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Joseph Redlhamer SJ (* 20. Oktober 1713 in Erlakloster; † 9. Juli 1761 in Wien; auch Redlhammer) war ein österreichischer Jesuit, römisch-katholischer Theologe, Philosoph und Hochschullehrer.
Leben
Redlhamer trat mit 18 Jahren in den Jesuiten-Orden ein. Er studierte, wurde dann Doktor der Philosophie und Theologie. Zunächst bekleidete er eine Stellung als Prediger in Großwardein, lehrte dann in Wien, Linz und Graz unter anderem Ethik. 1754 wurde der für seine Lehre beliebte und geachtete Redlhamer ordentlicher Professor und Examinator an der theologischen Fakultät der Universität Wien. Er starb während einer Vorlesung.
Werke (Auswahl)
Philosophia rationalis, Wien 1752 und 1755.
Philosophia naturalis seu Metaphysica, Ontologiam, Cosmologiam, Psychologiam et Theologiam naturalem complectens. II Tomi, Wien 1753, Warschau 1761.
Philosophia naturalis seu Physica generalis et particularis. 2 Bände, Wien 1755.
Tractatus de Deo uno et trino, Wien 1756.
De Incarnatione Verbi divini, Wien 1757.
De gratia Christi, 1758.
De virtutibus theologicis, 1759.
Literatur
Johann Georg Meusel: Lexikon der vom Jahr 1750 - 1800 verstorbenen teutschen Schriftsteller, Band 11, Fleischer, Leipzig 1813, S. 84.
Weblinks
Römisch-katholischer Theologe (18. Jahrhundert)
Philosoph (18. Jahrhundert)
Jesuit
Hochschullehrer (Universität Wien)
Person (Habsburgermonarchie vor 1804)
Geboren 1713
Gestorben 1761
Mann
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 4,983
|
Category: Building Construction
View Categories / Building Construction
Building in Cob, Pise and Stabilized Earth
By: C. Williams-Ellis with an Introduction By Gordon T. Pearson
Publisher: Dorset, UK, Donhead Publishing Ltd: 1999
This fascinating study, first published in 1919 then substantially revised in 1947, was based on experiments undertaken by the author, Clough Williams-Ellis into the use of pisé de terre and other earth based materials. It was written at a time when traditional building resources such as brick and timber were in short supply, and there was a need to consider the potential for using alternative materials in construction. Whilst earth building has not developed significantly in the UK since this book appeared, the recent efforts of the sustainable architecture movement has helped to stimulate a... View more info
Roof Slating and Tiling
By: Frank Bennett and Alfred Pinion with an Introduction By Richard Jordan and Tim Radcliffe
This is a facsimile of the 1948 edition Bennett and Pinion's classic work, first published in 1935. It provides an invaluable source of information on the various types of roof coverings that were traditionally used such as slates, clay tiles and shingles, and includes basic aspects such as sorting and holing slates through to more complex details such as random, diminishing slating and the tiling of swept and laced valleys. Contents: Roof covering; Slates and their characteristics; How a simple roof is slated; Groundwork; Slating generally; Manufacture and characteristics of roofing tiles;... View more info
The Geology of Building Stones
By: John Allen Howe; Introduction By David Jefferson
John Allen Howe's book, The Geology of Building Stones, written in 1910, was the first major reference work to feature information on the considerable range of building stones which were being used in the UK and which were still being quarried at that time. This important and useful publication, now reprinted by Donhead, offers very detailed information on the appearance and qualities of the various types of stone being used at that time, including granite, sandstones, limestones and other lesser known building stones, specific to certain geographical areas. It also includes a good introduc... View more info
English Leadwork: Its Art and History
By: Lawrence Weaver with an Introduction By Andrew Naylor
Lawrence Weaver's design reference work appeared in 1909, and is now available from Donhead in this re-printed facsimile edition. It describes and documents many examples of decorative leadwork, which being durable and attractive lends itself in its simplicity to a multitude of forms. Whilst examining in detail the history and workmanship to be found on fonts, statues, urns and vases, the book also includes more modest structures such as pipes, pipeheads and rain-water cisterns. The author also explores the use of lead in roofing, particularly for spires, steeples and domes, and points out t... View more info
Structural Appraisal of Traditional Buildings
By: Patrick Robson
Publisher: Hants, UK, Donhead Publishing Ltd: 2005
This book is a comprehensive guide to the common causes of structural damage. It examines the techniques for collecting evidence including desk study, visual inspection, distortion survey, testing and ground investigation as well as offering advice on managing liability. Before damage to a building can be remedied, the investigator has to discover the cause as well as predict the possible effects of the damage. This book provides an important study of the analytical skills necessary to achieve this. Practitioners in this field have no codes of practice or standards to fall back on – there a... View more info
By: Paul N. Hasluck with an Introduction By Patrick Baty
Developments in the use of paint analysis techniques for researching the painted interiors and exteriors of our most prestigious historic buildings has been extremely important in helping to maintain the integrity of historic structures while they are being conserved. It has given a broader dimension to architectural study, in many cases by showing how particular buildings and rooms were used, and also offering a better appreciation of the nature and constituents of historic paint. Paul Hasluck's useful little book, first published in 1897, will provide the conservation practitioner with a... View more info
The Weathering of Natural Building Stones
By: R.J. Schaffer with an Introduction By Dr Tim Yates
Printed Pages: 149 with numerous b/w illustrations. View more info
Building Construction Drawing
By: Richard B. Eaton; Introduction By Jonathan David, Normal England, and John Keenan
First published in six parts in the period 1914 to 1921 this volume has now been reprinted to provide a useful sourcebook for architects and other conservation specialists working on traditional buildings. This was one of the first books to include specifications and working drawings of joinery details, drawn on a large scale, which complemented the earlier better known construction 'pattern books ' of the nineteenth and early twentieth century. The book covers a wide range of details, with particular emphasis on joinery, including windows, doors, staircases, panelling, picture and chair ... View more info
Survey and Repair of Traditional Buildings: A Sustainable Approach
By: Richard Oxley
Understanding the unique requirements of traditional buildings is crucial to providing appropriate guidance on their care and repair. This book will help practitioners identify the particular issues relating to older buildings and the problems they may encounter when surveying and repairing them. With the use of examples, the author provides invaluable information on how traditional buildings perform, emphasizing the need for a sensitive and sustainable approach which also takes account of the specific needs of the building. The book examines all aspects to be included in any assessment for... View more info
Masonry, Bricklaying, and Plastering
By: Robert Scott Burn with an Introduction By Ian Pritchett
Robert Scott Burn wrote this book in 1871 at a time of great developments in science, industry and exploration, and when materials for engineering and building were constantly being improved and replaced. It offers, therefore, an interesting and useful coverage not only of traditional techniques and materials such as stone, brick and pisé. It also examines the developments in the use of cement for wall covering, as well as cement blocks to be used as artificial stone. This new reprint of the original work contains over 400 pages of text dealing with materials, practical construction technique... View more info
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 7,204
|
<?php
// @codingStandardsIgnoreFile
namespace Magento\Checkout\Test\Unit\Helper;
use \Magento\Checkout\Helper\Cart;
use Magento\Framework\App\Action\Action;
use Magento\Framework\DataObject;
use Magento\Quote\Model\Quote\Item;
class CartTest extends \PHPUnit_Framework_TestCase
{
/**
* @var \PHPUnit_Framework_MockObject_MockObject
*/
protected $urlBuilderMock;
/**
* @var \PHPUnit_Framework_MockObject_MockObject
*/
protected $requestMock;
/**
* @var \PHPUnit_Framework_MockObject_MockObject
*/
protected $scopeConfigMock;
/**
* @var \PHPUnit_Framework_MockObject_MockObject
*/
protected $cartMock;
/**
* @var \PHPUnit_Framework_MockObject_MockObject
*/
protected $checkoutSessionMock;
/**
* @var \PHPUnit_Framework_MockObject_MockObject|\Magento\Framework\Url\EncoderInterface
*/
protected $urlEncoder;
/**
* @var Cart
*/
protected $helper;
protected function setUp()
{
$this->requestMock = $this->getMockBuilder('Magento\Framework\App\Request\Http')
->disableOriginalConstructor()->getMock();
$objectManagerHelper = new \Magento\Framework\TestFramework\Unit\Helper\ObjectManager($this);
/** @var \Magento\Framework\App\Helper\Context $context */
$context = $objectManagerHelper->getObject(
'Magento\Framework\App\Helper\Context',
[
'httpRequest' => $this->requestMock,
]
);
$className = 'Magento\Checkout\Helper\Cart';
$arguments = $objectManagerHelper->getConstructArguments($className, ['context' => $context]);
$this->urlBuilderMock = $context->getUrlBuilder();
$this->urlEncoder = $context->getUrlEncoder();
$this->urlEncoder->expects($this->any())
->method('encode')
->willReturnCallback(function ($url) {
return strtr(base64_encode($url), '+/=', '-_,');
});
$this->scopeConfigMock = $context->getScopeConfig();
$this->cartMock = $arguments['checkoutCart'];
$this->checkoutSessionMock = $arguments['checkoutSession'];
$this->helper = $objectManagerHelper->getObject($className, $arguments);
}
public function testGetCart()
{
$this->assertEquals($this->cartMock, $this->helper->getCart());
}
public function testGetRemoveUrl()
{
$quoteItemId = 1;
$quoteItemMock = $this->getMock('\Magento\Quote\Model\Quote\Item', [], [], '', false);
$quoteItemMock->expects($this->any())->method('getId')->will($this->returnValue($quoteItemId));
$currentUrl = 'http://www.example.com/';
$this->urlBuilderMock->expects($this->any())->method('getCurrentUrl')->will($this->returnValue($currentUrl));
$params = [
'id' => $quoteItemId,
Action::PARAM_NAME_BASE64_URL => strtr(base64_encode($currentUrl), '+/=', '-_,'),
];
$this->urlBuilderMock->expects($this->once())->method('getUrl')->with('checkout/cart/delete', $params);
$this->helper->getRemoveUrl($quoteItemMock);
}
public function testGetCartUrl()
{
$this->urlBuilderMock->expects($this->once())->method('getUrl')->with('checkout/cart', []);
$this->helper->getCartUrl();
}
public function testGetQuote()
{
$quoteMock = $this->getMock('\Magento\Quote\Model\Quote', [], [], '', false);
$this->checkoutSessionMock->expects($this->once())->method('getQuote')->will($this->returnValue($quoteMock));
$this->assertEquals($quoteMock, $this->helper->getQuote());
}
public function testGetItemsCount()
{
$itemsCount = 1;
$this->cartMock->expects($this->any())->method('getItemsCount')->will($this->returnValue($itemsCount));
$this->assertEquals($itemsCount, $this->helper->getItemsCount());
}
public function testGetItemsQty()
{
$itemsQty = 1;
$this->cartMock->expects($this->any())->method('getItemsQty')->will($this->returnValue($itemsQty));
$this->assertEquals($itemsQty, $this->helper->getItemsQty());
}
public function testGetSummaryCount()
{
$summaryQty = 1;
$this->cartMock->expects($this->any())->method('getSummaryQty')->will($this->returnValue($summaryQty));
$this->assertEquals($summaryQty, $this->helper->getSummaryCount());
}
public function testGetIsVirtualQuote()
{
$isVirtual = true;
$quoteMock = $this->getMock('\Magento\Quote\Model\Quote', [], [], '', false);
$this->checkoutSessionMock->expects($this->once())->method('getQuote')->will($this->returnValue($quoteMock));
$quoteMock->expects($this->any())->method('isVirtual')->will($this->returnValue($isVirtual));
$this->assertEquals($isVirtual, $this->helper->getIsVirtualQuote());
}
public function testGetShouldRedirectToCart()
{
$storeId = 1;
$this->scopeConfigMock->expects($this->once())->method('isSetFlag')
->with(Cart::XML_PATH_REDIRECT_TO_CART, \Magento\Store\Model\ScopeInterface::SCOPE_STORE, $storeId)
->will($this->returnValue(true));
$this->assertTrue($this->helper->getShouldRedirectToCart($storeId));
}
public function testGetAddUrl()
{
$productEntityId = 1;
$storeId = 1;
$isRequestSecure = false;
$productMock = $this->getMock('\Magento\Catalog\Model\Product',
['getEntityId', 'hasUrlDataObject', 'getUrlDataObject', '__wakeup'], [], '', false);
$productMock->expects($this->any())->method('getEntityId')->will($this->returnValue($productEntityId));
$productMock->expects($this->any())->method('hasUrlDataObject')->will($this->returnValue(true));
$productMock->expects($this->any())->method('getUrlDataObject')
->will($this->returnValue(new DataObject(['store_id' => $storeId])));
$currentUrl = 'http://www.example.com/';
$this->urlBuilderMock->expects($this->any())->method('getCurrentUrl')->will($this->returnValue($currentUrl));
$this->requestMock->expects($this->any())->method('getRouteName')->will($this->returnValue('checkout'));
$this->requestMock->expects($this->any())->method('getControllerName')->will($this->returnValue('cart'));
$this->requestMock->expects($this->once())->method('isSecure')->willReturn($isRequestSecure);
$params = [
Action::PARAM_NAME_URL_ENCODED => strtr(base64_encode($currentUrl), '+/=', '-_,'),
'product' => $productEntityId,
'custom_param' => 'value',
'_scope' => $storeId,
'_scope_to_url' => true,
'in_cart' => 1,
'_secure' => $isRequestSecure
];
$this->urlBuilderMock->expects($this->once())->method('getUrl')->with('checkout/cart/add', $params);
$this->helper->getAddUrl($productMock, ['custom_param' => 'value']);
}
/**
* @param integer $id
* @param string $url
* @param bool $isAjax
* @param string $expectedPostData
*
* @dataProvider deletePostJsonDataProvider
* @SuppressWarnings(PHPMD.UnusedLocalVariable)
*/
public function testGetDeletePostJson($id, $url, $isAjax, $expectedPostData)
{
$item = $this->getMock('Magento\Quote\Model\Quote\Item', [], [], '', false);
$item->expects($this->once())
->method('getId')
->will($this->returnValue($id));
$this->requestMock->expects($this->once())
->method('isAjax')
->will($this->returnValue($isAjax));
$this->urlBuilderMock->expects($this->any())
->method('getCurrentUrl')
->will($this->returnValue($url));
$this->urlBuilderMock->expects($this->once())
->method('getUrl')
->will($this->returnValue($url));
$result = $this->helper->getDeletePostJson($item);
$this->assertEquals($expectedPostData, $result);
}
/**
* @return array
*/
public function deletePostJsonDataProvider()
{
$url = 'http://localhost.com/dev/checkout/cart/delete/';
$uenc = strtr(base64_encode($url), '+/=', '-_,');
$id = 1;
$expectedPostData1 = json_encode(
[
'action' => $url,
'data' => ['id' => $id, 'uenc' => $uenc],
]
);
$expectedPostData2 = json_encode(
[
'action' => $url,
'data' => ['id' => $id],
]
);
return [
[$id, $url, false, $expectedPostData1],
[$id, $url, true, $expectedPostData2],
];
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,115
|
Orientexpressen (franska/tyska: Orient-Express) var namnet på vissa tågförbindelser mellan Frankrike och östra Europa. Den ursprungliga betydelsen var sträckningen mellan Paris och Konstantinopel, vilken användes åren 1883–1977. Förbindelsen skapades av Compagnie Internationale des Wagons-Lits (CIWL). Därutöver har även andra östliga tågförbindelser från Paris, andra franska orter och även London använt namnet. Den sista/senaste reguljära linjen som använt namnet var tåg på sträckan Strasbourg–Wien fram till 2009.
Mannen bakom succén var belgaren Georges Nagelmackers (1845 - 1905).
Efter pressvisningen inför premiärturen från Paris 4 oktober 1883, så skrev de närvarande journalisterna entusiastiskt om tågets gränslösa lyx och skönhet. De förundrade passagerarna upplevde det som att de befann sig på ett av Europas finaste hotell, med fantastiska träpaneler, luxuösa skinnfåtöljer, silkeslakan och yllefiltar.
Också gourmeterna fick sitt lystmäte, genom de delikata rätter som skapades i restaurangvagnens minimala kök, bordens vita dukar, och tågets kunniga sommelierer som serverade utsökta viner i glittrande kristallglas.
Trafiken med Compagnie Internationale des Wagons-Lits (CIWL) nådde sin största omfattning under 1930-talet, då man hade nästan 2300 vagnar i trafik. Idag (2014) används namnet Orientexpressen för lyxcharter-linjen "Venice Simplon–Orient-Express", som främst kör på sträckan Paris–Venedig men även ibland på andra sträckor mellan västra och östra Europa (inklusive till Istanbul).
Historik
Den ursprungliga Orientexpressen
Den ursprungliga sträckningen, som kördes första gången 4 oktober 1883, gick mellan Paris och Konstantinopel via München, Wien och Giurgiu i Rumänien. Från Giurgiu åkte passagerarna båt över Donau till Ruse i Bulgarien, där de sedan fortsatte med tåg till Varna för att avsluta sin resa med båt till Konstantinopel. 1885 påbörjades en annan sträckning där resan gick med tåg från Paris via Wien till Belgrad och Niš, hästtransport till Plovdiv och slutligen tåg till Konstantinopel.
1889 startades en direktförbindelse till Konstantinopel. På den tiden gick Orientexpressen dagligen från Paris till Budapest, tre gånger i veckan fortsatte det till Belgrad och Konstantinopel och en gång i veckan till Bukarest och Constanța vid Svarta havet.
Senare samma år blev tågets östliga slutstation Varna i Bulgarien där passagerarna kunde fortsätta med båt till Konstantinopel. 1889 började tåget att gå utan avbrott hela vägen till Konstantinopel, vilket blev dess ostliga slutstation fram till 19 maj 1977. Stationen var Sirkecistationen i Gyllene hornet. Från hamnen vid stationen kunde passagerarna sedan åka vidare över Bosporen till Haydarpaşa där de kunde fortsätta resan med den turkiska järnvägen, TCDD.
Första världskriget
Starten av första världskriget gjorde att Orientexpressen drogs in. Den återupptogs 1918 och när Simplonpasset öppnades 1919 kunde förbindelsen dras i en sydligare sträckning via Milano, Venedig och Trieste. Denna sträckning kallades Simplon-Orientexpress och gick samtidigt som tågen fortsatte att gå längs den gamla sträckningen. Fördraget i Saint-Germain innehöll en klausul om att Österrike tvingades att acceptera tåget. Tidigare hade landet endast tillåtit internationella tåg att passera om de stannade i Wien. Simplon-Orientexpress blev snart den viktigaste tågförbindelsen mellan Paris och Konstantinopel.
Mellankrigstiden
1930-talet var Orientexpressens höjdpunkt då det fanns tre parallella förbindelser; Orientexpressen, Simplon-Orientexpress och Aarlberg-Orientexpress som gick via Zürich och Innsbruck till Budapest med sovvagnar om resenärerna fortsatte till Bukarest och Aten. Under den perioden fick Orientexpressen ett rykte om komfort och lyx, med sovvagnar som inkluderade fullständig service och restaurangvagnar som var kända för kökets höga kvalitet. Kungligheter, förnäma personer, diplomater, affärsmän och borgare reste med Orientexpressen. Varje tåg hade sovvagnar som gick från Calais till Istanbul vilket gjorde att tågen gick mellan europakontinentens båda ytterkanter.
Andra världskriget
När andra världskriget bröt ut 1939 ställdes Orientexpressen in och återupptogs inte förrän 1945. Under kriget körde det tyska järnvägsföretaget Mitropa några förbindelser till Balkanhalvön, men spåren saboterades ofta av jugoslaviska partisaner vilket gjorde att förbindelsen drogs in.
Efter kriget återupptogs förbindelserna förutom den som gick till Aten, där stängningen av gränsen mellan Jugoslavien och Grekland förhindrade att tågen kunde passera. Gränsen öppnades igen 1951 men stängningen av gränsen mellan Bulgarien och Turkiet 1951–1952 gjorde att tågen inte kunde nå fram till Istanbul. När järnridån föll i Europa, kunde förbindelsen fortsätta men de kommunistiska länderna bytte ut originalvagnarna mot de som användes av deras egna järnvägsföretag.
Direct-Orientexpress
1962 hade Orientexpressen och Arlberg-Orientexpress slutat att köras och den enda förbindelse som återstod var Simplon-Orientexpress. Denna ersattes 1962 av en långsammare sträckning som kallades Direct-Orientexpress och som körde dagligen mellan Paris och Belgrad samt två gånger i veckan mellan Paris och Istanbul samt Paris och Aten.
1971 slutade CIWL att äga vagnarna själva. Istället sålde eller leasade de vagnarna till olika nationella järnvägsbolag men de fortsatte att bemanna tågen. 1976 drogs direktförbindelsen mellan Paris och Aten in, och 1977 drogs Direct-Orientexpress in efter den sista resan mellan Paris och Istanbul som ägde rum 19 maj 1977.
Orient-Express, ett av Europas vanliga nattåg
Många trodde att indragningen av Direct-Orientexpress skulle innebära slutet för Orientexpressen, men namnet fortsatte användas, för förbindelsen mellan Paris och Budapest samt Paris och Bukarest. Detta fortsatte fram till 2001, då förbindelsen drogs ner till att endast gå mellan Paris och Wien. Den förkortades 2007 till Strasbourg–Wien. Namnet "Orient-Express" avsåg 2008 denna förbindelse. Det är ett vanligt EuroNight nattåg, och tar 10 timmar vilket ansågs mer lagom längd på ett nattåg än de tidigare 14 timmarna. Dessutom hade höghastighetståg införts Paris–Strasbourg kort innan vilket sparar två timmar restid. Den 13 december 2009 togs även sträckan Strasbourg–Wien ur trafik.
Venice-Simplon Orient Express
Venice-Simplon Orient Express, som är ett privatägt lyxtåg, började köras 1982 mellan Venedig och Calais (med anslutning mellan London och Calais med brittiska vagnar och fartyg). Tåget har gått där med vissa avbrott sedan dess. Det går även andra rutter. Vissa år har tåget gått till Istanbul. År 2013 gjorde det ett besök i Stockholm. Det är ett rent lyxturisttåg som stannar länge på vissa ställen. Det har bara har ett fåtal turer per år. Venice-Simplon Orient Express innehåller gamla Orientexpressvagnar från 1920-talet, noggrant restaurerade.
Populärkultur
Mordet på Orientexpressen
Källhänvisningar
Externa länkar
Sanningen bakom legenden
CIWL:s historia
Artikel som tar upp några av delarna i artikeln
Tåg
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,101
|
#include "css/test_rule.h++"
#include <core/debug.h++>
#include <core/string.h++>
#include <css/grammar.h++>
#include <css/property.h++>
#include <boost/spirit/home/x3.hpp>
namespace
{
using skui::core::string;
const string property_input = "align-content";
const string declaration_input = "align-content: center;";
const string declaration_block_input = "{ align-content: center; align-items: stretch; }";
}
int main()
{
using skui::test::check_rule_success;
skui::css::declaration_block declaration_block;
declaration_block.align_content = skui::css::align_content::center;
declaration_block.align_items = skui::css::align_items::stretch;
//check_rule_success(skui::css::grammar::declaration_block,
// declaration_block_input,
// declaration_block);
//check_rule_success(skui::css::grammar::property, property_input, skui::css::property::align_content, "property");
//check_rule_success(skui::css::grammar::declaration, declaration_input, std::make_pair(skui::css::property::align_content, skui::core::string("center")));
//check_rule_success(skui::css::grammar::declaration_block, declaration_block_input,
// std::unordered_map<skui::css::property, skui::css::grammar::value_type>{{skui::css::property::align_content, skui::css::align_content::center},
// {skui::css::property::align_items, skui::css::align_items::stretch}});
return skui::test::exit_code;
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,484
|
package org.drools.compiler.lang.api.impl;
import org.drools.compiler.lang.api.DescrBuilder;
import org.drools.compiler.lang.api.NamedConsequenceDescrBuilder;
import org.drools.compiler.lang.descr.NamedConsequenceDescr;
/**
* A builder implementation for NamedConsequenceDescr using a fluent API.
*/
public class NamedConsequenceDescrBuilderImpl<P extends DescrBuilder< ?, ? >>
extends BaseDescrBuilderImpl<P, NamedConsequenceDescr>
implements NamedConsequenceDescrBuilder<P> {
protected NamedConsequenceDescrBuilderImpl(final P parent) {
super(parent, new NamedConsequenceDescr());
}
public NamedConsequenceDescrBuilder<P> name( String name ) {
getDescr().setName( name );
return this;
}
public NamedConsequenceDescrBuilder<P> breaking( boolean breaking ) {
getDescr().setBreaking( breaking );
return this;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,835
|
Weldon es un lugar designado por el censo (en inglés, census-designated place) ubicado en el condado de Kern, California, Estados Unidos. Según el censo de 2020, tiene una población de 2303 habitantes.
Geografía
La localidad está ubicada en las coordenadas (35.644103, -118.309088). Según la Oficina del Censo, tiene un área total de 69.45 km², de la cual 69.06 km² son tierra y 0.39 km² son agua.
Demografía
Según la Oficina del Censo, en 2000 los ingresos medios de los hogares de la localidad eran de $22,857 y los ingresos medios de las familias eran de $26,500. Los hombres tenían ingresos medios por $35,573 frente a los $20,208 que percibían las mujeres. Los ingresos per cápita para la localidad eran de $15,243. Alrededor del 18.7% de la población estaba por debajo del umbral de pobreza.
De acuerdo con la estimación 2016-2020 de la Oficina del Censo, los ingresos medios de los hogares de la localidad son de $37,535. Alrededor del 42.2% de la población está por debajo del umbral de pobreza.
Referencias
Enlaces externos
Lugares designados por el censo en California
Localidades del condado de Kern
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,364
|
package com.amazonaws.services.simpleworkflow.flow.junit;
import java.util.List;
import org.junit.Test;
import org.junit.rules.MethodRule;
import org.junit.runners.BlockJUnit4ClassRunner;
import org.junit.runners.model.FrameworkMethod;
import org.junit.runners.model.InitializationError;
import org.junit.runners.model.Statement;
/**
* To be used instead of {@link BlockJUnit4ClassRunner} when testing
* asynchronous code. Requires {@link WorkflowTest} rule (annotated with @Rule)
* to be present in the tested class.
*
* @author fateev
*/
public class FlowBlockJUnit4ClassRunner extends BlockJUnit4ClassRunner {
private WorkflowTestBase workflowTestRule;
private long timeout;
private Class<? extends Throwable> expectedException;
public FlowBlockJUnit4ClassRunner(Class<?> klass) throws InitializationError {
super(klass);
}
@Override
protected Statement withPotentialTimeout(FrameworkMethod method, final Object test, Statement next) {
Test annotation = method.getAnnotation(Test.class);
timeout = annotation.timeout();
if (timeout > 0 && workflowTestRule != null) {
workflowTestRule.setTestTimeoutActualTimeMilliseconds(timeout);
}
return next;
}
@Override
protected List<MethodRule> rules(Object test) {
List<MethodRule> result = super.rules(test);
for (MethodRule methodRule : result) {
if (WorkflowTestBase.class.isAssignableFrom(methodRule.getClass())) {
workflowTestRule = (WorkflowTestBase) methodRule;
workflowTestRule.setFlowTestRunner(true);
if (timeout > 0) {
workflowTestRule.setTestTimeoutActualTimeMilliseconds(timeout);
}
if (expectedException != null) {
workflowTestRule.setExpectedException(expectedException);
}
}
}
return result;
}
@Override
protected Statement possiblyExpectingExceptions(FrameworkMethod method, Object test, Statement next) {
Test annotation = method.getAnnotation(Test.class);
Class<? extends Throwable> expected = annotation.expected();
if (expected != Test.None.class) {
expectedException = expected;
if (workflowTestRule != null) {
workflowTestRule.setExpectedException(expectedException);
}
}
return next;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,031
|
import { IStringDictionary, IDictionary } from "../../common/declarations";
import * as _ from "lodash";
import { injector } from "../../common/yok";
import { IApplePortalCookieService } from "./definitions";
export class ApplePortalCookieService implements IApplePortalCookieService {
private userSessionCookies: IStringDictionary = {};
private validUserSessionCookieNames = [
"myacinfo",
"dqsid",
"itctx",
"itcdq",
"acn01",
"DES",
];
private validWebSessionCookieNames = ["wosid", "woinst", "itctx"];
public getWebSessionCookie(cookiesData: string[]): string {
const webSessionCookies = _.cloneDeep(this.userSessionCookies);
const parsedCookies = this.parseCookiesData(
cookiesData,
this.validWebSessionCookieNames
);
_.each(
parsedCookies,
(parsedCookie) =>
(webSessionCookies[parsedCookie.key] = parsedCookie.cookie)
);
return _.values(webSessionCookies).join("; ");
}
public getUserSessionCookie(): string {
return _.values(this.userSessionCookies).join("; ");
}
public updateUserSessionCookie(cookiesData: string[]): void {
const parsedCookies = this.parseCookiesData(
cookiesData,
this.validUserSessionCookieNames
);
_.each(
parsedCookies,
(parsedCookie) =>
(this.userSessionCookies[parsedCookie.key] = parsedCookie.cookie)
);
}
private parseCookiesData(
cookiesData: string[],
validCookieNames: string[]
): IDictionary<{ key: string; value: string; cookie: string }> {
const result: IDictionary<{
key: string;
value: string;
cookie: string;
}> = {};
for (const c of cookiesData) {
const parts = c.split(";");
for (const cookie of parts) {
const trimmedCookie = cookie.trim();
const [cookieKey, cookieValue] = trimmedCookie.split("=");
if (
_.includes(validCookieNames, cookieKey) ||
_.some(validCookieNames, (validCookieName) =>
cookieKey.startsWith(validCookieName)
)
) {
result[cookieKey] = {
key: cookieKey,
value: cookieValue,
cookie: trimmedCookie,
};
}
}
}
return result;
}
}
injector.register("applePortalCookieService", ApplePortalCookieService);
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,698
|
\section{Introduction} \label{sec:intro}
Effective field theories (EFTs) describe the physics of systems with a separation of scales\footnote{Pedagogical introductions to EFTs can be found in
Refs.~\cite{Kaplan:1995uv,Phillips:2002da,Epelbaum:2010nr}.}.
A key element in any EFT is a power counting that organizes calculations
into an expansion in a dimensionless parameter or parameters, which are typically formed
from ratios of the low-energy and high-energy scales in the system under consideration.
We denote this parameter generically as $Q$. In the simplest case $Q=p/\Lambda_b$ is the ratio of the typical momentum, $p$,
of the process of interest to the break-down scale, $\Lambda_b$, of the EFT---i.e., the scale at which the first dynamics not explicitly
included in the EFT appears.
Even in more complex situations with many low-energy scales, the EFT expansion for $X$ can be denoted:
\begin{equation}
X=X_0 \sum_{n=0}^{\infty} c_n Q^n \;,
\label{eq:obsexp}
\end{equation}
where $X_0$ is the natural size of the observable $X$, and $\{c_n\}$ are dimensionless coefficients, some of which may be zero.
In most EFTs the expansion (\ref{eq:obsexp}) is inherited
directly from the EFT Lagrangian or potential---with suitable additions (e.g., terms
of the form $Q^n \log(Q)$) due to quantum corrections. In nuclear physics, however,
the dynamics is intrinsically non-perturbative, and there exists at least some sub-class of EFT graphs that
must be summed to all orders. The connection between
the Lagrangian and observables is then less direct. Nevertheless, a properly formulated EFT for
nuclear physics is expected to have a $Q$-expansion for observables of the form (\ref{eq:obsexp}) and
it is the properties of such expansions which are our concern in this paper.
A key benefit of the perturbative series (\ref{eq:obsexp}) is that it permits estimation of the error induced
by truncation at a finite order $k$: ``truncation errors". If the coefficients $c_n$ for an observable were
to vary significantly and unsystematically in size, the expansion (\ref{eq:obsexp})
would be unsuited to this end. However, experience, and the principle
of naturalness, suggest that the coefficients \emph{are}
typically of order one---even in the more complex nuclear context.
In Ref.~\cite{Furnstahl:2014jpg} we laid out a recipe for uncertainty quantification in
EFTs for nuclear physics. While they are not the only source of theory uncertainty,
truncation errors are often the dominant uncertainty in EFT calculations.
We argued that Bayesian methods~\cite{Schindler:2008fh}
provide an error bar,
with a well-founded
statistical interpretation,
that accounts for {\it all} sources of uncertainty in the EFT.
In particular, Bayesian methods are essential to the assessment of truncation error: assumptions
(or expectations) about the EFT are encoded
in ``prior probability distribution functions" (pdfs).
The Bayesian approach then proceeds by integrating out (``marginalizing'')
the coefficients of omitted terms to establish the truncation error.
The use of priors is often controversial because they can introduce
subjective judgments about, e.g., the meaning of naturalness, into
the computation. We argue that, on the contrary, introducing and stating
Bayesian priors on higher-order EFT coefficients
renders explicit in the calculation assumptions that are present but typically not articulated. This
allows such assumptions to be applied consistently, tested, and
modified in light of new information.
In this work we begin with the general formalism for computation of truncation errors discussed
in the context of perturbative QCD (pQCD) by Cacciari and
Houdeau in Ref.~\cite{Cacciari:2011ze} and further developed in
Refs.~\cite{Bagnaschi:2014wea,Bagnaschi:2014eva}, where it is called
$\overline{\rm CH}$\ (cf.~Ref.~\cite{Bagnaschi:2015iea} for a brief summary).
We rederive, adapt, and extend their prescription to EFT
expansions. We explore several different choices of prior for the coefficients
$\{c_n\}$ and examine---within some generic examples---how such prior choice affects the truncation-error estimate.
We then look specifically at the nuclear context, focusing on the extent to which such calculations justify
the uncertainty quantification (UQ) procedure typically adopted in EFTs. This procedure has recently been clearly stated and applied to nucleon-nucleon (NN) cross sections
by Epelbaum, Krebs,
and Mei{\ss}ner (henceforth EKM) in their fourth- and fifth-order applications of chiral EFT to these observables~\cite{Epelbaum:2014efa,Epelbaum:2014sza}.
(Introductions to chiral EFT can be found in Refs.~\cite{Weinberg:1978kz,Gasser:1983yg,Jenkins:1990jv,Bernard:2006gx,Bedaque:2002mn,Epelbaum:2005pn}.)
Note that here we do not deal with the extent to which truncation errors affect the low-energy constants (LECs) extracted from fitting
EFT expansions to data. This will be discussed in a separate publication~\cite{Wesolowski:2015}. Our focus here is solely on
estimating the truncation error at order $k$ for the series (\ref{eq:obsexp}), given the assumption of naturalness, and information on the
size of the coefficients $c_0, \ldots, c_k$.
In Section~\ref{sec:CH}, we provide a brief overview of the Bayesian rules
we will need and then adapt the CH\ prescription so that it is suitable
for application to EFT expansions.
We also enlarge the set of priors considered by CH.
In Section~\ref{sec:EKM}, this approach is applied to some two-body
observables considered by EKM, using their assumed breakdown scale to compare to their
error assessment. In Section~\ref{sec:scalechecking} we
explore methods to determine the breakdown scale
from the requirement that the EFT coefficients be consistent with naturalness.
In Section~\ref{sec:conclusion} we summarize our results.
\section{Adapting CH\ to EFT} \label{sec:CH}
\subsection{Setting up the problem}
Consider the perturbative series (\ref{eq:obsexp}) for the observable $X$. If the series is truncated at order $k$ then
the error induced is $X_0 \Delta_k$, where the scaled, dimensionless parameter that determines the truncation error is:
\begin{equation}
\Delta_k \equiv \sum_{n=k+1}^\infty c_n Q^n
\;,
\label{eq:Deltak_def}
\end{equation}
provided the series actually converges and is not solely asymptotic. For sufficiently small values of $Q$, the first omitted term $c_{k+1} Q^{k+1}$ is a good estimate for $\Delta_k$.
This leads to simplified formulas for the evaluation of DOB intervals. Below we will consider both this first-term approximation and evaluations at larger $Q$ that use several terms in $\Delta_k$. In either case this provides an estimate of the deviation of the series at order $k$ from the
true value of the observable---even if the series is asymptotic.
In Ref.~\cite{Cacciari:2011ze} Cacciari and Houdeau (hereafter ``CH") considered the case that the
series (\ref{eq:obsexp}) is a pQCD expansion. The expansion is then
in powers of the strong
coupling, $\alpha_s(\mu)$, where $\mu$ is a renormalization scale chosen
appropriately for the observable $X$. The optimal choice of $\mu$ is the
subject of much debate and many prescriptions in the literature. Indeed,
the variation of the truncated-at-order-$k$ expression for $X$ under an order-unity change
in $\mu$ is canonically used to estimate $\Delta_k$. This is justified because of the truncated expansion's residual dependence
on the renormalization scale $\mu$; the full sum should be independent
of $\mu$, so the variation with $\mu$ contains information about
omitted terms.
CH pointed out that varying the scale $\mu$ around an optimal value $\mu_0$, say, between $\mu_0/2$ and $2 \mu_0$, does
not yield an uncertainty with a straightforward statistical interpretation. They therefore
laid out a Bayesian probability-theory calculation of $\Delta_k$. Ultimately estimates from scale variation seem to coincide quite well
with the results of this more rigorous probabilistic analysis.
As we now describe, that analysis starts with priors for $\{c_n\}$ that encode the assumption that these pQCD coefficients
are of order unity (once the typical size of the observable $X$ is
factored out of the expression). It modifies them in light of information acquired as more orders
in the series for $X$ are computed, and ultimately obtains a
posterior pdf for $\Delta_k$. With this posterior in hand, either
the degree of belief (DOB) corresponding to a given
interval of values of the truncation error, or the range of truncation errors
corresponding to a specified
DOB, can be computed.
CH's analysis of truncation errors in pQCD took the case where the series
is in powers of $\alpha_s$, rather than $Q$. Later work~\cite{Bagnaschi:2014wea,Bagnaschi:2014eva} introduced a scale factor $\lambda$, such that the
expansion was in powers of $\alpha_s/\lambda$ (e.g., because the expansion parameter might really be $\alpha_s/\pi$
or include a color factor) and a possible combinatoric
factor (such as $n!$ from high-order renormalon contributions).
In this, termed the ``$\overline{\rm CH}$\ prescription", the assumption is modified to say that the coefficients in the perturbative series of an
appropriately chosen expansion parameter are distributed such that they
share a common upper bound. In EFT the rescaling by a factor $\lambda$ corresponds to the choice of a different breakdown scale for the EFT, and we discuss
this possibility in Section~\ref{sec:scalechecking}. We do not consider the combinatoric factor,
which has not been identified in EFT expansions for few-nucleon-system observables.
Since one of the low-momentum scales of which $Q$ is formed is the momentum at which the observable $X$ is measured,
the EFT expansion parameter is strongly dependent on kinematics. While the QCD expansion's convergence can be improved by matching the scale at which $\alpha_s$ is evaluated to that of the observable of interest, in EFT the dependence of $Q$ on momentum is intrinsic---not a matter of choice. Furthermore, the high-momentum scale, $\Lambda_b$, that specifies the radius of convergence of the EFT momentum expansion, may not be known {\it a priori}, it may only be able to be inferred from the behavior of the EFT series. This is a key difference between EFT and pQCD, since in pQCD, the value of $\alpha_s$ can always be specified. In EFT a value of $Q$ corresponding to a particular momentum must be chosen, and then checked for consistency. Complicating the choice of an appropriate $\Lambda_b$---and concomitantly the evaluation of $Q$---for many low-energy EFTs is that at least some of the $c_n$'s need to be extracted from data, either from $X$ itself or from other observables.
These differences from the pQCD situation are reflected in the need to check the naturalness of EFT coefficients for a given choice of expansion parameter, something that we discuss in detail in Section~\ref{sec:scalechecking}.
For the time being we assume that $\Lambda_b$ has been determined as part of the steps in the EFT analysis that yielded the coefficients $\{c_n: n=0, \ldots, k\}$. Empirically EKM found that
$\Lambda_b \approx 600$ MeV resulted in natural coefficients in their EFT series for neutron-proton scattering cross sections~\cite{Epelbaum:2014efa,Epelbaum:2014sza}. However,
the non-perturbative nature of NN scattering makes it unclear how naturalness for
EFT LECs results in these apparently natural values of $\{c_n: n=0, \ldots, k\}$ in the cross-section's expansion.
This connection is very clear for perturbative EFT expansions of interest in nuclear physics, e.g.,
the chiral expansion for the nucleon mass
(see Ref.~\cite{Schindler:2008fh}) and the expansion for energy per particle
of a dilute Fermi
system with natural-sized scattering length~\cite{Hammer:2000xg}. Regardless though, in either perturbative or non-perturbative cases, an incorrect choice of high-momentum scale, $\Lambda_b$, will result in coefficients that are {\it not} natural. This emphasizes the close connection between the assumption of a particular expansion parameter and the imposition of a naturalness prior.
\subsection{Conditional probabilities: definitions and rules}
We use the notation $\pdf(x|I)$ to denote the probability (density) of
$x$ given information $I$; thus $\pdf(\Delta_k|c_0, \ldots, c_k)$ is the
desired pdf for $\Delta_k$.
The specification
$c_0, \ldots, c_k$ suggests that $c_0$ is non-zero, but it is straightforward to generalize the results derived
here to the case where the first non-zero coefficient is $c_l$ with $l>0$ (as often is the
case in QCD) or that where some
intermediate coefficients are identically zero (as for chiral EFT in NN scattering
where $n=1$ does not appear).
Because the terminology, techniques, and manipulations of Bayesian statistics
may be unfamiliar to our intended audience, we include a brief overview
here of those aspects needed for the CH\ procedures~\cite{Sivia:06,Gregory:05}.
We indicate parenthetically some analogies to familiar manipulations in quantum
mechanics.
We emphasize that the correspondences are not to be taken literally.
Bayesian probabilistic inference is built on the sum and product rules.
If the set $\{x_i\}$ is exhaustive
and exclusive (cf.\ complete and orthogonal), then the sum rule says
that $\pdf(x_i|I)$ is normalized,
\begin{equation}
\sum_i \pdf(x_i | I) = 1
\quad \longrightarrow \quad
\int\!dx\, \pdf(x|I) = 1
\;,
\label{eq:sum}
\end{equation}
where the continuum version is integrated over the appropriate range of $x$.
But it further implies marginalization (cf.\ inserting a complete
set of orthonormal basis states):
\begin{equation}
\pdf(x|I) = \sum_j \pdf(x,y_j|I)
\;,
\end{equation}
or the continuum version
\begin{equation}
\pdf(x|I) = \int\!dy\, \pdf(x,y|I) = 1
\;,
\label{eq:marginalize}
\end{equation}
where $\pdf(x,y|I)$ is the joint probability of $x$ and $y$ given $I$.
We will apply this repeatedly, either to introduce new parameters or to
integrate out ``nuisance'' parameters.
Expressing $\pdf(x|I)$ in terms of the joint probability $\pdf(x,y|I)$
through Eq.~\eqref{eq:marginalize}
leads to progress by applying the product rule to relate it
to other pdfs:
\begin{equation}
\pdf(x,y|I) = \pdf(x|y,I)\,\pdf(y|I)
= \pdf(y|x,I)\,\pdf(x|I)
\;.
\label{eq:product}
\end{equation}
The first equality translates to: ``the joint probability of $x$ and $y$
is equal to the probability of $x$ given $y$ and $I$ times the probability
of $y$ given $I$.''
The second equality follows by symmetry, but when rearranged becomes
Bayes' theorem:
\begin{equation}
\pdf(x|y,I) = \frac{\pdf(y|x,I)\, \pdf(x|I)}{\pdf(y|I)}
\;,
\label{eq:Bayes}
\end{equation}
which here
relates the \emph{posterior} $\pdf(x|y,I)$ to the \emph{likelihood} $\pdf(y|x,I)$
given the \emph{prior} $\pdf(x|I)$ and the \emph{evidence} $\pdf(y|I)$.
These relations will enable us to derive the posterior for $\Delta_k$
in terms of assumed priors.
Another implication of the product rule follows when $x$ and $y$ are
mutually independent, which means that knowing $y$ doesn't affect the
probability of $x$, so that $\pdf(x|y,I) = \pdf(x|I)$. Then
Eq.~\eqref{eq:product} tells us that
\begin{equation}
\pdf(x,y|I) \longrightarrow \pdf(x|I)\,\pdf(y|I)
\;.
\label{eq:independent}
\end{equation}
In the following we sometimes omit the explicit $I$, but the specification of
prior information should always be assumed.
\subsection{CH synopsis and EFT correspondence}
We consider multiple priors that reflect the expectation that all coefficients
in the expansion of an observable in powers of $Q$ are of roughly the same size---or, more
precisely, they have a distribution with a characteristic size.
The fundamental assumption made by Cacciari and Houdeau in
Ref.~\cite{Cacciari:2011ze}
is that all coefficients of $\alpha_s$ in the pQCD series are
roughly the same size, which is implemented by treating them as
random variables having a shared
distribution with upper bound $\bar{c}$.
This assumption is motivated by empirical evidence from the behavior of such series.
But it may not be correct for EFT expansions, where the form (\ref{eq:obsexp})
is expected to result in coefficients which are $\mathcal{O}(1)$, not arbitrarily large.
\begin{table}[tb]
\caption{Prior pdfs.}
\label{tab:priors}
\begin{tabular}{c|cc}
set & $\pdf(c_n| \bar{c})$ & $\pdf(\bar{c})$ \\
\hline
A &
$\frac{\textstyle 1}{\textstyle 2\bar{c}}\,\theta(\bar{c}-|c_n|)$
& $\frac{\textstyle 1}{\textstyle \ln \cbar_{>}/\cbar_{<}}
\frac{\textstyle 1}{\textstyle\mathstrut\bar{c}}
\theta ( \bar{c} - \cbar_{<}) \theta( \cbar_{>} - \bar{c})$
\\[8pt]
B &
$\frac{\textstyle 1}{\textstyle 2\bar{c}}\,\theta(\bar{c}-|c_n|)$
& $\frac{\textstyle 1}{\textstyle\sqrt{2\pi}\bar{c}\sigma} e^{-(\log\bar{c})^2/2\sigma^2}$
\\[8pt]
C &
$\frac{\textstyle 1}{\textstyle\sqrt{2\pi}\bar{c}} e^{-c_n^2/2\bar{c}^2}$
& $\frac{\textstyle 1}{\textstyle \ln \cbar_{>}/\cbar_{<}}
\frac{\textstyle 1}{\textstyle\mathstrut\bar{c}}
\theta ( \bar{c} - \cbar_{<}) \theta( \cbar_{>} - \bar{c})$
\\[5pt]
\hline
\end{tabular}
\end{table}
To proceed we need to translate such a fundamental assumption into concrete
expressions for priors.
Cacciari and Houdeau do this through three supplementary assumptions
(which they call ``hypotheses'')~\cite{Cacciari:2011ze}, as follows.
\begin{itemize}
\item
The prior probability densities for coefficients at different orders are
independent in the sense of \eqref{eq:independent}. I.e., given an upper bound $\bar{c}$, the joint prior density
for coefficients factorizes:
%
\begin{equation}
\pdf(c_0, \ldots, c_n | \bar{c}) = \prod_{i=0}^n \pdf (c_i | \bar{c})
\;.
\label{eq:factorize}
\end{equation}
%
CH then also assume that $\pdf(c_i|\bar{c})$ is the same pdf for each $i$.
Thus the value of $\bar{c}$ is the most
knowledge obtainable from the known coefficients when predicting
possible values of unknown ones. In this way, we have isolated communication from the data about the sum of all omitted higher-order terms into one variable $\bar{c}$.
\item
Next we need a specific prior probability distribution for
$\pdf(c_i|\bar{c})$. In the interest of understanding the prior-dependence of our analysis, we test alternative implementations of naturalness in the priors.
The extent to which the posterior pdf for $\Delta_k$ is stable under different, but reasonable, choices of prior indicates the extent to which data on $\{c_n:n=0, \ldots, k\}$ is sufficiently informative to dominate the analysis.
When we know there is an upper bound to the coefficients, an application of maximum entropy dictates that the least-informative distribution is uniform for $|c_i| < \bar{c}$.
Such uniformity is additionally appealing because it can lead to simple, analytic results.
This uniform prior is the initial choice of Ref.~\cite{Cacciari:2011ze}. We employ it in priors we denote as ``Set A" and ``Set B" (see Table~\ref{tab:priors}), the difference being the prior pdf assumed for
$\bar{c}$ in the two cases (see below).
The priors of ``Set C" in Table~\ref{tab:priors} then correspond to the ensemble
naturalness assumption of Ref.~\cite{Schindler:2008fh}. This Gaussian prior follows
from the maximum-entropy principle assuming knowledge of testable information on the mean and standard deviation of the $c_n$'s~\cite{Sivia:06,Gull:98}
\begin{equation}
\label{eq:ensnat_conditions}
\left\langle \sum_{n=0}^{k} c_n^2 \right\rangle = (k+1)\bar{c}^2, \quad \left\langle c_n \right\rangle = 0
\;.
\end{equation}
We will see below that analyses with Sets A and B are insensitive to details of the distribution of $\{c_0, \ldots, c_k\}$: the only feature of the distribution that matters is the value of the largest of these $k+1$ lower-order coefficients. On the other hand, results under Set C priors are affected by the specific distribution of these coefficients, as well as by the largest value.
\item
Finally, the application of Bayes' theorem requires a prior for
$\bar{c}$: $\pdf(\bar{c})$.
Uniformity of $\ln\bar{c}$ is the only way to ensure unbiased expectations regarding the scale of $\bar{c}$~\cite{Jeffreys:1939}.
This log-uniform prior for $\bar{c}$ was chosen in Ref.~\cite{Cacciari:2011ze},
and so Set A of Table~\ref{tab:priors} is their choice of prior.
We also employ the log-uniform prior for $\bar{c}$ in Set C, there following Schindler
and Phillips in Ref.~\cite{Schindler:2008fh}. Such a prior cannot be normalized
for $\bar{c}$ in $(-\infty,\infty)$ and is therefore termed an ``improper prior".
Limiting the range of $\bar{c}$ through the use of $\theta$ functions
permits an examination of the otherwise ill-defined limiting behavior.
CH chose $\cbar_{<} = \epsilon$ and $\cbar_{>} = 1/\epsilon$
and take the limit $\epsilon\rightarrow 0$ at the end of the calculations. Thus,
the $\theta$ functions and associated $\ln\cbar_{>}/\cbar_{<}$ factor serve to regulate the
distribution so that the pdf is
always normalized. Taking the limit $\epsilon \rightarrow 0$ expresses complete
ignorance of the scale of $\bar{c}$, although we will also consider finite
ranges for the marginalization over $\bar{c}$, thereby rendering the priors more
informative.
In Refs.~\cite{Bagnaschi:2014wea,Bagnaschi:2014eva}, a more informative
$\bar{c}$ prior is considered based on the fact that the first
coefficient $c_0$ can be scaled out. The authors argue that in this case it is no longer necessary to allow for an arbitrarily large value for the other coefficients.
In consequence they assume $\bar{c}$'s prior is
a log-normal distribution about zero. We take this as Set~B of
Table~\ref{tab:priors}. Note that scaling the observable so that the first coefficient is order unity is also what we do for the EFT expansion, see Eq.~(\ref{eq:obsexp}).
\end{itemize}
In the case of prior information on the naturalness of coefficients that is different than that discussed here, maximum entropy can be used to derive how the different information should be reflected in alternative priors~\cite{Gull:98}. Such direct conversion from information on the interpretation of naturalness to prior pdfs facilitates rigorous derivation of the consequences of the concepts in question through the use of formal reasoning and the language of probability. We now show how this transpires by deriving the pdf for $\Delta_k$, initially refraining from specifying anything about the priors on $\{c_0, \ldots, c_k\}$.
\subsection{Posteriors and DOB intervals for $\Delta_k$}
Given the three assumptions described above and the prior sets of Table~\ref{tab:priors},
we can systematically derive the posterior for $\Delta_k$ by repeated
application of the sum and product rules and their logical Bayesian consequences.
At each step, we introduce a specific concept being built into the analysis.
For this general derivation we assume that
the coefficients start from $k=0$ and are all significant and non-zero (later we will modify the general results to treat the case of NN scattering in chiral EFT, where the orders are nominally $Q^0$, $Q^2$, $Q^3$, \ldots with $Q^1$ absent).
\begin{widetext}
\begin{enumerate}
\item \textbf{Formula for $\text{pr}\mathbf{(\Delta_k|c_0,...,c_k)}$:}
We seek $\pdf(\Delta_k| c_0,\ldots,c_k)$, which is the probability density
for the dimensionless residual, $\Delta_k$, given the known values of the first
$k+1$ coefficients. Because the true value of $\Delta_k$ depends only (explicitly)
on the unknown coefficients
$c_{n>k}$,
we insert them into the equation by
integrating over all their possible values using \eqref{eq:marginalize}
and \eqref{eq:product},
%
\begin{align}
\pdf(\Delta_k|c_0,\ldots,c_k) &=
\int\!
\pdf(\Delta_k|c_{k+1},c_{k+2},\ldots)
\, \pdf(c_{k+1},c_{k+2},\ldots | c_0,\ldots,c_k) \,
dc_{k+1} \, dc_{k+2}\, \cdots
\nonumber \\
&= \int \left[
\delta\left(\Delta_k - \sum_{n=k+1}^\infty c_n Q^n \right)
\right]
\, \pdf(c_{k+1},c_{k+2},\ldots | c_0,\ldots,c_k) \,
dc_{k+1} \, dc_{k+2}\, \cdots \;,
\label{eq:deltaeq}
\end{align}
%
where we have used
%
\begin{equation}
\pdf(\Delta_k|c_0,\ldots,c_k,c_{k+1},c_{k+2},\ldots)
=
\pdf(\Delta_k|c_{k+1},c_{k+2},\ldots)
=
\delta\left(\Delta_k - \sum_{n=k+1}^\infty c_n Q^n \right) \;.
\end{equation}
%
The latter is a direct consequence of Eq.~\eqref{eq:Deltak_def}.
Equation~\eqref{eq:deltaeq} states that, to get a specified $\Delta_k$ given a set of known coefficients,
we need to sum up all the different
combinations of $c_n$'s with $n > k$ that give us this $\Delta_k$, weighting each combination by
its probability given the known values of coefficients
$c_n$ for $n\leq k$. Note that all of these integrals over $c_n$ are from $-\infty$ to $+\infty$
in general, but in particular cases there may be constraints (e.g., a cross section
is positive, so the leading coefficient will be positive).
The probability density \eqref{eq:deltaeq} is
correctly normalized since the normalization integral over $\Delta_k$ can be performed using the delta function,
leaving the normalization integral for $\pdf(c_{k+1},c_{k+2},\ldots | c_0,\ldots,c_k)$,
which is unity.
\item \textbf{Independent priors:}
Our priors are based on the assumption that
$\bar{c}$ is the only information that gets transmitted to the
distribution of $c_{n}$ for $n>k$.
Thus, at this stage we introduce $\bar{c}$ as an intermediary in the pdf in
the integrand of Eq.~\eqref{eq:deltaeq}
via another marginalization integral, and apply this assumption:
%
\begin{align}
\pdf(c_{k+1},c_{k+2},\ldots | c_0,\ldots,c_k)
&= \int_0^\infty \!
\pdf(c_{k+1},c_{k+2},\ldots | \bar{c}, c_0,\ldots,c_k) \, \pdf(\bar{c} | c_0,\ldots,c_k)\, d\bar{c}
\nonumber \\
&= \int_0^\infty \!
\pdf(c_{k+1},c_{k+2},\ldots | \bar{c}) \, \pdf(\bar{c} | c_0,\ldots,c_k)\, d\bar{c}
\nonumber \\
&= \int_0^\infty
\Bigl[\prod_{n=k+1}^{\infty} \pdf(c_n | \bar{c})\Bigr]
\pdf(\bar{c} | c_0,\ldots,c_k)\, d\bar{c}
\;.
\label{eq:cbarfirst}
\end{align}
%
In the final equality we have used the assumption that the
$c_i$ distributions are independent, causing the joint densities for the $c_n$'s with $n>k$ to become the product
of independent densities $\pdf(c_n|\bar{c})$.
We will see that the imposition of Set A or Set C priors for $\bar{c}$ makes the limits on this integral finite.
\item
\textbf{Leading-term approximation:} We next assume
$\Delta_k \approx c_{k+1}Q^{k+1} \equiv \ensuremath{\Delta_k^{(1)}}$
in Eq.~\eqref{eq:deltaeq} and return later to relax this assumption.
By examining the effect of this assumption on DOB intervals, we will show that this approximation is quite appropriate for small values of $Q$.
This is the simplest way to
exploit the delta function, which then depends only on $c_{k+1}$.
After substituting Eq.~\eqref{eq:cbarfirst} into \eqref{eq:deltaeq}, the
$c_{k+2},\ldots$ integrals are just normalization integrals (equal to one),
leaving integrations over $c_{k+1}$ and $\bar{c}$:
%
\begin{align}
\pdf(\ensuremath{\Delta_k^{(1)}}|c_0,\ldots,c_k) &= \int_{-\infty}^\infty \int_0^\infty \bigl[
\delta(\ensuremath{\Delta_k^{(1)}} - c_{k+1} Q^{k+1})
\bigr]
\pdf(c_{k+1}|\bar{c}) \, \pdf(\bar{c} | c_0,\ldots,c_k)\, d\bar{c}\, dc_{k+1}
\nonumber
\\
&= \frac{1}{Q^{k+1}} \int_0^\infty \!
\pdf(c_{k+1} = \ensuremath{\Delta_k^{(1)}}/Q^{k+1} | \bar{c}) \,
\pdf(\bar{c} | c_0,\ldots,c_k)\, d\bar{c}
\;. \label{eq:ckplusone}
\end{align}
%
\item \textbf{Expanding the composite prior:}
The first pdf in the integrand of
\eqref{eq:ckplusone} may be directly evaluated for a given choice of prior,
but the second cannot. It can, however, be identified as being constructed
from the priors defined in Table~\ref{tab:priors}, via
application of Bayes' theorem:
%
\begin{align}
\pdf} % {\pdf_{\epsilon}(\bar{c} | c_0,\ldots,c_k) &=
\frac {\pdf} % {\pdf_{\epsilon}(c_0,\ldots,c_k | \bar{c})\, \pdf} % {\pdf_{\epsilon}(\bar{c})} {\pdf} % {\pdf_{\epsilon}(c_0,\ldots,c_k)}
\nonumber \\ &=
\frac {\pdf} % {\pdf_{\epsilon}(c_0,\ldots,c_k | \bar{c})\, \pdf} % {\pdf_{\epsilon}(\bar{c})}
{\int_0^\infty \pdf} % {\pdf_{\epsilon}(c_0,\ldots,c_k | \bar{c}')\, \pdf} % {\pdf_{\epsilon}(\bar{c}')\, d\bar{c}'}
\nonumber \\ &=
\frac {\displaystyle\Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c})\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c})}
{\displaystyle\int_0^\infty \Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c}')\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c}')\, d\bar{c}'}
\;.
\label{eq:BayesEps}
\end{align}
%
In the second line
we have introduced another marginalization over
$\bar{c}'$ in the denominator, while in the third line we apply the independence
assumption of Eq.~\eqref{eq:factorize}.
Combining \eqref{eq:BayesEps} and \eqref{eq:ckplusone} gives:
%
\begin{equation}
\pdf(\ensuremath{\Delta_k^{(1)}}|c_0,\ldots,c_k) =
\frac{ \displaystyle\int_0^\infty \!
\pdf(c_{k+1} = \ensuremath{\Delta_k^{(1)}}/Q^{k+1} | \bar{c}) \,
\displaystyle\Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c})\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c})
\, d\bar{c}}
{\displaystyle Q^{k+1} \int_0^\infty \Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c}')\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c}')\, d\bar{c}'}
\;.
\label{eq:BayesEps2}
\end{equation}
%
Now we can apply one of the sets of assumptions in Table~\ref{tab:priors},
which give us specific forms
to evaluate each of the pdfs in Eq.~\eqref{eq:BayesEps2}.
Note that if some of the $c_i$'s for $i < k$ are identically zero, there are
correspondingly fewer terms in the products of $\text{pr}(c_n | \bar{c})$ in
Eq.~\eqref{eq:BayesEps2}.
\item \textbf{Prior Set $\ensuremath{{\rm A}^{(1)}}$:}
Prior Set~A has been developed under the assumption
that identifying a maximum value $\bar{c}$ is a valid
concept.
We here start with a finite $\bar{c}$ range between $\cbar_{<}$ and $\cbar_{>}$ for which Eq.~\eqref{eq:BayesEps2} can be evaluated analytically.
If $\cbar_{<} = \epsilon$ and $\cbar_{>} = 1/\epsilon$
and we take the limit as $\epsilon \rightarrow 0$, we designate this as Set $\ensuremath{{\rm A}_{\epsilon}}$. Meanwhile, the superscript $^{(1)}$ is introduced to denote
the use of the first-term approximation.
For this prior choice, $\ensuremath{{\rm A}^{(1)}}$, the denominator of Eq.~\eqref{eq:BayesEps2} is directly evaluated
as there are only integrals over theta functions:
%
\begin{align}
\int_0^\infty \Bigl[\prod_{n=0}^{k} \pdf(c_n|\bar{c}') \Bigr] \,
\pdf} % {\pdf_{\epsilon}(\bar{c}')\, d\bar{c}'
&= \int_0^\infty
\Bigl[\prod_{n=0}^{k} \frac{1}{2\bar{c}'}\theta(\bar{c}'-|c_n|) \Bigr]
\frac{1}{\ln\cbar_{>}/\cbar_{<}} \,\frac{1}{\bar{c}'} \, \theta(\bar{c}'-\cbar_{<})
\theta(\cbar_{>} - \bar{c}')
\, d\bar{c}'
\nonumber \\
&= \frac{1}{2^{k+1}}\frac{1}{\ln\cbar_{>}/\cbar_{<}}
\int_{\max(\cbarsubk{k},\cbar_{<})}^{\cbar_{>}} \frac{1}{\bar{c}'{}^{k+2}}
\, d\bar{c}'
\;,
\end{align}
where we have followed CH~\cite{Cacciari:2011ze} and introduced the variable $\bar{c}_{(j)}$ to denote the maximum of the first $j+1$ coefficients:
%
\begin{equation}
\bar{c}_{(j)} \equiv \max(|c_0|,\cdots,|c_j|)
\;.
\label{eq:cbarkDef}
\end{equation}
%
The integration over $\bar{c}$ in the numerator of Eq.~\eqref{eq:BayesEps2} is similar, but contains the
extra pdf $\pdf(c_{k+1} = \ensuremath{\Delta_k^{(1)}}/Q^{k+1} | \bar{c})$ in the
integrand. Using the theta functions to once again define the integration bounds, the numerator simplifies to
\begin{equation}
\frac{1}{2^{k+2}} \frac{1}{\ln \cbar_{>}/\cbar_{<}} \theta\left( \cbar_{>} - \cbarsubk{k+1}\right) \int_{\max(\cbarsubk{k+1}, \cbar_{<})}^{\cbar_{>}} \frac{1}{\bar{c}^{k+3}} \, d \bar{c} \;.
\end{equation}
We can see now how regulating the integrals with $\cbar_{>}$ and $\cbar_{<}$ will allow
terms such as $\ln\cbar_{>}/\cbar_{<}$ (and most factors of 2)
to cancel between the numerator and denominator, after which we may choose to
take $\epsilon$ to zero in $\Aeps^{(1)}$ without consequence.
More generally, we assume that the integration range for $\bar{c}$ is wide enough that $\cbar_{<} < \cbarsubk{k} < \cbar_{>}$. The posterior then evaluates to:
\begin{equation}
\text{pr}(\ensuremath{\Delta_k^{(1)}}|\ensuremath{c_0,\ldots,c_k}) =
\frac{1}{Q^{k+1}} \frac{1}{2} \left(\frac{k+1}{k+2}\right)
\frac{\theta \left( \cbar_{>} - \cbarsubk{k+1} \right)}{ \cbarsubk{k}^{-(k+1)} - \cbar_{>}^{-(k+1)}}
\Scale[0.95]{
\begin{cases}
\cbarsubk{k}^{-(k+2)} - \cbar_{>}^{-(k+2)}
& \mbox{if }\left| \ensuremath{\Delta_k^{(1)}} \right| \leq \cbarsubk{k} Q^{k+1}
\vspace{2mm}
\\
\left(\frac{\textstyleQ^{k+1}}{\textstyle\bigl|\ensuremath{\Delta_k^{(1)}}\bigr|}\right)^{k+2} - \cbar_{>}^{-(k+2)}
& \mbox{if }\left| \ensuremath{\Delta_k^{(1)}} \right| > \cbarsubk{k} Q^{k+1}
\end{cases}
}
\;.
\end{equation}
If some of the coefficients are zero (e.g., the series
starts at $Q^l$ with $l>0$, or one or more
intermediate coefficients are zero) we can revise these formulas trivially:
the only change is that there are fewer theta functions in the
integrals. Taking $n_c$ to be the number of non-zero constants, we implement
this generalization by replacing
$k$ by $n_c-1$ everywhere except for powers of $Q$, which remain
$k+1$. Thus, the modified posterior for Set $\ensuremath{{\rm A}^{(1)}}$ is
%
\begin{equation}
\hspace{7mm}
\label{eq:setAposterior}
\text{pr}(\ensuremath{\Delta_k^{(1)}}|\ensuremath{c_0,\ldots,c_k}) =
\frac{1}{Q^{k+1}} \frac{1}{2} \left(\frac{n_c}{n_c+1}\right)
\frac{\theta \left( \cbar_{>} - \cbarsubk{k+1} \right)}{\cbarsubk{k}^{-n_c} - \cbar_{>}^{-n_c}}
\Scale[0.95]{
\begin{cases}
\cbarsubk{k}^{-(n_c+1)} - \cbar_{>}^{-(n_c + 1)}
& \mbox{if }\left| \ensuremath{\Delta_k^{(1)}} \right| \leq \cbarsubk{k} Q^{k+1}
\vspace{2mm}
\\
\left(\frac{\textstyleQ^{k+1}}{\textstyle\bigl|\ensuremath{\Delta_k^{(1)}}\bigr|}\right)^{n_c+1} - \cbar_{>}^{-(n_c+1)}
& \mbox{if }\left| \ensuremath{\Delta_k^{(1)}} \right| > \cbarsubk{k} Q^{k+1}
\end{cases}
}
\;,
\end{equation}
which simplifies to the corresponding equation of Ref.~\cite{Cacciari:2011ze} in the limiting case of $\Aeps^{(1)}$
\begin{equation}
\pdf(\ensuremath{\Delta_k^{(1)}} | c_0, \ldots, c_k) =
\left(\frac{n_c}{n_c+1} \right)
\frac{1}{2\cbarsubk{k}Q^{k+1}}
\begin{cases}
1 & \mbox{if }|\ensuremath{\Delta_k^{(1)}}| \leq \cbarsubk{k}Q^{k+1} \\
\left(\frac{\textstyle\cbarsubk{k}Q^{k+1}}{\textstyle\bigl|\ensuremath{\Delta_k^{(1)}}\bigr|}\right)^{n_c+1}
& \mbox{if }|\ensuremath{\Delta_k^{(1)}}| > \cbarsubk{k}Q^{k+1}
\end{cases}
\;.
\end{equation}
Note that this simple generalization is possible due to the identical treatment of the priors for each coefficient.
\item \textbf{Prior Sets $\ensuremath{{\rm B}^{(1)}}$ and $\ensuremath{{\rm C}^{(1)}}$:}
Neither Set~B nor Set~C priors allow for analytic integrals over $\bar{c}$, so the discussion here will necessarily be less extensive than that for Set~A.
In the first-term approximation the posterior for $\Delta_k$ can be reduced to a one-dimensional integral, whose evaluation must be left to numerical integration.
Inserting Set~C priors into Eq.~\eqref{eq:BayesEps2} results in
\begin{equation}
\label{eq:setCposterior}
\text{pr}(\ensuremath{\Delta_k^{(1)}}|\ensuremath{c_0,\ldots,c_k}) =
\frac{
\frac{\textstyle 1}{\textstyleQ^{k+1}} \frac{\textstyle 1}{\textstyle\sqrt{2\pi}}
\int\limits_{\cbar_{<}}^{\cbar_{>}} d \bar{c} \,
\exp{\left[-\frac{\left(\ensuremath{\Delta_k^{(1)}}\right)^2}
{2 \left(Q^{k+1}\right)^2\bar{c}^2} \right]}
\left(\frac{\textstyle 1}{\textstyle\strut\bar{c}}\right)^{n_c + 2}
\left[ \prod\limits_n e^{-c_n^2/2\bar{c}^2} \right]
}{
\int\limits_{\cbar_{<}}^{\cbar_{>}} d \bar{c}'\,\left(\frac{\textstyle 1}{\textstyle\bar{c}'}\right)^{n_c + 1}\left[ \prod\limits_n e^{-c_n^2/2\bar{c}'^2} \right]
}
\;,
\end{equation}
where products are assumed to run over all $n_c$ coefficients with defined prior distributions.
\item \textbf{DOB intervals: }
In the Bayesian framework, the posterior $\pdf(\Delta_k | c_0, \ldots, c_k)$
contains the complete
information we claim to have about the dimensionless residual $\Delta_k$.
In some applications we need to use the entire posterior because it is
very structured (e.g., multi-modal or simply non-gaussian), but here
we can capture most of the information with the choice of a small number
of degree-of-belief (DOB) intervals.%
\footnote{These are also called ``credibility" or ``credible" intervals.}
In particular, the DOB for a particular interval in $\Delta_k$ is
found simply by integrating $\pdf(\Delta_k | c_0, \ldots, c_k)$
over this interval. We could also start with a given DOB, e.g., the standard frequentist (gaussian) 68\% or 95\%, and determine the smallest interval that integrates
to that number. Or we could specify some other criterion for deciding the interval,
such as that it is symmetric about the mode.
In fact, the use of any of the priors
in Table~\ref{tab:priors} results in a smallest p\%-DOB interval
for $\Delta_k$ that is symmetric about the mode; following Ref.~\cite{Cacciari:2011ze} we
denote the corresponding dimensionless limits by $\pm d_k^{(p)}$.
Thus the implicit definition of this interval is
%
\begin{equation}
p\% = \int_{-d_k^{(p)}}^{d_k^{(p)}} \pdf(\Delta_k | c_0, \ldots, c_k)
\, d\Delta_k
\;.
\label{eq:integralford}
\end{equation}
%
In the limiting case of prior Set~$\Aeps^{(1)}$, this integral can be evaluated
explicitly~\cite{Cacciari:2011ze}:
\begin{equation}
d_k^{(p)} = \cbarsubk{k} \, Q^{k+1}
\times
\begin{cases}
\frac{\textstyle n_c+1}{\textstyle n_c}\, p\%
& \mbox{if } p\ \leq \frac{\textstyle n_c}{\textstyle n_c+1} \\
\Bigl[ \frac{\textstyle 1}{\textstyle (n_c+1)(1-p\%)} \Bigr]^{1/n_c}
& \mbox{if } p\ > \frac{\textstyle n_c}{\textstyle n_c+1}
\end{cases}
\label{eq:dcoeffs}
\;,
\end{equation}
where $n_c$ is again the number of non-zero known coefficients.
Thus, with these priors, the interval of
width $\cbarsubk{k} Q^{k+1}$ about the EFT prediction at order $k$ is a
$n_c/(n_c + 1)*100\%$ DOB interval, cf.\ Ref.~\cite{Cacciari:2011ze}.
Such a theory error bar has often been
assigned in previous EFT calculations, and---as we shall discuss further
in Section~\ref{sec:EKM}---corresponds to the prescription formalized in
Refs.~\cite{Epelbaum:2014efa,Epelbaum:2014sza}. It is important---e.g.,
in the context of error propagation---to keep in mind that this prior
leads to a distribution of probability for the truncation error that is
not Gaussian.
For the more general form of prior Set~$\ensuremath{{\rm A}^{(1)}}$, an analytic formula
for $d_k^{(p)}$ can still be found.
The explicit form of the integral depends on the $p\%$ value of interest,
because of the change in structure for
$\bigl| \ensuremath{\Delta_k^{(1)}} \bigr| > \cbarsubk{k} Q^{k+1}$.
Thus, we first calculate this transition value $\ensuremath{\left(p\%\right)_{\rm t}}$ by integrating
the maximal probability within the first region in which
$|c_{k+1}| \leq \cbarsubk{k}$ to obtain
\begin{equation}
\ensuremath{\left(p\%\right)_{\rm t}}
= \left[ \frac{\frac{1}{\strut\cbarsubk{k}^{n_c+1}} - \frac{1}{\strut\cbar_{>}^{n_c+1}}
}{
\frac{1}{\strut\cbarsubk{k}^{n_c}} - \frac{1}{\strut\cbar_{>}^{n_c}}} \right] \left(\frac{n_c}{n_c+1}\right) \cbarsubk{k}
\;.
\label{eq:pregion1}
\end{equation}
%
Now suppose we are interested in $p\%$ intervals for $p < p_t$.
Equation~\eqref{eq:pregion1} implies that the interval bounded by variation $\pm \cbarsubk{k} Q^{k+1}$ is a \mbox{$\ensuremath{\left(p\%\right)_{\rm t}}$-DOB interval}. Generally,
the DOB interval for Set~$\ensuremath{{\rm A}^{(1)}}$ is bounded by
\begin{equation}
\label{eq:aonedkpregion1}
\ensuremath{d_k^{(p)}} =\left[ \frac{\frac{1}{\strut\cbarsubk{k}^{n_c+1}} - \frac{1}{\strut\cbar_{>}^{n_c+1}}
}{
\frac{1}{\strut\cbarsubk{k}^{n_c}} - \frac{1}{\strut\cbar_{>}^{n_c}}} \right]^{-1} \frac{n_c+1}{n_c}\, p\% \, Q^{k+1} \qquad \mbox{if } p\% \leq \ensuremath{\left(p\%\right)_{\rm t}}
\;.
\end{equation}
When one is interested in larger $p\%$ values, it may be beneficial to take advantage of the normalization of the pdf to conduct an integration in only one region by integrating the second case of Eq.~\eqref{eq:setAposterior} on the interval $\left[\ensuremath{d_k^{(p)}},\infty\right]$.
Because $\cbarsubk{k+1} = c_{k+1}$ in this region, the theta function truncates this integration at $\ensuremath{\Delta_k^{(1)}} = \cbar_{>} Q^{k+1}$.
The resulting implicit expression for $\ensuremath{d_k^{(p)}}$ if $p\% > \ensuremath{\left(p\%\right)_{\rm t}}$ is thus
\begin{eqnarray}
\label{eq:aonedkpregion2}
(1-p\%)=\frac{1}{Q^{k+1}} \left(\frac{n_c}{n_c+1}\right) \frac{1}{ \frac{1}{\strut\cbarsubk{k}^{n_c}} - \frac{1}{\strut\cbar_{>}^{n_c}}} \left[ \frac{\left(\ensuremath{d_k^{(p)}} - \cbar_{>} Q^{k+1}\right)}{\cbar_{>}^{n_c+1}} +
\frac{\left(Q^{k+1}\right)^{n_c+1}}{n_c} \left(\frac{1}{\bigl(\ensuremath{d_k^{(p)}}\bigr)^{n_c}} - \frac{1}{(\cbar_{>} Q^{k+1})^{n_c}} \right) \right].\nonumber\\
\end{eqnarray}
For Set~$\ensuremath{{\rm B}^{(1)}}$, Set $\ensuremath{{\rm C}^{(1)}}$, or, indeed, for any of the sets if we do not make the first-term approximation,
the DOB interval $\ensuremath{d_k^{(p)}}$ can be found numerically from Eq.~\eqref{eq:integralford}
by integrating $\pdf(\Delta_k | c_0, \ldots, c_k)$
(e.g., from Eq.~\eqref{eq:setCposterior}) from zero until
the integral equals $p/2$.
We stress again the resulting DOB intervals are
\emph{not} standard
deviations and make no statement about the shape of the normalized
function which integrates to 0.68 between the bounds $\pm d_k^{(68)}$.
\item \textbf{Relaxation of first-term approximation:}
To relax the assumption that the first omitted term dominates, we introduce the generalized notation
%
\begin{equation}
\Delta_k \approx
\ensuremath{\Delta_k^{(1)}} + \sum_{m=k+2}^{k_{\rm max}} c_m Q^m \equiv \Delta_k^{(k_{\rm max}-k)} = \Delta_k^{(h)} \;,
\label{eq:tildeDeltak}
\end{equation}
%
where $k_{\rm max}$ is the highest-order coefficient kept in the sum of omitted
terms.
Returning to step 3 above,
we continue to use the $\delta$ function to eliminate the integral over
$c_{k+1}$, with the result that $\ensuremath{\Delta_k^{(1)}}$ is replaced by $\Delta_k^{(k_{\rm max}-k)}$ in
the subsequent expression and the integrations over $c_{m}$ for $m > k+1$
up to $m = k_{\rm max}$ remain. The generalization of Eq.~\eqref{eq:BayesEps2} is then
%
\begin{equation}
\pdf(\Delta_k^{(h)}|c_0,\ldots,c_k) =
\frac{ \displaystyle \int_{-\infty}^\infty \!\cdots\!\int_{-\infty}^\infty \int_0^\infty\!
\pdf(c_{k+1} = \Delta_k^{(h)}(Q)/Q^{k+1} | \bar{c}) \,
\displaystyle\Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c})\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c})
\, d\bar{c} \, \prod_{m=k+2}^{k_{\rm max}} \text{pr}(c_m | \bar{c})\,dc_m }
{\displaystyle Q^{k+1} \int_0^\infty \Bigl[\prod_{n=0}^{k} \text{pr}(c_n | \bar{c}')\Bigr] \pdf} % {\pdf_{\epsilon}(\bar{c}')\, d\bar{c}'}
\;,
\label{eq:BayesEpsFull}
\end{equation}
%
where there are $k_{\rm max} - k - 1$ integrals from $-\infty$ to $\infty$ in the numerator, in addition to the integral over the (positive) $\bar{c}$.
Note that if the first omitted term really does dominate,
then the integrals over higher
$c_m$'s are trivial normalization integrals, restoring the result of the first-omitted-term approximation.
\item \textbf{Summary:}
We have derived a general result for $\pdf(\Delta_k|c_0,\ldots,c_k)$
in Eq.~\eqref{eq:BayesEpsFull},
which is valid for any of the sets in Table~\ref{tab:priors}.
In most cases this expression must be evaluated numerically, for example by Monte Carlo
integration. By assuming the first omitted term dominates, we obtain
the much less involved integration in Eq.~\eqref{eq:BayesEps2}. Evaluating the
application of this approximation to Set~$\ensuremath{{\rm A}^{(1)}}$ yields the analytic result
in Eq.~\eqref{eq:setAposterior} while for Sets $\ensuremath{{\rm B}^{(1)}}$ and $\ensuremath{{\rm C}^{(1)}}$ integrals are left to be evaluated numerically---see, e.g.,
Eq.~\eqref{eq:setCposterior}.
Finally, DOB intervals can be derived from these posteriors
analytically for $\ensuremath{{\rm A}^{(1)}}$ (Eqs.~\eqref{eq:dcoeffs}, \eqref{eq:aonedkpregion1},
and \eqref{eq:aonedkpregion2})
and numerically for the others from Eq.~\eqref{eq:integralford}.
\end{enumerate}
\end{widetext}
\subsection{Representative examples}
\begin{figure*}[tbh!]
\includegraphics[width=0.32\textwidth]{Delta_k0_z0p33_setA_1000000.pdf}~~%
\includegraphics[width=0.32\textwidth]{Delta_k2_z0p33_setA_1000000.pdf}
\includegraphics[width=0.32\textwidth]{Delta_k4_z0p33_setA_1000000.pdf}
\caption{(color online) Posteriors for $\ensuremath{\Delta_k^{(1)}}$ under Set $\Aeps^{(1)}$ priors of Table~\ref{tab:priors}
for $k=0$, 2, and 4 with $Q=0.33$. In all cases, $c_n = 1$ was assumed.
The solid red curve is the analytic result from Eq.~\eqref{eq:setAposterior}, with the shaded regions
marking the 68\% and 95\% DOB intervals. The solid blue curve is the posterior $\Delta_k$ for
$\ensuremath{{\rm A}_{\epsilon}}$ once higher-order terms are included, with dot-dashed and dashed lines marking
the corresponding 68\% and 95\% DOB intervals.}
\label{fig:setAposterior}
\end{figure*}
\begin{figure*}[tbh!]
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig0p25_Delta_k2_z0p20.pdf}~%
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig0p50_Delta_k2_z0p20.pdf}~%
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig1p00_Delta_k2_z0p20.pdf}~%
\caption{(color online) Comparison of $\Delta_2$ for prior set \ensuremath{{\rm A}_{\epsilon}}\ (red solid line) and
B (blue solid line) for $\sigma=0.25$, $0.5$ and $1.00$ respectively. In each case $c_0,c_1,c_2$ are all set to
unity with an expansion parameter $Q = 0.2$. The DOB intervals are indicated as
in Fig.~\ref{fig:setAposterior}.}
\label{fig:compareABposteriors0p20}
\end{figure*}
\begin{figure*}[tbh!]
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig0p25_Delta_k2_z0p50.pdf}~%
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig0p50_Delta_k2_z0p50.pdf}~%
\includegraphics[width=0.32\textwidth]{setA_vs_setB_sig1p00_Delta_k2_z0p50.pdf}~%
\caption{(color online) Comparison of $\Delta_2$ for prior set \ensuremath{{\rm A}_{\epsilon}}\ (red solid line) and
B (blue solid line) for three values of $\sigma$ and $c_0,c_1,c_2$ all set to
unity with an expansion parameter $Q = 0.5$.
The DOB intervals are indicated as in Fig.~\ref{fig:setAposterior}.}
\label{fig:compareABposteriors0p50}
\end{figure*}
\begin{figure*}[tbh!]
\includegraphics[width=0.32\textwidth]{Delta_k2_z0p33_setA_vs_setC_a.pdf}~%
\includegraphics[width=0.32\textwidth]{Delta_k2_z0p33_setA_vs_setC_b.pdf}~%
\includegraphics[width=0.32\textwidth]{Delta_k2_z0p33_setA_vs_setC_c.pdf}~%
\caption{(color online) Comparison of $\Delta_2$ for prior set \ensuremath{{\rm A}_{\epsilon}}$^{(1)}$\ (red solid line)
and \ensuremath{{\rm C}_{\epsilon}}$^{(1)}$\ (blue solid line)---note both are in the leading-omitted-term
approximation---for three sets of $c_n$ values with an expansion parameter $Q = 0.33$.
These sets are (left-to-right) $\{c_n\}(a)\equiv \{1.0,1.0,1.0\}$, $\{c_n\}(b) \equiv\{1.0,0.5,0.1\}$,
and $\{c_n\}(c) \equiv \{1.0,0.1,0.1\}$.
The DOB intervals are indicated as in Fig.~\ref{fig:setAposterior}.}
\label{fig:compareACposteriors0p33}
\end{figure*}
Before applying the Bayesian framework developed by CH, and extended above,
to the specific problem of NN scattering, we make some
general observations on the form of the posteriors for $\Delta_k$
and the systematics of the
68\% and 95\% DOB intervals for various prior sets from
Table~\ref{tab:priors}.
We start with the set \ensuremath{{\rm A}_{\epsilon}}, defined by $\cbar_{<} = \epsilon$,
$\cbar_{>} = 1/\epsilon$, with $\epsilon \rightarrow 0$
(in practice all results here in which $\epsilon$ is invoked use $\epsilon = 0.001$).
The posterior distribution for $\ensuremath{\Delta_k^{(1)}}$ in Eq.~\eqref{eq:setAposterior},
which assumes the first omitted term dominates the error,
has a flat central plateau with power-suppressed tails.
This is illustrated by the red curves in Fig.~\ref{fig:setAposterior} for
$k=0$, $k=2$, and $k=4$, for $Q=0.33$. The heavy and light shaded regions show
the 68\% and 95\% DOB intervals, respectively.
From Eq.~\eqref{eq:dcoeffs}, the width of the posterior is given by
$\cbarsubk{k} Q^{k+1}$ times a number of order unity, so the dominant effect is that
the width decreases by a factor of $Q$ with each increase of $k$ by one.
In fact, only the maximum value of the $c_n$'s for a given $k$, $\cbarsubk{k}$, matters under this choice of prior; the distribution of those $c_n$'s is irrelevant.
The overall size of all DOB intervals then scales linearly with $\cbarsubk{k}$, so here $c_0$, \ldots, $c_k$ have all been set to one for simplicity.
For Set A priors the generalization to other cases is trivial.
To relax the first-term approximation we include the first four omitted terms in our computation of $\Delta_k$.
The result is then converged numerically in all cases shown, so in practice Set $Y^{(4)}$ ($Y=A$, $B$, or $C$) priors lead to the same results as
when arbitrarily many higher-order terms included in the truncation-error calculation. In consequence, we do not include superscripts below
when reporting results with terms beyond the first omitted one included in the computation of $\Delta_k$. Such calculations show
that the central plateau in the posterior becomes rounded (blue curve
in Fig.~\ref{fig:setAposterior}).
The corresponding effect on the DOB intervals depends on the value
of $k$; for $k\geq 2$ there is no significant
effect on the 68\% DOB intervals while the 95\% intervals are increased slightly.
If we use the more informative log-normal prior for $\bar{c}$ from set B, the tails are
more quickly suppressed than for set \ensuremath{{\rm A}_{\epsilon}}, to a degree that depends in detail on the values of
$\sigma$ and $Q$~\cite{Bagnaschi:2014eva,Bagnaschi:2014wea}.
Representative examples for $\Delta_2$
are shown in Figs.~\ref{fig:compareABposteriors0p20}
and \ref{fig:compareABposteriors0p50} for $Q=0.2$ and $Q=0.5$, respectively,
with $\sigma=0.25$, $0.5$, and $1.0$ respectively.
We see that the 68\% DOB and 95\% DOB intervals are smaller that those for \ensuremath{{\rm A}_{\epsilon}},
with the difference increasing with smaller $\sigma$.
The further extension of the tail for \ensuremath{{\rm A}_{\epsilon}}\ is not surprising
as we have allowed for the possibility of $\bar{c}$ having a large range.
As $\sigma$ gets larger, the posteriors for each $Q$ value
approach the \ensuremath{{\rm A}_{\epsilon}}\ result; once
$\sigma \geq 1.0$ there is very little difference between $\ensuremath{{\rm A}_{\epsilon}}$ and Set B for $k\geq 2$. $k=0$ and $k=1$ are more sensitive
to $\sigma$.
\begin{table*}[tbh]
\setlength{\tabcolsep}{9pt}
\caption{Resulting 68\% and 95\% DOB intervals for $\Delta_k$ using Set $\ensuremath{{\rm A}^{(1)}}$ with different choices for the minimum and maximum of the $\bar{c}$ prior. In all cases $\cbarsubk{k} = 1$.}
\label{tab:setA_approx2}
\begin{tabular}{c|c|c|c|c|c|c|c|c}
& min/max & $Q$ & $k=0$ & $k=1$ & $k=2$ & $k=3$ & $k=4$ \\
\hline
& 0.001/1000 & &
0.31 & 0.041 & 0.0073 & 0.00136 & 0.00026 \\
& 0.25/4.0 & 0.20 & 0.22 & 0.039 & 0.0072 & 0.00136 & 0.00026 \\
& 0.50/2.0 & & 0.18 & 0.035 & 0.0068 & 0.00132 & 0.00026 \\
\cline{2-8}
& 0.001/1000 & & 0.51 & 0.111 & 0.033 & 0.0101 & 0.0032 \\
68\% & 0.25/4.0 & 0.33 & 0.36 & 0.106 & 0.032 & 0.0101 & 0.0032 \\
& 0.50/2.0 & & 0.30 & 0.095 & 0.030 & 0.0098 & 0.0031 \\
\cline{2-8}
& 0.001/1000 & & 0.78 & 0.26 & 0.113 & 0.053 & 0.026 \\
& 0.25/4.0 & 0.50 & 0.55 & 0.243 & 0.112 & 0.053 & 0.025 \\
& 0.50/2.0 & & 0.45 & 0.22 & 0.106 & 0.051 & 0.025 \\
\hline\hline
& 0.001/1000 & & 1.96 & 0.103 & 0.0137 & 0.0023 & 0.00041 \\
& 0.25/4.0 & 0.20 & 0.47 & 0.077 & 0.0129 & 0.0022 & 0.00041 \\
& 0.50/2.0 & & 0.29 & 0.056 & 0.011 & 0.0020 & 0.00039 \\
\cline{2-8}
& 0.001/1000 & & 3.2 & 0.28 & 0.0614 & 0.0168 & 0.0050 \\
95\% & 0.25/4.0 & 0.33 & 0.77 & 0.21 & 0.058 & 0.0166 & 0.0050 \\
& 0.50/2.0 & & 0.48 & 0.152 & 0.048 & 0.0150 & 0.0047 \\
\cline{2-8}
& 0.001/1000 & & 4.91 & 0.645 & 0.21 & 0.0884 & 0.040 \\
& 0.25/4.0 & 0.50 & 1.16 & 0.48 & 0.201 & 0.087 & 0.040 \\
& 0.50/2.0 & & 0.73 & 0.35 & 0.166 & 0.079 & 0.038 \\
\hline
\end{tabular}
\end{table*}
We might expect that the Set B results with $\sigma > 1.0$ will be even closer to those from
Set A if we impose a range of $\bar{c}$ values in Set A that
reflects naturalness expectations.
Results of varying the range over which $\bar{c}$ is marginalized are shown in Table~\ref{tab:setA_approx2}, where
we compare DOB intervals for $\Delta_k$ with $k$ from 0 to 4.
For $k\geq 3$, the change in the range of $\bar{c}$ has no noticeable effect on either the 68\% or 95\%
DOB.
For $k=2$, effects are 5--10\% on the 68\% interval if a narrow range ($\bar{c}$ from 0.5 to 2.0) is employed. Effects on the 95\%
interval can be up to 20\% if this narrow range is employed at $k=2$.
\begin{table*}[tbh]
\setlength{\tabcolsep}{9pt}
\caption{DOB intervals for Sets \ensuremath{{\rm A}_{\epsilon}}\ and \ensuremath{{\rm C}_{\epsilon}},
with and without the leading omitted term
approximation, for $k=2$, with three sets of $c_n$ values.
These sets are
$\{c_n\}(a)\equiv \{1.0,1.0,1.0\}$, $\{c_n\}(b) \equiv\{1.0,0.5,0.1\}$,
and $\{c_n\}(c) \equiv \{1.0,0.1,0.1\}$. }
\label{tab:results_setC_approx1}
\begin{tabular}{c|c|c|c|c|c|c}
& $Q$ & $\Aeps^{(1)}/\ensuremath{{\rm A}_{\epsilon}}$ & $\Ceps^{(1)}/\ensuremath{{\rm C}_{\epsilon}}\ \{c_n\}(a)$ & $\Ceps^{(1)}/\ensuremath{{\rm C}_{\epsilon}}\ \{c_n\}(b)$
& $\Ceps^{(1)}/\ensuremath{{\rm C}_{\epsilon}}\ \{c_n\}(c) $ \\
\hline
& 0.20 & 0.0073/0.0073 & 0.0095/0.0097 & 0.0062/0.0063 & 0.0056/0.0057 \\
68\% & 0.33 & 0.033/0.033 & 0.043/0.045 & 0.028/0.029 & 0.025/0.026 \\
& 0.50 & 0.113/0.123 & 0.149/0.171 & 0.096/0.111 & 0.087/0.100 \\
\hline\hline
& 0.20 & 0.0137/0.0137 & 0.025/0.026 & 0.017/0.017 & 0.015/0.015 \\
95\% & 0.33 & 0.061/0.066 & 0.114/0.121 & 0.074/0.079 & 0.067/0.071 \\
& 0.50 & 0.21/0.25 & 0.40/0.46 & 0.26/0.30 & 0.23/0.27 \\
\hline
\end{tabular}
\end{table*}
The Set~C priors are qualitatively different from Set~A because they
correspond to an ensemble naturalness assumption for $\pdf(c_i|\bar{c})$,
which means that the distribution of $c_n$'s for a given $k$---and not just their
maximum---affects the result.
This is illustrated by the results in Table~\ref{tab:results_setC_approx1},
in which DOB intervals for $\Delta_2$ with prior choices \ensuremath{{\rm A}_{\epsilon}}\ and \ensuremath{{\rm C}_{\epsilon}}\
are compared.
Because $k=2$, the coefficients $c_0$, $c_1$, and $c_2$
are all influential; we consider three representative choices for their values.
The systematics going from $c_n$ sets $a$ to $b$ to $c$ show that having more $c_n$'s near one leads to larger DOB intervals.
Taking $c_n(b)$ to give generic results for a roughly even distribution of coefficients we find that the Set C vs.\ Set A comparison is
close: only a 10-15\% increase for the 68\% DOB and a roughly 20\% increase for
the 95\% DOB. (The Set A intervals are wider for all but the case in which all three known coefficients are 1.0.) This reflects the stronger central peaking of the Set C pdf under a reasonable distribution of the first three coefficients, as depicted (in the first-omitted-term approximation)
in Fig.~\ref{fig:compareACposteriors0p33}.
Such differences in DOB intervals under different prior choices will be amplified if $k=0$ or $k=1$.
Table~\ref{tab:results_setC_approx1} also assesses the approximation of keeping only the leading omitted
term in $\Delta_2$. Once $Q=0.5$ we see appreciable differences
between Set $\ensuremath{{\rm C}^{(1)}}$ and Set C results that include multiple higher-order terms,
but even then it is only about a 15\% effect on the error bar.
\section{Comparison to recent chiral EFT results for np scattering} \label{sec:EKM}
\subsection{EKM's truncation-error estimates}
Chiral perturbation theory ($\chi{\rm PT}$) encodes the consequences of QCD at
momenta of order the pion mass~\cite{Weinberg:1978kz,Gasser:1983yg,Jenkins:1990jv,Bernard:2006gx}. It can be used to compute the
interaction of single nucleons and pions for momenta well below the
chiral-symmetry-breaking scale, $\Lambda_{\chi {\rm SB}}$. $\chi$PT yields a purely perturbative expansion in powers of
$(p,m_\pi)/\Lambda_{\chi {\rm SB}}$ for low-energy pion-pion and pion-nucleon scattering. But, nuclei are bound
states, and will not be generated from such an expansion.
In the early 1990s Weinberg pointed out that the infrared enhancement associated
with multi-nucleon intermediate states meant that the $\chi$PT expansion
cannot be applied directly to the scattering amplitude in systems with
more than one nucleon~\cite{Weinberg:1990rz}. He
argued that the $\chi$PT Lagrangian and counting rules should instead be used
to compute an NN (or NNN or \ldots) potential up to some fixed order, $n$,
in $\chi$PT. Such an expansion can then be examined for convergence with $n$.
The $\chi$PT potential $V$ was computed to $O(Q^3)$ in
Refs.~\cite{Ordonez:1995rz,Epelbaum:1999dj,Entem:2001cg},
and to $O(Q^4)$ in Refs.~\cite{Entem:2003ft,Epelbaum:2004fk}.
Consistent three-nucleon forces have been derived and implemented in such an approach~\cite{VanKolck:1994yi,Epelbaum:2002vt}.
However, while there is a $\chi$PT expansion for $V$, the resulting nuclear binding energies
(and other observables) contain effects to all orders in the chiral expansion: there is
no obvious perturbative expansion for them. In practice, chiral EFT for few-nucleon systems
is often implemented as described in the previous paragraph, but with the Hamiltonian acting
only on a limited space: in
momentum space a cutoff $\Lambda$ in the range $450 < \Lambda < 800$ MeV must
be imposed~\cite{Marji:2013uia}. From now on when we use the term chiral EFT in the context
of few-nucleon systems we mean calculations that are carried out in this way. A formal justification of the $Q$-expansion (e.g., via the distorted-wave Born approximation
evaluation of higher-order contributions~\cite{Long:2011xw,Long:2011qx,Valderrama:2011mv} or use of a relativistic propagator~\cite{Epelbaum:2012ua,Epelbaum:2013ij}) requires a more sophisticated power counting~\cite{Nogga:2005hy,Birse:2009my,Phillips:2013fia}. Nevertheless, in practice, the convergence of chiral EFT calculations for observables can
be examined {\it a posteriori} to
see if they inherit the $Q$-expansion that has been used for the potential.
In two recent papers, EKM estimated
the errors that arise from truncation of the chiral EFT expansion
at a finite order~\cite{Epelbaum:2014efa,Epelbaum:2014sza}
(see also Ref.~\cite{Binder:2015wpa}).
Similar prescriptions have previously been used in other EFT contexts (see, e.g., Refs.~\cite{Phillips:1999hh,Griesshammer:2012we}).
Such estimates apply to individual observables (such as the total cross
section for neutron-proton scattering at a given lab energy or nucleon electric and magnetic polarizabilities).
They are independent of procedures used to
fit LECs to two-body scattering data at each order. While Bayesian analysis could also be applied to
those procedures that is not our concern here; it will be the focus of a future publication~\cite{Wesolowski:2015}.
Instead, EKM assume that the EFT expansion holds for individual observables $X(p)$, i.e.,
\begin{equation}
X(p)=X_0\sum_{n=0}^k c_n(p) Q^n \;,
\label{eq:EKMexp}
\end{equation}
with $Q$ the EFT expansion parameter, and $c_1=0$ in the Weinberg expansion for NN scattering in chiral EFT.
Cumulative sums at LO, NLO, N$^2$LO, N$^3$LO, and N$^4$LO are then given by:
\begin{eqnarray}
X^{\rm LO}(p)&=&c_0(p) \;, \\
X^{\rm NLO}(p)&=& \sum_{n=0}^2 c_n(p) Q^n \;, \\
X^{\rm N^jLO}(p)&=&\sum_{n=0}^{j+1} c_n(p) Q^n, \; j=2, 3, 4 \;.
\label{eq:partialsums}
\end{eqnarray}
EKM also assume that the dominant error at order $k$ comes from the first
omitted---($k+1$)$^{\rm th}$---term. Two ingredients
go into their estimate of this term. The first is to identify the EFT
expansion parameter $Q$, defined as
\begin{equation}
Q \equiv \max\left( \frac{p}{\Lambda_b},\ \frac{m_\pi}{\Lambda_b} \right)
\;.
\label{eq:Qexpansion}
\end{equation}
Note that, in contrast to pQCD, this is a momentum-dependent
expansion parameter, and so the expansion will perform differently at different kinematic points.
Furthermore, to know $Q$ we must identify $\Lambda_b$, the breakdown scale of the EFT.
In Refs.~\cite{Epelbaum:2014efa,Epelbaum:2014sza}, EKM estimate $\Lambda_b$
from error plots of the fit phase shifts. The second ingredient is to determine the shift beyond N$^j$LO as:
\begin{equation}
\Delta X^{\rm N^jLO}=Q^{j+2} {\rm max}(|c_0|, |c_1|, \ldots, |c_{j+1}|) \;,
\label{eq:DeltaX}
\end{equation}
where the $c_n$'s are defined as above.
In Refs.~\cite{Epelbaum:2014efa,Epelbaum:2014sza} the expressions for the theory
error are defined via differences of the partial sums (\ref{eq:partialsums}), but the result may
be summarized compactly according to Eq.~\eqref{eq:DeltaX}. The similarity of this prescription
to the simplest analytic form obtained above with \ensuremath{{\rm A}_{\epsilon}}$^{(1)}$ priors,
the CH procedure written in Eq.~\eqref{eq:dcoeffs},
is evident.
For a given observable, the value of $Q$ that
is identified defines the perturbative expansion parameter, and the EKM uncertainty
is the maximum coefficient times the first omitted power of $Q$. Up to factors
of order unity, this is what Eq.~\eqref{eq:dcoeffs} predicts
for the 68\% (``$1\sigma$'') DOB interval. There is then clearly a semi-quantitative
correspondence. We now make a quantitative comparison using the various
priors from Table~\ref{tab:priors}.
\begin{table}[tbh]
\setlength{\tabcolsep}{4pt}
\caption{Order-by-order calculations for $\sigma_{np}$ in mb
for $R= 0.9\,$fm
from EKM~\cite{Epelbaum:2014efa,Epelbaum:2014sza,Epelbaum:2015private}.
