándano** | blueberry
| el | **cacahuete** | peanut
| el | **coco** | coconut
| el | **dátil** | date
| el | **higo** | fig
| el | **hueso** | stone ( _in fruit_ )
| el | **kiwi** | kiwi fruit
| el | **ruibarbo** | rhubarb
**ESSENTIAL WORDS** __(feminine)__
---
| la | **castaña (asada)** | (roasted) chestnut
| la | **cereza** | cherry
| la | **frambuesa** | raspberry
| la | **fresa** | strawberry
| la | **fruta** | fruit
| la | **manzana** | apple
| la | **naranja** | orange
| la | **pasa** | raisin
| la | **pera** | pear
| la | **piel** | skin
| la | **(pieza de) fruta** | (piece of) fruit
| la | **piña** | pineapple
| la | **uva** | grape(s)
**USEFUL WORDS** __(feminine)__
| la | **avellana** | hazelnut
| la | **baya** | berry
| la | **ciruela** | plum
| la | **ciruela pasa** | prune
| la | **granada** | pomegranate
| la | **grosella espinosa** | gooseberry
| la | **grosella negra** | blackcurrant
| la | **grosella (roja)** | redcurrant
| la | **mandarina** | tangerine
| la | **mora** | blackberry
| la | **nuez** ( _pl_ nueces) | nut; walnut
| la | **pepita** | pip ( _in fruit_ )
| la | **vid** | vine
**USEFUL PHRASES**
un zumo de naranja/piña an orange/a pineapple juice
un racimo de uvas a bunch of grapes
maduro(a) ripe
verde unripe
pelar una fruta to peel a fruit
resbalar al pisar una cáscara de plátano to slip on a banana skin
#
furniture and appliances
**ESSENTIAL WORDS** __(masculine)__
---
| el | **armario** ( _Sp_ ) | cupboard; wardrobe
| el | **calefactor** | heater
| el | **congelador** | freezer
| el | **equipo (de música)** | stereo system
| el | **espejo** | mirror
| el | **frigo** | fridge
| el | **frigorífico** ( _Sp_ ) | fridge
| el | **mueble** | piece of furniture
| los | **muebles** | furniture
| el | **radiodespertador** | radio alarm
| el | **refrigerador** ( _LAm_ ) | fridge
| el | **reloj** | clock
| el | **ropero** ( _LAm_ ) | cupboard; wardrobe
| el | **sillón** ( _pl_ sillones) | armchair
| el | **teléfono** | telephone
| el | **transistor** | transistor
**IMPORTANT WORDS** __(masculine)__
| el | **aparador** | sideboard
| el | **aparato** | appliance
| el | **casete** | tape recorder
| el | **cuadro** | picture
| el | **escritorio** | (writing) desk
| el | **hervidor** | kettle
| el | **horno microondas** | microwave oven
| el | **inalámbrico** | cordless phone
| el | **lavavajillas** ( _pl inv_ ) | dishwasher
| el | **lector de CD/DVD** | CD/DVD player
| el | **piano** | piano
| el | **portátil** | laptop
| el | **sofá** | sofa
| el | **(teléfono) móvil** ( _Sp_ ) _or_ | mobile phone
| | **celular** ( _LAm_ ) |
| el | **vídeo** ( _Sp_ ) **,** el **video** ( _LAm_ ) | video recorder
**ESSENTIAL WORDS** __(feminine)__
| la | **balda** | shelf
| la | **cama** | bed
| la | **cocina (eléctrica/de gas)** | (electric/gas) cooker
| la | **estufa** | heater
| la | **habitación** ( _pl_ habitaciones) | room
| la | **lámpara** | lamp
| la | **lavadora** | washing machine
| la | **mesa** | table
| la | **pantalla (de lámpara)** | lampshade
| la | **radio** | radio
| la | **silla** | chair
| la | **televisión** ( _pl_ televisiones) | television
**IMPORTANT WORDS** __(feminine)__
| el | **arca** ( _fpl_ las arcas) | chest
| la | **aspiradora** | vacuum cleaner
| la | **librería** | bookcase
| la | **mesa de centro** | coffee table
| la | **pintura** | painting
| la | **plancha** | iron
| la | **radio digital** | digital radio
| la | **secadora** | tumble-dryer
**USEFUL WORDS** __(masculine)__
---
| la | **altavoz** ( _pl_ altavoces) | loudspeaker
| el | **asiento** | seat
| el | **cajón** ( _pl_ cajones) | drawer
| el | **camión de mudanzas** | removal van
| | ( _pl_ camiones ~ ~) |
| el | **carrito** | trolley
| el | **colchón** ( _pl_ colchones) | mattress
| el | **contestador** | answering machine
| el | **horno** | oven
| el | **mando a distancia** | remote control
| el | **marco** | frame
| el | **mobiliario** | furniture
| el | **operario de mudanzas** | removal man
| el | **paragüero** | umbrella stand
| el | **peso** | scales
| los | **postigos** | shutters
| el | **robot de cocina** ( _pl_ ~ s ~ ~) | food processor
| el | **secador (de pelo)** | hairdryer
| el | **taburete** | stool
| el | **teléfono inalámbrico** | cordless telephone
| el | **tocador** | dressing table
**USEFUL PHRASES**
un apartamento _or_ piso amueblado a furnished flat
encender/apagar el calefactor _or_ la estufa to switch the heater on/off
he hecho la cama I've made my bed
sentarse to sit down
poner _or_ meter algo en el horno to put sth in the oven
correr las cortinas to draw the curtains
cerrar los postigos _or_ las contraventanas to close the shutters
**USEFUL WORDS** __(feminine)__
---
| la | **alfombra** | rug
| la | **antena** | aerial
| la | **antena parabólica** | satellite dish
| la | **cadena de música** | music centre
| la | **cámara cinematográfica** | cine camera
| la | **cómoda** | chest of drawers
| las | **contraventanas** | shutters
| la | **cuna** | cradle; cot
| la | **estantería** | shelves
| la | **lámpara de pie** | standard lamp
| la | **lámpara halógena** | halogen lamp
| las | **literas** | bunk beds
| la | **máquina de coser** | sewing machine
| la | **máquina de escribir** | typewriter
| la | **mesilla de noche** | bedside table
| la | **moqueta** | fitted carpet
| la | **mudanza** | move
| la | **persiana** | blind
| la | **tabla de planchar** | ironing board
| la | **videocámara** | video camera, camcorder
**USEFUL PHRASES**
es un piso de 4 habitaciones it's a 4-roomed flat
¡ya está el desayuno/la comida/la cena! breakfast/lunch/dinner is ready!
#
geographical names
**ESSENTIAL WORDS**
---
| los | **Alpes** | the Alps
| | **Andalucía** | Andalusia
| el | **Atlántico** | the Atlantic
| | **Barcelona** | Barcelona
| | **Bruselas** | Brussels
| | **Castilla** | Castile
| | **Cataluña** | Catalonia
| la | **Costa del Sol** | the Costa del Sol
| el | **este** | the east
| las | **Islas Baleares** | the Balearic Islands
| las | **Islas Canarias** | the Canary Islands
| la | **Coruña** | Corunna
| | **Londres** | London
| | **Málaga** | Malaga
| | **Mallorca** | Majorca
| el | **Mar Cantábrico** | the Bay of Biscay
| el | **Mediterráneo** | the Mediterranean
| | **Menorca** | Minorca
| el | **norte** | the north
| el | **oeste** | the west
| el | **País Vasco** | the Basque Country
| el | **Peñón (de Gibraltar)** | the Rock (of Gibraltar)
| los | **Pirineos** | the Pyrenees
| | **Sevilla** | Seville
| la | **sierra** | mountain range
| el | **sur** | the south
| | **Vizcaya** | Biscay
| | **Zaragoza** | Saragossa
**IMPORTANT WORDS**
| | **Edimburgo** | Edinburgh
| el | **Támesis** | the Thames
**USEFUL WORDS**
---
| | **Atenas** | Athens
| | **Berlín** | Berlin
| la | **capital** | capital
| la | **comunidad autónoma** | autonomous region ( _of Spain_ )
| el | **Extremo Oriente** | the Far East
| | **Ginebra** | Geneva
| las | **Islas Británicas** | the British Isles
| la | **Haya** | The Hague
| | **Lisboa** | Lisbon
| | **Marruecos** | Morocco
| | **Moscú** | Moscow
| el | **Oriente Medio** | the Middle East
| el | **Oriente Próximo** | the Near East
| el | **Pacífico** | the Pacific
| | **París** | Paris
| | **Pekín** | Beijing
| el | **Polo Norte/Sur** | the North/South Pole
| la | **provincia** | province
| | **Roma** | Rome
| | **Varsovia** | Warsaw
| | **Venecia** | Venice
| | **Viena** | Vienna
**USEFUL PHRASES**
ir a Londres/Sevilla to go to London/Seville
ir a Andalucía to go to Andalusia
vengo de Barcelona/del País Vasco I come from Barcelona/the Basque Country
en el _or_ al norte in _or_ to the north
en el _or_ al sur in _or_ to the south
en el _or_ al este in _or_ to the east
en el _or_ al oeste in _or_ to the west
#
greetings and everyday phrases
**GREETINGS**
---
**hola** hello
**¿cómo está usted (** _or_ **estás)?** how are you?
**¿qué tal?** how are you?
**bien** fine ( _in reply_ )
**encantado(a)** pleased to meet you
**¿dígame?** hello ( _on telephone_ )
**buenas tardes** good afternoon; good evening
**buenas noches** good evening; good night
**adiós** goodbye; hello ( _when passing one another_ )
**hasta mañana** see you tomorrow
**hasta luego** see you later
**BEST WISHES**
**feliz cumpleaños** happy birthday
**feliz Navidad** merry Christmas
**feliz Año Nuevo** happy New Year
**felices Pascuas** happy Easter
**recuerdos** best wishes
**saludos** best wishes
**bienvenido(a)** welcome
**enhorabuena** congratulations
**que aproveche** enjoy your meal
**que le vaya (** _or_ **te vaya) bien** all the best
**que te diviertas (** _or_ **se divierta)** enjoy yourself
**buena suerte** good luck
**buen viaje** safe journey
**jesús** bless you ( _after a sneeze_ )
**salud** cheers
**a tu (** _or_ **vuestra** , _etc_ **) salud** good health
**SURPRISE**
---
**Dios mío** my goodness
**¿qué?, ¿cómo?** what?
**entiendo** oh, I see
**vaya** well, well
**pues...** well...
**(¿)de verdad(?), (¿)sí(?)** really(?)
**(¿)estás (** or **está) de broma(?)** you're kidding; are you kidding?
**¡qué suerte!** how lucky!
**POLITENESS**
**perdone** I'm sorry; excuse me
**por favor** please
**gracias** thank you
**no, gracias** no thank you
**sí, gracias** yes please
**de nada** not at all, don't mention it, you're welcome
**con mucho gusto** gladly
**AGREEMENT**
**sí** yes
**por supuesto** of course
**de acuerdo, vale** ( _Sp_ ) OK
**bueno** fine
**DISAGREEMENT**
---
**no** no
**que no** no ( _contradicting a positive statement_ )
**que sí** yes ( _contradicting a negative statement_ )
**claro que no** of course not
**ni hablar** no way
**en absoluto** not at all
**al contrario** on the contrary
**no me digas** well I never
**qué cara** what a cheek
**no te metas en lo que no te importa** mind your own business
**DIFFICULTIES**
**socorro** help
**fuego** fire
**ay** ouch
**perdón** (I'm) sorry, excuse me, I beg your pardon
**lo siento** I'm sorry
**qué pena** what a pity
**qué pesadez, qué rollo** what a nuisance; how boring
**estoy harto(a)** I'm fed up
**no aguanto más** I can't stand it any more
**vaya (por Dios)** oh dear
**qué horror** how awful
**ORDERS**
---
**cuidado** be careful
**para (** _or_ **pare)** stop
**oiga, usted** hey, you there
**fuera de aquí** clear off
**silencio** shh
**basta ya** that's enough
**prohibido fumar** no smoking
**vamos, venga** come on, let's go
**sigue** go ahead, go on
**vámonos** let's go
**OTHERS**
**no tengo (ni) idea** no idea
**quizá, quizás** perhaps, maybe
**no (lo) sé** I don't know
**¿qué desea?** can I help you?
**aquí tienes** there, there you are
**ya voy** just coming
**no te preocupes** don't worry
**no merece la pena** it's not worth it
**a propósito** by the way
**cariño, querido(a)** darling
**el (** _or_ **la) pobre** poor thing
**tanto mejor** so much the better
**no me importa** I don't mind
**a mí me da igual** it's all the same to me
**mala suerte** too bad
**depende** it depends
**¿qué voy a hacer?** what shall I do?
**¿para qué?** what's the point?
**me molesta** it annoys me
**me saca de quicio** it gets on my nerves
#
health
**ESSENTIAL WORDS** __(masculine)__
---
| el | **accidente** | accident
| el | **dentista** | dentist
| el | **doctor** | doctor
| el | **enfermero** | (male) nurse
| el | **enfermo** | patient
| el | **estómago** | stomach
| el | **hospital** | hospital
| el | **médico** | doctor
**IMPORTANT WORDS** __(masculine)__
| el | **algodón (hidrófilo)** | cotton wool
| el | **antiséptico** | antiseptic
| el | **comprimido** | tablet
| el | **dolor** | pain
| el | **esparadrapo** | (sticking) plaster
| el | **farmacéutico** | chemist
| el | **jarabe** | syrup
| el | **medicamento** | medicine, drug
| el | **paciente** | patient
| el | **resfriado** | cold
| el | **seguro** | insurance
**USEFUL PHRASES**
ha habido un accidente there's been an accident
ingresar en el hospital to be admitted to hospital
debe permanecer en cama you must stay in bed
estar enfermo(a) to be ill; sentirse mejor to feel better
cuidar to look after
me he hecho daño I have hurt myself
me he hecho un corte en el dedo I have cut my finger
me he torcido el tobillo I have sprained my ankle
se ha roto el brazo he has broken his arm
me he quemado I have burnt myself
me duele la garganta/la cabeza/ el estómago I've got a sore throat/ a headache/a stomach ache
tener fiebre to have a temperature
**ESSENTIAL WORDS** __(feminine)__
---
| la | **aspirina** | aspirin
| la | **cama** | bed
| la | **cita** | appointment
| la | **dentista** | dentist
| la | **doctora** | doctor
| la | **enferma** | patient
| la | **enfermera** | nurse
| la | **farmacia** | chemist's ( _shop_ )
| la | **médico** | doctor
| la | **pastilla** | tablet, pill
| la | **salud** | health
| la | **temperatura** | temperature
**IMPORTANT WORDS** __(feminine)__
| la | **ambulancia** | ambulance
| la | **camilla** | stretcher
| la | **clínica** | clinic, private hospital
| la | **consulta** | surgery
| la | **crema** | cream, ointment
| la | **cucharada** | spoonful
| la | **diarrea** | diarrhoea
| la | **enfermedad** | illness
| la | **escayola** | plaster cast
| la | **farmacéutica** | chemist
| la | **gripe** | flu
| la | **herida** | wound, injury
| la | **insolación** ( _pl_ insolaciones) | sunstroke
| la | **inyección** ( _pl_ inyecciones) | injection
| la | **medicina** | medicine
| la | **operación** ( _pl_ operaciones) | operation
| la | **paciente** | patient
| la | **píldora** | pill; the Pill
| las | **quemaduras del sol** | sunburn
| la | **receta** | prescription
| la | **sangre** | blood
| la | **tableta** | tablet
| las | **urgencias** | Accident and Emergency
| la | **venda** | bandage
**USEFUL WORDS** __(masculine)__
---
| el | **absceso** | abscess
| el | **acné** | acne
| el | **arañazo** | scratch
| el | **ataque** | fit
| el | **ataque al corazón** | heart attack
| el | **cáncer** | cancer
| el | **cardenal** | bruise
| el | **embarazo** | pregnancy
| el | **estrés** | stress
| el | **mareo** | dizzy spell; sickness
| el | **microbio** | germ
| el | **nervio** | nerve
| el | **preservativo** | condom
| los | **primeros auxilios** | first aid
| el | **pulso** | pulse
| el | **régimen** | diet
| el | **reposo** | rest
| el | **SAMU** | emergency medical service
| el | **sarampión** | measles
| el | **shock** | shock
| el | **sida** | AIDS
| el | **tónico** | tonic
| el | **vendaje** | dressing
| el | **veneno** | poison
**USEFUL PHRASES**
tengo sueño I'm sleepy
tengo naúseas I feel sick
adelgazar to lose weight
engordar to put on weight
tragar to swallow
sangrar to bleed
vomitar to vomit
estar en forma to be in good shape
reposar, descansar to rest
**USEFUL WORDS** __(feminine)__
---
| la | **amigdalitis** | tonsillitis
| las | **anginas** | sore throat; tonsillitis
| la | **apendicitis** | appendicitis
| la | **astilla** | splinter
| la | **cicatriz** ( _pl_ cicatrices) | scar
| la | **dentadura postiza** | false teeth
| la | **dieta** | diet
| la | **epidemia** | epidemic
| la | **fiebre del heno** | hay fever
| la | **migraña** | migraine
| la | **muleta** | crutch
| la | **náusea** | nausea
| las | **paperas** | mumps
| la | **pomada** | ointment
| la | **radiografía** | X-ray
| la | **recuperación** | recovery
| la | **rubeola** | German measles
| la | **silla de ruedas** | wheelchair
| la | **tos** | cough
| la | **tos ferina** | whooping cough
| la | **transfusión (de sangre)** | blood transfusion
| | ( _pl_ transfusiones (~ ~)) |
| la | **varicela** | chickenpox
| la | **viruela** | smallpox
**USEFUL PHRASES**
curar to cure; curarse to get better
gravemente herido(a) seriously injured
¿tiene seguro? are you insured?
estoy resfriado(a) I have a cold
¡eso duele! that hurts!; me duele it hurts!
respirar to breathe
desmayarse to faint
toser to cough
morir to die
perder el conocimiento to lose consciousness
llevar el brazo en cabestrillo to have one's arm in a sling
#
hotel
**ESSENTIAL WORDS** __(masculine)__
---
| el | **almuerzo** | lunch
| el | **ascensor** | lift
| el | **balcón** ( _pl_ balcones) | balcony
| los | **baños públicos** ( _LAm_ ) | toilets
| el | **bar** | bar
| el | **camarero** | waiter
| el | **cambio** | change
| el | **cheque** | cheque
| el | **cuarto de baño** | bathroom
| el | **depósito** | deposit
| el | **desayuno** | breakfast
| el | **director** | manager
| el | **equipaje** | luggage
| el | **hotel** | hotel
| el | **huésped** | guest
| el | **impreso** | form
| el | **maletero** | porter
| el | **número** | number
| el | **pasaporte** | passport
| el | **piso** | floor; storey
| el | **precio** | price
| el | **recepcionista** | receptionist
| el | **restaurante** | restaurant
| el | **ruido** | noise
| los | **servicios** | toilets
| el | **teléfono** | telephone
**USEFUL PHRASES**
quisiera reservar una habitación I would like to book a room
una habitación con ducha/con baño a room with a shower/ with a bathroom
una habitación individual a single room
una habitación doble a double room
**ESSENTIAL WORDS** __(feminine)__
---
| la | **cama de matrimonio** | double bed
| la | **camarera** | waitress
| las | **camas separadas** | twin beds
| la | **comida** | lunch; meal
| la | **comodidad** | comfort
| la | **cuenta** | bill
| la | **directora** | manager
| la | **ducha** | shower
| la | **entrada** | entrance
| la | **escalera** | stairs
| la | **estancia** | stay
| la | **fecha** | date
| la | **ficha** | form
| la | **habitación** ( _pl_ habitaciones) | room
| la | **huésped** | guest
| la | **llave** | key
| la | **maleta** | suitcase
| la | **media pensión** | half board
| la | **noche** | night
| la | **pensión** ( _pl_ pensiones) | guest house
| la | **pensión completa** | full board
| la | **piscina** | swimming pool
| la | **planta** | floor; storey
| la | **planta baja** | ground floor
| la | **recepción** | reception
| la | **recepcionista** | receptionist
| la | **salida de incendios** | fire escape
| la | **tarifa** | rate, rates
| la | **televisión** ( _pl_ televisiones) | television
| la | **vista** | view
**USEFUL PHRASES**
¿lleva algún documento de identidad? do you have any ID?
¿a qué hora se sirve el desayuno? what time is breakfast served?
limpiar la habitación to clean the room
"se ruega no molestar" "do not disturb"
**IMPORTANT WORDS** __(masculine)__
---
| el | **albergue** | inn
| el | **baño** | bathroom
| el | **interruptor** | switch
| el | **lavabo** | washbasin; bathroom
| el | **precio total** | inclusive price
| el | **recibo** | receipt
**USEFUL WORDS** __(masculine)__
| el | **cocinero** | cook
| el | **maître** | head waiter
| el | **sumiller** | wine waiter
| el | **vestíbulo** | foyer
**USEFUL PHRASES**
ocupado(a) occupied
libre vacant
limpio(a) clean
sucio(a) dirty
dormir to sleep
despertar to wake
"con todas las comodidades" "with all facilities"
¿podrían despertarme ( _or_ llamarme) mañana por la mañana a las siete? I'd like a 7 o'clock alarm call tomorrow morning, please
una habitación con vistas al mar a room overlooking the sea
**IMPORTANT WORDS** __(feminine)__
---
| la | **bañera** | bathtub
| la | **bienvenida** | welcome
| la | **camarera (de habitaciones)** | chambermaid
| la | **casa de huéspedes** | guest house
| la | **factura** | bill
| la | **guía turística** | guidebook
| la | **propina** | tip
| la | **reclamación** ( _pl_ reclamaciones) | complaint
**USEFUL WORDS** __(feminine)__
| la | **cocinera** | cook
**USEFUL PHRASES**
una habitación con media pensión room with half board
¿nos sentamos fuera _or_ en la terraza? shall we sit outside?
nos sirvieron la cena fuera _or_ en la terraza we were served dinner outside
un hotel de tres estrellas a three-star hotel
IVA incluido inclusive of VAT
# house – general
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aparcamiento** ( _Sp_ ) | car park; parking space
| el | **apartamento** | flat, apartment
| el | **ascensor** | lift
| el | **balcón** ( _pl_ balcones) | balcony
| el | **bloque de departamentos** ( _LAm_ ) | block of flats
| el | **bloque de pisos** ( _Sp_ ) | block of flats
| el | **comedor** | dining room
| el | **cuarto de baño** | bathroom
| el | **departamento** ( _LAm_ ) | flat, apartment
| el | **dormitorio** | bedroom
| el | **edificio** | building
| el | **estacionamiento** ( _LAm_ ) | car park; parking space
| el | **exterior** | exterior
| el | **garaje** | garage
| el | **interior** | interior
| el | **jardín** ( _pl_ jardines) | garden
| el | **mueble** | piece of furniture
| los | **muebles** | furniture
| el | **numéro de teléfono** | phone number
| el | **patio** | yard
| el | **piso** | floor, storey; ( _Sp_ ) flat,
| | | apartment
| el | **pueblo** | village
| el | **salón** ( _pl_ salones) | living room
| el | **sótano** | basement
| el | **terreno** | plot of land
**USEFUL PHRASES**
cuando vaya a casa when I go home
mirar por la ventana to look out of the window
en mi/tu/nuestra casa at my/your/our house
mudarse de casa to move house
alquilar un apartamento _or_ un piso to rent a flat
**ESSENTIAL WORDS** __(feminine)__
---
| la | **avenida** | avenue
| la | **bodega** | cellar
| la | **calefacción (central)** | (central) heating
| | ( _pl_ calefacciones (~es)) |
| la | **calle** | street
| la | **casa** | house
| la | **ciudad** | town; city
| la | **cocina** | kitchen
| la | **comodidad** | comfort
| la | **dirección** ( _pl_ direcciones) | address
| la | **ducha** | shower
| la | **entrada** | entrance
| la | **entrada para coches** ( _Sp_ ) | drive
| | _or_ **para carros** ( _LAm_ ) |
| la | **escalera** | stairs
| la | **habitación** ( _pl_ habitaciones) | room
| la | **llave** | key
| la | **parcela** | plot of land
| la | **pared** | wall
| la | **planta** | floor, storey
| la | **planta baja** | ground floor
| la | **plaza de parking** _or_ **de garaje** | parking space ( _in car park_ )
| la | **puerta** | door
| la | **puerta principal** | front door
| la | **sala de estar** | living room
| la | **urbanización** ( _pl_ urbanizaciones) | housing estate
| la | **ventana** | window
| la | **vista** | view
**USEFUL PHRASES**
vivo en una casa/en un apartamento _or_ un piso I live in a house /a flat
(en el piso de) arriba upstairs
(en el piso de) abajo downstairs
en el primer piso on the first floor
en la planta baja on the ground floor
en casa at home
**IMPORTANT WORDS** __(masculine)__
---
| el | **alojamiento** | accommodation
| el | **alquiler** | rent
| el | **baño** | toilet
| el | **césped** | lawn
| el | **dueño** | landlord; owner
| el | **humo** | smoke
| el | **lavabo** | toilet; washbasin
| el | **mantenimiento** | upkeep
| el | **mobiliario** | furniture
| el | **pasillo** | corridor
| el | **piso amueblado** | furnished flat
| el | **portero** | caretaker
| el | **propietario** | owner; landlord
| el | **rellano** | landing
| el | **tejado** | roof
| el | **trastero** | lumber room; ( _Mex_ ) cupboard
| el | **vecino** | neighbour
**USEFUL WORDS** __(masculine)__
| el | **ático** | penthouse; attic
| el | **chalet** ( _pl_ ~s) | bungalow; detached house
| el | **cristal** | window pane
| el | **despacho** | study
| el | **escalón** ( _pl_ escalones) | step
| el | **estudio** | studio flat
| el | **inquilino** | tenant; lodger
| el | **muro** | wall
| el | **parquet** ( _pl_ ~s) | parquet floor
| el | **piso piloto** | show flat
| el | **seto** | hedge
| el | **suelo** | floor
| el | **techo** | ceiling
| el | **timbre** | door bell
| el | **tragaluz** ( _pl_ tragaluces) | skylight
| el | **umbral** | doorstep
| el | **vestíbulo** | hall
| el | **vidrio** | window pane
**IMPORTANT WORDS** __(feminine)__
---
| la | **casa de campo** | cottage
| la | **chimenea** | chimney; fireplace
| la | **dueña** | landlady; owner
| la | **mudanza** | move
| la | **portera** | caretaker
| la | **propietaria** | owner; landlady
| la | **señora de la limpieza** | cleaner
| la | **vecina** | neighbour
| la | **vivienda** | housing
**USEFUL WORDS** __(feminine)__
| el | **ama de casa** ( _f pl_ amas ~ ~) | housewife
| la | **antena** | aerial
| la | **baldosa** | tile
| la | **buhardilla** | attic
| la | **caldera** | boiler
| la | **contraventana** | shutter
| la | **cristalera** ( _Sp_ ) | French window
| la | **decoración** ( _pl_ decoraciones) | decoration
| la | **fachada** | front ( _of house_ )
| la | **habitación de los invitados** | spare room
| la | **inquilina** | tenant; lodger
| la | **persiana** | blind
| la | **portería** | caretaker's room
| la | **puerta ventana** | French window
| la | **teja** | roof tile; slate
| la | **tubería** | pipe
| la | **vivienda de protección oficial** | council flat _or_ house
**USEFUL PHRASES**
llamar a la puerta to knock at the door
acaba de sonar el timbre the doorbell's just gone
desde fuera from the outside
dentro on the inside
hasta el techo up to the ceiling
#
house – particular
**ESSENTIAL WORDS** __(masculine)__
---
| el | **armario** | cupboard; wardrobe
| el | **bote de la basura** ( _Mex_ ) | dustbin
| el | **buzón** ( _pl_ buzones) | letterbox
| el | **cazo** | saucepan
| el | **cenicero** | ashtray
| el | **cepillo** | brush
| el | **cuadro** | picture
| el | **cubo de la basura** | dustbin
| el | **despertador** | alarm clock
| el | **espejo** | mirror
| el | **fregadero** | sink
| el | **frigorífico** ( _Sp_ ) | fridge
| el | **gas** | gas
| el | **grifo** | tap
| el | **interruptor** | switch
| el | **jabón** ( _pl_ jabones) | soap
| el | **lavabo** | washbasin; toilet
| la | **pasta de dientes** | toothpaste
| el | **póster** ( _pl_ ~es _or_ ~s) | poster
| el | **radiador** | radiator
| el | **refrigerador** ( _LAm_ ) | fridge
| el | **televisor** | television set
| el | **vídeo** ( _Sp_ ) _or_ **video** ( _LAm_ ) | video recorder
**USEFUL PHRASES**
darse un baño, bañarse to have a bath
darse una ducha, ducharse to have a shower
hacer la limpieza de la casa to do the housework
me gusta cocinar I like cooking
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua** ( _f_ ) | water
| la | **alfombra** | carpet, rug
| la | **almohada** | pillow
| la | **balanza** | scales
| la | **bandeja** | tray
| la | **bañera** | bath
| la | **cacerola** | saucepan
| la | **cafetera** | coffee pot; coffee maker
| la | **cazuela** | saucepan
| la | **cocina** | cooker
| las | **cortinas** | curtains
| la | **ducha** | shower
| la | **electricidad** | electricity
| la | **foto** | photo
| la | **lámpara** | lamp
| la | **lavadora** | washing machine
| la | **luz** ( _pl_ luces) | light
| la | **manta** | blanket
| la | **radio** | radio
| la | **refrigeradora** ( _LAm_ ) | fridge
| la | **sábana** | sheet
| la | **servilleta** | napkin
| las | **tareas domésticas** | housework
| la | **televisión** ( _pl_ televisiones) | television
| la | **toalla** | towel
| la | **vajilla** | dishes
**USEFUL PHRASES**
ver la televisión to watch television
en televisión on television
encender/apagar la tele to switch on/off the TV
tirar algo al cubo de la basura to throw sth in the dustbin
lavar _or_ fregar los platos to do the dishes
**IMPORTANT WORDS** __(masculine)__
---
| el | **bidé** | bidet
| el | **detergente (en polvo)** | washing powder
| el | **enchufe** | plug; socket
| el | **horno** | oven
| el | **lavavajillas** ( _pl inv_ ) | dishwasher; washing-up liquid
| el | **mueble de cocina** | cooker
| el | **polvo** | dust
**USEFUL WORDS** __(masculine)__
| el | **adorno** | ornament
| el | **almohadón** ( _pl_ almohadones) | bolster
| el | **cojín** ( _pl_ cojines) | cushion
| el | **cubo** | bucket
| el | **edredón nórdico** ( _pl_ edredones ~s) | duvet
| el | **horno microondas** | microwave oven
| el | **jarrón** ( _pl_ jarrones) | vase
| el | **molinillo de café** | coffee grinder
| el | **paño de cocina** | dishcloth
| el | **papel pintado** | wallpaper
| el | **picaporte** | door handle
| el | **trapo (del polvo)** | duster
**USEFUL PHRASES**
enchufar/desenchufar to plug in/to unplug
pasar la aspiradora to hoover
hacer la colada to do the washing
**IMPORTANT WORDS** __(feminine)__
---
| la | **aspiradora** | vacuum cleaner
| la | **bombilla** | light bulb
| la | **cerradura** | lock
| la | **colada** | (clean) washing
| la | **estufa** | heater
| la | **pintura** | paint; painting
| la | **receta** | recipe
| la | **ropa de cama** | bedclothes
| la | **ropa sucia** | (dirty) washing, laundry
| la | **sartén** ( _pl_ sartenes) | frying pan
| la | **señora de la limpieza** | cleaner
**USEFUL WORDS** __(feminine)__
| la | **basura** | rubbish
| la | **batidora** | blender
| la | **bayeta** | duster
| la | **escalera (de mano)** | ladder
| la | **escoba** | broom
| la | **esponja** | sponge
| la | **manta eléctrica** | electric blanket
| la | **moqueta** | fitted carpet
| la | **olla a presión** | pressure cooker
| la | **papelera** | waste paper basket
| la | **percha** | coat hanger
| la | **plancha** | iron
| la | **tabla de planchar** | ironing board
| la | **tapa** | lid
| la | **tapicería** | upholstery
| la | **tostadora** | toaster
**USEFUL PHRASES**
barrer to sweep (up)
limpiar to clean
recoger uno sus cosas to tidy away one's things
dejar uno sus cosas por ahí tiradas to leave one's things lying about
#
information and services
**ESSENTIAL WORDS** __(masculine)__
---
| el | **banco** | bank
| el | **billete (de banco)** | banknote
| el | **bolígrafo** | Biro®
| el | **buzón** ( _pl_ buzones) | postbox
| el | **cambio** | change
| el | **carnet** _or_ **carné de identidad** ( _Sp_ ) | ID card
| | ( _pl_ ~s ~ ~) |
| el | **cartero** | postman
| el | **céntimo de euro** | euro cent
| el | **cheque** | cheque
| el | **código postal** | postcode
| el | **contrato telefónico** | phone contract
| el | **correo electrónico** | email
| el | **documento de identidad** | ID card
| el | **empleado** | counter clerk
| el | **error** | mistake
| el | **euro** | euro
| el | **fax** | fax; fax machine
| el | **impreso** | form
| el | **ingreso** | deposit
| el | **justificante** | written proof
| el | **mensaje de texto** | text message
| el | **mostrador** | counter
| el | **prefijo** | dialling code
| el | **número** | number
| el | **paquete** | parcel
| el | **pasaporte** | passport
| el | **precio** | price
| el | **sello** | stamp
| el | **sobre** | envelope
| el | **teléfono** | telephone
| el | **tono de marcado** | dialling tone
**USEFUL PHRASES**
el banco más cercano the nearest bank
quisiera cobrar un cheque/cambiar dinero I would like to cash a cheque/change some money
**ESSENTIAL WORDS** __(feminine)__
---
| la | **caja** | check-out
| la | **carta** | letter
| la | **cartera** | postwoman; wallet;
| | | ( _LAm_ ) handbag
| la | **cédula de identidad** ( _LAm_ ) | ID card
| la | **compañía de teléfonos** | phone company
| la | **dirección** ( _pl_ direcciones) | address
| la | **empleada** | counter clerk
| la | **firma** | signature
| la | **información** | information; directory
| | | enquiries
| la | **libra (esterlina)** | pound (sterling)
| la | **llamada** | call
| la | **oficina de correos** | post office
| la | **oficina de información y turismo** | tourist information office
| la | **pluma** | pen
| la | **respuesta** | reply
| la | **tarjeta de crédito** | credit card
| la | **tarjeta de débito** | debit card
| la | **(tarjeta) postal** | postcard
**USEFUL PHRASES**
una llamada telefónica a phone call
llamar a algn por teléfono, telefonear a algn to phone sb
descolgar el teléfono to lift the receiver
marcar (el número) to dial (the number)
hola – soy el Dr Pérez _or_ el Dr Pérez al habla hello, this is Dr. Pérez
la línea está ocupada the line is engaged
no cuelgue hold the line
me he equivocado de número I got the wrong number
colgar to hang up
quisiera hacer una llamada internacional I'd like to make an international phone call
**IMPORTANT WORDS** __(masculine)__
---
| el | **archivo adjunto** | attachment
| el | **buzón de voz** ( _pl_ buzones ~ ~ ) | voicemail
| el | **cheque de viaje** | traveller's cheque
| el | **cibercafé** | internet café
| el | **contestador (automático)** | answerphone
| el | **correo** | mail
| el | **crédito** | credit
| el | **domicilio** | home address
| el | **gasto** | expense
| el | **impuesto** | tax
| el | **mail** ( _pl_ ~s) | email
| el | **monedero** | purse
| el | **pago** | payment
| el | **papel de carta** | writing paper
| el | **recargo** | extra charge
| el | **SMS** ( _pl inv_ ) | text message
| el | **talonario de cheques** | cheque book
| el | **telefonista** | operator
| el | **(teléfono) fijo** | landline
| el | **(teléfono) móvil** | mobile (phone)
| el | **telegrama** | telegram
| el | **tipo de cambio** | exchange rate
**USEFUL WORDS** __(masculine)__
| el | **apartado de correos** | PO box
| el | **auricular** | receiver
| el | **destinatario** | addressee
| el | **documento adjunto** | attachment
| el | **giro postal** | postal order
| el | **nombre de acceso (** _or_ **entrada)** | login
| | **al sistema** |
| el | **papel de envolver** | wrapping paper
| el | **remitente** | sender
| el | **tono de llamada** | ringtone
**IMPORTANT WORDS** __(feminine)__
---
| la | **banda ancha** | broadband
| la | **cabina telefónica** | callbox
| la | **contraseña** | password
| la | **cuenta (bancaria)** | (bank) account
| la | **estampilla** | stamp
| la | **guía telefónica** | telephone directory
| la | **llamada telefónica** | phone call
| la | **oficina de objetos perdidos** | lost property office
| la | **peseta** | peseta
| la | **ranura** | slot
| la | **recogida** | collection
| la | **recompensa** | reward
| la | **tarjeta telefónica** | ( _prepaid_ ) phonecard
| la | **tarjeta de recarga (del móvil)** | top-up (card)
| la | **telefonista** | operator
**USEFUL WORDS** __(feminine)__
| la | **carta certificada** | registered letter
| la | **destinataria** | addressee
| la | **llamada internacional** | international call
| la | **llamada local** | local call
| la | **llamada nacional** | inter-city call
| la | **oficina de cambio** | bureau de change
| la | **remitente** | sender
| la | **tarjeta SIM** ( _pl_ ~s ~) | SIM card
**USEFUL PHRASES**
he perdido la cartera I've lost my wallet
rellenar un impreso to fill in a form
en mayúsculas in block letters
hacer una llamada a cobro revertido to make a reverse charge call
**GENERAL SITUATIONS**
---
**¿cuál es su dirección?** what is your address?
**¿cómo se escribe?** how do you spell that?
**¿tiene cambio de 100 euros?** do you have change of 100 euros?
**escribir** to write
**responder** to reply
**firmar** to sign
**¿me puede ayudar por favor?** can you help me please?
**¿cómo se va a la estación?** how do I get to the station?
**todo recto** straight on
**a la derecha** to _or_ on the right; **a la izquierda** to _or_ on the left
**LETTERS**
**Querido Carlos** Dear Carlos
**Querida Ana** Dear Ana
**Estimado señor** Dear Sir
**Estimada señora** Dear Madam
**recuerdos, saludos** best wishes
**un abrazo de, un beso de, besos de** love from
**le saluda atentamente** _or_ **cordialmente** kind regards
**besos y abrazos** love and kisses
**atentamente** yours faithfully
**reciba un atento saludo, le saluda atentamente** yours sincerely
**sigue** PTO
**E-MaILS**
**mandarle un correo electrónico a algn** to mail _or_ email sb
**MOBILES**
**mandarle un mensaje de texto a algn** to text sb
**PRONUNCIATION GUIDE**
---
_Pronounced approximately as:_
**A** | **ah**
**B** | **bay**
**C** | **thay, say**
**D** | **day**
**E** | **ay**
**F** | **efay**
**G** | **khay**
**H** | **atchay**
**I** | **ee**
**J** | **khota**
**K** | **kah**
**L** | **elay**
**LL** | **elyay**
**M** | **emay**
**N** | **enay**
**Ñ** | **enyay**
**O** | **oh**
**P** | **pay**
**Q** | **koo**
**R** | **eray**
**S** | **essay**
**T** | **tay**
**U** | **oo**
**V** | **oobay** ( _Sp_ ) **, bay korta** ( _LAm_ )
**W** | **oobay doblay** ( _Sp_ ) **, doblay bay** ( _LAm_ )
**X** | **ekees**
**Y** | **ee griayga**
**Z** | **theta, seta**
#
law
**ESSENTIAL WORDS** __(masculine)__
---
| el | **abogado** | lawyer
| el | **accidente** | accident
| el | **carnet de identidad** ( _Sp_ ) ( _pl_ ~s ~ ~) | ID card
| el | **documento de identidad** | ID card
| el | **incendio** | fire
| el | **policía** | policeman
| el | **problema** | problem
| el | **robo** | burglary; theft
**IMPORTANT WORDS** __(masculine)__
| el | **atracador** | armed robber; mugger
| el | **atraco** | hold-up; mugging
| el | **consulado** | consulate
| el | **control policial** | checkpoint; roadblock
| el | **culpable** | culprit
| el | **daño** _or_ **los daños** | damage
| el | **ejército** | army
| el | **espía** | spy
| el | **gobierno** | government
| el | **guardia civil** | civil guard ( _person_ )
| los | **impuestos** | income tax
| el | **ladrón** ( _pl_ ladrones) | burglar; thief; robber
| el | **monedero** | purse
| el | **muerto** | dead man
| el | **permiso** | permission
| el | **propietario** | owner
| el | **testigo** | witness
**USEFUL PHRASES**
robar to burgle; to steal; to rob
¡me han robado la cartera! someone has stolen my wallet!
ilegal illegal; inocente innocent
no es culpa mía it's not my fault
¡socorro! help!; ¡al ladrón! stop thief!
¡fuego! fire!; ¡arriba las manos! hands up!
robar un banco to rob a bank
encarcelar to imprison; fugarse, escapar to escape
**ESSENTIAL WORDS** __(feminine)__
---
| la | **abogada** | lawyer
| la | **cédula de identidad** ( _LAm_ ) | identity card
| la | **culpa** | fault
| la | **documentación** | papers
| la | **identidad** | identity
| la | **policía** | police; policewoman
| la | **verdad** | truth
**IMPORTANT WORDS** __(feminine)__
| la | **atracadora** | armed robber; mugger
| la | **banda** | gang
| la | **cartera** | wallet; ( _LAm_ ) handbag
| la | **comisaría** | police station
| la | **culpable** | culprit
| la | **denuncia** | report
| la | **espía** | spy
| la | **Guardia Civil** | Civil Guard
| la | **guardia civil** | civil guard ( _person_ )
| la | **ladrona** | burglar; thief; robber
| la | **manifestación** ( _pl_ manifestaciones) | demonstration
| la | **muerta** | dead woman
| la | **muerte** | death
| la | **multa** | fine
| la | **pena de muerte** | death penalty
| la | **póliza de seguros** | insurance policy
| la | **propietaria** | owner
| la | **recompensa** | reward
| la | **testigo** | witness
**USEFUL PHRASES**
un atraco a mano armada a hold-up
raptar _or_ secuestrar a un niño to abduct a child
un grupo de gamberros a bunch of hooligans
en la cárcel in prison
pelearse to fight; arrestar to arrest; acusar to charge
estar detenido(a) to be remanded in custody
acusar a algn de algo to accuse sb of sth; to charge sb with sth
**USEFUL WORDS** __(masculine)__
---
| el | **arresto** | arrest
| el | **asesinato** | murder
| el | **asesino** | murderer
| el | **botín** ( _pl_ botines) | loot
| el | **cadáver** | corpse
| el | **crimen** ( _pl_ crímenes) | murder; crime
| el | **criminal** | criminal
| el | **detective privado** | private detective
| el | **disparo (de arma)** | (gun) shot
| el | **drogadicto** | drug addict
| el | **encarcelamiento** | imprisonment
| el | **estafador** | crook
| el | **gamberro** | hooligan
| el | **gángster** ( _pl_ ~s) | gangster
| el | **guarda** | guard; warden
| el | **guardia** | guard; policeman
| el | **inmigrante ilegal** | illegal immigrant
| el | **intento** | attempt
| el | **juez** ( _pl_ jueces) | judge
| el | **juicio** | trial
| el | **jurado** | jury
| el | **levantamiento** | uprising
| el | **pirómano** | arsonist
| el | **poli** | cop
| el | **preso** | prisoner
| el | **rehén** ( _pl_ rehenes) | hostage
| el | **rescate** | ransom; rescue
| el | **revólver** | revolver
| el | **secuestrador** | kidnapper; hijacker
| el | **secuestro** | kidnapping
| el | **secuestro aéreo** | hijacking
| el | **terrorismo** | terrorism
| el | **terrorista** | terrorist
| el | **traficante de drogas** | drug dealer
| el | **tribunal** | court
| los | **tribunales** | law courts
| el | **valor** | bravery
**USEFUL WORDS** __(feminine)__
---
| la | **acusación** ( _pl_ acusaciones) | the prosecution; charge
| el | **arma** ( _pl f_ las **armas** ) | weapon
| la | **asesina** | murderer
| la | **bomba** | bomb
| la | **cárcel** | prison
| la | **celda** | cell
| la | **criminal** | criminal
| la | **declaración** ( _pl_ declaraciones) | statement
| la | **defensa** | defence
| la | **detective privada** | private detective
| la | **detención** ( _pl_ detenciones) | arrest
| la | **droga** | drug
| la | **drogadicta** | drug addict
| la | **estafadora** | crook
| la | **fuga** | escape
| la | **gamberra** | hooligan
| la | **guarda** | guard; warden
| la | **guardia** | guard; policewoman
| la | **inmigrante ilegal** | illegal immigrant
| la | **investigación** ( _pl_ investigaciones) | inquiry
| la | **ley** | law
| la | **multa** | fine
| la | **pelea** | fight
| la | **pirómana** | arsonist
| la | **pistola** | gun
| la | **poli** | the cops; cop
| la | **prisión** ( _pl_ prisiones) | prison
| la | **presa** | prisoner
| la | **prueba** | proof
| las | **pruebas** | evidence
| la | **redada** | raid
| la | **rehén** ( _pl_ rehenes) | hostage
| la | **riña** | argument
| la | **secuestradora** | kidnapper; hijacker
| la | **suplantación de personalidad** | identity theft
| | ( _pl_ suplantaciones ~ ~) |
| la | **terrorista** | terrorist
| la | **traficante de drogas** | drug dealer
#
materials
**ESSENTIAL WORDS** __(masculine)__
---
| el | **acero** | steel
| el | **algodón** | cotton
| el | **caucho** | rubber
| el | **cristal** | glass
| el | **cuero** | leather
| el | **gas** | gas
| el | **gasoil** | diesel
| el | **hierro** | iron
| el | **metal** | metal
| el | **oro** | gold
| el | **plástico** | plastic
| el | **vidrio** | glass
**IMPORTANT WORDS** __(masculine)__
| el | **acero inoxidable** | stainless steel
| el | **aluminio** | aluminium
| el | **cartón** | cardboard
| el | **estado** | condition
| el | **hierro forjado** | wrought iron
| el | **ladrillo** | brick
| el | **papel** | paper
| el | **tejido** | fabric
**USEFUL PHRASES**
una silla de madera a wooden chair
una caja de plástico a plastic box
un anillo de oro a gold ring
en buen estado, en buenas condiciones in good condition
en mal estado, en malas condiciones in bad condition
**ESSENTIAL WORDS** __(feminine)__
---
| la | **lana** | wool
| la | **madera** | wood
| la | **piedra** | stone
| la | **piel** | fur; leather
| la | **plata** | silver
| la | **tela** | fabric
**IMPORTANT WORDS** __(feminine)__
| la | **fibra sintética** | synthetic fibre
| la | **seda** | silk
**USEFUL PHRASES**
un abrigo de piel a fur coat
un jersey de lana a woollen jumper
oxidado(a) rusty
**USEFUL WORDS** __(masculine)__
---
| el | **acrílico** | acrylic
| el | **alambre** | wire
| el | **ante** | suede
| el | **bronce** | bronze
| el | **carbón** | coal
| el | **cemento** | concrete
| el | **cobre** | copper
| el | **encaje** | lace
| el | **estaño** | tin
| el | **hilo** | thread
| el | **latón** | brass
| el | **lino** | linen
| el | **líquido** | liquid
| el | **mármol** | marble
| el | **material** | material
| el | **mimbre** | wickerwork
| el | **pegamento** | glue
| el | **plomo** | lead
| el | **raso** | satin
| el | **terciopelo** | velvet
| el | **tweed** | tweed
**USEFUL WORDS** __(feminine)__
---
| la | **arcilla** | clay
| la | **cera** | wax
| la | **cerámica** | ceramics
| la | **cola** | glue
| la | **cuerda** | string
| la | **escayola** | plaster
| la | **gomaespuma** | foam rubber
| la | **hojalata** | tin, tinplate
| la | **lona** | canvas
| la | **loza** | pottery
| la | **paja** | straw
| la | **pana** | corduroy
| la | **porcelana** | china
#
music
**ESSENTIAL WORDS** __(masculine)__
---
| el | **director de orquesta** | conductor
| el | **grupo** | band
| el | **instrumento musical** | musical instrument
| el | **músico** | musician
| el | **piano** | piano
| el | **violín** ( _pl_ violines) | violin
**USEFUL WORDS** __(masculine)__
| el | **acorde** | chord
| el | **acordeón** ( _pl_ acordeones) | accordion
| el | **arco** | bow
| el | **atril** | music stand
| el | **bombo** | bass drum
| el | **clarinete** | clarinet
| el | **contrabajo** | double bass
| el | **estuche** | case
| el | **estudio de grabación** | recording studio
| el | **fagot** | bassoon
| los | **instrumentos de cuerda** | string instruments
| los | **instrumentos de percusión** | percussion instruments
| los | **instrumentos de viento** | wind instruments
| el | **jazz** | jazz
| los | **metales** | brass
| el | **micrófono** | microphone
| el | **minidisco** | minidisc
| el | **oboe** | oboe
| el | **órgano** | organ
| los | **platillos** | cymbals
| el | **saxofón** ( _pl_ saxofones) | saxophone
| el | **solfeo** | music theory
| el | **solista** | soloist
| el | **tambor** | drum
| el | **triángulo** | triangle
| el | **trombón** ( _pl_ trombones) | trombone
| el | **violonchelo** | cello
**ESSENTIAL WORDS** __(feminine)__
---
| la | **batería** | drums, drum kit
| la | **directora de orquesta** | conductor
| la | **flauta** | flute
| la | **flauta dulce** | recorder
| la | **guitarra** | guitar
| la | **música** | music; musician
| la | **orquesta** | orchestra
**USEFUL WORDS** __(feminine)__
| la | **armónica** | harmonica
| el | **arpa** | harpe
| la | **batuta** | conductor's baton
| la | **composición** ( _pl_ composiciones) | composition
| la | **corneta** | bugle
| la | **cuerda** | string
| la | **gaita** | bagpipes
| la | **grabación digital** | digital recording
| | ( _pl_ grabaciones ~es) |
| la | **megafonía** | PA system
| la | **mesa de mezclas** | mixing deck
| la | **nota** | note
| la | **pandereta** | tambourine
| la | **solista** | soloist
| la | **tecla (de piano)** | (piano) key
| la | **trompeta** | trumpet
| la | **viola** | viola
**USEFUL PHRASES**
tocar _or_ interpretar una pieza to play a piece
tocar alto/bajo to play loudly/softly
tocar afinado/desafinado to play in tune/out of tune
tocar el piano/la guitarra to play the piano/the guitar
tocar la batería to play drums
Pedro a la batería Pedro on drums
practicar el piano to practise the piano
¿tocas en un grupo? do you play in a band?
una nota falsa a wrong note
#
numbers and quantities
**CARDINAL NUMBERS**
---
cero | **0** | zero
uno ( _m_ ), una ( _f_ ) | **1** | one
dos | **2** | two
tres | **3** | three
cuatro | **4** | four
cinco | **5** | five
seis | **6** | six
siete | **7** | seven
ocho | **8** | eight
nueve | **9** | nine
diez | **10** | ten
once | **11** | eleven
doce | **12** | twelve
trece | **13** | thirteen
catorce | **14** | fourteen
quince | **15** | fifteen
dieciséis | **16** | sixteen
diecisiete | **17** | seventeen
dieciocho | **18** | eighteen
diecinueve | **19** | nineteen
veinte | **20** | twenty
veintiuno(a) | **21** | twenty -one
veintidós | **22** | twenty-two
veintitrés | **23** | twenty-three
treinta | **30** | thirty
treinta y uno(a) | **31** | thirty-one
treinta y dos | **32** | thirty-two
cuarenta | **40** | forty
cincuenta | **50** | fifty
sesenta | **60** | sixty
setenta | **70** | seventy
ochenta | **80** | eighty
noventa | **90** | ninety
cien | **100** | one hundred |
**CARDINAL NUMBERS** ( _continued_ )
ciento uno(a) | **101** | a hundred and one
ciento dos | **102** | a hundred and two
ciento diez | **110** | a hundred and ten
ciento ochenta y dos | **182** | a hundred and eighty-two
doscientos(as) | **200** | two hundred
doscientos(as) uno(a) | **201** | two hundred and one
doscientos(as) dos | **202** | two hundred and two
trescientos(as) | **300** | three hundred
cuatrocientos(as) | **400** | four hundred
quinientos(as) | **500** | five hundred
seiscientos(as) | **600** | six hundred
setecientos(as) | **700** | seven hundred
ochocientos(as) | **800** | eight hundred
novecientos(as) | **900** | nine hundred
mil | **1000** | one thousand
mil uno(a) | **1001** | a thousand and one
mil dos | **1002** | a thousand and two
dos mil | **2000** | two thousand
dos mil seis | **2006** | two thousand and six
diez mil | **10000** | ten thousand
cien mil | **100000** | one hundred thousand
un millón | **1000000** | one million
dos millones | **2000000** | two million
**USEFUL PHRASES**
mil euros a thousand euros
un millón de dólares one million dollars
tres coma dos (3,2) three point two (3.2)
**ORDINAL NUMBERS**
---
primero(a) | **1º, 1ª** | first
segundo(a) | **2º, 2ª** | second
tercero(a) | **3º, 3ª** | third
cuarto(a) | **4º, 4ª** | fourth
quinto(a) | **5º, 5ª** | fifth
sexto(a) | **6º, 6ª** | sixth
séptimo(a) | **7º, 7ª** | seventh
octavo(a) | **8º, 8ª** | eighth
noveno(a) | **9º, 9ª** | ninth
décimo(a) | **10º, 10ª** | tenth
undécimo(a) | **11º, 11ª** | eleventh
duodécimo(a) | **12º, 12ª** | twelfth
decimotercero(a) | **13º, 13ª** | thirteenth
decimocuarto(a) | **14º, 14ª** | fourteenth
decimoquinto(a) | **15º, 15ª** | fifteenth
decimosexto(a) | **16º, 16ª** | sixteenth
decimoséptimo(a) | **17º, 17ª** | seventeenth
decimoctavo(a) | **18º, 18ª** | eighteenth
decimonoveno(a), decimonono(a) | **19º, 19ª** | nineteenth
vigésimo(a) | **20º, 20ª** | twentieth
**Note:**
Ordinal numbers are hardly ever used above 10th in spoken Spanish, and rarely at all above 20th. It's normal to use the cardinal numbers instead, except for **milésimo(a)**.
milésimo(a) | **1000º, 1000ª** | thousandth
dos milésimo(a) | **2000º, 2000ª** | two thousandth
millonésimo(a) | **1000000º, 1000000ª** | millionth
dos millonésimo(a) | **2000000º, 2000000ª** | two millionth
**FRACTIONS**
---
un medio | **1 /2** | a half
uno(a) y medio(a) | **1** **1 /2** | one and a half
dos y medio(a) | **2** **1 /2** | two and a half
un tercio, la tercera parte | **1 /3** | a third
dos tercios, las dos terceras partes | **2 /3** | two thirds
un cuarto, la cuarta parte | **1 /4** | a quarter
tres cuartos, las tres cuartas partes | **3 /4** | three quarters
un sexto, la sexta parte | **1 /6** | a sixth
tres y cinco sextos | **3 5/6** | three and five sixths
un séptimo, la séptima parte | **1 /7** | a seventh
un octavo, la octava parte | **1 /8** | an eighth
un noveno, la novena parte | **1 /9** | a ninth
un décimo, la décima parte | **1 /10** | a tenth
un onceavo, la onceava parte | **1 /11** | an eleventh
un doceavo, la doceava parte | **1 /12** | a twelfth
siete doceavos, las siete doceavas partes | **7 /12** | seven twelfths
un centésimo, la centésima parte | **1 /100** | a hundredth
un milésimo, la milésima parte | **1 /1000** | a thousandth
**USEFUL PHRASES**
ambos ( _f_ ambas), los dos ( _f_ las dos) both of them
un bocado de a mouthful of
un bote de a jar of; a tin _or_ can of
una botella de a bottle of
un botellín (de cerveza) a small bottle (of beer)
una caja de a box of
(gran) cantidad de lots of
una caña (de cerveza) a small glass of beer
cien gramos de a hundred grammes of
un centenar de (about) a hundred
un cuarto de a quarter of
tres cuartos de three quarters of
una cucharada de a spoonful of
una docena de (about) a dozen
un grupo de a group of
una jarra de a jug of; a mug of ( _beer_ )
un kilo de a kilo of
un litro de a litre of
la mayoría (de), la mayor parte (de) most (of)
media docena de half a dozen
medio litro de half a litre of
una loncha de jamón a slice of ham
un metro de a metre of
miles de thousands of
**USEFUL PHRASES**
la mitad de half of
un montón de a pile of
mucho(a) a lot of, much
muchos ( _f_ muchas) a lot of, many
multitud de, montones de loads of
un paquete de a packet of
un par de a pair of
un plato de a plate of
un poco de a little; some
una porción de a portion of
un puñado de a handful of
una rebanada de pan a slice of bread
un rebaño de a herd of ( _cattle_ ); a flock of ( _sheep_ )
una rodaja de merluza a slice of hake
un sobre de sopa a packet of soup
una taza de a cup of
un tazón de a bowl of
un terrón de azúcar a lump of sugar
un tonel de a barrel of
un trozo de papel/pastel a piece of paper/cake
a unos metros de a few metres from
un vaso de a glass of
varios several
a varios kilómetros de a few kilometres from
#
personal items
**ESSENTIAL WORDS** __(masculine)__
---
| el | **anillo** | ring
| el | **cepillo** | brush
| el | **cepillo de dientes** | toothbrush
| el | **champú** | shampoo
| el | **desodorante** | deodorant
| el | **espejo** | mirror
| el | **maquillaje** | make-up
| el | **peine** | comb
| el | **perfume** | perfume
| el | **reloj** | watch
**USEFUL WORDS** __(masculine)__
| el | **aftershave** | aftershave
| el | **broche** | brooch
| el | **colgante** | pendant
| el | **collar** | necklace
| el | **dentífrico** | toothpaste
| el | **diamante** | diamond
| los | **efectos personales** | personal effects
| el | **esmalte (de uñas)** | nail varnish
| el | **gemelo** | cufflink
| el | **kleenex ®** ( _pl inv_ ) | tissue
| el | **lápiz de labios** ( _pl_ lápices ~ ~) | lipstick
| el | **llavero** | key-ring
| el | **maquillaje** | make-up
| el | **neceser** | toilet bag
| el | **papel higiénico** | toilet paper
| el | **peinado** | hairstyle
| el | **pendiente** | earring
| los | **polvos compactos** | face powder
| los | **polvos para la cara** | face powder
| el | **quitaesmalte** | nail varnish remover
| el | **rímel** | mascara
| el | **rulo** | roller
| el | **secador** | hairdryer
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua de colonia** ( _f_ ) | eau de toilette
| la | **cadena** | chain
| la | **crema para la cara** | face cream
| la | **cuchilla de afeitar** | razor
| la | **joya** | jewel
| la | **maquinilla de afeitar** | (safety) razor
| la | **pasta de dientes** | toothpaste
| la | **pulsera** | bracelet
**USEFUL WORDS** __(feminine)__
| la | **alianza** | wedding ring
| la | **base de maquillaje** | foundation
| la | **brocha de afeitar** | shaving brush
| la | **crema de afeitar** | shaving cream
| la | **esponja** | sponge
| la | **espuma de afeitar** | shaving foam
| la | **manicura** | manicure
| la | **perla** | pearl
| la | **polvera** | (powder) compact
| la | **sombra de ojos** | eye shadow
**USEFUL PHRASES**
maquillarse to put on one's make-up
desmaquillarse to take off one's make-up
hacerse un peinado to do one's hair
peinarse to comb one's hair
cepillarse el pelo to brush one's hair
afeitarse to shave
lavarse los dientes, limpiarse los dientes to clean _or_ brush one's teeth
#
plants and gardens
**ESSENTIAL WORDS** __(masculine)__
---
| el | **árbol** | tree
| el | **césped** | lawn
| el | **jardín** ( _pl_ jardines) | garden
| el | **jardinero** | gardener
| el | **sol** | sun
**IMPORTANT WORDS** __(masculine)__
| el | **arbusto** | bush
| el | **banco** | bench
| el | **camino** | path
| el | **cultivo** | cultivation; crop
| el | **ramo de flores** | bunch of flowers
**USEFUL PHRASES**
plantar to plant
quitar las malas hierbas, desherbar to weed
regalar a algn un ramo de flores to give sb a bunch of flowers
cortar el césped to mow the lawn
"no pisar el césped" "keep off the grass"
a mi padre le gusta la jardinería my father likes gardening
**ESSENTIAL WORDS** __(feminine)__
---
| la | **flor** | flower
| la | **hierba** | grass
| la | **hoja** | leaf
| la | **jardinera** | gardener; flower bed
| la | **jardinería** | gardening
| la | **lluvia** | rain
| la | **planta** | plant
| la | **rama** | branch
| la | **rosa** | rose
| la | **tierra** | land; soil; ground
| las | **verduras** | vegetables
**IMPORTANT WORDS** __(feminine)__
| la | **abeja** | bee
| la | **avispa** | wasp
| las | **malas hierbas** | weeds
| la | **raíz** ( _pl_ raíces) | root
| la | **sombra** | shade; shadow
| la | **valla** | fence
| la | **verja** | gate
**USEFUL PHRASES**
las flores están creciendo the flowers are growing
en el suelo on the ground
regar las plantas to water the flowers
coger flores to pick flowers
irse a la sombra to go into the shade
quedarse en la sombra to remain in the shade
a la sombra de un árbol in the shade of a tree
**USEFUL WORDS** __(masculine)__
---
| el | **arriate** | flowerbed
| el | **azafrán** ( _pl_ azafranes) | crocus
| el | **brote** | bud
| el | **clavel** | carnation
| el | **cortacésped** | lawnmower
| el | **crisantemo** | chrysanthemum
| el | **diente de león** | dandelion
| el | **estanque** | (ornamental) pool
| el | **follaje** | leaves
| el | **girasol** | sunflower
| el | **gusano** | worm
| el | **huerto** | vegetable garden
| el | **invernadero** | greenhouse
| el | **invierno** | winter
| el | **jacinto** | hyacinth
| el | **lirio** | lily
| el | **lirio del valle** | lily of the valley
| el | **narciso** | daffodil
| el | **otoño** | autumn, fall
| el | **parterre** | flowerbed
| el | **pensamiento** | pansy
| el | **ranúnculo** | buttercup
| el | **rocío** | dew
| el | **rosal** | rose bush
| el | **sendero** | path
| el | **seto** | hedge
| el | **suelo** | ground; soil
| el | **tallo** | stalk
| el | **tronco** | trunk ( _of tree_ )
| el | **tulipán** ( _pl_ tulipanes) | tulip
| el | **verano** | summer
**USEFUL WORDS** __(feminine)__
---
| la | **amapola** | poppy
| la | **baya** | berry
| la | **campanilla** | campanula, bellflower
| la | **campanilla de invierno** | snowdrop
| la | **carretilla** | wheelbarrow
| la | **cerca** | fence
| la | **cosecha** | crop
| la | **espina** | thorn
| la | **herramienta** | tool
| la | **hiedra** | ivy
| la | **hortensia** | hydrangea
| las | **lilas** | lilac
| la | **madreselva** | honeysuckle
| la | **manguera** | hose
| la | **margarita** | daisy
| la | **mariposa** | butterfly
| la | **orquídea** | orchid
| la | **peonía** | peony
| la | **primavera** | spring; primrose
| la | **regadera** | watering can
| la | **semilla** | seed
| la | **violeta** | violet
#
seaside and boats
**ESSENTIAL WORDS** __(masculine)__
---
| los | **anteojos de sol** ( _LAm_ ) | sunglasses
| el | **bañador** | swimming trunks; swimsuit
| el | **bañista** | swimmer
| el | **barco** | boat; ship
| el | **barco de pesca** | fishing boat
| el | **bikini** | bikini
| el | **bote** | boat
| el | **mar** | sea
| el | **muelle** | quay
| el | **paseo** | walk
| el | **pescador** | fisherman
| el | **pesquero** | fishing boat
| el | **picnic** ( _pl_ ~s) | picnic
| el | **puerto** | port, harbour
| el | **puerto deportivo** | marina
| el | **remo** | rowing; oar
| el | **traje de baño** | swimming trunks; swimsuit
**IMPORTANT WORDS** __(masculine)__
| el | **cangrejo** | crab
| el | **castillo de arena** | sandcastle
| el | **fondo** | bottom
| el | **horizonte** | horizon
| el | **mareo** | seasickness
| el | **veraneante** | holiday-maker
**USEFUL PHRASES**
en la playa at the seaside; at _or_ on the beach
en el horizonte on the horizon
está mareado he is seasick
nadar to swim
ahogarse to drown
me voy a dar un baño I'm going for a swim
tirarse al agua, zambullirse to dive into the water
flotar to float
**ESSENTIAL WORDS** __(feminine)__
---
| el | **agua** ( _f_ ) | water
| la | **arena** | sand
| la | **bañista** | swimmer
| la | **barca** | boat
| la | **costa** | coast
| las | **gafas de sol** ( _Sp_ ) | sunglasses
| la | **isla** | island
| la | **natación** | swimming
| la | **pescadora** | fisherwoman
| la | **piedra** | stone
| la | **playa** | beach; seaside
| las | **quemaduras de sol** | sunburn
| la | **toalla** | towel
**IMPORTANT WORDS** __(feminine)__
| la | **colchoneta inflable** | airbed, lilo
| la | **crema (de protección) solar** | suncream
| la | **tabla de windsurf** | windsurfing board
| la | **travesía** | crossing
| la | **tumbona** | deckchair
| la | **veraneante** | holiday-maker
**USEFUL PHRASES**
en el fondo del mar at the bottom of the sea
hacer la travesía en barco to go across by boat
broncearse, ponerse moreno(a) to get a tan
estar moreno(a) to be tanned
sabe nadar he can swim
**USEFUL WORDS** __(masculine)__
---
| el | **acantilado** | cliff
| el | **aire de mar** | sea air
| el | **balde** | bucket
| el | **(barco de) vapor** | steamer
| los | **binoculares** | binoculars
| el | **bote de pedales** | pedalo
| el | **cabo** | headland
| el | **crucero** | cruise
| el | **cubo** | bucket
| el | **embarcadero** | pier
| el | **estuario** | estuary
| el | **faro** | lighthouse
| el | **guijarro** | pebble
| el | **marinero** | sailor
| el | **marino** | sailor; naval officer
| el | **mástil** | mast
| el | **naufragio** | shipwreck
| los | **náufragos** | shipwrecked people,
| | | castaways
| el | **océano** | ocean
| el | **oleaje** | swell
| el | **pedal** ( _Sp_ ) | pedalo
| los | **prismáticos** | binoculars
| el | **puente (de mando)** | bridge ( _of ship_ )
| los | **restos de un naufragio** | wreckage
| el | **salvavidas** ( _pl inv_ ) | lifeguard; lifebelt
| el | **socorrista** | lifeguard
| el | **timón** ( _pl_ timones) | rudder
| el | **transbordador** | ferry
**USEFUL WORDS** __(feminine)__
---
| las | **algas** | seaweed
| el | **ancla** ( _pl f_ las **anclas** ) | anchor
| la | **bahía** | bay
| la | **balsa** | raft
| la | **bandera** | flag
| la | **barca** | small boat
| la | **boya** | buoy
| la | **brisa marina** | sea breeze
| la | **carga** | cargo
| la | **concha** | shell
| la | **corriente** | current
| la | **desembocadura** | mouth ( _of river_ )
| la | **espuma** | foam
| la | **gaviota** | seagull
| la | **insolación** ( _pl_ insolaciones) | sunstroke
| la | **marea** | tide
| la | **marina** | navy
| la | **marinera** | sailor
| la | **marina** | sailor; naval officer
| la | **nave** | vessel
| la | **ola** | wave
| la | **orilla** | shore
| la | **pala** | spade
| la | **pasarela** | gangway
| la | **ría** | estuary
| la | **roca** | rock
| la | **salvavidas** ( _pl inv_ ) _or_ **socorrista** | lifeguard
| la | **sombrilla** | parasol
| la | **tripulación** ( _pl_ tripulaciones) | crew
| la | **vela** | sail; sailing
**USEFUL PHRASES**
tuve una insolación I had sunstroke
con la marea baja/alta at low/high tide
hacer vela to go sailing
# shopping
**ESSENTIAL WORDS** __(masculine)__
---
| el | **banco** | bank
| el | **billete (de banco)** | banknote
| el | **cambio** | change
| el | **céntimo** | cent
| el | **centro comercial** | shopping centre
| el | **cheque** | cheque
| el | **cliente** | customer
| el | **departamento** | department
| el | **dependiente** | shop assistant, sales assistant
| el | **descuento** | discount
| el | **dinero** | money
| el | **estanco** | tobacconist's
| el | **euro** | euro
| los | **grandes almacenes** | department store
| el | **hipermercado** | hypermarket
| el | **mercado** | market
| el | **número (de zapato)** | (shoe) size
| el | **precio** | price
| el | **regalo** | present
| el | **souvenir** ( _pl_ ~s) | souvenir
| el | **supermercado** | supermarket
| el | **talonario de cheques** | cheque book
| el | **vendedor** | salesman
**USEFUL PHRASES**
comprar/vender to buy/sell
¿cuánto cuesta? how much does it cost?
¿cuánto es? how much does it come to?
pagué veinte euros por esto, esto me costó veinte euros I paid 20 euros for that
en la carnicería/la panadería at the butcher's/bakery
**ESSENTIAL WORDS** __(feminine)__
---
| la | **agencia de viajes** | travel agent's
| la | **alimentación** | food
| la | **caja** | checkout; cash desk
| la | **carnicería** | butcher's
| la | **charcutería** | pork butcher's
| la | **clienta** | customer
| la | **compra** | purchase
| la | **dependienta** | shop assistant, sales assistant
| la | **farmacia** | chemist's
| la | **floristería** | flower shop
| la | **frutería** | fruiterer's
| la | **lista** | list
| la | **oficina de correos** | post office
| la | **panadería** | bakery
| la | **pastelería** | cake shop
| la | **perfumería** | perfume shop/department
| la | **pescadería** | fishmonger's
| la | **rebaja** | reduction
| las | **rebajas** | sales
| la | **sección** ( _pl_ secciones) | department
| la | **talla** | size
| la | **tarjeta de crédito** | credit card
| la | **tarjeta de débito** | debit card
| la | **tienda** | shop
| la | **tienda de alimentación** | grocer's
| | _or_ **de comestibles** |
| la | **vendedora** | saleswoman
| la | **verdulería** | greengrocer's
| la | **zapatería** | shoe shop
**IMPORTANT WORDS** __(masculine)__
---
| el | **artículo** | article
| el | **carnicero** | butcher
| el | **charcutero** | pork butcher
| el | **comerciante** | shopkeeper
| el | **comercio** | trade; shop
| el | **comercio justo** | fair trade
| el | **encargado** | manager
| el | **frutero** | fruiterer
| el | **mercadillo** | street market
| el | **monedero** | purse
| el | **mostrador** | counter
| el | **panadero** | baker
| el | **pastelero** | confectioner
| el | **peluquero** | hairdresser
| el | **pescadero** | fishmonger
| el | **rastro** ( _Sp_ ) | flea market
| el | **recibo** | receipt
| el | **tícket** ( _pl_ ~s) | receipt; ticket
| el | **vendedor de periódicos** | newsagent
| el | **verdulero** | greengrocer
| el | **zapatero** | cobbler
**USEFUL PHRASES**
sólo estoy mirando I'm just looking
es demasiado caro it's too expensive
algo más barato something cheaper
es barato it's cheap
"pague en caja" "pay at the checkout"
¿lo quiere para regalo? would you like it gift-wrapped?
debe de haber un error there must be some mistake
**IMPORTANT WORDS** __(feminine)__
---
| la | **biblioteca** | library
| la | **boutique** | boutique
| la | **calculadora** | calculator |
| la | **carnicera** | butcher
| la | **cartera** | wallet; purse; ( _LAm_ ) handbag
| la | **charcutera** | pork butcher
| la | **comerciante** | shopkeeper
| la | **encargada** | manager
| la | **escalera mecánica** | escalator
| la | **frutera** | fruiterer
| la | **librería** | bookshop
| la | **marca** | brand
| la | **panadera** | baker
| la | **pastelera** | confectioner
| la | **peluquera** | hairdresser
| la | **pescadera** | fishmonger
| la | **promoción** ( _pl_ promociones) | special offer
| la | **reclamación** ( _pl_ reclamaciones) | complaint
| la | **tintorería** | dry-cleaner's
| la | **vendedora de periódicos** | newsagent
| la | **verdulera** | greengrocer
| la | **vitrina** | display case; ( _LAm_ ) shop
| | | window
**USEFUL PHRASES**
¿algo más? anything else?
S.A. ( _= Sociedad Anónima_ ) Ltd
S.L. ( _= Sociedad Limitada_ ) limited liability company
y Cía & Co
"de venta aquí" "on sale here"
un coche de ocasión a used car
en oferta, de oferta on special offer
el café de comercio justo fair-trade coffee
**USEFUL WORDS** __(masculine)__
---
| el | **agente inmobiliario** | estate agent
| el | **color** | colour
| el | **escaparate** | shop window
| el | **ferretero** | ironmonger
| el | **gerente** | manager
| el | **joyero** | jeweller; jewellery box
| el | **librero** | bookseller
| el | **óptico** | optician
| el | **producto** | product
| los | **productos** | produce
| el | **recado** | errand
| el | **relojero** | watchmaker; clockmaker
| el | **tendero** | grocer
| el | **trato** | deal
| el | **videoclub** ( _pl_ ~s) | video shop
**USEFUL PHRASES**
ir a ver escaparates, ir de escaparates to go window shopping
horario opening hours
pagar en metálico to pay cash
pagar con un cheque to pay by cheque
pagar con tarjeta de crédito to pay by credit card
**USEFUL WORDS** __(feminine)__
---
| la | **agencia de viajes** | travel agent's
| la | **agencia inmobiliaria** | estate agent's
| la | **agente inmobiliario** | estate agent
| la | **caja de ahorros** | savings bank
| la | **cola** | queue
| la | **compra** | purchase; shopping
| las | **compras** | shopping
| la | **confitería** | sweetshop
| la | **droguería** | hardware shop
| la | **ferretera** | ironmonger
| la | **ferretería** | ironmonger's
| la | **gerente** | manager
| la | **joyera** | jeweller
| la | **joyería** | jeweller's
| la | **lavandería** | laundry
| la | **librería** | bookseller
| la | **mercancía** | goods
| la | **óptica** | optician; optician's
| la | **papelería** | stationer's
| la | **rebaja** | discount
| la | **relojera** | watchmaker; clockmaker
| la | **relojería** | watchmaker's; clockmaker's
| la | **sucursal** | branch
| la | **talla de cuello** | collar size
| la | **tendera** | grocer
| la | **venta** | sale
**USEFUL PHRASES**
en el escaparate in the window
ir de compras to go shopping
hacer la compra to do the shopping
gastar to spend
#
sports
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aerobic** | aerobics
| el | **ajedrez** | chess
| el | **arco** ( _LAm_ ) | goal
| el | **balón** ( _pl_ balones) | ball ( _large_ )
| el | **baloncesto** | basketball
| el | **balonvolea** | volleyball
| el | **billar** | billiards
| el | **campeón** ( _pl_ campeones) | champion
| el | **campeonato** | championship
| el | **campo** | field, ( _football_ ) pitch;
| | | ( _golf_ ) course; ( _basketball_ ) court
| el | **ciclismo** | cycling
| el | **crícket** | cricket
| el | **deporte** | sport
| el | **equipo** | team
| el | **esquí** | skiing; ski
| el | **esquí acuático** | water skiing
| el | **estadio** | stadium
| el | **fútbol** | football
| el | **gimnasta** | gymnast
| el | **golf** | golf
| el | **hockey** | hockey
| el | **juego** | game; play
| el | **jugador** | player
| el | **partido** | match, game
| el | **paseo** | walk
| el | **resultado** | result
| el | **rugby** | rugby
| el | **tenis** | tennis
**USEFUL PHRASES**
jugar al fútbol/tenis to play football/tennis
marcar un gol/un punto to score a goal/a point
llevar la cuenta de los tantos to keep the score
el campeón/la campeona del mundo the world champion
ganar/perder un partido to win/lose a match
mi deporte preferido my favourite sport
**ESSENTIAL WORDS** __(feminine)__
---
| la | **campeona** | champion
| la | **cancha** | ( _basketball/tennis_ ) court;
| | | ( _LAm_ ) field, ( _football_ ) pitch
| la | **cancha de tenis** ( _LAm_ ) | tennis court
| la | **equitación** | horse-riding
| la | **gimnasia** | gymnastics
| la | **gimnasta** | gymnast
| la | **jugadora** | player
| la | **natación** | swimming
| la | **partida** | game ( _chess etc_ )
| la | **pelota** | ball
| la | **pesca** | fishing
| la | **piscina** | swimming pool
| la | **pista** | track
| la | **pista de tenis** ( _Sp_ ) | tennis court
| la | **portería** | goal
| la | **tabla de windsurf** | windsurfing board
| la | **vela** | sailing; sail
**USEFUL PHRASES**
empatar to equalize; to draw
correr to run; saltar to jump; lanzar to throw
ganar _or_ derrotar _or_ vencer a algn to beat sb
entrenarse to train
el Liverpool gana por 2 a 1 Liverpool is leading by 2 goals to 1
un partido de tenis a game of tennis
es socio de un club he belongs to a club
ir de pesca to go fishing
ir a la piscina to go to the swimming pool
¿sabes nadar? can you swim?
hacer deporte to do sport
montar en bicicleta _or_ hacer ciclismo to go cycling
hacer vela to go sailing
hacer footing/alpinismo to go jogging/climbing
patín de cuchilla/de ruedas/en línea (ice) skate/roller skate/Rollerblade®
tiro al arco/al blanco archery/target practice
**IMPORTANT WORDS** __(masculine)__
---
| los | **bolos** | skittles
| el | **encuentro** | match
**USEFUL WORDS** __(masculine)__
| el | **adversario** | opponent
| el | **alpinismo** | mountaineering
| el | **árbitro** | referee; umpire ( _tennis_ )
| el | **atletismo** | athletics
| el | **bádminton** | badminton
| el | **boxeo** | boxing
| el | **buceo** | diving
| el | **chándal** | tracksuit
| el | **cronómetro** | stopwatch
| el | **descanso** | half-time
| el | **entrenador** | trainer; coach
| el | **espectador** | spectator
| el | **footing** | jogging
| el | **ganador** | winner
| el | **gol** | goal
| el | **hipódromo** | race course
| los | **Juegos Olímpicos** | Olympic Games
| el | **Mundial (de Fútbol)** | World Cup
| el | **parapente** | paragliding
| el | **patín** | skate
| el | **patinaje sobre hielo** | (ice) skating
| el | **perdedor** | loser
| el | **portero** | goalkeeper
| el | **principiante** | beginner
| el | **remo** | rowing; oar
| el | **resultado** | score
| el | **salto de altura** | high jump
| el | **salto de longitud** | long jump
| el | **squash** | squash
| el | **tanto** | goal; point
| el | **tiro** | shooting
| el | **torneo** | tournament
| el | **trineo** | sledge
**IMPORTANT WORDS** __(feminine)__
---
| la | **bola** | ball ( _small_ )
| la | **carrera** | race
| las | **carreras (de caballos)** | horse-racing
| la | **defensa** | defence
| la | **petanca** | pétanque
| la | **pista de esquí** | ski slope
**USEFUL WORDS** __(feminine)__
| la | **adversaria** | opponent
| la | **árbitra** | referee; umpire ( _tennis_ )
| la | **camiseta (de deporte)** | jersey, shirt
| la | **caña de pescar** | fishing rod
| la | **caza** | hunting
| la | **copa** | cup
| la | **Copa del Mundo** | World Cup
| la | **eliminatoria** | heat
| la | **entrenadora** | trainer, coach
| la | **esgrima** | fencing
| la | **espectadora** | spectator
| la | **estación de esquí** | ski resort
| | ( _pl_ estaciones de ~) |
| la | **etapa** | stage
| la | **final** | final
| la | **ganadora** | winner
| la | **jabalina** | javelin
| la | **lucha libre** | wrestling
| la | **perdedora** | loser
| la | **pesca** | fishing
| la | **pista de hielo** | ice rink
| la | **pista de patinaje** | skating rink
| la | **portera** | goalkeeper
| la | **principiante** | beginner
| la | **prórroga** | extra time
| la | **raqueta** | racket
| la | **red** | net
| la | **tribuna** | stand
| las | **zapatillas de deporte** | sports shoes; trainers
| las | **zapatillas de tenis** | tennis shoes
#
theatre and cinema
**ESSENTIAL WORDS** __(masculine)__
---
| el | **actor** | actor
| el | **ambiente** | atmosphere
| el | **anfiteatro** | dress circle
| el | **asiento** | seat
| el | **auditorio** | auditorium; audience
| el | **boleto** ( _LAm_ ) | ticket
| el | **cine** | cinema
| el | **circo** | circus
| el | **cómico** | comedian
| el | **espectáculo** | show
| el | **patio de butacas** | stalls
| el | **payaso** | clown
| el | **programa** | programme
| el | **público** | audience
| el | **teatro** | theatre
| el | **vestuario** | costume
| el | **videoclip** ( _pl_ ~s) | music video
| el | **western** ( _pl_ ~s) | western
**IMPORTANT WORDS** __(masculine)__
| el | **acomodador** | usher
| el | **actor principal** | leading man
| el | **ballet** ( _pl_ ~s) | ballet
| el | **cartel** | notice; poster
| el | **director** | director
| el | **entreacto** | interval
| el | **intermedio** | interval
| el | **maquillaje** | make-up
**USEFUL PHRASES**
ir al teatro/al cine to go to the theatre/to the cinema
reservar un asiento to book a seat
un asiento en el patio de butacas a seat in the stalls
mi actor preferido/actriz preferida my favourite actor/actress
durante el intermedio during the interval
salir a escena to come on stage
interpretar el papel de to play the part of
**ESSENTIAL WORDS** __(feminine)__
---
| la | **actriz** ( _pl_ actrices) | actress
| la | **banda sonora** | soundtrack
| la | **boletería** ( _LAm_ ) | box office
| la | **cómica** | comedian
| la | **cortina** | curtain
| la | **entrada** | ticket
| la | **estrella de cine** | film star
| la | **música** | music
| la | **obra (de teatro)** | play
| la | **ópera** | opera
| la | **orquesta** | orchestra
| la | **payasa** | clown
| la | **película** | film
| la | **sala** | auditorium; cinema
| la | **salida** | exit
| la | **sesión** ( _pl_ sesiones) | performance; showing
| la | **taquilla** | box office
**USEFUL PHRASES**
interpretar to play
bailar to dance
cantar to sing
filmar una película to shoot a film
"próxima sesión: 21 horas" "next showing: 9 p.m."
"versión original" "original version"
"subtitulada" "subtitled"
"localidades agotadas" "full house"
aplaudir to clap
¡bis! encore!
¡bravo! bravo!
una película de ciencia ficción/de amor a science fiction film/a romance
una película de aventuras/de terror an adventure/horror film
**IMPORTANT WORDS** __(masculine continued)__
---
| el | **primer actor** | leading man
| el | **protagonista** | star
| el | **subtítulo** | subtitle
| el | **título** | title
**USEFUL WORDS** __(masculine)__
| el | **anfiteatro** | circle
| los | **aplausos** | applause
| el | **apuntador** | prompter
| el | **argumento** | plot
| los | **bastidores** | wings
| el | **crítico** | critic
| el | **culebrón** ( _pl_ culebrones) | soap (opera)
| el | **decorado** | scenery
| el | **director de escena** | producer; stage manager
| el | **dramaturgo** | playwright
| el | **ensayo (general)** | (dress) rehearsal
| el | **escenario** | stage; scene
| el | **espectador** | member of the audience
| el | **estrado** | platform
| el | **estreno** | first night, premiere
| el | **foco** | spotlight
| el | **foso de la orquesta** | orchestra pit
| el | **gallinero** | the "gods"
| el | **guardarropa** | cloakroom
| el | **guión** ( _pl_ guiones) | script
| el | **guionista** | scriptwriter
| el | **musical** | musical
| el | **palco** | box
| el | **papel** | part
| el | **personaje** | character
| el | **productor** | producer
| el | **realizador** | director ( _cinema_ ); producer ( _TV_ )
| el | **regidor** | stage manager
| el | **reparto** | cast
| el | **serial** | serial
| el | **vestíbulo** | foyer
**IMPORTANT WORDS** __(feminine)__
---
| la | **acomodadora** | usherette
| la | **actriz principal** ( _pl_ actrices ~es) | leading lady
| la | **butaca** | seat
| la | **cartelera** | hoarding, billboard;
| | | listings section
| la | **comedia** | comedy
| la | **directora** | director
| la | **platea** | stalls
| la | **primera actriz** ( _pl_ ~s actrices) | leading lady
| la | **propina** | tip
| la | **protagonista** | star
| la | **reserva** | booking
**USEFUL WORDS** __(feminine)__
| la | **actuación** ( _pl_ actuaciones) | acting, performance
| la | **apuntadora** | prompter
| las | **candilejas** | footlights
| la | **crítica** | review; critics; critic
| la | **directora de escena** | producer; stage manager
| la | **dramaturga** | playwright
| la | **escena** | scene
| la | **escenografía** | scenery
| la | **espectadora** | member of the audience
| la | **farsa** | farce
| la | **función** ( _pl_ funciones) | performance
| la | **guionista** | scriptwriter
| la | **pantalla** | screen
| la | **platea** | stalls
| la | **productora** | producer
| la | **puesta en escena** | production
| la | **realizadora** | director ( _cinema_ ); producer ( _TV_ )
| la | **regidora** | stage manager
| la | **representación** | performance
| | ( _pl_ representaciones) |
| la | **serie** | series
| la | **tragedia** | tragedy
#
time
**ESSENTIAL WORDS** __(masculine)__
---
| el | **año** | year
| el | **cuarto de hora** | quarter of an hour
| el | **despertador** | alarm clock
| el | **día** | day
| el | **fin de semana** | weekend
| el | **instante** | moment
| el | **mes** | month
| el | **minuto** | minute
| el | **momento** | moment
| el | **reloj** | watch; clock
| el | **segundo** | second
| el | **siglo** | century
| el | **tiempo** | time
**USEFUL PHRASES**
a mediodía at midday
a medianoche at midnight
pasado mañana the day after tomorrow
hoy today
hoy en día nowadays
anteayer, antes de ayer the day before yesterday
mañana tomorrow
ayer yesterday
hace dos días 2 days ago
dentro de dos días in 2 days
una semana a week
una quincena a fortnight
todos los días every day
¿a qué día estamos?,¿qué día es hoy? what day is it?
¿cuál es la fecha de hoy? what's the date?
de momento at the moment
las tres menos cuarto a quarter to 3
las tres y cuarto a quarter past 3
en el siglo XXI in the 21st century
ayer por la noche last night, yesterday evening
**ESSENTIAL WORDS** __(feminine)__
---
| la | **hora** | hour; time ( _in general_ )
| la | **jornada** | day
| la | **mañana** | morning
| la | **media hora** | half an hour
| la | **noche** | night; evening
| la | **quincena** | fortnight
| la | **semana** | week
| la | **tarde** | afternoon; evening
**USEFUL PHRASES**
el año pasado/próximo last/next year
la semana/el año que viene next week/year
dentro de media hora in half an hour
una vez once
dos/tres veces two/three times
varias veces several times
tres veces al año three times a year
nueve de cada diez veces nine times out of ten
érase una vez once upon a time there was
diez a la vez ten at a time
¿qué hora es? what time is it?
¿tiene hora? have you got the time?
son las seis/las seis menos diez/las seis y media it is 6 o'clock/10 to 6/ half past 6
son las dos en punto it is 2 o'clock exactly
hace un rato a while ago
dentro de un rato in a while
temprano early
tarde late
esta noche ( _past_ ) last night; ( _to come_ ) tonight
**IMPORTANT WORDS** __(masculine)__
---
| el | **día siguiente** | next day
| el | **futuro** | future; future tense
| el | **pasado** | past; past tense
| el | **presente** | present ( _time_ ); present tense
| el | **retraso** | delay
**USEFUL WORDS** __(masculine)__
| el | **año bisiesto** | leap year
| el | **calendario** | calendar
| el | **cronómetro** | stopwatch
| el | **reloj de pie** | grandfather clock
| el | **reloj de pulsera** | wristwatch
**USEFUL PHRASES**
pasado mañana the day after tomorrow
dos días después two days later
el día antes _or_ el día anterior the day before
un día sí y otro no every other day
en el futuro in the future
un día libre a day off
un día de fiesta a public holiday
un día laborable a weekday
en un día de lluvia, en un día lluvioso on a rainy day
al amanecer, al alba at dawn
la mañana/tarde siguiente the following morning/evening
ahora now
**USEFUL WORDS** __(feminine)__
---
| las | **agujas** | hands ( _of clock_ )
| la | **década** | decade
| la | **Edad Media** | Middle Ages
| la | **época** | time; era
| la | **esfera** | face ( _of clock_ )
| las | **manecillas** | hands ( _of clock_ )
**USEFUL PHRASES**
llegas tarde you are late
llegas temprano you are early
este reloj adelanta/atrasa this watch is fast/slow
llegar a tiempo, llegar a la hora to arrive on time
¿cuánto tiempo? how long?
el tercer milenio the third millennium
no levantarse hasta tarde to have a lie-in
de un momento a otro any minute now
dentro de una semana in a week's time
el lunes que viene no el otro a week on Monday
la noche antes, la noche anterior the night before
en esa época at that time
#
tools
**ESSENTIAL WORDS** __(masculine)__
---
| el | **bricolaje** | DIY
| el | **manitas** ( _pl inv_ ) | handyman
| el | **taller** | workshop
**USEFUL WORDS** __(masculine)__
| el | **alambre (de espino)** | (barbed) wire
| los | **alicates** | pliers
| el | **andamio** | scaffolding
| el | **candado** | padlock
| el | **celo** ( _Sp_ ) | Sellotape®
| el | **chinche** ( _LAm_ ) | drawing pin
| el | **cincel** | chisel
| el | **clavo** | nail
| el | **destornillador** | screwdriver
| el | **durex ®** ( _LAm_ ) | Sellotape®
| el | **martillo** | hammer
| el | **muelle** | spring
| el | **pico** | pickaxe
| el | **pincel** | paintbrush
| el | **taladro** | drill
| el | **tornillo** | screw
**USEFUL PHRASES**
hacer bricolaje, hacer chapuzas to do odd jobs
clavar un clavo con el martillo to hammer in a nail
"recién pintado(a)" "wet paint"
pintar to paint
empapelar to wallpaper
**ESSENTIAL WORDS** __(feminine)__
---
| la | **cuerda** | rope
| la | **herramienta** | tool
| la | **llave** | key; ( _LAm_ ) tap
| la | **llave inglesa** | spanner
| la | **manitas** ( _pl inv_ ) | handywoman
| la | **máquina** | machine
**USEFUL WORDS** __(feminine)__
| la | **aguja** | needle
| la | **batería** | battery ( _in car_ )
| la | **caja de herramientas** | toolbox
| la | **cerradura** | lock
| la | **chinche** ( _LAm_ ) | drawing pin
| la | **chincheta** ( _Sp_ ) | drawing pin
| la | **cola** | glue
| la | **escalera (de mano)** | ladder
| la | **goma (elástica)** | rubber band
| la | **horca** | ( _garden_ ) fork
| la | **lima** | file
| la | **obra** | construction site
| la | **pala** | spade
| la | **pila** | battery ( _in radio etc_ )
| la | **sierra** | saw
| la | **tabla** | plank
| la | **taladradora** | pneumatic drill
| las | **tijeras** | scissors
**USEFUL PHRASES**
"prohibido el paso a la obra" "construction site: keep out"
práctico(a) handy
cortar to cut
reparar to mend
atornillar to screw (in)
desatornillar to unscrew
#
town
**ESSENTIAL WORDS** __(masculine)__
---
| los | **alrededores** | surroundings
| el | **aparcamiento** ( _Sp_ ) | car park; parking space
| el | **autobús** ( _pl_ autobuses) | bus
| el | **ayuntamiento** | town hall; town council
| el | **banco** | bank; bench
| el | **barrio** | district
| el | **bloque de departamentos** ( _LAm_ ) | block of flats
| el | **bloque de pisos** ( _Sp_ ) | block of flats
| el | **café** | café; coffee
| el | **carro** ( _LAm_ ) | car
| el | **centro de la ciudad** | town centre
| el | **cine** | cinema
| el | **coche** ( _Sp_ ) | car
| el | **edificio** | building
| el | **estacionamiento** ( _LAm_ ) | car park; parking space
| el | **habitante** | inhabitant
| el | **hotel** | hotel
| el | **mercado** | market
| el | **metro** | underground, subway
| el | **museo** | museum; art gallery
| el | **parking** ( _pl_ ~s) | car park
| el | **parque** | park
| el | **peatón** ( _pl_ peatones) | pedestrian
| el | **policía** | policeman
| el | **puente** | bridge
| el | **restaurante** | restaurant
| el | **suburbio** | suburb; slum area
| el | **taxi** | taxi
| el | **teatro** | theatre
| el | **tour** ( _pl_ ~s) | tour
| el | **turista** | tourist
**ESSENTIAL WORDS** __(feminine)__
---
| la | **boutique** | boutique
| la | **calle** | street
| la | **carretera** | road
| la | **catedral** | cathedral
| la | **ciudad** | town, city
| la | **comisaría** | police station
| la | **contaminación** | air pollution
| la | **esquina** | corner
| la | **estación (de trenes)** | (train) station
| | ( _pl_ estaciones (~ ~ )) |
| la | **estación de autobuses** | bus station
| | ( _pl_ estaciones ~ ~) |
| la | **fábrica** | factory
| la | **gasolinera** | petrol station
| la | **habitante** | inhabitant
| la | **lavandería automática** | launderette
| la | **oficina** | office
| la | **oficina de correos** | post office
| la | **parada de autobús** | bus stop
| la | **parada de taxis** | taxi rank
| la | **piscina** | swimming pool
| la | **plaza** | square
| la | **policía** | policewoman; police
| la | **tienda** | shop
| la | **torre** | tower
| la | **turista** | tourist
| la | **vista** | view
| la | **vivienda de protección oficial** | council flat
**USEFUL PHRASES**
voy a la ciudad _or_ al centro I'm going into town
en el centro (de la ciudad) in the town centre
en la plaza in the square
una calle de sentido único a one-way street
una zona muy urbanizada a built-up area
"dirección prohibida" "no entry"
cruzar la calle to cross the road
**IMPORTANT WORDS** __(masculine)__
---
| el | **abono** | season ticket
| el | **agente (de policía)** | police officer
| el | **alcalde** | mayor
| el | **atasco** | traffic jam
| el | **cartel** | notice; poster
| el | **castillo** | castle
| el | **cibercafé** | internet café
| el | **cruce** | crossroads
| los | **jardines públicos** | park
| el | **lugar** | place
| el | **monumento** | monument
| el | **parquímetro** | parking meter
| el | **quiosco de periódicos** | news stand
| el | **semáforo** | traffic lights
| el | **sitio** | place
| el | **tráfico** | traffic
| el | **transeúnte** | passer-by
| el | **zoológico** | zoo
**USEFUL PHRASES**
en la esquina de la calle at the corner of the street
vivir en las afueras to live in the outskirts
andar, caminar to walk
tomar el autobús/el metro, coger el autobús/el metro ( _Sp_ ) to take the bus/the underground
comprar una tarjeta multiviajes to buy a multiple-journey ticket
picar to punch ( _ticket_ )
**IMPORTANT WORDS** __(feminine)__
---
| la | **acera** | pavement
| la | **agente (de policía)** | police officer
| la | **alcaldesa** | mayor
| la | **biblioteca** | library
| la | **calle principal** | main street
| la | **calzada** | road
| la | **circulación** | traffic
| la | **desviación** ( _pl_ desviaciones) | diversion
| la | **estación de servicio** | petrol station
| | ( _pl_ estaciones ~ ~) |
| la | **iglesia** | church
| la | **máquina expendedora de** | ticket machine
| | **billetes** ( _Sp_ ) _or_ **de boletos** ( _LAm_ ) |
| la | **mezquita** | mosque
| la | **parte antigua** | old town
| la | **polución** | air pollution
| la | **sinagoga** | synagogue
| la | **tarjeta multiviajes** | multiple-journey ticket
| la | **transeúnte** | passer-by
| la | **zona azul** | restricted parking zone
| la | **zona industrial** | industrial estate
| la | **zona peatonal** | pedestrian precinct
**USEFUL PHRASES**
industrial industrial
histórico(a)historic
bonito(a) pretty
feo(a) ugly
limpio(a)clean
sucio(a) dirty
**USEFUL WORDS** __(masculine)__
---
| el | **adoquín** ( _pl_ adoquines) | cobblestone
| el | **barrio residencial** | residential area
| el | **callejón sin salida** ( _pl_ callejones ~ ~) | cul-de-sac, dead end
| el | **camino de bicicletas** | cycle path
| el | **carril bici** | cycle lane
| el | **cementerio** | cemetery
| el | **ciudadano** | citizen
| el | **cochecito (de niño)** | pram, buggy
| el | **concejo municipal** | town council
| el | **desfile** | parade
| el | **distrito** | district
| el | **edificio** | building
| el | **embotellamiento** | traffic jam
| el | **folleto** | leaflet
| los | **lugares de interés** | sights, places of interest
| el | **paradero de autobús** ( _LAm_ ) | bus stop
| el | **parque de bomberos** ( _Sp_ ) | fire station
| el | **paso de cebra** | zebra crossing
| el | **paso de peatones** | pedestrian crossing
| el | **pavimento** | road surface
| el | **rascacielos** ( _pl inv_ ) | skyscraper
| el | **sondeo de opinión** | opinion poll
**USEFUL WORDS** __(feminine)__
---
| las | **afueras** | outskirts
| la | **alcantarilla** | sewer
| la | **cafetería** | coffee shop, café; canteen
| la | **calle sin salida** | cul-de-sac, dead end
| la | **camioneta de reparto** | delivery van
| la | **cárcel** | prison
| la | **ciudadana** | citizen
| la | **cola** | queue
| la | **ciudad universitaria** | university campus
| la | **curva** | bend
| la | **estación de bomberos** | fire station
| | ( _pl_ estaciones ~ ~) ( _LAm_ ) |
| la | **estatua** | statue
| la | **farola** | street lamp
| la | **flecha** | arrow
| la | **galería de arte** | art gallery
| la | **isla peatonal** | traffic island
| la | **muchedumbre** | crowd
| la | **multitud** | crowd
| la | **muralla** | rampart
| la | **parada de autobús** | bus stop
| la | **población** ( _pl_ poblaciones) | population
| la | **señal de tráfico** | road sign
#
trains
**ESSENTIAL WORDS** __(masculine)__
---
| el | **andén** ( _pl_ andenes) | platform
| el | **asiento** | seat
| el | **AVE** | high-speed train
| el | **billete** ( _Sp_ ) | ticket
| el | **billete de ida** ( _Sp_ ) | single ticket
| el | **billete de ida y vuelta** ( _Sp_ ) | return ticket
| el | **billete sencillo** ( _Sp_ ) | single ticket
| el | **boleto** ( _LAm_ ) | ticket
| el | **boleto de ida** ( _LAm_ ) | single ticket
| el | **boleto de ida y vuelta** ( _LAm_ ) | return ticket
| el | **bolso** ( _Sp_ ) | handbag
| el | **compartimento** | compartment
| el | **descuento** | reduction
| el | **enlace** | connection
| el | **equipaje** | luggage
| el | **expreso** | fast train
| el | **freno** | brake
| el | **horario** | timetable
| el | **maletero** | porter
| el | **metro** | underground, subway
| el | **número** | number
| el | **oficial de aduanas** | customs officer
| el | **pasaporte** | passport
| el | **plano** | map
| el | **precio del billete** ( _Sp_ ) | fare
| | _or_ **del boleto** ( _LAm_ ) |
| el | **puente** | bridge
| el | **recargo** | extra charge
| el | **retraso** | delay
| el | **taxi** | taxi
| el | **tícket** ( _pl_ ~s) | ticket; receipt
| el | **tren** | train
| el | **vagón** ( _pl_ vagones) | carriage
| el | **viaje** | journey
| el | **viajero** | traveller
**ESSENTIAL WORDS** __(feminine)__
---
| la | **aduana** | customs
| la | **bici** | bike
| la | **bicicleta** | bicycle
| la | **boletería** ( _LAm_ ) | ticket office
| la | **bolsa** | bag
| la | **cafetería (de la estación)** | station buffet
| la | **cantina (de la estación)** | station buffet
| la | **cartera** | wallet; ( _LAm_ ) handbag
| la | **clase** | class
| la | **conexión** ( _pl_ conexiones) | connection
| la | **consigna** | left-luggage office
| la | **consigna automática** | left-luggage locker
| la | **dirección** ( _pl_ direcciones) | direction
| la | **entrada** | entrance
| la | **estación** ( _pl_ estaciones) | station
| la | **estación de metro** ( _pl_ estaciones ~ ~) | underground station
| la | **información** | information
| la | **línea** | line
| la | **llegada** | arrival
| la | **maleta** | suitcase
| la | **oficial de aduanas** | customs officer
| la | **oficina de objetos perdidos** | lost property office
| la | **parada de taxis** | taxi rank
| la | **petaca** ( _Mex_ ) | suitcase
| la | **reserva** | reservation
| la | **sala de espera** | waiting room
| la | **salida** | departure; exit
| la | **taquilla** | ticket office; locker
| la | **vía** | track, line
| la | **viajera** | traveller
**USEFUL PHRASES**
reservar un asiento to book a seat
pagar un recargo, pagar un suplemento to pay an extra charge, to pay a surcharge
hacer/deshacer el equipaje to pack/unpack
**IMPORTANT WORDS** __(masculine)__
---
| el | **coche-cama** ( _pl_ ~s~) | sleeping car
| el | **coche-comedor** ( _pl_ ~s~) | dining car
| el | **conductor** | driver
| el | **destino** | destination
| el | **ferrocarril** | railway
| el | **revisor** | ticket collector
**USEFUL WORDS** __(masculine)__
| el | **abono** | season ticket
| el | **baúl** | trunk
| el | **carnet joven** ( _pl_ ~s ~) | young persons' discount card
| el | **coche** | carriage
| el | **descarrilamiento** | derailment
| el | **jefe de estación** | stationmaster
| el | **maquinista** | engine-driver
| el | **panel informativo** | noticeboard
| el | **paso a nivel** | level crossing
| el | **silbato** | whistle
| el | **suplemento** | extra charge, supplement
| el | **trayecto** | journey
| el | **(tren de) mercancías** ( _pl_ (~es ~) ~) | goods train
**USEFUL PHRASES**
tomar el tren, coger el tren ( _Sp_ ) to take the train
perder el tren to miss the train
montarse en el tren to get on the train
bajar del tren to get off the train
¿está libre este asiento? is this seat free?
el tren lleva retraso the train is late
un vagón de fumadores/no fumadores a smoking/ non-smoking compartment
"prohibido asomarse por la ventanilla" "do not lean out of the window"
**IMPORTANT WORDS** __(feminine)__
---
| la | **barrera** | barrier
| la | **conductora** | driver
| la | **duración** ( _pl_ duraciones) | length (of time)
| la | **escalera mecánica** | escalator
| la | **frontera** | border
| la | **litera** | couchette
| la | **propina** | tip
| la | **RENFE** | Spanish Railway
| la | **revisora** | ticket collector
| la | **tarifa** | fare
**USEFUL WORDS** __(feminine)__
| la | **alarma** | alarm
| la | **etiqueta** | label
| la | **jefa de estación** | stationmaster
| la | **locomotora** | locomotive
| la | **maquinista** | engine-driver
| la | **vía férrea** | (railway) line or track
| las | **vías** | rails
**USEFUL PHRASES**
te acompañaré a la estación I'll go to the station with you
iré a buscarte a la estación I'll come and pick you up at the station
el tren de las diez con destino a/procedente de Madrid the 10 o'clock train to/from Madrid
#
trees
**ESSENTIAL WORDS** __(masculine)__
---
| el | **árbol** | tree
| el | **bosque** | wood
**USEFUL WORDS** __(masculine)__
| el | **abedul** | birch
| el | **abeto** | fir tree
| el | **acebo** | holly
| el | **albaricoque** | apricot tree
| el | **árbol frutal** | fruit tree
| el | **arbusto** | bush
| el | **arce** | maple
| el | **boj** | box tree
| el | **brote** | bud
| el | **castaño** | chestnut tree
| el | **cerezo** | cherry tree
| el | **chabacano** ( _Mex_ ) | apricot tree
| el | **chopo** | poplar
| el | **duraznero** ( _LAm_ ) | peach tree
| el | **espino** | hawthorn
| el | **follaje** | foliage
| el | **fresno** | ash
| el | **huerto** | orchard
| el | **limonero** | lemon tree
| el | **manzano** | apple tree
| el | **melocotonero** ( _Sp_ ) | peach tree
| el | **naranjo** | orange tree
| el | **nogal** | walnut tree
| el | **olmo** | elm
| el | **peral** | pear tree
| el | **pino** | pine
| el | **platanero** | banana tree
| el | **plátano** | plane tree
| el | **roble** | oak
| el | **sauce llorón** ( _pl_ ~s llorones) | weeping willow
| el | **tejo** | yew
| el | **tilo** | lime tree
| el | **tronco** | trunk
| el | **viñedo** | vineyard
**ESSENTIAL WORDS** __(feminine)__
---
| la | **hoja** | leaf
| la | **rama** | branch
| la | **selva (tropical)** | rain forest
**USEFUL WORDS** __(feminine)__
| la | **baya** | berry
| la | **corteza** | bark
| la | **encina** | ilex, holm oak
| el | **haya** ( _pl f_ las hayas) | beech
| la | **higuera** | fig tree
| la | **raíz** ( _pl_ raíces) | root
| la | **viña** | vineyard
#
vegetables
**ESSENTIAL WORDS** __(masculine)__
---
| el | **ajo** | garlic
| los | **champiñones** | mushrooms
| los | **chícharos** ( _Mex_ ) | peas
| los | **ejotes** ( _Mex_ ) | French beans
| los | **guisantes** ( _Sp_ ) | peas
| el | **pimiento** | pepper
| el | **tomate** | tomato
**USEFUL WORDS** __(masculine)__
| el | **apio** | celery
| el | **berro** | watercress
| el | **brécol** | broccoli
| el | **calabacín** ( _pl_ calabacines) | courgette
| el | **elote** ( _Mex_ ) | sweetcorn
| los | **espárragos** | asparagus
| los | **frijoles** ( _LAm_ ) | beans
| los | **garbanzos** | chickpeas
| el | **maíz (dulce** _or_ **tierno)** | sweetcorn
| el | **nabo** | turnip
| el | **pepino** | cucumber
| el | **perejil** | parsley
| el | **pimiento morrón** ( _pl_ ~s morrones) | (sweet) pepper
| el | **puerro** | leek
| el | **rábano** | radish
| el | **repollo** | cabbage
**USEFUL PHRASES**
cultivar verduras to grow vegetables
una mazorca de maíz ( _Sp_ ), una mazorca de choclo ( _Mex_ ) corn on the cob
**ESSENTIAL WORDS** __(feminine)__
---
| las | **arvejas** ( _LAm_ ) | peas
| la | **cebolla** | onion
| la | **coliflor** | cauliflower
| la | **ensalada** | salad
| las | **habichuelas** ( _LAm_ ) | French beans
| las | **judías verdes** ( _Sp_ ) | French beans
| la | **papa** ( _LAm_ , _Southern Sp_ ), | potato
| la | **patata** ( _Sp_ )
| las | **verduras** | vegetables
| la | **zanahoria** | carrot
**USESFUL WORDS** __(feminine)__
| la | **alcachofa** | artichoke
| las | **alubias** ( _Sp_ ) | beans
| la | **berenjena** | aubergine
| la | **calabacita** ( _Mex_ ) | courgette
| la | **calabaza** | pumpkin
| la | **cebolleta** | spring onion
| la | **col** | cabbage
| las | **coles de Bruselas** | Brussels sprouts
| la | **endibia** | endive, chicory
| la | **escarola** | curly endive
| las | **espinacas** | spinach
| las | **judías** | beans
| las | **judías blancas** | haricot beans
| la | **lechuga** | lettuce
| las | **legumbres** | pulses
| las | **lentejas** | lentils
| la | **remolacha** | beetroot
**USEFUL PHRASES**
zanahoria rallada grated carrot
biológico(a) organic
vegetariano(a) vegetarian
#
vehicles
**ESSENTIAL WORDS** __(masculine)__
---
| el | **autobús** ( _pl_ autobuses) | bus
| el | **autocar** | coach
| el | **avión** ( _pl_ aviones) | plane
| el | **barco de vela** | sailing ship; sailing boat
| el | **bote** | boat
| el | **bote de remos** | rowing boat
| el | **camión** ( _pl_ camiones) | lorry
| el | **carro** | cart; ( _LAm_ ) car
| el | **casco** | helmet
| el | **ciclomotor** | moped
| el | **coche** ( _Sp_ ) | car
| el | **coche de línea** | coach
| el | **helicóptero** | helicopter
| el | **medio de transporte** | means of transport
| el | **metro** | underground, subway
| el | **precio del billete** ( _Sp_ ) _or_ | fare
| | **del boleto** ( _LAm_ ) |
| el | **taxi** | taxi
| el | **transbordador** | ferry
| el | **transporte público** | public transport
| el | **tren** | train
| el | **vehículo** | vehicle
| el | **vehículo pesado** | heavy goods vehicle
**USEFUL PHRASES**
viajar to travel
ha ido a Barcelona en avión he flew to Barcelona
tomar el autobús/el metro/el tren, coger ( _Sp_ ) el autobús/el metro/el tren to take the bus/the subway/the train
montar en bicicleta to go cycling
se puede ir en coche you can go there by car
**ESSENTIAL WORDS** __(feminine)__
---
| la | **bici** | bike
| la | **bicicleta** | bicycle
| la | **camioneta** | van
| la | **caravana** | caravan
| la | **distancia** | distance
| la | **moto** | motorbike
| la | **motocicleta** | motorcycle, motorbike
| la | **parte de atrás** | back
| la | **parte de delante** | front
| la | **parte delantera** | front
| la | **parte trasera** | back
| la | **vespa ®** | scooter
**IMPORTANT WORDS** __(masculine)__
| el | **coche de bomberos** | fire engine
**IMPORTANT WORDS** __(feminine)__
| la | **ambulancia** | ambulance
| la | **grúa** | breakdown van
**USEFUL PHRASES**
reparar el coche de algn to repair sb's car
un coche de alquiler a hire car
un coche deportivo a sports car
un coche de carreras a racing car
un coche de empresa a company car
"coches de ocasión" "used cars"
arrancar to start, to move off
**USEFUL WORDS** __(masculine)__
---
| el | **aerodeslizador** | hovercraft
| el | **(barco de) vapor** | steamer
| el | **bulldozer** ( _pl_ ~s) | bulldozer
| el | **buque** | ship
| el | **camión articulado** ( _pl_ camiones ~s) | articulated lorry
| el | **camión cisterna** ( _pl_ camiones ~) | tanker
| el | **cochecito (de niño)** | pram, buggy
| el | **cohete** | rocket
| el | **hidroavión** ( _pl_ hidroaviones) | seaplane
| el | **jeep** ( _pl_ ~s) | jeep
| el | **navío** | ship
| el | **ovni (objeto volante** | UFO ( _unidentified flying object_ )
| | **no identificado)** |
| el | **petrolero** | oil tanker ( _ship_ )
| el | **planeador** | glider
| el | **platillo volante** | flying saucer
| el | **portaaviones** ( _pl inv_ ) | aircraft carrier
| el | **remolcador** | tug
| el | **remolque** | trailer
| el | **riesgo** | risk
| el | **submarino** | submarine
| el | **tanque** | tank
| el | **teleférico** | cable car
| el | **telesilla** | chairlift
| el | **tranvía** | tram
| el | **velero** | sailing ship; sailing boat
| el | **velomotor** | moped
| el | **yate** | yacht; pleasure cruiser
**USEFUL WORDS** __(feminine)__
---
| la | **barcaza** | barge
| la | **camioneta de reparto** | delivery van
| la | **canoa** | canoe
| la | **carreta** | waggon; cart
| la | **golondrina** | pleasure boat
| la | **lancha** | boat ( _small_ ); launch
| la | **lancha de salvamento** | lifeboat
| la | **lancha de socorro** | lifeboat
| la | **lancha neumática** | rubber dinghy
| la | **lancha rápida** | speedboat
| la | **locomotora** | locomotive
| la | **ranchera** | estate car
#
the weather
**ESSENTIAL WORDS** __(masculine)__
---
| el | **aire** | air
| el | **boletín meteorológico** | weather report
| | ( _pl_ boletines ~s) |
| el | **calor** | heat
| el | **cielo** | sky
| el | **clima** | climate
| el | **este** | east
| el | **frío** | cold
| el | **grado** | degree
| el | **hielo** | ice
| el | **invierno** | winter
| el | **norte** | north
| el | **oeste** | west
| el | **otoño** | autumn
| el | **paraguas** ( _pl inv_ ) | umbrella
| el | **parte meteorológico** | weather report
| el | **pronóstico del tiempo** | (weather) forecast
| el | **sol** | sun; sunshine
| el | **sur** | south
| el | **tiempo** | weather
| el | **verano** | summer
| el | **viento** | wind
**USEFUL PHRASES**
¿qué tiempo hace? what's the weather like?
hace calor/frío it's hot/cold
hace un día estupendo, hace un día precioso it's a lovely day
hace un día horrible it's a horrible day
al aire libre in the open air
hay niebla it's foggy
30° a la sombra 30° in the shade
escuchar el pronóstico del tiempo to listen to the weather forecast
llover to rain
nevar to snow
llueve it's raining
nieva it's snowing
**ESSENTIAL WORDS** __(feminine)__
---
| la | **estación** ( _pl_ estaciones) | season
| la | **lluvia** | rain
| la | **niebla** | fog
| la | **nieve** | snow
| la | **nube** | cloud
| la | **primavera** | spring
| la | **región** ( _pl_ regiones) | region, area
| la | **temperatura** | temperature
**USEFUL PHRASES**
brilla el sol the sun is shining
sopla el viento the wind is blowing
hace un frío que pela it's freezing
helarse to freeze
ha helado there's been a frost
fundirse to melt
soleado(a) sunny
tormentoso(a) stormy
lluvioso(a) rainy
frío(a) cool
variable changeable
húmedo(a)humid
el cielo está cubierto the sky is overcast
**IMPORTANT WORDS** __(masculine)__
---
| el | **chaparrón** ( _pl_ chaparrones) | shower
| el | **claro** | sunny spell
| el | **humo** | smoke
| el | **polvo** | dust
**USEFUL WORDS** __(masculine)__
| el | **aguacero** | downpour
| el | **amanecer** | dawn, daybreak
| el | **anochecer** | nightfall, dusk
| el | **arco iris** ( _pl inv_ ) | rainbow
| el | **barómetro** | barometer
| el | **cambio** | change
| el | **carámbano** | icicle
| el | **charco** | puddle
| el | **copo de nieve** | snowflake
| el | **crepúsculo** | twilight
| el | **deshielo** | thaw
| el | **granizo** | hail
| el | **huracán** ( _pl_ huracanes) | hurricane
| el | **pararrayos** ( _pl inv_ ) | lightning conductor
| el | **quitanieves** ( _pl inv_ ) | snowplough
| el | **rayo** | lightning
| el | **rayo de sol** | ray of sunshine
| el | **relámpago** | flash of lightning
| el | **rocío** | dew
| el | **trueno** | thunder
**IMPORTANT WORDS** __(feminine)__
---
| las | **precipitaciones** | rainfall
| la | **previsión meteorológica** | (weather) forecast
| | ( _pl_ previsiones ~s) |
| la | **sombrilla** | parasol
| la | **tormenta** | storm
| la | **visibilidad** | visibility
**USEFUL WORDS** __(feminine)__
| el | **alba** ( _pl f_ las albas) | dawn
| la | **atmósfera** | atmosphere
| la | **brisa** | breeze
| la | **bruma** | mist
| la | **corriente (de aire)** | draught
| la | **escarcha** | frost ( _on the ground_ )
| la | **gota de lluvia** | raindrop
| la | **helada** | frost ( _weather_ )
| la | **inundación** ( _pl_ inundaciones) | flood
| la | **luz de la luna** | moonlight
| la | **mejora** | improvement
| la | **nevada** | snowfall
| la | **ola de calor** | heatwave
| la | **oscuridad** | darkness
| la | **puesta de sol** | sunset
| la | **ráfaga de viento** | gust of wind
| la | **sequía** | drought
| la | **tormenta** | thunderstorm
| la | **ventisca** | snowdrift
# youth hostelling
**ESSENTIAL WORDS** __(masculine)__
---
| el | **albergue juvenil** | youth hostel
| los | **baños públicos** ( _LAm_ ) | toilets
| el | **bote de la basura** ( _Mex_ ) | dustbin
| el | **comedor** | dining room
| el | **cuarto de baño** | bathroom
| el | **cubo de la basura** | dustbin
| el | **desayuno** | breakfast
| el | **dormitorio** | dormitory
| los | **lavabos** | toilets
| el | **mapa** | map
| los | **servicios** ( _Sp_ ) | toilets
| el | **silencio** | silence
| el | **visitante** | visitor
**IMPORTANT WORDS** __(masculine)__
| el | **carnet de socio** ( _pl_ ~s ~ ~) | membership card
| el | **lavabo** | washbasin; toilet
| el | **saco de dormir** | sleeping bag
**ESSENTIAL WORDS** __(feminine)__
---
| la | **cama** | bed
| la | **(cama) litera** | bunk bed
| la | **cocina** | kitchen; cooking
| la | **comida** | meal
| la | **ducha** | shower
| la | **estancia** | stay
| la | **lista de precios** | price list
| la | **noche** | night
| la | **oficina** | office
| la | **sábana** | sheet
| la | **sala de juegos** | games room
| la | **tarifa** | rate( _s_ )
| las | **vacaciones** | holidays
| la | **visitante** | visitor
**IMPORTANT WORDS** __(feminine)__
| la | **caminata** | hike
| la | **excursión** ( _pl_ excursiones) | trip
| la | **guía** | guidebook
| la | **mochila** | rucksack
| las | **normas** | rules
| la | **ropa de cama** | bed linen
**USEFUL PHRASES**
pasar una noche en el albergue juvenil to spend a night at the youth hostel
quisiera alquilar un saco de dormir I would like to hire a sleeping bag
está todo ocupado there's no more room
#
supplementary vocabulary
The vocabulary items on pages 204 to 233 have been grouped under parts of speech rather than topics because they can apply in a wide range of circumstances. Use them just as freely as the vocabulary already given.
# **ARTICLES AND PRONOUNS**
**What is an article?**
In English, an **article** is one of the words _the_ , _a_ and _an_ which is given in front of a noun.
**What is a pronoun?**
A **pronoun** is a word you use instead of a noun, when you do not need or want to name someone or something directly, for example, _it_ , _you_ , _none_.
**algo** something; anything
**alguien** somebody, someone; anybody, anyone
**alguno/alguna** one; someone, somebody
**algunos/algunas** some, some of them; some of us, some of you, some of them
**ambos/ambas** both
**aquel/aquella; aquél/aquélla** that
**aquellos/aquellas; aquéllos/aquéllas** those
**cada** each; every
**cual** which; who; whom **lo cual** which
**cuál** what, which one
**cualquiera** any one; anybody, anyone **cualquiera de los dos/las dos** either ( _see also_ Adjectives)
**cualesquiera** ( _pl_ ) any ( _see also_ Adjectives)
**cuanto/cuanta** as much as
**cuánto/cuánta** how much
**cuantos/cuantas** as many as
**cuántos/cuántas** how many
**cuyo/cuya/cuyos/cuyas** whose **en cuyo caso** in which case
**demasiado/demasiada** too much
**demasiados** too many
**dos: los/las dos** both
**el/la** the
**él** he; him; it **de él** his
**ella** she; her; it **de ella** hers
**ello** it
**ellos/ellas** they; them **de ellos/ellas** theirs
**ese/esa; ése/ésa** that
**esos/esas; ésos/ésas** those
**este/esta; éste/ésta** this
**estos/estas; éstos/éstas** these
**la** her; it; you
**las** them; you
**le** him; her; it; you
**les** them; you
**lo** him; it; you
**los/las** the
**los** them; you
**me** me; myself
**mi/mis** my
**(el)mío/(la) mía/(los) míos/(las) mías** mine
**mismo/misma/mismos/mismas** same **mí mismo/misma; yo mismo/ misma** myself; **nosotros mismos/ nosotras mismas** ourselves; **sí misma; ella misma** herself; **sí mismo; él mismo** himself; **sí mismos/sí mismas; ellos mismos/ellas mismas** themselves; **ti mismo/ti misma; tú mismo/ tú misma; usted mismo/usted misma** yourself; **vosotros mismos/vosotras mismas; ustedes mismos/ustedes mismas** yourselves; **uno mismo/una misma** oneself
**mucho/mucha** a lot, lots; much ( _see also_ Adjectives; Adverbs)
**muchos/muchas** a lot, lots; many ( _see also_ Adjectives)
**nada** nothing **nada más** nothing else
**nadie** nobody, no one; anybody, anyone **nadie más** nobody else
**ninguno/ninguna** any; neither; either; none; no one, nobody **ninguno de los dos/ninguna de las dos** neither ( _see also_ Adjectives)
**ningunos/ningunas** any; none ( _see also_ Adjectives)
**nos** us; ourselves; each other
**nosotros/nosotras** we; us
**nuestro/nuestra/nuestros/ nuestras** our; ours **el nuestro/la nuestra/ los nuestros/las nuestras** ours
**os** you; yourselves; each other
**otro/otra** another, another one ( _see also_ Adjectives)
**otros/otras** others ( _see also_ Adjectives)
**poco/poca un poco** a bit, a little **dentro de poco** shortly
**pocos/pocas** not many, few
**que** who; that
**qué** what; what a
**quien/quienes** who; whoever
**quién/quiénes** who
**se** him; her; them; you; himself; herself; itself; themselves; yourself; yourselves; oneself; each other
**su/sus** his; her; its; their; your; one's
**(el) suyo/(la) suya /(los) suyos/ (las) suyas** his; her; its; their; your; hers; theirs; yours; one's own
**tal/tales** such
**tampoco** not...either, neither
**te** you; yourself
**ti** you
**todo/toda** (it) all **todo el mundo** everybody, everyone ( _see also_ Adjectives)
**todos/todas** all; every; everybody; everyone ( _see also_ Adjectives)
**tu/tus** your
**tú** you
**usted** you
**ustedes** you
**(el) tuyo/ (la) tuya/ (los) tuyos/(las) tuyas** yours
**un/una** a; an; one
**unos/unas** some; a few; about, around
**varios/varias** several
**vosotros/vosotras** you
**vuestro/vuestra/vuestros/ vuestras** your; yours **los vuestros/las vuestras** yours
**yo** I; me
# **CONJUNCTIONS**
**What is a conjunction?**
A **conjunction** is a word such as _and_ , _but_ , _or_ , _so_ , _if_ and _because_ , that links two words or phrases of a similar type, or two parts of a sentence, for example, _Diane and I have been friends for years_; _I left because I was bored_.
**ahora** though **ahora bien** however; **ahora que** now that
**antes: antes de que** before
**así: así (es) que** so **así pues** so
**aunque** although, though
**como** as
**conque** so, so then
**consiguiente: por consiguiente** so, therefore
**cuando** when; whenever; if
**cuanto: en cuanto** as soon as; as
**dar: dado que** since
**decir: es decir** that is to say
**desde: desde que** since
**después: después de que** after
**e** and
**embargo: sin embargo** still, however
**entonces** then
**fin: a fin de que** so that, in order that
**forma: de forma que** so that
**hasta: hasta que** until, till
**luego** therefore
**manera: de manera que** so that
**mas** but
**más: más que** more than
**menos: menos que** less than
**mientras** while; as long as **mientras que** whereas; **mientras (tanto)** meanwhile
**modo: de modo que** so that
**momento: en el momento en que** just as
**ni** or; nor; even **ni...ni** neither...nor
**o** or **o... o...** either... or...
**para: para que** so that
**pero** but
**porque** because
**pronto: tan pronto como** as soon as
**pues** then; well; since
**puesto: puesto que** since
**que** that
**ser: o sea** that is **a no ser que** unless
**si** if; whether **si no** otherwise
**siempre: siempre que** whenever; as long as, provided that
**sino** but; except; only
**tal: con tal (de) que** as long as, provided that
**tanto: por (lo) tanto** so, therefore
**u** or
**vez: una vez que** once
**vista: en vista de que** seeing that
**y** and
**ya: ya que** as, since
# **ADJECTIVES**
**What is an adjective?**
An **adjective** is a 'describing' word that tells you more about a person or thing, such as their appearance, colour, size or other qualities, for example, _pretty_ , _blue_ , _big_.
**abierto(a)** open
**absoluto(a)** absolute
**absurdo(a)** absurd
**académico(a)** academic
**accesible** accessible; approachable
**aceptable** acceptable
**acondicionado(a)** fitted out **con aire acondicionado** air-conditioned
**acostumbrado(a)** accustomed
**activo(a)** active
**acusado(a)** accused; marked
**adecuado(a)** appropriate
**admirable** admirable
**aéreo(a)** aerial
**aficionado(a)** keen
**afilado(a)** sharp
**afortunado(a)** fortunate, lucky
**agitado(a)** rough; agitated; hectic
**agotado(a)** exhausted
**agradable** pleasant, agreeable
**agresivo(a)** aggressive
**agrícola** agricultural
**agudo(a)** sharp; acute
**aislado(a)** isolated
**alegre** happy; bright; lively; merry
**alguno/alguna (** _before masc sing_ **algún)** some; any ( _see also_ Articles and Pronouns)
**algunos/algunas** some; several ( _see also_ Articles and Pronouns)
**alternativo(a)** alternating; alternative
**alto(a)** high; tall
**amargo(a)** bitter
**ancho(a)** broad; wide
**anciano(a)** elderly
**animado(a)** lively; cheerful
**anónimo(a)** anonymous
**anormal** abnormal
**anterior** former
**antiguo(a)** old; vintage; antique
**anual** annual
**apagado(a)** out; off; muffled; dull
**aparente** apparent
**apasionado(a)** passionate
**apropiado(a)** appropriate, suitable
**aproximado(a)** rough
**arriba: de arriba** top
**asequible** affordable
**asombrado(a)** amazed, astonished
**asombroso(a)** amazing, astonishing
**áspero(a)** rough
**atestado(a)** crowded; popular
**atento(a)** attentive; watchful
**atractivo(a)** attractive
**automático(a)** automatic
**avanzado(a)** advanced
**bajo(a)** low; short
**barba: con barba** bearded
**barbudo(a)** bearded
**básico(a)** basic
**bastante** enough; quite a lot of ( _see also_ Adverbs)
**bien** well-to-do
**bienvenido(a)** welcome
**blando(a)** soft
**breve** brief
**brillante** shining; bright
**brutal** brutal
**bruto(a)** rough; stupid; uncouth; gross
**bueno(a)** good
**cada** each; every
**caliente** hot; warm
**callado(a)** quiet
**cansado(a)** tired
**capaz** capable
**cariñoso(a)** affectionate
**caro(a)** expensive, dear
**cauteloso(a)** cautious
**central** central
**ceñido(a)** tight
**cercano(a)** close; nearby
**cerrado(a)** closed; off
**científico(a)** scientific
**cierto(a)** true; certain
**civil** civil; civilian
**claro(a)** clear; light; bright
**clásico(a)** classical; classic
**climatizado(a)** air-conditioned
**cobarde** cowardly
**comercial** commercial
**cómodo(a)** comfortable
**complejo(a)** complex
**completo(a)** complete
**complicado(a)** complicated; complex
**comprensivo(a)** understanding
**común** common; mutual
**concreto(a)** specific; concrete
**concurrido(a)** crowded; popular
**conmovedor(a)** moving
**consciente** conscious; aware
**conservador(a)** conservative
**considerable** considerable
**constante** constant
**contemporáneo(a)** contemporary
**contento(a)** happy; pleased
**continuo(a)** continuous
**convencional** conventional
**correcto(a)** correct, right
**corriente** ordinary; common
**cortado(a)** cut; closed; off; shy
**creativo(a)** creative
**cristiano(a)** Christian
**crítico(a)** critical
**crudo(a)** raw
**cuadrado(a)** square
**cualquiera (** _before masc and fem sing_ **cualquier)** any ( _see also_ Articles and Pronouns)
**cualesquiera** any ( _see also_ Articles and Pronouns)
**cuanto/cuanta** as much as
**cuánto/cuánta** how much
**cuantos/cuantas** as many as
**cuántos/cuántas** how many
**cultural** cultural
**curioso(a)** curious
**debido(a)** due, proper
**decepcionante** disappointing
**decidido(a)** determined
**delicado(a)** delicate
**delicioso(a)** delicious
**demasiado/demasiada** too much
**demasiados** too many
**democrático(a)** democratic
**derecho(a)** right
**desafortunado(a)** unfortunate
**desagradable** unpleasant
**desconocido(a)** unknown
**desesperado(a)** desperate
**desierto(a)** deserted
**desnudo(a)** naked; bare
**despejado(a)** clear
**despierto(a)** awake; sharp; alert
**despreocupado(a)** carefree; careless
**destruido(a)** destroyed
**detallado(a)** detailed
**diestro(a)** skilful
**difícil** difficult
**digno(a)** worthy; dignified
**diminuto(a)** tiny
**directo(a)** direct
**disgustado(a)** upset
**disponible** available
**dispuesto(a)** arranged; willing
**distinguido(a)** distinguished
**distinto(a)** different; various
**divertido(a)** funny, amusing; fun; entertaining
**dividido(a)** divided
**divino(a)** divine
**doble** double
**domesticado(a)** tame
**doméstico(a)** domestic
**dos: los/las dos** both
**dulce** sweet
**duro(a)** hard
**económico(a)** economic; economical
**efectivo(a)** effective
**eficaz** effective; efficient
**eficiente** efficient
**eléctrico(a)** electric
**electrónico(a)** electronic
**elemental** elementary
**emocionante** exciting
**emotivo(a)** emotional; moving
**encantador(a)** charming; lovely
**enmascarado(a)** masked
**enorme** enormous, huge
**enterado(a)** knowledgeable; well-informed; aware
**entero(a)** whole
**equivalente** equivalent
**equivocado(a)** wrong
**escandaloso(a)** shocking
**esencial** essential
**especial** special
**específico(a)** specific
**espectacular** spectacular
**espeso(a)** thick
**espiritual** spiritual
**estrecho(a)** narrow
**estricto(a)** strict
**estropeado(a)** broken (off); off
**estupendo(a)** marvellous, great
**estúpido(a)** stupid
**étnico(a)** ethnic
**evidente** obvious, evident
**exacto(a)** exact; accurate
**excelente** excellent
**excepcional** outstanding
**exclusivo(a)** exclusive
**exigente** demanding, exacting
**experto(a)** experienced
**éxito: de éxito** successful
**exitoso(a)** successful
**exquisito(a)** delicious; exquisite
**extra** extra; top-quality
**extranjero(a)** foreign
**extraño(a)** strange; foreign
**extraordinario(a)** extraordinary; outstanding; special
**extremo(a)** extreme
**fácil** easy
**falso(a)** false
**familiar** family; familiar
**famoso(a)** famous
**fatigoso(a)** tiring
**federal** federal
**feroz** fierce
**fijo(a)** fixed; permanent
**final** final
**financiero(a)** financial
**fino(a)** fine; smooth; refined
**firme** firm; steady
**físico(a)** physical
**flexible** flexible
**fluido(a)** fluid; fluent
**formal** reliable; formal; official
**frágil** fragile; frail
**frecuente** frequent
**fresco(a)** fresh; cool; cheeky
**fuerte** strong; loud
**futuro(a)** future
**general** general
**generoso(a)** generous
**genial** brilliant; wonderful
**gentil** kind
**genuino(a)** genuine
**global** global
**gordo(a)** fat; big
**grande (** _before masc sing_ **gran)** big; great
**grandioso(a)** grand; grandiose
**habitual** usual
**herido(a)** injured; wounded; hurt
**hermoso(a)** beautiful
**histórico(a)** historic; historical
**holgado(a)** loose
**honrado(a)** honest; respectable
**horrible** horrific; hideous; terrible
**horroroso(a)** dreadful; hideous; terrible
**humano(a)** human; humane
**ideal** ideal
**idéntico(a)** identical
**igual** equal
**ilegal** illegal
**iluminado(a)** illuminated, lit; enlightened
**ilustrado(a)** illustrated
**imaginario(a)** imaginary
**impar** odd
**importante** important
**imposible** impossible
**imprescindible** indispensable
**impresionante** impressive; moving; shocking
**inaguantable** unbearable
**incapaz (de)** incapable (of)
**increíble** incredible; unbelievable
**inculto(a)** uncultured
**indefenso(a)** defenceless
**independiente** independent
**indiferente** unconcerned
**individual** individual; single
**industrial** industrial
**inesperado(a)** unexpected
**inevitable** inevitable
**infantil** childlike; childish
**inflable** inflatable
**injusto(a)** unfair
**inmediato(a)** immediate
**inmenso(a)** immense
**inmune** immune
**inquieto(a)** anxious; restless
**intacto(a)** intact
**intencionado(a)** deliberate
**intenso(a)** intense; intensive
**interior** interior; inside; inner; domestic
**interminable** endless
**internacional** international
**interno(a)** internal
**interrumpido(a)** interrupted
**inútil** useless
**invisible** invisible
**izquierdo(a)** left
**junto(a)** together
**justo(a)** just, fair; exact; tight
**largo(a)** long
**legal** legal
**lento(a)** slow
**libre** free
**ligero(a)** light; slight; agile
**limpio(a)** clean
**liso(a)** smooth; straight; plain
**listo(a)** ready; bright
**llamativo(a)** bright; striking
**llano(a)** flat; straightforward
**lleno(a) (de)** full (of)
**lluvioso(a)** rainy, wet
**loco(a)** mad, crazy
**lujo: de lujo** luxurious
**lujoso(a)** luxurious
**magnífico(a)** magnificent; wonderful, superb
**maligno(a)** malignant; evil, malicious
**malo(a)** bad
**malvado(a)** wicked
**manso(a)** meek; tame
**maravilloso(a)** marvellous, wonderful; magic
**marcado(a)** marked
**más** more of a
**máximo(a)** maximum
**mayor** bigger; elder **el/la...mayor** the biggest...; the eldest...
**mecánico(a)** mechanical
**médico(a)** medical
**medio(a)** half; average
**medioambiental** environmental
**mejor** better **el/la mejor** the best
**menor** smaller; younger **el/la...menor** the smallest; the youngest
**menos** less of a
**mental** mental
**militar** military
**minucioso(a)** thorough; very detailed
**mismo(a)** same
**misterioso(a)** mysterious
**moderado(a)** moderate
**moderno(a)** modern
**mojado(a)** wet; soaked
**molesto(a)** annoying; annoyed; awkward; uncomfortable
**montañoso(a)** mountainous
**mucho/mucha** a lot of, lots of; much ( _see also_ Pronouns; Adverbs)
**muchos/muchas** a lot of, lots of; many ( _see also_ Pronouns)
**muerto(a)** dead
**mundial** worldwide, global
**mutuo(a)** mutual
**nacido(a)** born
**nacional** national; domestic
**nativo(a)** native
**natural** natural
**necesario(a)** necessary
**negativo(a)** negative
**ninguno/ninguna (** _before masc sing_ **ningún)** no; any ( _see also_ Pronouns)
**ningunos/ningunas** no; any ( _see also_ Pronouns)
**normal** normal; standard
**nuclear** nuclear
**nuevo(a)** new
**numeroso(a)** numerous
**obediente** obedient
**objetivo(a)** objective
**obligatorio(a)** compulsory, obligatory
**obvio(a)** obvious
**ocupado(a)** busy; taken; engaged; occupied
**oficial** official
**oportuno(a)** opportune; appropriate
**original** original
**oscuro(a)** dark; obscure
**otro/otra** another **a/en otro lugar** somewhere else; **otra cosa** something else; **otra persona** somebody else; **otra vez** again ( _see also_ Pronouns); **otros/ otras** other ( _see also_ Pronouns)
**pacífico(a)** peaceful; peaceable
**pálido(a)** pale
**par** even
**particular** special; particular; private
**patético(a)** pathetic
**peligroso(a)** dangerous
**peor** worse **el peor** the worst
**perdido(a)** lost; stray; remote
**perfecto(a)** perfect
**personal** personal
**pesado(a)** heavy; tedious
**picante** hot
**pie: de pie** standing (up)
**poco/poca** not much, little
**pocos/pocas** not many, few
**poderoso(a)** powerful
**polémico(a)** controversial
**polvoriento(a)** dusty; powdery
**popular** popular
**portátil** portable
**posible** possible; potential
**positivo(a)** positive
**práctico(a)** practical
**precioso(a)** lovely, beautiful; precious
**preciso(a)** precise; necessary
**preferido(a)** favourite
**preliminar** preliminary
**presentable** presentable
**presunto(a)** alleged
**previo(a)** previous
**primario(a)** primary
**principal** main
**privado(a)** private
**privilegiado(a)** privileged
**profundo(a)** deep
**prometido(a)** promised; engaged
**propio(a)** own
**próximo(a)** near, close; next
**psicológico(a)** psychological
**público(a)** public
**pueril** childish
**pulcro(a)** neat
**puntiagudo(a)** pointed; sharp
**puntual** punctual
**puro(a)** pure
**qué** what; which; what a
**querido(a)** dear
**químico(a)** chemical
**racial** racial
**radical** radical
**rápido(a)** fast, quick
**raro(a)** strange, odd; rare
**razonable** reasonable
**reacio(a)** reluctant
**real** actual; royal
**reciente** recent
**recto(a)** straight; honest
**redondo(a)** round
**refrescante** refreshing
**regional** regional
**regular** regular
**religioso(a)** religious
**repentino(a)** sudden
**repuesto: de repuesto** spare
**reservado(a)** reserved
**resistente** resistant; tough
**responsable (de)** responsible (for)
**revolucionario(a)** revolutionary
**ridículo(a)** ridiculous
**rival** rival
**romántico(a)** romantic
**rubio(a)** fair, blond
**ruidoso(a)** noisy
**rural** rural
**sabio(a)** wise
**sagrado(a)** sacred
**salvaje** wild
**salvo: a salvo** safe
**sanitario(a)** sanitary; health
**sano(a)** healthy **sano(a) y salvo(a)** safe and sound
**santo(a)** holy
**satisfecho(a) (de)** satisfied (with)
**seco(a)** dry
**secreto(a)** secret
**secundario(a)** secondary
**seguro(a)** safe; secure; certain; sure
**semejante** similar
**sencillo(a)** simple; natural; single
**sensacional** sensational
**sentado(a)** sitting, seated
**señalado(a)** special
**separado(a)** separate
**servicial** helpful
**severo(a)** severe
**sexual** sexual
**significativo(a)** significant; meaningful
**siguiente** next, following
**silencioso(a)** silent; quiet
**sincero(a)** sincere
**singular** singular; outstanding
**siniestro(a)** sinister
**situado(a)** situated
**sobra: de sobra** spare
**sobrante** spare
**social** social
**solemne** solemn
**sólido(a)** solid
**solo(a)** alone; lonely; black; straight, neat
**soltero(a)** single
**sombrío(a)** sombre; dim
**sonriente** smiling
**soportable** bearable
**sorprendente** surprising
**sospechoso(a)** suspicious
**suave** smooth; gentle; mild; slight
**sucio(a)** dirty
**superior** top; upper; superior
**supremo(a)** supreme
**supuesto(a)** assumed; supposed
**tal/tales** such
**tanto/tanta** so much
**tantos/tantas** so many
**técnico(a)** technical
**terrible** terrible
**típico(a)** typical
**tirante** tight; tense
**todo/toda** all ( _see also_ Pronouns)
**todos/todas** all; every ( _see also_ Pronouns)
**tolerante** broad-minded
**total** total
**tradicional** traditional
**tremendo(a)** tremendous
**triste** sad
**último(a)** last **el último** the latest
**ultrajante** offensive; outrageous
**único(a)** only; unique
**urgente** urgent
**útil** useful, helpful
**vacante** vacant
**vacío(a)** empty
**valiente** brave, ourageous
**valioso(a)** valuable
**valor: de valor** valuable
**variado(a)** varied
**varios/varias** several
**vecino(a)** neighbouring
**verdad: de verdad** real
**verdadero(a)** real; true
**viejo(a)** old
**vil** villainous; vile
**violento(a)** violent; awkward
**visible** visible
**vital** vital
**vivo(a)** living; alive; lively
**voluntario(a)** voluntary
# **ADVERBS AND PREPOSITIONS**
**What is an adverb?**
An **adverb** is a word usually used with verbs, adjectives or other adverbs that gives more Information about when, how, where, or in what circumstances something happens, or to what degree something is true, for example, _quickly_ , _happily_ , _now_ , _extremely_ , _very_.
**What is a preposition?**
A **preposition** is a word such as _at_ , _for_ , _with_ , _into_ or _from_ , which is usually followed by a noun, pronoun, or, in English, a word ending in -ing. Prepositions show how people or things relate to the rest of the sentence, for example, _She's at home_; _a tool for cutting grass_; _It's from David_.
**a** to; at; into: onto
**abajo** down; downstairs; below **allá abajo** down there
**absolutamente** absolutely
**acá** here, over here; now
**acerca: acerca de** about
**actualmente** at present
**acuerdo: de acuerdo** OK, okay
**adelante** forward **en adelante** from now on **hacia adelante** forward
**además** also; furthermore, moreover, in addition **además de** as well as; besides
**admirablemente** admirably
**afortunadamente** fortunately
**agradablemente** nicely
**ahora** now; in a minute **hasta ahora** so far
**alcance: al alcance** within reach
**allá** there, over there
**allí** there
**alrededor de** around
**ansiosamente** anxiously
**ante** before; in the face of; faced with **ante todo** above all
**antemano: de antemano** beforehand, in advance
**anteriormente** previously, before
**antes** before **antes de** before **cuanto antes** as soon as possible **lo antes posible** as soon as possible
**apartado: apartado de** away from
**aparte: aparte de** apart from
**apenas** hardly, scarcely; only
**aproximadamente** approximately
**aquí** here; now
**arriba** up; upstairs; above **allá arriba** up there
**así** like that; like this **así como** as well as
**atentamente** attentively, carefully; kindly
**atrás** behind; at the back; backwards; ago **hacia atrás** backwards
**aun** even **aun así** even so **aun cuando** even if
**aún** still, yet; even
**azar: al azar** at random
**bajo** low; quietly; under
**básicamente** basically
**bastante** enough; quite a lot; quite ( _see also_ Adjectives)
**bien** well; carefully; very; easily
**brevemente** briefly
**bruscamente** abruptly
**cambio: a cambio de** in exchange for; in return for **en cambio** instead
**camino: de camino** on the way
**casi** almost, nearly
**caso: en el caso de (que)** in the case of **en todo caso** in any case
**casualidad: por casualidad** by chance
**causa: a causa de** because of
**cerca (de)** close (to); near (to)
**claramente** clearly
**cómo** how
**como** like; such as; as; about
**completamente** completely
**con** with
**concreto: en concreto** specifically, in particular
**continuamente** constantly
**contra** against
**correctamente** correctly
**cortésmente** politely
**cuando** when
**cuándo** when
**cuanto: en cuanto a** as regards, as for
**cuánto** how much; how far; how
**cuenta: a fin de cuentas** ultimately **teniendo en cuenta** considering
**cuidado: con cuidado** carefully
**cuidadosamente** carefully
**curiosamente** curiously
**curso: en el curso de** in the course of
**de** of; from; about; by; than; in; if
**debajo** underneath **debajo de** under; **por debajo** underneath; **por debajo de** under; below
**débilmente** faintly; weakly
**delante** in front; at the front; opposite **delante de** in front of; opposite **hacia delante** forward **por delante** ahead; at the front
**demasiado** too; too much
**dentro** inside **dentro de** inside; in; within
**deprisa** quickly, hurriedly
**derecha: a la derecha** on the right
**desde** from; since
**desgraciadamente** unfortunately
**despacio** slowly
**después** later; after(wards); then **después de** after
**detrás** behind; at the back; on the back; after **detrás de** behind; **por detrás** from behind; on the back
**día: al día** per day
**diariamente** on a daily basis
**diario: a diario** daily
**donde** where; wherever
**dónde** where
**dondequiera** anywhere
**duda: sin duda** definitely, undoubtedly
**dulcemente** sweetly; gently
**durante** during; for **durante todo/toda** throughout
**efecto: en efecto** in fact
**ejemplo: por ejemplo** for example
**en** in; on; at; into; by
**encima** on top **encima de** above; on top of; **por encima** over; **por encima de** over; above
**enfrente (de)** opposite
**enseguida** right away
**entonces** then **desde entonces** since then; **hasta entonces** until then
**entre** among(st); between
**especialmente** especially, particularly; specially
**evidentemente** obviously, evidently
**exactamente** exactly
**excepción: con la excepción de** with the exception of
**excepto** except (for)
**extranjero: en el extranjero** overseas; abroad
**extremadamente** extremely
**fácilmente** easily
**fielmente** faithfully
**fin: por fin** finally; at last
**finalmente** eventually
**forma: de alguna forma** somehow **de esta forma** like that; like this; **de ninguna forma** in no way; **de otra forma** otherwise; **de todas formas** anyway
**francamente** frankly; really
**frecuentemente** frequently
**frente: frente a** opposite, facing; against
**fuera** outside; out **fuera de** outside
**gana: de buena gana** willingly, happily **de mala gana** reluctantly
**general: por lo general** as a rule
**generalmente** generally
**gracias: gracias a** thanks to
**gradualmente** gradually
**hacia** towards
**hasta** to, as far as; up to; down to; until
**honradamente** honestly
**igualmente** equally; likewise
**incluido** including
**inmediatamente** immediately
**intensamente** intensely
**izquierda: a la izquierda** on the left
**jamás** never; ever
**junto: junto a** close to, near; next to; together with **junto con** together with
**justamente** just; exactly; justly
**lado: al lado (de)** next door (to); near **al lado de** alongside; **al otro lado de** across; **de un lado a otro** to and fro; **por este lado (de)** on this side (of)
**largo: a lo largo de** along
**lejos (de)** far (from)
**ligeramente** lightly; slightly
**luego** then; later, afterwards **desde luego** certainly
**mal** badly; poorly; ill
**manera: de alguna manera** somehow **de esta manera** like that; like this; **de ninguna manera** in no way; **de otra manera** otherwise; **de todas maneras** anyway
**más** more; plus **el/la más** the most; **más allá de** beyond; **más bien** rather; **más cerca** closer; **más lejos** further; **más o menos** about; **más...que** more...than; **no más** no more
**medio: en medio de** in the middle of **por medio de** by means of
**mejor** better **el mejor** the best
**menos** less; minus **el/la menos** the least; **menos...que** less than; **por lo menos** at least
**mentalmente** mentally
**menudo: a menudo** often
**misteriosamente** mysteriously
**modo: de algún modo** somehow **de este modo** like that; like this; **de ningún modo** in no way; **de otro modo** otherwise; **de todos modos** anyway
**momento: en este momento** at the moment **en ese mismo momento** at that very moment
**mucho** a lot **no mucho** not much ( _see also_ Pronouns; Adjectives)
**muy** very
**naturalmente** naturally
**nerviosamente** nervously
**no** no; not
**nombre: en nombre de** on behalf of
**normalmente** normally; usually
**novedad: sin novedad** safely
**nunca** never; ever
**paciencia: con paciencia** patiently
**para** for; to **para atrás** backwards; **para la derecha** towards the right; **para siempre** forever
**parte: de mi parte** on my behalf **en cualquier parte** anywhere; **en gran parte** largely
**en otra parte** elsewhere **en parte** partly, in part; **en todas partes** everywhere; **por otra parte** on the other hand
**peligrosamente** dangerously
**peor** worse **el peor** the worst
**perfectamente** perfectly
**persona: por persona** per person
**personalmente** personally
**pesadamente** heavily
**pesar: a pesar de** despite; in spite of **a pesar de que** even though
**pie: a pie** on foot
**poco** not very; not a lot; not much **poco a poco** little by little, bit by bit
**por** because of; for; by; through **por qué** why
**precisamente** precisely, exactly
**primero** first
**principalmente** mainly
**principio: al principio** at first
**probable** likely
**probablemente** probably
**profundamente** deeply
**pronto** soon
**propósito: a propósito** deliberately; on purpose
**qué** how
**querer: sin querer** accidentally
**quién: de quién/de quiénes** whose
**rápidamente** fast, quickly
**rápido** quickly
**realidad: en realidad** in fact, actually
**realmente** really
**recientemente** recently, lately
**regularmente** regularly, on a regular basis
**relativamente** relatively
**repente: de repente** suddenly
**seguida: en seguida** right away
**seguido** straight on **todo seguido** straight on
**según** according to; depending on
**seguramente** probably; surely
**sencillamente** simply
**sentido: en este sentido** in this respect
**separado: por separado** separately
**ser: a no ser que** unless
**serio: en serio** seriously
**sí** yes
**siempre** always **como siempre** as usual
**siguiente: al/el día siguiente** next day
**silencio: en silencio** quietly; in silence
**silenciosamente** quietly, silently
**sin** without **sin embargo** still, however, nonetheless
**siquiera: ni siquiera** not even
**sitio: en algún sitio** somewhere **en ningún sitio** nowhere
**sobre** on; over; about
**solamente** only; solely
**sólo** only; solely **tan sólo** only, just
**suavemente** gently; softly; smoothly
**suelo: al suelo** to the ground **en el suelo** on the ground
**sumamente** highly, extremely
**supuesto: por supuesto** of course
**tal: tal como** just as **tal y como están las cosas** under the circumstances; **tal vez** perhaps, maybe
**también** also, too
**tampoco** not...either, neither
**tan** so; such **tan... como** as... as
**tanto** so much; so often **tanto más** all the more
**tarde** late **más tarde** later; afterwards
**temprano** early **más temprano** earlier
**tiempo: a tiempo** in time; on time **al mismo tiempo** at the same time; **mucho tiempo** long
**todavía** still; yet; even
**todo: en todo/toda** throughout **todo lo más** at (the) most
**total** in short; at the end of the day **en total** altogether, in all
**totalmente** totally, completely
**través: a través de** through; across
**vano: en vano** in vain
**velocidad: a toda velocidad** at full speed, at top speed
**ver: por lo visto** apparently
**vez: algunas veces** sometimes **cada vez más** more and more; **cada vez menos** less and less; **de vez en cuando** from time to time, now and then; **en vez de** instead of; **rara vez** rarely, seldom; **una vez** once; **una vez más** once more
**vía: en vías de** on its way to **en vías de desarrollo** developing; **en vías de extinción** endangered
**vista: de vista** by sight **en vista de** in view of
**voz: en voz alta** aloud; loudly **en voz baja** in a low voice
**ya** already **ya mismo** at once; **ya no** not any more, no longer
# **SOME EXTRA NOUNS**
**What is a noun?**
A **noun** is a 'naming' word for a living being, thing or idea, for _example_ , _woman_ , _desk_ , _happiness_ , _Andrew_.
**la abertura** opening
**el abismo** gulf
**el aburrimiento** boredom
**el abuso** abuse
**el acceso** access
**la acción** ( _pl_ acciones) action
**el acento** accent
**el ácido** acid
**el acontecimiento** event
**la actitud** attitude
**la actividad** activity
**el acuerdo** agreement; settlement
**la advertencia** warning
**la afirmación** ( _pl_ afirmaciones) claim
**la agencia** agency
**la agenda** diary
**el/la agente** agent
**la agitación** ( _pl_ agitaciones) stir
**el agujero** hole
**la alcantarilla** drain
**la alcayata** hook
**la alegría** joy
**el alfabeto** alphabet
**el alfiler** pin
**el/la aliado/a** ally
**el aliento** breath
**el alivio** relief
**el alma** ( _f_ ) soul
**el almacén** ( _pl_ almacenes) store
**el/la amante** lover
**la ambición** ( _pl_ ambiciones) ambition
**la amenaza** threat
**el/la amigo(a)** mate
**la amistad** friendship
**el amor** love
**el análisis** ( _pl inv_ ) analysis
**la anchura** breadth; width
**el/la anfitrión(ona)** host
**el ángel** angel
**el ángulo** angle
**la angustia** anguish
**el animal doméstico** pet
**la antigüedad** antique
**el anuncio** announcement
**el anzuelo** hook
**el apoyo** support
**la aprobación** ( _pl_ aprobaciones) approval
**la apuesta** bet; stake
**la armada** navy
**el arreglo** compromise
**la artesanía** craft
**el artículo** article; item
**la asociación** ( _pl_ asociaciones) association
**el asombro** astonishment
**el aspecto** aspect
**la astilla** splinter
**el asunto** affair
**el atajo** short-cut
**el ataúd** coffin
**la atención** ( _pl_ atenciones) attention
**el atentado** attempt
**la atracción; el atractivo** attraction
**la ausencia** absence
**la autoridad** authority
**la aventura** adventure; affair
**el aviso** notice
**la ayuda** assistance, help
**el/la ayudante** assistant
**el ayuntamiento** council
**el azar** chance
**la bala** bullet
**la bañera** tub
**la barandilla** rail
**la barrera** barrier
**el barril** barrel
**la base** base
**la batalla** battle
**la batería** battery
**la beca** grant
**el beso** kiss
**la Biblia** Bible
**la bolsa** bag
**la bomba** bomb
**la bondad** kindness
**el borde** edge
**la broma** joke
**el brote** outbreak
**el bullicio** bustle
**la burbuja** bubble
**el cable** cable
**la caja** box
**la calcomanía** transfer
**el cálculo** calculation
**el caldo** stock
**la calidad** quality
**la calma** calm
**el camino** path; way
**el campamento** camp
**la campaña** campaign
**el camping** ( _pl_ ~s) site
**el canal** channel
**el/la canguro** baby-sitter
**la cantidad** amount
**el caos** chaos
**la capa** layer
**la capacidad** ability; capacity
**el capítulo** chapter
**la característica** characteristic; feature
**la caridad** charity
**el/la catedrático(a)** professor
**el cazo** pot
**los celos** jealousy ( _sing_ )
**el centro** centre; focus; middle
**el centro turístico** resort
**la cesta** basket
**el chiste** joke
**el cielo** heaven
**el cierre** closure
**la cima** top
**el círculo** circle
**las circunstancias** circumstances
**la cita** quote; extract; appointment
**el/la civil** civilian
**la civilización** ( _pl_ civilizaciones) civilization
**la clase** sort; period
**la clasificación** ( _pl_ clasificaciones) classification
**la clave** code
**la codicia** greed
**la columna** column
**el columpio** swing
**la combinación** ( _pl_ combinaciones) combination
**el combustible** fuel
**el comentario** comment, remark
**el/la comentarista** commentator
**las comillas: entre comillas** inverted commas: in quotes
**la comisión** ( _pl_ comisiones) commission
**el comité** ( _pl_ comités) committee
**el compañero** fellow
**la comparación** ( _pl_ comparaciones) comparison
**la compasión** ( _pl_ compasiones) sympathy
**la competición** ( _pl_ competiciones) contest
**el/la competidor(a)** rival
**la comprensión** ( _pl_ comprensiones) sympathy
**el compromiso** commitment
**la comunicación** ( _pl_ comunicaciones) communication
**la comunidad** community
**la concentración** ( _pl_ concentraciones) concentration
**la conciencia** conscience
**la condecoración** ( _pl_ condecoraciones) honour
**la condición** ( _pl_ condiciones) condition; status
**la conducta** conduct
**la conexión** ( _pl_ conexiones) connection
**la conferencia** conference
**la confianza** confidence
**el conflicto** conflict
**el confort** comfort
**el congreso** conference
**la conmoción** ( _pl_ conmociones) shock; disturbance
**el conocimiento** consciousness; knowledge
**la consecuencia** consequence
**el consejo** advice
**la construcción** ( _pl_ construcciones) construction; structure
**el/la consumidor(a)** consumer
**el contacto** contact
**el contenido** content
**el contexto** context
**el contorno** outline
**el contraste** contrast
**la contribución** ( _pl_ contribución) contribution
**la conversación** ( _pl_ conversaciones) conversation
**la copia** copy
**el corazón** ( _pl_ corazones) heart; core
**la corona** crown
**el/la corresponsal** correspondent
**la corrupción** ( _pl_ corrupciones) corruption
**la cortesía** politeness
**la cosa** thing
**las cosas** stuff ( _sing_ )
**la costumbre** custom
**el crecimiento** growth
**el/la criado(a)** servant
**la crisis** ( _pl inv_ ) crisis
**la crítica** criticism
**el cuadro** picture
**la cuba** tub
**el cubierto** place
**el cuchicheo** whispering
**la cuenta** count **por su cuenta** of his own accord
**el cuento** tale
**la cuestión** ( _pl_ cuestiones) question
**la cueva** cave
**el cuidado** care
**la culpa** blame
**la cultura** culture
**la cuota** fee
**la curiosidad** curiosity
**los datos** data ( _pl_ )
**el debate** debate
**el deber** duty
**la decepción** ( _pl_ decepciones) disappointment
**la decisión** ( _pl_ decisiones) decision
**el defecto** fault
**la definición** ( _pl_ definiciones) definition
**el/la dependiente(a)** assistant
**la depresión** ( _pl_ depresiones) depression
**el/la derecho(a)** right **los derechos** fee
**el desagüe** drain
**el desarrollo** development
**el desastre** disaster
**el descanso** break
**el/la desconocido(a)** stranger
**la desdicha** unhappiness
**el deseo** desire; wish; urge
**el desgarrón** ( _pl_ desgarrones) tear
**la desgracia** misfortune
**el desorden** disorder; mess
**el destino** destiny; fate
**la destreza** skill
**la destrucción** ( _pl_ destrucciones) destruction
**la desventaja** disadvantage
**el detalle** detail
**la devolución** ( _pl_ devoluciones) refund; return
**el diagrama** diagram
**el diálogo** dialogue
**la diana** target
**el diario** diary; journal
**la diferencia** difference
**la dificultad** difficulty
**la dimensión** ( _pl_ dimensiones) dimension
**el Dios** God
**el/la diplomático(a)** diplomat
**el/la diputado(a)** deputy
**la dirección** ( _pl_ direcciones) direction
**la disciplina** discipline
**el discurso** speech
**la discusión** ( _pl_ discusiones) argument; discussion
**el diseño** design
**el dispositivo** device
**la disputa** dispute
**la distancia** distance
**la división** ( _pl_ divisiones) division
**el drama** drama
**la duda** doubt
**el eco** echo
**la economía** economics ( _sing_ ); economy
**la edición** ( _pl_ ediciones) edition
**el efecto** effect
**el ejemplar** copy
**el ejemplo** example **por ejemplo** for instance
**el/la elector(a)** elector
**la elegancia** elegance
**el elemento** element
**la encuesta** survey
**el/la enemigo(a)** enemy
**la energía** energy
**el entusiasmo** enthusiasm; excitement
**la envidia** envy
**la época** period
**el equilibrio** balance
**el equipo** equipment
**el error** mistake
**el escándalo** scandal
**el escape** leak
**la escasez** shortage
**la escritura** writing
**el esfuerzo** effort
**el espacio** space
**la espalda** back
**la especie** species ( _sing_ )
**el espectáculo** show; sight
**la esperanza** hope
**el espesor; la espesura** thickness
**el esquema** outline; diagram
**la estaca** stake
**la estancia** stay
**la estatua** statue
**el estilo** style
**la estrategia** strategy
**el estrés** stress
**la estructura** structure
**el estudio** studio
**la estupidez** ( _pl_ estupideces) stupidity
**la etapa** stage
**la excepción** ( _pl_ excepciones) exception
**el exceso** excess
**la excusa** excuse
**el/la exiliado(a)** exile
**el exilio** exile
**las existencias** stock
**el éxito** success
**la experiencia** experience
**el/la experto(a)** expert
**la explicación** ( _pl_ explicaciones) explanation
**la explosión** ( _pl_ explosiones) explosion **una explosión** a bomb blast
**las exportaciones** exports
**la exposición** ( _pl_ exposiciones) exhibition
**la expresión** ( _pl_ expresiones) expression
**la extensión** ( _pl_ extensiones) extent
**el extracto** extract
**el/la extranjero(a)** foreigner
**la fabricación** ( _pl_ fabricaciones) manufacture
**la facilidad** facility
**el factor** factor
**el fallo** failure
**la falta:** absence **falta (de)** lack (of)
**la fama** reputation
**el favor** favour
**la fe** faith
**la felicidad** happiness
**la fila** row
**la filosofía** philosophy
**el fin** end
**la flecha** arrow
**el fondo** background; bottom; fund
**el/la forastero(a)** stranger
**la forma** form; shape
**la fortuna** fortune
**el fracaso** failure
**la frase** sentence; phrase
**la frente** front
**el frescor, la frescura** freshness
**la fuente** source
**la fuerza** force; strength
**la función** ( _pl_ funciones) function
**la ganancia** gain
**el gancho** hook
**los gastos** expenses
**la generación** ( _pl_ generaciones) generation
**el gol** goal
**el golfo** gulf
**el golpe** bang; blow; knock
**la gotera** leak
**el grado** degree
**el gráfico** chart
**la grieta** crack
**el grito** cry
**el grupo** group
**la guía** guide
**el hambre** ( _f_ ) hunger
**el hecho** fact
**la higiene** hygiene
**la hilera** row
**el honor** honour
**los honorarios** fee
**la honra** honour
**el hueco** gap
**la huella** trace
**el humo** fumes ( _pl_ ); smoke
**el humor** humour
**la idea** idea **no tengo ni idea** I haven't a clue
**el idioma** language
**el/la idiota** fool; idiot
**la imagen** ( _pl_ imágenes) image
**la imaginación** ( _pl_ imaginaciones) imagination
**el impacto** impact
**el imperio** empire
**las importaciones** imports
**la importancia** importance
**la impresión** ( _pl_ impresiones) impression
**el impuesto** duty
**el impulso** urge
**la inauguración** ( _pl_ inauguraciones) opening
**el incidente** incident
**la independencia** independence
**el índice** index
**la indirecta** hint
**la infancia** childhood
**el infierno** hell
**la influencia** influence
**los ingresos** earnings
**el/la inspector(a)** inspector
**el instante** instant
**la institución** ( _pl_ instituciones) institution
**el instituto** institute
**las instrucciones** instructions
**el instrumento** instrument
**la intención** ( _pl_ intenciones) intention; aim
**el interés** ( _pl_ intereses) interest
**la interrupción** ( _pl_ interrupciones) interruption
**el intervalo** gap
**la investigación** ( _pl_ investigaciones) research
**la invitación** ( _pl_ invitaciones) invitation
**la ira** anger
**el jaleo** row
**el/la jefe(a)** chief
**el juego** gambling
**el juguete** toy
**la lágrima** tear
**la lata** can
**el/la lector(a)** reader
**la leyenda** legend; caption
**la libertad** freedom
**la licenciatura** degree
**el/la líder** leader
**la liga** league
**el límite** boundary; limit
**la limpieza** cleanliness
**la línea** line
**la liquidación** ( _pl_ liquidaciones) settlement
**la lista** list
**la literatura** literature
**el local** premises ( _pl_ )
**la locura** madness
**el logro** achievement
**la loncha** slice
**la longitud** length
**el lugar** site
**el lujo** luxury
**la luz** ( _pl_ luces) light **luz de la luna** moonlight
**el/la maestro(a)** master
**la magia** magic
**la manera** manner
**la máquina** machine
**la marca** brand; mark
**el marco** frame
**el margen** ( _pl_ márgenes) margin
**la máscara** mask
**la matrícula** fee
**el máximo** maximum
**la mayoría** majority
**el medio (de)** means (of)
**la mejora, la mejoría** improvement
**la memoria** memory
**la mente** mind
**el método** method
**la mezcla** mixture
**el miedo** fear
**el milagro** miracle
**la mina** mine
**el mínimo** minimum
**el ministerio** ministry
**la minoría** minority
**la mirada** glance
**la misa** mass
**la misión** ( _pl_ misiones) mission
**el misterio** mystery
**el mitin** ( _pl_ mítines) rally
**el mito** myth
**la moda** fashion; trend
**la molestia** annoyance
**el molino** mill
**el montón** ( _pl_ montones) mass; pile
**la moral** morals ( _pl_ )
**el mordisco** bite
**el motivo** pattern
**el motor** motor
**el muchacho** lad
**la muchedumbre** crowd
**la muestra** sample
**la muñeca** doll
**la naturaleza** nature
**el naufragio** wreckage ( _sing_ )
**la negociación** ( _pl_ negociaciones) negotiation
**el nervio** nerve
**la niñez** childhood
**el nivel** level
**el nombramiento** appointment
**la nota** note
**el número** number; issue
**la objeción** ( _pl_ objeciones) objection
**el objetivo** objective; purpose; target
**el objeto** object; goal
**las obras** works
**el odio** hate
**el/la oficial** officer
**la olla** pot
**el olor** smell
**la opción** ( _pl_ opciones) option
**la opinión** ( _pl_ opiniones) opinion
**la oportunidad** chance; opportunity
**la oposición** ( _pl_ oposiciones) opposition
**la orden** ( _pl_ órdenes) order
**la organización** ( _pl_ organizaciones) organization **organización benéfica** charity
**el orgullo** pride
**el origen** ( _pl_ orígenes) origin
**la oscuridad** darkness
**la paciencia** patience
**la página** page
**la paja** straw
**la palabra** word
**el palacio** palace
**el palo** stick
**el pánico** panic
**el paquete** pack; packet
**la pareja** pair
**la parte** part **parte de arriba** top; **parte delantera** front; **parte trasera** rear; **de parte de algn** on behalf of sb
**la partida** item
**el parto** labour **estar de parto** to be in labour
**el pasaje; el pasillo** passage
**la pasión** ( _pl_ pasiones) passion
**el paso** footstep
**el patrón** ( _pl_ patrones) pattern
**la pausa** pause
**el payaso** clown
**el pedazo** piece
**el pedido** order
**la pelea** row
**el peligro** danger
**la pena** distress; penalty
**el penalty** ( _pl_ penalties) penalty
**el pensamiento** thought
**el periódico** journal
**el periodo** period
**el/la perito(a)** expert
**el permiso** permission
**la persona** person
**el personal** personnel
**la perspectiva** prospect
**la pesadilla** nightmare
**la picadura** bite
**la pieza** piece; item
**la pila** battery; pile
**la pista** clue
**el placer** delight; pleasure
**el plan** plan; scheme
**el plato** dish
**la plaza** place
**el poder** power
**el poema** poem
**la política** politics ( _sing_ ); policy
**la póliza** policy
**el polvo** dust
**la pompa** bubble
**el porcentaje** percentage
**la porción** ( _pl_ porciones) portion
**el portavoz** ( _pl_ portavoces) spokesman
**la posibilidad** possibility
**la posición** ( _pl_ posiciones) position
**la práctica** practice
**la preferencia** choice
**el prefijo** code
**la pregunta** question
**el premio** award
**la preparación** ( _pl_ preparaciones) preparation
**los preparativos** arrangements
**la presencia** presence
**la presión** ( _pl_ presiones) pressure
**el presupuesto** budget; quote
**la princesa** princess
**el príncipe** prince
**el principio** beginning; principle
**la prioridad** priority
**el problema** problem; trouble
**el proceso** process
**el/la profesor(a)** master
**la profundidad** depth
**el programa** schedule
**la prohibición** ( _pl_ prohibiciones) ban
**el propósito** purpose **a propósito** on purpose
**la propuesta** proposal
**la prosperidad** prosperity
**la protección** ( _pl_ protecciones) protection
**la protesta** protest
**las provisiones** provisions
**el proyecto** plan
**la publicidad** publicity
**la puja** bid
**la punta** point
**la puntería** aim
**el punto** item; point **punto de partida** starting point; **punto de vista** point of view
**el/la querido(a)** darling
**la rabia** rage
**la raja** crack
**el rato** while
**la razón** ( _pl_ razones) reason
**la reacción** ( _pl_ reacciones) reaction; response
**la realidad** reality
**la rebanada** slice
**el/la rebelde** rebel
**el recado** message
**la recepción** ( _pl_ recepciones) reception
**la recesión** ( _pl_ recesiones) recession
**la reclamación** ( _pl_ reclamaciones) claim
**el recuerdo** souvenir
**el recurso** resource **como último recurso** as a last resort
**la red** network
**la reducción** ( _pl_ reducciones) reduction
**la reforma** reform
**la regla** period
**la reina** queen
**la relación** ( _pl_ relaciones) relationship
**la religión** ( _pl_ religiones) religion
**la reputación** ( _pl_ reputaciones) status
**el requisito** requirement
**la reserva** fund; stock
**la resistencia** resistance
**la resolución** ( _pl_ resoluciones) resolution
**el respecto: con respecto a** with regard to
**el respeto** respect
**la respiración** ( _pl_ respiraciones) breath
**la responsabilidad** responsibility
**la respuesta** reply; response
**los restos** remains; wreckage ( _sing_ )
**el resultado** outcome
**el reto** challenge
**el retrato** portrait
**la reunión** ( _pl_ reuniones) meeting
**la revista** magazine; journal
**el rey** ( _pl_ ~es) king
**el riel** rail
**el ritmo** pace
**el/la rival** rival
**la rodaja** slice
**el ruido** noise
**la ruina** ruin
**el rumor** rumour
**la ruptura** break
**la rutina** routine
**el sacrificio** sacrifice
**el/la santo(a)** saint
**la sección** ( _pl_ secciones) section
**el secreto** secret
**el sector** sector
**la sed** thirst
**la seguridad** security; safety
**la selección** ( _pl_ selecciones) selection; choice
**el sentido** sense; way
**el sentimiento** feeling
**la señal** sign; mark
**el señor** lord
**el servicio** service
**la sesión** ( _pl_ sesiones) session
**el significado** meaning
**el silbato** whistle
**el silencio** silence
**el símbolo** symbol
**el sindicato** trade union
**el sistema** system
**el sitio** place
**la situación** ( _pl_ situaciones) situation
**el/la socio(a)** member
**la soledad** loneliness
**el sollozo** sob
**la solución** ( _pl_ soluciones) solution
**la sombra** shadow
**el sondeo (de opinión)** poll
**el sonido** sound
**la sorpresa** surprise
**la sospecha** suspicion
**la subasta** auction
**el subtítulo** caption
**la subvención** ( _pl_ subvenciones) grant
**la suciedad** dirtiness
**el sueño** sleep
**la suerte** luck **buena/mala suerte** good/bad luck
**la sugerencia** suggestion
**el suicidio** suicide
**la suma** sum
**la superficie** surface
**la supervisión** ( _pl_ supervisiones) supervision
**el/la superviviente** survivor
**el/la suplente** substitute
**el surtido** choice
**la sustancia** substance
**el/la sustituto(a)** substitute
**la táctica** tactics ( _pl_ )
**el talento** talent
**la tapa** top
**la tapicería, el tapiz** ( _pl_ tapices) tapestry
**el tapón** ( _pl_ tapones) top
**la tarea** task
**la tarifa; la tasa** rate
**el teatro** theatre; drama
**la técnica** technique
**la tecnología** technology
**el tema** theme; issue
**la tendencia** trend
**la tensión** ( _pl_ tensiones) tension; strain
**la tentativa** attempt; bid
**la teoría** theory
**el territorio** territory
**el terrón** ( _pl_ terrones) lump
**el texto** text
**la tienda** store
**la timidez** shyness
**el tipo** type; kind; fellow, guy
**el tío** ( _Sp_ ) guy
**la tirada** edition
**el título** title
**el tomo** volume
**la tortura** torture
**el total** total
**la tradición** ( _pl_ tradiciones) tradition
**la trampa** trap
**la tranquilidad** calmness
**la transferencia** transfer
**el tratamiento** treatment
**el trato** deal; treatment
**la tristeza** sadness
**el trozo** bit; piece; slice
**el truco** trick
**el tubo** tube
**la tumba** grave
**el tumor** growth
**el turno** turn
**la unidad** unit
**la valentía** bravery, courage
**el valor** value
**el vapor** steam
**la variedad** variety; range
**la vela** candle
**el veneno** poison
**la ventaja** advantage; asset
**la verdad** truth
**la vergüenza** shame
**la versión** ( _pl_ versiones) version
**la victoria** victory
**la vida** life
**el vínculo** bond
**la violencia** violence
**la visita;** visit; visitor
**el/la visitante** visitor
**la vista** sight
**el volumen** ( _pl_ volúmenes) volume
**el/la voluntario(a)** volunteer
**el/la votante** voter
**la vuelta** turn; return **dar una vuelta** to go for a stroll; **dar una vuelta en bicicleta** to go for a bike ride
# **VERBS**
**What is a verb?** A **verb** is a 'doing' word which describes what someone or something does, what someone or something is, or what happens to them, for example, _be_ , _sing_ , _live_.
**abandonar** to abandon
**abrigar(se)** to shelter
**abrir** to turn on **abrir(se)** to open
**abrochar** to fasten
**aburrir** to bore **aburrirse** to get bored
**acabar de hacer algo** to have just done sth
**acampar** to camp
**aceptar** to accept
**acercarse (a)** to approach **acercarse a** to go towards
**aclarar(se)** to clear
**acompañar** to accompany; to go with
**aconsejar** to advise; to suggest
**acordarse de** to remember
**acostarse** to lie down
**acostumbrarse a algo/algn** to get used to sth/sb
**actuar** to act; to operate
**acusar** to accuse
**adaptar** to adapt
**adelantar** to go forward; to overtake
**adivinar** to guess
**admirar** to admire
**admitir** to admit
**adoptar** to adopt
**adorar** to adore
**adquirir** to acquire; to purchase
**afectar** to affect
**afirmar** to assert; to state
**agarrar** to catch; to grab; to grasp
**agradecer** to thank (for)
**aguantar** to bear
**ahorrar** to save
**ahuyentar** to chase (off)
**alcanzar** to reach **alcanzar a algn** to catch up with sb; **alcanzar a ver** to catch sight of
**alimentar** to nourish
**aliviar** to relieve
**almacenar** to store
**alojarse** to put up **alojarse con** to lodge with
**alquilar** to hire; to rent: to let
**amar** to love
**amenazar** to threaten
**amontonar** to stack
**andar** to walk
**anhelar** to long for
**animar** to encourage **animar a algn a hacer algo** to urge sb to do sth
**anunciar** to advertise; to announce
**añadir** to add
**apagar** to switch off; to turn off; to put out
**apagar** to turn off **apagarse** to fade
**aparecer** to appear
**apetecer** to fancy **me apetece un helado** I fancy an ice cream
**aplastar** to crush
**aplaudir** to applaud; to cheer; to clap
**aplazar** to postpone; to put back
**aplicar a** to apply to
**apostar (a)** to bet (on)
**apoyar** to support; to endorse **apoyar(se)** to lean
**apreciar** to appreciate
**aprender** to learn
**apretar** to press; to squeeze
**aprobar** to approve of; to endorse
**aprovechar** to take advantage (of)
**apuntar** to take down
**arañar** to scratch
**arrancar** to pull out
**arrastrar** to drag **arrastrarse** to crawl
**arreglar** to fix (up); to arrange; to settle **arreglárselas** to cope; to manage
**arrepentirse de** to regret
**arriesgar** to risk
**arrojar** to hurl
**arruinar** to ruin
**asar** to bake
**ascender** to promote
**asegurar** to assure; to ensure; to secure
**asentir con la cabeza** to nod
**asfixiar(se)** to suffocate
**asistir (a)** to attend
**asombrar** to amaze; to astonish
**asustar** to alarm; to frighten; to startle
**atacar** to attack
**atar** to attach; to tie
**atender** to treat **atender a** to attend to
**atraer** to attract
**atrasar** to hold up
**atreverse (a hacer algo)** to dare (to do sth)
**aumentar** to increase; to raise
**avanzar** to advance
**averiarse** to break down
**averiguar** to check
**avisar** to warn
**ayudar** to help
**azotar** to whip
**bailar** to dance
**bajar:** to come down; to go down; to lower **bajar (de):** to get off; **bajar de** to get out of
**balbucir** to stammer
**barrer** to sweep
**basar algo en** to base sth on
**batir** to whip; to beat
**besar** to kiss
**bombardear** to bomb
**brillar** to shine; to sparkle
**bromear** to joke
**burlarse de** to make fun of
**buscar** to look for; to search; to seek
**caerse** to fall (down) **se me cayó** I dropped it
**calcular** to estimate
**calentar(se)** to heat (up)
**callarse** to be quiet
**cambiar** to alter; to exchange **cambiar(se)** to change
**cancelar** to cancel
**cantar** to sing
**capturar** to capture
**carecer de** to lack
**cargar (de)** to load (with)
**causar** to cause
**cavar** to dig
**celebrar** to celebrate
**centellear** to sparkle
**cerrar:** to turn off: to close; to fasten **cerrar(se):** to shut; **cerrar con llave** to lock
**charlar** to chat
**chillar** to scream
**chismear** to gossip
**chocar con** to bump into
**chupar** to suck
**citar** to quote
**clasificarse** to qualify
**cobrar** to claim; to get
**coger** to catch; to grab; to seize
**colaborar** to collaborate
**coleccionar** to collect
**colgar** to hang (up)
**colocar** to place
**combinar** to combine
**comenzar (a)** to start (to)
**cometer** to commit
**compaginar** to combine
**comparar** to compare
**compartir** to share
**compensar** to compensate (for) **compensar por** to make up for
**competir en** to compete in
**complacer** to please
**completar** to complete; to make up
**comprar (a)** to buy (from)
**comprender** to comprise
**comunicar** to communicate
**conceder** to grant
**concentrarse** to concentrate
**concertar** to arrange
**concluir** to conclude; to accomplish
**condenar** to condemn; to sentence
**conducir** to lead
**conectar** to connect
**confesar** to confess
**confiar** to trust **confiar en** to rely on
**confirmar** to confirm
**confundir (con)** to confuse (with) **confundir a algn con** to mistake sb for
**congelar** to freeze
**conocer** to know
**conseguir** to achieve; to get; to secure **conseguir (hacer)** to succeed (in doing)
**considerar** to consider; to rate
**constar de** to consist of **hacer constar** to record
**constituir** to constitute; to make up
**construir** to build; to put up
**consultar** to consult
**consumir** to consume
**contar** to count **contar con** to depend on
**contemplar** to contemplate
**contener** to contain; to hold
**contestar** to answer
**continuar** to continue; to keep; to resume
**contribuir** to contribute
**controlar** to control
**convencer** to convince
**convenir** to suit
**convertir** to convert
**copiar** to copy
**correr** to run
**cortar** to cut (off); to mow
**costar** to cost
**crear** to create
**crecer** to grow
**creer** to believe; to reckon
**criar** to bring up
**criticar** to criticize
**cruzar** to cross
**cubrir (de)** to cover (with)
**cuchichear** to whisper
**cuidar** to look after; to take care of; to mind **cuidar de** to take care of
**cultivar** to cultivate
**cumplir** to accomplish; to carry out
**curar** to heal
**dañar** to harm
**dar** to give: **dar a** to overlook; **dar asco a** to disgust; **dar de comer a** to feed; **dar la bienvenida** to welcome; **dar marcha atrás** to reverse; **dar saltitos** to hop; **dar un paseo** to go for a stroll; **dar un puñetazo a** to punch; **dar una bofetada a** to slap; **dar vergüenza a** to embarrass; **dar vuelta a** to turn; **darse cuenta de algo** to become aware of sth; **darse por vencido** to give up; **darse prisa** to hurry;
**deber** must; to owe **deber hacer algo** to be supposed to do sth; **debo hacerlo** I must do it
**decepcionar** to disappoint
**decidir(se) (a)** to decide (to)
**decidirse (a)** to make up one's mind (to)
**decir** to say; to tell
**declarar** to declare **declarar culpable** to convict; **declararse en huelga** to (go on) strike
**decorar** to decorate
**dedicar** to devote
**defender** to defend
**definir** to define
**dejar** to leave **dejar caer** to drop
**deletrear** to spell
**demorar(se)** to delay
**demostrar** to demonstrate
**depender de** to depend on
**derribar** to demolish
**desanimar** to discourage
**desaparecer** to disappear
**desarrollar(se)** to develop
**descansar** to rest
**descargar** to unload
**describir** to describe
**descubrir** to discover; to find out
**desear** to desire; to wish
**deshacerse de** to get rid of
**deslizar(se)** to slip
**desnudarse** to strip
**despedir** to dismiss
**despegar** to take off
**despejar(se)** to clear
**despertar(se)** to wake up
**desprenderse** to come off
**desteñirse** to fade
**destruir** to smash
**desviar** to divert
**detener** to arrest
**determinar** to determine
**detestar** to detest
**devolver** to bring back; to give back; to send back **devolver a su sitio** to put back
**dibujar** to draw
**diferenciarse (de)** to differ (from)
**dimitir** to resign
**dirigir** to conduct; to direct; to manage
**disculparse (de)** to apologise (for)
**discutir** to argue; to debate; to discuss
**diseñar** to design
**disfrazar** to disguise
**disfrutar** to enjoy
**disminuir** to decline; to decrease; to diminish
**distinguir** to distinguish
**distribuir** to distribute
**divertir** to divert **divertirse** to enjoy oneself
**dividir** to divide; to split
**doblar** to fold **doblar(se)** to double
**dominar** to dominate; to master
**ducharse** to shower
**dudar** to doubt
**durar** to last
**echar** to pour: **echar a algn** to throw sb out; **echar a algn la culpa de algo** to blame sb for sth; **echar al correo** to post; **echar de menos** to miss; **echar una mirada a algo** to glance at sth; **echarse** to lie; **echarse a llorar** to burst into tears; **echarse a reír** to burst out laughing
**educar** to bring up; to educate
**ejecutar** to execute
**elegir** to choose; to select; to elect
**elogiar** to praise
**emocionar** to excite
**empatar** to draw, to tie
**empezar (a)** to begin (to)
**emplear** to employ
**empujar** to push
**encarcelar** to imprison
**encender** to switch on; to turn on; to light
**encerrar** to shut in
**encontrar** to find; to meet
**enfocar** to focus
**enjugar** to wipe
**enseñar** to teach; to show
**entender** to understand
**enterarse de** to hear about
**enterrar** to bury
**entrar (en)** to enter
**entregarse** to give oneself up; to surrender
**entrevistar** to interview
**enviar** to send
**envolver** to wrap up
**equivocarse** to make a mistake; to be mistaken
**erigir** to erect
**escapar (de)** to escape (from)
**escarbar** to dig
**escoger** to choose; to pick
**esconderse** to hide
**escuchar** to listen (to)
**especializarse en** to specialize in
**especular** to gamble
**esperar** to wait (for); to expect; to hope
**establecer** to establish; to set up **establecerse** to settle
**estallar** to blow up
**estar** to be **estar acostumbrado a algo/ algn** to be used to sth/sb; **estar de acuerdo** to agree; **estar de pie** to be standing; **estar dispuesto a hacer algo** to be prepared to do sth; to be willing to do sth; **estar equivocado** to be wrong; **estar involucrado en algo** to be involved in sth
**estirar(se)** to stretch (out)
**estrecharse la mano** to shake hands
**estrellar(se)** to crash
**estropear** to ruin **estropear(se)** to spoil
**estudiar** to study; to investigate
**evitar (hacer)** to avoid (doing)
**exagerar** to exaggerate
**examinar** to examine **examinarse** to sit an exam
**excitar** to excite
**exclamar** to exclaim
**excluir** to exclude; to suspend
**existir** to exist
**experimentar** to experience
**explicar** to explain
**explorar** to explore
**explotar** to explode
**exponer** to display
**exportar** to export
**expresar** to express
**exprimir** to squeeze
**expulsar temporalmente** to suspend
**extender** to spread: to extend **extender(se)** to spread out
**extrañar** ( _LAm_ ) to miss
**fabricar** to manufacture
**faltar** to be lacking; to fail
**felicitar** to congratulate
**fiarse de** to trust
**financiar** to finance
**fingir** to pretend (to)
**firmar** to sign
**flotar** to float
**fluir** to flow
**formar(se)** to form
**forzar a algn a hacer (algo)** to force sb to do (sth)
**fotografiar** to photograph
**frecuentar** to frequent
**freír** to fry
**funcionar** to work **(hacer) funcionar** to operate
**fustigar** to whip
**ganar** to earn; to gain
**garantizar** to guarantee
**gastar** to spend: to waste **gastar(se)** to wear (out)
**gemir** to groan
**golpear** to knock; to beat
**grabar** to record
**gritar** to shout; to scream; to cry
**guardar** to keep; to store
**guiar** to guide
**gustar** to like
**haber** to have
**hablar** to speak; to talk
**hacer** to do; to make; to bake **hacer añicos** to shatter; **hacer campaña** to campaign; **hacer comentarios** to comment; **hacer daño a** to hurt; **hacer las maletas** to pack; **hacer preguntas** to ask questions; **hacer público** to issue; **hacer señas** _or_ **una señal** to signal; **hacer una lista de** to list; **hacer una oferta** to bid; **hacer una pausa** to pause; **hacer una señal con la mano** to wave; **hacerse** to become; to get; **hacerse adulto** to grow up; **hacer(se) pedazos** to smash
**helarse** to freeze
**herir** to injure
**hervir** to boil
**huir** to flee; to run away _or_ off
**identificar** to identify
**iluminar(se)** to light
**imaginar** to imagine
**impedir** to prevent (from)
**implicar** to imply; to involve
**imponer** to impose
**importar** to matter; to mind; to care **¡no me importa!** I don't care!; **¿y a quién le importa?** who cares?
**impresionar** to impress
**imprimir** to print
**inclinar** to bend **inclinarse** to bend down
**incluir** to include
**indicar** to point out; to indicate
**influir** to influence
**informar** to inform
**inscribirse** to register
**insinuar** to hint
**insinuar** to imply
**insistir en** to insist on
**instruir** to educate
**insultar** to insult
**intentar** to attempt to
**interesar** to interest **interesarse por** to be interested in
**interrogar** to question
**interrumpir** to interrupt
**introducir** to introduce
**invadir** to invade
**investigar** to investigate
**invitar** to invite **invitar a algn a algo** to treat sb to sth
**ir** to go **ir a buscar a algn** to fetch sb; **ir bien a** to suit; **ir deprisa** to dash; **ir en bicicleta** to ride a bike
**irse** to go away
**irritar** to irritate; to aggravate
**jugar** to play; to gamble
**juntarse con** to join
**jurar** to swear
**justificar** to justify
**juzgar** to judge
**lamentarse** to moan
**lamer** to lick
**lanzar** to throw; to launch **lanzarse a** to rush into
**leer** to read
**levantar** to raise; to put up; to lift **levantarse** to get up; to rise
**limpiar** to clean
**llamar** to call **llamar por teléfono:** to ring; **llamarse** to be called
**llegar** to arrive
**llenar (de)** to fill (with)
**llevar:** to carry; to bear; to wear **llevar a cabo** to carry out; **llevarse** to take
**llorar** to cry, weep
**llover** to rain **llover a cántaros** to pour
**luchar** to fight; to struggle
**maltratar** to abuse
**manchar** to dirty
**mandar** to command, to order
**manifestarse** to demonstrate
**mantener** to maintain; to support **mantener el equilibrio** to balance
**marcharse** to depart; to leave
**medir** to measure
**mejorar(se)** to improve
**mencionar** to mention
**mentir** to lie
**merecer** to deserve
**meterse en** to get into
**mezclar** to mix
**mimar** to spoil
**mirar** to look (at); to watch **mirar fijamente** to stare at
**modificar** to adjust
**molestar** to annoy; to disturb; to trouble
**montar a caballo** to ride
**morder** to bite
**morir** to die
**mostrar** to hold up **mostrar(se)** to show
**mover** to move
**multiplicar** to multiply
**nacer** to be born
**necesitar** to need
**negar** to deny **negarse (a)** to refuse (to)
**negociar** to negotiate
**notar** to note
**obedecer** to obey
**obligar a algn a** to oblige sb to
**observar** to notice; to observe
**obstruir** to block
**obtener** to obtain
**ocasionar** to bring about
**ocultar** to hide
**ocupar** to occupy **ocuparse de** to deal with
**ocurrir** to occur
**odiar** to hate
**ofender** to offend
**ofrecer** to offer **ofrecerse a hacer algo** to volunteer to do sth
**oír** to hear
**oler** to smell
**olvidar** to forget
**operar a algn** to operate on sb
**oponerse a** to oppose; to object to
**organizar(se)** to organize
**otorgar** to award
**pagar** to pay
**pararse** to come to a halt, to stop
**parecer** to seem (to); to look **parecerse a** to look like, to resemble
**participar en** to take part in
**partir** to share **partir(se)** to split
**pasar** to pass; to overtake; to spend
**pedir** to request; to order **pedir a algn que haga algo** to ask sb to do sth; **pedir algo a algn** to ask sb for sth; **pedir algo prestado a algn** to borrow sth from sb
**pegar** to hit; to stick; to strike
**pensar** to think **pensar en** to think about; **pensar hacer** to intend to do
**perder** to miss: **perder a algn de vista** to lose sight of sb
**perdonar a** to forgive
**perdurar** to survive
**permitir** to allow, to permit, to let **permitirse** to afford
**perseguir** to pursue
**persuadir** to persuade
**pertenecer a** to belong to
**pesar** to weigh
**picar** to bite
**pinchar(se)** to burst
**planchar** to iron
**plegar** to fold
**poder** to be able to; can; might **¿puedo llamar por teléfono?:** can I use your phone?; **el profesor podría venir ahora:** the teacher might come now; **puede que venga más tarde** he might come later
**poner** to put; to lay **poner de relieve** to highlight; **poner en duda** to question; **poner en el suelo** to put down; **poner en orden** to tidy; **ponerse** to put on; **ponerse de pie** to stand up; **ponerse en contacto con** to contact
**portarse** to behave
**poseer** to own, to possess
**practicar** to practise
**precipitarse** to rush
**predecir** to predict
**preferir** to prefer
**preguntar (por)** to inquire (about) **preguntarse** to wonder
**prender fuego** to catch fire
**preocupar** to trouble; to bother **preocuparse (por)** to worry (about)
**preparar(se)** to prepare
**prescindir de** to do without
**presentar** to present; to introduce
**prestar** to lend
**prevenir** to warn
**prever** to foresee
**privar** to deprive
**probar** to prove
**producir** to produce
**prohibir** to ban; to forbid
**prometer** to promise
**pronosticar** to predict
**pronunciar** to pronounce
**propagarse** to spread
**proponer** to propose
**proteger** to protect
**protestar** to protest
**proveer** to provide
**publicar** to publish
**quedar** to remain **quedarse** to stay
**quejarse (de)** to complain (about)
**quemar** to burn
**querer** to want (to); to love; to like
**quitar** to remove **quitar algo a algn** to take sth from sb; **quitarse** to take off
**reaccionar** to react; to respond
**realizar** to fulfil; to realize
**reanudar** to resume
**recalcar** to emphasize; to stress
**rechazar** to reject
**recibir** to receive **recibirse** ( _LAm_ ) to qualify
**reclamar** to demand; to claim
**recoger** to pick (up); to collect; to gather
**recomendar** to recommend
**reconocer** to recognize
**recordar** to recall **recordarle a algn** to remind sb of
**recuperarse** to recover
**reducir(se)** to reduce
**reembolsar** to refund
**referirse a** to refer (to) **en lo que se refiere a...** as regards...
**reflejar, reflexionar** to reflect
**reformar** to reform
**regañar** to tell off
**regar** to water
**registrar** to register; to examine
**reír** to laugh **reírse de** to laugh at
**relajarse** to relax
**relatar** to report
**renovar** to renew
**reñir** to quarrel
**reparar** to repair, to mend
**repartir** to deal; to deliver
**repetir(se)** to repeat
**reponer** to replace **reponerse** to mend
**representar** to perform; to represent
**requerir** to require
**resbalar** to slide
**reservar** to book; to reserve
**resistir** to hold out **resistir(se)** to resist
**resolver** to solve
**respetar** to respect
**respirar** to breathe
**responder** to reply, to answer; to respond
**restaurar** to restore
**resultar** to prove
**retar** to challenge
**retirar(se)** to withdraw
**reunir(se)** to collect **reunirse** to gather; **reunirse con** to rejoin
**revelar** to reveal
**rodear (de)** to surround (with)
**romper(se)** to break; to tear; to burst
**ruborizarse** to blush
**saber a** to taste of
**saber** to know **sé nadar** I can swim
**sacar** to bring out; to take out **sacar brillo** to polish; **sacarse el título** to qualify
**sacudir** to shake
**salir** to emerge
**saltar** to leap
**saludar** to greet **saludar con la cabeza** to nod
**salvar** to rescue; to save
**secar(se)** to dry
**seguir** to follow **seguir haciendo algo** to go on doing sth
**sentarse** to sit (down)
**sentir** to be sorry **sentir(se)** to feel
**señalizar** to indicate
**ser** to be
**servir** to serve
**significar** to mean
**sobrevivir** to survive
**solicitar** to apply to; to seek
**soltar** to release
**sonar** to sound **(hacer) sonar** to ring
**sonreír** to smile
**sorprender** to surprise
**sospechar** to suspect
**subir** to climb; to come up; to go up **subir a** to board; to get on
**suceder** to happen
**sufrir (de)** to suffer (from) **sufrir un colapso** to collapse
**sugerir** to suggest
**sujetar** to fix
**suministrar** to supply
**suponer** to assume; to suppose; to involve
**surgir** to emerge
**suspender** to suspend; to fail
**suspirar** to sigh
**sustituir** to replace
**telefonear** to telephone
**temblar** to shake
**temer** to fear
**tender** to hold out
**tener** to have; to hold **tener antipatía a** to dislike; **tener cuidado** to be careful; **tener éxito** to be successful; **tener lugar** to take place; to come off; **tener mala suerte** to be unlucky; **tener miedo** to be afraid; **tener que** to have to; **tener que ver con** to concern; **tener razón** to be right; **tener suerte** to be lucky; **tener tendencia a hacer algo** to tend to do sth
**terminar** to end; to finish
**tirar** to throw away **tirar de** to pull
**tocar** to touch; to play; to ring
**tomar** to take
**torcer** to twist
**trabajar** to work
**traducir** to translate
**traer** to bring
**traicionar** to betray
**tranquilizar(se)** to calm down
**trasladar** to transfer
**tratar** to treat **tratar (de)** to try (to); **tratar con** to deal with
**unir** to join **unir(se)** to unite
**untar** to spread
**usar** to use
**vaciar(se)** to empty
**vacilar** to hesitate
**valer** to be worth
**variar** to vary
**vencer** to conquer, to defeat, to overcome
**vender** to stock **vender(se)** to sell
**venir** to come **venirse abajo** to collapse
**ver** to see
**visitar** to visit
**vislumbrar** to catch sight of
**vivir** to live
**volar** to fly
**volcar** to overturn
**volver** to come back; to go back; to return **volver(se)** to turn round; **volverse hacia** to turn towards
**votar** to vote
## ENGLISH
INDEX
The words on the following pages cover all of the ESSENTIAL and IMPORTANT NOUNS in the book.
absence
accident , ,
Accident and Emergency
accommodation
account
actor
actress
address ,
adults
advert(s)
aerobics
afternoon
age ,
agriculture
air , ,
air pollution ,
airbed ,
airport
airsickness
alarm clock ,
alcohol
alphabet
Alps
aluminium ,
ambition
ambulance
America
American ,
Andalusia
animal(s) , ,
ankle
anorak
answer
answerphone
antiseptic
apartment
aperitif
appearance
apple
appliance
application
appointment ,
apprenticeship ,
apricot
April
area ,
arm
armchair
armed robber ,
army
arrival ,
art gallery ,
article
ashtray ,
aspirin
Atlantic
atmosphere
attachment
audience
auditorium ,
August
aunt
au pair girl
author
autumn ,
avenue
baby
bachelor
back ,
bag , ,
baker
bakery
balcony ,
Balearic Islands
ball , ,
ballet
banana
band
bandage
bank , , ,
bank account
bank card
banknote ,
bar ,
barbecue
Barcelona
barrier
basement
basketball
Basque Country
bath
bathroom , , ,
bathtub
battery
Bay of Biscay
beach ,
bean
beard
beauty
bed , ,
bed linen ,
bedroom
bee
beef
beer
beginning of term
Belgian
Belgium
belt
bench ,
bicycle , ,
bidet
bike , ,
bikini
bikini bottoms
bill , ,
billboard
billiards
biology
bird , ,
Biro®
birth
birthday
blackboard
blanket
block of flats ,
blood ,
blouse
boarding card
boat , ,
body
bodywork
bonfire
book
bookcase
booking
bookshop
boot ,
border ,
boss , ,
bottle(s) ,
bottom
boutique ,
bowl
box ,
box office
boxer shorts
boy
boyfriend
bracelet
brake , ,
branch ,
brand
bread
break
breakdown
breakdown van
breakfast , ,
breathalyzer® test
brick
bridge , ,
Britain
British girl/woman
Briton ,
broadband
brother
brush ,
Brussels
budgie
building ,
bunch of flowers
bunk bed
burglar ,
burglary
bus ,
bus station
bus stop
bush
business
businessman/woman ,
bust
butane store
butcher
butcher's (shop)
butter
button
café ,
cafeteria
cage
cake
cake shop ,
calculator
calendar
calf ,
call
callbox
camcorder
camera
camp bed
camper ,
campfire
camping
campsite
can , , ,
Canada
Canadian ,
Canary Islands
cancellation
canned food
canteen
capital (city)
car , , ,
car door
car hire
car park , ,
car wash
carafe
caravan , , ,
cardboard
cards
career
careers adviser ,
caretaker , , ,
carpet
carriage
carrot
cart
cartoon
cash desk
cast
Castile
castle ,
cat , ,
Catalonia
cathedral
cauliflower
CD ,
CD/DVD/MP3 player ,
CD/DVD writer
cellar
cent
central heating
century
cereal
certificate
chain
chair
chairperson ,
chambermaid
champion ,
championship
change , ,
character
chauffeur ,
check-out ,
check-out assistant ,
checkpoint
cheek
cheese
chef ,
chemist , ,
chemist's (shop) ,
chemistry
cheque , ,
cheque book ,
cherry
chess ,
chest ,
chestnut
chicken
child ,
child benefit
chimney
chin
chips
chocolate
choice
Christian name
church
cider ,
cigar
cigarette
cinema , , ,
circus
city ,
civil guard , , ,
clarinet
class ,
classical music
classroom
cleaner , ,
climate ,
clinic
clock , ,
clothes
cloud
clown ,
club ,
clutch
coach
coast ,
coat ,
cobbler
cock ,
coffee ,
coffee pot/maker
coffee table
coffee with milk
Coke®
cold ,
collar
colleague ,
collection ,
collision ,
colour
comb
comedian ,
comedy
comfort ,
comic strip
compact disc
compartment
competition
competitive exam
complaint ,
complexion
comprehensive school
computer , ,
computer programmer ,
computer science
computer studies
concert ,
condition
conductor ,
confectioner
congratulations
connection , ,
consulate
contact lenses
contract
cook ,
cooker , ,
cooking
cordial
cordless phone
corkscrew
corner
corridor ,
Corunna
Costa del Sol
costume ,
cottage
cotton
cotton wool
couchette
council flat
counter
counter clerk ,
country , , ,
country people
countryman ,
countryside
countrywoman ,
course ,
court ,
cousin ,
cover charge
covering letter
cow ,
crab ,
cream ,
credit
credit card ,
cricket
crisis
crisps ,
croissant
crop
crossing
crossroads ,
culprit ,
cultivation
cup
cupboard , ,
curiosity
curtain(s) ,
customer ,
customs ,
customs officer , , ,
cycling ,
cyclist , ,
daddy
damage , ,
dance
dashboard
date ,
daughter
day , , ,
day off
days of the week
dead man/woman ,
death ,
death penalty
debit card ,
December
deckchair ,
decorator
defence
degree
delay , ,
demonstration
dentist ,
deodorant
department ,
department store
departure ,
departure gate
departure lounge
deposit ,
desk
dessert
dessertspoon
destination ,
detective novel
detergent
dialling code
dialling tone
diarrhoea
diesel , ,
diesel oil
digital camera
digital radio
dining car
dining hall
dining room ,
dinner
diploma
direction ,
director ,
directory
disco
discount
dish
dishes ,
dishwasher ,
display case
distance ,
district ,
diversion ,
divorce
DIY
doctor , , ,
dog , ,
door ,
dormitory ,
double bed
draught beer
drawing
dress
dress circle
drink
drive
driver , , ,
driving licence ,
driving school
drug
drum kit
drums
dry-cleaner's
duck ,
duration
dust , ,
dustbin , ,
Dutchman
Dutchwoman, Dutch girl
duty-free (shop)
DVD
ear
earth , ,
east ,
eau de toilette
ecology
Edinburgh
editor ,
education
egg
electric cooker
electrician
electricity
electronics
elephant
email ,
emergency exit
employee ,
employer
employment organisation
engagement
engine
engineer
England
English
Englishman
Englishwoman, English girl
enquiries
entertainment
entrance , , ,
entrance examination
envelope
environment
environmentalist
era
escalator , ,
estate
e-ticket
euro ,
euro cent
Europe
European ,
evening ,
event
ewe ,
exam
exchange
exchange rate
exercise book
exhaust fumes
exhibition
exit , ,
expense
experiment
expression
exterior
extra charge , , ,
eye ,
eyebrow
fabric ,
face ,
face cream
factory , ,
fair
fair trade
family
fare , , , ,
farm ,
farmer , , , , , , ,
farmer's wife
farmhouse ,
fashion
fast train
father
father-in-law
fault
fax
fax machine
February
fence , ,
ferry
festival ,
festivities
fiancé
fiancée
field , , ,
file ,
film , ,
film star ,
fine
finger
fire
fire engine
fire escape
fireman ,
fireplace
firework; firework display
first course
first name
fish , , ,
fish shop
fisherman/woman ,
fishing
fishing boat
fishmonger
fishmonger's
fixed price menu
fixed term contract
flat
flavour
flea market
flight
flight attendant ,
floor , , ,
flour
flower shop
flower(s) ,
flowerbed
flu
flute
fly
foal
fog
folder
food
foot
football
forecast ,
forehead
forest , ,
fork ,
form , ,
fortnight
foyer
France
free time
freezer
French
French beans ,
French loaf
Frenchman
Frenchwoman, French girl
Friday
fridge , ,
front
front door
fruit , ,
fruit juice
fruit tree
fruiterer
fruiterer's
frying pan
full board
fun fair
fur ,
furnished flat
furniture , ,
future , ,
future tense
game , ,
games console
games room ,
gang
garage , ,
garage owner ,
garden ,
gardener ,
gardening
garlic ,
gas , , ,
gas cooker
gate , ,
gear ,
geography
German , ,
Germany
girl
girlfriend
glass , ,
glasses
glove
goal ,
goalkeeper
gold
goldfish
golf
goose
government ,
grandchildren
granddaughter
grandfather
grandmother
grandparents
grandson
grant-aided school
grape(s)
grapefruit
grass
Great Britain
green salad
greengrocer ,
greengrocer's
greenhouse
Greens
grilled meat
grocer's
ground , , ,
ground floor/level ,
group
grown-ups
guest ,
guest house ,
guidebook ,
guitar
gym ,
gymnast ,
gymnastics
habit
hair , ,
hairdresser , ,
half an hour
half-board
hall
ham
hamburger
hamster
hand
hand luggage
handbag , , , , ,
handicrafts
handkerchief
handyman/woman ,
harbour
hard-boiled egg
hat
head
headlight(s) ,
headmaster
headmistress
health
heart
heat ,
heater , ,
heating
heavy goods vehicle
height
helicopter ,
helmet ,
hen ,
higher school-leaving course/certificate
high-speed train
highway code
hike , ,
hill ,
history
hitch-hiker ,
hitch-hiking
hoarding
hobby ,
hockey
hold-up
hole
holiday-maker ,
holidays ,
Holland
home address
homework ,
hood
horizon
horn
hors d'œuvres
horse ,
horse-racing
horse-riding
hospital
hot chocolate
hotel ,
hour
house
housework
housing
housing estate
hunger
hunter ,
husband ,
hypermarket
ice
ice cream
ID
ID card , ,
identity
identity card
identity theft
illness
inclusive price ,
income tax
industrial estate
information , ,
information desk
inhabitant(s) , ,
injection
injury
inn , ,
insect
institute of employment
instrument
insurance ,
insurance certificate
insurance policy ,
interior
internet
internet café ,
interval
interview
Ireland
Irishman
Irishwoman, Irish girl
iron ,
island ,
Italian ,
Italy
jacket
jam
January
jeans
jersey
jewel
job ,
job centre
job interview
job market
journey ,
jug
July
jumper
June
jungle
kettle
key , ,
kid
kilometre
kitchen ,
kitten
knee
knickers ,
knife ,
knitting
laboratory
lady
lake ,
lamb , ,
lamp , ,
lampshade
land ,
landing
landline
landlord/lady ,
languages
laptop
launderette ,
laundry
lawn
lawyer ,
leading lady
leading man
leaf , ,
leaflet
leather ,
lecture
left luggage locker/office
leg
leisure (activities)
lemon
lemonade
length (of time)
length
lesson(s)
letter
letterbox
library , ,
life
lift ,
light
light bulb
lighter
lilo
line
lion
list
listings section
litre
living room ,
lock
locker
London
look
lorry ,
lorry driver
lost property office ,
luggage , ,
lumber room
lunch , , ,
machine
magazine
maiden name
mail
main road
main street
Majorca
make (of car)
make-up ,
Malaga
man
manager , , , ,
map , , , ,
March
mare
marina
mark
market , ,
marmalade
marriage
match , , , ,
mathematics, maths
May
mayonnaise
mayor ,
meal , ,
means of transport
meat
mechanic ,
medicine ,
Mediterranean
meeting
melon
member
membership card
menu
metal
microwave oven
milk
milky coffee
miner
mineral water
Minorca
minute
mirror , , ,
mist
mistake ,
mixed salad
mobile phone , ,
mock exam
(modern) languages
moment
Monday
money
month ,
monument
mood
moped
morning
mosque
mother
mother-in-law
motorbike
motorcycle
motorcyclist ,
motorhome
motorist ,
motorway
MOT test
mountain ,
mountain bike
mountain range
mouse ,
moustache
mouth
move
mugger ,
mugging
multiple-journey ticket
mummy
museum ,
mushrooms
music , , ,
music video
musical instrument
musician ,
mustard
mutton
name
napkin
nationality
nature
neck
neighbour , , ,
nephew
Netherlands
news ,
news stand
newsagent
newspaper ,
next day
niece
night , , ,
nightdress
noise ,
north ,
(Northern) Ireland
nose
notebook
notice , ,
novel
November
nuclear plant
number , , , ,
nurse , , ,
nursery school
oar
October
office , , ,
official papers
oil ,
ointment
old town
olive
omelette
one-way street
onion
opera
operation
operator ,
optician
oral exam
orange
orchestra ,
outing ,
oven
overcoat
owner , , , ,
ox ,
pain
paint
painter ,
painting , ,
Pakistani ,
pal ,
pancake
pants ,
paper ,
papers
parasol
parcel
parents
park ,
parka
parking
parking meter
parking space , ,
Pakistani
parrot
party ,
passenger ,
passer-by ,
passport , , ,
past
past tense
pastry
pâté
path ,
patient ,
pavement
payment
PC , ,
PE
peace
peach
pear
peas ,
pedestrian ,
pedestrian precinct
pen
pen friend ,
pencil
pencil case
penknife
people
pepper ,
performance
perfume
perfume shop/department
permanent contract
permission
person ,
personal computer , ,
personal stereo
peseta
pétanque
petrol ,
petrol pump
petrol pump attendant
petrol station , ,
phone call
phonecard
phone company
phone contract
phone number
photo ,
physics
piano ,
picnic , ,
picture ,
piece of fruit
piece of furniture ,
pig ,
pill
pillow
pilot , ,
pineapple
pipe
pitch , ,
pity
pizza
place
place setting
plane ,
plane crash
plane ticket
planet
plant(s) ,
plaster cast
plastic
plate ,
platform
play ,
player ,
playground
playtime
plot of land ,
plug
plumber
pocket
pocket money
police , ,
police officer ,
police station ,
policeman , , ,
policewoman ,
politics
pollutant
pollution
pop music
pork
pork butcher
pork butcher's
pork chop
port
porter ,
post office , ,
postbox
postcard
postcode
poster , , ,
postman ,
postwoman ,
potato
pound (sterling)
power steering
practical class
prescription
present , ,
present tense
presentation
president ,
press
price , ,
price list
primary school
primary schoolteacher ,
printer
private hospital
private school
prize
problem
profession
program
programme , ,
programmer
progress
property
public holiday
public transport
publicity
puncture ,
pupil ,
puppy
purchase
purse , ,
pyjamas
Pyrenees
quality
quarter
quarter of an hour
quay
question ,
quiche
rabbit ,
race
radiator
radio , ,
radio alarm
railway
rain , ,
rain forest
raincoat
rainfall
raisin
raspberry
rate(s) ,
razor
reading ,
ready-made meals
receipt ,
reception
receptionist , ,
recipe ,
record
recorder
reduction ,
region ,
registration document
relative
rent
reply
report ,
reservation ,
restaurant , , ,
restricted parking zone ,
result ,
retirement
return ticket ,
review
reward ,
rice
right of way
ring
rise
river ,
road , , ,
road accident
road map
road surface
roadblock
roast
roast chicken
robber ,
rock
Rock (of Gibraltar)
roof
room , , ,
root
rope
rose
roundabout
rowing
rowing boat
rubber ,
rucksack ,
rug
rugby
rule
ruler
rules , ,
sail
sailing
sailing boat/ship
saint's day
salad ,
salami
sales
sales assistant , , ,
salesman/woman ,
salt
sand
sandal
sandcastle
sandwich
Saragossa
sardine
Saturday
saucepan ,
saucer
sausage
saxophone
scales
scenery
school ,
school friend ,
schoolboy
schoolgirl
science
scooter
Scot ,
Scotland
sea ,
seafood ,
seasickness
seaside
season ,
season ticket
seat , ,
seat belt ,
second
secondary school
secretary
self-service restaurant ,
semester
sentence
September
serial ,
service
set price
Seville
shade; shadow ,
shampoo
sheep
sheepdog
sheet ,
shelf
ship
shirt
shoe
shoe shop
shoe size ,
shop ,
shop assistant , , ,
shop keeper ,
shop window
shopping centre
shorts
shoulder
show ,
shower , , , , ,
showing
sideboard
signature
silence
silk
silver
SIM card
singer ,
singing
single ticket ,
single woman
sink
sister
site
situation
size , , , ,
skating rink
ski
ski slope
skiing
skin ,
skirt
skittles
sky ,
sleeping bag ,
sleeping car
slice
slipper
slot
slum area
small ads
smell
smile
smoke ,
snack
snails
snow
soap ,
sock
socket , ,
sofa
soft-boiled egg
soil , ,
soldier
solution
son
song
soundtrack
soup ,
south ,
South America
souvenir
sow
Spain
Spaniard ,
Spanish
Spanish railway
spanner
spare part
spare tyre
special offer
species
speed , ,
speed camera
spoon ,
spoonful
sport
spot
spring ,
spy ,
square
stadium
staffroom
stage manager
stainless steel
stairs ,
stalls ,
stamp ,
star , , ,
starter(s) ,
state school
station ,
station buffet
stay ,
steak
steel
stepfather/mother ,
stereo system
steward ,
sticking plaster
stomach ,
stone , ,
storey , , ,
storm
story
stove
strawberry
stream
street ,
street map
stretcher
strike
student ,
studies ,
study (of)
subject
subtitle
suburb
subway , ,
sugar
suit
suitcase , ,
summer ,
summer holidays
sun ,
sunburn ,
suncream
Sunday
sunglasses ,
sunny spell
sunset
sunshine
sunstroke
supermarket
surgery
surname
surroundings
sweets
swimmer ,
swimming , ,
swimming pool , , , , ,
swimming trunks ,
swimsuit ,
Swiss ,
Swiss girl, Swiss woman
switch ,
Switzerland
synagogue
synthetic fibre
syrup ,
table , ,
table football
tablespoon
tablet ,
tail
tap ,
tape
tape recorder ,
tart
task
taste
tax ,
taxi , , ,
taxi driver
taxi rank ,
tea
teacher , , ,
teaching
team
teapot
tear
teaspoon
teenager ,
telegram
telephone , ,
telephone directory
television , , ,
television set
temp ,
temperature , ,
temping agency
temporary contract
tennis
tennis court
tent
text message , ,
Thames
theatre , ,
theft
thief ,
thirst
throat
thumb
thunderstorm
Thursday
ticket , , , ,
ticket collector ,
ticket machine
ticket office ,
tie
tiger
tights
time , ,
timetable , ,
tin , , ,
tinned food
tin-opener
tip , , ,
title
toast
tobacco
tobacconist's ,
today's special
toilet , ,
toilets , , ,
toll
toll motorway
tomato ,
tongue
tool
tooth
toothbrush
toothpaste ,
top (of hill)
top-up card
torch
tortoise
tour
Tour of Spain
tourist , , , , ,
tourist information office
towel ,
tower ,
town ,
town centre
town council
town hall
toy
track , ,
tractor
trade
trade union
traffic , ,
traffic jam , ,
traffic lights ,
trailer
train ,
train driver
train station
transistor
translation
travel agent's , ,
traveller , , ,
traveller's cheque
tray ,
tree(s) , ,
trip , , ,
trolley ,
trousers
trout
truck
truth
T-shirt
Tuesday
tumble-dryer
turkey ,
TV
TV channel
twin beds
typist
tyre , ,
ugliness
umbrella ,
uncle
underground , ,
underground station
underwear
unemployed person
unemployment
uniform
United Kingdom
United States
university
unleaded petrol
upkeep
USA ,
usher
usherette
vacuum cleaner ,
valley
van , ,
vanilla
veal
vegetables , , ,
vehicle ,
video cassette
video game
video recorder , ,
view , ,
village , ,
vinegar
violin
visibility
visitor ,
voice ,
voicemail
volleyball
wage-earner ,
wages
waist ,
waiter , , ,
waiting room
waitress ,
Wales
walk , , ,
walking stick
wall
wallet , , ,
warden
wardrobe ,
washbasin , , , ,
washing
washing facilities
washing machine , ,
washing powder , ,
washing-up liquid
washrooms
wasp
watch ,
water , , , , ,
water skiing
way
weather ,
weather forecast ,
weather report
web designer
website
wedding
wedding anniversary
Wednesday
weeds
week ,
weekend ,
welcome
wellington boot
Welshman
Welshwoman, Welsh girl
west ,
western
wheel
widow
widower
wife ,
wind
wind farm
wind turbine
window
windsurfing board ,
wine
winter ,
witness ,
woman
wood , , ,
wool
word
work ,
worker ,
working life
workshop
world
wound
writing paper
written exam
written proof
wrought iron
yard
year ,
yoghurt
young man
young people
youth ,
youth club
youth hostel ,
zone
zoo ,
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evlutionz LLC is a silencershop.com "Buy-it-Local" partner and Silencer Shop fingerprinting Kiosk location. Email evlutionz@yahoo.com or TEXT 904-849-7874 if you have purchased a silencer from me on silencershop.com and need to have fingerprinting and passport photos done.
I would be thrilled to help you legally acquire a silencer. If you are in the market to buy a silencer, do yourself a favor and go to silencershop.com and see the evlutionz LLC pricing on silencers. If it isn't the lowest pricing that you see, please let me know and I will make it the lowest. With the constant addition of new products which are automatically set to the "suggested price" it is really hard to keep up with, but I am happy to see that the market has given us that wonderful first world problem and so many great choices. While you are there have a look at my reviews. Those reviews were completely unsolicited and I wasn't aware until recently that I have more 5-Star reviews than any other Silencer Shop "Buy -it-Local" partner in the entire state of Florida, and I am a one-man shop that is appointment only. Who would think that would be possible? I didn't, but I am apparently making an impression on my customers and it is humbling to see it in the form of those reviews. I will continue to give my best effort to maintain and grow that and will treat you like you will write that next 5 star review. My goals as a "Buy-it-Local" partner are to make silencer ownership as affordable as possible and to make your transaction as smooth and fast as possible. When your silencer is ready for pickup you will be notified immediately or within 24 hours maximum. No games here, just prompt service so you can get on with enjoying your purchase and protecting your hearing.
I have additional sources for silencer ordering and can get other brands and models that may not be in stock at Silencer Shop. Let me know what you want and I will provide an out the door price on it, transfer, fingerprinting, and passport photos included.
Transfers, including fingerprinting and passport photos are $100 (plus tax) for the first item and $75 (plus tax) for each additional item for up to one year from when the first fingerprints and passport photos are submitted. What can you expect in regards to service? You can expect me to do what I say I will quickly, notify you when the items arrive, and notify you within 24 hours of the approved Form's arrival if not immediately. No games, just prompt service.
Order what you want and forward the order confirmation email to evlutionz@yahoo.com. I will forward that same email back to the vendor with my FFL and SOT attached. Getting started really is that simple.
If you are not familiar with the process of legally owning a silencer, please email evlutionz@yahoo.com for information.
Are you not sure which silencer to get? Email evlutionz@yahoo.com for guidance on what might fit your firearm, needs, and budget.
I can even get you going in the right direction to own a suppressed 12 gauge shotgun…. | {
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{"url":"https:\/\/it.mathworks.com\/help\/signal\/ug\/upsampling-imaging-artifacts.html","text":"# Upsampling \u2014 Imaging Artifacts\n\nThis example shows how to upsample a signal and how upsampling can result in images. Upsampling a signal contracts the spectrum. For example, upsampling a signal by 2 results in a contraction of the spectrum by a factor of 2. Because the spectrum of a discrete-time signal is $2\\pi$-periodic, contraction can cause replicas of the spectrum normally outside of the baseband to appear inside the interval $\\left[-\\pi ,\\pi \\right]$.\n\nCreate a discrete-time signal whose baseband spectral support is $\\left[-\\pi ,\\pi \\right]$. Plot the magnitude spectrum.\n\nf = [0 0.250 0.500 0.7500 1];\na = [1.0000 0.5000 0 0 0];\n\nnf = 512;\nb = fir2(nf-1,f,a);\nHx = fftshift(freqz(b,1,nf,'whole'));\n\nomega = -pi:2*pi\/nf:pi-2*pi\/nf;\nplot(omega\/pi,abs(Hx))\ngrid\nylabel('Magnitude')\n\nUpsample the signal by 2. Plot the spectrum of the upsampled signal. The contraction of the spectrum has drawn subsequent periods of the spectrum into the interval $\\left[-\\pi ,\\pi \\right]$.\n\ny = upsample(b,2);\nHy = fftshift(freqz(y,1,nf,'whole'));\n\nhold on\nplot(omega\/pi,abs(Hy))\nhold off\nlegend('Original','Upsampled')\ntext(0.65*[-1 1],0.45*[1 1],[\"\\leftarrow Imaging\" \"Imaging \\rightarrow\"], ...\n'HorizontalAlignment','center')","date":"2021-10-20 16:35:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 4, \"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\": 0.6011618375778198, \"perplexity\": 2627.8546110070324}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323585322.63\/warc\/CC-MAIN-20211020152307-20211020182307-00185.warc.gz\"}"} | null | null |
Guy Fieri Serves Up Some Competition with a Side of Sibling Rivalry in 'Guy's Grocery Games: Family Style'
TV By The Numbers November 19, 2014
GUY FIERI SERVES UP SOME COMPETITION WITH A SIDE OF SIBLING RIVALRY IN "GUY'S GROCERY GAMES: FAMILY STYLE"
Four Episode Stunt Premieres Sunday, January 4th at 8pm ET/PT on Food Network
NEW YORK – November 19, 2014 – Guy Fieri's favorite things are food, fun and family, and he is bringing all three together in the New Year for a Guy's Grocery Games: Family Style showdown, premiering Sunday, January 4th at 8pm ET/PT on Food Network. The families will compete over four episodes, with each episode consisting of four teams made up of a different variation of family members, each including a chef, as they compete for a chance at the grand prize. Whether it is a child with two parents, a parent with two children or siblings working together, the families must navigate their way through the aisles of a grocery store, battling it out in different supermarket-themed obstacles, including shopping and cooking on a budget, cooking a meal with five ingredients or less, or the new game of station swap, among others. One-by-one the losing families must "check out" by a rotating panel of judges, featuring Melissa d'Arabian, Richard Blais, G. Garvin, Troy Johnson, Beau MacMillan, Catherine McCord and Aarti Sequeira. The last family standing goes on a shopping spree of a lifetime worth up to $20,000. These families know, live and love food, so don't miss all the laughs, tears, and sibling rivalries delivered Family Style!
Check out FoodNetwork.com/GroceryGames to get Guy's exclusive take on the family-style competition, learn more about the families competing, and see bonus behind-the-scenes photos and videos, including how Flavortown Market was built.
Premiering Sunday, January 4th at 8pm ET/PT "Family Style: Kid's Choice" Guy is constantly turning the tables, this time with kids choosing the meals. Four families face off in a brunch competition that includes a mandatory Red Light Special: raisins! In Budget Battle, families must make a comfort meal on a very uncomfortable budget. Then, the final teams must prepare a five-star dinner while playing Station Swap, a twisty new game that forces the families to trade kitchens and groceries. One family will go on a Shopping Spree worth up to $20,000. Competitors: Binbek Family, Landefeld Family, Lavin Family, Murphy Family Judges: Melissa d'Arabian, Richard Blais, Aarti Sequeira
Premiering Sunday, January 11th at 8pm ET/PT "Family Style: Sibling Rivalry" When four sets of siblings square off in a supermarket, sparks fly! The teams begin by making a family feast, but first they must agree on the 5 Ingredients or Less this challenge allows. Three families move on to make something stuffed using Guy's Grocery List of unique ingredients. Then in the feared game of chance, Food Wheel, the stakes are high as two families attempt to make an upscale dinner with strip steak and $7.15 worth of extra ingredients. The family that moves on will play for a chance to win up to $20,000 in the Shopping Spree. Competitors: Fraser Family, Grbic Family, Loza Family, Testa Family Judges: Richard Blais, Troy Johnson, Aarti Sequeira
Premiering Sunday, January 18th at 8pm ET/PT "Family Style: Kids Rule!" Four competing families start by joining the breakfast club, but this is Watch Your Weight so they can only cook with 5 lbs. of ingredients. Next, the families must make a hot lunch ABC-style, using only ingredients whose name begins with the letter R. The final two families go head-to-head in the dreaded game, Food Wheel. The winning family goes after the green stuff, up to $20,000 in the Shopping Spree! Competitors: Bruno Family, Chiovera Family, Roberts Family, Robertson Family Judges: Melissa d'Arabian, Richard Blais, Troy Johnson
Premiering Sunday, January 25th at 8pm ET/PT "Family Style: Food Feud" Chefs keep it all in the family with teams featuring husbands, wives, brothers, moms and even grandma! The pasta shelves are off-limits in Aisle Down, so our four families must really use their noodles to create their best dish. Next, three families have to come up with fresh ideas for making dessert from non-perishable items playing Meals from the Middle. The finalists must make their favorite family meal, but wait, this is Watch Your Weight, so they only get 5? lbs. of ingredients. Then, it's all hands on cart as the winning family goes on the Shopping Spree worth up to $20,000. Competitors: Casey Family, Parrish Family, Thurston Family, Vera Family Judges: Troy Johnson, Beau MacMillan, Catherine McCord
Guy's Grocery Games is produced by Relativity Lifestyle Television, a division of Relativity Television.
Category: Network TV Press ReleasesTagged: Guy's Grocery Games Ratings
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{"url":"https:\/\/2022.help.altair.com\/2022\/hwsolvers\/os\/topics\/solvers\/os\/analysis_fatigue_uniaxial_r.htm","text":"# Uniaxial Fatigue Analysis\n\nUniaxial Fatigue Analysis, using S-N (stress-life) and E-N (strain-life) approaches for predicting the life (number of loading cycles) of a structure under cyclical loading may be performed by using OptiStruct.\n\nThe stress-life method works well in predicting fatigue life when the stress level in the structure falls mostly in the elastic range. Under such cyclical loading conditions, the structure typically can withstand a large number of loading cycles; this is known as high-cycle fatigue. When the cyclical strains extend into plastic strain range, the fatigue endurance of the structure typically decreases significantly; this is characterized as low-cycle fatigue. The generally accepted transition point between high-cycle and low-cycle fatigue is around 10,000 loading cycles. For low-cycle fatigue prediction, the strain-life (E-N) method is applied, with plastic strains being considered as an important factor in the damage calculation.\n\nSections of a model on which fatigue analysis is to be performed must be identified on a FATDEF Bulk Data Entry. The appropriate FATDEF Bulk Data Entry may be referenced from a fatigue subcase definition through the FATDEF Subcase Information Entry.\n\n## Stress-Life (S-N) Approach\n\n### S-N Curve\n\nThe S-N curve, first developed by W\u00f6hler, defines a relationship between stress and number of cycles to failure. Typically, the S-N curve (and other fatigue properties) of a material is obtained from experiment; through fully reversed rotating bending tests. Due to the large amount of scatter that usually accompanies test results, statistical characterization of the data should also be provided (certainty of survival is used to modify the S-N curve according to the standard error of the curve and a higher reliability level requires a larger certainty of survival).\nWhen S-N testing data is presented in a log-log plot of alternating nominal stress amplitude ${S}_{a}$ or range ${S}_{R}$ versus cycles to failure $N$, the relationship between $S$ and $N$ can be described by straight line segments. Normally, a one or two segment idealization is used. (1) $S=S1{\\left({N}_{f}\\right)}^{b1}$\n\nfor segment 1\n\nWhere, $S$ is the nominal stress range, ${N}_{f}$ are the fatigue cycles to failure, ${b}_{l}$ is the first fatigue strength exponent, and $SI$ is the fatigue strength coefficient.\n\nThe S-N approach is based on elastic cyclic loading, inferring that the S-N curve should be confined, on the life axis, to numbers greater than 1000 cycles. This ensures that no significant plasticity is occurring. This is commonly referred to as high-cycle fatigue.\n\nS-N curve data is provided for a given material on a MATFAT Bulk Data Entry. It is referenced through a Material ID (MID) which is shared by a structural material definition.\n\n### Equivalent Nominal Stress\n\nSince S-N theory deals with uniaxial stress, the stress components need to be resolved into one combined value for each calculation point, at each time step, and then used as equivalent nominal stress applied on the S-N curve.\n\nVarious stress combination types are available with the default being \"Absolute maximum principle stress\". \"Absolute maximum principle stress\" is recommended for brittle materials, while \"Signed von Mises stress\" is recommended for ductile material. The sign on the signed parameters is taken from the sign of the Maximum Absolute Principal value.\n\nParameters affecting stress combination may be defined on a FATPARM Bulk Data Entry. The appropriate FATPARM Bulk Data Entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information Entry.\n\n### Mean Stress Correction\n\nGenerally, S-N curves are obtained from standard experiments with fully reversed cyclic loading. However, the real fatigue loading could not be fully-reversed, and the normal mean stresses have significant effect on fatigue performance of components. Tensile normal mean stresses are detrimental and compressive normal mean stresses are beneficial, in terms of fatigue strength. Mean stress correction is used to take into account the effect of non-zero mean stresses.\n\nThe Gerber parabola and the Goodman line in Haigh's coordinates are widely used when considering mean stress influence, and can be expressed as:\n\nGerber:(2) ${S}_{e}=\\frac{{S}_{r}}{\\left(1-{\\left(\\frac{{S}_{m}}{{S}_{u}}\\right)}^{2}\\right)}$\nGoodman:(3) ${S}_{e}=\\frac{{S}_{r}}{\\left(1-\\frac{{S}_{m}}{{S}_{u}}\\right)}$\nWhere,\n${S}_{m}$\nMean stress given by ${S}_{m}=\\left({S}_{max}+{S}_{min}\\right)\/2$\n${S}_{r}$\nStress Range given by ${S}_{r}={S}_{max}-{S}_{min}$\n${S}_{e}$\nStress range after mean stress correction (for a stress range ${S}_{r}$ and a mean stress ${S}_{m}$)\n${S}_{u}$\nUltimate strength\n\nThe Gerber method treats positive and negative mean stress correction in the same way that mean stress always accelerates fatigue failure, while the Goodman method ignores the negative means stress. Both methods give conservative result for compressive means stress. The Goodman method is recommended for brittle material while the Gerber method is recommended for ductile material. For the Goodman method, if the tensile means stress is greater than UTS, the damage will be greater than 1.0. For the Gerber method, if the mean stress is greater than UTS, the damage will be greater than 1.0, with either tensile or compressive.\n\nA Haigh diagram characterizes different combinations of stress amplitude and mean stress for a given number of cycles to failure.\n\nParameters affecting mean stress influence may be defined on a FATPARM Bulk Data Entry. The appropriate FATPARM Bulk Data Entry may be referenced from a fatigue subcase definition through the FATPARM Subcase Information Entry.\n\nFKM:\n\nIf only MSS2 field is specified for mean stress correction, the corresponding Mean Stress Sensitivity value ($M$) for Mean Stress Correction is set equal to MSS2. Based on FKM-Guidelines, the Haigh diagram is divided into four regimes based on the Stress ratio ($R={S}_{\\mathrm{min}}\/{S}_{\\mathrm{max}}$) values. The Corrected value is then used to choose the S-N curve for the damage and life calculation stage.\nNote: The FKM equations below illustrate the calculation of Corrected Stress Amplitude (${S}_{e}^{A}$). The actual value of stress used in the Damage calculations is the Corrected stress range (which is $2\\cdot {S}_{e}^{A}$). These equations apply for SN curves input by the user on the MATFAT entry (by default, any user-defined SN curve is expected to be input for a stress ratio of R=-1.0). For FKM equations applicable to spot weld analysis where the SN curve is input for a stress ratio of R=0.0, see the spot weld section below.\n\nThere are 2 available options for FKM correction in OptiStruct and are activated by setting UCORRECT to FKM\/FKM2 or MCORRECT(MCi) fields to FKM on the FATPARM entry.\n\nIf only MSS2 is defined and if UCORRECT\/MCORRECT(MCi) on FATPARM is set to FKM:\nRegime 1 (R > 1.0)\n${S}_{e}^{A}={S}_{a}\\left(1-M\\right)$\nRegime 2 (-\u221e \u2264 R \u2264 0.0)\n${S}_{e}^{A}={S}_{a}+M*{S}_{m}$\nRegime 3 (0.0 < R < 0.5)\n${S}_{e}^{A}=\\left(1+M\\right)\\frac{{S}_{a}+\\left(M}{3}\\right){S}_{m}}{1+M}{3}}$\nRegime 4 (R \u2265 0.5)\n${S}_{e}^{A}=\\frac{3{S}_{a}{\\left(1+M\\right)}^{2}}{3+M}$\nWhere,\n${S}_{e}^{A}$\nStress amplitude after mean stress correction (Endurance stress)\n${S}_{m}$\nMean stress\n${S}_{a}$\nStress amplitude\nIf only MSS2 is defined and if UCORRECT on FATPARM is set to FKM2:\nRegime 1 (R > 1.0) and Regime 4 (R \u2265 0.5)\nMean stress correction is not applied $M=0.0$\nRegime 2 (-\u221e \u2264 R \u2264 0.0)\n${S}_{e}^{A}={S}_{a}+M*{S}_{m}$\nRegime 3 (0.0 < R < 0.5)\n${S}_{e}^{A}=\\left(1+M\\right)\\frac{{S}_{a}+\\left(M}{3}\\right){S}_{m}}{1+M}{3}}$\nWhere,\n${S}_{e}^{A}$\nStress amplitude after mean stress correction (Endurance stress)\n${S}_{m}$\nMean stress\n${S}_{a}$\nStress amplitude\n$M$\nEqual to MSS2\n\nIf all four MSSi fields are specified for mean stress correction, the corresponding Mean Stress Sensitivity values are slopes for controlling all four regimes. Based on FKM-Guidelines, the Haigh diagram is divided into four regimes based on the Stress ratio ($R={S}_{\\mathrm{min}}\/{S}_{\\mathrm{max}}$) values. The Corrected value is then used to choose the S-N curve for the damage and life calculation stage.\n\nThere are 2 available options for FKM correction in OptiStruct and are activated by setting UCORRECT to FKM\/FKM2 and MCORRECT(MCi) fields to FKM on the FATPARM entry.\n\nIf all four MSSi are defined and if UCORRECT\/MCORRECT(MCi) on FATPARM is set to FKM:\nRegime 1 (R > 1.0)\n${S}_{e}^{A}=\\left({S}_{a}+{M}_{1}{S}_{m}\\right)\\left(\\left(1-{M}_{2}\\right)\/\\left(1-{M}_{1}\\right)\\right)$\nRegime 2 (-\u221e \u2264 R \u2264 0.0)\n${S}_{e}^{A}={S}_{a}+{M}_{2}{S}_{m}$\nRegime 3 (0.0 < R < 0.5)\n${S}_{e}^{A}=\\left(1+{M}_{2}\\right)\\frac{{S}_{a}+{M}_{3}{S}_{m}}{1+{M}_{3}}$\nRegime 4 (R \u2265 0.5)\n${S}_{e}^{A}=\\left({S}_{a}+{M}_{4}{S}_{m}\\right)\\left(\\left(\\left(1+3{M}_{3}\\right)\\left(1+{M}_{2}\\right)\\right)\/\\left(\\left(1+3{M}_{4}\\right)\\left(1+{M}_{3}\\right)\\right)\\right)$\nWhere,\n${S}_{e}^{A}$\nStress amplitude after mean stress correction (Endurance stress)\n${S}_{m}$\nMean stress\n${S}_{a}$\nStress amplitude\n${M}_{i}$\nEqual to MSSi\nIf all four MSSi are defined and if UCORRECT on FATPARM is set to FKM2:\nRegime 1 (R > 1.0) and Regime 4 (R \u2265 0.5)\nMean stress correction is not applied\nRegime 2 (-\u221e \u2264 R \u2264 0.0)\n${S}_{e}^{A}={S}_{a}+{M}_{2}{S}_{m}$\nRegime 3 (0.0 < R < 0.5)\n${S}_{e}^{A}=\\left(1+{M}_{2}\\right)\\frac{{S}_{a}+{M}_{3}{S}_{m}}{1+{M}_{3}}$\nWhere,\n${S}_{e}^{A}$\nStress amplitude after mean stress correction (Endurance stress)\n${S}_{m}$\nMean stress\n${S}_{a}$\nStress amplitude\n${M}_{i}$\nEqual to MSSi\nFor Spot Weld analysis, when the default S-N curves are used or if the field R on the SPWLD continuation line is set to 0.0 and UCORRECT is set to FKM, then the following FKM equations are used:\nRegime 1 (R > 1.0)\n${S}_{e}^{A}=\\left({S}_{a}+{M}_{1}{S}_{m}\\right)\\left(\\left(1-{M}_{2}\\right)\/\\left(\\left(1+{M}_{2}\\right)\\left(1-{M}_{1}\\right)\\right)\\right)$\nRegime 2 (-\u221e \u2264 R \u2264 0.0)\n${S}_{e}^{A}=\\left({S}_{a}+{M}_{2}{S}_{m}\\right)\/\\left(1+{M}_{2}\\right)$\nRegime 3 (0.0 < R < 0.5)\n${S}_{e}^{A}=\\frac{{S}_{a}+{M}_{3}{S}_{m}}{1+{M}_{3}}$\nRegime 4 (R \u2265 0.5)\n${S}_{e}^{A}=\\left({S}_{a}+{M}_{4}{S}_{m}\\right)\\left(\\left(1+3{M}_{3}\\right)\/\\left(\\left(1+3{M}_{4}\\right)\\left(1+{M}_{3}\\right)\\right)\\right)$\n\n### Damage Accumulation Model\n\nPalmgren-Miner's linear damage summation rule is used. Failure is predicted when:(4) $\\sum {D}_{i}=\\sum \\frac{{n}_{i}}{{N}_{if}}\\ge 1.0$\nWhere,\n${N}_{if}$\nMaterials fatigue life (number of cycles to failure) from its S-N curve at a combination of stress amplitude and means stress level $i$.\n${n}_{i}$\nNumber of stress cycles at load level $i$.\n${D}_{i}$\nCumulative damage under ${n}_{i}$ load cycle.\n\nThe linear damage summation rule does not take into account the effect of the load sequence on the accumulation of damage, due to cyclic fatigue loading. However, it has been proved to work well for many applications.\n\n## Strain-Life (E-N) Approach\n\nStrain-life analysis is based on the fact that many critical locations such as notch roots have stress concentration, which will have obvious plastic deformation during the cyclic loading before fatigue failure. Thus, the elastic-plastic strain results are essential for performing strain-life analysis.\n\n### Neuber Correction\n\nNeuber correction is the most popular practice to correct elastic analysis results into elastic-plastic results.\n\nIn order to derive the local stress from the nominal stress that is easier to obtain, the concentration factors are introduced such as the local stress concentration factor ${K}_{\\sigma }$, and the local strain concentration factor ${K}_{\\epsilon }$.(5) ${K}_{\\sigma }=\\sigma \/S$ (6) ${K}_{\\epsilon }=\\epsilon \/e$\nWhere, $\\sigma$ is the local stress, $\\text{\u03b5}$ is the local strain, $S$ is the nominal stress, and $e$ is the nominal strain. If nominal stress and local stress are both elastic, the local stress concentration factor is equal to the local strain concentration factor. However, if the plastic strain is present, the relationship between ${K}_{\\sigma }$and ${K}_{\\epsilon }$ no long holds. Thereafter, focusing on this situation, Neuber introduced a theoretically elastic stress concentration factor ${K}_{t}$ defined as:(7) ${K}_{t}^{2}={K}_{\\sigma }{K}_{\\epsilon }$\nSubstitute Equation 5 and Equation 6 into Equation 7, the theoretical stress concentration factor ${K}_{t}$ can be rewritten as:(8) ${K}_{t}^{2}=\\left(\\frac{\\sigma }{S}\\right)\\left(\\frac{\\epsilon }{e}\\right)$\nThrough linear static FEA, the local stress instead of nominal stress is provided, which implies the effect of the geometry in Equation 8 is removed, thus you can set ${K}_{t}$ as 1 and rewrite Equation 8 as:(9) $\\sigma \\epsilon ={\\sigma }_{e}{\\epsilon }_{e}$\n\nWhere, ${\\sigma }_{e}$ , ${\\epsilon }_{e}$ is locally elastic stress and locally elastic strain obtained from elastic analysis, $\\sigma$, $\\text{\u03b5}$ the stress and strain at the presence of plastic strain. Both $\\sigma$ and $\\text{\u03b5}$ can be calculated from Equation 9 together with the equations for the cyclic stress-strain curve and hysteresis loop.\n\n### Monotonic Stress-Strain Behavior\n\nRelative to the current configuration, the true stress and strain relationship can be defined as:(10) $\\sigma =P\/A$ (11) $\\epsilon ={\\int }_{l}^{l}\\frac{dl}{l}=\\mathrm{ln}\\left(1+\\frac{l-{l}_{0}}{{l}_{0}}\\right)$\n\nWhere, $A$ is the current cross-section area, $l$ is the current objects length, ${l}_{0}$ is the initial objects length, and $\\sigma$ and $\\text{\u03b5}$ are the true stress and strain, respectively, Figure 5 shows the monotonic stress-strain curve in true stress-strain space. In the whole process, the stress continues increasing to a large value until the object fails at C.\n\nThe curve in Figure 5 is comprised of two typical segments, namely the elastic segment OA and plastic segment AC. The segment OA keeps the linear relationship between stress and elastic strain following Hooke Law:(12) $\\sigma =E{\\epsilon }_{e}$\nWhere, $E$ is elastic modulus and ${\\epsilon }_{e}$ is elastic strain. The formula can also be rewritten as:(13) ${\\epsilon }_{e}=\\sigma \/E$\nby expressing elastic strain in terms of stress. For most of materials, the relationship between the plastic strain and the stress can be represented by a simple power law of the form:(14) $\\sigma =K{\\left({\\epsilon }_{p}\\right)}^{n}$\nWhere, ${\\epsilon }_{p}$ is plastic strain, $K$ is strength coefficient, and $n$ is work hardening coefficient. Similarly, the plastic strain can be expressed in terms of stress as:(15) ${\\epsilon }_{p}={\\left(\\frac{\\sigma }{K}\\right)}^{1\/n}$\nThe total strain induced by loading the object up to point B or D is the sum of plastic strain and elastic strain:(16) $\\epsilon ={\\epsilon }_{e}+{\\epsilon }_{p}=\\frac{\\sigma }{E}+{\\left(\\frac{\\sigma }{K}\\right)}^{1\/n}$\n\n### Cyclic Stress-Strain Curve\n\nMaterial exhibits different behavior under cyclic load compared with that of monotonic load. Generally, there are four kinds of response.\n\u2022 Stable state\n\u2022 Cyclically hardening\n\u2022 Cyclically softening\n\u2022 Softening or hardening depending on strain range\nWhich response will occur depends on its nature and initial condition of heat treatment. Figure 6 illustrates the effect of cyclic hardening and cyclic softening where the first two hysteresis loops of two different materials are plotted. In both cases, the strain is constrained to change in fixed range, while the stress is allowed to change arbitrarily. If the stress range increases relative to the former cycle under fixed strain range, as shown in the upper portion of Figure 6, it is called cyclic hardening; otherwise, it is called cyclic softening, as shown in the lower portion of Figure 6. Cyclic response of material can also be described by specifying the stress range and leaving strain unconstrained. If the strain range increases relative to the former cycle under fixed stress range, it is called cyclic softening; otherwise, it is called cyclic hardening. In fact, the cyclic behavior of material will reach a steady-state after a short time which generally occupies less than 10 percent of the material total life. Through specifying different strain ranges, a series of hysteresis loops at steady-state can be obtained. By placing these hysteresis loops in one coordinate system, as shown in Figure 7, the line connecting all the vertices of these hysteresis loops determine cyclic stress-strain curve which can be expressed in the similar form with monotonic stress-strain curve as: (17) $\\epsilon ={\\epsilon }_{e}+{\\epsilon }_{p}=\\frac{\\sigma }{E}+{\\left(\\frac{\\sigma }{{K}^{\\text{'}}}\\right)}^{1\/{n}^{\\text{'}}}$\nWhere,\n${K}^{\\text{'}}$\nCyclic strength coefficient\n${n}^{\\text{'}}$\nStrain cyclic hardening exponent\n\n### Hysteresis Loop Shape\n\nBauschinger observed that after the initial load had caused plastic strain, load reversal caused materials to exhibit anisotropic behavior. Based on experiment evidence, Massing put forward the hypothesis that a stress-strain hysteresis loop is geometrically similar to the cyclic stress strain curve, but with twice the magnitude. This implies that when the quantity ($\\text{\u0394}\\epsilon ,\\text{\u0394}\\sigma$) is two times of ($\\epsilon ,\\sigma$), the stress-strain cycle will lie on the hysteresis loop. This can be expressed with formulas:(18) $\\text{\u0394}\\sigma =2\\sigma$ (19) $\\text{\u0394}\\epsilon =2\\epsilon$\nExpressing $\\sigma$ in terms of \u0394\u03c3, $\\text{\u03b5}$ in terms of \u0394\u03b5, and substituting it into Equation 17, the hysteresis loop formula can be calculated as:(20) $\\text{\u0394}\\epsilon =\\frac{\\text{\u0394}\\sigma }{E}+2{\\left(\\frac{\\text{\u0394}\\sigma }{2K\\text{'}}\\right)}^{1\/n\\text{'}}$\nAlmost a century ago, Basquin observed the linear relationship between stress and fatigue life in log scale when the stress is limited. He put forward the following fatigue formula controlled by stress:(21) ${\\sigma }_{a}=\\sigma {\\text{'}}_{f}{\\left(2{N}_{f}\\right)}^{b}$\nWhere, ${\\sigma }_{a}$ is the stress amplitude, ${\\sigma }_{f}^{\\text{'}}$ is the fatigue strength coefficient, and $b$ is the fatigue strength exponent. Later in the 1950s, Coffin and Manson independently proposed that plastic strain may also be related with fatigue life by a simple power law:(22) ${\\epsilon }_{a}^{p}=\\epsilon {\\text{'}}_{f}{\\left(2{N}_{f}\\right)}^{c}$\nWhere, ${\\epsilon }_{a}^{p}$ is the plastic strain amplitude, $\\epsilon {\\text{'}}_{f}$ is the fatigue ductility coefficient, and $c$ is the fatigue ductility exponent. Morrow combined the work of Basquin, Coffin and Manson to consider both elastic strain and plastic strain contribution to the fatigue life. He found out that the total strain has more direct correlation with fatigue life. By applying Hooke Law, Basquin rule can be rewritten as:(23) ${\\epsilon }_{a}^{e}=\\frac{{\\sigma }_{a}}{E}=\\frac{\\sigma {\\text{'}}_{f}}{E}{\\left(2{N}_{f}\\right)}^{b}$\nWhere, ${\\epsilon }_{a}^{e}$ is elastic strain amplitude. Total strain amplitude, which is the sum of the elastic strain and plastic stain, therefore, can be described by applying Basquin formula and Coffin-Manson formula:(24) ${\\epsilon }_{a}={\\epsilon }_{a}^{e}+{\\epsilon }_{a}^{p}=\\frac{\\sigma {\\text{'}}_{f}}{E}{\\left(2{N}_{f}\\right)}^{b}+\\epsilon {\\text{'}}_{f}{\\left(2{N}_{f}\\right)}^{c}$\nWhere, ${\\epsilon }_{a}$ is the total strain amplitude, the other variable is the same with above.\n\n### Mean Stress Correction\n\nThe fatigue experiments carried out in the laboratory are always fully reversed, whereas in practice, the mean stress is inevitable, thus the fatigue law established by the fully reversed experiments must be corrected before applied to engineering problems.\n\nMorrow:\nMorrow is the first to consider the effect of mean stress through introducing the mean stress ${\\sigma }_{0}$ in fatigue strength coefficient by:(25) ${\\epsilon }_{a}^{e}=\\frac{\\left(\\sigma {\\text{'}}_{f}-{\\sigma }_{0}\\right)}{E}{\\left(2{N}_{f}\\right)}^{b}$\nThus, the entire fatigue life formula becomes:(26) ${\\epsilon }_{a}^{}=\\frac{\\left(\\sigma {\\text{'}}_{f}-{\\sigma }_{0}\\right)}{E}{\\left(2{N}_{f}\\right)}^{b}+{\\epsilon }_{f}^{\\text{'}}{\\left(2{N}_{f}\\right)}^{c}$\n\nMorrow's equation is consistent with the observation that mean stress effects are significant at low value of plastic strain and of little effect at high plastic strain.\n\nSmith, Watson and Topper:\nSmith, Watson and Topper proposed a different method to account for the effect of mean stress by considering the maximum stress during one cycle (for convenience, this method is called SWT in the following). In this case, the damage parameter is modified as the product of the maximum stress and strain amplitude in one cycle.(27) ${\\epsilon }_{a}^{SWT}{\\sigma }_{\\mathrm{max}}={\\epsilon }_{a}{\\sigma }_{a}={\\sigma }_{a}\\left(\\frac{\\sigma {\\text{'}}_{f}}{E}{\\left(2{N}_{f}\\right)}^{b}+\\epsilon {\\text{'}}_{f}{\\left(2{N}_{f}\\right)}^{c}\\right)$\n\nThe SWT method will predict that no damage will occur when the maximum stress is zero or negative, which is not consistent with the reality.\n\nWhen comparing the two methods, the SWT method predicted conservative life for loads predominantly tensile, whereas, the Morrow approach provides more realistic results when the load is predominantly compressive.\n\n### Damage Accumulation Model\n\nIn the E-N approach, use the same damage accumulation model as the S-N approach, which is Palmgren-Miner's linear damage summation rule.","date":"2022-11-30 10:09:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 129, \"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\": 0.6041725873947144, \"perplexity\": 2319.989409352945}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710734.75\/warc\/CC-MAIN-20221130092453-20221130122453-00771.warc.gz\"}"} | null | null |
Of all the products McIntosh has put out in the past few years this has really caught my attention. The classic McIntosh look embroidered onto a turntable, but wait, are those tubes? Perhaps giving a new definition to the term all-in-one for audiophiles, the newly announced MTI100 actually combines a 80 watt/channel (8 ohms) integrated amplifier with a vinyl turntable… and quite a bit more.
At first glance some might take pause at the vibration-sensitive source pushed so close to any other component, but it appears as though McIntosh has really thought the execution though. Let's be clear though, if speakers were included within the confines of the casework (as is actually the case for some products) things would be a little different. But this just-add-speakers scenario really does safely bring a lot to the…table.
A 7 pound aluminum platter, 3/8″ piece of glass and 1/4″ metal plate all help absorb vibrations and add stability within the architecture of the unit. Spinning the disc for beautiful music involves a belt-drive platter and 2-speed pulley, with an included Sumiko Olympia Moving Magnet cart providing the initial touchpoint. As one might expect, the power stage is class D and the two 12AX7 tubes power the pre. The phono section is separated and shielded for optimal performance in the small footprint.
On top of the basics, McIntosh didn't really hold back considering the amount of real estate they had to work with. For wireless on-the-go tap ins, Bluetooth 4.2 connectivity, for TV/gaming a digital optical input. Bonus points awarded for a dedicated subwoofer output, remote and even a headphone amplifier accessible from the front panel. Also on the front panel you can find power, volume and input selection. It's quite a smorgasbord of audio fun, especially considering the more traditional audiophile roots the McIntosh brand is typically known for.
McIntosh's dealer network is currently accepting preorders with shipping starting soon thereafter. The MSRP for the MTI100 is projected at $6,500 USD. Full presser below.
Binghamton, NY – January 24, 2019–McIntosh, the global leader in prestigious home entertainment and ultimate-quality audio for 70 years, is proud to announce the MTI100 Integrated Turntable. | {
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The federal government plays a crucial role in supporting states and local communities to prepare for, respond to and recover from disasters, but the federal role in recovery is not crucial, they mainly hand out cash. The states have their own cash, which allows the state to work on their own issues when they can. They also can use it to heal people through red cross and such.
However the government is responsible for helping where they can such as rescue teams, helicopters and the Coast Guard.
These people all help with the rescuing of people. This also includes the fire departments and police departments while the EMT's try and heal anyone in need. Another issue though is the government doesn't want to get involved when not needed, or if the state can do it faster. The reasoning for this is that the whenever the government intervenes there is much more paperwork required to get anything done. Florida has prepared by trying to evacuate anyone willing to do so, If the state can get everyone out that they can then they will have less people to worry about once the damage is done.
They have also told everyone what to do to keep them safe if they do choose to stay. They also acquire the correct amount of response personal needed, they stock stores with the last bit of resources they can to have their citizens survive without any power. Hurricane Michael was taken care of decently well, they had many things they had to cover and had done so. They shut down schools and stores, closed the roads and pretty much anything else that could pose any other problem.
Once the disaster is over there is much destruction and problems to address. They all have to think about all the people either dead or dying as well. Other nations such as Puerto Rico are still dealing with Hurricane Maria do to the lack of preparation, funds, and help. The disasters that can hit or start at any moment all of huge impacts on all of the people around it and the federal government is the only one that helps with natural disasters. Other countries do have emergency preparedness and they have similar situations. So they use all the communication that the certain country has to be used.
All in all government and state both play a huge role in the recovery of natural disasters. | {
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{"url":"http:\/\/en.wikiversity.org\/wiki\/Materials_Science_and_Engineering\/List_of_Topics\/Thermodynamics\/Zeroth_Law_of_Thermodynamics","text":"# Materials Science and Engineering\/List of Topics\/Thermodynamics\/Zeroth Law of Thermodynamics\n\nThe zeroth law of thermodynamics is a generalized statement about bodies in contact at thermal equilibrium and is the basis for the concept of temperature. The most common enunciation of the zeroth law of thermodynamics is:\n\n\"If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other.\"\n\nIn other words, the zeroth law says that if considered a mathematical binary relation, thermal equilibrium is transitive.\n\n## Temperature and the zeroth law\n\nIt is often claimed, for instance by Max Planck in his influential textbook on thermodynamics, that this law proves that we can define a temperature function, or more informally, that we can 'construct a thermometer'. Whether this is true is a subject in the philosophy of thermal and statistical physics.\n\nIn the space of thermodynamic parameters, zones of constant temperature will form a surface, which provides a natural order of nearby surfaces. It is then simple to construct a global temperature function that provides a continuous ordering of states. Note that the dimensionality of a surface of constant temperature is one less than the number of thermodynamic parameters (thus, for an ideal gas described with 3 thermodynamic parameter P, V and n, they are 2D surfaces). The temperature so defined may indeed not look like the Celsius temperature scale, but it is a temperature function.\n\nFor example, if two systems of ideal gas are in equilibrium, then $P1V1\/N1 = P2V2\/N2$ where $P_i$ is the pressure in the ith system, $V_i$ is the volume, and $N_i$ is the 'amount' (in moles, or simply number of atoms) of gas.\n\nThe surface $PV \/ N = \\mbox{const}$ defines surfaces of equal temperature, and the obvious (but not only) way to label them is to define T so that $PV \/ N = RT$ where R is some constant. These systems can now be used as a thermometer to calibrate other systems.","date":"2013-05-24 08:23:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 6, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8486681580543518, \"perplexity\": 336.8983604354659}, \"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-2013-20\/segments\/1368704368465\/warc\/CC-MAIN-20130516113928-00081-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
Q: How to remove input checkbox with jQuery I have a plugin which generates dynamically a list of categories.
I want to remove the input type checkbox select only from "Country" with jQuery. I have already tried with remove selector (on class .cat-item-15) but couldn't manage to make it work. Only for the specific li which is "Country". This way it removes all.
Is it possible to be applied only on "Country" li ?
I tried this way :
$(".cat-item-15 :checkbox").remove();
And here is the code I need to alter :
<li class="cat-item cat-item-15">
<label><input type="checkbox" name="ofait-items[]" value="15"> Country</label>
<ul class="children">
<li class="cat-item cat-item-53">
<label><input type="checkbox" name="ofait-items[]" value="53"> Canada</label>
</li>
<li class="cat-item cat-item-47">
<label><input type="checkbox" name="ofait-items[]" value="47"> United Kingdom</label>
</li>
<li class="cat-item cat-item-52">
<label><input type="checkbox" name="ofait-items[]" value="52"> USA</label>
</li>
</ul>
</li>
A: You could consider targeting the element in a few ways.
Target The Element Based On Its Value
jQuery supports attribute-based selectors which will allow you to target a specific element based on the value of one of it's attributes, so in this case, you could use :
$('.cat-item-15 :checkbox[value="15"]').remove();
Target The Element Based On Its Position
Since you know this will be the first checkbox that appears, you could remove it by using the :first selector :
$('.cat-item-15 :checkbox:first').remove();
Target The Element Based On Nearby Contents
Since you want to target the element that contains "Country", you can use the :contains() selector to find the particular <label> that contains that and remove it entirely :
$('.cat-item-15 label:contains("Country")').remove();
A: Your approach didn't work because the way that HTML is structured, all the other items are nested within the initial <li>. So if you remove that parent <li>, all the items within it will be removed as well.
If you want to remove just the input checkbox you can do something like:
$(".cat-item-15 :checkbox").first().remove();
If you need the word "Country" to disappear as well, then:
$(".cat-item-15 label").first().remove();
should work I think.
A: You should be able to use
$(".cat-item-15 :checkbox").first().remove();
or
$(".cat-item-15 :checkbox[value='15']").remove();
jsFiddle example
When you tried $(".cat-item-15 :checkbox").remove(); it failed because it selects all checkboxes that are descendants of any element with the class of cat-item-15, which was obviously too many.
:checkbox[value='15'] only selects checkboxes that have a value attribute of 15, and .first() just selects the first checkbox, so given your code either should work.
A: $('.cat-item-15 :checkbox').css("display") == "none";
or
$('.cat-item-15 :checkbox').hide();
A: You should use the below code:
$(".cat-item-15 input[type='checkbox']").remove();
It is so because, the input is a child of cat-item-15.
A: Try this:
$('.cat-item label:contains(Country) input').remove()
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<li class="cat-item cat-item-15"><label><input type="checkbox" name="ofait-items[]" value="15"> Country</label>
<ul class="children">
<li class="cat-item cat-item-53"><label><input type="checkbox" name="ofait-items[]" value="53"> Canada</label>
</li>
<li class="cat-item cat-item-47"><label><input type="checkbox" name="ofait-items[]" value="47"> United Kingdom</label>
</li>
<li class="cat-item cat-item-52"><label><input type="checkbox" name="ofait-items[]" value="52"> USA</label>
</li>
</ul>
</li>
A: you can use below code to remove checkbox in Country
$(".cat-item-15").children("label").children("input").remove()
A: You can use immediate child selector, if the structure needs to be same and value may be variable:
$(".cat-item-15 > label input:checkbox").remove();
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<li class="cat-item cat-item-15">
<label><input type="checkbox" name="ofait-items[]" value="15"> Country</label>
<ul class="children">
<li class="cat-item cat-item-53">
<label><input type="checkbox" name="ofait-items[]" value="53"> Canada</label>
</li>
<li class="cat-item cat-item-47">
<label><input type="checkbox" name="ofait-items[]" value="47"> United Kingdom</label>
</li>
<li class="cat-item cat-item-52">
<label><input type="checkbox" name="ofait-items[]" value="52"> USA</label>
</li>
</ul>
</li>
If the structure of HTML may vary but value remains same, then you can use:
$(".cat-item-15 :checkbox[value='15']").remove();
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<li class="cat-item cat-item-15">
<label>
<input type="checkbox" name="ofait-items[]" value="15">Country</label>
<ul class="children">
<li class="cat-item cat-item-53">
<label>
<input type="checkbox" name="ofait-items[]" value="53">Canada</label>
</li>
<li class="cat-item cat-item-47">
<label>
<input type="checkbox" name="ofait-items[]" value="47">United Kingdom</label>
</li>
<li class="cat-item cat-item-52">
<label>
<input type="checkbox" name="ofait-items[]" value="52">USA</label>
</li>
</ul>
</li>
Thanks!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,978 |
\section{Introduction}
Given a compact metric space $(X,d)$ and a positive integer $n$, it is natural to consider a subset $C\subseteq X$ that maximizes the minimum distance $\delta(C):=\min_{x,y\in C,x\neq y}d(x,y)$.
Such a subset, known as an \textbf{optimal $n$-code} for $(X,d)$, is guaranteed to exist by compactness.
Optimal codes are maximally robust to noise, since one can identify $x\in C$ from any noisy version $\hat{x}\in X$ that satisfies $d(\hat{x},x)<\delta(C)/2$.
Optimal codes have been an object of study ever since a legendary dispute in 1694 between Isaac Newton and David Gregory~\cite{casselman04}.
Consider the unit sphere $S^2\subseteq \mathbf{R}^3$ with distance inherited from the ambient Euclidean distance.
In our language, Gregory asserted that an optimal $13$-code $C$ for $S^2$ has $\delta(C)\geq1$.
Interest in spherical codes was rejuvenated in 1930 by the Dutch botanist Tammes, who studied the distribution of pores on pollen grains~\cite{tammes30}.
Thanks to this resurgence, Gregory was finally proved wrong in 1953 by Sch\"{u}tte and van der Waerden~\cite{schutte53}.
In 1948, Claude Shannon founded the field of information theory~\cite{shannon48}, which in turn motivated the pursuit of optimal codes over $\mathbf{Z}_2^n$ with Hamming distance.
Noteworthy optimal codes in this metric space include the Golay code~\cite{golay49} and the Hamming code~\cite{hamming50}.
This metric space can be viewed in terms of the Cayley graph on $\mathbf{Z}_2^n$ with generators given by the identity basis.
More generally, every graph produces a metric space consisting of the vertex set and the graph's geodesic distance.
In this language, the independence number of a graph is the largest $n$ for which an optimal $n$-code $C$ satisfies $\delta(C)>1$.
For example, the independence number of the Paley graph is of particular interest in number theory~\cite{chung89,hanson19}.
The connection between optimal codes and independence numbers has been rather fruitful, as the Lov\'{a}sz--Schrijver bound can be generalized to obtain useful bounds for a variety of metric spaces~\cite{delaat15}.
In 1996, Conway, Hardin and Sloane~\cite{conway96} posed the problem of finding optimal codes for Grassmannian spaces with \textbf{chordal distance}, defined as follows:
Given two subspaces $U,V\subseteq\mathbf{F}^d$ of dimension $r$ with principal angles $\{\theta_i\}_{i\in[r]}$, then $d(U,V)=(\sum_i\sin^2\theta_i)^{1/2}$.
In the time since this seminal paper, there has been a flurry of progress in the special case of projective spaces due in part to emerging applications in multiple description coding~\cite{strohmer03}, digital fingerprinting~\cite{mixon13}, compressed sensing~\cite{bandeira13}, and quantum state tomography~\cite{renes04}.
Most of this work takes a particular form:
Identify a collection $S$ of mathematical objects such that for every $s\in S$, there exists an explicit optimal $n$-code in $\mathbf{FP}^{d-1}$, where $n=n(s)$ and $d=d(s)$.
For example, one may take $S$ to be the set of regular two-graphs~\cite{seidel76}, $n(s)$ the number of vertices in $s$, and $d(s)$ the multiplicity of the positive eigenvalue of $s$; indeed, for every $s\in S$, one may construct an optimal $n$-code for $\mathbf{RP}^{d-1}$ known as an \textit{equiangular tight frame}~\cite{strohmer03}.
See \cite{fickus15} for a survey of these developments.
Due to this style of progress, the current literature on optimal codes for real projective spaces is rather spotty; while we have provably optimal $n$-codes for $\mathbf{RP}^{d-1}$ for infinitely many $(d,n)$, large gaps remain.
In what follows, we identify where these gaps first emerge.
It is straightforward to verify that for $n\leq d$, the optimal $n$-codes for $\mathbf{RP}^{d-1}$ correspond to orthogonal lines.
For $n=d+1$, the optimal $n$-codes are obtained from regular simplices centered at the origin; indeed, the lines spanned by the vertices correspond to an equiangular tight frame~\cite{strohmer03,fickus15}.
However, for $n=d+2$, the optimal $n$-codes for $\mathbf{RP}^{d-1}$ are unknown for most values of $d$.
In this paper, we focus on this minimal case.
Since $\mathbf{RP}^1$ is a circle, the $d=2$ case is uniquely solved by four uniformly spaced points.
The $d=3$ case is far less trivial, and was originally solved by Fejes T\'{o}th~\cite{fejes65} in 1965.
The optimal code is unique up to isometry, and can be obtained by removing any one of the six lines that are determined by antipodal vertices of the icosahedron.
A second treatment of this proof was provided by Benedetto and Kolesar~\cite{benedetto06} in 2006.
Finally, Fickus, Jasper and Mixon~\cite{fickus18} gave a third, more general treatment in 2018, and the ideas of their proof also solved the $d=4$ case.
This optimal code is unique up to isometry, and corresponds to the putatively optimal code provided by Sloane on his website~\cite{sloaneDatabase}.
Following~\cite{fickus18}, the putatively optimal codes for $d\in\{5,6\}$ can be expressed in terms of Gram matrices of unit-vector representatives of each line:
\begin{equation}\label{eq:winners}
\normalsize{G_5 := \scriptsize{\left[
\begin{matrix*}[r]
1 & -a & a & -a & \phantom{-}a & -a & a \\
-a & 1 & a & a & a & -a & a \\
a & a & 1 & -a & a & a & -a\\
-a & a & -a & 1 & a & -a & -a\\
a & a & a & a & 1 & a & a\\
-a & -a & a & -a & a & 1 & -a\\
a & a & -a & -a & a & -a & 1
\end{matrix*}\right]}, \quad
G_6 := \scriptsize{\left[
\begin{matrix*}[r]
1 & b & b & -b & b & c & b & -b\\
b & 1 & -b & -b & -b & -b & -c & -b\\
b & -b & 1 & -b & -b & -b & -b & -b\\
-b & -b & -b & 1 & b & -b & b & -b\\
b & -b & -b & b & 1 & -b & -b & b\\
c & -b & -b & -b & -b & 1 & b & -b\\
b & -c & -b & b & -b & b & 1 & b\\
-b & -b & -b & -b & b & -b & b & 1
\end{matrix*}\right]}}
\end{equation}
where $a>0$ is the second smallest root of $x^3-9x^2-x+1$, $b>0$ is the second smallest root of
\begin{equation}
\label{eq.6x8 coherence}
106x^6 - 264x^5 - 53x^4 + 84x^3 + 20x^2 - 4x - 1,
\end{equation}
and $c\in(0,b)$ is the fourth smallest root of
\[
53x^6+484x^5+814x^4-860x^3-347x^2+352x-32.
\]
Note that $\sqrt{1-a^2}$ and $\sqrt{1-b^2}$ are lower bounds on the minimum chordal distance of optimal $(d+2)$-codes for $\mathbf{RP}^{d-1}$ for $d\in\{5,6\}$, respectively.
Recently, Bukh and Cox~\cite{bukh19} proved the best-known upper bound on this minimum distance:
\begin{equation}
\label{eq.bukh--cox}
\delta(C)\leq\sqrt{1-\big(\tfrac{3}{2d+1}\big)^2},
\end{equation}
and furthermore, they characterized the codes that achieve equality in this bound, which occurs for every $d\equiv 1\bmod 3$.
In particular, this gives an alternate proof of the $d=4$ case.
As a result, the next open cases are $d\in\{5,6,8\}$.
In this paper, we resolve the cases of $d\in\{5,6\}$.
As conjectured, $G_5$ and $G_6$ above describe optimal codes for $\mathbf{RP}^4$ and $\mathbf{RP}^5$, which are unique up to isometry.
The next section reviews the preliminaries that set up our approach.
In particular, \cref{prop:fjm} (that is, Lemma~6 in~\cite{fickus18}) implies that every optimizer is necessarily an optimizer of one of a handful of subprograms.
These subprograms come in two different species, and in Section~3, we apply ideas from matrix and convex analysis to solve the first species; specifically, we determine the best possible $(d+2)$-codes that contain $d+1$ equiangular lines.
In Section~4, we apply this theory to the $d=5$ case, and we solve the second species with a clever application of cylindrical algebraic decomposition.
This approach does not scale to the $d=6$ case.
As an alternative, Section~5 introduces a method to convert numerical approximations of Stengle's Positivstellensatz certificates into honest certificates.
This allows us to tackle the $d=6$ case in Section~6, where we solve the second species of subprograms by computing numerical approximations of Positivstellensatz certificates using a Julia-based implementation of sum-of-squares programming.
We conclude in Section~7 by discussing opportunities for future work.
The proofs of our main results are computer assisted. Our computations were performed on a 3.4 GHz Intel Core i5, and we report runtimes throughout to help identify computational bottlenecks. While our code is far from optimized, we make it available with the arXiv version of this paper.
\section{Preliminaries}
We identify an $n$-code for $\mathbf{RP}^{d - 1}$ with a set of $n$ lines through the origin of $\mathbf{R}^d$. We seek to classify the optimal $n$-codes, that is, sets of $n$ lines for which the minimum angle between any two lines is maximized. The cosine of the minimum angle is known as the \textbf{coherence}, and so classifying optimal $n$-codes is equivalent to classifying sets of lines with the minimum coherence.
Let $U^{d \times n}$ denote the set of $d \times n$ real matrices with unit-norm columns. We can specify an $n$-code for $\mathbf{RP}^{d - 1}$ using a matrix $\Phi \in U^{d \times n}$ whose column vectors span the $n$ lines in $\mathbf{R}^d$. Let $B_n$ denote the group of $n \times n$ signed permutation matrices. Observe that $\Phi, \Psi \in U^{d \times n}$ specify the same $n$-code of (unordered) points in $\mathbf{RP}^{d - 1}$ if and only if there exists $P \in B_n$ such that $\Phi P^T = \Psi$. Moreover, $\Phi, \Psi \in U^{d \times n}$ specify the same $n$-code for $\mathbf{RP}^{d - 1}$ \emph{up to isometry} if and only if there exists $P \in B_n$ such that $P \Phi^T \Phi P^T = \Psi^T \Psi$. Let $E_{n,d}$ denote the rank-constrained elliptope
\[
E_{n,d} := \{G \in \mathbf{R}^{n \times n} : G = G^T, \operatorname{diag}(G) = \mathbf{1}, G \succeq 0, \operatorname{rank}(G) \leq d\}.
\]
We say that $G, G' \in E_{n,d}$ are \textbf{equivalent} if there exists $P \in B_n$ such that $P G P^T = G'$. Observe that the resulting equivalence classes correspond to isometry classes of $n$-codes for $\mathbf{RP}^{d - 1}$, and we can recover a representation $\Phi \in U^{d \times n}$ of one such $n$-code by decomposing $G = \Phi^T \Phi$. The coherence of the lines represented by $G$ is given by
\[
\mu(G) := \max_{1 \leq i < j \leq n} |G_{ij}|.
\]
Hence, our problem is equivalent to computing
\[
\mu_{n,d} := \inf\{\mu(G) : G \in E_{n,d}\}
\]
and classifying the corresponding optimizer(s), which necessarily exist by compactness. We say $G \in E_{n,d}$ is \textbf{optimal} if $\mu(G) = \mu_{n,d}$.
In principle, one may directly apply Tarski--Seidenberg~\cite{mishra93} to find optimal $G$, but in practice, quantifier elimination over the reals is slow. For example, cylindrical algebraic decomposition (CAD)~\cite{collins75} is known to have runtimes that are doubly exponential in the number of variables~\cite{davenport88}, which is already too slow for the values of $n$ that we are interested in. For this reason, we need to somehow reduce the problem size before passing to tools like CAD. To this end, in the special case where $n=d+2$, optimal $G \in E_{n, d}$ are known to satisfy certain (strong) combinatorial constraints:
\begin{prop}[Lemma~6 in~\cite{fickus18}]\label{prop:fjm}
Suppose $G \in E_{d + 2, d}$ is optimal and put $\mu = \mu(G)$.
Then
\[
G = I + \mu S + X,
\]
where $I$ is the identity matrix, the matrices $I$, $S$ and $X$ are symmetric with disjoint support, the entries of $X$ all reside in $[-\mu,\mu]$, and the entrywise absolute value $|S|$ is the adjacency matrix of either
(i) $K_{d+1}$ union an isolated vertex or (ii) the complement of a maximum matching.
\end{prop}
In what follows, we assume $n=d+2$ without mention.
\cref{prop:fjm} considerably reduces the search space for optimal $G\in E_{n,d}$.
Let $\mathcal{S}_1\subseteq\mathbf{R}^{n \times n}$ denote the set of symmetric $S$ for which $|S|$ is the adjacency matrix of $K_{d + 1}$ union an isolated vertex, and similarly, let $\mathcal{S}_2\subseteq\mathbf{R}^{n \times n}$ denote the set of symmetric $S$ for which $|S|$ is the adjacency matrix of the complement of a maximum matching.
Letting $\circ$ denote entrywise matrix product, then for each $S \in \mathcal{S}_1 \cup \mathcal{S}_2$, we consider the subprogram
\[
m(S)
:= \inf\{ \mu : I + \mu S + X \in E_{n, d}, (I + S)\circ X=0, -\mu\leq X_{ij} \leq\mu \}.
\]
\cref{prop:fjm} implies that $\mu_{n,d}=\min\{m(S):S\in\mathcal{S}_1\cup\mathcal{S}_2\}$, and we can recover each optimal $G \in E_{n, d}$ from the minimizers of $m(S)$.
We call $S \in \mathcal{S}_1 \cup \mathcal{S}_2$ \textbf{optimal} if $m(S) = \mu_{n, d}$.
Given $P\in B_n$, then $(\mu,X)$ is feasible in the program defining $m(S)$ if and only if $(\mu,PXP^T)$ is feasible in the program defining $m(PSP^T)$.
We may leverage this symmetry to further simplify our search for optimal $S$.
In particular, for each $i\in\{1,2\}$, the conjugation action of $B_n$ partitions $\mathcal{S}_i$ into orbits, and we say that two members of the same orbit are \textbf{equivalent}.
We may select a representative from each orbit to produce $\mathcal{R}_i\subseteq\mathcal{S}_i$.
Then
\[
\mu_{n,d}=\min\{m(S):S\in\mathcal{R}_1\cup\mathcal{R}_2\},
\]
and furthermore, every optimal $G\in E_{n,d}$ corresponding to an optimal $S\not\in\mathcal{R}_1\cup\mathcal{R}_2$ is equivalent to some optimal $G'\in E_{n,d}$ corresponding to an optimal $S'\in\mathcal{R}_1\cup\mathcal{R}_2$. We select the members of $\mathcal{R}_1$ to be zero in the last row and column and the members of $\mathcal{R}_2$ to be zero in the last $\lfloor n/2 \rfloor$ diagonal $2\times 2$ blocks. This determines the support of both types of matrices.
\begin{table}
\begin{tabular}{cccrrrcl}
$d$ & $n$ & $\mu$ & \qquad min polynomial & \qquad $|\mathcal{R}_1|$ & \qquad $|\mathcal{R}_2|$ & \qquad & optimality\\
\hline
$3$ & $5$ & $0.4473$ & $5x^2 - 1$ & $3$ & $6$ && Ref.~\cite{fejes65,benedetto06,fickus18}\\
$4$ & $6$ & $0.3334$ & $3x - 1$ & $7$ & $14$ && Ref.~\cite{fickus18,bukh19}\\
$5$ & $7$ & $0.2863$ & $x^3 - 9x^2 - x + 1$ & $16$ & $144$ && Thm.~\ref{thm:5by7}\\
$6$ & $8$ & $0.2410$ & Eq.~\eqref{eq.6x8 coherence} & $54$ & $560$ && Thm.~\ref{thm:6by8}\\
$7$ & $9$ & $0.2000$ & $5x - 1$ & $243$ & $49,127$ && Ref.~\cite{bukh19}\\
$8$ & $10$ & $0.1828$ & $19x^2 + 2x - 1$ & $2,038$ & $599,108$ && ---
\end{tabular}
\caption{Parameters of optimal $n$-codes for $\mathbf{RP}^{d-1}$ with $n=d+2$. Coherence $\mu$ is rounded to the next multiple of $10^{-4}$, and we provide the minimal polynomial of $\mu$ to specify its precise value. As a consequence of \cref{prop:fjm}, every optimizer is necessarily an optimizer of a subprogram specified by some $S\in\mathcal{R}_1\cup\mathcal{R}_2$, suggesting that one solves each of these subprograms; the sheer number of subprograms makes this approach infeasible for the $d=8$ case.
For the other cases, we provide the location(s) of the proof(s) of optimality.
\label{table.opt packings}}
\end{table}
As we will see, optimizing over $\mathcal{R}_1$ is easier than optimizing over $\mathcal{R}_2$, and we will apply different techniques to perform these optimizations.
Before discussing these techniques, we first determine the sizes of $\mathcal{R}_1$ and $\mathcal{R}_2$ to help establish which values of $d$ are amenable to this approach.
For every member of $\mathcal{R}_1$, the off-diagonal entries are only nonzero on the leading $(d+1)\times(d+1)$ principal submatrix.
Restricting to this submatrix, then the members of $\mathcal{R}_1$ are precisely the Seidel adjacency matrices of switching class representatives on $d+1$ vertices, which were counted by Mallows and Sloane~\cite{mallows75}.
In \cref{table.opt packings}, we report the size of $\mathcal{R}_1$ for $d\in\{3,\ldots,8\}$.
The size of $\mathcal{R}_2$ does not appear in the literature, and so we apply Burnside's lemma to formulate a fast algorithm that computes it.
Let $\mathcal{T}_2\supseteq\mathcal{R}_2$ denote the subset of $\mathcal{S}_2$ that is zero in the last $\lfloor n/2 \rfloor$ diagonal $2\times 2$ blocks. Next, consider the conjugation action of $B_n$ on $\mathcal{S}_2$, and let $F_2$ denote the largest subgroup of $B_n$ that acts invariantly on $\mathcal{T}_2$. Then our choice for $\mathcal{R}_2$ equates to representatives of orbits of the action of $F_2$ on $\mathcal{T}_2$. By Burnside, the size of $\mathcal{R}_2$ then equals the average number of points in $\mathcal{T}_2$ that are fixed by a random member of $F_2$. By construction, every member of $\mathcal{T}_2$ has the same support above the diagonal $E\subseteq\{(i,j):1\leq i<j\leq n\}$, and for each $P\in F_2$, the mapping $X\mapsto PXP^T$ over symmetric $X$ induces a signed permutation $P_E$ over $\mathbf{R}^E$, which enjoys a unique decomposition into disjoint signed cycles. If any of these cycles features an odd number of sign changes, then there is no $x\in\{\pm1\}^E$ for which $P_Ex=x$, and so $P$ has no fixed points in $\mathcal{T}_2$. Write $O\subseteq F_2$ for this subset of $P$'s. If $P\not\in O$, then the number of points fixed by $P$ equals $2^{k(P)}$, where $k(P)$ denotes the number of disjoint signed cycles in the decomposition of $P_E$. Overall, we have
\[
|\mathcal{R}_2|
=\frac{1}{|F_2|}\sum_{P\in F_2}
\left\{\begin{array}{cl}
0&\text{if }P\in O\\
2^{k(P)}&\text{else}
\end{array}\right\},
\]
which can be computed quickly by iterating over members of $B_n$. See \cref{table.opt packings} for the result of this computation for $d\in\{3,\ldots,8\}$.
In what follows, we describe our methodology for minimizing $m(S)$ subject to $S\in\mathcal{R}_1\cup\mathcal{R}_2$ in the cases where $d\in\{5,6\}$. In vague terms, our approach performs a computation for each $S$ and then compares the results. Considering \cref{table.opt packings}, we expect this approach to require about a thousand times as much runtime to resolve the next open case of $d=8$, even if the per-$S$ runtime matches the $d=6$ case (in reality, it is slower). As such, new ideas will be necessary to tackle this case.
\section{Codes from equiangular lines}
In this section, we prove results that will help us to estimate $m(S)$ for every $S\in\mathcal{R}_1$.
\begin{lem}\label{lem:eig}
Let $S \in \mathcal{R}_1$ and let $\lambda$ be the minimum eigenvalue of its leading $(d + 1) \times (d + 1)$ principal submatrix. Then $m(S) \in \{-\lambda^{-1}, \infty\}$.
\end{lem}
\begin{proof}
Suppose $m(S) \neq \infty$. Then there exist $\mu$ and $X$ such that
\[
I + \mu S + X \in E_{d + 2, d},
\qquad
(I + S)\circ X=0,
\qquad
-\mu\leq X_{ij} \leq\mu.
\]
In particular, $I + \mu S + X \succeq 0$, and so $I + \mu S' \succeq 0$, where $S'$ is the leading $(d + 1) \times (d + 1)$ principal submatrix of $S$. Furthermore, $I + \mu S'$ has rank at most $d$, and so $1 + \mu \lambda = 0$.
\end{proof}
The next result requires a definition:
We say $\{v_i\}_{i\in[l]}$ in $\mathbf{R}^d$ are conically dependent if there exists $j\in[l]$ and nonnegative $\{\alpha_i\}_{i\in[l]\setminus\{j\}}$ such that
\[
v_j
=\sum_{i\in[l]\setminus\{j\}}\alpha_iv_i.
\]
Otherwise, we say $\{v_i\}_{i\in[l]}$ are \textbf{conically independent}.
\begin{lem}\label{lem:eiginf}
Let $S \in \mathcal{R}_1$, suppose the minimum eigenvalue $\lambda < 0$ of its leading $(d + 1) \times (d + 1)$ principal submatrix $S'$ has multiplicity $1$, take $L\in\mathbf{R}^{(d+1)\times d}$ such that $LL^T = I - \lambda^{-1}S'$, and consider the pseudoinverse given by $L^\dagger=(L^TL)^{-1}L^T$.
\begin{itemize}
\item[(a)]
Suppose $\| L^\dagger y \|_2 < -\lambda$ for every $y \in \{\pm 1\}^{d + 1}$.
Then $m(S) = \infty$.
\item[(b)]
Suppose there exists a nonempty subset $\mathcal{Y}\subseteq \{\pm 1\}^{d + 1}$ such that $\{L^\dagger y\}_{y\in\mathcal{Y}}$ is conically independent, $\| L^\dagger y \|_2 < -\lambda$ for every $y \in \{\pm 1\}^{d + 1}\setminus\mathcal{Y}$, and for every $y\in\mathcal{Y}$, the matrix
\[
Z(y):=\begin{bmatrix}0 & y\\ y^T & 0\end{bmatrix}
\]
has the property that $S+Z(y)$ has minimum eigenvalue $\lambda$ with multiplicity $2$.
Then $m(S) = -\lambda^{-1}$ and the corresponding minimizers are given by $X=-\lambda^{-1} Z(y)$ for $y\in\mathcal{Y}$.
\end{itemize}
\end{lem}
\begin{proof}
First, $\lambda < 0$ since $S$ is a nonzero matrix with zero trace.
Hence, $I - \lambda^{-1}S' \succeq 0$, and since $I - \lambda^{-1}S'$ has rank at most $d$, there exists $L\in\mathbf{R}^{(d+1)\times d}$ such that $LL^T = I - \lambda^{-1}S'$.
In fact, $L$ has rank exactly $d$ since $\lambda$ is an eigenvalue of $S'$ with multiplicity $1$.
(a)
We will prove this claim by contraposition, and so we suppose $m(S) \neq \infty$.
By \cref{lem:eig}, it follows that $m(S) = -\lambda^{-1}$.
Set $\mu = m(S)$ and consider the set
\[
\mathcal{X} := \{X : I + \mu S + X \in E_{d + 2, d}, (I + S)\circ X=0, -\mu\leq X_{ij} \leq\mu\}.
\]
Since $m(S) \neq \infty$, a compactness argument gives that $\mathcal{X}$ is nonempty, and we may select $X \in \mathcal{X}$ and obtain a decomposition of the form $I + \mu S + X = A^TA$, where $A = [L^T~x]$ and $x \in \mathbf{R}^d$ is a unit vector satisfying $\| Lx \|_\infty \leq \mu = -\lambda^{-1}$.
Since $L$ has rank $d$, it holds that $\| Lx \|_\infty>0$.
Thus,
\begin{align*}
-\lambda
\leq \| Lx \|_\infty^{-1}
\leq \sup_{\|z\|_2=1} \| Lz \|_\infty^{-1}
= \sup_{z \neq 0} \frac{ \| z \|_2}{ \| Lz \|_\infty }
&= \sup_{y \in \operatorname{im}(L)\setminus \{0\}} \frac{\| L^\dagger y \|_2}{\| y \|_\infty}\\
&\leq \sup_{y \neq 0} \frac{\| L^\dagger y \|_2}{\| y \|_\infty}
= \sup_{y \in B_\infty^{d + 1}} \| L^\dagger y \|_2
=\max_{y \in \{\pm 1\}^{d + 1}} \| L^\dagger y \|_2,
\end{align*}
where the last step uses the fact that the maximum of a convex function over a compact polytope is achieved at a vertex of that polytope.
(b)
Since $\mathcal{Y}$ is nonempty, there exists $y$ such that $I-\lambda^{-1}(S+Z(y))$ is positive semidefinite with rank $d$, and so $m(S)\neq\infty$.
Then by \cref{lem:eig}, it holds that $m(S) = -\lambda^{-1}$.
It remains to show that the minimizers $X\in \mathcal{X}$ of the program defining $m(S)$ are $X=-\lambda^{-1}Z(y)$ for $y\in\mathcal{Y}$.
First, we show that $\| L^\dagger y \|_2=-\lambda$ for every $y\in\mathcal{Y}$.
To see this, fix $y\in\mathcal{Y}$ and consider the decomposition $I-\lambda^{-1}(S+Z(y))=A^TA$, where $A=[L^T~x]$.
Then $x$ has unit norm and $Lx=-\lambda^{-1}y$.
We apply $-\lambda L^\dagger$ to both sides and take norms to get $\| L^\dagger y \|_2=\|-\lambda x\|_2=-\lambda$.
As such,
\begin{equation}
\label{eq.max minus lambda}
\max_{y \in \{\pm 1\}^{d + 1}} \| L^\dagger y \|_2
=-\lambda.
\end{equation}
Next, we follow the proof of (a) to see that every $X\in \mathcal{X}$ yields a decomposition $I+\mu S+X=A^TA$ with $A=[L^T~x]$, where $x$ has unit norm and
\[
-\lambda
\stackrel{(*)}{\leq} \| Lx \|_\infty^{-1}
\stackrel{(\dagger)}{\leq} \sup_{\|z\|_2=1} \| Lz \|_\infty^{-1}
= \sup_{y \in \operatorname{im}(L)\setminus \{0\}} \frac{\| L^\dagger y \|_2}{\| y \|_\infty}
\stackrel{(\ddagger)}{\leq} \sup_{y \neq 0} \frac{\| L^\dagger y \|_2}{\| y \|_\infty}
=\max_{y \in \{\pm 1\}^{d + 1}} \| L^\dagger y \|_2
=-\lambda,
\]
where the last step comes from \eqref{eq.max minus lambda}.
By equality, we may conclude a few things.
First, equality in ($\dagger$) implies $x\in\arg\max\{\|Lz\|_\infty^{-1}:\|z\|_2=1\}$, and so a change of variables gives
\[
Lx
\in\arg\max\{\|y\|_\infty^{-1}:\|L^\dagger y\|_2=1,y\in\operatorname{im}(L)\}
\subseteq\arg\max\Big\{\tfrac{\|L^\dagger y\|_2}{\|y\|_\infty}:y\in\operatorname{im}(L)\setminus\{0\}\Big\}.
\]
Next, equality in ($*$) implies $\|Lx\|_\infty=-\lambda^{-1}$, and so we further have
\[
-\lambda Lx
\in\arg\max\{\|L^\dagger y\|_2:\|y\|_\infty\leq1,y\in\operatorname{im}(L)\}
\subseteq\arg\max\{\|L^\dagger y\|_2:\|y\|_\infty\leq1\},
\]
where the last step follows from equality in ($\ddagger$).
We claim that $\arg\max\{\|L^\dagger y\|_2:\|y\|_\infty\leq1\}=\mathcal{Y}$.
Our result follows from this intermediate claim since $-\lambda Lx=y\in\mathcal{Y}$ implies
\[
I+\mu S+X
=A^TA
=\begin{bmatrix}LL^T & Lx\\ x^TL^T & x^Tx\end{bmatrix}
=\begin{bmatrix}I-\lambda^{-1}S' & -\lambda^{-1} y\\ -\lambda^{-1} y^T & 1\end{bmatrix}
=I+\mu S- \lambda^{-1}Z(y),
\]
and so rearranging gives that every minimizer $X\in\mathcal{X}$ is of the form $X=-\lambda^{-1}Z(y)$, as desired.
We use convexity to prove $\mathcal{M}:=\arg\max\{\|L^\dagger y\|_2:\|y\|_\infty\leq1\}=\mathcal{Y}$.
First, we know $\mathcal{Y}\subseteq \mathcal{M}$ since the maximum of a convex function over a compact polytope is achieved at a vertex of that polytope.
For the sake of contradiction, suppose this containment is proper, that is, there exists $y_0\in \mathcal{M}\setminus\mathcal{Y}$.
By convexity, we may write $y_0=\sum_{v\in\{\pm1\}^{d+1}} c_v v$ with $c_v\geq0$ and $\sum_vc_v=1$.
In what follows, we show that $c_v>0$ for some $v\in\{\pm1\}^{d+1}\setminus\mathcal{Y}$.
Suppose otherwise that $c_v$ is only nonzero for $v\in\mathcal{Y}$.
Since $y_0\not\in\mathcal{Y}$, then there exists a subset $\mathcal{Y}'\subseteq\mathcal{Y}$ of size at least $2$ such that $c_v$ is nonzero precisely when $v\in\mathcal{Y}'$.
By assumption, $\{L^\dagger y\}_{y\in\mathcal{Y}'}$ is conically independent.
As such, picking $y_1\in\mathcal{Y}'$, it holds that $c_{y_1}L^\dagger y_1$ is not a positive scalar multiple of $\sum_{y\in\mathcal{Y}'\setminus\{y_1\}}c_y L^\dagger y$, and so
\begin{align*}
-\lambda
=\|L^\dagger y_0\|_2
=\bigg\|L^\dagger \sum_{y\in\mathcal{Y}'}c_y y\bigg\|_2
&=\bigg\|c_{y_1} L^\dagger y_1+\sum_{y\in\mathcal{Y}'\setminus\{y_1\}}c_y L^\dagger y\bigg\|_2\\
&<\|c_{y_1} L^\dagger y_1\|_2+\bigg\|\sum_{y\in\mathcal{Y}'\setminus\{y_1\}}c_y L^\dagger y\bigg\|_2
\leq \sum_{y\in\mathcal{Y}'}c_y\|L^\dagger y\|_2
=-\lambda,
\end{align*}
a contradiction.
Overall, it must be the case that $c_v>0$ for some $v\in\{\pm1\}^{d+1}\setminus\mathcal{Y}$.
Finally, $\|L^\dagger y_0\|_2=\|L^\dagger y\|_2=-\lambda$ for every $y\in\mathcal{Y}$ and $\|L^\dagger y_0\|_2\leq\sum_{v\in\{\pm1\}^{d+1}} c_v \|L^\dagger v\|_2$, and so
\begin{align*}
-\lambda
&=\frac{1}{1-\sum_{y\in\mathcal{Y}}c_y}\Big(\|L^\dagger y_0\|_2-\sum_{y\in\mathcal{Y}}c_y\|L^\dagger y\|_2\Big)\\
&\leq\frac{1}{1-\sum_{y\in\mathcal{Y}}c_y}\sum_{v\in\{\pm1\}^{d+1}\setminus\mathcal{Y}} c_v \|L^\dagger v\|_2
\leq \max_{v\in\{\pm1\}^{d+1}\setminus\mathcal{Y}}\|L^\dagger v\|_2
\leq -\lambda.
\end{align*}
By equality, we then conclude that $\max_{v\in\{\pm1\}^{d+1}\setminus\mathcal{Y}}\|L^\dagger v\|_2=-\lambda=\|L^\dagger y\|_2$ for every $y\in\mathcal{Y}$, which contradicts the fact that $\arg\max\{\|L^\dagger y\|_2:y\in\{\pm1\}^{d+1}\}=\mathcal{Y}$.
\end{proof}
\section{The optimal \texorpdfstring{$7$-code}{7-code} for \texorpdfstring{$\mathbf{RP}^4$}{RP4}}\label{5by7section}
In this section we fix $n = 7$ and $d = 5$ and prove the following classification.
\begin{thm}\label{thm:5by7}
$G \in E_{7,5}$ is optimal if and only if $G$ is equivalent to $G_5$, given in \eqref{eq:winners}.
\end{thm}
\begin{proof}
First, we recall the bounds on $\mu_{7,5}$ implied by the Bukh--Cox bound in \eqref{eq.bukh--cox} and the code represented by $G_5$ in \eqref{eq:winners}:
\begin{equation}\label{eq:5by7bounds}
\frac{3}{11} \leq \mu_{7,5} \leq 0.2863.
\end{equation}
These bounds will play a role in our analysis of both $\mathcal{R}_1$ and $\mathcal{R}_2$.
Let $\mathcal{T}_1$ denote the subset of $\mathcal{S}_1$ that is zero in its last row and column, and let $F_1$ be the subgroup of $B_n$ that acts invariantly on $\mathcal{T}_1$. Every member of $\mathcal{T}_1$ is equivalent to a matrix of the form
\begin{equation}\label{eq:r1n7}
\normalsize{
\scriptsize{\left[
\begin{array}{rrrrrrr}
0 & 1 & 1 & 1 & 1 & 1 & \phantom{\pm} 0\\
1 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & 0 & \pm 1 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & 0 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & 0 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0
\end{array}
\right]}
}
\end{equation}
and so we can generate orbits of $\mathcal{T}_1$ under the action of $F_1$ by generating the orbits of these $2^{10}$ matrices. We then build $\mathcal{R}_1$ by selecting one representative from each orbit of the form \eqref{eq:r1n7}, and this takes under one second.
For each $S \in \mathcal{R}_1$, we compute the minimum eigenvalue $\lambda$ of its leading $6 \times 6$ principal submatrix. By \cref{lem:eig} and \eqref{eq:5by7bounds}, we know that if $S$ is optimal, then $\frac{3}{11} \leq -\lambda^{-1} \leq 0.2863$, and this rules out all but two members of $\mathcal{R}_1$ from being optimal. For each of these two remaining members, we verify that $\lambda$ has multiplicity 1, compute $L^\dagger$ according to the setup of \cref{lem:eiginf}, and compute $\|L^\dagger y\|_2$ for every $y \in \{\pm 1\}^6$. In one case, we verify that $\|L^\dagger y\|_2 < -\lambda$ for every $y \in \{\pm 1\}^6$, and so this case is eliminated by \cref{lem:eiginf}(a). For the only remaining $S \in \mathcal{R}_1$, we obtain $\mathcal{Y} \subseteq \{\pm 1\}^6$ satisfying the hypotheses of \cref{lem:eiginf}(b) and set $\mu = -\lambda^{-1} \approx 0.2863$ with minimal polynomial $x^3 - 9x^2 - x + 1$. Applying \cref{lem:eiginf}(b) reveals that any minimizer $X$ for $m(S)$ leads to a Gram matrix $I + \mu S + X$ whose off-diagonal entries are all $\pm \mu$. This corresponds to a set of 7 equiangular lines in $\mathbf{R}^5$, unique up to isometry, reported by Bussemaker and Seidel as the complement of the 25th two-graph of order 7 in Table 1 of~\cite{bussemaker81}. To show that this configuration is optimal, we must still analyze $\mathcal{R}_2$.
Let $\mathcal{T}_2$ denote the subset of $\mathcal{S}_2$ with zero entries in its last 3 diagonal $2 \times 2$ blocks, and let $F_2$ be the subgroup of $B_n$ that acts invariantly on $\mathcal{T}_2$. Every member of $\mathcal{T}_2$ is equivalent to a matrix of the form
\begin{equation}\label{eq:r2n7}
\normalsize{\scriptsize{
\left[
\begin{array}{rrrrrrr}
0 & 1 & 1 & 1 & 1 & 1 & 1\\
1 & 0 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1\\
1 & 0 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & 0 & 0 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & 0 & 0 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
\end{array}
\right]},}
\end{equation}
and so we can generate orbits of $\mathcal{T}_2$ under the action of $F_2$ by generating the orbits of these $2^{12}$ matrices. We then build $\mathcal{R}_2$ by selecting one representative from each orbit of the form~\eqref{eq:r2n7}, and this takes under one minute.
For each member $S \in \mathcal{R}_2$, we build the corresponding Gram matrix $G = I + \mu S + X$ with variable entries $\{\mu, X_{23}, X_{45}, X_{67}\}$. We restrict $\mu$ according to \eqref{eq:5by7bounds} and $X_{23}, X_{45}, X_{67} \in [-\mu,\mu]$. If $S$ is optimal, then there must be a choice of $\mu$ and $X$ for which $G$ is positive semidefinite and of rank $5$. We can determine if such a choice of variables exists by solving the system of polynomial equalities and inequalities resulting from ensuring that each $6 \times 6$ minor of $G$ vanishes, some $5 \times 5$ minor of $G$ does not vanish, and each principal minor is nonnegative. In principle, a solution is provided by CAD, but even after our reduction to this $4$-variable system, its exceedingly slow runtime makes it necessary to relax our problem. We relax our rank and positive semidefinite constraints to simply ask for three $6 \times 6$ minors of $G$ to vanish, two of which are polynomials only in $\mu, X_{45}, X_{67}$, and the third of which is linear in $X_{23}$. Then after roughly two minutes, CAD reports that out of the 144 representatives $S \in \mathcal{R}_2$, only 11 allow the prescribed minors to vanish with $\mu$ satisfying \eqref{eq:5by7bounds} and $X_{23}, X_{45}, X_{67} \in [-\mu,\mu]$. Moreover, for each of these 11 representatives, $\mu$ is the root of $x^3 - 9x^2 - x + 1$ reported in Table 1 and $X_{23}, X_{45}, X_{67} \in \{\pm \mu\}$, and so each resulting Gram matrix corresponds to a set of equiangular lines with coherence $\mu$. Each of these Gram matrices has rank 5, and therefore correspond to the previously described set of 7 equiangular lines in $\mathbf{R}^5$.
\end{proof}
Our use of CAD here does not scale to the $d=6$ case, and so the next section describes an alternative approach involving Stengle's Positivstellensatz.
\section{Approximate Positivstellensatz}
Let $\mathbf{R}[x]=\mathbf{R}[x_1,\ldots,x_n]$ denote the set of polynomials with real coefficients and variables $x_1,\ldots,x_n$.
Let $\Sigma^2[x]$ denote the set of polynomials that can be expressed as a sum of squares of polynomials from $\mathbf{R}[x]$.
Given $f_1(x),\ldots,f_k(x),g_1(x),\ldots,g_l(x)\in\mathbf{R}[x]$, put $f:=\{f_i(x)\}_{i\in[k]}$ and $g:=\{g_j(x)\}_{j\in[l]}$, and consider the sets
\[
P(f):=\Big\{x\in\mathbf{R}^n:f_i(x)\geq0~\forall i\in[k]\Big\},
\qquad
Z(g):=\Big\{x\in\mathbf{R}^n:g_j(x)=0~\forall j\in[l]\Big\}.
\]
Then every polynomial in the cone
\[
C(f)
:=\bigg\{\sum_{I\subseteq[k]}s_I(x)\prod_{i\in I}f_i(x):s_I(x)\in\Sigma^2[x] ~ \forall I\subseteq[k]\bigg\}
\]
is nonnegative over $P(f)$, while every polynomial in the ideal
\[
I(g)
:=\bigg\{\sum_{j\in[l]}t_j(x)g_j(x):t_j(x)\in\mathbf{R}[x] ~ \forall j\in[l]\bigg\}
\]
is zero over $Z(g)$.
As such, writing $p(x)+q(x)=-1$ with $p(x)\in C(f)$ and $q(x)\in I(g)$ would certify that $P(f)\cap Z(g)$ is empty.
Amazingly, such a certificate is available whenever $P(f)\cap Z(g)$ is empty:
\begin{prop}[Stengle's Positivstellensatz~\cite{stengle74}]
The following are equivalent:
\begin{itemize}
\item[(a)]
$P(f)\cap Z(g)=\emptyset$.
\item[(b)]
$-1\in C(f)+ I(g)$.
\end{itemize}
\end{prop}
In principle, one may hunt for Positivstellensatz certificates by fixing $D\in\mathbf{N}$ and restricting to a search for $p(x)$ and $q(x)$ of degree at most $D$, as this reduces to a semidefinite program.
As a proof of concept, Parrilo and Sturmfels~\cite{parrilo03} applied this method to prove that
\begin{equation}
\label{eq.ps example}
S=\Big\{(x,y)\in\mathbf{R}^2:x-y^2+3\geq0,~y+x^2+2=0\Big\}
\end{equation}
is empty.
In reproducing this proof, we found the Julia implementation of sum-of-squares programming to be particularly user-friendly~\cite{bezanson17,dunning17}.
However, as an artifact of numerical optimization, the resulting degree-$4$ polynomials $p(x)$ and $q(x)$ have the property that $p(x)+q(x)+1$ is also a degree-$4$ polynomial, but all of its coefficients have absolute value smaller than $10^{-12}$.
Indeed, numerical optimization will generally fail to deliver an exact Positivstellensatz certificate, meaning we cannot directly apply Stengle's Positivstellensatz.
As an alternative, we introduce the notion of an \textbf{approximate Positivstellensatz certificate}, taking inspiration from the approximate dual certificates that arise in compressed sensing and matrix completion~\cite{gross11,foucart13}.
\begin{lem}[Approximate Positivstellensatz]\label{approxpsatz}
Suppose $r>0$ and $\|x\|_\infty< r$ for every $x\in P(f)\cap Z(g)$.
Then the following are equivalent:
\begin{itemize}
\item[(a)]
$P(f)\cap Z(g)=\emptyset$.
\item[(b)]
There exists $h(x)=\sum_\alpha c_\alpha x^\alpha\in 1+ C(f)+ I(g)$ such that
\begin{equation}
\label{eq.bound on coefficients}
\max_\alpha|c_\alpha|
\leq\Bigg[\sum_{k=0}^{\operatorname{deg}h(x)}\binom{n+k-1}{k}r^k\Bigg]^{-1}.
\end{equation}
\end{itemize}
\end{lem}
\begin{proof}
To see that (a) implies (b), set $h = 0$ and apply Stengle's Positivstellensatz. Now suppose $h \in1+ C(f)+ I(g)$ satisfies~\eqref{eq.bound on coefficients}. If $h = 0$, then (a) follows from Stengle's Positivstellensatz. Otherwise $h \neq 0$. If (a) fails, then there exists $x \in P(f)\cap Z(g)$, where $h$ satisfies
\[
1
\stackrel{(*)}{\leq}
h(x)
\leq|h(x)|
\stackrel{(\dagger)}{\leq} \max_\alpha|c_\alpha|\cdot \sum_\alpha |x^\alpha|
\stackrel{(\ddagger)}{<} \max_\alpha|c_\alpha|\cdot \sum_{k=0}^{\operatorname{deg}h(x)}\binom{n+k-1}{k}r^k
\stackrel{(\S)}{\leq} 1,
\]
a contradiction.
In particular, ($*$) follows from the fact that $h(x)\in1+ C(f)+ I(g)$, ($\dagger$) uses the triangle inequality, ($\ddagger$) applies our assumptions that $h\neq0$ and $\|x\|_\infty<r$ and the count of monomials of each degree $k$, and finally ($\S$) applies the bound \eqref{eq.bound on coefficients}.
\end{proof}
Returning to the example \eqref{eq.ps example}, one can easily prove a bound on $\max\{|x|,|y|\}$ for every $(x,y)\in S$.
For example, if $|x|\geq 3$, then
\[
2|x|
\geq|x+3|
\geq|y|^2
=|x^2+2|^2
\geq|x|^4,
\]
which implies $|x|\leq 2^{1/3}$, a contradiction.
As such, if $(x,y)\in S$, then it must hold that $|x|<3$, and therefore $|y|=|x|^2+2<11$.
Now that we know that $\max\{|x|,|y|\}<r:=11$ for every $(x,y)\in S$, we recall that our numerical optimizer produced a degree-$4$ polynomial $h(x,y)\in 1+ C(f)+ I(g)$ whose coefficients $c_\alpha$ all have absolute value smaller than $10^{-12}$.
A short computation shows
\[
\max_\alpha|c_\alpha|
\leq 10^{-12}
\leq \Bigg[\sum_{k=0}^{4}\binom{n+k-1}{k}r^k\Bigg]^{-1},
\]
meaning $h(x,y)$ serves as an approximate Positivstellensatz certificate that $S=\emptyset$.
When $r<1$, we note that \eqref{eq.bound on coefficients} can be replaced by the simpler bound
\begin{equation}
\label{eq.simpler bound}
\max_\alpha|c_\alpha|
\leq (1-r)^n,
\end{equation}
since in this case it holds that
\[
\sum_{k=0}^{\operatorname{deg}h(x)}\binom{n+k-1}{k}r^k
\leq \sum_{k=0}^{\infty}\binom{n+k-1}{k}r^k
=(1-r)^{-n}.
\]
We will apply this simpler bound in our classification of optimal $8$-codes for $\mathbf{RP}^5$.
\section{The optimal \texorpdfstring{$8$-code}{8-code} for \texorpdfstring{$\mathbf{RP}^5$}{RP5}}
In this section we fix $n = 8$ and $d = 6$ and prove the following classification.
\begin{thm}\label{thm:6by8}
$G \in E_{8,6}$ is optimal if and only if $G$ is equivalent to $G_6$, given in \eqref{eq:winners}.
\end{thm}
\begin{proof}
First, we recall the bounds on $\mu_{8,6}$ implied by the Bukh--Cox bound in \eqref{eq.bukh--cox} and the code represented by $G_6$ in \eqref{eq:winners}:
\begin{equation}\label{eq:6by8bounds}
\frac{3}{13} \leq \mu_{8,6} \leq 0.2410.
\end{equation}
These bounds will play a role in our analysis of both $\mathcal{R}_1$ and $\mathcal{R}_2$.
Let $\mathcal{T}_1$ denote the subset of $\mathcal{S}_1$ that is zero in its last row and column, and let $F_1$ be the subgroup of $B_n$ that acts invariantly on $\mathcal{T}_1$. Every member of $\mathcal{T}_1$ is equivalent to a matrix of the form
\begin{equation}\label{eq:r1n8}
\normalsize{\scriptsize{\left[
\begin{array}{rrrrrrrr}
0 & 1 & 1 & 1 & 1 & 1 & 1 & 0\\
1 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \phantom{\pm} 0\\
1 & \pm 1 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & 0 & \pm 1 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & 0 & \pm 1 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & \pm 1 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
\end{array}
\right]}}
\end{equation}
and so we can generate orbits of $\mathcal{T}_1$ under the action of $F_1$ by generating the orbits of these $2^{15}$ matrices. We then build $\mathcal{R}_1$ by selecting one representative from each orbit of the form \eqref{eq:r1n8}, and this takes under one minute.
For each $S \in \mathcal{R}_1$, we compute the minimum eigenvalue $\lambda$ of its leading $7 \times 7$ principal submatrix. By \cref{lem:eig} and \eqref{eq:6by8bounds}, we know that if $S$ is optimal, then $\frac{3}{13} \leq -\lambda^{-1} \leq 0.2410$, and this rules out all but two members of $\mathcal{R}_1$ from being optimal. Both of these are then ruled out by \cref{lem:eiginf}(a). Thus, no member of $\mathcal{R}_1$ is optimal, and so we proceed to investigate $\mathcal{S}_2$.
Let $\mathcal{T}_2$ denote the subset of $\mathcal{S}_2$ with zero entries in its diagonal $2 \times 2$ blocks, and let $F_2$ denote the subgroup of $B_n$ that acts invariantly on $\mathcal{T}_2$. Every member of $\mathcal{T}_2$ is equivalent to a matrix of the form
\begin{equation}\label{eq:r2n8}
\normalsize{\scriptsize{\left[
\begin{array}{rrrrrrrr}
0 & 0 & 1 & 1 & 1 & 1 & 1 & 1\\
0 & 0 & 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1\\
1 & 1 & 0 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1\\
1 & \pm 1 & 0 & 0 & \pm 1 & \pm 1 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0 & \pm 1 & \pm 1\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & \pm 1 & 0 & 0\\
\end{array}
\right]}}
\end{equation}
and so we can generate orbits of $\mathcal{T}_2$ under the action of $F_2$ by generating the orbits of these $2^{17}$ matrices. We then build $\mathcal{R}_2$ by selecting one representative from each orbit of the form \eqref{eq:r2n8}; it takes roughly 15 minutes to produce the 560 elements of $\mathcal{R}_2$.
For 558 members of $\mathcal{R}_2$, we will show that they are not optimal by proving $m(S) > 0.2410$. To do so, we introduce the decision variables $\{\mu, X_{12}, X_{34}, X_{56}, X_{78}\}$ and, for each member of $S \in \mathcal{R}_2$, build the symmetric matrix $G := I + \mu S + X$ with $(I + S) \circ X = 0$. Then by definition, $m(S)$ is the infimum of $\mu$ such that $G$ is positive semidefinite with rank $6$ and $-\mu \leq X_{ij} \leq \mu$. As in \cref{5by7section}, we will obtain a lower bound for $m(S)$ by completely relaxing the positive semidefinite constraint and partially relaxing the rank-6 constraint. However, unlike that case, we were not able to find a suitable relaxation for which CAD both provided the necessary lower bound on $m(S)$ and also terminated in a reasonable amount of time.
We introduce the polynomials
\[
f := \{f_i\}_{i \in [10]} = \{\mu - \tfrac{3}{13}\} \cup \{0.2410 - \mu\} \cup \{\mu \pm X_{j,j + 1}\}_{j \in \{1,3,5,7\}},
\]
and we let $g = \{g_i\}_{i \in [12]}$ denote a carefully selected set of $7 \times 7$ minors of $G$ for which at least one of the variables $X_{j,j + 1}$ has degree 0 or 1. Observe $P(f)\cap Z(g) = \emptyset$ implies $m(S) > 0.2410$, which then implies that $S$ is not optimal. For most $S \in \mathcal{R}_2$, we will show that $P(f)\cap Z(g)$ is empty by producing an approximate Positivstellensatz certificate. With $x = (\mu,X_{12},X_{34},X_{56},X_{78})$, we define
\begin{align*}
C_{m}(f) &:= \bigg\{\sum_{I\subseteq[10]}s_I(x)\prod_{i\in I}f_i(x):s_I(x)\in\Sigma^2[x],~\deg(s_I) \leq m ~ \forall I\subseteq[10]\bigg\},\\
I_{m}(g) &:=\bigg\{\sum_{j\in[12]}t_j(x)g_j(x):t_j(x)\in\mathbf{R}[x],~\deg(t_j) \leq m ~ \forall j\in[12]\bigg\}.
\end{align*}
By Stengle's Positivstellensatz, it suffices to produce $h_1 \in C_{m_1}(f)$ and $h_2 \in I_{m_2}(g)$ for which $h = 1 + h_1 + h_2$ satisfies \eqref{eq.bound on coefficients}. We use a Julia-based implementation~~\cite{bezanson17,dunning17} of sum of squares programming to obtain numerical solutions $\hat{h}_1 \in C_{m_1}$ and $\hat{h}_2 \in I_{m_2}$ for which $\hat{h}_1 + \hat{h}_2 \approx -1$, that is, $(\hat{h}_1,\hat{h}_2)$ provides a numerical approximation to a putative certificate that $P(f)\cap Z(g)$ is empty. We will promote $(\hat{h}_1,\hat{h}_2)$ to an honest certificate by carefully rounding. We write each scalar $s_I$ for $\hat{h}_1$ as a sum of squares and, for each term being squared, round its coefficients to five decimal places. We similarly round the coefficients for each scalar $t_j$ for $\hat{h}_2$ to five decimal places. Let $h_1 \in C_{m_1}(f)$ and $h_2 \in I_{m_2}(f)$ denote the resulting rounded polynomials with rational coefficients. As each of our five variables is less than $1/4$ in absolute value, we may use \eqref{eq.simpler bound} in place of \eqref{eq.bound on coefficients} so as to apply \cref{approxpsatz} and conclude that $P(f) \cap Z(g) = \emptyset$ whenever the largest coefficient of $1 + h_1 + h_2$ is at most $1/5$ in absolute value.
We apply this strategy to each $S \in \mathcal{R}_2$ with $m_1 = 2$. On a first run, we take $m_2 = 0$ and successfully eliminate 545 members of $\mathcal{R}_2$ in roughly 5 hours. On a second run, we take $m_2 = 1$ and eliminate another 13 members of $\mathcal{R}_2$ in roughly 8 minutes. This leaves us with only two members of $\mathcal{R}_2$ that could be optimal, and we proceed to use CAD to show that both are indeed optimal.
For these CAD queries, we again impose the constraint $f_i \geq 0$ for all $i\in[10]$, but we found that requiring $g_i = 0$ for all $i\in[12]$ resulted in CAD computations that did not terminate in a reasonable amount of time. We instead relaxed to only require $g_i = 0$ for a select few $i\in[12]$ that only depend on four of the five decision variables. For both of the remaining $S \in \mathcal{R}_2$, the corresponding CAD query reports that the optimal Gram matrix $G$ is equivalent to $G_6$. One of these computations takes roughly 18 minutes, while the other takes over three hours.
\end{proof}
\section{Discussion}
In this paper, we classified the optimal $(d+2)$-codes for $\mathbf{RP}^{d-1}$ for both $d\in\{5,6\}$.
The next open case in this direction is $d=8$.
Sloane's putatively optimal code~\cite{sloaneDatabase} is equiangular:
\[
\normalsize{
G_8:=
\scriptsize{\left[\begin{array}{rrrrrrrrrr}
1&-\mu&\mu&\mu&\mu&-\mu&\mu&\mu&-\mu&\mu\\
-\mu&1&-\mu&\mu&\mu&-\mu&\mu&\mu&\mu&\mu\\
\mu&-\mu&1&-\mu&\mu&-\mu&\mu&-\mu&\mu&-\mu\\
\mu&\mu&-\mu&1&\mu&-\mu&-\mu&-\mu&\mu&-\mu\\
\mu&\mu&\mu&\mu&1&\mu&-\mu&-\mu&-\mu&\mu\\
-\mu&-\mu&-\mu&-\mu&\mu&1&\mu&\mu&\mu&-\mu\\
\mu&\mu&\mu&-\mu&-\mu&\mu&1&-\mu&-\mu&-\mu\\
\mu&\mu&-\mu&-\mu&-\mu&\mu&-\mu&1&\mu&-\mu\\
-\mu&\mu&\mu&\mu&-\mu&\mu&-\mu&\mu&1&\mu\\
\mu&\mu&-\mu&-\mu&\mu&-\mu&-\mu&-\mu&\mu&1\\
\end{array}\right]},}
\]
where $\mu$ is given in \cref{table.opt packings}.
We expect that our current approach can already be used to partially tackle this case.
For example, our methods in Section~3 should be able to treat $\mathcal{R}_1$, but recall that it took 5 hours for us to rule out most of $\mathcal{R}_2$ in the $d=6$ case.
Considering $\mathcal{R}_2$ is over a thousand times larger in the $d=8$ case (see \cref{table.opt packings}), our methods should require the better part of a year to tackle this larger case.
For the record, our naive enumeration of the members of $\mathcal{R}_1$ is too slow for this case, but faster approaches are available, e.g., \cite{szollosi18}.
Still, $\mathcal{R}_2$ requires new ideas.
Is there a way to treat $\mathcal{R}_2$ in an analogous manner to our treatment of $\mathcal{R}_1$ in Section~3?
Previous work classified optimal codes for $S^2$ and for $\mathbf{RP}^2$ by leveraging spherical geometry and linear programming instead of Positivstellensatz~\cite{musin12,musin15,mixon19a}; perhaps an analogous approach is available here?
At the end of our approach, we use CAD to exactly optimize $G$ for any surviving $S\in\mathcal{R}_2$.
In the $d=8$ case, these CAD queries may not terminate in a reasonable amount of time.
We note that in the $d=6$ case, the Positivstellensatz step quickly produced an improved lower bound of $\mu_{8,6}\geq0.24$ before this CAD step, and including this information in our CAD query cut the three-hour runtime in half.
It might be possible to obtain improved lower bounds on $\mu_{10,8}$ even if CAD takes too long.
There might be some improvements available in our application of Positivstellensatz.
For example, we rounded our numerical approximations of Positivstellensatz certificates to five decimal places before using exact arithmetic to verify that the result satisfies the bound \eqref{eq.simpler bound}.
The exact arithmetic step might be faster if we had rounded to four decimal places (say), but we expect the bound \eqref{eq.simpler bound} to be violated if we round too much.
Next, in order for Positivstellensatz and CAD to have reasonable runtimes, we relaxed various determinant constraints.
While we have some heuristics for when a relaxation is good (e.g., some of the remaining polynomials have low degree in certain variables), this process remains an artform that deserves a careful treatment.
In prior work, numerical applications of Stengle's Positivstellensatz come in two different types.
The first type solves a sum-of-squares program numerically, and then performs what appears to be a handcrafted rounding step to ensure that $-1$ exactly resides in the set $C(f)+I(g)$; see~\cite{parrilo03}, for example.
This approach was not suitable for our purposes since we were solving hundreds of sum-of-squares programs.
The second type takes the numerical result that $h\approx-1$ resides in $C(f)+I(g)$ as sufficient evidence that $P(f)\cap Z(g)$ is empty; see~\cite{davis11}, for example.
Since this does not constitute a proof, it was also not suitable for our purposes.
Presumably, \cref{approxpsatz} could replace the ad-hoc strategy of the first type and give theoretical justification for the second type.
Furthermore, it would be interesting if \cref{approxpsatz} could provide sum-of-squares certificates of lower degree than Stengle's original Positivstellensatz.
Finally, we point out some problems that are adjacent to ours.
While we have focused on real projective spaces, the analogous question can be posed in complex projective spaces $\mathbf{CP}^{d-1}$.
Here, the optimal $n$-codes are known for $n\leq d+1$, but they are similarly mysterious for $n=d+2$.
Since $\mathbf{CP}^1$ is the $2$-sphere, the optimal $4$-code for $\mathbf{CP}^1$ is given by the vertices of the tetrahedron.
More generally, Bukh and Cox~\cite{bukh19} characterize the optimal $(d+2)$-codes for $\mathbf{CP}^{d-1}$ for every $d\equiv 2\bmod 4$.
These are the only solved cases.
For the $d=3$ case, Jasper, King and Mixon~\cite{jasper19} conjecture that the optimal $5$-code is given by the lines spanned by the columns of
\[
\left[\begin{array}{lllll}
a&b&b&c&c\\
b&a&b&cw&cw^2\\
b&b&a&cw^2&cw
\end{array}\right],
~a=\frac{\sqrt{13}+\sqrt{2+\sqrt{13}}-1}{3\sqrt{3}},
~b=\sqrt{\frac{1-a^2}{2}},
~c=\frac{1}{\sqrt{3}},
~w=e^{2\pi i/3}.
\]
Furthermore, King will buy a coffee for the first person to prove this conjecture~\cite{dustinBlog}.
Our methods do not easily transfer to this setting since sign patterns in the Gram matrix are no longer discrete.
The analogous question has also been posed in the sphere $S^{d-1}$, where the optimal $n$-codes are known for $n\leq 2d$.
For $n=2d+1$, little is known.
For $d=2$, the optimal code is given by five uniformly spaced points on the circle, and the $d=3$ case was solved by Sch\"{u}tte and van der Waerden~\cite{schutte51} in 1951.
Ballinger et al.~\cite{ballinger09} offer a conjecture that treats all dimensions simultaneously:
Let $S\in\mathbf{R}^{(d-1)\times d}$ be a matrix whose unit-norm columns form the vertices of a regular simplex.
The putatively optimal $(2d+1)$-code for $S^{d-1}$ is unique up to isometry and given by the columns of
\[
\left[\begin{array}{ccc}
1&\alpha&\beta\\
0&\sqrt{1-\alpha^2}\cdot S&-\sqrt{1-\beta^2}\cdot S
\end{array}\right],
\]
where $\alpha$ is the unique root between $0$ and $1/d$ of
\[
(d^3-4d^2+4d)x^3-d^2x^2-dx+1,
\]
and $\beta$ is the unique root between $-1$ and $1$ of
\[
\alpha x+\frac{1}{d-1}\sqrt{(1-\alpha^2)(1-x^2)}-\alpha.
\]
Our methods do not easily transfer to this setting since the contact graphs are far less dense, meaning the resulting programs have more decision variables.
\section*{Acknowledgments}
DGM was partially supported by AFOSR FA9550-18-1-0107, NSF DMS 1829955, and the 2019 Kalman Visiting Fellowship at the University of Auckland. HP was partially supported by an AMS-Simons Travel Grant.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,006 |
Special Permits; Possession of Deer Accidentally Killed by a Motor Vehicle
PROPOSED RULEMAKING
[58 PA. CODE CH. 147]
To effectively manage the wildlife resources of this Commonwealth, the Game Commission (Commission), at its October 5, 2004, meeting, proposed the following rulemaking:
Amend § 147.142 (relating to possession of deer accidentally killed by a motor vehicle) to permit the issuance of permit ''numbers'' rather than ''paper'' permits to validate lawful possession of road-killed deer and facilitate cost and personnel timesavings for the Commission.
The proposed rulemaking will have no adverse impact on the wildlife resources of this Commonwealth.
The authority for the proposed rulemaking is 34 Pa.C.S. (relating to Game and Wildlife Code) (code).
The proposed rulemaking was made public at the October 5, 2004, meeting of the Commission, and comments can be sent to the Director, Information and Education, Game Commission, 2001 Elmerton Avenue, Harrisburg, PA 17110-9797, until January 21, 2005.
1. Purpose and Authority
Currently, any individual who wishes to take possession of an accidentally road-killed deer shall apply for a possession permit through his local Commission regional office within 24 hours of taking possession of the deer. After the Commission receives an application for a permit, its personnel must commit time to completing and issuing the ''paper'' permit and recording its information. The cumulative cost of the time spent executing these tasks in addition to the postage costs for mailing a ''paper'' permit to each applicant is quite substantial. To promote cost and personnel timesavings, as well as streamline and simplify the permitting process, the Commission is proposing to amend § 147.142 to allow the issuance of permit ''numbers'' by phone rather than ''paper'' permits by mail. This should make it easier for applicants to receive a permit as well as make it less costly and time consuming for the Commission to issue the same.
Section 2901(b) of the code (relating to authority to issue permits) provides ''the commission may, as deemed necessary to properly manage the game or wildlife resources, promulgate regulations for the issuance of any permit and promulgate regulations to control the activities which may be performed under authority of any permit issued.'' Section 2102(a) of the code (relating to regulations) provides that ''The commission shall promulgate such regulations as it deems necessary and appropriate concerning game or wildlife . . . in this Commonwealth, including regulations relating to the protection, preservation and management of game or wildlife . . . in this Commonwealth.'' The proposed rulemaking is made under this authority.
2. Regulatory Requirements
The proposed rulemaking will require possession permit applicants to obtain a permit ''number'' rather than a ''paper'' permit to validate lawful possession of an accidentally road-killed deer.
3. Persons Affected
Persons who wish to take possession of an accidentally road-killed deer will be affected by the proposed rulemaking.
4. Cost and Paperwork Requirements
The proposed rulemaking should reduce cost and paperwork related to possession permits for accidentally road-killed deer.
The proposed rulemaking will be effective on final-form publication in the Pennsylvania Bulletin and will remain in effect until changed by the Commission.
6. Contact Person
For further information regarding the proposed rulemaking, contact Michael A. Dubaich, Director, Bureau of Law Enforcement, 2001 Elmerton Avenue, Harrisburg, PA 17110-9797, (717) 783-6526.
VERNON R. ROSS,
Fiscal Note: 48-197. No fiscal impact; (8) recommends adoption.
TITLE 58. RECREATION
PART III. GAME COMMISSION
CHAPTER 147. SPECIAL PERMITS
Subchapter H. PROTECTED SPECIMEN
§ 147.142. Possession of deer accidentally killed by a motor vehicle.
(a) A resident of this Commonwealth may immediately take possession of a deer accidentally killed on the highway and transport it to a place of safekeeping within this Commonwealth. The person taking possession shall [apply, through] contact a regional office or a local [commission] Commission officer, for a permit number within 24 hours after having taken possession of the deer. The permit number shall be considered a valid permit for the purposes of the act and this part and shall be valid for a period not to exceed 120 days from the date of issuance [and shall set forth other conditions which may be required. The deer shall be retained on the premises of the permittee unless otherwise provided on the permit]. The whole or any part of the deer may not be given to any person nor may any edible part be removed from the recipient's place of residence. The recipient may not sell or transfer the hide to another party except the hide may be given to the deer processor. Unused parts of the deer must be disposed of lawfully.
(b) It is unlawful:
(1) To possess a deer accidentally killed on the highway for more than 24 hours without applying for a permit number.
(3) To fail to comply with one or more conditions [on] of the permit.
[Pa.B. Doc. No. 04-2182. Filed for public inspection December 10, 2004, 9:00 a.m.] | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 637 |
Q: R Shiny key and actionButton binding to reactive values I'm trying to make a Shiny App work where the user can manipulate reactiveValues with either buttons or keys. Thus a minimal example would be to increment or decrement a counter with either the Up/Down actionButton or the U/D keys. The user should be able to use the keys without clicking anywhere on the screen first.
Based on the examples here on SO (Using enter key with action button in R Shiny, Shiny Responds to Enter and R Shiny key input binding), I came up with the script below. However, it doesn't react at all to the U/D keys. Buttons work as expected. Once I click on a button, it gets sort of "stuck" and I can use either the Enter or Space keys to repeat the button clicks, but the U/D key has still no effect. Any idea what could be wrong?
And this is the code I wrote:
library(shiny)
shinyApp(ui <- pageWithSidebar(
headerPanel("Test keyboard control"),
sidebarPanel(
tags$script(
'tags$head(
$(document).keydown(function(e)){
if (e.keyCode == 85) {
$("#upButton").click();
} else if (e.keyCode == 68) {
$("#downButton").click();
}
});'
),
actionButton("downButton", "Down"),
actionButton("upButton", "Up")
),
mainPanel(htmlOutput("text"))
),
server <- function(session, input, output) {
vals <- reactiveValues(count = 0)
observeEvent(input$downButton, {vals$count <- vals$count - 1})
observeEvent(input$upButton, {vals$count <- vals$count + 1})
output$text <- renderText(paste("Counter is:", vals$count))
}
)
A: The problem is that the input event only captures the keycode of the pressed key, which stays the same once the key is pressed. Shiny however only reacts if the event data changes. You need to set the event data to something new every time; e.g. the current time stamp. Look at this working example:
library(shiny)
shinyApp(ui <- pageWithSidebar(
headerPanel("Test keyboard control"),
sidebarPanel(
tags$script('$(document).on("keydown",
function (e) {
if(e.which == 68) {
Shiny.onInputChange("downButton", new Date());
} else if (e.which == 85) {
Shiny.onInputChange("upButton", new Date());
}
});
'),
actionButton("downButton", "Down"),
actionButton("upButton", "Up")
),
mainPanel(htmlOutput("text"))
),
server <- function(session, input, output) {
vals <- reactiveValues(count = 0)
observeEvent(input$downButton, {vals$count <- vals$count - 1})
observeEvent(input$upButton, {vals$count <- vals$count + 1})
output$text <- renderText(paste("Counter is:", vals$count))
}
)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,207 |
\section{Introduction}
All graphs in this paper are finite and undirected, and have no loops or parallel edges. For a graph $G$ we use $|G|$, $e(G)$, $\delta (G)$, $\Delta(G)$, $\alpha(G)$, $\chi(G)$ to denote the number
of vertices, number of edges, minimum degree, maximum degree, independence number, and chromatic number of $G$, respectively. The \dfn{complement} of $G$ is denoted by $\overline{G}$. For any positive integer k, we define $[k]$ to be the set $\{1, \ldots, k\}$. A graph $H$ is a \dfn{minor} of a graph $G$ if $H$ can be
obtained from a subgraph of $G$ by contracting edges. We write $G\succcurlyeq H$ if
$H$ is a minor of $G$.
In those circumstances we also say that $G$ has an \dfn{$H$ minor}. For positive integers $t, s$, we use $\mathcal{K}_t^{-s}$ to denote the family of graphs obtained from the complete graph $K_t$ by deleting $s$ edges. We use $K_t^-$, $K_t^=$, and $K_t^\equiv$ to denote the unique graph obtained from $K_t$ by deleting one, two and three independent edges, respectively; and
$K_t^<$ to denote the unique graph obtained from $K_t$ by deleting two adjacent edges. Note that $\mathcal{K}_t^{-1}=\{K_t^-\}$ and $\mathcal{K}_t^{-2}=\{K_t^=, K_t^<\}$.
A graph $G$ has \dfn{no $\mathcal{K}_t^{-s}$ minor} if it has no $H$ minor for every $H\in \mathcal{K}_t^{-s}$; and $G$ has a $\mathcal{K}_t^{-s}$ minor, otherwise. We write $G\succcurlyeq \mathcal{K}_t^{-s}$ if
$G$ has a $\mathcal{K}_t^{-s}$ minor.\medskip
Our work is motivated by Hadwiger's Conjecture~\cite{Had43}, which is perhaps the most famous conjecture in graph theory.
\begin{conj}[Hadwiger's Conjecture~\cite{Had43}]\label{HC} Every graph with no $K_t$ minor is $(t-1)$-colorable.
\end{conj}
\cref{HC} is trivially true for $t\le3$, and reasonably easy for $t=4$, as shown independently by Hadwiger~\cite{Had43} and Dirac~\cite{Dirac52}. However, for $t\ge5$, Hadwiger's Conjecture implies the Four Color Theorem~\cite{AH77,AHK77, RSST97}. Wagner~\cite{Wagner37} proved that the case $t=5$ of Hadwiger's Conjecture is, in fact, equivalent to the Four Color Theorem, and the same was shown for $t=6$ by Robertson, Seymour and Thomas~\cite{RST}. Despite receiving considerable attention over the years, Hadwiger's Conjecture remains wide open for all $t\ge 7$, and is considered among the most important problems in graph theory and has motivated numerous developments in graph coloring and graph minor theory.
K\"{u}hn and Osthus~\cite{KuhOst03c} proved that Hadwiger's Conjecture is true for $C_4$-free graphs of sufficiently large chromatic number, and for all graphs of girth at least $19$. Until very recently the best known upper bound on the chromatic number of graphs with no $K_t$ minor is $O(t (\log t)^{1/2})$, obtained independently by Kostochka~\cite{Kostochka82,Kostochka84} and Thomason~\cite{Thomason84}, while Norin, Postle and the second author~\cite{NPS20} improved the frightening $(\log t)^{1/2}$ term to $(\log t)^{1/4}$. The current record
is $O(t\log \log t)$ due to
Delcourt and Postle~\cite{DelcourtPostle}. \medskip
Given the notorious difficulty of Hadwiger's Conjecture, Paul Seymour in 2017 suggested the study of the following $H$-Hadwiger's Conjecture.
\begin{conj}[$H$-Hadwiger's Conjecture]\label{HHC} For every graph $H$ on $t$ vertices, every graph with no $H$ minor is $(t-1)$-colorable.
\end{conj}
Jakobsen~\cite{Jakobsen71b} in 1971 proved that every graph with no $K_7^{-}$ minor is $7$-colorable. It is not known yet whether every graph with no $K_7$ minor is $7$-colorable; some progress has been made in \cite{RST22}. For $H\in\{K_7^-, K_7^=, K_7^<\}$, proving that graphs with no $H$ minor are $6$-colorable also remains open. Kostochka~\cite{Kos14} proved that $H$-Hadwiger's Conjecture is true for graphs with no $K_{s,t}$ minor, provided that $t>C(s\log s)^3$. Very recently, Norin and Seymour~\cite{NorSey22} proved that every graph on $n$ vertices with independence number two has an $H$ minor, where $H$ is a graph with $\lceil n/2\rceil$ vertices and at least $ 0.98688\cdot {{|H|}\choose2}-o(n^2)$ edges. We refer the reader to a recent paper of the present authors~\cite{K84} on partial results towards Hadwiger's Conjecture for $t\le 9$; and recent surveys~\cite{CV2020, K2015,Seymoursurvey} for further background on Hadwiger's Conjecture. \medskip
Dirac in 1964 began the study of a variation of $H$-Hadwiger's Conjecture in~\cite{Dirac64b} by excluding more than one forbidden minor simultaneously; he proved that every graph with no $\mathcal{K}_t^{-2}$ minor is $(t-1)$-colorable for each $t\in\{5,6\}$.
Jakobsen~\cite{Jakobsen71a} in 1971 proved that every graph with no $\mathcal{K}_7^{-2}$ minor is $6$-colorable; this implies that $H$-Hadwiger's Conjecture is true for all graphs $H$ on seven vertices such that $\Delta(\overline{H})\ge2$ and $\overline{H}$ has a matching of size two. \medskip
Very recently, using the techniques developed in \cite{ KT05,RST} and generalized Kempe chains of contraction-critical graphs by Rolek and the second author~\cite{RolekSong17a}, the present authors considered the case when $t=8$ and proved the following result.
\begin{thm}[Lafferty and Song~\cite{K84}]\label{t:K84} Every graph with no $\mathcal{K}_8^{-4}$ minor is $7$-colorable. In particular, $H$-Hadwiger's Conjecture is true for all graphs $H$ on eight vertices such that $\Delta(\overline{H})\ge4$, and $\overline{H}$ has a perfect matching, a triangle and a cycle of length four.
\end{thm}
The purpose of this paper is to consider the next step and prove the following main result.
\begin{restatable}{thm}{main}\label{t:main} Every graph with no $\km{9}{6}$ minor is $8$-colorable. \end{restatable}
\cref{t:main} implies that $H$-Hadwiger's Conjecture holds for all graphs $H$ on nine vertices such that $H$ is not a subgraph of every graph in $ \km{9}{6}$. Following the ideas in \cite{K84}, our proof of \cref{t:main} utilizes an extremal function for $\km{9}{6}$ minors (see \cref{t:exfun}), generalized Kempe chains of contraction-critical graphs (see \cref{l:wonderful}), and the method for finding $\km{9}{6}$ minors from three different $K_6$ subgraphs in $7$-connected graphs on at least $19$ vertices (see \cref{l:threek6s}).
\begin{restatable}{thm}{exfun}\label{t:exfun} Every graph on $n\ge 9$ vertices with at least $5n-14$ edges has a $\km{9}{6}$ minor. \end{restatable} \medskip
\cref{t:exfun} is best possible in the sense that every $(K_8^=, 4)$-cockade on $n$ vertices has $5n-14$ edges but no $\km{9}{5}$ minor, where for a graph $H$ and an integer $k\ge1$, an $(H, k)$-cockade is defined recursively as follows: any graph isomorphic to $H$
is an $(H,k)$-cockade. Let $G_1$ and $G_2$ be $(H, k)$-cockades and let $G$
be obtained from the disjoint union of $G_1$ and $G_2$ by identifying a clique
of size $k$ in $G_1$ with a clique of the same size in $G_2$. Then the graph
$G$ is also an $(H,k)$-cockade, and every $(H,k)$-cockade can be constructed
this way. \medskip
This paper is organized as follows. In the next section, we introduce the necessary definitions and collect several tools which we will need later on. We prove \cref{t:main} in Section~\ref{s:coloring}, and \cref{t:exfun} in Section~\ref{s:exfun}.
\section{Notation and tools}
Let $G$ be a graph. If $x,y$ are adjacent
vertices of $G$, then we denote by $G/xy$ the graph obtained from $G$
by contracting the edge $xy$ and deleting all resulting parallel
edges. We simply write $G/e$ if $e=xy$. If $u,v$ are distinct nonadjacent vertices of $G$, then by
$G+uv$ we denote the graph obtained from $G$ by adding an edge
with ends $u$ and $v$. If $u,v$ are adjacent or equal, then we define
$G+uv$ to be $G$. Similarly, if $M\subseteq E(G)\cup E(\overline{G})$, then by
$G+M$ we denote the graph obtained from $G$ by adding all the edges of $M$ to $G$. Every edge in $\overline{G}$ is called a \dfn{missing edge} of $G$. For a vertex $x\in V(G)$, we will use $N(x)$ to denote the set of vertices in $G$ which are adjacent to $x$.
We define $N[x] = N(x) \cup \{x\}$. The degree of $x$ is denoted by $d_G(x)$ or
simply $d(x)$. If $A, B\subseteq V(G)$ are disjoint, we say that $A$ is \emph{complete} to $B$ if each vertex in $A$ is adjacent to all vertices in $B$, and $A$ is \emph{anticomplete} to $B$ if no vertex in $A$ is adjacent to any vertex in $B$.
If $A=\{a\}$, we simply say $a$ is complete to $B$ or $a$ is anticomplete to $B$. We use $e(A, B)$ to denote the number of edges between $A$ and $B$ in $G$.
The subgraph of $G$ induced by $A$, denoted by $G[A]$, is the graph with vertex set $A$ and edge set $\{xy \in E(G) \mid x, y \in A\}$. We denote by $B \setminus A$ the set $B - A$, and $G \setminus A$ the subgraph of $G$ induced on $V(G) \setminus A$, respectively.
If $A = \{a\}$, we simply write $B \setminus a$ and $G \setminus a$, respectively.
An $(A, B)$-path in $G$ is a path with one end in $A$ and the other in $B$ such that all its internal vertices lie in $G\setminus (A\cup B)$. We simply say an $(a, B)$-path if $A=\{a\}$. It is worth noting that each vertex in $A \cap B$ is an $(A, B)$-path.
For a positive integer $k$, a $k$-vertex is a vertex of degree $k$, and a $k$-clique is a set of $k$ pairwise adjacent vertices.
Let $\mathcal{F}$ be a family of graphs. A graph $G$ is \emph{$\mathcal{F}$-free} if it has no subgraph isomorphic to $H$ for every $H\in\mathcal{F}$. We simply say $G$ is $H$-free if $\mathcal{F}=\{H\}$. The \dfn{join} $G+H$ (resp. \dfn{union} $G\cup H$) of two
vertex-disjoint graphs
$G$ and $H$ is the graph having vertex set $V(G)\cup V(H)$ and edge set $E(G)
\cup E(H)\cup \{xy\, |\, x\in V(G), y\in V(H)\}$ (resp. $E(G)\cup E(H)$).
We use the convention ``$A:=$" to mean that $A$ is defined to be
the right-hand side of the relation.
Finally, if $H$ is a connected subgraph of a graph $G$ and $y \in V(H)$, we say that we \textit{contract $H \setminus y$ onto $y$} when we contract $H$ to a single vertex, that is, contract all the edges of $H$. \medskip
To prove \cref{t:main}, we need to investigate the basic properties of contraction-critical graphs. For a positive integer $k$, a graph $G$ is \dfn{$k$-contraction-critical} if $\chi(G)=k$ and every proper minor of $G$ is $(k-1)$-colorable.
Dirac~\cite{Dirac60} introduced the notion of contraction-critical graphs and proved \cref{l:alpha2} below; in the same paper he also proved that $5$-contraction-critical graphs are $5$-connected. The latter was then extended by Mader~\cite{7con} as stated in \cref{t:7conn}. It remains unknown whether every $k$-contraction-critical graph is $8$-connected for all $k\ge8$.
\begin{lem}[Dirac~\cite{Dirac60}]\label{l:alpha2} Let $G$ be a $k$-contraction-critical graph. Then for each $v\in V(G)$, \[\alpha(G[N(v)])\le d(v)-k+2.\]
\end{lem}
\begin{thm}[Mader~\cite{7con}]\label{t:7conn}
For all $k \ge 7$, every $k$-contraction-critical graph is $7$-connected.
\end{thm}
\cref{l:wonderful} on contraction-critical graphs turns out to be very powerful, as the existence of pairwise vertex-disjoint paths is guaranteed without using the connectivity of such graphs. Recall that every edge in $\overline{H}$ is a \dfn{missing edge} of a graph $H$.
\begin{lem}[Rolek and Song~\cite{RolekSong17a}]\label{l:wonderful}
Let $G$ be any $k$-contraction-critical graph. Let $x\in V(G)$ be a vertex of
degree $k + s$ with $\alpha(G[N(x)]) = s + 2$ and let $S \subset N(x)$ with
$ |S| = s + 2$ be any independent set, where $k \ge 4$ and $s \ge 0$ are integers.
Let $M$ be a set of missing edges of $G[N(x) \setminus S]$. Then there
exists a collection $\{P_{uv}\mid uv\in M\} $ of paths in $G$ such that
for each $uv\in M$, $P_{uv}$ has ends $u, v$ and all its internal vertices
in $G \setminus N[x]$. Moreover, if vertices $u,v,w,z$ with $uv,wz\in M$ are distinct, then
the paths $P_{uv}$ and $P_{wz}$ are vertex-disjoint.
\end{lem}
The proof of \cref{l:wonderful} uses Kempe chains. Using a result of Mader~\cite{7con} on rooted $K_4$ minors and the proof of \cref{l:wonderful}, the present authors~\cite{K84} proved a strengthened version of the remark given in \cite[Page 17]{RolekSong17a}.
\begin{lem}[Lafferty and Song~\cite{K84}]\label{l:rootedK4} Let $G$ be any $k$-contraction-critical graph. Let $x\in V(G)$ be a vertex of
degree $k + s$ with $\alpha(G[N(x)]) = s + 2$ and let $S \subset N(x)$ with
$ |S| = s + 2$ be any independent set, where $k \ge 4$ and $s \ge 0$ are integers.
If \[M=\{x_1y_1, x_1y_2, x_2y_1, x_2y_2, a_1b_{11}, \dots, a_1b_{1r_1}, \dots, a_mb_{m1}, \dots, a_mb_{mr_m}\}\] is a set of missing edges of $G[N(x)\setminus S]$, where the vertices $x_1, x_2, y_1, y_2, a_1, \dots, a_m,
b_{11}, \dots, b_{mr_m}\in N(x)\setminus S$ are all distinct, and for all $1\le i \le m$, $a_ib_{i1}, \dots, a_ib_{ir_i}$ are $r_i$ missing edges with $a_i$ as a common end, and $x_1x_2, y_1y_2\in E(G)$, then $G \succcurlyeq G[N[x]]+M$. \end{lem}
\begin{rem}\label{r:rootedK4} As observed in \cite{K84}, \cref{l:rootedK4} can be applied when \[M=\{x_1y_1, x_1y_2, x_2y_1, x_2y_2, a_1b_{11}, \dots, a_1b_{1r_1}, \dots, a_mb_{m1}, \dots, a_mb_{mr_m}\}\] is a subset of edges and missing edges of $G[N(x)\setminus S]$, where $x_1, x_2, y_1, y_2, a_1, \dots, a_m,
b_{11}, \dots, b_{mr_m}\in N(x)\setminus S$ are all distinct, and $x_1x_2, y_1y_2\in E(G)$. Under those circumstances, it suffices to apply \cref{l:rootedK4} to $M^*$, where $M^*= \{e\in M\mid e \text{ is a missing edge of } G[N(x)\setminus S])\}$. It is straightforward to see that $G\succcurlyeq G[N[x]]+M$.
\end{rem}
\begin{figure}[htb]
\centering
\includegraphics[scale=0.5]{3K5.png}
\caption{The nine possibilities for three $5$-cliques in Theorem~\ref{t:goodpaths}.}
\label{fig:threek5s}
\end{figure}
Finally we need a tool to find a desired $\km{9}{6}$ minor through three different $6$-cliques in $7$-connected graphs. This method was first introduced by Robertson, Seymour and Thomas~\cite{RST} to prove Hadwiger's Conjecture for $t=6$: they found a desired $K_6$ minor via three different $4$-cliques in $6$-connected non-apex graphs. The method was later extended by Kawarabayashi and Toft~\cite{KT05} to find a desired $K_7$ minor via three different $5$-cliques in $7$-connected graphs.
It is worth noting that \cref{t:goodpaths} corresponds to \cite[Lemma 5]{KT05}, where the existence of such seven ``good paths" follows from the proof of \cite[Lemma 5]{KT05}.
\begin{thm}[Kawarabayashi and Toft~\cite{KT05}]\label{t:goodpaths}
Let $G$ be a $7$-connected graph such that $|G| \geq 19$.
Let $L_1, L_2$, and $L_3$ be three different $5$-cliques of $G$ such that $|L_1\cup L_2\cup L_3|\ge 12$, that is, they fit into one of the nine configurations depicted in Figure~\ref{fig:threek5s}.
Then $G$ has seven pairwise vertex-disjoint ``good paths", where a ``good path" is an $(L_i, L_j)$-path in $G$ with $i \neq j$.
\end{thm}
\section{Coloring graphs with no $\km{9}{6}$ minor}\label{s:coloring}
We first use \cref{t:goodpaths} to prove a lemma that finds a $\km{9}{6}$ minor via three different $6$-cliques in $7$-connected graphs with at least $19$ vertices.
\begin{lem}
\label{l:threek6s}
Let $G$ be a $7$-connected graph such that $|G|\ge19$. If $L_1$, $L_2$, and $L_3$ are three $6$-cliques of $G$ satisfying \[\min\{|L_1 \setminus (L_2 \cup L_3)|, |L_2 \setminus (L_1 \cup L_3)|, |L_3 \setminus (L_1 \cup L_2)| \} \geq 1,\tag{$*$}\]
then $G$ has a $\km{9}{6}$ minor.
\end{lem}
\begin{proof} Suppose $G$ has no $\km{9}{6}$ minor. By the assumption ($*$), we see that $|L_1 \cap L_2\cap L_3| \le 5$, and $|L_i \cap L_j| \le 5$ for $1\le i<j\le 3$.
We first observe that $G$ is $\km{8}{5}$-free: suppose $G$ has an $H$ subgraph for some $H\in \km{8}{5}$. Since $G$ is $7$-connected, we see that there are at least seven pairwise disjoint $(V(H), V(C))$-paths in $G$ for every component $C$ of $G \setminus V(H)$. Thus we obtain a $\km{9}{6}$ minor by contracting a component of $G \setminus V(H)$ to a single vertex, a contradiction. It follows that $|L_1 \cap L_2\cap L_3| \ne 5$, and $|L_i \cap L_j| \ne 4$ for $1\le i<j\le 3$, else neither $G[L_1 \cup L_2\cup L_3]$ nor $G[L_i \cup L_j]$ is $\km{8}{5}$-free. We may assume that $|L_1 \cap L_2| \ge |L_1 \cap L_3| \ge |L_2 \cap L_3|$. \medskip
Suppose first $|L_1 \cap L_2| \le 1$. Let $L_i'$ be a $5$-clique of $L_i$ for each $i\in[3]$ such that $L_i\cap L_j=L_i'\cap L_j'$ for $1\le i<j\le 3$. Then $L_1', L_2'$ and $ L_3'$ fit into one of the five configurations in Figure~\ref{fig:threek5s}(a,c,d,g,i). By Theorem~\ref{t:goodpaths} applied to $L_1', L_2'$ and $ L_3'$, there exist seven pairwise vertex-disjoint ``good paths", say $Q_1, \ldots, Q_7$, between $L_1, L_2$, and $L_3$; we choose $Q_1, \ldots, Q_7$ so that $|V(Q_1)|+ \cdots+|V(Q_7)|$ is as small as possible. It follows that no internal vertex of each $Q_i$ belongs to $L_1 \cup L_2 \cup L_3$, and no vertex of $L_i\cap L_j$ belongs to a ``good path'' of length at least one. Let $t_{i,j}$ denote the number of ``good paths" between $L_i$ and $L_j$ for $1\le i<j\le 3$. We may assume that $t_{1,2}\ge t_{1,3}\ge t_{2,3}$. Then $3\le t_{1,2}\le 5$. We may further assume that $Q_6$ and $Q_7$ are $(L_1, L_2)$-paths of length at least one. Suppose $t_{1,2}= 5$. By contracting each of $Q_1, \ldots, Q_5$ to a single vertex, all the edges, but one, of $Q_6$ (that is, contracting $Q_6$ to a $K_2$), and all the edges, but one, of $Q_7$ (that is, contracting $Q_7$ to a $K_2$), we see that $G\succcurlyeq \km{9}{6}$, a contradiction. Thus $3\le t_{1,2}\le 4$. Recall that $ t_{1,3}\ge t_{2,3}$.
Let $x\in L_2$; in addition, let $y\in L_1\cup L_2$ with $y\ne x$ when $t_{1,2}=3$, such that neither $x$ nor $y$ is an end of any ``good path". But now contracting each of $Q_1, \ldots, Q_7$ to a single vertex, together with $x$ and $y$, yields a $ \km{9}{6}$ minor in $G$ when $t_{1,2}=3$, and contracting each of $Q_1, \ldots, Q_6$ to a single vertex and $Q_7$ to a $K_2$, together with $x$, yields a $ \km{9}{6}$ minor in $G$ when $t_{1,2}=4$, a contradiction.
This proves that $|L_1 \cap L_2| \ge 2$. Let $a_1, \ldots, a_p\in L_1\cap L_2$, where $p:=|L_1\cap L_2|$. Then $p=5$ or $2\le p\le 3$. \medskip
Suppose next $2\le p\le 3$.
By Menger's Theorem, there exist $6-p\ge3$ pairwise vertex-disjoint $(L_1 \setminus L_2, L_2 \setminus L_1)$-paths, say $Q_1, \ldots, Q_{6-p}$, in $G \setminus \{ a_1, \ldots, a_p\}$. But then we obtain a $\km{9}{6}$ minor in $G$ from $G[L_1\cup L_2]$ by contracting each of $Q_1, Q_2, Q_3$ to a $K_2$; in addition, contracting $Q_4$ to a single vertex when $p=2$, a contraction. \medskip
It remains to consider the case $p=5$. Let $x \in L_1 \setminus L_2 $ and $ y \in L_2 \setminus L_1 $. By the assumption ($*$), $x, y\notin L_3$. Let $z\in L_3\setminus (L_1\cup L_2)$. Since $G$ is $\km{8}{5}$-free, we see that $|L_1 \cap L_2\cap L_3|\le 2$, else $G[L_1\cup L_2\cup\{z\}]$ is not $\km{8}{5}$-free. Suppose $ |L_1 \cap L_2\cap L_3|= 2$. We may assume $a_4, a_5\in L_1 \cap L_2\cap L_3 $. Let $z'\in L_3\setminus(L_1\cup L_2)$ such that $z'\ne z$. Then $G\setminus \{a_4, a_5\}$ has five pairwise internally vertex-disjoint $(z, \{x, a_1, a_2, a_3, y\})$-paths, say $Q_1, \ldots, Q_5$. We may assume that $z'$ does not belong to $Q_1, \ldots, Q_4$. Let $Q_5^*$ be the $(z', w)$-subpath of $Q_5$ when $z'$ lies on $Q_5$, where $w$ is the other end of $Q_5$. Then $G\succcurlyeq \km{9}{6}$ from $G[L_1\cup L_2\cup\{z,z'\}]$ by contracting each of
$Q_1\setminus z, \ldots, Q_5\setminus z$ to a single vertex when $z'\notin V(Q_5)$; and each of $Q_1\setminus z, \ldots, Q_4\setminus z $, and $Q_5^* \setminus z'$ to a single vertex when $z'\in V(Q_5)$, a contradiction.
This proves that $ |L_1 \cap L_2\cap L_3|\le 1$. By Menger's Theorem, $G\setminus y$ has six pairwise vertex-disjoint $(L_3, L_1)$-paths, say $Q_1, \dotsc, Q_6$. We may assume that $a_i$ is an end of $Q_i$ for each $i \in [5]$. Then $x$ is an end of $Q_6$. We may assume further assume that $a_5\notin L_3$. But then we obtain a $\km{9}{5}$ minor in $G$ from $G[L_1\cup L_2\cup L_3]$ by contracting each of $Q_1, \ldots, Q_4, Q_5\setminus a_5, Q_6\setminus x$ to a single vertex, a contradiction.\medskip
This completes the proof of \cref{l:threek6s}.
\end{proof}
\begin{figure}[htb]
\centering
\includegraphics[scale=0.16]{6H.png}
\caption{Six $K_5$-free graphs $H$ with $|H|=9$ and $\alpha(H)=2$.}
\label{fig:counter}
\end{figure}
\begin{lem}
\label{l:H9}
Let $H$ be a graph such that $|H| = 9$ and $\alpha(H) = 2$.
Then $H$ contains $K_5$ or one of the graphs in Figure~\ref{fig:counter} as a spanning subgraph.
\end{lem}
\begin{proof}
Suppose $H$ is $K_5$-free, and $H_i$-free for each $H_i$ given in Figure~\ref{fig:counter}. We may assume that $H$ is edge-minimal subject to being $K_5$-free and $\alpha(H)=2$. Then $H$ has no dominating edge, where an edge $xy\in E(H)$ is dominating if every vertex in $V(H)\setminus\{x, y\}$ is adjacent to $x$ or $y$. This implies that $\Delta(H)\le7$ and \medskip
\noindent (a) no vertex in $N(v)$ is complete to $V(H)\setminus N[v]$ for each $v\in V(H)$. \medskip
Since $\alpha(H)=2$, we see that, for each $v\in V(H)$, $V(H)\setminus N[v]$ is a clique, and so $|H\backslash N[v]|\le4$ because $H$ is $K_5$-free. Then $\delta(H) \ge 4$ and $H[N(v)]$ is $K_4$-free for each $v\in V(H)$. By (a), $\Delta(H)\le 6$.
Let $x\in V(H)$ be a vertex of degree $\Delta(H)$. Let $N(x):=\{x_1, \ldots, x_{d(x)}\}$ and $V(H)\setminus N[x]:=\{y_1, \ldots, y_{8-d(x)}\}$. Suppose $d(x)=4$. Then $V(H)\setminus N[x]$ is a $4$-clique, and each $y_i$ is adjacent to exactly one vertex in $N(x)$. We may assume that $x_1y_1\in E(H)$. We may further assume that $x_1y_4\notin E(H)$ and $x_4y_4\in E(H)$. Then $\{x_2, x_3, x_4\}$ is a $3$-clique, and $x_1$ is complete to $\{x_2, x_3\}$ because $y_4$ is anticomplete to $\{x_2, x_3\}$. But then $x_4$ is complete to $\{y_2, y_3\}$ because $x_1$ is anticomplete to $\{x_4, y_2,y_3\}$, contrary to the fact that $\Delta(H)=4$. Suppose next $d(x)=6$. Then $V(H)\setminus N[x]=\{y_1, y_2\}$, and by (a), both $y_1$ and $y_2$ are $4$-vertices such that $y_1$ and $y_2$ have no common neighbor in $N(x)$. Thus $N(y_1)\cap N(x)$ and $N(y_2)\cap N(x)$ are disjoint $3$-cliques in $H$. But then $H$ contains $H_1$ as a subgraph, a contradiction. This proves that $d(x)=5$, and so $N(x)=\{x_1, \ldots, x_5\}$ and $V(H)\setminus N[x]=\{y_1, y_2, y_3\}$. \medskip
Suppose $H[N(x)]$ is $K_3$-free. Note that $\alpha(H[N(x)])=2$. Thus $H[N(x)]=C_5$, say with vertices $x_1, \ldots, x_5$ in order. Since $d(y_1)\le 5$, we may assume that $y_1$ is anticomplete to $\{x_4, x_5\}$. Then $y_1$ is complete to $\{x_1, x_2, x_3\}$. By (a) applied to $\{x_1, x_2, x_3\}$, we may further assume that $y_3$ is anticomplete to $\{x_1, x_2\}$. Then $y_3$ is complete to $\{x_3, x_4, x_5\}$ and so $y_2x_3\notin E(H)$. Then $y_2$ is complete to $\{x_1, x_5\}$; in addition, $y_2$ is adjacent to exactly one of $x_2$ and $x_4$ because $\alpha(H)=2$ and $\Delta(H)=5$. It follows that $H$ contains $H_2$ as a subgraph, a contradiction. This proves that \medskip
\noindent (b) $H[N(v)]$ contains $K_3$ as a subgraph for every $5$-vertex $v$. \medskip
Note that $\delta(H[N(x)])\ge 1$ because $H$ is $K_5$-free. Suppose $\delta(H[N(x)])= 1$. We may assume that $x_5x_4\in E(H)$ and $x_5$ is anticomplete to $\{x_1, x_2, x_3\}$. By (a), we may assume that $x_5y_1\notin E(H)$. Then $x_5$ is a $4$-vertex, $\{y_1, x_1, x_2, x_3\}$ is a $4$-clique, and $x_5$ is complete to $\{y_2, y_3\}$. By (a) applied to $\{x_1, x_2, x_3\}$, we may assume that $y_2$ is anticomplete to $\{x_2, x_3\}$. Suppose $x_4y_2\notin E(H)$. Then $x_4$ is complete to $\{x_2, x_3\}$ and $y_2x_1, x_4y_3\in E(H)$. Thus $H$ contains $H_3$ as a subgraph, a contradiction. It follows that $x_4y_2\in E(H)$. Then $x_4y_3\notin E(H)$, else $H$ contains $H_4$ as a subgraph. Note that each of $x_1, x_2, x_3$ is adjacent to exactly one of $x_4$ and $y_3$; and either $e_H(\{x_1, x_2, x_3\}, x_4)=2$ and $e_H(\{x_1, x_2, x_3\}, y_3)=1$, or $e_H(\{x_1, x_2, x_3\}, x_4)=1$ and $e_H(\{x_1, x_2, x_3\}, y_3)=2$. In the former case, we may assume that $x_1y_3, x_2x_4, x_3x_4\in E(H)$; thus $H$ contains $H_3$ as a subgraph, a contradiction. In the latter case, we may assume that $x_1y_3, x_2y_3, x_3x_4\in E(H)$; again $H$ contains $H_3$ as a subgraph by drawing the graph $H$ according to the $5$-vertex $y_1$, a contradiction. This proves that \medskip
\noindent (c)\, $\delta(H[N(v)])\ge 2$ for every $5$-vertex $v$. \medskip
By (b), we may assume that $\{x_1, x_2, x_3\}$ is a clique. Suppose $x_4x_5\notin E(H)$. Note that neither $x_4$ nor $x_5$ is complete to $\{x_1, x_2, x_3\}$, and no vertex in $\{x_1, x_2, x_3\}$ is anticomplete to $\{ x_4, x_5\}$. By (c), we may assume that $x_4$ is complete to $\{x_1, x_2\}$ and $x_5$ is complete to $\{x_2, x_3\}$. Then $x_1x_5, x_3x_4\notin E(H)$. Note that each $y_j$ is adjacent to at least two vertices in $N(x)$ for each $j\in[3]$. However, each of $x_1$ and $x_3$ is adjacent to at most one vertex in $\{y_1, y_2, y_3\}$; each of $x_4$ and $x_5$ is adjacent to at most two vertices in $\{y_1, y_2, y_3\}$; and $x_2$ is anticomplete to $\{y_1, y_2, y_3\}$. It follows that $e_H(\{y_1, y_2, y_3\}, N(x))=6$; and every $x_i$ is a $5$-vertex and every $y_j$ is a $4$-vertex for each $i\in[5]$ and $j\in[3]$. We may assume that $x_4$ is complete to $\{y_1, y_2\}$. Then $x_4y_3\notin E(H)$ and so $y_3$ is complete to $\{x_3, x_5\}$. But then $y_3$ is adjacent to $x_5$ only in
$H[N(x_3)]$, contrary to (c). We may assume that \medskip
\noindent (d)\, $H[N(v)]$ is $K_3\cup \overline{K}_2$-free for every $5$-vertex $v$.\medskip
It remains to consider the case
$x_4x_5\in E(H)$. Suppose $x_i$ is complete to $\{x_4, x_5\}$ for some $i\in[3]$, say $i=3$. We may assume that $x_1x_4\notin E(H)$ because $H[N(x)]$ is $K_4$-free. By (d) applied to $H[N(x)]$, we have $x_2x_5\notin E(H)$; in addition, either $x_1x_5, x_2x_4\notin E(H) $, or $x_1x_5, x_2x_4\in E(H) $. Since $e_H(\{y_1, y_2, y_3\}, N(x))\ge 6$, we see that $\{x_1, x_2\}$ is anticomplete to $\{x_4, x_5\}$. By (a), we may assume that $x_1y_3, x_4y_j\notin E(H)$ for some $j\in[3]$. Then $y_3$ is complete to $\{x_4, x_5\}$. Thus $j\ne 3$. We may assume that $j=1$. Then $y_1$ is complete to $\{x_1, x_2\}$. Since $H$ is $H_5$-free, we see that $y_2$ is not complete to $\{x_2, x_4\}$. We may assume that $x_2y_2\notin E(H)$. Then $y_2$ is complete to $\{x_4, x_5\}$ because $\{x_1, x_2\}$ is anticomplete to $\{x_4, x_5\}$. But then $H$ contains $H_6$ as a subgraph, a contradiction. This proves that no $x_i$ is complete to $\{x_4, x_5\}$ for each $i\in[3]$. By (c), we may assume that $x_2x_4, x_3x_5\in E(H)$. Then $x_2x_5, x_3x_4\notin E(H)$. By (a), we may assume that $x_5y_3\notin E(H)$. Then $y_3x_2\in E(H)$. By (d) applied to $H[N(x_2)]$, we have $y_3x_4\in E(H)$. By (a), we may assume that $x_4y_2\notin E(H)$. Then $x_4$ is anticomplete to $\{x_3, y_2\}$, and so $x_3y_2\in E(H)$. Thus $y_1$ is anticomplete to $\{x_2, x_3\}$, and so $y_1$ is complete to $\{x_4, x_5\}$. But then $x_4$ is a $5$-vertex such that $G[N(x_4)]=C_5$, contrary to (b). \medskip
This completes the proof of \cref{l:computer}.
\end{proof}
\begin{figure}[htb]
\centering
\includegraphics[scale=0.16]{6Hcolor.png}
\caption{Graphs in \cref{fig:counter} with bold vertices and edges depicted, and dashed edges added.}
\label{fig:wonderful}
\end{figure}
We are now ready to prove Theorem~\ref{t:main}, which we restate for convenience.\main*
\begin{proof} Suppose the assertion is false. Let $G$ be a graph with no $\km{9}{6}$ minor such that $\chi(G) \ge 9$.
We may choose such a graph $G$ so that it is $9$-contraction-critical. Then $\delta(G)\ge8$, $G$ is $7$-connected by \cref{t:7conn}, and $\delta(G) \le 9$ by \cref{t:exfun}.
Let $x\in V(G)$ be of minimum degree. Since $G$ is $9$-contraction-critical and has no $\km{9}{6}$ minor, by \cref{l:alpha2} applied to $G[N(x)]$, we see that $\delta(G)=9$ and $\alpha(G[N(x)]) = 2$. We next prove that $G[N(x)]$ contains a $5$-clique.
Suppose $G[N(x)]$ is $K_5$-free. By \cref{l:H9}, $G[N(x)]$ contains a spanning subgraph isomorphic to one of the graphs in Figure~\ref{fig:counter}. Let $A$ be the set of all bold vertices, $M$ be the set of all dashed edges and $e$ the bold edge in each $H_i$ given in Figure~\ref{fig:wonderful}. Since $G[N(x)]$ is $K_5$-free, we see that $A$ is not a clique in $G$. Let $S$ be a set of two nonadjacent vertices in $A$. Note that no vertex in $S$ is incident with any dashed edges in $M$. By \cref{l:rootedK4} applied to $G[N(x)]$ with $S$ and $M$ given above, we see that $G[N[x]]+M\succcurlyeq \km{9}{6}$ by contracting the bold edge $e$, a contradiction. This proves that $G[N(x)]$ contains a $5$-clique for all such $9$-vertices $x$ in $G$. Let $n_9$ denote the number of $9$-vertices in $G$. Then $e(G)\ge \big(9n_9+10(|G|-n_9)\big)/2=(10|G|-n_9)/2 $. By \cref{t:exfun}, $5|G|-15\ge e(G)\ge (10|G|-n_9)/2$. It follows that $n_9\ge30$. Then $G$ contains at least three pairwise nonadjacent $9$-vertices in $G$. Let $x_1, x_2, x_3\in V(G) $ be three pairwise nonadjacent $9$-vertices in $G$. For each $i\in[3]$, $G[N(x_i)]$ has a $5$-clique; let $L_i $ be a $6$-clique of $G[N[x_i]]$ such that $x_i\in L_i $. Then
\[\min\{|L_1 \setminus (L_2 \cup L_3)|, |L_2 \setminus (L_1 \cup L_3)|, |L_3 \setminus (L_1 \cup L_2)| \} \geq 1.\]
By \cref{l:threek6s}, $G\succcurlyeq\km{9}{6}$, a contradiction. \medskip
This completes the proof of \cref{t:main}.
\end{proof}
\section{An extremal function for $\km{9}{6}$ minors}\label{s:exfun}
Throughout this section, if $G$ is a graph and $K$ is a subgraph of $G$, then by $N(K)$ we denote
the set of vertices of $V(G)\setminus V(K)$ that are adjacent to a vertex of $K$.
If $V(K)=\{x\}$, then $N(K)=N(x)$.
It can be easily checked that for each vertex $x\in V(G)$, if $K$ is a component of $G\setminus N[x]$, then $N(K)$ is a minimal separating set of $G$. \medskip
Lemma~\ref{l:k4-} follows from the proof of Lemma~16 of J\o rgensen~\cite{Jor01}. A proof can be found in~\cite{K84}.
\begin{lem}[J\o rgensen~\cite{Jor01}]\label{l:k4-} Let $G$ be a $4$-connected graph and let $S\subseteq V(G)$ be a separating set of four vertices. Let $G_1$ and $G_2$ be proper subgraphs of G so that $G_1\cup G_2=G$ and $G_1\cap G_2=G[S]$. Let $d_1$ be the
largest integer so that $G_1$ contains pairwise disjoint sets of vertices
$V_1, V_2, V_3, V_4$ so that $G_1[V_j]$ is connected,
$|S\cap V_j|=1$ for $1\le j\le 4$, and so that the graph obtained from $G_1$ by contracting each of $G_1[V_1], G_1[V_2],G_1[V_3],G_1[V_4]$ to a single vertex
and deleting $V(G)\setminus \bigcup_{j=1}^4 V_j$ has
$e(G[S])+d_1$ edges. If $|G_1|\ge 6$, then \[e(G[S]) + d_1 \geq 5.\]
\end{lem}
We next prove a lemma that will be needed in the proof of Theorem~\ref{t:exfun}.
\begin{lem}
\label{l:computer}
Let $H$ be a graph on eight or nine vertices. If $\delta(H) \geq 5$, then
$H$ has a vertex $v$ such that $H \setminus v$ has a $ \km{7}{6}$ minor.
\end{lem}
\begin{proof} We may assume that $\delta(H) =5$ and every edge is incident with a $5$-vertex in $H$. Suppose $H \setminus v $ has no $\km{7}{6}$ minor for every $v\in V(H)$. Then $|H|=9$, else for any $5$-vertex $v$ in $H$, $e(H\setminus v)\ge 20-5=e(K_7)-6$, and so $H\setminus v$ has a $\km{7}{6}$ minor, a contradiction. We claim that some edge in $H$ belongs to at most two triangles. Suppose not. Then every edge in $H$ belongs to at least three triangles. Let $x$ be a $5$-vertex in $H$. Then $\delta(H[N(x)])\ge3$, and so $H[N(x)]$ contains $K_5^=$ as a spanning subgraph; in addition, every vertex in $H\setminus N[x]$ is adjacent to at least three vertices in $N(x)$. It follows that $H[N[x]\cup\{y\}]\succcurlyeq \km{7}{5}$, where $y\in V(H)\setminus N[x]$, a contradiction. Thus there exists an edge $uw\in E(H)$ such that $uw$ belongs at most two triangles. Let $H^*:=H/uw$. Then $e(H^*)\ge e(H)-3\ge 23-3=20$. Note that $|H^*|=8$. Similar to the case when $|H|=8$, we see that if $\delta(H^*)\ge5$, then $H^*\setminus v$ has a $\km{7}{6}$ minor for any $5$-vertex $v$ in $H$. Thus $\delta(H^*)\le 4$.
Let $v\in V(H^*)$ such that $d_{H^*}(v)\le4$. Then $ e(H^*\setminus v)\ge 20-4=e(K_7)-5$, and so $ H^*\setminus v$ has a $\km{7}{5}$ minor, a contradiction. \end{proof}
We are now ready to prove Theorem~\ref{t:exfun}, which we restate for convenience. \exfun*
\begin{proof} Suppose the assertion is false. Let $G$ be a graph on $n \geq 9$ vertices with $ e(G) \geq 5n-14$ and, subject to this, $n$ is minimum. We may assume that $e(G) = 5n-14$.
It is straightforward to check that $G\succcurlyeq \km{9}{6}$ when $n=9$. Thus $n \geq 10$. We next prove several claims. \medskip
\setcounter{counter}{0}
\noindent {\bf Claim\refstepcounter{counter} \label{c:d5} \arabic{counter}.}
$\delta(G) \geq 6$.
\begin{proof} Suppose $\delta(G)\le 5$. Let $x\in V(G)$ with $d(x)\le 5$. Then
\[e(G \setminus x) =e(G)-d(x)\ge (5n-14)-5 =5(n-1)-14.\]
Thus $G \setminus x $ has a $ \km{9}{6}$ minor by the minimality of $G$, a contradiction.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:triangles} \arabic{counter}.}
Every edge in $G$ belongs to at least five triangles. Moreover, $G[N[x]]=K_7$ if $x\in V(G)$ is a $6$-vertex, and $G[N[x]]$ contains a $K_8^\equiv$ subgraph if $x\in V(G)$ is a $7$-vertex.
\begin{proof}
Suppose there exists an edge $uv \in E(G)$ such that $uv$ belongs to at most four triangles. Then
\[e(G / uv) \ge (5n-14)-5 =5|G/uv| -14.\]
Thus $G /uv\succcurlyeq \km{9}{6}$ by the minimality of $G$, a contradiction. Since every edge in $G$ belongs to at least five triangles, we see that $G[N[x]]=K_7$ for each $6$-vertex $x$ in $G$, and $G[N[y]]$ contains a $K_8^\equiv$ subgraph for each $7$-vertex $y$ in $G$. \end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:n12} \arabic{counter}.}
$n\ge12$.
\begin{proof}
Suppose $10\le n\le 11$. Let $x\in V(G)$ be a vertex of degree $\delta(G)$. Then $d(x)\le 7$ because $e(G) = 5n-14$. By Claim~\ref{c:d5}, $6\le d(x)\le 7$.
Suppose $ d(x)=7$. Then $G[N[x]]$ contains a $K_8^\equiv$ subgraph by Claim~\ref{c:triangles}, and every vertex in $ V(G)\setminus N[x]$ is adjacent to at least five vertices in $N(x)$. But then $G\succcurlyeq G[\{v\}\cup N[x]] \succcurlyeq\km{9}{6}$ for each $ v\in V(G)\setminus N[x]$, a contradiction. Thus $d(x)=6$. Then $G[N[x]]=K_7$ by Claim~\ref{c:triangles}. Let $y, z\in V(G)\setminus N[x]$. Then $e_G(\{y, z\}, N(x))\ge 2(6-(n-8))=28-2n$. If $e_G(\{y, z\}, N(x))\ge 9$, or $e_G(\{y, z\}, N(x))\ge 8$ and $yz\in E(G)$, then $G[\{y, z\}\cup N[x]]\succcurlyeq \km{9}{6}$, a contradiction. Thus $ e_G(\{y, z\}, N(x)) =8 $ and $yz\notin E(G)$, or $6\le e_G(\{y, z\}, N(x)) \le 7 $. In the former case, there exists $w\in V(G)\setminus N[x]$ such that $w$ is complete to $\{y,z\}$. But then $G[\{y, z,w\}\cup N[x]]/wz\succcurlyeq \km{9}{6}$. Thus $6\le e_G(\{y, z\}, N(x)) \le 7 $ for any two vertices $y, z\in V(G)\setminus N[x]$. It follows that $n=11$, $V(G)\setminus N[x]$ is a $4$-clique, no vertex of $V(G)\setminus N[x]$ has degree at least eight, and at least three vertices of $V(G)\setminus N[x]$ are $6$-vertices in $G$. Thus $e_G(V(G)\setminus N[x], N(x))\le 12+1=13$. But then \[e(G)=e(G[N[x]])+e_G(V(G)\setminus N[x], N(x))+e(G\setminus N[x])\le 21+13+6< 5\times 11-14,\] which is impossible. \end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:55} \arabic{counter}.}
No three $6$-vertices in $G$ are pairwise adjacent.
\begin{proof}
Suppose there exist three distinct $6$ vertices, say $x, y, z$, in $G$ such that $\{x,y,z\}$ is a $3$-clique.
Then $|G \setminus \{ x, y,z \}|=n-3 \geq 9$ by Claim~\ref{c:n12}, and \[ e(G \setminus \{ x, y,z \}) = e(G)-15= 5(n-3) - 14.\]
Thus $G \setminus \{ x, y,z \}$ has a $\km{9}{6}$ by the minimality of $G$, a contradiction.
\end{proof}
Let $S$ be a minimal separating set of vertices in $G$, and let $G_1$ and $G_2$ be proper subgraphs of $G$ so
that $G=G_1\cup G_2$ and $G_1\cap G_2=G[S]$.
For each $i\in[2]$, let $d_i$ be the
largest integer so that $G_i$ contains pairwise disjoint sets of vertices
$V_1, \dots, V_p$ so that $G_i[V_j]$ is connected,
$|S\cap V_j|=1$ for $1\le j\le p :=|S|$, and so that the graph obtained from $G_i$ by contracting each of $G_i[V_1], \dots, G_i[V_p]$ to a single vertex
and deleting $V(G)\setminus \bigcup_{j=1}^p V_j$ has
$e(G[S])+d_i$ edges. It follows from the minimality of $G$ that for each $i\in[2]$,
\[ e(G_i) + d_{3-i} \le 5|G_1| - 15 \,\, \text{ if } |G_i|\ge9.\tag{$ \bigstar$}\]
\noindent {\bf Claim\refstepcounter{counter}\label{c:nodis7} \arabic{counter}.}
If $|G_i|=8$ for some $i\in [2]$, then $|S|\le 4$ and some vertex in $V(G_i)\setminus S$ is a $7$-vertex in $G$.
\begin{proof}
Suppose, say, $|G_1| = 8$. Let $C$ be a component of $G_2 \setminus S$. We first prove that $G_1\setminus S$ is connected. Suppose not. By Claims~\ref{c:d5} and \ref{c:triangles}, $G_1\setminus S$ must contain two nonadjacent $6$-vertices in $G$ with $G[S]=K_6$. Thus $G_1=K_8^-$ and so $G\succcurlyeq \km{9}{3}$ by contracting $C$ to a single vertex, a contradiction. Thus $G_1\setminus S$ is connected. We next prove that some vertex in $V(G_1)\setminus S$ is a $7$-vertex in $G$. Suppose no vertex in $V(G_1)\setminus S$ is a $7$-vertex in $G$. Then every vertex in $V(G_1)\setminus S$ is a $6$-vertex in $G$. By Claim~\ref{c:triangles} and the fact that $G_1\setminus S$ is connected, we see that $V(G_1)\setminus S$ is a clique of order $8-|S| $. By Claim~\ref{c:55}, $|V(G_1)\setminus S|\le 2$. By the minimality of $S$, every vertex in $S$ is adjacent to at least one vertex in $V(G_1)\setminus S$. It follows that $|V(G_1)\setminus S|= 2$ and $G_1=K_8^-$. But then $G\succcurlyeq\km{9}{2}$ by contracting $C$ to a single vertex, a contradiction. Finally, let $x\in V(G_1)\setminus S$ be a $7$-vertex in $G$. By Claim~\ref{c:triangles}, $G_1=G[N[x]]$ contains $K_8^\equiv$ as a spanning subgraph. Thus $|S|\le 4$, else $G\succcurlyeq\km{9}{6}$ by contracting $C$ to a single vertex. \end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:no7} \arabic{counter}.}
Neither $G_1$ nor $G_2$ has exactly eight vertices.
\begin{proof}
Suppose not, say $|G_1| = 8$. By Claim~\ref{c:nodis7}, $|S|\le 4$ and some vertex, say $x$, in $V(G_1)\setminus S$ is a $7$-vertex in $G$. By Claim~\ref{c:triangles}, $G_1$ contains $K_8^\equiv$ as a spanning subgraph.
We next prove that $|G_2|\ge 9$. Suppose $ |G_2|\le 8$. Note that $|G_2|\ge7$ by Claim~\ref{c:d5}. If $|G_2|=7$, then every vertex in $G_2\setminus S$ is a $6$-vertex. By Claims~\ref{c:triangles}, $G_2=K_7$, but then $V(G_2)\setminus S$ is a clique of order $7-|S|\ge3$ because $|S|\le 4$, contrary to Claim~\ref{c:55}.
Thus $|G_2|=8$ and $n=16-|S|$. By Claim~\ref{c:nodis7}, some vertex, say $y$, in $V(G_2)\setminus S$ is a $7$-vertex in $G$. By Claim~\ref{c:triangles}, $G_2$ contains $K_8^\equiv$ as a spanning subgraph.
Suppose $ |S|=4$. Then $G[S]=K_4$, else $G\succcurlyeq \km{9}{6}$ by contracting $G_2\setminus (S\cup\{y\})$ onto an end of a missing edge of $G[S]$. Thus $G_1=G_2=K_8^\equiv$, else say $G_1$ contains $K_8^=$ as a spanning subgraph, then $G[V(G_1)\cup\{y\}]\succcurlyeq\km{9}{6}$. But then $n=16-4=12$ and $e(G)=e(G_1)+e(G_2)-6=50-6=44<5\times 12-14$, a contradiction. Suppose next $ |S|= 3$. Then $n=13$; moreover, $G_1, G_2\in\{K_8^=, K_8^\equiv\}$, else say $G_1 $ contains $K_8^-$ as a subgraph, then $G[V(G_1)\cup\{y\}]\succcurlyeq \km{9}{6}$. But then $e(G[S])\ge2$ and $e(G)=e(G_1)+e(G_2)-e(G[S]) \le 26+26-2 =50<5\times 13-14$, a contradiction. Thus $|S|\le 2$. Then \[ 5(16-|S|)-14 = e(G)=e(G_1)+e(G_2)-e(G[S])\le 28+28-e(G[S]).\]
It follows that $|S|=2$, $G_1=G_2=K_8$ and $G[S]=\overline{K}_2$, which is impossible.
This proves that $|G_2|\ge 9$.
\medskip
Recall that $G_1$ contains $K_8^\equiv$ as a subgraph. It is easy to check that $e(G[S])+d_1={{|S|}\choose2}$. Note that if $|S|=4$, then $G_1=K_8^\equiv$, else $G\succcurlyeq \km{9}{6}$ by contracting a component of $G_2\setminus S$ to a single vertex. But then \begin{align*}
e(G_2)+d_1&=e(G)-e(G_1)+e(G[S])+d_1\\
&\ge 5n-14 -\big(28-\max\{0, 3(|S|-3)\}\big)+ {{|S|}\choose2} \\
&= \big(5\times (n-(8-|S|))-14\big) + 5\times (8-|S|) -\big(28-\max\{0, 3(|S|-3)\}\big)+{{|S|}\choose2}\\
&=(5 |G_2|-14) + 5\times (8-|S|) -\big(28-\max\{0, 3(|S|-3)\}\big)+{{|S|}\choose2}\\
&\ge 5|G_2|-14,
\end{align*}
contrary to ($ \bigstar$) because $ |S|\le 4$ and $|G_2|\ge 9$.
\end{proof}
Observe that, if $|G_1|\ge 9$ and $|G_2|\ge 9$, then by ($ \bigstar$), we have
\begin{align*}
5n - 14= e(G) &= e(G_1) + e(G_2) - e(G[S]) \\
& \le (5|G_1|-15-d_2)+(5|G_2|-15-d_1)- e(G[S]) \\
&= 5(n + |S|) - 30 - d_1 - d_2 - e(G[S]).
\end{align*}
It follows that
\[ 5|S| \ge 16 + d_1 + d_2 + e(G[S]) \, \, \text{ if } |G_1|\ge 9\, \text{ and } |G_2|\ge 9. \tag{$\blacklozenge$} \] \medskip
\noindent {\bf Claim\refstepcounter{counter}\label{c:not77} \arabic{counter}.}
If $|G_i|=7$, then $|G_{3-i}|\ge9$ for each $i\in[2]$. Moreover, $G[S]=K_5$ or $G[S]=K_6$.
\begin{proof}
Suppose $|G_1|=7$ but $|G_2|\le8$. By Claim~\ref{c:no7}, $|G_2|=7$.
By Claim~\ref{c:triangles}, $G_1=G_2=K_7$, and every vertex in $V(G_1)\setminus S$ is a $6$-vertex in $G$. By Claim~\ref{c:55}, $|V(G_1)\setminus S|\le 2$ and so $|S|\ge 5$. But then $n=14-|S|\le 9$, contrary to Claim~\ref{c:n12}. Since $G_1= K_7$ and $1\le |V(G_1)\setminus S|\le 2$, we see that $G[S]=K_5$ or $G[S]=K_6$.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:5conn} \arabic{counter}.}
$G$ is $5$-connected.
\begin{proof} Suppose $G$ is not 5-connected. Let $S$ be a minimal separating set of $G$, and $G_1, G_2, d_1, d_2$ be defined as prior to ($ \bigstar$). By Claim~\ref{c:not77},
$|G_1|\ne 7$ and $|G_2|\ne 7$. By Claim~\ref{c:no7}, $|G_1|\ge 9$ and $|G_2|\ge 9$. By ($\blacklozenge$),
$|S| \geq 4$, and so $G$ is $4$-connected. By Lemma~\ref{l:k4-}, $e(G[S])+d_1\ge5$. Note that $d_2\ge 1$ when $S$ is not a $4$-clique, and $e(G[S])=6$ when $S$ is a $4$-clique. In either case, we have $d_1 + d_2 + e(G[S])\ge6$, contrary to ($\blacklozenge$). \end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:almostclique} \arabic{counter}.}
If there exists $x \in S$ such that $S \setminus x$ is a clique, then $G[S] = K_5$ or $G[S] = K_6$.
\begin{proof} Suppose $S \setminus x$ is a clique but $G[S]\ne K_5$ and $G[S]\ne K_6$. Let $G_1$ and $G_2$ be as above. By Claim~\ref{c:not77},
$|G_1|\ne 7$ and $|G_2|\ne 7$. By Claim~\ref{c:no7}, $|G_1|\ge 9$ and $|G_2|\ge 9$. By Claim~\ref{c:5conn}, $|S| \geq 5$.
If $S$ contains a $7$-clique, then $G\succcurlyeq K_9^-$ by contracting a component of $G_1 \setminus S$ and a component of $G_2 \setminus S$ to two distinct vertices, a contradiction. Thus $5\le |S|\le 7$ and $S$ is not a clique.
Then $\delta(G[S]) =d_{G[S]}(x)\leq |S| - 2$.
Since $S\setminus x$ is a clique, we see that \[ d_1 = d_2 = |S| - 1 - d_{G[S]}(x)=|S| - 1 -\delta(G[S]). \]
It follows that \[ e(G[S]) ={{|S|-1}\choose 2}+d_{G[S]}(x)= {{|S|-1}\choose 2}+\delta(G[S]). \] This, together with ($\blacklozenge$), implies that
\begin{align*}
5|S| &\ge 16+d_1 + d_2 + e(G[S]) \\
&= 16 + 2(|S| - 1 -\delta(G[S])) + {{|S|-1}\choose 2}+\delta(G[S]) \\
&= 16+2(|S|-1)+(|S|^2 -3|S| + 2)/2 - \delta(G[S]) \\
&\ge 15+ (|S|^2 +|S|)/2 - (|S|-2)\\
&=17+(|S|^2 -|S|)/2,
\end{align*}
which is impossible because $5\le |S|\le 7$.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:k72} \arabic{counter}.}
$G$ is $\mathcal{K}_8^{-3}$-free.
\begin{proof}
Suppose $G$ has a subgraph $H$ such that $H\in \mathcal{K}_8^{-3}$. Since $G$ is $5$-connected,
we obtain a $\km{9}{6}$ minor in $G$ by contracting a component of $G \setminus V(H)$ to a single vertex, a contradiction. \end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:dnot6} \arabic{counter}.}
No vertex in $G$ is a $7$-vertex.
\begin{proof}
Suppose to the contrary that $G$ has a $7$-vertex, say $x$.
By Claim~\ref{c:triangles}, $G[N[x]]$ contains $K_8^\equiv$ as a spanning subgraph, contrary to Claim~\ref{c:k72}.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:onlyone5} \arabic{counter}.}
$G$ has at most two $6$-vertices. Moreover, if $G$ has exactly two $6$-vertices, then they must be adjacent.
\begin{proof}
Suppose to the contrary that $G$ has two distinct $6$-vertices, say $x, y$, such that $xy\notin E(G)$.
By Claim~\ref{c:triangles}, $N[x]$ and $N[y]$ are $7$-cliques in $G$. Then
$|N(x) \cap N(y)|\le 4$, else $G[N[x] \cup N[y]]=K_8^-$ (when $|N(x) \cap N(y)|=6$) or $G[N[x] \cup N[y]]\succcurlyeq \km{9}{4}$ (when $|N(x) \cap N(y)|= 5$), contrary to Claim~\ref{c:k72} in the former case, and the choice of $G$ in the latter case.
By Claim~\ref{c:5conn} and Menger's Theorem, there exist six pairwise internally vertex-disjoint $(x, y)$-paths $Q_1, \ldots, Q_6$. Then each $Q_i$ contains exactly one vertex in $N(x)$ and exactly one in $N(y)$. We may assume that $Q_1$ has at least four vertices with $ V(Q_1)\cap N(x)=\{x_1\}$ and $ V(Q_1)\cap N(y)=\{y_1\}$. Let $Q_1^*$ be the $(x_1, y_1)$-subpath of $Q_1$. Then $G\succcurlyeq\km{9}{3}$ by contracting all the edges of $Q_1^*\setminus y_1$, and $Q_2\setminus\{x, y\}, \ldots, Q_6\setminus\{x, y\}$, a contradiction. This proves that $6$-vertices are pairwise adjacent in $G$. By Claim~\ref{c:55}, $G$ has at most two $6$-vertices.\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:58} \arabic{counter}.}
No $6$-vertex is adjacent to an $8$-vertex or $9$-vertex in $G$.
\begin{proof}
Suppose to the contrary that there exists $xy \in E(G)$ such that $d(x) = 6$ and $d(y) \in\{8,9\}$.
By Claim~\ref{c:triangles}, $G[N[x]]=K_7$, $N[x]\subseteq N[y]$ and
$\delta(G[(N(y)])\ge5$. Then $d(y)=9$, otherwise $G\succcurlyeq G[N[y]]\succcurlyeq \km{9}{4}$, a contradiction. Let $ A:=N[y]\setminus N[x]$. Then $|A|=3$ because $xy\in E(G)$. Let $A:=\{a_1, a_2, a_3\}$.
Then either $e(\{a_1, a_2\}, N[x])\ge 10$, or $e(\{a_1, a_2\}, N[x])\ge 8$ and $a_1a_2\in E(G)$. But then $G[N[y]\setminus a_3]\succcurlyeq\km{9}{6}$ in both cases, a contradiction.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:disconnected} \arabic{counter}.} Let $x\in V(G)$ be an $8$-vertex or $9$-vertex in $G$, and let $M$ be the set of vertices of $N(x)$ not adjacent to all other vertices of $N(x)$.
Then there is no component $K$ of $G \setminus N[x]$ such that $M\subseteq N(K)$.
In particular, $G \setminus N[x]$ is disconnected if $x$ is an $8$-vertex.
\begin{proof}
Suppose such a component $K$ exists. Then every vertex in $M$ has a neighbor in $K$ because $M\subseteq N(K)$.
By Lemma~\ref{l:computer}, there exists $y \in N(x)$ such that $G[N(x)] \setminus y$ has a $\km{7}{6}$ minor.
If $y\notin M$, then $y$ is complete to $N[x]\setminus y$ and so $G[N[x]]\succcurlyeq\km{9}{6}$, a contradiction.
Thus $y\in M\subseteq N(K)$.
By contracting $K$ onto $y$, we obtain a $\km{9}{6}$ minor in $G$, a contradiction. This proves that no such component $K$ exists. Suppose $x$ is an $8$-vertex. By Claims~\ref{c:dnot6} and \ref{c:58}, every vertex in $M$ has degree at least eight, and thus every vertex in $M$ has a neighbor in $G \setminus N[x]$. It follows that $G \setminus N[x]$ is disconnected, as desired.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:dnot8} \arabic{counter}.}
No vertex in $G$ is an $8$-vertex.
\begin{proof}
Suppose to the contrary that $G$ has an $8$-vertex, say $x$. Suppose $G[N(x)]$ has a $5$-clique, say $A$. By Claim~\ref{c:triangles}, $\delta(G[N(x)])\ge 5$. It is straightforward to check that $e(G[N[x]])\ge 30=e(K_9)-6$, and so $G[N[x]]\succcurlyeq\km{9}{6}$, a contradiction. Thus $G[N(x)]$ is $K_5$-free. By Claim~\ref{c:disconnected}, let $C$ and $C'$ be two distinct components of $G \setminus N[x]$. By Claim~\ref{c:5conn}, $|N(C)|\ge5$ and $|N(C')|\ge5$. By Claim~\ref{c:almostclique} and the fact $G[N(x)]$ is $K_5$-free, we see that
each of $G[N(C)]$ and $G[N(C')]$ has two independent missing edges. Let $yz$ and $uv$ be a missing edge of $G[N(C)]$ and $G[N(C')]$, respectively, such that $ y\ne u, v$. Note that $e(G[N[x]])\ge 8+20=e(K_9)-8$. But then $G\succcurlyeq\km{9}{6}$ by contracting $C$ onto $y$ and $C'$ onto $u$, a contradiction.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:comporder1} \arabic{counter}.}
Let $x\in V(G)$ be a $9$-vertex in $G$.
Then $G\setminus N[x]$ is disconnected. Moreover, $|C|\ge2$ for every component $C$ of $G \setminus N[x]$.
\begin{proof} Suppose $G\setminus N[x]$ is connected. Let $M$ be the set of vertices of $N(x)$ not adjacent to all other vertices of $N(x)$.
By Claims~\ref{c:dnot6}, \ref{c:58} and \ref{c:dnot8}, every vertex in $M$ has degree at least nine, and thus every vertex in $M$ has a neighbor in $K:=G \setminus N[x]$. But then $M\subseteq N(K)$, contrary to Claim~\ref{c:disconnected}. \medskip
Next suppose there exists a component $C$ of $G \setminus N[x]$ such that $|C|=1$. Let $y$ be the only vertex in $C$. Suppose $y$ is not a $6$-vertex in $G$. Then $d(y)\ge 9$ by Claims~\ref{c:dnot6} and \ref{c:dnot8}, and so $N(C)=N(x)$, contrary to Claim~\ref{c:disconnected}. Thus $y$ is a $6$-vertex in $G$. By Claim~\ref{c:triangles}, $G[N[y]]=K_7$. But then $G[ \{x\}\cup N[y]]=K_8^-$, contrary to Claim~\ref{c:k72}.
\end{proof}
\noindent {\bf Claim\refstepcounter{counter}\label{c:comp9} \arabic{counter}.}
Let $x\in V(G)$ be a $9$-vertex in $G$.
Then for every component $C$ of $G \setminus N[x]$, there exists a vertex $v\in V(C)$ such that $d_G(v)=9$.
\begin{proof}
Suppose there exists a component $C$ of $G \setminus N[x]$ such that $d_G(v)\ne 9$ for every $v\in V(C)$. By Claim~\ref{c:comporder1}, $|C|\ge2$.
Observe that if all vertices in $V(C)$ are $6$-vertices in $G$, then $|C|=2$ by Claim~\ref{c:55} and $G[V(C)\cup N(C)]=K_7$ by Claim~\ref{c:triangles}; thus $G[\{x\}\cup V(C)\cup N(C)]$ is not $\km{8}{3}$-free, contrary to Claim~\ref{c:k72}. Thus there exists a vertex $y\in V(C)$ such that $d_G(y)\ne 6$. Since $d_G(v)\ne 9$ for every $v\in V(C)$, by Claims~\ref{c:dnot6} and \ref{c:dnot8}, we have $d_G(y)\ge10$. \medskip
Let $G_1 := G \setminus V(C)$ and $G_2 := G[V(C) \cup N(C)]$. Note that $|G_2|\ge11$ and $N(C)$ is a minimal separating set of $G$. By Claim~\ref{c:disconnected}, $N(C)\ne N(x)$.
Thus $|C|\ge 11-8=3$. Let $d_1$ be defined as in the paragraph prior to Claim~\ref{c:nodis7}.
Let $z \in N(C)$ such that $d_{G[N(C)]}(z) = \delta(G[N(C)])$. Let $d:=d_{G[N(C)]}(z)$.
By contracting $G_1 \setminus N(C)$ onto $z$, we see that $d_1 \geq |N(C)| - d - 1$. By ($ \bigstar$),
\[ e(G_2) \le 5(|C| + |N(C)|) - 15 - (|N(C)| - d - 1)=5|C| + 4|N(C)| + d - 14. \tag{a} \]
Now let $t := e_G ( C, N(C) )$ and let $p\le 2$ be the number of vertices in $V(C)$ that are $6$-vertices in $G$.
Then $e(G_2) = e(C) + t + e(G[N(C)])$.
Note that $2e(C) \geq 10(|C| - p) + 6\times p - t=10|C|-4p-t$ and $2e(G[N(C)]) \geq d|N(C)|$. Thus \[ 2e(G_2) =2e(C) +2 t + 2e(G[N(C)])\geq 10|C| - 4p + t + d|N(C)|. \tag{b} \]
Combining (a) and (b) yields \[ 10|C| + 8|N(C)| + 2d - 28 \ge 2e(G_2) \geq 10|C| - 4p + t + d|N(C)| \] and so \[ -t \ge d\big(|N(C)| - 2\big) - 8|N(C)| + 28-4p.\tag{c} \]
Note that $\delta(G[N(x)]) \geq 5$ by Claim~\ref{c:triangles}, and $N(C)$ is a subset of $N(x)$, so \[ d = \delta(G[N(C)]) \geq 5 - (9 - |N(C)|) = |N(C)| - 4. \]
This, together with (c), implies that
\begin{align*}
-t &\ge \big(|N(C)| - 4\big)\big(|N(C)| - 2\big) - 8|N(C)| + 28-4p \\
&= |N(C)|^2 - 14|N(C)| + 36-4p \\
&= \left( |N(C)|- 7\right)^2 -13-4p,
\end{align*}
so $-t \geq -13-4p$.
But then \[ |C|(|C|-1)\ge 2e(C) \geq 10|C|-4p-t \geq 10|C| - 4p-13-4p=10|C|-13-8p,\]
Since $2e(C)$ is even, we have
\[ |C|(|C|-1)\ge 2e(C) \geq 10|C| - 12-8p.\tag{d}\]
If $p\ge1$, let $w\in V(C)$ be a $6$-vertex in $G$. Then $G[N_G[w]]=K_7$ and thus $|N_G(w)\cap V(C)|\ge3$, else $G[\{x\}\cup N_G(w)]$ is not $\km{8}{3}$-free, contrary to Claim~\ref{c:k72}. Thus $|C|\ge4$ when $p\ge1$.
Suppose $p\le1$. Then (d) implies that $|C|\ge9$ and $e(C)>5|C|-14$; thus $ G\succcurlyeq C\succcurlyeq\km{9}{6}$ by the minimality of $G$, contrary to the choice of $G$. Thus $p=2$ and $|C|\ge4$. Then $(d)$ yields $ |C|= 4$ or $|C|\ge7$; and $e(C)\ge 5|C|-14$. By the minimality of $G$, we have
$ |C|= 4$ or $7\le |C|\le 8$. Let $w'\in V(C)$ be the other $6$-vertex in $G$. Suppose $|C|=4$. Then $V(C)$ is a $4$-clique in $G$ because $|N_G(w)\cap V(C)|\ge3$ as observed earlier. Let $y'$ be the vertex in $V(C)\setminus\{w,w',y\}$. Then $d_G(y')\ge10$. Recall that $N(C)\ne N(x)$. Thus there exist $x_1, x_2 \in N(x)\setminus N_G(w)$ such that $x_1$ is complete to $\{y', y\}$, and $x_2$ is adjacent to $x_1$ and some vertex in $N_G(w)\cap N(x)$. But then $G[N[x]\cup V(C)]\succcurlyeq\km{9}{6}$ by first contracting the edge $x_1x_2$ to a single vertex, and then $G[N[x]\setminus (\{x_1, x_2\}\cup N_G(w)\cap N(x))] $ to another single vertex, a contradiction. This proves that $7\le |C|\le 8$. Suppose $|C|=8$. Then (d) implies that $e(C)\ge 5\times 8-14=e(K_8)-2$ and so $C\in\km{8}{2}$, contrary to Claim~\ref{c:k72}. Thus $|C|=7$. By (d), we see that $C=K_7$ because $e(C)\ge 5\times 7-14=e(K_7)$. Note that each vertex in $V(C)\setminus\{w, w'\}$ is adjacent to at least four vertices in $N(x)$. It follows that there exists $x'\in N(x)$ such that $x'$ is adjacent to at least three vertices in $V(C)\setminus\{w, w'\}$. But then $G[N[x]\cup V(C)]\succcurlyeq\km{9}{6}$ by contracting $G[N[x]]\setminus x' $ to a single vertex, a contradiction. \end{proof}
To complete the proof, since $e(G)=5n-14$, we have $\delta(G)\le9$. By Claims~\ref{c:55}, \ref{c:dnot6} and \ref{c:dnot8}, let $x$ be a $9$-vertex in $G$. By Claim~\ref{c:comporder1}, $G \setminus N_G[x]$ is disconnected. Let $C$ be a component of $G \setminus N_G[x]$. We choose $x$ and $C$ so that $|C|$ is minimized. By Claim~\ref{c:comporder1}, $|C|\ge2$.
By Claim~\ref{c:comp9}, $C$ contains a $9$-vertex, say $y$, in $G$. Note that $N_G(x)\ne N(C)$ by Claim~\ref{c:disconnected}. Thus $N_G(x)\setminus N_G(y)\ne\emptyset$. Let $K$ be the component of $G \setminus N_G[y]$ containing $x$. Then $|K|\ge 2$ because $N_G(x)\setminus N_G(y)\ne\emptyset$. Note that $N_G(x)\cap N_G(y)\subseteq N(K)$, and every vertex in $N_G(x)\setminus N_G(y)$ belongs to $K$. Let $M$ be the set of vertices of $N_G(y)$ not adjacent to all other vertices of $N_G(y)$.
By Claim~\ref{c:disconnected}, $M\not\subseteq N(K)$.
Let $z \in M \setminus N(K)$.
Then $z \notin N_G(x)$, else $z\in N(K)$ because $x\in V(K)$. It follows that $z \in V(C)$.
Let $z'$ be a neighbor of $z$ in $G \setminus N_G[y]$.
Note that $z' \in \big(N_G(x)\setminus N_G(y)\big) \cup V(C)$. By Claims~\ref{c:dnot6}, \ref{c:58} and \ref{c:dnot8}, we see that $d_G(z)\ge9$ and so $d_G(z')\ge9$.
Suppose $z' \notin V(K)$. Then $z'\in V(C)$ because every vertex in $N_G(x)\setminus N_G(y)$ belongs to $K$. Let $C'$ be the component of $G \setminus N_G[y]$ that contains $z'$. Then $|C'|\ge2$ by Claim~\ref{c:comporder1}, and $C'$ is a proper subset of $C$, contrary to our choice of $x$ and $C$. This proves that $z' \in V(K)$, and so $z \in N(K)$, contrary to the choice of $z$. \medskip
This completes the proof of Theorem~\ref{t:exfun}.
\end{proof}
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\section{Introduction}
In modern mathematical treatments, we recognize the vector potential of a
gauge theory not as a globally defined function but as the section of a
gauge fiber bundle \cite{Wu:1976ge,Wu:1976qk}. In somewhat more
pedestrian terms, the vector potential can be defined as different
vector-valued functions in different coordinate patches of spacetime as long
as the distinct vector potentials are related by a gauge transformation on
the overlap of the coordinate patches (we will refer to this as ``gauge
patching'' of the vector potential). Gauge patching allows the description,
for example, of a constant magnetic field strength on a torus (the distinct
patches cover different unit cells) or the field of a magnetic monopole
(where the Bianchi identity $dF_2\neq 0$ can have no globally defined
solution). Analogs of both these examples for higher-rank form potentials
are important in string theory as harmonic background flux in compactifications
and higher-dimensional D-branes (and NS5-branes) that carry magnetic charges
for the fundamental potentials. The coupling between the magnetic current
and the potential is implicit in the patching and does not appear in the
action for the magnetic charge.
An alternative that displays the coupling of magnetic sources explicitly is to
double the number of gauge degrees of freedom by introducing dual field
strengths and corresponding potentials. In this so-called ``democratic''
formalism, the magnetic sources enter in the equations of motion (EOM) for the
dual potentials \cite{hep-th/0103233}.\footnote{Including auxiliary fields
to enforce duality constraints, the IIA and IIB supergravities are given
in a democratic formalism in \cite{Bandos:2003et,DallAgata:1998ahf}
respectively.}
The extra degrees of freedom are then removed by enforcing duality
conditions $F_{D-p-2}=\pm\star F_{p+2}$ at the level of the EOM. In the
democratic formalism, the action for magnetic charges includes the same
current-potential coupling as for electric charges, so the EOM of the magnetic
charges includes the dual field strengths. Nontrivial Bianchi identities
are enforced by the duality conditions. As a result, democratic formalisms
still require gauge patching around magnetic sources.
Because the gauge transformations in the transition regions between gauge
patches
are part of the definition of the potentials and also depend on the dynamical
magnetic currents, the gauge potentials are not independent degrees of
freedom --- they have a hidden dependence on the magnetic brane degrees of
freedom which should be considered explicit in the language of calculus of
variations. In quantum mechanical language, we need to separate the brane
and gauge degrees of freedom to serve as integration variables in the path
integral.
Interestingly, Dirac \cite{Dirac:1948um} provided a solution
in his early work on magnetic monopoles,\footnote{In fact, for monopoles,
\cite{Brandt:1977ks,Brandt:1976hk} showed that Dirac's formalism is
equivalent to defining potentials as sections in part by showing that some
gauge transformations move the Dirac string.}
which Teitelboim \cite{Teitelboim:1985yc}, Bandos \textit{et al.}
\cite{Bandos:1997gd},
and Lechner and co-workers
\cite{hep-th/0103161,hep-th/0007076,hep-th/0107061,hep-th/0203238,hep-th/0302108,hep-th/0402078,hep-th/0406083}
extended to magnetic $p$-branes.
The key idea is as follows:
Consider a field strength $\t F_{p+2}$ satisfying Bianchi identity
$d\t F_{p+2}=\beta\star j_{D-p-3}$ with $\beta$ a sign convention. Any conserved
current can be written as $\star j_{D-p-3}=d\star J_{D-p-2}$,\footnote{Assuming
there
are no harmonic forms on the full noncompact spacetime.} so a field strength
defined as $\t F_{p+2}\equiv dC_{p+1}+\beta \star J_{D-p-2}$ satisfies the Bianchi
identity; in this way, the magnetic coupling appears in the action.
There is actually one additional subtlety when the branes fill
all noncompact dimensions; $\star j_{D-p-3}=d\star J_{D-p-2}$ on a compact
manifold is inconsistent when there is net local charge,
so we must define instead $\star j_{D-p-3}-\star j_{D-p-3}^*=d\star J_{D-p-2}$,
where
$j_{D-p-3}^*$ is some specified reference current (see \cite{arXiv:1807.07401}
for details in the case of magnetic monopoles). Now, $C_{p+1}$ is patched
around the reference current, so dynamics of $j_{D-p-3}$ do not affect the
potential. The alert reader may note that a Gauss law constraint means that
the net charge must vanish on a compact manifold, but in string theory
charge may
dissolve in background flux, so the net charge of local objects need not
vanish. Reference currents are necessary to account for this fact.
There are a variety of choices for the form $J$ for a given magnetically
charged $p$-brane with worldvolume $\ensuremath{\mathcal{M}}$ and current $j_\ensuremath{\mathcal{M}}$. As described by
\cite{Teitelboim:1985yc}, we can consider a ``Dirac $(p+1)$-brane'' with
worldvolume $\ensuremath{\mathcal{N}}$ of boundary $\partial\ensuremath{\mathcal{N}}=\ensuremath{\mathcal{M}}-\ensuremath{\mathcal{M}}^*$. Then $J_\ensuremath{\mathcal{N}}$, the current of the
Dirac brane, satisfies $d\star J_\ensuremath{\mathcal{N}}=\star(j_\ensuremath{\mathcal{M}}-j_{\ensuremath{\mathcal{M}}^*})$. As we will see
below, both the brane and Dirac brane currents are delta-function supported.
A less singular option for $J$, used by
\cite{hep-th/0107061,hep-th/0203238,hep-th/0302108,hep-th/0402078,hep-th/0406083},
is given by the Chern kernel \cite{Chern1944,Chern1945},
which diverges only as a power law
near the current $j_\ensuremath{\mathcal{M}}$. In the following, we will mostly remain agnostic
about the nature of $J$, as our results are independent of this choice, but
we will often use the language of Dirac branes to be concrete and refer to
$J$ as the Dirac brane current as shorthand. It is also
worth noting that, even fixing to Dirac branes or Chern kernels, $J$ is
arbitrary up to its co-derivative, but the field strength $\t F$ is invariant.
Our goal is to extend this formalism to D-branes in the IIA and
IIB string theories, writing these theories in terms of Ramond-Ramond
(RR) potentials $C_{p+1}$
for $p\leq 3$. While \cite{hep-th/0406083} have already considered
(arbitrary intersections of) D-branes in the IIB theory by means of an anomaly
argument, we present a new derivation via duality from the democratic
formulation. In fact, \cite{hep-th/0406083} found several
new brane-induced terms in the IIB supergravity action, beyond the standard
coupling between currents and potentials, ie, the Wess-Zumino (WZ) action
for the D-branes. One set of new terms couples the Dirac brane
currents of magnetic branes to those of electric branes;
\cite{Deser:1997se} first
identified the analogous term in Maxwell electrodynamics. These terms are
related to charge quantization. Further, \cite{hep-th/0406083} found
a correction to the bulk Chern-Simons (CS) term involving Dirac brane currents.
We will emphasize how these terms are required for consistency of the
EOM and for gauge invariance. A key point in this story
is that D-brane currents are not conserved due to the WZ couplings,
but CS terms in the EOM and Bianchi identities cancel the anomaly via an
inflow argument \cite{hep-th/9512219,hep-th/0201221}; we give a detailed
accounting of the anomaly inflow in a general theory similar to that of
the RR forms. The necessity of reference currents also forces us to explain
what it means to integrate over a gauge-patched potential.
The plan of this paper is as follows. In section \ref{s:inflow}, we
demonstrate the anomaly inflow argument of \cite{hep-th/9512219,hep-th/0201221}
for a class of theories of form potentials which includes the RR potentials
of both type II supergravities. We pay particular attention to how the
inflow argument requires specific relations between various conventional
coefficients in the EOM and Bianchi identity and confirm the consistency
of the Dirac brane current with the inflow. Then
we consider an action principle for the generalized
theory of section \ref{s:inflow} and introduce the modified CS term in
section \ref{s:actions} through a novel derivation.
In section \ref{s:integration},
preliminary to our discussion of the supergravity actions, we find a
prescription for integrating potentials that are gauge patched around
magnetic sources, focusing on RR potentials in the 10D supergravities.
We then give a novel derivation of the new terms in the type IIB supergravity
action that were first described in \cite{hep-th/0406083} in section
\ref{s:typeIIB}. We also eliminate
redundant degrees of freedom in the self-dual 4-form potential, leading to
a noncovariant action for the RR fields and discuss gauge invariance.
Finally, in section \ref{s:typeIIA}, we derive the IIA supergravity action
including the Romans mass term \cite{Romans:1985tz} and D-branes for the
first time. It has long been known that D8-branes
source the Romans mass, and we show for the first time
how the corresponding Dirac 9-brane
currents reproduce the additional couplings of the massive IIA supergravity.
We also propose that additional WZ couplings on D-branes in the
massive theory \cite{hep-th/9603123,hep-th/9604119}
are a consequence of the Dirac brane currents and conjecture the presence of
other new WZ couplings on type IIA D-branes. We conclude with a brief
discussion of future directions and give our conventions and some
auxiliary results in the appendices.
A forthcoming companion paper \cite{freynew}
will demonstrate how Dirac's formalism
separates the brane and gauge degrees of freedom in a form useful for
dimensional reduction.
\section{Currents and anomaly inflow}\label{s:inflow}
In this section, we describe general brane currents and when they are not
conserved. We then see how anomaly inflow determines the coefficients of
several terms in the EOM and Bianchi identities and verify that the inflow
mechanism is always consistent with the Dirac brane formalism. Finally,
we apply our results to the 10D type II supergravity theories, making
explicit the allowed, self-consistent sign conventions.
\subsection{Currents and anomalies}\label{s:currents}
Mathematically speaking, currents are dual vectors to differential forms
(see \cite{griffithsharris} for a review), which includes form integration
over submanifolds of the appropriate dimensionality. In this respect, the
WZ action of a $p$-brane is the sum of $n$-currents acting on $n$-form
potentials:
\begin{eqnarray}
S_{WZ}&=&\sum_{q=0}^{p+1}\Gamma_{\ensuremath{\mathcal{M}}_{p+1},\ensuremath{\mathcal{G}}_q^{(p)}}(C_{p+1-q})\label{Ecouplings}\\
&=&\mu_p \int_\ensuremath{\mathcal{M}} \left(\sum_{q=0}^{p+1} [C_{p+1-q}]\wedge\ensuremath{\mathcal{G}}_q^{(p)}\right)
=\mu_p\int_\ensuremath{\mathcal{M}}\, [C]\wedge\ensuremath{\mathcal{G}}^{(p)}, \nonumber\end{eqnarray}
where $\ensuremath{\mathcal{M}}_{p+1}$ is the worldvolume,
$\ensuremath{\mathcal{G}}_q$ are a series of worldvolume $q$-forms defined on the brane, and
$\mu_p$ is the $p$-brane charge.
These may be defined to include pullbacks of spacetime forms.
After the second equality, we have defined $C$ and $\ensuremath{\mathcal{G}}^{(p)}$ as formal
sums over the
various rank forms [we will suppress the superscript $(p)$ on $\ensuremath{\mathcal{G}}$ when the
dimensionality or type of brane is clear from context].
Of course, the WZ action (\ref{Ecouplings}) only describes a brane's electric
couplings to the gauge fields. This is sufficient in a democratic formulation
but potentials of all ranks do not exist when only independent degrees of
freedom are included. As a result, a spacetime description of currents is
crucial. Since any dual vector $\Gamma_n$ is uniquely identified with a
differential form $j_n$ by the inner product
\beq{innerprod} \Gamma_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}(C_n)\equiv \int C_n\wedge \star j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}} \end{equation}
with the integration over spacetime, we can identify the $j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}$ as the
brane currents. Then the EOM and Bianchi identity
\begin{eqnarray}
d\star\t F_{p+2}&=&(-1)^{D-p-1}\star j_{p+1}+\cdots\quad\text{and}\nonumber\\
d\t F_{p+2} &=& \beta_{p}\star j_{D-p-3}+\cdots\label{eombianchi} \end{eqnarray}
give the electric and magnetic couplings, where $\beta_{p}$ is a sign chosen
by convention.\footnote{The sign on the current in the EOM is determined by
the canonical action
\begin{eqnarray}
S&=& \int d^Dx\sqrt{-g}\sum_p\left[-\frac{1}{2} |\t F_{p+2}|^2+
C_{p+1}\cdot j_{p+1}\right]\label{action1}\\
&=&\int \sum_p(-1)^{p(D-p)+1}\left[\frac 12 \t F_{p+2}\wedge\star\t F_{p+2}
+(-1)^D C_{p+1}\wedge \star j_{p+1}\right] .\nonumber\end{eqnarray}}
The current $j_{p+1}=\sum j_{\ensuremath{\mathcal{M}}_{p+q+1},\ensuremath{\mathcal{G}}_q}$ with the sum over all branes.
(On the flip side, all the currents of the same brane can be written as a
formal sum $j_\ensuremath{\mathcal{M}}=\sum_q j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}_q}$.)
Naively, the current for a $(p+q)$-brane with worldvolume form $\ensuremath{\mathcal{G}}_q$ is
\beq{branecurrents}
j^{\mu_1\cdots\mu_{p+1}}_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}(x) = \mu_{p+q}\int_{\ensuremath{\mathcal{M}}_{p+q=1}}\hat dX^{\mu_1}\wedge\cdots
\hat dX^{\mu_{p+1}}\wedge\ensuremath{\mathcal{G}}_q\,\delta^D(x,X) ,
\end{equation}
where $X^\mu$ are the embedding coordinates. This may be modified in
topologically nontrivial situations, such as when the brane in question is
actually the nontransversal intersection of two other branes. Nontransversal
intersections are the focus of
\cite{hep-th/9710206,hep-th/0402078,hep-th/0406083}.
As our goal is to emphasize writing the action in terms of independent
degrees of freedom, we base our results on the naive current
(\ref{branecurrents}); the adaptation to nontransversal intersections follows
from \cite{hep-th/0406083}.
The anomalies we consider are local in nature, so they must cancel
pointwise. While related, we emphasize that these anomalies are
separate from global anomalies that forbid certain brane configurations,
such as the Freed-Witten anomaly \cite{hep-th/9907189} or the magnetic D-brane
Gauss law constraint that $H_3$ integrate to zero over the worldvolume
(see \cite{hep-th/0201029,hep-th/0505208}). From the perspective of the WZ
action (\ref{Ecouplings}), they arise from a gauge variation
$\delta C=d\lambda$. Integrating the pullback by parts yields a term from the
brane boundary and one from $\hat d\ensuremath{\mathcal{G}}$. In some cases, these can cancel
between branes; for example, a D1-brane can end on a D3-brane, providing
a magnetic source for the D3-brane gauge field. The two anomalous terms cancel
in the summed current $j_2$.\footnote{In fact, this configuration can also
be described as a BIon solution of the D3-brane theory, in which case
there is manifestly no anomaly.}
However, if $\hat d\ensuremath{\mathcal{G}}$ contains the pullback of a
spacetime form, the cancellation must be by inflow associated with a
modified gauge transformation $\delta C$ as occurs in string theory.
From a spacetime point of view, we can consider the divergence of the brane
current
\begin{widetext}\begin{eqnarray}
(\star d\star j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}})^{\mu_1\cdots\mu_{p}}&=&(-1)^{(p+1)(D-p)}\mu_{p+q}
\int_\ensuremath{\mathcal{M}} \nabla_\nu
\left[\delta^D(x,X)\hat d X^\nu\wedge\hat dX^{\mu_1}\wedge\cdots \hat dX^{\mu_p}\wedge\ensuremath{\mathcal{G}}_q\right]
\nonumber\\
&=&(-1)^{D(p+1)+1}\mu_{p+q}\int_\ensuremath{\mathcal{M}} \hat d\left[\delta^D(x,X)\hat dX^{\mu_1}\wedge \cdots
\hat dX^{\mu_{p}}\wedge \ensuremath{\mathcal{G}}_q\right]\nonumber\\
&&+(-1)^{D(p+1)+p}\mu_{p+q}\int_\ensuremath{\mathcal{M}} \hat d X^{\mu_1}\wedge\cdots\hat dX^{\mu_p}\wedge\hat d\ensuremath{\mathcal{G}}_q\,
\delta^D(x,X)\ .
\label{divcurrent}\end{eqnarray}\end{widetext}
In an arbitrary Lorentzian metric, $\delta^D(x,X)$ is the biscalar
distribution, and the covariant derivative acts with respect to the
spacetime position $x$, but the derivative switches to the partial with
respect to $X$ as described in \cite{arXiv:1102.0529}.
We therefore see that the brane currents are not conserved:
\beq{nonconservation}
d\star j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}=(-1)^{D+q}\star\t\jmath_{\partial\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}-(-1)^{D}\star j_{\ensuremath{\mathcal{M}},\hat d\ensuremath{\mathcal{G}}},\end{equation}
where $\t\jmath$ is a $p$-form current for the boundary of the worldvolume.
Henceforth in this paper, we will assume that the boundary contributions
cancel with some of the worldvolume $\hat d\ensuremath{\mathcal{G}}$ contributions, so we will ignore
those terms from here out, returning to them in the companion paper
\cite{freynew}.
Consider then a single brane (ie, $\partial\ensuremath{\mathcal{M}}=0$) with $\hat d\ensuremath{\mathcal{G}}$ a
pullback of a nontrivial spacetime form $H_{r+1}$.
We will find that the anomalies cancel
when $\hat d\ensuremath{\mathcal{G}}_q = \sum_r \eta_{p,q,r} [H_{r+1}]\ensuremath{\mathcal{G}}_{q-r}$, where $H_{r+1}$ is
prototypically the field strength of a potential that does not
couple to the branes, and $\eta_{p,q,r}$ is some proportionality constant.
Then, using (\ref{idents}),
\begin{eqnarray}
\star j_{\ensuremath{\mathcal{M}},[H_{r+1}]\ensuremath{\mathcal{G}}_{q-r}} &=& \star\left(j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}_{q-r}}\cdot H_{r+1}\right)
\label{pullback2wedge}\\
&=&(-1)^{(r+1)(D-r-1)}H_{r+1}\wedge\star j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}_{q-r}} .\nonumber
\end{eqnarray}
We will find that $\eta$ is independent of the rank $q$ of the worldvolume
forms, so the anomaly for the total brane current is conveniently written as
\beq{nonconservation2}
d\star j_{p+1}= \sum_r (-1)^{r(D-r)}\eta_{p,r}H_{r+1}\wedge\star j_{p+r+1} .\end{equation}
\subsection{Anomaly inflow}\label{s:eombianchiinflow}
We consider a set of potentials $C_{p+1}$ (the RR potentials in string theory)
and corresponding gauge-invariant field strengths $\t F_{p+2}$, with an
additional set of field strengths
$H_{r+1}=dB_r$ assumed closed with pullbacks $[H_{r+1}]$ that appear in
$\hat d\ensuremath{\mathcal{G}}$ for some branes (with this coupling, those branes carry an electric
current for $B_r$, but $H_{r+1}$ remains closed).
The classical anomaly discussed in the previous section then
appears in the current whenever $H_{r+1}\neq 0$, whether it is a
topologically nontrivial flux or due to another brane source. It is a simple
generalization to add an extra index to $C$ or $B$ to have more than one
potential at each rank. Our discussion of the inflow is similar to comments
by \cite{hep-th/9512219} for M-theory and is implicit in \cite{hep-th/0406083}
for IIB string theory; \cite{hep-th/0201221}
gives a worldvolume argument for string theory. We are not
aware of a discussion in this full class of theories.
The general EOM for $C_{p+1}$ (to first order in $\t F_{p+2}$) has the structure
\begin{eqnarray}
d\star\t F_{p+2}&=&(-1)^{D-p-1}\star j_{p+1}\nonumber\\
&&+\sum_{r=0}^{D-p-3}\left[\alpha_{p,r} (\star\t F_{p+r+2})\wedge H_{r+1}\right.
\nonumber\\
&&\left.+ \t\alpha_{p,r}\t F_{D-p-r-2}\wedge H_{r+1}\right] ,\label{eomF2}\end{eqnarray}
where $\alpha,\t\alpha$ are constants. Meanwhile, the Bianchi identity is
\beq{bianchiF2}
d\t F_{p+2} = \beta_p \star j_{D-p-3}+\sum_{r=0}^{p+1}\t\beta_{p,r}\t F_{p-r+2}\wedge
H_{r+1} ;\end{equation}
$\beta_p$ is a sign convention, which can be chosen independently for
each field strength. For now, we treat the $\alpha,\t\alpha,\beta,\t\beta$
as independent constants, though there are relations among them in a
Lagrangian formulation of the theory; other conditions following from gauge
invariance are discussed in appendix \ref{a:invariance}.
The $\t\alpha$ terms follow from
CS terms in the action, while the $\alpha$ and $\t\beta$ terms arise from
terms in the field strength. To distinguish them from CS terms, we will
refer to the $\alpha$ and $\t\beta$ terms as ``transgression'' terms.
Theories with this structure include of course the type II supergravities
and also the dimensionally reduced theory of gravity and form potentials
on a torus, for example.
Current (non)conservation is related to the integrability conditions obtained
by taking the exterior derivative of the EOM and Bianchi identity.
For the EOM, we have
\begin{eqnarray}
d\star j_{p+1}&=& \sum_r \left[-(-1)^r \alpha_{p,r}+(-1)^{D-p}\t\alpha_{p,r}
\beta_{D-p-r-4}\right]\nonumber\\
&&\times\star j_{p+r+1}\wedge H_{r+1},\label{eomintegrability}\end{eqnarray}
leaving off terms that are independent of the brane currents.\footnote{These
must vanish separately. We discuss how this occurs and the relation to
gauge invariance in appendix \ref{a:invariance}.}
In other words, we see that the derivatives of the CS and transgression terms
localize on the currents as needed for an anomaly inflow.
Comparing to equation (\ref{nonconservation2}), we find
\beq{eominflow}
\eta_{p,r}=-(-1)^{D+(p+1)(r+1)}\alpha_{p,r}-(-1)^{pr}\t\alpha_{p,r}\beta_{D-p-r-4}\end{equation}
since the anomaly must cancel when only one $H_{r+1}$ background is nonvanishing.
In fact, this holds for any case where only one brane contributes to the
current, so we see that $\eta$ is independent of the worldvolume form rank.
Similarly, the Bianchi identity yields
\beq{bianchiintegrability}
d\star j_{D-p-3} = -\beta_p \sum_r \t\beta_{p,r}\beta_{p-r}\star j_{D-p+r-3}\wedge H_{r+1}
.\end{equation}
Cancellation of the anomaly then requires
\beq{bianchiinflow}
\eta_{D-p-4,r}=(-1)^{r(D-p)+p}\beta_p\beta_{p-r}\t\beta_{p,r} .
\end{equation}
Again, we see that $\eta$ is independent of $q$.
\subsection{Dirac brane currents}\label{s:diracbranes}
We will now see how Dirac brane currents in the field strengths fit into
the Bianchi identities using the constraint (\ref{bianchiinflow}).
Our discussion extends similar results in \cite{hep-th/0406083}.
To start, we need to consider how to extend the worldvolume form \ensuremath{\mathcal{G}}\ from the
brane worldvolume to the Dirac brane or, in the case $J$ represents a Chern
kernel, the entire spacetime. The key point is to choose the reference brane
worldvolume $\ensuremath{\mathcal{M}}^*$ homotopic to \ensuremath{\mathcal{M}}\ (so \ensuremath{\mathcal{N}}\ is continuous for a Dirac brane).
The extension of \ensuremath{\mathcal{G}}\ depends on its form. For D-branes, we will be
concerned primarily with the case that $\ensuremath{\mathcal{G}}=\ensuremath{\mathcal{G}}([B_2],\hat dA_1)$, where $A_1$
is the worldvolume gauge field. In this case, we continue to take $B_2$ as
given by the spacetime NSNS form (pulled back to \ensuremath{\mathcal{N}}\ as appropriate).
For the gauge field, we choose a fixed $A_1^*$ on $\ensuremath{\mathcal{M}}^*$ and an extension
$\b A_1$ to \ensuremath{\mathcal{N}}\ or spacetime that pulls back to $A_1$ on \ensuremath{\mathcal{M}}\ and $A_1^*$ on
$\ensuremath{\mathcal{M}}^*$. Then the Dirac brane current takes the form of (\ref{branecurrents})
with $\ensuremath{\mathcal{G}}$ promoted to the extension $\b\ensuremath{\mathcal{G}}$ and $X^\mu$ replaced by the
embedding coordinates $Y^\mu$ of \ensuremath{\mathcal{N}}. For a Chern kernel of a $(p+q)$-brane,
$\star J_{\b\ensuremath{\mathcal{G}}}\equiv (-1)^{(p+1)(q+1)}(\star J)\b\ensuremath{\mathcal{G}}$ (a similar formula holds
for Dirac brane currents when $\b\ensuremath{\mathcal{G}}$ is the pullback of a spacetime form
by virtue of (\ref{idents})).
Since the Dirac brane contribution to the field strength is given by the
Dirac brane's current, equation (\ref{nonconservation}) applies in the form
\beq{nonconservation3}
d\star J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{G}}} =(-1)^{D+q}\star\left(j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{G}}}-j_{\ensuremath{\mathcal{M}}^*,\ensuremath{\mathcal{G}}}\right)-
(-1)^D\star J_{\ensuremath{\mathcal{N}},\b d\b\ensuremath{\mathcal{G}}} .\end{equation}
Therefore, to cancel the dynamical current $j_{D-p-3}=\sum j_{\ensuremath{\mathcal{M}}_{D-p+q-1},\ensuremath{\mathcal{G}}_q}$
(summed over all branes) in the Bianchi identity (\ref{bianchiF2}),
we should define
\beq{transgression}
\t F_{p+2}=dC_{p+1}+(-1)^D\beta_p\star J_{D-p-2}
+\sum_{r=0}^{p+1} \t\beta_{p,r}C_{p-r+1}\wedge H_{r+1} ,\end{equation}
where the Dirac brane current is a sum over the corresponding Dirac branes
\beq{diracbranecurrent}
J_{D-p-2} = \sum (-1)^q J_{\ensuremath{\mathcal{N}}_{D-p+q-2},\b\ensuremath{\mathcal{G}}_q} \end{equation}
and $C_{p+1}$ includes the potential for the reference current for worldvolumes
$\ensuremath{\mathcal{M}}^*$. Then the current for the Dirac brane associated with a given physical
brane can be written as a formal sum $J_\ensuremath{\mathcal{N}}= \sum_q (-1)^q J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{G}}_q}$.
With this definition for the total Dirac brane current, the divergence
(\ref{nonconservation3}) and condition (\ref{bianchiinflow}) give
\begin{widetext}\begin{eqnarray}
d\star J_{D-p-2}&=&(-1)^D\star(j_{D-p-3}-j^*_{D-p-3}) -\beta_p\sum_{q,r}
(-1)^{q+(r+1)(p-r-1)}\t\beta_{p,r}\beta_{p-r}H_{r+1}\wedge\star J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{G}}_{q-r}}\nonumber\\
&=&(-1)^D\star(j_{D-p-3}-j^*_{D-p-3})+\beta_p\sum_r\t\beta_{p,r}\beta_{p-r}
\star J_{D-p+r-2}\wedge H_{r+1} .
\label{diracdiv}
\end{eqnarray}
Since $C_{p+1}$ contains the potential for the reference current,
\begin{eqnarray}
d\t F_{p+2} &=& \beta_p\star j_{D-p-3}+\sum_r \t\beta_{p,r}\left(dC_{p-r+1}+\sum_\ell
\t\beta_{p-r,\ell}C_{p-r-\ell+1}\wedge H_{\ell+1}+\beta_{p-r}\star J_{D-p+r-2}\right)
\wedge H_{r+1}\nonumber\\
&=& \beta_p\star j_{D-p-3}+\sum_r \t\beta_{p,r}\t F_{p-r+2}\wedge H_{r+1} .
\label{bianchireduced}\end{eqnarray}\end{widetext}
In other words, the co-derivative of the Dirac brane current is precisely
consistent with the appearance of Dirac brane currents in the transgression
term.
\subsection{Type II supergravity conventions}\label{s:sugraconventions}
We can now apply our results to set limits on possible sign conventions
in the 10D type II supergravities. Some of the restrictions we find below
(such as the alternating of signs in the duality conditions for the
democratic formulation) appear implicitly in the literature (see for example
the discussion of conventions in appendix A of \cite{arXiv:1609.00385}),
but we are not
aware of an explicit derivation from first principles.
While the D-brane WZ action identifies
\beq{DbraneG}
\ensuremath{\mathcal{G}}=e^{\ensuremath{\mathcal{F}}}\wedge
\sqrt{\frac{\hat A(4\pi^2\alpha' R_T)}{\hat A(4\pi^2\alpha' R_N)}} ,
\end{equation}
where $ \ensuremath{\mathcal{F}}=2\pi\alpha' F_2+\eta[B_2]$, $\hat A$ is the A-roof genus, and $R_T,R_N$
are the tangent and normal bundle curvatures, we will not consider the
$\alpha'$ corrections, instead restricting to $\ensuremath{\mathcal{G}}=\exp\ensuremath{\mathcal{F}}$. See
\cite{hep-th/0406083} for more on $\alpha'$ corrections in the IIB theory.
Both type II supergravities in this approximation have a single background
field strength $H_3=dB_2$ and, following from the above, a common sign
choice $\eta=\eta_{p,2}$ appearing in $\ensuremath{\mathcal{F}}$ for all $p$. Here, we will also
follow the typical choice of setting all $\t\beta_{p,2}\equiv\t\beta$, a
single sign choice for the transgression terms in each theory.
Starting with the IIB theory with only potentials $C_{p+1}$ for $p\leq 3$,
the EOM and Bianchi identities are
\begin{eqnarray}
d\star\t F_1&=&\star j_0+\alpha_{-1}\star\t F_3\wedge H_3,\nonumber\\
d\t F_1&=&\beta_{-1}\star j_8,\nonumber\\
d\star\t F_3&=&\star j_2+(\alpha_1\star\t F_5+\t\alpha_1\t F_5)\wedge H_3,\nonumber\\
d\t F_3&=&\beta_1\star j_6+\t\beta \t F_1\wedge H_3,\nonumber\\
d\star\t F_5&=&\star j_4+\t\alpha_3\t F_3\wedge H_3 ,\nonumber\\
d\t F_5&=&\beta_3\star j_4+\t\beta \t F_3\wedge H_3 .\label{IIBeqns}\end{eqnarray}
The appearance of both transgression and CS terms for the $\t F_3$ EOM is due
to the self-duality condition on $\t F_5$.
The constraint (\ref{eominflow}) tells us immediately that
$\eta=-\alpha_{-1}=-\t\alpha_3\beta_1=-\alpha_1-\t\alpha_1\beta_3$.
Meanwhile, the Bianchi
identities are consistent with (\ref{bianchiinflow}) for
$\eta=-\beta_{-1}\beta_1\t\beta =-\beta_{1}\beta_3\t\beta$. Finally, the
transgression terms in the EOM and Bianchi identity are related through
variation of the Lagrangian, leading to equation (\ref{coeffs}), which
implies $\alpha_{-1}=-\t\beta$ and $\eta=\t\beta$.
All told, there are two independent
sign choices, $\t\beta$ and $\beta_3$, with the signs in the Bianchi
identities alternating $\beta_3=-\beta_1=\beta_{-1}$.
The type IIA supergravity (including a possible mass term) has
\begin{eqnarray}
d\star\t F_0&=&0,\quad d\t F_{0}=\beta_{-2}\star j_9\nonumber\\
d\star\t F_2 &=&-\star j_1+\alpha_0\star\t F_4\wedge H_3 ,\quad d\t F_2= \beta_0
\star j_7+\t\beta\t F_0\wedge H_3\nonumber\\
d\star \t F_4&=&\star j_4+\t\alpha_2\t F_4\wedge H_3,\quad d\t F_4=
\beta_2\star j_5+\beta\t F_2\wedge H_3 .\label{IIAeqns}\end{eqnarray}
As in the IIB case, we find $\eta=\alpha_0=-\t\alpha_2\beta_2$ and
$\eta\t\beta=\beta_{-2}\beta_0=\beta_0\beta_2$. Derivation of the transgression
terms from the action gives also $\alpha_0=-\t\beta$, which tells us that
$\eta=-\t\beta$ and $\beta_0=-\beta_{-2}=-\beta_2$. There are once again
two independent sign choices, with the others determined.
In either supergravity, the democratic formulation has
\begin{eqnarray}
d\star\t F_{p+2} &=&(-1)^{p+1}\star j_{p+1}+\alpha_p \star\t F_{p+4}\wedge H_3 ,
\nonumber\\
d\t F_{p+2}&=&\beta_p\star j_{7-p}+\t\beta \t F_p\wedge H_3\label{democratic}\end{eqnarray}
for $-2\leq p\leq 8$ ($\t F_{p<0}\equiv 0$).
By comparison to the Bianchi identities above,
the duality relations must be $\star\t F_{D-p-2}=\mp \beta_p\t F_{p+2}$ (in IIA
and IIB respectively) for $p\leq 3$; in particular, $C_4$ satisfies the
self-duality relation $\star\t F_5=\beta_3\t F_5$.
Since the coefficients $\beta_p$ alternate signs in each
theory, so do the duality relations. Since the D-brane charge (vs antibrane)
is determined by the WZ coupling to $C_{p+1}$ in the democratic formulation,
these alternating signs mean that D$p$-branes with $p\geq 3$ enter the
Bianchi identities with alternating signs as well. The signs can only be
chosen the same if the transgression coefficients $\t\beta_p$ are distinct
for the different $\t F_{p+2}$. Finally, since the Bianchi identities for the
higher-rank field strengths have the same form, we have $\beta_p\beta_{p+2}=-1$
(i.e., alternating signs) for all $p$.
\section{Brane-modified Chern-Simons action}\label{s:actions}
Chern-Simons terms are familiar from the actions of both 10D type II
supergravities and the 11D supergravity. We emphasize here that the presence
of D-branes necessarily modifies those CS terms; by extension (through
duality, etc), M-branes in 11D and NS5-branes in 10D must also modify them.
The CS term modifications were first pointed out by \cite{hep-th/0406083};
here we give a new, simple, physically-motivated derivation in the theory
of the previous section, which we can apply to the 10D supergravities later.
The action
\begin{eqnarray}
S&=&\frac{1}{2\kappa_0^2}
\int \sum_p(-1)^{p(D-p)+1}\left[\frac 12 \t F_{p+2}\wedge\star\t F_{p+2}\right.
\nonumber\\
&&\left. +(-1)^D C_{p+1}\wedge \star j_{p+1}\vphantom{\frac 12}
\right]+S_{CS},\label{action}\end{eqnarray}
with Chern-Simons terms
\begin{eqnarray}
S_{CS} &=& \frac{1}{2\kappa_0^2}\sum_{p,r}\int \left[\gamma_{p,r}C_{p+1}\wedge
\t F_{D-p-r-2}\right.\nonumber\\
&&\left.+\t\gamma_{p,r}(\star J_{D-p-2})\wedge C_{D-p-r-3}\vphantom{\t F}
\right]\wedge H_{r+1}\label{CSaction}
\end{eqnarray}
reproduces the $C_{p+1}$ EOM (\ref{eomF2}), assuming that the
field strength is defined by equation (\ref{transgression}) with the Dirac
brane current (\ref{diracbranecurrent}). $\gamma_{p,r},\t\gamma_{p,r}$ are
some set of constants related to the EOM coefficients $\t\alpha_{p,r}$.
We have ignored kinetic terms for the closed field strengths $H_{r+1}$ as well
as the gravitational sector.
The canonical coupling between the potential and electric current in
(\ref{action}) determines the sign of the source term in (\ref{eomF2}), and
it also gives the WZ action for all the branes (i.e., there is no need for
an additional WZ action on the branes) up to a factor of the gravitational
coupling $2\kappa_0^2$, which can be accommodated by rescaling the brane
charges.
We discuss the invariance of this action and the field strength
(\ref{transgression}) under the gauge transformations of $C_{p+1}$ in the
absence of brane sources
in appendix \ref{a:invariance}, arriving at constraints
(\ref{gaugeconstraint1},\ref{gaugeconstraint4}), which also guarantee
that the Bianchi identity and EOM depend only on $\t F_{p+2}$ rather than
$C_{p+1}$ (in the absence of currents).
We also find the relationships (\ref{coeffs}) between the
EOM coefficients $\alpha_{p,r},\t\alpha_{p,r}$ and $\t\beta_{p,r},\gamma_{p,r}$
in the appendix.
While the $\gamma_{p,r}$ terms in $S_{CS}$ are familiar from, for example, the 10D
supergravities, the $\t\gamma_{p,r}$ terms require some explanation.
Without them, the Dirac brane currents are absent from the field strengths
in the $\t\alpha_{p,r}$ terms of the EOM. That would leave the EOM dependent
on the Dirac brane worldvolumes \ensuremath{\mathcal{N}}\ including the arbitrary reference branes
$\ensuremath{\mathcal{M}}^*$, which would clearly be inconsistent (in fact, that would be a
violation of gauge invariance in the magnetic context). So we consider
\begin{eqnarray}
\frac{\delta S_{CS}}{\delta C_{p+1}}&=& \sum_r \gamma_{p,r}\t F_{D-p-r-2}\wedge H_{r+1}
\label{vary1}\\
&&+\sum_r (-1)^{p(D-p-r)}\gamma_{D-p-r-4,r}\left(\t F_{D-p-r-2}\right.\nonumber\\
&&\left.-(-1)^D\beta_{D-p-r-4}\star J_{p+r+2}\right.\nonumber\\
&&\left.\vphantom{\t F} +(-1)^{(p+1)(D-p-r)}\t\gamma_{D-p-r-4,r}
(\star J_{p+r+4})\right)\wedge H_{r+1}\nonumber\end{eqnarray}
assuming the coefficients obey (\ref{gaugeconstraint4}). Therefore, we
require $\t\gamma_{p,r}=(-1)^{D-p}\beta_p\gamma_{p,r}$ to ensure that the EOM
are written only in terms of the field strengths.
We will later derive these and other new brane-induced terms for the type II
supergravities.
\section{Integrating patched potentials}\label{s:integration}
It is not immediately clear what it means to integrate over a quantity
including a potential with gauge patching because the potential is not
single valued in the overlap of coordinate patches: Either gauge is physically
acceptable. As a result, many authors, including
\cite{hep-th/9605033,hep-th/9710206,hep-th/0406083}
have suggested writing potential-current
couplings in terms of the gauge-invariant field strength. However, if we
attempt to write an action following that approach without the explicit
appearance of the potentials, the EOM will contain the arbitrary reference
currents $j^*_{p+1}$ (for electric sources).
Consider, for example, the action (\ref{action}) above
with the replacement $C_{p+1}(\star j_{p+1})\to(-1)^p\t F_{p+1}(\star J_{p+2})$.
Even ignoring transgression terms by setting $H_{r+1}\to 0$, the variation
of this term is $\delta C_{p+1}\wedge \star (j_{p+1}-j_{p+1}^*)$.
Here we give what is to our knowledge the first description of how to carry
out spacetime integrals including gauge-patched potentials.
The key idea is already present in \cite{Wu:1976qk}, who gave a prescription
for integrating the vector potential of Maxwell theory along a charged
particle worldline in the presence of a monopole. In sketch form our new
prescription for integration against other forms over spacetime is as
follows: Pick an
arbitrary division where the integrated potential switches from one gauge
to another. Then design the integral to be invariant under changes of
the division, a choice closely related to gauge invariance.
Since we are integrating over spacetime, we also have to
exclude the locus of magnetic charge, where the potential is undefined.
For simplicity, we work with RR potentials in string theory. Specifically,
we consider a set of potentials $C_{p+1}$ for $p$ either even or odd (as in
the IIA or IIB supergravity respectively).
Written as a formal sum of forms, the gauge-invariant field strengths are
$F=dC+\t\beta C H_3$ and the gauge transformations are
$\delta C=d\chi-\t\beta \chi H_3$, where $\t\beta$ is a single sign choice.
Depending on the application, the formal sum $C$ could include $p=-1$ to $8$
as in a democratic formulation of the supergravity or only a subset (e.g.,
$p=0,2$ in type IIA supergravity). Taking $p=0,H_3=0$, our prescription
also applies to standard electrodynamics. The field strengths do not
include Dirac branes, and the Bianchi identities are
$dF=\star (\beta j^*)+\t\beta F H_3$, where
$(\beta j^*)=\sum_p\beta_p j_{p+1}^*$ with $\beta_p$ a distinct sign choice
for each potential. Our results apply to any gauge-patched potential,
meaning $j^*$ could represent dynamical currents, but we will take $j^*$ to
be fixed reference currents. It is worth recalling that a high-dimension brane
with a worldvolume gauge field or in the presence of nonvanishing $B_2$
contributes to lower-rank currents, so $j^*_{p+1}$ may include currents smeared
over worldvolumes with dimension greater than $p+1$.
To define the spacetime integral $\int CK$, where $K$ is another formal sum of
forms, we note that the potentials $C$ are undefined on the collection of
branes that contribute to $j^*$. Contrast this to electric charges where
potentials simply diverge; for the example of a magnetic monopole, none of
the coordinate patches with well-defined potentials covers the monopole
location. Therefore, rather than integrating over all of spacetime, we excise
a small tube around the worldvolume of each magnetically charged brane with
boundary \P. After integrating, we will take the volume of the excluded tube
to vanish, so it becomes measure zero. In the presence of multiple magnetic
brane sources, \P\ has multiple components.
\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{integration.pdf}
\caption{Sketch of integration region with magnetic current $j^*$. Shaded
region inside \P\ is excluded; \ensuremath{\mathcal{Q}},$\ensuremath{\mathcal{Q}}'$ are possible separations of two gauge
patches.\label{f:integration}}
\end{figure}
Now consider the overlap region of two gauge patches (multiple gauge patches
are a straightforward extension, assuming the configuration is simple enough)
of potentials $C^\pm$ around some magnetic source.
On the overlap region, the two potentials are related
by the gauge transformation $C^+=C^-+d\zeta-\t\beta \zeta H_3$.
We choose a codimension-one surface \ensuremath{\mathcal{Q}}\ in the overlap region
such that the spacetime volume $\ensuremath{\mathcal{Q}}^\pm$ on either side of \ensuremath{\mathcal{Q}}\ is within
the coordinate patch where $C^\pm$ is valid respectively. This is just a
partition of spacetime into regions where each potential is used.
Note that \ensuremath{\mathcal{Q}}\ will generically intersect the boundary surface \P.
In the example of a monopole, this is just related to the fact that the
region where each potential is valid is given by a range of polar angle.
Figure \ref{f:integration} sketches the various surfaces for a current $j^*$.
Quantities integrated over \ensuremath{\mathcal{Q}}\ or \P\ are assumed to be pulled back to the
appropriate submanifold.
We now define the spacetime integral as
\beq{integral1}
\int C\wedge K \equiv \int_{\ensuremath{\mathcal{Q}}^+} C^+\wedge K + \int_{\ensuremath{\mathcal{Q}}^-} C^-\wedge K \pm\int_\ensuremath{\mathcal{Q}} \zeta\wedge K ,
\end{equation}
where the sign on the \ensuremath{\mathcal{Q}}\ integral depends on the orientation of the
integration measure. We will choose the positive sign below and take care to
account for signs due to the orientation.
This is sensible provided that the integral is unchanged under changes of
the arbitrary dividing surface \ensuremath{\mathcal{Q}}. Consider then changing $\ensuremath{\mathcal{Q}}\to\ensuremath{\mathcal{Q}}'$.
The change in the integral is
\begin{eqnarray}
&&\int_\ensuremath{\mathcal{Q}}^{\ensuremath{\mathcal{Q}}'} (C^- - C^+)\wedge K +\int_{\ensuremath{\mathcal{Q}}'}\zeta\wedge K -\int_\ensuremath{\mathcal{Q}} \zeta\wedge K \nonumber\\
&&=\int_\ensuremath{\mathcal{Q}}^{\ensuremath{\mathcal{Q}}'}\zeta\wedge\left[(-1)^pdK +\t\beta H_3\wedge K\right] -\int_{\b\P}
\zeta\wedge K ,\label{integral2} \end{eqnarray}
where $\int_\ensuremath{\mathcal{Q}}^{\ensuremath{\mathcal{Q}}'}$ indicates the region with boundary $\ensuremath{\mathcal{Q}}'-\ensuremath{\mathcal{Q}}-\b\P$
(that is, the region between \ensuremath{\mathcal{Q}}\ and $\ensuremath{\mathcal{Q}}'$ in figure \ref{f:integration})
and $\b\P$ is the region on \P\ between its intersections with $\ensuremath{\mathcal{Q}},\ensuremath{\mathcal{Q}}'$.
This will vanish provided $dK+(-1)^p\t\beta H_3 K=0$\footnote{Note that
$p$ is either even or odd for all potentials, so the same condition holds
for all terms in the formal sum.} and either $K$ has no
delta-function-like singularity (so the $\b\P$ integral vanishes as \P\
shrinks) or $\zeta K=0$ (for example, due to the legs of each form).
It is not a coincidence that $dK+(-1)^p\t\beta H_3 K=0$ is the same condition
for the integral (\ref{integral1}) to be gauge invariant under gauge
transformations $\chi$ that are globally defined over the integration region
and vanish on the boundary at infinity and \P.
Maxwell electrodynamics provides some simple examples. Consider a static
monopole of charge $g$ at the origin.
Then the simplest form for \P\ is a sphere of radius
$\epsilon$ around the origin. With the typical choices
$A_1^\pm= g(\pm 1-\cos\theta)d\phi$, \ensuremath{\mathcal{Q}}\ is any surface that intersects
\P\ in the limit $\epsilon\to 0$ and does not intersect the $z$-axis.
A simple choice for $Q$ is the $xy$-plane with transition function
$\zeta=2g\phi$. This prescription for integration
also works for harmonic flux with no magnetic sources on a compact manifold.
For example, we can consider a constant magnetic field on a square $T^2$,
which we can describe by vector potential $A_1=By dx$ in the first unit cell
$0\leq x,y<2\pi R$. To make the potential periodic in $y$, we must work
in a different gauge in each unit cell given by $2\pi R n\leq y<2\pi R(n+1)$
with gauge transition function $\zeta=-2\pi RBx$, but of course each gauge
is valid over the entire covering space. To integrate over the first
unit cell, we choose any curve \ensuremath{\mathcal{Q}}\ that runs from $x=0$ to $x=2\pi R$ within
the unit cell. A simple choice for \ensuremath{\mathcal{Q}}\ is the $x$-axis.
Integration by parts requires some care but is sensible for formal sums
$K=dk+(-1)^p\t\beta H_3 k$. We start by integrating by parts in $\ensuremath{\mathcal{Q}}^\pm$
separately to find
\begin{eqnarray}
\int C\wedge K &=& (-1)^p\int F\wedge k\label{byparts1}\\ &&+\int_\ensuremath{\mathcal{Q}} \left[\zeta\wedge K
+(-1)^p(C^+-C^-)\wedge k\right]\nonumber\\
&&-(-1)^p\int_{\P^+}C^+\wedge k-(-1)^p\int_{\P^-}C^-\wedge k ,\nonumber\end{eqnarray}
where $\P^\pm=\P \cap \ensuremath{\mathcal{Q}}^\pm$. Note that the integrals over $\P^\pm$ are
signed based on the orientation of the integration measure. The integral
over \ensuremath{\mathcal{Q}}\ is simply a surface term $-(-1)^p\zeta k$ over \P, which combines
with the $\P^\pm$ integrals. We have
\beq{byparts2}
\int C\wedge K = (-1)^p\left[\int F\wedge k-\int_\P C\wedge k\right] .\end{equation}
The first integral on the right-hand side
is over the same region as the original integral, i.e., all spacetime exterior
to \P, but it can extend to all spacetime since $F$ is globally defined
(assuming $k$ is globally defined).
It is tempting to think that the \P\ integral in equation (\ref{byparts2})
vanishes as \P\ shrinks. However, because $C$ does not have a well-defined
limit at the location of $j^*$, that is not always the case. There are three
cases of special interest. First, suppose that $k=\star J$ is given by a
Dirac brane current with boundary at other locations (so $J$ ``passes through''
\P). As a given component of \P\ shrinks, the pullback of $C$ approaches
the potential of the magnetic source in \P, which reverses orientation
compared to the $\star J$ on either side of \P.
As a second case, suppose $k=\star J$ is the Dirac
brane current emanating from the brane source inside \P. Then $J$ is aligned
along the worldvolume $\ensuremath{\mathcal{M}}^*$ and the radial direction inside \P, so $\star J$
has the same components as $C$ on \P\ as \P\ shrinks, and the integral
again vanishes. Finally, suppose that $k=d\kappa+(-1)^p\t\beta H_3\kappa$.
Since \P\ has no boundary, integration by parts gives
\beq{byparts3}
(-1)^p\int_\P C\wedge k = \int_\P F\wedge \kappa .\end{equation}
Assuming $\kappa$ is sufficiently smooth inside \P, we can replace the latter
by the integral of $(dF)\kappa$ over the excluded region inside \P\ in the
limit as \P\ shrinks. Then, we can replace $dF$ using the Bianchi identity
and keep only the delta-function-like term $\beta\star j^*$. After careful
accounting of signs,
\beq{byparts4}
\int C\wedge K = (-1)^p\int F\wedge k+\int (\beta\star j^*)\wedge\kappa ,\end{equation}
where both integrals on the right-hand side are taken over all spacetime.
In the above, we have ignored possible complications from brane intersections
or overlaps of three or more gauge patches in a nontrivial configuration.
Taking care with these will
potentially reproduce the modifications \cite{hep-th/0406083}
noted are necessary for nontransversal intersections.
Finally, we note that a variation of the potential $C$ can include a
variation of the gauge transition function $\zeta$, but it need not. In
particular, if $C^\pm \to C^\pm +\delta C$ for a globally defined variation
$\delta C$, the variation of the integral is well defined over all of
spacetime. No special prescription is needed for the integration.
\section{Type IIB supergravity}\label{s:typeIIB}
We now turn to the main result of this paper, the type II supergravity
actions in the presence of D-branes, starting with the IIB case.
We start by reminding the reader of the bosonic IIB action in the absence
of D-branes and using the result of section \ref{s:actions} to find the
modification to the CS term. Then we provide a novel derivation of this
term and other new terms involving Dirac brane currents by dualizing the
democratic formulation of the IIB supergravity. Keeping 10D covariance and
a self-dual 5-form field strength, we find agreement with
\cite{hep-th/0406083}, modulo terms involving anomalies on brane intersections
and $\alpha'$ corrections, which we do not consider. We also give a new
analysis of gauge invariance for this action. Finally, we separate
the 4-form potential and 5-form field strength into electric and magnetic
components and write a noncovariant action with D-brane contributions
in terms of the independent degrees of freedom only.
\subsection{Action and modified CS terms}
The gauge-invariant field strengths of the type IIB supergravity are
\begin{eqnarray}
\t F_1 &=& dC_0+\beta_{-1}\star J_9 ,\quad \t F_3=dC_2+\t\beta C_0\, H_3
+\beta_1\star J_7 ,\nonumber\\
\t F_5&=& dC_4+\t\beta C_2\wedge H_3+\beta_3\star J_5 ,\label{fieldIIB}
\end{eqnarray}
using the convention that all transgression terms have the same sign $\t\beta$.
Recall that $\beta_3=-\beta_1=\beta_{-1}$. Excluding local sources, the
action of the bosonic sector is
\begin{eqnarray}
S_{IIB}&=&\frac{1}{2\kappa_0^2}\int d^{10}x\sqrt{-g}e^{-2\phi}\left[R+4(\partial\phi)^2
\right]\label{actionIIB}\\
&&+\frac{1}{2\kappa_0^2}\int\left[\frac 12 e^{-2\phi}H_3\wedge\star H_3
+\frac 12 \t F_1\wedge\star \t F_1\right.\nonumber\\
&&\left.+\frac 12\t F_3\wedge\star\t F_3
+\frac 14\t F_5\wedge\star\t F_5+\frac 12\beta_3\t\beta\,
C_4\wedge\t F_3\wedge H_3\right] .\nonumber
\end{eqnarray}
The coefficient of the CS term is determined by the results of section
\ref{s:sugraconventions} and equation (\ref{coeffs}). Note that the $\t F_5$
kinetic term is halved because it is self-dual and contains duplicate degrees
of freedom.
As in section \ref{s:actions}, we can add D-brane currents to (\ref{actionIIB})
by adding Dirac brane currents to the field strengths and shifting the action by
\begin{eqnarray}
S_{IIB}&\to& S_{IIB}+\frac{1}{2\kappa_0^2}\int\left[C_0\wedge\star j_0+
C_2\wedge\star j_2\right.\nonumber\\
&&\left.+\frac 12 C_4\wedge\star j_4-\frac 12 \t\beta
(\star J_5)\wedge C_2\wedge H_3\right] .\label{actionIIBshift}
\end{eqnarray}
Here, $j_0$ is a scalar current associated with D$(-1)$-instantons, and
the last term, the CS term modification, includes the Dirac 4-brane current
as required to make the EOM gauge invariant. The coupling to $C_4$ has a
factor of $1/2$ due to the 5-form self-duality.
We also note that the relationship (\ref{coeffs}) between coefficients of the
action and EOM implies that we can replace
\begin{eqnarray}
&&\frac{\t\beta}{2}\int\left[\beta_3 C_4\wedge\t F_3\wedge H_3-(\star J_5)\wedge C_2\wedge H_3
\right]\nonumber\\
&&\ \rightarrow -\frac{\t\beta}{2} \int\left[\beta_3 C_2\wedge\t F_5\wedge H_3+
(\star J_7)\wedge C_4\wedge H_3\right]\label{CSreplace}
\end{eqnarray}
in the action to generate the same EOM for the RR gauge fields. (We will see
below that there are actually other terms also.)
Integration by parts to make this
replacement (up to surface terms) follows along the lines of section
\ref{s:integration} with a slight modification to account for the fact that
both potentials $C_2,C_4$ are patched. The integral on the boundary
\P\ vanishes, and the replacement (\ref{CSreplace}) holds with both
forms of the CS term following the prescription of section \ref{s:integration}
for integration.
Finally, we note that the action is sometimes written with an additional
CS term (see for example \cite{Johnson:2003gi})
\beq{extraCSIIB}
\frac{1}{2\kappa_0^2}\int\frac 14 B_2\wedge C_2 \wedge dB_2\wedge dC_2 .\end{equation}
In the absence of branes, this term is a total derivative and does not
contribute to the EOM. Even in the presence of D5-branes, it can be
written as the integral of $d(C_2^2 d(B_2)^2)$ following the integration
prescription given above. However, with both D5- and NS5-branes, this
term seems to be nonvanishing. Understanding its completion in the
presence of all sources and whether it remains topological is a task we
leave to the future.
\subsection{Dualization from democratic formulation}\label{s:dualization}
The EOM given in (\ref{democratic}) for the RR potentials
of type IIB supergravity in the democratic
formulation are given by the (pseudo)action
\begin{eqnarray}
S_{IIB,dem}&=&\frac{1}{2\kappa_0^2} \int \left[\frac 14 \t F_1\wedge\star\t F_1
+\frac 14 \t F_3\wedge\star\t F_3 +\frac 14 \t F_5\wedge\star\t F_5\right.\nonumber\\
&&\left. +
\frac 14 \t F_7\wedge\star\t F_7+\frac 14 \t F_9\wedge\star\t F_9
+\frac 12 C_0\wedge\star j_0 +\frac 12 C_2\wedge\star j_2\right.\nonumber\\
&&\left.
+\frac 12 C_4\wedge\star j_4+\frac 12 C_6\wedge\star j_6 +\frac 12 C_8\wedge\star j_8\right]
\label{democraticIIB}
\end{eqnarray}
(dropping the Einstein-Hilbert and dilaton and $B_2$ kinetic terms for
convenience) with the field strengths given by equation (\ref{fieldIIB})
and
\beq{fieldIIB2}
\t F_7=dC_6+\t\beta C_4\wedge H_3+\beta_5\star J_3 ,\quad
\t F_9=dC_8+\t\beta C_6\wedge H_3+\beta_7\star J_1 .\end{equation}
These also reproduce the Bianchi identities in
(\ref{democratic}).\footnote{Note that we are not considering type I
supergravity, so we do not include a D9-brane current, but it is a
straightforward generalization since $C_{10}$ does not have a dual potential.}
The EOM must be supplemented by duality relations between the higher- and
lower-rank field strengths. If we instead enforce the definitions
(\ref{fieldIIB2}) with Lagrange multipliers and identify those Lagrange
multipliers with the lower-rank field strengths, we can generate an
equivalent action for only the lower-rank potentials.
As in section \ref{s:integration}, the terms with potentials are over
spacetime with the reference currents removed, but other terms can be
integrated over the entire spacetime since they are smooth at the reference
currents and the punctures are zero measure.
Now we turn to removing the extra degrees of freedom from the action
(\ref{democraticIIB}). Start by adding Lagrange multipliers
\begin{eqnarray}
S_{IIB,dem}&\to& S_{IIB,dem}+\frac{1}{2\kappa_0^2}\int\frac 12\left[\lambda_1
\wedge\left(\t F_9-dC_8\right.\right. \nonumber\\
&&\left.\left.-\t\beta C_6\wedge H_3-\beta_7\star J_1\right)\right.
\label{lagrangeIIB}\\
&&\left.+\lambda_3\wedge \left(\t F_7-dC_6-\t\beta C_4\wedge H_3-\beta_5\star J_3\right)
\right] \nonumber
\end{eqnarray}
and treat $\t F_{7,9}$ as independent degrees of freedom.
The $\t F_{7,9}$ EOM give $\lambda_1=\star\t F_9,\lambda_3=\star\t F_7$.
Meanwhile, varying $C_{6,8}$ gives EOM
\beq{EOMpotIIB}
d\lambda_1=\star j_8,\quad d\lambda_3=\star j_6+\t\beta H_3\wedge\lambda_1 .\end{equation}
These are consistent with $\lambda_1\equiv\beta_{-1}\t F_1$ and
$\lambda_3\equiv\beta_1\t F_3$ recalling that $\beta_{-1}=-\beta_1$.
Imposing these identifications is equivalent to imposing the duality relations
of the democratic formulation.
The action is linear in $C_{6,8}$, so it may seem that imposing the EOM
(\ref{EOMpotIIB}) eliminates them. However, there are nontrivial surface
terms of the form
\begin{eqnarray}
-\frac{\beta_3}{2}&\!\!\!\!\!\!&\!\!\!\!\!\!
\int_\P \left(C_8\wedge\t F_1-C_6\wedge\t F_3\right)\nonumber\\
&=&
\frac{\beta_3}{2}\int\left(\beta_7 C_0\wedge\star j_0^*-\beta_5 C_2\wedge\star j_2^*
\vphantom{\frac 12}\right)\nonumber\\
&=&\frac 12\int\left(\vphantom{\frac 12}
C_0\wedge\star j_0^*+C_2\wedge\star j_2^*\right)\label{surfaceIIBduality} \end{eqnarray}
from integrating (\ref{lagrangeIIB}) by parts. [In the language of section
\ref{s:integration}, we have taken $C=C_4+C_6+C_8$ and
$K=d\lambda_1+(d\lambda_3-\t\beta H_3\lambda_1)-\t\beta H_3\lambda_3$, so
\P\ surrounds $j^*_{0,2,4}$.] Note that the electric reference currents $j_{0,2}^*$
are not excised from the integrals over $C_{0,2}$ (though excised
higher-dimensional reference branes may carry these currents).
At this point, the action has become
\begin{widetext}
\begin{eqnarray}
S_{IIB}&=&\frac{1}{2\kappa_0^2} \int \left[\frac 12 \t F_1\wedge\star\t F_1
+\frac 12 \t F_3\wedge\star\t F_3 +\frac 14 \t F_5\wedge\star\t F_5 +
\frac 12 C_0\wedge \star(j_0+j_0^*)+\frac 12 C_2\wedge\star( j_2+j_2^*)\right.\nonumber\\
&&\left. +\frac 12 C_4\wedge \star j_4 +\frac 12 \beta_3\t\beta C_4\wedge\t F_3\wedge H_3
-\frac 12 \t F_1\wedge\star J_1-\frac 12 \t F_3\wedge\star J_3\right] .
\end{eqnarray}
Finally, the last two terms split into terms involving the potentials and
those involving only Dirac brane currents. The former integrate by parts
using equation (\ref{diracdiv}) in IIB supergravity form
\beq{diracdivIIB}
d\star J_{p+2} = \star (j_{p+1}-j_{p+1}^*)-\t\beta \star J_{p+4}\wedge H_3 \end{equation}
(surface terms on \P\ vanish by reasoning given in section \ref{s:integration}),
leaving current terms and a remainder involving $\star J_5$.
All together, we have
\begin{eqnarray}
S_{IIB}&=&\frac{1}{2\kappa_0^2}\int \left[\frac 12 \t F_1\wedge\star \t F_1
+\frac 12\t F_3\wedge\star\t F_3 +\frac 14\t F_5\wedge\star\t F_5+C_0\wedge\star j_0+
C_2\wedge\star j_2+\frac 12 C_4\wedge\star j_4\right.\nonumber\\
&&\left. +\frac 12\beta_3\t\beta\, C_4\wedge\t F_3\wedge H_3-
\frac 12 \t\beta C_2\wedge(\star J_5)\wedge H_3+\frac 12\beta_3 \star J_1\wedge\star J_9
-\frac 12\beta_3\star J_3\wedge \star J_7\right] .\quad\qquad\label{actionIIB2}
\end{eqnarray}\end{widetext}
Some comments on the action (\ref{actionIIB2}) are in order. First, we note
the factor of $1/2$ on the $C_4-j_4$ coupling. It is well known that the
D3-brane charge must be reduced by half for the gauge EOM to work out correctly
for the self-dual 5-form (see \cite{hep-th/0105097} for example).
In fact, we made that
choice for the same reason in equation (\ref{actionIIBshift}). Here we see
that it is a consequence of dualization from the democratic action, where
all the potential-current couplings are halved. Second, we note
the appearance of the usual CS term and also the Dirac brane modification,
both of which are a consequence of transgression terms in the field strength
and in the divergence of the Dirac brane current. Finally, there are two
new terms involving Dirac brane currents for electrically and magnetically
charged branes. These terms were also found by \cite{hep-th/0406083} for IIB
supergravity and by \cite{Deser:1997se} for monopoles in electrodynamics.
In the monopole case, \cite{Deser:1997se} showed that these terms are
topological (do not contribute to the classical EOM) but are related to
charge quantization. However, in the type II supergravities, the Dirac brane
currents depend not just on the brane positions but also the brane gauge
fields and $B_2$, so they may not be purely topological (in either IIA or IIB
supergravity).
In our discussion of the IIA supergravity, we will see
that these terms can have physical importance even in the classical theory;
specifically, they will reproduce one of the CS terms of the massive IIA
theory. Further discussion of the contribution of $(\star J)^2$-type terms to
classical EOM will appear in \cite{freynew}.
\subsection{Gauge invariance}
We have now provided two novel derivations of the modified CS term (and also
found $J^2$-type terms when starting with the democratic action).
As it has not been discussed previously in the literature, it is important
to understand invariance of $S_{IIB}$ from (\ref{actionIIB2}) under gauge
transformations of the RR potentials, particularly because the CS terms are
not invariant on their own in the presence of branes, in contrast to the
usual presentation in the absence of branes.
The gauge transformations take the form
$\delta C=d\chi-\t\beta \chi H_3$ for globally defined forms $\chi_p$. Since
the integrals including the potentials $C$ have boundary at infinity and \P,
the $\chi_p$ should vanish on \P.
Before considering the final action (\ref{actionIIB2}),
it is worth commenting on the gauge invariance of (\ref{democraticIIB}).
The variation of the action is
\begin{eqnarray}
\delta S &=& \frac{1}{2\kappa_0^2} \int \frac 12 \left[ \chi_1\wedge\left(d\star j_2
-\t\beta H_3\wedge \star j_4\right)\right.\nonumber\\
&&\left. + \chi_3\wedge\left(d\star j_4
-\t\beta H_3\wedge \star j_6\right)\right.\label{gaugeIIBdem}\\
&&\left. + \chi_5\wedge\left(d\star j_6
-\t\beta H_3\wedge \star j_8\right)+\chi_7\wedge d\star j_8\right] .\nonumber
\end{eqnarray}
This vanishes by virtue of equation (\ref{nonconservation2}) with the
identification $\eta=\t\beta$.
On the other hand, the variation of the potential-current couplings in
(\ref{actionIIB2}) cannot all cancel. Fortunately, in the presence of
branes, the CS terms are also not gauge-invariant on their own. The variation
of the action is
\begin{eqnarray}
\delta S &=& \frac{1}{2\kappa_0^2} \int \left[ \chi_1\wedge d\star j_2+\frac 12
\chi_3\wedge d\star j_4-\frac 12 \t\beta \chi_1\wedge H_3\wedge\star j_4\right.\nonumber\\
&&\left.+\frac 12
\beta_3\t\beta \chi_3\wedge d\t F_3\wedge H_3-\frac 12 \t\beta \chi_1\wedge d\star J_5\wedge
H_3\right]\nonumber\\
&=& \frac{1}{2\kappa_0^2} \int \left[\t\beta \chi_1\wedge\star j_4\wedge H_3
\left(1-\frac 12 -\frac 12\right)\right.\nonumber\\
&&\left. +\t\beta \chi_3\wedge\star j_6\wedge H_3
\left(\frac 12-\frac 12\right)\right] =0 .\label{gaugeIIB}
\end{eqnarray}
The reference current $\star j_4^*$ does not appear because it lies in
the removed punctures, and
surface terms on \P\ vanish because the $\chi_p$ vanish on \P.
Note that the CS term with the Dirac brane current is necessary for invariance
under transformations of $C_2$.
\subsection{Noncovariant formulation for independent degrees of freedom}
\label{s:noncovariant}
To complete the action, \cite{hep-th/0406083} used
auxiliary variables with the Pasti-Sorokin-Tonin (PST)
formalism \cite{hep-th/9611100,hep-th/9701037}
to enforce the self-duality condition and maintain 10D
covariance.\footnote{Sen \cite{arXiv:1511.08220,arXiv:1903.12196}
has developed an alternate formalism also using
auxiliary fields to describe self-dual field strengths.}
Here, we determine the action for independent degrees of freedom only,
breaking 10D covariance and some of the $C_4$ gauge invariance. Making the
choice of degrees of freedom correctly can be useful in determining the
effective theory of a dimensional reduction; lack of 10D covariance is not
necessarily a disadvantage.
First, we need to identify independent degrees of freedom in $\t F_5$, which
we do by separating its components into two sets, ``electric'' components
$\t F_5^{(1)}$, which we treat as independent, and ``magnetic'' components
$\t F_5^{(2)}$ that satisfy $\t F_5^{(2)}=\beta_3\star\t F_5^{(1)}$.
The next task is to divide the potential also into
electric and magnetic components $C_4^{(1,2)}$. In some cases, it is possible
to make a clean division such that $C_4^{(1,2)}$ contribute only to
$\t F_5^{(1,2)}$ respectively. This is true, for example, of the nonvanishing
components of $C_4$ for the K\"ahler moduli of Calabi-Yau compactifications
even in the presence of background flux and warping
\cite{arXiv:0810.5768,arXiv:1308.0323,arXiv:1609.05904}. However, it is
not true in general. What is possible is to choose a set of magnetic components
$C_4^{(2)}$ that does not appear in $\t F_5^{(1)}$, while the complementary
set of electric components $C_4^{(1)}$ appears in both $\t F_5^{(1,2)}$. If we
ignore gauge invariance, the numbers of components in these sets are different.
To proceed, we fix our spacetime coordinates, including a spatial coordinate
$\t x$ (with $g_{\t x\mu}=0$ for $\mu\neq\t x$ for simplicity; we consider only
the case where we can do so). Then we label
any form with a leg along $\t x$ with $(2)$ and any form without a leg on $\t x$
with $(1)$. A prototype coordinate for $\t x$ is a spatial direction in a
Minkowski factor of a (possibly warped) product metric. This choice for
$\t F_5^{(1,2)}$ follows \cite{hep-th/0105097}, for example. For notational
convenience, we define $\t d=d\t x \partial_{\t x}$ and ${d\mkern-7mu\mathchar'26\mkern-2mu} =d-\t d$. Then
\begin{eqnarray}
\t F_5^{(1)}&=&{d\mkern-7mu\mathchar'26\mkern-2mu} C_4^{(1)}+\t\beta (C_2\wedge H_3)^{(1)}+\beta_3\star J_5^{(2)} ,
\nonumber\\
\t F_5^{(2)}&=&{d\mkern-7mu\mathchar'26\mkern-2mu} C_4^{(2)}+\t d C_4^{(1)}+
\t\beta (C_2\wedge H_3)^{(2)}+\beta_3\star J_5^{(1)} .\label{noncovF5}
\end{eqnarray}
To find the noncovariant action, we start with action (\ref{actionIIB2})
and project $\t F_5,(C_2H_3),J_5$ and $C_4$ onto electric and magnetic
components as above. Adding in a Lagrange multiplier, the relevant part
of the action is
\begin{eqnarray}
S&=&\frac{1}{2\kappa_0^2} \int\left[\cdots + \frac 14 \t F_5^{(1)}\wedge\star
\t F_5^{(1)}+\frac 14 \t F_5^{(2)}\wedge\star\t F_5^{(2)}\right.\nonumber\\
&&\left.
+\frac 12 C_4^{(1)}\wedge\star j_4^{(1)}+\frac 12 C_4^{(2)}\wedge\star j_4^{(2)}\right.
+\beta_3\t\beta C_4^{(1)}\wedge(\t F_3\wedge H_3)\nonumber\\
&&\left.
+\beta_3\t\beta C_4^{(2)}\wedge(\t F_3\wedge H_3)-\frac 12\t\beta\star J_5^{(1)}\wedge
(C_2\wedge H_3)\right.\nonumber\\
&&\left.-\frac 12\t\beta\star J_5^{(2)}\wedge(C_2\wedge H_3)
+\frac 12 \lambda_5\wedge\left(\t F_5^{(2)}-{d\mkern-7mu\mathchar'26\mkern-2mu} C_4^{(2)}-\t d C_4^{(1)}
\right.\right.\nonumber\\
&&\left.\left.-\t\beta(C_2\wedge H_3)^{(2)}
-\beta_3\star J_5^{(1)}\right)\right] .\label{selfdual1}
\end{eqnarray}
Note that a wedge product $A^{(1,2)} B$ chooses the $(2,1)$ components of
form $B$. We can now follow the same procedure as in the previous subsection,
finding $\lambda_5=\star\t F_5^{(2)}$ from the $\t F_5^{(2)}$ EOM, and the
duality relation $\lambda_5=\beta_3\t F_5^{(1)}$ plus $C_4^{(2)}$ EOM yield
\beq{noncovBianchi}
{d\mkern-7mu\mathchar'26\mkern-2mu} \t F_5^{(1)}=\t\beta (\t F_3\wedge H_3)^{(1)}+\beta_3\star j_4^{(2)} ,\end{equation}
which is the Bianchi identity following from (\ref{noncovF5}). It is also
the part of the covariant Bianchi identity with no legs along $\t x$.
There are two remaining finer points in the derivation. First,
we assume that $C_4^{(1)}$ is not patched on the surface surrounding $j_4^{(1),*}$
even though it appears in $\t F_5^{(2)}$. Second, we note that the
projection of the relation (\ref{diracdivIIB}) onto the magnetic components
involves both Dirac brane currents:
\beq{noncovdiracdiv}
{d\mkern-7mu\mathchar'26\mkern-2mu}\star J_5^{(1)}+\t d\star J_5^{(2)} =\star (j_4^{(1)}-j_4^{(1),*})
-\t\beta\left(\star J_7\wedge H_3\right)^{(2)} .\end{equation}
In the end, we find
\begin{widetext}\begin{eqnarray}
S&=&\frac{1}{2\kappa_0^2}\int\left[\cdots +\frac 12 \t F_5^{(1)}\wedge\star\t F_5^{(1)}
+C_4^{(1)}\wedge\star j_4^{(1)}+\frac 12\beta_3\t\beta C_4^{(1)}\wedge(\t F_3\wedge H_3)
-\frac 12\beta_3\t\beta \t F_5^{(1)}\wedge(C_2\wedge H_3)-\frac 12\beta_3\t F_5^{(1)}\wedge
\t d C_4^{(1)}\right.\nonumber\\
&&\left. -\frac 12\t\beta\star J_5^{(2)}\wedge(C_2\wedge H_3)
-\frac 12\t\beta C_4^{(1)}\wedge(\star J_7\wedge H_3)-\frac 12 C_4^{(1)}\wedge \t d \star J_5^{(2)}
+\frac 12 \beta_3\star J_5^{(1)}\wedge
\star J_5^{(2)}\right] .\label{selfdual2}
\end{eqnarray}\end{widetext}
Interestingly, the noncovariant action seems to mix
the two forms for the CS term equated in (\ref{CSreplace}). There are two
entirely new terms.
To validate the action (\ref{selfdual2}), we can check that it gives the
correct equations of motion for the potentials. The $C_4^{(1)}$ EOM follows
after some substitution; to write the EOM in terms of field strengths only,
we must rewrite ${d\mkern-7mu\mathchar'26\mkern-2mu}\t d C_4^{(1)}$ in terms of $\t F_5^{(1)}$ and recall
that $(\t F_3H_3)^{(2)}={d\mkern-7mu\mathchar'26\mkern-2mu}[(C_2H_3)^{(2)}]+\t d[(C_2H_3)^{(1)}]$.
After some cancellation,
\beq{C4EOMnoncov}
{d\mkern-7mu\mathchar'26\mkern-2mu} \star\t F_5^{(1)}+\beta_3\t d\t F_5^{(1)}=\star j_4^{(1)}
+\beta_3\t\beta (\t F_3\wedge H_3)^{(2)} .\end{equation}
Using the duality relation, this is also the part of the covariant EOM with
one leg along $\t x$, as expected.
The $C_2$ EOM is slightly more subtle, as we must
move the projection from $\delta C_2 H_3$ to other factors in wedge products
to get the full variation. In particular, the second
CS term contains $(\delta C_2 H_3)^{(1)} (C_2H_3)=-\delta C_2 (C_2H_3)^{(2)} H_3$.
To combine this with other terms to make the gauge-invariant $\t F_5^{(1)}$,
we must notice that $0=C_2 H_3^2=(C_2H_3)^{(1)}H_3+(C_2H_3)^{(2)}H_3$.
Further, we must notice that the variation of
$\t\beta C_4^{(1)} \t F_3 H_3-\t F_5^{(1)}\t d C_4^{(1)}$ yields
$\t\beta(d-\t d)C_4^{(1)}H_3=\t\beta{d\mkern-7mu\mathchar'26\mkern-2mu} C_4^{(1)}H_3$, also required to write
the EOM in terms of $\t F_5^{(1)}$. We see that
\beq{C2EOMnoncov}
d\star\t F_3=\star j_2-\t\beta\star\t F_5^{(1)}\wedge H_3-\beta_3\t\beta\t F_5^{(1)}
\wedge H_3\ .\end{equation}
Again, that is exactly as expected from the decomposition of the usual $C_2$
EOM.
As an alternate derivation, the action (\ref{selfdual2}) is in principle
equivalent to the action in section 5.3 of \cite{hep-th/0406083} with
the auxiliary scalar of the PST formalism gauge fixed to a specific form.
The remaining PST gauge symmetries (discussed for IIB supergravity in
\cite{DallAgata:1997gnw}) eliminate the components $C_4^{(2)}$.\footnote{We
thank D.~Sorokin for this and other provocative comments regarding this
subsection.} The companion paper \cite{freynew} will emphasize applications
where it is important to consider only independent degrees of freedom,
and (\ref{selfdual2}) will play a role there. This derivation highlights the
origin of the new terms in the covariant formulation.
\section{Type IIA supergravity}\label{s:typeIIA}
In this section, we give the type IIA supergravity action with D-brane
sources for the first time. We will first derive the action from the
democratic formulation, in which the brane-current couplings, i.e., the
brane WZ terms, are known, following the same techniques as used for the IIB
theory. We address gauge invariance under the RR gauge transformations and
verify that the action we obtain is consistent with the constraints discussed
in section \ref{s:actions}. We then discuss the well-known relation between
D8-branes and the massive IIA supergravity in light of our new action.
We will examine the role that Dirac brane currents play in generating the
couplings of the massive IIA theory, including terms proportional to the
mass parameter in D-brane WZ actions.
\subsection{Action, gauge invariance, and EOM}
As for the IIB theory, we start with a democratic (pseudo)action
(for the RR sector)
\begin{eqnarray}
S_{IIA,dem} &=& -\frac{1}{2\kappa_0^2} \int\left[ \frac 14 \t F_0\wedge\star\t F_0
+\frac 14 \t F_2\wedge\star\t F_2+\frac 14 \t F_4\wedge\star\t F_4\right.\nonumber\\
&&\left.+\frac 14 \t F_6\wedge\star\t F_6+\frac 14 \t F_8\wedge\star\t F_8
+\frac 14 \t F_{10}\wedge\star\t F_{10}\right.\nonumber\\
&&\left. +\frac 12 C_1\wedge\star j_1+\frac 12 C_3\wedge\star j_3
+\frac 12 C_5\wedge\star j_5+\frac 12 C_7\wedge\star j_7\right.\nonumber\\
&&\left.+\frac 12 C_9\wedge\star j_9\right]\label{democraticIIA}
\end{eqnarray}
and field strengths defined by
\begin{eqnarray}
\t F_0&=&m+\beta_{-2}\star J_{10} ,\nonumber\\
\t F_2 &=& dC_1+\t\beta m B_2+\beta_0\star J_8 ,\nonumber\\
\t F_4 &=& dC_3+\t\beta C_1\wedge H_3+\frac{m}{2}B_2^2+\beta_2\star J_6 ,\nonumber\\
\t F_6 &=& dC_5+\t\beta C_3\wedge H_3+\frac{m}{3!}\t\beta B_2^3+
\beta_4\star J_4\nonumber\\
\t F_8 &=&dC_7 +\t\beta C_5\wedge H_3+\frac{m}{4!} B_2^4+\beta_6\star J_2\ ,
\nonumber\\
\t F_{10}&=&dC_9 +\t\beta C_7\wedge H_3+\frac{m}{5!}\t\beta B_2^5
+\beta_8\star J_0 .\label{IIAfields}
\end{eqnarray}
Some of the field strength definitions (\ref{IIAfields}) require an explanation.
First, consistent with the possible presence of D8-branes, we include
the $\t F_0$ and $\t F_{10}$ field strengths, and we include a ``bare'' mass
parameter $m$ obeying $dm=\beta_{-2}\star j_9^*$. This and the choice
to add $m\exp(\t\beta B_2)$ to $\t F$ ensure that the Bianchi identities
of (\ref{IIAeqns}) are satisfied. These choices are consistent with the
massive IIA supergravity \cite{Romans:1985tz}.
Second, although $\t F_{10}$ automatically
has a trivial Bianchi identity simply by index counting, we include a
transgression term consistent with the gauge transformation of $C_9$
that leaves the D8-brane WZ action invariant. We also include a 0-rank
Dirac brane current though there is not a D$(-2)$-brane or associated
$j_{-1}$ current. Instead, we recall that each D$p$-brane has a series of
currents $j_{\ensuremath{\mathcal{M}}},j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{F}}},j_{\ensuremath{\mathcal{M}},\ensuremath{\mathcal{F}}^2/2},\cdots$ and Dirac brane currents
$J_{\ensuremath{\mathcal{N}}},J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{F}}},J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{F}}^2/2},\cdots$; the rank-0 Dirac brane current from
this series contributes to $J_0$, even though there is not a corresponding
D-brane current. To our knowledge, this is the first appearance of this current
in the literature.
From this point, derivation of the action for the lower-rank potentials
follows the same steps as in section \ref{s:dualization}. We find
\begin{widetext}\begin{eqnarray}
S_{IIA}&=&-\frac{1}{2\kappa_0^2} \int\left[ \frac 12 \t F_0\wedge\star\t F_0
+\frac 12 \t F_2\wedge\star\t F_2+\frac 12 \t F_4\wedge\star\t F_4
+C_1\wedge\star j_1+ C_3\wedge\star j_3+\frac 12 \beta_0\t\beta C_3\wedge\t F_4\wedge H_3
\right.\nonumber\\
&&\left. +\frac m4 \beta_0\t\beta C_3\wedge B_2^2\wedge H_3
-\frac 12 \t\beta C_3\wedge\star J_6\wedge H_3
-\frac 12 \left(\frac{m}{4!}B_2^4-\beta_0\star J_2\right)\wedge\left(m\t\beta\beta_0
B_2+\star J_8\right)\right.\nonumber\\
&&\left.
+\frac 12\left(\frac{m}{3!}\t\beta B_2^3+\beta_0\star J_4\right)\wedge\left(
\frac m2 \beta_0 B_2^2-\star J_6\right)
+\frac 12 \t F_0\wedge\left(\frac{m}{5!}\t\beta\beta_0 B_2^5+\star J_0\right)
\right] .\label{actionIIA}
\end{eqnarray}\end{widetext}
As in the IIB theory, we find a modified CS term and couplings between
Dirac brane currents of electrically charged and magnetically charged D-branes.
The last term is also of this type, but $\t F_0$ could also in principle
include the mass parameter.
It is worth noting that we recover the action of the pure massive IIA
supergravity (i.e. with no D-branes) for $j_{p+1},J_{p+2}\to 0$
\cite{Romans:1985tz} (or see
also \cite{hep-th/0103233}). The meaning of the mixing between
Dirac brane currents and $m\exp(\t\beta B_2)$ will become clear below.
Once again, the modified CS term has precisely the correct coefficients to
ensure that the EOM can be written in terms of the gauge-invariant field
strengths. Of course, this fact is related to gauge invariance of the action.
If we take gauge transformations $\delta C_1=d\chi_0$,
$\delta C_3=d\chi_2-\t\beta\chi_0 H_3$,
\begin{eqnarray}
\delta S &=& \frac{1}{2\kappa_0^2}\int\left[ \chi_0\left(d\star j_1+\t\beta
\star j_3\wedge H_3\right)\right.\label{varyIIA}\\
&&\left. +\chi_2\wedge\left(d\star j_3+\frac 12 \beta_0\t\beta
d\t F_4\wedge H_3-\frac 12 \t\beta d\star J_6\wedge H_3\right)\right] .\nonumber
\end{eqnarray}
Equation (\ref{nonconservation2}) implies that the $\chi_0$ terms cancel;
the $\chi_2$ terms also require the Bianchi identity and the divergence of
the Dirac brane current. The gauge invariance in fact ensures that the
integral over the potentials $C_1,C_3$ is well defined.
\subsection{The massive IIA theory from Dirac branes}
It is well known \cite{hep-th/9510017,hep-th/9510169} that D8-branes
are a source for the mass parameter of the Romans massive supergravity,
which is quantized in units of the D8-brane charge \cite{hep-th/9510227}.
As a review, since D8-branes are codimension one, $m$ is piecewise constant
and jumps by one unit of D8-brane charge at the position of each D8-brane,
for example on a $S^1/Z_2$ orientifold. We conjecture that, in fact, the
currents of the associated Dirac 9-branes describe all the additional
couplings of the massive IIA theory, whether described as a pure supergravity
or as the massless IIA theory in the presence of D8-branes and O8-planes.
Here, we present evidence in favor of this conjecture, point out some
remaining questions, and illuminate consequences.
Start by considering the Bianchi identity $d\t F_0=\star j_9$ on the interval
transverse to a set of parallel D8-branes. If we define
$\t F_0=m+\beta_{-2}\star J_{10}$, where $m$ is the bare
mass parameter, we see
that $m$ jumps by $\pm\mu_8$ at the location of each reference brane but
is otherwise constant. Meanwhile, $d\star J_{10}=\star(j_9-j_9^*)$, so
$\star J_{10}$ is also a step function equal to $\pm\mu_8$ between the
physical and reference branes. On the $S^1/Z_2$ orientifold, $m=0$ if half
of the reference D8-branes are coincident with each O8-plane. Alternately,
we can generate the massive supergravity by considering the massless IIA
theory on a circle. Then imagine an instantonic process in which a
D8/$\bar{\textnormal{D}}$8-brane pair appears transverse to the circle,
and then the
brane and antibrane move in opposite directions around the circle before
reannihilating. This process leaves behind a closed Dirac 9-brane
extending around the entire circle and filling spacetime
(there is a reference brane/antibrane pair
at the point of initial pair creation, which has no net
effect).\footnote{\cite{hep-th/9510227} also suggests this brane nucleation
process as a way to generate the bare mass parameter $m$.}
In both these cases, $\t F_0=-\beta_{0}N\mu_8$ for integer $N$, or
$\star J_{10}=-\beta_{0}\t F_0$.
Since the Dirac 9-brane fills spacetime, it is natural to treat the WZ
couplings on its currents as part of the bulk action. Ignoring any worldvolume
gauge fields, the Dirac brane currents are given by
\begin{eqnarray}
\star J_8 &=& -\beta_{0}\eta\t F_0 B_2,\quad
\star J_6=-\frac{\beta_{0}\t F_0}{2} B_2^2 ,\nonumber\\
\star J_4&=&-\frac{\beta_{0}\eta\t F_0}{6} B_2^3 ,\quad
\star J_2=-\frac{\beta_{0}\t F_0}{24} B_2^4 , \nonumber\\
\star J_0&=&-\frac{\beta_{0}\eta\t F_0}{120} B_2^5 .\label{massiveJ}
\end{eqnarray}
As a result, the field strengths become (with $\eta=-\t\beta$ from the anomaly
inflow)
\beq{massiveF}
\t F_2 =dC_1 +\t\beta \t F_0 B_2 ,\quad \t F_4 = dC_3+\t\beta C_1\wedge H_3
+\frac 12 \t F_0 B_2^2 ,
\end{equation}
standard for the massive supergravity. In terms of these field strengths,
the action (\ref{actionIIA}) in the absence of D-branes becomes
\begin{eqnarray}
S_{IIA}&=& -\frac{1}{2\kappa_0^2} \int \left[ \frac 12 \t F_0\wedge\star\t F_0
+\frac 12 \t F_2\wedge\star\t F_2+\frac 12 \t F_4\wedge\star\t F_4\right.\nonumber\\
&&\left. +\frac 12 \beta_0
\t\beta C_3\wedge dC_3\wedge H_3 +\frac{1}{2}\beta_0\t\beta\t F_0 C_3\wedge B_2^2\wedge H_3
\right.\nonumber\\
&&\left.
+\frac{1}{40} \beta_0\t\beta \t F_0^2 B_2^5 \right] .\label{massiveIIA}
\end{eqnarray}
This precisely matches the action for Romans massive supergravity given
above (there, $\t F_0\to m$).
In particular, if we consider the 10D spacetime as the boundary of an
11D spacetime, the last three terms together are
$(\beta_0\t\beta/2)\t F_4^2 H_3$ integrated in 11D, as expected. So we see
that the action for pure massive IIA supergravity follows from Dirac
brane currents. If we include both a bare mass parameter $m$ and the
Dirac branes (as is necessary generically in the presence of D8-branes),
we have $\star J_{10}=-\beta_0(\t F_0-m)$, which adjusts the coefficients
in equation (\ref{massiveJ}). With this change, the field strength definitions
(\ref{massiveF}) still hold, and the mixed terms in the action
(\ref{actionIIA}) are unchanged in terms of the physical $\t F_0$.
As a short aside, the last term in (\ref{massiveIIA})
is the sum of the $(\star J)^2$-type terms. Therefore, these
terms have physical consequences even in the classical theory. They are not
purely topological.
The interpretation of the mass parameter as the consequence of Dirac brane
currents raises a question about gauge transformations in the massive IIA
theory. Since the field strengths (\ref{massiveF}) contain the potential $B_2$,
they are gauge invariant only if the RR potentials also transform under
the $B_2$ gauge transformations. This still seems to be case when $\t F_0$
arises from D8-instantons as above. However, in the case where D8-branes are
present, the Dirac brane currents depend on $\b\ensuremath{\mathcal{F}}$, the extension of
the gauge-invariant D8-brane field strength. In that case, the $B_2$ gauge
transformation is compensated by a corresponding transformation of $\b A_1$.
When $\t F_0$ is a mix of bare mass parameter $m$ and $\star J_{10}$ in the
presence of D8-branes, it seems
that the gauge transformation of $C$ would depend only on $m$, not the
physical flux $\t F_0$.
Additional terms in the WZ action arise for D-branes in backgrounds with
$\t F_0\neq 0$, which \cite{hep-th/9603123,hep-th/9604119}
demonstrated for type IIA D-branes via T duality. These take the form
\beq{extraWZ}
S_{WZ,\t F_0} = \frac{\mu_p}{(p/2+1)!} \int_\ensuremath{\mathcal{M}} [\t F_0]\, \omega_{p+1}, \end{equation}
where $\omega_{p+1}$ is the Chern-Simons form defined by
$\hat d\omega_{p+1}=(\hat dA_1)^{(p+2)/2}$. We argue that these terms follow
naturally from the Dirac brane current $J_0$ and see that
these and other related WZ terms appear for all the IIA D-branes.
This Dirac brane current for a D$(2n-2)$-brane is
\begin{eqnarray}
J_0 &=& J_{\ensuremath{\mathcal{N}},\b\ensuremath{\mathcal{F}}^n/n!}=\sum_{\ell}
\frac{\mu_{2n-2}(2\pi\alpha')^\ell}{\ell!(n-\ell)!}\int_\ensuremath{\mathcal{N}} \b d\b\omega_{2\ell-1}
\wedge [B_2]^{n-\ell}\delta^{10}(x,Y)\nonumber\\ &=& -\sum_{\ell}
\frac{(2\pi\alpha')^\ell}{\ell!(n-\ell)!}\left[
j_{\ensuremath{\mathcal{M}},\omega_{2\ell-1}[B_2]^{n-\ell}} -j_{\ensuremath{\mathcal{M}}^*,\omega^*_{2\ell-1}[B_2]^{n-\ell}}\right.\nonumber\\
&&\left.\vphantom{j_\ensuremath{\mathcal{M}}}+(n-\ell)
J_{\ensuremath{\mathcal{N}},\b\omega_{2\ell-1}[H_3][B_2]^{n-\ell-1}}+\star d\star
J_{\ensuremath{\mathcal{N}},\b\omega_{2\ell-1}[B_2]^{n-\ell}}\right] .\label{J0current}
\end{eqnarray}
The first term, when substituted into the last term of the
action (\ref{actionIIA}),
is equivalent to a contribution
$S_{WZ}\propto [\t F_0]\omega_{2\ell-1}[B_2]^{n-\ell}$
to the D-brane's WZ action, where the $\ell=n$ term reproduces
(\ref{extraWZ}). The remaining terms are a similar coupling on the
reference brane, a Dirac brane coupling involving $H_3$ flux, and (after
integration by parts) a contact term between the Dirac brane and any
D8-brane.\footnote{While we presented (\ref{J0current}) in terms of a
Dirac brane, using the Chern kernel gives the same contributions with the
latter two terms extended over spacetime.}
This observation suggests that the additional WZ terms (\ref{extraWZ}) are
actually properly interpreted as Dirac brane couplings and should include
additional couplings to $B_2$. They reduce to (\ref{extraWZ}) in the
absence of $H_3$ flux and D8-branes; the additional term on the reference
brane does not contribute to the D-brane gauge field EOM because the
reference potential is fixed. Furthermore, (\ref{J0current}) immediately
implies that all type IIA D-branes have such couplings. So the action
(\ref{actionIIA}) leads to a prediction for D-branes in massive IIA
backgrounds. However, there is a puzzle. The $\t F_0\star J_0$ term in
the action is multiplied by a factor of $1/2$, so we have actually found
half of the WZ term suggested by T duality. A possible resolution is to note
that this term is analogous to the integration by parts of $C_{p+1}\star j_{p+1}$,
suggesting that we should include an extra $\t F_0\star J_0/2$ or perhaps
$m\star J_0/2$ (since the bare mass parameter depends on reference D8-branes)
already in action (\ref{democraticIIA}). The difficulty, of course, is that
adding this term to (\ref{actionIIA}) spoils agreement with the known action
for the massive IIA theory. Alternately, there could be a subtlety in the
derivation of these WZ terms by T duality in
\cite{hep-th/9603123,hep-th/9604119}. Specifically, it may be that any IIB
background dual to an allowed brane in the massive IIA theory involves an
orientifold, and the T duality rules in the presence of orientifolds can
introduce factors of 2 in bulk fields in comparison to T duality
without orientifolds. This could change the weight of the new WZ terms.
Resolving this puzzle is a question for the future.
\section{Discussion and future directions}\label{s:future}
We gave a brief introduction to the description of D-brane WZ actions
as they appear in the bulk supergravity action through D-brane and Dirac
brane currents. We initially went through an anomaly inflow argument
in terms of the nonconservation of D-brane currents and CS and transgression
terms in the EOM and Bianchi identities for the RR fields (for a generalized
version of the 10D type II supergravities). This discussion made explicit
several points that are implicit in the literature, including the allowed
sign conventions for the type II supergravity actions --- assuming there is
a common sign choice for transgression terms in the field strengths, there
is one independent choice of sign on a magnetic current in the Bianchi
identities. We then showed that reproducing the EOM in terms of gauge-invariant
field strengths requires a brane-induced modification to CS terms in the
action for the RR gauge fields. Inclusion of $\alpha'$ corrections in the
brane currents, such as the A-roof genus terms, is explained implicitly in
\cite{hep-th/0406083}, but an explicit description may be interesting.
Our main concern was to give actions for the IIB and IIA supergravities
with D-brane sources. As a preliminary, we explained how to integrate over
gauge-patched RR-sector potentials (or with similar gauge transformations).
A critical feature is the excision of the reference magnetic currents (around
which the potentials are patched), which leads to new surface terms.
We left any subtleties surrounding brane intersections to the future,
and these may be important in reproducing additional anomaly terms found in
\cite{hep-th/0406083}.
Up to those higher $\alpha'$ corrections and brane intersection terms,
we then reproduced the results of \cite{hep-th/0406083} for the action of
IIB supergravity with D-branes by dualizing the democratic formulation of
the theory. We uncovered the same brane-induced modification to the CS term
as well as couplings between Dirac brane currents. We also showed that both
the standard CS term and the brane-induced term are necessary for invariance
of the action under gauge transformations of the RR potentials. With an eye
toward dimensional reduction and other applications where accounting for
degrees of freedom is important, we further dualized the action, keeping only
half the degrees of freedom of the self-dual 4-form potential.
Finally, we presented the action of IIA supergravity with D-branes, including
the Romans mass parameter. This has a similarly modified CS term as the IIB
supergravity along with current-current couplings for Dirac brane currents,
though the latter are mixed with additional terms including the mass
parameter. We then demonstrated how Dirac brane currents carried by a
Dirac 9-brane reproduce the entire action of the massive IIA theory without
D-branes. In fact, Dirac brane currents associated with other D-branes
reproduce the form of additional WZ couplings on those branes in the massive
theory, which had been found by T duality \cite{hep-th/9603123,hep-th/9604119}.
However, these results raise some questions: In the Romans supergravity,
RR potentials transform under the Neveu-Schwarz--Neveu-Schwarz (NSNS)
gauge transformations, but should
the Dirac brane worldvolume potentials absorb those gauge transformations
instead? And what is the origin of the factor of 2 difference between
the new WZ couplings in massive supergravity as deduced from the Dirac brane
currents as opposed to T duality?
As we discussed in the introduction, Dirac's formalism separates the
brane and gauge field degrees of freedom. Identifying the correct degrees
of freedom is a critical task in a number of applications, including
determining the effective field theory of a dimensional reduction, for
example. (In fact, \cite{arXiv:1609.05904} used a variation on Dirac's
formalism to address the effective field theory of D3-branes in flux
compactifications.) We will return to this issue in a forthcoming
companion paper \cite{freynew}, compiling useful formulae for the dimensional
reduction of branes and fluxes. The companion paper will also describe
several magnetic brane configurations, including examples of smoothly
distributed magnetic monopole charge in electrodynamics and branes ending on
branes in string theory.
Looking further afield, other types of magnetic couplings and
magnetically charged branes in string theory are targets for this analysis.
First, a stack of D-branes carries a non-Abelian gauge theory, so extending
our results to non-Abelian worldvolume $F_2$ and to include noncommuting
worldvolume positions, which appear in the CS action of \cite{Myers:1999ps},
is an important task. Further, Lechner and co-workers
\cite{hep-th/0107061,hep-th/0203238,hep-th/0302108,hep-th/0402078}
and Bandos \textit{et al}. \cite{Bandos:1997gd}
have considered type IIA NS5-branes and M2- and M5-branes, and type IIB
NS5-branes would be a logical next step. An important issue, as we noted,
is understanding the supergravity action in the presence of both D-branes
and NS5-branes, particularly the ``extra'' CS term sometimes included in
the IIB supergravity action and which is topological except in the presence
of both D5- and NS5-branes. We also now know of numerous types of exotic
branes in string theory (along with KK monopoles), many of which also
presumably have associated Dirac brane currents. How do these affect
any effective gravitational and gauge action? We leave these intriguing
questions to the future.
\acknowledgments
ARF thanks K.~Dasgupta and R.~Danos for helpful discussions and K.~Lechner
and D.~Sorokin for correspondence.
ARF is supported by the Natural Sciences and
Engineering Research Council of Canada Discovery Grant program,
grants 2015-00046 and 2020-00054. Part
of this work was carried out while visiting the Perimeter Institute
for Theoretical Physics. Research at Perimeter Institute is supported
by the Government of Canada through the Department of Innovation,
Science and Economic Development and by the Province of Ontario
through the Ministry of Research and Innovation.
| {
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} | 5,180 |
George Steinmetz (* 1957) ist ein amerikanischer Soziologe.
Steinmetz besuchte von 1975 bis 1979 das Reed College, unterbrochen von einem Austauschjahr an der Universität Paris VI. 1980 erhielt er seinen B.A. in Deutscher Sprache und Literatur von der University of Wisconsin–Madison, wo er 1983 auch seinen M.S. in Soziologie machte. Anschließend studierte er bis 1985 an der Universität Mannheim und besuchte auch Veranstaltungen an der FU Berlin. 1985 kehrte er zurück an die University of Wisconsin-Madison, wo er 1987 zum Ph.D. promoviert wurde mit einer Dissertation über Sozialleistungen in Deutschland 1871–1914. Betreuer der Arbeit war Erik Olin Wright.
Anschließend erhielt Steinmetz eine Stelle an der University of Chicago, zunächst als Assistant Professor, ab 1994 als Associate Professor. 1997 wechselte er an die University of Michigan, wo er seit 2004 Charles-Tilly-Professor ist. Zwischen Juli 2008 und Juni 2009 war er zudem Professor of Sociology an der New School for Social Research in New York.
Steinmetz' Arbeitsschwerpunkte sind die Historische Soziologie, Kultursoziologie und soziologische Erkenntnistheorie.
Auszeichnungen (Auswahl)
2019: Siegfried-Landshut-Preis des Hamburger Instituts für Sozialforschung
2008: Mary Douglas Award, Vergeben von the Culture Section of the American Sociological Association (für The Devil's Handwriting)
Veröffentlichungen (Auswahl)
Monographien
The Colonial Origins of Modern Social Thought: French Sociology and the Overseas Empire, Princeton University Press, 2023, ISBN 978-0-691-23742-8.
Devil′s Handwriting: Precoloniality and the German Colonial State in Qingdao, Samoa, and Southwest Africa, University of Chicago Press, 2007, ISBN 978-0-226-77243-1.
Regulating the Social: The Welfare State and Local Politics in Imperial Germany, Princeton University Press, 1993, ISBN 978-1-4008-2096-2.
Herausgaben
Mit Didier Fassin: The Social Sciences in the Looking Glass: Studies in the Production of Knowledge, Duke University Press, 2023, ISBN 978-1-4780-1945-9.
Mit Timothy Rutzou: Critical Realism, History, and Philosophy in the Social Sciences, emerald, 2028, ISBN 978-1-78756-604-0.
Sociology and Empire: The Imperial Entanglements of a Discipline, Duke University Press, 2013, ISBN 978-0-8223-5258-7.
The Politics of Method in the Human Sciences: Positivism and its Epistemological Others, Duke University Press, 2005, ISBN 978-0-8223-3518-4.
State/Culture. State Formation after the Cultural Turn, Cornell University Press, 1999, ISBN 978-0-8014-3673-4.
Aufsätze & Artikel
"Ideas in Exile: Refugees from Nazi Germany and the Failure to Transplant Historical Sociology into the United States". In: International Journal of Politics, Culture, and Society 2010 (23), 1–27.
"German Exceptionalism and the Origins of Nazism: The Career of a Concept". In: Ian Kershaw, Moshe Lewin (Hrsg.): Stalinism and Nazism: Dictatorships in Comparison, 1997, 251–284-
"Social Class and the Reemergence of the Radical Right in Contemporary Germany". In: John R. Hall (Hg.): Reworking Class, Cornell University Press 1997, 335–368.
"The Myth of an Autonomous State: Industrialist, Junkers, and Social Policy in Imperial Germany". In: Geoff Eley (Hg.): Society, Culture, and the State in Germany, 1870-1930, University of Michigan Press 1996, 257–318.
"Die (un)moralische Ökonomie rechtsextremer Gewalt im Übergang zum Postfordismus". In: Das Argument, 1994 (23/1), 23–40.
"Fordism and the Immoral Economy of Right-Wing Violence in Contemporary Germany". In: Research on Democracy and Society, 1994 (2), 277–316.
Literatur
Schwerpunktheft Steinmetz, Mittelweg 36, Juni–Juli 2020, auch mit Texten Steinmetz'
Weblinks
http://lsa.umich.edu/soc/people/faculty/geostein.html
Einzelnachweise
Hochschullehrer (University of Michigan)
Soziologe (20. Jahrhundert)
US-Amerikaner
Geboren 1957
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,920 |
\section{INTRODUCTION}
At present, all published measurements of the CMB polarization used
discrete corrugated feeds to couple free-space to detectors.\cite{wollack2009opticalCouplingForCMB,padin2001cmbCBI,kovak2002cmbpolDASI,barnes2002cmbWMAPhorns,jones2003cmbBoomerang,barkats2005cmbpolCAPMAP,hinderks2009quad}
The use of corrugated feeds is motivated by the need for wide bandwidth,
good beam symmetry, minimal side lobes and low cross polarizations
while maintaining excellent transmission efficiency.\cite{clarricoats1984corrugatedHorns}
Next-generation imaging CMB polarimeters will use monolithic focal
plane detector arrays with hundreds of tightly packed detectors.\cite{lee2008polarbearCMBpol,niemack2010ACTpol,orlando2010BicepAndSpiderTESpolArrays,yoon2010spieTesPolarimetersForCMB}.
In this paper we describe one approach for producing monolithic arrays
of densely packed corrugated scalar feeds using micromachined Au-plated
Si which can be directly contacted to a monolithic array of superconducting
detectors (see Figure~\ref{fig:hornArrayAndDetectorArray}).
Extension of the conventional electroform approach to fabrication
of monolithic feed arrays is impractical. An alternative is metal
platelet arrays which consist of stacks of perforated metal plates
whose apertures' geometries define the horns' cross sections. A metal
platelet array with adequate performance for CMB polarimetry was demonstrated
with $91$-pixels at $95\,\mbox{GHz}$.\cite{bock2009opticalCouplingForCMB}
At NIST we are pursuing a new approach to fabricating monolithic corrugated
platelet arrays.\cite{britton2009ltd13siHornArray} Each layer in
the array is a Si wafer with photolithographically defined apertures.
Once assembled and Au-plated, these horn arrays are expected to feature
the same benefits as metal platelet arrays (including high thermal
conductivity) with the following additional advantages: (a) a thermal
expansion match to Si detector arrays, (b) more precise geometry reproduction
(and greater packing density), (c) smaller gaps between platelets
and (d) a straightforward path to arrays of thousands of feeds.\cite{britton2009ltd13siHornArray}
See Table~\ref{table:materialProperties} for a comparison of Si
with metals commonly used in platelet arrays.
\begin{figure}[b]
\begin{centering}
\includegraphics[width=0.5\columnwidth]{figures/feedArrayCouplingToDetectors}\caption{Illustration showing coupling between a monolithic corrugated Si platelet
feed array and a monolithic array of superconducting detectors fabricated
on Si.\cite{yoon2009ltd13proceedings} The detectors and Si feed array
are in direct thermal contact; there is no thermal expansion mismatch.\cite{britton2009ltd13siHornArray} }
\par\end{centering}
\label{fig:hornArrayAndDetectorArray}
\end{figure}
To demonstrate the feasibility of our approach, in 2009 we fabricated
and tested two corrugated feeds made of Si.\cite{britton2009ltd13siHornArray}
Subsequently a prototype monolithic Si array of $73$~corrugated
waveguides was also fabricated and tested. Currently underway at NIST
is the fabrication of a $50\,\mbox{mm}$ diameter array with $84$~horns
consisting of $33$~Si platelets. The platelets composing these devices
were machined in $76.2$~mm and $100\,\mbox{mm}$ diameter Si wafers
by use of photolithography and deep reactive ion etching (DRIE, see
Appendix.~A).
\begin{table}
\begin{centering}
\begin{tabular}{c|ccccc}
& $\rho\,\,[\mbox{kg}\cdot\mbox{m}^{-3}]$ & $c_{p}\,\,[\mbox{J}\cdot\mbox{m}^{-3}\cdot\mbox{K}^{-1}/10^{-6}]$ & \multicolumn{2}{c}{$\alpha\,\,[K^{-1}/10^{-6}]$ } & \multicolumn{1}{c}{$\lambda\,\,[W\cdot m^{-1}\cdot K^{-1}]$}\tabularnewline
& $\sim$300~K & $\sim$300 K & 100 K & 293 K & 297 K\tabularnewline
\hline
Al & 2698 & 2.37 & 12.2 & 23.1 & 236\tabularnewline
Cu & 8933 & 3.39 & 10.3 & 16.5 & 403\tabularnewline
Si & 2329 & 1.58 & -0.4 & 2.6 & 168 (at 173 K)\tabularnewline
\end{tabular}
\par\end{centering}
\caption{Comparison of structural materials used for horn arrays: $\rho$ is
density\cite{kayelaby1995constantsWeb}, $c_{p}$ is specific heat
(by volume)\cite{kayelaby1995constantsWeb}, $\alpha$ is coefficient
of thermal expansion\cite{kayelaby1995constantsWeb}, and $\lambda$
is thermal conductivity \cite{kayelaby1995constantsWeb}. }
\begin{centering}
\label{table:materialProperties}
\par\end{centering}
\end{table}
\section{CORRUGATED FEED DESIGN}
\label{sec:fhDesign}
\begin{figure}[b]
\begin{centering}
\includegraphics[width=0.6\columnwidth]{figures/feed_nist145ghz_03_profile_mod}\includegraphics[width=0.4\columnwidth]{figures/fh2_beforePlating}
\par\end{centering}
\caption{(left) Cross-section schematic of the prototype $150$ GHz corrugated
feed. The first six corrugation slots smoothly transform the fundamental
TE11 mode of the smooth-wall waveguide to the HE11 mode of the corrugated
section. A sine-squared profile is used in the flare section to the
aperture to achieve a more compact design than is possible with a
constant taper angle, with the added benefit of the location of the
phase center of the resulting beam that is coincident with the aperture
plane and is frequency-independent. (right) Photograph of a single
Si feed prior to electroplating. Features are (A) one of two clearance
holes filled with $4-40$ screws for holding together the platelets
during electroplating, (B) one of four holes for stainless alignment
dowels which mate with standard waveguides, and (C) is the horn aperture.
Corrugations are visible extending downward into the platelet stack
from the horn aperture. The translucent yellow is dried epoxy used
to adhere the platelets during electroplating. }
\label{fig:fh2schematicAndGlamorShot}
\end{figure}
The prototype corrugated horn design is driven by the needs of the
SPTpol and ACTpol receivers, both of which feature relatively fast
optics at the focal plane ($F\,\sim\,1.2$\textendash{}$1.3$). \cite{yoon2010spieTesPolarimetersForCMB,niemack2010ACTpol}
The input aperture diameter of the feed is determined by focal plane
sensitivity calculations, optimizing the tradeoff between beam spillover
efficiency and packing density. For the aforementioned receivers,
simulations indicate an optimum clear aperture diameter of $4.26\,\mbox{mm}$
(center-to-center packing distance of $5.26\,\mbox{mm}$ accounting
for the corrugation depths at the aperture), giving $34^{\circ}$
full width half maximum (FWHM) at nominal $150\,\mbox{GHz}$ operation.
The horn design follows standard practice. \cite{clarricoats1984corrugatedHorns,granet2005corrHornDesignPrimer}
It was optimized over the band from $122$~GHz to $170$ GHz, appropriate
for the $150$ GHz atmospheric window. The design was verified using
a modal-matching simulation package (Microwave Wizard by Mician, GmbH).\cite{nistComDisclaimer}
See Fig.~\ref{fig:fh2schematicAndGlamorShot} for a schematic.
The design was tested experimentally by fabrication and measurement
of a horn made from $60$ Si platelets each $250\,\mu\mbox{m}$ thick,
each corresponding to a ridge or a groove of a corrugation (see Figure~\ref{fig:fh2schematicAndGlamorShot}).
A metal seed layer (Ti:Au::$100\,\mbox{nm}$:$500\,\mbox{nm}$) was
deposited on the platelets mounted on an orbital platform canted at
$45^{\circ}$. Platelets were then stacked on stainless steel alignment
pins, clamped with a jig and adhered at the edges with an electrically
conductive epoxy. Platelet alignment accuracy by this approach was
$<\pm10\,\mu\mbox{m}$ layer-to-layer.\cite{britton2009ltd13siHornArray}
Subsequent electroplating of $3\,\mu\mbox{m}$ thick Cu followed by
$3\,\mu\mbox{m}$ thick Au was performed to ensure a high-conductivity
finish and to fill gaps between platelets ensuring electrical continuity.
Note that the thickness of electrolytically deposited metals is systematically
thinner in hard-to-reach high-aspect crevasses such as the corrugations
near the center of the platelet array.\cite{britton2009ltd13siHornArray}
Cited thicknesses are as measured on flat, superficial surfaces. Electroplated
copper was selected as an underlying layer due to its gap-filling
properties. The Au plating thickness was selected to be well in excess
of the skin depth of bulk Au: $90$~nm at $100$~GHz and $273\,\mbox{K}$.\cite{kayelaby1995constantsWeb,jackson1999a}.
\section{FEED PERFORMANCE}
\label{sub:fhPerformance}
A vector network analyzer (VNA) configured as described in Fig.~\ref{fig:mmWaveSetup2}
was used to characterize our horn's return loss, insertion loss and
far-field radiation patterns. The apparatus consisted of two horns:
a fixed transmitter (Tx) and a receiver (Rx) that pivoted about the
transmitting horn's phase center. The Rx horn was a commercially manufactured
corrugated metal horn for G-band (WR5). Simulated cross polarization
is $<-30\,\mbox{dB}$ and side-lobe amplitude is $<-25$~dB at $150$,
$180$ and $220$ GHz. Return loss and insertion loss were measured
with the horn aperture terminated against a microwave absorber or
a shorting metal plate, respectively. To measure H-plane and E-plane
beam patterns we used a $0^{\circ}$ or $90^{\circ}$ twist preceding
the Tx and after the Rx horns. Cross polarization measurements used
$45^{\circ}$ twists before the Tx horn and after the Rx horn. To
confirm proper operation of the system we used a pair of identical
metal horns in a test beam pattern measurement sweep. Manufacturing
errors in the waveguide twists and our angle-sweeping setup limited
the polarization aligment accuracy to $\sim\pm1^{\circ}$, resulting
in the leakage of the co-polar beam patterns dominating the nominal
cross-polar beam pattern data at the level of $\sim-23$ dB; this
represents an upper limit on the cross-polar levels of the prototype
Si feed.
Figures \ref{fig:fh2ReturnLoss}, \ref{fig:fh2InsertionLoss} and
\ref{fig:fh2BeamPattern145GHz} show the measured return loss, insertion
loss and far-field radiation pattern and cross polarization.
After the microwave measurements the horn was sliced in cross section
on a dicing saw. This permitted inspection of the horn's interior
for micromachining, assembly and metalization defects. In particular
we checked that the electroplated metal conformally coats sharp corners
and bridges (fills) platelet-platelet gaps. Of $94$ inspected corners
none were found without adequate metalization. Of $90$ inspected
platelet-platlet junctions three were found with unsatisfactory coating
of which only one which was certainly gapped.
\begin{figure}
\begin{centering}
\includegraphics[width=5in]{figures/vnaHornTestSetup}
\par\end{centering}
\caption{Schematic of feed test setup. It consists of two horns: a fixed transmitter
(Tx) and a receiver (Rx) that pivots about the transmitter's phase
center. The VNA S11 port is attached to the WR5 guide with a directional
coupler. A WR5-to-circular waveguide (CWG) transition interfaces with
the Tx horn. The VNA's S12 port is attached to the Rx horn. S11 was
calibrated at the calibration plane using a fixed short, sliding short
and sliding match. Since round calibration fixtures were unavailable,
horn measurements were compared with observation at the labeled check
point following the WR5-CWG transition. }
\label{fig:mmWaveSetup2}
\end{figure}
\section{SILICON FEED ARRAY}
In late $2009$ a prototype array structure with $73$ corrugated
waveguides was fabricated, temperature cycled (to $77\,\mbox{K}$)
and tested on the VNA. Testing methods and performance were similar
to the discrete Au-coated Si waveguides reported in $2009$.\cite{britton2009ltd13siHornArray}
Encouraged by the performance of this monolithic array of waveguides,
we are now fabricating a $50\,\mbox{mm}$ diameter array with $84$~horns
consisting of $33$~Si platelets (see Fig.~\ref{fig:cmb6ExplodedView}).
For corrugated feeds it is necessary to use $>4$ corrugations per
$\lambda$.\cite{clarricoats1984corrugatedHorns} Higher frequencies
require thinner, more fragile wafers. However, thin, large diameter
wafers are prone to fracture; handling $150$~mm diameter wafers
thinner than $500\,\mu\mbox{m}$ is not desirable. To address this
problem a two-tiered etch protocol was developed to permit the use
of thicker wafers ($\sim\lambda/4$) each defining a full corrugation
period. To reduce wafer handling the etch proceeded from a single
side in two stages. See Figure~\ref{fig:fabProcess} for a description
of the Si platelet fabrication process and Figure~\ref{fig:100mmWaferPics}
for images of Si platelets.
Typical wafer parameters for the Si used in the platelets are $0.001-0.005\,\Omega\cdot\mbox{cm}$
bulk resistivity (B doped, p-type), <100> crystal orientation (denoted
by wafer flat), double-side polished ($<0.5$~nm rms), $525\pm25\,\mu\mbox{m}$
thickness and $<20\,\mu\mbox{m}$ bow.
Individual platelets require metalization prior to stacking to facilitate
subsequent electrolytic plating. Metal deposition by evaporation proved
very robust in tests on individual feeds (Ti:Au::$100\,\mbox{nm}$:$500\,\mbox{nm}$)
and will be used for monolithic arrays as well. As with the individual
platelet feeds, platelet-platelet registration will be performed using
(removable) stainless dowels and clearance holes micromachined in
the Si. We are exploring use of epoxy and spring loaded clamps to
ensure that the the gap between platelets is minimal during electroplating
(Cu:Au::$3\,\mu\mbox{m}$:$3\,\mu\mbox{m}$).
\section{CONCLUSION}
\label{sec:conclusion}
We fabricated and tested Au-coated corrugated Si platelet waveguides,
waveguide arrays and horns. These devices exhibited performance comparable
to conventional all-metal devices. Our current work focuses on extending
these techniques to fabrication of monolithic waveguide arrays with
$600+$ individual pixels on $150$~mm wafers.
The flexibility of Si micromachining makes possible a wide varity
of microwave structures. For example, the 2-tiered etch recipe permits
overlap of adjacent horns' corrugations at the horn apertures for
greater packing density. A 3-tiered etch makes posible {}``ring-loaded''
corrugated horns with greatly increased spectral bandwidth for potential
multichroic detectors.\cite{mcmahon2009ringLoadedConversation,takeichi1971ringLoadedWaveguide}
\section*{APPENDIX A. SILICON DEEP ETCH}
\label{app:SiDRIE}
Plasma etching of silicon permits high aspect ratio features with
good repeatability and excellent mask selectivity. The NIST etcher
utilizes a variant of the BOSCH etch process optimized for silicon
deep etch ($>50\,\mu\mbox{m}$).\cite{larmer1992a,mcauley2001a} This
process forms nearly vertical sidewalls in silicon by interleaving
etch and surface passivation steps. The etch step is a chemically
active RF plasma ($\mbox{SF}_{6}$ and $\mbox{O}_{2}$) inductively
coupled to the wafer surface. The charged component of the plasma
is accelerated normal to the surface, enhancing its etch rate in the
vertical direction (tunable, $1-30\,\mu\mbox{m/min}$). The passivation
step ($\mbox{C}_{4}\mbox{F}_{8}$) coats all exposed surfaces including
sidewalls with a fluorocarbon polymer. Etch and passivation cycles
(typically $12$ and $8$ seconds respectively) are balanced so that
sidewalls are protected from over/under etching as material is removed
through the full wafer thickness. The cycled etching causes the sidewalls
to have a microscopic scalloped appearance with an amplitude of $100-500\,\mbox{nm}$
and a period of $200-1000\,\mbox{nm}$.\cite{mcauley2001a}
The primary etch mechanism for the $\mbox{SF}_{6}$/$\mbox{O}_{2}$
chemistry is due to chemical reactions between neutral atomic Fluorine
formed in the plasma and silicon at the wafer surface. Oxygen acts
to degrade the Fluorocarbon polymers ($\mbox{CF}_{x}$) to form gaseous
products. While other etch chemistries are possible, this is the most
common owing to the safety of the reactants and their selectivity
of silicon over commonly used etch masks (photoresist and silicon
oxide).\cite{flamm1990a,madou2002a} The gaseous products are pumped
away and do not redeposit on the process wafer. Structures with multiple
tiers per wafer are possible through the use of overlapping etch masks\cite{britton2009aplSiTraps}
or, at lower resolution, with roll-on photoresist.
DRIE permits fabrication of high-apect features in Si ($\sim50:1$
aspect ratio). Lateral resolution is limited by the greater of photolithography
resolution and etch aspect ratio. For example, in $250\,\mu\mbox{m}$
thick Si the NIST etcher's lateral resolution is $\pm5\,\mu\mbox{m}$
through the full wafer bulk even though our photolithography resolution
is $\sim3\,\mu\mbox{m}$. Radial variation in etch rate is ultimately
determined by aspects of the DRIE etch tool such as plasma uniformity;
we observe a radial (center to edge) variation of $<3\%$. Tools for
applying this process to wafers $150\,\mbox{mm}$ in diameter are
currently available in the NIST microfabrication facility. High resolution
wafer-scale Si etch tools are ubiquitous in Si MEMs foundries.
\section*{ACKNOWLEDGMENTS}
We thank the members of the ACT and SPT collaborations for their support
and interest in this research. We thank John J. Jost and Dave Walker
for suggestions on the manuscript. M.~D.~Niemack and K.~W.~Yoon
acknowledge support from the National Research Council. This work
was supported by NIST through the Innovations in Measurement Science
program. This proceeding is a contribution of NIST and is not subject
to U.S. copyright.
\begin{figure}
\begin{centering}
\includegraphics[width=0.75\columnwidth]{figures/fh2_return_loss_20100622}
\par\end{centering}
\caption{Simulated (solid, blue) and measured (solid, red) return loss. Also
shown (dotted) is the return loss of the rectangular-to-circular transition
necessary to mate to the Si feed. This transition is located beyond
the calibration point, and as such its intrinsic return loss contributes
to that of the Si feed's as shown above. See Fig.~\ref{fig:mmWaveSetup2}
for an explanation of the check point. The average return loss is
$<-20$~dB from $120$~GHz to $170$~GHz.}
\label{fig:fh2ReturnLoss}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=0.75\columnwidth]{figures/fh2_insertion_loss2_20100622}
\par\end{centering}
\caption{(solid trace) Implied insertion loss (IIL) is $(\mbox{S11}_{\mbox{horn}}^{2}-\mbox{S11}_{\mbox{CP}}^{2})/2$
where $\mbox{S11}_{\mbox{CP}}$ is measured with a short at the check
point (Fig.~\ref{fig:mmWaveSetup2}) and $\mbox{S11}_{\mbox{horn}}$
is measured with a short pressed against the output face of the horn.
This expression accounts for reflection from the WR5-CWG transition.
The average insertion loss is $\sim-0.2$~dB from $130$~GHz to
$170$~GHz. (dashed trace) IIL when the horn is intentionally misaligned
(lateral translation) with the circular waveguide (CWG) by $\sim0.1$
mm. }
\label{fig:fh2InsertionLoss}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=0.9\columnwidth]{figures/fh2_beam_pattern_fromKWY20100623}
\par\end{centering}
\caption{Plot of beam pattern and cross polarization at $130$, $150$ and
$170$~GHz. The solid traces are simulation while the points are
experiment. We conclude that from $130$~GHz to $170$~GHz the cross
polarization is $<-23$~dB, the side lobes are $<-25$~dB and beam
symmetry is good. }
\label{fig:fh2BeamPattern145GHz}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=0.8\columnwidth]{figures/201006_fabProcessSchematic2}\caption{Figure illustrating the the process flow to fabricate platelets in
Si. For clarity only a single pixel is shown; in practice all pixels
are fabricated in parallel for each platelet. A pair of overlapping
etch masks and the additivity of the DRIE etch process were exploited.
The lower, wide-feature mask was defined in $\sim1\,\mu\mbox{m}$
thermal $\mbox{SiO}_{2}$ using photolithography and a HF wet etch.
The upper narrow-feature mask was defined in $7\,\mu\mbox{m}$ photoresist
and patterned using photolithography. At the outset of etching, both
masks were patterned and adhered to the wafer. After an initial $250\,\mu\mbox{m}$
etch using the narrow-feature mask, it was stripped off with acetone
leaving behind the wide-feature mask. Residual DRIE passivation material
was stripped with Dupont EKC-265 heated to $75$~C.\cite{nistComDisclaimer}
To protect the etcher's chuck, Dupont MX5020 roll-on photoresist was
applied to the back-side of the wafer.\cite{nistComDisclaimer} The
second $250\,\mu\mbox{m}$ deep etch penetrates the wafer. The remaining
photoresist with acetone and a Si plug at the core of each aperture
falls out. The $\mbox{SiO}_{2}$ is removed with a HF wet etch. }
\par\end{centering}
\label{fig:fabProcess}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=0.49\columnwidth]{figures/400umDRIEsidewall}
\par\end{centering}
\caption{(left) Photograph illustrating typical cross section of a corrugation.
Note that wafer thickness varies wafer to wafer: $525\pm25\,\mu\mbox{m}$.
The target etch depth was $250\,\mu\mbox{m}$ (measured from the bottom).
This wafer was not metallized. }
\label{fig:100mmWaferPics}
\end{figure}
\begin{figure}
\begin{centering}
\includegraphics[width=0.9\columnwidth]{figures/23_cmb6_w-3}\caption{Perspective view of $23$ of the $33$ Si platelets that will be stacked
and metallized to form a $50\,\mbox{mm}$ diameter array with $84$~horns.
This planar array of corrugated platelet feeds will be integrated
with a matching arrays of NIST fabriacated OMT-coupled TES polarimeters
fabricated on Si and $\lambda/4$ Au-coated Si backshorts.}
\par\end{centering}
\label{fig:cmb6ExplodedView}
\end{figure}
\clearpage
\bibliographystyle{spiebib}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,708 |
Q: Calculator stack My understanding of calculators is that they are stack-based. When you use most calculators, if you type 1 + 2 [enter] [enter] you get 5. 1 is pushed on the stack, + is the operator, then 2 is pushed on the stack. The 1st [enter] should pop 1 and 2 off the stack, add them to get 3 then push 3 back on the stack. The 2nd [enter] shouldn't have access to the 2 because it effectively doesn't exist anywhere.
How is the 2 retained so that the 2nd [enter] can use it?
Is 2 pushed back onto the stack before the 3 or is it retained somewhere else for later use? If it is pushed back on the stack, can you conceivably cause a stack overflow by repeatedly doing [operator] [number] [enter] [enter]?
A: The only true stack based calculators are calculators which have Reverse Polish Notation as the input method, as that notation directly operates on stacks.
A: Conceptually, in hardware these values are put into registers. In simple ALU (Arithmatic Logical Units (i.e. simply CPUs)), one of the registers would be considered an accumulator. The values you're discussing could be put on a stack to process, but once the stack is empty, the register value (including the last operation) may be cached in these registers. To which, when told to perform the operation again, uses the accumulator as well as the last argument.
For example,
Reg1 Reg2 (Accumulator) Operator
Input 1 1
Input + 1 +
Input 2 2 1 +
Enter 2 3 +
Enter 2 5 +
Enter 2 7 +
So it may be a function of the hardware being used.
A: All you would need to do is retain the last operator and operand, and just apply them if the stack is empty.
A: There is an excellent description and tutorial of the Shunting-yard algorithm (infix -> rpn conversion) on wikipedia.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,818 |
The Palace of the Condes de Cirat (Spanish: Palacio de los Condes de Cirat) is a palace located in Almansa, Spain. It was declared Bien de Interés Cultural in 1990.