Lab energy $T_{\rm lab}$ and relative momentum $p_{\rm rel}$ are in units
of MeV. \label{tab:sigmanp_for_R0p9}
}
\begin{ruledtabular}
\begin{tabular}{ccrrrrr}
$T_{\rm lab}$ \strut & $p_{\rm rel}$ & $\sigma_{\rm LO}$ & $\sigma_{\rm NLO}$ &
$\sigma_{\rm N^2LO}$ & $\sigma_{\rm N^3LO}$ & $\sigma_{\rm N^4LO}$ \\
\hline
50 & 153 & 183.6 & 166.5 & 167.0 & 166.8 & 167.5 \\
96 & 212 & 84.8 & 75.1 & 78.3 & 77.5 & 78.0 \\
143 & 259 & 52.5 & 49.1 & 54.2 & 53.7 & 53.9 \\
200 & 307 & 34.9 & 35.9 & 42.6 & 43.2 & 42.7 \\
\end{tabular}
\end{ruledtabular}
\end{table}
\begin{table}[tbh]
\setlength{\tabcolsep}{4pt}
\caption{Order-by-order calculations for $\sigma_{np}$ in mb
for $R= 1.2\,$fm
from EKM~\cite{Epelbaum:2014efa,Epelbaum:2014sza,Epelbaum:2015private}.
Lab energy $T_{\rm lab}$ and relative momentum $p_{\rm rel}$ are in units
of MeV. \label{tab:sigmanp_for_R1p2}
}
\begin{ruledtabular}
\begin{tabular}{ccrrrrr}
$T_{\rm lab}$ \strut & $p_{\rm rel}$ & $\sigma_{\rm LO}$ & $\sigma_{\rm NLO}$ &
$\sigma_{\rm N^2LO}$ & $\sigma_{\rm N^3LO}$ & $\sigma_{\rm N^4LO}$ \\
\hline
50 & 153 & 159.4 & 164.8 & 165.6 & 167.2 & 167.9 \\
96 & 212 & 60.2 & 68.9 & 71.3 & 78.1 & 78.5 \\
143 & 259 & 30.8 & 38.6 & 41.4 & 52.6 & 52.7 \\
200 & 307 & 17.2 & 22.5 & 25.0 & 38.6 & 38.3 \\
\end{tabular}
\end{ruledtabular}
\end{table}
\begin{table}[tbh]
\setlength{\tabcolsep}{4pt}
\caption{Dimensionless coefficients from the expansion of
$\sigma_{np} = \sigma_{\rm LO} \sum_{n=0}^5 c_n Q^n$
for $R= 0.9\,$fm from Table~\ref{tab:sigmanp_for_R0p9},
with $Q = p_{\rm rel}/600\,$MeV. \label{tab:sigmanp_coeffs_for_R0p9}
}
\begin{ruledtabular}
\begin{tabular}{crrrrrrr}
$T_{\rm lab}$ & $c_0$ & $c_1$ & $c_2$ & $c_3$ & $c_4$ & $c_5$ \\
\hline
50 & 1.0 & 0.0 & $-1.43$ & 0.16 & $-0.26$ & 3.5\phantom{4} \\
96 & 1.0 & 0.0 & $-0.92$ & 0.86 & $-0.61$ & 1.07 \\
143 & 1.0 & 0.0 & $-0.35$ & 1.21 & $-0.27$ & 0.25 \\
200 & 1.0 & 0.0 & 0.11 & 1.44 & 0.25 & $-0.41$ \\
\end{tabular}
\end{ruledtabular}
\end{table}
\begin{table}
\setlength{\tabcolsep}{4pt}
\caption{Dimensionless coefficients from the expansion of
$\sigma_{np} = \sigma_{\rm LO} \sum_{n=0}^5 c_n Q^n$
for $R= 1.2\,$fm from Table~\ref{tab:sigmanp_for_R1p2},
with $Q = p_{\rm rel}/400\,$MeV. \label{tab:sigmanp_coeffs_for_R1p2}
}
\begin{ruledtabular}
\begin{tabular}{crrrrrrr}
$T_{\rm lab}$ & $c_0$ & $c_1$ & $c_2$ & $c_3$ & $c_4$ & $c_5$ \\
\hline
50 & 1.0 & 0.0 & 0.23 & 0.09 & 0.47 & 0.54 \\
96 & 1.0 & 0.0 & 0.51 & 0.27 & 1.43 & 0.16 \\
143 & 1.0 & 0.0 & 0.60 & 0.33 & 2.07 & 0.03 \\
200 & 1.0 & 0.0 & 0.52 & 0.32 & 2.28 & $-0.07$ \\
\end{tabular}
\end{ruledtabular}
\end{table}
\begin{figure}[bth]
\includegraphics[width=0.98\columnwidth]{CH_to_EKM_scaled_constants_R0p9_Lam600.pdf}
\caption{(color online) Chiral EFT expansion coefficients
from Table~\ref{tab:sigmanp_coeffs_for_R0p9} for $\sigma_{np}$ at four different energies
using potentials with regulator parameter $R=0.9\,$fm and $\Lambda_b = 600\,$MeV. Note that the coefficient
$c_5=3.5$ at $T_{\rm lab}=50$ MeV is off scale.}
\label{fig:scaledR0p9Lam600}
\end{figure}
\begin{figure}[bth]
\includegraphics[width=0.98\columnwidth]{CH_to_EKM_scaled_constants_R1p2_Lam400.pdf}
\caption{(color online) Chiral EFT expansion coefficients from Table~\ref{tab:sigmanp_coeffs_for_R0p9}
for $\sigma_{np}$ at four different energies
using potentials with regulator parameter $R=1.2\,$fm and $\Lambda_b = 400\,$MeV.
}
\label{fig:scaledR1p2Lam400}
\end{figure}
We note that in chiral EFT, having posited a $Q$ expansion,
we do not find the coefficients directly but extract them
from the calculations at different orders. In contrast, for the QCD expansions, the coefficients
are calculated independently of each other.
Thus the EFT application will require additional empirical verification, see Sec.~\ref{sec:scalechecking}.
\subsection{The pattern of EFT coefficients in EKM's result}
In Refs.~\cite{Epelbaum:2014efa} and \cite{Epelbaum:2015private}, results for
the neutron-proton total cross section at various energies are given for
several values of a coordinate-space regulator parameter $R$. These provide
empirical tests of the priors from Table~\ref{tab:priors}.
The order-by-order cross sections are given in Tables~\ref{tab:sigmanp_for_R0p9}
and \ref{tab:sigmanp_for_R1p2} for $R=0.9\,$fm and $R=1.2\,$fm, respectively.
In line with Eq.~\eqref{eq:obsexp},
we write the cross section at order $k$ in the chiral EFT expansion as
\begin{equation}
\sigma_{np}(E_{\rm lab}) \approx \sigma_{\rm ref} \sum_{n=0}^{k} c_n
\left(\frac{p}{\Lambda_b}\right)^n
\;,
\label{eq:sigmaexp}
\end{equation}
where $\sigma_{\rm ref}$ is a reference cross section that might be taken as
$\sigma_{\rm LO}$, as we do here, or the \ensuremath{{\rm N}{}^4{\rm LO}}\ result, or
the experimental value. The analysis is not sensitive to this choice.
The breakdown scale $\Lambda_b$ was identified in Ref.~\cite{Epelbaum:2014efa}
as $\Lambda_b = 600\,$MeV for cutoffs $R = 0.8$, 0.9,
and 1.0\,fm, $\Lambda_b = 500\,$MeV for $R =1.1\,$fm, and $\Lambda_b = 400\,$MeV
for $R = 1.2\,$fm. Note that this decrease in $\Lambda_b$ with increasing $R$
corresponds to the change in the regulator cutoff scale rather than a change in
the intrinsic underlying breakdown scale.
In Ref.~\cite{Furnstahl:2014jpg} it was emphasized that residuals
for a $k$th-order EFT calculation had two
types of errors: regulator artifacts dictated by the imposed cutoff
$\Lambda$ ($\sim 1/R$ in this context) and truncation errors in the Hamiltonian dictated by the underlying
breakdown scale $\Lambda_b$. EKM\ do not make this distinction
in their notation, i.e., they use $\Lambda_b$ for both.
Under the EKM choices for $\Lambda_b$, the dimensionless $c_n$ coefficients
are given in Tables~\ref{tab:sigmanp_coeffs_for_R0p9} and
\ref{tab:sigmanp_coeffs_for_R1p2} and Figs.~\ref{fig:scaledR0p9Lam600}
and \ref{fig:scaledR1p2Lam400} for the R=0.9 fm and R=1.2 fm cases respectively.
Although the coefficients in both cases are natural, rather different patterns are seen.
As discussed and illustrated by EKM
(e.g., see Fig.~2 of Ref.~\cite{Epelbaum:2014sza}), the softer cutoff shifts
contributions between different chiral orders so that the systematic pattern
of corrections is disrupted. In particular, corrections at orders \ensuremath{{\rm N}{}^2{\rm LO}}\ and
\ensuremath{{\rm N}{}^4{\rm LO}}, which are purely from non-analytic terms in the chiral expansion, become
heavily regulated by the soft cutoff.
This has the consequence
that the corresponding coefficients are anomalously small---which may, in turn result in \ensuremath{{\rm N}{}^3{\rm LO}}\ coefficients being somewhat large.
This pattern is seen in Fig.~\ref{fig:scaledR1p2Lam400}, but what is shown there
is insufficient to definitively
establish there is an inter-order correlation due to regulator artifacts. Here we
focus on the $R=0.9\,$fm example to ensure that the pattern is
primarily driven by the inheritance of
naturalness from the fit low-energy constants (LECs), and not by regulator artifacts that spring from a choice
of $R$ that makes the $\Lambda \sim 1/R$ effects predominate over the physics at
$\Lambda_b$ that was integrated out of the theory.
\subsection{DOB intervals from a Bayesian analysis}
There is a minimum of necessary information that must exist between the prior
and data in order for
the resulting posterior to accurately describe the above distributions.
Two extremes exist: a large supply of precise and accurate data paired
with an uninformative prior (or, even worse, an informative yet incorrect prior) and
a small amount of data paired with a precisely and accurately defined
prior. Each of these situations may result in realistic posteriors as lack of
information in one realm is compensated by abundance in the other. In practice,
though, we conduct analyses between these extremes. We are often able to define a
reasonable, and appropriately loose, prior that is subsequently
fine-tuned by a modest amount of data. We will now show that each
of the priors defined in Table \ref{tab:priors} may be considered reasonable
representations of naturalness in the EFT-coefficient distribution obtained in the
previous subsection. The DOB intervals that result from Bayesian analyses
using these priors show agreement and increased similarity at low $Q$ and high
$k$---where the strength of available data is greatest.
\begin{table*}[tbh!]
\setlength{\tabcolsep}{9pt}
\caption{DOB intervals for EKM $\sigma_{np}$ with $R=0.9\,$fm using prior Set $\Aeps^{(1)}$.}
\label{tab:EKMresults}
\begin{tabular}{c|c|c|c|c|c|c|c|c|}
DOB & $\mbox{E}_{\rm lab}$ & $Q$ & $\mbox{LO}'$ &$\mbox{LO}$& $\mbox{NLO}$ & $\mbox{\ensuremath{{\rm N}{}^2{\rm LO}}}$ & $\mbox{\ensuremath{{\rm N}{}^3{\rm LO}}}$ & $\mbox{\ensuremath{{\rm N}{}^4{\rm LO}}}$ \\
\hline
68\% & \multirow{2}{*}{50} & \multirow{2}{*}{0.255} & 0.40 & 0.102 & 0.024 & 0.0055 & 0.0013 & 0.00079 \\
$\times 183.6$\,mb & & & 73. & 19. & 4.4 & 1.0 & 0.24 & 0.15 \\
\hline
68\% & \multirow{2}{*}{96} & \multirow{2}{*}{0.354} & 0.55 & 0.20 & 0.045 & 0.0142 & 0.0047 & 0.0017 \\
$\times 84.8$\,mb & & & 47. & 17. & 3.8 & 1.2 & 0.40 & 0.15 \\
\hline
68\% & \multirow{2}{*}{143} & \multirow{2}{*}{0.432} & 0.68 & 0.29 & 0.082 & 0.038 & 0.015 & 0.0064 \\
$\times 52.5$\,mb & & & 35. & 15. & 4.3 & 2.0 & 0.81 & 0.34 \\
\hline
68\% & \multirow{2}{*}{200} & \multirow{2}{*}{0.511} & 0.80 & 0.41 & 0.136 & 0.089 & 0.043 & 0.021 \\
$\times 34.9$\,mb & & & 28. & 14. & 4.7 & 3.1 & 1.5 & 0.73 \\
\hline\hline
95\% & \multirow{2}{*}{50} & \multirow{2}{*}{0.255} & 2.6 & 0.650 & 0.061 & 0.0103 & 0.0022 & 0.0012 \\
$\times 183.6$\,mb & & & 470 & 120 & 11. & 1.9 & 0.40 & 0.23 \\
\hline
95\% & \multirow{2}{*}{96} & \multirow{2}{*}{0.354} & 3.5 & 1.25 & 0.115 & 0.027 & 0.0079 & 0.0027 \\
$\times 84.8$\,mb & & & 300 & 110 & 9.8 & 2.3 & 0.67 & 0.23 \\
\hline
95\% & \multirow{2}{*}{143} & \multirow{2}{*}{0.432} & 4.3 & 1.87 & 0.21 & 0.072 & 0.026 & 0.010 \\
$\times 52.5$\,mb & & & 230 & 98. & 11. & 3.8 & 1.4 & 0.53 \\
\hline
95\% & \multirow{2}{*}{200} & \multirow{2}{*}{0.511} & 5.1 & 2.6 & 0.35 & 0.17 & 0.071 & 0.033 \\
$\times 34.9$\,mb & & & 180 & 91. & 12. & 5.9 & 2.5 & 1.1 \\
\hline
\end{tabular}
\end{table*}
\begin{table*}[tbh!]
\setlength{\tabcolsep}{9pt}
\caption{DOB intervals for EKM $\sigma_{np}$ scaled by $\sigma_{\rm LO}$
with $R=0.9\,$fm. Results for prior Sets \ensuremath{{\rm A}_{\epsilon}}, B (with $\sigma = 1.0$), and \ensuremath{{\rm C}_{\epsilon}}, all without the leading-omitted-term approximation.}
\label{tab:EKMresults_setA_approx1}
\begin{tabular}{c|c|c|c|c|c|c|c|c|c|}
& set & $\mbox{E}_{\rm lab}$ & $Q$ & $\mbox{LO}'$ &$\mbox{LO}$& $\mbox{NLO}$ & $\mbox{\ensuremath{{\rm N}{}^2{\rm LO}}}$ & $\mbox{\ensuremath{{\rm N}{}^3{\rm LO}}}$ & $\mbox{\ensuremath{{\rm N}{}^4{\rm LO}}}$ \\
\hline
& \ensuremath{{\rm A}_{\epsilon}} & & & 0.43 & 0.11 & 0.025 & 0.0055 & 0.0013 & 0.00080 \\
&\ensuremath{{\rm C}_{\epsilon}} & 50 & 0.255 & 0.48 & 0.12 & 0.028 & 0.0053 & 0.0011 & 0.00056 \\
&B & & & 0.29 & 0.073 & 0.022 & 0.0052 & 0.0013 & 0.00076 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 0.59 & 0.21 & 0.048 & 0.015 & 0.0048 & 0.0018 \\
&\ensuremath{{\rm C}_{\epsilon}} & 96 & 0.354 & 0.69 & 0.25 & 0.060 & 0.019 & 0.0058 & 0.0021 \\
\multirow{2}{*}{68\%}& B & & & 0.40 & 0.143 & 0.043 & 0.014 & 0.0047 & 0.0017 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 0.74 & 0.32 & 0.089 & 0.040 & 0.016 & 0.0067 \\
& \ensuremath{{\rm C}_{\epsilon}} & 143 & 0.432 & 0.87 & 0.38 & 0.088 & 0.043 & 0.015 & 0.0059 \\
& B & & & 0.51 & 0.22 & 0.080 & 0.038 & 0.016 & 0.0065 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 0.91 & 0.46 & 0.15 & 0.097 & 0.046 & 0.022 \\
&\ensuremath{{\rm C}_{\epsilon}} & 200 & 0.511 & 1.08 & 0.58 & 0.14 & 0.096 & 0.041 & 0.019 \\
& B & & & 0.63 & 0.32 & 0.14 & 0.091 & 0.044 & 0.022 \\
\hline\hline
& \ensuremath{{\rm A}_{\epsilon}} & & & 2.7 & 0.69 & 0.066 & 0.011 & 0.0023 & 0.0013 \\
&\ensuremath{{\rm C}_{\epsilon}} & 50 & 0.255 & 3.3 & 0.85 & 0.089 & 0.014 & 0.0027 & 0.0013 \\
& B & & & 0.67 & 0.172 & 0.042 & 0.0091 & 0.0021 & 0.0012 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 3.8 & 1.3 & 0.13 & 0.030 & 0.0088 & 0.0030 \\
&\ensuremath{{\rm C}_{\epsilon}} & 96 & 0.354 & 4.8 & 1.7 & 0.20 & 0.050 & 0.0142 & 0.0049 \\
\multirow{2}{*}{95\%} & B & & & 0.97 & 0.34 & 0.088 & 0.026 & 0.0083 & 0.0029 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 4.7 & 2.0 & 0.24 & 0.083 & 0.030 & 0.012 \\
& \ensuremath{{\rm C}_{\epsilon}} & 143 & 0.432 & 6.0 & 2.6 & 0.29 & 0.114 & 0.038 & 0.014 \\
& B & & & 1.22 & 0.53 & 0.17 & 0.071 & 0.028 & 0.0115 \\
\cline{2-10}
& \ensuremath{{\rm A}_{\epsilon}} & & & 5.7 & 2.9 & 0.41 & 0.20 & 0.088 & 0.041 \\
& \ensuremath{{\rm C}_{\epsilon}} & 200 & 0.511 & 7.4 & 3.8 & 0.47 & 0.26 & 0.100 & 0.043 \\
& B & & & 1.53 & 0.78 & 0.29 & 0.173 & 0.081 & 0.040 \\
\hline
\end{tabular}
\end{table*}
\begin{figure}[b!]
\includegraphics[width=0.95\columnwidth]{EKM_Tlab_together_setA_eps_approx0.pdf}
\caption{(color online) Cross sections at different energies and orders from EKM, with
DOB intervals at each order using Set \ensuremath{{\rm A}_{\epsilon}}\ priors.
The thick error bars indicate 68\% DOB intervals while the thin
error bars indicate 95\% DOB intervals.}
\label{fig:EKM_Tlab_together_setA_eps_approx0}
\end{figure}
\begin{figure*}[tbp]
\includegraphics[width=0.85\columnwidth]{EKM_Tlab50_all_orders_multisets.pdf}
\hspace*{.3in}
\includegraphics[width=0.85\columnwidth]{EKM_Tlab96_all_orders_multisets.pdf}
\caption{(color online) Cross sections at 50\,MeV and 96\,MeV for all orders from EKM, with
DOB intervals at each order using a wide variety of prior sets. Note the change
in scale at each order.
The thick error bars indicate 68\% DOB intervals while the thin
error bars indicate 95\% DOB intervals. In each panel the dashed line is the result of the next-order calculation
(NLO at LO, N$^2$LO at NLO, etc.), shown to facilitate an assessment of the statistical consistency of
different prior choices.
For each prior choice, the intervals on
the left are from keeping only the first omitted term while those on the
right are including four omitted terms.
The shaded bands indicate the uncertainty from EKM.
}
\label{fig:EKM_Tlab_96_all_orders_all_sets}
\end{figure*}
\begin{figure*}[tbp]
\includegraphics[width=0.85\columnwidth]{EKM_Tlab143_all_orders_multisets.pdf}
\hspace*{.3in}
\includegraphics[width=0.85\columnwidth]{EKM_Tlab200_all_orders_multisets.pdf}
\caption{(color online) Cross sections at 143\,MeV and 200\,MeV for all orders from EKM, with
DOB intervals at each order using a wide variety of sets. Note the change
in scale at each order.The thick error bars indicate 68\% DOB intervals while the thin
error bars indicate 95\% DOB intervals. In each panel the dashed line is the result of the next-order calculation
(NLO at LO, N$^2$LO at NLO, etc.), shown to facilitate an assessment of the statistical consistency of
different prior choices.
For each prior choice, the intervals on
the left are from keeping only the first omitted term while those on the
right are including four omitted terms.
The shaded bands indicate the uncertainty from EKM.
}
\label{fig:EKM_Tlab_200_all_orders_all_sets}
\end{figure*}
In Fig.~\ref{fig:EKM_Tlab_together_setA_eps_approx0}, cross sections
from Table~\ref{tab:sigmanp_for_R0p9} for
$R = 0.9\,$fm at four
different energies are plotted order-by-order in the chiral expansion,
with error bars indicating the 68\% and 95\% DOB intervals if we
adopt prior set \ensuremath{{\rm A}_{\epsilon}}.
The $\mbox{LO}'$ error bars are from the calculation for the posterior
of $\Delta_0$ while the $\mbox{LO}$ error bars are from the posterior of
$\Delta_1$. When calculating $\Delta_1$ we have $k=1$ and $n_c=1$,
so the resulting error bar is simply $Q$ times the $\mbox{LO}'$ one.
This is the correct error estimate for a LO chiral
EFT calculation of NN scattering, as long as we know {\it a priori} that the coefficient
$c_1$ in the expansion (\ref{eq:sigmaexp}) is identically zero.
Cross sections at subsequent orders generally fall within the DOB
intervals of lower-order error analyses---in accord with the DOB intervals' statistical
interpretation. The order-by-order decrease in the error bars primarily
reflects the additional factors of $Q$ with each successive order.
The very conservative assumption for $\pdf(\bar{c})$ used here, which encodes ignorance
of its scale even though we anticipate naturalness, leads to long tails in the
posterior for the lowest orders and correspondingly large 95\% DOB intervals---
further reflecting the non-Gaussian nature of this distribution.
When we use a form for $\pdf(\bar{c})$ that reflects the expectation of naturalness,
the long tails are suppressed and the 95\% DOB intervals are closer to
``$2\sigma$'' errors, although the pdfs do remain non-Gaussian in general.
Table \ref{tab:EKMresults} is an analytical compilation of DOB intervals in
the limiting case of $\ensuremath{{\rm A}_{\epsilon}}$ with the leading-term approximation,
see Eq.~(\ref{eq:dcoeffs}). The top number in each cell has been calculated
using coefficients of Table~\ref{tab:sigmanp_coeffs_for_R0p9}, which are scaled
with the $\sigma_{\rm ref}$ corresponding to each energy.
The lower number is the resulting DOB interval in units of mb with the factor of $\sigma_{\rm ref}=\sigma_{\rm LO}$ included.
The 95\% DOB interval being more than 6 times broader than the corresponding
68\% DOB interval at $\mbox{LO}'$ and $\mbox{LO}$ emphasizes the strength of tails within these posteriors.
Representative numerical results for the various prior sets are given in
Table~\ref{tab:EKMresults_setA_approx1}. Though we omit mention of $\sigma_{\rm ref}$,
values here should also be multiplied by the energy-appropriate $\sigma_{\rm ref}$ (i.e., $\sigma_{\rm LO}$) to
obtain DOB values in units of mb. Systematically, we observe that the ratios of DOB intervals
between prior sets are the same across all 4 energies for $\mbox{LO}'$ and $\mbox{LO}$ as all $c_1$'s are
0 and we have scaled all $c_0$'s to the value 1.0. Thus, given the same set of
coefficients, all posteriors scale similarly with energy.
Table~\ref{tab:EKMresults_setA_approx1} also shows that the ensemble prior in
Set~$\ensuremath{{\rm C}_{\epsilon}}$ generally predicts 68\% DOB intervals quite similar to those from
Set~$\ensuremath{{\rm A}_{\epsilon}}$, with much greater variation for 95\% DOB intervals for the lower orders.
From this, we see that prior choice affects the structure of the tails
more significantly than the structure of the peak. This is indicative of the strength of information coming
from the data and the prior at different points in the distribution.
Though Set B results in significantly narrower DOB intervals at low $k$,
the EFT coefficients provide enough information for $k \geq 2$ to modify these posteriors into
agreement with those of Sets~$\ensuremath{{\rm C}_{\epsilon}}$ and~$\ensuremath{{\rm A}_{\epsilon}}$.
A comparison of Set~A results in
Table~\ref{tab:EKMresults_setA_approx1} with those in Table~\ref{tab:EKMresults}
shows that the approximation of keeping only the leading omitted term is
excellent for the 68\% DOB for $k>2$ and still quite good
for $k=1$ (which is the true leading order). This approximation always underestimates
the interval from including higher-order terms and worsens as the expansion
parameter $Q$ increases. Figures~\ref{fig:EKM_Tlab_96_all_orders_all_sets} and
\ref{fig:EKM_Tlab_200_all_orders_all_sets} show that this result is general and
that the approximation is better for the 95\% interval with a less
conservative prior for $\bar{c}$.
One outlier is the $k=5$ prediction
at $T_{\rm lab} = 50\,$MeV where we see consequences of a $c_5$ coefficient
known to have an anomalously large value, which is an artifact of the
fitting procedure~\cite{Epelbaum:2015private}.
Note that this results in the omission of the DOB interval for $\ensuremath{{\rm N}{}^4{\rm LO}}$
at 50 MeV with Set $A_{0.5-2}$ as $\cbar_{>}$ is then less than $\cbarsubk{k}$, so the distribution
is not defined in this case.
Overall, the prior sets $\ensuremath{{\rm A}_{\epsilon}}$ and $\ensuremath{{\rm C}_{\epsilon}}$ appear to be too conservative for
predictions at LO; we know that $\ensuremath{{\rm A}_{\epsilon}}$ and $\ensuremath{{\rm C}_{\epsilon}}$ have
incorporated less information than the alternatives so it is no surprise that
their posteriors are more widely distributed.
Importantly, we find that the posteriors for $\Delta_k$ for $k\geq 2$ are
largely insensitive to the choice of prior, even for the 95\%
DOB interval. As posteriors retain artifacts of the prior in inverse proportion
to the strength of the data, this similarity suggests that the data is
sufficiently informative that any reasonable prior is properly subservient
and thus able to adapt to evidence of the real world presented by the data.
\section{Choice of expansion parameter}
\label{sec:scalechecking}
In the previous section, the scale $\Lambda_b$ in the expansion parameter was
taken from Ref.~\cite{Epelbaum:2014efa}, where it
was extracted from error plots after the fit of the LECs.
This identification was certainly not rigorous in any statistical sense.
Therefore here we explore how $\Lambda_b$ can be extracted
from the convergence pattern of the EFT for observables.
In the case of pQCD,
Cacciari and Houdeau discussed using an expansion parameter
that is different from $\alpha_s$. They introduced a scale factor $\lambda$, so that the expansion
is in powers of $\alpha_s/\lambda$~\cite{Cacciari:2011ze}. This changes the expressions
for $\text{pr}(\Delta_k|c_0 \ldots, c_k)$ by a rescaling of the
expansion parameter $Q$ and a corresponding rescaling of the coefficients
themselves.
We can rewrite the series for an observable $X$ in terms of the rescaled expansion parameter and coefficients
as
\begin{equation}
X = X_0 \sum_{n=0}^\infty (c_n \lambda^n) \times \left(\frac{ Q}{\lambda}\right)^n \; .
\label{eq:lambda-tune-exp}
\end{equation}
In an EFT expansion this is equivalent to a rescaling of $\Lambda_b$ by a factor $\lambda$.
Subsequent papers explored procedures for determining the value
of $\lambda$ based on various criteria:
\begin{itemize}
\item In Refs.~\cite{Bagnaschi:2014eva,Bagnaschi:2014wea}, $\lambda$ was chosen
empirically by comparing the consistency of the computed
DOB intervals with known higher-order calculations.
An extra factor of $(n-1)!$ was also introduced along with $\lambda$ in
Eq.~\eqref{eq:lambda-tune-exp}---motivated by effects
from renormalon chains at higher orders in the expansion. The authors
denoted the resulting scheme $\overline{\rm CH}$.
We have no evidence for such a factorial in our EFT expansions and
do not consider it further here.
\item In Ref.~\cite{Forte:2013mda}, it was proposed that with the best expansion
parameter, the coefficients should form a normal distribution of mean $\mu$ and standard deviation $\sigma$.
This criterion was used to choose a value of $\lambda$. This approach is consistent
with naturalness for the $\{c_n\}$, as long as $\mu$ and $\sigma$ are both $\mathcal{O}(1)$.
\end{itemize}
Here we explore these procedures for tuning the expansion parameter in the
EKM cross sections, and we also suggest another criterion for assessing
$\lambda$ based on the assumption of naturalness in the EFT expansion for a
particular value of $\Lambda_b$. If a $\lambda$ emerges from such
analyses that is measurably different from one, it suggests that the true
breakdown scale of the EFT expansion is not $\Lambda_b$, but instead
$\Lambda_b \lambda$.
Given the limited
number of coefficients (20 at most) at our disposal from the EKM analysis, any statistical
procedure can only determine $\lambda$, and hence $\Lambda_b$, within sizable error bars.
Our goal in this section is less to determine $\Lambda_b$, than to
establish whether the choice $\Lambda_b=600$ MeV is consistent
with our other {\it a priori} assumptions and deductions about the convergence properties of the EFT.
\subsection{Consistency checks based on higher-order calculations}
In Refs.~\cite{Bagnaschi:2014eva,Bagnaschi:2014wea}
$\lambda$ was determined by checking the consistency of $\overline{\rm CH}$\ DOB intervals obtained with
expansion parameters $\alpha_s/\lambda$ in several large sets of pQCD
observables.
This is done by examining actual vs.\ expected success rates of the pQCD calculations.
As stated in Ref.~\cite{Jenniches}: ``For a finite set of observables
and a given model (with fixed parameters) at order $k$, the success rate is defined as the number
of observables whose subsequent-order contributions are within the uncertainty interval predicted
by the model.''
We want to use the observed success rates $n(p)/N$ for our EFT calculation to
infer the likelihood that $p$ is the true success rate---for many different
choices of $p$.
If each observable being considered is uncorrelated, the success
rate should follow a binomial distribution. Therefore the likelihood for $n$ successes amongst $N$ observables, given $p$, is
\begin{equation}
\text{pr}(n|p,N) = \frac{N!}{n!(N-n)!} p^n (1-p)^{N-n} \;.
\label{eq:binomial}
\end{equation}
We generalize the pdf (\ref{eq:binomial})
to its continuous version, the $\beta$-distribution:
\begin{equation}
\text{pr}(a,b|p,N) = \frac{(a+b-1)!}{(a-1)!(b-1)!}p^{a-1}(1-p)^{b-1} \;,
\label{eq:beta}
\end{equation}
with $a = n+1$ and $b=N-n+1$. We can then compute confidence intervals (CIs) on $n$ (or, equivalently $a$) for a given value of $p$ (in practice we will consider only
the 68\% and 95\% CIs). This can be done using standard integrals, and the result expressed in terms
of a range of success rates that are consistent with the chosen value of $p$.
As in Refs.~\cite{Bagnaschi:2014eva,Bagnaschi:2014wea}, we have calculations of the cross sections at several orders and energies
and are trying to determine
values of $\lambda$ that result in consistency between assumed values of $p$ and the resulting success rates $n$.
To do this, we take the set of 16 observables we have from the EKM results: calculations at LO, NLO, N$^2$LO, N$^3$LO for four different lab energies.
(Note that each observable must have a higher-order result to which it can be compared.) We then pick
a value of $\lambda$ and proceed
to assess the consistency of the success rates of the theory predictions for that $\lambda$ via this algorithm (adapted from pQCD to EFT for our purposes):
\begin{enumerate}
\item Select a grid of $p\%$ DOB intervals with $p$ ranging from 0 to 100.
\item Use the formalism laid out in Sections~\ref{sec:CH} and \ref{sec:EKM} to compute the $p\%$ DOB interval for each observable in the set.
\item For each next-order calculation that is within the DOB
interval of the previous order, count one success.
\item Take the number of successes and divide by the total number
of observables to get the actual success rate.
\item Compare the actual success rate for this value of $p$ with the 68\% and 95\% confidence intervals for the number of successes if $p$ were the true success rate, as computed from the distribution (\ref{eq:beta}).
\end{enumerate}
This algorithm generates a function of $p$ for this value of $\lambda$. If the curve is within the $68\%$ CI
for the entire range of $p$ values we say that the value of $\lambda$ is consistent at $1\sigma$ with the performance of the perturbative series. Moderate fluctuations outside the $1\sigma$ band over limited regions
of the entire $p$ domain can indicate a statistically consistent choice for $\lambda$, but the concern is with curves that end up systematically outside the $1\sigma$ region. This can occur in one of two ways.
If the curve starts to veer above the $1\sigma$ region then that indicates the EFT predictions are {\it too} successful.
The expansion parameter is overestimated, which means the EFT breakdown scale is underestimated. Alternatively, the function $n(p)/N$ may deviate well below the 68\% CI, in which
case the EFT is under-performing compared to statistical expectations. In that case the stated expansion parameter is too small, i.e., $\Lambda_b$ is overestimated.
We note that this interpretation is somewhat specific to EFT: in a case where we were confident of the expansion parameter in the series we could instead use this diagnostic to probe
whether different prior choices are too conservative or too aggressive.
Here though, we try to draw conclusions on the performance of the EFT expansion that are invariant under the choice of priors defined above. We thus implement this procedure for two different prior assumptions
on $\bar{c}$ and the coefficients $\{c_n\}$.
In each case we use the approximation that
the leading term dominates for computational ease.
The curves do not change substantially if we go beyond the first-omitted-term approximation.
We first consider Set $\Aeps^{(1)}$.
The results of computing $p\%$ success rates for various values of $\lambda$ are
shown by the lines in Fig.~\ref{fig:lam-success-plot-A}.
We include $68\%$ and $95\%$ confidence
bands to evaluate which $\lambda$ curves meet our consistency
criterion.
With only 16 observables, the confidence bands are fairly wide, but still the only
curve which falls completely within the $68\%$ interval is $\lambda = 1.3$. The original
expansion parameter at $\lambda = 1$ spends some time above the $1\sigma$ region, which may reflect that DOB intervals resulting from this prior are too conservative; i.e., the actual success rate
regularly exceeds the DOB that has been assigned. This is consistent with our
earlier observation that Set $\ensuremath{{\rm A}_{\epsilon}}$ priors produce overly conservative DOB intervals.
We also compute the intervals using Set $\Ceps^{(1)}$, which accounts for the effects
of each coefficient and is less conservative. The results are contained in
Fig.~\ref{fig:lam-success-plot-C}. We see that even for these assumptions,
the $\lambda=1$ curve gets outside the $1\sigma$ band. The plot suggests $\lambda = 1.1$ is a more consistent choice (other values near $\lambda=1.1$ will, of course, also be consistent).
Because the DOB intervals computed with Set $\Ceps^{(1)}$ priors are more
informed by the available coefficients, this result may suggest a small increase in the assigned breakdown scale
is appropriate. However, we note the small amount of data on EFT convergence that is being used here; almost all rescalings considered are consistent at the 2$\sigma$ level.
Such determinations of $\Lambda_b$ from success rates can be sharpened by considering the behavior of the EFT series for more observables.
\begin{figure}
\includegraphics[width=0.48\textwidth]{EKM_pdfs_0p9fm_A_new_colors.pdf}
\caption{(color online) Empirical determination of $\lambda$
by comparing results at different orders. The cross sections used are
the computations with the $R=0.9\,$fm regulator. Priors are Set A$_\epsilon^{(1)}$. For full explanation see text. \label{fig:lam-success-plot-A}}
\end{figure}
\begin{figure}
\includegraphics[width=0.48\textwidth]{EKM_pdfs_0p9fm_C_new_colors.pdf}
\caption{(color online) Empirical determination of $\lambda$
by comparing results at different orders. The cross sections used are
the computations with the $R=0.9\,$fm regulator. Priors are Set C$_\epsilon^{(1)}$. For full explanation see text.
\label{fig:lam-success-plot-C}}
\end{figure}
\subsection{Gaussian naturalness and the Forte method}
in Ref.~\cite{Forte:2013mda}, Forte et al.\ suggest that, for QCD expansions, the best $\lambda$ is the one that makes all
the expansion coefficients closest to the same size, which they interpret as a
statement that the coefficients should be normally distributed
around a single number $\mu$ with variance $\sigma^2$~\cite{Forte:2013mda}.
For a quantity for which the known information is a mean
and standard deviation, in
this case a particular coefficient $c_n$,
the method of maximum entropy results in a distribution that is a gaussian~\cite{Gull:98,Sivia:06}:
\begin{equation}
\text{pr}(c_n | \lambda, \mu, \sigma)
= \frac{1}{\sqrt{2 \pi}\sigma} \exp \left(
-\frac{(|c_n| \lambda^n - \mu)^2}{2\sigma^2} \right) \; .
\label{eq:cn-naturalness-gaussian}
\end{equation}
If we have several known coefficients, all of which are drawn from a distribution
with the same mean and standard deviation, the joint pdf
$\text{pr}(c_0, \ldots, c_k|\lambda, \mu, \sigma)$ becomes the standard likelihood function.
If $\sigma = \bar{c}$ and
$\mu = 0$ such a distribution corresponds to the Set C prior of
Table~\ref{tab:priors}.
Forte et al.\
consider the probability distribution for both $\mu$ and $\lambda$ given a
set of $\{c_n\}$~\cite{Forte:2013mda}. This can be obtained from \eqref{eq:cn-naturalness-gaussian} using
Bayes' theorem:
\begin{equation}
\text{pr}(\lambda, \mu | c_0, \ldots, c_k, \sigma) = \frac{\text{pr}(c_0, \ldots, c_k| \lambda, \mu, \sigma)
\, \text{pr}(\lambda, \mu| \sigma)}{\text{pr}(c_0, \ldots, c_k|\sigma)} \;.
\end{equation}
Forte et al.\ assign no prior information to $\lambda$ and $\mu$ other than
that both are larger than zero, and neither quantity depends on $\sigma$ \emph{a priori}.
They then take the prior and the evidence in the denominator to be an overall normalization factor
that is independent of $\lambda$ and $\mu$, and so do not calculate them
explicitly (cf.\ discussion of a scale-invariant prior for $\lambda$ below).
The pdf for $\lambda$ and $\mu$ can then be written
\begin{equation}
\text{pr}(\lambda, \mu | c_0, \ldots, c_k, \sigma) \propto \text{pr}(c_0, \ldots, c_k| \lambda, \mu, \sigma) \;,
\label{eq:forte-prob-lam-mu}
\end{equation}
meaning that maximizing the probability of $\lambda$ and $\mu$ is equivalent to
minimizing
\begin{equation}
\chi^2 = \sum_{i=1}^{N_O} \sum_{n=0}^k \left(\frac{|c_n^{(i)} | \lambda^n - \mu}{\sigma}\right)^2 \;,
\label{eq:chisqForte}
\end{equation}
where $\{c_n^{(i)}\}$ is the set of EFT coefficients found for the $i$th observable, and
$N_O$ is the number of observables being used to form the $\chi^2$. In our case $N_O=4$: the
cross sections at the four different energies analyzed by EKM~\footnote{In general there would be $N_0 n_c$ terms in the $\chi^2$ sum, but we omit the N$^4$LO coefficient from the 50 MeV cross section, since it is clearly an outlier. Our $\chi^2$ thus has 19 terms in the sum.}. Note also that for chiral EFT for NN scattering the coefficient
$c_1$ is known to be zero, and so the $n=1$ term should be omitted from the sum.
The assumption that
$\lambda$ has a uniform prior is not consistent with arguments regarding the invariance of the pdf under a change of scale~\cite{Jeffreys:1939}. In fact,
$\lambda$ should be treated as a scale parameter. So, in contrast to Ref.~\cite{Forte:2013mda},
we assign a uniform prior to the \emph{logarithm} of $\lambda$, resulting
in a probability distribution for $\lambda$
and $\mu$ that is:
\begin{equation}
\text{pr}(\lambda, \mu | c_0, \ldots, c_k, \sigma) \propto \frac{1}{\lambda} \times e^{-\chi^2/2} \; ,
\label{eq:mod-prob-lam-mu}
\end{equation}
with the parameter space for $\lambda$ and $\mu$ restricted to both being positive.
Assuming $\sigma=1$, we find the maximum of the probability \eqref{eq:forte-prob-lam-mu} for
the $R=0.9\,$~fm EKM coefficients occurs at $\lambda=0.92$, $\mu=0.69$. To consider
the pdf of $\lambda$ only, we marginalize over the parameter $\mu$ and maximize
$\text{pr}(\lambda|c_0,\ldots,c_k,\sigma)$ to find $\lambda = 1.01^{+0.18}_{-0.19}$,
which is consistent with the Forte {\it et al.} hypothesis at a 68\% DOB.
Larger $\sigma$'s generate still wider ranges. From this point of view too, then,
$\Lambda_b=600$ MeV is a consistent choice for the $R=0.9$ fm np scattering EFT-expansion coefficients.
\subsection{$\chi^2$ test}
Alternatively, we can demand that the mean of the $c_n$'s be fixed at
$\mu = 0$ and that the width $\sigma$ should affect the results as in Set~C
gaussian pdfs on the coefficients, where $\bar{c}$ is an important feature of
the prior. This leaves us with the probability
\begin{align}
\text{pr}(\lambda, \mu =0| c_0, \ldots, c_k, \sigma) \propto \frac{1}{\lambda} \exp\left(-\frac{\chi^2(\mu=0)}{2}\right) \; ,
\end{align}
where $\chi^2(\mu=0)$ is given by Eq.~\eqref{eq:chisqForte} with $\mu=0$.
We can then test whether, for a given $\lambda$, the data, i.e., the EKM coefficients from their $R=0.9$ fm calculation, follows a normal distribution with mean zero
and width $\sigma$. We do this by comparing $\chi^2(\mu=0)$ with the way that $\chi^2$ should be distributed for
a normal distribution with $19$ degrees of freedom.%
Once again, in order to do this we must fix $\sigma$. With the choice $\sigma=1$ we find $\lambda=1.09$
gives $\chi^2$ of 19---the central value one would expect for this many data points~\footnote{Including the N$^4$LO coefficient from the 50 MeV cross section lowers the
results for $\lambda$ by about 10\%.}. Using the rule of
thumb for large number of degrees of freedom, $N$,~\cite{NumericalRecipes} that the $\chi^2$ should
have a width of $\sqrt{2N}$ indicates that $\lambda$ could (68\% DOB) be anywhere
between 1.01 and 1.15. As in the previous subsection, choices of $\sigma > 1$ will increase this range of possibilities.
\subsection{Summary of expansion-parameter checks}
In any case, while none of these methods provide a crisp result for $\Lambda_b$ from the 19 data points analyzed, it is
reassuring that there is little evidence for a large change in $\Lambda_b$.
Minimally, EKM's estimate $\Lambda_b \approx 600\,$MeV
for their $R=0.9\,$fm calculation is consistent with these analyses, and the breakdown scale may in fact be a little higher.
Further investigations employing these techniques with EFT coefficients drawn from many more observables will provide more definitive answers.
\section{Summary and outlook} \label{sec:conclusion}
We have adapted and extended the Bayesian framework originally introduced in the context of pQCD by Cacciari and
Houdeau~\cite{Cacciari:2011ze} to evaluate truncation errors in EFT expansions.
Assumptions about the nature of the coefficients in the expansion are encoded as priors
on the coefficients of higher-order terms in the EFT series. The pdfs for these coefficients
then ultimately also include information on the distribution of coefficients at orders
that are calculated. Here we employed priors derived from the notion of
``naturalness" of EFT coefficients, i.e., the idea that they should be $\mathcal{O}(1)$
when the observable and the momentum of the process in question are measured
in appropriate units. We took the coefficients in the EFT expansion of cross sections
to be natural in this sense. Such a choice is uncontroversial for perturbative processes,
e.g., meson-meson scattering at momenta well below the chiral-symmetry-breaking
scale. It remains to be fully investigated for cross sections in nucleon-nucleon
scattering, where
the relationship between the underlying scales and observables is quite complex;
we rely here on an empirical validation (see Fig.~\ref{fig:scaledR0p9Lam600}).
We investigated the influence of two prior pdfs for EFT coefficients on the truncation errors. The first was the CH characterization of an upper bound
$\bar{c}$, the second was a Gaussian of width $\bar{c}$. We also investigated the influence of
priors on $\bar{c}$ itself on the results.
We did this in the context of representative examples in Section~\ref{sec:CH} and, in Section~\ref{sec:EKM}, using
results from the order-by-order calculations of neutron-proton cross
sections by Epelbaum, Krebs, and Mei\ss ner (EKM) in Ref.~\cite{Epelbaum:2014sza} (obtained with a regulator parameter
$R=0.9\,$fm). Combining the insights from both sections we find:
\begin{itemize}
\item Priors that reflect a natural size for $\bar{c}$ give similar
degree-of-belief (DOB) intervals at the lowest orders.
\item The resulting error bands are tighter than
those for which the scale of $\bar{c}$ is not constrained.
\item For higher orders, 68\% DOB intervals show little dependence on prior choice;
95\% DOB intervals have larger, but still quite small, dependence.
\end{itemize}
These results have wide applicability to observables---they can be used in many EFT contexts. In the case of neutron-proton scattering our formulas provide a statistical interpretation to
error bars obtained by EKM in Ref.~\cite{Epelbaum:2014efa}. Their error bar is obtained in the case that the distribution of coefficients is uniform, in which case it
is a $j/(j+1)*100\%$ DOB interval for the omitted terms in a N$^j$LO calculation. But, as already stated, truncation errors in these calculations at
NLO or beyond (i.e., which include at least two orders beyond leading) were only mildly dependent on
prior choice. In particular, the 68\% DOB intervals obtained in our Bayesian framework varied by at most 15\% amongst all the priors considered here, and the variation was less than that
in calculations beyond NLO. Error bands at a given order were also consistent with a statistical interpretation when compared with known higher-order results.
Truncation errors at leading order {\it are} sensitive to
prior choice, since--given the choice of scaling observable we made---almost no information on the pattern of coefficients emerges from a leading-order calculation. Comparison of the resulting error band with
the known results of NLO, N$^2$LO, N$^3$LO, and N$^4$LO calculations suggests that the CH choice of a $\theta$-function distribution for coefficients, and a scale-independent
distribution for the width of that $\theta$-function, is too conservative---at least for this case. Overall then, at sufficiently high order, the prior picked from Table~\ref{tab:priors} hardly matters---in practice $k=2$ may be enough. At lower orders priors provide a rigorous way to explore different assumptions about the pattern of
coefficients in the EFT.
Indeed, the application of Bayesian methods to data is often criticized because
of the apparently subjective selection of prior pdfs. However, the
priors manifest what would otherwise be implicit assumptions, so that they
can be tested. The information encoded in those assumptions is then modified
in light of subsequent data: in this case the distribution of low-order
coefficients influences the distributions computed for coefficients
that enter the assessment of the truncation error. Furthermore, the development
of specific pdfs for those higher-order coefficients allows a statistical interpretation
of the ``theory error"---or at least the part of it that results from the truncation of
the EFT series. This allows crisp answers to questions regarding, for example,
how theory error bars should be combined, or the extent to which theory errors
on different quantities are correlated. Those answers may have some sensitivity
to the choice of prior on the higher-order coefficients, but the advantage of the
Bayesian framework is that the consequences of prior assumptions about the distribution
of coefficients (Uniformly distributed or Gaussian? Natural or Scale-less?) can be traced
through to the statistical uncertainties on the EFT calculation. Those assumptions can then---if
necessary---be refined.
Such refinement may be necessary in light of the need to identify an EFT breakdown scale before extracting the (supposedly) $\mathcal{O}(1)$ coefficients which are input to our analysis.
Mis-identification of the breakdown scale is one manner in which a particular prior could fail. But, in this case, we showed in Sec.~\ref{sec:scalechecking} that
this breakdown scale $\Lambda_b=600$ MeV leads to success rates taken from the EFT predictions at four different energies, and for four different orders, that are statistically consistent with the DOB intervals resulting from our Bayesian formalism.
Furthermore, the distribution of coefficients with the $R=0.9$ fm regulator choice is consistent with a Gaussian distribution. Qualitatively a natural distribution is not seen for the coefficients obtained
using a second, larger, value of $R$. The calculation at this larger regulator radius reflects cutoff artifacts,
which leads to peculiar convergence of the EFT expansion. The breakdown of the EFT is then not set by $\Lambda_b$, but by the effects of this softer cutoff.
With the general formalism for probability distributions of EFT coefficients laid out here
it will be important to check when the EFT coefficients obtained over
a wide range of cutoff values and
observables are empirically consistent with the application of naturalness priors
to observables in the NN system.
The Bayesian approach to error estimation presented here is an alternative
to procedures that calculate error bands based on variation of the
EFT regulator, which could be a cutoff in either momentum or coordinate space.
While variation with regulator scale gives a lower bound on the uncertainty (theories should,
after all, be regulator invariant up to higher-order terms) the resulting error band has
no statistical interpretation.
A particular flaw is the arbitrariness of the interval in which the cutoff is varied;
for QCD this is only of mild concern, because the dependence on the regulator parameter is
only logarithmic. But running in the chiral EFT applied to NN scattering is much faster: it can contain
high positive powers of the regulator (momentum) scale. This concern is
exacerbated by the narrow range that is possible before encountering
irremediable cutoff artifacts or spurious deep bound states.
It is also the case that residual cutoff dependence only reflects the
contribution from omitted contact operators. These only enter the chiral expansion for NN observables
at even orders, and so examination of cutoff dependence alone may substantially
underestimate the EFT truncation error.
More generally, when computed using only cutoff variation, the error bands for predictions
of observables (as opposed to quantities used to fit EFT LECs) generically exhibit undesirable
systematics (e.g., sometimes growing wider with order) and often underestimate the
error when compared with actual higher-order calculations~\cite{Furnstahl:2014jpg}.
In contrast, the Bayesian assessment of truncation errors laid out here is applicable to all EFTs, admits a statistical interpretation
of truncation errors,
is justified when regulator parameters cannot be
varied widely, and predicts decreased
errors at \emph{all} orders---not just when new LECs are added.
The truncation-error assessment described here is just one piece of a broader framework for
EFT uncertainty quantification using Bayesian methods.
We have under development analogous procedures, together with a suite of diagnostic
tools, for parameter estimation and the assessment and propagation of errors---both statistical and truncation---in
fitted LECs and predicted observables.
Bayesian model selection is also well suited for addressing fundamental
questions in nuclear EFT, such as the comparative efficacy of theories with
different degrees of freedom, from pionless to chiral EFTs with and without
an explicit $\Delta(1232)$.
\acknowledgments{We are grateful to Evgeny Epelbaum for numerous discussions on these issues, and for sharing
results prior to publication. We also thank Harald Grie\ss hammer for a careful reading of, and useful suggestions regarding,
an early version of this manuscript. NMK thanks the KITP (Klco Institute for Theoretical Physics) for hospitality during the
completion of this research.
This work was supported in part by the National Science Foundation
under Grant No.~PHY--1306250, the U.S. Department of Energy under
grant DE-FG02-93ER40756, and the NUCLEI SciDAC Collaboration under
DOE Grant DE-SC0008533.}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 9,152
|
Crackdown on financial spread betting to weigh on IG Group revenue
Wed, Jul 25, 2018 - 5:50 AM
BRITISH online financial trading company IG Group lowered its revenue forecast for 2019 and said a regulatory clampdown on spread-betting will make some of its products less attractive.
The company, which provides online stockbroking and trading services to retail investors, said on Tuesday that it would return to growth after 2019.
The company's muted forecast comes as global regulators crack down on the fast-growing spread-betting industry to address concerns that high-risk speculative products are being offered to retail investors, leading to losses.
The European Securities and Markets Authority (ESMA) has said it would ban "binary" options sales to retail clients and restrict the sales of contracts for differences (CFDs) to protect investors from significant losses.
"As ESMA's product intervention measures are focused on the CFD industry, they risk creating an unlevel playing field by giving an advantage to other forms of leveraged trading products which are offered to retail clients," IG Group chief executive Peter Hetherington said.
"What you've had are regulatory rules that apply only to CFDs and are quite onerous, and will relatively make other products more attractive and relatively make CFDs less attractive," Mr Hetherington added.
Other products include traditional futures, options, warrants, and swaps, among twenty others, he said.
Binary options and CFDs are financial products that give an investor exposure to price movements in securities without actually owning the underlying assets such as a currency, commodity or stock.
IG, which was founded in 1974 as the world's first spread-betting firm, had already warned that ESMA's rules would risk pushing retail clients to providers based outside of the EU, resulting in poor client outcomes.
While most measures announced by the European regulator relate to retail clients, IG's client base is dominated by sophisticated traders.
"I think our clients are not happy with these new rules. And that is an understatement," Mr Hetherington said, adding that one in five of its customers had applied to be classified as "professional".
The company said it would continue to acquire licences to operate in additional jurisdictions and expects to go live as a forex dealer merchant in the US in the next five months.
IG also reported pretax profit of £280.8 million (S$503.3 million) in the year ended May, from £213.7 million, and higher than analysts' estimates of £273.9 million, according to company supplied consensus estimates.
IG Group and rivals Plus500 and CMC Markets have all reported healthy revenue growth as they signed up record numbers of customers, partly due to the bitcoin boom.
IG, which plans to create a subsidiary in Dusseldorf, also said it would have an EU licence in time for Britain's exit from the bloc next March. REUTERS
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 8,216
|
import {
Architect, BuildEvent, BuilderDescription,
TargetSpecifier,
} from '@angular-devkit/architect';
import { JsonObject, experimental, schema, strings } from '@angular-devkit/core';
import { NodeJsSyncHost, createConsoleLogger } from '@angular-devkit/core/node';
import { of } from 'rxjs';
import { from } from 'rxjs';
import { concatMap, map, tap, toArray } from 'rxjs/operators';
import { WorkspaceLoader } from '../models/workspace-loader';
import { Command, Option } from './command';
export interface ProjectAndConfigurationOptions {
project?: string;
configuration?: string;
prod: boolean;
}
export interface TargetOptions {
target?: string;
}
export type ArchitectCommandOptions = ProjectAndConfigurationOptions & TargetOptions & JsonObject;
export abstract class ArchitectCommand extends Command<ArchitectCommandOptions> {
private _host = new NodeJsSyncHost();
private _architect: Architect;
private _workspace: experimental.workspace.Workspace;
private _logger = createConsoleLogger();
// If this command supports running multiple targets.
protected multiTarget = false;
readonly Options: Option[] = [{
name: 'configuration',
description: 'The configuration',
type: String,
aliases: ['c'],
}];
readonly arguments = ['project'];
target: string | undefined;
public async initialize(options: ArchitectCommandOptions): Promise<void> {
return this._loadWorkspaceAndArchitect().pipe(
concatMap(() => {
const targetSpec: TargetSpecifier = this._makeTargetSpecifier(options);
if (this.target && !targetSpec.project) {
const projects = this.getProjectNamesByTarget(this.target);
if (projects.length === 1) {
// If there is a single target, use it to parse overrides.
targetSpec.project = projects[0];
} else {
// Multiple targets can have different, incompatible options.
// We only lookup options for single targets.
return of(null);
}
}
if (!targetSpec.project || !targetSpec.target) {
throw new Error('Cannot determine project or target for Architect command.');
}
const builderConfig = this._architect.getBuilderConfiguration(targetSpec);
return this._architect.getBuilderDescription(builderConfig).pipe(
tap<BuilderDescription>(builderDesc => { this.mapArchitectOptions(builderDesc.schema); }),
);
}),
).toPromise()
.then(() => { });
}
public validate(options: ArchitectCommandOptions) {
if (!options.project && this.target) {
const projectNames = this.getProjectNamesByTarget(this.target);
const { overrides } = this._makeTargetSpecifier(options);
if (projectNames.length > 1 && Object.keys(overrides).length > 0) {
throw new Error('Architect commands with multiple targets cannot specify overrides.'
+ `'${this.target}' would be run on the following projects: ${projectNames.join()}`);
}
}
return true;
}
protected mapArchitectOptions(schema: any) {
const properties = schema.properties;
const keys = Object.keys(properties);
keys
.map(key => ({ ...properties[key], ...{ name: strings.dasherize(key) } }))
.map(opt => {
let type;
const schematicType = opt.type;
switch (opt.type) {
case 'string':
type = String;
break;
case 'boolean':
type = Boolean;
break;
case 'integer':
case 'number':
type = Number;
break;
// Ignore arrays / objects.
default:
return null;
}
let aliases: string[] = [];
if (opt.alias) {
aliases = [...aliases, opt.alias];
}
if (opt.aliases) {
aliases = [...aliases, ...opt.aliases];
}
const schematicDefault = opt.default;
return {
...opt,
aliases,
type,
schematicType,
default: undefined, // do not carry over schematics defaults
schematicDefault,
hidden: opt.visible === false,
};
})
.filter(x => x)
.forEach(option => this.options.push(option));
}
protected prodOption: Option = {
name: 'prod',
description: 'Flag to set configuration to "prod".',
type: Boolean,
};
protected configurationOption: Option = {
name: 'configuration',
description: 'Specify the configuration to use.',
type: String,
aliases: ['c'],
};
protected async runArchitectTarget(options: ArchitectCommandOptions): Promise<number> {
const targetSpec = this._makeTargetSpecifier(options);
const runSingleTarget = (targetSpec: TargetSpecifier) => this._architect.run(
this._architect.getBuilderConfiguration(targetSpec),
{ logger: this._logger },
).pipe(
map((buildEvent: BuildEvent) => buildEvent.success ? 0 : 1),
);
try {
if (!targetSpec.project && this.target) {
// This runs each target sequentially.
// Running them in parallel would jumble the log messages.
return await from(this.getProjectNamesByTarget(this.target)).pipe(
concatMap(project => runSingleTarget({ ...targetSpec, project })),
toArray(),
).toPromise().then(results => results.every(res => res === 0) ? 0 : 1);
} else {
return await runSingleTarget(targetSpec).toPromise();
}
} catch (e) {
if (e instanceof schema.SchemaValidationException) {
const newErrors: schema.SchemaValidatorError[] = [];
e.errors.forEach(schemaError => {
if (schemaError.keyword === 'additionalProperties') {
const unknownProperty = schemaError.params.additionalProperty;
if (unknownProperty in options) {
const dashes = unknownProperty.length === 1 ? '-' : '--';
this.logger.fatal(`Unknown option: '${dashes}${unknownProperty}'`);
return 1;
}
}
newErrors.push(schemaError);
});
if (newErrors.length > 0) {
this.logger.error(new schema.SchemaValidationException(newErrors).message);
return 1;
}
} else {
throw e;
}
}
}
private getProjectNamesByTarget(targetName: string): string[] {
const allProjectsForTargetName = this._workspace.listProjectNames().map(projectName =>
this._architect.listProjectTargets(projectName).includes(targetName) ? projectName : null,
).filter(x => !!x);
if (this.multiTarget) {
// For multi target commands, we always list all projects that have the target.
return allProjectsForTargetName;
} else {
// For single target commands, we try try the default project project first,
// then the full list if it has a single project, then error out.
const maybeDefaultProject = this._workspace.getDefaultProjectName();
if (maybeDefaultProject && allProjectsForTargetName.includes(maybeDefaultProject)) {
return [maybeDefaultProject];
}
if (allProjectsForTargetName.length === 1) {
return allProjectsForTargetName;
}
throw new Error(`Could not determine a single project for the '${targetName}' target.`);
}
}
private _loadWorkspaceAndArchitect() {
const workspaceLoader = new WorkspaceLoader(this._host);
return workspaceLoader.loadWorkspace(this.project.root).pipe(
tap((workspace: experimental.workspace.Workspace) => this._workspace = workspace),
concatMap((workspace: experimental.workspace.Workspace) => {
return new Architect(workspace).loadArchitect();
}),
tap((architect: Architect) => this._architect = architect),
);
}
private _makeTargetSpecifier(options: ArchitectCommandOptions): TargetSpecifier {
let project, target, configuration, overrides;
if (options.target) {
[project, target, configuration] = options.target.split(':');
overrides = { ...options };
delete overrides.target;
} else {
project = options.project;
target = this.target;
configuration = options.configuration;
if (!configuration && options.prod) {
configuration = 'production';
}
overrides = { ...options };
delete overrides.configuration;
delete overrides.prod;
delete overrides.project;
}
return {
project,
configuration,
target,
overrides,
};
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,226
|
Q: Pass variable from web view to Xcode and store as NSString I am trying to pass a variable from a form filled out by a web view and store it as an NSString in Xcode. I have a signup page that stores the variable as a cookie. Then in another page I am trying to return that cookie as a variable and return it to Xcode. I think I am pretty close, but I need some assistance.
Xcode:
NSString *strURL = [NSString stringWithFormat:@"http://www.website.com/get_id.php"];
NSData *dataURL = [NSData dataWithContentsOfURL:[NSURL URLWithString:strURL]];
NSString *strResult = [[NSString alloc] initWithData:dataURL encoding:NSUTF8StringEncoding];
UIAlertView *alert = [[UIAlertView alloc]
initWithTitle:@"Your ID"
message:strResult
delegate:self
cancelButtonTitle:@"Dismiss"
otherButtonTitles:nil, nil];
[alert show];
return;
PHP:
<?php
$result = action($a, $b);
echo $result;
function action($a, $b){
$your_email = $_COOKIE["your_email"];
return $your_email;
}
?>
Thank you very much for your time and assistance!
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 9,596
|
Copyright © 1956 by Houghton Mifflin Harcourt Publishing Company
Copyright © renewed 1984 by Jane Eager and N. M. Bodecker
First Harcourt Young Classics edition 1999
First Odyssey Classics edition 1990
First published 1956
All rights reserved. Originally published in hardcover in the United States by Harcourt Children's Books, an imprint of Houghton Mifflin Harcourt Publishing Company, 1956.
For information about permission to reproduce selections from this book, write to trade.permissions@hmhco.com or to Permissions, Houghton Mifflin Harcourt Publishing Company, 3 Park Avenue, 19th Floor, New York, New York 10016.
www.hmhco.com
Cover illustration © 2016 by Peter Ferguson
Cover design by Whitney Leader-Picone
The Library of Congress has cataloged the hardcover edition as follows:
Eager, Edward.
Knight's castle/by Edward Eager; illustrated by N. M. Bodecker.
p. cm.
Sequel: The time garden.
Summary: Four cousins, Roger, Ann, Eliza, and Jack, have an extraordinary summer when, after an old toy soldier comes to life, they find themselves transported back to the days of Robin Hood and Ivanhoe.
[1. Magic—Fiction. 2. Space and time—Fiction. 3. Cousins—Fiction. 4. Knights and knighthood—Fiction.] I. Bodecker, N. M., ill. II. Title.
PZ7.E115Kn 1999
[Fic]—dc21 99-24557
ISBN: 978-0-544-67171-3 paperback
eISBN 978-0-547-89258-0
v4.0816
> _For my son_
>
> _FRITZ,_
>
> _Friend of knights_
>
> _and castles_
1
# The Blow
_It happened just the other day,_ to a boy named Roger.
Most of it happened to his sister Ann, too, but she was a girl and didn't count, or at least that's what Roger thought, or at least he thought that in the beginning.
Part of it happened to his cousins Jack and Eliza, too, but they didn't come in to it till later.
Roger and Ann lived with their mother and father in a pleasant small house in a pleasant small city, and until the blow fell life was very pleasant.
Their father was an understanding parent, often quite helpful and willing about such important things as building a rabbit hutch in the backyard or hanging the swing from the biggest oak tree. And even though he said he wasn't good with his hands (which was true), still part of the rabbit hutch stayed together quite nicely (though all the rabbits got away through the part that didn't), and one year the swing didn't fall down till nearly the end of summer.
And best of all, their father always read to them for an hour after dinner, even though they'd been able to read perfectly well to themselves for years now. This practice sometimes led to hot argument, because Roger was getting to be rather a yeomanly type and wanted to hear books like _The White Company_ and _The Scottish Chiefs,_ while Ann was becoming all too womanly, and leaned toward _Little Women_ and the Betsy-Tacy books. And their father would complicate matters by always wanting to read books like _Five Children and It,_ which he said was great literature. And Ann agreed that, next to the Betsy-Tacy books, it was.
Roger enjoyed science fiction books, too, but there their father drew the line. He said they were like having bad dreams on purpose, and if the Flying Saucers really _have_ landed, he didn't want to know about it. Roger called this Not Taking a Realistic Attitude. All the same, he really liked the magic books his father and Ann loved so, and back in the days when he was a child, before he got to be eleven, he had even hoped that some day something magic would happen to _him._ But nothing ever had, and that seemed to Roger to prove that there was no such thing. Or if there ever had been, probably modern science had done away with it long ago.
Their father always said how could he be sure, and besides, even if there weren't any such thing as magic, wasn't it pleasant to think that there might be? And in the discussion that would follow, their mother would sometimes pass through the room and cry out, and say honestly, their father was as much of a child as _they_ were, which Ann thought quite a compliment, though she was not sure their mother meant it as one.
Ann was eight, and believed nearly everything.
When their mother wasn't passing through the room and crying out, she was quite an understanding parent, too, except about the way Roger kept wanting more model soldiers when he had two hundred and fifty-six already, and the way all two hundred and fifty-six were always to be found all over the floor of his room, which she said passed all understanding.
And sometimes when Roger would start picking on Ann because she was a girl, and younger, their mother would get really cross, and say there would be none of that in _this_ house! Their mother said she knew just how Ann felt because _she_ had been a girl once, too, and the youngest of _four_ children, and what she had endured worms wouldn't believe!
But at other times she talked about what fun she and her sisters and brother had had; so Roger decided she couldn't have suffered so very much. And when he asked his Uncle Mark about it, his Uncle Mark said their mother had been a terror to cats and ruled the household with a rod of iron. And when he asked his Aunt Katharine, his Aunt Katharine said their mother had been a dear little baby, but went through a difficult phase as she grew older. He couldn't ask his Aunt Jane, because she was hardly ever there, being usually occupied hunting big game in darkest Africa or touring the English countryside on a bicycle.
But he decided their mother's childhood had probably been very much like their own, partly good and partly bad, but mostly very good indeed.
And so time went on, with few clouds to stir life's untroubled sea, until the day the blow fell.
The blow fell on a day in June. School had been over for only a few days, and the whole bright vacation lay ahead, waiting for them to make up their minds where to spend it. Their mother wanted to tour New England and stop at all the antique shops looking for old spice boxes, which she liked for some reason, and their father wanted to revisit an island in Canada, where he'd spent a wonderful summer once, back when the world was young.
Roger wanted to go somewhere yeomanly, like Sherwood Forest, but since everybody else seemed to think that was a bit far, he decided the Rocky Mountains were the next best thing. Ann didn't know where she wanted to go yet, but she thought probably Wampler's Lake, to be near her best friend Edith Timson. They were to have a big family conference about it that evening and decide.
But that afternoon their father came home from the office at half past three instead of half past five, and he didn't explain why, but said hello to Roger and Ann, just as though everything were perfectly usual, only somehow he didn't sound as though everything were.
And a few minutes later he and their mother went into the living room and shut the door, and their voices went on and on, for what seemed like practically forever.
Roger and Ann didn't know what to think of this odd behavior, but then they got interested in seeing who could draw the most horrible Frankenstein monster, and forgot about it. And after they'd drawn, and compared, and argued about which was most truly horrifying, Roger tried to persuade Ann to join him in a war of model soldiers. Only Ann was never terribly interested in model soldiers; so they played _Monopoly_ instead.
But after a few minutes of this, Ann got to thinking about that door being closed, though she didn't say anything about it to Roger. And after a few minutes more, Roger found himself wondering about those voices going on and on, though he didn't say anything about it to Ann.
And five minutes later all subterfuge failed, and they looked at each other and nodded with one accord, and put their _Monopoly_ game away (which was unusual of them) and went and stood on the stairway. The living room door was still closed, and from where they stood they could hear only an occasional unrevealing word, but the voices sounded serious.
"I sense divorce in the air," said Roger, who had been seeing too many old movies on television lately.
Ann shook her head. "They don't sound angry, just kind of worried. Do you suppose Father's done something _criminal?_ " (Ann had been seeing old movies on television, too.)
"Not Father," said Roger. "He's too nice and not half crafty enough. The police would catch him right away."
"Maybe they _have,_ " said Ann. But it turned out neither guess was right.
For the voices stopped and the door opened at last, as voices and doors will, and their mother and father came out, and looked at them with false bright smiles, and said it was time for dinner. And dinner was their mother's specially good meat loaf and popovers, but somehow the two children couldn't enjoy any of it, and every popover was as lead.
Finally Roger put his fourth popover down on his plate half-eaten, and burst into speech. "It's not fair," he said. "It's not fair, not telling us what's the matter, when anybody could see something _is!_ "
"We're not babies," Ann chimed in. "We can stand it, no matter how terrible."
"It's not terrible," their father said. "Only I'm afraid we won't get to the Rocky Mountains this summer, or Wampler's Lake, either."
And then he said he guessed he'd go and serve the dessert, and while he was out of the room their mother told them.
She told them their father had something wrong inside, and he was going to have to go to a hospital in Baltimore, Maryland, to have it made well. And because she didn't want to be separated from their father at a time like this, their mother was going to Baltimore, Maryland, too. And because it was all going to cost a lot of money, they wouldn't be able to send the children somewhere else for their vacation, and so she and Roger and Ann were going to have to spend the next few weeks in Baltimore, Maryland, and no one could tell how many weeks it would be, but maybe it would be the whole summer.
"Your father hopes you won't be too disappointed about the mountains and the lake," she finished.
Roger didn't say anything for a minute. Then he got red. Then he said, "It isn't that. It's Father."
"I know," said their mother.
"Is it serious?" said Roger.
"Doctor Reese is almost certain he'll be all right," said their mother.
"Almost," said Roger.
"I know," said their mother.
Ann didn't say anything. But when their father came in a second later with the dessert, which happened to be Royal Anne cherries and sponge cake, she ran to take the tray from him, as though its weight might be too much for his feeble strength.
And Roger jumped up and pulled their father's chair out for him, as though he might not be able to manage it alone.
And when they took their places at the table again, Ann didn't eat, but sat looking at their father with an expression on her face that Roger would have called icky if he hadn't had a sneaking suspicion that he was looking the same way himself.
Their father ate two Royal Anne cherries. Then he looked up and saw Roger and Ann. He swallowed hard, as if he were swallowing a pit in one of the cherries. Then he grinned.
"Look, kids," he said. "We may as well get this straight. I don't have a pain, and I'm not weak and pining away and having to be waited on. I've just got something mixed up inside that has to be straightened out, and we're going where the doctors are who can do that best. And we won't any of us have time to worry, because we've got to leave in three days and it'll take all that time to get ready."
After that, Roger and Ann found that their dessert went down more easily, though neither of them was ever able to feel quite the same about sponge cake or Royal Ann cherries again. Still, if their father could be brave, who were they to be behindhand?
Their mother was making plans. "Maybe we can stay with your Aunt Katharine while your father's in the hospital," she was saying.
"No, Martha," said their father. "We can't go wishing ourselves on people, like that."
"I don't know why not," said their mother. "My own sister. That beautiful big house."
"Even so," said their father, two words which were law in that house.
"I'll call her, anyway," said their mother. "Maybe she can find us an inexpensive hotel."
Ann and Roger looked at each other. The words didn't sound very promising, suggesting mean chandeliers with light bulbs that were too small, and long dark corridors and a draught coming in under the door. Still, this was no time for selfishness; so they volunteered to do the dinner dishes, and tried to cheer each other with bright conversation. Once Ann said, "Poor Father," and Roger said, "Yes," and once Roger said, "You forgot to scour the sink," and Ann said she was just going to.
When they came out of the kitchen their mother was just hanging up the telephone. "She insisted, Fred. I just knew she would," she was saying. "Children, we _are_ staying with Aunt Katharine after all. Now you'll have Jack and Eliza to play with."
"Oh," said Roger. Ann threw him an understanding look.
"Oh what?" said their mother.
"Nothing," said Roger. And then it was time for Ann to go to bed, and Roger to go upstairs for a half hour of tapering off before his own bedtime.
"Jack and Eliza!" muttered Ann to Roger, on the stairs. "Help!"
Up till two years ago their cousins Jack and Eliza had lived in the same town they did. The last they'd seen of Eliza she'd been just about the bossiest nine-year-old girl on her, or any other, block. As for Jack, all he cared about was his Leica camera, and spent all his time in his darkroom, only coming out for meals, or, as Ann once said wittily, to cast his shadow, like Groundhog Day.
"He's pretty good at baseball, though," said Roger.
"That," said Ann, "is small comfort."
"Ann, go to bed," said her mother, from below; so she did. But once there, she lay awake wondering about Baltimore, Maryland. All the words made her think of was a Baltimore oriole. She tried to picture a city all orange and black, like an oriole's feathers. After a bit she tiptoed over to the bookcase and found _The American Family Encyclopedia,_ Volume One, A—Boon. Baltimore, Maryland, she read, was the eighth largest city in the United States, population 859,100. Chief industries, iron and steel, straw hats, et cetera.
She got back into bed and shut her eyes, seeing a sky flaming with the orange of many steel forges, while in the black iron foundries below 859,100 dark figures labored, all wearing straw hats. "Only I should think the straw hats'd catch fire," she murmured to herself. A second later she was asleep.
In his room, Roger sat on the floor among the two hundred and fifty-six model soldiers, and absently started a small war. He wouldn't have done it if anyone had been looking, of course. Now that he was eleven, he kept the soldiers just as a collection. But when he felt lonely or unhappy, or when things went wrong, he sometimes still secretly played with them, for all the world as though he were still only ten-and-a-half.
Two hundred and seven of Roger's soldiers were modern ones, British grenadiers and such, that he had bought himself, or been given. Thirty-one were World War One veterans that had belonged to his father, and seventeen were survivors of the Spanish American War, and of many a nursery battle since the days of Roger's grandfather.
The two hundred and fifty-sixth soldier was much older, even, than any of these. No one knew exactly where it had come from in the first place, but Roger's father said it had been in his family for generations. No one could tell what kind of soldier it was, or even if it was a soldier at all, because all its paint was worn off, and its weapon, if any, had disappeared in the sands of time.
But it was the size of a model soldier, and Roger and his father before him, and _his_ father before _him,_ had played with it along with their own soldiers, though each one's father had said it was an antique and shouldn't be handled.
Roger called it the old one, and usually gave it special duties like being a sentinel or scout, so that it wouldn't be damaged in the heat of battle. Roger's battles (particularly when he felt lonely or unhappy) were usually very heated indeed.
But tonight even the familiar call to arms wasn't much comfort. There was a small skirmish, and several gallant privates bit the dust, but Roger's heart wasn't really in it, and after a minute or two he got into bed and put out the light. And if he took one of the soldiers to bed with him I hope you will not scorn him too much. A model soldier is not the same thing as a teddy bear at all. Taking a model soldier to bed with you is much more mature, and more manly, too.
It was the old one Roger held in his hand, and as he lay thinking about the weeks ahead in Baltimore, Maryland, he clutched it hard. Of course if their father were going to be all right, that was the main thing. But he wished something fun and exciting could happen to him in Baltimore, Maryland, too.
Just as he was thinking this thought, a voice spoke. It wasn't the voice of conscience, either. It seemed to come from somewhere very near Roger, and it seemed both cross and sleepy.
"A murrain!" it seemed to say. "Just as I was beginning to feel rested! Ah well, back into the fray, a soldier's lot is not a happy one, a plague on it! Still, needs must when duty calls! I could not love sleep half so much loved I not honor more!"
Roger sat up in bed. His hand tickled. For a second he could have sworn the old one was stirring in his grasp, stretching and yawning. Roger opened his hand quickly, and the old one fell to the floor by the side of the bed, landing in a standing position.
"Rough play, by the rood!" he seemed to say. A moonbeam shining through the window struck a silver glint from his battered countenance, and for a moment he seemed to be turning to the other soldiers lined up on the floor, as though giving them a word of command. And then for another moment it seemed as though all the soldiers were moving in the soft light, marching toward Roger:
Roger rubbed his eyes and opened them again. The soldiers were still now. Nothing had happened. Naturally.
"I must be sleepier than I thought," Roger said to himself. "I'm seeing things that aren't there." And he plumped up his pillow and put his head down on it and went to sleep.
2
# The Beginning
_The next three days were a flurry_ of activity and packing and meeting each other on the stairs at odd hours with armfuls of clothes. And of course the children would forget, sometimes for half days at a time, why they were going to Baltimore, Maryland, and just be happy and excited to be going anywhere.
Roger's packing took the longest. First he dumped the whole contents of his clothes basket and his dresser drawers into his suitcase, and that was quick, and the suitcase closed quite easily after he sat on it for a while, and he didn't actually have to _stand_ on it at all, hardly.
But then came the problem of choosing exactly the right-sized grocery carton from the pile in the attic, and then each of the two hundred and fifty-six soldiers had to be wrapped carefully in cotton and fitted into the box, not to mention sundry cannon, tanks, drawbridges, turrets from old broken castles, and other art treasures without which no boy's life can be truly rich and full.
Their mother went so far as to suggest that there were probably plenty of things to play with at Aunt Katharine's without taking toys along, but one glance at Roger's expression told her what a barbarous idea this was.
And quite soon the night of the third day came, and they were on the train. Roger and Ann had traveled in Pullman cars before, and there was nothing about this particular Pullman car to distinguish it from those they had known and loved in the past, except its name, which was Wah-Wah-Tay-See. Ann, who was making a collection of the names of Pullman cars, wrote this down on a special page in her notebook.
Their mother and father had a drawing room, and the two children were in the section nearest to it, Ann in the lower berth and Roger in the upper. And the dining car menu, like all menus in trains, had tonight's dinner listed in the middle, and then around the edges lots of far more interesting dishes that apparently no one was supposed to order, because their waiter looked very surprised when Ann asked for pickled mangoes and Roger called for a bottle of Apollinaris water. The children's mother tried to thwart them in this project, but their father gave her his well-known let-them-do-it-this-once look, and she subsided.
When they got back to their car after dinner, the usual nice old lady turned up in the section opposite, and wanted to talk to them about a dear little fairy who lived in a Pullman car. Roger and Ann were polite about this, and luckily it didn't go on for very long, because the train was getting into Baltimore, Maryland, early in the morning; so bedtime had to be early tonight.
And when Roger, in his pajamas, hung his head down over the edge of the berth and poked it through the green curtains to talk to Ann in the berth below, the usual cross other old lady in the upper berth next door rapped on the wall and said, "Quiet!"
So after that Roger lay still and tried to go to sleep, but he couldn't. Ann, down below, could look out on barns and towns and moonlight and hotdog stands, but he had only a curving wall and curtains and the dim light from the corridor to gaze at.
Pretty soon he decided he couldn't stand gazing at them any longer. He opened his curtains, let his feet down over the edge, swung wildly in space, and thumped to the floor.
He looked in on Ann. A gentle snore issued from under a mound of blankets. So then he knelt on the floor of the corridor and felt under the lower berth till he found the grocery carton of soldiers. He'd take a few of the top ones out and have a war in his berth, that's what he'd do.
To get the string off the box was but the work of a moment, but wasn't so noiseless a process as Roger would have chosen, and just as he had his hand inside the top flap, the cross old lady in the upper berth next door parted her curtains and glared down at him with a face so truly horrible that all Roger could do was gasp, grab the first soldier he found, shove the carton back, scramble up to his own berth and pull the curtains. He lay clutching the soldier, his heart beating fast, waiting for the old lady to call the conductor or pull the emergency cord and stop the train. But nothing of the kind happened.
What did happen was that he felt a tickling in his hand again, like the time before, and when he turned on the little light with his other hand he saw that what he held was the old one and he was talking.
"Newfangled flummery!" he was saying. "Modern inventions, industrial revolution, rush, rush, rush, choo-choo, crash, bang! A castle that stayed put was good enough for me, aye, and my forefathers before me, and when we sallied forth 'twas a gallant steed under us, aye, and a trusty sword in hand! By my halidom!" he added.
"What did you say?" said Roger.
"Thou heardst me," said the old one.
"I did not," said Roger. "You didn't say any of that. You didn't talk that other time, either. It was a dream. So's this."
The old one reached out his small metal hand and pinched Roger hard. For such a small pinch it hurt quite a lot.
"Ow," said Roger. And then he knew. And remembering from his reading that Psammeads and Phoenixes and Mary Poppins always had to be addressed with due deference, he made his voice very respectful indeed.
"Oh Old One," he said, "I take it back. I see it all now. You _are_ magic."
"Light dawneth," said the Old One.
"Why," said Roger, getting excited, "I suppose you must be the lucky charm of this family, like the Mouldiwarp of the House of Arden! Only I suppose you've been handed down from generation to generation till people forgot you were magic and just used you to play soldiers with! I'm sorry if we played too rough. And those times I forgot to pick you up and stepped on you afterwards by mistake. I hope the magic hasn't all gone out of you. It hasn't, has it? Did you come to make Father get well in Baltimore, Maryland? Because if I get a wish, that's what I wish."
The Old One said nothing, but Roger thought he grew a bit warmer in his hand. Encouraged, he went on.
"And if you still have any magic left in you after that, I wish we'd have an adventure in Baltimore, Maryland, while we're waiting."
"Quiet!" said the voice of the old lady next door. And she gave a really terrible rap on the partition at Roger's feet.
So Roger put out his light, and placed the Old One carefully on the pillow next to him, where the dim glow from the corridor could shine on his face. And just before he went to sleep, Roger heard the Old One speak again.
"Gadzooks!" he said. "Cannot a man retire in his old age but paltry striplings must be waking him from his soft sleep with their wearisome wishes? Wishes must be earned, sirrah! However," he added, and his voice was kinder, "wishes, like fishes, turneth up in strange dishes. Tomorrow is another day I always say." After that he was silent, and Roger knew somehow that he would not speak again, at least not now.
The next thing Roger knew, it was morning and his mother was telling him to wake up. And for the half hour after that all was bustle and squeak as he and Ann hurried to brush their teeth, hurried to pack away their pajamas and put on their clothes, and hurried to the dining car for breakfast.
Their mother had not been pleased to find the carton of soldiers untied, but she had already tied it up again, with a few pertinent remarks; so Roger put the Old One in his pocket.
And then the porter was brushing them off and they were pulling into Baltimore, Maryland, and Ann looked out of the window to see a city not orange and black, but gray with rain.
Their Aunt Katharine met them in the station. Eliza was with her, wearing her hair in pigtails and talking a blue streak. Jack was not to be seen, but a moment later the children caught a back view of him. He had his camera well in hand, and was focusing on some rather uninteresting-looking murals on the station ceiling.
"Wouldn't you know?" whispered Roger to Ann.
And then Aunt Katharine was kissing them and kissing their mother and shaking hands with their father, and Jack drifted up and took a picture of the whole group, and Eliza circled round all of them, telling all about a man she had heard of who had gone to the same hospital Roger's father was going to, and had practically _everything_ taken out, and learned to walk again perfectly well after a year.
"Really, Eliza," said Aunt Katharine, which was all she ever said when Eliza was awful.
And now a smartly dressed chauffeur had appeared and was dealing with the luggage, and Aunt Katharine turned to the children's mother. "You'll want to go to the hospital right away; so I thought I could take the children to a movie and lunch and then meet you at the house." And this was agreeable to all.
There was a bad moment when Roger and Ann said good-bye to their father, for a thought that didn't bear thinking couldn't help flashing through both their minds. But their father grinned and said, "I'll be seeing you," and after that they felt better. And their mother and father rode off in Aunt Katharine's big black car, while Jack summoned a taxi in rather a grown-up fashion, and the others got in.
On the way uptown Roger and Ann hung out the window looking for points of interest, but there weren't any till the cab stopped for a traffic light near a large statue. Ann read the name on the statue, _George Peabody._ She caught Roger's eye and they both started giggling, for no reason at all, as sometimes happens in families. To their surprise, Eliza giggled, too.
"George Cornbody," said Roger.
"George Squashbody," said Ann.
"George Beanbody," said Eliza. "George Applebody, George Prunebody."
Jack didn't say anything. He was leaning out the window of the cab, taking a picture of the statue. But after that Roger and Ann and Eliza felt friendlier, the way you do when you've all giggled at the same thing.
"Really, Eliza," said Aunt Katharine. "What movie shall we see?"
Jack and Eliza started talking at once. Jack wanted to see a picture about wheat growing that was full of interesting camera angles while Eliza was loud in asserting that _Scarface Returns_ was absolutely the only decent thing in town.
Aunt Katharine shook her head. "I thought _Ivanhoe_ ," she said. Roger's eyes glowed, for his father had read him the book last year. And everyone else had to admit that _Ivanhoe_ sounded just dandy.
And it was. It was in glorious Technicolor, and it was just about as yeomanly as a movie could be. Roger and Ann sat enthralled, and so, surprisingly enough, did Aunt Katharine. Jack quite approved of the photography, and as for Eliza, during the final combat between Ivanhoe and the wicked Knight Templar she bounced up and down in her seat and muttered, "Pow! Zowie! Wham!" till everybody sitting around said, "Shush," and Aunt Katharine said, "Really, Eliza."
But after the picture, as they sat eating a late and filling lunch of strange and wonderful seafood, Jack became critical.
"The tournament wasn't quite right," he said. "That isn't the way they did it, really."
"Were you ever _in_ one?" said Aunt Katharine, turning suddenly on her son.
"No," said Jack, surprised.
"Then don't talk about what you don't know about," said his mother. " _I_ thought it was quite a nice little tournament. Not like the ones King Arthur used to have, of course."
"Honestly, Mother," said Eliza. "Anybody'd think you'd been alive back then!"
Aunt Katharine blushed, and if you have read a book called _Half Magic_ you will know why. But all she said was, "Who wants what for dessert?" And there were seventeen things to choose from (because Roger counted), and that took silent concentration from everyone.
But a few minutes later Eliza looked up from her hot butterscotch ice-cream shortcake. "I don't see why he had to marry that old Rowena," she said. "Rebecca was lots prettier. Why couldn't he have married her?"
"That wasn't what the author wrote," said Roger, a bit shocked.
"Oh, that old Sir Walter Scott!" cried Eliza. "A lot he knew about anything!"
"Sir Walter Scott?" said Ann. "We have him in our _Authors_ game."
"You don't still play _Authors,_ do you?" said Eliza. "That's almost as babyish as _Old Maid_!"
After that Ann didn't feel so friendly about Eliza. Deciding not to talk, she got out her notebook, and started a new page headed, "Interesting Things About Baltimore, Maryland."
"Good movies. Good lunches. Statue of George Peabody," she wrote, and that seemed to be all the interesting things, so far. And then it was time to pay the bill.
As they rode to Aunt Katharine's house in another taxi, they passed a toyshop window, and Roger had an unworthy thought. He had hoped Aunt Katharine would give him and Ann presents; she usually did when she saw them. Still, they had had the movie and lunch, hadn't they? Roger decided his thought was _very_ unworthy and should be suppressed.
Their mother was waiting for them at Aunt Katharine's, and told them everything was fine with their father so far. And then Aunt Katharine took them to see their rooms. "You'll have the whole east wing to yourselves," she said.
"My," said Ann. "We shall be in the lap of luxury."
And they very nearly were. There was a big bedroom for their mother, with her own bath, and a smaller bedroom for Ann, and another bath, and another big room that would be Roger's room and a playroom combined.
And when Roger and Ann saw this room, they stood and stared.
There was a big, fancy dollhouse, with a family of dolls, in one corner, and in another was an immense castle, the most wonderful castle Roger had ever seen, rich with turrets and battlements and a portcullis and a pretend moat, and a keep with a front wall that swung out on a hinge, so you could see what was going on inside. The dollhouse and the castle were from Aunt Katharine.
"Only I told her what to get," said Eliza, proudly. "Except not the dollhouse. I despise dolls, don't you?"
So of course Ann, who didn't, had to pretend that she did, only not loud enough for Aunt Katharine to hear and have her feelings hurt.
And their Uncle Mark in New York City had sent a big box of model soldiers, but these weren't like any Roger had ever seen before. They were from a wonderful shop called The Knight's Castle, and there were no two alike. There were knights of all sorts with beards of divers colors, and some young ones with no beards at all. There were squires and pages and bowmen in Lincoln green, and a few obvious dastardly villains and half a dozen ladies of high degree. Ann was sure one of the bowmen in green was Robin Hood and Roger found a stalwart, handsome young knight that everyone agreed could be only Wilfred of Ivanhoe.
There was still another present, from Aunt Jane, sent all the way from London by air mail.
"Isn't that just like Jane?" said Aunt Katharine to their mother. "So dashing and extravagant." Aunt Jane was in London for the Coronation, of course.
Wherever there was the most going on, Aunt Jane usually was. "Eliza is just like her," their Aunt Katharine added in a low voice, but Ann heard her.
Aunt Jane's package, when opened, proved to contain a lot of little books in blue covers. Eliza pushed in ahead of the others, to see what they were. " _The Magic City_ by E. Nesbit," she said, in tones of scorn. "I read that _ages_ ago! Magic is baby stuff."
Roger opened his mouth to agree with her. Then he remembered last night. His hand went into his pocket and encountered the Old One, still lying there. He proceeded with caution. "I know what you mean," he said. "Of course there might be a _little_ something to it, though."
Eliza uttered a contemptuous snort.
And then the children's mother went downstairs with Aunt Katharine to have a good talk, and the children were left to play with the castle.
Only they couldn't get at the castle right now, because Jack was there before them, putting different knights in position in the different rooms and then taking their pictures.
Roger's fingers itched to get the knights out of Jack's hands. You could tell from the way he was setting them up that he didn't know a thing about the laws of chivalry. He just didn't have the touch. But after all, he was the host and Roger was the guest and had to be polite.
Eliza had no such scruples. "Get out of the way," she said, and pushed in next to her brother.
After that Roger decided it was free for all, and knelt down by the castle, jostling Eliza on one side and Jack on the other.
Ann would have liked to play quietly with her dollhouse in its corner but after what Eliza had said she didn't dare; so she joined the group around the castle.
"Let's have it be the one in _Ivanhoe,_ " said Eliza. "The one where the siege was."
"You mean Torquilstone?" said Roger, feeling rather superior.
"Whatever its name was," said Eliza.
So it was decided that the castle was to be that ill-starred fortress where the villains Bois-Guilbert and De Bracy held Ivanhoe and most of the other characters prisoner during the most exciting part of the story.
Luckily one of the knights had a Templar's shield; so he could be Bois-Guilbert, and Roger found a thin, overdressed one for De Bracy. Ann chose the darkest and most beautiful of the ladies to be Rebecca, and Eliza picked a simpering inferior-looking blonde for Rowena. Jack took pictures of the different characters.
There was a jester in the assortment, to be the jester Wamba, and an elderly knight made a fine Cedric the Saxon, Ivanhoe's father.
"Only he wouldn't be wearing just armor, silly," said Eliza. While Ann watched in alarm, she found some manicure scissors and went over to the dollhouse, and quickly made Cedric a scarlet cloak from the train of the ballgown of the mother doll, trimmed with fur cut from the same lady's fur coat.
The afternoon passed quickly and happily, save for a few moments when the strong personalities of Eliza and Roger met and clashed. By the time dinnertime came, the castle presented a spectacular appearance.
Bois-Guilbert was on the battlements pleading with Rebecca to give him her love and Rebecca was threatening to throw herself over the edge to the courtyard below. De Bracy was in a rich chamber of the castle pleading with Rowena to give him her love and Rowena was looking self-righteous.
Cedric the Saxon was in the dungeon with Wamba the jester beside him. Wilfred of Ivanhoe languished wounded in an upper room, his middle tied up in a bandage Eliza had made out of a dollhouse kitchen curtain.
A few stray knights, henchmen of the two villains, lounged about the castle courtyard, and at a safe distance outside on the greensward (carpet), Robin Hood and the Black Knight (a knight in black armor, naturally), with Maid Marian, who _would_ come along (Eliza chose the most athletic-looking of the ladies), lay in ambush with a band of trusty archers, waiting to attack the castle. Eliza made the ambush out of some fluffy green stuff from the dollhouse bath mat.
Jack thought they ought to have the wicked Prince John, too, and found a bearded knight with a crown and a squint who looked the part. There wasn't any logical place in the castle for him, and he belonged in another part of the story anyway; so Jack pushed back the sliding wrought-iron screen of the fireplace, and the space within made an excellent throne room. Jack put a few stray knights in there with him, for courtiers. An armchair from the dollhouse made an imposing throne.
Anybody left over was an attendant. Halfway through arranging these, Roger remembered his precious soldiers from home, still packed in their cotton. But then he decided their uniforms wouldn't go with the armor of the others, and besides, now that he had the castle full of knights, the charm of British grenadiers and Spanish War veterans paled. So he left them in their box on top of the bureau.
But he did take the Old One out of his pocket, and put him in the castle, among the attendants, just in case.
And then, just as it was the moment for the Black Knight and Robin Hood and their followers to begin attacking the castle, Aunt Katharine appeared in the doorway and said, "All right, time to wash your hands and faces for dinner."
There really couldn't have been a worse time for her to say this, and Eliza let her know it. "Honestly!" she fumed. "You'd think mothers just waited outside the door till they're _sure_ it's the wrong moment! We can't possibly come now; we're having a siege!"
"Really, Eliza," said Aunt Katharine. And then Eliza's father, who was Uncle John, appeared firmly in the doorway, and that was that.
Dinner was good, and the children had one small glass of wine each, which was interesting, but made Ann yawn all through her pecan pie until her mother said they had had a long day and Ann should go to bed now, but Roger could stay up and play for half an hour more.
"Good," said Eliza. "Let's have the siege."
Ann sent Roger a beseeching look.
"No," he said, nobly. "It wouldn't be fair without Ann."
"Let's have it, anyway," said Eliza, not nobly at all. But her father gave her a stern look and she subsided. And good nights were said, and five minutes later Roger sat on the floor of his room, to the sound of toothbrush noises from the bathroom, and gloated over the castle, and thought about the things he would do with it and the things that would happen in it, and pretty soon his head began to feel heavy, and he got up without being called, and went into the bathroom and brushed his teeth and put on his pajamas, and came out again and called good night to Ann, and climbed into bed.
He turned his light off, but the light from the hall (that Ann had asked to have left on) sent a golden glow into the room. It was a hot night, and pretty soon Roger pushed the bedclothes off, so that some of them slid down to the floor. The last thing he saw before sleep came was the castle, glimmering goldenly at him from across the room.
When he woke up the golden glow was gone and it was daylight. Right away he looked across the room, for the castle. Then he stared.
The castle was there, all right, but it seemed hundreds of times bigger, and yet at the same time it seemed hundreds of times farther away. And then Roger looked down, and he saw that he wasn't in his room at all. He was lying on a great plateau of white rock, and there must have been a landslide recently, for there was a fall of rock and rubble to one side, leading down to the grassy plain below. And then suddenly he remembered the Old One, and then he knew. This was the adventure he had asked for, and magic was happening to him at last.
He waited a minute to see what would happen next, and nothing did, and the castle stood there, its turrets gleaming at him in the bright sunlight, and it was plain to Roger that the first thing to do was get over there near it.
He started picking his way along the fall of rock, which seemed to be the only way down from the plateau. The rocks hurt his bare feet, and he wished the magic had been thoughtful enough to provide shoes. The way got steeper as he went along, and he slid the last half of it, skinning one knee.
No bones were broken, however, and he got to his feet and began the long walk across the flat greensward toward the castle. He felt rather conspicuous and a bit chilly in just his summer pajamas with the short trousers, and he felt rather small, too, as he drew near the castle's lofty walls and saw how _very_ lofty they were. Either the castle had grown to life size or he had shrunk to the height a toy soldier would be if he were eleven years old, and it didn't really matter which, because it came to the same thing in the end.
He began walking slower. He didn't exactly want to turn around and run, but he didn't exactly want to go on, either. At last he stood at the edge of the moat, looking up at the parapets, far above him. The castle presented a grim aspect. The drawbridge was up and the portcullis was down. The moat had real water in it now, and the water looked deep and cold. Roger shivered.
"So this is Torquilstone," he said aloud, trying to sound jaunty, "and I'm at the siege of it."
He wondered if he were meant to venture inside the castle, or if he hadn't better go find Robin Hood's attacking party instead. Yes, he decided, that would be much the safer plan.
But when he looked around for the besiegers, no living soul was in sight. He must remember to tell Eliza she was a good ambush-maker, when he got back. If he ever did.
At this moment a voice broke in on his thoughts. The voice came from a window slit in the watchtower next to the drawbridge.
"Halt, paltry knave," said the voice.
"I _am_ halted," said Roger. "Paltry knave yourself," he added, but he didn't add it very loud. The window slit was too narrow for him to see the face of the gatekeeper, but he could tell from his voice that he wouldn't like him at all. He sounded, in fact, like a foul churl.
"Stand where ye are," the churlish voice went on. "Come ye on aught of business with my lords, or mean ye mischief to us and ourn?"
"No, I'm just looking," said Roger. "Now I'll be going."
He turned to go. An arrow whistled past his ear, and then another. There was nothing for him to hide behind and if he ran he would be a perfect target; so he did the only thing he could think of. He fell flat on the greensward and shut his eyes.
Behind him he heard a creaking sound that could only be the drawbridge being lowered, a sight that doubtless would have been very interesting at some other time, only not now. Then came a sound of mailed boots on stone, and a foot spurned Roger where he lay.
There is nothing like being spurned by a mailed foot to make a person stop being frightened and start being angry instead. Roger sat up and glared around him indignantly.
Three men in armor stood looking down at him.
"What witless wight art thou," said one of them, "that cometh a-knocking at our door all half-naked of a morning?" He took Roger by the ear and pulled him to his feet.
"Ow," said Roger.
"Nay, 'tis a mere boy!" said another of the men.
"'Tis a sign! 'Tis witchcraft!" cried the third, in alarm. "A changeling boy out of Elfland left on our doorstep in his shift, pardie! What can it mean?"
"Don't be so superstitious, Lionel," said the first man. "More likely some scurvy Saxon trick. Be ye Saxon or Norman, boy? Parlez-vous français?"
"Non," said Roger, in one of the two French words he knew.
"Aha! What did I tell you? A Saxon spy!" cried the first man. "Quick! Hail him before our masters!"
And Roger was seized and trundled across the drawbridge and through the outer courtyard and into the great hall of the castle keep. Two of the men hurried off in different directions to fetch their masters, and the third man, Lionel, was left on guard.
Now that the worst seemed to be happening, Roger began to feel more cheerful, and even a bit reckless. After all, every magic adventure he'd ever read had turned out fine for the hero in the end. I do not know how he came to be so sure that he was the hero of this one, but he was. It is simply a thing that one knows, and if you have ever been the hero of an adventure yourself, you will understand.
He stood looking about the great hall interestedly. It was just about as yeomanly as a hall could be, what with trophies on the wall, deerskins on the floor, and a whole boar roasting merrily on a spit in the great fireplace.
Then he looked at Lionel. Lionel smiled nervously and backed away a few paces, and this gave Roger an idea. He decided to have some fun with the superstitious guard. He went on looking at him for a minute, and then suddenly he made a terrible face and uttered a sepulchral cry.
"Beware!" he cried.
Lionel jumped. "What didst thou say?"
"Woe!" Roger went on, pleased with the success of his efforts. "Wurra wurra. Pity the poor Normans on a day like this!"
Lionel was looking pale. "Wherefore sayest thou such?" he asked. "Whence earnest thou hither?"
"Wouldn't you like to know?" said Roger, forgetting to sound like a grim oracle and sounding like a mere boy. Then he recollected himself and started over. "Ask not the dread name of whence I came," he said, "but hearken to my dire words. This day bringeth doom to all Normans within this castle!"
"Oh, dear," said Lionel. "Doth it really? What shall I do to be saved?"
"Flee," said Roger.
Lionel turned, and started to flee. But at that moment Brian de Bois-Guilbert and Maurice De Bracy entered the hall.
Both knights were thoroughly out of sorts, because they had both just been interrupted in important love scenes, and both their ladies had just rejected their proposals. Bois-Guilbert in particular was in a vile mood. He stalked up to Roger and stood glaring down at him.
Roger began feeling less reckless. It is one thing to play with a toy castle and wish you were back in the golden days of chivalry, and it is another thing to be really there, and have one of the greatest villians in all legend stand glaring down at you and breathing the hot breath of wrath in your direction.
Bois-Guilbert went on glaring for what seemed like ages. Then he said, "So!"