References
Palaces in Castilla–La Mancha
Bien de Interés Cultural landmarks in the Province of Albacete
Almansa | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,772 |
{"url":"http:\/\/learn2adapt.com\/tag\/howto\/","text":"Warning: file_put_contents(H:\\root\\home\\csolved-001\\www\\learn2adapt\/wp-content\/mmr\/fa301849-1547099415.css.accessed): failed to open stream: Permission denied in H:\\root\\home\\csolved-001\\www\\learn2adapt\\wp-content\\plugins\\merge-minify-refresh\\merge-minify-refresh.php on line 550\nDec 18\n\n## L2A Links for December 18th\n\n\u2022 Developing Razor Sharp Focus with Zen Habits \u2013 If you\u2019ve just logged into Facebook or your email for the 10th time today or find yourself thinking in Facebook statuses throughout the day, it may be time to read Leo Babauta\u2019s eBook \u201cFocus: A simplicity manifesto in the age of distraction\u201d.\n\u2022 Kurt Vonnegut\u2019s Three Specialists for Change \u2013 Found an online passage quoting Kurt Vonnegut in \"Bluebeard\". One of my favorite summaries of how to put together a successful change leadership team.\n\nwritten by Jeff Kelly \\\\ tags: , , , , , , ,\n\nOct 13\n\n## L2A Links for October 13th\n\nwritten by Jeff Kelly \\\\ tags: , , , , , , , , ,\n\nMay 05\n\n## L2A Links for May 5th\n\nwritten by Jeff Kelly \\\\ tags: , , , , , , , , ,\n\nJun 15\n\nwritten by Jeff Kelly \\\\ tags: , , , , , , , , , , , , , , , , ,\n\nFeb 06\n\n## Jeff\u2019s del.icio.us bookmarks for February 6th\n\nThese are my links for February 6th:\n\n\u2022 Social Network Operating System : eLearning Technology \u2013 More great ideas from Tony Karrer. Good point on the obvious need for \"transportable open social graph\u2026 to leverage across applications.\" Also I wonder if the distinction of \"people\" and \"content\" is valid. Are we just not another form of content on t\n\u2022 Five Ways Women Learn \u2013 Learning Styles \u2013 Lifelong Learning \u2013 Interesting article from a book from back in the day. It raises tow questions immediately: How is this different than how men learn? and How does this manifest itself in how women learn from the Web and from collaborative learning?\n\u2022 LUNARR \u2013 LUNARR Works Smarter \u2013 Lunarr has a new take on the Enterprise 2.0 goal of improving collaboration. They take collaborative wiki-like editing and add email-like messaging system that associates messages with those documents.\n\u2022 Howcast \u2013 Howcast launched today to be the \"YouTube of instructional videos.\" It was started by three ex-GooTube employees. High audience participation: suggestions, voting on ideas, script editing, etc. A possible mecca for learning videos.\n\u2022 Time Warner Plans to Split AOL Businesses \u2013 New York Times \u2013 Just wanted to bookmark this as a \"follow-up\" to my February 1 post where I postulate that 2008 will see the splitting and spin-off of the three AOL businesses\u2026\n\nwritten by Jeff Kelly \\\\ tags: , , , , , , , , , , , , , , , ,\n\nWarning: file_put_contents(H:\\root\\home\\csolved-001\\www\\learn2adapt\/wp-content\/mmr\/aa910b25-1544458585.js.accessed): failed to open stream: Permission denied in H:\\root\\home\\csolved-001\\www\\learn2adapt\\wp-content\\plugins\\merge-minify-refresh\\merge-minify-refresh.php on line 550","date":"2019-04-24 20:14:05","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\": 0.8686103820800781, \"perplexity\": 7348.592869953493}, \"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\/1555578656640.56\/warc\/CC-MAIN-20190424194348-20190424220348-00322.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.adrian.idv.hk\/2019-10-25-youtube\/","text":"If you search \u201ccantopop\u201d in YouTube, you will find loads of music videos. Each of the video will bear a title. Below are some examples:\n\n HOCC\u4f55\u97fb\u8a69\u300a\u4ee3\u4f60\u767d\u982d\u300bMV\n\u6797\u4e8c\u6c76 Eman Lam - \u611b\u60c5\u662f\u4e00\u7a2e\u6cd5\u570b\u751c\u54c1\n[JOY RICH] [\u820a\u6b4c] \u5f35\u570b\u69ae - \u6709\u5fc3\u4eba(\u96fb\u5f71\u91d1\u679d\u7389\u84492\u4e3b\u984c\u66f2)\n\u5f35\u5b78\u53cb _ \u674e\u9999\u862d (\u9ad8\u6e05\u97f3)\n\u885b\u862d Janice Vidal - \u4f2f\u5229\u6046\u7684\u4e3b\u89d2 The Star Of Bethlehem (Official Music Video)\n\u5f35\u656c\u8ed2 Hins Cheung - \u9177\u611b (Hins Live in Passion 2014)\n\n\nCan we figure out the name of the artist and the name of the song from the title?\n\nThis problem is closely similar to the problem of segmentation in the first sight. The problem of Chinese segmentation is to identify phases from a string of characters, which then we can look up a dictionary or otherwise, identify each phases part of speech. One of the way to do segmentation is to train a hidden Markov model or using LSTM. However, I don\u2019t think this approach is applicable here \u2013 for a segmentation problem usually work on a fairly long sentence and train with a massive data, which the phases are supposed to be repeated fairly often. The problem here does not fit. Firstly, quite often we know how to segment the title: There are punctuations to group ideograph characters. Secondly, tagging the segmented phases by dictionary means we have a full dictionary of all artist names and songs, which the problem would be trivial if we have one and it can\u2019t cope with new entries.\n\nOf course, we can assume that the name of the song vs the name of the artist would bias to a different subset of characters. But we can also base on some contextual hints. For example, we can expect the phase inside \u300a..\u300b is the name of the song and the short phase closer to the beginning of the title is more likely than not the name of the artist. Instead of figuring out the rules to do this, we can learn through data and build an engine. Here I use scikit-learn.\n\n# Preparation of data\n\nWe collected a few hundred of cantopop titles from YouTube. Then we segmentize them and convert the tokens into features as follows:\n\ndef condense(tagged: Iterable[Tuple[str, str]]) -> Iterable[Tuple[str, str]]:\n\"Aggregate pairs of the same tag\"\ntag, string = None, ''\nfor t,s in tagged:\nif tag == t:\nstring += s\nelif tag is None:\ntag, string = t, s\nelse:\nyield (tag, string)\ntag, string = t, s\nif tag is not None:\nyield (tag, string)\n\ndef latincondense(tagged: Iterable[Tuple[str, str]]) -> Iterable[Tuple[str,str]]:\n\"Aggregate Latin words (Lu then Ll) into one tuple and mangle the space (Zs) type\"\ndash = ['-', '_', '\\u2500', '\\uff0d', ]\ntag, string = None, ''\nfor t,s in tagged:\nif (tag, t) == ('Lu','Ll'):\ntag, string = 'Lul', string+s\nelif tag is None:\ntag, string = t, s\nelse:\nif tag == 'Zs':\nyield (tag, ' ')\nelif tag in ['Pc','Pd'] and string in dash:\nyield ('Pd', '-')\nelse:\nyield (tag, string)\ntag, string = t, s\nif tag is not None:\nyield (tag, string)\n\ndef strcondense(tagged: Iterable[Tuple[str,str]]) -> List[Tuple[str,str]]:\n\"Condense latin string phases into one tuple, needs look ahead\"\nstrtype = ['Lu', 'Ll', 'Lul', 'Lstr']\ntagged = list(tagged)\ni = 1\n# Condense string into Lstr tag\nwhile i < len(tagged):\n# combine if possible, otherwise proceed to next\nif tagged[i][0] in strtype and tagged[i-1][0] in strtype:\ntagged[i-1:i+1] = [('Lstr', tagged[i-1][1]+tagged[i][1])]\nelif i>=2 and tagged[i][0] in strtype and tagged[i-1][0] == 'Zs' and tagged[i-2][0] in strtype:\ntagged[i-2:i+1] = [('Lstr', tagged[i-2][1]+' '+tagged[i][1])]\ni = i-1\nelse:\ni += 1\nreturn tagged\n\ndef features(title: str) -> List[dict]:\n'''Convert a title string into features'''\nstopword = ['MV', 'Music Video', '\u6b4c\u8a5e', '\u9ad8\u6e05', 'HD', 'Lyric Video', '\u7248']\nquotes = ['()', '[]', '\u300a\u300b', '\u3010\u3011', '\uff08\uff09', \"\u201c\u201d\", \"''\", '\"\"', ] # Ps and Pe, Pi and Pf, also Po\n# condense string with tags\ntagstr = strcondense(latincondense(condense( [(unicodedata.category(c), c) for c in title] )))\n# add other features: within quote (for diff quotes), is before dash, is\n# after dash, strlen count, tok count, Lo tok count, str is in name set, str\n# is in stopword set\nqpos = {}\nstrlen = 0\nLo_cnt = 0\nvector = []\n# position offset features, forward and backward\nfor i, (t, s) in enumerate(tagstr):\nvector.append(dict(\nstr=s, tag=t, ftok=i+1, flen=strlen, slen=len(s),\nstopword=any(w in s for w in stopword)\n))\nif t == 'Lo':\nLo_cnt += 1\nvector[-1]['fzhtok'] = Lo_cnt\nstrlen += len(s)\nfor tok in vector:\ntok.update({\n'titlen': strlen,\n'btok': len(vector) + 1 - tok['ftok'],\n'blen': strlen - len(tok['str']) - tok['flen'],\n})\nif 'fzhtok' in tok:\ntok['bzhtok'] = Lo_cnt + 1 - tok['fzhtok']\n# bracket features\nfor key in quotes + ['-']:\nqpos[key] = []\nfor tok in vector:\nif tok['tag'] == 'Pd':\nqpos['-'].append(tok['ftok'])\nelse:\nfor quote in quotes:\nif tok['str'] in quote:\nqpos[quote].append(tok['ftok'])\nbreak\nfor tok in vector:\ntry:\ntok['dashbefore'] = tok['ftok'] > min(qpos['-'])\ntok['dashafter'] = tok['ftok'] < max(qpos['-'])\nexcept ValueError:\npass\nfor quote in quotes:\nif not qpos[quote]:\ncontinue\ninquote = [1 for i,j in zip(qpos[quote][::2], qpos[quote][1::2]) if i < tok['ftok'] < j]\ntok[quote] = bool(inquote)\nreturn vector\n\n\nThe above code is to segmentize the title string based on the unicode character category, for we expects CJK ideograph and Latin alphabets mixed with punctuations and spaces. We do not try to further segmentize a string of CJK ideographs into phrases but treat it as a whole. We also normalize different forms of dash into one and identify stopwords based on substring matching. The features of each segmentized tokens are assigned based on length (titlen and slen), the position (ftok, btok, flen, blen, fzhtok, bzhtok, for counting forward and backward, based on characters and tokens), and neighbours (dashbefore, dashafter, (), [], \u300a\u300b, \u3010\u3011, \uff08\uff09, \u201c\u201d, '', \"\", mostly to identify whether the token is surrounded by a pair of different type of brackets\/quotes).\n\nWith these features created from the tokens, we manually label which one corresponds to the name of artist, name of the song, and everything else. Now we have a problem of multiclass classification: Only not sure which algorithm is the best to train and apply.\n\n# Comparing different classifiers\n\nThere is a beautiful chart at scikit\u2019s auto examples that compares different classifiers with different nature of data. Unfortunately this is only for 2D (two input features) but we have a higher dimension. We will forget about the graphics but focus only on the classification accuracy for now. Here is what we do for classification test:\n\n#!\/usr\/bin\/env python\n# coding: utf-8\n\n#\n# Classifier demo\n#\n# Some code are derived from\n# https:\/\/scikit-learn.org\/stable\/auto_examples\/classification\/plot_classifier_comparison.html\n\nimport pickle\n\nimport pandas as pd\nimport numpy as np\n# scikit-learn utility functions\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import classification_report\n# different classifiers\nfrom sklearn.linear_model import LogisticRegression\nfrom sklearn.neural_network import MLPClassifier\nfrom sklearn.neighbors import KNeighborsClassifier\nfrom sklearn.svm import SVC\nfrom sklearn.gaussian_process import GaussianProcessClassifier\nfrom sklearn.gaussian_process.kernels import RBF\nfrom sklearn.tree import DecisionTreeClassifier\nfrom sklearn.naive_bayes import GaussianNB\n\n#\n# Define classifiers\n#\n\nclassifiers = [\n(\"Logistic Regression\", LogisticRegression(solver='newton-cg', max_iter=1000, C=1, multi_class='ovr'))\n,(\"Nearest Neighbors\", KNeighborsClassifier(3))\n,(\"Linear SVM\", SVC(kernel=\"linear\", C=0.025))\n,(\"RBF SVM\", SVC(gamma=2, C=1))\n,(\"Decision Tree\", DecisionTreeClassifier(max_depth=5))\n,(\"Random Forest\", RandomForestClassifier(max_depth=5, n_estimators=10, max_features=1))\n,(\"Neural Net\", MLPClassifier(alpha=0.01, max_iter=1000))\n,(\"Naive Bayes\", GaussianNB())\n,(\"Gaussian Process\", GaussianProcessClassifier(1.0 * RBF(1.0)))\n]\n\n#\n# Prepare for plotting and classification\n# df is the input data of feature vectors and labels\n# incol is all feature columns\n# 'label' is the classification label, i.e., the expected result\n#\n\nX = df[incol]\ny = df['label']\n\n#\n# Train, evaluate, and plot\n#\n\n# preprocess dataset, split into training and test part\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=1841)\n\n# iterate over classifiers and plot each of them\nfor name, clf in classifiers:\n# train and print report\nclf.fit(X_train, y_train)\nscore = clf.score(X_test, y_test)\nprint(\"----\\n{} (score={:.5f}):\".format(name, score))\nprint(classification_report(y_test, clf.predict(X_test), digits=5))\n\n\nand this is the result:\n\nLogistic Regression (score=0.93935):\nprecision recall f1-score support\n\na 0.78919 0.76842 0.77867 190\nt 0.82099 0.73889 0.77778 180\nx 0.96966 0.98427 0.97691 1526\n\naccuracy 0.93935 1896\nmacro avg 0.85994 0.83053 0.84445 1896\nweighted avg 0.93746 0.93935 0.93814 1896\n----\nNearest Neighbors (score=0.91139):\nprecision recall f1-score support\n\na 0.74020 0.79474 0.76650 190\nt 0.78873 0.62222 0.69565 180\nx 0.94516 0.96003 0.95254 1526\n\naccuracy 0.91139 1896\nmacro avg 0.82470 0.79233 0.80490 1896\nweighted avg 0.90977 0.91139 0.90950 1896\n----\nLinear SVM (score=0.92563):\nprecision recall f1-score support\n\na 0.75661 0.75263 0.75462 190\nt 0.76608 0.72778 0.74644 180\nx 0.96419 0.97051 0.96734 1526\n\naccuracy 0.92563 1896\nmacro avg 0.82896 0.81697 0.82280 1896\nweighted avg 0.92458 0.92563 0.92505 1896\n----\nRBF SVM (score=0.83228):\nprecision recall f1-score support\n\na 0.97500 0.20526 0.33913 190\nt 1.00000 0.07778 0.14433 180\nx 0.82790 0.99934 0.90558 1526\n\naccuracy 0.83228 1896\nmacro avg 0.93430 0.42746 0.46301 1896\nweighted avg 0.85898 0.83228 0.77655 1896\n----\nDecision Tree (score=0.94304):\nprecision recall f1-score support\n\na 0.92715 0.73684 0.82111 190\nt 0.80460 0.77778 0.79096 180\nx 0.95990 0.98820 0.97385 1526\n\naccuracy 0.94304 1896\nmacro avg 0.89722 0.83427 0.86197 1896\nweighted avg 0.94187 0.94304 0.94118 1896\n----\nRandom Forest (score=0.90612):\nprecision recall f1-score support\n\na 0.94595 0.55263 0.69767 190\nt 0.86486 0.53333 0.65979 180\nx 0.90621 0.99410 0.94812 1526\n\naccuracy 0.90612 1896\nmacro avg 0.90567 0.69336 0.76853 1896\nweighted avg 0.90627 0.90612 0.89565 1896\n----\nNeural Net (score=0.95464):\nprecision recall f1-score support\n\na 0.88636 0.82105 0.85246 190\nt 0.85311 0.83889 0.84594 180\nx 0.97408 0.98493 0.97947 1526\n\naccuracy 0.95464 1896\nmacro avg 0.90452 0.88162 0.89262 1896\nweighted avg 0.95380 0.95464 0.95407 1896\n----\nprecision recall f1-score support\n\na 0.87571 0.81579 0.84469 190\nt 0.84066 0.85000 0.84530 180\nx 0.97332 0.98034 0.97682 1526\n\naccuracy 0.95148 1896\nmacro avg 0.89656 0.88204 0.88894 1896\nweighted avg 0.95095 0.95148 0.95109 1896\n----\nNaive Bayes (score=0.38238):\nprecision recall f1-score support\n\na 0.14082 0.98947 0.24656 190\nt 0.78049 0.35556 0.48855 180\nx 0.98747 0.30996 0.47182 1526\n\naccuracy 0.38238 1896\nmacro avg 0.63626 0.55166 0.40231 1896\nweighted avg 0.88298 0.38238 0.45083 1896\n----\nGaussian Process (score=0.94409):\nprecision recall f1-score support\n\na 0.79581 0.80000 0.79790 190\nt 0.84146 0.76667 0.80233 180\nx 0.97339 0.98296 0.97815 1526\n\naccuracy 0.94409 1896\nmacro avg 0.87022 0.84988 0.85946 1896\nweighted avg 0.94307 0.94409 0.94340 1896\n----\nQDA (score=0.10021):\nprecision recall f1-score support\n\na 0.10021 1.00000 0.18217 190\nt 0.00000 0.00000 0.00000 180\nx 0.00000 0.00000 0.00000 1526\n\naccuracy 0.10021 1896\nmacro avg 0.03340 0.33333 0.06072 1896\nweighted avg 0.01004 0.10021 0.01826 1896\n\n\nThe classification_report gives out precision (true positive over all positive, $\\frac{TP}{TP+FP}$), recall (true positive over all true, $\\frac{TP}{TP+FN}$), the $F_1$-score (i.e., simple harmonic mean of precision and recall), and the accuracy (fraction of correct classification). QDA is particularly bad and in fact, the model is failed to run because of some runtime error due to collinear input to discriminant analysis, probably yielded by intermediate results.\n\nNow this needs a bit of explanations. From the support figures, we can see that there is a large number of class x (neither artist name a nor song title t) and thus blindly classify everything into x gives quite good (80% accuracy) result anyway. So we should focus on the precision and recall of the other two classes. In this case AdaBoost, neural network, and decision tree all gives good result while other models are lagging behind.\n\nAmongst these models, Naive Bayes and Quadratic Discriminant Analysis are based on Bayes\u2019 rule. Namely, it involves computing the probability\n\nNaive Bayes: Assume that the marginal distribution of each feature $x_i$ conditioned on the classification result $y$ is independent of other features, i.e., $P(x_i\\mid y,x_1,\\cdots,x_{i-1},x_{i+1},\\cdots,x_n)=P(x_i\\mid y)$. Then we learn for the distribution of each features $P(x_i\\mid y)$, and classify based on highest probability, $\\hat{y} = \\arg\\max_y P(y)\\prod_i P(x_i\\mid y)$. Gaussian naive Bayes models $P(x_i\\mid y)$ as Gaussian.\n\nQuadratic discriminant analysis: The probability $P(X\\mid y)$ is modelled as a multivariate Gaussian distribution instead of dealing with each features independently. For each class output $y$ we may use a different covariance matrix $\\Sigma$ in the distribution. If we enforce all classes use the same $\\Sigma$, this will become linear discriminant analysis (LDA)\n\nThe models Logistic Regression and Gaussian Process Classifier are regression based:\n\nLogistic regression: Classification based on the function $\\hat{y}=\\sigma(w^Tx)$ for features $x$, learned weights $w$, and logistic function $\\sigma()$. Sometimes we will incorporate the classification result $y\\in\\{+1,-1\\}$ into the function for training, $\\hat{y}=\\sigma(y\\cdot w^Tx)$\n\nGaussian process classifier: Generalization of logistic regression, using $\\hat{y}=\\sigma(f(x))$ with kernel function $f()$. In the above case, the radial basis function is used.\n\nTwo models of support vector machine are used: the Linear SVM and RBF SVM, and the k-nearest neighbor is also closely related\n\nLinear SVM: Model the feature space as a high dimensional metric space and find the optimal hyperplane (a.k.a. the support vector) to separate the different classes based on the features\n\nRBF SVM: Using RBF kernel instead in the SVM. That is, instead of modeling the feature space as metric space, they are skewed by a kernel function before the support vector is found.\n\nk-Nearest neighbours: Similar to linear SVM, the feature space is presented as a metric space and then the classification on any query point is determined by simple majority voting amongst the $k$ nearest neighbours of the query point.\n\nThere are also three decision tree-based models:\n\nDecision tree: A simple flowchart of tests to determine the classification result\n\nRandom forest: multiple decision trees based on random subset of training data and then pick the best performing one\n\nAdaBoost: adaptive boosting (Freund and Schapire, 1996), by default it is a decision tree model. It begin with equal weight samples and iteratively trained the decision tree and afterwards assign heavier weight to those with wrong classifications.\n\nAnd finally a neural network, a.k.a. multilayer perceptrons. In here is 3-layer network with ReLU activation and 100 perceptrons in the middle layer.\n\nThe worst performing two, naive Bayes and QDA, are probably due to the assumption of Gaussian distribution as we have quite many boolean features that won\u2019t fit. The SVM models as well as the k-NN put the features in a metric space for learning. Because the discrete nature of boolean features is not an issue to find distance or hyperplane in the metric space, they are vastly better than naive Bayes and QDA. One further generalization is to allow linear combination of features. Both logistic regression and Gaussian process classification applies classification on such linear combination, and they works slightly better. Neural network is similarly, also involves a linear combination of features. But it applies the nonlinear activation functions twice and it seems such flexibility contributes to the improvement in performance.\n\nThe decision tree based models are from another school. It could be the best performing and most flexible as long as we increase the depth allowed. But it is also very easy to be overfit (unless the correlation between feature and output are very strong). The unstable performance amongst AdaBoost, decision tree, and random forest is an evidence of such.\n\nAdjusting the regularization parameter $C$ in SVM models and logistic regression models do not seem to do much help. The neural network models, however, can give a few percentage point difference in wrong hyper-parameters. In this case, the default 3-layer neural network with 100 perceptrons in the hidden layer seems to be enough. An additional layer gives no help at all. But if the regularization parameter alpha is too big, e.g., alpha=1, the system will perform worse for as much as 5%. It is also interesting to see the non-linear activation functions generally perform slightly better than the rectified linear function.\n\n# Preprocessing and other improvement attempts\n\nIt is quite often to see a machine learning exercise to normalise the data by scaling. We can do so on the non-boolean features, i.e., before feeding to the classifier, we mangle the dataframe first:\n\nfrom sklearn.datasets import make_classification\n\n# Scale transform vectors before learning\nscalecols = ['titlen', 'ftok', 'btok', 'flen', 'blen', 'slen']\nscaler = StandardScaler()\nscaler.fit(df[scalecols])\ndf[scalecols] = scaler.transform(df[scalecols])\n\n\nBut we have to be careful that the scaling is based on the data that it fit. We must save the scaler if we want to reuse the classifier. However, it does not seem to provide much help if we compare the $F_1$ scores before and after scaling. We can reasonably attribute this to the fact that the input features are not too exaggerated or diverse in magnitude.\n\nAnother approach is to modify the feature set. First we attempt to remove some features to avoid introducing noises to the model. We do this by comparing the correlation coefficient (between \u20131 to +1) of each feature to the class label, as follows:\n\n#\n# Numeric check: Correlation coefficient of features to labels\n# Here we build each label as an boolean column (valued 0 or 1) and find the\n# correlation coefficient matrix of a label column appended by all input feature\n# columns, then pick the first row into the new dataframe\n#\nindex = [\"a\", \"t\", \"x\"]\nfor label in index:\ndf[label] = df['label'].eq(label).astype(int)\n\n# Dataframe of correlation coefficients\ncorrcoef = pd.DataFrame({label: np.corrcoef(df[[label] + incol].T)[0][1:] for label in index},\nindex=incol).T\n# print the correlation coefficients with small values masked out\n.dropna(axis=1, how='all') \\\n.columns\nprint(corrcoef[sigfeats].to_string(float_format=\"{:.2f}\".format))\n\n\nand in this case, we have the following output:\n\n ftok btok flen blen fzhtok bzhtok () Lstr [] angle dashafter dashbefore square stopword\na -0.30 0.21 -0.30 0.20 0.23 0.55 nan 0.38 nan nan 0.21 -0.20 nan nan\nt nan nan nan nan 0.44 0.32 nan 0.35 nan 0.57 nan 0.11 0.12 nan\nx 0.23 -0.12 0.26 -0.12 -0.51 -0.64 0.14 -0.55 0.11 -0.39 nan nan nan 0.13\n\n\nSo these are the features that has an absolute value of correlation coefficient of larger than 0.1. If we use only these features in the classifiers we can see an observable improvement on the naive Bayes model as we no longer affected by the noise features. Not so significant improvement is also seen in decision tree-based models as well as metric space-based models such as SVM and nearest neighbours. Neural network models, however, does not seem to give significant difference. Likely because it already turned off the unimportant features by training.\n\nWe do not need to check for adding more features based on linear combination as most of the classification models will check on those. However, we tried to introduce ratio features such as presenting ftok as percentage position (i.e., ftok\/(ftok+btok), code below) but it turns out no improvement to the result.\n\ndf[\"tokpct\"] = df[\"ftok\"]\/(df[\"ftok\"] + df[\"btok\"] - 1)\ndf[\"lenpct\"] = (df[\"flen\"]+df[\"slen\"])\/(df[\"flen\"] + df[\"blen\"] + df[\"slen\"])\nincol += [\"tokpct\", \"lenpct\"]\n\n\n# Cheating to help\n\nBecause this exercise is focused on cantopop and there are finite number of artists of it. In fact, there are websites (such as https:\/\/mojim.com) that tracks all songs of cantopop and it can be a database to help us match. In order to make this more interesting, we do not try to match the song title but only the artist and see how such help can contribute to the performance.\n\nThis is the code we scrap all artist names:\n\nimport requests\nimport parsel\n\ndef curl(url):\n'''Retrieve from a URL and return the content body\n'''\nreturn requests.get(url).text\n\ndef gen_urls() -> List[str]:\n'''Return urls as strings for the artist names from mojim. Example URLs:\nhttps:\/\/mojim.com\/twzlha_01.htm\nhttps:\/\/mojim.com\/twzlha_07.htm\nhttps:\/\/mojim.com\/twzlhb_01.htm\nhttps:\/\/mojim.com\/twzlhb_07.htm\nhttps:\/\/mojim.com\/twzlhc_01.htm\nhttps:\/\/mojim.com\/twzlhc_33.htm\n'''\nfor a in ['a', 'b']:\nfor n in range(1, 8):\nyield \"https:\/\/mojim.com\/twzlh{}_{:02d}.htm\".format(a, n)\nfor n in range(1, 34):\nyield \"https:\/\/mojim.com\/twzlhc_{:02d}.htm\".format(n)\n\ndef _get_names() -> List[str]:\n'''Return names of artists from mojim'''\nfor url in gen_urls():\nhtml = curl(url)\nselector = parsel.Selector(html)\ntitles = selector.xpath(\"\/\/ul[@class='s_listA']\/li\/a\/@title\").getall()\nfor t in titles:\nname, _ = t.strip().rsplit(' ', 1)\nyield name\n\ndef get_names() -> List[str]:\n'''Return a long list of names'''\nreturn list(_get_names())\n\n\nand then we can add a boolean feature to tell if the token is a member of the set of all artist name scrapped.\n\nTogether with such new feature, it is obvious to see a few percent improvement in performance. Naive Bayes is significantly more accurate because of the high correlation between the new feature and one of the label. Others, such as decision tree and logistic regression and even neural network also have slight increase in accuracy. This boolean new feature is more of complimentary nature in these cases as the improvement is not much. In order words, the original set of features is enough to infer this newly added feature.\n\n# Preserving the model\n\nWe settle with 3-layer neural network with logistic activation and alpha=0.01. Once we trained the model, we preserve it for later use by pickle.\n\n# training\nclf = MLPClassifier(alpha=0.01, max_iter=1000, activation='logistic')\nclf.fit(X_train, y_train)\npickle.dump(clf, open(\"mlp_trained.pickle\", \"wb\"))\n\n# reuse\npredict = clf.predict(input_features)\n\n\n# An attempt to plot something\n\nSo far we didn\u2019t try to plot anything but it is good to visualize the data as the first step to get some insight on what we are dealing with. A good first step would be to plot the correlogram of features, which is to see how different features correlated to each other.\n\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\ncols = ['label'] + incol\nsns.pairplot(df[cols[:11]], kind=\"scatter\", hue=\"label\", markers=[\"o\", \"s\", \"D\"], palette=\"Set2\")\nplt.show()\n\n\nIt is very likely that we cannot find the covariance of boolean features. So we do not include them in the correlogram above. The diagonal of the correlogram are histograms of a single feature against the label, whereas the off-diagonal ones are scatter plots of two features. Therefore we can read from the diagonal whether a feature is discriminative to the classification, also from off-diagonal whether a label is clustered by some features.\n\nThen we can ask, whether there are some simple linear combination of features to be discriminative. We can do this based on principal component analysis and plot in 2D:\n\nfrom sklearn.decomposition import PCA\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\npca = PCA(n_components=2)\npca.fit(df[incol])\n\nplt.figure(figsize=(10,10))\nax = sns.scatterplot(data=pd.DataFrame(pca.transform(df[incol]), columns=[\"A\",\"B\"]).assign(label=df[\"label\"]),\nhue=\"label\", style=\"label\", x=\"A\", y=\"B\")\nax.set_title(\"Input data\")\nplt.show()\n\n\nor even 3D:\n\nfrom sklearn.decomposition import PCA\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\nimport seaborn as sns\n\npca = PCA(n_components=3)\npca.fit(df[incol])\n\nfig = plt.figure(figsize=(10, 10))\nxyz = pd.DataFrame(pca.transform(df[incol]), columns=[\"X\",\"Y\",\"Z\"])\ncolor = df[\"label\"].replace({'a':'r', 't':'g', 'x':'b'})\nax.scatter(xyz[\"X\"], xyz[\"Y\"], xyz[\"Z\"], c=color, s=10, alpha=0.3)\nax.set_title(\"Input data\")\nplt.show()\n\n\nIt is not so easy to show the decision boundary of each classifier. In fact, I don\u2019t know how to visualize that. My attempt would be to use the axes produced by PCA and map the decision boundary onto it. But this is not beautiful:\n\n#\n# Prepare for plotting using PCA axes\n#\n\nX = df[incol]\ny = df['label']\n\npca = PCA(n_components=2)\npca.fit(X)\n\n# get size limit of input data, for plotting purpose\nXpca = pca.transform(X)\nx_min, x_max = Xpca[:, 0].min() - .5, Xpca[:, 0].max() + .5\ny_min, y_max = Xpca[:, 1].min() - .5, Xpca[:, 1].max() + .5\n\n# generate input attributes\nranges = []\nfor c in incol:\nif c in numcols: # numeric cols\nranges.append(np.linspace(df[c].min(), df[c].max(), 10))\nelse: # boolean cols\nranges.append(np.linspace(0, 1, 2))\n\n# memory-save way to generate some data points to plot contour\ngriddf = pd.DataFrame([[np.random.choice(x) for x in ranges] for _ in range(5*N*N)], columns=incol)\ngridpca = pca.transform(griddf)\n\n# build a meshgrid according to input attributes. This will take a while\nxx, yy = np.meshgrid(np.linspace(x_min, x_max, N), np.linspace(y_min, y_max, N))\nzindex = np.ndarray(xx.shape, dtype=int)\nfor index in np.ndindex(*xx.shape):\ndist = np.linalg.norm(gridpca - np.array([xx[index], yy[index]]), axis=1)\nzindex[index] = np.argmin(dist)\n\n# Create plot helper\ndef plot(X, y, axis, title, **kwargs):\n\"Plot PCA-ized X over label Y in 2D scatter plot\"\nax = sns.scatterplot(data=pd.DataFrame(pca.transform(X), columns=[\"A\",\"B\"]).assign(label=y),\nhue=\"label\", style=\"label\", x=\"A\", y=\"B\", ax=axis, **kwargs)\nax.set_title(title)\nax.set(xlim=(x_min, x_max), ylim=(y_min, y_max))\n\n#\n# Train, evaluate, and plot\n#\n\ncm = plt.cm.RdBu\nf, axes = plt.subplots(4, 3, figsize=(21, 28)) # 3 col x 4 rows\naxes = axes.ravel() # unroll this into row-major 1D array\ni = 0\n\n# plot full input dataset\nplot(X, y, axes[i], \"All data\", legend=\"brief\")\n\n# preprocess dataset, split into training and test part\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=42)\n\n# Plot the test set\ni += 1\nplot(X_test, y_test, axes[i], \"Test\", legend=None)\n\n# iterate over classifiers and plot each of them\nfor name, clf in classifiers:\ni += 1\ni += 1\n# train and print report\nclf.fit(X_train, y_train)\nscore = clf.score(X_test, y_test)\nprint(\"\\n----\\n{} (score={:.5f}):\".format(name, score))\nprint(classification_report(y, clf.predict(X), digits=5))\n\n# Plot the decision boundary. For that, we will assign a color to each\n# point in the mesh [x_min, x_max]x[y_min, y_max].\ntry:\nif hasattr(clf, \"decision_function\"):\nZ = clf.decision_function(griddf)[:, 1]\nelse:\nZ = clf.predict_proba(griddf)[:, 1]\n\n# Put the result into a color plot\nzz = np.zeros(xx.shape)\nfor index in np.ndindex(zindex.shape):\nzz[index] = Z[zindex[index]]\naxes[i].contourf(xx, yy, zz, cmap=cm, alpha=.8)\n\n# Plot the training points\nplot(X_train, y_train, axes[i], name, legend=None)\nplot(X_test, y_test, axes[i], name, legend=None, alpha=0.6)\naxes[i].text(x_max-.3, y_min+.3, '{:.2f}'.format(score).lstrip('0'),\nsize=15, horizontalalignment='right')\nexcept:\npass # doesn't matter if error\n\nplt.tight_layout()\nplt.show()\n\n\nAs we can see in the above graph, some classifier is quite messy and some other can\u2019t even produce the contour. I am still looking for the right way to visualize this.\n\nThe Jupyter notebook for all the above is here.","date":"2020-01-26 08:04:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 24, \"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\": 0.43311768770217896, \"perplexity\": 5307.36647644492}, \"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\/1579251687958.71\/warc\/CC-MAIN-20200126074227-20200126104227-00230.warc.gz\"}"} | null | null |
module PlayFutsal
class Event < ActiveRecord::Base
#### Relations ####
belongs_to :match
belongs_to :event_type
belongs_to :athlete
belongs_to :other_athlete, :class_name => :athlete
#### Accessors ####
attr_accessible :minute,
:desc,
:athlete_id,
:event_type_id
#### Scopes ####
default_scope ->{ order :minute }
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,953 |
{"url":"https:\/\/www.numerade.com\/questions\/when-the-moon-is-directly-overhead-at-sunset-the-force-by-earth-on-the-moon-f_mathrmem-is-essentiall\/","text":"### Discussion\n\nYou must be signed in to discuss.\n##### Andy C.\n\nUniversity of Michigan - Ann Arbor\n\n##### Farnaz M.\n\nSimon Fraser University\n\nLectures\n\nJoin Bootcamp\n\n### Video Transcript\n\nquestion number 15 This is the moon and force by our on the moon is like this and at 90 degrees and other force by the sun on the moon is acting so the resultant off these two forces is magnitude off the resultant off these two forces is equal to under route 1.98 in 2. 10 to the power 20. Well, the square Plus they didn't wreck it. Four point 36 into 10 to the power 20 Holy square Because we know that the resultant off two forces magnitude off the resultant off two perpendicular forces is a call to F as, um is Squire plus as e m is square. So solving this, we will get the magnitude off the resultant force four point 78 into 10 to the power 20 Newton. This is the magnitude off the result in fourth F. Now let us find the X elation. X elation is equal to the net. Force F upon the mass off the moon, that force is four point 78 into 10 to the power contained Newton's. They were aided by the mosque seven point 35 in tow tend to the power 22 kg. This will give us the X elation off the moon. 6.5 Indo 10 to the power minus three meter per second Squired. This is the required X elation off the moon.\n\n##### Andy C.\n\nUniversity of Michigan - Ann Arbor\n\n##### Farnaz M.\n\nSimon Fraser University\n\nLectures\n\nJoin Bootcamp","date":"2021-07-29 08:58:43","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.23047780990600586, \"perplexity\": 2138.7316527929916}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046153854.42\/warc\/CC-MAIN-20210729074313-20210729104313-00151.warc.gz\"}"} | null | null |
import {getRegistrarAddress, getAddressByEns, entries, startAuctionAndBid, startAuction, newBid, unsealBid, sha3, shaBid, sealedBids} from './ensService';
import {getEstimateGas} from './dAppService';
const abi = require('ethereumjs-abi');
test.skip('getAddressByEns should not return "ENS not found" if the given .eth exists.', async () => {
const name = 'testing.eth';
const result = await getAddressByEns(name);
expect(result).not.toEqual('ENS not found');
});
test.skip('getAddressByEns should return a valid address if the given .eth exists.', async () => {
const name = 'testing.eth';
const result = await getAddressByEns(name);
// console.log(result)
expect(typeof result).toBe('string');
expect(result).toMatch(/^0x/);
});
test('entries', () => {
const name = 'testing';
const result = entries(name);
console.log(name, result);
expect(result).toEqual(expect.objectContaining({
state: expect.any(String),
deed: expect.any(String),
registrationDate: expect.any(Object),
value: expect.any(Number),
highestBid: expect.any(Number)
}));
// { state: 'Open',
// deed: '0x0000000000000000000000000000000000000000',
// registrationDate: 1970-01-01T00:00:00.000Z,
// value: 0,
// highestBid: 0 }
});
/* mytesting.eth myEtherWallet
{"name":"mytesting",
"nameSHA3":"0x82f348456fc18582707fcb29379d70dff8b75a12a13cf6343f98b394c83a1182",
"owner":"0x7c20badacd20f09f972013008b5e5dae82670c8d",
"value":"10000000000000000",
"secret":"testing",
"secretSHA3":"0x5f16f4c7f149ac4f9510d9cf8cf384038ad348b3bcdc01915f95de12df9d1b02"}
*/
/*
{"name":"testabc",
"nameSHA3":"0x847dd80d44a786b6ff021980b90757e6f716dd7df9022c9e0832fa33e21cf880",
"owner":"0x7c20badacd20f09f972013008b5e5dae82670c8d",
"value":"10000000000000000",
"secret":"testing",
"secretSHA3":"0x5f16f4c7f149ac4f9510d9cf8cf384038ad348b3bcdc01915f95de12df9d1b02"}
*/
test('getRegistrarAddress', () => {
console.log(getRegistrarAddress());
});
test.skip('sha3', () => {
const name = "mytesting";
const nameSHA3 = sha3(name);
const secret = "testing";
const secretSHA3 = sha3(secret);
console.log("name", name, nameSHA3);
console.log("secret", secret, secretSHA3);
expect(nameSHA3).toEqual("0x82f348456fc18582707fcb29379d70dff8b75a12a13cf6343f98b394c83a1182");
expect(secretSHA3).toEqual("0x5f16f4c7f149ac4f9510d9cf8cf384038ad348b3bcdc01915f95de12df9d1b02");
});
test.skip('startAuctionAndBid estimateGas', () => {
const name = 'ethmasks';
const result = getEstimateGas(startAuctionAndBid(name, 0.01, 0.02, 'testing', process.env.PRIVATE_KEY, 21));
console.log("startAuctionAndBid, estimateGas", result);
});
test.skip('startAuction', () => {
const name = 'mytesting';
const result = startAuction(name, process.env.PRIVATE_KEY, 21);
console.log("startAuction, txHash", result);
});
test.skip('newBid estimateGas', () => {
const name = "ethmask";
const result = getEstimateGas(newBid(name, 0.02, 0.05, "testing", process.env.PRIVATE_KEY, 21));
console.log("newBid, estimateGas", result);
});
test.skip('unsealBid', () => {
const name = 'testens';
const result = unsealBid(name, 0.01, 'testing', process.env.PRIVATE_KEY, 21);
console.log("unsealBid, txHash", result);
});
test.skip('sealedBids', () => {
const name = "testabc";
const secret = "testing";
const result = sealedBids(sha3(name), 10000000000000000, sha3(secret), process.env.PRIVATE_KEY, 21);
console.log("sealedBids result", result);
});
| {
"redpajama_set_name": "RedPajamaGithub"
} | 144 |
{"url":"https:\/\/en.m.wikisource.org\/wiki\/Dynamical_Theory_of_the_Electric_and_Luminiferous_Medium_III","text":"Dynamical Theory of the Electric and Luminiferous Medium III\n\nOn a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media. \u00a0(1897)\nby Joseph Larmor\n\nPhil. Trans. Roy. Soc. 190: 205\u2013300, 1897, Online\n\nSections 13-16 (pp. 221-231, especially p. 229) contain Larmor's version of the Lorentz transformation and the derivation of time dilation and length contraction.\n\nIntroductory\n\n1. In two previous memoires[1] it has been explained, that the various hypotheses involved in the theory of electric and optical phenomena, which has been developed by Faraday and Maxwell, can be systematized by assuming the \u00e6ther to be a continuous, homogeneous, and incompressible medium, endowed with inertia and with elasticity purely rotational. In this medium unitary electric charges, or electrons, exist as point-singularities, or centres of intrinsic strain, which can move about under their mutual actions; while atoms of matter are in whole or in part aggregations of electrons in stable orbital motion. In particular, this scheme provides an consistent foundation for the electrodynamic laws, end agrees with the actual relations between radiation and moving matter.\n\nAn adequate theory of material phenomena is necessarily ultimately atomic. The older mathematical type of atomic theory which regards the atoms of matter as acting on each other from a distance by means of forces whose laws and relations are gradually evolved by observation and experiment, is in the present method expanded end elucidated by the introduction of a medium through whose intervention these actions between the material atoms take place. It is interesting to recall the circumstance that Gauss in his electrodynamic speculations, which remained unpublished during his lifetime, arrives substantially at this point of view\u00a0; after examining a law of attraction, of the Weberian type, between the \"electric particles,\" he finally discards it and expresses his conviction, in a most remarkable letter to Weber,[2] that the key-stone of electrodynamics will be found in an action propagated in time from one \"electric particle\" to another. The abstract philosophical distinction between actions at a distance and contact actions, which dates for modern science from Gilbert's adoption of the scholastic axiom[3] Nulla actio fieri potest nisi per contactum, can have on an atomic theory of matter no meaning other than in the present sense. The question is simply whether a wider and more consistent view of the actions between the molecules of matter is obtained when we picture them as transmitted by the elasticity and inertia of a medium by which the molecules are environed, or when we merely describe them as forces obeying definite laws. But this medium itself, as being entirely supersensual, we must refrain from attempting to analyse further. It would be possible (cf. \u00a7 6) even to ignore the existence of an \u00e6ther altogether, and simply hold that actions are propagated in time and space from one molecule of matter to the surrounding ones in accordance with the system of mathematical equations which are usually associated with that medium\u00a0; in strictness nothing could be urged against such a procedure, though, in the light of our familiarity with the transmission of stress and motion by elastic continuous material media such as the atmosphere, the idea of an \u00e6thereal medium supplies so overwhelmingly natural and powerful an analogy as for purposes of practical reason to demonstrate the existence of the \u00e6ther. The aim of a theory of the \u00e6ther is not the impossible one of setting down a system of properties in which everything that may hereafter be discovered in physics shall be virtually included, but rather the practical one of simplifying and grouping relations and of reconciling apparent discrepancies in existing knowledge.\n\n2. It would be an unwarranted restriction to assume that the properties of the \u00e6ther must be the same as belong to material media. The modes of transmission of stress by media sensibly continuous were however originally formulated in connexion with the observed properties of elastic matter\u00a0; and the growth of general theories of stress-action was throughout checked and vivified by comparison with those properties. It was thus natural in the first instance to examine whether a restriction to the material type of elastic medium forms an obstacle in framing a theory of the \u00e6ther; but when that restriction has been found to other insuperable difficulties it seems to be equally natural to discard it. Especially is this the case when the scheme of properties which specifies an available medium turns out to be intrinsically simpler than the one which specifies ordinary isotropic elastic matter treated as continuous.\n\nA medium, in order to be available at all, must transmit actions across it in time\u00a0; therefore there must be postulated for it the property of inertia, \u2014 of the same kind as ordinary matter possesses, for there can hardly be a more general kind, \u2014 and also the property of elasticity or statical resistance to change either of position or of form. In ordinary matter the elasticity has reference solely to deformation; while in the constitution here assumed for the \u00e6ther there is perfect fluidity as regards form, but elastic resistance to rotational displacement.[4] This latter is in various ways formally the simpler scheme; elasticity depending on rotation is geometrically simpler and more absolute than elasticity depending on change of shape\u00a0; and moreover no phenomenon has been discovered which would allow us to assume that the property of elasticity of volume, which necessarily exists in any molecularly constituted medium such as matter, is present in the \u00e6ther at all. The objection that rotational elasticity postulates absolute directions in space need hardly have weight when it is considered that a definite space, or spacial framework fixed or moving, to which motion is referred, is a necessary part of any dynamical theory. The other fundamental query, whether such a scheme as the one here sketched could be consistent with itself, has perhaps been most convincingly removed by Lord Kelvin's actual specification of a gyrostatic cellular structure constituted of ordinary matter, which has to a large extent these very properties; although the deduction of the whole scheme of relations from the single formula of Least Action, in its ordinary form in which the number of independent variables is not unnaturally increased, includes its ultimate logical justification in this respect.\n\nOn Material Models and Illustrations of the \u00c6ther and its associated Electrons.\n\n3. Although the Gaussian aspect of the subject, which would simply assert that the primary atoms of matter exert actions on each other which are transmitted in time across space in accordance with Maxwell's equations, is a formally sufficient basis on which to construct physical theory, yet the question whether we can form a valid conception of a medium which is the seat of this transmission is of fundamental philosophical interest, quite independently of the fact that in default of the analogy at any rate of such a medium this theory would be too difficult for development. With a view to further assisting a judgment on this question, it is here proposed to describe a process by which a dynamical model of this medium can be theoretically built up out of ordinary matter, \u2014 not indeed a permanent model, but one which can be made to continue to represent the \u00e6ther for any assignable finite time, though it must ultimately decay. The \u00e6ther is a perfect fluid endowed with rotational elasticity; so in the first place we have \u2014 and this is the most difficult part of our undertaking \u2014 to construct a material model of a perfect fluid, which is a type of medium nowhere existing in the material world. Its characteristics are continuity of motion and absence of viscosity: on the other hand in an ordinary fluid, continuity of motion is secured by diffusion of momentum by the moving molecules, which is itself viscosity, so that it is only in motions such as vibrations and slight undulations where the other finite effects of viscosity are negligible, that we can treat an ordinary fluid as a perfect one. If we imagine an aggregation of frictionless solid spheres, each studded over symmetrically with a small number of frictionless spikes (say four) of length considerably less than the radius,[5] so that there are a very large number of spheres in the differential element of volume, we shall have a\n\npossible though very crude means of representation of an ideal perfect fluid. There is next to be imparted to each of these spheres the elastic property of resisting absolute rotation; and in this we follow the lines of Lord Kelvin's gyrostatic vibratory \u00e6ther. Consider a gyrostat consisting of a flywheel spinning with angular momentum ${\\displaystyle \\mu }$\u00a0, with its axis AB pivoted as a diameter on a ring whose perpendicular diameter CD is itself pivoted on the sphere, which may for example be a hollow shell with the flywheel pivoted in its interior; and examine the effect of imparting a small rotational displacement to the sphere. The direction of the axis of the gyrostat will be displaced only by that component of the rotation which is in the plane of the ring; an angular velocity ${\\displaystyle d\\theta \/dt}$\u00a0 in this plane will produce a torque measured by the rate of change of the angular momentum, and therefore by the parallelogram law equal to ${\\displaystyle \\mu d\\theta \/dt}$\u00a0 turning the ring round the perpendicular axis CD, thus involving a rotation of the ring round that axis with angular acceleration ${\\displaystyle \\mu \/i\\cdot d\\theta \/dt}$\u00a0, that is with velocity ${\\displaystyle \\mu \/i\\cdot \\theta }$\u00a0, where ${\\displaystyle i}$\u00a0 is the aggregate moment of inertia of the ring and the flywheel about a diameter of the wheel. Thus when the sphere has turned through a small angle ${\\displaystyle \\theta }$\u00a0, the axis of the gyrostat will be turning out of the plane of ${\\displaystyle \\theta }$\u00a0 with an angular velocity ${\\displaystyle \\mu \/i\\cdot \\theta }$\u00a0, which will persist uniform so long as the displacement of the sphere is maintained. This angular velocity again involves, by the law of vector composition, a decrease of gyrostatic angular momentum round the axis of the ring at the rate ${\\displaystyle \\mu ^{2}\/i\\cdot \\theta }$\u00a0; accordingly the displacement ${\\displaystyle \\theta }$\u00a0 imparted to the sphere originates a gyrostatic opposing torque, equal to ${\\displaystyle \\mu ^{2}\/i\\cdot \\theta }$\u00a0 so long as ${\\displaystyle \\mu \/i\\cdot \\int \\theta dt}$\u00a0 remains small, and therefore of purely elastic type. If then there are mounted on the sphere three such rings in mutually perpendicular planes, having equal free angular momenta associated with them, the sphere will resist absolute rotation in all directions with isotropic elasticity. But this result holds only so long as the total displacement of the axes of the flywheels is small: it suffices however to confer rotatory elasticity, as far as is required for the purpose of the transmission of vibrations of small displacement through a medium constituted of a flexible framework with such gyrostatic spheres attached to its links, which is Lord Kelvin's gyrostatic model[6] of the luminiferous working of the \u00e6ther. For the present purpose we require this quality of perfect rotational elasticity to be permanently maintained, whether the disturbance is vibratory or continuous. Now observe that if the above associated free angular momentum ${\\displaystyle \\mu }$\u00a0 is taken to be very great, it will require a proportionately long time for a given torque to produce an assigned small angular displacement, and this time we can thus suppose prolonged as much as we please: observe further that the motion of our rotational \u00e6ther in the previous papers is irrotational except where electric force exists which produces rotation proportional to its intensity, and that we have been compelled to assume a high coefficient of inertia of the medium, and therefore an extremely high elasticity in order to conserve the ascertained velocity of radiation, so that the very strongest electric forces correspond to only very slight rotational displacements of the medium: and it follows that the arrangement here described, though it cannot serve as a model of a field of steady electric force lasting for ever, can yet theoretically represent such a field lasting without sensible decay for any length of time that may be assigned.\n\n4. It remains to attempt a model (cf. Part I., \u00a7 116) of the constitution of an electron, that is of one of the point-singularities in the uniform \u00e6ther which are taken to be the basis of matter, and at any rate are the basis of its electrical phenomena. Consider the medium composed of studded gyrostatic spheres as above: although the motions of the \u00e6ther, as distinct from the matter which flits across it, are so excessively slow on account of its great inertia that viscosity might possibly in any case be neglected, yet it will not do to omit the studs and thus make the model like a model of a gas, for we require rotation of an individual sphere to be associated with rotation of the whole element of volume of the medium in which it occurs. Let then in the rotationally elastic medium a narrow tubular channel be formed, say for simplicity a straight channel AB of uniform section: suppose the walls of this channel to be grasped, and rotated round the axis of the tube, the rotation at each point being proportional for the straight tube to ${\\displaystyle AP^{-2}+PB^{-2}}$\u00a0: this rotation will be distributed through the medium, and as the result there will be lines of rotational displacement all starting from A and terminating at B: and so long as the walls of the channel are held in this position by extraneous force, A will be a positive electron in the medium, and B will be the complementary negative one. They will both disappear together when the walls of the channel are released. But now suppose that before this release the channel is filled up (except small vacuous nuclei at A and B which will assume the spherical form) with studded gyrostatic spheres so as to be continuous with the surrounding medium; the effort of release in this surrounding medium will rotate these spheres slightly until they attain the state of equilibrium in which the rotational elasticity of the new part of the medium formed by their aggregate provides a balancing torque, and the conditions all round A or B will finally be symmetrical. We shall thus have created two permanent conjugate electrons A and B; each of them can be moved about through the medium, but they will both persist until they are destroyed by an extraneous process the reverse of that by which they are formed. Such constraints as may be necessary to prevent division of their vacuous nuclei are outside our present scope; and mutual destruction of two complementary electrons by direct impact is an occurrence of infinitely small probability. The model of an electron thus formed will persist for any finite assignable time if the distribution of gyrostatic momentum in the medium is sufficiently intense: but the constitution of our model of the medium itself of course prevents, in this respect also, absolute permanence. It is not by any means here suggested that this circumstance forms any basis for speculation as to whether matter is permanent, or will gradually fade away. The position that we are concerned in supporting is that the cosmical theory which is used in the present memoirs as a descriptive basis for ultimate physical discussions is a consistent and thinkable scheme; one of the most convincing ways of testing the possibility of the existence of any hypothetical type of mechanism being the scrutiny of a specification for the actual construction of a model of it.\n\n5. An idea of the nature and possibility of a self-locked intrinsic strain, such as that here described, may he facilitated by reference to the cognate example of a material wire welded into a ring after twist has been put into it. We can also have a closer parallel, as well as a contrast; if breach of continuity is produced across an element of interface in the midst of an incompressible medium endowed with ordinary material rigidity, for example by the creation of a lens-shaped cavity, and the material on one side of the breach is twisted round in its plane, and continuity is then restored by cementing the two sides together, a model of an electric doublet or polar molecule will be produced, the twist in the medium representing the electric displacement and being at a distance expressible as due to two conjugate poles in the ordinary manner. Such a doublet is permanent, as above; it can be displaced into a different position, at any distance, as a strain-form, without the medium moving along with it; such displacement is accompanied by an additional strain at each point in the medium, namely, that due to the doublet in its new position together with a negative doublet in the old one. A series of such doublets arranged transversely round a linear circuit will represent the integrated effect of an electric polarization-current in that circuit; they will imply irrotational linear displacement of the medium round the circuit after the manner of vortex motion, but this will now involve elastic stress on account of the rigidity. Thus with an ordinary elastic solid medium, the phenomena of dielectrics, including wave-propagation, may be kinematically illustrated; but we can thereby obtain no representation of a single isolated electric charge or of a current of conduction, and the laws of optical reflexion would be different from the actual ones. This material illustration will clearly extend to the dynamical laws of induction and electromagnetic attraction between alternating currents, but only in so far as they are derived from the kinetic energy; the law of static attraction between doublets of this kind would be different from the actual electric law.\n\n6. According to the present scheme the ponderomotive forces acting on matter arise from the forces acting on the electrons which it involves; the application of the principle of virtual work to the expression for the strain-energy shows that, for each electron at rest, this force is equal to its charge multiplied by the intensity of the electric field where it is situated. It has been urged that a model of the \u00e6thereal electric field cannot be complete, and so must be rejected, unless it exhibits a direct mechanism by which the ponderomotive normal traction ${\\displaystyle F^{2}\/8\\pi }$\u00a0 is transmitted across the \u00e6ther from the surface of one conducting region to that of another: but the position can be maintained that such a representation would transcend the limitations belonging to a mechanical model of a process which is in part mechanical and in part ultra-mechanical. Indeed if this force were transmitted in the ordinary elastic senee, the transmitting stress would have to be of the nature of a self-balancing Faraday-Maxwell stress involving the square of the \u00e6ther-strain instead of its first power, and thus not directly related to elastic propagation. The model above described is so to speak made of \u00e6ther, and ought to represent all the tractions that exist in \u00e6ther, vanishing as they do over the surface of a conducting region: but the model does not in the ordinary sense represent matter at all, except in so far as the \u00e6thereal strain-form which constitutes the electron is associated with matter. It therefore cannot represent directly, after the manner of a stress across a medium, a force acting on matter, for that would from this ultimate standpoint be a force acting on a strain-form spreading from its nucleus all through the medium, not a traction on a definite surface bounding the matter.\n\nThe fact is that transmission of force by a medium, or by contact action so-called, remains merely a vague phrase until the strain-properties of that medium are described; the scientific method of describing them is to assign the mathematical function which represents its energy of strain, and thence derive its relations of stress by the principle of virtual work; a real explanation of the transmission of a force by contact action must be taken to mean this process. Now in an elastic medium permeated by centres of permanent intrinsic strain, whether it be the rotational \u00e6ther with its contained electrons, or an ordinary elastic solid permeated by polar strain-nuclei as described above, the specification of the strain-energy of the medium involves a mathematical function, not only of the displacement at each material point of the medium, but also of the positions of these intrinsic strain-centres which can move independently through it. To derive the play of internal force, this energy function must be varied with respect to all these independent quantities; the result is elastic tractional stress in the medium across every ideal interface, together with forcive tending to displace each strain-centre, which we can consider either as resisted by extraneous constraint preventing displacement of the strain-centre, or as compensated by the reaction of the inertia of the strain-form against acceleration.[7] Consider, for example, the analogy of the elastic solid medium, and suppose a portion of it to be slowly strained by extraneous force; two strains are thereby set up in it, namely that strain which would be thus originated if the solid were initially devoid of intrinsic strain, and that strain which has to be superposed in order to attain the new configuration of the intrinsic strain arising from the displacement of its nuclei. The latter part is conditioned by the displacement of these strain-centres, and in its production forces acting on them must be considered to assist, whose intensities may be determined as has been already done in the \u00e6thereal problem.\n\nThe attractions between material bodies are therefore not transmitted by the \u00e6ther in the way that mechanical tractions are transmitted by an ordinary solid, for it is electric force that is so transmitted: but neither are they direct actions at a distance. The point of view has been enlarged: the ordinary notion of the transmission of force, as framed mathematically by Lagrange and Green for a simple elastic medium without singularities, is not wide enough to cover the phenomena of a medium containing intrinsic strain-centres which can move about independently of the substance of the medium. But the same mathematical principles lead to the necessary extension of the theory, when the energy function thus involves the positions of the strain-centres as well as the elastic displacement in the medium; and the theory which in the simpler case answers fairly to the description of transmission by contact action has features in the wider case to which that name does not so suitably apply.[8] The strain-centres (that is, the matter) have, in the strict sense of the term, energy of position, or potential energy, due to their mutual configuration in the \u00e6ther, which can come out as work done by mutual forces between them when that configuration is altered, which work may be used up either in accumulating other potential energy elsewhere, or in increasing the kinetic energy of the matter, which is itself, in whole or in part, energy in the \u00e6ther arising from the movement of the strain-forms across it. Discussions as to transmission by contact are not the fundamental ones, as the above actual material illustration shows: the single comprehensive basis of dynamics into which all such partial modes of explanation and representation must fit and be coordinated is the formula of Stationary Action, including, as the particular case which covers all the domain of steady systems, the law that the mutual forces of such a system are derived from a single analytical function which is its available potential energy.\n\nThe circumstance that no mode of transmission of the mechanical forces, of the type of ordinary stress across the \u00e6ther, can be put in evidence, thus does not derogate from the sufficiency of the present standpoint. The transmission of material traction by an ordinary solid, which is now often taken as the type to which all physical action must conform, is merely an undeveloped notion arising from experience, which must itself be analysed before it becomes of scientific value: the explanation thereof is the quantitative development of the notion from the energy function by the method of virtual work in the manner indicated in \u00a7 10 infra. This orderly development of the laws of action across a distance, from an analytical specification of a distribution of energy pervading the surrounding space, is the essence of the so-called principle of contact action. It is precisely what the present procedure carries out, with such generalization as the scope of the problem demands; besides attaining a correlation of the whole range of the phenomena, it avoids the antinomies of partial theories which accumulate on the \u00e6ther contradictory and unrelated properties, and sometimes even save appearances by passing on to the simple fundamental medium those complex properties of viscous matter whose real origin is to be found in its molecular discreteness.\n\n\u00c6ther contrasted with Matter.\n\n7. The order of development here followed is thus avowedly based on the hypothesis that the \u00e6ther is a very simple uniform medium, about which it may be possible to know all that concerns us; and the present state of the theories of optics and electricity does much to encourage that idea. This procedure is of course at variance with the extreme application of the inductive canon, which would not allow the introduction of any hypothesis not based on direct observation and. experiment. But though that philosophy has abundantly vindicated itself as regards the secondary properties of matter, which are amenable to direct examination, its rigid application would debar us from any theory of the \u00e6ther at all, as we can only learn about it from circumstantial evidence. We could then merely go on heaping up properties on the \u00e6ther, on the analogy of what is known of matter, as circumstances necessitated; and this medium would be a sort of sink to dispose of relations that could not be otherwise explained. Whereas matter, with which we are familiar, is the really complicated thing on which all the maze of physical phenomena depends, so that it is doubtful whether much can ever be known definitely as to its ultimate dynamical constitution; our best chance is to try to approach it through the presumably simple and homogeneous \u00e6ther in which it subsists.\n\nFor example, it is found that the transmission of electrostatic force is affected by the constitution of the material dielectric through which it passes, and this is explained by a perfectly valid theory of polarization of the molecules of the matter: to press the analogy and ascribe the possibility of transmission through a vacuum to polarization of the rather may be convenient for some purposes of description, but in the majority of cases the impression is left that the so-called polarization of the rather is thereby explained. Whereas the processes being, almost certainly, of totally different character in the two cases, it will conduce to accurate thought to altogether avoid using the same term in the two senses, and to speak of the displacement of the \u00e6ther which transmits electric force across a vacuum as producing polarization in the molecules of a material dielectric which exists in its path, which latter in turn affects the transmission of the electric force by reaction. In trying to pass beyond this stage, we may accumulate descriptive schemes of equations, which express, it may be with continually increasing accuracy, the empirical relations between these two phenomena; but we can never reach very far below the surface without the aid of simple dynamical working hypotheses, more or less a priori, as to how this interaction between continuous \u00e6ther and molecular matter takes place.\n\n8. On the present view, physical theory divides itself into two regions, but with a wide borderland common to both: the theory of radiation or the kinetic relations of this ultimate medium; and the theory of the forces of matter which deals for the most part with molecular movements so slow that the surrounding rather is at each instant practically in an equilibrium condition, so that the material atoms practically act on each other from a distance with forcives obeying definite laws, derivable from the formula for the energy. It is only in electromagnetic phenomena and molecular theory that non-vibrational movements of the \u00e6ther are involved. The \u00e6ther not being matter, it need not obey the laws of the dynamics of matter, provided it obey another scheme of dynamical laws consistent among themselves; these laws must however be such that we can construct in the \u00e6ther an atomic system of matter which itself obeys the actual material laws. The sole spacial relations of the \u00e6ther itself, on which its dynamics depend, those namely of incompressibility and rotational elasticity, are thus to be classed along with the existing Euclidean relations of measurements in space (which also might a priori be different from what they are) as part of the ultimate scheme of mental representation of the actual physical world. The elastic and other characteristics of ordinary matter, including its viscous relations, are on the other hand a direct consequence of its molecular constitution, in combination with the law of material energy which is itself a consequence of the fact that the energies of the atoms are wholly located in the surrounding simple continuous \u00e6ther and are thus functions of their mutual configurations. In this way we come round again to an order of procedure similar to that by which Cauchy and Poisson originally based the elastic relations of material bodies on the mutual actions of their constituent molecules.\n\nConsider any two portions of matter which have a potential-energy function depending, as above explained, on their mutual configuration alone, the material movements being thus comparatively slow compared with the velocity of radiation; any displacement of them as a single rigid system, whether translational or rotational, can involve no expenditure of work; hence the resultant forcive exerted by the first system on the second must statically equilibrate that exerted by the second system on the first, these forcives must in fact be equal and opposite wrenches on a common axis; and the energy principle thus involves the principle of the balance of action and reaction, in its most general form. This stress, between two molecules, is usually sensible only at molecular range; hence the action of the surrounding parts on a portion of a solid body is practically made up of tractions exerted over the interface between them. Further, since rotation of the body without deformation cannot alter the potential energy of mutual configuration of the molecules, it follows that for a rectangular element of ordinary solid matter the tangential components of these tractions must be self-conjugate, as they are taken to be in the ordinary theory of elasticity. On the other hand, for a medium not molecularly constituted we can hardly treat at all of mutual configuration of parts, and the self-conjugate stress-relation will not be a necessary one.\n\nA certain similarity may be traced with the view of Faraday, who was disinclined to allow that ray-vibrations are transmitted by any medium of the molecular character of ordinary matter, but considered them rather as affections of the lines which represent electric force, the propagation being influenced by the material nuclei which in ponderable media disturb these lines. This propagation in time requires inertia and elasticity for its mathematical expression, and the problem of the free \u00e6ther is to find what kind of each is requisite.\n\n9. A theory which, like the present one, explains atoms of matter as made up of singularities of strain and motion in the \u00e6ther, is bound to look for an explanation of gravitation by means of the properties of that medium; it cannot avail itself of Cotes's dogma that gravitation at a distance is itself as fundamental and intelligible as any explanation thereof could be. In further development of the illustrative possibilities of the pulsatory theory of gravitation, mentioned in the previous papers, we can (ideally) imagine the pulsation to have been applied initially over the outside boundary of the \u00e6thereal universe, and thence instantaneously communicated throughout the incompressible medium to the only places that can respond to it, the vacuous nuclei of the electrons; and we can even imagine the pulsations thus established as spontaneously keeping time and phase ever after, when the exciting cause which established this harmony has been discontinued.\n\nIt has been noticed in Part I, \u00a7 103, that gravitation cannot be transmitted by any action of the nature of statical stress; for then the approach of two atoms would increase the strain, and therefore also the stress, and therefore also in a higher ratio the energy of strain which depends on their product, and hence the mutual forces of the atoms would resist approach. As gravitation must belong to the ultimate constituents of matter, that is on this theory to the electrons, and must be isotropic all round each of them, it would appear that no mediate \u00e6thereal representation of it is possible except the one here considered. The radially vibrating field might be described formally as the magnetic field of the electron considered as a unipolar magnet, necessarily of very rapidly alternating type because otherwise a field of gravitation would be an ordinary magnetic field. The bare groundwork of this hypothesis may thus be formally expressed in Maxwell's language and developed along his lines, by postulating that the electron is not only a centre of steady intrinsic electric force, but also a centre of alternating intrinsic magnetic force, instantaneously transmitted because it would otherwise involve condensation, each force being necessarily radial.[9] The unsatisfactory feature is that this radial quasi-magnetic field is introduced for the sake of gravitation alone, which does not present itself as in any direct correlation with other physical agencies.\n\nThe following sections are occupied chiefly with an attempt to logically systematize, and in various respects extend, the electric aspect of molecular theory. The preceding paper dealt mainly with the molecular side of directly \u00e6thereal phenomena, such as electric and radiative fields; of the present one the earlier part follows up the same subject, and the remainder relates to the actions of the molecules of polarized material bodies on one another, and the material stresses and physical changes thereby produced. As in the preceding papers, the quantitative results are to a large extent independent of any special theory of the constitution of matter, such as is here employed to bind together and harmonize the separate groups of phenomena, and to form a mental picture of their mutual relations; so far as they are electric they may be based directly on Maxwell's equations of the electric field in free space, which form a sufficient description of the free \u00e6ther, and have been verified by experiment. In the Faraday-Maxwell theory, however, as usually expounded, an explanation of these equations is found, explicitly or tacitly, in an assumption that the \u00e6ther is itself polarizable in the same manner as a material medium, and \u00e6ther is in fact virtually considered to be matter; on the present theory the equations for free space are an analytical statement of the ultimate dynamical definition of the continuous \u00e6thereal medium, and the polarization of material bodies with the resulting forcive are deduced from the relation of their molecules to this medium in which they have their being.\n\n10. In the modern treatment of material dynamics, as based on the principle of energy, the notion of configuration is, as above explained, fundamental. The potential energy, from which the forces are derived, is a function of the mutual configurations of the parts of the material system. In the case of forces of elasticity the internal energy is primarily a function of the mutual configurations of the individual molecules, from which a regular or organised part (\u00a7 49 infra) is separated which is expressible in terms of the change of configuration of the differential element of volume containing a great number of molecules, and from which alone is derived the stress that is mechanically transmitted. In connexion with the discussion of contact action in \u00a7 6 above, the mode of this derivation and transmission becomes a subject of interest.[10] In the first place the primary notion of a force as acting from one point to another in a straight line, has to be generalized into a forcive in Lagrange's manner on the basis of the principle of virtual work: then the forcive arising from the internal strain-energy of the element of volume of the material is derived by variation of this organized energy, and appears primarily as made up of definite complex bodily forcives resisting the various types of strain that occur in the element: then these forcives are rearranged, by the process of integration by parts, into a uniform translatory force acting throughout the element of volume of the material (which must compensate the extraneous applied bodily forcive) together with tractions acting over its surface. When this is done also for adjacent elements of volume, other tractions arise which must compensate the previous ones over the part of the surface that is common to the two elements; and thus the uncompensated traction is passed on from element to element until finally the boundary of the material system is reached where it remains uncompensated and must be balanced extraneously. The outstanding irregular part of the aggregate mutual potential energy of the individual molecules, which cannot be included in a function of strain of the element of volume, cannot on that account take part in the transmission of mechanical forces, and is evidenced only in local changes of the physical properties and temperature of the material. Cf. \u00a7 48 infra.\n\nThe other main division of the energy is the kinetic part, which is specified in terms of the rate of change of configuration of the material system with respect to an extraneous spacial framework to which its position is referred. Whatever notions may commend themselves a priori as to the impossibility of absolute space and absolute time, the fact remains that it has not been found possible to construct a system of dynamics which has respect only to the relative positions of moving bodies; and the reason suggests itself, that there is an underlying part of the phenomena, which does not usually explicitly appear in abstract material dynamics, namely, the \u00e6thereal medium, and that the spacial framework in absolute rest, which was introduced by Newton and was probably a main source of the great advance in abstract dynamics originated by the Principia, is in fact the quiescent underlying \u00e6ther. In this way the purely a priori standpoint is pushed away a stage, and we may find justification against the reproach that a philosophical formulation of dynamics should be concerned only with relative motions.\n\nRelation to Gas-Theory: Internal Molecular Energy.\n\n11. The kinetic theory of gases is considerably affected by the view here taken of the constitution of a molecule. In those simple and satisfactory features which are concerned only with the translatory motion of the molecules, it stands intact; but it is different with problems, like that of the ratio of the specific heats, which involve the internal energy. According to the usual hypothesis of the theory of gases, all the internal kinetic energy of the molecule is taken to be thermal and in statistical equilibrium, through encounters, with the translatory energy. But on the present view, the energy of the steady orbital motions in the molecule (including therein slow free precessions) makes up both the energy of chemical constitution and the internal thermal energy; while it is only when these steady motions are disturbed that the resulting vibration gives rise to radiation by which some of the internal energy is lost. The amount of internal energy can however never fall below the minimum that corresponds to the actual conserved rotational momenta of the molecule; this minimum is the energy of chemical combination of its ultimate constituents, while the excess above it actually existing is the internal thermal energy.[11] The present view requires that the energy of chemical constitution shall be very great compared with the thermal energy; but for this very reason our means of chemical decomposition are limited, so that only a part of that energy is experimentally realizable.[12] This being the case, the alteration produced by external disturbance in the state of steady internal motions of the molecule consists in the superposition on it of very slow free precessional motions, which have practically no influence on its higher free periods:[13] and this explains why change of temperature has no influence on the positions of the lines in a spectrum. As a gas at high temperature must contain molecules with all amounts of internal thermal energy from nothing upwards, we should on the other hand, on the ordinary gas-theory, expect both a shift of the brightest part of a spectral line when the temperature is raised, and also a widening of its diffuse margin.\n\nThe ordinary encounters between the molecules will influence this thermal energy or energy of slow precessional oscillation, without disturbing the state of steady constitutive motion on which it is superposed, therefore without exciting radiation, which depends on more violent disturbances involving dissociative action.\n\nOn this view the postulates of the Maxwell-Boltzmann theorem on the distribution of the internal energy in gases would not obtain, for the thermal energy of the molecule would not be expressible as a sum of squares. The ratio of the specific heats in a gas must still lie between 1 and ${\\displaystyle {\\tfrac {5}{3}}}$\u00a0; but the nature of the similarity of molecular constitution in the more permanent gases, which makes the ratio of the total thermal energy to the translatory energy either ${\\displaystyle {\\tfrac {5}{3}}}$\u00a0 or unity for most of them, would remain to be discovered. In those gases for which the latter value obtains, the energy of precessional motion in the molecule would be negligibly small, involving small resultant angular momentum and possibly small paramagnetic moment.\n\nThe necessity of a distinction such as that here drawn between the internal thermal energy and the energy of the vibratory disturbances of internal structure which maintain radiation, is well illustrated by the recent recognition (foreshadowed by Dulong and Petit's researches on the law of cooling) and application by Dewar of the remarkable insulating power of a vacuum jacket as regards heat. If this distinction did not exist, both conduction and convection must ultimately depend on transfer by ordinary radiation at small distances, as Fourier imagined; and it would not appear why convection by a gas, even when highly rarefied, is so much more efficient in the transfer of heat than radiation.\n\n12. The result obtained by Ramsay and Young, and others, that all over the gas-liquid range the characteristic equations of the substances on which they experimented proved to be very approximately of the form ${\\displaystyle p=aT+b}$\u00a0, where ${\\displaystyle a}$\u00a0 and ${\\displaystyle b}$\u00a0 are functions of the density alone, also supplies corroboration to this view. Expressing the increment of energy per unit mass ${\\displaystyle dE=Mdv+\\kappa dt}$\u00a0, we have for the increment of heat supplied ${\\displaystyle dH=dE+pdv}$\u00a0; and the fact that ${\\displaystyle dE}$\u00a0 and ${\\displaystyle dH\/T}$\u00a0 are perfect differentials shows immediately that M is equal to ${\\displaystyle -b}$\u00a0 and ${\\displaystyle \\kappa }$\u00a0 is independent of ${\\displaystyle v}$\u00a0, so that the total (non-constitutive) energy per unit mass consists of two independent parts, an energy of expansion and an energy of heating.[14] The latter part is the thermal energy of the individual molecules; it is a function of their mean states and velocities alone, and constitutes almost all the energy in the gaseous state. The former part is the energy of mutual actions between the molecules; it is negative and bears a considerable ratio to the whole thermal energy in the liquid state, in the case of substances with high latent heats of evaporation; for all gases except hydrogen, inasmuch as they are cooled by transpiration through a porous plug, ${\\displaystyle b}$\u00a0 is negative at ordinary densities. Cf. \u00a7 62, infra.\n\nThere would be no warrant for a view that the forces of chemical affinity fall off and finally vanish as the ultimate zero of temperature is approached. The translatory motions of the molecules would diminish without limit, and therefore also the opportunities for reaction between them, so that many chemical changes would cease to take place for the same reason that a fire ceases to burn when the supply of air is insufficient, or coal gas ceases to explode when too much diluted with air: but the energies of affinity exist all the time in probably undiminished strength, while the forces of cohesion are modified by the fall of temperature but not necessarily in the direction of extinction.\n\nThe Equations of the \u00c6thereal Field, with Moving Matter: various applications: influence of Motion through the \u00c6ther on the Dimensions of Bodies.\n\n13. Let (u, v, w) represent the total circuital current, and (u, v', w') the conducted part of it, which will be taken to include the current (u0, v0, w0) of migration of the free electric charge as this is in all cases very small in comparison; let (f', g', h') denote the electric polarization of the material, and (f, g, h) the \u00e6thereal elastic displacement, so that the total circuital displacement of Maxwell's theory is their sum (f\", g\", h\"); let the space of reference be fixed with respect to the stagnant \u00e6ther, and (p, q, r) be the velocity with which the matter situated at the point (x, y, z) is moving, and let \u03b4\/dt represent ${\\displaystyle d\/dt+pd\/dx+qd\/dy+rd\/dz}$\u00a0; let (P, Q, R) denote the electric force, namely that which acts on the electrons, and (P', Q', R') the \u00e6thereal force, that which produces the \u00e6thereal electric displacement (f, g, h); let \u03c1 denote density of free electric charge. Then the electromotive equations are[15]\n\n${\\displaystyle \\mathrm {P} =qc-rb-{\\frac {d\\mathrm {F} }{dt}}-{\\frac {d\\Psi }{dx}},\\quad \\mathrm {P} '=-{\\frac {d\\mathrm {F} }{dt}}-{\\frac {d\\Psi }{dx}},\\quad f={\\frac {1}{4\\pi \\mathrm {c} ^{2}}}\\mathrm {P} ',}$\n\nwhere\n\n${\\displaystyle \\mathrm {F} =\\int {\\frac {u}{r}}d\\tau +\\int \\left(\\mathrm {B} {\\frac {d}{dz}}-\\mathrm {C} {\\frac {d}{dy}}\\right){\\frac {1}{r}}d\\tau ,\\quad \\alpha ={\\frac {d\\mathrm {H} }{dy}}-{\\frac {d\\mathrm {G} }{dz}};}$\n\nand\n\n${\\displaystyle u=u'+{\\frac {\\delta f'}{dt}}+{\\frac {df}{dt}}+p\\rho ,}$\u00a0[16]\n\nwhere\n\n${\\displaystyle \\rho ={\\frac {d(f'+f)}{dx}}+{\\frac {d(g'+g)}{dy}}+{\\frac {d(h'+h)}{dz}}.}$\n\nFrom the formula for (P, Q, R) Faraday's law follows that the line integral of electric force round a circuit in uniform motion with the matter is equal to the time-rate of diminution of the magnetic flux through its aperture. The line-integral of the \u00e6thereal force (P', Q', R') round a circuit fixed in the \u00e6ther has the same value. Again if (F', G', H') be defined so that ${\\displaystyle F'=\\int u\/r.d\\tau }$\u00a0, we have\n\n${\\displaystyle a={\\frac {d\\mathrm {H} '}{dy}}-{\\frac {d\\mathrm {G} '}{dz}}+4\\pi \\mathrm {A} -{\\frac {d}{dx}}\\int \\left(\\mathrm {A} {\\frac {d}{dx}}+\\mathrm {B} {\\frac {d}{dy}}+\\mathrm {C} {\\frac {d}{dz}}\\right){\\frac {1}{r}}d\\tau ,}$\n\nso that\n\n${\\displaystyle \\alpha +{\\frac {d\\mathrm {V} '}{dx}}={\\frac {d\\mathrm {H} '}{dy}}-{\\frac {d\\mathrm {G} '}{dz}}}$\n\nwhere (\u03b1, \u03b2, \u03b3) is magnetic force and V' is the potential of the magnetism: hence Amp\u00e8re's law follows that the line integral of the magnetic force round any circuit is equal to times the total current that flows through its aperture. These two circuital relations are coextensive with the previous equations involving the vector potential, and can thus replace them, when the difference between (P, Q, R) and (P', Q', R') is inessential, that is (i) when the displacement currents are negligible, or (ii) when the matter is at rest; the quantity \u03a8 then enters as an arbitrary function in the integration of the equations.\n\nThe mechanical force acting on the matter, or ponderomotive force, is (X, Y, Z) per unit volume, where (\u00a7 38 infra)\n\n${\\displaystyle \\mathrm {X} =\\left(v-{\\frac {dg}{dt}}\\right)\\gamma -\\left(w-{\\frac {dh}{dt}}\\right)\\beta +\\mathrm {A} {\\frac {d\\alpha }{dx}}+\\mathrm {B} {\\frac {d\\alpha }{dy}}+\\mathrm {C} {\\frac {d\\alpha }{dz}}+f'{\\frac {d\\mathrm {P} }{dx}}+g'{\\frac {d\\mathrm {P} }{dy}}+h'{\\frac {d\\mathrm {P} }{dz}}+\\rho \\mathrm {P} .}$\n\nThe mechanical traction on an interface will be considered later (\u00a7 39). In a magnetic medium the magnetic force (\u03b1, \u03b2, \u03b3) differs from the magnetic flux (a, b, c) simply by not including the influence of the local Amperean currents; thus ${\\displaystyle \\alpha =a-4\\pi \\mathrm {A} }$\u00a0.\n\nWhen there is no conductivity, the free charge must move along with the matter, so that\n\n${\\displaystyle {\\frac {d\\rho }{dt}}+{\\frac {d\\rho p}{dx}}+{\\frac {d\\rho q}{dy}}+{\\frac {d\\rho r}{dz}}=0;}$\n\ntherefore, from the circuitality of the total current, we must have, identically,\n\n${\\displaystyle {\\frac {d\\rho }{dt}}={\\frac {d}{dx}}\\left({\\frac {\\delta f'}{dt}}+{\\frac {df}{dt}}\\right)+{\\frac {d}{dy}}\\left({\\frac {\\delta g'}{dt}}+{\\frac {dg}{dt}}\\right)+{\\frac {d}{dx}}\\left({\\frac {\\delta h'}{dt}}+{\\frac {dh}{dt}}\\right).}$\n\nThe latter is the same as the convergence of ${\\displaystyle (\\delta \/dt-d\/dt)\\ (f',\\ g',\\ h')}$\u00a0, which asserts (for the case of uniform motion that is contemplated) that mere convection of the polarized medium does not produce separation of free electricity. The relation between (f, g', h') and (P, Q, R) must be such as to strictly satisfy this equation. The quantity \u03a8 occurs in the equations of the field as an undetermined potential which is sufficient in order to conserve the condition of bodily circuitality ${\\displaystyle du\/dx+dv\/dy+dw\/dz=0}$\u00a0.\n\nIn order to express the conditions that must hold at an interface of transition, we notice that by definition F, G, H are continuous everywhere; but it is only when the media are non-magnetic that their rates of change along the normal (and therefore all their first differential coefficients) are also completely continuous. Across an interface the traction in the tether must be continuous, so that the tangential component of the \u00e6thereal force (P', Q', R') must be continuous, which is satisfied by continuity of \u03a8. The continuity of the total electric current secures itself without further condition by a compensating distribution of electric charge on the interface, that is by a discontinuity in d\u03a8\/dn. The tangential continuity of the elastic \u00e6ther requires that the tangential component of the magnetic force (\u03b1, \u03b2, \u03b3) must be continuous; the normal continuity of the magnetic flux is assured by the continuity of (F, G, H). It might be argued that if the electric force (P, Q, R) were not continuous tangentially, a perpetual motion could arise by moving an electron along one side of the interface and back again along the other side. But this reasoning requires that (p, q, r) shall be continuous across the interface, as otherwise the circuit returning on the other side could not be complete; and it also requires that there shall be no magnetization, as otherwise the mechanical force on the electrons in an element of volume, which is what we are really concerned with in the perpetual motion axiom, is different from the sum of the electric forces on the individual electrons, by involving (\u03b1, \u03b2, \u03b3) instead of (a, b, c). We can thus assert continuity of the tangential electric force only in the cases in which it is already involved in that of the tangential \u00e6thereal force; and consistency is verified. The aggregate of all these interfacial electromotive conditions is thus continuity of the vector potential (F, G, H), and of \u03a8, and of the tangential components of the magnetic force; they formally involve continuity of the tangential components of the \u00e6thereal force (P', Q', R'), and of the electric and magnetic fluxes. But further, in the equations from which Amp\u00e8re's circuital relation is derived above, it is only the normal space-variation of V' that is discontinuous; hence continuity of the tangential magnetic force is involved in that of F, G, H, \u03a8 by virtue of the mode of expression of (F, G, H) in terms of the currents and the magnetism. Thus there are in all cases only four independent interfacial conditions to be satisfied.\n\nThe scheme is thus far absolute, in the sense that the relations between the variables are independent of the special molecular constitution of the matter that is present. The system of equations must now be completed for material media by joining to it the relations which connect the conduction current in the matter with the electric force, and the electric polarization of the matter with the electric force, and the magnetic polarization of the matter with the magnetic force, in the cases in which these relations are definite and can be experimentally ascertained. In the simplest case of isotropic matter, polarizable according to a linear law, they are of types\n\n${\\displaystyle u'=\\sigma \\mathrm {P} ,\\quad f'=(\\mathrm {K} -1)\/4\\pi \\mathrm {c} ^{2}\\mathrm {P} ,\\quad \\mathrm {A} =\\kappa \\alpha .}$\n\nThe expression for \u03c1 leads in homogeneous isotropic media to\n\n${\\displaystyle \\mathrm {K} \\nabla ^{2}\\Psi =-4\\pi \\mathrm {c} ^{2}\\rho +(\\mathrm {K} -1)\\left\\{d\/dx(cq-br)+d\/dy(ar-cp)+d\/dz(bp-aq)\\right\\}}$\n\nso that \u03a8 is only in part an electrostatic potential. Inside a uniform isotropic conductor at rest, the condition of circuitality becomes ${\\displaystyle \\sigma \\nabla ^{2}\\Psi =d\\rho \/dt}$\u00a0; substituting this, we have ${\\displaystyle d\\rho \/dt+4\\pi c^{2}\\sigma \\mathrm {K} ^{-1}\\rho =0}$\u00a0, so that ${\\displaystyle \\rho =\\rho _{0}\\exp(-4\\pi \\mathrm {c} ^{2}\\sigma \\mathrm {K} ^{-1}t)}$\u00a0, showing that an initial volume density of free electricity would in that case be instantly driven to the boundary owing to the dielectric action. This proposition may be extended to aeolotropic media.\n\n14. The nature of the foregoing electric scheme may be elucidated by aid of some simple applications.\n\n(i.) When a conducting system is in steady motion so that there is no conduction current flowing into it, the electric force (P, Q, R) must be null throughout its substance. Thus for the case of a solid conductor rotating round an axis of symmetry in a uniform magnetic field parallel to that axis, with steady angular velocity \u03c9, the electric force in it, namely ${\\displaystyle (\\omega cx-d\\Psi _{1}\/dx,\\ \\omega cy-d\\Psi _{1}\/dy,\\ -d\\Psi _{1}\/dz)}$\u00a0, must be null, so that ${\\displaystyle \\Psi _{1}={\\tfrac {1}{2}}\\omega c(x^{2}+y^{2})+\\mathrm {A} }$\u00a0; the polarization in it is therefore null, but there is in it an \u00e6thereal displacement ${\\displaystyle -(4\\pi \\mathrm {c} ^{2})^{-1}(d\/dx,\\ d\/dy,\\ d\/dz)\\Psi _{1}}$\u00a0. In outside space, the electric force and \u00e6thereal force are each ${\\displaystyle -(d\/dx,\\ d\/dy,\\ d\/dz)\\Psi _{2}}$\u00a0, where \u03a82 is that free electrostatic potential which is continuous with the surface value ${\\displaystyle {\\tfrac {1}{2}}\\omega \\mathrm {c} (x^{2}+y^{2})+\\mathrm {A} }$\u00a0 at the conductor. Inside the conductor this purely \u00e6thereal displacement involves an electrification of volume density ${\\displaystyle \\rho =-\\omega c\/2\\pi \\mathrm {c} ^{2}}$\u00a0, which will be a density of free electrons or ions as all true electrifications are; while there is a compensating surface density \u03c3 equal to the difference of the total normal electric displacements on the two sides, that is to ${\\displaystyle (4\\pi \\mathrm {c} ^{2})^{-1}(d\\Psi _{2}\/dn_{2}+d\\Psi _{1}\/dn_{1})}$\u00a0, where dn2, dn1 are both measured towards the surface, the outside medium being air for which K is unity. The value of the constant A is determined by the circumstance that the aggregate of this volume and surface charge shall be null when the conductor is insulated and unelectrified, or equal to the given total charge when it is insulated and charged: when it is uninsulated, the constant is determined by the position of the point on it that is connected to Earth, and therefore at zero potential. The procedure of Part II., \u00a7 25 is thus justified, because there is in fact no dielectric polarization in the conductor, but only \u00e6thereal displacement.\n\nIt remains to consider whether the parts of this volume density \u03c1 and surface density \u03c3 of electrification are carried round with the conductor in its motion, or slip back through its volume and over its surface so as to maintain fixed positions in space. It is clear (as in Part II., \u00a7 27) that the same cause, namely, viscous diffusion of momentum among moving ions and molecules, which produces Ohmic resistance to a steady current, will lead to the electrons constituting electric densities being wholly carried on by the matter whenever a steady state is attained. This necessary consequence of the theory is in keeping with Rowland's classical experiments on convection currents. The excessively minute magnetic field due to these convection currents themselves has been neglected in the above analysis, which has enabled us to specify the slight redistribution of free charge on the rotating conductor when under the influence of a powerful extraneous magnetic field: when the magnetic field is due solely to its own motion the redistribution is of course absolutely negligible.\n\n(ii.) In the case of a dielectric (as also in the above) the restriction to a steady state and permanent configuration may be dispensed with; for the magnetic field arising from induced displacement currents can always be neglected in comparison with the inducing field. Thus, (a, b, c) being the extraneous inducing field, the electric forces inside and outside a rotating mass are\n\n${\\displaystyle (\\omega cx-d\\Psi _{1}\/dx,\\ \\omega cy-d\\Psi _{1}\/dy,\\ -\\omega ax-\\omega by-d\\Psi _{1}\/dz)}$\u00a0 and ${\\displaystyle -(d\/dx,\\ d\/dy,\\ d\/dz)\\Psi _{2}.}$\n\nAs there can be no free electrification,\n\n${\\displaystyle \\nabla ^{2}\\Psi _{1}=(1-\\mathrm {K} ^{-1})\\omega \\left\\{2c+x(dc\/dx-da\/dz)-y(dc\/dy-db\/dz)\\right\\}}$\u00a0 and ${\\displaystyle \\nabla ^{2}\\Psi _{2}=0;}$\n\nwhile at the surface\n\n${\\displaystyle \\Psi _{1}=\\Psi _{2}}$\u00a0, and ${\\displaystyle \\mathrm {K} \\ d\\Psi _{1}\/dn-(\\mathrm {K} -1)\\omega \\left\\{cxl+cym-(ax+by)n\\right\\}=d\\Psi _{2}\/dn,}$\n\nthe outside medium being air. If the dielectric body is a sphere rotating in a uniform field (0, 0, c) parallel to the axis, this gives by the usual harmonic analysis ${\\displaystyle \\Psi _{1}={\\tfrac {1}{3}}(1-\\mathrm {K} ^{-1})\\omega cr^{2}+\\mathrm {A} r\\ \\cos \\theta +\\mathrm {A} '}$\u00a0 and ${\\displaystyle \\Psi _{2}+\\mathrm {B} r^{-2}\\cos \\theta +\\mathrm {B} 'r^{-1}\\ }$\u00a0, where, r1 being the radius\n${\\displaystyle \\mathrm {A} =\\mathrm {B} \/r_{1}^{3}=-3\\mathrm {K} \/(2\\mathrm {K} +1)r_{1}.\\mathrm {A} '=-{\\tfrac {3}{2}}\/(\\mathrm {K} +2)r_{1}^{2}.\\mathrm {B} '=(\\mathrm {K} -1)\/(\\mathrm {K} +2).\\omega cr_{1}}$\u00a0; thus determining the electric potential \u03a82 in the space surrounding the rotating sphere.\n\n15. More generally, let us consider steady distributions of electric charges on a system of conductors and dielectric bodies in motion through the \u00e6ther. That there may be a steady state, without conduction currents, it is necessary that the configuration of the matter shall be permanent, and that its motion shall be the same at all times relative to this configuration and to the \u00e6ther, and also to the extraneous magnetic field if there is one: this confines it to uniform spiral motion on a definite axis fixed in the \u00e6ther. Referring to axes fixed in the material system, the vector potential has in the steady motion no time-variation: hence\n\n${\\displaystyle (\\mathrm {P,Q,R} )=-(d\/dx,\\ d\/dy,\\ d\/dz)\\mathrm {V} ,\\quad (\\mathrm {P',Q',R'} )=(\\mathrm {P} -qc+rb,\\ \\mathrm {Q} -ra+pc,\\ \\mathrm {R} -pb+qa).}$\n\nThe magnetic induction through any circuit moving with the matter being constant, (P, Q, R) is derived (\u00a712) from an electric potential function V. Inside a conductor the electric force must vanish, otherwise electric separation would be going on, therefore V must there be constant.\n\nWhen the surrounding dielectric is free space, the total current in it, referred to these axes moving with the matter, is ${\\displaystyle -(pd\/dx+qd\/dy+rd\/dz)\\ (f,\\ g,\\ h)}$\u00a0. When the velocity (p, q, r) of the matter is uniform, it then follows from Amp\u00e8re's circuital relation that ${\\displaystyle (a,\\ b,\\ c)=4\\pi (qh-rg,rf-ph,pg-qf)}$\u00a0. Hence (f, g, h), given by ${\\displaystyle 4\\pi \\mathrm {c} ^{2}f=\\mathrm {P} -qc+rb}$\u00a0, is expressed in terms of (P, Q, R) by equations of type ${\\displaystyle \\left(c^{2}-p^{2}-q^{2}-r^{2}\\right)f=\\mathrm {P} \/4\\pi -p\/4\\pi \\mathrm {c} ^{2}(p\\mathrm {P} +q\\mathrm {Q} +r\\mathrm {R} )}$\u00a0. The circuital quality of (f, g, h) thus gives the characteristic equation of the single independent variable V of the problem, in the form ${\\displaystyle \\nabla ^{2}\\mathrm {V} =c^{-2}(pd\/dx+qd\/dy+rd\/dz)^{2}\\mathrm {V} }$\u00a0, the boundary condition being that V is constant over each conductor.\n\nThus in the case of a system of conductors moving steadily through space with uniform velocity v in the direction of the axis of x, \u03b5 denoting ${\\displaystyle \\left(1-v^{2}\/c^{2}\\right){}^{-1}}$\u00a0 we have ${\\displaystyle (f,\\ g,\\ h)=(4\\pi \\mathrm {c} ^{2})^{-1}(\\mathrm {P} ,\\ \\epsilon \\mathrm {Q} ,\\ \\epsilon \\mathrm {R} )}$\u00a0, and therefore ${\\displaystyle (d^{2}\/dx^{2}+\\epsilon \\ d^{2}\/dy^{2}+\\epsilon \\ d^{2}dz^{2})\\mathrm {V} =0}$\u00a0. The distribution of electric force is therefore precisely the same as if the system were at rest, and the isotropic dielectric constant unity of the surrounding space changed into an aeolotropic one (1, \u03b5 \u03b5), cf. Part I. \u00a7115; and so would the surface density of true charge, which is the superficial discontinuity of total displacement, be the same, were it not that there is \u00e6thereal displacement inside the conductors which must be subtracted. The internal displacement current thence arising is ${\\displaystyle -(4\\pi \\mathrm {c} ^{2})^{-1}vd\/dx(0,-vc,vb)}$\u00a0; hence (a, b, c) is of the form ${\\displaystyle \\left\\{d\/dx,\\ (1+v^{2}\/c^{2})^{-1}d\/dy,\\ (1+v^{2}\/c^{2})^{-1}d\/dz\\right\\}\\phi }$\u00a0, by Amp\u00e8re's circuital relation: the circuitality of (a, b, c) then leads to a characteristic equation for Φ, which must be solved so as to give at the surface of the conductor a value for the normal component of (a, b, c) continuous with the already known outside value, and the internal displacement is thereby determined. There is no bodily electrification inside the conductors, since this displacement is circuital.\n\nWe can restore the above characteristic equation of V, the potential of the electric force, to an isotropic form by a geometrical strain of the system and the surrounding space, represented by ${\\displaystyle (x',\\ y',\\ z')=\\left(\\epsilon ^{\\tfrac {1}{2}}x,\\ y,\\ z\\right)}$\u00a0: the actual distribution of potential around the original system in motion corresponds then to that isotropic distribution of potential round the new system at rest which has the same values over the conductors. The \u00e6thereal displacements through related elements of area \u03b4S and \u03b4S', of direction cosines (l, m, n) and (l', m', n') in the two spaces, multiplied by 4\u03c0c\u00b2, will be\n\n${\\displaystyle -(ld\/dx+\\epsilon \\ md\/dy+\\epsilon \\ nd\/dz)V\\delta S}$\u00a0 and ${\\displaystyle -(l'd\/dx'+m'd\/dy'+n'd\/dz')V'\\delta S';}$\n\nof these the second is always ${\\displaystyle \\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0 times the first; thus the elements of surface for which the total displacement is null correspond in the two systems, and therefore the lines and tubes of total displacement also correspond, the flux of displacement in these tubes being ${\\displaystyle \\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0 times greater in the second system than in the first. But on account of the \u00e6thereal displacement in the interior, the outside tubes do not mark out the distribution of the charge on each conductor. If then a system of charged conductors has a velocity of uniform translation v through the \u00e6ther: and an auxiliary system at rest is imagined consisting of the original system and its space each uniformly expanded in the ratio ${\\displaystyle \\epsilon ^{\\tfrac {1}{2}}}$\u00a0 or ${\\displaystyle \\left(1-v^{2}\/c^{2}\\right){}^{\\tfrac {1}{2}}}$\u00a0 in the direction of the motion, and the charges on this new system are ${\\displaystyle \\epsilon ^{\\tfrac {1}{2}}}$\u00a0 times those on the actual system: then the fields of \u00e6thereal displacement of the two systems agree in the surrounding spaces so as to be the same across corresponding areas, but the distributions of the charges on the conductors do not thus exactly correspond. [These results are obtained on the supposition that the structure of the matter is not affected by its motion. The conductors on which these charges are situated will, however, if the results of the more fundamental analysis of \u00a716 are admitted, change their actual forms to a slight extent depending on (v\/c)\u00b2 when they are put in motion, and this change will react so that the distribution of charges and displacements will be the simple one there given.]\n\n16. The circumstances of propagation of radiation in a material medium moving with uniform velocity v parallel to the axis of x will form another example. We may here (\u00a713) employ the circuital relations, of types\n\n${\\displaystyle 4\\pi u={\\frac {d\\gamma }{dy}}-{\\frac {d\\beta }{dz}},\\quad {\\frac {\\delta \\alpha }{dt}}={\\frac {d\\mathrm {R} }{dy}}-{\\frac {d\\mathrm {Q} }{dz}}}$\n\nwhere\n\n${\\displaystyle u={\\frac {df}{dt}}+{\\frac {\\delta f'}{dt}},\\quad (f',\\ g',\\ h')={\\frac {K-1}{4\\pi c^{2}}}(\\mathrm {P,\\ Q,\\ R} ),\\quad (f,\\ g,\\ h)={\\frac {1}{4\\pi c^{2}}}(\\mathrm {P,\\ Q} +vc,\\ \\mathrm {R} -vb).}$\n\nThere readily results, on eliminating the electric force (P, Q, R),\n\n${\\displaystyle 4\\pi (u,\\ v,\\ w)=curl(\\alpha ,\\ \\beta ,\\ \\gamma ),\\quad \\mathrm {D} ^{2}\/dt^{2}(a,\\ b,\\ c)=4\\pi c^{2}curl(u,\\ v,\\ w),}$\n\nwhere\n\n${\\displaystyle \\mathrm {D} ^{2}\/dt^{2}=d^{2}\/dt^{2}+(\\mathrm {K} -1)(d\/dt+vd\/dx)^{2};}$\n\nwhich agrees with the equation obtained in Part I. \u00a7124 and Part II. \u00a713, leading to Fresnel's law of alteration of the velocity of propagation.\n\nNow let us consider the free \u00e6ther for which K and \u03bc are unity, containing a definite system of electrons which are grouped into the molecules of a material body moving across the \u00e6ther with uniform velocity v parallel to the axis of x; and let us remove the restriction to steadiness of \u00a7 15. We refer the equations of free \u00e6ther, in which these electrons are situated, to axes moving with the body: the alteration thus produced in the fundamental \u00e6thereal equations\n\n${\\displaystyle 4\\pi d\/dt.(f,\\ g,\\ h)=curl(a,\\ b,\\ c),\\quad -d\/dt.(a,\\ b,\\ c)=4\\pi c^{2}curl(f,\\ g,\\ h)}$\n\nis change of d\/dt into ${\\displaystyle d\/dt-v\\ d\/dx}$\u00a0, leading to the forms\n\n${\\displaystyle 4\\pi d\/dt.(f,\\ g,\\ h)=curl(a',\\ b',\\ c'),\\quad -d\/dt.(a,\\ b,\\ c)=4\\pi c^{2}curl(f',\\ g',\\ h');}$\n\nwhere\n\n${\\displaystyle (a',\\ b',\\ c')=(a,\\ b+4\\pi vh,\\ c-4\\pi vg),\\quad (f',\\ g',\\ h')=(f,\\ g-vc\/4\\pi \\mathrm {c} ^{2},\\ h+vb\/4\\pi \\mathrm {c} ^{2})}$\n\nfrom which eliminating the unaccented letters, neglecting (v\/c)\u00b3, and writing as before \u03b5 for ${\\displaystyle \\left(1-v^{2}\/c^{2}\\right)^{-1}}$\u00a0, we derive the system\n\n${\\displaystyle {\\begin{array}{ccc}4\\pi {\\frac {df'}{dt}}={\\frac {dc'}{dy}}-{\\frac {db'}{dz}}&&-(4\\pi \\mathrm {c} ^{2})^{-1}{\\frac {da'}{dt}}={\\frac {dh'}{dy}}-{\\frac {dg'}{dz}}\\\\\\\\4\\pi \\epsilon {\\frac {dg'}{dt}}={\\frac {da'}{dz}}-\\left({\\frac {d}{dx}}+{\\frac {v}{c^{2}}}{\\frac {d}{dt}}\\right)c'&&-(4\\pi \\mathrm {c} ^{2})^{-1}\\epsilon {\\frac {db'}{dt}}={\\frac {df'}{dz}}-\\left({\\frac {d}{dx}}+{\\frac {v}{c^{2}}}{\\frac {d}{dt}}\\right)h'\\\\\\\\4\\pi \\epsilon {\\frac {dh'}{dt}}=\\left({\\frac {d}{dx}}+{\\frac {v}{c^{2}}}{\\frac {d}{dt}}\\right)b'-{\\frac {da'}{dy}}&&-(4\\pi \\mathrm {c} ^{2})^{-1}\\epsilon {\\frac {dc'}{dt}}=\\left({\\frac {d}{dx}}+{\\frac {v}{c^{2}}}{\\frac {d}{dt}}\\right)g'-{\\frac {df'}{dy}}.\\end{array}}}$\n\nNow change the time variable from t to t', equal to ${\\displaystyle t-vx\/c^{2}}$\u00a0, so that ${\\displaystyle d\/dx+v\/c^{2}-d\/dt}$\u00a0 becomes d\/dx, and d\/dt becomes d\/dt', and these equations assume the form of an electric scheme for a crystalline medium at rest. Finally write x1 for ${\\displaystyle x\\epsilon ^{\\tfrac {1}{2}}}$\u00a0, a1 for ${\\displaystyle a'\\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0, f1 for ${\\displaystyle f'\\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0, dt1 for ${\\displaystyle dt'\\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0, keeping the other variables unchanged, and the system comes back to its original isotropic form for free \u00e6ther. Thus the final variables (f1, g1, h1) and (a1, b1, c1) will represent the \u00e6thereal field for a correlative system of electrons forming the molecules of another material system at rest in the \u00e6ther, of the form of the original one pulled out uniformly in the ratio ${\\displaystyle \\epsilon ^{\\tfrac {1}{2}}}$\u00a0 along its direction of movement; the electric displacements through corresponding areas in the two systems are not equal, but their molecules are composed of equal electrons and are situated at corresponding points, and the individual electrons describe corresponding parts of their orbits in times shorter for the latter system in the ratio ${\\displaystyle \\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0 or ${\\displaystyle \\left(1-{\\tfrac {1}{2}}v^{2}\/c^{2}\\right)}$\u00a0 while those less advanced in the direction of v are also relatively very slightly further on in their orbits on account of the difference of time-reckoning. Thus we have here two correlative systems each governed by the circuital relations, of the free \u00e6ther: (i) a system in which the electric and magnetic displacements are (f, g, h) and (a, b, c), moving steadily with uniform velocity v parallel to the axis of x, (ii) the same system expanded in the direction of x in the ratio ${\\displaystyle \\epsilon ^{\\tfrac {1}{2}}}$\u00a0 and at rest, the displacements at the corresponding points being ${\\displaystyle \\left(\\epsilon ^{-{\\tfrac {1}{2}}}f,\\ g-vc\/4\\pi c^{2},\\ h+vb\/4\\pi c^{2}\\right)}$\u00a0 and ${\\displaystyle \\left(\\epsilon ^{-{\\tfrac {1}{2}}}a,\\ b-4\\pi vh,\\ c+4\\pi vg\\right)}$\u00a0, and the molecules being situated in the corresponding positions with due regard to the varying time-origin. Inasmuch as the circuital relations form a differential scheme of the first order which determines step by step the subsequent stages of a system when its initial state is given, it follows that if these two \u00e6thereal systems are set free at any instant in corresponding states, they will be in corresponding states at each subsequent instant, their electrons or singularities being at corresponding points. If then the latter collocation represent a fixed solid body, the former will represent the same body in uniform motion; one consequence of the motion thus being that the body is shrunk in the direction of its velocity v in the ratio ${\\displaystyle \\epsilon ^{-{\\tfrac {1}{2}}}}$\u00a0 or ${\\displaystyle 1-{\\tfrac {1}{2}}v^{2}\/c^{2}}$\u00a0. It may be observed that there is here no question of verifying that the mechanical forces acting on the single electrons in the two cases are such as to maintain this correspondence; for in the present complete survey of the individual atoms there is no such entity as mechanical force, any more than there is on a free vortex ring in fluid; the notion of mechanical forces enters at a subsequent stage when we are treating of molecular aggregates considered as continuous bodies, and are examining the relations between the different groups into which our senses analyze their interactions (\u00a7 48).\n\nIf this argument is valid, it will confirm the hypothesis of FitzGerald and Lorentz, to which they were led as the ultimate resource for the explanation of the negative result of Michelson's optical experiments; and conversely it will involve evidence that the constitution of a molecule is wholly electric, as here represented. The reasoning given in Part II., \u00a7 13, was insufficient, because the correlation between the two systems was not there pushed to their individual molecules.\n\n1. 'Phil. Trans.,' 1894, A., pp. 719-822; 1895, A, pp. 695-743; referred to subsequently as Part I. and Part TI. [In the abstract of the present Memoir, 'Roy. Soc. Proc.,' 61, on p. 281, line 6, read ${\\displaystyle 2\\pi n'^{2}+\\int i'd\\mathrm {F} }$\u00a0 for ${\\displaystyle 2\\pi n'^{2}}$\u00a0; line 35 read ${\\displaystyle {\\tfrac {2}{3}}\\cdot {\\tfrac {4}{5}}\\pi i'^{2}}$\u00a0 for ${\\displaystyle {\\tfrac {4}{5}}\\pi i'^{2}}$\u00a0; and on p. 284, line 18, read ${\\displaystyle m\/2c\\cdot \\mathrm {E} \\left(1-m^{2}\\right)}$\u00a0 for ${\\displaystyle \\mathrm {E} \\left(1-m^{2}\\right)}$\u00a0.\n2. Gauss, Werke, V., p. 629, letter to WEBER of date 1845\u00a0; quoted by Maxwell, \"Treatise\" II., \u00a7 861. After the present memoir had been practically completed, my attention was again directed, through a reference by Zeeman, to H. A. Lorentz's Memoir \"Le Th\u00e9orie Electromagnetique de Maxwell et son application aux corps mouvants,\" Archives N\u00e9erlandaises 1892, in which (pp. 70 seqg.) ideas similar to the above are developed. The electrodynamic scheme at which he arrives is formulated differently from that given in \u00a7 13 infra, the chief difference being that in the expression for the electric force (P, Q, R) the term ${\\displaystyle -d\/dt}$\u00a0 (F, G, H) is eliminated by introducing the \u00e6thereal displacement (f, g, h). This applies also to the later \"Versuch einer Theoric . . . in bewegten K\u00f6rpern,\" 1895. The author remarks on the indirect manner in which dynamical equations had to be obtained, mainly on account of the absence of any notion as to the nature of the connexion between the stagnant \u00e6ther and the molecules that are moving through it. \"Dans le chemin qui nous a conduit \u00e0 ces \u00e9quations nous avons rencontr\u00e9 plus d\u2019une difficult\u00e9 s\u00e9rieuse, et on sera probablement peu satisfait d\u2019une th\u00e9orie qui, loin de d\u00e9voiler le m\u00e9canisme des ph\u00e9nomenes, nous laisse tout au plus l\u2019espoir de le d\u00e9couvrir un jour\" (\u00a7 91). In the following year (1893) similar general ideas were introduced by von Helmholtz, in his now well-known memoir on the electrical theory of optical dispersion, in which currents of conduction are included: but his argument is very difficult, and the results are in discrepancy with those of Lorentz and the present writer in various respects in which the latter agree; moreover they are not consistent with the optical properties of moving material media. Both these discussions, of Lorentz and of von Helmholtz, are in the main confined to electromotive phenomena: the treatment of the mechanical forces acting on matter in bulk would require for basis a theory of the mechanical relations of molecular media such as is developed in this paper. The results in the paper by Zeeman, above referred to, \"On the Influence of Magnetism on the Light emitted by a substance,\" Verslagen Akad. Amsterdam, Nov. 28, 1896, have an important bearing on the view of the dynamical constitution of a molecule that has been advanced in these papers, and illustrated by calculation in an ideal simple case in Part I., \u00a7\u00a7 114-8; cf. 'Roy. Soc. Proc.' 60, 1897, p. 514. [See 'Phil. Mag.,' Dec. 1897: where the loss of energy by radiation from the moving ions is also examined.]\n3. Gilbert, de Magnete, 1600,\n4. I find that the rotational \u00e6ther of MacCullagh, which was advanced by him in the form of an abstract dynamical system (for reasons similar to those that prompted Maxwell to finally place his mechanism of the electric field on an abstract basis) was adopted by Rankine in 1850, and expounded with full and clear realization of the elastic peculiarities of a rotational medium: by him also the important advantage for physical explanation, which arises from its fluid character, was first emphasized. Cf. Miscellaneous Scientific Papers, pp. 63, 160. In Rankine's special and peculiar imagery, the \u00e6ther was however a polar medium or system (as contrasted with a body) made up of polarized nuclei (Cf. Part I., \u00a7\u00a7 37-8) whose vertical atmospheres, where such exist, constitute material atoms. The supposed necessity of having the vibration at right angles to the plane of polarization also misled him to the introduction of complications into the optical theory, such as \u00e6olotropic inertia, and to deviations from MacCullagh's rigorous scheme.\n5. The use of these studs is to maintain continuity of motion of the medium without the aid of viscosity; and also (\u00a7 4) to compel each sphere to participate in the rotation of the element of volume of the medium, so that the latter shall be controlled by the gyrostatic torques of the spheres.\n6. Lord Kelvin, 'Comptes Rendus,' Sept. 1889: 'Math, and Phys. Papers,' III., p. 466.\n7. Thus when the medium is in equilibrium, there is in it only the static intrinsic strain diverging from these centres, which gives rise to the forces between them; but when it is disturbed by radiation or otherwise, there is also the strain thence arising.\n8. An analogous principle applies in the vortex-theory illustration of matter. If we consider rigid cores round which the fluid circulates, they are moved about by the fluid pressure: but if we consider vortex-rings, say with vacuous cores, these are mere forms of motion that move across the fluid, and if we take them to represent atoms, the interactions between aggregations of atoms cannot be traced by means of fluid pressures, but can only be derived from the analytical character of the function which expresses the energy.\n9. Two steady magnetic poles of like sign would repel each other: but in the case of two poles pulsating in the same phases there is also an inertia term in the fluid \u00e6thereal pressure, and the result is as stated above. Cf. Hicks, ' Proc. Camb. Phil. Soc.,' 1880, p. 35.\n10. It is here assumed that the direct action between the molecules is sensible only at molecular distances, which would not be the case if the material were electrically polarized. The statement also refers solely to transmitted mechanical stress of the ordinary kind: more complicated types, not expressible by surface tractions alone, are put aside, as well as molecular conceptions like the Laplacian intrinsic pressure in fluids, Cf. \u00a7\u00a7 44-6 infra.\n11. As a concrete illustration, we can imagine two ideal atoms, each consisting of a single gyrostat enclosed in a suitable massless case, coming into mutual encounter. We may imagine that neither of them has any internal heat; so that the internal energy of each is the minimum that corresponds to its steady gyrostatic momentum, and the axis of each gyrostat therefore keeps a fixed direction in space. The result of the encounter will be that the axis of each gyrostat acquires steady wobbling or free processional motion, so that its internal energy is increased at the expense of the energy of translation of the atoms; but in this the simplest case there will be no unsteady vibration, such as could be radiated away. If however there are also other types of momenta associated with the atom, for example if the case of the gyrostat is not massless, the encounter will leave vibrations about the new state of steady motion, which if of high enough period will lead to loss of energy by radiation.\n12. Ideas somewhat similar to the above are advanced by Waterston in his classical memoir of 1845 on gas-theory, recently edited by Lord Rayleigh; 'Phil. Trans.' (A), 1892, p. 51.\n13. Cf. Thomson and Tait, 'Nat. Phil.' \u00a7 345 xxiv.\n14. Cf. G. F. FitzGerald, 'Roy. Soc. Proc.' 42, 1887: cf. also Clausius' early ideas on 'disgregation.'\n15. This scheme forms an improved summary of that worked out in Part II. \u00a7\u00a7 15-19; the expressions there assigned for \u03c1 and \u03a8 have here been corrected, and (u0, v0, w0) is merged.\n16. [Added Sept. 14.\u2014The term \u03b4f'\/dt in u arises as follows. In addition to the change of the polarization in the element of volume, df\/dt, there is the electrodynamic effect of the motion of the positive and negative electrons of the polar molecule. Now the movement of two connected positive and negative electrons is equivalent to that of a single positive electron round the circuit formed by joining together the ends of their paths: and a similar statement holds when there are more than two electrons in the molecule. Hence the motion of a polarized medium with velocity (p, q, r), which need not be constant from point to point, produces the electrodynamic effect of a magnetization (${\\displaystyle rg'-qh',\\ ph'-rf,\\ qf'-pg'}$\u00a0) distributed throughout the volume: cf. Part I, \u00a7 125. And it has been shown in Part II, \u00a7 31 that any distribution of magnetism (A, B, C) may be represented as a volume distribution of electric current equal to curl (A, B, C), which is necessarily circuital, together with a surface current sheet equal to (${\\displaystyle Bn-Cm,\\ Cl-An,\\ Am-Bl}$\u00a0). Thus, when (p, q, r) is uniform and (f, g', h') is circuital, the above magnetic distribution is equivalent to a current system (${\\displaystyle pd\/dx+qd\/dy+rd\/dz)\\ (f,\\ g',\\ h')}$\u00a0 together with current sheets on interfaces of discontinuity: this system is to be added on to d\/dt (f, g', h') in order to give the full electrodynamic effect. Thus in these special circumstances the formulation in the test is correct in so far as it leads to the correct differential equations for the element of the medium: the integral expression there given for F is however only correct either when it is reduced to the differential form ${\\displaystyle -\\nabla ^{2}\\mathrm {F} \/4\\pi =u+d\\mathrm {C} \/dy-d\\mathrm {B} \/dz}$\u00a0, which is derivable on integration of its second term by parts, or else when, the velocity of the matter still being uniform, discontinuous interfaces are replaced in the analysis by gradual though rapid transitions. These conditions are satisfied in all the applications that follow: but they would not be satisfied for example in the problem of the reflexion of radiation from the surface of moving matter.\nBut a formulation which is preferable to the above, in that it is absolutely general, is simply to implicitly include the above virtual magnetization directly in (A, B, C) and consequently change from \u03b4f'\/dt to df'\/dt in the expression for u: this will also involve that the relation ${\\displaystyle \\mathrm {A} =\\kappa \\alpha }$\u00a0. which occurs lower down shall be replaced by ${\\displaystyle \\mathrm {A} =\\kappa \\alpha +rg'-qh'}$\u00a0, but there will be no further alteration in the argument of the text. The boundary conditions of the text are unaltered.]\n\nThis work is in the public domain in the United States because it was published before January 1, 1928.\n\nThe longest-living author of this work died in 1942, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 80 years or less. 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Space Lifestyle Magazine is a general interest consumer digital edition magazine on space and the space sector. We incorporate full feature stories, video and animation on all things space related. From the professional to those with a passing interest in things space, the digital edition allows readers to catch a quarterly perspective on space with their computer screen, iPhone, or iPod touch.
Established in 2002 by Elon Musk , the founder of PayPal and the Zip2 Corporation, SpaceX has already developed two brand new launch vehicles, established an impressive launch manifest, and been awarded COTS funding by NASA to demonstrate delivery and return of cargo to the International Space Station. Supported by this order book and Mr. Musk's substantial resources, SpaceX is on an extremely sound financial footing as we move towards volume commercial launches.
Our design and manufacturing facilities are located near the Los Angeles International airport, leveraging the deep and rich aerospace talent pool available in Southern California . Our extensive propulsion and structural test facilities are located in Central Texas. We currently have launch complexes available in Vandenberg and Kwajalein Island , and in April 2007 we were granted use of and began developing Space Launch Complex 40 at Cape Canaveral.
The New Mexico Spaceport Authority will plan, develop and operate the first inland commercial spaceport. Spaceport America will provide vertical and horizontal launch services and facilities for the new generation of commercial and government space launch vehicles. Our goal is to achieve commercial vertical and horizontal launch programs, training, research and development, testing, entertainment, tourism, education and community relations as well as bringing related industry to New Mexico for economic growth. Spaceport America will attract global customers for suborbital flights.
Spaceport Sweden represents the combined expertise of several Kiruna-based Swedish companies whose successful development has earned them international respect. Their reputation for service consistently attracts attention with regards to aerospace operations, testing and tourism.
Spaceport Sweden is a co-operation between the Swedish Space Corporation, ICEHOTEL, Kiruna Airport and Kirunas business-development company Progressum.
The aim of Spaceport Sweden is to make Kiruna Europeans first and most obvious place for personal suborbital spaceflight.
Special Aerospace Services (SAS) is a newly formed aerospace Systems, Services, and Software company established by former highly experienced NASA, FAA, and Industry professionals. SAS provides effective space systems engineering, space systems, and flight software assurance/IV&V solutions to NASA, existing aerospace industry, and the emerging commercial spaceflight industry. Our team has worked on every successful U.S. Expendable Launch System, supported emerging launch systems through our FAA experienced staff, and have worked on existing and emerging space access solutions for NASA, Air Force, and US Government agencies.
Team 1st provides sales, training, and support for eInstruction products which include the Classroom Performance System (CPS), ExamView and ExamView Learning Series, and the InterWrite Pad, Board, and Workspace software. Our products advance student achievement through teamwork, collaboration and real-time assessment. We provide immediate feedback at the classroom level as well as facilitating district-wide management of shortcycle assessments. Strategic implementation of eInstruction products has been shown to have a positive impact on a school's AYP, Adequate Yearly Progress.
Verge is a highly motivated venture capital fund that invests in seed-stage, high-growth ventures right here in New Mexico. This partnership focuses on opportunities at the earliest stages of their development, even if the business plan hasn't been fully built out. Sure, there's a certain amount of ambiguity at this stage, but there's also the potential for a very high return. And the Principals at Verge know a little something about that.
The Village of Hatch is located approximately 22 miles from Spaceport America and is the closest municipality to the Spaceport. The Governor's office and the New Mexico Spaceport Authority has often referred to the Village as "the most aggressive and helpful community in support of Spaceport America". As a rural Village of less than 2,000 residents we must speak up to be heard. We are the home of the Internationally known Hatch Chile Festival drawing 20,000+ visitors each year over Labor Day weekend and have recently achieved the status of a Certified Community in New Mexico indicating we are a business friendly community. Please visit our website or stop by our booth during ISPCS 2008 to see what we might be able to do for you.
White Sands Missile Range is 4 Million acre facility; controlled airspace; rocket propulsion; component/whole body testing; flight safety; endo/exo-atmospheric launch; telemetry, radar, high-altitude optical tracking; meteorology; robotics; high wireless commo; vacuum/altitude chamber; liq propellant; solar radiation/nuclear effects; unmanned aerial systems; EM interference; Climatic; Dynamics; Accredited Chemistry Lab; Coop(spaceport, universities, national lab, and Tech Corridor); Crew Explor Vehicle, sounding rocket; community launch programs; START Treaty compliant; Space Harbor Runway on-site; low fuel to reach orbit. | {
"redpajama_set_name": "RedPajamaC4"
} | 487 |
These two patients have been on a weight loss program and have reached their goals.
The first patient, Duncan, a six year old Labradoodle, started on a weight loss program in November. His weight in November was 27kg or 59.4lbs. Duncan came in for a nutritional consult and it was decided that he needed to lose 15lbs.
Duncan is a very active dog and loves to go hiking so exercise was not a problem he just needed the right nutrition. Duncan's new diet was a reducing diet that is low in fat, high in fibre which helps reduce body fat while ensuring that he feels full. It also has high levels of carnitine which increases lean muscle mass. It has antioxidants that defend the cells from free radicals which promotes a healthy immune system.
In order for Duncan to lose weight, he needed full cooperation of his family. Duncan was in every 2 weeks so we could check his weight. We also had to cut back on his treats drastically which was very hard because Duncan, who is part Labrador retriever, really loves his food. When he comes in for his weight checks he assesses all of our food shelves to see what we have, he usually tries to pick out a few bags of cat food or treats from the treat section. It was important for him to still have a treat or two so we put him on a low fat dental chew that not only tastes good but reduces plaque and tartar.
It took six months for Duncan to reach his goal weight so it was a big commitment. It was important for Duncan to not lose the weight too quickly. Ideally it is 1% a week which worked out to be 1kg per month which Duncan achieved. His family reports that his energy levels have increased dramatically since his weight loss and he is now able to go running with his family.
The second patient, Zeus, an 11 year old Golden Retreiver, started on a weight loss program in May, 2010. Zeus weighed 52kg or 114lbs at this time. During his exam it was decided that he needed to lose 22lbs.
Zeus started on the same reducing diet that Duncan was on. For Zeus it was incredibly important to lose the weight. We wanted him to be very healthy during his senior years. Dogs that are overweight are more prone to be at a high risk for a number of abnormalities such as exercise intolerance, joint problems such as arthritis and ruptured ligaments, diabetes, problems with the digestive system such as pancreatitis and constipation, and it increases the workload on their heart. The plan for Zeus was to reduce his weight by 4.5lbs a month. Zeus lost the weight perfectly each month.
His family was very diligent and in 6 months Zeus was at his ideal weight. As you can see from his photo's Zeus looks fantastic. He is now on a maintenance diet and at his last veterinary check-up he had so much energy we had a hard time examining him. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,035 |
package com.mercadopago.android.px.testcheckout.pages;
import com.mercadopago.android.px.testcheckout.assertions.CheckoutValidator;
import com.mercadopago.android.testlib.pages.PageObject;
import static android.support.test.espresso.Espresso.pressBack;
public class DiscountDetailPage extends PageObject<CheckoutValidator> {
public DiscountDetailPage() {
// This constructor is intentionally empty. Nothing special is needed here.
}
public DiscountDetailPage(final CheckoutValidator validator) {
super(validator);
}
public PaymentMethodPage pressCloseToPaymentMethod() {
pressBack();
return new PaymentMethodPage(validator);
}
public InstallmentsPage pressCloseToInstallments() {
pressBack();
return new InstallmentsPage(validator);
}
public OneTapPage pressCloseToOneTap() {
pressBack();
return new OneTapPage(validator);
}
@Override
public DiscountDetailPage validate(final CheckoutValidator validator) {
validator.validate(this);
return this;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,450 |
{"url":"https:\/\/datascience.stackexchange.com\/questions\/25526\/how-to-create-domain-rules-from-raw-unstructured-text-using-nlp-and-deep-learnin","text":"# How to create domain rules from raw unstructured text using NLP and deep learning?\n\nHow to create domain rules from raw unstructured text using NLP and deep learning techniques ? For example for the below text on symptoms of Dengue, all three look pretty similar but if you want to make sure a person is having Dengue you want to exact definite common minimum rules out of these raw text , so as to confirm a person is having Dengue. Can someone give reference to some research or blogs where similar problem has been solved ?\n\n1) Symptoms of dengue fever include severe joint and muscle pain, swollen lymph nodes, headache, fever, exhaustion, and rash.\n\n2) High fever and at least two of the following:\nSevere eye pain (behind eyes)\nJoint pain\nMuscle and\/or bone pain\nRash\nMild bleeding manifestation (e.g., nose or gum bleed, petechiae, or easy bruising)\nLow white cell count\n\n3) Aching muscles and joints\nBody rash that can disappear and then reappear\nhigh fever\npain behind the eyes\nvomiting and feeling nauseous\n\n\nFor the above three extracts commons rule would look like\n\n1) Fever\n2) Joint and muscle pain\n4) Rash\n\n\u2022 How could you define a labeled data for this type of problems? \"exact definite common minimum rules out of this raw text, so as to confirm a person is having Dengue.\"? what an objective metric you could define? May 10 '18 at 18:39\n\nI think your question can be solved using Case Based Reasoning .\n\nBasic principle how it works is, you need to train the model using whole lot of different cases which you have. Based on the symptoms which you give the outcome is predicted(which disease).\n\nPlease refer to the links below for deep diving into the topic, appended couple of links with respect to health care industry:\n\nDo let me know if you need any additional information.\n\n\u2022 If you got what you were looking for, you can accept the answer. Let me know If you need any more explanation. Mar 21 '18 at 1:23\n\nYou can look into topic models like LDA to discover the most common topics. Preprocessing, like removing stop words, stemming and using n-grams and then applying LDA usually produces better results.\n\nYou can also use embedding together with neural nets to discover important words. Googles MLCC has a nice example.","date":"2022-01-24 23:51:21","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\": 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\": 0.5256788730621338, \"perplexity\": 2640.9421273365847}, \"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-2022-05\/segments\/1642320304686.15\/warc\/CC-MAIN-20220124220008-20220125010008-00548.warc.gz\"}"} | null | null |
// ******************************************
// * *
// * THIS IS A GENERATED FILE. DO NOT EDIT! *
// * SEE .xml FILE WITH SAME NAME *
// * *
// ******************************************
#ifndef ZORBA_RUNTIME_SEQUENCES_SEQUENCES_H
#define ZORBA_RUNTIME_SEQUENCES_SEQUENCES_H
#include "common/shared_types.h"
#include "runtime/base/narybase.h"
#include <zorba/internal/unique_ptr.h>
#include "runtime/base/narybase.h"
#include "runtime/core/path_iterators.h"
#include "zorbatypes/integer.h"
namespace zorba {
class NodeHandleHashSet;
class AtomicItemHandleHashSet;
/**
*
* op:concatenate
*
* Author: Zorba Team
*/
class FnConcatIteratorState : public PlanIteratorState
{
public:
std::vector<PlanIter_t>::const_iterator theCurIter; //iterator pointing to the child that is currently being processed
std::vector<PlanIter_t>::const_iterator theEndIter; //
FnConcatIteratorState();
~FnConcatIteratorState();
};
class FnConcatIterator : public NaryBaseIterator<FnConcatIterator, FnConcatIteratorState>
{
public:
SERIALIZABLE_CLASS(FnConcatIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnConcatIterator,
NaryBaseIterator<FnConcatIterator, FnConcatIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnConcatIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnConcatIterator, FnConcatIteratorState>(sctx, loc, children)
{}
virtual ~FnConcatIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
void openImpl(PlanState&, uint32_t&);
void resetImpl(PlanState&) const;
};
/**
*
* Summary: Returns a sequence of positive integers giving the positions
* within the sequence $seqParam of items that are equal to $srchParam.
*
* The collation used by the invocation of this function is determined
* according to the rules in 7.3.1 Collations. The collation is used when
* string comparison is required.
*
* The items in the sequence $seqParam are compared with $srchParam under
* the rules for the 'eq' operator. Values that cannot be compared, i.e.
* the 'eq' operator is not defined for their types, are considered to be
* distinct. If an item compares equal, then the position of that item in
* the sequence $seqParam is included in the result.
*
* If the value of $seqParam is the empty sequence, or if no item in
* $seqParam matches $srchParam, then the empty sequence is returned.
*
* The first item in a sequence is at position 1, not position 0.
* The result sequence is in ascending numeric order.
*
* Author: Zorba Team
*/
class FnIndexOfIteratorState : public PlanIteratorState
{
public:
uint32_t theCurrentPos; //the current position in the sequence
store::Item_t theSearchItem; //the item to search for
XQPCollator* theCollator; //the collator
FnIndexOfIteratorState();
~FnIndexOfIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnIndexOfIterator : public NaryBaseIterator<FnIndexOfIterator, FnIndexOfIteratorState>
{
protected:
int theFastComp; //
public:
SERIALIZABLE_CLASS(FnIndexOfIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnIndexOfIterator,
NaryBaseIterator<FnIndexOfIterator, FnIndexOfIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnIndexOfIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children,
int fastComp)
:
NaryBaseIterator<FnIndexOfIterator, FnIndexOfIteratorState>(sctx, loc, children),
theFastComp(fastComp)
{}
virtual ~FnIndexOfIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* If the value of $arg is the empty sequence, the function returns true;
* otherwise, the function returns false.
*
* Author: Zorba Team
*/
class FnEmptyIterator : public NaryBaseIterator<FnEmptyIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnEmptyIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnEmptyIterator,
NaryBaseIterator<FnEmptyIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnEmptyIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnEmptyIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnEmptyIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* If the value of $arg is not the empty sequence, the function returns true;
* otherwise, the function returns false.
*
* Author: Zorba Team
*/
class FnExistsIterator : public NaryBaseIterator<FnExistsIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnExistsIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnExistsIterator,
NaryBaseIterator<FnExistsIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnExistsIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnExistsIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnExistsIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns the sequence that results from removing from arg all but one of a
* set of values that are eq to one other. Values of type xs:untypedAtomic are
* compared as if they were of type xs:string. Values that cannot be compared,
* i.e. the eq operator is not defined for their types, are considered to be
* distinct. The order in which the sequence of values is returned is implementation
* dependent. In zorba, we return the first item that is not a duplicate and
* throw away the remaining ones.
*
* Author: Zorba Team
*/
class FnDistinctValuesIteratorState : public PlanIteratorState
{
public:
bool theHasNaN; //indicates whether NaN was found in the sequence
std::unique_ptr<AtomicItemHandleHashSet> theAlreadySeenMap; //hashmap for doing the duplicate elimination
FnDistinctValuesIteratorState();
~FnDistinctValuesIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnDistinctValuesIterator : public NaryBaseIterator<FnDistinctValuesIterator, FnDistinctValuesIteratorState>
{
public:
SERIALIZABLE_CLASS(FnDistinctValuesIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnDistinctValuesIterator,
NaryBaseIterator<FnDistinctValuesIterator, FnDistinctValuesIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnDistinctValuesIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnDistinctValuesIterator, FnDistinctValuesIteratorState>(sctx, loc, children)
{}
virtual ~FnDistinctValuesIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns a new sequence constructed from the value of the first parameter with
* the value of third parameter inserted at the position specified by the value
* of the second parameter.
*
* Author: Zorba Team
*/
class FnInsertBeforeIteratorState : public PlanIteratorState
{
public:
xs_integer theCurrentPos; //the current position in the sequence
xs_integer thePosition; //
store::Item_t theTargetItem; //
FnInsertBeforeIteratorState();
~FnInsertBeforeIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnInsertBeforeIterator : public NaryBaseIterator<FnInsertBeforeIterator, FnInsertBeforeIteratorState>
{
public:
SERIALIZABLE_CLASS(FnInsertBeforeIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnInsertBeforeIterator,
NaryBaseIterator<FnInsertBeforeIterator, FnInsertBeforeIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnInsertBeforeIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnInsertBeforeIterator, FnInsertBeforeIteratorState>(sctx, loc, children)
{}
virtual ~FnInsertBeforeIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns a new sequence constructed from the value of aTarget with the item at
* the position specified by the value of aPosition removed.
*
* Author: Zorba Team
*/
class FnRemoveIteratorState : public PlanIteratorState
{
public:
xs_integer theCurrentPos; //the current position in the sequence
xs_integer thePosition; //the position to delete
XQPCollator* theCollator; //the collator
FnRemoveIteratorState();
~FnRemoveIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnRemoveIterator : public NaryBaseIterator<FnRemoveIterator, FnRemoveIteratorState>
{
public:
SERIALIZABLE_CLASS(FnRemoveIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnRemoveIterator,
NaryBaseIterator<FnRemoveIterator, FnRemoveIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnRemoveIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnRemoveIterator, FnRemoveIteratorState>(sctx, loc, children)
{}
virtual ~FnRemoveIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:reverse
*
* Author: Zorba Team
*/
class FnReverseIteratorState : public PlanIteratorState
{
public:
std::stack<store::Item_t> theStack; //
FnReverseIteratorState();
~FnReverseIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnReverseIterator : public NaryBaseIterator<FnReverseIterator, FnReverseIteratorState>
{
public:
SERIALIZABLE_CLASS(FnReverseIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnReverseIterator,
NaryBaseIterator<FnReverseIterator, FnReverseIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnReverseIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnReverseIterator, FnReverseIteratorState>(sctx, loc, children)
{}
virtual ~FnReverseIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:subsequence
*
* Author: Zorba Team
*/
class FnSubsequenceIteratorState : public PlanIteratorState
{
public:
xs_long theRemaining; //
bool theIsChildReset; //
FnSubsequenceIteratorState();
~FnSubsequenceIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnSubsequenceIterator : public NaryBaseIterator<FnSubsequenceIterator, FnSubsequenceIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSubsequenceIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSubsequenceIterator,
NaryBaseIterator<FnSubsequenceIterator, FnSubsequenceIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSubsequenceIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSubsequenceIterator, FnSubsequenceIteratorState>(sctx, loc, children)
{}
virtual ~FnSubsequenceIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
void resetImpl(PlanState&) const;
};
/**
*
* zorbaop:subsequence-int
*
* Author: Zorba Team
*/
class SubsequenceIntIteratorState : public PlanIteratorState
{
public:
xs_long theRemaining; //
bool theIsChildReset; //
SubsequenceIntIteratorState();
~SubsequenceIntIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class SubsequenceIntIterator : public NaryBaseIterator<SubsequenceIntIterator, SubsequenceIntIteratorState>
{
public:
SERIALIZABLE_CLASS(SubsequenceIntIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(SubsequenceIntIterator,
NaryBaseIterator<SubsequenceIntIterator, SubsequenceIntIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
SubsequenceIntIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<SubsequenceIntIterator, SubsequenceIntIteratorState>(sctx, loc, children)
{}
virtual ~SubsequenceIntIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
void resetImpl(PlanState&) const;
};
/**
*
* zorbaop:sequence-point-access
*
* Author: Zorba Team
*/
class SequencePointAccessIteratorState : public PlanIteratorState
{
public:
bool theIsChildReset; //
SequencePointAccessIteratorState();
~SequencePointAccessIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class SequencePointAccessIterator : public NaryBaseIterator<SequencePointAccessIterator, SequencePointAccessIteratorState>
{
public:
SERIALIZABLE_CLASS(SequencePointAccessIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(SequencePointAccessIterator,
NaryBaseIterator<SequencePointAccessIterator, SequencePointAccessIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
SequencePointAccessIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<SequencePointAccessIterator, SequencePointAccessIteratorState>(sctx, loc, children)
{}
virtual ~SequencePointAccessIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
void resetImpl(PlanState&) const;
};
/**
*
* Returns $arg if it contains zero or one items. Otherwise, raises err:FORG0003.
*
* Author: Zorba Team
*/
class FnZeroOrOneIterator : public NaryBaseIterator<FnZeroOrOneIterator, PlanIteratorState>
{
protected:
bool theDoDistinct; //
public:
SERIALIZABLE_CLASS(FnZeroOrOneIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnZeroOrOneIterator,
NaryBaseIterator<FnZeroOrOneIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnZeroOrOneIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children,
bool doDistinct = false)
:
NaryBaseIterator<FnZeroOrOneIterator, PlanIteratorState>(sctx, loc, children),
theDoDistinct(doDistinct)
{}
virtual ~FnZeroOrOneIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns $arg if it contains one or more items. Otherwise, raises err:FORG0004.
*
* Author: Zorba Team
*/
class FnOneOrMoreIterator : public NaryBaseIterator<FnOneOrMoreIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnOneOrMoreIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnOneOrMoreIterator,
NaryBaseIterator<FnOneOrMoreIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnOneOrMoreIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnOneOrMoreIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnOneOrMoreIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns $arg if it contains exactly one item. Otherwise, raises err:FORG0005.
*
* Author: Zorba Team
*/
class FnExactlyOneIterator : public NaryBaseIterator<FnExactlyOneIterator, PlanIteratorState>
{
protected:
bool theRaiseError; //
bool theDoDistinct; //
public:
SERIALIZABLE_CLASS(FnExactlyOneIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnExactlyOneIterator,
NaryBaseIterator<FnExactlyOneIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnExactlyOneIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children,
bool raiseError = true,
bool doDistinct = false)
:
NaryBaseIterator<FnExactlyOneIterator, PlanIteratorState>(sctx, loc, children),
theRaiseError(raiseError),
theDoDistinct(doDistinct)
{}
virtual ~FnExactlyOneIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* This function assesses whether two sequences are deep-equal to each other. To
* be deep-equal, they must contain items that are pairwise deep-equal; and for
* two items to be deep-equal, they must either be atomic values that compare equal,
* or nodes of the same kind, with the same name, whose children are deep-equal.
*
* Author: Zorba Team
*/
class FnDeepEqualIterator : public NaryBaseIterator<FnDeepEqualIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnDeepEqualIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnDeepEqualIterator,
NaryBaseIterator<FnDeepEqualIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnDeepEqualIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnDeepEqualIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnDeepEqualIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Hashing semi/anti join iterator.
*
* First producer goes in the result if a match in the second producer is
* found/not found. The order of the first producer is retained. No duplicate
* elimination is performed.
*
* Author: Zorba Team
*/
class HashSemiJoinIteratorState : public PlanIteratorState
{
public:
NodeHandleHashSet* theRightInput; //
HashSemiJoinIteratorState();
~HashSemiJoinIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class HashSemiJoinIterator : public NaryBaseIterator<HashSemiJoinIterator, HashSemiJoinIteratorState>
{
protected:
bool theAntijoin; //
public:
SERIALIZABLE_CLASS(HashSemiJoinIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(HashSemiJoinIterator,
NaryBaseIterator<HashSemiJoinIterator, HashSemiJoinIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
HashSemiJoinIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children,
bool antijoin = false)
:
NaryBaseIterator<HashSemiJoinIterator, HashSemiJoinIteratorState>(sctx, loc, children),
theAntijoin(antijoin)
{}
virtual ~HashSemiJoinIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Sortmerge based semijoin iterator.
*
* First producer goes in the result if a match in the second producer is found.
* Precondition: both inputs must be sorted.
* Postcondition: the order of the first producer is retained.
*
* If either of the inputs is guaranteed to contain no duplicates, then the
* output will be duplicate-free. Otherwise the output may contain duplicates.
*
* Author: Zorba Team
*/
class SortSemiJoinIterator : public NaryBaseIterator<SortSemiJoinIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(SortSemiJoinIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(SortSemiJoinIterator,
NaryBaseIterator<SortSemiJoinIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
SortSemiJoinIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<SortSemiJoinIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~SortSemiJoinIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
* fn:count
* Author: Zorba Team
*/
class FnCountIterator : public NaryBaseIterator<FnCountIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnCountIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnCountIterator,
NaryBaseIterator<FnCountIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnCountIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnCountIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnCountIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:avg
*
* Author: Zorba Team
*/
class FnAvgIterator : public NaryBaseIterator<FnAvgIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnAvgIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnAvgIterator,
NaryBaseIterator<FnAvgIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnAvgIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnAvgIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnAvgIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns a value obtained by adding together the values in $arg. If $zero is
* not specified, then the value returned for an empty sequence is the xs:integer
* value 0. If $zero is specified, then the value returned for an empty sequence
* is $zero.
*
* Author: Zorba Team
*/
class FnSumIterator : public NaryBaseIterator<FnSumIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSumIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSumIterator,
NaryBaseIterator<FnSumIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSumIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSumIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnSumIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:sum with arguments xs:double
*
* Author: Zorba Team
*/
class FnSumDoubleIterator : public NaryBaseIterator<FnSumDoubleIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSumDoubleIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSumDoubleIterator,
NaryBaseIterator<FnSumDoubleIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSumDoubleIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSumDoubleIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnSumDoubleIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:sum with arguments xs:float
*
* Author: Zorba Team
*/
class FnSumFloatIterator : public NaryBaseIterator<FnSumFloatIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSumFloatIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSumFloatIterator,
NaryBaseIterator<FnSumFloatIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSumFloatIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSumFloatIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnSumFloatIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:sum with arguments xs:decimal
*
* Author: Zorba Team
*/
class FnSumDecimalIterator : public NaryBaseIterator<FnSumDecimalIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSumDecimalIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSumDecimalIterator,
NaryBaseIterator<FnSumDecimalIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSumDecimalIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSumDecimalIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnSumDecimalIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* fn:sum with arguments xs:integer
*
* Author: Zorba Team
*/
class FnSumIntegerIterator : public NaryBaseIterator<FnSumIntegerIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnSumIntegerIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnSumIntegerIterator,
NaryBaseIterator<FnSumIntegerIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnSumIntegerIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnSumIntegerIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnSumIntegerIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
* op:to
* Author: Zorba Team
*/
class OpToIteratorState : public PlanIteratorState
{
public:
xs_integer theCurInt; //the current integer
xs_integer theFirstVal; //first integer
xs_integer theLastVal; //last integer
OpToIteratorState();
~OpToIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class OpToIterator : public NaryBaseIterator<OpToIterator, OpToIteratorState>
{
public:
SERIALIZABLE_CLASS(OpToIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(OpToIterator,
NaryBaseIterator<OpToIterator, OpToIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
OpToIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<OpToIterator, OpToIteratorState>(sctx, loc, children)
{}
virtual ~OpToIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Returns the sequence of element nodes that are in the target document and have
* an ID value matching the value of one or more of the IDREF values supplied in
* $arg. The target document is the document containing $node, or the document
* containing the context item (.) if the second argument is omitted.
*
* Author: Zorba Team
*/
class FnIdIteratorState : public DescendantAxisState
{
public:
bool theIsInitialized; //
std::vector<zstring> theIds; //
store::Item_t theDocNode; //
rchandle<store::AttributesIterator> theAttrsIte; //
FnIdIteratorState();
~FnIdIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnIdIterator : public NaryBaseIterator<FnIdIterator, FnIdIteratorState>
{
public:
SERIALIZABLE_CLASS(FnIdIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnIdIterator,
NaryBaseIterator<FnIdIterator, FnIdIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnIdIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnIdIterator, FnIdIteratorState>(sctx, loc, children)
{}
virtual ~FnIdIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* The effect of this function is identical to fn:id in respect of elements that
* have an attribute with the is-id property. However, it behaves differently in
* respect of element nodes with the is-id property. Whereas the fn:id, for legacy
* reasons, returns the element that has the is-id property, this function returns
* the element identified by the ID, which is the parent of the element having the
* is-id property.
*
* Author: Zorba Team
*/
class FnElementWithIdIteratorState : public DescendantAxisState
{
public:
bool theIsInitialized; //
std::vector<zstring> theIds; //
store::Item_t theDocNode; //
rchandle<store::AttributesIterator> theAttrsIte; //
FnElementWithIdIteratorState();
~FnElementWithIdIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnElementWithIdIterator : public NaryBaseIterator<FnElementWithIdIterator, FnElementWithIdIteratorState>
{
public:
SERIALIZABLE_CLASS(FnElementWithIdIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnElementWithIdIterator,
NaryBaseIterator<FnElementWithIdIterator, FnElementWithIdIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnElementWithIdIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnElementWithIdIterator, FnElementWithIdIteratorState>(sctx, loc, children)
{}
virtual ~FnElementWithIdIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
* fn:idref
* Author: Zorba Team
*/
class FnIdRefIteratorState : public DescendantAxisState
{
public:
bool theIsInitialized; //
std::vector<zstring> theIds; //
store::Item_t theDocNode; //
rchandle<store::AttributesIterator> theAttrsIte; //
FnIdRefIteratorState();
~FnIdRefIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnIdRefIterator : public NaryBaseIterator<FnIdRefIterator, FnIdRefIteratorState>
{
public:
SERIALIZABLE_CLASS(FnIdRefIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnIdRefIterator,
NaryBaseIterator<FnIdRefIterator, FnIdRefIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnIdRefIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnIdRefIterator, FnIdRefIteratorState>(sctx, loc, children)
{}
virtual ~FnIdRefIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
* fn:doc
* Author: Zorba Team
*/
class FnDocIterator : public NaryBaseIterator<FnDocIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnDocIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnDocIterator,
NaryBaseIterator<FnDocIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnDocIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnDocIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnDocIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
* fn:doc-available
* Author: Zorba Team
*/
class FnDocAvailableIterator : public NaryBaseIterator<FnDocAvailableIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnDocAvailableIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnDocAvailableIterator,
NaryBaseIterator<FnDocAvailableIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnDocAvailableIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnDocAvailableIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnDocAvailableIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Summary: returns a list of environment variable names that are suitable for
* passing to fn:environment-variable, as a (possible empty) sequence of
* strings.
*
* The function returns a sequence of strings, being the names of the environment
* variables in the dynamic context in some implementation-defined order.
*
* Author: Zorba Team
*/
class FnAvailableEnvironmentVariablesIteratorState : public PlanIteratorState
{
public:
store::Iterator_t theIterator; //the current iterator
FnAvailableEnvironmentVariablesIteratorState();
~FnAvailableEnvironmentVariablesIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnAvailableEnvironmentVariablesIterator : public NaryBaseIterator<FnAvailableEnvironmentVariablesIterator, FnAvailableEnvironmentVariablesIteratorState>
{
public:
SERIALIZABLE_CLASS(FnAvailableEnvironmentVariablesIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnAvailableEnvironmentVariablesIterator,
NaryBaseIterator<FnAvailableEnvironmentVariablesIterator, FnAvailableEnvironmentVariablesIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnAvailableEnvironmentVariablesIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnAvailableEnvironmentVariablesIterator, FnAvailableEnvironmentVariablesIteratorState>(sctx, loc, children)
{}
virtual ~FnAvailableEnvironmentVariablesIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Summary: Returns the value of a system environment variable, if it exists.
*
* If there is no environment variable with a matching name, the function returns
* the empty sequence.
*
* Author: Zorba Team
*/
class FnEnvironmentVariableIterator : public NaryBaseIterator<FnEnvironmentVariableIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnEnvironmentVariableIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnEnvironmentVariableIterator,
NaryBaseIterator<FnEnvironmentVariableIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnEnvironmentVariableIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnEnvironmentVariableIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnEnvironmentVariableIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Summary: The fn:unparsed-text function reads an external resource (for
* example, a file) and returns its contents as a string.
*
* Author: Zorba Team
*/
class FnUnparsedTextIterator : public NaryBaseIterator<FnUnparsedTextIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnUnparsedTextIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnUnparsedTextIterator,
NaryBaseIterator<FnUnparsedTextIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnUnparsedTextIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnUnparsedTextIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnUnparsedTextIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Because errors in evaluating the fn:unparsed-text function are
* non-recoverable, these two functions are provided to allow an application
* to determine whether a call with particular arguments would succeed.
*
* Author: Zorba Team
*/
class FnUnparsedTextAvailableIterator : public NaryBaseIterator<FnUnparsedTextAvailableIterator, PlanIteratorState>
{
public:
SERIALIZABLE_CLASS(FnUnparsedTextAvailableIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnUnparsedTextAvailableIterator,
NaryBaseIterator<FnUnparsedTextAvailableIterator, PlanIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnUnparsedTextAvailableIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnUnparsedTextAvailableIterator, PlanIteratorState>(sctx, loc, children)
{}
virtual ~FnUnparsedTextAvailableIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
/**
*
* Reads an external resource and returns its contents as a sequence of strings,
* separated at newline boundaries.
*
* Author: Zorba Team
*/
class FnUnparsedTextLinesIteratorState : public PlanIteratorState
{
public:
std::unique_ptr<std::istream, StreamReleaser>* theStream; //the current stream
internal::StreamResource* theStreamResource; //the current iterator
FnUnparsedTextLinesIteratorState();
~FnUnparsedTextLinesIteratorState();
void init(PlanState&);
void reset(PlanState&);
};
class FnUnparsedTextLinesIterator : public NaryBaseIterator<FnUnparsedTextLinesIterator, FnUnparsedTextLinesIteratorState>
{
public:
SERIALIZABLE_CLASS(FnUnparsedTextLinesIterator);
SERIALIZABLE_CLASS_CONSTRUCTOR2T(FnUnparsedTextLinesIterator,
NaryBaseIterator<FnUnparsedTextLinesIterator, FnUnparsedTextLinesIteratorState>);
void serialize( ::zorba::serialization::Archiver& ar);
FnUnparsedTextLinesIterator(
static_context* sctx,
const QueryLoc& loc,
std::vector<PlanIter_t>& children)
:
NaryBaseIterator<FnUnparsedTextLinesIterator, FnUnparsedTextLinesIteratorState>(sctx, loc, children)
{}
virtual ~FnUnparsedTextLinesIterator();
zstring getNameAsString() const;
void accept(PlanIterVisitor& v) const;
bool nextImpl(store::Item_t& result, PlanState& aPlanState) const;
};
}
#endif
/*
* Local variables:
* mode: c++
* End:
*/
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,661 |
\section{Autohomeomorphisms}
In what follows $\Aut$ denotes the autohomeomorphism group of~$\Nstar$,
and $\Triv$~denotes the subgroup of trivial autohomeomorphisms.
\begin{question}\label{q.triv.normal}
Can $\Triv$ be a proper normal subgroup of $\Aut$, and if \emph{yes} what is
(or can be) the structure of the factor~group $\Aut/\Triv$;
and if \emph{no} what is (or can be) $[\,\Triv:\Aut\,]$?
\comments
A very concrete first step would be to investigate what can one say about an
autohomeomorphism~$h$ that satisfies $h^{-1}\circ\Triv\circ h=\Triv$.
A related question: what is the minimum number of autohomeomorphisms
necessary to add to $\Triv$ to get a generating set for~$\Aut$?
Of course that number is~$0$ when $\Aut=\Triv$,
but can it be non-zero and finite?
\end{question}
If $h\in\Aut$ then $I(h)$ denotes the family of subsets of~$\omega$
on which $h$~is trivial, that is, $A\in I(h)$ iff there is a function
$h':A\to\omega$ such that $h(B^*)=h'[B]^*$ whenever $B\subseteq A$.
If $I(h)$ contains an infinite set then $h$~is \emph{somewhere trivial},
otherwise $h$~is totally non-trivial.
The ideal $I(h)$ determines an open set $O_h$: the union
$\bigcup\{A^*:A\in I(h)\}$; its complement~$F_h$ is closed and could be
said to be the set of points of~$\Nstar$ where $h$~is truly
non-trivial.
\begin{question}
Does the existence of a (totally) non-trivial automorphism imply that
$\Aut$ is simple?
\comments
This question asks more that the opposite of question~\ref{q.triv.normal};
a yes answer here would imply a no answer there, but a negative answer
there could go together with a negative answer here.
\end{question}
\begin{question}
Is it consistent with $\MA+\neg\CH$ that a totally non-trivial
automorphism exists?
\comments
The answer yes.
This was established by Shelah and Stepr\=ans in~\cite{MR1896046}.
Consistency is the best one can hope for: the conjuction of $\MA_{\aleph_1}$
and $\OCA$ implies that all autohomeomorphisms of~$\Nstar$ are
trivial, this was proved by Veli\v{c}kovi\'c in~\cite{MR1202874}.
\end{question}
\begin{question}
Is it consistent to have a non-trivial automorphism, while for every
$h\in\Aut$ the ideal~$I(h)$ is the intersection of finitely many prime ideals?
\comments
In topological terms: can one have non-trivial autohomeomorphisms but only
very mild ones; the set of points where an autohomeomorphism is truly
non-trivial is always finite.
\end{question}
\begin{question}
Is every ideal $I(h)$ a $P$-ideal (if every automorphism is somewhere trivial)?
\comments
Of course this question only makes sense in case $I(h)$ is not equal
to the ideal of finite sets.
Also, if \emph{every} autohomeomorphism is somewhere trivial then
every $I(h)$~is a tall ideal and hence the set of points of non-triviality
is nowhere dense.
\end{question}
\begin{question}
If every automorphism is somewhere trivial, is then every automorphism
trivial?
\comments
This is undecidable.
Shelah proved the consistency of ``all autohomeomorphisms are trivial'',
see~\cite{MR1623206}.
Shelah and Stepr\=ans proved the consistency with $\MA_{\aleph_1}$
of ``every autohomeomorphism is somewhere trivial, yet there is a non-trivial
autohomeomorphism'' in~\cite{MR1271551};
as noted above they proved in~\cite{MR1896046} that $\MA$~does not imply
that all autohomeomorphisms are somewhere trivial.
\end{question}
Given a cardinal $\kappa$ call an autohomeomorphism~$h$
\emph{weakly $\kappa$-trivial} if the set
$\{p:p\not\RKeq h(p)\}$ has cardinality less than~$\kappa$.
Here $p\RKeq q$~means that $p$ and~$q$ have the same type, i.e.,
$q=\pi^*(p)$ for some permutation~$\pi$ of~$\N$.
\begin{question}
For what cardinals $\kappa$ is it consistent to have that all
autohomeomorphisms are $\kappa$-weakly trivial?
\comments
Since a trivial autohomeomorphism is weakly $1$-trivial we see
that $\kappa=1$ is a possibility.
And of course the candidates are less than or equal to~$2^\cee$.
\end{question}
\begin{question}
If $h$ is weakly $1$-trivial is $h$ then trivial?
\comments
This is a uniformization question: if for every $p\in\Nstar$
there is a permutation~$\pi_p$ such that $h(p)=\pi_p^*(p)$ is there then
one (almost) permutation~$\pi$ of~$\Nstar$ such that $h(p)=\pi^*(p)$ for
all~$p$?
\end{question}
\begin{question}
($\MA+\lnot\CH$)
if $p$ and $q$ are $P_\cee$-points\pri{Pc-point@$P_\cee$-point}
is there an $h$ in $\Aut$ such that $h(p)=q$?
\comments
This is undecidable.
Shelah and Stepr\=ans proved the consistency of $\MA+\lnot\CH$ with
``all autohomeomorphisms are trivial''
in~\cite{MR935111}; in this model there are $\cee$~many autohomeomorphisms
and $2^\cee$~many $P_\cee$-points.
Stepr\=ans proved the consistency of a positive answer in~\cite{MR1239060}.
\end{question}
In the investigations into the previous question the following
equivalence relation was used: $p\equiv q$ means that there are two partitions
$\{A_n:n\in\omega\}$ and~$\{B_n:n\in\omega\}$ of~$\N$ into finite sets such that
$$
(\forall P\in p)(\exists Q\in q)(\forall n)
\bigl(\card{P\cap A_n}=\card{Q\cap B_n}\bigr)
$$
The following question was left open.
\medskip
\begin{question}
Is $\equiv$ different from $\RKeq$ in $\ZFC$\pri{ZFC@\ZFC}?
\comments
\end{question}
\section{Subspaces}
\begin{question}
For what $p$ are $\Nstar\setminus\{p\}$
and $\betaN\setminus\{p\}$ non-normal?
\comments
This question had the word `equivalently' after the `and' (in parentheses).
Since $\Nstar\setminus\{p\}$ is closed in $\betaN\setminus\{p\}$ there is an
implication between the non-normality of these spaces but we do not know
whether that implication is reversible.
Thus this question may actually be two separate ones.
\end{question}
\begin{question} Is it consistent that there is a non-butterfly
point\pri{non-butterfly point} in $\Nstar$?
\comments
We call $p$ a butterfly point if there are disjoint sets~$A$ and~$B$ such
that $p$~is the only common accumulation point of~$A$ and~$B$,
that is: $A^d\cap B^d=\{p\}$.
\end{question}
\begin{question}
Is it consistent that $\Nstar\setminus\{p\}$ is $C^*$-embedded in~$\Nstar$
for some but not all~$p\in\Nstar$?
\comments
The answer is yes: in~\cite{MR1434375} Alan Dow showed that
in the Miller model $\Nstar\setminus\{p\}$ is $C^*$-embedded iff $p$~is not
a $P$-point.
There are $P$-points in the Miller model: every ground-model $P$-point
generates a $P$-point in the extension.
\end{question}
\begin{question}
What spaces\pri{subspace!of $\beta\omega$} can be embedded in $\beta\omega$?
\comments
This is a very general question and a definitive answer looks out of reach
for now, even for closed subspaces.
The Continuum Hypothesis implies that the closed subspaces of $\beta\omega$
are exactly the compact zero-dimensional $F$-spaces; in fact, these are also
exactly the closed $P$-sets in~$\Nstar$.
The implication does not reverse: in~\cite{MR1152978} it is shown that the
every compact zero-dimensional $F$-space is a (closed) subspace of~$\Nstar$
in any model obtained by adding $\aleph_2$~many Cohen reals to a
model of~$\CH$.
Dow and Vermeer proved in~\cite{MR1137221} that it is consistent that
the $\sigma$-algebra of Borel sets of the unit interval is not the quotient
of any complete Boolean algebra.
By Stone duality, this yields a compact basically disconnected space,
hence a compact zero-dimensional $F$-space, of weight~$\cee$ that cannot
be embedded into any extremally disconnected space, in particular
not into~$\betaN$.
Some $\ZFC$ results are available.
For instance: if $X$~is a compact space of countable cellularity
that is a continuous image of~$\Nstar$ then its projective cover~$E(X)$
can be embedded in~$\Nstar$ as a $\cee$-OK set (a weakening of the notion
of a $P$-set).
This was proved by van~Mill in~\cite{MR637426} and applies to all separable
compact extremally disconnected spaces as well as to the projective covers
of Suslin lines and of Bell's ccc non-separable remainder~\cite{MR624458}.
Van Douwen proved in unpublished work that every $P$-space of weight~$\cee$
(or less) can be embedded into~$\betaN$.
In fact he proved that for every infinite cardinal~$\kappa$ every $P$-space
of weight~$2^\kappa$ can be embedded in~$\beta\kappa$.
The argument was sketched and extended in~\cite{MR674103} and we summarize
it here for the reader's convenience.
Let $X$ be a $P$-space of weight~$2^\kappa$ and embed it into the Cantor cube
$C=2^{2^\kappa}$ of weight~$2^\kappa$.
Next consider the projective cover~$\pi:E(C)\to C$ of this cube.
The Cantor cube is a group under coordinatewise addition modulo~$2$, so
for every $p\in C$ the map $\lambda_p:x\mapsto x+p$ is a homeomorphism; this
homeomorphism lifts to a homeomorphism $\Lambda_p:E(C)\to E(C)$ with the
property that $\pi\circ\Lambda_p=\lambda_p\circ\pi$.
Now take one point~$u_0\in E(C)$ that maps to the neutral element~$0$ of~$C$
and consider the subspace $X'=\{\Lambda_p(u_0):p\in X\}$ of~$E(C)$.
Using the fact that regular open sets in~$C$ are, up to permutation of the
coordinates, of the form $U\times2^I$ where $U$~is regular open
in the Cantor set~$2^\omega$ and $I=2^\kappa\setminus\omega$, one shows
that $\pi$~is actually a homeomorphism from~$X'$ to~$X$.
Finally then, as $\pi$~is irreducible and $C$~has density~$\kappa$,
the density of~$E(C)$ is equal to~$\kappa$ as well.
Therefore there is a continuous surjection $f:\beta\kappa\to E(C)$ and one
can take a closed subset~$F$ of~$\beta\kappa$ such that $f\restr F$~is
irreducible and onto.
As $E(C)$~is extremally disconnected this restriction is a homeomorphism
and we find our copy of~$X$ in~$F$.
The extension mentioned delivers more but at a cost:
one embeds $\beta X$ in a suitable Cantor cube, possibly of a larger
weight than that of~$X$ itself.
What this delivers is that the copy of~$X$ in $\beta\lambda$
(where $\lambda$ may be larger than the $\kappa$ above) is $C^*$-embedded.
Thus we get the general statement that every $P$-space can be $C^*$-embedded
in a compact extremally disconnected space.
This argument also shows that $2^{\aleph_0}=2^{\aleph_1}$ implies that
$\beta\omega_1$ embeds into~$\betaN$.
For $\beta\omega_1$ embeds into the Cantor cube $2^{2^{\omega_1}}$, which under
our assumption is the same as~$2^\cee$.
The latter is a continuous image of~$\betaN$ and an irreducible preimage
of~$\beta\omega_1$ will be homeomorphic to~$\beta\omega_1$.
If $2^{\aleph_0}<2^{\aleph_1}$ then $\beta\omega_1$ can not be embedded
into~$\Nstar$ because its weight, which is $2^{\aleph_1}$, is larger than that
of~$\Nstar$.
\end{question}
\begin{question}\label{q.P-sets}
Describe the closed $P$-sets\pri{P-set@$P$-set} of $\Nstar$.
\comments
This has a quite definitive answer under $\CH$: every compact zero-dimensional
$F$-space can be embedded in~$\Nstar$ as a $P$-set.
What we are looking for are properties that can be established in~$\ZFC$,
or provably can not.
For example: one cannot prove in~$\ZFC$ that there is a $P$-set homeomorphic
to~$\Nstar$ itself, see~\cite{MR976360}, or that there is a $P$-set
that satisfies the ccc, see~\cite{MR1253914}.
One can ask if cellularity less than~$\cee$ is at all possible.
There are various nowhere dense closed $P$-sets that one can write down
explicitly.
To give two familiar examples, among many, we consider the density
ideal~$\calI_d$ and the summable ideal~$\calI_\Sigma$.
The first is defined by
$$
I\in\calI_d \text{ \quad iff \quad}\lim_{n\to\infty}\frac1n|A\cap n|=0
$$
and
the second as
$$
I\in\calI_\Sigma \text{ \quad iff \quad}\sum_{n\in A}\frac1n \text{ converges.}
$$
These ideals have been studied widely but we would like to know: what are
the topological properties of the nowhere dense closed $P$-sets
$$
F_d=\Nstar\setminus\bigcup\{A^*:A\in\calI_d\}
\text{ \quad and \quad}
F_\Sigma=\Nstar\setminus\bigcup\{A^*:A\in\calI_\Sigma\}
$$
Rudin established in~\cite{MR0216451}
that $F_d$ contains no $P$-points and even that no countable
set of $P$-points accumulates at a point of~$F_d$.
Indeed let $u$ be a $P$-point and observe first that for every~$n$ there
is an $i_n<n$ such that $U_n=\{m\in\N: m\equiv i_n\pmod{n}\}$ belongs
to~$u$.
Because $u$~is a $P$-point there is then a $U\in u$ such that $U\subseteq^*U_n$
for all~$n$.
But this implies $U\in\calI_d$, so $u\notin F_d$.
Because $F_d$ is a $P$-set this implies that no countable set of $P$-points
has accumulation points in~$F_d$.
There are certain similarities between the two sets and $\N^*$ itself.
Consider the map $f:\N\to\N$, defined by $f(n)=k$ iff $k!<n\le(k+1)!$.
It is an elementary exercise to show that
$$
\limsup_{n\to\infty}\frac1n|f\preim[X]\cap n|=1
\text{ \quad en \quad}
\sum_{n\in f\preim[X]}\frac1n=\infty
$$
whenever $X$~is an infinite subset of~$\N$.
This implies that $\beta f$ maps both $F_d$ and $F_\Sigma$ onto~$\Nstar$
and it allows for the lifting of many combinatorial structures on~$\Nstar$
to these sets.
It is clear that the restriction of~$\beta f$ to $\Nstar$ is an open map
onto~$\Nstar$ itself, whether its restrictions to $F_d$ and~$F_\Sigma$
are open as well is less clear.
\end{question}
\begin{question}
Which compact zero-dimensional $F$-spaces admit an open map onto~$\Nstar$?
\comments
This question is related to Van Douwens paper~\cite{MR1062775}, where open
maps are used to transfer information from $\Nstar$ to other remainders.
As a special case one can investigate whether the sets~$F_d$ and~$F_\Sigma$
from the Question~\ref{q.P-sets} admit open maps onto~$\Nstar$
(if the map~$\beta f$ given there does already not do so).
\end{question}
\begin{question}\label{q.c-OK}
Is there a nowhere dense copy of $\Nstar$ in $\Nstar$ that is
a $\cee$-OK-set in $\Nstar$?
\comments
Alan Dow showed in~\cite{MR3209343} that there a nowhere dense copy
of~$\Nstar$ that is not of the form~$\cl{D}\setminus D$ for some countable
and discrete subset~$D$ of~$\Nstar$.
This was later improved by Dow and van Mill in~\cite{DowVanMill21} to a nowhere
dense copy that is a weak $P$-set.
In light of the comments for question~\ref{q.P-sets} the present question
asks for the best that we can get in~$\ZFC$.
Most likely the answer to this question will require a new idea as the
constructions in the papers cited above produce sets that are definitely
not $\cee$-OK in~$\Nstar$.
\end{question}
\begin{question} Is every subspace of $\Nstar$ strongly zero-dimensiona
\pri{strongly zero-dimensional|see{zero-dimensional, strongly}
\pri{zero dimensional!strongly}?
\comments
It is clear that every subspace is zero-dimensional and that closed subspaces
are even strongly zero-dimensional but for general subspaces this question
is quite open.
Until recently it was not even known whether there was an example of a
zero-dimensional $F$-space that is not strongly zero-dimensional.
see~\cite{MR4384168}.
If the answer is negative then a secondary question suggests itself immediately:
is there an upper bound to the covering dimension of subspaces of~$\Nstar$?
\end{question}
\begin{question}
Is every nowhere dense subset of $\Nstar
\pri{subset!nowhere dense!of $\Nstar$
\pri{nowhere dense subset|see{subset, nowhere dense}} a
$\cee$-set\pri{c-set@$\cee$-set}?\label{q.cee-set}
\comments
That the answer is positive is called by some ``The $\cee$-set conjecture''.
In~\cite{MR1056181} Simon proved that this question is the same as
``Is there a maximal nowhere dense subset in~$\Nstar$?''.
The questions are the same in that the answer ``no'' to one is equivalent to
the answer ``yes'' to the other:
Every nowhere dense set in $\Nstar$ is a $\cee$-set if
and only if every nowhere dense set in $\Nstar$ is a
nowhere dense subset of another nowhere dense set
(this is the order that we are considering).
There is a purely combinatorial reformulation of this question,
denoted $\RPC(\omega)$ in~\cite{MR991597}: if $\calA$ is an infinite maximal
almost disjoint family then $\calI^+(\calA)$ has an almost disjoint refinement.
Here, $\calI^+(\calA)$ is the family of sets not in the ideal~$\calI(\calA)$
generated by~$\calA$ and the finite sets and an almost disjoint refinement
is an almost disjoint family~$\calB$ with a map $X\mapsto B_X$
from $\calI^+(\calA)$ to~$\calB$ such that $B_X\subseteq^* X$ for all~$X$.
\end{question}
\begin{question}
Does there exist a completely separable maximal almost disjoint family?
\comments
This question is related to Question~\ref{q.cee-set} because by
\cite{MR991597}*{Theorem~4.19} a positive answer to that question
implies the existence of an abundance of completely separable maximal almost
disjoint families; where a maximal almost disjoint family~$\calA$
is \emph{completely separable} if it is itself an almost disjoint
refinement of~$\calI^+(\calA)$.
Whether completely separable maximal almost disjoint families exist is a
problem first raised by Erd\H{o}s and Shelah in~\cite{MR319770}.
Currently the best result is due to Shelah who showed
in~\cite{MR2894445} that the answer is positive if $\cee<\aleph_\omega$
and that a negative solution would imply consistency of the existence of
large cardinals.
It is not (yet) clear whether this question and Question~\ref{q.cee-set}
are equivalent.
Thus far \emph{constructions} of completely separable maximal almost disjoint
families (in some model or another) could always be adapted to
prove~$\RPC(\omega)$, but there is currently no proof of~$\RPC(\omega)$ from
the \emph{mere existence} of such a family.
\end{question}
\begin{question}
Describe the retracts of $\betaN$ and $\Nstar$, as well as their
\emph{absolute} retracts.
\comments
A retract of $\betaN$ is necessarily a closed separable extremally
disconnected subspace.
It is known that a compact separable extremally disconnected can be embedded
as a retract of~$\betaN$.
If~$X$ is such a space then there is a continuous surjection $f:\betaN\to X$
and if $K$~is such that $f\restr K$ is irreducible then $f\restr K$~is
a homeomorphism to~$X$ and $(f\restr K)^{-1}\circ f$ is a retraction
of~$\betaN$ onto~$K$.
Shapiro \cite{MR810825} and
Simon \cite{MR0869226} have shown independently and by quite different means
that not every closed separable subset of~$\betaN$ is a retract.
This gives rise to the notion of an absolute retract of~$\betaN$: a (sub)space
that is a retract irrespective of how it is embedded.
Bella, B\l{}aszczyk and A. Szyma\'nski proved in~\cite{MR1295157}
that if $X$ is compact, extremally disconnected, without isolated points
and of $\pi$-weight~$\aleph_1$ or less then $X$~is an absolute retract for
extremally disconnected spaces iff $X$~is the absolute of one of the following
three spaces: the Cantor set, the Cantor cube $\vphantom{2}^{\omega_1}2$,
or the sum of these two spaces.
This shows that under~$\CH$ there are very few absolute retracts of~$\betaN$.
We have less information about the retracts of~$\Nstar$, absolute or not.
Of course if a subset of~$\Nstar$ is a retract of~$\betaN$ then it is a retract
of~$\Nstar$ as well.
We do not know whether the converse is true, for separable closed subsets
of course.
We do know that non-trivial zero-sets are not retracts.
Such a set is of the form $Z=\Nstar\setminus\bigcup_{n\in\omega}A_n^*$, where
the $A_n$ are infinite and pairwise disjoint subsets of~$\N$.
We write $C=\bigcup_{n\in\omega}A_n^*$.
Now the closure of~$C$ is a $P$-set in~$\Nstar$, it is the union of~$C$
and the boundary of~$Z$, and if we one
point~$u_n\in A_n^*$ for each~$n$ then $K=\cl\{x_n:n\in\omega\}$ is a copy
of~$\betaN$ and $K^*=K\setminus\{x_n:n\in\omega\}$ is a $P$-set in the boundary
of~$Z$ and hence in~$Z$.
If we now take assume $r:\Nstar\to Z$ is a retraction then $r\restr K^*$~is
the identity and for all but finitely many~$n$ we must have $r(x_n)\in K^*$.
But this would imply that $K^*$ is separable, a contradiction.
\end{question}
\section{Individual Ultrafilters}
\question\label{PandQ}
Is there a model in which there are no $P$-points\pri{P-point@$P$-point} and
no $Q$-points\pri{Q-point@$Q$-point}?
\comments
The Continuum Hypothesis implies that both kinds of points exist.
If $\cee=\aleph_2$ then at least one kind exists; this depends on the
value of~$\dee$.
If $\dee=\cee$ then $P$-points exist, in fact Ketonen showed in~\cite{MR433387}
that then every filter of cardinality less than~$\cee$ can be extended
to a $P$-point.
In the present case, if $\dee<\cee$ then $\dee=\aleph_1$ and then
the result of Copl\'akov\'a and Vojt\'a\v{s} from~\cite{MR863903} applies
to show that there are $Q$-points; this relies on the fact that the Nov\'ak
number of~$\Nstar$ is at least~$\aleph_2$, see~\cite{MR0600576}.
The current methods for creating models without $P$-points involve iterations
with countable supports and these invariably produce models
where $\cee=\aleph_2$, and hence these will contain $Q$-points.
A recent exeption is~\cite{MR3990958}, where models without $P$-points
and arbitraily large continuum are constructed.
However $\dee=\aleph_1$ in these models, hence these contain $Q$-points
as well.
\endquestion
\begin{question}
Is there a model in which there is a rapid
ultrafilter\pri{rapid ultrafilter|see{ultrafilter, rapid}
\pri{ultrafilter!rapid} but in which
there is no $Q$-point\pri{Q-point@$Q$-point
\pri{ultrafilter!$Q$-point|see{$Q$-point}
\index{ultrafilter!$P$-point|see{$P$-point}
\index{ultrafilter!$Q$-point|see{$Q$-point}
\pri{ultrafilter!$P$-point|see{$P$-point}}?
\comments
In~\cite{MR4246814} it was shown that the existence of a countable non-discrete
extremally disconnected groups implies the existence of rapid ultrafilters.
\end{question}
\begin{question}
What are the possible compactifications of spaces of the form $\N\cup\{p\}$
for $p\in\Nstar$?
\comments
Of course for every $p$ we have $\beta(\N\cup\{p\})=\betaN$.
There are points where this phenomenon persists: Dow and Zhou showed that
is $f:\betaN\to{}^\cee2$ is continuous and onto and $K\subset\Nstar$ is a
closed set such that $f\restr K$ is irreducible and onto then
for \emph{every} point in~$K$ \emph{every} compactification of~$\N\cup\{p\}$
contains a copy of~$\betaN$, see~\cite{MR1676677}.
Other examples of spaces of the form~$\N\cup\{x\}$, where $x$~is the only
non-isolated point, for which every compactification contains~$\betaN$
were constructed by Van~Douwen and Prszymusinski in~\cite{MR532957}.
\smallskip
The case of scattered compactifications has received considerable interest.
In~\cite{MR107849} Semadeni asked whether $\N\cup\{p\}$ always has a scattered
compactification.
In~\cite{MR263030} Ryll-Nardzewski and Telgarski proved that the answer
is yes if $p$~is a $P$-point and the Continuum Hypothesis holds;
the compactification is a version of the compactification~$\gamma\N$
of Franklin-Rajagopalan from~\cite{MR283742},
where $\gamma\N\setminus\N$ is a copy of the
ordinal~$\omega_1+1$ and $p$~corresponds to the point~$\omega_1$.
In~\cite{MR410671} Jayachandran and Rajagopalan constructed a scattered
compactification of $\N\cup\{p\}$, where $p$~is a $P$-point limit
of a sequence of $P$-points.
Solomon, Telgarsky and Malykhin, in \cite{MR448298}, \cite{MR461441},
and~\cite{MR478101}, respectively, exhibited points~$p$ in~$\Nstar$
such that $\N\cup\{p\}$ has no scattered compactification.
Malykhin's paper and the paper~\cite{MR461442} by Telgarsky contain
investigations of the structure of the (complementary)
sets~$S$ and~$\mathit{NS}$ of points for which $\N\cup\{p\}$ does and
does not have
a scattered compactification respectively.
The set~$\mathit{NS}$ is quite rich: it contains the closures of all of its
countable subsets and it is upward closed in the Rudin-Frol\'ik order.
This richness foreshadowed a later result of Malykhin's
from~\cites{Malykhin:betaNandnotCHa,Malykhin:betaNandnotCHb}:
in the Cohen model it is the case that for \emph{every} point
$p\in\Nstar$ \emph{every} compactification of~$\N\cup\{p\}$
contains a copy of~$\betaN$; in particular $\mathrm{NS}=\Nstar$ in this model.
\end{question}
\begin{question}\label{nonremote
Is there $p\in\Nstar$ such that
$\{A\in p:A$~is closed and nowhere dense in~$\Q$ and without
isolated points$\}$ is a base for $p$?
\comments
To eliminate possible confusion: we wrote $p\in\Nstar$ to emphasize that
we are asking for an ultrafilter on the countable \emph{set of rationals},
that has a base that is closely connected to the topological structure of the
\emph{space of rationals}.
One could ask the question in the opposite direction: is there a point~$x$
in $\beta\Q\setminus\Q$ (where $\Q$~carries its normal topology) that,
when considered as an ultrafilter of closed sets has a base consisting
of closed nowhere dense copies of~$\Q$ and that also generates a real
ultrafilter on the set~$\Q$.
These ultrafilters were dubbed `gruff ultrafilters' by Van Douwen.
This question is still open but there are many consistent positive answers:
\begin{itemize}
\item Van Douwen \cite{MR1192307}: from $\MA_{\mathrm{countable}}$,
\item Coplakova and Hart \cite{MR1676672}: from $\bee=\cee$,
\item Ciesielski and Pawlikowski \cite{MR1997781}: from a version of
the Covering Property Axiom (hence in the Sacks model),
\item Mill\'an \cite{MR2182932}:
from the same assumption a $Q$-point with this property,
\item Fern\'{a}ndez-Bret\'{o}n and Hru\v{s}\'{a}k \cite{MR3539743}:
from a parametrized $\diamond$-principle,
from $\dee=\cee$,
and in the random real model;
a correction in~\cite{MR3712981} points out that in the third case
one needs to add $\aleph_1$~many Cohen reals first
\end{itemize}
\end{question}
\begin{question}
Is there a $p\in\Nstar$ such that whenever $\langle x_n:n\in\omega\rangle$ is
a sequence in $\Q$ there is an $A\in p$ such that $\{\,x_n:n\in A\,\}$
is nowhere dense?
\comments
Such ultrafilters are called \emph{nowhere dense}.
A $P$-point is nowhere dense: it will have a member~$A$ such that
$\{x_n:n\in A\}$ converges to a point or is closed and discrete.
On the other hand, in~\cite{MR1690694} Shelah showed that it is consistent
that there are no nowhere dense ultrafilters.
In~\cite{MR1833478} it is shown that a nowhere dense ultrafilter exists
iff there is a $\sigma$-centered partial order that does \emph{not}
add a Cohen real.
Research into this type of problem was initiated by Baumgartner
in~\cite{MR1335140}:
the general situation involves a set~$S$ and a notion of smallness on~$S$,
usually expressed in terms of ideals.
One then calls an ultrafilter $u$ on~$\N$ small if for every map $f:\N\to S$
there is a member of~$u$ whose image under~$f$ is small.
\end{question}
\section{Dynamics, Algebra, and Number Theory}
\begin{question}\label{q.max.orbitcl
Is there a point in $\Nstar$ that is not an
element of any maximal orbit closure\pri{orbit closure!maximal}?
\comments
In this problem we consider the integers $\Z$ rather than~$\N$ and the
shift map~$\sigma$, defined by $\sigma(n)=n+1$.
The orbit of~$u\in\Nstar$ is the set $\{\sigma(u):n\in\Z\}$ and its
closure~$C_u$ is the \emph{orbit closure} of~$u$.
\end{question}
\begin{question}
Is there an infinite strictly increasing sequence of
orbit closures\pri{orbit closure}?
\comments
This problem is related to the previous problem: if there is no increasing
sequence of orbit closures then the family of orbit closures is well-founded
under reverse inclusion and every point is in some maximal orbit closure.
A negative answer to this question,
and hence to Question~\ref{q.max.orbitcl},
was announced recently by Zelenyuk.
\end{question}
\begin{question}
Is there a $p\in\Nstar$ such that for every pair of commuting
continuous maps $f,g:\Cantor\to\Cantor$ there is an $x\in\Cantor$
such that $\plim f^n(x)=\plim g^n(x)=x$?
\comments
This question is related in two ways to Furstenberg's multiple recurrence
theorem, which states that commuting continuous self-maps of the Cantor set
have common recurrent points.
Using ultrafilters one can state this theorem as: for every pair of commuting
continuous maps $f,g:\Cantor\to\Cantor$ there are~$p\in\Nstar$ and
$x\in\Cantor$ such that $\plim f^n(x)=\plim g^n(x)=x$.
So the first connection to our question is clear: is there one single
ultrafilter that works for all pairs.
The second connection is the question whether Furstenberg's theorem holds
for the Cantor cube~$\Cantorc$?
If it does then the answer to our question is positive.
To see this note first that there are $\cee$~many pairs
of commuting self-maps of~$\Cantor$,
enumerated these as $\{\orpr{f_\alpha}{g_\alpha}:\alpha<\cee\}$.
These determine one pair $\orpr fg$ of commuting self maps of~$\Cantorc$:
write $\Cantorc$ as $\Cantor[\cee\times\omega]$, and let
$f=\prod_{\alpha<\cee}f_\alpha$ and $g=\prod_{\alpha<\cee}g_\alpha$.
The maps~$f$ and~$g$ commute and if $x\in\Cantor[\cee\times\omega]$~is a
common recurrent point then $\plim f^n(x)=\plim g^n(x)=x$ for some~$p\in\Nstar$.
But then also $\plim f_\alpha^n(x_\alpha)=\plim g_\alpha^n(x_\alpha)=x_\alpha$ for
all~$\alpha$.
\iffalse
For the converse, assume $p$~is as in the question and let $f$ and $g$ be
commuting self-maps of~$\Cantorc$.
A standard closing-off argument will show that for every countable subset~$A$
of~$\cee$ there is a larger countable subset~$B$ such that $f$ and~$g$ factor
through the partial product~$\Cantor[B]$; that is, there are self-maps $f_B$
and~$g_B$ of~$\Cantor[B]$ such that $\pi_B\circ f=f_B\circ\pi_B$ and likewise
for~$g$, where $\pi_B$~is the projection.
This yields a point~$x_B\in\Cantor[B]$ such that
$\plim f_B^n(x_B)=\plim g_B^n(x_B)=x_B$.
The set $F_B=\{y\in\Cantorc:x_B\subseteq y\}$ is closed and closed under
$p$-limits, that is, if $y\in F_B$ then $\plim f^n(y)$ and $\plim g^n(y)$
are in~$F_B$.
{\slshape Nu nog even aan elkaar plakken \dots}
\fi
\end{question}
\begin{question}\label{nwdperm}
For what nowhere dense sets\pri{nowhere dense set}
$A\subseteq\Nstar$ do we have $\bigcup_{\pi\in S_\N}\pi[A]\neq\Nstar$?
\comments
Here $S_\N$ denotes the permutation group of~$\N$.
It is consistent to assume that this happens for all nowhere dense sets.
In~\cite{MR0600576} Balcar, Pelant and Simon studied~$\enn$, the Nov\'ak number
of~$\Nstar$, defined as the smallest number of nowhere dense sets needed to
cover~$\Nstar$.
The inequality~$\cee<\enn$ is consistent and yields the consistency
of ``for all nowhere dense sets'';
it follows from~$\CH$ (because $\enn\ge\aleph_2$),
but is also consistent with other values of~$\cee$.
The inequality $\enn\le\cee$ is also consistent and that case there is not such
an easy way out and it becomes an interesting project to investigate whether
the permutations of individual nowhere sets do, or do not, cover~$\Nstar$
in~$\ZFC$.
Permuting a singleton will not yield a cover, as $|\Nstar|=2^\cee$.
Less obvious is Gryzlov's result from~\cite{MR782711} that the permutations
of the set~$F_d$ from Question~\ref{q.P-sets} do not form a cover.
This was improved by Fla\v{s}kov\'a in~\cite{MR2337416}: the permutations
of the larger set~$F_\Sigma$ do not cover~$\Nstar$ either.
For another natural nowhere dense subset of~$\Nstar$ the permutations of which
may, or may not, cover~$\Nstar$.
Identify $\N$ with $\N\times\N$ and for~$k\in\N$ and $f:\N\to\N$ write
$U(f,k)=\{\orpr mn:m\ge k$ and~$n\ge f(m)\}$.
The set $B=\bigcap_{f,k}U(f,k)^*$ is nowhere dense and it is well known
then $\bigcup_{\pi\in S_\N}\pi[B]$ consists of all non $P$-points of~$\Nstar$.
Hence the permutations of~$B$ cover~$\Nstar$ iff there are no $P$-points.
\end{question}
\begin{question}
For what nowhere dense sets\pri{nowhere dense set}
$A\subseteq\Nstar$ do we have
$\bigcup\{h[A]:h\in\Aut\}\neq\Nstar$?
\comments
This question is more difficult than the previous one.
For example, singleton sets still do not provide covers in~$\ZFC$, but the
easy counting argument is replaced by the non-trival fact that $\Nstar$~is not
homogeneous.
We have no information about the sets $F_d$ and $F_\Sigma$ in this context,
except for the general fact that under~$\CH$ the space~$\Nstar$ cannot be
covered by nowhere dense $P$-sets, see~\cite{MR548097}.
Also, in~\cite{MR620204} it was shown that it is consistent that
$\Nstar$~can be covered by nowhere dense $P$-sets,
and the principle~$\NCF$ (Near Coherence of Filters) implies that
$\Nstar$~is even the union of a \emph{chain} of nowhere dense $P$-sets,
see~\cite{MR1261700},
but the sets in these covers are unrelated to the sets~$F_d$ and~$F_\Sigma$.
It is also unclear whether any one of the individual sets in these families
will produce a cover when moved around by the members of~$\Aut$.
The answer for the set~$B$ remains the same because
the union $\bigcup\{h[B]:h\in\Aut\}$ consists of all non-$P$-points.
\end{question}
\iffalse
\begin{question}[Deze vraag gaat weg maar ik wil de nummers niet veranderen]
Can $\orpr{\beta\N}{+}$ be embedded in $\orpr{\N^*}{+}
\pri{binary operation!on $\beta\omega$}?
\comments
Strauss showed in~\cite{MR1190430}
that $\orpr\betaN+$ cannot be embedded in $\orpr\Nstar+$.
Specifically, if $\varphi:\betaN\to\Nstar$ is a continuous homomorphism
then the image of~$\varphi$ must be finite.
\end{question}
\begin{question}[Deze vraag gaat naar achteren maar ik wil de nummers niet veranderen]
Are there $p$, $q$, $r$ and $s$ in $\N^*$ such that $p+q=r\times s
\pri{binary operation!on $\beta\omega$}?
\comments
\end{question}
\begin{question}[Deze vraag gaat naar achteren maar ik wil de nummers niet veranderen]
What are the maximal subgroups of $\orpr{\beta\N}{+}$ and
$\orpr{\beta\N}{\times}$\pri{binary operation!on $\beta\omega$}?
\comments
\end{question}
\begin{question}[Deze vraag gaat weg maar ik wil de nummers niet veranderen]
Let $X$ be $\beta\omega$ or $\Nstar$.
If $h: X^2\to X^2$ is a homeomorphism, is there a disjoint open
cover $\mathcal{U}$ of $X$ such that for all $U,\,V\in\mathcal{U}$ the map
$h\restr U\times V$ is elementar
\pri{elementary map|see{map, elementary}}\pri{map!elementary}?
\label{q.elem.homeo}
\comments
The answer is positive.
In~\cite{MR1933577} Farah proved a more general result than asked for
in this problem and problem~\ref{q.map.simple}:
Assume $Z$ is a $\betaN$-space, $X$~is compact, $\kappa$~i an arbitrary
cardinal and $f:X^\kappa\to Z$ is continuous.
Then $X^\kappa$~can be covered by finitely many clopen rectangles such
that $f$ depends on at most one coordinate on each one of them.
A $\betaN$-space is one in which the closure of every countable discrete
subset, if compact, is homeomorphic to~$\betaN$.
\end{question}
\begin{question}[Deze vraag gaat weg maar ik wil de nummers niet veranderen]
Let $X$ be $\beta\omega$ or $\Nstar$.
If $\varphi: X^2\to X$ is continuous, is there a disjoint open
cover $\mathcal{U}$ of $X$ such that for all $U,\,V\in\mathcal{U}$ the map
$\varphi\restr U\times V$ depends on one coordinate? \label{q.map.simple}
\comments
The answer is positive, see the comments to problem~\ref{q.elem.homeo}.
\end{question}
\fi
\section{Other}
\begin{question}\label{q.Katowice}
Are $\omega_0^*$ and $\omega_1^*$ ever homeomorphi
\pri{homeomorphism!of $\omega^*$ and $\omega_1^*$}?
\comments
This is known as the Katowice Problem, or rather the last remaining case of
this problem.
It was posed in full by Marian Turza\'nski, when he was in Katowice
(hence the name of the problem).
The general question is:
if $\kappa$ and~$\lambda$ are infinite cardinals, endowed with the discrete
topology, and the remainders $\kappa^*$ and~$\lambda^*$ are homeomorphic
must the cardinals~$\kappa$ and~$\lambda$ be equal?
Since the weight of $\kappa^*$ is equal to~$2^\kappa$ it is immediate that
the Generalized Continuum Hypothesis implies a yes answer.
In joint work Balcar and Frankiewicz established that the answer is actually
positive without any additional assumptions,
\emph{except possibly for the first two infinite cardinals}.
More precisely, see~\cites{MR0461444,MR511955}:
If $\orpr\kappa\lambda\neq\orpr{\aleph_0}{\aleph_1}$
and $\kappa<\lambda$ then the remainders $\kappa^*$ and~$\lambda^*$
are not homeomorphic.
The paper~\cite{MR3563083} contains a list of the current known of consequences
of~$\omega_0^*$ and~$\omega_1^*$ being homeomorphic; all but one of these
can be made to hold in a single model of~$\ZFC$.
By Stone-duality the Katowice problem can be formulated algebraically:
are the quotient (Boolean) algebras~$\pow(\omega_0)/\fin$
and~$\pow(\omega_1)/\fin$ ever isomorphic?
In this form the question even makes sense in~$\ZF$: in models without
non-trivial ultrafilters the spaces~$\omega_0^*$ and~$\omega_1^*$ are empty
(and so trivially homeomorphic) but the structures of the algebras may still
differ.
\end{question}
\begin{question}
Is there consistently an uncountable cardinal $\kappa$ such that
$\omega^*$ and $U(\kappa)$ are homeomorphic?
\comments
This problem is part of the uniform version of the Katowice problem,
Question~\ref{q.Katowice}.
The full question asks whether for distinct infinite cardinals $\kappa$
and~$\lambda$ spaces $U(\kappa)$ and $U(\lambda)$ of \emph{uniform}
ultrafilters can be homeomorphic, or algebraically whether the quotient
algebras $\pow(\kappa)/[\kappa]^{<\kappa}$
and~$\pow(\lambda)/[\lambda]^{<\lambda}$ can be isomorphic.
This is Question~47 in~\cite{MR588216}, where we also find the information
that, in general, the algebra $\pow(\kappa)/[\kappa]^{<\kappa}$ has
cardinality~$2^\kappa$ and is $\mu$-complete for~$\mu<\cf\kappa$ but
not $\cf\kappa$-complete.
Therefore we can concentrate on cases where $2^\kappa=2^\lambda$ and
$\cf\kappa=\cf\lambda$.
In~\cite{MR1103989} Van Douwen investigated the statements~$S_n$:
$$
\hbox{if $\kappa\neq\aleph_n$ then $\pow(\kappa)/[\kappa]^{<\kappa}$ and
$\pow(\omega_n)/[\omega_n]^{<\aleph_n}$ are not isomorphic}.
$$
Thus, our question is whether it is consistent that $S_0$ is false.
Van Douwen showed that there is at most one~$n$ for which $S_n$~is false,
but the proof offers no information on the location of that~$n$ (if any)
as it simply establishes the implication
``if $m<n$ and $S_m$~is false then $S_n$~holds''.
\end{question}
\begin{question}
What is the structure of the sequences
$\langle n((\Nstar)^n): n\in\N\rangle$
and $\langle wn((\Nstar)^n): n\in\N\rangle$?
\comments
Here $n$ and $wn$ denote the Nova\'k and weak Nov\'ak numbers, defined
as the minimum cardinality of a family of nowhere dense sets that covers
the space, or has a dense union, respectively.
It is clear that if $N$~is nowhere dense in a space~$X$ then $N\times Y$
is nowhere dense in the product~$X\times Y$.
This shows that, in general, $n(X\times Y)\le\min\{n(X),n(Y)\}$ and likewise
for~$wn$.
It follows that both sequences in our question are non-increasing and hence
must become constant eventually.
One could ask when they do become constant.
For $wn$ this is undetermined: in~\cite{MR1641157} Shelah and Spinas showed
that for every~$n$ there is a model in
which $wn((\Nstar)^n)> wn((\Nstar)^{n+1})$.
In particuler $wn(\Nstar)>wn(\Nstar\times\Nstar)$ is possible,
in~\cite{MR1751223} the latter inequality was shown to hold in the Mathias
model.
For the Nov\'ak numbers of the finite powers nothing is known as yet.
\end{question}
\iffalse
\begin{question}[Deze vraag gaat weg maar ik wil de nummers niet veranderen]
Is it consistent that $n(\Nstar)>n(\Nstar\times\Nstar)
\pri{nomega@$n(\Nstar)$}, that $wn(\Nstar)>wn(\Nstar\times\Nstar)
\pri{wnomega@$wn(\Nstar)$}?
\comments
Yes, to the second part of the problem.
Shelah and Spinas showed in~\cite{MR1751223} showed that that
$wn(\Nstar) > wn(\Nstar\times\Nstar)$ holds in the Mathias model.
\end{question}
\fi
\begin{question}
What is the status of the statement
that all Parovichenko spaces are co-absolute (with~$\Nstar$)?
\comments
This question is related to Parovichenko's theorem from~\cite{MR0150732},
which states that under~$\CH$ all Parovichenko spaces are homeomorphic
to~$\Nstar$.
Of course Parovichenko spaces were named after this theorem was proved:
they are compact, zero-dimensional $F$-spaces of weight~$\cee$ without isolated
points in which every non-empty $G_\delta$-set has non-empty interior.
For the nonce we say that a space is of \emph{Parovichenko type} if it
satisfies the conditions above, except for possibly the weight restriction.
In \cite{MR612009} Broverman and Weiss proved that under~$\CH$ all spaces
of Parovichenko~type of $\pi$-weight~$\cee$ are co-absolute (with~$\Nstar$).
They also established that if~$\CH$ fails and $\cee=2^{<\cee}$ then there
is a Parovichenko space that is not co-absolute with~$\Nstar$.
They also proved that $\omega_0^*$ and~$\omega_1^*$ are co-absolute or,
in algebraic terms that the Boolean algebras~$\pow(\omega_0)/\fin$
and~$\pow(\omega_1)/\fin$ have isomorphic completions, which shows that
completions do not have a direct effect on Question~\ref{q.Katowice}.
In~\cite{MR648079} Williams also established the $\pi$-weight result and
showed that $\Nstar$ is co-absolute with a linearly ordered space.
In~\cite{MR676966} Van Mill and Williams improved the negative result
of Broverman and Weiss: if our statement holds then not only do we
have $\cee<2^{<\cee}$, but even $\cee<2^{\aleph_1}$.
In~\cite{MR759135} Dow proved that the equality $\cf\cee=\aleph_1$
already implies that all Parovichenko spaces are co-absolute.
The definition of the absolute as the Stone space of the Boolean algebra
of regular open sets makes sense for any compact space, so one may also seek
co-absolutes of~$\Nstar$ among spaces that are not zero-dimensional.
In~\cite{MR234422} Comfort and Negrepontis showed that under~$\CH$ if
$X$~is locally compact and $\sigma$-compact, but not compact, and if
$\bigl|C(X)\bigr|=\cee$ then the set of $P$-points in~$X^*$ is homeomorphic
to the $G_\delta$-modification of the ordered space~$2^{\omega_1}$;
Parovichenko had already established this fact for~$\Nstar$ in~\cite{MR0150732}.
This implies that for such spaces the remainders share a homeomorphic
dense subspace and hence that all such remainders are co-absolute
with~$\Nstar$, still under~$\CH$ of course.
So, for example, under~$\CH$ the spaces~$\Nstar$ and $\Hstar$ are co-absolute.
In~\cite{MR1619290} Dow showed that in the Mathias model $\Nstar$ and~$\Hstar$
are not co-absolute.
\end{question}
\begin{question}
Let $X$ be a compact space\pri{compact space} that can be mapped
onto~$\Nstar$.
Is $X$ non-homogeneous\pri{compact space!non-homogeneous}?
\comments
Since $\Nstar$ maps onto~$\betaN$, a space as in the question will also
map onto~$\betaN$.
If the weight of~$X$ is at most~$\cee$ then Theorem~4.1\,(c) of~\cite{MR644652}
applies and we find that $X$~is indeed non-homogeneous.
\end{question}
\begin{question}
Is it consistent that every compact space\pri{compact space}
contains either a convergent sequence\pri{sequence!convergent}
or a copy of~$\betaN$\pri{copy!of~$\beta\omega$}?
\label{q.efimov}
\comments
Efimov asked in~\cite{MR0253290} whether every compact space contains
either a convergent sequence or a copy of~$\betaN$ and a counterexample
is now called a \emph{Efimov space}.
In~\cite{hart:efimov} one finds a survey of the status of the problem
in~2007; it lists various consistent Efimov spaces, which explains
why the present formulation asks for a consistency result.
We mention here some of the additional results that have been obtained
in the meantime.
To begin there is a positive answer in~\cite{MR3164725} to Question~1
from~\cite{hart:efimov}:
Martin's Axiom, or even the equality $\bee=\cee$, implies that there is
a Efimov space.
In addition there has been progress on two related questions due to Juh\'asz
and Hu\v{s}ek.
The latter asked whether every compact Hausdorff space contains either
a convergent $\omega$-sequence or a convergent $\omega_1$-sequence; Juh\'asz'
question is stronger: must a compact Hausdorff space that does not contain
a convergent $\omega_1$-sequence be first-countable?
A counterexample to Hu\v{s}ek's question would be a Efimov space because
$\betaN$~contains a convergent $\omega_1$-sequence.
In~\cite{MR1707489} one finds a result that provides many models in which
Juh\'asz' question, and hence that of Hu\v{s}ek's, have a positive answer.
One of these models satisfies $\bee=\cee$, hence Efimov's question is strictly
stronger than that of Hu\v{s}ek's.
\end{question}
\begin{question} Is there a locally connected continuum such that every proper
subcontinuum contains a copy of~$\betaN$?
\comments
There are various continua that have the property that every proper
subcontinuum contains a copy of~$\betaN$: the remainders
$\beta\R^n\setminus\R^n$ all have this property for example.
The reason is that they are $F$-spaces, hence the closure of every countable
relatively discrete subset is a copy of~$\betaN$.
However, these remainders are not locally connected; indeed if a space~$X$
is not pseudocompact then one can use an unbounded continuous function
to exhibit points in~$X^*$ at which neither $\beta X$ nor $X^*$~is locally
connected, see~\cite{MR96195}.\par
In~\cite{MR1934264} we find a construction, from~$\CH$, of a locally connected
continuum without non-trivial convergent sequences.
This construction, an inverse limit in which all potential convergent
sequences are destroyed, can be modified with some extra bookkeeping to yield
a locally connected continuum in which every infinite subset contains
a countable discrete subset whose closure is homeomorphic to~$\betaN$,
still under~$\CH$ of course.\par
This leaves the question for a $\ZFC$-example open but also suggest some further
variations.
The example has the property that \emph{some} countable relatively discrete
subsets have $\betaN$~as their closures.
One can ask whether one can ensure this for \emph{all} countable relatively
discrete subsets, or whether one can even make all countable subsets
$C^*$-embedded.
The reason for this is that a compact $F$-space cannot be locally connected,
hence we would like how close to an $F$-space a locally connected continuum
can be.\par
We would also like to know whether there is a natural example that answers
our question; natural in the sense that one can simply write it down, as in
``$\betaN$~is a compact space without convergent sequences'' and
``$\Hstar$~is a continuum in which every proper subcontinuum contains
a copy of~$\betaN$''.
\end{question}
\begin{question}
Is there an extremally disconnected normal locally compact spac
\pri{extremally disconnected!normal!locally compact
\pri{locally compact space!normal!extremely disconnected}
that is not paracompact\pri{compact space!not paracompact}?
\comments
The ordinal space $\omega_1$ is locally compact and normal, but not paracompact.
There are, however, various additional assumptions that when added
to local compacness and normality will ensure paracompactness.
Extremal disconnectedness may or may not be such an assumption:
Kunen and Parsons showed in~\cite{MR540504} that if $\kappa$~is weakly compact
then $\beta\kappa\setminus U(\kappa)$~is normal and locally compact but not
paracompact.
As weak compactness is a large cardinal property the answer to this question
can go many ways: a consistent counterexample, a real counterexample, or
even an equiconsistency result involving a large cardinal.
The weaker property of basic disconnectedness does not work, as shown
by Van Douwen's example in~\cite{MR546947}.
In this paper Van Douwen attributes the present question to Grant Woods.
\end{question}
\begin{question}
Is every compact hereditarily paracompact space of weight at most~$\cee$ a
continuous image of~$\Nstar$?
Is every hereditarily c.c.c.\ compact space a continuous image of~$\Nstar$?
\comments
These questions are part of the general problem of identifying
the continuous images of~$\Nstar$.
Przymusi\'{n}ski proved in~\cite{MR671232} that all perfectly normal
compact spaces are continuous images of~$\Nstar$.
One can therefore look for weakenings of perfect normality that still
make the space an image of~$\Nstar$.
The present two properties are such weakenings and they have
not been ruled out yet.
Another weakening, first-countability, was ruled out by Bell
in~\cite{MR1058795}: the $\aleph_2$-Cohen model contains a first-countable
compact space that is not a continuous image of~$\Nstar$; this space is
also hereditarily metacompact.
In the same paper Bell showed that the compact ordered space~$2^{\omega_1}$
(with the lexicographic order) is an image of~$\Nstar$.
Theorems~15 and~17 in Chapter~1 of~\cite{MR0220252} imply that every
compact ordered space that is first-countable is a continuous image of the
latter space, hence also of~$\Nstar$.
In connection with the latter result we note that it is consistent with
the negation of~$\CH$ that all linear orders of cardinality~$\cee$ are
embeddable into the Boolean algebra~$\powNfin$, see~\cite{MR567675}.
By a combination of the Stone and Wallman dualities this implies that
it is consistent with $\neg\CH$ that every compact ordered space of
weight~$\cee$ is a continuous image of~$\Nstar$.
This was later generalized in~\cite{MR1095691} to the consistency of
Martin's Axiom for $\sigma$-linked partial orders, the negation of~$\CH$,
and the statement that all compact spaces of weight~$\cee$ are continuous
images of~$\Nstar$.
In both cases the proof constructs an embedding of a universal linear order
or a universal Boolean algebra of cardinality~$\cee$ into~$\powNfin$.
This raises the question whether there is a universal compact space
of weight~$\cee$; one that maps onto all such spaces.
The answer is negative, see~\cite{MR1707489}*{Section~6}.
\end{question}
\begin{question}
Is there a universal compact space of weight~$\aleph_1$?
\comments
If $\CH$ holds then $\Nstar$ is such a space, but even without $\CH$ it still
maps onto every compact space of weight~$\aleph_1$.
So $\Nstar$ would answer the question positively without the restriction that
the desired space should have weight~$\aleph_1$.
\end{question}
\iffalse
\begin{question}[Deze gaat weg, maar eerst de nummers bewaren]
Is every hereditarily c.c.c.\ compact spac
\pri{compact space!hereditarily \ccc}\pri{ccc@\ccc!hereditarily}
a continuous image of~$\Nstar$?
\comments
\end{question}
\fi
\begin{question}
Investigate ultrafilters as topological spaces.
\comments
This is a very general question, so let us discuss some specific ones that
may be investigated.
An ultrafilter can be viewed as a subspace of the Cantor set~$\Cantor$,
if one identifies a subset of~$\omega$ with its characteristic function.
Of course this makes ultrafilters separable metric spaces, and hence
relatively well-behaved.
But not too well-behaved: free ultrafilters are non-measurable and do not
have the property of Baire.
To begin one can repeat many of the investigations into the Rudin-Keisler
order using more general kinds of maps.
We know $p\leRK q$ means that there is a map $f:\N\to\N$ such that $f(q)=p$.
The map~$f$ determines a continuous map from~$\Cantor$ to itself, so
the following definition suggests itself at once: say $p\le_c q$ if there
is a continuous map $f:\Cantor\to\Cantor$ such that $f[q]=p$.
One can ask whether $p\le_cq$ and $q\le_cp$ together imply that $p\equiv_cq$,
which means that there is a homeomorphism of~$\Cantor$ that maps $p$ to~$q$.
The structure of the partial order~$\le_c$, minimal elements, incomparable
elements, etc., would warrant investigation as well.
There is no reason to stop here of course: one can ask the same questions
about Borel maps of any specific order, of maps of arbitrary Baire classes.
One need not work with maps on~$\Cantor$, though that may make life easier,
one can investigate what it means for two ultrafilters to be homeomorphic,
or what it means that one is a continuous image of the other.
The methods of~\cite{MR1277880} may be of use in determining the possible
sizes of sets of ultrafilters that are incomparable in this sense.
We note that an ultrafilter can be homeomorphic to at most $\cee$ many other
ultrafilters: if $f:p\to q$ is a homeomorphism then Lavrentieff's theorem
implies that $f$ can be extended to a homeomorphism of $G_\delta$-subsets
of~$\Cantor$, and the number of such homeomorphisms is equal to~$\cee$.
The paper~\cite{MR2879361} contains many results on the topology of
ultrafilters.
\end{question}
\iffalse
\begin{question}
Suppose that $p\le_\alpha q$ and $q\le_\alpha p$. Are $p$ and $q$
$\RK$-equivalent\pri{ultrafilters!\RK-equivalent},
or can they be mapped to each other by a Baire
isomorphism\pri{Baire isomorphism|see{isomorphism, Baire}
\pri{isomorphism!Baire} of class $\alpha$?
\comments
\end{question}
\begin{question}
Do $\le_\alpha$-minimal points exist, and can they be characterized?
\comments
\end{question}
\begin{question}
Do $\le_\alpha$-incomparable points exist?
\comments
\end{question}
\fi
\begin{question}
Is the space of minimal prime ideals of $C(\Nstar)$ \emph{not}
basically disconnected?
\comments
For a commutative ring~$R$ we let $mR$ denote the set of minimal prime ideals
endowed with the hull-kernel topology.
In~\cites{MR0144921,MR194880} Henriksen and Jerison studied this space and
asked whether $mC(\Nstar)$~is basically disconnected.
In the papers~\cite{MR958091} and~\cite{MR1057626} various conditions were
found that imply $mC(\Nstar)$~is \emph{not} basically disconnected.
For example, $\MA$~implies that $mC(\Nstar)$ is not even an $F$-space
(\cite{MR958091}).
In~\cite{MR1057626} it was shown that the equality $\cf[\dee]^{\aleph_0}=\dee$
suffices to show that $mC(\Nstar)$~is not basically disconnected.
Failure of this equality entails the existence of inner models with measurable
cardinals.
The actual consequence, called~\textbf{Mel}, of this equality that was used
in the proof identifies $\N$ with~$\Q$ and asks for a $P$-filter~$\calF$
on~$Q$, and two countable disjoint dense subsets $A$ and $B$
of $\R\setminus\Q$ such that the closure in~$\R$ of every member
of~$\calF$ meets both $A$ and~$B$.
Thus, to show that $mC(\Nstar)$ is not basically disconnected it suffices
to show that \textbf{Mel} holds, or the following stronger, but possibly more
manageable, statement: the ideal of nowhere dense subsets of $\Q$ can be
extended to a $P$-ideal.
\end{question}
\begin{question}
Is there a c.c.c.\ forcing extensio
\pri{forcing extension!\ccc}\pri{ccc\ccc{}!forcing extension}
of~$L$ in which there are no $P$-points\pri{P-point@$P$-point}?
\comments
The consistency of the nonexistence of $P$-points was proven by Shelah,
see~\cite{MR728877} and also~\cite{MR1623206}*{VI\,\S4}.
After this there have been various attempts to (dis)prove the existence
of $P$-points in various standard models.
Quite often the outcome was that ground model $P$-points remained ultrafilters
and $P$-points in the extension.
A notable exeption is the Silver model: in~\cite{MR3990958} we find a proof
that iterating Silver forcing $\omega_2$ times with countable supports produces
a model without $P$-points; the same holds for the countable support product
of arbitrarily many copies of the partial order.
This establishes the consistency of the nonexistence of $P$-points
with arbitrarily large values of~$\cee$.
A question that is still open is whether $P$-points exist in the random real
model.
If not then this would answer the present question positively.
If there are $P$-points in this model then our question gains interest
as it is as yet unknown whether c.c.c.\ forcing can be used to kill
$P$-points.
\end{question}
\begin{question}
What is the relationship between ultrafilters of small character
(less than~$\cee$) and $P$-points?
\comments
One of the first ultrafilters of small character can be found
in~\cite{MR597342}*{Exercise~VII.A10}; it is a simple $P_{\aleph_1}$-point
constructed by iterated forcing over a model of~$\neg\CH$.
There are many more examples of ultrafilters of small character but their
constructions seem to involve $P$-points in some form or another.
A common method is to start with a model of~$\CH$ and enlarge the continuum
while preserving some ultrafilters; these will then have character~$\aleph_1$,
which is smaller than~$\cee$.
Almost always these `indestructible' ultrafilters are $P$-points (or stronger)
and remain $P$-points in the extension.
There are a few exceptions, see~\cite{MR987317} for instance, but there the
ultrafilters are built using $P$-points and these are preserved as well.
\end{question}
\iffalse
\begin{question}\label{charquest}
Is there a model in which there are no $P$-points\pri{P-point@$P$-point},
but there is an ultrafilter of character\pri{ultrafilter!of small character}
less than~$\cee$?
\comments
Deze en de volgende vraag samenvoegen tot een vraag over hoe ultrafilters
van klein karakter te maken.
\end{question}
\begin{question}
Is there a model in which there is an ultrafilter of characte
\pri{ultrafilter!of small character} less than~$\cee$ without any
$P$-point below it in the Rudin-Keisler order\pri{Rudin-Keisler order}?
\comments
\end{question}
\fi
\begin{question}
We let $\Spchi$ denote the set of characters of ultrafilters on~$\N$,
the \emph{character spectrum} of~$\N$.
The general question is what one can say about this set.
\comments
We know that $\cee\in\Spchi$, and that $\Spchi=\{\cee\}$ is possible.
In \cite{MR2365799} Shelah showed the consistency of there being
three cardinals $\kappa$, $\lambda$, and $\mu$ such that
$\kappa,\mu\in\Spchi$ and $\lambda\notin\Spchi$.
The construction uses a c.c.c.~forcing over a ground model in which
the three cardinals are regular, $\lambda$~is measurable, and there is another
measurable cardinal below~$\kappa$.
In~\cite{MR2847327} he extended this result by showing how build,
given two disjoint sets $\Theta_1$ and~$\Theta_2$ of regular cardinals,
a cardinal-preserving partial order that forces $\Theta_1$ to be a subset
of~$\Spchi$ and $\Theta_2$ to be disjoint from it; the construction requires
$\Theta_2$ to consist of measurable cardinals.
The same paper also contains models in which $\{n:\aleph_n\in\Spchi\}$ can be
any subset of~$\N$, starting from infinitely many compact cardinals.
This answers a question from~\cite{MR1686797}, namely whether if there
are ultrafilters of character~$\aleph_1$ and~$\aleph_3$ there must be one
of character~$\aleph_2$, but at the cost of large cardinals.
This leaves open the question whether the conjunction of
$\aleph_1,\aleph_3\in\Spchi$ and $\aleph_2\notin\Spchi$ can be proven
consistent from the consistency of just~$\ZFC$.
To be very specific we ask whether there is an ultrafilter of
character~$\aleph_2$ in the model(s) of~\cite{MR597342}*{Exercise~VII.A10},
where one starts with a model of~$\cee=\aleph_3$, and in the side-by-side
Sacks model where $\cee=\aleph_3$.
\end{question}
\begin{question}
Is there consistently a point in $\Nstar$ whose
$\pi$-character\pri{pi-character@$\pi$-character} has
countable cofinality?
\comments
The paper~\cite{MR1686797} contains a wealth of material on $\pi$-characters
of ultrafilters, including a model with an ultrafilter of
$\pi$-character~$\aleph_\omega$.
Unlike the results on the character spectrum the reults on the $\pi$-character
spectrum do not require large cardinals.
\end{question}
\begin{question}
Is it consistent that $t(p,\Nstar)<\chi(p)$\pri{tpomega@$t(p,\Nstar)$
\pri{chip@$\chi(p)$} for some $p\in\Nstar$?
\comments
There are plenty of compact spaces with points where the tightness is smaller
than the character; the one-point compactification of the any uncountable
discrete space will do: the tightness at the point at infinity is countable,
the character of the point is not.
Let us remark that no point of $\Nstar$ has countable tightness: certainly
at $P$-points the tightness is uncountable; if $p$~is not a $P$-point
then it lies on the boundary of a zero-set~$C$ and in the closure of its
interior, but the closure of every countable subset of that interior
is a subset of that interior.
This implies that $t(p,\Nstar)=\chi(p)=\cee$ if~$\CH$ holds, hence the
question for a consistency result.
As an aside we mention that there are consistent examples
of regular extremally disconnected spaces of countable tightness:
in~\cite{MR0458392} and~\cite{MR461464} one finds constructions of
extremally disconnected $S$-spaces.
The constructions use $\clubsuit$ and that some extra assumption is necessary
is shown in~\cite{MR615971}: there are no extremally disconnected $S$-spaces
if $\MAnotCH$~holds.
Both \cite{MR461464} and~\cite{MR615971} contain constructions of extremally
disconnected $S$-spaces in~$\betaN$.
\end{question}
\iffalse
\begin{question}
Are there $p$ and $q$ with $\I_p$\pri{Ip@$\I_p$} and $\I_q$ not homeomorphic?
\label{q.different.Ip}
\comments
Dow and Hart showed in~\cite{MR1282963} that $\CH$ implies that all
continua~$\I_p$ are mutually homeomorphic, and applied
\cite{MR828984}*{Theorem~2.2} to prove the converse implication.
Dow strengthened that converse implication by proving that $\lnot\CH$
implies that there is a family~$A$ of $2^\cee$~many ultrafilters
on~$\omega$ such that the continua in the family $\{\I_p:p\in A\}$ are
mutually non-homeomorphic, \cite{MR2823685}.
This also provides one half of the answer to problem~\ref{q.how.many}.
This shows that $\CH$ is equivalent to the statement that all
continua~$\I_p$ are mutually homeomorphic.
\end{question}
\begin{question}
Are there cut points in $\I_p$\pri{cut points!in $\I_p$} other than the
points~$f_p$ for $f:\omega\to I$?
\comments
This was answered in~\cite{MR1216810}:
under $\CH$ every $\I_p$ has cut points not of the form~$f_p$, and
in Laver's model for the Borel Conjecture all cut points of all~$\I_p$
are of the form~$f_p$.
\end{question}
\begin{question}
How many subcontinua does $I_p$\pri{subcontinua!of $I_p$} have?
\label{q.how.many}
\comments
The answer is~$2^\cee$.
Interestingly the proofs are quite different depending whether $\CH$ holds
or not; also, both arguments work in the context of~$\Hstar$, where
$\HH$~is the half line~$[0,\infty)$.
Dow proved that $\lnot\CH$ implies that there is a family~$A$ of
$2^\cee$~many ultrafilters on~$\omega$ such that the continua in the family
$\{\I_p:p\in A\}$ are mutually non-homeomorphic, \cite{MR2823685}.
This also provides one half of the answer to problem~\ref{q.different.Ip}.
Dow and Hart proved that $\CH$ implies the existence of a family of
$2^\cee$~many mutually non-homeomorphic indecomposable subcontinua
in~$\Hstar$, see~\cite{MR3414878}.
\end{question}
\fi
\begin{question}
If $C(\omega+1,\C)$\pri{Comega+1@$C(\omega+1)$} admits an
incomplete\pri{norm!incomplete} norm then does
$C(\betaN,\C)$\pri{Cbetaomega@$C(\beta\omega)$} admit one too?
\label{analyse.1}
\comments
This question is related to a conjecture\slash question of Kaplansky's about
algebra norms on the spaces~$C(X,\C)$, with $X$ compact.
The question is whether every algebra norm is equivalent to the
sup-norm~$\|{\cdot}\|_\infty$.
The answer is positive if the norm is complete, hence the question became
whether every algebra norm on~$C(X,\C)$ is complete.
The book~\cite{MR942216} surveys the solution to this problem:
under~$\CH$ every~$C(X,\C)$ carries an incmplete algebra norm
(Dales and Esterl\'e) and it is consistent
that every algebra norm on every~$C(X,\C)$ is complete (Solovay and Woodin).
The present question comes from the results that if $C(\betaN,\C)$~admits
an incomplete norm then so does every~$C(X,\C)$, and
if \emph{some}~$C(X,\C)$ carries an incomplete norm then so
does~$C({\omega+1},\C)$.
In short it asks whether all compact spaces are equivalent for Kaplansky's
conjecture.
The question can be translated into terms of individual ultrafilters and this
leads to some interesting subquestions.
A seminorm on an algebra is a function that satisfies all conditions of an
akgebra norm except for the condition that non-zero elements should have
non-zero norm.
An algebra is semi-normable if it carries a non-trivial seminorm.
For a point $p$ of $\betaN$ we let $A_p$ denote the quotient algebra
$M_p/I_p$, where $M_p=\{f\in C(\betaN,\C):f(p)=0\}$, and
$I_p=\{f\in C(\betaN,\C):(\exists P\in p)(f\restr P=0)\}$.
We also let $c_0$ be the subalgebra of~$C(\betaN,\C)$ of functions
that vanish on~$\Nstar$ and we let $c_0/p$ denote the quotient algebra
$c_0/(c_0\cap I_p)$.
We now have Theorem~2.21 in~\cite{MR942216} shows why we should be interested
in these algebras:
The algebra $C(\betaN,C)$~admits an incomplete norm iff for some~$p$
the algebra~$A_p$ is seminormable, and $C({\omega+1},\C)$ admits an incomplete
norm iff for some~$q$ the algebra~$c_0/q$ is seminormable.
We see that \emph{if} there is a $p$ such that $A_p$ is seminormable \emph{then}
there is a~$q$ such that $c_0/q$~is seminormable.
The present question ask wether this implication can be reversed.
Further questions regarding these algebras suggest themselves:
is it the case that the seminormability of~$A_p$ implies that of~$c_0/p$?
in other words can we get $q=p$ in the previous paragraph?
Also, what is the answer to the stronger version of our question:
if $c_0/p$~is seminormable is the $A_p$ seminormable too?
We recommend \cite{MR942216}*{Chapters~1, 2 and~3} for more detailed
information on this question.
\end{question}
\iffalse
\begin{question}
If $p\in\Nstar$ and $c_0/p$\pri{c0p@$c_0/p$} is
seminormable\pri{seminormable}, is $A_p$\pri{Ap@$A_p$} seminormable?
\comments
\end{question}
\begin{question}
If $p\in\Nstar$ and $A_p$\pri{Ap@$A_p$} is
seminormable\pri{seminormable}, is $c_0/p$\pri{c0p@$c_0/p$} seminormable?
\comments
\end{question}
\begin{question}\label{analyse.4}
If $p\in\Nstar$ and $A_p$\pri{Ap@$A_p$} is weakly
seminormable\pri{seminormable!weakly}, is $A_p$ seminormable\pri{seminormable},
or is $A_q$ for some other $q$?
\comments
\end{question}
\fi
\begin{question}
($\MA+\lnot\CH$\pri{MACH@$\MA+\lnot\CH$}) Are there $\Gap$ and $p$
($P$-point, selective) such that $p\subseteq I_\Gap^+$?
\comments
Here $\Gap$ denotes a Hausdorff-gap in~${}^\omega\omega$ and
$I_\Gap$ is the ideal of sets over which $\Gap$~is filled.
S. Kamo \cite{MR1138202} proved that if $V$~is obtained from a model of~$\CH$
by adding Cohen reals then in~$V$ an ideal is a gap-ideal iff it is
$\le\aleph_1$-generated.
Also, $\CH$~implies that any nontrivial ideal is a gap-ideal.
The commentary in~\cite{MR2023411} mentions a further preprint by Kamo,
\cite{kamo1993}, where it is shown that, under $\MA+\lnot\CH$,
for every Hausdorff gap~$\Gap$ there are both selective ultrafilters and
non-$P$-points consisting of positive sets (with respect to the
gap-ideal~$I_\Gap$).
Also under $\MA + \lnot\CH$ there is a selective non-$P_{\aleph_2}$-point
that meets every gap-ideal.
Unfortunately we were unable to locate this preprint and verify these
statements.
\end{question}
\section{Orders}
\begin{question}
Is there for every $p\in\Nstar$ a $q\in\Nstar$
such that $p$ and $q$ are $\leRK$-incomparabl
\pri{ultrafilters!$\leRK$-incomparable}?
\comments
This question has a long history; it is as old as the Rudin-Keisler order
itself.
In~\cite{MR314619} Kunen constructed two points that are $\leRK$-incomparable.
In~\cite{MR540490} Shelah and Rudin proved that there is a set of $2^\cee$
incomparable points.
In~\cite{MR0863940} Simon proved that these points may be taken to
be $\aleph_1$-OK.
In~\cite{MR1277880} Dow showed that that there are many more situations
where such sets may be constructed.
However, none of these results shed light on the present question.
Some partial results are available: in~\cite{MR931732} Hindman
proved: if $p$ is such that $\chi(r)=\cee$ whenever $r\leRK p$ then there
is a point that is incomparable with~$p$, so the answer to the present question
is positive if all ultrafilters have character~$\cee$.
Furthermore if $\cee$~is singular and $\chi(p)=\cee$ then again there is a
point that is incomparable with~$p$.
The latter result was extended by Butkovi\v{c}ov\'a in~\cite{MR1045131}:
if $\kappa<\cee$ is such that $\cee<2^\kappa$ then for every ultrafilter
of character~$\cee$ there are $2^\kappa$~many ultrafilters incomparable
with it.
Note that these results all impose conditions on individual ultrafilters
in order to find an incomparable point; only the condition
``all ultrafilters have character~$\cee$'' answers this question directly.
In~\cite{MR1623206}*{XVIII~\S4} Shelah proved that it is consistent that
up to permutation there is one $P$-point.
\end{question}
We recall the definition of the Rudin-Frol\'ik order: we say $p\leRF q$ if
there is an embedding $f:\betaN\to\betaN$ such that $f(p)=q$.
This is a preorder that induces a partial order on the types of ultrafilters.
To see this note that $p\leRF q$ implies $p\leRK q$: given~$f$ take a partition
$\{A_n:n\in\N\}$ of~$N$ such that~$A_n\in f(n)$ for all~$n$.
The map $g=\bigcup_n(A_n\times\{n\})$ satisfies $p=g(q)$ and shows $p\leRK q$.
As usual $p\lRF q$ will mean $p\leRF q$ plus not-$q\leRF p$, and this is
readily seen to be equivalent to there being an embedding $f:\betaN\to\Nstar$
such that~$f(p)=q$.
The Rudin-Frol\'ik order is tree-like: if $p,q\leRF r$ then $p\leRF q$
or $q\leRF p$.
And due to the relation with~$\leRK$ we see at once that $\{p:p\leRK q\}$
always has cardinality at most~$\cee$.
In many papers on the Rudin-Frol\'ik order Frol\'ik's original notation
is employed where one writes $X=f[\N]$, and $q=\Sigma(X,p)$ as well
as $p=\Omega(X,q)$.
\begin{question}
For what cardinals $\kappa$ is there a strictly decreasing chain
of copies of~$\betaN$ in $\Nstar$ with a one-point intersection?
\label{q.one-point}
\comments
This question is related to decreasing chains in~$\leRF$.
A decreasing sequence of copies of~$\betaN$ determines and is determined
by a sequence $\langle X_\alpha:\alpha\in\delta\rangle$ of countable
discrete subsets of~$\Nstar$ with the property
that $X_\alpha\subseteq\cl{X_\beta}\setminus X_\beta$ whenever $\beta\in\alpha$.
Take a point~$p$ in the intersection of the sequence;
then $\langle\Omega(X_\alpha,p):\alpha\in\delta\rangle$ is a decreasing
$\leRF$-chain.
To ensure that this chain does not have a lower bound one should make sure
that $p$~is not an accumulation point of a countable discrete subset
of the intersection.
Having a one-point intersection is certainly sufficient for this.
In~\cite{MR863908} Van Douwen showed that it is possible to have a chain
of length~$\cee$ with a one-point intersection.
In~\cite{MR633575} and~\cite{MR1007490} we find constructions of decreasing
$\leRF$-chains of type~$\omega$ and of type~$\mu$ for uncountable~$\mu<\cee$
respectively.
The latter two constructions provide a point in the intersection of
a suitable chain of copies of~$\betaN$ that is not an accumulation point of
a countable discrete subset of that intersection.
We want to know when in these cases the intersection can be made to be a
one-point set.
\end{question}
\begin{question}
If $\kappa\le\cee$ has uncountable cofinality and if
$\left\langle X_\alpha:\alpha<\kappa\right\rangle$ is a strictly
decreasing sequence of copies of~$\betaN$ with intersection~$K$,
is there a point~$p$ in~$K$ that is not an accumulation point of any
countable discrete subset of~$K$?
\comments
This is related to Question~\ref{q.one-point}: the chains of copies of~$\betaN$
in the positive results were chosen with care.
We want to know if that care is necessary.
\end{question}
\begin{question} What are the possible lengths of unbounded $\RF$-chain
\pri{RF-chain@$\RF$-chain!unbounded}?
\comments
Since every point has at most~$\cee$ predecessors every chain has cardinality
at most~$\cee^+$.
In~\cite{MR633575} we find a point with exactly $\aleph_0$~many predecessors,
with the order type of the set of negative integers.
Every unbounded chain will have cardinality at least~$\cee$
(this follows from results in~\cite{MR277371}*{Theorem~2.9} or~\cite{MR698391}),
so the cardinality of an unbounded chain is equal to either~$\cee$ or~$\cee^+$.
In~\cite{MR730151} and~\cite{MR817833} Butkovi\v{c}ov\'a constructed unbounded
chains of order-type~$\cee^+$ and~$\omega_1$ respectively.
What other order-type are possible?
Can one prove that a chain or order-type~$\cee$ (or its cofinality)
exists, irrespective of~$\CH$?
\end{question}
\begin{question}
Is every finite partial order embeddable in the Rudin-Keisler order?
\comments
See MathOverFlow \texttt{https://mathoverflow.net/questions/375365}.
To get a positive answer it suffices to embed every finite power set
into this order.
It is relatively easy to adapt the construction of two incomparable
ultrafilters to yield an embedding of the power set of~$\{0,1\}$
(see~\cite{ruitje}),
but an embedding of the power set of~$\{0,1,2\}$ already poses unexpected
difficulties.\par
The analogous question for the Rudin-Frol\'ik order has an easier answer.
This order is tree-like in that the predecessors of a point are linearly
ordered, and every point has $2^\cee$ many successors.
This implies that every finite rooted tree, and only those among the finite
partial orders, can be embedded into this order.
\end{question}
\section{Uncountable Cardinals}
\begin{question}\label{q.small.chi}
Is there consistently an uncountable cardinal $\kappa$ with
$p\in U(\kappa)$ such that~$\chi(p)<2^\kappa
\pri{ultrafilter!of small character!on uncountable cardinals}?
\comments
It is well known that if $\kappa$~is an infinite cardinal then there
are $2^{2^\kappa}$~many uniform ultrafilters on~$\kappa$ that have
character~$2^\kappa$, see~\cite{MR1454}.
It is also well known that, and referred to in other questions, that it
is consistent that there are ultrafilters on~$\N$ of character less than~$\cee$.
Of course the Generalized Continuum Hypothesis implies that every uniform
ultrafilter on every~$\kappa$ has character~$2^\kappa$, but we are not aware
of any consistency result the other way for uncountable cardinals.
We formulate two special cases of our question:
\begin{itemize}
\item Is it consistent to have uniform ultrafilter on~$\omega_1$ of
character~$\aleph_2$ (with $\aleph_2<2^{\aleph_1}$ of course)?
\item Is it consistent to have a measurable cardinal $\kappa$ with
a $p\in U(\kappa)$ such that $\chi(p)<2^\kappa$?
\end{itemize}
The first question simply looks at the smallest possible case and the second
question asks, implicitly, if having a uniform ultrafilter of small
character is actually a large-cardinal property of~$\aleph_0$.
There has been recent activity in this area;
the paper~\cite{MR3832086} deals with the character spectrum of uncountable
cardinals of countable cofinality, and in~\cite{MR4081063} one finds models
with $\you_\kappa<2^\kappa$ for $\kappa=\cee$ and for $\kappa=\aleph_{\omega+1}$.
These results use large cardinals in the ground model: the spectrum result
uses a supercompact and many measurables; the results for~$\cee$
and~$\aleph_{\omega+1}$ use a measurable and supercompact cardinal respectively.
\end{question}
\begin{question}
Is it consistent to have cardinals $\kappa<\lambda$ with points
$p\in U(\kappa)$ and $q\in U(\lambda)$ such that $\chi(p)>\chi(q)
\pri{ultrafilter!of small character!on uncountable cardinals}?
\comments
This is a follow-up question to Question~\ref{q.small.chi}:
if uniform ultrafilters of small character are at all possible, how
much variation can we achieve among various cardinals?
\end{question}
\begin{question}
If $\kappa$ is regular and uncountable, $\calF$ is a countably
complete uniform filter on $\kappa$ then what is the cardinality
of the closed set $U_\calF=\{u\in U(\kappa):\calF\subseteq u\}$?
\comments
In case $\kappa$ is measurable one can use a measure ultrafilter to create
filters~$\calF$ such that $U_\calF$ is finite or a copy of~$\beta\lambda$,
for any $\lambda<\kappa$.
For other cardinals the set $U_\calF$ will always be at least infinite and
given the nature of~$\beta\kappa$ the cardinality will be closely related
to numbers of the form~$2^{2^\lambda}$ for $\lambda\le\kappa$.
For the closed unbounded filter the answer is~$2^{2^\kappa}$: using
a family of $\kappa$~many pairwise disjoint stationary sets and an independent
family on~$\kappa$ of cardinality~$2^\kappa$ one can produce a map from~$U_\calF$
onto the Cantor cube of weight~$2^\kappa$.
\end{question}
\begin{question}
Assume that $\kappa$ is regular, that $\kappa\subseteq X\subseteq\beta\kappa$
is such that $[X]_{<\kappa}=X$ and $\beta_X\kappa=X$.
Now if $Y$ is a closed subspace of a power of $X$, is then also
$X$ a closed subspace of a power of $Y$?
\comments
Some notation: $[X]_{<\kappa}$
denotes $\bigcup\{\cl B:B\in[X]^{<\kappa}\}$, and
if $\kappa\subseteq X\subseteq\beta\kappa$ then $\beta_X\kappa$~is
the maximal subset of~$\beta\kappa$ such that every function from~$\kappa$
to~$X$ has a continuous extension from~$\beta_X\kappa$ to~$X$.
\end{question}
\begin{question}
Are there $\kappa$ and $p\in U(\kappa)$ such that $|\R_p|>|\R_p/\equiv|=\cee
\pri{cardinality!of ultrapower}\pri{ultrapower!cardinality of}?
\comments
Here $\R_p$ denotes the ultrapower of~$\R$ by the ultrafilter~$p$.
The relation~$\equiv$ is that of Archimedean equivalence:
$a\equiv b$ means that there is an~$n\in\N$ such that both $\abs{a}<\abs{nb}$
and $\abs{b}<\abs{na}$.
\end{question}
\begin{question}
Is there a $C^*$-embedded bi-Bernstein set\pri{bi-Bernstein set}
in $U(\omega_1)$\pri{Uomega1@$U(\omega_1)$}?
\comments
\end{question}
\begin{question}
Are there open sets $G_1$ and $G_2$ in $U(\omega_1)
\pri{open set!in $U(\omega_1)$} such that
$\cl{G_1}\cap\cl{G_2}$ consists of exactly one point?
\comments
\end{question}
\section{New problems}
\begin{question}
Is every compact space of weight at most~$\aleph_1$ a $1$-soft remainder
of~$\omega$?
\comments
A compactification~$\gamma\N$ of~$\N$ is $1$-soft if for every subset~$A$
of~$\N$ with $\cl A\cap\cl(\N\setminus A)\neq \emptyset$ there is an
autohomeomorphism~$h$ of~$\gamma\N$ that is the identity
on~$\gamma\N\setminus\N$ and is such that $\{n\in A:h(n)\notin A\}$ is
infinite.
See Question~351527 on MathOverFlow, \cite{flow351527},
and also the papers \cite{MR4142223} and~\cite{MR4266612} for related
information.
\end{question}
\begin{question}
Are the autohomeomorphisms of $\Nstar$ induced by the shift map
$\sigma:n\mapsto n+1$ and by its inverse conjugate?
\comments
See~\cites{MR1035463,MR4138425}.
Under~$\CH$ the autohomeomorphism group of $\Nstar$ is simple, yet it has
the maximum possible number of conjugacy classes:~$2^\cee$.
This suggests questions about the number and nature of conjugacy classes
of this group, in $\ZFC$ or under various familiar extra set-theoretical
assumptions.
\end{question}
\begin{question}
Does $\Nstar$ have a universal autohomeomorphism?
\comments
This is a question with many possible variations.
The definition of universality that we adopt here is as follows:
$f:\Nstar\to\Nstar$ is universal if for every closed subspace~$F$ of~$\Nstar$
and every autohomeomorphism~$g$ of~$F$ there is an embedding $e:F\to\Nstar$
such that $g=e^{-1}\circ (f\restr e[F])\circ e$.
One can ask whether there is a universal autohomeomorphism at all,
whether the shift~$\sigma$ is universal (for autohomeomorphisms without
fixed points),
whether there is a universal autohomeomorphism just for autohomeomorphisms
without fixed points.
The authors have shown that there is a universal autohomeomorphism of~$\Nstar$
under~$\CH$ and that there is no trivial universal autohomeomorphism.
See~\cite{HartvanMill2021}.
We also note that $\N$ has a universal permutation:
take a permutation of~$\N$ that has infinitely many $n$-cycles, for every~$n$,
and infinitely many infinite cycles (copies of~$\Z$ with the shift).
Every other permutation of~$\N$ can be embedded into this one.
\end{question}
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\section*{I. INTRODUCTION}
In the past decades more and more experimental data come out with the establishment and running of several high energy accelerators\cite{OPAL}\cite{PDG14}. The focus on heavy quarks has spread from mesons to baryons, partly because of the discovery of the flavor and spin symmetries in QCD, $SU(2)_{f}\times SU(2)_{s}$, in the heavy quark limit and the establishment of the heavy quark effective theory~(HQET)\cite{Isgur1989}-\cite{Georgi1990}. On the experimental side, there have been many new experimental results about $b$-baryons\cite{PDG14}\cite{Akers1996}-\cite{Abe1997}. The lifetime of $\Lambda_{b}$ was given by several experiments\cite{OPAL}. The widths of the nonleptonic decay $\Lambda_{b}\rightarrow \Lambda J/\Psi$\cite{CDF1997} as well as the semileptonic decay $\Lambda_{b}\rightarrow \Lambda_cl^{-}\bar{\nu}$ were measured\cite{DELPHI1995}\cite{DELPHI2004}. Besides, the branching ratios of two-body decays such as $\Lambda_{b}\rightarrow\Lambda_{c}\pi$\cite{CDF2007122002},~$\Sigma^{*}_{c}\rightarrow\Lambda_{c}\pi$ and $\Sigma_c\rightarrow\Lambda_{c}\pi$\cite{CDF2011012003} have been listed in PDG's booklet. CDF has measured decay widths of $\Sigma^{*}_{b}\rightarrow\Lambda_{b}\pi$ and $\Sigma_{b}\rightarrow\Lambda_{b}\pi$ since 2010\cite{CDF2007202001}. All of these measurements help to test theoretical studies for heavy baryons.
Although the heavy quark symmetries can be used to simplify the physical processes where heavy hadrons are involved, in most cases HQET itself can not give the final phenomenological predictions for the decay properties. Hence one still has to adopt nonperturbative QCD models in the end. Among them, there are QCD sum rules, the Bethe-Salpeter~(BS) equation, the chiral perturbation theory, the potential model, the bag model, the instanton model, the relativistic and nonrelativistic quark models, etc.. Applying these models one can calculate weak transition form factors for, for instance, $\Lambda_{b}\rightarrow\Lambda_{c}$, and consequently the semileptonic decay width directly because the lepton pair can be separated from the hadronic weak transition.
The matrix element of $\Lambda_{b}\rightarrow\Lambda_{c}$ can be expressed by six transition form factors because of Lorentz covariance,
\begin{eqnarray}
\langle\Lambda_{c}(v',s')|\bar{c}(\gamma_{\mu}-\gamma_{\mu}\gamma_{5})b|\Lambda_{b}(v,s)\rangle&=&\bar{u}_{\Lambda_{c}}(v',s')[F_{1}(\omega)\gamma_{\mu}+F_{2}(\omega)\nu_{mu}+F_{3}(\omega)\nu'_{\mu}\nonumber\\
&&~~~~~-G_{1}(\omega)\gamma_{\mu}\gamma_{5}-G_{2}(\omega)\nu_{\mu}\gamma_{5}-G_{3}(\omega)\nu'_{\mu}\gamma_{5}]u_{\Lambda_{b}}(v,s),\label{1}
\end{eqnarray}
\noindent where $v'$ and $v$ are the velocities of $\Lambda_{c}$ and $\Lambda_{b}$ respectively, $\omega=v'\cdot v$, $s'$ and $s$ are the spins of $\Lambda_{c}$ and $\Lambda_{b}$ respectively, $u_{\Lambda_c}(v',s')$ and $u_{\Lambda_b}(v,s)$ are the Dirac spinors of $\Lambda_c$ and $\Lambda_b$, respectively, $F_{i}$ and $G_{i} ~(i=1,2,3)$ are the Lorentz scalar form factors. There is only one form factor~(the Isgur-Wise function) remained when we take off all the corrections in the $1/m_{Q}$ expansion. When we take first order corrections into account\cite{Georgi1990},
\begin{eqnarray}
&&F_{1}=G_{1}\Bigg[1+\bigg(\frac{1}{m_{c}}+\frac{1}{m_{b}}\bigg)\frac{\bar{\Lambda}}{1+\omega} \Bigg],\nonumber\\
&&F_{2}=G_{2}=-G_{1}\frac{1}{m_{c}}\frac{\bar{\Lambda}}{1+\omega},\\
&&F_{3}=-G_{3}=-G_{1}\frac{1}{m_{b}}\frac{\bar{\Lambda}}{1+\omega},\nonumber\label{2}
\end{eqnarray}
\noindent where $\bar{\Lambda}$ is a parameter which is defined as the mass difference $m_{\Lambda_{Q}}-m_{Q}$ in the limit $m_{Q}\rightarrow\infty$. There is one independent form factor such as $F_{1}$ in this case.
As a formally exact equation to describe the hadronic bound state, the BS equation is an effective method to deal with nonperturbative QCD effects. With HQET, the BS equation has already been applied to the heavy hadron systems. In the limit $m_{Q}\rightarrow\infty$, we found that the BS equations for the heavy baryons $\Lambda_{Q}$ are greatly simplified. When the quark mass is very heavy compared with the QCD scale, $\Lambda_{QCD}$, the light degrees of freedom in a heavy baryon $\Lambda_{Q}$ become blind to the flavor and spin quantum numbers of the heavy quark because of the $SU(2)_{f}\times SU(2)_{s}$ symmetries. Therefore, the angular momentum and the flavor quantum numbers of the light degrees of freedom become good quantum numbers that can be used to classify heavy baryons, and $\Lambda_{Q}$ corresponds to the state in which the angular momentum of the light degrees of freedom is zero. So it is natural to regard the heavy baryon as composed of one heavy quark and a light diquark. When $1/m_{Q}$ corrections are taken into account, since the isospin of $\Lambda_{Q}$ is zero, the isospin of the light degrees of freedom is also zero, therefore, the spin of the light degrees of freedom should also be zero in order to guarantee that the total wave function of $\Lambda_{Q}$ is antisymmetric. Hence the spin and isospin of the light degrees of freedom are still fixed even when $1/m_{Q}$ corrections are taken into account. Therefore, we still treat $\Lambda_{Q}$
as composed of a heavy quark and a scalar light diquark. In this picture, we established the BS equations of $\Lambda_{Q}$ to second order in the $1/m_Q$ expansion assuming the kernel contains two parts, a scalar confinement term and a one-gluon-exchange term. In the present work, we will apply the BS equation to calculate the semileptonic and nonleptonic decay widths to second order in the $1/m_Q$ expansion.
The remainder of this paper is organized as follows. In Sec. II we will review the BS equation for $\Lambda_{Q}$ to second order in the $1/m_{Q}$ expansion briefly. In Sec. III we will express the six form factors for $\Lambda_b\rightarrow\Lambda_c$ transition in terms of the BS wave functions of $\Lambda_{Q}$ to second order in the $1/m_{Q}$ expansion and give the numerical results. In Sec. IV we will deduce the numerical results for the semileptonic decay width of $\Lambda_{b}\rightarrow\Lambda_{c}l\bar{\nu}$ and nonleptonic decay widths of $\Lambda_{b}\rightarrow\Lambda_{c}P(V)$~(where $P$ denotes pseudoscalar mesons and $V$ denotes vector mesons
) by applying the numerical results of form factors we get in Sec. III. We will also compare our results with the experimental data. Finally, Sec. V is reserved for summary and discussion.
\section*{II. BS EQUATION FOR ~$\Lambda_{Q}$ TO SECOND ORDER IN THE ~$1/m_{Q}$ EXPANSION}
As we discussed in Introduction, $\Lambda_{Q}$ is regarded as a bound state of a heavy quark and a light scalar diquark. Hence we can define the BS wave function of $\Lambda_{Q}$ as the following\cite{Guo1996}:
\begin{eqnarray}
\chi(x_{1},x_{2},P)=\langle 0|T\psi(x_{1})\varphi(x_{2})|\Lambda_{Q}(P)\rangle,\label{3}
\end{eqnarray}
\noindent where $\psi(x_{1})$ and $\varphi(x_{2})$ are the field operators of the heavy quark at position $x_{1}$ and the light scalar diquark at position $x_{2}$, respectively, $P=m_{\Lambda_{Q}}v$ is the momentum of $\Lambda_{Q}$, and $v$ is its velocity. Let $m_{Q}$ and $m_{D}$ represent the masses of the heavy quark and the light diquark in the baryon, $\lambda_{1}=\frac{m_{Q}}{m_{Q}+m_{D}}$, $\lambda_{2}=\frac{m_{D}}{m_{Q}+m_{D}}$, and $p$ represent the relative momentum of the two constituents. Then, the BS wave function in momentum space is defined as
\begin{eqnarray}
\chi(x_{1},x_{2},P)=e^{iPX}\int\frac{d^{4}p}{(2\pi)^{4}}e^{ipx}\chi_{P}(p),\label{4}
\end{eqnarray}
\noindent where $X=\lambda_{1}x_{1}+\lambda_{2}x_{2}$ is the coordinate of the center of mass and $x=x_{1}-x_{2}$.
It is straightforward to prove that the BS equation for $\Lambda_{Q}$ has the following form in momentum space\cite{Lurie1968}:
\begin{eqnarray}
\chi_{P}(p)=S_{F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K(P,p,q)\chi_{P}(q)S_{D}(p_{2}),\label{5}
\end{eqnarray}
\noindent where $p_{1}=\lambda_{1}P+p$, $p_{2}=-\lambda_{2}P+p$ are the momenta of the heavy quark and the light scalar diquark, respectively, $K(P,p,q)$ is the kernel which is defined as the sum of two particle irreducible diagrams, $S_{F}(p_{1})$ and $S_{D}(p_{2})$ are propagators of the heavy quark with momentum $p_{1}$ and the light diquark with momentum $p_{2}$,
\begin{eqnarray}
S_{F}(p_{1})=\frac{i}{\slashed{p}_{1}-m_{Q}+i\varepsilon},\label{6}
\end{eqnarray}
\begin{eqnarray}
S_{D}(p_{2})=\frac{1}{p_{2}^{2}-m_{D}^2+i\varepsilon}.\label{7}
\end{eqnarray}
In order to solve the BS equation for $\Lambda_{Q}$ to second order in the $1/m_{Q}$ expansion, we rewrite Eq.~(\ref{5}) as the following:
\begin{eqnarray}
\chi_{0P}(p)+\frac{1}{m_{Q}}\chi_{1P}(p)+\frac{1}{m_{Q}^{2}}\chi_{2P}(p)&=&\bigg(S_{0F}(p_{1})+\frac{1}{m_{Q}}S_{1F}(p_{1})+\frac{1}{m_{Q}^{2}}S_{2F}(p_{1})\bigg)\int\frac{d^{4}q}{(4\pi)^{4}}\bigg(K_{0}(P,p,q)\nonumber\\
&&+\frac{1}{m_{Q}}K_{1}(P,p,q)+\frac{1}{m_{Q}^{2}}K_{2}(P,p,q)\bigg)\times\Big(\chi_{0P}(q)+\frac{1}{m_{Q}}\chi_{1P}(q)\nonumber\\
&&+\frac{1}{m_{Q}^{2}}\chi_{2P}(q)\Big)S_{D}(p_{2}),\label{8}
\end{eqnarray}
\noindent where we have expanded the BS wave function, the propagator of the heavy quark, and the kernel to $1/m^{2}_{Q}$.
It is easy to show that $S_{D}$ remains unchanged in the $1/m_{Q}$ expansion. Then, by comparing the two sides of Eq.~(\ref{8}) at each order in $1/m_{Q}$, we have the following equations:
\noindent to leading order in the ~$1/m_{Q}$ expansion:
\begin{eqnarray}
\chi_{0P}(p)=S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^4}K_{0}(P,p,q)\chi_{0P}(q)S_{D}(p_{2}),\label{9}
\end{eqnarray}
to first order in the~$1/m_{Q}$ expansion:
\begin{eqnarray}
\chi_{1P}(p)&=&S_{1F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{0}(P,p,q)\chi_{0P}(q)S_{D}(p_{2})+S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{1}(P,p,q)\chi_{0P}(q)S_{D}(p_{2})\nonumber\\
&&+S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{0}(P,p,q)\chi_{1P}(q)S_{D}(p_{2}),\label{10}
\end{eqnarray}
to second order in the~$1/m_{Q}$ expansion:
\begin{eqnarray}
\chi_{2P}(p)&=&S_{2F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{0}(P,p,q)\chi_{0P}(q)S_{D}(p_{2})+S_{1F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{1}(P,p,q)\chi_{0P}(q)S_{D}(p_{2})\nonumber\\
&&+S_{1F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{0}(P,p,q)\chi_{1P}(q)S_{D}(p_{2})+S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{2}(P,p,q)\chi_{0P}(q)S_{D}(p_{2})\nonumber\\
&&+S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{1}(P,p,q)\chi_{1P}(q)S_{D}(p_{2})+S_{0F}(p_{1})\int\frac{d^{4}q}{(2\pi)^{4}}K_{0}(P,p,q)\chi_{2P}(q)S_{D}(p_{2}).\label{11}
\end{eqnarray}
In our previous work\cite{Zhang2013}, we found that:
\begin{eqnarray}
&&\chi_{0P}(p)=\phi_{0P}(p)u_{\Lambda_{Q}}(v,s),\nonumber\\
&&\chi^{+}_{1,2P}(p)=\frac{1+\slashed{v}}{2}\chi_{1,2P}(p)=\phi^{+}_{1,2P}(p)u_{\Lambda_{Q}}(v,s),\\
&&\chi^{-}_{1,2P}(p)=\frac{1-\slashed{v}}{2}\chi_{1,2P}(p)=\phi^{-}_{1,2P}(p)\slashed{p}_{t}u_{\Lambda_{Q}}(v,s)\nonumber\label{12}
\end{eqnarray}
\noindent where we use the variables $p_{l}=v\cdot p-\lambda_{2}m_{\Lambda_{Q}}$ and $p_{t}=p-(v\cdot p)v$, $\phi_{0P}(p)$ and $\phi^{\pm}_{1,2P}(p)$ are scalar functions.
As before, we assume the kernel has the following form:
\begin{eqnarray}
&&-iK_{0}=1\otimes1V_{1}+v^{\mu}\otimes(p_{2}+p'_{2})^{\mu}V_{2},\nonumber\\
&&-iK_{1}=1\otimes1V_{3}+\gamma^{\mu}\otimes(p_{2}+p'_{2})^{\mu}V_{4},\\
&&-iK_{2}=1\otimes1V_{5}+\gamma^{\mu}\otimes(p_{2}+p'_{2})^{\mu}V_{6},\nonumber\label{13}
\end{eqnarray}
\noindent where the first parts on the right hand represent the scalar confinement terms while the second parts represent the one-gluon-exchange terms.
\begin{center}
\begin{figure}[htbp]
\includegraphics[height=6cm]{diquark-onegluon-diquarkvetex.pdf}
\caption{~Diquark-gluon-diquark vetex, $\mu$ and $\alpha$ are the Lorentz and color indices of the gluon, respectively.}
\end{figure}
\end{center}
Defining the variable $W^{2}_{P}=\sqrt{p^{2}_{t}+m^{2}_{D}}$ and using the following relation
\begin{eqnarray}
m_{\Lambda_{Q}}=m_{Q}+m_{D}+E_{0}+\frac{1}{m_{Q}}E_{1}+\frac{1}{m^{2}_{Q}}E_{2},\label{14}
\end{eqnarray}
\noindent where $E_{0}$, $E_{1}$, and $E_{2}$ represent the binding energies, we have the BS equations for the scalar functions in Eq.~(\ref{12}) in leading order, first order and second order in the $1/m_{Q}$ expansion:
\begin{eqnarray}
&&\tilde{\phi}_{0P}(p_{t})=-\frac{1}{2(m_{D}+E_{0}-W_{P})(W_{P})}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]\tilde{\phi}_{0P}(q_{t}),\label{15}\\
&&\tilde{\phi}^{+}_{1P}(p_{t})=0,\label{16}\\
&&\tilde{\phi}^{-}_{1P}(p_{t})=\frac{1}{2}\tilde{\phi}_{0P}(p_{t}),\label{17}\\
&&\tilde{\phi}^{+}_{2P}(p_{t})=\frac{-1}{2(m_{D}+E_{0}-W_{P})W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]\tilde{\phi}^{+}_{2P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\frac{-1}{2(m_{D}+E_{0}-W_{P})W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}(p_{t}\cdot q_{t}-q^{2}_{t})\tilde{V}_{4}\tilde{\phi}^{-}_{1P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\frac{-1}{2(m_{D}+E_{0}-W_{P})W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{5}-2W_{P}\tilde{V}_{6}]\tilde{\phi}_{0P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\frac{-1}{4(m_{D}+E_{0}-W_{P})W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]p_{t}\cdot q_{t}\tilde{\phi}^{-}_{1P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\Big[\frac{p^{2}_{t}}{8(m_{D}+E_{0}-W_{P})W_{P}}+\frac{E_{2}}{(p_{l}+m_{D}+E_{0}+i\varepsilon)^{2}(p^{2}_{l}-W^{2}_{P}+i\varepsilon)}\Big]\nonumber\\
&&~~~~~~~~~~~~~~\times\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]\tilde{\phi}_{0P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\frac{-1}{4(m_{D}+E_{0}-W_{P})W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[p_{t}\cdot q_{t}-p^{2}_{t}]\tilde{V}_{4}\tilde{\phi}_{0P}(q_{t}),\label{18}\\
&&\tilde{\phi}^{-}_{2P}(p)=\frac{1}{4W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]\frac{p_{t}\cdot q_{t}}{p_{t}\cdot p_{t}}\tilde{\phi}^{-}_{1P}(q_{t})\nonumber\\
&&~~~~~~~~~~~~~~+\frac{1}{4W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}\bigg(1+\frac{p_{t}\cdot q_{t}}{p_{t}\cdot p_{t}}\bigg)\tilde{V}_{4}\tilde{\phi}_{0P}(q)\nonumber\\
&&~~~~~~~~~~~~~~+\frac{1}{8W_{P}}\int\frac{d^{3}q_{t}}{(2\pi)^{3}}[\tilde{V}_{1}-2W_{P}\tilde{V}_{2}]\tilde{\phi}_{0P}(q),\label{19}
\end{eqnarray}
\noindent where we have defined $\tilde{\phi}(p_{t})\equiv\int\frac{dp_{l}}{2\pi}\phi(p)$ and applied the covariant instantaneous approximation in the kernel,~$\tilde{V_i}=V_i|_{p_l=q_l}~(i=1,\ldots6)$.
The numerical results of these scalar functions were given in our previous work\cite{Zhang2013}, and in that paper we discussed why Eqs.~(\ref{16}) and (\ref{17}) hold.
\section*{III. $\Lambda_{b}\rightarrow\Lambda_{c}$ FORM FACTORS TO $1/m^{2}_{Q}$ }
In this section we will express the six form factors for the $\Lambda_{b}\rightarrow\Lambda_{c}$ weak transition in terms of the BS wave functions to second order in the $1/m_{Q}$ expansion and give their numerical results.
On the grounds of Lorentz invariance, the matrix element for $\Lambda_{b}\rightarrow\Lambda_{c}$ can be expressed as in Eq.~(\ref{1}).
On the other hand, the matrix element for $\Lambda_{b}\rightarrow\Lambda_{c}$ can be related to the BS wave functions of $\Lambda_{b}$ and $\Lambda_{c}$ as the following:
\begin{eqnarray}
\langle\Lambda_{c}(v',s')|\bar{c}(\gamma_{\mu}-\gamma_{\mu}\gamma_{5})b|\Lambda_{b}(v,s)\rangle=\int\frac{d^{4}p}{(2\pi)^{4}}\bar{\chi}_{P'}(p')(\gamma_{\mu}-\gamma_{\mu}\gamma_{5})\chi_{P}(p)S^{-1}_{D}(p_{2}),\label{20}
\end{eqnarray}
\noindent where $P'~(P)$ is the momentum of $\Lambda_{b}~(\Lambda_{c})$ and $p~(p')$ is the relative momentum defined in the BS wave function of $\Lambda_{b}(v,s)~(\Lambda_{c}(v',s'))$.
As we did before, we can express the BS wave functions of $\Lambda_{b}$ and $\Lambda_{c}$ in the terms of the scalar functions $\phi_{0P}(p)$ and $\phi^{\pm}_{1,2P}(p)$ to second order in the $1/m_{Q}$ expansion
\begin{eqnarray}
\bar{\chi}_{P'}(p')&=&\bar{\chi}_{0P'}(p')+\frac{1}{m_{c}}\bar{\chi}_{1P'}(p')+\frac{1}{m^{2}_{c}}\bar{\chi}_{2P'}(p')\nonumber\\
&=&\bar{u}_{\Lambda_{c}}(v',s')\bigg[\phi_{0P'}(p')+\frac{1}{m_{c}}\bigg(\phi^{+}_{1P'}(p')+\slashed{p}'_{t}\phi^{-}_{1P'}(p')\bigg)+\frac{1}{m^{2}_{c}}\bigg(\phi^{+}_{2P'}(p')+\slashed{p}'_{t}\phi^{-}_{2P'}(p')\bigg)\bigg],\label{21}\\
\chi_{P}(p)&=&\chi_{0P}(p)+\frac{1}{m_{b}}\chi_{1P}(p)+\frac{1}{m^{2}_{b}}\chi_{2P}(p)\nonumber\\
&=&\bigg[\phi_{0P}(p)+\frac{1}{m_{b}}\bigg(\phi^{+}_{1P}(p)+\slashed{p}_{t}\phi^{-}_{1P}(p)\bigg)+\frac{1}{m^{2}_{b}}\bigg(\phi^{+}_{2P}(p)+\slashed{p}_{t}\phi^{-}_{2P}(p)\bigg)\bigg]u_{\Lambda_{b}}(v,s).\label{22}
\end{eqnarray}
Substituting the above twe equations into Eq.~(\ref{20}) and comparing with Eq.~(\ref{1}) we can obtain the form factors in terms of the BS wave functions. To simplify our results, we define
\begin{eqnarray}
&&\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(\beta p')\phi_{P}(p)(p^{2}_{l}-W^{2}_{p})=F_{(\alpha P',\beta P)},\label{23}\\
&&\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p_{t\nu}\phi_{\beta P}(p)(p^{2}_{l}-W^{2}_{p})=f_{1(\alpha P',\beta P)}v_{\nu}+f_{2(\alpha P',\beta P)}v'_{\nu},\label{24}\\
&&\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p'_{t\nu}\phi_{\beta P}(p)(p^{2}_{l}-W^{2}_{p})=f_{3(\alpha P',\beta P)}v_{\nu}+f_{4(\alpha P',\beta P)}v'_{\nu},\label{25}\\
&&\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p'_{t\mu}p_{t\nu}\phi_{\beta P}(p)(p^{2}_{l}-W^{2}_{p})=f_{5(\alpha P',\beta P)}g_{\mu\nu}+f_{6(\alpha P',\beta P)}v'_{\mu}v_{\nu}+f_{7(\alpha P',\beta P)}v_{\mu}v'_{\nu},\label{26}
\end{eqnarray}
\noindent where $F_{(\alpha P',\beta P)}$ and $f_{i(\alpha P',\beta P)}~(i=1,\ldots7)$ are functions of $\omega$, and $\alpha,~\beta=0,1,2$. With the aid of $p_{t\nu}v^{\nu}=p_{t}\cdot v=0$,~$p'_{t\nu}v'^{\nu}=p'_{t}\cdot v'=0$ and $v^{2}=v'^{2}=1$, it is easy to see that
\begin{eqnarray}
&&f_{1(\alpha P',\beta P)}=-\omega f_{2(\alpha P',\beta P)},\label{27}\\
&&f_{2(\alpha P',\beta P)}=\frac{1}{1-\omega^{2}}\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p_{t}\cdot v'\phi_{\beta P}(p)(p^{2}_{l}-W^{2}_{P}),\label{28}\\
&&f_{3(\alpha P',\beta P)}=\frac{1}{1-\omega^{2}}\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p'_{t}\cdot v\phi_{\beta P}(p)(p^{2}_{l}-W^{2}_{P}),\label{29}\\
&&f_{4(\alpha P',\beta P)}=-\omega f_{3(\alpha P',\beta P)},\label{30}\\
&&f_{5(\alpha P',\beta P)}=\frac{1}{3}\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{\alpha P'}(p')p'_{t}\cdot p_{t}\phi_{P}(\beta p)(p^{2}_{l}-W^{2}_{P}),\label{31}\\
&&f_{6(\alpha P',\beta P)}=0,\label{32}\\
&&f_{7(\alpha P',\beta P)}=-\frac{1}{\omega}f_{5(\alpha P',\beta P)}.\label{33}
\end{eqnarray}
Then, we can express the six form factors, $F_{i},~G_{i}~(i=1,2,3)$, as follows:
\begin{eqnarray}
&&F_{1}(\omega)\nonumber\\
&&=-i\bigg[F_{(0P',0P)}+\frac{1}{m_{b}}\bigg(f_{1(0P',1P^{-})}-f_{2(0P',1P^{-})}\bigg)+\frac{1}{m^{2}_{b}}\bigg(F_{(0P',2P^{+})}+f_{1(0P',2P^{-})}-f_{2(0P',2P^{-})}\bigg)\nonumber\\
&&+\frac{1}{m_{c}}\bigg(-f_{3(1P'^{-},0P)}+f_{4(1P'^{-},0P)}\bigg)+\frac{1}{m^{2}_{c}}\bigg(F_{(2P'^{+},0P)}-f_{3(2P'^{-},0P)}+f_{4(2P'^{-},0P)}\bigg)\nonumber\\
&&+\frac{1}{m_{b}m_{c}}\bigg(-2f_{5(1P'^{-},1P'^{-})}-(1+2\omega)f_{7(1P'^{-},1P'^{-})}\bigg)\bigg],\label{34}
\end{eqnarray}
\begin{eqnarray}
&&F_{2}(\omega)=-i\bigg[\frac{2}{m_{c}}f_{3(1P'^{-},0P)}+\frac{2}{m^{2}_{c}}f_{3(2P'^{-},0P)}+\frac{2}{m_{b}m_{c}}\bigg(f_{3(1P'^{-},1P^{+})}+f_{7(1P'^{-},1P^{-})}\bigg)\bigg],\label{35}\\
&&F_{3}(\omega)=-i\bigg[\frac{2}{m_{b}}f_{2(0P',1P^{-})}+\frac{2}{m^{2}_{b}}f_{2(0P',2P^{-})}+\frac{2}{m_{b}m_{c}}\bigg(f_{2(1P'^{+},1P^{-})}+f_{7(1P'^{-},1P^{-})}\bigg)\bigg],\label{36}
\end{eqnarray}
\begin{eqnarray}
&&G_{1}(\omega)\nonumber\\
&&=-i\bigg[F_{(0P',0P)}+\frac{1}{m_{b}}\bigg(f_{1(0P',1P^{-})}+f_{2(0P',1P^{-})}\bigg)+\frac{1}{m^{2}_{b}}\bigg(F_{(0P',2P^{+})}+f_{1(0P',2P^{-})}+f_{2(0P',2P^{-})}\bigg)\nonumber\\
&&+\frac{1}{m_{c}}\bigg(f_{3(1P'^{-},0P)}+f_{4(1P'^{-},0P)}\bigg)+\frac{1}{m^{2}_{c}}\bigg(F_{(2P'^{+},0P)}+f_{3(2P'^{-},0P)}+f_{4(2P'^{-},0P)}\bigg)\nonumber\\
&&+\frac{1}{m_{b}m_{c}}\bigg(2f_{5(1P'^{-},1P'^{-})}-(1-2\omega)f_{7(1P'^{-},1P'^{-})}\bigg)\bigg],\label{37}
\end{eqnarray}
\begin{eqnarray}
&&G_{2}(\omega)=-i\bigg[\frac{2}{m_{c}}f_{3(1P'^{-},0P)}+\frac{2}{m^{2}_{c}}f_{3(2P'^{-},0P)}+\frac{2}{m_{b}m_{c}}\bigg(f_{3(1P'^{-},1P^{+})}+f_{7(1P'^{-},1P^{-})}\bigg)\bigg],\label{38}\\
&&G_{3}(\omega)=i\bigg[\frac{2}{m_{b}}f_{2(0P',1P^{-})}+\frac{2}{m^{2}_{b}}f_{2(0P',2P^{-})}+\frac{2}{m_{b}m_{c}}\bigg(f_{2(1P'^{+},1P^{-})}-f_{7(1P'^{-},1P^{-})}\bigg)\bigg],\label{39}
\end{eqnarray}
\noindent where the superscripts "$\pm$" of $P$ or $P'$ correspond to $\phi^{(\pm)}_{1,2P}$ or $\phi^{(\pm)}_{1,2P'}$.
We assume that in the weak transition of $\Lambda_{b}\rightarrow\Lambda_{c}$ the diquark behaves as a spectator, so the four momenta of the diquarks in the initial and final baryons are the same, that is,
\begin{eqnarray}
p_{2}=p'_{2}.\label{40}
\end{eqnarray}
Substituting $p_{2}=p-\lambda_{2}m_{\Lambda_{Q}}v$,~$p=p_{t}+(v\cdot p)v$ and $v\cdot p=p_{l}+\lambda_{2}m_{\Lambda_{Q}}$ into Eq.~(\ref{40}), we get
\begin{eqnarray}
p_{t}+p_{l}v=p'_{t}+p'_{l}v'.\label{41}
\end{eqnarray}
Defining ~$v'_{t}=v'-(v\cdot v')v=v'-\omega v$ and $\theta$ be the angular between $p_{t}$ and $v'_{t}$, we have
\begin{eqnarray}
&&p_{t}\cdot v'_{t}=-|p_{t}||v'_{t}|\cos\theta=-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta,\label{42}\\
&&p'_{l}=-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta+p_{l}\omega,\label{43}\\
&&p'_{t}\cdot v=(1-\omega^{2})p_{l}+\omega|p_{t}|\sqrt{\omega^{2}-1}\cos\theta,\label{44}\\
&&p'_{t}\cdot p_{t}=|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta-\omega p_{l}|p_{t}|\sqrt{\omega^{2-1}}\cos\theta,\label{45}\\
&&|p'_{t}|^{2}=|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+p^{2}_{l}(\omega^{2}-1)-2\omega p_{l}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta,\label{46}\\
&&(p'_{l})^{2}-W^{2}_{P'}=p^{2}_{l}-W^{2}_{P}.\label{47}
\end{eqnarray}
Then all $p'_{l}$ and $p'_{t}$ in $F$ and $f_{i}~(i=1-7)$ can be replaced by $p_{l}$ and $p_{t}$. Take $F_{(0P',0P)}$ as an example:
\begin{eqnarray}
&&F_{(0P',0P)}=\int\frac{d^{4}p}{(2\pi)^{4}}\phi_{0P'}(p')\phi_{0P}(p)(p^{2}_{l}-W^{2}_{P})\nonumber\\
&&~~~~~~~~~~~=\int\frac{d^{4}p}{(2\pi)^{4}}\frac{-i}{(p'_{l}+m_{D}+E_{0}+i\varepsilon)(p'^{2}_{l}-W^{2}_{P'}+i\varepsilon)}\int\frac{d^{4}k}{(2\pi)^{4}}\big[V'_{1}(k,p'_{t})+(p'_{l}+k_{l})V'_{2}(k,p'_{t})\big]\phi_{0P'}(k)\nonumber\\
&&~~~~~~~~~~~~~\times\frac{-i}{(p_{l}+m_{D}+E_{0}+i\varepsilon)(p^{2}_{l}-W^{2}_{P}+i\varepsilon)}\int\frac{d^{4}q}{(2\pi)^{4}}\big[V_{1}(q,p_{t})+(p_{l}+q_{l})V_{2}(q,p_{t})\big]\phi_{0P}(q)(p^{2}_{l}-W^{2}_{P})\nonumber\\
&&~~~~~~~~~~~=\int\frac{d^{4}p}{(2\pi)^{4}}\frac{-1}{(p'_{l}+m_{D}+E_{0}+i\varepsilon)(p_{l}+m_{D}+E_{0}+i\varepsilon)(p^{2}_{l}-W^{2}_{P}+i\varepsilon)}\int\frac{d^{4}k}{(2\pi)^{4}}\big[V'_{1}(k,p'_{t})\nonumber\\
&&~~~~~~~~~~~~~+(p'_{l}+k_{l})V'_{2}(k,p'_{t})\big]\phi_{0P'}(k)\int\frac{d^{4}q}{(2\pi)^{4}}\big[V_{1}(q,p_{t})+(p_{l}+q_{l})V_{2}(q,p_{t})\big]\phi_{0P}(q)\nonumber\\
&&~~~~~~~~~~~=\int\frac{d^4p}{(2\pi)^4}\frac{-1}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta+p_{l}\omega+m_{D}+E_{0}+i\varepsilon)(p_{l}+m_{D}+E_{0}+i\varepsilon)(p^{2}_{l}-W^{2}_{P}+i\varepsilon)}\nonumber\\
&&~~~~~~~~~~~~~\times\int\frac{d^{4}k}{(2\pi)^{4}}\big[V'_{1}(k,p'_{t})+(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta+p_{l}\omega+k_{l})V'_{2}(k,p'_{t})\big]\phi_{0P'}(k)\int\frac{d^{4}q}{(2\pi)^{4}}\big[V_{1}(q,p_{t})\nonumber\\
&&~~~~~~~~~~~~~+(p_{l}+q_{l})V_{2}(q,p_{t})\big]\phi_{0P}(q)|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+p^{2}_{l}(\omega^{2}-1)-2\omega p_{l}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}\nonumber\\
&&~~~~~~~~~~~=\frac{(2\pi i)}{2\pi}\int\frac{d^3p_t}{(2\pi)^3}\frac{-1}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})(-W_{P}+m_{D}+E_{0})(-2W_{P})}\int\frac{d^3k_t}{(2\pi)^3}[\tilde{V}'_1(k_t,p'_t)\nonumber\\
&&~~~~~~~~~~~~+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_2(k_t,p'_t)]\int\frac{dk_l}{2\pi}\phi_{0P'}(k)\int\frac{d^3q_t}{(2\pi)^3}[\tilde{V}_1(q_t,p_t)-2W_p\tilde{V}_2(q_t,p_t)]\nonumber\\
&&~~~~~~~~~~~~\times\int\frac{dq_l}{2\pi}\phi_{0P}(q_l)|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}\nonumber\\
&&~~~~~~~~~~~=\int\frac{d^{3}p_{t}}{(2\pi)^{3}}\frac{-i}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\nonumber\\
&&~~~~~~~~~~~~~-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})\big]\tilde{\phi}_{0P'}(k_{t})\frac{1}{(-W_P+m_D+E_0)(-2W_P)}\int\frac{d^3q_t}{(2\pi)^3}[\tilde{V}_1(q_t,p_t)-2W_p\tilde{V}_2(q_t,p_t)]\nonumber\\
&&~~~~~~~~~~~~~\times\tilde{\phi}_{0P}(q_t)|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}\nonumber\\
&&~~~~~~~~~~~=\int\frac{d^{3}p_{t}}{(2\pi)^{3}}\frac{-i}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\nonumber\\
&&~~~~~~~~~~~~~-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})\big]\tilde{\phi}_{0P'}(k_{t})\tilde{\phi}_{0P}(p_{t})|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}\nonumber\\
&&~~~~~~~~~~~\equiv\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\tilde{\phi}_{0P}(p_{t}),\label{48}
\end{eqnarray}
\noindent where we have done a contour integration with $p_l=-W_P+i\varepsilon$ as the pole and defined $\tilde{\phi}(q_t)\equiv\int\frac{dq_l}{2\pi}\phi(q)$, and
\begin{eqnarray}
g_{0P'}(p_{t},\cos\theta)&&\equiv\frac{-i}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\-W_{P}\omega)\nonumber\\
&&\times\tilde{V}'_{2}(k_{t},p'_{t})\big]\tilde{\phi}_{0P'}(k_{t})|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}.\label{49}
\end{eqnarray}
In the same way we can also get,
\begin{eqnarray}
&&F_{(0P',2P^{+})}=\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\tilde{\phi}^{+}_{2P}(p_{t}),\label{50}\\
&&F_{(2P'^{+},0P)}=\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{2P'^{+}}(p_{t},\cos\theta)\tilde{\phi}_{0P}(p_{t}),\label{51}\\
&&f_{1(0P',1P^{-})}=-\omega f_{2(0P',1P^{-})},\label{52}\\
&&f_{1(0P',2P^{-})}=-\omega f_{2(0P',2P^{-})},\label{53}\\
&&f_{2(0P',1P^{-})}=\frac{1}{2(1-\omega^{2})}\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\big(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\big)\tilde{\phi}_{0P}(p_{t}),\label{54}\\
&&f_{2(0P',2P^{-})}=\frac{1}{(1-\omega^{2})}\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\big(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\big)\tilde{\phi}^{-}_{2P}(p_{t}),\label{55}\\
&&f_{3(1P'^{-},0P)}=\frac{1}{2(1-\omega^{2})}\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\big[W_{P}(\omega^{2}-1)+|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\big]\tilde{\phi}_{0P}(p_{t}),\label{56}\\
&&f_{3(2P'^{-},0P)}=\frac{1}{(1-\omega^{2})}\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{2P'^{-}}(p_{t},\cos\theta)\big[W_{P}(\omega^{2}-1)+\omega|p_{t}|\sqrt{\omega^{2}-1}\cos\theta\big]\tilde{\phi}_{0P}(p_{t}),\label{57}\\
&&f_{4(1P'^{-},0P)}=-\omega f_{3(1P'^{-},0P)},\label{58}\\
&&f_{4(2P'^{-},0P)}=-\omega f_{3(2P'^{-},0P)},\label{59}\\
&&f_{5(1P'^{-},1P^{-})}=\frac{1}{12}\int\frac{d^{3}p_{t}}{(2\pi)^{3}}g_{0P'}(p_{t},\cos\theta)\big[|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos\theta+W_{P}|p_{t}|\omega\sqrt{\omega^{2}-1}\cos\theta\big]\tilde{\phi}_{0P}(p_{t}),\label{60}\\
&&f_{7(1P'^{-},1P^{-})}=-\frac{1}{\omega}f_{5(1P'^{-},1P^{-})},\label{61}
\end{eqnarray}
\noindent where we have defined
\begin{eqnarray}
&&g_{2P'^{+}}(p_{t},\cos\theta)\nonumber\\ &\equiv&\frac{-i}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})}\bigg\{\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})\big]\tilde{\phi}^{+}_{2P'}(k_{t})\nonumber\\
&&+\frac{1}{2}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big(2p'_{t}\cdot k_{t}-k^{2}_{t}-p'^{2}_{t}\big)\tilde{V}'_{4}(k_{t},p'_{t})\tilde{\phi}_{0P'}(k_{t})+\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{5}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{6}(k_{t},p'_{t})\big]\nonumber\\
&&~\times\tilde{\phi}_{0P'}(k_{t})+\frac{1}{4}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})\big]p'_{t}\cdot k_{t}\tilde{\phi}_{0P'}(k_{t})\nonumber\\
&&+\big(\frac{-p'^{2}_{t}}{4}+\frac{-E_{2}}{(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega+m_{D}+E_{0})}\big)\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\big[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})\big]\nonumber\\
&&~\times\tilde{\phi}_{0P'}(k_{t})\bigg\}|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}},\label{62}\\
&&g_{2P'^{-}}(p_{t},\cos\theta)\nonumber\\
&\equiv&i\frac{1}{4W_{P}}\Bigg[\int\frac{d^{3}k_{t}}{(2\pi)^{3}}[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})]\frac{p'_{t}\cdot k_{t}}{p'_{t}\cdot p'_{t}}\phi^{-}_{1P'}(k_{t})\nonumber\\
&&+\int\frac{d^{3}k_{t}}{(2\pi)^{3}}\bigg(1+\frac{p'_{t}\cdot k_{t}}{p'_{t}\cdot p'_{t}}\bigg)\tilde{V}'_{4}(k_{t},p'_{t})\phi_{0P'}(k_{t})+\frac{1}{2}\int\frac{d^{3}k_{t}}{(2\pi)^{3}}[\tilde{V}'_{1}(k_{t},p'_{t})+2(-|p_{t}|\sqrt{\omega^{2}-1}\cos\theta-W_{P}\omega)\tilde{V}'_{2}(k_{t},p'_{t})]\nonumber\\
&&~\times\phi_{0P'}(k_{t})\Bigg]|_{p'_{t}=\sqrt{|p_{t}|^{2}+|p_{t}|^{2}(\omega^{2}-1)\cos^{2}\theta+W^{2}_{P}(\omega^{2}-1)+2\omega W_{P}|p_{t}|\sqrt{\omega^{2}-1}\cos\theta}}.\label{63}
\end{eqnarray}
The three dimensional integrations in Eqs.~(\ref{48}), (\ref{50})-(\ref{61}) can be reduced to one dimensional integrations by using the following identities:
\begin{eqnarray}
&&\int\frac{d^{3}q_{t}}{(2\pi)^{3}}\frac{\rho(q^{2}_{t})}{[(p_{t}-q_{t})^{2}+\mu^{2}]^{2}}=\int\frac{q^{2}_{t}dq_{t}}{4\pi^{2}}\frac{2\rho(q^{2}_{t})}{(p^{2}_{t}+q^{2}_{t}+\mu^{2})^{2}-4p^{2}_{t}q^{2}_{t}},\label{64}\\
&&\int\frac{d^{3}q_{t}}{(2\pi)^{3}}\frac{\rho(q^{2}_{t})}{(p_{t}-q_{t})+\delta^{2}}=\int\frac{q^{2}_{t}dq_{t}}{4\pi^{2}}\frac{\rho(q^{2}_{t})}{2|p_{t}||q_{t}|}ln\frac{(|p_{t}|+|q_{t}|)^{2}+\delta^{2}}{(|p_{t}|-|q_{t}|)^{2}+\delta^{2}},\label{65}
\end{eqnarray}
\noindent where $\rho(q^{2}_{t})$ is some arbitrary function of $q^{2}_{t}$.
In our model we have several parameters, $\alpha_{seff}$, $\kappa$, $Q^{2}_{0}$, $m_{D}$, $E_{0}$, $E_{1}$ and $E_{2}$. The relationship between $\alpha_{seff}$ and $\kappa$ is independent of the heavy quark mass in the diquark model, hence $\alpha_{seff,\Lambda_{b}}=\alpha_{seff,\Lambda_{c}}$ for the same $\kappa$. As discussed in our previous work, we let $\kappa$ vary between $0.02GeV^{3}$ and $0.08GeV^{3}$. The parameter $Q^{2}_{0}$ can be chosen as $3.2GeV^{2}$ from the data for the electromagnetic form factor of the proton\cite{Ansel1987}. From the BS equation solutions in the meson case, it has been found that the values $m_{b}=5.02GeV$ and $m_{c}=1.58GeV$ give theoretical results which are in good agreement with experiment\cite{Jin1992}. With Eq.~(\ref{14}), It is easy to see that
\begin{eqnarray}
m_{D}+E_{0}+\frac{1}{m_{Q}}E_{1}+\frac{1}{m^{2}_{Q}}E_{2}=0.62GeV,\label{66}
\end{eqnarray}
\noindent if we use $m_{\Lambda_{b}}=5.64GeV$. In order to guarantee that the binding energies $E_{0}$, $E_{1}$ and $E_{2}$ are negative, we assume the minimum value of $m_{D}$ is $650MeV$ and the maximum value of $m_{D}$ is chosen as $800MeV$. One notes that $E_{1}\sim\Lambda_{QCD}E_{0}$, $E_{2}\sim\Lambda_{QCD}E_{1}$, and hence we further assume that $E_{1}=\delta E_{0}$, $E_{2}=\delta E_{1}=\delta^{2}E_{0}$. The value of $m_{D}+E_{0}$ is dependent on $\delta~(0.1-0.4)$. Now with the BS equations to the $1/m^{2}_{Q}$ order in the $1/m_{Q}$ expansion we had in our previous work, we give the numerical results of all the six form factors in Figs.~\ref{fig:14} and \ref{fig:15}.
\begin{figure}[ht!]
\includegraphics[scale=0.55]{650mevsecondorderF1G1.pdf}
\includegraphics[scale=0.55]{800mevsecondorderF1G1.pdf}
\caption{The numerical results for $F_i~(i=1,2,3)$ and $G_1$ for $\kappa=0.02GeV^3$~(solid line) and $\kappa=0.08GeV^3$~(dashed line) to the second order in $\frac{1}{m_Q}$ expansion with $m_D=650Mev$~(left one) and $m_D=800MeV$~(right one). From top to bottom we have $F_1$,~$G_1$,~$F_3$ and $F_2$, respectively.}
\label{fig:14}
\end{figure}
\begin{figure}[ht!]
\includegraphics[scale=0.55]{650mevsecondorderF2F3G2G3.pdf}
\includegraphics[scale=0.55]{800mevsecondorderF2F3G2G3.pdf}
\caption{The numerical results for $F_2$,~$F_3$,~$G_2$ and $G_3$ for $\kappa=0.02GeV^3$~(solid line) and $\kappa=0.08GeV^3$~(dashed line) to the second order in $\frac{1}{m_Q}$ expansion with $m_D=650Mev$~(left one) and $m_D=800MeV$~(right one). From top to bottom we have $G_3$,~$F_3$,~$F_2$ and $G_2$, We can barely figure out $F_2$ from $G_2$ because they are almost the same.}
\label{fig:15}
\end{figure}
\section*{IV. APPLICATIONS TO $\Lambda_{b}\rightarrow\Lambda_{c}l\bar{\nu}$ AND $\Lambda_{b}\rightarrow\Lambda_{c}P(V)$ }
\textbf{A. Semileptonic decay $\Lambda_{b}\rightarrow\Lambda_{c}l\bar{\nu}$}\\
When the mass of the lepton can be neglected, the semileptonic decay form factors of baryons $1/2^{+}\rightarrow1/2^{+}$ can be expressed as following:
\begin{eqnarray}
\langle\Lambda_{2}(P_{2})|J^{V+A}_{\mu}|\Lambda_{1}(P_{1})\rangle=\bar{u}(P_{2})\Big[\gamma_{\mu}(F^{V}_{1}+F^{A}_{1}\gamma_{5})+i\sigma_{\mu\nu}q^{\nu}(F^{V}_{2}+F^{A}_{2}\gamma_{5})\Big]u(P_{1}),\label{67}\nonumber\\
\end{eqnarray}
\noindent where $J^{V}_{\mu}$ and $J^{A}_{\mu}$ represent vector current and axial-vector current, respectively, $u(P_{1,2})$ is the Dirac spinor of $\Lambda_{1,2}$, $q_{\mu}=(P_{1}-P_{2})_{\mu}$ is the four momentum transfer, and form factors $F^{V,A}_{i}(i=1,2)$ are functions of $q^{2}$. The terms containing $q^{\mu}$ do not contribute to the semileptonic decay when $m_{lepton}=0$.
Comparing Eq.(\ref{67}) with Eq.(\ref{1}) and noting that $\Lambda_{1}$ is $\Lambda_{b}$ while $\Lambda_{2}$ is $\Lambda_{c}$, we can get the relationships between $F^{V,A}_{1,2}$ and $F_{i}$, $G_{i} (i=1,2,3)$:
\begin{eqnarray}
&&F^{V}_{1}-(m_{\Lambda_{b}}+m_{\Lambda_{c}})F^{V}_{2}=F_{1},\label{68}\\
&&2m_{\Lambda_{c}}F^{V}_{2}=\frac{m_{\Lambda_{c}}}{m_{\Lambda_{b}}}F_{2}+F_{3},\label{69}\\
&&F^{A}_{1}+(m_{\Lambda_{b}}-m_{\Lambda_{c}})F^{A}_{2}=-G_{1},\label{70}\\
&&2m_{\Lambda_{c}}F^{A}_{2}=-\bigg(\frac{m_{\Lambda_{c}}}{m_{\Lambda_{b}}}G_{2}+G_{3}\bigg).\label{71}
\end{eqnarray}
We have to add QCD corrections into the differential decay width because they are comparable with $\frac{1}{m_{Q}}$ correction. Therefore, the form factors are changed to the following\cite{Korner1992}:
\begin{eqnarray}
F^{QCD}_{1}(\omega)=F_{1}(\omega)-iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}v_{1},\label{72}\\
F^{QCD}_{2}(\omega)=F_{2}(\omega)+iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}v_{2},\label{73}\\
F^{QCD}_{3}(\omega)=F_{3}(\omega)+iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}v_{3},\label{74}\\
G^{QCD}_{1}(\omega)=G_{1}(\omega)-iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}a_{1},\label{75}\\
G^{QCD}_{2}(\omega)=G_{2}(\omega)+iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}a_{2},\label{76}\\
G^{QCD}_{3}(\omega)=G_{3}(\omega)+iF_{(0P',0P)}\frac{\alpha_{s}}{\pi}a_{3},\label{77}
\end{eqnarray}
\noindent where $v_{i}$ and $a_{i}(i=1,2,3)$ are QCD corrections\cite{Neubert1992}.
Now with Eqs.~(\ref{68})-(\ref{77}), $F^{V,A}_{1,2}$ with QCD corrections can be expressed as
\begin{eqnarray}
&&F^{V}_{1}(\omega)=F^{QCD}_{1}(\omega)+\bigg(\frac{1}{2}+\frac{m_{\Lambda_{c}}}{2m_{\Lambda_{b}}}\bigg)F^{QCD}_{2}(\omega)+\bigg(\frac{m_{\Lambda_{b}}}{2m_{\Lambda_{c}}}+\frac{1}{2}\bigg)F^{QCD}_{3}(\omega),\label{78}\\
&&F^{V}_{2}(\omega)=\frac{1}{2m_{\Lambda_{b}}}F^{QCD}_{2}(\omega)+\frac{1}{2m_{\Lambda_{c}}}F^{QCD}_{3}(\omega),\label{79}\\
&&F^{A}_{1}(\omega)=-G^{QCD}_{1}(\omega)+\bigg(\frac{1}{2}-\frac{m_{\Lambda_{c}}}{2m_{\Lambda_{b}}}\bigg)G^{QCD}_{2}(\omega)+\bigg(\frac{m_{\Lambda_{b}}}{2m_{\Lambda_{c}}}-\frac{1}{2}\bigg)G^{QCD}_{3}(\omega),\label{80}\\
&&F^{A}_{2}(\omega)=-\frac{1}{2m_{\Lambda_{b}}}G^{QCD}_{2}(\omega)-\frac{1}{2m_{\Lambda_{c}}}G^{QCD}_{3}(\omega).\label{81}
\end{eqnarray}
$v_i$ and $a_i~(i=1,2,3)$ can be expressed respectively as\cite{Neubert1992}:\\
\begin{eqnarray}
v_{1}&=&\frac{1}{3}\Big(K_{V}+2D^{V}_{1}+2D^{V}_{2}+2(\omega-1)D^{V}_{3}\Big),\label{82}\\
v_{2}&=&\frac{2}{3}D^{V}_{2},\label{83}\\
v_{3}&=&\frac{2}{3}D^{V}_{1},\label{84}\\
a_{1}&=&\frac{1}{3}\Big(K_{A}-2(\omega-1)D^{A}_{3}\Big),\label{85}\\
a_{2}&=&\frac{2}{3}\Big(D^{A}_{2}-2D^{A}_{3}\Big),\label{86}\\
a_{3}&=&-\frac{2}{3}\Big(D^{A}_{1}-2D^{A}_{3}\Big),\label{87}
\end{eqnarray}
\noindent where\\
\begin{eqnarray}
K_{V}&=&-\Big(2\big[\omega r(\omega)-1\big]ln\frac{m_{\Lambda_{b}}m_{\Lambda_{c}}}{\lambda^{2}}+C_{V}(Z,\omega)\Big),\label{88}\\
K_{A}&=&-\Big(2\big[\omega r(\omega)-1\big]ln\frac{m_{\Lambda_{b}}m_{\Lambda_{c}}}{\lambda^{2}}+C_{A}(Z,\omega)\Big),\label{89}\\
D^{V}_{1}&=&\Big(1-\frac{1}{2}Z\Big)r(\omega)-\Big(1+\frac{1}{2}Z\Big)\chi(\omega)-\frac{Z}{1-Z}\phi(\omega),\label{90}\\
D^{V}_{2}&=&\Big(1-\frac{1}{2Z}\Big)r(\omega)-\Big(1+\frac{1}{2Z}\Big)\chi(\omega)-\frac{1}{Z(Z-1)}\phi(\omega),\label{91}\\
D^{V}_{3}&=&-\frac{Z}{(1-Z)^{2}}\phi(\omega),\label{92}\\
D^{A}_{1}&=&\Big(1+\frac{1}{2}Z\Big)r(\omega)-\Big(1-\frac{1}{2}Z\Big)\chi(\omega)+\frac{Z}{1-Z}\phi(\omega),\label{93}\\
D^{A}_{2}&=&\Big(1+\frac{1}{2Z}\Big)r(\omega)-\Big(1-\frac{1}{2Z}\Big)\chi(\omega)+\frac{1}{Z(Z-1)}\phi(\omega),\label{94}\\
D^{A}_{3}&=&\frac{Z}{(1-Z)^{2}}\phi(\omega),\label{95}
\end{eqnarray}
\noindent with the following definitions:\\
\begin{eqnarray}
r(\omega)&=&\frac{1}{\sqrt{\omega^{2}-1}}ln(\omega+\sqrt{\omega^{2}-1}),\label{96}\\
Z&=&\frac{m_{c}}{m_{b}},\label{97}\\
C_{V}(Z,\omega)&=&5+G(\omega)+2H(\omega)-2(2\omega-1)r(\omega)-\frac{3}{2}\Big(\frac{1+Z^{2}}{Z}r(\omega)-\frac{1-Z^{2}}{Z}\chi(\omega)\Big)+\phi(\omega),\label{98}\\
C_{A}(Z,\omega)&=&5+G(\omega)+2H(\omega)-2(2\omega-1)r(\omega)-\frac{1}{2}\Big(\frac{1+Z^{2}}{Z}r(\omega)-\frac{1-Z^{2}}{Z}\chi(\omega)\Big)-\phi(\omega),\label{99}\\
\chi(\omega)&=&\frac{1}{1-2Z\omega+Z^{2}}\Big(2ZlnZ+(1-Z^{2})r(\omega)\Big),\label{100}\\
\phi(\omega)&=&\frac{(1-Z)^{2}}{1-2Z\omega+Z^{2}}\Big(G(\omega)+1-\omega r(\omega)\Big),\label{101}\\
G(\omega)&=&\frac{1}{1-2Z\omega+Z^{2}}\Big((Z^{2}-1)lnZ-2Z(\omega^{2}-1)r(\omega)\Big)-2,\label{102}\\
H(\omega)&=&\omega r(\omega)lnZ+h(\omega)+2-\frac{\omega}{\sqrt{\omega^{2}-1}}\Big[L_{2}(1-Zy_{-})-L_{2}(1-Zy_{+})\Big],\label{103}\\
y_{\pm}&=&\omega\pm\sqrt{\omega^{2}-1},\label{104}\\
L_{2}(x)&=&-\int^{x}_{0}dt\frac{ln(1-t)}{t},\label{105}\\
h(\omega)&=&\frac{\omega}{2\sqrt{\omega^{2}-1}}\Big[L_{2}(1-y^{2}_{-})-L_{2}(1-y^{2}_{+})\Big].\label{106}
\end{eqnarray}
In Ref.~\cite{Korner1992}, K$\ddot{o}$rner and Kr$\ddot{a}$mer regarded the semileptonic decay $\Lambda_1\rightarrow\Lambda_2+l+\nu_l$ as a quasi two-body decay $\Lambda_1\rightarrow\Lambda_2+W_{off-shell}$ followed by the leptonic decay $W_{off-shell}\rightarrow l+\nu_l$. In the zero-lepton-mass approximation only the $J^P=1^+,~1^-$ components of $W_{off-shell}$ participate in the decay~($1^+$ corresponds to axial-vector current while $1^-$ to vector current). They defined helicity amplitudes $H^{V,A}_{\lambda_2~\lambda_W}$ where $\lambda_2$ and $\lambda_W$ are the helicities of the daughter baryon and the $W_{off-shell}$ boson, respectively. They are related to the invariant form factors through\cite{Korner1992}:\\
\begin{eqnarray}
\sqrt{q^{2}}H^{V}_{\frac{1}{2}~0}=\sqrt{Q_{-}}\Big[(M_{1}+M_{2})F^{V}_{1}-q^{2}F^{V}_{2}\Big],\label{107}\\
H^{V}_{\frac{1}{2}~1}=\sqrt{2Q_{-}}\Big[-F^{V}_{1}+(M_{1}+M_{2})F^{V}_{2}\Big],\label{108}\\
\sqrt{q^{2}}H^{A}_{\frac{1}{2}~0}=\sqrt{Q_{+}}\Big[(M_{1}-M_{2})F^{A}_{1}-q^{2}F^{A}_{2}\Big],\label{109}\\
H^{A}_{\frac{1}{2}~1}=\sqrt{2Q_{+}}\Big[-F^{V}_{1}-(M_{1}-M_{2})F^{A}_{2}\Big],\label{110}
\end{eqnarray}
\noindent where $Q_{\pm}=(M_1\pm M_2)^2-q^2$ with $M_1$ and $M_2$ being the masses of $\Lambda_1$ and $\Lambda_2$, respectively. The remaining helicity amplitudes can be obtained with the help of the parity relations:
\begin{eqnarray}
H^{V}_{-\lambda_{2}~-\lambda_{W}}=+H^{V}_{\lambda_{2}~\lambda_{W}},\label{111}\\
H^{A}_{-\lambda_{2}~-\lambda_{W}}=-H^{A}_{\lambda_{2}~\lambda_{W}}.\label{112}
\end{eqnarray}
The differential decay width of the semileptonic decay $\Lambda_b\rightarrow\Lambda_c l\bar{\nu}$ is
\begin{eqnarray}
\frac{d\Gamma}{Adq^{2}}&=&2\cdot\frac{q^{2}p}{48m^{2}_{\Lambda_{b}}}\bigg(|H^{V}_{\frac{1}{2}~1}+H^{A}_{\frac{1}{2}~1}|^{2}+|H^{V}_{-\frac{1}{2}~-1}+H^{A}_{-\frac{1}{2}~-1}|^{2}\nonumber\\
&&~~~~~~~~~+|H^{V}_{\frac{1}{2}~0}+H^{A}_{\frac{1}{2}~0}|^{2}+|H^{V}_{-\frac{1}{2}~0}+H^{A}_{-\frac{1}{2}~0}|^{2}\bigg),\label{113}
\end{eqnarray}
\noindent where $p$ is the norm of the three dimensional momentum of daughter $\Lambda_c$. $p$ and $A$ can be expressed as:
\begin{eqnarray}
&&p=\frac{\sqrt{m^{4}_{\Lambda_{b}}+m^{4}_{\Lambda_{c}}+q^{4}-2m^{2}_{\Lambda_{b}}m^{2}_{\Lambda_{c}}-2m^{2}_{\Lambda_{b}}q^{2}-2m^{2}_{\Lambda_{c}}q^{2}}}{2m_{\Lambda_{b}}}\nonumber\\
&&~~~=m_{\Lambda_{c}}\sqrt{\omega^{2}-1},\label{114}\\
&&A=\frac{G^{2}_{F}}{(2\pi)^{3}}|V_{cb}|^{2}B(\Lambda_{c}\rightarrow ab),\label{115}
\end{eqnarray}
\noindent where $V_{cb}$ is the Cabibbo-Kobayashi-Maskawa matrix element and $B(\Lambda_c\rightarrow ab)$ is two-body decay branching ratio of $\Lambda_c\rightarrow ab$.
With the help of $dq^{2}=2m_{\Lambda_{b}}m_{\Lambda_{c}}d\omega$, one can get the differential decay width in terms of $\omega$:
\begin{eqnarray}
\frac{d\Gamma}{Ad\omega}&=&\frac{m^{2}_{\Lambda_{c}}\sqrt{\omega^{2}-1}q^{2}}{12m_{\Lambda_{b}}}\bigg(|H^{V}_{\frac{1}{2}~1}+H^{A}_{\frac{1}{2}~1}|^{2}+|H^{V}_{-\frac{1}{2}~-1}+H^{A}_{-\frac{1}{2}~-1}|^{2}\nonumber\\
&&~~~~~~~~~+|H^{V}_{\frac{1}{2}~0}+H^{A}_{\frac{1}{2}~0}|^{2}+|H^{V}_{-\frac{1}{2}~0}+H^{A}_{-\frac{1}{2}~0}|^{2}\bigg)\nonumber\\
&=&\frac{m^{2}_{\Lambda_{c}}\sqrt{\omega^{2}-1}q^{2}}{6m_{\Lambda_{b}}}\bigg(|H^{V}_{\frac{1}{2}~1}|^{2}+|H^{A}_{\frac{1}{2}~1}|^{2}+|H^{V}_{\frac{1}{2}~0}|^{2}+|H^{A}_{\frac{1}{2}~0}|^{2}\bigg).\label{116}
\end{eqnarray}
With Eqs.~(\ref{107})-(\ref{110}), one can immediately get
\begin{eqnarray}
&&\sum|H|^{2}\nonumber\\
&=&\bigg(|H^{V}_{\frac{1}{2}~1}|^{2}+|H^{A}_{\frac{1}{2}~1}|^{2}+|H^{V}_{\frac{1}{2}~0}|^{2}+|H^{A}_{\frac{1}{2}~0}|^{2}\bigg)\nonumber\\
&=&2m_{\Lambda_{b}}m_{\Lambda_{c}}\Bigg\{\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)(-F^{2}_{(0P',0P)})\nonumber\\
&&~~~~+\frac{1}{m_{b}}\Bigg[-2\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})F_{(0P',0P)}\nonumber\\
&&~~~~~~~~~~+12\eta^{-1}(\omega-\eta)f_{2(0P',1P^{-})}F_{(0P',0P)}\Bigg]\nonumber\\
&&~~~~+\frac{1}{m_{c}}\Bigg[-2\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})F_{(0P',0P)}\nonumber\\
&&~~~~~~~~~~+12(\omega\eta-1)f_{3(1P'^{-},0P)}F_{(0P',0P)}\Bigg]\nonumber\\
&&~~~~+\frac{1}{m^{2}_{b}}\Bigg[-\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)\Big(f^{2}_{1(0P',1P^{-})}+\eta^{-2}f^{2}_{2(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+2\eta^{-1}f_{1(0P',1P^{-})}f_{2(0P',1P^{-})}+2(F_{(0P',2P^{+})}+f_{1(0P',2P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})\nonumber\\
&&~~~~~~~~~~\times F_{(0P',0P)}\Big)-\eta^{-2}\Big(2\omega(3+\eta^{2}-2\omega\eta+2\eta^{2})-8\eta\Big)f^{2}_{2(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+12\eta(\omega-\eta)(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})f_{2(0P',1P^{-})}\Bigg]\nonumber\\
&&~~~~+\frac{1}{m^{2}_{c}}\Bigg[-\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)\Big(f^{2}_{4(1P'^{-},0P)}+\eta^{2}f_{3(1P'^{-},0P)}\nonumber\\
&&~~~~~~~~~~+2\eta f_{4(1P'^{-},0P)}f_{3(1P'^{-},0P)}+2(F_{(2P'^{+},0P)}+f_{4(2P'^{-},0P)}+\eta f_{3(2P'^{-},0P)})\nonumber\\
&&~~~~~~~~~~\times F_{(0P',0P)}\Big)-\Big(2\omega(3+\eta^{2}-2\omega\eta+2\eta^{2})-8\eta\Big)f^{2}_{3(1P'^{-},0P)}\nonumber\\
&&~~~~~~~~~~+12(\omega-\eta)(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})f_{3(1P'^{-},0P)}\Bigg]\nonumber\\
&&~~~~+\frac{1}{m_{b}m_{c}}\Bigg[-2\eta\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)f_{7(1P'^{-},1P^{-})}F_{(0P',0P)}\nonumber\\
&&~~~~~~~~~~-2\bigg(\frac{4\omega\eta-2\eta^{2}-2}{1+\eta^{2}-2\eta\omega}-4\bigg)(1+\eta^{-1})f_{7(1P'^{-},1P^{-})}F_{(0P',0P)}\nonumber\\
&&~~~~~~~~~~-2\bigg(\frac{2\omega+2\omega\eta^{2}-4\eta}{1+\eta^{2}-2\omega\eta}+4\omega\bigg)\big(f_{1(0P',1P^{-})}f_{4(1P'^{-},0P)}+\eta f_{1(0P',1P^{-})}f_{3(1P'^{-},0P)}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})}f_{4(1P'^{-},0P)}+f_{2(0P',1P^{-})}f_{3(1P'^{-},0P)}\big)\nonumber\\ &&~~~~~~~~~~+2\eta^{-1}\Big(2(3+\eta^{2}-2\omega\eta+2\eta^{2})-8\omega\eta\Big)f_{3(1P'^{-},0P)}f_{2(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+12(\omega\eta-1)(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})f_{3(1P'^{-},0P)}+12\eta^{-1}(\omega-\eta)\nonumber\\
&&~~~~~~~~~~\times(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})f_{2(0P',1P^{-})}\Bigg]\nonumber
\end{eqnarray}
\begin{eqnarray}
&&~~~~+\frac{\alpha_{s}}{\pi}v_{1}(\omega-1)F_{(0P',0P)}\Bigg[-2\bigg(\frac{(1+\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)+6(1+\eta)\big(\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\big)\Bigg]\nonumber\\
&&~~~~+\frac{\alpha_{s}}{\pi}v_{2}(\omega-1)F_{(0P',0P)}\Bigg[2\bigg(\frac{(1+\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big(\frac{1+\eta}{2}\Big)-6(1+\eta)\nonumber\\ &&~~~~~~~~~~\times\Big[\eta^{-1}\frac{1}{m_{b}}\big(\frac{1+\eta}{2}\big)f_{2(0P',1P^{-})}+\frac{1}{m_{c}}\big(\frac{1+\eta}{2}\big)f_{3(1P'^{-},0P)}+\frac{1}{2}\Big(F_{(0P',0P)}\nonumber\\ &&~~~~~~~~~~+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big]\nonumber\\
&&~~~~~~~~~~+\big(1+\eta^{2}-2\omega\eta+2(1+\eta)^{2}\big)\Big(\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}+\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\Big)\Bigg]\nonumber\\
&&~~~~+\frac{\alpha_{s}}{\pi}v_{3}(\omega-1)F_{(0P',0P)}\Bigg[2\bigg(\frac{(1+\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big(\frac{1+\eta}{2\eta}\Big)-6(1+\eta)\nonumber\\ &&~~~~~~~~~~\times\Big[\eta^{-1}\frac{1}{m_{b}}\big(\frac{1+\eta}{2\eta}\big)f_{2(0P',1P^{-})}+\frac{1}{m_{c}}\big(\frac{1+\eta}{2\eta}\big)f_{3(1P'^{-},0P)}+\frac{\eta^{-1}}{2}\Big(F_{(0P',0P)}\nonumber\\ &&~~~~~~~~~~+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big]\nonumber\\
&&~~~~~~~~~~+\big(1+\eta^{2}-2\omega\eta+2(1+\eta)^{2}\big)\Big(\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}+\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\Big)\Bigg]\nonumber\\
&&~~~~+\frac{\alpha_{s}}{\pi}a_{1}(\omega+1)F_{(0P',0P)}\Bigg[-2\bigg(\frac{(1-\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)+6(1-\eta)\big(\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~-\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\big)\Bigg]\nonumber\\
&&~~~~+\frac{\alpha_{s}}{\pi}a_{2}(\omega+1)F_{(0P',0P)}\Bigg[2\bigg(\frac{(1-\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big(\frac{\eta-1}{2}\Big)-6(\eta-1)\nonumber\\ &&~~~~~~~~~~\times\Big[\eta^{-1}\frac{1}{m_{b}}\big(\frac{1-\eta}{2}\big)f_{2(0P',1P^{-})}-\frac{1}{m_{c}}\big(\frac{1-\eta}{2}\big)f_{3(1P'^{-},0P)}+\frac{1}{2}\Big(F_{(0P',0P)}\nonumber\\ &&~~~~~~~~~~+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big]\nonumber
\end{eqnarray}
\begin{eqnarray}
&&~~~~~~~~~~+\big(1+\eta^{2}-2\omega\eta+2(1-\eta)^{2}\big)\Big(-\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}+\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\Big)\Bigg]\nonumber\\
&&~~~~+\frac{\alpha_{s}}{\pi}a_{3}(\omega+1)F_{(0P',0P)}\Bigg[2\bigg(\frac{(1-\eta)^{2}}{1+\eta^{2}-2\omega\eta}+2\bigg)\Big(F_{(0P',0P)}+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}\nonumber\\
&&~~~~~~~~~~+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big(\frac{\eta-1}{2\eta}\Big)-6(\eta-1)\nonumber\\ &&~~~~~~~~~~\times\Big[\eta^{-1}\frac{1}{m_{b}}\big(\frac{1-\eta}{2\eta}\big)f_{2(0P',1P^{-})}-\frac{1}{m_{c}}\big(\frac{1-\eta}{2\eta}\big)f_{3(1P'^{-},0P)}+\frac{\eta^{-1}}{2}\Big(F_{(0P',0P)}\nonumber\\ &&~~~~~~~~~~+\frac{1}{m_{b}}(f_{1(0P',1P^{-})}+\eta^{-1}f_{2(0P',1P^{-})})+\frac{1}{m_{c}}(f_{4(1P'^{-},0P)}+\eta f_{3(1P'^{-},0P)})\Big)\Big]\nonumber\\
&&~~~~~~~~~~+\big(1+\eta^{2}-2\omega\eta+2(1-\eta)^{2}\big)\Big(\eta^{-1}\frac{1}{m_{b}}f_{2(0P',1P^{-})}+\frac{1}{m_{c}}f_{3(1P'^{-},0P)}\Big)\Bigg]\Bigg\}\label{284}\nonumber\\
&&~~~~+O\Big(\frac{1}{m^{3}_{Q}}\Big)+O\Big(\alpha^{2}_{s}\Big)+O\Big(\frac{\alpha_{s}}{m^{2}_{Q}}\Big),\label{117}\nonumber\\
\end{eqnarray}
\noindent where $\eta=m_{\Lambda_c}/m_{\Lambda_b}$.
By using the numerical results of form factors we get in Section III, and substituting Eqs. (\ref{82})-(\ref{106}) and (\ref{117}) into Eq. (\ref{116}), one can get the plots for $\frac{d\Gamma}{Ad\omega}$ shown in Fig. \ref{fig:4} for $m_D=0.65GeV$ and $m_D=0.8GeV$, where we also show explicitly the effects of $1/m_Q$, $1/m^2_Q$ and $QCD$ corrections. For other values of $m_D$ the results change only a little.
\begin{figure}[!ht]
\includegraphics[scale=0.55]{dgamma650mev.pdf}
\includegraphics[scale=0.55]{dgamma800mev.pdf}
\caption{The numerical results for $A^{-1}(d\Gamma/d\omega)$ for $\kappa=0.02GeV^3$~(solid lines) and $\kappa=0.08GeV^3$~(dot-dashed lines) with $m_{D}=0.65GeV$~(left one) and $m_D=0.8GeV$~(right one). From top to bottom we have the predictions without $1/m_Q$ and $QCD$ corrections, with $1/m_Q$ corrections, with $1/m_Q+1/m^2_Q$ corrections, with $1/m_Q$ and $QCD$ corrections, and with $1/m_Q+1/m^2_Q$ and $QCD$ corrections, respectively.}
\label{fig:4}
\end{figure}
We have the total decay width for $\Lambda_b\rightarrow\Lambda_c l\bar{\nu}$ after integrating over $\omega$. The numerical results are shown in Table \ref{tab:1} for $m_D=0.65GeV$ and $m_D=0.8GeV$, and for $\kappa=0.02GeV^3$~($\kappa=0.08GeV^3$). $\Gamma_0$, $\Gamma_{1/m_Q}$, $\Gamma_{1/m_Q+1/m^2_Q}$, $\Gamma_{1/m_Q+QCD}$ and $\Gamma_{1/m_Q+1/m^2_Q+QCD}$ are the decay widths without $1/m_Q$ and $QCD$ corrections, with $1/m_Q$ corrections, with $1/m_Q+1/m^2_Q$ corrections, with $1/m_Q$ and $QCD$ corrections, and with $1/m_Q+1/m^2_Q$ and $QCD$ corrections, respectively.
\begin{table}
\begin{center}
\caption{Predictions for the decay widths for $\Lambda_{b}\rightarrow\Lambda_{c}l\bar{\nu}$ in units $10^{10}s^{-1}B(\Lambda_c\rightarrow ab)$ for $V_{cb}=0.0398/0.042$\cite{PDG14}.}
\begin{tabular}{|c|c c c|}\hline
$m_{D}(GeV)$ & $\Gamma_{0}$ & $\Gamma_{1/m_{Q}}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}}$ \\ \hline
$0.65$ & $3.74/4.17(5.39/6.01)$ & $3.35/3.72(4.92/5.47)$ & $3.15/3.49(4.65/5.18)$ \\
\hline $0.80$ & $4.34/4.78(5.18/5.76.)$ &
$3.87/4.36(4.76/5.28)$ & $3.66/4.08(4.59/5.09)$ \\
\hline $m_{D}(GeV)$ & $\Gamma_{1/m_{Q}+QCD}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}+QCD}$ & \\
\hline $0.65$ & $2.41/2.68(3.58/3.98)$ & $2.15/2.46(3.28/3.65)$ & \\
\hline $0.80$ & $2.79/3.06(3.46/3.84)$ & $2.48/2.88(3.24/3.60)$ & \\
\hline
\end{tabular}\label{tab:1}
\end{center}
\end{table}
From Figure \ref{fig:4}, it is clear to see that $1/m_Q$ corrections, $1/m^2_Q$ corrections and $QCD$ corrections all reduce the differential decay width. From Table \ref{tab:1} it is easy to see that the decay width of $\Lambda_b\rightarrow\Lambda_c l\bar{\nu}$ is $(2.15\sim3.60)\times10^{10}s^{-1}B(\Lambda_c\rightarrow ab)$ after taking $1/m_Q$ corrections, $1/m^2_Q$ corrections and $QCD$ corrections into account. This result agrees with the experimental result $(2.5\sim5.1)\times10^{10}s^{-1}B(\Lambda_c\rightarrow ab)$\cite{DELPHI2004}.\\
\textbf{B. Nonleptonic decays $\Lambda_{b}\rightarrow\Lambda_{c}P(V)$}\\
The Hamiltonian describing nonleptonic decays $\Lambda_b\rightarrow\Lambda_cP(V)$~($P$ and $V$ stand for pesudoscalar and vector mesons, respectively) reads\cite{Buchalla1996}
\begin{eqnarray}
H_{eff}=\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}(a_{1}O_{1}+a_{2}O_{2}),\label{118}
\end{eqnarray}
\noindent with $O_1=(\bar{D}U)(\bar{c}b)$ and $O_2=(\bar{c}U)(\bar{D}b)$, where $U$ and $D$ are the field operators for light quarks involved in the decay, and $(\bar{q}_1q_2)=\bar{q}_1\gamma_{\mu}(1-\gamma_5)q_2$ is understood. The parameters $a_1$ and $a_2$ in Eq. (\ref{118}) are defined as $a_1=c_1+c_2/N_c$, $a_2=c_2+c_1/N_c$, where $c_1$ and $c_2$ are Wilson coefficients, and $N_c$ is the effective color number factor caused by Fiertz transformation. $N_c$ does not equal to 3 in general because of the part that can not be factorized. Therefore, $a_1$ and $a_2$ are treated as free parameters to be determined by experiments. Since $\Lambda_b$ decays are energetic, the factorization assumption is applied so that one of the currents in the Hamiltonian (\ref{118}) is factorized out and generates a meson $P(V)$\cite{Bjorken1989}\cite{Dugan1991}. Thus the decay amplitude of the two body nonleptonic decay becomes the product of two matrix elements, one is related to the decay constant of the factorized meson ($P$ or $V$) and the other is the weak transition matrix element between $\Lambda_b$ and $\Lambda_c$,
\begin{eqnarray}
M^{fac}(\Lambda_{b}\rightarrow\Lambda_{c}P)=\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}<P|A_{\mu}|0><\Lambda_{c}(P')|J^{\mu}|\Lambda_{b}(p)>,\label{119}\\
M^{fac}(\Lambda_{b}\rightarrow\Lambda_{c}P)=\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}<V|V_{\mu}|0><\Lambda_{c}(P')|J^{\mu}|\Lambda_{b}(p)>,\label{120}
\end{eqnarray}
\noindent where $<0|A_{\mu}|P>$ and ~$<0|V_{\mu}|V>$ are related to the decay constants of the pseudoscalar meson or the vector meson respectively by
\begin{eqnarray}
<0|A_{\mu}|P>=if_{P}q_{\mu},\label{121}\\
<0|V_{\mu}|V>=f_{V}m_{V}\epsilon_{\mu},\label{122}
\end{eqnarray}
\noindent where $q_{\mu}$ is the momentum of the meson emitted from the
$W$-boson and $\epsilon_{\mu}$ is the polarization vector of the emitted
vector meson. It is noted that in the two-body nonleptonic
weak decays $\Lambda_b\rightarrow\Lambda_cP(V)$ there is no contribution from the
$a_2$ term since such a term corresponds to the transition of $\Lambda_b$
to a light baryon instead of $\Lambda_c$.
The general form for the amplitude of $\Lambda_b\rightarrow\Lambda_cP(V)$ are
\begin{eqnarray}
M(\Lambda_{b}\rightarrow\Lambda_{c}P)&=&i\bar{u}_{\Lambda_{c}}(P')(A+B\gamma_{5})u_{\Lambda_{b}}(P),\label{123}\\
M(\Lambda_{b}\rightarrow\Lambda_{c}V)&=&\bar{u}_{\Lambda_{c}}(P')\epsilon^{*\mu}(A_{1}\gamma_{\mu}\gamma_{5}+A_{2}P'_{\mu}\gamma_{5}+B_{1}\gamma_{\mu}+B_{2}P'_{\mu})u_{\Lambda_{b}}(P).\label{124}
\end{eqnarray}
On the other hand, the matrix element for $\Lambda_b\rightarrow\Lambda_c$ can be expressed by using Lorentz invariance
\begin{eqnarray}
<\Lambda_{c}(P')|J^{\mu}|\Lambda_{b}(p)>&=&\bar{u}_{\Lambda_{c}}\Big[f_{1}(q^{2})\gamma_{\mu}+if_{2}(q^{2})\sigma_{\mu\nu}q^{\nu}+f_{3}(q^{2})q_{\mu}\nonumber\\
&&-\big(g_{1}(q^{2})\gamma_{\mu}+ig_{2}(q^{2})\sigma_{\mu\nu}q^{\nu}+g_{3}(q^{2})q_{\mu}\big)\gamma_{5}\Big],\label{125}
\end{eqnarray}
\noindent where $f_i$, $g_i~(i=1,2,3)$ are Lorentz scalars. The relations between $f_i$, $g_i$ and form factors $F_i$, $G_i$ in Eq.~(\ref{1}) are
\begin{eqnarray}
f_{1}&=&F_{1}+\frac{1}{2}(m_{\Lambda_{b}}+m_{\Lambda_{c}})\bigg(\frac{F_{2}}{m_{\Lambda_{b}}}+\frac{F_{3}}{m_{\Lambda_{c}}}\bigg),\label{126}\\
f_{2}&=&\frac{1}{2}\bigg(\frac{F_{2}}{m_{\Lambda_{b}}}+\frac{F_{3}}{m_{\Lambda_{c}}}\bigg),\label{127}\\
f_{3}&=&\frac{1}{2}\bigg(\frac{F_{2}}{m_{\Lambda_{b}}}-\frac{F_{3}}{m_{\Lambda_{c}}}\bigg),\label{128}\\
g_{1}&=&G_{1}-\frac{1}{2}(m_{\Lambda_{b}}-m_{\Lambda_{c}})\bigg(\frac{G_{2}}{m_{\Lambda_{b}}}+\frac{G_{3}}{m_{\Lambda_{c}}}\bigg),\label{129}\\
g_{2}&=&\frac{1}{2}\bigg(\frac{G_{2}}{m_{\Lambda_{b}}}+\frac{G_{3}}{m_{\Lambda_{c}}}\bigg),\label{130}\\
g_{3}&=&\frac{1}{2}\bigg(\frac{G_{2}}{m_{\Lambda_{b}}}-\frac{G_{3}}{m_{\Lambda_{c}}}\bigg).\label{131}
\end{eqnarray}
The decay width for $\Lambda_b\rightarrow\Lambda_cP$ is \cite{Cheng1992}\cite{Pakvasa1990}
\begin{eqnarray}
\Gamma(\Lambda_{b}\rightarrow\Lambda_{c}P)=\frac{|\overrightarrow{P}'|}{8\pi}\Bigg[\frac{(m_{\Lambda_{b}}+m_{\Lambda_{c}})^{2}-m^{2}_{P}}{m^{2}_{\Lambda_{b}}}|A|^{2}+\frac{(m_{\Lambda_{b}}-m_{\Lambda_{c}})^{2}-m^{2}_{P}}{m^{2}_{\Lambda_{b}}}|B|^{2}\Bigg],\label{132}
\end{eqnarray}
\noindent where $A$ and $B$ are related to the form factors by
\begin{eqnarray}
A&=&\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{P}\big[(m_{\Lambda_{b}}-m_{\Lambda_{c}})f_{1}+m^{2}_{P}f_{3}\big],\label{133}\\
B&=&\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{P}\big[(m_{\Lambda_{b}}+m_{\Lambda_{c}})g_{1}-m^{2}_{P}g_{3}\big].\label{134}
\end{eqnarray}
The decay width for $\Lambda_b\rightarrow\Lambda_cV$ is \cite{Cheng1992}\cite{Pakvasa1990}
\begin{eqnarray}
\Gamma(\Lambda_{b}\rightarrow\Lambda_{c}V)=\frac{|\overrightarrow{P}'|}{8\pi}\frac{E_{\Lambda_{c}}+m_{\Lambda_{c}}}{m_{\Lambda_{b}}}\Bigg[2(|S|^{2}+|P_{2}|^{2})+\frac{E^{2}_{V}}{m^{2}_{V}}(|S+D|^{2}+|P_{1}|^{2})\Bigg],\label{135}
\end{eqnarray}
\noindent where
\begin{eqnarray}
S&=&-A_{1},\label{136}\\
D&=&-\frac{|\overrightarrow{P}'|^{2}}{E_{V}(E_{\Lambda_{c}}+m_{\Lambda_{c}})}(A_{1}-m_{\Lambda_{b}}A_{2}),\label{137}\\
P_{1}&=&-\frac{|\overrightarrow{P}'|^{2}}{E_{V}}\Bigg[\frac{m_{\Lambda_{b}}+m_{\Lambda_{c}}}{E_{\Lambda_{c}}+m_{\Lambda_{c}}}B_{1}+m_{\Lambda_{b}}B_{2}\Bigg],\label{138}\\
P_{2}&=&\frac{|\overrightarrow{P}'|}{E_{\Lambda_{c}}+m_{\Lambda_{c}}}B_{1},\label{139}
\end{eqnarray}
with
\begin{eqnarray}
A_{1}&=&-\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{V}m_{V}[g_{1}+g_{2}(m_{\Lambda_{b}}-m_{\Lambda_{c}})],\label{140}\\
A_{2}&=&-2\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{V}m_{V}g_{2},\label{141}\\
B_{1}&=&\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{V}m_{V}[f_{1}-f_{2}(m_{\Lambda_{b}}+m_{\Lambda_{c}})],\label{142}\\
B_{2}&=&2\frac{G_{F}}{\sqrt{2}}V_{cb}V^{*}_{UD}a_{1}f_{V}m_{V}f_{2}.\label{143}
\end{eqnarray}
Then from Eqs. (\ref{126})-(\ref{143}), we obtain the numerical results for $\Lambda_b\rightarrow\Lambda_cP(V)$ decay
widths by using the results for $F_i$ and $G_i~(i=1,2,3)$ at $q^2=m^2_{P,V}$ from BS equations. In
Tables~\ref{tab:2} and~\ref{tab:3} we list the results for $m_D=0.65GeV$ and $m_D=0.8GeV$, respectively. One can see that the results change only a little with $m_D$. The numbers
without (with) brackets correspond to $\kappa=0.02GeV^3~(
\kappa=0.08GeV^3)$. Again, the subscripts "$0$", "$1/m_Q$",
"$1/m_Q+QCD$", "$1/m_Q+1/m^2_Q$" and "$1/m_Q+1/m^2_Q+QCD$" stand for the results without $1/m_Q$, $1/m^2_Q$ and $QCD$
corrections, with $1/m_Q$ corrections, with both $1/m_Q$ and
$QCD$ corrections, with $1/m_Q$ and $1/m^2_Q$ corrections, and with $1/m_Q$, $1/m^2_Q$ and $QCD$ corrections, respectively. In the calculations we have
taken the following decay constants:
\begin{eqnarray}
&&f_{\pi}=132MeV,~~~~f_{D_{s}}=241MeV,~~~~f_{D}=200MeV,~~~~f_{K}=156MeV.\nonumber\\
&&f_{\rho}=216MeV,~~~~f_{K^{*}}=f_{\rho},~~~~f_D=f_{D^{*}},~~~~f_{D_s}=f_{D^{*}_s}.\nonumber
\end{eqnarray}
\begin{table}[ht!]
\begin{center}
\caption{When $m_{D}=650MeV$, the nonleptonic decay widths for ~$\Lambda_{b}\rightarrow\Lambda_{c}P(V)$ for $\kappa=0.02GeV^3$(~$\kappa=0.08GeV^3$), in units ~$10^{10}s^{-1}a^{2}_{1}$, with $V_{cb}=0.0398/0.042$.}
\begin{tabular}{|c|c c c|}\hline
$Process$ & $\Gamma_{0}$ & $\Gamma_{1/m_{Q}}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}}$ \\ \hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\pi^{-}$ & $0.24/0.27(0.45/0.50)$ & $0.28/0.31(0.53/0.58)$ & $0.32/0.35(0.60/0.66)$ \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}_{s}$ & $0.77/0.86(1.20/1.33)$ & $0.88/0.98(1.42/1.59)$ & $0.98/1.09(1.57/1.75)$\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}$ & $0.028/0.032(0.044/0.049)$ & $0.032/0.036(0.055/0.060)$ & $0.035/0.040(0.062/0.068)$\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{-}$ & $0.017/0.019(0.033/0.036)$ &
$0.020/0.022(0.038/0.043)$ & $0.023/0.026(0.042/0.048)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\rho^{-}$ &
$0.32/0.35(0.61/0.67)$ & $0.37/0.41(0.70/0.78)$ & $0.43/0.47(0.81/0.89)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{*-}$ &
$0.017/0.019(0.031/0.035)$ & $0.020/0.022(0.035/0.038)$ & $0.023/0.025(0.038/0.042)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}$ &
$0.021/0.023(0.032/0.036)$ & $0.023/0.026(0.037/0.041)$ &
$0.025/0.028(0.041/0.046)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}_{s}$ & $0.59/0.65(0.95/1.04)$ & $0.68/0.76(1.03/1.15)$ & $0.75/0.84(1.11/1.25)$\\
\hline
$Process$ & $\Gamma_{1/m_{Q}+QCD}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}+QCD}$ & \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\pi^{-}$ & $0.22/0.25(0.43/0.48)$ & $0.26/0.30(0.53/0.59)$ & \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}_{s}$ &
$0.76/0.85(1.21/1.34)$ & $0.90/0.98(1.31/1.46)$\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}$ & $0.027/0.030(0.043/0.048)$ & $0.030/0.034(0.048/0.055)$ &\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{-}$ & $0.016/0.018(0.032/0.035)$ & $0.020/0.022(0.037/0.042)$ &\\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\rho^{-}$ &
$0.30/0.33(0.58/0.65)$ & $0.34/0.38(0.64/0.0.72)$ &\\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{*-}$ &
$0.016/0.018(0.031/0.034)$ & $0.018/0.020(0.033/0.036)$ &\\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}$ &
$0.020/0.022(0.031/0.035)$ & $0.022/0.024(0.036/0.042)$ &\\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}_{s}$ & $0.57/0.64(0.94/1.03)$ & $0.63/0.71(1.01/1.12)$ &\\
\hline
\end{tabular}\label{tab:2}
\end{center}
\end{table}
\begin{table}[ht!]
\begin{center}
\caption{When $m_{D}=800MeV$, the nonleptonic decay widths for ~$\Lambda_{b}\rightarrow\Lambda_{c}P(V)$ for $\kappa=0.02GeV^3$(~$\kappa=0.08GeV^3$), in units ~$10^{10}s^{-1}a^{2}_{1}$, with $V_{cb}=0.0398/0.042$.}
\begin{tabular}{|c|c c c|}\hline
$Process$ & $\Gamma_{0}$ & $\Gamma_{1/m_{Q}}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}}$ \\ \hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\pi^{-}$ & $0.27/0.30(0.50/0.55)$ & $0.31/0.35(0.57/0.64)$ & $0.35/0.39(0.66/0.73)$ \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}_{s}$ & $0.84/0.93(1.28/1.41)$ & $0.96/1.06(1.53/1.74)$ & $1.05/1.17(1.72/1.92)$\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}$ & $0.031/0.035(0.048/0.054)$ & $0.036/0.040(0.060/0.066)$ & $0.039/0.044(0.068/0.074)$\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{-}$ & $0.020/0.022(0.037/0.040)$ &
$0.023/0.025(0.042/0.046)$ & $0.026/0.029(0.046/0.053)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\rho^{-}$ &
$0.36/0.40(0.66/0.73)$ & $0.41/0.46(0.77/0.85)$ & $0.45/0.52(0.86/0.94)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{*-}$ &
$0.019/0.022(0.035/0.040)$ & $0.022/0.025(0.041/0.046)$ & $0.024/0.028(0.046/0.052)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}$ &
$0.023/0.026(0.036/0.039)$ & $0.026/0.029(0.040/0.045)$ & $0.029/0.032(0.044/0.050)$ \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}_{s}$ & $0.65/0.73(1.04/1.15)$ & $0.75/0.84(1.15/1.27)$ & $0.84/0.94(1.24/1.38)$ \\
\hline
$Process$ & $\Gamma_{1/m_{Q}+QCD}$ & $\Gamma_{1/m_{Q}+1/m^{2}_{Q}+QCD}$ & \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\pi^{-}$ & $0.25/0.28(0.48/0.53)$ & $0.29/0.34(0.55/0.63)$ & \\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}_{s}$ &
$0.82/0.91(1.27-1.40)$ & $0.95/1.04(1.35/1.51)$ &\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{-}$ & $0.030/0.034(0.047/0.053)$ & $0.034/0.039(0.051/0.058)$ &\\
\hline $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{-}$ & $0.019/0.021(0.035/0.039)$ & $0.022/0.025(0.042/0.047)$ & \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\rho^{-}$ &
$0.34/0.38(0.64/0.71)$ & $0.38/0.44(0.72/0.89)$ &\\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}K^{*-}$ &
$0.018/0.020(0.034/0.038)$ & $0.020/0.023(0.038/0.042)$ & \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}$ &
$0.022/0.025(0.034/0.037)$ & $0.024/0.028(0.037/0.041)$ & \\
\hline
$\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}D^{*-}_{s}$ & $0.63/0.70(1.02/1.14)$ & $0.71/0.79(1.13/1.25)$ & \\
\hline
\end{tabular}\label{tab:3}
\end{center}
\end{table}
From Tables~\ref{tab:2} and~\ref{tab:3}, one can see that $1/m_Q$ and $1/m^2_Q$ corrections enlarge the decay widths while $QCD$ corrections reduce them. Taking $\Lambda^{0}_{b}\rightarrow\Lambda^{+}_{c}\pi^{-}$ as an example, the decay width with $1/m_Q$ corrections is $17\%$ bigger than that without any corrections, and the decay width with $1/m_Q$ and $1/m_Q^2$ corrections is $14\%$ larger than that with just $1/m_Q$ correction. The experimental data for decay width of $\Lambda_b\rightarrow\Lambda_c\pi$ is $(0.14\sim0.69)\times10^{10}s^{-1}$\cite{CDF2007122002}, and the numerical result from our model is $(0.26\sim0.63)\times10^{10}s^{-1}a^2_1$. As we know, $a_1=c_1+c_2/N_c$, $c_1=1.1502$, $c_2=-0.3125$\cite{Deshpande1995}\cite{Fleischer1997}, $N_c=2\sim5$\cite{Guo20072007}\cite{Chen1999}, so that $a_1\sim O(1)$. Our theoretical result matches the experimental data if we take $a\simeq1$. There are not experimental data for other processes. Our predictions for these processes will be tested in the future.
\section*{V. Summary and discussion}
In the present work, we assume that a heavy baryon $\Lambda_Q$ is composed of a heavy quark and a scalar light diquark. Besed on this picture we analyze the $1/m^2_Q$ corrections to the BS equation for $\Lambda_Q$ and apply the results to calculate the six weak decay form factors $F_i$, $G_i~(i=1,2,3)$. We find that they mostly depend on $\kappa$ and depend only a little on the diquark mass, $m_D$. Then we apply the numerical results of these six form factors to calculate the differential and total decay widths for the semileptonic decay $\Lambda_b\rightarrow\Lambda_cl\bar{\nu}$, and the nonleptonic decay widths for $\Lambda_b\rightarrow\Lambda_cP(V)$. Not only $1/m_Q$ and $1/m_Q^2$ corrections, but also $QCD$ corrections are taken into account because the last one is comparable with $1/m_Q$ corrections. One can see that the numerical results for the decay widths mostly depend on $\kappa$. The decay width for $\Lambda_b\rightarrow\Lambda_cl\bar{\nu}$ is ($2.15\sim3.60)\times10^{10}s^{-1}$ when we consider all the corrections mentioned above, and it matches the experimental data, ($2.5\sim5.1)\times10^{10}s^{-1}$. The decay width for $\Lambda_b\rightarrow\Lambda_c\pi$ is $(0.26\sim0.63)\times10^{10}s^{-1}a^2_1$, and it agrees with the experimental data, $(0.14\sim0.69)\times10^{10}s^{-1}$, when the color factor $N_c=2\sim5$, and hence, $a_1\simeq1$. We also give predictions for other processes including $\Lambda_b\rightarrow\Lambda_cD_s^-$, $\Lambda_b\rightarrow\Lambda_cD^-$, $\Lambda_b\rightarrow\Lambda_cK^-$, $\Lambda_b\rightarrow\Lambda_cP^-$, $\Lambda_b\rightarrow\Lambda_cK^{\star-}$, $\Lambda_b\rightarrow\Lambda_cD^{\star-}$, and $\Lambda_b\rightarrow\Lambda_cD_s^{\star-}$. These predictions will be tested in future experiments.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,914 |
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ISBN 978-0-316-41627-6
E3-20190129-JV-NF-ORI
# CONTENTS
Cover
Title Page
Copyright
Dedication
Epigraph
Foreword by Darrell "Condor" Gary
[Prologue
Palm Desert, California, 2018](prologue.xhtml)
[1. Admission Price
Over Southern California, December 1956](chapter001.xhtml)
[2. First Tribe
Texas to Naval Air Station North Island, San Diego, Spring 1957](chapter002.xhtml)
[3. The Navy Way
North Island, June 1958](chapter003.xhtml)
[4. Fight Club
Off San Clemente Island, California, 1959](chapter004.xhtml)
[5. Where Are the Carriers?
Off the Saigon River, South Vietnam, November 3, 1963](chapter005.xhtml)
[6. The Path to Disillusionment
Pearl Harbor, Hawaii, January 1967](chapter006.xhtml)
[7. Yankee Station Education
Yankee Station, off the coast of Vietnam, Early 1968](chapter007.xhtml)
[8. Starting Topgun
Naval Air Station Miramar, California, Fall 1968](chapter008.xhtml)
[9. The Original Bros
Miramar, 1969](chapter009.xhtml)
[10. Secrets of the Tribe
Miramar, 1969](chapter010.xhtml)
[11. Proof of Concept
Miramar, 1969](chapter011.xhtml)
[12. Topgun Goes to War
Yankee Station, Spring 1972](chapter012.xhtml)
[13. The Last Missing Man
Yankee Station, January 1973](chapter013.xhtml)
[14. The Peace That Never Was
Yankee Station, February 1973](chapter014.xhtml)
[15. End of the Third Temple
Tel Nor Air Base, Israel, October 6, 1973](chapter015.xhtml)
[16. Return with Honor
Forty miles off South Vietnam, April 29, 1975](chapter016.xhtml)
17. Topgun and the Tomcat
[18. Black Shoes
Aboard USS _Wichita_ , 1978](chapter018.xhtml)
[19. The Best and the Last
Somewhere in the Indian Ocean, November 1980](chapter019.xhtml)
[20. One More Goodbye
Somewhere in the Pacific, Spring 1982](chapter020.xhtml)
21. Saving Topgun
[22. Will We Have to Lose a War Again?
(or, Back to the Future in an F-35)](chapter022.xhtml)
Photos
Acknowledgments
Glossary of Acronyms and Terms
Topgun Officers in Charge and Commanding Officers
Photo Credits
Newsletters
_For Mary Beth_
**God bless all naval aviators, past, present, and future.**
# FOREWORD
We who served at the Navy Fighter Weapons School are bound together as brothers. It is a fifty-year-old culture of excellence, and an extraordinary aviation legacy. The pilots call it Topgun. Where did it come from? How did I get to be a part of it? How did they?
Our journey is brilliantly portrayed in this book, seen through the eyes of the man whose innovative leadership was based on the enduring principles of our tradition. Dan Pedersen risked his career to accomplish a seemingly impossible task. His success has endured for more than fifty years now.
I first met "Yank" in 1968, when I was assigned as an instructor in Fighter Squadron 121 (VF-121) at Naval Air Station Miramar, California, also known as Fightertown USA. Our job was to transition pilots and naval flight officers into a new fighter aircraft, the F-4 Phantom. Over the course of six months we trained them to fly the Phantom day or night, in any weather, anywhere in the world, from the pitching decks of aircraft carriers.
As a twenty-four-year-old lieutenant with two combat tours to Vietnam, I was in awe of the Navy's fighter community, and the people with whom I served. Dan cut an imposing figure at six feet three inches, with penetrating hazel eyes and a John Wayne swagger that exuded self-confidence, with the ability and experience upon which reputations are built within our tight-knit community. He was the Hollywood image of a fighter pilot, seldom appearing without his Ray-Ban sunglasses.
As the head of the tactics phase of VF-121's curriculum, Dan was disciplined, focused, and demanding of himself and others. He established high standards of performance, constantly reinforcing the mantra that "In combat second best is dead last." Yet he also possessed a good sense of humor, insisted upon leading by personal example, and seldom phrased anything as a question. One exception: Sometimes he would stride up to a student and ask, "Hey there, tiger. Are you ready for this hop?" When Dan was named to start the new fighter aviation schoolhouse, we all knew it was in good hands. General George Patton said it best: "Wars are fought with weapons, but they are won by men." Even in today's environment of geopolitical complexity and the sophistication of the fifth-generation jets and weapon systems, it is still the man in the machine who will bring victory. That human resource is the work product of Topgun.
Topgun's mission was to challenge the status quo. To do that, Dan selected eight young, very junior officers with unique experience, ability, and passion. His vision and leadership gave us direction. His words gave us inspiration: "There is an urgency here beyond anything we have ever done." We were using "Yankee ingenuity," hard work, combat experience, and imagination to fix a problem. Too many of our brothers were dying over Vietnam, and we could make a difference.
Topgun became a culture of excellence that over the past five decades has consistently produced the Navy's most accomplished, innovative, and adaptive warriors as well as the most compassionate and inspirational leaders. The course has expanded from four weeks to twelve and a half. The school is responsible for providing training in air combat maneuvering and weapon systems deployment for Navy and Marine Corps squadrons, advanced predeployment training for fleet units, and the development of new tactics to confront emerging threats. Its founding principles have been carefully guarded and preserved. The extraordinary qualities of leadership demonstrated by each generation have ensured its survival in the face of resource constraints, professional envy, and PC careerists.
When I have the opportunity to meet the young instructors today, I recognize that while we are from different eras with different equipment, the mission remains unchanged: to control the skies over the battlefield and do whatever is necessary to support our forces on the ground or at sea and ensure their survival.
As I reflect on the humble beginnings of this storied institution, I am struck by several facts. None of us among the original nine officers who established Topgun imagined that we would be a part of an aviation legacy that would span five decades, change the course of tactical aviation in the United States and around the world, and influence aircraft and weapon systems design and pilot training.
The current sophistication and capability of the Navy's aircraft and weapons is beyond anything the original nine could have imagined at the time. Today, the complexity of the battlefield and volume of information available to the pilot are nearly overwhelming. What has not changed are the human elements that make Topgun relevant. The school is still run by junior officers. Then, as now, the focus was upon finding individuals who possessed the following traits:
• A passion for the mission, necessary to sustain the individual in an extreme environment.
• Leadership by personal example—a compassionate, inspirational person willing to take responsibility.
• Extraordinary airmanship required to operate in so unforgiving an environment.
• Humility derived from a sense of being part of something much greater than oneself.
• Subject matter expertise that is beyond reproach.
• A work ethic that will drive that person to do whatever it takes for however long it takes to ensure success.
• Personal discipline to endure the rigorous training and attention to detail required to constantly perform at an optimum level.
• Integrity, adaptability, innovation, and a willingness to challenge the status quo.
• Credibility established through demonstrated performance sustained over time.
All of this is refined in the furnace of uncompromising peer review. The extreme selection process and the rigorous training ensure that Topgun's culture of excellence and its legacy will endure.
As I meet the young officers serving on the staff today, it is strongly affirming to see that our legacy and the future of this nation are in such good hands. The brotherhood of Topgun today remains strong.
For the first time, in this book, the story of Topgun's creation and evolution is told by the man who made it happen at the start. Dan is rightly regarded as the "Godfather of Topgun." His book will take its place among the finest combat aviation memoirs of his generation. It deserves the interest of anyone who appreciates high performance and how it is handed down through generations.
_—Darrell "Condor" Gary Topgun's junior Original Bro_
# PROLOGUE
**Palm Desert, California**
**2018**
Though I'm eighty-three years old, I still look up like a kid whenever I hear an airplane passing overhead. Sometimes it'll be a pair of Super Hornets smoking over the desert. Watching them thunder past just under the Mach, I'll get the same electrified thrill I got the first time I lit the afterburner on an F4D Skyray and blasted off North Island's runway to find myself two minutes later at fifty thousand feet.
There is no other rush like it. It is visceral. It fills you with a sense of rapture that only exists out there on the razor's edge.
We flew almost whenever we wanted, and often whatever we wanted. It was all about who you knew. If you wanted a new flying experience after duty hours, there were certain guys, like the Navy chief in maintenance control—the keeper of the keys—who'd give you a wink and send you up for the sheer fun of it. After all, you were a naval aviator.
Sometimes, a World War II F6F Hellcat from the local Palm Springs Air Museum will fly over our house. I'll look up and think, _Yeah. Flew one at North Island_. Beautiful ride, that old tail dragger. The museum also owns a P-51 Mustang that sometimes buzzes by on weekends. Seeing it takes me back to a poker game in Monterey one night. We'd taken a dentist for his last dime, but he wanted to keep playing. He asked for credit. Having heard that he owned a hangar with two P-51s in there, I asked him for a ride. He agreed, and I beat him. Twice. And that's how many times I got to fly that sleek Luftwaffe killer.
When my dad died and I moved my mom up to Port Angeles, Washington, I'd take an F-4 Phantom and cruise north through the Sierra Nevadas and the Cascades, seldom getting above five hundred feet. With nobody in sight, just pristine wilderness, lakes, and rivers, I wound around those mountain peaks, feeling freer and more alive than I ever did on the ground. I'd land at Whidbey Island and spend the weekend with my mom before returning to my command on Sunday afternoon.
We have some helicopters in our area, Jet Rangers and such. Their choppy, eggbeater sound puts me in the cockpit of a Sea King I once flew all the way up the West Coast, tracing the beach, just above the whitecaps, from San Diego to Washington State. Beachcombers, swimmers, kayakers, surfers—they all looked up toward the _thup-thup-thup_ of our rotors. Sometimes I waved back, feeling blessed for such moments, doing something so few ever get to do.
Where else could you do such things but in the Navy?
I don't fly anymore. It's a function of age, not of desire or heart. One of my "Original Bros" at Topgun, seventy-four-year-old Darrell Gary, still straps himself into his own Russian Yak and stunts about the sky. It was the same plane our enemies learned to fly before tangling with us over Vietnam. Darrell formed his own precision aerobatics team with a group of former U.S. pilots and one Brit. "I hate taking time out of my day to eat, sleep, and excrete," Darrell likes to say. "We can sleep when we're dead."
How can you not love that man? We nine Original Bros were cut from that same cloth. Darrell and Mel, Steve, Smash, Ski, Ruff, J. C., and Jimmy Laing. In civilian life, you rarely encounter people of similar temperament, focus, ability, and passion. Maybe it's because only rarely are people thrown together to fight for a failing cause on guts and pride, while surrounded by hostility that pushes you ever closer together.
In the 1960s, America fought in Vietnam with the wrong planes, unreliable weapons, bad tactics, and the wrong senior civilian leadership. A lot of important things were broken. But we loved what we did, and treasured the relationships built in aircraft carrier–ready rooms and bars from North Island to the Philippines. The Navy had given us a home filled with committed, driven men who shared the same passion. When the air war started in earnest, we were tested by months of exhaustion that showed the deeper meaning of our connections.
Operation Rolling Thunder began in 1968. As we flew combat missions, striking Secretary of Defense Robert McNamara's hand-selected targets, we lost planes and men almost every day. Flying from Yankee Station, the area in the Gulf of Tonkin where the aircraft carriers operated, we learned what it was like to sit at a wardroom table surrounded by empty chairs. Half the time we never knew what happened to them. Maybe another pilot noticed an enemy surface-to-air missile launch or caught a fleeting glimpse of a burning American plane heading toward the jungle below. Sometimes we'd hear the aircrew requesting help on the ground, dodging enemy patrols and calling for rescue. When the helicopters went in, the North Vietnamese were often waiting. They shot up the helicopters and their escorting planes. We sometimes got our man and lost three more in the process.
We were flying not just for each other. We were flying for each other's families. The man on your wing usually had a wife, maybe some children. You took care of him to take care of them. We all faced moments where we risked our lives for each other to ensure the contact teams did not knock on our brother's door back in San Diego, Lemoore, or Whidbey Island.
When the enemy scored, the families were devastated. You seldom see that written about. But we've all come home to tell widows and fatherless kids how sorry we were. We gave them what peace we could. The truth is, that loss never goes away. It warps the rest of their lives as they wrestle with the pain. That old adage "Time heals all wounds"? Bull. Fifty years on, I've seen those families still break down in tears as they talk of their fallen aviator.
You don't get over that kind of pain. You just learn to live around it. It becomes part of who you are, and for us out on Yankee Station, that grief motivated us to sacrifice for each other.
Not everyone could hack it. There were days on Yankee Station when I watched aircrews lose their nerve. All of a sudden, some mysterious mechanical issue came up and a flight had to be scrubbed. Sometimes it happened when the plane was on the catapult and ready to launch. They just couldn't bring themselves to face—again—the most fearsome air defense network in the world, erected by the North Vietnamese, with Russian help, around Hanoi. On rare occasions, some men turned in their wings and went home rather than face that crucible again. It was easier to fly for an airline.
Twenty-one different aircraft carriers operated for more than 9,100 total days in the Gulf of Tonkin. In three years, the Navy lost 532 aircraft in combat. Including other operational losses associated with that war, the Navy had 644 aviators killed, missing, or taken prisoner of war. The total fixed-wing aircraft losses of the Navy, Marine Corps, and Air Force together exceeded 2,400. Of course, it was intensely personal. Darrell Gary lived with nine guys in two houses on the beach in La Jolla when he went through training. After their first trip to Yankee Station, six came home.
Worse, we were losing the larger war. Destroying the targets given to us by the Pentagon seemed to make no difference in the war to the south. The losses mounted, and the MiGs started seeking us out. The North Vietnamese possessed a small but well-trained air force, proxied by their Chinese and Soviet allies. As good as it was, they were not in the same league as the Soviet Air Force, so it sent shock waves through the Navy when North Vietnamese pilots started shooting us down. During the Korean War, the North Korean Air Force was virtually wiped out in the opening months. A decade later, the Vietnamese MiGs gave us a real fight. They shot down one of ours for every two MiGs that we claimed. We considered the loss rate intolerable, given our long history of deeply one-sided kill ratios. In World War II, U.S. naval aviators crushed the Japanese in the central Pacific on the way to Tokyo, with Hellcat pilots, who scored three-fourths of the Navy's air-to-air victories, posting a kill ratio on the order of nineteen to one. In Vietnam, we simply were not allowed to win, so the Navy bureaucracy did what bureaucracies do best: It continued on course. Micromanaged from Washington, D.C., we made the same mistakes month after month. It nearly crippled U.S. naval aviation.
In January 1969, a plain-spoken carrier skipper named Frank Ault wrote a report to the chief of naval operations detailing deadly flaws in our fighter tactics and weapons systems. His list of complaints was a long one, and the Navy decided to act. Unfortunately, many in senior commands worried more about their careers than about fixing the problem. By approving the creation of an air combat postgraduate school—which we quickly named Topgun—they gave the appearance of doing something to change things. Under President Johnson's and Secretary McNamara's leadership, the Navy bureaucracy seemed more interested in appearing to solve problems than risking failure by actually trying to solve them. They gave the leadership of Topgun to a relatively junior officer—me.
The eight men who joined me in a condemned trailer at Naval Air Station Miramar in late 1968 had gone into the war thinking we were the best pilots in the world flying the best aircraft armed with the best weapons. The North Vietnamese showed us otherwise. We were ready to do whatever it took to find a way to win.
The community we loved was in crisis, and for whatever reason it fell to us to help find a way forward. As we got started, not a man among us was willing to put his career over doing the right thing. We went to war against conventional thought. We asked questions, sought out answers, chopped red tape. We broke rules. We borrowed, stole, or horse-traded for everything we needed. Ultimately, the Bros created a revolution from nothing but pride and devotion.
I want to tell you about the Bros. I want to tell you about our community, how it was in the years before Vietnam when we frittered away the birthright of victory that our forebears had handed and chose to stake our future on untested technology. I want to tell you about a few of us who kept the legacy alive, flying off the books, in ways that were never discussed in professional spaces, lest the wrong ears hear. Most of all, I want to tell you about the founding days of Topgun and its enduring legacy. It stands as proof that a small group of driven individuals can change the world. We live today in times of great uncertainty with problems that seem unsolvable. The Bros faced that in 1968. Topgun is a reminder that things can be changed.
Along the way, I hope to leave you with an appreciation of the cost. Naval aviation back then wasn't just a job or career; it was a monastic calling. You had to love it more than anything else in your life to stick with it when things went so wrong. That primacy of position in our lives wrought havoc with everything else not connected to our ready rooms. We became outsiders in our own nation, unable to relate even to the people we grew up with back home. Darrell learned this when he attended his high school reunion in Oakland. He had nothing in common with even his oldest friends. Alienated by the experience, he turned around and flew straight back to the brotherhood that had become his home. He never attended another reunion.
It wasn't just old friends we left behind. Our families took a backseat to our flying and our responsibilities as officers. The glamour of marrying a handsome, fit fighter pilot with a bright career ahead soon wore thin as we served at sea and our spouses remained behind. How many women stand for another love in their husband's life? Each night when we were on Yankee Station, the unknown gnawed at them. They feared for their pilots. Our wives never knew when a contact team might appear on the porch. Every time the doorbell rang, they cringed with dread. Late-night phone calls produced a panic. So it had to be. For us, flying always came first.
One night I was aboard ship, ready to take my first ship command, when I got a phone call. Somehow my eight-year-old son had found my direct number. I answered. He was crying. He begged me not to leave.
"Please, Dad. Come back... everyone else has a dad home with them. I don't."
Those words linger. Neither of us ever forgot them.
Every naval aviator had moments like these. It was our reality on the ground. I have one regret in my twenty-nine-year career: It was brutal on my family.
That's the deeper story, beyond the Hollywood portrayal of us. All too often, we are painted with the Val Kilmer "Iceman" stereotype—cool, capable speed addicts who live on the edge for the sheer thrill. We live harder, party harder, womanize harder, and are somehow larger than life.
This book will challenge the stereotype. We are flesh and blood. We live in a dangerous world that whipsaws us from elation to fear in a heartbeat. This brotherhood conceals its emotions to outsiders, so perhaps some of it is our fault. Yet to me, what I saw my brothers achieve out in the fleet is even more remarkable because we are only human and as fallible as everyone else. The difference is the consequences of those fallibilities. When you are dodging missiles over Haiphong or landing aboard a flattop in the middle of a tropical storm, mistakes are often fatal.
I can't fly anymore, but my heart is still up there. Lying in my yard and watching these jets stream past, I try to figure their speed and altitude. I've been doing it so long I know their schedules. When an aircraft is late, I wonder if the crew got hung up at the gate, or if the taxiway was jammed. It's one of many ways I keep myself in the game. Pushing a jet through the sky will always be my abiding love.
# CHAPTER ONE
# ADMISSION PRICE
**Over Southern California**
**December 1956**
Sixty-five and sunny; blue skies all the way home. God, how I loved December in California. No snow, no shoveling the walk to the driveway. Just plans for Christmas dinner in the backyard as the last rays of sunlight bathed the L.A. basin in golden hues.
From the matte gray cockpit of my Lockheed T-33 jet trainer, I looked down at the suburban sprawl born of the postwar housing boom. The orange groves were vanishing, replaced by blocks of little pink houses and picket fences that looked like Legos from my twenty-thousand-foot vantage point.
_I used to shine shoes down there. Lee's Barbershop in Whittier._
I shifted my eyes from the scene below to scan the instrument panel of my "T-bird." Altimeter, heading, airspeed indicator, turn and bank indicator, vertical velocity gauge. I swept them all in a heartbeat, trained to do so by the best pilots in the world until each scan of the dials and gauges was an act of unconscious muscle memory.
My path to Pensacola began right down there. At Los Alamitos, I enlisted in the U.S. Navy as a seaman recruit. The naval air station was full of World War II vintage aircraft. As an apprentice engine mechanic in a reserve squadron, I worked on the F4U Corsair. When that legendary gull-winged beauty became a relic in the jet age, the unit I was attached to became the first in the reserves to get jets. A young lieutenant helped me to make the transition. He took me flying in his two-seater. Inspired, I applied to the Naval Aviation Cadet program, which sent enlisted men to flight training in Pensacola. With the help of that generous lieutenant, I passed the exams and made the cut. In 1955, I decamped to the famous naval aviation training center on the Florida panhandle.
Now the long-sought reward was close enough to touch. As long as I kept my grades up, I'd stand an excellent chance of flying jet fighters with gold Navy wings on my chest.
That morning over the L.A. basin, we whistled through the wild blue in technology that would have dazzled those who flocked to California looking for work two decades before. The age of the Joads and Okies was long gone. The jet age was upon us, and I embraced it with all my heart.
To the people down below, this may not have meant a thing. They were going about their peaceful lives, caring for family, stressed out over work and the growing traffic. Some would open the _Los Angeles Times_ as they sipped their morning coffee for a keyhole view to the outside world. Eight hundred and ninety-six drunk driving arrests in the county this Christmas season was a headline in the _Times_ that morning. Beside that story, a tiny blurb described how the Japanese were detecting radiation in the atmosphere. That could only mean the Russians had detonated yet another nuclear bomb.
Vice President Richard Nixon talked of the ten thousand Hungarian refugees the Air Force was flying to the United States for a new lease on life. Victims of Soviet oppression, they'd fought and lost in the Budapest uprising. When Russian armor rolled through their streets, they were lucky to have survived.
The people below me could not imagine such a life. Living in their orderly tract houses, they enjoyed well-kept lawns, sidewalks full of playing kids, and a sense of peace underwritten by men such as I had come to know in the past year. Home for the holiday, I would soon join them guarding our ramparts in the Cold War. The morning was simply gorgeous. The engine's whine was like music to me, the soundtrack to my new life. I was entering a profession unlike any I'd ever dreamed of.
My dad, a veteran of World War II, had served in Europe in the Army Signal Corps, keeping communications flowing between the front lines and headquarters. He came home to Illinois in 1945 to find his job had been filled. Victory in Europe cost him his career, and he found himself forced to start over in middle age with a family depending on him. Never showing us the fear he surely felt, he moved us to California, believing that every problem can be overcome by hard work. He got a job laying pipelines in Palm Springs. After a shift in the sun, which baked his Scandinavian skin to leather, he would come home with twelve-hour days in his eyes. He never complained; he worked and lived for us. His example of resilience instilled in me that same devotion. I was blessed and knew it.
There was a difference, though. I loved every second in the cockpit. This wasn't work; it was freedom. Every flight pushed our personal boundaries and revealed that we were capable of more. With each test, we grew as aviators and young men. Along the way, achievement became a drug. I couldn't wait for the next jump forward toward a fleet assignment. From the tie-cutting ceremony after I soloed to the first time I landed aboard an aircraft carrier, it was a journey marked with memorable moments. A year at Pensacola gave me a sense of identity and purpose that I never felt back home.
I wanted Mary Beth Peck to pin my aviator's wings on me at graduation. We had met in high school at a church function; I was seventeen, she was fourteen. Even in Southern California, with probably the highest concentration of beautiful girls anywhere, she made everyone else look ordinary. Blonde hair, eyes like the sky at twenty thousand feet. It took only one conversation to realize she wasn't just a beautiful face. Mary Beth possessed a soft-spoken eloquence and powerful intellect.
We courted properly, and our families grew close as we fell in love. She had written me every day since I'd left home to seek this new path through life. No matter how tough it got at Pensacola, I never let my head hit the pillow until I'd filled a page for her in return.
We had not seen each other since I left Los Alamitos for Pensacola. I'd left home a boy, working my way through junior college. That morning, I returned at the controls of a modern jet trainer, the double solo bars of an advanced naval aviation cadet on my chest. Christmas break was my chance to show her and our families the man I was becoming.
Wings banked now, the T-bird's polished aluminum skin reflected the sun as Bill and I began our approach to Marine Corps Air Station El Toro in Irvine. The base's distinctive double-cross runways stuck out among the tract homes and orange groves. El Toro served as home to some of the greatest combat aviators America ever produced: Joe Foss, Marion Carl, John L. Smith—the men who had stopped the Japanese advance in the Pacific during World War II. Most of the people in Orange County knew little of that legacy, but from the moment I started training, we naval aviation cadets were immersed in the heritage that was ours if we proved ourselves worthy.
At Pensacola, we flew the SNJ Texan and the T-28. On my first morning there, our drill sergeant woke us in the barracks with the rattle of his nightstick along the steel frames of our bunks, then double-timed us out to an aging hangar beside the seaplane ramp. In the very same building where some of naval aviation's pioneers established our tradition, the drill sergeant smoked us with forty minutes of PT. Each morning started with the same ritual. We worked out in the hangar among the ghosts of those who had paved the way for us. Thanks to them, naval aviation became the rebel branch of the service, always striving to develop new ideas, new technology, and new ways of fighting that would send the age of the battleship into history. From the battles of the Coral Sea and Midway to the Great Marianas Turkey Shoot, they transformed the U.S. Navy into the most effective naval fighting force on the planet.
Everywhere we went at Pensacola, we felt that tradition and it was an honor to be invited to be part of it. Would my generation contribute to perpetuate it in the years ahead? One thing for sure, I was not going to be the one who washed out and went home to be just another college kid with ducktail hair, working odd jobs to cover tuition.
Where other cadets bought cars and spent time in town, drinking at Trader John's and other local aviator watering holes, I made a point of staying on base. My dad's ethic became mine. I studied and worked hard. I was determined to be among the top cadets who upon graduation would be handed the keys to the latest and greatest fighter jets our country produced.
After Basic School at Pensacola, we were required to take a cross-country instrument flight to California, the final stage before we finished Advanced School in Beeville, Texas. The fringe benefit of this last evolution was a chance to visit home.
As we started our descent toward El Toro, Bill Pierson, my instructor in the rear seat, coached me over the intercom. I eased the throttle back and entered the landing pattern. Gear and flaps down, nose flared, I set the T-bird onto the runway. I taxied to the ramp by base operations, shut down the engine, and opened the canopy. Bill jumped out to grab a cup of coffee while our airplane got refueled. I pulled my helmet off and slid on the pair of Ray-Bans that I'd purchased at the Pensacola PX. They were a little over-the-top Hollywood for a cadet. In Florida and Texas I usually only wore them to the beach. What the heck. It was California.
Mary Beth stood on the tarmac, looking up at me with my parents at her side. She was a vision in an angora sweater and below-the-knee skirt. Wearing flat-heeled shoes and with her hair down, she had a smile on her face. Maybe just a hint of awe as well. I could hope.
I unstrapped and climbed out, dressed in a khaki flight suit, a matching jacket, and Navy-issue chukka boots. I'd barely made it down the ladder when she wrapped her arms around me. In an instant, the year of separation seemed like an eyeblink. I knew beyond a doubt, this was the woman I wanted to marry.
Bill watched from the doorway to base ops, a paper cup of coffee in hand. He was a veteran of Korea and countless days at sea. He had shared moments like this one and knew their power. He also knew to stay clear and let me have it; for that I was grateful. The holiday break passed quickly.
I was born in Moline, Illinois, in 1935, and my father served in the army during World War II. My parents were immigrants and I was a first-generation American. Dad, named Orla or Ole, was born in Denmark in 1912 and his parents, Olaf and Mary Pedersen, immigrated the next year. My mother, Henrietta, was one of three beautiful sisters from the Isle of Man. She met Dad at a high school basketball game.
I remember the smell of potato sausage in Mom's kitchen on the evening we ate Christmas dinner on the back porch. That was a Danish tradition passed down from my paternal grandfather. When I was a kid in Moline, I'd rush from school to his little Scandinavian specialty store, passing barrels of pickled fish. A pot of that potato sausage would be simmering on the stove, filling the place with the scent of home and warmth.
My first flying experience had been in 1946, not long after dad returned from Europe. My father was intrigued with aircraft, as he had some experience with B-25 bombers near the end of the war. One evening, at Moline Airport, he said we were going flying. What a surprise for a ten-year-old boy. The flight was in darkness, early in the evening in a prewar Ford Trimotor, distinctive with its three clattering Wright engines and corrugated aluminum skin. I marveled even then at the beauty of being aloft at night.
Before I went to Beeville, Mary Beth gave me a Christmas gift. I unwrapped it to discover a gold signet ring with a tiny diamond inset on its flat face. She had my initials inscribed on it along with _1956_ and _Love, Beth_ on the inside. She was a freshman at Whittier College working in the student union cafeteria. She must have gone into debt to pull this off.
All too soon, this beautiful interlude ended. My instructor met me at El Toro a few days after Christmas. I wore the ring on my right hand as I kissed Mary Beth goodbye on the ramp. Soon I would be an officer and a gentleman. I'd ask her father for permission to propose. We'd start a life in the Navy together. A final hug, no tears, and I scrambled up the ladder and into the cockpit. As Bill Pierson and I taxied out to the runway, I saw her waving goodbye to her naval aviation cadet.
When I landed at Beeville, my first jet fighter awaited me on the flight line. She was a Grumman F9F Panther, a well-traveled aircraft whose dark blue aluminum skin was dotted with patched-over bullet holes. Like my instructor, she was a veteran of Korea, her paint dulled by years of service. With her straight wing and her sub–Mach 1 top speed, the Panther had been relegated to stateside pastures, where she helped train the next generation of naval aviators.
I stood under my bird and shared a _Bridges at Toko-Ri_ moment. How many times had I seen that movie? A dozen? The flying scenes were spectacular. The poignancy of the love story and the fact that pretty much everyone dies in the end was lost to my visions of glory. That first morning with that Panther, I climbed into the cockpit and fell in love.
She was a delight to fly, balanced on the controls and fast for a first-generation, single-engine jet. Alone in the cockpit, I tried aerobatics with her and shot up towed sleeves with her four 20mm cannons. The thrill of it left me craving more.
As we closed in on the final lap of our training, a few boxes remained to be checked. One included a cross-country formation flight to Dallas and back. Three of us cadets took off with a storm closing in on us. The cloud ceiling was under a thousand feet. Speeding over the Texas countryside, we hugged the earth in an arrowhead formation at about five hundred feet, each of us taking turns in the lead. Two miles behind, our instructor trailed along in another F9F observing us at the edge of visibility. The weather worsened. Visibility diminished. We reached Dallas, landed safely. After resting and refueling, we flew back in the afternoon.
At four hundred miles an hour, a Panther travels almost two football fields a second. You have to think a step or two ahead at all times, or the speed simply overwhelms your ability to respond. Get behind the aircraft, and the struggle to catch up will make you mistake-prone. The best pilots ride the wave and are always thinking a move or two ahead of the aircraft. You have very little time to react to something. So when something suddenly flashed _between_ our three Panthers, I was stunned. Looking in my rearview mirror, I saw a red-lit radio relay tower stretching skyward into the overcast. We were at five hundred feet. Those radio towers were fifteen hundred feet tall. It was only an act of God that kept one of us from careening into it with fatal results.
We landed back at Beeville shaken but intact. Our instructor taxied to the ramp several minutes later, and I felt a swell of anger rise in me. _Where were you? Miles behind us out of sight when we almost flew into that tower?_
After I calmed down, the lesson came into focus. When you're a fighter pilot, alone in that cockpit, your fate is in your hands. Blaming others is just a dodge. It's no way to grow or improve. It was up to me to see that radio tower. No one else.
Near misses aside, I ranked near the top of my class in the final stage of advanced training. I felt myself developing into a confident young pilot. Inevitably, such self-realizations will lead the universe to knock you down a peg. Mine was a brutal humbling with lifelong implications.
That day I was supposed to fly a graded check flight in a T-bird with an instructor named Tony Biamonte. We planned and briefed a flight to Foster Air Force Base near Victoria on a day when a solid wall of clouds marched over the Lone Star State to twenty-five thousand feet. Visibility was at a minimum, even down on the deck. In the days before ground control radar, pilots navigated by low-frequency radio signals called LFR. It was still in use as a redundant backup system in the 1950s, and every cadet needed to know how to use it in a pinch. This weather called for it.
We took off into the soup, spiraling upward until we broke into blue skies above twenty-five thousand. Tony sat in the rear seat; I was in the front. Victoria was only about fifty miles away, so this was a quick flight. After checking in with Foster control, I started our descent. We went from blue skies to a world of swirling grays so thick I could barely see our wingtip fuel tanks.
Being inside a cloud is a disorienting experience. Look outside the cockpit too long at the dark heart of a cloud, and you'll lose all sense of up or down, inverted or upright. Mesmerized, you won't be able to tell if your wings are level, if you're in a bank, or if you're dropping out of the sky. With no frame of reference, your senses go haywire. The same thing can happen while flying at night. In moments like these, you bet your life on your instruments. You have to trust them, not what your body is telling you. It can be hard to believe the gauges over the wisdom in your own gut.
I was wrestling with that phenomenon while trying to carefully listen to the LFR signals telling me where I was in relation to the runway. I could feel myself starting to stretch to keep hold of the situation and stay ahead of the aircraft.
As we began our descent, I tried to keep a mental picture of where I thought we were. That mental picture was crucial. You have to see your bird in the air in your mind's eye, erasing the clouds and overcast until the landscape below comes into focus. You build the picture with the radio signals. Each Morse code letter, either an A, an N, or a Null, gave you a sense of your position. As I dropped into the pattern, I listened as the letters changed. With each new Morse code signal, I updated my mental picture.
At about two thousand feet, I had us on our downwind leg of the pattern. This meant we were running parallel to the runway a few thousand feet to the side. As we passed ninety degrees to the edge of the runway, I heard the Morse code letter change. That was the cue to make a turn onto the final approach. One more turn and I'd have this box checked.
We were still in heavy overcast, the T-bird buffeted by turbulence. Between studying my instruments, prepping the aircraft for landing, and trying to listen to the radio signals, I grew confused and uncertain.
_Is my mental picture wrong?_
The signal changed. New letter.
_Wait, which end of the runway have I reached? Which way to turn?_
I thought I knew where we were, but my confusion destroyed my confidence.
I turned the wrong way, sending the T-bird directly away from the end of the runway. I realized my mistake within seconds. Stopping our descent, I called the tower, fessed up, and asked to return to a holding pattern.
I could feel Tony's presence behind me right then. I had screwed up. Naval aviation is an unforgiving calling. One error and people—including yourself—die. In training, even a few seconds' worth of a wrong turn will count against you.
It certainly did here. Tony scrubbed the exercise, telling me to return to Beeville instead. I flew back, tense and upset with myself, seething at the mistake. When we got back on the ground, he asked, "You know what you did wrong?"
"Yeah." I explained what had happened, mentioning that I corrected the mistake very quickly.
He nodded agreement on that last point. Still, he did not let me off the hook. "I want you to fly this check ride again."
I'd failed a flight, the only one in eighteen months of training. He saw the expression on my face and tried to reassure me. "Listen. Dan, everybody gets one down check. Don't worry about it. It is a good lesson in humility."
I hit the books harder than ever. I studied LFR approaches. I flew the mission profile in the base simulators every day. I went back to the basics and studied Morse code again. There was no way I was going to fail again. In my obsession to succeed, I jettisoned every routine aspect of my life and used the extra minutes to study. That first night, my head hit the pillow, and as I fell off into an exhausted near-coma, a part of my brain felt like I'd forgotten to do something.
_I haven't written Mary Beth._
For the first time since I'd left home for cadets, I'd failed to finish a letter to her.
The next night, the same thing happened. I was falling behind. Her letters arrived like clockwork. Now I'd missed two days and I foolishly let my responsiveness slide even further.
All week, I remained singularly focused. Life distilled down to one thing: Learn LFR approaches and do it right the second time. Mary Beth and every other aspect of my life took a temporary backseat as I worked to overcome my error. No cell phones or long-distance to explain; besides, I was too embarrassed. Big mistake.
This was my initiation into the constant battle all naval aviators face: the demands of the job versus the need for a personal life. The job is so demanding that it almost always wins. In a civilian career, balancing professional and personal lives requires careful attention, but it can be done. In naval aviation, there is no balance. The job always has to come first.
At home, she checked her mailbox every day to find it empty. She went from puzzled to alarmed to deeply hurt as each afternoon brought the same empty box. My grandkids would call this "ghosting." Imagine you and your love have been texting on your phones day after day while separated for some reason. Suddenly, one of you stops. A few hours might not seem significant, but the communication becomes one-way. The stress level rises. A day passes. Then two. Wondering becomes an agony. No explanation—the person simply vanished, became a ghost.
The word _ghosting_ hadn't made it to Webster's English Dictionary yet, but that week in 1957, it's exactly what I did to Mary Beth as I focused on passing the check ride. When I climbed back into the T-bird for the do-over, the hard work paid off: I aced the flight, landed the aircraft without issue, and returned to Beeville with my confidence restored.
Tony died two months later during a similar LFR check ride with another naval aviator. Life in aviation, even in training, was deadly serious. It required everything you have. Living an intensely focused, out-of-balance life wasn't just an expression of our passion for flying. It was required in order to survive.
That was one of my last check rides. I finished advanced training and didn't slip in the class rankings. With the ordeal behind me, I wrote Mary Beth for the first time in several weeks. I couldn't bring myself to tell her about my brush with failure. How could I explain my poor judgment in a letter? I decided to wait until I returned home to explain it to her in person. I needed her to see me as infallible, the confident pilot who'd climbed out of the T-bird at Christmas, rocking those Ray-Bans and beige chukka boots. So I took the path of least resistance: I wrote as if nothing had happened. I didn't even acknowledge vanishing for all those days. I just picked up where I'd left off.
On March 1, 1957, I got my wings. The graduation ceremony in Corpus Christi was almost anticlimactic. I wanted Mary Beth to pin my wings on me, but flying to Texas was not financially feasible for her or my folks. Instead, my flight training roommate and friend from home, Al Clayes, pinned my wings on my chest that day. I did the same honor for this newly commissioned U.S. Marine aviator.
The Navy commissioned us all ensigns and made Big Al a Marine second lieutenant. We were officers and gentlemen at last, waiting for our first assignments with increasing trepidation. Through the grapevine, I'd heard that there were very few jet fighter pilot slots available on the West Coast that spring. I wanted to be back in California, close to home and Mary Beth, so I'd asked for duty on my side of the country.
When my orders arrived, I tore open the envelope, running through my worst-case scenarios, the first of which was blimps. Yes, the 1950s Navy still flew airships. We called them "poopy bags." Nobody wanted to go from flying Panthers and T-birds to puttering around at seventy knots with a gigantic bag of gas over your head. No thank you. Then there was ASW. Antisubmarine warfare. This meant multiengine flying and interminably long patrols over open ocean, where everyone aboard tried not to fall asleep.
I took a breath, looked down at my orders, and read the official verbiage directing me to report in thirty days to San Diego.
I read it twice. Then a third time just to be sure I wasn't dreaming.
I was going to a squadron known as VF(AW)-3.
V stood for heavier than air. No blimps for me.
F stood for fighters.
AW stood for all-weather.
I'd done it. I was going to be a jet fighter pilot.
I was on the road to Topgun.
# CHAPTER TWO
# FIRST TRIBE
**Texas to Naval Air Station North Island, San Diego**
**Spring 1957**
It's 2300 here in the California desert, eleven o'clock in the civilian world. I come out every night and sit by the pool at the same time with my wife's two little white-poofball Maltese pups. They curl up under my lounge chair, which I'll adjust to be flat. Then I'll lay here and look up into the night and wait.
The stars are old friends, of course. We all did our share of night flying. At sea aboard an aircraft carrier, the air wings assigned the rookie pilots night flights based on the phase of the moon. A first-timer would need to land by the light of a full moon. If he hit that forty-foot zone in which the tailhook can catch a wire—as it will have to on a carrier or heaven help you—the next time he flies, the moon will be a crescent. Less light, more challenging. The biggest test came on nights with no moon—and bad weather. Nothing gives a naval aviator more gut-check moments than a night carrier landing in a heavy sea. It takes a special breed of cat to do it consistently, that's for sure.
Whenever the moon looks like the base of a thumbnail, I remember when I commanded the carrier USS _Ranger_. Somewhere in the Pacific, under a sliver moon, our air wing conducted night ops. One of our young pilots had trouble getting get his F-14 Tomcat back down on the deck. As he made his approach and the landing signal officer (LSO) talked him toward that number-three wire, I watched from my bridge chair. I could tell he was "killing snakes in the cockpit." That means he was overcontrolling the aircraft. He was feeling overwhelmed and his heart rate was spiked. We'd all been there. The LSO told him to go around and try again. We call that a wave-off.
He did, and the same thing happened. His bucket was full. He was battling fear, the darkness, his instruments, the procedures needed to bring the bird back aboard. It got away from him again.
All night, he tried to land on the _Ranger_. Twice he had to climb above the clouds to refuel from an airborne tanker. I finally had to call him on the radio, something ship captains almost never do. We leave talking to the pilots to the air boss or their squadron commanders.
"Look, son, we're into the wind and we're not going anywhere. We're here for you, and we've got all night. Just relax a bit and smooth it out."
Those are the moments I loved the most—the kind of mentoring and loyalty to each other I never found anywhere else but inside the brotherhood of naval aviation.
That nugget took twelve passes before he was safely on the flight deck. Now think about that. Each approach is a gut-check moment. The deck may be moving with the swells and you can't see the horizon in the darkness. You're utterly reliant on the LSO and your instruments. A mistake can kill you. Worse, if you make that mistake as you touch down, you'll probably kill others, too. Even when we weren't in combat, the stakes were high.
Twelve tries in, he made a perfect landing. Maybe in the civilian world, some manager would give a young employee twelve chances, but I doubt it. In our world, we knew what to do. We sent him right back up the very next night. And when the time came to land, he rolled into his approach like a fleet veteran and caught the number-three wire like a seasoned tail hooker. Later in his career he flew with the Navy's famous demonstration team, the Blue Angels.
Love of aviation led us to our careers, but we all stayed in the service because of the people. Men like the ones who had gotten us through nights like that.
My first unofficial act as an ensign in the U.S. Navy was to buy a car. My gang of new officers, at lunch for the first time at the officers' club in Corpus Christi, Texas, decided that at least one of us needed to have a set of wheels. We rolled dice to see who would go down to the dealership, and I lost.
I picked out a brand-new 1957 Ford Fairlane. Raven black with black and colonial white matching interior. Sidewalls straight out of _American Graffiti_. I drove home from Texas in my new ride, eager to see Mary Beth, make amends, and take her for a spin. I had thirty days of leave before I needed to report to VF(AW)-3, and I intended to use every minute of it courting my girl.
The morning after I got home, I drove the Fairlane over to Whittier College. I found Mary Beth working at the cafeteria in the student union. She seemed unusually quiet. As I showed her the new car, I knew something was wrong.
"Beth, is something on your mind?"
She hesitated, searching for words.
"You didn't write," she said. "I didn't get any letters for a while."
I was about to explain, when she said, "Dan, I'm seeing someone. When you didn't write. Well, he was persistent. I gave in." I didn't know what to say. He was a football player at the college. They'd been seeing each other for only a few weeks.
I went home to regroup. My folks' house was a sad place that evening. I stayed around town for two more weeks, marking time and feeling increasingly like an outsider in my own home. It was the first taste of alienation most of us naval aviators experienced as we began our journey into the brotherhood. The layers of our old lives would fall away like leaves in the months to come. Nuggets—rookie naval aviators—still had some connections to the outside civilian world, but already we were seeing them strained to the limits by the demands of flying high-performance aircraft. Increasingly, our lives were whittled down to the job, the people working with us, and a few problematical connections on the ground.
It was a brutal process for all of us. Hollywood often portrays us as skirt-chasing, hard-drinking types without delving deeper into the situation. The truth was, by the time you reached your first squadron, those superficial nights with beautiful girls were all that naval aviators had room for in their lives. The problem arose when we tried to form deeper connections. The love of my life was the first sacrifice I made for those wings of gold.
When sticking around town became intolerable, I decided to report early to my new squadron. While I was packing, my mom came to me and watched me fill my suitcase.
"Dan," she said gently, "Mary Beth has made her choice. You've got to respect that."
I wanted to win her back. My mom could see right through me.
"Don't do it. Don't interfere. That isn't your place. It wasn't meant to be." One thing we did not do in the Pedersen household was defy our mother. Her words followed me all the way to San Diego.
Joining your first squadron is a life event for naval aviators. You make lifelong friends and the lessons in the air come at you like a firehose. Your mind needs to be clear; you've got to be ready for the challenges ahead. If you're not, you're going to have an accident. No matter what area of naval aviation you're in, it is deeply unforgiving of mistakes.
In downtown San Diego, I found the Coronado Ferry at the end of Broadway and drove the Fairlane aboard. My mind was anything but clear. I wasn't joining the squadron two weeks early that day, I was running from home and the life I'd wanted but could not have.
At North Island, the guard at the front gate gave me directions to VF(AW)-3. I barely noticed the planes coming and going off the runways as I drove past long lines of attack jets, patrol planes, and fighters. The squadron had its own high-security compound. Fenced off, patrolled by guards with leashed attack dogs, it stood in stark contrast to the relatively relaxed security at the main entrance. It was my first indication that my new squadron was a distinctive one.
I parked by the hangar after showing my orders a second time at the guard station. I reached across the bench seat, grabbed my fore-and-aft cap along with the manila envelope containing my orders, and went to check in at the admin office.
The officer of the day greeted me warmly with a "Welcome aboard" and a handshake. He took me to meet the squadron's executive officer, Commander Eugene Valencia.
Meeting the exec was a formal call, part of the ritual when a new guy came aboard. I was led to his office, stepped inside, and introduced myself.
Round-faced, solidly built, with slightly thinning hair, my new XO happened to be the third-highest U.S. Navy ace of World War II, one of the great legends of our community. In one engagement over the Japanese home islands in April 1945, he shot down six enemy planes. He finished the war with twenty-three flags on the side of his F6F Hellcat.
I was a raw ensign fighting to hide a broken heart. The man introducing himself to me held the Navy Cross and six Distinguished Flying Crosses. I was in awe. Yet Commander Valencia was anything but arrogant. He greeted me and set me at ease with his relaxed, unassuming nature. It was hard to believe that a man with so many accomplishments could be so grounded and approachable.
From the XO's office, the officer of the day led me to the hangar. He explained that the squadron stood on twenty-four-hour alert as a component of the North American Air Defense Command. VF(AW)-3 was the only U.S. Navy fighter squadron assigned to protect America's shores. We were the anomalies—naval aviators under direct U.S. Air Force control. At any moment of the day or night, two crews stood ready to scramble and be airborne within five minutes. More crews waited in the ready room on ten-minute alert. Should the order be given, they would run to the aircraft waiting in front of the hangar and launch down Runway 18 in a mad dash.
It was the height of the Cold War. The great threat to the American homeland wasn't intercontinental ballistic missiles; it was Soviet nuclear-armed bombers. In case of World War III, our job was to get to the incoming Red Air Force bombers before they could hit Southern California.
The Navy gave us the best equipment, the most advanced electronics—and the best crews. Every year there was a competition to see which outfit was the best squadron protecting American airspace. Every year, a two-star Air Force general came to North Island to bestow that award—it always went to the lone Navy unit in the mix. It was a tremendous point of pride for the Navy, and for VF(AW)-3.
I was allowed to poke my head into the ready room for just a short minute that afternoon. The crews were lounging there in their flight suits, waiting for the Klaxon to sound. The officer of the day said, "Why don't you go get your flight gear and put it in your new locker." He pointed out a bank of them in the main hangar. When I found my assigned locker, I opened it up to find that it was full of somebody else's stuff.
"I think there's been a mistake," I said.
The officer of the day looked stricken. "Sorry about that. We forgot to clear it out."
_Clear it out?_
"That locker belonged to the lieutenant j.g. you're replacing. He was killed a little while back. Accident. Go ahead and throw everything away. The rest of his effects already went to his family."
I walked back to the locker and stared at the items inside with a new perspective. A ratty old T-shirt hung on one hook. A few other knickknacks and toiletries sat on the shelf. Then I noticed something unusual. A pair of eyes were staring back at me. I reached in and pulled off the top shelf a tiny stuffed mouse. It was about two inches tall, with big eyes, soft gray fur, and a tail. The toy seemed out of place in a fighter pilot's locker.
Was it a gift to his child, never delivered because of that last, fatal flight? Was it a gift from his child to him? If it was a lucky talisman that served as a reminder of who waited for him back home, I hated to think it had failed him.
Suddenly, I didn't want to know. Talk about an attitude adjustment. My problems seemed trivial, selfish, compared to the death of the mouse's owner.
I trashed the shirt and toiletries. But as the mouse hovered over the can, I held it there and regarded it again. _Who am I to throw away another man's mouse?_
I took the little guy back to my flight bag and made him a nest deep inside. As I stowed my gear in the reclaimed locker, his cartoon eyes stared up at me from beside my helmet. I set my Ray-Bans on the shelf, closed the locker, and headed off to get a room assignment in the bachelor officers' quarters. After I unpacked, I went to the ready room to meet the squadron.
Ties off. Formality forgotten, one of my new squadron mates greeted me with a grin and said, "Welcome to the best squadron in the United States Air Force!" Mom had told me to go make the best life I could. Carry on. Move forward. Easy things to say. Yet here I was, surrounded by men driven by the same passion for flight that burned in me. They were achievers, hard chargers, type A. The kind of men whose respect, once earned, offered meaning never found anywhere else. These men were among the best pilots in the Navy, and here they were opening a place for me in their circle. That night, I found my tribe, the men who would teach me to be a fighter pilot.
# CHAPTER THREE
# THE NAVY WAY
**North Island**
**June 1958**
The buzz of the Klaxon sent us scrambling. Unidentified aircraft inbound. Pilots drinking coffee and playing acey deucey in the ready room were always waiting for this moment. I was on "alert five" status, ready to be airborne, in case of a contingency, within five minutes. The Klaxon started us sprinting to the flight line. We climbed into our cockpits, taxied to Runway 18, and did a rolling takeoff with an unrestricted climb.
The aircraft we called the Ford was officially known as the Douglas F4D Skyray. It was a tailless aerodynamic marvel created by legendary designer Ed Heinemann. It looked like something straight out of a sci-fi movie with its missile-shaped nose and rakish bat wing. It was so hot that to earn cockpit time in this beast, each pilot in VF(AW)-3 first had to fly three hundred hours in the older F3D Skyknight interceptor. The trick in that single-seater was to learn to handle the radar and speed procedures by yourself.
I could feel the Pratt & Whitney J57 engine surging as I checked the instruments. At 140 knots, I rotated to climb attitude about thirty degrees, while sucking up the landing gear and turning to the assigned vector to find my target. Everything in the green. The Skyray streaked for the heavens like a homesick angel.
Continuing to pull back on the stick, I reclined until my nose had moved from thirty degrees to sixty. Almost straight up now, I accelerated with the afterburner pushing the aircraft to the perfect climb speed. I passed ten thousand feet in fifty-five seconds. The stars lay dead ahead.
Two minutes and thirty-six seconds later, I was at fifty thousand feet. On a clear day, from this vantage point nine miles above the Pacific, I could see the Sierra Nevada to the north, far past Los Angeles. To the east the Colorado River snaked around Yuma, Arizona.
The target was somewhere out there in the night, ahead and below me. The Mount Laguna radar station and the Manual Air Direction Center at Norton Air Force Base coached me toward it until I detected the target with my own sensors. The Skyray had a secret airborne radar installed in the nose. It was a circular cathode ray tube screen with a hood attached to it. To see it in daylight, the pilot leaned forward and put his eyes into the hood to watch the radar beam sweep left to right. If that seems like a dangerous way to fly, you get used to it. Westinghouse built a turn and bank indicator, an attitude gyro, into the screen. We could fly the aircraft with our eyes on the radar scope. The radar controls were just aft of the throttle, so we'd fly with our right hand on the stick and run the radar with our left.
Thanks to our burner, we could reach a target in mere minutes. Our powerful radar could spot the enemy long before we could see them visually. The target pulsed onto my radar screen and I started the lock-on procedure. The screen displayed a small circle. Our job was to ease it over the target dot. That done, we were ready to fire when the target was in range. We could fire dozens of unguided 2.7-inch rockets to hit our target.
The Skyray rolled out of the Douglas Aircraft factory at El Segundo with four cannons and sixty-five shells per gun. With the advent of unguided rockets and heat-seeking air-to-air missiles, the Navy deemed the guns so much needless weight. They were removed, and their ports faired over. Welcome to the dawn of Push Button Warfare.
In these peacetime intercepts, we always needed to establish visual sight of the target to figure out what it was. I dropped down on the target to discover on this night, like almost every other intercept, that our bogey was a wayward airliner. I flew along with it for a few minutes, wondering if the passengers inside could see me out there off their wing. My nav lights were switched off, so I would have just been a ghostly outline to anyone who happened to be peering out their porthole window.
No threat to the country on this night. Mission accomplished; time to return to North Island. That afterburner sucked almost three thousand pounds of fuel—461 gallons—just to get to fifty thousand feet. We were fast, could scale the stars at Buck Rogers rates, but the Skyray did not have a lot of endurance, even with two external fuel tanks slung under the wings. She was a sprinter, built to counter a threat we hoped we would never face.
I headed back for North Island and eased into the pattern, passing over the Hotel del Coronado, always checking out the pool as I paralleled the beach. On final approach, the Skyray demanded full attention. Unlike the T-bird, which was a beautifully balanced and stable bird, the Ford was twitchy, nervous, and laterally unstable. That instability gave it tremendous maneuverability and roll rate, but it was not for a novice pilot. They were tricky to land on carriers. Nuggets had to fly in an older interceptor before getting the keys to the Ford.
You couldn't see very well when you were coming in hot, thirty degrees nose up. The Skyray landed so nose-high that Ed Heinemann designed a retractable tail skid with a small wheel embedded in it. When we extended the landing gear, the skid lowered and locked into place. If you landed properly, the skid would be the first part of the aircraft to contact the runway, followed by the main wheels, then the nose wheel.
I spotted the approach lights near the end of the runway. They stood on tall wooden poles like streetlights on steroids. I was wary of them. They could disorient you, especially on foggy nights. I put the nose on the centerline, scanned the instrument panel, and eased off the throttle. The Ford descended toward the runway on a ground-controlled radar approach on glide path, on centerline, until touchdown.
Two months into my time with VF(AW)-3, I received a call at home in the middle of the night ordering me back to North Island. I was living with several of the other pilots in a rental house on Coronado, so I was close by. At the compound I discovered that a lieutenant j.g. friend had flown into one of those approach lights in dense fog, after getting disoriented on final. His F4D exploded and killed him instantly. The skipper made me the assistant accident investigating officer; it fell to me to go with the squadron commander and a chaplain to break the news to his wife.
After that terrible doorway moment on her front porch, I returned to the field to spend the morning helping to clear the wreckage off the runway. That was the worst and hardest duty I ever had in my twenty-nine-year career. Part of the task required finding my friends' remains. We spent hours collecting pieces, and I thought about his newly widowed wife and their children.
His death left me ultra-careful as I made those night approaches, especially in bad weather. After dark, thick fog usually moved in from the bay and North Island. It made for very difficult, near-zero-visibility landings. Sometimes the fog proved so thick that we diverted to the naval air station at El Centro or another local strip. The fog is what got my friend. In his final seconds, it disoriented him and he clipped one of those stanchions. It was both a tragedy and cautionary tale.
These Skyrays were the wave of the future. If we did our jobs right, we'd never even see the Soviet bomber we blew out of the sky. In the months to come, beyond-visual-range attacks would become the order of the day, thanks to the advent of two key pieces of technology: the Sidewinder and Sparrow air-to-air missiles. These were the first generation of guided weapons. The Sidewinder, officially known as the AIM-9, used infrared sensors to track and destroy a target. The longer-ranged Sparrow relied on radar guidance.
In September 1958, our allies in the Taiwanese Air Force took the Sidewinder to war. They mounted them on their vintage F-86 Sabres. Through the end of that summer, the Taiwanese had been fighting a bitter air war against the Red Chinese Air Force, which was equipped with the newer Soviet-built MiG-17 Fresco.
The Taiwanese pilots scored history's first guided missile kill on September 24. The Sidewinder came as a complete shock to the Communists. Before the fight ended, the new missile helped them knock down about ten MiG-17s. The fight validated the enormous investment in missile technology we were making all through the 1950s. Of course, combat creates totally unanticipated moments. On that day, one of the Sidewinders failed to explode after spearing a MiG-17's wing. The Chinese pilot returned to base with his prize stuck in his aircraft, and within weeks the Russians were reverse-engineering our ultra-secret technological marvel. A few years later, in Vietnam, we would face those Russian-made Sidewinder knockoffs—we called them AA-2 Atolls.
After the Sidewinder's inaugural success in combat, the Department of Defense, Air Force, and Navy moved quickly toward long-range guided missile technology. The day of the Red Baron's swirling dogfights over the Western Front in World War I seemed a thing of the past. No longer did you have to close within a few hundred feet to score a kill. Pilots could shoot an enemy plane out of the sky long before getting into dogfight range. The Navy and Air Force agreed with the DoD whiz kids, who decided the day of close-range air combat was over. The new fighters would have multiple pylons for missiles, but no internal gun. Why waste space and weight for such an anachronism?
In my squadron, the senior leadership came of age in the World War II and Korean War era. Their combat experience looked a lot more like the Red Baron's day than our Buck Rogers dot wars on a radar screen. Nobody influenced me more than our executive officer, ace Eugene "Geno" Valencia, who took several of us young pilots under his wing and mentored us. In after-hours bull sessions at the famous air station I Bar, or the base officers' club, he would sometimes open up and talk about fighting the Japanese in the skies over the Pacific. As a young nugget, I relished the stories. In 1957, Geno had taken me to a big gathering of naval aviators in Rosarito Beach, Baja California, Mexico. It was known as the Tailhook Convention. As Geno's aide-de-camp, I carried the briefcase full of scotch. I heard sea stories and hangar tales that set my hair on end from some of the Navy's greatest aviation legends. Another time, Geno took some of us junior officers to an American Fighter Aces convention. I had devoured the memoirs of the World War II aces, looking for lessons I could apply to my career. We met some of America's best fighter pilots, and we absorbed everything they told us. All of them had fought Zeroes and MiGs. We wanted to be them!
They told us how, during the Pacific War, they learned to avoid getting into a turning dogfight with more-maneuverable Japanese fighters. Trying to turn with the more agile Japanese planes would get your tail shot off. So they took their shot and flew away—"One pass, haul ass" was the axiom. They learned to work together in pairs, cooperating to make sure that an enemy couldn't latch on to a pilot's tail. The other American pilot was always ready to turn toward his partner and stick his guns in the enemy's face.
My flight leader, Bill Armstrong, explained to me that in Korea, the opposite was the case. The tactics of World War II would get a pilot killed going up against a Communist MiG-15. Those jets were faster and flew higher than anything the Navy had, including the hot F9F Panther I had flown in training. Given the MiG's speed advantage, the horizontal plane became the Panther's playground. It could out-turn the MiG-15. So in just six years, we changed tactics altogether. "One pass, haul ass" went away and U.S. fighter pilots found their advantage in the sharp-turning dogfight.
In the missile age, it was all changing again. At least that's what the Navy believed. We would simply be directed by ground control to a point in the sky, lock our little circle on the dot, and let loose with a missile. No more seat-of-the-pants maneuvering in sharply turning fights. Technology promised a revolution.
Classically, the fighter jocks flew in many roles. We flew close to bomber formations, covering them en route to a target. We intercepted enemy bombers, tangling with their own fighter escort. We carried out sweeps in search of anything in the air to shoot down. We even carried out bombing missions ourselves, supporting troops by dropping napalm along the front lines. Fighters were jacks-of-all-trades, with the primary job of driving the enemy from the skies so our own planes could operate without interference. Each of these missions involved close-in dogfighting. The Navy concluded that long-distance radar interception would make all of these tactics obsolete. A flight of missile-armed fighters would stand off and destroy targets without ever needing to engage at close range. Just watch that cathode ray tube, secure the lock, and release the missiles. The bombing mission would be handed over to dedicated attack squadrons.
In our tight-knit group, some of us didn't like where the Navy was heading. The old ways had developed for a reason. Had air warfare really changed? It turned out, there was another factor at play here. It had everything to do with budgets. Through the mid-1950s, training for the kind of Korean War dogfighting we'd experienced proved both expensive and dangerous. Blasting off the runway and going climbing to fifty thousand feet at the edge of the sound barrier put a great deal of stress on an airframe. So, for reasons of safety, every plane came with a designated service life. The defense contractor guaranteed the airframe could withstand a certain number of flight hours before needing to be replaced. Somewhere in the Pentagon, some bean counter concluded that the heavy G loads of dogfight training wore out aircraft at least five times faster than simple intercept flights did. And dogfight training cost lives. Men made mistakes in those twisting, turning mock duels. They exceeded the limits, and died in unrecoverable spins or midair collisions. The loss of expensive aircraft could be (painfully) overcome, but the loss of well-trained pilots who took years to learn the ropes was a double blow.
So during my time at VF(AW)-3, the old ways were outlawed. Dogfighting—officially known as air combat maneuvering (ACM)—was forbidden. In 1960, the year before I left for my next assignment, the Navy shuttered the last of the old schools that trained fighter pilots to dogfight, the Fleet Air Gunnery Unit at El Centro. From then on, air combat maneuvering was banned. If you were caught "hassling," as we called dogfighting, your career could end.
The edict against dogfighting divided our squadron into three factions. Our senior leadership, whose experience ran counter to everything the Navy was now doing, had fought in two wars and had seen friends die. Having spent years away from their families on fleet deployments, they focused on being dads and husbands. At the end of their careers, they were content to mentor us nuggets on the ground, share their experiences, and teach us how to be leaders. They left the bulk of the flying to the younger guys.
In the second camp were the junior officers who bought into the new way. They never hassled, never pushed their Skyrays to the edge of the flight envelope.
The third group, a quiet group of young tigers, thought otherwise. I was one of them. And we decided to do something about it.
# CHAPTER FOUR
# FIGHT CLUB
**Off San Clemente Island, California**
**1959**
Do you remember the day when you first got the keys to your folks' car? Or maybe you salvaged some wreck off a lot, put in some wrench time, and took it out to see what it could do? In the 1950s, car-crazy high school kids always seemed to know where the street races were happening. Southern California had plenty of abandoned military airfields. And runways make great drag strips. Kids would take their beloved rides out there on Friday nights and tear around the old runways. Decades after those racing strips had disappeared, an underground racing scene developed. It was portrayed very well in the film _The Fast and the Furious_. The underground races were never formally organized. Just a few whispers at lunch and we made a deal to meet at a certain time and place. The network spread the word, one kid at a time.
Well, we developed a similar sort of underground subculture with supersonic fighters. Off the California coast, about eighty miles west of San Diego, there's a sector of restricted airspace that encompasses San Clemente Island. It's a military reservation. Air controllers call it Whiskey 291. The U.S. Navy squadrons in Southern California use it for training exercises. That was our playground.
I first heard about the West Coast's illicit dogfighting scene one night after hours in a San Diego bar. It might have been the Hotel del Coronado, or a Mexican restaurant where we knocked back tequila. It was certainly not at the North Island Officers' Club, or in the ready room. Too many "ears" could make things difficult.
We were free to fly almost whenever we wanted. Our squadron had plenty of aircraft and our chain of command encouraged us to get stick time. Almost always we could find a valid reason to fly. Sometimes we'd check out a bird for a weekend to practice cross-country navigation. I'd go to Texas, or Oklahoma, or Arizona. Once, when one of my fellow nuggets, Don Hall, was getting married in Phoenix, I flew a Ford to be part of the wedding. I can't imagine doing that in today's Navy.
Here's the thing: You learn by _doing_. Those of us who lived to fly learned our craft by flying a lot. We intercepted wayward airliners, and did our own troubleshooting when things went wrong with our birds. The men I most admired in the Navy were old-school fighter pilots. I wanted to be a throwback, ready to face adversity on my own wits. One look at the Eastern Bloc order of battle and it was clear that if World War III broke out, we were going to be heavily outnumbered. I imagined a zombie apocalypse with airplanes. We would pick off the first ones with our sniper rifles, our missiles. But behind them there would be more rushing at us. And a sniper rifle is the wrong weapon to have when they're grabbing for your shirttails.
What would happen to us when our missiles were gone? Our Fords we flew had no gun. And we were no longer being taught how to win a dogfight. It felt like a big gap in our combat aviator toolbox.
One Friday afternoon after a long week standing on alert, I went to the maintenance shop and signed out a Ford. I had heard at the bar that Friday afternoons before cocktail hour was the best time to find our version of a street race.
I took off from North Island and headed west for Whiskey 291, the unwritten rules in mind. One of them established a "hard deck" at five thousand feet. This meant that the fight was over the moment you dipped below that altitude. It was a nod to safety. If you ran into trouble and entered a spin, you'd need that altitude to recover. Aside from that, it was the Wild West. You'd find somebody who was willing to fight, give each other a hand signal, and get it on. What happened in Whiskey 291 stayed in Whiskey 291, unless you met your opponent later and had the chance to talk over drinks. There were no debriefs. No reports. No paper trail at all.
By joining this "fight club," we were keeping the flame alive for a certain way of being a fighter pilot. Three of the five junior officers from VF(AW)-3 whom I lived with on North Island loved this business, and in the months to come we would spend a lot of unofficial time hassling with other aircraft out over the Pacific. It was a whole lot of fun. It was also serious. We were preserving our birthright as naval aviators.
The first time I went out there, south of San Clemente, I was amazed at what I found. Marine A-4 Skyhawks, Air National Guard F-86L interceptors, Air Force F-100 Super Sabres, and lots of Navy guys flying F-8 Crusaders. There were even a few other Fords from North Island. The word had spread far beyond the Navy community, and the services mixed it up with fierce relish because they all were going through the same institutional evolution away from air combat that we in naval aviation were experiencing.
Mel Holmes, who later became one of my Original Bros at Topgun, served at North Island in a utility squadron just a few hangars down from my compound at the same time I was there. Mel loved to hassle out at Whiskey 291. Though I didn't know him at the time, I'd like to think we went head-to-head out there.
I learned the ropes that first time out. Pick your opponent, roll up alongside, and give the signal—the signal being the "bird." A smile and wave, and a forty-five-degree break in opposite directions. A break means we rolled the wings and turned one way. The guy to the left broke forty-five degrees left. The guy on the right broke forty-five degrees right. We'd extend out away from each other for several seconds until we were a few miles distant, then we began the fight.
We turned into each other, pushing throttles forward in what to the uninitiated looked like an aerial game of chicken in Mach 1 fighters. Approaching head-to-head or close to it, two fighters inevitably passed each other close aboard. We called this the Merge. Closing somewhere north of a combined thousand miles an hour meant the Merge is over in mere seconds. Before a collision, we'd break away, showing our first, best move. That was when the hassle began.
There was no script for what happened after the Merge. We reacted to each other, flying our aircraft as best we could. We learned that power is king. Power gives you the ability to climb above a fight to reenter it with even more energy in a diving attack. Power means you can push your bird in a tighter and tighter turn and maintain your airspeed longer.
The Ford had tons of power. It was nimble, quick, and a hard target. It was an adrenaline rush to push to the edge of its performance envelope. Usually just a full turn or two was enough to determine who was going to win. The hassles rarely lasted more than five minutes. But that's an eternity in aerial combat, a world where split seconds make the difference between victory and defeat.
When we had enough and were ready to admit defeat—maybe our opponent gained position at six o'clock and never let go—we waggled our wings, pulled up alongside our opponent, and flew wing to wing. Sometimes we smiled unseen behind our oxygen masks and waved. _Nice fight, brother_. Sometimes we just eyeballed each other, pissed off that somebody had gotten the better of us. Invariably somebody out there was a little better than I was, but each time I went out, win or lose, I improved.
These fights required real physical endurance. The hard maneuvering threw you around inside the cockpit and put heavy G forces on your body. That first day left me almost intoxicated with exhaustion. I felt more alive in that world than anywhere else. The rush is that powerful.
Afterward, I decided I'd go out and hassle at Whiskey 291 every chance I could. I wanted to learn, and the best way to learn was by running up against a pilot with more experience than you. If you lost, you lived to learn again. But some of our guys would rather die than lose. They were the ones I looked for. We'd push our birds to the absolute utmost, and sometimes beyond.
If the planes were different models, it sometimes came down to what airframe had more power and agility. Both pilots would pull the stick into their stomachs, draining power to tighten their turns as they tried to gain an edge on their opponent. The most aggressive pilots would "pull well into the buffet," as we said. A fighter on the verge of a stall falls out of controlled flight for a moment, then recovers. You can feel it in the seat of your pants and in the stick. Then the entire aircraft shakes. If you keep pulling and don't ease up, the fighter will stall, snap-roll inverted, and begin falling. It's easy for your opponent to whip around and eat your lunch. The best pilots know exactly how far to pull into the buffet and keep the plane from stalling. In the air, tiny advantages make a difference.
More than once, I watched two planes battling it out in the vertical, going straight up after each other like rockets, burners lit. They'd reach the edge of their respective flight envelope and enter an inverted spin. You could tell it had happened when the engine's smoke trail started streaming over the plane's belly and beyond the nose as the plane sank earthward, tail first, wings no longer gripping the sky. Those were dangerous moments, but with enough altitude for seven or eight revolutions, you could pull out of it.
I learned the basics of air combat in those hassles. Never lose sight of your opponent: "Lose sight, lose the fight." Never go vertical unless you can own it, meaning you have enough pure engine power to blast skyward and leave your opponent unable to follow you and hammer you from behind. Turning fights are like back-alley brawls. When similar aircraft engage like that, the difference is pilot skill and aggressiveness. The winner usually is the one with the most guts to push his aircraft to its aerodynamic limit.
To win, you had to feel the aircraft, know exactly where you were based on visual cues with the horizon or the ground. Maybe you take a quick look at your fuel gauge, or glance at the altimeter once or twice. But that was it. This kind of flying requires your eyeballs out of the cockpit as much as possible. If you glance down in the middle of a scrap at a pivotal moment, you're liable to lose your target in the split second it takes your brain to process and your eyes to refocus on the switch from instruments to blue sky.
Every pilot had his own bag of tricks. We learned by watching other guys beat us with them. Others we picked up in late-night shop talk in the Coronado bars. Unusual maneuvers, little ways to extract just a bit more performance from your aircraft and other jewels, were shared and discussed. The knowledge—and liquor—flowed with equal speed in those sessions.
Sometimes we ignored the hard deck. That's when it truly became a game played on guts, the two of us twisting and turning in a roller-coaster maneuver we called the "rolling scissors." I'd see my opponent coming in behind me, looking to make a high-speed pass. To counter, I'd pull up and roll inverted. The attacker would pass right below my canopy, and so I'd lower the nose and roll back toward him in a dive. This made my pursuer my target—though a fleeting one. I would have a tiny window to take a high-deflection shot at him as he pulled hard into me, then he had the chance to barrel roll and pursue me as I went past. Each time we crossed paths—that was the scissors. Picture the flight paths intersecting like the X of a pair of scissors, chopping away at the sky. Two evenly matched pilots could do this over and over. Often we dropped below five thousand feet and stayed after each other until we were on top of the whitecaps. Real combat has no hard deck.
In this way we preserved our perishable skill sets and kept alive the fading art of the dogfight. The rest of the Navy was letting it slip away in the early 1960s. I flew whenever I could. Holidays were great times to hassle, because the married guys were home with their families and the pace of activity on base relaxed. I was still trying to get over Mary Beth, so I'd climb in a Ford and go look for a good fight.
Some of the best pilots flew the Navy's Vought F-8 Crusader. In later years, the F-8 would be called "the last of the gunfighters" because it carried four 20mm cannon and five hundred shells. The F-8 community had learned to dogfight in the Fleet Air Gunnery Unit, which disbanded in 1960. They were indeed the last of their breed. And boy, were they good.
We could outclimb the F-8, but they could reach 1,200 mph in burner, while we could only get to just above Mach 1—740 mph. The Crusader, in the hands of a good pilot, was a world-beater. With a Skyray, we needed a turning contest. That big bat wing gave us the edge here, and we could turn inside the heavier F-8. Drag 'em down to the hard deck (or below) and turn and fight. That was our win. The best F-8 guys knew better, and they stayed in the Crusader's envelope, using their speed and power, where they could dictate the terms of the fight.
Fighting against different types of planes was useful. It taught me more than fighting against the same type of plane I was piloting. In later years at Topgun we would call it "dissimilar air combat training." But back in the late 1950s, we didn't have a name for it. We just intuited it based on experience. Each fight with a different type of aircraft, each with its own advantages and weaknesses, taught us how to exploit our edge and minimize theirs. How did we learn? By losing. Failure is a teacher. Be honest with yourself, extract the lessons, and you'll never make that error again. I spent many long flights back to North Island replaying what I did wrong, so that on my next bout in the interservice fight club, I'd bring the heat and win. When we founded Topgun, this part of the experience in Whiskey 291 became a very important component of our culture.
A few days before Christmas in 1958, it was a quiet time at the squadron. Most everyone had gone home. I had been going home on weekends. I was eager to have news about Mary Beth. On one visit I saw her after a Whittier College football game. She was with her new beau. I waved at her, trying to hide my sadness. As she offered a furtive wave, I noticed tears in her eyes. After that, I went home less frequently and spent my weekends flying.
One day down at maintenance control, I checked out a Ford and took off out over the ocean. It was a crisp winter morning, without a cloud in the sky. Once I got to altitude, I could see for almost two hundred miles. The view was simply breathtaking.
Instead of heading out to San Clemente, I turned north toward Los Angeles and my folks' home. I hadn't gone far when a pair of contrails caught my attention off to my right. They were _vertical_ contrails, in the restricted airspace around Edwards Air Force Base.
_Somebody is getting it on._
I couldn't resist. I banked my Skyray east to see who was hassling. I came upon an F-8 locked in a wild duel with an Air National Guard F-86. As I closed, I could see from the markings that the Crusader belonged to a squadron based at Miramar. Those guys were damn good. To my surprise, though, the F-86 pilot was eating the F-8's lunch. As I closed in, the Crusader quit. The two planes linked up, and the F-8 waggled his wings and broke for home.
I slid alongside the Sabre. _I'm your Huckleberry._
The National Guard pilot studied me and my Ford. He nodded. I nodded. He flipped me the bird—the magic signal—and I flipped it back.
Game on.
We broke forty-five degrees and separated to a distance of about seven miles. Before turning back for the Merge, I checked my altitude. Twenty-seven thousand feet. Part of me wondered if this was too risky. On such a clear day, surely people below could see what we were doing. What if someone called Edwards, reporting us?
No time to worry. I checked those concerns as I wheeled around and barreled straight for the F-86 with the pride of my service on the line. It was time to avenge my Crusader brother.
The Sabre and I hit the Merge at more than a thousand miles an hour, and I broke hard to start the fight that suited the F4D best: a horizontal turning battle.
I made a one-eighty and saw him already in the horizontal, turning for me. Wings vertical, we watched each other from out of the tops of our canopies. A full three-sixty later, he had gained a good angle on me, closing on my tail. I started to sweat. I turned as sharply as I could, and the plane began to buffet, losing speed. By the second revolution, the Air National Guard pilot was pinned to my six.
In a real combat situation, tracer rounds would have been streaking past my windscreen. I had to do something fast, so I lit the afterburner and went vertical. No way could a Korean War–vintage aircraft hang with me there.
I rocketed straight up, trading energy for altitude. When I got up above him, I could trade it back. I came down on him in a subsonic dive and made a pass. He juked out of the way and rolled into a dive after me.
As my Skyray pushed toward Mach 1, the F-86 stayed on me. I pulled back up into the vertical, but found I couldn't shake him. I had the superior aircraft; he was the superior pilot. In two and a half minutes, with the Sabre on my six, I had to admit defeat. I rocked my wings. He joined up on me as we made a slow turn toward the L.A. basin. He nodded and saluted me. I returned it, then headed for North Island.
Not long after I landed, somebody told me I had a phone call from the Air National Guard's 146th Fighter Wing at Van Nuys. A lump formed in my throat. Had I been reported? On the other line was a major, probably one of the wing's squadron leaders. He asked me if I'd been up in an F4D over Edwards airspace. I said yes.
"You're not bad, son," he said, "but you've got a lot to learn."
We talked the fight over. I learned his F-86 had an afterburner too. Earlier versions didn't. I wondered if that's how he beat me. At length, I finally said, "Hey, no other phone calls, okay, sir?"
"Oh, no calls. I wouldn't do that to you, son." He knew the rules of the game.
We hung up, and I never spoke to him again. But boy, the lesson he gave me that holiday's eve lingered for the rest of my career. When you pick a fight, you better know the capabilities of the aircraft you are facing. And it's a dangerous mistake to assume you're better than your opponent. When you start a fight, you should always assume you're facing the very best. Otherwise, chances are you're going to have a really bad day.
The road to my longest season of bad days began almost as soon as I got my orders to leave VF(AW)-3. I reported to VF-121 at Miramar to transition to a brand-new McDonnell Douglas bird, the F3H Demon. In late 1962, I joined the Black Lions of Fighter Squadron 213 (VF-213). In February 1963, we deployed on board the carrier USS _Hancock_ and spent the next eight months in the western Pacific.
Naval aviation is the tip of the American spear. Wherever trouble brews, the aircraft carriers go. When the _Hancock_ went into the South China Sea our purpose was to send a message to the Red Chinese: Lay off Taiwan.
It was not a pleasant experience.
# CHAPTER FIVE
# WHERE ARE THE CARRIERS?
**Off the Saigon River, South Vietnam**
**November 3, 1963**
Black night. No moonlight for the nuggets. Not even a star visible thanks to the storm clouds stacked from a thousand feet on up to heaven. USS _Hancock_ 's wooden flight deck was slick from intermittent tropical downpours. The old girl was almost twenty years old now, a carrier built in wartime with funds raised by the John Hancock life insurance company. This wooden deck had seen everything from fires inflicted by exploding Japanese kamikazes to raging typhoons off Southeast Asia. She sat in mothballs during Korea, but as the Cold War intensified, the need for more flight decks grew urgent. The Navy pulled her from the fleet reserve in Bremerton, Washington, and updated her with an angled flight deck and four steam catapults for jet operations.
Two decades after joining the fight against Imperial Japan, the _Hanna_ found itself in the middle of a new crisis in the western Pacific.
Aboard this storied flattop, I sat in the cockpit of my McDonnell F3H Demon interceptor on the alert five catapult, watching the deck crew hustle around me. Lacking inspiration? Watch a deck crew in action, especially at night. It was one of the most tightly choreographed performances you'll ever see. Every member of that team worked in complete harmony in one of the most dangerous work environments you can imagine. Their margin for error is so slight—one wrong move and the sailor can get sucked into an engine or blown overboard by the exhaust blast. Yet they work in this danger zone of roaring afterburners and high-tension cables with fearlessness and focus. It is an awesome sight to see.
That night, I couldn't see much. Just flashlights moving around and glowing yellow wands giving me signals from the deck on the left side of the cockpit. I could just make out the dim outlines of the flight-deck crew by the glow of their lights.
The conductor of this little symphony was called the shooter. An experienced commissioned officer, he wore a yellow shirt and carried a pair of those yellow glowing wands. He gave the order to fire the catapult when the time came to send me on my way.
Getting ready to go, another yellow shirt, the flight-deck director, waved me forward to the catapult track. I eased off the brakes. As the nose wheel reached the catapult shuttle and nestled in, I set the brakes again and made sure the foldable wings were locked in place. Sailors swarmed under the Demon. Red-shirted ordnancemen pulled the arming pins out of my four AIM-7 Sparrow missiles, our radar-guided air-to-air weapons. Another team slung a bridle behind my nose wheel and attached it to the shuttle in the catapult track. I felt a bump as the Demon went into tension, the catapult locked and loaded, ready to sling me off the bow.
I wasn't supposed to be on the catapult that night. I was due for shore leave in Hong Kong, one of the best of all possible ports of call. Great food and nightlife, and deals on Rolex watches. Before we could enjoy any of it, the _Hancock_ received an emergency sail order. We weighed anchor at 0830 and sped southwest with a pair of destroyers. We had no idea what was happening, other than that some kind of crisis was afoot and a carrier was needed off Vietnam.
My very first cruise gave me a front-row seat to U.S. naval power projection in action. Deployed to WestPac, we guarded the sea lanes, trained off the coast of Japan, and flew the flag at various ports of call. Our F3H Demons intercepted Soviet bombers that periodically dropped down to snoop on us. We'd chase them as soon as our radars caught them coming down from Vladivostok. When the Tupolev Tu-95 Bears took their photos of us, we wanted a Demon in the frame. Proving up our ability to destroy them at will was a game we played with the Russians for the entire Cold War. More than once, I watched a Russian gunner wave at me as I snapped pictures through the canopy. Such moments were rare and fleeting, just two aircrew at the tip of the spear, making momentary personal contact at altitude over the world's largest ocean.
Truth was, my transfer to VF-213 and the two ensuing deployments were like the sophomore blues. On my first deployment, the Black Lions were led by a skipper who pushed the young guys hard. Too hard, occasionally. As the squadron safety officer, I watched him make several bad decisions and finally couldn't stand idly by. After one of our pilots, apparently exhausted, died in a preventable deck accident—after landing and getting free of the arresting cable, he just slid to the edge of the flight deck and fell over to his death—I urged the skipper to dial it down or other guys were going to die. He ignored me, and later wrote up an unsatisfactory fitness report that described me as "disloyal." This second deployment went more smoothly without him.
When it was conceived in the early 1950s, the Demon was powered by a Westinghouse J40, supposedly a world-beater. It proved to be a dog. It failed constantly, killed pilots, and never produced the thrust the Demon needed to be an effective interceptor. The Navy canceled the Westinghouse contract and equipped the F3H with an Allison engine designed for the B-66 bomber. Even with the upgrade, transitioning from the Skyray to the Demon was like trading in a Porsche for a Dodge.
In cold, wet weather, the engines tended to fail when the metal housing around the Allison shrank, causing the turbine blades to scrape the inside of the enclosure. Though this merited a full redesign of the engine, there was no money in the Navy budget for it. Instead, the manufacturer shaved a small amount off the turbine blades. Problem solved, right? Yes. But the solution detuned the engine, leaving the Demon underpowered and slow to accelerate. Once up to flying speed, it handled nicely enough, though it was no bat-winged Ford.
I do miss my days flying that plane. You never forget taking off from a carrier. At night and ready to launch, the deck crew raises the jet blast deflector, a sheet of hardened steel that protects everyone aft of my Demon from the engine's exhaust. Scanning the instruments, I see that everything is in the green. A quick glance forward reveals nothing but blackness. I can't even see the end of the flight deck.
The red shirts back out from beneath my wings, having armed my missiles. A final check by other crewmen and I'm clear to go. Advancing the throttles, I hear the engine spool up.
I look over at the shooter's yellow wands. He signals me to light the afterburner. A whoosh and bright reddish glow erupt behind me as a long tongue of flame shoots out the Demon's exhaust pipe. Seconds away now.
I lean my head back, pressing against the ejection seat. If you don't, you'll have a sore neck as the catapult slings you forward. Simultaneously, I use the catapult grip that holds my throttle in place, so my hand doesn't reflexively pull it backward as I accelerate. Lastly, I jam my right elbow into my hip, so I don't accidentally pull the control stick back, overrotate the nose, and stall out. You can easily do that on a pitch-black night with absolutely no horizon. What a way to go.
The shooter leans forward and brings his wand down to the deck—the launch order.
The catapult fires, and the shuttle rushes in its track toward the bow. I go from zero to a 150 miles an hour in two seconds flat.
God, I miss it.
Halfway toward the bow of the deck and I am already flying the aircraft. In such moments, you don't look out at the darkness ahead. Rather, you're entirely focused on the instruments once your eyeballs are uncaged and your vision returns. A moment later, I feel the wheels leave the deck. The bridle drops free, and I raise the landing gear.
Nothing to it, really. That night, I sped to altitude and to my assigned patrol station off the Saigon River, never breaking clear of the weather. What a terrible night to be flying, but the situation in South Vietnam was briefed to be critical. Of course, they didn't give us any details. If we'd been able to watch the evening news broadcast back home, we'd have learned that an Army-led coup was underway in Saigon against Ngo Dinh Diem, the despot who had run the country into the ground over the past eight years. Regime loyalists and rebels battled in the streets as chaos engulfed the nation. Diem and his brother had been captured by rebels the day before and rumors abounded that they had either committed suicide or had been executed.
The Navy wanted the _Hancock_ on scene should the situation spin out of control. If an evacuation of the American military advisers in the country was necessary, we would provide air cover. That night, though, exactly what I could do with my air-to-air missiles, in storm clouds above twenty thousand feet, was anyone's guess.
I patrolled in complete darkness. Somewhere behind me was my wingman, but we never had visual on each other from the moment we left the _Hancock_ 's deck. It was that kind of night.
I don't remember who was up with me that night, but if it was Lieutenant John Nash, I know I wouldn't have needed to worry about him. Nash joined the Black Lions not long after I arrived. He was serious, intense, and utterly driven. What he lacked in humor aboard ship he more than made up for in the air. He was a relentless, aggressive pilot who backed up his self-confidence with simply incredible flying. He was one of the rarest: a man seemingly born to fly, as if it were coded into his DNA. In later years, I counted him among the ten best fighter pilots I've ever known. He coined the phrase "I'd rather die than lose." That was his mission statement. He lived it fully, in training and in combat. I would later use his enormous talent when I chose him as an Original Bro at Topgun.
The Demon was equipped with an excellent airborne radar system. As I bored holes in the cave-dark night, I kept my eyes on the radar. Could those Russian Bears drop down for a visit this far from Vladivostok? Did the North Vietnamese have an air force? I had no idea. But somebody wanted us up there that night for a reason.
I peered out into the darkness for a moment. It was easy to get vertigo in such black conditions. Try standing in a closet with the lights off for ten or twenty minutes, and you'll start to lose your balance. Your inner ear gets confused. Your senses send confusing messages to your brain. Now imagine that closet moving at 450 knots, without any point of reference in sight. Again, you embrace your instrument training and trust the gauges and dials on the panel in front of you.
This is all well and good until the power fails and your panel lights go out. A Demon did that to me on our first cruise the year before, and I never quite trusted the bird afterward.
That night was very similar to this one, except we broke out above the cloud layer at fifteen thousand feet. No moon, no visible horizon. My Demon suffered electrical failure and the lights went out in the cockpit. A wind-powered auxiliary unit was supposed to deploy in such a situation, but that failed as well. There I was, surrounded by absolute darkness, using a ninety-degree-angled flashlight to periodically check my instruments. I was flying that mission with our squadron executive officer, Lieutenant Commander Joe Paulk, who realized my predicament and came to my rescue.
Joe signaled to me with his flashlight, _Follow me_ , and pointed back to _Hancock_ 's latest position.
It was an eerie sensation flying on his wing in the dark en route to the _Hancock_ 's waiting deck. I forced myself to keep my wings level relative to his wing and belly navigation lights. I used small, precise control inputs, made easier by Joe's smooth flying.
We broke out of the cloud layer about a mile and a half astern of the ship. We could see the white strobes beckoning us. I continued flying Joe's wing until his lights went out and he turned away to give me a clear shot at the deck.
The electrical failure had knocked out my radio, which meant I could not talk to the landing signal officer. All I could do was watch his lights: A green one meant to keep coming. Flashing reds would be the dreaded wave-off—go around and try again. I didn't have enough fuel for that, so if I missed I'd have to eject, trusting that somebody would find me in the stormy sea.
I made it down and felt the tail hook catch one of the deck wires. The Demon lurched to a halt. A close call for sure, but it wasn't over.
The next night, while flying the same Demon, the same thing happened again. I was on Joe's wing, and he brought me back to the _Hancock_ in an encore performance. I landed safely after another gut-check approach. Perhaps we joked about him saving me twice. Fighter pilots never like to reveal weakness or fear to each other. The fact is, I went belowdecks and sat alone for a while, trying to drink a cup of coffee as I tried to figure the odds of _two_ electrical failures on consecutive moonless nights. That same aircraft had flown perfectly twice during the daylight between my events.
I said a prayer in the wardroom, coffee cup in hand. _Thank you, God, for making sure Joe was there to help me get back to my family._
Over the South Vietnamese coast, a year later, my radar swept the sky ahead of me and found nothing. The panel lights glowed reassuringly as my eyes scanned across the instruments. Nothing out of the ordinary. Just another night in heavy weather on the ocean frontier. Still, those two electrical failures remained in the back of my mind. Should the worst happen, I had triple checked my ninety-degree flashlight to make sure it worked and remained in easy reach in a flight suit pocket. Little pieces of gear can make all the difference in a critical moment.
My radio crackled. The controller on the ship below gave me a vector. Something was up offshore and he wanted us to drop down to investigate. Into the heart of the scud layer we went, navigation lights burning orange holes in the milky soup around us.
At fifteen hundred feet, we still had not found the bottom of the cloud layer. Suddenly, a muzzle flash lit the blackness below. Another flash strobed the sky, revealing holes in the cloud layer. A warship was down there on the water, firing its main batteries. I began to get vertigo.
_Get a hold of yourself, Dan. Trust the instruments._
Dizzy and lightheaded, I felt like I was floating. My body told me we were heading one way while my instruments told a completely different story. I might have been descending but did not know how to move the stick. Finally, returning to my instruments, I was able to recover from the vertigo.
A final salvo of naval gunfire, like yellow-red lightning, flared underneath me. I forced myself to focus on the instrument panel while my world tilted crazily. When the sensation passed, I leveled off and reported the gunfire to our controller on the _Hancock_. "What do you want me to do?" I asked.
What could we do? We didn't have bombs or unguided rockets. The Demon was configured for an air-to-air fight. It had a pair of cannon, but the Black Lions rarely flew with loaded guns—the shells were extra weight that the already underpowered bird didn't need. The _Hancock_ ordered us to return to the ship. We banked away from whatever fighting raged on the wavetops and fought our way through the overcast for another white-knuckle carrier landing.
When I was three miles astern, they gave me corrections to stay on the centerline of the glide path all the way to the deck. The ship appeared ahead of me. I held my approach and listened as the LSO coached me down. I dropped on the deck and felt the hook catch the three wire. Good landing. The aircraft functioned beautifully, and I lived to record another night landing in my logbook.
After my wingman got down safely, we went below for the debrief. Who had been shooting at whom? We never learned. Maybe it was one of our destroyers offshore, supporting some of our advisers in some battle right off the beach. Maybe it was a South Vietnamese warship shooting at rebel units involved in the coup. It was a foretaste of what was to come in the years ahead. We'd just witnessed a naval action almost a year before the Gulf of Tonkin incident pulled America into Vietnam's civil war.
Somewhere after midnight, my head hit the pillow. Sleep did not come. I couldn't help dwelling on the narrow margin we lived in on these night missions. Bad weather. Vertigo. System failures. Landing in total darkness. The risks never gave me pause. Well, unless we lost somebody. I just never thought it might be me. But things were different for me now, and in that moment, I felt mortal.
Mary Beth had gotten married to her football player. I never tried to win her back. Her marriage was the final nail in the coffin of my wishful thinking. I had to let her go. Eventually, I met a wonderful young woman in Coronado, Maddi, and married her in 1959. A year later, our daughter, Dana, arrived. My wife and I began a seventeen-year journey in Navy life, with far too much time apart.
Flying is a dangerous game of risk versus reward. Push too far and you pay the price. Before I joined the Black Lions, I only had to look out for myself and my squadron mates. Different game now. I lived for two others who depended on me. Becoming a family man coincided with my first fleet assignment aboard the _Hancock_. My 1962 deployment lasted from February to November. We got back to the West Coast and started training for the next one, running simulated intercepts in our Demons three or four nights a week. On that schedule, even when we were at home we were not really home. I've already explained what that did to families. Our 1963 deployment began in the spring after being home for less than six months. Hugs, goodbyes, tears on cheeks. Dana's little hand pressed into mine. Then back to the ship to manage a long-distance relationship through handwritten letters, voice messages on cassette tapes, and an occasional phone call.
The second parting for my family was worse than the first. I didn't want to be a stranger to my own daughter, but what choice did I have? The Navy needed me on the other side of the Pacific; it was my sworn duty to go.
We did not stay long off South Vietnam. The new military junta restored order surprisingly quickly in the wake of Diem's death even as the war against the Communist insurgency continued. Three weeks later, after John F. Kennedy was shot to death in Dallas, Lyndon Johnson was sworn in as president. The _Hancock_ sailed for home port a few days after the assassination. We reached San Diego on December 15, 1963, to a joyous reunion. It was our last peacetime holiday season for a decade, and the only "home by Christmas" moment that many of us ever shared.
# CHAPTER SIX
# THE PATH TO DISILLUSIONMENT
**Pearl Harbor, Hawaii**
**January 1967**
I stood at attention on the flight deck of the _Enterprise_ as the world's first nuclear-powered aircraft carrier steamed slowly in the channel past Hospital Point. A couple of tugs hove to, but were not needed. Every skipper in the Navy knew this channel like his own hometown.
Ahead and off to port, USS _Arizona_ lay in her grave. Above the national memorial, her flag flew proudly, the Stars and Stripes full in the wind. Beneath it lay the remains of more than a thousand sailors, killed on the first day of war on December 7, 1941, a full generation earlier. The USS _Arizona_ Memorial is the closest thing to a shrine that the Navy has, this side of John Paul Jones's crypt at the Naval Academy. Ever since that day of infamy, it has been tradition to render honors to those sailors whenever a warship arrives in Pearl Harbor. A flight-deck parade was the order of the day. A voice came over the ship's loudspeaker, "Attention on deck, hand salute!" As one, the crew of the _Enterprise_ touched our foreheads with our right hands and held position.
I'd done this before aboard the _Hancock_ , but it was different now, and everyone could feel it. Some of my shipmates held back tears in their eyes. After three years of war, we knew the cost. All those men, entombed in that shattered hull. Airpower did this.
After this short stop at Pearl, my unit, Fighter Squadron 92, would be on its way to Yankee Station, the patch of water in the Gulf of Tonkin where our carriers operated against the North Vietnamese. VF-92, known as the Silver Kings, would join President Johnson's three-year-long air campaign against North Vietnam, Operation Rolling Thunder.
I held the salute as we steamed past the _Arizona_ , oil still rising to the surface from her rusted fuel bunkers after all these years. The white memorial was filled with people, civilian tourists mainly, who looked away from the names of the dead to behold the Big E sliding through the channel with a thousand men at rigid attention in their tropical whites.
I'd returned from sea duty aboard _Hancock_ just as the last hopes to avert war in Vietnam were dashed. As the Gulf of Tonkin incident drew the United States into an open-ended, overt commitment, I received orders sending me to the fleet antiair warfare training center at Point Loma in San Diego. While other aviators went to war, I was on the beach, helping the Navy evolve from analog technology to digital battle management, developing computer systems for our shipboard combat information centers. After two cruises on _Hancock_ it was a welcome rest. I enjoyed two good years ashore with my wife and daughter.
In August 1964, the president authorized airstrikes against Communist targets. On August 5, Everett Alvarez, the son of Mexican immigrants who settled in Salinas, California, was shot down while piloting an A-4 Skyhawk bomber. The first U.S. naval aviator to be taken by the North Vietnamese, he endured more than eight years of torture in captivity.
I thought of the friends I'd lost since that first accident a few months after joining VF(AW)-3. Since then, the roster of the killed, missing, or wounded had grown long. Vietnam was chewing us up just as the Navy was trying to maintain America's global commitments elsewhere, from the Atlantic to the Indian Ocean. A lot of guys started getting out. When Rolling Thunder started, I was home. I was tempted to get out too. The airlines were hiring, offering salaries double or triple what we made as naval aviators. But I wasn't wired to be an airline pilot.
Whenever I was in San Diego, I went to North Island to see an old neighbor from my VF(AW)-3 days, Roger Crim. He was in charge of test flying the aircraft that had been patched up at the maintenance and overhaul facility. He usually let me check out a repaired bird. Thanks to him and one of his chiefs, I was able to fly everything from an F6F Hellcat to the aircraft that replaced the Demon, its larger, twin-engine cousin, the McDonnell F-4 Phantom II.
The first time I flew the Phantom, feeling the rush of reaching Mach 2, convinced me to stay in the Navy. When my tour of duty ashore came to an end, I arranged to receive orders to train to fly the new fighter, before joining a squadron on the _Enterprise_.
After ten years of flying fighters, I felt ready and confident. I'd aced the F-4 training at VF-121, the West Coast's replacement air group (RAG) for the Phantom community. This squadron prepared all new F-4 crews for their Vietnam deployments. We flew constantly, training hard at our beyond-visual-range missile intercepts. We even got to shoot a drone down with a Sparrow, one of the only times I'd actually fired one of these new high-tech weapons. On the ground, our instructors gave us intelligence briefs and taught us about our weapons and sensor systems. Then came survival training. We had to escape and evade the enemy force (our instructors) as if we had ejected into hostile territory. After a few days, I was captured—everyone was—and thrown into a thirty-six-by-twenty-four-inch wooden box with just a couple of breathing holes. When I made the mistake of revealing to the "enemy" guards my fear of spiders, they made sure to let me live with one for a while in that box. One cold night it crawled right across my face. This, of course, was nothing next to what the North Vietnamese were doing to our downed aviators.
After a few days in Pearl, we were on our way west to Sasebo, Japan. Our arrival was met by massive protests. Students and radicals opposed the Vietnam War. Others protested the first-ever appearance of a nuclear-powered ship not far from Nagasaki, which had been devastated by an atomic bomb on August 9, 1945. Armed with clubs and throwing rocks, the protesters tried to storm the base. The police, wielding truncheons, water cannon, and bare knuckles, needed two days to return the Japanese city to its natural state: quiet law and order. Things were raw then. When the carrier _Oriskany_ called at Sasebo around the same time we did, we learned that its air wing had lost half its aircraft over North Vietnam, and had suffered a third of its aircrews either killed, wounded, or missing in action. Their casualty list eventually included Lieutenant j.g. John McCain, the future senator from Arizona who was captured in October 1967.
Only a few weeks before our ships crossed paths, one of _Oriskany_ 's F-8 pilots, Lieutenant Commander Dick Schaffert, fought an epic duel against six North Vietnamese MiG-17s and MiG-21s. He had been escorting an A-4 Skyhawk strike when they were attacked. Schaffert fired all three of his Sidewinder missiles, but each malfunctioned or missed. When he switched to his 20mm cannon, the high-G maneuvering jammed the pneumatic feed system, leaving him defenseless. Nevertheless, he stalemated the MiGs with an exceptional display of flying before slipping away on the dregs of his remaining fuel. Other _Oriskany_ fighters showed up a moment later and downed one of the MiGs. They fired seven missiles in that fight. Only one hit.
Aboard the _Enterprise_ , we didn't know any of this at the time, but there was enough scuttlebutt to give us a sense that the intel briefings back in California had been anything but thorough. We didn't know what we didn't know. The enemy was a mystery to us. We didn't know their current capabilities; we didn't know anything about their tactics. The intelligence officers who briefed us talked a lot about the antiaircraft weapons we would face, as well as the surface-to-air missiles the North Vietnamese received from the Soviet Union. We heard that MiG interceptors were based near Hanoi, but learned little of those airfields, or the geography and weather of North Vietnam. I assumed that as we got closer to Yankee Station, we would receive more thorough briefings and get an accurate air order of battle—basically a list of North Vietnamese forces arrayed against us. That never happened. The reports that could have helped us turned out to be highly classified.
Though we were supposed to be heading to Yankee Station, a crisis developed off North Korea. En route to Subic Bay in the Philippines, we received orders to reverse course and speed to the Korean Peninsula. The North Koreans had sent a commando team to assassinate the president of South Korea, then captured a U.S. Navy vessel, USS _Pueblo_ , in international waters. Four torpedo boats, MiG-21 fighters, and two submarine chasers pursued the little intelligence-gathering ship. Their gunfire killed a sailor from Oregon. The North Koreans then boarded the ship, captured the crew, and began torturing them. They also scooped up enough classified material and encryption gear to allow the Soviets to read certain types of U.S. Navy communications for the next twenty years.
It was humiliating. We were locked in a war seemingly without end, and now another one seemed to be flaring. The Big E steamed off Korea as a show of force.
We arrived on station to face terrible winter weather. We sailed through blizzards and snow squalls that left us unable even to see the end of the flight deck from the ship's island. Then Washington told us we would be flying patrols in these storms. Of the almost hundred pilots aboard, only six were selected to fly in that horrible weather. I was tapped to fly wing on our squadron commander, Commander T. Schenck Remsen.
Nicknamed "Skank," Remsen was one of the rarest of leaders. A talented pilot, he led from the front and always took the toughest assignments. He had a natural energy about him that inspired the junior officers, and his concern for their well-being engendered absolute loyalty to him. Naturally, when word arrived that we needed to fly a patrol along the Korean coast in a snowstorm at night, Skank took the mission.
The flight deck turned out to be covered in ice. The crew had to assist us to our F-4 Phantoms so we didn't slip and fall. Once in the cockpits, we were towed to the catapults, so we didn't slide around on the ice. A night cat shot is always an experience. Add snow flurries and heavy seas and you've got a real adventure.
We climbed above twenty thousand feet but never broke free of the storm. It was so thick that Skank and I couldn't even see each other. My back-seater, Dennis Duffy, tracked him on radar and we followed a few miles behind. Snow and ice lashed our Phantoms. The windscreen was a kaleidoscope of snowflakes. It was like flying through a snow globe.
The _Enterprise_ finally vectored us to a holding pattern before we returned to the ship. As our approach time drew near, I thought it strange that they never gave us a weather report. We started our descents individually through the heart of the blizzard. Visibility was almost nil. Skank went in to land first, guided by radar from the ship. He saw nothing on that first approach. No lights, no carrier. Just blizzard and blackness. The landing signal officer said, "You sounded good when you went by us!"
When he finally landed, Skank and the landing signal officer talked to me as I swung around the ship again. Stay low. Follow the ship's wake. I got down as close to the water as I dared. Forty feet, maybe. The flight deck sits sixty-five feet off the swells. A red light began flashing in my cockpit. Low fuel. This was it. Either land or eject into the frigid seas and see how good our survival suits really were. Our life expectancy in the freezing water was five minutes. No thanks.
In the darkness, I found the carrier's white wake and followed it until I spotted the drop lights on the ship's stern ahead. They were _above_ me. The landing signal officer told me to climb. I pulled the nose up. As the Phantom's nose topped the ramp, I pushed the stick forward, and an instant later, pulled back up. This was an old trick a World War II ace named Zeke Cormier taught me. It saved my and Dennis's lives that night. The Phantom touched the deck, the tail hook caught an arresting wire, and we jerked to a stop.
As we waited for the deck crew to clear us, my knees trembled and my feet shook on the brake pedals. Of all the flying I'd done to date, this was the most demanding. Why somebody in Washington wanted us in the air that night is anyone's guess. I can't think of what we accomplished in our ninety-minute sortie, other than perhaps impress the North Korean radar operators, who undoubtedly tracked our progress through the weather. We had risked our lives for nothing. Who were these politicians to play games with our lives? I'd never questioned our chain of command before, at least not above the squadron level. We trusted that our leadership would not saddle us with needless risk. But that flight was the first step down a path of disillusionment we all experienced in the western Pacific. I sat in the squadron ready room with a mug of hot coffee and a bag of popcorn. _You're all right, man. You can enjoy life again_. But our problems only got worse from there.
Not long after our _Pueblo_ diversion, the _Enterprise_ 's air wing went into battle over North Vietnam. I flew my first combat missions filled with assumptions and expectations based on the stories I'd been told by the combat veterans I'd known. They had ripped a swath through our enemies in a way that has rarely been equaled in history. I expected to do the same over North Vietnam. But that was not how Operation Rolling Thunder rolled.
Conceived in Washington by Secretary of Defense Robert McNamara and approved by President Johnson, our bombing campaign was meant not to destroy the enemy's ability to wage war. It wasn't designed to demolish their air defense network, so we could operate over North Vietnam with impunity. It had nothing to do with tangible results or victory. It had everything to do with sending gradual messages to Hanoi. Where I had expected to be the tip of the spear, we were instead the thumb and forefinger of Lyndon Johnson's gradual escalation of pressure on the North Vietnamese. We weren't allowed to apply pressure anywhere that it might hurt. We were allowed just to pinch their metaphorical shoulder as a warning that if they didn't behave, we would pinch harder.
Gradual escalation of pressure on an enemy was a strategy conceived by people who probably had never even been in a schoolyard fight against a bully. Imagine the school bell's ringing at the end of the day. You head out to walk home, and along the way you see a bully beating up on a younger kid. You go over to help, but instead of knocking down the bully, you tap him lightly on the back of the head and say, "Keep that up, and I'll get serious!"
What's the bully going to do?
The Rolling Thunder campaign was LBJ's personal billy club. He would send us to smack the North Vietnamese for sending supplies and troops to the insurgents, then order unilateral stand-downs—known as bombing pauses—to give the North Vietnamese time to internalize the punishment and heed its lesson. But the pauses just gave them time to rearm. The American response seemed only to embolden Hanoi and convince its leadership that we were more worried about widening the war and possibly fighting China or the Soviet Union than we were about defeating them. They used the bombing pauses to resupply and prepare for the next onslaught. A lot of Americans died as a result. Some were friends of mine.
On Yankee Station, the _Enterprise_ air wing learned what this meant to individual aircrews. Johnson and McNamara micromanaged the losing air war from Washington, D.C., going so far as to pick our targets. There were perhaps 150 worthwhile things to bomb in North Vietnam. Airfields, military bases, supply facilities, power plants, bridges, rail centers, oil and lubricant facilities, a few steel mills, and of course Haiphong's port facilities. As both China and Russia wanted to be Hanoi's primary ally, they tried to one-up each other with military support. Large convoys of weapons and war matériel flowed across the Chinese border into Vietnam, while the Russians heavy-hauled tanks and surface-to-air missile systems via cargo ships to Haiphong Harbor. The enemy thus had sanctuary to bring in whatever was needed, and for years.
Afraid of escalating the war, the Johnson administration refused to sanction attacks on Haiphong Harbor or the shipping there. As we started flying missions up north, we would pass near those cargo ships as they waited their turn to offload at the docks. We could see their decks crammed with weatherized MiGs and surface-to-air missiles that would shortly be used against us.
But we couldn't hit them. And we couldn't mine the harbor, either. What a tragedy. The simple execution of an off-the-shelf aerial mining plan, long before perfected during World War II and carried out in three days, could have shut down that big port—the only one of its kind in North Vietnam. But the word from the White House was no.
Those big surface-to-air missiles, as large as telephone poles, would spear up into the sky after our aircraft, homing on their radar signatures. They took a heavy toll. We could seldom bomb the missile sites for fear we might kill their Russian advisers.
When the North Vietnamese began flying Russian-and Chinese-built MiG fighters, the Navy and Air Force asked Washington for permission to bomb their airfields. The request was denied. Categories of targets that could not be struck under any circumstances included dams, hydroelectric plants, fishing boats, sampans, and houseboats. They also included, significantly, populated areas. Seeing the military value of these restrictions, the North Vietnamese placed most of their SAM support facilities and other valuable cargo near Hanoi and Haiphong—places we were forbidden to strike. The airfields around Hanoi became sanctuaries for the MiGs; the commander in chief of U.S. Pacific Command, Admiral Ulysses S. Grant Sharp, who had overall responsibility for the air war, urged the Joint Chiefs of Staff to lift the crippling restrictions. Meanwhile, the enemy fighter pilots could sit on their runways in their planes without fear of attack, waiting to scramble when our bombers showed up.
Eventually, Johnson and McNamara caved to pressure and agreed to allow strikes on the airfields. Yet they micromanaged even this, picking specific airfields and leaving others out of bounds. "It was always necessary virtually to beg target authorization out of Washington bit by piece," Admiral Sharp wrote. Instead of letting the Navy launch a blitz that might break the back of the North Vietnamese Air Force, we hit a few air bases at a time while leaving the rest unscathed.
Postwar research suggests that Hanoi occasionally received updated target lists about the same time we did on Yankee Station. Our own State Department passed the list to North Vietnamese via the Swiss government in hopes that Hanoi would evacuate civilians from the target areas. Of course they cared little about that. They simply used the valuable intel to duck the next onslaught, moving MiGs out of harm's way and bolstering antiaircraft artillery and surface-to-air missile batteries in the target areas for good measure. Destroying the MiGs on the ground proved difficult enough, but we were also ordered not to attack them in the air unless they could be visually identified and posed a direct threat.
This was a setup for failure. And it got a lot worse.
Those rules of engagement negated the way we had trained to fight in the air. The value of our F-4 Phantoms was their ability to destroy enemy planes from beyond visual range. The AIM-7 Sparrow was the ultimate expression of that new way of fighting. Track and lock with the radar system, loose the missile from ten miles out, and say goodbye to a MiG. This is how the Navy trained us to fight. We abandoned dogfight training because of the Navy's faith in missile technology. Most of our aircrews didn't know how to fight any other way. Yet our own rules of engagement kept us from using what we were taught.
The rules of engagement specifically prohibited firing from beyond visual range. To shoot a missile at an aircraft, a fighter pilot first needed to visually confirm it was a MiG and not a friendly plane. The thought of inadvertent or accidental shootdown of our brothers was of course intolerable. It did happen, sadly, in the heat of combat. Yet three years along, the training squadron in California was still teaching long-range intercept tactics to the exclusion of everything else. Our training was not applicable to the air war in Vietnam.
This played directly into the kind of fight the MiG pilots wanted.
The MiG-17 was a nimble fighter armed with cannons, but no missiles. It was old school, derived from the lessons the Soviets learned in the Korean War. With such a plane, the North Vietnamese needed to get in close and track our planes with their gunsights. They would sometimes wait to open fire on us until they were within six hundred feet. Here we were, trained to knock planes down at ten miles. The F-4 carried only missiles; it did not have an internal gun because contractors and the Pentagon believed the age of the dogfight was over.
We brought our expensive high tech into this knife fight in a phone booth. The result? The MiG pilots scored a lot more heavily than they should have.
That one-versus-six fight that the _Oriskany_ 's Dick Schaffert survived illustrated another problem. He started the day with four AIM-9 Sidewinders. On deck, just before launch, one of the missiles was found to be nonfunctional and was pulled off his aircraft. That left him three. He fired all of those at the MiGs, but none hit. His gun failed him, too.
Our weapons didn't work as advertised. I'd like to say this was an anomaly, but the exact same thing happened before Pearl Harbor with our torpedoes. Those weapons were the high-tech wizardry of the 1930s, which meant they were expensive. The Navy couldn't afford to go blow up their torpedoes in training shoots. Instead, they used a dummy warhead that would cause the torpedo to float after its run. Very few live warheads were ever detonated prior to 1941.
So imagine the surprise when the torpedoes proved to be unreliable. They ran in circles. They didn't explode. The Navy bureaucracy resisted any suggestion that the torpedoes were malfunctioning, blaming instead the frontline sailors who were supposedly using the weapons improperly. It wasn't until 1943 that the problem was finally identified and solved. It was a purely technical issue.
Over Vietnam, our Sparrow missiles usually malfunctioned or missed. So did the AIM-9 Sidewinders. How could we not have known this prior to 1965? Well, history repeats: The weapons were so expensive that the Navy could not afford to use them in training. Live-fire shooting was done against drones flying straight and level, like an unsuspecting bomber might be caught doing. We didn't know we had a problem until the weapons had to be deployed against fighters.
While we never lost air superiority over North Vietnam, the MiGs and their pilots remained a significant threat. Their success against us pointed to a larger and more ominous problem: If the 170-odd MiGs of the North Vietnamese Air Force could inflict so many casualties on us, what would happen in a war with the Warsaw Pact and the Soviets, where they would outnumber us in the air maybe five to one? If Vietnam was a preview of our performance, we would be chewed up and overwhelmed.
We had to find a way to win in spite of these technical problems and political interference. Robert McNamara was a numbers guy. Under him, the Pentagon measured success in the ground war by the body count. In the air, the metric was the number of sorties flown over North Vietnam. One sortie equals one plane flying one mission. A ten-plane raid resulted in ten sorties. This became a delusional world. A sortie counted in the total even if our bombers were forced to dump their payloads short of the target, which often happened when MiGs appeared.
Facing pressure to generate sorties, the carriers were worn ragged. Aircraft handling crews worked twelve hours on, twelve off, spotting and respotting the decks, launching strikes, recovering aircraft, arming and refueling the birds, racing to meet the sortie rate required of them. Each pilot often flew twice a day, with each mission taking several hours to brief and debrief. We flew to the edge of fatigue and beyond. Aviators who were shot down and recovered were back in action in a short few days. During the _Oriskany_ 's December 1967 MiG battle, Commander Schaffert flew with an undiagnosed broken back because no other pilots were available. The injury prevented him from turning his neck to check his tail. To compensate, he unstrapped his shoulder harness and swiveled his whole upper torso. If he had to eject, he probably would have died. The Bear, as he was called, is a combat legend in naval aviation. He survived Vietnam to become a respected author on the war's history.
While the tempo took a heavy toll, it also led to needless tragedies, including major fires aboard our carriers that were the result of exhausted crews making mistakes. Scores of sailors and aviators died in those accidents, and the fires on two carriers were serious enough to risk the loss of the ship.
We were losing good men needlessly in the push to maintain the sortie rate. Why? Competition between the services. With the Air Force and Navy battling furiously for appropriations, both were determined to outdo the other in sorties flown.
In 1967, just before the _Enterprise_ arrived in the Gulf of Tonkin, the Navy and Air Force ran into a severe shortage of ordnance. With peacetime levels of production unable to supply the war's demands, the Pentagon resorted to buying back thousands of bombs that had been sold to our NATO allies, paying inflated rates. They took old iron bombs out of World War II–era storage. The carriers still had to fly many missions short on bombs. Instead of two planes carrying the available ordnance, six or eight would be used. That way, when McNamara saw the daily numbers, he didn't see any drop in the Navy's performance.
When the war revealed these weaknesses, the Washington bureaucracy was so moribund it could not find solutions. It kept us doing the same thing over and over with the same results: The North Vietnamese doubled down in supporting the insurgency in South Vietnam while we flew ourselves to exhaustion.
This has been a fast summary of a pervasive, serious, multilayered crisis. I can assure you it was far harder to experience it than it has been to write about it. The problem has been well explained in many other books. But it was real. It was tragic. And it was a bitter experience for those of us who survived it.
The only difference in my telling is that I would be given the responsibility of doing something to fix the problem. I'll get to that story in a moment. But first I'll have to show you how a carrier air wing survived a tour on Yankee Station in 1968.
# CHAPTER SEVEN
# YANKEE STATION EDUCATION
**Yankee Station, off the coast of Vietnam**
**Early 1968**
I stood in the locker space next to our squadron ready room, donning G-suit, boots, gloves, and packing my survival gear for the next mission. I reached into my locker and grabbed my Ray-Bans. More than a decade old, they came with me on almost every flight. As I took my helmet from my flight bag, I found my little stuffed mouse. Still there in his nest, beaten up from transoceanic travel, he peered out at me with the same stoic expression that caught my eye in that unvacated locker at North Island.
_Hey there, fella._
The mouse was my good-luck charm. Thousands of hours in high-performance jets. Combat over Vietnam. Night landings aboard old carriers—that critter saw me through all of it. I thought about giving him to Dana. She was eight now and would probably love him. Then I remembered his original owner. I had no right to gift this toy. His home would always be in my flight bag. I'd have to get my little girl something else when I got home.
When. Not if.
I gave the mouse another look, then returned the bag to my locker. Helmet in hand, I almost forgot my National Match Colt .45 pistol in its shoulder holster. Another good-luck charm that I had flown with ever since my father-in-law, Coronado's assistant chief of police, gave it to me. Retrieving it, I was good to go.
I wanted a MiG. Badly. All us fighter pilots did. But those North Vietnamese pilots were cagey and elusive, thanks to their radar ground control and the handcuffs that were locked on the wrists of those who wanted to destroy them. Weeks would pass without any American spotting a MiG. Then suddenly they would come streaking out of nowhere to tear into our thirty-plane strike formations.
I had yet to encounter one on any of my flights over North Vietnam.
Day after day, we flew missions from Yankee Station to hammer targets of questionable value. We bombed truck convoys when we could find them on search and destroy missions. They moved mostly at night in total darkness. We bombed supply depots and occasionally went after power plants, as well as military barracks long flattened by the squadrons who had deployed before us. We went after bridges and SAM sites. Very occasionally, we received permission from Washington to hit the MiG airfields around Hanoi.
The F-4 was designed from the ground up to be a Mach-plus interceptor. It was supposed to be the bane of all Soviet-built strategic bombers. Over Vietnam, the Phantom became perhaps the most versatile multirole aircraft America ever produced. Still with its interceptor heart, it functioned as an escort fighter, a utility strike bomber, and, south of the Demilitarized Zone, a close air support attack aircraft.
We were doing it all, learning on the job how best to carry out our missions. And they were never the same. But the two-a-days over the North, usually one at night, left us worn out. Lack of quality sleep also put our nerves on edge at times. We grew easily frustrated. Some people started to withdraw under the pressure, the exhaustion, and the grief over losing so many friends. This didn't happen in my squadron. Skank and the other senior pilots set the example by flying almost all the difficult missions with the junior crews, while never griping about the targets or the rules of engagement. They were great pilots as well as tremendous inspirations to all of us. Skank kept us focused and working as a team, taking care of each other as we flew daily into harm's way. In our air wing, all of the squadrons were led by example. It wasn't always that way, as some other outfits experienced.
We were losing guys to SAMs, flak, and even marauding MiGs whose pilots, well directed by radar, would launch slashing attacks into our formations. They were particularly adept at hitting the Air Force F-105 Thunderchief fighter-bombers, forcing them to jettison their ordnance and sparing the targets from being struck again.
Naval aviation and the Air Force will always be rivals as well as brothers in arms. In 1968, I felt for those Thud pilots, who took heavy losses over North Vietnam. Out of 833 F-105s built by Republic, 382 went down in Southeast Asia. Those Thud pilots were like our A-4 Skyhawk drivers—courageous and dedicated American heroes.
This afternoon, it was our turn to go beard the North Vietnamese lion. Dressed, armed, and ready to go, the pilots on the scheduled mission walked into the Strike Operations Center for the briefing. We usually went to the Strike Ops Center because that's where the ship's intelligence officers worked. We considered them lazy and figured they had no idea where our ready rooms were, so we made it easy and went to them.
As we entered, I caught sight of the day's map and my heart sank. No chance of MiGs on this run. The target area straddled the DMZ between North and South Vietnam at a place called Khe Sanh.
At the end of January, the North Vietnamese Army launched a major attack against a series of special forces outposts and the Marine firebase at Khe Sanh, which sat up on top of a flat-topped hill with all sides exposed. The embattled American and South Vietnamese troops were soon surrounded, deluged with artillery fire, and cut off from overland resupply. Helicopters and transport planes trying to get into the small airfield at Khe Sanh faced a gauntlet of antiaircraft weapons on their approach, then mortar fire as they touched down on the runway. A night assault by the North Vietnamese managed to break through the base defenses, but before they could exploit the penetration, a Marine platoon counterattacked into the charging enemy troops. In a swirling fight that evolved into a brawl with bayonets, rifle butts, and bare knuckles, the Marines threw them back.
They were holding on with sheer guts and firepower. Overhead, two Air Force B-52 Stratofortresses gave the Marines support by carpet-bombing the enemy's positions. Marine aircraft, other Air Force fighter-bombers, and now the Yankee Station air wings were joining the fight to save the firebase and the lives of the valiant men enduring the siege.
We launched late that afternoon and flew two hundred miles to our marshaling station above Khe Sanh. With the battle filling the surrounding valleys with gray-black smoke, we had only glimpses of what was happening below. The airfield was a scene of carnage. Burnt-out aircraft lay pushed to the side of the runway, victims of the mortar barrages. The base itself looked like a lunar landscape, with thousands of shell craters overlapping in the soft reddish soil.
I checked in with the Marine forward air controller whose job it was to guide us onto target. He was down there, right among those young American kids, enduring the artillery barrages and night assaults alongside them. With his radios and expertise, he was their fist of God. He was probably a Marine aviator as well, so he spoke our language and understood our perspective.
The forward air controller heard my check-in radio call and responded immediately. The situation sounded dire from his description. North Vietnamese troops were massing just beyond the wire for another night assault, and he wanted me to hit them with everything under my wings before darkness gave them the opportunity to attack again.
The late day offered a rare cloudless sky. The blue stretching above me contrasted with the ugly coils of smoke and flame filling the valley under my Phantom's nose. After receiving my instructions, I started down to begin my run.
"Keep your speed up, five hundred knots, four hundred feet, they'll be shooting at you," called the forward air controller. "Drop all your Snakes on my signal. Remember, there are Marines on the wire, just off your left wing."
I carried a dozen five-hundred-pound Mark 82 Snake Eye bombs. When we dropped these, spring-loaded air brakes or fins would deploy, and the bombs would fall virtually straight down at the point of release. It made for a very accurate weapon, plus it gave us aircrew time to get away from their explosions and fragment patterns when we were dropping from low altitude.
I leveled off at four hundred feet, going five hundred knots. The Phantom sped through clouds of smoke. From the hills to our right, small-arms fire erupted and my back-seater, Dennis Duffy, and I could see the muzzle flashes. Moments later, red-orange tracers laced the sky ahead and level with us.
With my high speed, I wasn't so concerned with taking hits from those North Vietnamese troops on the right of us whose tracers were horizontal, but I was terrified of blowing the run and dropping my Snakes on the Marines near the wire by accident. Earlier, an inexperienced Navy pilot did just that by accident and wounded some of our men.
The idea of killing Americans with a misplaced bomb? Well, I knew I would never get over that if it happened.
I listened carefully to every word the forward air controller said. If I wasn't exactly level, the bombs might fall right or left of the target area, depending on where my wings were to the horizon. Holding steady while every bad guy with an AK-47 seemed to be shooting at me was no easy feat. In fact, it was the toughest flying I'd ever done.
I checked my heading. Wings level. A split second later, the forward air controller called, "Drop! Drop! Drop!"
I pickled the Mark 82s. The F-4 lurched upward as the six thousand pounds of bombs came off our hardpoints and began falling toward the ground. Simultaneously, I pushed the throttle further and lit the burner. The Phantom's twin J79 engines responded and we pulled up with five Gs back to where we belonged—far above the fray.
Duff, my back-seater, said, "Let's haul ass, Kemosabe!"
As we climbed, my throat constricted, heart filled with dread while we waited to hear from the forward air controller. Toughest part of the mission is waiting for the results from the big grunt FAC.
_Oh shit. Did I just kill a bunch of Marines?_
No word from the controller. The altimeter needle spun as we speared through three thousand feet. The seconds ticked off. No word. Behind me, Dennis was probably twisted in his ejection seat, trying to see where our bombs had landed.
_Oh shit..._
The radio filled with static, then the forward air controller's voice shouted, "Great run! Great run! Right on target!"
I started to breathe again. Then a big smile formed under my oxygen mask. We'd done a few of these close air support runs in training, and a couple more over South Vietnam on our way to Yankee Station, but nothing like this. Those Marines were dangerously close to the release point.
One by one, my division of Phantoms made their runs, then we formed up and flew back to the ship, or home plate, as we called it. For days we flew these missions, supporting those desperate Marines. It felt good to be doing something useful. Every North Vietnamese we took out by our bombs was one less rifle pointed at our men below.
The Marines held. And as a joint Army, Marine, and South Vietnamese rescue force battled its way up Highway Nine to break the siege, the _Enterprise_ air wing returned to its regularly scheduled programming over North Vietnam.
We flew day and night in any kind of weather. We flew alpha strikes, which were large, unwieldy raids of thirty or more planes. We F-4s provided escort against the MiG threat, or went in to suppress air defenses while A-4 Skyhawk attack planes struck the targets. We flew two-and four-plane armed recce missions, searching for anything worthwhile Washington allowed us to bomb.
Because we owned the airspace over their country, the North Vietnamese took to sending war matériel and men south to the war zone under the cover of darkness. To counter this, we flew at night, hunting for their vehicle convoys in hopes of catching them on the roads heading south.
The North Vietnamese guarded those truck convoys with light antiaircraft guns mounted on armored cars that looked a lot like the ones we built and supplied to the Soviets during World War II. With heavy machine guns or light cannon, they could hammer at us as we dove down to make our attacks.
The rules of engagement made it much easier for them to hit us. Washington dictated that we drop flares first, identify any trucks as military vehicles, then dive down under the flare light to deliver our attacks. The enemy quickly figured this out. Whenever we dropped a flare, their gunners would lace the illuminated area below it with tracers and exploding antiaircraft shells. We'd dive through all that incoming and get a split-second opportunity to release our bombs.
Once again, it would have been really nice to have had an internal 20mm cannon for such moments. We could have strafed our way in and suppressed some of the fire coming back at us. Instead, we just had to take it. There is nothing more frustrating than being a target that can't fight back until your bombs impact behind you.
One night, I was leading a two-plane armed reconnaissance patrol looking for movement on Highway One, which ran down the coastline. Near the port of Vinh, perhaps 160 miles from Hanoi, we caught sight of a couple of dim lights on the road.
_There are no friends of mine down there, that's for sure._
Free from concern for a friendly fire incident, we looped around and decided to attack west to east along the road. Normally, either we'd make a pass and drop a flare, or one plane would drop the flare while the other attacked under it. Better yet, sometimes we delayed our attack until the flare burned out and most of the flak had stopped. We were a whole lot smarter than those rules of engagement writers back in D.C., and our being unpredictable gave the North Vietnamese gunners fits.
_I'm tired of getting shot at. Screw the flares._
We carried cluster bombs that night. Think of these things as mother bombs that open up and released to spew dozens of small baby bomblets all over the area below. These hit the ground, detonate, and do their damage with thousands of whirring fragments of shrapnel. They were designed to kill troops in the open, but we found that they could cut through unarmored vehicles and set them afire. A good drop with a full load of cluster bombs from an F-4 would create a kill zone hundreds of meters in every direction. They were devastating weapons and much feared.
Down we went, my wingman trailing offset, just behind me. I released first. He followed a heartbeat later, and as we pulled off target and climbed into the dark night, two full loads of cluster bombs lit up a truck convoy filled with munitions and barrels of fuel. The fiery streaks in the air above Highway One could be seen for miles. Pilots patrolling the coast that night saw the fireworks on the horizon and asked, "What's happening down at Vinh?" That night we put a dent in the logistical train supplying the Tet Offensive in the South. These were moments to savor.
After we returned to the ship, I got a surprise. Following the debrief, some staff weenie stormed up to me and threatened to court-martial me for violating the rules of engagement. That flare I didn't drop? Yeah, that could have cost me my career, thanks to the rules of engagement and lockstep thinking of noncombat officers. I told him to pound sand. The attack was one of the most successful missions the squadron flew. It was also a reminder that in McNamara's war, the margin between a court-martial and a valor award was thin.
The missions continued, as did the losses. There were nights I got back to my bunk struggling with despair. Seeing friends die is never an easy thing. At times, you think you grow hard to it. Other times, their deaths open wounds that the heart simply cannot heal. On those nights, I would crawl under the covers and lay there, unable to sleep despite my exhaustion, mind racing.
_Could we have done anything different? Could he have gotten out and we just didn't see the chute? Fortunately, none of them were from my squadron._
I'd try not to think about their families back home, but the faces of the wives and kids would sometimes elude those efforts, and they would come back to me in a rush. I found through my Navy career that some men revel in the challenge and rush of combat. That pace off Vietnam? It was their hunting ground. Me, I never got to that point. Combat was a responsibility, even a sacred duty. That moment as we passed the _Arizona_ was a reminder of that legacy and the connection we combat pilots shared in it. I took it very seriously, of course, but I never liked it. Those men I would never see again, those families I would see too soon again—they were the cost of that adrenaline rush others craved. That was a burden I couldn't carry and love at the same time.
The enemy always had a say, and that was the wild card in combat. You could do everything right. Your division could do everything right. Your chain of command could make every right decision and lead from the front, like Skank did. Yet we faced a cunning, devoted, and frankly courageous enemy who found ways to surprise us with new tricks.
On those sleepless nights, my brain refusing to shut off, I would think of those empty wardroom chairs. We lost some excellent pilots. All the talent in the world was not enough when fate called your number.
I didn't go to church much after I left home, but I never lost my devotion. As the missions grew tougher and the roster of the dead and missing grew longer, I relied heavily on that faith to see me through. Knowing that there is a purpose, that it wasn't all about capricious random acts of chance that could kill us, gave me a measure of comfort that made getting into the cockpit every morning an easier task.
In those sleepless nights, which most of us out on Yankee Station had, we did our best not to think of home. It could make you cautious, hesitant in the air, get you killed. If you were wise, you never looked past the next dawn. Some combat vets would tell new guys, "Assume you're never coming back, truly believe it, and you will make it home." It was a psychological paradox of battle.
In my darkest times, I would think of Mary Beth. The heart loves who it loves. Nothing can change that. While I had not spoken to her or seen her in over a decade, I remembered every nuance of her face. I worked on my marriage every day I was home in California. I loved my wife and always would, whether we made it through the ordeals of combat and separation or not. But in my most honest moments, I knew Mary Beth would always be the love of my life, and it gave me comfort to know she was out there in the world. Most people never find their soul mate. At least I knew who mine was, even if I never saw her again.
After weeks of nonstop operations, we left Yankee Station and set course for Subic Bay for a rest period. We were wound as tight as humans can be. If you've ever watched the opening scenes of the movie _Das Boot_ , you may understand the craziness we unleashed at the Cubi Point Officers' Club. These breaks from combat offered a chance to release the tension. It came out in spasms of partying, womanizing for a lot of the guys, stunts, pranks, and rivers of alcohol.
The club sat on a hill overlooking Subic Bay's mile-and-a-half-long runway. With a thatched roof, a concrete floor, and disposable plastic or metal furniture, the place pulled off the stereotypical tropical dive bar aura perfectly. We drank the beer that helped make Andrés Soriano one of the richest men in history. His San Miguel beer cost ten cents a bottle and there was plenty to be found.
The place had catered to nearly every naval aviator who's ever done a WestPac cruise. The walls memorialized them, and in that respect our tropical dive bar was part museum, part memorial to those who came before us. Every squadron contributed plaques or photographs or memorabilia. It lent the place a hallowed feel, and in later years after Subic Bay closed down and the Navy left, the Cubi Point O Club was almost perfectly replicated back in Pensacola at the National Naval Aviation Museum. It was that important to us.
We had some unique features built into the place over the years. A local engineer and some junior officers built a small catapult track including an old aircraft cockpit with a tail hook release handle. Its propulsion system was nitrogen-powered and shot you down a short track. If you didn't get the arresting hook down to catch a wire you ended up in a tank of lukewarm water. Actually, it was probably mostly beer, though I suspected that late at night some junior officers had added other ingredients. Loud cheers followed any attempt, successful or not. The "cat track" was indifferent to the rank of the man in the cockpit. One night I watched the secretary of the Navy get very wet a couple of times.
The coiled tension sprang out of us in other ways. With lots of alcohol came an erosion of self-restraint, and those resentments built up on Yankee Station leached out of us at times. There were arguments and fights. Having learned on Yankee Station that rank alone did not make you a leader, we did not consider every superior as such. Leaders had courage, skill, and a willingness to set a good example. They took the toughest missions while working harder than everyone else. Those who did not measure up were obeyed only because of their rank and the fact that we were devoted to the discipline our Navy had instilled in us.
One night, an air wing commander who was roundly despised by his men somehow triggered his junior officers. Rank forgotten, the young guys started throwing punches. The air wing commander fought back, but, outnumbered, he was beaten to the deck. Still he refused to quit. He called out his men to bring it on, and they went at it again. Nobody intervened. That was an internal affair best resolved as warriors will. When the beatdown ended and the air wing commander lay on the deck, bloody and put in his place, his pilots looked down at him and one shouted, "Now we're even, CAG."
When you're asked to risk your life day after day for a cause that often made no sense, bound by rules that made it more likely you would die, poor leadership was often the final straw. That night, I felt grateful we had Skank Remsen leading us into the fray.
After about a week in the Philippines, we rotated back to Yankee Station, stopping along the way at a point off South Vietnam for a combat refresher. This was Dixie Station, from which we launched missions in direct support of the men fighting on the ground. There was little AAA, and no surface-to-air missiles here in the South, so these missions gave us a chance to get our heads back in the game before heading north to continue the Rolling Thunder campaign.
At the end of March, in a speech declaring that he would not run for reelection in November, Lyndon Johnson changed the entire dynamic of the air war. He announced an immediate suspension of all bombing attacks north of the 20th parallel. Just like that, Rolling Thunder was over, neutralized by a lame-duck president.
Up until then, the MiGs had been forced to operate from China, reducing their effectiveness. When LBJ told the world where we would not be bombing anymore, he essentially told the North Vietnamese we were giving their fighter regiments a safe space again. At the same time, the new restrictions greatly reduced the Air Force's role in the air war over North Vietnam. The onus to continue it fell on the Navy.
The MiGs returned to their nests around Hanoi, the pilots rested and better trained than in the past. They studied our tactics and developed their own new ones to counter ours. It didn't take them long to come after us.
On May 7, 1968, five of our F-4s ran into what they thought was a pair of MiG-21 interceptors, one of which was piloted by Nguyen Van Coc, an ace with six American planes to his credit. The MiGs took off from Xuan Airfield and sped after an EKA-3B Skywarrior, an all but defenseless electronic warfare aircraft and tanker.
The plan was to use our Sparrow missiles and engage the MiGs once they'd been radar identified. With the airspace north of the 20th parallel essentially free of Air Force aircraft, radar could suffice to identify MiGs as they took off. No longer did we need visual identification to fire. We were going to use our interceptors as intended: missile platforms for beyond-visual-range missile shots.
The sky was hazy with broken clouds, making it perfect for our all-weather F-4s. Instead, the battle was a confused affair on both sides from the get-go. Our Phantoms raced to intercept and rescue the Skywarrior's crew, whose jamming efforts failed. As the F-4s closed, local ground defenses mistook the MiGs for American aircraft. NVA antiaircraft gunners lit up their own planes. They broke off the intercept and circled over Do Luong until their ground controller sent them after the Phantoms.
The MiGs spotted the F-4s in heavy cloud cover at about nine thousand feet. It turned out that the two lead MiG-21s tracked on American radar were bait. Trailing them were two other MiG-21s staying low over the treetops to hide from our sensors.
Four on five were the odds, and two F-4s encountered the MiGs first. A pair of Sparrows left the rails but lost their locks, missing their targets. As a cat-and-mouse game developed in the clouds, one of the F-4s got separated from the others. Nguyen Van Coc, low on fuel at this point, was about to turn for home when the lone F-4, flown by Lieutenant Commander Einar Christensen, a pilot from our air wing staff, and Lieutenant j.g. Lance Kramer, crossed in front of him. Nguyen Van Coc fired a pair of heat-seeking missiles—copies of the Sidewinder captured a decade before during the air battles of the Taiwan Strait.
One of the missiles struck home, knocking the F-4 out of the air. Christensen and Kramer managed to eject, and they were subsequently rescued. They were the North Vietnamese ace's ninth and final air-to-air victory.
Two days later, a pair of Big E Phantoms tangled with three MiG-21s, possibly four. The F-4 crews fired four Sparrows but did not score a confirmed kill. Fortunately, all of our aircraft returned that day. The MiGs were getting more aggressive, and I was getting more and more eager to encounter them.
On May 23, 1968, I led an element of two F-4s in Skank Remsen's division during a BarCAP patrol. BarCAP was short for barrier combat air patrol. It put us on station between our carrier task force and the North Vietnamese coast in such a way that we could quickly intercept any MiGs launching from the fields around Hanoi.
Usually these were boring missions where nothing happened. The MiGs made rare appearances, but never when I was up there. This day turned out to be different. A group of MiG-21 interceptors—those latest and greatest examples of Communist high tech donated to the North Vietnamese cause—sped off one of their runways and climbed out toward the coast, looking for trouble.
This was the moment every fighter pilot wants. While I never liked combat, I did want to find out just how good I really was. The years of hassling off San Clemente—the secret fight club that kept the art of air combat alive in the fleet—those moments of risking aircraft and career boiled down to what we could do with our aircraft when challenged by the enemy's MiGs.
Our ship-based radars picked up the MiG launch almost right away. The controller called us and gave us a vector. Skank pointed his nose toward the shore; my wingman and I did the same. Power on, J79s roaring, we sped toward the fight of our careers.
As we closed, the controller called out, "Bandits, bandits! You're clear to fire!"
It was a perfect intercept. Textbook. The MiG-21s appeared on our airborne radars. Our rear-seaters stared at the scopes, calling out targets and seeking a lock for our long-range Sparrow missiles. We'd been taught to shoot those AIM-7s at about twelve miles. Skank held our fire and narrowed the range, hoping to give us a better chance at a kill.
We achieved lock-on with good missile ready lights. We had our targets. They were coming at 12 o'clock, so it would be a perfect shot. Sparrows worked best when fired head-on.
Skank was about to fire when our radios squawked, "Silver King, this is Red Crown, Salvo! Salvo! Salvo!" It was an order to break off the attack and get out of the area.
We turned back toward the fleet, puzzled. A moment later, our controller amplified the warning. The guided missile cruiser USS _Long Beach_ had been hiding offshore with its electronics shut down. Steaming in her place in our defensive screen was a smaller destroyer. The North Vietnamese knew the general range of our surface-to-air missiles and knew that the destroyers carried older variants that didn't have very good range. Thinking they were clear of any surface-to-air missile threat, they launched those MiG-21s. They ran right into that cruiser.
After we detected them, the _Long Beach_ lit up its radar and weapon systems. From sixty-five miles away, they locked on to the MiGs—just as we were about to engage. A barrage of Talos surface-to-air missiles from that warship went streaking over us. We were forced to break contact. The MiG-21s ran for home. One was shot down and another one was probably hit as well. It was one of only three surface-to-air missile kills by the Navy during the Vietnam War.
I could have not cared less about that success. Those cruiser sailors had poached our MiGs and denied us a chance to see how good we really were. And they had actually fired, it seemed, with no regard for our presence, a dangerous roll of the dice. We landed on the Big E bitterly disappointed. If we had fired at twelve miles, maybe things would have been different. The missions continued, but I didn't see another MiG.
It was a tough cruise, but it left us all with an indelible lesson in what real leadership looks like. Some time later, leading a strike mission at low altitude, Skank Remsen took a rifle round through the cockpit, straight through both thighs. He took his leg restraints, slid them up both legs, cinched them tight, and used them as tourniquets. He then flew one hundred and fifty miles and successfully landed aboard the carrier. Flight deck medical staff got him out of the airplane and rushed him to surgery. He refused medical evacuation to a stateside hospital and remained on board to heal. Two weeks later that tough old hombre was back in the saddle, flying combat missions with his boys. Now that's my idea of real leadership.
On June 14, F-4s from our sister carrier, USS _America_ , got into a scrap with some older MiG-17s. The Phantom crews tried to knock them down with Sparrows and managed to get four off in the short fight. All four missed. Two days later, the _America_ lost an F-4 from VF-102 in a dogfight with MiG-21s. Four more Sparrows went downrange, but not a single one struck home. The crew ejected over North Vietnam. The pilot was captured, his rear-seater killed.
We'd lost two Phantoms in a month, fired more than a million dollars' worth of high-tech smart weapons, and suffered one KIA, one MIA. This was a shocking development, especially since neither the air wing from the Big E nor the _America_ had managed to offset the losses with a kill.
A couple nights later, I was part of a flight of F-4s that provided air cover for a Navy helicopter searching for two Phantom crewmen from VF-33 off the _America_. They'd been shot down by a SAM deep inside North Vietnam, and the helo, piloted by Clyde Lassen and LeRoy Cook, ran a gauntlet of ground fire while skirting the treetops in the darkness.
My back-seater Duffy and I circled the scene. We carried air-to-air missiles and nothing else that night, which made us feel truly useless. A 20mm gun at least would have allowed us to dive down and strafe the enemy gunners shooting up the helicopter. No gun gave us no recourse but to stay above and help coordinate the rescue and communications while stewing over our helplessness.
Lassen couldn't find the F-4 crew, and the crew couldn't locate the helo. His rotors hit some trees on his first rescue attempt. Lassen decided to try again. Low on fuel, he flicked on his navigation lights. And every North Vietnamese soldier in the area opened fire on them. The jungle below was a web of muzzle flashes and tracers.
The aviators on the ground spotted the lights and tried to move toward the helicopter. John Holzclaw, the pilot, dragged his back-seater, Zeke Burns, to a clearing. The ejection and hard landing had broken Zeke's leg, and his survival depended on his front-seater's stamina and determination.
Lassen touched down in a rice paddy, his crew chief and copilot laying down fire to suppress the North Vietnamese with his M-16 rifle. LeRoy Cook, the copilot, fired his weapon through the helicopter's open side window. The downed Americans reached the helo and were helped aboard. The crew chief, Bruce Dallas, jumped in, and the battle-damaged bird sped for the coast. They made it to an offshore cruiser and landed on her helo deck with five minutes of fuel remaining. Lassen earned America's highest award for bravery, the Medal of Honor, for his actions that night. In my many months of combat on Yankee Station, it was the bravest and most selfless act I witnessed. After that night, I never forgave the Navy for failing to arm the F-4 Phantom II with a gun.
That rescue proved to be one of the last missions we flew from Yankee Station that June. We were getting ready to head home by this point, having been out since the beginning of the year. The MiGs were getting increasingly active, and in June we fought them three more times. Thirteen Sparrows were fired in those three engagements, but none of them hit.
We left Yankee Station in July, just as things reached a boiling point. On July 10, a VF-33 Phantom crew brought down a MiG with a Sidewinder shot. That helped ease the pain a bit, but a month later, the air wing that replaced ours launched off USS _Constellation_ and was intercepted by MiG-21s. In the ensuing fight, a Sidewinder fired at a MiG locked on to a passing F-4 and brought it down. The crew ejected and reached the ground, only to be captured before the search and rescue helo could get to them.
As those two final summer acts played out, the Big E and Air Wing Nine returned to the United States. We were worn out, beat up, and bitter. Between the end of February and the end of June, our hundred-man air wing had lost thirteen killed or captured, ten bombers, an F-4, and a Vigilante reconnaissance plane. Something was very, very wrong.
If we were going to regain the dominance that was naval aviation's birthright, we would need to make changes. My orders were cut: I had been assigned to the Phantom fleet replacement squadron at Naval Air Station Miramar. As luck would have it, there, in the bustling enclave of Fighter Squadron 121, I would have the chance to help solve our costly, tragic problem.
# CHAPTER EIGHT
# STARTING TOPGUN
**Naval Air Station Miramar, California**
**Fall 1968**
Fightertown USA. That's the long-standing nickname of the naval air station whose Spanish name, Miramar, doesn't seem to suit the place. There's no "view of the sea" from its location fifteen miles north of San Diego, five miles in from the coast—at least not until you've gone wheels up and are flying west on what the air controllers call a Sea Wolf departure. No, the unofficial nickname painted on Hangar One is a much better fit. On the runways, ramps, and taxiways of the sprawling complex, the shriek of jet engines and the smell of aviation fuel was constant.
If my love of flight had been tested by the war, I still never shook the habit of lifting my eyes to the sky whenever a jet roared overhead. Who was it? How was he doing? What's going on? As an instructor, it was my job to keep track of my nuggets.
When I parked my sea bag at Miramar again, this time to serve as a tactics instructor at Fighter Squadron 121, I found the pace of daily life clipping along at a fast wartime tempo. The whole West Coast naval shore establishment had ramped up to support the war in Vietnam, and VF-121 was hauling a heavy load. As the fleet replacement squadron for all F-4 Phantom squadrons based on the West Coast, it had a clientele that included all the carrier air wings in the Pacific. As I mentioned earlier, we called it the RAG, based on its name during World War II, a replacement air group. Each type of aircraft had its own RAG squadron supporting it: the A-1 Skyraider, A-3 Skywarrior, A-4 Skyhawk, A-6 Intruder, A-7 Corsair II, F-8 Crusader, and various antisubmarine and early warning aircraft. Fighting 121 handled the F-4 community. Anytime a carrier lost a Phantom, we produced a replacement plane and a two-man crew. It was but a short flight from our runway to the flight deck of a carrier bound for Yankee Station. We understood the reality that loss and death were a part of our trade. A lot of good men never came home. Whenever word came of another aircrew killed, captured, or missing, it haunted us. In 1968, no one at Miramar was in the mood to fool around.
Our fighter squadron was the largest in the whole Navy when I was there. It had an average of about seventy F-4Bs and F-4Js assigned to it, and 1,400 officers and enlisted men, including administrative and maintenance staff. A squadron that big did not go to war. A home-bound training command, it made sure the squadrons that operated from our aircraft carriers at sea were at full strength and ready to go. Given how poorly the air war was going, the squadron's nickname, the Pacemakers, was apt. You might say the war was on life support as our losses mounted. So we did our part to keep the pipeline full, turning out new aviators as the war whittled away at our ranks. In 1969 the RAG would graduate more than 150 pilots and RIOs to fly the Phantom. No group of F-4 drivers, RIOs, maintainers, and mechanics that I ever knew had a stronger claim on their pride.
I was an instructor in the advanced tactics phase (or department) of the squadron. A good man, Lieutenant Commander Sam Leeds, was head of tactics. Our students had been through the mill by the time they got to us. After they got their wings, ground schools somewhere had taught them how to fight fires; survive isolation on water, on land, and as prisoners; read and report air intelligence; use their cockpit instruments; and master the many systems of our McDonnell Douglas fighter aircraft. Basic air combat tactics was my area. Young pilots always had smiles on their faces when they got to our phase of training. With me, they got to do some real flying. At the same time, they were going through a series of intensive lectures; this flight phase had them learning basic aircraft aerodynamics, instrument flying, basics of air-to-air interception, weapons, navigation, electronic warfare, and carrier qualifications (it can't be said often enough: finding a moving carrier at night and landing on its flight deck is not for the faint of heart). The tactics we taught them were nothing advanced. The syllabus was standard Navy tactical doctrine, complying with all the restrictive published guidelines about how the F-4 Phantom should be flown. They learned how to fire their weapons, drop bombs, and use long-range radar to intercept a distant target. It was like an undergraduate education, about as advanced as Biology for English Majors, just the essentials of flying and maneuvering in an F-4 and using its weapons to defeat another pilot or destroy a target on the ground.
What kept us from pushing the aerodynamic limits was the attitude of risk aversion that commonly afflicts training. The worst thing we could do, as far as our higher headquarters was concerned, was lose a plane. So twice a day, when I took new Phantom pilots and their back-seaters up to fly, we played it safe. We did air combat maneuvering, or ACM, but always within strict safety parameters. We never let them fly below ten thousand feet. You might say the Navy didn't want to risk voiding the warranties on their new planes. As a result, the program lacked combat realism. The first time RAG pilots saw the radical maneuvers that modern jets were capable of, tracers were flying. Their eyes had not been opened. That's not how you want to send a young man off to war.
Even still, by the time the students finished our phase of training, they were ready for further training, and ready for assignment to the fleet. The daily tempo of flight training was dangerous enough. The enemy took things to another level. He always gets a vote, a wise person once said, and in the skies over North Vietnam the enemy was voting in droves. Finally the time came for the Navy to do something about it.
Not long after my arrival, late in December, Sam Leeds called me into his office and showed me a thick document bound in a blue cover. It was a study issued by the Naval Air Systems Command. Its title, "Report of the Air-to-Air Missile System Capability Review," hardly sounded like a blockbuster. But this study, produced by Captain Frank Ault, the captain of the _Coral Sea_ , was an impressive, consequential piece of work.
About two hundred pages long, it was a top-to-bottom exploration of the reasons for our failure in air-to-air combat over North Vietnam. Captain Ault's project had been a long time coming. It began in the summer of 1968, when he led a team that tackled the problem of the Sparrow missile. Building on that and other studies, he pulled in more than two hundred people to a symposium at the Naval Air Missile Test Center at Point Mugu, north of Los Angeles. There were pilots, commanders, and managers and technicians from Raytheon, Westinghouse, and McDonnell Douglas, all the major fighter weapons contractors. No one had put together the entire picture of the problem like Ault had. It was the first time the whole air combat system—our fighters, their missiles, and fire-control systems—had been studied holistically, from design and acquisition to operations and logistics. Ault wanted to understand weapons systems "from the womb to the tomb," as he liked to say. His conclusions were far-reaching.
Sam Leeds called my attention to one particular recommendation in the report. He flipped to here and pointed to the eleventh of the fifteen items listed in paragraph 6, "Aircrew Training." It was there that Ault advised the chief of naval operations and the commander of Naval Air Forces, Pacific, to "establish, as early as possible, an Advanced Fighter Weapons School in RCVW-12* at NAS Miramar for both the F-8 and the F-4." These were the words that gave birth to Topgun. Apparently, the idea of such a school had already been under discussion at the RAG's parent command. Like any good idea, it required a brave soul to stick his neck out to become reality. Captain Ault's report put the idea front and center on some important desks.
Sam and I knew that any Miramar-based tactics training program would run through us. He looked at me and said, "Dan, why don't you take it?"
I suppose this was generous of him. He had both experience and seniority over me. He could have led the effort himself. But he already had a great job waiting for him. He was in the final running to command the first fighter squadron that would fly the new F-14 Tomcat. (Tom Cruise would help make that beautiful Grumman jet famous in the movie.) Sam could easily have taken the assignment to start the new schoolhouse and then handed it off to me when his time came to go fly F-14s. But he felt that the school should have the same leadership from the beginning, for continuity's sake. He said as much, and strongly.
It was settled then and there. I made a quick, fateful decision: I'd do it.
When Sam and I informed our skipper, Commander Hank Halleland, that I had agreed to serve as the Navy Fighter Weapons School's first officer in charge (OIC), he had only one directive. "Don't kill anybody, and don't lose an airplane." That did happen from time to time, so we took the warning seriously. He also made it clear that the Navy was funding us on thin wooden nickels. We would have no classroom space, ready room, or administrative office, no maintainers and mechanics assigned to us, no airplanes of our own, only loaners. And, of course, we would have no money. The new graduate school would subsist by forage, hunting and gathering in the forgotten corners of Miramar. There was one more thing. Our deadline for preparing a curriculum and having it ready for the first class of students was short: sixty days. Aside from all that, I suppose the job was a real plum.
Soon we started calling the school Topgun. We weren't the first to use this fine nickname. There was an annual air weapons competition that used the name until about 1958. The aircraft carrier _Ranger_ , which I would later command, called itself "the Top Gun of the Pacific Fleet." Our friends and rivals at Miramar who flew the older F-8 Crusader called themselves "the last of the gunfighters." Their own schoolhouse was established by the same paragraph in the Ault report that gave birth to us, but as that old fighter was on its way out, their tactics initiative did not last long.
I've often reflected on the sheer happenstance of how leadership of Topgun fell to me. I didn't know it at the time, but it was larger and more important than anything I had ever undertaken before. It was the chance of a lifetime to effect much-needed change. Its success would take the passage of years, requiring the work of the many fine aviators who followed me. But our new graduate school in fighter combat was greater than any one man or group of men. It would grow roots and flourish. It would transcend its own mission and stand for excellence and commitment of the purest kind. Its legacy would last for decades. None of that was expected in December 1968. It was a job to do.
The program almost seemed designed to fail. I say that because the Navy considers nothing very important that's not run by an admiral. I was a thirty-three-year-old lieutenant commander, three pay grades below flag rank. That the Navy gave leadership of Topgun to someone so lowly speaks to what it thought of our chances. We easily could have crashed nose first. We were going to disrupt the traditional way of teaching tactics. I'll say more on that later, but most real tactical aviation training took place out in the fleet. The skippers of the fleet squadrons thought they owned tactics. Topgun threatened that approach. Thus, we could easily fail.
In the Navy, the failure of any group can inflict collateral career damage on superiors in the chain of command. The damage was usually in proportion to the rank of the failing commander. If Topgun crashed and burned, my own career would take a hit. Yet my humble rank meant that the senior officers standing over us would suffer no blemish on their record. Our failure could be written off to the stumbling of youngsters who, while well intended, were not up to the task. That's probably why a guy like me got to be the first OIC of Topgun. It sounds like a much bigger deal today, knowing what we know.
Being in that dicey position, I took comfort in having Hank Halleland's support. He quickly proved himself a friend from the beginning, helping us find people and resources. The pedigree of the Ault report helped too. The higher echelons at Pacific Naval Air Forces headquarters and at the Pentagon had to pay attention, since the CNO himself had endorsed the study.
But the war didn't care, not a lick. And the war was the reason Topgun was born. It awaited our return, ready to kill any of us who showed up unprepared. Next time we reported in for a WestPac cruise, we would need to perform a lot better. Lives hung in the balance.
I've always tried to keep in mind something that was famously well expressed by another fighter pilot in another day: God is my copilot. When I look back at how we pulled it together, it's clear to me that the acting hand was far mightier than my own. I prayed for the gift of discernment to make it work. It wasn't going to be easy, but everything we would need was at our fingertips there in Fightertown USA.
Captain Ault described what had to be done, but—bless him for his wisdom and foresight—he said nothing about _how_ it should be done. He prescribed the creation of the Navy Fighter Weapons School but did not say what it should teach, how it should be taught, or how it should be set up. Today, an initiative like that would involve millions being spent on special studies and outside experts. Until they were unanimous in their conclusions, nothing would start happening. The paper pushing would take years. In 1969, I was left to my own devices. With the wise council of Hank Halleland and some other trusted voices around Miramar at my disposal, I thought I might have a puncher's chance. I went right to work.
Topgun was best understood as a graduate school. It functioned essentially like a teachers' college for fighter pilots. Our job was not just to teach pilots to be the hottest sticks in the sky. It was to teach pilots _to teach other pilots_ to be the hottest sticks in the sky. Our first class of students, handpicked by their squadron commanders to join us at Miramar in sixty short days, would spend about five weeks with us and then return to their units to spread to their peers what we had taught them. In this way the Navy hoped to leverage a multiplier effect, seeding new ideas in a geometric progression as a class of eight went out to teach eight times sixteen more.
The way to true mastery of anything is to learn it to the point that you can teach it to someone else. My first task, then, was to find instructors with a talent for teaching, pilots with the gift for delivering a complex lesson in a way that made it stick. Our expectations were sky-high. Not just of our students, but of ourselves. With only sixty days to develop new offensive dogfighting tactics for the Phantom, redefine the way Sparrows and Sidewinders were used, write the curriculum and lesson plans, create a flight syllabus with briefing and debriefing guides, and recruit our first class of pilots from the fleet, there was hardly an hour to waste.
Around the time Sam Leeds showed me the Ault report, I hosted a group of Israeli pilots at my home in San Diego. Heading the group was Lieutenant Colonel Eitan Ben Eliyahu. He had a superb reputation as a fighter pilot and leader. Danny Halutz, another future head of the Israeli Air Force, was part of the group. When I met these guys, the IAF was making the transition from the French-built Dassault Mirage to the Phantom. They were visiting Miramar to learn what they could. I learned a few things from Ben Eliyahu in particular, and we became good friends.
Over good American barbecue, listening closely to everything they said, I discerned that Israeli fighter squadrons believed strongly in the power of technical specialization. In each technical area, Ben Eliyahu explained, one man was designated to serve as the lead specialist. Radar, weapons, ordnance, aerodynamics, tactics—each domain had its wizard. The division of labor would prove to be an efficient way to assemble a team and develop a technical curriculum on a short schedule. That was the approach I used in selecting Topgun's first instructors.
Reflecting on what the Israelis had revealed to me, I decided that eight men would be the right number to cover the subjects we needed to master. Four pilots and four RIOs would join me as Topgun's founding cadre of instructors. These eight dynamic, smart, persuasive, and articulate young officers would help me pull our program together ahead of our hot start in March. I didn't think I could manage more people than that while developing the school and continuing to teach and fly in the RAG—all of our instructors would have double duty—and doing everything that serving as the OIC entailed. There was little time to waste in assembling the team, designing a curriculum in collaboration with them, corralling assets, and finding a way to turn around the air war that was going south eight thousand miles away on the other side of the Pacific.
Look around any room and you'll realize that your people are everything. It doesn't matter if it's a business, a charity, a government agency, or a military unit. Your people are your destiny. We had to be successful or our careers and reputations would be finished. And that would be the least of it. If we failed, we would return to a war using the same tactics burdened by the same politically driven rules of engagement. That would just mean more of the same: lost friends and a brotherhood strained to the limit by the demands of war we were not allowed to win.
I didn't have to look far for good people to help me fulfill this unexpected charge. The pool of combat-seasoned talent at the RAG was deep, which was helpful because there was no time to do the paperwork necessary to transfer people to us from other units. The instructors who had been teaching with me in the tactics phase were all combat-experienced, with lots of flight time in the F-4. They flew every day, putting new pilots through the paces. I knew all of them—and not just as pilots, but as _teachers_. Their reputations among the student pilots at Miramar were as important to me as their standing as warriors. When the time came to choose my "original eight," the right names came quickly to mind. I talked to each of them, had them read the Ault report, and described the enormous task we faced in building a graduate-level program with an advanced curriculum and preparing to teach it within sixty days.
I don't remember the exact words of my initial presentation, but it was based around the sentiment that we were being challenged to revive our heritage as naval aviators—to learn how to dogfight again. Captain Ault had empowered line aviators to have a voice. I was not surprised when I learned that the author of the section of the report that recommended creation of Topgun was a salty F-8 Crusader pilot, Captain Merle Gorder. In spite of the rivalries between the Crusader and Phantom communities, we were virtually the same tribe, going all the way back to World War II when our predecessors flying piston-engine, propeller-driven fighters had purchased our birthright in blood. With this as my message, I was able to get every one of my recruits to join me in the new venture.
The pilots I invited to join Topgun as instructors were Lieutenants Mel Holmes, John Nash, Jim Ruliffson, and Lieutenant j.g. Jerry Sawatzky. I called them into my office one by one and explained the idea of the Fighter Weapons School as referenced in the Ault report. To a man, they did not hesitate to sign on. We had long been vocal about the changes we thought were needed to win the air war in Vietnam. Here was the chance to do something about it.
Mel Holmes was a first-round pick in anybody's book. I had seen a lot of pilots fly, fight, and work. None was better than Mel. I considered him to be hands down the finest F-4 Phantom pilot in the world in early 1969. Tall, handsome, and self-confident, he was a natural leader with strong opinions. He had been born and reared in northeastern Oregon, a rural outback that bred tough, independent people. One time when Mel was golfing at the base course at Miramar, he hit a drive into the weeds. That was bad news for the nest of rattlesnakes he walked into while looking for his ball. When his buddies saw him hacking away with his seven-iron, slaughtering those serpents in the grass, Holmes had his nickname: Rattler. He had one trait in spades and I strongly doubt it's teachable: a bone-deep, hardwired, electric-fire sense of aggression. It manifested itself on the basketball court, where he was hell on wheels. An athletic scholarship had paid for an education his family could not otherwise have afforded. But its biggest dividends were paid in the air. When Mel strapped himself into the cockpit of a fighter aircraft, whatever separated the flight surfaces from the man at the controls simply disappeared. He had as much natural talent as anyone I've known. No pilot I ever knew beat Mel consistently one-on-one. So he was a perfect candidate to specialize in tactics and aerodynamics at Topgun.
I chose John "Smash" Nash for the way his heart and mind worked together. Though he was the one member of the original eight who hadn't taught in the RAG's tactics phase, I knew him well from our early days flying McDonnell F3H Demons from the _Hancock_ back in '63, a year that he and I were both lucky to have survived. John was at his best when he was pitted against a supposedly superior fighter pilot. Any suggestion that a mismatch was at hand triggered his competitive fire. His motto, "I'd rather die than lose," bore it out. Most combat pilots are wired that way. What made Nash special was the way he combined that fire with hyperattention to detail. Anyone who showed any degree of inattention to the fine points of something he was trying to teach got a hard dose of his Mississippi wrath. Most of our students were smart enough to avoid a second helping. Nash expected perfection from them and usually got it. He was as much an asset on the ground as in the air. His talent for technical research kept our ideas about tactics built on a deep base of fact. Nash was a systems guy. He told his students, "Automobiles, aircraft, and air-to-air missiles are built to fail. Expect problems and anticipate them." I considered his fusion of traits—detail-driven aggression—to be the best possible mind-set for a Topgun instructor.
Jim Ruliffson probably put out more pure intellectual wattage than any of us. No one understood the Phantom's electronic and avionics systems better than he did. With his superb technical mind and training in electrical engineering, he was a natural to spearhead our effort to master the Sidewinder and Sparrow missile systems. In the subtle differences in performance between these high-tech weapons, not to mention the optimal parameters of their use, was the critical margin between life and death. This was Jim's specialty. A fine stick and great tactician, he was a protégé of Duke Hernandez, a great one from the East Coast fighter community. "Cobra" Ruliffson distinguished himself with his superb gift for teaching this complex material to aircrews in a way that let them retain and use it.
Jerry Sawatzky, or "Ski Bird," as I called him, had played linebacker for Bear Bryant at Alabama. He was big, imposing, and highly energetic, but also very unassuming and one of the most likable people I ever flew with. He had survived a horrific fire on the carrier USS _Forrestal_ , which claimed thirty-nine men from his squadron in July 1967. A born teacher, he was one of the first ensigns assigned to fly the Phantom when it was the fleet's hottest, newest ride. He knew the plane inside and out, and he was magic in an F-4. With his keenly aggressive way, he was known to "bend the jet," as we said. Jerry had great situational awareness, which was vital in fighter combat. It's very easy and all too dangerous to focus on the enemy you're about to shoot. A pilot has to stay alert to what's happening in the cube of air that extends several miles around him as all the players move at high speed in different directions. Jerry could teach others how to develop their awareness and retain it. He was also good at looking at an aerial encounter from the enemy's point of view. Holmes and Nash rated him very highly, which told me a lot. Ski Bird was a prince of a teammate. We appreciated him for being as reliable as gravity, usually showing up ten minutes early for a scheduled brief. He was just the kind of instructor we needed, since our job was to throw away the manual and push our aircraft beyond its factory limits.
Holmes, Nash, Ruliffson, and Sawatzky were my first four pilot instructors. But I hope I've made clear how important the radar intercept officers are. Without a good back-seater in his F-4, no fighter pilot gets far in an air battle. Topgun's four founding RIOs were the best that were available anywhere. At the head of the pack was John "J. C." Smith, whom I invited right away. He might have been the finest RIO there ever was.
In June 1965, flying from USS _Midway_ , J. C. and his pilot, Commander Lou Page, scored the Navy's first air-to-air kill of the Vietnam War. The head-on tangle with a pair of MiG-17s was a by-the-book radar intercept, and their Sparrow performed as advertised. Moments later, their wingman, Jack Batson, shot down a second MiG. Of course the Pentagon was elated. As far as I know, these were the only "pure intercept" victories the Navy scored in the entire war. Soon thereafter the Vietnamese stopped playing our game and the radar-guided AIM-7 Sparrow seldom again delivered on the promises of its marketing brochure.
J. C. was colorful. He talked a mile a minute and at times never seemed to stop. That element of his personality made him a great RIO. A good back-seater never stops talking until his pilot issues the command "Go cold mike." J. C. was especially good with new pilots. Whenever I had one who needed some help, I'd prescribe for him a flew flights with J. C. in his rear seat. That always got him up to speed. J. C. lived the Christian life with his wife, Carol. Teaching others was his forte. He was a pretty fair negotiator too.
Another of my RIOs was Jim "Hawkeye" Laing. A youngster, just twenty-three, he was so quiet in person that you'd never know what a tiger he was in the rear seat. During his two combat tours in Vietnam, flying from USS _Kitty Hawk_ , he and his pilot flamed a MiG-17 in a wild fight near Haiphong Harbor. Laing survived two ejections in barely a month. The second was harrowing in the extreme. Hawkeye and his pilot, Denny Wisely, landed well inland in a thick jungle, where they became the objects of an epic search and rescue mission. As the helo looked for them, John Nash courageously remained overhead, covering the rescue to the limit of his fuel while under fire from enemy gunners. He received a well-deserved Silver Star. Laing, with his notable history of survival against the odds, gave Topgun an element of moral strength and never-quit resilience that was enormously valuable. He took all of his hard lessons in stride and always came back for more. A deeply religious family man, Jim imbued Topgun with his never-say-die spirit. He was one of the steadiest, most stalwart, spiritual, and reliable men I have ever known. When he spoke, everybody listened. He was a generalist who contributed to each area of the curriculum. He could teach with the best and was a quality leader who was always ready to help anyone who needed it.
Our other Smith—Steve—had all the essential skills of a top-grade RIO but stood apart from everybody for his skills as a salesman, organizer, and grifter for all seasons. Steve-O could talk a Bedouin out of his camel, ride it to Alaska with a load of shaved ice, and sell it all at a premium to an Eskimo. He had a great laugh and darkly handsome looks that drew an enviable share of female attention. I guess we didn't begrudge him those successes, because he was a world-class organizer and had a work ethic that outdid mine. He was a self-starter, keeping a daily to-do list in his pocket, and it was a rare sunset when he hadn't scratched off every item. "Rebel" was at his best when I gave him free rein and didn't ask too many questions.
Our junior RIO, Lieutenant j.g. Darrell Gary, was the youngest man in our cadre of founders. He had every attribute I wanted in an instructor—mature (beyond his years), confident (beneath his years), and very hardworking. If Darrell looked a bit too much like a movie star fighter pilot to be an actual fighter pilot, we had to accept what God gave him and be glad for it. It was plentiful. Some pilots were smarter than he, and others were more experienced, but none was more driven. Though his after-hours activities were diverse and even legendary, as often as not they involved important professional work. In cadet training, while everybody else was asleep in their racks, Darrell would often be found sequestered in the head, sitting on a throne with a flashlight in one hand and a textbook in the other. That's part of the reason he graduated at the top of his class in naval flight officer school. He came to VF-121 in 1968, after two combat tours in the _Kitty Hawk_. It was hard to miss his extreme self-assurance. Because evolution tells us that birds with that trait tend to become extinct, we gave Darrell a call sign to match: Condor. It was designed to encourage him toward humility. But all these years later I can finally say it. Darrell was one of Topgun's sharpest lecturers, gifted with a probing tactical mind. He is one of the most aggressive, intelligent men I have ever known and is a natural innovator whom people followed willingly.
Our last find was an ace in the hole of sorts, even though he was a nonaviator. When Steve Smith met Chuck Hildebrand, Chuck was working as an intelligence officer, bored and unhappy, in one of Miramar's F-8 photoreconnaissance squadrons. Steve talked him up a little, recognized his useful talent, and helped arrange his transfer—all on the same day. Chuck was the perfect man to serve as Topgun's intelligence officer. He was a human vacuum cleaner. He got the inevitable nickname "Spook." Tall, studious, professorial in bearing despite his youth, he never stopped collecting documents for our reference library, detailing the capabilities of enemy aircraft and pilots. Without Spook, Topgun would have needed many more years to emerge as a research library for fighter pilots and the center of knowledge that it quickly became.
And that was our team. I like to think that their being in one place, the right place, at precisely the right time was the work of a power greater than me. With the team assembled, all we needed was a place to call home.
One Friday afternoon, Steve Smith, foraging in a remote part of NAS Miramar, near the base operations center, found an abandoned, dilapidated modular trailer. It was perfect. He chatted up an off-duty public works crane operator and offered him a case of scotch if he would make delivery to our area of the base. Later that afternoon, the ten-by-forty-foot structure was hoisted aloft and relocated to a space adjacent to VF-121's hangar. Over the weekend, we laid in new flooring, repainted it with bright red trim, and hung a sign on the door announcing the existence of the Navy Fighter Weapons School.
While the rest of us renovated our find, Steve went scrounging and stole a bunch of office furniture and a couple of classified document safes from God knows where. Legend had it he bagged some of it from the Air Force. Wherever it came from, we filled our formerly condemned trailer with all the trappings of a real classroom and called it home. By Monday morning, Topgun was officially in business.
# CHAPTER NINE
# THE ORIGINAL BROS
**Miramar**
**1969**
The famous movie that borrowed our name—and we all still love it—might make you suspect that we were a self-obsessed bunch, that it must have been a constant battle of egos between the students and even the instructors inside that stolen trailer and on our training flights out of Miramar. Television shows like _Baa Baa Black Sheep_ , with its over-the-top portrayal of Major Gregory "Pappy" Boyington and Marine Fighter Squadron 214 as a gang of misfits, created that sense too.
Speaking for the Original Bros, I'll say that for six and a half days a week, we were scholars, even monks. No PhD in astrophysics ever worked harder to understand the facts of the physical universe than we did at Topgun ahead of the arrival of our first class of students in early 1969. Our mission was to master the full combat capability of our airplane and its weapons and turn around the air war. As skipper I set the tone and made decisions. But the Topgun instructors emerged as the intellectual drivers of our attempt to redefine the flight envelopes of the F-4 Phantom and its missiles. That was our most important work, and the foundation of the Topgun legacy.
Pilots were dying because our missiles were not designed to operate in a dynamic, high-G, high-angular-rate environment. That's a technical way of saying that an air-to-air brawl moves so fast that a fighter pilot should never trust a missile to win it for him. Certainly, the pilot had to be smarter than the missile. It was simply a killing tool, like a throwing knife. But a man must know how to use it perfectly, every time.
One thing we saw was that our missiles were taking a beating day and night aboard ship. Carrier ordnance personnel had to manhandle those heavy things, and they got knocked around. Whenever a pilot landed with his missiles still aboard, the weapons absorbed a stiff, debilitating concussion. You have to know your weapon and its limitations as surely as you do your airplane. So we went to school on them to uncover every shortfall. There were many shortfalls and some very technical solutions.
The forward thinkers in Washington who had eulogized the day of the dogfight knew nothing of what it was like to be part of an alpha strike arriving over Hanoi. They couldn't picture thirty Navy planes inbound, with sometimes fifteen enemy SAMs rising toward you. They couldn't see the crowd of unidentifiable radar and visual contacts in the sky swelling and commingling as MiGs reached altitude and approached us, or the surprise of an Air Force formation arriving unannounced over the target, right when things were getting sporty. The ever-present AAA and even small-arms fire made for a chaotic dynamic as you rolled along at six hundred knots.
As I've perhaps belabored, the rules of engagement required us to make visual identifications of targets before firing. Telling friend from foe meant getting close enough practically to see him through your windscreen. Good luck with that. By the time you got within recognition distance of a MiG closing head-on with you, your advanced radar-guided missile was about as useful as a fence post strapped to your wing. In the first three years of the war, our pilots had fired nearly six hundred missiles at enemy planes, scoring a kill on about sixty. If you're keeping score, that's one in ten. More often than not, those agile little MiGs, having ducked our first swing, would be on our tails showering us with explosive cannon shells sooner than our wingmen could shout, "Bandit on your six—break right!" Something had gone wrong. It was our job to follow Captain Frank Ault's suggestion and solve the problem from the ground up.
Some of the most productive hours of my professional life were spent in the trailer. A couple of cinder blocks were the staircase to the left-side door that put you in our operations center. It had a desk and a chair, some cabinets, a pair of safes that Steve Smith had liberated to hold our classified documents, plus the inevitable Navy coffee mess. For students there were six tables in two rows of three, flanking a narrow center aisle, and a dozen chairs. At the far end of the room was a chalkboard and a podium, with barely enough room for an instructor to stand. There was a small window on one end and two on the side. Armed with our youthful ideas about what the U.S. Navy was doing wrong, we went about rewriting the rules of tactical air warfare in the F-4 Phantom.
Mel took charge of our effort to deconstruct the aerodynamic capabilities of the F-4, revise its performance envelope, and discover its true capabilities in the air, well beyond the parameters set by McDonnell Douglas. We developed the Topgun curriculum in searching, impassioned conversations, illustrated by fast work at the chalkboard. To build a curriculum in air-to-air tactics, all you had to do was get Mel Holmes, John Nash, and Jerry Sawatzky talking a bit. The others would join in, and we'd be on our way. Once it got rolling, you'd better be strapped in with a five-point harness and taking notes fast, because it was going to be a wide-open discussion.
Rattler might lead off by discussing his thoughts on a trick of the tactical trade that was too advanced to teach in the RAG. By the time we were finished, we had something important in the making: an outline that became a lesson plan that became a flight syllabus and a curriculum, broken down and assigned to the instructor specializing in that technical area. All of it was reviewed over and over again as each instructor presented the material to the other Bros.
John Nash was my expert on air-to-ground tactics. Phantoms were, after all, sold to the military as "fighter-bombers," and we couldn't ignore the second part of its mission while going to school on the first. Nash was the best among us in that specialty. He was a master air-to-air tactician as well.
Cobra Ruliffson did a lot of his best work away from Miramar. He was a frequent visitor to the Raytheon offices in Massachusetts. Working with the engineers who built the Sparrow, he took apart the flight dynamics of our problematic missile. The actual parameters of the Sparrow's sensors and electronics had never seemed to inform the tactics. There were optimal times and places to fire a Sparrow, and if you didn't know the kinematics and the process times, or the shifting matrix of G forces, angular rates, and track crossing angles that your choice of moment to fire imposed upon your missile, you weren't going to hit anything. Jim grasped all the factors of time and space that defined the air-to-air missile's proper use. By the time his study was aligned with our new understanding of the Phantom's own performance parameters, its flight envelope, we had a better weapon on our hands.
Doing all of this on a sixty-day deadline meant for some busy days.
Our beautiful F-4 had some important things going for it. One of them was the pair of General Electric J79 turbojets that made the plane accelerate like a rocket. Earlier U.S. fighters had used their superior engine power to gain an advantage over the agile MiG, soaring high above a fight and diving back down when they saw a chance to kill. We called this tactic "using the vertical." Developing it for the Phantom, for which it had never been envisioned, would be one of our top priorities.
While we were preparing the curriculum, I joined Chuck Hildebrand and J. C. Smith on trips to Langley, Virginia. Only by visiting CIA headquarters, we discovered, could we get access to the highly classified air action reports from the carrier squadrons off Vietnam. It was funny that they were originally unavailable to us, seeing as the squadrons we had belonged to were their authors in the first place. Still, without top-secret clearances, we needed cooperation from our contacts at the CIA. On one trip from Washington back to Miramar, J. C. and I hand-carried two briefcases full of classified debriefs—reports that were full of valuable lessons that had been paid for with blood.
Before we could teach our material we had to study and learn it cold ourselves. We created, collated, and corrected the curriculum at a fever pace, working all hours to refine it, hunting and pecking with two fingers on manual typewriters, red-lining each other's drafts, and rehearsing our lectures to each other. This last part was key. As we took turns at the podium in the trailer, we faced withering scrutiny from our fellow instructors. In the military, this is known as a "murder board." No hiccup in presentation style, no slip of the tongue, no glitch in dress or personal appearance was too small to be seized upon and corrected on the spot. We knew we would be ineffective lecturing to our top-notch students if we were anything less than bulletproof. How would they believe in us at Topgun if we couldn't deliver a graduate-level lesson well? In the meantime, we began reaching out to the fleet squadrons to recruit our first students.
The founding class would consist of two representatives from four Phantom squadrons, a total of four pilots and four RIOs. Steve Smith, our best salesman, was put in charge with the guidance that he recruit from both the East and West Coasts. He had quite a time of it making these cold calls. He would ask for the executive officer, inviting him to nominate his best junior officers, one pilot and one RIO, to join us for a five-week class in advanced tactics. After Steve made his pitch, the XO usually said something like this:
"Sorry, who the hell are you?"
Steve would explain. If he ever suggested that the XO's higher headquarters might already know of our existence—"Sir, haven't you been briefed about our school by your air wing commander?"—he often found the situation escalating. The squadron CO himself would get on the horn. And that's when the inquisition really got going.
"I don't know who are, son. Do you really expect me to cut loose my best guys and send them to you? By the way, what makes you think you can teach tactics better than I can?"
At that point Steve would have to up the ante by explaining that participating squadrons were responsible not only for sending us two aviators, but also a Phantom and some maintenance people to keep it up. Sometimes this news was agitating.
Steve didn't close every sale. Often the CO, miffed, hung up and queried the Pentagon about Topgun's status and standing. That's when our top cover paid off. The Navy Department's highest headquarters for air warfare, known as "OP-05," always set the skipper straight.
Steve's persuasive gifts paid off best when he was talking to East Coast guys. The fact that Topgun was based at the gateway to the Southeast Asian war zone was useful. "Are you aware of what's going on here at Miramar?" Steve would say. "We're considering inviting one of your squadrons to join us. Their chances will be better if they have combat experience. Do they?" With East Coast units the answer almost always was no. This had a way of building desire. Over time, Steve created buzz—and demand.
As the roster of Class One came together, we tested some of our finished lesson plans on students in the RAG. We were seeing them regularly anyway, because all of Topgun's instructors were still teaching the basics in VF-121. One day in the middle of February, Mel Holmes and I did a two-plane training hop, putting a pair of student RIOs through the paces in long-range radar interception. I was cooking along in full afterburner about a hundred miles off the California coast, approaching San Clemente Island, when I felt a thump. My warning panel lit up. There was a fire in my right engine.
As I shut it down, my back-seater, Lieutenant j.g. Gil Sliney, ran through the emergency checklist while Mel eased in close for a visual inspection, trying to see through all the smoke. We were about thirty miles from Miramar, off La Jolla, when the seven-liter liquid oxygen canister mounted in the tail of my Phantom exploded. It tore the tail section clean off my bird. End over end we tumbled. Time slowed down. We plummeted. In my headset I think I heard Mel's voice.
"Dan, you guys eject, eject!"
Gil pulled the handle and we rocketed out of the doomed jet. We fell in a parabola toward the ocean, strapped into our ejection seats at twenty-one thousand feet.
It's odd how time passes in a crisis. Inspired by the flood of adrenaline into my system, I had the time to look down over La Jolla and notice the scenic cove. My helmet visor was gone, but somehow my Ray-Bans were still hanging on. _I've got to save them_ , I thought. Those sunglasses had been with me since my Pensacola training days. No way did I want to lose them now. I reached up, shucked them off my face, and stuffed them into a zippered pocket on my flight suit.
It was then that I realized, as I fell through space, that I was still attached to my ejection seat. This was a problem. The heavy apparatus was supposed to separate automatically by action of a powerful spring activated by a barostat at twelve thousand feet.
Falling toward the sea, I looked around for Gil's chute and was relieved to see it drifting down, behind and above me. Disengaging myself manually from the ejection seat and falling clear, I pulled the D-ring to pop my chute. Nothing happened. I yanked it again, harder, and the cable broke off in my gloved hand. I was falling at terminal velocity, fourteen feet per second or like a rock. Somehow, I had to get my hands on the chute pack.
Short on time and altitude, I pulled myself up the risers and reached my chute pack. I thought of my wife and kids and home and it was God who gave me the strength, I'm sure. Reaching the parachute pack, I opened it with my hands and the chute flew free. The beautiful white blossom swelled above me, jerking me upright and into a lazy but short descent. _Thank you, my dear Lord_.
Looking down at the cold water, I saw dark sleek shadows swimming just below the surface. There wasn't much time to think about what that meant. My chute had opened so low—Mel said it was about twenty-four hundred feet—that I had time only for two swings back and forth in the harness before I hit the drink. Almost at once, my small life raft deployed. When I climbed in, I did double time, because I thought I was avoiding the sharks. A moment later, a pair of large gray sea creatures launched themselves up against my raft, parking their snub noses on the edge of it. Dolphins. Chortling excitedly, they stayed with me until the rescue helo arrived from the carrier _Bonhomme Richard_.
As the rotor wash sprayed me with salt water, the helo crew hauled me heavenward. I wondered about Gil, and there he was, reclined on the deck of the cabin and beaming. The rescuers had been quick to snag him. As Gil, elated, gave me a sidelong man-hug, I warned him that I'd kill him if he tried to kiss me. He didn't. Clearly it was not the day for either one of us to die.
An accident investigation revealed a defect in the aging original bar springs of the Phantom's ejection seat. The Navy surmised that this problem, which was fleetwide, was the reason five pilots had been lost during night ejections. I doubt Gil and I would have made it if our mishap had happened after dark. After a medical checkup on the _Bonnie Dick_ , we boarded a C-1 Trader and with a nighttime catapult shot were on our way home to Miramar.
It was just another day in the life, full of routine danger and little of what passes for glory. As for the nights, my young instructors knew how to blow off steam. The Topgun social circuit was in place from our first day at Miramar. It reached from Downwinds, the beachfront O club at Coronado, to Bully's in San Diego and all the way up to La Jolla, where Bully's had another location and where Condor and Hawkeye Laing rented a house that became famous. Right on the beach, at 259 Coast Boulevard, was a little white stucco house that we started calling the "Lafayette Escadrille." A refrigerated keg was always on tap and the doors were never locked. It and the two houses across the street, which were rented by other young Miramar pilots, attracted an entourage that included everybody from San Diego State coeds to members of the San Diego Chargers pro football team. Darrell never knew who he was going to have to throw out of his bedroom when he rolled in from Miramar on a Friday night. But all of us lived and breathed for the work we did at Topgun. Of course, anything we did off base was meant solely to keep our edges sharp for the work that really mattered.
A few days after my unprogrammed cold swim, I was back to work. Having finalized the Topgun curriculum and completed most of the murder-boarding, we were ready to receive our young sticks from the fleet. We would have to be on our game. Because we were going to make these guys into world-beaters.
On March 3, 1969, in our stolen trailer at Fightertown USA, Topgun's Class One convened. All eight attendees had come from Pacific-based squadrons, VF-142 and VF-143, just off a Vietnam deployment with USS _Constellation_. They were some of the finest junior officers in the fleet, all combat-experienced aviators, all graduates of the Naval Academy, career Navy. We didn't take reservists. Their names were Jerry Beaulier, Ron Stoops, Cliff Martin, and John Padgett. The RIOs were Jim Nelson, Jack Hawver, Bob Cloyes, and Ed Scudder. The instructors and I sensed quickly that their COs had chosen well. All were sharp and well prepared.
After fifteen years in the Navy, I had learned a few things about leadership. If you had not attended Annapolis or ROTC in college, you learned it not by express instruction, but by absorption of example. You got it on the job. Some of it came by negative example: "Don't be like Commander What's-his-name." But most of my role models were helpful and even inspiring. I've mentioned Gene Valencia and Skank Remsen. But many fine aviators were mentors to me. Their lessons always resonated. They taught me what kind of leader I needed to become.
When the legendary Swede Vejtasa was a wing commander at Miramar, he welcomed every new class in the RAG more or less like this. "Okay, boys, training command was fun, because each of you did well. You wouldn't be in fighters if you hadn't. Now the _fun's over_. When you finish, you are headed to war, maybe immediately. Pay attention! Learn everything you can about your aircraft and its capabilities, the tactics, and the standard operating procedures. They may well save your life. Dismissed."
Swede was telling those nuggets what they needed to hear. With advanced talents such as these eight, however, I felt no need to be heavy. I issued a heartfelt "Welcome aboard" and said we had been charged with an important purpose. I introduced my instructor team and told them who they all were. I explained that we would all learn together along the way. The main thing for any skipper to bear in mind is this: The troops need to know he's interested in their welfare. This is true regardless of the leader's personal communication style. Hard-asses can care, too. Some leaders give lip service to caring, but what a leader does to show it is far more important. I wanted my instructors to challenge them—but always constructively. We would aspire to build their confidence, not destroy it. They were professionals and future mentors in training. So we were going to show them how it was done.
I closed by saying, "There is an urgency here beyond anything we have ever done. We hold lives in our hands." These words still fill me with conviction today.
Our students had little time to settle in before we got to work. The first week was mostly lectures. Before the sun was up, at 0430 on the day after they arrived, we started the classroom work with a daily briefing. We reviewed the sad state of affairs on Yankee Station, talked about how we meant to change it. Our study of the after-action reports revealed one thing that all of us knew pretty well. Dogfights were over in a hurry. The critical moment was the Merge, when two jets passed a few hundred yards apart. The enemy's next move after that point told you a lot. Is he aggressive? Does he turn toward you sharply, confidently, put the pressure on you? Or does he hesitate for a critical second and a half and let you make the next move? The smart fighter pilot leads with his strength—his first best move. Because it's probably all going to be over in less than a minute. The elapsed time from Merge to kill was thirty to forty-five seconds. Everything you knew had to come together in that vanishing moment of life or death.
We flew a couple of times to let our students shake off the rust. There wasn't much of it to shake. Flying two-seat TA-4 Skyhawks as "aggressors," in the role of the enemy, we learned quickly that these were no beginners. They climbed the learning curve quickly. I respected their abilities, as I did with all my opponents.
The pace of the program accelerated once we began flying a lot. After the first week or so, we ran two or three training sorties every day. With instructors playing the role of aggressors, we would put the students in different scenarios, flying all the basic permutations—1 vs. 1, 2 vs. 1, 1 vs. 2, 2 vs. 2, 4 vs. 2, 4 vs. 4, and 2 vs. 4.
A dogfight is a true physical ordeal. When a fighter aircraft is flown hard, it shakes you like a plummeting roller coaster on the verge of collapse. You're buffeted from side to side, helmet hammering the Plexiglas canopy, harness digging into your shoulders and hips. G forces cause blood to surge and drain from your extremities, including your head. Our program tested not only a student's body, but his mind.
With four or even five separate test engagements on every flight, you can do the math and then imagine the strain this places on a pilot. It beats you up and sometimes, on the most instructive days, drains you to your core. ACM is a full-contact sport played on the edge of life and death. The fast pace of operations exhausted even well-conditioned aircrews. We were especially zonked after starting the day with an 0430 briefing. To allow for recuperation, we alternated schedules. After an early day in the air, the next morning we slept in, meeting in the classroom at 0630 or 0700. We worked almost around the clock, eating when we could, usually from a food truck that rolled onto the 121 ramp. We were that lady's favorite customers, devouring her sliders and hot dogs, heavy on the mustard and onions.
There were a couple of names for the MiG-killing new tactic we developed for the F-4 community. It basically involved flying a Phantom like a Saturn V rocket. Straight up. Sometimes we called it "using the vertical envelope." It was also known as the "high yo-yo." But the name we settled on was inspired by the shape of the airspace we used while flying it. J. C. Smith called it the Egg, and the moniker stuck. That was the shape our Phantoms traced, rocketing up and coming back down. I should point out that Topgun did not invent this maneuver. The guys in the F-8 Crusader community had been using "the vertical option" for years. Our breakthrough was applying it to the fighter of our day, the F-4 Phantom, an aircraft that was never supposed to perform such tricks but that proved very well suited for it thanks to its powerful engines.
The maneuver really did break new ground. In the safety-conscious cocoon that was the RAG, what little dogfighting we did stayed in the horizontal plane. The vertical was something that only a few rebellious instructors fooled around with from time to time. You might guess the names. Mel, he was one. I had used it in my "fight club" days off San Clemente a decade before. The best pilots we encountered in those after-hours hassles always used the vertical. I learned from the best out there, just as Mel had when he was stationed at North Island.
None of our students had ever flown an F-4 Phantom like a space vehicle out of Cape Canaveral. None ever forgot his first experience of the "pure vertical." With the student in the rear seat we'd fly somewhere out over the ocean or the desert of El Centro, then start the demonstration. Lighting the afterburners, I accelerated to five hundred knots, then hauled the stick back into my gut. Since the Phantom had no trouble reaching Mach 2 in level flight, it wasn't hard to fly straight up. We sank into our seats as the airplane began to climb. With those twin J79s cooking away, we pointed our nose to the stars. I held it. And held it. And held it some more. Our nose was still pointed high. Despite the enormous thrust of the engines, the big brute eventually started to decelerate. That was when the student in the rear seat got worried.
As we lost speed, trading kinetic energy for the potential energy of altitude, the basic aerodynamics of lift came into play. Airplanes aren't engineered to grip the sky at very low speeds. The airfoil of the wing just can't do its work. A maneuver like this is a no-no in any RAG. At low speed but under full power, the airframe starts to vibrate ever so slightly.
At that point most aviators want to push the nose over and let gravity get them moving again. They want airflow rushing over that swept wing to resume giving them lift. But that wasn't what we were doing. Not yet. Both hands on the stick, elbows against my ribs, I kept the nose high with absolutely no aileron input.
As the Phantom sat atop that towering parabola, engines still putting out full power but with our airspeed feeling like it was near zero, we started what's known as a tail slide. It's an unnatural thing for a heavy jet to do. Properly done, though, it's safe. The engines hiccupped, belched some flame and smoke, but they never quit.
At this point, I'd often hear hollering in my headphones. "Do something!" The poor student was along for the ride, helpless. But I couldn't worry about that. I needed him to experience the physical sensations of this unusual "flight profile"—and know he could live through it. Because this was where the magic happened. Anyone who's tossed one of those little balsawood gliders into the air with the adjustable wing shoved all the way forward has seen how elegantly a three-ounce toy plane rises up and falls back. That was basically what we were doing here.
If this were a combat scenario, we would have left our enemy well behind as we rocketed heavenward. Now as we turned back over at the top, my RIO scanned the sky below to help me find him. It was hard for him if he wasn't tracking closely. It was tricky to keep an eye on your prey, sitting there upside down, G forces pulling you. But if you paid attention throughout the maneuver, you'd know where your target was. That was bad news for a MiG. We were going to turn him into a bag of dust.
Normally our Phantoms flew in pairs. The formation was known as the Loose Deuce—two planes flying in line abreast. As soon as we made contact with an enemy, one F-4 would attack, beginning a turning fight. The other would skyrocket into the vertical, as I have just described. While the enemy was busy with the wingman, turning and veering in the horizontal plane, he would have little chance of seeing the other Phantom as it rocketed to the top of the Egg. I would use these unbothered seconds to choose a flight path that put the enemy dead center in my missile envelope.
Technique was critical as I came off the afterburners, pressed my foot down on the rudder pedal, and fed in some rudder. As the nose of the plane began to fall through, pointing back down to earth, we began a dive that allowed us to regain airspeed. We took a vector to lead the enemy or latch on to his tail, keeping enough distance to set up a good missile shot.
This was the important tactical evolution we developed at Topgun. I would explain it to my rear-seater on the intercom system as we went along, and gave him a debriefing on the way back to base. Because his turn at the stick was just moments away.
By the time we landed back at Miramar and taxied to the octagon, as the rotary refueling facility installed there on the taxiway is known, my student was completely exhilarated, realizing that we'd just rewritten the rules. As I shut down the port engine for a hot refueling, ground crews hustling in our giant NASCAR-like circular pit stop, my student could hardly wait to try to fly the Egg himself. As soon as the refueling was done, we switched seats, taxied around, and took off again.
Out over the desert or the ocean, I'd coach him through the vertical maneuver. He had never dreamed a Phantom could do it, but our rugged machine performed the same way every time. Once the student decided he could trust it, he was exhilarated to fly the F-4 as it was never supposed to be flown.
Back on the ground, there was always a lot of laughing and hollering from the front cockpit. The student would be ready to beat his chest. And trust me on this: Once four or five twentysomethings have an experience like that, the energy level at the O club that evening is something to see. If you walk in and witness it, the buzz you'll hear isn't rowdy idiocy. It's the sound of people believing in themselves, in their aircraft, in their weapons, in their leadership, and in their ability to win a war when it all comes together.
The day to start worrying about your military is the Friday night you go into an officers' club and everybody's quiet, staring into their beer.
We knew that the RAG's emphasis on radar interception was not going to help us in Vietnam, where visual identification of a target was required by the rules of engagement. It especially worried us that the missiles were still treated as infallible when experience showed us they were anything but. So when nuggets were told that they could get a kill with their AIM-9B Sidewinder if they fired it within a thirty-degree arc of the enemy's tail—and that was the only parameter they thought they needed—we knew we had considerable work ahead of us. Truth was, a missile shot was exceptionally difficult when your target was maneuvering for his life and angles were sharp. Jim Ruliffson broke this down at the level of circuitry to show why targets needed to be led a little in order for the infrared sensor to have time to activate and acquire the target after the missile had launched from the plane. That short lag was causing a lot of missiles to fly uselessly around Southeast Asia. Out in the fleet squadrons, those busy COs didn't have a lot of time or space to troubleshoot and innovate.
Flying every day, we worked on all of this, and hard. We developed the Egg in a way that made excellent use of our two-plane Loose Deuce formation. As one Phantom tangled with the opponent at some lower altitude, the other Phantom soared heavenward to set up a kill on the next pass. Working in tandem against an opponent, two pilots could alternate turning and dogfighting and soaring to the top of the Egg, trading status as "free" and "engaged" fighters. It enabled them to keep constant pressure on a MiG, slowly running him out of altitude, airspeed, energy, and eventually fuel, until they could kill his ass. (That off-color language isn't what I was raised to speak. But war isn't pretty and killing is the name of the game. I see no reason to sanitize this reality.)
The Loose Deuce tactic reflected Topgun's culture, which empowered junior officers to act and speak freely. There was no leader/wingman hierarchy in our tactics, which left either fighter free to attack, depending on who sighted a bogey first. Loose Deuce was versatile and aggressive. Certainly it was a far cry from the Air Force's tactic, the Fluid Four, which in spite of its adjective was quite rigid, giving the initiative and most opportunities to the flight leader.
The confidence we invested in our students was well placed. They continued learning fast, and after three or four days of our brand of rocketry, the skeptics came around. Soaring and plunging to and from the top of the Egg, they got educated fast while squaring off with instructors flying as aggressors, and with guest pilots from other squadrons flying F-8 Crusaders, Air Force F-4s, F-86s, F-100s, and other types. The spirit of our tribe caught hold of them deeply, and they became the second generation of believers.
They were good, and their confidence grew. That had its own dangers. We had no alternative but to live dangerously and feel comfortable doing it. Some ego is essential. I considered our rivalry with the pilots of VF-124, the RAG squadron that flew the F-8 Crusader at Miramar, as healthy up to a point. Their long, sleek, gape-mouthed gunfighter was a heck of an older bird. We went head-to-head with them often and a couple of their guys were as good as it got. Moose Myers, Boyd Repsher, and Jerry "Devil" Houston come to mind. I never passed up a chance to fight them. God help the MiG driver who ran into their like on a clear day.
But technology is usually on the side of the newer airplane. A well-flown Phantom did not lose to an F-8 in a 1 vs. 1 contest. Mel went undefeated 1 vs. 1 against the Crusader after 1968, and he fought them constantly. One time I went 1 versus 2 with a Crusader squadron skipper and his wingman. Though they were both good sticks, I was up 3–0 at the end of the third engagement, flying our A-4E Mongoose, even though I was the "1." Feeling pretty good about it, I listened in on their radio conversation. The skipper said, "What the shit is going on here? Damn it, we have to go back and retrain." I'm sure they did, but training wasn't the problem. The problem was that their plane had seen its best day. It was on the way out. But the F-8 guys, bless 'em, never lost their attitude. A lot of them transitioned to the F-4 as the war dragged on. Some of us could not resist the impulse to keep them humble.
In their hangar at Miramar was a glass case containing a beautiful longsword. Its origins were dubious, but the squadron claimed it had been wielded by a twelfth- or thirteenth-century Crusader. They treated it as some kind of holy talisman and generally guarded it accordingly. One night we caught them in a lapse. Some of our guys staged a clandestine operation to liberate the relic. Our student Jerry Beaulier did the honors, sneaking in and taking the sword from its case. The next day at the O club, our guys led a show-and-tell with the blade during happy hour. Some F-8 guys were present. A fracas ensued. Somehow the Topgunners managed to escape with their prize.
We later showed mercy and returned the Crusader sword, with a finishing touch. Marland "Doc" Townsend, a senior instructor and future skipper of VF-121, attached a placard to it certifying that it had been carried aloft at Mach 2. That was a sore point because the Crusader maxed out short of that. I was briefed later on the fistfight that developed in the bar afterward, but neglected to write an after-action report.
Life at Topgun was a fight club every day. As the instructors flew against the students, it was natural for the students to want to take a scalp now and then. If one of them beat Rattler, Smash, Sawatzky, Cobra, or me, it could help his service reputation. They seldom did it. But by the end of the syllabus and its twenty-six flights, it did happen. There was plenty of pride to be taken in that. I tried to keep them grounded. Everybody gets beaten now and then, I told them. If you managed to beat Mel and were smart, you understood it was dangerous to pump up your ego. The lesson there was that if Mel could get beat, anyone could. I considered this attitude the heart of professionalism. And as for my instructors, from time to time I had to warn them, "No egos, fellas. We're here to teach."
All that said, I couldn't always keep Rattler and Nash from wanting a piece of each other. Though these guys were close, they were just so strong-willed. Nash was a real needler. He could piss off the pope. He was always working on Mel. Maybe he didn't like the consensus that Holmes was the most talented Phantom pilot we had. I understood this and watched them carefully.
One day during a 2 vs. 1 with a student, they mixed it up hard. Mel and the student were the 2, going against Nash, who was flying an adversary aircraft. It turned into the Rattler versus Smash show, a contest of greats. It happened more than once, and we had a serious offline discussion. I had to lay down the law once again: no dogfighting between Topgun instructors. We were there to teach, not to feed our egos. Too much was at stake. I was mindful of Halleland's warning. One accident could scuttle us, the skipper had said. If Nash and Holmes stayed on this course, very likely one or both would be making a long trip back to the trailer on foot, with a popped parachute bundled up under his arm. Losing a plane could number our days.
No, I didn't want my pilots living on the pride of whom they could beat. All of us were in the same fraternity. When, say, Jerry Beaulier was finished with Topgun, I wanted to be sure how he would do against a MiG—and maybe unsure how I would fare against him. If we did our job, we'd have made him pretty dangerous. That's where any good instructor will find his pride.
# CHAPTER TEN
# SECRETS OF THE TRIBE
**Miramar**
**1969**
Only in 2013 did the U.S. government finally declassify its reports on a secret Defense Intelligence Agency project to test actual MiGs. Part of the effort went by the name of Have Doughnut. That program was made possible after an Iraqi pilot defected to Israel in 1966, delivering his prize MiG-21 to the West. A bit later, a Syrian pilot mistakenly landed in Israel with his MiG-17 and another operation was born. The DIA called that one Have Drill.
We were in the middle of teaching Class One at Topgun when our friends up the highway at Air Test and Evaluation Squadron Four, or VX-4, let us in on the secret of the captive MiGs. The squadron's CO, Commander James R. Foster, often invited us to his base at Point Mugu, north of Los Angeles, to join the fun on their Friday "fight of the week" event. His guys, all of them seasoned test pilots, were always ready to try out some new tactic in a new plane. We tried never to miss the show.
One weekend Foster invited J. C. Smith and me to his ready room, where he showed us film of U.S. planes dogfighting against a MiG-21. This really got our attention. It was footage from an American test range. Jim explained that he and his chief of projects, Marine major Don Keast, had been going to a forbidden zoo in the Nevada desert where these exotic animals were being tamed. The heavily restricted airspace had several names. Paradise Ranch. Groom Lake. Dreamland. Area 51.
Naturally, we expressed interest in having a turn. In the spring of 1969, Foster worked channels to secure approval for the leadership of Topgun to go to Dreamland for a week and see it for ourselves. The project was so secret that when we flew from San Diego to Nellis Air Force Base, near Las Vegas, we weren't allowed to tell our families anything about our destination, let alone what we would be doing.
From Nellis we took a cab into the city, where, across from the Las Vegas Hilton, there was a small hotel that was run by the CIA. The barkeeper at the watering hole there, known as O'Brien's, must have owned a security clearance. He had a professional's knowing attitude and never asked questions as we unwound during our overnight stay. The next morning before sunrise we would be back in the taxicab to the air base for a flight to the safari park where the MiGs lived.
It's probably not wise for me to describe a lot of what I saw at Area 51. The way the base was laid out, it was hard to see much. You'd man your airplane in the hangar and they'd pull you out. The hangars and taxiways seemed to have been arranged to block your lines of sight in most directions. That was fine by me. Highly sensitive programs went on there that I don't believe the public had an immediate need to know about. The CIA's A-12 Oxcart program—better known by its Air Force name, the SR-71 Blackbird strategic reconnaissance aircraft—was one. Other classified activities went on there at night, which may account for why we never stayed over on our days to fly. We clocked out at closing time and were back to O'Brien's by dusk.
But what we learned during the day was just invaluable. While the TA-4 and F-86H did a fair impersonation of a MiG-17, and the F-5 could stand in for a MiG-21, there was no substitute for the real thing. When I first saw the 17 up close, my instant feeling was trepidation, as I would soon be flying it. Sitting on its stubby nose and leaning over the windscreen to look into the cockpit, I was impressed for better and worse. It was old, rough, simple, heavy, and beautiful in its way. The avionics were crude, lacking the power-boosted controls of U.S. aircraft. I gave the fuel gauge a double take. This bird carried only eighteen hundred pounds of fuel, less than one-eighth of what a Phantom's tanks held.
I got six or seven flights in the adversary plane. It was agile to be sure, but I still felt like I was flying a very fast anvil. My frequent opponent at Dreamland was one of Jim Foster's crackerjacks at VX-4, Ron "Mugs" McKeown. He was a superb pilot. He concealed a considerable intellect behind his breezy self-confidence and ready willingness to do mischief. Tough, too. At the Naval Academy, he went undefeated for three years in the boxing ring. Mugs and I would spend most of a day flying head-to-head and swapping roles, Phantom for MiG. A former Air Force test pilot school graduate, Mugs was used to flying a lot of different aircraft. He was damn good in a MiG. The plane was so quick to run out of gas, even without using its afterburner, that you had to make your moves and score your points fast. You had to learn the rhythm of how to fight it. If you did, you could be dangerous.
Another pilot at VX-4, Lieutenant Commander Foster "Tooter" Teague, claimed that no Navy pilot who flew against the MiG-17 beat it 1 vs. 1 the first time out. That may not have been true, but either way, Major Boyd was right that the Communist plane had its advantages. Of course, we knew that already. It turned out that Doc Townsend, who had preceded Hank Halleland as skipper of the Phantom RAG, had, unbeknownst to me, flown against the MiG-21 at Dreamland a few years before we started Topgun. Townsend's work, though very highly classified, apparently had given the F-4 community its initial push to fly beyond prescribed boundaries in ACM. He seems to have passed down a lot of what he had learned to Sam Leeds at the RAG.
There was no better way to validate our tactics than to try them out at Dreamland. Once the Air Force guys got used to seeing us, we were allowed to fly straight to the base that did not exist from Miramar. We'd taxi in before sunrise, park our airplanes, go to the hangar, and sometimes grab a combat nap. We were in the skies at first blush of dawn. We never filed a flight plan. One day I flew a brand-new F-4J out to evaluate it against MiGs. Fresh from the factory in St. Louis, that Phantom smelled like a new car. It had, among other things, an improved radar and fire-control system that we were anxious to try out.
I should say here that the captured MiGs weren't supposed to be flown in dogfights. "ACM evaluation" was not the purpose of their Nevada residency. They had been obtained by the Air Force for "technical research." The blue suits were measuring engine temperatures, high-and low-end airspeeds, doing all the stuff they did in testing at Edwards Air Force Base. Accordingly, the three-star general who was in charge of the Air Force units at Groom Lake allowed no dogfighting. There could be no such risky behavior on his watch. We saw it differently. There were tactics to prove up. So we bent a few rules. If the Air Force chose to skip our flight briefs or debriefs, which they did, who were we to insist upon wasting their time? We got ourselves on the schedule and did our own thing. I suppose this was the closest we ever came to resembling characters in the old TV show _Baa Baa Black Sheep_. Forgiveness is easier to request than permission.
When Mugs met me at the hangar, enthused as he always was, he said he was scheduled to fight a MiG-17 and asked to borrow my airplane. It was still hot from my ferry flight, but I saw no reason to refuse him. He said something about wanting to test a new evasive maneuver when he flew that afternoon against one of the greats at VX-4, Tooter Teague, who had worked with Jim Foster in getting naval pilots' access to the MiGs. It was foolproof, he said, though adding that the maneuver had never been tried in an F-4. It was cheeky of Mugs to announce this after talking me out of that hot rod. As he taxied to the fuel pit, topped off, and accelerated down the runway, I suspected I'd been had.
Even if that was the case, I didn't want to miss the show. Mugs McKeown and Tooter Teague going 1 vs. 1 was always worth seeing. Both men were top-tier test and evaluation guys. You never knew what you might see. So I checked out another Phantom belonging to VX-4 and joined them in the airspace over Area 51.
Circling at a safe distance, with J. C. in the rear seat, I watched them merge and start a dogfight. Neither seemed to be getting an edge on the other and the tangle descended to lower and lower altitudes. Then Mugs tried his maneuver. He turned so sharply that his plane skidded and momentarily "departed controlled flight," as we say. Regaining it, he flipped over, inverted, and entered a stall once again. This was graduate-level flying, PhD sort of stuff. I can't do justice to the adventurous aerodynamics of it without moving my hands around a lot and using technical language.
After the stall Mugs was not able to regain control. Tooter broke character as an enemy aggressor and was trying to give Mugs some help over the radio. Mugs said something like "I got it." But he never saved his plane from its spinning descent toward the desert.
As the F-4J tumbled below five thousand feet, the hard deck through which we were never supposed to descend, Tooter and I both yelled, "Mugs, get out!"
Cool as a test pilot, he said, "I'm departing the airplane."
As if in slow motion, the Phantom arced toward the earth for the last time. Mugs or his RIO, Pete Gilleece, pulled the ejection handle.
_Foom-foom!_ Two small rockets went off, two seats followed, and—thank God—two parachutes opened in the sky. And two million dollars' worth of factory-fresh Navy flying machine erupted in flames in the desert.
As Mugs and Pete continued their nylon descent, they drifted directly toward the churning fireball. Fortunately, the desert whipped up a breeze that carried them to a landing maybe two hundred feet from the flames. They felt a pretty toasty heat wave but walked away without a scratch.
I wasn't sure the same would be said of Topgun.
After a mishap involving a multimillion-dollar piece of equipment, Uncle Sam required an investigation. And that worried me. Any report of the loss of a VF-121 plane at Topgun would imperil the program as it struggled to make its way. Since I had checked that Phantom out of Hangar One, we were responsible for it. Hank Halleland's warning rang in my ears.
When I landed and returned to the hangar, I made the call to Hank to break the news. I was surprised to find out that Jim Foster had reached my skipper first. Jim explained to him that it had been his pilot who carried out the maneuver while doing VX-4 business. Hank must have smiled as he said to Jim, "Okay. If that's true, you just bought yourself an airplane." With those words, the test-and-evaluation squadron took the hit and Topgun was off the hook.
Jim, to his eternal blessing, took the additional trouble of reporting the incident directly to Washington, instead of to Pacific Naval Air Forces headquarters. By reporting it to Rear Admiral Edward L. "Whitey" Feightner, the chief of naval fighter studies, he saved Vice Admiral William F. Bringle at AirPac from having to deal with it. (I promise you Bringle knew of the incident about fifteen minutes after it happened.) That double trick made our crashed bird VX-4's loss and let everybody avoid a grilling from our West Coast headquarters. No one wanted to see Topgun shot down, for we had come so far in such a short time.
Taking our leave of Dreamland that evening and flying back to Miramar in a VX-4 jet, J. C. and I drank well at the officers' club. Topgun would see another day. Where do we get men of Jim Foster's and Hank Halleland's courage? They never seemed to forget that we were at war.
The Air Force was slow to get wind of what we were doing with those precious captive toys at Area 51. We kept no written records of the dogfighting. Routine maintenance paperwork was our only paper trail. The reporting and debriefs were all done verbally after each flight, safely back at Miramar, within our tribe, over a beer or two in the trailer late at night, or at the officers' club.
Mel Holmes and I were invited to visit the Air Force Fighter Weapons School at Nellis to brief them on what we were doing at Miramar. I was curious to check in at their gun shop and learn more about the General Electric M61 Gatling gun pods they mounted to their Phantoms. (We decided not to use them.) Nothing the Air Force was doing entered the homegrown Topgun curriculum. Our cultures were so different, and that was reflected in our tactics. We did know that Colonel Lloyd "Boots" Boothby, a USAF pilot at Nellis, was as aggressive as we were, but had to hide it. He and some other good men, including Windy Schaller, one of the chief test pilots, were deeply frustrated with the rigidity.
Topgun couldn't avoid a rivalry with the U.S. Air Force. It wasn't about politics to us. It was about flying and ideas. Sure, it bothered us to hear the Air Force claim it had created the first fighter weapons school. (If that was true in name, it wasn't true in substance—or result.) It's bad ideas that lose wars and get people killed.
The most vocal advocate of the Air Force thinking at the time was Major John Boyd. In 1969 he was making a lot of speeches promoting his "energy-maneuverability" theory of air-to-air warfare. Simply put, it's a mathematical formula that tries to reduce fighter aircraft performance to a single value based on the plane's speed, thrust, aerodynamic drag, and weight. First put forward in 1964, it had reportedly been used by the Air Force to design new fighters such as the F-15 Eagle and F-16 Fighting Falcon, outstanding planes, as we all know. When Topgun was getting launched, Holmes, Jerry Sawatzky, and I attended classified conferences to keep current, and we'd see Boyd at several of them. Eventually, after we were established, we were invited to make presentations of our own.
In 1969, Mel and Ski gave a talk at Tyndall Air Force Base in Florida. John Boyd followed them, pitching his theory. There was some good debate, and Mel remembers Air Force officers starting to challenge their catechism. A particularly brave captain once questioned the Fluid Four concept by asking why a wingman with more tactical experience than his flight leader should be forbidden from taking a kill when he had it. That one ruffled some feathers. In the Q&A, though, Major Boyd made an infamous remark. He said that no U.S. pilot should ever dogfight a MiG, because his theory proved mathematically that since the enemy plane performed better throughout the flight envelope than the F-4, taking on a MiG was a good way to end up hanging from a parachute or a whole lot worse.
The problem with any theory is the baggage of its assumptions. We thought Major Boyd was making some rather large ones and considered his analysis suspect as a result. In the base auditorium at Tyndall that day, Ski poked Mel in the ribs.
"Why don't you say something, Rattler."
Mel stood up and proposed to the Air Force officer that he was underrating a few things. Namely people. Mel said that while weapons might have parameters and airplanes theoretical values, no algorithm could predict much if it excluded the most important factor of all: the skill, heart, and drive of the pilot in the cockpit. The moment of truth was the Merge. It was then that you had your chance to take the measure of a man.
"Sir," Mel said, "I just don't think you can know anything about another pilot before the first turn. And if you don't know that, then you can't say that a MiG-17 will win every time."
That needed saying.
The best I can recall, Major Boyd didn't really engage. He replied by restating his claim. "Thank you for that view, Lieutenant, but you can't fight MiGs in an F-4. We'll lose wars that way."
We would see about that.
John Boyd was intelligent, patriotic, and good at a great many things. From this exchange, we concluded that one of them was deriving big ideas that aspired to universality but did not reckon with the human heart. In aerial combat, technical factors were important. Some of them could be modeled. But no model could tell the whole story. Major Boyd was not wrong. His theory was simply incomplete. He also completely misjudged the F-4. We were no slouches at the science, either. With Cobra Ruliffson's technical acuity and hard work, we had fused hard data with equally hard experience. It ended up showing exactly how a Phantom could smoke a MiG, almost every time.
The energy-maneuverability theory had little to say about tactics or the people who made them work. The pilot is the key part of the equation, though as a variable it cannot be quantified. Out at Miramar, as students and instructors bent the jet and flew beyond the limits, we were trying to turn the man in the cockpit into a weapon. As adversary pilots, Mel, Ski, Cobra, Nash, and I were enjoying the role, flying, debriefing, and adjusting from the enemy point of view. Day after day and flight after flight, we were helping our students meet the challenge. We were making them part of the equation.
Men surely are weapons, and, as I said, ideas matter. I'd venture to say that any engagement pitting Major Boyd and any of his handpicked three against Mel, Jim, Nash, and Sawatzky would have had an instructive outcome. (And okay, I guess I have to say it: I could have filled in for any of them to equal result.) Adherence to strict rules and restrictions meant almost certain defeat against well-trained pilots fighting under no such restrictions. And this is why we say Topgun never existed before the Navy set up at Miramar. No schoolhouse that required adherence to fixed ideas, reduced airplanes to numbers, or considered its instructors as "priests" could ever be Topgun in our book. The final tallies over Vietnam would eventually tell the tale.
While Topgun's forays to Area 51 were never discussed at Miramar (the handful of us who were cleared to go treated the classification seriously), those flights were incredibly valuable. Our experiences there went straight into our 0430 briefings, and from there were used to refine the Topgun syllabus. We learned some important thing about the MiGs, and for that we were in debt to our friends at VX-4.
Slowly but surely, we were gaining confidence that when our junior officers went back to the war, they would be the dogfighters—and teachers—that their country needed in a desperate hour.
# CHAPTER ELEVEN
# PROOF OF CONCEPT
**Miramar**
**1969**
Topgun's students became crisp, smart, quick, deadly, and confident. They knew the performance envelopes of their airplanes and missiles, maneuvered quickly to exploit them, and handled all the switch interfaces in the cockpit efficiently. They demonstrated their ability to fly the Egg tactics to perfection and use the high yo-yo out of a two-plane Loose Deuce formation to fillet and fry aggressor pilots almost every time out. Their final exam was a special treat: an unrestricted Sparrow and Sidewinder shoot against live maneuvering targets.
Steve Smith was in charge of our BQM-34 Firebee drone live-fire exercises, generously provided to us by Jim Foster's squadron up the road at Point Mugu. These remote-controlled jet-powered gunnery targets, built by the Ryan Aeronautical Company, had been around since the 1950s. Unlike towed targets and the more common drones, which did not maneuver, the BQM-34s were flown by an operator on the ground. They were capable of more than six hundred knots and could fly up to sixty thousand feet. In the hands of a Phantom instructor like Steve-O, well, that twenty-two-foot-long target had a fair chance of giving even a good pilot fits. While it didn't have the power to soar vertically, it was plenty maneuverable, capable of sharp twists and break turns. Though we were a little worried about the possibility of accidents flying such a hot rod from the ground in a live-fire exercise, we figured the risk was worth it. Topgun's students needed this experience against a thinking opponent before we sent them back to war. At the Pacific Air Missile Test Range, some of our young guys were so good that they destroyed the wildly evading drones, then shot some more missiles to pick off the falling parts. After a success like that, the confidence soared and they were on final approach to graduation day in early April. As it approached, we had another surprise in store for them—a flight out to Area 51 to take a turn against a real live MiG as I related in the previous chapter. For students, it was a crowning moment in their young careers.