"Hello," said Roger, trying to smile in an offhand manner.
"Silence," said Bois-Guilbert. "I perceive that thou art a vile spy. Thou shalt hang from the castle battlements for the crows to pick at, as a warning to all Saxons!"
"Nay!" cried Maurice De Bracy, ever the less evil of the two villians. "'Tis too harsh a punishment. He is but a child."
"He is no child," gibbered Lionel, excitedly, "but an elfish spirit come to warn us of disaster!"
"Tush, Lionel," said De Bracy. "What old wives' tale is this?"
"Take note of his garb, sir!" Lionel went on, almost in tears and pointing to Roger's summer pajamas. "Saw ye ever the like of that on mortal boy? Nay, but be sure the small fiends dress so, down below, what with the hot climate and all!" Fearfully his hand shot out and caught Roger by the collar of his pajama jacket. He saw the label inside the collar, and recoiled. "B. V. D.!" he read, in tones of horror. "Meaneth not that 'Bene volens diabolus,' or 'Best wishes from the devil?'"
"Pish, Lionel," said De Bracy. "Thy Latin waxeth rusty." But his voice sounded a bit worried, all the same.
Bois-Guilbert was made of sterner stuff.
"Go to," he said. "Never yet did Brian de Bois-Guilbert quail before witch or warlock. I defy the foul fiend. And besides, I don't believe it, anyway. Kneel, minion." And he pushed Roger rudely to his knees before him. "Confess who hath sent ye hither and from what Saxon pigpen ye hail!"
"Nobody sent me. I came of my own accord," said Roger. "From Baltimore, Maryland."
"I know no merrie land save England," said De Bracy. "And la belle Normandie, of course."
"Quiet!" said Bois-Guilbert. "Who conducteth this inquiry, anyway? Minion," he said again to Roger, "for the last time I bid ye speak. What is your errand here?" And he, too, spurned Roger with his mailed foot.
Once again the spark of anger glowed in the soul of Roger. "All right," he said, in words more spunky than yeomanly. "All right! I came to help the good guys beat the bad guys! And that means you!"
Bois-Guilbert burst into unpleasant laughter. "And didst think a Templar's cheek would pale before a minikin _your_ size?" he cried. "Away with him to the dungeon for the rats to nibble till he is ready to speak the truth!"
Maybe it was the mention of the rats that did it. Because if Roger had thought twice, he'd have gone quietly to the dungeon and bided his time, and let the story go on from there, and the ending might have been very different. There might have been a fair jailer's daughter to set him free, or there might have been a secret passage from the dungeon, or the rats might have proved friendly, and nibbled his bonds instead of him.
But which of these fascinating things would have happened will never be known, for Roger didn't think twice. He lost his temper instead, which is a dangerous thing to lose when you are in the middle of a magic adventure.
"Your time is up, Templar!" he cried. "Might as well throw in the sponge now! Wilfred of Ivanhoe beats you in the end, anyway, you know!"
"Ha!" cried Bois-Guilbert. "So _he_ is thy master, is he?" He spat elegantly into a corner. " _That_ for Wilfred of Ivanhoe! Knowest thou not he fell wounded at the end of the tournament and none hath seen him since? Where's your Wilfred of Ivanhoe now? Dead, that's where!"
"A lot you know about it!" said Roger, throwing precaution to the winds. "He's lying wounded right here in this castle now!"
"Oh, he is, is he?" said Bois-Guilbert, interestedly.
"Yes, he is," said Roger. "Rebecca's been taking care of him."
"Oh, she hath, hath she?" said Bois-Guilbert.
"Yes, and then when the castle catches fire he gets rescued," said Roger.
"Oh, the castle catcheth fire, doth it?" said Bois-Guilbert.
"Yes, and you know what? Robin Hood and his band are waiting outside right now, getting ready to besiege you, and guess who's with them? The Black Knight, that's who! Only do you know who it really is? It's King Richard, back from the Crusades, in disguise!" Roger finished triumphantly.
"Oh, it is, is it?" said Bois-Guilbert.
"Yes, it is," said Roger.
"One thing more," said Bois-Guilbert. "About this fire in the castle. Where doth it start?"
"Well," said Roger, "in the book it starts in the fuel magazine, but in the movie it starts in the dungeon."
"I know not this word movie," said Bois-Guilbert, "but just to be on the safe side . . . Guards, ho!" he suddenly called.
Men in armor started pouring into the room from all sides, and it was then that Roger realized, too late, what he had done. He had been overconfident. He had been boastful and too full of himself, and he had given the whole show away, and betrayed Ivanhoe and his friends into the hands of their enemies! Even so, he couldn't understand it. This wasn't the way the story went, at all!
"Form bucket brigades!" Bois-Guilbert was saying. "Some in the dungeon and some in the fuel magazine. Observe fire prevention rules. Watch out for flying sparks! Put out any flame thou seest!"
Some of the guards scurried off to do his bidding.
"You can't do that; it's not in the book!" cried Roger, running up to Bois-Guilbert.
"What is this talk of books?" said the Templar. "Out of my way!" He gave Roger a push to one side, and turned to some of the others. "Fetch me hither the wounded knight Rebecca hath been tending," he said grimly. "Stay not to be over-gentle with him, neither!"
"I didn't mean it! I take it back! It isn't him!" Roger cried, forgetting all grammar and running up on Bois-Guilbert's other side, to pummel at him vainly, as high up as he could reach.
But already more guards had hurried away to fetch Ivanhoe, and Bois-Guilbert, shaking Roger off, turned to the rest of his followers. "To arms!" he cried. "Enemies are without! A scurvy outlaw band led by him who calleth himself the Black Knight. But we shall be ready for them. Hugo, prepare the molten lead. De Bracy, wave a white pennon from the parapet and ask for parley. When the Black Knight steppeth upon the drawbridge, Hugo, empty thy caldron."
"What, and kill the king?" said De Bracy.
"Oh, no," said Roger.
"Prince John will thank us for it," said the Templar. "Besides, how were we to know who he was? People who goeth about in disguise can just take the consequences. The molten lead will make him unrecognizable, anyway."
"I'll have no part in it," said Maurice De Bracy.
"Good for you," said Roger.
"Oh, very well," said Bois-Guilbert. "Do I have to do everything myself around here?" And he turned and started for the courtyard.
Roger, made brave by guilt and fear, ran to bar the way. "Treason! Murder! Help!" he cried.
The Templar looked down at him with a face of utter exasperation. "Really!" he said. "Will no one cage this bratling for me?"
Ready hands seized Roger and dragged him back, and for a moment he decided he was going to end up in the dungeon with the rats after all. But there was an interruption.
The guards who had been sent to fetch Ivanhoe returned, carrying that gallant knight, still wounded and palely loitering upon a litter. They set the litter down, and Rebecca rushed in after them and flung herself on her knees beside him. A moment later Rowena rushed in, pushed Rebecca out of the way, and flung herself on _her_ knees where Rebecca had been.
Bois-Guilbert stood looking at his enemy with a cruel smile. "So we meet again," he said, "and for the last time, I think. Thou shalt rue the day thou unhorsed Bois-Guilbert in the field! But ere I finish _thee,_ thou shalt see the end of that Lion-heart king thou servest. Guards, up with him and after me!" And once more he turned and strode through the courtyard.
The nearest guards lifted Ivanhoe and bore him after the Templar, and the whole multitude hurried along after _them,_ curious to see the fine sport. Roger broke away from his captor and ran along with the others, and if a tear stained his cheek as he thought of the disaster he had brought upon those he had come to help I do not think you will blame him.
Suddenly, to his surprise, a friendly hand caught hold of his, and he looked up to see Rebecca, running along beside him and smiling at him with her kind sad eyes.
"Weep ye for Richard and Ivanhoe, boy?" she said. "Weep not. Fortune may yet change."
"Don't," said Roger, pulling his hand away and feeling guiltier than ever. "You wouldn't if you knew."
The people ran through the courtyard and up the stairs till they gained the roof. Then they stood in sudden hush. Bois-Guilbert was already at the parapet, waving his white pennon of truce and calling for colloquy with the Black Knight, and down below the Black Knight, tall and noble, was coming forward for the supposed parley. The drawbridge had been lowered and the Black Knight was just stepping upon it, and up above, crouched behind his battlement, the villainous Hugo was just tilting his horrid, steaming caldron.
And it was then that Roger knew what he had to do. He lowered his head, butted his way through the crowd, and with a mighty effort hoisted himself up onto the battlements, between Hugo and Bois-Guilbert. He leaned from its dizzy heights and called, "Chiggers! Look out below! Cheezit!"
The Black Knight looked up. "Who saith so?"
"Me. Roger," was all Roger could think of to say. But it was enough. The Black Knight jumped back just in time, and the molten lead splashed hotly and harmlessly upon the empty stones below.
And then the men of Robin Hood, furious at the trick that had been played, leaped into action and the siege of Torquilstone began. A green-clad archer appeared from behind every bush and tree, and arrows fell like deadly rain.
The followers of Bois-Guilbert, caught all unprepared on the castle roof, made a fine target, and many fell under that first flight of arrows.
And now Robin's men ran up nearer the castle, and their bows twanged again, and the noise of their battle cries echoed round the walls of Torquilstone.
And while they should have been calling, "A Robin, a Robin," or possibly "A Richard, a Richard," it seemed to Roger that they were saying, "A Roger, a Roger!"
Wilfred of Ivanhoe, though still pale, had leaped from his litter, seized a sword from a varlet standing near him, cleaved the varlet in half, and was now cutting a swath through the men of Torquilstone, taking them all on singlehanded, while Rebecca helped him by tripping up any who would attack him from the rear, and Rowena helped him by turning away and holding her ears.
Only Brian de Bois-Guilbert took no part in the battle that raged within and without the castle. He stood glaring at Roger, where he still clung to his lofty parapet.
"Witch-brat!" he said viciously. "Thou shalt learn what it meaneth to thwart me, when thy brains lie dashed out on the stones below!" And he seized Roger by a foot to thrust him over and down.
Roger looked down at the stones and didn't like what he saw. Then he looked at Bois-Guilbert and liked him even less. Then, just as all hope failed, he remembered something.
"I'm not afraid of you!" he cried. "You're not even real! You wouldn't even _be_ Bois-Guilbert, if I hadn't said you were! You're nothing but a lead soldier!"
"What?" cried Bois-Guilbert, his face deathly pale and his voice a mere whisper. "What didst thou say?"
"Lead soldier!" Roger repeated wildly. "That's all any of you are! Lead soldiers, lead soldiers, lead soldiers!"
Bois-Guilbert fell back shuddering before him, and the fighting men dropped their swords and all the people fell on their knees, and a murmur of awe ran from lip to lip among the crowd.
"The Words of Power!" cried some, and "The Elfish Charm!" cried others, and "I said 'twas no mortal boy!" cried Lionel.
And Roger jumped down from his perch and pushed his way through them, and as he did so they seemed to grow paler and dimmer, and as he ran down the stairs the walls of the castle seemed to grow fainter, the way the picture on your television set does when a tube is ailing and your mother has to send for the man.
In the courtyard a figure with a white beard appeared in Roger's path. Roger didn't recognize him but he seemed to recognize Roger, and to shake his head at him rather sorrowfully as he ran past. And yet just before everything faded out completely there seemed to be a twinkle in the figure's dim eye.
And now the castle had vanished and the sound of battle had died away, and all around and before Roger was nothing but gray mist. Then suddenly the plateau loomed whitely in his path as he ran, and he had just strength enough to scramble up the rock path to the top before darkness overtook him and he knew no more.
The next thing he _did_ know, it was still dark, and he was sitting up in bed, and his mother was standing over him. "Did you have a bad dream?" she said. "You pushed the covers all off onto the floor."
"Yes," said Roger, sleepily, "I had a dream. Some of it was bad. Some of it wasn't, though. Anyway, it's over." And he rolled over and went back to sleep.
But it wasn't over.
3
# The Magic City
_When Roger woke up_ for the second time it was morning, and the castle was its normal self again, and yet he remembered it all too clearly when it hadn't been. And looking back on his behavior in the cold light of morning, he decided it could only be called un-yeomanly!
Of course there had been that one stirring moment when he saved the Black Knight's life, and the air rang with shouts of "À Roger, à Roger!" He guessed lots of people he knew would call a moment like that the high point of their whole lives.
But on the other hand the Black Knight's life wouldn't have needed saving if Roger hadn't given him away in the first place. And then at the end what did he do but run away without waiting to see who won the siege?
He wondered whether he would ever have a second chance, or if the whole thing was a mere failure. And it was as he was lying there wondering that Ann came bouncing into the room and sat on the bed (and on part of Roger) and said, "Let's play. Let's play with the castle."
"Go away. It's too early. I'm asleep," said Roger.
Eliza appeared in the doorway in her pajamas and bathrobe. "Let's play with the castle," she said.
"He says he's asleep," said Ann.
"I'll fix that," said Eliza. She laid hold of Roger and pulled. Roger kicked out. A small table bit the dust and several knees were skinned.
Jack appeared in the doorway. "What's the matter?" he asked.
"It's Roger," said Ann, from the sidelines. "He won't play with the castle."
"Oh. Well, I guess it's his castle," said Jack. He went out again.
Roger got up from the floor, got back into bed, and pulled the covers over his head. They came out at the foot. His bare toes emerged, and he could not feel that he made a dignified picture. He sat up again.
Eliza was staring at his bare feet with an expression of disdain. "It's not fair," she said. "Here we've been waiting all night to start playing with the castle, and you've been in here in the thick of it, just _glutting_ yourself with it till you're tired of it!"
"That's not it," said Roger.
"What is, then?" said Eliza.
Roger didn't answer. The two girls sniffed, put their noses in the air, and went out arm in arm.
Breakfast was no better. Ann and Eliza made private jokes and giggled together. They did not address Roger. Roger felt depressed.
He wished he could ask them to play with the castle, but he couldn't. Now that he had known the knights in all their lifelike glory, just merely playing with them didn't seem possible. It would be a mockery.
Not only that, but there was the wish he had made about his father's getting well in Baltimore, Maryland. The Old One had said wishes had to be earned, and Roger felt that his behavior last night could not have done his father one bit of good.
But after breakfast their mother took them to see their father, and he didn't seem a bit worse, and they stayed for lunch and Roger was cheered. And when they got back to Aunt Katharine's, Jack asked him if he wanted to see some pictures being developed, and it was surprising how interesting photography turned out to be.
Ann heard Roger laughing in the darkroom, and was encouraged. She opened the door. " _Now_ can we play with the castle?"
Roger turned on her with a face of fury. " _Now_ see what you've done!" he said. "You've ruined the negatives. _Never_ open the door of a darkroom!"
It was Ann's turn to feel depressed. She wandered upstairs to Roger's room. Eliza was curled up on the bed, reading _The Magic City._ "I'd forgotten what a good book this is," she said.
"I tried it," said Ann, "but the words were too big." She sat down on a chair, feeling lonely. Eliza glanced at her.
"Oh, all right," she said, in a long-suffering voice. "I suppose I'll have to start over, and read it to you."
" _Would_ you?" said Ann, in surprise. Really, she thought, Eliza could be quite nice, once you were used to her. Her bark was worse than her bite. And she read out loud beautifully, putting in all the expression.
_The Magic City_ proved to be all about a boy named Philip, who built a town of blocks and books and ornaments and peopled it with all his toys, and then one night the town came to life, and Philip found himself in the middle of it, and the magic adventures began.
"This," said Ann, after chapter one, "is a good book."
"This," she said, after chapter two, "is one of the crowned masterpieces of literature which have advanced civilization."
Eliza put the book down. She looked from the book to the castle in a significant manner. "What are we waiting for?" she said.
Ann looked shocked. "We couldn't. What about Roger?"
"He won't mind. It won't be _playing_ with it at all, exactly. We won't even _touch_ the castle, hardly. We'll detour round it, sort of. He'll never even know."
"Well," said Ann, hesitating.
Half an hour later Jack and Roger came into the room. Roger was whistling a merry tune that broke off in the middle as he stopped and stared.
The castle was still there and the dollhouse was still there and Prince John still held court in the fireplace. But all around and between and among them, the room was littered with books and ashtrays and tumblers turned upside down till it looked as though someone were holding a rummage sale on the floor. And down on the carpet, amid the coffee cups and boxes and perfume bottles sat Ann and Eliza, with two pairs of manicure scissors, busily cutting roses out of the flowered quilt from the dollhouse master bedroom and gluing them onto wooden matchsticks.
"What are you doing?" said Roger.
"Making a magic city," said Ann, happily, balancing one of the matchsticks upright on the carpet and sticking it there with some Scotch tape. "This is the rose garden."
"Well, you can just unmake it again," said Roger.
It was then that the mild and agreeable nature of Ann suffered a change. She got up and threw the scissors down on the floor. "I hate you," she said. "You're mean. And spoilsport and doggish in the manger!"
Jack looked at the city. "What's wrong with it?" he said, reasonably.
Roger looked at it, too. A sidewalk of stone blocks led away from the castle, flanked by a double row of glittering columns that ended suddenly where the supply of old ginger ale bottles had given out. There was an imposing building made of books, labeled "Public Library," and another beautiful one made of different-colored cakes of soap, labeled "Public Baths." And since you can always find more drinking glasses and glass ashtrays and perfume bottles than you can anything else when you're building a magic city, the whole area sparkled with transparent domes and pinnacles.
"It's too modern," Roger said. "All that glass. It looks all streamlined. It isn't yeomanly. Castles didn't have sidewalks."
"This one does," said Ann.
"It's a good city. If you like that kind of thing," said Jack, looking down on it from his superior height of twelve-and-a-half years. "I vote it stays." And he went out of the room.
"Majority rules," said Eliza. "Three out of four."
"But it's all changed around and everything's spoiled!" Roger burst out desperately. "It just isn't Torquilstone any more! I hoped maybe I'd have a second chance, and now I _know_ it won't happen again, and I never will!"
"Never will what?" said Eliza.
"Nothing," said Roger.
"Come on, Ann," said Eliza. "Let's go finish our book someplace else. He's crazy. Let him tear the old city down if he wants to."
"No, it's all right," Roger said. "Let it stay."
"Well, it won't be any fun unless we all do it together," said Ann. And she started out of the room after Eliza.
Roger had a change of heart. Ann was right; things _were_ more fun when you did them together. "Wait," he started to say. But a closing door was his only answer.
The rest of Roger's day is better left untold. Let other pens dwell on guilt and misery. Suffice it to say that night came at last, and another day dawned, as usual, and Roger woke up with the sun in his eyes. He looked across at the castle. The castle looked back at him, small and toylike. Not a thing had happened. The magic was over. He had had his chance and he had failed.
Then suddenly as he looked he remembered the old man with the white beard he had met in the castle. And he went over and found the Old One and held him in his hand.
"Oh Old One," he said, "what's wrong? Is it the mistakes I made or is it because Ann built the city?"
To his joy he felt the familiar sensation of the Old One growing warm in his hand, and the tiny, leaden voice began to speak.
"Ods bodikins!" said the Old One. "Hath it come to this? Hath the race sunk so low that all useful knowledge is forgotten, by the mass? Modern education, psychoanalysis, nuclear physics, a pox on it! What booteth thy newfangled fads and fancies if thou forgettest the good old rule that magic goeth by threes?"
"Do you mean . . ." began Roger.
"Canst count, sirrah? Didst thou think magic hath naught else to do but be waiting on thee hand and foot, day in, day out, maybe yes, maybe no, whenever it please thy puling fancy? Think thyself lucky if it smile on thee one night in three!"
"The third night's tomorrow," said Roger.
"Grand news," said the Old One.
There was a silence. Roger waited. Then he said, "Is there anything else? That I ought to know?"
The Old One was already growing colder in his hand, but his voice came again, only fainter.
"And didst think thou couldst do it all alone, selfish? Rode ever knight on gallant quest without his gentle lady to speed him on and hark to his tale and tell him how he should have done it differently? 'Oh woman, in our hour of ease uncertain, coy and hard to please, when pain and anguish wring the brow a ministering angel thou,' as the poet saith. A trusty friend may oft prove helpful, too. Not to speak of cousins."
"Oh," said Roger. "Yes. I see what you mean."
"Then act upon it," said the voice, dying away. And the Old One lay cold and silent in Roger's hand.
"I will," said Roger. "Right away. I was just going to."
"What did you say?" said Ann, coming into the room in her nightgown.
"Nothing," said Roger, from force of habit. Then he went on quickly. "Yes, I did, too. I was talking to _him._ " And he told Ann all about it, and Eliza came in in the middle of it, and asked questions, and he had to start over, and tell it again, from the beginning. Ann believed it right away, the way she always did, but Eliza was disposed to scoff.
"The boy's raving," she said. "Too much reading has turned his feeble brain."
Roger shook his head. "Honest," he said.
"Scout's honor?" said Eliza.
"By my halidom," said Roger.
And of course after that Eliza believed, and was all too ready to run the whole thing, and wanted the magic to start happening right away.
"It can't," said Roger. "Not till tomorrow night."
"Why not?"
"Hast thou sunk so low that thou hast forgotten the good old rule that magic goeth by threes?"
"Well, I think it's silly of it," said Eliza.
"I hate arithmetic," said Ann.
"I think it makes it more interesting," said Roger. "And it gives us time to plan. The first thing is to get the castle back the way it was."
"Why?" said Eliza.
"I think we ought to go by the book. Just to be on the safe side."
" _They_ didn't," Ann pointed out. "Once the magic began and you got to be their size, they did just as they pleased. _I_ mean to do just as I please from the start!"
Roger began to see what the Old One meant about women.
"After all," Ann went on, "you had your chance. I think we ought to take turns from now on. I get this turn, 'cause I'm your sister. And I don't think we ought to plan at all. I think we ought to build just whatever comes into our heads, and then leave it up to _them._ I think it'll be more exciting that way."
This was such a long and spunky speech for Ann to make that the others were too surprised to argue.
"I guess it's only fair," said Roger. "Don't say I didn't warn you. Have it your own way."
"Good," said Ann.
"I get dibs on next time," said Eliza.
After breakfast they tried to interest Jack in the magic, but he would have none of it. He said he had too much to do to listen to a lot of nutty talk, and went off to his darkroom to develop the pictures he'd taken to replace the ones Ann had spoiled when she walked into the darkroom yesterday.
Ann and Eliza and Roger didn't mind. They were too busy roaming the house, collecting material for the magic city. An old toy chest in Eliza's room yielded a store of battered playthings, and Ann added toy autos and parts of electric train to the city with reckless abandon. Roger and Eliza invaded the kitchen, and borrowed so many cookie cutters and jelly molds that the cook cried out and said she'd have to speak to the madam.
But Aunt Katharine, except for the times when she was defending her art treasures from the children's eager clutches, was so delighted at how well they were getting along that she made little objection, and, as Ann put it, the hours moved on oiled wheels until pretty soon it was the fateful night. The city by this time was terrible and wonderful to behold. I shall not attempt to tell you what it was like. It defied description.
One thing the children were careful to do, and that was to leave a wide cleared avenue from the hall door to Roger's bed. "Otherwise we might never find each other once it starts," said Ann, "and it'd be like those awful books where the characters get separated and you can't keep track of anybody."
And then she had another idea, and added one final touch. Her final touch was a statue, or at least that's what Ann said it was, to stand in the park in front of the castle. The statue was composed of a can of pea soup, balanced on an iron trivet. It was labeled, "St. George Peabody."
And then it was bedtime. Nobody was sure how far into the house the magic would reach, and Eliza's room was way over in another wing, but that didn't discourage Eliza.
"Meet me by midnight when the lone wolf howls," she whispered to Ann. And as soon as the heavy feet of grown-up interference were safely out of the way, a howl like a rather small and cautious wolf's was heard, and a lone figure came tiptoeing into Ann's room and got into her bed.
"How now, you secret, black and midnight hag?" said the figure.
"Shush," said Ann. "It won't happen if we talk."
But the night when you want to go to sleep most is always the night when you can't, as you may have noticed yourself on nights before Christmas. And not only that, but Ann had decided they should wear their bathrobes and slippers to bed, for Roger had told them how silly he felt, arriving at Torquilstone in just his pajamas and bare feet, and the extra clothes and crowded conditions made things hot and difficult. And not only that, but it was a single bed. And not only that, but Eliza proved to be a tosser and a turner and a talker.
"What do you hope happens?" she whispered. "I hope there's a battle and a siege and we get to rescue somebody from durance vile. Maybe we can fix it so Ivanhoe marries Rebecca, too."
"Shush," said Ann.
"I wouldn't mind having a deadly combat with that Brian, either," Eliza went on, thoughtfully. "Move over. Your elbow's in my back."
Ann sighed, and squashed herself against the wall.
But at long last sleep came and knitted up Eliza's raveled sleeve of care, and after that Ann was still awake for a while, and then all of a sudden she wasn't.
When she woke up she knew it had begun. It was still dark in her room, and her bed hadn't turned into a plateau and was still just a bed, but somehow she knew it was time. She shook Eliza. "Wake up," she said.
"Man the battlements," muttered Eliza, hitting out. "The Normans are attacking."
"You're dreaming," said Ann. "Wake up. This is real."
Eliza opened her eyes and staggered to the door after Ann. And then she wasn't sleepy anymore.
Where the hall should have been there wasn't any hall, just great airy space, and far above them a round shining globe that might have been the hall light back in unmagic times.
And from up ahead, where the door of Roger's room had been, came a blaze of light and a deafening roar. Ann and Eliza ran over drab stubbly earth (the hall carpet had been brown) in the direction of the light and the noise. Then they stopped.
"My," said Ann. "It _is_ streamlined, isn't it?"
The magic city had grown to life-size, and the beastlike roar was the sound of its traffic, as all the motorized vehicles from Eliza's toy-chest whizzed about its avenues. And all its buildings were modern with glass and chromium, and glaring with electric lamps and neon signs, and that was the blaze of light. It was like the middle of New York City, only more so. Except that riding the trucks and sports cars and parts of old electric trains were knights in armor and ladies in tall headdresses. Few of them were expert drivers, and all of them were exceeding the speed limit.
Ann eyed the city dubiously. "I didn't think it'd be like this, exactly," she said.
Eliza had no qualms. "Come on!" she cried. "Into the jaws of death rode the six hundred!" And she pulled Ann forward into the heart of the traffic.
A varlet in a Yellow Cab skidded toward them on two wheels and they had to jump for the curbstone.
"Let's find Roger," said Ann.
They looked ahead, and far in the distance they saw a small figure clambering down a fall of rock. They ran toward it. A bus came along, going their way, and Eliza hailed it and pushed Ann up the step before her.
"What about money?" said Ann.
"Who knows?" said Eliza. "Maybe magic will provide."
But it didn't. When they thrust their hands in their bathrobe pockets, nothing was in them but the usual linings and handkerchiefs and cooky crumbs.
"Fares, please," said a guard, appearing beside them firmly.
Ann and Eliza got off the bus.
But they'd already ridden halfway across the city, and the running figure of Roger was much nearer now. A second later he ran up to them. They stood in a doorway, shouting to be heard over the city's noise.
"Isn't this keen?" said Eliza.
"No, it's not. It's horrible," said Roger. He turned on Ann. "What did I tell you? You've just practically ruined the whole age of knighthood, that's all!"
"I know," said Ann. "I didn't realize."
"I don't know what you mean," said Eliza. "I think we've done a noble deed. We've brought the poor things out of the dark ages and given them all the comforts of modern civilization!"
A knight rode by on a motorcycle. He had his fair lady with him, in the sidecar. Roger averted his eyes. "It's sacrilege," he said.
A crash was heard in the distance, as several cars collided. Police cars arrived on the scene, sounding their sirens.
"The only thing is," admitted Eliza, "they don't seem to be very _good_ at it yet. Maybe we improved them too _quickly._ "
Traffic was now hopelessly snarled, and all the knights and ladies were blowing their horns. A factory whistle screamed, and more knights and ladies emerged for lunch hour, reading comic books and movie magazines. One of the knights jostled against Roger.
"I crave thy pardon, gentle sir," said Roger.
"Get outa the way, stoopid," said the knight, shoving past. From somewhere nearby a band started playing, "Sh-Boom, Sh-Boom."
"This is awful," said Roger. "We might just as well not have come. It's not like magic at all. It's just like ordinary times back home."
"Let's go somewhere where it's quieter," said Ann.
Even Eliza agreed, and the three children turned a corner into a shabby alleyway of small, hutlike houses looking like nothing so much as cardboard boxes hastily painted to resemble stonework.
"I never saw this part," said Ann. "Who built it?"
"I did," said Roger. "It may not be pretty but at least it's more old-time. At least it's more in keeping."
No one was in sight but a veiled lady, stepping toward them. "Good morning, children," she said. "How do you feel?"
"Hello," said Eliza. "I feel all right."
"Have you been vaccinated for contagious diseases?" said the lady. "Have a cough drop." And she produced one from a pocket first-aid kit.
"No, thank you," said Ann. "Are you the district nurse? I didn't know we had one."
The lady threw back her veil, and smiled at Ann and Eliza and Roger with her kind beautiful sad dark eyes.
"Why, you're Rebecca!" cried Ann. "What are you doing here?"
"Visiting the sick," said Rebecca, "and doing good."
"Oh, for Heaven's sake," said Eliza. "The story _said_ you went like that in the end. _I_ think it's a shame. If you'd only waited, Ivanhoe would have seen the light some day. You could have married him, and visited the sick in your spare time!"
Rebecca shook her lovely head. "It was not to be."
"Then he _did_ marry Rowena?" said Eliza.
"Not yet. They are to be married when the siege of Torquilstone is over."
"The siege? Is it still going on?" Roger joined in. "Who's winning?"
"It goes on all the time," said Rebecca, sadly, "and no one ever wins." Then she looked at him more closely. "But I know you! You're Roger! Have you come to save us? The way you did before?"
"Did I?" said Roger, pleased.
"Of course you did. With your Elfish magic."
"I wasn't sure," said Roger. "We elves forget things."
"You saved us," went on Rebecca, "and then you disappeared in a cloud of glory, and then a terrible thing happened. A mighty sorceress cast a spell over the whole country."
"Oh, dear," said Ann. "Did she?"
"Yes, she did," said Rebecca. "And you can see for yourselves what followed. All that noise, and newfangled inventions, and everybody rushing and nobody getting anywhere! Nobody speaking the old ancient yeomanly talk any more, either. You can walk a whole city block without hearing a single 'By my halidom!' And you can imagine what happened to the siege."
"It went to pot," guessed Eliza.
"That's exactly where it went," said Rebecca. "Oh, they still fire a few arrows on weekdays between two and four, but nobody takes it seriously anymore. They let the servants take care of it, mostly." Her voice trembled with emotion. "And Wilfred of Ivanhoe's sword grows rusty and they say he just lies in bed all day and reads science fiction!"
"Why, how perfectly disgusting!" said Eliza.
"I thought you liked it modern, this way," said Ann.
"I don't any more," said Eliza. "I think it's perfectly disgusting."
"It is," said Rebecca. "But now Roger has come back, everything will be changed!"
"What?" said Roger. "Oh, of course. Sure it will. We'll have to do something."
"What'll we do?" said Ann.
"Start a revolution," said Eliza. "Down with progress. Bring back the horse."
"Sort of an Underground Movement," said Roger. "We could have secret meetings."
"With passwords," said Ann.
"I'll be the beautiful female spy," said Eliza.
"Splendid!" Rebecca clapped her hands. "And then when we're all organized, surely Ivanhoe will see the error of his ways!"
"He'd better," said Eliza, "or else!"
They were all so excited by now that they weren't looking around them much, as they walked along. Now Ann did look ahead, and said, "Oh!" in a surprised way, and the others looked, too.
Coming toward them was a knight in armor riding a gallant steed.
"Well!" said Eliza. "There's at least _somebody_ around here who hasn't changed!"
"Doesn't he look beautiful?" said Ann.
"Not so dusty," said Roger.
"Just like old times!" breathed Rebecca, with glowing eyes and clasped hands.
But as the knight drew nearer, they saw that his armor was rusty, and his steed, though still gallant, was spavined and rheumy with age. His shield and all his clothing were black, and the visor of his helmet was down, hiding his face. His pace was slow, and he hung his head and seemed a prey to utter melancholy.
"Good morrow, fair lady," he said, his voice coming indistinctly from behind the closed visor. "How farest thou on this dark and dreary day?"
"He talks old ancient yeomanly language still," whispered Eliza.
"That I do, lass," said the knight, whose ears seemed to be sharp, in spite of his closed helmet.
"A murrain on newfangled inventions, say I! What was good enough for me is good enough for me! By the rood!" he added.
"It doeth my heart good to hear thee speak so," cried Rebecca, falling easily into the old speech, herself.
"Doth it now?" said the knight. "And how goeth it with thy gentle heart this morning?"
"Better than for many a moon," said Rebecca, "now that Roger hath returned."
"Indeed?" said the knight, looking at Roger, and Eliza did not think he sounded pleased.
"That's right," said Roger. "We're organizing everybody who wants to go back to the good old days. You can be our first recruit. What's your name?" Then he didn't think that sounded old-timeish enough. "How call they you, fair sir? And open thy visor, that we may see thy face and know thee friend."
"Nay," said the knight. "I have sworn a vow. My shield be black in mourning for the death of chivalry, and my visor remaineth forever shut that I may not see the light of this modern world till the old days returneth. Men call me the Unknown Knight."
"What a beautiful sentiment," said Rebecca.
"Thinkst thou so?" said the knight. "Then may I be thy champion and fight for thee, and mayhap win thy heart?"
"Nay," said Rebecca, regretfully. "'Tis too late. Another claimeth it."
"What?" said the knight angrily. "Beateth it still for Wilfred of Ivanhoe, that mewling, puling milksop?"
"Oh sir!" cried Rebecca. "Say not so, for thou woundest my very soul!"
"Milksop I say and milksop he be!" cried the knight, getting excited. "And a mollycoddle and a lie-abed-late and a novel-reader and a space-happy dreamer and a rascally knave of a Saxon churl!"
At this Roger grew hot under the collar and would have spoken up, but Eliza spoke first. "Why, sirrah!" she said. "How thou talkest! Be thee not Saxon thyself?"
"To be sure, lass, to be sure," said the knight, quickly. He leaped from his horse and knelt before Rebecca. "Forgive me, gentle lady," he said. "My righteous anger was too much for me."
Rebecca was touched. "And no wonder," she said. "Thou art too noble, that is thy trouble. I forgive thee readily." And she put out her hand.
The knight seized it and covered it with kisses, pushing his visor part way up to do so. "Blessings on thy kind heart," he cried, "and thy soft dusky cheek, and thy dark eyes a man might drown in, and thy beauty fit to drive a fellow mad!"
"Why, sir!" said Rebecca, drawing back in alarm.
But Eliza, who had been watching the knight closely, stepped up to him suddenly as he knelt, and pulled his visor the rest of the way open. And the knight leaped up and his eyes flashed fire and his mustaches bristled, and even though his Templar's shield was camouflaged with black paint, the three children knew him right away for none other than Brian de Bois-Guilbert, and Roger wished he had brought a sword.
"Oh Rebecca," cried Bois-Guilbert, "vouchsafe me but one smile from thy sweet eyes. Be kind to me as thou wert to the Unknown Knight!"
"Fie, false Templar!" cried Rebecca. "For shame! Thoughtst thou to woo me in disguise and win aught but my scorn?"
"Thou'rt mine now," said the Templar, catching her by the arm, "and none shall come between us!"
"Oh, won't they?" said Roger, squaring up to him and putting up his fists. "Let her go!" And he aimed a blow at Bois-Guilbert's midsection.
"Let her go!" echoed Eliza, running up daringly to trip the false knight from behind.
"Avaunt, moppets!" said Bois-Guilbert, sweeping them from his path with a brutal arm. He smiled cruelly down at Roger as he sprawled on the sidewalk. "Thou and I hast met before, methinks. Had I time, I would settle thy hash now for good and all. Take care that we meet not again." And he leaped to the saddle and swung Rebecca up behind him.
"Wait!" cried Roger, scrambling to his feet and clutching vainly at the bridle.
"You'll be sorry!" said Eliza.
"Oh, yes?" said Bois-Guilbert. "Thou and who else shalt make me? Thinkst thou any knight in this degenerate age dare follow me to the Dolorous Tower? Because that's whither we goeth!"
"Nay, Templar, not that!" cried Rebecca, in the first words of fear the children had heard pass her lips. And her olive cheek paled.
"Aye," said the Templar, his face set in grim lines. "Brian de Bois-Guilbert dareth even that for thee! Giddy-up." And the spavined steed remembered its glorious past and made a surprisingly gallant dash down the alleyway.
Ann and Eliza and Roger dashed after it, and round the corner into the busy avenue. Far in the distance they saw the horse and its riders disappearing in a cloud of dust. And villain though Bois-Guilbert was, Roger couldn't help admiring the masterful way he was steering his steed through the crowd of badly driven motor cars.
"One thing you have to admit," he said. "He may be a vile dastard but he's still yeomanly!"
"Never mind about that now!" said Eliza. "Come on."
"Where?" said Ann.
"Where do you suppose?" said Eliza. She pointed.
Across the city, the turrets of Torquilstone glittered against the sky. With one accord, the three children turned and ran toward them.
4
# The Dolorous Tower
_As they ran through the streets_ of the degraded city, not a single knightly scene met their gaze. Those of the populace who weren't out joyriding were sitting inside looking at wrestling matches on television. It was sickening.
And when they reached the castle, the state of the siege looked even more sorry than Rebecca had told them. Not a single attacker or defender was insight. The drawbridge was down and the portcullis was up. The three children ran over the one and under the other and into the courtyard. A discouraging sight awaited them.
Two guards sat playing gin rummy and smoking cigarettes. Their helmets were off and their armor was loosened. They looked thoroughly out of training and unfit for combat.
"Go away," said one of them, without looking up. "All deliveries use the back door."
"We're not a delivery, we're important messengers," said Ann.
"It's a matter of life and death," said Eliza.
The guard yawned. "Mister Ivanhoe is not at home. Come back on Tuesday."
Roger was disgusted at the lax and corrupt behavior of the guards. He banged his fist on the table. "Poltroons, take us to thy master at once!"
"Who are you?" said the guard, insolently.
"I'm Roger," said Roger.
The guard tittered. "A likely story!" he said. "Everyone knows there never was any such person. Nobody believes that old myth nowadays. Nowadays Roger's just a word you use at the end of conversations."
"Roger. Like that. It means oke," said the second guard.
"Oak? Oh, you mean oke," said Roger.
Eliza, who had been fuming at this delay, now burst out. "He is _too_ Roger," she said, "and this"—pointing at Ann—"is a mighty sorceress. You'd better let us in or you'll be sorry. I'm a pretty well-known witch, myself!"
The second guard turned to his friend. "Maybe it's true, Perce. They've got on pajamas, the way they say Roger did when he done the deed and won the battle! They talk the old ancient yeomanly language, too!"
"I couldn't take the responsibility," said Percy, for that was the first guard's fitting name. "Not for some old impostors. It's your deal." And he returned to his game.
The second guard winked at Roger. "Run along in, kids," he said. "One flight up and the first door on your right. Don't say we sent you."
And the three children pushed past the guards and ran through the great hall of the castle, shuddering at its new modern glass and chromium furniture, and up the stairs.
The first door to the right was open, and they looked in on a disillusioning spectacle. For a minute even Eliza was speechless.
Wilfred of Ivanhoe, in dressing gown and slippers, lay on a couch deep in study. He still wore a bandage round his middle, and he also wore a pair of horn-rimmed spectacles. His face looked pale and thin and scholarly. He was reading a book with a red cover, and every so often he stopped and made a note. Roger recognized the book at once. It was called _The Angry Planet,_ and he had brought it with him from home, and Ann had used it when she built a public library for the Magic City.
Across the room from Ivanhoe sat Rowena. She had grown much plumper, and was lolling in an armchair, eating chocolate-covered cherries.
"My dear," Ivanhoe was saying, "did you know that Mars is only one-third as big as the earth and so the force of gravity is only one-third as strong?"
"Pass the stuffed dates," said Rowena.
Ivanhoe didn't hear her. He was making a note. Rowena sighed. Then she put on a coaxing expression. "Ivanhoe, when will the siege be over? When will we be married?"
"One moment, my dear," said Ivanhoe. He finished working out his arithmetic problem. "Amazing! That would mean that the Martians must be eighteen feet tall. Otherwise they'd bounce."
"Not necessarily," said Roger from the doorway. "They might be made of something heavier than we are. They might be made of lead. They might be wide instead of high."
"Don't talk so fast," said Ivanhoe, his pencil traveling madly over the paper. "I can't get it all down."
"Who are you?" said Rowena. "How dare you enter this chamber unannounced?"
"I'm Roger," said Roger.
"You don't say?" Ivanhoe looked up with a smile of welcome. "Come in, my dear fellow! Forgive my not getting up. My old wound still troubles me. Sit down. I'm delighted to see you. The old stories always _said_ you'd come again some day. To finish the siege, but we don't have to talk about that now, do we?"
"Yes, we do," said Rowena. "I'd _like_ to talk about it. You said you'd marry me when the siege was over, but how can the siege be over if you never fight?"
"Please, my dear," said Ivanhoe. "Not now. Roger must have lots more interesting things to tell us. Coming from Elfland, he must know all kinds of things. Tell me"—and he turned to Roger again—"how high exactly _is_ the moon?"
"The moon," said Roger, promptly, "is two hundred and thirty-nine thousand miles from the earth. Approximately."
"Fascinating," said Ivanhoe. "Is it inhabited?"
"I don't know," said Roger. "Nobody knows."
"Then you can't be Roger," said Ivanhoe. "Roger knows everything."
"Not quite," said Roger, modestly. "I'm only in six-one-A. Now about that siege."
"I'm afraid my fighting days are over," said Ivanhoe. "My old wound, you know."
"Wilfred, that's just your imagination," said Rowena. "That old wound must have healed by now. Goodness knows I make you enough bandages, don't I?"
"Not like the kind Rebecca used to make," said Ivanhoe.
Rowena looked hurt. "Wilfred!" she said. "I thought we agreed never to mention that name!"
But the mention of Rebecca had roused Eliza from her spellbound silence at the door. "Oh, for Heaven's sake!" she interrupted. She marched straight into the middle of the room and stood looking down scornfully. "Wilfred of Ivanhoe, you get right up this minute!" she said. "While you're just lying there, Brian de What's-his-name has kidnapped Rebecca!"
"What?" Ivanhoe leaped up. "Why didn't you say so before?"
"I was just going to," said Roger, sheepishly. "I kind of got sidetracked."
Ivanhoe strode across the room, his eyes flashing fire behind their spectacles. "Perfidious wretch! He shall die for this!"
"Now, Wilfred," said Rowena, following him fussily, "it isn't as if it were the first time. In my opinion people who go round getting themselves kidnapped don't deserve a bit of sympathy! You don't see anyone kidnapping _me,_ do you?"
"No," muttered Ivanhoe, "I certainly don't." He was rummaging in a corner. "Where is my new armor? What have you done with my helmet? What is this sticky stuff all over my best sword? Have you been using it to toast marshmallows again?"
"Wilfred," said Rowena, "you get right back on that couch. You're not well."
"A minute ago you wanted me to get up and fight."
"A minute ago," said Rowena, "was different."
"Tush to thy puling," said Ivanhoe, falling into the old yeomanly talk now there was occasion for it. "Hold this cuirass."
"I won't," said Rowena.
"All right, _thou_ holdst it, then," said Ivanhoe to Ann, who was nearest. And Ann reached up and held it for him to put on, feeling very romantic and like a lady in a storybook.
The armor was a bit large for him, now he had grown thinner, but he looked quite knightly in it, particularly after he took off his spectacles, which he did because they wouldn't fit under the helmet. "By my halidom!" he cried, when the armor was all on. "I feel like a new man! My old wound scarce troubleth me at all!"
Eliza nudged Roger, and Roger formally introduced Ivanhoe to Ann the mighty sorceress and Eliza the well-known witch. Ivanhoe assured them he was honored, and made a low bow and kissed their hands, while Ann and Eliza giggled, and blushed, and tried to make grand sweeping curtsies, and looked, in Roger's opinion, very silly.
"And now," said Ivanhoe, "where hath the vile villain taken her?"
"To the Dolorous Tower, he said," said Eliza, "wherever that is."
Ivanhoe turned pale, as Rebecca had before him. "It lieth in the Outer Wastes, beyond the edge of the world," he said.
"You mean in Outer Space?" Roger's eyes glowed.
Ivanhoe nodded. "Thou mightst say that it doth. In a way."
"Golly!" said Eliza. This adventure was getting better and better, after all.
Ann didn't think it was. She thought it was getting worse and worse. But before she could say so, there was an interruption.
"That settles it!" said Rowena to Ivanhoe. "You're not going gallivanting off into any Outer Space after any old Rebecca! Why, you might never come back!"
"That's true," said Ivanhoe, brightening and sounding as though he rather liked the idea. "I might never! Besides," he went on, "this giveth me a good chance to try out my Flying Saucer. I've always wanted to."
"Flying Saucer?" cried Ann, in utter alarm. "You don't have one of _those,_ do you? Don't look at _me_!" she said quickly to Roger. "I didn't put _that_ in!"
"I know," said Roger. " _I_ did."
"Then you're just as bad as I am," said Ann.
"Come along," said Ivanhoe.
"Stop!" said Rowena, barring their way, but they pushed past her and went down the stairs and through the courtyard and out of the castle.
Ann, who had never so much as been up in an airplane in all her eight years and three months, was a prey to conflicting emotions. She didn't want to go up in a Flying Saucer, but she wanted even less to say so, because that would be putting herself in a class with Rowena, which was not a place where she ever wanted to be.
And now Ivanhoe was leading them behind the castle, and there the Flying Saucer waited, lashed down and straining at its moorings like a live thing. Eliza recognized it at once. "Why, that's part of our breakfast set," she said. "It's Wedgewood."
"Edgeworld," Ivanhoe corrected her. "A pretty thought, is it not? I thought of it. It saileth over the edge of the world. Gettest thou the point?"
"Yes," said Ann, with sinking heart. "I do."
An attendant with a white beard helped them up the ladder into the Saucer. This time Roger recognized him. It was the Old One. He did not speak, but winked at Roger and Eliza, and gave Ann an encouraging pat on the head. This comforted Ann a little, but not much.
They took their places on the rim of the saucer, Ann between Roger and Ivanhoe. "What makes it go?" Roger wanted to know.
Ivanhoe shook his head. "I know not I never dared ride it before." This did not add to Ann's confidence.
The next minute the mechanism, whatever it was, started, and she was thrown heavily against the armored Ivanhoe, who hurt. And the _next_ minute they rose, spinning, straight up in the air.
At first the sensation was horrible, like a thousand Empire State Building elevator rides mixed up with a thousand merry-go-rounds, but by the time the machine gained its top speed it was revolving so fast that the children hardly realized it was turning at all, any more than you feel the earth turning under your feet, as the schoolbooks would have you believe it does.
After a bit Ann took courage to look down over the edge. She saw the castle and the city fast disappearing below, and before them not the ghost of shores, before them only shoreless skies.
"This is super," said Roger, hanging his head over the edge next to her, and shouting against the wind.
"Is it?" said Ann.
"Look!" said Eliza, pointing.
They looked. Far above and ahead of them, but coming nearer every second, hung a round shining globe.
"The moon!" cried Eliza, in tones of wild excitement, and "The moon!" cried Roger, in tones of awe, and "The moon!" breathed Ivanhoe in such a tone as Columbus might have used on a certain famous occasion.
"The moon?" said Ann, doubtfully. It didn't look quite right to her. It reminded her of something else.
"We can make it if we just keepeth on," Ivanhoe was saying.
"What about Rebecca?" Ann reminded him.
"Ah yes. I was almost forgetting," said Ivanhoe, with something almost like regret.
"Too bad," said Eliza.
"Maybe some other day," said Roger.
They all peered down over the edge again. The city had vanished, except for a faint glow in the far distance. Otherwise there was nothing to be seen but vast, airy, empty moonlit nothingness. "We had best land at once," said Ivanhoe. "We be over the edge of the world right now."
"How do we make it go down?" Roger wanted to know.
"I know not," Ivanhoe admitted. "What thinkst thou if we all make ourselves as heavy as we can, and then bear down hard?"
This didn't seem very scientific to Roger, but strange to say, it did the trick. The Edgeworld plunged straight downward in the neat habit of all Flying Saucers, with no sissy business of gliding and banking, like your mere airplanes, and at last, after what felt like a thousand _more_ Empire State elevator rides (only going down this time, which is far worse), it came to rest as lightly as a large feather on something that felt pleasantly like solid earth.
"Where are we?" said Eliza, clambering down the portable ladder and looking round at the scenery (only there wasn't any).
"The Outer Wastes," said Ivanhoe.
"No, it isn't," said Ann, jumping down and feeling the familiar stubble underfoot. "It's the hall . . ." But she was interrupted.
"Hist!" said Ivanhoe, a little distance away. "Hark!"
They harked. From somewhere not far off a voice was speaking, and it was the voice of Brian de Bois-Guilbert.
And then, only a little way across the stubbly plain, they saw a tower built all of yellow metal, palely shining in the moonlight. And inside the tower Rebecca languished in durance vile, while Bois-Guilbert stood outside looking in at her, and uttered a cruel laugh.
"'Tis the Dolorous Tower!" whispered Ivanhoe. And he and Roger and Eliza and Ann moved stealthily nearer.
Bois-Guilbert stood with his back to them, and he didn't turn around as they crept close. "Relent, Rebecca," he was saying. "Proffer me but one kind word, else I must leave thee to perish in this lonely prison on this blasted heath."
"Nay," said Rebecca.
"Rebecca," said Bois-Guilbert again, "think what thou art saying! Do not force me to do this dread deed, for it grieveth me greatly. Only smile on my suit, and thou art free. And if thou lovest me not yet, mayhap thou canst learn."
"Never," said Rebecca.
"Rebecca, for the third and last time," said the Templar, getting exasperated, "stop being so stubborn! Recollect that thou art my prisoner, alone and with none to aid thee!"
"Not so," cried Ivanhoe, stepping forth into a shaft of moonlight, so that he shone all silvered on the darkling plain. "Turn, Templar, and meet thy end!"
"What?" said Bois-Guilbert, turning angrily. "Who asked thee to interrupt? How earnest thou hither, anyway? Never mind," he added quickly, as Ivanhoe started describing the Flying Saucer. "Don't tell me. I don't want to hear about it. Back to thy books, stargazer, ere I make thee see stars of a different color!"
"Bully!" cried Roger, stepping forth next to Ivanhoe.
"Fiend!" cried Eliza, stepping forth next to Roger.
"Shame on you!" cried Ann, stepping forth on the end of the line.
When he saw the three children, the Templar's dark visage whitened. "What, thou again?" he said. "And thou and thou? Witch brats, do I have to find ye in my path every time I'm just getting started? Surely 'tis an evil omen and ye were born to be my bane! Nonetheless, I fight!" And he fell upon Ivanhoe with naked sword.
And there raged such a conflict, on that dark heath, as has seldom been seen outside the pages of romantic fiction. Steel rang on steel and harsh cries sounded. Bois-Guilbert thwacked Ivanhoe and Ivanhoe thwacked him right back again. Roger and Eliza jumped up and down in excitement. Rebecca clung to the bars of the prison, her eyes shining. Ann watched with clasped hands.
The slow minutes passed, filled with clashes and grunts and heavy breathing. For a long time none could say who would be victor on that bloody battleground. And though one was good and one evil, none could help but admire the fighting form of both.
Then, at last, training told its tale.
Too long had the limbs of Ivanhoe lain stretched in studious ease upon his couch; too long had he stayed absent from the courts of tourney. Besides, he didn't have his glasses on and he couldn't see. Too long had his keen eyes been strained with poring over stirring tales of interplanetary travel and scientific experiment.
A mighty blow of the Templar's sword brought him crashing to his knees. He dropped his sword. Then he couldn't see to find it. As he crawled on his hands and knees, vainly looking for it, the Templar took careful aim.
"Take care!" cried Rebecca, from within the tower.
"Do something!" said Ann, her fingers digging into Roger's arm.
"I can't. Can I? It wouldn't be right. Would it?" said Roger. "Two against one?"
"At a time like this," said Eliza, "who cares? All is fair in love and war!" And she ran to Bois-Guilbert and tried to find a gap in his armor, to bite him.
But it was too late. The Templar's sword came crashing down on Ivanhoe's helmet in a mighty blow, and the hapless hero sank unconscious beneath it.
"Now for the death thrust," said Bois-Guilbert, pulling out his dagger.
"Help him, Roger," called Rebecca from the tower. "Use thy Elfish magic!"
"I would if I could," said Roger, "but I can't. I don't have any. Honest I don't. That's all a mistake. I'm not an elf. I'm a boy."
"Farewell to hope, then," said Rebecca. "Spare his life, Templar, and I am thine!"
"No, don't do that! Wait!" cried Eliza.
"Hocus pocus," muttered Roger. "Might as well try anything once. Abracadabra. Allez-oop." He stopped to see if anything magic would happen, but of course nothing did.
Ann was sniffling. Roger was pale. Eliza was gritting her teeth. Then suddenly her face cleared.
"What are we so worried about?" she said. "It isn't as if they were real. They're nothing but a lot of lead soldiers!"
"Stop!" Roger opened his mouth to cry, but it was too late.
"What didst thou say?" said Bois-Guilbert, dropping his sword.
"What didst thou say?" said Ivanhoe, coming to and sitting up and looking around.
"Lead soldiers, lead soldiers, lead soldiers!" said Eliza.
"The Words of Power!" cried Rebecca, from the Dolorous Tower. "The Elfish Magic!" And right away the disappearing began.
Ivanhoe and Rebecca and Bois-Guilbert grew dim and then transparent, and then they simply weren't there at all, and the gray mist came swirling down and blotted out everything, and the next Roger and Ann and Eliza knew, they were sitting on the floor of the hall outside Ann's door, looking at some toy knights and a saucer and a yellow tin wastebasket upside down with a toy lady standing on top of it, and a round shining globe that was no longer a moon but just a hall light.
"The Outer Wastes," said Roger, pointing at the wastebasket. "The Dolorous Tower."
"What happened?" said Eliza.
"You said the Words of Power," said Roger. "Didn't I tell you about them?" And he told her about them now.
The children's mother chose this moment to appear in the hall.
"Up playing at this hour, the idea," she said. "It's one o'clock in the morning. How did that saucer get on the floor?"
"It flew there," said Ann, stupidly. She was still dazed by the suddenness with which the adventure had ended.
"This," said their mother, "is no time for funny jokes. Roger and Eliza, go back to your own rooms. Ann, go to bed. You've all been dreaming. And I only hope you haven't started walking in your sleep, too, because that would be the Last Straw!"
After that there was really nothing to do but trail back to their separate rooms. Roger knocked some of the Magic City over as he trailed through his, but he didn't care. It had been a mistake. If there were any more adventures and if he had anything to say about them, they were going to be yeomanly, like the first one. Magic and modernness just didn't mix.
Eliza, on the way to _her_ room, was thinking about the battle and how thrilling it had been. She wondered if Ivanhoe had lived to tell the tale, and if Rebecca had ever got out of the Dolorous Tower, and what had happened next.
Ann, in her bed in _her_ room, was wondering the same thing, and wondering if she would ever know the answer.
"Magic things goeth by threes," she said to herself. "Does that mean the next adventure'll be the last one?"
She was still wondering when she fell asleep.
5
# The Greenwood Tree
_Roger woke up the next morning_ to a chinking and a clinking and a coming and going of feet, all adding up to what he recognized all too well as the sound of Putting Away.
He opened his eyes and looked across the room. The Magic City was gone, except for the castle in one corner with a part of the park and the statue of St. George Peabody, and the dollhouse in the next corner, and some fake trees along the wall in between, and Prince John's court in the fireplace.
And in the middle of the room stood his mother, gazing round at her handiwork as though she found it good.
Roger sat up in bed. His mother met his accusing look. "I know," she said, defensively, "but it just Had To Be. Think of the poor maid who's supposed to clean in here."
At this moment Ann came rushing in from the hall. "They're gone!" she cried.
"What are?" said their mother.
"Who?" said Roger.
"Ivanhoe and Rebecca and that Brian." She turned on their mother. "What did you do with them?"
Their mother gestured vaguely toward the castle. "Whatever I found I put over there somewhere."
"Oh! Now we'll never know how they would have got back if you hadn't!" Ann wailed.
"Honestly!" said their mother. "You'd almost think the things were _alive!_ "
Ann and Roger exchanged a look.
On the way to breakfast they met Eliza. She was full of excited plans. "What'll we do next?" she said. "It's my turn this time, 'cause I said dibs on it. What'll we make happen tonight?"
"Nothing," said Roger. "We can't." And he reminded her about magic going by threes.
"It would!" said Eliza, bitterly. "You'd almost think it _tried_ to make things harder! How'll we exist in the meantime?"
"The meantime of what?" said Jack, coming into the dining room behind them.
"You wouldn't believe it if we told you," said Roger. And they proceeded to.
Luckily the custom at Aunt Katharine's was the sensible one of having the children eat by themselves, except on special occasions; so they were able to tell Jack all through breakfast with no fear of grown-up scoffing, and spill as much maple syrup as they wanted to, in their enthusiasm, without the tyranny of table manners to interrupt.
When they'd finished they could see he was impressed.
" _Now_ do you believe in magic?" said Ann.
"There might be something to it," Jack admitted. "Maybe not magic, exactly. Maybe kind of extrasensory perception, more. Maybe next time I'd better come along. Look at it scientifically."
"Huh uh," said Roger. "No more science."
"Not that old science fiction stuff, _real_ science," said Jack. "Examine the facts. I'll bring my camera. "
"That'll be nice," said Ann.
They all went up to Roger's room. "Just where did it happen?" said Jack, looking around and sniffing the air, as an inquiring photographer and scientific detective should.
"It's no use. It's too late. Mother picked up," Ann told him bitterly.
"That reminds me," said Roger. He went over and investigated the castle. Their mother had piled the soldiers every which way in the keep, and it took a long time to get them sorted.
Eliza was boss, because it was her adventure next. Under her direction, they put Robin Hood and the Black Knight and Maid Marian and some Merry Men out among the fake trees, and lined up De Bracy and his followers in besieging formation outside the castle again. They stood various courtiers and attendants about the lower chambers (Rowena was still sulking in her upper one), but they couldn't find Ivanhoe or Rebecca or Brian de Bois-Guilbert anywhere.
"Let's get the Old One," said Ann.
"Who's he?" said Jack.
They told him.
But when Eliza took the Old One from the castle, and asked him what had happened to Ivanhoe and the others, he didn't answer, and at first he was so cold in their hands that they were afraid the magic was over for good. Jack was beginning to look skeptical when all of a sudden the Old One _did_ warm up a little, as though to show them it wasn't over, but that was all he would do.
"Interesting," said Jack, feeling the warm Old One. "Peculiar phenomenon. Probably some quality in the metal. Retains heat."
"Why wouldn't he answer?" said Ann.
"Maybe we're not meant to know," said Roger. "Maybe we're meant to not do anything about it, and just wait till the third night."
"That's going to be hard," said Ann.
"Hard," said Eliza, "is not the word. I for one shall go raving tearing mad."
But it turned out that she didn't. And the three days passed quicker than you would have believed. Once you're friends with people, it's surprising how much you can find to do with them, even without magic to Light the Way.
Roger went on learning about photography from Jack, and met some of Jack's friends and hacked around with them, and played a lot of baseball and in general decided Jack wasn't really half so bad as he had painted him.
Ann didn't have such an easy time. With Roger so busy, she was left to Eliza's tender mercies, and the difference between eight years old and eleven-and-a-half loomed large. But Eliza was surprisingly nice, and offered to play hopscotch with her, and jacks, and one day she gave a tea party for Ann, and asked all her friends to meet her.
Ann was grateful, though she didn't enjoy the conversation much, which was mostly about which boys on the block were the best-looking. Nor did she prove proficient in dancing the Lindy, when the big girls tried to teach her how. She would rather have stayed in her room and investigated her new dollhouse, but she suppressed this thought. Eliza, she felt somehow, would disdain it.
And at last the third night came.
There had been some worry about sleeping arrangements, but their mothers were so pleased at what good friends they were getting to be that they raised no objections when Eliza wanted a cot put up in Ann's room, and Jack asked to sleep on Roger's couch.
That night four bathrobed figures assembled before the castle. It had been a big day of baseball, and Jack got down on the floor now and started moving De Bracy and his followers around in different formations, demonstrating how Roger could have won the game if he'd played differently.
"Don't!" said Ann. "Once you start moving them around you never can tell _what_ might happen!"
"What could happen?" said Jack.
"Almost anything," said Eliza. "You don't know what that magic's like when it's roused!"
"Ah, don't pay any attention to them," said Roger suddenly and basely, full of his new manly importance as Jack's friend. "They're just a couple of crazy girls."
After that, Ann did not take much part in the conversation.
Eliza's reaction to being called a crazy girl was different. In the process of her reaction a chair leg came off and the floor was scratched, but no one was seriously hurt.
"One thing I've been wondering," said Roger, when peace had been restored. "Why doesn't the Old One ever talk to us when we run into him? I mean, when we meet him in the magic part. All he ever does is kind of smile and wink."
"Yes," said Eliza. "You'd think he could at least give us advice and steer our faltering steps."
"Maybe he can't," said Jack. "When you see him in the magic part—I mean the old-time part," he corrected himself, for he still wasn't ready to admit the magic was real, "why, then he's in _his_ _own time._ He can't get out of it into yours, any more than you can get into his."
"But we do," said Eliza.
"Not ackcherly," said Jack. "You're still yourselves, all the time you're back there. You're not really part of that time at all. You're sort of just visiting."
All this about two kinds of time was too deep for Ann. And when she said so, and Jack tried to explain, Roger betrayed her again.
"She won't get it," he said. "She's too young."
Ann felt depressed. Not only was she a girl, but she was too young. There didn't seem to be much future for anybody who was both these things. She gave Roger a wounded look, and turned away from him to the others. "Isn't it bedtime?" she said.
"For once in my life," said Eliza, "I wish it were."
"We could set the clock ahead," suggested Roger. He felt a little guilty and smiled at the back of Ann's neck, trying to make her turn around, but she wouldn't.
Jack shook his head. "That's no good. It wouldn't be scientific. Might spoil the whole thing."
So then Ann said she was going to bed anyway, and Eliza went with her. And then Roger remembered to warn Jack about the Words of Power; so he wouldn't use them by accident, and cut off the adventure in full flower, the way Eliza had. After that he tried to think whether there were anything more he should tell Jack, and there didn't seem to be. He forced a yawn. "Ho hum," he said. "Might as well hit the sack, too."
"What for?" said Jack. "It's early."
"I just guess I will," said Roger. And he got into bed.
If the truth must be told, he was feeling sorry for the things he'd said about Ann, and the way she had looked after he'd said them. The sooner the magic began the sooner everything would be right again.
Jack went on talking to him from across the room, but Roger shut his eyes and began taking long breaths, pretending he was asleep. Pretty soon, as so often happens when you do this, he was.
Jack strapped his camera on, in readiness for whatever striking scene might occur, and lay down on the couch, but he still felt wide awake. After a bit he got up and tiptoed across the room and stood looking down at Roger. Roger's eyes were shut.
And reassured that Roger wasn't awake, to see him being so childish, Jack tiptoed over to the fake trees near the castle, and knelt down and started playing with Robin Hood and his band, for all the world as though he were a boy of eleven, and not a man of nearly thirteen.
He had the Merry Men hunt a deer. Then he had them hold an archery contest. Robin Hood won easily, by shooting the petals off a daisy, one by one.
After that, Jack lay back on the carpet. He'd just stretch out here a minute, he told himself; then he'd get into bed. Strange as it seemed and early as it was, he felt suddenly very, very sleepy.
When Roger woke up and saw the familiar plateau stretching around him and knew that the magic was happening, he scrambled to his feet and hurried down the rocky path to the plain below. Far away toward the horizon he made out two dim figures hurrying toward him. Roger ran and the figures ran, and they met on the greensward.
"I'm sorry," were the first words of Roger.
"What for?" said Ann.
"You know," said Roger.
"What are you talking about?" said Eliza.
"Nothing," said Ann, but she felt better. "Where's Jack?"
"He slept that way," said Roger, pointing at a far plateau that had been Jack's couch. The three of them hurried across the plain. But as they neared the plateau, they couldn't see any sign of human habitation. And when they came right up to it, they saw that the plateau was smooth and unruffled, as though it hadn't been slept on all night.
"If that isn't just _like_ that magic!" Eliza cried indignantly. "It got to him ahead of us. He's probably somewhere in the middle of it right now, being scientific and ruining _my_ adventure! Come on!"
"Where?" said Ann. "We don't know where he is, or Ivanhoe, or anybody!"
"Start with the castle," said Roger. "That's always the beginning of everything. Our Social Studies book says in medieval times the castle was the hub of all activity."
The three of them ran toward the familiar towers of Torquilstone. As they hurried through the park, they could see figures moving up ahead.
"The siege must be still going on," said Roger, pointing.
"Oh, is that what they're doing?" said Ann. "That isn't what it looks like."
And now, as they drew nearer, the others saw that Ann was right. What was going on didn't look like a siege at all. A ball came hurtling through the air, but it didn't seem to be a cannonball, exactly. Some sort of stick flashed in the sun, but it didn't seem to be a pikestaff, or a quarterstaff, either.
And then they were very close, and loud voices rang on the bright air.
"He striketh thrice!" cried the first voice, in loud, official-sounding tones. "Out upon him!"
Other voices interrupted angrily. "Nay!" they cried. "A pox on thee! 'Twas a ball! Slay the Umpire!" And all the figures surged together in a quarreling knot.
Roger and Ann and Eliza came to a halt near some varlets who were looking on. "What's happening?" Roger asked one of them.
"It be ye sport of Base Ball," said the varlet. "The Norman team claimeth a ball but the Umpire saith them nay. It be ye olde Rhubarb."
"Good grief," said Roger. "Has the siege come to this? This is worse than last time."
Ann did not say "I told you so" to her brother. She merely gave him a meaningful look.
"Jack ought to be here," said Eliza. "He'd be in his glory. Where do you suppose he is?"
"Never mind about that now," said Roger. "The point is, who's winning?"
"It be a tie," said the varlet. "Naught to naught in ye sixth."
And now the quarrel (or rhubarb) seemed to be over, and the Saxons and Normans straggled back to their positions. A dignified-looking, white-haired gentleman who seemed to be the Umpire tossed the ball back into play, and the children saw that it was the Old One. He raised his eyebrows at Roger, but did not speak.
Meanwhile a tall Norman had stepped up to home plate, swinging his bat. At sight of him a murmur ran through the crowd. Some cheered and cried, "Up the Normans!" while others booed.
"Who is it?" hissed Roger to the varlet.
"'Tis the greatest Norman of them all," said the varlet. "'Tis Babe De Bracy. 'Tis ye Sultan of Swatte."
And then, as all eyes were fixed on the mighty Norman, a shameful thing happened. The Lady Rowena appeared on the battlements of the castle, no longer slothful and chocolate-fed, but slim and lovely, her blonde hair streaming on the wind. And as Roger and Eliza and Ann watched, horrified, she waved a lily-white hand at De Bracy. The mighty batsman bowed low in her direction, and she blew him a kiss.
"Why, the traitorous thing!" said Ann. "Imagine!"
"Isn't that just like her?" said Eliza.
The booing from the Saxon fans, which had grown louder when the Lady Rowena appeared, died down, and again Babe De Bracy approached home plate, his bat swinging.
But again there was an interruption. The portcullis of the castle moved upward, the drawbridge creakingly descended, and two figures advanced across it, on horseback. One was bearded and elderly, and the three children recognized him right away. It was Cedric the Saxon, Ivanhoe's father. Wamba the jester rode by his side.
De Bracy left the baseball diamond and strode over to the two horsemen. "What meaneth this?" he said. "Doth the castle surrender?"
Cedric the Saxon drew himself up proudly. "Never," he cried, "while breath remaineth in me to defend it! I but crave leave to depart to seek my vanished son."
"Thy son is dead, methinks," said De Bracy, "else why hath he not returned?"
"Dead fiddlesticks!" cried Rowena, appearing suddenly on the drawbridge beside them and interrupting. "Run off with that Rebecca, more likely!"
"Temper, temper!" said Wamba.
"Peace, fool," said Rowena.
"For shame," said Cedric the Saxon, glaring at Rowena. "Smiling on the enemy and making thy great eyes at him from the very battlements of our Saxon stronghold, I saw thee!"
"I must needs smile at someone," said Rowena, "and none other was forthcoming. Besides, all the ladies smile at the Sultan of Swatte." And she batted her eyes at De Bracy.
"Faugh!" said Cedric the Saxon. "I shall find my son, if he be living, and he shall return to save our merrie land from these degenerate games. Sultan of Swatte, indeed! My son shall swatte _thee!_ " And he turned his haughty glare upon De Bracy.
"Take care, gaffer," said the Norman. "Who cometh begging favors must needs speak more discreetly. Nonetheless, none can say Maurice De Bracy was ever an ungenerous foe. Depart in peace and seek thy son. But proceed with caution, for thou art old and thy fool but a fool." He strode back to the baseball diamond. "Play ball!" he cried, and the game began again.
Ann and Roger and Eliza ran after Cedric and Wamba. "Wait!" Roger called. "Take us with you; we want to find him, too!"
The two riders reined in their horses. "'Tis Roger!" cried Wamba. "And the witch and the sorceress with him! Now surely we are in luck, for they have come to set us on the right path."
"Lead me to my son, elf-child," said Cedric the Saxon, "and I shall bless thy name forever."
"I can't," said Roger. "I don't know where he is."
"We know where he _was,_ " put in Ann, "but he's not there any more."
"Then surely my son is dead," cried Cedric, "if the magic of Elfland itself cannot find him!"
"Not necessarily," said Roger.
"You'd be surprised what all we don't know," said Eliza.
"We know he's not _that_ way, though," said Ann, pointing ahead through the park toward the greensward and the distant plateaus. "We've _been_ there."
So Cedric the Saxon and Wamba turned their horses toward the grove of trees on their left, and Roger climbed up with Wamba, and Cedric lifted Eliza and Ann up to ride with him in a kind of double pillion, and they set off to look for Wilfred of Ivanhoe.
As they went along, the trees grew thicker and taller till they found themselves in a deep forest. The earth was carpeted with acorns and beech-mast, and the sunlight, sifting through the foliage above, turned the air the color of new young leaves; so that it was a green wood indeed. Once a deer galloped across their path, looking so free and beautiful and lordly that Ann and Eliza and Roger caught their breaths in sheer wonder.
It was a second after that that they heard a twanging sound, and something they thought was a bird flew by, over their shoulders. Only then they knew that it hadn't been a bird, because there was another twanging sound, and an arrow suddenly thrilled in the heart of an oak tree just ahead.
They pulled up short, their hearts beating fast. All at once the forest seemed alive with laughing men in green jerkins and hose. And in the midst of them, and grinning at Eliza and Roger and Ann, stood a familiar figure.
"Isn't this swell?" it said. "I guess there ackcherly _is_ magic, after all."
When Jack awoke after going to sleep on the carpet, he found himself lying on cool grass at the edge of a wood. For a minute he couldn't think where he was; then he remembered. He jumped to his feet and walked into the wood, swinging a stick he fashioned from a fallen oak branch, and wondering what was going to happen next.
What happened next was a twanging noise in his ear, and something came flying through the air, straight at him. There was no time to duck, but he'd always been a good man with a fastball; so he quickly took his stance, and struck at the flying thing with his oak staff.
And he wasn't the batting champion of several Baltimore, Maryland, vacant lots for nothing. His stick hit the flying thing squarely, but instead of sailing over the fence and out, as it would have if it had been a baseball, it just stuck there on the end of the stick, and when he looked at it he saw that it was an arrow that had gone halfway through the stout oak.
The next thing he knew, a handsome man in green had appeared from behind a tree and was applauding him.
"Well played, boy!" said the man.
"Thanks," said Jack.
"But what is thy business in Sherwood Forest?" the strange man went on. "And art thou rich or poor, that I may know whether to rob thee or call thee friend?"
"Sherwood Forest?" said Jack. "Gee. Of course. And you're Robin Hood."
The man in green bowed. "Naturally."
A thrill went through Jack, and he reached for his everready camera. This would be the best picture yet. Not only that, but it would prove the magic had been real, afterwards.
"Hold still a second," he said. "Smile, please. There." And he clicked the shutter.
"What be yon?" said Robin Hood. "Some newfangled wizardry or other?"
"Sort of," said Jack. "I'll send you a copy if it comes out. Gosh. Robin Hood. Could I shake your hand, sir?" And he held his own hand out. "My name's Jack."
"Well met, Jack!" said Robin Hood, gripping it manfully. "With thy quick eye and thy ready hand and wizardry besides, thou shouldst go far in the outlaw trade. Wouldst care to join my merry band?"
"Oh boy!" said Jack. "Wouldst I ever!"
Robin Hood blew a blast on his hunting horn, and outlaws appeared from behind every tree; Maid Marian in a green gown, and Will Scarlet in scarlet, and Allan-a-Dale with his lute, and a huge fellow who could only be Little John. And after that, Jack didn't care whether the magic were real or not. Whatever it was, it was super.
Then, just as Robin was taking Jack around and introducing him to his comrades, another bowman in green came running into the clearing and stood there, getting his breath back.
"What news, Will Stutely?" said Robin Hood.
"Travelers approaching, sir," said Will Stutely. "On horseback, and richly caparisoned, to judge by the jingling!"
"Oho!" said Robin Hood. "More rich booty to plunder and divide among the deserving poor! To your posts, gentlemen!"
There was a sort of flicker, and Jack rubbed his eyes. Except for Robin Hood and himself, not a soul was to be seen. Robin clapped him on the shoulder. "Thy first taste of outlawry, boy!" he said. "Keep by me." And he whisked Jack behind an elm, where they lay crouched together as the unsuspecting horsemen moved into the clearing, jingling as they came.
Only the jingling wasn't caused by rich caparisons, but by Wamba's jester's bells, and when Robin Hood saw who the horsemen were he laughed mightily (but silently) in Jack's ear.
"Marry, 'tis old friends," he breathed. "Nonetheless, we shall give them a scare, for old times' sake." And fitting a shaft to his bow, he sent it whirring past the travelers, and then sent its fellow deep into the heart of an oak tree directly in their path.
"Help!" cried Wamba, falling off his horse and then trying to hide under it.
"Indians!" cried Ann, who wasn't thinking.
"No, it isn't; it's . . ." began Roger. But at that moment Robin Hood jumped laughing out from behind his tree, and the other outlaws jumped laughing out from behind theirs, and Jack came grinning up to Ann and Eliza and Roger.
When Robin Hood heard of Ivanhoe's disappearance he swore a mighty oath, and when he heard that Roger himself had come again, to join in the search for the missing hero, he came up to Roger and bowed low before him.
"Sir," he said, "this is a great honor."
"Oh, that's all right," said Roger. "It's mutual."
"Thou art too kind," said Robin Hood. "We must have a feast to celebrate the occasion. Men, roast the deer!" And the hearts of the four children thrilled at these truly yeomanly words.
"Is there time, though?" said Roger. "Shouldn't we get searching?"
"Searchers require sustenance," said Robin Hood. "Tonight we feast. Tomorrow we join in the hunt."
"I crave thy pardon," said a tall figure in black armor who had appeared out of the shadows. "Didst say Wilfred of Ivanhoe was lost while on some deed of derring-do? Hath the moon-mad dreamer then recovered from his stargazing?"
"Don't blame him. That wasn't his fault," said Roger. He pointed at Ann. "This mighty sorceress here did that."
"Then death to her," said the Black Knight, putting his hand on his sword.
"Oh dear," said Ann.
"Nay!" said Roger, quickly. "She hath reformed."
"She'd better!" muttered the Black Knight. But he took his hand off his sword. "And Wilfred is the old knightly Ivanhoe once more?"
"Well." Roger hesitated.
"Of course he's a little bit out of practice," said Ann.
"But the last time we saw him, he was rescuing a maiden," said Eliza.
"My, my, just like old times," beamed the Black Knight. "I feel like a new man. Richard is himself again!"
"Sire," said Roger. "I've been wondering. Why don't you come back to your throne and drive Prince John and the Normans out and make everything good again!"
"Marry, mayhap I will!" said Richard. "If the old age of chivalry returneth, who am I to be behindhand? Must find dear old Wilfred first, however. After that, who knoweth?"
So that night all was feasting, and if Ann and Roger and Eliza found the taste of roast venison disappointing (maybe because of the deer they had seen all alive and beautiful in the forest), at least they were too well brought up to say so. And dessert, which was wild strawberry junket and frumenty, was dandy.
After the feast, toasts were drunk and songs were sung, and they all lay back in the shade of the spreading greenwood tree and Jack wished this magic, if that's what it was, would go on forever.
And then the strange thing happened. A bird fluttered into the clearing and all around the company, almost brushing their faces with its wings, before it flounced to a perch on the limb of a nearby oak. And somehow all of them knew that this was no ordinary bird.
"'Tis a falcon!" said Little John.
"With its jesses broken and trailing, the poor strayed thing!" said Maid Marian.
"And if I mistake not, with some paper or other tied unto them," said Robin Hood, striding from his place to look up at the bird. "Could it be 'tis a message for someone here present?"
And now everyone was clustering around the falcon in the tree, and making what everyone hoped were reassuring noises.
"There, there," said Maid Marian.
"Nice falcon," said Ann.
"Soo, boss," said Much the Miller, who was of a rustic background.
The falcon merely fixed them with its glittering eye.
"Wait," said Robin Hood. And he climbed the tree as one who knew no fear, and the falcon seemed to respect this, and allowed itself to be carried to earth with no struggles, or biting and tearing. Robin Hood untied the paper and glanced at it. Then he gave a cry, and read it aloud:
> "To Whom It May Concern:
>
> "We are all three of us prisoners in the Giants' Lair. Help.
>
>> (Signed)
>>
>> |
>>
>> |
>>
>> Wilfred I.
>>
>> ---|---|---
>>
>> |
>>
>> |
>>
>> Rebecca Y.
>>
>> |
>>
>> |
>>
>> Brian de B. G."
Immediately the air was filled with a babble of excited talk.
"My son!" cried Cedric the Saxon.
"Giants! Ugh! Sooner them than me!" cried all the outlaws.
"Brian de Bois-Guilbert?" said the Black Knight with a snort. "Is Wilfred hobnobbing with _that_ dastard?"
"It's not his fault," Roger told him. "They were fighting together the last time I saw them. They probably got taken prisoner together. He probably won't like being rescued by us any more than we'll like rescuing him. It's probably just a case of any port in a storm."
"Where's this Giants' Lair?" said Jack.
Robin Hood looked grave. "It lieth beyond the forest, at the world's end," he said. "Rumor hath it that the giants who dwell therein are ogres of the most deadly variety, though of course I have never seen them, myself. Few have, and lived to tell the tale. Indeed the legend runneth that no man may enter that grimly habitation of his own free will."
"How do we save them then?" asked Roger.
"The one creature for whom 'tis said the door standeth ever open," said Robin Hood, "is a little girl."
Eliza pushed forward eagerly. After all, this was supposed to be her adventure.
Robin Hood looked her over. "Thou mightst do," he said, "but little still would be better."
All eyes turned to Ann. Ann felt small. "You mean me?"
"To a mighty sorceress," said Robin Hood, "all things should be possible."
"Yes," said Ann dubiously, "I suppose they should."
"We of course," went on Robin, "would accompany you as far as possible, stand by to be of what aid we can, et cetera."
"What about me? Can't I go along?" asked Roger. Ann threw him a grateful look.
"Under certain circumstances," admitted Robin, "'tis said that a small boy also may enter those hideous halls."
"Me too?" asked Jack.
Robin Hood looked at him, and there seemed to be a twinkle in his eye. "Thou art grown near to man's estate, boy," he said. "But while the legend runneth that the door standeth open only for a little girl, there is another legend that only a certain youth may conquer the dread monsters within. I should say that if the lady meaneth to undertake this journey, she would do very well to have thee along!"
"Good," said Jack. He grinned at Ann, and winked.
"Count me in," said Roger. "Me, too," said Eliza.
Everybody seemed to be waiting for Ann to say something. She looked round at them all, and swallowed. She thought of how much she liked Ivanhoe and Rebecca, and how, even though Brian de Bois-Guilbert might be wicked as wicked, he was still a knight and deserved a knightly death, not one at horrid giant hands (or teeth). And she hoped she sounded brave, because she didn't feel brave at all.
"All right," she said. "I'll try."
A cheer burst from the lips of Robin Hood and his men. Eliza threw her arms round Ann. Jack thumped her on the back.
Ann looked at Roger. Roger looked at Ann. "Pretty good," he said, "for a girl."
And that made Ann feel best of all.
6
# The Giants' Lair
_Once the die was cast,_ Ann wanted to start for the Giants' Lair right away and get it over with, and so did Roger and Jack and Eliza. But Robin Hood shook his head.
"Ye must rest and store up your strength," he told them. "Who knoweth what ordeals ye may undergo before ye see old Sherwood again?" And Ann and Roger and Jack and Eliza had to agree that who knew, indeed?
But getting to sleep that night was not easy for any of them, particularly Ann, even though their couches were of fragrant bracken and their pillows scented with pine needles, and even though Maid Marian came and told them soothing stories of the sunnier side of outlaw life.
And when Ann finally did drop off, she had the most bloodcurdling dreams all night.
But the forest birds woke them cheerfully in the morning, and tomorrow was, as usual, another day, and all was swash and buckle as they made ready for the journey, and then all too soon they _were_ ready, and the procession started off through the trees, in the opposite direction from Torquilstone Castle.
At first the going was easy, and foxgloves glowed like purple and white candles, and birds warbled their native woodnotes wild, and Allan-a-Dale sang tirra lirra, and Ann might almost have believed they were bound on a party of pleasure, instead of a deed of derring-do.
But as the day wore on things got different. No more flowers bloomed under the trees, which were mostly dead or blasted by lightning, anyway. And around their splintered trunks hung stringy, thorny briers that slapped the travelers scratchingly in the face and seemed to be trying to hold them back. The sun went behind a cloud. A thin cold wind blew down their necks. A carrion crow flew over.
"We're getting near," said Robin Hood.
And Ann and Eliza and Roger and Jack could see that the forest ended just ahead, not thinning out and trailing away gradually, like a respectable forest, but stopping suddenly, as though all life had been cut off at one fell swoop.
"The Giants' Lair!" said Robin, pointing.
Ann and Eliza and Roger and Jack knew what they expected to see—a grim, half-ruined castle like one of the drawings of Mr. Charles Addams in _The New Yorker,_ with bats flying around and toads on the terrace and a wolf at the door, and maybe a horrible head glaring from a window.
They stopped at the edge of the forest.
"Hideous, isn't it?" said Robin Hood. "Like nothing ever built by human hands!"
Ann and Eliza and Roger and Jack looked. It wasn't like a Charles Addams drawing at all. Except that it was about a hundred times normal size, what they saw was a perfectly ordinary house, such as you might see in any perfectly ordinary suburb today, with white paint and green blinds and a neat lawn and flowerbeds.
Maid Marian averted her eyes. "How dreadful!" she shuddered. "Robin, can we leave these innocent children to go in there alone?"
"There's nothing wrong," said Jack. "It's just a house only it's too big."
"It's just like any old house back home," said Eliza, disappointed. "I think it's boring."
"There's no accounting for tastes," said Maid Marian.
Ann didn't say anything. There was something familiar about the house, but she couldn't think what it was.
"And now," said Robin Hood, "this is where you must leave us. We shall be waiting here if there be any little thing we can do."
"Good luck," said Marian, kissing Ann.
"Tell old Wilfred chin up from me," said the Black Knight.
"Save my son," said Cedric the Saxon.
"We'll try," said Roger.
He and Eliza and Ann and Jack got down from their horses.
"But stay," said Robin Hood. "I was forgetting. Thou bearest no arms."
"Do we have to?" said Ann. "I'd rather not."
"I wouldn't," said Eliza, swaggering.
Robin Hood looked at them. Again there seemed to be a twinkle in his eye. "Methinks," he said, "that Jack at least should bear some weapon."
The Black Knight stepped forward, and in this moment he looked every inch King Richard the Lionhearted. He drew his sword from its sheath. "This blade," he said, "hath fought right valiantly against Saracens abroad and traitors at home. Take it, and may it do yet one more bright deed for Merrie England."
"Thanks a lot," said Jack.
And he and Roger and Eliza and Ann started walking across the lawn.
But as they drew nearer the house it kept looking bigger and bigger, and the four children felt smaller and smaller in the middle of the vast grassy expanse. There were no fierce cries from within and nothing pounced at them out of the front door. But they felt better when they gained the shelter of a hedge at the side of the house. And beyond the hedge they saw a cellar window.
The window was open what probably seemed only a crack to it, but to small Ann and Roger and Jack and Eliza it was a great yawning cavern. They slithered through the hedge, ran forward stealthily, crouched on the vast sill and looked into the room below.
What they expected to see was a grisly dungeon, with chains, and somebody grinding somebody else's bones to make his bread. That would have been unpleasant, but only to be expected. But that wasn't what they saw at all.
What they saw was a perfectly ordinary-looking rumpus room. If it hadn't been so big it might have looked rather jolly. If the people in it hadn't been so big they might have looked rather jolly, too.
They were a man (if you could call him that) and a woman (or at least a female) and a little girl (if you could describe as little a being that was at least four times as tall as Jack). Their cheeks were of a pink-and-white, china-like perfection, and their eyes were blue and staring, with long curling lashes, and their lips parted, showing pearly teeth.
And no matter what they said or did, they never stopped smiling. After a while, Ann wished they wouldn't.
There was something else peculiar about the room, too. There didn't seem to be enough furniture to go round. And Ann noticed that the train of the female giant's red velvet gown seemed to have been cut away, leaving a jagged edge. And the man giant's tail-coat didn't have any tails. And the little girl giant had blonde corkscrew curls on one side of her face, but on the other side she didn't have any. And suddenly Ann knew the secret of the Giant's Lair. She turned to Eliza to tell her.
"Shush," said Eliza. "Look." And she pointed.
The giant family was squatting down now, and gazing at something on the floor, but Ann couldn't see what it was. Then she heard a piteous voice.
"Oh, please do not play with me any more!" it cried. "I am so tired!" It was the voice of Rebecca.
And far down on the floor, the four children made out the forms of Ivanhoe and Brian de Bois-Guilbert, standing one on each side of Rebecca as though to protect her.
The voice of the female giant now made itself heard.
"Why, the very idea! What impudence. Don't you pay a bit of attention to what the horrid little thing says. You play with them. Play just as hard as you can. Play house with the girl and soldiers with the boys."
"Yes, Mama!" said the child giant. And she picked Rebecca up and started undressing her, and then got tired of that halfway through and put her down in a draft, and took hold of Ivanhoe and Bois-Guilbert instead, and started marching them up and down the floor in a childish and elementary manner.
Ann and Roger and Eliza looked at each other with indignation.
"It's an insult to the whole order of knighthood!" sputtered Roger.
" _I_ think it's an outrage!" said Eliza.
"What have those giants got there? Dolls?" said Jack.
"No, that's Ivanhoe and Rebecca and Bois-Guilbert," Ann told him. "It's dolls that have got _them!_ "
For of course that was the secret of the Giants' Lair. It was the neglected dollhouse Aunt Katharine had given Ann, that she had never played with, except to plunder its rooms when she was furbishing the Magic City.
"I knew there was something wrong with that dollhouse the minute I saw it," Eliza was saying now to Ann.
"You're right," said Ann. "They're not nice dolls."
The little girl doll (or giant) now decided to play war and make Ivanhoe and Bois-Guilbert have a deadly combat. She did this in crude fashion by holding one of them in each hand and then knocking them together, hard.
"Sorry, old man," said Bois-Guilbert. "Was that my boot in thy left eye?"
"'Twas not thy fault, old fellow," said Ivanhoe. "Oops! Did I crack thy crown? Blame not me. Blame this monstrous child."
"I do," said Bois-Guilbert. "I blame her more than I can say. And more of the same from her I will not suffer!" And he drew his sword and attacked the giant child.
Of course to her it was as the prick of a mere pin, but she immediately dropped both knights on the floor (stunning them badly) and began to cry, in the whining tone of all crying dolls.
"Mama," she cried. "It hurt me!"
"Why, the vicious thing," said her mother.
"We won't have any more of that!" said the father giant. "They are not fit pets for you to play with! They should be destroyed!"
At this the child giant began to cry louder, but her mother soothed her. "Wait," she said. "I have an idea. Come with me, and Mama will put some iodine on your finger, and then we will come back and Papa will get his pliers and remove their stings. Then you may play with them just as much as you want to."
And the child giant suffered herself to be led away, her father pausing only long enough to put Ivanhoe and Rebecca and Bois-Guilbert on a table, for safekeeping.
As soon as they'd gone, Eliza said, "Pssst."
Rebecca looked around the room.
"Up here," said Ann.
Rebecca's eyes found the window, high up near the ceiling, and her face lighted. "'Tis Roger!" she cried. "And the witch and the sorceress with him!"
"Then haply we may hope again," said Ivanhoe.
"Oh Roger," said Bois-Guilbert, humbly. "Thou and I hast crossed swords more than once in days of yore, but fetch us out of this prison and I shall atone for my many sins!"
"Well, for Heaven's sake!" said Eliza, in surprise. "How you've changed, haven't you?"
"We'll save you all if we can," said Roger. "Anyway, we'll try."
"Wait there," said Jack.
"We needs must," said Ivanhoe, peering down from the table. "Other choice offereth there none."
Roger and Ann and Jack and Eliza scrambled out from their perch on the windowsill (for the drop from there was even higher than the drop from the table) and ran around the house looking for a way to the cellar. At last they found some steps leading down, with a door at the bottom.
"For a little girl," said Roger, "the door standeth ever open."
Even as he spoke and even as they looked, the door swung wide of its own accord. But getting to it was another matter.
"Take a giant step," said Eliza, bitterly, looking down at the series of perilous drops before them. But they managed it at last by hanging from the edge of each step with their hands, and then letting go. They arrived at the bottom, whole but somewhat jolted.
And once in the cellar, they faced the problem of how to get Rebecca and Ivanhoe and Bois-Guilbert down from the table.
"Use thy Elfish magic," suggested Ivanhoe.
"You don't ever seem to understand about that," said Roger. "There isn't any. At least there is, but we can't use it. We're sort of _in_ it!"
But it was vain to attempt to explain. "Come, come," said Ivanhoe. "Thou art merely being modest."
"Think how thou hast saved us in the past," said Rebecca.
"Our fate is in thy hands," added Bois-Guilbert, piously. "Heaven hath sent thee to us in our hour of need."
After that the children had to think of something, and it was Ann who saw the end of a skein of yarn hanging down from the table, where the female giant had been knitting, and it was Jack who had the strength to pull a whole mass of the great floppy stuff down to the floor, and it was Roger and Jack who made the rope ladder, and it was Eliza who looked on and told them how to do it. Ann kept watch at the door.
"Sister Ann, what do you hear?" said Roger.
"Awful screams," said Ann. "They're putting on the iodine."
"Good," said Eliza.
At last the ladder was ready, and Ivanhoe and Bois-Guilbert, pulling as hard as they could on the other end of the yarn, managed to heave it up to the table.
"Ladies goeth first," said Ivanhoe to Rebecca.
"Nay," said Bois-Guilbert. "One of us strong men should precede her, to aid in her descent and break her fall shouldst she tumble."
"What a goodly thought, old man!" said Ivanhoe. "Go thou, and I shall come third."
"Not at all, my dear fellow," said Bois-Guilbert. "After thee!"
"My, you two certainly are pals all of a sudden," said Roger.
"We have sworn brotherhood," said Ivanhoe. "Brian is a new man. He hath reformed."
"Rebecca hath reformed me," said Bois-Guilbert. "It helped to pass the time. Besides, what is chivalry for, if two knights do not unite against a common enemy? Old Wilfred and I have been through thick and thin together in this dungeon."
"There is a great deal of good in old Brian," said Ivanhoe. "We are . . . What was the word Roger hath used?"
"We are pals," said Bois-Guilbert, gripping Ivanhoe by the hand.
"Good," said Eliza. "Now let's hurry."
But which of the two knights would finally have gone down the yarn ladder first will never be known. For now heavy feet were heard on the stairs, and the three smiling giants appeared in the doorway. They stood looking around the room.
"Someone has been leaving the cellar door open," said the father giant, crossing to shut it.
"Someone has been snarling up my knitting," said the mother giant, seizing the yarn ladder and pulling it apart beyond repair.
"Someone has been trying to steal my playthings," cried the little-girl giant, "and there they are now!" And she pointed at Roger and Jack and Ann and Eliza.
"Well, well," said her father. "More pets for you to play with. Aren't you the lucky girl?" And he leaned over to pick up Ann.
Ann's heart quailed, though she tried not to let it. And Eliza stepped forward courageously.
"Don't you touch her!" she said. "You'll be sorry! She may not look it, but she's a mighty sorceress. It just so happens I'm a pretty powerful witch, myself. Beware!"
"And I," said Roger, drawing himself up to his full small height, "am the great Roger. You've probably heard of me."
"No," said the giant, "I haven't. And what's more, I don't believe you." And he leaned over them again with his menacing smile.
"Help!" cried Eliza, in sudden alarm. "Jack! Use your sword!"
Jack brandished the blade King Richard had given him.
The giant's face retreated quicker than it had advanced. "What did you say?" he said.
"I told him to use his sword," said Eliza. "He will, too."
"But what was that you called him?" said the giant.
"Jack," said Eliza. "That's his name."
The child giant screamed. The mother giant turned pale.
"I don't believe you," said the father giant again, but his voice trembled. "If that's Jack, where's his beans?"
This time it was Roger who understood. "He's not that Jack," he said. "He's the other one. He's Jack the . . ."
"Don't say it!" cried the giantess, clutching her offspring to her. "Not before the child!" The three giants gazed at Jack in terror.
"What's the matter with them?" said Jack.
"They think you're Jack the Giant Killer," said Ann.
"Okay," said Jack. "What do I do? Kill them?"
Roger looked doubtful. "Do you suppose we have to?"
"Think of the blood," said Ann. "So _much_ of it!"
"Only it'd probably be sawdust," said Roger.
"And they'd probably go right on smiling," said Eliza. "I couldn't stand it."
While this discussion was going on, the father giant had been edging toward the table. Now he suddenly caught up Ivanhoe and Rebecca and Bois-Guilbert and held them high in the air.
"I'll teach you to come invading people's homes with your nasty murdering friends," he said. "If he doesn't put away his sword, I'll smash them to smithereens."
Ann and Roger and Eliza gazed up in horror at their captive friends. Jack was so startled that he dropped his sword on the floor.
"Pay no heed," called Rebecca to Jack, from somewhere up near the ceiling, which was of skyscraper height. "Take up thy blade!"
"If we die, 'twill be in a good cause," said Ivanhoe.
"I have been a miserable wretch," said Bois-Guilbert, his voice muffled by the giant's hand, but with a sincere ring in it. "But at least I repented before 'twas too late."
"Wait," said Roger to the giant. "Can't we talk this over sensibly? Maybe we could work out some kind of truce."
"What makes you so mean?" said Ann. "What have we ever done to you?"
"Well, really! Well may you ask," said the mother doll (or giant). "It isn't that we mind being played with day and night and wheeled in baby carriages till it's monotonous. Oh no! Nor being undressed and put to bed when we aren't sleepy, and dropped on our heads and left out in the rain, either! That's just part of the normal scheme of things. It's what we were made for. We even enjoy it, in a way. It makes us feel Somebody Cares! But _you_ "—her voice trembled and she sounded hurt—"never played with us at all!"
Ann blushed and felt ashamed of herself but Eliza was scornful. "I certainly didn't," she said. "I wouldn't stoop to it."
"Very well," said the mother giant. "Very well. That's your privilege. But when it comes"—and her voice swelled with righteous wrath—"to invading our privacy and spoiling our interior decoration and cutting up the very clothes off our back, why _then_ I say it's time to draw the line, and it's no wonder we're striking back! And don't pretend you didn't do it," she went on, pointing at Ann's hand with the birthstone ring with the tiny agate, "because I'd know that hand anywhere! And _that_ "—she pointed at Eliza's hand with the bitten fingernails—"is the hand that helps it!"
"Only now they've got little," said the child giant.
"And now," said the father, snatching up Jack's sword from the floor, "they're in our power."
The giant family glowered down at Ann and Eliza.
"What have you done with my red velvet train?" said the mother giant.
"My coattails?" said the father giant.
"My side-curls?" said the little girl giant.
"My fur coat? The best bath mat? The drawing room armchair? The kitchen curtains? The roses from the quilt?" said all three.
Ann blushed guiltily. "I'm sorry," she said.
"We didn't think you'd mind," said Eliza.
"Mind?" said the mother giant. "Mind? Have we no feelings? Have we no hearts? Are we things of wood and china?"
"Give us back what you stole," said the father giant. "Then maybe we can talk of truces."
"We can't," said Ann, unhappily.
"We don't have them anymore," said Eliza.
"Then bid your friends good-bye forever," said the giant. And again he raised Ivanhoe and Rebecca and Bois-Guilbert in the air, to dash them to pieces on the floor.
"Wait!" cried Ann. "We'll find them for you! We'll bring them back!"
"We'll go on a quest!" said Eliza.
But there was an interruption. "Ah, what does it matter?" said Jack, forgetting for a moment that he had shrunk to toy-soldier size and remembering only his boyish scorn for girls' playthings. "They're just a lot of dolls, anyway!"
"Don't!" cried Roger and Ann and Eliza in one voice, gripped by the same horrid fear. But they were too late.
For these words proved just as powerful as others that shall be nameless, and the mist rolled down, and the giants and Ivanhoe and Rebecca and Bois-Guilbert started growing transparent, and the last thing Roger and Ann and Jack and Eliza saw before everything disappeared completely was the whole wall of the Giant's Lair sort of swinging out and away from them, as though they were in an earthquake.
The next they knew, they were standing in Roger's room looking down at an open dollhouse. Inside the dollhouse were a father doll and a mother doll and a little girl doll and the small figures of Ivanhoe and Rebecca and Bois-Guilbert, lying where the children's mother had put them when she picked up, three days ago.
"Oh!" cried Ann, looking at Jack with a face of utter displeasure. "You might know some _boy_ would spoil everything!"
"How was I to know?" said Jack. He turned to Roger. "That's not what you said the Words of Power were."
"It's the same principle," said Roger. "You might have guessed. I did."
"I don't see how," said Jack.
"Maybe he used his head," snapped Eliza. "And this was supposed to be my adventure and you spoiled it before I got to be leader at all, hardly."
There was a silence.
"Robin Hood was keen, though," said Jack.
The others looked at him coldly. "And now he's still waiting at the edge of the wood for us to come back, and maybe we never will!" said Ann.
"Ivanhoe and Rebecca and that Brian'll be killed, of course," said Eliza, joining in in that spirit of making everything as gloomy as possible that can be such a pleasure at such times.
"And the Normans'll win the siege, and the whole thing'll be ruined," said Roger.
"I don't see that it's my fault at all," said Jack. "You can't expect an experiment to come out right if people don't give you the right facts."
"Oh, leave him alone," said Eliza, pityingly. "He's too old to know better."
And they did.
7
# The Quest
_"Now then," said Eliza._ "What'll we do?"
It was the next day, and hope reigned again in the hearts of the four children.
"Well, the first thing," said Ann, "is to remember all the things we took out of the dollhouse, and find them and put them back."
Eliza shook her head. "That's too easy. Better wait till the magic starts again and go on a quest, like I said."
"But we'll never find all the things when we're small," Ann wailed.
Roger was firm. "Eliza's right. Any other way would be just sissy and cheating."
"But Ann's partly right, too," said Jack. "We can't move all that furniture if we're soldier-size."
"We'll have to compromise," said Roger.
"What's that?" said Ann.
The other three proceeded to show her what it was by taking Prince John's throne from behind the sliding fire screen and putting it back in the dollhouse, where it became the best parlor armchair once more. And all the other furniture that would be too heavy to move, later, they put back now, but the smaller things they left where they were, to be quested for when the magic began.
"I get to plan the quest," said Eliza. "Last time doesn't count as my turn at all. The door stood open for Ann, and Jack nearly was a giant killer, and Roger was the great Roger. I hardly did anything."
And the others all saw that to agree would be the way of much less resistance.
"We ought to make a list," Eliza went on, "of all the things we have to find, and take it along, to prod our sluggish brains."