One evening at the Miramar O club while Class One was winding down, we designed what has endured ever since as the official Topgun flight-suit patch. Steve Smith and Mel Holmes sketched it out on a napkin: a MiG-21 in a Phantom's gunsight reticle and pipper. In Washington, people who had time to worry about such things thought it might offend the Russians. I made one call to Vice Admiral Bringle's office and the complaint went away. The patch design perfectly reflected the origin story of Topgun, and it has survived basically unchanged for fifty years. Every graduate of the Navy Fighter Weapons School wears it with pride.
As that small emblem got around the fleet, people noticed. As the reputation of Topgun flourished and grew, the fleet squadrons began calling _us_. Very soon Steve had the pleasure of explaining that all our billets were full, but that he'd be glad to keep their names on file.
The story of the patch, like so many other stories about Topgun, suggested the wisdom of letting junior officers be in charge. If the Navy's decision to put a fresh-caught lieutenant commander in charge seemed like risk avoidance at first, I see now that our insurgency could have succeeded in no other way. Without the great creativity, focus, and pace of younger men, we wouldn't have gotten it done. We were never more openly controversial than we had to be, but we had to rock their boat. You can get away with it, if you know what your mission is and you're damn good. We were.
The graduates of Class One returned to the fleet with a changed way of thinking, a patch, and a Topgun training manual. It was a master document that captured everything we had taught them and made it teachable. As training officers, they were the evangelists of the Egg and the lords of the Loose Deuce, and they set to work remaking the fleet squadrons in our image. Meanwhile, Class Two showed up, and we started the cycle all over again, hustling hard to update the lessons and the program documentation. There was no time to breathe easy.
To think all of this came together in about ninety days and took root in a stolen trailer. On the day Steve got that crane operator to perform a little larceny in exchange for a case of scotch, we never imagined it would become the nerve center of the Navy's evolving effort to improve its fighter tactics and doctrine for the next fifty years. But that's exactly what happened. Never was a man more fortunate to have God as his copilot.
Right after Class Two graduated, Vice Admiral Bringle, as ComNavAirPac, made a formal request to his boss, Admiral John J. Hyland, the commander in chief of the Pacific Fleet, officially to establish the Navy Fighter Weapons School at Miramar effective July 1, 1969. This meant everything to our fledgling graduate school. For the first time, we had explicit validation from the top of our chain of command, unprecedented for a project led by junior officers. Around the same time, that world-beating RIO, J. C. Smith, relieved me as Topgun's officer in charge. The handover was easy. He had been with me every step of the way. Continuity like that helped Topgun grow roots—just what Sam Leeds had ensured by letting me have the job in the first place.
In October, I went to Washington to brief the Pentagon on our experiences at the Topgun schoolhouse. Our syllabus was approved by the CNO himself. Later that year, Commander Richard Schulte relieved Hank Halleland as skipper of VF-121, our parent command. In Dick Schulte, Topgun continued to be fortunate in its friends. He personally arranged for the acquisition of four new adversary aircraft for our school. The A-4E Mongoose was far more capable than the two-seat TA-4s we had been flying as adversaries in "dissimilar" air combat maneuvering.
One Friday at the O club in the early days, Tooter Teague tried to sell me on using the Air Force's F-86H Sabre as our principal aggressor. The debate went long into the night and was settled the following morning in the air, F-86 versus A-4E. We bent those two jets hard. The moment of truth came when Tooter tried to match me in a vertical climb. He had no chance, not even in burner. It ended with his aircraft stalling, going into an inverted spin, and falling out of control like a dropping maple leaf. At that point he agreed with me that the Mongoose should be Topgun's aggressor of choice. No more borrowing aircraft from the RAG, in other words. We were free to soup them up as we wanted, removing all excess weight. The Mongoose's superior performance and constant availability enabled us to develop an expanded dissimilar ACM curriculum as well. A few months later, the Topgun curriculum got its first test in the crucible of war.
When our student Jerry Beaulier deployed with Fighter Squadron 142, the Ghostriders, on USS _Constellation_ in March 1970, it continued to be a strange time on Yankee Station. The air war was still on hold while President Johnson's White House held peace talks with North Vietnam. Though the carriers were striking at enemy supply lines running into South Vietnam through Laos and Cambodia, targets in North Vietnam were off-limits. That meant U.S. planes weren't flying where the bandits were. As usual, there had not been much of a threat to our carriers from enemy aircraft. Not since September 1968 had a U.S. pilot killed a MiG.
In the twelve months since receiving his Topgun patch and returning to his squadron, Jerry had been serving as VF-142's weapons-and-tactics officer, teaching what he knew but enjoying little opportunity to see anyone use it. That changed in March, when it seemed the MiGs were ranging farther south than they had been.
On Saturday, March 28, Jerry and his RIO, Steve Barkley, were idling in their F-4J, standing on the catapult in alert five status, ready for a quick launch. When the radar control ship reported four bandits inbound toward the carrier that afternoon, Beaulier and his air wing commander, Paul Speer, were launched off the _Constellation_ 's deck. Directed to take a westerly vector toward the oncoming enemy, still eighty-seven miles out, they were cleared to fire at once (they got a break from the usual rules of engagement requiring visual identification).
As the radar calls kept coming and the range closed, they saw no sign of the MiGs. The Phantom pair pressed ahead. It was Beaulier who first sighted the enemy fighters ahead and above him, at about twenty-five thousand feet. Following the Loose Deuce doctrine, Jerry alerted Speer and took lead, stoking his afterburners and accelerating into a climbing turn to intercept. The two MiGs spotted the Americans and separated, the leader climbing and his wingman breaking into a right turn. Beaulier took the enemy wingman while Speer went after the leader.
As he closed with the number two MiG, Beaulier realized, I suspect, in the space of those first twenty seconds, that his excitement had led him to stray from proper technique. He was fighting in the horizontal. In climbing to engage his enemy directly, he had lost too much airspeed to attack effectively. He dove again to regain it, pulling seven Gs at the bottom. He found the MiG descending with him. Looking to avoid a turning fight, he returned to what we had taught him. He pulled up sharply to initiate the Egg maneuver, rocketing vertically. The MiG had no chance to keep up.
Meanwhile, down below, Commander Speer had seemed to unnerve his own MiG. Its pilot turned wide and left the fight. Speer was turning back toward Beaulier to clear Jerry's tail when Jerry's MiG saw Speer. The North Vietnamese pilot fired a heat-seeking Atoll missile at the approaching Phantom. The head-on shot missed.
Up and up Beaulier's Phantom went. With RIO Barkley keeping him oriented, telling him the MiG shooting at Speer was no threat, Jerry focused on setting up his shot. Arcing over the top, he saw that their opponent was vulnerable. The MiG had lost sight of him. The enemy pilot banked right then reversed sharply left, as if looking for his pursuer.
This last maneuver was a fatal mistake. It gave Jerry a clean shot up the enemy's tailpipe. With the tone of a Sidewinder lock buzzing in his helmet earphones, he pressed the trigger and his missile left the rail. It tracked true and exploded underneath the MiG. A shower of steel fragments sliced into the enemy plane and set it on fire.
Trailing flames like a torch, the MiG sailed along, rocking its wings. Beaulier pulled up sharply to avoid running past him, slid in behind him again, and fired another missile. This one finished him. Just like he had done in the drone shoot at Topgun.
Back on the flight deck of the _Constellation_ , the celebration started immediately. Paul Speer, a large man, gave diminutive Jerry a bear hug and lifted him off his feet. Champagne, strictly forbidden, flowed. Later that day a Hanoi radio broadcast confirmed the MiG loss. In Washington, the politics of the peace talks forced the Pentagon to make smoke. Other than a brief announcement of a MiG being downed—the kill was said to have been scored by Phantoms that were escorting photoreconnaissance aircraft—the Navy kept a lid on the story.
Back at Miramar, we wondered who the MiG killer was. We worked our private channels as best we could. When word came back that an unnamed aircrew from the _Constellation_ had gotten it, we were thrilled. The carrier's two fighter squadrons had sent us Topgun's first class. We had wondered if there would ever be another dogfight over Vietnam, and were thrilled to think we might have a case study bearing out our tactics. When it was finally confirmed that the MiG killers were Beaulier and Barkley, we were ecstatic. It validated not only what we taught, but our school's very existence.
The highly classified after-action report of their engagement went back to the Pentagon, where the aviation and intel offices studied it in depth. Eventually we listened to the voice tapes of Jerry, Barkley, Speer, and his RIO. As we expected, there was no excitement there. They sounded like they were discussing a particularly important grocery list. Jerry went on to fly 220 missions in the F-4 Phantom. Topgun never taught a better one. Some said his success produced the impetus, then and there, to begin the process of turning Topgun into a proper naval command.
As our humble detachment within VF-121 saw its influence grow, we attracted some interesting visitors. Some very good foreign pilots served on exchange at the RAG. Foremost among these, in terms of talent and experience, was the British contingent. As their Fleet Air Arm had been transitioning to the F-4, the Brits sent some capable pilots and back-seaters to train with us. They passed through VF-121 much as other foreign exchange pilots did, serving in the RAG tactics section at the time we were forming Topgun. Their senior man was Commander Dick Lord, who was exceptional in the air. All of them, including Dick Moody, Peter Jago, and Colin Griffin, were very professional. While I could not involve them officially in Topgun—Dick had returned to England by the time we started—the Royal Navy exchange pilots performed valuable service within the RAG, especially flying as adversaries.
And they were great fun on the ground. As Condor sums it up, "What we learned from them was how to play mess rugby in our whites at the Admiral Kidd O Club in San Diego; how to pass out in our plates at a dining in; and how to leave our breakfast on the ramp and still make our takeoff times." Contrary to headlines in the British press a few years ago, British pilots had nothing to do with the formation of Topgun. The revisionist history has been disappointing. But it never diminished our affection for the exchange Brits, whether it be in a tavern or in the air.
In 1970, the Great One himself came for a visit to our trailer: Brigadier General Robin Olds. His fighting days were behind him now, but what glorious days they were. In World War II, he became an ace in both the P-38 Lightning and the P-51 Mustang, something no one else ever did, finishing the war as a squadron commander at the age of twenty-two. In 1966 and 1967, his fighter wing was so prolific that the comedian Bob Hope called it "the world's leading distributor of MiG parts." Robin led the way with four kills—a record that stood until 1972. He walked on water as far I was concerned.
When Dick Schulte and I invited Robin to be a guest of honor at one of our monthly Super Happy Hours at Miramar, Olds was serving as commandant of cadets at the U.S. Air Force Academy in Colorado Springs. He quickly accepted, but on one condition. He said he would come only if we let him fly. Though he was a second-generation West Pointer, he had none of the high attitude you often find in academy graduates. Robin cared only about results. It didn't matter what ring you wore. But we were happy to give him this little perk. We put him on the schedule for an ACM hop in an F-4.
I didn't know whether Robin was current in that aircraft. We figured he had never flown a Navy model. He arrived with flight gear and was clearly ready to go. After we gave him a quick cockpit checkout, away he went. J. C. Smith was his rear-seater and Mel Holmes flew on his wing.
The first engagement was a 2 vs. 1. The skilled duo of Robin and Rattler made short work of the aggressor. Rattler went low and got the bogey turning, leaving Robin to fly free and get the kill. So far so good. In the next engagement, a 2 vs. 2, Robin and Mel took on a pair of A-4Es flown by Dick Schulte and T. R. Swartz, a MiG killer from the A-4 tribe. (T.R., a former F-8 pilot, scored the only air victory of the war by a Skyhawk pilot.)
It was Mel who located them. Mel and Robin had briefed in advance how they would use the Loose Deuce formation, and Mel took the lead, turning toward them, reaching the Merge, and beginning a turning horizontal dogfight against the closest aggressor plane. The other A-4 wasn't to be found at the moment. Mel, as the "goat," was setting up his A-4 enemy to be bagged by Robin. That's when things fell apart.
The Air Force legend did not show. Having spotted the other Mongoose, he went tearing off after it. As Mel radioed to Olds, "Hey, I'm engaged," Robin was on the chase, leaving Mel in favor of trying to get his fangs into the second bandit.
Meanwhile, Swartz gained an edge on Rattler, conducting the dogfight expertly at low altitude, exploiting all the dancing ability of the lightweight, fast-rolling, tightly turning, rapidly accelerating Mongoose. It ended with Mel getting bagged. Believe me, that didn't happen often. It happened here only because his partner quit the tactical plan.
Back on the ground Robin climbed down from the cockpit, enthused. He had enjoyed the chance to wring out a fighter again and get a kill. But he pulled me aside. "Your back-seater talked the entire time. He never shut up!" He was right. J. C. usually never stopped talking. Especially when there was a serious mistake to correct. I still have to laugh. If a triple ace wearing a star was doing it wrong, Lieutenant Commander Smith would not be too shy to tell him. It was part of what made him the best RIO of his day.
At the debrief, J. C. Smith continued talking to Robin—just the way junior officers always talked at Topgun. He was just reviewing our rulebook, dogging his superior officer for not staying with Mel. If Robin ever got his wing out of joint over it, we saw no sign. Despite his deeply ingrained ideas about fighter tactics, and his commitment to the Air Force's Fluid Four, he finally conceded the wisdom of our tactic. "You've got it right," he told me. I doubt the Air Force ever adopted our formation afterward, but it did me a world of good to know that Robin Olds seemed convinced. He would eventually upset the wrong people with his outspokenness on the errors of his service over Vietnam. I would have done anything to persuade this brilliant tactician, warrior, and disruptor to transfer to Miramar. Major command should have been his due.
Handsome, well spoken, and charming, he filled the bill like a rock star that evening, drawing a huge crowd. His speech was superb and very well received.
In May 1971 Commander Roger Box succeeded J. C. Smith as officer in charge of Topgun. A two-tour combat aviator and Navy test pilot, Roger had an agenda. He believed the time had come for Topgun to become a stand-alone command. At the time, it was still just a department within the Phantom RAG. The RAG had the authority to move aircraft and people in and out of Topgun at its discretion. Without control of its own assets, the school in theory could have been out of business overnight if the RAG decided its needs were more important than the Fighter Weapons School's.
But Roger had an ace up his sleeve: the sympathy of the commander of Fleet Air Miramar, Captain Armistead "Chick" Smith. Roger, having served on his fighter wing staff, enjoyed good relations with him and approaching him for help springing Topgun free of control by the RAG. But there were problems. The CO of the RAG squadron at the time was Commander Don "Dirt" Pringle, a highly capable, well-respected officer who could overwhelm people merely with his presence. Under pressure to keep the RAG producing, Pringle didn't want to lose any of his prized aircraft to a separate Topgun command. He needed the A-4Es especially for his tactics shop. He was also hoping to begin doing what Topgun had been doing.
A key player in the fight for Topgun independence turned out to be Lieutenant Commander Dave Frost, one of Roger Box's instructors and a brilliant tactician who succeeded Cobra Ruliffson as schoolhouse specialist in the Sparrow missile. He was member of the Annapolis class of 1963, and had graduated in the second Topgun class.
Dave and his fellow instructors wanted to build on what the first generation of Topgun had accomplished. The manual needed updating, particularly because of all the real-world data the fleet was sending back as they began bagging MiGs. With our program getting results over North Vietnam, there was increased demand as well. We needed more adversary aircraft and skilled pilots than ever. But those resources were being pulled in three directions: training RAG students; supporting Topgun classes; and working with the fleet's adversary training program to prepare deploying squadrons for combat. Something had to give.
On the way back from a tactical conference at VX-4, Frosty and fellow instructors Dave Bjerke, Goose Lorcher, and Pete Pettigrew stopped for dinner in Malibu. They compiled their notes and drew diagrams on paper napkins. The changes that emerged from the "Malibu Conference" were used to update the F-4 tactics manual and maintenance plans.
They thought that as the school evolved it could have a greater impact as an independent command. But Pringle resisted. Scarcity of resources wasn't the only reason. There was also the issue of prestige. Though the public didn't know about Topgun yet, the wider Navy certainly did, and the Air Force had taken notice too. Whichever command "owned" the Navy Fighter Weapons School stood to play a large role in defining the direction of tactics and training. Its officers stood to have their careers enhanced.
That spring Roger Box's influence with Chick Smith began showing some promise. Like all good leaders, Chick usually got people to work together. He directed a ninety-day trial period in which Topgun would operate semi-independently. At the end of that period, Chick would hold a conference to evaluate whether the trial balloon rose or popped. They blocked out some aircraft and people as their own and moved forward independently. Roger managed the ninety days without a hitch. Before the evaluation could take place, he was selected to command a fleet squadron. Dave Frost was left to represent Topgun at a showdown with the Miramar brain trust. Roger's absence wasn't going to help the schoolhouse's cause at that meeting, which was bound to be contentious.
The evening before the decisive meeting, Commander Pringle called Dave to the VF-121 headquarters, where Pringle and his exec pressed him to declare the three-month test a failure, so that everybody could simply continue business as usual. But Frost had done his homework. He came loaded with data showing how much better Topgun had performed when it was operating separately. Though he realized it might hurt his career, he held his ground, defending Topgun like an accomplished attorney making his case. The meeting broke up in disagreement at 9 p.m. They all knew they would reconvene the next morning to finish their arguments, then it would be up to Captain Smith.
The next morning, neither side conceded anything and temperatures rose. Having heard enough, Smith pounded the table, stunning the participants, who had never seen the Fleet Air Miramar commander so agitated. Smith and his aide left the room. After what seemed like hours they returned, and the temperature in the room seemed to drop about ten degrees. Because the verdict was in: Topgun would become a separate command.
It was a quiet celebration at Miramar. I was away on a cruise, and most of the other Original Bros had gone to new duty stations too. Until the decision could be implemented, Topgun's instructors would continue to have responsibilities at the RAG. But the school was now in a real official competition for operating assets, people, aircraft, and funds. It would take a strong team to make it come together.
In January 1972, Captain Smith cut the order. Topgun became a permanent detachment, appearing on the RAG organizational chart with a solid line instead of a dotted line connecting it to Chick Smith's headquarters. That little tweak to the org chart made all the difference. Suddenly we were assured of adequate staffing, equipment, fuel, and operating funds. Our program was free of its former parent organization.
Roger Box became Topgun's first commanding officer, rather than "officer in charge." His tenure was brief. When he was transferred to the fleet on short notice, Mugs McKeown picked up the torch. He had the seniority, charisma, and talent to handle the job well. But he too was set to deploy to Tonkin Gulf. With his departure, Dave Frost, Roger's advocate extraordinaire, became the skipper, serving until Mugs returned from the fleet and relieved him.
In the spring of 1972, after President Nixon restarted the aerial bombing of North Vietnam, Topgun's graduates started tallying victories. By the time Operation Linebacker began, we'd graduated several more classes and were loaded for bear when the air war resumed in earnest.
One afternoon Frosty got a call from Washington. It was his old rival, Dirt Pringle. The former skipper of the RAG had moved on to an influential billet: executive assistant to Admiral Elmo Zumwalt, the chief of naval operations himself. For an upcoming meeting of the Joint Chiefs of Staff, the CNO wanted to present a review of the air-to-air box score. Frosty was to address an Air Force group at Nellis Air Force Base to discuss tactics and organization as well as demonstrate the use of our adversary program. As he put it, "The Navy was going to poke the Air Force in the eye." Dave worked up a presentation of the new Navy tactics. As he and his guys had just revised the Topgun manuals, it was a fairly easy assignment.
The room was crowded—obviously word had gotten around. Dave explained how Topgun operated, and noted the cautious approach the USAF took to air combat training. All of their dogfighting was F-4 against F-4. Never did an Air Force pilot see a plane imitating a MiG.
He got a lot of pushback during the question-and-answer session. A couple of accented voices stood out at the back of the room. As it happened, the Air Force Fighter Weapons School at Nellis had some Israelis among their foreign exchange pilots. One of them was my friend Eitan Ben Eliyahu. He and his cohort, the talented and cerebral Asher Snir, who had twelve and a half kills, had fine reputations that preceded them. Impatient, I suppose, with all the discussion of a matter they considered settled, one of them stood up and said, basically, "We agree with the Navy!" That seemed more or less to end the argument for the moment.
Some Air Force pilots were catching on in the meantime. Junior officers were alive to the dynamism of the Navy's Loose Deuce cruising formation, and the offensive potential of exploiting the Egg. The USAF also began to understand the value of dissimilar combat training, as well as the tactics and culture of the Loose Deuce. The blue suits learned fast, and the training environment became one of mutual respect with a healthy exchange of ideas.
The Air Force sent two Nellis instructors to fly with Topgun for a week. Major Richard "Moody" Suter, who had flown with us at Area 51, and Captain Roger Wells were experienced tacticians. The two pilots spent a week flying in the front seat of the TA-4s, seeing everything from 1 vs. 1 up to 4 vs. 4. Quickly absorbing the nuances of Topgun's syllabus, they returned to Nellis to start urging the Air Force's leadership to come around. Moody, like the great Steve Smith, could sell sand to an Arab. In late 1972, within a few months of the Miramar visit, the "junior service" stood up its first dedicated aggressor squadron, eventually maintaining a force of two dozen T-38 Talons and F-5 Tigers to mimic enemy planes and tactics. The cross-pollination of Topgun's tactics into the Air Force's training would not bear fruit in time to help it reverse its fortunes in the Vietnam War, but the foundation had been laid for a longer-term, mutually beneficial relationship.
Topgun would influence the development of the next-generation fighter, the F-14 Tomcat. We were consulted on new aircraft requirements and weapons acquisition as well. But the future of fighter aviation seemed a distant concern in 1972 as the ground war in Vietnam took a turn for the worse.
# CHAPTER TWELVE
# TOPGUN GOES TO WAR
**Yankee Station**
**Spring 1972**
After the Tet Offensive and the siege at Khe Sanh in early 1968, the U.S. presence in Vietnam diminished, both on the ground and in the air. By the spring of '72, with President Nixon's policy of "Vietnamization" requiring South Vietnam to handle its own defense, only ten thousand American troops remained in country. About a hundred aircraft were on hand in the country to support them. Another hundred or so planes were based in Thailand. Two carriers on Yankee Station fielded another 140 aircraft. Watching this drawdown in U.S. forces, our enemy prepared a massive ground offensive against the South.
On March 30, thirty thousand North Vietnamese Army soldiers, supported by a hundred tanks acquired from Red China, invaded South Vietnam. A few days later, another twenty thousand troops, also supported by tanks, struck South Vietnam from Laos. They were the vanguard of a Communist army that would ultimately field three hundred thousand troops and six hundred armored vehicles.
The South Vietnamese Army, caught by surprise, buckled. When desperate Allied soldiers called for ground support, the Air Force and Marine Corps squadrons in country were hamstrung by the monsoon season. What aircraft did get through faced shoulder-fired SA-7 missiles, which took a heavy toll. Within a week, the situation grew dire.
To stem the tide, President Richard Nixon unleashed the full weight of American airpower. Air Force F-4 squadrons flew in from all over the world, and the rotation plan that kept two carriers on Yankee Station was replaced by a full-on surge. Soon the _Coral Sea_ , _Hancock_ , _Kitty Hawk_ , and _Constellation_ were operating in the Gulf of Tonkin, with the _America_ , _Midway_ , and _Saratoga_ ready to deploy. It would be the largest concentration of naval airpower since World War II. With the restrictive rules of engagement rescinded or modified, it was a different war.
On May 10, President Nixon ordered the mining of Haiphong Harbor and other North Vietnamese ports, putting a stop to Soviet deliveries of MiGs and surface-to-air missiles. Meanwhile, Air Force, Marine Corps, and Navy planes hammered North Vietnamese supply lines. Bridges collapsed under a barrage of first-generation smart weapons, including laser-guided bombs, delivered by Navy Grumman A-6 Intruders and A-7 Corsair IIs. Air Force B-52 Stratofortresses struck MiG airfields around Hanoi.
The enemy tried to defend these important targets. Flying MiG-21 and MiG-19 interceptors, the North Vietnamese pilots found themselves in wild dogfights with USAF F-4 Phantoms. On May 10, three MiG-19s went down to air-to-air missiles, but the North Vietnamese pilots scored two kills. The Air Force continued to use the old-style World War II–era tactics that we found so limiting. During the climax of the morning's air battles, a three-kill F-4 pilot named Major Robert Lodge and his rear-seater, Captain Roger Locher, had just fired a missile at a MiG when another one slipped behind them. Lodge's wingman called out a warning, but it was too late. The MiG pilot opened fire with his cannon and tore the Phantom apart. Major Lodge stayed with the aircraft to give his back-seater a chance to escape. Locher ejected and was eventually rescued after an epic escape and evasion experience. Lodge was killed in action. The Air Force pilots were brave men and good aviators; yet their service's failure to learn the lessons of Rolling Thunder's air battles cost them. On day one of Operation Linebacker, the Air Force barely topped a one-to-one kill ratio in air combat.
The Navy was on a different path. North Vietnamese MiGs encountered a new Navy. The alpha strikes included electronic countermeasures aircraft that jammed the radio frequencies the North Vietnamese pilots used. When they ran into Topgun-trained pilots, the tactics we developed at Miramar changed the game altogether.
The _Constellation_ 's air wing hit the Haiphong area on May 10. Thirty jets sped over the beach, the pilots determined to inflict maximum damage on a vital target area that had been off-limits for virtually the entire war. Flying escort in an F-4J Phantom was Lieutenant Curt Dosé, who had finished second in his 1971 Topgun class, where he represented my old squadron, VF-92. When Dosé returned from Topgun, he became the weapons training officer. His knowledge and experience percolated throughout the squadron and changed how it fought.
As Dosé and his section leader, Austin "Hawk" Hawkins, orbited between the enemy airfields and the target area, the MiG-21s began to rise. Our radar picket ship, USS _Chicago_ , detected the enemy activity at Kep airfield. In the past, we would have been forced to wait for the MiGs to come to us and pose a threat. Now, with the handcuffs removed, the U.S. pilots could break straight for Kep. The Navy planes took only a few minutes to arrive.
At five thousand feet, Curt Dosé spotted two MiGs waiting to take off on the north end of the runway, plus a few more in revetments in the dispersal area. Dosé called to Hawkins, "Silver Kite, in-place turn port. Go!" Both Phantoms went to burner and dove for the deck, breaking the speed of sound on the way down. The MiG-21s, alerted now, lifted off the runway and jettisoned their external fuel tanks.
Dosé in the lead, the Phantoms streaked right over Kep's patchwork asphalt and concrete runway at Mach 1. The sudden switch from the cooler air at altitude down to the humidity down low caused Dosé's canopy to fog, obscuring his view of the fleeing MiG-21s. He shut off the air-conditioner system, which cleared the cockpit almost immediately, and picked up both MiG-21s again.
The chase took them down the treetop level and below. More than once, Dosé lifted a wing to avoid hitting branches. They wound around rolling hills as the MiGs played for time, trying to get their speed up while their fellow pilots launched from Kep to come to their rescue.
Behind the MiGs, with more energy and speed, Dosé and his leader controlled the fight. As the range narrowed and the MiGs passed through thirty degrees in their left turn, Dosé pulled the stick back and maneuvered from a lag pursuit into a perfect setup behind one of the MiGs. His Sidewinder growled in his ear and he fired the missile at about fifteen hundred feet. It missed, exploding behind the MiG. He fired a second missile. This one streaked straight into the MiG's tailpipe. A moment passed before the enemy plane blew apart, killing its pilot.
The lead MiG remained. Hawkins had expended his Sidewinders at it, which either lost tracking or malfunctioned. By now, the pursuit had taken the F-4 pilots back around toward Kep in this left-turn chase. Down to his Sparrow missiles now, Dosé asked Jim McDevitt, his back-seater, if he could get a lock on the MiG. They were too low; the ground clutter kept interfering with the missile's ability to track the enemy aircraft.
For a brief few seconds, the Americans and North Vietnamese were at an impasse. Without guns, the F-4s couldn't finish off the MiG, and with their remaining missiles outside their performance envelope, they would either need to break contact or figure out something else, all while blasting over the treetops at 550 knots.
Dosé, an aggressive and instinctive pilot, was not about to break contact. Instead, he pitched up into the vertical in a sort of barrel roll to try and fire a Sparrow in front of the fleeing MiG. He knew it wouldn't hit, but he hoped to spook the North Vietnamese pilot enough to get him to abandon his turn and give Hawkins a good shot at him.
While inverted at the top of the barrel roll, Dosé automatically checked his six. The other pair of MiG-21s on the runway were right behind them at their five o'clock and closing.
Dosé called them out, and both Phantom drivers broke hard right, toward their attackers, then went to full burner again. They broke through the sound barrier on their way to almost a thousand miles an hour. That sort of maneuver would have left a MiG-17 in the dust. A MiG-21? That Russian fighter possessed exceptional power and speed, and of course the always worrisome guns. A MiG-21 was climbing right up Hawkins's six. The enemy pilot looked to have the F-4 cold.
There was still one trick in the Topgun toolbox. The classified Have Doughnut program at Area 51 had taught us that at such speeds, the MiG-21 couldn't maneuver like an F-4. The two Americans broke hard into each other in a crossing turn, making an X in the sky. The Loose Deuce tactics worked beautifully as the cross turn cleared each other's tails.
Just then, the MiG pilot launched one of the Sidewinder copies known as the AA-2 Atoll missile. Hawkins's tight break defeated the missile—it exploded behind his F-4. The miss combined with the F-4s crossing maneuver convinced the MiG pilot he couldn't stay in this fight. He fled for Kep after Dosé stuck his nose at him and went after him. The Topgun grad gave up the pursuit and rendezvoused with Hawkins for the return to the _Constellation_.
The next day the phone rang at Dosé's parents' house in La Jolla. Captain Robert Dosé had served as a naval aviator during World War II and had experienced his own dogfights in the western Pacific. The caller, a Navy insider who knew the significance of what had happened, told Dosé's dad, "Bob, your boy got a MiG yesterday."
Bob and Curt Dosé became the only Navy father and son pilots to down enemy aircraft.
That fight over Kep was just a warm-up for the rest of the Navy's day over North Vietnam on May 10. The _Constellation_ 's air wing refueled and rearmed for a second alpha strike set for the afternoon against the railyard at the port of Hai Duong. The air wing flew straight into a mass MiG intercept, creating the largest single dogfight of the Vietnam War.
The MiGs raced into the strike group, initially blowing past the escorting F-4s. A pair of MiG-17s caught an A-7 Corsair down low and gave chase. The frantic American pilot called out, "MiG on my tail! I've got a MiG on my tail!"
Overhead, Topgun graduates Matt Connelly and his RIO, Lieutenant Tom Blonski, were covering the strike just north of the target area. They heard the call for help, but without any context, they couldn't rush to the rescue.
"Where are you?" Matt called out over the radio before banking hard to check the sky below. Sure enough, he and Blonski caught sight of the two MiG-17s hard on the heels of a lone A-7. The Corsair driver was trying to shake them with a hard left turn, but the MiG-17s stayed with him.
It would be a race to see who got into position to shoot first. The A-7 fled, the MiG-17s in hot pursuit. Matt rolled right and dove nearly inverted after the MiGs, keeping them on his nose. As he approached their altitude, he rolled left and pulled in behind them. It was a masterful maneuver, but he still ended up about sixty degrees off the lead MiG's tail and he couldn't get a good tone with his Sidewinder.
He fired anyway. The MiG pilot saw the launch and reacted instantly, pulling straight up and flipping inverted in an Immelmann. The 17 flashed right over Matt and Tom's canopy and vanished behind them.
The Topgun grad leveled out and lit his burners. The F-4 extended away from the fight, then Matt used the vertical, intending to get above the MiGs before dropping like an anvil on them for a second pass.
Instead, as his F-4 streaked into a near-vertical climb, both pilot and RIO discovered they had just flown into the middle of a wild dogfight involving almost fifty friendly and North Vietnamese aircraft.
A MiG sped right across their nose, bending into a right-hand turn. Matt rolled after him and turned hard to pull enough lead to get a missile shot. The MiG started to roll slowly left. Knowing from our Topgun curriculum that one of the MiG-17 Fresco's weaknesses was its roll rate at high speeds, and also knowing that its pilot had a blind spot directly to his rear thanks to the bulky ejection seat, Matt exploited the situation. As the MiG rolled out of the turn, the F-4 slid directly behind his tailpipe about a mile away. Unable to see the F-4, the MiG pilot began rolling left. Connelly nailed him with a Sidewinder. He felt the heat of the blast as his aircraft flew through it.
Another MiG-17 sped across Matt's nose in a shallow right bank. He gave chase, and suddenly the North Vietnamese pilot started rolling left in a near duplication of their first kill.
Matt stayed in his blind spot and triggered another Sidewinder. This one lost lock briefly, then reacquired the target and blew its tail clean off. After a brush with another MiG that ended up almost flying wing on them at one point, Matt and Tom lit out for the _Constellation_ , their weapon rails empty and two kills to their credit.
In the fight that day were other crews with Topgun experience, including Randy "Duke" Cunningham. While Randy had not graduated from the Navy Fighter Weapons School, he'd sat in on so many classes and flown so many aggressor missions with us in the backseat of a TA-4 that he might as well have been a grad. Everything he learned in our trailer he brought with him to Air Wing Nine's VF-96, the Fighting Falcons. He even took my call sign. I had chosen "Duke" because so many people said my voice sounded like John Wayne. Some even said I looked like him. When Randy came along he said he wanted the moniker for himself. I had no problem with it, so I changed to "Yankee." Shortened to "Yank," it served me well.
That day over Hai Duong, Randy and his back-seater, William "Irish" Driscoll, knocked down three MiGs using our vertical tactics. As they tried to leave the area, a surface-to-air missile shot them down. Both men were picked up in the water not far from the coast. Duke and Willy had scored two kills earlier in the year, making them the first Navy aces of the Vietnam War.
Altogether, the first day of Operation Linebacker highlighted just how far we'd come since 1968. The Navy's F-4 crews flamed eight MiGs without loss, while the Air Force got three for two Phantoms shot down. The death of Major Lodge came as an especially difficult blow to the Air Force units based in Thailand. He was one of the best pilots in the theater, the weapons guru for his F-4 wing, with three kills to his credit.
The Topgun training made a significant difference, as testified by most of the participants of the day's action. Our Navy crews still faced some of the same deficiencies we had encountered four years before during Rolling Thunder—malfunctioning missiles and the lack of an internal gun being the two most significant—but with the right tactics and training, the F-4 became a true MiG killer.
Eight days later, Topgun grad Lieutenant Henry "Black Bart" Bartholomay and his RIO, Oran Brown, shot down a MiG-19 while flying with the _Midway_ 's air wing. The MiG-19 was not an aircraft we had trained against at Dreamland, but many of the same rules applied to it as to the other MiGs.
The following month, Tooter Teague of VX-4 ended up in a wild fight. Though Tooter was not a Topgun instructor or graduate, he had worked closely with us as we stood up our graduate school. He had spent time at Area 51 while flying the MiGs, so he knew the enemy's rides intimately.
On June 11 Tooter led his squadron, VF-51 off the _Coral Sea_ , on an escort mission while the rest of the air wing pounded targets around Nam Dinh. The MiGs defending the area often used a ridgeline to mask their intercept approaches from radar. The intel guys on the _Coral Sea_ figured this out, and radar control set up Teague to bounce the MiGs should they try.
Sure enough, they caught four MiGs as they hugged the far side of the ridge. Teague and his wingman surprised them and shot two of them down. The crews worked as an integrated team, one F-4 pressing an attack while the other covered him, then reversing roles to take down a second one.
By mid-June, the Navy's kill ratio during Linebacker stood at almost twelve to one, a 600 percent increase over what we had managed during Rolling Thunder. The Navy's high command was ecstatic; the North Vietnamese Air Force clearly was demoralized. That spring, a MiG-17 pilot encountered a Navy F-4 and ejected on the spot before he even came under fire. They had no answer for our new tactics and teamwork. By the summer of 1972, the MiGs focused on attacking the Air Force while avoiding U.S. flights originating from Yankee Station. Our MiG-hungry Topgun grads didn't like it, but the tactical switch provided stark testimony as to which service they thought they could score against. Sadly, the Air Force fought the 1972 air campaign essentially as it had Rolling Thunder. Adherence to the Fluid Four formation cost them aircrews. Of the fifty-one aircraft the Air Force lost during Operation Linebacker, twenty-two went down to the guns and missiles of the North Vietnamese MiGs. During the same time, the Navy lost just four birds to MiGs. The Marines lost an F-4 to a MiG and scored one in return. From the start date of the Topgun program to the end of the war, the Navy's overall kill ratio was twenty-four to one. Its ratio for the entire war, beginning to end, would stand at twelve to one.
The Air Force crews voiced their opinions on the formations and tactics, wanting to make changes, but their chain of command proved inflexible. It cost them dearly in June, when the MiGs shot down three Air Force F-4s without a loss, the single worst air-to-air engagement of the war for the United States. The MiGs scored two more kills against the Air Force before the end of June. The Air Force failed to score in return. At the start of July, the Air Force F-4s had claimed seventeen MiGs in 1972 for the loss of ten aircraft in those dogfights. It was a valiant performance by some very brave men. Sadly the poor loss ratio, 1.7 to 1, could be traced to inadequate training and inflexible tactics.
While the Air Force struggled, I was in Washington overhearing a lot of buzz about Topgun and its success. Our little trailer with its stolen furniture truly became the nexus of a revolution that, once started with that first class back in '69, spread through our entire fighter force. Before Linebacker ended in October, 60 percent of the MiGs flamed by our men on Yankee Station went down at the hands of Topgun grads, or fleet F-4 air crews trained by the initial cadre of graduates of NFWS. The results blew all the bureaucratic opposition to Topgun right off the map. Of course, there always remained some latent animosity or jealousy by other factions of the Navy, including the attack aviators. (It only got worse when the first _Top Gun_ movie became so popular a decade later.) For a few years, the naval aviation fraternity wasn't as strong as I had thought. Individual careers seemed to be more important than the satisfaction of building a winning team.
That June, I called Miramar and talked to Jerry Kane, who was running the show then. I told him that eyes had been fully opened in D.C. They saw the value of Topgun at last. Even better, there was talk of making Topgun an independent command.
On July 7, 1972, it finally happened. I missed the ceremony at Miramar, as did most of the Original Bros, but we were there in spirit. Our bond was formed back in 1968 and '69, at Miramar. What we did in those two years was the most important thing we would ever do for our country. One look at the Air Force's experience in '72 convinced me that Topgun saved a lot of lives. I thought of the families, the "cruise widows," and the kids at North Island missing their dads, and I felt like I'd played a role in making sure they would have a homecoming.
Our successes over North Vietnam were tempered by those losses. Don Hall, an A-7 Corsair squadron commander on _KittyHawk_, was among them. My old buddy from VF(AW)-3 suffered engine failure during a night landing and was killed in the ensuing crash out in WestPac. Suzy, his widow, raised their two boys and never remarried. That beautiful lady passed not long after her sons graduated from college. How many more would have suffered like her if we had adhered to failing ways?
Meanwhile, the situation in South Vietnam stabilized as a result of the success of Operation Linebacker. The strikes up north choked off between 60 and 70 percent of the supplies the enemy needed to sustain their offensive against our forces. Hanoi agreed to begin peace negotiations in Paris in October, and Nixon suspended the air campaign while those talks proceeded. You have to wonder how many lives could have been saved had Rolling Thunder been carried out the same way from the beginning. The war would have taken a very different course had we done things in 1964 the way we learned to do them in 1972.
As Linebacker unfolded, I was stuck stateside, wanting only to get into the fight and bag my own MiG. After years of training to do it, seeing friends go off and succeed or die trying, I went to bed some nights thinking about Yankee Station. Our signals intelligence guys—the ones who listened in on North Vietnamese radio chatter—believed they had identified a MiG pilot with over ten American planes to his credit. Known as "Colonel Tomb," he was said to fly like the Red Baron had in World War I—above the fray, lurking to pick off American stragglers as they sought refuge back over the sea. Years after the war, we discovered that Colonel Tomb didn't actually exist. The top North Vietnamese MiG ace of the war was Nguyen Van Coc with nine kills.
In the moment, though, as the war raged, I wanted to meet this Colonel Tomb in the air and make him test his ejection seat. It became a personal goal. I wanted revenge for all my friends he had killed or forced into the torture camps. But mostly I was looking to prove I was better than their best.
In December 1972, the peace talks broke down. The Hanoi contingent walked away from Paris and refused to set a date to return. Furious, Nixon ordered a renewed bombing campaign, throwing the full weight of Strategic Air Command's massive B-52 bombers against the North. As the fighting flared again in what would be called Linebacker II, or the Christmas Bombings, I was mere days from getting a new assignment that would send me out to Yankee Station with one of the best fighter squadrons in the Navy. Perhaps I would have a chance at personally extending the Topgun winning streak.
# CHAPTER THIRTEEN
# THE LAST MISSING MAN
**Yankee Station**
**January 1973**
Home with my family for a rare Friday night together, I was barbecuing steaks, thinking about taking an after-dinner swim with the kids, when the phone rang. I went to pick it up, sensing something was wrong. As it turned out, I was right. The executive officer of Fighter Squadron 143, the Pukin' Dogs, was missing in action in South Vietnam. That pilot, Harley Hall, was a friend of mine.
The squadron was in a state of shock. It also needed a new XO. Which accounted for my emergency orders to pack up within twenty hours and begin the long journey out to the _Enterprise_.
Harley's fateful mission, I couldn't help but think, might well have been the last of the entire war. With the Paris peace talks showing progress, it figured to be over soon. Harley made sure he led what he knew could have been naval aviation's swan song over North Vietnam. He never came home.
I first met Harley in 1966, when we were going through the Phantom RAG at Miramar. He became one of the most gifted pilots of his generation, and had commanded the Blue Angels. He'd just gotten married to his girlfriend, Mary Lou Marino, in a little church in Santa Barbara. Crossed swords. Dress whites. Gloves. The works. They were a great-looking couple, so devoted to each other. They had a five-year-old daughter and were expecting their second child. I never really got to know Mary Lou, but Harley—I would have followed him anywhere. Most everyone who flew with him felt he would become chief of naval operations someday.
His junior officers flat-out worshipped Harley H. Hall. A charismatic leader, he always took the toughest missions. He mentored the younger guys and looked out for their well-being. He was scheduled to take command of the squadron when it returned to Miramar, and I was to become his exec. The only change now was an acceleration in the schedule.
Eventually I learned the whole story behind his disappearance. That strike from the _Big E_ launched on the afternoon of January 27. Ernie Christensen was one of the last men to speak to Harley. Ernie saw him on the flight deck and offering a quick greeting, then climbed into his plane. The Dogs were going to hit a river harbor about fifteen miles off Quang Tri.
Guided by a forward air control aircraft, Harley rolled in to hit some barges, then made two runs on a cluster of trucks. As he pulled up after his second run, his F-4J shuddered from repeated shrapnel strikes. Calmly he reported to his wingman, "Mayday, Mayday. I'm hit. Heading 'feet wet.'" Turning for the coast, he hoped to reach the water before he and Al would have to eject. The closer to the coast they bailed out, the better their chance to survive.
His Phantom flew sluggishly and Harley reportedly struggled to keep the aircraft under control. His wingman, Terry Heath, spotted him a few miles from the target area, staggering along at about four thousand feet.
"I've got you," his wingman said. "But you're on fire." Flames streamed from the port wing, spreading toward the fuselage. Still, Harley stayed with it, fighting for every second. Then the fire reached his hydraulic system. When he lost control of the plane, Harley and his back-seater, Phillip A. "Al" Kientzler, were out of time. They ejected. Harley's wingman saw them swinging in their chutes, descending about a half mile apart onto an island at the confluence of two rivers.
The area was crawling with enemy troops. As the two naval aviators swung in their chutes, ground fire erupted below them. Al was wounded in the leg as he descended. Harley was seen to reach the ground and start running for cover.
Harley's wingman swept over the area, trying to establish contact. An enemy soldier fired an SA-7 that barely missed. A moment later, a second missile streaked out of the jungle. Only hard maneuvering saved that F-4, and the brave pilot refused to leave his exec.
Racing to the scene to coordinate the search and rescue operation was the Air Force forward air controller. Flying an OV-10 Bronco, he and his back-seater were not so lucky. An SA-7 leapt up out of the tree line and struck their aircraft. As it went down, the two men ejected. Their chutes opened, and though enemy ground fire reached up at them, they too hit the ground safely. At length the pilot was heard on the radio saying, "Looks like I'm going to be captured." His radio circuit clicked back again as the North Vietnamese troops shot at him. "Oh my God! I'm getting hit. Oh my God!" Then silence. The enemy finally tied them to a couple of trees and decapitated them. A South Vietnamese special operations team found their bodies a few days later.
Harley Hall became a POW, but unlike Al Kientzler he was never released. And so in the last hours of the war, the men of Fighting 143 had their hearts torn out one final time.
The first night of peace since 1964 was no time for celebration. I struggled to make sense of the loss of one more friend as I told my kids that Dad had to go away again. As I pulled my gear together, I found my little mouse still in his nest in my flight bag. Through fifteen years and countless stations, he had seen me through. _Hey, little fella. We're heading back to the_ Big E. _I'm gonna need all your mojo for this ride_. I found my old Ray-Bans, carefully tucked away in their case. As I packed them with the rest of my gear, it struck me that they'd been with me through my entire career. _Who keeps a fifteen-year-old set of sunglasses? Maybe it's time for a new pair_. The distractions were welcome, because they kept me from dwelling on my larger concerns. I had tried to be a good husband and father, but these constant separations took a toll.
The next morning, I shared yet another goodbye with my family. My wife and I knew the chance of combat was probably pretty low, given that the peace accords were signed and our prisoners of war were soon to be returned. If all went according to schedule, it would be only a few weeks instead of months this time. We were pros at this by now.
My oldest, Dana, was in her first year of high school that winter. Through all the other goodbyes, she had learned to be tough and stoic. After recovering from the shock of my impending emergency deployment, she handled it like a superstar. My little guy, Chris, was a different story. Almost five now, he looked up at me with tear-streaked cheeks, letting it all out. I gave him an especially long hug as we waited for my friend Jack Bewley to take me to the airport in his antique Bentley sedan.
At Lindbergh Field, I caught a flight to SFO, then Seattle, where I secured a seat on a mostly empty Pan Am 747 bound for Manila. I curled up across three seats and slept for most of the trip.
Twenty-four hours later, a Navy C-2 took me aboard at Cubi Point and flew me out to the carrier. The squadron's CO, Gordon Cornell, met me on the flight deck. Gordo was a warrior's warrior, a man who'd flown everything from F9F Panthers to F-8 Crusaders and F-4 Phantoms. Wounded in action over North Vietnam in 1966, he went on to earn two Distinguished Flying Crosses and seventeen Air Medals.
"Really glad to see you, Yank. Sorry it had to be under such terrible circumstances."
I shook his hand and asked how the Dogs were doing.
"They're Dogs, Dan. They'll always be okay. They're a tough bunch. Bonded, as Harley would have wanted."
Still clutching my hand, he seemed to reconsider this. He added, "They're hurting, badly. Some of the guys can't wait to get home and help out Mary Lou and the kids."
There was sadness in his eyes. The shooting war was over, but we all had wounds to heal.
# CHAPTER FOURTEEN
# THE PEACE THAT NEVER WAS
**Yankee Station**
**February 1973**
The Dogs were a quiet lot when I joined them in the ready room. Their anguish was palpable as they discussed how they might intercept Harley as the North Vietnamese moved him north to Hanoi. If we could pinpoint his location, maybe we could combine a strike package with a combat search and rescue mission and get him and Al out of there. With the war theoretically over, of course, neither Washington nor our admiral would have ever authorized such a mission.
Was the war really over? It didn't feel like it. Sure enough, the fragile cease-fire broke down. Both sides were at fault, and at times the flare-ups were serious enough to endanger the peace accord. Of course, the North Vietnamese supply influx into South Vietnam continued through Laos, where the fighting became intense. The Communist rebels stood a good chance of overrunning the pro-American government there, and they sensed the time was ripe now that we were, as our ambassador to Laos put it, "cutting and running."
The North Vietnamese used a road that ran through Laos and into South Vietnam. This supply route, which we had bombed for years, was known to us as the Ho Chi Minh Trail. Dubbed Operation Barrel Roll, the air campaign stretched from 1964 into 1973 and continued after the peace accords were signed. American aircraft, including B-52s, flew hundreds of sorties in support of the crumbling Laotian army.
Back home, the Paris Agreement was hailed as a victory. Our POWs were coming home. Our troops were pulling out. South Vietnam would survive and have the right to determine its own fate.
But only the U.S. troop pullout was real. The war in Laos continued, and the _Big E_ 's air wing went back into the fight, bombing Communist insurgents and their lines of supply. Far from celebrating the war's end, we found ourselves in the midst of another one that nobody at home even knew had gone on for nine years.
Well west of the Vietnam border, we hit a truck convoy on the Ho Chi Minh Trail. Flying low and slow, an Air Force forward air controller marked targets for us with smoke rockets. We rolled in and hammered them with bombs. During another pass, the forward air controller's plane took a critical hit from ground fire. When he crash-landed on a small dirt road, we had another rescue mission to cover.
Far from the coast, we were going to have trouble getting him out, but we stayed over him, wishing yet again that the F-4 had an internal gun. We could have killed a lot of bad guys with a 20mm Vulcan Gatling gun that day. At last, another aircraft from his unit arrived and managed to land in a patch of open ground. When they hauled their comrade aboard, we thankfully avoided a repeat of what happened the day Harley and Al ejected.
As the weeks wore on, the squadron's mood shifted from shock and grief to stubborn resolve. The guys carried out their missions, flying in an air corridor that took us past Quang Tri practically every day. I could not have been prouder. Gordo and Harley had selected and trained well. Lieutenant Terry Heath ranked among the best, a pilot who thoroughly understood the F-4 and could take most anyone in a dogfight. Having been on Harley's wing that day over South Vietnam, he was affected by the loss particularly hard. He'd risked his life repeatedly to find out what happened to Harley and Al. His poise and character helped keep things together.
If only the larger war had followed his example. All around South Vietnam, the Americans were turning out the lights. The final prisoner release took place in March. On the twenty-ninth, the last of the American combat troops climbed aboard transport aircraft at Saigon for the long journey home.
Before crossing the Pacific for Pearl, we stopped at Subic Bay. Those nights at the Cubi Point Officers' Club were the wildest, hard-drinkingest I'd ever seen. The guys really unleashed, like dozens of overwound springs suddenly releasing their tension. In retrospect, it was probably the first real act of healing for the squadron.
On June 7, 1973, the _Enterprise_ arrived at Pearl Harbor. During our arrival salute to USS _Arizona_ in 1968, we were filled with anticipation of what combat would be like. Now we had names to mourn. As I stood rendering another salute to our lost battleship, I thought about our POWs such as Jim Stockdale and Harley Hall, Ron Polfer, J. B. Souder, Arvin Chauncey, Robby Reisner, Coal Black, and Dieter Dengler, to name a few. They were tortured, beaten, and psychologically run down. They were forced to sign confessions, starved, denied medical care, and, to add a final insult, used as propaganda tools when actress Jane Fonda showed up in Hanoi, with television cameras rolling, to fawn over our enemy. Some of these men never came home.
In March, most of these POWs returned to America. Harley was not among them. The mystery of his fate was never unraveled. Al Kientzler was told by a guard that his pilot had died in his chute, but Lieutenant Heath saw him running from his landing spot into some nearby trees. We'd received intelligence tracing his handover from unit to unit all the way to Hanoi.
The worst fear for all of us wasn't death. It was ending up like some of the Korean War crews shot down over enemy territory. Never handed back at the end of hostilities, they simply vanished. Rumors abounded over the years that some ended up in Soviet gulags, wasting away in Siberia, forgotten by everyone but their families. When we heard that Harley had not been released, the nightmare we all feared became his reality.
We were different men when we arrived at Pearl that spring day. It would take time for each of us to sort out what that meant. I guess that process started in Hawaii. Few of our squadron took the chance to go on liberty there. It was the only stay at Pearl I ever made where most of my men remained aboard. We caught up on sleep and considered our futures. With the war over, did we want to stay in the Navy? The airlines were paying well for good pilots. A peaceful, lucrative, and far more family-friendly career waited for them on the other side of the gate. Gordo would be moving on to another command. That meant I'd be moved up and given the squadron.
Just before we arrived at Pearl, we received a priority message ordering VF-143 and our sister fighter squadron on the _Enterprise_ , VF-142, to turn around and redeploy in fifty-one days. Breaking the news to our men was going to be tough. And it could cost the Navy some good people. Honestly, I wouldn't blame any of them for getting out. Already we were due for a mass exodus. As we faced other threats—the Russians, the Chinese, more chaos in Southeast Asia and the Middle East—we needed to keep our talent. That would be a major leadership challenge in the weeks ahead.
We sailed out of Pearl a few days later, California bound. When I came aboard, the guys told me stories of the ship's last view of home. When the _Big E_ was set to sail from Alameda in the Bay Area, antiwar activists tried to storm the base or delay the carrier's departure by swarming the boat basin with small boats. The Navy and Coast Guard fended them off, and the _Enterprise_ sailed on schedule. But a sour feeling prevailed when the carrier steamed under the Golden Gate Bridge. The country was poorly led and bitterly divided. A good portion of the public simply hated the military. I like to think those who felt that way were just ignorant. If they knew us, perhaps they would have come around. Maybe peace would bring some perspective and understanding. Or maybe that was asking too much of people who called us baby killers and spat on returning veterans in airports. We felt our universities were playing a role in spreading this poisonous, hateful view among younger Americans.
Halfway home, Gordo and I broke the news to the squadron of our quick return to sea. This time, the Navy was sending us to the East Coast to deploy on USS _America_ for operations in the Mediterranean Sea. Cruises in the Med usually meant we would operate near the Middle East, the other major flashpoint of the Cold War. We promised to do our best to make it a "vacation cruise."
Four hundred miles from the California coast, the _Big E_ launched her air wing. The attack squadrons flew to Whidbey Island, Washington, and Naval Air Station Lemoore, in central California. While some of the Dogs sped for Miramar, the rest of the squadron came home on Navy DC-9s when the ship made port in Alameda.
Those of us who flew into Miramar were in for a treat. We landed, taxied to the ramp, and parked our Phantoms side by side, arrayed before our families. Waving American flags, holding our kids on shoulders and cheering, they were a sight that stirred us all. We climbed out of our planes to meet a herd of kids. Many of them put on their dads' big flight helmets and were lifted into the cockpits so that their fathers could patiently explain what the myriad instruments and switches did. As Dana and Chris found me, their mom trailing after them, my family was reunited again. Steak and baked potatoes were on the menu that night. Afterward, I made sure we finally took the swim that got derailed on the last night of the war six months earlier. It was a long one, with a lot of joyful splashing.
Every fighter pilot wants command of his own squadron. When I learned I was to become the skipper of the Pukin' Dogs, I made sure to bone up on squadron lore. It began in 1953, at the end of the Korean War. The insignia of VF-143 was a winged griffin, a mythological predator with the body of a lion and the head and wings of an eagle. During a squadron function, one of the pilots tried to craft a snarling griffin out of papier-mâché. It ended up looking like a dog with wings, hunched over in the throes of misery, coughing up something it had eaten. Seeing it, one of the wives exclaimed, "My God, it looks like a puking dog!" Ever after, VF-143 had its proud nickname. For all the challenges ahead, I relished the opportunity.
The change-of-command ceremony was a formal affair with full dress whites, VIP admirals, and well-rehearsed speeches. When I parked and got out of my car, I heard something tear. The rear seam of my pants had split open, exposing my white Navy briefs. I couldn't believe it. There was no time to bolt for the base tailor shop. Gordo, whom I was relieving, was ready for our joint entrance, and all the guests and troops were waiting. When I walked to the platform, I hoped nobody would be checking my six.
When my turn came at the podium, I made a point of keeping my tail away from the crowd. As I began my speech, I heard a stir behind me. Though the crowd was none the wiser, the small group of VIPs had a clear view of my loose deuce. I heard a few quiet cheap shots in their muffled hilarity. I made my remarks in spite of my mortification. At that point the air wing commander took the mic and said, "Well, ladies and gentlemen, it sure is a bit breezy today!" I could only laugh. After a quick turn at the base tailor, I hustled to the reception at the O club.
With less than two months before deployment, the squadron went right to work. The leadership lessons I'd learned in the fleet and applied at Topgun were my basis for everything we did. Lesson one: Above everything, take care of your people. My men needed to feel valued. After the shared hardships out on Yankee Station, the grief over Harley's loss, and the chaos unfolding in the streets back home, beyond the front gate, we closed ranks. With those outward pressures pushing in on us, we became one of the tightest bunches I've ever known.
Another lesson was to take good care of your aircraft. Among the first things I did at Miramar was make sure the squadron kept the aircraft it had flown on the _Enterprise_ on its most recent deployment. Usually a returning squadron sent its planes through a maintenance cycle and took new aircraft from inventory. The crew chiefs, maintainers, and plane captains hated this. Out on the _Big E_ , they had gotten to know their current aircraft like family. Each Phantom has little quirks that make it perform just a bit differently from the others of its type. Some have issues. Some are unusually reliable. Once our maintainers figured all this out, they knew how to dote on them and the squadron gained a performance edge. At the end of the cruise, our F-4s had the most beautiful paint jobs and were free of corrosion. I pulled strings that let us keep these same aircraft as we prepared to go to the Mediterranean.
We broke for a trip to Las Vegas at the end of August for an enormous reunion of American aviators of all services who had flown in Vietnam. We would unofficially welcome back the 166 men taken prisoner by the North Vietnamese. Some three thousand of us and our wives gathered at the Hilton. There were many spontaneous mini-reunions that night as old friends saw each other for the first time in years. The happiness touched everyone. The war over, the years of hardship in the rearview mirror at last, our former POWs were ready to pick up their lives and careers. What an enormous challenge. Some came home knowing nothing of the Summer of Love, the Watts riots, the Kent State shootings, or the assassinations of Martin Luther King and Robert F. Kennedy. Their last experience of America predated acid rock and Woodstock. Fitting into the here and now and getting to know their families again tested the former POWs all over again.
I was chatting with old friends and our wives that night when somebody wrapped his arms around my shoulders and said, "Hello, Yank." I turned in my seat to see Ron Polfer. "Pompadour," as he was called by the guys at VF-121, was shot down flying a Vigilante reconnaissance plane. Punching out at about seven hundred knots cost him his eardrums, a few broken bones, bruises to his whole body, and capture by the North Vietnamese. But he survived to return and become chairman and president of Zeiss International. Arvin Chauncey, an attack pilot and liberty buddy of mine, greeted me in the same warm fashion. I had not seen him since the day he was shot down too. Throughout the evening, Bob Hope and many other friends of the military entertained us and turned it into a night most of us will never forget. The song of the evening was "Born Free," which few managed to sing without tears rolling down their cheeks.
Shortly after our Vegas interlude, the Pukin' Dogs said farewell to Miramar one more time. Yet another goodbye with our families. Chris clung hard to me again. Every time he did that it became harder to leave. No matter how tough the man, no matter how much combat experience and passion for flying he has, the sight of your little boy brokenhearted by your departure never fails to hit home.
At least we weren't being sent to Yankee Station.
We climbed into our Phantoms and flew east to Norfolk, and the rendezvous with our new home, the carrier USS _America_.
The Mediterranean, home of the U.S. Sixth Fleet, became a powder keg on October 6. That was the day our Israeli friends awoke to the greatest crisis of their lives: an imminent Arab invasion. The nation of Israel responded to that gathering storm with a massive preemptive strike.
When the Yom Kippur War started, I was at Norfolk with the Dogs. All I could do was hope my Israeli friends, Eitan Ben Eliyahu and Dan Halutz and the rest of them, were out there knocking MiGs down and laying waste to ground targets. I'm sure they felt the same as their American friends at Miramar headed to Vietnam in 1969. We all knew that the proxy nations we fought were but tentacles of a common enemy: the Soviet Union.
Our deployment to the Med was undertaken in this light. In January 1974, the _America_ and its battle group sailed across the Atlantic to join the Sixth Fleet, then began a series of port-of-call stops from Barcelona to Athens. The pace was slow and easy. We flew, but not too much to wear us out. The ports we visited—it was indeed a vacation cruise. We explored the ruins of classical Italy; we saw Sicily and the Greek islands of Corfu and Rhodes. After the strains of Vietnam, this Med cruise turned out to be exactly what the Pukin' Dogs needed.
We would make periodic sweeps through the eastern Med to show the flag, then return to Athens for some time ashore. The guys in the squadron pooled resources and rented a beach house in a resort town called Glyfada. That became our base of operations when ashore, and the pilots would crash in every nook and cranny of the place at night. We'd have to step over each other to get to the head in the middle of the night. Psychologically, the Mediterranean cruise prepared us for peace better than anything could have.
I ran the squadron as best I could with men like Skank Remsen and Gene Valencia as my inspirations. One of the things I did was get hold of a theater-grade popcorn machine. Our maintenance guys found a place for it in their area, and we charged ten cents a bag. The money we made went into a squadron fund to be used for the morale and welfare of the Dogs. Twice on the deployment, guys lost a family member back home. Both times, we secured emergency leaves for them, using the popcorn fund to buy their plane tickets. The popcorn fund also bought all the pilots and naval flight officers a white or blue turtleneck, a blue blazer, gray flat-front slacks, and cordovan loafers to wear during our nonuniform time ashore. (As we were in Europe now, not the Cubi officers' club, I insisted that my men be sharply dressed.) We looked superb, and in a crowded club we could spot each other a mile away. It was a great way to boost our sense of pride.
Every great leader I knew made a point of taking care of his chief petty officers. This was important, as the chiefs oversee the nuts-and-bolts operations that keep the squadron functioning. The enlisted crew worked directly for the chiefs, not for the officers—a point that good officers never forget. I made a point of getting to know our chiefs, drinking coffee with them from time to time to hear the view from the hangar deck. Their input was vital to the morale and effectiveness of the squadron. At times, the chiefs invited me to eat with them in their mess. I was grateful for those opportunities—and took the opportunity to return the favor when we were on deployment in the Mediterranean.
I had asked Vice Admiral Bob Baldwin at AirPac if the Navy would consider chartering a 747 for us. The idea was to fly out our wives and girlfriends to enjoy a mid-deployment break while we were in Greece. Such a gesture would help improve retention, I said. And Admiral Baldwin went to bat for us, recognizing the high cost of training someone to replace any of the high performers in my squadron in 1973. Halfway through our cruise, a United Airlines 747 landed in Athens with the squadron's wives and fiancées. We spent ten days in Glyfada together. The family that celebrates together stays together. Of all the experiences I had in the Navy during my career, this interlude in Greece ranks as one of the best. There would be no airline pilots coming out of this deployment, thanks to Admiral Baldwin.
One day at the fleet landing at Athens, I watched our chief warrant gunner, Bob King, dive into the water. He swam all the way to Glyfada to wade ashore and surprise the gang at the beach house. He had been a SEAL in Vietnam. Though he was always tight-lipped about his time out there, he did once tell me how he had escaped a jam by crawling to a river at night and floating downstream as patrols of North Vietnamese troops searched for him. Along the way, a snake wrapped itself around him and began warming itself. He drew his Ka-Bar knife and cut the snake's head off as he drifted along. He was a great man who was revered by every man in the Dogs, including me. Imagine having men of such capability and deep experience at your disposal every day.
Our chiefs were uniformly superb. My own plane's crew chief, Tony Baker, set the example every day with his work ethic and attention to detail. My aircraft was always well prepared and ready to go, thanks to him. All that hard work, yet it turned out not one of our chiefs had ever flown in an F-4. At the end of our seven-month cruise to the Med, as we were preparing to return to Norfolk, I realized that because several of our naval flight officers lived on the East Coast and didn't need to fly home, our squadron would have five or six empty seats. Why not let the senior chiefs fly back with the air wing? I put out the word, and the chiefs pounced on the chance to experience a catapult launch and a fast ride home.
As we passed through the Strait of Gibraltar and began the long transatlantic crossing, the squadron completed seven months on deployment without a single accident, a remarkable achievement. Morale, at rock bottom the previous year, was sky-high. The Dogs were walking tall with our swagger back, ready for whatever the Navy threw at us.
A few hundred miles from Norfolk, our F-4s began launching for the cross-country flight back to Miramar. With me in the backseat of my F-4 on this flight was our J79 specialist, Chief Jim "Frenchie" Ireland. He was nothing short of a prodigy. He knew more about the inner workings of our power plants than any other man I ever met in uniform. As we chatted over the intercom during our flight, I could hear the excitement and happiness in every word he said to me. We refueled in midair over Tennessee before heading on to Roswell, N.M., for an overnight.
The next day, our sixteen Phantoms entered the pattern over Miramar. Fightertown was abuzz. Flags were waved, signs were held high. As we touched down, taxied to the ramp, cut our engines, and opened our canopies, our families surged toward our birds. For the chiefs who had never flown before, this was an incredible moment. To the surprise of their families, they climbed out of the cockpits in full flight gear. Frenchie's wife reached him just as our brown shoes touched the ramp. She wrapped her arms around him and gave him one hell of a kiss, then grabbed me for a thank-you-skipper kiss that left me mirroring Jim's smile.
Quickly on her heels was my son, Chris, giving me a little-man bear hug. My daughter, Dana, pushed right in for a long hug. My girl, always a bit more reserved, was halfway through high school now, and I'd missed much of it. I needed to be there for her. Finally, Maddi reached my side. We'd had ups and downs over the years. Our marriage had taken big hits during my time at sea. But I was in it for the long haul and wanted to make it work. Our embrace on the ramp made me think we had a chance.
My Dogs, surrounded by family, were headed home. Wrenched by the experience of Vietnam, they seemed reenergized and ready for more. When the _America_ reached Norfolk the next day, the remainder of the Dog crew flew home in Navy C-9s. Everybody celebrated in their own way, but the joy seemed universally shared. It was the best homecoming I ever had.
# CHAPTER FIFTEEN
# END OF THE THIRD TEMPLE
**Tel Nor Air Base, Israel**
**October 6, 1973**
I would learn only after returning from the Med how the Yom Kippur War threatened the Middle East with Armageddon—and that Topgun had played a small part in averting what could have been a worldwide tragedy of the first order.
On October 6, 1973, as I explained earlier, Israel faced down an Arab army almost a million soldiers strong. Dan Halutz lay in bed that morning, unaware that these troops, supported by thousands of tanks and armored vehicles, were poised to strike against the Israel Defense Forces. His first indication that something was amiss came when an A-4 Skyhawk blew over his house at treetop level.
Dan belonged to the legendary 201 Squadron, known as "The One." Colonel Ben Eliyahu was its deputy commander. The One was considered the elite outfit of the Israeli Air Force, and as such received the latest and most technologically advanced fighter in the Jewish state's inventory: the F-4 Phantom. The Miramar RAG would play a vital role in the squadron's survival in combat.
In the Six-Day War of June 1967, the Israelis had responded to the imminent threat of an Arab invasion with a preemptive strike. Now, while Prime Minister Golda Meir wrestled with how to deal with the geopolitics of what Israeli intelligence could clearly see coming, the head of the Israeli Air Force ordered all squadrons to be armed and ready to carry out a strike. But when Henry Kissinger, the U.S. secretary of state, made it known to the Israelis that they would not receive any American support if they attacked first, Meir made the decision to absorb the Arab onslaught. At midday on October 6, the air force countermanded the original order, telling the squadrons to be prepared for air defense. While the ground crews pulled bombs and air-to-ground missiles off Israel's fighter-bombers, the Arab invasion began. Waves of Egyptian and Syrian fighters and bombers thundered over Israel, attacking airfields, antiaircraft batteries, headquarters, and other command facilities. Our friends from the Miramar RAG days suddenly found themselves in dire straits.
Those who got aloft fought with almost superhuman tenacity. Two F-4 Phantoms from 201 Squadron rose to meet an incoming raid that included twenty-eight Egyptian MiGs. Outnumbered fourteen to one, the two crews maneuvered wildly, shooting threats off each other's tails in a desperate, sprawling dogfight. When it ended, seven MiGs were smoking holes in the desert. Both Israeli F-4s landed safely back at base.
There was a swagger to the Israeli Air Force, born from repeated victories over the Arab nations that had attacked them since the War of Independence in 1948. When the IAF rose to attack the advancing Arab armies, however, they had some of the swagger knocked out of them when they ran into a brand-new threat: the mobile SA-6 surface-to-air Russian-made missile launcher.
As they rushed to support three thousand forward-deployed Israeli troops against ten times that number of Syrian troops on the Golan Heights, the Israeli Air Force was unprepared for the SA-6. Phantoms and Skyhawks exploded in the flames as missiles knocked them out of the sky. By the end of the day, the Israelis had lost forty planes—almost 10 percent of their entire Air Force.
The next morning, the Skyhawks and Phantoms went after those SA-6 launchers, which the Syrians had moved forward to defend their frontline troops from air attack. Unable to detect the SA-6s' new radar emissions, the Israeli crews could only eyeball the incoming missiles. By then, it was usually too late. Dan's squadron, The One, was shot to pieces over the Golan Heights. In five wild minutes, a Syrian SAM battery was annihilated at the price of four Israeli F-4s shot out of the sky.
At the same time, the Egyptians crossed the Suez Canal and invaded the Sinai with almost two hundred thousand troops, supported by tanks and armored vehicles. The surface-to-air missile batteries of the invaders also took a heavy toll of Israeli planes on this southern front.
Colonel Ben Eliyahu and his squadron attacked the Egyptian bridges thrown across the Suez Canal that day. To avoid the missile threat, they flew right down low on the dunes before climbing suddenly to release their weapons. They hit the bridges with surprising accuracy.
When a dozen Egyptian MiG-17s bombed the Israeli headquarters for the southern front, Ben Eliyahu and his men turned and went after them. In the ensuing dogfight, Ben Eliyahu scored his second confirmed kill, sending a MiG-17 into the desert sand. His wingman flamed two more, and a fourth crashed into the ground while maneuvering against Colonel Ben Eliyahu.
For all the air-to-air success, the Israeli Army could not stop the Arab offensive, and the Israeli Air Force was taking losses it could not sustain or afford. It was a dreadful situation. On the ground, Israeli frontline units were simply being overrun. One unit defending the Golan Heights was down to its last half dozen tanks. The Syrians arrayed hundreds against them.
Israeli defense minister Moshe Dayan went to see Golda Meir. In a sober tone, Dayan said to her, "Prime Minister, this is the end of the Third Temple."
In other words, Israel was about to be overrun and crushed.
Prime Minister Meir ordered thirteen Hiroshima-sized nuclear warheads to be assembled and placed on surface-to-surface missiles and under the wings of an F-4 squadron based at Tel Nof. The nukes were deployed out in the open, so that American intelligence satellites could see it happening. In later years there was debate over the degree to which this impressed Nixon and Kissinger. Some accounts say the threat of a nuclear war in the Middle East was a powerful impetus to what followed.
Nixon ordered a full-scale emergency resupply effort for the Israelis. From U.S. Army bases in Germany, stocks of latest-generation antitank missiles were loaded into Air Force transports and flown to Israel, even as the air battles raged. It seemed my country, which had done so many things wrong in Southeast Asia, finally did something right.
In the United States, Phantoms and Skyhawks were pulled straight out of Air Force and Navy squadrons and forwarded to Israel to replace the planes lost to those deadly SA-6s. The majority of our NATO allies lent exactly zero assistance. Cowed by the threat of an OPEC oil embargo, NATO refused to help Israel in its hour of crisis, though the Dutch and the Portuguese, to their credit, allowed our flights to land and refuel in their countries.
On October 14, Colonel Ben Eliyahu led his Phantoms on a deep strike against the Egyptian MiG-21 base at Mansura. A wild fight erupted down on the deck as MiGs clashed with Phantoms and the base was pummeled with bombs. Ben Eliyahu locked on to a MiG-21, whose pilot maneuvered wildly, trying to buy time as his wingman came to his rescue. Ben Eliyahu's navigator twisted around in his seat and spotted that second MiG-21 sliding into firing position behind them.
Rather than breaking off his pursuit, Ben Eliyahu stuck with his MiG. He opened fire with his 20mm cannon—the latest version of the F-4 came with an internal gun—and watched as the MiG exploded in flames and augered in. A split second later, his RIO shouted, "Break! Break!" Ben Eliyahu bent the Phantom into a tight turn. The MiG-21 driver behind him, obviously inexperienced, tried to follow and pushed his aircraft too far. It spun in and crashed not far from the Israeli's first kill. Once again, it was considered a squadron kill. In any other air force, Ben Eliyahu would have become an ace that day.
As he took over the squadron command, he and Dan Halutz flew nonstop. In seventeen days, Dan flew forty-three combat missions. The pace was so intense that a major general came to Colonel Ben Eliyahu and recommended the squadron stand down and get some rest.
"Under absolutely no circumstances," came Ben Eliyahu's response. A warrior to the core, he would help save his nation or die trying. There would be no rest until one or the other happened. In this intense war of survival, only winning counted.
The squadron went into action day and night. They led attacks deep into Egyptian territory. On one mission against a communication center, MiGs intercepted them again. Colonel Ben got on the tail of one panicky MiG-21 pilot, who saw the writing on the wall and ejected. The squadron received credit for that one too.
The days of flying and fighting wore The One down. They lost brothers in nearly every fight, and each day fewer and fewer planes and crews remained. Yet the bombings and destruction of MiGs helped blunt the Arab advance. Finally, Israeli ground forces retook the Golan Heights, and drove into Syria, too, smashing the Syrian Army and leading Iraq and Jordan to send troops to defend Damascus.
As the tide turned, the first American F-4s and A-4s started to arrive to replace the near-crippling losses. Topgun played an unheralded role in this pivotal moment.
Mugs McKeown was the skipper of the Navy Fighter Weapons School at the time. After Roger Box stood it up as an independent squadron, and Dave Frost held the reins in the summer of '72, Mugs arrived from Yankee Station to run the shop. One Friday, halfway through the current class, word came that the Israelis needed his aggressor A-4E Mongooses. The maintenance people spent all weekend repainting them in Israeli markings and camouflage. Some F-4s were also promised to the Israelis, and a call for volunteers went out to fly them from Miramar to the combat zone. Every naval aviator present at that meeting volunteered.
Almost a hundred F-4s from Air Force units headed east to join the Israelis. More Navy Phantoms soon followed. A half dozen Israeli pilots arrived at Miramar three days after Mugs got orders to give up the shop's A-4s. A serious, secretive bunch, the Israeli pilots expressed profound gratitude for the help.
The Israelis flew the Topgun A-4s across the country and crossed the Atlantic, tanking en route before stopping in Portugal or Spain. For the American crews who delivered aircraft straight to Tel Nof, they discover not just an air force at war, but an entire people. The families of the flight crews lived in tents around the runways. Wives hung laundry out to dry next to missile batteries. Their country and lives were threatened. There could be no greater stakes for any patriot. The dynamics of the situation were so very different from the Vietnam War. More than a few of the U.S. pilots would have gladly stayed and flown into combat with the Israelis.
Three weeks into the war, a Russian cargo vessel carrying nuclear weapons steamed out of the Black Sea into the eastern Med, bound for Alexandria. Soviet-manned Scud missile batteries operating in Egypt included at least one tactical nuclear warhead each. American intelligence discovered that fact when overflights spotted the unique trucks the Soviets used to transport such deadly weapons. As a result of these discoveries, senior U.S. officials—apparently without the approval or foreknowledge of President Nixon—took the country to an upgraded nuclear alert, DEFCON 3.
The Russians saw the U.S. response and interpreted it as a panicky overreaction. After a series of long internal discussions in Moscow, the Soviets decided Syria and Egypt were not worth a global thermonuclear holocaust. The ship carrying nukes dropped anchor in Alexandria, but did not unload. The Kremlin's diplomats started leaning on its Arab allies to end the war.
Peace broke out on October 23, 1973. The Israeli counteroffensives cleared the Golan Heights, captured significant chunks of Syrian territory, drove the Egyptians largely out of the Sinai, and even established footholds on the west side of the Suez Canal. In that sense, it was a catastrophic defeat for the Arab alliance. But in truth it had been a near-ruin thing. The Israeli Air Force was battered and exhausted, with just seventy or so Phantom crews left standing. The Israelis admitted to the loss of over a hundred aircraft—almost a quarter of their entire complement of combat aircraft. With only a few exceptions, these planes went down to latest-generation Soviet-built missiles.
Those three weeks were rough ones indeed. They were worse for the Arab air forces, whose fighter pilots found themselves completely overmatched by the better-trained Israelis. Boyd may have had his equations, but at Topgun, we trained to the man in the cockpit. The better pilot will almost always win, no matter the odds, situation, or planes. The Israelis fought savage air battles against ridiculously long odds—and tore the guts out of their enemies. The exact kill ratio will never be known, as the Egyptians concealed the extent of their losses, as did the Israelis. Our Israeli friends claimed more than 440 Arab aircraft destroyed, most of them in air combat. Current sources show the number of Israeli air-to-air kills at around 83. The American influence was significant, but it boiled down to the men in the cockpit. They had performed as well as fighter pilots ever have.
Meanwhile, the Yom Kippur War precipitated a crisis at Topgun. With only a single aggressor A-4 remaining after the transfers to the Israelis, the school could not function. The October class graduated on schedule, but Mugs canceled the next one while they scrambled to solve this problem.
Since its inception, Topgun had faced ongoing jealousies and bureaucratic hostility. We fought our battles for resources and respect early on, and slowly gained both through any means necessary. The year before, thanks to Dave "Frosty" Frost making his career-risking stand, Topgun became an independent command with its own aircraft. Now, with our war in Vietnam over, some careerists above and around Topgun began to question the need for such a school, especially one that was an independent command. This is where it hurt Topgun to be run by junior officers. Lieutenant commanders and lieutenants usually do not have the political horsepower to fend off serious threats.
Fortunately, Mugs McKeown was a special kind of skipper. He intuited the threat. If Topgun owned no aggressor aircraft, the school would have no way to function independently. Bill Driscoll, Duke Cunningham's back-seater and the only Navy RIO ace of the Vietnam War, was a Topgun instructor at the time. He and the others running the school all sensed a pivotal moment was at hand. The Navy either refused to buy new jets or had no aircraft to spare in the aftermath of Vietnam. The animosity toward Topgun from the staff officers who came up through the ranks of attack aviation led to many closed doors. If Mugs didn't fix his aircraft shortage, Topgun might just dry up and blow away. Death by bureaucratic atrophy.
A fighter to the core, he'd earned his nickname while boxing at the Naval Academy. He also played running back for Navy in its glory year of 1960, when the team was ranked fourth in the nation and beat the number one Washington Huskies. Thanks to his time training with the Air Force, Mugs knew a lot of people outside Navy circles. He networked with men who became members of Congress and Air Force leaders who ended up in key commands.
While working the phones, Mugs learned from an old friend at VX-4 that the Air Force just stashed a pair of broken-down T-38 Talon fighter trainers at the Navy test facility at China Lake, where they were to be turned into target drones and blown up.
Mugs and his executive officer at the time, Jerry Sawatzky, went down to China Lake to take a look. The planes were in bad shape. The engine intakes were full of desert dust; the ejection seats were nonfunctional; they were missing parts and even had flat tires. Still, they were better than nothing.
With the help of Northrop, Topgun got those aircraft ready for flight. Mugs and Jerry flew them to Miramar, where the school's maintainers discovered that none of their support equipment would work with the new planes. Basic things like engine stands, hoists, and a cache of spare parts would be needed to get the birds functional. The mechanics improvised, pulling the engines out by hand and laying them on mattresses inside a hangar, but that was a stopgap. They needed a proper logistical setup for these planes.
It became a race against time. The school could not afford to keep canceling class. That would attract too much attention from the wrong crowd above Topgun. So Mugs reached out to an old friend from his test pilot school days, Major Richard "Moody" Suter, who played the central role later on in establishing the Air Force's big multinational exercise, Red Flag. Mugs made a backroom deal with Suter, trading a shipment of stylish USN leather flight jackets for the parts and equipment Topgun needed.
An Air Force C-130 flew the gear into Miramar, which caught the eye of an AirPac admiral, who reportedly began asking questions.
"Is there an Air Force detachment arriving?"
"No sir, all that gear is for Topgun."
_"What?"_
Mugs embodied the attitude that had played a foundational role in Topgun's history: Don't ask for permission—get it done and beg for forgiveness. Quickly the T-38s were up and flying, filling the gap until other aircraft arrived.
Not long after, in January 1974, Mugs lost his executive officer. Jerry called him one night and told him he couldn't hack the pace anymore. He was a former enlisted pilot who had become an officer like I had, through the Naval Aviation Cadet (NAVCAD) program. He was trying to finish college and had just gotten married. Too many balls in the air, and he knew Topgun needed an XO with his entire heart in the job. He asked to be relieved, and Mugs let him go.
The next morning, Jack Ensch walked into the Topgun offices to find Jerry cleaning out his desk. Jack had just come off nine months of medical rehab for his wounds and injuries incurred during his shootdown and imprisonment in North Vietnam.
"What's going on?" Jack asked his friend.
"I quit," Jerry answered. "You're the XO now."
The news caught Jack by surprise. He had come to Topgun as Mugs's special projects officer, a slot created for him so he'd have a place to work until his next assignment.
The connection between Mugs and Jack is one of the finest examples of the bond naval aviators build with each other. Mugs was an only child growing up, and in his most serious moments, he told Jack, "You know, you're the brother I always wanted and never had."
The two men flew in combat together, knocking a pair of MiG-17s out of the sky in May 1972. During one fight, as they were vectored after some MiGs, Jack called out from the RIO's position in their F-4, "Let's go get 'em, Mugs. I'm right behind ya."
Chuckling, Mugs told him, "Knock that shit off. This is serious."
Thirteen days later, Mugs left Yankee Station to take over Topgun. Jack stayed on the carrier. He was flying with another pilot, Mike Doyle, when they took a SAM hit and ejected. Doyle was killed. Jack suffered grievous injuries during his ejection, and was captured and taken to a North Vietnamese prison camp.
As Mugs heard the news, he had just learned that they were to receive the Navy Cross for their two-kill engagement in May. It was the second-highest award for valor that existed. Mugs said he would accept it only with Jack by his side. Eight months after Jack was released, he and Mugs stood shoulder to shoulder in a ceremony attended only by their families and a few VIPs. Together as brothers, they received their Navy Crosses.
Now at Topgun, Jack would be right behind Mugs again. The two would help usher in a new era for the school and its capabilities, ensuring that Topgun kept Navy fighter aviation the best in the world during some difficult years.
In the spring of 1974, I was still in the Med with the _America_ and my Dogs. I was in Palma de Mallorca, Spain, during a port of call, having a drink in a waterfront hotel, when I noticed an airline flight crew entering the lounge. They were from El Al, the Israeli airline. One of the flight attendants approached me.
"Are you Commander Dan Pedersen?"
"I am."
"I have something for you from your friends in Israel."
She handed me a small box. No note. No card. Just a box. She walked away without another word.
Inside, I found a beautiful fourteen-karat gold Star of David attached to a gold link chain. The gift was completely anonymous.
_How did they find me?_
I thought right then of the barbecue at my place in San Diego, where I met Colonel Ben Eliyahu, Dan Halutz, and the other Israelis for the first time. No-nonsense, secretive, eager to learn. Professional to the core. Then I remembered a conversation we had had. I asked Ben why his people were so serious.
"Daniel, you will understand when you are in combat, getting ready to fire at your enemy, and you realize you are flying over your home, where your wife and children are."
They had lived our worst nightmare and prevailed.
I resolved to visit Israel someday to renew those friendships. Maybe I would even find out who had sent that beautiful gift.
I put it on and wore it for the rest of my Navy career as part of my basic kit. Little mouse. Fifties Ray-Bans. Star of David on my chest, reminding me that friendships can sometimes help save nations.
# CHAPTER SIXTEEN
# RETURN WITH HONOR
**Forty miles off South Vietnam**
**April 29, 1975**
For naval aviation, the problem of Vietnam never seemed to go away.
Lieutenant Darrell "Condor" Gary stood before the assembled pilots and RIOs of VF-51. In Darrell's short career, he'd been thrown into the air war over North Vietnam before completing his RAG training back in the late '60s as an F-4 back-seater. Two tours there and he came home in time for me to pull him into Topgun as one of our instructors. He subsequently went to flight school, became an F-4 pilot, and went through Topgun as a student before heading out to the carrier USS _Coral Sea_ and his first overseas deployment as a fighter pilot.
In 1975, he was a young lieutenant tasked with delivering one of the most painful briefs the squadron would ever receive: It fell to Condor to bring them the news that we were abandoning our allies once and for all.
The disaster began the previous month, when North Vietnam launched a new offensive against our allies in the Central Highlands. For the past eighteen months, Congress had steadily whittled down U.S. military aid to South Vietnam. Suffering shortages of spare parts, ammunition, and lubricants, the army of the Republic of Vietnam was in a deplorable state of readiness. America was partially responsible for that.
The North Vietnamese offensive threw eighty thousand troops into the Central Highlands. Our allies buckled under the onslaught. As we pulled out in the early 1970s, we tried to train the South Vietnamese Army, but never overcame the corruption, malfeasance, and frequent cowardice of their officer corps.
Prime Minister Nguyen Van Thieu appealed to President Gerald Ford for $300 million worth of emergency military aid. Congress balked, in part because everyone could see that the South Vietnamese Army was coming apart at the seams.
Thieu ordered the army to stage a strategic withdrawal to defend key cities and strategic locations. Under heavy pressure, the South Vietnamese Army found roads clogged with fleeing refugees. The withdrawal bogged down. Officers panicked. One general told his troops, "Every man for himself." It became a rout.
This surprised the North Vietnamese. Sensing an opportunity, the Communist army converged on Saigon, overrunning our former air base at Da Nang and capturing dozens of South Vietnamese Air Force aircraft.
Chaos descended on the South. By April Fools' Day, it was clear our allies were doomed unless the United States came to the rescue. No amount of money could save the South Vietnamese military by this point; only a massive employment of airpower and ground troops could turn the situation around. We flew in dozens of heavy transport aircraft to Tan Son Nhut Air Base to extract as many people as possible.
There were horrible tragedies as the evacuation unfolded. On the fourth of April, a C-5 Galaxy, the largest aircraft in the world, suffered mechanical failure with 250 orphaned children aboard. The crew turned around and crash-landed at Tan Son Nhut, killing 153 children and adults. The Communists marched on the air base as the evacuation gained steam. As the North Vietnamese advanced, commercial airliners were thrown into the effort. Should Tan Son Nhut become unusable, helicopters would be our only other option to get our people out of harm's way. The air base was soon untenable as the NVA closed.
The U.S. task force off the South Vietnamese coast, anchored by the carriers _Enterprise_ , _Coral Sea_ , _Midway_ , and _Hancock_ , were the evacuation's last best hope.
On April 29, Darrell briefed his squadron as it prepared to serve as MiG combat air patrol (MiGCAP) for the last-ditch evacuation off rooftops and makeshift helicopter pads around Saigon. At the American embassy, the final embarkation point, personnel chopped down trees to create a second helicopter landing zone. The situation was chaotic in the extreme.
Darrell reviewed the latest intel as dispassionately as he could, but beneath the façade he felt an overwhelming sense of disappointment and grief. The war that had consumed his youth was coming to an end with America abandoning her ally. We were finally about to quit on the conflict that had spanned his entire adult life. The mood at VF-51 was somber. There was none of the usual wisecracking. If the Communists took over, the consequences would be horrific. Tens of thousands of innocents would be rounded up and shot or thrown into labor camps. With four U.S. carriers offshore, why should we let it happen?
Darrell went over the rules of engagement. As ever, Washington-style thinking prevailed. We could not engage unless our planes or helicopters came under direct fire first. If MiGs attempted to intercept the rescue effort, Fighting 51 was cleared to shoot only if they posed a threat. The eighty helicopters used in the evacuation would fly to USS _Midway_ , the receiving ship. The other carriers would support. The surface fleet formed a barrier between coast and carriers, ready to help in any way they could. When Darrell was finished, the aviators rose from their seats and headed toward their aircraft.
The helicopters began arriving over Saigon as the lead elements of the North Vietnamese army reached the outskirts of the city. Yet the Communists did not interfere with the evacuation. Fearing it could trigger full-scale American intervention at the eleventh hour, the North Vietnamese held back. The MiGs made no appearance, nor did the attack aircraft they'd captured at Da Nang. The biggest threat to the helos came from rogue disgruntled South Vietnamese troops. Small-arms fire raked them as they landed on rooftops and at the embassy tennis courts.
Overhead, Darrell and the other aviators of Fighting 51 could see smoke rising over the embassy in downtown, where the last of the staff burned top-secret documents and millions of dollars' worth of cash. Toasted hundred-dollar-bill ashes rained down on the crowd from the incinerator's smokestack. Helicopters touched down on rooftops, picked up loads of people, and turned for the fleet.
Some neighborhoods under curfew looked empty. The only vehicles on the streets were ambulances that had been pressed into service. Mobs of people hauled their luggage and all the cash they could scrounge up, desperate to get out of the city with their children before the Communists stormed the palace gates. Streaming out of every inlet, moorage, and slough came boats, sampans, luggers, rafts, scows of every sort, hundreds flowing into a great exodus, looking like ants on leaves as they rode the waves in search of salvation. It was a humanitarian crisis unlike anything since the final days of World War II. Millions would be consumed by it.
Darrell and the rest of his flight loitered as long as fuel allowed, then turned for home as another group of F-4s arrived to take up station. The flight back to the _Coral Sea_ was one that the youngest of Topgun's Original Bros would never forget. Below his F-4, the evacuation armada carpeted the ocean to the horizon, pushing through the swells toward the Navy task force. It represented one thing: freedom. The sight of it was heartbreaking.
Toward midmorning, the first South Vietnamese Army helicopters appeared above the fleet. Flown by pilots who knew their country was in its death throes, they sought now to save themselves and their families. As the boats struggled along, the helos raced back and forth, delivering refugees to the _Midway_ before turning around and going back for more.
As Darrell landed aboard the _Coral Sea_ , steaming about ten miles from the _Midway_ , he headed to debrief, helmet in hand, sobered by what he had witnessed. This was the end. We had never been allowed to win. He had a bird's-eye view of the consequences of it that day. They would be felt for decades to come.
The next morning, at 0500, the U.S. ambassador to a country that no longer existed climbed aboard a CH-46 Sea Knight helicopter and departed the embassy in Saigon. Three hours later, the last Americans—U.S. Marines—were pulled out and carried out to the fleet. That was it. South Vietnam surrendered unconditionally later that morning.
One Memorial Day, years after the war, Jim Laing and Darrell Gary were drinking a beer at Bulley's together. Both were well into their civilian lives. They started wondering about their old friends and how many in their circle they really lost back in those days. They grabbed a cocktail napkin and started writing down names. The first three names belonged to fallen aviators from the nine guys they had rented beach houses with in the early days of Topgun at the Lafayette Escadrille. From there, the list grew. They reached for more cocktail napkins. By the time their memories ran out, forty-three names filled a small pile of napkins. Those were just their friends. Half had been lost in combat, half in training. The personal cost of a war lost will always be the names and faces of friends. The larger consequences beggared the imagination.
With the last flight to the _Midway_ from the embassy grounds, 1,373 Americans and 5,595 Vietnamese were helicoptered to the naval task force. Another 65,000 fled by boat, later to be picked up by one of the forty ships offshore. The fixed-wing airlift from Tan Son Nhut pulled out another 50,493, including almost 2,700 orphans. They were the lucky ones. In the immediate aftermath of South Vietnam's collapse, more than 150,000 civilians vanished, most either executed outright or thrown into concentration camps. Saigon was renamed Ho Chi Minh City, a memorial to the unknown masses of dead. Somewhere between 1 and 4 million Vietnamese perished from 1955 to 1975. In Cambodia, another 300,000 were killed. Laos lost between 20,000 and 60,000. In the years ahead, the killing would continue as Communist insurgents toppled the governments of Laos and Cambodia. From 1975 to 1979, the Khmer Rouge, a regime that swept to power in the wake of America's exit from the region, murdered or starved to death about 2.5 million people out of a population of 8 million—more than 30 percent of the entire nation. When Americans look back at Vietnam, we remember the domestic unrest. We think, too, of the 58,000 names memorialized on that long black marble wall in Washington. Those are important to remember. But few want to discuss the other consequences of America's lost war.
As the naval armada covered the evacuation off the Vietnam coast in April 1975, I was headed for the Philippines. The honor of serving as squadron commander had prepared me for a higher command. At Subic Bay, I caught up with the _Coral Sea_ and went aboard as the prospective commander of Air Wing Fifteen.
I won't belabor the mood aboard ship. Everyone was ready to forget. Fortunately, the ship was scheduled to steam south for Perth, Australia, to celebrate the Battle of the Coral Sea, the 1942 naval victory that helped save Australia from Japanese invasion.
The air wing needed the lift of a friendly port of call with one of our closest and most loyal allies. The Aussies always treated us sailors with tremendous affection and kindness, even when our own countrymen didn't. It was also a good way for me to get to know the men and make the transition from the current skipper, Commander Inman "Hoagy" Carmichael.
We departed Cubi Point after only a short stay, steaming through the Sunda Strait, where the heavy cruiser USS _Houston_ had made its epic last stand a generation before. The men were looking forward to the excitement waiting for them in Perth. Each morning, I saw Condor running on the flight deck, getting back in shape for the merriment ahead.
It was not to be. As Darrell put it, "One morning, I woke up and went for my run, and realized the sun was on the wrong side of the ship." Another emergency had developed, and so the president had asked where the carriers were. The _Coral Sea_ was the closest, and we received orders sending us racing north at flank speed.
The Cambodians had seized an American-flagged and -owned cargo container ship. Now the ship was in Khmer Rouge hands, and the crew was somewhere ashore, locked up in what looked like an exact repeat of the 1968 _Pueblo_ incident.
Would we never be free of this place?
The ship was named the _Mayaguez_. It had departed South Vietnam with cargo that included almost eighty containers full of military equipment and material from the American embassy in Saigon. The skipper of the _Mayaguez_ was supposed to sail to Thailand. En route, he accidentally passed inside Cambodian territorial waters. On May 12, 1975, as we headed south for Perth, a small boat crewed by Khmer Rouge forces sped out to the _Mayaguez_ and fired a rocket-propelled grenade across its bow only a few miles off the island of Poulo Wai. The captain of the _Mayaguez_ , Charles Miller, ordered full stop and began broadcasting an SOS. The Khmer Rouge boarded the ship and ordered the vessel to Poulo Wai.
The next morning, two U.S. Navy patrol aircraft discovered the _Mayaguez_ and took ground fire while making a low-level pass to confirm the ship's identity. The Khmer Rouge moved the ship to an anchorage just north of Koh Tang island, where our planes found her.
President Gerald Ford announced to the world that he considered this an act of piracy. The _Pueblo_ incident in 1968 had become an open wound for the United States, for months embarrassing the Johnson administration. After the humiliation of South Vietnam's defeat and the blow to American prestige it inflicted, the president was in no mood to show weakness. He ordered the ship seized and the crew rescued. The _Coral Sea_ 's air wing would provide air support and strike targets on the Cambodian mainland.
By rights, I should have been leading the air wing, but Hoagy Carmichael was not about to give up his command when we were going back into combat. I don't blame him; I would have done the same thing. I would ride this out beside our task force commander, Rear Admiral Bob Coogan.
Around WestPac, a rescue force was cobbled together under Seventh Air Force command. The plan called for Air Force helos to stage the Marines out of an air base in Thailand. En route on the night of the thirteenth, one of the birds crashed, killing twenty-three men. That put the operation on hold, at least until the _Coral Sea_ reached the area.
The next morning, Air Force F-111s and A-7 Corsairs discovered the captive American crew aboard a fishing boat. The Khmer Rouge planned to take them to the mainland, making rescuing them far more difficult. The planes bombed and strafed in front of the vessel and shot up several patrol boats, sinking one, but that failed to dissuade the Khmer Rouge. The fishing boat continued on its way, and the planes overhead eventually lost sight of it. There were conflicting reports as to exactly where the crew was taken. Some thought they'd been taken back to Koh Tang. Other sources thought they were on the mainland.
On the afternoon of the fourteenth, President Gerald Ford ordered the Seventh Air Force to execute a helicopter assault on Koh Tang island and the _Mayaguez_. The forces landing on the island were to find the crew, if they were there, while another team helicoptered onto the _Mayaguez_ and steamed it out to international waters.
Just before the rescue force went in, Admiral Coogan received a direct call from President Ford and Secretary of State Henry Kissinger. I was with him in the _Coral Sea_ 's flag quarters and listened with great interest. President Ford ordered the carrier to strike targets on the Cambodian mainland, including port facilities and a nearby naval base.
"Admiral," the president said, "go get our ship and crew back. It's your show. Use all available means, but no nukes."
I wondered how many times our commanders on Yankee Station had heard such a command. Not even Nixon had ever expressed such a clear and explicit willingness to let us fight.
The rescue mission began at dawn on May 15. As the strike aircraft catapulted away and Marines in Air Force helicopters sped toward Koh Tang, I led a dozen F-4s on a fighter sweep over the mainland. Approaching Phnom Penh, we increased speed and dove down to the deck. Two dozen J79s shook the streets as we rocketed along at five hundred knots at just five hundred feet. We were there in case some MiGs wanted to make trouble. None showed up. Meanwhile, the size and suddenness of the air strike let them know America was serious.
Darrell Gary, who was scheduled to fly later in the day, climbed up the ladder to the _Coral Sea_ 's flight deck. Because the initial strike quickly obliterated the targets so completely, Darrell's flight was scrubbed. We meant business—and showed it.
Unfortunately, these were the days before a unified Special Operations Command and quick-reaction forces. The hastily thrown-together rescue group from multiple services operated with inaccurate intelligence and a complete misread of the situation on the island. The CIA believed Koh Tang was lightly defended, if at all. In fact, more than a hundred Khmer Rouge troops held the island to deter their Communist brothers from North Vietnam, who had laid claim to these patches of turf off the Indochinese coast.
Our Marines rolled into hot landing zones laced with machine-gun and rocket-propelled grenade fire. From the ship, Darrell watched as several CH-53 heavy transport helicopters took hits. One crashed offshore after receiving two RPG hits. The survivors were in the water for hours until a gig from one of our escorts pulled them to safety. Included in those survivors was the Marine forward air controller, who somehow found an Air Force survival radio that he used to call targets for the A-7 Corsairs overhead. Clinging to wreckage, the radio's batteries slowly failing, he gave everything he had to try and secure help for the embattled Marines pinned down in the landing zone.
Three CH-53 Jolly Green Giants went down during the rescue operation. Fifteen Marines were killed on Koh Tang and fifty more wounded during the fighting that raged throughout the day.
Meanwhile, our attack aircraft saturated the _Mayaguez_ with tear gas. An American warship raced into the anchorage with a company of Marines aboard. An hour after the assault on the island began, the Marines, clad in gas masks, swarmed aboard the cargo ship and found it abandoned. We had our ship back. Where was the crew?
The Khmer released them, sending them back out to sea, where a Navy patrol plane spotted them. Another American warship steamed to the vessel and pulled the crew aboard just before the lunch hour.
The final act played out through the afternoon as the Air Force tried to extract the Marines from the landing zones. Heavy fire repeatedly drove them off, and one battle-damaged Jolly Green force-landed on the _Coral Sea_ 's deck. Our maintainers swiftly patched it up. A few hours later, it went back into action.
The fighting raged, and our frustration level grew. The birds kept taking hits, and the Marines were reporting heavy casualties. By dinner, the Air Force brought in an AC-130 gunship and five C-130s carrying fifteen-thousand-pound bombs known as BLU-82s, nicknamed Daisy Cutters. They were the biggest, most destructive conventional weapons in the American arsenal.
The first one detonated as Darrell and others watched from our deck. Darrell saw the enormous explosion followed by the shock wave the blast unleashed. It obscured the island and swept right across the _Coral Sea_ , causing the huge carrier to shudder from its impact.
As darkness fell, another Jolly Green staggered out of the moonless night. The massive helicopter carried a crew of five and managed to pull aboard thirty-four Marines before suffering engine trouble. The crew set down on the carrier's deck, and when its ramp dropped, almost three dozen wounded Marines tumbled out onto the flight deck.
Our ship's corpsmen raced to help them, triaging the wounded and lining them up on one of our elevators. The air wing's senior master chief went from man to man, offering water and words of support, giving them anything they needed. Even those who weren't wounded suffered from dehydration after twelve hours of combat in the tropical heat. The wounded on the elevator were lowered to the hangar deck, then carried by corpsmen and volunteers to our medical facilities, where surgeons operated through the night. They saved every one of those wounded Marines.
That night, a young second lieutenant was given a bunk in Darrell's stateroom. He was shocked and exhausted, with a _What in the hell just happened?_ expression on his face. Forty-eight hours before, he was living an easy life on Okinawa. He woke up, ended up in a hot LZ, and watched some of his men die.
During the last part of the evacuation, that officer saw a C-130 make a run right in front of his position, dropping a BLU-82. A parachute opened above the bomb, and it swung down to land practically on his Marine platoon. It didn't go off. The mother of all bombs turned out to be a dud. Thank God.
In less than three weeks, the _Coral Sea_ and her air wing had witnessed the final evacuation of South Vietnam, then taken part in what is now called the last battle of the Vietnam War. The fifteen Marines killed on Koh Tang island became the final men whose names were etched into the wall in Washington a decade later. Three more Marines, declared missing in action on the island, were captured by the Khmer Rouge and later beaten to death.
Though the cost was high, we got our ship and crew back. There was no repeat of the _Pueblo_ incident. The Communist Khmer Rouge did not have time to inspect or offload the cargo, which meant whatever secrets lay inside the containers from our embassy remained safe. The U.S. government has never divulged their contents.
Aboard the _Coral Sea_ , we were heartened by President Ford's willingness to let us off the leash. My new air wing performed brilliantly, destroying all of its assigned targets. It would take time and years to figure out how best to handle crisis situations as this one. The aborted attempt to rescue our hostages in Iran in 1980 would be another case study in how not to conduct such operations. They became the catalyst for changes that gave our military the flexibility to handle any such task the world might throw our way. For now, President Ford had shown our adversaries some of the strength and resolve that might have helped us during the LBJ years.
After we took our wounded Marines to Subic Bay, we steamed south for Perth and a ten-day port call. The Aussies welcomed us with a great hospitality. We were treated like family everywhere we went. The crew drank and laughed with our friends from down under and put the scars of the war in their rearview mirrors. By the end of it I was so exhausted from all the free drinks and parties that I crawled into my bunk and slept the sleep of a free man. The world was at peace for the first time in ten years.
# CHAPTER SEVENTEEN
# TOPGUN AND THE TOMCAT
While I was out with my air wing aboard the _Coral Sea_ , the Navy began its first major evolution into the post-Vietnam era. The renaissance centered on a new and potent fighter aircraft whose design Topgun helped influence, the Grumman F-14 Tomcat.
Our work at Topgun in 1969 and 1970 continued to spark a rethinking of naval aviation and its role. Thanks to the efforts of so many dedicated commanders and junior officers, Topgun would not only survive the transition to peacetime, but would undergo a new golden age that helped shape how we would fight for the next twenty years.
In combat aviation, no aircraft is forever. Our beloved Phantom served a long and useful service life. But the future was within view even on the day that I accepted the assignment to lead Topgun in 1969. My old friend from Miramar, Sam Leeds, took command of Fighter Squadron One, the first unit that was assigned the new F-14, in October 1972, based on USS _Enterprise_. Later that year, VF-124, the Crusader fleet replacement squadron whose sword we stole and hauled around at Mach 2, stopped training pilots to fly the obsolescent F-8 and began training the first Tomcat pilots.
The last of the carrier-deploying Phantom squadrons made the transition to the Tomcat in 1987—a fifteen-year overlap during which both F-4s and F-14s served well and capably at the same time.
One of my few regrets is that I never had the pleasure of being part of the Tomcat tribe. When I had the chance, I would log some time just sitting in that Grumman-built bird, daydreaming about the things I could have done with someone like J. C. Smith or Hawkeye Laing in my rear seat.
Of course, the F-14 Tomcat almost never made it into the world, thanks to Secretary of Defense Robert S. McNamara, who loved to think he knew people's business better than they did. In 1968, he tried to force the Navy to adopt the hulking F-111 fighter-bomber for use on aircraft carriers.
Imagine SecDef's chagrin when a mere three-star admiral, the head of naval aviation at the Pentagon, decided to stand in his way. That truth-telling sailor, Tom Connolly, testified to Congress, "There isn't enough thrust in Christendom to make that airplane into a fighter." And he won. The Navy avoided being saddled with the "Flying Edsel," so named by its unhappy Air Force pilots because its chief advocate, Secretary McNamara, had been president of Ford Motor Company. McNamara took his revenge, denying Vice Admiral Connolly a deserved promotion to a fourth star. But the last word belonged to the Navy. It paid tribute to a great man by naming its new world-beating fighter aircraft after him. The legendary Tomcat was born. Though it fell right in line with other Grumman felines in history—Wildcat, Hellcat, Bearcat, Tigercat—the name was the artful final act in a Pentagon dogfight.
Where the F4D Skyray was like a Porsche and a Phantom like a muscle car, the F-14 Tomcat was a supercharged Cadillac: big, comfortable, the plushest ride in fighter aviation. It had a roomy cockpit, and the instrumentation, controls, and switches were well laid out, placing its systems easily to hand. A long bubble canopy offered visibility for the pilot and RIO vastly better than the F-4's. Grumman even thought to install a "hassle handle" on the rear instrument panel. During combat, the rear-seater could grab hold of it, gaining leverage to twist in his seat and check for a threat astern, between the Tomcat's twin tails.
The Tomcat, like the Phantom, was a twin-engine interceptor, designed mainly for fleet defense. But unlike the Phantom, the Tomcat was saved by Grumman's attention to its heritage: Their designers found a way to mount it with a powerful 20mm Gatling cannon. Topgun had a hand in that particular development. When the Navy's project officer from the Pentagon showed up at Nellis to pitch the F-14's coming glory as a missile shooter, future Topgun CO Mugs McKeown and I were on hand to ask, "Where's the gun?" I admit, we knocked around that projects officer pretty well that day. Ultimately the Tomcat was built with that Gatling gun tucked in the fuselage below the cockpit. The hollow moan of the six-barrel Vulcan rotary cannon can never be forgotten by those who've felt and heard it. Six thousand rounds per minute has a useful effect on an enemy pilot's psychology, too. Vice Admiral Tom Connolly was the one who took our input at the Pentagon and made a gun-armed Tomcat a reality.
The gun was great to have, but the advanced AIM-54 Phoenix air-to-air missile could really reach out and touch someone. Tracking up to six targets simultaneously with her Hughes AWG-9 multimode pulse-Doppler radar, one F-14 could destroy them out beyond one hundred miles with the Phoenix. At nearly half a million dollars apiece, the Phoenix blew through budgets nearly as fast as it chased down targets at Mach 5. Considerations of weight would leave the typical Tomcat weapons load-out short of the six it was designed to carry. The more typical load-out was four Phoenix carried on mounts on the aircraft's belly, and two Sparrows and two Sidewinders hanging from the wings. The final Tomcat variation, the F-14D, was known as the Bombcat. The versatile machine could carry the GPS-guided precision bomb known as a Joint Direct Attack Munition, as well as Paveway laser-guided bombs, a centerline reconnaissance system, or an infrared targeting pod. With that Gatling gun added in, Navy air wings were equipped to deliver a heck of a lot of firepower.
The Tomcat had a variable-geometry wing. It could retract, sweeping back almost flush with the fuselage, twenty degrees off the tail, or extend to nearly full stretch at sixty-eight degrees for takeoff and slow flight, adjusting automatically to maximize performance at any airspeed. With the wings swept back, she resembled a lethal bird of prey, but was still surprisingly maneuverable (the fuselage itself was shaped to produce aerodynamic lift). Once her Pratt & Whitney engines were replaced by the more reliable General Electric F110 and updated avionics, the thirty-eight-million-dollar fighter had power to spare.
When the movie came out in 1986, the Tomcat became a star. It would stand as the symbol of Topgun and naval aviation generally for decades. It would rival the Phantom as a favorite among fighter pilots and aviation enthusiasts alike. Plenty of squadrons continued operating the F-4 as the Tomcat made its way to the fleet. But the future was closing with us fast as I wound down my tour as air wing commander in the _Coral Sea_. At Miramar, Topgun continued its original mission of preparing to handle the threat of what lay ahead.
In 1975, the year Tomcats began deploying in larger numbers, Topgun went through a major evolution in the way it taught air combat maneuvering. This was made possible by new technology. The Cubic Corporation, based in San Diego, working with Navy engineers, devised a special telemetry pod that could be mounted on an aircraft's Sidewinder missile pylon. Dave Frost flew some of the first tests around 1972, exploring ways to capture a full, reviewable record of a dogfight within defined airspace over our combat training ranges. The so-called air combat maneuvering range (ACMR) would revolutionize how our fighter pilots were educated. It enabled us to push beyond a problem that hampered us in Topgun's early days. The problem looked like this.
The scene: Hangar One at Miramar. A student aircrew is slumped in their seats, exhausted after four or five dogfights in the mission just completed. Their faces are lined with the impressions of their oxygen masks cinched tight to stay in place under heavy G. Their flight suits are stained with sweat from the physical exertion of high-speed maneuvering. Before them stands their instructor, tall at the podium, resplendent in his tailored blue Topgun flight suit, his debrief polished by the murder boards, carefully consulting his notes of each student's moves. Topgun had long since embraced the good news/bad news approach to enlightenment. Sometimes, especially early in a class, it was difficult to find good news. But delivering and dissecting bad news was how people learned after taking a licking.
The instructor would say, "Cruiser, by offsetting on the third engagement you made a good initial turn after the Merge, and I had to go vertical to avoid an overshoot. At that point you seemed to lose sight of me—is that right? Rowdy, did you see me from the backseat?"
The instructor would turn to the chalkboard and diagram the fight as his notes from his knee board and memory permitted. But these data sources were fallible, especially when the mind that produced them was under strain of G forces, short on blood as all the aircraft changed speeds and altitudes. Multiply that complexity by the four or five engagements that typically took place in one flight, and the human senses can short-circuit trying to apprehend it all. A cassette tape recording of the radio calls could help, but only so much. The instructor had to do what he could to determine who did what to whom and derive the appropriate lessons. We used to say, "First man to the chalkboard wins the fight."
Captain Ault and his people anticipated this problem well in advance. His famous 1969 report had described the need for an electronic monitoring system to sort out the precise choreography of every ACM flight. Merle Gorder, the author of the report's recommendations, advised the major fighter commands on each coast to establish an ACMR, noting that cost estimates and plans were already available thanks to a report jointly filed in November 1968 by the Applied Physics Laboratory and Johns Hopkins University.
Less than a decade later, the potential of that system was realized at Topgun's range in Arizona, east of Marine Corps Air Station Yuma. Telemetry made it possible for the new system to record the myriad data of an air-to-air engagement in a given block of airspace, including the altitudes, speeds, headings, G forces, weapon status, everything. It gave our instructors a choice between a "God's-eye view" and switchable individual perspectives from any cockpit in the fight. Now that an unblinking electronic eye could show whether a pilot had fired his missile within its performance envelope, gone were the days of "I gotcha" versus "You did not." The ground stations would relay the hard data to a central station on the range and then via microwave data link to Miramar. With every squeeze of a trigger, the system would run numbers and function as an umpire, calling kill or no kill. It made possible a renaissance in fighter combat training.
With Mugs and Jack Ensch leading the way, Topgun's leadership in this new era was rock solid. Together, they fostered and perpetuated the elite atmosphere we started in the F-4 days, all while integrating new technology and concepts. Mugs and his always-useful political connections helped get the command a new fleet of aggressor aircraft, including a number of former South Vietnamese F-5 Freedom Fighters whose pilots had escaped with them to Thailand before the fall of Saigon. Finally Topgun had resources, access to almost whatever it needed, plus first-rate aircraft with which to teach. From those first days inside the condemned trailer back in 1969, we had come a long, long way.
When foreign aircrews came to the United States to train, they universally wanted to come to Topgun, something that left the Air Force and its Red Flag program feeling slighted. The staff at Miramar greeted everyone from Saudi princes to French Mirage pilots—and of course more hard-drinking Brits, whose antics on the ground matched their skill in the air.
The irrepressible Darrell Gary was right at the center of this evolution. Perhaps nobody else in the Navy was as connected to Topgun as Condor was through the 1970s. He first joined us as an RIO in 1969, the youngest of our nine. He served with skill and dedication as an instructor before going to flight school and becoming an F-4 pilot. He graduated from Topgun and returned to VF-51, then he and I crossed paths once again aboard the _Coral Sea_ during the _Mayaguez_ incident. After that cruise, he returned to Topgun for a third time. As an instructor pilot, and the project officer for the air combat maneuvering range at Yuma, Condor became a leading light in the technological revolution that took Topgun to a new level.
When Condor briefed the four-star in charge of USAF Tactical Air Command about the ACMR, the general said he didn't like the system. Darrell asked him why. The response was, "Because my guys know that everyone can see the mistakes as well as the good maneuvering. It will increase the accident rate. My guys would rather die than look bad." Darrell sensed he was only half joking.
It wasn't just Topgun instructors who needed to see the battle space in granular time-motion detail. Our fleet operators needed it, too, and thanks to new technology, they were getting it. The latest airborne early warning (AEW) aircraft were equipped with powerful radars that could detect the enemy at great ranges and target him. The state of the art was embodied by the E-2 Hawkeye's twenty-four-foot rotating dome, which covered hundreds of square miles of radar airspace. The five-man crew included three specialists—a combat information officer, an air control officer, and a radar operator—who were shoehorned in "the tunnel," a tight, confined workspace in the rear crammed with scopes, dials, and switches. The system for managing all that data required an enormous amount of expertise.
The full name of the Miramar command, as it happened, was Fighter and Airborne Early Warning Wing, Pacific Fleet (ComFitAEWWingPac). The early warning aircraft community there had its own fleet readiness squadrons and a tactical school they called Top Dome. As fleet air defense required real-time information to be reliably exchanged, data link became increasingly important. Although Hawkeyes and fighters often worked together in exercises, they didn't have the type of hand-in-glove integration that Topgun fostered. In the years when Cobra Ruliffson and Hawk Smith were in charge, Topgun worked hard to change that.
Ruliffson conceived of a program to cultivate and sharpen the skill of our E-2 aircrews, the Maritime Air Superiority Threat (MAST) program, or "Topscope," and pitched it to the chief of naval operations in 1976. The new schoolhouse began in 1978. The following year, Topgun put ninety-four men through its five-week course, while next door, the four-week Topscope program graduated 109 aircrewmen and "air intercept controllers." In 1980, the two programs were formally consolidated and the curriculum expanded to six weeks.
These postwar developments came just in time to help save the supercarrier. The Russians, well aware of the threat our carrier battle groups represented, had spent decades devising ways to defeat them. Though they never were able to build their own supercarriers, they did come up with some weapons and aircraft that put our command of the sea at risk.
The Tu-22M Backfire bomber first flew in 1969. It joined operational squadrons in 1972 as a dedicated carrier killer. Armed with air-to-surface missiles with a three-hundred-mile range, the Tu-22M could race toward a carrier battle group at Mach 2 and fire a salvo of deadly missiles before our antiaircraft weapons could hit them. Each Backfire could carry four or more of these missiles. An attack by a full Backfire regiment—about forty planes—could throw almost two hundred missiles at our ships, overwhelming our defenses from stand-off distance. These long-range missiles could carry either conventional or nuclear warheads. In a worst-case scenario, one missile could destroy an entire battle group costing billions of dollars, manned by thousands of young Americans.
The discovery of the threat posed by Soviet Backfire bombers justified very serious concern in our senior command at the start of the 1970s. We had to counter that threat for the supercarrier to survive. The combination of the F-14, E-2, and the Phoenix missile system was our answer. The F-14's long legs allowed us to patrol greater distances from the carrier. The E-2 gave us radar coverage well away from the fleet. It also ensured we would have radar coverage when the battle group was running on "EMCON" control—with all of its electronic emissions shut down, to keep the Soviets from detecting our ships. The Phoenix gave us our own stand-off response to the Tu-22 threat. Its hundred-mile-range enabled Tomcat aircrews to engage the Backfires far from the battle group.
It fell to Topgun to create these tactics. Through the late 1970s and early 1980s, Topgun sharpened our capability both in long-range interception and fighter-on-fighter dogfighting. When Monroe Smith was CO, he developed a tactic known as the "chainsaw." The idea was to keep Tomcats on patrol at their maximum range from the carriers. This required a constant cycle of E-2 Hawkeyes, Tomcats, and aerial refueling tankers. Together, they would create a defensive barrier two hundred miles from the battle group. It was easy to reinforce them with fighters on alert five status. The E-2 Hawkeyes would orbit nearby, providing radar coverage and control extending hundreds more miles out. When the Backfires appeared, the Tomcats could hit their burners, close the distance quickly, and fire their Phoenix missiles. Russian aircrews became painfully aware of the power of our argus-eyed orbiting radars. With in-flight refueling, Tomcats could chase Russians almost without limit, held back only by the constraints of our aircrews' endurance. We could only hope that the Phoenix would have been more reliable than the troubled Sparrow.
At Miramar, Topgun expanded its program to better prepare aircrews—fighter and early warning aircraft alike—for the challenge of fleet air defense. They got a broad-based understanding of how fighters could destroy other fighters while also protecting carriers from a Russian aerial swarm. We wanted to kill the archers rather than the arrows. The Miramar schoolhouse sent MAST teams to the East Coast to brief F-14 and E-2 squadrons on the latest Soviet anticarrier capability and how to counter it. At times, the Russians demonstrated their tactics against us. In the early 1980s, they actually launched a simulated attack on the _Enterprise_ and _Midway_ , closing to within 120 miles. As we monitored the exercise, we in turn learned a lot about how the Backfires planned to do business. We altered our tactics accordingly.
When Lonny "Eagle" McClung was the CO at Topgun in 1980 and 1981, he enlisted the Air Force to help him train his F-14 pilots to defeat the long-range Soviet cruise missile threat. It turned out the SR-71 Blackbird strategic reconnaissance aircraft was a superb imitator of a cruise missile. He would arrange for the boys from Beale Air Force Base to take off in their Blackbirds and track inbound toward the coast, starting far south of San Clemente Island. Topgun would station F-14s at ten-mile intervals along the radial of their approach, with their radars looking south. When the radars locked on a Blackbird, the Tomcat pilots would turn on their afterburners and climb, looking to gain a favorable position to shoot a Phoenix. With the stunning speed of the SR-71 faithfully matching an inbound antishipping missile, students learned how little time they had to set up a kill. The higher and faster they were, the more likely they were to achieve a good solution. According to Eagle, that meant climbing to forty thousand feet. There's no better way than to learn by doing, by experiencing those closure rates firsthand.
Thank God we never found out if any of these tactics worked. In a full-scale war with the Soviets, we would have faced not just hundreds of Backfire bombers, but older Tu-16 jet bombers and the venerable Tu-95 Bears as well. Well supported with electronic warfare aircraft and perhaps even fighter escort, the Soviet air armadas could have launched thousands of missiles at our battle groups. No tactic or weapon system is foolproof. Even if we were 99 percent successful in defeating their attacks, that 1 percent could have been enough to devastate the fleet.
As this threat took shape and Topgun responded through the postwar years, I was at sea more often than not. Commanding an air wing that included four F-4 Phantom squadrons, as well as attack aircraft, bombers, tankers, early warning planes, and helicopters, was one of the most challenging and fun jobs I ever had. In some ways, it is also a naval aviator's last hurrah with the fleet. Once you get promoted out of air wing command, your flying days are limited. Until that day comes, however, air wing commanders are expected to fly every type of plane in their inventory. It was a hair-on-fire experience. In the space of a few days, I might fly an F-4 Phantom, an A-6 Intruder, and a helicopter. In battle, I would have been leading strikes and coordinating the attacks of my individual squadrons.
The job is a culmination of everything learned earlier in a naval aviator's career. All the lessons, all the mentoring by other officers comes together in the way an air wing commander chooses to lead his men. Creating a culture of excellence, of openness and of self-evaluation so that your crews can improve and grow, is an essential element to success. Aboard the _Coral Sea_ , I used the leadership techniques we developed at Topgun to set the framework, then I let my squadron commanders run their own shows without micromanaging them.
Our F-4 squadrons trained to tackle both the bomber threat and air-to-air combat with enemy fighters. The days of obsessively focusing on one mission set were over. We had learned the lessons of the 1960s, of Vietnam and the Topgun solutions. Now the new order of the day was to be a flexible force capable of responding to any threat.
It was an exciting time, and I cherished every moment. I knew that once it came to an end, I would have to let the younger guys do the flying. With the F-14 coming into the fleet in ever-increasing numbers, that was a bittersweet thing for me to accept. On one hand, with my career thriving, I could look forward to a staff job with Task Force 77, then my own carrier someday. On the other hand, I would have given almost anything to blast through the speed of sound in an F-14 heading for fifty thousand feet. I had come a long way from my days flying Fords from North Island.
One of the sweetest moments of my career took place at the officers' club at the Long Beach naval shipyard when my air wing was ashore. As CAG, I was invited to be the keynote speaker at the Daedalian Society, a wonderful aviation advocacy organization. I don't remember what I said to them. I do remember one man who lingered in his seat at the front table afterward. He was small and unassuming. He carried himself in an understated way. All the great ones do. It was General Jimmy Doolittle.
I am not easily overwhelmed, but when the general motioned me to his table and we fell into a conversation about aviation and everything related to it, I was overcome with gratitude—and awe. Imagine his courage, carrying out the famous Tokyo strike in April 1942 that bears his name. Leading a flight of sixteen Army bombers from an old straight-deck aircraft carrier when the war seemed nearly lost, he undertook a mission that was hard to tell from suicide. The general invited me to retire to the bar, where we drank a scotch and talked about what had been going on with my air wing on the _Coral Sea_. I took it as a high honor that he took the time with me. It suggested I might have done something right in my career. It was a most memorable drink with a great man.
In 1976 I stepped out of the cockpit for one last time as a full-time aviator and said farewell to my air wing. The Navy promoted me to captain, and now I was a senior officer at last. While I'd still get to fly from time to time, the truth was that my days as a combat aviator were over. I suppose it would have been harder to take had there been nothing but desk jobs on the horizon for me. Thank God, that was not the case. Ronald Wilson Reagan was my commander in chief. The prestige of naval aviation and the military generally was set for a resurgence, after many years in the doldrums following the withdrawal from Vietnam. It was a fine time for a newly minted captain to take command. I was going to sea as the skipper of my own ship.
# CHAPTER EIGHTEEN
# BLACK SHOES
**Aboard USS _Wichita_**
**1978**
Naval aviators are always considered a component of a total ship's company when serving aboard a carrier. This is true when we are acting either as a flying part of her air wing, or as a ship's officer. It should be understood that there are many nonflying jobs on board requiring seasoned naval aviator expertise. True, the aircraft and flight crews are the most visible and well known, the raison d'être of the vessel, but they are still only a component. It takes about five thousand sailors to get those ninety airplanes and their crews to where they need to go, but when you are part of the brown shoe, or aviation, set, much of that is invisible. We are focused on our squadrons, our air wing, and our flying. What the ship's company is doing represents almost a different universe to us, including engineering, navigation, supply, medical, dental, communication and, very importantly, the flight and hangar decks.
Decades ago, experience dictated that it was always best for a naval aviator to command our aircraft carriers due to the unique types of command decisions they made and the complexity of operating aircraft at sea. As a result, the career path for pilots and aircrew led through the traditional side of the Navy. Before they went to an aircraft carrier, they were designated a surface warfare officer or officer of the deck of an aircraft carrier. After I attended the Prospective Commanding Officers Course in Rhode Island, the Navy gave me command of my first ship, the replenishment oiler USS _Wichita_ (AOR-1).
Talk about a wake-up call. From flying fighters at Mach 2, I found myself navigating the Pacific at twelve knots on the bridge of a forty-thousand-ton, 660-foot-long behemoth crewed by twenty-two officers and four hundred men. While we had two Boeing H-46 Sea Knight helicopters to help run "vertical replenishment" missions between our ship and those we serviced, for the first time in my career I had virtually no connection to flying fixed-wing aircraft. It was a big transition for me personally.
Why does the Navy send fighter pilots to command supply ships? Because prior to achieving the ultimate prize, aircraft carrier command, you must demonstrate your ability to command and operate a large ship at sea. You have to show you will never collide with another ship or run aground. More importantly, you need to learn the complex logistics of fleet operations. It is actually a stroke of institutional genius. During World War II, we needed to find ways to keep our carriers on station thousands of miles from port. This was no small challenge. A carrier crew consumes massive amounts of food and basic items like toothpaste, toilet paper, chewing gum, and cigarettes. The ship itself needs enormous amounts of fuel oil, aviation gas, and lubricants. To keep the carriers at sea functioning, we built an entire fleet of logistics ships that could transfer all those consumables at sea. It revolutionized the way the Navy projected power. Thirty years after the war, we had refined it to an art form.
When a big carrier came alongside us at sea, my crew would send across lines to the carrier, then run hoses linked with big connections and hose trolleys that move in and out on a steel cable to transport and replenish the carrier's supply of aviation fuel and bunker fuel. Our two helicopters, meanwhile, hauled sling loads of palletized supplies to the flight deck. In a few hours, the carrier was full up and ready to look for trouble.
Occasionally, we would replenish two ships at once, usually at night. I remember refueling a supercarrier and a foreign destroyer at the same time in open ocean, all three warships riding the swells together within a football field's length abreast. It took a lot of shiphandling skill for the receiving ships to do this, and even today few other navies have this kind of capacity. It is the secret behind our ability to operate anywhere in the world for as long as necessary.
Learning the logistical side of battle group operations was important to commanding a supercarrier. Thus, taking a supply ship to sea to work with the flattops was one of the stepping-stones to commanding a carrier of your own. Again, the keys to success were: "Don't hit anyone and never run her aground." If you were always on time and always filled out your customer's entire order, you would stay in the running for a supercarrier. Remember, there are always plenty of naval aviators, but only a few handfuls of ships like the _Wichita_ , and even fewer supercarriers. Competition for command of one of those beautiful ships is understandably intense. It is well worth the study, time, and effort.
My great challenge came later in 1978 when the _Wichita_ headed to the shipyard at Hunters Point, San Francisco, to undergo a refit and modernization. Aside from Candlestick Park, home of the 2–14 49ers that year, Hunters Point is a legendarily bad neighborhood, riddled with crime and drugs. We were slated to be at the shipyard for nine months. Our first problem: Where to billet the crew? I didn't want them to live aboard ship while it was being dry docked and overhauled, so I set off in search of suitable housing. A floating barracks ship was not available. We settled on an unused nice four-story building on the shipyard grounds, which the owner allowed us to convert into land-based crew quarters for the duration. We filled it with beds, televisions, and a keg of beer every afternoon at 5:30. The crew hung a sign out front reading "The _Wichita_ Hilton." It made a nice hotel and my crew were out of the dirt and noise of a ship in overhaul.
In a weird, urban farm sort of twist, the shipyard owner allowed a number of barnyard animals to roam the place at random. I'd see pheasants, chickens, and even guinea hens scuttling about the vegetation along the bay in the shadow of the 49ers' stadium. Well, the crew saw them too, and we had a number of cooks who caught those little buggers and served them to our sailors. The shipyard owner only complained after one of his prize goats went missing the morning after the crew held a raucous barbecue. The goat, my boys swore, was last seen swimming the bay, heading toward Alameda.
It was here that I began to learn the biggest challenge every skipper faced in the Carter-era Navy: personnel issues. In the post-Vietnam years, with the draft ending and the birth of the all-volunteer military, we faced a lot of shortages in specialized areas, as I discovered when my new ship's doctor arrived at Hunters Point.
The fleet suffered a significant shortage of physicians back then. The _Wichita_ wasn't supposed to be allotted a doctor, but I made a stink about that and was able to pry one loose. I think they gave me Dr. Jack Methner as punishment for shaking the tree.
He showed up in a new Porsche 911 convertible, which he drove right up to the gangway and parked in my slot. He jumped out, and we got our first look at his long, flowing white hair, chest full of ribbons, and a gaudy disco-era gold chain around his neck. He wore a tropical white uniform that looked out of place against our uniform of the day, khakis.
I found out later that the service was so short of doctors that he went straight to the fleet without any indoctrination training. This made his four rows of ribbons more than suspect. When asked, he shrugged, and with a Cheshire Cat smile said, "My recruiter told me to go get them."
He would be a project I never fully was able to tame. Jack was taken belowdecks by my executive officer and ordered to remove the ribbons and get a haircut. His first attempt at the latter turned out to be little more than a trim to his daring mane, so the XO sent him back to get a true high and tight. It never happened. Only a nice trim. I suppose they knew he was going to be the one giving them physicals.
Dr. Jack may have been a project, but he meant well and was a fine doctor and became a treasured friend when we left the service. He signed up with the Navy to see the world after becoming both a general practitioner and a psychiatrist. He had such an active mind (and libido) that I think he just got bored back in Texas and lit off for some high adventure in uniform.
The issues we faced as a Navy included racial tensions and a lot of drug use. It was a difficult time, stretching back to the Vietnam War, when a full-fledged race riot broke out aboard USS _Kitty Hawk_ , resulting in dozens of injuries. Fortunately, as the Navy became more integrated, efforts were made to ensure better treatment for our African-American sailors. Gradually, such measures worked to overcome the most significant problems.
Drugs were another matter entirely. For many ships at sea, everything from angel dust to heroin, pot, and cocaine proved to be readily available. Some sailors took to making money on the side by dealing to their buddies. They received regular shipments through the U.S. Postal Service. We were not allowed to screen or censor incoming packages, so the flow from stateside drug dealers to those aboard ship could not be interdicted or shut off. The Navy's criminal investigation service was caught completely unprepared for the influx of narcotics into the fleet, and it would be years before they caught up. Our only hope was to catch the dealers actually making transactions, something that happened infrequently at best simply because we lacked the means to do it.
I saw only a few of these cases among the _Wichita_ 's crew. The vast majority of my sailors were dedicated and hardworking professionals. In fact, we convinced our chain of command to let our ship's chiefs oversee and manage the overhaul. I figured nobody was more dedicated than our chiefs, and nobody knew the ship as well as they did. Why not let them take the lead? It turned out to be a great success. We completed the work two months early and came in two million dollars under budget, something that had never happened before.
One night, as we were getting ready to take the _Wichita_ out to sea after the overhaul, I was working late. My ten-year-old son, Chris, got ahold of my ship-to-shore number and called my cabin. I picked up and heard him crying.
"Dad, you can't leave."
I thought about all the goodbyes since 1968. Time after time, he'd seen me fly out of his life at the controls of an F-4.
"I have to, Chris."
"Everyone else at school has a dad. I don't. You can't leave."
I thought of that barbecue in '73 when the phone call came telling me of Harley's disappearance and how my little guy clung to me as I said goodbye.
Navy life dictates an episodic family life. It is sometimes cruel and always hard. That night, all my accolades and promotions meant nothing. In that moment, I wasn't a ship's captain preparing to go to sea. I was just a dad who chose a career that would take me away from my son yet again. Nothing I could say could stem his tears. We sailed the next morning.
Given my own family experience, I always tried to be sensitive to my sailors. The best we could do was focus on the job at hand and look forward to mail calls and a few moments on the phone in port somewhere.
In April 1979, our sea trials went flawlessly, and we returned to the Far East to support our supercarriers out there. The _Wichita_ received the Battle "E," the Pacific Fleet's award for most efficient ship in our type.
During the _Wichita_ 's adventures in the Pacific, Doc Jack's inexperience with Navy tradition bubbled to the surface again. He was unused to the ocean, and being cooped up on our forty-thousand-ton floating home started to get to him. As we returned to Pearl Harbor from WestPac after about a month at sea, I could see the good doc's morale starting to suffer. I called him to my cabin and gave him a special mission. He would fly a helicopter to Honolulu, then on to Fort DeRussy to set up liberty accommodations at the Navy R&R center. And I asked him to plan a dinner reception for all the officers the night we got into Pearl.
When we docked at Ford Island a day later, I peered down from the bridge to see Doc Jack racing up to the berth in a convertible Mercedes-Benz, three gorgeous women in back and beside him. He waved to the crew lined up along the main deck. The crew stared in utter astonishment at the spectacle. Of course, right at that moment the base admiral rolled up in his sedan to make the traditional welcoming call. We'd been ready for him and extended our amidships officers' brow to bring him aboard.
Doc, clueless as ever to protocol, ignored the admiral completely, grabbed his three dates and scampered up the brow, and saluted the ensign ahead of our visiting dignitary. This sort of breach of naval propriety could cause havoc to careers and ships' companies if the admiral so wished. We saw it happen and dreaded the fallout.
The admiral came aboard a few minutes later. As per custom, I hurried to go meet him in my cabin, where we would drink coffee and talk shop.
I rushed down to the cabin to discover not just the admiral waiting for me, but Doc Jack and the three gorgeous women he'd somehow met in one night ashore. For a split second, I saw my career flash before my eyes. Then the admiral gave me a sideways glance, a half-smile, and I realized he was thoroughly enjoying the company. Doc's party that night was a shot in the arm for our ship's officers. Weeks at sea can wear out any man no matter how much he loves the smell of salt air and the ocean spray on his face.
We had another kind of morale boost later on, one that affected the entire crew and remains one of the most meaningful moments in my own career.
One beautiful day, south of Baja, Mexico, after sailing from Hawaii, _Wichita_ was awaiting a rendezvous with the USS _Constellation_ battle group in four days. We were killing time, but my crew was tired and needed a break, so I requested a visit at Mazatlán for a night or two of R&R. There was a storm to the south, but it looked okay for a short visit.
We enjoyed the food and beverages at Señor Frog's. Then the storm started to move north, so we got underway early and headed for Cabo San Lucas. A couple of sailors missed the ship's movement, and I left instructions with our liaison in Mazatlán to send them via slow bus to Tijuana for the shore patrol. That evolved into a weeklong trek, often stopping for food and water. Next time, those lads sailed with the rest of us.
I fell asleep on the bridge wing about daylight and slept for a couple of hours. When I woke I went in the bridge to listen to the radio. I caught an unusual change in the channel, and heard two men in two sailboats discussing their plight. One was a cardiologist and his wife whose boat was dead in the water. It was the _Infinity_ 's maiden voyage, and she had run with too much sail during the night, lost the mast, and fouled the running gear. The other boat contained a dentist and his family with five children. They were both lost, but the dentist could still sail.
Immediately we got our two helicopters searching even as I noticed two big cumulus cloud formations or thunderstorms over Baja. I took a bearing to each, which we triangulated, and asked both boats to do the same. They passed their bearings to us so we could chart them.
After confirming his position, the dentist departed for port in Magdalena Bay. Then I sent the helicopters to locate the _Infinity_. We found the boat just about dark and tried to pass a towline, but it washed overboard twice before we got a hookup. We took the _Infinity_ in tow for about ten hours, brought it to the entrance to Magdalena Bay, and handed her off to the Mexican coast guard.
During the night I learned that the doctor was recovering from open-heart surgery, and his wife conned that beautiful sailboat in our wake. It was not the typical Navy service to the fleet, but it was the right thing to do. Plus, the impact it had on my crew was substantial. A typical American wants to help, wants to do right by Emerson's admonishment to leave the world a little better place than he found it. This was one of those moments for all of us. Late that night, as we churned north, running from the storm, I looked aft to see almost all my off-duty sailors lining the stern railing. They were keeping the couple aboard the _Infinity_ company, reassuring them that the _Wichita_ would take good care of them. They took turns talking to the surgeon's wife as she stood at the wheel, cracking jokes and keeping her relaxed. The heart on display that night is a memory I will always cherish.
We reached Magdalena Bay safely, said goodbye, and departed to join up with the _Constellation_. But after I reported the rescue, an admiral in San Diego wanted to see me. He threatened to court-martial me for endangering my ship. My master chief, who came with me to see him, spoke up right then. "Our actions were safe and in the proudest traditions of the naval service at sea, which includes helping and protecting those in danger," he told the admiral. He added that the press would not react well to the court-martialing of a ship's captain who had just saved American lives. The admiral dropped the matter.
The Navy is an up-or-out organization. If you do not continue to achieve at a high level, you don't make the next selection board list on the command ladder. In the fall of 1980, after two years with the _Wichita_ , I received new orders. It was a major moment in my career. It would determine if I went to a staff post ashore, or was entrusted with a new command at sea.
I opened my orders, hopeful and confident. I thought we did a great job with the _Wichita_ , but that admiral could make trouble.
I unfolded the orders and read them. Then read them again.
The Navy was giving me an aircraft carrier.
# CHAPTER NINETEEN
# THE BEST AND THE LAST
**Somewhere in the Indian Ocean**
**November 1980**
The tropical sun beat down on the flight-deck crew of USS _Ranger_ as they choreographed the morning launch cycle. Tomcats first. Sidewinders and Sparrows mounted and armed, the big birds taxied one by one to the catapults, where the nose gear was attached to the piston. As the aircraft was put "in tension" with the catapult, the catapult officer signaled the pilot to push the throttles to full power and select afterburners. One last check of his instruments, and the pilot gave the salute for "All go" (or turned his lights on if it was at night). The cat officer snapped a salute to the pilot, then touched his wand to the deck, pointed toward the bow. This was the signal, "Launch 'em!" and the big piston hauled the Tomcat down the deck. Trailing two long tongues of flame, she took to the sky as another pair of Tomcats taxied to the catapults. Going from zero to 150 knots in two seconds was a real kick in the ass.
The _Ranger_ was my ship now. Perched on the bridge, seated in a barber chair with "Skipper" stenciled on its back, I watched the bustle of the flight deck from the best seat in the house. I was forty-six, still wearing the Ray-Bans I bought in Pensacola and the Star of David chain around my neck. My little mouse from North Island was tucked away in the captain's cabin a few yards aft from this chair. My three talismans served every day as a reminder of who I was and where I came from since first climbing into a cockpit in Pensacola.
It was here that I learned why it is so important for an aviator to command a supercarrier. That ballet on the flight deck? We all had seen it from the cockpit of our Phantoms back in the day. But when we were coming aboard, it was just us and the landing signal officer working together to get our wheels back on the deck. There was another component to that which was largely invisible to the guys in the cockpit. The landing signal officer, the air boss, and the captain communicated constantly, asking for course and speed alterations depending on the velocity of the wind over the deck and how the seas were running. That coordination becomes crucial in bad weather or at night. The planes don't just line up on the carrier—the carrier lines up and maintains course perfectly for the planes.
Once I had six A-6 Intruders in the landing pattern with a thunderstorm bearing down on us. I was in constant contact with the air boss and landing signal officer, who confirmed what they needed. As the winds became more erratic, we altered course to keep the wind coming over the angled deck, where the planes landed. By the time we brought home all six birds, we had turned that big ship a full sixty degrees. Without the nuanced understanding of what the men in the cockpit were experiencing, there was no way a captain of a carrier could do his job to greatest effect in such moments.
I took command of the _Ranger_ and its five thousand sailors at Subic Bay on October 20, 1980. I relieved former Topgun CO Roger Box, who had taken the ship the previous year after the _Ranger_ collided at night with a tanker near the Straits of Malacca, one of the busiest sea lanes in the world. The tanker almost sank, and the carrier suffered heavy damage to its bow and two fuel tanks. After temporary repairs at Subic, the carrier steamed to Japan to complete the work. As a result of the incident, the skipper was relieved of command and Box given the ship.
Consecutive commanders of Topgun now took the _Ranger_ to sea. After eleven years of classes, Topgun's graduates, instructors, and skippers had spread throughout the fleet, energizing it with our ethos and leadership style. We had never thought this far down the road about where our careers would take us into surface commands. Still, the values and leadership methods we used could be equally applied here on the _Ranger_ 's bridge, and I made a point of doing so.
I addressed my whole crew daily so that everyone felt a part of the team. Twice a day, my master chief and I toured different decks and compartments, getting to know the sailors. In some spaces far belowdecks, the men not only never saw sunlight while at sea, but they'd never seen a captain come through their compartments. The _Ranger_ displaced more than eighty thousand tons. She was over a thousand feet long and divided into more than two thousand spaces. With our five thousand–plus sailors aboard, we were a small-sized, nautically mobile American city. Trying to get into every space and compartment was akin to trying to do the same in a comparable-sized town in the heartland. I visited as many as I could, usually with our master chief, Dave Hobbs.
On those twice-a-day trips belowdecks, I could get to know our sailors. The majority of these nineteen-and twenty-year-olds were aboard for the right reasons. They wanted to serve their country, learn a trade or skill, or go to college after their stint at sea. Others saw the Navy as their career, wanting to rise through the enlisted ranks like Master Chief Hobbs had. But a troublesome few, perhaps about 4 percent of the _Ranger_ 's crew, had fallen into the cycle of drugs and crime. A kid on angel dust was capable of anything. It was a hideous and totally unexpected problem. Until I held my first shipboard command, I hadn't had contact with drugs or drug users. Naval aviators were insulated from them. You can't drop acid and work on a carrier flight deck at night.
In the first months on the _Ranger_ , we faced drug-related issues on a daily basis. When our investigators finally caught one of the most notorious dealers, we made sure he got a bad-conduct discharge. We tossed out another one not long after. It felt like throwing bricks into the Grand Canyon. Somebody else took their place and the flow of drugs remained a problem.
Sabotage was an issue as well. Draftees opposed to the war carried out more than two dozen acts of sabotage aboard the _Ranger_ alone. Before I took command, one sailor caused millions of dollars of damage by dropping a paint scraper into some critical rotating machinery. It delayed the _Ranger_ 's redeployment to WestPac for months. It was hard to track down the culprits. My predecessor, Roger Box, had to deal with a saboteur who crept into the hangar deck and activated the firefighting system. The chemical foam from pressured lines made a huge mess. When it happened to me, the whole hangar deck got doused while it was full of aircraft. The air wing was furious, but an investigation turned up no suspects.
Master Chief Dave Hobbs and I settled on a creative approach. The morning after the event, in my daily address over the intercom, I explained what had happened and the damage it had done. "Whoever did this, I'm offering you a deal. Today, and today only, I urge you to come forward to discuss this with us. We'll help you." I provided a secure phone number that our saboteur could call.
That night my bedside phone buzzed. Dave was on the line. "He's called in," he said. After a short negotiation, the culprit walked into the master chief's office. I hustled down to confront him and find out what the kid thought he was doing. As I entered, I saw our saboteur. He was a desperate-looking, emaciated kid of maybe twenty—hollowed eyes, the gaunt, skeletal face of a person in the grip of addiction. Looking at him, I couldn't be angry. Here was the embodiment of the cancer afflicting our navy, and our culture back home. What started out as a fun diversion for this kid had taken over his life.
He admitted he was addicted to angel dust—PCP. He couldn't explain his behavior, but was devastated by what he was doing. He pleaded for help.
We put him in protective custody. The damage and extra work he had caused everybody earned him considerable wrath from the crew. Had his identity become known, Dave and I feared he would be beaten by angry sailors or sent for a nighttime swim with the sharks. Later, we sent him to San Diego, where he underwent treatment for his drug addiction.
The obvious answer to the drug problem aboard our ships was to interdict the supply. All we needed to do was check the incoming packages sent from the States, and our long days at sea would have taken care of the situation. Whatever supplies had been smuggled aboard before our departure would have been quickly consumed, and our addicts would have been forced to go through withdrawal as a result.
We couldn't do that. The legal system ruled that our sailors had a right to privacy, and their packages could not be opened or searched. This changed later, and during the post-9/11 years, anything coming or going to or from a war zone was thoroughly searched. Contraband, including alcohol (often disguised as mouthwash), drugs, weapons, and weapon parts, was confiscated by the postal system. If only we could have done that in 1980, lives could have been saved.
Personnel issues occupied the majority of my time. Talk to any teacher, and they will tell you that the disciplinary cases in their classroom may include only two or three kids, but those two or three kids take up half their day trying to keep everything under control. It was the same aboard the _Ranger_.
Occasionally I glimpsed the stress and hardship the sailors endured as a result of their home lives back in the States. Dear John letters flowed into the ship with depressing frequency, and many of my men suffered serious heartbreak while we patrolled our nation's distant ramparts. Some dealt with it by focusing on their jobs and throwing themselves into their work with renewed intensity. Others tried everything they could to get home. This included jumping overboard. We had a number of cases like that until we broadcast on the ship's internal television system photos of the sharks in our area that fed on the garbage the Navy's ships released from our compactors. Once the men saw the teeth on those things, nobody willingly went overboard.
One evening while in port, I got a call telling me we had a sailor sitting on a flight-deck rail, bleeding from his arms. He was threatening to jump seventy feet to a concrete pier beneath him. I was attending a dinner reception at the time and was wearing my tropical white uniform. I dropped everything, sped back to the ship, and found the young sailor brokenhearted and sobbing. He held a pair of scissors in one hand, which he'd used to slash his wrists.
I talked to the young fellow, trying to coax his story out. Haltingly, he related to it me. It was a sad story, a mess of his own creation that now left him trapped. In his mental condition, death seemed to be the only way out. At length, I was able to coax him off the rail. He came over to me and grabbed me, hugging me desperately. We got him below to sick bay where the corpsmen treated his self-inflicted injuries. As I watched him depart, I realized my tropical whites were smeared with his blood. It turned out he had gotten both of his girlfriends pregnant.
Through it all, we showed the flag at ports of call from Thailand to Kenya and Sri Lanka while operating in the Persian Gulf on what we called Gonzo Station. This was near the end of the Iran hostage crisis, and we anxiously awaited word to attack. That word never came, but we were armed and ready.
The Iranians never tested us with their air force, which included a batch of F-14 Tomcats we had sold them just before the revolution deposed our ally, the shah. I sure wanted them to try. I had two squadrons of Tomcats—the two oldest and most storied units in the Navy (VF-1 and VF-2)—filled with hard-charging, type A fighter pilots who wanted a crack at Iranians as bad as anyone.
We didn't face the kind of threat from the Iranians that we did from the Soviet Backfire regiments, so we usually armed our F-14s with a mix of Sparrows, Sidewinders, and Guns, leaving the Phoenix missiles aboard ship. Whenever we went through the Strait of Hormuz into the Persian Gulf, we cycled our Tomcats off the deck and pushed them out between our ship and the edge of international waters within sight of the Iranian coast. Any low-flying Iranian bandits would have been caught the moment they were "in play" over neutral waters, and we would have torn them apart.
Instead of risking aircraft, they decided to harass us with fast-moving PT boats, something our battle group's destroyers and cruisers dealt with very effectively.
During intense operational cycles, a typical air wing usually loses five or six engines a month to "foreign object damage," or FOD. This can be any stray piece of metal like a screw, a bolt, or a nut that has fallen onto the flight deck that gets sucked into an intake and wrecks the engine's turbine blades. It is a constant problem, both at sea and on land, that is solved by frequent walkdowns by our sailors to find anything that could harm our aircraft. Of course, with the available crew, it was impossible to find every little nut or screw that fell into the tie-downs in the deck.
We computed that we needed three hundred to four hundred men for a thorough FOD search, but the flight-deck crew just couldn't provide that many bodies. I hit upon an idea from my visits to the ship's belowdecks spaces. I announced that at a specific time, called by the air boss who runs the flight deck, everyone not engaged in an essential job could report to the deck, breathe the sea air, get some exercise, and help eliminate FOD.
Sometimes I got on the 1MC circuit and encouraged the crew to come up and "smell the roses." While I got some laughs, it worked, and I often saw engineering "snipes" and mess cooks stretching themselves in search of the elusive FOD. Moreover, I offered three days' liberty to those who found a very small screw painted a particular color, usually black. That got the crew's attention. We even had cooks in aprons doing walkdowns.
_Ranger_ 's program was a huge success. We went 107 days without FOD damage, and the concept spread Navy-wide.
We stayed out on Gonzo Station keeping an eye on the Iranians and flying every day through the first weeks of 1981. In March, we headed back to Subic Bay and a much-needed break. As we reached the Strait of Malacca, the busiest shipping bottleneck in the world, my air wing commander asked if we could launch a few aircraft. I agreed. It made sense to get some eyes up there. It was a Friday morning, March 20, 1981, a day none of us ever forgot.
From my seat on the port side of the bridge, I watched the deck crew launch a couple of A-6 Intruder bombers. They fanned out ahead of us as we steamed east through the strait and into the South China Sea.
As our birds flew along, they caught sight of a tiny boat drifting on the swells. Circling back, they made a pass and reported it crowded with people. Apparently it was without power. It had no sails. They were just drifting with the tide. It was a humid, steamy day without even the benefit of a small breeze. The people on the boat were largely exposed to the sun's full strength.
We plotted the boat's position, and I ordered our ship to intercept it. Late that afternoon, we spotted it. The vessel was perhaps forty feet long with a tiny enclosed wheelhouse, and every square inch of it seemed to be covered by people. They were lying inert, one atop another, piled together in such terrible physical condition that some were said to be hallucinating. Most were too weak to even sit up and stare at the enormous supercarrier bearing down on them. A few had scraps of clothing. Most were bare from the waist up. Some had no clothes at all.
Our helicopters circled overhead, snapping photographs as we hove to and began rescuing these people. Some had to be taken aboard in stretchers lowered down to the boat. They had been at sea for two weeks after fleeing the violence continuing to plague Vietnam. Not long into their journey to freedom, the boat's engine failed. Food ran out first. Water soon followed. There were 138 people aboard a boat meant to hold, at most, 25. They grew weak. Several people died. The day we rescued them, we were told the survivors were considering cannibalism to survive.
We arrived just in time.
Our crew sprang into action, doting on the survivors with incredible tenderness. Our medical staff treated them for dehydration, heat exhaustion, and many other ailments, getting fluids in them with IV bags. Our tailors and parachute riggers sewed them clothing while our cooks prepared meals. It didn't take long for the crew and the refugees to bond. It was a beautiful sight, one of those unexpected moments in life where what you do plays a critical role in the well-being of others.
They were ordinary folks from Vietnam who had risked everything to escape an oppressive regime still killing or imprisoning its own people. Among those we rescued was a Vietnamese soldier who had deserted to seek a new life away from the fury and violence. It was impossible not to be affected by their ordeal, and by what they had risked everything for—the same things that drove generations to American shores.
We took them to Subic Bay with us, where the Philippine government gave them sanctuary. We later found out their ordeal was far from over. The Filipinos treated them poorly. Food and clean water became scarce in their refugee camp. Ultimately, though, most of the 138 were able to immigrate to the United States, where they started new lives on the West Coast as American citizens.
As they waited for their chance to fly east to our nation, my ship's company suffered a terrible tragedy. A young airman named Paul Trerice collapsed and died while we were in Subic Bay about three weeks after we rescued the refugees.
Trerice was a sad story, a twenty-year-old from Michigan whose time in uniform was a case study of the devastation wrought by drugs in our Navy. Having served for three years, he had never been promoted. In fact, he was in frequent trouble and even tried to desert twice. His squadron commander disciplined him repeatedly, though he was no stranger to our correctional custody training unit [CCU]. (Some people mistakenly call it the brig, which was totally separate.) Nothing seemed to work. He remained an often belligerent hard case who frustrated his squadron commander. I never met this sailor, but his death changed my life forever.
The ship had just returned from a five-day visit to Hong Kong, where he was an unauthorized absentee. He was next in the CCU that April of 1981. My understanding from the Navy investigation that followed his death is that, combative as always, he fought with a couple of our senior petty officers, who then took him up on the flight deck and ordered him to start jogging. It was routine exercise in the sweltering Subic Bay heat. Trerice had previously been restricted to bread and water as a result of his combativeness. As he was running, he collapsed. Taken below, he began to have seizures. Thirty minutes later, medical personnel arrived to treat him, but sadly, he died soon after. The Navy determined he had gone into cardiac arrest as a result of heat exhaustion.
During the investigation, it came to light that he'd been smoking marijuana with several other sailors inside one of our S-3 Vikings in the hangar. Our chaplain came to see me months after Paul Trerice's death to tell me that he'd been treating him and his addiction for a year as part of the CREDO Program. It wasn't just pot; much more serious and dangerous drugs were in the picture. I asked, "Why didn't you tell me earlier?" The chaplain shook his head, saying, "That was between him and God."
The captain is ultimately responsible for everything that happens on his ship. Despite all the good things we accomplished and the high level at which the crew had performed, I knew this tragedy would have a reckoning. We commenced a Judge Advocate General investigation on the way home.
We arrived in San Diego in May, where I was summoned before the commander of Naval Air Forces, Pacific, Vice Admiral Robert "Dutch" Schoultz. Based on the way Trerice was treated while in the custody unit, the admiral issued me a nonpunitive letter of caution.
After he announced his decision in the matter, Schoultz said, "Dan, I'd like you to take _Ranger_ on her next cruise."
Of course I said yes.
# CHAPTER TWENTY
# ONE MORE GOODBYE
**Somewhere in the Pacific**
**Spring 1982**
I sat in my captain's cabin, holding Mary Beth's letter like a precious gem. Two pages. I read and reread it until I had committed every sentence to memory. I still could not believe it had found its way to me, that she would be thinking of me all these decades after our parting outside the Whittier College cafeteria.
_Dan, I want you to know that I know the kind of man you are and will always be. Your friends know it too, and they refuse to believe the things being said about you in the newspapers._ The tragedy had been big news in the _Detroit Free Press_ , the _Los Angeles Times_ , and the _San Diego Union-Tribune_.
She reached out to me, knowing how devastating the media storm must have been. Then the _New York Times_ , _Playboy_ magazine, and the network nightly news all picked up the story. It became a national spectacle. Paul Trerice's death was without a doubt a terrible tragedy, but how it sparked a media frenzy shocked and mystified me. In 1981, 4,699 members of the U.S. military—all branches—died while in service to their country. It was a time of peace, and none of those deaths resulted from combat operations. Accidents, suicides, a scattering of murders, heart attacks, strokes—they happen.
Of all those, Trerice's was the only one that riveted the press for months. The death was a terrible tragedy that inflicted lifelong suffering on his family. For that, there was no excuse. Could it have been prevented? I asked that question every day for years. I just don't know. I think if we had known the extent of his apparent drug addiction, we might have been able to steer him to treatment instead of to the Correctional Custody Training Unit for his desertions and other acts. I thought about the saboteur we had sent to drug treatment, giving him another chance at a good life. I wish we had been able to do the same for Paul Trerice and his family. By the time his drug use came to light, it was too late to help him.
The West Coast press wasn't interested in my view of this. It tore into me with astonishing cruelty, relying on sources that included the two drug dealers we'd kicked out of the Navy to show me as a nautical tyrant, recklessly endangering the lives of my crew with sadistic punishments meted out on a whim. I became a Cold War version of Captain Bligh. Calls came from all over the country for my head.
My family received death threats almost daily for months. Hate mail poured in, especially from Michigan. The Trerice family filed several lawsuits against the Navy. One named me as a defendant. It was almost unheard of for an active-duty officer to be sued over something that happened in the line of duty.
In all the turmoil, this letter from Mary Beth arrived. We hadn't spoken since the Eisenhower years. I hadn't seen her since the football game where she gave me that cautious half-wave from the hip, tears in her eyes. It didn't matter. I thought about her very often.
I resolved to write her back and thank her, to tell her what her words of support meant to me. I had gone from being a respected naval aviator and ships captain whose peers had put my name on the admiral's list a year early, to the embodiment of every negative stereotype about the Navy and its officers.
I was putting my pen to the paper when I paused. _Don't do it. She made her choice. You have to honor it._
Mary Beth was still married to her football player. I was married too. Given how I still felt for her, writing her back would be a betrayal. It would also open up that wound again. I'd be in touch with the person I'd always loved and could never share my life with. As bad as the media attacks had been, suffering that would be far worse.
I never wrote her back. Instead, I carried the letter with me aboard the _Ranger_ for a month as the media firestorm continued. Each night, I reread it to remind myself that there were those I cared about who refused to believe what was being written about me and my style of leadership.
One day, I realized I was beginning to rely too heavily on it. I couldn't write her. I couldn't reestablish contact. In the moment, I needed to focus on my crew and my ship, and find the strength to ignore the publicity.
A federal court finally tossed the lawsuits, a decision that was upheld on appeal. But the blowback from Trerice's death affected a lot of good officers and petty officers aboard the _Ranger_. I did what I could to protect them, and by then my own career hung in the balance.
On June 11, 1982, I left the _Ranger_ for a shoreside staff position. This was the classic career progression on the way to flag rank, and I was given a plum job serving as deputy chief of staff for current operations under the commander in chief, Pacific Fleet, at Pearl Harbor. It's probably the busiest I had ever been in the service, but the job historically had its rewards. It was known as an "admiral maker." About a year into this job, I got a summons to Washington from the chief of naval operations. In his office, with the door closed, we discussed what I faced going forward with the Navy. One of Michigan's senators had made Trerice's death a personal crusade. The CNO believed that this was motivated by the fact that Trerice's family members were substantial donors to the senator and the CNO saw the senator's attacks on the Navy as essentially political theater as he faced a difficult reelection campaign.
Whatever the motivation, when the lawsuits were dismissed by both of the federal courts that heard it, and the Navy inquiry concluded that the death was a tragic accident, the senator used his position on the Senate Armed Services Committee to block my promotion to admiral.
Our CNO fought for me. I'd had a good record from Topgun, with the two deployments with the _Ranger_ , where we went two years without an aircraft accident, something no other carrier in the fleet had done during that period. But I was a political liability. Though the CNO urged me to stay the course, he was forced to pull my name off the admiral's list for 1983. I loved the Navy. What would I do without it? Yet I came to the conclusion that if I stayed, I wouldn't be able to win this fight. The senator would be reelected, and his opposition to my promotion would never waver. If the Navy resisted again, there could be fallout that would harm the service I loved. That's just how Washington worked. I resigned my staff position and retired two weeks later, on March 1, 1983, after twenty-nine years, one month, and one day in uniform.
As the Reagan administration continued boosting defense spending in the early '80s and I finished my tour as commanding officer of the _Ranger_ , Topgun was in the hands of a terrific CO, Ernie Christensen. He had excellent access to Navy Secretary John F. Lehman, and constantly worked on him to elevate the Navy Fighter Weapons School position in the chain of command so that our rivals within the Pentagon bureaucracy would leave us alone.
The culture of Topgun and its larger Miramar tribe was always its own best critic. In 1982, in fact, the reviews were mixed. The fast pace of fleet operations, which were pushing our carriers to operate ever forward, close to Soviet territory, in line with President Reagan's aggressive new Maritime Strategy, had cut into training time and limited the availability of our very busy fleet pilots to go to Miramar. While proficiency in air combat maneuvering was high, it seemed that Topgun graduates were no longer having such a dramatic impact on squadron training. Part of the reason was all the new squadrons that were being created to field the F-18 Hornet, which was arriving in Navy inventories in large numbers. With twenty-four squadrons getting equipped with the Hornet from 1982 to 1985, the Navy didn't have enough graduates to go around.
And yet Topgun's influence within the Navy grew ever wider. The school sent detachments to the Philippines, Japan, and Saudi Arabia to work directly with forward-deployed air wings. We ran "road shows" for them, organizing lectures, booking simulator time, and conducting battle group defense exercises. Our Mobile Training Teams, meanwhile, visited our NATO allies. Norway and Germany were particularly receptive, and Topgun instructors relished assignments to help them get the most out of their F-5s, F-104s, and F-16s. Our Navy cousins in the surface warfare community, meanwhile, tried to use Topgun-style training to make commanders of frigates, destroyers, and cruisers into better warriors. As I heard it, though, our way of giving a lot of voice to junior officers was a problem for the more tradition-bound parts of the Navy.
With all of this going on, it was only a matter of time before the larger public began to get wind of Topgun. In 1983, _California_ magazine published an article about Topgun, focusing on a single F-14 Tomcat crew. When movie producers Jerry Bruckheimer and Don Simpson read it, they saw the potential for a movie set in the world of Fightertown USA. The XO of Topgun at the time, Mike "Wizzard" McCabe, hosted the moviemakers at Miramar to explore the idea. After the producers hired screenwriters Jim Cash and Jack Epps to create the script, they approached the Navy about supporting the project.
The CNO, Admiral James Holloway, ended up granting them full cooperation on the condition that the Navy have the right to approve the script. With that agreement in place, two aircraft carriers were made available to the filmmakers, as well as several F-14 Tomcats modified to carry cameras. With the Navy billing the Paramount production team $7,800 per flying hour, Tony Scott began shooting in June 1985.
Though Scott said he wanted originally to make " _Apocalypse Now_ on an aircraft carrier," the producers thought better of that dark idea. Bruckheimer and Simpson wanted to make "a rock-and-roll movie about fighter pilots." And that was _Top Gun_ ,* released to much fanfare in May 1986.
The plot was built around the rivalry of two Topgun student pilots, Lieutenants Pete "Maverick" Mitchell, played by Tom Cruise, and Tom "Iceman" Kazansky, played by Val Kilmer. Tom Skerritt pretty well nailed the role of their skipper, Mike "Viper" Metcalf, conveying the character of Topgun leadership and the rigor of the training in a way that reflected reality far better than the conflict between the youngsters did. The one character in the film who might have seemed to be a Hollywood fabrication, Charlie Blackwood—the female lead played by Kelly McGillis—was actually inspired by a real person. This was Christine H. Fox, a mathematician who went to Miramar as a field analyst to advise the commander of the Airborne Early Warning Wing. Though she had little direct contact with Topgun, her boss, Rear Admiral Thomas J. Cassidy—who happened to be the Navy's liaison to the film producers—was so impressed with her that he persuaded the filmmakers to change Tom Cruise's love interest from an aerobics instructor to a brainy tactical consultant. Christine Fox went on to serve as a deputy secretary of defense, making her the highest-ranking woman in the history of the Pentagon.
Who would have expected such a film to be a boon to feminism? Because as we all know, the testosterone in that movie ran hot. It portrayed Topgun more as a glorified intramural tournament than as the academically rigorous graduate schoolhouse it really is. But hand it to Tony Scott and his team: The aerial photography was among the finest ever shot. Among the technical advisers was Captain (later Rear Admiral) Pete Pettigrew, a Vietnam MiG killer and Topgun instructor, who also appeared onscreen. Some nitpicking aside, they did very fine work demonstrating the F-14's capabilities in great shots set up by Mr. Scott and his cinematographer, Jeffrey L. Kimball, with a soundtrack that seemed to pull you into the cockpit for the ride. The film topped the U.S. box office that year, narrowly beating _Crocodile Dundee_. It eventually earned more than $350 million worldwide and won an Oscar for best original song ("Take My Breath Away" by Giorgio Moroder and Tom Whitlock, performed by Berlin).
Having watched some of the filming, Pete Pettigrew was impressed with Meg Ryan, in the role of the wife of Goose, Maverick's RIO. He says she cried on cue for twenty-two straight takes. I think Anthony Edwards stole the show as Goose. His son's experience as a Topgun pilot is the focus of the sequel, _Top Gun: Maverick_ (coming in 2020), which I consider a deserved tribute to the importance of a pilot's eyes and ears in the rear seat.
Several Topgun instructors got camera time in the publicity campaign. Asked about Maverick's cocky character, one of them said, "Well, he has the right stuff, but with that attitude we wouldn't let him in the back door." That's how we felt about egos in my day. It makes for good entertainment but isn't what you want in your ready room. The loner glory seeker—the maverick—doesn't last. He kills himself trying to impress people. Topgun wants solid, mature professionals, maybe touched by a divine spark of inspiration, but intelligent warriors who fight with the head, heart, and hands.
However, Navy Secretary Lehman wrote just recently that the bravado was meant with a particular audience in mind: the Russians. "The swashbuckling, confidently professional naval aviators kicking their ass was exactly the message we had intended to project, but it was not quite the nuanced approach conducive to diplomacy." No, it wasn't. But who knows? The movie as a psychological warfare operation might have helped push the Soviet Union to collapse just five years later.
It's easy to take shots at a film, because realism is seldom its primary goal. No Topgun pilot would ever invert himself and fly upside down, canopy to canopy, with an enemy pilot. And the maneuver where Maverick bagged his instructor by pulling up and reducing power to idle, causing the instructor to overshoot, is nothing more than what Jerry Beaulier has called a "kill self" maneuver. But there was no disputing the movie's value to naval aviation. It attracted hordes of new potential aviators and sailors to recruiting offices, which was definitely the Navy's goal. Admiral Holloway said that when applications from qualified candidates to go to Pensacola surged past the training quotas by 300 percent, he got Secretary of Defense Caspar Weinberger to approve "banking" the applications, spreading them over the next three years to assure the supply of candidates. The Air Force tried to keep pace. Reports circulated of their recruiters setting up in lobbies of theaters showing the film.
Few people outside the aviation community remember that a real tragedy marred the shooting of the film. In September 1985, the famed aerobatics champion and air-show favorite Art Scholl was killed while filming an aerial sequence in a camera-equipped biplane. Unable to recover from an inverted spin, he went into the water with his two-seater Pitts Special about five miles off Encinitas. The film was dedicated to his memory.
While the movie provided a shot in the arm for the Reagan-era Navy and its recruitment goals, there were unintended consequences within naval aviation that affected Topgun for years to come. The other communities, especially our attack crews, felt slighted by the movie. It stirred old resentments, and as the 1980s came to a close, the school faced another series of bureaucratic assaults that I believe were designed to cripple it.
Of course, I was a civilian by then, for the first time since I was selling shoes in downtown Whittier. I had challenges of my own. I went from commanding a supercarrier off the Persian Gulf to being another casually dressed California businessman. My entire social circle was gone. When I returned to California that spring, I felt like a refugee in my own hometown. I was almost fifty years old, starting over from scratch. I needed to find a new sense of normal.
For me, normal was waking up in my cabin to the smell of salt air coming through a brass porthole. It was the heavy jolt of a catapult launch, and the euphoria of breaking Mach 1 in a vertical climb. It was long, beautiful night flights across our country, and the sense of purpose I felt when we saved lives at sea. It was the fear of flying strikes into North Vietnam, and the honor of leading Topgun, alongside some of the finest young men America ever produced. It was welcoming old friends back from the Hanoi Hilton, and holding membership in a brotherhood that defined my entire adult life. In civilian life, there was no normal for me.
I struggled. My first marriage did not survive the many deployments of the 1970s. Being gone so much finally drove a wedge between us that could not be removed. I married a second time while serving in surface ships. Ever the optimist, I guess. It wasn't meant to be. The best part of our time together was the birth of my third child, a daughter. For beautiful Candice, I will always be grateful.
I could have gone into the defense industry like so many other retired military officers do—great salaries, great benefits. I refused to do that. I'd long since concluded that many of the problems we faced originated in the procurement system and the defense industry's influence in Washington and the Pentagon. I didn't want to use the military-corporate revolving door that makes the influence possible.
Instead, I went into business for myself in Southern California. The leadership principles I learned in the Navy played a large role in my success. So did a great businessman named Joe Sinay, who took me under his wing and mentored me. We became close friends over the years, and I owed him a tremendous debt of gratitude.
My folks passed, Dad first, then Mom a few years later. Even so, whenever I had business in the Los Angeles area, I'd make a point of getting back to Whittier to see my mom's oldest and closest friend, Louise Seacrest. She was ninety-four, sharp as ever, and the only family I had left there.
One night, after I'd taken her to dinner, she turned to me and said, "Dan, I've known you almost all your life. I have never seen you so miserable."
I thought I'd been doing a good job hiding it.
"Yeah, I'm pretty unhappy."
"I have the answer for you."
She pulled out a notepad and pen, scrawled on it, then tore the sheet off and handed it to me. I looked down at a phone number.
"Call it. Do it now. You should have done it thirty years ago."
I had no idea what she was talking about.
"Dan, Mary Beth is single. Call the number."
I was speechless. I'd lost touch with our mutual friends long ago. With my mom gone, I had no conduit to information about Mary Beth. I had no idea her marriage had ended too.
I had a car phone that I used for work, and after I saw my mom's friend to her door, I returned to my sedan and called the number. Mary Beth's mom answered the phone. I introduced myself, unsure if she would remember me. She was happy to hear from me, and we talked for several minutes, catching up. Then she gave me Mary Beth's number. I made the call.
Her voice sounded exactly the same, and for an instant I was back under the nose of that T-33 at El Toro, home for Christmas with her rushing into my arms.
"Beth, this is Dan Pedersen."
Dead silence on the phone.
I said my name again.
Thinking this was a prank call from her brother, pretending to be me, she scolded me. This was not how I expected it to go.
I promised her I was not her brother. We started laughing with an effortlessness I hadn't felt in years.
"Are you in town? Where are you?" she asked.
"Put a pot of coffee on, I'll be right over."
She gave me her address and I began breaking speed limits.
I stepped out of the car in front of a well-kept condominium, dressed in a polo shirt, slacks, and good loafers. (Always wear a good pair of shoes, just in case you have the luck to run into the love of your life.)
The front door opened, and there she was, Mary Beth, looking as breathtakingly beautiful thirty years later as she'd been in every thought and memory that I had carried across the oceans. It seemed almost surreal. Thirty years. I never thought I would see her again. I realized I had felt her absence every day. It lessened with time, but never left me.
Who was I really thinking about on the day I ejected from my crippled F-4, chute opening late, swinging once, twice, before slamming into the water off La Jolla? It was the woman in front of me, dressed fabulously as always, looking at me with so much happiness and excitement.
I stepped toward her as she smiled and opened her arms. I reached her and went in for a hug. She had something more in mind. A gentle kiss, warm and open. Connecting. Not the kind you give an old friend; the kind you give your long-lost love.
I felt a strange sensation right then. The hole inside me disappeared. Time and distance held no meaning in the moment. When our lips parted, all I could see were her brown eyes looking into mine.
In them, I saw at last I was home.
# CHAPTER TWENTY-ONE
# SAVING TOPGUN
As I write this, I'm eighty-three years old. I still look up whenever a plane passes overhead. Now you know why. Flying was one great love of my life. For thirty years, it consumed everything, gave me everything I ever felt was valuable and valued. It gave me a home, both in the air and on sea or land. In the end, though, Mary Beth came along and showed me what I had been missing. More and better family moments. Love and connection between my kids that I never got to share while searching for targets south of Haiphong.
It is past midnight now. The moon is rising, and the airliners are still passing by as we sit beside the pool here. Truth is, I have only one regret: I should have found a way to spend more time with Dana, Chris, and Candice, who was born in 1980. In retrospect, there was no way either of my first marriages was going to survive the constant deployments, the politics, and the press coverage. They were fine women; I will always care about them, and I hope they will forgive me for my priorities and pursuits when we were together.
In time of war, our country needed us. I couldn't walk away when my friends were fighting for their lives against those flaming telephone poles and MiG-17s. When you take the oath and don the uniform, it changes you. It changes your priorities.
Take a look right there. See that light moving in the sky? I bet she's a 737 outbound from LAX. I see her every night around this time. Right on schedule; no delays at the gate or surly passengers, I guess.
God, how I loved flying. On a night like this, you could see for hundreds of miles at forty thousand feet. Crystal black sky overhead, lit with an infinite number of galaxies and their stars, the glittering cities below, like diamonds reflecting sunlight. Earth and life in all their beauty. Until you see it for yourself and feel how it opens you up and then hooks you like an addict, you'll never know what a transformative experience flying can be.
There aren't many military aircraft in this part of the sky at night anymore. With the budget cuts and the spare parts crisis, the crews just don't get much flight time. If I dwell on it, I worry about where we're going and what will happen to Topgun.
In 1993, the end of our rivalry with the Soviet Union triggered massive budget cuts and base closures. The peace dividend forced the Marines to move from El Toro to Miramar, which crowded Topgun out of the picture. Those running the show decided to move us to Fallon, Nevada, where it would fall under the Naval Strike Air Warfare Center, or "Strike U." Just like that, the plot of land with the dubious "view of the sea" where we had first parked our stolen trailer was no longer home. The attack aviators in the chain of command scored a decisive victory by forcing this move, one that ultimately imperiled our legacy.
Resentment against the fighter community and Topgun ran high in the mid-1990s. Not all of that was a result of the rock-star status the movie seemed to give us within the public. The controversy over the alleged sexual assaults at the Tailhook Convention in 1991 left a stain on naval aviation. As Rolland G. "Dawg" Thompson, then Topgun's CO, put it, "Topgun represented, to many, the last bastion of fighter aviation—the hallmark of what many on the outside of our culture despised at the time."
From the beauty, beaches, and pulse of Southern California, Topgun decamped for a place that seemed at times like the edge of civilization. The press paid a lot of attention to this, and as our trucks moved out, people lined the freeway holding signs, saying goodbye and wishing us well. More than one Topgun wife cried as they drove into Fallon, seeing the valley's desolation, feeling the high desert heat on their faces, and thinking of what they had left behind in San Diego. Their beautiful homes and fine schools—gone.
The chief of naval operations at the time, Admiral Jeremy Michael Boorda, protected us quite well, mandating that while the graduate school would come under the umbrella of Strike U, it would remain its own command. Based on Topgun principles of training, Strike U had once set high standards for the attack aviators that it trained. But by the time Dawg's boys began arriving, along with their eighteen Hornets and four Tomcats, the strike aircraft instructors were no longer even murder-boarding their lectures during instructor qualification. They didn't even have their own aircraft to fly and teach with.
Nineteen ninety-six was a year of tragedy for the Navy. The CNO, Admiral Boorda, took his life, leaving a note that explained his shame over wearing an unearned valor award on his uniform. After his death, Topgun apparently lost the last flag officer in a position to protect the school. With his passing, Topgun was demoted from an independent command to just a department of Strike U, under a two-star, a rear admiral.
I tell you, it broke my heart when we lost that fight. It broke the heart of all of us who'd devoted so much of our lives to create and foster Topgun, who had risked their careers to keep it going in the face of increasing hostility. Our success was living testimony to the ability of dynamic, creative, motivated junior officers to do great things. Was this message considered dangerous or something? I don't know.
I do know they even tried to take the name Topgun away from us. When Dawg showed up at Fallon one day after Admiral Boorda's death, he found that the Strike U headquarters building no longer had a sign reading "Topgun." It had been replaced with "N7," an obscure bureaucratic designator for the Navy Fighter Weapons School.
Boorda was replaced by Admiral Jay Johnson (who to this day remains the last aviator to become CNO). Dawg took this as a bad sign at first, as Johnson was a friend of the incoming Strike U commander, Rear Admiral Bernie Smith. Merging the attack and fighter communities into a single entity threatened to dilute our culture. But give Admiral Smith credit. Seeing what was at risk, he put Thompson in charge of all training. At the decommissioning change-of-command ceremony, Dawg invited his boss as guest speaker, just to make sure he was in attendance. That's where the Topgun skipper made a dramatic declaration: "I will compromise my career before I compromise the standards of this organization." He would make good on the promise.
The Strike U establishment at Fallon ended up leaving the Topgun Bros alone, though their wives were very unhappy with the way they were treated by the established social clique at Fallon. It mattered. The divisive atmosphere hurt morale badly, which was part of why more than a few well-qualified people turned down orders to go to Topgun. Its prestige had been badly diminished by making it just a department in the "Strike U" with command leadership going from a junior officer to a rear admiral.
Dawg realized he had to change things. Leveraging his position as director of training, he required Topgun's instructors to become involved with the strike curriculum too. "The game plan was that they were not going to absorb us; we were going to absorb them," he said. That was easier said than done. The schism persisted.
But so did Topgun. With Dawg flying top cover to preserve the integrity of the program, his junior officers did what they've always done—they continued the mission. This is how bureaucratic warfare is waged in the military. Organizations come and organizations go, but they can often be saved by someone who is willing to swallow his pride and pursue a matter of principle with calm conviction. I credit Rolland Thompson for saving the program in a very difficult time. When one of his instructors, Richard W. "Rhett" Butler, returned as CO of the Topgun department six years later, he was gratified to notice that the "N7" label on the wall was gone. It had been changed to "Topgun Training Department."
It's not well realized even in our community how precarious our existence was during the move from Miramar to Nevada. Reportedly about 80 percent of the junior instructor pilots were prepared to leave the Navy. But with Dawg's leadership guiding the success of the combined strike fighter training program, most all of them stayed for a full tour. If not for our resilient group of JOs, who were given strong direction by their devoted leader, Topgun might well have ceased to exist.
I try not to think about all this needless bureaucratic infighting, especially on gorgeous nights like this one. I come out here by the pool for peace. Sometimes I relive the best moments of my career and feel that old sense of pride return. You know, though? As much as I loved the flying, the best moments to me now were those where we saved lives. The couple stranded off Baja, the boat full of dying refugees we rescued in the South China Sea. Those were the best moments.
It is one of life's great beauties—and mysteries—how things put in motion years before can well up from the past to alter your present. The boat full of refugees turned out to be one of those pivotal episodes in my life. Many years later, in 1998, I received a call from the Navy's chief of information in Washington. He told me that one of the survivors we rescued in the South China Sea back in 1981 wanted to meet with me. He had been thirteen years old when his mother, brother, and two sisters paid for passage aboard that decrepit boat. He never forgot the sight of our carrier pulling alongside, the big number "61" painted on the side of the island superstructure. Now he wanted to thank me in person for stopping and saving 138 strangers.
I readily agreed, thinking we would just talk on the phone. Instead, the Navy asked if we could meet on the set of _Good Morning America_. I'll tell you what, I never thought that a moment on a soundstage would lead to so many great things in my life. Lan Dalat came on camera next to me, and from that first greeting, I knew we were destined to be close.
His family stayed for several months in the refugee camp on Luzon before emigrating to Washington State. Later, they moved to Southern California in search of a warmer climate that was a bit more like home for them. Lan and his siblings suffered bullying in the public school system. They were called names, derided for being "boat people." It was a tough and sometimes cruel end to childhood as he came of age in his adopted country, but the opportunities America offered were seized upon by his family.
All four kids graduated from college and embarked on highly successful careers, starting families along the way. Lan asked me to come speak at his college graduation, and later at his commissioning ceremony in the U.S. Army. I did the same with his brother Tony, who served in the Army's Special Operations Command during the war in Afghanistan.
More than just about anyone I've ever known, Lan Dalat and his family understand the real heart and real power of America, and they devoted their lives to defending those things.
Want to know the best part of their story? At least to me, anyway, but I'm biased of course. When Lan got married and had a baby boy, they named him Dan, after me. I think about that and get emotional. I almost lost my tribe, my brotherhood, when I left the Navy in 1983. In my worst and most isolated moments, I made plans to refit a 110-foot oceangoing tug so I could once again sail away to sea. I was going to ride the Pacific waves to Japan, the Philippines, or wherever else the wind and stars took me. It sounded romantic. It would have been desperately lonely.
I went from that low point to reconnecting with Mary Beth. Then Lan Dalat and his family entered my life. Old friends retired from the Navy, and almost all the Original Bros settled down close by in Southern California.
On March 1, 1983, I started my new life as an alienated civilian, unsure what my path might be in a country I had defended all my life but no longer knew. In the end, my new normal became a full and happy life, filled with love and friendships and family—my kids, Beth's kids (we have a Brady Bunch–sized clan these days), and the men I went to war with back in our youth.
Topgun's Original Bros get together for dinner periodically, though there are only seven left of the original nine as I write this. Beth and I waited over a year after our doorway moment, then I flew her to Denmark and married her in the church my dad had been baptized in as a child before his family, just like Lan's, made the journey to America's shores.
Beth and I made up for lost time in the 1990s and after the turn of the millennium. We worked together, built things together, explored and traveled and celebrated life. She was my missing part, and when she fit into my heart again, there were no more bad days.
I do worry, though, that those who took our place in the cockpit will face bad days in the years to come.
# CHAPTER TWENTY-TWO
# WILL WE HAVE TO LOSE A WAR AGAIN?
## (or, Back to the Future in an F-35)
Just like the old F-4 Phantom, the F-14 Tomcat will live long in the memories of fighter pilots. The famous plane met its end in 2006. Focused on acquiring the Tomcat's replacement, the F-18 Hornet, and the A-12 Avenger II stealth bomber, an upgrade for the A-6 Intruder, the Navy decided there wasn't enough money to keep the Tomcats flying. It didn't help the old bird's cause that the secretary of defense, Dick Cheney, seemed to have it in for New York's congressional delegation. Grumman Aircraft was located on Long Island. As the Pentagon's axe fell, it was a sad case of the new and the expensive driving out the affordable and the reliable. When Secretary Cheney ended the lives of those two iconic Grumman carrier planes, the Intruder and the Tomcat, the future got a whole lot more costly.
The Navy's $4.8 billion contract with McDonnell Douglas and General Dynamics to build the A-12 became a fiasco of lawsuits. It never produced a single aircraft. The litigation lasted twenty-three years, ending with the contractors repaying some $400 million to the government. Stealth technology was at the heart of the dispute. The contractors said that they could not deliver on schedule with the government withholding classified data on its requirements for radar-evading features. They had a point. According to former Topgun skipper Lonny "Eagle" McClung, "The A-12 was in the black world"—highly classified. "You could not take the material to your desk. You had to read it in a vault." But the Pentagon seemed to be putting a great deal of faith in stealth.
"We were selling our soul for stealth," Eagle said. "The attitude in the Pentagon was that if we did not come up with stealth, the USAF would own the strike mission. I kept saying that somewhere in some dark basement in Eastern Europe was a group of guys wearing glasses about as thick as Coke bottles who were figuring out how to defeat stealth.... The airplane had a lot of problems. Cancelling the thing saved the Navy from itself."*
In the end, the F-18 was reengineered to handle the A-12's mission. Today the Super Hornet, as the F/A-18's E and F models are known, is performing that role well enough, though with a combat range that doesn't come close to the old Tomcat's.
How sad that the only F-14s that you'll find in service today are flying for the government of Iran, which began acquiring them in 1976, when Tehran's leaders were friendly to the United States and we were happy to help them counter the Soviet Union's vaunted MiG-25 Foxbat. Decades after America lost Iran, following the rise of the ayatollah, Secretary Cheney killed the F-14 in part to shut down the availability of spare parts for the Persian Tomcat squadrons. But somehow, to this day, Iran is proving up the F-14's reliability and maintainability by flying it alongside Russian bombers on strikes into Syria. (I can remember that some Iranian pilots were posted at VF-121 at Miramar on foreign exchange, back in the day. All they did, I remember, was chase American women and spend money on fancy new cars. They were lousy students.)
When I poke around the Internet today, catching up with the posts on my naval aviation mail lists, I find a lot of comments from chief petty officers who maintained the F-14 when it was in its prime. Their constant refrain, in essence, is "OMG, if only we had that airplane again." Most of these guys are really sharp. They want the Navy to retool and resume building Tomcats, upgraded a bit but mostly just like they were. I feel as they do. The evolution toward high technology has pushed us backward in many ways. And the Iranians are having a laugh, I'm sure, still flying one of the best fighter aircraft ever built to serve the U.S. Navy.
There's nothing new about an old guy with all the answers. So, at the risk of playing to type, please allow this former aircraft engine mechanic to complain that our country has been put at risk by the Pentagon's fascination with stealth technology. We've lost the lessons we learned painfully in the 1960s. We worship at high technology's altar and are on the verge of selling our souls. Stealth is like a zombie—a very expensive zombie. It's coming back to life to haunt us.
The new aircraft that is supposed to replace the F/A-18 someday is Lockheed Martin's F-35 Lightning II. The stealth-equipped "multi-purpose aircraft" is designed to do all things. Three different models of this "fifth-generation" plane are in development to meet the needs of the Navy, Marine Corps, and Air Force. We ought to have learned a lesson from the failure of Robert McNamara's F-111 "Flying Edsel," which was supposed to serve both the Air Force and Navy. But we did not. So now comes the F-35 in three flavors: the Air Force A model, the Marine Corps B model (a short takeoff/vertical landing model that will replace the AV-8 Harrier jump jet), and the Navy F-35C.
With total program costs figuring to exceed a trillion dollars, the F-35 is the most expensive weapons system in history.* The unit production cost of the Navy variant (not counting development and testing costs) has been pegged north of $330 million and growing.†
The late, great John Nash used to say that modern aircraft components are designed to fail. Defense contractors have done a good job ensuring the profit margin in "line-replaceable units," as they call spare parts today. In total, over the life of the program, the parts will cost more than the aircraft do. Think of the inkjet printer you bought at the office warehouse for $75. The ink cartridges will set you back half again that amount every six months. That's basically true in the high-performance aircraft business, too.
The F-35 is so expensive I fear we'll end up with a fleet full of beautiful new nuclear-powered supercarriers with partially empty flight decks. There's simply no way the U.S. Treasury can afford to buy the numbers we'll need to fill out the air wings.
The F-35's problems are many, from the tail hook, which basically just didn't work, to the oxygen system for the pilot, to the super-sophisticated helmet, built with advanced sensors, an information-packed visor display, and the ability to aim weapons by line of sight, based on the pilot's head movements. The unit price for that fancy dome was $400,000, but who knows what it really costs? The total program cost of this aircraft continues to rocket skyward like an F-4 Phantom heading to the top of the Egg. Meanwhile, the nickname for the F-35 among pilots who have lost confidence in it is "the penguin." It flies like one.
No one agency can fix this problem. Not the Navy or the other services, not the defense contractors, and not Congress. Each of these has powerful incentives to avoid doing the right thing. The lucrative subcontracts associated with the F-35 are spread strategically across most every congressional district in America. With so many House members having a stake in the program, it is assured to have broad-based political support, regardless of its actual capabilities or costs. So when a defense contractor proposes a new feature for the new aircraft, even if it's not one that the Navy's frontline squadrons want or need, there's nobody on hand to say no. Why would some rear admiral at the Pentagon stand in the way of a "yes" vote for the Navy's appropriations in the House of Representatives by turning down the unwanted bells and whistles? A lot of those admirals, you know, have golden parachutes waiting for them after they retire—a well-paying job as an executive vice president at that one-and-the-same company. Should he risk the windfall by asking questions?
One question deserves to be whether we even need such expensive capabilities as stealth in our planes. I'm not so sure. New sensors that are within the current capability of Russia and China to field don't even use radar waves. These infrared search-and-track devices can detect the friction heat of an aircraft's skin moving through the atmosphere, as well as disturbances in airflow.
Yet the defense contractors' marketing brochures, and a few pilots too, assure us that the F-35 is "transformational." According to the Lockheed Martin website, "With stealth technology, advanced sensors, weapons capacity and range, the F-35 is the most lethal, survivable and connected fighter aircraft ever built. More than a fighter jet, the F-35's ability to collect, analyze and share data is a powerful force multiplier enhancing all airborne, surface and ground-based assets in the battlespace and enabling men and women in uniform to execute their mission and come home safe."
That pitch makes the F-35 sound like an early warning aircraft—transformational indeed. It doesn't say anything about winning a dogfight. Maybe that's the point, because the pilots who have a lot of experience flying the "penguin" say it's no dogfighter. My ears are ringing from the echo of the nonsense we heard in the '60s about the F-4 Phantom transforming the fighter pilot's traditional mission.
At Topgun in my day, a pilot had to log a minimum of thirty-five to forty flight hours every month to be considered combat-ready. This is no longer possible. As the F-35 continues to swallow up the money available to naval aviation, the low rate of production all but ensures that our pilots will not soon gain the flight hours that they need to get good. For the past few years Super Hornet pilots have been getting just ten to twelve hours per month between deployments—barely enough to learn to fly the jet safely. The F-35 has far less availability. Its pilots have to rely on simulators to make up the deficit. Its cost per flight hour is exorbitant.
But the magnitude of the problem of the F-35 is probably best understood in terms of time rather than money. And here it is in a nutshell: We are twenty-seven years into the development cycle of that plane.
After twenty-seven years and untold billions spent, no fully operational version of the F-35 has reached a U.S. squadron. That's right. Development started in 1992, yet it has not achieved operational status in any of the services that have ordered it.* The photos we see of the aircraft flying are misleading. Not one of these planes is ready for combat. The Israelis claim to have used the export model of the F-35 in an engagement. I don't know if that's true, but it's possible the lucrative foreign market for the plane helps explain its undeserved longevity after nearly three decades of delays and cost overruns. Israel, Japan, and South Korea are supposedly on board to buy it, as are the eight other "partner nations" who are helping to develop it. Unfortunately, the program has run so long that one of those partners, Turkey, is on the verge of no longer being a U.S. ally. (Maybe they'll still fulfill their contract with Lockheed to keep supplying important parts for the F-35 as they cozy up to the Russians.)
Twenty-seven years. That's more than a generation. Compare that to the development timeline of the F-14 Tomcat. The elapsed time from the Navy's first request for proposals to the deployment of the F-14 in the fleet was four years. Yes, four years. With the F-18 Hornet, it was nine years.
Now twenty-seven?
Something is rotten in Washington, and one day, sadly, we will lose a war because of it. Maybe that tragic result will serve to wake up our political and defense establishments and give them the courage to begin removing the rot.
Meanwhile, the state of the art in air-to-air combat as it's actually practiced over the battlefields of the world doesn't seem to have advanced very much. The future looks a lot like the past. Let me tell you a very recent story.
On June 18, 2017, Lieutenant Commander Michael "Mob" Tremel, a Topgun graduate and former instructor, took off from USS _George H. W. Bush_ in an F/A-18E Super Hornet. Flying a close air support mission near Raqqa, Syria, he led four Super Hornets inland to join a "stack" of jets waiting their turn to bomb Islamic State positions. That was when he and his cohorts detected the Syrian aircraft. The approaching pilot ignored numerous warnings to turn away. After a Sukhoi Su-22 Fitter made a bombing run on allied troops, Commander Tremel engaged.
Adhering to the rules of engagement, he made visual identification and fired an AIM-9X Sidewinder. The enemy pilot detected the launch and dropped flares. The missile, "spoofed" in spite of all its advanced features, missed. Tremel switched to a radar-guided AMRAAM—the Sparrow's replacement—and fired. The eight-minute affair ended with the Syrian plane exploding, leaving Tremel to dodge a cloud of debris. The pilot, Captain Ali Fahd, ejected and floated to earth below his chute. It was the first victory by an American fighter pilot since the spring of 1999, when Air Force pilots bagged three Yugoslav MiG-29s in the Kosovo War.
In the 2017 action, three of the four Hornet pilots were Topgun grads, so they would be well qualified to teach us the lessons here, which are familiar. First, high technology can still be foiled by simple countermeasures. Missiles are never a sure thing. But the real lesson was that, against the fashionably futuristic expectations, Tremel was forced to fight in close visual range because the rules of engagement required it. Why spend fortunes on technology that our own rules of engagement make useless?
Even if its many problems are solved and it's fielded in numbers that matter, the F-35 and its beyond-visual-range capability will mean nothing if the pilot has to see and identify his target before shooting it. That has been true now for more than forty years. As Condor says, "If you can see him, he can see you, and you're in a dogfight." This is not where the "penguin" is at its best. At least it will, apparently, have a gun. That's one thing they might be getting right.
I was a pretty good fighter pilot, but I might be old-fashioned. I devoutly believe that simpler is better. I've learned that lesson repeatedly in my career. After thirty years in naval aviation, I can tell you what a plane can do in the air by looking at its engine specs and the sweep of its wings and its tail. Few planes I've seen are better dogfighters than the tried-and-true F-5, the old Northrop birds we used at Topgun as aggressors. Some are still in service today.
At night, sometimes while I lay beside the pool watching the jets and satellites ease by overhead, I use my imagination to design my ultimate fighter aircraft. I'd make it a basic hot rod, a single-seater akin to the old F-5. Light, maneuverable, and compact—hard to see in a fight. I'd want it cheap, easy to mass-produce and replace should we start taking losses in combat over time.
The cockpit systems will be engineered to avoid overwhelming the pilot's senses with data. My pilots will not be emotionally and mentally overloaded by the bells and whistles that characterize the fifth-generation cockpit. The Navy busts its budgets by installing integrated command and control electronics, but most pilots I know don't touch them. So we'll get rid of them. My guys won't need a non-combatant staffer or distant admiral somewhere hearing all their comms and butting in to micromanage. The only conversations they'll need are with a good radar controller somewhere, their mother carrier, and their squadron mates.
That little hot rod will cost less than ten million dollars apiece, and so we'll never have to sell it to a foreign country. Except to the Brits and the Israelis, of course. With the money we save, the enlisted men in the maintenance hangar will have everything they need. The defense contractors can golf on their own dime.
Give me a few hundred planes like the F-5N, with a reliable gun, a lead-computing gunsight, four Sidewinders, electronic countermeasures support, and pilots who get forty or fifty flight hours a month, and we'll beat any air force that's bankrupting its nation with fifth-generation stealthy penguins. Pilot retention problems will go away.
Because the basic truth of fighter combat remains the same: It is not the aircraft that wins a fight, it's the man in the cockpit. Flying is a perishable skill. It has to be practiced constantly and maintained on a consistent basis. That isn't happening anymore, thanks to the year-to-year budgeting process called for by "the sequester" and its defense cuts. And on that count, looking back, I can see that as bad as things looked to us over Vietnam, my comrades and I may well have flown in the best of times.
Darrell "Condor" Gary's logbook for June 1976 shows that he flew forty-six flights that month for a total or 65.5 hours, including five in the F-4N Phantom, seventeen in the A-4E Skyhawk, and twenty-four in the F-5E Tiger. All of these were real air combat maneuvering flights, not cross-country transits. With that much time in the air, Condor says, you couldn't avoid becoming proficient as a warrior.
My boys will all be dogfighters. With enough planes in inventory, we can return to the days when any pilot who's in good with the senior chief in maintenance control can check out a bird and go find a "fight club" somewhere off the coast. That's how we'll sharpen our edge in dogfighting again. Give those boys lots of flight hours under heavy-caliber leadership and they'll win almost every time. I feel so strongly about the need for more pilot training that I'd propose this: We should consider tapping our federal petroleum reserve for jet fuel production, so that our aviation training commands can keep new pilots flying every day. If we wait until we're at the threshold of a war before doing it, it will be too late.
I run through this mental exercise often. Always I come back to our Topgun axiom: What matters is the man, not the machine. So let's talk about what a good fighter pilot candidate looks like. Over the years and thousands of aviators I've known, I noticed the best shared some common traits.
A good pilot should have a strong family background with a patriotic mindset and a self-starting work ethic. He should believe in something greater than himself while remaining self-reliant and confident without being overbearing. (Some ego is necessary—I wouldn't want a soul filled with doubt flying my wing.) An athletic background helps, because when properly coached at the right age, youngsters learn trust, teamwork, and goal setting. They'll need all those things in the air. I'll pass on anybody who displays his participation trophies. Self-esteem without real accomplishment will make anyone crash and burn. Give me a committed B student with a boiling will to win over an A-plus scholar with a careerist agenda, and we'll be on our way.
Finally, it's important to have a sincere interest in the history and lore of your calling. Good pilots strive constantly for self-improvement. In my first years in the Navy, I had the opportunity to meet the World War II generation and hear their stories and lessons. I read every air combat memoir I could and gleaned a lot of little things from them that helped me in my journey. We lived on the edge of life and death, and the margin between them was narrow. I think Jimmy Doolittle bought me a scotch because he saw that we had shared residency there. History is a wellspring of lifesaving lessons. No one really invents anything.
Successful leaders recognize those traits and encourage them, even at the risk of bending a rule—or a jet—once in a while. Just like we did in Miramar every day, and much as you saw in that thirty-three-year-old movie, long may it stream. In between its scenes of beach volleyball, romantic sunset motorcycle rides along the runway, and crazy, dangerous moves in the air, the movie has some important messages. It reminds me of better days. And I think that reminder can help us today, if we let it.
Well, that's what naval aviation would look like if I were King of Everything. Since I'm not, I think I ought to call it a night. Come on inside; I have one last thing to show you.
I kept my 1950s Ray-Bans until just a few years ago, when I replaced the lenses and gave them to my granddaughter, at her request, as a Christmas gift. After fifty years, I figured it was time for a new pair. My youngest daughter, Candice, ended up with my Star of David and gold chain. But I still have my little mouse. After all the sea duty he endured, he enjoys a cushy retirement on my bookshelf. From time to time I look at him and say, _It was a hell of a ride, wasn't it, little fella?_
He is surrounded by books and other treasured items from my career. But what I value most was my time at Miramar with the Bros. Their enduring friendships are my real treasures, not any physical things in my library. Topgun will always be the centerpiece of my career and my life's most important accomplishment. None of it would have happened without the Bros, or the ever-present hands of God.
In 1956, at Whiting Field, in Florida, I entered primary flight training to become a naval aviator. We flew the legendary North American SNJ. Those well-worn birds were usually oil-streaked, like this one.
Ensign Pedersen at NAS North Island, 1959, with my first operational squadron, VF(AW)-3. Flying the F4D Skyray, I learned from such great pilots as World War II ace Eugene Valencia.
Standing twenty-four-hour alerts with our "Fords," we were always ready to intercept a Soviet bomber attack before it reached the West Coast.
An F-4 Phantom intercepts a Soviet Tu-95 Bear somewhere over the western Pacific. These encounters were usually quite friendly.
America's first nuclear-powered carrier, USS _Enterprise_ , became my home on Yankee Station in 1967. In four months, our air group lost thirteen of its hundred pilots.
An F-4 Phantom releases a load of Mark 82 bombs over South Vietnam. By 1967, the Navy was suffering from a shortage of bombs.
Four North Vietnamese pilots with twenty U.S. aircraft to their credit at a runway near Hanoi. We were not prepared for close-in dogfights against the agile MiG-17. Defeating the Russian-built interceptors became the founding premise of Topgun.
The boldfaced names were my Original Bros at Topgun. I told them our mission would be the most important thing we did in our military careers. "We hold lives in our hands."
Jim "Hawkeye" Laing, one of our Original Bros, stands beside his F-4 Phantom prior to the first strike against Kep Airfield near Hanoi in April 1967. Laing was shot down during this mission and was later rescued by helicopter.
Jim Laing was the only Original Bro to eject twice as a result of battle damage over North Vietnam. This stunning photo, taken by Jim's wingman, shows him ejecting on April 24, 1967, after the strike on Kep. His pilot ejected a split second later.
Mel "Rattler" Holmes was the finest Phantom pilot in the Navy in 1969. Tough, relentlessly aggressive in the air and on the ground, Mel was a key part of Topgun's initial success as our tactics and aerodynamics specialist.
Darrell "Condor" Gary and Jim Laing aboard _Kitty Hawk_ on Yankee Station, on April 24, 1967, hours before Jim and his pilot were shot down and later rescued.
Jerry "Ski-Bird" Sawatzky towers over Mike Guenther, one of our adversary pilots, as they stand in front of a pair of A-4 Skyhawks. Jerry was a natural teacher at Topgun and a superb aviator too.
Once we had our team assembled, we needed an office and classroom space. Steve Smith found this abandoned modular trailer and paid a crane operator a case of scotch to deliver it to our area at Miramar.
Mel Holmes and Steve Smith designed the Topgun patch in the Miramar officer's club one night on a cocktail napkin. Complaints that it might offend the Russians soon ceased.
At Topgun, we painted our aggressor A-4s in camouflage schemes used by air forces around the world. Some of those paint jobs rendered the little aircraft almost invisible.
Here I am with J. C. Smith in a TA-4 Skyhawk belonging to Ken Wiley's VF-126. Ken's Skyhawks became Topgun's initial adversary aircraft.
A MiG-21 flies over Area 51. Captured Soviet aircraft played a key role in helping us develop the tactics to defeat them.
From April through October 1972, during Operation Linebacker, F-4 squadrons downed twenty-one MiGs, losing just four aircraft in return. The stunning success validated the Topgun program.
Though we learned to beat the MiGs, the war ended in defeat in 1975. Condor flew high cover the day the last Americans were evacuated from rooftops around Saigon. Meanwhile, the South China Sea was carpeted with hundreds of vessels filled with refugees fleeing the North Vietnamese Army.
After Vietnam, Topgun continued teaching new generations of fighter pilots. Here, a Topgun instructor demonstrates maneuvering an F-14 Tomcat against a MiG-21 during a class in the mid-1970s.
An adversary TA-4 painted in a Soviet Air Force scheme.
One of Topgun's F-5 adversary aircraft goes vertical off the California coast. The Freedom Fighter did a fine impression of a MiG.
After leaving Topgun, I took over VF-143 and in 1976 commanded the _Coral Sea_ air wing.
The F-14 Tomcat reached the fleet in the mid-1970s and served until 2006. Made famous by the movie _Top Gun_ , the F-14 was beloved by all who flew it. I regret that I never did.
When the Navy promoted me to captain in 1978, my flying days were over. I commanded the fleet replenishment ship USS _Wichita_ then took the aircraft carrier _Ranger_ to the Persian Gulf.
At sea aboard the _Wichita_ , I'm in the dark jacket surrounded by the bridge crew. The ship won several highly coveted Battle Efficiency Awards ("Battle E's") for superior performance in an operating environment.
The _Ranger_ and one of her escorts replenish at sea. Taking command at Subic Bay in October 1980 was the capstone of my career.
Monroe "Hawk" Smith was my air ops officer on the _Ranger_. He was the skipper of Topgun from 1976 to 1978.
Mary Beth and me at my parents' home in Whittier, California. I flew home from flight training in Texas over Christmas 1956.
Mary Beth and I reconnected thirty-two years after our breakup. We were married in Denmark, in the church that had baptized my father. The ring on my finger is the one she gave me for Christmas in 1956.
The Navy and Air Force have staked their futures on the F-35 Lightning II. Development of the so-called Joint Strike Fighter (some pilots call it the "penguin") began in 1992. Twenty-seven years later, we do not yet have a fully operational squadron and it is the most expensive weapons program in history.
Mel Holmes, myself, Darrell Gary, and Jim Laing at Condor's house in Southern California in April 2017, almost fifty years after we stood up Topgun.
# ACKNOWLEDGMENTS
This book has been in the works for about eighteen months. It all started when Jim Hornfischer, president of Hornfischer Literary Management, contacted one of Topgun's Original Bros, Darrell Gary in San Diego, to discuss a legacy book to be written and published in time for the fiftieth anniversary of Topgun. As I had been the original Topgun leader during the formation of the Navy Fighter Weapons School in 1968 and 1969, Jim felt I should tell Topgun's story by way of a personal memoir. Jim helped us develop the idea, brought our proposal to New York, and set us up with Hachette Books, my estimable publisher.
For the first year of this effort, I had the honor of working closely with naval aviation's premier historian, Barrett Tillman. Barrett's work is the gold standard of naval aviation history, based on his dozens of books and hundreds of articles in his award-winning career. Working under an extremely short deadline, we thoroughly researched and co-wrote the original draft, providing accuracy and authentication while we recounted most of the story. It was the experience of a lifetime to share my naval aviation career and Vietnam experience with this fine man. He is a walking encyclopedia of naval aviation. Our relationship has grown.
When the original manuscript was delivered, it was decided that more could be added to the story. In the final two months in which the book was finalized, John R. Bruning Jr. helped me to transform it into what it is today. John and I became fast friends as we worked daily to adapt the original manuscript on a tough schedule. It was a true pleasure to work with and learn from him. He has authored or co-authored twenty-one military books, including _House to House_ , _Outlaw Platoon_ , _Level Zero Heroes_ , _The Trident_ , and _Indestructible_ , and has embedded with our combat ground forces in the Afghanistan war. He is one special American.
As my literary agent, Jim Hornfischer navigated the project from beginning to completion and helped shape the final manuscript. An author in his own right (recipient of the Samuel Eliot Morison Award for his work, which includes _The Fleet at Flood Tide_ , _Neptune's Inferno_ , _Ship of Ghosts_ , and _The Last Stand of the Tin Can Sailors_ ), he is a skilled literary guide who worked tirelessly to help me tell this story the right way.
It truly was a once-in-a-lifetime experience to recall and relive my life and Navy career with the assistance of these gifted professional gentlemen. The true legacy of the Navy Fighter Weapons School would not have been told without their devotion and close involvement. They can fly my wing anytime.
My publisher at Hachette Books, Mauro DiPreta, has been a great advocate for this book and a skilled editor of the manuscript. Thanks also to his very capable assistant, David Lamb, and to the rest of the Hachette Books publishing team, including associate publisher Michelle Aielli, marketing director Michael Barrs, and senior publicist Sarah Falter. All of them play key roles in the work of bringing a new book to the public.
The founding instructors of Topgun, the Original Bros as we call each other, gave life to the new organization and have been friends of mine since we began our association more than fifty years ago. My thanks to these great patriots: Darrell Gary, Mel Holmes, Jim Ruliffson, John Nash, Jerry Sawatzky, Steve Smith, J. C. Smith, Jim Laing, and Chuck Hildebrand. With the outstanding leadership of succeeding generations, including forty-two skippers, numerous young instructors, and the always-hard-working enlisted maintenance crews and staff, the Navy Fighter Weapons School grew to international fame. I thank you all for the risks you took, your sacrifices and those of your families, and your superb performance over many decades. This story, our story, is one that I've longed to tell. I hope I've done it right, because we all did it right, back when our country needed us. You were then, and you are today, the best of the best.
Special thanks to the Navy's greatest sailors. Master Chief David M. Hobbs, a great friend with whom I served in USS _Ranger_ , is at the very top of that list.
It was my family who made everything possible. My grandfather, Arthur Lamp, was my guiding light. My folks, Orla and Henrietta Pedersen, always encouraged me.
Lastly, my wonderful Mary Beth: This book is dedicated to you for your sustained and sustaining support and love for all these many years. You made it all complete.
# GLOSSARY OF ACRONYMS AND TERMS
**AAA:** | Antiaircraft artillery
---|---
**AAW:** | Antiair warfare
**ACM:** | Air combat maneuvering
**ACMI:** | Air combat maneuvering instrumentation
**ACMR:** | Air combat maneuvering range
**AIM:** | Air intercept missile
**AOR:** | Underway replenishment ship
**Bandit:** | Hostile aircraft
**BarCAP:** | Barrier combat air patrol
**Bogey:** | Unidentified aircraft
**BOQ:** | Bachelor officers' quarters
**CAG:** | Air wing commander
**CAP:** | Combat air patrol
**CCA:** | Carrier controlled approach
**CNO:** | Chief of naval operations
**CO:** | Commanding officer
**ComFit:** | Commander, Fighter and Airborne Early Warning Wing
**ComNavAirPac:** | Naval Air Force, U.S. Pacific Fleet
**CV:** | Aircraft carrier
**CVN:** | Nuclear-powered aircraft carrier
**CVW:** | Carrier air wing
**DCNO:** | Deputy chief of naval operations
**ECM:** | Electronic countermeasures
**FAGU:** | Fleet Air Gunnery Unit
**FAST:** | Fleet air superiority training
**FRS:** | Fleet replacement squadron (RAG)
**GCA:** | Ground-controlled approach
**IFF:** | Identification friend or foe transponder
**IP:** | Instructor pilot
**J.G.:** | Junior grade
**JO:** | Junior officer
**LSO:** | Landing signal officer
**MCAS:** | Marine Corps Air Station
**MiGCAP:** | MiG combat air patrol
**NAS:** | Naval air station
**NFWS:** | Navy Fighter Weapons School (Topgun)
**NAWDC:** | Naval Air Warfare Development Center (previously NSAWC)
**NSAWC:** | Naval Strike and Air Warfare Center
**OP-05:** | Office of the CNO, deputy chief of naval operations for air
**RAG:** | Replacement air group (FRS)
**RIO:** | Radar intercept officer
**ROE:** | Rules of engagement
**SAM:** | Surface-to-air missile
**TarCAP:** | Target combat air patrol
**VA:** | Attack squadron
**VAW:** | Airborne early warning squadron
**VF:** | Fighter squadron
**VF(AW):** | All-weather fighter squadron
**VFA:** | Strike fighter squadron
**VS:** | Antisubmarine squadron
**VX:** | Air test and evaluation squadron
**WestPac:** | Western Pacific
**XO:** | Executive officer
# TOPGUN OFFICERS IN CHARGE AND COMMANDING OFFICERS
**Officers in Charge**
**1969** | Dan A. "Yankee" Pedersen
---|---
**1969–71** | John C. "J. C." Smith
**Commanding Officers**
**1971–72** | Roger E. "Buckshot" Box
---|---
**1972–73** | David E. "Frosty" Frost
**1973–75** | Ronald E. "Mugs" McKeown
**1975** | John K. "Sunshine" Ready
**1975–76** | James H. "Cobra" Ruliffson
**1976–78** | Monroe "Hawk" Smith
**1978–79** | Jerry L. "Thunder" Unruh
**1979–81** | Lonny K. "Eagle" McClung
**1981** | Roy "Outlaw" Cash Jr.
**1982–83** | Ernest "Ratchet" Christensen
**1983–84** | Christopher T. "Boomer" Wilson
**1984** | Joseph "Joedog" Daughtry Jr.
**1984–85** | Thomas G. "Otter" Otterbein
**1985–86** | Daniel L. "Dirty" Shewell
**1986–88** | Frederic G. "Wigs" Ludwig Jr.
**1988–89** | Jay B. "Spook" Yakeley III
**1989–90** | Russell M. "Bud" Taylor II
**1990–92** | James A. "Rookie" Robb
**1992–93** | Robert L. "Puke" McLane
**1993–94** | Richard "Weasel" Gallagher
**1994–96** | Thomas "Trotts" Trotter
**1996–97** | Rolland G. "Dawg" Thompson
**1997–99** | Gerald S. "Spud" Gallop
**1999–2001** | William "Size" Sizemore
**2001–03** | Daniel "Dix" Dixon
**2003–04** | Richard W. "Rhett" Butler
**2004–05** | Thomas M. "Trim" Downing
**2005–06** | Mike R. "Trigger" Saunders
**2006–07** | Keith T. "Opie" Taylor
**2007–08** | Michael D. "Dice" Neumann
**2008–09** | Daniel L. "Undra" Cheever
**2009–10** | Paul S. "Dorf" Olin
**2010–11** | Matthew L. "Yodel" Leahey
**2011–12** | Steven T. "Sonic" Hejmanowski
**2012–13** | Kevin M. "Proton" McLaughlin
**2013–14** | James D. "Cruiser" Christie
**2014–15** | Edward S. "Stevie" Smith
**2015–16** | Michael A. "Chopper" Rovenolt
**2016–18** | Andrew "Grand" Mariner
**2018–** | Christopher "Pops" Papaioanu
# PHOTO CREDITS
Photos courtesy of the author, except for the following: (here, here) U.S. Navy photograph; (here, here) U.S. Navy photograph (here) National Archives photo courtesy of Jack "Ordy1" Cook; (here) U.S. Navy photograph; (here) courtesy of Jim Laing (here) U.S. Navy photograph; (here) U.S. Navy photograph; (here, here) U.S. Navy photograph; (here, here) U.S. Navy photograph (here) courtesy of Darrell Gary; (here, here, here) U.S. Navy photograph; (here) U.S. Navy photograph; (here, here) U.S. Navy photograph; (here, here) U.S. Navy photograph; (here, here) U.S. Navy photograph; (here, here) U.S. Navy photograph; (here) © John Bruning (here) © Jim Hornfischer.
* That's the acronym for Readiness Air Wing 12, which was VF-121's parent command at Naval Air Station Miramar.
* Although the Navy always uses the term "Topgun" in one-word form, the filmmakers insisted upon using two words. I guess it looks better that way on movie posters—or on the cover of a book, like this one.
* McClung is quoted here from Barrett Tillman's fine book _On Wave and Wing: The 100-Year Quest to Perfect the Aircraft Carrier_ (Washington, DC: Regnery History, 2017), p. 272.
* Valerie Insinna, "4 Ways Lockheed's New F-35 Head Wants to Fix the Fighter Jet Program," _Defense News_ , July 14, 2018, www.defensenews.com/digital-show-dailies/farnborough/2018/07/10/4-ways-lockheeds-new-f-35-head-wants-to-fix-the-fighter-jet-program/. Accessed by the author on August 23, 2018.
† Winslow Wheeler, "How Much Does an F-35 Actually Cost?," _War Is Boring_ , Medium, July 27, 2014, https://medium.com/war-is-boring/how-much-does-an-f-35-actually-cost-21f95d239398. Accessed by the author on August 23, 2018.
* In 2015, the Marine Corps prematurely declared its version, the F-35B, operational, although its systems, including its eight million lines of software code, remain plagued with problems.
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# Contents
1. Cover
2. Title Page
3. Copyright
4. Dedication
5. Epigraph
6. Foreword by Darrell "Condor" Gary
7. Prologue Palm Desert, California, 2018
8. 1. Admission Price Over Southern California, December 1956
9. 2. First Tribe Texas to Naval Air Station North Island, San Diego, Spring 1957
10. 3. The Navy Way North Island, June 1958
11. 4. Fight Club Off San Clemente Island, California, 1959
12. 5. Where Are the Carriers? Off the Saigon River, South Vietnam, November 3, 1963
13. 6. The Path to Disillusionment Pearl Harbor, Hawaii, January 1967
14. 7. Yankee Station Education Yankee Station, off the coast of Vietnam, Early 1968
15. 8. Starting Topgun Naval Air Station Miramar, California, Fall 1968
16. 9. The Original Bros Miramar, 1969
17. 10. Secrets of the Tribe Miramar, 1969
18. 11. Proof of Concept Miramar, 1969
19. 12. Topgun Goes to War Yankee Station, Spring 1972
20. 13. The Last Missing Man Yankee Station, January 1973
21. 14. The Peace That Never Was Yankee Station, February 1973
22. 15. End of the Third Temple Tel Nor Air Base, Israel, October 6, 1973
23. 16. Return with Honor Forty miles off South Vietnam, April 29, 1975
24. 17. Topgun and the Tomcat
25. 18. Black Shoes Aboard USS Wichita, 1978
26. 19. The Best and the Last Somewhere in the Indian Ocean, November 1980
27. 20. One More Goodbye Somewhere in the Pacific, Spring 1982
28. 21. Saving Topgun
29. 22. Will We Have to Lose a War Again? (or, Back to the Future in an F-35)
30. Photos
31. Acknowledgments
32. Glossary of Acronyms and Terms
33. Topgun Officers in Charge and Commanding Officers
34. Photo Credits
35. Newsletters
# Navigation
1. Begin Reading
2. Table of Contents
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{"url":"https:\/\/yutsumura.com\/possibilities-for-the-number-of-solutions-for-a-linear-system\/","text":"# Possibilities For the Number of Solutions for a Linear System\n\n## Problem 102\n\nDetermine whether the following systems of equations (or matrix equations) described below has no solution, one unique solution or infinitely many solutions and justify your answer.\n\n(a) $\\left\\{ \\begin{array}{c} ax+by=c \\\\ dx+ey=f, \\end{array} \\right.$ where $a,b,c, d$ are scalars satisfying $a\/d=b\/e=c\/f$.\n\n(b) $A \\mathbf{x}=\\mathbf{0}$, where $A$ is a singular matrix.\n\n(c) A homogeneous system of $3$ equations in $4$ unknowns.\n\n(d) $A\\mathbf{x}=\\mathbf{b}$, where the row-reduced echelon form of the augmented matrix $[A|\\mathbf{b}]$ looks as follows:\n$\\begin{bmatrix} 1 & 0 & -1 & 0 \\\\ 0 &1 & 2 & 0 \\\\ 0 & 0 & 0 & 1 \\end{bmatrix}.$ (The Ohio State University, Linear Algebra Exam)\n\nContents\n\n## Hint.\n\nRecall that possibilities for the solution set of a system of linear equation is either no solution (inconsistent) or one unique solution or infinitely many solutions.\n\nA homogeneous system is a system with zero constant terms.\nA homogeneous system always has the zero solution.\n\n## Solution.\n\n(a) Note that by the given condition $a\/d=b\/e=c\/f$, the numbers $b, e, c$ are not zero. The augmented matrix of the system is\n$\\left[\\begin{array}{rr|r} a & b & c \\\\ d & e & f \\end{array}\\right]$.\nWe apply the elementary row operations as follows.\n\n\\begin{align*}\n&\\left[\\begin{array}{rr|r}\na & b & c \\\\\nd & e & f\n\\end{array}\\right] \\xrightarrow{R_1-\\frac{a}{d}R_2}\n\\left[\\begin{array}{rr|r}\n0 & 0 & 0 \\\\\nd & e & f\n\\end{array}\\right] \\xrightarrow{R_1\\leftrightarrow R_2}\n\\left[\\begin{array}{rr|r}\nd & e & f\\\\\n0 & 0 & 0\n\\end{array}\\right]\\\\\n& \\xrightarrow{\\frac{1}{d}}\n\\left[\\begin{array}{rr|r}\n1 & e\/d & f\/d\\\\\n0 & 0 & 0\n\\end{array}\\right].\n\\end{align*}\nHere in the first step, we used the relation $a\/d=b\/e=c\/f$.\nThe last matrix is in reduced row echelon form with rank $1$ and it does not have a row of the form $[00|1]$. Therefore the system is consistent and there are $1(=\\text{the number of unknowns }-\\text{ rank})$ free variable, hence there are infinitely many solutions.\n\n(b) The system is homogeneous, thus it has the zero solution. Since the coefficient matrix $A$ is singular, the system has non-zero solution as well.\nTherefore, the only possibility is that the system has infinitely many solutions.\n\n(c) A homogeneous system has the zero solution hence it is consistent. Since there are more unknowns than equations, the system must have infinitely many solutions.\n\n(d) The last row of the reduced row echelon form matrix of the augmented matrix is $[000|1]$.\nIt corresponds to the equation\n$0x_1+0x_2+0x_3=1.$ Equivalently, this is $0=1$ and this is impossible. Thus the system has no solution (an inconsistent system).\n\nFor which choice(s) of the constant $k$ is the following matrix invertible? \\[A=\\begin{bmatrix} 1 & 1 & 1 \\\\ 1...","date":"2019-10-15 04:24:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9688833355903625, \"perplexity\": 203.09041623093268}, \"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\/1570986655864.19\/warc\/CC-MAIN-20191015032537-20191015060037-00052.warc.gz\"}"} | null | null |
\section{Introduction}
The electroweak form factors are sets of functions that are used to
parameterize the structure of the nucleon as seen by the electromagnetic and
the weak probes.
While a wealth of data and theoretical predictions exist for the
electromagnetic form factors (see, e.g.,
\cite{Gao:2003ag,Friedrich:2003iz,Hyde-Wright:2004gh} and references
therein), the nucleon form factors of the isovector axial-vector current,
the axial form factor $G_A(q^2)$ and, in particular, the induced pseudoscalar
form factor $G_P(q^2)$, are not as well-known (see, e.g.,
\cite{Bernard:2001rs,Gorringe:2002xx} for a review).
However, there are ongoing efforts to increase our
understanding of these form factors.
The value of the axial form factor at zero momentum transfer is defined as
the axial-vector coupling constant $g_A$ and is quite precisely
determined from neutron beta decay.
The $q^2$ dependence of the axial form factor can be obtained
either through neutrino scattering or pion electroproduction
(see \cite{Bernard:2001rs} and references therein).
The second method makes use of the so-called Adler-Gilman relation
\cite{Adler:1966} which provides a chiral Ward identity establishing a connection between charged
pion electroproduction at threshold and the isovector axial-vector current
evaluated between single-nucleon states (see, e.g.,
\cite{Scherer:1991cy} for more details).
The induced pseudoscalar form factor $G_P(q^2)$ is even less known than
$G_A(q^2)$.
It has been investigated in ordinary and radiative muon capture
as well as pion electroproduction.
Analogous to the axial-vector coupling constant $g_A$, the induced pseudoscalar
coupling constant is defined through $g_P = \frac{m_\mu}{2m_N}G_P(q^2=-0.88
m_\mu^2)$, where $q^2=-0.88\, m_\mu^2$ corresponds to muon capture kinematics
and the additional factor $\frac{m_\mu}{2m_N}$ stems
from a different convention used in muon capture.
For a comprehensive review on the experimental and theoretical situation
concerning $G_P(q^2)$ see for example \cite{Gorringe:2002xx}.
A discrepancy between the results in ordinary and radiative
muon capture has recently been addressed in \cite{Clark:2005as}.
Theoretical approaches to the axial and induced pseudoscalar form factors
include the early current algebra and PCAC calculations
\cite{Adler:1966,Nambu:1997wb,Sato:1967},
various quark model (see, e.g.,
\cite{Tegen:1983gg,Hwang:1984sz,Boffi:2001zb,Merten:2002nz,Ma:2002xu,
Khosonthongkee:2004qm,Silva:2005fa})
and lattice calculations \cite{Liu:1992ab}.
For a recent discussion on extracting the axial form factor in the
timelike region from $\bar p + n\to \pi^- +\ell^-+\ell^+$
($\ell=e$ or $\mu$)
see \cite{Adamuscin:2006bk}.
Chiral perturbation theory (ChPT)
\cite{Weinberg:1978kz,Gasser:1984yg,Gasser:1984gg,Gasser:1988rb} is the
low-energy effective theory of the standard model and as such
allows model-independent calculations of nucleon properties (see
\cite{Bernard:1995dp,Scherer:2002tk} for an introduction).
The axial form factor has been addressed in the framework of
heavy-baryon ChPT
\cite{Bernard:1992ys,Bernard:1993bq,Fearing:1997dp,Bernard:1998gv}.
In principle, when considering a charged transition there is
a third form factor, the induced
pseudotensorial form factor $G_T(q^2)$.
As will be explained below, this form factor vanishes when combining
isospin symmetry and charge-conjugation invariance and therefore
is not considered in this work \cite{Weinberg:1958ut}.
Experimentally the induced pseudotensorial form factor is found
to be small \cite{Wilkinson:2000gx,Minamisono:2001cd}.
Finally, defining the pion-nucleon form factor in terms
of the pseudoscalar quark density and
using the partially conserved axial-vector current (PCAC)
relation allows one to determine the pion-nucleon form factor, once
the axial and induced pseudoscalar form factors are known.
In this paper we calculate the axial, the induced
pseudoscalar, and the pion nucleon form factors of the nucleon in manifestly
Lorentz-invariant ChPT up to and including order ${\cal O}(p^4)$.
The renormalization procedure is performed in the framework of
the infrared renormalization of \cite{Becher:1999he}.
In its reformulated version \cite{Schindler:2003xv}, this renormalization
scheme allows for the inclusion of further degrees of freedom.
In the following we will include the $a_1$ axial-vector meson
as an explicit degree of freedom.
It needs to be pointed out that in a strict chiral expansion up
to order ${\cal O}(p^4)$ the results will not differ from the ones
obtained in the standard framework.
However, explicitly keeping all terms generated from the considered diagrams
involving the axial-vector meson amounts to a resummation of
higher-order contributions.
This phenomenological approach has shown an improved
description of the electromagnetic form factors of the nucleon
\cite{Kubis:2000zd,Schindler:2005ke} when the $\rho$, $\omega$,
and $\phi$ mesons are included.
This paper is organized as follows: In
Sec.~\ref{sec:Def} the definitions and some important properties
of the relevant form factors are given.
Section~\ref{sec:Lag} contains the effective Lagrangians used in the present
calculation.
We present and discuss the results for the form factors with and without
the inclusion of the axial-vector meson $a_1$ in
Sec.~\ref{sec:Results}. Section~\ref{sec:Sum} contains a short
summary.
\section{\label{sec:Def}Definition and properties of the isovector axial-vector
current}
In QCD, the three components of the isovector axial-vector current
are defined as
\begin{equation}
A^{\mu,a}(x)\equiv \bar{q}(x)\gamma^\mu\gamma_5
\frac{\tau^a}{2}q(x), \quad
q=\left(\begin{array}{c}u\\d\end{array}\right),\quad a=1,2,3.
\end{equation}
The operators $A^{\mu,a}(x)$ satisfy the following properties
relevant for the subsequent discussion:
\begin{enumerate}
\item Hermiticity:
\begin{equation}\label{Aherm}
A^{\mu,a\dagger}(x) = A^{\mu,a}(x).
\end{equation}
\item Equal-time commutation relations with
the vector charges:
\begin{equation}\label{AIsospin}
[Q^a_V(t),A^{\mu,b}(t,\vec x)]=i\epsilon^{abc}A^{\mu,c}(t,\vec x).
\end{equation}
\item Transformation behavior under parity:
\begin{equation}\label{Aparity}
A^{\mu,a}(x) \stackrel{\cal P}{\mapsto} -A_\mu^a(\tilde x),\quad
\tilde x^\mu=x_\mu.
\end{equation}
\item Transformation behavior under charge conjugation:
\begin{eqnarray}
A^{\mu,a}(x)&\stackrel{{\cal C}}{\mapsto}&A^{\mu,a}(x),
\quad a=1,3, \nonumber \\
A^{\mu,2}(x)&\stackrel{{\cal C}}{\mapsto}&-A^{\mu,2}(x).
\end{eqnarray}
\item Partially conserved axial-vector current (PCAC) relation:
\begin{equation}
\label{pcac}
\partial_\mu A^{\mu,a}=i\bar{q}\gamma_5\{\frac{\tau^a}{2},{\cal M}\}q,
\end{equation}
where ${\cal M}=\mbox{diag}(m_u,m_d)$ is the quark mass matrix.
\end{enumerate}
Assuming isospin symmetry, $m_\mu=m_d=\hat m$, the most general
parametrization of the isovector axial-vector current
evaluated between one-nucleon states in terms of axial-vector covariants
is given by
\begin{equation}\label{FFDef}
\langle N(p')| A^{\mu,a}(0) |N(p) \rangle = \bar{u}(p')
\left[\gamma^\mu\gamma_5 G_A(q^2)
+\frac{q^\mu}{2m_N}\gamma_5 G_P(q^2)
\right]
\frac{\tau^a}{2}u(p),
\end{equation}
where $q_\mu=p'_\mu-p_\mu$ and $m_N$ denotes the nucleon mass.
$G_A(q^2)$ is called the axial form factor and
$G_P(q^2)$ is the induced pseudoscalar form factor.
From the Hermiticity of Eq.~(\ref{Aherm}), we find that
$G_A$ and $G_P$ are real for space-like momenta ($q^2\leq 0$).
In the case of perfect isospin symmetry
the strong interactions are invariant under ${\cal G}$ conjugation, which is a
combination of charge conjugation $\cal C$ and a rotation by $\pi$ about the 2
axis in isospin space (charge symmetry operation),
\begin{equation}
{\cal G}={\cal C}\exp(i\pi Q_V^2).
\end{equation}
The presence of a third so-called second-class structure
\cite{Weinberg:1958ut} of the type $i\sigma^{\mu\nu}q_\nu\gamma_5$ in the
charged transition would indicate a violation of $\cal G$ conjugation.
As there seems to be no clear empirical evidence for such a
contribution \cite{Wilkinson:2000gx,Minamisono:2001cd}
we will omit it henceforth.
Similarly, the nucleon matrix element of the pseudoscalar density
$P^a(x)=i\bar q(x) \gamma_5 \tau^a q(x)$
can be parameterized as
\begin{equation}
\label{GpiN}
\hat m \langle N(p')| P^a (0) | N(p) \rangle =
\frac{M_\pi^2 F_\pi}{M_\pi^2 - q^2}
G_{\pi N}(q^2)i\bar{u}(p') \gamma_5 \tau^a u(p),
\end{equation}
where $M_\pi$ is the pion mass and $F_\pi$ the pion decay constant.
Equation (\ref{GpiN}) {\em defines} the form factor
$G_{\pi N}(q^2)$ in terms of the QCD operator $\hat m P^a(x)$.
The operator $\hat m P^a(x)/(M_\pi^2 F_\pi)$ serves as
an interpolating pion field and thus $G_{\pi N}(q^2)$ is also referred to as
the pion-nucleon form factor for this specific choice of the interpolating
pion field \cite{Bernard:1995dp}.
The pion-nucleon coupling constant $g_{\pi N}$ is defined through
$G_{\pi N}(q^2)$ evaluated at $q^2=M_\pi^2$.
As a result of the PCAC relation, Eq.\ (\ref{pcac}), the three form
factors $G_A$, $G_P$, and $G_{\pi N}$ are related by
\begin{equation}
\label{ff_relation}
2m_N G_A(q^2) + \frac{q^2}{2m_N} G_P(q^2) =
2\frac{M_\pi^2 F_\pi}{M_\pi^2 - q^2} G_{\pi N}(q^2).
\end{equation}
\section{\label{sec:Lag}Effective Lagrangian and power counting}
The calculation of the isovector axial-vector current form factors
of the nucleon requires both the purely mesonic as well as the one-nucleon
part of the chiral effective Lagrangian up to order ${\cal O}(p^4)$,
\begin{equation}\label{LagBasic}
{\cal L}_{\rm eff} = {\cal L}_{2} + {\cal L}_{4} + {\cal L}^{(1)}_{{\pi}N} +
{\cal L}^{(2)}_{{\pi}N} + {\cal L}^{(3)}_{{\pi}N} + {\cal L}^{(4)}_{{\pi}N}
+ \cdots.
\end{equation}
Here, $p$ collectively stands for a ``small'' quantity such as the
pion mass, a small external four-momentum of the pion or of an
external source, and an external three-momentum of the nucleon.
The pion fields are contained in the $2\times 2$ matrix $U$,
\begin{eqnarray}\label{U}
U(x) &=& u^2(x) = \exp\left(\frac{i \Phi(x)}{F}\right), \\
\Phi &=& \vec{\tau}\cdot \vec{\phi} = \left(
\begin{array}{cc}
\pi^0 & \sqrt{2}\pi^+ \\ \sqrt{2}\pi^- & -\pi^0
\end{array}\right),
\end{eqnarray}
and the purely mesonic Lagrangian at order ${\cal O}(p^2)$ is given by
\cite{Gasser:1984yg}
\begin{equation}\label{L2}
{\cal L}_2=\frac{F^2}{4}\mbox{Tr}\left[D_\mu U (D^\mu
U)^\dagger \right] + \frac{F^2}{4}\mbox{Tr}\left[\chi U^\dagger
+ U \chi^\dagger\right].
\end{equation}
The covariant derivative $D_\mu U$ with a coupling to an external
axial-vector field $a_\mu=\tau^a a^a_\mu/2$ only is given by
\begin{displaymath}\label{covDer}
D_\mu U = \partial_\mu U -i a_\mu U -i U a_\mu\,,
\end{displaymath}
while $\chi$ is defined as
\begin{displaymath}\label{chi}
\chi=2B(s+ip),
\end{displaymath}
with $s$ and $p$ the scalar and pseudoscalar external sources,
respectively.
$F$ denotes the pion decay constant in the chiral limit,
$F_\pi = F[1+{\cal O}(\hat{m})] = 92.42(26)$ MeV \cite{Yao:2006}.
We work in the isospin-symmetric limit $m_u=m_d=\hat m$, and
the lowest-order expression for the squared pion mass is
$M^2=2 B\hat m$, where
$B$ is related to the quark condensate
$\langle\bar{q}q\rangle_0$ in the chiral limit
\cite{Gasser:1984yg,Colangelo:2001sp},
$\langle\bar u u\rangle_0=\langle\bar d d\rangle_0=-F^2 B$.
For the mesonic Lagrangian at order ${\cal O}(p^4)$ we only list
the term that contributes to our calculation,
\begin{equation}\label{L4}
{\cal L}_4=\cdots + \frac{l_4}{8}\mbox{Tr}\left[D_\mu U (D^\mu
U)^\dagger \right]\mbox{Tr}\left[\chi U^\dagger + U
\chi^\dagger\right] + \cdots\,.
\end{equation}
The complete list for the $SU(2)$ case can be found in \cite{Gasser:1988rb}.
The lowest-order pion-nucleon Lagrangian is given by
\cite{Gasser:1988rb}
\begin{equation}\label{LagpiN1}
{\cal L}^{(1)}_{\pi N}=\bar{\Psi}\left(i D\hspace{-.57em}/\hspace{.1em} -
m
+ \frac{\texttt{g}_A}{2}\,
\gamma^\mu\gamma_5 u_\mu \right) \Psi,
\end{equation}
with $m$ the nucleon mass and
$\texttt{g}_A$ the axial-vector coupling constant both
evaluated in the chiral limit.
For the nucleonic Lagrangians of higher orders we only display those terms
that contribute to our calculations.
A complete list of terms at orders ${\cal O}(p^2)$ and ${\cal O}(p^3)$ can
be found in \cite{Gasser:1988rb,Fettes:2000gb}.
At second order the Lagrangian reads
\begin{eqnarray}\label{LagpiN2}
{\cal L}_{{\pi}N}^{(2)} &=& c_1 \mbox{Tr}(\chi_{+})\bar\Psi\Psi
- \frac{c_2}{4m^2}\left[ \bar{\Psi}\mbox{Tr}\left(u_\mu
u_\nu\right)D^\mu D^\nu \Psi + \mbox{h.c.} \right]
+ \frac{c_3}{2}\,\bar{\Psi}\mbox{Tr}\left(u_\mu u^\mu\right)\Psi\nonumber\\
&&-\frac{c_4}{4}\bar\Psi\gamma^\mu\gamma^\nu [u_\mu ,u_\nu ]\Psi
+\cdots ,
\end{eqnarray}
while at order ${\cal O}(p^3)$ we need
\begin{equation}\label{LagpiN3}
{\cal L}_{{\pi}N}^{(3)} =
\frac{d_{16}}{2}\bar{\Psi}\gamma^\mu\gamma_5\mbox{Tr}(\chi_+)u_\mu\Psi
+\frac{d_{22}}{2}\bar{\Psi}\gamma^\mu\gamma_5
\left[D_\nu,F_{\mu\nu}^-\right]\Psi
+\cdots\,.
\end{equation}
There are no contributions from ${\cal L}^{(4)}_{{\pi}N}$ in our calculation.
The Lagrangians contain the building blocks
\begin{eqnarray*}\label{Buildblocks}
D_\mu\Psi &=&\left(\partial_\mu +\Gamma_\mu\right)\Psi,\\
\Gamma_\mu &=&
\frac{1}{2}\,\left[ u^\dagger \left( \partial_\mu -ia_\mu \right)u
+ u \left( \partial_\mu -ia_\mu \right)u^\dagger \right],\\
u_\mu &=& i\left[ u^\dagger \partial_\mu u -u \partial_\mu
u^\dagger-i (u^\dagger a_\mu u + u a_\mu u^\dagger)\right],\\
\chi_+&=&u^\dagger\chi u^\dagger+u\chi^\dagger u,\\
F^-_{\mu\nu} &=& u^\dagger(\partial_\mu a_\nu-\partial_\nu a_\mu
-i[a_\mu,a_\nu])u
+u(\partial_\mu a_\nu-\partial_\nu a_\mu
+i[a_\mu,a_\nu])u^\dagger,
\end{eqnarray*}
where we only display the external axial-vector source $a_\mu$.
In order to include axial-vector mesons as explicit degrees of freedom we
consider the vector-field formulation of \cite{Ecker:yg} in which the
$a_1(1260)$ meson is represented by $A_\mu=A_\mu^a \tau^a$.
The advantage of this formulation is that the coupling of the axial-vector
mesons to pions and external sources is at least of order ${\cal O}(p^3)$.
A complete list of possible couplings at this order can be found in
\cite{Ecker:yg}.
The calculation of the contributions to the isovector axial-vector
form factors only requires the term
\begin{equation}\label{LagAVMmeson}
{\cal L}_{{\pi}A}^{(3)} = \frac{f_A}{4}
\mbox{Tr}(A_{\mu\nu}F^{\mu\nu}_{-}),
\end{equation}
where
\begin{displaymath}
A_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu
\end{displaymath}
with
\begin{displaymath}
\nabla_\mu A_\nu=\partial_\mu A_\nu+[\Gamma_\mu,A_\nu].
\end{displaymath}
The coupling of the axial-vector meson to the nucleon starts at
order ${\cal O}(p^0)$.
The corresponding Lagrangian reads
\begin{equation}\label{LagAVMNuc}
{\cal L}_{NA}^{(0)} = \frac{g_{a_1}}{2} \bar{\Psi} \gamma^{\mu}
\gamma_5 A_\mu \Psi.
\end{equation}
A calculation up to order ${\cal O}(p^4)$ would in principle
also require the Lagrangian of order ${\cal O}(p)$.
However, there is no term at this order that is allowed by the symmetries.
In addition to the usual counting rules for pions and nucleons
(see, e.g., \cite{Scherer:2002tk}), we count the axial-vector
meson propagator as order ${\cal O}(p^0)$, vertices from ${\cal
L}_{{\pi}A}^{(3)}$ as order ${\cal O}(p^3)$ and vertices from
${\cal L}_{AN}^{(0)}$ as order ${\cal O}(p^0)$, respectively
\cite{Fuchs:2003sh}.
\section{\label{sec:Results}Results and Discussion}
\subsection{\label{sec:without}Results without axial-vector mesons}
The axial form factor $G_A(q^2)$ only receives contributions from
the one-particle-irreducible diagrams of Fig.~\ref{Irreduc}.
The unrenormalized result reads
\begin{eqnarray}\label{GA}
{G_A}_0(q^2) &=&\texttt{g}_A +4 M^2 d_{16} -d_{22}q^2
-\frac{\texttt{g}_A}{F^2}I_{\pi}
+2\frac{\texttt{g}_A}{F^2}M^2 I_{{\pi}N}(m_N^2)
\nonumber \\
&& +8\frac{\texttt{g}_A}{F^2}m_N
\left\{c_4\left[M^2I_{{\pi}N}(m_N^2)-I_{{\pi}N}^{(00)}(m_N^2)\right]
-c_3 I_{{\pi}N}^{(00)}(m_N^2) \right\}\nonumber \\
&& -\frac{\texttt{g}_A^3}{4F^2}
\left[ I_{\pi}-4m_N^2 I_{{\pi}N}^{(p)}(m_N^2)
+4m_N^2(n-2)I_{{\pi}NN}^{(00)}(q^2)\right.\nonumber\\
&&\left.
+16m_N^4 I_{{\pi}NN}^{(PP)}(q^2) +4m_N^2 t I_{{\pi}NN}^{(qq)}(q^2)
\right].
\end{eqnarray}
The definition of the integrals can be found in the appendix.
To renormalize the expression for $G_A(q^2)$ we
multiply Eq.~(\ref{GA}) by the nucleon wave function
renormalization constant $Z$ \cite{Becher:1999he},
\begin{equation}\label{ZNuc}
Z = 1-\frac{9 \texttt{g}_A^2 M^2}{32\pi^2 F^2}
\left[\frac{1}{3}+\ln\left(\frac{M}{m}\right)\right]+
\frac{9 \texttt{g}_A^2 M^3}{64\pi F^2 m},
\end{equation}
and replace the integrals with their infrared singular parts.
The axial-vector coupling constant $g_A$ is defined as $g_A=G_A(q^2=0)
=1.2695(29)$ \cite{Yao:2006} and we obtain for its quark-mass expansion
\begin{equation}
\label{gAexpand}
g_A=\texttt{g}_A+g_A^{(1)}M^2+g_A^{(2)}M^2\ln\left(\frac{M}{m}\right)
+g_A^{(3)} M^3 +{\cal O}(M^4),
\end{equation}
with
\begin{eqnarray}
g_A^{(1)} &=& 4d_{16}-\frac{\texttt{g}_A^3}{16\pi^2F^2}\,, \nonumber\\
g_A^{(2)} &=&
-\frac{\texttt{g}_A}{8\pi^2F^2}(1+2\texttt{g}_A^2)\,, \nonumber\\
g_A^{(3)} &=& \frac{\texttt{g}_A}{8\pi F^2 m}(1+\texttt{g}_A^2)
-\frac{\texttt{g}_A}{6\pi F^2}(c_3-2c_4),
\end{eqnarray}
where all coefficients are understood as IR renormalized parameters.
These results agree with the chiral coefficients obtained in
HBChPT \cite{Kambor:1998pi,Bernard:2006te} as well as the IR calculation
of \cite{Ando:2006xy}.
It is worth noting that an agreement for the analytic term
$g_A^{(1)}$ cannot be expected in general.
For example, when expressed in terms of the renormalized couplings
of the extended on-mass-shell (EOMS) renormalization scheme of
\cite{Fuchs:2003qc}, the $g_A^{(1)}$ coefficient is given by
\cite{Ando:2006xy}
\begin{displaymath}
4 d_{16}^{EOMS}-\frac{\texttt{g}_A}{16\pi^2 F^2}(2+3\texttt{g}_A^2)
+\frac{c_1 \texttt{g}_A m}{4\pi^2 F^2}(4-\texttt{g}_A^2).
\end{displaymath}
Such a difference is not a surprise, because the use of different
renormalization schemes is compensated by different values of the
renormalized parameters.
For a similar discussion regarding the chiral expansion of the
nucleon mass, see \cite{Fuchs:2003qc}.
The axial form factor can be written as
\begin{equation}\label{GAexpansion}
G_A(q^2)=g_A+\frac{1}{6}\,g_A\,\langle r^2_A\rangle\, q^2 +
\frac{\texttt{g}_A^3}{4F^2}H(q^2),
\end{equation}
where $\langle r^2_A\rangle$ is the axial mean-square radius
and $H(q^2)$ contains loop contributions and satisfies $H(0)=H'(0)=0$.
The low-energy coupling constants (LECs) $d_{16}$ and $d_{22}$ are thus
absorbed in the axial-vector coupling constant $g_A$ and the axial
mean-square radius $\langle r^2_A\rangle$.
The numerical contribution of $H(q^2)$ is negligible which can be
understood by expanding $H$ in a Taylor series in $q^2$.
Such an expansion generates powers of $q^2/m^2$ where the individual
coefficients have a chiral expansion similar to Eq.~(\ref{gAexpand}).
For the analysis of experimental data, $G_A(q^2)$ is conventionally
parameterized using a dipole form as
\begin{equation}\label{GAPara}
G_A(q^2)=\frac{g_A}{(1-\frac{q^2}{M^2_A})^2},
\end{equation}
where the so-called axial mass $M_A$ is related to the axial root-mean-square
radius by $\langle r^2_A\rangle^\frac{1}{2}=2\sqrt{3}/M_A$.
The global average for the axial mass extracted from neutrino scattering
experiments given in \cite{Liesenfeld:1999mv} is
\begin{equation}\label{MAv1}
M_A = (1.026 \pm 0.021)\,\mbox{GeV},
\end{equation}
whereas a recent analysis \cite{Budd:2003wb} taking account of updated
expressions for the vector form factors finds a slightly smaller value
\begin{equation}\label{MAv2}
M_A = (1.001 \pm 0.020)\,\mbox{GeV}.
\end{equation}
On the other hand, smaller values of $(0.95\pm 0.03)$ GeV and
$(0.96\pm 0.03)$ GeV have been obtained in \cite{Kuzmin:2006dh} as world
averages from quasielastic scattering and $(1.12\pm 0.03)$ GeV
from single pion neutrinoproduction.
Finally, the most recent result extracted
from quasielastic $\nu_\mu n\to \mu^- p$ in oxygen nuclei reported by
the K2K Collaboration, $M_A=(1.20\pm 0.12)$ GeV, is considerably
larger \cite{Gran:2006jn}.
The extraction of the axial mean-square radius from
charged pion electroproduction at threshold is motivated by
the current algebra results and the PCAC hypothesis.
The most recent result for the reaction $p(e,e'\pi^+)n$ has been obtained
at MAMI at an invariant mass
of $W=1125$ MeV (corresponding to a pion center-of-mass momentum of
$|\vec{q}^\ast|=112$ MeV) and photon four-momentum transfers of $-k^2=0.117$,
$0.195$ and 0.273 GeV$^2$ \cite{Liesenfeld:1999mv}.
Using an effective-Lagrangian model
an axial mass of
\begin{displaymath}
\bar{M}_A=(1.077\pm 0.039)\,\mbox{GeV}
\end{displaymath}
was extracted, where the bar is used to distinguish the result from the
neutrino scattering value.
In the meantime, the experiment has been repeated including an
additional value of $-k^2=0.058$ GeV$^2$ \cite{Baumann:2004} and is currently
being analyzed.
The global average from several pion electroproduction experiments
is given by \cite{Bernard:2001rs}
\begin{equation}\label{MApi}
\bar{M}_A=(1.068\pm 0.017)\,\mbox{GeV}.
\end{equation}
It can be seen that the values of Eqs.~(\ref{MAv1}) and
(\ref{MAv2}) for the neutrino scattering experiments are smaller
than that of Eq.~(\ref{MApi}) for the pion electroproduction
experiments.
The discrepancy was explained in heavy baryon chiral
perturbation theory \cite{Bernard:1992ys}.
It was shown that at order ${\cal O}(p^3)$ pion
loop contributions modify the $k^2$ dependence of the electric dipole amplitude
from which $\bar{M}_A$ is extracted.
These contributions result in a change of
\begin{equation}\label{deltaMA}
\Delta M_A = 0.056 \,\mbox{GeV},
\end{equation}
bringing the neutrino scattering and pion electroproduction
results for the axial mass into agreement.
Using the convention $Q^2=-q^2$ the result for the axial form factor
$G_A(q^2)$ in the momentum
transfer region $0\,\mbox{GeV}^2\leq Q^2 \leq 0.4\,\mbox{GeV}^2$
is shown in Fig.~\ref{GAwithout}.
The parameters have been determined such as to reproduce the axial
mean-square radius corresponding to the dipole parameterization with
$M_A=1.026$ GeV (dashed line).
The dotted and dashed-dotted lines refer to dipole parameterizations
with $M_A=0.95$ GeV and $M_A=1.20$ GeV, respectively.
As anticipated, the loop contributions from $H(q^2)$ are small
and the result does not produce enough curvature to describe the data
for momentum transfers $Q^2 \ge 0.1\, \mbox{GeV}^2$.
The situation is reminiscent of the electromagnetic case
\cite{Kubis:2000zd,Fuchs:2003ir} where ChPT at ${\cal O}(p^4)$
also fails to describe the form factors beyond $Q^2 \ge 0.1\,
\mbox{GeV}^2$.
The one-particle-irreducible diagrams of Fig.~\ref{Irreduc} also contribute
to the induced pseudoscalar form factor $G_P(q^2)$,
\begin{equation}\label{GPirr}
G_P^{irr}(q^2) = 4m_N^2 d_{22} + 8m_N^4
\frac{g_A^3}{F^2}I_{{\pi}NN}^{(qq)}(q^2)\,.
\end{equation}
Furthermore, $G_P(q^2)$ receives contributions from the pion pole graph of
Fig.~\ref{PiPoleDia}.
It consists of three building blocks: The coupling of the external axial
source to the pion, the pion propagator, and the ${\pi}N$-vertex,
respectively.
We consider each part separately.
The renormalized coupling of the external axial source to a pion
up to order ${\cal O}(p^4)$ is given by
\begin{equation}\label{api}
\epsilon_A \cdot q F_\pi \delta_{ij},
\end{equation}
where the diagrams in Fig.~\ref{APiDia} have been taken into
account and the renormalized pion decay constant reads
\begin{equation}\label{Frenorm}
F_\pi = F \left[ 1+\frac{M^2}{F^2}l_4^r
- \frac{M^2}{8\pi^2F^2}\ln\left(\frac{M}{m}\right)+{\cal O}(M^4)
\right].
\end{equation}
We have used the pion wave function renormalization constant
\begin{equation}\label{Zpi}
Z_\pi = 1-\frac{2M^2}{F^2}\left[ l_4^r+\frac{1}{24\pi^2}\,\left(
R-\ln\left(\frac{M}{m}\right) \right) \right],
\end{equation}
with $l_4^r$ the renormalized coupling of Eq.~(\ref{L4}) and
$R=\frac{2}{n-4}+\gamma_E-1-\ln(4\pi)$.
The renormalized pion propagator is obtained by simply
replacing the lowest-order pion mass $M$ by the expression for the
physical mass $M_\pi$ up to order ${\cal O}(p^4)$,
\begin{equation}\label{Mphys}
M^2_\pi = M^2+\Sigma(M^2_\pi) = M^2\left[ 1 +\frac{2M^2}{F^2}\left( l_3^r
+\frac{1}{32\pi^2}\ln\left(\frac{M}{m}\right) \right)
\right].
\end{equation}
The ${\pi}N$ vertex evaluated between on-mass-shell nucleon states
up to order ${\cal O}(p^4)$ receives contributions from the
diagrams in Fig.~\ref{PiNDia} and the unrenormalized result for a
pion with isospin index $i$ is given by
\begin{eqnarray}\label{PiNVertex}
\Gamma(q^2)\gamma_5 \tau_i &=& \left( -\frac{\texttt{g}_A}{F}m_N
+2\frac{M^2}{F}m_N(d_{18}-2d_{16}) +\frac{\texttt{g}_A}{3F^2}m_N I_{\pi}
-2\frac{\texttt{g}_A}{F^3}M^2 m_N I_{{\pi}N}(m_N^2)\right. \nonumber \\
&& -8\frac{\texttt{g}_A}{F^2}m_N^2
\left\{c_4\left[M^2I_{{\pi}N}(m_N^2)-I_{{\pi}N}^{(00)}(m_N^2)\right]
-c_3 I_{{\pi}N}^{(00)}(m_N^2) \right\} \nonumber \\
&&\left. +\frac{\texttt{g}_A^3}{4F^3}m_N\left[ I_{\pi} +4mN^2 I_{NN}(q^2)
+4m_N^2 M^2 I_{{\pi}NN}(q^2)
\right]\right)\gamma_5 \tau_i\,.
\end{eqnarray}
To find the renormalized vertex one multiplies with
$Z\sqrt{Z_\pi}$ and replaces the integrals with their infrared
singular parts.
However, the renormalized result should not be confused with the
pion-nucleon form factor $G_{\pi N}(q^2)$ of Eq.\ (\ref{GpiN}).
In general, the pion-nucleon vertex depends on the choice of the field
variables in the (effective) Lagrangian.
In the present case, the pion-nucleon vertex is only an auxiliary
quantity, whereas the ``fundamental'' quantity (entering chiral Ward
identities) is the matrix element of the pseudoscalar density.
Only at $q^2=M_\pi^2$, we expect the same coupling strength, since
both $\hat m P^a(x)/(M_\pi^2 F_\pi)$ and the field
$\phi_i$ of Eq.\ (\ref{U})
serve as interpolating pion fields.
After renormalization, we obtain for the pion-nucleon coupling
constant the quark-mass expansion
\begin{equation}
\label{gpiNexpand}
g_{\pi N}=\texttt{g}_{\pi N}
+ g_{{\pi}N}^{(1)} M^2
+ g_{{\pi}N}^{(2)} M^2 \ln\left(\frac{M}{m}\right)
+ g_{{\pi}N}^{(3)}M^3
+{\cal O}(M^4)\,,
\end{equation}
with
\begin{eqnarray}
\texttt{g}_{\pi N}&=&\frac{\texttt{g}_A m}{F}\,,\nonumber\\
g_{{\pi}N}^{(1)}&=&-\texttt{g}_A\frac{l_4^r m}{F^3}
- 4\texttt{g}_A\frac{c_1}{F}
+\frac{2(2d_{16}-d_{18})m}{F}
-\texttt{g}_A^3\frac{m}{16\pi^2F^3} \,, \nonumber\\
g_{{\pi}N}^{(2)} &=&-\texttt{g}_A^3\frac{m}{4\pi^2F^3} \,, \nonumber\\
g_{{\pi}N}^{(3)} &=&\texttt{g}_A\frac{4+ \texttt{g}_A^2}{32\pi F^3}
-\texttt{g}_A\frac{(c_3-2c_4)m}{6\pi F^3}\,,
\end{eqnarray}
where all coefficients are understood as IR renormalized parameters.
These results agree with the chiral coefficients obtained in
\cite{Becher:2001hv}.
In the chiral limit, Eq.\ (\ref{gpiNexpand}) satisfies the
Goldberger-Treiman relation $\texttt{g}_{\pi N}=\texttt{g}_A m/F$ \cite{GT}.
The numerical violation of the Goldberger-Treiman relation as expressed
in the so-called Goldberger-Treiman discrepancy \cite{Pagels:1969ne},
\begin{equation}
\label{GTdiscrepancy}
\Delta=1-\frac{m_N g_A}{F_\pi g_{\pi N}},
\end{equation}
is at the percent level, $\Delta=(2.44^{+0.89}_{-0.51})$ \% for
$m_N=(m_p+m_n)/2=938.92$ MeV, $g_A=1.2695(29)$, $F_\pi=92.42(26)$
MeV, and $g_{\pi N}=13.21^{+0.11}_{-0.05}$ \cite{Schroder:rc}.
Using different values for the pion-nucleon coupling constant such as
$g_{\pi N}= 13.0\pm 0.1$ \cite{Stoks:1992ja}, $g_{\pi N}= 13.3\pm
0.1$ \cite{Ericson:2000md}, and $g_{\pi N}= 13.15\pm 0.01$
\cite{Arndt:2006bf}
results in the GT discrepancies $\Delta=(0.79\pm 0.84)$ \%,
$\Delta=(3.03\pm 0.81)$ \%, and $\Delta=(1.922\pm 0.363)$ \%,
respectively.
The chiral expansions of $g_A$ etc.~may be used to relate the
parameter $d_{18}$ to $\Delta$ \cite{Becher:2001hv},
\begin{equation}
\label{Delta_d_18}
\Delta=-\frac{2 d_{18} M^2}{\texttt{g}_A}+{\cal O}(M^4).
\end{equation}
Note that $\Delta$ of Eq.\ (\ref{GTdiscrepancy}) and
$\Delta_{GT}$ of \cite{Becher:2001hv,Schroder:rc} are related
by $\Delta_{GT}=\Delta/(1-\Delta)$.
In particular, the leading order of the quark mass expansions of
$\Delta$ and $\Delta_{GT}$ is the same.
The induced pseudoscalar form factor $G_P(q^2)$ is obtained by
combining Eqs.~(\ref{GPirr}), (\ref{Frenorm}), (\ref{Mphys}) and
the renormalized expression for Eq.~(\ref{PiNVertex}).
With the help of Eqs.\ (\ref{GTdiscrepancy}) and (\ref{Delta_d_18})
it can entirely be written in terms of known physical
quantities as \cite{Bernard:1994wn}
\begin{equation}\label{GPwoResult}
G_P(q^2)=-4\frac{m_N F_\pi g_{{\pi}N}}{q^2-M^2_\pi}-\frac{2}{3}m_N^2 g_A
\langle r_A^2\rangle + {\cal O}(p^2).
\end{equation}
The $1/(q^2-M_\pi^2)$ behavior of $G_P$ is not in conflict with
the book-keeping of a calculation
at chiral order ${\cal O}(p^4)$, because
the external axial-vector field $a_\mu$ counts
as ${\cal O}(p)$, and the definition of the matrix element contains a
momentum $(p'-p)^\mu$ and the Dirac matrix $\gamma_5$
so that the combined order of all ingredients in the matrix element ranges
from ${\cal O}(p)$ to ${\cal O}(p^4)$.
The terms that have been neglected in the form factor $G_P$ are of
order $M^2$, $q^2/m^2$ and higher.
Using the above values for $m_N$, $g_A$, $F_\pi$ as well as
$g_{{\pi}N}=13.21^{+0.11}_{-0.05}$, $M_A=(1.026\pm 0.021)$ GeV,
$M=M_{\pi^+}=139.57$ MeV and $m_\mu=105.66$ MeV \cite{Yao:2006} we
obtain for the induced pseudoscalar coupling
\begin{equation}\label{gP}
g_P = 8.29^{+0.24}_{-0.13}\pm 0.52,
\end{equation}
which is in agreement with the heavy-baryon results $8.44\pm 0.23$
\cite{Bernard:1994wn} and $8.21\pm 0.09$ \cite{Fearing:1997dp}, once the
differences in the coupling constants used are taken in consideration.
The first error given in Eq.~(\ref{gP}) stems only from the empirical
uncertainties in the quantities of Eq.~(\ref{GPwoResult}).
As an attempt to estimate the error originating in the truncation
of the chiral expansion in the baryonic sector we assign a relative error
of $0.5^k$, where $k$ denotes the diffence between the order that has
been neglected and the leading order at which a nonvanishing result appears.
Such a (conservative) error is motivated by, e.~g., the analysis
of the individual terms of Eq.~(\ref{gAexpand}) as well as the
determination of the LECs $c_i$ at ${\cal O}(p^2)$ and to one-loop accuracy
${\cal O}(p^3)$ in the heavy-baryon framework \cite{Bernard:1997gq}.
For $g_P$ we have thus added a truncation error of 0.52.
Figure \ref{GPwithout} shows our result for $G_P(q^2)$ in the
momentum transfer region $-0.2\,\mbox{GeV}^2\leq Q^2 \leq
0.2\,\mbox{GeV}^2$.
One can clearly see the dominant pion pole contribution at
$q^2\approx M^2_\pi$
which is also supported by the experimental results of
\cite{Choi:1993vt}.
Using Eq.\ (\ref{ff_relation}) allows one to also determine the
pion-nucleon form factor $G_{\pi N}(q^2)$ in terms of the results for
$G_A(q^2)$ and $G_P(q^2)$.
When expressed in terms of physical quantities, it has the particularly
simple form
\begin{equation}
\label{GpiNresult}
G_{\pi N}(q^2)=\frac{m_N g_A}{F_\pi}+g_{\pi N}\Delta \frac{q^2}{M_\pi^2}
+{\cal O}(p^4).
\end{equation}
We have explicitly verified that the results agree with a direct
calculation of $G_{\pi N}(q^2)$ in terms of a coupling to an external
pseudoscalar source.
Observe that, with our definition in terms of QCD bilinears, the
pion-nucleon form factor is, in general, {\em not} proportional
to the axial form factor.
The relation $G_{\pi N}(q^2)=m_N G_A(q^2)/F_\pi$ which is sometimes
used in PCAC applications implies a pion-pole dominance for
$G_P(q^2)$ of the form $G_P(q^2)=4m_N^2 G_A(q^2)/(M_\pi^2-q^2)$.
However, as can be seen from Eq.\
(\ref{GpiNresult}), there are deviations at
${\cal O}(p^2)$ from such a complete pion-pole dominance assumption.
The difference between $G_{\pi N}(q^2=M_\pi^2)$ and $G_{\pi N}(q^2=0)$
is entirely given in terms of the GT discrepancy \cite{Bernard:1995dp}
\begin{equation}\label{GpNDiff}
G_{\pi N}(M_\pi^2)-G_{\pi N}(0)=g_{\pi N}\Delta.
\end{equation}
Parameterizing the form factor in terms of a monopole,
\begin{equation}\label{Monopole}
G_{\pi N}^{{\rm mono}}(q^2) = g_{\pi
N}\frac{\Lambda^2-M^2}{\Lambda^2-q^2}\,,
\end{equation}
Eq.~(\ref{GpNDiff}) translates into a mass parameter $\Lambda=894$
MeV for $\Delta=2.44$ \%.
\subsection{\label{sec:with}Inclusion of the axial-vector meson $a_1(1260)$}
The contributions of the axial-vector meson to the form
factors $G_A$ and $G_P$ at order ${\cal O}(p^4)$ stem from the diagram in
Fig.~\ref{AVMDia}.
We do not consider loop diagrams with internal axial-vector meson
lines that do not contain internal pion lines, as these vanish in
the infrared renormalization employed in this work.
With the Langrangians of Eqs.~(\ref{LagAVMmeson}) and (\ref{LagAVMNuc}) the
axial form factor receives
the contribution
\begin{equation}\label{GAAVM}
G_A^{AVM}(q^2) = - f_A g_{a_1} \frac{q^2}{q^2-M_{a_1}^2}\,,
\end{equation}
while the result for the induced pseudoscalar form factor
reads
\begin{equation}\label{GPAVM}
G_P^{AVM}(t) = 4 m_N^2 f_A g_{a_1} \frac{1}{q^2-M_{a_1}^2}\,.
\end{equation}
The Lagrangians for the axial-vector meson contain two new LECs, $f_A$ and
$g_{a_1}$, respectively.
However, we find that they only appear through the combination
$f_A g_{a_1}$, effectively leaving only one unknown LEC.
Performing a fit to the data of $G_A(q^2)$ in the momentum region
$0\,\mbox{GeV}^2\leq Q^2 \leq 0.4\,\mbox{GeV}^2$ the product of
the coupling constants is determined to be
\begin{equation}\label{ConstantFitted}
f_A g_{a_1} \approx 8.70.
\end{equation}
Fig.~\ref{GAwith} shows our fitted result for the axial form factor
$G_A(q^2)$ at order ${\cal O}(p^4)$ in the momentum region
$0\,\mbox{GeV}^2\leq Q^2 \leq 0.4\,\mbox{GeV}^2$ with the $a_1$
meson included as an explicit degree of freedom.
As was expected from phenomenological considerations, the
description of the data has improved for momentum transfers
$Q^2\gtrsim 0.1\,\mbox{GeV}^2$.
We would like to stress again that in a strict chiral expansion
up to order ${\cal O}(p^4)$ the results with and without axial
vector mesons do not differ from each other.
The improved description of the data in the case with the
explicit axial-vector meson is the result of a resummation of
certain higher-order terms.
While the choice of which additional degree of freedom to
include compared to the standard calculation is completely
phenomenological, once this choice has been made there exists a
systematic framework in which to calculate the corresponding
contributions as well as higher-order corrections.
It can be seen from Eq.~(\ref{GAAVM}) that in our formalism the
axial-vector meson does not contribute to the axial-vector
coupling constant $g_A$.
The pion-nucleon vertex also remains unchanged at the given order,
while the axial mean-square radius receives a contribution.
The values for the LECs $d_{16}$ and $d_{18}$ therefore do not change,
while $d_{22}$ can be determined from the new expression for the
axial radius using the value of Eq.~(\ref{ConstantFitted}) for the
combination of coupling constants.
In Fig.~\ref{GPwith} we show the result for $G_P(q^2)$ in the
momentum transfer region $-0.2\,\mbox{GeV}^2\leq Q^2 \leq
0.2\,\mbox{GeV}^2$.
Also shown for comparison is the result without the explicit
axial-vector meson.
One sees that the contribution of the $a_1$ to $G_P(q^2)$ for
these momentum transfers is rather small and that $G_P(q^2)$ is
still dominated by the pion pole diagrams.
The form factors $G_A$ and $G_P$ are related to the
pion-nucleon form factor via Eq.~(\ref{ff_relation}).
For the contributions of the axial-vector meson we find
\begin{equation}\label{WAAVM}
2m_N G_A^{AVM}(q^2)+\frac{q^2}{2m_N} G_P^{AVM}(q^2) = 0\,,
\end{equation}
so that the pion-nucleon form factor is not modified by
the inclusion of the $a_1$ meson.
\section{Summary}\label{sec:Sum}
We have discussed the nucleon form factors $G_A$ and
$G_P$ of the isovector axial-vector current in manifestly Lorentz-invariant
baryon chiral perturbation theory up to and including order ${\cal O}(p^4)$.
The main features of the results are similar to the case of
the electromagnetic form factors at the one-loop level.
As far as the axial form factor is concerned, ChPT can neither predict
the axial-vector coupling constant $g_A$ nor the mean-square axial radius
$\langle r^2_A\rangle$.
Instead, empirical information on these quantities is used to absorb the
relevant LECs $d_{16}$ and $d_{22}$ in $g_A$ and $\langle r^2_A\rangle$.
Moreover, the use of a manifestly Lorentz-invariant framework does not
lead to an improved description in comparison with the heavy-baryon
framework, because the re-summed higher-order contributions are negligible.
The induced pseudoscalar form factor $G_P$ is completely
fixed from ${\cal O}(p^{-2})$ up to and including ${\cal O}(p)$,
once the LEC $d_{18}$ has been expressed in terms of the Goldberger-Treiman
discrepancy.
Using $g_{\pi N}=13.21$ for the pion-nucleon coupling constant,
we obtain for the induced pseudoscalar coupling
$g_P = 8.29^{+0.24}_{-0.13}\pm 0.52$.
The first error is due to the error of the empirical quantities entering
the expression for $g_P$ and the second error represents our estimate for the
truncation in the chiral expansion.
Defining the pion field in terms of the PCAC relation allows one to
introduce a pion-nucleon form factor which is entirely determined in terms
of the axial and induced pseudoscalar form factors.
Assuming this pion-nucleon form factor to be proportional to the
axial form factor leads to a restriction for $G_P$ which is not supported
by the most general structure of ChPT.
In addition to the standard treatment including the
nucleon and pions, we have also considered the axial-vector meson $a_1$
as an explicit degree of freedom.
This was achieved by using the reformulated infrared
renormalization scheme.
The inclusion of the axial-vector meson effectively results in
one additional low-energy coupling constant which we have determined by a fit
to the data for $G_A$.
The inclusion of the axial-vector meson results in a considerably improved
description of the experimental data for $G_A$ for values of $Q^2$ up to
about $0.4$ GeV$^2$, while the contribution to $G_P$ is small.
\acknowledgments
M.R.S.~and S.S.~would like to thank H.W.~Fearing and J.~Gasser for
useful discussions and the TRIUMF theory group for
their hospitality.
This work was made possible by the financial support from the
Deutsche Forschungsgemeinschaft (SFB 443), the Government of Canada,
and the EU Integrated Infrastructure Initiative Hadron
Physics Project (contract number RII3-CT-2004-506078).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 335 |
<?php
/**
* This file is part of the Minty templating library.
* (c) Dániel Buga <daniel@bugadani.hu>
*
* For licensing information see the LICENCE file.
*/
namespace Minty\Extensions;
use Minty\Compiler\TemplateFunction;
use Minty\Extension;
class Debug extends Extension
{
public function getExtensionName()
{
return 'debug';
}
public function getFunctions()
{
return [
new TemplateFunction('dump', 'var_dump')
];
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,452 |
A hurdle model is a class of statistical models where a random variable is modelled using two parts, the first which is the probability of attaining value 0, and the second part models the probability of the non-zero values. The use of hurdle models are often motivated by an excess of zero's in the data, that is not sufficiently accounted for in more standard statistical models.
In a hurdle model, a random variable x is modelled as
where is a truncated probability distribution function, truncated at 0.
Hurdle models were introduced by John G. Cragg in 1971, where the non-zero values of x were modelled using a normal model, and a probit model was used to model the zeros. The probit part of the model was said to model the presence of "hurdles" that must be overcome for the values of x to attain non-zero values, hence the designation hurdle model. Hurdle models were later developed for count data, with Poisson, geometric, and negative binomial models for the non-zero counts .
Relationship with zero-inflated models
Hurdle models differ from zero-inflated models in that zero-inflated models model the zeros using a two-component mixture model. With a mixture model, the probability of the variable being zero is determined by both the main distribution and the mixture weight. Specifically, a zero-inflated model for a random variable x is
where is the mixture weight that determines the amount of zero-inflation. A zero-inflated model can only increase the probability of , but this is not a restriction in hurdle models.