"I'll get my notebook," said Ann.
" _Can_ we take things?" Roger wondered. "We never have."
"We take the clothes we're wearing," said Eliza, "if that signifies."
"And I took my camera," said Jack.
"You did? I never noticed," said Eliza.
"I forgot about it myself," said Jack. "I only took that one picture of Robin Hood, and then I forgot all about developing that."
"Let's go do it now," said Roger. And the two boys departed for the darkroom while Ann and Eliza worked on the list.
"What did we use the father giant's coattails for?" Eliza tried to remember.
"I can't think," said Ann. "I know where the child giant's side-curls went, though." She giggled at the thought of where they had gone. Then she ran to get her notebook, but she couldn't find a pencil (as who ever can?) and the talk turned to other matters.
Pretty soon Roger and Jack came back and reported that the picture of Robin Hood hadn't turned out.
"It must have been overexposed," said Jack, but Roger thought there might be more to it than that.
And so the rest of that day and all the next one passed in fun and games and harmless ploys, and always the fateful third night drew ever nearer. And as to what it might bring, Eliza decreed that they should try not to even think about it. Because planning had never paid in the past, nor meddling, either.
It was on the afternoon of the third day that the telephone call came. Roger and Ann's mother answered it, and after the first few words she turned perfectly white. "Yes," she said. "Yes. Of course." Something about the way she said it made everybody in the room stop talking in mid-word and look at her. Then she hung up.
Aunt Katharine went to her quickly and they left the room together, and could be heard murmuring in low voices in the hall. The four children sat in silence in the living room, where they'd all been playing rummy when the call came, and Ann and Roger remembered other low voices that had gone on and on, that day back at home, and they were worried.
And then Aunt Katharine came back in and told them that it had been the hospital calling, and that the doctors had decided their father had to have an operation right away, today.
"Your mother's going straight out there now," she said. "I'm going with her." And she went to the phone to see about getting a room at the hospital where she and the children's mother could stay tonight till the worry was over.
Roger and Ann went upstairs to find their mother. The three of them didn't talk very much, but each one knew how the other two felt, and Roger and Ann were quiet and helpful about such things as packing their mother's bag for her and remembering what she ought to put in.
Their mother didn't even say good-bye, just kissed them both hard. And then she was gone. And pretty soon Jack and Eliza came upstairs, and the four of them drifted into Roger's room and sat, and nobody said anything much, but you could tell that Jack and Eliza were feeling friendly and sympathetic and wondering what they could do to help, and yet there didn't seem to be anything.
After a while Eliza got red and stared at the floor and said, "Look. Does the magic _have_ to happen tonight? Maybe you'd rather it didn't. Maybe it could be indefinitely postponed."
"No," said Roger, unhappily. "Even if it could, it can't," he went on, not very clearly.
"Don't worry about us," said Jack quickly. "We'll understand."
"Sure," said Eliza. "Maybe I could have my adventure next week. Maybe we can fix it with the Old One."
"No, don't do that!" said Roger. "It's _got_ to be tonight!"
"Why?" said Eliza.
But Roger looked so desperate that Jack gave his sister a surreptitious kick, and she did not repeat her question. Instead she asked if Roger and Ann would like to take a walk, but Roger said he thought they ought to stay, in case there were a message. And guessing that maybe they wanted to be alone, Eliza and Jack went away.
And when they'd gone, Roger told Ann a thing he'd been keeping to himself all this time. He told her about the wish he'd made that their father would get well in Baltimore, Maryland.
"And the Old One said wishes have to be earned," he told her anxiously. "And you see I _haven't_ earned it, and this is my last chance. This is a warning."
Ann's eyes grew solemn. "Let's talk to him," she said. And she went and found the Old One and held him in her hands and stroked him lovingly, and after a while he rather reluctantly warmed up and began to speak.
"Ods fish," he said. "Degenerate times, generation of vipers, posterity is just around the corner and welcome to it! Canst thou not decide a single thing for thyself any more? Have courage and steadfast hearts gone down the drain, pardie?"
"It isn't that," said Ann. "We try. And we mean well, but something always happens."
"Ah yes," said the Old One. "Good intentions. Forsooth we all know what road paveth itself with _them!_ On the other hand, if at first thou succeedeth not, try subsequently. And never forget the good old rule that magic goeth by threes."
"Can't you tell us any more, sir?" said Roger. "We _know_ that."
The Old One gave him rather a sharp look. "Dost thou?" he said. "Art thou sure?" Then his eyes grew dreamy and his voice seemed to come from farther away. "Meseemeth I remember an ancient rune for just such cases as thine," he murmured. "How didst it run? Ah yes." And he recited slowly:
> _"Sword from stone the hero taketh—_
>
> _Then the snowbound sleepers waketh!_
>
> _Wisdom then the hero learneth!_
>
> _Wishes then the hero earneth!"_
And after that he wouldn't say another word, and he grew cold and heavy as lead (which he was) in Ann's hand.
"What did all that mean?" said Roger, as Ann put the Old One back in the castle. "Swords in the stone? That's the wrong story."
"And snowbound sleepers," said Ann, "only there aren't any. We didn't put any snow in. Did we?" But she wrote the ancient rune down in her notebook, anyway.
It was a few minutes after that that the phone rang. It was their mother. She said the operation was over and everything was fine so far. Roger sent a silent look of gratitude in the direction of the castle and the Old One. So far, so good.
And then Jack and Eliza came in from their walk, and Roger and Ann showed them the ancient rune, and they couldn't figure it out, either, though they all tried till dinnertime and all through dinner and after dinner, and Jack even consulted his book on secret codes, to no avail.
"Maybe there's more in it than meets the eye," said Eliza. "Maybe it doesn't mean what it says. Maybe it's kind of symbolic. Maybe it's something else we're supposed to quest for. Something that looks like a sword or a stone."
"What looks like a stone besides a stone?" said Ann.
Nobody knew. And then all of a sudden the hours, which usually moved on laggard feet on magic nights, decided to cooperate for once, and it was bedtime.
Roger stayed awake for a while after the others, in case the telephone should ring again, but it didn't. All was still, save for the breathing of Jack on his couch. The gentle rhythm lulled Roger, and soon he knew no more. And soon after that the magic began.
The four cousins met on the usual greensward. Four pairs of eyes shone with eagerness and four hearts beat faster with the excitement of the quest. Where to begin was the question of the hour.
"I remembered one thing," said Ann. "I know where the red velvet train went, and part of the fur coat, too. Cedric the Saxon's got them on."
"And he's way over in Sherwood Forest," said Roger, "and the other things are in the castle, mostly."
"We'll have to separate," said Jack.
"Who'll go where?" said Ann.
"You and Jack take the castle," said Eliza, assuming command. "I'll go with Roger. Then each fair lady will have a champion to save her from worse than death, whatever that is."
"Are you nervous?" said Ann to Roger, privately.
"Yes," he admitted.
"I know," said Ann.
"So much depends on it," said Roger.
"Yes," said Ann.
"What depends on what?" said Eliza, coming up to them.
"Why, the quest depends on us," said Roger. But that wasn't what he was thinking of.
And now all clasped hands in a solemn good-bye. "Good luck," Roger said. "Watch out for Normans." And he and Eliza turned toward Sherwood.
Ann and Jack watched them out of sight; then they set off for Torquilstone.
As they drew near the castle and passed through the park with the statue of St. George Peabody, the rose trees pinkly perfumed the air.
"There's something we can start with," said Ann. "The roses from the quilt." She checked off an item on the list in her notebook, and they both started picking.
"Did you plant this many?" Jack asked after a while.
"I don't see how we could have," said Ann, wearily.
"They must have spread." They went on picking. Then suddenly a hand seized Ann by the shoulder. She turned in its grasp. A guard stood eyeing them sternly. He wore a peculiar uniform Ann had never seen before.
"Picking flowers in public parks is forbidden by the Leader," he said. "Punishable by twenty years' imprisonment. You are under arrest."
"But I put them there in the first place!" cried Ann. "I am the mighty sorceress!"
"Magic," said the guard, even more sternly, "is _specially_ forbidden by the Leader. Punishable by burning at the stake, at _least._ Guards, ho!"
But before more guards could appear, Jack grabbed Ann's hand. "Come on," he said, and clutching their armfuls of roses to them, they ran. The guard gave chase, but they dodged among the shrubbery and lost him.
"What do you suppose has happened?" Ann whispered pantingly as they ran. "Who's this Leader?"
"I don't know," Jack whispered back. "Something terrible must have gone wrong."
"After we were so careful, too," said Ann. "You'd think that magic did it on purpose!" And after that she saved her breath for running.
The park was left behind now, and they were on unfamiliar ground. Then, just as Ann reached her last gasp, they saw a sort of great high-ceilinged building ahead, with black iron hangings pushed back at the sides, and they knew where they were.
Jack pulled Ann to a stop. "Lurk!" he whispered. "Maybe we can find out what's up." And they crept toward the curtained chamber, lurked behind the nearest drapery, and peered through its iron folds.
Prince John stood in the middle of the room, surrounded by more oddly-uniformed guards. He wore a peculiar-looking cap on his head, and he was in a fury.
"Answer me!" he was shouting. "Who hath stolen my throne?"
"We know not, oh Leader," said a guard, raising his arm in a peculiar salute.
"Then find out!" snapped Prince John. "What was the use of my seizing the throne in the first place if ye let the first Tom, Dick or Harry who cometh along steal it the moment my back be turned?"
Ann and Jack looked at each other. Now they knew who was Leader in England, and why England was no longer merry.
Then Jack thought of his camera. This was too good a shot to miss. He reached for it, took careful focus, and Ann heard him snap the shutter. Unfortunately Prince John heard him, too.
"A spy!" he cried. "Seize him!"
Rough hands grasped Jack and dragged him from his hiding place. Other hands seized Ann and dragged her after Jack. And at that very moment the guard who had tried to arrest them in the rose garden came puffing up behind them, just to make things worse.
"Hold them!" he cried. "They be both of them mighty sorcerers. The small one hath confessed it."
"Mayhap 'tis they who hath stolen the throne," suggested a guard.
"Their garb is strange, like to that of Roger," whispered another.
"Silence!" cried Prince John. "Hath not thy Leader forbidden that name to be mentioned? There is no Roger." He glared at Ann and Jack and saw the camera. "What be yon devil's instrument?"
"It isn't," said Jack. "It's a camera. I just took your picture. And there is too a Roger. He's my cousin."
"What a camera may be," said Prince John, "I neither know nor care. But making pictures behind this iron curtain"—and he pointed to the draperies—"is punishable by death. So is believing in Roger, let alone being related to him. To the dungeon with them. They shall be burnt at sunrise."
And Ann and Jack were dragged away.
"How did it happen? Where did all these terrible new ideas come from?" Ann said to Jack as they were hustled along. " _We_ certainly didn't put them in!"
"Maybe they just sort of leaked in from the outside world," said Jack. "Goodness knows there's enough of them around!"
The dungeon, when they got to it, proved to be so full already that they could hardly squeeze in.
"No wonder," said Jack, "with practically all the pleasures of life forbidden now!"
"Exactly," said the nearest prisoner. "I could not agree with thee more!"
Ann recognized him right away. It was the Norman knight, Maurice De Bracy. "What are _you_ doing in jail?" she asked. "I thought Prince John was a friend of yours!"
"No longer," said De Bracy, grimly. "Now he calleth himself Leader, he is no man's friend. He hath become the worst tyrant in history. Some of us fellows finally got up a little petition against him."
"Sure," said Jack. "I know. The Magna Charta."
"Why, yes. How didst thou guess? 'Twas no use, though. He found out about it and clapped us all in jail. We are waiting now, to be burnt at sunrise."
"Why, so are we!" said Ann.
"Practically everybody is," said De Bracy, gloomily.
"Where's Rowena?" Ann wondered. "You seemed to be awfully good friends the last time I saw you."
The Norman's face darkened. "Never speak that name," he said. "'Twas she who betrayed me. She maketh her great eyes at the Leader now. She hopeth to be Leaderess. When the guards arrested me, she laughed."
"I'm not a bit surprised," said Ann. "She never was good enough even for you, let alone Ivanhoe. I always kind of liked you. For a villain, you weren't bad at all."
"Thanks," said De Bracy, blushing modestly. "Then perhaps in that case thou wouldst not mind rescuing me and my comrades? I have heard tell that thou art a mighty sorceress."
"Oh," said Ann, blushing now in her turn. "Well, about that." Then she broke off, staring at his luxurious curling blond whiskers. She had almost forgotten about the quest. Now she remembered. "All right," she said. "But first there's just one thing."
"Anything, anything," said De Bracy.
"First," said Ann, "I'll have to cut off your beard."
"What?" The Norman's hand flew up to cover his beautiful whiskers protectively. He stood glaring at her in mistrust.
"I need it," said Ann, "for my mighty sorcery. Besides, it will soon grow out again," she added, feeling sorry for his knightly dignity.
"Well," said De Bracy reluctantly, offering her his sword, "see that thou cuttest clean and pullest not the short hairs." And he laid his head trustfully down on the stone windowsill.
One clean sweep, and the beard was in Ann's hands. She put it carefully with the roses, and checked off another item in her notebook. For the beard was what she had made of the small giant's side-curls one day when she decided De Bracy's face needed an extra touch. Now if she could just remember about the coattails.
"Well?" said De Bracy, when a minute had gone by and nothing had happened. "When doth the mighty sorcery begin?"
"Wait," said Ann, playing for time. "I can't do it all alone. I have to wait for Roger and the witch."
Another minute passed.
"When will they be coming?" said De Bracy.
"Pretty soon," said Ann. "I hope."
"Where are they now?" said De Bracy.
Ann couldn't keep up the pretense any longer. Her lip trembled. "I wish I knew," she said.
While all this was happening, Roger and Eliza were steadily trudging over the plain toward the forest. When they came to the shrubbery at the edge of the wood, Eliza stopped and picked a few leaves.
"Here," she said, handing them to Roger. "The giants' bath mat."
And they were in Sherwood itself. But the mighty forest seemed different today. No birds sang in its trees, no deer galloped gaily down its corridors. Even Eliza's bright conversation dwindled. Suddenly she grabbed Roger's arm. "Chiggers!" she said.
Roger stopped short. Someone was watching them, from behind a tree just ahead. It was a man in Lincoln green, but his jerkin was frayed and worn and his hose had holes in the knees. He had a bow in his hand, but he seemed to lack the strength to use it. He was staring at them with cold, unfriendly eyes that burned in a face so thin and worn that they didn't recognize him at first. Then they did, and ran to him with joyful cries of "Robin!"
But Robin Hood made an effort and raised his bow threateningly. "Stop where ye are, false prophets!" he cried. "Ye have tricked us with lies and led us astray that the vile Prince—I will not call him Leader for he certainly leadeth not _me_ —might pillage our noble greenwood and rob us of our livelihood!"
"No we didn't. Honest," said Roger.
"We were unavoidably detained," said Eliza.
"We couldn't help it. It was magic. It does that sometimes," said Roger.
At last Robin Hood was convinced. "Then thank Heaven ye have returned," he said. "It hath been horrible."
And he raised his horn and blew a faint but cheered-up blast, and the rest of the outlaws came out of their woodsy hiding, but so changed and weary that Roger would not have known them, and with many missing from their ranks.
Then as they sat on the ground, Robin told Roger and Eliza what De Bracy had told Ann, all about how Prince John was Leader now. And he told them how Prince John had rounded up all the deer in the forest for a collective farming experiment, so that the merry men were reduced to living on berries and tree bark. And how afterwards when they were weakened he had hunted them down with his terrible new army.
Many had been wounded and many more had deserted and fled. But the best men of the band were still loyally hoping for Roger and Ivanhoe to return and lead them to crush Prince John forever.
"Had I my trusty sword by me I shouldst have done it long ago," said the Black Knight. "Where is it?"
"Goodness," said Roger. "It must be in the Giants' Lair, still!" And he and Eliza told them about their adventure with the giants (leaving out the parts that were too magic for them to understand).
"And the mighty Jack?" said Robin Hood, "and the small sorceress?"
Eliza told about their quest, and how Ann and Jack must be somewhere in Torquilstone Castle this very minute.
"Then woe betide them!" cried Maid Marian. "The Prince hath taken it, and is burning folk at sunrise right and left!"
At this, Roger wanted to turn back and rescue Ann right away, but the others dissuaded him. "They've probably found everything and got away by this time," said Eliza. "They're probably on their way here right now. They'll probably be turning up any minute."
"Besides," said Robin Hood, "my men are in no condition to attack." So it was decided that Robin and the Black Knight should ride with Roger and Eliza to the Giants' Lair, while the others rested and consumed what rations they had, in preparation for battle.
"I hate to do this," said Eliza, after she had explained to Cedric the Saxon about needing his cloak for the quest. "Won't you be cold?"
"If 'twill aid my son," said Cedric, "what matter if back and side go bare?" And Friar Tuck said he'd lend him his extra habit, anyway.
The journey to the Lair passed quickly, and Robin and the Black Knight waited at the edge of the wood while Roger and Eliza hurried across the giants' lawn. And the door stood open for Eliza, and the three smiling giants appeared in it.
They were more civil than they had been before, and thanked the children for the return of the furniture. The mother giant was a bit sniffy about the worn condition of Cedric's cloak, but when she put the velvet next to her gown it attached itself and suddenly looked as good as new. And the bits of fur grew back into the fur coat beautifully.
The bath mat, alas, was never quite the same, and looked more like a group of leaves than a bath mat for the rest of its life, but the female giant actually smiled and said she liked it better that way. "Quite artistic."
Eliza then asked to see the prisoners, and sure enough, Ivanhoe still had his bandage on under his armor, and though it now made rather a mussy pair of kitchen curtains, the giant family agreed that it would be quite a souvenir.
As for the rest of the things, Roger explained that his sister was bringing those, but had been delayed. "Couldn't you trust us?" he asked. "Couldn't you let our friends go now, sort of on credit?" And Eliza joined her voice to his, assuring the giants that they would have their other belongings back soon.
"Why not?" said the mother giant. "I have heard of getting things on the installment plan, and this must be what it means."
"Well," said the father giant, "I pride myself on being a fair giant. Two may leave, but one must stay as hostage."
"Allow me," said Bois-Guilbert, nobly. "Let the best man win. The extra wait will give me more time to repent, anyway."
"Thanks a lot, old man," said Roger, before Ivanhoe could start being self-sacrificing, too. "That's darn nice of you."
And he and Eliza grabbed Ivanhoe and Rebecca and ran out of the house and across the lawn with them, to where Robin Hood and the Black Knight waited. And the giant let them take the Black Knight's sword with them, just to show what a fair giant he really was.
Once the Black Knight found its hilt in his hand again he declared himself ready to tame a thousand Saracens, let alone one measly Leader, who was only his little brother, anyway! And Robin Hood started looking less thin and worn, already.
When they reached the clearing all was excitement, as the outlaws prepared horses and weapons for the coming battle. Roger noticed a silver-bearded figure busying itself in the thick of the activity. He thought he knew who the silver-bearded one was, but every time he tried to get near him to make sure, the bearded one was suddenly somewhere else.
But each place he had been, the horses suddenly looked sturdier and the weapons sharper and keener and the merry men stronger and merrier, till at last, when Robin wound his horn in the signal for departure, it was a lusty and mettlesome battalion that set out for Torquilstone. No one would have known them for the starving outcasts they had been a few hours before.
Eliza rode by the side of Roger. "Don't look now," she said, after a few minutes, "but hark behind you."
Roger harked. "Father," Ivanhoe was saying to Cedric the Saxon, "this may make thee very angry, but my troth is plighted to Rebecca. I can never marry the Lady Rowena now."
"Son," said Cedric, "it doth not make me angry one whit. Thy Rebecca is a maid of courage and honor, and bonny besides. As for the Lady Rowena, she hath proved herself a false jade. I say down with her."
"So _that's_ all right," said Eliza.
Yes, thought Roger to himself, things were looking up. Hope sang high in his heart as he galloped toward Torquilstone.
Meanwhile, in the dungeon, Maurice De Bracy was getting restless. "Really!" he said to Ann, crossly. "Half the day hath passed now, and no sorcery!"
"I know," said Ann, unhappily. "I'm sorry."
"So far as I can see, cutting off my beard hath not done one speck of good. Canst thou not at least put it back on again?"
"No," said Ann. "I can't."
"Humph!" said De Bracy. "Thy magic seemeth pretty small pumpkins to me."
Jack was standing by one of the barred windows, looking out. "That's what _you_ think," he said, suddenly.
There was a confused noise from outside, and a sound of running feet. Then voices began to shout, and their words sent a thrill through each prisoner's heart. "To arms!" said the voices. "The enemy is attacking!"
Jack grinned at Ann. "You see?" he said to De Bracy triumphantly.
De Bracy went down on one knee before Ann. "I take it back," he said. "Hail, mighty sorceress!"
"Don't mention it," said Ann.
At that moment bolts were shot back, keys turned in locks, and the great dungeon door swung wide. A man appeared in the doorway. He wore a silver beard, and if Roger had seen him, he'd have wondered how he got here so quickly from Robin Hood's camp.
The bearded one said nothing, and nothing needed to be said. With one accord the prisoners streamed out of the dungeon to freedom, and as they passed, the bearded one handed each a weapon from a seemingly endless store he had with him. Ann and Jack came last.
"Hello," said Ann. "You're awfully helpful all of a sudden. Does that mean it's a good sign?"
The Old One said nothing, but he winked at Ann before he disappeared.
"Come on!" said Jack. And he and Ann raced out of the dungeon. Then they flattened themselves against the side of the building just in time. For Prince John himself appeared right in front of them, riding by at the head of his army.
"Follow your Leader!" he was shouting as he rode past. "We are twice their strength and have better weapons besides! Wait till we have them in our power! _Then_ heads will roll!"
He and his army dashed out the castle gates, and Ann turned to Jack. "Let's get somewhere where we can see!"
Of course Jack yearned to be in the battle, but he didn't think he should leave Ann unprotected. "Let's try the roof," he said. "Maybe we can help from there." So they ran through the courtyard and up the stairway to the battlements.
The varlet Hugo was already there, tending some cauldrons of molten lead, as usual. Jack took him by surprise and threw him over the edge, and his molten lead after him. Then he dusted his hands and turned to photographing the scene below.
Ann looked and caught her breath. The armies were spread out beneath, like a bright-colored moving tapestry. Trumpets sounded, and flights of arrows soared like fireworks. Then the front lines crashed together, like two great waves meeting in a storm. And Prince John's men _were_ stronger, and the line of Lincoln green wavered and fell back, and Ann shut her eyes.
But Prince John had reckoned without De Bracy and the other escaped prisoners, who now came charging onto the field and attacked him from the rear. Caught between two fires, the Prince's men hesitated, and in the pause Robin's forces rallied and came at them with renewed vigor.
When Ann cautiously opened her eyes and looked again, the two armies were tangled in a free-for-all, and none could say who was winning, but anyone could see Prince John was hard pressed.
And now the tide of battle swung nearer the castle, and Ann and Jack gasped. There, riding the crest of it, was Eliza. She had borrowed a helmet and shield from somebody, and was laughing and whacking about her like some wild battle goddess, her boastful cries ringing on the air.
And there, just behind Eliza, Ann saw Roger. He wasn't laughing but he was fighting just as hard. The next minute another turn of the tide swept them both out of sight.
But now Prince John seemed to feel that enough was enough. He and his men turned tail and cut their way back through De Bracy's followers till they gained the castle. Ann and Jack were afraid they might try to defend it, and find them on the roof, but the Prince and his men merely packed up their goods and chattels, and did a few other things, before escaping by a back door, just as the triumphant merry men rode up to the front one, to claim Torquilstone for Richard Lionheart.
And Ann and Jack went running down from the parapet to be the first to offer their congratulations.
"Oh, good, you're still alive," said Eliza, galloping up beside Roger, as the victorious army surged toward the castle. "I cut off four heads and cleaved three knights in two. How did you do?"
"All right, I guess," said Roger. Actually he had fought with valor and joined in several quite good deadly combats. But battles, he decided, were more fun when they were pretend ones than when they were real, even magically real. He had seen his duty and he had done it, but he didn't want to talk about it.
There was a slight delay at Torquilstone, for Prince John had left the drawbridge up. But Robin Hood gallantly swam the moat and forced his way into the guardtower and let down the bridge.
And at that moment the portcullis went up, and Ann and Jack appeared in the opening.
"Hi," said Jack to Robin Hood. "Come on in. The battle was fine."
And the gallant army trooped over the bridge, and the four cousins were reunited, and the voice of Eliza rang loud on the courtyard air, as she boasted of her prowess upon the field.
In the castle keep Rowena came smiling up to them, carrying a banner she had hastily embroidered that said, "Victory!" She tried to fling herself into Ivanhoe's arms, but Rebecca was already there, and repulsed her. So then she came swarming up to Robin Hood and Roger, but to no avail. She was roundly snubbed by everybody.
"Traitress," said King Richard, "we have heard of thy faithless dealings. Thou art under arrest. Away with her."
Rowena was hustled away to the dungeon.
"And now," said King Richard, "what say ye all to a feast to celebrate our victory and refresh our war-weary limbs?" And all the weary warriors cheered.
"Only no roast venison, please," said Eliza.
"Is this the happy ending?" Ann whispered to Roger, as several dozen minions scurried away to the kitchen. "Have you earned the wish already, do you suppose?"
"It seems as if," said Roger, "but I don't see how it can be. I haven't done a thing yet, really. And what about the ancient rune?"
"That's right," said Ann. "I forgot."
"I didn't," said Roger. "I've been thinking about it all the time."
"Let's think some more," said Ann. And she got her notebook out and studied it.
Maurice De Bracy, who had been looking unhappy ever since Rowena was hustled away, now stepped forward and started to kneel before the king and say something. But before he could, there was an interruption.
The minions who had been sent to prepare the feast came running back into the room, all talking at once and wringing their hands and saying, "Wurra wurra." When King Richard finally got sense out of them, it turned out that before Prince John's men left the castle, they had thrown away or poisoned every bit of food in the kitchens, and there wasn't a smidgin left to have a small meal with, let alone a feast.
And just as this blow was sinking in, Little John, who had been left in charge of the guard at the gates, came hurrying in with a face of doom. "'Tis that Prince John," he cried. "He be back with more army than before! He hath surrounded us! The park and the castle we still hold, but that be all!"
Everyone went running to look. It was true. Beyond the park and all around the castle on every side stretched a ring of armed men.
"'Tis a blockade! He meaneth to starve us out!" cried Robin Hood.
"You see?" said Roger to Ann.
"What a scurvy trick! If that be not just like him!" said King Richard. "But he hath not won the game yet! Robin, call your men. Ivanhoe, follow me! We shall carve our way out!"
"My men couldn't stand it," said Robin Hood. "Not on an empty stomach. I couldn't, either."
"Nor I," said Ivanhoe. "And speak not of carving, for thou makest my mouth water."
"Hm," said King Richard. "Now that thou mentionest it, I feel very much the same." He turned to Roger. "Methinks there be only one among us who can help us now."
"Who, me?" said Roger.
King Richard nodded solemnly. "What is thy Elfish counsel? What shall we do?"
Roger gulped. He looked at King Richard and Robin Hood and Ivanhoe and they looked back at him with appeal in their eyes, and he didn't have a thought in his head.
"Wait a minute," he said. "Maybe I'll think of something."
Everybody waited.
Ann had heard all this, but only with part of her mind. The other part was still thinking about the ancient rune. Her eyes went from her notebook to the park with the statue of St. George Peabody, and back to her notebook again. And an idea started forming in her mind.
She thought of something, and then she thought of something else. And then she knew what she had to do. She supposed she ought to tell Roger and let _him_ do it, but he was busy just now.
The only thing was, she would have to go away for a little while to do it, and she didn't want her going to disturb any of the others. Maybe if she left quietly, no one would notice. Maybe she could even slip away alone and come back again without anyone's knowing she had been gone.
So, not using her voice at all, but just saying them in her mind, Ann thought two words. I leave you to imagine what words they were.
But it seemed that Words of Power are Words of Power whether you speak them out loud or not. For the mist came down and the castle disappeared, and the next minute Ann was back in Roger's room, and Eliza and Jack were standing glaring at her with expressions of utter exasperation.
"What in the world did you do that for?" said Jack.
"Just when it was getting interesting, too!" said Eliza.
Ann paid them no heed. "I worked it out! I worked out the ancient rune!" she cried, turning to tell Roger.
Then she broke off. Roger wasn't there.
8
# The Ending
_"Where is he?" said Ann,_ stupidly, gazing at where Roger should have been.
" _I_ don't know," said Jack, looking around the room. "I hardly know where I am myself, yet."
"We must have left him behind," said Eliza. "He must be back there in the magic, still."
"And now we'll have to wait three days before we find out," said Jack.
"Oh dear," Ann wailed. "I thought I could just get away and back by myself, but if you're here, too, then it's over, just like the other times. Only if that's true, why didn't he come along? He always got home all right before. Last time, and the Flying Saucer time, and that first time when we weren't with him!"
She broke off and her face paled, as a horrid possibility dawned. "Oh dear," she said. "Magic goeth by threes."
"You mean the words only work three times for each one, and now he's had his, and he's _stuck_ there?" said Eliza. " _Forever?_ "
Jack nodded solemnly. "It stands to reason."
A worse thought occurred to Eliza. "And now you've made me use my third time, and if we go back again to get him I'll be stuck, too, and so will you!"
Ann set her chin stubbornly. "Maybe we won't," she said. "Maybe now I know the rune it'll be all different."
"What rune?" said Eliza.
"The ancient rune," said Ann.
"You mean you've guessed it?" said Jack.
"Yes, but I haven't time to talk about it now," said Ann. "I have to do something."
She reached down and picked the Old One up, from the castle. "Oh Old One," she said, "you needn't answer, and don't bother warming up if it's any trouble, but please couldn't you not count this time and let us go back as soon as I've finished? I know what the rune means now. Wait and see."
She put the Old One back in the castle and ran out of the room. Her feet were heard clattering on the stairs.
"Where's she going?" said Jack. He and Eliza ran into the hall and hung over the stairwell.
From below came a sound of drawers opening and shutting, and a clatter of cutlery.
"She's in the kitchen," said Jack. "What's she doing?"
"She's crazy," said Eliza. "It's all been too much for her and her mind's given way."
Ann came running back up the stairs, an intent expression on her face and something in her hand. She hurried past Jack and Eliza without a word, and into Roger's room.
"What was that in her hand?" said Eliza.
"It looked like a can-opener," said Jack.
"It couldn't be," said Eliza.
They followed Ann into the room. Ann went over to the castle and did something. Then she went to Roger's bureau. There was a big tied-up box on top of the bureau, and she undid the string and opened the lid. So far as Jack and Eliza could see, there was nothing in the box but a lot of cotton.
"There," said Ann. "Now we can go. At least I hope we can." She looked over toward where the Old One was, in the castle. "Did I guess right? Can we go now? Please?"
"You mean you interrupted everything and spoiled it all just to come back and do _that?_ " said Jack.
"I told you," said Eliza. "The girl's balmy. Stark, raving daft!" But she was wrong.
And Ann paid her words no heed. "Look!" she said, pointing to the walls of the room.
Jack and Eliza looked where she pointed. There weren't any walls. And the gray mist came swirling, and it was just like the other times, only backwards, because the next moment they were standing in the park before Torquilstone Castle, and Ivanhoe and Rebecca and Robin Hood and King Richard and a whole crowd of others were standing there, too, and everybody was cheering.
The children looked to see what all the shouting was for. And then they knew.
Roger was staring at the floor, trying desperately to think of a way out, when he heard Ann utter the Words of Power.
For though Ann merely thought them, the words were so powerful that the sound of them rang and echoed through the room, and everyone heard.
And despair filled the heart of Roger.
This was the end. And now Ann had given up and deserted, and she was probably perfectly right to, and something told Roger this was his last chance, and he'd never earn his wish now.
He waited for the gray mist to carry him away, but it didn't. What he saw now was what Ivanhoe and Rebecca and Bois-Guilbert and the giants had seen on other occasions, and if Roger hadn't been beyond all caring, it would have been interesting to watch.
For a bright cloud descended and enveloped Ann and Jack and Eliza and sailed away with them, and left Roger standing right where he was.
And then he, too, remembered about magic going by threes, and he felt even worse. Not only had he failed, but he was lost here in this magic world forever! And he knew it was only what he deserved.
"Thy friends have gone," said King Richard, after a moment. "I presume thou hast sent them on some magic errand to save us?"
"No," said Roger, "I didn't. I wish I had. I would have if I could have thought of any."
"Can it be," said the king, "that they have fled?" And a frown of anger clouded his brow.
"I guess that's what they've done," said Roger, looking at his feet.
"But then surely we must despair," cried the king, paling, "if magic itself giveth us up as hopeless!"
"Yes," said Roger. "I guess you might as well. I'm sorry. It's all my fault."
"Dost mean that thou hast betrayed us on _purpose?_ " cried King Richard, outraged. "Is thy magic _black?_ "
"Not exactly," said Roger, "but it might as well be. I'm just plain no good at it. I don't have the touch. I thought I did, but I don't. And you don't know the worst part."
The worst part, of course, was about his father, but he couldn't talk about that. He could only think about it, and he did.
But it was then, in Roger's darkest hour, that help came.
Little John, who had gone to check with the guard, came running back in again.
"A miracle, sire!" he cried. "Help from the skies!"
More guards came running in after him, shouting. "The sword! The sword!" cried some. And others cried, "The statue!"
Everyone ran into the park. Sure enough, from the statue of St. George Peabody a great sword protruded. It hung at a peculiar angle, as though someone had stuck it in at the top, and then levered it down to one side.
"Behold," said Little John, "a great hand hath appeared from above, and placed it there!"
"Many have tried, but none can pull it forth," cried those who were nearest the statue, and had been trying.
"What can it mean?" everybody was saying.
But Roger had remembered the ancient rune, and he knew what it meant. At least he thought he did. And his heart gave a great leap.
And like the young King Arthur before him, he stepped up to the sword, and took it by the hilt, and it came away easily in his hands. He looked up, and there was the Old One, standing beside him smiling at him. And for the first time in all the magic adventures, the Old One spoke.
"Sword from stone the hero taketh," he said.
And then a great cheer went up from the whole multitude. For out of the cloven statue gushed a stream of rich liquid and a delicious aroma pervaded the air. And all the hungry people came with ramekins and pannikins and bowls, and drank from that fount of plenty. And a cloud of glory descended from the sky and brought Ann and Jack and Eliza with it, and Roger saw Ann smiling at him, and he realized what it was that she had done.
"Have some soup," he said, and Ann knew that in those words he was saying all the things that nobody can ever say, particularly when he is a boy talking to his little sister.
And she and Roger and Eliza and Jack agreed afterwards that it was the best pea soup they ever tasted.
It seemed to have other properties, too—added vitamins, maybe. For as its rich warmth coursed through their veins, all the knights and yeomen felt suddenly refreshed and strong again, and couldn't wait to fall upon the army of the dastard Prince.
"Follow me, Ivanhoe's men!" cried Wilfred, and Robin Hood blew his hunting horn, and all their loyal band gathered round them.
"Wait," called a voice. It was the Old One. He pointed. "The Snowbound Sleepers!"
Everyone looked.
Far in the distance whitely gleamed a snowcapped mountain nobody remembered ever having seen before. And all the people cried out, "More miracles!"
For strains of martial music were heard from the mountain, and down its side marched a company of such soldiers as the eyes of chivalry had never yet gazed upon.
"Wow!" said Jack. "The U.S. Marines to the rescue!"
"Well, sort of," said Ann, modestly.
As Eliza said later, it was like a Memorial Day parade. There were British grenadiers singing _The British Grenadiers,_ and modern G.I.'s singing _The Beer Barrel Polka,_ and 1918 doughboys singing _Over There!_ And last and most impressive of all, marched the Spanish War veterans. "Remember the Maine!" they cried. "Remember Teddy Roosevelt! Charge!"
And the men of Prince John gave way and scattered before them and they kept on marching straight up to the castle.
Roger looked at them with love and pride, and realized that only he knew the record and capabilities of each and every one of them, and only he was fitted to be their general. Brandishing the sword he had pulled from the stone, he took his place at their head, and Jack and Robin Hood and King Richard and Ivanhoe fell into line just behind him, and the merry men followed after.
But when they saw the whites of the enemy's eyes, and Roger waved his sword in the command to fire, and when the Prince's soldiers heard gun-powder for the first time, they fell on their knees holding their ears in craven surrender, and Prince John fled all by himself.
And they hunted him over hill, over dale, through bush and through brier, till in the end he took refuge in Sherwood Forest, which was foolish of him, because Robin Hood knew every tree and every inch of it, and they found the wretched Prince at last, cowering behind a bush, alone and miserable and Leader of nobody. And they marched him back a prisoner to Torquilstone.
His judgment was pronounced by King Richard that very day, in the castle keep. All were present. Prince John made a contemptible picture, as he sniveled in the prisoner's dock.
"Come, come," said King Richard. "Crying will get thee nowhere. Thou wert ever the same, e'en when we were boys together. Nothing but a pest!"
"To the block with him!" called somebody.
"Melt him down," called somebody else, "in his own molten lead!"
"Nay," said the king. "I cannot slay my own brother, richly though he deserve it. Go forth," he said to Prince John, "to lead a hermit's life alone in the wilderness, bereft of thy title, and let all men shun thee forever."
And Prince John slunk away.
"But won't he come back and make more trouble later?" whispered Ann, who was seated on the king's left. "Later on in history?"
King Richard shook his head. "History no longer hath meaning for us now. And what is even better, after this no more terrible ideas from the world outside can penetrate here. Time standeth still from now on, and the golden age of chivalry endureth forever, now that the hero"—and here he nodded at Roger, who was seated upon his right hand—"hath set us free."
Roger started to protest at this, but now Maurice De Bracy stepped forward and knelt before the king.
"Sire," he said, "I started to say this before, but there was an interruption. I have been thy enemy in the past, but I have repented. I crave pardon and shall do any penance thou wishest."
"De Bracy," said Richard, "thou wert ever an honorable foe, and thou hast fought valiantly in the recent battles. I pardon thee."
"I crave another boon," said De Bracy. "If it please thee, set free the Lady Rowena, who now languisheth in durance vile. Traitress or not, I love her and would have her for my bride."
"Oh, very well," said King Richard, "though sooner you than me. Take her far from here and let living with her be thy penance."
And Rowena was brought from the dungeon and fell into De Bracy's arms. So _that_ was all right.
There was still the quest unfinished, but Ivanhoe and Rebecca volunteered to stop off and deliver the final installment at the Giants' Lair, on their wedding journey. And at last Ann remembered what she had done with the father giant's coattails.
She hadn't done anything with them. She had cut them off, and then forgotten about them, and put them down somewhere. They finally turned up in the scullery, where the kitchenmaid had cut them up for dishcloths. King Richard had them laundered, and Rebecca tied them up in a neat package with De Bracy's beard and the roses, which were sadly wilted by now.
And then the four children said a fond good-bye to Ivanhoe and Rebecca, who were anxious to depart on their honeymoon.
"Now we'll never know what finally became of Bois-Guilbert," said Ann.
"He's probably so reformed by now he probably won't be fit for normal life," said Eliza. "He'll probably go enter a monastery." And I believe that is probably exactly what he did.
Roger was getting anxious to depart now, too, for something told him it was time. But King Richard said he couldn't possibly leave till he and Robin Hood gave a banquet in his honor. And in spite of all that Roger could, and did, say, they gave it for him that night.
And after the banquet everyone drank to Roger, and then came a cry of "Speech! Speech!" from the whole company, and Roger stood up and faced them all.
"Thanks a lot," he said, "and I just want to say I don't deserve any of it. I haven't been a hero a bit. The first time I came there wouldn't have been any trouble if I hadn't started it by talking too much. And the next two times I wasn't a speck of help to hardly anybody. And this last time there wouldn't have been any sword in the stone, or any army for me to be general of, if Ann hadn't worked out the secret rune when I couldn't, and she did just about the whole thing, and if there's any toasts going to be drunk, they ought to be to her. And I drink to her now."
And he drained his glass, and then smashed it on the stone floor, and sat down and blushed and didn't look at anybody, though Ann was looking at him and smiling for all she was worth.
But to his surprise the cheers now were louder than they had been before, and Robin Hood cried that that was the most heroic speech he ever did hear, pardie! And the Old One came all the way around the table and shook Roger's hand.
"Wisdom now the hero learneth," he said.
Roger looked at him. "You mean?"
"Wait," said the Old One. And he turned to the others. "Three cheers for Roger," he cried, "and may his name live forever, for the way he hath led soldiers!"
"He led soldiers! Led soldiers! Led soldiers!" cheered the whole company, and these were the most beautiful Words of Power (or of anything else) that Roger had ever heard in his life.
And the gray mist came down for the last time, and wafted the four children away in its soft nothingness, and the next Roger knew he was lying in bed and it was a bright morning of sun and blue sky, and his mother was standing over him with such a smile on her face that Roger knew he must have earned his wish at last, and it had come true.
Later that day he learned how his father had come through better than anyone had expected, and he was going to be fine. In fact, he was going to be better so soon that he could leave the hospital in just a little while now, and they were going to spend the rest of the summer on an island in a lake in the mountains on the boundary between New England and Canada, because that was the nearest they could get to the four different vacations the family had wanted.
"Though after the magic," said Eliza, when the four children were alone, "even the desertest island would seem paltry."
"I don't know," said Roger. "I'll be kind of glad to get back to normal. Not that it wasn't wonderful," he added quickly. "At least most of it was."
"And now we'll never see them again," said Jack. "I'm going to miss that Robin Hood. Those were the days."
"We can still play with them," said Ann. "I think they'll kind of _know._ "
"I never did get my special adventure," said Eliza. "It turned out to be somebody else's every time."
"Maybe that was on purpose," said Jack, grinning at her. "Maybe that was just to teach you."
Eliza looked surprised. Then slowly a smile spread over her face. "Well, for Heaven's sake," she said. "If that wouldn't be just like that magic's impudence! Trying to teach _me_ moral lessons! Maybe you're right, though," she added, seriously. Maybe that's why it came into our lives, to make noble characters of us. I learned not to be bossy, and Ann learned to be brave and think for herself."
"And I learned there ackcherly is magic," said Jack.
"And I learned wisdom," said Roger, looking so smug and holy that Jack and Eliza fell on him and held him down and sat on him while Ann tickled his feet till he admitted that maybe he did have a _little_ more to learn, still.
"I wish I could give you a picture to remember it all by," said Jack, when peace reigned again. "I had a keen one of you leading the army, but it didn't come out. None of them did."
"I didn't think they would, somehow," said Ann.
"I wonder if we'll ever have another summer together," said Roger.
"I wonder if it'll be a magic one," said Jack.
"Wottest thou not that all magic goeth by threes?" said Eliza. "Maybe we'll have two more!"
"Time will tell," said Ann. And it did.
1
## The Lake
_It was Martha who saw the lake_ first. It was Katharine who noticed the sign on the cottage, and it was Mark who caught the turtle, and it was Jane who made the wish. But it was Martha who saw the lake first. The others didn't see it until at least ten seconds later. Or, as Katharine put it, at long last when all hope was despaired of, the weary, wayworn wanderers staggered into sight of the briny deep.
This, while poetic, was not a true picture of the case. They really weren't so wayworn as all that; the lake was only fifty miles from home. But cars didn't go so fast thirty years ago as they do today; so they had started that morning, their mother and Martha and Mr. Smith their new stepfather in front, and Jane and Mark and Katharine and the luggage in the tonneau, which is what people called the back seat in those days, and Carrie the cat wandering from shoulder to shoulder and lap to lap as the whim occurred to her.
At first spirits were high, and the air rang with popular song, for this was going to be the four children's first country vacation since they could remember. But two hours in a model-T Ford with those you love best _and_ their luggage is enough to try the patience of a saint, and the four children, while bright and often quite agreeable, were not saints. It was toward the end of the second hour that the real crossness set in.
"That lake," said Jane, "had better be good when we finally get to it. If ever."
"Are you sure we're on the right road?" said Mark. "That crossroad back there looked better."
"I want to get out," said Martha.
"You can't," said their mother. "Once you start that, all pleasure is doomed."
"Then I want to get in back," said Martha.
"Don't let her," said Katharine. "She'll wiggle, and it's bad enough back here already. Sardines would be putting it mildly."
"Just cause I'm the youngest, I never get to do anything," said Martha.
"That's right, whine," said Katharine.
"Children," said their mother.
"I," said Mr. Smith, "suggest we stop and have lunch."
So they did, and it was a town called Angola, which interested Mark because it was named after one of the countries in his stamp album, but it turned out not to be very romantic, just red brick buildings and a drugstore that specialized in hairnets and rubber bathing caps and Allen's Wild Cherry Extract. Half an hour later, replete with sandwiches and tasting of wild cherry, the four children were on the open road again.
Only now it was a different road, one that kept changing as it went along.
First it was loose crushed stone that slithered and banged pleasingly underwheel. Then it gave up all pretense of paving and became just red clay that got narrower and narrower and went up and down hill. There was no room to pass, and they had to back down most of the fourth hill and nearly into a ditch to let a car go by that was heading the other way. This was interestingly perilous, and Katharine and Martha shrieked in delighted terror.
The people in the other car had luggage with them, and the four children felt sorry for them, going back to cities and sameness when their own vacation was just beginning. But they forgot the people as they faced the fifth hill.
The fifth hill was higher and steeper than any of the others; as they came toward it the road seemed to go straight up in the air. And halfway up it the car balked, even though Mr. Smith used his lowest gear, and hung straining and groaning and motionless like a live and complaining thing.
"Children, get out," said their mother. So they did.
And relieved of their cloying weight, the car leaped forward and mounted to the brow of the hill, and the four children had to run up the hill after it. That is, Jane and Mark and Katharine did.
Martha was too little to run up the hill. She walked. And nobody gave her a helping hand or waited for her to catch up, and she felt deserted and disconsolate, and the backs of her knees ached. When she arrived at the top, the others were already in the car and urging her on with impatient cries. But she didn't get in the car. She threw herself down among the black-eyed Susans at the side of the road to get her breath. She glanced around. Then she jumped up again.
"Look!" she cried, pointing.
The others looked. Below them and to one side was the lake. They could see only part of it, because land and trees got in the way, but the water lay blue and cool, and there were cattails and water lilies, and from somewhere in the distance came the put-put of a motorboat.
Then Jane and Mark and Katharine started to get back out of the car, and they all clamored to go running right down to the lake now, and take their bathing suits and jump into it.
Mr. Smith had a lenient look in his eye, and their mother must have seen this, for she became firm.
"All in good time," she said. "First things first. Wait till we get to the cottage and unpack."
So Martha climbed back in the car, not feeling out of breath at all anymore, and they drove on till they came to a gate. Mark jumped out and opened the gate, and closed it after them, and then they drove over a rolling pasture, and there were sheep staring stupidly and a few rams looking baleful, and then another gate, and beyond it a grove of trees, and in the grove was the cottage.
And of course before there could be any base thought of unloading the car, the four children had to explore every inch of the cottage and the grounds around it, only not going near the water, because their mother's word was law and they kept to the letter of it. But they could see the lake from every window and between the silver birches that picturesquely screened the front.
And naturally there was a hammock slung between two of the birches, and better still there was a screened porch with cots on it that ran around three sides of the cottage, and that was where the children would sleep. And there were three little rooms with more cots in them downstairs and another cot in the corner of the living room, for rainy nights, only of course there wouldn't be many of those.
There was a big kitchen, and a big room upstairs for their mother and Mr. Smith, and that was all of the cottage.
"I'm sorry it isn't any better," they heard Mr. Smith saying to their mother. "It was the best I could do so late in the season."
The four children couldn't imagine what he meant. So far as they could see, the cottage was all that was ideal.
Next came a horrid interval of unloading and unpacking, but few would wish to hear about that. Suffice it to say that at last the four children emerged in their new bathing suits, and the lake was waiting.
Mark and Katharine were the first to emerge from the cottage. As they waited impatiently for the others, Katharine noticed a sign by the front door. It was of rustic letters made from pieces of tree branch, and they hadn't seen it before because it was the same color as the cottage's brown shingles. "Magic by the Lake," it said.
Katharine looked at Mark, a wild guess in her eyes. "Do you suppose?" For the four children had had experience of magic, or at least a kind of half magic, in the past.
(After the half magic was over, they wondered if they'd ever have any magic adventures again, and in the book about it it says it was a long time before they knew the answer. And here it was only three weeks later, and already Katharine was ready for more. But if you think three weeks isn't a long time for four children to be without magic, I can only say that it seemed a long time to _them._ )
"Could it be going to start again already?" Katharine went on.
Mark shook his head. "Nah," he said. "It's too soon. We couldn't be _that_ lucky. That's just one of those goofy names people give things. You know, like 'Dreamicot' and 'Wishcumtrue.' Doesn't mean a thing."
And then Jane and Martha appeared, and their mother and Mr. Smith with them, and there was a race for the small private beach that went with the cottage. And the beach proved to be perfection, first pebbles and tiny snail shells, then soft sand and shallow water for Martha and Katharine, and farther on a diving raft for those like Jane and Mark, who had passed their advanced tests at the "Y" and could swim out deep.
You all know what going swimming is like, and it is even better when it's your first swim from your own private beach in the first lake you've ever stayed at.
After an hour of bliss, there was the usual rumor among the grown-ups that maybe they'd been in long enough, and after an hour more even the four children were ready to admit there might be more to life than paddle and splash. Just merely lying in the sun on the sand might be even better. So they did that until their mother cried out and said they would catch their deaths. Then reluctantly they went back to the cottage and put on blue jeans (Mark) and old dresses (the three girls) and set out to explore the rest of the grounds.
They found a nice rustic summerhouse on the high point of the shore that would be useful for sitting in and watching the sunset and listening to the water and the mosquitoes. And down on an inlet, round the corner from the beach, was the boathouse.
The boathouse, when investigated, proved to contain a flat-bottomed rowboat and a trim red canoe named _Lura,_ after the first name of Mrs. Kutchaw, from whom they'd rented the cottage. The four children had met Mrs. Kutchaw and did not think Lura an appropriate name for her, but the canoe was dandy. Only their mother, when consulted, said they'd better not take the canoe out without a grown-up along, just yet. But the flat-bottomed rowboat they could use, if they were careful.
"Better stay close to shore," said Mr. Smith. "There are parts of this lake in the middle where they've never found bottom."
This impressed the four children very much, and they now had even more respect for the lake than they'd had before. As Mark said, it must be some lake.
None of them had ever done any rowing at all, and of course they all had to try. But after Martha lost an oar and Mark nearly fell in rescuing it, and Katharine almost shipwrecked them on an unhandy sandbank, it was decided that Jane and Mark should take charge, and the other two lay back in luxury and were passengers.
"This is keen," said Mark, after a bit. "I've got the crude inkling of it now, just about."
"I've almost figured out how not to catch crabs already," said Jane, plying the other oar and belying her words by sending a sizable jet of water all over Katharine.
But the shore was slipping by them visibly now, and they explored its possibilities with eager eyes. After their own grove of trees came a cottage or two, then more trees, then more cottages closer together, till up ahead the four children saw a little settlement, with a hotel and a dance pavilion and a soft-drink stand and a pier.
"That must be Cold Springs," said Jane, for that was the unusual name of the resort on this side of the lake.
All the cottages had boats, and most of the boats were on the water now, and when Mark saw a large excursion launch called the _Willa Mae_ heading toward them from the hotel pier, he decided traffic conditions were too difficult for beginners and turned the rowboat around.
So they rowed back along the shore and decided which cottages they liked the looks of, and chose a pink one with curlicues as their favorite, till they came in sight of their own house and beach, already looking familiar and homelike. They rowed round the bend toward the boathouse, but the inlet was so inviting, what with water lilies gleaming whitely, and frogs sitting on lily pads looking bemused, and dragonflies hovering over the water, that Mark and Jane shipped their oars, and the four children drifted gently in the afternoon sun. It was then that Martha saw the turtle swimming past.
It was Mark who caught it. It was a big turtle, and it looked even bigger as he deftly scooped it up and landed it in the bottom of the boat.
"Watch out, maybe it's the snapping kind," said Jane.
But the turtle merely gave one look at the four children and withdrew into its shell in scorn.
"Put it back," said Katharine, who was of a tender heart. "It's not happy here."
"It will be," said Mark. "I'll build it a tank. I'll catch lots more and train them."
But when they had put the boat away and carried the turtle tenderly to the shade of a friendly oak, building a tank right now seemed all too energetic. The four children sat in the shade, lazily eating an occasional gooseberry from a convenient bush, and talked, instead. The turtle still refused to make friends. Its apparently headless, footless shell lay upon the ground nearby.
"This summer," said Katharine, "is going to be a thing of beauty and a joy forever."
"Not quite," said Jane. "It's the middle of July already. Two more months and prison doors will yawn. And I get Miss Martin for seventh grade next year. Help!" And she fell back in a deadly swoon at the thought, and lay pulling up blades of grass and nibbling the juicy white bits off the bottom.
"Why couldn't we have found this place way back at the beginning of vacation?" said Katharine.
"If we had, we wouldn't have found the half-magic charm and Mother wouldn't have got married," said Mark.
"And there wouldn't have been any Uncle Huge to rent a cottage _for_ us," said Martha, for that was the charming name she insisted on calling Mr. Smith, whose given name was Hugo.
"Maybe there would have," said Jane. "If I could find a magic charm right on Maplewood Avenue, it stands to reason there must be lots of it lying around still, just waiting for the right person to come along. Meaning me," she added smugly, and whistled through a blade of grass.
"Have you noticed the name on the cottage?" Katharine asked.
Martha and Jane hadn't. Katharine told them.
"Pooh," said Mark. "I told her that doesn't mean a thing. Just a goofy name."
"Maybe it does," said Katharine. "Maybe it means exactly what it says. Maybe there's a secret passage in the wall, and a wishing well, and buried treasure in the cellar!"
"And a dear little fairy in the keyhole," said Mark scoffingly. "Bushwah!"
"Magic by the lake," said Martha, trying out the words to herself. "Doesn't it sound lovely? Don't you wish it _were_ true?"
" _I_ certainly do," said Jane.
There was a silence. The turtle stuck its head out of its shell.
"Now you've done it," it said.
# Buy the Book
Visit www.hmhco.com or your favorite retailer to purchase the book in its entirety.
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# About the Author
EDWARD EAGER (1911–1964) worked primarily as a playwright and lyricist. It wasn't until 1951, while searching for books to read to his young son, Fritz, that he began writing children's stories. In each of his books he carefully acknowledges his indebtedness to E. Nesbit, whom he considered the best children's writer of all time—"so that any child who likes my books and doesn't know hers may be led back to the master of us all."
# Contents
1. Title Page
2. Contents
3. Copyright
4. Dedication
5. The Blow
6. The Beginning
7. The Magic City
8. The Dolorous Tower
9. The Greenwood Tree
10. The Giants' Lair
11. The Quest
12. The Ending
13. Sample Chapter from MAGIC BY THE LAKE
14. Buy the Book
15. Read More from the Tales of Magic Series
16. About the Author
|
{
"redpajama_set_name": "RedPajamaBook"
}
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Latin America's Leaders
**About the Authors**
RUT DIAMINT is professor of international relations in the Department of Political Science and International Studies at Universidad Torcuato di Tella, researcher at the National Council for Scientific and Technological Research (CONICET) and a member of the Advisory Committee of Club de Madrid and the UN Secretary General Advisory Board on Disarmament Matters. She has been visiting professor at Columbia University, and has received scholarships from Fulbright, the Woodrow Wilson International Center for Scholars, the PIF programme of the Canadian government, the Tinker Foundation, the UN Commission for Peace Studies and the US Studies Center for US–Mexican Studies, University of California at San Diego.
LAURA TEDESCO is associate professor of political science at Saint Louis University, Madrid Campus, and at Instituto de Empresa, Madrid. She has received scholarships from the British Council, the Foreign and Commonwealth Office and CONICET (Argentina) and grants from the British Academy and the Open Society Institute. She has taught at Universidad de Buenos Aires, FLACSO, the University of Warwick and the University of East Anglia. She has been a consultant for UNICEF and worked as an analyst for FRIDE, Spain.
Latin America's Leaders
RUT DIAMINT AND LAURA TEDESCO
_Latin America's Leaders_ was first published in 2015 by Zed Books Ltd,
The Foundry, 17 Oval Way, London SE11 5RR, UK.
www.zedbooks.co.uk
Copyright © Rut Diamint and Laura Tedesco 2015
The rights of Rut Diamint and Laura Tedesco to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act, 1988.
Typeset in Monotype Bulmer by Lumina Datamatics Ltd.
Index: John Barker
Cover designed by www.stevenmarsden.com
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying or otherwise, without the prior permission of Zed Books Ltd.
A catalogue record for this book is available from the British Library.
ISBN 978-1-78360-103-5 hb
ISBN 978-1-78360-102-8 pb
ISBN 978-1-78360-104-2 pdf
ISBN 978-1-78360-105-9 epub
ISBN 978-1-78360-106-6 mobi
_To Alex, Simona, Ema, Matilda, Luna and Rita_
| Contents
---|---
| LIST OF FIGURES AND TABLES
| ACKNOWLEDGEMENTS
| Introduction
CHAPTER 1 | How to study leaders
CHAPTER 2 | Models of democratic leadership
CHAPTER 3 | Leadership in the context of a stable party system: Uruguay and Colombia
CHAPTER 4 | Leadership in the context of a crisis: Argentina and Ecuador
CHAPTER 5 | Leadership in the context of the collapse of a party system: Venezuela
CHAPTER 6 | Rethinking political leadership
| LIST OF INTERVIEWS
| NOTES
| BIBLIOGRAPHY
| INDEX
Figures and Tables
FIGURE 1.1 | Hypothesis
---|---
FIGURE 1.2 | Dimensions of leadership
FIGURE 1.3 | The leader–supporter relationship
TABLE 1.1 | Selection criteria for the case studies
FIGURE 1.4 | Access to their first political post
TABLE 1.2 | How the leaders assess democracy
TABLE 2.1 | Self-interested and common-interested leaders
TABLE 2.2 | The democracy enhancer
TABLE 2.3 | The ambivalent democrat
TABLE 2.4 | The soft power usurper
TABLE 2.5 | The power usurper
Acknowledgements
This book is the result of seven years of collaborative study. We began to debate the democratic quality of Latin American political leaders in 2008. In the beginning our discussions were part of informal meetings. Slowly we became more intrigued about political leaders in Latin America and a literature review started to take shape. We realized that the bibliography on political leadership in the region was very limited. Although political leaders have always been important in our region, academics have neglected their study, while internationally the bibliography about political leadership was growing. Thus, we established an agenda to discuss research questions on leadership, and at the beginning of 2009 started to work on a research proposal.
Our project was accepted by the Foundation of Open Society Institute (FOSI) in Washington, DC. We want to thank María Victoria Wigodsky, who shared our enthusiasm for and preoccupation over political leaders. FOSI gave us generous financial support for three years, which allowed us to conduct interviews in Buenos Aires, Bogotá, Caracas, Montevideo, Quito and Washington.
We were able to manage the project, prepare events and organize the interviews thanks to a fantastic team of collaborators in different countries. Juan Pablo Ochoa (Quito); Juan Pablo López Gross (Caracas); Ariadne García (Montevideo); Ivonne Patricia León (Bogotá) and María Belén Fernández Milmanda, Valentina Waisman and Elliot Sucari (Buenos Aires) have been the best group of assistants that a researcher can have. They prepared the agenda for the interviews, listened to all the interviews and transcribed them, wrote some of the reports and literature reviews and managed to work with two difficult directors who were miles apart.
Many friends and colleagues helped us discover and explore the fascinating world of politicians. We would like to thank María Matilde Ollier, John Magdaleno, Carlos de la Torre, Miguel Serna, Jorge Lanzaro, Alejo Vargas Velásquez, Benigno Alarcón, Osvaldo Hurtado, Susanne Gratius, Carlos Gervasoni, Enrique Peruzzotti, Juan Carlos Torre, Lorenza Sebesta, Ernesto Calvo, César Montúfar, Betty Amores, Normay Wray, Adrián Bonilla, Simón Pachano, Pablo Celi, Bertha García, Julián González Guyer, Martín Balza, Alberto Curiel, Arlene Tickner, Francine Jacome, Johanna Mendelson Formann, Michael Shifter, José Miguel Vivanco, Adam Isacson, Andrés Serbin, Juan Rial, Domingo Erwin, Heather Booth and Albis Muñoz.
Mary Ingram helped us with translation and editing. Kika Sroka-Miller, our editor at Zed Books, has been fabulous, patient and always happy to help us.
We could not have done our work without the generosity of our interviewees. We enjoyed every interview. There was a bit of everything: professionalism, tension, laughter, friendliness and a lot of information. Some of them opened up their houses to us. Others waited for us in bars or restaurants. But most of the interviews took place in government buildings, which allowed us to witness the beauty of some congresses and houses of government but also to see much decadence. We want to thank wholeheartedly all of our interviewees. Both of us have learned a lot from all of them.
INTRODUCTION
History does not move forward in a straight line but when skilled and determined leaders push, it does move forward
Samuel Huntington, _The Third Wave_ (University of Oklahoma Press, 1992)
Latin America is widely known for its leaders. It is a continent that has produced political leaders that have gained global recognition – for good and ill. It is closely associated with leaders whose political projects have resonated far beyond their own countries. In Argentina, Juan Domingo Perón inspired a particular kind of nationalist populism. In Chile, the name of Augusto Pinochet became almost synonymous with the brutality of military dictatorship. Fidel Castro still stands as an emblematic figure of revolutionary resistance – and, for many, of undemocratic rule. In more recent times, Hugo Chávez developed a leftist project that attracted followers and critics around the world. The novels of writers like Gabriel García Márquez and Mario Vargas Llosa have given us memorable literary figures based on the popular image of the Latin American _caudillo_.
In the last decade, Latin America has experienced a variety of political trends. And, crucially, the marked differences between Latin American states have much to do with contrasting leadership styles. As the region made the transition from dictatorship to democracy and then into a prolonged debt crisis, the intensity of its challenges gave birth to very different types of leaders. In Brazil, Uruguay and Chile, a succession of skilful and consensus-building leaders were pivotal in laying the foundations for liberal democracy. In Argentina, Ecuador, Bolivia, Nicaragua and Venezuela leaders have taken office on more divisive platforms. In these countries, such leaders command huge numbers of both acolytes and detractors. Love them or hate them, it is undeniable that these men and women have exerted a defining influence over their respective countries' political development.
These twin trends form the subject of this book. First, leadership matters in Latin America, probably more than in any other region. Secondly, a greater diversity of leadership styles has taken root in the region during the last decade. We will show not only how and why leadership styles matter, but that there is a strong link between the structure of party systems and different leadership styles.
A neglected issue
Since the return of democracy to Latin America, there has been an explosion of powerful leaders. However, very little has been written regarding their influence on democratic quality. Surprisingly, despite the fact that Latin America's history is full of strongmen, strongwomen and _caudillos_ , little attention has been paid to their impact on _how well_ democracy works. The list of Latin America's very recent powerful and charismatic leaders includes a military officer, a bishop, a trade unionist, a former _guerrillero_ and many women. Their legacies have been complex. Some of them were able to stabilize the economy but to the detriment of political democracy. Some deepened democratic quality but failed in economic management. Others helped to make their societies more equal but undermined civil liberties. Few have been able to achieve economic growth and a more just income distribution without jeopardizing democracy.
This book explores the reasons behind the emergence of different types of leader in post-crisis scenarios. It does this in five Latin American countries. We began the research because we wanted to understand the reasons why the return to democracy has not changed Latin America's tendency to generate extremely dominant leaders. Recently, the region has witnessed the rise and fall of powerful political leaders, alongside the collapse or fragmentation of party systems. Twenty-one presidents were either removed from office or forced to resign from 1985 to 2012. The continent's political class has become the centre of international attention with the emergence of dominant leaders such as Hugo Chávez, Rafael Correa, Álvaro Uribe and Cristina Fernández de Kirchner. Latin America is today associated with certain types of populist leader. Indeed, this is widely seen as the region's distinctive contribution to contemporary political models. While expanding political and social rights, these leaders have polarized political debates and widened divisions between their citizens. This book asks why Latin America has produced such leaders. It finds the explanation in a series of domestic political conditions related to the nature of political parties. We uncover how this lies behind Latin America's modern paradox: the expansion and deterioration of democracy have advanced hand in hand. Indeed, in recent decades, different groups in the region have been included in the democratic game through the expansion of individual rights. This was the case in Bolivia and Ecuador with their indigenous communities and in Venezuela through the inclusion of economically and socially marginalized groups. However, at the same time other pillars of liberal democracy deteriorated, such as the political party system, the separation of powers or freedom of press. Here we understand democracy in its liberal form. It is characterized by fair, free and competitive elections; a political party system, separation of powers and protection of human rights, civil rights and political rights. The pillars of liberal democracy are limited government, horizontal accountability, individual rights and civil liberties. To sum up, a liberal democracy combines open political competition and the protection of individual rights (Held 1996; Youngs 2015).
This is a study of political leadership from different perspectives. First, we review the main concepts of leadership, looking specifically at the relationship between leaders, political context and followers. Secondly, we offer an analysis of political leaders in Latin America which is based on semi-structured interviews with former presidents, former and current vice-presidents, party leaders and legislators. The book draws extensive material from a three-year research project that included field trips, interviews, seminars and publications. The 285 interviews with politicians have provided us with a wealth of information about their ideals, goals, frustrations and perceptions about domestic politics and democracy. The interview material on politicians' perceptions, ideas and beliefs leads into a critical analysis of their performance and democratic quality. Thirdly, the book offers a comparative study of five countries in the region – Argentina, Colombia, Ecuador, Venezuela and Uruguay. Across these case studies, we point to the national conditions that shape different types of leader. In this way, we contribute to a comparative political leadership research agenda which aims to help with theory-building and testing empirical cases (Helms 2012: 9). Fourthly, based on our interviews and primary research, the book provides a new _typology_ of democratic leaders.
Situating the debate
Traditionally, academic literature on Latin American studies has focused more on the transition process, the state and economic reforms, the crises of political parties and the phenomena of neoliberalism and populism (Mainwaring and Scully 2010; Fukuyama 2008; Panizza 2005; O'Donnell 1995). Political leadership has been superficially included in the debates about presidentialism and parliamentarism (Diamond et al. 1999). More recently, the concept has gained some prominence owing to the emergence of political representation crises (Linz and Valenzuela 1994; Pérez-Liñán 2009; Fabbrini 2009). The rise of personalistic and populist leadership styles in Latin America has also been researched (Malamud 2010; Edwards 2009; Philip and Panizza 2011). Conventional wisdom presents this trend as an ideological challenge to liberal democracy led by charismatic individuals.
However, this book suggests that leadership styles in Latin America are better explained if contextualized within the different political party systems of each country. The study analyses the emergence of different types of political leader in Latin America, looking specifically at five countries. These countries were chosen because they have all suffered political and economic crisis – but with very different results. Five presidents were expelled in Argentina, three in Ecuador, one in Venezuela and none in Uruguay and Colombia between 1993 and 2005. Analysts argue that 'crisis offer excellent opportunities for studying political leadership in action' (Boin et al. 2012: 119). Crises are unique moments at which 'who leads matter' (Lord 2003: xiii). This book argues that some countries of the region, in post-crisis scenarios, seem to have fallen into a political trap marked by strong leaders who are democratically elected but once in power devote themselves to corrupting the political regime and maintaining themselves in power.
Locating itself within debates over the quality of democracy, this book looks at the relationship between leadership styles and broader political processes. Good-quality democracy is like an extremely intricate and finely tuned machine. When working to perfection, the machine produces high-quality output. But much effort is needed to build the machine and get it working properly, and its very complexity leaves it vulnerable to breakdown. The temptation is to look for a shortcut. Voters turn to leaders who promise solutions without going through the tortuous process of building such an elaborate and fragile machine. Their very impatience to see democracy's promises fulfilled installs leaders with an impoverished understanding of democracy's machinery. This study is concerned with the operators of democracy, those responsible for the quality of the product. It is about those who are in charge of what we might call 'democracy craft'. We start from the assumption that the importance of leaders in the working of democracy is paramount and that they should be considered as pivotal for understanding the widespread deterioration in democratic quality. They should also be recognized when they enhance democracy.
In addition to the above, this book also examines the challenges encountered by the authors in conducting research in five different countries; fixing interviews with politicians and listening to them. The book offers both a critical analysis of political leaders and the vicissitudes of interpreting a politician's words. Thus, based on interviews with politicians, this book narrates what politicians who are currently in office think about democracy, their role, their impact and ideas. When politicians are currently under so much scrutiny and criticism, this book explains the conditions that allow so many 'bad' politicians to survive in domestic politics and able to diminish democracy. The book combines analyses with a narrative on the challenges posed by such research in political science.
What will follow
The main contributions of this book are a typology of democratic leaders; a qualitative analysis of 285 interviews with political leaders; and the story behind the management of a research project.
The book has six chapters. Chapter 1 describes the making of the research project. In 2008 we began to discuss the predicaments of political leaders in Latin America. It took us around one year to put together a research project. In this chapter we narrate the different steps of this process: How did we formulate different research questions and hypotheses? Why did we choose to interview politicians? How did we organize the questionnaires?
In 2009 the project was approved by the Foundation of Open Society Institute in Washington, DC. Thanks to this grant we were able to conduct 285 interviews in five capital cities with former presidents, former vice-presidents, incumbent vice-presidents, legislators and party leaders. The interviews were conducted between 2009 and 2012.
The first chapter has two main aims. It explains our research method and presents the problems that a researcher encounters when analysing political leaders. The chapter does not offer a pure academic perspective. Rather it tells the story behind a four-year project which was managed by one director in Buenos Aires, another director in Madrid and a team of seven research assistants in different countries. Our purpose is to discuss the main difficulties found during the development of the project. Thus the chapter offers ideas about the design of the interviews, the dichotomy between qualitative and quantitative approaches and the management of a huge flow of information coming from literature reviews, interviews and seminars.
Chapter 2 outlines our conceptualization of political leadership. Following mainstream debates on political leadership, we discuss definitions of leaders, context and followers. The chapter explores the Latin American context and offers brief analysis of the political scenarios of the five case studies. Based on a qualitative analysis of the 285 interviews conducted in Caracas, Bogotá, Buenos Aires, Montevideo and Quito, the chapter offers a typology of democratic leaders. The typology was articulated by putting together different institutional settings and the characteristics of leaders which were discussed in the interviews.
Chapters 3, and test the typology in Uruguay and Colombia, Argentina and Ecuador, and Venezuela, respectively. We decided to divide the case studies according to their institutional settings. Therefore, Uruguay and Colombia are analysed together since their political party system has a high degree of institutionalization. Argentina and Ecuador are studied in Chapter 4 as two cases in which the degree of institutionalization of the party system is low. Venezuela is examined in Chapter 5. There are three main reasons why Venezuela is a case on its own. First, we were not able to interview Chávez's followers. We contacted members of the Partido Socialista Unido de Venezuela (PSUV), legislators from the party, journalists and academics who had a pro-Chávez stand but none of them accepted to be interviewed. Therefore the interviews were biased. Moreover, we arrived in Caracas when news about President Hugo Chávez's health were released. The interviews were monopolized by current affairs. It was a big effort to try to follow our questionnaire. Secondly, Venezuela was the only country from our basket which underwent a collapse of its political party system. Lastly, Hugo Chávez as a political leader was unique.
These three chapters are very different. In the case of Uruguay and Colombia, the interviews were not monopolized by discussions about one particular leader. In Uruguay, our interviewees gave us interesting quotes that we reproduce anonymously. But they were reluctant to provide a detailed analysis of José Mujica's leadership. They perceived political leadership as a collective phenomenon. In the case of Colombia, there were many references to the different styles of leadership of Álvaro Uribe and Juan Manuel Santos. However, most of our respondents emphasize the analysis of the political context in which leadership is exercised. Indeed, the issue of political violence monopolized the interviews.
In the case of Argentina and Ecuador, the interviews were more concentrated on the analysis of the leadership of Néstor Kirchner, Cristina Fernández de Kirchner and Rafael Correa. Issues such as clientelism, populism and strong presidentialism were discussed in almost all interviews. Thus, the responses of our interviewees allow us to offer some quantitative analysis. During the interviews, some policies were discussed as examples of how leadership was exercised. We have included some analysis of these policies, which has also helped us to structure our typology of leaders.
The chapter on Venezuela is a combination of a study of policies, especially those that were discussed in the interviews, and a qualitative analysis of the interviews. As we said, the interviews in Caracas were monopolized by the leadership of Hugo Chávez, his illness and the February 2012 primary elections. We made an effort to discuss how leadership could be exercised by the younger politicians who have created the new political parties.
Therefore, there are differences in how each case study is presented. Rather than trying to standardize the analysis, we prefer to respect the differences that emerge from the interviews. We believe that these differences enrich the comparative analysis.
Chapter 6 discusses the conclusions of our research and further explores the value of our typology. The evidence presented here has uncovered a complex and fluid relationship which indicates that the degree of political party institutionalization and the forms of political competition influence leadership styles. The key element is the degree of autonomy that leaders can carve out in contexts of over- or low institutionalization of political parties. Listening to politicians in Argentina and Ecuador, it became clear that leaders have a notable capacity to ignore rules and citizens' demands by building clientelist networks and concentrating power in their own hands. In Uruguay, politicians are held accountable by their parties and their autonomy is limited. In Venezuela, Hugo Chávez has been able to rewrite the institutions of the state, concentrate power in his hands and hollow out state power. In Colombia, the political system is contaminated by violence. The institutions of the state and the degree of institutionalization of the political party system are still able to control political leaders. Paradoxically, they can avoid concentration of power but they cannot avoid corruption and violence.
The book argues that certain political conditions allow for the emergence of different types of leader. It offers a new typology of democratic leaders that highlights their impact on the quality of democracy.
CHAPTER 1
How to Study Leaders
Introduction
Our research was motivated by questions about the democratic quality of political leaders in Latin America. How could leaders who had successfully established democracy in their countries take political paths that would lead to a gradual deterioration of the quality of the democratic institutions? What motivates some leaders to employ populist, clientelistic methods to build or strengthen their power? Why are so many young politicians so naive and inefficient that they quickly lose power?
We observed different type of leaders in Latin America. We wanted to discover why in some countries excellent democratic leaders emerge while in others populist, inefficient or corrupt leaders prevail. The literature suggests a combination of elements linked to the historical and cultural context, the strength of state institutions and the extent of democratic practice among the citizens of the country in question. What we did not find were texts that laid out the thinking of politicians themselves. Therefore we decided to interview politicians. We wanted to know their perspective on the democratic quality of political leaders and the political conditions that help the emergence of different types of leader.
We knew, then, what we wanted to do but still had to decide how to carry out the research. Therefore we consulted both books and experts. Before we coordinated the interviews we undertook a literature review. Our first discovery was that there is very little written about leadership in academic texts, especially in Latin American political science. Although one of the classic texts on leadership, _The Prince_ by Niccolò Machiavelli, had recognized the importance of leaders in any political project, modern political science had concentrated more on the structure of parliaments, political party systems, elections and the relations between the branches of state power, omitting the subject of leadership.
We also discovered that most of the literature on leadership was in the field of business studies, concentrating on private sector performance. Although some of the ideas in these studies can be applied to our field, we needed a different approach. In studies on business, negotiation and strategy, there are a lot of resources on both the study and training of leaders. But this material cannot really be applied to the study of political leaders. There are major differences between leading businesses and leading countries. Typically studies on leadership focus on an analysis of the personalities of the individuals. However, they tend to be more of a psychological examination of their good and bad points rather than a political discussion. Our interest was shared by other academics who had started to investigate the subject of leadership more systematically (Lord 2003; Kellerman 2004, ; Bueno de Mesquita and Smith 2011; Nye 2008; Helms 2012).
In order to establish a line of questioning for future interviews we carried out a series of informal meetings with colleagues in Buenos Aires and Madrid, and ran the questions by opinion poll specialists for their input. Thinking about questions for future interviewees was the first concrete task of this research. The project was taking shape. We wrote it up and submitted it to different foundations. In August 2009 the Foundation Open Society Institute in Washington, DC, approved our project and in October we started work.
The study took four years and covered five different cases, which enabled us to offer comparative analysis. It entailed ten study trips, 319 interviews in six countries, seven seminars organized in Toronto, Buenos Aires, Quito and Madrid, the writing of research reports, work documents and journalistic articles, the editing of a book in Spanish, and finally the writing of this book. It involved a team of seven research assistants in five countries.
Here we intend to discuss how we organized our material and conducted the research. This chapter is not strictly methodological. It is not always easy to implement what methodological texts stipulate. Often the researcher changes their hypothesis, variables and ideas and in many cases this means starting again from scratch. We had to grapple with social science methodological rules, but what we seek to convey stems more from concrete experience than scientific theories.
This chapter also covers the unexpected elements that any social scientist can encounter when they seek to explain political reality.
Defining our hypothesis and case studies
The initial hypothesis of this research holds that the deep-rooted authoritarian tradition in Latin America protected those in power from having to engage in any real deep and meaningful transformation of the democratic system. A consequence of this, we maintain, was the destruction of any new democratic leadership. Our assumption was that the traditional modes of behaviour such as clientelism, _caudillismo_ , authoritarianism, the desire to hold on to power indefinitely, and corruption helped to explain the numerous political crises which have been the scourge of the region throughout the last three decades. Other countries, by contrast, worked to institutionalize political systems that broadened democracy.
Given that this is a rather sweeping assumption, we set out from the beginning to compare different cases in order to be able to reach some generalization, since, as Morlino says, 'comparison makes it possible to control for the hypothesis' (Morlino 1991: 14). In addition, a comparative study helps to construct assumptions and identify trends that we hoped would shed some light on how change could improve the democratic quality of leaders.
The examples we chose adhered to traditional comparative criteria, i.e. cases with similarities as well as differences. We used the Mill difference method (Pérez-Liñán 2007: 8–10) to identify cases in which we assumed that the leadership was democratic and others in which we held that the leadership characteristics were less democratic.
To begin with, we took a series of social phenomena which we considered to be tied to the rise of different types of leadership, as were the crises, the problems of political representation and the fragmentation of political parties. Our dependent variable was initially the democratic quality of the political leaders. As a first step in the research we defined democratic quality by taking as a basis the study by Barreda, which measures this quality as a function of five dimensions: 1) political rights and civil liberties; 2) responsiveness of the government; 3) level of participation; 4) accountability; and 5) rule of law, or rather the validity of the legal system (Barreda 2011: 270).
However, as our research progressed, we modified our initial hypothesis and refocused the study. We argue that the quality of the democracy could be considered as a product of the type of leadership and thus we began to focus more on the different types of leader. What we observed was that many Latin American leaders were elected democratically but once in power they seek to destroy the institutions and democratic processes, establishing legal frameworks to enable them to remain in power. Many of them succeeded, others came up against the power of the institutions themselves or popular discontent. This diversity suggests that the political context could explain the emergence of different types of democratic leaders. One of the factors that seems to have explanatory power was the degree of institutionalization of the political party system.
With these early observations and an extensive bibliographical review we began to formulate a different hypothesis: i.e. the quality of the leaders could be related to the degree of institutionalization of the political parties and of the state. This hypothesis enabled us to focus on the variance of the leaders. Leaders do not rise from a vacuum, so we assumed that the different institutional arrangements promoted the emergence of different types of leaders (the independent variable). In addition, since a leader has to win over supporters so as to become a leader, the second independent variable was the relationship that the leader established with the voters. Hence we began our study of political leaders with the assumption that leadership has three components: the leader, the followers and the context, as per Figure 1.1.
FIGURE 1.1 Hypothesis
The next step was to define each category. In order to explore different elements of the leadership relationship we took five dimensions: a) how leaders entered politics; b) whether they had a suitable background for holding an executive or legislative position; c) their values and ambitions; d) the relationship with their followers and the media; and e) their readiness to innovate and use new technology (Figure 1.2).
FIGURE 1.2 Dimensions of leadership
With regard to context, we reviewed the literature on the subject of the institutionalization of political systems, a topic which has been widely covered. In particular, following Mainwaring and Scully (), Alcántara () and Ollier (, ), we used the concepts of high and low institutionalization of political parties. First, a party system is institutionalized when parties have continuity in terms of internal rules and inter-party competition procedures. Secondly, institutionalized parties are well established in society and have ideological consistency. They generate ideas, programmes, proposals and government plans that allow citizens to understand the party's aims. Thirdly, parties are the vehicle for political representation, providing a legitimate way to gain access to government. They are also a vehicle for representing interests; they are channels for interest groups to make their voices heard. Fourthly, the internal organization of institutionalized parties is coherent with efficient instruments for internal discipline to avoid and punish corruption (Mainwaring and Scully 1995; Alcántara 2004). Analysts have concluded that institutionalization does not guarantee high-quality democratic institutions, but that a low degree of institutionalization weakens any type of democracy (Mainwaring and Scully 1995: 21). A non-institutionalized party system increases the chances of arbitrary decisions being taken. If the parties are weak, or the rules are not clear and transparent, force, violence or mass movements become ways to gain power and access to government. If rules and procedures are flexible and change constantly, the system leaves room for manipulation, which in turn benefits parties or leaders, thus ruining the political and legal pillars of a democratic system. Parties can be hijacked by interest groups, which end up gaining privileged access to government posts or influence over the decision-making process. This amplifies the differences between interest groups and citizens, and makes the system unjust rather than democratic. A low degree of institutionalization also increases the likelihood of a personalist, populist leader coming to power, particularly in presidential systems (Mainwaring and Scully 1995: 22). If the system is obscure and party discipline is erratic, the level of autonomy can easily increase. Here we understand politicians' autonomy as their capacity to be isolated from citizens, political parties and/or to 'make decisions at odds with citizen demands' (Fukuyama 2013: 10).
Measurement of followers/supporters was more complicated since we did not want to limit ourselves solely to the relationship between populist leaders and their supporters. In order that we could consider different levels of adherence to leaders, we used concepts tested in interviews. They referred to three aspects which stem from the concept of participation (Hagopian 2005: 41–90): the type of communication (personal, media, only in political campaigns, group, individual); aim of the link (electoral, permanent, intermittent); and the transparency of the management. We also tested the way in which advisers are incorporated as another source of link with supporters (see Figure 1.3).
FIGURE 1.3 The leader–supporter relationship
The second stage was to choose the case studies (Deslauriers 2004: 31). We began by selecting Argentina and Ecuador. Both countries had undergone major political chaos with presidential crisis, exhaustion of the party system and questioning on the part of society. Secondly, we chose Uruguay and Colombia, because they share some characteristics, such as having undergone crisis situations and changes in their two-party systems while maintaining a stable party system and consistent, lasting political careers. Lastly, we chose Venezuela, which was quite unique, with a major political crisis followed by the emergence of a strong leader who was able to secure political stability (see Table 1.1). We would have liked to have included more cases for comparison since broader studies in the field of social sciences enable the formulation of generalized classifications. However, our project had a set amount of financing which forced us to balance academic criteria with concrete reality. We had to discard research on Brazil, Chile and Peru, all of which was very interesting. There was only a limited time to carry out the research and this did not stretch to more than the five cases we chose. As Patton stated, 'having weighed the evidence and considered the alternatives, evaluators and primary stakeholders make their sampling decisions, sometimes painfully, but always with the recognition that there are no perfect designs' (Patton 1990: 181).
TABLE 1.1 Selection criteria for the case studies
All the cases have one common characteristic and lack one of the other attributes (Pérez-Liñán 2007: 9–13). Following qualitatively oriented comparative methods, our aim was to compare the conditions or causes in different historical contexts with a holistic and interpretative approach. Our ultimate purpose was to understand and interpret the differences and similarities in political leadership issues in the region. We believe that by focusing our comparison on the similarities and differences between our case studies, they 'can tell us a great deal about the way governments function' (Peters 1998).
The design of the research and of the sample
The research project posed many methodological questions. From the start we opted to conduct a comparative, qualitative study. We argue that a qualitative study is more relevant for social science (Flick 2012: 15). However, we accept that, gradually, studies in political science have become more embedded in different methods of quantitative research. Despite the dominance of quantitative studies, social scientists tend to consider it more useful to use a qualitative approach when dealing with a limited number of cases (Morlino 1991: 16–17). Moreover, the originality of this research lies in the information produced by the interviews with politicians. We wanted to use the narrative of the interviews, the stories that were told and the impressions that were given rather than limit ourselves to a quantitative approach.
However, the qualitative analysis exhibited some problems as well as benefits. Given especially the nature of the comparative case study, we tried to control 'the sources of variance in the ex-ante selection of the cases, rather than through ex-post manipulation of data' (Peters 1998). In other words, we endeavoured to make the sample as representative as possible, by analysing the political representation of parliaments in each case study. However, we confronted some significant issues about the conceptualization of the sample.
One of the main challenges was to define who would fall into the category of political leader. The choice led to many controversies in the early discussions. One classification which involved a very small margin of error was legislators. They constitute a relatively homogeneous universe and therefore an averagely rigorous sample. In addition it was a reasonably fair sample since their numbers are in proportion to support for their political party.
However, as is often the case in social science, reconciling methodology with reality is not easy. First, there are important differences among the legislators. There are some who have been elected many times and others who are in their first term in Congress. Some are close to the press and their ideas are better known by the general public. Others can be good political operators within their parties but have limited visibility. Being a national deputy who represents a large district with a large electorate is not the same as being a national deputy representing a province with few inhabitants. Some legislators have held important positions in the executive or high-ranking party positions, while others are new to the political game. In fact, a distribution of the interviewees by party membership, reflecting the percentage obtained in elections, does not necessarily ensure a fair distribution in their universe as a function of the objectives we had established.
Secondly, as indicated by Taylor and Bogdan (: 36), it was not possible to determine beforehand who would fit into that universe. This means that for each of the five cases we could draw up a table that illustrates representation criteria as a function of the votes obtained by each political party. We could consider those criteria with information from the media to compare legislators with a greater public exposure with those who are either new or less well known. We could also include the degree of involvement in executive power. But we could not guarantee that the legislators we chose were actually prepared to be interviewed, and many of them were not. Although we had identified our universe, many of those selected did not answer our requests for interview. We were therefore concerned that we would end up with an arbitrary sample which would make it difficult to extrapolate results and establish causal relationships (Gerring 2008: 156–7).
One way of dealing with this problem was to select a universe that was not based on a proportional sample but that considered well-known people in the political sphere. This was the solution we chose, and we consider that despite the problems with regard to distribution, it was easier to achieve a balanced representation. Given that we could not obtain a balanced representation of political parties according to their distribution in Congress, we opted to choose leaders as a function of their importance in terms of the political agenda. Hence we decided to increase our sample to include political leaders both in parliament and outside it. This involved another benefit because we realized that we could not confine our concept of political leader to the purely legislative and we wanted the opportunity to interview politicians in the executive and party apparatus.
The definition of this universe was closely related to the method involved in deciding on the population of our study. Our approach was to speak with ten colleagues in each of the five countries with whom we had worked previously. We asked them to provide a list of the ten most politically influential people and leaders who had had a distinguished political career. We also asked them to provide us with contact details for the individuals, such as their telephone numbers, email addresses and name of the institution they belonged to. We appreciated that the data could be skewed by virtue of the relationship with our contact, where they worked or the political party they belonged to. Hence we spent time comparing the list with the local press to be sure that the political leaders our contacts had suggested did indeed appear frequently in the local news. We also applied a specific time frame and regional spread so that we were not simply including politicians in the capital cities of the countries involved. We also included local academic specialists in the field of political science and political journalists who could help us draw an accurate picture of the political scene pertaining at the time of the interviews.
We were aware of the bias that could creep into our sample given our use of such heterogeneous criteria. However, in line with Azorín and Crespo (: 69), we believe that the 'the optimal design of the sample could only be achieved by relying on knowledge of the population'. As is widely accepted in the social sciences, similarities between the components of the universe are not previously given properties but distinctions made by the observer (Mandujano Bustamante 1998: 3; Salgado 1990: 349). Therefore, having defined in basic terms the characteristics of those we wanted to make up our universe, we chose cases that met those conditions according to the information provided by opinion pollsters, key contributors and local leaders. This was an intentional sample (Patton 1990: 100–105; Deslauriers 2004: 58; Pla 1999: 296), derived from a theoretical concept.
The lists could easily contain over 200 names. Hence we decided to organize a ranking according to the number of times the person had been suggested by our colleagues, and this cut the list down to sixty individuals.
Then our assistants began the difficult job of trying to find a way of speaking with the potential interviewees by internet or telephone. The research assistants compiled information from public sources to build up a complete profile of each candidate. This helped to guard against any bias towards specific political parties.
We told all the people that we contacted that we had been given their name by an important source. Since it is difficult to gain access to politicians we realized that more influential sources could open more doors for us as well as foster a greater degree of trust between ourselves and the interviewee (Taylor and Bogdan 1987: 38; Deslauriers 2004: 39–40). This worked well in most countries apart from Venezuela. We did not experience many difficulties in speaking to the politicians on the lists. Unless they had no space in their diaries or were travelling, the politicians were happy to speak to us, again with the exception of Venezuela.
We asked the people who responded positively and quickly to us whether they could also suggest names of people we could interview. This also meant we avoided omitting relevant people so we had a greater understanding of the domestic political process in each country (Gerring 2008: 181–3).
While in the letters to our colleagues we explained our objectives and asked for their help in designing the interviews, in the letters to interviewees we included a summary of our project and the aim of the interviews, emphasizing that our work was purely for academic purposes and that we would not publish anything without their prior approval. Recording the interviews tended to create a degree of tension. We tried to mitigate against this by stating firmly that they would not be quoted, nor would any other personal characteristics be mentioned that would identify them. As Flick has noted, recording people's speech reveals things about them that it is difficult to control (Flick 2012: 68), and following Taylor and Bogdan's recommendations (1987: 80–81) we also took written notes if the person made a specifically pertinent comment.
The method of choosing the universe cannot be optimal in terms of its methodological validity (Elster 2010: 218–19; Deslauriers 2004: 28–30). However, we made an a priori classification of the categories to define the interviewees and we respected those criteria in the interviews. In each country we planned between forty and forty-five interviews with legislators, party leaders and politicians who had been or who were in the executive. We also interviewed between ten and fifteen academics and journalists who helped us to identify and interpret political trends, social problems, issues on the domestic agenda, etc. These were very important in helping us to illustrate the institutional background against which the leaders were operating. Most of the interviews were carried out during our study trips. Others were carried out by our local assistants. This brought the average number of interviews up to ninety per country.
Interviews were largely carried out in a single week. Our local assistants accompanied us to the interviews, which helped to systematize the type of interview we wanted and to train them so that they could do the job themselves. Since we had so little time in each place, the agenda was packed. We undertook between seven and eight interviews a day, some together and some separately. At the end of each day we evaluated our observations. We read notes and discussed any doubts so that we could make any necessary changes for the next day's interviews. Then, as recommended by López Estrada and Deslauriers (: 12): 'it is very important to write up the notes immediately after each interview. For that to be possible, the transcript should be considered part of the interview itself. The passage of time, contacts with other people and doing other activities can act against us. We should remember that we forget quickly.'
Many of the leaders we contacted wanted more information about the reason for the interviews. Some wanted to have the questions in advance, but we tried not to comply with this as it would detract from our aim of having an open discussion in which the interviewees could freely express themselves. We had taken into consideration Jon Elster's suggestion. He said that 'explaining behaviour is often in the situation and not in the person' (Elster 2010: 206). In other words, answers formulated in advance by the interviewee (or their adviser) put a distance between the two people when the actual interview takes place. It is also worth mentioning the variety of places where the interviews took place: an office in Congress, a personal office, party headquarters or, as happened in Caracas, our hotel to avoid being punished for speaking to foreigners.
Carrying out the interviews
An important aim of our work was to instil a degree of confidence in us on the part of the interviewees so that they would be prepared to answer our questions frankly. As they had not met us beforehand, we ran the risk, as is usual in interviews, that we would give off the wrong signal about what our real objectives were. There was not very much that we could really do to gain their trust other than being punctual, thanking them for meeting us, showing an interest in listening to them and avoiding any sort of prejudice or criticizing what they said (López Estrada and Deslauriers 2011: 9–12). Some of the meetings were long and rather heated. Others constituted the bare minimum to comply with having offered to do the interview at all. Altogether we can attest that they were very enriching.
We learned something from every interview. Most politicians want to be known and are expansive by nature. They were concerned about reaching out to their supporters and establishing good communications. This was helpful, and most of the interviews ended up being very long conversations about their political careers, their values and how they saw the prevailing climate. A major issue for them is how to stay in power or at the very least how to stay in politics. They do not want to disappear. Hence the media constitutes a valuable resource for them to spread their political message. Some had mistaken us for journalists and were disappointed that we were not. Appearing in the media was of more interest to them than being in an academic report.
We also came to appreciate their limitations. In some cases we were surprised at the lack of knowledge that many had about international affairs and their rather parochial outlook. In a lot of cases there was a marked inability to criticize themselves.
In light of our results, we are happy with the way we conducted the interviews. As López Estrada and Deslauriers (: 1, 6–7) point out, 'the interview has enormous potential to allow us to reach the mentality of people, but also to gain access to their vital side so we learn about their daily life and social relationships'. We were extremely careful about choosing topics of conversation that would allow us to collect a lot of data so that we could evaluate and analyse their political careers. Our aim was to listen to the politicians; hence the interviews were semi-structured around open-ended questions, so as to give interviewees the opportunity to speak extensively about their careers and domestic politics. In each case we started with a question that allowed the interviewee to speak without too many interruptions. However, although we did not stick rigidly to the questionnaires, we did want to repeat a few formal well-defined questions in order to encourage each speaker to talk about topics that interested them. If we had not had some similarities in the questioning, we would not have discovered the indicators that enabled us to establish comparisons and generalize about the leaders of the region.
The process of putting together the interview had a number of aspects. Since there was no agreement in the literature about the qualities of a political leader, the selection criteria came from our own conceptualization of the topic more than from secondary sources that dealt with similar subjects.
The categories of questions
We chose five themes to help us identify what sort of leader we were interviewing. They were: a) their entry into politics; b) their qualification to hold an executive or legislative position; c) their values and ambitions; d) their relationship with their supporters and the media; and e) their ability to innovate and use technology. We could explain in detail how we chose the five categories but it seems more important to point out that while we used a set format for the interviews, we did change the questions somewhat, adding some which came from previous conversations and leaving aside topics that did not generate interesting material.
The data were difficult to group together: 'a problem may be that narrative material is generally not linear, and paragraphs from transcribed interviews may contain elements relating to several categories' (Elo and Kyngäs 2008: 113). Bearing in mind that 'codification is a means of deconstructing data: the researcher takes an element of information, removes it and isolates it, classifies it with others of the same type, deindividualises it, decontextualises it' (Deslauriers 2004: 70), the five themes we present largely comply with the evaluations that came up in the interviews. Thus codification reproduces the data according to codes derived from the material collected during the project or rather built on the responses of the interviewees and the framework of our survey.
With regard to how they entered politics, and in line with Kane and Patapan (: 4), we were interested to know whether their nomination as a candidate stemmed from political competition, since that is an essential characteristic of a democratic regime. It was also important to us to ascertain how important the interviewee considered that question to be. In other words we wanted to know whether the interviewee made any reference to the legitimacy with which they held their position.
In examining access to politics, we wanted to know whether they had had a mentor, whether they came from a political family, how they had won their first public office and what qualities they thought they had to have been selected. On this point there were considerable similarities between older politicians. It was quite common for them to have started their political career in university militancy, and their replies referred to role models that had influenced their development as well as things they had read. Meanwhile, the younger interviewees tended to belong to social organizations and not to have role models or any particularly inspiring texts.
In the chart below (Figure 1.4) we can see that university militancy was a frequent channel into political life. Except for Uruguay, which has rather fixed rules governing a career in a political party, in the other three cases (Argentina, Colombia and Ecuador) it is the main source of entry into politics. In Venezuela it did not have a marked influence. This can possibly be attributed to the fact that traditionally entry into politics was via the two traditional political parties (COPEI and Acción Democrática). In addition the sample from this country includes hardly any official legislators, so the issue of access for new leaders does not represent the new generations of politicians who emerged during the presidencies of Hugo Chávez.
FIGURE 1.4 Access to their first political post
* In Venezuela we were able to interview only politicians from the opposition parties. Therefore this chart does not include those who come from the armed forces.
** In Uruguay a high percentage (26 per cent) come into politics because of family relations.
_N_ = 285
We were also interested in what training or preparation they had had to carry out an executive or legislative job. Our questions referred to the necessary qualities for the job as well as characteristics they considered most important for their career. Was education or practical experience more important? Did it require them to have done a similar type of job or was political militancy more valuable? It is worth emphasizing that we did not start out with an elitist idea of leadership qualities, we did not have any prejudices with regard to university education, and we valued equally a politician from a union organization or local militancy. In the few cases where the legislators or politicians had started their careers in trade unions, there was a generational difference. The older ones stressed the effect of reading and political debate while the younger ones talked only of militancy.
We also asked whether they had had any formal training to prepare them for a political career, since one assumption of our research was that schools of leadership do not really influence political careers.
The third item in the interviews, analysis of values and ambitions, aims to analyse what aspects of their political activity they value most and what topics involved in the game of democratic politics are important to the interviewee. For example, we asked how they built consensus between party members and with the opposition, knowing that if we asked whether it was important to seek consensus we would obviously get a positive answer. Going against the expectations of the interviewee was always risky (Taylor and Bogdan 1987: 72–4). Politicians know what is correct. However, we found on various occasions that politicians were so sincere they harmed themselves. For instance, some politicians told us without any shame that they had engaged in some financial shenanigans to gain their position, that they had gained it thanks to nepotism or that they had no single quality to justify holding their current position.
At this stage we introduced questions about how they valued democracy. We tried to get the leaders to talk about democracy. We were interested to see what the politicians understood by democracy, what ideas they had about everyday democracy and how they experienced democracy in their daily life. We understood that 'the vision for democracy is a fundamental characteristic of democratic leadership since it creates the environment that leaders and followers pursue to improve their society and nation in terms of the demand for democracy' (Choi 2007: 251).
Table 1.2 shows the degree of understanding of democracy among the leaders. A high percentage (between 39 and 51 per cent) considers democracy a guarantor of power division. In Venezuela, as a consequence of the social rhetoric of the twenty-first century, most emphasized the importance of protecting minorities. The lowest percentage relates to responses about guaranteeing political management. This was not really considered an important characteristic of democracy by many of the leaders. The answers were more diverse than these five categories, but despite the variations it was possible to group them.
TABLE 1.2 How the leaders assess democracy
_N_ = 285
On the subject of valuing democracy, we introduced questions about populism and clientelism as ways of exercising leadership. We expected the leaders to respond that these political practices were negative, in line with the tacit consensus that predominates in Western democracies. In order to avoid any false responses, the questions covered issues such as what elements would be lost in the relationship with activists and voters if we put to one side clientelistic policies. Who would be most affected if we limited excessively clientelistic practices? How would you respond to the concrete demands of supporters?
Finally we also asked about the role of political parties and whether that had changed or whether they kept the same party traditions. What effect had the political party had on their political career? How did they feel the political party had contributed positively or negatively to their career? We asked how they defined their electorate and the mechanisms the party employed to support their candidates. We also explored ideas about the formation of alternative policies and how politicians who changed party were considered.
With regard to their supporters and the media, in order to discover how the respondents understood the making of politics, we included questions about their everyday routine, communication with their constituents and the process of selection of their advisers. We asked whether they met with their supporters personally, how many they saw a month and how they managed follow-up to their requests. In order to assess their openness to new forms of making politics, we asked questions about generational change, gender and class.
Most studies on leadership have neglected to consider the importance of supporters in empowering or limiting leaders. For us, supporters play a fundamental role, especially in countries where the institutions are weak, the political parties are in disarray and leaders tend to concentrate power in their own hands. The recent presidential crises in the region have shown that 'informed citizens no longer accept the role of passive audience. They want to be actors, not spectators' (Darcy de Oliveira 2008: 120). Therefore the interviews gave the politicians the opportunity to talk about their experiences with their supporters and to expand upon the relations they had with them at a personal level and via social networks. Other questions referred to how they chose to communicate with voters.
With regard to how they put together a team, we started by asking how many assistants they had, what functions they performed and how they had contacted them. In just two instances out of 285 people we interviewed did they choose their assistants via open competition. This point was very telling. As for their advisers, the legislators did not seem to believe in any sort of democratic, open and transparent method to choose them. Legislators select their advisers from among their political party, their friends or relatives. In a few exceptional cases the respondents mentioned taking into account technical or intellectual ability. After the interviews, we reached the conclusion that how they put together their team of advisers is a good indicator of how democratic the leader is.
Finally the interviews also included questions about innovation and use of technology. We wanted to know whether the respondent was aware of changes in political debates, and whether they felt that society was demanding a different discourse. Most of the politicians used new technology, web pages, Twitter and Facebook, but the majority could not really say how they benefited from them or how they could gain the most from these tools. Although this technology creates dynamic interaction and we tend to believe that it democratizes politics, the leaders we interviewed continued to hold that the more traditional ways of recruiting party members and supporters were the best. Many indicated that nothing could replace face-to-face contact and walking through neighbourhoods to reach out to potential supporters despite technological progress. Many said that they left it to their younger advisers to communicate with voters and make use of technology.
The interviews were long. Few lasted less than an hour. Some of the leaders talked at great length about their careers, others talked more about democratic and political values, and others were almost incapable of sticking to the questionnaire, preferring instead to talk about current domestic political issues. It is not our intention here to narrate the 285 interviews at length. Nevertheless, the following pages encapsulate the most interesting findings, presenting our respondents' ideas about their political career and the qualities of political leaders.
Politicians' perceptions
The first question in the interviews was 'Why did you enter politics?' This question gave politicians the chance to talk about their political career. In many cases, especially in Argentina, Colombia and Uruguay, the opportunity to get into politics is related to family connections. Our respondents emphasized that they were born into a Peronist family, a Liberal family or a Colorado family. Very few of them rebelled and followed the opposition. One Colombian senator from the Conservative Party said that he started out in politics when he was twelve years old. Many of them discovered their ability to lead a group from an early age in school. The word 'vocation' came up in the majority of the interviews. In the five countries the majority of our respondents explained that they understood politics as social service. Legislators from rural areas mostly entered politics through community service in their towns. Particularly in Colombia, many respondents stressed that they entered politics to help their country to end political violence. In Venezuela, the younger politicians entered politics to oppose Hugo Chávez.
We were aware of the fact that our respondents could reply with answers they believed created a good impression. Probably this is why many replies were 'I entered politics because I had a vocation for public service', 'I wanted to end injustice' or 'I wanted to improve the life in my community'. Many respondents argued that their personal aims were of secondary importance and that their main objective was to serve the community. Yet the majority of our respondents did seem to believe that they had a real vocation for public service.
The second question was 'How and why did you get your first job in politics?' Sixty-three per cent of the respondents in Argentina said that it was militancy either in university or in their political party which opened the door for their first job. Thirty-four per cent said that their first job came through personal relations. In Ecuador, 65 per cent pointed out that they got their first job through militancy in the parties, university or a social movement. Forty-five per cent of our Uruguayan respondents told us that it was through militancy in political parties and 23 per cent through activism in university. In Venezuela 34 per cent got their first job thanks to militancy in political parties, 33 per cent in social movements and 11 per cent in university. In Colombia 40 per cent of our interviewees got their first job through militancy in political parties and 36 per cent thanks to family connections.
Talking about personal qualities necessary to become leaders, the respondents gave very different answers. We have grouped them in two categories: personal qualities and militancy. In the first group, the following answers appeared repeatedly in the majority of the interviews: intuition, strong personality, hard worker, willpower, good oratory skills and persuasiveness. In Uruguay honesty was mentioned many times as a quality and a need. In the case of Argentina, politicians were very critical, highlighting the problems rather than the qualities. One legislator said that politicians were very arrogant and that the Congress was a 'bonfire of vanities'. In the second group of answers, the most common replies referred to ideological coherence, many years of militancy in the party and the ability to create consensus and to talk to political opponents. Other answers that were interesting included: 'my brother is the governor', 'my father's death opened the door to attain the national level' or 'female quotas opened the door'.
Charisma was also widely discussed in the interviews. Most of our respondents did not consider charisma as something extraordinary. It seems for them that most leaders in the region have some degree of charisma. They associated charisma with high popularity and a strong personality. The dark side of charisma was also brought up in the interviews. Many respondents argued that many of their colleagues become arrogant, individualist and selfish.
Another quality which was mentioned in the interviews was the capacity to debate. A senator in Uruguay said that political debate helps to define personal positions, to clarify ideological preferences and to manifest your values.
A young _Asambleísta_ in Ecuador recognized the lack of political training and formation among the new generation of leaders by pointing out that 'we need to discuss concepts, ideologies and political traditions, we need to build a government plan, to study the current situation and to plan the short-term future'. We found that the absence of training and formation was a feature of all the countries considered in this study. Despite the fact that there are a significant number of schools organized by political parties, social movements, international organizations and churches, our respondents agreed that young militants and politicians do not have proper training and formation. This was a more acute concern in Argentina and Ecuador because of the recent renovations that opened the door to younger generations of politicians. Respondents in Colombia and Uruguay recognized that a political career was more structured and thus politicians were gaining experience over time.
We also asked about communication with followers. Most of our respondents said that they were active on Facebook and Twitter. According to our research, the majority of our interviewees used the platform to upload activities and promote themselves but they were not very interactive with the followers. It was very common to hear expressions about preferring the old type of communications and the face-to-face meetings. We were told by many respondents in our five countries that 'the main political theatre is the street'; 'to be in the street with the people is our aim'; 'in politics you have to be connected to people'; 'political parties have to be closer to the people'. The younger generation was more inclined to combine the internet platforms and the personal contact with followers.
Having discussed leaders' qualities, we asked about leaders' deficiencies. The shortfalls mentioned most often were in relation to honesty, ethics, tolerance and transparency. Some of the respondents suggested that to improve the democratic quality of leaders it was necessary to tackle corruption and increase accountability and transparency in private affairs. Thirty-six per cent thought that the separation between the public and private spheres should be clearer.
One of the last questions which actually sprang more out of curiosity than methodology was to ask whether any other family member (partner, children, brothers or sisters) was in politics. This produced some surprising answers. Some said that they would not consider it a good choice for their children to go into the same profession. From that we deduced that they considered a career in politics to be rather negative and that they did not want their children to experience problems similar to theirs. In other cases it was surprising how many family members had had political careers, demonstrating both nepotism and power dynasties. In only a few cases did a respondent express regret that nobody had followed in their footsteps.
In one of the most important questions we gave our respondents the opportunity to explain how they conceptualized democracy. In every country more than 30 per cent replied that democracy is a regime that guarantees division of power. One member of PAIS in Ecuador said that 'democracy can ensure that the executive does not interfere with the legislative'. Democracy was also considered a guarantor of political representation and protection of minorities.
Unanimously democracy was named as the best form of government. In Ecuador, 69 per cent of the respondents argued that democracy can control leaders. One _Asambleísta_ said 'democracy need citizens who are well informed'. In Colombia the emphasis was on democracy as a political regime with tolerance and transparency. It was also pointed out that democracy should promote a clear division between private and public affairs. In Uruguay, 40 per cent of respondents argued that democracy guarantees political representation and 20 per cent that it protects all political ideologies. In Argentina, politicians talked about accountability and consensus. Finally, in Venezuela, democracy was seen as a political regime that promotes tolerance.
Legislators in their buildings
Politicians know that when they speak they should show some vocation to work for the public good. In an interview, the leader knows what they should say to be perceived positively by an interviewer. However, we found other ways to assess political leaders. For the most part the interviews with legislators took place in parliamentary buildings. We visited legislative palaces and annexes, since both contained parliamentary offices. Some legislators had their own private offices whilst others met us at their party headquarters. We learned a lot about democracy in each of the countries simply by seeing these buildings and observing the way people worked.
The most modern parliamentary building is in Ecuador. The National Assembly in Ecuador is a new building which replaced the Congress that burnt down in March 2003. It is a modern, light, transparent building with large windows. Its modernity contrasts starkly with the run-down area in which it is situated. The legislators' offices are bright and spacious. The Assembly was a very dynamic space with corridors full of legislators, advisers and journalists and offices full of visitors and people in meetings. It was easy to get into the building despite the usual identity checks. Some of the offices had open spaces where commissions could hold meetings. In some instances, while we were waiting to speak to people, we felt as though we were participating in the meetings as they were held with the doors open. All of this gave us the feeling that this building was an accessible space. We were well received in the Asamblea Nacional, the members gave us their time and hospitality without any problem. Beyond customary Andean friendliness, the Ecuadorean interviewees exemplified the existing polarization in the country and were very clear as to whether they were in favour or against the government of Rafael Correa.
The Argentine Congress has two main buildings: the Palace and the Annexe. The Palace is an imposing building with a green dome. It is opposite but some distance away from the Casa Rosada, which is the headquarters of the executive. The Annexe is in front of the Palace and is a modern, tall, largely glass building. We went to both the Palace and the Annexe and both gave us a similar impression. One afternoon in September 2010 we were waiting in the part of the Palace where the senators have their offices. It is an old grand building with very high ceilings and a magnificent wide marble staircase. We were asked to sit in a huge room just outside the senator's office. The leather chairs were old, broken and dirty but we sat down anyway. While we waited we looked at the lights on the staircase and one of us asked quietly, 'Who stole the lampshade?' Another one of us looked at the oak door and asked, 'And who stole the door handle?' On that floor, in the waiting room, there were neither lampshades nor door handles. We had not lost our past glory but had probably stolen it from ourselves. Who are the people who take things from the Senate? They must be Argentines because we found it hard to believe that a foreigner would come into this building to take a few mementos. Do they put the things on display in their homes like trophies? Do their family and friends look proudly at the lampshades and door handles stolen from the Senate? Is nobody ashamed of this stupid robbery?
If the Palace had a sort of faded glory from another time that we will never recover, the Annexe embodies more current misery. The air-conditioning pipes are bare and dirty. The lifts suggest that they are not maintained regularly. On leaving the lift on any of the floors you are faced with a labyrinth of corridors that have few signs and are dark, dirty, hostile and unkempt. The offices of the deputies are small with narrow staircases and are rather claustrophobic. The degree of deterioration and dirt in the legislative offices surprised us and showed us the neglect that has been introduced into Argentine politics during the years of democracy. One senator told us how difficult it was even to get the curtains in his office washed. Nobody seemed to care about the dirt, the dust or what had happened to the lampshades. Argentina, like its legislative buildings, is going through a bad time politically and old contradictions are mixing with constant neglect. Stealing a lampshade or enriching oneself illegally to the tune of a million dollars goes unnoticed. We had the feeling that in Argentine politics nobody cared about anything.
In Uruguay there is also a Palace and an Annexe. The Palace is quite similar to the one in Argentina and has a sunny internal patio with arabesques and paintings. The building is well looked after and clean. The Annexe is a rectangular building with five floors. When you reach any of the floors there is a person to show you where the legislator's office is. Off the hall there are wide welcoming corridors with comfortable clean seats that do not have holes in them. All the offices which lead on to this corridor have windows, so it is possible to see all the people who work with the legislators. These wide corridors act like impromptu meeting rooms, where you see different legislators talking, having mate, making coffee. They walk past each other and greet each other there, including us when we were waiting to be seen. We met with the legislators we had interviewed in these corridors and they greeted us pleasantly. The Annexe is a simple, clean, welcoming building. These wide corridors encourage people to greet each other and to talk. They are places where everyone knows everyone else; they understand and respect each other. The building is like Uruguayan politics because, as the legislators repeated over and over again to us, they all know each other and that helps to keep corruption under control; nobody wants to stand out and they like to talk until they come to an agreement. The Annexe and the Palace in Montevideo show a Uruguayan political culture that is friendly, respectful and which encourages dialogue. In the corridors there was a feeling of camaraderie and respect. There were no missing lampshades or door handles and the buildings are surrounded by wide avenues, as in the rest of the city. The respect and harmony in both buildings reflect the style of doing politics in Uruguay.
The parliamentary office in Colombia also has an imposing structure, like a traditional court. Wide corridors link the legislators' offices and everything is well looked after. As in the Ecuadorean Assembly there is an atmosphere of intense activity and dynamism with the obvious sense of camaraderie that was so palpable in the Uruguayan parliament. The interviews with left-wing legislators included in some cases heartbreaking anecdotes about threats, exile or assassinations. There was a grief and sadness among some left-wing representatives that was impossible to ignore. Many of the interviews were rather like confessions. The harsh political struggle in Colombia heavily influenced our conversations with legislators. This also had an impact on the security measures required to enter the parliamentary offices. These controls and mistrust permeate the Colombian political game.
Venezuela was a very special case. The governing party officials would not speak to us, nor would any of the opposition legislators speak to us in the Congress. Most of the interviews took place in our hotel. Some opposition legislators admitted that they did not want to be seen with foreign interviewers. We had to spend time convincing a lot of the opposition legislators that our work was academic rather than journalistic. One of the people we interviewed stated that because we were backed by a US organization official party politicians would not speak to us. Consequently we did not visit the Congress or the offices of any legislators. The cessation of the political game and social fragmentation stopped us from evaluating this political space.
If the buildings reveal aspects of the prevailing democracy in each of the countries we visited, we have no hesitation in stating that the best-functioning democracy was in Uruguay. Second place would go to Colombia, with the proviso that many of the stories we heard inside the buildings showed that democracy is a façade for a terribly unequal, unjust and violent regime. Ecuador showed a contradictory face – a new transparent building in a deteriorating neighbourhood. This contrast enabled us to see the paradox of contemporary Ecuador, where the new mixes with the old, where the renewal promised by Rafael Correa involves many of the old guard. It has become another _caudillista_ , clientelistic government within which it is only possible to see a few new elements. It was the Argentine Congress which had the worst effect on us. It appeared to be frozen in time between past glory and present misery. Venezuela left us rather frustrated as we could not get to know anybody with any parliamentary power – if that indeed exists there. Their buildings were closed to us.
At the beginning we had never thought that buildings would contribute to our study. We had not anticipated that in our initial debates, nor was it included in our questionnaires. It was, however, a helpful factor that supported our other findings. The buildings said a great deal about the political game in each country. This was obvious. Often theories do not take into account such observations, as Deslauriers (: 86) pointed out: 'above all qualitative research seeks to show that grand theories can be shown as useless if they are prisoners of a conceptual framework'. Nonetheless, an open-minded, attentive researcher can find useful data in facts and situations that do not correspond to more traditional classifications and which have a tremendous richness.
Conclusions
This chapter explains how we carried out the research. It is not a traditional methodological chapter. Our aim is to show the real process of preparing and carrying out research about political leaders.
We began by addressing the main motivation that has driven this research: the democratic quality of political leaders in Latin America. We explained the different hypotheses that we developed and how the literature review helped us to refocus the study. One of the most important findings of this stage of the research was the need to contextualize the study of leaders historically.
The chapter also described the process of selecting the case studies. We wanted to explore political leadership in stable and unstable political contexts, and therefore we chose five case studies which provided us with a variety of scenarios.
The design of the research, methodological questions and doubts about the sample were also discussed with the aim of explaining the difficulties that we encountered.
We also offered an analysis of the interviews and of the way in which we articulated the questions. We have included some analysis about why the interviewees enter politics, their personal ambitions and aspirations, and their relationship with their followers.
The interviews were the pillar of our research. The opportunities to meet with former presidents, former vice-presidents and legislators gave us a unique opportunity to analyse political leaders. We also discovered that the parliament buildings provide some ideas about the political context. From a personal standpoint, we had the chance to meet 285 leaders, many of whom had been very important actors in the politics of their respective countries. We learned a great deal about them, and many of them engendered in us a rather sad disappointment. Altogether, though, it was a very enriching experience which we have outlined in these pages.
With all this material we faced a huge challenge: how to unravel ideas about leaders and democratic quality from almost 600 hours of conversation? This was a tough task, and we present the main contours in the following pages. We discovered that our respondents connected leaders to legal frameworks, opposition and power. Thus we have articulated different models of democratic leaders taking into account these three elements. In the following pages, the reader will find a suggested classification of democratic leaders.
CHAPTER 2
Models of Democratic Leadership
Introduction
The premise of this book is that the quality of leaders is fundamental to the overall performance of political regimes. We understand leadership as a power relationship between an individual and a group of followers established in a concrete historical context. Leaders can transform the context, and persuade followers to accept change. Leaders in democratic countries can enhance or undermine democracy. In this chapter we offer a new typology of democratic leaders which takes into account the impact that leaders can have on the quality of democracy.
The chapter is divided into four sections. The first section discusses definitions of leaders and analyses their relation with followers and the context in which they operate. The second section presents the context of our research. Based on the interviews, this section briefly analyses the political scenarios in which leadership is exercised in Argentina, Colombia, Ecuador, Venezuela and Uruguay. It also studies the main political trends that can help us to explain the reasons for the emergence of new powerful leaders. The third section studies different typologies of leaders and presents a new typology based on the conclusions of our research. It offers a typology of leaders based on different institutional settings. Indeed, we depart from the assumption that 'context plays a relevant and unavoidable role in democratic leadership' (Teles : 13). The last section concludes with a discussion of the relationship between the context and the emergence of different types of leader.
The leader, the followers and the context
A leader is a person who leads a group of people, a country or an organization. The leader defines the agenda and motivates the group to follow it. In general terms, leaders give directions and provide solutions to common problems. There are many definitions of leadership but most of them include more or less the same pillars: power, influence, inspiration, guidance, vision, ability to understand the context, to diagnose weaknesses and strengths and to set the agenda with goals and effective solutions.
Political leadership is the ability to influence, motivate and inspire. An individual becomes a political leader because he is able to modify the course of events (Blondel 1987). A leader should be able to make a difference, and to influence his followers' attitudes, beliefs, demands and needs (Masciulli et al. ). He has to have the capacity to interpret citizens' aspirations and to understand the national interest. He needs to motivate citizens to follow him. He must be capable of understanding the historical context, the complexity of different political scenarios and the alternative solutions available. The leader has to interpret the problems, prescribe ends and means to solve them. The leader has to present his personal visions to attract and mobilize followers (ibid.). A leader should be able to 'bend' the context and his followers (Teles : 5). However, his power has to be limited by the institutions of the state and the followers. Powerless institutions and/or followers make political leadership unpredictable and probably undemocratic.
As suggested by Nye (), the leader has to create the group, set the agenda and the strategy to achieve it. He has to help to build the group's identity. However, a leader can also emerge from a group of people who have coalesced around specific objectives. In this case, the leader has to accept the challenge and set the strategy to achieve the goals.
Analysts have also agreed that the definition of political leadership has strong cultural and historical contextual components. These components should be taken into account when political leadership is defined and analysed (Masciulli et al. 2009). It has also been argued that political leadership should be studied historically and comparatively (Teles : 1).
The leadership literature endows a democratic leader with a significant number of qualities. A democratic leader is identified as an individual who has vision, courage to innovate, integrity, intelligence, shrewd judgement, tolerance, flexibility, the ability to implement changes and absorb information, to interpret different views and to build consensus (ibid.; Brown 2014).
There is no leader without power or followers because a leader exists if and only if there is a group of people that supports his agenda. Leadership and power go together, establishing an asymmetrical relationship: 'political leadership implies holding a certain "amount of power", but the opposite is not true – it is possible to have power (for instance, in hierarchical relations) without being a leader' (Teles 2012: 117). Power has been defined many times before. Lukes' () definition understands power as the capacity to make or resist changes. Dahl () explains power as the ability to make others do what they would not have done otherwise. This could be achieved by coercion or persuasion. These different approaches divide power, according to Nye (), into hard and soft power. The first is identified with threats or privileges and it is used to make others change their actions, attitudes and or/decisions. On the other hand, soft power is the capacity to obtain results by inducement and persuasion with no manipulation. Soft power seems to be an essential attribute of a democratic leader. Nye (ibid.) argues that effective leadership requires a combination of soft and hard power, known as smart power.
As there is no leader without followers, even bad leaders have them. The followers have a crucial role in monitoring what the leader does, pushing for transformation or abandoning the leader. People follow leaders for different reasons. In politics, we follow leaders in the hope that they can solve our problems and manage public goods. They give us a political identity and ideals. They are inspirational and persuade us that they know how to govern. Bittner () argues that followers evaluate leaders according to two main factors: character (looking at honesty and compassion) and competence (looking at intelligence and strength). There are important biases in the way followers perceive political leaders. In general terms, leaders from conservative parties seem to be considered more competent while left-wing leaders are seen to have more honesty and compassion (ibid.).
Thus, followers matter; their role is crucial in legitimizing, passively or actively, both good and bad leaders. In order to understand the emergence and endurance of bad leaders, followers are as relevant as the leaders themselves. Above all, followers matter because 'those who can bring a leader to power can also bring the leader down' (Bueno de Mesquita and Smith 2011: 59). Hirschman () conceptualizes followers' attitudes as exit, voice and loyalty. Through these, followers seem to have the key to discarding a bad leader. The main problem is that, in the literature, leaders remain overvalued and followers undervalued, despite the fact that followers are crucial to limiting leaders' powers, especially now with the spread of information (Kellerman ). If followers abandon the leader, then he loses power and the leadership relationship is gone. The followers are no longer there to legitimize the leader's authority.
Leadership studies tend to concentrate on the 'strongman', paradoxically proclaiming what they want to avoid, which is the cult of the leader (Burns 1978). This is closely related to the personalization of politics. Teles (: 3) points to a set of changes that have helped the process of personalization: institutions accord more relevance to individual politicians than to collectivities; electoral campaigns are centred on individuals; politics is understood as a competition between leaders and political preferences are formed by individual political actors. This trend had already been highlighted by Fabbrini () when he confronted the increasing power of the democratic Prince with the deterioration of political parties. Both studies attempt to emphasize that the political leader makes a difference. This is the case in strongly controlled democracies where the systems of checks and balances work, but much more so in countries with weak institutions. We argue that, in an institutionally weak political scenario, some political leaders can become necessary causes, understood as the 'outcome would not have occurred if the cause had been absent' (Mahoney et al. 2009: 118). Following Barrington Moore's idea of 'no bourgeoisie, no democracy', can it be argued 'no Chávez, no _Revolución Bolivariana_ ' or 'no Correa, no _Revolución Ciudadana_?' We advance the idea that there is a combination of political factors that help the emergence of a political leader and help him to become a necessary cause. Taking into consideration the five countries that we study for this book, we would suggest that the degree of institutionalization of political parties seems to be a crucial factor with explanatory power.
If the leader is an individual who has power and is in charge of creating a group, an identity, an agenda and a strategy, what or who creates a leader? For some analysts a leader is an individual born with specific abilities that can be developed in school, the workplace or in a political environment. Others would argue that a leader emerges thanks to historical conjunctures (Tucker 1977). The classical example given for the latter is Winston Churchill, who was a secondary politician in Great Britain until the beginning of Second World War. Our analysis should be placed within the latter category since we aim to observe the different domestic political factors that promote the emergence of different types of leaders in Latin America. In this book we are interested in exploring the political conjunctures that inspire the emergence of different leaders. As Masciulli et al. () argue, leadership is a historically concrete phenomenon. Therefore, the research needs to take into consideration beliefs, values, characters, power relations, ethical and unethical values, attitudes and actions of formal and informal institutions. Thus, the historical and cultural-institutional context is essential to analyse patterns of political leadership (Nye 2008). As Kellerman (: xiv) puts it, 'leadership does not take place in a vacuum. All leader–follower stories are set in the particular contexts within which they unfold.' We followed two debates that help us to highlight the need for the contextualization of leaders. The halo effect (Thorndike 1920a, 1920b) explains that a leader can be praised or demonized to such an extent that is impossible to assess his achievements or failures in a balanced way. Thus, our perception of a leader can be contaminated by making inferences on the basis of a general impression (Rosenzweig 2007). Indeed, we could judge the leader by the country's economic performance, simply accepting the idea that achieving economic growth is the outcome of a good leadership and an economic recession the outcome of a bad one. The halo effect can be very damaging because it can compromise our analysis. The romance of leadership (Meindl et al. 1985) can also undermine the objectivity of the study. This was particularly important as we were analysing political leaders in a region which historically has a messianic view of leadership. Because of the interviews, we faced the risk of understanding events only in terms of leadership. In other words we risked being biased in associating leaders only with political outcomes in a positive or negative sense. We argue that the contextualization of leadership helps us to overcome this risk. Most importantly, we selected our interviewees from different political backgrounds which contributed to our receiving different perceptions of leaders and political processes. Despite our precautions, the study of leaders is always risky and can easily be influenced by the halo effect or a romantic perspective. There is a higher risk when political leadership is studied in regions with long traditions of strong leaders. The halo effect was omnipresent in the interviews in Venezuela and Ecuador, where society has been deeply polarized by Hugo Chávez and Rafael Correa, respectively. To place the leaders in their political context improves the chances of avoiding a romantic perspective.
Through 285 interviews with political leaders in Latin America, we aim to understand and explain the historical and cultural-institutional context in which leadership is exercised and to explore the political causes that explain the emergence of different types of leaders. We observe that in Latin America, the political context is mainly dominated by historically powerful leaders, mobilized followers and weak institutions.
The scenario of our research
Since 1985, and owing to social revolts or parliamentary pressure, twenty-one Latin American presidents have left government abruptly. In this context, the democratic deficit or the gap between citizens' aspirations and their level of satisfaction increases. In many countries, democracy may be seen as the preferred form of government, but in many states society remains 'deeply sceptical when evaluating how democracy works' (Norris : 5). In Latin America 79 per cent of citizens believe that democracy is the best political regime but only 57 per cent of them are satisfied with its results (Latinobarómetro 2013). While followers may have been able to provoke the fall of presidents, they have not managed to avoid the re-emergence of deep-rooted political practices under subsequent administrations. Thus, presidential crises in Latin America showed that followers can get rid of bad presidents but have been unable to ensure that the newcomer will be any better. Therefore one of our questions is why followers could be wise enough to dismiss bad leaders but not sagacious enough to prevent the access of new bad leaders.
The context of our research is marked by the post-presidential crises scenario in Latin America. In our region presidents stand out. Presidential leaders matter more in presidential and semi-presidential regimes and even more under majoritarian electoral systems and two-party systems (Webb et al. 2012). It has been argued that presidents have become 'guardians of the laws and symbols of national values' (Lord 2003: xii). Citizens look to presidents for justice and inspiration and, therefore, the character of presidents, their values, beliefs, behaviour, traditions and ideas, matters. When all these seem to have become extremely relevant, the 'personal integrity in our leaders seems both more fragile and more necessary than ever' (ibid.: xii).
The recent presidential crises seemed to be a short-term solution but did not solve the long-term democratic deficit. We have identified a significant fault in most Latin American democracies: there are no clear paths for the formation of democratic leaders and no tools to avoid undemocratic, dishonest and/or inefficient leaders being elected. Political parties have been losing ground as the institutions which enable politicians to gain expertise and be selected for public office. As Fabbrini () has pointed out, there has been a process whereby power has increased for individual politicians but deteriorated for political parties. This process, previously known as presidentialization, had already been identified by Juan Linz (). His analysis highlighted presidentialism's rigidity. Linz (ibid.: 55) argued that in time of crisis the negative risks of presidentialism increase, 'ranging from the death of the incumbent to serious errors in judgment committed under the pressure of unruly circumstances'. Thus presidential rule is less predictable and often weaker than alternatives. Increasing presidential powers makes the president stronger and the risks higher. Presidentialism, combined with extraordinary powers, places the destiny of the nation in the hands of one individual and Linz (ibid.: 69) cleverly pointed out that 'heavy reliance on the personal qualities of a political leader... is a risky course'. Latin America provides too many examples of presidentialism under different conceptualizations, such as _caudillismo_ or populism. Indeed, in Latin America extreme presidentialism has gone hand in hand with populism and a low degree of institutionalization. The recent presidential crisis deepened this situation. The fall of presidents affected the political parties more than the leaders themselves. In fact, in many cases the legacy of the presidential crisis was the emergence of another strong leader.
In Latin America our context is dominated by historically powerful leaders, mobilized followers and weak institutional settings. This was the scenario presented to us in the interviews. With the exception of our Uruguayan respondents, the interviewees refer to powerful presidents when asked about leaders. Presidents concentrate executive power and in many cases they usurp power from other institutions, especially the legislative. Presidents in Latin America disempower the institutions to empower themselves. The followers deify or hate them, and politics is played in the extremes of a very polarized society in which democracy becomes blurred.
Our research led us to conclude that some Latin American countries seem to have fallen into a political trap: weakly institutionalized regimes undermine political competition which in turn helps leaders increase their autonomy and subsequently the quality of democracy deteriorates. Leaders become autonomous and democracy becomes dependent on their actions. This trap was described in many of the 285 interviews undertaken for this study: the logic behind it seems to be that concentration of power, despite its negative consequences, secures political stability.
For the purpose of this study, Argentina, Colombia, Ecuador, Venezuela and Uruguay were chosen because all suffered similar deep political and/or economic crises. However, the outcomes were different: five presidents were expelled in Argentina, three in Ecuador, one in Venezuela and none in Uruguay and Colombia. In Argentina, Ecuador and Venezuela the crises brought about the fragmentation or collapse of the party systems and the emergence of strong leaders. Economic crises became political crises. In contrast, in Uruguay the 2002 crisis neither affected the political party system nor did it become a political crisis. However, the traditional political parties lost the elections and the Frente Amplio won the presidency for the first time since its creation in 1971, without affecting the political system. Colombia's long conflict has been managed with a high degree of institutionalization of its political party system and an inexplicable level of political stability. While the political parties underwent important transformation following the constitutional reform of 1991 and the 2003 political reform, political stability and a high degree of institutionalization allowed a strong leader such as Álvaro Uribe to come to power but also helped to control his political ambitions.
In Latin America the majority of political parties have not modernized following the transition to democracy. Of course, the parties have assumed the defence of democracy as one of their main pillars but most of them have been unable to democratize their internal institutions and internal organization, their ways of accessing power, debates and discourse. Many parties lack advisory teams or think tanks that could structure their political thought, strategies, tactics and an agenda for government. Some of the political parties are mere electoral machines, organized around one strong leader. If we believe that democracy still functions through political parties, their problems will be seen to cause a low-quality democracy and will be reflected in the poverty of public policies and agendas for government. The deterioration of political parties makes a low-quality democracy more likely. The decay of political parties is concealed by the emergence (or the construction) of charismatic leaders (OEA and PNUD 2009). Many Latin American political parties, rather than control or monitor their leaders, deify them and provide them with a wealth of power resources. Leaders are increasing their power while political parties are fading away (Fabbrini 2009). In electoral campaigns, leaders seemed to have replaced parties and debates. Indeed, elections are more related to the personal characteristics of leaders than to the policies and government objectives that they represent. Most of the messages seem to be ambiguous, made for a television audience rather than for politically aware citizens. In this context, populist leaders spread. While political parties are unable or unwilling to control or monitor their leaders, populism and clientelism seem to expand and flourish.
State institutions are also crucial in overseeing democratic leaders' behaviour. If institutions legitimize leadership, they should be able to monitor it. The formal institutions of the state have been considered, mainly by John Locke, as tools to secure the rights of the led (Kellerman 2004: 16). The institutions should have the capacity to restrain the power of the leader. The combination of powerful leaders and weak institutions distorts the pillars of liberal democracy. The institutions' weakness increases expectations of leaders' capacity to solve the problems that the political system has been unable to clear up. Citizens look for powerful leaders to compensate for the weakness of the formal institutions of a political regime. But in the long term, strong leaders become an obstacle to the strengthening of formal institutions. Indeed, strong political leaders may well not find incentives to empower institutions that could control or monitor their activities. In Latin America, most of the strong leaders have not worked towards the strengthening of formal political institutions.
By the end of the 1990s, politics in Latin America altered with the emergence of new, populist, leaders. Here we analyse only some conceptualizations of populism since leadership can adopt many populist forms. There are too many definitions of populism and, paradoxically, some analysts argue that it is a difficult political phenomenon to grasp. Germani's (, ) definition is still very influential. Populism was conceptualized as a stage on the path towards modernization that basically helped to include the working class in politics. De la Torre () offers three historical categories: classical populism, which was born out of the import substitution industrialization process; neopopulism, which was the product of the end of industrialization and the implementation of neoliberal policies; and radical populism, which emerged with the collapse of neoliberalism. The former president of Brazil, Fernando Henrique Cardoso, argues that populism means the exercise of power without institutional mediation or control. It is mainly based on the direct relationship between the leader and the followers, which is based on the exchange of political or social goods (Botana 2006). Other analysts have interpreted populism as a tendency to reduce the number of veto players in politics and the power of institutional control (Navia and Walker 2010).
In order to understand populism, analysts have traditionally related this political phenomenon to economic inequality. Most of the works presented by De la Torre and Peruzzotti () argue that populism emerges when an economically dominant elite perpetuates itself in power. Therefore, populism is understood as a response to that political and economic domination.
Here we argue that the leader is crucial in the development of a populist model. Without a leader, populism cannot flourish. Usually the populist leader has some degree of charisma. The discourse of a populist leader builds a strong polarization between 'them and us'. While populism is presented as a political tool for inclusion and a vehicle for change, in recent decades populism has been unable to generate long-lasting wealth redistribution. Despite its revolutionary rhetoric, populism has not produced deep transformations in economic structures. However, it has persisted since it established a political regime that allows millions of citizens to have access to social goods. The Venezuelan case is the best example of this.
This phenomenon goes hand in hand with clientelism. Citizens receive social benefits in exchange for political loyalty (Abente Brun and Diamond 2014). Leaders receive votes in exchange for the distribution of social or other benefits. The equation means that both actors win and thus there are no incentives for change.
Our research reveals powerful leaders who most of the time use populism and clientelism to increase and maintain power. These powerful leaders usually usurp power from other institutions of the state, manipulate the rules and weaken democracy. Followers are polarized – while some support the leader, others hate him. Their political participation can be either controlled by the leader or non-existent. However, when crises hit, followers are ready to expel the leader, looking for another saviour. Their participation in political parties had declined but they fill the streets to support their new leader or to show their discontent.
The makers of democracy in Latin America seem to be more worried about their role in the political process than in the end result of the process. Rather than working to improve the quality of democracy, the majority of political leaders seem to be more concerned with increasing their share of power to achieve a privileged position. Leaders in Latin America think of power as hard power, democracy as concentration of power in the executive and leadership as requiring a strong political figure who can surpass the limits imposed by laws and institutions. According to one of our respondents politics has become a 'bonfire of vanities' and leaders seem to be more important than democracy.
Categorizing the leaders
Inevitably, when studying leaders, the researcher is inundated by ethical ideas about good and bad, right and wrong. Nye's contribution () is related to the conceptualization of the word good: a leader can be good in moral terms or according to his degree of efficiency. Even if the goals are morally wrong, the leader could still be considered good if he is able to achieve them. He could be efficient but morally wrong. On the contrary, good leadership should be good both ethically and instrumentally. Unfortunately we have to agree with Masciulli et al. () that 'if we decide to limit the studied universe of leaders by weeding out all tyrants, egoistic "power-wielders" and morally deficient individuals, the remaining number of cases might be too few from which to draw any meaningful conclusions'.
The number of typologies of leaders has recently increased, especially those that differentiate leaders in the private sector (Harvard Business School 2011; Kellerman 2004; Nye 2008). Typologies help us to categorize objects or subjects. In the case of leaders, they help us to put some logical order among the different types that have traits in common or that are extremely different. To put some order into the varieties of leaders helps us to discover trends and foresee the influence that leaders could have at the national or international level. Typologies help us to draw a map of differences and similarities in the emergence and the performance of leaders.
A classical typology of leaders was designed by Aristotle drawing a line between self-interested leaders and common-interested leaders (Table 2.1). His typology is based on the number of leaders, their motivation and result. His typology is a valued-based, nominal typology.
TABLE 2.1 Self-interested and common-interested leaders
| Motivation and result
---|---
Number of leaders | Self-interested | Common-interested
One | Tyranny | Kingship
Few | Oligarchy | Aristocracy
Many | Democracy | Polity
SOURCE: Masciulli et al. ()
The difference between attempting to reach self-interest and common interest can correlate to what Kellerman (: 34) calls ethical and unethical leadership. The ethical leader put his followers' needs before his own, has private virtues such as courage and temperance and exercises his leadership in the interests of the common good. Bueno de Mesquita and Smith (: xviii) present a more brutal argument by which 'politics is about getting and keeping political power. It is not about the general welfare of "We, the people".' By analysing dictators and exploring the reason why 'bad behavior is almost always good politics', they argue that politics is about individuals, each motivated to do what is good for them, not what is good for others (ibid.: xix). Therefore, from their perspective, there is no leader who is willing to achieve only the common interest unless it implies also achieving self-interest.
Other typologies of leader, outlined by Max Weber (), Burns () and Deutsch (), are more related to the functioning of the leadership relation. Max Weber organized his typology around his idea of the different types of domination. Thus, there are different types of leaders according to the kind of domination that they exert: traditional, rational-legal or charismatic. The most studied one is the charismatic domination, in which the leader is gifted with extraordinary powers and is able to transform the political scenario. James MacGregor Burns () identifies two basic types: the transactional and the transforming. Most of the leadership relations are transactional: leaders and followers exchange one thing for another such as jobs for votes, or tax benefits for campaign contributions. The transforming leader aims to satisfy higher needs and engages the follower fully. The result is a relationship of mutual stimulation. Deutsch's typology is simpler since it divides the leaders according to the power resources they hold: strong and weak (Deutsch 1990). Kellerman () offers a typology of bad leaders that includes seven different types: incompetent, rigid, intemperate, callous, corrupt, insular and evil. However, she also argues that there are two main categories: 'bad as ineffective and bad as unethical' (ibid.: 32). Most ineffective leaders are judged such because of the means they employ to follow their goals. In general, most leaders define reasonable objectives but fail to reach them.
We offer a new typology of democratic leaders which has been built through a qualitative analysis of the 285 interviews conducted in Bogotá, Buenos Aires, Caracas, Montevideo and Quito. In order to build up the typology, we have analysed three elements: the political context, the ability of the leader to lead and the impact of the leader on the quality of democracy. We developed a typology which is based on three dimensions: the relationship between the leader and the rule of law; his efforts to achieve consensus or to provoke polarization and his methods of increasing power. Our typology of democratic leaders is normative with an emphasis on the impact that leaders can have on democratic quality.
From the analysis of the interviews, we have identified four different groups of democratic leaders: democracy enhancers, ambivalent democrats, soft power usurpers and power usurpers.
Democracy enhancers include leaders who push for the building or reinforcement of democratic institutions, accept power limits imposed by state institutions, respect and promote democratic rights and civil liberties and leave their posts on time. They are usually inclined to share power and responsibility, build consensus and avoid polarization. This type of leader belongs to a political party in which he has developed his career. The party tends to maintain its principles and norms and has some internal rules to monitor the performance of its members. Therefore, democracy enhancers are not autonomous. Following Aristotle's typology, these are leaders who aim to enhance the common interest. According to Kellerman's idea, they are ethical leaders. Democracy enhancers are more inclined to use soft power. They are categorized as rule developers, bridge builders and respectful of the limits imposed by state institutions (Table 2.2).
TABLE 2.2 The democracy enhancer
Rule developer | Pushes for the building or reinforcement of democratic institutions
---|---
| Promotes and respects horizontal accountability
| Promotes and respects democratic rights and civil liberties
| Respects freedom of the press
Bridge builder | Builds consensus
| Tolerant
| Works with his cabinet
| Inclined to share power and responsibility
Respectful | Accepts power limits imposed by state institutions
| Leaves his post on time
The ambivalent democrat respects people's rights, works in a cooperative manner but seeks to accumulate personal power. This type of leader believes that strengthening his position requires negotiation and making concessions. He is able to work in a team and can work with the opposition. However, the ambivalent democrat has a clear tendency to accumulate power. The leader accepts normative regulations but gives himself a leading role in their application. Unlike the democracy enhancer he respects but does not strengthen democratic institutions. The ambivalent democrat can actually end up weakening democracy in his bid to increase his own personal power. He follows rules and is a receptive leader and a soft challenger (Table 2.3).
TABLE 2.3 The ambivalent democrat
Rule-obedient | Respects democratic rights and civil liberties
---|---
| Respects freedom of the press
| Respects horizontal accountability
Receptive | Accepts consensus
| Relatively tolerant
| Works with his cabinet
| Sporadically works with the opposition
Soft challenger | Challenges power limits imposed by state institutions
| Agrees to share power and responsibility
| Leaves his post on time
The soft power usurper navigates between challenging and accepting the rule of law and state institutions. The historical context becomes crucial since it can allow or block the leader's ability to gain autonomy. In crises, the collapse of party systems, situations of extreme violence or abrupt changes in the international context, this politician can take advantage of these exceptional phenomena to reduce the scope for action of other institutions. However, at some point in this power-building process, a break is applied by his party, the judiciary, the legislative power or even societal pressure. On these occasions the soft power usurper retreats in the hope of new favourable conditions arising that will enable him to fit the political game to his own personal or collective aims. Nevertheless, this retreat is never total, so each new advance is a step towards a greater degree of autonomy than at the beginning. The leader is conscious of his strategy and knows that at some stage he will be able to confront the restrictions posed by the system. Hence a central resource is to win legitimacy by gaining the support of society. To do this he engages in activities to win over supporters, possibly providing them with concrete benefits. A leader's popularity is a useful tool to convince detractors about the cost of changing the agenda. This does not necessarily require populist policies but it does call for action that has a high symbolic value for the population. The soft power usurper has more faith in his personal power than in political rules. If he can, he tends to go against the normative framework to accumulate power or ensure the permanency of his government. The soft power usurper always takes advantage of any favourable situation to weaken his opponents or to dominate press coverage. He is not worried about party control or the needs of the citizenry. The political party is merely a vehicle by which he achieves his aims. Soft power usurpers have no compunction about using resources to divide public opinion or insult their opponents. Democracy for the soft power usurper is most definitely a means not an end. This type of leader is a rule challenger, a soft polarizer and a power builder (Table 2.4).
TABLE 2.4 The soft power usurper
Rule challenger | Sporadically manipulates constitutional or electoral instruments
---|---
| Sporadically usurps power from institutions
| Uses clientelism and populism to increase his personal power
| Undermines civil liberties and freedom of the press
| Undermines horizontal accountability
Soft polarizer | Accepts polarization
| Somewhat intolerant
| Avoids a power-sharing decision-making process
Power builder | Capacity to ignore the rules and citizens
| Attempts to undermine political opposition
| Ideologically strong
| Wish to perpetuate himself in government
| Accords more importance to personal promotion than to democracy
In turn, power usurpers accumulate power by absorbing it from other state institutions, either by minimizing the role of the legislative or by undermining the independence of the judiciary. Power usurpers are democratic leaders since they have been elected in free elections. In some cases, they are very popular leaders, who have achieved more than 50 per cent of the vote. However, while democratically legitimate in origin, some end up manipulating constitutional or electoral instruments to increase personal power, thus worsening the quality of democracy. Power usurpers can be part of a political party, but the party tends to be a mere tool to augment power or win elections. In many cases, the party has been created to support the leader or is manipulated to increase the leader's power. This type of leader does not accept power-sharing decision-making processes. They are autonomous and, by usurping power, they increase their capacity to ignore rules and citizens while in government. Power usurpers believe that they are the only legitimate representatives of their people. Politics becomes embedded in them. In Latin America, power usurpers usually establish populism and clientelism as political instruments to retain power. They tend to aspire to perpetuating themselves in power. They could be considered self-interested leaders or unethical leaders according to Aristotle and Kellerman, respectively. Power usurpers are prone to hard power. They are defined as rule manipulators, polarizers and power maximizers (Table 2.5).
TABLE 2.5 The power usurper
Rule manipulator | Manipulates constitutional or electoral instruments
---|---
| Usurps power from institutions
| Uses clientelism and populism to increase his personal power
| Undermines civil liberties and freedom of the press
| Undermines horizontal accountability
Polarizer | Increases the polarization of society
| Intolerant
| Does not accept a power-sharing decision-making process
Power maximizer | High capacity to ignore the rules and citizens
| Undermines political opposition
| Ideological polarization
| Perpetuates himself in government
| Accords more importance to personal promotion than to democracy
We do not offer this typology as an end explanation; rather its aim is to be a reliable tool to classify leaders and understand their impact on the quality of democracy.
Conclusion
When we developed our study, one of the main trends in Latin America was the deterioration of political parties with the reinforcement of presidentialism. Our typology reflects that. We have suggested four types of leaders and we describe them according to their relation with the rules (obey, challenge or manipulate), the opposition (polarize, tolerate or build consensus) and power (share, concentrate or usurp). We want to emphasize that the four types describe democratic leaders who have been elected by free and fair elections. Our typology advances the idea that they can became illegitimate owing to the way they subsequently exercise power.
In the following pages we use our typology to analyse leaders in each of our case studies. First, we examine the context, offering an analysis of the post-crises scenarios. Secondly, we lay out the qualitative analysis of the interviews. Finally, we examine case studies using our typology. Therefore what follows has two levels of analysis. First, we contextualize the understanding and the exercise of leadership at the national level. Secondly, we confront our typology with specific cases which were discussed in the interviews, such as Álvaro Uribe or Cristina Fernández de Kirchner.
As our study contextualizes leadership, we suggest that the emergence of different types of leader has to be explained by a combination of domestic conditions and individuals' ability, and therefore we combine these two different levels.
The next chapter shows how the combination of strong parties in different political contexts gave rise to distinct leaderships in Uruguay and Colombia.
CHAPTER 3
Leadership in the Context of a Stable Party System: Uruguay and Colombia
Introduction
In the second chapter we set out the different types of leadership in our typology, which we based on the arguments expressed by the politicians we interviewed. The two cases we discuss in this chapter both have stable political systems and strong political parties but went through very different crises. The political responses to these crises were also different. While in Uruguay the response followed the democracy enhancer leadership model, in Colombia we see the ambivalent democrat model.
According to the literature, political parties should have institutionalized mechanisms to control their leaders (Fabbrini 2009: 209; Valenzuela 2004: 5–19). This is indeed the case in both Uruguay and Colombia, but with different degrees of intensity. From the fifty-six interviews we carried out in Uruguay it was clear that the Uruguayan political class understood the historical context in which they were operating and could introduce new alternative policies without upsetting the institutional foundation of the country. Uruguay has a collective leadership rather than an individual one. It can interpret problems and find solutions without breaking with existing norms. If there is a change of administration from one party to another, the leaders strengthen the democratic institutions and accept the limits imposed by legislation. They are politicians who stimulate political competition and do not seek to subjugate their opponents. Politics is based on responsibility and consensus-building. When in power, governments broaden the spectrum of rights and civil liberties and then step down without having changed the rules to their own benefit. The political race is considered to be a long, slow process with distinct stages. Their democratic leaders are not autonomous but work within an institutional framework that they strengthen and respect.
Colombia has had a stable exclusive two-party system. The Liberal Party (Partido Liberal, PLC) and the Conservative Party (Partido Conservador, PC) dominated the political scene from the middle of the nineteenth century until the end of the last century, when there was a degree of opening of the party system. This domination brought about personalist leaders and a concentration of power in them. However, the party system held firm. The division of powers also functions well. Following our fifty-four interviews we categorize the Colombian political class as being closest to the ambivalent democrat model. On a number of occasions there were attempts to change the legal framework but the institutions imposed limits on these reforms. Leaders respected state and party rules even though they did try to take more power for themselves. This led to a peculiar crisis situation. Unlike the economic and political imbalances in the other cases in our study, the Colombian crisis was the product of political violence and the break-up of the state's monopoly over security. Colombia has at times departed from democratic rules and then at others embraced them more fully. Our interviews in Colombia enabled us to observe how the different political forces interact and compete within a set framework of regulations. But it was also clear that the political game involves a degree of rather shady dealing and clientelist practices that erode the system.
This chapter analyses the different leadership types in Uruguay and Colombia. We first look at the political contexts, in particular the party political system in Uruguay and constitutional reform in Colombia. Secondly, we offer a detailed examination of our interviews, comparing the party systems with the types of leadership. Thirdly, using our leadership typology, we outline the types of leader that pertain to each country. The final section puts forward some ideas about the leadership types that emerge in stable party systems.
Contexts and systems at times of crisis
Uruguay
In the democracy index published in 2013 by the Economist Intelligence Unit (), Uruguay is the only country in South America to be considered a full democracy. The only other qualifying Latin American country in this group of twenty-six countries is Costa Rica. Chile is in thirty-fourth place. Then, farther down the list, starting with forty-sixth place, there are other countries from the region such as Panama, Brazil and Mexico. The index is based on five categories: electoral processes and pluralism, civil liberties, functioning of government, political participation and political culture. In the case of Uruguay, the categories of civil liberties and electoral processes and pluralism score 10, while political participation scores less than 5. Political culture scores 7.5 and the functioning of government 8.57. Obviously there are a few weaknesses in this index. Nonetheless, it is an instrument that shows something quite clear: Uruguay stands out as a positive beacon of democracy in the region. This is even clearer within the framework of our comparative study on political leadership.
The relative calm enjoyed by the Uruguayan political system hides dynamic innovative processes. Uruguay has a stable and pluralist party system with a culture of consensus rather than polarization (Lanzaro 2001; Cason 2002). Pluralism is a long-standing characteristic that grew out of the balance of power between the different political forces. Although Uruguay is a country where politicians are well known by name, Uruguayan leaders such as Jorge Batlle, Julio María Sanguinetti, Luis Lacalle, Tabaré Vázquez and José Mujica did not personalize politics. They did not seek to concentrate power in their own hands or hold on to power indefinitely (Diamint and Tedesco : 39).
The Argentine crisis in 2001 caused a lot of turbulence for the Uruguayan banking system. Uruguayan banks received a large number of deposits from Argentine citizens who were trying to escape the collapse of their economy. In 2002 some of the deposits began to be withdrawn, which risked the security of the Uruguayan banks. President Jorge Batlle of the Colorado Party decided to step in to bail out some of the banks but not others, thereby increasing uncertainty. The banking crisis and the situation in Argentina led to social unrest and looting. But the citizens did not demand 'all must go' ( _que se vayan todos_ ). President Batlle ended his term in office with a very low approval rating but the party system did not disintegrate. At the end of his mandate in 2004, the Colorado Party had only ten deputies and three senators. Batlle won a seat in the Senate, heading the Colorado list, but he refused to take it, blaming himself for his party's defeat.
Uruguay had been a stable democracy from 1918 until it broke down in 1973 with the administration of President Juan María Bordaberry. He allowed a civil–military dictatorship to be installed, which lasted until 1985. Following the failure of a plebiscite in 1980, which the military hoped would legitimize their rule, a process was set in motion to achieve a consensus with civil society. To this end, the military sought the involvement of the political parties. The parties that were 'frozen' during the dictatorship were in a good position to rejoin political society once the political arena was reopened (Rial 1990: 24; González 1985). The Naval Club Pact led to an opening of politics with the inclusion of left-wing parties and their legalization. Although the armed forces tried to stonewall over the amnesty created in the pact, they did agree to allow the legalization of Frente Amplio.
These first elections brought Julio María Sanguinetti (1985–90), of the Colorado Party, to power. He had proved himself an able negotiator with the military, which agreed to step down peacefully. The National Party (known also as the Blancos) suffered a degree of fragmentation and division but began to reconstruct itself thanks to a young politician, Luis Alberto Lacalle (1990–95), and some alternative policies. During the presidency of Jorge Luis Batlle Ibáñez (2000–05), who came from a traditional political family, the country suffered the 2002 financial crisis. The devaluation of the peso and an increase in public debt had a definitive effect on the result of the presidential elections of 31 October 2004. Batlle's rival from five years previously, Tabaré Vázquez (–) of the Frente Amplio, won the presidency.
The victory of Frente Amplio marked a fundamental change for the Uruguayan political system. As Lanzaro and De Armas said (: 3): 'the change – which is major but which takes place with state institutions and plurality intact and effective political competition – culminates with the victory of the Left in the 2004 elections, its entry into national government'. This profound transformation took place within the limits stipulated by democracy, the Constitution and Uruguayan law. Consequently, despite the crisis, the political system did not collapse, or even tremble a little. Instead it was strengthened. The arrival of Frente Amplio injected some dynamism into politics, which had previously been dominated by an old leadership and a small number of elites who essentially exchanged power periodically.
Some analysts maintain that a transition took place from a two-party system of the Blanco and Colorado parties to a two-party system between the Frente and the old political parties (De Armas 2010; Luna 2007). While Gustavo de Armas considers the Frente to be a maverick party, other analysts, such as José Rilla (), believe it to be simply a new form of traditional party. Many academics agree that both the traditional two-party system and the new one which includes the Frente have created a political culture free of extremes. The system absorbs conflict and moderates disagreements (Buquet and Chasquetti 2005; González 1985).
This post-transition process demonstrated that democracy is fully embedded in the country and that crises can be resolved through institutional mechanisms. As Daniel Buquet (: 141) explains: 'the Uruguayan political system – very stable, institutionalized and consolidated in comparative terms – is also more complex than those in other countries in the region. The most complicating factor is the internal factionalism in Uruguayan political parties and the resulting difficulties this creates within the legislature.' The internal make-up of the political parties fosters rivalry in local committees. This creates a political system with many divisions and potential alliances. The factions within each party have their own conflicts and group loyalties. But there is no disloyalty, nobody changes party, nor is there any instability. Internal party disagreement does not spill over into institutions. Hence the establishment of a new party did not break the political system. There were some changes but continuity and respect for established rules prevailed. The presidents since the return to democracy have had different political ideologies but they have all been democracy enhancers.
Colombia
The Colombian political system is defined by contradictions: legitimacy and democratic stability coexist with extreme poverty, the absence of the state in rural areas, political violence, ideological intolerance, human rights violations and corruption. With an institutionalized party system, free elections and a political class with extensive experience in public policy, Colombia is surprising because it has maintained its democratic appearance while resorting to political violence.
When people talk about the Colombian political system, they tend to point out that the country has the oldest political parties in Latin America. In that respect it is similar to Uruguay. It also, like Uruguay, has a two-party system which arose in the middle of the nineteenth century. The Liberal (1848) and Conservative (1849) parties had an iron grip on power based on alternation. The Colombian political elite is an urban and provincial political class tied to concentrated economic power.
Colombian politics is dominated by an elite composed of a few traditional families who essentially take it in turns to hold power. These traditional elites in both urban and rural areas are key to understanding how Colombia has maintained a degree of political stability within the context of a long civil war. In the words of one of the politicians we interviewed, 'these elites have managed to maintain order, the presence of the state and the economic development of the country where it mattered while ignoring the rest of the country as being rather unimportant in their bid to enrich themselves'.
The two traditional parties, the Liberals and Conservatives, had different characteristics at the beginning. The Liberals promoted liberty, free education, federalism, the separation of Church and state and universal suffrage. The Conservatives were in favour of strong unitary governments, a dominant position for the Church, centralism and restricted voting. Both parties have members from different social classes. They have set up a pragmatic alliance with the Frente Nacional, which allows them to alternate in power (Dávila Ladrón de Guevara 1997).
It is interesting to observe how even nowadays politics remains the preserve of the same families. This is clear from the words of a Liberal Party representative. He said he had forged his political career climbing each rung of the ladder. He claimed, 'I am not the son of a politician, I am not from a rich family, I am not a member of a political elite. I am simply a citizen who forged his own path.' However, farther on in the interview, it was revealed that his parents worked in politics, they were from a military family and that his grandfather was friends with the Liberal leader Jorge Eliécer Gaitán, who was assassinated in 1948. However, even those who do not consider themselves part of the old elite are still part of the traditional political class. To understand this elitism better, a note in the magazine _Semana_ () talked about the recent presidential elections in 2014 and stated that 'among genealogists in Colombia there is a tradition of finding out which of the presidential candidates is a descendant of the Ibáñez sisters'. They were two sisters at the time of independence who are famous not only for their beauty but also because one of them, Bernardina, was Simón Bolívar's lover, and the other, Nicolasa, was General Santander's lover. In the presidential elections of that year there were two descendants: the president, Juan Manuel Santos, and the Polo (PDA, Polo Democrático Alternivo) candidate, Clara López Obregón. This mark of origin drives home the point that Colombian politics is elitist.
Once the historical period known as ' _La Violencia_ ' was over, a phase of stability known as the National Front Regime (1958–74) began. Under this agreement, the two parties shared power, dividing up the posts in public administration and public corporations between themselves. According to some analyses this system became a single-party regime with no formal opposition but which was defined superficially as bi-party (Ramírez Huertas 2009: 32).
The regime was based on the exclusion of third political forces or new parties. There were some smaller parties such as the Colombian Communist Party (PCC), which was formed in 1930, and the Revolutionary Independent Labour Movement (MOIR), set up in 1969. These parties did not, however, achieve any parliamentary representation (Morales 1978: 56–73; Urrego Ardila 2013: 135–45). This elitist exclusive political system led to depoliticization and abstention on the part of society. It is possible that this was a factor in encouraging the guerrilla movement to come into being. They demanded a more egalitarian and inclusive form of politics. That fictitious democratic legality forced opponents to operate outside the system. It is also worth remembering that Colombia not only has the oldest political parties in Latin America, it also has the oldest guerrilla movement in the region.
The 1991 constitutional process was an opportunity to increase political representation (Restrepo 2006). Nevertheless, the results were not very successful. According to some analysts, the reform did not bring about renewal but stagnation. Ramírez Huertas holds that after more than twelve years since the Colombian Constitution was promulgated, nothing had changed. He maintains that the new Constitution consolidated the lack of party discipline and electoral microenterprises (Ramírez Huertas 2009: 40–41). Other analysts claim that the Constitution promised reconciliation but that the 'political class was not renewed. It became corrupted, allied itself with new sectors or foreign interests to the detriment of the well-being of the community' (Semana 2011).
The fragmentation and volatility of electoral preferences have prompted analysts to characterize the party system as multiparty (Batlle and Puyana 2011: 27–57). In every election many parties are formed and then disbanded but put forward national and local lists of candidates. For example, the Democratic Alliance, which was made up of members of the former guerrilla movement M-19, was practically wiped out. Leaders, such as Noemí Sanín, who do gain some political space and who attract a high percentage of votes do not manage to create a party. Antanas Mockus, who was a professor and rector at the University of Colombia, went from being a much-praised manager, promoter of honest management and a citizens' culture for peace, to being a creator or candidate of various political groupings. In 2010 Mockus joined the Green Party and fought against Juan Manuel Santos in the second round. On 9 June 2011, Mockus left the Green Party and announced his retirement from politics.
There is another strange contradiction in Colombian politics between a country in the midst of guerrilla and paramilitary violence and one with consistently good economic growth indices. That economic development did not, however, lead to an increase in democracy: 'economic growth helped to reduce absolute poverty and to a lesser extent income inequality since the middle of the first decade of the twenty-first century. Nevertheless, Colombia is still one of the most unequal countries in the world' (Estudios Económicos de la OCDE 2013: 9; Bonilla González 2011: 46–65).
As the 1991 reform did not modernize the party system or restore popular faith in political representation it was necessary to introduce other changes. The demand for this was what brought Álvaro Uribe (2002–10) to power. The failure of previous presidents to solve the problem of the guerrillas opened up the game to a new type of leadership. The changes proposed by Uribe generated some doubts about democratic institutionality. There were suspicions that some judges were being tempted by hefty payments from the government to permit immediate re-election to be introduced. Congress approved a Political Reform in 2003. Thanks to this, President Uribe was re-elected in May 2006 with 62.2 per cent of the vote (Leal and Roll 2013; Durán Escalante 2006: 113–35). A crushing victory which did not provide for greater democratic access for the citizenry.
We could agree that since it came into being as a state, Colombia has had a democratic image which masks a different reality. Initially we classed Uruguay and Colombia as being similar cases. In both examples we see a system of democratic leadership. But the interviews told a different story. The dominant and exclusive party system allows for a kind of ambivalent democrat. The context enables new parties to emerge but they are ephemeral. They do not manage to survive three consecutive electoral contests. Rodríguez Rincón defines this harshly as: 'we are not in the presence of real parties but electoral microenterprises which brandish improbable party banners' (Rodríguez Rincón 2006). Based on the interviews we carried out for our five case studies, we suggest that the party system and its degree of institutionalization are crucial to the emergence of different types of leadership. We argue that a fragmented, exclusive party system does not generate democratic leadership. Colombia helps to structure this argument.
Party systems and types of leadership
Uruguay
Both the party system and access to power in Uruguay involve clear rules which have helped to ensure well-defined political careers (Botinelli 2008). Leaders begin their political careers at local level as _ediles_. The next step along the road is to enter Congress as an alternate deputy. Some end up being senators, which is considered the peak of their political career. In Uruguay senators are most definitely considered the political elite (ibid.). This structured and long career is what explains how old the politicians are. In the interviews, time and again we were told that a leader of fifty-five years of age is considered young in Uruguayan politics. Seventy-one per cent of the political leaders we interviewed owed their positions to having worked their way up the echelons of their political party.
In Uruguay, the vast majority of politicians stay in the same party for their entire life. An academic we interviewed summarized the relationship between politicians and their parties: 'in Uruguay _outsiders_ are _insiders_ , you cannot be a pure _outsider_ within this system; you have to go through party channels'. Staying in one party and the stability of the political careers have strengthened a political class which had to manage the transition to and consolidation of democracy. It is an educated and engaged elite. Some 45 per cent of those interviewed have a university degree and 40 per cent also have a postgraduate qualification.
Political parties have been vital actors in the formation of the Uruguayan state. In the words of one interviewee: 'the traditional parties as a political administrative structure came before the state but also pre-dated the constitution of the Uruguayan nationality... the parties are central to the formation of our identity'. The coexistence of the political parties and their role in public administration have led to a politics of consensus, cooperation between the Blancos and the Colorados and institutional stability (Rilla 1999).
The arrival of the Frente Amplio heralded change but without any need to abolish the traditional parties or destroy existing rules. The Frente also breathed new life into the elite. According to available data, the left-wing parliamentarians are more diverse in terms of gender and professions linked to the social and human sciences. There is also a greater proportion of working people and trade union members (Serna 2005).
One of the Frente leaders defined it as being 'a political and programmatic agreement rather than ideology, which has helped to preserve the identity of each of the individual members'. Party membership is very important in Uruguay as a means of entering politics. Some 45 per cent of those we interviewed were party members, family tradition accounted for 26 per cent, and involvement in student politics accounted for 23 per cent.
The political parties are central to political life as the basis of policy-making and for promoting ideas and strategies. Politics still has local support bases and the party is also a sort of social club. One Blanco party deputy explained Uruguayan politics to us like this: 'Uruguay is not a country of extremes but averages. It is not a country of definite colours but of shades of colour. We do not like harsh words or taking risks. The state has the role of protector to play. In addition we have codes in Uruguay which keep everything in check. We never stop talking to each other in Uruguay.' This concept of politics made it possible to open up the political game and manage the leftover Blancos and Colorados.
In addition, Uruguayan society believes in democracy. In a study on the public image of legislative power, 73 per cent of those surveyed agreed with the phrase 'without political parties there could be no democracy' and 77 per cent agreed that 'without parliament there could be no democracy' (Buquet 2014: 3).
Their leaders respect the laws. President Tabaré Vázquez, despite belonging to a new party, did not change the rules of the game but actually consolidated the political system. Garcé (: 500–501) comments that 'Vázquez managed to achieve unparalleled levels of popularity and approval for his administration'. Garcé attributes this popularity to three facts: 'He made use of three things at his disposal: accountability, trips abroad and inaugurating public works' (ibid.: 501). The country continued unchanged even when in 2009 an ex-guerrilla, José Mujica, won the election. Garcé gives this explanation: 'the first steps in Presidente José Mujica's term confirm the "party-centric hypothesis": in Uruguay people don't govern, parties do' (ibid.: 530). All the points made by our interviewees conform to the model of democracy enhancer. There is no dissent between the three Uruguayan parties: in Uruguay there is a stable predictable political system.
We were very interested to hear time and again the word 'learning' from our interviewees. One female senator told us how during her years in prison she had the opportunity to think and learn. This helped her to understand how a 'Uruguayan citizen in the 1980s was very different from one in the 1970s'. She also maintained that 'we learn the most important political lessons from defeat'. This predisposition to learning, self-criticism and historical analysis is not to be found in our interviews with Argentines, Ecuadoreans or Venezuelans. The Frente and their politicians learned from past experience and pushed for change to ensure that they could represent voters in a relevant manner. José Mujica, who was spoken to about his guerrilla past, also talked of learning when he said: 'To some people I represent the 1970s when the world was very much bipolar. We have learned that in the game of liberal democracy we can do a great deal. We do not have the right to sacrifice one or two generations in the name of utopias' (Danza and Tulbovitz 2015: 66).
Our interviewees agreed that clientelism exists. The type that exists in Uruguay is what we call vertical clientelism, which is that between politicians and political supporters. Around 62 per cent of the interviewees identified clientelism as the exchange of benefits for votes. In the main these benefits are offering jobs to the party faithful or members of the party. The word clientelism was largely used in connection with political parties during the interviews: 'for many years citizens demanded jobs from the state owing to the lack of other employment. And that is what encouraged clientelism.' In the interviews many of the politicians explained clientelism as a party political instrument which is falling into disuse since the introduction of technology into public affairs is increasing transparency and competition when it comes to employment. Most of the interviewees considered clientelism as a necessary evil and something that will be difficult to eradicate. Most Uruguayan leaders (66 per cent) consider that clientelism is linked to the political culture and functions as a means of domination. The fundamental difference with countries such as Argentina, Ecuador or Venezuela is that clientelism does not seem to be used as a tool to increase personal power. Clientelism was actually described as a party policy that benefited members and supporters once their party had come to power. In our meetings, however, it was clear that the interviewees considered clientelism to be a problem for each of the three main parties in Uruguay.
The case of Uruguay was crucial for this study. Uruguay is very different from Argentina, Ecuador and Venezuela. The stable institutionalized party system, free and fair elections and a deep-rooted democratic political culture combine to produce democratic leaders. By contrast, party systems with a low degree of institutionalization or a high degree of autonomy (Argentina and Ecuador, and Venezuela, respectively) encourage power usurpers to come to the fore. Our qualitative analysis of the interviews carried out in Uruguay demonstrates that the extent to which the party system is institutionalized is the most significant variable in determining leader type. Uruguayan political parties are key to guarding against concentration of power. In addition, leaders are considered to be citizens. One Colorado deputy explained this very clearly: 'there is daily contact with politicians in Uruguay. You can go for a coffee and see Mujica [the president] at the next table having coffee with his wife or a friend. And he is the president of the republic. You can see ministers playing football and you can just sit down and watch. A while ago a report was published about whether legislators used bodyguards and it had not occurred to any of them to use them. I think that is good. We also do not have guards on legislative buildings here.' Although the country has had some very important leaders who have had a profound effect on its history, Uruguay has managed to avoid power usurpers. Under its two presidents, the Frente Amplio improved social conditions, carried out a tax reform and brought about a twenty-four-point fall in unemployment. The popularity of both leaders – Vázquez and Mujica – did not translate into any change in the electoral system.
The post-crisis scenario did not provoke any breaking of the rules. In the case of Uruguay it was the citizens who, when faced with the 2002 economic crisis, channelled their demands through the party system. The winning party, Frente Amplio, did not resort to weakening the opposition. Our interviewees maintained that this stability was not the result of strong or charismatic leaders but rather of trust in the democratic system and the strength of the political parties.
Colombia
The Colombian study also demonstrates the importance of political parties. However, as was to be expected, the interviews focused largely on the topics of political violence and corruption. The crisis in Colombia is one of global governability of its territory. Colombia has two faces. The judicial system seems to function and many corrupt politicians go to prison. But prison does not seem to be a deterrent. Even if they spend a few years in prison, their family can carry on in politics on their behalf. The stolen money is not recovered. Hence while the justice system might well pursue the corrupt, the arrogance of the political class explains just how little they are dissuaded from wrongdoing by the threat of punishment or even imprisonment. The combination of political violence and an efficient justice system that actually does not really deter crime means that there is no such thing as democratic order in Colombia.
Some writers suggest that Colombians are used to sectarian and not very democratic politics. Pizarro explains that 'in Colombia there is no culture of democratic opposition. Neither the one-party hegemonic governments of the past nor the Frente Nacional provided fertile ground for that culture to flourish' (Pizarro Leongómez 1996: 218–19). However, this does not fully explain the political careers of the presidents. For example, Andrés Pastrana Arango, Uribe's predecessor, had a stellar career in politics using the tools of democracy. He was part of the traditional political elite since his father, Misael Pastrana Borrero, had been president of the republic between 1970 and 1974 and leader of the Colombian Conservative Party. His son was the first mayor of Bogotá to be elected by popular vote (1988–90). Then he was a senator of the republic. In 1998 he was elected president with 51 per cent of the vote, defeating the Liberal candidate, Horacio Serpa.
Pastrana was responsible for negotiating the Colombia Plan with the United States, which provided financial support to the Colombian government to help counteract the insurgency in exchange for efforts to fight drug production and trafficking. Of the total, 51 per cent of the resources were destined to support programmes to improve social conditions and respect for human rights and strengthen state institutions. The efforts to fight the guerrillas were to run in parallel with democratic strengthening. However, the Colombia Plan really focused on combating drug trafficking and fighting the Revolutionary Armed Forces of Colombia (Fuerzas Armadas Revolucionarias de Colombia, FARC), and so had a heavy military component. With the arrival of Uribe in the presidency, this repressive aspect intensified. At the start of 2002 Pastrana considered his strategy to have failed and suspended the peace process with the FARC. His party was decimated in the elections. Uribe capitalized on the discontent, placing the breakdown in the peace negotiations at the heart of his campaign.
His predecessor, Ernesto Samper, was elected in the Liberal Party primaries, meaning that his presidential candidacy had come about as a result of following democratic procedures. But he was accused of accepting a large campaign donation from drug traffickers. Under his government violence escalated both among common criminals and the far-right paramilitary organizations, the Self-Defence Units of Colombia (Autodefensas Unidas de Colombia, AUC), and the left-wing guerrillas.
We can, therefore, observe the existence of institutionalized political careers but which have some characteristics that are more common in uninstitutionalized systems. Cárdenas Ruiz points out three current trends in Colombian politics: the rise of personalist governments, disaffection with parties and lack of ideological identity. 'Faced with the question "describe with one word what politics means to you" 33 per cent of those surveyed associated it with corruption, 10 per cent with injustice, 9 per cent with democracy, 5 per cent with the common good, and 18 per cent did not know how to describe it' (Cárdenas Ruiz 2012). This dominance of corruption as a political evil is substantiated also by a LAPOP study: 'It is worth pointing out that in 2012 Colombia was ranked first among the countries for the level of perception of corruption, with an average of 82 points on a scale of 0 to 100' (Rodríguez Raga and Seligson 2012: 95, 206).
All of these characteristics help to explain the emergence of a leader such as Álvaro Uribe, who combined authoritarianism with popularity. Uribe stands out in the Colombian context as a soft power usurper – a type of usurpation supported by a large majority who are not interested in 'the rule of law, constitutional guarantees, judicial process, democratic institutions, checks and balances as laid out in the 1991 Constitution, national or international laws' (Mejía Quintana 2009). Despite his rather different ideological leaning, Álvaro Uribe, like Rafael Correa in Ecuador, Hugo Chávez in Venezuela or Cristina Fernández de Kirchner in Argentina, mobilized his supporters and had a fixed logic of friends/enemies. The majority of those interviewed from the opposition party, the Alternative Democratic Pole (Polo Democrático Alternativo), were convinced that the Uribe coalition government was controlled by para-politicians, rural and urban leaders linked to the paramilitary organizations. However, Uribe's high level of popularity and speeches about defeating the guerrillas were not enough to win him a third victory. His leadership did eventually come up against the relative autonomy of the state institutions, which defended democracy and limited his ability to concentrate power in his hands.
For its part, the leadership of Juan Manuel Santos had more in common with that of the more traditional leaders in Colombia. His approach demonstrated that Colombia had maintained the tradition of ambivalent democrat. Santos is conciliatory and he seeks consensus. Santos also has the media on his side by virtue of his family. He is a president who returned to democratic legality. Santos also began a concerted effort to negotiate with the FARC.
One possible explanation as to why the electorate switched preferences from Uribe to Santos is that although Uribe managed to re-establish a degree of public order, he did so in rather illegitimate ways. Having achieved a degree of order, society then preferred a candidate who would reinstate democratic rules. Although President Santos corrected a lot of his predecessor's 'deviations', he did not focus on improving the political system, reforming party finance or reducing clientelism.
In the following section we are going to examine these differences through the lens of our leadership typology. The information gained from our interviews provides key data to achieve this.
The profile of leadership
Uruguay
We argue that in Uruguay leaders are democratic enhancers. The interviews revealed a model of leadership which matches our description of Uruguay as a rule developer, a bridge builder and respectful of democracy (see Table 2.2).
Rule developer
Our interviews in Uruguay revealed just how important respect for the rule of law is in that country. Hence leadership is considered to be a support for and promoter of democratic institutions, horizontal accountability and civil rights and liberties. One opposition legislator said that 'when a law has the support of all the parties, it is symbolically as well as formally stronger'. Laws are so important that a Colorado leader said that 'we have to prioritize the defence of democratic values and the rule of law'. Leaders aim to promote civil rights and freedoms.
In Uruguay party activism is politics. Some 71 per cent of the politicians we interviewed got their jobs thanks to having worked in their political parties. This does not mean there is an absence of trade union or student activism but rather that leadership largely emerges from political parties. The party system is stable. The bi-party system broke down but the Frente Amplio injected new life into the political system, strengthening the institutions.
Control over the leaders is carried out at all levels. Society holds them to account in the party conferences, in which citizens can question their representatives. Their peers hold them to account; as one Frente Amplio deputy said: 'we have an important degree of social control here, we have a small population and actually we all know each other so there is a degree of social control whereby anybody who shows off is told off'. Another deputy also said that the opposition exerts a degree of control over leaders: 'I spend a lot of my time monitoring things, asking for reports, calling ministers.'
President Tabaré Vázquez implemented the 'Democratic Uruguay' programme, the main idea of which was to make public administration more transparent and to open up political power to civil society. The main instrument to achieve this was the Strategy for Fostering Citizen Participation. Meanwhile, President Mujica donated his presidential salary to the poor. Mujica said: 'We know these things won't change the world but we increase our commitment to society. This is a moral and ethical obligation' (FM Centro 2015).
One opposition deputy stressed how actually a concentration of power frightens the Uruguayan political class: 'the only problem with democracy is that sometimes a party can win over 50 per cent of the vote. Then democracy, which is essentially political freedom, the majority governing, can lose respect for minorities. Then we stop being a democracy and we start to get used to things that are rather more at home in dictatorial regimes. Then we do not have the liberal game that needs majorities and minorities to find solutions.'
Political leadership in Uruguay is understood from the perspective of respect for institutions and the promotion of the rule of law. Fifty-eight per cent of our interviewees maintained that the main function of democracy is to guarantee the division of powers.
In the Uruguayan interviews, the leaders interpreted leadership as a collective issue. The parties and institutions of the state are a fundamental pillar of political leaderships.
Bridge builder
All the interviews in Montevideo emphasized the importance of political consensus. Political competition in Uruguay is not a zero-sum game. One Blanco deputy said that 'political activity is largely about negotiation, articulation and consensus'. President Mujica himself also stressed this idea. He said that his presidency would be a question of 'negotiate, negotiate, negotiate until it is unbearable' (El País ).
One of the interviewees explained that reaching consensus with the opposition is important but 'consensus without losing your identity. We have to be careful otherwise people will think we are all the same. We have different ideologies and a different vision for the country.' Political consensus is valued given the differences that separate the parties.
Uruguayan leaders understand politics as responsibility. As a leader of Frente Amplio said: 'there is no need for consensus but there is a need for compromise'. That compromise, as an ex-minister from Frente Amplio said, is what binds together the policies of state: 'I believe we created a consciousness within the Uruguayan political system of the need to seek and articulate agreement, with the broadest possible support, and approved by the political system as a whole'. Another interviewee said that 'the magic of Uruguay is that nobody can crush anybody'.
A Colorado deputy expressed similar ideas: 'The democratic system is the best because it makes for consensus. We have a non-confrontational style. You can have strong convictions but still respect the other person's point of view. We also respect those who behave differently since none of us can claim to be the masters of truth.' This idea of consensus-building and respect for others seems to be a quality shared by all members of the Uruguayan political class.
The inclination to share power was very clear from the ideas about accepting the limits of the governing party. An important member of Frente Amplio said: 'Frente Amplio accepted that only half the population voted for us. There is another half which did not support us and we have to consider them too. There is a good relationship between the different parties. It is a shared collective vision, shared although there are a few social issues on which we disagree (such as abortion and euthanasia)'.
A well-known political scientist explained this collective vision: 'even when the leader is very important such as Tabaré or Mujica, they are still leaders of parties, groups and sectors. They are still connected and can be voted down. That to me is a key point about democracy that nobody is above everything.' Power for Uruguayan leaders is not a personal attribute. It is a joint project with the community. Consensus-building and tolerance are natural attributes for Uruguayan political leaders.
This tradition will probably continue under Tabaré Vázquez, who took office in March 2015. Vázquez said that in government he will hold a dialogue with all political forces. In his victory speech on being elected he said: 'We can celebrate a climate of peace, respect, and republican sentiment today. It is our nation's way of being an achievement for all Uruguayans' (El País 2014). To understand this dominant democratic climate in Uruguay, it is worth listening to the eloquence of his opponent at the ballot box: 'the results will be praised, respected and defended. We are not supporters of majorities who make mistakes but majorities who lead' (ibid.). Both candidates show great tolerance.
Vázquez won in the second round of voting with 53.6 per cent of the vote. This was the largest victory in a second round since the current electoral system was introduced in 1996. Tabaré Vázquez became the president to garner the most votes in the last seventy years. Luis Lacalle Pou, his rival, won 41.1 per cent of the vote. One conclusion from the 2014 elections is that 'apart from the numbers, Uruguay deepened the democratic values that have characterized the government since the return to democracy in 1986: whoever governs respects the institutions of the republic and the democratic rules of the game' (ibid.). These conclusions back up our depiction of Uruguayan leaders as democracy enhancers.
Respectful
The characteristic that defines Uruguay and sets it apart from its neighbours is that it is political parties rather than individuals which lead the country. The political parties provide an identity to a group, understand their situation, set an agenda and propose solutions. In the Uruguayan context the party is the necessary channel for mediation (Garcé 2009: 110). A Frente Amplio senator described this enthusiastically: 'in Uruguay party loyalty is important for everything, but people do it with pride, Blancos, Colorados and Frenteamplista. The people also do it with pride and respect each other.'
There is a party system and fixed rules of the political game. As a Blanco party leader said, 'governability is high in this country because of the strength of the institutions'. Uruguayan politicians do not break the rules or change the constitution. They do not pass laws to benefit themselves personally. A Frente Amplio deputy stated very clearly: 'the candidate is nothing more than an instrument by which to express the ideas of the political party but alone they cannot govern'.
This idea also comes over in President Mujica's evaluation: 'I would have liked to have done more but at least I tried to convey a very republican image, to drive home the fact that nobody is better than anybody else and that the president is just like any other member of society, that he is not above the people and that morally I have been loyal to the interests of the country' (El Espectador 2014).
An analysis of the changes to the _Ley de Caducidad_ proposed by Vázquez and Mujica exemplifies this devotion to the law. When Vázquez discovered, in October 2005, that the law did not apply to fifty cases of clandestine removal and forced disappearances of Uruguayan citizens, he saw a way of advancing human rights policy but without going against the law. He held a plebiscite on 25 October 2009, on the day of the election. The Supreme Court, in a unanimous judgement, declared that Articles 1, 3 and 4 of the _Ley de Caducidad_ were unconstitutional. Six days later, once José Mujica had won the election, the Uruguayan electorate voted that the constitutional amendment would make part of the _Ley de Caducidad_ invalid. The votes in favour of the measure averaged 48 per cent, but over 50 per cent was required for it to pass. As a result there was no reform and the _Ley de Caducidad_ remained unchanged. Neither Vázquez nor Mujica tried to force the issue to achieve their objective.
In Uruguay institutions are respected: 'when a party comes to power its head, its president, becomes the president of all Uruguayans. This is also what brings about large governing coalitions,' explained a Colorado deputy. 'In Uruguay we know the limits of power. And we all respect them.'
Analysis of the interviews carried out in Uruguay helped to formulate our argument. Domestic political conditions and especially the degree of institutionalization of political parties are an important variable in explaining different types of leadership.
Colombia
Classifying leadership in Colombia was very difficult since it combines democratic elements with a very specific reality: violence. A well-known lawyer explained that there are formally democratic institutions in Colombia but taken as a whole they are very far from being democratic: 'Colombia has a democratic side and a violent side. This ambiguity is most obvious when you consider that the legal system coexists with a permanent state of exception.' The country is criss-crossed by serious structural violence. This was also remarked upon by a senator from the Alternative Democratic Pole (Polo Democrático Alternativo): 'in Colombia violence makes the political struggle very hard. Here nobody gives up their armoured cars, nobody. I have two armoured cars and five escorts which I consider normal. If you see the statistics you will see that every day a mayor is killed, somebody is kidnapped. In a nutshell, the Colombian state is a long way from having the monopoly over weapons. There are very powerful armed organizations on all sides.'
In Colombia we carried out interviews just after the start of Juan Manuel Santos' first term in office. Many of our interviewees commented on the differences in leadership style between Santos and Uribe (see Table 2.3).
Rule-obedient
Colombia has a democratic creed. There is a widespread belief among the political class that it is a democratic country. Several interviewees mentioned the importance of the rule of law to the Colombian political community.
Presidents have respected the freedom of the press. This has been under threat because of the state of violence in the country. For example, Andrés Pastrana agreed to a request from the Secretariat of the Inter-American Press (Secretaría Interamericana de Prensa, SIP) for clear instructions to be given to members of the security forces. They asked that journalists in conflict zones not be considered as military targets and that they not be subjected to any threats or intimidation (El Tiempo 2000). Pastrana explained his decision, saying: 'as a leader I understand and agree with the overriding principle that people who hold political power should respect freedom to inform and be informed as the best counterweight to power'.
President Santos has mentioned on several occasions the importance of safeguarding press freedom: 'freedom of the press, freedom of expression, the right to criticize, the right to demonstrate for or against something or some government is the essence of democracy. That is why I have always defended that right clearly and wholeheartedly' (Presidencia de la República 2013). He also agreed to open up the negotiations with the FARC in Cuba following criticism that they were taking place in secret. Our interviewees agreed that Santos did not have any problems with the media.
Many of our respondents suggested that political parties should not be overly conditioned by current events but rather should have a degree of ideological cohesion and long-term plan for the country. In the words of one deputy: 'a strong party, with an ideology, is very important for democracy. It is the fundamental basis for democracy.' When asked 'what is the role of political parties?' 52 per cent of the interviewees chose the option 'to structure the democratic game'.
In Colombia, as in Uruguay, we found traditional political parties. But in the case of Colombia these parties coexist with new organizations and their leaders often switch party. For example, President Juan Manuel Santos is the leader of the U party (Partido Social de Unidad Nacional), set up by Álvaro Uribe in 2005. Before that Santos was a member of the Liberal Party. For his part, Uribe was elected senator in the most recent elections in 2014 for the Democratic Centre (Centro Democrático). Leaders and parties seem to be quite flexible. A Liberal Party senator mentioned that 'parties are blooming in Colombia, I myself set up two because it was really easy to get 30,000 signatures'. However, political parties do not have the degree of coherence they had prior to 1991.
One of our interviewees claimed that most Colombian leaders do not take apart or build the democratic state but they do accept the rules of the game, even political violence. One representative of the Green Party said that 'nearly all the congressional presidents in the last ten years have been investigated by the Supreme Court and are in jail'. There is a permanent tension between corruption and the limits imposed by institutions. But as the Green Party representative explained, this illegality is part of Colombian culture, and although many congressmen end up in prison, 'several of them have their wives in Congress; they are in prison and their wives are in Congress with exactly the same votes that they won themselves'.
Receptive
Ambivalent democrats seek to build consensus by working on occasion with the opposition. In Colombia there is an old tradition of inter-party agreements. For example, in 2002, President Pastrana had organized the Common Front for Peace Multi-party Commission (Comisión Pluripartidaria del Frente Común por la Paz). He had also arranged a referendum on changes to the political system, inviting the opposition to lead the 'no' campaign.
In part as a consequence of the ongoing war, recent Colombian history has seen a host of multiparty initiatives to try to bring about peace. This is one of the characteristics that most of our interviewees see in President Santos. He asked the opposition to unite to work for peace and to reach an agreement with Venezuela. As a U senator commented, 'Santos is a great negotiator. He is a strategist. He is a man who likes building large coalitions. He is the heir to a tradition of political parties and mediation. He has the media, institutions and financial institutions on his side.' A social leader added that Santos 'up to now has maintained the independence and division of power, the system of checks and balances that exists in a liberal democracy.' According to most of our interviewees, Santos wants to share power.
The political party system in Colombia has historically not promoted polarization. According to one of our interviewees, the polarization engendered by Álvaro Uribe can be considered an exception. There is openness and tolerance but they do not necessarily translate into a broadening of democracy. In sum, this particular combination of exclusion and violence on one hand and tolerance, consensus and traditionalism on the other creates a pragmatic and little-ideologized power play.
Between soft challenger and power builder
The ambivalent democrat is a soft challenger. They are leaders who seek to accumulate personal power. In this process it is likely that they will seek to defy institutional power. However, they appreciate their limits and tend to agree to include their opponents. The leader accepts the law but tries to favour his own position. Unlike democracy enhancers, they respect but do not strengthen democracy. In the case of Colombia, the best example of this is Álvaro Uribe. Uribe oscillated between defying and accepting institutional rules. In our categorization Uribe can be considered a leader who unites the characteristics of ambivalent democrat and soft power usurper (see Table 2.4).
The Colombian institutions were able to put limits on some of Uribe's excesses, particularly his desire to stand for re-election after two consecutive terms. However, he did exploit his favourable situation to weaken his opponents and dominate press coverage. He did not hold back from using a number of resources to divide public opinion and insult his opponents. He created the National Social Unity Party or U party, which served as a vehicle to further his own personal aims. However, he was unable to limit the power of the Colombian state institutions and finally accepted the Electoral Court's decision that denied his request for constitutional reform to enable him to seek a third mandate.
According to some legislators we interviewed, Uribe was actually a product of the Colombian political system. The rise of Uribe can be interpreted as a consequence of specific political conditions. The crisis of representation of the political parties and civil weariness with the violence seem to have created the favourable conditions necessary for Uribe to win the elections.
Uribe achieved a special combination of efficiency and populism. From our perspective, the way he exercised power involved a manipulation of state institutions, the media and his party. For example, a report in the _Washington Post_ stated that North American money, equipment and training for elite Colombian intelligence units to help combat drug trafficking were used to carry out undercover operations and campaigns to discredit the Supreme Court, and members of the opposition and civil society groups (DeYoung et al. ).
Uribe was very tough with the guerrillas and both his repressive Democratic Security Policy (Política de Seguridad Democrática) as well as the matter of 'false positives' defied existing laws. Finally, the 2003 Anti-Terrorist Law broke a number of national treaties. It was strongly criticized by opposition congressmen and NGOs, who demanded that the armed forces be stripped of their judicial role.
Society as a whole went along with these methods and Álvaro Uribe enjoyed a lot of popularity. Despite reports that linked Uribe with the paramilitaries, his repressive security programme brought a degree of calm to the population. Operations of doubtful legality succeeded in reducing the power of the FARC. Uribe's real aim was to achieve a greater degree of security for the citizenry. He did this by accumulating power and weakening the existing bi-party system. Tackling inequality and building a new party system were not on his agenda (Galindo Hernández 2007: 148, 152).
Despite all these excesses, a Liberal senator we interviewed pointed out that 'nine members of the Constitutional Court said no to re-election and nothing happened, nobody shed a tear, nobody went out to demonstrate in Bolívar Square'. Even a young leader from the U party recognized that 'our great attachment to the rule of law came about because there is an institutional culture so it was possible to stop Álvaro Uribe by institutional means'. That led us to agree that Uribe is a leader who combines characteristics from both models.
Uribe exploited his position of popularity with the electorate to cut away at the power of his opponents. A Liberal Party senator told us, 'Uribe is a clear leader but polarized the country.' As we characterized in our leader typology, soft power usurpers use polarization as a means of asserting their leadership.
The answer to why the population did not react when confronted by an authoritarian leader seems to be clientelism. A Green Party leader commented, for example, that 'Boyacá in particular is a department with a very strong political tradition. It is a department where you can buy peasants with meat, beer and bricks.' Sixty-nine per cent of our interviewees said that people expect clientelism so it carries on. One deputy admitted that 'politicians generate a need among society to keep asking for things'.
A senator from the Liberal Party talked about clientelist skills: 'The electoral process is corrupt here. The merits of the candidates are not important, the only thing that matters is money and you can buy leaders of all sizes.' Uribe's success is attributable to the problem of violence, if we consider the argument put forward by one important bureaucrat in the executive: 'It is very difficult to achieve any form of democratic consolidation in a country in the middle of the type of violence we face, violence that threatens the freedom and peace of the population.' His charisma also had something to do with his popularity. Uribe captivated the population. He was also very intransigent with the opposition parties but did not wipe them out. He taunted them in ways that were more appropriate to street brawls than political debate.
A female senator from the U party admitted that the party was made up of people representing a range of ideas. The party did not have a clear identity nor the organizational tradition of the Liberal or Conservative parties. The party was seen as a vehicle for consolidating the Uribe project. The Uribe slogan 'Firm hand, big heart' struck a chord with voters who wanted peace. Uribe's response was to try to destroy the FARC. Hence he introduced the Democratic Security Policy. Ideologically it was nothing more than strongarm tactics. It worked. It restored confidence on the part of ordinary Colombians and won their support by using concrete decisions to resolve long-standing conflicts. Disillusionment turned to hope. However, it was along this road that Uribe let slip his democratic principles, but the population was not worried. What mattered was ending the violence. This is why the period of Álvaro Uribe has been described as authoritarian modernization (Rodríguez Garavito 2005: 14; Rodríguez Rincón 2006: 73). The president peddled hope and abused his position to gain results. This led to an increase in his power, which is why he is considered a power builder.
It is important to remember, though, that press freedom was not curtailed. Even a U party leader commented: 'the anti-Uribe criticism in Colombia was thanks to the fact that the media was free to express its views'. We see this combination again in the case of respect for civil rights, even though some practices went against established democratic rules.
The use of nationalist rhetoric, patriotic symbols and repression through the Democratic Security Policy all validated his strategy. But he could not remain in power. Uribe did not manage to become a power usurper. Despite the political violence in Colombia, the strength of the institutions and the degree of institutionalization of the political parties constrained a leader who swung from being an ambivalent democrat to a soft power usurper.
After Uribe's time in office, Santos restored the political style that had been the norm before. Colombian political tradition is a peculiar combination of clientelism, party disobedience, electoral microenterprises, corruption and factional organization, according to Ramírez Huertas (: 29). Santos did not confront the institutions but neither did he strengthen them.
Colombia has faced challenges to its institutions and rule of law. It is a country with territorial and institutional vacuums but it maintains a democratic appearance. But this is not a full democracy. In our interviews in Bogotá debate about the differences between Santos and Uribe was crucial. In our model, Santos is rule-obedient and Uribe a rule challenger. Several interviewees agreed that Juan Manuel Santos reinstated the country's best liberal traditions, which had been broken by Álvaro Uribe.
Conclusion
The case of Uruguay indicates that the degree of institutionalization of the political party system is a crucial element in understanding the emergence of different types of leader.
The interviews in Colombia show a political scenario that combines, paradoxically, stability and political violence. While the political party system seems to be institutionalized, political violence can be considered an excuse for the emergence of power usurpers. Indeed, Álvaro Uribe used the problem of political violence to attempt to increase his power. He was only partially successful. Despite political violence, the institutions in Colombia were able to block the emergence of a power usurper.
Is a stable party system a condition for excluding power usurpers? Uruguay and Colombia seem to suggest this conclusion. Therefore, collapse or fragmentation of a party system could increase the possibilities for the emergence of power usurpers. The following cases, Argentina and Ecuador, witnessed the deterioration of their party systems after deep economic crisis. We now apply our typology to politically unstable contexts to be able to answer the following questions: Does the degree of institutionalization of the party system make a difference with regard to different types of leader? Is our typology appropriate to explain leaders in Argentina and Ecuador? Are post-crisis scenarios fertile times for democracy enhancers or power usurpers?
As in this chapter, we present the following cases in two levels of analysis – analysis of the political context and of individual leaders.
CHAPTER 4
Leadership in the Context of a Crisis: Argentina and Ecuador
Introduction
Argentina and Ecuador underwent economic and political crises at the beginning of the 2000s. In each case the post-crisis scenario was dominated by the emergence of strong political leaders who have been able to achieve economic and political stabilization. In this chapter, we present an analysis of political leadership in those two countries. It is based on the results of 118 interviews in Buenos Aires and Quito with legislators, former presidents, former vice-presidents and party leaders. They discussed with us the post-crisis scenarios, the fall and rise of different political leaders, the role of the political parties and the main features of the new political leaders.
This chapter starts by analysing the 2001 crisis in Argentina. It briefly explores different leadership models that emerged before and after the crisis. The second section studies the long crisis that Ecuador faced from 1995. The section suggests some ideas about the emergence of Rafael Correa. The third section offers an analysis of the post-crisis scenario in both countries. The fourth section presents the conceptualization of political leaders in Argentina and Ecuador. This is based on qualitative analysis of the interviews undertaken in Buenos Aires and Quito. It considers our typology of leaders and examines different examples from both countries. The conclusion offers some ideas about the political conditions that prompt the emergence of different types of leader.
The reasons for the crises
Between December 2001 and January 2002, politically and economically Argentina came to a standstill. In 2001, Argentinian president Fernando de la Rúa was forced to resign, owing to his inability to rescue the economy from a deep and long recession. The slogan chanted in the streets was _que se vayan todos_ ('all must go'). However, the political crisis was resolved by the old elite that still dominated the political landscape: the Peronist Party, created in 1945, and the Radical Party, formed in 1890.
An economic recession began in 1994 with the Mexican crisis and deepened in 1998 after Brazil's devaluation, bringing to an end a period of economic growth and stability that had started in 1991. In his second term in office Carlos Menem was unable to adjust the economic strategy to the recession and increased the external and internal public debt. The convertibility plan became a straitjacket that prevented the government devaluing to regain international competitiveness (Tedesco 2002; Corrales 2002). In 1999, a political alliance between the Radical Party and a new political formation, FREPASO, won the general elections with promises to maintain the convertibility plan while fighting corruption, reducing unemployment and strengthening judicial independence. After less than a year in office, the government was accused of having bribed senators to approve a labour reform. The political alliance collapsed and the Radical Party was left to govern alone. President Fernando de la Rúa was incapable of rescuing the economy from the recession and, cornered by social demonstrations, resigned in December 2001 (Ollier 2001). In just a week, four presidents were appointed and quickly resigned. One of them, Adolfo Rodríguez Saá, declared a default on the national debt. Finally, Congress elected Eduardo Duhalde, who had been defeated in the 1999 general elections.
Although a weak president, Eduardo Duhalde managed to achieve economic and political stability. He called for national elections to be held in April 2013. Carlos Menem won 24 per cent of the national vote followed by Néstor Kirchner, who received 22 per cent. Both of them were Peronists but ran for the presidency with different political formations. As neither obtained a majority, a second round was needed, but Menem, fearing a defeat, stood down and Kirchner became president (Levitsky and Murillo 2008).
With only 22 per cent of the vote, Néstor Kirchner faced many challenges. After 2001, political parties were deeply fragmented. Indeed, the 2003 elections featured three different candidates from the Peronist Party and three from the Radical Party. Peronists failed to agree on a presidential candidate. Radicalism was divided, two candidates formed different parties, and one, Leopoldo Moreau, was the Radical candidate who received less than 3 per cent of the total vote. This fragmentation illustrated the delegitimization of politics that has been encapsulated by the slogan _que se vayan todos_.
With a weak mandate, Kirchner had to build political power in a volatile context. From the very beginning, he signalled change. First, he aimed to build power within Peronism, but also wanted to include left-wing political actors and parties. This was known as _transversalidad_ , and its aim was to create a new political formation clearly identified with the left wing and what is known as _progresismo_. Kirchner was quite successful and a significant number of politicians and intellectuals joined his Frente para la Victoria. Secondly, Kirchner reformed the Supreme Court, which has been expanded by Carlos Menem from five to nine members. Menem created what was known as an 'automatic majority'; those new members approved most of the government's proposals. Kirchner pushed for the resignation of the new members, and in 2006 the Supreme Court reverted to its five-member status. Thirdly, Kirchner reactivated a strong policy to prosecute those guilty of human rights violations during the 1976 military dictatorship. These three initiatives seemed to bring political renovation to the post-crisis scenario (Levitsky and Murillo 2008; Quiroga 2010).
However, President Kirchner very quickly did a U-turn, reverting to a traditional Peronist strategy of building up power and reducing judicial independence. Indeed, in 2005, when electoral lists needed to be organized, Kirchner turned to the General Confederation of Labour (CGT), which has been a traditional Peronist ally, and to the Peronist mayors of Buenos Aires Province. In order to build his power, Kirchner implemented a clientelist logic and made clear that, in Argentina, power is built through the executive (Quiroga 2010: 55).
Economic or political crises have been the excuse used by different democratic presidents to increase the power of the executive. Raúl Alfonsín, Carlos Menem, Fernando de la Rúa, Eduardo Duhalde, Néstor Kirchner and Cristina Fernández de Kirchner have adjusted the rule of law to their political purposes. This practice had been on the increase over the years, strengthening the power of the president and his/her autonomy. As a consequence, political institutions have become less important and more dependent on the executive's decisions. As Argentina has been in crisis mode pretty much continually since 1983, the concentration of power in the executive, as a requirement to resolve economic or political chaos, has become a key policy in this democratic era. Presidents increased their autonomy by taking power from the political parties and state institutions, especially the Congress. We would suggest that all the presidents since the return to democracy fall into two main categories: soft power usurper and ambivalent democrat (see Table 2.3 and Table 2.4).
While Raúl Alfonsín can be considered an ambivalent democrat, Carlos Menem, Fernando de la Rúa, Eduardo Duhalde, Néstor Kirchner and Cristina Fernández de Kirchner can be defined as soft power usurpers.
Raúl Alfonsín had the huge task of establishing democracy in Argentina. He could be considered as rule-obedient, receptive and a soft challenger. He promoted prosecution and punishment for those who committed human rights violations during the military dictatorship. However, after sentencing in the trial involving the _Juntas Militares_ , Alfonsín tried to interfere in the justice system to avoid new trials against all military officers involved in human rights abuses. He also undermined the power of the Congress when, for instance, he changed the national currency by decree. However, he did respect civil rights and liberties and freedom of the press. He was tolerant but he did not try to achieve consensus with the Peronist Party or the trade unions; on the contrary, in his first months he promoted legislation which tried to neutralize the power of the unions. He did work with his cabinet and sporadically worked with some sectors of the Peronist opposition. He respected the power limits imposed by state institutions.
Carlos Menem, Fernando de la Rúa, Eduardo Duhalde, Néstor Kirchner and Cristina Fernández de Kirchner were closer to the definition of a soft power usurper. Most of them have been challenged by economic difficulties. These crises were not seen as a window of opportunity to reform politics or political parties; on the contrary, each crisis seemed to deepen undemocratic policies such as concentration of power in the executive, abuse of presidential decrees, interference in the justice system and use of clientelism to build political power and populism to secure power (see Table 2.4).
However, while Carlos Menem was quite successful in building and using autonomy from his political party and state institutions, Fernando de la Rúa and Eduardo Duhalde proved unable to build autonomy or concentrate power in their hands to maintain their position. An early conclusion is that a crisis or a post-crisis scenario per se does not guarantee that politicians can increase autonomy. A combination of domestic conditions and the leader's ability is more likely to explain the success of Menem, Néstor Kirchner and Cristina Fernández de Kirchner.
The reasons for the crisis in Ecuador
In Ecuador, economic instability and unpopular government decisions brought about the collapse of the political party system. Historically Ecuador had strong political leaders. Juan José Flores, José María Velasco Ibarra and León Febres Cordero are, among others, examples of the strong _caudillos_ that have dominated Ecuador's political history. Political parties have also been historically significant. By the end of the 1990s, Ecuador's party system seemed to be consolidated around the Partido Social Cristiano, the Partido Roldosista Ecuatoriano, Izquierda Democrática and Democracia Popular. There were also new initiatives such as Movimiento Pachakutik.