See also
Zero-inflated model
Truncated normal hurdle model
References
Statistical models | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,822 |
{"url":"https:\/\/notesformsc.org\/page-table\/","text":"# Page Table\n\nMost OS allocate a page table for each process. A pointer to the page table is stored in the PCB of the process. When the dispatcher start a process, it must reload the user registers and define the correct hardware page table from the stored user page-table.\n\nThe hardware page table can be implemented in many ways. The simplest form of page table can be build using high speed registers for better efficiency. The CPU dispatcher reloads these register like other registers and instructions to modify the page-table registers are privileged, so only OS can change the memory map.\n\nExample, DEC PDP-11\n\nThe address has 16-bit and page-size is 8 KB.\n\nThe use of registers is good for memory with small size such as 256 entries in page table. But, in modern computer the size of entries is 1 million cannot use fast registers.\n\nThe page-table is kept in main memory and a page-table base register (PTBR) points to the page table. To change page-table entries, you only need to change the value of PTBR.\n\nTo access memory location i, we must index into the page-table, using the value in the PTBR, offset by page number for i. This provides us with a frame number and together with offset value gives us the physical address. Then we can access the memory.\n\nThis scheme requires two memory access for a byte, therefore, slowed the memory access by a factor of 2.\n\n1. One memory access for the page-table entry\n2. Another memory access for the byte.\n\nThe above approach is also slow.\n\nThe standard solution is to use a Translation Look-aside Buffer (TLB).\n\n\u2022 The TLB is associative, high-speed memory.\n\u2022 Each entry consist of two parts \u2013 a key or a tag and a value.\n\u2022 When an item is presented, it is compared with all the keys. If a match is found, then the corresponding value is returned.\n\u2022 Number of entries in TLB is small, usually between 64-1024.\n\n### TLB With Memory Page Table\n\nThe working of TLB is as follows:\n\n\u2022 CPU generates the logical address.\n\u2022 Its page number is presented to TLB.\n\u2022 If page is found, obtain frame number\n\u2022 Access the memory.\n\u2022 If not page not found, it is called TLB miss, a memory reference to the page table must be made.\n\u2022 When frame number obtained, use it to access memory.\n\u2022 Add the page and frame number to the TLB, so next reference we can find it quickly.\n\u2022 If the TLB is full, then OS must use one entry for replacement (using page replacement algorithm).\n\n### Other Features Of TLB\n\n\u2022 Some entries are wired down(cannot be replaced). The TLB entries for kernel code are wired down.\n\u2022 Some TLB store address-space identifiers (ASIDs) in each TLB entry. An ASID uniquely identify process and provide address space protection for that process.\n\u2022 TLB tries to resolve a virtual page, if ASID of process and a virtual page does not match. It is a TLB miss.\n\u2022 For several processes, if TLB does not support separate ASIDs, then flush or erase TLB for next executing process.\n\u2022 Otherwise, TLB will refer to valid virtual addresses of previous process and refer to incorrect physical addresses.\n\nThe percentage of time a page is found in the TLB is called a hit ratio.\n\nAn 80% hit ratio means pages are found 80% of time. If it takes 20 nanoseconds to search TLB. If it takes 100 nanoseconds to access memory.\nthen,\nIt takes 120 nanoseconds for mapped-memory access when page is in TLB.\n\nIf the page is not found in TLB which takes 20 nanoseconds\nIt takes 100 nanoseconds to access the page-table in memory.\nIt takes 100 nanoseconds to access the byte from memory.\n\nThe total of 220 nanoseconds to access memory.\n\nTo find the effective memory access time, we weight the case by its probability:\n\nEffective memory access time = 80\/100 * 120 + 20\/100 * 220 = 96 + 44 = 140 nanoseconds.\n\nThe slowdown is 40% (from 100 to 140 nanoseconds)\n\nFor 98% hit ratio,\n\nEffective memory access time = 98\/100 * 120 + 2\/100 * 220 = 196 117.6 + 4.4 = 122 nanoseconds\n\nThe increased hit ratio produces only 22 % slowdown.\n\n### Memory Protection In Paging\n\nMemory protection in paged environment is accomplished by protection bit with each frame number. These bits are kept in the page-table. One bit can define page to be read-write or read-only.\nWhen the page physical address is being computed, the protection bit is verified to prevent write on a read-only page. If such an attempt is made then it cause a hardware trap.\n\nOne additional bit is included with each entry, a valid-invalid bit by operating system. If the bit is set to valid, the page is in the process\u2019s virtual address space. If bit is set to invalid, the page is not in virtual address space, resulting in a trap.\n\nSuppose a 14-bit address space , with page size 2kb( 211 bytes). The number of pages are 14 \u2013 11 = 3 =214\/ 211= 23= 8 pages\n\nIf the process is restricted to use only 0 to 10453, then all other addresses are set to invalid. The invalid address inside a page are unused and cause internal fragmentation.\n\n10453\/2048 = 5 page (10240 addresses) + 213 addresses. But the entire 6th page is considered as valid. This is internal fragmentation.","date":"2022-11-30 03:51:53","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\": 0.2800597548484802, \"perplexity\": 3458.868487878216}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710719.4\/warc\/CC-MAIN-20221130024541-20221130054541-00283.warc.gz\"}"} | null | null |
<?php declare(strict_types=1);
namespace Darvin\Utils\Twig\Extension;
use Darvin\Utils\ObjectNamer\ObjectNamerInterface;
use Twig\Extension\AbstractExtension;
use Twig\TwigFilter;
/**
* Object namer Twig extension
*/
class ObjectNamerExtension extends AbstractExtension
{
/**
* @var \Darvin\Utils\ObjectNamer\ObjectNamerInterface
*/
private $objectNamer;
/**
* @param \Darvin\Utils\ObjectNamer\ObjectNamerInterface $objectNamer Object namer
*/
public function __construct(ObjectNamerInterface $objectNamer)
{
$this->objectNamer = $objectNamer;
}
/**
* {@inheritDoc}
*/
public function getFilters(): array
{
return [
new TwigFilter('utils_name_object', [$this->objectNamer, 'name']),
];
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,322 |
Green Creative products selected for the Illuminating Engineering Society's 2013 Progress Report
Date Announced: 31 Oct 2013
BURLINGAME, CA - GREEN CREATIVE LLC, the commercial grade LED lighting manufacturer proudly announces the selection of its PAR38 19W, MR16 7W High CRI, and MR16 High Output lamps by the Illuminating Engineering Society for the 2013 Progress Report.
Each year the Illuminating Engineering Society's (IES) prestigious Progress Report showcases unique and innovative products significant to the lighting industry. The IES Progress Committee is dedicated to following developments in the art and science of lighting throughout the world and prepares the Progress Report as a yearly review of achievements for the Illuminating Engineering Society. Accepted products will be presented at the IES Annual Conference held in Huntington Beach, CA on October 28th.
Submitting products for the first time, GREEN CREATIVE went three for three on submissions. "We are extremely honored to have three of our products selected for the 2013 Progress Report out of the few hundred submissions," said Matt Leonard, GREEN CREATIVE'S Product Manager. "We feel our products are at the forefront of LED lighting and embody the type of technological innovation valued by lighting professionals and end users."
One product recognized was the new PAR38 19W lamp. A member of GREEN CREATIVE'S Generation 3 PAR family, this lamp's design and performance upgrades set it apart from traditional LED PAR lamps. The innovative CoolSink advanced thermal management system enhances lumen maintenance and lifetime by lowering the operating temperature of the LED and power supply. In addition, the lamp's new MirOptic lens uses a series of multiple integrated reflectors to maximize light distribution and minimize optical loss. This 120W halogen replacement emits soft and pleasant light with low glare and high illuminance.
Data sheet available here: http://www.gc-lighting.com/wp-content/uploads/GREEN-CREATIVE-LED-PAR38-19W.pdf
Joining the PAR38 19W lamp in the 2013 Progress Report is the MR16 7W HIGH CRI lamp. The signature lamp of GREEN CREATIVE'S CRISP SERIES features typical CRI 95, R9 95, and R13 95 values. This compact light combines exceptional color rendering with high lumen output and at 66 LPW, is the most efficient high CRI MR16 50W replacement available today.
Watch this video to learn more about CRI and this CRISP SERIES lamp: http://www.youtube.com/watch?v=DuxJ2HJf9-4.
Data sheet available here: http://www.gc-lighting.com/wp-content/uploads/GREEN-CREATIVE-LED-CRISP-SERIES-MR16-7W-High-CRI.pdf
The third product accepted by IES was the MR16 7W High Output lamp. This powerful lamp has a 1:1 halogen form factor and produces 525 lumens in Warm White. With an industry leading efficacy of 75 LPW, this lamp is available in 4 CCT and 2 beam angles and is ENERGY STAR qualified in 2700K, 3000K, and 4000K.
Data sheet available here: http://www.gc-lighting.com/wp-content/uploads/GREEN-CREATIVE-LED-MR16-7W-HO.pdf
These products are available through GREEN CREATIVE distributors. For more information on where to purchase these products near you or how to become a distributor, please contact GREEN CREATIVE at: sales@gc-lighting.com or (866) 774-5433.
About GREEN CREATIVE LLC
GREEN CREATIVE is a major solid state lighting development and manufacturing company dedicated to bringing to market the latest in LED technology. The company is committed to providing only relevant high performance LED lamps and fixtures that have been rigorously engineered, manufactured and tested for the demanding commercial market. More information about GREEN CREATIVE is available at www.gc-lighting.com. For all of the latest updates follow GREEN CREATIVE on Twitter and LinkedIn.
Green Creative +1-866-774-5433
E-mail:info@gc-lighting.com
Web Site:www.gc-lighting.com | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,620 |
Copyright © 2006 by David and Leigh Eddings
All rights reserved.
Warner Books
Hachette Book Group
237 Park Avenue
New York, NY 10017
Visit our website at www.HachetteBookGroup.com.
The Warner Books name and logo are registered trademarks of Hachette Book Group, Inc.
First eBook Edition: August 2006
ISBN: 978-0-7595-6797-9
Contents
Copyright
Preface
Mount Shrak
Chapter 1
Chapter 2
Chapter 3
The Journey
Chapter 1
Chapter 2
The Temple Of Aracia
Chapter 1
Chapter 2
Up From The Beach
Chapter 1
Chapter 2
Alarming News
Chapter 1
Chapter 2
Chapter 3
THe Horse-Soldiers
Chapter 1
Chapter 2
Chapter 3
The Violation Of The Temple
Chapter 1
Chapter 2
The Gifted Student
Chapter 1
Chapter 2
Chapter 3
The Defenders Of The Faith
Chapter 1
Chapter 2
Chapter 3
The Commander
Chapter 1
Chapter 2
Confusion
Chapter 1
Chapter 2
The Tribe Of Old-Bear
Chapter 1
Chapter 2
A Report From The North
Chapter 1
The Plea Of Alcevan
Chapter 1
The Dream Of Omago
Chapter 1
Chapter 2
Chapter 3
The Visitor
Chapter 1
Be No More
Chapter 1
Chapter 2
The Decline Of The Temple
Chapter 1
Chapter 2
Chapter 3
The Blizzard
Chapter 1
Chapter 2
The Alternate
Chapter 1
Chapter 2
Chapter 3
The Visit Of Sorgan Hook-Beak
Chapter 1
The Nest
Chapter 1
The Last Generation
Chapter 1
Chapter 2
Chapter 3
Epilogue In The Land Of Dreams
Chapter 1
Chapter 2
Chapter 3
By David and Leigh Eddings
THE DREAMERS
Book One: _The Elder Gods_
Book Two: _The Treasured One_
Book Three: _Crystal Gorge_
THE BELGARIAD
Book One: _Pawn of Prophecy_
Book Two: _Queen of Sorcery_
Book Three: _Magician's Gambit_
Book Four: _Castle of Wizardry_
Book Five: _Enchanters' End Game_
THE MALLOREON
Book One: _Guardian of the West_
Book Two: _King of the Murgos_
Book Three: _Demon Lord of Karanda_
Book Four: _Sorceress of Darshiva_
Book Five: _The Seeress of Kell_
_B ELGARATH THE SORCERER_
_P OLGARA THE SORCERESS_
_T HE RIVAN CODEX_
THE ELENIUM
Book One: _The Diamond Throne_
Book Two: _The Ruby Knight_
Book Three: _The Sapphire Rose_
THE TAMULI
Book One: _Domes of Fire_
Book Two: _The Shining Ones_
Book Three: _The Hidden City_
_T HE REDEMPTION OF ALTHALUS_
_H IGH HUNT_
_T HE LOSERS_
_R EGINA'S SONG_
**Preface**
Those of us who devote our lives to the care of Mother were greatly concerned by her rage after the disaster of "blue fire" which had consumed so many of her warrior children. It is the duty of the warrior children to die if it is necessary to achieve that which Mother wants, but deaths beyond counting reduce our numbers and weaken the overmind which guides us all. And, truly, the weakening of the overmind lessens all of us who live but to serve our beloved Mother.
We are told by those who came before us that Mother had been content in the nest which shelters us all until—in times long past—the weather changed and in each season there was less to eat than there had been in previous seasons. It had been then that Mother had sent forth those servants we call "the seekers of knowledge," and in time they returned and told Mother that beyond the high hills that surround our homeland there was much to eat. And this warmed Mother's heart. It came to her that should those who search for things to eat go beyond the high hills and bring back much to eat, she could spawn yet more children—and then even more—and soon our numbers would be so great that no other mothers would dare to send _their_ children out to fight with us for things-to-eat, since we would destroy their children and soon they would be alone in their nests screaming in despair.
And so it was that Mother began to alter the children which would go forth from the nest to search for things-to-eat in the lands beyond the high hills. And many were her alterations, for the man-things that dwelt in the lands beyond the high hills were very clever and they used weapons that were _not_ parts of their bodies.
And this gave Mother great concern, for it is most unnatural for _any_ creature to take up things that are not parts of their bodies to use as weapons. Then it came to Mother that if the man-things could do this, could not _her_ children do so as well? She sent forth more of the seekers of knowledge to find creatures who had unusual parts of their bodies that gave them advantages in the search for things-to-eat.
And the seekers of knowledge returned in time with much that Mother might find useful. There were creatures without legs that had long, sharp teeth that could instantly kill anything the creature without legs saw as something-to-eat. There were other creatures who had eight legs rather than six who could turn the insides of things-to-eat into liquid that the eight-legged creature could conveniently drink. There were creatures with hard shells that covered and protected their bodies, and there were still other creatures with hard, sharp mouth-parts that could cut pieces off the thing that was being eaten.
The more dear Mother considered it, the more she thought that the teeth of the creature that had no legs might be the most effective.
Then, in seasons beyond counting, Mother put generation after generation to work on the high hills that stood between our nest and the land of the sunset. There were burrows that would safely take Mother's children beyond the peaks of the high hills, and there were many flat stones piled on the slope of the high hill that appeared to have once been nests of the man-things, and it seemed that the empty nests might be useful to deceive the man-things.
In time, all was complete, and Mother waited as the elder divinities grew older and less responsive. Then, in the springtime of this present year, all was ready, and Mother commanded the children to attack the man-things clustered near the top of that particular high hill.
And great was the consternation of the man-things when the servants of our mother crossed the empty ground to attack the pile of rocks the man-things had gathered at the top of that high hill. But the man-things knew not that most of the servants of dear Mother were creeping through burrows that went beneath that high hill to come out in various rock-piles lying on the sunset side of the high hills.
And Mother rejoiced, for victory was now in her grasp.
But it was not to be, for disaster came down on the servants in the burrows. Two of the high hills did most suddenly burst into flame, hurling liquid fire high into the spring sky. It was not the liquid fire in the sky that brought grief to Mother, however. It was the liquid fire that ran down through the burrows that made the servants of dear Mother vanish as if they had never been.
And when word of this reached Mother, she shrieked in agony, and all who lived but to serve her shrieked as well, for our overmind was made less by this disaster.
Now, the seekers of knowledge had spent much time over generations in the lands of the man-things, and they had come to learn the way by which the man-things used noises to communicate with each other. And many of the seekers of knowledge had learned how to make the noises the man-things called "speech." And so it was that when our beloved Mother decided that we should go down into the land of longer summers where there was much to eat, the seekers went up the slope of the high hills to gather information about the man-things of that region.
And while the seekers worked on this task, beloved Mother brought forth many new forms for the warrior children. The new forms were well-designed to overcome the many advantages the man-things appeared to have had in the land of the sunset.
And when the seekers returned, they were sorely discontented, for the man-things had told them many things that were not true. In truth it would appear that the man-things said more things that were _not_ true than were truly true. The seekers had discovered _one_ thing that they felt to be most important, however. Although that which ruled the land of longer summers was called Veltan, there was another man-thing called Omago, who had far, far more power than did the one called Veltan. The Omago thing was not yet fully aware of this power, and it had never used it. There was yet another man-thing called Ara, however, who shared this knowledge with the Omago thing, but it never spoke with the Omago thing about that power.
As the new hatch of the warrior servants matured, beloved Mother sent them toward the land of longer summers, and we all believed that our warrior servants would most easily overcome the man-things, and the land of longer summers would be ours before the seasons changed.
But it was not so, for many man-things had come to the land of longer summers, and they had piled up endless stacks of flat stones to impede our progress toward what was rightfully ours. And once again, the cursed man-things used things that were _not_ parts of their bodies as weapons. We had encountered the flying sticks before, though none of us had been able to understand just _how_ the man-things could make the sticks fly. Some of us were quite sure that the sticks were live things that were controlled by various man-things. When the man-thing said "fly," the stick obeyed. Then, when the stick was in mid-flight, the man-thing spoke again and said "kill." And the stick did that.
We searched and searched for sticks that would obey commands, but we found them not.
The man-things had used other weapons as well. The long stick did not fly, but it was nearly as cruel as were the flying sticks. The long sticks had wide points that were alien, having no relation to the stick itself. The points were very sharp, and they easily penetrated the bodies of the warrior servants.
It came to us that many of the man-things we had encountered were not related to the man-things that occupied the land of the sunset and now the land of longer summers.
The struggle on the slope was long and difficult, and our beloved Mother sent many new-form servants into the struggle, but they could not overcome the man-things who hid themselves behind their protective rock-piles, rising to their feet only to kill those of us who were attacking.
Much disturbed were those of us who are the _true_ servants of beloved Mother when she insisted that we should take her from the nest to the region where the conflict was taking place. _Her_ safety must always be our first obligation, but Mother saw no reason to be concerned. She is immortal, of course, but the conflict was raging in the land of longer summers. The nest was safe, but the region of conflict was not.
She _was_ Mother, however, so we had no choice but to obey her.
Then yet another group of man-things came rushing up from far down in the land of longer summers, and that particular group appeared to have some other goal than the defeat of Mother's warrior servants. There were many reports from the seekers that the man-things which had been fighting Mother's warrior servants were stepping aside to let the new group pass through without restraint.
And the new group of man-things rushed to the top of the slope that led down to Mother's region and then they ran on down that slope—almost as if they could not even see Mother's warrior servants. We have learned—much to our sorrow—that most of the man-things are extremely clever, but the new group of man-things seemed to have little or no thought as they blindly rushed down the slope toward something which only they could see.
And Mother's warrior servants of several altered forms killed the mindless man-things by the thousands, but the other mindless man-things paid no heed to the fate of their companions, but continued their rush down the slope toward that which only they could see.
And then it was that enormous amounts of water burst forth from the upper face of the high hill above us, and Mother's warrior servants and the mindless man-things alike were engulfed in water and carried down the slope to certain destruction.
And Mother screamed in anguish even as those of us who live but to serve her carried her back toward the safety of the nest, for it was now clear that water could be as deadly as fire, and that the land of longer summers was now and forever beyond our reach.
Great was the grief of our beloved Mother, but in time the seekers of knowledge persuaded her that there were still two regions beyond the high hills that were not now and forever blocked off from us. There was the land of the sunrise and the land of shorter summers. Many were the arguments between those warrior servants who favored the land of shorter summers and those who favored the land of the sunrise, and those arguments became more heated until those who preferred shorter summers and those who favored sunrise began to kill each other.
And finally, to prevent more of the killing, beloved Mother chose shorter summers, and once she had chosen, the killing stopped.
The seekers were much interested in a low-tree that flickered and put out light and dark clouds which lay close to the ground or rose high up into the sky, for they saw that low-tree as a way to kill the man-things from a long way off, and that would put none of the servants of our beloved Mother in peril.
And the seekers were much pleased when they discovered that the low-tree was most generous, and freely it shared its flickers and clouds with other low-trees of its own kind.
Now other seekers had gone into the high hills that blocked off the land of shorter summers, and they soon found a narrow pathway that went through the high hills and emerged in a well-concealed manner in the land of shorter summers.
Cautious was our beloved Mother, however, and she sent forth servants that could make the noises of the man-things to deceive the man-things and to set them at war one with the other, for it had come to the overmind that the man-things on occasion hated each other even more than they hated us, and gladly would they kill each other, and that would make things easier for Mother's warrior servants.
We proceeded across the flat place where there are no things-to-eat and came at last to the narrow pathway that led from Mother's region to the land of shorter summers. Much were we discontented when we arrived there, however, for the man-things had once more piled flat rocks on top of other flat rocks to block our path.
We now had a means to drive them away, however. The seekers entered several nesting places in the high hills below the flat rock-pile of the man-things, there to make piles of the low-trees that flicker inside the nesting places, and dense black clouds passed over their rock-pile, and then the man-things turned and fled, leaving the pathway open to the warrior servants.
Beloved Mother rejoiced and told the warrior servants to move rapidly along the narrow pathway toward the land of shorter summers, for now the low-trees—which almost certainly loved Mother almost as much as do we who serve and protect her—continued to drive the man-things away.
And so it was that the warrior servants swarmed up the narrow pathway with victory almost certainly within their reach.
But then a man-thing that was _not_ a breeder as most of the man-things are unleashed something that no one has ever seen before. We, the servants of beloved Mother, have encountered the fires of the man-things before, but the man-thing who was not a breeder sent a huge wave of fire that was _not_ yellow down the pathway. The fire was blue instead, and it consumed warrior servants uncounted as it rushed on down the narrow path and even beyond.
That in itself was horrid beyond anything we had yet encountered, but then the man-thing which was _not_ a breeder called forth yet another blue fire at the foot of our narrow path. And _that_ blue fire rose higher than the pile of flat rocks the man-things had built, and it showed no indication that it would ever stop burning.
And yet once again, our beloved Mother screamed in agony, and we who serve her also screamed.
So great was Mother's fury that she listened to a suggestion of one of the seekers—a suggestion she would not even have considered had she been more calm. The seeker declared that since there was only one part of this land that was _not_ blocked, the man-things would certainly know that Mother's warrior servants would attack them from that direction, and their numbers would be enormous. "You will need many, many warrior servants to overcome the man-things, beloved Vlagh," she said. "Can you possibly spawn out more this time than you did when we attacked the other directions?"
"Many, many more," dear Mother replied. "I will bury the man-things in freshly hatched spawn. I _will_ have the land of the sunrise, and my children will feed on the remains of all the man-things that contaminate this entire land that is—and always will be— _mine_."
We did not wish to remind beloved Mother that a spawn of that size would severely reduce any future spawns to the point that there would hardly be enough new care-givers to see to her needs, and seasons uncountable would pass before she could spawn more. We tried as best we could to bring this to her attention, but she paid little heed and commanded us to carry her straightaway to the spawning chamber. And, since it is required, we did as she commanded.
Should disaster come again, however, the children of future spawns will be so limited that as the seasons plod on by, the nest of our beloved Mother will have few—if any—care-givers to see to her needs, and in time, it may be that she will dwell here alone.
[MOUNT
SHRAK](YoungerGods_toc.html#part_1)
**1**
It was well past midnight, and Zelana was standing alone on the balcony of what big brother Dahlaine called his "War Chamber." It seemed to Zelana that those fancy names had always been one of Dahlaine's failings. For some reason he seemed to feel a need to give almost _everything_ some kind of stupendous title. If he'd spend as much time _solving_ a problem as he usually spent coming up with a name for it, things might go a bit smoother for him.
Right now, however, Zelana was trying to swallow some very peculiar events. It seemed that they had a mysterious helper who could pull miracles out of her hat—or sleeve—without any kind of warning at all.
Down in baby brother Veltan's Domain, Longbow had been plagued with a series of very peculiar dreams which were being rammed into his mind by an entity he always called "our unknown friend," despite the fact that he'd told Zelana and the others that he recognized the voice—but he couldn't quite attach a name to the speaker. Zelana knew that Longbow's mind was too sharp to start getting fuzzy about something _that_ important, so it was quite obvious that "unknown friend" had been tampering with him in ways Zelana could not even begin to comprehend.
There was one thing that was abundantly clear, however. Not only could "unknown friend" erase memories, she could also break—or just ignore—some very important rules. Zelana and her family were _not_ permitted to kill things. "Unknown friend," however, had manipulated the members of the Trogite Church with her "sea of gold" and lured them into a confrontation with the Creatures of the Wasteland. Then, when the two enemy forces were locked in what would almost certainly have turned out to be a war of mutual extinction, "unknown friend" had obliterated them _all_ with an enormous wall of water that she'd pulled up from about six miles down below the face of the earth.
It seemed that their friend had powers that Zelana could not even imagine, although she was almost positive that their friend was using the Dreamers to assist her.
The more Zelana thought about it, the more certain she became that Eleria's flood and Yaltar's twin volcanos had _also_ originated in the mind and imagination of "unknown friend."
The involvement of the Dreamers had been confirmed when the children's shared vision had mentioned "a fire unlike any fire we have ever seen," which had produced the blue inferno that had obliterated what had almost certainly been an entire hatch of the Vlagh.
That, of course, brought Aracia's idiotic attempt to conceal Lillabeth's Dream right out into the open. Aracia had always been obsessed with her own divinity, but now—probably because of the overdone adoration of those assorted indolents who had identified themselves as her clergy—Aracia's mind had begun to slip, and she seemed to be convinced that she was now the most important creature in the entire universe. Her absurd attempt to conceal Lillabeth's Dream had been a clear indication that sister Aracia's mind was starting to come apart.
The more that Zelana thought about it, though, the more she remembered that Aracia had _always_ been more than a little unwilling to go to sleep and relinquish her Domain to Enalla. It seemed that deep down, Zelana's sister _hated_ Enalla. The length of their sleep-cycle made change inevitable. Zelana ruefully recalled the time in the distant past when she'd awakened to find her Domain covered with ice that must have been at least two miles deep. It had taken Dahlaine weeks to explain _that_ to Zelana's satisfaction. He'd assured her that the inevitable thaw had already begun, but it had been almost five centuries before the ice was gone, and Zelana's Domain didn't look at all the way it had when she'd drifted off to sleep. Perhaps even more disturbing had been the fact that the creatures she'd come to know in her previous cycle were all gone, and strange new animals had arrived to replace them. Dahlaine had used the term "extinction," and that had chilled Zelana all the way down to her bones. She'd had almost no contact with Aracia during that particular cycle, but she was almost positive that her sister had somehow twisted things around in her mind so that she could blame Enalla for those eons of ice and the disappearance of almost all of the creatures that had been present in her Domain when she'd gone to sleep.
Something like that _was_ the sort of thing Aracia would do.
Zelana was growing more and more weary now, and she'd be more than willing to hand the responsibilities of the Domain of the West to Balacenia—the adult version of Eleria—but she was almost positive that Aracia wouldn't see things that way at all, _and_ her priesthood was probably in a state of near-panic by now. Whether they liked it or not, Aracia _would_ go to sleep very soon, and Enalla would replace her. Zelana had caught a few hints from Eleria that Enalla—the _real_ version of Lillabeth—had some plans that Aracia's priests wouldn't like very much at all.
"It might almost be worth staying awake long enough to watch," she murmured to herself. " _Almost_ ," she added, "but not quite." As closely as she could determine, "sleep-time" was no more than a few months away. She'd long since decided that the pink grotto on the Isle of Thurn would be the place where she'd sleep this time. The pink dolphins would sing her to sleep, and she might even have dreams of her own this time—dreams of a Land of Dhrall without a Vlagh, and a land where her friends did not grow old and pass away, and where she could sing and write poetry, and where it was always spring and the flowers never wilted. Now _that_ might be the best of dreams.
"I _thought_ I could feel your presence here, dear sister," Dahlaine said as he joined Zelana on the balcony over the "lumpy map" of his Domain. "You seem to be troubled. What's bothering you so much?"
"Aracia, of course," Zelana replied. "I think her mind is slipping even more than it was when she tried to conceal Lillabeth's Dream. I wish that there was some way that we could put her to sleep a few months early this time. Then we could all concentrate on the Vlagh and stop worrying about our sister."
"It probably _would_ make things a lot easier."
"What _is_ it about Aracia that makes her start to go to pieces at the end of every cycle?" Zelana demanded. "I was thinking back, and as closely as I can remember, Aracia's never once gone off to sleep without fighting it every step of the way. Why does she _do_ that?"
Dahlaine shrugged. "Inferiority, most likely. When you include our alternates, there are eight of us altogether, and as closely as I've been able to determine, our alternates trade off authority in the same way that we do. That suggests that Aracia's the dominant one for only twenty-five thousand years. Then she has to wait for a hundred and seventy-five eons for dominance to return. For some reason, she just can't _stand_ that. She yearns to be at the center of the entire universe. If I remember correctly—and I usually do—the last time she was dominant, she literally wallowed in her position. Of course there weren't any developed humans around back then, so _she_ was the only one around who could adore her, but as I remember, her self-adoration was more than a little extreme."
Zelana smiled. "Maybe you and I should join Veltan when our next waking cycle rolls around. I'm sure he was just trying to make a joke of it—we all know how much Veltan enjoys jokes—but he told me on one occasion that he might just go back and camp out on the moon when Aracia's next cycle of dominance comes along, and I think he was about half-serious when he said it."
"That's our baby brother for you. Any time responsibility comes along, Veltan runs away." Dahlaine scratched his cheek. "It probably wouldn't have made much difference in eons past, but there are humans in our various Domains now. I don't know about _you_ , dear sister, but I will _not_ permit Aracia to run roughshod over the people of _my_ Domain."
"You almost sound like you're thinking about declaring war on our sister."
"I'd hardly call it a war, Zelana. Aracia's people are supposed to spend every waking moment adoring her, so they wouldn't pose much of a threat."
"You're putting our sister in the same category as holy—but crazy—Azakan of the Atazak Nation of your own Domain, big brother," Zelana said. Then she frowned. "There _are_ quite a few similarities, though, aren't there?"
"Except that Aracia actually _has_ the power to make things happen. Poor Azakan spent most of his time ordering the earth and sky to obey him, but I don't think they paid very much attention. Aracia, however, has a certain amount of power, so she _can_ make things happen if she feels the need."
"Maybe so, but none of us are permitted to _use_ that power if killing things is going to be involved. If Aracia steps over that line, she'll probably vanish right then and there," Zelana suggested. "And if _Aracia_ vanishes, will _we_ still be here? There's a linkage between the four of us, Dahlaine, and if _one_ of us ceases to exist, isn't it quite possible that we'll _all_ just vanish?"
"You're starting to give me a headache, Zelana."
"At least it's still there to ache, mighty brother."
"I think we've had _one_ stroke of good luck, Zelana. Your pirate chief has persuaded Commander Narasan not to just pack up and go home. We're going to need forts in Long-Pass, and when someone says 'forts,' he's usually talking about Trogites. Did _you_ have anything to do with Sorgan's little scheme?"
"No, big brother. As closely as I can determine, Hook-Beak came up with that all by himself. Of course, the likelihood that he'll be able to swindle a lot of gold out of Aracia probably played a large part in his decision, but right up beside his greed is his friendship for Narasan. He'll keep Aracia so flustered that she probably won't even remember that Narasan exists. He'll go on down to Aracia's absurdly overdone temple and persuade our none too bright sister that he'll be more than happy to defend her— _if_ she'll give him enough gold."
"What's he going to defend her _against_?" Dahlaine asked. "The servants of the Vlagh will be coming down Long-Pass, so they won't be anywhere _near_ Aracia's temple."
Zelana smiled. "If I know Sorgan—and I _do_ —he'll come up with ways to keep Aracia—and her clergy—so terrified that they won't even _think_ about sending anybody up Long-Pass to pester Narasan while he's building forts."
It wasn't much later when the door to Dahlaine's map room opened slightly, and Eleria looked in. "Ah, _there_ you are, Beloved," she said to Zelana. "We should have guessed that you'd be in here conferring with dear old Grey-Beard."
"Mind your manners, Eleria," Zelana chided her Dreamer.
"I'm sorry, Old Grey-Beard," Eleria said with one of her mischievous grins. "We've been looking for you and the Beloved for hours now."
"We?" Dahlaine asked curiously.
"Big-Me and I. Mother wants us to talk with you."
"Mother?" Zelana asked, feeling suddenly baffled.
"We _all_ have a mother, you know, Beloved. Big-Me can explain it much better than I can, I'm sure." Then Eleria came on inside the large room, and immediately behind her was an extremely beautiful lady.
Dahlaine gasped. "What are you _doing_ , Balacenia?" he demanded. "You're not supposed to be awake yet."
"Grow up, Dahlaine," the lady replied. "Your little game almost tore the world apart. We've had a lot of trouble smoothing things over, and we're not even supposed to be awake yet."
Zelana was staring at the lady. "Are you _really_ —" She almost choked at that point.
"Yes, Beloved, I _am_ your alternate. Our Domain is still under your control, however. I promise that I won't tamper—unless Mother tells me—us—to." She put her hand on Eleria's shoulder. "This can be terribly confusing sometimes. This is Little-Me. You know her as Eleria, which is sort of all right, I suppose. She makes me laugh quite often, and laughter's good for the soul—or so I've been told. There _is_ something I've been curious about, though. Where in the world did she come up with her hugs and kisses ploy? She has poor Vash so confused that he doesn't know exactly what to do."
Zelana suddenly smiled. "The idea came to Eleria back in the pink grotto when she was very, very young. She can kiss a pink dolphin into submission in no time at all." Then she looked rather closely at Balacenia, her alternate. "The resemblances are definitely there, Balacenia. You _are_ , in fact, a grown-up version of Eleria the Dreamer. How is it that the two of you can both be in the same place at the same time?"
"It's just a little complex, Beloved. Actually, we're _not_ here at the same time. Actually, I'm not even really here. I'm still sound asleep, and what we're all seeing right now is _my_ Dream."
"That's not possible!" Dahlaine protested.
"Why—and how—am I here, then?" Balacenia demanded. "Your little game was very clever, Dahlaine, but it got away from you almost right at the beginning. You _thought_ that you could step around us with your 'infant' hoax, but it started to come apart when Eleria had her first Dream. That was the one when she saw the very beginning of this world. Then, a little later in the Land of Maag she had a variety of Dream that you didn't even anticipate. She had what _we_ call a 'warning dream,' and it was _that_ Dream that saved Longbow and his friends from the intentions of the Maag called Kajak. _You_ might not have been aware of what that Dream suggested to _us_. Dreams can be warnings as well as predictions."
"That _did_ startle me just a bit," Dahlaine admitted. "I'd sort of believed that _I_ might have some control over the Dreams, but the children keep slipping around me."
"Actually, it's Mother who's guiding the Dreamers. She picked up your little game, and she's doing things with it that you couldn't even imagine."
"Mother?" Dahlaine sounded startled. "We don't _have_ a mother."
"Where did we come from, then?" Balacenia demanded.
"You'll really like her, Dahlaine," Eleria said. "She can do all kinds of fun things. She was the one who took me down under the sea so that I could pick up my pink pearl. That's what started all this, remember?"
"She's the mother of the whole universe, Dahlaine," Balacenia added, "and she's more than a little peeved with you right now. The outlanders are all right, I suppose, but Mother was—and still is—dealing with it in her own way."
"That will do, Balacenia," a melodious voice came through the open doorway. "Why don't you let _me_ deal with this?" Then a misty sort of form that seemed to be pure light came through the open doorway. "What were you thinking of when you hired all those outlanders to come here and fight this war for you, Dahlaine?"
"You _do_ know that we have limitations, don't you?" Dahlaine demanded. "Now that I think about it, if you're who Balacenia says you are, _you're_ probably the one who came up with them. You may have forgotten, but we aren't permitted to kill things—even when they're attacking us. We needed armies, so we went out into the world to hire outlanders to do the killing for us."
"That particular limitation might just be a little outdated," the glowing presence conceded. "Right at first, there were very few living things here, and we didn't want to lose any of them—at least not until the populations had grown to the point that extinction was no longer a distinct possibility. When the incursions by the Creatures of the Wasteland began, I was going to take care of it myself, but before I could even start, the whole Land of Dhrall was crawling with outlanders. You've got to learn to trust me, Dahlaine."
"Longbow suggested something you might want to consider, though." Zelana stepped in. "The assorted outlanders _are_ helping us to hold back the Creatures of the Wasteland, but Longbow seems to think that it's much more important that the more greedy outlanders come to realize that the people of the Land of Dhrall are quite capable of making life very unpleasant for _any_ invaders. The outlanders are helping, but they're also learning. The greed of the Amarite Church down in the Trogite Empire was almost legendary, but _you_ dealt with that in a way that advised _all_ outlanders that an attempted invasion of our part of the world could be a ghastly mistake."
"And your blue fire in Crystal Gorge made it more obvious," Dahlaine added. "Nobody in his right mind walks into fire. Some of the more greedy outlanders might _want_ to come back, but I don't think they will." He hesitated. "You seem to be very attached to us, for some reason," he said rather carefully.
"You _are_ my children," the glowing form replied, "and I _will_ protect you. You've come a long, long way, but you might want to go back a bit and have a look at where—and when—this began."
Zelana's mind suddenly reeled as memories came rushing back from so far in the distant past that there was no word for that many years. The suggestion of the hazy figure of glowing light had seemed to set off bells inside Zelana's mind.
Dahlaine's eyes suddenly went very wide as—evidently—the same memories came flooding over him.
"All in all, you did quite well, my son," Misty Lady continued. "Your notion of the Dreamers was brilliant, and it's worked almost perfectly—except that you'll have to come up with a way to persuade the Dreamers to reunite with their previous identities. Things are just a little touchy this time, however, so I want all of you children to back away and let _me_ deal with the situation in Aracia's Domain. It's almost reached the point that she'd rather die than hand her Domain over to Enalla. We've _got_ to get her under control, because she's getting very close to total insanity. If she crosses that line, we'll lose her, and that will lead to a disaster—not immediately, maybe—but if she's a raving lunatic when she wakes up from her sleep-cycle, the entire Land of Dhrall will be at risk—and _that_ risk will make the invasion of the Creatures of the Wasteland look like some child's game by comparison."
**2**
Zelana was certain that it was just after sunrise when the commanders of the outlander forces, led by the bleak-faced Longbow, came through the door and out onto the balcony that encircled Dahlaine's map room.
"The map seems to have changed a bit," Longbow said, looking down at the map Dahlaine had put in place after Balacenia and the strange, mist-covered figure of "Mother" had left.
Dahlaine shrugged. "We've finished here in my part of the Land of Dhrall," he explained, "so I laid out a 'lumpy map' of sister Aracia's Domain. Ordinarily, we'd have relied on Aracia for a map, but her view of her Domain is just a bit vague, since she almost never leaves her temple."
"Being worshiped _would_ probably take quite a bit of time," Sorgan Hook-Beak said, peering down at the well-illuminated map. "Just exactly where _is_ this 'temple-town' that's got everybody so worked up?"
Dahlaine reached out with his hand, and a bright beam of light came from his forefinger and illuminated a spot on the representation of the east coast.
"That's a useful idea there, Lord Dahlaine," Sorgan said, "particularly when we're all standing ten feet or so above the map."
"It _does_ seem to work fairly well," Dahlaine replied modestly.
"And where's this 'Long-Pass' that everybody keeps on talking about?"
Dahlaine's glowing little spot of light moved along the eastern edge of the map to a sizeable replica of a bay with a fairly wide river running down to it.
"Then the river's not in any way connected to your sister's temple-town?" Sorgan asked.
Dahlaine shook his head. "The east coast of the Land of Dhrall gets some savage floods almost every year," he explained. "Aracia didn't want her temple destroyed that often, so she had her servants build it farther south where there aren't any major rivers coming down out of the mountains. The ground's sort of marshy, but Aracia's workers laid in a substantial base before they started construction."
"How long ago was it when they built the temple?" Keselo asked.
"Eight—maybe ten—centuries ago, wouldn't you say, Zelana?" Dahlaine asked.
"You couldn't prove that by me, brother mine," Zelana replied. "I was living in my grotto on the Isle of Thurn then."
"Do all those priests who worship your sister plant crops of any kind near the temple?" Sorgan asked.
Dahlaine shook his head. "The farmers of Aracia's Domain deliver large amounts of food to keep most of our sister's priests quite fat, at least."
"Fat seems to show up quite often in the world of priests," Longbow observed.
"Professional hazard, wouldn't you say, big brother?" Zelana suggested. "Priests spend much of their time stuffing food into their mouths."
"And that makes them so fat that their hearts wear out and they fall over dead," Dahlaine added.
"Now _there's_ an idea," Rabbit said. "If we just happened to pile twenty or thirty tons of food on the steps of sister Aracia's temple, her priests would eat themselves to death inside a week."
"I _like_ that notion, brother," Zelana said. "We wouldn't violate our limitations by providing food for dear Aracia's priests, would we? And if they ate too much and fell over dead, it wouldn't be _our_ fault, would it?"
Dahlaine squinted at the ceiling. "You might want to take that up with Mother, Zelana. If we feed Aracia's priests too much and they die as a result, wouldn't that almost be the same as poisoning them?"
"Spoilsport," Zelana grumbled. "Can you imagine how much screaming would come from Aracia's temple if she woke up one morning to discover that all of her priests had died during the night?"
"We'll keep the idea in reserve, dear sister," Dahlaine said. "Let's push on, though." He looked at Narasan. "Who would you say is the head of sister Aracia's priesthood?"
"They call him Takal Bersla," Narasan replied, "and he's almost as fat as Adnari Estarg of the Amarite Church was—before that overgrown spider had him for lunch. Bersla has made a career out of oration. He spends hours every day telling your sister how holy she is, and Aracia's almost paralyzed by Bersla's overdone speeches. Padan kept track one day not long after we'd arrived at Aracia's temple, and Bersla talked to your sister for six straight hours. Then he ate lunch—a lunch that would have overstuffed four or five normal people—and then he stood up and orated for another five or six hours. The man's a talking machine, but your sister can't seem to get enough of all that tedious adoration."
"It sounds to me like she's getting even worse, Dahlaine," Zelana observed. "She drinks in adoration in almost the same way that a drunkard pours beer into his mouth."
"It's not a good sign, Lord Dahlaine," Sorgan said. "If her mind has slipped _that_ far, getting her attention might be a little difficult."
"Not necessarily, cousin," Torl disagreed. "If this Bersla priest is the main adorer in Lady Aracia's temple, and he wound up dead some morning, you could probably get her immediate attention."
"Maybe so, Torl," Sorgan agreed, "but how do we know that he'll die at any time in the near future?"
Torl slid his hand down into the top of his boot and pulled out a long, slender dagger. "I can almost guarantee that, cousin," he said, flourishing his dagger.
"It _has_ got some possibilities, Lord Dahlaine," Sorgan said. "If your sister's sitting on her throne some morning and several of her priests drag the body of her favorite underling into her throne room to show her that somebody—or some _thing_ —slipped into her temple and butchered her head priest, she'd go to pieces. Then, if I tell her that the stab-wounds in Bersla's body were almost certainly caused by the teeth of one of the bug-people, she'd start paying very close attention to anything I said. I could feed her all kinds of wild stories about bug-people creeping around through the halls of her temple killing off her priests by the dozens."
"Wouldn't she demand to see the bodies?"
Sorgan shrugged. "If she wants to look at bodies, we'll _show_ her bodies. Torl might have to sharpen his dagger six or eight times a day, but that's all right."
"Thanks, cousin," Torl said sourly.
"Don't mention it, Torl," Sorgan replied.
"I'd say that the separation of Long-Pass from Aracia's temple will work out very well for you," Longbow suggested to Sorgan and Narasan a bit later. "You can sail on down to that river-mouth, and those of you who'll be going on up Long-Pass can go ashore while Sorgan goes on down to pacify Aracia. She and her servants won't even know that you're anywhere in that pass, so she won't be issuing commands for you to rush on down south to defend _her_."
"That's a very good idea, Longbow," Narasan agreed. "I'm sure that the only thing that interests Bersla will be the defense of the temple. He doesn't care at all about what happens to the ordinary people of Aracia's Domain. He wouldn't so much as turn a hair if all the rest of Aracia's Domain was overrun by the bug-people."
"There's a thought, Captain Hook-Beak," Keselo said. "If you send out some scouts and they report back that the bug-men are eating all of the peasants, the priests will be afraid to come out of the temple and take a look for themselves. They'll hole up inside the temple itself—almost as if they were prisoners."
"It _would_ keep them out from underfoot," Sorgan agreed. Then he looked at his friend Narasan. "You've been there, but I haven't," he said. "Did you see anything at all like building material near the temple? Rocks or logs or anything like that? If we're going to go through the motions of _looking_ like we're building a defensive wall of some kind, we'll need to put up something that _looks_ like a fort."
"You're not going to find anything like rocks—or even logs—in marshy country, Sorgan," Narasan replied.
"Ah, well," Sorgan said, "the temple's there anyway. It shouldn't be _too_ hard to knock it down so that we can build a fort."
"Our sister will come apart at the seams if you do that, Sorgan," Zelana told him.
"And you'll be able to hear her priests screaming from ten miles away," Dahlaine added.
"Not after my scouts come back and report that the bug-people are eating the farmers alive, I won't," Sorgan disagreed. "When the fat ones hear _that_ , they might even offer to help. Just how big would you say that temple is, Narasan?"
"About a mile or so square," Narasan replied.
"You're not serious!"
"The priesthood's been building Aracia's temple for centuries, Sorgan," Dahlaine said.
"You should be able to build quite a wall with that much stone, Sorgan," the warrior queen Trenicia said.
"The screaming's likely to go on for a long time, though," Veltan added.
"Not if the stories my scouts bring back from the countryside are awful enough, it won't," Sorgan disagreed. "If the priests hear about a bug that's twelve feet tall and rips out a man's liver when it gets hungry, they'll run for cover and tell us to do whatever's necessary to hold back the monsters— _and_ they'll be hiding so far back in the temple that they won't see daylight for at least a month."
"I _like_ it!" Narasan said enthusiastically.
"That's the way we'll do 'er then, old friend," Sorgan replied with a broad grin.
Zelana smiled. The unlikely seeming friendship between Sorgan and Narasan seemed to be growing stronger and stronger, and now it appeared that they'd do almost anything to help each other.
While their men were preparing for the long march to the east coast of Dahlaine's part of the Land of Dhrall, Sorgan, Narasan, and several others spent most of their time carefully studying the map.
"I'm going to need those ships as soon as you unload your men down in Aracia's temple-town, Sorgan," Narasan reminded his friend. "I'll still have more than half of my army sitting on that beach on the east coast."
"No problem," Sorgan replied. "The ships would only clutter up the harbor of temple-town anyway. Then too, if Aracia's priests look at your ships _too_ long, they might decide that they want a navy so that they can go out to sea to preach to the fish." He frowned slightly. "Do the people down there actually call their city 'temple-town'? Most places have fancier names."
"The priests—and Aracia herself—never refer to the place as a town, Sorgan," Narasan explained. "The people who live out beyond the walls might have a different name, I suppose, but the people you'll be dealing with just speak of 'the temple.' It's entirely possible, I guess, that _most_ of the priests aren't even aware of the buildings and houses outside the temple walls. For them, the temple is the whole world."
"That's stupid," Sorgan said.
"I think that's the word most people use when they're talking about _any_ priesthood, Sorgan," Narasan said with a faint smile.
Longbow had been studying the map, and he gestured to Sorgan.
The Maag captain joined him. "Do you see anything that might go wrong?" he asked.
"Not _so_ far, friend Sorgan. It just came to me, though, that most of _your_ fleet is still sitting in the bay over there."
"They'd _better_ be," Sorgan replied. "I sent Skell over there to keep a tight grip on them."
"I'm sure that more archers will be very useful once we're in Long-Pass, and it's only a few days south of where your ships are anchored to the village of Old-Bear, where hundreds of archers are sitting around telling stories to each other. If Skell picked them up and carried them on up to that fishing village on the coast, they'd only be a few days behind us, and they'll probably reach the upper mouth of Long-Pass before the bug-people come storming out of the Wasteland."
"That's not a bad idea at all, Longbow," Sorgan approved. "It'll keep the sailors busy, and it'll give Narasan some help when he's likely to need it."
"I definitely approve," Narasan said, "and I'll take all the help I can get."
Longbow continued to stare at Dahlaine's replication of Eastern Dhrall. "There's this range of low, rounded hills running down along the east side of the Land of Dhrall. I think that when we reach that range, I'll lead the archers of Tonthakan on down that way, and Old-Bear's archers won't be _too_ far behind us. We'll most likely be at the upper end of Long-Pass even before Narasan's fort-builders get there. We can make sure that there won't be any surprises for the Trogites when they go up there to build forts."
"I'll get word to Skell," Sorgan said. Then he looked over at his friend. "How many forts were you planning to build?" he asked Narasan.
"As many as the Vlagh gives me time to build," Narasan replied. "I'd go for one fort every mile or so down that pass if I've got enough time. The bug-people don't like forts, so I'll make things as unpleasant for them as I possibly can."
"How are you going to keep the bugs from smoking you out again like they did down in Crystal Gorge?" Rabbit asked.
"Veltan and I can take care of that if it's necessary," Dahlaine said, "but I don't think the bugs will try that again. The prevailing wind down there comes in out of the east, and if they tried greasy smoke again, that wind would blow it right back in their faces."
"The Vlagh almost has to be desperate this time, big brother," Veltan said. "The other three regions have been blocked off, so this is the only way left. If she doesn't win _this_ time, she'll spend the rest of eternity trapped out there in the Wasteland. She'll do almost anything to get her servants past you."
"We'll have to make sure that she doesn't succeed then, little brother," Dahlaine said quite firmly.
It was somewhat later, and all of the outlanders had gone to their beds. Zelana and her brothers lingered in the map room, however. All three of them were quite certain that they'd soon be getting more instructions. Longbow had also remained behind, but he didn't say why.
It was perhaps midnight when the door opened and Balacenia and her glowing, mist-covered companion joined them on the balcony. "One of you will have to go to sister Aracia's temple with Sorgan," the Misty Lady told them.
"I'll take care of that," Veltan volunteered. "Aracia thinks of me as an immature creature without much of a brain, so she won't pay any attention to me."
"That's not a bad idea, Veltan," the lady said. "Keep a very close eye on Aracia. She's right on the verge of going to pieces, and if her brain flies apart, you'll need to tell Zelana and Dahlaine about it. The three of you might need to step on her to keep her from breaking the rules. We _don't_ want to lose her."
Longbow was standing off to one side, and he had a peculiarly startled expression on his face.
Then, after Balacenia and her glowing companion had left the large room, the usually grim-faced archer suddenly began to laugh.
"What's so funny, Longbow?" Zelana asked.
"Nothing all that important," he replied. But then he laughed again.
Zelana found that to be very irritating, but she wasn't sure just exactly why.
**3**
Early the next morning the assorted armies were preparing to march, and Longbow joined Zelana near the mouth of Dahlaine's cave. "It might save a bit of time if Chief Old-Bear knows that the Maag longships are coming," he suggested.
Zelana smiled. "You'd like to have me fly on down there to let him know, I take it?"
"If it's not too much trouble," Longbow replied.
"And if it is?"
"Do it anyway."
"Longbow!" Zelana exclaimed. "Are you actually giving me orders now?"
"Let's just call it a strong suggestion."
"That means the same thing, doesn't it?"
"Approximately, yes, but it's more polite."
"Things might go more smoothly for you if you'd learn how to smile."
"The air's very cold right now, Zelana," he replied. "Smiling when it's cold is hard on one's teeth."
"Did Dahlaine have time to take a look at that worn-down mountain range off to the east for you?"
Longbow nodded. "His thunderbolt took him on down there at first light this morning," he said. "When he came back, he told us that we wouldn't have any trouble."
"Who are you taking with you when you veer off from the main army?"
"Mostly the local hunters," he replied. "Kathlak will lead the Tonthakans, and Two-Hands will bring the Matans. Ekial and the Malavi horse-soldiers will go with us as well. Actually, that was Narasan's suggestion. He's going to need his ships to carry his army down to the mouth of Long-Pass, and the Malavi don't like to ride in ships. They'll probably be more useful at the upper end of Long-Pass anyway."
"Things should go quite smoothly for you and your people," Zelana said. "That's unless you get caught in a blizzard, of course."
"I think your older brother's going to take care of that," Longbow replied. "He's very good at dealing with the weather."
"How far is it from where you and your men will turn south to the upper end of Long-Pass?" Zelana asked.
"If Dahlaine's map is accurate, it's about a hundred and sixty miles," Longbow said. "I'm sure we'll be able to cover thirty miles a day, and that puts us about five and a half days out. We'll be there before Narasan's ships drop him off at the lower end of the pass. I'm sure that we'll be able to keep the Creatures of the Wasteland out of the upper end of the pass."
"That's all that really matters, I suppose," Zelana said.
Just then Sorgan and Narasan came out of Dahlaine's cave. "Don't worry about a thing, Narasan," Sorgan was saying. "I'll keep Lady Zelana's sister so busy that the notion of causing you any problems won't even cross her mind."
"I appreciate that, my friend," Narasan replied. "If I never _see_ Lady Zelana's sister again, it'll be about six weeks too soon."
Sorgan grinned. "The nice part of this is that she's going to _pay_ me to keep her out of your hair."
Then Eleria's adult person came out of the cave with the warrior queen Trenicia. "Are we almost ready, Beloved?" Balacenia asked Zelana.
"Beloved?" Zelana asked, slightly startled.
"A lot of Eleria's been rubbing off on me," Balacenia replied.
"She's good at that."
Trenicia had joined Narasan and Sorgan, and Balacenia stepped closer to Zelana. "I've been catching a few hints that Trenicia's becoming very attached to Narasan," she said quietly.
"She _wants_ him," Zelana replied. "I spoke with her about that after she and Narasan walked out on Aracia. In many ways Trenicia doesn't think—or behave—like a woman. I made a few suggestions, and she seems to be following them."
"Do you really think she'll catch him?"
"Probably. She can be quite charming when she sets her mind to it." Zelana smiled. "It might sound a bit peculiar, but I've noticed over the years that women who want to catch a man use themselves as bait. I don't know if Trenicia's managed to hook Narasan yet, but it probably won't take her much longer." Then Zelana yawned. "Sorry," she said. "I'm getting to the point that I can barely keep my eyes open."
"I'm sure that this silly war will end very soon," Balacenia said, "and when it does, Eleria and I'll take you home and put you to bed." Then she paused and her expression suddenly became very, very familiar. "Won't that be neat?" she said, using one of Eleria's favorite remarks.
Zelana laughed and took her alternate in her arms. "Eleria calls this a 'hug,'" she explained.
"Yes," Balacenia agreed, "and now I see why she likes them so much. Any time you feel like hugging, Beloved, I'll be right here."
Zelana laughed, and then she yawned again.
[THE
JOURNEY](YoungerGods_toc.html#part_2)
**1**
Sub-Commander Andar was more than a little grateful that Chief Two-Hands of the Matan Nation had given him one of the thickly furred bison-hide cloaks as Commander Narasan's army began the march from Mount Shrak to the east coast of the Land of Dhrall. It was early winter now, and it was bitterly cold in the grassland of Matakan. Andar had grown up in Kaldacin, the capital city of the Trogite Empire, and sometimes during the winter months there it grew chilly enough to put a thin layer of ice on the nearby ponds, but Andar had never before seen a lake or pond that had been frozen solid from the surface all the way down to the bottom in a huge block of solid ice. "How do you people find water to drink when it's this cold, Tlindan?" he asked one of the nearby Matans.
"There's quite a bit of water in that pond," Tlindan replied.
"It's frozen solid," Andar pointed out.
"You'd have to melt it," Tlindan said. "Most of the time we melt snow when we need water, but ice _will_ melt if you're really thirsty and there's no snow nearby." The fur-cloaked Matan squinted across the browned grass toward the horizon. "We don't usually spend much time outdoors during the winter. We sort of hole up in our lodges instead. If a man inside his lodge keeps his fire going, it's fairly warm inside, and a pot-full of snow will melt down in an hour or so. Ice takes longer, but it _will_ melt—eventually. Most of us don't care all that much for ice. It takes quite a while to melt, even if the lodge is very warm."
"How do you melt it when you're out in the open and it's very cold?"
"The best way I've found is to chip the ice with a hand-axe. If you tried to use an axe with a handle, you'd probably break it up into small pieces. You want very tiny chips of ice, since bigger ones take longer to melt. Then, when you've got what looks like enough, you scoop them into a pot. Then you scrape together a fair-sized heap of dried grass, put your pot in the middle of the heap, and then set fire to the grass. You'll have water to drink in almost no time at all."
"Isn't the water a bit hot for drinking?"
Tlindan shrugged. "Add some more ice to cool it down. In the wintertime, I sort of like to drink warm water. Your stomach will spread the warmth around, and you'll feel better all over—except for your feet, of course. Everybody's feet are cold in the winter."
"How can _anybody_ live in a place like this?"
Tlindan spread out his hands. "The hunting's very good, and winter doesn't really last all that long. We don't usually spend much time out of our lodges in the wintertime. It's a very good time to catch up on your sleep. Twelve-hour naps are sort of nice when there's nothing going on outside. A man who takes twelve-hour naps feels all rested when spring arrives."
Andar looked up at the grey clouds rolling off toward the east. "Is it cloudy like this all winter long?" he asked the native.
"Fairly often, yes. Dahlaine's playing with the clouds this year, though. Usually we get blizzards here during the winter season."
"Blizzards?"
"Heavy snowstorms. A good blizzard can put twelve feet of snow down in about a day and a half. When that happens, _nobody_ goes outside. They're not really _bad_ things, though. When the snow melts off in the spring, the grass gets _lots_ of water, and it grows very fast. That gives the bison herds plenty to eat, and they're nice and fat when we go hunting. Weather works _for_ you, if you know how to get along with it." Then he squinted up at the sky. "We'll probably have to stop and set up camp fairly soon. It'll be dark before much longer."
"It's just barely past noon," Andar protested.
"That's one of the things you should know about the north country. In the wintertime up here, the days are only six or seven hours long, and nighttime comes very fast."
Andar frowned. "We can talk more later," he said. "I think I'd better go warn Commander Narasan that night's almost here." He walked rapidly toward the front of the column. "I think we might have a bit of a problem, Commander," he said.
"Now what?" Narasan demanded in a peevish-sounding voice.
"It's going to start getting dark before long. One of the Matans warned me about that. We aren't going to have daylight for much longer."
"It's only a few hours past noon, Andar."
"The Matan told me that there's no more than six or seven hours of daylight up here in the wintertime."
Narasan scowled. "I think we'd better go have a chat with Lord Dahlaine, Andar. We've got a long way to go to reach the east coast, and we're going to need longer days—or it'll be summer before we reach the coast."
"It's not really all that much of a problem, Narasan," Dahlaine said. "I'm sure you remember my toy sun. She—and sister Zelana's fog-bank—helped us quite a bit down in Veltan's Domain."
"I should have remembered that," Narasan said. "How many extra hours a day would you say she'll be able to give us?"
"How many do you want? She enjoys putting out light, so she'll give you as many extra hours of light as you want."
Narasan squinted across the frozen grassland. "She puts out heat as well as light, doesn't she?"
"She kept the inside of my cave warm and cozy when Ashad was just a baby."
"That might even be more valuable than light," Narasan said. Then he looked at Dahlaine. "This isn't really any of my business," he said, "but you don't feel hot and cold in the same way that we do, do you?"
"I know that they exist," Dahlaine replied. "I think I see where you're going with this, Narasan. It's not a bad idea, now that you mention it. If my pet gives you and your men light _and_ heat, you'll be able to go much farther each day, won't you?"
"I'd say at least an extra five miles," Narasan estimated. "Possibly even an extra seven or eight." Then he winced. "That _might_ just disturb my men quite a bit, though."
"I didn't quite follow you there, Narasan."
"Ten miles a day is one of the articles of faith in a Trogite army, Lord Dahlaine. Individual soldiers could exceed that, I'm sure, but when they're marching together, ten miles is the limit. Anything any farther is viewed as an abomination. It's a custom, and we Trogites are big on customs." He shrugged. "It actually grows out of the inevitable delays that keep cropping up when you're moving a hundred thousand men."
"Wouldn't you say that 'rest time' has something to do with the ten-miles-a-day limitation, Commander?" Andar suggested.
"Rest time?" Dahlaine asked.
"Another custom, Lord Dahlaine," Narasan explained. "We're expected to give our men a quarter of each hour spent marching to catch their breath. It makes a certain amount of sense in mountain country, but it's a bit foolish on flat land." His eyes hardened. "I think it might just be time to abolish that foolishness. If we can add an extra few miles to each day's march, we'll almost certainly reach the east coast of your Domain several days earlier than we'd originally planned. I'd say that it's worth a try. Then too, if it's warmer, we won't have to worry too much about blizzards, will we?"
Dahlaine grinned. "It might make them a little sulky," he said, "but I think I'll be able to make them quit pouting. Let's see how far my pet can go. I don't think we'll want mid-summer, but early autumn might be sort of nice."
"Whatever you think best, Lord Dahlaine," Narasan said.
"You're very good at putting all sorts of things together, Narasan," Dahlaine observed.
"That's what an army-commander is supposed to do, Lord Dahlaine. Our people come up with all kinds of ideas, and we're supposed to fit them together to construct a plan that might work. There are many people in my army who are much more clever than I am, but that doesn't hurt my feelings very much. _My_ job involves putting their assorted ideas together to come up with something that'll work and won't get _too_ many of my men killed."
"Aren't you just a little bit out of uniform, Padan?" Andar asked his friend as they set out early the following day.
"I'm supposed to look like a Maag," Padan explained. "Narasan suggested it to Sorgan. The Maags aren't too good at defending cities—burning, yes; defending, no. I'll stay in the background so Aracia's priesthood won't recognize me, and I'll give Sorgan details when he needs them. The idea is to have us put something together that'll _look_ enough like a fort to deceive the priests into believing that we've come up with something impregnable. I'm not as good as Gunda when it comes to building forts, but I should be able to come up with something that _looks_ like a fort."
"Right up until the wind starts blowing," Andar said.
"Be nice," Padan said. Then he scratched at his cheek.
"Problems?" Andar asked.
"Sorgan suggested that I should let my whiskers grow. He said that most Maags wear beards, and if I want to _look_ Maagish, I should get a bit more shaggy. He didn't bother to tell me that the thing itches all the time."
"Maags might not notice that, Padan," Andar replied with a faint smile. "You'd think that people who live out at sea would bathe more often. I'd almost be willing to bet that the Maags are the native home of fleas and lice."
"You're in a grumpy sort of mood today, Andar."
"Homesick, I suppose," Andar admitted. "I miss Kaldacin. It's corrupt and it doesn't smell too good, but it _is_ home."
"If Lord Dahlaine's correct, this will be the last war here in the Land of Dhrall. There's only one path left open to the Creatures of the Wasteland. Once this last one's closed off, we'll all be able to go on back home and sit around counting all the lovely money we've picked up here."
"It'll be a lot cleaner now that the Church of Amar has been eliminated," Andar added. "I don't know if you noticed the similarities between the priests of 'Holy Aracia' and the high-ranking clergymen of the Church of Amar."
"They're all fat, if that's what you mean," Padan agreed. "Did I ever get around to congratulating you for that horror story you foisted off on the fat priest called Bersla?"
"There _was_ a certain amount of truth involved, Padan," Andar protested. "We've all heard stories about the famines that show up every so often. When people are starving, they _do_ sometimes revert to cannibalism—except that they'll eat people who are already dead. I was fairly sure that the prospect of being eaten alive might frighten Bersla enough that he'd start paying attention to what was happening out in the real world."
"The fact that his hair was standing straight up and his eyes were bulging out of their sockets sort of hints that he was getting your point."
"We can hope, I suppose. His sense of his own superiority rubbed me the wrong way. He behaves as if the common people of Aracia's Domain were nothing more than cattle whose only purpose in life is to feed _him_ , and Aracia's mind has slipped so far that she believes just about anything he ever tells her."
"I hate to admit this—again—" Padan said, "but I think Keselo's scheme might be the best one any of us will ever come up with. If Sorgan sends out scouts and they report back that the bug-people are coming and that they're _awful_ , I'm fairly sure that all those fat priests will try to take cover, and they'll all be so far down in the basement that they won't have any idea of what's _really_ happening. If they're all busy hiding, they won't even _know_ that Sorgan's been tearing down certain parts of the temple to build that wall."
Now that Dahlaine's little toy sun was giving them much more daylight—as well as warmer weather—the combined armies were making much better time than they'd made during that first dreadful day, so they reached the low mountain range off to the east much sooner than any of them had thought possible.
The worn-down range of mountains had a familiar quality that Andar found rather pleasant. In many ways they were very much like the mountains off to the south of Kaldacin, so Andar found them to be quite beautiful. They weren't as rugged and imposing as the mountains in the Domains of Zelana, Veltan, and Dahlaine had been. The young scholar, Keselo, had told them that mountains were much like people. As they grew older, their rough edges were worn down by the passing years, and they were much gentler.
"I think this is far enough for today," Commander Narasan announced. "Put the men to work setting up camp. We'll be splitting up tomorrow, so it might not be a bad idea to talk things over before we're separated."
"Good idea," Dahlaine agreed. "Longbow told us that he was going to lead the Tonthakans, Matans, and the Malavi horse-soldiers south along this mountain range to the upper end of Long-Pass while the Trogites and Maags go over to the coast to sail south. That's the way we decided to do this back at Mount Shrak, and I don't see any reason to change things."
"You didn't tell him, I take it," Ekial the Malavi said to the bleak-faced Longbow.
"I didn't really want to alarm him—or his sister, Zelana," Longbow replied.
"Alarm?" Zelana asked the archer. "What are you up to now?"
"I _will_ be leading the others, Zelana," Longbow replied, "but I'll be quite some distance ahead of them. Kathlak, Ekial, and Two-Hands know where they're going, so they won't need me around to keep pointing them south. I'll go on ahead and make sure that the Creatures of the Wasteland haven't reached these mountains yet. Then I'll go on down Long-Pass to the sea. I'll probably be there when the ships arrive, and I'll be able to pass along anything I've seen to our friends."
"That's too much of a risk," Zelana declared. "You can't just run around by yourself like that."
"You can come along, if you'd like," Longbow told her with a faint smile. "Somebody has to go ahead—somebody who knows enough about the servants of the Vlagh to know what he's looking for. That means _me_ , Zelana. I know more about the Creatures of the Wasteland than anybody else does, and I know exactly what I'll have to do to stay out of their sight. I've been doing this for a long, long time, Zelana, so I won't be in any real danger."
"You're going to insist, I take it?" Zelana said.
"I thought I just did. You worry too much, Zelana. It'll make you old if you're not careful."
"I'm already old," she snapped.
"But you don't want it to show, now do you? I'll be just fine, Zelana. I know _what_ has to be done and _how_ to do it. Nobody else does, so I'll have to do it myself." He looked around at the others. "I know that many of you would like to help, but you'd just be in my way. I'll see you down at the mouth of Long-Pass in a few days, my friends," he said, and then he turned and ran smoothly off to the south. Andar was quite certain that Longbow's decision had grown perhaps more out of his desire to be alone. Longbow didn't really like—or need—other people around him. He was definitely the most solitary man Andar had ever encountered.
**2**
Andar had been careful to keep his opinion of the warrior queen Trenicia strictly to himself, of course, but she was always there when he needed to speak with the commander. It wasn't that she ever interfered or anything like that, but just her presence made Andar uncomfortable.
It _might_ have been the massive sword she had belted to her waist that disturbed Andar so much. Women were not _supposed_ to carry weapons like that. Women were supposed to be soft and gentle—and subservient, of course. It seemed to Andar that Trenicia's very _existence_ was a violation of some natural law dating back to the beginning of time.
Of course Andar had never even _heard_ of the Isle of Akalla until the Trogite fleet had reached the temple of Lady Zelana's sister early last autumn. The notion of a place where women were dominant was so unnatural that Andar was almost positive that it was some kind of hoax. He was quite certain that a _man_ was the true leader on the isle, and that Trenicia was nothing more than an elaborate deception.
But she could run for at least a half a day, and her shoulders were even larger than Andar's were. She had all of the characteristics of a warrior—except that she was a woman. Commander Narasan treated her with respect, and the two of them seemed to get along quite well.
As the army continued the march to the east, Andar continued his private argument with himself. Queen Trenicia wasn't really supposed to be with them—but she was. Queen Trenicia was supposed to be in some fancy palace surrounded by servants who were supposed to respond to her every whim—but she wasn't.
Andar's whole world seemed to be turning upside down, and he didn't like that at all. "I really wish that we'd stayed home," he muttered to himself.
They reached the coast several days later, and the Trogite ships were still anchored where they'd been when Commander Narasan's army had disembarked to begin the long march to Mount Shrak.
Then Sorgan Hook-Beak rowed over to the _Victory_ , and Narasan was already standing at the rail waiting for him. "We need to talk, Narasan," Hook-Beak called.
"Of course," Narasan replied. "The weather, maybe?"
"Very funny," Sorgan said without smiling. "Can we get down to business?"
"Sorry," Narasan apologized.
"I've been talking with several of the men who were with you when you arrived at the temple of Lady Zelana's crazy sister. I gather from what your men told me that the priests aren't any too bright. If I was going to be dealing with people who had something besides air between their ears, I _might_ be able to get away with an advance force, but from what I've heard, the 'Holies' down there wouldn't even know what I was talking about. I'm going to have to make it simple for them by putting my whole army down on the beach at the same time. Then I'll be able to persuade Lady Zelana's stupid sister that I've got enough men to protect her and her 'holy of holies' when the bugs attack her precious temple."
" _And_ to find out how much gold she'll be willing to pay?" Narasan asked.
"That _is_ sort of important, Narasan. Anyway, if we agree that putting my entire army ashore will be the best way to go, I'm going to need about a hundred of those wallowing tubs of yours to get me and my people in place."
"It makes sense, friend Sorgan. As soon as you get your men ashore, though, release those ships. I've got a lot of men who'll still be camped here, and I'm fairly sure I'm going to need them when the Creatures of the Wasteland come storming in." He looked rather speculatively at his friend. "Would it bother you if I made a few suggestions about dealing with Lady Zelana's sister?"
"Not one little bit, Narasan. You know her and I don't."
"First off," Narasan said, "push up your price just a bit. Money doesn't mean anything to Aracia, so she probably won't pay any attention. When you talk with her, act sort of arbitrary. Tell her that if she doesn't agree to do things your way, you'll take your men back to the ships and sail away. She _will_ pay what you ask and agree to keep her priests from interfering, but agreeing with everything you say will make her feel a bit on the defensive side. You'll need to use any lies or ideas you can think of to keep her that way. If she believes that you've got the upper hand, she'll do just about anything you demand of her. Always be abrupt—and even arbitrary—particularly when you announce that you're going to tear down a major part of her temple to get the material you'll need to build a fort. Don't ask her; _tell_ her. Her fat head-priest will probably start screaming as soon as you announce that you're going to dismantle a major part of her temple. I don't know if I'd kill him right there on the spot, but you can make a few threats—draw your sword or hit him in the mouth with your fist. Always keep Aracia off balance if you possibly can."
"You can be a very nasty fellow when you set your mind to it, old friend," Sorgan said with a broad grin.
"That's where I made my mistake when _I_ was there, friend Sorgan. I avoided 'nasty' because I was trying to be polite. 'Polite' doesn't work when you're dealing with someone like Aracia. Push her—and keep pushing. Don't give her time to object."
"A suggestion, if I may?" Andar said, stepping in.
"I'll take all the help that I can get," Sorgan declared.
"I'd say that Keselo came up with the best answer," Andar said. "Pick out the best liars in your army and send them out into the countryside to pretend that they're scouting. When they come back, you'll want them to start telling stories about all the terrible things the bug-people are doing to the ordinary peasants—eating them alive, pulling out their livers, having their eyeballs for dessert—that sort of thing. If Aracia's priesthood is totally terrorized, Aracia will do almost anything you tell her to do."
"You're even nastier than Narasan," Sorgan noted.
"I received my training from the best, Captain Hook-Beak," Andar replied modestly.
"We'll try it your way then," Sorgan declared. Then he grinned. "I've got a hunch that I'm going to have a lot more fun than you two will. You'll have to face _real_ bugs. All I'll have to do is deal with imaginary ones to make sure that big sister's frightened enough to do just about anything I tell her to do."
"I think you'll do just fine, friend Sorgan," Commander Narasan said with an answering grin.
It took several days to load the Maags on board the ships Sorgan had borrowed, and then, when all was ready, the burly Maag joined Narasan and the others on board the _Victory_. "We're just about ready to start," he advised. "If it's all right, I'll go on ahead. It won't take long to unload my men, and then I'll send the ships back here to pick up the rest of Narasan's men and take them on down to the mouth of Long-Pass. I'll send word of how things are going from time to time, but I don't really expect much in the way of trouble."
"Keep our sister off balance as much as you can, Sorgan," Zelana told him. Then she looked at Dahlaine. "I've found that the unexpected always seems to startle Aracia," she said.
"I pretty much agree with the scheme to drop horror stories on Aracia—and her priesthood," Dahlaine replied. "If it goes the way I _think_ it will, the priests will be so frightened that they won't be able to deliver all those flattering orations, and that alone will shake Aracia right down to her roots."
"Your sister has roots, Dahlaine?" the beautiful lady called Ara asked with a sly smile. "If she does, then maybe we could transplant her—in the middle of the night, probably. When her priests wake up and find that she's gone, they won't have any idea at all about where she's gone—or why—and it's likely that their minds will shut down."
"I'm not at all sure that something like that would work, dear lady," Dahlaine replied. "Aracia's priests spend all their time groveling in her throne room whether she's there or not. Groveling is an art form among the priests of Aracia."
"Doesn't that make them sort of meaningless?" Ara's husband suggested.
For the life of him, Andar could not think of any reason at all just _why_ the two neighbors of Lord Veltan were present here on the _Victory_ —except, perhaps, for the glorious food Ara presented to Narasan and his friends when mealtime arrived. Without a doubt, Ara was probably the finest cook in the whole world, but why did she and her husband always participate in these serious meetings?
"Build good forts, friend Narasan," Sorgan said then. "I _don't_ want the bug-people sneaking up behind me when I'm busy swindling holy old Aracia."
"We'll do the best we can, Sorgan," Narasan replied with a grin. "Swindle away for all you're worth, and we'll keep the bug-people out of your hair."
The weather was holding—probably because Dahlaine told her to—so the remaining ships in the fleet made good time as they sailed on down to the mouth of Long-Pass. The ships that had carried Sorgan's Maags down to Aracia's temple had turned around and they'd passed Narasan's fleet two days ago, and they were probably picking up the numerous cohorts that had stayed behind. It wouldn't be much longer before the entire army would be reunited and marching up the pass toward whoever—or whatever—would soon be invading.
[THE
TEMPLE
OF
ARACIA](YoungerGods_toc.html#part_3)
**1**
It was late afternoon when the hundred Trogite tubs Sorgan had borrowed from Narasan hauled into the harbor of the temple-town of Zelana's elder sister. Sorgan, Veltan, and Padan were standing in the bow of the _Ascension_ , the lead ship, and Sorgan was more than a little astonished by the enormity of the temple. Narasan had told him that the silly thing was about a mile square—which might be easy to say—but Sorgan realized that saying and seeing were altogether different. "It seems to go on forever," he said to Veltan in an awed sort of voice.
"I'm sure that Aracia likes to think so," Veltan replied.
"Most of it's empty, though," Padan advised. "It's not what I'd call jam-packed with priests and her church hangers-on. I nosed about when we first arrived last autumn, and there aren't really that many people living there."
"Fat Takal Bersla was probably responsible for the overdone size of the silly thing," Veltan added. "It's one of the many myths he's foisted off on my big sister. He _claims_ that there are thousands and thousands of priests living in that absurdity. Aracia's absolutely certain that she has worshipers beyond counting living here, but she never bothers to look. There might be thousands and thousands of creatures living here, but most of them are probably mice."
"Or spiders," Padan added. "I roamed around in that foolishness last fall, and _most_ of the corridors in 'Holy Temple' are jammed to the ceiling with cobwebs."
"It's nothing but a hoax, then?" Sorgan asked.
"A 'holy hoax,' Captain Hook-Beak," Veltan corrected. "Aracia devoutly believes that the absurdity her priests have foisted off on her is a sign of her overwhelming importance."
"That's pathetic," Sorgan declared.
"That's a fair description of my sister, yes," Veltan agreed.
"We've got company coming," Padan said, pointing across the bay. "I'd say that it's most probably fat old Bersla coming out here to find out what we want."
"That thing doesn't look at all like Longbow's canoe," Sorgan observed.
"It's not really the same thing, Sorgan," Veltan agreed. "Longbow's canoe is designed to carry one man. The ugly thing coming out here to meet us is designed for show. Bersla yearns to be important, and he thinks that having hundreds of men paddling him out here makes him _look_ important."
Sorgan squinted at the approaching boat. "It looks to me like it was made out of a single tree trunk."
"That's fairly common here in the Land of Dhrall," Veltan said. "They're called 'dugouts,' probably because making them involves scraping out most of the log with sharp stones. I've never actually seen one built before, but I'm told that most of them are partially hollowed out with fire—very well-controlled fire, of course. There _are_ certain advantages, though. A boat made from a single log wouldn't leak, would it?"
"Maybe not," Sorgan said, "but if it doesn't have a keel, it'll probably roll over any time one of the paddlers sneezes or hiccups."
"That _has_ happened here fairly often, Captain Hook-Beak," Veltan said, smiling. "Stately—but not very bright—Bersla doesn't understand _why_ just yet but it might come to him—eventually."
"That's pure stupidity!" Sorgan declared.
"I'd say that's a fair description of Bersla, yes. You've already met Aracia herself back in _my_ Domain, so you don't really need Bersla to introduce you to her. He's terribly impressed with himself. He'll demand to know why you're here, but I'd suggest that you tell him that you're here to see Aracia herself, not some servant."
"Won't that offend him?"
"Probably, yes. I'd say that you should tell him that you're too important to talk to servants. When we reach the temple, I'll introduce you to my sister and tell her that you'll defend her temple _if_ she'll pay you enough."
"That sounds good to me," Sorgan replied. "How should I behave? Am I supposed to bow to her or any of that other nonsense?"
"A certain amount of arrogance wouldn't hurt. Tell her that you're the mightiest warrior in the world, so you're worth your weight in gold—that sort of thing. One thing you should always remember. _Don't_ let her give you orders. Tell her that you'll do what's necessary to defend her, and you don't want any interference from her or her priesthood. Get that established right away. You're going to be tearing down a large part of her temple, so there'll be a lot of screaming from the priests. Tell them that you have her permission, and that they should mind their own business. Pull out your sword, if you have to."
"Or maybe even if I don't, right?"
"Now you're getting the idea. I think you'll do just fine, but you'll have to push my sister back into a corner as well, and that might take a few days."
"It'd better not, Veltan," Padan said. "Captain Hook-Beak _has_ to persuade your sister to let him do things _his_ way, but he can't drag it out for _too_ long. They'll have to reach an agreement _before_ he unloads his men and frees up all the ships here in the harbor. Those ships are vital to Narasan, because half of his army is still sitting on that beach up in Lord Dahlaine's territory."
"He _does_ have a point there, Veltan," Sorgan said. "I promised Narasan that I'd release his ships as soon as possible, and I don't lie to my friends."
"I can manipulate a few things," Veltan said, frowning slightly. "A good following wind _would_ recover a day or two. We can give you that much time to manipulate my sister if you need to. After that, you might have to be sort of arbitrary in your dealings with Aracia."
"I don't see much of a problem there, Veltan," Sorgan declared. "I _am_ a Maag, after all, and we _invented_ arbitrary."
The obviously unstable log-boat pulled alongside the _Ascension_ , and the grossly fat priest rose to his feet to stand in the bow—which struck Sorgan as an act of sheer stupidity. "We have beheld your approach to the temple of Holy Aracia," he declared in a rolling sort of voice, "and we must know of your purpose here."
Veltan stepped forward. "I am Veltan," he said, "the younger brother of she who guides you."
"I have not heard of you," Bersla declared in a haughty tone of voice. "Surely Holy Aracia would have advised me that she has a brother besides Mighty Dahlaine."
"I wouldn't depend on Aracia very much if I were you, fat man. Her mind isn't all that stable anymore."
"Blasphemy!" Bersla exclaimed in a shocked tone.
"Not if it's true, it isn't," Veltan disagreed. "I see that you're going to need some convincing. Watch closely, fat man, and pay close attention. This is your only chance to avoid my resentment." Then Veltan slowly rose up into the empty air above the _Ascension_ to stand on nothing but air.
Fat Bersla went pale, and his eyes bulged almost out of their sockets.
"I can go higher, if you'd like," Veltan said. "I could even take you up into the air with me, if that would convince you. I am unlimited, Takal Bersla. If need be, I can carry you all the way up to the moon—but I don't think you'd like that very much. There's nothing to eat on the moon, and no air to breathe, so you'd probably die almost immediately."
"I believe you!" Bersla declared in a shrill voice. "I believe you!"
"Isn't he just the nicest fellow?" Veltan mildly asked the others.
It took the trembling Bersla a while to recover. "I pray you, Lord Veltan," he said, "why have you come here?"
"It should be obvious, priest of my sister," Veltan replied. "The Creatures of the Wasteland will soon invade my dear sister's Domain, and I have brought fearless warriors to drive them away."
"Eternally grateful shall we be if you succeed, Lord Veltan."
"Were you planning to live eternally, High Priest Bersla?" Veltan asked with feigned astonishment.
"Ah—we will pass this on to generations as yet unborn, timeless Veltan," Bersla amended. "May I speak now with the chieftain of these mighty warriors who have come from afar to defend our Holy Aracia?"
"I don't waste my time speaking with servants," Sorgan declared as roughly as he could. "Let's go talk with your sister, Veltan."
"That cannot _be_!" Bersla protested. "Holy Aracia's time is all filled for this day. As you may know, however, _I_ speak for Divine Aracia when it seems necessary."
"Not to _me_ , you don't," Sorgan declared. "I only talk with those who have gold."
Sorgan and Veltan conferred briefly, and then a sailor with nothing else to do untied a rope that held a well-built skiff in place, and then he lowered it over the side.
"That is not permitted!" Bersla declared. "No alien ships or boats may go ashore in Holy Aracia's Domain."
"You don't think for one minute that I'm going to ride to the beach in that unstable canoe of yours, do you?"
"It is perfectly sound," Bersla declared.
"Of course it is," Sorgan replied sarcastically. "At least it might be as long as you leave it on the beach. It's when you push it out into the bay that it tends to roll over without much warning. How many times has that happened so far this month?"
Bersla began to splutter a denial, but there was a muscular oarsman sitting just behind the fat priest, and he held one hand up with the fingers stretched wide and two fingers of his other hand clearly visible. Then he winked at Sorgan.
"Let me guess," Sorgan said to Bersla then. "I've got a strong hunch that your tree-stump tub has rolled out from under you seven times already this month."
Bersla's eyes went wide. "How did you—?" Then he broke off.
"Instinct, fat man," Sorgan replied. "I've spent most of my life at sea, so I know a lot about things that happen out on the water. Logs _always_ roll over in the water when you don't want them to, and seven's a lucky—or unlucky—number, be it logs or dice." He made a slight gesture to the muscular oarsman, and the fellow nodded. "Let's go hit the beach, Veltan," Sorgan said then. "I want to meet your sister, and then I'll look around. If I'm going to defend her territory, there are a lot of things I'll need to know."
"How in the _world_ did you know that Bersla's log-canoe had rolled over seven times already this month?" Veltan asked as Sorgan rowed the skiff toward the beach.
"You weren't watching very closely if you missed it," Sorgan replied with a broad grin. "When I asked the fat priest how many times his log-boat had rolled over, one of the oarsmen held up seven fingers."
"Why would he do that?"
"I haven't got any idea. I'm going to talk with him later and find out, though. It's entirely possible that he might turn out to be very useful later on."
"Does he know that you want to talk with him?"
"Of course he does. I don't want to hurt your feelings, Veltan, but you don't pay very close attention to what's going on around you. That oarsman gave me a wink when he held up his fingers, and I pointed at my mouth after I threw 'seven' into the fat priest's face. Pointing your finger at your mouth can mean two things—'let's eat' or 'let's talk.' Everybody knows that."
"It _does_ make sense, I suppose."
"Are we going to have any trouble getting in to see your sister?"
"Probably not," Veltan replied. "Aracia knows who I am, after all, and as soon as she sees me, she'll know that I've got some information for her. I'll introduce you to her, and then we can get down to business."
It had seemed to Sorgan when he'd been on board the Trogite ship out in the bay that there'd been a kind of coherence about Aracia's temple, but as the skiff came closer to shore he began to see some glaring inconsistencies. "I don't want to sound critical or anything, Veltan," he said, "but there's a sort of slapdash quality about your big sister's palace. Didn't the people who were building it ever get together and establish some rules? In some places, the stones are very smooth, but in others they're rough and lumpy."
"There _do_ seem to be quite a few inconsistencies," Veltan agreed. "I'd say that the assorted work crews didn't have anything to do with each other. Some of them appear to have spent a great deal of time polishing the stones, while others concentrated on piling up more rocks."
"Something on the order of 'prettier' or 'bigger,' you mean?"
"That probably comes very close, Sorgan. I don't imagine that Aracia really cared much one way or the other. As long as her temple kept growing, she was probably quite happy."
"She's not really very bright, is she?"
"I wouldn't go quite _that_ far. Aracia has different needs than the rest of us do. She desperately needs adoration, and her priests spend all of their time adoring her. I'm fairly sure that they didn't spend _much_ of that vital time telling the work crews who were building the temple how to proceed, and that's what probably led to these inconsistencies."
"It's possible, I guess." Sorgan turned and looked a bit more closely at the beach. "No piers," he grumbled.
"Building piers would take the work crews away from expanding big sister's temple," Veltan explained.
"We'll have to climb all over her right away," Sorgan said.
"I didn't quite follow that."
"We'll need piers when we unload the people from about a hundred Trogite tubs, Veltan," Sorgan declared. "They _won't_ be willing to swim in the dead of winter, you know."
"Good point there," Veltan said. "I think I'll have to cheat," he added glumly.
"Cheat?"
"I'll make the piers myself. I know what they look like, and I'll be able to set them up much faster than the temple work crews possibly could. Then, too, if _I_ do it, we won't have to listen to all the sniveling and complaining we'd get if we pulled the crews away from their 'Holy' task of expanding my sister's temple until it's fifty or a hundred miles square."
"Which probably won't take them much more than a few hundred years," Sorgan added.
They pulled the skiff up onto the beach and then walked directly up to Aracia's temple.
When they reached the entrance, however, Sorgan's heart almost stopped beating. "Is that door made out of what I _think_ it is?" he gasped.
"Oh, yes," Veltan replied. "There might be a bit of bracing here and there, but most of it _is_ gold."
"There must be a ton of it!" Sorgan exclaimed.
"More than that, I'd say," Veltan replied. "Gold is very heavy, and that's quite a large door."
"Are you saying that your sister just leaves it right out in the open like that?"
"It's fairly safe, Sorgan. I doubt if a hundred men—or even two hundred—would be able to pick it up and carry it. Let's go on inside and have our little chat with my sister, shall we?"
"Who are you, and why have you profaned the temple of Holy Aracia with your presence?" an officious-sounding young lady demanded as Veltan and Sorgan entered the corridor beyond the golden door.
"My name is Veltan," Sorgan's friend replied. "You may have heard of me—assuming that my sister remembers the rest of her family. You can go tell her that I'm here—or step aside and I'll go tell her myself."
"You would not dare. I am Alcevan, the priestess of Holy Aracia, and I speak for her in all matters."
"Aracia has women priests now?" Veltan said, sounding more than a little startled. "Does Bersla know about this?"
The young lady sneered. "Fat Bersla only knows what Holy Aracia and I want him to know. He might _think_ that he's the most important person in Aracia's Domain, but that's no longer true. _I_ am the one who speaks for Holy Aracia now, for I am her High Priestess and always will be."
"That's very nice, I suppose," Sorgan told her, "but you're going to be a doormat if you don't get out of the way." He put his hand on his sword-hilt in a threatening gesture.
Her eyes went very wide, and she turned and fled.
"Now _that's_ something I wouldn't have expected," Veltan said. "It seems that things are getting more and more complicated here in Aracia's Domain."
"The little lady _could_ have been just making this up," Sorgan said.
"It's possible, maybe," Veltan replied. "I think we'd better keep our eyes open, though. If the young woman was telling us the truth, Aracia's playing a different game now." He squinted slightly. "I think maybe you should hold on to this attitude you just threw into Alcevan's face. Be sort of rough and abrupt. Let's keep Aracia off balance if we possibly can."
Sorgan was somewhat startled by the sheer size of the room at the end of the corridor. At the very center, of course, was a massive marble pedestal topped by a golden throne and backed with dark red drapes. Zelana's sister was sitting on the throne, and the little lady Alcevan was kneeling before her and babbling.
Veltan went directly to the pedestal. "I wouldn't pay too much attention to anything the young lady's telling you, dear sister," he said. "We had a slight misunderstanding out in the corridor. I wasn't aware of the fact that you were now accepting women as members of your priesthood."
Aracia straightened, glaring at her younger brother. "Who is this pagan, Veltan?" she demanded. "And why have you profaned my holy temple with his presence?"
"You know who I am, sister of Zelana," Sorgan declared. "We met in Veltan's Domain last summer. He brought me here to defend you and your people when the bug-things invade, but since you and your stupid priests don't appreciate that, I'll just go back out to the harbor and sail away. From what I've seen so far here in the Land of Dhrall, I'd imagine that the Vlagh will have you for breakfast some day very soon." And then he stormed out of the room, winking at Veltan as he went by.
Veltan's voice came softly out of nowhere. "Maybe just a trifle extreme there, Sorgan."
"I think maybe I got carried away just a bit," Sorgan admitted. "Your sister and that uppity lady-priest of hers irritated me more than a little."
Veltan's laugh came out of nowhere. "On second thought, Sorgan, don't change a thing. I'm quite sure that my sister will come around fairly soon. Go on back out to your ship and wait. I'm almost certain that she'll send someone out to talk with you before long."
"I hope you're right, Veltan," Sorgan replied. "I didn't leave myself very much room to wiggle out of this."
**2**
The husky oarsman from Bersla's log-canoe was leaning over the rail of the _Ascension_ when Sorgan rowed his skiff out from the beach. "How did things go in the silly temple?" he asked when Sorgan pulled the skiff neatly in beside the ship.
"Things are sort of up in the air right now," Sorgan replied.
"If I understood what your signal meant a while back, you wanted to talk with me about something."
"I'll be right with you," Sorgan replied, starting up the rope ladder hanging down from the rail.
"This is a real fancy boat you've got here," the native said.
"It's not mine," Sorgan replied, swinging his leg over the rail. "I borrowed it from a friend." Then he squinted at the beefy native. "I'm just guessing here," he said, "but I take it that you don't have much use for that fat priest."
"He might make pretty good bait if I wanted to go fishing for sharks."
"It'd take a very big shark to eat that much," Sorgan said with a grin. "If that's the way you feel about him, why did you go to work for him?"
"Free food. I don't have to work very hard, and Fat Bersla makes sure that we get fed regularly. We don't eat as much as _he_ does, but nobody else in the whole world eats as much as Bersla does."
"It definitely shows," Sorgan agreed. "You seem to keep track of how often that log-canoe of his rolls over."
"That's only natural, since I'm the one who rolls it."
"Do you want to run that past me again? I didn't quite follow you."
"It's the easiest thing in the world to do," the native said with a broad grin. "All I have to do to get poor Fat Bersla soaking wet is lean toward one side or the other. As long as everybody is sitting up straight, the canoe will keep on sitting upright in the water. One quick lean toward one side or the other rolls that thing in the blink of an eye. Any time Bersla starts to relax, I tip his canoe over."
"What for?"
"I don't like him. Nobody _really_ likes him. If _I_ don't roll his canoe every now and then, one of the other paddlers _will_. Bersla hasn't gone home dry for about three years now. _We_ get wet, too, but our clothes dry in a hurry. Bersla's clothes are thick and fancy, so they take at least a week to dry out. That's a big part of what this is all about. He has to keep on giving us food to eat, whether he goes out in his canoe or not."
"You and I are going to get along just fine," Sorgan said. "What's your favorite kind of food?"
"Meat. Everybody likes meat."
"I'll see what I can do to chase down some meat for you."
"What will you want in exchange?"
"Information, my friend. Information. What's your name, anyway?"
"Platch," the native replied. "What's yours?"
"Sorgan Hook-Beak."
"How did you _ever_ get a name like that?"
"I had to work for it a long time ago. Let's go have something to eat, shall we?"
"I thought you'd never ask," Platch replied.
Veltan came into the large cabin at the stern of the _Ascension_ early the following morning. "It took me a while, but I managed to calm my sister just a bit. I explained some of the peculiarities of the Maag culture to her— _after_ she'd sent the priestess Alcevan off on some meaningless errand. I made quite a big issue of what good warriors your people are. Aracia's very arrogant, but she _does_ know that her priests would be useless in a confrontation with the Creatures of the Wasteland."
"Unless the bugs happen to be hungry," Sorgan added.
"I mentioned that, yes. When you get right down to it, though, it's very unlikely that Aracia or any of her servants will even _see_ any of the servants of the Vlagh. Your scouts will tell the assorted priests that the bugs are out there and that they're living on a steady diet of people, but all that we're _really_ doing is diverting their attention from the _real_ invasion—the one that's pointed at Long-Pass."
"How would you say I should approach your sister?" Sorgan asked. "I might have been just a little too rough yesterday."
Veltan squinted at the cabin ceiling. "You might want to be a bit more polite today—not _too_ polite, of course. Swagger a bit and brag about what a great warrior you are and how you defeated the servants of the Vlagh back in sister Zelana's Domain and helped Narasan in _mine_. Then tell her that you want to talk about gold. Gold doesn't mean anything to Aracia, but she'll probably try to make you lower your price. That's when you should storm out again and come back out to this ship. Try to make it look like you're just about ready to sail off and leave her here to fight her own war. This is _very_ important, Sorgan. Don't ever back down when you're dealing with Aracia. She _will_ come around when she realizes that you mean what you say."
"You people play very rough games with each other, don't you?"
"Indeed we do," Veltan agreed. Then he smiled slyly. "Fun though," he added.
Sorgan rowed the skiff back to the beach. Veltan offered to take up a set of oars to help, but Sorgan said "no" quite firmly. "I'm not trying to offend you, Veltan, but things go much more smoothly if there's only one man rowing. We'd both look sort of silly if we were soaking wet when we went back into that throne room. If we happened to do something wrong, we could tip this skiff over _almost_ as fast as Platch can roll Bersla's log canoe."
"Did he ever tell you why he does that every so often?" Veltan asked.
"It takes the wind out of the fat man's sails," Sorgan replied with a chuckle. "A man who's soaking wet and dribbling water all over the floor doesn't look very important. Platch despises Bersla, so he keeps him wet most of the time."
Sorgan rowed the skiff up onto the same beach where he had beached her the previous day, and then he and Veltan went on up through the assorted buildings lying outside the temple.
Sorgan looked longingly at the ornate temple door. "I don't suppose—" He left it hanging.
Veltan shook his head. "Sister Aracia wouldn't hold still for that, Sorgan. We _might_ encounter the same objections when we tell my sister that we're going to have to tear down some of the outer reaches of her temple, but that door is much too important in my sister's eyes for her to agree to it as your price. Then too, how would you move it? It weighs tons, and even if you managed to get your hands on it, the sheer weight would sink any ship you could bring into the harbor. Stick to the gold blocks, Sorgan. They're much more convenient."
They passed through the long corridor and entered the throne room. Fat Bersla was delivering a flowery speech, comparing Zelana's sister to a sunrise, a hurricane, and an earthquake. Aracia's attention, however, seemed to be a bit divided, since the young priestess Alcevan was standing beside the throne whispering on and on. Sorgan sensed a certain competition there. It seemed that Bersla and Alcevan were each doing everything they could think of to get Aracia's attention.
Sorgan walked up to the marble pedestal and looked Aracia right in the face—which was probably against all the rules. "Well now," he said. "Veltan tells me that you're ready to listen to what I say."
"Not right now," Aracia replied with a note of irritation in her voice. "Takal Bersla is addressing me now."
Sorgan drew his sword. "That's not really much of a problem, you know. He'll stop talking just as soon as I kill him."
"You wouldn't _dare_!" Aracia exclaimed.
"Watch me," Sorgan suggested in an offhand sort of way. "You've got a problem, and I'm here to solve it. Let's dispense with all this foolishness and get down to business." He purposefully crossed the marble floor to where Bersla had just stopped talking. The word "kill" seemed to have gotten his attention.
"You _have_ finished your speech, haven't you?" Sorgan asked, moving the point of his sword back and forth about six inches from Bersla's face.
Bersla nervously backed away. "Holy Aracia will protect me," he declared, still backing up.
"How?" Sorgan asked. "You _did_ know that she's not permitted to kill things, didn't you? I don't have those restrictions. I can kill anything—or anybody—whenever I feel like it. You've got a very simple choice, fat man. What it all boils down to is shut up or die. The choice is entirely yours, though, but you'd better hurry. My sword's very thirsty right now."
Bersla flinched back, and then he ran out of the room.
Veltan was smiling. "I'd say that there's a certain charm to Hook-Beak's directness, wouldn't you, dear sister?"
"I will not tolerate this!" Aracia almost screamed.
"I think you'd better," Sorgan said bluntly. "I came here to protect you and your people—for money, of course—so let's get down to business. I'll start protecting right after you pay me."
" _I_ will decide when—and how much," Aracia declared. She was obviously trying to regain control in this situation.
"That might be very true, Lady Aracia," Sorgan said, "but _I'm_ the one who'll say yes or no. Be nice to me, lady, because _I'm_ the only one willing to protect you. You've offended your big brother _and_ your sister, so they won't have anything to do with you. That sort of says that _I'm_ the most important person in the whole wide world, wouldn't you say?"
Aracia gave him a cold, superior sort of look. "How much do you want?" she asked.
"Oh, I don't know," Sorgan replied. "How does one hundred blocks of pure gold sound to you?"
"That's absurd!"
"It is, isn't it? Let's make it _two_ hundred, then."
She stared at him, her eyes suddenly gone wide.
"It's entirely up to you, lady. That's the price. Take it or leave it." Then he turned and walked toward the door, not even bothering to look back.
"I'll pay! I'll pay!" Aracia almost screamed.
"That's more like it," Sorgan said. "Now you can see just how easy I am to get along with."
"He leaned on her, Padan," Veltan told their friend the next morning. "Very, very hard."
"I wish I'd been there to see that," Padan said with an evil sort of grin.
"Your whiskers aren't quite long enough to make it safe for you to roam around in the temple, Padan," Sorgan told the Trogite. "Give them another week before you visit that holy absurdity. You're not wearing your Trogite uniform, and that _might_ be enough, but let's not take any chances yet. We want you to look entirely different before you start making any public appearances." He scratched his cheek. "I think maybe you and Rabbit should talk this over. Rabbit's got a fair idea of the horror stories he's going to tell Veltan's sister, but I think you might want to add a few other stories as well. We've seen quite a few different varieties of the bug-people, and we'll want to throw them all in Aracia's face—in bits and pieces, of course. Let's say that the first time you'll sorta concentrate on the snake-bugs that we encountered in Zelana's Domain. Then move on to the bug-bats and the turtle-shell bugs. Hold off on the spider-bugs for quite some time. _That's_ the _really_ scary one. I still have nightmares about people having their insides turned into a liquid that the spider drinks right out of them."
"It _did_ eliminate Jalkan and Adnari Estarg, Captain Hook-Beak," Padan said. "A lot of us in Commander Narasan's army are quite sure that was the nicest thing anybody—or any _thing_ —could have done for us."
Sorgan smiled. "If I remember right, Gunda wanted to make that a national holiday down in Trog-land. I'll be sending Ox, Ham-Hand, and Torl out as well. Maybe you should all get together and decide which awful each one of you should present to Aracia and her assorted priests. Each one of you should have a different story to wave in Aracia's face. Remember that she _was_ down in Veltan's Domain, so she knows about _most_ of the varieties of bugs. Let's add a few new ones, though—bird-bugs, maybe, or wolf-bugs and lion-bugs. Maybe the group of you should get together and decide how you're going to spread these stories out and make them sound real. The whole idea is to give them _new_ awfuls every so often, and each awful should be worse than the previous ones. We want to make Aracia's priests so terrified that they'll be afraid to come out of the temple to see the awfuls themselves." Then he had a sudden idea, and he looked at Veltan. "You know how to make images of things that aren't really there, don't you?"
"More or less," Veltan admitted. "Where are we going here?"
"Let's say that our scouts come back with stories about some terrifying varieties of bugs. Then, maybe a day or so later, the priests and other servants actually _see_ those very same bugs."
"I can do that, yes," Veltan admitted. "I'll need to stay quite a ways away from Aracia when I do it, though. If I'm too close to her, she'll be able to feel what I'm doing."
"We'll probably be out along the west side of her temple. That's quite some distance from the main temple here. The higher-ranking priests will probably be hiding out in cellars and what-not, but I'm sure we'll be able to come up with some reason for a few of the lower-ranking priests to be out there with us. If you whip up some nasty images, they'll probably run back to Aracia yelping and squealing. Let's keep your sister so terrified that she can't think straight. We want her to order all of her priests to come home to the temple to join up with the ones already here. We don't want _any_ of her priests out there catching whiffs of the invasion of Long-Pass. Let's make sure that Narasan can get his job done without any interference from your sister or her overweight priests."
"You're getting very good at this sort of thing, Sorgan."
"Practice, Veltan, practice. And if worse comes to worse, we can borrow a few of the children. I'm almost positive that Eleria could scare your older sister into convulsions, if that's what we really need. We're pulling off a hoax here, but let's make it seem so real that _nobody_ who works for your sister will even dare to come out of the temple to have a look for themselves."
[UP
FROM
THE
BEACH](YoungerGods_toc.html#part_4)
**1**
It was late afternoon on a cold, grey winter day when the _Victory_ hauled into a narrow bay where a sluggish-looking river came down through a range of low, rounded mountains.
"This must be the place, Andar," Gunda said to his friend as the sailors lowered the sails of the _Victory_ and dropped the anchor. "Lord Dahlaine's map only showed one river coming down out of the mountains along this stretch of the east coast."
"It looks to be quite a bit wider than the streams and rivers we encountered off to the west," Andar observed.
"And fairly quiet as well," Gunda added. "That doesn't particularly hurt my feelings, though. Waterfalls and rapids are pretty to look at, but trying to get around them isn't much fun at all."
"I _knew_ it," Andar said.
"Knew what?"
"Longbow said he'd be waiting for us here, and there he is."
"I don't—" Gunda started, but then he too saw the leather-clad archer sitting on a log not far from the river mouth. "That's Longbow, all right," he said. "If he says he's going to do something or be someplace, you might as well believe him. I learned never to argue with him during that first war in Lady Zelana's Domain."
"If I was reading Lord Dahlaine's map right, he had hundreds of miles ahead of him when he led the Malavi and those natives down along that mountain range," Andar said, sounding more than a little baffled.
"The first rule when you're dealing with Longbow is always to believe him when he tells you something," Gunda said with a slight smile. "It may not be true when he says it, but it _will_ turn out to be true in the long run. If Lady Zelana doesn't wiggle her fingers to make things happen, Longbow's _other_ friend—the one who conjures up tidal waves on dry land or sets fire to a mountain range when she gets irritated— _will_. Don't _ever_ cross Longbow if you can possibly avoid it. That's the best way I know of to stay alive."
Narasan and the overly clever Keselo came out of the cabin at the stern of the _Victory_ , and they joined Gunda and Andar at the starboard rail. "I'd say that we made good time," Narasan observed.
"Not _too_ bad," Gunda agreed, "but Longbow outdid us. He's camped on the beach, and he's probably been waiting for us for a month or so at least."
"I see that you're filling in for Padan in the funny remarks department," Narasan said in a sour tone. "If you are, you'd better practice just a bit. Padan would have added all sorts of irritating comments to _that_ one."
"Give me a little time, Narasan," Gunda replied. "My sense of humor's sort of rusty—the weather, no doubt."
"Longbow should be able to tell us if the bug-people are coming up out of the Wasteland," Keselo said. "That's what we _really_ need to know."
Gunda squinted at the narrow bay. "I was sort of hoping that we'd be able to get closer to the beach," he said. "If the men have to row ashore from this far out, it'll take us several days to get everybody on shore."
"We won't be going anywhere for several days anyway, Gunda," Narasan said. "Half of the army's still camped on that beach up in Dahlaine country. Sorgan's scheme _should_ keep Aracia out of my hair, but when he borrowed half of the fleet, he slowed things down for us quite a bit. Let's go ashore and have a little chat with Longbow. We really need to know if the bugs are moving yet."
"How far would you say it is to the top of Long-Pass from here?" Narasan asked when several Trogites met with the archer.
"About a hundred and twenty miles, Narasan," Longbow replied. "Dahlaine's map was fairly accurate."
Narasan winced. "That's not exactly good news, Longbow," he said. "At ten miles a day, that's twelve days at least."
"Is ten miles a day some sort of religious obligation?" Longbow asked the commander.
"No, not really," Narasan replied. "It's based on reality. One man alone can cover much more ground, but when you're dealing with an army of a hundred thousand, ten miles a day is about the best you can hope for."
"But your fort-builders wouldn't _really_ have to move that slowly, Narasan," Longbow declared. "Friend Gunda here is the expert, so he'll know how many of your men we'll need to get the job done. If I were to guide—or maybe lead—your fort-builders up the pass, I'm sure that I'd have them up there in four days, and they could have _most_ of the work finished by the time you and the rest of your army reached the top."
"It's just not done like that, Longbow," Gunda protested. "An army's not an army if it gets all split up like that."
"Don't be in such a rush, Gunda," Andar suggested. "It's very likely that we're going to _need_ those forts and we'll definitely need them _before_ the bug-people come charging across the Wasteland. I suppose we could give some thought to blocking them off somewhere about halfway down the pass, but I'd say that blocking them right up at the top of the pass would work better."
"He's got a point there, Gunda," Narasan agreed. "We're not fighting an ordinary enemy, and we _don't_ want them to get into the pass if we can possibly come up with a way to keep them out." Then he looked at Longbow. "Can you _really_ get the fort crew to the head of the pass in just four days?" he asked.
"Not all of them maybe," Longbow replied, "but enough of them to get started. The Tonthakans, Matans, and the Malavi can hold our enemies back for a while, but I'm sure that forts are absolutely essential."
"I see your point," Narasan agreed. "All right, then, take the fort crews on up to the head of the pass as quickly as you possibly can. If we don't block off Long-Pass, there's a fair chance that poor old Sorgan will be facing _real_ bug-people instead of assorted imaginary ones."
Gunda shrugged. "If that's the way you want it, glorious leader, that's the way we'll do it." Then he squinted at Andar. "Are you feeling up to a long hike in short time?" he asked.
"That's up to the commander, Gunda," Andar replied. "If he wants me to go along, I'll go, and we could turn it into a race, if you'd like. I can probably run at least as fast as you can."
Gunda was seriously discontented by Longbow's scheme to rush the building crews up to the head of the pass. Spreading the army out in potentially hostile territory wasn't a good idea at all, and he was highly skeptical when Longbow announced that he could march the construction gangs to the top of the pass in a mere four days. Longbow himself probably wouldn't have any trouble covering that much ground in four days, but Longbow wasn't familiar with all the delays that can crop up when several thousand men are moving in the same direction. Gunda's years in Narasan's army had taught him a fairly simple rule—"Always expect the worst, and you'll seldom be disappointed."
The grumbling and complaining began before they even started up the pass the following morning. When Longbow said "at first light" he meant it, and that didn't sit too well with most of the men in the construction crews.
It didn't take Gunda very long to put his finger on the source of much of their problem. Longbow was a tall man, and Trogites, for the most part, were significantly shorter. Gunda didn't bother to keep count, but he was almost positive that he had to take two steps for every one of Longbow's. Most Trogites, it appeared, almost had to run to keep up with the archer.
"He moves very fast, doesn't he?" the farmer Omago suggested.
Gunda wasn't sure just why Omago had joined them, but he decided not to ask any questions just now. "He steps right along," he agreed. "If somebody happened to take six or eight inches off each one of his legs, things might be a lot more pleasant for the rest of us."
"I think it might have something to do with the fact that he's a hunter," Omago said. "From what I've heard, all hunters move fast, because they don't eat if they just plod along."
"That probably has a lot to do with it," Gunda agreed.
"Hunting might be exciting," Omago said, "but turnips don't run away, so we don't have to chase them."
"I've never been involved in farming or hunting," Gunda said. "Down in the Empire, we just buy our food. We don't have to grow it or chase it down to shoot it full of arrows."
"Did I hear correctly?" Omago asked then. "Somebody told me that Trogite soldiers are born and raised in those forts down there."
"Not quite _all_ of us," Gunda replied. "It's mostly just the officers. We start out playing soldier, but then we move on to being real ones."
"Isn't it sort of dangerous to hand real weapons to little children?"
Gunda smiled. "We don't get _real_ weapons until we're older," he replied. "We start out with wooden swords, and there are quite a few old veterans keeping an eye on us. Then, when the weather's bad, they tell us war stories. There was an old sergeant named Wilmer who could spend hours telling us stories about wars the army had fought in the past. I'd say he was probably one of the greatest storytellers who've ever lived. He could keep us sitting on the edge of our chairs for hours."
"The stories the older farmers tell _us_ when we're little boys aren't really very exciting," Omago said. "Stories about bugs eating our crops used to show up quite often."
"That's what _this_ war is all about, though, wouldn't you say? Of course, this one's just a little different. This time, the bugs are eating _people_ , not just crops." Then he saw something quite interesting. "Excuse me a minute, Omago," he said. "I need to mark something." He went to a fair-sized oak tree and tied a length of red string around it. "A good spot for a fort," he explained. "Narasan told me to keep my eyes open while we're going through the pass and mark any place that might be a good spot for a fort."
"Are you saying that you're going to build forts _this_ far down the pass?"
"Only if the bug-people give us enough time, Omago. If things work out right, we'll build a fort every mile or so. If the bug-people _do_ decide to come down this way, we'll be able to make it _very_ expensive for them."
"You Trogites are most certainly the finest soldiers in the world," Omago declared. "We're very lucky that Veltan was able to persuade Commander Narasan to come here and help us. I keep hearing stories that your commander had given up soldiering and had taken up begging instead."
Gunda shrugged. "He made a blunder in a war, and his nephew was killed. Narasan couldn't live with that—until Veltan came along and told him that it was time to go to work again."
Omago smiled. "Veltan can be very persuasive when he needs to be."
"He is indeed," Gunda agreed. "He threw some things at Narasan that jerked our commander out of his gloom, that's for sure. Narasan was sure that the world was coming to an end, and time would stop. Veltan told him that time didn't, and never would, have an end—or a beginning either."
"He was wrong there," Omago said. "Time may never have an end, but it definitely had a beginning. There was a time when the universe wasn't, but it suddenly appeared. _That_ was when time began."
"Just when did that happen?" Gunda asked curiously.
"It's very hard to say," Omago replied. "It was before the world—or the sun—came into existence, so Veltan wasn't around."
"Where did you pick up this story, Omago?"
Omago frowned. "I'm not really sure," he admitted. "I just somehow know that it happened that way. Isn't that odd?"
"This Land of Dhrall is the native home of odd, Omago," Gunda said. "We'd better pick up our pace, my friend," he suggested. "Longbow's getting a fair distance ahead of us, and if we don't keep up, he'll get very grouchy. If we keep strolling along like this, he might send us to bed without supper."
Omago laughed, and they both began to walk faster.
The sun was setting off to the west when Longbow decided that they'd gone far enough. Gunda breathed a sigh of relief at that point. He was fairly sure that he didn't have another mile left in him.
"We'll need to go a little farther tomorrow," Longbow said.
" _Farther?_ " Gunda protested. "I'm not sure I'll be able to stand up tomorrow morning, much less walk more than a mile."
"You spend too much time lying around when you're riding on boats, Gunda," Longbow replied. "You'll be in much better shape when we reach the head of the pass." Then he looked back down the pass where the last of the Trogites were stumbling up toward where they'd soon be setting up their night's camp. "Did Narasan happen to tell you why he sent so many men?" he asked.
"Narasan doesn't explain too many things to me anymore, Longbow. All it does is confuse me."
"But ten thousand men to build one fort?"
"That might depend on just how big a fort we're talking about."
They had beans for supper, of course, but Gunda was sure that he could eat almost anything by then. He put out guards and then fell asleep almost immediately.
**2**
Longbow had been quite obviously not at all pleased when Commander Narasan designated some ten thousand of his men as "fort-builders." Andar had privately agreed with the archer, but he chose not to make an issue of it. The more he thought about it, though, the more he realized that the idea might have some merit.
He went looking for Longbow and found him still awake. "I take it that you aren't too happy with the commander's generosity, Longbow."
"I wouldn't call foisting that many people off on me 'generosity,' Andar," Longbow replied in a sour sort of voice.
"There _is_ something we might want to consider, though," Andar said.
"Oh?"
"About how wide would you say that the upper end of this pass is?"
"I'd say fifty feet at the most."
"That would put almost two hundred men to work on every foot of our projected fort, wouldn't it?"
"I'm not sure that building a fort out of people would be a very good idea, Andar."
"It might be just a little difficult to feed them if they're piled up on top of each other," Andar agreed. "But since we've got a surplus of people, we _could_ put the extra ones to work building a second fort a mile or so on down the pass. That way, there'd only be five thousand standing on top of each other in each fort."
"That's _still_ going to be badly crowded."
"If it seems that way when we get up there, we could build even _more_ forts. If we've got four solid, well-made forts blocking off the Creatures of the Wasteland, life might start to become very unpleasant for them, wouldn't you say? We'll have archers and spear-men standing on top of those forts and Malavi horse-soldiers slashing at them from both sides. I'd say that each fort could cost them a half-million or so of their companions. If we keep on erecting new forts every mile or so, the Vlagh's likely to run out of warriors before her army even gets halfway down the pass."
"Maybe sending ten thousand fort-builders up the pass wasn't such a bad idea after all," Longbow agreed. "Do you think Gunda will go along with us on this?"
"Not right at first, maybe, but after a day or so of watching his men falling over each other, he'll probably listen to our suggestion."
Longbow looked at Andar in a speculative way. "I've noticed several times that you're more clever—and practical—than either Gunda or Padan. Why does Narasan pay so much attention to those two and ignore you?"
"It has to do with our childhood, Longbow," Andar explained. "We were all children in the army compound in Kaldacin, but we didn't all live in the same barracks. Narasan, Gunda, and Padan were childhood friends, because they all lived in the same barracks. Brigadier Danal and I lived in a different barracks, so Narasan didn't know us as well as he knew Gunda and Padan." Andar smiled briefly. "In a way I'm _earning_ my position while Gunda and Padan get theirs for free. Narasan's perceptive enough to know that I'm not a dunce. These wars here in the Land of Dhrall have been most useful for me. It's reached the point that Narasan depends on me almost as much as he depends on Gunda and Padan." He glanced off to the east. "The sun's coming up," he noted, "the _real_ one, I think. Dahlaine's toy might still be asleep. I think you might want to start out now, and I'll tell Gunda that it's time to go. If you step right along, you'll get farther and farther ahead of him. Gunda should get the point in an hour or so, and he'll start pushing the men. They like him, so they'll do as he tells them."
"They don't like you as much as they like Gunda, do they?"
Andar shrugged. "Being liked isn't that important, Longbow. It's getting the job done that counts."
The river that had carved out Long-Pass over the extended eons was wider and more gentle than the frothy, tumbling brooks in the more rugged mountain ranges in other parts of the Land of Dhrall. In some ways the river rather closely resembled the streams in the southern region of the Trogite Empire. Andar pulled his mind back from that particular comparison, since it reminded him of the death of Commander Narasan's gifted young nephew Astal. Narasan had never come right out and admitted it, but Andar was fairly sure that he'd been secretly pleased when word reached him that Gunda and Padan had arranged to have Astal's murderers assassinated by a number of professional killers.
It seemed to Andar that the river that flowed down through Long-Pass was wider than it should be. The unseasonable warmth caused by Dahlaine's pet sun appeared to be melting ice and snow farther on up the pass. Had anyone ever told him when he'd still been living in Kaldacin that it might be possible to have a glowing little sun as a house pet, he was quite sure that he'd have had _that_ particular informant sent off to some lunatic establishment.
Longbow, who evidently could get by on very little sleep, roused them before daybreak the following morning. It was bitterly cold, and Gunda saw something that was very rare down in the Empire. Any time somebody spoke, a cloud of steam came out of his mouth to accompany the words. "I thought we were far enough to the south that we wouldn't blow out steam when we talked," he said when he and his friends were eating breakfast.
"It happens up in the mountains fairly often," Longbow said. "It can be quite useful when you're hunting—or fighting a war. It's fairly easy to find out just where the animals—or your enemies—are."
"Do the bugs blow out steam when they talk to each other in the same way that people do?"
Longbow shook his head. "Most bugs don't talk with words the way we do," he said. "They talk with touch instead. Most bugs don't even _have_ voices."
"They _do_ make noises, Longbow."
Longbow nodded. "They rub their legs together to _make_ the noises you've heard, Gunda, and the noises they make aren't words. Bugs don't _need_ words. They all know what they're supposed to be doing, so they don't have to talk about it."
"Were you able to see the Wasteland when you came down that mountain range, Longbow?" Keselo asked their friend.
"Fairly often, yes."
"Are the bugs moving out there yet?"
"I saw a few—quite a long way out in the Wasteland. I'd say that the ones I saw are probably scouts. The overmind needs to know whether we're here or not and how many of us there are. The main force is probably quite a way behind the scouts."
"How far behind you would you say that the Tonthakans, Matans, and Malavi are?"
"Just a few days would be about all. The Malavi would be quite a bit farther south, of course."
"But you _still_ outran them, didn't you?"
"Probably," Longbow replied with a shrug. "Horses get tired after a while."
"But you don't, do you? You can run all day long, can't you?" Keselo's voice was strangely intense.
"If necessary, yes. You seem to be concerned, Keselo. What's bothering you so much?"
"There are times, friend Longbow, when I'm not absolutely sure that you're human."
"We don't live the same kind of lives, Keselo," Longbow replied. "I almost never walk. I run instead. Your body gets used to doing things the way you want it to. I've trained my body to run. When you get down to it, walking tires me much more than running does." He looked off to the east. "It's almost daylight," he told them. "You'd better tell your men to get started, Gunda. Days don't last very long in the wintertime."
It was about mid-morning that day when they rounded a turn in the pass and came to something that noticeably brightened Gunda's day. Andar waded across the now-shallow river and rubbed his hand down a weather-worn rock face.
"Well?" Gunda called.
"It's granite, all right," Andar called back. "It's been worn down until it's quite smooth, but there are cracks here and there, so we should be able to pry quite a bit of it free."
"You Trogites seem to be very fond of that particular variety of stone," Omago said.
"It's the very best that there is," Gunda replied. "If you want something to last for a long, long time, build it out of granite. It's heavy and hard, and if you know what you're doing, you can chip it into blocks. If we have access to granite, and the bug-people aren't right on top of us when we get to the head of the pass, we'll be able to build a fort that _nobody_ will be able to get past. A well-built overhang makes it almost impossible to climb up the outer face, and the archers and spearmen will delete 'almost.' Give me and my crew about three days, and the bug invasion will stop right there at the head of the pass, and that sort of translates into 'we just won another war,' wouldn't you say?"
"That's what this is all about," Omago agreed.
Then Longbow came back down the pass. "Why have we stopped?" he asked Gunda.
"We just came across a sizeable deposit of the best building material in the whole world," Gunda replied smugly. "Give my men and me a few days and we'll have an impregnable fort at the head of the pass."
"We're talking about that grey rock, aren't we?"
"That's it."
"We might as well move along, then," Longbow suggested. "Almost all of the rock at the head of the pass is the same as that rock face on the other side of the river. Your men won't have to come down here and dig up building material. It's lying all over the ground up at the head of the pass."
"Let's move right along, then, Longbow," Gunda said, concealing a broad grin. "All this shilly-shallying around is just wasting time."
Longbow gave him a hard look and then he turned around and continued his hike.
"Wasn't that just a little bit—?" Omago started.
"It's good for Longbow, friend Omago," Gunda said. "It'll take some of the wind out of his sails."
They made camp for the night as dusk settled down over the pass, and Gunda was quite happy when he came to realize that his legs and back weren't aching nearly as badly as they'd been the previous evening.
He slept very well that night, and he even woke up before Longbow came around to rouse him. "You're already up and moving?" the archer said. "What an amazing thing."
"Don't beat me over the head with it," Gunda replied. "When do you think we'll reach the head of the pass?"
"Late tomorrow," Longbow said, "or early the following day." Then he smiled, and that slightly startled Gunda. Longbow almost never smiled. "We have company," he announced.
"Way out here?" Gunda demanded. "Who's foolish enough to join us out here in the wilderness?"
"Zelana herself," Longbow replied. "She has some information for us."
"Let's go see what she has to say," Gunda said, throwing back his blankets.
Zelana was sitting near the riverbank, and she looked rather pensive. Gunda, as always, was more than a little awed by her presence. Lady Zelana was by far the most beautiful woman Gunda had ever seen, and just her presence set him to trembling. He reminded himself over and over that she was _not_ a woman in the usual sense of that word. She was an immortal goddess instead, and she was quite probably at least a million years old.
"Are you all right?" Longbow asked her. "You seem to be a little unhappy about something."
"It's nothing important, Longbow," she replied. "I'm approaching sleep-time, is all. There were many, many things I wanted to do during this cycle, but I seem to be running out of time." Then she stretched up her arms and yawned. "It's getting closer," she said. "My nap seems to be creeping up on me from behind." Then she straightened. "Let's get down to business. I rode the wind out over the Wasteland late yesterday to see what the Vlagh is up to. She's sent out many of her servants to nose around and find out what we're up to, and I don't think she likes what they've been telling her. She doesn't really have very many choices this time. Long-Pass here is her only possible invasion route, and I'm sure that she knows that you're coming up the pass to block her off, and she doesn't like that one little bit."
"What a shame," Longbow said with no hint of a smile.
"It stops being funny right about now, Longbow," Zelana told him. "After I'd had a look at the Vlagh's scouts, I drifted farther out into the Wasteland, and from what I saw, I'd say that the Vlagh's throwing everything she's got at us this time. There are limitations on just how many eggs she can lay at any one time. She's _supposed_ to hold enough back to maintain the population of her nest. I'd say that she's ignoring that this time. From what I was able to see, she has close to five times as many warriors as she's had during the previous wars, and they're all coming this way."
"How long would you say it's likely to take for her children to reach us up here?" Gunda asked.
"Five or six days anyway."
"That's probably all that I'm going to need," Gunda said. "We'll have the fort erected and manned before the Vlagh gets here. From what Longbow told me, the head of the pass isn't very wide, and I'm sure that our fort will be complete before the Vlagh even gets close. Once that fort's complete and well-manned, the Vlagh can stand out there beating her head against it until next summer, but she won't get past—no matter how many of her children she sends to attack."
[ALARMING
NEWS](YoungerGods_toc.html#part_5)
**1**
It took the better part of two days to get Sorgan's army ashore, and then Sorgan and Padan rowed over to the _Victory_ to speak with Brigadier Danal.
"That takes care of things here, Danal," Sorgan told the lean, stubborn officer. "Convey my thanks to Narasan, and tell him that I'll stay in touch."
"I'll do that, Captain," Danal replied.
"How long would you say it's going to take you to get the rest of his army down to the mouth of Long-Pass?"
Danal squinted. "The ships will be empty when we go north," he said, "and that should save us a day. Loading the troops on these ships will take a couple of days, and then four days to the mouth of the pass. Then two more days to unload. I make it to be twelve days to two weeks. Even if the bug-men have reached this side of the Wasteland, the Malavi and those archers from the North will be able to hold them off until Gunda's got some forts in place." Then he smiled slightly. "You don't necessarily have to tell Narasan that I said this, but your little side-trip gave me a wonderful opportunity to avoid all that tedious business of building forts."
"That's what friends are for, Danal," Sorgan said with a grin. "If you happen to meet Lady Zelana up there, tell her that I said hello."
"I'll do that, Captain Hook-Beak."
"Oh, and tell Narasan that I'll keep the _Ascension_ here. I'm going to need a private place to confer with my men. I don't want one of Lady Aracia's fat priests eavesdropping when I'm telling my men what to do."
"I'm sure he'll understand, Captain," Danal replied. "You have a nice war now."
"I'd hardly call what we're going to do here a war, Danal. It's just going to be an imitation."
"Those are the very best kind," Danal said.
Sorgan and Padan climbed down the rope ladder to their skiff. "I like that man, Padan," Sorgan said. "We get along just fine."
"He's a very good soldier," Padan agreed.
They rowed across to the _Ascension_ and joined several Maags in the rear cabin.
"All right, then," Sorgan said. "The Trogite fleet will sail at first light tomorrow, and they'll pick up the rest of Narasan's men and take them on down to the mouth of Long-Pass to fight the _real_ war. In the meantime, we'll get started on the imitation war here. I don't _think_ Aracia has any people up in that vicinity, but we'll want to make sure that no word of what's happening up there reaches her. I don't think she'd pay much attention to anything that's not going on here in the vicinity of her temple, but we should probably block off any roads or trails coming down here from up in the Long-Pass region."
"I'll send some men up there to take care of that, cousin," Torl said.
"Good," Hook-Beak said approvingly.
"Have you worked out a plan yet?" Padan asked the Maag.
Sorgan grinned. "Oh, yes," he replied. "I'm going to take some men to Aracia's throne room. I'll tell her that they're scouts, and they'll find out what they can about the upcoming invasion of the bug-people. Then I'll tell her how dangerous things are going to be for those scouts and make a big issue of how many varieties of invaders we'll come up against. Then I'll send the men on their way, and they'll march out about a mile or so and then set up camp in some fairly well-concealed place."
"Wouldn't you say that a mile is just a little too close?" Padan asked.
Sorgan shook his head. "I want them to be close enough to be able to hear the sound of a horn. I'm going to work on Aracia to build up her fright. Then, when she's filled to the brim with terror, I'll send word out to the west side of her temple, and one of the men there will toot a horn. When the imitation scouts hear it, they'll come running back and start piling 'awful' all over Aracia and the fat ones who worship her." He squinted. "Torl," he said to his cousin, "I'll send Rabbit out there with you. He's very clever, and between the two of you, you should be able to come up with stories that'll send Aracia and her fat priests screaming and searching for safe places to hide. I'd say that you two should put things together so that this nonexistent invasion by the bug-people starts out with moderately awful and then builds up to pure horror. You'll have several days to work on these stories, so use lots of imagination. Then too, I think you all might want to practice looking frightened. Bulge out your eyes, shiver like crazy, and scream once in a while. The whole idea here is to frighten everybody to the point that they'd sooner die than go outside the temple and have a look for themselves. _If_ we can scare them enough, the notion of going north to pester Narasan will never occur to any of them. They won't know that Narasan's there anyway, but I want those priests to be so frightened that they won't even _consider_ following an order to go anywhere away from this central temple. We'll use terror instead of bars, but this silly temple _will_ be a prison if we do this right."
Padan was just a bit surprised by the level of sophistication Sorgan's scheme indicated. "Maags aren't supposed to be that clever," he murmured to himself.
"I think you'd better come along, Padan," Sorgan said when they went out onto the deck of the _Ascension_. "I'm going to be playing a game of sorts, so I might miss a few reactions of Aracia or her assorted priests. If you happen to notice any degree of skepticism, let me know immediately. We _don't_ want any doubts floating around at this point." Then he turned to his cousin. "Gather up the men who'll be going with you and come along. I'll give you your marching orders right there in the temple. I want Aracia and her priests to see you leave so that they'll recognize you when you come back. Try to look brave and strong when I send you out, and frightened and timid when you come back. I'll make an issue of how skilled you are as warriors when you march out. Then, when you come back whimpering, Aracia will believe just about everything you tell her about all the awful-awful you've witnessed."
"This is a side of you I don't think I've ever seen before, cousin," Torl said. "You're an excellent deceiver, aren't you?"
"I'm probably the best," Sorgan replied. "Let's go frighten Zelana's sister for an hour or so, and then _I_ can come back to the _Ascension_ and rest for a while. I've been running steadily for about three days now."
They rowed on to the beach just below Aracia's temple and then walked on up to the golden door. Evidently word had gotten out, and no priest—or priestess—tried to interfere as they marched on along the corridor that led to the throne room.
The fat priest Bersla was delivering another oration of praise when they entered Aracia's throne room. His majestic voice faltered when Sorgan marched in, however.
"Are you just about through?" Sorgan asked in a flat, unfriendly tone of voice.
"I was just about to leave, mighty Sorgan."
"No," Sorgan said abruptly, "stay. There's something I want you to see."
"As you wish, mighty Sorgan," Bersla replied in a squeaky sort of voice.
Sorgan approached the throne. "I've looked around your temple here, Lady Aracia," he said, "and we've got a lot of work ahead of us, I think, but for right now we need information—what kind of bugs are coming this way, anything new and unusual approaching, how close they are to where we are right now." Then he gestured at Rabbit and Torl. "These men are the best, so they'll be leading the scouting parties. I'm _hoping_ that some of them will live long enough to bring back the information we need. There are many different varieties of bug-people. We know about quite a few of those, but there might be others as well. If there are, I want to know about them. We _don't_ want any surprises. We already know that bugs can come at us from under the ground, from up in trees, and even out of the empty air. There's one variety that's part bug and part bat, and it flies around biting people, and the people die immediately."
Aracia shuddered. "How in the world did these things come into existence?"
Sorgan shrugged. "Their queen—the one called 'the Vlagh'—comes up with the idea for these various creatures, and then she lays eggs. When the eggs hatch, there's a whole new variety of bug. Worse yet, she lays those eggs by the thousands."
"They'd only be infants," the priestess Alcevan said. "They wouldn't be much of a danger for quite some time."
"I see that you've never spent much time around bugs," Sorgan said. "Bugs only live for about six weeks, and then they die. The infancy of a bug only lasts for three or four days, and then it's a full-grown adult, and it'll kill anything the Vlagh wants it to kill. They're not intelligent enough to be afraid of anything. I've seen two or three of them still attacking a fort after we've killed thousands of their friends. They just keep coming until they die."
"That's absurd!" Bersla declared.
"You'd better be ready for _lots_ of absurd when the bug-people attack," Torl said. "About the only thing we've found that gets their attention is fire. When you set fire to something, it tends to get a little confused."
Then Sorgan gestured toward the door. "Take your men and go out there and see what you can find out. Don't get _too_ many of your men killed by taking chances. I need information, not dead friends. Find out what you can and then hurry back, and be very careful. You can die some other time. _This_ time I want live men who can tell me what I need to know."
Sorgan had moved his main force to the far western side of Aracia's temple. "If there really _was_ going to be an invasion by the bug-people, they'd reach this part of Aracia's temple first," he told Padan. "That means that we'll need some kind of fort here to persuade Aracia and her priests that we _are_ going to protect them. It won't have to be _too_ close to a real fort. The temple itself isn't really that well-built, so the priests wouldn't recognize _real_ construction even if it walked up and bit them on the nose. We'll move a few of the building blocks and maybe knock down a tower or two. Then we'll have the men pretend to be building some kind of fort and let it go at that. What we'll _really_ be doing will be terrifying Aracia and her priests to the point that they'll be afraid to come out of the central temple."
"If this works out the way we want it to, we'll have pulled off one of the greatest hoaxes of all time, Captain," Padan said.
"Naturally," Sorgan boasted. "No matter what I do, I'm always the best." Then he laughed. "Sorry, Padan," he said then. "It was just too good an opportunity to let slip by."
"Where's Veltan?" Padan asked. "I haven't seen him for the last few days."
"He's nosing around over in the main temple," Sorgan replied. "I need to know how much of our silly story the priests—and Aracia, of course—have swallowed whole. If there are any doubts over there, we might have to play some more exotic games." Then he shivered. "Let's get in out of the weather, Padan," he said. "I _hate_ winter."
They went on back inside to a room that had a stove, and it wasn't too much later when Veltan joined them.
"Well, Sorgan," he said, "you've managed to terrify my sister's priesthood."
"That was sort of what we had in mind, wasn't it?" Sorgan asked. "That's why we've been waving bugs around every time we're near any priest."
"It's _you_ , not the bugs, that has them worried, Sorgan. They're desperately trying to come up with some way to reduce your grip on Aracia. They're afraid of you, and they hate you. It seems that you've got a tighter grip on Aracia than even _we_ could imagine. I think it all goes back to Bersla. He had Aracia wrapped around his little finger with those stupid orations of his. Then you came along and pushed him back into a corner and threatened to kill him if he said one more word. He's had Aracia under his control for years now, and then you walked in and took her away from him in just a day or so. Aracia had the title, but Bersla had the power. Now he doesn't anymore."
"Poor, poor Fat Bersla," Sorgan murmured smugly.
"Now we come to the interesting part, Sorgan," Veltan said. "Bersla wants to kill you—or persuade some lesser priest to do the job for him."
"They don't even have weapons, Veltan," Sorgan scoffed.
"They _do_ have knives, you know. They're made of stone, but a good hard stab in the back with a stone knife will penetrate your skin and go in far enough to do very serious damage to your vital organs. Bersla's doing everything he can think of to persuade some minor priest to stab you in the back. Quite a few of them are very interested by the offers Bersla has been waving in their faces. Instant promotion to the higher priesthood sounds very nice to young, ambitious priests who don't stand too high in the Church of Aracia."
"It sort of sounds like I should have borrowed one of those iron breastplates from Narasan before I even came down here," Sorgan muttered.
**2**
After a bit of thought, Hook-Beak spoke briefly with his first and second mates, Ox and Ham-Hand, and after that, the two big Maags followed their captain wherever he went in Aracia's temple. Ox was carrying his huge battle-axe, and any time Hook-Beak spoke with one of Aracia's overfed priests, the hulking Maag touched up the already razor-sharp axe-blade with a hefty whetstone that made a shrill sound as Ox drew it across the axe-blade.
The priests of Aracia got the point almost immediately.
Veltan, who had frequently demonstrated his ability to listen without being seen, advised Sorgan that the priests of Aracia had stumbled over a truth in their desperate search for some way to loosen Sorgan's grasp on Aracia. They had taken to denouncing Hook-Beak and his men as opportunistic swindlers. "They keep telling each other that there's no such thing as a bug-man, Sorgan," Veltan reported. "They're claiming that you and your men are waving 'bug-men' around as a way to leech more and more gold out of Aracia."
"That's ridiculous, Veltan," Sorgan protested. "I know for a fact that Lady Aracia has actually _seen_ the bug-people. I was standing right beside her down in your Domain when the bug-people and the Trogite priests were busy killing each other."
"I know," Veltan replied. "I think big sister has been keeping that to herself. The last thing she wants here is to have all of her priests come down with panic. If they run away, she'll be all alone here."
"We're going to have to do something about this, Veltan," Sorgan said. "The priests are obviously scraping this off the wall, but it looks to me like they've accidentally stumbled over the truth. Bug-people are real, but they aren't coming through _this_ part of Aracia's country." Then he looked speculatively at Veltan. "Maybe it's time for you to start making people believe that they're seeing something that's not really there, can't you?" he asked.
"If it's absolutely necessary," Veltan replied. "I don't want to do it too soon, though. She _can_ sense things like that if I leave the illusions in place for too long."
"I think a few brief glimpses might serve our purpose, Veltan. We want to confirm Aracia's belief that the bug-men are invading _this_ part of her Domain, _and_ to persuade the priests that I'm not lying and that Aracia _knows_ that I'm not. I think I'll go have a little talk with Torl and Rabbit. If they come running out of that farmland off to the west and there are images of several huge bugs right behind them, Aracia will probably go into hiding and this scheme the priests came up with will fall apart right then and there, wouldn't you say?"
"I think it's worth a try, Sorgan," Veltan agreed. "I've briefly touched Aracia's mind a few times since we arrived, and she's absolutely convinced that the Vlagh is out to get _her_ personally. She's sure that the Vlagh wants to kill her, and she's terrified."
"She can't actually die, can she? I mean she's immortal, isn't she?"
"Yes, she is, but she's drifting toward senility, so she's not sure of _anything_ anymore. This has happened several times before. All of us get a little vague when we're approaching the end of one of our cycles, but Aracia tends to take it to extremes."
"I had a talk with Torl and Rabbit last night," Sorgan said the next morning in the cabin of the _Ascension_. "Now they know about Veltan's illusions, and they'll make some show of fighting them off. The only problem we might have is that Aracia has to _see_ this imitation skirmish, and she almost never comes out of that silly throne room of hers."
"We've got some time to play with, Sorgan," Padan said. "You might want to have your men get started on the fort. Then, when its base is in place, you could invite holy Aracia to come out and have a look." Padan scratched his bearded cheek. "I suppose that technically you'll need her permission to continue, so a visit would be very appropriate. If Veltan and your scouts know when she'll be there, they'll be able to put on a show for her that'll send her running for cover— _and_ , after that, she'll dismiss any priest who tries to tell her that you're a swindler." Then he laughed as he remembered something that had happened in Kaldacin several years ago.
"What's so funny?" Sorgan asked.
"The Church of Amar down in the Empire has a fair number of dungeons scattered about. When a priest blunders and insults one of his superiors, they lock him in a hole in the ground and throw away the key. I'd imagine that Bersla would lose quite a bit of weight if Aracia had him locked up in a dungeon where all he had to eat would be bread and water."
Sorgan frowned slightly. "I wonder if we could get away with that," he murmured.
The Maags were busy knocking down walls that afternoon. Padan saw that they were very good at destroying things. Building, however, might cause them a few problems.
A young priest came scurrying out of the central temple with a look of horror on his face. "What are you _doing_?" he screamed.
"We need a fort to hold off the bug-people," Sorgan replied. "When we saw that nobody lives here in this part of the temple, we decided to modify it just a bit. There are quite a few similarities between forts and temples. Did you ever notice that? Anyway, things are going along fairly well. Give us a week or so, and the invasion of the bugs will stop right here." Then he looked rather speculatively at the young priest. "He looks pretty husky to me, Padan. If Lady Aracia wants this fort in place to defend her temple, she might just order all of her priests to come here and lend us a hand. The exercise would probably be good for them, wouldn't you say?"
"I'm sure it would," Padan agreed. "If we were to sweat some of the fat off them, they'd probably live longer." He looked at the now-horrified young priest. "If you were to step in and lend us a hand with our fort here, you _might_ even live past your thirtieth birthday. And if you were to _really_ bear down, you _might_ even live to be forty. Look at all the extra life you'll get out of a few weeks of hard work."
The young priest turned and fled at that point.
Sorgan laughed. "I think that might eliminate any further objections," he said. "The notion of doing _real_ work doesn't seem to sit very well with Aracia's priesthood."
"What an amazing thing," Padan agreed.
Their imitation fort was coming along quite well now that Sorgan had leaned on his men and ordered them to follow Padan's instructions. They had what _looked_ like a solid base about ten feet tall running along the west side of Aracia's temple.
"It's not really all that substantial, Sorgan," Padan admitted, "but Aracia wouldn't even recognize a _real_ fort. I don't know that you want to wait too much longer. I'm sure that her priests are trying everything they can think of to discredit you. Let's not give them _too_ much more time before she sees the skirmish between your men and the imitation bugs Veltan's going to conjure up. That's going to verify our scam and scare Aracia's stockings off. After that, we'll be home free."
"You're probably right, Padan. I'll have a quick talk with Veltan, and he can go on out and start Torl and Rabbit this way while you and I go to the throne room and tell Aracia that we want to show her what we've accomplished so far."
"What are you going to do if she refuses to come out here?"
Sorgan shrugged. "I'll tell her that all work stops until she comes out here and approves of what we've done so far. No matter what her priests have been telling her, she's still terrified by the Vlagh, so she won't take any chances. She knows that her priests would be useless in a war, so she'll do just about anything to stay on the good side of me."
Bersla was orating again, but for once Aracia didn't even seem to be listening.
"Where have you been?" she demanded of Sorgan when he entered the opulent throne room.
"Off on the west side of your temple, lady," Sorgan replied. "My men have been building a fort to hold off the bug-people. It looks fairly good to me so far, but maybe you should come there and take a look. My men and I have always specialized in tearing forts down, not building them. If you have any suggestions, now's the time to make them. There's a fairly significant difference between a temple and a fort that you might want to think about. A temple says 'come in,' but a fort says 'stay out.' I think you'll see what I mean when we get there."
"Holy Aracia is otherwise occupied right now, outlander," the priestess Alcevan declared arrogantly.
"Listening to Bersla, you mean?" Sorgan asked. "Has he said anything new and different today? I'm sure that Lady Aracia has heard every speech that he's cobbled together a hundred times or more. You could listen, if you'd like, and then when Lady Aracia returns you can sum them up for her."
"Do you _really_ need to have me look at this fort of yours, Sorgan?" Aracia asked.
"This is _your_ temple, Lady Aracia," Sorgan replied. "If the bugs destroy it, your priests will have to build you a new one, and that might take them a while—quite a _long_ while, I'd say, since fat people wear out in just a short time when they're doing real work. I suppose you could set up your throne in an open field somewhere, but I don't think very many of your priests would like to make speeches when it's raining on them. Let me put it to you in the simplest of terms, lady. Come and look, or all work stops. We can't go any farther without your approval."
Aracia's eyes went wide and she stood up. "Let's go look, Captain Hook-Beak," she said.
"Now, that's more like it," Sorgan said approvingly.
"It's called a catapult, lady," Sorgan explained. "The Trogs invented it. Up north in your brother's Domain, it worked out quite well. It was originally invented to throw rocks at the enemy, but we used it to throw burning pitch at the bug-people. If you want to get somebody's—or some _thing's_ —immediate attention, set him on fire."
"I see that you're still putting sharp stakes in the ground," Aracia noted.
Sorgan nodded. "We've got gallons and gallons of the venom we leeched out of dead bugs down in Zelana's Domain. We dip the stakes in that venom before we plant them in the ground. When a bug-man steps on one of those, he dies almost immediately. It's a quick way to get rid of a _lot_ of enemies."
"Is _that_ as high as you're going to make your fort, Sorgan?" Aracia asked.
"No, ma'am, that's just the base. There'll be another ten feet on top of that part of the fort."
"Ho, Cap'n," one of the Maags shouted. "I think the scouts are coming back, but it looks to me like they're being chased by bug-people."
Sorgan swore. "I _told_ those idiots to be careful!" he exclaimed. Then he took Aracia by the arm. "Let's get up on top of the fort. It'll be safer there."
Aracia's face had gone pale, and her eyes seemed filled with terror.
"Over that way, Cap'n," Padan said in a fair imitation of the Maag dialect. "There's a ladder a short way down along the wall. Once we get up on top, I'll kick the ladder away."
"That's not a bad idea, Black-Beard," Sorgan agreed.
"Black-Beard?" Padan muttered.
"Sorry," Sorgan said softly. "You've got to have a Maag kind of name, and that was about the best I could come up with."
They reached the ladder and scrambled on up. "Leave the ladder where it is for now, Black-Beard," Sorgan said. "If one of our scouts gets clear of the bug-people, we want him up here. I need to know just exactly what happened out there."
"Aye, Cap'n," Padan replied.
"Shouldn't I return to the main temple?" Aracia asked.
Sorgan shook his head. "It's not safe now, Lady Aracia," he said. "My men and I can protect you up here on this wall, but those narrow corridors wouldn't be safe." Then he looked out toward the west. "There!" he said, pointing at a berm no more than a hundred feet away. "My men are doing something right for a change. They took some high ground and it looks to me like they're holding it. There are probably a lot of dead bugs on the far side."
"Isn't that Rabbit with the others?" Padan asked.
"That's Rabbit, all right," Sorgan agreed. "He's got that bow he made down in Veltan country."
"I didn't know that he had a bow," Padan said.
"He spent too much time with Longbow," Sorgan declared.
"Now _that's_ the one I'd like to see out there," Padan said. "If there's only one Longbow and a thousand bug-men, put your money on Longbow. He'll kill every one of them."
"Our men are holding that berm," Sorgan said. "The bug-people _aren't_ going to get past them."
"Those bug-things aren't very big, are they?" Aracia said then.
"You don't really see very many big ones, Your Majesty," Padan said. "Now and then the Vlagh will _make_ a big one, but most of them are what Rabbit calls 'teenie-weenies.'"
"The little rascal just came down off that berm," Sorgan said, "and he's running this way."
"He probably wants to report, Cap'n," Padan suggested. "You made a big issue of that when you sent them out to scout around. You told them all to stay alive so that they could tell you things that you needed to know."
The little smith came scrambling up the ladder and then stood there puffing. "We hit a snag out there, Cap'n," he wheezed.
"Catch your breath before you report, Rabbit," Sorgan said.
"Aye, Cap'n," the little smith said. Then he stood breathing deeply for a few moments. "Things went real good for a while, Cap'n," he started again. "Just about the only breed of bugs we saw were those little ones, but when we started back, Torl caught a few glimpses of great big ones. I ain't exaggerating one little bit, Cap'n. They stood almost ten feet tall, and they probably weighed close to a ton."
"You're not serious!" Sorgan exclaimed.
"I'm afraid I am, Cap'n. This wall our people made here just won't work. If those big ones are as strong as the others, they'll smash down your fort here with their bare hands and then throw the bits and pieces out into the Wasteland just to get rid of them."
"You'd better round up the men, Black-Beard," Sorgan said to Padan. "This wall here's going to have to be at least twice as high and three times as thick if it's going to hold off the giant bug-people." Then he took Aracia's arm again. "There's not much you or your people are going to be able to do to help us. Right now I'd say that blocking off most of the corridors your people included when they built the temple would be the best thing to do. You don't really want more than one hallway leading there."
**3**
The men out on the berm continued to shout and to roll large rocks down the empty far side to make it appear that there were still enemies charging their position. Queen Aracia stayed very close to Sorgan, but she seemed to be growing more and more calm. "The bug-people are truly hideous, aren't they, Captain Hook-Beak?" she asked.
"Oh, yes. The first time I ever saw one of them was right after Eleria's flood had come rushing down the ravine to almost swamp the village of Lattash. That flood drowned bug-people by the hundreds, and their bodies were washed on down to the village. _That_ was when my men and I found out that those little bug-people had snake fangs and they were deadly. I almost gave your sister's gold back to her and sailed on back home at that point."
"You were actually afraid? I didn't think you knew the meaning of the word 'afraid.'"
"I wasn't quite ready for snake-bugs—or maybe bug-snakes—at that time. It took a while for me to get used to the notion. I have Longbow to thank for that. There's a man who isn't afraid of anything."
"I know," Aracia said. "I spoke with him a few times when I was observing the war in Veltan's Domain. Is he really as good as everybody says he is?"
"Better, probably," Sorgan replied. "If your sister had been lucky enough to have ten men like Longbow, she wouldn't have needed me." Sorgan shaded his eyes and peered down at the ridge lying to the west of the fort. "My men aren't rolling rocks or throwing spears anymore, and that sort of says that they've managed to kill all of the bug-people who'd been pursuing them."
"It's safe for me to return to the main temple, then?" Aracia asked.
"Let's hold off until morning, lady," Sorgan said. "Let's not take any unnecessary chances." Then he looked questioningly at his employer. "Would it offend you if I had something to eat?" he asked her.
"Not in the slightest, Captain," she replied. "I think I'll nibble on the sunset while you have supper."
"I'm _never_ going to get used to that," Sorgan said. "How can _anybody_ live on nothing but light?"
"It's one of our advantages," Aracia replied. "We don't need food, and we don't need sleep—not during our ordinary cycle, anyway. It's almost sleep-time now, though. I can feel it creeping up on me. I _wish_ it would wait, though. I've got a lot of things that need to be taken care of, and I don't think I've got enough time."
"If it's all right with you, Lady Aracia, we'll wait until the sun's up tomorrow morning before we go back to your main temple. Let's be sure that there aren't any bug-people hiding in the corridors there."
"Whatever you think best, Captain Hook-Beak."
Padan felt a bit puzzled. It seemed to him that once Queen Aracia had been separated from her priesthood, she was almost normal. She _also_ seemed to be developing a certain attachment to Sorgan Hook-Beak. The Maag's roughshod approach seemed to be bringing Aracia right to the brink of normalcy.
The dawn came, and Sorgan, along with Ox, Ham-Hand, Padan, and Rabbit, accompanied Aracia to her throne room. They paused briefly at the door while Aracia listened. When she heard what was being said on the other side, her eyes narrowed and her face went bleak. "Absolute scoundrels," she said. "Why was I ever foolish enough to believe anything they told me?"
"We all make mistakes, lady," Sorgan said rather placatingly.
"Well, I've made more than enough," Aracia said. Then she looked Sorgan right in the face. "I'm paying you to defend me, mighty Sorgan," she said. "You may earn some of that pay right here and now. I don't want _any_ of those priests to come within ten feet of me."
"I think we can handle that, yes," Sorgan said. "I take it that you're planning to hurt their feelings just a bit."
"Watch," she replied. "Watch and learn." Then she literally slammed the throne room door open.
"Clear the way!" Sorgan bellowed. "Stand aside or die!" And he drew his sword.
It seemed to Padan that Sorgan might have taken it just a bit farther than necessary, but he drew his own sword to back Sorgan up. Then the party marched across the throne room in Aracia's wake.
"Great was our concern for you, most holy Aracia," Bersla of the big belly declared.
"But not quite great enough to move you to come looking for me, I noticed," Aracia replied.
"But—"
"Close your mouth!" Aracia snapped. Then she looked at Sorgan. "If he says anything else, kill him!" she ordered.
"It will be my pleasure, most holy," Sorgan replied with a florid bow that seemed to Padan to be totally out of character.
Aracia's face grew hard and cold. "Much have I considered the merits—or the lack of merit—of those here in this room today," she declared. "I have seen greed, cowardice, indolence, o'erwhelming self-esteem, and a total lack of anything at all that even remotely resembles honor. That, however, is about to change. Hear my command, my worshipers, and obey me—lest ye die."
"She definitely has a way with words, doesn't she?" Padan whispered to Sorgan.
"She's getting their attention, that's for sure," Sorgan replied, concealing his smile with one hand.
"Moreover," Aracia continued, "those who do _not_ obey, and escape their rightful punishment will no longer be priests and therefore no longer welcome in my temple. Hear my command and obey without question. Gather together and proceed straight forth to that part of my holy temple which lies to the west. There will you—one and all—give assistance to those who have come here to defend me. You will do what they require without hesitation or complaint, and you will continue your labor until our defenses are complete." Then she motioned to Sorgan. "I'm not really very good at this, am I?" she said with some shame.
"You're doing just fine, lady," Sorgan replied. "You even surprised _me_ just now."
"I must have done something right then. Now, what do you think I should do to any of these halfwits who refuse?"
"I've had a fair degree of success with a whip, lady," Sorgan replied. "Fifty lashes is usually about right. Then, after the others have seen a few of those floggings, I usually don't get any more arguments."
"I'm not sure if I could do something like that, Captain Hook-Beak."
"That's what you're paying _me_ to do, lady. I'll take care of it for you." Then he turned to his second mate. "Herd them on out of here, Ham-Hand," he said.
"Aye, Cap'n," Ham-Hand replied.
Padan suddenly laughed when a peculiar thought came to him.
"What's so funny?" Sorgan asked.
"Since those priests will be working with our men, they should probably eat the same kind of food."
"Beans?" Sorgan asked.
"It _would_ be fair, Sorgan, wouldn't you say?"
Sorgan started to laugh.
[THE
HORSE-SOLDIERS](YoungerGods_toc.html#part_6)
**1**
Prince Ekial of the Land of the Malavi had been just a bit edgy about the presence of Lord Dahlaine's pet sun. She was giving them all the light they needed, and she _was_ holding back the bitter chill of winter there in the far north, but the concept of using a miniature sun as a house-pet made Ekial just a bit nervous. The "What ifs" kept nagging at him.
He'd spent some time with Longbow in Dahlaine's "map room" carefully studying Dahlaine's miniature duplication of the rounded-down range of mountains Longbow had decided would be the best course to follow on their way on down to the upper end of Long-Pass. Ekial hadn't made a big issue of it, but he was rather looking forward to being separated from the Trogites and the Maags. They'd been very useful during the war in Crystal Gorge, but their superior attitude had rubbed Ekial the wrong way on several occasions, so he felt a certain relief when the mountain range became visible on the eastern horizon.
Longbow's friend, Red-Beard, pulled his horse, Seven, in alongside Ekial. "How's our day gone so far?" he asked.
" _Mine_ just got a bit better," Ekial replied. "Now we've reached the mountains, we'll be moving off in a different direction from the Trogites and the pirates. That will probably warm my heart. Don't get me wrong, Red-Beard, I _like_ them, but they move so slow. I could have been here three days ago."
"That's one of the nice things about riding a horse," Red-Beard agreed. "Old Seven here doesn't move very fast, but he could run circles around those foot-soldiers. Of course, he won't have to run for a while. I get to sit here until Skell delivers the archers from Chief Old-Bear's tribe. Then Seven and I'll guide them on down to the upper end of Long-Pass."
"Longbow told me that the archers of that tribe are the best in the whole world," Ekial said.
Red-Beard smiled. "Every tribe believes that they're the best," he said. "Longbow himself _is_ the best in the world, but the others in his tribe aren't nearly as good as he is." Red-Beard hesitated slightly. "You don't necessarily have to tell him that I said that he's the best," he added. "He doesn't need to know that I believe that."
Ekial laughed. "Your secret's safe with me, friend Red-Beard," he said. Then he added, "Doesn't he _ever_ smile?"
"Oh—once or twice a year, I'd say. Every so often he'll even smile three times if it's a very good year."
Longbow would be going on ahead, so getting the Tonthakans and Matans to the west end of Long-Pass would be Ekial's responsibility.
Longbow asked him if he had the route firmly in mind.
"I spent as much time looking at Dahlaine's map as _you_ did, Longbow," Ekial replied. "Won't it be just a little dangerous for you to travel alone, though? The bug-people _will_ be coming this way. That much is certain. I _could_ send a party of horsemen with you."
Longbow shook his head. "They'd only slow me down," he replied.
"You don't _really_ believe that you can run faster than a horse, do you?" Ekial demanded.
"Not faster," Longbow replied. "Longer beats faster almost any time at all."
"How long would you say that you can run?"
"Twenty hours or so, anyway, and I _can_ eat while I'm running."
"That raises another problem, friend Longbow," Red-Beard said. "Horses are nice enough, I suppose, but they _do_ have to eat, and I don't see very much grass around here."
"I was just about to ask you the same question," Ekial told the archer. "We _have_ to find grass."
Longbow shrugged. "Tell your men to keep their eyes out for bison. They eat grass just like your horses do. When you see a bison with his head down, he's probably eating. Chase him away and you'll have happy horses in just a little while. Is there anything else?"
"Is it always _this_ cold around here in the wintertime?"
"The local people have told me that it is. Be glad that it's cold now, though. If it starts to warm up, there's probably a blizzard coming your way."
"I've heard the locals talking about blizzards a few times," Ekial said. "Are they _really_ all that bad?"
"You might want to talk with Two-Hands about that. He was caught in one near the village of Asmie when he was very young. He had to dig a cave in the snow to survive."
Ekial shuddered, and decided not to pursue that. "Let's move on, shall we?" he suggested.
Since Dahlaine's little toy sun would be going with the Maags and Trogites, there wasn't too much daylight left, so they set up camp for the night before they'd gone very far to the south. Ekial was fairly sure that they should start out at first light each day. The horses could cover a fair distance in six or seven hours, but the Tonthakans and Matans couldn't move that fast, and to make things even worse, the Malavi were going to have to find grass for their horses every day, and that promised to slow things down to a crawl.
Longbow had set off the following morning.
"What's your hurry, Longbow?" Ekial asked.
"When I reach the upper end of Long-Pass, I'll need to go on down to the mouth so that I can guide the Trogites back up to the most likely places for them to build their forts."
"You're going to wear out your shoes, Longbow. That's about four hundred miles, you know," Ekial remarked.
Longbow shrugged. "Whatever it takes."
Ekial, somewhat regretfully, sent his friend Ariga and a sizeable number of other horse-soldiers off to the south to scout the eastern edge of the Wasteland to determine if the bug-people were anywhere in sight yet. He'd have much preferred to lead that scouting party himself, but he was fairly sure that wouldn't sit too well with Kathlak and Two-Hands. It was tedious—even boring—to plod along with the foot-soldiers, but it _was_ sort of necessary.
There was a slight cloudiness that day, and the thin clouds made the sun look sort of pale and sickly. Winter was a very depressing time of year.
Ekial was about to call a halt for the day when Two-Hands and Longbow's Tonthakan friend, Athlan, came up through the rounded foothills to join him. "There's company coming, Ekial," Chief Two-Hands reported.
"Oh? Who might that be?"
"It might be almost anybody," Athlan said. "They're still a good ways off, but we're almost positive that they aren't people-people. They look like bug-people to me."
"Where?" Ekial asked sharply.
"They're a few miles out in sand-country," Two-Hands said. "We might have missed them, but they're kicking up a lot of dust. We can't give you any kind of details, since they're still several miles away, and the dust pretty much conceals them."
"If Long-Pass is going to be their invasion route, what are they doing a hundred and sixty miles north of that pass?" Ekial demanded.
"I haven't the foggiest idea," Two-Hands admitted. "I suppose that it _might_ be possible that they're planning to cross over the mountains and then go south through the foothills on the other side to someplace about halfway down Long-Pass. That _would_ put them behind the Trogites if the fort-builders are going to concentrate on blocking the pass on the west end."
"How many of them would you say there are?" Ekial asked.
"It's a little hard to tell," Athlan said. "They're quite a ways out in that desert, and the dust pretty much conceals them. I'd say several hundred thousand at least. The dust cloud's at least ten miles wide, so we aren't talking about a couple dozen or so."
Ekial started to swear.
**2**
They kept a close eye on the creatures out there in the desert for the next several hours, but it didn't seem to Ekial that their enemies were in any great hurry. He mentioned that to Longbow's friend Athlan when the archer returned to report that he'd just located a sizeable meadow with lots of grass just ahead.
Athlan scratched his cheek. "From what Longbow told me a while back, this will probably be our last war with the children of the Vlagh," he said. "I asked him once a few weeks ago if we'd be fighting the bug-people for the rest of our lives. That's when he told me about the twin volcanos in Zelana's Domain, and the sudden flood in Veltan's part of the Land of Dhrall. Neither the bug-people nor anybody else will be able to attack _those_ two regions."
" _And_ that wall of blue fire in Crystal Gorge closes the only route up to Dahlaine's territory as well," Ekial added.
"It did that, all right," Athlan agreed. "I go cold all over when I think about _that_ disaster. I've seen blue fire before—usually in swamps, where it's just a faint flicker dancing on top of the water. The blue fire in Crystal Gorge went _way_ past a flicker, though." Athlan paused. "He _did_ tell you about that 'unknown friend,' didn't he?"
"Oh, yes. I wasn't sure just how much of what he said I should believe—but that was before the blue fire went roaring down Crystal Gorge. If Longbow's got a friend who can do things like _that_ , why does he need to hire outlander armies?"
"It wasn't Longbow who hired you, Prince Ekial. I've heard that it was Dahlaine. Longbow himself doesn't _need_ any outside help. I'm not trying to offend you, Prince Ekial, but once Longbow told me that bringing outlander armies here to the Land of Dhrall really only had one purpose. You're here to see just how terrible the people who live here can be if somebody from another part of the world decides that he wants all the gold in the Land of Dhrall. After what happened to those idiots from the Trogite Church in Veltan's Domain, I'm sure that every outlander who's here realizes what a terrible mistake it'd be to come here with some notion of getting rich. People who offend us _don't_ get rich. They get dead—soon—instead."
The weather turned bitterly cold that night, and Ekial didn't like that at all. "Why can't it warm up just a bit?" he complained to Chief Two-Hands.
"You don't really want that to happen, Prince Ekial," Two-Hands replied. "A brief warm spell usually means that there's a blizzard on the way, and you _don't_ want to come up against one of those. The warm spell goes away rather quickly, and it's suddenly ten times colder than it was before—at least it _seems_ that way. The wind cuts into you like a knife, and the snow whirling around you blots out everything more than two or three feet away."
"Longbow told me that you had to burrow down under the snow during a blizzard once," Ekial said.
"Oh, _yes_!" Two-Hands said. "I was wearing one of our bison-hide robes, and it _still_ felt like I was getting frozen into a solid block of ice. I couldn't see anything beyond two feet away because the snow was so thick. I could barely see my hand in front of my face. I didn't know which way was which, and it was getting colder and colder by the minute. I knew that if I didn't get in out of that wind, I'd freeze to death. My only option at that point was to burrow down into a snow-bank. I knew that my burrow wouldn't be toasty warm, but at least it would protect me from that screaming wind. That's when I discovered that snow will pack up if you lean your back against it and push. I was finally able to open up a chamber about the same size as a small room in a very small house. There was air to breathe, and if I got thirsty, I could eat a few handfuls of snow. I happened to have a couple of slabs of smoked meat in my belt-pouch, so I had shelter, water, and food. I stayed there for a few days, and then I took a look outside. It'd stopped snowing, so I made my way back to Asmie—just in time to witness my own funeral. You wouldn't _believe_ how upset people become when the guest of honor at a funeral shows up and he's still breathing." He smiled then. "Word of what I'd done got spread around all over the village, and the young boys of Asmie thought it might be a lot of fun to make snow tunnels around the village in the dead of winter." He shrugged. "It gives them something to do, and it keeps them in out of the weather. Last winter eight or nine boys built what amounted to a palace under the snow on the south side of Asmie. They made miles of tunnels and they had large chambers here and there. It kept them out of mischief, so I didn't scold them or anything. I _did_ order them to mark the locations of their tunnels and meeting halls, though. It's not really safe to walk over the top of a snow-tunnel. The women of the tribe mentioned that to me fifteen or twenty times a day, as I recall."
"Are we at all likely to get hit with a blizzard like _that_ one?" Ekial asked.
Two-Hands shook his head. "Dahlaine's got a very tight grip on the weather just now. I'm not really sure exactly why, though. From what I've heard, I could go a whole lifetime without seeing that older sister of his. I guess she's gone completely crazy."
"Oh, _that's_ nice," Ekial said. "Why should we bother to save her? Let the bug-people eat her and have done with it."
Two-Hands shook his head. "If the Vlagh gets her feet into people-country—where there _is_ food—she'll lay millions and millions of eggs. That's what these wars have been all about, really. The Vlagh wants the whole world, and if she wins just one war here, she'll spread out and _take_ it. It won't just be Dahlaine's sister who'll be eaten, it'll be the entire world, and all the people of the world will be nothing but something to eat."
Ekial felt a sense of horror welling up from his stomach at that point.
"There are thousands and thousands of those bug-things coming this way from that desert out there, Ekial," Ariga reported a few days later when Ekial's horse-soldiers, the Tonthakan archers, and the Matan spear-throwers reached the narrow opening at the upper end of Long-Pass.
"Why don't you just go on out there and kill them?" Ekial asked.
"You're joking, of course," Ariga said.
"Well, maybe," Ekial conceded, "but not entirely. We've got to hold those things out there back until the Trogites get here and build a fort. We have a sizeable number of Tonthakan archers here now, and Matan spear-throwers as well. We've worked with them before, and things turned out quite well."
"I think I get your point, Ekial. See if I've got it right. The archers and spear-throwers sort of stay out of sight while _we_ gallop on out there and nudge the bug-people into trying to chase us down."
"Nudge?" Ekial asked.
"We have lances, remember? We gallop on out to where the bug-people are busy sneaking, and we skewer a few dozen with our lances. Then we gallop on back. The bug-people should be very angry because we just killed quite a few of their friends and relatives, so they try to chase after us. That's when we lead them into the range of the arrows and spears. In short, we lead them, and the archers and spear-men kill them. Isn't that sort of what you had in mind?"
"I'd say that it's worth a try, Ariga, but let's hold off until morning. The Tonthakans and Matans are probably worn down just a bit, so let's give them some time to rest before we put them to work."
"You're getting better at this, Ekial."
"Practice," Ekial replied modestly.
**3**
"I think we were right about why those bug-people were coming across that desert miles and miles to the north of this pass," Kathlak the Tonthakan said the next day. "I sent out some scouts, and they told me that there _are_ enemies in the hills and along the ridges on both sides of this pass. I'd say that what happened in Crystal Gorge taught them a lesson. They learned that having enemies up above you doesn't make for very pleasant days. It looks like they learned very fast. If there _are_ bug-people up above this pass when the Trogites are coming up here to build forts, life could get very exciting for them. I'd say that cleaning off those hills and ridges might be even more important than killing the ones coming toward the upper end of the pass."
"Those bug-things seem to be more clever than everybody was telling us they are," Two-Hands added. "They seem to learn much faster than we'd been told they could."
Ekial swore. "I'm afraid that you two might be right," he said. "Clearing off the ridges along the sides of the pass is probably much more important than thinning out the herd coming across that Wasteland. If the Trogites are blocked off, we'll be in deep trouble."
"A suggestion—if it's all right," Kathlak said.
"I'll listen to almost anything right now," Ekial admitted.
"There are trees up along those rims," Kathlak said, "and Tonthakans are skilled at hunting in a forest. The Matans are more accustomed to open country. If I led _my_ people up into these tired, worn-out old mountains, _we_ could probably deal with the bug-people up there, and that would leave Two-Hands and his spear-throwers free to deal with the enemies coming in off the desert, wouldn't you say?"
"It _does_ make sense, Ekial," Two-Hands agreed. "Throwing spears in a forest is mostly a waste of time—and spear-points. If we let the Tonthakans deal with the enemies hiding in the forest, your horse-soldiers and my spear-throwers should be able to thin out the bugs coming across the desert, don't you think?"
"I suppose we can give it a try," Ekial agreed.
"How long would you say that it's likely to take for the Trogites to get up here?" Kathlak asked.
"I wouldn't start looking for them tomorrow," Ekial replied. "I think there might be some law down in Trog-land that forbids a soldier to walk more than ten miles a day."
"That's ridiculous!" Kathlak exclaimed.
Ekial smiled faintly. "Laws are supposed to be ridiculous, aren't they? Gunda explained it to me once. A Trogite army moves as a group, as I understood what he was saying. That means that the army can only move as fast as the slowest man can walk, and they spend a lot of their time resting."
"If that's as fast as they can go, they don't really _need_ to rest, do they?"
"I guess that it's a custom, and customs don't really _have_ to make sense. It's about a hundred and twenty miles from the beach at the bottom of the pass up to here, so we're not likely to see any Trogites for twelve days or so. That gives us twelve days to clear away the bugs along the rims of the pass and thin out the ones crawling through the sand out here. We've got plenty to do, so I suppose we should get started."
There was a mindless quality about the Creatures of the Wasteland that chilled Ekial. It appeared that they were not intelligent enough to be afraid, so they kept on trying to do what they'd been told to do despite the fact that they were running directly into the face of certain death. To some degree they _looked_ like people, but they definitely didn't _think_ like people. On one occasion during the war in Crystal Gorge, Longbow had told Ekial that the servants of the Vlagh were totally unaware of their mortality. "They seem to think that they'll live forever. Of course they don't have any idea of what 'forever' means. A bug lives in a world of now, and that's all that they can understand. Yesterday was too long ago for them to have any memory of it, and tomorrow will probably never arrive."
"Idiocy!" Ekial had exclaimed.
"That's a fair description, yes," Longbow had blandly agreed. "Many things that work quite well when your enemies are people _won't_ work when they're bugs."
"What would you say is the best way to deal with an enemy that's too stupid to be afraid?"
"I've had a fair amount of success with killing every one I see, friend Ekial."
"All right, then," Ekial said to a number of his friends the next morning, "try to remember that the enemies we'll encounter might _look_ like people, but they aren't. Don't waste time trying to frighten them, because you _can't_ frighten them. They have no idea of what 'afraid' means."
"They might start to understand after a lot of their friends get killed," Skarn said.
"That's the whole point, Skarn. The bug-people don't _have_ friends—at least not in the way that _we_ understand the word. They don't have enough time to grow friendly with other bugs. They live for six weeks, and then they die of the bug version of 'old age.' They take orders from the Vlagh, and that's the only relationship they have. They'll _try_ to follow the Vlagh's orders, and they won't understand what 'danger' means. If we just happened to kill every bug out there but just left one of them alive, that last one would keep on trying to attack us."
"That's stupid!" Orgal declared.
"It goes a long way _past_ 'stupid,' Orgal. Nobody I know of has yet invented a word that describes how brainless the bug-people really are. They don't know _how_ to think. They _are_ poisonous, though, so don't get too close to them. Use your lances, but try not to break them. Concentrate on killing the ones that are close to the bottom of this slope. Don't go galloping out into that silly desert. All _we're_ supposed to do is hold the bugs back until the Trogites get up here and build the fort. As soon as the fort's in place, we're probably going to be out of work."
[THE
VIOLATION
OF THE
TEMPLE
](YoungerGods_toc.html#part_7)
**1**
It seemed to Ox that Captain Hook-Beak was more than a little disturbed by Lady Aracia's sudden change of position. As long as she'd been willing to sit on her throne listening to the overdone orations of praise, she hadn't caused the slightest bit of inconvenience. Now that she realized just how totally useless her priests were, Sorgan and the other Maags would have to come up with ways to step around their new—and unwanted—helpers.
"I think you'd better pass the word to the other captains, Ox," Sorgan said when they'd returned to the _Ascension_. "We need to talk this over and come up with some way to keep all those silly priests from finding out what we're _really_ doing here."
"I'll take care of it, Cap'n," Ox replied. Then he went out onto the deck of the _Ascension_ , lowered the skiff, and rowed back to the beach.
It took him a couple of hours to gather up most of the Maag ship-captains, and it was well past midnight before Sorgan could advise the other captains that things had radically changed.
"Everything was going just the way we wanted it to go," he said, "but then the lady who's paying us came to her senses and woke up. She ordered all those fat priests to go out to the west wall of that silly temple to lend us a hand."
"Why didn't you just tell her that we don't _need_ those people, Sorgan?" a captain called Squint-Eye demanded.
"She took me by surprise," Sorgan admitted. "That was the last thing I expected from her. She's not nearly as stupid as we all thought. She came down on those lazy priests of hers _very_ hard. She threatened to kick any one of them who refused to help us out of the priesthood and banish him from her temple."
"I wish I'd been there to see that," a captain called Gimpy said. "I'll bet that most of the faces of those priests fell right off."
"They didn't seem too happy, that's for sure. Now, how are we going to get those fools out from underfoot?"
"Ah, Cap'n," Ox said then, "would you like to hear a suggestion?"
"Sure."
"We've pretty much blocked off that west side of the temple, wouldn't you say?"
"All except for adding another ten feet or so to our fake fort. Where are you going with this, Ox?"
"The west side's just about finished, Cap'n," Ox replied, "but the south side hasn't been touched yet, and the imitation bug-people will attack from any direction we want them to, wouldn't you say?"
Sorgan blinked.
"I'd say that solves your problem, Hook-Beak," Squint-Eye said. "You could have saved us all a lot of time if you'd learned to listen to your first mate. It sounds to me like he's about three jumps ahead of you."
"Or maybe even four," Gimpy added.
"I'm not really sure, Cap'n," Ox replied when Sorgan started asking questions as soon as the other Maag ship-captains had left the _Ascension_. "The whole idea seemed to come to me while you were telling the other captains about the problem Lady Zelana's sister dropped on us."
"Now you're starting to sound like Longbow," Sorgan said. "Did you hear some lady's voice coming from no place at all?"
"It wasn't a lady's voice, Cap'n. I'm sure that I've heard it before, though. If the idea's as good as I think it is, it most likely came from somebody who knows Lady Aracia very well."
"Veltan, maybe?"
Ox shook his head. "No, I'm sure it wasn't Veltan. Whoever it was didn't have to say very much to me to get the point across. About all our _other_ friend said to me was 'Why not send those worthless priests down to the south wall of the temple and put them to work _there_ instead of where the work's almost finished? Keep them busy, but out from underfoot.' Then it all seemed to come together, and it made a lot of sense. I didn't mean to embarrass you or anything like that, but as soon as I thought my way through the whole notion, I just started to tell you about it without waiting until we were alone."
"Well, _whoever_ it was solved our problem for us, and I don't embarrass all that easy." Then Sorgan scratched his cheek. "I think we might want to take Rabbit and Torl along with us. We'll need to have them tell Lady Aracia that they saw a different group of bug-people sneaking down toward the south wall while we were holding off the west wall from the attack of their friends."
"You might want to talk with Veltan, Cap'n," Ox suggested. "If we can persuade Lady Aracia to send the fat people to the south wall, a few sightings of bug-people creeping through the bushes would confirm what we tell Lady Aracia, and I'm sure that reports of those sightings will get back to her real soon."
"Give our new friend my thanks, Ox," Sorgan said with a broad grin. "Whoever he is, he's doing most of the work for us in this imitation war."
"I'll pass that on the next time he stops by, Cap'n," Ox replied.
Then Sorgan smiled. "Now that I've had enough time to think my way through this, I'd say that maybe Squint-Eye and Gimpy should be the ones who should oversee those modifications of the south wall. It'll give them something to do instead of dropping clever remarks on me every time I turn around."
"I'm sure that they'll feel honored that you suggested them to Lady Aracia, Cap'n," Ox replied with no hint of a smile.
The following morning Ox went out from the west wall of the temple to the berm where Torl and Rabbit had staged their imitation invasion. "The Cap'n wants you two to go with him to talk with Lady Aracia," he told them. "He wants you to say that you saw quite a few bug-people sneaking around toward the south wall of her temple."
"That _would_ make a certain amount of sense," Torl agreed. "If this was _really_ a war, that's the sort of thing the bug-people would do."
"You might be right there," Ox said, "but that's not why he's doing it. He doesn't want all those fat priests underfoot while he's setting up his deception. There'll be things going on that ain't none of their business, and he wants to make certain sure that none of them are around when him and Veltan start playing games."
"That's my cousin." Torl chuckled.
**2**
Fat Bersla was nowhere in sight when they entered the throne room, and the snippy little priestess Alcevan seemed to have taken his place. She glared at Captain Hook-Beak when he led the Maags into the room.
"I'll get right to the point here, Lady Aracia," Sorgan said. "There's something we might have overlooked. It seems that the bug-people might just be getting a bit more clever. This little fellow here is known as Rabbit, the smith on the _Seagull_ —my own ship—and Rabbit's much more clever than he lets on. When my scouts were holding back the new varieties of bug-people, Rabbit noticed that there were quite a few of the older ones who _weren't_ trying to attack that berm. Why don't you tell her what you saw, Rabbit?"
"Aye, Cap'n," Rabbit replied. "What I saw didn't seem to make any sense, Lady," Rabbit told Zelana's sister. " _Most_ of them were charging toward that berm we'd raised up to hold them off, but then I caught a kind of flicker back in the bushes behind where the new bugs were charging. I looked a bit closer and saw quite a few of the little ones we've seen before sneaking down through the thick bushes. They were staying low, but I _was_ able to see that there were _hundreds_ of them back there, and it seemed to me that they weren't the least bit interested in the war their big brothers were fighting around our berm. They were going almost due south, and that wasn't where the war was being fought. Now, the Cap'n and his men have built a fairly good fort along that west wall of your temple, but we don't have even one single soldier on that south wall, and the construction isn't really very good. Now, _if_ those other bug-people _are_ planning an attack on that side of your temple, they'll probably be able to walk right in without no trouble at all."
"I'm sure you can see where this is going, Lady Aracia," Sorgan said. " _My_ people can hold the west wall of your temple without much trouble now that we've modified it. That south wall isn't very good, and I'd say that it's not really strong enough to hold back a mosquito. I thank you for your concern and your offer of help, but I'd say that beefing up that south wall's a lot more important right now. I strongly suggest that you send your priests south instead of west."
"I will do as you command, mighty Sorgan," Aracia declared, "but as soon as you and your people have beaten back the invaders, we must go forth from the temple and gather up all of my people who live beyond the temple walls and bring them _here_ so that they'll be safe. We must _not_ permit the servants of the Vlagh to destroy them."
The priestess Alcevan looked sharply at Aracia. "You cannot bring all those commoners here into the holy temple. They are not sanctified, and their presence here will _defile_ your holy temple!"
"The people— _my_ people—are far more significant than the indigents who call themselves priests," Aracia declared. "If you should find their presence here offensive, feel free to go forth from the temple to seek out a different god to worship. If you would continue to worship _me_ , you _will_ do as I tell you to do, and _this_ I say: The commons _will_ join us here, and you and the other priests will see to their needs. _You_ will eat only after _they_ have eaten, and you will surrender your beds and your warm clothes to them without question or complaint. The _people_ come first in my eyes, and you will serve _them_ even as you would serve _me_ —or I will send you away. You will no longer contaminate my temple."
Alcevan's face went pale, and her expression was one of chagrin.
"Well now, Cap'n," Ox said quietly. "It sort of looks like maybe Zelana's sister's starting to grow up."
"Let's not make a big issue of that just yet, Ox," Sorgan replied. "She _might_ just change her mind again after she's gone a week or so without any adoration."
[THE
GIFTED
STUDENT](YoungerGods_toc.html#part_8)
**1**
Keselo had also had some problems with Lord Dahlaine's "toy sun." His education at the University of Kaldacin had taught him that a sun needed a certain volume before it qualified as a true sun. Dahlaine's little toy violated almost everything Keselo had learned or worked out for himself. He knew that most of the rules didn't apply to the members of Dahlaine's family, but still—
The toy sun stayed with them all the way to the coast.
They reached the large bay where the Trogite ships Commander Narasan had hired in Castano were anchored, and Sorgan's Maags had taken about half of that fleet and sailed on south to bamboozle Lady Zelana's sister.
"I'm glad that Sorgan's the one who'll have to deal with that crazy woman," Gunda said. "I got more than enough of her the last time we were down here."
"She set _my_ teeth on edge just a bit, too," Andar agreed.
"All right, gentlemen," Commander Narasan, who'd just come up from the beach, said. "We're not going to board _our_ ships for several days. Let's give Sorgan and his men a good head start. Go tell the men to set up camp and have the cooks fix something for supper."
"Beans?" Gunda asked with a definite note of distaste in his voice.
"What a marvelous idea, Gunda," Commander Narasan said with mock enthusiasm. "Beans will be just fine. I wonder why _I_ didn't think of that."
After they'd loaded about half of Commander Narasan's army on board the remaining ships, they sailed on south under a gloomy sky, and they reached the narrow bay at the mouth of the river that had carved out Long-Pass at some time in the long-distant past. Just the notion of the eon after eon it must have taken that river to reach the sea made Keselo shudder. Time, it appeared, had no meaning for rivers and mountains.
They'd dropped anchor, and there on the beach—as they all probably should have expected—the archer Longbow was waiting for them.
"I will _never_ understand how he can cover so much ground in so little time," Keselo muttered to himself.
Keselo was just a bit surprised when Commander Narasan included _him_ in the group of men who knew how to build forts that Longbow would lead ahead of the rest up to the top of the pass.
"How are your legs holding out, Keselo?" Narasan had asked.
"They seem all right to me, sir," Keselo replied.
"Good. I think that maybe you should go along with the fort-builders. Gunda's just about the best fort-builder in the entire Trogite Empire. You could learn a lot by watching him."
Keselo resented that just a bit. He _had_ taken courses in architecture at the University of Kaldacin, so he already knew all about building walls.
"I'm not trying to offend you," Narasan added. "Gunda and Andar are sort of stuck in stone when it comes to fort-building. Their minds are locked in 'the good old-fashioned way' when it comes to forts. You're intelligent enough to come up with things that won't even occur to them— _and_ you can be diplomatic enough not to offend them with your shiny _new_ ideas."
"I can _try_ , I suppose, sir," Keselo agreed a bit dubiously. "I'm not sure they'll listen, though."
"Talk louder, then."
When Longbow had objected to leading so many men to the head of the pass, Keselo took him aside.
"It's a precaution, Longbow," Keselo tried to explain. "Commander Narasan doesn't like to take chances. We've had quite a few surprises here since last spring, so the commander wants to be sure that there'll be enough men up at the head of the pass to deal with anything the Vlagh throws at us."
"That's why we have the Malavi, Tonthakans, and Matans, Keselo," Longbow objected.
"I mentioned that to him," Keselo replied. Then he smiled faintly. "The commander has opinions, Longbow. He's not positive that our friends will do what they're supposed to do. That's why he overloaded us just a bit."
"Ten thousand men is his idea of 'just a bit'?" Longbow asked.
The protests that had arisen when Longbow abolished the traditional "rest period" were long and loud. Keselo had long believed that those quarter-hour lounges were totally unnecessary, but the common soldiers viewed them as something on the order of a divine right. But Keselo estimated that they'd covered three times more distance than they normally would have.
"He's going too fast," Gunda grumbled.
"This _is_ sort of an emergency, sir," Keselo suggested. "If we don't reach the head of the pass before the bug-people do, things will probably start to get ugly. Once the fort's in place, our men should be able to rest. Up until then, we don't really _have_ much time for rest, wouldn't you say?"
"You're probably right," Gunda conceded, "but that doesn't abolish my right to complain, does it?"
"Not at all, sir, but I wouldn't complain too much when Longbow's around. He might decide to run tomorrow instead of just walk fast. I've come to know him very well during the past three seasons, and the first rule when you're dealing with Longbow is 'don't irritate him if you can possibly avoid it.'"
"I think he's right, Gunda," Andar agreed. "We want that fort in place as soon as possible." He paused. "Are you open to a suggestion?"
"I'll listen," Gunda replied.
"We've got four or five times as many men as we'll really need, right?"
"I'll know better after I've seen the ground I'll be working on," Gunda replied, "but I _am_ just a bit overloaded with workers. Where are you going with this, Andar?"
"Why build only one fort at a time? We've got all those extra men, so why keep them all at the head of the pass? I could take maybe half of them and build a second fort a mile or so on down the pass. That should give you someplace to run to when the bug-people make your fort too hot to hold on to."
"Thanks a lot, Andar," Gunda said in a voice reeking with sarcasm. Then he squinted. "You know, if we put the men to work on other forts every mile or so on down the pass, we could probably hold back the invaders until sometime next summer."
"Brilliant," Andar said rather dryly.
"You've been thinking along the same lines, haven't you, Andar?"
"It did sort of occur to me, yes."
"Why didn't you say something?"
"I just wanted to see how long it was going to take you to get the point, Gunda," Andar replied with mock sincerity.
Keselo smiled. Things seemed to be going quite well.
They were three days up from the beach when the horse-soldier Ekial came riding down the pass. He reined in his horse when he reached Longbow. "You seem to be making fairly good time, friend Longbow," he said.
"Not _too_ bad," Longbow replied. "Have you seen any sign that the Creatures of the Wasteland are coming east yet?"
"Oh, they're coming, all right," Ekial said. "Ariga's got scouts out in that desert, and they've told us that there are thousands and thousands of the bug-people coming east."
"Have your people got any kind of idea about how much longer it's going to take them to reach the head of this pass?"
"I'd say that they're still a week or ten days away. There's a bit of a diversion that's already here, though."
"Oh? What's that?"
"When we were coming south, we saw a sizeable number of bug-people coming across the sand. Kathlak, the chief of the Tonthakans, suggested that the bugs might have realized that things can get very unpleasant for people as well as for bugs if they've got enemies above them. When we reached the head of the pass, I sent horsemen down along the rims on both sides of this pass, and sure enough, there _were_ bug-people on those rims. If we'd left them there, they'd have been dropping boulders on Narasan's army every time they got a chance. Kathlak's archers took care of that for us. The bug-men up on those rims suddenly started sprouting arrows. There may still be a few of them up there hiding in the bushes, but they aren't likely to cause any problems."
"Have the archers of Old-Bear's tribe joined you yet?" Longbow asked.
"They're still a day or so away. Your friend Red-Beard came on ahead to let us know that they were on the way. They'll probably reach the head of the pass at about the same time your fort-builders do."
Gunda joined them.
"You brought a lot of men with you," Ekial noted.
"That was Narasan's idea," Gunda told him. "He's always believed that more is better. He might be right this time, though. I'm sure that _I_ won't need all those men, so I'll hand the surplus off to Andar, and he'll be able to build _another_ fort about a mile on down the pass. If the Vlagh gives us enough time, we'll have a fort standing every mile or so down the pass, and our enemy will run out of bugs before she gets halfway down."
Then he looked at the lean, scar-faced horse-soldier. "Have you had your supper yet?" he asked.
"I've been a little busy," Ekial replied.
"I can't offer anything very exciting," Gunda said, "but you're welcome to join me if you want."
"I could probably eat," Ekial said.
"Let's go do it then."
**2**
The river that came down through Long-Pass was somewhat wider than the one in Crystal Gorge, but not nearly as wide as the one that had been the source of the Falls of Vash. Keselo realized that the Falls of Vash weren't there anymore, and the river now rushed down to that inland sea that had drowned a generation of the children of the Vlagh _and_ quite nearly all of the clergy of the Church of Amar. To Keselo's way of thinking, that particular disaster had purified the Trogite Empire to no small degree.
Despite Longbow's best efforts, it was about mid-morning on the fifth day when they reached the upper end of Long-Pass and Gunda caught his first glimpse of the projected fort site. "It's only fifty feet across!" he exclaimed.
"About that, yes," Longbow agreed.
"Didn't you tell Narasan how tight this is?"
"As I remember, I described it to him four or five times," Longbow replied.
"Why in the world did he send so many men up here?"
"I think it's called 'more is better,' or something like that, friend Gunda."
"You were right, Andar," Gunda said to his friend. "If I tried to jam ten thousand men into that skinny little opening, they'd be falling all over each other."
"It's about fifty feet wide, I'd say," Andar agreed.
"If that much," Gunda replied. "It widens out just a bit when it gets up near the rim on either side, but that won't be much of a problem."
"How long would you say building a fort there is likely to take?" Andar asked.
Gunda shrugged. "Three days—maybe four. There's plenty of granite lying around here. Squaring it off won't take too long." Gunda pursed his lips. "I think twenty feet high should do the job. When the main army gets up here, they'll have those poisoned stakes. If we plant those to the front like we've done before, I don't think very many bug-people will even reach the fort. We've got archers and spear-men—and those horse-soldiers as well. The Vlagh can send ten thousand or so bug-people here to attack the fort, but a dozen or so at most will actually reach it. Why don't you drop back a mile or so and find a good place to build that second fort you mentioned. When you find it, let me know, and I'll send you half of our men. We'll see how our first two forts turn out, and then we might want to move on to four. Give us a couple of weeks and we'll have at least a dozen forts blocking off this pass. That might just make poor old Vlagh feel sort of grouchy."
"Poor baby," Andar replied in mock sympathy.
"If you don't have access to mortar, you keep things in place with weight," Gunda was explaining to Keselo the following day. "The blocks should be squared off, of course, but it's the sheer weight that'll make your fort impregnable."
"That's a very useful thing to know, Sub-Commander," Keselo replied with mock enthusiasm. Gunda was very proud of his reputation as a master fort-builder, and it didn't really cost Keselo very much to heap praise on his superior.
"Now, then," Gunda continued. "Every three or four layers you should connect the upper blocks to the lower ones with interlocking grooves."
"I was wondering about that," Keselo replied with a perfectly straight face. "My big problem, though, is how you can lock the battlements in place."
"That _does_ get a little tricky," Gunda replied. "You're picking this up quite rapidly, Keselo. Give me a little time and I'll make a first-rate fort-builder out of you."
Along with four or five professors of architecture at the University of Kaldacin, Keselo privately added.
"If you're not busy with something else," Gunda said then, "why don't you drop on back down the pass and see how Andar's fort is coming along. Andar and I _should_ keep in touch."
"I'll go on down there immediately, sir," Keselo replied, snapping to attention. Right now he'd be more than happy to get away from Gunda's tedious lectures.
"I was just about to send somebody up to Gunda's fort to fetch you, Keselo," Sub-Commander Andar said. "A messenger just came up here from the main army. Commander Narasan wants to see you."
"Am I in trouble?" Keselo asked.
"Not that I know of. The messenger wasn't too specific, but I think Commander Narasan wants you to go on down to that silly temple to advise Sorgan that everything up here is pretty much the way we want it to be. The forts _will_ be in place when the bug-people try to attack."
Keselo frowned. "The commander _could_ have sent somebody else down to the temple, and that messenger would have reached Sorgan long before I'll be able to."
Andar shrugged. "You know Sorgan much better than an ordinary messenger would have, _and_ your rank would tell Sorgan that he's significant to Commander Narasan. What Sorgan's doing down there's a little silly, maybe, but it _will_ keep Veltan's sister off our backs. I'm sure that the commander has things he wants Sorgan to know about, and Sorgan probably has information for the commander as well. They both trust you, Keselo, so I've got a sort of hunch that you'll be doing a lot of traveling back and forth between the pass and the temple before this is all over. I'll send word on up to Gunda to let him know that the commander's got a job for you."
"I'd appreciate that, sir," Keselo said. Then he considered the distance he'd be traveling for the next several weeks. "I wonder if Ekial might lend me a horse," he murmured to himself.
**3**
Commander Narasan's tent had seen better days. It had been patched so many times that there were several areas where even the patches had been patched. Near the center there was a stove that put out small amounts of heat, but quite a bit of smoke. The commander was seated at a small table carefully examining a rudimentary map. "You made good time, Keselo," he said when Keselo entered the tent. "I sent the messenger up the pass only two days ago."
"Downhill is quite a bit easier than uphill, sir," Keselo replied.
"How's the fort coming along?"
"Which one, sir?"
Commander Narasan raised one eyebrow.
"Sub-Commanders Gunda and Andar talked things over after they'd seen how narrow the gap was at the head of the pass, sir," Keselo explained. "They agreed that they had far more men than they needed to build the fort that'd block off that gap, so Sub-Commander Andar took half of the men a mile or so on down the pass, and he's building a second fort. I wouldn't exactly call it a race, but there _is_ a certain amount of competitiveness involved."
The commander smiled faintly. "That always seems to come floating to the surface when Gunda's involved," he said.
"He _is_ a soldier, Commander," Keselo replied. "He fights wars, and war _is_ the ultimate competition, wouldn't you say?"
"You're an extremely perceptive young man, Keselo. Now, then, how well do you and Sorgan get along?"
"He thinks I'm just a little stuffy, sir. That's one of the drawbacks of an extensive education. The word 'sir' seems to offend him for some reason."
"He _does_ believe you when you tell him something, doesn't he?"
"I believe so, yes, sir. I've never had any reason to lie to him."
"I think you talked yourself into a lot of traveling, Keselo."
"Sir?" Keselo was a bit confused.
"Sorgan and I will need to pass information back and forth to each other, and we both trust you to give us the absolute truth."
"I'm honored that you feel that way about me, sir."
"I've been in touch with one of the ship-captains in the bay at the mouth of this pass, and he has a small, swift sloop that's been quite useful in the past. When you reach the bay, he'll lend you the sloop and a couple of sailors who know how to use it. They'll be able to deliver you to Sorgan in about a half a day. Then, after you've spoken with old Hook-Beak, you can come back and tell _me_ anything he wants me to know. When you see him, tell him that Gunda's fort—and Andar's—are nearly complete. I'm sure that he'll want to send word to me about how well his hoax is coming. Now, then, can you think of anything you might need to make these journeys a bit easier—and faster?"
"Yes, sir," Keselo replied. "I think I can. It might take me a while to learn how to ride one of Prince Ekial's horses, but we might want to consider that. There may be a few times when speed will be essential, and a horse is sort of a land version of that sloop, wouldn't you say?"
"I'd say that you can think about twice as fast as anybody else in the army, Keselo. I'll send word to Prince Ekial, and there _will_ be a horse waiting for you on the beach when you return."
"And a Malavi as well, sir?" Keselo added. "I'll need somebody there to teach me how to ride a horse, because I don't really know _anything_ about horses."
The swift little sloop the captain of the _Triumph_ provided for Keselo's trip down the coast to the harbor of Lady Aracia's temple made the voyage in just over a half a day, and the two skilled sailors who'd rowed her south pulled alongside the _Ascension_ in the early afternoon.
Keselo climbed up the rope ladder and spoke with the extremely tall Maag known as Tree-Top. "I've got some information for Captain Hook-Beak," Keselo told the towering Maag. "I think it might be best if I spoke with him here on the _Ascension_ rather than in the temple. I'm fairly sure that Commander Narasan and Captain Hook-Beak would prefer to keep the priests in Lady Aracia's temple from finding out that they're in contact with each other."
"You're probably right," Tree-Top agreed. "I'll get word to the cap'n that you're here."
"How have things been going down here?" Keselo asked.
Tree-Top laughed. "The cap'n seems to have got hisself on the good side of the crazy lady who owns this place. The other day she ordered all them fat priests of hers to go out to the west to lend the cap'n and his men some help. You could hear the screaming for miles when she said that. It quieted down some after the cap'n had several of them fat priests flogged, though."
"Did Lady Aracia actually let him _do_ that?" Keselo was more than a little startled.
"It looked to me like it made her real happy. I'll send a man ashore to let the cap'n know that you're here, and then maybe you can tell me what's happening up there where the _real_ war's going on."
Keselo was more than a little surprised that Sorgan had somehow managed to bring Lady Aracia over to his side. Before Veltan and Lady Zelana had pulled the Trogite army out of this temple-town, it had seemed that the priests had been making all the decisions here, and Lady Aracia had been little more than a figurehead. Sorgan had somehow managed to wake her up, though, and that _might_ just change a lot of things.
"It was really a mistake that turned into something very useful, Captain Sorgan," Keselo admitted. "None of us knew for certain just when the servants of the Vlagh would come rushing up out of the Wasteland—or how many there'd actually be. The commander wasn't entirely sure that the Tonthakans, Matans, and the Malavi would be able to hold the bug-people off, so he sent ten thousand men up the pass with Sub-Commander Gunda—more for security than for fort-construction. When we reached the head of the pass, we saw that the opening was only fifty feet across— _and_ the bug-people were still quite a long way out in the Wasteland. Sub-Commanders Gunda and Andar talked it over a bit, and they decided to build two forts instead of just one."
"That's the sort of thing I'd expect from Gunda," Sub-Commander Padan, who was now sporting a beard, said.
"Actually, sir, it was Sub-Commander Andar who came up with the notion. Sub-Commander Gunda was too busy inventing new swear words about then. When I left, those two forts were almost finished, and Gunda and Andar were discussing the possibility of putting the construction crews to work on _four_ new forts."
He hesitated slightly. "When I first got here, Tree-Top was telling me that Lady Aracia might just be coming to her senses."
"She's starting to think," Sorgan replied. "Her lazy priests just got themselves put to work, and they're not too happy about that." Then Captain Hook-Beak grinned rather slyly. "What's _really_ making them unhappy is what we're feeding them. They're used to fancy food, and beans don't sit very well with them."
"Did Lady Aracia actually accept the stories about bug-people here in the vicinity of her temple?" Keselo asked. "Nobody's ever actually _seen_ any of them, have they?"
"Veltan's been lending us a hand," Sorgan replied. "He's been cooking up images for the entertainment of his sister and her chubby priests. I've got men out there pretending to fight off the bugs, and those priests—and even Lady Aracia herself—have been catching very brief glimpses of those images. _That's_ the thing that brought Aracia over to our side. She suddenly woke up and realized that her priests were almost totally worthless. You should have _heard_ the speech she made to the priests. That lady can be a tiger when it's necessary."
"You've done something here that nobody else has ever been able to do, Captain Hook-Beak," Keselo noted.
"I had Veltan's help, Keselo," Sorgan replied. "I'm positive that it was _his_ images that brought her around."
"Tree-Top told me that you had a few of the priests flogged."
Sorgan nodded. "That definitely cut back all the complaining," he said.
"Are those priests actually working alongside your men? Wouldn't that suggest to some of them that what they've been hearing about, and catching a few glimpses of, is nothing but a hoax?"
Sorgan shook his head. "Rabbit came up with a story that sent the priests down to the south wall of the temple—bugs sneaking through the bushes and a few other all-out lies. Now the priests are tearing the southern buildings apart, and leaving my men alone here on the west side so that we can cook up more horror stories. Tell Narasan that we've got things pretty much under control down here, and you _might_ want to tell him— _and_ Lady Zelana and Lord Dahlaine—that Lady Aracia _seems_ to be coming to her senses."
"That _might_ just be the best news they've had since last spring, Captain," Keselo agreed.
Keselo was a bit startled when he saw that the Malavi waiting for him on the beach at the mouth of Long-Pass was Prince Ekial himself. The two of them had met during the war in Veltan's Domain the preceding summer, and they'd gotten along with each other quite well, but Keselo was quite certain that Ekial had more serious matters to attend to.
The sailors who'd been rowing the scruffy little skiff pulled the bow of the skiff up onto the sandy beach, and Keselo stepped out onto the sand. "What are you doing down here, Prince Ekial?" Keselo asked.
Ekial shrugged. "Friend Narasan tells me that you'd like to learn how to ride a horse," he replied. "I wasn't doing anything important, so I thought I might as well come on down here and teach you myself."
"I'm honored, Prince Ekial."
"We're friends, Keselo," Ekial replied. "We don't have to wave our titles in each other's face like that. Actually, I was starting to get just a little bored up there watching Gunda and Andar building forts."
"Have there been any signs of the Creatures of the Wasteland approaching the upper end of the pass yet?"
"A few," Ekial replied. "I'd say that the ones we've seen so far are just scouts. Let's get on with this, shall we? It's likely to take you a few days to get used to sitting on a horse's back, so we'd better get started." He reached out and put his hand on the front shoulder of a rangy horse with a saber-scar across its nose. "This is Bent-Nose, and he's a fairly sensible animal. He doesn't bite very often, and he almost never kicks somebody who walks behind him. He's old enough not to get excited every time somebody walks by, but he's not so old that he'd rather rest than run. Now, the first thing you need to do is let the horse get to know you. I brought some apples along, and horses _love_ apples. If you give a horse an apple, he'll follow you for a day or so at least. Then you want to scratch his ears and pet his nose. He needs to be able to recognize your smell."
"I didn't realize that it was so complicated," Keselo confessed. Then he remembered something. "If horses like apples, isn't it possible that they'd like other sweet things as well?"
"They might, yes. What did you have in mind?"
Keselo reached into his pocket and took out several pieces of candy. "I've always had a sort of weakness for this," he admitted. "It might be a sign that I never really grew up. Try one, and see what you think."
Ekial took one of the lumps of candy and popped it into his mouth. "Oh, my goodness," he said. "I think you might have just made a huge jump forward in the taming of horses, friend Keselo. Let's see how Bent-Nose feels about this."
Ekial held a piece of candy out to the horse. Bent-Nose sniffed at the candy, and his ears perked up. Then he rather carefully took the candy into his mouth.
It seemed to Keselo that the horse almost shivered with delight. Then he nuzzled at Keselo's hand.
"You _do_ have more, don't you?" Ekial asked.
"A couple of pounds, I think," Keselo replied. "I'll check my pack, but I always keep plenty of candy."
"I think you're on to a winner, friend Keselo. If things go as fast as I think they will, you'll be riding Bent-Nose before noon tomorrow."
It took Keselo a while the following day to learn the rudiments of mounting and dismounting, but Bent-Nose was most cooperative, and then Ekial said that they might as well ride on up the pass to report in to the commander. Bent-Nose and Ekial's horse Bright-Star moved on up the pass at a canter, and Keselo was quite pleased with how much easier it was to ride rather than walk—at least during the first morning of their journey. By the time they stopped for the night, however, Keselo realized that there were some drawbacks involved in riding.
"It takes a while for your backside to toughen up," Ekial explained. "Walk around a little bit, and that should ease the pain in your backside. You might want to eat standing up for a few days, though."
"How far would you say we came today?" Keselo asked.
"Forty miles or so," Ekial replied. "We haven't been pushing the horses very hard. Uphill is always a bit slower than downhill."
"We should make it up to the top of the pass in two more days, then. Have Gunda and Andar finished their forts yet?"
"As closely as _I_ could determine, yes. Of course I'm not really all that familiar with forts."
"Have the Creatures of the Wasteland made any attacks?"
"They hadn't when I left that end of the pass. The Tonthakan archers had pretty well cleared the rims on both sides of the pass, so I'm fairly sure that friend Narasan's army has reached the top by now."
"I'd say that we're about as ready to meet the invaders as we'll ever be, then."
"They won't get past us," Ekial agreed. "We might have to sit up there for a few months, but eventually that thing called the Vlagh will run out of soldiers, and that's what this is all about, wouldn't you say?"
"Sorgan seems to think that your sister's coming to her senses," Keselo told Lady Zelana and Lord Dahlaine on the evening of the day when he and Ekial had reached the top of Long-Pass. "She's begun to realize just how totally worthless her priests really are. Their so-called 'adoration' is nothing but a ruse to make their own lives easier, and their contempt for the common people _really_ angered her. Sorgan's clever mock invasion seems to have brought her face-to-face with reality, and she came down very hard on those who had elevated themselves to the priesthood. She ordered them to go to work helping Sorgan's men build fortifications." Keselo grinned then. "Quite a few of her priests refused, but after Sorgan had them flogged with whips, the refusals stopped. A good number of priests decided to run away along about then, but absurd though it might seem, that huge temple only has one door, and Sorgan put a hundred or so of his men at that door, so nobody's leaving. Like it or not, Aracia's priesthood _will_ do honest work for a while."
Lord Dahlaine laughed. "That, all by itself, makes these attempted invasions by the servants of the Vlagh worth more than anything else that's happened in the last four or five centuries."
Then Commander Narasan and Ekial came down from Gunda's fort at the head of the pass. "It looks like we've got company coming," Commander Narasan reported. "The Wasteland off to the west isn't empty anymore."
"How many would you say there are?" Lord Dahlaine asked.
"I wouldn't even want to try to make a guess, My Lord," the commander replied. "They seem to stretch from horizon to horizon as far off to the west as I can see."
[THE
DEFENDERS
OF THE
FAITH](YoungerGods_toc.html#part_9)
**1**
Torl had been greatly impressed by Veltan's imaginary bug-men. The images had looked so real that several of the Maags standing on top of the berm had turned and fled when the images had briefly appeared.
Of course that had added a sense of reality to the incident, and Lady Zelana's sister now totally believed everything cousin Sorgan told her. Just hearing the word "invasion" was one thing but actually _seeing_ what had appeared to be real, live bugs was something entirely different. That single incident had turned Lady Aracia into a true believer.
That was _definitely_ causing some problems for her priests. Lady Aracia's priests had scoffed at the notion that the bug-people were anything but a hoax cousin Sorgan had come up with as a way to get his hands on all the gold in the temple. But now the priests had been sent to the rudimentary south wall of the temple, where several bulky, bad-tempered Maags worked the poor fat priests as hard as they could for ten or twelve hours a day on a diet of nothing but beans. That generated a lot of sniveling, which amused Torl no end.
"Just keep an eye on them, Torl," Sorgan instructed. "I don't _think_ they'll try anything violent. Priests aren't notorious for that sort of behavior, but desperate people do desperate things every so often."
"I'll watch them, cousin," Torl promised. "It'll probably bore me to tears, but not as much as building this imitation fort does."
"It's not _that_ bad a fort, is it?" Sorgan objected.
"Watch out for mice, Sorgan," Torl advised. "If a mouse happened to bump your fort with his shoulder, the whole thing might tumble down around your ears."
"Very funny, Torl. Go watch those fat priests, but stay out of sight. You're _supposed_ to be fighting off the invasion of the bug-people. Let's not stir up any suspicions in Lady Aracia."
"It shall be as thou hast commanded, mighty leader."
"Do you really have to do that, Torl?" Sorgan asked.
"It's good for you, cousin," Torl replied. "I'll go watch those fat priests get skinny, and I'll keep you advised."
"Do that." Then cousin Sorgan went back to his imitation fort.
Torl had been exploring the somewhat makeshift temple Lady Aracia's priests (or their younger relatives) had been building (badly) for the last several centuries. As Torl had reported to Sorgan, _most_ of the temple consisted of empty rooms and wandering corridors that didn't really go anyplace. Torl was fairly certain that Lady Aracia believed with all her heart that there were thousands of priests living here so that they could adore her in groups. As closely as Torl had been able to verify, however, there were probably no more than a couple hundred of them. The "thousands and thousands of priests" hoax obliged the ordinary farmers of Lady Aracia's Domain to deliver enormous amounts of food to the temple. Her brave priests sacrificed themselves by eating at least ten times more food than was really good for them.
As Torl moved through the empty temple, he wondered just _who_ had done all this meaningless construction. It occurred to him that in all probability assorted relatives of the established priests had realized that the life of a priest of Aracia was a life of luxury unmarred by honest work, but their relatives of high rank had most likely put a price on the aspirations of their younger relatives, and the price was most likely six or seven rooms or a hundred feet of corridor. Quite probably, Fat Bersla escorted Lady Aracia on periodic tours of these empty corridors and vacant rooms to show her how her temple was expanding. He assumed there was a lot of scrambling around by lesser priests to make all this empty space appear to be occupied. When he got right down to it, Torl viewed the whole thing as pathetic—and Aracia herself was probably the most pathetic.
Then, from some distance off, he heard some people talking. Torl recognized the voices of Fat Bersla and the tiny priestess Alcevan. Torl moved quietly along the corridor to see if he could get close enough to hear what they were saying. Whatever it was that they were discussing didn't seem to be making them happy.
Fat Bersla was speaking in a whining kind of voice that definitely set Torl's teeth on edge. "I have spent most of my life praising that simple-minded woman, and I'd finally reached the point where she was almost totally under my control. Then that pirate came out of nowhere with his absurd story and snatched her out of my grasp. Now she'll do almost anything he tells her to do without even consulting me."
"We have a matter of greater concern, Takal Bersla." The strange-sounding voice of priestess Alcevan cut in to Bersla's sniveling. "If there's any truth to the legends of this land, ancient Aracia is right on the verge of drifting off to sleep."
"She never sleeps!" Bersla declared.
"You mean that you've never _seen_ her sleep, mighty Takal. No one living has, because she's been awake for twenty-five thousand years. There weren't even any people around when she woke up this time. The legend still tells us that she _will_ sleep—soon—and she will be replaced by another divinity who goes by the name of Enalla."
"I spoke with Holy Aracia on one occasion some years ago," another man-priest with a rasping sort of voice declared, "and she told me that the child-Dreamer Lillabeth is in reality this Enalla who will succeed our beloved Aracia."
"That _can't_ be true!" Bersla exclaimed. "Child Lillabeth has no interest at all in the religion of Holy Aracia. On many occasions I have delivered masterful orations praising Holy Aracia whilst child Lillabeth was present, and she inevitably fell asleep before the end of the first hour of my praise. She has no interest in religion or priests or temples. If this Enalla is really the adult Lillabeth, she will have no need of priests or temples or hymns of praise. She will abandon the temple, and when the local people come to understand her disinterest, they will turn their backs on us, and we will surely perish."
"That couldn't happen to a better group," Torl muttered. Then he squinted at the ceiling. "I wonder just how long Fat Bersla could stay alive if nobody bothered to feed him. He could probably absorb his own fat for a while, but he'd run dry eventually."
"Holy Aracia advised me that child Lillabeth was what she called 'a Dreamer,'" the raspy-voiced priest declared. "She said that Lillabeth could cause things to happen with her Dreams that were quite beyond anything Holy Aracia or her brothers or sister could ever bring to pass. These events, as I understood what Holy Aracia told me, are what are called 'natural disasters'—floods, earthquakes, volcanos—and such. Have a care when you approach child Lillabeth, for she can—most certainly—cause the sky to fall down on you."
"That's absurd," Alcevan scoffed.
"I wouldn't be so sure, Alcevan," Bersla disagreed. "Holy Aracia herself told me of several disasters other Dreamer-children had caused to happen—floods, volcanoes, and other events almost beyond human conception. It would appear that these innocent children are _not_ innocent when they Dream. The gods live by a law that they will never kill anything. The Dreamers, however, have no such restriction."
Alcevan suddenly chuckled. "I'd say that we have a very simple solution to our problem, then. We know that there's some kind of connection between Lillabeth and Enalla. Enalla will live forever, of course, but Lillabeth? I'm not so sure about her. She eats food, and she goes to sleep. That suggests that she's _not_ an immortal, and that makes things very easy for us."
"I didn't quite follow that, Alcevan," Bersla said.
"All we have to do is order some novice to kill her, you dunce. If Lillabeth's dead, Enalla will be dead as well. They _are_ the same person, after all."
"It wouldn't work," Bersla declared. "Aracia can hear our thoughts—particularly any thought that threatens the life of Lillabeth. Aracia _loves_ that spoiled little brat."
"Let _me_ deal with that, Takal Bersla," Alcevan said then. "Since Lillabeth is _really_ Enalla, she'll be the one who'll usurp Aracia's throne once Aracia goes to sleep. Aracia, however, desperately wants to retain her position as the god of the East, and she'll do _anything_ to hold her throne."
Torl turned and walked as swiftly as he dared through the dimly lighted corridor that led to the west wall of the temple. As soon as he came out into the open area that was no longer closed in by stone blocks, he went looking for cousin Sorgan. "I think we've got a serious problem, cousin," he said.
"Another one?" Sorgan said. "What's the world coming to?"
"Are you about finished with the tired old jokes, Sorgan?" Torl demanded. "Why don't you try to laugh at this one? I just heard that priestess called Alcevan come up with a plot to kill Aracia's Dreamer."
"You said _what_?"
"You heard me, cousin. Alcevan seems to think that if Lilglabeth died, Enalla would cease to exist. Those priests desperately want to keep Aracia in charge here, since she's their only access to a life of luxury. They seem to believe that if Enalla dies—or just ceases to exist—Aracia will have to stay awake and continue providing them with everything they want."
Cousin Sorgan's face hardened. "I think we'd better take this to Veltan," he said.
It didn't take them very long to find Zelana's baby brother. He was watching Sorgan's men as they continued the construction of cousin Sorgan's imitation fort, and he didn't look very impressed.
"We need to talk, Lord Veltan," Sorgan said. "I think we might have an emergency of sorts coming before too long."
"Somebody's going to sneeze, and your fort will collapse?" Veltan suggested.
"The fort's not really significant," Sorgan replied. "It's just there to make your big sister feel more secure. It's not like there was going to be a real invasion. Cousin Torl here just overheard something that we'll have to deal with—soon. Tell him what you heard, Torl."
"I was sort of wandering around in this badly-put-together temple a little while back, and I just happened to hear some of your sister's priests talking. They're _very_ unhappy about Aracia's approaching nap time. They know that when she drifts off, your granddaughter Enalla will take charge here."
"Granddaughter?" Veltan seemed a bit startled.
"You and the rest of your family _are_ related to the younger generation, aren't you? I suppose we could call Enalla your niece, if that would be closer."
"We _are_ related, Torl," Veltan said with a faint smile, "but I doubt that any word you could come up with would explain the relationship."
"Don't try to explain it to me, Lord Veltan," Torl said. "I probably wouldn't understand you anyway, and all it'd do would be to give me a headache. The priests I heard talking were trying to come up with some way to keep your sister awake. The little priestess Alcevan came up with a plan that the other priests seem to think might actually work."
"Oh?"
"This gets just a little ugly, so brace yourself. Alcevan seems to have found out that the Dreamer Lillabeth is actually Enalla. Enalla, like the rest of you, doesn't need to eat or sleep, _but_ Lillabeth _does_. Alcevan told the other priests that Enalla might be immortal, but Lillabeth probably isn't. Then she went on to suggest that if some novice priest just happened to murder Lillabeth, Enalla would just vanish. I don't know if it would work that way, but the other priests seemed to think it might be worth a try."
"That's horrible!" Veltan exclaimed.
"The next question is, would it work?" Sorgan said.
"I don't think so," Veltan replied, "but let's not take any chances." Then he frowned. "I didn't know that my sister _had_ any women priests," he said.
"As far as we know, this Alcevan's the only one," Sorgan said. "The other priests don't seem to like her very much, but your sister spends a lot of time listening to her." He smiled. "I think Eleria might refer to her as one of the 'teenie-weenies,'" he said. "That particular term showed up fairly often in Zelana country. Eleria herself was a teenie-weenie, and so was Rabbit. Then, when we encountered the bug-snake-people, Eleria called _them_ teenie-weenies as well."
Veltan shrugged. "There _are_ small people here in Aracia's Domain. From what you just told me, this Alcevan priestess throws a lot of weight around—quite possibly because Aracia _told_ her to. Let's go give Lillabeth some protection. We don't want to take any chances here."
"She almost never comes here to spend any time with me," the little girl complained. "I think she hates me because I had that Dream."
"No, Lillabeth," Veltan replied. "It's the war that's bothering Aracia so much. It'll be over soon, and then things should go back to the way they're supposed to be."
"Do wars always take this long, Uncle Veltan?"
"I really don't know, child," Veltan replied. "This is the first war we've ever had here in the Land of Dhrall. Torl here knows much, much more about wars than I do."
Lillabeth looked at Torl. "How long do the wars last in your part of the world?" she asked.
Torl shrugged. "Sometimes they're over in about half an hour," he replied. "Others can go on for years and years. This one here is supposed to be over by springtime."
"And then everything will go back to the way it's supposed to be?" the little girl asked.
"Who knows?" Torl said. "The world changes all the time, and that means that nothing ever really stays the same."
"They get better, you mean?"
"Sometimes they do, but sometimes they get worse."
Veltan winced, but he didn't say anything.
Then the door of Lillabeth's room opened, and a young priest who couldn't have been much older than fifteen or so came into the room. He was just a bit pale, and his hands were shaking. "What are you people doing here?" he demanded.
"We just came by to visit my niece," Veltan replied.
"Your niece?"
Veltan nodded. "I'm Aracia's younger brother. We don't get chances to visit very often. Did someone tell you to stop by for some reason?"
"Ah—I was just supposed to look in to make sure that the little girl is all right and doesn't need anything," the young fellow replied just a bit too quickly.
"I'm here now," Veltan told him, "and I'll take care of anything she needs. Was there anything else?"
"Well—no, I guess not."
"Good. You can go now then. Tell whoever sent you that Lillabeth is just fine and that I'm here to make sure that she stays that way."
"I'll do that," the young fellow said, nervously backing toward the door.
Veltan smiled. "You have a nice day," he said blandly.
The young man fled.
"That was the one, Torl," Veltan said. "Alcevan promised him a quick elevation in rank if he did what she wanted him to do."
"You can hear what people are thinking, can't you, Veltan?" Torl asked.
"Usually, yes. I don't always _want_ to, but it's there if I need it. I'll stay here with Lillabeth. Why don't you follow that nervous young priest? He _might_ be the only one Alcevan hired, but let's make sure, if we can."
"I'll get right on it, Lord Veltan," Torl replied, going to the door.
**2**
The pale young priest was trembling noticeably and not walking very fast as he moved along one of the dusty corridors of Aracia's temple. Torl was quite sure that he knew why the young man was reluctant to report his failure to Alcevan. The little priestess was quite obviously not the sort who'd be willing to accept failure, so the young man was almost certainly moving toward a blistering reprimand.
He finally reached one of those dusty, unoccupied rooms that didn't even have a door, but, unlike the other chambers on both sides of the corridor, there was a dim light in this one. "I'm back, Holy Alcevan," the young fellow said in a trembling voice. "I wasn't able to do what you asked, though. The little girl wasn't alone. There was a stranger who called himself Veltan there, along with one of those barbarians. I think I'll have to wait a while before I try again."
"There's no real problem, Aldas," the priestess replied. "We have plenty of time, so try again some other day."
"Oh, I will, I will," the young priest vowed. "Believe me, the time will come—sooner or later—when I'll find the little girl alone, and then I'll do that which you want me to do."
"Excellent, Aldas," the little priestess said. "I knew that I could depend on you."
"I'll go back immediately, Holy Alcevan," the young man promised. "I'll watch for days and days until I can get the little girl alone, and then—" His voice abruptly stopped, and Torl heard a gurgling sound.
Torl blinked. "She _didn't_!" he exclaimed under his breath. The stream of red blood coming through the doorway, however, said that she _had_. Alcevan quite obviously was _not_ prepared to accept failure.
"I stayed back out of sight until she left the room, Veltan," Torl said somewhat later after Lillabeth had gone to sleep. "I'm not sure just exactly how she did it with a stone knife, but the poor boy's throat had been cut from ear to ear. First she told him that everything was all right, and then she killed him right there on the spot."
Veltan's face hardened. "She's even worse than I thought," he said. "She's after something here, and it's obvious that she'll go to any length to get it. I'm quite sure that she's _not_ what she appears to be."
Torl suddenly grinned. "I don't really think fat old Bersla will be around very much longer, do you?"
"Interesting notion, Torl. Be very careful, but try to keep an eye on her. We _might_ just be looking at extreme ambition here. If that's the case, she'll do almost anything to replace Bersla as the high priest—or Takal, as the local term has it—but it might go even further."
"Are you saying that she wants to replace your _sister_?"
"I wouldn't rule it out, Torl. Alcevan wants _something_ , but I don't think we know for sure just _what_ it is. How familiar are you with all these silly corridors here in the temple?"
"I think I've got a nodding acquaintance with _most_ of them, Veltan," Torl replied. "Of course I come across a new one every so often, but those are the ones that don't really go anywhere. I can find my way around without much trouble."
"Good. Stay out of sight as much as possible, but do what you can to find out just exactly what Alcevan's goal _really_ is."
"I'll see what I can do, Veltan," Torl promised, "but I think _you_ should stay close to Lillabeth. She needs protection right now."
"I'll get right on it, Torl," Veltan replied in an obvious imitation of something Torl had said earlier.
"Ha," Torl replied in the same flat tone Gunda always used. "Ha. Ha. Ha."
Veltan burst out laughing at that point.
Torl had found an unused corridor that went past the back side of Aracia's throne room. Like most of the rest of the temple, it was not well-made, and Torl had been able to hear what was going on in the throne room. He crept through the shoddy corridor until he could hear voices. Then he put his ear to the wall.
"We don't know this Enalla person who'll replace you when you lie down to rest, Holy Aracia," Alcevan was saying, "but isn't it possible that she'll decide to usurp your temple and tell us that _she_ is the true god of your Domain and order us to bow down and worship _her_ instead of you? Of course, after a few generations, nobody will even remember that you were ever here."
"Is there no way, Divine Aracia, that you can delay the arrival of this Enalla?" Bersla asked. "We have the invasion by the Creatures of the Wasteland in progress right now. Could you not remain here with us until they are driven back? You are wise beyond our understanding, but this Enalla person will have only recently awakened from her long sleep, so she will be as helpless as a child. Should the Creatures of the Wasteland o'erwhelm your people, is it not possible that the Vlagh itself will assume your holy throne?"
Then Aracia's voice, colder than ice, replied. "These matters are none of your concern—neither of your concerns. I will, before this season ends, go to my rest. Enalla _is_ my alternate, and my Domain _will_ be hers while I sleep. You _will_ obey her in all things." She paused and then spoke again in an icy tone. "Why is it that you two are not at the south wall of my temple as I have commanded?"
Bersla floundered a bit. "Most of the priesthood labors there as you commanded, Most Holy. Some few of us, however, have remained here to see to your needs."
"I _have_ no needs, Bersla. You should know that by now." Then Aracia paused, and her voice became even more cold. "You were fully aware of that, were you not, Takal Bersla? This 'see to my needs' pose of yours is but a way to avoid strenuous labor, is it not?"
"We can _not_ leave you unprotected, Divine One," Alcevan declared.
"Brave are you indeed, small, inconsequential person," Aracia replied in a voice dripping with sarcasm. "First you defy _me_ , and then you will attempt to hold back the servants of the Vlagh, which will most certainly kill you and then eat you. Hear me now, both of you. Proceed at once to the south wall of my temple and give aid to those who have already obeyed my commands. Should that not suit you, go from this holy temple and do not _ever_ return. Know, moreover, that when you depart from here, I will mark you, and neither one of you will ever be permitted to come back to within my walls. Choose, Bersla and Alcevan, and know that which course you choose will not in any way concern me."
Torl heard the sound of hurried footsteps, and the throne room door opened—and then closed.
Torl pressed one hand over his mouth to muffle the sound of his laughter. Then he went west again through the dusty corridor to tell cousin Sorgan and Veltan about this sudden change in Veltan's sister.
After a little while, Torl realized that he was whistling as he went.
**3**
"She really came down hard on those two," Torl reported when he rejoined Sorgan and Veltan at the west wall. "They were trying their best to persuade her to stay awake and keep Enalla from taking over, but she told them to either go to the south wall and do what she'd told them to do, or leave the temple and never come back."
"Well," Veltan said with a smile. "It seems that my sister has finally come to her senses." Then he looked curiously at Torl. "How did you manage to get into the throne room without being seen?"
"I wasn't inside," Torl said. "I was in one of those cobwebby corridors that just happened to have a crack in the wall. I could hear everything that was going on in there, and they didn't know that I was listening. There seem to be quite a few of those old corridors in the vicinity of the throne room."
"They were probably put there by certain previous high priests to give them someplace where they could hear what was going on without being seen," Veltan replied. "They've always wanted that advantage to make sure that no other priest was getting ahead of them."
"Are the politics here always so complicated, Veltan?" Sorgan asked.
"That sort of depends on whose territory we're talking about," Veltan replied. "Things in Dahlaine's Domain are a bit more formal than they are in Zelana's Domain and mine, but Aracia's church takes politics out to the far end—or it did until just recently. Now that Aracia's come to her senses, she _might_ even go so far as to abolish her church." Then he smiled again. "And if Aracia doesn't, Enalla almost certainly will. The priests of her church will probably have to go out and find honest work before spring arrives."
"Poor babies," Sorgan said in mock sympathy.
[THE
COMMANDER
](YoungerGods_toc.html#part_10)
**1**
Trenicia, the warrior queen of the Isle of Akalla, was seriously discontented with winter. The Matans had generously provided her with a double-layered bison-hide cloak, but she still spent most of her time shivering and complaining.
Her language was very colorful, Commander Narasan noted with a faint smile as his army marched up through Long-Pass. Trenicia had, in effect, joined Narasan's army when they'd both walked off and left Veltan's older sister screaming about their desertion. Aracia's arrogance knew no bounds, and the thought that they would all just walk away and leave her totally undefended sent her right up through the ceiling. "I wonder how Sorgan's doing," he muttered as he and Trenicia walked through a gloomy afternoon.
"I didn't quite catch that, dear Narasan," Trenicia said in a milder tone of voice.
"Just thinking out loud, Your Majesty," Narasan replied.
"I thought that we'd discarded the 'Your Majesty' foolishness," she said a bit tartly.
"Sorry," Narasan apologized. "Habit, probably. Down in the Empire, people are very interested in rank, so we grow accustomed to spouting terms of respectfulness. They don't really _mean_ anything, but we wave them around anyhow. I'm just a bit concerned about Sorgan's scheme, is all. He's one of the few friends I have, and I don't want to lose him."
"You have _me_ as your friend, Narasan," Trenicia said. "That's all you really need. Someday we might want to talk about friendship. In time, friendship grows into something more interesting, and I'd say that we've almost reached that point."
Narasan actually blushed, though he couldn't for the life of him think why.
"Is your face turning red for some reason other than the beastly chill in this region?" Trenicia asked. "If you're having a problem, feel free to tell me all about it."
"I'm sure it's only the weather, dear friend Trenicia."
"Spoilsport," she replied accusingly.
"I'm not entirely sure that Sorgan's sophisticated enough to float his scheme past Aracia—or her priests. He can _tell_ them that his scouts have actually seen the bug-people invading, but I don't know if they'd accept that."
"He has Veltan to help him, dear Narasan. That's all the help he'll probably need." Then she paused. "How in the world did you get so attached to a Maag pirate?" she asked. "I thought that Maags and Trogites were supposed to be natural-born enemies."
Narasan shrugged. "We've been allied with each other in three wars so far, and we've learned to trust each other. If he keeps things simple, he shouldn't have many problems, but sometimes Sorgan goes to extremes. All we _really_ need is for him to keep Aracia and her priests out of my hair here in Long-Pass."
"That shouldn't be _too_ hard," Trenicia said. "We're not talking about intelligent people here. Relax, dear Narasan. I'm sure that everything down in the temple's going exactly the way we want it to."
It was about noon when the main army reached the back side of a fairly standard Trogite fort. Trenicia wasn't at all impressed. "Is that the best your men can do?" she demanded.
"This is the _back_ side, Trenicia dear," Narasan explained. "It's the _front_ side that holds back the enemy. The back side is designed to make it easy for our soldiers to get inside the fort."
"What if your enemy sneaks around behind you?"
"Would the word 'how' offend you? The fort blocks off the entire pass in this spot. Believe me, dear, we Trogites have been building forts for centuries, we've come up with answers to just about all the 'what ifs' anybody can come up with. About the only one that concerns us is what's called 'burrowing.' That's when your enemy digs a deep hole in the ground some distance back from your fort and then starts to dig a tunnel."
"I _knew_ that there had to be a weakness!" Trenicia exclaimed triumphantly.
"Take a look around, dear," Narasan suggested. "You won't see very much dirt. This is a mountain pass, and that means that it's mostly rock. I guess it's theoretically possible to burrow through solid rock, but I'd say that it'd take at least ten years to get as far as the front side of the fort—and another four or five years to burrow _under_ the fort to get to the back side."
Trenicia glared at him for a moment, but then she laughed. "I _was_ being just a bit silly there, wasn't I? It's just that I _hate_ forts. The notion of being locked in one place for years and years makes me want to scream."
"You made very good time, sir," Sub-Commander Andar said when Narasan and Trenicia joined him at the front of the fort.
"Not as good as you and Gunda made," Narasan replied. "How in the world were you able to cover a hundred and twenty miles in four and a half days?"
"Longbow discarded several customs, sir," Andar replied with a faint smile. "First he abolished the standard rest period."
"How was he able to persuade the men to do that? That custom's been locked in stone for centuries now."
"He used the cooks as the key to unlocking it, sir."
"The cooks? I don't quite follow you there."
"He put the cooks at the head of the column, sir," Andar explained. "He must have made a few threats, because the cooks did their best to keep up with him. That put breakfast, lunch, and supper farther and farther ahead of the men who felt the need to rest. It took the men a day or so to get his point. 'Rest or eat' is a little brutal, but it _did_ get his point across. Sauntering along more or less vanished along about then, and running became all the rage—particularly after that lady cook from Lord Veltan's Domain took charge of the preparation of the meals. An occasional gust of wind went down the pass, and it carried the smell of her cooking down to the men who'd been stubbornly insisting that their right to rest was more important than anything else in the whole world. The pace of the army picked up quite noticeably at that point."
"That Longbow's an absolute genius," Narasan declared.
"I'd say so, yes," Andar agreed. "It seems that when he wants something, he always comes up with a way to get it."
"How far on up the pass is Gunda's fort?" Narasan asked then.
"Almost exactly a mile, sir," Andar replied. "That might vary a few times as we go on down the pass, but we'll always be quite close to a mile."
"I suppose I'd better go on up and say some nice things about Gunda's fort," Narasan said then.
"I'm sure he'll appreciate that, sir," Andar said with no hint of a smile.
Since it was obviously going to take the rest of the day for the main army to get past Andar's fort, Narasan and Trenicia went on ahead to Gunda's fort. Longbow was there, of course, and Narasan had learned quite some time back that when he needed information about the Creatures of the Wasteland, Longbow was the man to speak with.
Gunda's fort went quite a ways farther than the standard Trogite one in that there were huge boulders mixed in with the standard granite blocks. "It wasn't really my idea, Narasan," Gunda conceded. "Prince Ekial took a look at our rock wall and suggested that bigger rocks might add a bit. Then he had a fair number of his men start dragging those boulders here. I was more than a little surprised when I saw the size of the rocks a dozen or so horses could drag across the ground. No matter how many bug-people come charging up here, this is as far as they're going to get."
"Have you seen any of them yet?" Narasan asked.
"Oh, yes," Gunda replied. "They're still about five miles away, but there are thousands of them out there. Prince Ekial and his horse-soldiers are slowing them down quite a bit, but they _will_ reach this fort before too much longer."
"The main army's not far behind, Gunda," Narasan assured his friend. "They're climbing over Andar's fort right now, but I'd say that your fort will be fully manned by about noon tomorrow."
"They _do_ have those poisoned stakes with them, don't they?"
"Oh, yes. Your impregnable fort's going to be even _more_ impregnable after we've planted those stakes to the front. Andar told me that there _were_ quite a few bug-people up on the rims of the pass."
"They're still there, Narasan," Gunda replied, "but they're dead now. Kathlak's archers went on up there and showered them with poisonous arrows. There are a lot of trees up on those rims, and once the main army gets here, I'd suggest that we send a good number of them up there with axes. Catapults are always nice to have on hand when your enemies are charging. If we do this right, this will be about as far as our enemies will get."
"Why have you got people building more forts then?" Queen Trenicia asked.
"Just a precaution, ma'am," Gunda replied. "Things sometimes go wrong no matter what we do, and those extra forts will give us someplace to fall back to if it turns out to be necessary. As our mighty commander here says quite often, 'Always expect the worst, and be ready for it.' If it doesn't turn out that way, it's a pleasant surprise, but we don't take any chances."
"You're a gloomy sort of fellow, aren't you, friend Narasan?" Trenicia said.
"Maybe," Narasan conceded, "but I _am_ still alive."
"That's all that really matters, dear one," Trenicia said with a fond smile.
**2**
"Where's Prince Ekial?" Narasan asked the Malavi Ariga the following morning when they were all gathering for the customary conference.
"Ekial is giving instruction to that young Keselo on riding a horse. The two of them get along well with each other," Ariga replied.
Narasan nodded, then looking around at everyone, he said, "First, of course, the question is how far away from here is the enemy—and how many of them are there?"
"I drifted out over the Wasteland yesterday," Lady Zelana said, "and it looked to me like the Vlagh was throwing everything she's got at us this time."
"And how many would that be, ma'am?" Gunda asked.
"A half million at least," Zelana replied. "Probably closer to a whole million."
"She's definitely pushing her luck, then," Lord Dahlaine declared. "In the past she's always kept a great number of her children in reserve."
"Children?" Trenicia asked in a startled voice.
"I know that it sounds very unnatural, Queen Trenicia," Dahlaine replied, "but the Vlagh gives birth to _all_ of her servants. Of course she doesn't have children in the same way that human mothers do. She lays eggs instead. Evidently, she realizes that this will be her last chance to gain dominion of some part of the Land of Dhrall that's out beyond the Wasteland, so with the exception of the ones that take care of her in her nest, she's probably emptied the place out. If things turn out the way we want them to, she'll have very few servants left if this attack falls apart the way that the previous ones have."
"And that would mean that she'll be out of business, wouldn't it?" Andar said.
"I'm not completely positive about that," Lady Zelana disagreed. "It'll take her a long, long time to build the number of her children back up, but as long as she's there, she'll still be a danger for us."
"We'll have to kill her then," Trenicia said bluntly.
Zelana winced. "We're not allowed to do that," she replied.
"That's why you hired _us_ , isn't it?" Trenicia suggested. "If the best that we can do is block her off, she'll go back to her nest and lay more eggs, and next spring she'll attack again."
"Not quite _that_ soon, Queen Trenicia," Dahlaine disagreed. "It might take as long as another century for her to produce enough children to pose any significant threat, but—" He left it hanging there.
"Cut off her food," Two-Hands of Matan said bluntly. "Doesn't no food mean no new calves? You _can_ play with the weather, Dahlaine. You've demonstrated that several times already this year. A drought might be the best answer."
"Or possibly a flood," the farmer Omago from Veltan's Domain suggested. "That worked extremely well last summer."
"I'd say that we can decide which way we should go _after_ we've stopped the army that's coming to visit us here," Longbow said then.
"How long would you say it's likely to take the bug-people to get into position to attack Gunda's fort, Longbow?" Narasan asked.
"A week or ten days," Longbow replied. "Right now I'd suggest working on catapults. They worked rather well last autumn in the north country."
"I'll put the men to work on those," Gunda agreed.
It was about noon on the following day when Ekial and Keselo came up to the back side of Gunda's fort. Narasan was a bit surprised by how well Keselo was riding the horse Ekial had provided. "You two made good time," Narasan said as they dismounted.
"That's because young Keselo here is a natural-born horseman," Ekial declared. "It didn't take him more than a couple hours to get old Bent-Nose there so attached to him that the silly horse wants to sleep with him now."
"Bent-Nose?" Narasan asked. "Isn't that an odd sort of name for a horse?"
"When he was quite a bit younger, we were fighting horsemen from a different part of our country, and one of the enemies slashed the horse across the nose with his saber. When the cut healed, the scar changed the shape of the horse's nose. 'Bent' might not be too accurate, but it sounds better than 'swelled-up,' wouldn't you say?"
"I see what you mean." Then Narasan looked inquiringly at Keselo. "How did you manage to get on the good side of the horse so fast?" he asked curiously.
Keselo smiled. "I just happened to have some candy in my pack-sack, sir," Keselo replied, "and Bent-Nose seems to have a sweet tooth. After two small pieces of candy, he was following me around like a puppy dog."
"Bribery, Keselo? I'm shocked."
"I wouldn't really call it 'bribery,' Commander," Keselo protested. "I'd say that 'a treat for a friend' would come closer."
Ekial laughed. "The young man was nice enough to give me the recipe for that candy, so if I don't eat it all myself, I'll be able to get on the good side of just about every horse in the Land of Malavi." Then his scarred face grew more serious. "Have the bug-people made any attacks yet?"
Narasan shook his head. "Longbow says that they'll probably wait until all of their relatives join them. I was talking with Ariga, and he advised me that the Malavi had come up with a scheme to disrupt the advance of our enemies."
"Lances, most likely," Ekial said.
Then Lord Dahlaine and Lady Zelana came out of the back side of Gunda's fort and joined them. "What did Sorgan say about our sister, Keselo?" Lady Zelana asked.
Keselo told them Aracia had finally come to her senses, thanks to Veltan's images of assorted varieties of bug-people, and then she came down on her priests— _hard_ —and on the little priestess Alcevan.
"A priestess?" Narasan said in astonishment. "I didn't even _know_ that Aracia _has_ female priests."
"I gathered that Alcevan's entry into the priesthood was fairly recent. Fat Bersla orates his adoration, but tiny Alcevan _whispers_ hers—continuously, even while Bersla's performing. She sounds a lot like an ordinary priest trying to get Aracia's undivided attention— _but_ she was recently involved in an attempt to murder Aracia's Dreamer, Lillabeth."
"She's trying to kill Lillabeth?" Dahlaine exclaimed.
"That's what Sorgan told me, sir," Keselo replied. "He said that she'd already bribed a young priest to kill the little girl, but the priest showed up in Lillabeth's play-room when several other people—Sorgan included—were there. The priest reported back to Alcevan that the time wasn't right yet, but that he'd take care of it when there was nobody about. Alcevan told him that was a wonderful idea, and then she cut the young man's throat from ear to ear. Sorgan's fairly sure that she doesn't want anybody who knows what she's doing to stay alive for very long. Veltan believes that Alcevan has her eye on Aracia's throne and she'll routinely kill any accomplice after they've either done what she wanted them to do—or failed, for that matter. I'd say that the life expectancy of _anybody_ who goes to work for little Alcevan will be just about one day. After that, he'll be dead meat."
"That's terrible!"
"Look on the bright side, Lord Dahlaine. Every priest she kills now will be one less that _we'll_ have to kill when this is over." He looked over at Ekial. "That's called 'thinning the herd' down in Malavi-land, isn't it?"
It was late that afternoon when Red-Beard, riding the horse he called Seven, led the archers of Longbow's tribe—or the Old-Bear tribe—down to the upper end of Gunda's fort. Longbow, of course, went out to greet them, and Narasan, as a courtesy, went with his tall, somber friend.
"Ho, Longbow," a lean archer with steely eyes greeted his friend.
"Tracker," Longbow replied with a nod. "What took you so long?"
"We ran into some of the Creatures of the Wasteland," the one Longbow had called Tracker replied. "Red-Beard here told us that there had been several encounters with them along that worn-out old mountain range. I think that the Vlagh doesn't really want _too_ many archers standing in the path of her children when she sends them up here. Evidently she's learned that we can eliminate her children without much difficulty, so she'd rather not have us to come up against. It took us a little while, but we cleaned them out of our way. Oh, Chief Old-Bear told us to give you his regards."
"How's he doing?"
"The same as always, Longbow. You should know that by now. He can still bend his bow, and his arrows always go just where he wants them to go."
"Is One-Who-Heals feeling any better?" Longbow asked. "Word reached us that he was quite ill a month or so ago."
"We thought that the bad news had reached you by now. We lost him, Longbow. He died a few days before the Maag called Skell sailed into our bay."
Longbow sighed. "We're all made less by that," he said mournfully. "He was one of the wisest men in all the Land of Dhrall. Was he ever able to identify the disease that took him from us?"
"I don't think it was really a disease, Longbow. Old age would probably come closer. He was at least ninety years old, and not too many people live much longer than that."
"That's true, I suppose. I think that out of respect for him we should exterminate all the servants of the Vlagh and leave her sitting alone on that hive of hers."
"She'll just lay more eggs, Longbow."
"Maybe—but then again, maybe not. Oh, this is Commander Narasan of the Trogite Empire. You probably met him during the war in the Domains of Zelana and Veltan."
Tracker nodded. "He's been very helpful."
"We try," Narasan replied. "What is it that gave you the name 'Tracker'?" he asked.
"It's what he does, friend Narasan," Longbow explained. "Tracker can follow any animal—or man—just about anyplace they go. He can find tracks laid down on solid rock—or so I've been told—and I wouldn't be at all surprised to find out that he can track fish as well."
"Only if the water isn't too deep, friend Longbow," Tracker said. "I don't really swim very well, so fish can usually get away from me. The little rascals can move very fast when they need to."
"Let's go on back to Gunda's fort, gentlemen," Narasan suggested. "It's a bit chilly out here, and I'm sure your men would be very happy to get something to eat along about now."
"What a great idea," Longbow said without cracking a smile.
The arrival of the members of Longbow's tribe seemed to have changed their friend quite a bit. Longbow had always seemed to be a solitary sort of man, but now that he had his friends here, he even smiled on occasion.
The next morning, just after sunrise, the bug-people began a steady march toward the steep slope that led up to Gunda's fort at the upper end of Long-Pass.
Ekial's horsemen savaged them as they advanced, but it didn't seem to Narasan that the bug-people were slowing their pace very much.
During the previous night, however, the men from the main army had reached Gunda's fort and had delivered the barrels of naphtha, pitch, and tar. Gunda had then moved his catapults into position and the catapult crews were carefully mixing the three elements in preparation for launching fire missiles.
"Did you speak with Ekial, Gunda?" Narasan asked. "We don't want to start throwing fire at our friends, you know."
"We've got it all worked out, Narasan," Gunda replied. "We're falling back on toots. When Ekial and his men hear the horns blowing, they'll get clear. Then the catapult crews will set fire to enough bug-people to persuade the other ones to go play somewhere else."
"That's the most brutal way to make war on somebody that I've ever heard of," Trenicia said.
"In the long run, it probably saves a lot of their lives, dear," Narasan told her. "Even the stupidest enemy in the world will turn and run when he sees his friends engulfed in fire. The bug-people aren't any too bright, but even _they_ will probably turn and run when it starts raining fire."
"Then we've just won another war, wouldn't you say?"
"I'm not at all that certain, dear," Narasan replied, looking out at the massed Creatures of the Wasteland marching up the slope. "We don't have an unlimited supply of fuel for our fire missiles, and when we run out, the enemies will most probably resume their advance."
"Right up until they reach the poisoned stakes," Gunda added. "Then after they come through the stakes, the archers from Longbow's tribe and Kathlak's Tonthakan archers will shower them with poisoned arrows. If any of the bug-people get past _that_ , the Matan spear-throwers will greet them. I'd say that dear old Vlagh's going to lose about half of her army on that slope, and then they'll come face-to-face with this fort. They're _not_ going to get past us, but even if they do, they'll come up against Andar's fort a mile or so down the pass—and more forts farther on down the pass. The Vlagh may have started out with a million or so soldiers, but she'll be lucky if she's got even a dozen left after a week or so."
CONFUSION
**1**
Rabbit was fairly sure that Fat Bersla and tiny Alcevan would be nowhere near any place along the rickety southern wall of the temple where _most_ of Aracia's priests were engaged in honest work and endless complaints about it— _and_ about the steady diet of beans. Gimpy and Squint-Eye were Maag ship-captains, but they'd been put in charge of the construction of what passed for the south wall more because they'd irritated Sorgan than because they were good builders. Rabbit was quite sure that the two of them weren't certain just how many of Aracia's lazy priests were supposed to be working on that wall. That should have made it quite easy for Bersla and Alcevan to slip away. "Except that there won't be much for Bersla to eat—except maybe for cobwebs," Rabbit muttered. "I think I'd better go see if I can find those two," he decided. "If they're still trying to come up with a way to kill Aracia's little Dreamer, I'd better stay right on top of them."
Given Bersla's need for _lots_ of food, Rabbit was quite sure that they wouldn't be too far from the nearest kitchen.
He roamed around in the dark, dusty corridors near the rickety south wall of the temple, searching more with his ears than his eyes, and as luck had it—or possibly destiny—he heard the priestess Alcevan talking in her peculiar voice. "Stay calm, Takal Bersla," she was saying. "I still have my hands on a fair number of novice priests. In the light of all this chaos, nobody's really paying much attention to the various corridors leading from here to the central temple, so sooner or later one of my agents _will_ get through and kill the spoiled brat Lillabeth, and that should put Aracia back under our control."
"I'm not sure that you're right, Alcevan," Bersla disagreed. "I know Aracia much better than you do, and she's totally independent now. The old Aracia would _never_ have dismissed me the way this new one did. She's not at all the same as she was before that cursed pirate Sorgan arrived. She _used_ to rely on me for all things, but now she turns to Sorgan instead."
"That's the work of the younger goddess Enalla, you fool," Alcevan declared. "Once Enalla's gone, Aracia will be ours again. That's why we _must_ kill the child Lillabeth. She's Enalla in disguise. When _she_ dies, Enalla also dies."
"You could be right, I suppose," Bersla admitted dubiously.
That struck Rabbit as more than just a little bit peculiar. Bersla was the highest-ranking priest in Aracia's temple, but it seemed to Rabbit that the Fat Man was falling in line with the recently arrived Alcevan every time she opened her mouth. She seemed to have some kind of overpowering grip on the head of the Church of Aracia. "I think that maybe I'd better go warn Veltan that these two _still_ want to kill that little girl," he muttered.
"She's still sending those low-rank young priests through the corridors to come here and try to kill Lillabeth, Veltan," Rabbit advised Zelana's younger brother when they met in the cabin of the _Ascension_ later that day. "She's absolutely certain that Lillabeth is really Enalla in disguise, and that if Lillabeth is killed, Enalla will die as well."
"She doesn't fully understand what's happening, Rabbit," Veltan replied, leaning back in the bulky chair near the broad window on the stern side of the cabin. Then a rueful sort of expression came over his face. "Of course, I'm not all that sure that _I_ do either. When Eleria started to refer to Balacenia as 'Big-Me,' it startled me more than a little. The Dreamers and the younger gods _are_ connected in ways that Dahlaine didn't anticipate when he came up with his scheme, and they're connected with each other in ways that none of us could have imagined."
"They share their dreams with each other, you mean?"
"Exactly. We weren't ready for that. _We_ tend to avoid each other as much as possible, but our younger counterparts are much more closely linked."
"You know that you _could_ take Lillabeth over to the cap'n's fort on the west wall. If he put out the word that _no_ priest will be permitted to go there, Alcevan's scheme would go to pieces, wouldn't you say?"
"It probably would, Rabbit," Veltan agreed, "but I think I'd better keep her right here. I can protect her here, and I've got a strong feeling that I should stay very close to my big sister. Aracia's more or less come to her senses, but she might start veering off again. That priestess Alcevan is about ten times more clever than Fat Bersla will ever be, and if she wheedles her way back into Aracia's presence, she'll probably start pushing big sister off balance again."
"You could be right, I guess," Rabbit agreed. "When we first got here, we were all sure that Fat Bersla was the main one in your sister's priesthood, but when I heard the Fat Man talking with Teenie-Weenie, she was calling all the shots. There's something very strange about her, and I think maybe we should all do what we can to find out just what that is. Fat Bersla makes speeches, but 'Teenie' spends all of her time whispering to your big sister." Then Rabbit stopped, and he felt just a bit foolish. " _You_ could listen to those whispers, couldn't you?"
"Probably, yes."
" _And_ neither Alcevan or your big sister would know that you're listening, would they?"
"Aracia _might_ sense my presence, but I think I could conceal it from her."
Rabbit shook his head. "Bad idea, I think. If you're busy eavesdropping who's going to look out for Lillabeth?"
Veltan's expression became a bit sheepish. "I seem to have overlooked that," he admitted. "Why don't I have a talk with Zelana instead? She can either protect Lillabeth, or do our eavesdropping for us."
"That's probably the best idea right there," Rabbit agreed. Then he remembered something from the previous summer. "I think I know of a way to stop those novice priests from coming here," he said.
"Oh?"
"I'll need a lot of spiderwebs that are quite a bit thicker than the ones the local spiders have been spinning in the hallways here in your sister's temple. You _do_ remember what happened to Jalkan and that churchman from the Trogite Empire, don't you?"
Veltan shuddered. "I don't think I'll _ever_ forget that."
"If I gather those beginner priests together and warn them that there are spiders in those hallways that are almost as big as horses and then describe what happened to Jalkan and the Trogite priest down in your territory, Alcevan's going to have a lot of trouble hiring killers, I think." Then Rabbit squinted at Zelana's younger brother. "You can make just about anything you want to, can't you, Veltan?" he asked.
"What exactly do you think you'll need?"
"Bones, mostly—but not just random bones scattered around. I think complete skeletons would be best. That way anybody who comes across one of them will know that he's looking at a dead person rather than a fox or a cow, and it might be useful if the skeleton has a few rags attached as well—rags that look like they used to be those robes all of Aracia's priests wear."
"And maybe a brief image of a very large spider—or ten—scampering around in those corridors?" Veltan suggested.
"You _can_ do that, can't you?" Rabbit said. "I'd forgotten about that. If we have a few sightings of spiders that are ten feet across, human skeletons wearing bits and pieces of priest robes, and spiderwebs as thick as anchor ropes, _nobody_ with his head on straight will go anywhere near those corridors."
"I like it!" Veltan declared with a wicked grin. "Go back to the south side of the temple and start telling stories, Rabbit. I'll make sure that anybody who ventures into one of those corridors sees things so terrible that he'll _never_ go back again."
"I think we just sank Alcevan's boat," Rabbit said with a broad grin.
"I'm fairly sure that she'll never be able to give those halfwit young priests what she's promising," Rabbit told the two Maags, Gimpy and Squint-Eye, "but around here, a promotion is worth more than gold. I'm going to need some verification, though. If it's not too much trouble, put on long, worried faces and talk about some of your sailors who went along one of those corridors and never came back."
"You're a nasty little fellow, Rabbit," Captain Squint-Eye said. Then he assumed the facial expression that had given him his name. "Maybe if we had one of those imitation skeletons you were telling us about dressed in Maag clothes and armed with Maag weapons, the limp-brained priests will get your point."
"And maybe put up some danger signs at this end of those hallways," Captain Gimpy added. "You know, a red sign with a big picture of a spider painted on it. If we pile up enough awfuls for those halfwits to see, not one of them will even consider going back to the main temple, no matter _what_ the little lady priest offers them. It's a lot like that old Maag saying that has to do with gold, wouldn't you say? 'You've got to be alive to spend it' gets right to the point, doesn't it?"
"And Gimpy and I'll announce that we want all those priests to come to an 'emergency conference,' and then you can dump awful-awful all over them," Captain Squint-Eye added. Then he laughed. "You know, something like this is even more fun than a war."
"Of course," Rabbit agreed. "Deception is always more fun than war, and, if you do it right, you don't even have to bleed."
**2**
No, Rabbit," Captain Hook-Beak said. "I think _you'd_ better do it. You and Torl and several others have been passing on stories about your encounters with imaginary bug-people ever since we first got here. I'll back you up, of course, but the lazy priests would believe _you_ a lot sooner than they'd ever believe me." He paused, staring out across the berm his men had built out to the front of the west wall. "Don't go _too_ far, though. When you get right down to it, all you're really going to do down by the south wall is set things up for the appearance of those imitation skeletons wearing priest robes that Veltan's going to conjure up. Keep your description of what the spider-bugs have been doing to the local priests those imitation skeletons are going to represent pretty much accurate. Don't get too creative. The real thing down in Veltan's Domain was awful enough, so you won't have to take it much farther."
"That's the way we'll do 'er, Cap'n," Rabbit agreed. "I'll start out by telling them that the spider-bugs slipped past us before we even started building walls and that they're hiding in _most_ of those hallways. Then I'll move on into a description of what happened to Jalkan and Adnari Estarg. That should set things up for Cap'n Gimpy to uncover those imitation skeletons."
"You're _very_ good at this sort of thing, Rabbit," Sorgan said admiringly.
"I've had lots of practice, Cap'n," Rabbit replied. "All I had to do to keep Ox and Ham-Hand from putting me to doing _real_ work was to stand there tapping on my anvil with a hammer. I'm a natural-born expert when it comes to deception."
"Except that Longbow saw right through you the first time he ever met you," Sorgan added.
"Longbow don't count, Cap'n," Rabbit replied. "He sees through everything."
Rabbit was almost certain that Takal Bersla would _not_ be present during Captain Squint-Eye's "emergency conference." He was too well-known, for one thing, and, since he'd gained his position in the temple by making speeches, he probably wouldn't care to listen to speeches delivered by someone else. The priestess Alcevan would almost certainly want to be present, though, since the term "emergency" strongly suggested that something had come up that would make her hired assassins very reluctant to do what she wanted them to do. Rabbit was very well acquainted with all the tricks a small person could use to watch and listen without being seen, so he ran his eyes carefully over the gathered crowd of priests to see if he could locate her.
Then a brief flicker of movement caught his eye, and there was Alcevan, crouched low among the ruins of the poorly constructed wall along the south side of the temple. She was in the shadows, so nobody would even know that she was there— _if_ she stayed still and didn't move. Either she didn't know that, or she was positive that nobody would be looking for her. Rabbit, however, _had_ been searching, and he'd just found what he wanted. "I don't think she's going to like this very much," he murmured to himself as Captain Gimpy climbed up onto a large stone block to speak to the gathered priests.
"Captain Squint-Eye and me decided that there's something you priests really ought to know about, since your lives could very well depend on your knowing what it is," Gimpy declared. "To keep it short, our scouts saw quite a few bug-people sneaking through the bushes toward this south wall, and that's why you're here to lend us a hand. There was something that'd happened earlier, though, that our scouts didn't know about." He put his hand on Rabbit's shoulder. "This little fellow has actually _seen_ a certain variety of bugs in the corridors that lead to the main temple, so he can tell you what they look like and just how dangerous they are."
"I'll do my best, Cap'n Gimpy," Rabbit said. Then he looked out at the not really too interested priests. "This will be the fourth war we've had with the bug-people since last spring, and I've managed to live through all four of them—so far, anyway. There are dozens and dozens of different kinds of bug-people. Most of them are fairly stupid, so we've been able to outsmart them three times already. An entirely different kind of bug showed up in the second war last summer, and that's the bug that somehow got into these corridors. Most bugs have six legs, but these ones we've seen in these corridors have eight. Now, _most_ bugs chase things—or people—that they want to eat. The eight-legged ones set traps, though."
"That's absurd," one of the priests declared.
"Not really," Rabbit disagreed. "Most of the corridors here in the temple have spiderwebs all over the walls and hanging down from the ceiling. The spider-bug we encountered last summer was fifty or a hundred times bigger than any other spider I've ever seen. We had two different enemies in that war off to the south. One of the enemies was the bug-people, of course, but the other one came from Trog-land, and _they_ came here to look for gold, and they thought that they saw more gold than they'd ever seen before lying out there in the Wasteland."
Rabbit smiled then. "We had two enemies, and they were running toward each other. It wouldn't have been very polite to interfere with either one of them, so we just got out of the way. The Trog-landers encountered bug-people with poisonous fangs, and that eliminated quite a few of them. But then the Trogs came up against the spider-bugs we've been talking about here. The huge spider-bugs had spun out their webs, and a fair number of Trogs got snared in those webs. Then the spider-bugs came out of their hiding places and bit the snared up Trogs. The venom of the ordinary bug-people is so poisonous that it kills people instantly. The venom of the spider-bug works differently, though. It dissolves the innards—hearts, livers, lungs, and so on—so the person caught in the web has had most of his insides turned into a liquid. A spider doesn't have to chew its food. It drinks it instead. The Trogs were snared in those webs, so they couldn't move. Then, any time the spider got hungry again, it'd just tiptoe along the web, bite a hole in one of the Trogs, and then drink a gallon or so of the liquid that used to be the insides of the trapped Trog. The screaming when that happened isn't the kind of screaming you really want to hear."
"Are you saying that those men were still alive after their insides were dissolved?" an older, chubby priest demanded skeptically.
"I've never heard a dead man scream," Rabbit replied. "I'd guess that the spider wants fresh food, so its venom dissolves things, but doesn't kill. _That's_ what you'll be coming up against if you try to go back through those corridors to the main temple."
"We _have_ managed to recover what was left of several of the victims of those overgrown spiders." Captain Gimpy smoothly stepped in. "There wasn't really very much of them left—except for their bones. It looks to me like spider venom doesn't dissolve bones, so we can show you what condition you're likely to be in after one of the spiders eats most of you." Then he pulled back a tarp to reveal four skeletons. Gimpy tapped one of the skeletons with his foot. " _This_ one was probably a Maag before the spider ate most of him. He was wearing fairly standard Maag clothes, though, so that sort of identifies him. The other three . . . ?" Gimpy shrugged. "Maybe one of you can identify the clothing on those others. Clothes are about all we've got to work with. Bones are bones, and they all look pretty much the same."
The priests all shrank back from Gimpy's suggestion. Rabbit was fairly sure that none of them had ever _seen_ a human skeleton before. Finally, one of the older priests ordered a novice to go look. The young man turned pale and hesitantly approached Veltan's recently manufactured skeletons. "It's sort of hard to tell, Your Reverence," he said in a trembling voice. "There are only a few rags attached to any one of these three."
"What color are the rags?" the old man demanded.
"Black, Your Reverence."
"I'd say that sort of answers the question," Gimpy declared. "Maags don't wear black clothes. It's considered to be unlucky. You priests here _all_ wear black robes, though, so those three skeletons are—or were—almost certainly priests who served Lady Aracia. I want all of you to take a good hard look at those three skeletons. If you happen to get some kind of urge to go back to the main temple, you'll almost certainly end up looking exactly like these three do. Of course, dead people don't really care what they look like, do they? They're too busy being dead to worry about their appearance. It's entirely up to you men, though. I'm not going to make staying out of those hallways an order. You might have very important things to do back in the main temple, and your chances of actually _reaching_ the main temple aren't very good, but that's up to you. I won't interfere with anybody's religious obligations."
Rabbit rather casually looked at the tumbled-down wall where Alcevan had been hiding, and he saw that the look she was giving Cap'n Gimpy was filled with frustration and hatred.
"I'd say that poor 'Teenie-Weenie' just got cut off at the pockets," Rabbit murmured, doing his very best to avoid laughing out loud.
[THE
TRIBE
OF
OLD-BEAR](YoungerGods_toc.html#part_12)
**1**
The weather had turned bitterly cold as Red-Beard, mounted on the horse he called "Seven," led Skell and the archers of Old-Bear's tribe south along a worn-down mountain range toward the upper end of Long-Pass. The Matans of Tlantar Two-Hands _had_ given Skell and the other Maag seamen those densely furred bison-hide cloaks, but the chill was still brutal.
The archers of Old-Bear's tribe were very interested in Red-Beard's horse, and Longbow's friend described the "slash and run" tactics of the Malavi in some detail.
"That might be all right in open country," an archer called Sleeps-With-Dogs said, "but I don't think it'd work out too well in the forest."
"You're probably right," Red-Beard admitted, "but most of the country here in the North or off to the East is open. If I remember right, you were with us down in Veltan's Domain, and the country above the Falls of Vash didn't have very many trees. A forest is good for hunting, but when you get into open country, the distance between here and there seems to go on forever. That's when a horse becomes _very_ useful. You don't have to do your own walking—or running—if you've got a horse." Then he gave the archer from Longbow's tribe a curious look. "How in the world did you come up with a name like 'Sleeps-With-Dogs'?" he asked.
The archer shrugged. "I found out quite some time ago that having dogs in your lodge in the wintertime means that you're not going to need very much firewood. If you bed down with three or four dogs, you'll stay nice and warm. The fleas are sort of troublesome, but not as much as ice is."
"I might give that a try myself," Red-Beard said. "I'm sure that Seven here gives off heat when he sleeps, but he sleeps standing up."
"What made you decide to call him 'Seven'?" the archer asked.
Red-Beard laughed. "That wasn't my idea at all. His original owner was a gambler, and he just _loved_ to play dice-games. As I understand it, seven's a very important number when you're playing dice-games. When the Malavi were sailing north on board quite a few Trogite ships, they didn't really have much to do, so they gambled, just to pass the time. I've heard that Seven's original owner won a lot of money in those dice-games—right up until the other Malavi found out that he'd been cheating. They threw him off the ship into deep water, and since he'd never learned how to swim, he sank like a rock."
"Drowned?"
"You couldn't prove that by me, Sleeps-With-Dogs," Red-Beard replied, "but after he'd been under water for an hour or so the other Malavi divided up what he'd left behind, and they gave _me_ old Seven here. He's a sensible old horse, and he and I get along very well. I don't have to walk much now, and I don't force him to run. It works out fairly well for the both of us."
"How much farther would you say it is to this Long-Pass place?" Skell asked Red-Beard.
"Dahlaine's map said that it's about a hundred and sixty miles from where we started down along this mountain range," Red-Beard replied. "I'd say that we're about halfway there, Captain Skell. Since it took us four days to get _this_ far, it'll probably take us another four days to get to where we're going."
"I was sort of afraid that it might take that long," Skell said sourly.
"Have you heard anything at all about what cousin Sorgan's up to down in Lady Aracia's temple?" Skell asked Red-Beard as they set out the next morning.
"Deception for the most part, I've been told," Red-Beard replied.
"Zelana's big sister wants everybody in the world who owns a sword to run down there and defend her. I've heard that Sorgan told her that he could hold off the bug-people _if_ she'd pay him a lot of gold."
"That's Sorgan, all right," Skell said with a faint smile. "My cousin is probably the greatest cheater in the world. Before I left to go fetch the archers from Old-Bear's tribe, people were saying that the bugs would attack through Long-Pass, and that Aracia's temple wasn't in any danger at all, and that Aracia herself wasn't either. How in the world did cousin Sorgan manage to squeeze any gold at all out of her?"
"He lied, of course. You know how Sorgan is. From what I've heard, his plan was to send people who can lie with a straight face out into the farmland and come back with all kinds of horror stories about bug-people living on a steady diet of people-people. That's supposed to keep Aracia's holy-holies penned up inside the temple while the _real_ warriors are fighting off the bugs in Long-Pass." Then Red-Beard tugged at his whiskers. "If what I've heard about Zelana's sister comes anywhere close to being true, she wants—even _needs_ —to have the bug-people attack her holy temple. If they don't bother to attack her, it would sort of mean that she's not very important to them, wouldn't it? She just couldn't stand that, you know. She _has_ to be important, and if the bugs just ignored her, she'd shrivel up and blow away. I think _that's_ what your cousin is counting on. Aracia will believe any lie he—or one of his paid liars—tells her, because she _has_ to believe."
"That's the saddest thing I've ever heard," Skell declared. "She'd rather die than be ignored."
"Except that she _can't_ die," Red-Beard said. "In some ways that makes it even sadder, wouldn't you say? She'll live forever, but nobody's ever going to pay any attention to her."
Skell shuddered and changed the subject. "Sorgan always manages to have all the fun," he said sourly. "A war against an enemy who isn't really there would be a lot easier than a real war."
"He took your brother Torl with him," Red-Beard said. "From what I've heard, Torl's probably one of the greatest liars in the whole world."
"He's good at that, all right," Skell agreed. "Have any new varieties of bug-people shown up yet?"
"I wouldn't know for sure," Red-Beard replied. "I've been riding poor old Seven here back and forth across this part of the Land of Dhrall since late last fall, so I haven't been anywhere near the Wasteland."
"Is learning how to ride a horse very difficult?" Skell asked curiously.
"That sort of depends on the horse. Old Seven here is fairly placid and easy to get along with. Most of the Malavi horses are much more frisky than Seven, and that doesn't hurt my feelings one little bit. Seven can't run as fast as most of the other Malavi horses, but I'm not in _that_ big a hurry to get from here to there."
"I'll go along with you there, Red-Beard," Skell agreed.
A fair number of Old-Bear's archers had gone on ahead that afternoon, and along about sunset the main party reached the campsite on the bank of a wide river that flowed down out of the mountain range. Somewhat to Skell's surprise, the archers had managed to kill several of the bison that grazed nearby. "I've been told that it's very difficult to kill those bison with arrows," Skell said to the archer called Tracker.
"Not if you've got metal arrowheads," Tracker replied. "Stone arrowheads aren't as sharp, and metal cuts through much easier. We'll have fresh meat for supper tonight. Your cousin Sorgan gave us exactly what we needed to make our lives more pleasant."
"I'm sure that he'll be glad to hear that. Did you happen to encounter any bug-people?"
"We saw a few of them, but they were holding back for some reason."
"I've been meaning to ask one of you people a question," Skell said then.
"I'll answer it if I can," Tracker said.
"Over in the Land of Maag, we almost never see a bug roaming around in the wintertime, but the bugs out in the Wasteland don't seem to pay any attention to the fact that it's turned very cold."
Tracker shrugged. "The Vlagh does all sorts of things that other bugs don't," he replied. "Our shaman, One-Who-Heals, told us that the Vlagh wants the Wasteland all to herself. The other bugs hole up in the wintertime, but the Vlagh's children don't. They break into the nests of the other bugs, kill them all, and then run back to the Vlagh's nest with all the food the other bugs had stored up for the winter."
"That's terrible!" Skell exclaimed.
"'Terrible' pretty much describes the Vlagh, yes," Tracker replied with a faint smile. "If I understand it right, she wants the whole world, and she wants her children to eat everything—and everybody—who lives there. For her, more food means more children."
"We've got to get rid of that monster!" Skell declared.
"You should take that up with Longbow, Skell. That's his lifelong goal. After one of the Vlagh's children killed Misty-Water, Longbow set out to kill the Vlagh, and sooner or later, he'll probably do just that."
"Who was Misty-Water?" Skell asked.
Tracker sighed. "She was the daughter of Chief Old-Bear, and she and Longbow were right on the verge of mating. One of the servants of the Vlagh killed her, though, and now killing the Vlagh is Longbow's only real goal in life."
"That explains a lot of the things about Longbow that I didn't really understand," Skell said. "I'm glad that he's on _our_ side. Having Longbow for an enemy would cut back a man's life-expectancy by quite a bit, wouldn't you say?"
"Almost back to nothing at all," Tracker agreed.
**2**
It was about noon on a cloudy day when they reached the upper end of Long-Pass, and Skell was forced to concede that Gunda's fort was very impressive.
"I can't really take credit for all those boulders in the front wall," Gunda said. "Ekial and the Malavi hitched their horses to rocks almost as big as houses and dragged them here. I don't think the bug-people will have much fun trying to climb that wall, particularly now that we've got all those archers you just brought here."
Then Longbow and the Trogite army commander Narasan came out to greet Longbow's friends.
"Ho, Longbow," Tracker called.
"What took you so long?" Longbow asked with a faint smile.
"We ran into some of the Creatures of the Wasteland. Red-Beard said that they've been sneaking around quite a bit. I don't think the Vlagh's too happy about all the archers her people are going to come up against. They didn't rush us or anything, but they _were_ watching. Oh, Chief Old-Bear told us to give you his regards."
"How's he doing?"
"The same as always. He can still put arrows where he wants them."
Skell went over to the south side of Gunda's fort to speak with the other Maag sailors who'd come along with Longbow's friends. "I want you men to behave yourselves," he told them. "Don't insult the Trogites or the natives. They're on _our_ side in this war, so don't make fun of them."
"We've heard all this before, Skell," a bearded sailor said.
"Good. Now you've heard it again. Maybe if you hear it often enough, it'll start to seep through into your mind."
"We've been using Keselo as our go-between, Skell," Commander Narasan said the following morning. "He has access to a fast sloop that can take him down to the temple-town in about half a day, so your cousin can keep him up to date on what's happening down there." Narasan smiled then. "Keselo came up with another idea as well. Prince Ekial gave him a horse called Bent-Nose, and Keselo tamed the horse in about a half a day."
"With a whip?"
Narasan laughed. "No, not really. He even startled Ekial when he used candy instead. It seems that a horse will do almost anything for candy. That means that Keselo can reach your cousin in about a day and a half, and he can bring information back to us in about the same amount of time."
"I'd start watching my tail feathers very close, Commander," Skell said. "A young fellow as clever as Keselo might start to have ambitions, and he _might_ just decide that he'd be a better commander than even you are."
"He _does_ show quite a bit of promise," Narasan agreed. "Anyway, your cousin has persuaded Queen Aracia that the bug-people are running all over her Domain, and she's even gone so far as to order all those fat, lazy priests of hers to go help your cousin build forts to hold back the Creatures of the Wasteland. The priests aren't very happy about that, but they're even _un_ happier about the steady diet of beans Sorgan offers them three times a day."
Skell laughed. "Sorgan's very good at things like that," he said.
"Indeed he is, and he's keeping Aracia and all of her priesthood so frightened that they don't even know that we're fighting the _real_ war up here in Long-Pass."
"That's all that really matters, I guess," Skell replied.
[A
REPORT
FROM
THE
NORTH](YoungerGods_toc.html#part_13)
**1**
"She moves right along, that's for sure," Red-Beard said to Keselo as the sloop cut through the waters of Long-Pass bay.
"When you add oarsmen to a good following wind, you're not going to stay in one place for very long," Keselo agreed.
"How did you get stuck with being the messenger boy between Narasan and Sorgan?" Red-Beard asked the young Trogite.
Keselo shrugged. "I spent a lot of time with Sorgan during the war in Lady Zelana's Domain, and we got to know each other quite well. Commander Narasan felt that using somebody Sorgan knew and trusted as the messenger would work out better for all of us. Sorgan will tell _me_ things he wouldn't mention to a stranger or some low-ranking soldier who doesn't know what's really going on." Then he smiled. "I'm not really complaining about it, Red-Beard. Prince Ekial gave me Bent-Nose, so I don't have to walk very much."