Like other countries in the region, Ecuador was able to stabilize its economy at the beginning of the 1990s. Thanks to this stabilization, the country received foreign investment and achieved economic growth. However, in 1995, under the presidency of Sixto Durán Ballén, the war against Peru over a border dispute started a period of political and economic uncertainty that exploded in 2002.
In 1996 Abdalá Bucaram won the elections with the Partido Roldosista Ecuatoriano. As soon as he took office, he changed his economic preferences and turned from a populist strategy to a neoliberal one which promoted privatization and a currency scheme quite similar to the convertibility plan implemented in Argentina. While Carlos Menem in Argentina and Alberto Fujimori in Peru were able to transform themselves from populist to neoliberal advocates without jeopardizing their popularity, Bucaram could not. Seven months after he was elected, he faced a huge popular demonstration against the austerity measures and mounting corruption. Bucaram was impeached and political instability deepened. From his impeachment until Rafael Correa's election, Ecuador witnessed more economic instability and unpopular government decisions that finally caused the collapse of the political party system. There were seven presidents in less than ten years. After the 'dollarization' of the economy, President Jamil Mahuad was forced to resign in January 2000, leading to another period of political uncertainty that did not end when Lucio Gutiérrez won the 2002 general elections (Freidenberg 2008).
After participating in the 2000 coup against Mahuad, Gutiérrez formed the Partido Sociedad Patriótica, which, in an alliance with Movimiento Pachakutik, helped him to win the 2002 presidential elections (Van Cott 2008). Their platform was based on the transformation of the neoliberal agenda and the fight against corruption; but, once he was in office, Gutiérrez reversed his strategy and was unable to maintain his power. He broke his political alliance with left-wing parties and moved closer to the conservative Partido Social Cristiano (PSC). However, this alliance did not last very long and the PSC and Movimiento Pachakutik pushed for Gutiérrez's impeachment (Montúfar 2008). He was finally dismissed in 2005 owing to increasing social unrest and demonstrations, which were held mainly in Quito. As in Argentina, the slogan was _que se vayan todos_. But in Ecuador this became a reality. The political party system collapsed and a thoroughgoing revival of the political elite took place. The traditional parties, from both left and right, were discredited. Former finance minister Rafael Correa won the 2006 presidential elections and assumed office in January 2007. He presented a strong discourse against the so-called _partidocracia_ ('partycracy', a negative term used to describe old, traditional political parties). He did not present candidates for the legislative branch, paving the way for its transformation. The new assembly was formed in 2008, with a somewhat renewed political elite.
Lucio Gutiérrez and Rafael Correa had some similarities. They could be considered outsiders and newcomers and both were highly critical of the political system, promoting an _antisistema_ discourse. So what are the reasons that explain Gutiérrez's failure and Correa's success? Martín Tanaka () argues that Rafael Correa benefited from oil price increases. Thus, Tanaka answers the question combining leadership and economic conditions. During 2005, revenues from oil increased by 40 per cent (El Universo 2005). Ecuador enjoyed record-breaking oil prices from 2007 to 2012 (El Comercio 2013). Not surprisingly, Correa's government has taken advantage of this situation. However, the oil boom in itself cannot be considered the only reason behind Correa's success. His ability to capitalize on the oil price increase also needs to be taken into consideration.
Rafael Correa became minister of finance when Alfredo Palacio succeeded Lucio Gutiérrez. In his four months as minister, he achieved high popularity. He promoted a closer relationship with Venezuela while being critical of the pressures from the World Bank to implement austerity measures and the negotiations for a free trade agreement with the United States. Like Hugo Chávez in Venezuela, Correa understood the dissatisfaction of citizens with the neoliberal agenda, the role of the multinational institutions and the austerity measures. He built up his political discourse, emphasizing Ecuador's sovereignty. Finally, seven months after leaving the government, Correa founded a political movement, Patria Altiva i Soberana (Proud and Sovereign Fatherland), whose objectives were political sovereignty, regional integration and poverty relief. Correa understood the political mood that dominated Ecuador at that time.
The political turmoil that Ecuador was witnessing had some similarities with the background to the emergence of Hugo Chávez in Venezuela and Evo Morales in Bolivia. In the case of Ecuador, traditional parties and new actors such as Partido Sociedad Patriótica or Movimiento Pachakutik proved unable to tackle the economic and political crisis that affected the country from 1995. This caused the relationship between the citizens and their representatives to break down. Gutiérrez's electoral win showed that citizens were ready to accept outsiders with the mandate to transform the system. While Gutiérrez did not particularly promote change in the economy, Rafael Correa proposed a complete political and economic renovation (Mainwaring 2008).
First, Correa represented a unifying figure in a historically divided country: between the coast and the Andes, between the urban and rural environments and many ethnic divisions. He is one of few political leaders who has been able to develop a national leadership. Secondly, Correa has transformed clientelism by centralizing and institutionalizing it through the plan _Bono de Desarrollo Humano_. According to data from the Ministry of Social and Economic Inclusion (MIES), in 2014 approximately 1.9 million people qualified to receive the _Bono_ – a monthly benefit of US$50, for families living below the poverty line, as defined by the Ministry of Social Development. Traditionally, clientelism in Ecuador was mainly conducted at the local level as a negotiation tool between local barons and urban elites, particularly in Quito and Guayaquil. Political parties were territorially based and structured more locally than ideologically. Gradually, these became more involved in representing local interests and closely related to local clientelist networks. Rafael Correa severed these ties and managed to impose direct clientelism without intermediaries, ignoring local barons. The _Bono de Desarrollo Humano_ is nationally distributed through an electronic card and cashpoints; so no local intermediaries are required. Thirdly, Correa's attacks on political parties turned out to be very popular. He rejected political parties from the very beginning, and this strategy has been so successful that politicians are still cautious about mentioning the rebirth of political parties (Conaghan and De la Torre 2008; De la Torre 2013a). The collapse of the political party system prompted a high degree of turnover, with the inclusion of young people and women following that of indigenous movements.
In a context of low institutionalization Correa appeared able to take the country out of a period of political stagnation. He was perceived by many as the solution to Ecuador's deep economic and political crisis. However, he gradually became a polarizing leader, with a tendency to concentrate power and use populist and clientelist tactics (De la Torre 2013b). Like many leaders before him, he attempted to consolidate power by presenting himself as the only solution and the only representative of the people. Moreover, the 2013 elections show that the political system has not recovered. Rafael Correa won with 57 per cent of the total vote followed by Guillermo Lasso, a businessman who created a political formation to present its candidacy. Lasso received 22 per cent of the total vote followed by Lucio Gutiérrez with only 6 per cent. Politics in Ecuador is divided between an opposition still open to newcomers and outsiders and a concentration of power in Correa's hands.
As in the Argentine case, it seems that in Ecuador leaders make a difference. Rafael Correa achieved what Abdalá Bucaram, Lucio Gutiérrez and others could not accomplish. Before Rafael Correa came on the scene, Ecuador had seven presidents in ten years. The list starts in 1997 with the fall of Abdalá Bucaram. Five presidents occupied the Palacio de Carondelet (Fabián Alarcón, Jamil Mahuad, Gustavo Noboa, Lucio Gutiérrez and Alfredo Palacio) until political stability was achieved with the arrival of Rafael Correa. In this context, it is difficult to categorize them within our typology of leaders because they stayed in government for short periods of time. They were unable to develop any leadership style either because they were inefficient – probably they did not have the ability to lead – or because they were thrown out by social mobilizations owing to their incapacity to stabilize the economy or to avoid adjustment policies.
Leaders such as Carlos Menem, Néstor Kirchner and Rafael Correa had the ability to interpret people's needs and expectations, to communicate charismatically their objectives, to gain people's trust and to build political power. Our typology can be applied to those who have the ability to lead. In Ecuador, after many years of political chaos, Rafael Correa was able to take the country out of its misery.
The post-crisis scenarios
In Argentina, the 2001 post-crisis scenario brought to the fore the existing fragmentation of traditional political parties, but also a significant degree of turnover at the municipal level and in the national Congress. After the crisis, new political parties emerged: Coalición Cívica in 2002; Propuesta Republicana in 2005; and Generación para un Nuevo Encuentro Nacional in 2007. However, only 12 per cent of respondents in Argentina believed that new actors had been incorporated in the post-crisis political system and only 28 per cent thought that political practices had actually changed.
The country seems to have moved from its traditional two-party system to one with a (fragmented) dominant party surrounded by new small parties or Peronist splits. The Peronist Party is not only fragmented and contradictory, but is also highly decentralized, with different leaders fighting to control as many political barons as possible in an attempt to conquer national power. This scenario is not very different from the preceding one: one leader monopolizes power at the top while many politicians fight against each other to praise 'the one and only' so as eventually to succeed him.
In this regard, the diagnosis was conclusive: 74 per cent of the legislators interviewed opined that the main political problem in Argentina is the combination of strong leaders with weak political parties. The main political parties have been unable to change the historic trend of strong leaders. The Radical Party has been dominated by Hipólito Yrigoyen, Leandro Alem, Ricardo Balbín and Raúl Alfonsín, and Peronism by Juan Perón, Carlos Menem and Néstor and Cristina Kirchner. Political parties in Argentina seem to need strong leaders to win elections and maintain power. In this context, political parties can become flexible, functional institutions at the service of the leader.
On the other hand, around 30 per cent of legislators believed that parties are also chameleons, deserting and dumping leaders when these become powerless. Thus, parties in Argentina seem to be considered as power machines that only serve strong leaders. Fifty-seven per cent of respondents also argued that most political parties lack ideas, can switch ideologies readily and opportunistically, and that leaders are prepared to break from their parties to increase personal power. Party discipline is absent and leaders easily jump from one party to another. Although most interviewees argued that the main feature of Argentina's political system is the lack of rules, we did find a set of clear and concise 'rules' that are used to increase and maintain power. Politics is a process of power construction through a clientelist logic of exchanging votes, jobs or money. In Argentina, power is achieved through different clientelist channels. Provincial political barons in government are able to distribute a high number of public posts and manage public funds that are crucial to maintaining their clientelist networks. Thanks to this political and economic power, provincial barons usually hold the key to presenting names for the electoral lists. Once elected, these political leaders continue to exchange votes for money, loyalty, support or jobs. These exchanges occur among legislators, politicians in the executive, local political barons and clients. The exchange is political capital, which helps politicians maintain their power, job and privileges. The national leader builds his power by keeping wide networks of clientelist relations, exchanging national funds for the control of provinces, political support for re-elections, jobs and social programmes (Lodola 2009; Szwarcberg 2012). As a result of this individually driven power-building process, political parties remain on the margins.
Clientelism is a tool used by a power usurper to increase his power. In the Argentine case, we observed that politicians – national leaders or provincial barons – practise clientelism as power usurpers. These clientelist networks were widely explained in the interviews. When asked whether these are the complex steps of political negotiations, 88 per cent of interviewees considered that, rather than building consensus or aiming to agree on political issues, the main goal of these processes was to maintain individual power, benefits and privileges. In fact, clientelism was considered a permanent feature: 84 per cent of our respondents argued that clientelism, conceptualized as a tool to increase power through the use and abuse of public resources, was impossible to eradicate. Moreover, 65 per cent answered that clientelism persisted because it was essential to the type of political domination exercised by politicians. Thus, it can be concluded that politics does have clear 'rules' and that leaders can build up personal power independent of political parties. From the long conversations held with politicians, the puzzle of the Argentine case is expressed in the relationship between a low degree of institutionalization of political parties and the autonomy of strong political leaders.
In Ecuador, Correa and his new PAIS movement were seen by 45 per cent of our respondents (including some from the opposition) as a fresh start in a politically stagnant country. However, the renewal of the political elite did not break with old political practices: 90 per cent of our respondents argued that clientelism continues to be a strong political tool. Moreover, Ecuador has always had strong political leaders. Rafael Correa continues that tradition. However, some changes were identified.
A considerable number of respondents, 48 per cent, agreed that during the Correa administration there have been innovations in political practices: 42 per cent of them referred to innovations in communication methods between politicians and citizens; 41 per cent referred to innovations being due to the inclusion of new actors and 17 per cent saw innovations in the degree of the government's transparency.
The collapse of the political party system prompted a high degree of turnover, with the inclusion of young people and women following that of indigenous movements. Studies on elite circulation are rare in Ecuador. Some of the available bibliography centres on the study of the candidates for the 2007 Constitutional Assembly. Of the candidates interviewed for that study, 75.5 per cent had not held political office before and 79.6 per cent had not previously held a job in a political party. Only 34.7 per cent had begun their political career in a political party (Freidenberg 2008). Despite these newcomers, the Assembly followed historical trends: 50 per cent of its members had university degrees, 38.8 per cent had postgraduate degrees and 43.7 per cent had undertaken postgraduate studies abroad. In a country where only 11 per cent of the population goes to university (Viteri Díaz 2006), despite Correa's Citizen Revolution, the assembly was co-opted by a small elite. In 2010, according to data from the Legislative Assembly's website, 82.2 per cent of its members had a university degree.
Thus, the changes that Correa achieved are combined with a significant degree of continuity. Rafael Correa was perceived by many as the solution to Ecuador's deep economic and political crisis; however, he gradually became a polarizing leader, with a tendency to concentrate power and use populist and clientelist tactics (De la Torre 2013b). Like many leaders before him, he attempted to consolidate power in a personalized fashion, presenting himself as the only solution and the only representative of the people.
As in Argentina, in Ecuador clientelism is considered a structural problem and a tool for political domination: in Quito 56 per cent of our respondents defined clientelism as the use and abuse of public resources to gain political benefits. On the other hand, 34 per cent emphasized that citizens exhibited a clientelist logic: they expected some type of benefit in exchange for their participation in politics. Clientelism is a two-way problem, where responsibility falls on politicians as well as citizens. While Correa neutralized the power of local barons, 90 per cent of our respondents agreed that clientelism is still used as a tool to maintain power through a network of exchanges of benefits for political loyalty.
We have identified different types of clientelism and divided them into horizontal and vertical clientelism. Horizontal clientelism is the exchange of political favours and/or money for political support among politicians, i.e. between legislators in the National Congress, between legislators and provincial barons or members of the executive. Vertical clientelism is that between politicians and political supporters. While politics in Argentina seems to have both types, Ecuador is more prone to the vertical model. While in Argentina 47 per cent of respondents mentioned horizontal clientelism, in Ecuador only 10 per cent referred to it. In Ecuador, 56 per cent considered clientelism as a misuse of public resources to obtain political benefits and 34 per cent recognized it as a tool to exchange votes for benefits. Therefore, 90 per cent of our Ecuadorean respondents recognized the existence of what we considered vertical clientelism.
In Argentina, horizontal clientelism was described by 47 per cent of our respondents. They used catchphrases such as _dos contratos por una ley_ (referring to the exchange of jobs in Congress for positive support for legislation) or _política del trueque_ (barter politics). In Ecuador, vertical clientelism was summarized as _quien más da, más votos recibe_ (meaning the politician that gives the most gets the majority of votes).
Clientelism, personalism and weak or fragmented political parties were the main features of the post-crisis scenario identified by most of our respondents in both Argentina and Ecuador. There are some significant differences. In Argentina, traditional political parties, such as the Peronists and Radicals, were weakened by the crisis and became very fragmented. New parties emerged and there was a slow but constant turnover of elites. In Ecuador, most of the traditional parties lost power and representation; they are struggling to survive or re-emerge in a context of a thoroughgoing and fast elite revival. However, both political systems are still embedded in old political practices: clientelism as a political tool that opens up doors for political corruption and excessive presidentialism or personalism with strong leaders who embrace populism as a tool to decrease the number of veto players, weakening the system of checks and balances and the level of political accountability.
The responses of our interviewees helped us to design our classification of leaders. Argentina and Ecuador offer key guidelines for exploring the main features of soft power usurpers. In both cases, the economic chaos was an excuse to usurp power from other state institutions and increase the power of the president.
Conceptualizing political leadership
Argentina
In Argentina our respondents characterized leaders as strong or weak according to their ability to accumulate power. The interviews gave a clear message: 64 per cent of our interviewees believed that political leadership was decadent. The story told by our respondents showed strong leaders, a low degree of institutionalization of political parties, low party competition and unstable and flexible rules. Most of the leaders in Argentina seem to encapsulate the features of rule challenger, soft polarizer and power builder. The interviews in Argentina were conducted during the first presidency of Cristina Fernández de Kirchner and thus we mainly discussed her leadership style.
Cristina Fernández de Kirchner was first elected to the Santa Cruz legislature in 1991. Between 1995 and 2007, she was repeatedly elected to the National Congress, both as deputy and senator. When her husband, President Néstor Kirchner, announced that he would not seek re-election in 2007, Cristina was promoted as his successor. She won the 2007 elections with almost 45 per cent of the total vote. She was the candidate of the Frente Para la Victoria (Front for Victory), a political organization which included mainly Peronists, members of the Radical Party and of small parties from the left. Her vice-president was Julio Cobos from the Radical Party.
Between rule challenger and rule-obedient
Fernández de Kirchner is a leader who combines elements of soft power usurper and ambivalent democrat. Respondents mentioned the use of clientelism and populism to increase her personal power, the concentration of power in the executive to legislate in key areas, together with respect for democratic rights, civil liberties and freedom of press. She can be considered a rule challenger and rule-obedient. Indeed, when her attempts to modify or implement new rules were not successful, she accepted these results. This was the case with Resolution 125 which pitted the government against the agricultural sector.
Cristina Fernández had, at the very beginning of her government, an absolute majority in Congress. Taking advantage of this majority she promoted an increase in the agricultural export tax. This would be the third increase in one year. Resolution 125 indicated that the tax would be flexible, which meant that it would increase or decrease following price fluctuations. The increase that the president was proposing in March 2008 was from 35 per cent to 44 per cent for soya beans and from 32 per cent to 39 per cent for sunflower seeds. This proposal prompted a major confrontation with the agricultural exporters. Historically, Argentina's economy has been agriculture-led. Moreover, landowners and agricultural exporters, from big or small farms, had been historically anti-Peronist. However, Fernández de Kirchner had won in many small towns in rural areas so she seemed to have the support of the owners of small farms. Despite this, there was strong opposition to the new increase. This was a turning point for her government and her first big political failure. The resolution was not approved in the Congress. The negative vote of her vice-president, the Radical Julio Cobos, buried the government's proposal. She did, however, accept the result.
There was another political confrontation in which Fernández de Kirchner was able to accept her limits. The executive power in Argentina has the capacity to legislate through the Necessity and Urgency Decrees (NUDs). They are issued by the president and have the force of law. According to the 1994 Constitution they can be used in exceptional circumstances. The president has used NUDs to introduce changes in the national budget, to approve the use of national reserves to pay the debt, to implement social programmes, to nationalize the pension funds and to regulate private provision of health services. The use of national reserves to pay the debt was reduced by the president of the Central Bank, who was later sacked, and by the justice system. Finally, the president had to annul the first NUD and issue a new one (Levy Yeyati and Novaro 2013). In this case, Fernández made some concessions but got her way and the government was able to use the Central Bank reserves to pay the debt. She explained her tactics by saying 'if we go backwards, we do it to gain strength and jump further' (ibid.: 218).
Our respondents agreed that leaders in Argentina have to be strong. Sixty-two per cent argued that strong leaders are a necessity because there are no rules and the political parties are weak. One senator emphasized that 'Argentines like authoritarian leaders, those who are above the law. These leaders give us security and stability. We do not realize that those leaders will end up abusing power. They will become a problem. In every crisis we look for someone who is going to rescue us.' Cristina Fernández was considered one of those strong leaders. Rather than rescuing Argentina from a crisis, her role was to continue what her husband had started. Both aimed to rebuild the state, which had collapsed in 2001, to change the economic strategy, emphasizing the role of the government in the management of the economy, and to rewrite national history. They were able to pursue their objectives thanks to the soya boom which helped Argentina's economy to recover with 9 per cent economic growth in 2010 and 2011.
While the majority of our respondents seemed to prefer strong leaders, 46 per cent argued that collective leadership should be promoted, pointing to the examples of the Frente Amplio in Uruguay and the Concertación in Chile. However, 73 per cent of interviewees pointed out that a sizeable majority of Argentines understand political leadership as individual and authoritarian. This perspective is confirmed by politics in Argentina. As one deputy said, 'the history of political parties is monopolized by the history of their leaders'. Forty-four per cent stated that this type of leader does not promote political renovation. For instance, 32 per cent of respondents from the Radical Party pointed out that Raúl Alfonsín became, in the long term, one of the most important obstacles to the renovation of the Radical Party. One member of his government argued that Alfonsín concentrated power in his hands, blocking the inclusion of new, younger members.
Thus, Fernández de Kirchner was no exception – a strong, powerful leader who challenged the rules while at the same time accepting some of the limits imposed by the law and state institutions. As one political leader told us, 'leaders in Argentina are always trying to challenge the law and the institutions. If they succeed, they go ahead. If they fail, they will accept the limits and try again later or by other means.'
Not so soft a polarizer
The Argentine president is closer to a power usurper. She is a polarizer, intolerant, and does not share power in the decision-making process. She concentrates power in her hands and takes decisions with a small circle of advisers; some of them are not part of her cabinet.
The polarization of Argentine society was exacerbated under her leadership, most specifically during the 2008 confrontation with the agricultural sector. The old Peronist confrontation between the working class and the oligarchy came alive. Although she lost her battle there, it was a historical moment with two main legacies.
First, a new Peronist movement emerged. La Cámpora is a youth organization that was formed by Máximo Kirchner, son of Cristina and Néstor. It firmly supports the Kirchner government. Many of its members are the children of Peronist militants of the 1970s who disappeared during the military dictatorship. Fernández de Kirchner appointed a significant number of its members to her administration. Secondly, Fernández de Kirchner's image was damaged because of her failure to pass Resolution 125, and she lost the legislative elections in 2009. So the legacy of the confrontation with the agricultural sector was mixed. On the one hand, while La Cámpora was created in 2003, it was after the confrontation that it emerged nationally as a strong, very active, supporter of the government. On the other hand, the government was weakened by losing its majority in Congress.
The emergence of a new movement renewed the government. Paradoxically, the renovation meant the resurrection of old Peronist styles, and Fernández de Kirchner deepened the polarization of society between her followers and her detractors. Her government became involved in a long confrontation with a media conglomerate, Grupo Clarín. This fight also started during the confrontation with the agricultural sector. The Grupo Clarín owned one of the main newspapers as well as TV channels and many radio stations. The government proposed a law to limit the power of the conglomerate. The law, known as _Ley de Medios_ (Media Law), established certain rules and procedures for the distribution of TV and radio licences. It was passed in 2009. Grupo Clarín appealed but its appeal was rejected by the Supreme Court in 2013. This means that all media conglomerates have to adjust their size according to the new law. The battle was won by the government. In the meantime, the confrontation exacerbated the political polarization. Our respondents portrayed a scenario which was highly divided between those who followed Cristina Fernández and those who opposed her. One senator pointed out that the government was damaging the democratic system through the promotion of political confrontation. Sixty-three per cent of interviewees argued that the president attempted to increase her power by undermining political actors. One deputy who belonged to the Peronist Party had a different opinion: 'the president is strengthening democracy by limiting the power of powerful newspapers'.
Power builder and maximizer
Both Kirchners were described in our interviews as power builders and power maximizers. Clientelism, as a tool to use and abuse state revenues, and concentration of power were the main pillars that took Néstor Kirchner from his weak beginning to becoming another strongman in Argentina's politics. There are two legal tools behind these pillars: the co-participation law (23.548), which was passed in 1988 as a transitory regime, is still in place, and the emergency law (25.561), passed during the 2002 crisis, has been extended until December 2015. These two laws, together with decrees from the executive, allow the government to use resources from outside the national budget. Some economists have argued that since 2003 the government was able to access, without the approval of parliament, around US$52 million that can be used discretionally (Clarín 2011). By undermining the inflation rate and economic growth figures, the government has been able to receive more revenues than those included in the national budget. Thanks to the NUD issued by the executive and the discretion allowed by the emergency co-participation laws, both the Kirchner administrations have been able to use state resources to build political power.
Ideologically they were both very strong and articulated. They promoted a different narrative ( _el relato_ ) which attempted to create a hegemonic discourse. In 2003, the Congress annulled the Full Stop and the Due Obedience laws which were passed during the Alfonsín government to limit the number of trials against those who committed human rights violations. In 2004, in the Military Academy, Kirchner ordered that the portraits of General Jorge Rafael Videla and Reynaldo Bignone, who were de facto presidents during the dictatorship, be taken down. These were symbolic gestures to show that the government was committed to the defence of human rights. Both Néstor and Cristina Kirchner structured a discourse which argued that nothing had been done to tackle historical human rights violations under successive democratic governments.
There was further manipulation of information with the intervention of the National Institute of Statistics and Census (INDEC) in January 2007. The idea behind the intervention was to control data, especially when the inflation rate began to escalate (Levy Yeyati and Novaro 2013).
In our interviews, both Néstor Kirchner and Cristina Fernández de Kirchner were portrayed as leaders who would use any tool to maximize power. The laws, the new narrative and the intervention of the INDEC are examples of tools that challenge the rule of law. They both defied the institutions of the state and attempted to ignore rules. Ideologically they have been strong and highly articulated, which has helped to undermine an already weak political opposition.
Ecuador
Political leaders have had a profound effect on Ecuador. Many of those we interviewed agreed that Ecuadorean history can be told by talking about its leaders, including the incumbent president, Rafael Correa. Eighty-six per cent of our interviewees defined Ecuadorean political leaders as strong and keen to monopolize power. Analysis of Correa's leadership pointed to polarization and a permanent debate that we heard in all the interviews. Correa engenders strong confrontational feelings and opinions. According to our respondents, Correa combines elements of a power usurper and a soft power usurper. At the very beginning of his presidency, he could be considered a democratic enhancer, since he promoted the building of democratic institutions such as the 2008 Constitution and the new Assembly.
Rule challenger and rule developer
From the very beginning, Rafael Correa challenged state institutions. He wanted to re-create the state, limit the power of old political actors and traditional political parties, transform the economy, leaving behind the neoliberal strategy, increase social expenditure and achieve sovereignty in the energy and the financial sector. For the 2007 elections he did not have candidates for the Congress. One of our respondents pointed out that Correa considered the Congress and the traditional political parties 'responsible for Ecuador's political decadence'. As soon as he took office, he asked the Tribunal Supremo Electoral (Supreme Electoral Tribunal) to organize a referendum to ask citizens about the formation of a Constituent Assembly. The Tribunal sent his proposal to Congress, where Correa had only marginal support. Fifty-seven congressmen opposed the initiative. The Tribunal dismissed them because they were blocking an electoral process. Correa supported that decision. This was the first confrontation that Correa had with a state institution. One of the dismissed congressmen told us that 'it became clear that Correa was breaking down the traditional political regime'. Indeed, in order to re-create the state, Correa had to dissolve the old regime. In this period, he presented elements of a power usurper and a democratic enhancer since he undermined and rebuilt democratic institutions.
His proposal to form a Constituent Assembly succeeded with 81 per cent of the total vote. In the elections to form the Assembly, Correa's movement Alianza PAIS won almost 70 per cent of the total vote. The Constituent Assembly wrote a new Constitution, which was ratified by a referendum with 63.9 per cent of the vote. With significant popular support, Correa had changed the main pillars of the state.
Gradually, Correa started a confrontation with the press through the judiciary. In 2011, he began a judicial process against the newspaper _El Universal_. The paper had strongly criticized Correa's management of the police revolt of 2010. The newspaper called the president a dictator who had committed crimes against humanity by ordering people to fire at the policemen. The trial ended with a victory for Correa. _El Universal_ had to pay 40 million dollars in compensation and the director and some journalists were sentenced to three years in jail. Finally, Correa pardoned them. Before and after this case, the relationship between the president and the opposition media had been tense. The interviews reflected this polarization. Respondents who supported the president blamed the media for trying to demonize Correa. Other interviewees argued that the president had undermined press freedom because he could not accept any criticism. It is interesting to highlight that 37 per cent of our respondents who supported the president agreed that Correa did not accept 'no for an answer and found it very difficult to accept any criticism'.
In 2011, the president promoted a referendum to modify some articles from the 2008 Constitution and from the Penal Code. Issues related to public security, environment, justice, the banking system and the media were affected. There were ten questions, some of them quite complex. The results were tight. In some of the questions the sum of the negative answers, the blank answers and the invalid ones was higher than that for the affirmative answer. However, Correa said that only the valid votes should be considered, which meant his proposal succeeded.
These examples show that Rafael Correa began as a democratic enhancer promoting a new Constitution which could be considered as one of the most progressive in the region. He was gradually becoming a soft power usurper by confronting the press, polarizing society and increasing his personal power. According to 55 per cent of the interviewees, Correa believes that the whole process of transformation came from him. This means that President Rafael Correa does not consider his leadership to be a relationship with his supporters in a specific time and space but rather a range of personal qualities which has led him to become the unopposed leader of Ecuador since 2007. Several opinions voiced in the interviews suggest that the president considers himself to be the only representative of the will of the people (whether supporter or opponent, citizen or politician) so the only options for everyone else are to stand with him or alone.
Our interviewees highlighted one quality about the president in particular – that he believes in generational change so that the government includes plenty of young bureaucrats. A former adviser to the president said that on coming to power 'they clashed with the existing institutions and the 1998 Constitution' but over time the drive to innovate weakened and all that was left was a desire to remain in office, thanks in particular to the popularity of the president.
Thus far Correa has achieved and appears able to maintain leadership for the nation as a whole. This is considered by many interviewees as a very important political achievement, since Ecuador is in many respects a divided country – divided between mountains and coast, urban and rural areas. Another of the president's achievements, according to the interviewees, is the government's social conscience, which is a marked change from the past.
Correa has transformed clientelism by centralizing and institutionalizing it by means of the _Bono de Desarrollo Humano_ (Human Development Bonus) plan. However, while this has provided much-needed social investment, it has also been plagued with inefficiency and corruption and limited citizen participation. A so-called 'bonocracy' has also sprung up. This refers to the exchange of _Bonos_ for support for the government. Thirty-six per cent of our interviewees agreed that institutionalized clientelism was very obvious in this government and that populist approaches and traditional strongman leaders persist.
A complex combination of democratic enhancer and soft power usurper, President Rafael Correa was the main topic of conversation in all the interviews. While our respondents agreed that he is a national leader who has been able to transform Ecuador, those in opposition fear that he is forgetting his democratic values and beginning to approximate our power usurper model. For instance, 47 per cent of our interviewees expressed doubts about the relationship between the government and the Constitution. They maintained that the Constitution could end up being a 'straitjacket' if the government continues to increase its personalist and authoritarian characteristics. One PAIS legislator pointed to the obvious contradiction between an almost perfect Constitution and the government. He said 'PAIS should demand that the President adhere more closely to the Constitution'.
Polarizer
Rafael Correa considers his leadership to be pivotal in helping Ecuador to begin a new process of independence (De la Torre 2013a). His discourse has polarized society by accusing traditional political parties of being responsible for the many crises that the country has faced since the 1990s. The president perceives himself as the only force behind the Citizens' Revolution ( _Revolución Ciudadana_ ). Those who opposed his plans have been labelled traitors. He has confronted all of them: the _partidocracia_ , the press (criticized as mediocre and corrupt by the president) and the old style left, especially indigenous movements and ecologists (ibid.).
The interviews in Quito gave us a strong feeling of the polarization and intolerance that abound in politics. We were able to interview five politicians (members of the Assembly and former members of Correa's government) who had become deeply disillusioned. They argued that Correa had 'kidnapped the spirit of the 2008 Constitution' and his main objective was to maintain his power. The innovative and revolutionary feeling of the first years was gone. The government was described as a 'technocratic government that discouraged social movements and debate'. They portrayed Correa as intolerant and obsessed with personal power. One of our respondents argued that Correa has developed a messianic discourse: 'he is the people'. He told us that many times the president used phrases such as 'I am the leader, I am the one who got the votes, I know what has to be done'.
One of the interviewees referred to Correa as an icon who combines the beginning and the end, who can promote passion and become the centre of the universe, the one who decides who is bad and who is good: 'every Saturday he stops at the pulpit and reads the gospel for that week'. There is no doubt that Correa arouses strong conflicting feeling and opinions. A close collaborator of the government who left described Correa as a very intelligent academic, a clever man with a great capacity for leadership but with little political experience and somebody who 'cannot understand and never has understood that he is only in power because society as a whole generated the right conditions'. According to one of the young leaders, who founded Ruptura de los 25, his experience of the political ascent of Correa is that: 'in Ecuador building up leadership requires you to show strength'.
Power maximizer
Many of our respondents began to admire Rafael Correa in 2005 when he was finance minister. It was clear then that he had the ability to lead. His discourse concentrated on recovering Ecuador's sovereignty. This helped him to become very popular. Among our respondents, 56 per cent believed that Correa was 'the solution for the country'. However, 34 per cent of them stated that the president has also become a problem.
One of the main problems mentioned was the lack of political parties. However, 87 per cent of the interviewees firmly rejected them. One of them even said, 'political parties do not exist any more'. A government minister was one of the few people who suggested that the political parties were something that still needed to be sorted out and that the traditional parties needed to be restructured to take into account the changes in Ecuadorean society since 2007.
One of the politicians we interviewed summed up recent party history: 'When the democratic process began in 1979 there were three types of party: the old traditional parties that had existed for many years, such as the conservatives and socialists, the new ideological parties (Democratic Left and Popular Left) and the new populist parties (Concentration of Popular Forces). Under democratic rule the parties began to adopt populist practices while the old parties disappeared. The new parties also adopted clientelist practices with strong leaderships, corporativism and short-term policy vision'. According to our respondents, before 2007 there were three main political actors: strong leaders, weak political parties and citizens who took to the streets each time they were politically dissatisfied.
Opposition leaders agreed that the political party system in Ecuador had failed, but they mainly blamed Correa for the dismantling of the parties. Seventy-nine per cent of the opposition politicians we interviewed agreed that government assaults on the political parties had been very effective, so much so that many party leaders were ashamed of their parties. Indeed, Correa's attacks on political parties turned out to be very popular. He rejected political parties from the very beginning, and this strategy has been so successful that politicians are still cautious about mentioning the rebirth of political parties. One leader maintained that the president had demonized politics and politicians and that nowadays many leaders say repeatedly 'I am not a politician'. Political parties' reputations are so damaged that most interviewees prefer to regard their organizations as 'movements'. It is definitely the case that the decline of the political parties was also directly related to their lack of transparency, their understanding of politics as merely a means of peddling influence and privileges for one sector of society. It was also related to the lack of institutionalization, which also affects the state as a whole.
Conclusion
The scenarios that arise out of crises show similarities and differences. In the two countries new leaders came to power. While Néstor Kirchner and Cristina Fernández de Kirchner were traditional but marginal politicians, Rafael Correa was an _outsider_. The three were launched on to the national scene because of a power vacuum following the crisis. The severity of the crisis was used as an excuse to justify the usurpation of power. The concentration of power in the executive was absorbed into an image of democratic stability and governability.
Argentina and Ecuador show that a post-crisis scenario increases the likelihood that soft power usurpers or power usurpers will emerge. The analysis of the four countries presented so far shows the need to contextualize the study of leaders. Leaders are not born in isolation; they are the product of political parties and the political careers that they develop within the party's rules. If parties are in decline, fragmented, clientelist and dysfunctional; if rules are flexible and uncertain and if discipline is absent, and accountability and transparency are low or non-existent, then the likelihood of having usurpers increases. The winner-takes-all logic, together with a lack of pluralism, tolerance and consensus politics, also explains the emergence of usurpers.
In the case of Argentina and Ecuador it was important to recall the bibliography on the halo effect to tackle the degree of polarization among our respondents: some demonize the Kirchners and Correa, others love them. This was also essential to analyse our following case, Venezuela. This country experienced a collapse of its party system and the emergence of a unique leader, Hugo Chávez. We now apply our typology to the case of the charismatic leader who radically transformed Venezuela.
CHAPTER 5
Leadership in the Context of the Collapse of a Party System: Venezuela
Introduction
Venezuela combines strong political parties and strong leaders such as Rómulo Betancourt, Carlos Andrés Pérez and the dictator Marcos Pérez Jimenez. These leaders were strong _caudillos_ with a populist approach. They appealed to nationalistic sentiment with a clever use of political symbols. Political parties were also strong. Acción Democrática was founded in 1941 and COPEI (Comité de Organización Política Electoral Independiente) in 1946. Both parties dominated Venezuelan politics from the 1940s to the 1990s. The end of the so-called _democracia pactada_ (Karl 1986; Magdaleno 2013) meant the collapse of the traditional political parties and the emergence of a new strong leader.
In this chapter, we present an analysis of fifty-seven interviews conducted in Caracas between October 2011 and March 2012. This is a very different chapter from the others. On one hand, we were unable to interview any member of the Partido Socialista Unido de Venezuela (PSUV, United Socialist Party of Venezuela), any member of the government or any journalist who supported Hugo Chávez. All our efforts to persuade them of the academic nature of our research were in vain. According to the opposition leaders the negative answers could be because members of the PSUV and the government did not want to be seen with foreigners and were suspicious about how their words would be used. Nobody wanted to take the risk of being quoted in a foreign newspaper. The PSUV, it was explained to us, is a very hierarchical organization and its members would not risk their position by meeting with us. Therefore we interviewed only members of the opposition parties such as Movement for Socialism (Movimiento al Socialismo), Radical Cause (Causa Radical), the Red Flag Party (Partido Bandera Roja), Project Venezuela (Proyecto Venezuela), A New Era (Un Nuevo Tiempo), Justice First (Primero Justicia) and For Social Democracy (Por la Democracia Social, PODEMOS) and other parties from the Mesa de Unidad Democrática (MUD).
On the other hand, when we arrived in Caracas in October 2011, the nation was still in shock after the announcement in June that the president had cancer. Moreover, the political opposition was reorganizing itself to present candidates for the primary elections in February 2012. For the first time they would present a candidate for the presidential elections who would be elected in open primaries. The illness of the president and the primaries were the main worries of our interviewees. We had to make enormous efforts to keep the interviews focused on our questionnaire. We have to confess that often the interviews took a long time because it was fascinating to listen to all the rumours about Chávez's health and to all the analysis of the primaries' results.
In order to comply with the structure of the book, we have decided not to include the multiple political scenarios that were presented to us in the interviews. In this chapter, as in the previous chapters, we are analysing the post-crisis scenario, the emergence of Hugo Chávez and the conceptualization of political leaders as presented in the interviews.
The reasons for the crisis
Although it came as a surprise, the ease with which the Venezuelan political party system was dismantled could have been foreseen if historical details had been deeply analysed. After the 1958 political agreement, the political party system became highly institutionalized with a very low degree of electoral competition. The options were scarce: the Christian Democratic Party, known as COPEI, and Democratic Action (AD), which was the social democratic option.
The _Punto Fijo_ accord consolidated a democratic regime with two well-established political parties and a low degree of electoral competition. The aim of the pact was to achieve political stability and to avoid the return of authoritarian regimes. The 1958 pact implemented a shared government since the parties committed themselves to accept election results and to include members of AD and COPEI in each government. Although this was seen as one of the pillars of Venezuelan democracy, in the long run it became one of its main problems. Political parties and politicians became too comfortable within a system that secured them a place in government despite electoral results. This increased their level of autonomy, which in the long term transformed itself into impunity. Both parties became resistant to any political change. Moreover, as governors and mayors were named by the president, clientelism was at its peak during this period of territorial centralization. This political system was legalized and legitimized with the 1961 Constitution, and it was defined as a 'populist system of elite conciliation that imposed a system of negotiations, transactions and compromises' (Magdaleno 2013: 239).
From the time of the government of Rómulo Betancourt (AD, 1959–64) Venezuela began a process of consolidation of democracy. The 1968 elections were a turning point when Rafael Caldera from COPEI won the vote. This was the first alternation in power and the first opportunity to test the _Punto Fijo_ accord. One of the journalists interviewed for this research pointed out that 'the _Punto Fijo_ had political titans'. In the 1973 elections, Carlos Andrés Pérez won the presidency and the political party system seem to be consolidated (Rey 1998). This process of democratic consolidation has to be understood in its historical context. Magdaleno () argues that the huge increase in oil revenues helped the governments from AD and COPEI to expand public expenditure and meet social demands. In 1972 the oil revenues were 7,884 million bolivars, in 1974 they reached 36,448 million; in 1980, 45,331 million, and in 1981, 70,886 million (ibid.). Oil revenues were around 70–80 per cent of the total public revenues (Romero 1996).
We suggest that the combination of high oil revenues and political stability explains the high degree of autonomy that the political parties acquired in Venezuela. In terms of political stability, the _Punto Fijo_ accord guaranteed that AD and COPEI would be in government. There were no threats from other political actors. These two political parties became very powerful with a high degree of influence over domestic matters. There were no other political actors who could challenge their power (Crisp 1997).
If Argentina and Ecuador are examples of low institutionalization and Uruguay presents a degree of institutionalization that seems to balance the political system, then Venezuela, after 1958, shows an over-institutionalization of the political party system that gives parties and politicians a high degree of autonomy. In the case of Venezuela, we will go a step farther to suggest that in the long term the _Punto Fijo_ coalition ensured the iron law of oligarchy, as explained by Robert Michels (). The elected were dominating the electors with a high degree of autonomy. Here, we argue that the degree of political parties' autonomy depends on the democratic quality of electoral competition. If electoral competition is weak, political parties increase their autonomy and capacity to ignore citizens and rules. The _Punto Fijo_ in Venezuela gave parties a high degree of autonomy (Ellner 1988). The long-term consequences of the _Punto Fijo_ pact were that AD and COPEI became over-autonomous, too powerful, and too corrupt. Politicians were so isolated that they did not spot the signs of popular discontent.
During the oil boom, the governments of Carlos Andrés Pérez (1974–79) and Luis Herrera Campins (1979–84) increased the public debt. In 1974, the external and internal debt totalled 10,176 million bolivars; in 1979 the total was 54,533 million, and in 1981 66,654 million (Romero 1996). By the end of the 1970s, Venezuela began to show signs of political and economic exhaustion: a highly indebted and oil-dependent economy managed by politicians who were gradually unable to maintain political consensus. The impact that oil had on Venezuelan politics has been analysed before (Karl 1986, ). Here we would like to emphasize that the AD and COPEI leadership was economically sustained by oil price increases, especially from 1973 (Magdaleno 2013). However, Corrales () points out that from 1973 to 1983, the oil boom became an obstacle to any economic reform in Venezuela. Indeed, governments chose fiscal expansion as their main economic strategy, since economic opportunities were considered infinite during the price boom. However, once the international context changed, the Venezuelan governments were forced to amend their strategy. The external debt crisis that affected Latin America from 1982 and the end of the oil boom made it impossible to continue with the policies of fiscal expansion and redistribution of oil revenues.
In 1989, Carlos Andrés Pérez from AD won the elections with 52 per cent of the total vote. The COPEI candidate obtained 40 per cent of the vote, showing a strong polarization of the results. However, there were two political parties which were gaining in strength: Movimiento al Socialismo (MAS) and La Causa Radical. Both had been created in 1971 from divisions within the Communist Party, and, although in the presidential elections they received less than 5 per cent of the vote, in the regional elections they achieved better results, winning two governorships. AD obtained 39 per cent of the vote; COPEI, 31 per cent; and MAS, 17 per cent. This showed that political and territorial decentralization could end the monopoly of power shared by AD and COPEI (El País 1989). It was the first time, since 1958, that the domination of AD and COPEI was threatened.
The 1980s have been defined as the era of disillusion; many frustrations emerged since the Great Venezuela promised by Carlos Andrés Pérez in the 1970s never happened (Romero 1996; Magdaleno 2013). This could explain why, only three and a half weeks and after taking office, Carlos Andrés Pérez was confronted by the social revolt known as the _Caracazo_. In February 1989, Pérez increased the price of petrol and urban transport, which unleashed social unrest that ended with 276 dead. The _Caracazo_ made evident the wide gap between politicians and citizens. Carlos Andrés Pérez was a strong leader, popular and populist, who had won the elections with more than 50 per cent of the vote, but after less than a month in government he became terribly unpopular. He had inherited a bankrupt country with a fiscal deficit of 9.4 per cent of GDP and the largest current-account deficit in Venezuelan history (Reid 2007). After Pérez's impeachment, Rafael Caldera won the 1993 elections with only 30 per cent of the total vote. After the collapse of the second-largest bank, Banco Latino, Caldera reintroduced Pérez's reform programme but under a different name: _Agenda Venezuela_.
It is relevant to ask why the economic reforms were strongly opposed in Venezuela when other Latin American countries, such as Argentina and Peru, implemented them. Magdaleno () offers three reasons to explain this rejection. First, the 1970s and 1980s established a populist political culture based on the redistribution of oil revenues. Secondly, there was internal opposition from AD and COPEI to the economic reforms. Therefore, political actors were no longer able to achieve consensus, especially on economic strategy. Thirdly, Carlos Andrés Pérez was a very popular politician who overestimated his ability to implement an economic adjustment. A deteriorating economic situation with leaders who were unable to read citizens' demands and the need for political renewal were the precursor of the collapse of the _Punto Fijo_ accord and its political stability.
We suggest that Venezuela is a case of over-institutionalization of the political party system with low, undemocratic, electoral competition that allows political parties to be autonomous. Through the _Punto Fijo_ , the traditional parties themselves guaranteed their position in government. Thus, over-institutionalization can give parties a high degree of autonomy. While the emergence of the Frente Amplio in Uruguay benefited electoral competition by breaking the traditional equilibrium between Blancos and Colorados, in the long run the _Punto Fijo_ accord in Venezuela provoked a deterioration of electoral competition (Tedesco and Diamint 2013). Owing to the appearance of a new political actor, the Frente Amplio, Uruguay avoided an over-institutionalization of its political party system and a deterioration in electoral competition. Venezuela did not. Here again we can see leadership from a collective perspective that, in this case, negatively led to the emergence of an autonomous, strong, leader. The _Punto Fijo_ political class undermined the degree of representation and political competition, provoking a change of regime that deepened the undermining of democracy with the emergence of Hugo Chávez.
There are six main factors that should be considered to understand the emergence of Hugo Chávez in Venezuela. First, the political elite, rather than facing the challenges posed by the _Caracazo_ , continued to be immersed in party politics and ignored, or misunderstood, citizens' demands. Secondly, governments from different political parties were no longer effectively dealing with economic problems, which eroded the legitimacy of state institutions and political parties. Thirdly, owing to the economic problems, AD and COPEI were undergoing internal crisis and a confrontation between them that undermined their political coalition. Fourthly, the traditional political parties were no longer able to channel social demands. Fifthly, Hugo Chávez understood the _Caracazo_ message and citizens' rejection of austerity measures and the neoliberal agenda. Lastly, he offered a very simple discourse that blamed political parties and politicians for the economic crisis.
Hugo Chávez was able to build power and autonomy outside the old party system. The control of the armed forces and the oil rents together with the creation of an extensive social programme to improve the quality of life of urban and rural marginal sectors allowed him to concentrate power in his hands for fourteen years. His government was legitimized, and his autonomy increased thanks to many victories in elections and referendums.
The post-crisis scenario
The story of Hugo Chávez is well known. Chávez was a military officer who, in 1982, formed a movement within the armed forces known as Ejército Bolivariano Revolucionario-200 (Bolivarian Revolutionary Army-200), later called Movimiento Bolivariano Revolucionario-200 (Revolutionary Bolivarian Movement-200). He emerged as a political figure with the attempted military coup of February 1992. He was imprisoned and released in 1994 by President Rafael Caldera. McCoy (: 67) emphasizes that Chávez was eligible to run for office because he was never convicted and thus 'he quietly began to build an impressive campaign throughout the country'. In 1997 he created his own political party, Movimiento Quinta República (MVR, Fifth Republic Movement). He won the elections in 1998 with 56 per cent of the total vote.
One of our respondents stated that this election marked the end of an era. Venezuelans were angry with the political elite of the _Punto Fijo_ and Chávez was offering them a transformation. A union leader explained: 'Hugo Chávez was a product of the end of a historical period in Venezuela'. Sixty-two per cent of our respondents agreed that the president had a high approval rating because citizens believed that he cared about them, and especially about the poorest. In our interviews, most of the political opponents recognized Chávez's charisma and his ability to communicate and to talk to the underprivileged. One of our respondents argued that Chávez was able to give the poor a role as a political actor.
In his presidential oath he proclaimed: 'I swear before God and my people that upon this moribund Constitution I will drive forth the necessary democratic transformations so that the new republic will have a Carta Magna befitting these new times' (Marcano and Barrera 2007). Chávez was clear from the very beginning that he would transform state institutions. Indeed, in order to concentrate power in his hands and to create a system of presidentialist domination, Chávez started a process that would create new institutions and transform old ones to eliminate the system of checks and balances. It was the beginning of a period that would concentrate power in the hands of the president, undermining the rule of law.
In order to change the Constitution, Chávez called for a public referendum to form a Constitutional Assembly. The referendum took place on 25 April 1999 and Chávez's proposal won with 88 per cent of the vote. In August of that year, the Constitutional Assembly proclaimed itself sovereign, replacing the Congress that had been elected in 1998 and the Supreme Court. This was the beginning of a long process that entailed the modification of the balance of power between the legislative, the executive and the judiciary. The Assembly gave itself powers to dismiss state officials it considered corrupt. The Constitutional Assembly replaced the members of the Supreme Tribunal of Justice, the National Electoral Council and the Attorney General. Finally the Assembly wrote a new Constitution. In December 1999 there was a referendum to adopt the Constitution, which was approved by 72 per cent of the vote.
The new law was 'the most heavily presidentialist constitution in contemporary Latin America' (Corrales and Penfold 2007: 186). It included more rights and protection for indigenous people and women and established the rights to education, housing, healthcare and food. It increased the presidential term from five to six years with a single re-election and allowed people to recall presidents by referendum. The Congress became a unicameral body, the National Assembly. The president had the power to legislate and to call for public referendums without support from the Assembly. The military obtained more powers and a role in the government, on the grounds that they have to ensure public order and aid national development. The political parties could not receive public financing. Finally, the executive also gained control over the National Electoral Council, which governs electoral affairs.
With the new Constitution and the new Assembly, President Chávez dismantled the old political regime and began a process of power concentration in the executive. He became a firm power usurper with all the features that we defined: he challenged the rules, polarized society and maximized his power (see Table 2.5).
One of the instruments that Chávez used to usurp power from other institutions was the so called _Leyes Habilitantes_ (Habilitating Laws). These laws, approved by the National Assembly, gave power to the president to legislate. Thus, the president took over the role of the legislative. In 1999, Chávez asked for approval of a _Ley Habilitante_ that allowed him to legislate by decree. The Assembly sanctioned the law for a six-month period. During this period Chávez approved fifty-three decrees, mainly on economic and financial issues.
In 1999, Chávez launched Plan Bolivar 2000. Around 70,000 members of the armed forces would help to repair roads, schools and hospitals and offer free medical care and vaccinations. The Plan Bolivar gave a new role to the armed forces and was the antecedent of the _Misiones_ (community-based social plans).
Three main pillars would be developed by Chávez to increase and maintain his power: the _Misiones_ , elections and referendums. One of our respondents explained that there were many elections and referendums but participation was low. He argued that citizens felt incorporated into politics through Chávez and did not feel the need to vote.
In 2000 Venezuela held elections in July and December to elect the president, members of the National Assembly, governors, mayors and city councillors. Chávez was re-elected with almost 60 per cent of the vote. In the National Assembly, his supporters won 101 seats out of 165. In November 2000, the Assembly passed another _Ley Habilitante_ which gave the president the power to legislate throughout one year. In this period forty-nine decrees were passed on issues pertaining to natural resources, especially legislation regarding land and hydrocarbons. In 2001 the government introduced a new hydrocarbon law to increase its control over the oil industry. They increased the royalties and introduced the formation of mixed companies whereby PDVSA, the national oil company, would have joint control with private companies over the oil industry. By 2006, all the agreements with private companies were controlled by PDVSA. The president was not only usurping power from other institutions of the state but also from private companies.
After the attempted coup in 2002, and thanks to an oil windfall, Chávez launched the _Misiones_ , which helped him to increase his power by captivating the hearts of millions of poor Venezuelans. The _Misiones_ helped him to win the 2004 recall referendum. He won 59 per cent of the vote. After this victory, he used his majority in the National Assembly to change twelve judges in the Supreme Court. While the _Leyes Habilitantes_ helped him to overrule the legislative, the change of twelve judges was a clear move to neutralize any type of independence or opposition in the judiciary. This was another tool that allowed Chávez to usurp power.
The _Misiones_ became a pillar of Chávez's power and increasing popularity. Sixty-seven per cent of our respondents in Caracas defined clientelism as an exchange of benefits for votes; 93 per cent agreed that the _Misiones_ were a clientelist tool; 43 per cent believed that clientelism persists because it is functional to a specific form of political domination and 28 per cent argued that clientelist policies replace the state when it fails to provide public services. Clientelism is criticized, but 57 per cent of our respondents argued that it is very effective when the aim is to accumulate power. However, in unequal countries such as Venezuela, social policies are crucial to improve income distribution. According to ECLAC, in 1998 49 per cent of Venezuelans were considered to be poor (CEPAL 2012). In 2011, the percentage of poor people in the country had decreased to 27 per cent. All our respondents said that in the case of a Mesa de la Unidad Democrática (MUD, Democratic Unity Roundtable) government, the _Misiones_ should be continued. The political abuse of social policies, which could be considered as clientelism, does not erase the need to establish measures to change the situation of the poorest.
In October 2004 there were regional elections. Chávez's supporters won twenty-one out of twenty-three state governments and more than 90 per cent of the municipalities (Corrales and Penfold 2007). By 2005 the opposition was in disarray. Most of the opposition decided to boycott the National Assembly elections in December 2005. Consequently Chávez's partisans won all the seats in the Assembly. In the 2006 presidential elections, Chávez won with 63 per cent of the vote. At this time, he created the PSUV, which was an umbrella organization that encompassed all leftist political parties that supported the Chávez regime. By 2007, 5.7 million people belonged to the PSUV (Cannon 2009). He argued that this umbrella organization would have a bottom-up structure to help the emergence of new leaders, but in reality this did not happen and the PSUV became a mere follower of a strong leader (ibid.).
With or without the PSUV, Chávez was a great communicator and a highly popular president. One of our respondents emphasized that Chávez was able to speak in very simple terms and his message was clear to anybody. Another respondent suggested that he was a postmodern _caudillo_ : a military, Christian strong man.
In January 2007, Chávez asked again for the approval of a _Ley Habilitante_. He got it for eighteen months. This law allowed him to legislate on energy; economic, social and financial issues; tax reforms; state institutions and popular participation. He sanctioned fifty-nine laws during this exceptional period.
After the 2006 victory, Chávez was expanding his power and stepping up his persecution of political opponents. The government would not renew the licence of RCTV, the biggest opposition television station. A law was passed to make it very difficult for NGOs to receive foreign donations. Finally, 'those on the list of the 3.4 million people who signed the petition for the recall referendum found themselves liable to be sacked from government jobs and denied public services, from passports to loans and contracts' (Reid 2007: 172).
There was another referendum in December 2007 to reform sixty-nine articles of the Constitution. The amendments encompassed indefinite re-election for the president and all elective officials, changing the presidential term from six years to seven, the militarization of the country with the president able to create Strategic Zones in any area of the Venezuelan territory and suspend democratic rights, the creation of new forms of popular participation, such as _Consejos del Poder Popular_ or _Células Sociales_ , and the establishment of a socialist democracy. The changes were rejected by 50.65 per cent of the vote, which showed the degree of polarization that Venezuela achieved during the Chávez regime. This was the first time that Chávez had lost an election. Since 1999, he had won eleven votes in elections and referendums.
After this defeat, the opposition camp gained new momentum. The Mesa de la Unidad Democrática (MUD, Democratic Unity Roundtable) was established in 2008 and by 2010 included fifty political parties from the centre, centre-left and centre-right. The main unifying factor of the MUD was its opposition to Hugo Chávez. The main member parties were Democratic Action and COPEI, the two parties which dominated Venezuelan politics from 1959 to 1999. Other parties that joined the MUD were the Movement for Socialism (Movimiento al Socialismo), Radical Cause (Causa Radical), the Red Flag Party (Partido Bandera Roja), Project Venezuela (Proyecto Venezuela), A New Era (Un Nuevo Tiempo), Justice First (Primero Justicia) and PODEMOS. Despite the collapse of the political party system and President Chávez's assaults, a large number of the MUD still believed that political parties were relevant for democracy. Indeed, 49 per cent of our respondents agreed that political parties should be the pillars of a democratic political regime, and 24 per cent believed that they are the main channels for citizens' demands; but 11 per cent were more negative, seeing political parties as mere tools for the accumulation of power. However, as Chávez's discourse has been very successful in presenting the political parties as inefficient and corrupt, even young politicians were careful when debating the role of political parties.
Under the Constitution, President Chávez could not stand for election again so he called for another referendum in February 2009 to abolish the two-term limit for all public offices. His proposal won with 54 per cent of the total vote. He had secured a chance of indefinite re-election.
In 2010 there was another _Ley Habilitante_ for eighteen months as a response to violent storms in the country. During these eighteen months, fifty-four laws were passed. Chávez asked for special powers to legislate on infrastructure, transport, public services, housing, development and urban and rural land. He was also able to legislate on citizen security, national defence, international cooperation and economic issues.
By 1999, President Chávez had achieved complete control of all the institutions of the state. As one of our respondents put it, 'the executive had kidnapped all the powers of the state'. Chávez was also breaking the boundaries between the president and the state.
In the September 2010 election for the National Assembly the MUD won around 47 per cent of the vote nationally. This new situation, with the emergence of a political opponent, changed dramatically when in June 2011 Chávez announced from Cuba that he had cancer.
Since the 2007 defeat, the political scenario in Venezuela had changed. The opposition was becoming stronger and Chávez was weaker because of his illness. The October 2012 elections were very different from previous ones under the Chávez regime. The president was ill and the opposition was united. The MUD held open primaries in February 2012. Around three million citizens voted in the primaries and Henrique Capriles, from Primero Justicia, won with 63 per cent of the vote. In October, Chávez won the presidential elections with 55 per cent of the vote. Capriles received 44 per cent. Chávez became extremely ill and was unable to take office in January 2013. He died in March and new elections were held in April. Nicolás Maduro, Chávez's elected successor, won 50.61 per cent of the vote and Henrique Capriles won 49.12 per cent.
No doubt Chávez fundamentally changed Venezuelan politics in the short and in the long term. He also changed how political leadership is understood, and this is the issue that we analyse in the next section.
Conceptualizing political leadership
Although our respondents opposed President Chávez, all of them agreed that he was a charismatic leader. They all praised his ability to communicate with his followers, his capacity to engage with the underprivileged, his talent for speaking for a long time and his powerful image. They also pointed to his aggressive speeches and his authoritarian and paternalistic style. They emphasized that Chávez created a leadership style that was difficult to emulate and impossible to forget. Most of them agreed that the new, younger leaders who were emerging in the MUD were trying to follow Chávez's style in one way or another. For instance, one of our respondents explained that Chávez concentrated his discourse at the micro level, talking with his followers about problems in their neighbourhood, their local school or clinic. The younger generation of leaders was doing the same, leaving aside discussions about economic strategy, the problems of infrastructure and urban violence.
Chávez was defined as an omnipotent, charismatic leader. He was paternalistic and caring to some and authoritarian and arrogant to others. He polarized society, provoking love and hatred. One of our respondents suggested that Chávez created a reality show; he sacked ministers on television, sang, made jokes, got angry with his political opponents and insulted the United States. Every time he appeared on television, he put on a show. He seduced his followers. He was a politician and an entertainer. He transformed the image of the political leader. From the time Chávez appeared on the political scene, Venezuelans were seduced into a personality cult. His followers were charmed and enchanted by him. Many of our respondents agree that Chávez has became a messianic figure.
His type of leadership had two contrasting effects. For his followers he was a caring father, fighting for their interests, protecting them and providing them with goods and services through the _Misiones_. He represented the majority of Venezuelans; he was considered one of them. He understood their situation, spoke their language, taught them about their rights and made them feel important. For his opponents, he was an authoritarian, populist, clientelist president whose main aim was to concentrate power in his hands. 'Chávez wins in all games where he polarizes and confronts,' said an opposition leader. However, all of our respondents stated that he could not be considered a dictator. Although there were some human rights violations, persecutions of political opponents, a reduction in the freedom of expression and civil liberties, our interviewees pointed out that Chávez was not like the Latin American dictators of the 1970s. In fact, 93 per cent of our respondents agreed that the 1999 Constitution expanded human rights guarantees, improving women's rights and indigenous rights. Nevertheless, 87 per cent stated that there was discrimination on political grounds, and permanent attacks on the independence of the judiciary and on the freedom of the press.
There was also consensus among our interviewees that the emergence of Chávez provoked a renewal of political elites. He also transformed the understanding of politics and of leadership. The interviews described a type of leader who was democratic, legitimate, charismatic, a polarizer and omnipotent, clientelist and authoritarian. It was a complex characterization which combined democracy and authoritarianism. Indeed, Chávez organized many elections and referendums while manipulating the institutions of the state, especially the system of checks and balances.
In our typology he was a power usurper. Chávez was simultaneously a rule challenger, a polarizer and a power maximizer. He was democratically elected and used elections and referendums to transform state institutions and increase his power. The _Leyes Habilitantes_ were a tool to usurp power from the legislative. Changing the judges of the Supreme Court in 2004 undermined the power and the independence of the judiciary. When he lost the 2007 referendum, he called for a new one in 2009 to approve indefinite re-election. He was using referendums and elections to concentrate power in his hands. President Chávez also employed clientelism and populism to increase his personal power. This was very evident in the establishment of the _Misiones_. Indeed, in 2003 his popularity was decreasing and the _Misiones_ provided a huge boost.
A charismatic leader, a polarizer, a rule challenger and a power maximizer, Hugo Chávez displays all the features of a power usurper. However, we would like to suggest that the undermining of civil liberties and the freedom of the press was not extreme. There was a combination of persecution of opponents and an important degree of freedom to criticize the government.
Regarding the role of the political parties, all of our respondents were very cautious about it. Hugo Chávez, like Rafael Correa in Ecuador, had been very successful in his attacks on political parties, especially AD and COPEI. However, as mentioned above, 49 per cent of our respondents agreed that political parties are key to a democratic political regime, 24 per cent believed that parties are the main channels for social demands and, from a more negative perspective, 11 per cent defined political parties as mere tools for the accumulation of power.
One of the unintended consequences of the _Punto Fijo_ accord was the discrediting of the main political parties, AD and COPEI. According to 75 per cent of our respondents the new parties, such as Movement for Socialism (Movimiento al Socialismo), Radical Cause (Causa Radical), the Red Flag Party (Partido Bandera Roja), Project Venezuela (Proyecto Venezuela), A New Era (Un Nuevo Tiempo), Justice First (Primero Justicia) and PODEMOS, had a responsibility to show that they could be different. One of the main objectives of the February 2012 primaries was to demonstrate that. We conducted interviews with young leaders from all of these new political groupings and they all agreed that to defeat Chávez, unity under the umbrella of the MUD was necessary. These political parties did not have strong ideological differences. Their aim was to renovate politics and to organize the opposition to Chávez. As one young leader stated, 'what unites us is our opposition to the president'.
In the interviews Chávez was also characterized as a polarizing leader. Here we would like to reiterate that all our respondents were from the opposition movements and considered Chávez the main problem in Venezuelan politics. Under his presidency, the country became highly polarized. He provoked love and hatred. Eighty-three per cent of our respondents argued that Chávez was always able to deepen and take advantage of the polarization because a majority of Venezuelans supported his policies. One of our respondents emphasized that he also created fear among his supporters by proclaiming that the opposition would dismantle the _Misiones_.
President Chávez, argued most of our respondents, became the only voice in politics in Venezuela. His leadership was understood as direct, since there were no intermediaries between him and his people. In the eyes of our respondents, the PSUV had never attempted to become a communication channel between the leader and his followers.
His charismatic leadership was screened on TV. He made politics a big show with his TV programme _Aló Presidente_ , which was broadcast every Sunday from 11 a.m. until he was done talking. Cameras followed him around the country, showing the results of his Bolivarian Revolution and his power. Enrique Krauze (Nolan 2012) pointed out that ' _Aló Presidente_ gives Venezuelans at least the appearance of contact with power, through his verbal and visual presence, which may be welcomed by people who have spent most of their lives being ignored'. Eighty-seven per cent of our respondents agreed that Chávez's innovation was the economic, social and political inclusion of millions of underprivileged citizens. This was also his main contribution – the young leaders from the new political organizations recognized in the interviews that the poorest of the poor could no longer be ignored by Venezuelan politicians. Chávez had politically activated the poor sectors of society and highlighted the African and indigenous roots of Venezuela's population (Trinkunas 2002: 42). This initiated the establishment of a sacred relationship between Chávez and his followers. One of our respondents argued that Venezuelans understand leadership with a religious touch.
In our interviews the conceptualization of leadership was defined by Chávez's style. The political opposition expressed the opinion that a leader has to have charisma, strong personality and a paternalistic attitude. However, 86 per cent of our respondents mentioned the Chilean Concertación as the ideal type of political leadership. The young leaders of the opposition in Venezuela preferred collective political leadership, criticizing Chávez's concentration of power. Ninety-two per cent of the interviewees agreed that one of the main problems of Chávez's style of leadership is that the president becomes the only guarantor of the political model. They also stated that they wanted to find a happy medium between strong leaders who could oppose Chávez and a collective leadership to avoid an extreme concentration of power.
Based on our interviews, we suggest that the collapse of the _Punto Fijo_ accord together with the discrediting of the traditional political parties helped the emergence of a strong leader who was able to transform the institutions of the state and politics. Chávez is an extreme example of a power usurper. In a context of over-institutionalization of the political party system, an economic crisis opened the door to outsiders and anti-systemic leaders. In our research, Venezuela, Ecuador and Argentina indicate that these situations help the emergence of power usurpers. If the economic crisis is reversed and a period of economic growth (thanks to an oil or soya boom) follows, the probability of having a power usurper increases.
The power usurper is a leader who has three main features: he is a rule challenger, a polarizer and a power maximizer. He is a rule challenger because he manipulates constitutional or electoral instruments. In the case of Chávez, he changed the Constitution and the electoral system to concentrate power in his hands and undermine any opposition from the legislative or the judiciary. Through the four _Leyes Habilitantes_ , Chávez usurped power from the legislative. Chávez used clientelism and populism to increase his personal power, undermined civil liberties, undermined press freedom and horizontal accountability.
The power usurper is also a polarizer. As mentioned before, Chávez increased the polarization of society. He was intolerant of his opponents and refused to share the decision-making process. Chávez took advantage of the failures of the _Punto Fijo_ to discredit traditional political parties. Even when in 2007 there was a new student movement which opposed Chávez's referendum, he referred to them as 'the children of the old regime'. Our respondents from the new political organizations argued that it has taken a monumental effort to overcome the bad reputation of the parties.
Concentration of power is one of the main aims of a power usurper, which illustrates the third feature of being a power maximizer. The leader has a high capacity to ignore the rules and citizens' demands. He undermines political opposition, perpetuates himself in power and believes that he is more important than democracy. Usually, the power usurper is highly ideological. Through his ideology, Chávez motivated and inspired millions of Venezuelans. A young leader from an opposition party told us how significant it was to see previously excluded citizens holding the Constitution as if it were the Bible. Chávez was without doubt a great orator and he convinced his followers that he cared about each of them. However, he also used his speeches to confront his political opponents, whom he considered his enemies. A traditional politician who was a member of COPEI recognized Chávez's ability to discredit political parties and political opponents.
In the interviews, the Venezuelan political leaders described Chávez as an extreme power usurper. It became clear that the president had rewritten the concept of leader. We wanted to explore how political leadership, independently of Chávez's style, was understood by our respondents, so we asked them to explain what type of political leader the MUD would offer. All our respondents from the different political parties that were included in the MUD agreed that leadership should be collective with political parties as its main pillars. One representative said, 'parties have been strengthened. People understood the importance of having these mechanisms of political mediation.' After so many years of strong leaders, they suggested that Venezuela was ready for a different kind of leadership. The example of the Concertación in Chile was mentioned in 87 per cent of the interviews. However, they also recognized the need to find a charismatic leader; 92 per cent argued that a Chávez political opponent should be young and charismatic. They also stated that a government from the opposition should continue with the _Misiones_. As one of our respondents explained, 'the _Misiones_ are now a need in Venezuela'.
Despite the fact that most of our respondents gave priority to the strengthening of political parties, they also pointed out that whoever emerges from the MUD should be a strong leader. One of the young politicians of a new political party said, 'most of the people will vote for the strongest leader'. However, they also emphasized the importance of building consensus and dialogue to mark a crucial difference with the Chávez government.
A charismatic, strong, young leader supported by empowered political parties and a promoter of dialogue and consensus was the ideal leader, according to our respondents. Their main aim was to reform politics and to depolarize society.
We would suggest that in our typology such a leader is closer to an ambivalent democrat or a democracy enhancer. After so many years of a power usurper in government, our respondents argued for the building or reinforcement of democratic institutions, the promotion of horizontal accountability and respect for democratic rights and civil liberties. They aimed to establish consensus so that they could be considered bridge builders. Finally, they expressed the need to respect the limits imposed by state institutions. It is important to highlight that these were their goals. Whether they follow them strictly if one day they are in government, or whether they continue to exercise a leadership more similar to our model of the power usurper, is beyond our analysis since they are still outside the Palacio de Miraflores.
Conclusion
The collapse of the party system opens the door to power usurpers. In the case of Venezuela, Hugo Chávez was the consequence of the failures of the _Punto Fijo_. However, it is essential to emphasize that Chávez was unique. He was extremely charismatic. Above all, he was a great communicator and understood his citizens' demands.
Our study indicates that in order to understand the emergence of Chávez it is essential to examine the slow deterioration of the traditional party system. This does not mean that the collapse of a party system necessarily brings in a charismatic leader, but it does make the appearance of a power usurper more likely.
Having analysed our five cases studies, our aim is now to present our general conclusions by answering the following questions: In what way does our typology help to understand political leadership? Does it help to advance the study of leaders? Does it say something about the democratic qualities of the leaders?
CHAPTER 6
Rethinking Political Leadership
We began this research because we wanted to discover the impact that political leaders have on the quality of democracy. As the research was developing, different questions arose: Why has the return to democracy not changed the tendency to generate strong leaders? Why did recent presidential crises end with the emergence of strong leaders? Can domestic conditions explain the emergence of different types of leader?
We believed that the key to answering these questions was the leaders themselves. Using material from 285 interviews, we argue that the emergence of different types of leader is intrinsically related to the political context, and especially to the degree of institutionalization of the political party system. We observe that it is also related to the degree of electoral competition and the autonomy that a leader can establish, free of other political actors. This situation promotes the emergence of a soft power usurper or a power usurper. Argentina, Ecuador and Venezuela show that the logic behind this scenario is that the concentration of power is considered necessary to secure political stability.
Leaders in Uruguay and Colombia present a different picture. They tell us that if parties are strongly institutionalized, then leaders find it more difficult to gain autonomy. Indeed, Uruguay in particular shows that institutionalized political parties do have power to control and limit leaders' autonomy. In Colombia, Álvaro Uribe's aspirations to continue in government met effective resistance from the judiciary.
In post-crisis scenarios countries can fall into a political trap: Argentina, Ecuador and Venezuela show that opponents can get rid of bad presidents but have been unable to make sure that the newcomer will be any better. We have considered the question of why Latin American voters have often ejected bad, undemocratic leaders from office, but then voted in new leaders who turn out to be just as bad for democratic quality. The answer lies in the state of political parties. Our research shows that the deterioration of political parties undermines the possibility of training democratic leaders and the tools needed to prevent undemocratic leaders taking power. Political parties are key in the formation and monitoring of new generations of democratic leaders.
The cases of Argentina, Ecuador and Venezuela help us to explore why the return to democracy has not changed Latin America's tendency to generate strong leaders (soft power usurpers or power usurpers). Rather than a democratization of political parties, what happened during the 1980s and the 1990s was that parties became increasingly disconnected from citizens' demands. They became almost redundant, challenged by powerful leaders.
We observe that in post-crisis scenarios, the deterioration of the political party system allows presidents to disempower institutions in order to empower themselves. In this context soft power usurpers and power usurpers can prevail and the quality of democracy declines.
The combination of strong leaders and weak institutions erodes the pillars of liberal democracy. Our respondents in Argentina, Ecuador and Venezuela seem to suggest that citizens look for powerful leaders to compensate for the weakness of political parties. In the long term, power usurpers do not have the incentives to empower institutions that could control or monitor their activities. In Argentina, Ecuador and Venezuela leaders seem to be more important than democracy. They have a striking capacity to ignore rules and citizens' demands.
With the exceptions of those in Uruguay and Colombia, the majority of our respondents thought of power as hard power; of democracy as concentration of power; and of leadership as strength. In Uruguay, our respondents talked in terms of soft power, power distribution among the different institutions of the state and of collective leadership. In Colombia, strong political leaders have been effectively controlled and monitored by democratic institutions.
In Uruguay political parties and citizens seem to be as important as democracy. In Colombia, even in a context of political violence, institutions seem to be as important as democracy. In Uruguay and Colombia politicians are held accountable by their parties and state institutions – and their autonomy is limited.
The value of our typology
Theoretically, the book emphasizes that the study of political leaders needs to be contextualized. Leaders are a historical product. However, they are also able to transform the context. They are both makers and products of political history. Thus, in order to understand their emergence and their legacy, the research has to be contextualized. The book suggests that a combination of domestic conditions and leaders' ability is key to understanding political leadership.
The contextualization explained the different institutional settings that promoted the emergence of different types of leaders. Most analysis of leaders in Latin America presents general perspectives that highlight the strongman or _caudillo_. Here we propose a more sophisticated approach. Our typology uses factors related to: political context; leaders' ability to lead; and leaders' impact on the quality of democracy. It is based on three dimensions: the leader's attitude towards the rule of law; whether the leader seeks consensus or provokes polarization; and the methods the leaders uses to increase power.
This is a theoretical construction, an ideal type which differs from real-life cases. The typology is not an end in itself. It is a tool to explore and compare different types of leaders, how and why they emerge and their impact on the quality of democracy.
Our typology is not inductive. First we analysed the political scenarios. Secondly, we conducted the interviews. Thirdly, we looked for trends, relations, differences and similarities. Finally, we articulated the typology.
The qualitative analysis derived from the interviews helped us to construct the different types of leader based on three factors: their relation with the rule of law, their ability to build consensus or promote polarization and their style of building power. These three factors implicitly show the democratic quality of the different leadership types since they are based on the relations that leaders establish with a range of political elements: the Constitution, electoral laws, institutions of the state, civil liberties, horizontal accountability, polarization, tolerance, autonomy, power sharing, citizens, political opposition and personal power. In this sense, the typology provides a comprehensive framework in which examine the democratic quality of leaders. Here lies the originality of our contribution, namely that we characterize democratic leaders through their actions. Does the leader work with his cabinet? Does he listen to the opposition? Does he manipulate norms to perpetuate himself in government? Is he tolerant?
We suggest that our typology encapsulates the components to distinguish the degree of democraticness of political leaders and offers four ideal types which include extreme and moderate. We hope that this typology offers guidelines for how leaders' political influence can also be studied in other parts of the world.
This book also offers ideas about conducting research on political leaders. We have described the difficulties encountered in basing our research on interviews with politicians. The current debate about quantitative or qualitative research influenced the design of the research project from the beginning. We are aware that our decision to privilege the qualitative research might be questioned. However, we argue that the originality of this research comes from the in-depth analysis of 285 interviews with politicians and the comparative perspective.
We hope that the book presents some questions that could become the subject of broader research agendas. However, our hope is also that leaders and citizens become more interested in this type of research because they have the key to provoke change. Leaders can use our typology as a guide to become democratic enhancers. For citizens it can be a tool to demand accountability. Scholars can consider it as a step to help expand the study of democratic leadership.
After many years working on leaders we have mixed feelings about the future of democracy. Politicians have been able to offer us a comprehensive diagnosis of the impact of leaders on the quality of democracy. However, very few were prepared to suggest ideas for democratizing politics and leaders. They seem to be more concerned about the short term, elections and their continuation in office than the long-lasting reward of building a more democratic society.
List of Interviews
ARGENTINA
1. **2 November 2009. José Pampuro.** National Senator for the province of Buenos Aires (2005–11), Victory Front (Frente para la Victoria, PJ).
2. **25 November 2009. Marcelo Stubrin.** Ex-National Deputy (1983–85, 1985–89 and 1995–99) for the Radical Civic Union (Unión Cívica Radical, UCR).
3. **4 December 2009. Graciela Fernández Meijide.** Ex-National Deputy for the City of Buenos Aires (1993–95).
4. **4 December 2009. Carlos Snopek.** National Deputy for Jujuy (2005–09).
5. **9 December 2009. Federico Storani.** Ex-National Deputy for the province of Buenos Aires (1983–85, 1985–89, 1993–97, 1997–99, 2003–07).
6. **9 December 2009. Graciela Giannettasio.** National Deputy for the province of Buenos Aires (2007–11).
7. **10 December 2009. Vilma Ibarra.** National Deputy for the City of Buenos Aires (2007–11).
8. **11 December 2009. Héctor Recalde.** National Deputy for the province of Buenos Aires (2005–09).
9. **1 February 2010. José Luis Machinea.** Ex-Minister of Economy and Finance (December 1999–March 2001).
10. **16 February 2010. Héctor Flores.** National Deputy for Buenos Aires (2007–11) for the Civic Coalition (Coalición Cívica, CC).
11. **26 February 2010. Carlos Álvarez.** Ex-Vice-President (December 1999, October 2000).
12. **8 March 2010. Jesús Rodríguez.** Secretary General of the National Committee of the Radical Civic Union (Unión Cívica Radical, UCR). Ex-National Deputy (1983–87, 1987–91, 1993–97, 1999–2003).
13. **16 March 2010. Marcos Peña.** Secretary General of Buenos Aires City Government (Propuesta Republicana, PRO).
14. **18 March 2010. Héctor Álvaro.** National Deputy for Mendoza (2007–11) for the Citizen Collaboration Party. Founder of Popular Commitment in Mendoza.
15. **23 March 2010. Margarita Stolbizer.** National Deputy for the province of Buenos Aires (2009–13), for the Generation for National Togetherness (Generación para un Encuentro Nacional, GEN). President and founder of GEN.
16. **25 March 2010. Adrián Pérez.** National Deputy for the City of Buenos Aires (2003–07, 2007–11) for the Civic Coalition (Coalición Cívica, CC).
17. **26 March 2010. Enrique Nosiglia.** Ex-Minister of the Interior (1987–89).
18. **29 March 2010. Cecilia Merchán.** National Deputy for Cordoba (2007–11) for the Free Movement of the South (Movimiento Libres del Sur).
19. **29 March 2010. Diego Kravetz.** Legislator for the City of Buenos Aires for the Victory Front (Frente para la Victoria) (2003–07, 2007–11).
20. **5 April 2010. Gabriela Michetti.** National Deputy for the City of Buenos Aires (2009–13) for Propuesta Republicana, PRO.
21. **6 April 2010. Liliana Fellner.** National Senator for Jujuy (2005–11). Victory Front (Frente para la Victoria).
22. **6 April 2010. Cristian Gribaudo.** National Deputy for the province of Buenos Aires (2007–11). Propuesta Republicana, PRO.
23. **3 June 2010. Rubén Giustiniani.** National Senator for Santa Fe (2003–09, 2009–15). Socialist Party (Partido Socialista).
24. **8 June 2010. Eduardo Torres.** National Senator for Misiones (2007–11). Renewal Front (Frente Renovador).
25. **11 June 2010. María Eugenia Estenssoro.** National Senator for the City of Buenos Aires (2007–13). Civic Coalition (Coalición Cívica).
26. **5 July 2010. Rossana Bertone.** National Deputy for Tierra del Fuego (2001–05, 2005–09, 2009–13). Victory Front (Frente para la Victoria).
27. **8 July 2010. Martín Sabbatella.** National Deputy for Buenos Aires (2009–13).
28. **4 December 2009.** Santiago Leiras. Academic.
29. **7 December 2009. Juan Carlos Torre.** Professor and researcher at the Torcuato di Tella University – Department of Political Science and International Relations.
30. **11 February 2010. Hugo Yasky.** General Secretary of the Workers' Central of the Republic of Argentina (Central de Trabajadores de la República Argentina, CTA).
31. **12 February 2010. Monseñor Jorge Pedro Casaretto.** Bishop of San Isidro. President of Social Pastoral Care of Argentina (Pastoral Social Argentina).
32. **18 February 2010. Carlos de la Vega.** President of the Argentine Chamber of Commerce (Cámara Argentina de Comercio, CAC).
33. **25 February 2010. Mauro González.** President of the Federation of Young Entrepreneurs of Argentina (Federación Argentina de Jóvenes Empresarios, FEDAJE).
34. **3 March 2010. Susana Rueda.** Ex-Secretary General of the CGT (2003–04), Secretary for Institutional Relations and Policy at the ATSA Santa Fe.
35. **26 March 2010. Enrique Mantilla.** President of the Chamber of Exporters of Argentina (Cámara Argentina de Exportadores, CERA). Winner of the Konex Prize for Business Leader of the Year 2008.
36. **11 December 2009. Diana Maffia.** Deputy for the City of Buenos Aires (2007–11). Academic Coordinator of the Hannah Arendt Institute. Civic Coalition (Coalición Cívica).
37. **8 February 2010. Ramiro Etchegaray.** Head of the Buenos Aires office of the Contemporaneous Foundation (Fundación Contemporánea).
38. **8 February 2010. Martín Boccacci.** Coordinator of Strategic Thinking at the Contemporaneous Foundation (Fundación Contemporánea).
39. **9 February 2010. Camilo Vedia.** Moisés Lebensohn Institute of Thinking. Radical Youth (Juventud Radical).
40. **15 February 2010. Ramiro Tagliaferro.** Provincial Deputy for Buenos Aires (2007–11). Propuesta Republicana, PRO.
41. **23 March 2010. Juan González.** Alternative Popular University (Rosario university grouping). Secretary for policy training for the Rosario Peronist Youth.
42. **25 March 2010. Victoria Buratti.** Secretary for Education and Training of the Digital PJ.
43. **29 March 2010. Roberto Magliano.** Head of the Policy Formation Programme at the Juan Perón Institute of Higher Studies.
44. **30 March 2010. Nicolás Fernández Arroyo.** Director of the Municipal Leader Programme, Centre for Public Policy Implementation for Equity and Growth (Centro de Implementación de Políticas Públicas para la Equidad y el Crecimiento, CIPPEC).
45. **31 March 2010. Carlos Rizzuti.** Vice-President of the Civil Association for Popular Studies (Asociación Civil de Estudios Populares, ACEP).
46. **31 March 2010. Marcelo Ferreira.** Coordinator of I-Gen. (Institute of Studies for a New Generation).
47. **31 March 2010. Eduardo Beltrán.** Coordinator of the PROFIM-ICDA at the Catholic University of Cordoba and the Konrad Adenauer Foundation.
48. **8 April 2010**. **Silvina Viazzi.** Coordinator of Training for the Argentine Productive Movement (Movimiento Productivo Argentino, MPA).
49. **18 May 2010. Alan Clutterbuck.** Managing Council for the Policy Action Network Movement (Movimiento Red de Acción Política, RAP).
50. **18 May 2010. Paula Montoya.** Managing Council for the Policy Action Network Movement (Movimiento Red de Acción Política, RAP).
51. **27 May 2010. Martín Galanternik.** Founder and Executive Director of MINU. Member of the board of the Federal Youth Platform of Argentina.
52. **27 May 2010. Ilaina Rabbat.** Member of the Latin American School for Young Social Action (Escuela Latinoamericana para la Actoría Social Juvenil, ELASJ).
53. **1 June 2010. Alicia Ciciliani.** Secretary of the Centre for Municipal and Social Studies (Centro de Estudios Municipales y Sociales, CEMUPRO). Socialist Party of Santa Fe.
54. **July 2010. Lucas Sebastián Duran.** Member of the Radical Civic Union (Unión Cívica Radical).
ECUADOR
55. **13 November 2009. Osvaldo Hurtado.** Ex-President of Ecuador (1981–84). President of the Corporation for Developent Studies (Corporación de Estudios para el Desarrollo, Cordes).
56. **26 April 2010. Wilfredo Lucero.** Ex-President of the National Congress (2004–06). Deputy for the Democratic Left (Izquierda Democrática) (1996–98, 1988–92, 2003–07).
57. **26 April 2010. Rafael Dávila.** Assembly member for the Loja province for the Citizens' Conscience Movement (2009–13). Ex-Deputy for the Popular Democracy Party (1998–2000, 2003–05).
58. **26 April 2010. Paco Moncayo.** Ex-chief of the Joint Command of the Armed Forces of Ecuador (1995–98). Ex-mayor of the city of Quito (2001–05, 2005–08) for the Democratic Left Party. Assembly member for the province of Pichincha representing the Municipal Movement (2009–13).
59. **26 April 2010. Lucio Gutiérrez.** Ex-President of Ecuador (2003–05). Founding leader of the Patriotic Society Party.
60. **27 April 2010. Arturo Donoso.** Adviser to the governments of Osvaldo Hurtado, Rodrigo Borja and Sixto Durán.
61. **27 April 2010. Alberto Acosta.** President of the Constituent Assembly (2008). Ex-Minister of Energy (2007). Economic analyst. Professor/researcher at FLACSO Ecuador in Economics.
62. **27 April 2010. Betty Amores.** National Assembly member for Alianza PAIS (2009–13).
63. **28 April 2010. Francisco Ulloa.** Assembly member of the Democratic Popular Movement for the province of Cotopaxi (2009–13).
64. **28 April 2010. Fausto Cobo.** Deputy for the province of Pichincha for the Patriotic Society Party (2007).
65. **28 April 2010. Pedro Páez.** President of the board of the Central Bank of Ecuador. Ex-Minister and coordinator of economic policy (2007–09).
66. **28 April 2010. Jorge Escala.** National Assembly member for the MPD (2009–13).
67. **28 April 2010. Andrés Páez.** Assembly member for Pichincha for the Democratic Left (2009–13).
68. **29 April 2010. Pedro Saad.** Ex-communist leader.
69. **29 April 2010. Luis Fernando Torres.** Deputy for the province of Tungurahua for the Social Christian Party (2004–07).
70. **30 April 2010. Alexandra Vela.** Ex-National Deputy for the Popular Democracy Party (1998–2002).
71. **30 April 2010. Norman Wray.** Constituent Assembly member for the Breakaway 25 movement (Movimiento Ruptura de los 25) (2008). Councillor for the city of Quito (2009–13).
72. **30 April 2010. Virgilio Hernández.** Assembly member for the province of Pichincha for the Alianza PAIS (2009–13).
73. **3 May 2010. Alexandra Ocles.** National Secretary for the Social, Popular and Nationalities Movements of Ecuador in the government of Rafael Correa (2009–10). Member of the Breakaway 25 movement (Movimiento Ruptura de los 25).
74. **3 May 2010. Rodrigo Borja.** Ex-President of Ecuador (1988–92). Founder leader of the Democratic Left.
75. **3 May 2010. Sandra Alarcón.** Director of the Christian Democratic Union Party.
76. **5 May 2010. Dr César Montúfar.** Assembly member for Pichincha province representing the National Democratic Consensus Movement (2009–13).
77. **5 May 2010. Dr Rossana Alvarado.** Assembly member for the province of Azuay for Alianza PAIS (2009–13).
78. **18 May 2010. Dr María Paula Romo.** Assembly member for the province of Pichincha (2009–13). Member of the Breakaway 25 movement (Movimiento Ruptura de los 25).
79. **18 May 2010. Mariangel Muñoz.** Assembly member for the province of Azuay for Alianza PAIS (2009–13).
80. **25 May 2010. Linda Machuca.** Assembly member representing immigrants for Alianza PAIS (2009–13).
81. **26 May 2010. Silvia Salgado.** National Assembly member for the coalition between Alianza PAIS and the Ecuadorean Socialist Party (2009–13).
82. **26 May 2010. Marco Murillo.** Assembly member for the province of Chimborazo (2009–13). Member of the Amauta movement. Ex-leader of the FEINE. President of the Collective and Community Rights Commission of the National Assembly.
83. **2 June 2010. Fabricio Villamar.** Councillor for Quito for the National Democratic Consensus movement (2009–13).
84. **2 June 2010. Pedro de la Cruz.** National Assembly member for Alianza PAIS (2009–13).
85. **8 June 2010. Pablo Lucio-Paredes.** Constituent Assembly member for the Future Now movement (2008).
86. **15 June 2010. Ana María Larrea.** Under-Secretary of the Organization and Structure of the State of the National Secretariat of Planning and Development (Secretaría Nacional de Planificación y Desarrollo, SENPLADES).
87. **18 June 2010. Rafael Quintero.** Under-Secretary for multilateral affairs in the Ecuadorean chancellorship. Socialist leader.
88. **24 June 2010. Aminta Buenaño.** Assembly member for the province of Guayas for Alianza PAIS (2009–13).
89. **29 June 2010. Galo Lara.** Assembly member for the Los Ríos province for the Patriotic Society Party (2009–13).
90. **23 April 2010. Pablo Celi.** Director of the Sociology and Political Science School at the Central University of Ecuador.
91. **24 April 2010. Berta García.** Professor at the Pontificia Catholic University of Ecuador.
92. **26 April 2010. Jaime Arciniegas.** Union leader, ex-president of the Ecuadorean Confederation of Free Union Organizations (Confederación Ecuatoriana de Organizaciones Sindicales Libres, CEOSL) (2003–06).
93. **26 April 2010. Rocío Rosero.** Leader of the Ecuadorean feminist movement.
94. **27 April 2010. Ruth Hidalgo.** Sub-Director and legal adviser of the Citizen Participation Corporation.
95. **27 April 2010. Simón Jaramillo.** Citizen Participation Corporation.
96. **27 April 2010. Adrián Bonilla.** Director of FLACSO Ecuador.
97. **28 April 2010. Simón Pachano.** Coordinator of the Policy Studies Programme at FLACSO Ecuador.
98. **28 April 2010. Paco Rhon.** Director of the Andean Centre for Popular Action (Centro Andino de Acción Popular, CAAP).
99. **28 April 2010. Carlos de la Torre.** Professor/researcher at FLACSO Ecuador.
100. **29 April 2010. Diego Cano.** Head of the Federation of Petroleum Workers of Ecuador.
101. **29 April 2010. Franklin Ramírez.** Professor/researcher at FLACSO Ecuador.
102. **29 April 2010. Fernando Villavicencio.** Ex-petroleum workers' leader, political activist, member of the Democratic Pole Movement (Movimiento Polo Democrático).
103. **17 May 2010. Ricardo Ulcuango.** Indigenous leader, ex-deputy of the Pichincha province for the Pachacutik movement (2003–07). Ex-Vice-President of the Confederation of Ecuadorean Indigenous Nationalities (Confederación de nacionalidades indígenas ecuatorianas, CONAIE).
104. **31 May 2010. Delfín Tenesaca.** President of the indigenous organization ECUARUNARI.
105. **7 June 2010. Marlon Santí.** President of the Confederation of Ecuadorean Indigenous Nationalities (Confederación de nacionalidades indígenas ecuatorianas, CONAIE).
106. **7 June 2010. Luis Andrango.** President of the National Federation of Peasant, Indigenous and Black Organizations of Ecuador (Federación nacional de organizaciones campesinas, indígenas y negras del Ecuador, FENOCIN).
107. **3 May 2010. Ernesto Aranibar.** Director of the Democracy Now Corporation (Ágora Democrática, IDEA).
108. **4 May 2010. Sandy Quimbaya.** Coordinator of the NDI headquarters.
109. **13 May 2010. Jimmy Bejarano.** Director of the school of leadership of the National Democratic Consensus movement.
110. **28 May 2010. Patricio Coba.** Director of the 'Manuel Córdova Galarza' Institute of Policy Formation, an institute of the Democratic Left party.
111. **1 June 2010. Raúl Proaño.** Director of the school of citizenship of the Truirbas collective.
112. **8 June 2010. Dolores Padilla.** Coordinator of Leadership Projects at the Esquel Foundation.
113. **9 June 2010. Carla Bonilla.** Coordinator of Leadership Projects at the Konrad Adenauer Foundation.
114. **18 June 2010. Juan Pablo Espinoza.** Director of the school of leadership of Movimiento Ruptura de los 25.
115. **22 June 2010. Norma Mayo.** Director of the CONAIE school of leadership for indigenous women.
116. **23 June 2010. Stalin Vargas.** Director of the Popular Democratic Movement school of policy training.
117. **1 July 2010. Adriana Egas Aráuz.** Christian Democratic Union, Christian Democratic Youth.
118. **1 July 2010. Andrés de la Vega Grunauer.** Member of Alianza PAIS.
VENEZUELA
119. **3 October 2011. Ramón Guillermo Aveledo.** Executive Secretary of the Mesa de Unidad Democrática (MUD).
120. **4 October 2011. Biagio Pileri.** Deputy of the MUD representing the state of Yaracuy.
121. **5 October 2011. Fausto Maso.** Journalist, speaker, political analyst.
122. **5 October 2011. Freddy Guevara.** Councillor for the metropolitan area of Caracas (2008–12) and President of the Citizens' Security Commission and DDHH of the city.
123. **5 October 2011. Stalin González.** Deputy for Caracas in the National Assembly for the Nuevo Tiempo party.
124. **5 October 2011. María Corina Machado.** Deputy for Miranda state (2011–15).
125. **5 October 2011. Ramón José Medina.** Coordinator of International Affairs at the MUD.
126. **6 October 2011. Teodoro Petkoff.** Venezuelan politician, journalist and economist.
127. **6 October 2011. Pedro Benítez.** Coordinator of the MUD.
128. **6 October 2011. Héctor Constant.** Bureaucrat at the Ministry of Foreign Affairs in the 'Pedro Gual' Institute of High Diplomatic Studies.
129. **6 October 2011. Carlos Ocariz.** Mayor of the Sucre municipality for Justice First (Primero Justicia).
130. **7 October 2011. Guillermo Miguelena.** Secretary for International Affairs at the Youth Bureau of Democratic Action (Acción Democrática).
131. **5 October 2011. Luis Velásquez.** Deputy for the Caracas metropolitan area for the Partido Voluntad Popular.
132. **7 October 2011. Alejandro Vivas.** Deputy for the Caracas metropolitan area. COPEI party.
133. **7 October 2011. Juan Guaido.** Deputy in the National Assembly for the state of Vargas. Partido Voluntad Popular.
134. **14 October 2011. Tomas Guanipa.** Secretary General of the Partido Primero Justicia. Deputy in the National Assembly for the state of Zulia.
135. **29 November 2011. Rodolfo Rodríguez.** Deputy in the National Assembly for Anzoategui. AD party.
136. **21 December 2011. Angel Medina.** Deputy in the National Assembly for Miranda. AD party.
137. **21 December 2011. Edgar Zambrano.** Deputy in the National Assembly for the state of Lara. AD party.
138. **3 October 2011. Feliciano Reyna.** President of Solidarity Action (Acción Solidaria).
139. **3 October 2011. Carlos Correa.** Director of Public Space – area of human rights.
140. **3 October 2011. Luis Vicente León.** President of Datanalisis.
141. **4 October 2011. Alfredo Padilla.** Union member and member of the International Workers Organization.
142. **4 October 2011. Albis Muñoz.** Ex-President of Fedecamaras.
143. **4 October 2011. Deborah Van Berkel.** Vice-President, Venezuelan Institute of Social and Political Studies (Instituto Venezolano de Estudios Sociales y Políticos, INVESP).
144. **4 October 2011. Alejandro Oropeza.** Director of Projects – Legal Consultant at the Hannah Arendt Observatory.
145. **4 October 2011. Heinz Sonntag.** Director General of the Hannah Arendt Observatory.
146. **5 October 2011. Georg Eickhoff.** Director of the Konrad Adenauer Foundation (KAS).
147. **5 October 2011. Marino Alvarado Betancourt.** Director of the Venezuelan Programme for Education and Action on Human Rights (Programa Venezolano de Educación-Acción en Derechos Humanos, PROVEA).
148. **6 October 2011. José Manuel González de Tober.** Ex-business leader at Fedecamaras.
149. **6 October 2011. Diana Vegas Castro.** Director of the Centre for Service of Popular Action (CESAP).
150. **7 October 2011. Aldo de Santis.** Coordinator of the Centre of Public Policy (IFEDEC).
151. **22 October 2011. Miguel Sabal.** Director of the Present Future Foundation.
152. **17 December 2011. Isabel Carmona.** Democratic Action Training School.
153. **18 December 2011. Benigno Alarcón.** Director of the school of social and community leaders at the Andrés Bello Catholic University (Universidad Católica Andrés Bello, UCAB).
154. **3 October 2011. Germán Carrera.** Doctor of History.
155. **5 October 2011. Francine Jacome.** Director of the Venezuelan Institute of Social and Political Studies (Instituto Venezolano de Estudios Sociales y Políticos, INVESP) and Regional Director of Research at the Regional Network of Economic and Social Research (Coordinadora Regional de Investigaciones Económicas y Sociales, CRIES).
156. **6 October 2011. John Magdaleno.** Political scientist at USB. Specialist in social science data analysis at the Central University of Venezuela (Universidad Central de Venezuela, UCV).
157. **6 October 2011. Carlos Luna Ramírez.** Teaching adviser at the Delegation of the School of Political and Administrative Studies at the Central University of Venezuela.
158. **7 October 2011. María Teresa Romero.** Professor at the UCV.
159. **7 October 2011. Carlos Romero.** Professor at the UCV.
160. **7 October 2011. Nicmer Evans.** Teacher at the School of Sociology at the UCV.
161. **5 October 2011. Marisela Boada.** Leader of the PSUV, Metropolitan Deputy.
162. **5 October 2011. Luis Velasquez.** Deputy for the metropolitan area of Caracas. Partido Voluntad Popular.
163. **7 October 2011. Alejandro Vivas.** Deputy for the metropolitan area of Caracas. COPEI party.
164. **7 October 2011. Juan Guaido.** Deputy in the National Assembly. Partido Voluntad Popular.
165. **14 October 2011. Tomas Guanipa.** Secretary General, Partido Primero Justicia.
166. **4 November 2011. Alfonzo Marquina.** Deputy in the National Assembly for Miranda. UNT party.
167. **4 November 2011. Juan Carlos Caldera.** Deputy in the National Assembly for Miranda. Partido Primero Justicia.
168. **29 November 2011. Rodolfo Rodríguez.** Deputy in the National Assembly for Anzoategui. Democratic Action Party.
169. **21 December 2011. Ángel Medina.** Deputy in the National Assembly for Miranda. Democratic Action Party.
170. **21 December 2011. Edgar Zambrano.** Deputy in the National Assembly for the state of Lara. Democratic Action Party.
171. **5 October 2011. Ángel Lugo.** Political Secretary of Democratic Action.
172. **22 October 2011. Miguel Sabal.** Director of the Present Future Foundation.
173. **17 December 2011. Isabel Carmona.** Democratic Action Training School.
174. **1 July 2010. Juan Pablo López Gross.** Member of the Voluntad Popular party.
175. **1 July 2010. María Francia Herrera.** Member of Partido Primero Justicia.
COLOMBIA
176. **10 October 2011. Rafael Pardo.** Leader of the Liberal Party (2010). Senator of the Republic (2002–06). Professor and researcher, University of los Andes.
177. **10 October 2011. Jorge Robledo.** Senator of the Alternative Democratic Pole (Polo Democrático Alternativo) (2010–14).
178. **10 October 2011. José Darío Salazar.** President of the National Conservative Directorate.
179. **10 October 2011. Camilo González Posso.** Director of the Institute of Development for Peace (Instituto de Desarrollo para la Paz, INDEPAZ).
180. **10 October 2011. Salud Hernández Mora.** Journalist on _El Tiempo_.
181. **11 October 2011. Armando Benedetti.** Senator of the U party (2010–14).
182. **11 October 2011. Carlos Amaya.** Representative of the Green Party.
183. **11 October 2011. Roy Barreras.** Senator of the U party (2010–14).
184. **11 October 2011. Angelino Garzón.** Vice-President of the nation in the presidency of Juan Manuel Santos Calderón.