"Horses _are_ sort of fun, aren't they?" Red-Beard said. "And they _do_ move a lot faster than we can."
"That's the _good_ part of the task Commander Narasan dropped on me. Bent-Nose does all the running and these two sailors do the rowing. All I have to do is sit."
Red-Beard smirked. "I wouldn't spread that around too much, Keselo," he said. "If other men find out how easy life becomes when you've got a horse, they might decide to poach old Bent-Nose from you, and you'll go back to walking." He looked across the bay at the shoreline. "I sort of hate to admit this," he admitted, "but this sloop moves _almost_ as fast as my canoe."
"I saw you and Longbow moving back and forth out in the bay of Lattash," Keselo replied. "You were both going very fast, but I'm not sure I'd care to ride in a boat made of tree-bark."
"The tribes of Zelana's Domain have been using tree-bark canoes for a long, long time, Keselo. You wouldn't want to drop a heavy rock into one of them, but they move very fast and very quiet. That's important when you're hunting. Where do you usually have your conferences with old Hook-Beak when you get down to temple bay?"
"Sorgan kept one of the ships that carried his army on down to the temple harbor," Keselo replied. "She's named the _Ascension_ , and she serves Sorgan's purposes very well. She gives him a private place to confer with his men without worrying about being overheard, and since there's quite a bit of trickery involved in what he's doing there, privacy's fairly important. It also gives _me_ a place to speak with him without being seen by any of Lady Aracia's priests. Of course, we don't really have to worry about that now, since Sorgan tricked her into sending _all_ of her priests on down to the south wall of the temple to help the Maags build defenses to hold off their imaginary enemies—maybe not quite all _that_ imaginary now, though. Veltan's been able to conjure up images of bug-things so awful that even the Maags are about half afraid of them."
The sloop heeled over sharply when they reached open water and the two sailors who'd been manning the oars stood up and reset the sails.
"Sorgan thinks of everything, doesn't he?" Red-Beard suggested.
"Actually, he listens well. _Most_ of these deceptions come from men like Rabbit or Torl. Sorgan polishes them a bit and then waves them in Aracia's face."
Red-Beard was staring at the shoreline. "This baby _really_ moves," he said. "Trying to keep up with her would probably sprain my shoulders if I was in my canoe."
"It's the sail, Red-Beard," Keselo explained. "Why strain yourself if the wind's doing all the work?"
It was about mid-afternoon on a cold, cloudy day when the sloop hauled into the harbor of what Keselo called temple-town, and the two skilled sailors rowed the sloop up alongside a large, squared-off Trogite ship anchored alone in the harbor. As Red-Beard probably should have anticipated, Sorgan and Veltan were standing at the rail of the _Ascension_ watching. Red-Beard straightened and looked up at the two friends. "Zelana and Dahlaine sent me down here to advise you two that the archers of Old-Bear's tribe are in place at the upper end of Long-Pass," he called up to them.
"Come on board, Red-Beard—and you too, Keselo," Sorgan told them. "Let's avoid all this shouting back and forth. Aracia _seems_ to be improving, but let's not get her started again."
Red-Beard and Keselo climbed up the rope ladder and joined Sorgan and Veltan on the deck of the _Ascension_. Then Sorgan led them all into the oversized cabin at the stern, where Rabbit and Torl were waiting.
"Will I get to see these imaginary bugs you've been showing Aracia?" Red-Beard asked Veltan.
"They couldn't _be_ much better," Veltan replied. "My big sister's finally come to her senses, and she ordered all her priests to go help the Maags."
"They're in the way, naturally," Rabbit said, "but at least they're out of the throne room, so Queen Aracia doesn't have to listen to them all day every day."
"Is she really buying that story about invading bugs?" Red-Beard asked.
"Veltan's images look pretty real—out in the open where everybody can see them—for like maybe a half a minute or so," Sorgan's cousin Torl replied.
"I don't _really_ want them to be in sight for very long," Veltan explained. "My sister's chubby priests wouldn't know a bug from a cow, but we _don't_ want Aracia herself to look at them too closely or too long. Aracia's starting to come to her senses, and _she_ knows what the bug-people _really_ look like. If she smells this hoax of ours, her head might start to come apart, and she'll go back to being adored. That's the _last_ thing we want. She's finally come to realize that her priests are totally worthless, and we want to keep it that way. We'll let her catch brief glimpses of our imaginary bug-people, but 'brief' is the important word right now."
Then Keselo looked at Red-Beard. "I haven't been that far up the pass for quite a while now," he said. "You just came down the pass, friend Red-Beard. How many forts are in place now?"
"Eight, if I counted right," Red-Beard replied, "and there are several others being constructed right now. I'd say that poor old Mama Vlagh's going to lose a lot of puppies this time out."
"What a shame," Sorgan replied sardonically.
"We _could_ send her a note of sympathy, Captain Hook-Beak," Keselo suggested, "but I don't think she knows how to read—or just exactly what a note is. She might just crumple it up and eat it."
Sorgan squinted. "I don't suppose that anybody happened to bring any poison with him," he said.
"We _should_ be able to come up with _something_ that'll kill her—or at least make her terribly sick," Red-Beard added.
"Don't rush me," Sorgan said. "I'm working on it."
"Squint-Eye and Gimpy weren't keeping very close track of all the priests Aracia sent down to the south wall to help them," Sorgan was saying the following morning after breakfast on board the _Ascension_ , "so there was quite a bit of sneaking back to the main temple going on. The ordinary priests were more interested in getting something to eat besides beans, but the priestess Alcevan was still trying to send young priests there to kill Lillabeth."
"You said _what_?" Red-Beard demanded.
"We've got it all under control, Red-Beard," Rabbit said. "There are several priests who are terrified by the coming change-over. They know that Aracia will be going off to sleep before long, and then Enalla will take over. They're quite sure that Enalla will abolish the priesthood and order them to tear down the temple. This Alcevan priestess is a newcomer, and she's positive that if Lillabeth dies, so will Enalla, and Aracia will _have_ to stay awake. There were a few attempts before Aracia sent _all_ of her priests off to the south wall to help build the fort. Alcevan was sending novice priests back to the main temple to kill Aracia's Dreamer every chance she had, but we put a stop to that."
"How?" Red-Beard asked.
"More imitation bugs." Sorgan chuckled. "Rabbit remembered what had happened to Jalkan and Adnari Estarg back in Veltan country. He spoke with Veltan about it, and now there are cobwebs that look like anchor ropes in every corridor leading back to the main temple, and every so often a spider that's about ten feet across skitters through the shadows. Squint-Eye and Gimpy described what happened to Jalkan and that Trogite Adnari several times, and then Veltan made several skeletons that were wearing scraps of what _looked_ like the material of those priestly robes. The apprentice priests stopped paying attention to Alcevan about then. The notion of being dissolved and then slurped up by a ten-foot spider had terrified them to the point that _nothing_ Alcevan offered even interested them one little bit. All those priests are bunched up by the south wall, and they won't go _near_ any of those hallways."
Red-Beard laughed. "These hoaxes seem to be getting better and better," he noted. "Who's guarding the little girl, though?"
"Torl's got a hundred men stationed all around Lillabeth's room," Sorgan replied. "They're some of the biggest men in our whole army, and they've got some _very_ ugly weapons. _Nobody's_ going to get anywhere _near_ that little girl, we'll see to that. Most of those priests aren't at all interested in Alcevan's scheme, though. They're all terribly disappointed by the food Squint-Eye and Gimpy are offering. They're used to eating very fancy food, and a steady diet of beans doesn't sit too well with them. Gimpy told them that they had a choice, but when he said, 'You can eat beans, or you can eat dirt,' it didn't go over very well."
[THE
PLEA
OF
ALCEVAN](YoungerGods_toc.html#part_14)
**1**
Balacenia was floating in the air above the temple of Aracia to keep an eye on things. Since she would be the dominant god during the next cycle, Balacenia felt a certain responsibility, even though she wasn't supposed to wake up yet. Dahlaine's "grand plan" had in effect split each one of the younger gods right down the middle. From what she'd seen during several brief encounters with the other younger gods, their Dreamer alternates were pretty much the same as their real personalities. Eleria, however, seemed almost to be a total stranger. She _definitely_ had her own personality, and it did not even remotely resemble Balacenia's. They were now so far apart that Balacenia was almost positive that they'd never be able to completely unite again. Balacenia sighed. "At least I'll have somebody to talk with when I'm lonesome."
Balacenia had some very serious doubts about Sorgan's declaration that Aracia had returned to sanity. Zelana's older sister had always been a towering egomaniac, totally convinced that she was the most important being in the entire universe. That, of course, had opened the door for a number of self-appointed "priests" who'd found their way to lives of luxury over the past several eons. They'd made lifelong careers of piling counterfeit adoration on Aracia, and she'd wiggled like a puppy and begged for more.
Over the countless centuries, Aracia's priests had spread the word that she'd _really_ like to have a glorious temple built for her, and they'd managed to persuade the common citizens that it was _their_ duty to construct it. Unfortunately, nobody had bothered to draw up an overall plan, so Aracia's "glorious temple" was a hodgepodge of corridors that didn't go anywhere, chambers without doorways, and extensive unroofed areas.
Aracia spent most—if not all—of her time in her throne room, so she had no real awareness of how ridiculous her glorious temple really was. It was a mile square, though, and the word "mile" seemed to thrill Aracia right down to her bones, and she sat contented in her glorious throne room on her glorious throne, accepting the glorious adoration of generation after generation of lazy priests.
Then, quite suddenly during Sorgan's imitation invasion hoax, Aracia had changed direction—to the horror of her priests. Her voice suddenly became steel-hard, and she commanded her priests to go out and do some honest work for a change.
"It just doesn't fit," Balacenia complained. She was catching a strong odor of tampering here, but she had no idea of who might be trying to change things.
Then her eye caught a flicker of movement outside the unstable east wall of Aracia's temple. Rabbit's "spider hoax" had terrified everybody in Aracia's Domain, and terrified people don't wander around alone—particularly not after the sun goes down.
Curious, Balacenia drifted lower and saw a small person wearing a priest robe scurrying along outside the rickety temple wall. "That almost _has_ to be that self-appointed priestess called Alcevan," Balacenia murmured. "What's she up to now?" Then she remembered Veltan's imitation spiders, and that explained just _why_ Alcevan was staying outside the temple, and it also suggested that Alcevan desperately needed to talk with Aracia.
Then she thought of Torl's description of an unused corridor that just happened to have a crack in the wall where he'd been able to listen to what was happening without being seen. "I'd say that 'sneak around' time just got here," she murmured to herself.
She drifted down through the poorly constructed roof of Aracia's temple and settled in Torl's dusty corridor. She could even see Torl's footprints in the dust, and that made things very simple.
"Please don't leave us, dear one!" Balacenia heard Alcevan's peculiar-sounding voice coming through the crack Torl had found. There was a desperation in the voice, but also just a hint of insincerity.
"You're just wasting your time—and mine—Alcevan," Aracia's cold voice declared. "I have no choice. My cycle nears its end. I _must_ sleep, and soon. I cannot remain awake when my cycle ends."
"You must _try_ , dear one!" Alcevan's voice was almost shrill. "We do not know this Enalla creature, but I am almost positive that she'll abolish your church—or even worse, change it so that the people—and priests—of your Domain will worship _her_ instead of you."
Balacenia caught a brief smell of a very peculiar odor. Then Aracia's attitude—and even her voice—changed. "I will _not_ permit that! The church is _mine_!"
"Could you not delay her awakening, dear one?" Alcevan asked. "Surely you can stay with us for just a few more years."
Aracia, it seemed, even considered that. Then she spoke in an ominous tone. "Maybe I can at that," she said. "And I think I know of a way to keep Enalla from _ever_ usurping this throne that is rightfully mine."
"And which way is that, dear one?" Alcevan asked, though it was obvious to Balacenia that the small priestess already knew.
"You don't need to know that just yet, Alcevan," Aracia declared.
Balacenia could catch bits and pieces of Aracia's thoughts. Her brain was fairly scrambled, but the word "kill" kept cropping up.
"I think I'd better warn Veltan about this. His big sister isn't quite as sane as Sorgan seems to think she is."
The Trogite ship called the _Ascension_ that Narasan had given to Sorgan was anchored in the harbor, and Balacenia sensed Veltan's presence in the large cabin at the ship's stern. Fortunately, he was alone, and Balacenia was certain that the two of them needed to talk privately. She could have just drifted down to the deck of the _Ascension_ and then knocked on the cabin door, but she chose at the last minute to just suddenly appear in Veltan's presence with no warning.
Veltan visibly flinched when she dropped into the cabin. "What are you _doing_?" he demanded.
"I just thought I'd drop by and warn you that there's a great deal of trouble coming your way, Uncle Veltan," Balacenia replied. "I was sort of keeping an eye on things in your big sister's temple, and I saw that little priestess Alcevan sneaking along the east wall. She went on inside, and I used that corridor Sorgan's cousin found to get close enough to the throne room to eavesdrop. I hate to tell you this, Uncle Veltan, but that little priestess Alcevan just put a stop to your sister's journey into the land of people who aren't crazy."
"You aren't supposed to be doing that sort of thing yet," Veltan protested.
"Don't worry so much about 'supposed to,' Uncle. I just discovered that Alcevan isn't at all what everybody seems to think she is. Actually, she's a bug."
Veltan's head came up sharply. "What are you talking about?" he demanded.
"I was talking about Alcevan the bug. Weren't you listening? This _has_ happened before. If you think back, you'll remember that tribe in Tonthakan who were positive that they'd been terribly insulted—right up until the Maag called Ox brained a couple of men—who turned out _not_ to be men. Alcevan's of that same variety of bug."
"How do you know that?"
"I could smell her. She's emitting the same kind of odor the ones in Tonthakan were, so Aracia believes everything Alcevan tells her, and she's coming very close to trying to keep Enalla from taking over here by killing Lillabeth."
"She wouldn't _do_ that. It's totally forbidden."
"'Forbid' just blew out of the window. Aracia is all wound up, and the word 'kill' keeps coming into her mind. I'm almost positive that Aracia believes that if she kills Lillabeth, it'll almost certainly kill Enalla as well. I think it's time for a conference, Veltan. Why don't you go speak with Dahlaine and Zelana? The other Dreamers are with them. I'll snatch Lillabeth out of Aracia's temple."
"That might be just a bit tricky, Balacenia," Veltan said. "Sorgan's cousin Torl has a hundred oversized Maags there guarding her."
"So?"
Veltan blinked. Then he laughed a bit ruefully. "I keep forgetting who you really are, Balacenia. You're not at all like Eleria, are you?"
Balacenia sighed. "Not really. I love her, but she goes her own way. I don't think we'll be able to merge when this is all over, but we can worry about that later. Right now, getting Lillabeth to safety is more important than anything else. Where do you think we should meet?"
Veltan frowned. "I'd say Mount Shrak. It's the most secure place. The snow's probably ten feet deep up there, and that should definitely keep the bugs from getting close enough to hear what we're saying."
"Good idea. We need to make some decisions. If necessary, we might _all_ have to come down on Aracia with both feet. Let's get started, Uncle. We've got a long way to go, and not very much time."
It wasn't particularly difficult for Balacenia to take Lillabeth right out from under the noses of Torl and the hundred massive sailors Sorgan had sent to guard her. The Maags guarded doors and hallways, but they didn't guard the roof. Many things were coming back to Balacenia now, and she had no difficulty passing down through the roof to join the little girl who was _really_ Balacenia's sister Enalla. "We've got an emergency, Lillabeth," Balacenia declared, "and we're all supposed to meet with the elders up at Mount Shrak."
"Why didn't Aracia come here and take me there?" Lillabeth demanded.
"There's a war out there, Lillabeth," Balacenia reminded her sister. "Aracia's very busy right now." She paused. "I don't suppose you remember how to fly," she said.
"I've never tried," Lillabeth said. "I'm sure that Aracia would be terribly upset if I suddenly sprouted wings."
"We don't use wings, Lillabeth. There's a much easier way to do it. I'll carry you. You're not really all that heavy."
"You're the grown-up Eleria, aren't you?"
"Well—sort of. Eleria and I are much farther apart than you and Enalla are."
"When the time comes, will I have to grow up before I become Enalla? Or will there just be a poof, and I'll be all grown up?"
"We've never done this before, Lillabeth," Balacenia replied. "I think each one of us will have to make it up when the time comes." She held out her hand. "Shall we go?" she said.
Lillabeth's eyes went very wide when the two of them passed up through the roof of Aracia's temple. "How can you _do_ that?" she said in a trembling voice.
"It has to do with thought, little sister," Balacenia replied. "Aracia could do it, if she ever left her throne room. There are all sorts of things we can do that ordinary people don't even think about. Just look at the scenery, Lillabeth. I'll take care of this."
"Where are we going?"
"I told you, Mount Shrak. You've been there, so it shouldn't bother you."
They rose up through the chill winter air until Balacenia located a wind coming out of the southeast. She latched onto it, and it carried them in a generally northwesterly direction. Balacenia had always enjoyed riding the wind. It was an easy way to go from here to there, since the wind did all the work.
"How high up in the air are we?" Lillabeth asked in a trembling sort of voice.
"That doesn't really matter, child," Balacenia replied. "Don't let the height bother you. I won't let you fall."
"I've never been up this high in the air before," Lillabeth said. "The world's a lot bigger than I thought it is. How far is it from one side to the other?"
"The world doesn't _have_ sides, child. It's round—almost like a ball, but it's much larger than an ordinary ball. There are thousands of miles between one side of the world and the other."
Lillabeth peered down at the earth far below. "Why is it all white like that?"
"It's covered with snow, Lillabeth."
"Like that snow we saw back in Lattash last spring?"
"I'd almost forgotten that you were there with the rest of us," Balacenia admitted. Then she pointed on ahead. "That's Mount Shrak there. The rest of the family should be there by now. I'd say that you should listen, but don't say very much. They're likely to say things about Aracia that you won't like, but just keep your feelings to yourself. The whole purpose of this meeting is to come up with a way to keep Aracia from hurting you."
"She wouldn't do that!" Lillabeth protested.
"I wouldn't be too sure, Lillabeth. Aracia's mind isn't working the way it's supposed to right now. That's what this meeting's all about. If we don't get her mind to working right, we could lose her."
Balacenia began their descent, and they came down just outside the entrance to Dahlaine's cave. She was just a bit out of practice, but things seemed to be returning to normal.
The two of them went on inside, and they soon reached the part of the cave Dahlaine used for living quarters.
"Did you have any problems?" Veltan asked.
"I don't _have_ problems, Uncle," Balacenia teased him. "You should know that by now. Torl's men were guarding the doors, but I went into Lillabeth's room through the ceiling. Then we came out the same way. It'll probably be three or four days before anybody in the temple discovers that Lillabeth isn't there anymore."
"Let's get on with this," Dahlaine said. "Veltan told us that you've discovered that one of sister Aracia's priests is a disguised servant of the Vlagh."
"Priestess, Uncle," Balacenia corrected. "I can't be sure just how she managed to persuade Fat Bersla and the others that women can be priests just like men can. She _might_ have used that odor you encountered in Tonthakan, but that's not really important. She's got your sister completely under her control now, and she's doing her best to drive Aracia into killing Lillabeth here."
"She can't _do_ that!" Dahlaine exclaimed.
"Not since I grabbed Lillabeth and brought her here, she can't," Balacenia reminded him. "Our problem now is how we are going to deal with that smelly bug."
"Kill it," Yaltar, the childish form of Vash, said bluntly.
"Didn't you tell him that we're not permitted to do that, Uncle Veltan?" Balacenia asked.
"I didn't get into too many details," Veltan admitted.
"We could always send for Longbow," Eleria said. "He kills bugs all the time."
"Or maybe Ox," Dahlaine's Dreamer Ashad said.
Then there came a glow of light out of the passage that led to the outside of Mount Shrak, and Ara was there. "What seems to be the problem, children?" she asked.
"One of the bug people has stolen the Beloved's big sister," Eleria replied. "We'd like to get her back, but we don't know exactly how."
"Which one of you discovered that?" Ara asked.
"It was Big-Me," Eleria replied. "You know how clever Big-Me can be."
Ara frowned slightly. "Who's she talking about?"
"That would be me," Balacenia said. "She's had a peculiar way of talking ever since she started playing with the dolphins. There's a woman called Alcevan down in Aracia's temple who pretends that she's a priestess. I overheard her talking with Aracia and she was letting out that peculiar odor the servants of the Vlagh use to confuse people. She's come very close to persuading Aracia that when Enalla takes charge in the East, she'll usurp the temple and the priesthood and make everybody in Aracia's Domain worship _her_. Aracia accepted that absurdity, and she was getting very close to murdering Lillabeth here as a way to destroy Enalla. Just to be safe, I snatched Lillabeth and brought her here."
Ara's face went cold. "Aracia should know that she's not permitted to kill _anything_."
"I'm sure that she knows that," Dahlaine said, "but we've seen this sort of thing before. Once one of the bug-people unleashes that odor, people lose their grip on reality. We've been trying to come up with an answer, but we haven't gotten very far yet. We're working on it, though. We'd be more than happy if you can give us a solution."
Ara squinted at him. "First off, you can't send Lillabeth back to that silly temple. She's too innocent to protect herself, but Enalla can. I'll help her a bit, and she'll look exactly like Lillabeth. Then, when Aracia commands her to die, Enalla can block that command with no trouble and—we can all hope—she'll prevent Aracia from going _too_ far. If she goes over the forbidden line, she'll cease to exist."
"Die, you mean?" Ashad asked.
"Not exactly. She just won't be there anymore. She'll simply vanish."
"That's the last thing we want," Dahlaine said. "Aracia's never really been very stable. She's obsessed with her divinity, and sooner or later she's almost certain to step over that forbidden line. I think it's altogether possible that we'll lose her, no matter what we do. Then we'll have to replace her."
"Make a new person, you mean?" Ashad asked.
"Maybe. We'll see."
Balacenia saw the perfect answer standing right there, but she was fairly sure she'd have trouble convincing Dahlaine, so she kept it to herself for now.
[THE
DREAM
OF
OMAGO](YoungerGods_toc.html#part_15)
**1**
Ara was humming softly to herself as she prepared a breakfast for the Trogites who were manning Gunda's fort at the head of Long-Pass. The weather had turned bitterly cold, but Ara's kitchen was pleasantly warm. The Trogite army cooks used stoves made of iron, but that didn't suit Ara one little bit. Iron stoves didn't produce constant temperatures, and constant temperature was the key to good cooking. She'd tried one of the iron stoves when she and Omago had first reached Gunda's fort, and the results had been disastrous. Omago was almost immediately aware of her dissatisfaction, and he had built her a stove much like the one back in their kitchen near Veltan's house, and Ara had always been more comfortable with a stove made of fired bricks. Her ovens were exactly where they were supposed to be. Different foods needed different heats, and Ara had always depended on distance from the fire to precisely control the heat in each oven. The Trogite army cooks could prepare large amounts of food, but quite a bit of it was overcooked—almost burned—and much of it was still half-raw. The Trogite soldiers were very brave, so they didn't complain when half of their food was partially burned and the other half was not even very warm.
Ara was still very concerned by child Balacenia's discovery that Aracia was almost totally under the control of one of the servants of the Vlagh. Lillabeth would be safe, though, and that was all that really mattered. Ara smiled faintly. Aracia—and her buggish priestess—were likely to be very surprised when they encountered what _appeared_ to be the child Lillabeth, but in reality was the younger goddess Enalla. With Enalla and Balacenia there to block them, Aracia and Alcevan wouldn't have any chance at all of achieving their goal. Dahlaine had been more than a little reluctant to admit that Aracia wouldn't be around much longer, but his sister was quite obviously out of her mind, and very soon she would almost certainly cease to exist.
"Good morning, dear heart," Omago said as he came into the kitchen.
"You finally woke up, I see," Ara said. "Here it is almost daylight, and you're only now getting out of bed. Aren't you feeling well?"
"Not really, dear," Omago replied. "I had a very peculiar dream last night."
"Oh?"
"You and I were drifting in a strange place where there wasn't much light at all."
"What exactly do you mean by 'drifting'?" Ara asked.
"We seemed to be just floating up in the air," Omago replied, "except that there wasn't any air."
Ara put down her large spoon. "I think that maybe everybody has one of those 'floating' dreams every now and then." She smiled. "I suppose that it might mean that we're all secretly envious of birds. They can fly, but we can't."
"I wasn't really thinking about birds, Ara, and I've never had a 'floating dream' before. Anyway, everything around us seemed to be moving toward an extremely bright light—so bright that it hurt my eyes just to look at it."
"It must have been the sun, then."
Omago shook his head. "It was even brighter than the sun, Ara—much, much brighter. Anyway, everything kept moving faster and faster as it rushed toward that bright light. Then the light started to shrink down, growing smaller and smaller until it wasn't any bigger than my thumbnail, but it was still growing brighter. Then everything went darker than night, and for some reason that I couldn't understand at all, you and I both said ' _Now!_ ' and the light was there again, but it definitely wasn't shrinking anymore. It was growing larger and larger so fast that I couldn't even keep track of it. The light almost seemed to be exploding and spreading out, shoving the darkness aside as it went."
Ara was suddenly cold all over. This wasn't supposed to be happening. "Just how long did that last, dear heart?" she asked, trying to keep her voice calm and ordinary.
"I couldn't really say, Ara. It was still expanding—or growing, maybe—when I suddenly woke up. Something very strange was going on. It's very, very cold in the sleep chambers of this fort, but I was covered with sweat as if I'd been out in my fields in the middle of summer."
Ara smiled. "I'd say that your dream was very useful, then, dear, dear Omago. You were feeling cold, and your dream warmed things up for you."
"It definitely made me feel warmer. Anyway, before I woke up, that immense light had started to spin off bits and pieces that whirled out in bright little chunks, spinning and flying. They seemed to remind me of stars, for some reason."
"Maybe you should talk with Dahlaine, dear Omago. He might be willing to pay a lot for a dream like the one you just had."
Omago smiled faintly. "Will it be long before breakfast?" he asked. "I think I should walk around just a bit and see if I can shake off what's left of that dream."
"You have about a half hour, dear heart," Ara replied. "Go out in the open and throw the dream away. Don't forget to put on your fur cape, though."
Omago nodded and went out of Ara's kitchen.
"How did he _do_ that?" Ara demanded out loud. "We agreed that he wouldn't remember any of this for years and years. He's supposed to be an ordinary man, but no ordinary man is going to have dreams about something that happened millions of years ago."
There had been a certain practicality in Omago's decision to transform himself into an ordinary human with no memories at all of his real identity. The man-creatures were a recent development, and, unlike most other creatures, it appeared that they were able to think at a much more complex level than the other living creatures on this particular world. Omago had decided that the best way to understand the man-creatures would be to duplicate their experiences and abilities by living out the life of an ordinary human here in the Land of Dhrall. He might have been able to try it elsewhere, but this world and this particular region were most important right now.
Omago's description of his dream had raised certain memories for Ara. Her mind went back to the time before time when she'd been awareness only, with no body. Her awareness had moved about the universe through endless eons, searching, searching for something—anything—that might dispel her dreadful loneliness.
And then Omago's awareness had reached out to her, and she'd no longer been alone.
For eons uncountable they had drifted together, growing more attached to each other as they searched for other awarenesses. But as far as they'd been able to determine, there were none.
And then, with no warning whatsoever, there was light—a light so intense that Ara could not bear to look at it. "What _is_ that thing?" she demanded.
"I couldn't really say, dear heart," Omago's awareness replied. "I've never seen anything like it before."
"Make it go away."
"How? It's millions of times larger than anything I've ever seen before, and other things that are also bright seem to be joining it. I think that something very important is about to happen."
"Why now, and not before?"
"I'm not sure that there's a difference between now and before, Ara."
"That just changed, dear Omago. That bright thing makes 'now' very important."
"I think you might be right, dear Ara. Something just started that didn't exist before."
"Is it my imagination, or is the bright thing growing smaller—and even brighter?"
Omago gasped. "Come away!" he shouted in the silence of her mind. "We can't stay here! We'll be destroyed if we do!"
"We'll be _what_?"
"We'll cease to exist. Come with me— _now_!"
And quite suddenly, Ara was no longer only thought. She had a tangible body, and Omago had one as well. He reached out and took her hand in his, and they turned and fled from the now tiny bright light.
And then, for some reason neither of them understood, they both said, " _Now_."
And time began as the tiny light stopped being tiny and suddenly flared out to enormity, engulfing the darkness as it went.
Then Omago seized Ara's new form and carried her away, and she suddenly realized that they were moving even faster than the light.
In time—now that time existed—the light slowed, and the vast light began to break into smaller pieces Omago called "suns," but Ara called them "the children of the light." That seemed nicer than "suns" to Ara, but she chose not to make an issue of it with Omago. Then, in the endless eons that plodded along in time, the various suns _also_ bore children that Omago called "worlds." Eventually, of course, the worlds _also_ had children. Trees and grass came first, but then other living things began to appear, primarily in the oceans of the various worlds. Life, as Ara understood it to be, began in worlds uncountable in the vastness of the universe.
The universe continued to expand, but Ara and Omago concentrated their attention on a specific world _and_ on what appeared to be a subcontinent that Ara named "Dhrall." It was a nice-sounding name that didn't really mean anything. "I think that might be a perfect place for a bit of experimentation, dear heart," she said to Omago. "This form you've given us seems to be most practical. Creatures that resemble us would probably be able to do many things that other creatures would find quite impossible." She held up one of her hands. "This alone would give our creatures an enormous advantage over creatures that only have feet. How were you able to invent hands when the time came for us to have bodies as well as awareness?"
Omago smiled. "Think back, dear heart," he told her. "We were in a very dangerous place, and we needed to leave—in a hurry. I wanted something that I could use to grab hold of you and pull you off to safety. If you'd like, we could call them 'Ara-grabbers,' I suppose."
"Not if you want me to say anything to you for the next million years, you won't," Ara replied tartly.
"I was only teasing, dear," Omago replied. He looked down at the land they called Dhrall. "I think it might be quite a long time before we'll be able to experiment, though. That land below is still at a very primitive level of development. I don't think _any_ life-forms will appear on this world until the fire-mountains go to sleep."
"You're probably right, dear heart," Ara agreed. "This might be a good time for some exploration. This particular part of the world might be very nice after it cools down, but I think it might be a good time for us to find out what the rest of this world looks like, don't you?"
"That might take a long time, my love," Omago replied a bit dubiously.
"Not if I fly, it won't."
"You're going to sprout wings?"
"Why would I want to bother doing that? I'll just set my body aside and go exploring with my awareness."
Omago blinked. "I never thought of that," he admitted. "Are you sure that you can separate yourself from your body, though?"
"We'll find out in just a moment or two. I won't be long, dear heart. I don't think I'll really need to count pebbles or anything like that. All we need right now is a general idea of the shape of the various other bits and pieces of land here on this world. Take a nap or something. I'll be back in a day or so."
Ara felt a tremendous sense of freedom when she separated her awareness from her body. It was a nice enough body, but the limitations it imposed on her mind had been almost intolerable. Now she was free again, and she soared off into the sky.
The sea that lay to the west of the Land of Dhrall was extensive, but Ara's awareness found no signs of life there. "Ah, well," she sighed. "It looks as if we'll have to start from the beginning."
That took some of the joy away. It appeared that this particular world was barren, totally devoid of any form of life.
When she reached the land mass on the western side of the empty sea, she saw no signs of plants of any kind. There _were_ mountains, however, but many of them were spouting fire miles and miles into the air.
"Oh, stop that," she told the mountains irritably.
And they did.
That startled Ara more than a little. "Good babies," she told them and then turned toward the south. _If_ she could stop these eruptions with just a word, this plan she and Omago had devised _might_ not be as difficult as it had previously seemed.
The land to the south was far less rugged than the land to the west had been, and Ara saw no telltale columns of smoke rising into the air. Evidently there _were_ no fire-mountains down here—or if there were, they had exhausted their supply of molten rock.
"That's more like it," Ara said with a certain satisfaction.
She roamed about in the sky for several days and found even more regions with no fire-mountains. After another few days, she turned north to return to the Land of Dhrall. Omago was probably starting to worry, so it was time to go home.
**2**
"Where have you _been_?" Omago demanded when Ara's awareness returned to the Land of Dhrall and rejoined her body. "I was starting to think that I'd lost you forever."
"You're not going to get away from me _that_ easy, dear heart," she replied. "Actually, you'll never get away from me at all, so don't even think about it. We'll still be locked together when the universe is old and grey. I more or less found out what we needed to know. There _are_ fire-mountains in other parts of this world, but not as many, and they aren't spitting fire nearly as far up into the air as the ones here in the Land of Dhrall are. I'd say that this is the newest part of this world."
"Did you encounter any life-forms at all?"
"Not on dry land. I sensed a few very primitive forms of life in the seas, but they've got a long way to go before they'll start coming up on dry land."
Omago looked out across the rolling sea. "We seem to have come here at the right time, then. We might want to experiment just a bit. We've seen many forms of life on other worlds, and they have characteristics that might be very useful. If we really _want_ to, I'm sure that we could create a creature with wings _and_ a level of intelligence that no bird-thing will ever have. Then we could _also_ create an intelligent creature with gills, and that one could live out its life in the sea."
Ara shook her head. "No, dear heart," she said. "We _know_ exactly what kind of creature we want here, and wings or gills wouldn't fit, and they could cause problems later on. _Our_ creatures should resemble _us_. Our body-forms will prove to be the best, I think, so let's not start tampering."
"Oh," Omago said then, "this part of the world already has a life-form much like some of those we've encountered on other worlds."
"Could you be just a bit more specific, dear heart?" Ara asked. "Exactly what _is_ this creature?"
"It's primarily a bug, dear," Omago replied. "It has six legs, a sort of shell to keep other creatures from eating it, and a tendency to live in caves. I very briefly touched what passes for a mind, and this bug-creature is very ambitious. It wants this entire world, and it's creating children by the thousands to take this world for it. It calls itself 'the Vlagh,' which most probably means 'mother.' I'm quite sure that any creatures _we_ make will have to deal with it."
"I've been considering this for quite some time now, dear heart," Ara said to Omago some time later. "You and I aren't limited to this particular world. Things have a way of popping out when we least expect them, and if some emergency breaks out on another world, we could very well have to go deal with it no matter what's in the wind here."
"It's possible, I suppose," Omago conceded. "I take it that you've come up with an answer?"
"I think we need children, dear heart," Ara replied.
Omago's face suddenly turned bright red.
"Is there some sort of problem with that?" Ara asked with wide-eyed innocence.
Omago blushed even more, and Ara laughed with pure delight. "Are we having some problems with the idea, dear, dear Omago?" Then she fondly touched his face. "We don't necessarily have to do it that way, you know. We have alternatives available to us. I can call them up with a snap of my fingers—and they wouldn't be of much use if they were infants anyway. Once they're in place, you and I can sort of fade back and let _them_ deal with any ordinary problems while you and I take care of more extraordinary ones."
"I don't know, dear heart," Omago said a bit dubiously. "If we give them absolute power, they could make some disastrous mistakes."
"Not if we put some limitations on them, they won't. 'No killing' should probably be at the top of the list, wouldn't you say?"
"Definitely."
"Of course, if we don't permit them to kill, that would mean that they won't eat."
"We can get around that if we have to," Omago said. "They can absorb light instead of food."
"Very good," Ara agreed. "Then too, they'll need to be awake all the time as well. Emergencies crop up without much warning, so I don't think they should need sleep."
"No creature stays awake eternally, Ara."
"I'll work on that and see what I can come up with."
"It won't work, dear heart," Omago said when Ara described her concept of the god creatures who would rule the Land of Dhrall.
"What's the matter with it?" Ara demanded.
"Females are very pretty, but I think we'll need males as well."
"What for? They aren't going to have children."
"Would you be contented if _I_ wasn't around?"
"Bite your tongue!" Then Ara felt just a little foolish. "For some reason it just never occurred to me that we'd need males as well as females."
"Something else too, dear," Omago continued. "I think we should give some serious thought to producing ordinary creatures who'll closely resemble these gods. We want the gods to have a sense of responsibility. That in itself will keep them from wandering off."
"Now _that's_ a very good idea, Omago," Ara agreed. Then something came to her. "You _do_ realize that we'll be creating an entirely new species, don't you?"
"So?" Omago replied blandly.
"You're making this very complicated, dear heart," Ara complained.
"That's all right, Ara. Complications make things much more interesting, don't they?"
Ara glared at him for a moment, but then she laughed.
**3**
Ara was quite sure that Omago's form and hers should also be the forms of the gods of the Land of Dhrall. "The time may come when we'll need to speak with them, dear heart," she told her mate, "and they won't be disturbed if we resemble them to some degree. Then, when we create their worshipers, they should also resemble their gods—and us as well."
"Not a bad idea at all," Omago agreed. "The time may come some day off in the future when we'll need to blend in with the worshipers and their gods, and it'll be much easier if we all have the same number of arms and legs. Shall we begin?"
"Why don't you make the bodies, dear? Just the general shape. I'll build their faces, and then we can both work on their characteristics. We'll want them to have individual identities and personalities, wouldn't you say?"
"You're very creative, Ara," Omago observed.
"Details, dear heart. Fine art grows out of details. In a certain sense what we're about to conjure up _will_ be fine art. They'll need awareness as well as bodies, and we'll want them to think like we do as well as resemble us."
"A thought before we begin," Omago said then. "They should probably have memories when they become conscious. I think they should believe that they've always been here, and that this day is just an ordinary day like one of several million others." Then he frowned. "They may _think_ that they've lived for thousands of years, but you and I will both know better. They _will_ live for a long, long time, but eventually the years will catch up with them, and they'll need to sleep for quite some time to refresh their minds."
"Who's going to mind the Land of Dhrall when they drift off to sleep, dear one?" Ara protested.
Omago scratched his cheek. "If we do this right and don't permit any weaknesses to crop up, I'd say that they'll be good for about twenty-five eons, and then they'll _have_ to sleep for the same amount of time."
"There goes our grand plan," Ara observed.
"Not really, dear one," Omago said with a sly grin. "All we'll need is a second generation to take over when the elders start to snore. We decided that four gods would be sufficient, but it seems that we were wrong. We'll need eight instead. The first four will tend to things for about twenty-five eons. Then _they'll_ go to sleep, and the second four will take over. If they pass it back and forth like that, they should all survive for a long, long time, and that's what this has been all about. You and I must _not_ be tied down here. We have other responsibilities as well as this one. Let's get started, dear heart. This might take a while."
Omago was nice enough not to protest when Ara declared that _she_ would name the gods—both the elders and the youngsters. Omago was not particularly poetic, but Ara could weave names by the dozens. After much thought, she named the elder gods Dahlaine, Zelana, Veltan, and Aracia. There was a musical quality about those names that Ara found very attractive. The younger gods—when the time came for them to wake up—would be Balacenia, Vash, Enalla, and Dakas.
Omago carefully planted those names in the minds—and false memories—of the assorted gods, and then he stepped out of sight and stirred the awareness of the four elders.
"What's going on here?" the grey-bearded, but still only three or four minutes old, Dahlaine demanded.
"I was just about to ask you that same question, big brother," the goddess Zelana declared. "As I remember, I was looking at a range of mountains, but they're not there anymore."
"I'm not sure that I'm right, Dahlaine," the youthful Veltan declared, "but it seems to me that you called us together to warn us about something you called the Vlagh."
"Ah," Dahlaine replied, "now it comes back to me. I've spent many, many eons watching insects. I pretty much understand the ones that have been around for a long, long time, but this Vlagh insect seems to have a number of troublesome ambitions."
"That's absurd, Dahlaine," the goddess Aracia declared. "Bugs can't think coherently enough to have anything even remotely resembling ambition. All _she_ wants to do is lay eggs—by the thousands."
"Exactly," Dahlaine replied. "The Vlagh seems to think that if she lays enough eggs, her children will run out and steal the world from us. She seems to think that the whole world rightfully belongs to _her_."
"Not while _I'm_ around, she won't," Veltan declared. "If she even tries to usurp any part of my domain, I'll tie all six of her legs into a knot so tight that it'll take her years to get unraveled."
"Can we watch, baby brother?" Zelana asked with some show of enthusiasm.
"Feel free, big sister," Veltan replied. "If the Vlagh comes south, I'll climb all over her."
Ara smiled. The memories Omago had planted in the minds of these newly created godlings had convinced them that they'd been around for eons and eons instead of just the few minutes that they'd _really_ been here. "Everything seems to be working the way we want it to, dear heart." She sent her thought to her mate. "The false memories you gave them are firmly in place. Do you think we should make the younger ones as well right now?"
"We don't really need them right now, Ara," Omago replied.
"When do you think we should start making their worshipers?"
"Let's hold off on that for a while," Omago said. "I think these elders will need some time to adjust before we make the ordinaries who'll worship them. There are enough animals here to make these elders know that they aren't the only life-form in this world."
"Are we pretty much finished here?" Ara asked.
"I think so, yes."
"Maybe we should drift around and have a look at the other lands on this world," Ara suggested. "If there are people in _those_ lands, we might need people here as well."
"Let's go look then," Omago agreed.
Omago was more than a little reluctant to set his body aside and revert to awareness only when they left the Land of Dhrall to look at the other lands.
"It's much, much faster, dear heart," Ara advised. "There are several limits involved if you drag your body along. All we need to do is look, and our awareness can take care of that."
"It just seems so unnatural to do it that way," Omago complained.
"What's 'natural' got to do with anything?" Ara demanded. "You and I are from another time and place, so the rules of _this_ time and place don't apply to us. Just try it, Omago. I've done this before, remember? There are—or may be—things we need to know before we make any decisions, so let's get on with it."
"All right." Omago surrendered.
Ara smiled. "See? That wasn't too hard at all, was it?"
They separated their awareness from their bodies and crossed the rolling sea lying to the west of the Land of Dhrall.
"Is that what I think it is?" Omago's thought silently asked.
"Where?" Ara asked.
"Right at the edge of the water," Omago replied. "I don't think it's an animal of any kind."
"It's standing on its hind legs," Ara agreed, "and it _does_ have hands. I don't think any animals have hands. What's it doing down there?"
"I think it might be trying to kill a fish-creature," Omago replied. "That's probably why it's carrying that long, pointed stick. It's probably hungry, but very primitive. Let's move on, dear heart. There might be more advanced people in other lands. If they're all as primitive as this one, I think we can hold off on providing the gods of the Land of Dhrall with worshipers."
They drifted on down toward the south, and when they reached the land beyond the sea, they saw a fair number of collections of what appeared to be rude huts.
"Shelters," Omago surmised. "Protection from bad weather. If they're intelligent enough to build things like that, they almost have to be people."
"And that smoke says that they've discovered fire," Ara added. "They may have found out that fire will protect them from cold weather." Then she peered down at a fair-sized collection of huts. "What in the world is _that_ one doing?" she demanded. "It appears to be a female, and it's got part of some other animal propped up over an open fire."
"It smells quite interesting," Omago added. "I'd say that the she-thing found a way to make animal flesh taste better."
"Now _that's_ something that never occurred to me," Ara said. "Raw meat would probably taste a lot like blood." She considered the notion and decided to try it when they returned to the Land of Dhrall. "I know that you'd rather wait a while before we made worshipers for the gods we've already created, but if the Vlagh tries to usurp the Land of Dhrall, we're going to need people. The gods we just created aren't permitted to kill, but it seems that people don't have that kind of restriction. They might not want to _eat_ the children of the Vlagh, but killing doesn't _always_ involve eating."
"I think you're right, dear heart," Omago agreed. "I thought it might be best to wait a while before we introduced worshipers, but that might have been a serious mistake."
They drifted on farther to the south and saw that the people of that area ate roots and berries and other forms of plant life as well as animal flesh.
Ara was quite certain that they should create man-things as well as gods to inhabit the Land of Dhrall, and, unlike the gods, the man-things would need food. Raw food would keep the man-things alive, but food that had been placed in the vicinity of fire would almost certainly taste better.
That thought alone opened all kinds of doors for Ara.
[THE
VISITOR](YoungerGods_toc.html#part_16)
**1**
It was bitterly cold at the head of Long-Pass, and even the shaggy bison-hide robes Chief Tlantar Two-Hands of the Matan Nation had provided us didn't entirely keep the chill away. I'd found a fairly well protected place in Gunda's fort, and after the sun had gone down and I'd finished eating supper, I decided that it might not be a bad time to catch up on my sleep. The Malavi had held back the Creatures of the Wasteland, so there was nothing much for me to do, and, though I wouldn't admit it to my outlander friends, the days and days of running down along that tired old mountain range and through Long-Pass itself had taken a lot out of me. Evidently, the years were catching up with me.
I drifted off to sleep, and, as had been happening more and more frequently here lately, I had a dream of the time when I was very young and I was living in the lodge of Chief Old-Bear. In those days the only thing on my mind had been Misty-Water, Old-Bear's beautiful daughter, and in my dreams I saw her again and again, and just the sight of her made me go weak all over. Even when I was asleep and dreaming, I knew that one day something would happen that would come very close to destroying me. I always pushed that aside, though, and fixed my attention entirely on my vision of she who would one day be my mate.
"Wilt thou hear me, brave warrior?" the now familiar voice of my "unknown friend" reached out to me. I knew who she really was now, but just her interruption of my dream irritated me.
"Now what?" I demanded harshly.
"Be nice," she scolded me.
"I'm sorry," I apologized. "I had something else on my mind just now. Was there something you wanted to tell me?"
"Nay," she replied. "I come to thee to ask, not to tell."
"That's unusual. Is there a problem of some kind?"
"One whom thou dost know quite well hath done that he was not supposed to do as yet."
"I suppose you could spank him and send him to bed without any supper," I suggested. She still had me a bit irritated.
"I don't find that particularly amusing, Longbow," she told me, lapsing out of her antique formality. Her familiar voice confirmed what I had come to realize back at Mount Shrak.
"I'm sorry," I apologized. "Just exactly was it that this friend of ours did that he was not supposed to do?"
"He dreamed," she retorted, and her irritation was fairly obvious.
"One of _those_ dreams?"
"Not exactly, no. He didn't cause a flood or set fire to a mountain as the children do. He reached back instead and discovered his _true_ identity. He's not supposed to do that yet."
"And why is that?"
"You don't need to know that, Longbow."
I shrugged. "Then I guess I won't need to talk with him. Those are the rules, unknown friend. If you don't talk to me, I won't talk to Omago."
"How did you know—" She left it hanging.
"You're fairly obvious, Ara. Omago's your mate, and that's why you're so upset. Why is it that Omago's not supposed to know who he really is?" Then something came to me. "You two have been mated since the beginning of time, haven't you?"
" _Before_ the beginning of time, actually," she replied. "Time began when we both said 'now' at the same moment. That's when everything started—and _that_ lay at the core of Omago's dream, and he's not supposed to know about it yet. That was the whole idea behind what he was trying to accomplish. We needed to know about the _true_ nature of you man-things, so Omago blotted out all his memories of the past so that he could live the life of an ordinary man-thing. But now he's sneaking around things he's not supposed to know about. Curiosity is one of his great failings."
"Just exactly when was it when you two ordered time to begin? I mean, how many years?"
"There's no word for that number, Longbow. A million millions doesn't even come close."
"Just exactly what was happening back then that you two found so important?"
"It was when the universe began."
"The universe has always been there, hasn't it?"
She shook her head. "There wasn't _anything_ back then. Not even Omago and I existed in our present forms. We were awareness only, and it took us a long, long time to even find each other. We can talk about that some other day. The important thing right now is that one of our children will try to do something that's forbidden, and she will cease to exist when she does that. I fear that Omago will not be able to bear her obliteration."
"We're talking about Aracia here, aren't we?"
"I did not say that."
"You didn't have to. It _is_ fairly obvious, you know." Then I suddenly saw where this was going. "She's going to try to kill the little girl named Lillabeth, isn't she?"
"I do fear that you are correct."
"She can't _do_ that!"
"I know, and her attempt will obliterate her." There was a kind of agony in her voice.
"Can't you stop her? As far as I can determine, there's nothing that you _can't_ do."
"That's in the world of things, dear Longbow. I can't do that in the world of thought. When Aracia tries to destroy Lillabeth—or Enalla, actually—she'll step over the forbidden line."
"And she'll die?"
"She _can't_ die, Longbow. She'll just cease to exist."
"Isn't that what dying means?"
"No. It goes quite a bit farther."
"And it's _that_ you're afraid of, isn't it, Ara?"
"How did _you_ come to know who I am?"
"You're extremely upset, so you've been letting some things slip. I probably should have realized that from the very beginning. You _are_ Aracia's mother, after all, and just the thought of her obliteration is tearing pieces out of your heart."
"I think that maybe it's _Dahlaine_ who needs a good spanking. His 'Dream' idea seems to be working quite well, but it appears that it's setting off some other Dreams that aren't supposed to happen just yet."
"Such as the one _I'm_ having right now?"
"This one's altogether different, my son."
"Maybe someday you'll get around to telling me just exactly _how_ it's different, Mother."
All right, it was a silly thing to say, but it was just too good an opportunity to let slip by. "Am I supposed to go to my room now?" I asked her.
"No. You're supposed to go to the place where Omago's sleeping and try to keep him from going all to pieces."
"I'll get right on it, Mother."
"Will you _stop_ that?" she flared.
"Anything you say, Ara."
[BE
NO
MORE](YoungerGods_toc.html#part_17)
**1**
Your presence there should conceal Enalla and me from Aracia, Little-Me," Balacenia told me while we drifted through the chill air above Aracia's silly temple.
"I'm not sure that I follow you, Big-Me," I told her. "If everybody's right, the Beloved's older sister has had her mind turned off by the bug-woman they call Alcevan. If her mind isn't there anymore, she won't recognize anybody, will she?"
"That's one of the things we need to find out, Eleria," Big-Me replied. "If Aracia's mind is still working to some degree, we _might_ be able to pull her out of Alcevan's grasp."
"I wouldn't get my hopes up too much, Big-Me," I told her. "That stink Alcevan's using on Aracia is probably about the same as the one that showed up in Tonthakan in Dahlaine's part of the world. If we had Ox and his war-axe here, he could probably solve the problem for us."
Big-Me shook her head. "The others and I have talked it over already," she said. "Alcevan could very well turn out to be the key that'll lock the Vlagh away permanently, so we don't want anybody to kill her just yet."
"Why not just send for Veltan?" I asked. "If he took the Vlagh to the moon and left her there, she'd never be able to come back, would she?"
"I'm not sure that Veltan could do that, Eleria. That might step over the line that we don't want Aracia to cross. We all love Veltan too much to take any chances."
"Just what do you want me to do, Balacenia?" I asked her.
"What happened to 'Big-Me'?" she asked with a faint smile.
"There's nothing wrong with 'Balacenia,'" I told her. "It's a very pretty name, and I like to use it every now and then when I'm talking with you. Just what do you want me to do?"
"Why don't you just tell Enalla—who'll appear to be Lillabeth—the stories about the pink dolphins you played with when you were younger?" She paused. "You _do_ know that it was the time you spent with those dolphins that separated us so much that we'll probably never be able to merge again, don't you?"
"The Beloved didn't mention it," I replied, "but I'd more or less come to realize it myself. Don't worry about it so much, Big-Me. We might not be such a bad thing, you know. There will be two of us during the next cycle, so we'll be able to get a lot more done. Don't forget that Longbow's _mine_ , though."
"You love him, don't you?"
"Of course. I think we all love Longbow, don't we?"
Balacenia sighed. "We may all love him, but _you're_ the one who owns him."
"I wouldn't say 'owns.' Nobody owns Longbow. I think that if we got right down to it, we'd find that _he_ owns _us_. I wouldn't let my hope of pulling Aracia back to normal build up too much, Big-Me. You don't have to mention this to the others, but I'm almost positive that we've lost Aracia permanently. Little Stinky has her pretty much tied down."
"Stinky?" Big-Me said with a little laugh. "That _does_ identify Alcevan, doesn't it? You're absolutely perfect, Little-Me."
"I don't know about 'perfect,' Big-Me. I _do_ have my share of faults, you know. Anyway, 'Stinky' sort of came to me from nowhere, and I scraped it off the wall. Sometimes I have trouble finding the right word when I'm using people-talk. I still speak—and think—in the language of the pink dolphins." I paused, as I almost always do. Then I said, "Isn't that neat?"
And Big-Me broke down and laughed.
Balacenia sort of faded out of sight as we drifted down through the shabby roof of Aracia's poorly constructed temple. I could still sense her presence, but she wasn't visible anymore. Enalla was sitting in Lillabeth's ornate room, and she looked so much like Lillabeth that she even startled me. I had met Lillabeth during the war in the Beloved's Domain last spring, and I'd joined her during our joint recitation of her Dream—to the great chagrin of Aracia, who'd been desperately trying to hide that Dream—so even though I knew that she was really Enalla, I felt quite comfortable with her.
"We _are_ the same person, Eleria," Lillabeth's other personality reminded me in a voice that was a bit more mature than Lillabeth's. "We're much the same as you and Balacenia are."
"Not entirely, sister," Balacenia's voice told her. "Eleria here spent most of her time with the pink dolphins during her early childhood, and I'm afraid that the dolphins permanently separated us."
"Why did Zelana permit that?" Enalla demanded.
"The Beloved had her mind on music and poetry," I explained. "She was very fond of the pink dolphins, and after Dahlaine dropped me in her lap, she knew that somebody—or some _thing_ —would have to nurse me. That's when she turned to Meeleamee."
"Dolphins have names?" Enalla asked, sounding a bit startled.
"Oh, yes," I replied, "and they also have a language. The Beloved speaks their language, so she could call out to Meeleamee when she discovered that I couldn't live on just light the way she does. Meeleamee nursed me, and in some sense she was the mother I never had."
"Aracia just handed me off to a fair number of local women to nurse me," Enalla said. "I never grew as close to any of them as you did to Meeleamee. They nursed me, but I never grew attached to any of them."
"That's probably what kept you from having any fun when you were a baby. The pink dolphins seemed to think that teaching me how to swim was almost as important as nursing me was. I could swim like a fish long before I learned how to walk."
"Why don't you tell me all kinds of stories about your pink dolphins, Eleria?" Enalla whispered. "Balacenia and I are fairly sure that might persuade Aracia that we're just an empty-headed pair of little girls." Then she spoke louder. "How in the world could a baby possibly learn how to swim?" she asked as if she was terribly interested.
"It's not really all that difficult, Lillabeth," I replied. "Meeleamee wasn't the only female dolphin who was nursing me. There were many others as well, and more of them turned up in that pond inside the grotto when they heard that I was rewarding the ones that nursed me with kisses."
"So _that's_ where you picked up your kiss-kiss habit," Enalla said. "I've always wondered about that."
"I found out early that kisses and hugs will get you almost anything you want, Lillabeth," I told her. "I kissed Longbow into submission in about five minutes. Anyway, the pink dolphins began to herd fish into the grotto so that I could learn how to feed myself. Once a baby starts to grow teeth, nursing the child can start to be quite painful. Dolphins are sea-animals, so they live on a steady diet of fish. They started to give me bits and pieces of fish, and after a while they decided to teach me how to catch fish by myself. They were all very pleased when I caught and ate my very first fish."
"I've noticed that there aren't any fires in Zelana's grotto. How were you able to cook the fish you were eating?"
I shrugged. "I didn't cook them. It might be a little hard to keep a fire burning if it's under water."
"Are you saying that you ate those fish _raw_?"
"Of course. That's one of the reasons Meeleamee and the others gave me pieces of raw fish when they were weaning me off a steady diet of dolphin milk. I was _so_ proud when I caught and ate my first fish in the little shallow pool at the mouth of the grotto. The fishing was much better out in deep water, though, so I didn't miss too many meals."
"Are you saying that Zelana approved?"
"The Beloved doesn't eat anything at all—except for light, of course, so she turned the feeding over to the dolphins."
"I've always been curious about just why you always call her 'the Beloved.'"
"That's what the dolphins called her. I picked it up from them, but I used _her_ language instead of theirs. Of course that's fairly recent. I spoke 'dolphin' long before I learned how to speak in 'people.' I didn't care _too_ much for the name they gave me, though. They called me 'Beeweeabee,' which translates into 'Short-Fin-With-No-Tail.' I was much happier when the Beloved named me Eleria. I still swam with the dolphins when I got hungry. And then one day Meeleamee introduced me to an old cow-whale—who probably wasn't a whale at all—and she led me on down to the bottom of the sea where an oyster opened its shell and gave me the pink pearl that started to give me Dreams as soon as I rejoined the Beloved in her pink grotto."
"Zelana mentioned that," Enalla-Lillabeth said. "Did that first Dream you had go all the way back to the beginning of the world?"
"That's what the Beloved told me," I said. "From what I saw in the Dream, the whole world was on fire."
"I wouldn't take it any further back, Little-Me." Balacenia's voice came silently to me. "If Aracia happens to still be listening, we don't want her to know where—and when—your Dream _really_ began."
"How did _you_ know about that?" I demanded.
"Eleria," Balacenia's silent voice came to me again, "we _are_ the same person, you know, so _I_ can remember your Dream as well as you can. I remember that when your Dream began, the universe wasn't there, and neither was time."
"Then you saw Mother and Father too?"
"Of course I did, Little-Me."
I felt just a little pouty about that. I'd always believed that the earliest part of the Dream was mine alone—something on the order of a gift from Mother and Father because I was their favorite child. Big-Me had just filched my gift, and I didn't like that one little bit.
"We'll talk about that some other time, Little-Me," Balacenia said. "We _don't_ want Aracia to find out about it. She'll do something even _more_ stupid if she knows the whole story of the Dream. Let Enalla-Lillabeth talk for a while now. Ask them about life here in this silly temple. That should draw Aracia's attention away from _your_ Dream. Let's stay on the safe side."
"Sometimes it almost made me want to throw up," Lillabeth told me. "Fat Bersla could go on for hours and hours telling Aracia how wonderful she is. It made me sick to my stomach, but Aracia just couldn't get enough of it. She adores being adored, so those speeches were meat and drink. She didn't seem to realize that he was waving what he called his adoration in her face every chance he got for one reason and one only. As long as she hungered for what he called his adoration, he didn't have to do any honest work, and not working has always been Fat Bersla's main goal in life."
Then Big-Me spoke silently to Enalla. "Don't get _too_ specific, dear sister," she said. "Alcevan the bug might be listening, and her purpose right now is persuading Aracia to kill Lillabeth—and you, of course. The bug-people _really_ want Aracia to live—or stay awake—for a while longer, because they can control her. I'm quite sure they know that they won't have that kind of control of you, and that's why they want Aracia to kill you."
"Then they don't know about what will happen to Aracia if she even tries to do that, do they?"
"It's not one of those things we mention very often," Big-Me replied.
"There is _one_ thing that I don't quite understand," Enalla admitted. "So far as I can determine, Alcevan is the only female priest in Aracia's Domain. How did she manage to foist that off on dear old Bersla?"
"Dear old 'Stinky' probably used her gift to pull it off," Big-Me replied.
"Stinky?" Enalla silently asked, trying quite hard to keep from laughing.
"That's what Little-Me calls her," Balacenia replied. "She _does_ use an odor to control people, and that's probably how she pulled Fat Bersla into line." Then she paused. "I'm not entirely positive that she actually stinks terribly, but just that name alone takes her down a peg or two, wouldn't you say?"
"I think I'll keep that name tucked under my arm," Enalla said. "It might be very useful at some time in the not-too-distant future." Then she sighed. "I was fairly sure that Sorgan Hook-Beak's deception had brought Aracia to her senses. You wouldn't _believe_ the look of pure horror on Bersla's face when Aracia ordered him—and all the other priests—to go on down to the south wall of the temple to help construct the stronger defenses. How did Stinky manage to escape and come back here and steal Aracia from us again?"
"She went out over the wall and came back here out on open ground," Big-Me replied. "She'd been trying to send novice priests back here to murder Lillabeth—in much the same way she tried before Aracia ordered her to go down to the south wall."
"Are you saying that there are novices out there so stupid that they'd believe her after she cut the throat of the first assassin she sent here to murder Lillabeth—or me?" Enalla demanded.
"I'd imagine that news of that killing didn't get around very much," Big-Me replied. "It wasn't as if Alcevan had left the body lying in the throne room or anything like that. Anyway, her plan fell apart after that clever little Maag called Rabbit came up with a way to make just about everybody too terrified to even _think_ about coming back here through the corridors."
"Oh?"
"He managed to make everybody believe that there were giant spiders creeping around in the corridors, and that being killed—and eaten—by a spider is the most hideous fate in all the world."
"Even worse than snake-bites?"
"Much, much worse, dear sister," Big-Me declared. "Nobody—and I _do_ mean _nobody_ —would even consider taking that kind of a chance, no matter what kind of reward has been offered."
"Why don't we just send for Longbow, Big-Me?" I suggested. "He could kill Stinky from so far away that her odor wouldn't reach him."
"That might just be the best idea of all, Balacenia," Enalla said. "Once we get rid of Stinky, Aracia should return to good sense."
"Except that Longbow's involved in the war up in Long-Pass," Big-Me replied. "I'm afraid that Stinky is _our_ problem, and we'd better solve it very soon."
**2**
"I think it's time for you to go to sleep, child Eleria," Mother's voice came to me.
"You said _what_?" I demanded.
"You're going to have to Dream, Eleria. That's probably the only way we'll be able to prevent Aracia from destroying herself—and I'm not sure even _that_ will be enough. Alcevan has warped Aracia's mind to the point she thinks that she's immune to what's almost certain to be the result of her attempt to obliterate Lillabeth. I'm hoping that your Dream will bring her back to her senses."
"You want me to pretend that I'm asleep and then tell her a story so awful that she won't _dare_ to try to kill Lillabeth?"
"Drop 'pretend,' Eleria," Mother told me. "You _will_ be asleep, and you _will_ have a Dream. Then you and Enalla—who _appears_ to be Lillabeth—will recite the Dream in unison, in the same way that you and Lillabeth did last autumn. Aracia _knows_ that the Dreams have power far beyond anything she can do, and your Dream _should_ frighten her enough to make her reconsider Alcevan's suggestion."
"What if it doesn't?"
"We'll lose Aracia," Mother bluntly replied, "and I'm not sure what the result will be."
I knew that I was asleep. That's one of the things that separates "those" Dreams from ordinary ones. The Dream that Mother provided was moderately terrible, and I was fairly sure that it would give Aracia some second thoughts.
But it didn't turn out that way. Aracia—or Alcevan, the bug—was already ahead of us. The door to Lillabeth's nursery banged open, and Aracia, wild-eyed with fury and with her hair tangled and sticking out in all directions, burst into the room. She was screaming what sounded much like curses in a hoarse voice. Little Stinky was right behind her with an expression of victory on her face.
"I have Dreamed." Lillabeth, who was really Enalla, and I began to recite the content of the Dream Mother had given me, but I saw almost immediately that Aracia wasn't even listening. I suppose that it's possible that Alcevan the bug had turned her ears off.
"Foul usurper!" Aracia screamed at the child she thought was Lillabeth. "Violator of my temple! I have cared for thee with all my heart, but thy first act when I have gone to my sleep will be to betray me. Know ye that thou shall _not_ have this temple, nor the worship of those who serve me, for I must banish thee now and forever from the world of the living, wicked child. Be no more, wicked Lillabeth!" Aracia screamed. "Exist no longer!"
For about a moment she stood in one place as if she had just been frozen, and then, as my Dream had predicted, she gradually began to change from what appeared to be human into tiny speckles of light—even as she had in my Dream. Her outward shape didn't seem to change, but it now consisted of those specks of light. I was quite sure that Big-Me and Enalla had simply turned her command around and thrown it back at her, but the more I thought about it, the more I realized that her command had turned on her all by itself. Had Enalla and I been allowed to describe my Dream, would that have saved Aracia? I do not know. If killing is forbidden, telling someone—or something—to die, _might_ just destroy the speaker rather than the intended victim. From what I could make out of Aracia's face, she had an expression of sheer horror on what passed for her face. Then her face was gone, and the specks of light grew brighter and brighter. Then there was an enormous burst of pure light, and Aracia wasn't there anymore.
Alcevan howled in frustration, and then she fled as Lillabeth began to weep and moan in her grief. Enalla was standing with Big-Me near the door, so poor Lillabeth was suffering her grief all by herself. I took her in my arms and held her. It wasn't really all that much in the way of comforting her in her time of sorrow, but it was the best I could come up with.
Lillabeth was still weeping when Veltan came rushing into the room. "What was that awful noise just now?" he demanded.
I wasn't feeling very kindly toward _anybody_ just then, so I answered Veltan's stupid question in a cold, blunt tone of voice. "Your sister just destroyed herself. She came in raving and with Stinky right behind her. Then she commanded Lillabeth to be no more. Since that's forbidden, her curse—or whatever you want to call it—turned and flew right back into her face, and she suddenly turned into little speckles of very bright light. The speckles grew brighter and brighter, and then there was a huge burst of pure light, and your sister wasn't there anymore." I had decided _not_ to reveal my involvement to any members of the family. If Mother wanted to tell them, that was up to her, but I chose to keep my mouth shut.
Veltan went suddenly very pale, and then he also began to weep as his sorrow overwhelmed him.
Then Mother suddenly appeared. "What's going on here?" she demanded—as if she didn't know.
"Aracia came here with that bug-thing that calls herself Alcevan right behind her," I replied. "I'd say that Alcevan turned her odor loose and persuaded Aracia to try to destroy Lillabeth. I couldn't prove that Alcevan was responsible, but she _was_ there, and Aracia ignored a very important rule and ordered Lillabeth to dissolve—or something like that—but her order turned around and dissolved her instead. I'm afraid you just lost one of your babies, Mother, and there isn't enough of Aracia left to even try to bury."
Mother touched her finger to her lips and then gave me a very stern look to keep Veltan and the others in the room from finding out what had _really_ happened. Then she spoke in that voice she uses to reach out to her assorted children. "Dahlaine," she said, "and Zelana. We've got a crisis here in Aracia's silly temple. You'd better come here as fast as you can, and bring the children."
Lillabeth was still weeping when the others joined us in her room, and I was still doing my best to comfort her. But then, at Mother's suggestion, I'm sure, Enalla took Lillabeth into _her_ arms, and Mother told me to repeat the story of Aracia's self-destruction for the others.
"It's better without her," Vash of Veltan's Domain declared.
"No, Vash," Big-Me disagreed. "Actually, it's worse. We're one god light now, and that throws everything out of balance. If we don't do something to correct that, it won't be long, I'm afraid, before we'll all be joining her."
"Don't be absurd, Balacenia," Mother told Big-Me. "All you have to do is replace her."
"With who?" Enalla, still holding Lillabeth in her arms, demanded. Then she turned to speak to Dahlaine. "You'd better come up with something very soon, big brother, or we'll _all_ be turning into gleaming dust."
Mother, quite naturally, was about three jumps ahead of Enalla—and all the rest of us as well. "The answer is really very simple, dear Enalla," she said. Then she smiled at me. "You'll have plenty of time to get used to the idea, Eleria," she told me. "It's going to be twenty-five eons before you'll have to take Aracia's place as the goddess of the East. Your childhood with the pink dolphins has separated you from Balacenia—or 'Big-Me'—so much that you aren't the same anymore. That leaves you floating around with nothing to do, so _you'll_ replace poor Aracia." She paused a moment and then threw my own favorite remark right back in my face. "Won't that be neat?" she demanded.
[THE
DECLINE
OF THE
TEMPLE](YoungerGods_toc.html#part_18)
**1**
Sorgan Hook-Beak of the Land of Maag was sleeping in his imitation fort that night. He'd have much preferred sleeping on the _Ascension_ out in the harbor, but it _was_ fairly essential for him to keep up the pretense of the mock invasion of the bug-people, and sleeping on board a ship out in the harbor _might_ just make Lady Aracia more than a little suspicious. Now that she'd come to her senses and ordered all of her fat, lazy priests to help build the defensive walls around her temple, staying on the good side of her _was_ fairly important.
It was just after midnight, as closely as Sorgan could determine, when cousin Torl came into Sorgan's room, accompanied by Lady Zelana's Dreamer, Eleria.
"What are you two doing running around at night like this?" Sorgan demanded.
"Lady Zelana told me to bring the little girl here so that she can tell you something that _might_ be fairly important, cousin," Torl replied.
"What is it now?" Sorgan grumbled.
Eleria gave him a little smirk. "The Beloved thought that you ought to know that the lady who hired you isn't around anymore."
"Where did she go?"
"That's a little hard to say, Captain Hook-Big," Eleria replied. "She broke one of the rules, and she went poof."
"Poof?"
"That's about as close as I can come to describing what happened. She came into Lillabeth's room and commanded her to 'be-no-more,' but now _she's_ the one who no longer exists."
"Who did it? I mean, who ordered her to stop being alive?"
"She did—all by herself. I think it's built into the gods. They're not allowed to kill things, so when one of them tries to do that, it comes back and hits them right in the face. Didn't the Beloved explain that to you when you first came here to work for her?"
Sorgan blinked as a horrid possibility crashed in on him. "My gold!" he exclaimed. "Did _that_ all go 'poof' when she did?"
"I sort of doubt that, Hook-Big," Eleria replied. "The temple's still there, so the gold probably is as well. You could go look, I suppose, but we've got something else to worry about now."
"What's happening?" Sorgan demanded.
"There are a lot of people in the temple who just lost their god. I don't think it's going to be much longer before a war breaks out. Now that Aracia isn't around to tell them to behave, things are probably going to get a little messy in the temple. I think you'd better send somebody down there to keep an eye on things."
"And to find the storeroom where Aracia kept all her gold," Sorgan muttered to himself. That could wait, though. He turned to look at cousin Torl. "Did that young Trogite Keselo leave the harbor yet?" he asked.
"I doubt it," Torl replied. "It was almost dark when he went out to the _Ascension_. He'll probably go north again when daylight comes along."
"Good," Sorgan said with a certain relief. "Go on out to the _Ascension_ and tell Keselo what just happened here. We _definitely_ want Narasan to know about it, so as soon as Keselo reaches Long-Pass, he'd better climb up on his horse and go up the pass to whatever fort Narasan's holed up in and tell him that Lady Zelana's sister isn't around anymore."
"Sound thinking, cousin," Torl agreed.
"I'm glad you liked it. Then I want you to nose around in the temple and see what's going on there—and see if you can locate the strong-room where Aracia kept all of her gold. She doesn't need it anymore, but _we_ do."
"I'll see what I can find, cousin," Torl replied. Then he took Eleria by the hand, and the two of them went back toward the main temple.
Sorgan gave some thought to Eleria's warning. The priests of the temple didn't really pose much of a threat, but there was no point in taking any chances. He went to the chamber where Ox and Ham-Hand slept and woke them up.
"What's afoot, Cap'n?" Ox asked.
"We just got a nasty surprise," Sorgan told him. "It seems that Lady Aracia lost her grip on things again—probably because that little priestess—who's really a bug—turned that smell loose on her the way she did before, and Lady Aracia went crazy. She rushed into the room where her Dreamer lived and ordered her to stop living. I guess that's against all the rules, so Aracia's not around anymore."
"She just fell over dead?" Ham-Hand asked.
"From what Eleria said—and she was there—there wasn't enough of Aracia left to fall over. Eleria used the word 'poof' to describe what happened. I guess Aracia's body just faded away, and it was replaced by little speckles of light. Then the light went out, and there wasn't anything called Aracia anymore. That probably sent all those fat, lazy priests right straight up the wall. When they come down, they'll start scheming against each other, and the 'holy temple' is very likely to be ankle-deep in blood."
"What a shame," Ox said.
"Isn't it, though?" Sorgan agreed. "We don't want them out here, though, so take some sizeable parties of men along the corridors that lead to the main temple and block them off."
"We've already been paid, Cap'n," Ham-Hand said. "Why don't we just take that money and run?"
"Because there's probably a lot _more_ money piled up somewhere in the main temple. I'm not about to just walk away and leave it behind. My cousin Torl's in the main temple right now to see what's _really_ happening there, and in his spare time, he's checking every room in that part of the temple for gold. Once he finds it, we're all going to become very, very rich."
Torl came back out to the fort a couple days later, and he had a peculiar expression on his face when he entered Sorgan's chamber.
"Are we having a problem, cousin?" Sorgan asked him.
"You wouldn't _believe_ what's going on in that main temple, cousin," Torl replied. "Those people have all gone crazy."
"Exactly what do you mean by 'crazy,' cousin?" Sorgan asked.
"Right at first they were falling back on simple murders—all the usual ones like knife in the back, cutting throats, and bashing out brains with clubs or big rocks. They've been killing each other by the dozens. I'd say give it another day or so and there'll be open war over there. There's already a lot of blood splashed on the walls, but there'll probably be an ocean of blood when they move on to a full-scale war."
"Were you able to locate Aracia's gold-room?"
"Not yet. I came back out here to warn you that things are very dangerous in that part of the temple."
"I appreciate that, Torl. I've already got men blocking off every corridor that leads to the main temple."
"Good thinking, Sorgan. Have you heard anything from Veltan yet?"
"Not a word. I'd say that he's got a family emergency on his hands right now. His older sister just vanished—or just stopped being anyplace anymore, and that might bring down a whole lot of trouble. Get on back to the main temple, cousin, but watch your back. We _really_ want to find that gold storeroom. We're nailed down here until we locate it."
**2**
It was about mid-morning on the following day when the fat priest called Bersla came around the outer wall of the temple to Sorgan's makeshift fort. Sorgan was just a bit surprised by the fact that Bersla was traveling alone. If the oarsman Platch had been right, Bersla never went anywhere all by himself.
"Well, now," Sorgan called from the outer wall of his makeshift fort, "if it isn't Holy Takal Bersla. Does Lady Aracia want to talk with me about something?" He watched the Fat Man closely, and, as he'd more or less anticipated, Bersla's face suddenly went very pale. Then he pulled himself together. "I speak for Holy Aracia in a matter of some urgency, mighty Sorgan. It would appear that the foul servants of That-Called-the-Vlagh have infiltrated the Holy Temple, and even as we speak, they are creeping about with murder only on their minds. Now, I, of course, would be more than willing to face the foul servants of the Vlagh alone, but Holy Aracia has commanded me to speak with you."
"I'll be more than willing to listen, Takal Bersla," Sorgan declared. "Let's keep this sort of to ourselves, though. One of my men at the gate will show you the way to my quarters, and I'll meet you there."
Sorgan was rubbing his hands together as he went down the narrow flight of stairs toward the central yard of his fort. If anybody in the whole temple would know exactly where Aracia's gold was hidden, it would be Fat Bersla.
He went into the room where he usually slept, and a few minutes later a burly Maag escorted the priest into Sorgan's room. After the sailor had left, Sorgan squinted at the priest. "I hadn't heard that the bug-people had managed to get inside the temple, and I've got men watching just about every square foot of the place. How did they manage to get past my people?"
Bersla floundered for a moment, and then he said, "Tunnels, I've been told. As I understand it, these creatures can chew their way through solid rock."
"Indeed they can, Takal," Sorgan replied. "During the first war off to the west in Lady Zelana's Domain, thousands of bug-people came swarming up out of tunnels that'd taken them centuries to chew through solid rock. Tunnels are the most effective way to get under walls and buildings without being seen. Now, then, let's get something out of the way right now. These sneaking bugs aren't spiders, are they? If I even mention the word 'spider,' I'll be lucky to have a dozen men left by morning."
Bersla looked a bit startled. "I'm sure they aren't spider-bugs. Spiders have eight legs, don't they?"
"That's what I've been told," Sorgan replied.
"We're safe, then. The bugs crawling through the tunnels under the temple have six legs, not eight."
"That's a relief. Now, then, how are we going to go about this? If I put several thousand men in the temple hallways, they should be able to push the bugs off balance."
"You are the warrior, mighty Sorgan," Bersla replied. "I know little or nothing of such things."
"All right, then," Sorgan said. "How much will you pay me to keep you alive?"
"I know very little about money, brave Sorgan," Bersla admitted. "I do, however, have access to many blocks of the yellow metal your people call gold."
"There's the answer right there, Takal Bersla," Sorgan said. "Each evening when you're still alive, give one of those blocks to my cousin Torl. One is an easy number to remember, so neither one of us will be confused. Let's start with a couple dozen of my men. If Torl thinks that won't be enough, I'll send more to guard you."
Bersla heaved a huge sigh of relief, and his hands almost stopped trembling.
"I'll send an escort with you back to the main temple, Takal," Sorgan said. "You won't have to go back outside the walls now. I've got men blocking off the corridors, but they'll let you pass. After all, you and I are friends now, aren't we?"
"Indeed we are, mighty warrior," Bersla declared. "Indeed we are."
Sorgan probably should not have been particularly surprised the next morning when the tiny priestess Alcevan came out to the fort with a request that was almost identical to the one Takal Bersla had made the previous afternoon. At least, unlike Bersla, she didn't try to foist on Sorgan an absurdity about bug-people creeping through tunnels as Bersla had. "The Church of Divine Aracia is now divided, Captain Hook-Beak," she declared. "The one who elevated himself to 'High Priest' believes that he alone can speak for Holy Aracia, and he has dispatched assassins to murder those of us who know full-well that his self-aggrandizement did _not_ come from Holy Aracia. Since I live only to serve her, Bersla has commanded his henchmen to concentrate on _me_ in advance of all others, for I am the _true_ leader of the clergy in Aracia's holy temple. I can _not_ permit him to usurp my position. So I must be protected from Bersla's villains. I will pay you much to defend me. Name your price, and gladly will I pay."
"Oh, I don't know," Sorgan said. "How does one gold block a day sound to you?"
"Most reasonable, Captain Hook-Beak. Should I send the gold here?"
"Those corridors aren't really safe, Priestess," Sorgan replied. "My cousin Torl will be right there in the temple. Why don't you just give him one of those gold blocks every morning? Torl _loves_ gold, so he won't let anything happen to the lady who gives him a gold block every morning at breakfast time."
"It shall be as you have requested, mighty Sorgan," the tiny priestess agreed.
It was all Sorgan could do to keep from laughing out loud. There were two people in the temple who hated each other with a passion, and now they were _both_ paying Sorgan a block of gold every day to protect them from each other.
It was about noon two days later when Torl came back out to Sorgan's imitation fort with four blocks of gold. "I can't for the life of me find out where the treasure-room is located, cousin," he declared. "Bersla and Alcevan never leave that throne room but morning and evening, one of them hands me one of these gold blocks."
"The pay's very good, cousin," Sorgan said. "And the work's not really very hard." Then he frowned. "The only drawback is how long it's likely to take us to empty out the treasure-rooms—assuming, of course, that they're each filching these blocks from a different room. For all we know, they could both be taking the blocks out of the same room."
"If that's the case, that room _will_ get emptied eventually."
"That's all right with me, Torl," Sorgan said. "One day with no pay, and we're out of here."
"They probably _will_ kill each other as soon as we're gone, cousin," Torl said.
"And we'll both be terribly sad when that happens, won't we?" Sorgan suggested with a wicked grin.
"I don't really think that's going to break my heart, cousin," Torl replied. "It might bend it just a little, but I'm fairly sure it won't break."
"You _do_ have a fairly strong heart, cousin," Sorgan agreed.
Then they both laughed.
**3**
It was later that same day when Veltan came crashing in on his pet thunderbolt. As usual, the loud crash shook Sorgan right down to his toenails. "Where have you been?" he demanded of Lady Zelana's younger brother.
"We _did_ have a family emergency, Sorgan," Veltan replied.
"I know," Sorgan said. "What are you doing about it?"
"We haven't really decided yet. Is anything unusual going on down here?"
"I think it's called 'church politics,' Veltan," Sorgan replied, "which is a polite way of saying 'open war.' Takal Bersla and tiny little Alcevan are right on the verge of going all out. So far, all they've been doing is sending out murderers to kill off various members of the opposing side. Bersla and Alcevan both know that they're in mortal danger, so they've both hired _me_ to protect them. I've got men over in the main church keeping the churchies apart." Then he grinned. "Actually, this upcoming war has turned into a golden—and I _do_ mean 'golden'—opportunity for me. A while back Takal Bersla hired me to protect him, and the next morning teenie-weenie Alcevan came by, and she _also_ hired me. Each one of them pays me a gold block every day to keep them alive, so this is turning into a profitable little war for me. They hate each other all the way down to the ground, and I'm fairly sure that there are a couple of _other_ things they'd like for me to do, and they are almost certain to make me even more interesting offers before too many days go by."
"You're not _really_ going to get involved at that level, are you?"
"Of course not, Veltan. I will take the gold, though. Then I'll just take the money and run."
"That's terrible!" Veltan exclaimed.
"I know," Sorgan admitted. "Fun, though."
Torl came out to the fort a few days later to bring the loot to Sorgan. "I think you might want to take a fairly close look at these blocks, cousin," he said. "I _think_ I've found the gold-block warehouse. If you look at the blocks, you'll see that each one of them has quite a bit of sand ground in along one side."
"Why would anybody do _that_?" Sorgan demanded.
"It's a way to hide the gold, cousin. That coat of sand makes these gold blocks look like ordinary building blocks."
"Well, sort of, I suppose. What's the point of doing that, though?"
"It's a way to hide the gold. I _have_ found the place where Aracia kept all her gold."
"Well, _finally_!" Sorgan said. "Where is it?"
"In her throne room, cousin. Actually, Holy Aracia's throne room is walled in with solid gold that's been disguised to make it look like ordinary bricks. I scraped a few places with my knife when nobody was watching, and sure enough, every brick I scraped was actually a gold block."
"That throne room is enormous!" Sorgan exclaimed.
"It is indeed, cousin, and it's walled in with solid gold. I'd say that _one_ of Aracia's priests—possibly Takal Bersla—came up with the idea even before Narasan's Trogite army arrived here last autumn. We've spent days and days looking for the gold warehouse, and it's been right there in front of us every time we went into the throne room. We're going to need a _lot_ of ships to carry our gold when we leave this place."
Sorgan began to tremble violently. "I think I'd better go over there and have a close look," he said. "I don't think we've got enough ships in the whole Land of Dhrall to carry _that_ much gold, and I'm _not_ going to just sail away and leave most of it behind."
"It's safer here, cousin," Torl declared. "They won't know that we're in this hidden corridor, and quite some time ago I pried out a couple of ordinary stone blocks so that I could _see_ what they were doing in that silly throne room, as well as hear what they were saying to each other." He paused for a moment. "If I'd just reached in through the holes I'd made in this wall, I could have gathered up several dozen of those gold bricks."
"You missed your chance, Torl," Sorgan said with a faint smile. Then he peered through Torl's small opening. He was just a bit startled when he saw fat Takal Bersla sitting on Aracia's gold throne. "Isn't that pushing things just a bit?" he asked Torl. "Aracia's only been gone for a week or so, and now the Fat Man has sort of usurped her throne."
Torl shrugged. "At least it protects his back if somebody tries to kill him. Then, too, he almost certainly believes that he's going to come out the winner in this skirmish he's having with Alcevan."
"My fellow priests," Bersla declared in his oratorical voice, "dear Holy Aracia has gone forth to look upon the creatures who are currently invading this most holy of the four Domains of the Land of Dhrall. It is by her command that I have taken her place here. She has spoken to me, and only _I_ know what she wants."
"Over there, Sorgan," Torl whispered, pointing toward the far side of the throne room.
Sorgan peered across the room and saw a sizeable party of hooded priests coming through the main door of Aracia's throne room. They crossed the oversized room to the throne Bersla had usurped, and then they knelt down in seeming adoration—all of them except one. That one came forward with a tray heaped with exotic food.
"That's _one_ way to get the Fat Man's attention," Torl whispered.
"The _best_ way," Sorgan agreed softly.
Takal Bersla looked very pleased, and he eagerly reached out to take the overloaded tray. Then he began to take large bites of the assorted food heaped on the tray, and he wasn't paying much attention to the hooded ones kneeling before him.
Then the one who had given Bersla the tray pushed back the hood, and Sorgan was startled to see the small priestess Alcevan. With a look of triumph she opened her robe and pulled a broad dagger that was obviously of Maag origin out of her waist sash.
"Where did she get one of our daggers?" Torl exclaimed.
"Stole it, most likely," Sorgan replied. "She _is_ a bug, after all, and the bugs steal everything they can put their claws on."
Then Alcevan stood up and lunged directly at Fat Bersla, driving the dagger all the way to the hilt into the Fat Man's belly.
Bersla dropped the food he'd been wolfing down and screamed as he tried to wrest the dagger from the little priestess. Alcevan was obviously much stronger than she appeared to be. She pushed Bersla's hands out of her way and slowly ripped him up the middle with that very sharp dagger.
Bersla screamed, trying to hold in his intestines, which were spilling out of Alcevan's gash.
Several dozen of Bersla's followers rushed toward the throne, but the hooded ones who'd accompanied Alcevan met them with swords and spears. The followers of Bersla died by the dozens as Bersla, still screaming, clutched at his surging-out innards.
Alcevan had already moved on, however. She seized Bersla by the hair at the back of his head, pulled it, and then began to saw at his throat with the sharp dagger.
Bersla's screams suddenly stopped and huge amounts of blood came squirting out of the gash in his throat.
That _should_ have finished it, Sorgan believed, but Alcevan wasn't through yet. She continued to slash and saw at Bersla's neck until his head finally came free. Then Alcevan lifted Bersla's detached head by the hair. "Behold Divine Bersla!" she shouted. "Follow him if you choose, and you shall soon go with him to the house of the dead! Truly I say to you, _I_ now rule here in the holy temple."
"Now _that's_ something I never expected," Torl declared. "That little one's a savage, isn't she?"
"No, cousin," Sorgan disagreed. "Actually, she's a bug, and I wouldn't be at all surprised if she ate all the remains of poor old Bersla."
"That might take her quite a while," Torl observed. "She's not very big, and there's a whole lot of Bersla sprawled out on that throne."
Sorgan shrugged. "Maybe she'll just have a banquet for all the assorted priests who supported her."
"And kill any of them who refuse to eat their share?"
"That's possible, I suppose," Sorgan said. "Right now, though, you and I had better come up with some way to get all the gold building blocks out of this throne room and then haul them down to the harbor. I've got a hunch that 'take the money and run' might just go on for quite a long time."
[THE
BLIZZARD](YoungerGods_toc.html#part_19)
**1**
Tlantar Two-Hands wasn't particularly surprised when a sudden blizzard came sweeping in out of the north. Dahlaine had held the normal snowstorms back while the various armies had come down along the mountain range to the mouth of Long-Pass, but now that they were all in place, that was no longer necessary. It appeared that winter had much resented being cut off from her normal entertainments, and now that she was free, she seemed to want to unleash at the same time all the previous storms that Dahlaine had prohibited before.
Tlantar had no problems with that. He and his friends had the fort of Gunda the Trogite for shelter, but the Creatures of the Wasteland were all right out in the open where winter could bury them all under twenty-foot snowdrifts.
On about the third day of the screaming blizzard, Longbow the archer suggested that a few of them should probably go up to the top of Gunda's wall and see just exactly what was going on down on the slope leading up from the Wasteland to the mouth of Long-Pass.
"How long would you say this is likely to continue?" Gunda asked Tlantar after Longbow had led them to the top.
Two-Hands shrugged. "A week or so at least," he replied. "Dahlaine has held winter back for quite some time, so it's likely to take her a while to get over her frustration. I've noticed that winter is like that. She hates it when she's not permitted to play with her toys. I wouldn't say that _we've_ got much to worry about. Your fort here will give us all the protection we're likely to need. The bug-people are right out in the open, though, so this won't be a very pleasant time for them."
"Oh, the poor, poor babies," Gunda said with a wicked sort of grin. "Dear old Mama Vlagh will probably lose a lot of her children before this snowstorm goes away."
"It's not impossible," Two-Hands agreed. "They won't be able to see for more than a few feet, and there's nothing on that slope for them to see anyway, and nothing to shelter them. Most of them will probably be frozen solid by the time spring arrives."
Gunda pulled his bison-hide cloak tighter about him. "Have you seen all that you need to see, Longbow?" he asked the tall archer. "I'd really like to get back inside where it's warm. My feet are starting to get very cold."
"Let's go back inside, then," Longbow agreed.
They went on back down the narrow stairway to the lower part of the fort and rejoined Sleeps-With-Dogs and the farmer Omago from Veltan's Domain in a sizeable room with a solid stove standing against one of the rock walls. Two-Hands had noticed that the Trogites were very fond of stoves, in spite of the fact that their homeland almost never received much snow.
"Is that snowstorm out there letting up at all?" Sleeps-With-Dogs asked.
"I'd say that it's getting worse," Longbow told his friend.
"Ah, well," Sleeps-With-Dogs said, "this lodge made of stone should hold it off. Are the bug-people up to anything?"
"That's just a bit hard to say," Longbow replied. "The snow's so thick that we couldn't see more than a few feet."
"How cold would you say it is out there?" Omago asked.
Gunda laughed. "I didn't try it, but I'd say that if a man happened to spit anyplace out there, the spit would turn into ice before it hit the ground." He looked around. "This is a very good fort, I guess, but if it keeps snowing and getting colder every minute, we might not need it at all. The bug-people will all freeze to death before they even get up here." He gave Tlantar a speculative look. "This blizzard is Lord Dahlaine's way to stop the bug-people right in their tracks, isn't it? I mean, he _can_ do that, can't he?"
Two-Hands shook his head. "Dahlaine's not permitted to kill things. _We_ can kill them, but _he_ can't. I'd say that this blizzard is just a natural reaction of winter to Dahlaine's decision to hold the weather back until _we_ all got here. As soon as Dahlaine loosened his grip on her, she threw all the storms down this way at the same time. The seasons get very cranky when somebody interferes with their personal entertainment."
"Are you saying that the seasons can actually think?"
"I wouldn't call it thinking, friend Gunda." Longbow stepped in. "Things build up as time passes, and winter things build up more than things in the other seasons. This particular storm probably didn't originate in winter, though. I took a quick look down Long-Pass when we started to come back down from the top of the wall. It's snowing very hard on the slope that comes up out of the Wasteland, but it's hardly snowing at all down in Long-Pass. I'd say that _somebody's_ tampering."
"Your 'unknown friend' maybe?" Gunda asked.
"It's altogether possible, wouldn't you say? She _is_ on our side, after all, and every bug the blizzard kills is one less that _we'll_ have to kill."
"That takes a lot of the fun out of _this_ war, Longbow," Gunda complained.
"I suppose you could scold her if you're feeling cheated," Longbow replied mildly.
"Ah—no, I don't think I'll do that," Gunda said. "I _definitely_ don't want to irritate _that_ one."
"Sound thinking," Two-Hands noted.
Narasan, the chief of the Trogites, had been conferring with Gunda's friend Andar in the fort that was about a mile down the pass from this one, and he came up to Gunda's fort the next morning with his constant companion, the warrior queen Trenicia. "Is somebody tampering again?" he asked when he joined Gunda and his friends in the central room of the fort. "All we were getting down in Andar's fort were a few random snowflakes, but that's a serious snowstorm off to the west."
"Longbow here thinks that it might be his unknown friend again," Gunda replied. "After some of the things she did down in Veltan-land last summer and what she did a month or so ago in Dahlaine-land, this snowstorm is the sort of thing she seems to like. She's got the bug-people all pinned down on that slope that comes up out of the Wasteland, and they're probably all very busy freezing to death."
"I just wish that our friend out there could come up with a way to eliminate the Vlagh," Narasan said. "Once the Vlagh is gone, we'll all be able to go back home."
The farmer Omago smiled. "We'll miss you terribly, Com-mander," he said, "but you have things that need to be done when you return to your homeland, don't you?"
"I'm sure that we do," Narasan replied. "I think I'd like to get to know our new emperor a little better. He's pretty much destroyed the Trogite Church, but there are some other things he might want to consider. Selling the higher-ranking members of the clergy as slaves was most appropriate, but I think it's about time to take a hard look at the whole idea of slavery."
"I don't know about that," Gunda said. "If he tries to abolish slavery, the people who own slaves and the rascals who sell them will put a sizeable price on his head."
"Now _there's_ a thought," Narasan said. "If we hired on to protect him, we could ask just about any price, wouldn't you say?"
"The Palvanum would come unraveled if we stuck our hands _that_ deep into the imperial treasury," Gunda replied.
"Maybe it's time to take a hard look at the Palvanum as well, Gunda," Narasan suggested. Then he looked around at the others in the room. "This is an internal matter in the Empire, and I don't think our friends here would be very interested. Right now we'll need to concentrate on what we'll need to do here when it stops snowing."
Two-Hands was catching a strong odor of ambition. When Narasan returned to his homeland again, he'd probably become extremely important in the Trogite Empire, and sooner or later he could very well take the imperial throne for himself. Two-Hands smiled. If that _did_ happen, he was fairly sure that he knew exactly who would be the empress in the Land of Trog.
It was about mid-morning on the following day when the young Trogite soldier Keselo rode up to the back of Gunda's fort. The blizzard had subsided a bit during the night, but the snow was still piling up on the slope below the fort.
Keselo climbed down off his horse and came on into the fort. He touched one hand to his forehead in what the Trogites called a salute when Narasan joined him.
"Is there a problem of some kind?" Narasan asked him.
"There's no easy way to say this, sir," Keselo replied. "It seems that Lady Zelana's sister doesn't exist anymore."
"You said _what_?" Narasan exclaimed.
"I didn't see it personally, sir, but Captain Sorgan told me to get up here as fast as I could and let you know what happened. If I understood him correctly, Lady Aracia ordered the little Dreamer Lillabeth to vanish—or die—or something like that."
"She killed that baby?" Narasan exclaimed.
"She might have been trying, sir," Keselo replied, "but that's not what happened. As soon as she said it, she just disintegrated. At least that's what Eleria told Sorgan. Her body turned into little speckles of light. Then the lights all faded, and Lady Aracia wasn't there anymore. Captain Sorgan had spoken with Veltan, and Veltan told him that his sister had tried to do something that's prohibited, and when she attempted to do that, she was obliterated."
"Dear Gods!" Narasan exclaimed. "Who's in charge down there now?"
"I suppose you could say that it's the child Lillabeth, sir," Keselo replied, "but Captain Sorgan has seen her a time or two, and she's no longer a child, and her name is Enalla now."
"Are all those fat priests worshiping this Enalla now?" Gunda asked.
Keselo shook his head. "Captain Hook-Beak told me that she ordered them not to, and then she sent word out to the local farmers that they didn't need to deliver food to the temple anymore."
"My goodness," Narasan said mildly. "What are the priests supposed to eat now?"
"Their shoes, probably, sir."
"What moved Lady Aracia to try to do something that's absolutely forbidden?" Gunda demanded.
"Captain Sorgan told me that it was the same thing that caused those problems in the Tonthakan Nation in Lord Dahlaine's part of the Land of Dhrall, sir. There was a tiny little priestess called Alcevan who was able to control Lady Aracia with an odor—in much the same way that those two controlled the chief up in Tonthakan—up until the Maag called Ox brained the both of them with his axe."
"It would seem that the Vlagh is playing games again," Gunda growled.
"So it would seem, sir," Keselo agreed. "Oh, one other thing. Captain Hook-Beak asked me to advise you that his men are going to take all the gold they can get their hands on down there, and then they'll come on up here to lend us a hand— _and_ to share the gold with us."
Narasan blinked in astonishment, and then he started to laugh.
**2**
It took several more days for the lopsided blizzard to move off to the south, and when the pale winter sun returned, it more or less confirmed Longbow's assessment of the storm. The slope leading up from the Wasteland was covered with deep snow, but it appeared that very little snow had fallen into Long-Pass. Two-Hands now agreed that something very unusual had conjured up this particular blizzard.
As soon as the weather cleared, Gunda put most of his men to work clearing the snow off the top of the wall while the young Trogite called Keselo gathered the catapult crews near the back side of the fort, where they all carefully mixed several liquids together to produce the fire-missiles that had proved to be extremely useful during the war in Crystal Gorge.
That might have disturbed Two-Hands more than just a little. Arrows and spears were one thing, but balls of liquid fire were quite another. Had their enemies in this war and the previous one been people-people, Two-Hands would have protested quite extensively. But bug-people were quite a different matter. Setting fire to bugs didn't bother Two-Hands at all.
The Trogite soldiers were still busily clearing away the snow piled high on the top of the wall when Longbow's friend, Sleeps-With-Dogs, came up to join them. He peered down the slope for a few moments, and then pointed out a sizeable number of snow-piles down there. "Shouldn't the wind have blown those away?"
"That would sort of depend upon how tightly those snow-piles are packed," Two-Hands replied. Then he gave it some thought. "Now that you mention it, though, those piles shouldn't really be there. The wind should have carried them away quite some time ago."
"Doesn't that sort of suggest that those piles aren't natural?" Sleeps-With-Dogs suggested.
"Indeed it does," Two-Hands agreed. "I'd say that the bug-people sort of improvised shelters to protect themselves from the weather, and we weren't able to see what they were doing because the blizzard was hiding everything down there. It's a good thing that _one_ of us still had his eyes open."
"If we're at all close to being right, before too much longer a bug will show up down there—unless they're going to try to burrow their way up here under the snow," Sleeps-With-Dogs said.
"If any of them try that, they won't live very long," Gunda declared. "There are a thousand or so poisoned stakes down under all that snow, and one little scratch from one of those stakes will kill anything that tries to come up here—either on top of the snow or down underneath. One-Who-Heals gave us that idea, and those stakes have probably killed more bug-people than all the rest of us put together have."
"One-Who-Heals was probably the wisest man in all the Land of Dhrall," Sleeps-With-Dogs said proudly.
"We heard that he'd died not too long ago," Gunda said. "What killed him, anyway?"
"Old age," Sleeps-With-Dogs replied. "No matter how many wars we win, old age will end up killing us all."
"That's a gloomy way of looking at things," Gunda said in a sour tone of voice.
"Always look on the dark side, friend Gunda," Sleeps-With-Dogs replied. "Then, if you get killed with an arrow or a spear, it brightens things up, wouldn't you say?"
Two-Hands covered his mouth so that Gunda couldn't see his grin.
It was not much later when the side of one of the snow-heaps down on the slope buckled outward and a somewhat larger than usual bug-man kicked its way out into the open.
"Am I seeing things right?" Gunda asked. "It looks to me like that overgrown bug is wearing one of the bison-hide cloaks that the Matans gave us to keep us from freezing to death."
"It's possible, I suppose," Longbow agreed. "I'd say that it's much more likely that the Vlagh saw how useful they are, and she modified a new hatch to add those cloaks."
"He's carrying a spear as well," Two-Hands noted. "Can the Vlagh take things _that_ far?"
"The bugs have been stealing those spears for a long time now," Gunda said. "They pillage battlefields to steal weapons from dead men."
"I wouldn't worry too much about that, Gunda," Longbow said. "Spears will reach out quite some distance, but arrows reach farther, and we have a lot of archers here—and fire-missiles as well. I've noticed that the Vlagh usually depends on numbers when she goes to war, but numbers don't mean much when the bug-people come up against arrows and fire-missiles."
"You know," Kathlak, Longbow's Tonthakan friend, said, "I noticed the same thing during the Crystal Gorge war. What do you think, Longbow? Should we start picking them off as soon as they come out of those snow-piles, or should we wait until most of them are out in the open?"
"Let's hold off until they get closer," Longbow replied. "Let's not waste arrows trying to hit them at long range. Then too, the snow's quite shallow up here at the top of the slope, and Ekial has horse-soldiers more or less hidden near the upper end of Long-Pass. We should be able to drop thousands of bug-people with our arrows, and then the horse-soldiers will be able to kill many, many more."
Two-Hands saw that the bug-people weren't able to move very fast as they came by the thousands up the slope. It was quite obvious that they weren't at all familiar with snow and its drawbacks. After a few hundred of the bug-people had waded through the snow, they'd packed it down to the point that it was very nearly solid ice, and nobody—man or bug—can move very fast when walking on ice.
"What do you think, Longbow?" Kathlak asked.
"They're probably close enough now," Longbow agreed. "Do you want to give the order?"
"Why don't _you_ do it?" Kathlak suggested. " _Nobody_ argues with _you_ when you give orders."
"All right," Longbow agreed. Then he took a long breath and shouted, "Shoot!"
The arrows swept out in a vast wave from the top of Gunda's fort, and the front ranks of the advancing enemies toppled like fresh-cut wheat. The piles of dead bug-men were almost like a wall that blocked off the advance of the ones coming up the slope behind those first ranks. Then the horse-soldier Ekial shouted, "Charge!" and his men galloped across the upper end of the slope, killing thousands more of their enemies.
Then there came the sound of a trumpet, and the horse-soldiers pulled back. Two-Hands was just a bit awed by how smoothly things had gone for them. Then the young Trogite called Keselo shouted "Shoot!," but he wasn't talking about arrows. Great gobs of burning pitch came over the front wall of Gunda's fort, and absolute chaos brought the charge of the bug-men to a dead stop as burning bugs ran this way and that through the snow.
"Don't they know that all they have to do to put out those fires is roll around in the snow?" Two-Hands asked Longbow.
"Not really," Longbow replied. "These particular bugs come from a desert, so they probably don't know that snow is just another form of water."
The winter sun was going down off to the west, and it touched the clouds of smoke with light that the smoke made bright red.
"I've always sort of liked sunsets," Gunda said. "The best thing about a sunset is that it means supper-time, and I'm starting to get very hungry."
[THE
ALTERNATE](YoungerGods_toc.html#part_20)
**1**
Omago's Dream had released his memories of times long past, and now he knew just who—and what—he really was, and that knowledge had shaken him down to his very core.
Now that things were quieter, he felt that the time had come for him to get a better grip on that stunning reality, but he needed to be alone for that. And so, as midnight approached, he went up to the top of the main wall of Gunda's fort at the head of Long-Pass.
The weather was bitterly cold, but it came to Omago from out of the distant past that he was immune to weather—cold or hot—and he had no real need of air to breathe or food to eat. He sent his memory back to the time some thirty years ago when he'd first revealed his plan to Ara.
"It's something we need to know, dear heart," he'd explained. "The minds of the man-things here in the Land of Dhrall are unlike the minds of any of the other creatures here, and I think the best way to find out just why would be to erase all previous memories and live out the life of an ordinary man-thing."
"I don't see any particular value in your plan, Omago," Ara had replied. "A prince or a chieftain might have _some_ knowledge you'd find useful, but the ordinaries have trouble distinguishing night from day."
"They're not really _that_ bad, Ara. Princes and chieftains have very little contact with reality. They spend most of their time trying to _avoid_ reality. I've been considering the life of an ordinary farmer—most probably in the Domain of Veltan of the South."
"Why there, dear heart?"
"Apple-blossoms, Ara," he'd replied. "I think they're the most beautiful flowers I've ever encountered in this world—or any others in this part of the universe. I _need_ beauty, Ara. That's why we've been together for so long. Your beauty has held me captive since the beginning of time when we first added forms to our awareness."
"Flattery won't get you very far, Omago."
"Oh, I'm not so sure about that, dear heart," Omago had replied with a sudden smile. Then he'd grown more serious. "There's another reason that I think I should stay close to Veltan. As far as I can determine, he's the best teacher of all the gods. Dahlaine's too busy being important, and Vash and Dakas are just a bit abrupt and not really very bright."
"What's wrong with the females?"
"Males and females don't think alike, Ara. Haven't you ever noticed that? I have a strong feeling that something very important will happen in the Land of Dhrall. The man-things of this world will continue to exist, or will become extinct, because of something that will take place in that obscure part of this world. There's a creature there that wants to obliterate them, and if the man-things are obliterated there, they'll also be eliminated in _all_ parts of this world. I need to find out what that thing is and stop it—or even destroy it, if I have to."
Ara had sighed. "You aren't giving me too much room here, dear heart," she'd accused him. "Go ahead with this game of yours, but I'm _not_ going to let you play alone. I'll be with you, like it or not, and I know who you _really_ are. If you make any serious mistakes, I'll be there, and I'll be able to step in if it's necessary."
"I _would_ miss you, dear heart," Omago confessed.
"Don't worry, Omago. I'll see to it that you don't."
Omago clearly remembered the early years of his alternate identity when Veltan had given the young man a surprisingly complete education. As the young man had grown older, the other farmers of the region had taken to using him as a "messenger-boy" of sorts to convey information to Veltan rather than going up the hill to Veltan's massive house on their own. It wasn't that they were actually afraid of Veltan, but he _was_ a god, after all. The farmer version of Omago had dutifully carried that information up to Veltan's house, and as time went on, he'd added his own assessment of the various farmers of the region. For example, he'd told Veltan that the little farmer called Selga was much more interested in gaining Veltan's respect than he was in passing warnings and the like to the local god.
The farmer version of Omago hadn't had much interest in women during his early years, and the elder version knew exactly why. Ara had quite obviously been tampering. Omago actually laughed when he realized that.
"What's so funny?" Ara's voice came out of nowhere along about then.
"Nothing, dear heart," Omago lied. "I just remembered something that was sort of amusing, is all."
Then Omago the elder quite vividly remembered Ara's rather blunt proposal. Her words still jumped out at him. "My name is Ara," she'd begun. "I'm sixteen years old, and I _want_ you."
"It _did_ get right to the point," the elder conceded, "but it might have been just a little too specific to drop on someone as innocent as my alternate was."
The more Omago considered things, though, it came to him that his true identity had unobtrusively stepped in on several occasions. When Veltan had given the young farmer version of Omago the iron knife, it had been the eternal version that had guided the younger one through the invention of the spear.
The older version had also nudged the younger into the notion of what Keselo had called "The Phalanx." The younger Omago was not as totally innocent as he'd appeared right at first—largely because the elder Omago had been tampering for all he was worth. The grand plan of the original Omago seemed to have had quite a few holes in it.
When the foul-mouthed Jalkan had insulted Ara, however, young Omago had punched him squarely in the face without any help at all from eternal Omago, and he'd done it so fast that it had actually startled his eternal awareness.
"He _did_ show some promise there," eternal Omago murmured with a faint smile.
He spent the next hour or so remembering the experiences of his alternate personality. Despite his lack of training, younger Omago had been clever and resourceful during the war in Veltan's Domain, and even more so during the war in the North.
"Enough of that," he murmured. He and his mate had been drawn to the Land of Dhrall by their certainty that _something_ would happen here that would prevent the extermination of the man-things here on this world. The events here during the past three seasons had made it abundantly clear that That-Called-the-Vlagh would be the exterminator. If she succeeded _here_ , she would move on to the other parts of this world and delete the man-things in each of those as well. Given a few years, there would no longer _be_ man-things anywhere on this world, and then the Vlagh would produce offspring by the millions, and they would spread out and kill off all other living creatures. "Not as long as I'm around, they won't," Omago vowed to himself. The more he thought about it, the more certain he became that the Alcevan creature would be the key to the obliteration of the man-things, and if they stopped Alcevan, they could surely stop the Vlagh as well.
But how?
"Have we turned into night-creatures now, Omago?" the somber-faced archer Longbow asked.
Omago was startled. "Can't you make a little noise before you do that, Longbow?" he demanded.
"That might be just a little difficult, friend Omago," Longbow replied, holding up one of his feet and pointing at the soft leather shoe he wore.
"You could always cough, or something," Omago said sourly.
"Is there some reason why you're still awake in the middle of the night?" Longbow asked.
"Something that might turn out to be very important," Omago replied. "It's important enough anyway that I don't think I'll sleep very much until I find some way to deal with it."
"Oh?"
"The Vlagh has many servants—or children, actually—but most of them are as stupid as rocks. If what I've heard actually happened, the Alcevan creature is far, far more intelligent. If that's true, the children of the Vlagh will quite probably defeat us. I _think_ , however, that I've come up with a way to defeat _her_ instead. What I really need right now is more information about the nature of her servants."
Longbow's expression changed slightly at that point. "You're not _really_ just an ordinary farmer, are you, Omago?" he asked.
"Well—" Omago left it sort of up in the air.
"I didn't really think so. I don't think your mate would have been very interested in somebody whose main purpose in life was picking apples or growing beans."
Omago felt just a bit crestfallen about then. "Have I been _that_ obvious?"
Longbow smiled. "I've come to know Ara very well since the war in Veltan's Domain. You two have been here for a long, long time, haven't you?"
"From even before the beginning, yes."
"But you weren't aware of that until just recently, right?"
"How did you know _that_?" Omago demanded.
"You probably shouldn't have told your mate about that dream you'd had. She was _very_ upset when you told her about it. She wanted _me_ to do something about it. I'm not sure just _what_ she wanted me to do, but she laid it in my lap. That's why we're having this present conversation. What made you think that it was time to shed that farmer pose and become the _real_ eternal Omago?"
Omago smiled. "Ara does that every so often," he said. "She didn't really like the idea of a simple-minded Omago, but now she wants to defend him—even though he's not particularly useful now. My original intention was to be just an ordinary farmer so that I'd understand the man-things here in the Land of Dhrall. You people here do things that nobody else in this whole world would ever do. I wanted to see things the way that the native people of the Land of Dhrall see them, but evidently my mind has ways to step around any restrictions I've laid upon it—probably when an emergency pops up."
"Omago," Longbow asserted then, "we've been neck-deep in emergency since last spring. Did your mind just now wake up to that?"
"I think it might have been the Alcevan creature that shook it awake. The Vlagh—or her children—have come up with a way to eliminate people— _all_ people, I think. That odor they use makes people believe whatever the Vlagh _wants_ them to believe. It was fairly crude over in Tonthakan, but the Alcevan creature took it much, much farther, and eliminated Aracia in the process. I'll get to Alcevan in good time, but right now I think I need to know more about the Vlagh creature herself."
"I've seen her servants many times," Longbow replied, "but the only time I've ever seen _her_ was back in Veltan's Domain when her servants were carrying her back out into the Wasteland. What is it that you want to know about her?"
"I need to know where she lives, and just who takes care of her."
"You might want to speak with Dahlaine," Longbow suggested. "He's fairly busy right now, though. I think that Keselo might be able to tell us quite a lot about the world of bugs. He told me once that he used study as an excuse to avoid doing honest work, and he spent a lot of time studying the world of fishes and birds—maybe he studied bugs as well. Why don't we go wake him up? As long as you and _I_ are awake, we might as well rouse him too, wouldn't you say?"
"My teachers at the University of Kaldacin weren't really all that interested in insects," Keselo told them when they asked him about the world of bugs. "They had a fair grasp of the nature of bees, of course, since honey can be quite valuable. They also warned us about locusts and ants, but that was about as far as it went. I _have_ picked up quite a bit of information about the Vlagh from Dahlaine, though. Maybe you should ask _him_. When you get right down to it, though, I've picked up just about everything I know about bugs from _you,_ Longbow—and from your Shaman, One-Who-Heals. Is it at all possible that the Vlagh had your shaman killed because he knew too much about her and her children?"
"That gives me another good reason to kill her," Longbow said. Then he paused. "Male bugs aren't really very important, are they?"
"Only at breeding time," Keselo replied. "There's no such thing as a king bee—or a king ant."
"Has Dahlaine ever found the exact location of the nest of the Vlagh?" Omago asked.
"Oh, yes," Keselo replied. "He knows _exactly_ where she is. If it was permitted, he could probably obliterate her and all of her children." The young Trogite frowned. "That's one thing I've never understood. Dahlaine is a god, and he can do almost anything—except kill any living creature. I wouldn't be at all surprised if chopping down a tree would obliterate _him_."
"It worked quite well recently," Longbow said. "Aracia _really_ wanted to obliterate Enalla. Wars between various people aren't really all that significant, but a war between gods might just set the world on fire."
"Has Dahlaine ever described the servants of the Vlagh?" Omago asked. "I mean, just exactly what are they supposed to do?"
"They feed Mother," Keselo replied, "and keep her warm, of course. I'm just guessing here, but I'd say that if there wasn't anything for the Vlagh to eat, her servants would offer her themselves, and they'd set themselves on fire if she started to shiver. Self-sacrifice seems to show up quite often in the nest of the Vlagh."
"I think we might be getting somewhere now," Omago said. "The Vlagh has been modifying her children since last spring. She's been turning them into imitation people—except that they have no sense at all of self. If there was some way that we could give them a sense of personal identity, they might not be so eager to sacrifice themselves."
"Persuade one of the others to do it instead, maybe?" Keselo suggested.
"That would probably be the first step," Omago agreed.
"They'd have to have names then," Keselo added. "The name lies at the very core of personal identity." He hesitated slightly. "I didn't come up with that all by myself," he admitted. "One of my teachers at the university dropped it on us. He made quite an issue of it when he told us that a man without a name is not a man. He never got around to telling us just exactly what a man without a name really was, though."
"We'll have to pick up Rabbit before we go out into the Wasteland," Longbow reminded them.
Omago blinked, and then he felt a bit embarrassed. "We _will_ , won't we?" he said. "I should have thought of that myself."
"And now we are—or will be—four," Keselo declared quite formally. Then he laughed. "Sorry," he apologized. "It was just too good an opportunity to let slide by."
**2**
Are you certain that we're really going to need that Maag called Rabbit?" Omago asked Longbow and Keselo a bit later.
"He's very clever," Keselo replied, "and on several occasions he's come up with ways to accomplish things that never would have even occurred to me." The young Trogite smiled. "It just wouldn't be the same without him," he added.
"Do either of you have any idea of exactly where I might be able to locate him?"
"Sorgan Hook-Beak would know," Longbow replied, "and Sorgan's almost certainly in Aracia's temple—stealing everything of value in that oversized building. I can go down there and find him, if you like."
"I'll take care of it, Longbow," Omago replied. "I have certain advantages that aren't available to you."
"You're going to fly, I take it."
"Well—sort of," Omago said. "I can go from here to there very fast when it's necessary."
"You have a tame thunderbolt the same as Dahlaine has?" Keselo asked.
Omago smiled. "Not exactly," he said. "Why don't we just leave it there? It's one of those things you _really_ don't want to know about. Rabbit and I should be here in a day or so. Then we can go to the nest of the Vlagh and see what we can do to disrupt things for her."
Omago went down the stone staircase to the center of Gunda's fort, and when he was out of the sight of Longbow and Keselo, he rose rapidly up into the still, night-dark air and willed himself to the shabby stone building Aracia's overweight priests had constructed to make their owner happy.
He sent out his thought in search of Rabbit, but the little smith wasn't there. He _did_ sense the presence of Sorgan's cousin Torl, however, and he dropped down into the temple to have a few words with the clever Maag. "I've been looking for Rabbit," he said, "but I can't seem to find him anywhere here."
"You're the farmer called Omago, aren't you?" Torl asked.
"That's me all right," Omago replied. "Longbow the archer wants to have a few words with Rabbit, but I can't find the little fellow."
"He's out in the harbor on board that Trogite tub called the _Ascension_ ," Torl said. "We found out that the bricks that made the walls of Aracia's throne room are actually gold blocks and cousin Sorgan put Rabbit to work melting them down and making small blocks out of them. A big gold block is worth too much to waste on little things. Smaller gold blocks work better." He squinted at Omago. "Do you think you could row a skiff across the harbor to the _Ascension_?" he asked. "I'd row you out there myself, but cousin Sorgan has me busy doing other things now."
"I can manage, Torl," Omago said. "I thank you for the information. I could have spent a week or more looking for Rabbit here in this overdone temple. Give your cousin my regards."
"I'll do that, Omago," Torl replied.
Omago went back outside the temple and located the _Ascension_ out in the harbor. Then he willed himself from the beach to the ship's deck, and he could clearly hear the sound of a hammer pounding on something made of iron near the ship's bow.
"Ah, there you are, Rabbit," he said to the little smith. "Why are you working in the middle of the night like this?"
"Cap'n's orders," Rabbit said sourly. "He doesn't really trust all the sailors here on this oversized tub, and I'm working with gold, so the cap'n would rather that I didn't do it out in the open in broad daylight."
"I heard a somewhat peculiar sound up here when I first came up on the deck of this boat. Does gold really ring like a bell when you tap it with your hammer?"
"That was the mold," Rabbit explained. "The gold the cap'n stole from Lady Aracia's temple was mostly used for disguised bricks that had been used to make her throne room. I've been melting it down and pouring it into molds. After it hardens, I tap the back of the mold to make the gold blocks break loose."
"Ah, now I understand." Omago glanced at the half-dozen or so gold blocks lying on Rabbit's anvil. "Those aren't really very big, are they?"
"Four ounces each," Rabbit said. "That was Torl's idea. Those great big blocks Lady Zelana gave us are pretty enough, but they're too big to use for money—unless you're buying ships—or maybe a house in Kormo or Weros. Torl told the cap'n that we needed smaller blocks if we wanted to buy food. We don't have coins over in the Land of Maag. We use plain gold blocks instead, and Torl was right when he said that bags and bags of these four-ounce blocks could be very useful." Then he grinned at Omago. "The size and shape suggest something different, wouldn't you say?"
"I didn't quite follow you there," Omago admitted.
"They don't have any spots on them, but they're exactly the same shape and same size as dice. Maags are very familiar with dice, but I've never heard of a dice-game played with gold dice. The cap'n came up with the idea all by himself. These gold dice will be the Maag version of money if the idea gets spread around."
"Clever," Omago said. "Longbow sent me here to fetch you. He and Keselo need you."
"I don't know if I can get away, Omago," Rabbit said a bit dubiously. "The cap'n _really_ wants me to convert a lot of the gold bricks our people are stealing out of Lady Aracia's temple into these dice-shaped blocks. If I try to sneak off, he'll have a lot of men out there trying to chase me down."
"I'll see to it that they don't catch you, Rabbit."
"Really? Just how do you plan to do that?"
Omago was fairly certain that Rabbit wouldn't believe him if he were to answer that question, so he went off in a different direction. "Sleep, Rabbit," he said quite calmly. Then he caught the suddenly comatose little Maag and carried him several hundred feet up into the air above the temple harbor. "You look sort of tired anyway, Rabbit," he murmured. Then he turned slightly and returned to Gunda's fort at the head of Long-Pass.
"That was quick!" Keselo declared, sounding more than a little astonished.
"I cheated just a little," Omago admitted. "I don't know if you'll believe this, but Sorgan Hook-Beak has filched a lot of gold from Aracia's temple. Then he put Rabbit to work melting gold and pouring it into molds the size and shape of the dice some people use when they're gambling. Rabbit told me that Sorgan planned to use those gold dice as money when he returns to the Land of Maag."
Keselo blinked. "Now _that's_ something that never would have occurred to me," he said.
"Sorgan's very good at doing things that other people would never think of doing," Longbow said. Then he looked rather closely at the sleeping little Maag. "He _is_ all right, isn't he, Omago?" he asked.
"He's just fine," Omago replied, "and he'll be well rested come morning."
"I don't really think we should wait until daylight before we leave," Keselo said. "Too many people are likely to start asking us questions if they see us going down that snowy slope after the sun comes up."
"That raises another question, Omago," Longbow said. "If we start walking across the Wasteland in broad daylight, the bug-people are likely to be all over us."
"Only if they can see us, friend Longbow," Omago replied. "And I can guarantee that they _won't_ see us."
"You're going to make us invisible?" Keselo asked.
"Not really invisible," Omago replied. "'Unnoticeable' might describe it better. The bug-people will _look_ at us, but they won't _see_ us."
"You can _do_ that?" Keselo exclaimed.
Omago shrugged. "Zelana does it all the time," he said, "and if _she_ can do it, so can I. Shall we go?"
"Let's see if I've got this straight," Rabbit said after Omago had roused him from his sleep and Longbow had told him just exactly where they were going and what they were going to do when they got there. "Are you saying that just the four of us are going to hike out across the Wasteland, break into the palace of the Vlagh, and then persuade her children to run off and leave her there all by herself?"
"Approximately, yes," Omago replied. "It's probably going to be quite a bit more complicated than what you just suggested, but that pretty much sums it up, yes."
"Have you people been drinking grog or something?" Rabbit demanded. "The bug-people have killed thousands and thousands of people-people, and you three seem to think that you can walk right through them with no problems at all."
Keselo stepped in at that point. "You're going to have to adjust your thinking, Rabbit," he told the little smith. "Omago might _look_ like an ordinary farmer, but he has at least as much power as his mate, and we've all seen the sort of things Ara can do. The bug-people won't be able to see us when we cross the Wasteland and enter the nest of the Vlagh. They won't even know that we're there, so we'll be able to do anything we want to do."
"Butcher the Vlagh, maybe?" Rabbit asked in a voice dripping with skepticism.
"You're going to have to show him what you can do, Omago," Longbow said. "Rabbit needs to _see_ things before he'll accept them."
"And just for the fun of it, you might want to show us that 'unnoticeable' trick that's supposed to get us safely across the Wasteland," Keselo added.
Omago shrugged. "Whatever makes you gentlemen happy," he said. He rose up through the chill winter air until he was standing about forty feet above his friends. "Does this answer any of your questions, Rabbit?" he asked the little Maag. "Now then, I want all of you to watch me very closely." Then he reached out and touched their minds.
"Where did he go?" Rabbit demanded.
"I'm still here, Rabbit," Omago called. "You just can't see me anymore, that's all."
"Are you saying that you're invisible?"
"No. You're just not paying any attention to me is all. Here, watch this." He brushed away their insensibility, and they all seemed to be startled by his sudden reappearance.
"Are you sure that you can include _us_ in this little game?" Keselo asked a bit dubiously.
Omago laughed. "I can make a mountain range disappear if I really want to," he replied. "It'll still be there, but nobody will be able to see it. This isn't really all that unusual, you know. Zelana does it all the time."
"Are you saying that you're as powerful as Lady Zelana is?" Rabbit demanded.
" _More_ powerful, Rabbit," Omago replied. "She'll probably get better when she grows up, but she's still got a long way to go. Does that answer all the questions you have? We have quite a long way to go, so we'd better get started."
**3**
The chill wind sweeping across the rock-strewn Wasteland had a distinctly mournful sound to it that Omago found quite depressing. There were several reasons why they should hurry, but Omago knew in his heart that what was really pushing him was the sad song of the wind.
After they'd gone down the slope to the west of Gunda's fort, Omago fell back to what he'd always called the "skip-ship" method of crossing empty ground. He didn't mention it to the others, and he was fairly sure that they weren't even aware of the fact that he was cheating. When his skips reached about ten miles each, however, Longbow held up one hand. "I don't think this is a very good idea, friend Omago," he said.
"What was that?"
"These jumps of yours are covering too much ground. We _could_ pop out right in the middle of a large group of bug-people, and they're making just enough noise to catch the enemy's attention. The jumps are all right, of course, but I'd hold them back to one mile apiece if I were you."
"Did I miss something?" Rabbit asked.
"If you look at the mountains on the east side of the Wasteland, you'll notice that they seem to be jumping fairly often. A mountain peak that was fairly close is suddenly a long ways away." Longbow smiled at Omago. "I really think we should play it a little safer, don't you?"
"Do you catch _everything_ , Longbow?" Omago demanded rather peevishly.
"I'm _supposed_ to, friend Omago. Part of my job involves keeping my friends out of danger. If we keep going at this pace we'll arrive very suddenly at our destination. We don't _really_ want to reach the nest of the Vlagh before the sun goes down, and we don't want to go inside until _some_ of the servants of the Vlagh drift off to sleep, do we?"
Omago sighed. "I guess not," he reluctantly agreed.
It was only a few days later when they reached a peculiar-looking rock peak that jutted up out of the barren desert called The Wasteland. "I think that's it," Omago quietly told his friends.
"There _do_ seem to be quite a lot of bugs scampering around outside that pile of rocks," Rabbit agreed.
"It looks almost like a fort, doesn't it?" Keselo said. "I don't think I've ever seen a peak that looks very much like that one, though. What could cause something like that?"
"Erosion," Omago told him. "At one time, what's now called The Wasteland was the bottom of a fairly large sea, and water tends to eat rock. Give a sea a few million years, and it'll turn just about every rock along its shore into sand."
"If I understand what you're saying about this peak," Rabbit said, "it's the 'nest' the bug-people all live inside."
"Not quite _all_ of them, Rabbit," Longbow said. "Quite a few of them have been out in the open killing people. That's why we call this a 'war,' isn't it?"
"Very funny, Longbow," Rabbit said. "What I was getting at is that bugs don't build fires—or didn't until the war up in the North. If they don't build fires, what do they use to give them light inside that mountain?"
"Many bugs don't _need_ light, Rabbit," Keselo said. "They find their way around in dark places with touch, not sight. Then too, there _are_ certain bugs that generate light from inside their bodies. Some people call those particular bugs 'fireflies,' but there isn't any fire involved, and I've heard that those bugs are beetles, not flies."
"We'll know more once we get inside," Longbow said in a bleak voice. "One thing, though. I want you all to know that the Vlagh is _mine. I'm_ the one who's going to kill her."
_That_ took Omago by complete surprise, and it disturbed him more than a little. _He_ had come up with something entirely different, but it was now fairly obvious that he and Longbow needed to talk about this— _soon_.
"That cave-mouth at the center of the peak is almost certainly the main entrance to the nest," Keselo told them quietly as dusk began to settle over the Wasteland.
"There are a lot of bugs going in and out of that cave," Rabbit noted. "Even if they can't see us, we'll probably be bumping into a lot of them inside the cave."
"I can deal with that," Omago assured the little smith. Then he looked around. "What _is_ that buzzing sound?" he demanded rather irritably.
"I don't hear anything," Rabbit said.
Omago glanced at Longbow and then at Keselo. "Can either of you hear it?" he asked.
They both shook their heads.
"Is it possible that you're listening to the Vlagh herself?" Keselo asked. "I've heard about what's called 'the overmind.' Maybe the Vlagh's giving orders to her children, and you're eavesdropping. You _do_ have capabilities that we don't."
"It _is_ a possibility, Omago," Longbow agreed. "Is there some way that you might be able to understand what the Vlagh's overmind is saying to her children? If we knew what she wants them to do, we'd have a tremendous advantage."
Omago frowned. "That hadn't occurred to me," he admitted. "I think what she's telling them will be more clear once we're inside the cave."
"This might just turn into a very easy war," Rabbit said. "If you can listen in while the bug-queen is giving orders to her children, we should be able to stop them before they even get started."
"Let's go on inside," Omago told his friends. "If I can still hear the buzzing when we're in the cave, we should look into it."
The walls of what had appeared from the outside to be nothing more than a natural opening in the side of the mountain were as smooth as the walls of Veltan's house off to the south. Polished walls—particularly in a mountain cave—seemed to Omago to be more than a little absurd, but they'd obviously given the children of the Vlagh something to do when they weren't busy invading people country.
There were many bug-people moving in or out of the cave, and even though they most certainly couldn't see Omago and his friends, they almost politely stepped out of their way. As Omago moved farther and farther into the cave, the irritating buzz became louder and more distinct. He probed at that sound with his mind, and after a few false starts, his mind captured the meaning of what the Vlagh was telling her children. "Care for the little ones" came through quite clearly. "Take them to a place where it is not cold, and feed them much, for they will soon grow larger and will take on their tasks. Fail me not if you would go on living, for the little ones are most precious to me."
Rabbit had gone on ahead, and his expression when he rejoined them was a bit awed.
"What's wrong?" Longbow asked his little friend.
"You're not going to believe just how big the chamber at the end of this tunnel is, Longbow," Rabbit said. "I couldn't even _see_ the far wall."
"Is there light there?" Keselo asked.
"If you want to call it that," Rabbit replied. "There are quite a few of those fire-bugs mixed in with the ordinary ones. They don't really put out very much light, but it's not pitch-black in there."
"Did you see the Vlagh herself?" Longbow asked.
Rabbit shook his head. "The bug-people are all looking at something that looks a lot like a large clump of spiderwebs that's hanging down from the ceiling."
"That would be a cocoon," Keselo said. "Certain bugs wrap themselves in webbing when they're changing their form—or when they're giving birth to a new generation of puppies—or whatever you call baby-bugs."
Longbow's face went cold and bleak. "That would most likely be the Vlagh herself, wouldn't it?" he asked Omago.
"Definitely," Omago agreed. Then he decided that it was time to clear something up. "Don't start reaching for your bow or your arrows, friend Longbow. I have other plans for the Vlagh."
"Oh?"
"Once you hear what I have in mind, I'm sure that you'll approve."
"Surprise me," Longbow said.
Omago shrugged. "The Vlagh will live forever, and I'll see to it that she'll suffer every moment of that eternal time."
"I'll listen," Longbow promised.
The "Care for the little ones" buzz was repeated over and over, even though the cocoon was still intact, and Omago was quite sure that "the keepers" knew what they were supposed to do. It took him a while to blot out the buzz-sound, and once it was no longer audible, he reached out and began to duplicate that sound with a completely different message. "You are the best of all who serve me," he buzzed to the care-givers. "Let others attend to this new hatch, for you have much more important duties. Go forth from our eternal nest and prepare to defend it from the man-things who even now approach across the land that produces no food. The fate of this nest depends entirely upon you."
"How did you _do_ that?" Rabbit whispered to Omago as virtually _all_ of the bug-people rushed into the passageway that led to the outside of the peak.
"I think the most significant term would be 'cheating,' my little friend. I duplicated that buzzing noise and ordered nearly every bug in this vast chamber to run outside and hold back an imaginary invasion."
"Aren't they supposed to take care of the puppies?" Rabbit demanded.
"They _were_ , yes. But the 'overmind' just gave them new orders." Omago looked around the vast chamber that had been filled with bug-people until he'd issued his counterfeit command. "There aren't very many of the Vlagh's servants left in here, are there?" he observed.
And then he broke out laughing.
[THE
VISIT
OF
SORGAN
HOOK-BEAK](YoungerGods_toc.html#part_21)
**1**
Commander Narasan of Kaldacin was more than a little disturbed by the sudden disappearance of the enemy army. Not even the recent blizzard had driven the bug-people back, and they'd continued their mindless charges up the slope toward Gunda's fort despite the steady rain of arrows and fire missiles and the savage attacks by Prince Ekial's horse-soldiers. But now, for no reason Narasan could determine, the bug-people had ceased their attacks, and for all anybody in Gunda's fort could tell, they'd abandoned the slope and gone back out into the barren Wasteland.
To make things even worse for Narasan, Queen Trenicia of the Isle of Akalla was nowhere to be found in the fort, and her absence troubled Narasan more than he'd care to admit, even to himself. Trenicia was boisterous, sometimes arrogant, and prone to take terrible chances when they weren't necessary, but Narasan felt a dreadful isolation when she wasn't around. She'd irritated him many times during the war in Lord Dahlaine's domain in the north of the Land of Dhrall, and it was fairly obvious that she intended to continue that here in Long-Pass. "If she'd just tell me where she was going," he muttered to himself as he stood on the high front wall of Gunda's fort looking down the snow-covered slope toward the Wasteland. "I'm not going to order her around, but I need to know where she is."
"Ah, _there_ you are," Narasan's friend, Sub-Commander Padan, said, joining Narasan on top of the wall. "Are there any signs at all of the bug-people on that slope?"
"Nothing at all," Narasan replied. "I suppose it's possible that they've gone back to burrowing."
"That would take them years, Narasan," Padan scoffed. "I came up here to advise you that we've got company coming up Long-Pass."
"Who's that?"
"Our dear old friend, Sorgan Hook-Beak. A runner just came up the pass to warn you that he's on his way up here to scold you about something. The runner told me that Sorgan's very discontented about something."
"Now what?" Narasan grumbled.
"I haven't got a clue, glorious leader," Padan replied.
"Do you _always_ have to do that, Padan?" Narasan complained.
"Every now and then, yes. Shall we go down and greet him and see what he has to say? Or would you rather find someplace to hide?"
Narasan's friend, the burly Sorgan Hook-Beak, reached the rear gate of Gunda's fort about a half hour later, and he had his shaggy Matan bison-robe pulled tightly around him. "Is there some kind of emergency up here, friend Narasan?" he demanded.
"Our enemies aren't charging up the slope to the west of Gunda's fort," Narasan replied. "I wouldn't call that an emergency, though. Let's get in out of the cold, and then you can tell me about your problem."
"It _is_ a bit crisp up here," Sorgan agreed. "Lead the way, my friend. I'll be happy to follow."
At Padan's suggestion they went through a long corridor that led to the kitchen of Ara, the mate of the farmer Omago. It was the warmest place in the whole fort, and Sorgan, after his long hike up the pass, was probably hungry.
"We don't want to intrude, Ara," Narasan said, "but Captain Hook-Beak here has been out in the cold for several days, and I'd imagine that something to eat might make his belly very happy."
"It doesn't disturb me at all, Narasan," the beautiful Ara said. "Warm him up a bit, and I'll give him a lunch."
"That won't hurt my feelings one little bit, ma'am," Sorgan said, pulling off his bison-hide cloak. "Your mate has probably been away for several days now," he added. "That's why I came up here to talk with friend Narasan here." Then he looked at Narasan. "That's why I asked you if there was some kind of emergency up here. Omago came down to temple-town looking for Rabbit. I guess they talked for a little while, and now we can't locate either one of them. It's almost like they just disappeared."
"Was Rabbit doing anything important?"
"Very, _very_ important, Narasan. We found tons and tons of gold in Lady Aracia's temple, and Rabbit's been modifying gold bricks for us, but now he's gone. I've got several other men working on the modification, but they're not nearly as good as Rabbit."
"Just where did you find this gold, friend Sorgan?"
"You're not going to believe this, but the walls of Lady Aracia's throne room were made of solid gold blocks."
"When did that happen?" Narasan demanded. "When I was down there, her throne room was made of ordinary bricks."
"They might have _looked_ ordinary," Sorgan replied, "but _somebody_ down there was clever enough to disguise them."
"How did they do that?"
"As close as we were able to determine, they sprinkled sand on the molten gold while it was still cooling in the molds. The sand stuck to the gold and made it look like clay bricks. I'd say that _one_ of those lazy priests was clever enough to disguise the gold—to keep _us_ from finding out that it was there." He looked around. "Have you got anything to drink around here?" he asked.
"I'll go fetch a jug or two, Captain," Padan said, walking toward the door.
"How can people _live_ in a place where it gets this cold?" Sorgan asked Narasan.
"Those bison-hide cloaks help quite a bit," Narasan replied.
"I'd hate to spend much time outside if I didn't have one, _that's_ for sure," Sorgan agreed. "Oh, before I forget, I'm going to need several more of your ships down there in the harbor before long. The _Ascension_ is a nice enough ship, I guess, but she can't carry all that gold by herself."
"How much are we talking about here, Sorgan?"
"What's the next word up from 'tons,' Narasan? We're a long way above 'tons' already, and there's still more that we haven't pulled out of the temple yet."
"I'd like to see some of it, Sorgan. I'm not calling you a liar or anything, but still—"
"I thought you'd never ask, Narasan," Sorgan said. Then he untied a leather pouch from his belt, opened it, and poured several fairly small gold blocks out onto the table just as Padan returned with two fairly large jugs.
"Pretty," Padan said, looking at the gold scattered across the table, "but why are you making such small chips?"
"I'm stealing another idea from you Trogites," Sorgan admitted. "We don't have gold coins over in the Land of Maag. We've got copper coins, brass ones, and a few made of silver, but for some reason, nobody there has ever considered gold coins."
"Square ones?" Narasan asked. "I don't think I've ever seen square coins."
"It was Rabbit's idea. He said that if we put out square coins, everybody would know that they came from the Land of Maag."
"Shouldn't you stamp a picture of somebody on those blocks?" Padan asked.
"A picture? Of who?"
"You, probably. You're the one who came up with the idea, after all, and if your picture is stamped into every one of them, the other Maags will think of you as their emperor."
"That never occurred to me," Sorgan admitted. "How do people go about doing that?"
"Etch the picture on the end of an iron rod, set the rod on the face of one of your gold blocks, and then rap the blank end with a hammer."
"How did you plan to distribute your new coins, friend Sorgan?" Narasan asked.
Sorgan shrugged. "I'll buy things—ships, houses, land. When you get right down to it, I probably _will_ be the emperor of Maag, since I'll own everything there, and I'll be able to hire an army to make everybody there bow down to me. And friend Narasan here will be able to buy the Trogite Empire too, since half of the gold will be his."
"How did you come up with _that_ idea, Sorgan?" Narasan asked, more than a little surprised.
"We're partners, friend Narasan, and I never cheat a partner. You should know that by now."
"I seem to be about neck-deep in emperors," Padan said. Then he pulled the cork out of one of the jugs he'd just carried into the room. "Let's drink to that, shall we?" he suggested.
"I thought you'd never ask," Sorgan declared with a broad grin.
Ara had been checking her assorted ovens, and then, with a sort of reluctant expression on her beautiful face, she joined Narasan and Sorgan at the large table where they'd been talking with each other for the better part of an hour. "I think there's something you gentlemen should know," she said.
"It's almost supper-time?" Sorgan asked her with a grin on his face.
"Very funny, Hook-Beak," she replied. "I don't want to ruin your day, mighty soldiers, but my mate has decided to put an end to this war right about now."
"So _that's_ why he came down to temple-town and filched Rabbit," Sorgan said.
"I think you just lost me, friend Sorgan," Narasan said.
"The farmer's clever enough to realize that Longbow, Rabbit, and your man Keselo have made an excellent team during the previous wars. I'm fairly sure that if we looked around we wouldn't find _any_ of them here in Gunda's fort." He looked at Ara then. "As I understood what people have been saying correctly, you and your mate can stay in touch with each other even if you're a thousand miles apart. That suggests that you know exactly what he and his friends are up to."
"Oh, yes, and a thousand miles only begins to describe how far we can reach when we need to. Up until quite recently, he wasn't fully aware of that. Then he had a Dream that went much farther than the Dreams of the children."
"A Dream about what's going to happen out in the Wasteland?" Narasan asked.
"No. That's sort of beside the point, though. Omago's Dream told him just who—and what—he really is. Now he knows that _he_ can eliminate the Vlagh and all of her puppies. He picked up that team that's been so useful in the past, and they went across the Wasteland to the nest of the Vlagh."
"Isn't that sort of dangerous?" Narasan asked. "As far as we can tell, the Wasteland's crawling with the children of the Vlagh."
"Not anymore," Ara replied, "and even if they _were_ out there by the thousands, they wouldn't be able to see our friends."
"When would you say that they'll reach the nest of the Vlagh?" Narasan asked.
"Actually, distance doesn't mean anything to Omago, and neither does time. They're there already."
"What's at the core of his scheme?" Sorgan asked.
"He's blotted out the sound of her voice. She'll _try_ to give her children orders, but they won't be able to hear her. Omago has usurped her voice, so now her children are obeying _him_ instead of her. The Vlagh just recently laid a million or so eggs. When the eggs hatched, Vlagh's children went to the 'care-givers,' who are _supposed_ to care for each new hatch. Since Omago had blotted out the Vlagh's orders to the 'care-givers,' they didn't recognize the baby bugs, so they ate them."
Sorgan suddenly gagged. "They're eating their own children?" he exclaimed.
"They don't _know_ that the new hatch comes from the Vlagh herself," Ara replied. "To them, the new hatch is nothing but small caterpillars. Omago advised me that the Vlagh started screaming when the 'care-givers' ate every single puppy she had created. Omago's certain that she'll scream for a long, long time."
"How long?" Narasan demanded.
"Omago used the word 'forever' when he explained it to Longbow. You might not want to accept this, but Longbow put his arrows away after Omago told him 'forever.' He had obviously planned to kill the Vlagh, but when my mate told him that the Vlagh would scream out her grief for millions of years, that would be much, much more satisfactory than shooting her full of arrows could _ever_ be."
"If there aren't going to be any more hatches, the bug-people will probably die out before long, won't they?" Sorgan asked.
"Define 'before long,' Hook-Beak," Ara replied.
"I don't know," Sorgan admitted. "A year or so at the most, I'd say."
"No bug has _ever_ lived that long," Ara said. "Four to six weeks is about as far as they can go. The Vlagh will still be there, but she'll be alone—and screaming—for the next million years—or so."
"If that's what's happening, you and your men don't need to stay here, friend Narasan," Sorgan said. "Your men would be much more useful down there in temple-town guarding all that gold."
"What's been going on down there since Lady Aracia vanished?" Narasan asked his friend.
"I think it's called 'mutual extinction,'" Sorgan replied with a wicked grin. "The priests have been killing each other every chance they get. That little priestess Alcevan gutted poor old Fat Bersla right in the throne room. Bersla had usurped Lady Aracia's throne, and little Alcevan came up to him and knelt down as if she wanted his blessing. I guess he was thinking it over, but then Alcevan jumped forward with a knife and gutted him right then and there. I didn't see it myself, but I've heard that his innards spilled out all over the floor of the throne room. It's a messy way to kill somebody, but it _does_ work—eventually."
"I've heard quite a bit about that Alcevan," Ara said. "I think I'll make a suggestion to my mate. It might not be a bad idea to send her back home to the nest. Then she'll be able to sit somewhere and listen to her mother scream out her grief for the next million or so years."
"She couldn't possibly live _that_ long," Narasan protested.
"Throw 'possibly' away, dear Narasan," Ara replied. "If I want Alcevan to be in the nest listening to her mother's screams for the next million or so years, she _will_ , I can guarantee that. Killing is _one_ way to get revenge, but _not_ killing is sometimes more satisfactory."
It was about mid-morning the following day when the warrior queen Trenicia came up the slope that led down to the Wasteland, and she was accompanied by Prince Ekial.
"Where have you been?" Narasan demanded when Trenicia entered Gunda's fort.
"My," she said, "aren't _we_ grouchy this morning?"
"I've asked you several times to let me know _before_ you go scouting around."
"You didn't _really_ think I paid any attention, did you? You needed some information, so I went out and gathered it for you. That slope _appears_ to be deserted, but it's _not_. There are thousands of bug-people down there, but they're all dead."
"Who—or what—killed them?" Narasan asked, more than a little startled.
"I'd say that it was the weather," she replied. "Isn't that the way you saw it, Prince Ekial?"
"She's right about that, friend Narasan," Ekial replied. "The peculiar thing is that every one of them we saw was still standing up."
"Let's go on inside," Narasan suggested. "Sorgan Hook-Beak is here, and he'll want to know about this too."
"It _is_ just a bit chilly out here," Trenicia said. Then she reached out and patted Narasan's cheek. "You worry too much, Narasan. I'm a big girl now, and I _do_ know how to take care of myself."
They went on inside the fort and found Sorgan, who was talking with Gunda and the pretty lady Ara. "What's happening, Narasan?" Sorgan asked.
"It appears that the slope to the west of this fort isn't as deserted as we all thought it was," Narasan replied. "There are still bug-people down there, but they're all dead."
"Arrows?" Sorgan asked.
Narasan shook his head. "Cold weather, I've been told. Tell him what you saw, Trenicia."
"It seemed a bit peculiar to me that the horde of bug-people who'd been charging up that slope for several weeks had just vanished—without even leaving any footprints in the snow," Trenicia told Hook-Beak, "so I went on down to have a look. The bug-people are still there, but they aren't moving. I'd say that they all froze to death." She drew out her heavy sword and ran her thumb along the edge of the blade and winced. "It's going to take me _weeks_ to grind away all those nicks," she complained. "I chopped several of the bug-people into pieces, and they were all frozen solid. For some reason they just stopped moving, and the weather turned them all into blocks of ice."
"The bug-people aren't very clever," Sorgan said, "but standing out in the open when it's as cold as it's been here lately is senseless."
"Of course it is," Ara replied. "The bug-people don't _have_ any sense. That's what 'the overmind' was all about. Now that Omago has shut down the Vlagh's voice, the overmind can't contact her children. They're waiting for orders, but they aren't getting any. They don't know what to do, so they just stand there and freeze."
"It seems that they stood there for much too long," Sorgan observed.
"Not too long for _me_ , they didn't," Narasan said with a faint smile.
"I'd take it as a great kindness if you'd let me know where you're going _before_ you go running off, Trenicia," Narasan told the warrior queen again when they were alone in Narasan's quarters. "When I discovered that you were gone, I thought that I'd lost you, and that almost made me want to die. _Please_ don't do that anymore, dear heart."
Trenicia's eyes suddenly went very wide as she stared at Narasan. Then quite suddenly they were filled with tears. She threw her arms about him and held him tightly.
"Are you all right, Trenicia?" Narasan asked.
"I'm just fine," she replied with tears streaming down her face. "You just called me 'dear heart,' and that means that you love me, doesn't it?"
"I thought you already knew that."
"Well, I had some hopes, but you never came right out and said it before."
"We'd have gotten to it eventually," Narasan told her with a faint smile. "Please forgive me, dear heart. I've never had these feelings before, so I'm just a bit clumsy when I try to let you know how I feel."
"You're doing just fine, dear heart," she said, wiping her eyes. "The only problem I can see is that I'll probably break down and cry every time you call me 'dear heart.'"
"That's all right," he said. "It should wash the dust out of your eyes."
"Must you _always_ be so practical?" she complained.
"Practical is what I'm supposed to be, Trenicia," he told her. "It keeps my people alive. Why don't I save 'impractical' just for you?" Then he laughed and fondly embraced her.
[THE
NEST](YoungerGods_toc.html#part_22)
**1**
Keselo was having more than a little difficulty with the true identity of the farmer Omago. He realized that he _should_ have had some suspicions, in view of the evidently unlimited capabilities of Omago's mate. For some reason, however, it had never occurred to him that Omago could probably hurl disasters on the Creatures of the Wasteland in much the same way that Ara could.
The more that Keselo thought about it, though, the more he realized that Omago could almost certainly "tamper" with those around him so that they'd all look upon him as just an ordinary farmer with no unusual talents.
Of course, if what Omago had told them back in Gunda's fort had been true, Omago had even deceived himself. In his search for understanding of the people of the Land of Dhrall, Omago had erased all knowledge of just who—and what—he really was, and he'd grown up as just an ordinary farmer who planted grain and vegetables, watched them grow all summer, and then harvested them when autumn arrived.
It appeared, however, that a certain part of Omago's mind knew exactly who—and what—he really was, and when it became necessary, that part of Omago's mind stepped over the "farmer" subterfuge and took over. That meant that Keselo and his friends were dealing with an entirely different Omago—one who could, and would, step over "impossible" whenever it suited him. He'd gone down to Aracia's temple-town, picked up Rabbit, and returned to Gunda's fort at the head of Long-Pass in slightly more than an hour. Then, to make things even worse, Omago had made them all "unnoticeable"—evidently a variation of invisibility—and then had started taking ten-mile steps across the Wasteland toward the nest of the Vlagh—up until Longbow had firmly suggested that those long jumps _might_ cause some problems.
And so it was that late in a cold winter day they had reached "the nest" of the Vlagh.
"Are we going to go through that cave to the Vlagh's main chamber, or are you going to 'poof' us in there?" Rabbit asked Omago.
"Poof?" Omago asked, sounding just a bit puzzled.
"You know what I mean," Rabbit replied. "Lady Zelana 'poofs' every time she gets a chance."
"Let's just walk in," Longbow suggested. "If we happen to get into trouble in the main chamber, we might need to know which way to go when we run away."
"You still don't entirely trust me, do you, Longbow?" Omago asked.
"You're doing fine so far," Longbow replied, "but if anything can possibly go wrong, it probably will. If it doesn't though, we can all be pleasantly surprised."
Keselo was awestruck when Omago responded to his question about the peculiar shape of the peak that was the nest of the Vlagh by describing erosion in a manner that indicated that he'd actually witnessed something that had taken thousands of years to occur. Then he remembered that Longbow had told him that Omago and Ara had been around since before the beginning of time.
Rabbit seemed to be concerned about the probability that the entire nest would be totally dark, "since bugs don't know much about building fires, do they?"
Keselo reached back to what One-Who-Heals had taught him and remembered something the shaman had briefly mentioned about bugs called fireflies that generate light inside their bodies. "But there isn't any fire involved," he said. "Or so I've been told. I've never actually _seen_ one of them myself."
As dusk settled down over the nest of the Vlagh, Omago led them to the mouth of the cave that almost certainly led to the home of the Vlagh herself. He stopped before they entered, however, and asked his friends again if they could hear a buzzing sound. They all listened carefully, but it seemed that Omago was still the only one who could hear it.
" _Is_ it possible that you're listening to the voice of the Vlagh herself?" Keselo asked.
"It _is_ a possibility, I suppose," Omago conceded. "Let's go on into the cave. The sound might become more clear when we get closer to the Vlagh."
The cave had seemed to be a natural opening in the side of the mountain peak when they'd seen it from the outside, but just a few yards in, the walls were very smooth, and they even looked polished. There were quite a few bug-people moving around in the cave, and Keselo was almost startled when he saw several of them who glowed in the dark.
"Living lamps, I see," Rabbit noted. "The Vlagh seems to think of almost everything, doesn't she?"
"I'd say that she's been filching again," Keselo added. "I'd swear that I've already seen thirty or forty different varieties of bugs—beetles and ants and locusts, and flies—as well as several that have wings."
"Then there are the ones that look like worms—except that they've got fifty or a hundred legs," Longbow added.
"There are a lot of other varieties that we haven't seen yet as well," Omago said.
"How does she manage to keep the peace?" Keselo demanded. "It's more than a little weird to see natural enemies all bunched together like this."
"That _might_ turn out to be very useful," Omago said. "If these bugs start killing each other, we won't have to do very much except stand around and watch."
"Those are the very best kind of wars," Rabbit said. "Am I going to keep on being invisible even if I go on ahead?" he asked. "We probably ought to know what's there, wouldn't you say?"
"They won't see you, friend Rabbit," Omago assured the little smith. "It probably wouldn't be a bad idea for you to go have a look, now that you mention it. I don't like surprises all that much."
As Keselo, Longbow, and Omago moved through the seemingly endless cave, they noted that the more recent hatches of the Vlagh were much larger than the ones that had preceded them. "It would seem that the Vlagh was greatly impressed by the Maags," Longbow observed.
"That's not really a very good idea," Keselo said. "Bigger children have bigger appetites, and there's not really that much food out here in this desert, is there?"
"Other bugs is about all," Longbow replied. "Of course, that might have been part of the idea. There _are_ other nests and 'queens,' if we want to use that term. If the Vlagh's idea was to eliminate all the other bug-tribes out here in the Wasteland, 'hungry children' could be quite useful."
When Rabbit came back with a slightly awed expression on his face and told them about the big, open chamber at the end of the tunnel, Omago became very quiet.
Keselo explained that the big cluster of spiderweb Rabbit had seen was called a cocoon. Though Rabbit and Longbow were listening to him, Keselo noticed that Omago was standing off to one side, listening to something that only he could understand.
"Don't make any noises," Longbow cautioned them. "We'd better take a look at this 'cocoon' thing."
Omago came along behind the rest of them, but Keselo was fairly certain that their friend was very busy now with something else.
They entered what Rabbit had called "the throne room," and Keselo was stunned by the incredible number of assorted bugs crawling across the floor and up the walls in the dim light given off by the few glowing "fire insects." Keselo turned to speak to Omago, but Omago had a look of intense concentration on his face, and he waved Keselo off.
"Where's this 'cocoon' thing you mentioned?" Longbow quietly asked Rabbit.
"I'd say that it's probably in the very center of this cavern," the little Maag replied. "It's a little hard to see from this far back, because there are thousands of bugs between us and that silly bird's nest."
Keselo winced slightly. "Bird's nest" didn't exactly fit.
"Get back against one of the walls," Omago told them. Keselo noted that their friend had a wicked sort of grin on his face. "Several thousand of these servants are just about to leave, and we don't want to get trampled."
"Aren't they supposed to stay here and tend to the baby-bugs?" Keselo asked.
"They just received new orders," Omago replied.
"The Vlagh told them to go away?"
"They _think_ she did, but _I'm_ the one they're obeying."
"How did you manage that?" Rabbit asked.
Omago shrugged. "I shut off the buzz that was coming from the Vlagh, and then I buzzed a new set of orders. I told them that invaders were coming across the Wasteland, and I ordered most of the care-givers to go out of the cave and fight off all those evil people-people. A few of them will stay behind to care for the new hatch that's just about to come out of the cocoon. I'm almost certain that the Vlagh will come out of the cocoon before the new hatch does, and I want enough care-givers here in the cave to make the Vlagh believe that everything's all right. She's in for a very nasty shock before long, and her screaming will probably go on for quite a long time—a long, long, long time, if I've done this right."
"Have you _ever_ done anything wrong?" Keselo demanded, feeling more than a little irritated.
"Not that I can remember," Omago replied.
After the last of the departing care-givers had left the vast central chamber of the nest of the Vlagh, Omago assured his friends that they were still "unnoticeable" so they crossed the now virtually empty central chamber of the nest to take a closer look at their enemy.
The upper part of the cocoon began to bulge out, a fair sign that the Vlagh was squirming her way out into the open.
Keselo gasped as the Vlagh came into sight. "That's impossible!" he exclaimed.
"Not really," Omago disagreed. "We probably should have expected this."
"That's not the _real_ Lady Aracia, is it?" Rabbit demanded.
"No," Omago said. "She's gone for good. She _was_ the ruler of the East, though, and she was behaving as if she was the queen of the entire Land of Dhrall. The Vlagh thinks that _she's_ the queen, so her duplication of Aracia makes a certain amount of sense. You might want to approve, Rabbit. You don't really want to see the _real_ Vlagh. Nine feet tall the last time I looked and with six legs, waving antennae, and mandibles that could turn rocks into dust. Aracia wasn't quite as beautiful as Zelana, but she was much nicer to look at than the Vlagh is in her real form."
"There's something moving in the bottom of that cocoon," Longbow said then.
"The new hatch," Omago said. "They won't resemble adult bug-people—or Aracia either, for that matter."
The bottom of the web began to give way, and a cluster of worm-shaped infants came wriggling out.
"Caterpillars?" Rabbit said in a voice charged with disbelief.
"It's the standard form of the infant bug-people," Omago explained. "After they've been fed for a week or so, they assume the shape the Vlagh's got in mind for them. They have plenty of feet to get them from here to there and an overpowering appetite. The remaining care-givers have a lot of work ahead of them, I'd say. But I don't think they'll be doing much 'caring.'"
"They're still wriggling out of that cocoon," Keselo said. "How many of them would you say have just hatched?"
"A quarter of a million anyway," Omago replied. "More, probably. The Vlagh needs a _lot_ of servants just now."
The new "puppies" scurried across the floor of the vast chamber toward the greatly reduced "care-givers," and they were making sounds not unlike the crying of newborn humans. Keselo couldn't translate what the infants were saying, but he was quite sure that "feed me!" was a significant part of it.
The "care-givers" didn't seem to be very interested—at least not until the howling newborns reached the area near the west side of the chamber.
Then something happened that wasn't supposed to happen. One of the "care-givers" reached down and snatched up one of the babies and examined it as if the care-givers had never before seen any infant bugs.
Then, evidently satisfied with what it saw, the servant stuffed the caterpillar-like infant into its mouth and bit down hard. The other "care-givers" watched closely, and then they too snatched up infant bugs and stuffed them into their mouths.
"They're eating the babies!" Rabbit exclaimed.
"So it would seem," the farmer Omago agreed. "Isn't that nice of them?"
At that point, the imitation Aracia standing near the cocoon began to scream.
"Now I think you'll put your arrows aside, Longbow," Omago suggested. "The Vlagh's doing exactly what we want her to do."
"How long would you say that she's going to continue the screaming?" Longbow asked.
Omago shrugged. "Forever, most likely," he said.
"It won't really be very hard for her to lay a new batch of eggs, will it?" Longbow asked.
"Not in the least," Omago replied. "Of course, the eggs will never hatch. That's the main reason we came here, friend Longbow. The Vlagh won't produce any live servants now. I'd say that the Vlagh will never have any children—or warriors either. From here on until the end of time, the Vlagh will never produce another child, and after about six weeks she's going to be all alone here in her nest—weeping and screaming. Does that satisfy your need for vengeance, mighty hunter?"
"Her screaming _is_ sort of beautiful, isn't it?" Longbow agreed, "and I wouldn't for all the world want to interrupt her." Then he carefully slid the arrow he'd been holding back into his quiver.
[THE
LAST
GENERATION](YoungerGods_toc.html#part_23)
**1**
It came to Rabbit that they shouldn't really be surprised that Omago was more than just a farmer. Omago's mate, the beautiful Ara, could do things that not even the gods of the Land of Dhrall could duplicate. A woman with _that_ kind of power wouldn't be very interested in a man whose main goal in life was to grow lots of turnips. So Rabbit was not surprised that Omago understood the nature of the creatures that confronted them in the throne room of the nest.
The bulging eyes of every bug on the chamber floor, those who were partway up the walls, and even those clinging to the ceiling were fixed on the strange cocoon as if it were some kind of holy object.
"We seem to have arrived right on time, then," Omago said. "The Vlagh is instructing the horde of 'care-givers' to take good care of this new hatch."
Omago was staring at the cocoon, and then he suddenly laughed. "I think that does it," he murmured. Then he frowned again, and what appeared to be almost all of the bug-people in the vast chamber suddenly rushed toward the narrow tunnel that led back to the outside.
"Why didn't you just send them _all_ away?" Rabbit wanted to know.
"I need the few that are left, Rabbit. They're going to do something that's probably going to make the Vlagh start screaming, and she'll probably keep it up for a long, long time."
Since Rabbit and the others were still invisible to the remaining bugs, they crossed the now nearly empty chamber to get closer to the cocoon.
It was then that the cocoon split with a ripping sound as a very familiar figure came crawling through the web.
Rabbit flinched back. "I thought she was dead!" he exclaimed.
"That's not quite accurate, little friend," Omago said. "What we're looking at is _not_ a reborn Aracia. I'd say that Alcevan told the Vlagh that Aracia had been the queen of the East, and the Vlagh evidently decided to alter her form until she resembled Zelana's elder sister. It _is_ quite a bit more attractive than the Vlagh's _real_ form could ever be, and the Vlagh has always adored adoration. In some ways, the Vlagh and Aracia are very much like sisters. Even bugs have a certain sense of vanity. Then too, the Vlagh might have a certain amount of deception in what passes for her mind."
The Vlagh, disguised as Lady Aracia, made a peculiar buzzing sound as countless many-legged worms scrambled across the nearly empty floor of the nest. They rushed to where the bugs called "care-givers" were waiting, and they all began to make a sort of squeaky sound.
"I don't speak bug," Rabbit told Keselo, "but I'd guess that the puppies are all saying, 'feed me, feed me, feed me.'"
"That probably comes fairly close, yes," Keselo agreed. "Now that Omago has chased out _most_ of the puppy-feeders, the baby bugs might have to wait in line for quite a long time."
"Do you think they'd know how to stand in line?"
"Probably not," Keselo replied. "I'd say that we're about to see a very interesting fight any minute now."
It wasn't exactly a fight they saw, however. The full-grown bugs looked at the tiny worms with legs for a moment or two, and then they began to eat them, snatching them up with their front claws and biting off their heads.
The Vlagh began to scream, but the "care-givers" paid no attention and continued their feast.
"I think the Malavi call that 'thinning out the herd,' don't they?" Rabbit said.
"I believe I've heard them use that term, yes," Keselo agreed.
"Big Mommy doesn't seem to like it very much," Rabbit added.
"I think you might have spent too much time in the vicinity of Eleria," Keselo suggested. Then he looked at Longbow and Omago. "I'd say that our friend Longbow might be having a bit of a problem right now," he said. "He'd _really_ like to shoot a dozen or so arrows into Big Mommy, but her screams are probably the most beautiful music he's ever heard."
"It _is_ a pleasant sort of sound, isn't it?" Rabbit agreed. Then he looked around at the vast chamber. "What do you think, Keselo? Should we stay here and listen to Big Mommy sing, or should we snoop around in the other parts of the nest and find out how all the other buggies are reacting to this disaster?"
"That might not be a bad idea," Keselo agreed. "I'm fairly sure that the other bug-people are filled with confusion, but maybe we should go look and make sure."
**2**
If it's all right with you, Omago," Rabbit said to their friend, "Keselo and I talked it over, and it seems to us that taking a quick look at the other parts of this fort—or whatever it is—might be a good idea. If the bugs are all coming apart, fine and dandy, but if they look like they're about to go charging out to kill all the people-people in the vicinity, we ought to know about it."
"That's a very good idea, Rabbit," Omago said. "We've all spent so much time concentrating on the Vlagh that we haven't really paid much attention to her children. Now that her mind isn't functioning anymore, her children might try to do almost anything, and we'd better know about it."
"They don't really live very long, do they?" Rabbit asked.
"No. Four to six weeks is about all. Now and then you might come across one that's seven or eight weeks old, but I don't think we'll ever see one that's older than that."
"I think we're going to need a torch," Keselo said. "There are probably bugs out there that can see in the dark, but my eyes aren't quite that good."
Omago reached into the canvas bag hanging from his belt and took out a pale, round object that appeared to be glass. "Use this," he said, handing the glass ball to Keselo. "When you need some light, squeeze it, and it'll give you all the light you need. When you want darkness, loosen your grip."
Keselo examined the round ball rather closely. "I don't really see anything in this that could produce light," he said.
"It isn't in there," Omago said with a faint smile. "It's in here." And he tapped his forehead.
"Oh," Keselo said. "I probably should have realized that."
"That's our Keselo for you," Rabbit said. "He seems to need to know how everything works. Don't let him get too close to the moon, Omago. He'll probably take her apart to find out what keeps her up in the night sky."
"Curiosity isn't a bad thing, Rabbit," Omago replied.
"I was only teasing," Rabbit said. "It's all right to tease your friends, isn't it? Come along, Keselo," he said then. "Let's go out and see if we can find any of Big Mommy's puppies."
"Big Mommy?" Omago asked, sounding a bit perplexed.
"It's sort of what's called an 'in-house joke,' Omago," Rabbit said. "I'd explain it, but it'd take much too long. Shall we go, Keselo?"
"We might as well," Keselo agreed.
The far wall of the vast main chamber was at least a mile from the place where the "care-givers" were eating the Vlagh's babies, but the Vlagh's screams were still quite audible. "She's got a big mouth, hasn't she?" Rabbit said to his friend.
"Oh, yes," Keselo agreed. "I wouldn't want to try to sleep anywhere within ten miles of this place." Then he pointed at a part of the back wall about fifty yards off to the left. "It looks to me like there's a sizeable hole in the wall over there. It might lead to another part of the nest."
"Squeeze that light ball," Rabbit suggested. "Let's make sure that it works before we go crawling into any dark places."
"Omago wouldn't lie to us, Rabbit."
"I'm not saying that he would. The light ball probably works just fine when _he_ squeezes it, but let's make sure that it'll work for you as well. Always test equipment _before_ you need to use it."
"If it makes you happy," said Keselo, squeezing Omago's toy.
When the glass ball began to glow, Rabbit nodded. Then he looked around at the vast chamber that was still echoing to the screams of the Vlagh. "This might take us quite a while, Keselo," he suggested. "If this mountain—or whatever we want to call it—is jam-packed full of bug-people, there could be hundreds of chambers where they hole up when they're not out in the open eating people-people."
"We'll never know for sure until we take a look," Keselo said. "The more we see, the more we'll know."
The hole in the rear wall that Keselo had seen was not exactly what Rabbit would have called a doorway, but there were many signs that it was used fairly often by the assorted children of the Vlagh. When Rabbit and Keselo crawled through the hole, they came out in what appeared to be a shaft that reached far, far up in this imitation mountain.
"I think we're in trouble," Rabbit said.
"Oh?"
"We didn't think to bring a ladder."
Keselo squinted up. "The walls of this shaft aren't really very smooth," he noted. "It looks to me like there are plenty of handholds on the sides of the shaft."
"Bugs have hands now?" Rabbit said, pretending that he was astonished.
"Funny, funny, Bunny," Keselo replied sarcastically.
"Bunny?" Rabbit protested.
"I filched that one from Eleria," Keselo replied with a faint smile. "Let's see if we can make our way up this shaft. If it gets too risky, we'll go back and see if Omago can create a ladder for us."
They climbed slowly up the wall of the shaft, and Rabbit noticed that there were many, many small round holes in the solid rock. Evidently generations of bugs had been climbing up and down the shaft for hundreds of years. "It looks to me like there are quite a few openings in the walls of this up and down corridor," he said.
"Separate quarters, most likely," Keselo suggested. "I'd say that the various kinds of bug-people avoid each other when they possibly can."
"Just ahead," Rabbit whispered. "I just saw a bug poke its head out of that hole in the wall just ahead of us."
"Do you think it might have seen us?"
"Probably not. It seemed to be looking _up_ the shaft instead of down. To get down to the bald truth, Keselo, I'm not really thrilled by the notion of crawling into a hole in the wall that _might_ just be filled to the brim with hungry bugs."
"I'm with you all the way on that one, Rabbit," Keselo replied. Then he leaned back slightly and peered up the gloomy shaft. "There's a much larger opening about fifteen feet above the little one just ahead of us. That one might be a safer one to investigate."
"I _do_ like the word 'safe,' my friend," Rabbit agreed.
They carefully climbed up the rugged shaft wall until they reached the larger opening. Rabbit quickly poked his head around the edge of the opening and then jerked it back. "No bugs," he whispered. "Are we still invisible?"
"I think the word Omago used was 'unnoticeable,'" Keselo replied. "I'd say that it's still in place. If any one of the bugs had actually seen us, she'd be making a lot of noise by now."
"I'm _never_ going to get used to the idea that all our enemies are women."
"I wouldn't think of them as 'women,' Rabbit," Keselo said. "Female is one thing, but 'women' is something entirely different."
The larger opening appeared to be the mouth of a cave of some sort, and, much like the cave that had led to the vast chamber down below, this cave _also_ led to a much, much larger room. When the two of them reached that chamber, they stopped. There were thousands of bugs there, but they were not all of the same variety, and the different kinds of bugs were staying away from each other, for some reason. Each group was all clustered together in the same place, and it seemed to Rabbit that there was a growing antagonism in the clusters of some varieties of bugs. Some of the groups seemed to be speaking inaudible sounds and others were reaching out with their front legs to touch the front legs of others. "I don't imagine that you learned bug-language when you were going to school," he whispered to his friend.
"We don't have the right kind of equipment to talk bug, Rabbit," Keselo replied. "Most of the time, bugs communicate by touching each other. If their language involves sound, like ours does, they make the sound by rubbing their legs against each other. Bug language would have to be quite simple, I think. They aren't really overloaded with brains, after all. I'm just guessing here, but I'd say that 'kill, kill, kill,' is about as far as the language of bugs would go."
Something suddenly occurred to Rabbit. "Are you up for an experiment of sorts, friend Keselo?" he asked.
"That might depend on just what kind of experiment we're talking about."
"Omago can do all sorts of peculiar things, wouldn't you say?"
"I think I'd take it quite a bit farther than 'peculiar.' What did you have in mind?"
"Why don't you hold out that light ball Omago gave you and squeeze it?"
"Do you want to announce that we're here to about a half-million unfriendly bugs? Are you out of your mind?"
"I don't think they'll see it, Keselo. Omago wouldn't give us something that'd put us in any danger, would he? I'm sure that _we'll_ see the light coming from that glass ball, but I'm just as sure that the bugs won't."
"A light that only _we_ can see?"
"Something like that _would_ be sort of Omago-ish, wouldn't you say?"
Keselo frowned. "That was a rotten thing to do, Rabbit," he complained. "It _is_ a definite possibility, and it's raised my curiosity so much that I almost _have_ to try it."
"You worry too much, Keselo," Rabbit said. "If it works the way I _think_ it will, we'll have a tremendous advantage."
"And if it doesn't work?"
Rabbit shrugged. "We've got a clear path back to that shaft. We can escape if we really have to. Try it. Think of the advantage. We'll have light, but the bugs will still be in the dark."
Keselo took the glass ball out from under his shirt. "Just don't get in my way if we have to make a run for it, Rabbit."
"Don't worry about a thing, friend Keselo," Rabbit said. "I can run at least twice as fast as you can, so I won't get in your way at all."
"I've _got_ to find out if your absurd idea will actually work, Rabbit," Keselo complained. "It _shouldn't_ work that way, but I'll fly apart if I don't try it and find out." He raised the glass ball up over his head, and the growing light coming from Omago's toy grew brighter and brighter as Keselo's hand squeezed it.
"You can let it go now, Light-Bearer Keselo," Rabbit told his friend. "The light's as bright as the noon sun, but the bugs out there don't seem to be able to see it."
"Oh, the poor babies," Keselo said. He began to squeeze and release in rapid succession, and the light went on and off as Keselo's hand told it to.
"Show-off," Rabbit scolded. And then he laughed.
They came across several familiar bug-people as they went farther back into the huge chamber. There were a lot of the snake-bugs that had made things so unpleasant in the ravine above the village of Lattash in one area, and Rabbit was a bit surprised to see several of the glowing fire-bugs mixed in with the snake-bugs. "It looks to me like the fire bugs are almost welcome in the vicinity of nearly every other kind of bug," he said to Keselo.
"You're probably right," Keselo agreed. "Light can be very useful. I wouldn't be at all surprised if the other bugs even feed the ones that glow in the dark."
"The bug-people pay for light, you mean?"
"It's not out of the question, friend Rabbit." Then Keselo stopped and pointed at the ceiling. "Bug-bats," he said.
"It's almost like old times, isn't it?" Rabbit said. "Let's not get them excited. I didn't bring any fish-nets along this time."
As they moved farther back into the chamber, they encountered several more of the familiar varieties of bug-people, and quite a few others they'd never seen before. "What would you say that shaggy one whose hands drag on the floor might be?" Rabbit asked.
"Some sort of ape," Keselo replied.
"I don't think we ever came across any of those, did we?"
"Not that I recall, we didn't. It's probably a variety that didn't turn out very well. The Vlagh experimented all the time, I'd say, and she probably turned out more useless creatures than good ones."
"Junk-bugs?" Rabbit suggested.
"That's probably as good a term as any," Keselo agreed.
Then a kind of roaring sound came from farther back in the chamber. "If that's what I _think_ it is, we're very lucky that we didn't encounter any of them in these various wars. It sounded very much like a lion to me."
"What's a lion?"
"A very, very large cat. I've heard that a full-grown lion weighs about five hundred pounds, and it's got long, sharp teeth and deadly claws. It's a tropical animal, though, so it probably wouldn't have been of much use in the Land of Dhrall—except possibly down in Veltan's Domain."
The roaring continued, but there was also another sound echoing from the walls up ahead.
"It sounds to me like there's a fair amount of 'unfriendly' on up ahead," Rabbit noted.
"That's not at all unlikely," Keselo agreed. "As long as 'Big Mommy' was running things, her children probably tolerated each other, but Omago broke her grip on her puppies, and now her children are all trying their very best to kill each other."
"Something to eat might be involved as well," Rabbit added. "This isn't called 'the Wasteland' just for fun. There's nothing to eat here except rocks—and the neighbors, of course."
"Good point," Keselo agreed. "Let's have a look and see just how savage all of this really is. The nest might be empty much sooner than we all thought it would be."
"What a shame," Rabbit replied with mock regret. And then he laughed.
"I don't think I've ever seen a six-legged cat before," Rabbit said as the two friends moved along the chamber wall toward the violent encounter between several varieties of bug-people.
"The Vlagh probably blundered on that one," Keselo replied. "She's never fully understood why many creatures don't need that many legs, so it seems that six legs show in these imitations quite often."
"She must have paid more attention when she conjured up that one called Alcevan, then," Rabbit said. "She looked like a real woman—a little small, maybe, but she had everything else that a woman's supposed to have."
"I'd say that Alcevan was the best one the Vlagh ever produced. In many ways Alcevan is even better than the Vlagh herself, and when you add that odor, the little imitation priestess came very close to winning the war in temple-town."
"You might say that she even won a war for _us_ when she gutted out Takal Bersla. Torl was watching when that happened, and Torl's seen a lot of nasty things happen to people, but he told Cap'n Sorgan that he almost threw up when Alcevan spilled poor Bersla's insides all over the temple floor."
"It couldn't have happened to a nicer fellow," Keselo agreed. "We might want to stay back just a bit, Rabbit," he said then. "I see several varieties of bugs approaching those lion-bugs, and I suspect that open war is just about to break out."
"You're right there, friend Keselo," Rabbit agreed. "I see a dozen or so very large spiders on the other side of this chamber, as well as the lion-bug, some beetles that look like they're wearing armor, and some wasp-bugs flying around with their stingers held at the ready. Do _all_ bugs have those great big eyes?"
"They want—and _need—_ to see everything, Rabbit." Then Keselo gasped. "What is _that_ thing?" he exclaimed.
Rabbit stared at the creature Keselo had just pointed out. "She actually tried to imitate Longbow!" he exclaimed.
"It looks that way to me too," Keselo agreed, "but it has six limbs instead of only four, and it's carrying two bows instead of only one."
"Now _this_ I want to see," Rabbit declared. "If that thing shoots two arrows at the same time, it can kill more of its enemies than any other bug thing could ever manage."
Keselo and Rabbit watched closely, and sure enough, the archer bug was killing two lion-bugs—or beetle-bugs—at the same time. The dead bugs with arrows in them began to pile up.
"She's good," Rabbit reluctantly admitted. "Longbow never misses, but he only uses one bow."
"Look out!" Keselo exclaimed as a heavy crashing sound came from overhead.
Rabbit and Keselo pulled back from the large chamber as the overhead ceiling began to shatter. They could see a new kind of bug above them, and they had big rocks in their claws.
"They're _huge_!" Keselo exclaimed. "They have to be at least ten feet tall, and they're slamming boulders down on the top of the ceiling. The whole thing will collapse any time now."
Then a flock of the bug-bats came flapping in overhead, and they began attacking the lion-bugs and the bug-archers.
"That's it!" Rabbit declared. "Let's get out of here, Keselo. It's time to go on back and tell Omago what's going on in this part of the nest. Give them a couple of days, and there won't be _any_ bugs left alive anywhere in this nest."
"What a shame," Keselo murmured, and then the two of them ran back toward the central shaft, and they didn't even laugh very much.
**3**
When the two explorers returned to the main cavern, the Aracia creature was still screaming, but no other bugs were around anymore.
"I wasn't sure just _what_ 'Vlagh' was supposed to mean back in the old days," Rabbit said. "That's why we called her Big Mommy. But I _do_ know what it means now."
"Oh?" Keselo stepped in. "What's that?"
"I'd say that 'all alone' comes pretty close, wouldn't you?"
"Not quite, friend Rabbit," Longbow said. "If you listen carefully, you'll hear some other screams coming from a different part of the nest. The pretty lady delivered another screamer while you two were roaming around in the nest. The one called Alcevan is back home now, and she'll be able to listen to Big Mommy's screams for a long, long time."
"Except that she won't _live_ for a long time, will she?" Keselo asked.
"Pretty Ara took care of that before she brought Alcevan here," Omago replied. "Alcevan will live for as long as Big Mommy keeps screaming. Artistic screaming deserves an audience, wouldn't you say? There are solid stone walls between those two, so they won't see each other or be able to speak to each other. They'll exchange screams, and that's all."
"Duets _are_ a bit nicer than solos," Keselo said.
"It's all over, then, isn't it?" Rabbit said, feeling just a bit sad that his days in the Land of Dhrall were coming to an end.
"Are you saying that you'll actually _miss_ this war, Rabbit?" Longbow asked.
"Not the war as much as I'll miss the friends I've made here." Then he snapped his fingers. "What do you think, Keselo?" he asked. "Should we tell Longbow about the imitation of him that Big Mommy made just a while back?"
"Are you sure that it won't offend him?" Keselo asked.
"It's real hard to offend Longbow, friend Keselo," Rabbit said. "Anyway, Longbow, it seems that you _really_ impressed Big Mommy with your bow and your arrows—enough, anyway, that she made her own version of you. It wasn't at all bad, either. Of course, it was a bug, so it had six legs instead of only four. After it'd learned to stand up on its two hind legs, it had four arms to work with. That meant that it could hold two bows and shoot two arrows at the same time. It wasn't a half-mile away like you are, but up to a hundred or so paces away from its enemies, it could kill them two at a time." Then an odd notion came to him. "I'd be willing to bet that Omago here could modify you just a bit and give you an extra two arms—or maybe take a quick look at an octopus and give you _six_ arms altogether. You could kill a whole army all by yourself if you were built that way."
Longbow smiled faintly. "Very interesting, friend Rabbit," he said. "And just where were you planning to set up your arrow factory after Omago gives me all those extra arms? I'll need a _lot_ of arrows, you know."
Rabbit winced. "I'll forget all about this if you will, friend Longbow," he said.
"Whatever seems right to you, little friend." Then he looked at Omago. "Are we finished here?" he asked.
"Unless you'd like to stay and listen to the Vlagh scream and wail," Omago replied.
Longbow shrugged. "After you've heard a few hours of screaming, it starts to get a bit boring. Why don't we go back to Gunda's fort and let everybody know that the war's over now, and that it's not very likely that it'll come back."
"Good idea," Omago agreed. "Let's go."
"Why didn't you just drive a dozen or so arrows into her, Longbow?" Sorgan asked the archer after Omago had described the current condition of the Vlagh to their friends in the large room at the center of Gunda's fort a few days later.
Longbow shrugged. "Omago persuaded me not to," he replied. "She might have taken a minute or so to die if I'd driven an arrow into her. Now that all her children are dead and she'll never lay any more eggs that will give her other children, she'll remain in that nest screaming in agony until the end of time. In a certain sense she's paying for each and every one of our friends that the bug-people killed. I'd say that she probably _wanted_ me to kill her, but I've always made a point of _never_ giving the Vlagh anything she wanted."
"So she's all alone in that hole in the ground screaming her lungs out," Sorgan said. "I think I'll go with Longbow on this one. Let her scream. She's not close enough to any town to keep the people awake."
"Not exactly all alone, Captain," Omago said. "My dear Ara grabbed the bug-woman called Alcevan and jammed _her_ into the Vlagh's nest as well. She'll never _see_ her mother, but she _will_ hear her screaming. She'll scream as well—and probably for just as long. I'm sure that most of you have come to realize that you never want to do _anything_ that offends my mate, and Alcevan stepped over that line when she pushed Aracia into Lillabeth's playroom. Aracia ceased to exist, but Alcevan will exist—and suffer—for all eternity."
"That goes quite a bit farther than getting a plateful of raw beans for supper," Rabbit said.
"A _lot_ farther, yes."
"That pretty much brings an end to all these wars here in the Land of Dhrall, doesn't it?" the Trogite Commander Narasan said as Zelana and her young brother Veltan entered the room.
"Not _yet_ , friend Narasan," Rabbit's captain declared. "Things aren't over here until we've stored all that gold we found in Aracia's temple on board our ships." He pursed his lips and then spoke to Zelana and Veltan. "Why don't we just forget about the gold you two offered us to come here and fight this war?" he said.
"Generosity, Sorgan?" Zelana said with a certain surprise.
Sorgan shook his head. "Not really," he replied. "Caution would be more accurate. We've got tons of gold down there in the temple, and too _much_ gold would probably sink our ships."
"Wise decision there, Captain Hook-Beak," Veltan agreed.
Then Eleria and her big sister Balacenia came in to join them. "Where have you _been_ , Bunny?" Eleria demanded.
"Several of us had to go out into the Wasteland to put the Vlagh out of business, baby sister," Rabbit replied.
"Isn't he just the nicest person we've ever seen?" Eleria said to the others as she climbed up into Rabbit's lap. "You _do_ owe me a lot of kisses, though, Bunny," she said. "Fair is fair, after all. When you all took off like that you didn't leave anybody at all here to give me kisses, so it's time for you to start paying me what you owe me."
"I'll get right on it, baby sister," Rabbit promised.
The discussion of what had happened in the nest of the Vlagh went on for most of the rest of that day. Then at the supper table when they were all feasting on Ara's magnificent cooking, the warrior queen Trenicia turned to Commander Narasan. "Now that this is all over here in the Land of Dhrall, what are _our_ plans, brave leader?"
"We have plenty of time to discuss that, dear Queen Trenicia," Narasan replied.
"How much time?" she pressed.
"I'd say the rest of our lives, glorious Trenicia," Narasan replied bluntly.
"You said _what_?" she demanded.
"I thought it was very clear, dear queen," Narasan said. "Get a firm grip on this, Your Majesty. You will _not_ leave me—not ever. You are _mine_ now."
"And _you_ are _mine_ ," she replied just as fervently.
"We can discuss this when we're alone," Narasan said, looking slightly embarrassed by his own possessive remarks.
"Right," Trenicia replied, standing up. "Let's go. I've been waiting for _this_ particular discussion for months now." Then she paused. "What took you so long?" she asked.
Narasan actually blushed at that point.
It was much later that night, but Rabbit found that he just couldn't sleep. His memories of all the things that had happened here in the Land of Dhrall kept coming back to haunt him. In an odd sense, he was no longer totally a Maag. He still hungered for riches, of course, but that wasn't all that unique. Keselo found gold to be at least as pretty as Rabbit did, and Prince Ekial was also attracted to gold. Longbow, however, was indifferent to it. His central goal in life had always been the destruction of the Vlagh and all her offspring. At the last moment, though, Longbow had set his arrow aside after Omago had advised him that in her current state of total isolation, the Vlagh might have welcomed four or five arrows to end her eternal grief.
"This is the strangest place," Rabbit murmured as he wandered around the dark corridors of Gunda's fort. "I'm quite sure that I _will_ miss it—and the friends I've met since I came here. My life will seem sort of empty for a long, long time, I'm afraid."
Then he drew in a long breath. "This isn't going anywhere," he muttered. "I might as well go back to bed and see if I can get some sleep."
He was quite sure that he wouldn't, though, but he went back to give it another try.
[EPILOGUE
IN
THE
LAND
OF
DREAMS](YoungerGods_toc.html#part_24)
**1**
I'm not sure that this is really a very good idea, Vash," Balacenia said to her brother as the younger gods and their elders gathered in Dahlaine's home inside Mount Shrak. "Dahlaine's people-people have access to this place. I'm sure that they're nice enough, but this is a matter they probably shouldn't know about. There are almost certain to be some arguments, and I don't think we want people to know that the gods don't agree about _everything_ , do you?"
"You may have a point there, dear sister," Vash agreed. He squinted at Omago and Ara, who were standing somewhat apart from the others. "I'll go mention your reservations to Mother and Father. Where would you say we should go?"
"Where else, Vash?" Balacenia replied.
"That place is _ours_ , Balacenia," Vash objected.
"I know, and it's so beautiful that all the others should agree with almost anything we say. We _have_ had a few visitors there from time to time, and they've always agreed with anything we tell them."
"I'll see what I can do, mighty leader."
"Why are you throwing _that_ in my face, Vash?"
"You might as well get used to it, Balacenia. You _will_ be the Dominant this time. I'll go see what Mother and Father have to say."
"Oh, bless you, Vash," Balacenia replied.
"Bless?"
"Just practicing, baby brother. I haven't been the Dominant for a long, long time. If I remember right, blessings make the others wiggle like puppies."
Vash grunted and went off to speak with Omago and Ara.
"Do you pick on him like that all the time, Big-Me?" Eleria asked.
"Only when it's necessary, Little-Me."
After Vash had spoken briefly with Omago and Ara, he came back across the chamber. "They agreed that this might not be the best place to have this meeting," he reported. "They'll speak with Dahlaine about it. He'll listen to _them_ , but he might resent it if you and I were the ones who make the suggestion."
"Those two can be _very_ useful," Balacenia agreed.
"I don't see what's wrong with Mount Shrak here," Dahlaine objected. "I can keep all the local people out of here."
"I'm sure you can, dear Dahlaine," Ara said, "but it's winter here and sort of gloomy. I've seen this Land of Dreams Vash and Balacenia created out of pure imagination, and it's probably the most beautiful place in the entire universe. We have an important decision to make, and beauty will make it nicer."
"I still don't see why it's necessary to go there," Dahlaine grumbled.
"I learned a long time ago that it's not wise to offend the lady who runs the kitchen," Omago said.
"I don't _need_ food, Omago," Dahlaine replied. "Kitchens don't interest me, because I don't eat."
"You ought to try it sometime," Omago suggested. He frowned just a bit. "I suppose there might have been some obscure reason for that 'don't eat or sleep' rule, but I think it's out of date now."
"How do we get to this imitation place?" Dahlaine asked.
"Your Dreamer, Ashad—who's really Dakas—knows the way, big brother," Balacenia told him. "We had a meeting there a while back. There were several things we needed to agree about, so we all went to the Land of Dreams to make some necessary decisions."
They all went on out through the long tunnel to the cave-mouth that opened out onto the snow-covered grassland. Then each of the Dreamers—or younger gods—took his or her elder by the hand, and they all rose up into the chill winter sky.
Unlike the others, however, both of Balacenia's hands were full. She and Eleria could not merge as the others did, so she was obliged to carry both Zelana and her alternate. Balacenia was quite certain that Eleria was the only possible successor for Aracia, but she was fairly sure that Eleria would violently object. There had to be something that only Ara and Omago could offer Eleria that would make the little girl willing to accept divinity. "I think I'm going to have to work on that a bit," she murmured.
"I didn't quite catch that, dear," Zelana said.
"Just thinking out loud, Zelana. It's a habit I picked up back in the days before people existed."
"That was a very lonely time, as I recall," Zelana agreed. "I used to recite poetry to trees and sing songs to Mother Sea."
"Did she like your songs?"
"Some of them, yes. I could always tell which songs she liked, because she'd fill the sky with rainbows."
"And if she didn't like them?"
"Hailstorms, as I recall."
Balacenia winced. "Did you ever teach Eleria how to sing?"
Zelana nodded. "It was a mistake, though. Her voice is so beautiful that it'd fill Mother Sea's eyes with tears. It worked rather well if the weather had turned dry, though. Eleria can probably stir up a three-day rainstorm if we really need it. Is this Land of Dreams much farther away?"
"No," Balacenia replied. "It could be right here, if Vash and I wanted it to be. Vash is stirring up the aurora, though. Nobody argues with anybody else when the aurora's in bloom."
The younger gods gently lowered their elders down onto the Land of Dreams, and Balacenia saw that Vash had outdone himself in the creation of the current aurora. They usually sort of lingered along the horizon, but this one seemed to be rising up from meadows and mountains on all sides of the Dreamland, and the beauty almost took Balacenia's breath away.
"Tell me, Vash," Veltan said to the real version of Yaltar, "whatever possessed you and Balacenia to conjure up this beautiful place?"
"It was a long, long time ago, Uncle. There weren't any people—or animals, for that matter—and Balacenia and I were looking at twenty-five eons with nothing to do except maybe watch grass grow. After a few centuries of that, we really needed something else to look at. Balacenia had caught a brief glimpse of an aurora along the northern horizon, and then she and I drifted on up north—actually into the Domain of Dakas. I suppose you could say that we stole an aurora from Dakas and then planted it in a place that didn't really exist—except in our Dream, of course. We spent centuries here soaking in the beauty of our Dream. It made that empty cycle bearable."
"I'll concede that it's much, much prettier than the moon was when Mother Sea sent _me_ there," Veltan admitted. "Of course the moon lied to me when she told me that Mother Sea was still angry with me for tampering with her color."
"You can't really trust the moon, Uncle," Vash said.
Dakas gently lowered Dahlaine onto the Land of Dreams, and old Grey-Beard, evidently still a bit irritated, glanced around. "We have something very important to attend to," he told them all, "and looking at the imaginary scenery here is just a waste of time."
"There's no great rush, Uncle," Dakas said. "Time doesn't really exist here. When Balacenia and Vash brought us here last summer, it seemed like we'd been here for months and months, but that was only a dream. When we woke up again, we were all back home and only one night had passed. We can take our time making our decision because time doesn't mean anything here. A century—or even an eon—can crawl past, and the world won't be a day older."
Omago and Ara were still caught up in the glory of the aurora, but Veltan, with a slightly worried look on his face, quietly approached them. "Just how are we going to create a god to replace sister Aracia?" he asked them.
"She's already here, Veltan," Omago replied. "All we have to do is persuade her to take up the position—if that's the right term."
Veltan looked around. "I don't see any unfamiliar faces," he said.
"Of course you don't, dear Veltan," Mother Ara said. "You've probably known her since she was a baby. You _did_ visit Zelana in her grotto a few times after the children arrived, didn't you?"
"Well, yes, but—" Veltan stopped, and his eyes went wide as he stared at Eleria. "Are you saying that you're going to pile _two_ Domains on poor Balacenia's shoulders?"
"We wouldn't do that, dear Veltan," Ara said. "Eleria and Balacenia were separated a long, long time ago." She paused briefly. "That's in baby-terms, of course. Eleria was too independent, and Balacenia enjoyed her company so much that she didn't put any restrictions on her. It _could_ be, I suppose, that Mother Sea and Father Earth _knew_ that Aracia would destroy herself eventually, so they made Eleria very special."
"Why is everybody always talking about me like that, Big-Me?" Eleria asked.
"Because you're so special, Little-Me," Balacenia replied. "Isn't being special a lot of fun?"
"Not for me it isn't," Eleria said. "I'm not feeling the least bit goddish, so tell the others to go pick somebody else."
"Who?" Balacenia replied. "There's nobody else available. You spent your childhood playing with the pink dolphins, and that separated you and me so much that we'll never be able to meld into a single person again. You already have as much power—or even more—than any of the rest of us—elder or younger—have. Like it or not, you _will_ replace Aracia when Enalla starts feeling sleepy."
"I don't _want_ it!" Eleria almost shouted, stamping her foot on the ground.
"'Want' has nothing to do with it, dear Little-Me," Balacenia said rather bluntly. "Like it or not, you _will_ be the goddess of the East when Enalla goes to sleep."
Eleria was definitely sulky after Balacenia had harshly dropped the truth on her. Eleria had always been able to persuade various people to do what she wanted them to do, but Balacenia had just deliberately slammed that door in Eleria's face. She gave her sweet little alternate some time to sulk before she moved on. "Stop pouting so much, Little-Me," she said. "Zelana's coming, so don't get her all upset." Then she paused. "You _do_ know that we absolutely _must_ replace Aracia—soon."
"What do you mean by 'soon,' Big-Me?" Eleria demanded. "Enalla—or Lillabeth—will run things in the East for the next twenty-five eons, won't she?"
"Yes, she will, and that gives _you_ twenty-five eons to grow accustomed to the _new_ Eleria."
"No! No! No!" Eleria screamed, stamping her foot on the ground again.
"Don't do that, Little-Me," Balacenia scolded her. "You're just being silly." Then she paused and spoke more quietly. "You _do_ realize, don't you, that the _real_ gods, Omago and Ara, will have to give you anything you want to persuade you to accept Aracia's silly temple?"
" _Anything?_ " Eleria replied, looking suddenly more interested.
"You name it, Little-Me, and they'll have to give it to you."
"Are you absolutely certain sure about that, Big-Me?"
"Tell them to kick down all the mountains or grab the moon and throw her away, and they'll _have_ to do what you tell them to do."
"Well now," Eleria replied. "Isn't _that_ interesting?"
**2**
Balacenia and Eleria went across the Land of Dreams to a nearby grassy hilltop where Ara was showing the aurora to her mate.
"It's beautiful, dear heart," he said to Ara. "It looks almost like the whole sky is suddenly in bloom."
Ara smiled fondly. "You have always loved blossoms, dear heart, but I doubt that you've ever seen the sky in bloom before."
"When Vash and I were constructing this land, we spent a lot of time making her pretty. The outside world way back then wasn't really very attractive, so Vash and I concentrated on beauty," Balacenia explained.
"And you did very, very well," Omago said.
"Do you suppose we could get down to business here?" Eleria asked rather tartly.
"Mind your manners, Little-Me," Balacenia chided.
"I'm being as polite as I can, Big-Me. I'm not the least bit interested in replacing that monster who destroyed herself trying to kill Lillabeth. I do _not_ want a temple, and I do _not_ want any part of a priesthood pretending to adore me. I'd much rather go back to the pink grotto so I can play with my dolphins and tend to the Beloved while she's asleep. Why does there have to be an extra goddess in the East anyway? Just tear down that silly temple and tell the fat priests that their life of luxury is over. Let Lillabeth and Enalla take care of things there."
"It won't work that way," Omago explained. "They will return to being one single identity, small one."
"That's 'Little-Me,'" Eleria corrected.
"I didn't quite follow that," Omago conceded.
"Everybody knows that Balacenia is 'Big-Me,' and I'm 'Little-Me,'" Eleria replied. Then she gave Omago an arch—and very familiar—look. "Now you owe me a hug," she told him.
"I'd be just a little careful along about now, Omago," Balacenia cautioned. "Eleria's been hugging people into submission for years now. When she wants something, she'll hug it out of you."
"Tattle-tale," Eleria accused her alternate. Then she looked back at Omago and Ara. "What's so important about having two goddesses in the East?"
"Balance, Little-You," Omago explained. "If there aren't two divinities in each region, it will be _out_ of balance, and it could very well irritate Mother Sea and Father Earth. You saw what happened when Yaltar—who's really Vash—unleashed those volcanos at the head of the ravine above Lattash, and they were only toys compared to what Father Earth can do if he's irritated. Let's keep things safe, Little-You."
"I _like_ him," Eleria said to Ara. "Does he hug good?"
Ara looked more than a little startled by _that_ question. "As far as I can remember I've never had any reason to complain," she replied, blushing slightly.
"Good. Hugs are very important, you know."
Omago actually looked just a bit embarrassed, and Balacenia covered her mouth to conceal her grin.
"All right," Eleria said. "All this talking is very nice, and now we know each other much better, so here comes the question you've been waiting for. What's in this for me?"
"You'll be a goddess, Little-You," Ara replied.
"Why would I want anything _that_ silly? If I asked my pink dolphins to adore me, they'd giggle me right out of the water and never let me go back in again. You're going to have to come up with something better."
"Such as what, Little-You?" Ara asked.
"Don't rush me," Eleria replied. "I'm working on it. I'll get back to you as soon as I make my decision." Then she turned and started on back down the hill again. "Are you coming, Big-Me?" she asked Balacenia.
They went on down the hill and paused in a grove of blossom-covered trees.
"You did very, very well, Little-Me," Balacenia praised her little blonde alternate. "You were blunt enough to get their immediate attention, and then you left them both up in the air when you told them that you hadn't yet decided what you really want."
"That's easy, Big-Me," Eleria replied. "I want them to leave me alone."
"They won't do that, Little-Me. What's your next choice? Make it as impossible as you can."
"What I really don't understand is why they want to drop this thing on me. If they wanted somebody who'd done more than anybody else to defeat the Vlagh, they'd have chosen Longbow. He's the one who actually won the war against the bugs, you know. Not only that, he's just about the best in the world when it comes to hugs."
"Is that all you ever think about, Little-Me?" Balacenia demanded a bit peevishly.
"Hugs _are_ important, Big-Me." Then Eleria peered out through the blossom-covered tree-limbs. "Here comes the Beloved. Maybe _she_ can solve this problem for us."
"What are you two up to now?" Zelana asked rather shortly.
Balacenia shrugged. "Little-Me doesn't want to be a goddess, and she _definitely_ doesn't want to replace crazy Aracia."
"Be nice," Zelana murmured absently.
"I was just telling Big-Me here that if Omago and Ara wanted to elevate somebody to godhood, they should talk with Longbow. If anybody in the world has earned immortality, it's Longbow. If he hadn't been there, all the outlanders—and the native people as well—would have been eaten by the bugs."
Zelana sighed. "Even if Ara and Omago offered him the position, Longbow would turn them down. He doesn't really want anything. His life has been totally empty since the death of Misty-Water."
"That's the answer then," Balacenia declared.
"Revive Misty-Water, you mean," Eleria said. "We may not look very much alike, Big-Me, but we think almost exactly the same—or hadn't that come to you just yet?" Then she turned to Zelana. "Ara and Omago _could_ do that, couldn't they, Beloved?"
Zelana frowned. "It's altogether possible, I think. They'd have to go back in time, but they do that all the time."
"And then we'd have a happy Longbow instead of the gloomy one we all know and love. I'd say that it's worth trying. If I tell Ara and Omago that Misty-Water is my price, they might decide to go pester somebody else."
Balacenia had a strong feeling that she was missing something that might be extremely important, but she just couldn't put her finger on it.
"It _is_ theoretically possible, dear heart," Ara told her mate after Eleria had laid her demand upon them.
"I know that, yes, dear," Omago replied, "but won't it disrupt many, many things that have already come to pass?"
"They _won't_ have come to pass way back then, will they?" Eleria disagreed.
Then several things clicked together for Balacenia, and it made everything so simple that she almost laughed. "As I understand it, you two can move events forward or backward in time, can't you?"
"It's not really all that difficult, child. In the past we've had to correct many mistakes. Worlds are not really as solid as they might appear to be," Ara explained.
Then Balacenia looked at Omago. "You recently destroyed the Vlagh, didn't you?"
"No. All I did was render all the incipient eggs she'd been bearing in her abdomen for eons and eons null and void. She might still be able to lay eggs, but they'll never come to life."
"You can move things backward or forward in time, can't you? If you'd done that a long time back, the Vlagh wouldn't have posed any threat to the Land of Dhrall, would she? _And_ , if she wasn't a threat, the elder gods wouldn't have had any reason to go hire outlander armies to come here and fight a war, would they?"
"That's brilliant, Balacenia!" Ara exclaimed. "The way things stand now, there will always be a danger that outlander gold-seekers will invade the Land of Dhrall. But if they don't even know that it's here, they'll never even try to invade."
"And Longbow will be mated with Misty-Water," Eleria insisted, "and the world will be more beautiful."
"And you will agree to accept the Domain of the East as its goddess with no more arguments, right?" Omago asked shrewdly.
"On only one condition," Eleria answered.
"And what is that?"
"You'll give me hugs whenever I need them," Eleria insisted.
Omago smiled. "I think I can manage that, little one," he replied.
"You see how easy things are when you do them right, Big-Me?" Eleria said to Balacenia.
**3**
There was never any question that the gods—both elder and younger—would attend the ceremony that would unite Longbow with Misty-Water, the daughter of Chief Old-Bear. One of the advantages of divinity was their ability to make themselves look familiar to the ordinary man-things of Old-Bear's tribe.
Balacenia found the deerskin clothing worn by the natives quite attractive, actually.
The one thing that startled Balacenia—and all the other gods as well—was the appearance of the young Longbow. The more familiar elder Longbow almost never smiled and there seemed to be perpetual grief in his eyes. The young Longbow smiled almost continually, and the first time Balacenia saw the beautiful Misty-Water, she knew exactly why. Balacenia had seen many, many beautiful women in her almost endless life, but Misty-Water was far and away the most beautiful Balacenia had ever encountered. Her hair was black and glossy, but her skin was pale white. Her eyes were very large, and they were almost permanently locked on Longbow.
"She _is_ a pretty one, isn't she?" Zelana said between yawns. Had it not been for the upcoming ceremony that would join Longbow and Misty-Water, Zelana would almost certainly be sleeping by now.
Oddly, since this joining had been _her_ idea, Eleria didn't seem to like Misty-Water very much. "Could you maybe put a pimple on her nose, Beloved?" she asked Zelana as the day of the ceremony grew closer.
"Why in the world would I want to do something like that, dear child?" Zelana asked mildly.
"I hate to admit it, Beloved," Balacenia said, "but I'm catching a few hints of jealousy in Little-Me's behavior."
"Does she _have_ to be that pretty?" Eleria demanded. "Longbow's always been _mine_ , and now she's stealing him right out from under me." Then she looked at the young Longbow. "Isn't he _gorgeous_?" she demanded.
"I'm not sure if 'gorgeous' is customarily used to describe male humans," Zelana replied. "He looks much nicer without that perpetual scowl on his face, though."
It was about noon when the shaman of the tribe, One-Who-Heals, came out of his lodge at about the same time that Chief Old-Bear escorted Longbow, dressed in golden deerskin, and Misty-Water, garbed in white leather, out to the open area at the center of the village. Old-Bear spoke quite formally when he addressed his friend. "These two children would be mated, Wise Shaman, and I have therefore summoned you to determine if it might be so."
"And does this union have the approval of their parents, mighty Chief?" One-Who-Heals formally replied.
"I am the parent in question, Wise Shaman," Old-Bear replied, "and I do fully approve."
"And is this your true wish, brave Longbow?" One-Who-Heals asked.
"With all my heart, Wise Shaman," Longbow replied in a voice much richer than Balacenia had ever heard coming from him before.
"And is this also _your_ true wish, fair Misty-Water?"
"I have no other wish, One-Who-Heals," the beautiful young woman replied in a voice that was almost musical. "And know this, Wise Shaman. Should you refuse to join us, I will surely die before tomorrow's dawn. Longbow will ever be my heart and my soul, and without him, my life will have no meaning."
"I wouldn't crowd _that_ one," Balacenia murmured to her relatives. "If One-Who-Heals is foolish enough to refuse her, _he'll_ probably be dead before the sun goes down."
"I didn't fully understand Longbow before," Veltan admitted. "But everything just fell into place. I'm quite sure that when this ceremony is over, we'll be looking at the two happiest people in the world."
"And perhaps the saddest as well," Balacenia added, pointing at Eleria, whose eyes were filled with tears.
"Does any member of the tribe object to this union?" One-Who-Heals asked.
"That wouldn't really be a very good idea, would it?" Balacenia said quietly to the other gods. "If Longbow didn't kill the objector, Misty-Water probably would."
Then One-Who-Heals straightened and raised his hand. "Since none objects, it falls to me to declare that Longbow and Misty-Water are now joined, and never will they be parted."
The members of the tribe all cheered—at least _most_ of them did. There were a few young men, and several young women, who chose _not_ to cheer. They _were_ wise enough not to denounce the joining, though.
And then the celebration began. Quite nearly every member of the tribe spoke briefly with Longbow and Misty-Water, congratulating them on their joining. Balacenia was almost positive that One-Who-Heals was really redundant. The joining of Longbow and Misty-Water had long since taken place in their hearts and minds, and nothing would ever separate them.
The congratulations of the members of the tribe continued until almost evening, and then, to Balacenia's astonishment, Zelana approached the happy couple. "Know ye both," she said quite formally, "that your joining was decreed by the gods of the Land of Dhrall—both elder and younger—eons ago—for in your joining lies perfection. Love has now found a home, and she will stay with you forever."
Then Zelana seemed to almost slump as if she were about to collapse.
"Get her home!" Dahlaine rasped. "She should have gone to sleep months ago."
"Take her other hand, Little-Me," Balacenia told Eleria. "Let's get her back to the pink grotto and put her to bed before the sun goes down."
"I'll come with you," Ara said. "Zelana is our most precious child, so let's see to her well-being."
"What were you thinking of, Zelana?" Ara demanded when they reached the pink grotto and bedded the Beloved down in her own bed.
"There was an emergency, Mother," Zelana replied. "I doubt if I could have slept at all if I hadn't seen it all the way through to the end. Balacenia is _good_ , mind you, but _I_ knew what was in the wind and how to veer it away. Of course as it turned out, she's at least as clever as I am. Toward the end of my cycle, though, I was _very_ worried about what would happen if _Eleria_ had to take charge. Until just recently, I didn't even _know_ Balacenia."
"We're encouraged to keep it that way, Beloved," Balacenia replied.
"Beloved?" Zelana asked with a faint smile.
"That's Eleria's term, of course, but it seems to have rubbed off on me, for some reason. Sleep well, dear Zelana. 'Little-Me' and I will keep things going as they should."
Zelana sighed. "It's time for me to sleep, I think." Then she smiled at Eleria. "Tell me 'night-night,' little one, and I'm sure that I'll slip right off."
"Have some nice dreams, Beloved," Eleria said, tucking Zelana's blanket up under her chin.
Balacenia had slowly backed away. "It just occurred to me, Mother, that we're going to lose all of our outlander friends, since they won't be coming here now."
Eleria quietly moved away from Zelana's bed. "You didn't sound very happy, Big-Me," she said. "What is it now?"
"My clever notion has just robbed us of a good number of very close friends. Rabbit, Keselo, Gunda, Ox, and all of our other friends won't be coming here because we won't need them now. The Vlagh is gone now—or at least totally alone—so she won't be stirring things up."
"I'm going to miss Bunny," Eleria said, "and Keselo as well." Then she blinked. "Oh, dear," she said.
"Yes, Little-Me?" Balacenia replied. "Was there something?"
"We went to a lot of trouble to attach Trenicia to Narasan, and that just went out the window. Trenicia has no reason at all to even recognize Narasan."
Balacenia frowned. "You might be right there, Little-Me," she admitted.
"Why don't you girls let _me_ take care of that?" Mother Ara said. "Narasan eventually _will_ have to take charge of the Trogite Empire, and I'll arrange things so that Trenicia will pay him a call—sometime in the past, I think. Trenicia's _almost_ as good as anybody else with her weapons, and Narasan will be in a lot of danger if he tampers with the Empire. Trenicia _will_ be able to protect him. Then, in time, we'll probably see something very much like what we saw this morning. Trenicia and Narasan _will_ be joined. I'll see to that personally."
"Isn't it handy to have Mother around like this, Little-Me?" Balacenia said. "I'm sure that we'll want to stay here until Zelana goes deeper into her sleep cycle. Then you and I had better go talk with Enalla. I'm fairly sure that she'll knock that silly temple all to pieces before long, but you're going to need someplace to sleep. It's going to be a long, long time before you wake up and take over in your Dominion."
"Wouldn't it be all right if I just stayed here with the Beloved, Big-Me? I know that when I wake up, I'll have to go over to the East and take charge, but until then I'd really rather sleep here with the Beloved."
"What do you think, Mother?" Balacenia asked Ara.
"I don't see any problems with her staying here with Zelana, Big-Me," Mother replied. "There are many things she'll need to know, and if she's here in the pink grotto, I'll know where to find her."
"Whatever you think best, Mother," Balacenia agreed.
Balacenia was fully aware of her position as the dominant god of the Land of Dhrall during this cycle, but she was quite sure that Dakas and Vash could get along quite well without her interference for a few hundred years. Enalla was probably busy tearing down Aracia's temple and chasing off the fat men who called themselves priests. Mother Ara was there to keep Enalla from going _too_ far, and that gave Balacenia some free time to consider things. She knew that she was going to miss a number of the outlanders who'd been such good friends this past year. Her suggestion to Father that he move the time when the Vlagh had lost all her children had eliminated any need for outlanders—friends or not. Balacenia sighed. "They were delightful and very dear to me," she murmured, "but things are much better this way. Nobody dies, and I still have all those memories."
She let those memories return as she sat in the pink grotto with blessed Zelana and dearly loved Little-Me while she let her mind drift back through the year that had just passed. That year no longer existed, of course, but her memories of it were precious. "I think I'll keep them tucked away," she said out loud. "I'll be able to share them with children—and others as my cycle moves along."
"Did you say something, Big-Me?" Eleria asked, emerging from her sleep.
"Just thinking out loud, Little-Me," Balacenia replied. "Go back to sleep and join once more with the Beloved."
"I'll do that, Big-Me," Eleria replied, "just as soon as you stop all this chattering."
Balacenia laughed then and looked fondly at her alternate. "I really could use a hug, though," she said.
"Why didn't you say so in the first place, Big-Me?" Eleria replied. "Come over here, and I'll hug you all to pieces. I _am_ the best hugger in all the world, you know."
"Indeed I do, Little-Me," Balacenia said. Then she went to Eleria's small bed and collected several years' worth of hugs.
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{"url":"https:\/\/blog.openmined.org\/split-neural-networks-on-pysyft\/","text":"Update as of November 18, 2021: The version of PySyft mentioned in this post has been deprecated. Any implementations using this older version of PySyft are unlikely to work. Stay tuned for the release of PySyft 0.6.0, a data centric library for use in production targeted for release in early December.\n\nSummary: In this blog we are going to provide an introduction into a new decentralised learning methodology called, \u2018Split Neural Networks\u2019. We\u2019ll take a look at some of the theory and then dive into some code which will allow us to run them on PySyft.\n\n## Privacy and the Data industry\n\nHistorically, machine learning architectures have been built upon the assumption that all machine learning algorithms are to be centralised, where both the training data and the model are in the same location and known to the researcher. However, there is a growing appetite for learning techniques to be applied to domains where data is traditionally sensitive or private, i.e healthcare, operational logistics or finance. In healthcare, these kinds of applications have the capacity to improve patient outcomes through enhanced diagnostic accuracy and through the augmentation of doctor to patient time efficiency using competent clinical decision support systems.\n\nHowever, until recently there has been a barrier in the way of this kind of innovation, data privacy. It\u2019s currently not possible for data owners to truly know that their data hasn\u2019t been sold on, used for something they didn\u2019t previously consent to or held onto for far longer than intended. This leads to a problem of trust between data processors and data owners. When data has been gathered, it\u2019s even more difficult to adequately manage the consent of its owners. This makes the traditional, centralised, industry model impossible to apply to data practices post GDPR.\n\nFor these reasons, centralised learning architectures have become either an impediment to innovation or a privacy hazard for the data owners involved. Either research on private data is blocked due to privacy ramifications or it goes ahead with potentially disastrous social and political consequences for the subjects of the data.\n\nThe tech sector still races to catch up with one of the landmark innovations of our time; blockchain. However, while distributed ledger technology is going to be at the core of the next generation of the internet, it only marks the start of a greater transformation in system architectures. The genie which has left the bottle here is decentralisation.\n\nThis principle has been adopted in order to build tools where the decentralisation of resources and multi-owner governance enshrine the citizens right to privacy and security. This opens the door to innovation through an information resource which has previously been inaccessible; private data. A community at the front of this transformation is OpenMined. Their private AI tool is called PySyft.\n\n## Split Neural Network\n\nTraditionally, PySyft has been used to facilitate federated learning. However, we can also leverage the tools included in this framework to implement distributed neural networks. These allow for researchers to process data held remotely and compute predictions in a radically decentralised way. First introduced by MIT in December 2018, SplitNNs represent a brand new architectural mechanic for privacy-preserving ML researchers to play with.\n\n### What is a SplitNN?\n\nThe training of a neural network (NN) is \u2018split\u2019 across two or more hosts. Each model segment is a self contained NN that feeds into the segment in front. In this example Alice has unlabelled training data and the bottom of the network whereas Bob has the corresponding labels and the top of the network. The image below shows this training process, where Bob has all the labels and there are multiple Alices with X data [1]. Once the first Alice has trained, she sends a copy of her bottom model to the next Alice. Training is complete once all Alices have trained.\n\n### Why use a SplitNN?\n\nThe SplitNN has been shown to provide a dramatic reduction to the computational burden of training while maintaining higher accuracies when training over large number of clients [2]. In the figure below, the Blue line denotes distributed deep learning using splitNN, the red line represents federated learning (FL) and the green line labels Large Batch Stochastic Gradient Descent (LBSGD).\n\nTable 1 shows computational resources consumed when training CIFAR 10 over VGG. Theses are a fraction of the resources of FL and LBSGD. Table 2 shows the bandwidth usage when training CIFAR 100 over ResNet. Federated learning is less bandwidth intensive with fewer than 100 clients. However, the SplitNN outperforms other approaches as the number of clients grow[2].\n\n### Training a SplitNN\n\nPredictions made with a SplitNN are quite simple. All we have to do is get our data, make a prediction using the bottom segment and send that prediction to the next model segment. When that segment receives the prediction, we make a new prediction using previous one as our input data. We then send it onward to the next model. We keep going until we reach the end layer. At the end of the prediction, we have our final prediction and a computation graph for each model. Computation graphs document the transformation from the input data to the prediction and are useful in the backprop phase.\n\nIn PyTorch, the computation graph allows the autograd function to quickly differentiate variables used in a function w.r.t a loss function. Autograd produces gradients which we can then use to update the model. However, in PyTorch, this method was not designed to be distributed. We don\u2019t have all the variables in the computation graph in one place in order to do this automatic calculation. In our method, we get around this by performing partial backprop on each model segment as we work the loss backward. We achieve this by sending the relevant gradients back as we go.\n\nConsider the example of the computation graph below. We want to compute gradients all the way back to W\u2080 and B\u2080, which are the weights and biases in Network 1. However, our model splits at A\u2081. This is the output of Network 1 and the input of Network 2. To get around this, we compute the loss of O, the output of Network 2, and calculate the gradients back to A\u2081, W\u2081 and B\u2081. We then send the computed gradients of A\u2081 back to Network 1 and use them to continue the gradient calculation at that location. Once we have gradients all weights and biases all the way back to W\u2080 and B\u2080, we can step in the direction of these gradients.\n\nWe repeat this over epochs to train the model. Once we have trained over a sufficient number of epochs, we send the model segments back to the researcher. The researcher can then aggregate the updated segments and keep the trained model.\n\n## Implementing SplitNN\n\nNext we will go into a little code example where we use splitNN to predict upon the MNIST dataset. First we define our SplitNN class. This takes a set of models and their linked optimisers as its input.\n\nclass SplitNN:\ndef __init__(self, models, optimizers):\nself.models = models\nself.optimizers = optimizers\n\ndef forward(self, x):\na = []\nremote_a = []\n\na.append(models[0](x))\nif a[-1].location == models[1].location:\nelse:\n\ni=1\nwhile i < (len(models)-1):\n\na.append(models[i](remote_a[-1]))\nif a[-1].location == models[i+1].location:\nelse:\n\ni+=1\n\na.append(models[i](remote_a[-1]))\nself.a = a\nself.remote_a = remote_a\n\nreturn a[-1]\n\ndef backward(self):\na=self.a\nremote_a=self.remote_a\noptimizers = self.optimizers\n\ni= len(models)-2\nwhile i > -1:\nif remote_a[i].location == a[i].location:\nelse:\ni-=1\n\nfor opt in optimizers:\n\ndef step(self):\nfor opt in optimizers:\nopt.step()\n\n\nWe then import all of our regular imports for training with PySyft, set up a torch hook and pull in the MNIST data.\n\nimport numpy as np\nimport torch\nimport torchvision\nimport matplotlib.pyplot as plt\nfrom time import time\nfrom torchvision import datasets, transforms\nfrom torch import nn, optim\nimport syft as sy\nimport time\nhook = sy.TorchHook(torch)\n\n\nNext we define our network which will be distributed. Here we are going for a simple, three-layer network. However, we can do this for a network of any size or shape. Each segment is it\u2019s own self-contained network. All that matters is the shape of the layer where one segment joins to the next. The sending layer must have an equal output shape to the receiving layers input shape. For more information on how the model parameters were chosen for this particular dataset, read this great tutorial.\n\ntorch.manual_seed(0) # Define our model segments\ninput_size = 784\nhidden_sizes = [128, 640]\noutput_size = 10\nmodels = [\nnn.Sequential(\nnn.Linear(input_size, hidden_sizes[0]),\nnn.ReLU(),\n),\nnn.Sequential(\nnn.Linear(hidden_sizes[0], hidden_sizes[1]),\nnn.ReLU(),\n),\nnn.Sequential(\nnn.Linear(hidden_sizes[1], output_size),\nnn.LogSoftmax(dim=1)\n)\n]\n# Create optimisers for each segment and link to them\noptimizers = [\noptim.SGD(model.parameters(), lr=0.03,)\nfor model in models\n]\n\n\nNow it\u2019s time to define some workers to host our models, and send the models to their locations.\n\n# create some workers\nalice = sy.VirtualWorker(hook, id=\"alice\")\nbob = sy.VirtualWorker(hook, id=\"bob\")\nclaire = sy.VirtualWorker(hook, id=\"claire\")\n\n# Send Model Segments to model locations\nmodel_locations = [alice, bob, claire]\nfor model, location in zip(models, model_locations):\nmodel.send(location)\n\n\nNext we build the splitNN. All that is required for this to work is for the model segments to be in their starting locations and paired to their respective optimisers.\n\n#Instantiate a SpliNN class with our distributed segments and their respective optimizers\nsplitNN = SplitNN(models, optimizers)\n\n\nNext we define a train function. The usage of splitNN is fairly similar to a conventional model. All that is required is a second back-propagation phase to push gradients back over the segments.\n\ndef train(x, target, splitNN):\n\n#2) Make a prediction\npred = splitNN.forward(x)\n\n#3) Figure out how much we missed by\ncriterion = nn.NLLLoss()\nloss = criterion(pred, target)\n\n#4) Backprop the loss on the end layer\nloss.backward()\n\n#5) Feed Gradients backward through the network\nsplitNN.backward()\n\n#6) Change the weights\nsplitNN.step()\n\nreturn loss\n\n\nFinally we train, sending data to starting locations as we go.\n\nfor i in range(epochs):\nrunning_loss = 0\nimages = images.send(models[0].location)\nimages = images.view(images.shape[0], -1)\nlabels = labels.send(models[-1].location)\nloss = train(images, labels, splitNN)\nrunning_loss += loss.get()\n\nelse:\nprint(\"Epoch {} - Training loss: {}\".format(i, running_loss\/len(trainloader)))\n\n\nThe full example can be seen here on the PySyft Github.\n\n## Conclusion\n\nThere you have it, a new tool to rival federated learning in terms of accuracy, computational complexity and network resources. Follow for more updates relating to privacy-preserving methodologies such as Homomorphic Encryption and Secure Multi-Party Computation.\n\nIf you enjoyed this then you can contribute to OpenMined in a number of ways:\n\n### Star PySyft on GitHub\n\nThe easiest way to help our community is just by starring the repositories! This helps raise awareness of the cool tools we\u2019re building.\n\n### Try our tutorials on GitHub!\n\nWe made really nice tutorials to get a better understanding of Privacy-Preserving Machine Learning and the building blocks we have created to make it easy to do!\n\nThe best way to contribute to our community is to become a code contributor! If you want to start \u201cone off\u201d mini-projects, you can go to PySyft GitHub Issues page and search for issues marked Good First Issue.","date":"2022-01-19 02:26:06","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\": 0.3059029281139374, \"perplexity\": 1760.8312228844327}, \"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-2022-05\/segments\/1642320301217.83\/warc\/CC-MAIN-20220119003144-20220119033144-00639.warc.gz\"}"} | null | null |
SPRAYER TESTING CHANGES COMING INTO FORCE
As part of the Sustainable Use Directive (SUD), pesticide application equipment (PAE) testing became a legal requirement in 2016. Any machine applying a professional pesticide must be tested by the specified dates and at regular intervals thereafter.
Ian Forman, National Sprayer Testing Scheme (NSTS) manager says, "To explain this in a bit more detail, the change affects sprayers that are more than 5 years old and have a boom width over 3 metres, air blast sprayers, aircraft, and train sprayers. Currently a test is required every 5 years, but from 26th November it changes to every 3 years. So, for any sprayer of this type tested before November 2017, a re-test is due by that date.
"It is also important to note that sprayers tested any time after 26th November 2017, the test is only valid for 3 years, so if your sprayer was tested for example in June 2018, the next test is due in June 2021."
For all other types of PAE, which includes boom sprayers 3 metres and under, weed wipers, slug pellet and granular applicators and a range of other machines, the requirements remain unchanged at 6 yearly cycles for retest.
Ian continued, "Crop assurance scheme requirements haven't changed so sprayers are still required to be tested annually. Regular testing is important in helping to ensure safe and accurate application of pesticides, protecting the environment and waterways, but also helping to safeguard the availability of products for the future. A regularly tested machine will reduce the risk of breakdowns, when timing of applications can be crucial for efficient control of weeds, pests and diseases.
"The need for an integrated pest management (IPM) plan to be carried out helps ensure that when the decision has been made to use a pesticide, that the equipment is calibrated and has been tested to a standard that will apply the product in a safe and sustainable way." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,202 |
Online Service offers access to environmental information.
Environmental Data Resources Inc. Oct 31, 2006
EDR OnDemand(TM) online subscription service allows real-time aggregation and access to environmental information from more than 800 federal, state, local, and tribal sources. EDR OnDemand Corporate and EDR OnDemand Legal facilitate environmental financial reporting and allow law firms and corporations to conduct research for acquisition of assets and new construction projects. Service enables users to perform research from any location with Internet access.
Environmental Data Resources Launches EDR OnDemand(TM), an Online Interface Providing Real-Time Access to Environmental Data
First Service of its Kind to Give Corporations and Attorneys Instant Access to Data from More Than 800 Environmental Databases
Research that previously took days can now be completed in matter of minutes
MILFORD, Conn., Oct. 12 // -- Environmental Data Resources Inc. (EDR) announced today the launch of EDR OnDemand(TM), an online, subscription service that allows real-time aggregation and access to environmental information from more than 800 federal, state, local, and tribal sources. EDR's Corporate, Legal and Government Services Division provides law firms and corporations the tools they need to conduct environmental research in an efficient and effective manner that has never before been available. To learn more about EDR OnDemand, visit www.edrnet.com/ondemand.
Law firms and corporations conduct environmental research for due diligence in the acquisition of new assets, new construction projects, environmental audits, background research for litigation and increasingly for compliance purposes and environmental financial reporting. Environmental financial reporting has been an area of particular concern for EDR's clients recently due to new accounting and regulations standards, such as the FIN47 ruling by the Financial Accounting Standards Board, which have spurred an increased demand for environmental information from corporations. For all of these needs, EDR OnDemand Corporate and EDR OnDemand Legal provide superior services to manually searching relevant local databases, which has traditionally been a time-intensive, inexact and costly process.
"Overwhelmingly, our corporate and attorney clients tell us that the largest challenge they have with conducting environmental research has been the tremendous amount of time it takes to simply gather the appropriate data from various environmental and government sources," says Robert Barber, EDR's Chief Executive Officer. "We are thrilled to be providing a new and valuable service that expedites this research process, resulting in significant cost savings for our clients. Not only does EDR OnDemand provide fast and powerful research capabilities, but it also simplifies the overall environmental information collection process and ensures no databases are missed through manual error."
EDR OnDemand is subscription based, allowing corporations and law firms to pay an annual fee to have unlimited access to research. Through an easy-to-use, Web-based application, users can perform the research they need from any location with Internet access.
Barber continued, "The EDR OnDemand service allows our corporate and attorney clients to take full advantage of our position as the country's leading provider of environmental data reports. Clients can rely on EDR OnDemand as a comprehensive, single source of information for their environmental research needs. The product ultimately helps them gain control of the research process while significantly reducing time and costs."
About EDR
Environmental Data Resources Inc. (EDR) is the nation's premier provider of environmental risk information services and reports. The company offers current, prior use and regulatory compliance information services tailored to either a specific property address or company name. EDR offers these services to all participants in a real estate transaction, including the lender, environmental engineer, buyer, seller, attorney and insurer. The company's Market Research Group provides strategic data and analysis on environmental due diligence trends, including market surveys, newsletters, and workshops. Established in 1991, EDR's headquarters are in Milford, Connecticut; regional offices are located throughout the United States. EDR is wholly owned by DMG Information Inc., the business information division of Daily Mail and General Trust, plc (DMGT). For more information, visit www.edrnet.com.
Source: Environmental Data Resources Inc.
Web site: www.edrnet.com/
http://www.edrnet.com/ondemand
Service enables secure online collaboration.
Email Reputation Service is based on machine-learning.
TUV Presents MediaMind Appliance Search Engine That Uses Both AI and Time Code for Generating Search Results
Online Tool assesses employee satisfaction.
Software offers online hotel reservations. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,944 |
{"url":"https:\/\/hydro-informatics.com\/documentation\/glossary.html","text":"# Glossary\u00b6\n\nUsing common and consistent vocabulary is vital for working in teams. This section exemplifies a glossary with technical terms recurring in this eBook.\n\nAdvection is the motion of particles along with the bulk flow. The properties (e.g., heat) of an advected particle or substance are conserved. Mathematically, advection of incompressible fluids (e.g., water) is described by the Continuity equation [KC08].\n\nAnabranch\n\nAn anabranched river (section) is characterized by one or more side channels diverting from the main river stem. Anabranching (or also anastomosing) channels occur primarily in alluvial channel beds where more sediment is available than the water runoff can transport (transport capacity-limited rivers). Thus, an anabranching river has high sediment loads and channel avulsion is likely to occur during floods [HN07, NK96, RPLV17]. This eBook shows an example for an anabranching river section in the morphdynamic modeling tutorial in Fig. 154.\n\nFrench: Anabranche\nGerman: Flussarm\n\nAnastomosing rivers\n\nSee Anabranch.\n\nASCII\n\nThe American Standard Code for Information Interchange (ASCII) is an encoding standard for text on computers. The development of ASCII goes back to telegraphy and was first published in 1961 for the Latin alphabet. It was later extended by other alphabets and special characters [Mac80]. ASCII code represents characters in the form of numbers. For instance, the ASCII code 65 represents uppercase A (utf-8 encoding). In Python applications, ASCII code numbers can be useful to iterate through the alphabet (e.g., alphabetic column names), where chr(ASCII) returns a letter as a function of the system encoding. For instance, in Python, print(chr(78)) returns uppercase N for utf-8 encoding (default on many Linux systems). To find out the encoding type of your Python installation, open a Python terminal, tap import sys and sys.getdefaultencoding().\n\nBedload (also referred to as bed load) $$Q_b$$ (or $$q_b$$ for unit bedload) in kg$$\\cdot$$s$$^{-1}$$ (or kg$$\\cdot$$s$$^{-1}\\cdot$$m$$^{-1}$$) is a special type of Sediment transport describing the displacement of coarse particles by rolling, sliding, and\/or jumping on the riverbed. In river hydraulics, the so-called Dimensionless bed shear stress or also referred to as Shields parameter [Shi36] is often used as the threshold value for the mobilization of sediment from the riverbed. The dimensionless expression of bedload transport is [Ein50]:\n\n$\\Phi_b = \\frac{q_b}{\\rho_{w} \\sqrt{(s - 1) g D^{3}_{pq}}} \\approx \\frac{Q_b}{0.5\\cdot(b + B)\\rho_{w} \\sqrt{(s - 1) g D^{3}_{pq}}}$\n\nwhere $$\\rho_{w}$$ is the density of water; $$s$$ is the ratio of sediment grain and water density (typically 2.68) [Sch17]; $$g$$ is gravitational acceleration; $$D_{pq}$$ is the grain diameter of which $$pq \\%$$ of the mixture are finer; and $$b$$ and $$B$$ are the channel bottom and surface width, respectively (or cell width\/height in a 2d numerical model).\n\nRead more about the calculation of bedload in this eBook in the Python exercises or the Telemac2d-Gaia tutorial. In numerical models, bedload transport is often computed using the Exner equation.\n\nIn addition, the term traveling bedload refers to a transport mode that is similar to wash load, but without suspended load [Pit16, YWZ+09].\n\nFrench: Charriage\nGerman: Geschiebtransport\n\nBoussinesq\n\nThe Boussinesq approximation of the Continuity equation assumes that density variations can be neglected except for the gravity term (i.e., in the vertical momentum equations). In addition, the Boussinesq approximation assumes that a fluid is incompressible and that wave motion is inviscid [SV60].\n\nBraiding\n\nA braiding river morphology refers to anabranched channel networks with high bedload supply, mostly located in moderately steep mid-land to mountain rivers [LW57, Ros94].\n\nFig. 157 A braided-channel section of the Devolli River (Albania). Source: Sebastian Schwindt (2021)\n\nCFL\n\nIn the field of hydrodynamics, the abbreviation CFL commonly refers to the Courant-Friedrichs-Lewy condition, which represents a convergence criterion for the numerical solution to the Navier-Stokes partial differential equations. The CFL applies to explicit time integration schemes that may become unstable for large time steps as a function of the size of mesh cells. Today, most numerical software uses an internal value for the CFL to adaptively calculate the maximum time step that is required for the stability of explicit solvers. In 2d modelling, the CFL condition is defined as $$c_{cfl}={u_x \\cdot \\Delta t}\/\\Delta x + {u_y \\cdot \\Delta t}\/\\Delta y$$, where $$\\Delta t$$ is the time step, $$\\Delta x$$ and $$\\Delta y$$ are grid cell sizes in $$x$$ and $$y$$ directions of the coordinate reference system, and $$u_x$$ and $$u_y$$ are the flow velocities in the $$x$$ and $$y$$ directions. An explicit solver is assumed to be stable when $$c_{cfl} \\leq c_{cfl, crit}$$, where the critical value $$c_{cfl, crit}$$ for the CFL condition must be smaller than 1.0. To this end, numerical modelling software, such as BASEMENT, uses a default value of $$c_{cfl, crit} = 0.9$$.\n\nFrench: Nombre de Courant\nGerman: CFL-Zahl\n\nClogging\n\nRiverbed clogging describes the sedimentation of the porous coarse sediment matrix of the hyporheic zone under and along gravel-cobble-bed rivers. We differentiate between external and internal clogging: external clogging affects surficial layers and is a direct consequence of the deposition of fine, cohesive sediment; internal clogging occurs in deeper layers of the hyporheic zone and is the consequence of spontaneous percolation or grain sorting at the surface [BR87, Sch92].\n\nFig. 158 Example of outer riverbed clogging of a coarse sediment matrix with fine muddy sediment. Picture: Sebastian Schwindt (2021).\n\nFrench: Colmation\/colmatation\nGerman: Kolmation\n\nContinuity equation\n\nThe differential form of the continuity equation is $$\\frac{\\partial \\psi}{\\partial t}+\\mathbf{u} \\cdot \\nabla \\psi = 0$$ where $$\\psi$$ is a constant of the particle\/substance in consideration and $$\\mathbf{u}$$ is the fluid velocity vector. The $$\\nabla$$ operator is literally a vector of partial differential operators $$\\frac{\\partial}{\\partial x_i}$$ where $$x_i$$ refers to the dimensions of the flow field. In the case of steady flow (no variability in time) the advection equation becomes $$\\mathbf{u} \\cdot \\nabla \\psi = 0$$ [KC08].\n\nThe mass continuity equation of an incompressible fluid, such as water, considers the constant $$\\Psi$$ as a mass and has the form $$\\nabla \\cdot \\mathbf{u} = 0$$ or $$\\frac{\\partial u_i}{\\partial x_i} = 0$$ [KC08].\n\nFrench: \u00c9quation de continuit\u00e9\nGerman: Kontinuit\u00e4tsgleichung\n\nConvection\n\nConvection encompasses Advection and Diffusion [KC08]. Thus, convection is fluid motion because of bulk transport (water flowing in a river with reference to Advection) and dispersion of a fluid component from high-density to low-density regions (Diffusion) in the flow field (e.g., an ink drop dispersing in a river).\n\nFrench: Convection\nGerman: Konvektion\n\nCRS\n\nA Coordinate Reference System (CRS), also referred to as Spatial Reference System (SRS), is an orientation unit system to geographically locate objects in a map. The CRS involves an origin ($$x$$=0.0 and $$y$$=0.0) and a projection. Objects of one map can be put into another map through the transformation of their CRS with respect to the coordinates and the projection. Read more about CRS in the section on Projections and Coordinate Systems.\n\nFrench: Syst\u00e8me de coordonn\u00e9es\nGerman: Koordinatenreferenzsystem \/ Koordinatenbezugsystem (KBS)\n\nCSV\n\nThe Comma-Separated Values (CSV) file format describes the structure of a text file storing simply structured data. The file name extension is *.csv, which may also contain Tab-Separated Values (TSV). The separator (i.e., comma, semicolon, or tab) sign delimits (or separates) colon values in one line of a *.csv file. Spreadsheet software, such as Libre Office Calc, enables to import and process *.csv files for cell-formula based data analyses.\n\nDEM\n\nA Digital Elevation Model (DEM) represents the bare Earth\u2019s topographic surface excluding objects such as buildings or trees. In contrast, a Digital Surface Model (DSM) includes objects such as trees or buildings. In addition, a Digital Terrain Model (DTM) represents similar data to a DEM and both DEM and DTM can be used synonymously in many regions of the world. However, in the United States, a DTM refers to a Vector (regularly spaced points) dataset while a DEM is a Gridded Cell (Raster) Data dataset. The translation into other languages does not go along with the same definition of a DEM, DSM, and DTM, and the following translations refer to the English definitions rather than the same (translated) words.\n\nFrench for DSM: Mod\u00e8le num\u00e9rique d\u2019\u00e9l\u00e9vation (MNE)\nGerman for DSM: Digitales H\u00f6henmodell (DHM)\n\nFrench for DEM: Mod\u00e8le num\u00e9rique de terrain (MNT)\nGerman for DEM: Digitales Oberfl\u00e4chenmodell (DOM)\n\nFrench for DTM: Mod\u00e8le num\u00e9rique d\u2019\u00e9l\u00e9vation (MNE)\nGerman for DTM: Digitales Gel\u00e4ndemodell (DGM)\n\nUltimately, there are many options for correct DEM-terminology depending on the region where you are. Now, what is the correct term in which language? There is no universal answer to this question and a good choice is to be patient with the communication partner.\n\nDiadromous fish guilds migrate between the sea and freshwater in their life cycle, as opposed to potamodromous fish that only migrates in freshwater regions. Within diadromous fish guilds, further distinction is made between sub-guilds [Mye49]:\n\n\u2022 Anadromous fish live in the seas and migrate to freshwaters, mainly for reproduction. Examples for anadromous fish are sea trout (Salmo trutta trutta) or Pacific salmon (Oncorhynchus).\n\n\u2022 Catadromous fish live in freshwaters and migrate to the sea for reproduction. An example for catadromous fish is American eel (Anguilla rostrata).\n\n\u2022 Amphidromous fish migrate regularly between the sea and freshwaters. An example for amphidromous fish is round goby (Neogobius melanostomus) [LSK+19].\n\nDiffusion\n\nDiffusion is the result of random motion of particles, driven by differences in concentration (e.g., dissipation of highly concentrated particles towards regions of low concentration). Mathematically, diffusion is described by $$\\frac{\\partial \\psi}{\\partial t} = \\nabla \\cdot (D \\nabla \\psi)$$ where $$\\psi$$ is a constant of the particle\/substance in consideration; $$D$$ is a diffusion coefficient (or diffusivity) in m$$^2$$\/s, which is a proportionality constant between molecular flux and the gradient of a substance (or species). The $$\\nabla$$ (nabla) operator is a vector of partial differentials $$\\frac{\\partial}{\\partial x_i}$$ where $$x_i$$ refers to the dimensions of the flow field [KC08].\n\nFrench: Diffusion\nGerman: Diffusion\n\nDimensionless bed shear stress\n\nThe dimensionless bed shear stress $$\\tau_x$$ (in the literature often called $$\\theta$$) is derived from the shear forces that act on the riverbed as a result of flowing water. $$\\tau_x$$ is a key parameter in the calculation of Bedload transport where many semi-empiric equations assume that a sediment grain is mobile when a particle size-related, critical value of the dimensionless bed shear stress is exceeded. This critical value of dimensionless bed shear stress is also referred to as Shields parameter. To this end, $$\\tau_x$$ is calculated based on hydraulic characteristics and the characteristic grain size $$D_{pq}$$ [Kra32, VK30]:\n\n$\\tau_{x} = \\frac{R_h~\\cdot~S_e}{\\left(s-1\\right)~\\cdot~D_{pq}}$\n\nwhere $$R_h$$ is the hydraulic radius (cf. calculation in the 1d hydraulic Python exercise); $$S_{e}$$ is energy slope; and $$s$$ is the ratio of sediment grain and water density (typically 2.68) [Sch17]. $$R_h$$ may be substituted by water depth in wide rivers with monotonous cross-sectional shape and for (grid) cells of a 2d numerical model.\n\nGerman: Dimensionslose Schubspannung\n\nEcho sounder\n\nAn echo sounder emits an acoustic signal under water, which is reflected by the objects of the underwater landscape. Echo sounding is an active Sonar technique and enables the creation of an underwater DEM, which is also referred to as bathymetry. To perform echo sounding a probe must be installed on a boat that requires a minimum navigable water depth. In addition, the use of the echo sounder (probe) itself also requires a minimum water depth to operate with little noise inference. Therefore, by experience, a minimum water depth of 1-2 m is necessary to survey the bathymetry of a river by echo sounding. Echo sounding can be performed with single-beam (one underwater spot) or multi-beam (underwater surface) devices.\n\nFrench: \u00c9chosondeur \/ Sondeur acoustique\nGerman: Echolot \/ F\u00e4cherecholot\n\nExner equation\n\nThe Exner [Exn25] equation yields sediment mass conservation in a hydro-morphodynamic model (see also the TELEMAC-Gaia tutorial) and expresses that the time-dependent Topographic change rate $$\\frac{\\partial \\eta}{\\partial t}$$ equals the unit sediment (Bedload) fluxes $$q_b$$ over the boundaries [BRP03, Hir71]:\n\n$\\frac{\\partial \\eta}{\\partial t} = -\\frac{1}{\\epsilon}\\frac{\\partial q_b}{\\partial x}$\n\nwhere $$\\epsilon$$ is the porosity of the active transport (riverbed) layer, and $$\\eta$$ is the thickness of the active (riverbed) transport layer.\n\nFrench: \u00c9quation de Exner\nGerman: Exner-Gleichung (?)\n\nFroude number\n\nThe Froude number $$Fr$$ is the ratio between inertia and gravity forces and it is a key number of wave propagation. Thus, $$Fr$$ states whether information can be transmitted in upstream direction or not [Cho59, Hag10, HS09]:\n\n$\\begin{split} Fr^2 = \\frac{Q^2}{A^3 g} \\frac{\\partial A}{\\partial h}\\begin{cases} < 1 \\rightarrow \\mbox{ subcritical flow (upstream and downstream wave propagation)} \\\\ = 1 \\rightarrow \\mbox{critical flow (standing waves in upstream direction)} \\\\ > 1 \\rightarrow \\mbox{ supercritical flow (downstream wave propagation only)} \\end{cases} \\end{split}$\n\nThe transition from supercritical flow to subcritical flow is called hydraulic jump. For a rectangular cross section $$A$$, the Froude number becomes:\n\n$Fr = \\frac{u}{\\sqrt{g \\cdot h}}$\n\nThe Froude number is also the basis for scaling many sediment transport phenomena in open channel flow [Yal71, Yal77].\n\nFrench: Nombre de Froude\nGerman: Froude-Zahl\n\nGeoTIFF\n\nThe Georeferenced Tag Image File Format (GeoTIFF) links geographic positions to Gridded Cell (Raster) Data images. A GeoTIFF involves multiple files containing the tagged image itself (*.tif file), a world file (*.tfw file) containing information about the geographic reference and projection system, and potentially an *.ovr file that links the GeoTIFF with other resource data. Read more at the Open Geospatial Consortium\u2019s standard for GeoTIFF.\n\nGeomorphic heterogeneity\n\nGeomorphic heterogeneity describes the spatial pattern of gemorphic units (e.g., Riffle pool) within the River corridor. It describes the non-uniformity of a river compared with a monotonous trapezoidal or rectangular artificial channel [Woh22].\n\nGuild\n\nAn ecological guild describes a group of species that share common ecosystem resources. Species in a guild are not necessarily related to each other, nor do they necessarily use similar ecological niches. The term guild was introduced by Root [Roo67] and is used in ecohydraulics to describe (physical) habitat preferences of fish species and their lifestages. For instance, we may differentiate between reophilic and limnophilous fish guilds. In addition, we can distinguish between fish spawning guilds, and potamodromous, oceanmodromous and diadromous migration guilds.\n\nFrench: Guilde (f)\nGerman: Gilde (w)\n\nHDF\n\nThe Hierarchical Data Format (HDF) provides the *.h5 (HDF4) and *.h5 (HDF5) file formats that store large datasets in an organized manner. HDF is often used with high-performance computing (HPC) applications, such as numerical models, to store large amounts of data output. This eBook impinges on HDF datasets in the BASEMENT tutorial where xdmf files represent the model output, and in the TELEMAC tutorials. In particular, TELEMAC builds on mesh and boundary files of the EnSim Core that is described in the user manual of the pre- and post-processing software Blue KenueTM (the newest Blue Kenue installer contains an updated version of the user manual). Understanding the HDF format significantly facilitates troubleshooting structural errors of computational meshes for numerical models.\n\nHyporheic zone\n\nThe hyporheic zone is the space under and along rivers where surface water and groundwater exchange takes place. The exchange processes of a functional, non-clogged hyporheic zone are important for the ecosystem, in particular for fish spawning [BFM+98].\n\nKrylov space\n\nKrylov (sub) spaces are used in numerical approximation schemes for finding solutions to sparse (many zero entries), high-dimensional linear systems [BH74]. To this end, Krylov (sub) space methods use Gaussian elimination (e.g., LU decomposition) to speed up calculations [Gut07].\n\nFrench: Sous-espaces de Krylov \/ M\u00e9thode de la puissance it\u00e9r\u00e9e\nGerman: Krylowraum\n\nIAHR\n\nThe International Association for Hydro-Environment Engineering and Research (IAHR) is an independent non-profit organization that unites professionals in the field of water resources. The IAHR has multiple branches and publishes several journals in collaboration with external publishing companies. Read more about the IAHR at https:\/\/www.iahr.org.\n\nLidar\n\nLight Detection and Ranging (LiDAR or lidar) uses laser pulses to measure earth surface properties such as canopy or terrain elevation. The laser pulses are sent from a remote sensing platform (fix station or airborne) to surfaces, which reflect the pulses with different speed (time-of-flight informs about terrain elevation) and energy pattern (leaves behave differently than rock). In its raw form, lidar data is a point cloud with various, geo-referenced information about the reflected signal. Lidar point clouds for end users are typically stored in las format or compressed laz format. las-formatted data are much faster to process, but also much larger than laz-formatted data. For this reason, lidar data are preferably transferred in laz format, while the las format is preferably used for processing lidar data.\n\nLimnophile\n\nThe term limnophile is used as a noun in reference to species that prefer to live in calm waters. Thus, limnophilous species, such as common rudd (Scardinius erythrophthalmus), colonize slow-flowing to stagnant fresh water regions. Unlike limnophilous species, reophilic species prefer fast flowing regions (see also Reophile).\n\nFrench: inconnue\nGerman: Limnophil\n\nLU decomposition\n\nA lower-upper (LU) decomposition applies to the solution of linear systems (matrices) by re-organizing a matrix of equations into an upper and a lower triangular matrix. Thus, LU decomposition is a form of Gaussian elimination, which is typically applied in numerical analysis (e.g., Telemac2d) or machine learning.\n\nFrench: D\u00e9composition LU\nGerman: LR Zerlegung (Gau\u00dfsches Eliminationsverfahren)\n\nMPI\n\nIn computing, MPI stands for Message Passing Interface, which is a portable message passing standard. MPI is implemented in many open-source C, C++, and Fortran applications to enable parallel computing.\n\nNavier-Stokes equations\n\nThe general form of the Navier-Stokes equations describes the motion of a Newtonian fluid and expresses the conservation of mass and momentum [Bat00]. The Navier-Stokes equations is a special type of Continuity equation that is derived from Cauchy\u2019s equation (conservation of momentum). The equation simplifies with the assumption of incompressible fluids and reduces to the Euler equation when viscous effects are negligible, which is generally the case in far distance from the boundaries [KC08]. A theoretical, exact solution of the Navier-Stokes equations would yield a perfect description of many natural processes. However, the underlying system equations involves more unknown parameters than equations. For this reason, rigorous simplifications (e.g., the Shallow water equations) and numerical approximations with considerably larger computational effort than for an analytical solution are necessary for the solution of the Navier-Stokes equations. Simplification hypotheses are, for example, a hydrostatic pressure distribution (leading to the shallow water equations) or the assumption that a fluid is incompressible.\n\nFrench: \u00c9quations de Navier-Stokes\nGerman: Navier-Stokes-Gleichungen\n\nOceanodromous\n\nOceanodromous fish guilds exclusively live in oceans. while oceanodromous fish may encounter diadromous fish (migrate from the sea to freshwaters), they will very likely never meet potamodromous fish [Mye49]. Examples for oceanmodromous fish are Atlantic mackerels (Scomber scombrus) or Atlantic herring (Clupea harengus).\n\nOperating System\n\nAn Operating System (OS) manages the hardware of a computer, software (resources), and services for any program you want to install.\n\nFrench: Syst\u00e8me d\u2019exploitation\nGerman: Betriebssystem\n\nPlane bed\n\nA plane bed refers to a type of riverbed that is characterized by irregular bedforms with distant, varying confinement, often in transition between transport capacity-limited and sediment supply-limited river sections [Sch17].\n\nFig. 159 Example of a plane bed river section at the Drance (VS, Switzerland). Picture: Sebastian Schwindt (2016).\n\nPotamodromous\n\nPotamodromous fish guilds live and migrate in freshwater regions. Their migration is mostly due to reproduction. The difference with diadromous fish is that those migrate from the sea to freshwater regions. In addition, potamodromous fish will very likely never meet oceanmodromous fish [Mye49]. Examples for potamodromous fish are eal (Anguilla anguilla) and river trout (Salmo trutta fario).\n\nRating curve\nReophile\n\nThe term reophile is used as a noun in reference to species that prefer to live in fast-flowing water. In addition, a distinction is made between reophilic A and B species. Reophilic A species (e.g., brown\/river trout Salmo trutta (fario) or minnow Phoxinus phoxinus) colonize the main stream of a river at all lifestages. Reophilic B species (e.g., gudgeon Gobio gobio) occupy calmer flow regions (e.g., oxbows) in some lifestages. Unlike reophilic species, limnophilic species (e.g., common rudd Scardinius erythrophthalmus) prefer calm (stagnant) flow regions (see also Limnophile).\n\nFrench: inconnue\nGerman: Reophil\n\nReynolds number\n\nThe Reynolds number $$Re$$ relates viscous forces to inertia and is a key parameter for flow turbulence [Cho59]:\n\n$\\begin{split} Re = \\frac{u h}{\\nu} \\begin{cases} < 800 \\rightarrow \\mbox{ laminar flow} \\\\ \\geq 800 \\mbox{ and } \\leq 2000 \\rightarrow \\mbox{ transitional flow} \\\\ > 10000 \\rightarrow \\mbox{ turbulent flow} \\end{cases} \\end{split}$\n\nWhere $$\\nu$$ denotes the kinematic viscosity (10$$^{-6}$$ m$$^{2}$$ s$$^{-1}$$ for water at 20$$^{\\circ}$$C). In gravel-cobble bed rivers, inertia forces are typically dominant compared with viscous forces; therefore $$Re$$ is generally larger than 2000 and the flow is turbulent [Cho59, Woh00].\n\nFrench: Nombre de Reynolds\nGerman: Reynolds-Zahl\n\nRich Text Format\n\nThe proprietary Rich Text Format (RTF) wraps raw text in functional blocks that enable graphically flavored Word-like processors to identify document properties such as font size and type. Common RTFs are, for instance, docx or odf and enable exchanging text files between different Word-like processors on different operating systems.\n\nRiffle pool\n\nRiffle-pool (or pool-riffle) sequences are a sequence of fast-flowing, shallow flow units and deeper, slower flowing units of a river, where the dimensions of one unit correspond approximately to one channel width [Lis79]. The maintenance of riffle-pool channels requires sufficient sediment supply during smaller floods and a velocity reversal when those floods occur [CGB+09].\n\nFig. 160 A pool-riffle sequence at the American River close to Sacramento (CA, USA). Source: Sebastian Schwindt (2018)\n\nRiver corridor\n\nThe river corridor embraces the active river channel(s), floodplains, and the hyporheic zone underneath [Woh22].\n\nRiverbed clogging\n\nSee Clogging.\n\nSaint-Venant equations\n\nThe French mathematician Adh\u00e9mar Jean Claude Barr\u00e9 de Saint-Venant introduced dimensional simplifications of the Navier-Stokes equations. For simple cross-sections, the one-dimensional (1d), cross-section averaged Saint-Venant equations can be applied, and represent the baseline for the Manning-Strickler Formula (cf. the 1d Hydraulics Python exercise). The two-dimensional (2d), depth-averaged Saint-Venant equations are more frequently referred to as the Shallow water equations, which imply a hydrostatic pressure distribution [GA11].\n\nFrench: \u00c9quations (de Barr\u00e9) de Saint-Venant\nGerman: Saint-Venant-Gleichungen\n\nSand bed\n\nSand bed rivers are characterized by the abundance of fine sediment and sand bars. Compared with a gravel bed, a sand bed tends to have higher suspended load. This type of morphology is often observed lowland and coastal regions where the the hypothetic energy grade is low is less intense than in steeper regions [Kle05, ZF94].\n\nFig. 161 Dune bedforms of a sand bed in a side channel of the Inn River in Bavaria, Germany. Source. Sebastian Schwindt (2022)\n\nSediment transport\n\nFluvial sediment transport encompasses two modes of particle displacement: (1) suspended load and (2) bedload (see figure below). Finer particles with a weight that can be carried by the fluid (water) are transported as Suspended load. Coarser particles rolling, sliding, and jumping on the channel bed are transported as Bedload. There is third type of transport, the so-called wash load, which is finer than the coarse bed load, but too heavy (large) to be transported in suspension [Ein50]. The units for sediment transport are for an integral flow cross-section kg$$^3\\cdot$$s$$^{-1}$$ or per unit width kg$$^3\\cdot$$s$$^{-1}$$m$$^{-1}$$.\n\nFrench: Transport solide\nGerman: Sedimenttransport\n\nSediment yield\n\nThe sediment yield is the amount of sediment eroded per unit area (tons$$\\cdot$$km$$^{-2}\\cdot$$year$$^{-1}$$) of a watershed [GHW06].\n\nFrench: Apport solide\nGerman: Feststoffeintrag\n\nShallow water equations\n\nIn shallow (i.e., small water depths) and wide waters (many rivers), the assumption of hydrostatic pressure distribution can be made to simplify the Navier-Stokes equations. The corresponding simplified form of the Navier-Stokes equations is referred to as the shallow water equations. The shallow water equations imply that vertical flow velocity is negligible compared to horizontal (and longitudinal) flow velocity. This assumption is valid in many river systems, but there are several cases for which the shallow water equations are not suited [KC08].\n\nFor instance, the depth-averaged shallow water equations are not suited for any pressurized flows (e.g., at weirs or in pipes). This eBook recommends to use the shallow water equations only when the water depth is smaller than a 1\/20 times the characteristic wavelength (e.g., flood waves or in tsunami\/oceanic models) and when the water depth is smaller than 1\/10 of the wetted channel width. The application of the shallow water equations is featured in this eBook with the tutorials on 2d numerical modeling (i.e., in the BASEMENT and Telemac2d chapters).\n\nFrench: \u00c9quations (de Barr\u00e9) de Saint-Venant\nGerman: Flachwassergleichungen\n\nShields parameter\n\nThe Shields [Shi36] parameter $$\\tau_{x,cr}$$ (in the literature also often named $$\\theta_{cr}$$) is a dimensionless value of critical bed shear stress for sediment mobility. For this reason, the Shields parameter is also often referred to as dimensionless critical bed shear stress. Flow conditions and grain sizes with a Dimensionless bed shear stress $$\\tau_x$$ smaller than the Shields parameter curve are considered immobile. Vice versa, flow conditions and grains associated with a Dimensionless bed shear stress larger than the Shields parameter are considered mobile. In fully turbulent flow, the Shields parameter can be taken as a constant value of approximately 0.047$$\\pm$$0.15 [Kra32, SJ83, VK30]. To evaluate if a grain is in motion, its Dimensionless bed shear stress value is plotted against its dimensionless diameter $$D_x$$ in the so-called Shields diagram (also referred to as the Hunter-Rouse [Rou65] diagram). $$D_x$$ is calculated for any grain with a diameter $$D_{pq}$$ (in m) as [Ein50]:\n\n$D_x = \\left[\\frac{(s-1)\\cdot g}{\\nu^2}\\right]^{1\/3}\\cdot D_{pq}$\n\nwhere $$s$$ is the ratio of sediment grain and water density (typically 2.68); $$g$$ is gravitational acceleration; and $$\\nu$$ is the kinematic viscosity of water ($$\\approx$$10$$^{-6}$$m$$^{2}$$ s$$^{-1}$$) [Sch17]. Read the definition of Dimensionless bed shear stress for the calculation of $$\\tau_{x}$$. Figure 162 shows the Shields diagram where the Shields curve is plotted based on descriptions in Guo [Guo02].\n\nFig. 162 The Shields parameter $$\\tau_{x,cr}$$ (critical dimensionless bed shear stress) for grain mobility as a function of the dimensionless particle diameter $$D_x$$, according to Guo [Guo02] (image source: Schwindt [Sch17]).\n\nBeyond grain size and local hydrodynamics, $$\\tau_{x,cr}$$ is also a function of global channel roughness and slope, relative submergence and bedload transport intensity .\n\nSpawning guild\n\nDifferent groups of fish (i.e., fish guilds) have different practices and preference for spawning their eggs. In ecohydraulics, a distinction is made, for instance, between fish guilds that prefer to build nests in the surface of the riverbed (lithophilous) or glue their eggs to sediment (psamnophilous) or plants (phytophilous). Also, pelagophilous fish release their eggs into the free-flowing water.\n\nSuspended load is a special type of Sediment transport describing the displacement of fine particles with the bulk flow.\n\nFrench: Transport en suspension\nGerman: Schwebstofftransport\n\nSMS 2dm\n\nSMS (Surface-water Modeling System) is a proprietary software suite from Aquaveo for surface water modeling. 2dm file format is natively produced with SMS and represents a computational grid with x, y, and z coordinates of nodes along with node ids. The developer\u2019s wiki provides a comprehensive description of the file format.\n\nSonar\n\nSound navigation and ranging (Sonar) is a technique for locating objects in space and underwater by emitting sound pulses. An active Sonar system, such as radio detecting and ranging (radar), emits and receives sound signals to map objects underwater (time-of-flight measurement). Passive Sonar detects signals emitted by an object itself (e.g., vibrations from fish motion or Whale chant), but cannot accurately map underwater objects.\n\nSRS\n\nSee CRS.\n\nStage-discharge relation\n\nA stage-discharge relation (also referred to as rating curve) plots discharge (in m$$^3$$\/s or CFS) as a function of water surface elevation function (in m above sea level or ft) at a specific river cross-section. Most stream gauging stations have a regularly calibrated stage-discharge relation that is often maintained by a state authority. This is why, it is mostly state authorities that provide stage-discharge functions for their gauging stations online, such as the state of Bavaria at the M\u00fchldorf am Inn gauge.\n\nFrench: Courbe d\u2019\u00e9talonnage \/ Courbe hauteur-d\u00e9bit \/ Courbe de tarage\nGerman: Wasserstands-Abfluss Beziehung, bzw. Abflusskurve \/ Abflussschl\u00fcsselkurve \/ Eichkurve\n\nStep pool\n\nStep pools are a type of morphological units, typically found in steep mountain rivers. They are characterized by high gradients (exceeding 2%) and a rough surface composed of cobble and bedrock [GONK08].\n\nSTL\n\nThe Standard Tessellation Language (STL) file format is native to a three-dimensional (3d) printing CAD software type called stereolithography. An STL file describes 3d structures in the form of unstructured triangulated surfaces with arbitrary units.\n\nThalweg\n\nThe term Thalweg stems from old German spelling for valley (today: Tal) and should be more correctly referred to as Talweg. The literal translation of Talweg is valley path and originally refers to a line that longitudinally connects the lowest points of valley cross-section profiles. Geomorphologists sometimes use slightly different definitions of Talweg. International law is more explicit, referring to the Thalweg as the primary navigable channel at boarders between two countries.\n\nFrench: talweg \/ thalweg\nGerman: Talweg\n\nTopographic change\n\nTopographic change is the increase or decrease in elevation of the Earth\u2019s surface as a function of time. Conceptually, tracking topographic changes could consist of a simple comparison (i.e., subtraction) of elevation changes at two different moments. However, topographic change detection is not quite that simple, since every measurement technique has spatial inaccuracies with regards to the exact location and elevation of recorded points. For this reason, methods have been developed that, based on a level of detection (LoD), generate topographic change maps conveying and accounting for spatial uncertainty. Depending on the method, either strict global LoD raster [PW17] or less strict pixel-based LoD values [WBDS10] are used to remove uncertainty from topographic change maps. Topographic change maps also enable the visualization of soil loss (i.e., erosion), which is a growing challenge for agriculture and beyond. To this end, the USGS developed a publicly available website that is dedicated to topographic change (visit https:\/\/usgs.gov).\n\nFrench: Changement du terrain (non-technique)\nGerman: Topografischer Wandel (kein technischer Begriff)\n\nxdmf\n\nThe eXtensible Data Model and Format (XDMF) library provides standard routines for exchanging (scientific) datasets that result from high performance computing (HPC) tasks. XDMF files redundantly store light and heavy data in XML and HDF5 format and Python interfaces exist for both formats. Thus, XDMF or XMF files are often linked to a *.h4 or *.h5 (HDF) file that contains heavy simulation datasets.","date":"2023-02-08 12:37:37","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\": 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\": 0.4908776879310608, \"perplexity\": 4278.448291603776}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764500813.58\/warc\/CC-MAIN-20230208123621-20230208153621-00346.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.weegy.com\/Home.aspx?ConversationId=FE1E5CC2","text":"Multiply 1 1\/2*6 2\/3\nQuestion\nUpdated 206 days ago|2\/24\/2018 7:49:32 PM\nThis conversation has been flagged as incorrect.\nFlagged by jeifunk [2\/24\/2018 7:49:01 PM]\nOriginal conversation\nUser: Multiply 1 1\/2*6 2\/3\n\nWeegy: Multiplication (often denoted by the cross symbol \"?\") is the mathematical operation of scaling one number by another. [ It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division). Because the result of scaling by whole numbers can be thought of as consisting of some number of copies of the original, whole-number products greater than 1 can be computed by repeated addition; for example, 3 multiplied by 4 (often said as \"3 times 4\") can be calculated by adding 4 copies of 3 together: 3 \\times 4 = 3 + 3 + 3 + 3 = 12.\\!\\, Here 3 and 4 are the \"factors\" and 12 is the \"product\". Educators differ as to which number should normally be considered as the number of copies, and whether multiplication should even be introduced as repeated addition.[1] For example 3 multiplied by 4 can also be calculated by adding 3 copies of 4 together: 3 \\times 4 = 4 + 4 + 4 = 12.\\!\\, Multiplication of rational numbers (fractions) and real numbers is defined by systematic generalization of this basic idea. Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths (for numbers generally). The area of a rectangle does not depend on which side you measure first, which illustrates that the order numbers are multiplied together in doesn't matter. In general the result of multiplying two measurements gives a result of a new type depending on the measurements. For instance: 2.5 \\mbox{ meters} \\times 4.5 \\mbox{ meters} = 11.25 \\mbox{ square meters},\\!\\, 11 \\mbox{ meters\/second} \\times 9 \\mbox{ seconds} = 99 \\mbox{ meters}.\\!\\, The inverse operation of multiplication is division. For example, 4 multiplied by 3 equals 12. Then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number. Multiplication is also defined for other types of numbers (such as complex numbers), and for more abstract constructs such as matrices. ]\nkitchencatlover|Points 162|\n\nUser: Multiply 1 1\/2*6 2\/3\n\nWeegy: Multiplication (often denoted by the cross symbol \"?\") is the mathematical operation of scaling one number by another. [ It is one of the four basic operations in elementary arithmetic (the others being addition, subtraction and division). Because the result of scaling by whole numbers can be thought of as consisting of some number of copies of the original, whole-number products greater than 1 can be computed by repeated addition; for example, 3 multiplied by 4 (often said as \"3 times 4\") can be calculated by adding 4 copies of 3 together: 3 \\times 4 = 3 + 3 + 3 + 3 = 12.\\!\\, Here 3 and 4 are the \"factors\" and 12 is the \"product\". Educators differ as to which number should normally be considered as the number of copies, and whether multiplication should even be introduced as repeated addition.[1] For example 3 multiplied by 4 can also be calculated by adding 3 copies of 4 together: 3 \\times 4 = 4 + 4 + 4 = 12.\\!\\, Multiplication of rational numbers (fractions) and real numbers is defined by systematic generalization of this basic idea. Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths (for numbers generally). The area of a rectangle does not depend on which side you measure first, which illustrates that the order numbers are multiplied together in doesn't matter. In general the result of multiplying two measurements gives a result of a new type depending on the measurements. For instance: 2.5 \\mbox{ meters} \\times 4.5 \\mbox{ meters} = 11.25 \\mbox{ square meters},\\!\\, 11 \\mbox{ meters\/second} \\times 9 \\mbox{ seconds} = 99 \\mbox{ meters}.\\!\\, The inverse operation of multiplication is division. For example, 4 multiplied by 3 equals 12. Then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number. Multiplication is also defined for other types of numbers (such as complex numbers), and for more abstract constructs such as matrices. ]\nkitchencatlover|Points 162|\n\nUser: Calculate 7 3\/8+9.125=\n\nUser: 21. Find percent notation for the fraction notation in the sentence. In one company, two out of every ten employees use all their sick time. What percent use all their sick time?\n\nUser: In one company, two out of every ten employees use all their sick time. What percent use all their sick time?\n\nUser: The number 37000 when expressed in scientific notation is\n\nWeegy: it is 3\nposhful14|Points 20|\n\nUser: Find the difference of 23 and (32 - 9)\n\nWeegy: 23+23= 46\ntina.pie88|Points 46|\n\nQuestion\nUpdated 206 days ago|2\/24\/2018 7:49:32 PM\nThis conversation has been flagged as incorrect.\nFlagged by jeifunk [2\/24\/2018 7:49:01 PM]\nRating\n3\n1 1\/2 * 6 2\/3\n= 3\/2 (20\/3)\n= 10\nAdded 206 days ago|2\/24\/2018 7:48:36 PM\n3\n23 - (32 - 9)\n=23 - 23\n=0\nAdded 206 days ago|2\/24\/2018 7:48:57 PM\n3\n7 3\/8 + 9.125\n= 59\/8 + 9.125\n= 33\/2\n= 16 1\/2\nAdded 206 days ago|2\/24\/2018 7:49:32 PM\n\n27,346,123\n*\nGet answers from Weegy and a team of really smart live experts.\nPopular Conversations\nMultiply (2x + 8)(4x + 7).\nWeegy: 3(4x + 2x) = 8; User: Multiply (2m + 3)(m2 \u2013 2m + 1).\nWhere did the D-Day invasion occur during World War II? A. ...\nWeegy: D-Day invasion occur in France. User: What reason was given for the German annexation of Austria in 1938? ...\nWhich of the following was a reason for the collapse of the Soviet ...\nWeegy: A flawed, underperforming economy was a reason for the collapse of the Soviet Union. User: Which of the ...\nThe Incident Command System (ICS) is only applicable to large, ...\nWeegy: The Incident Command System (ICS) is a standardized management tool for meeting the demands of small or large ...\nS\nL\nPoints 1024 [Total 1335] Ratings 14 Comments 884 Invitations 0 Offline\nS\nR\nL\nR\nP\nR\nP\nR\nR\nR\nR\nPoints 412 [Total 1296] Ratings 3 Comments 292 Invitations 9 Offline\nS\nL\nR\nP\nR\nP\nR\nP\nR\nPoints 351 [Total 1126] Ratings 3 Comments 291 Invitations 3 Offline\nS\nL\nP\nP\nP\nPoints 281 [Total 1157] Ratings 0 Comments 281 Invitations 0 Offline\nS\nL\nR\nPoints 34 [Total 151] Ratings 0 Comments 34 Invitations 0 Offline\nS\nPoints 33 [Total 33] Ratings 1 Comments 23 Invitations 0 Offline\nS\nPoints 14 [Total 14] Ratings 0 Comments 14 Invitations 0 Offline\nS\nPoints 10 [Total 10] Ratings 0 Comments 0 Invitations 1 Offline\nS\nL\n1\nR\nPoints 2 [Total 1453] Ratings 0 Comments 2 Invitations 0 Offline\nS\nPoints 2 [Total 2] Ratings 0 Comments 2 Invitations 0 Offline\n* Excludes moderators and previous\nwinners (Include)\nHome | Contact | Blog | About | Terms | Privacy | \u00a9 Purple Inc.","date":"2018-09-19 09:29:05","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\": 0.8575174808502197, \"perplexity\": 1821.019543152489}, \"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-2018-39\/segments\/1537267156096.0\/warc\/CC-MAIN-20180919083126-20180919103126-00127.warc.gz\"}"} | null | null |
\section{Introduction}
With the sharp proliferation of the Internet of Thing (IoT) devices
and the rising need of mission-critical services, timely delivery
of information has become increasingly important in real-time status
update systems, such as environmental monitoring in smart city, vehicle
tracking in autonomous driving, and video surveillance in smart home,
whose performance strongly depends on the freshness of the status
updates received by the destination \cite{palattellaInternetThings5G2016,schulzLatencyCriticalIoT2017,abd-elmagidRoleAgeofInformationInternet2019}.
The Age of Information (AoI) has been recently introduced to measure
information freshness from the receiver\textquoteright s perspective
\cite{kaulRealtimeStatusHow2012}. Particularly, it is defined as
the time elapsed since the generation of the most recent status update
packet received by the destination. In general, the smaller the AoI
at the destination, the fresher the received status update. The AoI
jointly characterizes the packet delay and the packet intergeneration
time, which distinguishes AoI from conventional metrics, such as delay
and throughput. Such a superiority of AoI for evaluating the information
freshness in various wireless networks has been demonstrated in recent
studies \cite{kaulRealtimeStatusHow2012,kaulStatusUpdatesQueues2012,kostaAgeInformationPerformance2018,xuOptimizingInformationFreshness2020}
by resorting to queueing theory.
An IoT network mainly consists of three components, i.e. the IoT device,
the communication network, and the destination node. As such, to optimize
the information freshness in terms of the AoI for the IoT, it is of
great importance to control the status update process, which has attracted
significant research attention in recent years \cite{hsuSchedulingAlgorithmsMinimizing2020,sunUpdateWaitHow2017,bedewyAgeoptimalSamplingTransmission2018,liuUAVAidedDataCollection2020,ceranAverageAgeInformation2019,tangMinimizingAgeInformation2020,zhouJointStatusSampling2019,lengAgeInformationMinimization2019a,abd-elmagidReinforcementLearningFramework2020,abd-elmagidAoIOptimalJointSampling2020}.
Particularly, authors in \cite{hsuSchedulingAlgorithmsMinimizing2020}
studied the AoI optimal packet transmission policy with random information
arrivals under a transmission capacity constraint. In the case where
the IoT device generates status updates at will, the authors in \cite{sunUpdateWaitHow2017}
studied the AoI minimization problem with a single device, where a
zero-wait policy was shown to be non-optimal. Minimizing the average
AoI in a status update system with multiple devices was further studied
in \cite{bedewyAgeoptimalSamplingTransmission2018}. Two age-optimal
data collection problems were investigated to minimize the average
AoI and peak AoI for UAV enabled wireless sensor networks in \cite{liuUAVAidedDataCollection2020}.
An optimal status updating scheme with hybrid Automatic Repeat request
(ARQ) was proposed in \cite{ceranAverageAgeInformation2019} to minimize
the average AoI under a constraint on the average number of transmissions.
By considering the restriction from bandwidth and power consumption
constraints, a dynamic scheduling algorithms was developed to minimize
the average AoI of industrial IoT networks in \cite{tangMinimizingAgeInformation2020}.
The authors in \cite{zhouJointStatusSampling2019} designed a joint
status sampling and updating to minimize the average AoI under an
average energy cost constraint. Further, by empowering the sensor
nodes with energy harvesting techniques, recent work \cite{lengAgeInformationMinimization2019a}
developed the age-aware primary spectrum sensing and update strategy
for an energy harvesting cognitive radio. Meanwhile, the wireless
energy transfer procedure and scheduling of update packet transmissions
were jointly optimized by authors in \cite{abd-elmagidReinforcementLearningFramework2020},
who further extended their research by considering the sampling cost
in \cite{abd-elmagidAoIOptimalJointSampling2020}.