185. **12 October 2011. Mauricio Ernesto Ospina Gómez.** Senator of the Polo Democrático Alternativo (2010–14).
186. **12 October 2011. Iván Cepeda.** Representative of the Polo Democrático Alternativo (2010–14).
187. **12 October 2011. David Luna.** Member of the Chamber of Representatives of Colombia.
188. **12 October 2011. Germán Navas Talero.** Representative in the Chamber for the Polo Democrático Alternativo (2010–14).
189. **12 October 2011. Marta Lucia Ramírez.** Ex-Minister of Defence (2002–03).
190. **13 October 2011. Clara López Obregón.** Mayor of Bogotá (2011).
191. **13 October 2011. Wilson Arias.** Representative in the Chamber for the Polo Democrático Alternativo.
192. **13 October 2011. Germán Varón.** Representative in the Chamber for Cambio Radical (2010–14).
193. **13 October 2011. Dr Alberto Echavarría.** Vice-President for Judicial and Social Affairs of the National Association of Entrepreneurs of Colombia (Asuntos Jurídicos y Sociales de la Asociación Nacional de Empresarios de Colombia, ANDI).
194. **13 October 2011. Gloria Inés Ramírez Ríos.** Senator of the Polo Democrático Alternativo (2010–14).
195. **13 October 2011. Horacio José Serpa.** Councillor elect for Bogotá for the Liberal Party (2012–15).
196. **13 October 2011. John Sudarsky.** Senator of the Green Party (2010–14).
197. **13 October 2011. Jonathan Forero.** Adviser to the head of the Bogotá Council. Youth President of the U party.
198. **14 October 2011. Gustavo Gallón.** Colombian Commission of Lawyers (1988–2011).
199. **14 October 2011. Luis Eduardo Celís.** Coordinator of the public policy for peace, Corporación Nuevo Arco Iris.
200. **14 October 2011. Lázaro Ramírez.** President of the Colombian Union of Young Democrats (Unión Colombiana de Jóvenes Demócratas, UCJD).
201. **11 October 2011. Pedro Santana.** President of Long Live the Citizenry.
202. **12 October 2011. Olga Lucía Gómez.** Director of the Free Country Foundation.
203. **14 October 2011. Mauricio Romero Vidal.** Director of the Observatory of Armed Conflict, Corporación Nuevo Arco Iris (2008–11).
204. **10 October 2011. María Victoria Llorente.** Principal Researcher for the Group and Executive Director of the Foundation for Ideas for Peace (Fundación Ideas para la Paz, FIP).
205. **11 October 2011. Alejo Vargas Velásquez.** Professor, National University, and Director of the Research Group on Security and Defence.
206. **12 October 2011. Alexandra Barrios.** Director of the Electoral Observer Mission (Misión de Observación Electoral, MOE).
207. **12 October 2011. Francisco Leal Buitrago.** Honorary professor at the National and Los Andes universities.
208. **12 October 2011. Oscar Fernando Sevillano.** Assistant researcher, Observatory of Armed Conflict of the Corporación Nuevo Arco Iris (2006–).
209. **14 October 2011. Fernán González.** Researcher at CINEP and ex-director of the institute.
210. **9 February 2012. Ángela Robledo.** Representative in the Chamber for the Green Party.
211. **21 February 2012. Maritza Martínez.** Senator, U party (2010–14).
212. **9 March 2012. Gilma Jiménez.** Senator, Green Party.
213. **21 March 2012. Marco Aníbal Avirama.** Senator, Independent Social Alliance Party (Partido Alianza Social Independiente, ASI).
214. **28 March 2012. Germán Carlosama.** Senator, Colombian Indigenous Authorities Party (Partido Autoridades Indígenas de Colombia, AICO).
215. **29 March 2012. Rodrigo Villalba.** Senator, Colombian Liberal Party.
216. **8 May 2012. Édgar Espíndola.** Senator, National Integration Party (Partido de Integración Nacional, PIN).
217. **8 May 2012. Antonio Correa.** Senator, National Integration Party (Partido de Integración Nacional, PIN).
218. **8 May 2012. Juan Carlos Salazar.** Representative in the Chamber of the National Integration Party (Partido de Integración Nacional, PIN).
219. **9 May 2012. Eduardo Carlos Merlano.** Senator, U party.
220. **1 March 2012. Carolina Montoya.** School of Government, MIRA movement.
221. **12 March 2012. Paola Andrea Pinilla.** Hernán Echavarría Olozága Political Science Institute (Instituto de Ciencia Política, ICP).
222. **14 March 2012. Miguel Galvis.** 'People's' School of policy formation, Independent Social Alliance Party (Partido Alianza Social Independiente, ASI).
223. **15 March 2012. Álvaro Forero.** Leadership and Democracy Foundation, young politicians' training programme.
224. **28 March 2012. Dr Arnobio Cordoba.** Director, Phelps Stokes Foundation – Colombia.
225. **17 April 2012. Alfonso Amaya Parra.** Alberto Lleras Camargo School of Government, Los Andes University.
226. **23 April 2012. Carlos Martínez.** Centre for Conservative Party Thought.
227. **25 April 2012. Hugo Guerra.** Liberal Thought Institute (Instituto de Pensamiento Liberal, IPL).
228. **4 May 2012. Catalina Nava.** Youth member of the Polo Democrático Alternativo.
229. **1 July 2010. Jessica Pamela Obando Burgos.** Colombian Liberal Party.
URUGUAY
230. **21 March 2011. Dr Julio Ma. Sanguinetti.** Senator of the Republic (2005–10) and Constitutional President of Uruguay (1985–90, 1995–2000).
231. **21 March 2011. Fitzgerald Cantero Piali.** National Deputy for Montevideo for the Colorado Party (2010–15).
232. **22 March 2011. Jorge Saravia.** Senator of the Republic for Frente Amplio.
233. **22 March 2011. Pablo Mieres.** Leader of the Independent Party.
234. **22 March 2011. Alfonso P. Varela.** President of the National Chamber of Commerce and Services of Uruguay.
235. **23 March 2011. Heber da Rosa.** Senator of the Republic, National Alliance, National Party (2010–15).
236. **23 March 2011. Rafael Michelini.** Senator of the Republic for Frente Amplio – Liber Seregni Front (2010–15).
237. **23 March 2011. Carlos Julio Pereyra.** Ex-President of the Board of the National Party (2008–09).
238. **23 March 2011. Raúl Sendic.** President of ANCAP (petroleum, gas and alcohol refinery).
239. **23 March 2011. Francisco Gallinal.** Senator of the Republic, National Unity, National Party (2010–15).
240. **23 March 2011. Alberto Couriel.** Senator of the Republic, Frente Amplio – Space 609 (2010–15).
241. **23 March 2011. Luis Rosadilla.** Minister of Defence (2010–). Deputy of the Popular Participation Movement (Movimiento de Participación Popular, MPP) (2005–09).
242. **23 March 2011. Dr Luis Alberto Lacalle.** Senator of the Republic, National Party (2010–15).
243. **24 March 2011. Danilo Astori.** Vice-President of the Republic (2010–11).
244. **25 March 2011. Felipe Michelini.** National Deputy, Frente Amplio (2010–15).
245. **25 March 2011. Juan Castillo.** Coordinator of the Secretariat of International affairs – PIT CNT (trade union workers' plenary).
246. **11 April 2011. Lucía Topolansky.** Senator of the Republic, Frente Amplio – Space 609/MPP (2010–15).
247. **11 April 2011. Carlos Moreira.** Senator of the Republic, National Alliance, National Party (2010–15).
248. **11 April 2011. José Bayardi.** National Deputy for Montevideo, Frente Amplio. Minister of Defence (2008–09).
249. **12 April 2011. Jorge Luis Batlle Ibáñez.** Ex-President of Uruguay (2000–05), Colorado Party.
250. **12 April 2011. Alberto Casas.** National Deputy for the Department of San José, National Party (2010–15).
251. **12 April 2011. Carmelo Vidalín.** National Deputy for the Department of Durazno, National Party (2010–15).
252. **12 April 2011. Jorge Chediak.** Minister of the Supreme Court of Justice (2009–).
253. **12 April 2011. Ricardo Berois.** National Deputy for the Department of Flores, National Party (2010–15).
254. **13 April 2011. Álvaro Delgado.** National Deputy, National Party, National Unity (2010–15).
255. **13 April 2011. Amin Niffouri.** National Deputy for the Department of Canelones, List 400, National Party (2010–15).
256. **14 April 2011. Jorge Gandini.** National Deputy for Montevideo, National Party (2010–15).
257. **14 April 2011. Nelson Mancedo.** Secretary of Finance of the Broad Front. Member of the Uruguayan Communist Party.
258. **14 April 2011. Verónica Alonso.** National Deputy for Montevideo, National Party (2010–15).
259. **14 April 2011. Constanza Moreira.** Senator of the Republic, Frente Amplio, Space 609 (2010–15).
260. **14 April 2011. Eduardo Fernández.** Secretary General of the Socialist Party (2006–).
261. **26 April 2011. Graciela Matiaude.** National Deputy for the Department of Canelones, Colorado Party, Let's Go Uruguay (2010–15).
262. **27 April 2011. Dr Alfredo Solari.** Senator of the Republic, Colorado Party, Let's Go Uruguay (2010–15).
263. **28 April 2011. Gustavo Penadés.** Senator of the Republic, National Party, National Unity (2010–15).
264. **29 April 2011. Pedro Saravia.** National Deputy for the Department of Cerro Largo, National Party (2010–15).
265. **9 May 2011. Martín Tierno.** National Deputy for the Department of Durazno, Frente Amplio, Space 609 (2010–15).
266. **9 May 2011. Andrés Lima.** National Deputy for the Department of Salto, Frente Amplio (2010–15).
267. **11 May 2011. Daniel Bianchi.** National Deputy for the Department of Colonia, Colorado Party, Let's Go Uruguay (2010–15).
268. **16 May 2011. Gustavo Cersósimo.** National Deputy for the Department of San José, Colorado Party, Let's Go Uruguay (2010–15).
269. **19 May 2011. Sebastián Sabini.** National Deputy for the Department of Canelones, Frente Amplio, Space 609 (2010–15).
270. **21 March 2011. Romeo Pérez.** Political scientist, President of the Council of the Latin American Human Economy Centre (Centro Latinoamericano de Economía Humana, CLAEH) (2010–13).
271. **22 March 2011. Eduardo Bottinelli.** Director of the FACTUM consultancy.
272. **12 April 2011. Juan Gabito Zóboli.** Director of the 'Manuel Oribe' Institute.
273. **13 April 2011. Adolfo Pérez Piera.** Ex President of the Council for Transparency and Public Ethics (Junta de Transparencia y Ética Pública, JUTEP).
274. **14 April 2011. Luis E. González.** Director and co-founder of CIFRA.
275. **14 April 2011. Agustín Canzani.** Director of the Líber Seregni Foundation.
276. **25 April 2011. Milton Castellano.** Director of the Cuesta Duarte Institute.
277. **25 April 2011. Gonzalo Kmaid.** Director of Projects and Senior Researcher at CIFRA.
278. **21 March 2011. Daniel Buquet.** Academic at the Institute of Political Science, Faculty of Social Sciences, University of the Republic.
279. **24 March 2011. Adolfo Garcé.** Academic, Political Science Institute, Faculty of Social Sciences (UDELAR).
280. **12 May 2011. Miguel Serna.** Academic. Researcher and professor in the Sociology Department at the Faculty of Social Sciences, University of the Republic.
281. **13 May 2011. Jorge Lanzaro.** Academic. Researcher at the Political Science Institute, University of the Republic.
282. **13 May 2011. Dr José Rilla.** Academic. Professor at the Faculty of Social Sciences, University of the Republic.
283. **14 May 2011. Gustavo Adrián de Armas.** Academic. Sociologist, Faculty of Social Sciences, University of the Republic.
284. **15 May 2011. Hebert Gatto.** Ex-Professor of Political Science at the University of the Republic.
285. **1 July 2010. Damián Payotti de León.** Frente Amplio. University of the Republic.
WASHINGTON, DC
286. **5 March 2012. Miriam Harmer.** Legislative adviser. Specialist in foreign relations for Republican Senator Mike Lee (Utah).
287. **5 March 2012. Joan Caivano.** Assistant to the President and Director of Special Projects at the Inter-American Dialogue.
288. **6 March 2012. Dan Fisk.** Republican International Institute.
289. **6 March 2012. Jorge Arguello.** Ambassador of the Argentine Republic to the United States.
290. **6 March 2012. Daniel Erikson.** Senior Adviser on Western Hemisphere Affairs at the US Department of State.
291. **6 March 2012. Michael Shifter.** President of the Inter-American Dialogue.
292. **6 March 2012. José Miguel Vivanco.** Director, Division of the Americas, Human Rights Watch.
293. **7 March 2012. Miriam Kornblith.** Regional Director of the Latin America and Caribbean Programme, National Endowment for Democracy.
294. **7 March 2012. Heather Booth.** President of the MidWest Academy.
295. **7 March 2012. Augusta Babson.** Official in public diplomacy at the US Department of State, Office of the Principal Adviser to the Secretary for Civil Society and Emerging Democracies.
296. **7 March 2012. Robert Creamer.** Political and strategy consultant.
297. **8 March 2012. José Miguel Insulza.** Secretary General of the Organization of American States (OAS).
298. **8 March 2012. Melanie Sloan.** Executive Director of Citizens for Responsibility and Ethics in Washington (CREW).
299. **8 March 2012. Jim Swigert.** Senior Associate and Regional Director for Latin America and the Caribbean at the National Democratic Institute (NDI) for international affairs.
300. **8 March 2012. Theodore Piccone.** Senior Fellow and Deputy Director, Foreign Policy at the Brookings Institution.
301. **9 March 2012. Sam Farr.** US representative for California's 17th congressional district, serving since 1993. Member of the Democratic Party.
302. **9 March 2012. Nina M. Serafino.** Expert in international security, foreign affairs, defence, Commercial Service Division of the research service at the Library of Congress.
303. **9 March 2012. Enrique Fernandez Toledo.** Deputy Chief of Staff of the Democratic Representative for Illinois, Luis Gutiérrez.
304. **9 March 2012. Tina Huang.** Foreign affairs officer, Bureau of Western Hemisphere Affairs, State Department.
305. **9 March 2012. Francisco Javier González.** Director of the Bureau of Western Hemisphere Affairs, State Department.
306. **5 March 2012. Mark Sullivan.** Specialist in international security, Congressional Research Service on Foreign Relations, Defence and Trade.
307. **6 March 2012. Arturo Valenzuela.** Professor of Government and Director of the Centre for Latin American Studies at Georgetown University. United States Assistant Secretary of State for Western Hemisphere Affairs, nominated by President Barack Obama.
308. **7 March 2012. Christopher Arterton.** Academic. Professor of Political Management at the George Washington University Graduate School of Political Management (GSPM).
309. **7 March 2012. Luis Matos.** Professor at George Washington University.
310. **8 March 2012. James Thurber.** Professor and Director of the Centre for Congressional and Presidential Studies.
311. **7 March 2012. Mark Feierstein.** Associate administrator of USAID for Latin America and the Caribbean.
312. **6 March 2012. Silvio Waisbord.** Associate professor and Director of the Graduate Programme at the School of Media and Public Affairs at George Washington University.
NEW YORK
313. **28 February 2012. Jimmy Tom.** Director of the NY Centre Foundation, NY Library.
314. **29 February 2012. Kenneth Erickson.** Graduate Centre, City University of New York (CUNY).
315. **1 March 2012. Heraldo Muñoz.** Under-Secretary General of the UN Development Programme (UNDP) (May 2010). Regional Director of the UNDP for Latin America and the Caribbean.
316. **1 March 2012. Gerardo Noto.** Specialist on the Democratic governability programme, Regional Board for Latin America and the Caribbean.
317. **1 March 2012. Roland Rich.** Chief Executive of the UN Democracy Fund (UNDEF). Official in charge, United Nations Office for Project Services (UNOP).
318. **2 March 2012. Victoria Murillo.** Professor of Political Science and International Relations at the Universities of Columbia and Yale.
319. **2 March 2012. Susan L. Woodward.** Professor in the Political Science Programme at the Centre for Graduate Studies, City University of New York (CUNY).
Notes
INTRODUCTION
. In order to avoid 'he/she' we have decided to use 'he' as our default pronoun.
CHAPTER 1
. Our research project included trips to Washington, DC, and New York to discuss our main ideas with academics and consultants. The total number of interviewees is 319. However, only 285 of them were political leaders in Bogotá, Buenos Aires, Caracas, Montevideo and Quito.
. In this book we refer only to interviews conducted with politicians, legislators and party leaders. We do not include interviews with academics and journalists.
. The interviews were conducted between 2009 and 2013. It is well known that the use of this new technology, especially Twitter, has become more important over the last two years.
CHAPTER 2
. This list includes Hernán Siles Zuazo (Bolivia, 1985), Raúl Alfonsín (Argentina, 1989), Fernando Collor de Mello (Brazil, 1992), Jorge Serrano (Guatemala, 1993), Carlos Andrés Pérez (Venezuela, 1993), Jean-Bertrand Aristide (Haití, 1994 and 2004), Joaquín Balaguer (Dominican Republic, 1996), Abdalá Bucaram (Ecuador, 1997), Raúl Cubas (Paraguay, 1999), Jamil Mahuad (Ecuador, 2000), Alberto Fujimori (Peru, 2000), Valentín Paniagua (Peru, 2001), Fernando de la Rúa (Argentina, 2001), Alberto Rodríguez Saá (Argentina, 2001), Ramón Puerta (Argentina, 2002), Gonzalo Sánchez de Lozada (Bolivia, 2003), Eduardo Duhalde (Argentina, 2003), Lucio Gutiérrez (Ecuador, 2005), Carlos Mesa (Bolivia, 2005), Manuel Zelaya (Honduras, 2009) and Fernando Lugo (Paraguay, 2012).
CHAPTER 3
. The 2011 UNDP Report on Human Development in Colombia states that 52 per cent of property is held by just 1.15 per cent of the population (La Vanguardia 2011).
. The period of ' _La Violencia_ ' lasted from 1948 to 1957, especially under the dictatorship of Gustavo Rojas Pinilla (1953–57). Terrible atrocities were committed during that time. For example, the head of the Liberal Party, Jorge Eliécer Gaitán, was assassinated on 9 April 1948 in a street uprising known as the _Bogotazo_. Over 200,000 civilians were killed (Morales 1978: 59).
. The scandal of false positives was reported in 2008 and involved members of the Colombian army. The soldiers killed innocent civilians and then made out that they were dead guerrillas. These murders were presented as successes in the fight against the FARC. These extrajudicial executions were denounced nationally and internationally by Philip Alston, special reporter to the UN for arbitrary executions, in May 2010.
CHAPTER 4
. In Argentina fifty-four interviews were conducted between December 2009 and August 2010 and in Ecuador sixty-four interviews were conducted between April and August 2010.
. After resignations and deaths, the Court now has five members.
. Raúl Alfonsín issued ten, Carlos Menem 545, Fernando de la Rúa 74, Eduardo Duhalde 160 and Néstor Kirchner between 236 and 270 (Carrera 2013). Cristina Fernández had issued thirty-two NUDs up to December 2014.
. La Cámpora takes its name from Héctor J. Cámpora, a loyal follower of Juan Péron. Cámpora was president in 1973. He prepared the way for Perón to return to the Casa Rosada.
. Our respondents mentioned Juan José Flores (the first president, who served for three periods: 1830–34, 1839–43 and 1843–45), Gabriel García Moreno (president 1859–65 and 1869–75), José Eloy Alfaro (president 1897 and 1901 and 1906–11), José María Velasco Ibarra (president for five periods: 1934–35, 1944–47, 1952–56, 1960–61 and 1968–72), León Febres Cordero (president 1984 and 1988) and Rafael Correa (president from 2007).
. Ecuadorean constitutional history has been volatile. From 1830 to the present there have been twenty Constitutions; the last was approved under the Correa government in 2008. All the interviewees praised the current Constitution and it is definitely a progressive, modern, broad legal framework which includes social rights such as the right to live well, the right of people and groups to priority attention, legal instruments on biodiversity and natural resources and rules of organization for political parties.
. One of our interviewees stated that, for example, 90 per cent of the rural inhabitants of Cotopaxi receive the _Bono_.
. This refers to the weekly radio programme that Rafael Correa broadcasts on Saturday mornings.
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Index
Acción Democrática (AD), Venezuela, , , –,
advisers, leaders incorporating,
Alcántra, M.,
Alfonsín, Raúl, –,
Alternative Democratic Pole, Colombia,
ambivalent democrats, –, ; Colombia,
Anti-Terrorist Law, Colombia 2003,
_antisistema_ discourse,
Argentina, , –, , –, , –, , , , , ; Congress building, , –; Emergency law 2002, ; horizontal clientilism, ; military dictatorship crimes and trials, , ; polarization, ; political party fracturing, ; presidential power concentration, ; Presidents expelled, ; Resolution , , ; soya boom, ; 2001 crisis, , ,
Aristotle, , ; leader typology,
authoritarianism, Latin America,
Azorín, F.,
Ballén, Sixto Durán,
Banco Latino, collapse of,
Barreda, M.,
Battle Ibáñez, Jorge Luis, –
Betancourt, Rómulo, ,
Bignone, Reynaldo,
Bittner, A.,
Blanco party, Uruguay, –, ,
Bogdan, R., ,
Bogotá, ,
Bolívar, Simón,
Bolivia, , ; indigenous communities,
Bolivarian Revolution, Venezuela,
_Bono de Desarrollo Humano_ , ,
Bordaberry, Juan María, dictatorship,
Borrero, Misael Pastrana,
Boyacá province, Colombia,
Brazil, , , ; 1998 devaluation,
Bucaram, Abdalá, , ; impeachment of,
Buenos Aires, , –, , –
Buquet, Daniel,
Burns, James McGregor,
business studies, leadership studies,
Caldera, Rafael, , ; _Agenda Venezuela_ ,
Capriles, Henrique,
Caracas, , ,
_carazaco_ , –
Cardoso, Fernando Henrique,
case studies, variables,
Castro, Fidel,
_caudillos_ , , , , ; postmodern,
Causa Radical, , ,
Chavez, Hugo, , , –, , , , , , , , , –, –, –, –; _Aló Presidente_ TV programme, ; as power usurper, , ; communication ability, , ; elites renewal, ; micro level discourse, ; polarization,
checks and balances,
Chile, , ,
Churchill, Winston,
Citizen's Revolution, Ecuador,
clientilism, –, , , , , , , , , –, , , , , ; definitions, , ; direct, ; logics of, ; types, ; vertical,
Co-Participation law, Argentina 1988,
Coalición Cívica,
Cobos, Julio, ,
Colombia, –, , –, , , , , , ; ambivalent democracy, , ; Communist Party, ; Conservative Party, _see below_ ; Constitution, ; Constitutional Court, ; constitutional reform, ; contradictions, ; corruption perception, ; Electoral Court, ; elitist politics, –; left-wing legislators, ; 1991 reform, ; Plan, –; political party institutionalization, ; political violence, , ; territorial vacuums, ; traditional elite, ; two-party system, ,
Colorado party, Uruguay, –, –, , , –,
Common Front for Peace Multi-party Commission,
Communist Parties: Colombia, ; Venezuela,
competition, political, , ,
Concertación party, Chile, , ,
_Consejos del Poser Popular_ ,
consenus politics, , , ; building of, ; culture of, ; establishing of, ; Uruguay,
Conservative party, Colombia, , , ,
Constituent Assembly, Ecuador proposal,
Constitutional Assembly, Venezuela,
COPEI, , , –, , ,
Corrales, J.,
Correa, Rafael, , , , , , , , –, , –, –, ; Citizen Revolution, ; emergence of, ; oil price benefit, ; PAIS movement, ; polarizing discourse,
corruption, , , , –, ,
Costa Rica,
Cuba,
Dahl, R.,
De Armas, Gustavo, –
De la Rúa, Fernando, , –
De la Torre, C.,
De Mesquita, Bueno,
debate, capacity to,
debt crisis, Latin America,
democracy enhancement, ; Uruguay,
democracy: buildings symptomatic, –; enhancers, ; 'craft', ; Latin American 'deficit', –; leaders, , leaders impact, , liberal, , public-private division, , quality of, , ,
Democratic Action, Venezuela,
Democratic Alliance, Colombia,
Democratic Centre,
Democratic Security Policy,
'Democratic Uruguay' programme,
Deslauriers, J-P., –,
Deutsch, K.,
dictators, ,
Duhalde, Eduardo, –
ECLAC,
economic crises, Latin America,
economic inequality, populism link,
economic reforms, Venezuela lack,
Economist Intelligence Unit, democracy index,
Ecuador, , –, –, , , –, , , , , , ; Assembly, ; Alianza PAIS, ; _caudillismo_ , ; 'dollarization', ; follower-leader relations, ; indigenous communities, ; Legislative Assembly elite, ; National Assembly building, ; political parties collapse, ; Presidents expelled, ; 2008 constitution, , ; 2011 referendum, ; vertical clientilism,
Ejército (Movimiento) Bolivariano Revolucionario,
_El Universal_ , Correa dispute with,
elections: competition, , ; personalized,
Elster, Jon,
Fabbrini, S., ,
Facebook, ,
FARC, –, , ,
Febres Cordero, León,
Fernández de Kirchner, Cristina, –, , –,
Flick, U.,
Flores, Juan José,
followers/supporters, -leaders relation, –, , , –,
Foundation of Open Society Institute, ,
Frente Amplio, Uruguay, , , –, , –, , ; legalization,
Frente Nacional, ,
Frente para la Victoria, ,
Fujimori, Alberto,
Gaitán, Jorge Eliécer,
Garcé, A.,
García Márquez, Gabriel,
Generación para un Nuevo Encuentro Nacional, Argentina,
General Confederation of Labour, Argentina,
Germani, G.,
governments, personalized,
Green Party, Colombia, –, ,
Grupo Clarín, Argentina, –
guerrilla movement, Colombian longevity,
Gutiérrez, Lucio, –
halo effect, –,
hard power, ,
Hirschman, A.,
Huertas, Ramírez, ,
Huntington, Samuel,
Ibáñez, Bernadina,
Ibáñez, Nicolasa,
import substitution industrialization,
indigenous people, Venezuela protection,
interviews, , ; locations, ; methodological validity, ; qualitative analysis, –; questionnaires, ; sample design, ; transcribing, ; values and ambitions analysis,
interviwees, choice methodology, –
Kane, J.,
Kellerman, , –,
Kirchner, Cristina _(seeFernández de Kirchner)_
Kirchner, Máximo, , Néstor, , –, –, , –,
Krauze, Enrique,
La Cámpora movement, Argentina,
La Causa Radical, Venezuela,
Lacalle Pou, Luis Alberto, –,
Lanzaro, J.,
LAPOP,
Lasso, Guillermo,
Latin America: economic crises, ; external debt crisis, ; political context,
leaders: advisers choice, ; agenda creating, ; communication methods, ; democratic quality, , , ; face-to-face meetings, , ; family connections, –; media relations, , ; non-legislative, ; politics entry, –; political qualities, ; Presidential, ; typologies of, –, , , , –
leadership: analysis lack, ; collective, , ; comparative research, ; conceptualization, , ; contextualization, ; ethics question, ; populist, ; romance of, –; studies, ; typologies,
legislators, differences,
_Ley de Caducidad_ , Uruguay,
_Ley de Medios_ , Argentina,
_Leyes Habilitantes_ , –, –, ,
liberal democracy, ; pillars of,
Liberal party, Colombia, ,
Linz, Juan, –
Lópea Estrada, –
López Obregón, Clara,
Locke, John,
Lukes, S.,
Machiavelli, Niccoló,
Madrid, , ; seminars,
Maduro, Nicolás,
Magdaleno, J., ,
Mahuad, Jamil, 2000 coup against,
Mainwaring, S.,
Masciulli, J., ,
McCoy, J.L.,
media, leaders relation with, ,
Menem, Carlos, –, –
mentors, political leaders,
Mesa de la Unidad Democrática (MUD), , , –, , –
methodology: research methods, ; social sciences,
Mexico, ; 1994 crisis,
Michels, Robert,
Mill difference method,
Ministry of Social and Economic Inclusion, Ecuador,
minorities: protection of issue, ,
_misiones_ , Venezuela, –, –,
Mockus, Antanas, –
Montevideo, ,
Moore, Barrington,
Morales, Evo,
Moreau, Leopoldo,
Morlino, L.,
Movimiento al Socialismo (MAS), Venezuela, , , –,
Movimiento Bolivariano,
Movimiento Pachakutik, –,
Movimiento Quinta República,
Mujica, José, , , –, –,
National Front Regime, Colombia,
National Institute of Statistics and Census,
National Party, Uruguay,
National Social Unity Party, Colombia, , –
Naval Club Pact,
Necessity and Urgency Decrees, Argentina,
nepotism, ,
new technologies, leaders use of,
Nicaragua,
Nye, J., –,
Ollier, M.M.,
PAIS, Ecuador, ,
Palacio de Miraflores,
Palacio, Alfredo,
Panama,
parliament buildings, ; security,
Partido Bandera Roja, , ,
Partido Social Cristiano,
Partido Socialista Unido de Venezuela (PSUV), , , –
Partido Sociedad Patriótica, ,
Pastrana Arango, Andrés, , –
Patapan, H.,
Patria Altiva i Soberana, Ecuador,
Patton, M.Q.,
PDVSA oil company, Venezuela,
Pérez Jimenez, Marcos,
Pérez, Carlos Andrés, , –; impeachment,
Perón, Juan Domingo, ,
Peronist party, Argentina, –,
Peru, , ; Ecuador war with,
Peruzzotti, E.,
Pinochet, Augusto,
Pizarro, Leongómez E.,
Plan Bolivar,
pluralism,
PODEMOS, Venezuela, , ,
political class, Latin America, ; Colombian elites, ; families,
political parties: balanced representation, ; career entry, ; Chavez discourse, ; collapse of, , , ; Colombia switching, ; conferences, ; deterioration of, , , , , ; discredited, ; Ecuador failure, , –, ; factionalism, ; fracturing of, ; fragmentation, , ; institutionalization level, –, –, , , , ; leaders relation to, , ; losing ground, ; loyalty, ; nature of, ; over-autonomous, ; over-institutionalized, –, , ; Presidential vehicle, –; system collapse, ; traditional recruiting, ; Uruguayan state role, ; Venezuela collapse, ; votes,
political representation: crises, ; parliaments, ; party vehicles, ; personalization of,
political science, quantitive research,
political violence: Colombia, ; use of,
Polo party, Colombia, ,
populism, , , , , ; conceptualizations of, –; nationalist, ; presidential system,
power: definitions, ; dynasties,
Presidentialism, –; crises, ; reinforcement,
press freedom issue, , ,
Primero Justicia, , –,
_progresimo_ ,
Propuesta Republicana,
Proyecto Venezuela, , ,
_Punto Fijo_ , –, , , ; collapse of, , ; failures of,
qualitative research, privileged,
questionnaires, interviews,
Quito, , , –, , ; seminars,
Radical Party, Argentina, –, , –
RCTV, Venezuela,
referendums, Venezuela, , –,
research, methods, ; qualitative,
Revolutionary Independent Labour Movement, Colombia,
Rilla, José,
Rincón, Rodríguez,
Rodríguez Saá, Adolfo,
Ruiz, Cárdenas,
rule of law, , ,
Ruptura de los , Ecuador,
Samper, Ernesto,
Sanatander, General,
Sánchez-Crepo, J.L.,
Sanguinetti, Julio María, –
Sanín, Noemí,
Santos, Juan Manuel, , , , –, –,
Scully, T.R.,
Secretariat of the Inter-American Press,
self-criticism,
Self-Defence Units of Colombia,
Serpa, Horacio,
Smith, A.,
social goods, access to,
soft power, , , ; usurpers, –, , ,
sovereignty discourse, Ecuador,
state, the: formal institutions of, ; security monopoly,
Strategic Zones, Venezuela,
strategy, leaders,
Supreme Court: Argentina reform, –; Venezuela,
Tanaka, Martín,
Taylor, S.J., ,
technology, leader use of, ,
Teles, F.,
tolerance, democracy marker,
Toronto, seminars,
trade unions, political career start,
Twitter, ,
two-party systems,
U party, Colombia,
Un Nuevo Tiempo, , ,
universities: leaders educated, ; political careers from, ,
Uribe, Álvaro, , , , , , –, –, –, ; Democratic Security Policy, ; judiciary resistance,
Uruguay, , –, , –, , , , –, , –, , , ; banking system, ; honesty respected, ; National Assembly building, ; party system, ; political entry methods, ; political party factionalism, ; Strategy for Fostering Citizen Participation, ; 2002 financial crisis, ,
USA (United States of America), , ; Chavez insults,
Vázquez, Tabaré, –, , , , –
Vargas Llosa, Mario,
Velasco Ibarra, José María,
Venezuela, –, , –, , , , , , , , , , , , ; attempted coup 1992, ; attempted coup 2002, ; Constitution, 1961, ; interview difficulty, ; military role, ; 1989 election, ; 1999 Constitution, , ; oil revenues, –; poor people activated, ; poverty, ; President expelled, ; 2000 elections, ; 2007 referendum, , ; 2009 referendum, ; 2012 primary elections, , ; younger politicians,
Videla, Jorge Rafael,
voters, communication with,
Weber, Max,
Western democracies, tacit consensus,
World Bank,
|
{
"redpajama_set_name": "RedPajamaBook"
}
| 7,338
|
"Unfortunately physics does not have all the answers about the why of the universe. The questions, which can not be solved by logic of the physic laws open a space for existential problems. Some of us consult religions [...] Others practice performance art."
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,049
|
{"url":"http:\/\/clay6.com\/qa\/20824\/angle-between-lines-of-force-and-equi-potential-surface-is-","text":"# Angle between lines of force and equi-potential surface is?\n\n(A) 180 degrees (B) 30 degrees (C) 90 degress (D) 45 degrees\n\nEquipotential surface is perpendicular to line of forces. Hence the answer is 90 degrees.","date":"2018-04-23 23:16:23","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\": 0.701255202293396, \"perplexity\": 1483.7084557872536}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-17\/segments\/1524125946256.50\/warc\/CC-MAIN-20180423223408-20180424003408-00366.warc.gz\"}"}
| null | null |
package com.tvd12.ezyfox.annotation;
import java.lang.annotation.ElementType;
import java.lang.annotation.Retention;
import java.lang.annotation.RetentionPolicy;
import java.lang.annotation.Target;
/**
* Indicates that a class configure which packages bean context need to load.
*
* @author tavandung12
*/
@Retention(RetentionPolicy.RUNTIME)
@Target({ElementType.TYPE})
public @interface EzyPackagesToScan {
/**
* packages to load.
*
* @return array of package names
*/
String[] value() default {};
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,892
|
Q: Three.js hide radial segments Is there any way to remove or hide radial segments from ConeBufferGeometry, CylinderBufferGeometry etc ? I'm new to 3D and three.js so I don't really know is it some crucial part of these geometries or I can hide it.
A: What do you mean? What are the "radial segments"? If you remove the outer surface all you're left with is a disc from the bottom of a cone or 2 discs from the ends of the cylindar.
If you wanted just a disc use a CircleBufferGeometry. If you wanted the ends gone then read the docs. They make it pretty clear there is an option to remove the ends
https://threejs.org/docs/#api/en/geometries/ConeBufferGeometry
https://threejs.org/docs/#api/en/geometries/CylinderBufferGeometry
Otherwise you can make your own custom geometry
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,900
|
Running Resources
"Fear holds us back. Belief moves us forward.
What do you have to lose?"
Runner. Dreamer. Mother of Five.
At 26, Beatie Deutsch just wanted to get back in shape after giving birth to 4 babies in 6 years. Inspired by her husband who recently rode a 180-miles on a bicycle for charity, she decided she would run a marathon.
It wasn't anything she'd done before but she didn't want to show up at her next family reunion to lose the annual beach race (again).
She trained four days a week for four months and placed sixth in the Tel Aviv Marathon. So she decided to run another one. And another. And another.
When she found out she was pregnant, Beatie kept running (under a doctor's supervision) and a year after she started training, she ran the Tel Aviv Marathon at 7 months pregnant in 4 hours and 8 minutes. She ran another marathon just a few months after giving birth.
Although she had never thought about being a professional runner, Beatie realized she was meant to run. She is currently training for the 2020 Olympics. "Running touches the core of what it means to be human," she says. "It allows me to experience gratitude on the deepest level, pushes me beyond my limits and gives me the strength to face challenges and define myself in every area of my life."
RUNNING & RELIGION
This natural runner caught the eye of the public not only because she ran a marathon well into her 3rd trimester, but also because she was the only runner wearing a head covering and a long skirt.
Beatie Deutsch is an Orthodox Jew. But for her, running isn't separate from her religious beliefs, it's sustained by it. "Our role in the world is to take the raw material God has given us and to use it to the fullest. I have a talent for running," she explains. "G-d gave me these strengths and talents. My motto is: believe in the impossible, give all you have and ask G-d for His assistance."
Even when she trains, Beatie maintains her modest attire: her necklines cover her
collarbone, her sleeves cover her elbows, and her skirts cover her knees. As a married woman, she always runs in a headscarf that covers her hair. She feels empowered by the idea that female athletes don't have to expose their bodies to win championships. "I'm proud that I can still pursue my dreams without sacrificing my values," she says.
"There are a lot of messages out there telling runners to look and dress a certain way,
but it doesn't have to be all about how your body looks when you run."
For Beatie, the modest clothing is also a practice in humility. As an athlete she recognizes how easily she could fall prey to the idea that she is solely responsible for her success. "When I dress modestly I remind myself that my speed is a gift from God, and it's not me that deserves the credit. It helps keep me in check and connected to who I truly am at my core -- a body AND soul with a piece of God inside of me. "
Born and raised in the United States, Beatie lived in Washington, New Jersey, and Chicago before she moved to Israel in 2000, where she lives with her husband and 5 children.
© 2020 - Beatie Deutsch | All rights reserved. Site creation and athlete management by My Guys Marketing.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 3
|
Manuel Vignau Pemartin (Auloron e Senta Maria, Bearn (França) mitjans del segle XVIII - Reus, 31 de gener de 1828) va ser un comerciant d'aiguardent francès instal·lat a Catalunya.
Va fundar una companyia amb Joan Larrard, amb el qual havia emigrat d'Auloron a Reus cap al 1730, amb el nom de "Juan Larrard y Compañia" i es dedicaren al comerç d'exportació de vins i aiguardents fins ben entrat el . Tenien com a centre comercial i habitatge la Casa de Larrard & Vignau, davant de l'església de Sant Francesc de Reus, un edifici que encara avui es conserva. Juntament amb el seu soci Joan Larrard i d'altres comerciants francesos, van estudiar a mitjans del la possibilitat de construcció d'un canal navegable de Reus a Salou, i en va fer un projecte presentant-lo a l'ajuntament, demanat els drets d'explotació perpètua. Aquest projecte, amb variants, es va iniciar el 1805, però va ser impossible de tirar endavant per la Guerra del Francès. El 1776 Manuel Vigmau es va casar amb Teresa de Miró i Bover, filla de Pau de Miró i Roig, un ciutadà honrat reusenc i doctor en dret. El 1796 Manuel Vignau va ser afavorit ell també amb el títol de ciutadà honrat. A més de la societat amb Larrard, era apoderat a Reus de la firma "Robert Herrier y Cia", dedicats al comerç de vins i grans. Va aconseguir de fer-se una fortuna i tenia una tomba pròpia a l'església de sant Francesc, davant de casa seva. Va fer diversos préstecs a la seva cunyada, Rosa Guardiola i Guasch, vídua d'un germà de la seva dona, Josep de Miró i Bover, per tal que recuperés diverses partides de terra venudes a carta de gràcia del Mas de Bover, el casal familiar. Vidu de Teresa de Miró, el 1811 es va casar amb Maria Veciana i de Miró, filla de Felip Veciana i Dosset, comandant general de les Esquadres de Catalunya.
Referències
Bearnesos
Morts a Reus
Comerciants reusencs
Empresaris francesos
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 3,204
|
\section{Introduction}
In recent years, approaches to molecular transport based on density-functional theory (DFT) in combination with the non-equilibrium Green's function formalism (NEGF) have received considerable attention in the literature, driven by the rapid progress in experimental work on realizing single-molecule nanodevices.\cite{Agrait2003,Venkataraman2006,Osorio2007,Quek2007} A number of research codes,\cite{Taylor2001,Xue2002,Qian2007} as well as the TranSIESTA,\cite{Soler2002,Brandbyge2002,Stokbro2003a} TurboMole\cite{Ahlrichs1989,Evers2003,Rothig2006,Arnold2007} and SMEAGOL\cite{Rocha2006} production codes have been developed. The attractiveness of the approach is based on the strengths of DFT for treating realistic atomistic and molecular transport configurations self-consistently, starting from an \emph{ab initio} quantum chemical description, combined with an intuitive mapping to a Landauer-type expression for the conductance and current through the Green's function formalism.\cite{Meir1992,Datta2000}
The NEGF+DFT approach, already at the LDA level of theory, is known to work particularly well for transport in the strongly coupled regime\cite{Mozos2002,Stokbro2003} and through off-resonant transport levels.\cite{Li2008} It has, for example, been used for metallic wires and non-conjugated hydrocarbons (alkanes).\cite{Mozos2002,Li2008,Prasongkit2010,Zanolli2010}
The strengths of DFT in this approach are, however, balanced by known weaknesses of the often-used approximate exchange-correlation potentials (\emph{e.g.}~LDA), which introduce self-interaction errors\cite{Perdew1981,Toher2005,Toher2007} and incorrect charging behavior due to the lack of a correct derivative discontinuity.\cite{Koentopp2006} The failure of common exchange correlation functionals to predict excited many-body states, as well as their mean-field character, hampers a proper handling of dynamic Coulomb correlations. This renders the method less suitable for weakly-coupled systems, particularly when one or more resonances are present inside the bias-window.
Nonetheless, despite the attractiveness of conceptually better-founded methods such as the GW approximation for dynamical response,\cite{Aryasetiawan1998,Thygesen2009} computational tractability has favored the popularity of the NEGF+DFT approach, especially when combined with better functionals from \emph{e.g.}~the GGA family. The approach has, for example, led to a better understanding of charge transport in thiolated phenyl systems\cite{Stokbro2003,Xue2003a,Xue2003b,Arnold2007} and single-molecule magnets,\cite{Barraza-Lopez2007,Park2010} among other systems of interest.
Recent work on \emph{e.g.} self-interaction corrections,\cite{Toher2005,Toher2007} accounting for lead-renormalization and dielectric effects\cite{Neaton2006,Quek2007,Mowbray2008,Kaasbjerg2008} and better functionals for the description of molecule-substrate interfaces,\cite{Baer2010} also strongly suggest that some of the problematic issues can be handled satisfactorily.
Moreover, the problems with accounting for dynamical Coulomb correlations are less pronounced in the strong-coupling regime and when studying off-resonant transport, which is why NEGF+DFT performs well there. But even outside these regimes, while \emph{e.g.}~exact peak positions may not be accurate, the qualitative trends obtained by the method are still quite useful for understanding transport through molecular devices.
It is in this spirit that we report on an efficient NEGF+DFT method implemented in the BAND periodic-system DFT code,\cite{Velde1991,Wiesenekker1991,Velde2001} (sister-code to the ADF molecular DFT code) which allows us to study novel single-molecule systems. A number of unique features of BAND, in particular the freedom to choose the number of dimensions in which periodicity is imposed, enables us to perform accurate modeling of the contacts, as well as of the electric potential in the presence of a gate. This will help to resolve a number of the issues critical to the full understanding of experimental results, although a full treatment of the Coulomb potential in the presence of a gate electrode has not yet been implemented in our method. \\
In the following section (\ref{Formalism}), we will briefly review the NEGF formalism underlying our approach, which has been described in detail elsewhere.\cite{Datta1997} Section \ref{Implementation} then discusses our implementation schematically, commenting on some subtle points relating to the peculiarities of BAND and critical to the efficiency of the calculations. In particular, we discuss the partitioning of the model system in \ref{Partitioning}, the treatment of the Hamiltonian obtained from the periodic band-structure calculation in \ref{Tight-binding}, and how we obtain surface Green's functions and self-energies, coupling the infinite leads to an ``extended molecule,'' in \ref{Surface}. In section \ref{Alignment} (and appendix \ref{AlignmentTests}) we then discuss the technical issue of the alignment of the potential between computational stages.
The details of the non-equilibrium calculations are treated in section \ref{NEqPMat}.
Once the alignment has been determined self-consistently, we proceed to the transport-calculation proper, for a molecular system of interest. Calculations we have performed to validate our code are discussed in sections \ref{Transport1D} and \ref{Transport3D}. In the 1D case we present benchmark results on Li and Al chain systems, and in the general 3D case we discuss our study of transport through benzenedithiol and oligo-phenylene-ethynylene-dithiols, as archetypal molecular wires, between Au electrodes, which form a family of structurally related junctions. This is reflected in the character of their zero-bias transmission near the Fermi level $\epsilon_f$, where there is a progressive closing of the transport gap mirroring the decreasing gas-phase HOMO-LUMO gap. We further examine the details of the symmetries of the orbitals which are found to couple in transport, finding them again related across the family, and finally we show the results of calculations under moderate bias, which illustrates the screening effect of the electrodes and supports the common-practice of using the zero-bias transmission $T(\epsilon)$ for systems under low-bias.
\section{Overview of the NEGF+DFT Approach}\label{Formalism}
In order to model the molecular system and the contacts to which it is connected using \emph{ab initio} techniques, we need to reduce the size of the system being modeled from a molecule between infinitely large contacts to something more manageable. To this end we use the ``extended molecule'' (EM) scheme,\cite{Xue2002,Brandbyge2002} illustrated in Fig.~\ref{fg:extendedmolecule}. The system is partitioned into a central extended molecule comprised of the actual molecule and some connecting parts of the leads on each side. This extended molecule, in turn, is then connected to true semi-infinite bulk leads via a well-defined metal-metal interface. Thus, in our model the leads are described by a finite-dimensional Hamiltonian $H$ corresponding to a portion of true bulk metal, corrected by a self-energy $\Sigma$ containing the response of the leads.
The key benefits of modeling the system in this way are first that we are able to place the interface between the leads and the active portion of the single-molecule system between metal layers, an interface which is much better understood than the complex molecule-metal binding geometries which may occur. The details of these binding geometries may then be varied, without the need to recalculate the contributions from the bulk contacts.
A subtler point is that, as argued by Evers \emph{et al.}\cite{Rothig2006,Arnold2007}, this approach allows us to increase the size of the extended molecule in order to test convergence to transport properties which correspond to truly bulk-reservoir electrodes, which they have shown for tight-binding chains and cluster Au electrodes of varying sizes.
Furthermore, the metallic parts of the extended molecule allow us to take simple polarization effects in the leads into account. Finally, the approach allows us to derive an expression for the propagator for the entire extended molecule in a simple way, which we discuss in section \ref{Implementation}.
\begin{figure}
\includegraphics[width=\columnwidth]{img/ext-molecule}
\caption{Schematic geometry of the extended molecule (physical molecule and portion of the contacts to which it is attached) and semi-infinite bulk portion of the contacts.}\label{fg:extendedmolecule}
\end{figure}
Our treatment of the metallic contacts is a Kohn-Sham based periodic band-structure calculation, as implemented in the BAND density-functional code.\cite{Velde1991,Velde2001} The code uses localized basis-functions, of either Slater-type orbital (STO) or numerical atomic orbital (NAO) type, usually complemented by frozen-core approximations of the inner electron shells of the atoms in the system. Smooth radial confinement of the basis functions can be applied using a Fermi-Dirac function of the distance from the nucleus. The code also supports variable periodicity, ranging from 0D (none), 1D (chain), 2D (slab) and finally to 3D (bulk) geometries.\\
First, a calculation is performed in the band-structure DFT code BAND to obtain the Fock matrix for a bulk unit cell, from the self-consistent density which enters the Kohn-Sham Hamiltonian $\mathcal{H}^\text{\tiny KS}$:
\begin{align}\label{ks}
\mathcal{H}^\text{KS}(\bm{r}) = &-\frac{1}{2} \nabla^2 - \sum_n \frac{Z_n}{|\bm{r} - \bm{r}_n|} + V_\text{H}[n](\bm{r}) + V_\text{xc}[n](\bm{r})\;,
\end{align}
where $V_\text{H}[n](\bm{r})$ (the Hartree potential) is the solution of the Poisson equation with boundary conditions corresponding to the chemical potentials in the electrodes. The density is constructed from the occupied Kohn-Sham orbitals as $n(\bm{r}) = \sum_{i_\text{occ}} \left| \phi_i(\bm{r}) \right|^2$.
In the following, it should be kept in mind that the Kohn-Sham Hamiltonian depends on the bias voltage and the electron density, though these dependencies are usually omitted for compactness of notation. In BAND we represent the Hamiltonian \eqref{ks} in a non-orthogonal basis, and so find the Fock matrix as $H^\text{\tiny KS} = [ \langle\phi_i|\mathcal{H}^\text{\tiny KS}|\phi_j\rangle]$ and the overlap matrix as $S^\text{\tiny KS} = [ \langle\phi_i|\phi_j\rangle]$. From the Fock and overlap matrices for the bulk leads we calculate the surface Green's functions $g_c(\epsilon)$ by an efficient recursion algorithm.\cite{Sancho1985,Henk1993} We then find the corresponding self-energies $\Sigma_{1,2}(\epsilon)\sim\tau g_c(\epsilon) \tau^\dagger$ of the contacts (1,2 for source and drain, respectively and $\tau$ the coupling between layers in the leads), which are then combined with the Hamiltonian of the extended molecule to find the full Green's function:
\begin{equation}\label{GF1}
G_\text{\tiny EM}(\epsilon) = \biggl( \epsilon\,S_\text{\tiny EM} - H_\text{\tiny EM} -\left(\Sigma_1(\epsilon)+\Sigma_2(\epsilon)\right)\biggr)^{-1}\;.
\end{equation}
where $G(\epsilon),\;\Sigma_{1,2}(\epsilon)$ refer to the retarded (causal) Green's function and self-energies, respectively.
The Green's functions are then used in a modified self-consistent field (SCF) approach based on the density derived from the Green's function:
\begin{align}\label{SCF2}
\nonumber \phi^{(0)}_j(\bm{r}) \rightarrow n^{(0)}(\bm{r}) \rightarrow \;&H^\text{\tiny KS} +\Sigma_1 + \Sigma_2 \rightarrow G(\epsilon) \rightarrow \rho \rightarrow n^{(1)}(\bm{r}) \rightarrow \\ \nonumber &H^\text{\tiny KS} +\Sigma_1 + \Sigma_2 \rightarrow G(\epsilon) \rightarrow \rho \rightarrow n^{(2)}(\bm{r}) \rightarrow\\ &\ldots
\end{align}
which may be compared to the usual SCF cycle in DFT:
\begin{align*
\phi^{(0)}_j(\bm{r}) \rightarrow n^{(0)}(\bm{r}) \rightarrow H^\text{\tiny KS} \rightarrow \phi^{(1)}_j(\bm{r})
\rightarrow n^{(1)}(\bm{r}) \rightarrow H^\text{\tiny KS} \ldots
\end{align*}
If we assume that the contacts each couple only with the central extended molecule, then we can simplify the general Green's function formalism and obtain the density matrix from the Green's function at each iteration as an integral over the real-valued energies:
\begin{align}\label{density2}
\nonumber \rho = \frac{1}{2 \pi} \int \mathrm{d}\epsilon\; [\; &G(\epsilon) \Gamma_1(\epsilon) G^{\dagger}(\epsilon) f(\epsilon,\mu_1) \\+ &G(\epsilon) \Gamma_2(\epsilon) G^{\dagger}(\epsilon) f(\epsilon,\mu_2)\;]\;.
\end{align}
$\Gamma(\epsilon)$ is defined as $i\left( \Sigma(\epsilon)-\Sigma^\dagger(\epsilon)\right)$ for each contact. $\mu_1$ and $\mu_2$ are the chemical potential of source and drain electrodes. The bias voltage follows as $V_b = \frac{\mu_1-\mu_2}{e}$.
This is general to the case of differing chemical potentials (\emph{e.g.} biased devices or different contact materials), but doesn't take \emph{e.g.} direct coupling between leads into account. In the equilibrium case with a single chemical potential in both leads, the expression further simplifies to:
\begin{align}\label{density1}
\rho = -\frac{1}{\pi}\int \mathrm{d}\epsilon\; \im{G(\epsilon)} f(\epsilon,\mu)\;.
\end{align}
When the SCF cycle \eqref{SCF2} converges, some interesting properties of the molecular system may be evaluated, using the converged $G(\epsilon)$ to obtain \emph{e.g.} the density of states (DOS) by:
\begin{align}\label{DOS}
D(\epsilon) &= -\frac{1}{ \pi} \tr{ \im{ \,G(\epsilon)\,}\,S }\;,
\end{align}
and the current by a Landauer-like expression, with $T(\epsilon) \sim \trr{ \Gamma_1 G \Gamma_2 G^{\dagger} }$ such that:
\begin{align}\label{Current}
I &= \frac{2e}{h} \int \mathrm{d}\epsilon\; \trr{ \Gamma_1(\epsilon) G(\epsilon) \Gamma_2(\epsilon) G^{\dagger}(\epsilon) } \left( f(\epsilon,\mu_1) - f(\epsilon,\mu_2) \right)\;.
\end{align}
The integral above is over the real line, but can be performed much more efficiently by using analytic continuation and complex contour integration.\cite{Zeller1982}\\
An important technical issue is that the offset of the potential cannot be expected to be the same in the junction geometry as that used for the bulk metal calculation for the contacts, due both to the controlled approximation in the tight-binding fit, and the much larger intrinsic issue of a floating-potential effect in the periodic band-structure code. The latter arises because in any band-structure DFT code the potential, and thus the Hamiltonian, are only determined up to some additive constant, \emph{i.e.} $H$ and $H+\ensuremath{\Delta\phi} \, S$ give the same spectrum for constant offset $\ensuremath{\Delta\phi} $. However, as our approach to transport involves several stages (bulk calculation of contacts, self-energy calculation, self-consistent alignment and transport calculation), we must take care to ensure that the (arbitrary) offset in the potential is consistent across all stages.
To find the offset $\ensuremath{\Delta\phi} $, an alignment calculation is carried out next, such that for the contacts in the transport calculation, it holds that:
\begin{align*}
H^\text{\tiny KS} \approx H^\text{\tiny TB} + \ensuremath{\Delta\phi} \cdot S^\text{\tiny TB}\;,
\end{align*}
to within some acceptable tolerance. Once converged, we proceed to the calculation of an arbitrary molecular system, which may be under bias.
\section{Overview of the Implementation}\label{Implementation}
\subsection{System Partitioning}\label{Partitioning}
The partitioning illustrated in Fig.~\ref{fg:extendedmolecule} is made precise in terms of the operators in the formalism in Fig.~\ref{fg:extendedmolecule2}. The partitioning of the Hamiltonian into extended molecule ($H_m$) plus contacts ($H_c = H_1\oplus H_2$) is as follows:
\begin{align}\label{partitioning}
H &= \left(
\begin{array}{ccc}
H_m & \tau_1^\dag & \tau_2^\dag \\
\tau_1 & H_1 & 0 \\
\tau_2 & 0 & H_2 \\
\end{array}
\right) \equiv
\left(
\begin{array}{cc}
H_m & \tau^\dag \\
\tau & H_c \\
\end{array}
\right)
\end{align}
such that the Green's function for the entire system is determined by inverting:
\begin{align}\label{matGF}
(\epsilon\,S - H)G(\epsilon)=I\;.
\end{align}
\begin{figure}
\includegraphics[width=\columnwidth]{img/Illustration/Partitioning}
\caption{Schematic geometry of the extended molecule and semi-infinite bulk portion of the contacts indicating the regions on which each operator in the formalism is active}\label{fg:extendedmolecule2}
\end{figure}
The specific approximation behind this partitioning is that we require the full Hamiltonian for contacts and extended molecule to be correct in the Kohn-Sham sense at each iteration, while the density matrix need only be correct for the extended molecule. This is justified by its spatial separation from the (expected) field- and charge-errors at the edges of the finite system. The errors there, in turn, are minimized by replacing $H_{1,2}$ by the stored bulk operators, as we discuss in section \ref{Alignment}.
\subsection{Tight-binding Representation of $H^\text{\tiny KS}$}\label{Tight-binding}
From the bulk calculation, the Fock matrix is known with respect to BAND's basis functions for many Bloch boundary conditions, represented by a dense set of Bloch wavevectors $\bm{k}$ inside the Brillouin zone. We search for a tight-binding Fock matrix, given in terms of BAND's localized
basis functions, which reproduces BAND's Fock matrices as closely as possible.
The basis functions
are denoted $\left| \phi_i^\alpha\rangle\right.$, where $i$ denotes a unit cell and $\alpha$ denotes a particular orbital type:
\[
\langle \bm{r} | \phi^\alpha_i \rangle = \phi^\alpha (\bm{r} - \bm{r}^\alpha_i).
\]
Here, $\bm{r}^\alpha_i$ is the position of the atom in unit cell $i$ about which the $\alpha$-orbital is centered. Taking the cell index $i=0$ without loss of generality, we denote the real-space tight-binding matrix elements in relation to $k$-space as:
\begin{align}
H^\text{\tiny TB}_{\alpha\beta}(\bm{k}) &= \sum_{\bm{R}_j} \; H^\text{\tiny TB}_{i\alpha,j\beta} \; e^{i\bm{k}\cdot\bm{R}_j}\;,
\end{align}
The requirement that the matrix on the left-hand side is equivalent to BAND's Fock operator suggests that:
\begin{align*}
F = \sum_{\alpha\beta} \sum_l \left|H_{\alpha\beta}^\text{\tiny TB}(\bm{k}_l) - H_{\alpha\beta}^\text{\tiny KS}(\bm{k}_l)\right|^2\;,
\end{align*}
be minimized with respect to the real-space matrix elements $H^\text{TB}_{i\alpha,j\beta}$.
This minimization is done using the L-BFGS algorithm,\cite{Press2007} with a cut-off radius
which is increased as needed to meet a user-specified tolerance for the fit.
As each element of the tight-binding fit is calculated using only the lattice positions and the reference value of the Fock matrix, it can be calculated independently, so that this calculation is trivially parallelized, with linear scaling in the number of cores.
We emphasize, however, that we make a tight-binding \emph{fit} $H^\text{\tiny{TB}}$ of $H^\text{\tiny KS}$ in terms of the (known) lattice of the contact, as opposed to switching to a traditional tight-binding \emph{model} for the electronic structure. These TB Fock and overlap matrices, together with the lattice, then form the input for our calculation of the surface Green's functions. \\
\begin{figure
\includegraphics[width=.8\columnwidth]{img/Illustration/Tubes2}
\caption{Narrow tube (NT) in the infinite contact based on a single unit cell. Partitioning based on principal layers, which due to electronic screening interact only with neighboring principal layers (discussed in section \ref{Surface}).}\label{fg:players}
\end{figure}
\begin{figure
\includegraphics[width=.8\columnwidth]{img/Illustration/Tubes}
\caption{Wide tube (WT) in the infinite contact based on an $\ell\times\ell$ grid of unit cells in the surface plane. Compare Fig.~\ref{fg:players} for the relation with the narrow tube. }\label{fg:tube}
\end{figure}
We now have a set of Fock and overlap matrices corresponding to $\bm{k}$-vectors in the Brillouin zone, from which we can calculate self-energies, for a `tube' extending into the contact as in Fig.~\ref{fg:players}. From these, we can calculate self-energies on the same grid of $\bm{k}$-vectors. We assume the number of $\bm{k}$ vectors in the Brillouin zone to be $N^2$.
From these matrices, it is then possible to calculate their counterparts for a wider tube with periodic boundary conditions, see Fig.~\ref{fg:tube}. We now denote the original (narrow) tube by NT, and the wide tube as WT.
We assume that the 2D unit cell of the wide tube is an integer multiple ($\ell \times \ell$) of that of the narrow tube.
Within the narrow tube, we can write the Fourier transform of the matrix $M$ (which may be the Hamiltonian or the overlap matrix) for any wave vector $\bm{k}$ as
\[
M^\text{NT}_{\alpha \beta} (\bm{k}) = \sum_{\bm{r}_\|} M_{\alpha,\beta} (\bm{r}_\|) e^{i \bm{k} \cdot \bm{r}_\|},
\]
where the sum $\sum_{\bm{r}_\|}$ is over \emph{all} relative positions $\bm{r}_i^\alpha-\bm{r}_j^\beta$ within the large volume
corresponding to the $N^2$ $\bm{k}$-vectors in the two-dimensional BZ in the surface plane.
Taking the wide tube with periodic boundary conditions (i.e.\ at the $\Gamma$-point), we have
\[
M^\text{WT}_{\alpha\beta} (\bm{r}_\|) = \sum_{\bm{R}^\text{WT}} M_{\alpha \beta} (\bm{r}_\| + \bm{R}^\text{WT})\;,
\]
where $\bm{R}^\text{WT}$ is any $m\cdot\bm{a}_1^w+n\cdot\bm{a}_2^w$, linear combination of wide-tube basis vectors ($\bm{a}_i^w = \ell\bm{a}_i$ in terms of the NT basis vectors).
This equation expresses the periodicity of $M^\text{WT}$.
On the other hand we can write:
\[
M_{\alpha\beta}(\bm{r}_\| + \bm{R}^\text{WT}) = \frac{(2\pi)^2}{\Omega} \int d^2 k\; M_{\alpha\beta} (\bm{k})
e^{i \bm{k} \cdot (\bm{r}_\|+\bm{R}^\text{WT})}.
\]
Combining these two ingredients, we can write
\[
M^\text{WT}_{\alpha\beta} (\bm{r}) = \sum_{\bm{R}^\text{WT}} \frac{1}{N^2} \sum_{\bm{k}_\text{BZ}} M_{\alpha\beta}(\bm{k}_\text{BZ})
e^{i \bm{k} \cdot \left(\bm{r}_\| + \bm{R}^\text{WT} \right)}.
\]
The sum over the wide tube vectors $\bm{R}^\text{WT}$ singles out the reciprocal lattice vectors (lying inside the NT Brillouin zone)
of the wide tube:
\[
\sum_{\bm{R}^\text{WT}} e^{i \bm{k} \cdot \bm{R}^\text{WT}} = \frac{N^2}{\ell^2} \sum_{\bm{K}^\text{WT} \,\in\, BZ^\text{NT}}
\delta(\bm{k} - \bm{K}^\text{WT}),
\]
from which we immediately have:
\[
M^\text{WT}_{\alpha\beta} (\bm{r}_\|) = \frac{1}{\ell^2} \sum_{\bm{K}^\text{WT} \,\in\, \text{BZ}^\text{NT}} M^\text{NT}_{\alpha\beta}(\bm{K}^\text{WT})
e^{i \bm{K}^\text{WT} \cdot \bm{r}_\|}\;.
\]
This expression tells us how to obtain the matrix elements between any two points inside the wide tube from the matrix elements on
the reciprocal lattice points of the WT, lying inside the Brillouin zone of the NT.
\subsection{Surface Green's Function and Self-Energies}\label{Surface}
Equation \eqref{matGF} for the matrix Green's function in the case of a non-orthogonal basis
yields the matrix relation:
\begin{align}
\left( \begin{array}{cc}
I_m & 0 \\
0 & I_c \\ \end{array} \right) &=
\left( \begin{array}{cc}
\epsilon S_m - H_m & \epsilon S_{\tau}^{\dagger} - \tau^{\dagger} \\
\epsilon S_{\tau} - \tau & \epsilon S_c - H_c \\ \end{array} \right)
\left( \begin{array}{cc}
G_m & G_{mc} \\
G_{cm} & G_c \\ \end{array} \right)
\end{align}
(omitting the $\epsilon$-dependence from the Green's functions on the right-hand side) from which follow closed expressions for the propagator $G_m$ of the extended molecule using self-energies, in the presence of a contact:
\begin{align}
G_m(\epsilon) &= \left( \epsilon S_m - H_m - (\epsilon S_{\tau}^{\dagger} - \tau^{\dagger}) G_c(\epsilon) (\epsilon S_{\tau} - \tau) \right) ^{-1}\;,
\end{align}
and we identify:
\begin{align*}
\Sigma_c(\epsilon) \equiv (\epsilon S_{\tau}^{\dagger} - \tau^{\dagger}) G_c(\epsilon) (\epsilon S_{\tau} - \tau)
\end{align*}
as the self-energy of the contacts, which may be split as $\Sigma_1+\Sigma_2$.\footnote{In the literature $\Sigma = \tau g \tau^\dagger$ is often used as the definition of the self-energy; then $\tau$ corresponds precisely to our $(\epsilon S_{\tau} - \tau)$ expression for the coupling of device and contact.} For two contacts we specify the propagator further as $G(\epsilon)=\left( \epsilon S_m - H_m - \Sigma_1 - \Sigma_2 \right)^{-1}$, and it is this subsystem which we subsequently focus on.\\
Two further remarks are important before continuing. First, we note that the determination of $\Sigma_c$ only requires knowing the surface couplings in $(G_{\text{c}})_{i j\, \in\,\text{surf}}$, which makes this practical to implement in a DFT code with localized basis functions (such as BAND). Second, we note that while the above is an exact description within the limits of the one-electron picture (\emph{i.e.} neglecting electron-electron interaction beyond the mean-field level), in practice when calculating by an approximate method such as an actual DFT implementation, we need to be aware of the consequences of the limited spatial extent of the extended molecule, which may be felt by the central region due to the Hartree term in the potential if it is insufficiently screened. Generally, for metals, the screening is strong enough to justify the approach for contacts of a few atomic layers.\\
Now, our approach to obtaining the Green's function $G$ relies on the fact that the metallic system has a finite interaction-range in real-space due to electronic screening. This implies a local-- and neighbor-coupling structure of the Fock matrices which is tridiagonally structured as $( \tau,\; h,\; \tau^\dagger )$ in a basis organized into adjacent layers of atoms, and similarly tridiagonally structured as $( s_\tau,\; s,\; s_\tau^\dagger )$ for the overlap matrix.
We introduce the concept of ``principal layers,'' because it is well known that electronic screening limits the interaction range of the Coulomb potential to just a few atomic layers in a metal.\cite{Ashcroft1976} This implies that we can give a description in terms of blocks of 3-4 atomic layers called a ``principal layer,'' which interact only with the neighboring principal layers. Together with the use of localized basis functions, this allows us to use the structure of a Hamiltonian matrix as in equation \eqref{H_principal_layers} corresponding to principal and adjacent (interacting) layers, as illustrated in Fig.~\ref{fg:players}.
\begin{align}\label{H_principal_layers}
H=\left(
\begin{array}{ccccc}
h & \tau^\dagger & 0 & \cdots &\\
\tau & h & \tau^\dagger & 0 & \cdots\\
0 & \tau & h & \tau^\dagger & 0\\
\vdots & 0 & \ddots & \ddots & \ddots \\
\end{array}
\right)\;.
\end{align}
We consider the metal as being composed of an infinite number of layers in space, and then find the relation between elements of the Green's function for $2^k$ and $2^{k+1}$ principal layers by recursively eliminating the layers in between.\cite{Sancho1985,Henk1993}
From this we obtain the Green's function for the surface and the bulk of an infinite contact, and can study the latter's convergence with respect to the bulk calculation in BAND. This method is easily extended to evaluation over a Monkhorst-Pack grid\cite{Monkhorst1976} in $k$-space, and parallelized in energy.
This approach converges quickly, and a sample calculation of the surface and bulk DOS is illustrated in Fig.~\ref{fg:dosconverges} for different grid densities in $k$-space in the plane of the contacts. In principle this $k$-space dependence also carries over to the alignment and transport calculations, and in the previous section we discussed a method for the construction of an expanded self-energy for the contacts. However, we will present only calculations in the $\Gamma$-point approximation in the remainder of this paper.
\begin{figure
\includegraphics[width=\columnwidth]{img/Al-kgrid/Multiplot}
\caption{Convergence of the bulk aluminum DOS with increasingly dense grid in $k$-space.
Top: bulk DOS from the Green's function ({\bf red}) compared with normal DFT calculations ({\bf green}): convergence for finer $k$-grids. Bottom: surface DOS for a [111]--cut surface (from the surface Green's function), which cannot be obtained directly from DFT. DFT calculations performed with the LDA functional, using a DZP-quality basis-set.}\label{fg:dosconverges}
\end{figure}
The key computational steps in this stage of the calculation are the complex contour integrals over the Green's functions (expressions \eqref{density2}--\eqref{density1}), which are a much more efficient way\cite{Zeller1982} to evaluate the density matrix from the Green's function than direct integration over the real line. The reason for the latter is that in general $G(\epsilon)$ may have poles quite near the real axis, necessitating a very dense integration grid, while the contour may be taken safely away from these in the upper half of the complex plane, drastically reducing the computational effort.
We pre-calculate the contours themselves and the corresponding self-energies $\Sigma_{1,2}(\epsilon_i)$ over all points on the contour $\{\epsilon_i\}$, given that the self-energies can be calculated independently for each energy point on the contour.
\subsection{Potential Alignment and Determination of the Fermi Level}\label{Alignment}
As noted above, the zero of the potential is not uniquely determined in this type of DFT calculation. As our approach to transport involves a sequence of relatively independent computations (bulk calculation of contacts, self-energy calculation, self-consistent alignment and transport calculation), we must ensure that the (arbitrary) offset in the potential is consistent across all stages, keeping in mind that the self-energies also implicitly reference the chemical potential of their respective contact: $\Sigma_{1,2}(\epsilon_i;\mu_{1,2})$.
A number of codes take different approaches to this,\cite{Stokbro2003a,Rocha2006} but we are not aware of any approach that has handled the problem self-consistently to date.
In order to ensure the alignment of the potentials in the leads (and their self-energies) with those of the extended molecule, we first note that there is a natural criterion for determining the offset: the charge neutrality of bulk material. Clearly, the chemical potential is directly related to the number of electrons in the metal. Consequently, when the unbiased extended molecule is itself composed of the same material as the contacts, we can self-consistently determine the offset by requiring the (valence) charge on the extended molecule to equal the bulk (valence) charge for the same number of atoms. We tune this charge by iteratively shifting the potential during the SCF until the criterion is met. We have also implemented a novel constrained-DIIS (CDIIS) scheme in our code to accelerate the convergence of this alignment procedure for difficult systems; this is briefly outlined in appendix \ref{DIIS}.\\
\begin{figure
\includegraphics[width=.98\columnwidth]{img/Illustration/Potentials-2}
\caption{Differing computational stages' zeros of the potential induce differing chemical potentials which are reconciled in alignment. Shown is the analog of Fig.~\ref{fg:extendedmolecule2}, where we now include the contact offset $\ensuremath{\Delta\phi} _0$ and fine-tuning of charge-neutrality $\ensuremath{\Delta\phi} _1$ as discussed, yielding a consistent $\mu_\text{true}$ after alignment.}\label{fg:potentialzeros}
\end{figure}
Our approach is to split the shift into the two components illustrated in Fig.~\ref{fg:potentialzeros}. The first is the offset between the bulk run (periodic cell, used to construct the self-energies for the semi-infinite contacts) and the alignment run (longitudinally aperiodic transport geometry composed of contacts + extended molecule). This offset is estimated at each iteration as follows:
\begin{align}
\ensuremath{\Delta\phi} _0 = \frac{1}{n_\text{bas}}\displaystyle\sum_{i\in\text{C1}\oplus\text{C2}} \frac{\left(H_{ii}^\text{\tiny TB}-H_{ii}^\text{\tiny KS}\right) }{ S_{ii} }\;,
\end{align}
where $n_\text{bas} = n_\text{bas}^\text{C1} + n_\text{bas}^\text{C2}$ is the dimension of the basis of the Hamiltonian for the two contacts and $H^\text{\tiny TB}$ and $H^\text{\tiny KS}$ refer to the tight-binding representation of these bulk contact Hamiltonians and the transport geometry's contact Hamiltonians respectively (see Fig.~\ref{fg:extendedmolecule}).
We now shift the system by the offset: $H^\text{\tiny KS} \rightarrow H^\text{\tiny KS} + \ensuremath{\Delta\phi} _0\, S^\text{\tiny KS}$. Next, we overwrite the Hamiltonian and overlap matrix $S^\text{\tiny KS}$ of the contact regions by those obtained from the bulk calculations, which do not suffer from edge effects and are now aligned with the rest of the system. This is updated at each iteration, allowing for fluctuations in the density-dependent potential $V[n({\bf r})]({\bf r})$, such that the extended system is always as close as possible to be precisely aligned with the bulk contacts' potential.\footnote{Convergence of these shifts is a natural heuristic for the proper alignment of the system with this algorithm.}
The second shift is the correction to the extended system which brings the Fermi level into alignment with the implicit chemical potential encoded in the open-boundary self-energies. We obtain it by determining the density matrix from the Green's function for the extended system via equation \eqref{density1}, which yields the valence charge over the extended molecule region by tracing over the relevant basis functions as $\trr{\rho S}_\text{\tiny EM}$. This is in practice typically not charge-neutral. To achieve $Q_\text{\tiny EM} \rightarrow Q_\text{valence}$ we use an offset to ensure charge neutrality, which is calculated iteratively:
\begin{align}
\ensuremath{\Delta\phi} _1\itr{k+1} = \ensuremath{\Delta\phi} _1\itr{k} + \alpha\left(\tr{\rho S}_\text{\tiny EM} -Q_\text{valence}\right)
\end{align}
until convergence is achieved. The shifts $\ensuremath{\Delta\phi} _1$ are applied to the entire system. Note that the parameter $\alpha$ has the dimensions of a capacitance, and indeed can be chosen proportional to the inverse of the density of states, evaluated at the Fermi-energy. In practice, such an implementation easily becomes numerically unstable, and we have opted for a fixed, small mixing parameter $\alpha$ instead.
Both shifts, $\ensuremath{\Delta\phi} _0,\,\ensuremath{\Delta\phi} _1$, must converge for the alignment stage to be considered successful. This procedure may be accelerated by extending the DIIS scheme\cite{Pulay1980} as outlined in appendix \ref{DIIS}, and we illustrate a representative performance of the accelerated method in Fig.~\ref{fg:Al.ShiftConvergence-cdiis} for a 1D Al chain, as well as in figures Figs.~\ref{fg:Au.ShiftConvergence1}-\ref{fg:Au.ShiftConvergence2} for Au contacts. Moreover, for each set of contacts we discuss, we check that re-running the alignment ``bulk'' geometry as a zero-bias transport calculation using the shifts calculated as static inputs indeed results in charge-neutrality in the extended molecule.\\
To summarize, when the SCF calculation converges, we have obtained two potential shifts: the contact shift $\ensuremath{\Delta\phi} _0$
and the charge-neutrality shift $\ensuremath{\Delta\phi} _1$. The former is a runtime iterative adjustment to ensure that the active region of the transporting system is aligned to the bulk Hamiltonians with which the contacts are overwritten, while the latter is a runtime constant which ensures that the potential of the entire system is such that a bulk extended molecule is precisely charge neutral. This in turn determines the Fermi level completely. The alignment calculation is separate from our transport calculations, and performed once for every new set of contacts.
The subtlety of our approach lies in realizing that by aligning the transport system to the bulk calculation, we tie it to the picture of contacts as reservoirs with well-defined chemical potentials. Consequently, from this point onward the Fermi level is no longer an estimated quantity, but an exactly known and fixed quantity, stemming directly from the bulk periodic contact calculation.\\
The procedure outlined here performs well in practice, correcting the offsets illustrated in Fig.~\ref{fg:potentialzeros}, and produces a PDOS on the extended molecule which matches the PDOS of the bulk contacts very well, see section \ref{Transport1D}.
The resulting electronic structure, moreover, compares well with a bulk calculation of the true periodic system, as shown in appendix \ref{AlignmentValidation}.
\subsection{Non-equilibrium Calculations}\label{NEqPMat}
The procedure described in the previous section yields the ``total shift'' $\ensuremath{\Delta\phi} =\ensuremath{\Delta\phi} _0+\ensuremath{\Delta\phi} _1$, and from this point on $\ensuremath{\Delta\phi} _1$ is a constant shift applied at every iteration during a transport run. However, in order to treat the non-equilibrium transport case, we also need to consider both the effects of the applied bias and fields, and the calculation of the non-equilibrium density from the NEGF formalism.
The system in the transport run is, as we have outlined, shifted from the unmodified $H^\text{\tiny KS}$ for the extended molecule with contacts to the correct potential zero as $H+(\ensuremath{\Delta\phi} _0+\ensuremath{\Delta\phi} _1)S$. To this we add the bias $\phi_b(\bf r)$ and (possibly) gate $\phi_g(\bf r)$ fields being applied to extended molecule region.\footnote{Not to the deep contacts and self-energies, which are already at the right chemical potentials.} The potential profile implementing these fields is usually a ramp whose end points lie sufficiently far from the electrodes' surface for the layers of contact material in between to sufficiently screen the local distortions and produce the correct self-consistent potential drop within the extended-molecule region.\footnote{In our implementation a number of models in these two classes are available.} We discuss this further for the case of biased gold-phenyl-gold junctions in section \ref{bias} below.
In order to calculate the current in the presence of a bias voltage, we need to calculate the non-equilibrium density matrix. Our approach is splitting expression \eqref{density2} into the equilibrium term we have used thus far, and a new non-equilibrium correction, given by the following expressions \eqref{density3a}-\eqref{density3b}, analogous to the approach of Stokbro \emph{et al.}:\cite{Stokbro2003a}
\[
\rho = \frac{1}{2 \pi} \int \mathrm{d}\epsilon\; [G(\epsilon) \Gamma_1 G^{\dagger}(\epsilon) f(\epsilon,\mu_1) + G(\epsilon) \Gamma_2 G^{\dagger}(\epsilon) f(\epsilon,\mu_2)],
\]
which may be worked out to yield:
\begin{align}\label{density3a}
\nonumber \rho &= \underbrace{-\frac{1}{\pi}\int \mathrm{d}\epsilon\; f(\epsilon,\mu_1)\im{G(\epsilon)}}_{\rho^\text{A}_\text{eq}} \\
&+ \underbrace{\frac{1}{2\pi}\int \mathrm{d}\epsilon\; [f(\epsilon,\mu_1)-f(\epsilon,\mu_2)]G(\epsilon)\,\Gamma_2(\epsilon) \,G^\dagger(\epsilon)}_{\rho_\text{neq}^\text{A}}
\end{align}
or equivalently:
\begin{align}\label{density3b}
\nonumber \rho &=\underbrace{-\frac{1}{\pi}\int \mathrm{d}\epsilon\; f(\epsilon,\mu_2)\im{G(\epsilon)}}_{\rho^\text{B}_\text{eq}} \\
&+ \underbrace{\frac{1}{2\pi}\int \mathrm{d}\epsilon\; [f(\epsilon,\mu_2)-f(\epsilon,\mu_1)]G(\epsilon)\,\Gamma_1(\epsilon) \,G^\dagger(\epsilon)}_{\rho_\text{neq}^\text{B}}\;.
\end{align}
$\rho_\text{eq,neq}^\text{A}$ and $\rho_\text{eq,neq}^\text{B}$ are two equivalent ways of obtaining the equilibrium and non-equilibrium density matrix, from which we obtain the terms by a weighted average.
The equilibrium terms' integrals may be evaluated as before by complex contour integration, but it is important to observe that the argument underpinning the analytic continuation into the complex plane was the localization of the poles of $G(\epsilon)$ in the lower half-plane. This is no longer true for the more complicated pole structure of terms like $G(\epsilon)\,\Gamma_1 \,G(\epsilon)^\dagger$, and so the non-equilibrium integral must be evaluated along a dense grid as near to the real axis as is reasonable, while avoiding numerical inaccuracies due to nearby poles.
\section{Transport in 1D Systems}\label{Transport1D}
\subsection{Li Chains}
In section \ref{Alignment} we outlined the use of a self-consistent procedure to fix the potential zero and the Fermi level consistently for the full system of extended molecule with contacts, by requiring charge neutrality of a bulk ``extended molecule.'' If we apply this to a 1D Li chain, we obtain a charge-density profile and HOMO wavefunction as illustrated in Fig.~\ref{fg:Li-Charge-Density}, where these are compared with the bulk result obtained from a conventional periodic DFT calculation, using the LDA exchange-correlation functional and a single-$\zeta$ (SZ) basis-set for Li. The lattice spacing (2.876 \AA) for the cell was obtained by energy minimization, using the same LDA functional and basis for consistency.
\begin{figure
\includegraphics[width=.8\columnwidth]{img/Li/Sextuple-Cell}\vspace{.6cm}
\includegraphics[width=\columnwidth]{img/Li/Alignment-System}\vspace{.6cm}
\caption{Bulk charge density profile (solid) and HOMO wavefunction (hatched) calculated in a bulk 1D chain (top) and the converged alignment configuration for our finite extended system (bottom). Both were calculated using LDA and a SZ basis-set. Edge effects on the outer atoms on the finite chain are clearly visible, but in the inner extended-molecule region there is excellent agreement, including the 4-atom periodicity of the wavefunction.\label{fg:Li-Charge-Density}}
\end{figure}
We point out that the exact 4-atom periodicity observed in Fig.~\ref{fg:Li-Charge-Density} is a signature result: we can derive the ``HOMO'' level (the highest occupied state in the infinite system) from a model of fermion sites in a finite chain by filling the outer $s$-orbital of Li at each site. Take a $M+1$-site chain of length $L$, with lattice constant $a$, which will hold $2(M+1)$ electrons. Each electron will sit in a band formed by a standing wave pattern because of the periodic boundary conditions, and so:
\begin{align*}
\psi_n(x) = e^{i\, \pi n x/L}\;.
\end{align*}
The states may be labeled by the $2(M+1)$ set of $k_n = \pm\frac{\pi n}{L}$ instead, where the maximum value of $N$ is $M/2$ such that:
\begin{align}\label{lambda1}
\lambda_\text{max} &= \frac{2\pi}{k_\text{max}} \sim 4a
\end{align}
Consequently, the wavelength of the highest occupied mode in the infinite chain is 4 lattice spacings, which is exactly what we see in Fig.~\ref{fg:Li-Charge-Density}.
The PDOS and transmission are illustrated in Fig.~\ref{fg:transmission-Li}, where we note that the transmission has a clear plateau at $G_0$ corresponding to the transmission through a single channel over the range of energy corresponding to nonzero density of states in the chain. The prediction of the wavefunction shape of the highest occupied mode is general for a single electron in an outermost atomic shell without degeneracy, such as the Li $2s$ orbital, as opposed to the Al chain (see below). We also note oscillations in the DOS and transmission, which likely reflect the finite extent of the contacts (the edges acting as scattering potentials), and the bad screening of a 1D chain in particular.\\
\begin{figure
\includegraphics[width=\columnwidth]{img/Li/Multiplot}
\caption{(a) Zero-bias transmission through and (b) density of states of the 1D Li chain (using a SZ basis set), showing a single $s-$band providing transport as we expect, with a range in energy corresponding to the (projected) DOS on each part of the model structure.}
\label{fg:transmission-Li}
\end{figure}
We next performed a zero-bias transport calculation with a H$_2$ molecule placed in between the chain contacts. We calculate the transmission and PDOS for the structure under zero bias, see Fig.~\ref{fg:transmission-LiH2Li}.
We observe that the transmission is reduced in the presence of the H$_2$, an effect of H$_2$ partially interrupting the transport path through the s-orbitals in $1$s$^22$s$^1$ Li chain (transmission $\sim 1$, effectively an ideal Landauer conductance channel). The H$_2$ LUMO does have an s-orbital character, and so there is transport as it does in fact couple more broadly to a number of Li states, but its coupling to the Li is different, so that the transmission becomes somewhat attenuated at different energies along the band.
On the high-energy side of the DOS plots, we also note a lone peak in the extended-molecule DOS: this corresponds to the LUMO orbital of H$_2$, and since its resonance is beyond the limited extent of the Li chain's DOS, it should not couple in transport. That is indeed what we observe in the transmission: the lack of a feature at the corresponding energy in the top panel of Fig.~\ref{fg:transmission-LiH2Li}. The HOMO and LUMO+1 levels, by contrast, are considerably further away, and do not couple at all.\\
\begin{figure
\includegraphics[width=\columnwidth]{img/Li-H2-Li/Multiplot}
\caption{(a) Zero-bias transmission through and (b) density of states of the 1D Li chain with an H$_2$ molecule (using a SZ basis set on Li, DZ basis on H$_2$). We see a decline of the transmission when a H$_2$ molecule is placed in the junction. Given the small size of the molecule, its primary effect is to slightly weaken the coupling in the chain.}
\label{fg:transmission-LiH2Li}
\end{figure}
A similar analysis can be performed for experimentally more realistic Al chains. The key difference is the addition of electrons, which now contribute both $s-$ and $p-$ bands for transport, as we discuss in appendix \ref{Al.Chains}, where we find otherwise very similar results.
\section{Transport in General 2-terminal Systems}\label{Transport3D}
\subsection{Building Au Contacts}
Before we proceed to transport calculations using ``bulky'' Au contacts, which will be used as a building block in all following sections, we first discuss their construction. We will emphasize, in particular, the difference between applying transverse periodic boundary conditions\xspace and their omission. We begin the discussion with figures Fig.~\ref{fg:Au.Transmissions}-\ref{fg:Au.geoms}, where we illustrate 3 representative geometries one might use for the contacts, and the transmission through their bulk structure (\emph{without} molecules). These are all FCC stacked with a (111) face perpendicular to the axis, and we compare a transverse $2\times 2$--atom surface with the $3\times 3$--surface case, the latter both with and without {periodic boundary conditions\xspace}. Calculations were performed with the LDA functional and a SZ basis with 11 valence electrons.
\begin{figure
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au.pbc/3x3/Transmission_63}}\\
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au.nopbc/3x3.slanted/Transmission_42}}
\caption{Transmission through the ``bulk'' Au contacts (LDA calculations using a SZ, 11$e$ basis per atom). {\bf a)} with and {\bf b)} without periodic boundary conditions\xspace. Note the transmission plateaus at integer units of the conductance quantization $G_0$, as we expect from a system that is essentially a larger-diameter version of a single Au-atom chain. }\label{fg:Au.Transmissions}
\end{figure}
In appendix \ref{AlignmentTests} we show the convergence of the alignment shifts (Figs.~\ref{fg:Au.ShiftConvergence1}-~\ref{fg:Au.PDOS.Compares}), with the conclusion that in contrast to the case without periodic boundary conditions\xspace, the shifts obtained in order to converge the extended-molecule structure with periodic boundary conditions\xspace can be quite large.\footnote{We emphasize that this is an algorithmically-determined rather than an arbitrarily imposed shift, and that as we illustrate in Fig.~\ref{fg:Au.PDOS.Compares}, the PDOS indicate that the structure is correctly converged.}
It appears that for the case of periodic boundary conditions\xspace, the bulk run in BAND is significantly offset in potential with respect to the alignment and transport runs. The strong difference with the alignment run argues for fixing the Fermi level via the correction $\ensuremath{\Delta\phi} _0+\ensuremath{\Delta\phi} _1$ (as opposed to simply neglecting a numerical error incorrectly assumed small). The continuing difference in the transport run further argues for a dynamic (runtime) correction $\ensuremath{\Delta\phi} _0$, as implemented, rather than assuming a static correction $\ensuremath{\Delta\phi} _0$ in transport.
In Fig.~\ref{fg:Au.Transmissions}, the typical transmission characteristics of these ``bulk'' junctions exhibit clear conductance plateaus, as we expect from what is essentially a ``bulky'' monatomic chain. We note that the number of channels found is similar near the Fermi level, while further away, in particular in the region from -8 to -2 eV, the structure \emph{without} periodic boundary conditions\xspace is considerably noisier, and has fewer channels.
This may be due in part to the electrons moving to the surface boundaries in the structure without periodic boundary conditions\xspace, effectively reducing the number of transport channels.
\begin{figure
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.nopbc/bdt-2x2-slanted}}\\
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.nopbc/bdt-3x3-slanted}}\\
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.nopbc/3x3/geom-2}\label{fg:unslanted}}
\caption{Au contacts' geometry for {\bf a)} the $2\times 2$ surface case, {\bf b)} the $3\times 3$ surface case, both with hollow-site binding with 2.40 \AA\xspace Au-S distance. {\bf c)} An alternate $3\times 3$ surface used in calculations with bias, resp. with periodic boundary conditions, \emph{cf}. Fig.~\ref{fg:Au-BDT-Au_3x3_pbc_geom_II}. Calculations performed using the LDA functional and a SZ basis with 11 valence electrons.}\label{fg:Au.geoms}
\end{figure}
Having examined the alignment, convergence and bulk structure of the extended-molecules in different cases, we now proceed to single-molecule calculations. We will mainly use $3\times 3$ surfaces of Au, both with and without periodic boundary conditions\xspace.
\subsection{Benzenedithiol Junctions}
We now consider the well-studied ``test case'' of a gold-benzenedithiol-gold (Au--BDT--Au) junction.\cite{Xue2003a,Xue2003b,Stokbro2003,Stokbro2003a,Nara2004,Pontes2006} The contacts are designed in the same way as in the previous section, with Au (111) faces consisting of $2\times 2$ and $3\times 3$ atoms,
shown in Fig.~\ref{fg:Au.geoms}. Except where stated otherwise, we perform transport calculations in our code and gas-phase calculations in ADF using the LDA functional with a SZ basis on the Au contacts and a TZP basis on the molecule. In Fig.~\ref{fg:AuBDT.Transmission1} we present the results of our calculations without periodic boundary conditions\xspace.
\begin{figure
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.nopbc/2x2.slanted/Transmission_24}\label{fg:2x2}}\\
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.nopbc/3x3.slanted/Transmission_27}\label{fg:3x3}}\\
\caption{Transmission through the Au--BDT--Au junction, using {\bf a)} $2\times 2$ and {\bf b)} $3\times 3$
Au contacts without periodic boundary conditions. We see that the transport gap opens, becoming recognizably linked to the smooth structure visible below in Fig.~\ref{fg:Au-BDT-Au_3x3_pbc_geom_II} for the case of periodic boundary conditions\xspace. The main peaks map between the two sets of calculations, and we illustrate the orbitals that play the dominant role for the $3\times 3$ case in Fig.~\ref{fg:AuBDT.orbitals} below.}\label{fg:AuBDT.Transmission1}
\end{figure}
We first note that
on increasing the size of the surface perpendicular to transport, there is a
relatively quick convergence to a recognizable result with a broad HOMO-like peak below $\epsilon_f$, followed by a 2--3 eV low-conductance gap separating it from a LUMO peak beyond the gap, around 2 eV. This confirms that the size of contacts does matter to the calculation, though the major features already become established for modest contact sizes.
\begin{figure
\subfloat[LUMO+1, acts as LUMO]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-LUMO+1}}
\subfloat[LUMO, does not couple]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-LUMO+2}}\\
\subfloat[HOMO]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-LUMO}}
\subfloat[H$_\text{A}$: apparent HOMO state on fragment]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-HOMO}\label{fg:appH}}\\
\subfloat[H$_\text{B}$: apparent HOMO-1 state on fragment]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-HOMO-1}\label{fg:appH-1}}
\subfloat[HOMO-1]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-HOMO-2}}\\
\subfloat[HOMO-2, does not couple]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-HOMO-3}}
\subfloat[HOMO-3, couples below -2eV]{\includegraphics[width=.5\columnwidth]{img/Au-BDT-Au.nopbc/3x3/fragment-au-HOMO-4}}
\caption{Transport-coupled orbitals of the BDT junction,
ordered by decreasing chemical potential. {\bf a)--c)} and {\bf f)--h)} are the fragment's orbitals nearest the Fermi level, which are labeled by correspondence to their gas-phase counterparts. {\bf d)--e)} are two examples of intermediate states that are the present in the fragment but not the neutral BDT molecule, and survive the thiolate coupling to Au adatoms instead of the terminal -SH bond.}\label{fg:AuBDT.orbitals}
\end{figure}
\begin{figure
\subfloat[]{\includegraphics[width=\columnwidth]{img/Phenyls/bdt_peaks}}\\
\subfloat[]{\includegraphics[width=\columnwidth]{img/Phenyls/bdt_peaks2}}
\caption{Transmission and peak decompositions for the $3\times 3$ Au--BDT--Au junction. Distance between clearest frontier peaks at -0.26 eV and 1.68 eV suggests an effective gap of roughly 1.93 eV. (a) Illustrates the decomposition onto the main gas-phase orbitals, while (b) also includes the H$_\text{A}$ and H$_\text{B}$ orbitals of Fig.~\ref{fg:appH} and Fig.~\ref{fg:appH-1}.\label{fg:bdt.peaks}}
\end{figure}
Fig.~\ref{fg:AuBDT.orbitals} shows the main orbitals derived from the BDT molecule, labeled by their correspondence to the gas-phase orbitals. We use these in order to construct Fig.~\ref{fg:bdt.peaks}, showing the compositions of the peaks in the transmission through the Au--BDT--Au junction near $\epsilon_f$.
We have determined these by using a fragment-decomposition technique, outlined in \ref{decompositions}, in which we project the eigenstates of the transport calculation onto the orbitals of a molecular fragment. As a fragment we use the gas-phase BDT molecule geometry with thiolate bonds to a single Au atom on each side (outermost H's of the gas-phase BDT are removed, leaving an Au--S bond), as expected for the preferred bonding of a molecule ending on a thiol group, \emph{e.g.} BDT, to an Au surface.\cite{Love2005,Hoft2006,Romaner2006}
We can identify the orbitals of the fragment with those of either the BDT molecule or radical, and this flexibility also provides extra information on the complicated orbital compositions which we find in the junction. We find that adding the Au adatoms induces the formation of hybrid Au--BDT--Au states which may couple well in transport, labeled H$_\text{A}$ and H$_\text{B}$ in Fig.~\ref{fg:AuBDT.orbitals}, to reflect their energy ordering as the ``apparent'' HOMO and HOMO-1 states on the fragment. We discuss their role in more detail later. The rest of the states in Fig.~\ref{fg:AuBDT.orbitals} are labeled by their correspondence to the orbitals of gas-phase BDT. We now focus on the geometry of Fig.~\ref{fg:3x3} in particular, as we later use it to model OPE-2 and OPE-3 as well.
We find that the broad HOMO-resonance appears to be mainly composed of 2 separate peaks, which we identify by our decomposition analysis as the HOMO and HOMO-1 peaks of the gas-phase BDT molecule, with a bit of HOMO-3 playing a role as well. H$_\text{A}$ and H$_\text{B}$ also appear here. In the fragment they are split by about 120 meV, and appear as a result of hybridization with Au, or more generally, for collinear termination on the thiol (\emph{i.e.} they also occur when the -SH bond in gas-phase BDT is collinear). This suggests that they may represent a bonding/anti-bonding pair which interferes nearly perfectly destructively, and as a result does not contribute much to transport.\cite{Hoffmann1971,Solomon2010} In this context we further note that despite the $\sim 120$ meV splitting, they indeed consistently appear in roughly equal measure in each contribution in Fig.~\ref{fg:bdt.peaks}b, once coupled to Au.
The LUMO and HOMO-2 states, by contrast, are sufficiently localized to the center of the molecule that do not couple in transport; rather, for the unoccupied states it is the LUMO+1 which appears as the lowest unoccupied transport peak above the transport gap. We return to this point in discussing the OPE-series in the next section.
We do find the HOMO-2 peak present in our decomposition around -2.45 eV, and as a considerably more pure state, consistent with the lack of coupling to the Au contacts. By contrast, the HOMO-3 has an orbital structure which suggests coupling in transport, and it is present, mixed with the HOMO and HOMO-1 states, in Fig.~\ref{fg:bdt.peaks}. This may suggest an analogy to the HOMO-2 states of the OPE-series.\\
Finally, we also remark on the presence of some small discontinuities in the transmissions in Fig.~\ref{fg:AuBDT.Transmission1}, in the $3\times 3$ case near \emph{e.g.} -0.4 eV, -0.1 eV and 0.5 eV. We have investigated these using the projected DOS on the molecule proper, extended molecule and deep contacts. We find that these are not numerical artifacts, but rather are related to effects in the potential in the contacts. While these may be relevant for very sharp, needle-like contacts, they would probably not play a role for relatively large, bulk-like electrodes. \\
While we remarked that the results of Fig.~\ref{fg:AuBDT.Transmission1} indicate a gradual convergence towards a ``bulk'' face result (the single benzenedithiol atom coupled to an infinite plane of Au on each side), they should be distinguished from the ``classic'' Au--BDT--Au junction results calculated using DFT+NEGF in the literature.\cite{Stokbro2003,Xue2003a,Xue2003b}
The difference is the absence of periodic boundary conditions here, a relatively important modeling decision not typically discussed in the early literature, in large part because few codes allow for explicitly breaking transverse periodicity. We illustrate this difference explicitly in Fig.~\ref{fg:AuBDT.Transmission2} below, which should be compared with Fig.~\ref{fg:3x3}.
The implications of the use of periodic boundary conditions for a junction with such a small face evident in Fig.~\ref{fg:Au-BDT-Au_3x3_pbc_geom_II}, where we see that the model in this case is qualitatively more similar to a self-assembled monolayer than to a true single-molecule configuration. Conversely, the geometry without periodic boundary conditions\xspace are particularly useful for modeling the small, needle-shaped contacts used in break-junction experiments. This difference has consequences for the conductance of the system,\cite{Liu2005} but for larger inter-molecular separation this need not be an issue per se, as long as the system being modeled is not actually needle-like in geometry.\\
\begin{figure
\subfloat[]{\label{fg:AuBDT.Transmission2}\includegraphics[width=.85\columnwidth]{img/Au-BDT-Au.pbc/Transmissions_Comparison} }\\
\subfloat[]{\label{fg:Au-BDT-Au_3x3_pbc_geom_II}\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.pbc/Au-BDT-Au_3x3_pbc_geom_II}}\caption{{\bf a)} Transmission through the Au--BDT--Au junction with periodic boundary conditions\xspace, compared with the previous result without periodic boundary conditions\xspace,
Fig.~\ref{fg:AuBDT.Transmission1}. {\bf b)} Implied geometry of the model $3\times 3$ Au--BDT--Au junction, using periodic boundary conditions. Overall, we observe a further opening of the gap and a broadening of the HOMO-like peaks, which themselves are reduced in magnitude back to $G_0$ transmission.}
\end{figure}
Finally, for Fig.~\ref{fg:AuBDT.Transmission2} we find the same general picture in terms of peaks (compositions not illustrated).
The predominance of the HOMO, HOMO-1 and their ``apparent'' counterpart states in transport is, moreover, in excellent agreement with the findings of Stokbro and others.\cite{Stokbro2003,Kondo2006}
Our work indicates that the convergence towards this bulk result is primarily dependent on having a sufficient number of transport channels available in the contacts to couple to, as in Fig.~\ref{fg:Au.Transmissions}. This has implications for contacts which do not couple to as many channels, where a broad peak from the strongly-coupled regime may break apart into a number of narrower (less strongly-coupled) resonances, though still enabling transport. A noteworthy feature is that the transmission \emph{at} the Fermi level\ $T(\epsilon_f)$ may be significantly reduced, bringing the value closer to the experimental one,\cite{Ulrich2006,Hybertsen2008} where one typically would expect to be in the weakly-- rather than strongly-coupled regime.