As seen above, the AoI has been widely used as a performance metric
to characterize the information freshness over time. It does, however,
disregard the content carried by the updates and the current knowledge
at the receiver. A natural question that then emerges is whether measuring
the freshness of updates through the AoI alone is sufficient. Several
recent attempts have been made to answer this question \cite{sunSamplingDataFreshness2019,kamEffectiveAgeInformation2018a,zhongTwoFreshnessMetrics2018,tangSchedulingMinimizeAge2020,maatoukAgeIncorrectInformation2020}.
The pros and cons of these metrics are elaborated in the following.
\begin{itemize}
\item Authors in \cite{sunSamplingDataFreshness2019} utilized mutual information
between the state of the physical process and the received updates
at the destination to evaluate the information freshness. The mutual
information quantifies the amount of information that the received
updates carry about the current value of the physical process. Although
the destination has no knowledge of the current value of the physical
process, it is proved that the mutual information is a non-negative
and non-increasing function of AoI if the physical process is a stationary
Markov chain and the sampling times are independent of the value of
the physical process. Therefore, the mutual information can be computed
by the destination via the AoI. However, for more general cases where
the sampling policy needs to be devised based on the causal knowledge
of the value of the physical process, the mutual information is not
necessarily a function of the age. In this light, how to compute the
mutual information at the destination is unknown.
\item In \cite{kamEffectiveAgeInformation2018a}, the authors proposed a
metric, called sampling age, which is the time difference between
the last ideal sampling time and the first actual sampling time. The
ideal sampling time is the most recent time at which the state of
the physical process changed relative to the last received update.
However, the ideal sampling time is not available to the destination
and hence the sampling age cannot be obtained by the destination.
\item The Age of Synchronization (AoS) was proposed in \cite{zhongTwoFreshnessMetrics2018}
to measure how long the information at the receiver has become desynchronized
compared with the physical process. It is defined as the time difference
between the current time and the earliest update generation time after
the previous synchronization time \cite{tangSchedulingMinimizeAge2020}.
Similar to the AoI, the AoS drops when the destination receives a
status update packet. However, unlike the AoI which begins to increase
immediately after the reception of a status update packet at the destination,
the AoS remains to be zero and does not increase until the sensor
generates a new status update packet. However, the destination does
not know the generation time of the earliest update after the previous
synchronization until it receives this update. Hence, the AoS cannot
be calculated at the destination.
\item The Age of Incorrect Information (AoII) was proposed in \cite{maatoukAgeIncorrectInformation2020}
to address the real-time remote estimation problem. The AoII combines
a time penalty function and an estimation error penalty function that
reflects the difference between the current estimate at the destination
and the actual state of the physical process. As such, the AoII will
increase with time when the receiver stays in an erroneous state.
Computing the AoII at the destination requires that the state of the
physical process is available to the destination in any time slot.
Otherwise, the estimation at the destination and the state of the
physical process cannot be compared to compute the estimation error
penalty function in the AoII. However, the destination cannot observe
the state of the physical process until it receives the status update
packet. Therefore, the AoII cannot be computed by the destination.
\end{itemize}
In summary, mutual information cannot be computed if the sampling
times are determined by using causal knowledge of the value of the
physical process, while the other three metrics are only available
to the transmitter rather than the destination. Since the last three
metrics cannot be computed by the destination, they cannot be applied
in the scenario where the sensor has no computing capability and the
destination is in charge of decision-making. This is also the scenario
we focus on in this work. Moreover, even if the sensor has the computing
capability, the above three metrics require the continuous sensing
of the physical process, which would induce noticeable energy consumption.
In this paper, we concentrate on the scenario where the receiver aims
to conduct timely detection of status changes in the underlying physical
process only based on its received update packets. In practice, a
status change won\textquoteright t be detected until an update generated
after the change point is successfully delivered to the destination
for the first time. However, it is impossible to know the exact time
instant of a status change unless the physical process is monitored
continuously. Therefore, it is challenging to design the optimal updating
policy to balance the information freshness and the energy consumption.
On the one hand, sampling and transmitting at a higher frequency incurs
a higher energy consumption of the sensor. On the other hand, sampling
at a lower frequency results in staleness in detecting a status change
or even a miss detection. The error-prone wireless channel further
worsens the situation, since the update packet may be dropped due
to channel outage. As a result, the receiver could be fooled into
believing that no change in state has taken place. Motivated by all
this, we introduce a utility function from the receiver's perspective
that depicts both the passage of time and the change of information
content. We further investigate this utility in a status update system
consisting of a sensor and a destination. In particular, the sensor
monitors the real-time status of a physical process, which is modeled
by a discrete time Markov chain with uniform stationary distribution,
and transmits status update packets to the destination. In our earlier
work \cite{linAverageAgeChanged2020a}, we investigated the effects
of content change on the information freshness and designed the optimal
status updating policy in an IoT system. However, the model of the
physical process is limited to the two-state Markov chain with the
equal transition probabilities. The key contributions of this paper
are summarized as follows:
\begin{itemize}
\item Motivated by the fact that a status change will not be perceived by
the destination until an update generated after the change instant
is successfully delivered, we introduce a new age-based utility,
referred to as Age of Changed Information (AoCI), that characterizes
the information freshness via the updates received by the destination.
The word ``changed'' refers to the newly received update that brings
new content different from the previous one at the destination. The
AoCI takes into account the information content of the updates and
the current knowledge at the destination. It will increase when the
update with the same status information is received.
\item We formulate the status updating problem as an infinite horizon average
cost Markov Decision Process (MDP) with the goal of minimizing the
weighted sum of the AoCI and the update cost. By incorporating the
AoCI into the cost function of the MDP, the sensor is made to sample
and transmit at a higher frequency when the same status information
is continuously received, thereby potentially reducing the miss detection.
We analyze the properties of the value function without specifying
the state transition model of the physical process. Armed with these
properties, we show that the optimal updating policy has a special
structure with respect to the AoCI and identify the condition on the
return probability of the physical process under which the special
structure exists. A structure-aware relative policy iteration algorithm
is then proposed to obtain the optimal updating policy with low complexity.
\item We study two special cases, where the return probability satisfies
the condition. In the first case, by giving an example that the
state of the underlying physical process transits with equiprobability,
we simplify the MDP and prove that the optimal policy is of threshold
type. We also derive the optimal threshold in closed-form, which sheds
insight on how the system parameters affect the threshold policy.
Particularly, we prove that the optimal threshold is non-increasing
with transmission success probability and the number of states of
the physical process, but is non-decreasing with the update cost.
We generalize the example in the first case by studying the periodic
Markov model of the physical process in the second case. Simulation
results highlight interesting insights on the effects of the system
parameters and show the superiority of the optimal updating policy
over the zero-wait policy.
\end{itemize}
The rest of the paper is organized as follows: Section II provides
a description of the system model and a definition for the proposed
performance metric. In Section III, we present the MDP formulation
and analyze the structure of the optimal policy. Two special cases
are then analyzed in Section IV. Simulation results are presented
in Section V, followed by the conclusion in Section VI.
\section{System Overview \label{sec:System-Overview}}
\subsection{System Model}
\begin{figure}[tp]
\centering
\includegraphics[width=0.5\textwidth]{figure/SystemModel}\caption{\label{fig:SystemModel}An illustration of a status update system
monitoring a physical process.}
\end{figure}
As shown in Fig. \ref{fig:SystemModel}, we consider a status update
system consisting of a sensor and a destination, where the sensor
performs simple monitoring tasks, such as reading temperature, and
the destination could be a monitor or an actuator. The status update
system is assumed to be time-slotted. The sensor may produce a status
update about the underlying time-varying process (a.k.a. generate-at-will)
in each time slot and send it over an unreliable wireless channel
to the destination. The sensor could also remain idle in one time
slot. Let $a_{t}\in\{0,1\}$ be the action of the sensor in the $t$-th
slot, where $a_{t}=1$ indicates that the sensor samples and transmits
an update, and $a_{t}=0$, otherwise. Any update's transmission time
is assumed to be equal to one slot length. Moreover, the slot length
is normalized to unity, without loss of generality. In general, each
update would entail a cost $C_{u}$, including the sampling cost and
the transmission cost, where the cost for sampling is assume to be
negligible compared to that of transmission.
Assume that the underlying time-varying physical process is modeled
by a $M$-state discrete time Markov chain $\{X_{t};t\in\mathbb{N}\}$
with $X_{t}\in\{1,2,...,M\}$, where $M\geq2$. The period of each
state is equal to the length of one slot, and the transition occurs
at the beginning of each slot just before the sampling decision. We
assume that all the state of the Markov chain have have uniform stationary
distribution.
We assume that the fading of channels in each slot stays constant
but varies independently over various slots. We also assume that an
update is transmitted by the sensor at a fixed rate, and channel state
information is only available at destination. As such, the transmission
in each time slot may fail because of an outage and thus the loss
of the packet could be described by a memoryless Bernoulli process.
Specifically, let $h_{t}\in\{0,1\}$ denote whether the transmission
succeeds or fails, where $h_{t}=1$ indicates that the transmission
is successful, and $h_{t}=0$, otherwise. We define the success probability
as $\Pr\{h_{t}=1\}=p_{s}$ and the failure probability as $\Pr\{h_{t}=0\}=p_{f}=1-p_{s}$.
After the destination receives the update packet, a single-bit acknowledgement
is fed back instantaneously without error. We assume that the failed
update will be discarded, and if the sensor decides to transmit in
the next slot, a new status update will be generated.\footnote{The reason why we sample and transmit a new status update rather than
retransmit a failed update lies in two aspects. On the one hand,
according to the studies in \cite{ceranAverageAgeInformation2019},
in the context of AoI, it is better not to retransmit an undecoded
packet with the classical ARQ protocol, where failed transmissions
are discarded at the destination and the receiver tries to decode
each retransmission as a new message. This is because the probability
of a successful transmission is the same for a retransmission and
for the transmission of a new update. On the other hand, in this work
we focus on the scenario that the sensor performs simple monitoring
tasks, such as reading temperature, and hence, the cost for generating
status packets is assumed to be negligible compared to that of transmission.
Then, the energy costs for transmitting a new update and retransmitting
a failed update are almost the same. Altogether, we choose to transmit
a new update when the transmission failure occurs.}
\subsection{Freshness Metric}
We assume that at the beginning of a slot a status update is generated
and transmitted, and the destination will receive it at the end of
the slot if the transmission succeeds. The AoI, commonly used to quantify
the freshness of the information, is specified as the time elapsed
since the generation of the latest status update received by the destination.
Suppose that the latest status update successfully received by the
destination was generated at the time instants $U(t)$, i.e., $U(t)=\max\{g_{i}\mid d_{i}\leq t\}$,
where $g_{i}$ and $d_{i}$ represent the time instants when the update
$i$ is generated and delivered, respectively. Then, the AoI at the
beginning of slot t is given by
\begin{equation}
\delta_{t}=t-U(t).
\end{equation}
The proposed metric, AoCI, is different from the AoI in that the AoCI
not only captures the time lag of the update received at the destination,
but also includes variations in the information content of these updates.
In particular, the AoCI only declines when the newly received update
content differs from the previous one, and boosts otherwise. Let us
denote by $n(t)=\max\{i|d_{i}\leq t\}$ the index of the latest update
the destination receives at the end of slot $t$. We let $Y_{j}$
denote the information content of update $j$. It is worth noting
that $Y_{j}$ is equal to the state of the physical process in the
slot when update $j$ was generated, e.g., $Y_{n(t)}=X_{U(t)}$. Let
us denote by $m(t)=\max\{j|Y_{j}\neq Y_{n(t)},d_{j}\leq d_{n(t)}\}$
the index of the most recently update which has different content
from the latest update $n(t)$ got. Then, we can define the AoCI at
the beginning of slot $t$ as
\begin{equation}
\Delta_{t}=t-U'(t),\label{eq:AoCI}
\end{equation}
where $U'(t)=\min\{g_{k}|d_{m(t)}<d_{k}\leq d_{n(t)}\}$ represents
the generation time of the next successfully received update after
$m(t)$. Noting that all the update packets that have been successfully
received after $m(t)$ have the same content as the latest one received.
We set the upper limits to the AoCI and the AoI, which are denoted
by $\hat{\Delta}$ and $\hat{\delta}$, respectively.
In slot $t$ where a status update is received successfully, we denote
by $D_{t}\in\{0,1\}$ an indicator for whether the content of the
newly received update varies from that of the previously received
update. If $D_{t}=1$, then the newly received update has different
content. Otherwise, it has the same content. Particularly, the content
change probability is defined as
\begin{align}
\Pr(D_{t}=1) & \overset{(a)}{=}\Pr(Y_{n(t)}\neq Y_{n(t)-1})\overset{(b)}{=}1-p_{r}(\delta_{t}),
\end{align}
where $p_{r}(\delta_{t})=\Pr(X_{U(t)}=X_{U(t)-\delta_{t}})$ is the
return probability that the state of the physical process remains
the same after $\delta_{t}$ steps. In the above equation, (a) holds
due to the definition of $D_{t}$, and (b) holds because of the fact
that $Y_{n(t)}=X_{U(t)}$ and $Y_{n(t)-1}=X_{U(t)-\delta_{t}}$.\footnote{Note that the time difference between two consecutive samples at the
sensor is $\delta_{t}$. Therefore, the update $n(t)-1$ was generated
at $U(t)-\delta_{t}$, and its content $Y_{n(t)-1}$ is the same as
the state of the physical process at $U(t)-\delta_{t}$, i.e., $X_{U(t)-\delta_{t}}$. } According to (\ref{eq:AoCI}), if a new status update generated by
the sensor is received successfully by the destination (i.e., $a_{t}=1,h_{t}=1$)
and it contains different content from the update previously received
(i.e., $D_{t}=1$), then the AoCI decreases to one; otherwise, the
AoCI increases by one. Then, the dynamics of the AoCI is given by
\begin{equation}
\Delta_{t+1}=\begin{cases}
1, & a_{t}=1,h_{t}=1,D_{t}=1;\\
\min\{\Delta_{t}+1,\hat{\Delta}\}, & \text{otherwise}.
\end{cases}\label{eq:Dynamic}
\end{equation}
For ease of exposition, we demonstrate how the AoCI and the AoI evolve
over time in Fig. \ref{fig:AOI figure}, where the dotted line represents
the AoI and the solid line represents the AoCI.
\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{figure/AoIDynamics_new}\caption{\label{fig:AOI figure}An illustration of the AoCI and the AoI in
a time-slotted status update system.}
\end{figure}
\subsection{Problem Formulation}
The aim of this paper is to find an update policy $\pi=(a_{0},a_{1},\ldots)$
that minimizes the total average cost, which is defined as the weighted
sum of the AoCI and the update cost. By defining $\Pi$ as a set of
stationary and deterministic policies,\footnote{A policy is said to be stationary and deterministic if it is time
invariant and chooses an action with probability one.} our problem is formulated as follows:
\begin{equation}
\min_{\pi\in\Pi}\limsup_{T\rightarrow\infty}\frac{1}{T}\stackrel[t=0]{T}{\sum}\mathbb{E}[\Delta_{t}+\omega a_{t}C_{u}],\label{eq:Problem}
\end{equation}
where $\omega$ is the weighting factor and the expectation is taken
with respect to the distribution over trajectories induced by $\pi$
together with the transition probabilities.
\textcolor{red}{}
\begin{figure*}[tb]
\begin{equation}
\begin{cases}
\Pr(\bm{s}_{t+1}=(\min\{\Delta+1,\hat{\Delta}\},\min\{\delta+1,\hat{\delta}\})|\bm{s}_{t}=(\Delta,\delta),a_{t}=0)=1,\\
\Pr(\bm{s}_{t+1}=(\min\{\Delta+1,\hat{\Delta}\},\min\{\delta+1,\hat{\delta}\})|\bm{s}_{t}=(\Delta,\delta),a_{t}=1)=p_{f},\\
\Pr(\bm{s}_{t+1}=(\min\{\Delta+1,\hat{\Delta}\},1)|\bm{s}_{t}=(\Delta,\delta),a_{t}=1)=p_{s}p_{r}(\delta),\\
\Pr(\bm{s}_{t+1}=(1,1)|\bm{s}_{t}=(\Delta,\delta),a_{t}=1)=p_{s}(1-p_{r}(\delta)),
\end{cases}\label{eq:state-transition}
\end{equation}
\hrulefill
\end{figure*}
\section{Optimal Update Policy Design \label{sec:Updating-Policy-Design}}
\subsection{MDP Formulation}
The optimization problem in (\ref{eq:Problem}) can be cast into an
infinite horizon average cost Markov decision process $(\mathcal{S},\mathcal{A},\Pr(\cdot|\cdot,\cdot),C(\cdot,\cdot))$,
where each element is described as follows:
\begin{itemize}
\item States: The state of the MDP at time slot $t$ is defined to be the
tuple of the AoCI and the AoI, i.e., $\bm{s}_{t}\triangleq\left(\Delta_{t},\delta_{t}\right)$.
Since both the AoCI and the AoI are bounded by their upper limits,
the state space $\mathcal{S}$ is finite.
\item Actions: The action at time slot $t$ is $a_{t}$ and the action set
is $\mathcal{A}=\{0,1\}$.
\item Transition Probability: Let $\Pr(\bm{s}_{t+1}|\bm{s}_{t},a_{t})$
denote the transition probability that state transits from $\bm{s}_{t}$
to $\bm{s}_{t+1}$ by taking action $a_{t}$ at slot $t$. Because
the event of packet transmission and that of content change are independent,
according to the AoCI evolution dynamics (\ref{eq:Dynamic}), the
transition probability is represented as in (\ref{eq:state-transition})
and $\Pr(\bm{s}_{t+1}|\bm{s}_{t},a_{t})=0$ otherwise.
\item Cost: We let $C(\bm{s}_{t},a_{t})=\Delta_{t}+\omega a_{t}C_{u}$ denote
the instantaneous cost at state $\bm{s}_{t}$ given action $a_{t}$.
\end{itemize}
The above MDP is a finite-state finite-action average-cost MDP. According
to \cite[Theorem 8.4.5]{putermanMarkovDecisionProcesses2005}, there
exists a deterministic stationary average optimal policy for the finite-state
finite-action average-cost MDP if the cost function is bounded and
the MDP is unichain, i.e., the Markov chain corresponding to every
deterministic stationary policy consists of a single recurrent class
plus a possibly empty set of transient states. Below, we examine these
two conditions. First, the cost of the above MDP is bounded since
the instantaneous cost is defined as the weighted sum of the AoCI
and the energy consumption. Second, since the state $(\hat{\Delta},\hat{\delta})$
is reachable from all other states, the induced Markov chain has a
single recurrent class. Hence, the MDP is unchain. Altogether, there
exists a stationary and deterministic optimal policy. The optimal
policy $\pi^{*}$ to minimize the total average cost can be obtained
by solving the following Bellman equation \cite{dimitrip.bertsekasDynamicProgrammingOptimal2007}:
\begin{equation}
\theta+V(\bm{s})=\min_{a\in\{0,1\}}\left\{ C(\bm{s},a)+\sum_{\bm{s}'\in\mathcal{S}}\Pr(\bm{s}'|\bm{s},a)V(\bm{s}')\right\} ,\forall\bm{s}\in\mathcal{S},\label{eq:Bellman}
\end{equation}
where $\theta$ is the optimal value to (\ref{eq:Problem}) for all
initial state and $V(\bm{s})$ is the value function which is a mapping
from $\bm{s}$ to real values. Moreover, for any $\bm{s}\in\mathcal{S}$,
the optimal policy can be given by
\begin{equation}
\pi^{*}(\bm{s})=\arg\min_{a\in\{0,1\}}\left\{ C(\bm{s},a)+\sum_{\bm{s}'\in\mathcal{S}}\Pr(\bm{s}'|\bm{s},a)V(\bm{s}')\right\} .\label{eq:optimal-policy}
\end{equation}
We can seen from (\ref{eq:optimal-policy}) that the optimal policy
$\pi^{*}$ depends on the value function $V(\cdot)$. Unfortunately,
there is usually no closed-form solution for $V(\cdot)$ \cite{dimitrip.bertsekasDynamicProgrammingOptimal2007}.
Therefore, numerous numerical algorithms have been proposed in the
literature, such as policy iteration and value iteration. Nonetheless,
owing to the curse of dimensionality these approaches are typically
computationally exhausting, and few insights can be leveraged for
optimal policy. Hence, in the sequel, we study the structural properties
of the optimal updating policy.
To analyze the structure of $\pi^{*}$, we introduce the state-action
value function $Q(\bm{s},a)$, which is defined as
\begin{equation}
Q(\bm{s},a)=C(\bm{s},a)+\sum_{\bm{s}'\in\mathcal{S}}\Pr(\bm{s}'|\bm{s},a)V(\bm{s}'),
\end{equation}
for all $\bm{s}\in\mathcal{S}$ and $a\in\mathcal{A}$. Note that
$Q(\bm{s},a)$ is related to the RHS of the Bellman equation in (\ref{eq:Bellman}).
The optimal policy can also be expressed in terms of $Q(\bm{s},a)$,
i.e.,
\begin{equation}
\pi^{*}(\bm{s})=\arg\min_{a\in\{0,1\}}Q(\bm{s},a),\quad\forall\bm{s}\in\mathcal{S}.\label{eq:optimal-policy-Q}
\end{equation}
\subsection{Structural Analysis and Optimal Policy}
Before we present the main theorem, we first show the key properties
of the value function $V(\Delta,\delta)$ in the following lemmas.
\begin{lem}
\label{lem:value function monotony wrt AOCI}The value function $V(\Delta,\delta)$
is non-decreasing with $\Delta$ for any $\delta$.
\end{lem}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof v-function AoCI}.
\end{IEEEproof}
\begin{lem}
\label{lem:slope wrt aoci}Given $\delta$, we have $V(\Delta_{2},\delta)-V(\Delta_{1},\delta)\geq\Delta_{2}-\Delta_{1}$
for any $\Delta_{2}\geq\Delta_{1}$.
\end{lem}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-slope wrt aoci}.
\end{IEEEproof}
\begin{lem}
\label{lem:slope wrt aoi}For any $\Delta$ and $\delta_{1}\leq\delta_{2}$,
if $p_{r}(\delta_{1})-p_{r}(\delta_{2})\leq\frac{\delta_{2}-\delta_{1}}{\mathop{V_{k}(\Delta+1,1)}-V_{k}(1,1)}$
for any $k\in\mathbb{Z}_{\geq0}$, we have $V(\Delta,\delta_{1})-V(\Delta,\delta_{2})\leq\delta_{2}-\delta_{1}$,
where $V_{k}(\cdot)$ is the value function obtained in the value
iteration algorithm.
\end{lem}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-slope wrt aoi}.
\end{IEEEproof}
Then, we present the structure of the optimal updating policy in the
following theorem.
\begin{thm}
\label{thm:threshold-structure-general}Given $\bm{s}=(\Delta,\delta)$,
if $p_{r}(1)-p_{r}(\delta+1)\leq\frac{\delta}{\mathop{V_{k}(\Delta+1,1)}-V_{k}(1,1)}$
for any $\Delta$ and $k\in\mathbb{Z}_{\geq0}$, the optimal updating
policy has a special structure for any $\delta$, that is, if $\Delta\geq\underline{\Delta}(\delta)$,
then $\pi^{*}(\bm{s})=1$, where $\underline{\Delta}(\delta)$ is
the minimum integer value satisfying $p_{s}(1-p_{r}(\delta))\Delta-p_{s}\delta-\omega C_{u}\geq0$.
\end{thm}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-threshold-structure}.
\end{IEEEproof}
It is noteworthy that the special structure in Theorem 1 is different
from the threshold structure defined in available studies \cite{zhouJointStatusSampling2019,maatoukAgeIncorrectInformation2020},
where the optimal policy is to update when $\Delta$ is no less than
the threshold and the optimal policy is to keep idle otherwise.
We then propose a low-complexity relative policy iteration algorithm
to compute the optimal policy based on the special structure of the
optimal updating policy presented in Theorem \ref{thm:threshold-structure-general}.
Although the exact value of the threshold is not available in the
general case, we can still reduce the computational complexity for
obtaining the optimal policy by exploiting the special structure.
This is because the threshold structure only relies on the properties
of the value function. Particularly, if $p_{r}(1)-p_{r}(\delta+1)\leq\frac{\delta}{\mathop{V_{k}(\hat{\Delta},1)}-V_{k}(1,1)}$
and $p_{s}(1-p_{r}(\delta))\Delta-p_{s}\delta-\omega C_{u}\geq0$
hold,\footnote{According to Lemma 1, $V_{k}(\hat{\Delta},1)\geq V_{k}(\Delta,1)$
for $1\leq\Delta<\hat{\Delta}$. Therefore, if $p_{r}(1)-p_{r}(\delta+1)\leq\frac{\delta}{\mathop{V_{k}(\hat{\Delta},1)}-V_{k}(1,1)}$,
then $p_{r}(1)-p_{r}(\delta+1)\leq\frac{\delta}{\mathop{V_{k}(\Delta+1,1)}-V_{k}(1,1)}$
for any $\Delta$.} then it is optimal to update for the state $(\Delta,\delta)$. Therefore,
we can determine the optimal action immediately (Lines 6-7 in Algorithm
1). Otherwise, we have to perform the minimization to find the optimal
action (Lines 8-9 in Algorithm 1). Since Algorithm 1 is a monotone
policy iteration algorithm, the policy $\pi_{k}(\bm{s})$ and value
function $V_{k}(\bm{s})$ will finally converge when $k$ increases.
The details of the proposed relative policy iteration algorithm is
summarized in Algorithm 1. By taking the advantage of the special
structure of the optimal policy, the complexity of the policy improvement
step in the relative policy iteration algorithm can be reduced. Since
the upper limits of the AoCI and the AoI are $\hat{\Delta}$ and $\hat{\delta}$,
respectively, the cardinality of the state space is $\left|\hat{\Delta}\right|\times\left|\hat{\delta}\right|$.
According to \cite{littmanComplexitySolvingMarkov1995}, the computational
complexity saving for each iteration in the structure-aware policy
iteration algorithm is $O\left(\left(\left|\hat{\Delta}\right|\times\left|\hat{\delta}\right|\right)^{2}\right)$.
\begin{algorithm}[tb]
\caption{Relative Policy Iteration based on the Threshold Structure}
\begin{algorithmic}[1]
\STATE Initialization: Set $k=0$ and $\pi_{0}(\bm{s})=0$ for all
state $\bm{s}=(\Delta,\delta)\in S$, select a reference state $\bm{s}^{\dagger}$
and set $V_{0}(\bm{s}^{\dagger})=0$.
\REPEAT
\STATE $\pi_{k+1}(\bm{s})\leftarrow0$.
\medskip{}
Policy Evaluation:
\STATE Given policy $\pi_{k}(\bm{s})$, compute the value of $\theta_{k}$
and $V_{k}(\bm{s})$ by solving the following $|S|$ linear equations:
$\begin{cases}
\theta_{k}+V_{k}(\bm{s})=C(\bm{s},\pi_{k}(\bm{s}))+\\
\qquad\sum\limits _{\bm{s}'\in\mathcal{S}}\Pr(\bm{s}'|\bm{s},\pi_{k}(\bm{s}))V_{k}(\bm{s}'),\\
V_{k}(\bm{s}^{\dagger})=0.
\end{cases}$
\medskip{}
Policy Improvement:
\FOR{$\bm{s}=(\Delta,\delta)\in S$}
\IF{$p_{r}(1)-p_{r}(\delta+1)\leq\frac{\delta}{\mathop{V_{k}(\hat{\Delta},1)}-V_{k}(1,1)}$
and $p_{s}(1-p_{r}(\delta))\Delta-p_{s}\delta-\omega C_{u}\geq0$}
\STATE $\pi_{k+1}(\bm{s})\leftarrow1$.
\ELSE
\STATE $\pi_{k+1}(\bm{s})\leftarrow\arg\min\limits _{a\in\mathcal{A}}\{C(\bm{s},a)+\sum\limits _{\bm{s}'\in\mathcal{S}}\Pr(\bm{s}'|\bm{s},a)V_{a}(\bm{s}')\}$.
\ENDIF
\ENDFOR
\STATE $k\leftarrow k+1$.
\UNTIL{$\pi_{k+1}(\bm{s})=\pi_{k}(\bm{s})$ for all $\bm{s}\in\mathcal{S}$.}
\STATE $\pi^{*}\leftarrow\pi_{k+1}$.
\RETURN the optimal policy $\pi^{*}$.
\end{algorithmic}
\end{algorithm}
\section{Special Case Study\label{sec:Special-Case-Study}}
In this section, we study two special cases, where the return probability
of the physical process satisfies certain conditions.
\subsection{Case 1}
We first consider a special case where the return probability $p_{r}(\delta)$
is irrespective of $\delta$, i.e., $p_{r}(\delta_{1})=p_{r}(\delta_{2})\neq0$
for any $\delta_{1}\neq\delta_{2}$. It is easy to see that the condition
in Theorem \ref{thm:threshold-structure-general} is satisfied in
this special case and the optimal updating policy has a threshold
structure with respect to the AoCI.
One example for this special case is that the state of the underlying
physical process transits with equiprobability. The one-step state
transition probability matrix for $M$-state discrete time Markov
chain is given by
\begin{equation}
\Pr(X_{t+1}|X_{t})=\left[\begin{array}{cccc}
p_{c} & p_{c} & \ldots & p_{c}\\
p_{c} & p_{c} & \ldots & p_{c}\\
\vdots & \vdots & \ddots & \vdots\\
p_{c} & p_{c} & \ldots & p_{c}
\end{array}\right],\label{eq:transition-matrix-2}
\end{equation}
where $p_{c}=\frac{1}{M}$. Since the $\delta$-step state transition
probability matrix $\Pr(X_{t+\delta}|X_{t})$ is the same with $\Pr(X_{t+1}|X_{t})$
for all $\delta$, we have $p_{r}(\delta)=1/M$.
In this case, we can simplify the MDP formulated in Section \ref{sec:Updating-Policy-Design}.A.
In particular, the state at slot $t$ is only the AoCI, i.e., $s_{t}=\Delta_{t}$,
and the state transition probability in (\ref{eq:state-transition})
can be simplified as
\begin{equation}
\begin{cases}
\Pr(s_{t+1}=\min\{\Delta+1,\hat{\Delta}\}|s_{t}=\Delta,a_{t}=0)=1,\\
\Pr(s_{t+1}=\min\{\Delta+1,\hat{\Delta}\}|s_{t}=\Delta,a_{t}=1)=p_{f}+p_{s}p_{r},\\
\Pr(s_{t+1}=1|s_{t}=\Delta,a_{t}=1)=p_{s}(1-p_{r}),
\end{cases}
\end{equation}
and $\Pr(s_{t+1}|s_{t},a_{t})=0$ otherwise.
Based on the simplified state and transition probability, we present
the monotonicity property of $V(s)$ in the following lemma.
\begin{lem}
\label{lem:lemma2}The value function $V(s)$ is non-decreasing with
$s$.
\end{lem}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-Lemma 2}.
\end{IEEEproof}
Next, in the following theorem, we give results on the structure of
the optimal updating policy.
\begin{thm}
\label{thm:threshold type}The optimal policy has a threshold structure,
that is, if $\pi^{*}(s_{1})=1$, then $\pi^{*}(s_{2})=1$ for all
$s_{2}\geq s_{1}$.
\end{thm}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-Theorem-1}.\emph{}
\end{IEEEproof}
According to Theorem \ref{thm:threshold type}, the optimal policy
can be represented as a threshold policy, which is given by
\begin{equation}
\pi^{*}(s)=\begin{cases}
1, & \text{if }s\ge\Omega,\\
0, & \text{otherwise},
\end{cases}\label{eq:Threshold}
\end{equation}
where $\Omega$ is the threshold at which the switching occurs. Under
the threshold policy, we proceed with analyzing the total average
cost of any threshold $\Omega$ in the asymptotic regime.
\begin{lem}
\label{lem:total average cost}Let $p_{z}\triangleq p_{f}+p_{s}p_{r}$.
When $\hat{\Delta}$ goes to infinity, for any given threshold $\Omega$,
the total average cost $J(\Omega)$ of the threshold policy approaches
to $J(\Omega)=J_{1}(\Omega)+J_{2}(\Omega)$, where
\begin{align}
J_{1}(\Omega)= & \frac{1-p_{z}}{\Omega(1-p_{z})+p_{z}}\left(\frac{\Omega(\Omega-1)}{2}+\frac{\Omega}{1-p_{z}}+\frac{p_{z}}{(1-p_{z})^{2}}\right),
\end{align}
and
\begin{equation}
J_{2}(\Omega)=\frac{\omega C_{u}}{\Omega(1-p_{z})+p_{z}}.
\end{equation}
\end{lem}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-expected value of average cost}.
\end{IEEEproof}
By leveraging the above results, we can proceed to find the optimal
threshold value $\Omega^{*}$.
\begin{thm}
\label{thm:closed-form} The asymptotically optimal threshold $\Omega^{*}$
of the optimal updating policy is given by
\begin{equation}
\Omega^{*}=\arg\min(J(\left\lfloor \Omega'\right\rfloor ),J(\left\lceil \Omega'\right\rceil )),\label{eq:optimalThreshold}
\end{equation}
where $\Omega'=\frac{\sqrt{p_{z}+2\omega C_{u}(1-p_{z})}-p_{z}}{1-p_{z}}.$
\end{thm}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-closed-form}.
\end{IEEEproof}
\begin{cor}
\label{cor:optimal-threshold}The asymptotically optimal threshold
$\Omega^{*}$ is non-decreasing with the update cost $C_{u}$, but
is non-increasing with transmission success probability $p_{s}$ and
the number of states of the physical process $M$.
\end{cor}
\begin{IEEEproof}
See Appendix \ref{subsec:Proof-of-Corollary1}.
\end{IEEEproof}
Fig. \ref{fig:Optimal threshold} illustrates the asymptotically optimal
threshold $\Omega^{*}$ of the optimal updating policy with respect
to $p_{s}$ under different $C_{u}$. The asymptotically optimal threshold
is shown to be non-increasing with $p_{s}$. This is because, before
the destination successfully receives an update packet, the sensor
has to sample and transmit more times when $p_{s}$ is small. Hence,
updating the status is productive only when the AoCI is large. We
can also observe that the asymptotically optimal threshold is non-decreasing
with $C_{u}$. This indicates that the sensor will remain idle until
the AoCI is large, if the update cost is high. Hence, the optimal
policy is able to achieve a balance between the AoCI and the update
cost.
\begin{figure}[tp]
\centering
\includegraphics[width=0.5\textwidth]{figure/OmegaStarWRTpsM2pc12w1}\caption{\label{fig:Optimal threshold}The asymptotically optimal threshold
$\Omega^{*}$ versus $p_{s}$ ($M=2$, $p_{c}=0.5$, and $\omega=1$).}
\end{figure}
Fig. \ref{fig:Optimal threshold withMps=00003D1} shows the asymptotically
optimal threshold $\Omega^{*}$ of the optimal updating policy with
respect to $M$ under different $C_{u}$. We can observe that the
asymptotically optimal threshold is non-increasing with $M$. This
is due to the fact that the return probability $p_{r}$ is large,
when $M$ is small. In other words, the received status update is
more likely to contain the same content with the previous one. Hence,
it is more cost-efficient to have a larger threshold at a smaller
$M$. We note that the reason why $\Omega^{*}$ becomes constant when
$M$ becomes large is due to the fact that $\Omega'$ converges as
$M$ grows and so do $\left\lfloor \Omega'\right\rfloor $ and $\left\lceil \Omega'\right\rceil $.
\begin{figure}[tp]
\centering
\includegraphics[width=0.5\textwidth]{figure/OmegaStarWRTMps1pc1Mw1}\caption{\label{fig:Optimal threshold withMps=00003D1}The asymptotically optimal
threshold $\Omega^{*}$ versus $M$ ($p_{c}=1/M$, $p_{s}=1$, and
$\omega=1$).}
\end{figure}
\subsection{Case 2 }
In this case, we consider that $p_{r}(1)=0$ and $p_{r}(\delta)\geq0$
for $\delta>1$. It is also easy to see that the condition in Theorem
\ref{thm:threshold-structure-general} is satisfied in this special
case and the optimal updating policy has a special structure with
respect to the AoCI as given in Theorem \ref{thm:threshold-structure-general}.
The optimal updating policy can also be obtained via Algorithm 1.
The example for this case is the physical process modeled by periodic
Markov chain. For instance, the Markov model could be a $M$-state
one-dimensional random walk with the state transition probability
matrix given by
\begin{equation}
\Pr(X_{t+1}|X_{t})=\left[\begin{array}{cccccc}
0 & p_{c} & 0 & \ldots & 0 & 1-p_{c}\\
1-p_{c} & 0 & p_{c} & \ldots & 0 & 0\\
\vdots & \vdots & \vdots & \ddots & & \vdots\\
p_{c} & 0 & 0 & \ldots & 1-p_{c} & 0
\end{array}\right],\label{eq:transition-matrix-3}
\end{equation}
where $p_{c}\in(0,1)$ and $M$ is even. Every state of this Markov
chain is periodic with period 2. Hence, the return probability $p_{r}(\delta)$
is $0$ when $\delta$ is odd, and is positive when $\delta$ is even.
In Figs. \ref{fig:Structure of optimal policy-1} and \ref{fig:Structure of optimal policy pc(1/M,1/M-1)},
we illustrate the analytical results of Theorem \ref{thm:threshold-structure-general}
when Markov model of the physical process is a one-dimensional random
walk with 4-state and 6-state, respectively. The period of both Markov
chain is 2. In both figures, the optimal updating policy is shown
to have a special structure with respect to the AoCI for any $\delta$.
In fact, the structure of the optimal policy unveils a tradeoff between
the AoCI and the update cost. Particularly, if the AoCI is small,
it is not efficient for the sensor to send the status update to the
destination due to the update cost. It can also be seen that the optimal
action $\pi^{*}=0$ does not appear in the whole state space of the
AoCI if the AoI is high. This is due to the fact that the AoCI is
always no less than the AoI and it is more efficient to generate a
new status update due to the outdated information at the destination
with the high AoI.
\begin{figure}[tp]
\centering
\includegraphics[width=0.5\textwidth]{figure/K=4p=0_5ps=0_8w=1Cu=12}\caption{\label{fig:Structure of optimal policy-1}Structure of the optimal
policy for different values of $\delta$ for one-dimensional random
walk ($M=4$, $p_{c}=0.5$, $p_{s}=0.8$, $C_{u}=12$, and $\omega=1$).}
\end{figure}
\begin{figure}[tp]
\centering
\includegraphics[width=0.5\textwidth]{figure/K=6p=0_5ps=0_8w=1Cu=12}\caption{\label{fig:Structure of optimal policy pc(1/M,1/M-1)}Structure of
the optimal policy for different values of $\delta$ for one-dimensional
random walk ($M=6$, $p_{c}=0.5$, $p_{s}=0.8$, $C_{u}=12$, and
$\omega=1$).}
\end{figure}
\section{Simulation Results \label{sec:Simulation-Results}}
In this section, the simulation results of the optimal updating policy
are presented to examine the effects of system parameters. The performance
of the optimal updating policy is also compared with that of two baseline
policies, i.e., zero-wait policy and sample-at-change policy. In zero-wait
policy, the sensor samples and transmits the status update at each
time slot. While in sample-at-change policy, a new update is generated
only when the state changes relative to the previous received update
at the destination. Note that the sample-at-change policy is genie-aided
and can achieve the minimum AoCI.
\subsection{Performance Evaluation in the Special Case 1}
\begin{figure}[tb]
\centering\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentPsAboutRewardW=1Cu=12M=2pc=05}}
\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentPsAboutAoCIandCostW=1Cu=12M=2pc=05}}
\caption{\label{fig:Comparision-ps}Comparison between the optimal policy,
sample-at-change policy, and zero-wait policy ($M=2$, $p_{c}=0.5$,
$C_{u}=12$ and $\omega=1$). (a) The total average cost versus $p_{s}$.
(b) The average AoCI and the average update cost versus $p_{s}$.}
\end{figure}
In Fig. \ref{fig:Comparision-ps}, we compare the total average cost
of the optimal policy and two baseline policies with respect to $p_{s}$.
It can be observed in Fig. \ref{fig:Comparision-ps}\,(a) that the
optimal policy outperforms the zero-wait policy. Moreover, as $p_{s}$
increases, there is a larger reduction in the total average cost.
The reason can be explained with the aid of Fig. \ref{fig:Comparision-ps}\,(b).
Although the zero-wait policy gains a smaller AoCI, it bears a constant
update cost. In contrast, the optimal policy can trade off the AoCI
for the update cost. Particular, in the optimal policy, the sensor
remains idle until the AoCI is larger than a threshold, thereby inducing
a large AoCI. However, the optimal policy has a smaller update cost
than the zero-wait policy. We also observe that the sample-at-change
policy outperforms the optimal policy at first. As $p_{s}$ increases,
the optimal policy beats the sample-at-change policy, because the
update cost of the optimal policy declines as $p_{s}$ increases.
Hence, the optimal policy is more cost-efficient.
\begin{figure}[tb]
\centering\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentMAboutRewardW=1ps=1Cu=12pc=1M}}
\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentMAboutAoCIandCostW=1ps=1Cu=12pc=1M}}
\caption{\label{fig:Comparision bewteen op and zwp different M pc=00003D1/M-1}Comparison
between the optimal policy, sample-at-change policy, and zero-wait
policy ($p_{c}=1/M$, $p_{s}=1$, $C_{u}=12$ and $\omega=1$). (a)
The total average cost versus $M$. (b) The average AoCI and average
update cost versus $M$.}
\end{figure}
In Fig. \ref{fig:Comparision bewteen op and zwp different M pc=00003D1/M-1},
we compare the total average cost of the optimal policy and two baseline
policies with respect to $M$, where $p_{c}$ is set to be $1/M$.
We can see in Fig. \ref{fig:Comparision bewteen op and zwp different M pc=00003D1/M-1}\,(a)
that the optimal policy outperforms both baseline policies. Moreover,
for both the optimal policy and the zero-wait policy, when $M$ grows,
the total average cost decreases. As shown in Fig. \ref{fig:Comparision bewteen op and zwp different M pc=00003D1/M-1}\,(b),
the average AoCI of the optimal policy is larger than that of the
zero-wait policy, whereas the average update cost of the optimal policy
is smaller than that of the zero-wait policy. The average AoCI decreases
with the increasing of $M$ because the received status update is
more likely to have a new content with a large $M$. The average update
cost is affected by $M$ and the optimal threshold simultaneously.
The increase of the average update cost when $M=4$ is due to the
decrease of the optimal threshold as shown in Fig. \ref{fig:Optimal threshold withMps=00003D1}.
When the optimal threshold is fixed, the average update cost decreases
as $M$ increases. We also observe that the total average cost of
the sample-at-change policy increases with $M$. This is because the
return probability decreases with $M$ and the sample-at-change policy
approaches the zero-wait policy as $M$ increases.
\subsection{Performance Evaluation in the Special Case 2}
\begin{figure}[tb]
\centering\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentPsAboutRewardW=1Cu=12M=4p=02}}
\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentPsAboutAoCIandCostW=1Cu=12M=4p=02}}
\caption{\label{fig:Comparision-ps-2}Comparison between the optimal policy,
sample-at-change policy, and zero-wait policy ($M=4$, $p_{c}=0.2$,
$C_{u}=12$ and $\omega=1$). (a) The total average cost versus $p_{s}$.
(b) The average AoCI and the average update cost versus $p_{s}$.}
\end{figure}
In Fig. \ref{fig:Comparision-ps-2}, we compare the total average
cost of the optimal policy and two baseline policies with respect
to $p_{s}$. It can be observed that the optimal policy outperforms
both two baseline policies. As $p_{s}$ increases, both the AoCI and
the update cost of the optimal policy decline. This is because the
AoCI can be reset with fewer transmission when $p_{s}$ is large.
The AoCI of both baseline policy decreases with the increase of $p_{s}$.
However, the update cost of the zero-wait policy remains constant
and the update cost of the sample-at-change policy increases with
$p_{s}$. In particular, the sample-at-change policy degenerates to
zero-wait policy when $p_{s}=1$. As a result, the performance gain
of the optimal policy is larger when $p_{s}$ is larger.
\begin{figure}[tb]
\centering\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentWAboutRewardPs=05Cu=12M=4p=02}}
\subfloat[]{\centering
\includegraphics[width=0.5\textwidth]{figure/DifferentWAboutAoCIandCostPs=05Cu=12M=4p=02}}
\caption{\label{fig:Comparision bewteen op and zwp different w}Comparison
between the optimal policy, sample-at-change policy, and zero-wait
policy ($M=4$, $p_{c}=0.2$, $p_{s}=0.5$ and $C_{u}=12$ ). (a)
The total average cost versus $\omega$. (b) The average AoCI and
average update cost versus $\omega$.}
\end{figure}
In Fig. \ref{fig:Comparision bewteen op and zwp different w}, we
compare the total average cost of the optimal policy and two baseline
policies with respect to $\omega$. From Fig. \ref{fig:Comparision bewteen op and zwp different w}\,(a),
we can observe that the total average cost of three policies increase
with the weighting factor $\omega$. The three policies are coincident
when $\omega=0$, which implies that the sensor under the optimal
policy would sample and transmit in each time slot. As $\omega$ increases,
the total average cost of the zero-wait policy and the sample-at-change
policy grow linearly. This is because these two baseline policies
cannot adapt to the weighting factor and its average AoCI and average
update cost are constant, as shown in Fig. \ref{fig:Comparision bewteen op and zwp different w}\,(b).
On the contrary, the optimal policy is able to adjust according to
$\omega$. When $\omega$ grows larger, the AoCI is traded off to
obtain a smaller update cost. Therefore, the optimal policy can strike
a balance between the AoCI and the update cost.
\section{Conclusion\label{sec:Conclusion}}
In this paper, by identifying the ignorance of information content
variation in the conventional AoI, we have proposed the AoCI as an
age-based utility to quantify information freshness. The AoCI not
only measures the freshness by the passage of time but also captures
the information content of the updates at the destination. We have
further investigated the updating policy in the status update system
by taking into account both the AoCI and the update cost, and formulated
the status updating problem as an infinite horizon average cost MDP.
We have analyze the properties of the value function without specifying
the state transition model of the physical process. Based on these
properties, we have proved that the optimal updating policy has a
special structure with respect to the AoCI and identify the condition
on the return probability of the physical process under which the
special structure exists. Equipped with this, we have provided a structure-aware
relative policy iteration algorithm to obtain the optimal updating
policy with low complexity. We have also studied two special cases
where the condition holds. In the special case where the state of
the underlying physical process transits with equiprobability, we
have proved that the optimal policy is of threshold type and derived
the closed-form of the optimal threshold. We have also proved that
the optimal threshold is non-increasing with respect to transmission
success probability and the number of states of the physical process,
respectively, but is non-decreasing with respect to the update cost.
Results from the simulation have shown the impacts of the unreliable
channel and the physical process on the total average cost. By comparing
the optimal updating policy with the zero-wait policy and the sample-at-change
policy, it is shown that the optimal updating policy achieves a balance
between the AoCI and the update cost and yields a substantial performance
boost in terms of the total average cost compared to zero-wait policy.
| {
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\section{Introduction}
\label{sec:intro}
The forthcoming experimental perspectives for in-medium heavy-light quark meson spectroscopy, in particular at FAIR, are accompanied by the need for sophisticated theoretical analyses, e.\,g.\ \cite{tolos09,blaschke,yasuisudoh13a,he,hilger09,wang11}. When utilizing QCD sum rules \cite{svz79,rry,narison}, this requires a thorough discussion of heavy-quark condensates in general, and, in particular, in the nuclear medium \cite{suzukigubler13}. Therefore, the heavy-quark expansion (HQE), originally developed for the heavy two-quark condensate \(\langle \bar{Q}Q \rangle\) in vacuum, is extended to four-quark condensates and to the in-medium case, thus going beyond previous approaches, e.\,g.\ \cite{narison13}. Specific formulas are derived and presented.
\section{Recollection: HQE in vacuum}
\label{sec:HQE_vac}
In \cite{genbroad}, a general method is introduced for vacuum condensates involving heavy quarks \(Q\) with mass \(m_Q\). The heavy-quark condensate is considered as the one-point function
\begin{align}
\langle 0 | \bar{Q}Q | 0 \rangle = -i \int \frac{d^4p}{(2\pi)^4} \langle 0 | \text{Tr}_\text{c,D}\; S_{\!\! Q}(p) | 0 \rangle
\label{eq:formula_HQEofQQ}
\end{align}
expressed by the heavy-quark propagator \(S_{\!\! Q}\) in a weak classical gluonic background field in Fock-Schwinger gauge, \(S_{\!\! Q}(p) = \sum_{k=0}^\infty S^{(k)}_{\!\! Q} (p)\) with \(S^{(k)}_{\!\! Q} (p) = (-1)^k S_{\!\! Q}^{(0)}(p) \gamma^{\mu_1}\tilde{A}_{\mu_1} S_{\!\! Q}^{(0)}(p) \ldots \gamma^{\mu_k}\tilde{A}_{\mu_k} S_{\!\! Q}^{(0)}(p)\), incorporating the free heavy-quark propagator \(S_{\!\! Q}^{(0)}(p) = (\gamma^\mu p_\mu + m_Q)/(p^2 - m_Q^2)\) and the derivative operator \(\tilde{A}\) emerging from a Fourier transform defined as \(\tilde{A}_\mu = \sum_{m=0}^\infty \tilde{A}_\mu^{(m)}\) with \(\tilde{A}_\mu^{(m)} = -\frac{(-i)^{m+1} g}{m!(m+2)} \left( D_{\alpha_1} \ldots D_{\alpha_m} G_{\mu\nu}(x) \right)_{x=0} \partial^\nu \partial^{\alpha_1} \ldots \partial^{\alpha_m}\) \cite{hilger11,zsch11}. In this way, the heavy-quark propagator interacts with the complex QCD ground state via soft gluons generating a series expansion in the inverse heavy-quark mass. The compact notation \eqref{eq:formula_HQEofQQ} differs from \cite{genbroad}, but provides a comprehensive scheme easily extendable to in-medium condensates. The first HQE terms of the heavy two-quark condensate \eqref{eq:formula_HQEofQQ} reproduce \cite{genbroad}:
\begin{align}
\langle 0 | \bar{Q}Q | 0 \rangle & = - \frac{g^2}{48\pi^2 m_Q} \langle G^2 \rangle - \frac{g^3}{1440\pi^2 m_Q^3} \langle G^3 \rangle - \frac{g^4}{120\pi^2 m_Q^3} \langle (DG)^2 \rangle + \ldots
\label{eq:HQEofQQ}\\
& = \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQ_GG}}} \!\!\!\!\!
+ \; \left( \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQ_GGG}}} \!\!\!\!\!
+ \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQ_GGGnonloc}}} \!\!\!\!\! \right) \;
+ \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQ_4q}}}\!\!\!\!\! + \; \ldots \nonumber
\end{align}
with the notation
\begin{align}
\langle G^2 \rangle & = \langle 0 | G^A_{\mu\nu} G^{A\,\mu\nu} | 0 \rangle \, , \\[1ex]
\langle G^3 \rangle & = \langle 0 | f^{ABC} G^A_{\mu\nu} {G^{B\,\nu}}_\lambda G^{C\,\lambda\mu} | 0 \rangle \, , \\
\langle (DG)^2 \rangle & = \langle 0 | \bigg( \sum_{f} \bar{q}_{f} \gamma_\mu t^A q_{f} \bigg)^2 | 0 \rangle \, .
\end{align}
The graphic interpretation of the terms in \eqref{eq:HQEofQQ} is depicted too: the solid lines denote the free heavy-quark propagators and the curly lines are for soft gluons whose condensation is symbolized by the crosses, whereas the heavy quark-condensate is symbolized by the crossed circles \cite{bagan86}. An analogous expression for the mixed heavy-quark gluon condensate can be obtained along those lines which contains, however, a term proportional to \(m_Q\). The leading-order term in \eqref{eq:HQEofQQ} was employed already in \cite{svz79} in evaluating the sum rule for charmonia.
The vacuum HQE method was rendered free of UV divergent results for higher mass-dimension heavy-quark condensates by requiring at least one condensing gluon per condensed heavy-quark \cite{bagan85,bagan86}, which prevents unphysical results, where the condensation probability of heavy-quark condensates rises for an increasing heavy-quark mass.
\section{Application of HQE to in-medium heavy-light four-quark condensates}
\label{sec:HQE_qqQQ}
The above method can be extended to in-medium situations. Our approach contains two new aspects: (\(i\)) formulas analogous to equation~\eqref{eq:formula_HQEofQQ} are to be derived for heavy-quark condensates, e.\,g.\ \(\langle \bar{Q} \slashed{v} Q \rangle\), \(\langle \bar{Q} \slashed{v} \sigma G Q \rangle\), \(\langle \bar{q} \slashed{v} t^A q \bar{Q} \slashed{v} t^A Q \rangle\), which additionally contribute to the in-medium operator product expansion (OPE) and (\(ii\)) medium-specific gluonic condensates, e.\,g.\ \(\langle G^2/4 - (vG)^2/v^2 \rangle\), \(\langle G^3/4 - f^{ABC} G^A_{\mu\nu} {G^{B\,\nu}}_\lambda G^{C\,\lambda\kappa} v^\mu v_\kappa / v^2 \rangle\), enter the HQE of heavy-quark condensates for both, vacuum and additional medium condensates, where \(\langle \ldots \rangle\) denotes Gibbs averaging.
We are especially interested in heavy-light four-quark condensates entering the OPE of \(D\) and \(B\) mesons, inter alia, in terms corresponding to the next-to-leading-order perturbative diagrams with one light-quark (\(q\)) and one heavy-quark (\(Q\)) line cut. There are 24 two-flavour four-quark condensates in the nuclear medium \cite{thomas07} represented here in a compact notation by \(\langle \bar{q} \Gamma T^A q \bar{Q} \Gamma' T^A Q \rangle\), where \(\Gamma\) and \(\Gamma'\) denote Dirac structures and \(T^A\) with \(A=0,\ldots,8\) are the generators of \(S\! U(3)\) supplemented by the unit element (\(A=0\)). We obtain the analogous formula to \eqref{eq:formula_HQEofQQ} for heavy-light four-quark condensates:
\begin{align}
\langle \bar{q} \Gamma T^A q \bar{Q} \Gamma' T^A Q \rangle = -i \int \frac{d^4p}{(2\pi)^4} \langle \bar{q} \Gamma T^A q \; \text{Tr}_\text{c,D} \left[\Gamma' T^A S_{\!\! Q}(p) \right] \rangle \, .
\end{align}
The leading-order terms of this HQE are obtained for the heavy-quark propagators \(S_{\!\! Q}^{(1)}\) containing \(\tilde{A}_\mu^{(1)}\) and \(S_{\!\! Q}^{(2)}\) with leading-order background fields \(\tilde{A}_\mu^{(0)}\):
\begin{align}
\langle \bar{q} \Gamma T^A q \bar{Q} \Gamma' T^A Q \rangle & = -i \int \frac{d^4p}{(2\pi)^4} \langle \bar{q} \Gamma T^A q \; \text{Tr}_\text{c,D} \left[\Gamma' T^A \left( S_{\!\! Q}^{(1)}(p) + S_{\!\! Q}^{(2)}(p) + \ldots \right) \right] \rangle
\label{eq:expan_HQEofQQqq}\\[2ex]
& = \langle \bar{q} \Gamma T^A q \bar{Q} \Gamma' T^A Q \rangle^{(0)} + \langle \bar{q} \Gamma T^A q \bar{Q} \Gamma' T^A Q \rangle^{(1)} + \ldots
\label{eq:firstterms_HQEofQQqq}\\
& = \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQqq_4q}}} \!\!\!\!\!
+ \!\!\!\!\! \parbox[c][15mm][c]{20mm}{\mbox{\includegraphics[width=2cm]{HQEofQQqq_GGqq}}}\!\!\!\!\! + \; \ldots \, . \nonumber
\end{align}
Evaluation of the first term of the expansion \eqref{eq:firstterms_HQEofQQqq} for the complete list of two-flavour four-quark condensates in \cite{thomas07} gives three non-zero results:
\begin{align}
\langle \bar{q} \gamma^\nu t^A q \bar{Q} \gamma_\nu t^A Q \rangle^{(0)} & = -\frac{2}{3}\frac{g^2}{(4\pi)^2}\left( \log\frac{\mu^2}{m_Q^2} + \frac{1}{2} \right) \langle \bar{q} \gamma^\nu t^A q \sum_f \bar{q}_f \gamma_\nu t^A q_f \rangle \, , \\
\langle \bar{q} \slashed{v} t^A q \bar{Q} \slashed{v} t^A Q \rangle^{(0)} & = -\frac{2}{3}\frac{g^2}{(4\pi)^2}\left( \log\frac{\mu^2}{m_Q^2} + \frac{2}{3} \right) \langle \bar{q} \slashed{v} t^A q \sum_f \bar{q}_f \slashed{v} t^A q_f \rangle \, , \\
\langle \bar{q} t^A q \bar{Q} \slashed{v} t^A Q \rangle^{(0)} & = -\frac{4}{3}\frac{g^2}{(4\pi)^2}\left( \log\frac{\mu^2}{m_Q^2} - \frac{1}{8} \right) \langle \bar{q} t^A q \sum_f \bar{q}_f \slashed{v} t^A q_f \rangle \, ,
\end{align}
where logarithmic singularities are calculated in the \(\overline{\text{MS}}\) scheme, \(\mu\) is the renormalization scale, and \(t^A= T^A\) for \(A = 1,\ldots,8\). The non-zero contributions for the second term of \eqref{eq:firstterms_HQEofQQqq} read
\begin{align}
\langle \bar{q}q \bar{Q}Q \rangle^{(1)} & = -\frac{1}{3}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle \bar{q}q G^A_{\mu\nu} G^{A\, \mu\nu} \rangle \, , \\
\langle \bar{q} t^A q \bar{Q} t^A Q \rangle^{(1)} & = -\frac{1}{6}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle d^{ABC} \bar{q} t^A q G^B_{\mu\nu} G^{C\, \mu\nu} \rangle \, , \\
\langle \bar{q} \gamma_5 q \bar{Q} \gamma_5 Q \rangle^{(1)} & = - \frac{1}{4}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle i \bar{q} \gamma_5 q G^A_{\mu\nu} G^{A}_{\alpha\beta} \varepsilon^{\mu\nu\alpha\beta} \rangle \, , \\
\langle \bar{q} \gamma_5 t^A q \bar{Q} \gamma_5 t^A Q \rangle^{(1)} & = - \frac{1}{8}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle i d^{ABC} \bar{q} \gamma_5 t^A q G^B_{\mu\nu} G^{C}_{\alpha\beta} \varepsilon^{\mu\nu\alpha\beta} \rangle \, , \\
\langle \bar{q} \slashed{v} q \bar{Q}Q \rangle^{(1)} & = -\frac{1}{3}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle \bar{q} \slashed{v} q G^A_{\mu\nu} G^{A\, \mu\nu} \rangle \, , \\
\langle \bar{q} \slashed{v} t^A q \bar{Q} t^A Q \rangle^{(1)} & = -\frac{1}{6}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle d^{ABC} \bar{q} \slashed{v} t^A q G^B_{\mu\nu} G^{C\, \mu\nu} \rangle \, , \\
\langle \bar{q} \sigma_{\mu\nu} t^A q \bar{Q} \sigma^{\mu\nu} t^A Q \rangle^{(1)} & = -\frac{5}{6}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle f^{ABC} \bar{q} \sigma_{\mu\nu} t^A q G^{B\,\nu}{}_\lambda G^{C\, \lambda\mu} \rangle \, , \\
\langle \bar{q} \sigma_{\mu\nu} t^A q \bar{Q} \sigma_{\alpha\beta} t^A Q g^{\mu\alpha} v^\nu v^\beta \rangle^{(1)} & = - \frac{5}{3}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle f^{ABC} \bar{q} \sigma_{\mu\nu} t^A q G^{B\,\nu}{}_\alpha G^{C\, \alpha\beta} v^\mu v_\beta \rangle \, , \\
\langle \bar{q} \gamma_5 \gamma_\lambda t^A q \bar{Q} \sigma_{\mu\nu} t^A Q \varepsilon^{\mu\nu\lambda\tau} v_\tau \rangle^{(1)} & = -\frac{5}{6}\frac{g^2}{(4\pi)^2} \frac{1}{m_Q} \langle f^{ABC} \bar{q} \gamma_5 \gamma_\lambda t^A q G^B_{\alpha\beta} G^{C\, \beta}{}_\gamma \varepsilon^{\gamma\alpha\lambda\tau} v_\tau \rangle \, ,
\end{align}
where \(f^{ABC}\) is the anti-symmetric structure constant of the color group and the corresponding symmetric object \(d^{ABC}\) is defined by the anti-commutator \(\{ t^A , t^B \} = \delta^{AB}/4 + d^{ABC} t^C\).
\section{Summary and Conclusions}
\label{sec:sum}
The extension of the OPE for QCD sum rules of \(\bar{q}Q\) and \(\bar{Q}q\) mesons by four-quark condensates to mass dimension 6 yields heavy-light condensate contributions requiring HQE in a nuclear medium. The necessary steps to generalize the vacuum HQE \cite{genbroad} to cover in-medium situations are described and a general formula for the HQE of in-medium heavy-light four-quark condensates is presented. The two leading-order terms of this expansion for the complete list of two-flavour four-quark condensates \cite{thomas07} have been evaluated. In leading-order the results contain known condensate structures, thus, reducing the number of condensates entering the sum rule evaluation of mesons composed of a heavy and a light quark. It can be seen that the series does not exhibit a simple expansion in \(1/m_Q\), not even in vacuum. Therefore, the lowest order terms are not suppressed by inverse powers of \(m_Q\) as for \(\langle \bar{Q}Q \rangle\), challenging the omission of heavy-light four-quark condensates, as often done in previous sum rule analyses.
\begin{acknowledgement}
This work is supported by BMBF 05P12CRGHE and the Austrian Science Fund (FWF) under project no. P25121-N27.
\end{acknowledgement}
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Anjar (Gujarat), March 18, 2017: Welspun India Ltd., one of the world's leading home textiles manufacturer, has forayed into new technologies in its Technical Textile Business with its state-of-the-art Needle Entangled Advance Textile Plant in Anjar. The plant was inaugurated by Minister of Textiles, Smriti Irani on March 18.
Further, Welspun has invested INR 100 crore to set up a fresh state- of- the-art fully automated cut and sew unit in the made-ups segment with a capacity of 10 mn units per annum.
The new initiatives are a testimony of Welspun's commitment in enhancing employment opportunities in the region,particularly for the women workforce.
Welspun India Ltd, part of USD 2.3 billion Welspun Group, is one of the world's largest home textile manufacturers. With a distribution network in more than 50 countries and world class manufacturing facilities in India, it is the largest exporter of home textile products from India. Supplier to 17 of Top 30 global retailers, the Company has marquee clients like Bed Bath & Beyond, Costco, Kohl's, Wal-Mart and Macy's to name a few. | {
"redpajama_set_name": "RedPajamaC4"
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{"url":"http:\/\/math.stackexchange.com\/questions\/232165\/residues-and-laurent-expansion\/232181","text":"Residues and Laurent expansion\n\nHow can I prove that the coefficient of $(z-z_0)^{-1}$ when $f(z)$ has a pole of order $m$ at $z=z_0$ is given by: $$a_{-1}=\\frac{1}{(m-1)!}\\frac{d^{m-1}}{dz^{m-1}}\\left[(z-z_0)^mf(z)\\right]_{z=z_0}$$ ?\n\n-\n\nLet $f(z)=\\sum\\limits_{n=-m}^{\\infty}a_n(z-z_0)^n$ be the Laurent expansion of $f$ at $z_0$. Then $g(z)=(z-z_0)^mf(z)$ is holomorphic around $z_0$ and its Taylor expansion at $z_0$ is $g(z)=\\sum\\limits_{n=0}^{\\infty}a_{n-m}(z-z_0)^n$. Therefore, $a_{-1}=\\frac{1}{(m-1)!}g^{(m-1)}(z_0)$, and the conclusion follows.\nYou mean $g(z)=(z-z_0)^m f(z)$ \u2013\u00a0 M. Strochyk Nov 7 '12 at 14:28\n@richard and putting $n-m=x$ we can find any $a_x$ using $$a_x=\\frac{1}{(m+x)!}g^{(m+x)(z_0)}$$. Is that correct? \u2013\u00a0 Ivan Lerner Nov 28 '12 at 14:11","date":"2015-04-26 08:41:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9656980037689209, \"perplexity\": 176.82786415979103}, \"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-2015-18\/segments\/1429246654114.44\/warc\/CC-MAIN-20150417045734-00312-ip-10-235-10-82.ec2.internal.warc.gz\"}"} | null | null |
Q: How to search a data from one range to another range in Realm database I am working in a Realm database. I am saving some data in the database. Say name,age,address,phone number.
I am using list view to view the data in the UI.
My question is if I am saving names which are not in order(not in alphabetical order) then how to sort them in order.
And one more question is after sorting the names I wanna view only few names in the list view(say if i type range as from C to H) C=represents the names starting with C likewise H.
Can anyone please help me in this.
A: To get data in sorted order, use like this
RealmResults<DataModel>resultsd =
realm.where(DataModel.class)
.findAllSorted("name");
For second questions, use like this
RealmResults<DataModel>resultsd =
realm.where(DataModel.class)
.contains("name","c").or().contains("name","h").findAll();
A: https://realm.io/docs/java/latest/api/io/realm/RealmQuery.html#lessThan-java.lang.String-java.util.Date-
You use: lessThan and greaterThan or between()
final RealmResults<Dog> puppies = realm.where(Dog.class).greaterThan("age", 2).lessThan("age", 10).findAll();
As far as I know ,this also works with Strings, so if greaterThan("name", "C") it will have names with C.
And for sorting, you can use Collections.sort() on the arraylist before adding to Realm, but sorting and then adding to the DB will have no effect. Cause the data that you get when querying for RealmResults, is based on the query you make.
For the query to sort, you can to:
RealmResults<Dog>results = realm.where(Dog.class).findAllSorted("name");
| {
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Home » Articles » Future Watch – Setting the stage for regeneration Over 52660 entries
Thursday, 30th November 2017
Future Watch – Setting the stage for regeneration
With cities' night time economy being seen as increasingly important in the future, Tim Foster, partner at Foster Wilson Architects, reflects on how theatre design projects that put placemaking at their core can catalyse regeneration.
Following the debate around placemaking in recent years it is apparent that the term means many different things to differ- ent people. Local community activists believe it is about community participation and the making of places in which people have ownership, while property people believe it is about creating a congenial environment which will attract people to their develop- ments, making them easier to sell or rent for a good return: the reality probably lies somewhere in between.
As quoted in a recent article in The Guardian, the US academic Richard Florida – considered to be the guru of placemaking – told the mayors of major American cities in 2002 that attracting 'hipsters' to their towns was crucial. "Don't waste money on stadi- ums and concert halls, or luring big companies with tax breaks. Instead, make your town a place where hipsters want to be, with a vibrant arts and music scene and a lively cafe culture. Embrace the 'three T's' of technology, talent and tolerance, and the 'creative class' will come flocking."
This is really the same cycle that Jane Jacobs described in her seminal work 'The Death and Life of Great American Cities', published in 1961, whereby districts fall into decay, the artists move in attracted by the cheap rents, the hipsters and coffee shops follow, the area regenerates, forcing the rents back up and the artists and original residents to move on. You only have to look at certain areas of London, like Shoreditch and Dalston, to see this gentrification process in action. There are obvious winners, mainly the early adopters, but there are also losers, particularly the low paid service workers who can no longer afford to live in the place where they have their roots.
So despite the casualties, placemaking as a catalyst for regenera- tion is here to stay, and most policymakers, now understand the benefits. There is also a growing consensus that cultural facilities, be they art galleries, music venues or theatres, have an important part to play in making places where people want to be. Generally, these facilities need to arise organically and are not imposed from outside. There are many examples of how small independent theatres, particularly in London, have contributed to the regenera- tion of their areas, such as The Tricycle in Kilburn, The Almeida in Islington and The Arcola in Dalston. They now occupy thriving high streets, which are almost unrecognisable from what they were 20 years ago.
It is worth considering the economic impact that theatres can have on the night-time economy. Take for example the data published by
The Society of London Theatres, who represent commercial theatre owners, which showed that in 2016, West End theatres had a gross revenue of £644m, VAT receipts of £107m, 14 million attendances and 76 per cent of seats filled. The London Theatre Report of 2014, which surveyed all theatres, both commercial and not-for- profit, found there were 241 theatres in London with 110,000 seats, 22 million attendances a year and nearly 20,000 people employed by theatres.
This is a lot of people generating a lot of footfall, who not only go to the theatre but also use transportation, restaurants and shops and visit other attractions. The West End of London is an extreme and unique example, but the same principles apply in any urban centre with a vibrant night-time economy, where cultural facilities are an important driver. In 2013 the Local Government Association published a report on how investment in arts and culture affects local economies, identifying five key impacts: attracting visitors, creating jobs, attracting businesses, revitalising places and develop- ing talent.
With such evidence, the role of cultural facilities in driving wellbeing, regeneration and local economies is undeniable, but how are the different players in the development cycle responding?
Planning & local authorities
It is worth noting that The National Planning Policy Framework of 2012 requires local authorities to prepare local plans which support cultural wellbeing and deliver sufficient community and cultural facilities to meet local needs. This was not included in the original draft, and it was only because of a campaign led by the national advisory public body for theatres, the Theatres Trust, that any reference to culture was included at all. However it is there now and local authorities should be pressed to act on it. Some local authorities do understand the community and commercial benefits that a cultural plan can bring, but not all.
My practice, Foster Wilson Architects, is involved in two local authority-led projects for cultural buildings as part of larger regen- eration projects. The Ovalhouse in Brixton is part of a large housing development led by Lambeth Council to provide a new home for an established theatre, create much needed cultural facili- ties in central Brixton, and help boost the night time economy. In Taunton we are looking at the enlargement of the existing Brewhouse Theatre and Arts Centre, a council-led regeneration project to create a cultural quarter in the centre of the town, which has been designated by the Government as a Garden Town. Both these projects show how local authorities are prioritising support- ing their existing cultural organisations, while at the same time serving a wider regeneration agenda designed to add value and create places which people actually want to live in.
It is not just local authorities that are recognising the positive economic impact of theatres. There is a growing trend for develop- ers to provide new cultural facilities or support existing ones as part of their plans. This is happening for a variety of reasons, which may include a requirement to replace an existing theatre, a demand for community benefit under a Section 106 agreement, or a straightforward commercial judgement about the contribution theatres make to the vibrancy of a neighbourhood.
For example, The St James Theatre, now renamed The Other Palace, replaced the old Westminster Theatre, which was previously on the site, providing a new theatre with residential development above. The new Bridge Theatre at One Tower Bridge forms part of a large development by Berkeley Homes and occupies an area origi- nally designated as 'cultural space', although neither the local authority nor the developer knew quite what that meant when the original planning approval was granted. At the Regents Place devel- opment, British Land have lent their support to the existing New Diorama Theatre because they understand its importance in creat- ing a cohesive community.
At a time when funding for theatres is increasingly hard to come by, the financial support of developers is to be welcomed, but needs to be handled with care to make sure they meet their obligations – and planning authorities have an important role to play in ensuring this happens.
Theatre as social space
Another growing trend, which theatres are increasingly embracing, is the creation of open, welcoming democratic foyer spaces, which are open to all in the daytime, and engage with the public realm. The traditional model of theatres that open their doors an hour before the performance and close them again after it finishes is rapidly disappearing.
While many theatres have been open all day for many years, the transformative development is the digital economy, where increas- ing numbers of people work online and do not need to be in conventional offices. Theatre foyers can be an ideal place to hang out, to work and to have meetings, provided there is the all-impor- tant wi-fi connection and good food and drink available. Obviously the location needs to be convenient and the design of the frontage as open and permeable as possible, but these are characteristics most theatres have anyway.
The most obvious example of this trend is the use of the foyers at The National Theatre and Southbank Centre in London, which are so full of people with laptops they are starting to be overwhelmed. This is a nice problem to have. It brings people into the building, who might otherwise not come in, and can generate a valuable income stream from the sale of food and drinks, as a well as creat- ing a sense of place.
Most theatres do much more than putting on performances, and community engagement is an important part of what they do. This may include school visits, drama workshops, dance classes, yoga and pilates. An interesting recent project, The Storyhouse in Chester, combines a new theatre with a public library, which brings a whole extra level of community engagement to the building, ensuring it is full of life all day long.
I think it is worth highlighting that theatre people are remarkably good at creating theatre quickly and with very few resources. They are in the business of making performances, which are ephemeral – here today and gone tomorrow. This is the antithesis of conven- tional architecture, which is by definition permanent, so if you want a pop-up performance or an interesting 'meanwhile' use to help generate activity, then there is no one better to help you do it.
In conclusion, theatre buildings play a vital role in the economic and cultural wellbeing of communities and are key drivers of
the local economy, the impact of which is often far greater than their modest means – if that isn't placemaking, I don't know what is.
Tim Foster is partner at Foster Wilson Architects
Council-led regeneration – Taunton's Brewhouse Theatre and Arts Centre
The Ovalhouse in Brixton is part of a large London housing development
Foster Wilson Architects | {
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\section{Introduction}
Figure \ref{fig:teaser} shows a high scoring detection from an object detector
with HOG features and a linear SVM classifier trained on a large database of
images. \changed{\emph{Why} does this detector think that sea water looks like a car?}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/teaser_fp.png}
\vspace{-.5em}
\caption{An image from PASCAL and a high scoring car detection from
DPM \citep{felzenszwalb2010object}. Why did the detector fail?}
\label{fig:teaser}
\vspace{-.5em}
\includegraphics[width=\linewidth]{figs/teaser_fp_vis.png}
\vspace{-1em}
\caption{We show the crop for the false car detection from
Figure \ref{fig:teaser}. On the right, we show our visualization of the HOG
features for the same patch. Our visualization reveals that this false alarm
actually looks like a car in HOG space.}
\label{fig:teaser2}
\vspace{-1.5em}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{figs/false-positives.png}
\caption{We visualize some high scoring detections from the deformable parts
model \citep{felzenszwalb2010object} for person, chair,
and car. Can you guess which are false alarms? Take a minute to study
this figure, then see Figure \ref{fig:topdetsrgb} for the corresponding RGB
patches.}
\label{fig:topdets}
\vspace{-1em}
\end{figure*}
Unfortunately, computer vision researchers are often unable to explain the
failures of object detection systems. Some researchers blame the features,
others the training set, and even more the learning algorithm. Yet, if we wish
to build the next generation of object detectors, it seems crucial to
understand the failures of our current detectors.
In this paper, we introduce a tool to explain some of the failures of object
detection systems. We present algorithms to visualize the
feature spaces of object detectors. Since features are too high dimensional for
humans to directly inspect, our visualization algorithms work by inverting
features back to natural images. We found that these inversions provide an
intuitive visualization of the feature spaces used by object
detectors.
Figure \ref{fig:teaser2} shows the output from our visualization algorithm on the
features for the false car detection. This visualization reveals that,
while there are clearly no cars in the original image, there is a car hiding
in the HOG descriptor. HOG features see a slightly different visual world than
what we see, and by visualizing this space, we can gain a more intuitive
understanding of our object detectors.
Figure \ref{fig:topdets} inverts more top detections on PASCAL for a few
categories. Can you guess which are false alarms? Take a minute to study the
figure since the next sentence might ruin the surprise. Although every
visualization looks like a true positive, all of these detections are actually
false alarms. Consequently, even with a better learning
algorithm or more data, these false alarms will likely persist. In other words,
the features are responsible for these failures.
\begin{figure}
\includegraphics[width=\linewidth]{figs/teaser-multiple.pdf}
\caption{Since there are many images that map to similar features, our method recovers multiple images that are diverse in image space, but match closely in feature space.}
\label{fig:multiple}
\end{figure}
The primary contribution of this paper is a general algorithm for visualizing
features used in object detection. We present a method that inverts visual
features back to images, and show experiments for two standard features in object detection,
HOG and activations from CNNs. Since there are many images that can produce equivalent
feature descriptors, our method moreover recovers multiple images that are perceptually
different in image space, but map to similar feature vectors, illustrated in Figure \ref{fig:multiple}.
The remainder of this paper presents and analyzes our visualization algorithm.
We first review a growing body of work in feature visualization for both
handcrafted features and learned representations. We evaluate our inversions
with both automatic benchmarks and a large human study, and we found our
visualizations are perceptually more accurate at representing the content of a
HOG feature than standard methods; see Figure \ref{fig:example} for a
comparison between our visualization and HOG glyphs. We then use our
visualizations to inspect the behaviors of object detection systems and analyze
their features. Since we hope our visualizations will be useful to other
researchers, our final contribution is a public feature visualization toolbox.\footnote{Available online at \url{http://mit.edu/hoggles}}
\section{Related Work}
Our visualization algorithms are part of an actively growing body of work in
feature inversion. \cite{oliva2001modeling}, in early work, described a simple
iterative procedure to recover images given gist descriptors.
\citet{weinzaepfel2011reconstructing} were the first to reconstruct an image
given its keypoint SIFT descriptors \citep{lowe1999object}. Their approach
obtains compelling reconstructions using a nearest neighbor based approach on a
massive database. \cite{d2012beyond} then developed an algorithm to reconstruct
images given only LBP features \citep{calonder2010brief,alahi2012freak}. Their
method analytically solves for the inverse image and does not require a
dataset. \cite{kato2014image} posed feature inversion as a jigsaw puzzle
problem to invert bags of visual words.
\begin{figure}
\includegraphics[width=\linewidth]{figs/teaser2.png}
\caption{In this paper, we present algorithms to visualize features. Our visualizations are more perceptually intuitive for humans to understand.}
\label{fig:example}
\vspace{-1em}
\end{figure}
Since visual representations that are learned can be difficult to interpret,
there has been recent work to visualize and understand learned features.
\cite{zeiler2013visualizing} present a method to visualize activations from a
convolutional neural network. In related work, \cite{simonyan2013deep}
visualize class appearance models and their activations for deep networks.
\cite{girshick2013rich} proposed to visualize convolutional neural networks by
finding images that activate a specific feature. \changed{\cite{deephoggles}
describe a general method for inverting visual features from CNNs by
incorporating natural image priors.}
While these methods are good at reconstructing and visualizing images from
their respective features, our visualization algorithms have some advantages.
Firstly, while most methods are tailored for specific features, the
visualization algorithms we propose are feature independent. Since we cast
feature inversion as a machine learning problem, our algorithms can be used to
visualize any feature. In this paper, we focus on features for object
detection, and we use the same algorithm to invert both HOG and CNN features.
Secondly, our algorithms are fast: our best algorithm can invert features in
under a second on a desktop computer, enabling interactive visualization, which
we believe is important for real-time debugging of vision systems. \changed{Finally, our algorithm
explicitly optimizes for multiple inversions that are diverse in image space, yet match in feature space.}
Our method builds upon work that uses a pair of dictionaries with a coupled
representation for super resolution \citep{yang2010image,wang2012semi} and
image synthesis \citep{huangcoupled}. We extend these methods to show that
similar approaches can visualize features as well. Moreover, we incorporate
novel terms that encourage diversity in the reconstructed image in order
to recover multiple images from a single feature.
Feature visualizations have many applications in computer vision. The computer
vision community has been using these visualization largely to understand object recognition
systems so as to reveal information encoded by features
\citep{zhangspeeding,sadeghi2013fast}, interpret transformations in feature
space \citep{cheninferring}, studying diverse images with similar features
\citep{tatu2011exploring,equiv}, find security failures in machine learning systems
\citep{biggio2012poisoning,weinzaepfel2011reconstructing}, and fix problems in
convolutional neural networks
\citep{zeiler2013visualizing,simonyan2013deep,bruckner2014ml}. With many
applications, feature visualizations are an important tool for the
computer vision researcher.
Visualizations enable analysis that complement a recent line of papers that
provide tools to diagnose object recognition systems, which we briefly review
here. \cite{parikh2011human,parikh2010role} introduced a new paradigm for
human debugging of object detectors, an idea that we adopt in our experiments.
\cite{hoiem2012diagnosing} performed a large study analyzing the errors that
object detectors make. \cite{divvala2012important} analyze part-based
detectors to determine which components of object detection systems have the
most impact on performance. \cite{liu2012has} designed algorithms to highlight
which image regions contribute the most to a classifier's confidence.
\cite{zhuwe} try to determine whether we have reached Bayes risk for HOG. The
tools in this paper enable an alternative mode to analyze object detectors
through visualizations. By putting on `HOG glasses' and visualizing the world
according to the features, we are able to gain a better understanding of the
failures and behaviors of our object detection systems.
\section{Inverting Visual Features}
We now describe our feature inversion method. Let $x_0 \in
\mathbb{R}^{P}$ be a natural RGB image and $\phi = f(x_0) \in \mathbb{R}^Q$ be
its corresponding feature descriptor. \changed{Since features are many-to-one functions,} our goal is to invert the features $\phi$
by recovering a \emph{set} of images $\mathcal{X} = \{x_1, \ldots, x_N\}$ that all map to
the original feature descriptor.
We compute this inversion set $\mathcal{X}$ by solving an optimization problem. We wish
to find several $x_i$ that minimize their reconstruction error in feature space
$\left|\left| f(x_i) - \phi \right|\right|_2^2$ while simultaneously appearing
diverse in image space. We write this optimization as:
\begin{equation}
\begin{aligned}
\mathcal{X} = \argmin_{x, \xi} &\sum_{i=1}^N \left|\left| f(x_i) - \phi \right|\right|_2^2 + \gamma \sum_{j<i} \xi_{ij} \\
\textrm{s.t.} \quad &0 \le S_A(x_i, x_j) \le \xi_{ij} \; \forall_{ij}
\end{aligned}
\label{eqn:objective-multiple}
\end{equation}
The first term of this objective favors images that match in feature space and
the slack variables $\xi_{ij}$ penalize pairs of images that are too similar to
each other in image space \changed{where $S_A(x_i, x_j)$ is the} similarity cost, parametrized by $A$,
between inversions $x_i$ and $x_j$. A high similarity cost intuitively means
that $x_i$ and $x_j$ look similar and should be penalized. The hyperparameter
$\gamma \in \mathbb{R}$ controls the strength of the similarity cost. By
increasing $\gamma$, the inversions will look more different, at the expense of
matching less in feature space.
\subsection{Similarity Costs}
There are a variety of similarity costs that we could use. \changed{In this work,} we use costs of the form:
\begin{align}
S_A(x_i, x_j) = (x_i^T A x_j)^2
\label{eqn:similarity}
\end{align}
where $A \in \mathbb{R}^{P \times P}$ is an affinity matrix. Since we are
interested in images that are diverse and not negatives of each other, we
square $x_i^T A x_j$.
The identity affinity matrix, i.e.\ $A = I$, corresponds to comparing inversions
directly in the color space. However, more metrics are also possible, \changed{which we describe now.}
\emph{Edges:} We can design $A$ to favor inversions that differ in edges. Let
$A = C^T C$ where $C \in \mathbb{R}^{2P \times P}$. The first $P$ rows of $C$
correspond to the convolution with the vertical edge filters
$\left[\begin{smallmatrix}-1 & 0 & 1\end{smallmatrix}\right]$ and similarly the
second $P$ rows are for the horizontal edge filters
$\left[\begin{smallmatrix}-1 & 0 & 1\end{smallmatrix}\right]^T$.
\emph{Color:} We can also encourage the inversions to differ only in colors.
Let $A = C^T C$ where $C \in \mathbb{R}^{3 \times P}$ is a matrix that averages
each color channel such that $Cx \in \mathbb{R}^3$ is the average RGB color.
\emph{Spatial:} We can force the inversions to only differ in certain spatial
regions. Let $A = C^T C$ where $C \in \mathbb{R}^{P \times P}$ is a binary
diagonal matrix. A spatial region of $x$ will be only encouraged to be
diverse if its corresponding element on the diagonal of $C$ is $1$. Note we can
combine spatial similarity costs with both color and edge costs to encourage
color and edge diversity in only certain spatial regions as well.
\subsection{Optimization}
Unfortunately, optimizing equation \ref{eqn:objective-multiple} efficiently is challenging because
it is not convex. \changed{Instead, we will make two modifications to solve an approximation:}
\begin{figure}
\includegraphics[width=\linewidth]{figs/paired-dict-tutorial-2.png}
\caption{Inverting features using a paired dictionary. We first project the feature vector
on to a feature basis. By jointly learning a coupled
basis of features and natural images, we can transfer coefficients estimated from features
to the image basis to recover the natural image.}
\label{fig:pair-tutorial}
\end{figure}
\changed{\emph{Modification 1:} Since the first term of the objective depends on the feature function $f(\cdot)$, which is often not convex nor differentiable, efficient optimization is difficult. Consequently, we approximate an image $x_i$ and its features
$\phi = f(x_i)$ with a paired, over-complete basis to make the objective convex.
Suppose we represent an image $x_i \in \mathbb{R}^P$ and its feature $\phi \in
\mathbb{R}^Q$ in a natural image basis $U \in \mathbb{R}^{P \times K}$ and a
feature space basis $V \in \mathbb{R}^{Q \times K}$ respectively. We can
estimate $U$ and $V$ such that images and features can be encoded in their
respective bases but with shared coefficients $\alpha \in \mathbb{R}^K$:
\begin{align} x_0 = U\alpha \quad \textrm{and} \quad \phi = V\alpha \end{align}
If $U$ and $V$ have this paired representation, then we can invert features by
estimating an $\alpha$ that reconstructs the feature well. See Figure
\ref{fig:pair-tutorial} for a graphical representation of the paired
dictionaries.}
\changed{
\emph{Modification 2:} However, the objective is still not convex when there are multiple outputs. We approach solving equation \ref{eqn:objective-multiple} sub-optimally using a greedy approach.
Suppose we already computed the first $i-1$
inversions, $\{x_1, \ldots, x_{i-1}\}$. We then seek the inversion $x_i$ that
is only different from the previous inversions, but still matches $\phi$.
}
Taking these approximations into account, we solve for the inversion $x_i$ with
the optimization:
\begin{equation}
\begin{aligned}
&\alpha_i^* = \argmin_{\alpha_i, \xi} ||V\alpha_i-\phi||_2^2 + \lambda ||\alpha_i||_1 + \gamma \sum_{j=1}^{i-1} \xi_j \\
& \textrm{s.t.} \quad S_A(U\alpha_i, x_j) \le \xi_j
\end{aligned}
\label{eqn:pair-inverse}
\end{equation}
where there is a sparsity prior on $\alpha_i$ parameterized by $\lambda \in
\mathbb{R}$.\footnote{We found a sparse $\alpha_i$ improves our results. While
our method will work when regularizing with $||\alpha_i||_2$ instead, it tends to
produce more blurred images.} After estimating $\alpha_i^*$, the inversion is
$x_i = U\alpha_i^*$.
\begin{figure}
\includegraphics[width=1\linewidth]{figs/pd-pairs.jpg}
\caption{Some pairs of dictionaries for $U$ and $V$. The left of every pair is the gray scale dictionary element and the right is the positive components elements in the HOG dictionary. Notice the correlation between dictionaries.}
\label{fig:pair-basis}
\end{figure}
The similarity costs can be seen as adding a weighted Tikhonov
regularization ($\ell 2$ norm) on $\alpha_i$ because
\begin{align*}
S_A(U \alpha_i, x_j) = \alpha_i^T B \alpha_i \quad
\textrm{where} \quad
B = U^T A^T x_j^T x_j A U
\end{align*}
Since this is combined with lasso, the optimization
behaves as an elastic net \citep{zou2005regularization}.
Note that if we remove the slack variables ($\gamma =
0$), our method reduces to \citep{vondrick2013hog} and only produces one
inversion.
As the similarity costs are in the form of equation \ref{eqn:similarity}, we can
absorb $S_A(x; x_j)$ into the $\ell 2$ norm of equation \ref{eqn:pair-inverse}.
This allows us to efficiently optimize equation \ref{eqn:pair-inverse} using an
off-the-shelf sparse coding solver. We use SPAMS \citep{mairal2009online} in
our experiments. The optimization typically takes a few seconds to produce each
inversion on a desktop computer.
\subsection{Learning}
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{figs/elda1.png}
\caption{We found that averaging the images of top detections from an exemplar
LDA detector provide one method to invert HOG features.}
\label{fig:elda}
\end{figure*}
The bases $U$ and $V$ can be learned such that they have paired coefficients.
We first extract millions of image patches $x_0^{(i)}$ and their corresponding
features $\phi^{(i)}$ from a large database. Then, we can solve a dictionary
learning problem similar to sparse coding, but with paired dictionaries:
\begin{equation}
\begin{aligned}
\argmin_{U, V, \alpha} \; & \sum_{i} ||x_0^{(i)} - U\alpha_i||_2^2 + ||\phi^{(i)} - V\alpha_i||_2^2 + \lambda ||\alpha_i||_1 \\
\textrm{s.t.} \quad &||U||_2^2 \le \psi_1, \; ||V||_2^2 \le \psi_2 \
\end{aligned}
\label{eqn:pairobj}
\end{equation}
for some hyperparameters $\psi_1 \in \mathbb{R}$ and $\psi_2 \in \mathbb{R}$.
We optimize the above with SPAMS \citep{mairal2009online}. Optimization
typically took a few hours, and only needs to be performed once for a fixed
feature. See Figure \ref{fig:pair-basis} for a visualization of the learned
dictionary pairs.
\section{Baseline Feature Inversion Methods}
In order to evaluate our method, we also developed several baselines that we use for
comparison. We first describe \changed{three} baselines for single feature inversion, then discuss two
baselines for multiple feature inversion.
\subsection{Exemplar LDA (ELDA)}
Consider the top detections for the exemplar object detector
\citep{hariharan2012discriminative,malisiewicz2011ensemble} for a few
images shown in Figure \ref{fig:elda}. Although all top detections are false
positives, notice that each detection captures some statistics about the query.
Even though the detections are wrong, if we squint, we can see parts of the
original object appear in each detection.
We use this observation to produce our first baseline.
Suppose we wish to invert feature $\phi$. We first train an exemplar LDA
detector \citep{hariharan2012discriminative} for this query,
$w = \Sigma^{-1}(y - \mu)$
where $\Sigma$ and $\mu$ are parameters estimated with a large dataset.
We then score $w$ against every sliding window in this database. The feature
inverse is the average of the top $K$ detections in RGB space:
$f^{-1}(\phi) = \frac{1}{K} \sum_{i=1}^K z_i$ where $z_i$ is an image of a
top detection.
This method, although simple, produces reasonable reconstructions,
even when the database does not contain the category of the feature template.
However, it is computationally expensive since it requires running an object detector across a large database.
\changed{Note that} a similar nearest neighbor method is used in brain research to
visualize what a person might be seeing \citep{nishimoto2011reconstructing}.
\subsection{Ridge Regression}
We describe a fast, parametric
inversion baseline based off ridge regression.
Let $X \in \mathbb{R}^P$ be a random variable representing a gray scale image and $\Phi \in \mathbb{R}^Q$ be a random variable of its corresponding feature. We define
these random variables to be normally distributed on a $P+Q$-variate Gaussian
$P(X, \Phi) \sim \mathcal{N}(\mu, \Sigma)$
with parameters
$\mu = \left[\begin{smallmatrix}
\mu_X & \mu_{\Phi}
\end{smallmatrix}\right]$ and $
\Sigma = \left[\begin{smallmatrix}
\Sigma_{XX} & \Sigma_{X\Phi} \\
\Sigma_{X\Phi}^T & \Sigma_{Y\Phi}
\end{smallmatrix}\right]$.
In order to invert a feature $y$, we calculate the most likely image from
the conditional Gaussian distribution $P(X | \Phi = \phi)$:
\begin{align}
f^{-1}(y) &= \argmax_{x \in \mathbb{R}^D} P(X = x | \Phi = \phi)
\end{align}
It is well known that a Gaussian distribution have a closed form conditional mode:
\begin{align}
f^{-1}(y) = \Sigma_{X\Phi} \Sigma_{\Phi\Phi}^{-1} (y - \mu_{\Phi}) + \mu_X
\end{align}
Under this inversion algorithm, any feature can be inverted by a single matrix
multiplication, allowing for inversion in under a second.
We estimate $\mu$ and $\Sigma$ on a large database. In practice, $\Sigma$ is not positive definite; we add
a small uniform prior (i.e., $\hat{\Sigma} = \Sigma + \lambda I$) so $\Sigma$
can be inverted. Since we wish to invert any feature, we assume that $P(X,
\Phi)$ is stationary \citep{hariharan2012discriminative}, allowing us to efficiently learn the covariance across
massive datasets. For features with varying spatial dimensions, we invert a feature by marginalizing
out unused dimensions.
\subsection{Direct Optimization}
We now provide a baseline that attempts to find images that, when we compute features on it, sufficiently match the original descriptor. In
order to do this efficiently, we only consider images that span a natural image basis.
Let $U \in \mathbb{R}^{D \times K}$ be the natural image basis. We found using the first $K$ eigenvectors of $\Sigma_{XX} \in \mathbb{R}^{D \times D}$ worked well for this basis. Any image $x \in \mathbb{R}^D$ can be encoded by coefficients $\rho \in \mathbb{R}^K$ in this basis: $x = U \rho$. We wish to minimize:
\begin{equation}
\begin{aligned}
&f^{-1}(y) = U\rho^* \\
&\textrm{where} \quad \rho^* = \argmin_{\rho \in \mathbb{R}^K} \left|\left| f(U\rho) - y \right|\right|_2^2
\end{aligned}
\label{eqn:highfreq-objective}
\end{equation}
Empirically we found success optimizing equation \ref{eqn:highfreq-objective} using
coordinate descent on $\rho$ with random restarts.
We use an over-complete basis corresponding to sparse Gabor-like filters for
$U$. We compute the eigenvectors of $\Sigma_{XX}$ across different scales and
translate smaller eigenvectors to form $U$.
\subsection{Nudged Dictionaries}
In order to compare our ability to recover multiple inversions, we describe two
baselines for multiple feature inversions.
Our first method modifies paired
dictionaries. Rather than incorporating similarity costs, we add noise to a feature to create a slightly different inversion by ``nudging'' it in random directions:
\begin{equation}
\begin{aligned}
&\alpha_i^* = \argmin_{\alpha_i} ||V\alpha_i-\phi + \gamma \epsilon_i||_2^2 + \lambda ||\alpha_i||_1\\
\end{aligned}
\end{equation}
where $\epsilon_i \sim \mathcal{N}(0_Q, I_Q)$ is noise from a standard normal distribution \changed{such that
$I_Q$ is the identity matrix}
and $\gamma \in \mathbb{R}$ is a hyperparameter that controls the strength of the diversity.
\subsection{Subset Dictionaries}
In addition, we compare against a second baseline that
modifies a paired dictionary by removing the basis elements that were
activated on previous iterations. Suppose the
first inversion activated the first $R$ basis elements. We
obtain a second inversion by only giving the paired dictionary the other
$K-R$ basis elements. This forces the sparse coding to use a disjoint basis
set, leading to different inversions.
\section{Evaluation of Single Inversion}
We evaluate our inversion algorithms using both qualitative and quantitative
measures. We use PASCAL VOC 2011 \citep{Everingham10} as our dataset and we
invert patches corresponding to objects. Any algorithm that required training
could only access the training set. During evaluation, only images from the
validation set are examined. The database for exemplar LDA excluded the
category of the patch we were inverting to reduce the potential effect of
dataset biases. Due to their popularity in object detection, we first focus on
evaluating HOG features.
\begin{figure}
\captionsetup[subfigure]{labelformat=empty}
\centering \subfloat[Original]{ \shortstack{
\includegraphics[width=0.18\linewidth]{figs/aeroplane_47_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/sheep_199_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/tvmonitor_204_orig.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/pottedplant_100_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cat_456_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bottle_519_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cow_231_orig.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/bicycle_181_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bird_490_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bus_9_orig.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/train_311_orig.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/diningtable_181_orig.jpg}
} }
\subfloat[ELDA]{ \shortstack{
\includegraphics[width=0.18\linewidth]{figs/aeroplane_47_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/sheep_199_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/tvmonitor_204_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/pottedplant_100_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cat_456_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bottle_519_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cow_231_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bicycle_181_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bird_490_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bus_9_avg.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/train_311_avg.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/diningtable_181_avg.jpg}
} }
\subfloat[Ridge]{ \shortstack{
\includegraphics[width=0.18\linewidth]{figs/aeroplane_47_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/sheep_199_gmm.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/tvmonitor_204_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/pottedplant_100_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cat_456_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bottle_519_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cow_231_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bicycle_181_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bird_490_gmm.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bus_9_gmm.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/train_311_gmm.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/diningtable_181_gmm.jpg}
} }
\subfloat[Direct]{ \shortstack{
\includegraphics[width=0.18\linewidth]{figs/aeroplane_47_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/sheep_199_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/tvmonitor_204_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/pottedplant_100_ggs.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/cat_456_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bottle_519_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cow_231_ggs.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/bicycle_181_ggs.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/bird_490_ggs.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bus_9_ggs.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/train_311_ggs.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/diningtable_181_ggs.jpg}
} }
\subfloat[PairDict]{ \shortstack{
\includegraphics[width=0.18\linewidth]{figs/aeroplane_47_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/sheep_199_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/tvmonitor_204_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/pottedplant_100_pdl.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/cat_456_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bottle_519_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/cow_231_pdl.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/bicycle_181_pdl.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/bird_490_pdl.jpg} \\
\includegraphics[width=0.18\linewidth]{figs/bus_9_pdl.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/train_311_pdl.jpg}\\
\includegraphics[width=0.18\linewidth]{figs/diningtable_181_pdl.jpg}
} }
\caption{We
show results for all four of our inversion algorithms on held out image
patches on similar dimensions common for object detection.}
\label{fig:results}
\end{figure}
\subsection{Qualitative Results}
We show our inversions in Figure \ref{fig:results} for a few object categories.
Exemplar LDA and ridge regression tend to produce blurred visualizations.
Direct optimization recovers high frequency details at the expense of extra
noise. Paired dictionary learning tends to produce the best visualization
for HOG descriptors. By learning a dictionary over the visual world and
the correlation between HOG and natural images, paired dictionary learning
recovered high frequencies without introducing significant noise.
\begin{figure*}
\centering
\includegraphics[width=0.45\linewidth]{figs/color/2008_002588.jpg}\hspace{2em}\includegraphics[width=0.45\linewidth]{figs/color/2011_003115.jpg}\\
\vspace{0.2em}
\includegraphics[width=0.45\linewidth]{figs/color/2011_002983.jpg}\hspace{2em}\includegraphics[width=0.45\linewidth]{figs/color/2008_002910.jpg}\\
\vspace{0.2em}
\includegraphics[width=0.45\linewidth]{figs/color/2011_001822.jpg}\hspace{2em}\includegraphics[width=0.45\linewidth]{figs/color/2011_001282.jpg}\\
\caption{We show results where our paired dictionary algorithm is trained to
recover RGB images instead of only grayscale images. The right shows the
original image and the left shows the inverse.}
\label{fig:color}
\end{figure*}
Although HOG does not explicitly encode color, we found that the paired
dictionary is able to recover color from HOG descriptors. Figure
\ref{fig:color} shows the result of training a paired dictionary to estimate
RGB images instead of grayscale images. While the paired dictionary assigns
arbitrary colors to man-made objects and indoor scenes, it frequently colors
natural objects correctly, such as grass or the sky, likely because those
categories are strongly correlated to HOG descriptors. We focus on grayscale
visualizations in this paper because we found those to be more intuitive for
humans to understand.
\changed{
We also explored whether our visualization algorithm could invert other
features besides HOG, such as deep features. Figure \ref{fig:qual-icnn} shows
how our algorithm can recover some details of the original image given only
activations from the last convolutional layer of \cite{krizhevsky2012imagenet}.
Although the visualizations are blurry, they do capture some important visual
aspects of the original images such as shapes and colors. This suggests that our visualization algorithm
may be general to the type of feature.}
\begin{figure}
\centering
\captionsetup[subfigure]{labelformat=empty}
\subfloat[Original]{
\includegraphics[width=0.32\linewidth]{figs/2009_002457-gray.jpg}
}
\subfloat[PairDict (seconds)]{
\includegraphics[width=0.32\linewidth]{figs/2009_002457-pd.jpg}
}
\subfloat[Greedy (days)]{
\includegraphics[width=0.32\linewidth]{figs/2009_002457-greedy.jpg}
}
\caption{Although our algorithms are good at inverting HOG, they are not perfect, and struggle to reconstruct high frequency detail. See text for details.}
\label{fig:notperfect}
\end{figure}
\begin{figure}
\captionsetup[subfigure]{labelformat=empty}
\centering
\subfloat[Original $x$]{
\includegraphics[width=0.32\linewidth]{figs/recursion1.jpg}
}
\subfloat[$x' = \phi^{-1}\left(\phi(x)\right)$]{
\includegraphics[width=0.32\linewidth]{figs/recursion2.jpg}
}
\subfloat[$x'' = \phi^{-1}\left(\phi(x')\right)$]{
\includegraphics[width=0.32\linewidth]{figs/recursion3.jpg}
}
\caption{We recursively compute HOG and invert it with a paired dictionary. While there is some information loss,
our visualizations still do a good job at accurately representing HOG features. $\phi(\cdot)$ is HOG, and $\phi^{-1}(\cdot)$ is the inverse.}
\label{fig:recursion}
\end{figure}
\begin{figure}
\centering
\captionsetup[subfigure]{labelformat=empty}
\subfloat[$40 \times 40$]{
\includegraphics[width=0.23\linewidth]{figs/chair-big.jpg}
}
\subfloat[$20 \times 20$]{
\includegraphics[width=0.23\linewidth]{figs/chair-medium.jpg}
}
\subfloat[$10 \times 10$]{
\includegraphics[width=0.23\linewidth]{figs/chair-small.jpg}
}
\subfloat[$5 \times 5$]{
\includegraphics[width=0.23\linewidth]{figs/chair-tiny.jpg}
}
\caption{Our inversion algorithms are sensitive to the HOG template size.
We show how performance degrades as the template becomes smaller.}
\label{fig:pyramid}
\end{figure}
While our visualizations do a good job at representing HOG features, they have
some limitations. Figure \ref{fig:notperfect} compares our best visualization
(paired dictionary) against a greedy algorithm that draws triangles of random
rotation, scale, position, and intensity, and only accepts the triangle if it
improves the reconstruction. If we allow the greedy algorithm to execute for an
extremely long time (a few days), the visualization better shows higher
frequency detail. This reveals that there exists a visualization better than
paired dictionary learning, although it may not be tractable \changed{for large scale experiments}. In a related
experiment, Figure \ref{fig:recursion} recursively computes HOG on the inverse
and inverts it again. This recursion shows that there is some loss between
iterations, although it is minor and appears to discard high frequency details.
Moreover, Figure \ref{fig:pyramid} indicates that our inversions are sensitive
to the dimensionality of the HOG template. Despite these limitations, our
visualizations are, as we will now show, still perceptually intuitive for
humans to understand.
\subsection{Quantitative Results}
We quantitatively evaluate our algorithms under two benchmarks. Firstly, we use an automatic
inversion metric that measures how well our inversions reconstruct original
images. Secondly, we conducted a large visualization challenge with human
subjects on Amazon Mechanical Turk (MTurk), which is designed to determine how
well people can infer high level semantics from our visualizations.
\emph{Pixel Level Reconstruction:}
We consider the inversion performance of our algorithm: given a HOG feature
$y$, how well does our inverse $\phi^{-1}(y)$ reconstruct the original pixels
$x$ for each algorithm? Since HOG is invariant up to a constant shift and
scale, we score each inversion against the original image with normalized cross
correlation. Our results are shown in Table \ref{tab:inversionobjective}.
Overall, exemplar LDA does the best at pixel level reconstruction.
\emph{Semantic Reconstruction:}
While the inversion benchmark evaluates how well the inversions reconstruct the
original image, it does not capture the high level content of the inverse: is
the inverse of a sheep still a sheep? To evaluate this, we conducted a study on
MTurk. We sampled 2,000 windows corresponding to objects in
PASCAL VOC 2011. We then showed participants an inversion from one of our
algorithms and asked participants to classify it into one of the 20 categories. Each
window was shown to three different users. Users were required to pass a
training course and qualification exam before participating in order to
guarantee users understood the task. Users could optionally select that they
were not confident in their answer. We also compared our algorithms against the
standard black-and-white HOG glyph popularized by \citep{dalal2005histograms}.
\begin{figure}
\centering
\includegraphics[width=12em]{figs/vis/121.jpg}\hspace{2em}
\includegraphics[width=12em]{figs/vis/13.jpg}
\includegraphics[width=12em]{figs/vis/23.jpg}\hspace{2em}
\includegraphics[width=12em]{figs/vis/34.jpg}
\includegraphics[width=12em]{figs/vis/37.jpg}\hspace{2em}
\includegraphics[width=12em]{figs/vis/54.jpg}
\includegraphics[width=12em]{figs/vis/61.jpg}\hspace{2em}
\includegraphics[width=12em]{figs/vis/74.jpg}
\caption{\changed{We show visualizations from our method to invert features
from deep convolutional networks. Although the visualizations
are blurry, they capture some key aspects of the original images, such as shapes and colors. Our visualizations are inverting
the last convolutional layer of \cite{krizhevsky2012imagenet}.}}
\label{fig:qual-icnn}
\end{figure}
\begin{table}
\centering
\begin{tabular}{l | c c c c c}
Category & ELDA & Ridge & Direct & PairDict \\
\hline
aeroplane & \textbf{0.634} & \textbf{0.633} & 0.596 & 0.609 \\
bicycle & 0.452 & \textbf{0.577} & 0.513 & 0.561 \\
bird & \textbf{0.680} & 0.650 & 0.618 & 0.638 \\
boat & \textbf{0.697} & 0.678 & 0.631 & 0.629 \\
bottle & \textbf{0.697} & 0.683 & 0.660 & 0.671 \\
bus & 0.627 & \textbf{0.632} & 0.587 & 0.585 \\
car & 0.668 & \textbf{0.677} & 0.652 & 0.639 \\
cat & \textbf{0.749} & 0.712 & 0.687 & 0.705 \\
chair & \textbf{0.660} & 0.621 & 0.604 & 0.617 \\
cow & \textbf{0.720} & 0.663 & 0.632 & 0.650 \\
table & \textbf{0.656} & 0.617 & 0.582 & 0.614 \\
dog & \textbf{0.717} & 0.676 & 0.638 & 0.667 \\
horse & \textbf{0.686} & 0.633 & 0.586 & 0.635 \\
motorbike & 0.573 & \textbf{0.617} & 0.549 & 0.592 \\
person & \textbf{0.696} & 0.667 & 0.646 & 0.646 \\
pottedplant & \textbf{0.674} & \textbf{0.679} & 0.629 & 0.649 \\
sheep & \textbf{0.743} & 0.731 & 0.692 & 0.695 \\
sofa & \textbf{0.691} & 0.657 & 0.633 & 0.657 \\
train & \textbf{0.697} & 0.684 & 0.634 & 0.645 \\
tvmonitor & \textbf{0.711} & 0.640 & 0.638 & 0.629 \\
\hline
Mean & \textbf{0.671} & 0.656 &0.620 & 0.637\\
\end{tabular}
\caption{We evaluate the performance of our inversion algorithm by comparing
the inverse to the ground truth image using the mean normalized cross
correlation. Higher is better; a score of 1 is perfect.}
\label{tab:inversionobjective}
\end{table}
\setlength{\tabcolsep}{2pt}
\begin{table}
\centering
\begin{tabular}{l | c c c c c | c}
Category & ELDA & Ridge & Direct & PairDict & Glyph & Expert \\
\hline
aeroplane & 0.433& 0.391& 0.568& \textbf{0.645}& 0.297 & 0.333\\
bicycle & 0.327& 0.127& 0.362& 0.307& \textbf{0.405} & 0.438 \\
bird & 0.364& 0.263& \textbf{0.378}& 0.372& 0.193 & 0.059\\
boat & 0.292& 0.182& 0.255& \textbf{0.329}& 0.119 & 0.352\\
bottle & 0.269& 0.282& 0.283& \textbf{0.446}& 0.312 & 0.222\\
bus & 0.473& 0.395& \textbf{0.541}& 0\textbf{.549}& 0.122 & 0.118\\
car & 0.397& 0.457& \textbf{0.617}& 0.585& 0.359 & 0.389\\
cat & 0.219& 0.178& \textbf{0.381}& 0.199& 0.139 & 0.286 \\
chair & 0.099& 0.239& 0.223& \textbf{0.386}& 0.119 & 0.167\\
cow & 0.133& 0.103& \textbf{0.230}& 0.197& 0.072 & 0.214\\
table & 0.152& 0.064& 0.162& \textbf{0.237}& 0.071 & 0.125\\
dog & 0.222& 0.316& \textbf{0.351}& 0.343& 0.107 & 0.150\\
horse & 0.260& 0.290& 0.354& \textbf{0.446}& 0.144 & 0.150\\
motorbike & 0.221& 0.232& \textbf{0.396}& 0.224& 0.298 & 0.350\\
person & 0.458& 0.546& 0.502& \textbf{0.676}& 0.301 & 0.375\\
pottedplant & 0.112& 0.109& \textbf{0.203}& 0.091& 0.080 & 0.136\\
sheep & 0.227& 0.194& \textbf{0.368}& 0.253& 0.041 & 0.000\\
sofa & 0.138& 0.100& 0.162& \textbf{0.293}& 0.104 & 0.000\\
train & 0.311& 0.244& 0.316& \textbf{0.404}& 0.173 & 0.133\\
tvmonitor & 0.537& 0.439& 0.449& \textbf{0.682}& 0.354 & 0.666\\
\hline
Mean & 0.282& 0.258& 0.355& \textbf{0.383} & 0.191 & 0.233
\end{tabular}
\caption{We evaluate visualization performance across twenty PASCAL VOC
categories by asking MTurk participants to classify our inversions. Numbers are
percent classified correctly; higher is better. Chance is $0.05$. Glyph refers
to the standard black-and-white HOG diagram popularized by
\citep{dalal2005histograms}. Paired dictionary learning provides the best
visualizations for humans. Expert refers to MIT PhD students in computer vision
performing the same visualization challenge with HOG glyphs.}
\label{tab:userstudy}
\end{table}
Our results in Table \ref{tab:userstudy} show that paired dictionary learning
and direct optimization provide the best visualization of HOG descriptors for
humans. Ridge regression and exemplar LDA perform better than the glyph, but
they suffer from blurred inversions. Human performance on the HOG glyph is
generally poor, and participants were even the slowest at completing that
study. Interestingly, the glyph does the best job at visualizing bicycles,
likely due to their unique circular gradients. Our results overall suggest that
visualizing HOG with the glyph is misleading, and richer visualizations from
our paired dictionary are useful for interpreting HOG features.
Our experiments suggest that humans can predict the performance of object detectors
by only looking at HOG visualizations. Human accuracy on
inversions and state-of-the-art object detection AP scores from
\citep{felzenszwalb2010cascade} are correlated with a Spearman's rank
correlation coefficient of 0.77.
We also asked computer vision PhD students at MIT to classify HOG glyphs in order to
compare MTurk participants with experts in HOG. Our results are summarized
in the last column of Table \ref{tab:userstudy}. HOG experts performed slightly
better than non-experts on the glyph challenge, but experts on glyphs did not
beat non-experts on other visualizations. This result suggests that our
algorithms produce more intuitive visualizations even for object detection
researchers.
\section{Evaluation of Multiple Inversions}
\changed{Since features are many-to-one functions, our visualization algorithms should be able to recover multiple inversions
for a feature descriptor.
We look at the multiple inversions from deep network features because these features appear to be robust to several invariances.}
To conduct our experiments with multiple inversions, we inverted features from the AlexNet convolutional
neural network \citep{krizhevsky2012imagenet} trained on ImageNet
\citep{deng2009imagenet,russakovsky2014imagenet}. We use the publicly
available Caffe software package \citep{Jia13caffe} to extract features. We use
features from the last convolutional layer (pool5), which has been shown to
have strong performance on recognition tasks \citep{girshick2013rich}. We
trained the dictionaries $U$ and $V$ using random windows from the PASCAL VOC
2007 training set \citep{Everingham10}. We tested on two thousand random
windows corresponding to objects in the held-out PASCAL VOC 2007 validation
set.
\begin{figure}[t]
\centering
\subfloat[Affinity = Color]{
\includegraphics[width=0.47\linewidth]{figs/color-qual.pdf}
}
\hspace{0.01\linewidth}
\subfloat[Affinity = Edge]{
\includegraphics[width=0.47\linewidth]{figs/edge-qual.pdf}
}
\vspace{1em}
\subfloat[Nudged Dict]{
\includegraphics[width=0.47\linewidth]{figs/baselineA-qual.pdf}
}
\hspace{0.01\linewidth}
\subfloat[Subset Dict]{
\includegraphics[width=0.47\linewidth]{figs/baselineB-qual.pdf}
}
\caption{We show the first three inversions for a few patches from our testing
set. Notice how the color (a) and edge (b) variants of our method tend to
produce different inversions. The baselines tend to either similar in image
space (c) or do not match well in feature space (d). Best viewed on screen. }
\label{fig:qual}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=0.48\linewidth]{figs/qual1/edge-matrix.jpg}
\hspace{0.02\linewidth}
\includegraphics[width=0.48\linewidth]{figs/qual1/edge-matrix-2.jpg}
\caption{The edge affinity can often result in subtle differences. Above, \changed{we show a difference matrix} between the first three inversions that highlights differences between
all pairs of a few inversions from one CNN feature. The margins show the inversions, and the inner black squares show the absolute difference. White means larger difference. Notice that our algorithm is able to recover inversions with shifts of gradients.}
\label{fig:edge}
\end{figure}
\subsection{Qualitative Results}
We first look at a few qualitative results for our multiple feature
inversions. Figure \ref{fig:qual} shows a few examples for both our method (top
rows) and the baselines (bottom rows). The 1st column shows the result of
a paired dictionary on CNN features, while the 2nd and 3rd show the
additional inversions that our method finds. While the results are blurred,
they do tend to resemble the original image in rough shape and color.
The color affinity in Figure \ref{fig:qual}a is often able to produce inversions
that vary slightly in color. Notice how the cat and the floor are changing
slightly in hue, and the grass the bird is standing on is varying slightly. The
edge affinity in Figure \ref{fig:qual}b can occasionally generate inversions with
different edges, although the differences can be subtle. To better show the differences
with the edge affinity, we visualize a difference matrix in Figure \ref{fig:edge}.
Notice how the edges of the bird and person shift between each inversion.
\begin{figure}[t]
\centering
\includegraphics[width=0.8\linewidth]{figs/hog-equiv.jpg}
\caption{\changed{The block-wise histograms of HOG allow for gradients in the
image to shift up to their bin size without affecting the feature descriptor.
By using our visualization algorithm with the edge affinity matrix, we can
recover multiple HOG inversions that differ by edges subtly shifting. Above, we
show a difference matrix between the first three inversions for a downsampled
image of a man shown in the top left corner. Notice the vertical gradient in
the background shifts between the inversions, and the man's head move
slightly.}}
\label{fig:multiple-hog}
\end{figure}
The baselines tend to either produce nearly identical inversions or inversions
that do not match well in feature space. Nudged dictionaries in Figure
\ref{fig:qual}c frequently retrieves inversions that look nearly identical.
Subset dictionaries in Figure \ref{fig:qual}d recovers different inversions,
but the inversions do not match in feature space, likely because this baseline
operates over a subset of the basis elements.
\changed{
Although HOG is not as invariant to visual transformations as deep features, we can
still recover multiple inversions from a HOG descriptor. The block-wise histograms of HOG allow for
gradients in the image to shift up to their bin size without affecting the feature descriptor. Figure \ref{fig:multiple-hog}
shows multiple inversions from a HOG descriptor of a man where the person shifts slightly between each inversion.
}
\subsection{Quantitative Results}
We wish to quantify how well our inversions
trade off matching in feature space versus having diversity in image space. To
evaluate this, we calculated Euclidean distance between the features of the
first and second inversions from each method, $||\phi(x_1) -
\phi(x_2)||_2$, and compared it to the Euclidean distance of the inversions in
Lab image space, $||L(x_1) - L(x_2)||_2$ where $L(\cdot)$ is the Lab
colorspace transformation.\footnote{We chose Lab because Euclidean distance in this
space is known to be perceptually uniform \citep{jain1989fundamentals}, which
we suspect better matches human interpretation.} We consider one inversion
algorithm to be better than another method if, for the same distance in feature space, the
image distance is larger.
We show a scatter plot of this metric in
Figure \ref{fig:eval1} for our method with different similarity costs. The thick
lines show the median image distance for a given feature distance. The overall
trend suggests that our method produces more diverse images for the same
distance in feature space. Setting the affinity matrix $A$ to perform color
averaging produces the most image variation for CNN features in order to keep
the feature space accuracy small. The baselines in general do not perform as
well, and baseline with subset dictionaries struggles to even match in feature space, causing the
green line to abruptly start in the middle of the plot. The edge affinity
produces inversions that tend to be more diverse than baselines, although this effect
is best seen qualitatively in the next section.
We consider a second evaluation metric designed
to determine how well our inversions match the original features. Since
distances in a feature space are unscaled, they can be difficult to interpret, so we use a
normalized metric. We calculate the ratio of distances that the inversions make to the original
feature: $r = \frac{||\phi(x_2) - f||_2}{||\phi(x_1) - f||_2}$ where $f$ is the original
feature and $x_1$ and $x_2$ are the first and second inversions. A value of $r = 1$ implies
the second inversion is just as close to $f$ as the first. We then compare the ratio $r$ to
the Lab distance in image space.
\begin{figure}[t]
\centering
\includegraphics[trim=15em 1em 15em 1em,clip,width=\linewidth]{figs/eval.pdf}
\caption{We evaluate the
performance of our multiple inversion algorithm. The horizontal axis is the
Euclidean distance between the first and second inversion in CNN space and the
vertical axis is the distance of the same inversions in Lab colorspace.
\changed{This plot suggests that incorporating diversity costs into the inversion are
able to produce more diverse multiple visualizations for the same reconstruction error.}
Thick lines show the median image distance for a given feature distance.}
\label{fig:eval1}
\end{figure}
\begin{figure}[t]
\centering
\subfloat[Color]{\includegraphics[width=0.32\linewidth]{figs/ratio_rgb_axis.png}}
\hspace{.01em}
\subfloat[Identity]{\includegraphics[width=0.32\linewidth]{figs/ratio_standard_axis.png}}
\hspace{.01em}
\subfloat[Edge]{\includegraphics[width=0.32\linewidth]{figs/ratio_edge_axis.png}}
\\
\subfloat[Nudged Dict]{\includegraphics[width=0.32\linewidth]{figs/ratio_baseline_axis.png}}
\hspace{.01em}
\subfloat[Subset Dict]{\includegraphics[width=0.32\linewidth]{figs/ratio_delete_axis.png}}
\caption{We show density maps that visualize image
distance versus the ratio distances in feature space: $r = \frac{||\phi(x_2)-f||_2}{||\phi(x_1)-f||_2}$.
A value of $r = 1$ means that the two inversions are the same distance from the original feature. Black means most dense
and white is zero density. Our results suggest that our method with the affinity matrix set to color averaging produces more diverse
visualizations for the same $r$ value.}
\label{fig:eval2}
\end{figure}
We show results for our second metric in
Figure \ref{fig:eval2} as a density map comparing image distance and the ratio of
distances in feature space. Black is a higher density and implies that the
method produces inversions in that region more frequently. This experiment
shows that for the same ratio $r$, our approach tends to produce more diverse
inversions when affinity is set to color averaging. Baselines frequently performed poorly,
and struggled to generate diverse images that are close in feature space.
\section{Understanding Object Detectors}
\changed{While the goal of this paper is to visualize object detection
features, in this section we will use our visualizations to inspect the
behavior of object detection systems. Due to our budget for experiments, we focus
on HOG features.}
\subsection{HOGgles}
Our visualizations reveal that the world that features see is slightly
different from the world that the human eye perceives. Figure
\ref{fig:seeintodarkA} shows a normal photograph of a man standing in a dark
room, but Figure \ref{fig:seeintodarkB} shows how HOG features see the same
man. Since HOG is invariant to illumination changes and amplifies gradients,
the background of the scene, normally invisible to the human eye, materializes
in our visualization.
In order to understand how this clutter affects object detection, we visualized
the features of some of the top false alarms from the Felzenszwalb et al.\
object detection system \citep{felzenszwalb2010object} when applied to the
PASCAL VOC 2007 test set. Figure \ref{fig:topdets} shows our visualizations of
the features of the top false alarms. Notice how the false alarms look very
similar to true positives. While there are many different types of detector
errors, this result suggests that these particular failures are due to
limitations of HOG, and consequently, even if we develop better learning
algorithms or use larger datasets, these will false alarms will likely persist.
Figure \ref{fig:topdetsrgb} shows the corresponding RGB image patches for the
false positives discussed above. Notice how when we view these detections in
image space, all of the false alarms are difficult to explain. Why do chair
detectors fire on buses, or people detectors on cherries? By
visualizing the detections in feature space, we discovered that the learning
algorithm made reasonable failures since the features are deceptively
similar to true positives.
\subsection{Human+HOG Detectors}
Although HOG features are designed for machines, how well do humans see in HOG
space? If we could quantify human vision on the HOG feature space, we could get
insights into the performance of HOG with a perfect learning algorithm
(people). Inspired by Parikh and Zitnick's methodology
\citep{parikh2011human,parikh2010role}, we conducted a large human study where
we had Amazon Mechanical Turk participants act as sliding window HOG based object
detectors.
We built an online interface for humans to look at HOG visualizations of window
patches at the same resolution as DPM. We instructed participants to either classify
a HOG visualization as a positive example or a negative example for a category.
By averaging over multiple people (we used 25 people per window), we obtain a
real value score for a HOG patch. To build our dataset, we sampled top
detections from DPM on the
PASCAL VOC 2007 dataset for a few categories. Our dataset consisted of around $5,000$
windows per category and around $20\%$ were true positives.
\begin{figure}
\centering
\subfloat[Human Vision]{
\includegraphics[height=18em]{figs/seeintodark_original.jpg}
\label{fig:seeintodarkA}
}
\subfloat[HOG Vision]{
\includegraphics[height=18em]{figs/seeintodark_inverse.jpg}
\label{fig:seeintodarkB}
}
\caption{Feature inversion reveals the world that object detectors see. The left
shows a man standing in a dark room. If we compute HOG on this
image and invert it, the previously dark scene behind the man emerges. Notice
the wall structure, the lamp post, and the chair in the bottom right hand
corner.}
\label{fig:seeintodark}
\end{figure}
Figure \ref{fig:hoggles} shows precision recall curves for the Human + HOG based
object detector. In most cases, human subjects classifying HOG visualizations
were able to rank sliding windows with either the same accuracy or better than
DPM. Humans tied DPM for recognizing cars, suggesting that performance may be
saturated for car detection on HOG. Humans were slightly superior to DPM for
chairs, although performance might be nearing saturation soon. There appears to
be the most potential for improvement for detecting cats with HOG. Subjects
performed slightly worst than DPM for detecting people, but we believe this is
the case because humans tend to be good at fabricating people in abstract
drawings.
We then repeated the same experiment as above on chairs except we instructed
users to classify the original RGB patch instead of the HOG visualization. As
expected, humans have near perfect accuracy at detecting chairs with
RGB sliding windows. The performance gap between the Human+HOG detector and Human+RGB detector
demonstrates the amount of information that HOG features discard.
\begin{figure}
\centering
\includegraphics[width=0.48\linewidth]{figs/chair-hoggles.pdf}
\includegraphics[width=0.48\linewidth]{figs/cat-hoggles.pdf}
\includegraphics[width=0.48\linewidth]{figs/car-hoggles.pdf}
\includegraphics[width=0.48\linewidth]{figs/person-hoggles.pdf}
\caption{By instructing multiple human subjects to classify the visualizations, we show
performance results with an ideal learning algorithm (i.e., humans) on the HOG
feature space. Please see text for details.}
\label{fig:hoggles}
\end{figure}
\begin{figure*}
\centering
\includegraphics[height=6.7em]{figs/models/car_4_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/person_2_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/bottle_6_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/bicycle_2_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/motorbike_2_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/pottedplant_4_parts.jpg}\hspace{0.1em}\includegraphics[height=6.7em]{figs/models/pottedplant_4_parts_hog.jpg} \\
\vspace{0.5em}
\includegraphics[height=6.7em]{figs/models/train_4_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/bus_2_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/horse_2_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/tvmonitor_4_parts.jpg}\hspace{0.5em}
\includegraphics[height=6.7em]{figs/models/chair_4_parts.jpg}\hspace{0.1em}\includegraphics[height=6.7em]{figs/models/chair_4_parts_hog.jpg}
\caption{We visualize a few deformable parts models trained with
\citep{felzenszwalb2010object}. Notice the structure that emerges with our
visualization. First row: car, person, bottle, bicycle, motorbike, potted
plant. Second row: train, bus, horse, television, chair. For the right most
visualizations, we also included the HOG glyph. Our visualizations
tend to reveal more detail than the glyph.}
\label{fig:prototypes}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=\linewidth]{figs/false-positives-rgb.png}
\caption{We show the original RGB patches that correspond to the
visualizations from Figure \ref{fig:topdets}. We print the original patches on
a separate page to highlight how the inverses of false positives look
like true positives. We recommend comparing this figure side-by-side with
Figure \ref{fig:topdets}.} \label{fig:topdetsrgb}
\end{figure*}
Our experiments suggest that there is still some performance left to be
squeezed out of HOG. However, DPM is likely operating very close to the
performance limit of HOG. Since humans are the ideal learning agent and they
still had trouble detecting objects in HOG space, HOG may be too lossy of a
descriptor for high performance object detection. If we wish to significantly
advance the state-of-the-art in recognition, we suspect focusing effort on
building better features that capture finer details as well as higher level
information will lead to substantial performance improvements in object
detection. Indeed, recent advances in object recognition have been driven
by learning with richer features \citep{girshick2013rich}.
\subsection{Model Visualization}
We found our algorithms are also useful for visualizing the learned models of an
object detector. Figure \ref{fig:prototypes} visualizes the root templates and
the parts from \citep{felzenszwalb2010object} by inverting the
positive components of the learned weights. These visualizations provide hints on which
gradients the learning found discriminative. Notice the detailed structure
that emerges from our visualization that is not apparent in the HOG glyph. Often, one can recognize the category of the detector by only looking at the
visualizations.
\section{Conclusion}
We believe visualizations can be a powerful tool for understanding object
detection systems and advancing research in computer vision. To this end, this
paper presented and evaluated several algorithms to visualize object detection
features. We hope more intuitive visualizations will prove useful for the
community.
\emph{Acknowledgments:} We thank the CSAIL Vision Group
for many important discussions. Funding was provided by a NSF GRFP to CV, a
Facebook fellowship to AK, and a Google research award, ONR MURI N000141010933
and NSF Career Award No. 0747120 to AT.
\bibliographystyle{spbasic}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,677 |
\section{Introduction}
Quantum entanglement is not only of interest in the interpretation
of the foundation of quantum mechanics, but also a resource useful
in quantum information processing and quantum computation. A measure
of the entanglement in a state of two qubits is the Wooters
concurrence \cite{wootters1}. For pure bipartite states one also
uses the Von Neumann entropy of the reduced density matrix for
either of the parties \cite{bennett1,popescu} to measure the
entanglement. For a simple example, which has been proposed by
Jordan \textsl{et al.} \cite{jordan}, we have shown that in the
quantum evolution a modified entanglement fidelity exhibits the
behavior similar to that of the concurrence \cite{xiang}. In this
paper we investigate other two quantities, the \textit{entropy
exchange} and the \textit{coherent information}
\cite{schumacher1,schumacher2}, by deriving analytic expressions for
the system proposed by Jordan \textsl{et al.}. From these we obtain
relations between them and the concurrence in the quantum evolution
and discuss the possibility of using them as measures of the
entanglement.
We begin with a brief discussion of noisy quantum processes and
their mathematical descriptions. $R$ and $Q$ are two quantum systems
and the joint system $RQ$ is initially prepared in a pure entangled
state $\ket{\Psi^{RQ}}$. The system $R$ is dynamically isolated and
has a zero internal Hamiltonian, while the system $Q$ undergoes some
evolution that possibly involves interaction with the environment.
The evolution of $Q$ might represent a transmission process via some
quantum channel for the quantum information in $Q$. In general, the
evolution of $Q$ can be represented by a quantum operator
$\varepsilon^{Q}$, which gives the mapping from the initial state to
the final state
\begin{eqnarray}
\rho^{Q'}=\varepsilon^{Q}(\rho^{Q}).
\end{eqnarray}
Here, $\rho^{Q}=\mbox{Tr} _{R}{\ket{\Psi^{RQ}}\bra{\Psi^{RQ}}}$ which
represents the initial state of system $Q$, and after the dynamical
process the final state of the system becomes $\rho^{Q'}$. In the
most general case, the map $\varepsilon^{Q}$ must be trace
preserving and is a linear positive map \cite{stinespring,kraus}, so
it can represent all unitary evolutions. The evolution may also
include unitary evolving interactions with an environment $E$.
Suppose that the environment is initially in state $\rho^{E}$. The
operator can be written as
\begin{eqnarray}
\varepsilon^{Q}(\rho^{Q})&=&\mbox{Tr} _{E}{U\left(\rho^{Q}\otimes\rho^{E}\right) U^{\dag}}\nonumber\\
&=&\mbox{Tr} _{E}{U\left( \rho^{Q}\otimes\sum_{i}{p_{i}|i\rangle\langle i|}\right) U^{\dag}}\nonumber\\
&=&\sum_{j}{E_{j}^{Q}\rho^{Q} E_{j}^{Q\dag}}, \label{operation}
\end{eqnarray}
where $\sum_{i}{p_{i}|i\rangle\langle i|}$ is the spectral
decomposition of $\rho^{E}$ with $\{ |i\rangle \}$ being a base in
the Hilbert space $\mathcal{H}_{E}$ of the environment $E$, and
$E^{Q}_{j}=\sum_{i}{\sqrt{p_{i}}\langle j|U|i\rangle}$. The final
state of $RQ$ is
\begin{eqnarray}
\rho^{RQ'}&= &\mathcal{I}^{R}\otimes\varepsilon^{Q}(\rho^{RQ})\nonumber\\
&=&\sum_{j}{(1^{R}\otimes E^{Q}_{j})\rho^{RQ}(1^{R}\otimes
E^{Q}_{j})^{\dag}}. \label{operation2}
\end{eqnarray}
The \textit{entropy exchange} $S_{e}$ is defined as
\cite{schumacher1}
\begin{eqnarray}
S_{e}=-\mbox{Tr} {\rho^{RQ'}\log{\rho^{RQ'}}}. \label{se1}
\end{eqnarray}
It is the von Neumann entropy of the final state of the joint system
$RQ$. Throughout this paper we use $\log$ to denote $\log_{2}$. The
intrinsic expression of the entropy exchange is given by
$S_{e}=S(W)$, $S(\rho)$ is the von Neumann entropy of density
operator $\rho$ and $W$ is a density operator with components (in an
orthonormal basis)
\begin{eqnarray}
W_{ij}=\mbox{Tr} {E^{Q}_{i}\rho^{Q} E^{Q\dag}_{j}}. \label{w1}
\end{eqnarray}
The entropy exchange is an intrinsic property of $Q$, depending only
on $\rho^{Q}$ and $\varepsilon^{Q}$. It is a measure of the
information exchanged between system $Q$ and the environment during
evolution $\varepsilon^{Q}$. If there is no interaction between
system $Q$ and the environment, i.e., $\varepsilon^{Q}$ is a unitary
operator, then after the dynamical process the final state of the
joint system $RQ$ is still a pure state. This means that in this
case the entropy exchange equals zero. A complete discussion of the
entropy exchange can be seen in Refs.
\cite{schumacher1,schumacher2,barnum}. In Ref. \cite{xiang} we show
that the modified entanglement fidelity (MEF) admirably reflects the
entanglement preservation. The MEF is defined as
\begin{eqnarray}
F_{e}=\max_{U^{Q}}\bra{\Psi^{RQ}}(1^{R}\otimes
U^{Q})\rho^{RQ'}(1^{R}\otimes U^{Q})^{\dag}\ket{\Psi^{RQ}},
\label{f}
\end{eqnarray}
where $U^{Q}$ is a unitary transformation acting on $Q$. A
connection between the MEF and the entropy exchange is given by the
\textit{quantum Fano inequality} \cite{schumacher1},
\begin{eqnarray}
h(F_{e})+(1-F_{e})\log(d^{2}-1)\geq S_{e}, \label{fano}
\end{eqnarray}
where $h(\rho)=-\rho\log\rho-(1-\rho)\log(1-\rho)$ and $d$ is the
number of the complex dimensions of the Hilbert space ${\cal H}$
describing system $Q$. We can easily find that when $F_{e}=1$, i.e.,
the entanglement is admirably preserved in the evolution process,
$S_{e}$ equals zero. This implies that there may be some connection
between the entropy exchange and the measures of the entanglement,
e.g., the concurrence.
Another important intrinsic quantity is the \textit{coherent
information} $I_{e}$. It is defined as \cite{schumacher2}
\begin{eqnarray}
I_{e}=S(\rho^{Q'})-S(\rho^{RQ'})=S(\rho^{Q'})-S_{e}.
\label{i}
\end{eqnarray}
For classical systems, $I_{e}$ can never be positive since the
entropy of the joint system $RQ$ can never be less than the entropy
of the subsystem $Q$. But, for quantum systems, $I_{e}$ may take
positive value. For example, if $\rho^{RQ'}$ is an entangled pure
state, then $\rho^{Q'}$ is a mixed state, implying that
$S(\rho^{Q'})>0$ and $S(\rho^{RQ'})=0$. Thus, $I_{e}$ can be
regarded as a measure of the ``nonclassicity'' of the final joint
state $\rho^{RQ'}$, or, in other words, the degree of the quantum
entanglement retained by $R$ and $Q$.
Now we discuss a simple example introduced by Jordan \textsl{et al.}
in their work \cite{jordan}. For this example we can give analytic
expressions of the entropy exchange and the coherent information
from which the relations between them and the concurrence can be
obtained. We consider two entangled qubits, $A$ and $B$, and suppose
that qubit $A$ interacts with a control qubit $C$. Then $A$, $B$ and
$C$ respectively correspond to systems $Q$, $R$ and environment $E$
discussed above. We suppose that the initial states of the three
qubits are
\begin{eqnarray}
\Lambda=\rho^{AB}\otimes\frac{1}{2} 1_{c} \label{w},
\end{eqnarray}
where $\rho^{AB}$ is the initial state of joint system $A$ and $B$.
According to the Schmidt theorem \cite{schmidt}, a pure state of two
$\frac{1}{2}$-spins can be decomposed as
\begin{eqnarray}
\ket{\Psi}&=&e^{-i\varphi/2}\cos(\frac{\theta}{2})\ket{{\bf
n}}_{A}\ket{{\bf
m}}_{B}\nonumber\\
&~~~~&+e^{i\varphi/2}\sin(\frac{\theta}{2})\ket{{\bf
-n}}_{A}\ket{{\bf -m}}_{B}, \label{www}
\end{eqnarray}
where ${\bf n}$ and ${\bf m}$ are two points on the Poincar\'{e}
sphere, and the subscript specifies the related qubit $A$ or $B$.
The ``angle'' $\theta$ in Eq. (\ref{www}) determines the degree of
entanglement in the state. The angle satisfies $0\leq\theta\leq\pi$,
$\theta=0$ and $\theta=\pi$ correspond to the product states, and
the maximal entanglement is obtained for $\theta=\frac{\pi}{2}$.
Without losing generality we set the initial state of the joint
system $A$ and $B$ as
\begin{eqnarray}
\ket{\psi}=\cos\left(\frac{\theta}{2}\right)\ket{+z}_{A}\ket{-z}_{B}
+\sin\left(\frac{\theta}{2}\right)\ket{-z}_{A}\ket{+z}_{B},
\label{initial state}
\end{eqnarray}
where $\ket{\pm z}$ represent the eigenstates of $\sigma_{z}$ with
eigenvalues $\pm 1$. So the density matrix
$\rho^{AB}=\ket{\psi}\bra{\psi}$. For simplicity, we omit the
``azimuthal angle" $\varphi$, as factor $e^{\pm i\varphi/2}$ can be
absorbed in eigenstates $\ket{\pm z}$ and has no effect on the final
results.
We suggest an interaction between qubits $A$ and $C$ described by
the unitary transformation
\begin{eqnarray}
U=e^{-i t H} \label{u},
\end{eqnarray}
where
\begin{eqnarray}
H=\frac{\lambda\sigma^{A}_{z}}{2}(\ket{\alpha}\bra{\alpha}-\ket{\beta}\bra{\beta})
\label{h}
\end{eqnarray}
with $\lambda$ being the strength of the interaction, and
$\ket{\alpha}$ and $\ket{\beta}$ are two orthonormal vectors for
system $C$. Then the changing density matrix for joint system of $A$
and $B$ can be calculated as
\begin{widetext}
\begin{eqnarray}
\rho^{AB'}&=&\mbox{Tr} _{c}{\left[(U\otimes1^{B})\Lambda(U\otimes1^{B})^{\dag}\right]}
=\mbox{Tr} _{c}{\left[(U\otimes1^{B})(\ket{\psi}\bra{\psi}\otimes\frac{1}{2}1_{c})(U\otimes1^{B})^{\dag}\right]}\nonumber\\
&=&\left(
\begin{array}{c}
0~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0\\
0~~~~~~~\cos^{2}\left(\frac{\theta}{2}\right)~~~~~~~~~~~~~~~~~~~~~\cos(\lambda
t)\cos\left(\frac{\theta}{2}\right)\sin\left(\frac{\theta}{2}\right)~~~~~~~~~~~~~~~~0\\
0~~~~~~~\cos(\lambda
t)\cos\left(\frac{\theta}{2}\right)\sin\left(\frac{\theta}{2}\right)~~~~\sin^{2}\left(\frac{\theta}{2}\right)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0\\
0~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~0
\end{array}\right). \label{dm}
\end{eqnarray}
\end{widetext}
The changing density matrix $\rho^{AB'}$ usually represents a mixed
state. In order to quantify the entanglement we adopt the Wootters
concurrence \cite{wootters1} defined as
\begin{eqnarray}
C(\rho)\equiv\max[0,\sqrt{\lambda_{1}}-\sqrt{\lambda_{2}}-
\sqrt{\lambda_{3}}-\sqrt{\lambda_{4}}],
\end{eqnarray}
where $\rho$ is the density matrix representing the investigated
state of the joint system of $A$ and $B$, $\lambda_{1}$,
$\lambda_{2}$, $\lambda_{3}$, and $\lambda_{4}$ are the eigenvalues
of $\rho\sigma^{A}_{2}\sigma^{B}_{2}\rho^{\ast}
\sigma^{A}_{2}\sigma^{B}_{2}$ in the decreasing order, and
$\rho^{\ast}$ is the complex conjugation of $\rho$.
\begin{figure}[htb]
\centering
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{resub1.ps}\\
{(a)$\;\theta=\pi/4$}
\end{minipage}%
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{resub2.ps}\\
{(b)$\;\theta=\pi/3$}
\end{minipage}
\vspace*{0.5cm}
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{resub3.ps}\\
{(c)$\;\theta=\pi/2$}
\end{minipage}%
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{resub4.ps}\\
{(d)$\;\theta=3\pi/4$}
\end{minipage}
\caption{Evolutions of the entropy exchange $S_{e}$ (solid line) and
the concurrence $C$ (dashed line). We take $\hbar$=1 so that
$\lambda t$ is dimensionless.}
\label{fig1}
\end{figure}
From Eq. (\ref{dm}) we can obtain
\begin{eqnarray}
C(\rho^{AB'})=\sin\theta|\cos{\lambda t}|.
\end{eqnarray}
It is found that at time $\lambda t=\frac{\pi}{2}$, the state
$\rho^{AB'}$ is changed from the initial entangled state at $t=0$ to
a separable state, while at time $\lambda t=\pi$ the state
$\rho^{AB'}$ returns to the state with the initial entanglement. We
can also find that if the initial state is a product state, i.e.,
$\theta=0$ or $\theta=\pi$, the concurrence always equals zero.
Using Eqs. (\ref{operation}), (\ref{w}), (\ref{u}), and (\ref{h}),
we obtain the quantum operation on qubit $A$,
\begin{eqnarray}
\varepsilon^{A}(\rho^{A})&=&\mbox{Tr} _{C}{U(\rho^{A}\otimes\rho^{C})U^{\dag}}\nonumber\\
&=&\mbox{Tr} _{C}{U\left(\rho^{A}\otimes(\frac{1}{2}(\proj{\alpha}+\proj{\beta}))\right)U^{\dag}}\nonumber\\
&=&\frac{1}{2}e^{-i \sigma^{A}_{3}\left(\frac{\lambda
t}{2}\right)}\rho^{A}e^{+i \sigma^{A}_{3}\left(\frac{\lambda
t}{2}\right)}\nonumber\\
&~~~~&+\frac{1}{2}e^{+i \sigma^{A}_{3}\left(\frac{\lambda
t}{2}\right)}\rho^{A}e^{-i \sigma^{A}_{3}\left(\frac{\lambda
t}{2}\right)}. \label{expression}
\end{eqnarray}
So $E^{A}_{\alpha}=\frac{1}{\sqrt{2}}e^{-i
\sigma^{A}_{3}\left(\frac{\lambda t}{2}\right)}$ and
$E^{A}_{\beta}=\frac{1}{\sqrt{2}}e^{+i
\sigma^{A}_{3}\left(\frac{\lambda t}{2}\right)}$. Substituting them
into Eq. (\ref{w1}) and noting that $\rho^{A} \equiv
\mbox{Tr} _{B}{(\rho^{AB})}=\left(
\begin{array}{c}
\cos^{2}\left(\frac{\theta}{2}\right)~0~~~~~~~~~\\
0~~~~~~~~~~\sin^{2}\left(\frac{\theta}{2}\right)
\end{array}\right)$, we can get the density matrix $W$ in Eq. (\ref{w1}) as
\begin{widetext}
\begin{eqnarray}
W=\frac{1}{2}\left(\begin{array}{c}
1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\cos(\lambda t)-i\sin(\lambda t)\cos(\theta)\\
\cos(\lambda t)+i\sin(\lambda
t)\cos(\theta)~~1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\end{array}\right). \label{w2}
\end{eqnarray}
Thus, we have
\begin{eqnarray}
S_{e}=&-&\frac{1}{2}\left[1-\sqrt{\cos^{2}(\lambda
t)+\cos^{2}(\theta)\sin^{2}(\lambda
t)}\right]\log\left\{\frac{1}{2}\left[1-\sqrt{\cos^{2}(\lambda
t)+\cos^{2}(\theta)\sin^{2}(\lambda
t)}\right]\right\}\nonumber\\
&-&\frac{1}{2}\left[1+\sqrt{\cos^{2}(\lambda
t)+\cos^{2}(\theta)\sin^{2}(\lambda
t)}\right]\log\left\{\frac{1}{2}\left[1+\sqrt{\cos^{2}(\lambda
t)+\cos^{2}(\theta)\sin^{2}(\lambda t)}\right]\right\}. \label{se}
\end{eqnarray}
\end{widetext}
We can also directly calculate $S_{e}$ by using Eq. (\ref{dm}) and
Eq. (\ref{se1}). From Eq. (\ref{se}), we find that if the initial
state is a product one, i.e., $\theta=0$ or $\theta=\pi$, the
entropy exchange always equals zero.
The evolutions of the entropy exchange $S_{e}$ and the concurrence
$C(\rho^{AB'})$ are depicted in Fig. \ref{fig1}. We can see that the
entropy exchange exhibits the behavior \textsl{opposite} to that of
the concurrence in the quantum evolution. During the evolution
$\varepsilon^{A}$, the more information exchanged between $A$ and
``environment'' $C$, the more entanglement between $A$ and $B$ is
lost.
Now we discuss the coherent information $I_{e}$. By using Eq.
(\ref{dm}) we find that $\rho^{A'}= \mbox{Tr} _{B}{(\rho^{AB'})}=\left(
\begin{array}{c}
\cos^{2}\left(\frac{\theta}{2}\right)~0~~~~~~~~~\\
0~~~~~~~~~~\sin^{2}\left(\frac{\theta}{2}\right)
\end{array}\right)$, so from Eq. (\ref{i}) we can obtain $I_{e}$.
The evolutions of the coherent information $I_{e}$ and the
concurrence $C(\rho^{AB'})$ are depicted in Fig. \ref{fig2}. It can
be seen that $I_{e}$ exhibits the behavior very similar to that of
the concurrence in the quantum evolution, although their values are
not exactly consistent with each other at all moments.
\begin{figure}[htb]
\centering
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{5.ps}\\
{(a)$\;\theta=\pi/4$}
\end{minipage}%
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{6.ps}\\
{(b)$\;\theta=\pi/3$}
\end{minipage}
\vspace*{0.5cm}
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{7.ps}\\
{(c)$\;\theta=\pi/2$}
\end{minipage}%
\begin{minipage}[c]{0.5\columnwidth}
\centering
\includegraphics[width=1\columnwidth,
height=0.8\columnwidth]{8.ps}\\
{(d)$\;\theta=3\pi/4$}
\end{minipage}
\caption{Evolutions of the coherent information $I_{e}$ (solid line)
and the concurrence $C$ (dashed line). }
\label{fig2}
\end{figure}
The negative correlation between the entropy exchange and the
concurrence is a striking feature of the quantities. In this example
the range of $S_{e}$ is in $(0,1)$, where the left-hand side of the
Fano inequality (\ref{fano}) is a monotonic decreasing function of
the MEF $F_{e}$. This means that for a quantum operation with a
given $S_{e}$ there should be an upper bound of $F_{e}$. In Ref.
\cite{xiang} we have shown that $F_{e}$ exhibits the behavior
similar to that of the concurrence in the quantum evolution. So for
a quantum operation giving $S_{e}$ there is also an upper bound of
the concurrence. This only gives a rough correlation between the
concurrence and the entropy exchange. Owing to the simplicity of the
example we are able to obtain the analytical expressions of $F_{e}$
and $S_{e}$ and to illustrate the definite negative correlation
between them. In this sample the effect of the environment is
represented by only a single qubit ($C$). In Eq. (\ref{w}), we
assumed the initial state of qubit $C$ is a mixed one. For a more
complicated environment we may introduce an extra system, e.g., a
qubit $D$, in addition to qubit $C$. If this new qubit purifies the
initial state, then all the results obtained above are retained. In
fact, we can regard the system $AB$ and the environment $CD$ as a
new joint system and assume that the initial state of this joint
system is a pure state. After a quantum operation which represents
the interaction between subsystems $A$ and $C$, the final state of
the joint system must be a pure state too, so the entropy exchange
can also be seen as a measure of the entanglement between $AB$ and
$CD$. The information exchange between $A$ and $C$, which is the
result of the interaction, will cause the entanglement between $AB$
and $CD$, and decrease the entanglement between $A$ and $B$. This
results in the opposite behavior between the entropy exchange and
the concurrence in the quantum evolution. This also means that the
entanglement between $A$ and $B$ and the entanglement between $AB$
and $CD$ have negative correlation. Thus, the conclusion about the
negative correlation between the entropy exchange and the
concurrence may be extended to the case of environment having two
qubits but the initial state being purified. In other cases where
the environment includes more qubits but there are no correlations
between them, the effect of every qubit in the environment should be
similar to that of the single qubit investigated in this example.
The coherent information $I_{e}$ depends only on $\rho^{Q}$ and
$\varepsilon^{Q}$ and is used to measure the amount of quantum
information conveyed in the noisy channel. We imagine that the
initial state of system $Q$ is $\rho^{Q}$ which arises from the
entanglement between $Q$ and a reference system $R$. Now the goal of
Alice in $Q$ is to send the initial state $\rho^{Q}$ to Bob via a
quantum channel (which can be described by $\varepsilon^{Q}$) and
establish an entanglement between reference system $R$ and Bob's
output system $Q'$. The coherent information $I_{e}$ can express the
degree of achieving this aim. In above investigation we just model
the time evolution of quantum information transmitted via a noisy
quantum channel described by the interaction with a control qubit.
By comparing the coherent information $I_{e}$ and the concurrence,
we find that $I_{e}$ is indeed a good measure for the capacity of a
quantum channel to transmit the entanglement.
In summary, for an example modeling interaction with environment we
derive the analytic expressions of the entropy exchange and the
coherent information. From these we find that both the entropy
exchange and the coherent information have profound correlations
with the measure of the entanglement.
\vskip 0.5 cm
{\it Acknowledgments} This work was supported by the State Key
Programs for Basic Research of China (Grants No. 2005CB623605 and
No. 2006CB921803), and by National Foundation of Natural Science in
China Grant No. 10474033 and No. 60676056.
\bigskip
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,552 |
Walt Whitman High Wins Five Cappie Awards
Tech skills triumph
Sets, Brian Clarkson, Matthew Lewis, and Hailey Laroe, Walt Whitman High School, "Frankenstein." Photo by Steve Hibbard.
By Bonnie Hobbs
Potomac — Walt Whitman High won five starry statuettes for technical excellence at Sunday night's 13th annual Cappie Awards at The Kennedy Center in Washington, D.C. It received the honors for Stage Crew, Sound, Sets, Lighting, and Special Effects and Technology for its production of "Frankenstein."
Senior Brian Clarkson accepted the Cappie for Special Effects and Technology. "It feels amazing," he said. "I was nervous going onstage, though; I'm normally behind the scenes. But this award means that all our hard work paid off."
Chelsea Cook, Homeschool ITS, of Burke won the Returning Critic Award.
Clarkson said he and his team of Jonathan Kluger and Nikolas Allen "incorporated everything from dry-ice fog to small, flash-pot sparkers on stage to produce the mood of the scene, build suspense and bring everything to life." Following graduation, Clarkson plans to study aviation at Jacksonville University in Florida to someday become a pilot.
Alex Allen (Nikolas's twin), Lydia Carroll and Lindsay Worthington won the Sound award. "I'm surprised and overjoyed at the same time," said Alex. "We weren't expecting this."
Carroll called their victory incredible. "I've been in this field four years, and it's so unreal," she said. "We put so much blood, sweat and tears and hard work into it. Alex and I mixed the effects and ran the microphones, and Lindsay put together the soundtrack."
Representing the Sets award, junior Matthew Lewis said, "It's amazing. Our production process was so compressed for this show that we were all surprised at how fast we put it together. We rebuilt our set three times in five weeks to get it right."
But as the set designer and master carpenter, he said the final product was worth it. "It was impressive," said Lewis. "It had a lot of moving portions, including parts in Frankenstein's lab that were entirely moved by hand by the stage crew."
Juniors Nikolas Allen and Andrew Elman captured the Lighting Cappie. "It's really exciting," said Elman.
Added Allen: "We worked really hard — especially during 'Hell Week,' the week before the show — and we had a great lighting team."
Accepting the Stage Crew award were juniors James London and Daniel Levine. "I'm proud of the tech crew that worked so closely and so well with us," said London. Levine said they were lucky to have London as their stage manager because he was such a good leader.
"The tech crew students worked so hard on this show," added Levine. "And it's really touching that the Cappies puts such an emphasis on the hard work that goes on backstage."
Overall, Westfield High won the most Cappies, garnering 10, including Best Musical, for "Crazy for You." The Best Play winner, McLean High, also took home five awards, including Lead Actor and Lead Actress in a Play, for its production of "A View from the Bridge." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,264 |
The 1884 Dakota Apartments - 1 West 72nd Street
In 1992 nearly a century of black grime was removed from the building, exposing Hardenbergh's warm palette of brick and stone. photo by Ajay Suresh
Although it was inventor and actor Isaac Merritt Singer who founded the Singer Sewing Machine Company; it was Edward Cabot Clark who made it a success. Clark had been Singer's attorney since 1848 and the two became business partners. A marketing genius, Clark's innovative ideas--like accepting trade-ins for newer models--made the Singer Company an enormous success and the partners millionaires.
Edward Clark diversified into real estate development and quickly turned his attention to the rocky, mostly undeveloped Upper West Side. He was outspoken in his intentions to make the West Side as affluent as the East. He encouraged landowners to work together, mutually investing in property, and issuing restrictive covenants on construction.
In 1880 Clark embarked on an ambitious project—the erection of a first-class apartment building that would engulf the blockfront of Eighth Avenue (later Central Park West) between 72nd and 73rd Streets. His speculation was both aggressive and risky. Years later The New York Times would remind its readers that the area "was in the heart of a squatter's shanty district, where goats and pigs were more frequently encountered than carriages in the muddy streets."
Architect Henry Janeway Hardenbergh's plans, filed on October 1, 1880, called for an eight-story "Dorchester stone and brick Family Hotel" with an estimated cost of $1 million (more than 24 times that much in today's dollars). Clark christened his projected building The Dakota. Manhattan lore is fond of saying that Clark's friends chided him that it was so far away from the established city that it could be in the Dakota Territory. But in fact, the name was almost assuredly merely a product of Clark's fascination with the West.
Clark was faced with the challenge of attracting moneyed residents to an apartment building at a time when multifamily living was considered middle-class at best. And so, his apartments would offer everything found in an upscale private home. The ceiling heights ranged from 15.5 feet on the first floor to 12 feet at the topmost. No two of the scores of fireplaces were identical, and imposing scale was emphasized throughout the building. Some drawing rooms were 20 by 40 feet, and the parlors, libraries and dining rooms were sumptuous. Floors were inlaid with cherry, oak and mahogany. The Manufacturer and Builder reported that the apartments would have "from five to twenty rooms in each; some are supplied with kitchens, and others have only dining-rooms. On the main floor, at the Eighth avenue and Seventy-second street corner, is to be a large restaurant, including a dining hall and café, with private dining-rooms connected."
Entrances are located on the four corners of the courtyard. At the southeast corner were the restaurant, private dining rooms and cafe. from the collection of the Library of Congress
The most lavish apartment was intended for Clark and his family. Its drawing room was the size of a ballroom—24 by 49 feet—with two massive crystal chandeliers and fireplaces at either end. It contained a total of 17 rooms and 17 fireplaces. The expensive details included silver-plated doorknobs and hinges.
Clark would never see his apartment completed. On October 14, 1882, Edward C. Clark died of malarial fever, two years before the end of construction. But his project forged ahead without him.
To maximize floor space in the apartments, Clark and Hardenbergh had eliminated most of the servants' rooms and relocated them to the top two floors, which they shared with the laundry and trunk storage rooms. The second floor held apartments for out-of-town guests so the need for guest bedrooms in the apartments was unnecessary, as well.
Cast iron staircases with marble treads were deemed fireproof. photo by Fred R. Conrad, The New York Times
In its May 1882 issue The Manufacturer and Builder reported on the progress. "There will be seven hydraulic elevators, and the same number of stairways in iron and marble. The woodwork will be elaborately carved." Hardenbergh assured residents their privacy by placing the entrances within a gated courtyard. The main carriage gate--a 20-foot high arched entrance--opened onto 72nd Street. On the opposite end of the courtyard was a smaller "tradesmen's gate" where delivery wagons entered, trash and ashes were removed, and through which the servants came and went. (In the 20th century the tradesmen's gate received the romantic name "The Undertaker's Gate," despite that it was most likely never used for that purpose.)
The courtyard allowed residents to get in and out of their carriages in privacy. The Daily Graphic, September 10, 1884 (copyright expired)
On October 21, 1882 The Record & Guide described the style as being "in the main, a reminiscence of French Renaissance." Architectural critics have argued the point for more than a century. It has been described as German Renaissance, Chateauesque, Brewery Brick, and even "Victorian Kremlin." In fact, it is a melding of historic styles--Hardenbergh's own hybrid.
The Dakota, which the Record & Guide said was "the very earliest attempt on a large scale to attract fashion to the west side of the park," was completed in 1884. By then the cost had risen to "between $1,500,000 and $2,000,000," according to the journal, which added on February 7, 1885, "the rents range from $1,000 to $5,600."
For that, however, residents enjoyed upscale amenities. Maids arrived every day, as did porters who removed the ashes, and replaced coal and firewood for the stoves and fireplaces. Laundry was taken away and returned freshly cleaned and ironed. The main floor restaurant was in the style of an English baronial hall; but for those tenants who preferred to eat in, meals would be delivered and served by the restaurant staff. On the roof was a promenade with gazebos and pergolas and canopied sunshades. And for the more athletically inclined the adjoining lot to the side held private tennis courts for residents' use.
from The Sanitary Engineer, 1885 (copyright expired)
On October 27, 1884 the Daily Graphic entitled an article "A Description of One of the Most Perfect Apartment Houses in the World" and called The Dakota "the largest, most substantial, and most conveniently arranged apartment house of the sort in this country."
A glimpse of the rooftop promenade and a pergola can be seen in this 1965 photograph by the Historic American Buildings Survey. from the collection of the Library of Congress
Among the early residents were the family of Theodor Steinway, of Steinway & Sons; music publisher Gustav Shirmer and his wife; John Browning, the founder of the Upper West Side's exclusive Browning School for boys; and Edward Bascomb Harper, president and founder of the Mutual Reserve Fund Life Insurance Company. Others included John D. Adams of the chewing gum firm; and engineer John B. McDonald who built the first subway.
The completed building was surrounded by unpaved streets and vacant lots. from the collection of the Library of Congress
The New York Sun found the extravagance of some residents inexcusable. In an article in May 1890 it complained "A tenant with a five years' lease in the Dakota flats has spent $5,000 in decorating the walls of his apartment." (It was a large amount, equal to nearly $150,000 today.) But those who lived in The Dakota could well afford it.
It was no coincidence that Frederick G. Bourne, president of the Singer Sewing Machine Company, had an apartment here. He nearly lost his life on February 23, 1897 when he went for a ride in Central Park. His relaxing jaunt turned terrifying when his saddle horse was spooked and began galloping down the Park Driveway. Bourne was thrown to the pavement, breaking his arm. The Tribune reported "he was taken to his home in the Dakota flats…in a carriage."
After the turn of the century the laundry was moved from the top floor to a large boiler room under the tennis courts. On the afternoon of April 18, 1910 several employees were at work there, including 52-year old Ellen Cleary, who was working on a steam wringer. Suddenly the massive boiler exploded. The Evening Telegram reported "A huge piece of iron struck her in the leg and she fell to the floor unconscious." All the other employees ran from the room in panic; but when the danger seemed to have subsided, they rushed back.
"James Williams, an employee of the place, saw the woman was badly injured and made a tourniquet of a sheet, which he placed above the wound to stop the flow of blood." An ambulance arrived to find that "the Cleary woman's leg had been almost torn off and was hanging by shreds of flesh. He immediately amputated the limb." The force of the explosion had broken out several of the lower floor windows.
The tradition of the heads of the Singer Sewing Machine Company residing in The Dakota continued with Sir Douglas Alexander and his wife, the former Helen Hamilton Gillespie. Alexander was the sixth president of the firm which he had joined as a clerk in his native Canada in 1891. Upon his appointment to the Board of Directors in 1896 the couple moved to New York. He was created a baronet of Edgehill, near Stamford, Connecticut, on July 2, 1921 by King George V. Lady Alexander died in their Dakota apartment on March 19, 1923.
By 1959 the tenant list, while still highly affluent, had somewhat changed. Nan Robertson, writing in The New York Times on September 7, 1959, grouped the residents into three categories: "the diplomatic corps, upper-echelon show business and publishing." Included in the diplomatic contingent were the ambassadors to the United States of the Netherlands, Portugal, Finland and the former Ambassador from the Soviet Union. "Theatrical tenants, to name a few," said the article, "are Boris Karloff, Eric Portman, Judy Holliday, Jose Ferrer and his wife, Rosemary Clooney, Zachary Scott and his wife, Ruth Ford, Jo Mielziner, the set designer, and Sidney Kingsley, the playwright." C. D. Jackson, a top executive of Time, Inc. occupied the 17-room Edward C. Clark apartment on the sixth floor.
The Dakota still maintained a staff of 52, described by Robertson as "like wondrous fossils from the Age of Gracious Living." And it was still owned by the Clark family. One resident said "You never saw a building so superbly maintained. The bronze is petted, the mahogany oiled, the brass rubbed, the floors waxed." By now the former warren of servants' rooms on the eight and ninth floors were rented "to a chosen few tenants for $25 and $30 a month."
With motion picture stars inside, The Dakota became a film celebrity in its own right in 1968 with it served as the location of Roman Polanski's psychological horror film Rosemary's Baby.
photo by Half Sigma
In 1973 singer John Lennon and his wife, Yoko Ono, moved into an apartment, adding their names to those of other famous residents like Leonard Bernstein, Roberta Flack and Lauren Bacall. Two years later, on January 26, 1975 a catty journalist suggested that the two had split up, writing in a Twin Falls, Idaho newspaper "Yoko still lives in their expensive New York City Dakota Apartment and drives around town in the Lennon limo. John is hanging out with a swinging black dancer on Manhattan's West Side."
Seven years later the couple had acquired five apartments consisting of 26 rooms, plus a ground-floor office. On the night of December 8, 1980, the Lennons left the building headed to a recording session. A fan, Mark Chapman, approached John and asked him to autograph a copy of "Double Fantasy," Lennon's latest album. He did so, writing "John Lennon, 1980." Several hours later the Lennons returned home. John stepped back through the gate to the crowd of fans to sign autographs. Chapman was still there and he emptied his .38-calibre pistol into Lennon's back and left arm. The former Beatle was pronounced dead upon arrival at the hospital.
Many of the 1884 interior details remain throughout. photo via Brown Harris Stevens
Today The Dakota is regarded as America's second most famous address--the first being 1600 Pennsylvania Avenue. While almost ever other Victorian apartment house fell from fashion or, more often, was demolished, The Dakota never lost its upscale reputation. And, also unlike most, its interiors are for the most part secured. Residents who wish to modernize their apartments are required to store any architectural elements--like mantels or woodwork--so they can be reinstalled later.
Posted by Tom Miller at 12:24 PM
Labels: central park west, henry j. hardenbergh, upper west side, west 72nd street
Architect Henry Janeway Hardenbergh's plans, filed on October 1, 1800. I believe you meant to say October 1, 1880.
Andrew Porter September 22, 2020 at 10:22 AM
Wonderful history and details I didn't know. Thanks!
Marc Sell September 24, 2020 at 7:58 PM
Amazing to hear they require preservation of the interior elements removed during any shortsighted renovation so the next buyer can undo the foolish improvements done by a prior owner.
The 1910 John M. Bowers House - 45 East 65th Street
Common Buildings With Uncommon Fire Escapes - 233-...
The Sadly Abused 1884 Nos. 254 and 256 West 88th S...
The Lost San Remo Hotel - Central Park West and 75...
The William Dolan House - 105 West 16th Street
An "Elegant Flathouse" - 42 Morton Street
The Charles C. Stillman Mansion - 9 East 67th Street
The Henry E. Montgomery House - 115 East 30th Street
The Lost Bethel African Methodist Episcopal Church...
The James B. Thomson House - 203 West 14th Street
The Chauncey S. Traux House - 7 East 67th Street
Wooden Relics -- 185 to 189 Ninth Avenue
The James Baldwin Residence -- 81 Horatio Street
The Wm. A. Nash House - 19 West 73rd Street
The Lost 1849 London Terrace - 23rd Street from 9t...
The Surviving Relic at 108 West 14th Street
The Arthur W. Popper House - 48 East 66th Street
The 1862 College of St. Francis Xavier Bldg - 39 W...
The 1846 Cornelius Ackerman House - 58 Horatio Street
The 1929 Master Building - 310-312 Riverside Drive
The Lost 1797 N. Y. State Prison - Christopher Str...
Robert Mook's 1869 Cast Iron 483-485 Broadway
A Stunning Transformation - 629 Park Avenue
The 1885 Make-Over of 30 Downing Street
H. & H. Brien's 1871 793 Sixth Avenue
The Dr. Wm. Holmes Stewart House - 222 West 79th S... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
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package com.lithium.mineraloil.selenium.elements;
import lombok.experimental.Delegate;
import org.apache.commons.lang3.StringUtils;
import org.openqa.selenium.By;
import java.util.ArrayList;
import java.util.List;
import java.util.stream.IntStream;
import static java.util.concurrent.TimeUnit.SECONDS;
public class ImageElement implements Element<ImageElement> {
@Delegate
private final ElementImpl<ImageElement> elementImpl;
ImageElement(Driver driver, By by) {
elementImpl = new ElementImpl(driver, this, by);
}
private ImageElement(Driver driver, By by, int index) {
elementImpl = new ElementImpl(driver, this, by, index);
}
public List<ImageElement> toList() {
List<ImageElement> elements = new ArrayList<>();
IntStream.range(0, locateElements().size()).forEach(index -> {
elements.add(new ImageElement(elementImpl.driver, elementImpl.by, index).withParent(getParentElement())
.withIframe(getIframeElement())
.withHover(getHoverElement())
.withAutoScrollIntoView(isAutoScrollIntoView()));
});
return elements;
}
public String getImageSource() {
Waiter.await().atMost(Waiter.INTERACT_WAIT_S, SECONDS).until(() -> StringUtils.isNotBlank(getAttribute("src")) || StringUtils.isNotBlank(getCssValue("background-image")));
if (StringUtils.isNotBlank(getAttribute("src"))) {
return getAttribute("src");
} else {
return getCssValue("background-image");
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,384 |
{"url":"http:\/\/www.mathemafrica.org\/?p=13590","text":"I have decided to start writing some posts here, and this is my first post. I would like to introduce trig substitution by presenting an example that you have seen before. Trig substitution is one of the techniques of integration, it\u2019s like u substitution, except that you use a trig function only.\n\nLet\u2019s get into the example already!\n\n$\\int_{-1}^{1} \\sqrt{1-x^2} dx$\n\nIf you equate the integrand to y (and get $x^2+y^2=1$, $y\\geq 0$), you should be able to see that this is the area of the upper half of a unit circle. The answer to this definite integral is therefore the area of the upper half of the unit circle (yes, the definite integral of f(x) from a to b gives you the net area between f(x) and the x-axis from x=a to x=b), is $\\frac{\\pi}{2}$.\n\nWe relied on the geometrical interpretation of the integral to solve the definite integral, but can we also show this algebraically?\n\nYes, mathematics is beautiful and does allow us to do that. Consider\u00a0the part of a unit circle that is on the\u00a0first quadrant (it may help to draw a diagram), if you draw a straight line from the origin to the circle at an angle of $\\theta$ and construct a triangle, you should see that hypotenuse is 1 (the radius of the unit circle), the adjacent and the opposite are x and y respectively, this makes $\\cos{\\theta}=x$, cool? If not cool, see the diagram\u00a0here\u00a0.\n\nIf we are going to make any trig substitution, it is natural to choose\u00a0$\\cos{\\theta}=x$ , (\u00a0$\\sin{\\theta}=x$ would also do the job, but lets stick to the natural one for now, it will get clear later). This substitution will make the radical disappear (this is one of the top reasons why we like trig substitution, you will see later on in the course)! Please stop reading and attempt the problem with the substitution $\\cos{\\theta}=x$, and see how far you get.\n\nNow that you have attempted the problem , let\u2019s get to the evaluation (the fun part).\n\n$\\int_{-1}^{1} \\sqrt{1-x^2} dx$\u00a0= $2\\int_{0}^{1} \\sqrt{1-x^2} dx$ \u00a0 \u00a0 \u00a0because the integrand is an even function.\n\nIf $x=\\cos{\\theta}$ then $dx = -sin{\\theta}d\\theta$ this should transform our integral to\n\n$-2\\int_{arccos(0)}^{arccos(1)} \\sqrt{1-(cos{\\theta})^2} \\sin{\\theta}d\\theta =-2\\int_{\\frac{\\pi}{2}}^{0} \\sqrt{1-(cos{\\theta})^2} \\sin{\\theta}d\\theta$ \u00a0,\n\nwe may switch the limits and introduce a negative, and get\u00a0\u00a0$2\\int_{0}^{\\frac{\\pi}{2}} \\sqrt{1-(cos{\\theta})^2} \\sin{\\theta}d\\theta$, \u00a0this simplifies to an integral we can work with,\u00a0$2\\int_{0}^{\\frac{\\pi}{2}} \\sin^2{\\theta}d\\theta$ .\n\nRecall that $\\sqrt{\\sin^2{\\theta}} = |\\sin{\\theta}|$ but we have dropped the absolute value signs because $\\sin{x} \\geq 0$ \u00a0 on \u00a0 $[0,\\frac{\\pi}{2}]$, I am confident that you will\u00a0be able to use the double angle formula to finish the question. You should find that the algebra confirms the geometry.\n\nAnd, there goes my first post! This was fun! \ud83d\ude00","date":"2020-05-30 05:26:31","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\": 35, \"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\": 0.9546084403991699, \"perplexity\": 234.29646122572228}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347407289.35\/warc\/CC-MAIN-20200530040743-20200530070743-00037.warc.gz\"}"} | null | null |
{"url":"https:\/\/brilliant.org\/problems\/all-i-need-is-a-friend\/","text":"# An algebra problem by vishwathiga jayasankar\n\nAlgebra Level 2\n\nHow many zeros are there in the following graph $$y = f(x)$$?\n\n\u00d7","date":"2018-07-20 22:30:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.42915695905685425, \"perplexity\": 4456.953498307663}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-30\/segments\/1531676591837.34\/warc\/CC-MAIN-20180720213434-20180720233434-00224.warc.gz\"}"} | null | null |
«Марсе́ль» () — французский телесериал с Жераром Депардьё в главной роли, созданный Дэном Франком. Сериал является первым шоу сервиса Netflix, произведённым во Франции. Премьера сериала состоялась 5 мая 2016 года; также первые два эпизода были показаны на телеканале TF1.
6 июня 2016 года Netflix продлил сериал на второй сезон, который вышел 23 февраля 2018 года. Сериал был закрыт после второго сезона.
Сюжет
Робер Таро (Жерар Депардьё) был мэром Марселя более двадцати лет. На очередных выборах у него появляется сильный соперник — бывший протеже Люка Баррес (Бенуа Мажимель).
В ролях
Жерар Депардьё — Робер Таро
Бенуа Мажимель — Люка Баррес
Жеральдин Пелас — Рашель Таро
Стефани Колияр — Жулия Таро
Надя Фаре — Ванесса д'Абранте
Производство
Первый сезон из восьми эпизодов был заказан 10 июля 2015 года; премьера состоялась 5 мая 2016 года. Съёмки второго сезона стартовали 18 апреля 2017 года.
Отзывы критиков
Примечания
Ссылки
Официальный сайт
Марсель (2 сезон) русский трейлер сериала
Телесериалы Франции 2016 года
Драматические телесериалы Франции
Телесериалы на французском языке
Оригинальные программы Netflix
Телесериалы, сюжет которых разворачивается во Франции | {
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El Nino Ventures Inc.
Management and Directors
Corporate Governance Policy
Charter of the Audit Committee
Murray Brook Project
Slide Presentation
AGM2021
Tel: 1.613.659.2773, 1.604.685.1870 or Toll free 1.800.667.1870
TSXV: ELN OTC Pink: ELNOF FSE: E7QP
Sedar
Opt-in to our distribution list to receive company news
El Nino Ventures amends press release of April 26, 2011
ELN News May 24 2011
May 24, 2011, Vancouver, Canada -- El Niño Ventures Inc. ("ELN" and the "Company") (TSX.V: ELN; Frankfurt: E7Q) wishes to announce that, further to its press release of April 26, 2011, the Company has granted, effective today, an aggregate 3,710,00 stock options, not 4,000,000 stock options as disclosed in the April 26th press release. The Company has granted these options to various directors, officers, employees and consultants of the Company at an exercise price of $0.17 per common share for a period of five years. The foregoing is subject to regulatory approval.
About El Nino Ventures
El Niño Ventures Inc. is an international exploration company, focused on exploring for Copper/Cobalt in the Democratic Republic of Congo ("DRC") and Lead, Zinc and Copper in New Brunswick, Canada.
In Canada, El Nino holds a 50% interest in an extensive base metal project located within the Bathurst mining camp in Bathurst, New Brunswick, where earlier drilling campaigns have been carried out on several historical deposits of lead, zinc and copper mineralization within the large claim block owned 50% ELN, 50% Xstrata Zinc.
El Niño subsequently entered into an option agreement with Votorantim Metals Canada Inc. and Xstrata Zinc Canada whereby Votorantim may earn a 50% interest in El Niño's landholdings by expending $10 million over 5 years and may further increase its interest in El Niño's landholdings to 70% by expending an additional $10 million over a further two years. (Please see release dated May 4, 2010,).
In February 2011, ELN announced that a $5 million exploration program has begun consisting of airborne and ground geophysics and will include a 10,000 metre drill program which is slated for commencement in the spring of 2011. (See press release dated February 23, 2011).
In January 2011, ELN announced that it has provided notice to Votorantim Metals Canada Inc. (Votorantim) to enter into an Option Agreement on the Murray Brook Massive Sulphide /Polymetallic Deposit, situated in the Bathurst Mining Camp in New Brunswick, Canada. (See press release dated January 20, 2011). Drilling has been initiated on this project.
El Nino's management is aggressively seeking to acquire additional projects on an International scale that meet our corporate objectives. This includes base and precious metal properties within Africa and North America.
El Nino has approximately $2.5 million in cash with no debt.
On behalf of the shareholders and board of directors of El Nino Ventures, I would like thank you for your ongoing support.
"Harry Barr"
Harry Barr, Chairman and Acting CEO
Corporate: Jay Oness -- jay@elninoventures.com
Investor Relations: Toll free 1.800.667.1870
2303 West 41st Avenue, Vancouve, B.C. V6M 2A3
Email: info@elninoventures.com
TSX Venture Exchange or its Regulation Services Provider (as that term is defined in the policies of the TSX Venture Exchange) accepts responsibility for the adequacy or accuracy of this release.
Note: this release contains forward-looking statements that involve risks and uncertainties. These statements may differ materially from actual future events or results and are based on current expectations or beliefs. For this purpose, statements of historical fact may be deemed to be forward-looking statements. In addition, forward-looking statements include statements in which the Company uses words such as "continue", "efforts", "expect", "believe", "anticipate", "confident", "intend", "strategy", "plan", "will", "estimate", "project", "goal", "target", "prospects", "optimistic" or similar expressions. These statements by their nature involve risks and uncertainties, and actual results may differ materially depending on a variety of important factors, including, among others, the Company's ability and continuation of efforts to timely and completely make available adequate current public information, additional or different regulatory and legal requirements and restrictions that may be imposed, and other factors as may be discussed in the documents filed by the Company on SEDAR (www.sedar.com), including the most recent reports that identify important risk factors that could cause actual results to differ from those contained in the forward-looking statements. The Company does not undertake any obligation to review or confirm analysts' expectations or estimates or to release publicly any revisions to any forward-looking statements to reflect events or circumstances after the date hereof or to reflect the occurrence of unanticipated events. Investors should not place undue reliance on forward-looking statements.
You can view the Next News Releases item: Tue Jul 12, 2011, El Niño Ventures Announces $1,000,000, 6650 Meter Drill Program at Murray Brook Massive Sulfide Deposit, New Brunswick in the Bathurst Mining Camp
You can view the Previous News Releases item: Tue May 17, 2011, El Nino Ventures Inc Announces Board Member Resignation
You can return to the main News Releases page, or press the Back button on your browser. | {
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Le barrage de Ludila est un barrage sur la rivière Jinsha (nom donné au cours supérieur du Yangzi Jiang), situé dans la province du Yunnan en Chine. Il est associé à une centrale hydroélectrique de , comprenant 6 turbines de chacune . Sa production électrique moyenne est estimée à .
Il s'agit d'un barrage-poids en béton compacté au rouleau (BCR). Il forme un lac de retenue d'un volume de .
Sa construction a débuté en 2006. Les premiers générateurs ont été mis en service en 2013, les derniers en . Le coût de construction total a atteint .
Le barrage a dû être vidé pour cause de malfaçon.
Cascade hydroélectrique du Jinsha moyen
Le barrage de Liyuan est le septième barrage d'une cascade hydroélectrique sur le Jinsha moyen, qui en comportera huit au total : Longpan, Liangjiaren, Liyuan, Ahai, Jinanqiao, , Ludila et Guanyinyan. Sur cette section de entre Shigu et Panzhihua, le fleuve Yangzi Jiang chute de , offrant un potentiel hydroélectrique considérable.
Notes et références
Articles connexes
Yangzi Jiang
Liste des barrages hydroélectriques les plus puissants
Hydroélectricité en Chine
Ludila
Ludila | {
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{"url":"http:\/\/homotopytypetheory.org\/2014\/02\/24\/composition-is-not-what-you-think-it-is-why-nearly-invertible-isnt\/","text":"## Composition is not what you think it is! Why \u201cnearly invertible\u201d isn\u2019t.\n\nA few months ago, Nicolai Kraus posted an interesting and surprising result: the truncation map |_| : \u2115 \u2192 \u2016\u2115\u2016 is nearly invertible. This post attempts to explain why \u201cnearly invertible\u201d is a misnomer.\n\nI, like many others, was very surprised by Nicolai\u2019s result. I doubted the result, tried to push the example through using setoids (the clunky younger sibling of higher inductive types), succeeded, and noted that the key step was, unsurprisingly, that the notion of \u201crespecting an equivalence relation\u201d for a dependent function involved transporting across an appropriate isomorphism of the target types. I accepted it, and added it to my toolbox of counterexamples to the idea that truncation hides information. It was surprising, but not particularly troubling; my toolbox had already contained the example that, for any fixed $x$ of any type, $\\sum_y (y = x)$ is contractible, even though $x = x$ might not be; hence erasure of contractible types results in full proof irrelevance, contradicting univalence. More precisely, if inhabitants of contractible types are judgmentally equal, then we can apply the second projection function to the judgmental equality (x; p) \u2261 (x; refl) and obtain p \u2261 refl for any proof p : x = x.\n\nOthers had more extreme reactions. This post made some people deeply uncomfortable. Mike Shulman became suspicious of judgmental equality, proposing that \u03b2-reduction be only propositional. When I brought this example up in my reading group last week, David Spivak called it a \u201chemorrhaging wound\u201d in our understanding of homotopy type theory; this example deeply violated his homotopical intuition, and really required a better explanation.\n\nWhat follows is my attempt to condense a four hour discussion with David on this topic. After much head-scratching, some Coq formalization, and a decent amount of back-and-forth, we believe that we pinpointed the confusion to the notion of composition, and didn\u2019t see any specific problems with judgmental equality or \u03b2-reduction.\n\nTo elucidate the underlying issues and confusion, I will present a variant of Nicolai\u2019s example with much simpler types. Rather than using the truncation of the natural numbers \u2016\u2115\u2016, I will use the truncation of the booleans \u2016Bool\u2016, which is just the interval. All code in this article is available on gist.\n\nWe construct a function out of the interval which sends zero to true and one to false, transporting across the negb (boolean negation) equivalence:\n\nDefinition Q : interval \u2192 Type\n:= interval_rectnd Type Bool Bool (path_universe negb).\nDefinition myst (x : interval) : Q x\n:= interval_rect Q true false ....\n\nThe ... in the definition of myst is an uninteresting path involving univalence, whose details are available in the corresponding code.\n\nThe corresponding Agda code would look something like\n\nQ : interval \u2192 Type\nQ zero = Bool\nQ one = Bool\nQ seg = ua \u00ac_\n\nmyst : (x : interval) \u2192 Q x\nmyst zero = true\nmyst one = false\nmyst seg = ...\n\nWe can now factor the identity map on Bool through this function and the inclusion i:\n\nDefinition i (x : Bool) : interval := if x then zero else one.\nDefinition id_factored_true : myst (i true) = true := idpath.\nDefinition id_factored_false : myst (i false) = false := idpath.\n\n(Note: If we had used \u2016Bool\u2016 rather than the interval, we would have had a slightly more complicated definition, but would have had judgmental factorization on any variable of type Bool, not just true and false.)\n\nNicolai expounds a lot more on the generality of this trick, and how it\u2019s surprising. My discussion with David took a different route, which I follow here. As a type theorist, I think in $\\Pi$s, in dependent functions; Nicolai\u2019s trick is surprising, and tells me that my intuitions about functions don\u2019t carry over well into type theory, but nothing more. As a category theorist, David thinks in morphisms of types; Nicolai\u2019s trick is deeply disturbing, because the truncation morphism is fundamentally not invertible, and if it\u2019s invertible (in any sense of the word), that\u2019s a big problem for homotopy type theory.\n\nLet\u2019s look more closely at the interface of these two pictures. It is a theorem of type theory (with functional extensionality) that there is an equivalence between dependent functions and sections of the first projection. The following two types are equivalent, for all $A$ and all $Q~:~A \\to \\texttt{Type}$:\n\n$\\displaystyle\\prod_{x : A} Q(x)\\quad\\simeq\\quad\\sum_{f : A \\to \\sum\\limits_{x : A} Q(x)} \\left(\\prod_{x : A} \\texttt{pr1}(f(x)) = x\\right)$\n\nSo what does myst look like on the fibration side of the picture?\n\nWe have the following pullback square, using 2 for Bool and I for the interval:\n\nThe composition myst_sig_i \u2261 myst_sig \u2218 i induces the section myst_pi_i corresponding to the \u03b2-reduced composite myst \u2218 i, which Nicolai called id-factored. (This is slightly disingenuous, because here (as in Nicolai\u2019s post), \u2218 refers to the dependent generalization of composition.) In Coq, we can define the following:\n\nDefinition myst_sig : interval \u2192 { x : interval & Q x }\n:= \u03bb x \u21d2 (x; myst x).\nDefinition myst_sig_i : Bool \u2192 { x : interval & Q x }\n:= \u03bb b \u21d2 myst_sig (i b).\nDefinition myst_pi_i : Bool \u2192 { x : Bool & Q (i x) }\n:= \u03bb b \u21d2 (b; myst (i b)).\n\nDavid confronted me with the following troubling facts: on the fibrational, $\\Pi$ as sections of $\\Sigma,$ side of the picture, we have myst_sig_i true = myst_sig_i false, but myst_pi_i true \u2260 myst_pi_i false. Furthermore, we can prove both the former equation and the latter equation in Coq! But, on the other side of the picture, the dependent function side, we want to identify these functions, not just propositionally (which would be bad enough), but judgementally!\n\nSo what went wrong? (Think about it before scrolling.)\n\nThose of you who were checking types carefully probably noticed that myst_sig_i and myst_pi_i have different codomains.\n\nThe reason they have different codomains is that we constructed myst_sig_i by composing morphisms in the fibrational picture, but we constructed myst_pi_i by composing functions on the dependent function side of the picture. Dependent function composition is not morphism composition, and involves the extra step of taking the morphism induced by the pullback; if we want to recover morphism composition, we must further compose with the top morphism in the pullback diagram:\n\nWe can also see this by shoving dependent function composition across the $\\Pi$-$\\Sigma$ equivalence, which I do here in Coq.\n\nWe have explained what the mistake was, but not why we made it in the first place. David came up with this diagram, which does not commute, expressing the mistake:\n\nType theorists typically think of dependent functions as a generalization of non-dependent functions. In sufficiently recent versions of Coq, \u2192 is literally defined as a $\\Pi$ type over a constant family. Category theorists think of $\\Pi$ types as a special case of morphisms with extra data; they are sections of the first projection of a $\\Sigma$. Non-dependent functions are (isomorphic to) morphisms in the category of types. Composition of non-dependent functions is composition of morphisms. But there is another embedding: all functions (dependent and non-dependent) can be realized as sections of first projections. And this embedding does not commute with the isomorphism between non-dependent functions and morphisms in the category of types. Saying, the identity (judgmentally) factors through dependent function composition with a particular non-dependent function, is very, very different from saying that the identity morphism factors through the corresponding morphism in the category of types.\n\nSo the issue, we think, is not with judgmental equality nor judgmental \u03b2-reduction. Rather, the issue is with confusing dependent function composition with morphism composition in the category of types, or, more generally, in confusing dependent functions with morphisms.\n\nAnd as for the fact that this means that truncation doesn\u2019t hide information, I say that we have much simpler examples to demonstrate this. When I proposed equality reflection for types with decidable equality, Nicolai presented me with the fact that $\\sum_{y : A} (y = x)$ is contractible, even when $A$ is not an hSet, which he discovered from Peter LeFanu Lumsdaine. Because we can take the second projection, we can obtain non-equal terms from equal equal terms. I would argue that the solution to this is not to reduce the judgmental equalities we have in our type-theory, but instead, as Vladimir Voevodsky proposes, make judgmental equalities a first class object of our proof assistant, so that we have both a reflected, non-fibrant, extensional, judgmental equality type a la NuPrl, and a fibrant, intensional, propositional equality type a la Coq and Agda. (I believe Dan Grayson has implemented a toy proof checker with both of these equality types.) I think that the question of what can be done when you hypothesize judgmental equalities is under-studied in homotopy type theory, and especially under-formalized. In particular, I\u2019d like to see an answer to the question of which propositional equalities can safely be made judgmental, without compromising univalence.\n\nThis entry was posted in Code, Foundations, Higher Inductive Types and tagged . Bookmark the permalink.\n\n### 13 Responses to Composition is not what you think it is! Why \u201cnearly invertible\u201d isn\u2019t.\n\n1. jessemckeown says:\n\n\u2026 guessing off the top of my head (so I may be wrong, as often enough\u2026 ), if one can hypothesize judgmental equalities, then one can talk about reduced suspensions\/joins\/pushouts, and talk directly about equivariance puzzles, and strictly equational theories\u2026 I would guess there should be really-and-truely no problem with defining simplicial types\u2026 it might be nice; but I\u2019ve had such a fun time just trying to figure out how to do without all of those, too!\n\n2. Mike Shulman says:\n\nFor what it\u2019s worth, Nicolai\u2019s trick made me more suspicious of judgmental equalities not because it violated my homotopical\/categorical intuition. In fact, it fit perfectly with my intuition, once I compiled it out in categorical language; I certainly wouldn\u2019t call it a hemorrhaging wound! Rather, I was just bothered that judgmental equality can \u201csweep a nontrivial transport under the rug\u201d, as I said in that comment.\n\n\u2022 Mike Shulman says:\n\nHaving now read your post more carefully, it doesn\u2019t reduce my suspicion of judgmental equalities any. You\u2019re absolutely right, of course, that dependent function composition is not just categorical composition but also involves a pullback. But I don\u2019t think that that really has much to do with the paradox, although it\u2019s certainly a necessary thing to understand before tackling the paradox. The paradox is that we have a function $i:2\\to I$, and a dependent function $\\mathsf{myst}$, such that for any $x:2$ we have $\\mathsf{myst}(i(x))\\equiv x$. Whatever dependent function composition means on the categorical side, the point is that we (naively) expect the element $i(x)$ to have forgotten the identity of $x$, whereas we can actually recover $x$ from it by applying the operation $\\mathsf{myst}$. And the reason that is possible, it seems to me, is because judgmental equality can hide what on the categorical level would be a transport across a nontrivial isomorphism.\n\nYour example of $\\sum_{y:A} (x=y)$ is nice to make a connection to, but it took me a few minutes to extract from it a paradox that looks the same as Nicolai\u2019s. Here\u2019s what I came up with: take $A=S^1$ and $x=\\mathsf{base}$. Then we have $i:\\mathbb{Z} \\to \\sum_{y:S^1}(\\mathsf{base}=y)$ defined by $i(n) = (\\mathsf{base},\\mathsf{loop}^n)$, and the codomain of $i$ is contractible. But $\\mathsf{pr}_2(i(n)) = \\mathsf{loop}^n$, from which we can extract $n$. Did you have something simpler in mind?\n\n\u2022 jessemckeown says:\n\nI\u2019m having difficulty figuring what you mean by \u201chide\u201d in saying \u201cjudgmental equality can hide what on the categorical level would be a transport across a nontrivial isomorphism\u201d, but let that wait; what I think is going on, in both Nikolai\u2019s example and your pr_2 example, is that the proof assistant is doing fewer computations than homotopical thinking would expect: the term you\u2019re giving *does* have type the universal cover of $\\mathbb{S}^1$, which universal cover *is* contractIBLE, but neither coq nor agda bother to apply the contraction\/extract a normal form in that type (which is actually the prudent thing to do when normal forms are not guaranteed). It just remembers the term itself untill there is a beta reduction to do \u2014 and this is sort-of what I meant last time by singing about cofibrations in every comment. The free space of the physical universe we live in seems to be contractible, at least at the level of detail we can discern, but we aren\u2019t surprised that we can remember where things in it are, relative to eachother.\n\nAnd so, while there doesn\u2019t seem to be a type to say this, the term you\u2019re giving *also* has the form $z\\in \\mathbb{Z} \\mapsto (0, f_0 \\in F_0)$ for $x : \\mathbb{S}^1 \\mapsto F_x : \\mathrm{Type}$ an appropriate dependent type. Because neither coq (nor agda) actually thinks \u201cthat\u2019s in a contractible type, let me contract it\u201d, we can do the violence of pretending that $\\mathrm{pr}_2$ is a map to $F_0$, rather than a dependent map.\n\nTo put it in Nikolai the magician\u2019s terms, \u201ca term of type $\\|\\mathbb{N}\\|_0$\u201d doesn\u2019t actually constitute mere evidence that I\u2019ve chosen a natural number! The only actual terms in $\\|\\mathbb{N}\\|_0$ are of the form $\\pi (n)$, and neither coq nor agda thinks \u201cthis is in a contractible type, let me contract it\u201d.\n\n\u2022 Mike Shulman says:\n\nI wouldn\u2019t focus too much on coq or agda; the paradox is a paradox with the theory, not just some implementation of it. I think I see your point that a homotopy theorist may expect all terms in a contractible type to get \u201cliterally\u201d identified somehow, but I don\u2019t think there\u2019s any sense in which such an identification could be regarded as a \u201ccomputation\u201d. For one thing, whether or not a given type is contractible is not decidable!\n\nAs some of us were just discussing in a github issue, a newcomer to type theory does have to get over the expectation that things s\/he is used to regarding as \u201cidentical\u201d are not judgmentally identical, hence not literally interchangeable in the theory. In other words, the \u201cequality\u201d of mathematics is propositional equality, not judgmental equality. And once you\u2019ve come to terms with that, I don\u2019t think there\u2019s any additional \u201ccomputation\u201d on terms of a contractible type that could be expected: any two such terms are already (propositionally) equal.\n\nFor what I mean by \u201chiding a nontrivial isomorphism\u201d, see my other comment.\n\n\u2022 Jason Gross says:\n\nI was originally thinking of $\\sum_{y:\\texttt{Type}}(y = \\texttt{Bool})$. I believe this type is isomorphic to the interval, and yields the same construction as what I did above. But your construction works too.\n\nEdit: More precisely, there a map $i : \\texttt{Bool} \\to \\sum_{y}(y = \\texttt{Bool})$ defined by $i(\\texttt{true}) = (\\texttt{Bool}; \\texttt{refl})$ and $i(\\texttt{false}) = (\\texttt{Bool}; \\texttt{ua\\ negb})$; we have , I believe, $\\texttt{transport\\ idmap\\ }\\texttt{pr}_2(i(b))\\ \\texttt{true} = b$.\n\n3. Thanks for posting this explanation, a clarification can only help. I am surprised and happy that my construction has triggered so many discussions. Ultimately, however, the paradox is just what paradoxes use to be: a counter-intuitive construction, but not in any sense a \u201cproblem\u201d that one has to do something about (maybe I have not made that clear enough in my original post). The core is, to say it in Mike\u2019s words (I cannot think of anything better), that we \u201ccan sweep a nontrivial transport under the rug\u201d, but I don\u2019t think that this has any bad consequences. It only says that we have to adjust our intuition to the theory (you argue in that direction if I understand correctly).\nThanks for the pointer to Dan\u2019s implementation, I was not aware of that. I agree with Jason and Jesse that we should try to figure out which judgmental equalities can safely be considered, and I am also thinking about this.\nOne small side remark:\n\n(Note: If we had used \u2016Bool\u2016 rather than the interval, we would have had a slightly more complicated definition, but would have had judgmental factorization on any variable of type Bool, not just true and false.)\n\nMartin has observed that the truncated version of bool can be given the same judgmental properties as the interval (see his Agda code), so there is really no actual difference.\n\n\u2022 Jason Gross says:\n\nThe problem is the other way; I do not think the interval can be given the judgmental properties of truncation (unless we have some kind of judgmental eta for the interval, or more commutation rules for pattern matching). In particular, I don\u2019t see how to define |_| for the interval in such a way that applying the interval eliminator to it reduces appropriately.\n\n\u2022 Ok, but then I don\u2019t understand why you need this direction here. I thought you should have used the truncation of bool, but instead, you used the interval and explained why that is justified; and I supported that justification.\n\n\u2022 Jason Gross says:\n\nI need that direction if I want judgmental factorization of the function, rather than just judgmental factorization on constructors. The purpose of the parenthetical note was to explain why I used the interval rather than \u2016Bool\u2016 (the types and proofs are a bit simpler), and to note that this resulted in slightly weaker judgmental properties (that the judgmental factorization only occurs on constructors (true and false) and not arbitrary variables).\n\nIf that didn\u2019t answer your question, I fear we may be talking past each other (or writing incomplete thoughts); I re-read your two sentences three or four times, and came to a different conclusion about what they said and how to respond each time.\n\n\u2022 Okay, thanks, now I see what you meant. (I just did not understand that you wanted to make everything work for the interval, rather than making it work for ||Bool|| and using the interval as a tool.)\n\n4. jessemckeown says:\n\nOh! I think I get now what you Mike are saying with \u201chiding\u201d a nontrivial isomorphism; the clunkier way I\u2019d phrase it is that we implicitly have a \u201cpair\u201d (x ; f) : { x : S1 & x = 0 } and another chosen identification _ : x = 0 because x happens to be litterally 0\u2026 you may well have said exactly that already. The fact that naive equivalences could be either adjointified or Joyalized (and that these have essentially the same fiber maps) was a case of a similar coincidence.\n\nI didn\u2019t ever mean that a proofchecker *should* collapse types we\u2019ve shown or supposed contractible; leaving it alone, I\u2019m sure, is really the right thing. The lesson, if you will, that I\u2019m drawing from this all is that a proofchecker is not a secure chanel for obfuscation.\n\n\u2022 Mike Shulman says:\n\nHmm, I\u2019m not saying you\u2019re wrong, but I don\u2019t see why that\u2019s what I\u2019m saying. (-:\n\nActually, on further reflection, maybe \u201chiding\u201d is the wrong word.","date":"2014-07-29 08:40:17","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\": 45, \"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\": 0.8286435604095459, \"perplexity\": 986.0910556990042}, \"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-2014-23\/segments\/1406510266894.52\/warc\/CC-MAIN-20140728011746-00132-ip-10-146-231-18.ec2.internal.warc.gz\"}"} | null | null |
Браян Літтл () — анлгійське ім'я та прізвище.
Відомі носії
Вільям Браян Літтл (1942–2000) — американський підриємець
Браян Літтл (футболіст) (1953) — ангілйський футболіст і тренер
Сторінки зі списками однофамільців-тезок | {
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Album Review: Of Legions – Face Value
Anthony Matthews - 16 February 2018 17 February 2018
Release Date: 16th February 2018
Label: Self Release
In theory, Of Legions represent a British take on the traditionally American dominated Hardcore genre. With a spike in popularity, thanks to bands like, Knocked Loose, Code Orange and fellow Brits Gallows, hardcore bands are in a place where they can grace Warped Tour as well as enjoy Grammy nominations. Stoke band Of Legions are the latest band to try and infuse energetic Hardcore Punk and slabs of heavy metal. On paper this is a winning combination, combining a British-Punk ethos to a well-established genre, with a dash of metal and deathcore influence added for special measure. All said, it adds for a winning combination, unfortunately, 'Face Value' doesn't lives up to what the band have set up for themselves, or the genre of which they are a part of.
My main grievance with this album, comes down to its disappointing recording and production, which is a shame; being a massive fan of the DIY underground scene as well as heavy music. I am fully aware of the chaotic, spur of the moment, emotional ethos surrounding hardcore punk, however, with the vast majority of songs having vocals and often other instruments following a seemingly different time signature to each other, it gets old fast. The off beat nature is particularly grinding when the band change time signatures at multiple points during a track which, with no pertaining themes, means it's easy to get lost within a song, thinking the track has skipped or even changed. Perhaps these were conscious song writing decisions, but aside from stand out track 'Suicidal Thoughts', the nine songs of 'Face Value' seem to merge into mess of blastbeats, fuzzy riffs and endlessly strained vocals. In regard to production, the vocals are far too high in the mix most of the time, leaving the important instruments to blend together, which as already mentioned leads to this forgettable album of blurred songs. However, the few times that the instrumentals are given their time to shine like the breakdown in 'La Familia' or on Deathcore dominated final track 'Wormfeeder' they really do come into their own and present a band with promising attributes.
It's this last point that makes the album so disappointing as the band is clearly able to create tracks and moments of chaos that truly work together (as oxymoronic as that sounds). Instead, Of Legions attempt to presents 'Face Value' as as a packing a 'serious blow to the senses' and in a way, I think they may be right but not in the way that they had hoped. However, despite my reservations, it would be good to keep an ear out for the band in the future, and I do hope that they could release a more well-rounded and professional record in the future.
Favourite Tracks: Wormfeeder, No Loyalty
Tagged British Hardcore, FACE VALUE, Hardcore, Heavy metal, of legions, UK Metal
Album Review: Barren Womb – Old Money / New Lows
Home Wrecked release new video and announce a new EP! | {
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{"url":"https:\/\/www.physicsoverflow.org\/23161\/bulk-boundary-cutoffs-in-ads-cft","text":"+ 2 like - 0 dislike\n878 views\n\nI'm studying the holographic entanglement entropy (HEE) in this paper (Ryu-Takayanagi, 2006). In section 6.3 they compute the HEE for a segment in a 2D CFT. To do so, they obtain the corresponding geodesic in the bulk (in the Poincar\u00e9 patch) and compute its length.\n\nI understand all that process, but I'm having some trouble when they introduce the cutoff. The metric diverges when $z\\to0$ so we introduce a cutoff $\\epsilon>0$, I understand that. But then they say\n\nSince $e^\\rho\\sim x^i\/z$ near the boundary, we find $z\\sim a$\n\nHere, $\\rho$ is the hiperbolic radial coordinate un the global coordinates for AdS,\n\n$$ds^2 = R^2(-\\cosh^2\\rho\\ d\\tau^2 + d\\rho^2 + \\sinh^2\\rho\\ d\\Omega^2)$$\n\n$x^i$ and $z$ are coordinates in the Poincar\u00e9 patch,\n\n$$ds^2 = \\frac{R^2}{z^2}(dz^2-dt^2+\\sum_i(dx^i)^2)$$\n\nAnd $a$ is the inverse of the UV cutoff of the CFT in the boundary, that is, the spacing between sites.\n\nI have two problems:\n\n1) First, I don't see why near the boundary $e^\\rho\\sim x^i\/z$. I made up the relations between both coordinate systems and I find more complicated relations than that (even setting $z\\sim0$).\n\n2) Even assuming the previous point, I don't understand why we obtain that relation between the CFT and the $z$ cutoff.\n\nThis post imported from StackExchange Physics at 2014-09-02 07:57 (UCT), posted by SE-user David Pravos\n1. To see why the relation has to hold, you have to acknowledge that it needs to transform the line elements you have written down into each other. One can see that this is true by taking the logarithm on both sides, which yields $$\\rho=\\log{x^i}-\\log{z}.$$ Taking the derivative of this expression and squaring it gives $\\mathrm{d}\\rho^2=\\mathrm{d}z^2\/z^2$, which clearly transforms between the terms in the metric covering the holographic direction.\n2. As is explained in section 6.1, at the cutoff position $\\rho_0$, which is close to the boundary, we have the relation $$\\exp{\\rho_0}\\sim \\frac{L}{a},$$ which implies $z\\sim a$.\n Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the \"link\" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)\u00a0\u00a0 Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\\varnothing$ in the following word:p$\\hbar$ysicsOve$\\varnothing$flowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.","date":"2018-09-19 12:53:22","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.8249680995941162, \"perplexity\": 607.439713037694}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-39\/segments\/1537267156224.9\/warc\/CC-MAIN-20180919122227-20180919142227-00406.warc.gz\"}"} | null | null |
Today we have the action packed wedding of Mimi and Thang for you.
Mimi & Thang started with traditional tea ceremonies at their respective parent's homes before having a garden ceremony with their family and friends at Boulevard Gardens Indooroopilly.
The weather was looking ominous for most of the morning but had thankfully held off during their garden ceremony. We even had a burst of sunshine just as Mimi started to walk down the aisle!
But the heavens opened up as soon as we started the location portraits. Thankfully I keep some great under cover locations handy for just such an occasion and we had heaps of (dry) fun! | {
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\section{Introduction}
Questions of equilibration and thermalization in isolated quantum
many-body systems have experienced an upsurge of interest both from
the theoretical and the experimental side over the last decades
\cite{polkovnikov2011, gogolin2016, dalessio2016}.
In this context, the eigenstate thermalization
hypothesis (ETH) has been established as a key concept to explain the
emergence of thermodynamic behavior, by assuming a certain matrix structure of
physical operators ${\cal O}$ in the eigenbasis of generic Hamiltonians
${\cal H}$ \cite{deutsch1991, srednicki1994, rigol2005}.
Specifically, let ${\cal O}_{mn} = \bra{m}{\cal O}\ket{n}$ denote the matrix
element of ${\cal O}$ within the eigenstates $\ket{m}$ and
$\ket{n}$ of ${\cal H}$, then the ETH ansatz reads
\cite{dalessio2016,srednicki1999}
\begin{equation}\label{Eq::ETH}
{\cal O}_{mn} =
O(\bar{E})\delta_{mn}+\Omega^{-\tfrac{1}{2}}(\bar{E})f(\bar{E},
\omega)r_ {mn}\ ,
\end{equation}
where $\omega= E_m - E_n$
is the difference between the eigenenergies $E_m$ and $E_n$ with mean
energy $\bar{E} =
(E_m + E_n)/2$, $O(\bar{E})$ and $f(\bar{E}, \omega)$ are smooth
functions of their arguments, and $\Omega(\bar{E})$ is the
density of states. Furthermore, the $r_{mn} = r_{nm}^\ast$ are
conventionally assumed to be \mbox{(pseudo-)}random Gaussian
variables with zero mean and unit variance. (For earlier works,
see also \cite{Feingold1986, Feingold1991}.)
While the ETH is an assumption and a formal proof is
absent, its validity (including the Gaussian distribution of the $r_{nm}$) has
been numerically confirmed for a variety of models and
observables
\cite{santos2010, beugeling2014, beugeling2015, kim2014, steinigeweg2013,
Mondaini2016, mondaini2017,
jansen2019, LeBlond2019}. Generally, the ETH is believed to hold for
nonintegrable
models and physical (for instance, spatially
local) observables.
In contrast, the ETH is violated in integrable systems due to their extensive
number of integrals of motion \cite{essler2016}, as well as in strongly
disordered models
which undergo a transition to a many-body localized phase in one dimension
\cite{nandkishore2015}. In these cases, the
off-diagonal matrix elements $r_{nm}$ deviate from the Gaussian
distribution \cite{LeBlond2019, Luitz2016}. In addition,
models exhibiting a weaker violation of the ETH, such as, e.g., models
featuring so-called
``quantum scars'', where rare less entangled states are embedded in an
otherwise
thermal spectrum, have recently attracted a
significant amount of interest (see, e.g., \cite{Shiraishi2017, Turner2018}).
While the formulation of the ETH in Eq.\ \eqref{Eq::ETH} is
conventional~\cite{dalessio2016}, it is to some degree incomplete with
regard to the statistical properties of the ${\mathcal O}_{mn}$. Specifically,
for a given ${\cal H}$ and ${\cal O}$, the matrix elements ${\cal O}_{mn}$ are
predetermined, and therefore the notion of \mbox{(pseudo-)}randomness of the
$r_{nm}$
needs to be carefully defined.
In the spirit of the Bohigas-Giannoni-Schmit conjecture
\cite{Bohigas1984}, we here advocate the strongest point of
view, that below a certain energy scale all statistical
properties of the
off-diagonal matrix elements would match those of a Gaussian random ensemble.
The central question of this paper is therefore to what
extent the matrix elements ${\cal O}_{mn}$ can be represented as {\it
independently} drawn
random numbers?
Clearly, all ${\cal O}_{mn}$ cannot be random in the
strict sense as they
are constrained by the fact that the observables have to obey various algebraic relations (e.g.\
${\mathcal O}^2= \mathbb{1}$ in case of ${\cal O}$ being a Pauli matrix acting
on an individual spin). Furthermore, correlations between the $r_{mn}$
are necessary to reproduce the growth of certain four-point
correlation functions in chaotic systems \cite{Foini2019, Chan2019, Murthy2019}.
Likewise, the consistency of relaxation dynamics in local systems also requires
the $r_{mn}$ to be correlated \cite{Dymarsky2018}.
We therefore arrive at the important conclusion that the onset
of random-matrix behavior has to be limited
to matrix elements ${\mathcal O}_{mn}$ within a certain energy window specified
by the relevant energy scale $\Delta E_{\rm RMT}$.
In this paper, we test the ETH in the case of a local spin operator in the
eigenbasis of the
paradigmatic spin-$1/2$ XXZ chain,
for which we break integrability by means of (i) an additional next-nearest
neighbor interaction or (ii) a single-site magnetic field in the center of the
chain. (See Refs.\ \cite{Brenes2020_1, Brenes2020_2, Pandey2020, Santos2020}
for related studies of the ETH and the emergence of quantum
chaos in these models.)
Going beyond the ``standard'' indicators of the ETH, we particularly
investigate the
existence of the
scale $\Delta E_{\rm RMT}$ below which random matrix theory (RMT) prevails.
To this end, we establish the eigenvalue spectrum of ${\cal O}$ as a sensitive
probe of the correlations between the ${\cal O}_{mn}$.
While the spectrum of the full spin operator includes only two eigenvalues
$\pm1/2$, we particularly focus on the spectrum of band submatrices at a
fixed energy
density $\bar E$ where the ${\cal O}_{mn}$ are restricted
to a narrow band $|E_n-E_m|\leq \omega_c$.
For such band submatrices, we demonstrate that the ${\cal O}_{mn}$ are in
convincing agreement
with conventional indicators of the ETH in the following sense:
(i) the diagonal matrix
elements form a ``smooth'' function of energy $O({\bar E})$, (ii) the
off-diagonal matrix
elements follow a Gaussian distribution with a variance $f^2(\bar{E},\omega)$
that depends smoothly
on the mean energy and
respective energy difference,
and
(iii) the ratio between the variances of diagonal and off-diagonal elements for
small
$\omega$ takes on the value predicted by RMT.
However, despite (i) - (iii) being satisfied, we find that the eigenvalues
of the band
submatrices for $\omega_c$ larger than a certain value $\Delta E_{\rm
RMT}$ still exhibit clear signatures of the original operator, implying
correlations between matrix elements.
At the same time, when the bandwidth is sufficiently decreased, the spectrum
takes on an approximately
semicircular shape, marking the transition where genuine random-matrix behavior
occurs.
\subsection{Outline and reader's guide}
While our main goal is to demonstrate the
existence of the scale $\Delta E_\text{RMT}$, this paper includes a
detailed discussion of standard indicators of the ETH extensively studied in
this context. A reader already familiar with numerical
studies of the ETH, including works \cite{dalessio2016, deutsch1991,
srednicki1994, rigol2005, srednicki1999, santos2010, beugeling2014,
beugeling2015, kim2014, steinigeweg2013,
Mondaini2016, mondaini2017,
jansen2019, LeBlond2019}, may go directly to the relevant sections concerned
with the
investigation of $\Delta E_\text{RMT}$. This paper is
structured as follows. In Sec.\ \ref{Sec::Setup}, we introduce
the models and observables and describe our approach to
study the ETH. In particular, the spectrum of band
submatrices as a probe for the onset of random-matrix behavior is discussed
in Sec.\ \ref{Sec::IndiRMT}. Our numerical results are then presented in Sec.\
\ref{Sec::Results}. Specifically, we present data for ``standard'' indicators
of the ETH in Sec.\ \ref{Sec::Standard}, while the main results
concerning the existence of the scale $\Delta
E_\text{RMT}$ are analyzed in Sec.\ \ref{Sec::EVs}. A summary and
discussion
is given in Sec.\ \ref{Sec::Summary}, where we put our findings
into context with previous studies of the ETH and outline future directions of
research.
\section{Setup}\label{Sec::Setup}
\subsection{Models and observable}
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig1.eps}
\caption{(Color online) Level-spacing distribution $P(s)$ of (a) ${\cal
H}_\text{XXZ}$, (b) ${\cal H}_1$, and (c) ${\cal H}_2$. The parameters are
chosen as $\Delta = 1.5$, $\Delta^\prime = 1.2$, $h_{L/2} = 1$, and $L = 18$.
Correct extraction of $P(s)$ requires unfolding of the
spectrum.}
\label{Fig1}
\end{figure}
In order to test the ETH ansatz \eqref{Eq::ETH}, we consider different
(integrable and nonintegrable) quantum spin chains. A convenient starting point
is provided by the
one-dimensional XXZ model with open boundary conditions,
\begin{equation}\label{Eq::XXZ}
{\cal H}_\text{XXZ} = \sum_{\ell = 1}^{L-1} S_\ell^x S_{\ell+1}^x + S_{\ell}^y
S_{\ell+1}^y + \Delta S_{\ell}^z S_{\ell+1}^z\ ,
\end{equation}
where $L$ denotes the number of lattice sites,
$S_\ell^{x,y,z}$ are spin-$1/2$ operators at site $\ell$, and $\Delta$ is an
anisotropy in the $z$ direction. (In the following, we set the anisotropy to
$\Delta = 1.5$.) While ${\cal H}_\text{XXZ}$ is integrable in
terms of the Bethe ansatz, we break integrability by
either an additional next-nearest neighbor interaction of strength~$\Delta'$
\cite{steinigeweg2013, Rigol2010, richter2018_3},
\begin{equation}\label{Eq::H1}
{\cal H}_{1} = {\cal H}_\text{XXZ} + \Delta^\prime \sum_{\ell = 1}^{L-2}
S_\ell^z S_{\ell+2}^z\ ,
\end{equation}
or by means of a single-site magnetic field $h_{L/2}$ in the center of the
chain \cite{Barisic2009, Brenes2020_1, Brenes2020_2, Pandey2020, Santos2020,
Santos2004},
\begin{equation}\label{Eq::H2}
{\cal H}_{2} = {\cal H}_\text{XXZ} + h_{L/2} S_{L/2}^z\ .
\end{equation}
Note that, although not written explicitly in Eqs.\
\eqref{Eq::XXZ}-\eqref{Eq::H2}, we furthermore always include a small magnetic
field at the
first
lattice site, $h_1S_1^z$ with $h_1 = 0.1$, which breaks the spin-flip and
reflection symmetry of the model.
While ${\cal H}_\text{XXZ}$ and
${\cal H}_{1,2}$ conserve the total magnetization $S^z = \sum_\ell S_\ell^z$,
all results presented in this paper are obtained for the largest symmetry
subspace which corresponds to $S^z = 0$ and has dimension
\begin{equation}
{\cal D} = \binom{L}{L/2}= \frac{L!}{(L/2)!(L/2)!}\ .
\end{equation}
For $L = 18$, which is the largest
system size we
can treat numerically, we have ${\cal D} = 48620$.
Moreover, our simulations are performed for a representative choice
of the integrability-breaking parameters, i.e., $\Delta^\prime = 1.2$ and
$h_{L/2} = 1$, for which both ${\cal H}_1$ and ${\cal H}_2$ are robustly
nonintegrable (see also Refs.\ \cite{steinigeweg2013, Santos2004,
Barisic2009, Rigol2010, richter2018_3} for other
parameter choices).
The transition from the integrable XXZ chain to the nonintegrable models ${\cal
H}_1$ and ${\cal H}_2$ can for instance be seen from the level-spacing
distribution
$P(s)$ which is shown in Fig.\ \ref{Fig1}. While the level spacings follows
the
Poisson distribution in the integrable case, $P(s)$ matches the
Wigner-Dyson distribution for ${\cal H}_{1,2}$. In this
context, let us note that the field $h_1$ at the
edge of the chain does not break integrability of
${\cal H}_\text{XXZ}$ \cite{Santos2004}, while the single impurity
$h_{L/2}$ in the center of the chain induces the onset of chaos
\cite{Barisic2009, Santos2004}.
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig2.eps}
\caption{(Color online) (a) The ETH ansatz \eqref{Eq::ETH} is studied for the
spin-$1/2$ operator $S_{L/2}^z$ written in
the eigenbasis of the respective Hamiltonian ${\cal
H}$. The oval shaded area indicates matrix elements around
a fixed value of ${\bar E}$ where the density of states is approximately
constant, while the smaller square-shaped shaded area
indicates a
submatrix in this energy window. (b) For
square-shaped submatrices with dimension ${\cal D}^\prime <
{\cal D}$, the
ratio $\Sigma^2(n,\mu)$ defined in Eq.\ \eqref{Eq::SigRat} between the
variances of diagonal and
off-diagonal
matrix elements is obtained for regions of size $\mu$ shifted along the
diagonal. Note that the matrix shown here comprises actual data for the example
of ${\cal H}_1$ and $L = 12$. (c) We introduce a cutoff frequency $\omega_c$,
where off-diagonal
matrix elements are set to zero,
${\cal O}_{mn} = 0$, if $|E_m - E_n| > \omega_c$, resulting in a band matrix
with relative bandwidth $W/{\cal D}^\prime$. We study how the
distribution of eigenvalues
$\lambda_1^{\omega_c},\dots,\lambda_{{\cal D}'}^{\omega_c}$ of the
submatrix evolves upon reducing $\omega_c$.}
\label{Fig2}
\end{figure}
For nonintegrable models such as ${\cal H}_{1,2}$, it is a general
expectation that the matrix elements of physical observables ${\cal O}$
will follow the eigenstate
thermalization hypothesis \cite{dalessio2016}.
In this paper, we test the ETH for the case of a local spin-$1/2$ operator
acting on
the
central lattice site of the chain,
\begin{equation}\label{Eq::Obs}
{\cal O} = S_{L/2}^z\ .
\end{equation}
Specifically, we employ full exact diagonalization to obtain the matrix
elements ${\cal
O}_{mn}$.
Note that the indices $m$ and $n$ always
refer to the eigenbasis of ${\cal H}$. The
${\cal O}_{mn}$ are real numbers for the chosen operator
and the symmetry subspace.
\subsection{Testing the ETH and the onset of
RMT}\label{Sec::TestETH}
In the following, we
introduce the quantities studied in this paper. An accompanying
sketch is provided in Fig.~\ref{Fig2}. A reader
familiar with the ``standard'' indicators of the ETH may directly
go to Sec.\ \ref{Sec::IndiRMT}.
\subsubsection{Indicators of diagonal ETH}
The ETH ansatz \eqref{Eq::ETH} consists of the
diagonal part and the off-diagonal part. The diagonal part of the ETH asserts
that the function $O(\bar{E})$ becomes ``smooth'' in
the thermodynamic limit $L \to \infty$. In particular, the eigenstate-to-eigenstate
fluctuations ${\cal O}_{mm} - {\cal O}_{m+1m+1}$ should rapidly decrease
with the system size $L$.
One way to test this statement is to study the variance
$\sigma^2_\text{d}(\bar{E})$ of the diagonal matrix elements,
\begin{equation}\label{Eq::VarDiag}
\sigma^2_\text{d}(\bar{E}) = \frac{1}{N_{\bar{E}}}
\sum_{m} [{\cal O}_{mm}]^2 -
\left(\frac{1}{N_{\bar{E}}}\sum_{m} {\cal O}_{mm}\right)^2\ ,
\end{equation}
where the sum runs over all $N_{\bar{E}}$ eigenstates $\ket{m}$ with
eigenenergies $E_m \in [\bar{E}-\Delta E/2,\bar{E}+\Delta E/2]$ in a
microcanonical
energy window around a fixed $\bar{E}$. For nonintegrable systems including
our cases, it has been found that $\sigma^2_\text{d}(\bar{E})$ decreases
exponentially with increasing $L$, while the scaling for integrable models is
polynomial see, e.g., \cite{dalessio2016, beugeling2014, steinigeweg2013,
alba2015}.
\subsubsection{Indicators of off-diagonal ETH}
Next, in order to test the off-diagonal part of the ETH, we consider
matrix elements
${\cal O}_{mn}$ in a (sufficiently narrow) energy window around a fixed
$\bar{E}$, where $\Omega(\bar{E})$ is approximately constant, which facilitates
the analysis of the $\omega$ dependence of $f(\bar{E},\omega)$
and of the distribution of the ${\cal O}_{mn}$, see Fig.\ \ref{Fig2}~(a).
A useful quantity in this
context is the average over matrix elements in a small $\omega$
interval, which we denote in this paper by an overline. For instance, the
average over $|{\cal O}_{mn}|^2$ in an interval of width
$\Delta \omega \ll \omega$ (with
fixed $\bar{E}$) is given by
\begin{equation}
\overline{|{\cal O}_{mn}|^2}(\omega) =
\frac{1}{N_\omega}\sum_{\substack{n,m \\ E_m-E_n \approx \omega}}
|{\cal O}_{mn}|^2\ ,
\end{equation}
where the sum runs over all $N_\omega$ matrix elements with
$E_m - E_n \in [\omega -\Delta\omega/2,\omega+\Delta \omega/2]$. Plotting
$\overline{|{\cal O}_{mn}|^2}(\omega)$ versus $\omega$ yields the function
$f^2(\bar{E},\omega)$, cf.\ Eq.\
\eqref{Eq::ETH}, except for an
overall prefactor \cite{LeBlond2019, Serbyn2017, Richter2019}.
Assuming the ${\cal O}_{mn}$ have zero mean, i.e.,
$\overline{{\cal O}_{mn}} = 0$, (which holds with a very high accuracy), we study
the following quantity recently introduced in Ref.\ \cite{LeBlond2019}, which is sensitive to the distribution of $r_{nm}$,
\begin{equation}\label{Eq::Gamma}
\Gamma(\omega) = \overline{|{\cal O}_{mn}|^2}/\overline{|{\cal O}_{mn}|}^2\ .
\end{equation}
When $\overline{{\cal O}_{mn}} = 0$, the nominator in Eq.\
\eqref{Eq::Gamma} coincides with the variance of the ${\cal O}_{mn}$ while the
denominator is the squared mean of the folded distribution.
In particular, if ${\cal O}_{mn}$ were to follow the Gaussian distribution,
$\Gamma(\omega) = \pi/2$. The value we find numerically in Sec.\
\ref{Sec::Results} is very close.
To further confirm that the distribution
$P({\cal O}_{mn})$ of
the ${\cal O}_{mn}$ is indeed
Gaussian, we plot the histogram of ${\cal O}_{mn}$ from narrow windows with
fixed $\bar{E}$ and $\omega$, see Fig.~\ref{Fig5} below.
Next, we consider square-shaped submatrices of ${\cal O}$ of
dimension
${\cal D}^\prime < {\cal D}$ around a fixed mean energy
$\bar{E}$.
In
Fig.\ \ref{Fig2}~(b), an example for such a submatrix comprising actual
numerical data is shown. As a further check that the ${\cal
O}_{mn}$ are normally distributed,
we calculate the ratio
$\Sigma^2(n,\mu)$ between the variances of diagonal and off-diagonal matrix
elements for eigenstates in (small) regions $[n-\mu/2,n+\mu/2]$ of width $\mu$
[cf.\ Fig.\
\ref{Fig2}~(b)],
\begin{equation}\label{Eq::SigRat}
\Sigma^2(n,\mu) = \frac{\sigma_\text{d}^2(n,\mu)}{\sigma_\text{od}^2(n,\mu)}\ .
\end{equation}
Here $\sigma_\text{d}^2(n,\mu)$ and $\sigma_\text{od}^2(n,\mu)$ are defined
analogously to the variance in Eq.\
\eqref{Eq::VarDiag}, see also \cite{Note} for details.
For an actual random matrix drawn from the Gaussian orthogonal ensemble
(GOE), $\Sigma^2_\text{GOE} = 2$. Agreement with the GOE was anticipated in
\cite{dalessio2016} and then verified numerically in, e.g., \cite{mondaini2017,
jansen2019, Dymarsky2019}.
Our results for $\Sigma^2(n,\mu)$ in Sec.\ \ref{Sec::Results} are also in
agreement with the GOE value.
\subsubsection{Indicators of correlations between off-diagonal matrix
elements}\label{Sec::IndiRMT}
While the indicators of ETH given in Eqs.\
\eqref{Eq::VarDiag} - \eqref{Eq::SigRat}
have
been studied before, this work particularly scrutinizes the presence of
correlations between the ${\cal O}_{mn}$. To this end, we
consider the
eigenvalue distribution of the submatrices with dimension ${\cal D}'<{\cal
D}$ around mean energy ${\bar E}$ [see Fig.\ \ref{Fig2}~(b)], and show that it
provides a much more sensitive probe of the statistical properties of the
${\cal O}_{mn}$.
For a full random matrix with all matrix elements being independent, the
eigenvalue distribution will follow the celebrated Wigner's semicircle
\cite{dalessio2016, Mehta2004}.
In contrast, if
there are
correlations
between the ${\cal O}_{mn}$, deviations from the semicircle shape should
emerge. Importantly, we find
that the eigenvalue spectrum unambiguously shows that the $r_{nm}$ can not be
represented as {\it independent} Gaussians variables, even though
all standard indicators of the ETH are fulfilled, see Sec.\ \ref{Sec::EVs}
below. We note that this finding is in accord with recent
theoretical arguments from Ref.\ \cite{Dymarsky2018}. In particular,
Ref.\ \cite{Dymarsky2018} showed that consistency with transport in a quantum
many-body system imposes
constraints on the matrix elements entering the ETH and requires them to be
correlated. The strongest constraint is provided by the slowest mode
probed by the operator ${\cal O}$. For instance, consider a system exhibiting
diffusive transport with ${\cal O}$ being coupled to the diffusive quantity
(such a scenario is realized in the present paper as ${\cal O} =
S_{L/2}^z$ and spin transport is presumably diffusive in the nonintegrable
models ${\cal H}_{1,2}$ \cite{Bertini2020}). In this case, the slowest Fourier
mode is expected to decay as $\propto e^{-t/\tau}$ with $\tau \propto L^2/D$
and $D$ being the diffusion constant. While this picture would suggest that the
${\cal O}_{mn}$ should become stuctureless and independent for frequencies
below $\tau^{-1} \propto L^{-2}$, Ref.\ \cite{Dymarsky2018} proved that the
scale $\Delta E_\text{RMT}$, below which genuine random-matrix may
occur, in fact has to be parametrically smaller, $\Delta E_\text{RMT} \lesssim
(1/\tau)/L\sim L^{-3}$. The bound $\Delta E_\text{RMT}
\lesssim
(1/\tau)/L$ with $\tau$ being the time scale of the
slowest mode applies to any
kind of transport. Therefore, in full generality, $\Delta
E_\text{RMT} \propto 1/L^{2}$ is the loosest possible bound in a local
system.
Studying the signatures discussed below, we
demonstrate in the present
work that the scale $\Delta E_\text{RMT}$ indeed exists. Moreover, while we do
not explicitely
address its scaling with $L$, we specifically show that $\Delta E_\text{RMT}$
is drastically smaller than the scales where ``standard'' indicators of the ETH
are already well fulfilled.
To identify the scale at which the transition to RMT behavior
occurs, we
analyze how the
eigenvalue distribution depends on the width $W$ of the band, see Fig.\
\ref{Fig2}~(c). Specifically, let $\omega_c$
denote some cutoff frequency. Then we define the new operator ${\cal
O}^{\omega_c}$ with matrix elements
\begin{equation}\label{Eq::BandMat}
\mathcal{O}_{mn}^{\omega_c} = \begin{cases}
{\cal O}_{mn}, &|E_m-E_n| < \omega_c \\
0, &\text{otherwise}
\end{cases}\ ,
\end{equation}
resulting in a band matrix with the relative bandwidth $W/{\cal D}^\prime$.
Band random matrices have been extensively used in physics to model quantum
systems and study their properties \cite{Casati1990,
Fyodorov1991, Kus1991, Fyodorov1996, Borgonovi2016, Dabelow2020}. Furthermore,
the largest eigenvalues of full (square) and band submatrices have been studied
in
\cite{Dymarsky2019,Dymarsky2018,Dymarsky2019_2} in connection with the
transition from integrability to chaos as well as relaxation dynamics and
thermalization.
However, to the best of our knowledge, the full eigenvalue distribution of
(band) submatrices of local operators has not been previously considered as
a quantity to characterize the presence of
correlations between the matrix elements ${\cal O}_{mn}$.
Provided all matrix elements are independent and
identically distributed (except for an overall amplitude which may depend
on $\omega$), the eigenvalue distribution of band random matrices is
expected to converge towards a semicircle for small $W/{\cal D}'$
\cite{Kus1991}, although there are
corrections at intermediate $W/{\cal
D}'$ and the detailed shape is more complicated \cite{Molchanov}, see
Appendix~\ref{App::RMT}.
In addition to {\it band} submatrices, we also consider the eigenvalue
distribution of {\it full} submatrices with varying dimension ${\cal
D}^\prime$ in Appendix \ref{App::Square}. One advantage of keeping ${\cal
D}^\prime$ fixed and varying $W$,
however, is that the number of eigenvalues remains unchanged and is
comparatively large. As shown in Appendix \ref{App::Square}, the
properties of the smaller full submatrices are in fact similar and
consistent with our findings for the band submatrices
\eqref{Eq::BandMat}.
Given the ordered eigenvalues $\lambda_\alpha^{\omega_c}$ obtained by
diagonalizing $ \mathcal{O}^{\omega_c}$ for the cutoff frequency
$\omega_c$, an important quantity characterizing ${\cal
O}^{\omega_c}$ is the mean ratio $\langle r_{\omega_c}
\rangle$ of adjacent level spacings,
\begin{equation}
\label{r}
\langle r_{\omega_c} \rangle= \frac{1}{N_r}\sum_\alpha
\frac{\text{min}\lbrace
\Delta_\alpha,\Delta_{\alpha+1} \rbrace}{\text{max}\lbrace
\Delta_\alpha,\Delta_{\alpha+1} \rbrace} \ ,
\end{equation}
where $\Delta_\alpha = |\lambda_{\alpha+1}^{\omega_c} -
\lambda_{\alpha}^{\omega_c}|$ denotes the gap between two adjacent eigenvalues
and the averaging is performed over a number (here $N_r \approx {\cal
D}^\prime/2$) of gaps around the center. For a
random matrix drawn from the GOE, one expects $
r_\text{GOE}\approx 0.53$,
while for uncorrelated Poisson distributed eigenvalues, one finds $
r_\text{Poisson}
\approx 0.39$ \cite{Oganesyan2007}.
In addition to $\langle r_{\omega_c} \rangle$, the central quantity in this
paper is the full eigenvalue distribution
$P_{\omega_c}(\lambda)$ of the band submatrix ${\cal O}^{\omega_c}$,
\begin{align}\label{Eq::Distri}
P_{\omega_c}(\lambda) &= \frac{1}{{\cal D}^\prime}\sum_{\alpha = 1}^{{\cal
D}^\prime}
\delta(\lambda-\lambda_{\alpha}^{\omega_c})\ ,
\end{align}
where $\delta(\cdot)$ denotes the delta function, and it is understood that
individual peaks are collected in small bins such that $P_{\omega_c}(\lambda)$
forms a ``continuous'' distribution.
Given the corrections to the semicircle
distribution for band random matrices with intermediate $W/D'$,
a particularly simple and effective scheme to test the randomness of ${\cal
O}^{\omega_c}$ is to compare the eigenvalue distribution $P_{\omega_c}(\lambda)$
with the eigenvalue distribution of the suitably randomized $\widetilde{{\cal
O}}^{\omega_c}$. For a similar comparison of the properties of
bare and sign-randomized matrices, see \cite{Cohen2001, Kottos2001}.
Specifically, $\widetilde{{\cal O}}^{\omega_c}$ is
constructed by assigning random signs to the individual
matrix elements ${\cal O}_{mn}^{\omega_c}$ (while keeping $\widetilde{{\cal
O}}^{\omega_c}$ hermitian),
\begin{equation}\label{Eq::TildeO}
\widetilde{{\cal O}}^{\omega_c}_{mn} = \begin{cases}
{\cal O}^{\omega_c}_{mn}\ , & 50\%\
\text{probability} \\
(-1){\cal O}^{\omega_c}_{mn}\ , & 50\%\
\text{probability}
\end{cases}\ .
\end{equation}
If the matrix elements ${\cal O}^{\omega_c}_{nm}$ were random, we expect that the
eigenvalue distribution would remain
unchanged under this
``sign randomization''. In contrast, if the matrix elements of ${\cal
O}^{\omega_c}$ are correlated, these correlations will be erased by
the randomization procedure and the eigenvalue distribution of the original and randomized matrices
will be different. In order to quantify the difference (and its
dependence on $\omega_c$) between
$P_{\omega_c}(\lambda)$ and the distribution
$\widetilde{P}_{\omega_c}(\lambda)$
of the randomized operator, we introduce
\begin{equation}
d_2(\omega_c) = \int_{-\infty}^{\infty} [P_{\omega_c}(\lambda) -
\widetilde{P}_{\omega_c}(\lambda)]^2\ \text{d}\lambda\ ,
\end{equation}
where $P_{\omega_c}(\lambda)$ and $\widetilde{P}_{\omega_c}(\lambda)$ should be
understood as the continuous distributions resulting from a binning
procedure [see below Eq.\ \eqref{Eq::Distri}].
If $d_2(\omega_c) \to 0$, both distributions are very similar, which will
be
interpreted as a further indication that the matrix elements ${\cal
O}_{mn}^{\omega_c}$ are randomly distributed.
\section{Results}\label{Sec::Results}
Let us now turn to our numerical results for the matrix structure of
$S_{L/2}^z$ in the eigenbasis of the two
nonintegrable models ${\cal H}_1$ and ${\cal H}_2$. The properties of
diagonal and off-diagonal matrix
elements are discussed in Secs.\ \ref{Sec::Diag} and
\ref{Sec::OffDiag}
respectively, while Sec.\ \ref{Sec::EVs} presents results for the eigenvalue
distribution of band submatrices. Additional results for the integrable
XXZ chain can be found in Appendix~\ref{App::Int}.
\subsection{``Standard'' indicators of the ETH}\label{Sec::Standard}
\subsubsection{Diagonal matrix elements}\label{Sec::Diag}
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig3.eps}
\caption{(Color online) Diagonal matrix elements of $S_{L/2}^z$ in the
eigenbasis of (a) ${\cal H}_1$ and (b) ${\cal H}_2$, for system sizes $L =
14,16,18$. The shaded area indicates the energy window $E_m/L \in
[-0.15,-0.05]$ which is used in the
following to further study the properties of off-diagonal matrix elements. For
the example of ${\cal H}_1$, the
inset in (a) shows that the variance $\sigma_\text{d}^2(\bar{E})$ of the
${\cal O}_{mm}$ in this window decreases exponentially with increasing
$L$.}
\label{Fig3}
\end{figure}
As a first step, we study the diagonal part of the ETH.
To this end, Figs.\ \ref{Fig3}~(a) and (b) show the matrix
elements ${\cal O}_{mm} = \bra{m} S_{L/2}^z\ket{m}$
as a function of the corresponding energy
density $E_m/L$ for ${\cal H}_{1,2}$ and different system
sizes $L = 14,16,18$.
For energy densities in the center of the
spectrum, we find that the ``cloud'' of matrix elements becomes narrower with
increasing $L$ \cite{steinigeweg2013, beugeling2014, Brenes2020_1}. This
finding is in good accord with the ETH prediction that the
${\cal O}_{mm}$ should form a ``smooth'' function of energy in the
thermodynamic
limit $L \to \infty$.
At the edges of the spectrum, the scaling with $L$ is
significantly slower. Especially for ${\cal
H}_1$ [Fig.\ \ref{Fig3}~(a)] and $E_m/L \gtrsim 0.2$, the ${\cal
O}_{mm}$ are found to fluctuate very strongly. This can be
understood as follows. The
eigenstates of ${\cal H}_1$ with the highest energies are
weakly dressed domain-wall states. Consider, for instance, the states
$\ket{n_1}
=
\ket{\uparrow \cdots \uparrow \downarrow \cdots \downarrow}$ and $\ket{n_2} =
\ket{\downarrow \cdots \downarrow \uparrow \cdots \uparrow}$ (note that
$\ket{n_1}$ and $\ket{n_2}$ are not exact eigenstates). While $\ket{n_1}$ and
$\ket{n_2}$ have almost the same energy, one finds that
$\bra{n_1}S_{L/2}^z\ket{n_1} \approx 1/2$ whereas $\bra{n_2}S_{L/2}^z\ket{n_2} \approx
-1/2$ such that ETH is not satisfied. We expect the range of energy densities
where the ETH applies to increase with $L$.
Given the distribution of the ${\cal O}_{mm}$, we
restrict ourselves in the following to eigenstates in an energy
window $E_m/L \in [-0.15,-0.05]$ which is close to the center of the
spectrum (shaded area in Fig.\ \ref{Fig3}). As
shown in the inset of Fig.\ \ref{Fig3}~(a),
the variance $\sigma_\text{d}^2(\bar{E})$ of the ${\cal O}_{mm}$ in this
window decays approximately
exponentially with $L$ (at least for the system sizes numerically available),
indicating that the diagonal part of the ETH is fulfilled.
\subsubsection{Off-diagonal matrix elements}\label{Sec::OffDiag}
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig4.eps}
\caption{(Color online) [(a),(b)] Running averages
$\overline{|{\cal O}_{mn}|^2}$ of matrix elements in the energy window
$\bar{E}/L
\in [-0.15,-0.05$], calculated for system sizes $L = 14,16,18$ and
frequency bins of width $\Delta \omega = 0.01$. [(c),(d)] Close-up of the
low-frequency regime using a bin width of $\Delta \omega = 5\times
10^{-4}$. Note that both the
horizonal and the vertical axis have been rescaled.
Panels (a) and (c) show results for ${\cal H}_1$, while (b) and
(d) show data for ${\cal H}_2$. The shaded area in panels (a) and (b) indicates
the $\omega$ range which is probed when considering a square-shaped
submatrix with eigenstates in an energy interval of width $\Delta E/L = 0.1$.}
\label{Fig4}
\end{figure}
Let us now analyze the properties of the off-diagonal matrix elements
${\cal O}_{mn} = \bra{m} S_{L/2}^z \ket{n}$.
In view of the previous results for the diagonal matrix elements in Fig.\
\ref{Fig1}, we focus on eigenstates with mean energy density
$\bar{E}/L \in [-0.15,-0.05]$ as said above.
For matrix elements in this window, running averages $\overline{|{\cal
O}_{mn}|^2}$ of their absolute squares
are shown in Figs.\ \ref{Fig4}~(a) and (b)
as a function of $\omega$ both for ${\cal H}_1$ and
${\cal H}_2$. The data are obtained for frequency intervals of width $\Delta
\omega = 10^{-2}$ and system sizes $L = 14,16,18$. Overall, the
situation is qualitatively similar for the two models ${\cal H}_{1,2}$. Namely,
$\overline{|{\cal
O}_{mn}|^2}$ decays comparatively slowly at low
frequencies, while a substantially quicker (presumably superexponential
\cite{Abanin2015, Avdoshkin2019}) decay
can be
found at higher $\omega$.
In Figs.\
\ref{Fig4}~(a) and (b) the values of $\overline{|{\cal
O}_{mn}|^2}$ for different $L$ form smooth curve which collapse on each
other when rescaled by the
respective Hilbert-space dimension ${\cal D}$. [The rescaling
by ${\cal D}$ accounts for the factor $\Omega^{-\tfrac{1}{2}}(\bar{E})$
in Eq.\ \eqref{Eq::ETH}.] Except for a
prefactor, these smooth curves correspond to the function $f^2(\bar{E},\omega)$
from the ETH ansatz~\eqref{Eq::ETH}.
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig5.eps}
\caption{(Color online) [(a),(b)] $\Gamma(\omega)$ for matrix elements in
the energy window
$\bar{E}/L \in [-0.15,-0.05$] and
system sizes $L = 14,16,18$. The dashed line indicates the value $\pi/2$ for a
Gaussian distribution. The shaded area indicates
the $\omega$ range which is probed when considering a square-shaped
submatrix with eigenstates in an energy interval of width $\Delta E/L = 0.1$.
[(c),(d)] Distribution $P({\cal O}_{mn})$ of off-diagonal
matrix elements for $L =
18$ and $\omega = 0.2,0.4,\dots,2$ (arrow). The data are
collected in
frequency bins $[\omega-\Delta \omega/2,\omega+\Delta \omega/2]$ with $\Delta
\omega = 0.002$. (a) and (c) show results for
${\cal H}_1$, while (b) and
(d) show data for ${\cal H}_2$.}
\label{Fig5}
\end{figure}
For a more detailed analysis of $\overline{|{\cal
O}_{mn}|^2}$, Figs.\ \ref{Fig4}~(c) and (d) show a close-up
of the low-frequency regime (note that the horizontal and the vertical
axis have been rescaled to account for possible finite-size
effects at such small $\omega$). For both ${\cal H}_1$ and ${\cal H}_2$, we
observe
that $\overline{|{\cal
O}_{mn}|^2}$ clearly approaches a nonzero value as $\omega \to 0$ with an
approximately constant plateau for small $\omega L^2$, where
the data collapse achieved by the $L^2$-rescaling indicates diffusive spin
dynamics
(see also the
discussion in Ref.\ \cite{Brenes2020_2}).
Next, in order to study the distribution of the ${\cal O}_{mn}$, Figs.\
\ref{Fig5}~(a) and (b) show the
frequency-dependent ratio
$\Gamma(\omega)$, defined in \ Eq.\ \eqref{Eq::Gamma}. For small
$\omega$, we find that $\Gamma(\omega)$ is close to the
Gaussian value $\pi/2$, while visible deviations appear at higher
frequencies. However, these
deviations decrease with the increasing system size $L$,
indicating that the ${\cal O}_{mn}$ follow a Gaussian distribution over a
wide range of
frequencies if $L$ is sufficiently large.
In addition, the full distribution $P({\cal O}_{mn})$ of the off-diagonal
matrix elements is shown in
Figs.\
\ref{Fig5}~(c) and (d) for system size $L = 18$ and
frequencies $\omega = 0.2,0.4,\dots,2$. For all curves shown, we find that
$P({\cal O}_{mn})$ is
indeed well described by the Gaussians with zero mean (see also Refs.\
\cite{beugeling2015, LeBlond2019, Luitz2016}). The
width of the Gaussians is found to decrease with increasing $\omega$, which is
consistent with the data for $\overline{|{\cal
O}_{mn}|^2}$ shown in Figs.\ \ref{Fig4}~(a) and (b).
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig6.eps}
\caption{(Color online) [(a),(b)] Ratio $\Sigma^2(n,\mu)$ between the
variances of diagonal and off-diagonal matrix elements for two different
square sizes $\mu = 100,1000$ and all embeddings $n \in [1+\mu/2,{\cal
D}'-\mu/2]$. The data are obtained for system size $L = 18$ and the dashed line
indicated the value $\Sigma_\text{GOE}^2= 2$ predicted from RMT. [(c),(d)]
Average value
$\overline{\Sigma^2(\mu)}$ versus $\mu$ for system sizes $L = 14,16,18$. Note
that for the largest system size $L = 18$, the maximum $\mu = 2\times 10^3$
shown here is still considerably smaller than the full submatrix dimension
${\cal D}^\prime \approx 1.3\times 10^4$.
Panels (a) and (c) show data for ${\cal H}_1$ while (b) and (d) show data for
${\cal H}_2$.}
\label{Fig6}
\end{figure}
Let us finally comment on the shaded gray area at low frequencies in Figs.\
\ref{Fig4}~(a), (b) and Figs.\ \ref{Fig5}~(a), (b). This area indicates the
frequency range
which is covered when considering a square-shaped submatrix in the interval
$\bar{E}/L \in [-0.15,-0.05]$, cf.\ Fig.\ \ref{Fig2}. Specifically,
since this interval has a width $\Delta E/L = 0.1$, the largest energy
difference for $L = 18$ is $\omega_\text{max} = 0.1 L = 1.8$.
Therefore, when studying the eigenvalue distribution of such a submatrix further
below, we are probing the region where $\overline{|{\cal
O}_{mn}|^2}$ varies comparatively slowly and $\Gamma(\omega) \approx \pi/2$.
To conclude the analysis of the off-diagonal matrix elements, Figs.\
\ref{Fig6}~(a) and (b) show the ratio $\Sigma^2(n,\mu)$ between the variances
of
diagonal and off-diagonal matrix elements. Specifically, the data are obtained
for $L = 18$ with two
different square sizes $\mu = 100,1000$ and all possible embeddings along the
diagonal of the submatrix with dimension ${\cal D}^\prime$. (Note that for the
chosen energy window, we have ${\cal D}^\prime \approx {\cal D}/4$.)
For small $\mu =
100$, we find that $\Sigma^2(n,\mu)$ fluctuates around the
GOE value $\Sigma_\text{GOE}^2 = 2$, both for ${\cal H}_1$ and ${\cal
H}_2$. Increasing the square size to $\mu =
1000$, we observe that the fluctuations of $\Sigma^2(n,\mu)$ are visibly
reduced. For the larger value of $\mu$, $\Sigma^2(n,\mu)$ is still rather
close to
$\Sigma_\text{GOE}^2$ for ${\cal
H}_1$, while clear deviations between
$\Sigma^2(n,\mu)$ and $\Sigma_\text{GOE}^2$ can be seen in the case of
${\cal H}_2$.
Figures \ref{Fig6}~(c) and (d) show
the averaged
value,
\begin{equation}
\overline{\Sigma^2(\mu)} = \frac{1}{{\cal D}'-\mu}\sum_{n=1+\mu/2}^{{\cal
D}'-\mu/2} \Sigma^2(n,\mu)\ ,
\end{equation}
calculated from all embeddings $n \in [1+\mu/2,{\cal
D}'-\mu/2]$.
We find that $\overline{\Sigma^2(\mu)} \approx \Sigma_\text{GOE}^2$ for small
$\mu$, while $\overline{\Sigma^2(\mu)}$ monotonously grows with increasing
$\mu$ (this growth is particularly pronounced in the case of ${\cal
H}_2$). This behavior of $\overline{\Sigma^2(\mu)}$ follows from
the $\omega$ dependence of
$\overline{|{\cal
O}_{mn}|^2}$ discussed in Fig.\ \ref{Fig4}. Since
$\overline{|{\cal
O}_{mn}|^2}$ decreases with increasing $\omega$, the variance
$\sigma_\text{od}^2(n,\mu)$ likewise decreases with increasing $\mu$, simply because matrix
elements at higher frequencies are included.
Comparing $\overline{\Sigma^2(\mu)}$ for different system sizes,
we find that $\overline{\Sigma^2(\mu)}$ remains closer to $\Sigma_\text{GOE}^2$
for a wider range of $\mu$ as $L$ increases (see also
\cite{jansen2019}).
Therefore in the thermodynamic limit $L \to \infty$ one can expect ${\cal
O}_{nm}$ to approach an actual random matrix drawn from the GOE, at least
for a finite region around the diagonal.
To summarize, in this subsection we considered different quantities
conventionally
considered as standard indicators of ETH.
The results presented in Figs.\ \ref{Fig3} - \ref{Fig6} confirm
that the matrix structure of the local spin-$1/2$ operator ${\cal O} =
S_{L/2}^z$
in the eigenbasis of the nonintegrable models ${\cal H}_{1,2}$ is
in good agreement with the ETH ansatz \eqref{Eq::ETH}, at least for the chosen energy
window close to the center of the spectrum.
Nevertheless, in the next subsection, we will show that the matrix elements
${\cal
O}_{mn}$ within this energy window can not be considered as fully
uncorrelated, i.e., the standard indicators in Figs.\ \ref{Fig3} -
\ref{Fig6} are not sufficient when it comes to the statistical properties of
the ${\cal
O}_{mn}$.
\subsection{Beyond ``standard'' indicators: Eigenvalue
distribution of band submatrices}\label{Sec::EVs}
We now turn to the eigenvalue distribution for the band
submatrices centered around $\bar{E}/L = -0.1$ with $\Delta E/L = 0.1$.
First we discuss the ratio of the adjacent level spacings
$\langle r_{\omega_c} \rangle$ defined in \eqref{r}, which is shown in Fig.\
\ref{Fig7} versus $W^2/{\cal D}^\prime$ [panels (a) and (b)] as well as
versus $\omega_c$ [panels (c) and (d)].
We find that the
behavior of $\langle
r_{\omega_c} \rangle$ is very similar for ${\cal H}_1$ and ${\cal H}_2$.
Specifically, over a wide range of $\omega_c$, $\langle r_{\omega_c} \rangle
\approx 0.53$ approximately matches the
GOE value, while the transition towards
the Poissonian value $\langle r_{\omega_c} \rangle \approx 0.39$ occurs when the
bandwidth becomes too narrow.
The crossover from $r_\text{GOE}$ to $r_\text{Poisson}$ can be understood from
the well-known fact that the eigenstates of a band random matrix with a
sufficiently small value of $W^2/D'$ are localized and the eigenvalues become
uncorrelated \cite{Fyodorov1991}.
In order to avoid localization effects while studying the eigenvalue
distribution $P_{\omega_c}(\lambda)$, we restrict our analysis to $\omega_c
\gtrsim 0.03$ (shaded area in Fig.\ \ref{Fig7}), such that $\langle
r_{\omega_c} \rangle \approx r_\text{GOE}$.
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig7.eps}
\caption{(Color online) Mean ratio $\langle r_{\omega_c} \rangle$ of adjacent
level spacing of the operator ${\cal O}^{\omega_c}$ versus [(a),(b)] the
scaling parameter $W^2/{\cal D}'$, and [(c),(d)] the cutoff frequency
$\omega_c$. Panels (a) and (c) show data for ${\cal H}_1$ while (b) and (d)
show data for ${\cal H}_2$. The data is obtained for system sizes $L = 16,
18$ and the dashed horizontal lines indicate the GOE value
$r_\text{GOE} \approx 0.53$ and the Poisson value $
r_\text{Poisson} \approx 0.39$. For our analysis of
$P_{\omega_c}(\lambda)$, we restrict ourselves to $\omega_c
\gtrsim 0.03$ [shaded area in (c) and (d)], such that $\langle
r_{\omega_c} \rangle \approx r_\text{GOE} $.}
\label{Fig7}
\end{figure}
In Fig.\ \ref{Fig8}, we show the full spectrum
$P_{\omega_c}(\lambda)$ for ${\cal H}_{1,2}$ with $L = 18$ and four
exemplary choices of the cutoff frequency $\omega_c$. Specifically, we have
chosen $\omega_c = 1.8$ (i.e.\ the full nonband submatrix), as well as $\omega_c
\approx 1$, $\omega_c \approx 0.4$,
and $\omega_c \approx 0.03$, which are all above the transition point of
$\langle r_{\omega_c} \rangle$.
In all cases, we compare the spectrum of the bare operator
${\cal O}^{\omega_c}$ to the distribution
$\widetilde{P}_{\omega_c}(\lambda)$ of the sign-randomized version
$\widetilde{{\cal O}}^{\omega_c}$, see Eq.\ \eqref{Eq::TildeO}.
As can be clearly seen in Figs.\ \ref{Fig8}~(a) and (b),
$P_{\omega_c}(\lambda)$ and $\widetilde{P}_{\omega_c}(\lambda)$
differ strongly for the largest $\omega_c$ considered. Specifically,
while $\widetilde{P}_{\omega_c}(\lambda)$ closely follows the semicircle
law appropriate for random matrices, $P_{\omega_c}(\lambda)$
still exhibits pronounced peaks at $\pm 1/2$, which is reminiscent to the
original spectrum of the
spin-$1/2$ operator.
This deviation between
$P_{\omega_c}(\lambda)$ and $\widetilde{P}_{\omega_c}(\lambda)$ illustrates
that the matrix elements ${\cal O}_{mn}$ of a small submatrix cannot
automatically be considered as independent
random
variables, notwithstanding all standard indicators of ETH being in agreement
with the Gaussian distribution. This is a main result of the present
paper.
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig8.eps}
\caption{(Color online) Eigenvalue distributions $P_{\omega_c}(\lambda)$ and
$\widetilde{P}_{\omega_c}(\lambda)$ of bare and sign-randomized
submatrices in the energy window $\bar{E}/L \in [-0.15,-0.05]$ for system size
$L = 18$. The cutoff frequencies are chosen as [(a),(b)] $\omega_c = 1.8$
(i.e.\ the full nonband
submatrix of dimension ${\cal D}' < {\cal D}$),
[(c),(d)] $\omega_c \approx 1$, [(e),(f)] $\omega_c \approx 0.4$, and
[(g),(h)] $\omega_c \approx 0.03$. For
comparison, the solid curves indicate a semicircle distribution. Left
column shows data for ${\cal H}_1$, while right column shows data for
${\cal H}_2$. The skewed distribution in the case of ${\cal H}_2$
can be explained by the diagonal matrix elements
${\cal O}_{mm}$ [see Fig.\ \ref{Fig3}~(b)] which have a mean that (i) is
nonzero within the energy window and (ii) grows with $E$, in contrast to the
case of ${\cal H}_1$, cf. Fig.\ \ref{Fig3}~(a).}
\label{Fig8}
\end{figure}
Lowering the cutoff frequency to $\omega_c \approx 1, 0.4$ and $\omega_c
\approx 0.03$
[see Figs.\ \ref{Fig8}~(c)-(h)], we find that the spectra of the
bare and the randomized submatrices become more and more similar. Especially
for
${\cal H}_1$, $P_{\omega_c}(\lambda)$ and
$\widetilde{P}_{\omega_c}(\lambda)$ are very similar for $\omega_c \approx 0.4$
and virtually indistinguishable from each
other for $\omega_c \approx 0.03$. Moreover, the bulk of the spectrum is
convincingly described by a
semicircular distribution (the width of the semicircle shrinks with $\omega_c$),
while small deviations from a perfect semicircle
can be
observed at the spectral edges. This similarity of
$\widetilde{P}_{\omega_c}(\lambda)$ and $P_{\omega_c}(\lambda)$ as well as
their
semicircular shape can be interpreted as an indication that the correlations
between the matrix
elements are significantly reduced for frequencies
around and below $\omega \lesssim \Delta E_{\rm RMT}\approx 0.4$, i.e., on
these
smaller scales the ${\cal
O}_{mn}$ can be represented as independent random variables.
This is another central result of the present work.
Let us emphasize that the full distribution
$P_{\omega_c}(\lambda)$ is sensitive to the RMT scale $\Delta E_{\rm RMT}$
while the mean gap ratio $\langle r_{\omega_c} \rangle$ takes on the GOE value
for
all $\omega_c$ considered in Fig.~\ref{Fig8}.
\begin{figure}[tb]
\centering
\includegraphics[width=\columnwidth]{Fig9.eps}
\caption{(Color online) $d_2(\omega_c)$ for (a) ${\cal H}_1$, and (b) ${\cal
H}_2$. System sizes are chosen as $L = 14,16,18$. The dashed vertical lines
indicate the approximate
location of $\Delta E_\text{RMT}$ below which random-matrix behavior occurs.}
\label{Fig9}
\end{figure}
Comparing properties of ${\cal H}_1$ and ${\cal H}_2$, we find that
$P_{\omega_c}(\lambda)$ and $\widetilde{P}_{\omega_c}(\lambda)$ still
differ visibly for $\omega_c \approx 0.4$ in the case of ${\cal H}_2$, see
Fig.\ \ref{Fig8}~(f), but become very similar for the smaller
$\omega_c \approx 0.03$, see Fig.\ \ref{Fig8}~(h). This is in accord with
Fig.\ \ref{Fig9} below, which suggests that
$\Delta
E_{\rm RMT} \approx 0.1$ is smaller in the case of ${\cal H}_2$.
While it certainly would be desirable to study the eigenvalue distribution
$P_{\omega_c}(\lambda)$ for even smaller values of ${\omega_c}$ in a controlled
manner, this is difficult to do numerically as the value of $W$ and the
relative
bandwidth size $W/{\cal D}'$ become too small. Likewise, if one instead
diagonalizes full nonband submatrices with smaller dimension ${\cal
D}^\prime$, see Appendix \ref{App::Square}, the number of eigenvalues becomes
significantly reduced, which complicates the analysis.
Finally, Figs.\ \ref{Fig9}~(c) and (d) show the difference $d_2(\omega_c)$
between the two distributions $P_{\omega_c}(\lambda)$ and
$\widetilde{P}_{\omega_c}(\lambda)$. Consistent with our previous observation
in Fig.\ \ref{Fig8}, we find that $d_2(\omega_c)$ decreases upon reducing
$\omega_c$. Moreover, the decrease is slower in the case of ${\cal H}_2$. The
minimum of $d_2(\omega_c)$ is reached around the values of $\omega_c$ which we
associate with $\Delta E_{\rm RMT}$ ($\Delta E_{\rm RMT} \approx 0.4$ in
case of ${\cal H}_1$ and $\Delta E_{\rm RMT} \approx 0.1$ in case of ${\cal
H}_2$), and $d_2(\omega_c)$ remains low for
smaller~$\omega_c$.
\section{Discussion}\label{Sec::Summary}
In this paper we have studied matrix elements of the spin-$1/2$ operator
${\cal O} = S_{L/2}^z$ in the eigenbasis of two nonintegrable
quantum spin chains. Specifically, we have considered the one-dimensional XXZ
model in the
presence of two different integrability-breaking perturbations: an
additional next-nearest neighbor interaction and a single-site magnetic field
in the center.
For these models and an energy window close to the center of the spectrum, we
have shown that the matrix elements of ${\cal O}$ are in good agreement with
the eigenstate thermalization hypothesis ansatz in the sense that (i) variance of
the diagonal matrix elements decreases exponentially with the increasing system
size, (ii) the off-diagonal matrix elements follow a Gaussian distribution with
a variance that depends smoothly on the energy difference $\omega$, and (iii)
the ratio between the variances of diagonal and off-diagonal matrix elements
approximately takes on the value predicted by random matrix theory.
Overall, our results are in full agreement with previous works
\cite{Brenes2020_1, Brenes2020_2, Pandey2020, Santos2020} and the conventional
expectation that for local operators and nonintegrable Hamiltonians
the ETH is satisfied.
The central question of this paper was to study to what extent
off-diagonal matrix elements ${\cal O}_{mn}$ can be treated as
independently drawn random variables. To this end, we have considered
submatrices around a fixed mean energy $\bar{E}$ and restricted the
${\cal O}_{mn}$ to lie inside a sufficiently narrow band $|E_n-E_m|\leq
\omega_c$. We have established the form of the full eigenvalue distribution to
be a sensitive
probe to correlations between matrix elements. By comparing
the eigenvalue distribution of the band submatrix with its
sign-randomized counterpart \eqref{Eq::TildeO},
we have shown that the ${\cal O}_{mn}$ cannot be considered as independently
distributed, even
on scales where ${\cal O}_{mn}$ follow a Gaussian distribution with a
variance that varies comparatively slowly with $\omega$, i.e., on the scales
where the ETH
function $f(\bar{E},\omega)$ is approximately constant.
Specifically, while the spectrum of the
sign-randomized matrix closely
followed the semicircle law, matching the theoretical expectation for a random
matrix, the
eigenvalue distribution of the original submatrix was found to exhibit
signatures
of the spin operator, implying
correlations between the matrix elements. When the cutoff frequency $\omega_c$
is sufficiently reduced, we have found that the
eigenvalue distribution of the original and the sign-randomized operator
become similar and well described by a semicircle.
The energy scale $\Delta E_{\rm RMT}$ when this transition occurs marks the
onset of validity of the random-matrix behavior.
It should be noted that many important results rooted in the ETH are not
sensitive to the statistics of the off-diagonal matrix elements ${\cal
O}_{mn}$. This includes the central argument that the ETH ensures
thermalization \cite{rigol2005, Rigol2012, dalessio2016}, which essentially
relies on the exponential smallness of the ${\cal O}_{mn}$.
At the same time, within the contemporary understanding of
ETH, it is often assumed that matrix elements posses additional statistical
properties
matching the GOE (or some other appropriate Gaussian ensemble), see
e.g.~\cite{beugeling2015,dalessio2016,Luitz2016,mondaini2017}.
In this work, we have
advocated that below a certain energy scale all statistical
properties of the
off-diagonal matrix elements would match
those of a Gaussian random matrix. We have provided numerical evidence that
this onset of random-matrix behavior takes place below a certain energy
scale $\Delta E_\text{RMT}$ for specific models and
observables. Our results suggest that for frequencies $\omega < \Delta
E_\text{RMT}$, the notion of \mbox{(pseudo-)}randomness of the $r_{mn}$
entering the
ETH can be interpreted in an even stricter sense.
At the same time, we have clearly seen that
the scale $\Delta E_\text{RMT}$, where this transition to genuine random-matrix
behavior occurs, is distinctly
smaller than the scales on which ``standard'' indicators of the ETH are
fulfilled.
Our work raises a number of straightforward questions. First, we note that our
numerical observation $\Delta E_{\rm
RMT} \ll E_\tau$ mirrors the analytical bound $\Delta E_{\rm RMT}
\lesssim E_\tau/L$ established in \cite{Dymarsky2018}, where
$E_\tau$
is defined as the width of the plateau of
$f(\bar{E},\omega)$ (note that $E_\tau$ is sometimes referred to as Thouless
energy
\cite{Serbyn2017}). A natural question would be to establish
the scaling of $\Delta E_{\rm RMT}$ with the system size $L$ and,
in particular, to investigate if $(\Delta E_{\rm RMT})^{-1}$ can be associated
with the time scale of late time chaos at which the dynamics of
various observables is captured by RMT \cite{Cotler2017, Cotler2019,
Moudgalya2019, Schiulaz2019}.
Another direction is to contrast the behavior in
chaotic systems with the integrable counterparts. We repeat the analysis of
section \ref{Sec::Results} for the integrable XXZ model in the Appendix
\ref{App::Int}. One particular observation to point out is that
off-diagonal matrix elements in the integrable case also can be regarded as
random and independent, although not Gaussian, below a certain
energy scale.
We leave for the future the question of better understanding this transition,
and the universal properties of ${\cal O}_{mn}$ in the integrable case.
Eventually, one avenue of research is to characterize the nature of the
correlations between off-diagonal matrix elements for $\omega > \Delta
E_\text{RMT}$, and to understand their potential impact on self-averaging
properties of the ${\cal O}_{mn}$ exploited in various works \cite{Richter2019,
Richter2020, Dabelow2020, Nation2019}.
At the same time, it would be interesting to study the connection between
universal properties of ${\cal O}_{mn}$ at small frequencies and transport,
which could be diffusive or ballistic \cite{Bertini2020}.
\subsection*{Acknowledgements}
We thank M. Bergfeld and M. Lamann for discussions and helpful comments on the
manuscript. This work has been funded by the Deutsche Forschungsgemeinschaft
(DFG) -
Grants No.\ 397107022 (GE 1657/3-1), No.\ 397067869 (STE
2243/3-1), No.\ 355031190 - within the DFG Research Unit FOR 2692.
A.\ D.\ acknowledges support of the Russian Science Foundation (Project No. 17-12-01587).
| {
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Posted on wow keren bisa menjadi ipnsirasi buat semua orang .bahwa kelemahan/kekurangan jangan dianggap sebagai kelemahan, tapi jadikan suatu kekuatan yang sangat luar biasa .salut semoga Mas Habibi bisa jadi motivator seperti Nick Vujicic Sang Motivator sukses kelas dunia yang Tanpa Kaki Dan Tangan.
no, they really dont go on sale BUT THEY SELL OUT FAST so I woudln't wait too long. Your best chance for a sale would be to get them from a place like macy's that offers you a discount to open a credit card- then put them on the card and you'll get like 20% off- which would be about 30-35 bucks. Remember though you wont get the discount if you run up the credit card bc of interest. E bay is another place you may find a small discount, but idk if it's worth the risk. I bought mine at dillards- and they are worth every cent of the $ 160 i spent on them.
zei kai grafei akoma autos?egrafe palia tis feyrails tou sto ram, apo otan efyge to diavaza me megalyteri eyxaristisi.Apla na toniso oti stin periptosi tou diafimisti n. dimou h fysiki epilogi leitourghse sosta kai den tha afhsei os ateknos kapoion apogono tou piso.
Happy Day After New Year and many more to all my Streeter friends. Sorry to hear about all the siskcens. My philosophy is have it early and get it over with for the year. Mark and I too had a very quiet New Years Eve. I made bacon wrapped scallops with a peach glaze and we had shrimp cocktails. Also, a bottle of champagne too. Needless to say I made it to see Pitbull sing my favorite song on New Year's Rockin' Eve and we turned in at 9:45p.m. It was a great night though. Hope everyone has a great happy healthy prosperous new year.
Hope everyone had a happy and safe New Year's Eve like Ralph, ours was low key as Dan and I are rcenveriog from respiratory infections and strep yuk! I hope all the Streeters and their families have a wonderful and healthy 2012 let's raise a glass to more Seeley memories in 2012!!!
Janis- I'll agree with better and beoldr. Can't think of anyone who wants to get bigger; taller maybe, not bigger. And there is a helluva lot of room for getting brighter!
Bullying is a common wrklpoace phenomenon. If a boss is a old hand and employess are new the boss bullies ( depending on his personality, experinces, values and upbringing), if the boss is new employees are old then the boss gets bullied, especially if he is under promotion and the juniors are permanant.In all other situations too group dynamics is always on. It is upon you to win support of some of the employees. Form a cliche in the legion and survive and earn your bread.
Good a1V I should cnirately pronounce, impressed with your web site. I had no trouble navigating through all tabs and related info ended up being truly easy to do to access. I recently found what I hoped for before you know it at all. Reasonably unusual. Is likely to appreciate it for those who add forums or something, site theme . a tones way for your customer to communicate. Nice task.. | {
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Hey everyone! We recorded this at CCLivingwater after the Wednesday night service. The guys were practicing for the outreach that they will do at the Coffee Depot on Thursday night. We had a good time messing around.
After Wednesday night service, the Joyce's (Segmon's family) invited many of us over their house for an evening dinner. It was incredible, they had lumpia, and empanadas (Philippino food) we thought that this was the main course. We found out that it was just the appetizer. The main course was Turkey, pancit, pork, chicken, rice, you name it, it was there. We had a blast! In the center picture is Segmon's sister Melissa, Dad Ben, and Mom Guiua.
We had a great time at CCLivingwater. Pastor Jerry gave a great message Wednesday night. Anytime we bring out the camera, the hams all want to get in the picture. What is cool about Livingwater is that after service, the young people jump on the instruments and start jamin for Jesus.
Today we had the opportunity to take a drive down the Coast to CC Costa Mesa and Hunnington Beach. In the center picture, this was taken in front of the entrance to Calvary Costa Mesa. Pastor Chuck a few months ago had this fountain installed in the courtyard. After we took this shot, we headed over to the bookstore and purchased some CD's. The picture up top, was taken at the Pier in Hunnington Beach. It was a cold afternoon and the surf has been high. Surprisingly, there were only a few surfers out there. It was Itsuki's first visit to the Southern California beaches.
Friday night the Youth group at CCLivingwater had their Christmas party at the Horne's house. They had such a blast. Like always, the gift exchange got the most laughs. As the youth look back on 2005, they have so many good memories. Praise God, next year will even be better.
Yesterday Itsuki Kudaka arrived safely from Okinawa. She will be with us for 2 weeks, spending time getting to know the Church family at Livingwater. She will also attend the CC Missions conference in Murrieta. It is such a blessing to have her here.
Thursday night we were blessed with the opportunity to head out to Bakersfield and visit with Pastor Gil and his family. After a time of fellowship at Gil's gamestor, we headed out to Delano and had a wonderful time of fellowship with the body. It was a blessing to see the beginnings of a new work in that area. Please continue to lift up Pastor Gil and the fellowship in Delano. We believe that this is just the beginning of great things in this area.
This is a great picture of the students at CCBC Jerusalem. For those of you who do not know, Rosie (center left) has been serving at the Bible College for about 2 years. Her mother and brothers attend CCLivingwater in California. It is such a blessing to see the students serving and loving the Lord there in Israel. Please continue to pray for everyone at CCBC. They will begin their next semester in early February. We love you guys.
We had a fun Friday afternoon. Segmon's sister (pictured in the center photo) works at Disneyland, but her last day was Saturday. Segmon hooked it up so when we arrived in California, we were able to take the family for the day. Everyone had a blast! It is cold in California, I am so glad that we took our coats. Because we arrived in California the day before, we tired out quick and called it a day, towards the early evening. Thank you again Joyce for blessing us, and may the Lord bless you as you move on to other things.
Hey everyone, this is Mike Langley in Pakistan. He emailed me the other day and said that things are going well, but he misses everyone back at home (Okinawa). Mike is in Pakistan helping with Relief efforts from the earthquake that hit a month ago. Pictured above is Mike refereeing a basketball game for the guys on one of thier free times away from work duty. Please continue to pray for Mike and all the servicemen and women who are serving oversees. Remember, many of them will be gone this Christmas season, and the best thing that we can do, is to lift them up before our Heavenly Father in Prayer. God bless all of you oversees and remember that we love you. Pastor Tommy and your church family.
Sunday mornings the Jr. Highers at Calvary Okinawa meet downstairs for thier own Sunday morning service. Pictured above is Vunder praying and Natsumi interprets for the Japanese speakers.
These are the latest pictures send from Nile in Italy. The guys had a great time visiting the land. They were able to attend some of the Calvarys in Rome. As you can see from Damien, no missions trip is complete with out trying some of the local food. That is one big burger Pastor Rick.
We are back in Okinawa, and the wheels get turning. Thursday we had M.E.L.T. (my english lunch time) and Tim Newell resumes duties in ministry. Tim and Ayu are back from thier honeymoon and serving the Lord together.
Monday we were also invited to minister at Central Philippines University. Rob was able to lead in worship and we taught the students on "the renewed life in Christ". It was a great time, Rob also met some skaters on the campus and fit right in. Also, on the campus we were invited to visit thier butterfly sanctuary on the campus. If you would like to see more picts, click onto http://photos.yahoo.com/philippinestrip2005 We put up a lot more pictures. | {
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