\subsection{OPE--series Junctions}
We now proceed by considering the first two of the thiol-anchored oligophenylene-ethynylene family of molecules. Except where stated otherwise, we again perform transport calculations in our code and gas-phase calculations in ADF using the LDA functional with a SZ basis on the Au contacts and a TZP basis on the molecule. We show the results of modeling OPE-2 and OPE-3 single-molecule junctions, with 2 and 3 phenyl rings respectively; the junction geometries are illustrated in Fig.~\ref{fg:OPE.geom}a--b respectively. These calculations use the same contacts as with BDT, and therefore have a common and well-determined Fermi level $\epsilon_f$, as discussed previously. These molecules have also been studied experimentally as promising benchmark systems in molecular electronics.\cite{Reichert2002,Mayor2003,Xiao2005,Huber2008}
\begin{figure
\subfloat[Au--OPE-2--Au Junction Geometry]{ \includegraphics[width=\columnwidth]{img/OPE/ope2-3x3-slanted}\label{fg:OPE2.geom} }\\
\subfloat[Au--OPE-3--Au Junction Geometry]{ \includegraphics[width=\columnwidth]{img/OPE/ope3-3x3-slanted}\label{fg:OPE3.geom} }
\caption{Geometry of $3\times 3$ atom (111) surface Au--OPE-2--Au and Au-OPE-3--Au junctions, both without periodic boundary conditions. Hollow-site binding with 2.40 \AA\xspace Au-S distance, compare Fig.~\ref{fg:Au.geoms}.}\label{fg:OPE.geom}
\end{figure}
\begin{figure
\includegraphics[width=\columnwidth]{img/Phenyls/ope2_peaks}
\caption{Peak compositions near $\epsilon_f$ for the Au--OPE-2--Au junction. Distance between clearest frontier peaks at -0.25 eV and 1.33 eV suggests an effective gap of roughly 1.6 eV.}\label{fg:OPE2.transmission}
\end{figure}
\begin{figure
\subfloat[LUMO, see Fig.~\ref{fg:AuBDT.orbitals}]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-LUMO+1}}
\subfloat[HOMO]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-LUMO}}\\
\subfloat[H$_\text{A}$: apparent HOMO state on fragment]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-HOMOb}}
\subfloat[H$_\text{B}$: apparent HOMO-1 state on fragment]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-HOMOa}}\\
\subfloat[HOMO-1]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-HOMO-1}}
\subfloat[HOMO-2]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-2/fragment-au-HOMO-2}}\\
\caption{{\bf a)--f)} Fragment transport-coupled orbitals nearest the Fermi level (compare Fig.~\ref{fg:AuBDT.orbitals}). We note again H$_\text{A}$ and H$_\text{B}$, the ``apparent'' HOMO and HOMO-1 states, which are now more localized at the interface and whose wavefunctions do not extend all the way across the molecule.}\label{fg:OPE2.Combi}
\end{figure}
The transmission through a junction composed of OPE-2 coupled to $3\times 3$ atom Au (111) face contacts is illustrated in Fig.~\ref{fg:OPE2.transmission}, where the peak decompositions are constructed as outlined above for BDT. The fragment states to which the figure refers are illustrated in Fig.~\ref{fg:OPE2.Combi}, again labeled according to the gas-phase OPE-2 molecule's orbitals. In combination with these orbitals, we analyze the nature of transport, and the relation to the single-phenyl BDT system discussed previously.\\
The electronic structure near $\epsilon_f$ immediately recalls the results for the BDT junction. We again find a broad resonance, now split over three peaks below the Fermi level which are identified with the HOMO-2, --1 and HOMO states. The broad peaks are further composed of mixtures with the H$_\text{A}$ and H$_\text{B}$ states of the Au-OPE fragments and Au-derived states that are mainly localized at the Au-S bond. Beyond the transport gap, at 1.5 eV, we again find a peak which is identified predominantly with the gas-phase LUMO. This is a state which on the OPE-2 (and OPE-3) junction has an orbital symmetry that immediately recalls the LUMO+1 of BDT. The LUMO+1 states on these two molecules, conversely, recall the LUMO of BDT, and do not play a strong role in transport due to the localization of electrons away from the contacts.\\
\begin{figure
\includegraphics[width=\columnwidth]{img/Phenyls/ope3_peaks}
\caption{Peak compositions near $\epsilon_f$ for the Au--OPE-3--Au junction. Distance between clearest frontier peaks at -0.25 eV and 1.52 eV suggests an effective gap of roughly 1.8 eV.}\label{fg:OPE3.transmission}
\end{figure}
\begin{figure
\subfloat[LUMO]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-LUMO+1}}
\subfloat[HOMO]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-LUMO}}\\
\subfloat[H$_\text{A}$: apparent HOMO state on fragment]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-HOMOb}}
\subfloat[H$_\text{B}$: apparent HOMO-1 state on fragment]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-HOMOa}}\\
\subfloat[HOMO-1]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-HOMO-1}}
\subfloat[HOMO-2]{\includegraphics[width=.5\columnwidth]{img/OPE/OPE-3/fragment-au-HOMO-2}}\\
\caption{{\bf a)--f)} Fragment transport-coupled orbitals nearest the Fermi level (compare figures Fig.~\ref{fg:AuBDT.orbitals} and Fig.~\ref{fg:OPE2.Combi}). We again note H$_\text{A}$ and H$_\text{B}$, again the ``apparent'' HOMO and HOMO-1 states, and analogues of Fig.~\ref{fg:OPE2.Combi} {\bf c)--d)} which are again localized mostly near the S atom, and as with OPE-2 have wavefunctions which do not extend all the way across the molecule.}\label{fg:OPE3.Combi}
\end{figure}
\begin{figure
\includegraphics[width=\columnwidth]{img/OPE/Transmissions_Slanted_log}
\caption{Comparison of transmissions on log-scale showing evolution of main features near the Fermi level as molecule in junction is varied from 1 to 3 phenyl rings. Opening of the transport gap is visible, as well as narrowing of the peaks near $\epsilon_f$ and a general spectral shift backwards of the HOMO-like peaks.}\label{fg:MultiRingComparison}
\end{figure}
For OPE-3, the transmission is illustrated in Fig.~\ref{fg:OPE3.transmission} together with the peak decompositions. The orbitals referred to are illustrated in Fig.~\ref{fg:OPE3.Combi}, which further confirms the picture nature of transport in this family. When comparing with the Au--BDT--Au and Au--OPE-2--Au junctions' results, it appears that the gap slightly reopens. This, however, still appears to be part of a progression towards a smaller transport gap for the longer molecules, following the trend towards smaller HOMO-LUMO gap. This is illustrated in the log-scale plot of Fig.~\ref{fg:MultiRingComparison}, where we show the transmission for OPE-4 and OPE-5 junctions as well.
Again, it is the gas-phase HOMO which dominates the conductance near the Fermi level, with the HOMO-1 and HOMO-2 below it composing the lower-lying peaks. The LUMO dominates beyond the transport gap around 1.5--2 eV. The LUMO of OPE-3 again recalls the LUMO+1 orbital of BDT found to compose the ``effective LUMO'' peak there, and so we confirm the role of the orbital symmetries between the respective ``LUMO,'' HOMO, HOMO-1 and HOMO-2 states for each of the three molecules.
The H$_\text{A}$ and H$_\text{B}$ states, see Fig.~\ref{fg:OPE3.Combi}, are likewise present in all 3 junctions, but as the molecule becomes larger, they become more localized in nature than conjugated, and so should play progressively less of a role in transport through the longer molecules of the family. However, in practice, we find them present in roughly similar proportion to the HOMO and HOMO-1 states in the broad peaks right below $\epsilon_f$ in our decompositions for all 3 systems, as well as in the low-conductance transport gap, which suggests that, as argued above, these two states may not really be contributing to transport.
The big picture then, appears to be a slightly erratic change of the gap, which seems to converge from the third or fourth member of the OPE$-n$ family on, narrowing the gap as the number of phenyl-rings in the junction molecule increases. As pointed out by Ke \emph{et al.},\cite{Ke2007} this should converge to a gap similar to the infinite-OPE-chain band gap of $\sim 1.7$ eV,\footnote{The value of $\Delta\sim 1.72$ eV calculated by us using the BAND code, with 1D periodicity using LDA with a TZP basis set to match the transport calculations; compare $\sim 1.5$ eV as calculated using GGA with unspecified basis set, by Ke \emph{et al.}} dominated by the molecular orbitals as the influence of the contacts begins to decrease with wire length. We remark that using carbon nanotube contacts, they observe similarly erratic behavior where the gap-size is concerned. Finally, we remark on the clear trend towards steadily lower values of $T(\epsilon_f)$ as the molecular wire length increases, also visible in Fig.~\ref{fg:MultiRingComparison}.
\subsection{Finite Bias Calculations}\label{bias}
Finally, we briefly consider calculations of transport through BDT under bias, using the perpendicular-face contacts of Fig.~\ref{fg:unslanted}, and the same basis set as before.
In Fig.~\ref{fg:BDT_bias_profile} we show the potential drop averaged transverse to the transport direction, and observe that the potential is already relatively stable within a few layers of the extended molecule's inner surface. The potential drop is mostly over the thiol end-groups, which may be contrasted with a slightly lower slope of the potential averaged over the core benzene fragment within the extended molecule region, in agreement with the results of Datta \emph{et al.}\cite{Liang2004} and Xue and Ratner.\cite{Xue2002}
\begin{figure
\subfloat[]{\includegraphics[width=.95\columnwidth]{img/Au-BDT-Au.bias/Fixed-vs-Iterative01b} \label{fg:BDT_bias_profile}}\\
\subfloat[]{\includegraphics[width=.8\columnwidth]{img/Au-BDT-Au.bias.slanted/Transmissions_Comparison_3} \label{fg:AuBDT.bias}}
\caption{{\bf a)} Potential drop with fixed ramps starting at $0.5d, 1.5d$, and $2.5d$ from the innermost Au layer of the device region, where $d$=2.88\AA\xspace the interlayer spacing. $500$mV bias is applied, results are relative to a zero-bias self-consistent calculation. Molecule with nearest Au neighbors indicated, together with vertical black lines showing position of subsequent layers of Au. Note the decreased slope of the potential drop over the benzene ring, as compared with the Au-S bond region. {\bf b)} Transmission through the biased $3\times 3$ Au--BDT--Au junction, as compared with the unbiased result, both without periodic boundary conditions\xspace.}
\end{figure}
We also illustrate the influence of adjusting the location at which the ramp begins further back into the junction. We see that the largest charge accumulation at the interface occurs when the ramp is initiated between the first layers at $-0.5d$ from the innermost Au layer (where $d$ is the interlayer spacing), suggesting that it should begin further back to avoid this. However, we see that as we move the ramp further back, the junction has more difficulty screening the applied potential, reflected in the longer extent of its deviation from $\pm250$mV deeper into the contacts. This implies practical limitations on minimum junction depth, which are likely more relevant in our models without periodic boundary conditions\xspace, given their lower capacity to screen high fields inside the conducting leads.
In Fig.~\ref{fg:AuBDT.bias} we plot the transmission on logarithmic scale, compared with the zero-bias calculation of Fig.~\ref{fg:3x3}. We see that the main effect is the shift in Fermi level and the attenuation of the peaks, as is commonly observed in the presence of an electric field. There do not appear to be further large changes for this relatively small bias, and all prominent features are still clearly recognizable.\\
\section{Conclusions}
A combination of the NEGF approach with a DFT description of the bulk contacts is a flexible, efficient and scalable computational method for transport calculations on realistic geometries of single-molecule devices. A key advantage of our implementation is the ability to break periodicity in 1-3 dimensions within a band-structure code, which allows accurate simulation of the metal contacts for different systems, while allowing us to simulate geometries akin to \emph{e.g.} mechanically controlled break junctions without the need to impose periodic boundary conditions\xspace.
We have studied one-dimensional chains and found transport behavior that is expected based on simple theoretical considerations, and then extended our scope to three-dimensional junctions involving a series of phenyl-ring molecules from the OPE-family with related gas-phase electronic structures. For benzenedithiol we recover the signature transmission characteristic with periodic boundary conditions\xspace, but if we go beyond this by breaking periodicity we gain a deeper understanding of the more complex transmission-peak structure, as the simple broad HOMO-like peak is separated into smaller peaks that we identify with particular molecular orbitals hybridizing with Au in transport. This may better reflect what happens in experiments with sharp nanocontacts.
Such characteristic features are seen to evolve in a clear way for the OPE-based molecular wires as well, with the orbitals determining transport near the Fermi level clearly related to the orbital symmetries we identify across the family of molecules. In particular, we see a related cluster of occupied orbitals near $\epsilon_f$ which dominate transport. As we consider progressively longer molecular wires, we find an at first erratic trend, leading finally to convergence in reducing the transport gap between these and the lowest unoccupied-level resonances. Finally, in the low-bias regime, we find that for the simplest phenyl junction the symmetry of coupling ensures that we find no significant spectral shifts, but we do find amplification and attenuation of specific transmission features.
In looking towards the future, we would note first the utility of the implementation of a gate,\cite{Stadler2008a,Kaasbjerg2008} an end to which work is already underway in our group. Beyond adding a gate as a next step, we envision an extension to a model for the weak-coupling regime using discrete-charge-state Green's functions, along the lines of recent work by Mirjani and Thijssen,\cite{Mirjani2011} for which we anticipate the utility of our underlying charge-constrained DIIS algorithm, here used for convergence acceleration.
\begin{acknowledgments}
We acknowledge financial support by the FOM Foundation within Project-86 and from the EU FP7 program under the ``ELFOS'' grant agreement. This work was also sponsored by the National Computing Facilities Foundation for the use of supercomputer facilities, with financial support from the Netherlands Organization for Scientific Research, NWO. We would also like to thank M. Leijnse for the initial development work in BAND, P. Philipse and A. Yakovlev for their assistance in the development process, and G. Labadze and J.S. Seldenthuis for fruitful discussions.
\end{acknowledgments}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 4,043
|
{% extends "tardis_portal/portal_template.html" %}
{% load static from staticfiles %}
{% block script %}
<script type="text/javascript">
$('.canWrite').live('click', function(){
if($(this).is(':checked'))
{
var canReadBox = $(this).siblings(".canRead");
canReadBox.attr('disabled', true);
canReadBox.attr('checked','checked')
}
else
{
var canReadBox = $(this).siblings(".canRead");
canReadBox.attr('disabled', false);
canReadBox.removeAttr('checked')
}
});
var refreshFunctionFor = function($toggle) {
return function(data, textStatus, jqXHR) {
if (data.success) {
if ($toggle.hasClass('tokens_shown')) {
$toggle.click();
$toggle.click();
} else {
$toggle.click();
}
} else {
alert('An error occurred. Please try again later');
}
};
};
$('.token_delete').live('click', function(evt){
evt.preventDefault();
var $toggle = $($(this).attr('data-toggle_selector'));
$.post(this.href, {}, refreshFunctionFor($toggle));
});
$(document).ready(function() {
$('.create_token_link').click(function(evt){
evt.preventDefault();
var $toggle = $(this).siblings('.access_list_token_toggle');
$.post(this.href, {}, refreshFunctionFor($toggle)); // TODO error-handling
});
//beginswith, endswith
String.prototype.beginsWith = function(t, i) { if (i==false) { return
(t == this.substring(0, t.length)); } else { return (t.toLowerCase()
== this.substring(0, t.length).toLowerCase()); } }
String.prototype.endsWith = function(t, i) { if (i==false) { return (t
== this.substring(this.length - t.length)); } else { return
(t.toLowerCase() == this.substring(this.length -
t.length).toLowerCase()); } }
$('.access_list1').hide().end().find('.access_list_user_toggle').click(function() { $(this).siblings('.access_list1').toggle(); });
$('.access_list2').hide().end().find('.access_list_group_toggle').click(function() { $(this).siblings('.access_list2, .access_list3').toggle(); });
//$('.access_list3').hide().end().find('.access_list_external_toggle').click(function() { $(this).next().toggle(); });
$('.access_list3').hide();
$('.access_list_token_toggle').click(function(evt){
evt.preventDefault();
var $this = $(this);
var $access_list = $this.siblings('.access_list');
var $icon = $this.find('span')
$this.toggleClass('tokens_shown');
$icon.toggleClass('ui-icon-circle-triangle-e ui-icon-circle-triangle-s');
if ($this.hasClass('tokens_shown')) {
$access_list.load(this.href);
$access_list.show();
} else {
$access_list.hide();
}
});
$('.token_url').live('click', function(evt) {
evt.preventDefault();
});
$('.token_url').live('mouseup', function(evt) {
if (evt.which == 1) { // left-click
if (confirm('Click OK to login as a token user.\nOr click cancel and right-click and "copy shortcut" or "copy link location" or similar')) {
window.location.href = this.href;
}
}
});
var loadingHTML = "<img src='{% static "images/ajax-loader.gif"%}'/>";
// Format a row for display in the user autocomplete dropdown.
function formatRow(row) {
username = '';
for (var i = 0; i < row.auth_methods.length; i++) {
auth_method = row.auth_methods[i].split(':');
user = auth_method[0];
auth_method = auth_method[2];
username += ' "' + user + '" at ' + auth_method + '<br/>';
}
username = '<br/><small>Accounts:<br/>' + username + '</small>';
return displayName(row) + username;
}
// Get a sensible name to display in a text field based on a user object.
function displayName(row) {
if (row.first_name && row.last_name)
name = row.first_name + ' ' + row.last_name;
else if (row.first_name)
name = row.first_name;
else if (row.last_name)
name = row.last_name;
else if (row.email)
name = row.email;
else
name = row.username;
return name;
}
// Convert list of user dicts to data objects for JQuery autocomplete.
function parseUserList(data) {
var array = new Array();
for (var i=0;i<data.length;i++) {
array[array.length] = { data: data[i], value: data[i].toString(), result: displayName(data[i]) };
}
return array;
}
// user access list
$(".access_list_user_toggle").toggle(function(){
var href = $(this).attr("href");
var $target = $(this).siblings('.access_list1');
$target.html(loadingHTML + "</br>");
$target.load(href, function() {
$(document).ready(function() {
$("#id_entered_user").keypress(function() {
// Reset autocomplete user when typing in the user edit field.
$(this).siblings("#id_autocomp_user").val('');
$(this).siblings("#id_authMethod").attr('disabled', '');
});
// Load user list and activate field autocompletion
$.ajax({
'dataType': 'json',
'url': '/ajax/user_list/',
'success': function(users) {
$("#id_entered_user").autocomplete({
'source': _.bind( function(query, callback) {
var authMethod = $("#id_authMethod").val();
callback(
userAutocompleteHandler(
query.term, this.users, authMethod));
}, { 'users': users })
});
}
});
$("#user.form_submit").unbind('click');
$("#user.form_submit").click(function(event) {
event.preventDefault();
var entered_user = $(this).siblings("#id_entered_user").val();
var autocomp_user = $(this).siblings("#id_autocomp_user").val();
if (autocomp_user != "") {
// Use the details from the autocomplete.
autocomp_user = autocomp_user.split(":");
var username = autocomp_user[0];
var authMethod = autocomp_user[1];
} else {
// Autocomplete failed. Use the entered username as-is.
var username = entered_user;
var authMethod = $(this).siblings("#id_authMethod").val();
}
var experiment_id = $(this).siblings(".experiment_id").val();
var users_div = $(this).parents('.access_list1').children('.users');
var canRead = $(this).siblings(".canRead").is(':checked');
var canWrite = $(this).siblings(".canWrite").is(':checked');
var canDelete = $(this).siblings(".canDelete").is(':checked');
var permissions = '/?authMethod=' + authMethod + '&canRead=' + canRead + '&canWrite=' + canWrite + '&canDelete=' + canDelete;
action = experiment_id + '/access_list/add/user/' + username + permissions;
$.ajax({
'async': false,
'global': true,
type: "GET",
url: action,
success: function(data) {
if (data.beginsWith("<div class=", true) == true) {
users_div.hide().append(data).fadeIn();
// todo this is a duplicate function..
$(".remove_user").unbind('click');
$(".remove_user").click(function() {
var href = $(this).attr("href");
remove_user = $(this);
$.ajax({
'async': false,
'global': false,
'url': href,
'success': function (data) {
val = data;
if(val == "OK") {
remove_user.fadeOut(300, function(){ remove_user.parents('.access_list_user').remove(); });
}
else { alert(val); }
}
}); // end ajax
return false;
}); // end remove user
}
else {
val = data;
alert(val);
}
},
error: function(data) { alert('Error adding user'); }
});
return false;
});
$(".remove_user").unbind('click');
$(".remove_user").click(function() {
var href = $(this).attr("href");
remove_user = $(this);
$.ajax({
'async': false,
'global': false,
'url': href,
'success': function (data) {
val = data;
if(val == "OK") {
remove_user.fadeOut(300, function(){ remove_user.parents('.access_list_user').remove(); });
}
else { alert(val); }
}
}); // end ajax
return false;
}); // end remove user
});
});
var $icon = $(this).find('span');
$icon.toggleClass('ui-icon-circle-triangle-e ui-icon-circle-triangle-s');
}, function(){
var $icon = $(this).find('span');
$icon.toggleClass('ui-icon-circle-triangle-e ui-icon-circle-triangle-s');
});
// group access list
$(".access_list_group_toggle").toggle(function(){
var $icon = $(this).find('span');
$icon.toggleClass('ui-icon-circle-triangle-e ui-icon-circle-triangle-s');
var href = $(this).attr("href");
var $target = $(this).siblings('.access_list2, .access_list3');
$target.html(loadingHTML + "</br>");
$target.load(href, function(){
$(document).ready(function(){
var users = null;
var groups = (function () {
var val = null;
$.ajax({
'async': false,
'global': false,
'url': '/ajax/group_list',
'success': function (data) { val = data; }
});
return val;
})();
$(".creategroup").live('click', function()
{
if($(this).is(':checked'))
{
$(this).parents('.access_list2').find('.newgroup').show();
}
else
{
$(this).parents('.access_list2').find('.newgroup').hide();
}
});
// TODO: Replace with Bootstrap typeahead
$(".groupsuggest").typeahead({
'source': groups.split(" ~ ")
});
$("#group.form_submit").unbind('click');
$("#group.form_submit").click(function(event) {
event.preventDefault();
var experiment_id = $(this).parents('.access_list2').find(".experiment_id").val();
var usersuggest = $(this).parents('.access_list2').find(".usersuggest").val();
var groupsuggest = $(this).parents('.access_list2').find(".groupsuggest").val();
var authMethod = $(this).parents('.access_list2').find("#id_authMethod").val();
var groups_div = $(this).parents('.access_list2').children('.groups');
var create = $(this).parents('.access_list2').find(".creategroup").is(':checked');
var canRead = $(this).parents('.access_list2').find(".canRead").is(':checked');
var canWrite = $(this).parents('.access_list2').find(".canWrite").is(':checked');
var canDelete = $(this).parents('.access_list2').find(".canDelete").is(':checked');
var permissions = '/?authMethod=' + authMethod + '&create=' + create + '&canRead=' + canRead + '&canWrite=' + canWrite + '&canDelete=' + canDelete + '&admin=' + usersuggest;
action = experiment_id + '/access_list/add/group/' + groupsuggest + permissions;
$.ajax({
'async': false,
'global': true,
type: "GET",
url: action,
success: function(data) {
if (data.beginsWith("<div class=", true) == true) {
groups_div.hide().append(data).fadeIn();
// todo this is a duplicate function..
$(".remove_group").unbind('click');
$(".remove_group").click(function() {
var href = $(this).attr("href");
remove_group = $(this);
$.ajax({
'async': false,
'global': false,
'url': href,
'success': function (data) {
val = data;
if(val == "OK") {
remove_group.fadeOut(300, function(){
remove_group.parents('.access_list_group').remove();
});
}
else { alert(val); }
}
}); // end ajax
return false;
}); // end remove group
}
else {
val = data;
alert(val);
}
},
error: function(data) { alert('Error adding group!'); }
});
return false;
});
$(".remove_group").unbind('click');
$(".remove_group").click(function() {
var href = $(this).attr("href");
remove_group = $(this);
$.ajax({
'async': false,
'global': false,
'url': href,
'success': function (data) {
val = data;
if(val == "OK") {
remove_group.fadeOut(300, function(){
remove_group.parents('.access_list_group').remove();
});
}
else { alert(val); }
}
}); // end ajax
return false;
}); // end remove group
});
});
},function(){
var $icon = $(this).find('span');
$icon.toggleClass('ui-icon-circle-triangle-e ui-icon-circle-triangle-s');
});
});
</script>
{% endblock script %}
{% block style %}
<style type="text/css">
.experiment-row {
margin-top: 1ex;
margin-bottom: 2ex;
}
</style>
{% endblock %}
{% block content %}
<div class="page-header">
<h1>Experiment Access Controls</h1>
</div>
{% if experiments %}
<div class="container-fluid">
{% for experiment in experiments %}
<div class="row-fluid experiment-row">
<div class="span12">
<h4><a href="{% url 'tardis_portal.view_experiment' experiment.id %}">{{ experiment.title }}</a></h4>
<div>
<span style="float:left;">
User Access
</span>
<a href="{% url 'tardis.tardis_portal.views.retrieve_access_list_user' experiment.id %}" class="access_list_user_toggle fg-button small fg-button-icon-solo ui-corner-all">
<span class="ui-icon ui-icon-circle-triangle-e"></span>
</a>
<div style="clear:both;"></div>
<div class="access_list1"></div>
</div>
<div>
<span style="float:left;">
Group Access
</span>
<a href="{% url 'tardis.tardis_portal.views.retrieve_access_list_group' experiment.id %}" class="access_list_group_toggle fg-button small fg-button-icon-solo ui-corner-all">
<span class="ui-icon ui-icon-circle-triangle-e"></span>
</a>
<div style="clear:both;"></div>
<div class="access_list2"></div>
</div>
<div>
<span style="float:left;">
External Access
</span>
<a href="{% url 'tardis.tardis_portal.views.retrieve_access_list_external' experiment.id %}" class="access_list_group_toggle fg-button small fg-buton-icon-solo ui-corner-all" title="show/hide">
<span class="ui-icon ui-icon-circle-triangle-e"></span>
</a>
<div style="clear:both;"></div>
<div class="access_list3"></div>
</div>
<div>
<span style="float:left;">
Token Access
</span>
<a title="show/hide" id="token_toggle_{{experiment.id}}"
href="{% url 'tardis.tardis_portal.views.retrieve_access_list_tokens' experiment.id %}"
class="access_list_token_toggle fg-button small fg-button-icon-solo ui-corner-all"
style="float:left;">
<span class="ui-icon ui-icon-circle-triangle-e"></span>
</a>
<a title="Create Token"
href="{{ experiment.get_create_token_url }}"
class="create_token_link fg-button small fg-button-icon-solo ui-corner-all"
style="float:left;">
<span class="ui-icon ui-icon-plusthick"></span>
</a>
<div style="clear:both;"></div>
<div class="access_list" style="display:none;"></div>
</div>
</div>
</div>
{%endfor %}
</div>
{% else %}
<p>There are no experiments under your control.</p>
{% endif %}
{% endblock %}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,377
|
Q: How to properly add proguard to application? I have added pro guards to my Android application, but it makes too much on resposne files and provide to crash an application during launching.
This is my build.gradle settings of optimizing and reducing code
minifyEnabled true
shrinkResources true
debuggable false
manifestPlaceholders = [crashlyticsCollectionEnabled:"true"]
proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
in android manifest
<application
<meta-data
android:name="firebase_crashlytics_collection_enabled"
android:value="${crashlyticsCollectionEnabled}" />
[...]
in proguard-rules.pro
-keep class com.google.android.gms.** { *; }
-keep class com.google.firebase.** { *; }
-keep class com.package.packageandroid2.endpoints.responses.** { *; }
-keep class * extends com.package.packageandroid2.endpoints.** { *; }
-keep class * extends com.package.packageandroid2.PackageApplication.** { *; }
-keep class * extends com.package.packageandroid2.** { *;}
error
Process: com.package.dev.staging, PID: 9574
java.lang.RuntimeException: Unable to create application com.package.packageandroid2.PackageApplication: zh.d: Could not create instance for [Single:'a9.p']
at android.app.ActivityThread.handleBindApplication(ActivityThread.java:6465)
This is the place where is Single class
package com.package.packageandroid2.endpoints.responses
sealed class ResponseId {
abstract val count: Int
data class Single(val id: Int) : ResponseId() {
override val count: Int = 1
}
data class Multiple(val ids: List<Int>) : ResponseId() {
override val count: Int = ids.count()
}
}
From my perspective I keep classes that could provide to crash. What could be the problem here?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 8,593
|
package com.google.flightmap.parsing.esri;
import com.google.flightmap.common.io.StreamUtils;
import com.google.flightmap.parsing.esri.data.Point;
import com.google.flightmap.parsing.esri.data.Polygon;
import com.google.flightmap.parsing.esri.data.Shapefile;
import java.io.File;
import java.io.IOException;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
public class ShapefileReader {
private final static int NULL_SHAPE = 0;
private final static int POLYGON = 5;
private final File shapefile;
/**
* Input buffer. Initialized by calling {@link #open()}.
*/
private ByteBuffer buf;
public ShapefileReader(File shapefile) {
this.shapefile = shapefile;
}
/**
* Reads shape file data. This method cannot be called twice.
*
* @return Contents of shape file
*/
public synchronized Shapefile read() throws IOException {
open();
final Shapefile shapefile = readFileHeader();
readRecords(shapefile);
return shapefile;
}
/**
* Loads contents of shapefile in memory and initializes input buffer.
*/
private synchronized void open() throws IOException {
final byte[] contents = StreamUtils.getBytes(shapefile);
buf = ByteBuffer.wrap(contents);
}
/**
* Reads shape file header and returns new Shapefile object.
*/
private synchronized Shapefile readFileHeader() throws IOException {
buf.order(ByteOrder.BIG_ENDIAN);
final int fileCode = buf.getInt();
for (int i = 0; i < 5; ++i) {
final int unused = buf.getInt();
if (unused != 0) {
throw new RuntimeException("Unexpected unused value: " + unused + " (should be 0).");
}
}
final int length = buf.getInt();
buf.order(ByteOrder.LITTLE_ENDIAN);
final int version = buf.getInt();
final int shapeType = buf.getInt();
final double xMin = buf.getDouble();
final double yMin = buf.getDouble();
final double xMax = buf.getDouble();
final double yMax = buf.getDouble();
final double zMin = buf.getDouble();
final double zMax = buf.getDouble();
final double mMin = buf.getDouble();
final double mMax = buf.getDouble();
return new Shapefile(fileCode, length, version, shapeType, xMin, yMin, xMax, yMax, zMin, zMax,
mMin, mMax);
}
/**
* Reads shape records from the buffer and populates {@code shapefile}.
*/
private synchronized void readRecords(final Shapefile shapefile) {
while (buf.hasRemaining()) {
buf.order(ByteOrder.BIG_ENDIAN);
final int recordNumber = buf.getInt();
final int contentLengthWords = buf.getInt();
buf.order(ByteOrder.LITTLE_ENDIAN);
final int shapeType = peekInt();
if (shapeType != 0 && shapeType != shapefile.shapeType) {
throw new RuntimeException("Unexpected record shape type: " + shapeType +
" (should be " + shapefile.shapeType + " or 0).");
}
switch (shapeType) {
case NULL_SHAPE:
continue;
case POLYGON:
final Polygon polygon = readPolygon(recordNumber);
shapefile.addPolygon(polygon);
break;
default:
throw new RuntimeException("Shape type not supported: " + shapeType);
}
}
}
/**
* Reads an int from the buffer without changing its position.
*/
private synchronized int peekInt() {
final int position = buf.position();
final int val = buf.getInt();
buf.position(position);
return val;
}
/**
* Reads a polygon shape record from the buffer.
*/
private synchronized Polygon readPolygon(final int recordNumber) {
// Byte order MUST be LITTLE_ENDIAN
final double shapeType = buf.getInt();
if (shapeType != POLYGON) {
throw new IllegalStateException("Invalid shape type for polygon: " + shapeType);
}
final double xMin = buf.getDouble();
final double yMin = buf.getDouble();
final double xMax = buf.getDouble();
final double yMax = buf.getDouble();
final int numParts = buf.getInt();
final int numPoints = buf.getInt();
// Get number of points per part
final int[] pointsPerPart = new int[numParts];
final int[] partsStartingIndices = new int[numParts];
for (int i = 0; i < numParts; ++i) {
partsStartingIndices[i] = buf.getInt();
if (i > 0) {
pointsPerPart[i-1] = partsStartingIndices[i] - partsStartingIndices[i-1];
}
}
pointsPerPart[numParts-1] = numPoints - partsStartingIndices[numParts-1];
// Get parts (and points...)
final Polygon.Part[] parts = new Polygon.Part[numParts];
for (int currentPart = 0; currentPart < numParts; ++currentPart) {
final int pointsInPart = pointsPerPart[currentPart];
final Point[] points = new Point[pointsInPart];
for (int i = 0; i < pointsInPart; ++i) {
points[i] = readPoint();
}
parts[currentPart] = new Polygon.Part(points);
}
return new Polygon(recordNumber, xMin, yMin, xMax, yMax, parts);
}
/**
* Reads a {@link Point} from the buffer.
*/
private synchronized Point readPoint() {
final double x = buf.getDouble();
final double y = buf.getDouble();
return new Point(x,y);
}
public static void main(String args[]) {
try {
final String filename = args[0];
final ShapefileReader reader = new ShapefileReader(new File(filename));
System.out.println(reader.read());
} catch (Exception ex) {
ex.printStackTrace();
System.exit(1);
}
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 1,090
|
Q: How to convert searchTwitter results (from library(twitteR)) into a data.frame? I am working on saving twitter search results into a database (SQL Server) and am getting an error when I pull the search results from twitteR.
If I execute:
library(twitteR)
puppy <- as.data.frame(searchTwitter("puppy", session=getCurlHandle(),num=100))
I get an error of:
Error in as.data.frame.default(x[[i]], optional = TRUE) :
cannot coerce class structure("status", package = "twitteR") into a data.frame
This is important because in order to use RODBC to add this to a table using sqlSave it needs to be a data.frame. At least that's the error message I got:
Error in sqlSave(localSQLServer, puppy, tablename = "puppy_staging", :
should be a data frame
So does anyone have any suggestions on how to coerce the list to a data.frame or how I can load the list through RODBC?
My final goal is to have a table that mirrors the structure of values returned by searchTwitter. Here is an example of what I am trying to retrieve and load:
library(twitteR)
puppy <- searchTwitter("puppy", session=getCurlHandle(),num=2)
str(puppy)
List of 2
$ :Formal class 'status' [package "twitteR"] with 10 slots
.. ..@ text : chr "beautifull and kc reg Beagle Mix for rehomes: This little puppy is looking for a new loving family wh... http://bit.ly/9stN7V "| __truncated__
.. ..@ favorited : logi FALSE
.. ..@ replyToSN : chr(0)
.. ..@ created : chr "Wed, 16 Jun 2010 19:04:03 +0000"
.. ..@ truncated : logi FALSE
.. ..@ replyToSID : num(0)
.. ..@ id : num 1.63e+10
.. ..@ replyToUID : num(0)
.. ..@ statusSource: chr "<a href="http://twitterfeed.com" rel="nofollow">twitterfeed</a>"
.. ..@ screenName : chr "puppy_ads"
$ :Formal class 'status' [package "twitteR"] with 10 slots
.. ..@ text : chr "the cutest puppy followed me on my walk, my grandma won't let me keep it. taking it to the pound sadface"
.. ..@ favorited : logi FALSE
.. ..@ replyToSN : chr(0)
.. ..@ created : chr "Wed, 16 Jun 2010 19:04:01 +0000"
.. ..@ truncated : logi FALSE
.. ..@ replyToSID : num(0)
.. ..@ id : num 1.63e+10
.. ..@ replyToUID : num(0)
.. ..@ statusSource: chr "<a href="http://blackberry.com/twitter" rel="nofollow">Twitter for BlackBerry®</a>"
.. ..@ screenName : chr "iamsweaters"
So I think the data.frame of puppy should have column names like:
- text
- favorited
- replytoSN
- created
- truncated
- replytoSID
- id
- replytoUID
- statusSource
- screenName
A: I know this is an old question, but still, here is what I think is a ``modern'' version to solve this. Just use the function twListToDf
gvegayon <- getUser("gvegayon")
timeline <- userTimeline(gvegayon,n=400)
tl <- twListToDF(timeline)
Hope it helps
A: Try this:
ldply(searchTwitter("#rstats", n=100), text)
twitteR returns an S4 class, so you need to either use one of its helper functions, or deal directly with its slots. You can see the slots by using unclass(), for instance:
unclass(searchTwitter("#rstats", n=100)[[1]])
These slots can be accessed directly as I do above by using the related functions (from the twitteR help: ?statusSource):
text Returns the text of the status
favorited Returns the favorited information for the status
replyToSN Returns the replyToSN slot for this status
created Retrieves the creation time of this status
truncated Returns the truncated information for this status
replyToSID Returns the replyToSID slot for this status
id Returns the id of this status
replyToUID Returns the replyToUID slot for this status
statusSource Returns the status source for this status
As I mentioned, it's my understanding that you will have to specify each of these fields yourself in the output. Here's an example using two of the fields:
> head(ldply(searchTwitter("#rstats", n=100),
function(x) data.frame(text=text(x), favorited=favorited(x))))
text
1 @statalgo how does that actually work? does it share mem between #rstats and postgresql?
2 @jaredlander Have you looked at PL/R? You can call #rstats from PostgreSQL: http://www.joeconway.com/plr/.
3 @CMastication I was hoping for a cool way to keep data in a DB and run the normal #rstats off that. Maybe a translator from R to SQL code.
4 The distribution of online data usage: AT&T has recently announced it will no longer http://goo.gl/fb/eTywd #rstat
5 @jaredlander not that I know of. Closest is sqldf package which allows #rstats and sqlite to share mem so transferring from DB to df is fast
6 @CMastication Can #rstats run on data in a DB?Not loading it in2 a dataframe or running SQL cmds but treating the DB as if it wr a dataframe
favorited
1 FALSE
2 FALSE
3 FALSE
4 FALSE
5 FALSE
6 FALSE
You could turn this into a function if you intend on doing it frequently.
A: I use this code I found from http://blog.ouseful.info/2011/11/09/getting-started-with-twitter-analysis-in-r/ a while ago:
#get data
tws<-searchTwitter('#keyword',n=10)
#make data frame
df <- do.call("rbind", lapply(tws, as.data.frame))
#write to csv file (or your RODBC code)
write.csv(df,file="twitterList.csv")
A: For those that run into the same problem I did which was getting an error saying
Error in as.double(y) : cannot coerce type 'S4' to vector of type 'double'
I simply changed the word text in
ldply(searchTwitter("#rstats", n=100), text)
to statusText, like so:
ldply(searchTwitter("#rstats", n=100), statusText)
Just a friendly heads-up :P
A: Here is a nice function to convert it into a DF.
TweetFrame<-function(searchTerm, maxTweets)
{
tweetList<-searchTwitter(searchTerm,n=maxTweets)
return(do.call("rbind",lapply(tweetList,as.data.frame)))
}
Use it as :
tweets <- TweetFrame(" ", n)
A: The twitteR package now includes a function twListToDF that will do this for you.
puppy_table <- twListToDF(puppy)
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 4,884
|
\section{Introduction}
Proposed by Aharony, Bergman, Jafferis and Maldacena (ABJM)
\cite{ABJM} the duality relation between the $D=3$ $\mathcal N=6$
superconformal Chern-Simons-matter theory with the $U(N)\times
U(N)$ gauge symmetry and level $k$ and M-theory on the $AdS_4\times(
S^7/\mathbf Z_k)$ background provided the novel instance of the
gauge fields/strings correspondence. Whenever $N,k\to\infty$ with
the t'Hooft coupling $\lambda=N/k$ fixed the dual theory reduces
to the IIA superstring on the $AdS_4\times\mathbb{CP}^3$ background.
So one of the pivotal problems in exploring the ABJM duality is to
construct and quantize the string theory on
$AdS_4\times\mathbb{CP}^3$. The problem of constructing the
superstring action on $AdS_4\times\mathbb{CP}^3$ including the
fermions has been addressed in \cite{AF}-\cite{GSWnew}. In Ref.
\cite{AF} there was applied the supercoset approach previously
proposed to obtain the Green-Schwarz (GS) superstring action on
the $AdS_5\times S^5$ superbackground \cite{MT}, \cite{Kallosh}. The
basic observation is that the symmetry group $SO(2,3)\times SU(4)$
of the bosonic background can be viewed as the bosonic subgroup of the
$OSp(4|6)$ supergroup that also includes 24 fermionic generators. The
action constructed in \cite{AF} using the $OSp(4|6)/(SO(1,3)\times
U(3))$ supercoset element includes 10 bosonic and 24 fermionic\footnote{Equal in number to the Type IIA supersymmetries
preserved by the $AdS_4\times\mathbb{CP}^3$ background.} degrees
of freedom, is invariant under the $8-$parameter $\kappa-$symmetry
transformations and is classically integrable. Such supercoset
action corresponds to the complete superstring action on
$AdS_4\times\mathbb{CP}^3$ with 32 fermions \cite{GSWnew}, in
which the $\kappa-$symmetry gauge freedom has been partially
fixed. Since $S^7$ admits the Hopf fibration representation as
$\mathbb{CP}^3\times U(1)$ \cite{Pope}, \cite{Volkov} the complete superstring action on
$AdS_4\times\mathbb{CP}^3$ can be constructed by performing the
double dimensional reduction \cite{DHIS} of the membrane action on the $D=11$
maximally supersymmetric background $AdS_4\times S^7$
\cite{Plefka98} that can also be viewed as the supercoset manifold
$OSp(4|8)/(SO(1,3)\times SO(7))$. This complete action on
$AdS_4\times\mathbb{CP}^3$ describes all possible superstring
motions and allows a wider choice of the $\kappa$-symmetry gauges
compared to the supercoset action. However, whether it is
integrable remains unclear.
Among possible $\kappa-$symmetry gauge conditions a special role
is played by the light-cone type gauges. In flat superspace it is
the light-cone gauge in which the GS equations of motion linearize and the model can be straightforwardly
quantized. Light-cone type gauge conditions also appear to be useful in exploring the string theory on $AdS_5\times S^5$ (see \cite{found} for review and
references). The
superstring model on $AdS_4\times\mathbb{CP}^3$, as well as its Penrose limit have
been studied in the light-cone type gauges in \cite{Nishioka}-\cite{Dukalski}. Here we consider the
superstring action on the $AdS_4\times\mathbb{CP}^3$ background
beyond the $OSp(4|6)/(SO(1,3)\times U(3))$ supercoset approach in the fermionic light-cone gauge corresponding to the choice of the light-like directions
within the $D=3$ Minkowski boundary of $AdS_4$ \footnote{Analogous $\kappa-$symmetry gauge conditions were proposed in \cite{MTlc} for the
$AdS_5\times S^5$ superstring.}. Similarly to our previous paper
\cite{0811} we elaborate on the presentation of the $AdS_4\times S^7$ background isometry superalgebra $osp(4|8)$ as the $D=3$ extended superconformal algebra
and the transformation of the Cartan forms to the
superconformal basis\footnote{The splitting of the fermionic generators/coordinates into the supersymmetry/superconformal ones w.r.t. the symmetry
of the Minkowski boundary of $AdS$ was introduced in \cite{9807115}, \cite{Kallosh2}, \cite{PST} for the study of brane models on the $AdS\times S$
backgrounds.}. To make the exposition more self-contained
we start by reviewing the $OSp(4|8)/(SO(1,3)\times SO(7))$
supercoset membrane action and its dimensional reduction to the
superstring action on $AdS_4\times\mathbb{CP}^3$. The details of the notation, spinor and isometry algebras are taken to the Appendixes.
\section{The supermembrane on $AdS_4\times S^7$ and its reduction to the $D=10$ IIA superstring on $AdS_4\times\mathbb{CP}^3$}
The $D=11$ supermembrane action on the $AdS_4\times S^7$ background \cite{Plefka98} is given by
\begin{equation}\label{membrane}
S=-\int\limits_{V} d^3\xi\sqrt{-g^{(3)}}+S_{WZ},
\end{equation}
where $g^{(3)}$ is the determinant of the induced world-volume metric
\begin{equation}
g^{(3)}_{\underline i\underline j}=E^{\hat m}_{\underline
i}E_{\underline j\hat m}
\end{equation}
and the Wess-Zumino (WZ) term
\begin{equation}
S_{WZ}=s\int\limits_{\mathcal M_4} H_{(4)}
\end{equation}
is presented as the integral of the closed 4-form
\begin{equation}
H_{(4)}=\frac{i}{2}F^{\hat\alpha}\wedge\mathfrak{g}^{\hat m\hat
n}{}_{\hat\alpha}{}^{\hat\beta}F_{\hat\beta} \wedge E_{\hat
m}\wedge E_{\hat n}+\varepsilon_{m'n'k'l'}E^{m'}\wedge
E^{n'}\wedge E^{k'}\wedge E^{l'}
\end{equation}
over the 4-dimensional auxiliary hypersurface $\mathcal M_4$, whose boundary coincides with the supermembrane world volume $V$.
The first term has the same structure as in the flat superspace
\cite{BSTown}, while the second term is the contribution of the nonzero bosonic
4-form of the background. The $D=11$ supervielbein bosonic components $E^{\hat
m}=(E^{m'},E^{I'})=(G^{0'm'},\Omega^{8I'})$ consist of the $AdS_4$
and $S^7$ vielbeins $G^{0'm'}$ and $\Omega^{8I'}$ that are the Cartan forms
corresponding to the $so(2,3)/so(1,3)$ and $so(8)/so(7)$
generators $M_{0'm'}$ and $V^{8'I'}$ respectively. Together with the
fermionic 1-forms $F^{\hat\alpha}\equiv F^{\alpha A'}$ associated
with the $osp(4|8)$ fermionic generators $O_{\hat\alpha}\equiv
O_{\alpha A'}$ they satisfy the $osp(4|8)$ Maurer-Cartan (MC)
equations
\begin{equation}\label{MCmemb}
\begin{array}{rl}
dG^{0'm'}&=2G^{m'}{}_{n'}\wedge G^{0'n'}+\frac{i}{4}F^{\alpha A'}\wedge C_{A'B'}\Gamma^{m'}_{\alpha\beta}F^{\beta B'},\\
d\Omega^{8I'}&=2\Omega^{I'J'}\wedge\Omega^{8J'}-\frac{i}{4}F^{\alpha A'}\wedge\Gamma^5_{\alpha\beta}\gamma^{I'}_{A'B'}F^{\beta B'},\\
dF^{\alpha A'}&=-\frac12G^{m'n'}\wedge F^{\beta
A'}\Gamma_{m'n'\beta}{}^\alpha-G^{0'm'}\wedge F^{\beta
A'}\Gamma_{m'\beta}{}^\gamma\Gamma^5{}_\gamma{}^\alpha\\
&+\frac12\Omega^{I'J'}\wedge F^{\alpha
B'}\gamma^{I'J'}{}_{B'}{}^{A'}-\frac12\Omega^{8I'}\wedge F^{\alpha
B'}\gamma^{I'}{}_{B'}{}^{A'}
\end{array}
\end{equation}
that can be derived by taking into account Eq.(\ref{cf}) below and the $osp(4|8)$ (anti)commutation relations in the form (\ref{so8in7}), (\ref{antic}), (\ref{so8fermitransin7}), (\ref{so23fermitransin4}) given in Appendix B. These MC equations are used to show the closeness of $H_{(4)}$.
To verify the $\kappa-$invariance of the membrane action (\ref{membrane}) consider the following variation of the fermionic vielbein components
\begin{equation}\label{kappavar}
F_{\hat\alpha}(\delta_\kappa)=\Pi_{\hat\alpha}{}^{\hat\beta}\kappa_{\hat\beta}(\xi),
\end{equation}
where the matrix $\Pi_{\hat\alpha}{}^{\hat\beta}$ has the form
\begin{equation}
\Pi_{\hat\alpha}{}^{\hat\beta}=\delta^{\hat\beta}_{\hat\alpha}+\frac{q}{\sqrt{-g^{(3)}}}\varepsilon^{\underline i\underline j\underline k}E^{\hat m_1}_{\underline i}E^{\hat m_2}_{\underline j}E^{\hat m_3}_{\underline k}\mathfrak{g}_{\hat m_1\hat m_2\hat m_3\hat\alpha}{}^{\hat\beta},
\end{equation}
accompanied by $E^{\hat m}(\delta_\kappa)=0$. Using that $dH_{(4)}=0$ the variation of $H_{(4)}$ reduces to
\begin{equation}\label{Hvar}
\delta_\kappa H_{(4)}=id\left(F^{\hat\alpha}\mathfrak{g}_{\hat m\hat n\hat\alpha}{}^{\hat\beta}F_{\hat\beta}(\delta_\kappa)\wedge E^{\hat m}\wedge E^{\hat n}\right).
\end{equation}
Substituting (\ref{kappavar}) into (\ref{Hvar}) and performing the $\gamma-$matrix
rearrangements using the formulae adduced in \cite{TFSusy} yields the expression for the
Wess-Zumino 4-form variation
\begin{equation}
\delta_\kappa H_{(4)}=id\left(F^{\hat\alpha}\mathfrak{g}_{\hat m\hat
n\hat\alpha}{}^{\hat\beta}\kappa_{\hat\beta}\wedge E^{\hat
m}\wedge E^{\hat n}-\frac{6q}{\sqrt{-g^{(3)}}}\varepsilon^{\underline
i\underline j\underline k}\varepsilon^{\underline i'\underline
j'\underline k'}(E_{\underline i}\cdot E_{\underline
i'})(E_{\underline j}\cdot E_{\underline j'})E_{\hat m\underline
k'}F^{\hat\alpha}_{\underline k}\mathfrak{g}^{\hat
m}{}_{\hat\alpha}{}^{\hat\beta}\kappa^{\hat\beta}\right).
\end{equation}
It has to be canceled by the $\kappa-$variation of the kinetic
term of (\ref{membrane}) that is defined by the variation of the
induced metric determinant $g^{(3)}$. Taking into account that the
$\kappa-$variation of the bosonic vielbein reads
\begin{equation}
\delta_\kappa E^{\hat m}=-\frac{i}{2}F^{\hat\alpha}\mathfrak{g}^{\hat m}{}_{\hat\alpha}{}^{\hat\beta}F_{\hat\beta}(\delta_\kappa)
\end{equation}
one obtains
\begin{equation}
\delta_\kappa\sqrt{-g^{(3)}}=\frac{i}{4\sqrt{-g^{(3)}}}\varepsilon^{\underline
i\underline j\underline k}\varepsilon^{\underline i'\underline
j'\underline k'}(E_{\underline i}\cdot E_{\underline
i'})(E_{\underline j}\cdot E_{\underline j'})E^{\hat
m}_{\underline k'}F^{\hat\alpha}_{\underline k}\mathfrak{g}_{\hat
m\hat\alpha}{}^{\hat\beta}\kappa_{\hat\beta}-\frac{3iq}{2}F^{\hat\alpha}\mathfrak{g}^{\hat
m\hat n}{}_{\hat\alpha}{}^{\hat\beta}\kappa_{\hat\beta}\wedge
E_{\hat m}\wedge E_{\hat n}.
\end{equation}
The $\kappa-$invariance condition of the action (\ref{membrane})
then fixes the values of the numerical coefficients
$s=\pm\frac14$, $q=\mp\frac16$ \footnote{Such choice of the value
of $q$ makes the matrix $\Pi_{\hat\alpha}{}^{\hat\beta}$ the
projector that eliminates half components of the transformation
parameter $\kappa^{\hat\alpha}(\xi)$.} so that the final form of
the WZ term is given by
\begin{equation}
S_{WZ}=\pm\frac14\int\limits_{\mathcal M_4}\left(\frac{i}{2}F^{\hat\alpha}\wedge\mathfrak{g}^{\hat m\hat
n}{}_{\hat\alpha}{}^{\hat\beta}F_{\hat\beta} \wedge E_{\hat
m}\wedge E_{\hat n}+\varepsilon_{m'n'k'l'}E^{m'}\wedge
E^{n'}\wedge E^{k'}\wedge E^{l'}\right).
\end{equation}
Dimensional reduction of the $D=11$ supermembrane action to the
$D=10$ Type IIA superstring was described for general
superbackground in \cite{DHIS}. The vielbeins are chosen not to
depend on the reduction direction coordinate $y\in[0,2\pi)$.
However, when the bosonic components of the supervielbein receive
contribution $E^{\hat m'}_y$ proportional to the differential $dy$
of the $U(1)$ coordinate\footnote{As is the case for the
$OSp(4|8)/(SO(1,3)\times SO(7))$ supercoset elements considered in
\cite{GSWnew} and here.} the local Lorentz rotation in the tangent
space has to be performed
\begin{equation}
E^{\hat m}\rightarrow L^{\hat m}{}_{\hat n}E^{\hat n},\quad
F^{\hat\alpha}\rightarrow
L^{\hat\alpha}{}_{\hat\beta}F^{\hat\beta},\quad L^{\hat m}{}_{\hat
n}\in SO(1,10),\ L^{\hat\alpha}{}_{\hat\beta}\in Spin(1,10)
\end{equation}
with the parameters determined by $E^{\hat m'}_y$ to bring the
supervielbein bosonic components to the Kaluza-Klein ansatz form
\begin{equation}\label{kkanzatz}
(LE)^{\hat m'}=\mathrm E^{\hat m'},\quad (LE)^{11}=\mathrm E^{11}=\Phi(dy+A),
\end{equation}
where $\mathrm E^{\hat m'}$ is the bosonic part of the $D=10$
supervielbein that does not depend on $y$ and $dy$, the $D=10$ IIA
superfield $\Phi=e^{2\phi/3}$ is related to the dilaton $\phi$,
and $A$ is the RR 1-form potential. For the fermionic components
of the $D=11$ supervielbein the reduction ansatz is
\begin{equation}\label{kkfermviel}
(LF)^{\hat\alpha}=E^{\hat\alpha}+e^{-2\phi/3}\chi^{\hat\alpha}\mathrm E^{11}:\quad
E^{\hat\alpha}=(Lf)^{\hat\alpha}-(LF_y)^{\hat\alpha}A,\
\chi^{\alpha}=(LF_y)^{\hat\alpha},
\end{equation}
where $E^{\hat\alpha}$ are the $D=10$ supervielbein fermionic
components, $\chi^{\hat\alpha}$ is the dilatino superfield and there has been
separated the $dy$-dependent contribution to the $D=11$ supervielbein fermionic components
\begin{equation}\label{fermviel}
F^{\hat\alpha}=f^{\hat\alpha}+dyF^{\hat\alpha}_y.
\end{equation}
Upon identification of $y$ with the world-volume compact direction coordinate the kinetic term of the membrane action (\ref{membrane}) reduces to the Nambu-Goto string action in the Kaluza-Klein frame
\begin{equation}
\int\limits_V d^3\xi\sqrt{-g^{(3)}}\rightarrow\int\limits_\Sigma
d\tau d\sigma\Phi\sqrt{-g^{(2)}},
\end{equation}
where $g^{(2)}=\det g^{(2)}_{ij}$ is the determinant of the
induced world-sheet metric
\begin{equation}
g^{(2)}_{ij}=\mathrm E^{\hat m'}_i\mathrm E_{\hat m'j},
\end{equation}
while the membrane WZ term reduces to the integral of the NS-NS 3-form over the auxiliary 3-dimensional hypersurface $\mathcal M_3$, whose boundary coincides with the superstring world-sheet $\Sigma$
\begin{equation}\label{wzred}
\int\limits_{\mathcal M_4} H_{(4)}\rightarrow \int\limits_{\mathcal M_3}H_{(3)}.
\end{equation}
To specificate the above discussion let us describe the
transformation of the $so(8)$ Cartan forms to the
$\mathbb{CP}^3\times U(1)$-basis that exhibits the Hopf fibration
realization of $S^7$ necessary to perform the double dimensional
reduction and also of the $sp(4)$ Cartan forms to the $D=3$
conformal basis. For the $OSp(4|8)/(SO(1,3)\times SO(7)$ supercoset element $\mathscr G$ the $SO(1,3)\times SO(7)$ covariant decomposition
of the Cartan forms reads
\begin{equation}\label{cf}
\mathscr G^{-1}d\mathscr G=G^{m'n'}M_{m'n'}+G^{0'm'}M_{0'm'}+\Omega^{I'J'}V^{I'J'}+\Omega^{8I'}V^{8I'}+F^{\alpha
A'}O_{\alpha A'}.
\end{equation}
The first two terms correspond to the $D=3$ conformal sector
and after the transformation of the generators to the conformal basis, as described in Appendix B, are brought to the form
\begin{equation}
G^{m'n'}M_{m'n'}+G^{0'm'}M_{0'm'}=G^{mn}M_{mn}+\Delta D+\omega^m P_m+c^m K_m,
\end{equation}
where
\begin{equation}
\omega^m=G^{0'm}-G^{3m},\quad c^m=G^{0'm}+G^{3m},\quad \Delta=-G^{0'3}.
\end{equation}
The $AdS_4$ vielbein components, used in constructing the superstring action, in the conformal basis are expressed as
\begin{equation}\label{adsvielbein}
G^{0'm}=\frac12(\omega^m+c^m),\quad G^{0'3}=-\Delta.
\end{equation}
The third and the fourth terms in (\ref{cf}) correspond to the $so(8)$ generators and 1-forms and further decompose as
\begin{equation}\label{cfso8}
\Omega^{I'J'}V^{I'J'}+\Omega^{8I'}V^{8I'}=\Omega^{IJ}V^{IJ}+\Omega^{78}V^{78}+\Omega^{8I}V^{8I}+2\Omega^{7I}V^{7I}.
\end{equation}
To perform the dimensional reduction of the $AdS_4\times S^7$ membrane action one is required to change the generator basis to that corresponding to
the Hopf fibration realization of the 7-sphere (see Appendix B).
Then the two last terms in (\ref{cfso8}) corresponding to the $so(8)/(so(2)\times
so(6))$ coset generators acquire the form
\begin{equation}
\Omega^{8I}V^{8I}+2\Omega^{7I}V^{7I}=\Omega_a T^a+\Omega^aT_a+\tilde\Omega_a\tilde T^a+\tilde\Omega^a\tilde T_a,
\end{equation}
where
\begin{equation}
\begin{array}{c}
\Omega_a=\Omega^7{}_{4a}-\frac{i}{2}\Omega^8{}_{4a},\quad\Omega^a=-\Omega^{74a}-\frac{i}{2}\Omega^{84a},\\
\tilde\Omega_a=-\Omega^7{}_{4a}-\frac{i}{2}\Omega^8{}_{4a},\quad\tilde\Omega^a=\Omega^{74a}-\frac{i}{2}\Omega^{84a}
\end{array}
\end{equation}
and $\Omega^{7(8)}{}_{4a}=\Omega^{7(8)I}\rho^I_{4a}$, $\Omega^{7(8)4a}=\Omega^{7(8)I}\tilde\rho^{I4a}$. The 1-forms
\begin{equation}
\Omega^8{}_{4a}=i(\Omega_a+\tilde\Omega_a),\quad\Omega^{84a}=i(\Omega^a+\tilde\Omega^a)
\end{equation}
will be used in constructing the superstring action.
Changing the basis in the $so(6)\oplus so(2)$ sector that is described by the first two terms in (\ref{cfso8}) yields
\begin{equation}\label{cfso6so2}
\Omega^{IJ}V^{IJ}+\Omega^{78}V^{78}=\tilde\Omega_a{}^b\tilde
V_b{}^a+\tilde\Omega_b{}^b\tilde
V_a{}^a+\Omega_a{}^4V_4{}^a+\Omega_4{}^aV_a{}^4+hH,
\end{equation}
where
\begin{equation}
\begin{array}{c}
\tilde\Omega_a{}^b=\Omega_a{}^b-\delta^b_a\Omega_c{}^c+\delta^b_ah,\quad\tilde\Omega_b{}^b=-2\Omega_b{}^b+3h,\\
\Omega^{78}=-\tilde\Omega_a{}^a-h,
\end{array}
\end{equation}
and the $so(6)$ Cartan forms have been decomposed into the $u(3)$ $\Omega_a{}^b$ and $su(4)/u(3)$ $\Omega_a{}^4$, $\Omega_4{}^a$ ones as
\begin{equation}
\Omega_A{}^B=\frac{i}{2}\Omega^{IJ}\rho^{IJ}{}_A{}^B=\left(
\begin{array}{cc}
\Omega_a{}^b &\Omega_a{}^4\\
\Omega_4{}^b &\Omega_4{}^4
\end{array}\right),\quad
\Omega_4{}^4=-\Omega_a{}^a.
\end{equation}
The 1-form $h$ in (\ref{cfso6so2}) corresponds to the fiber direction of $\mathbb{CP}^3\times U(1)$.
The fermionic sector of (\ref{cf}) decomposes as follows
\begin{equation}
\begin{array}{c}
F^{\alpha A'}O_{\alpha A'}=\bar F^{\alpha A}\bar O_{\alpha A}+F^\alpha_AO^A_\alpha\\
=\omega^\mu_A Q^A_\mu+\bar\omega^{\mu A}\bar Q_{\mu A}+\chi_{\mu A}S^{\mu A}+\bar\chi^A_\mu\bar S^\mu_A,
\end{array}
\end{equation}
where the generators have been split into the supersymmetry and superconformal ones (see Eq.(\ref{susygen})) accompanied by the corresponding
splitting of the Cartan forms
\begin{equation}\label{defsconff}
\bar F^{\alpha A}=\sqrt{2}\left(
\begin{array}{c}
\bar\omega^{\mu A}\\
\bar\chi^A_\mu\\
\end{array}\right),\quad
F^\alpha_A=\sqrt{2}\left(
\begin{array}{c}
\omega^\mu_A\\
\chi_{\mu A}\\
\end{array}\right).
\end{equation}
The MC equations (\ref{MCmemb}) in the novel basis
acquire the form
\begin{equation}
\begin{array}{rcl}
d\omega^m&=&2G^m{}_n\wedge\omega^n+2\Delta\wedge\omega^m-2i\omega^\mu_A\sigma^m_{\mu\nu}\bar\omega^{\nu A},\\
dc^m&=&2G^m{}_n\wedge c^n-2\Delta\wedge c^m-2i\chi_{\mu A}\tilde\sigma^{m\mu\nu}\bar\chi^A_\nu,\\
d\Delta&=&\omega^m\wedge
c_m+i\omega^\mu_A\wedge\bar\chi^A_\mu+i\bar\omega^{\mu
A}\wedge\chi_{\mu A}
\end{array}
\end{equation}
for the Cartan forms from the $AdS$ sector,
\begin{equation}
\begin{array}{rcl}
d\Omega_a&=&-i\tilde\Omega_a{}^b\wedge\Omega_b-i\tilde\Omega_b{}^b\wedge\Omega_a-i\varepsilon_{abc}\Omega_4{}^b\wedge\tilde\Omega^c+2\varepsilon_{abc}\bar\omega^{\mu b}\wedge\bar\chi^c_\mu,\\
d\Omega^a&=&-i\Omega^b\wedge\tilde\Omega_b{}^a-i\Omega^a\wedge\tilde\Omega_b{}^b+i\varepsilon^{abc}\Omega_b{}^4\wedge\tilde\Omega_c-2\varepsilon^{abc}\omega^\mu_b\wedge\chi_{\mu c},\\
d\tilde\Omega_a&=&-i\tilde\Omega_a{}^b\wedge\tilde\Omega_b+i\tilde\Omega_b{}^b\wedge\tilde\Omega_a+2ih\wedge\tilde\Omega_a-i\varepsilon_{abc}\Omega_4{}^b\wedge\Omega^c-2\omega^{\mu}_{a}\wedge\chi_{\mu 4}+2\omega^\mu_4\wedge\chi_{\mu a},\\
d\tilde\Omega^a&=&-i\tilde\Omega^b\wedge\tilde\Omega_b{}^a+i\tilde\Omega^a\wedge\tilde\Omega_b{}^b-2ih\wedge\tilde\Omega^a+i\varepsilon^{abc}\Omega_b{}^4\wedge\Omega_c+2\bar\omega^{\mu a}\wedge\bar\chi_{\mu 4}-2\bar\omega^{\mu 4}\wedge\bar\chi^a_\mu,\\
d\tilde\Omega_a{}^a&=&-i\Omega_a\wedge\Omega^a+\frac{i}{2}\tilde\Omega_a\wedge\tilde\Omega^a+\frac{i}{2}\Omega_a{}^4\wedge\Omega_4{}^a-\omega^\mu_a\wedge\bar\chi^a_\mu+\bar\omega^{\mu a}\wedge\chi_{\mu a},\\
dh&=&\frac{i}{2}\tilde\Omega_a\wedge\tilde\Omega^a+\frac{i}{2}\Omega_4{}^a\wedge\Omega_a{}^4-\omega^\mu_4\wedge\bar\chi^4_\mu+\bar\omega^{\mu
4}\wedge\chi_{\mu 4}
\end{array}
\end{equation}
for the Cartan forms from the $so(8)$ sector and
\begin{equation}
\begin{array}{rcl}
d\omega^\mu_a&=&\Delta\wedge\omega^\mu_a+\frac12G^{mn}\wedge\omega^\nu_a\sigma_{mn\nu}{}^\mu-\omega^m\wedge\tilde\sigma_m^{\mu\nu}\chi_{\nu a}-i\tilde\Omega_a{}^b\wedge\omega^\mu_b+i\tilde\Omega_b{}^b\wedge\omega^\mu_a\\
&-&i\Omega_a{}^4\wedge\omega^\mu_4+i\tilde\Omega_a\wedge\bar\omega^{\mu 4}-i\varepsilon_{abc}\Omega^b\wedge\bar\omega^{\mu c},\\
d\omega^\mu_4&=&\Delta\wedge\omega^\mu_4+\frac12G^{mn}\wedge\omega^\nu_4\sigma_{mn\nu}{}^\mu-\omega^m\wedge\tilde\sigma_m^{\mu\nu}\chi_{\nu 4}+2ih\wedge\omega^\mu_4-i\Omega_4{}^a\wedge\omega^\mu_a-i\tilde\Omega_a\wedge\bar\omega^{\mu a},\\
d\chi_{\mu a}&=&-\Delta\wedge\chi_{\mu a}-\frac12G^{mn}\wedge\sigma_{mn\mu}{}^\nu\chi_{\nu a}+c^m\wedge\sigma_{m\mu\nu}\omega^\nu_a-i\tilde\Omega_a{}^b\wedge\chi_{\mu b}+i\tilde\Omega_b{}^b\wedge\chi_{\mu a}\\
&-&i\Omega_a{}^4\wedge\chi_{\mu 4}+i\tilde\Omega_a\wedge\bar\chi^4_\mu-i\varepsilon_{abc}\Omega^b\wedge\bar\chi^c_\mu,\\
d\chi_{\mu 4}&=&-\Delta\wedge\chi_{\mu
4}-\frac12G^{mn}\wedge\sigma_{mn\mu}{}^\nu\chi_{\nu
4}+c^m\wedge\sigma_{m\mu\nu}\omega^\nu_4+2ih\wedge\chi_{\mu
4}-i\Omega_4{}^a\wedge\chi_{\mu
a}-i\tilde\Omega_a\wedge\bar\chi^a_\mu
\end{array}
\end{equation}
and c.c. for the fermionic 1-forms.
In what follows we shall specialize to the $OSp(4|8)/(SO(1,3)\times SO(7))$ representative in the form of the "dressed" $OSp(4|6)/(SO(1,3)\times U(3))$ supercoset element
\begin{equation}\label{48cosetel}
\mathscr G=\mathscr G_{OSp(4|6)/(SO(1,3)\times
U(3))}e^{yH}e^{\theta^\mu_4Q^4_\mu+\bar\theta^{\mu 4}\bar Q_{\mu
4}}e^{\eta_{\mu 4}S^{\mu 4}+\bar\eta^4_\mu\bar S^\mu_4},
\end{equation}
where
\begin{equation}\label{46cosetel}
\mathscr G_{OSp(4|6)/(SO(1,3)\times U(3))}=e^{x^mP_m+\theta^\mu_aQ^a_\mu+\bar\theta^{\mu a}\bar Q_{\mu a}}e^{\eta_{\mu a}S^{\mu a}+\bar\eta^a_\mu\bar S^{\mu}_a}e^{z^aT_a+\bar z_aT^a}e^{\varphi D}
\end{equation}
is the $OSp(4|6)/(SO(1,3)\times U(3))$ supercoset element considered in \cite{0811}. It is
parametrized by the $D=3$ $\mathcal N=6$ super-Poincare coordinates
$x^m,\theta^\mu_a,\bar\theta^{\mu a}$ supplemented by the
coordinates $\eta_{\mu a},\bar\eta^a_\mu$ associated with the
superconformal generators, the coordinates $z^a,\bar z_a$
parametrizing $\mathbb{CP}^3$ and the coordinate $\varphi$ related to the radial
direction of $AdS_4$. The expressions for the Cartan forms corresponding
to the supercoset element (\ref{46cosetel}) have been derived in \cite{0811}.
The form of the supercoset element (\ref{48cosetel}) is governed
by the requirement of the absence of the vielbein dependence on
the reduction direction coordinate $y$ that can be satisfied by
placing $e^{yH}$ to the left from the factors corresponding to
the broken supersymmetries of the background, whenever the differential acts from
the right. The differentials of the factors corresponding to the broken supersymmetries give contributions to the $sp(4)$
Cartan forms, the forms associated with the broken
supersymmetries and the $U(1)$ direction. After the commutation of
$\mathscr G^{-1}_{OSp(4|6)/(SO(1,3)\times U(3))}d\mathscr G_{OSp(4|6)/(SO(1,3)\times U(3))}$ with the factors
corresponding to the broken supersymmetries the $osp(4|6)$ Cartan
forms $\mathcal C$ become $\mathcal N=4$ superfields $\mathcal
C(\theta_4,\bar\theta^4,\eta_4,\bar\eta^4)$. There also appear the
contributions proportional to the broken supersymmetries generators and
$\tilde T_a$, $\tilde T^a$, $V_a{}^4$, $V_4{}^a$, $H$ generators.
\section{$AdS_4\times\mathbb{CP}^3$ superstring in the light-cone gauge}
The fermionic light-cone gauge condition we consider
\begin{equation}\label{lcfermi}
\theta^2_A=\bar\theta^{2 A}=\eta_{1 A}=\bar\eta_{1}^{A}=0
\end{equation}
is characterized by setting to zero the coordinates associated
with the generators $Q^A_2$, $\bar Q_{2 A}$, $S^{1A}$, $\bar
S^1_A$ that have negative charge w.r.t. the $so(1,1)$ generator
$M^{+-}\equiv2M^{02}$ from the Lorentz group acting on the
Minkowski boundary of $AdS_4$
\begin{equation}
[M^{+-},Q^A_2]=-Q^A_2,\quad [M^{+-},\bar Q_{2A}]=-\bar Q_{2A},\quad [M^{+-},S^{1A}]=-S^{1A},\quad [M^{+-},\bar S^1_A]=-\bar S^1_A.
\end{equation}
Other fermionic generators have positive $so(1,1)$ charge
\begin{equation}
[M^{+-},Q^A_1]=Q^A_1,\quad [M^{+-},\bar Q_{1A}]=\bar Q_{1A},\quad [M^{+-},S^{2A}]=S^{2A},\quad [M^{+-},\bar S^2_A]=\bar S^2_A.
\end{equation}
Respective coordinates can be denoted as follows
\begin{equation}
\theta^1_A\equiv\theta^-_A\equiv\theta_A,\quad\bar\theta^{1A}\equiv\bar\theta^{-A}\equiv\bar\theta^A,\quad
\eta^{1}_{A}\equiv\eta^{-}_{A}\equiv\eta_A,\quad\bar\eta^{1A}\equiv\bar\eta^{-A}\equiv\bar\eta^A
\end{equation}
and become the physical degrees of freedom of the superstring in the gauge (\ref{lcfermi}).
In the light-cone gauge the constituents of the $AdS_4$ vielbein (\ref{adsvielbein}) reduce to
\begin{equation}\label{omega}
\begin{array}{c}
\omega^m=e^{-2\varphi}(dx^m-id\theta_a\sigma^m\bar\theta^a+i\theta_a\sigma^md\bar\theta^a)-id\theta_4\sigma^m\bar\theta^4+i\theta_4\sigma^md\bar\theta^4+dy\omega^m_y,\quad\omega^m_y=4\theta_4\sigma^m\bar\theta^4,\\
c^m=-ie^{2\varphi}(d\eta_a\tilde\sigma^m\bar\eta^a-\eta_a\tilde\sigma^md\bar\eta^a)-
id\eta_4\tilde\sigma^m\bar\eta^4+i\eta_4\tilde\sigma^md\bar\eta^4+dyc^m_y,\quad c^m_y=4\eta_4\tilde\sigma^m\bar\eta^4,\\
\Delta=d\varphi.
\end{array}
\end{equation}
The $\mathbb{CP}^3\times U(1)$ vielbein components acquire the form
\begin{equation}\label{omega84a}
\Omega^8{}_{4a}=i(\Omega_a-2e^{-\varphi}\hat\eta_a\eta_4dx^+),\quad\Omega^{84a}=i(\Omega^a+2e^{-\varphi}\hat{\bar\eta}{}^a\bar\eta^4dx^+),
\end{equation}
\begin{equation}
\Omega^{87}=h+\tilde\Omega_a{}^a,
\end{equation}
where
\begin{equation}
h=dy-e^{-2\varphi}\eta_4\bar\eta^4dx^+,
\end{equation}
\begin{equation}
\hat\eta_a=T_a{}^b\eta_b+T_{ab}\bar\eta^b,\quad\hat{\bar\eta}{}^a=T^a{}_b\bar\eta^b+T^{ab}\eta_b
\end{equation}
and the matrix $T_{\hat a}{}^{\hat b}$ has been defined in Eq.(64) of \cite{0811}.
The Cartan forms $\Omega_a$, $\Omega^a$ and $\tilde\Omega_a{}^a$ in the light-cone gauge become purely bosonic quantities equal to
$\Omega_{\mathbf ba}{}^4$, $\Omega_{\mathbf b4}{}^a$ and $\Omega_{\mathbf ba}{}^a$ respectively given by Eq.(65) of \cite{0811}. Then the $S^7$ part of the target-space metric acquires the Kaluza-Klein form
\begin{equation}
ds^2_{S^7}=\Omega^{8I'}\Omega^{8I'}=\Omega^{87}\Omega^{87}+ds^2_{CP^3}=(dy+a)^2+ds^2_{CP^3},
\end{equation}
where
\begin{equation}
a(d)=\tilde\Omega_a{}^a-e^{-2\varphi}\eta_4\bar\eta^4dx^+
\end{equation}
and
\begin{equation}
ds^2_{CP^3}=-\Omega^{8}{}_{4a}\Omega^{84a}.
\end{equation}
In analogy with (\ref{fermviel}) in the Cartan forms (\ref{defsconff}) associated with the supersymmetry and superconformal generators it is also
possible to single out the terms proportional to the reduction direction coordinate differential $dy$
\begin{equation}
\omega^\mu_A=\tilde\omega^\mu_A+dy\omega^\mu_{yA},\quad\bar\omega^{\mu
A}=\bar{\tilde\omega}{}^{\mu A}+dy\bar\omega^{\mu A}_y,\quad
\chi_{\mu A}=\tilde\chi_{\mu A}+dy\chi_{y\mu
A},\quad\bar\chi^A_\mu=\bar{\tilde\chi}{}^A_\mu+dy\bar{\chi}{}^A_{y\mu}.
\end{equation}
In the light-cone gauge the $dy-$independent components are given by
\begin{equation}\label{omega-a}
\tilde\omega^\mu_a=e^{-\varphi}\left(
\begin{array}{c}
\hat d\theta_a+dx^1\hat\eta_a\\
dx^+\hat\eta_a
\end{array}\right),\quad
\bar{\tilde\omega}{}^{\mu a}=e^{-\varphi}\left(
\begin{array}{c}
\hat d\bar\theta^a+dx^1\hat{\bar\eta}{}^a\\
dx^+\hat{\bar\eta}{}^a
\end{array}\right);
\end{equation}
\begin{equation}\label{chi-a}
\tilde\chi_{\mu a}=\left(
\begin{array}{c}
0\\
e^{\varphi}\hat d\eta_a
\end{array}\right),\quad
\bar{\tilde\chi}{}^a_\mu=\left(
\begin{array}{c}
0\\
e^{\varphi}\hat d\bar\eta^a
\end{array}\right),
\end{equation}
where $\hat d\theta_a(\hat d\eta_a)=T_a{}^bd\theta_b(d\eta_b)+T_{ab}d\bar\theta^b(d\bar\eta^b)$, $\hat
d\bar\theta^a(\hat d\bar\eta^a)=T^a{}_bd\bar\theta^b(d\bar\eta^b)+T^{ab}d\theta_b(d\eta_b)$, and
\begin{equation}\label{omega-4}
\tilde\omega^\mu_4=\left(
\begin{array}{c}
d\theta_4+d\varphi\theta_4+e^{-2\varphi}dx^1\eta_4\\
e^{-2\varphi}dx^+\eta_4
\end{array}\right),\quad
\bar{\tilde\omega}{}^{\mu 4}=\left(
\begin{array}{c}
d\bar\theta^4+d\varphi\bar\theta^4+e^{-2\varphi}dx^1\bar\eta^4\\
e^{-2\varphi}dx^+\bar\eta^4
\end{array}\right);
\end{equation}
\begin{equation}
\tilde\chi_{\mu 4}=\left(
\begin{array}{c}
0\\
d\eta_4-d\varphi\eta_4
\end{array}\right),\quad
\bar{\tilde\chi}{}^4_\mu=\left(
\begin{array}{c}
0\\
d\bar\eta^4-d\varphi\bar\eta^4
\end{array}\right).
\end{equation}
The components of $F^{\hat\alpha}_y$ acquire the form
\begin{equation}\label{omega-y}
\omega^\mu_{y4}=\left(
\begin{array}{c}
2i\theta_4\\
0
\end{array}\right),\quad
\bar\omega^{\mu 4}_y=\left(
\begin{array}{c}
-2i\bar\theta^4\\
0
\end{array}\right);
\end{equation}
\begin{equation}\label{chiy}
\chi_{y\mu 4}=\left(
\begin{array}{c}
0\\
2i\eta_4
\end{array}\right),\quad
\bar\chi^4_{y\mu}=\left(
\begin{array}{c}
0\\
-2i\bar\eta^4
\end{array}\right).
\end{equation}
For the $OSp(4|8)/(SO(1,3)\times SO(7))$ supercoset element (\ref{48cosetel}) the
consequence of the absence of the vielbein dependence on the
reduction direction coordinate $y$ is that the $AdS_4$ vielbein
components (\ref{omega}) acquire the contributions proportional to
$dy$. To remove them, i.e. to bring the bosonic components of the supervielbein to the
Kaluza-Klein ansatz form (\ref{kkanzatz}), the local Lorentz
rotation in the tangent space needs to be performed. Since the
$\mathbb{CP}^3$ vielbein components (\ref{omega84a}) do not
contain the contributions proportional to $dy$, the necessary
frame rotation $L$ involves only tangent to the $AdS_4$ directions and
the one tangent to the U(1)-fiber direction on $S^7$ labeled by
"11" in the $11d$ context
\begin{equation}
\left(\begin{array}{c}
\mathrm E^{m'}\\
\mathrm E^{11}
\end{array}\right)=
L\left(\begin{array}{c}
G^{0'm'}\\
\Omega^{87}
\end{array}\right).
\end{equation}
The entries of the matrix $L$
\begin{equation}
L=\left(\begin{array}{cc}
L^{m'}{}_{n'}& L^{m'}{}_{7}\\
L^7{}_{m'}&L^7{}_7
\end{array}\right)\in SO(1,4)
\end{equation}
in the light-cone gauge are given by
\begin{equation}
L^{m'}{}_{n'}=\delta^{m'}_{n'}-\frac12G^{0'm'}_yG^{0'}_{yn'},\quad
L^{m'}{}_7=-G^{0'm'}_y,\quad L^{7}{}_{m'}=G^{0'}_{ym'},\quad
L^7{}_7=1,
\end{equation}
where
\begin{equation}
G^{0'm'}_y=\left(\frac12(\omega^m_y+c^m_y),0\right)=2\Theta(1,0,-1,0),\quad \Theta=\theta_4\bar\theta^4+\eta_4\bar\eta^4
\end{equation}
is the $D=1+3$ light-like vector. Corresponding Lorentz rotation acting on the
supervielbein fermionic components is generated by the matrix
\begin{equation}
L^{\hat\alpha}{}_{\hat\beta}=\delta^{\hat\alpha}_{\hat\beta}-\frac12G^{0'}_{ym'}\mathfrak{g}^{m'\hat\alpha}{}_{\hat\gamma}\mathfrak{g}^{11\hat\gamma}{}_{\hat\beta}.
\end{equation}
As a result transformed bosonic components of the $D=11$ supervielbein in the light-cone basis equal
\begin{equation}\label{tbv}
\begin{array}{c}
\mathrm E^{+}=\frac12e^{-2\varphi}dx^+,\quad\mathrm E^{-}=\frac12e^{-2\varphi}dx^-+\varpi-2e^{-2\varphi}\Theta^2dx^++4\Theta(\tilde\Omega_a{}^a-e^{-2\varphi}\eta_4\bar\eta^4dx^+),\\
\mathrm E^1=\frac12e^{-2\varphi}dx^1,\quad\mathrm E^3=-d\varphi,\\
\mathrm E^{11}=dy+A(d),\quad A(d)=a(d)-e^{-2\varphi}\Theta dx^+
\end{array}
\end{equation}
where $x^{\pm}=x^2\pm x^0$ and
\begin{equation}
\varpi=ie^{-2\varphi}(d\theta_a\bar\theta^a-\theta_ad\bar\theta^a)+i(d\theta_4\bar\theta^4-\theta_4d\bar\theta^4)+ie^{2\varphi}(d\eta_a\bar\eta^a-\eta_ad\bar\eta^a)+i(d\eta_4\bar\eta^4-\eta_4d\bar\eta^4).
\end{equation}
Note that in the light-cone gauge the superfield
$\Phi=\sqrt{1+G^{0'm'}_yG^{0'}_{ym'}}$ turns to unity for the
chosen normalization. Correspondingly the transformed fermionic
components $(Lf)^{\hat\alpha}$ of the supervielbein read
\begin{equation}\label{tchi-a}
(L\tilde\chi)_{\mu a}=\left(
\begin{array}{c}
0\\
e^{\varphi}\hat d\eta_a+2ie^{-\varphi}\Theta\hat\eta_adx^+
\end{array}\right),\quad
(L\bar{\tilde\chi}){}^a_\mu=\left(
\begin{array}{c}
0\\
e^{\varphi}\hat d\bar\eta^a-2ie^{-\varphi}\Theta\hat{\bar\eta}{}^adx^+
\end{array}\right)
\end{equation}
and
\begin{equation}\label{tchi-4}
(L\tilde\chi)_{\mu 4}=\left(
\begin{array}{c}
0\\
d\eta_4-d\varphi\eta_4+2ie^{-2\varphi}\Theta\eta_4dx^+
\end{array}\right),\quad
(L\bar{\tilde\chi}){}^4_\mu=\left(
\begin{array}{c}
0\\
d\bar\eta^4-d\varphi\bar\eta^4-2ie^{-2\varphi}\Theta\bar\eta^4dx^+
\end{array}\right).
\end{equation}
Other fermionic vielbein components (\ref{omega-a}), (\ref{omega-4}), (\ref{omega-y}), (\ref{chiy}) remain unaffected. Altogether they define the
Kaluza-Klein form of the fermionic vielbein (\ref{kkfermviel}).
Then using (\ref{omega84a}) and (\ref{tbv}) we find the expression for the
induced world-sheet metric in the fermionic light-cone gauge (\ref{lcfermi})
\begin{equation}
g^{(2)}_{ij}=g^{AdS}_{ij}+g^{CP}_{ij},
\end{equation}
where
\begin{equation}
\begin{array}{rl}
g^{AdS}_{ij}=&\frac12(\mathrm E^+_i\mathrm E^-_{j}+\mathrm
E^+_{j}\mathrm E^-_i)+\mathrm E^1_i\mathrm E^1_j+\mathrm
E^3_i\mathrm
E^3_j\\[0.2cm]
=&\frac18e^{-4\varphi}(\partial_i x^+\partial_j x^-+\partial_j
x^+\partial_i x^-)+\frac14e^{-4\varphi}\partial_i x^1\partial_jx^1
+\partial_i\varphi\partial_j\varphi\\[0.2cm]
+&\frac14e^{-2\varphi}[\partial_ix^+(\varpi_j+4\Theta\tilde\Omega_{ja}{}^a)+
\partial_jx^+(\varpi_i+4\Theta\tilde\Omega_{ia}{}^a)]-4e^{-4\varphi}\theta_4\bar\theta^4\eta_4\bar\eta^4\partial_ix^+\partial_jx^+
\end{array}
\end{equation}
and
\begin{equation}
\begin{array}{rl}
g^{CP}_{ij}=&-\frac12(\Omega^{84a}_i\Omega^8_j{}_{4a}+\Omega^{84a}_j\Omega^8_i{}_{4a})\\[0.2cm]
=&\frac12(\Omega_{ia}\Omega^a_j+\Omega_{ja}\Omega^a_i)+e^{-\varphi}[\partial_ix^+(\Omega_{ja}\hat{\bar\eta}{}^a\bar\eta^4
-\Omega^a_j\hat\eta_a\eta_4)+\partial_jx^+(\Omega_{ia}\hat{\bar\eta}{}^a\bar\eta^4-\Omega^a_i\hat\eta_a\eta_4)]\\[0.2cm]
+&4e^{-2\varphi}\hat\eta_a\hat{\bar\eta}{}^a\eta_4\bar\eta^4\partial_ix^+\partial_jx^+.
\end{array}
\end{equation}
The superstring WZ term is determined by the integral of the NS-NS 3-form
(\ref{wzred})
\begin{equation}
H_{(3)}=\frac{i}{4}(E^{\hat\alpha}\mathfrak{g}^{\hat m'\hat
n'}{}_{\hat\alpha}{}^{\hat\beta}\chi_{\hat\beta}\wedge\mathrm
E_{\hat m'}\wedge\mathrm E_{\hat
n'}+E^{\hat\alpha}\mathfrak{g}^{\hat
m'11}{}_{\hat\alpha}{}^{\hat\beta}\wedge
E_{\hat\beta}\wedge\mathrm E_{\hat
m'})-\varepsilon_{m'n'k'l'}\mathrm E^{m'}\wedge\mathrm
E^{n'}\wedge\mathrm E^{k'}L^{l'}{}_7
\end{equation}
that in the fermionic light-cone gauge (\ref{lcfermi})
can be presented as the total differential of the
2-form
\begin{equation}
\begin{array}{rl}
B_{(2)}=&\frac{1}{2}e^{-4\varphi}(\theta_4\bar\theta^4+\eta_4\bar\eta^4)dx^1\wedge
dx^+\\[0.2cm]
+&\frac14e^{-2\varphi}(d\theta_4\bar\eta^4-d\eta_4\bar\theta^4+\eta_4d\bar\theta^4-\theta_4d\bar\eta^4)\wedge
dx^+\\[0.2cm]
+&ie^{-2\varphi}(\theta_4\bar\eta^4-\eta_4\bar\theta^4)dx^+\wedge\tilde\Omega_{a}{}^a
+ie^{-\varphi}\hat\eta_a\theta_4dx^+\wedge\Omega^a+ie^{-\varphi}\hat{\bar\eta}{}^a\bar\theta^4dx^+\wedge\Omega_a\\[0.2cm]
+&e^{-2\varphi}\hat\eta_a\hat{\bar\eta}{}^adx^1\wedge
dx^++\frac12e^{-2\varphi}(\hat\eta_a\hat d\bar\theta^a+\hat
d\theta_a\hat{\bar\eta}{}^a)\wedge dx^+.
\end{array}
\end{equation}
So the Polyakov representation of the $AdS_4\times\mathbb{CP}^3$ superstring action in the fermionic light-cone gauge (\ref{lcfermi}) becomes
\begin{equation}
S_{l.c.}=-\frac12\int\limits_\Sigma d\tau
d\sigma\sqrt{-\gamma}\gamma^{ij}(g^{AdS}_{ij}+g^{CP}_{ij})\pm\int\limits_\Sigma
d\tau d\sigma B_{(2)},
\end{equation}
where $\gamma_{ij}$ is the auxiliary world-sheet metric. The
bosonic light-cone gauge condition can be fixed in various ways,
in particular, within the Hamiltonian approach \cite{MTlc}, \cite{found}.
\section{Conclusion}
We have obtained the $AdS_4\times\mathbb{CP}^3$ superstring
action in the light-cone gauge, in which both light-like
directions lie on the Minkowski boundary of the $AdS_4$ part of the background. In deriving
it we employed the double dimension reduction of the supermembrane
action on the $AdS_4\times S^7$ background constructed in
\cite{Plefka98} using the supercoset approach. To perform the
dimensional reduction it is necessary to change the generator
basis in the $so(8)$ sector of the $osp(4|8)$ isometry superalgebra of $AdS_4\times S^7$ superbackground to
exhibit the Hopf fibration realization of the 7-sphere. In the
$sp(4)$ sector the generators have been transformed to the $3d$
conformal basis. As a result the fermionic generators and coordinates
naturally split into corresponding to the (un)broken Poincare and conformal
supersymmetries. The kinetic term of the
resultant action includes the contributions up to the 4th order in
the space-time fermions and the WZ term is of the 2nd order similarly to the $AdS_5\times S^5$ superstring case \cite{MTlc}. There
can be taken simplifying limits of the action analogous to those
considered for the $AdS_5\times S^5$ superstring (for review see
\cite{found}). It can also be used to study the string states with zero quantum numbers from the $\mathbb{CP}^3$ sector within the semiclassical approximation \cite{GKP}, \cite{FT}, whose application for the $AdS_4\times\mathbb{CP}^3$ superstring has been initiated in \cite{semiclas}.
\section{Acknowledgements}
The author is obliged to A.A.~Zheltukhin for stimulating discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 2,794
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You can read all about Abi and Phil's big day below. In a change for 2019 blogs, I'll be really narrowing down the image selection on the page to my favourite 30 or so images. I'd love you then to take 3 minutes out of your day to sit back, watch and listen to Abi & Phil's wedding photography on their unique slideshow video, linked below. I really think music adds something, so it's worth a listen!
Abi and Phil were married at the lovely St Mary's Church, Lamberhurst, followed by a marquee reception in the grounds of Abi's sister and brother in law's amazing house – which was a truly stunning venue to have access to!
A lot of us Brits are the same when it comes to the weather – moan when it's too hot and long for cooler days and then can't wait for summer to come around. On a cold, wintry day in the UK I thought I'd throw back to a beautiful wedding from last summer, which was on one of the hottest days of the year – a real scorcher!
I started the day by joining Abi and family at their reception location, where preparations were in full swing outside and in. The marquee was up and the flowers being finished off by Lara and her team from Darling and Wild including an amazing full-length statement piece across the front of the top table – stunning!
Due to England's progress in the World Cup, an outdoor screen was hastily being erected for the footie fans to keep one eye on during the drinks reception….
Once Abi was into her dress it was time for me to head off to the Church to join Phil, photograph guest arrivals and then await the arrival of the bridal party.
After the touching wedding ceremony, everyone made their way back to the stunning wedding reception venue to enjoy canapes, provided by the ever-excellent Mint Dining and drinks in the sun – as there was so much space, everyone found their own spots to relax and enjoy themselves – some in the shade, some soaking up the rays and some by the football screen!
Once the groups were done, I took Abi and Phil for some couples portraits as we went exploring the woodlands in the grounds – the shade was a brief respite from the sun!
After the drinks reception it was time for everyone to head into the rather warm marquee for the wedding breakfast. Once everyone had been seated and service had started – watched over by Michael from Wedding Day Butlers – I took a quick 5 minutes to chill out – literally – in the walk in wine and beer fridge – bliss!
After my quick break it was time for the speeches with some very touching funny moments and a special present for the bride, that her father in law had bought in the hope of a girl all those years ago – handed over to the first honoury daughter.
Then it was straight into the cake cut and then first dance. Everyone soon joined Abi & Phil on the dance floor until the heat took over. The dancing took a small break whilst we all enjoyed the rest of the evening sunshine.
I'd kept an eye on the sunset so quickly whipped the Bride and Groom off up the field for a few more quick portraits before it was time for us to set up ready for the finale – the fireworks!
Congratulations to Abi & Phil – what a stunning day!
|
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{"url":"https:\/\/questioncove.com\/updates\/51def067e4b076f7da415ae5","text":"OpenStudy (anonymous):\n\nLet tan x=12 and cot y=16. What is cot X + tan Y ?\n\n4 years ago\n\nuse these identity : tan = 1\/cot cot = 1\/tan\n\n4 years ago\n\nif tan x = 12 then cot x = 1\/tan x = 1\/12 while if cot y = 16 then tan y = 1\/cot y = 1\/16\n\n4 years ago\n\nso, cot x + tan y = 1\/12 + 1\/16 = ... ?\n\n4 years ago\nOpenStudy (anonymous):\n\n0.1458\n\n4 years ago\nOpenStudy (anonymous):\n\nis that correct\n\n4 years ago\n\n1\/12 + 1\/16 = 4\/48 + 3\/48 = 7\/48 = 0.1458 you are right\n\n4 years ago\nOpenStudy (anonymous):\n\nThank you so, so much very grateful !!!!! ;D\n\n4 years ago","date":"2017-11-18 10:06:18","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\": 0.803307831287384, \"perplexity\": 9220.738283712011}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-47\/segments\/1510934804724.3\/warc\/CC-MAIN-20171118094746-20171118114746-00123.warc.gz\"}"}
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{"url":"https:\/\/www.physicsforums.com\/threads\/electric-flux-through-the-semisphere.130739\/","text":"# Electric Flux through the semisphere\n\n1. Sep 4, 2006\n\n### YoungILoveYou\n\nHello, if we have an electric field E parallel to X axis and a semisphere with axis parallel to X axis, which is the electric flux through the semisphere?\n\n2. Sep 4, 2006\n\n### Andrew Mason\n\nThe flux is:\n\n$$\\phi = \\int E\\cdot dA$$\n\nSince flux is a dot product of the field and area, the flux through the semisphere is the same as the flux through the projection of the semisphere onto the yz plane (which is perpendicular to x axis).\n\nAM\n\n3. Sep 5, 2006\n\n### YoungILoveYou\n\nAnother thing.\nIf there is a sphere centered at the origin, with radius R, the Flux is zero?\nI think that is similar to cube example!\n\nhttp:\/\/img153.imageshack.us\/my.php?image=cubeqq7.jpg\n\nWhat do you think?\n\nBye\n\n4. Sep 5, 2006\n\n### Tomsk\n\nYes, if there's no charge inside it, which there wouldn't be with that field, I think. If there is a charge inside the sphere, the flux is Q\/epsilon0.","date":"2017-04-30 01:32:34","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\": 0.7612172961235046, \"perplexity\": 716.2766129158368}, \"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-2017-17\/segments\/1492917123635.74\/warc\/CC-MAIN-20170423031203-00220-ip-10-145-167-34.ec2.internal.warc.gz\"}"}
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I spent five years in Tokyo, taking my camera wherever I went. Now I've assembled a book of my favourite photos from that time. I called the book streets without names . So if you've ever wanted to see Asia or if you just like street photos, have a look. The whole thing begins here.
Thanks for the quick response i have a follow up question with my situation as a foreign worker. Can i still work here in alberta havingy work permit til nov2015 and file an outland process for spousal sponsorship? Or should i really leave canada while its ongoing?
You should be able to stay in Canada. In fact, the visa office in Manila will ask for your passport early in the process (after about six weeks, once your husband has been approved as a sponsor). You won't, at that point, be able to leave the country. I believe that you should look into "dual intent".
And by all means, get all the information you can from CIC.
I was hoping that it was 100% make-up. But I suppose you never know.
Great pictures Mike. Love the texture.
that is some hard-core ikke-ikke onna. they must turn the dial on the sunbed to beyond the max to get their faces that dark!
Kinda sad that the fad has passed on. I guess the kids'll have to come up with something new.
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{"url":"https:\/\/crypto.stackexchange.com\/tags\/bcrypt\/hot?filter=all","text":"# Tag Info\n\n45\n\nThe hash returned by bcrypt.hashSync is more than the hash itself, it contains all parameters needed by bcrypt. You do not need to store anything else yourself, this information is everything bcrypt needs to hash and compare an incoming password. The actual hash was computed by combining the password and salt, so no worries there. The structured data is ...\n\n30\n\nComing up with a specific number is hard. Realistically, all three options take you well out of the realm of ever having more than the absolute worst passwords brute-forced by an attacker. The primary gain of scrypt and argon2 over bcrypt is a hit to parallelism due to the addition of memory requirements. GPUs with thousands of cores will need (but don't ...\n\n30\n\nIs this really more secure than using bcrypt with a complexity of 11 or 12 ? It depends. Obviously if you consider everything on their servers compromised this isn't more secure than using a higher workload for the password hashing scheme (PHS). If you assume they can guard their pepper better than their password database then the passwords are ...\n\n26\n\nThe algorithms themselves just output binary (i.e. bytes) if you read their specifications. It's the implementation in API's and applications that output the hexadecimals and\/or base64. Sometimes there are also ad hoc standards \/ common practice that specifies a certain output format. This is for instance the case for the output of the bcrypt password ...\n\n25\n\nUsing Base64\/HEX has nothing to do with security of a hash algorithm. Base64 and HEX are ways to represent binary data, which is the actual output of a hash algorithm. Base64 is shorter simple because it uses a larger charset than HEX. (64 characters vs 16 characters) Besides, algorithms like SHA-256 and SHA-512 are only \"unsafe\" when used for password ...\n\n16\n\nIntroduction BCrypt is a password-based KDF (far from state-of-the-art, but better than PBKDF2, because BCrypt requires sizable RAM, which greatly increases the cost of hardware-accelerated password search). Bcrypt is based on the block cipher Blowfish, with the initial processing of the password reminiscent of Blowfish's key preprocessing. Bruce Schneier'...\n\n14\n\nI understand that the Global \"pepper\" means that a DB dump protects the hashes until that pepper is found, and then each hash is still salted per user, but how much would that slow down people reversing the passwords in the event of a DB leak over simply bcrypting them ? If you use AES with a random 128-bit key (the smallest key size), an attacker who ...\n\n13\n\nYour core problem is the fact that you only have about 20 bits of entropy at most (assuming users pick fully random 6-digit PINs which most probably won't). 20 bits of entropy also means that it takes an attacker at most 1,000,000 times the amount of work that you invest for verification to find the password, but the attacker can greatly parallelize the ...\n\n11\n\nSHA-512 is a cryptographic hash while bcrypt is a password hash or PBKDF (password based key derivation function). SHA-512 has been designed to be fast. You don't want any delays when validating a signature, for instance. There is no reason for generic cryptographic hashes to be slow. bcrypt on the other hand is a password hash that performs key ...\n\n10\n\nAny time there is a choice and password search is an issue, one should prefer scrypt or perhaps bcrypt to stretched-md5, or even PBKDF2. The reason is that scrypt and bcrypt provide better security, by requiring a bigger investment in hardware (in particular, RAM) for the would-be password cracker, assuming parametrization yielding the same runtime for ...\n\n10\n\nYou are correct, Blowfish is a reversible cipher if you know the key. Bcrypt has three parameters it uses to hash a password: Salt Password Cost It derives a key using the salt, password and cost to encrypt the well known text \"OrpheanBeholderScryDoubt\" and not the password itself. So verification would be performing the encryption again on this string and ...\n\n10\n\nSo in general, isn't this equivalent to what Bcrypt and PBKDF2 do in terms of password storage security? PBKDF2, yes, pretty much. The only real difference is that salt\/password are used the other way around, with the password mixed in at every step. Bcrypt, however, is different. In your case an attacker only needs a small amount of memory compared to ...\n\n8\n\nLet's get terminology right. If you talk of \"unknown s\" then s is not a salt; when some piece of data is secret, we call it a key. And your \"hash function\" is then a MAC. In the context of \"password hashing\", such things are sometimes called \"peppering\" (as always, technical terminology is, at its core, a collection of bad puns). If your MAC is correct (i.e....\n\n8\n\nIn many cases, 0x00 is treated as end of string. That is where the problem comes into play. So if I passed password\\x00defgreallylongpassword into bcrypt, the password would be terminated after password due to the null byte. That is a very insecure password and can easily be found with a dictionary attack. No one types null bytes into a password field, ...\n\n7\n\nIt's called a key derivation function because that's what you'd typically use its output for \u2014 as a key for some other cryptographic algorithm. (Of course, you can also use the output of Bcrypt for other purposes, e.g. storing it in a database as a password hash, but that's really a secondary use case.) In general, key derivation functions (KDFs) ...\n\n6\n\nProbably because a simple cascade would only be stronger against some attacks, while opening the door to more implementation bugs. While bcrypt and scrypt are password-hashing functions, much of what is in the answers to this question about combining hash functions applies here. Different constructions give preimage resistance and PRF-ness, and which is ...\n\n6\n\nThe threat model of password storage is that of server compromision, where the attacker gain access to the database and server code. The attacker can then run the code to test password candidates, possibly making modifications, porting to faster platform, etc. The attacker will not bother computing the fake hash and fake salt. So this scheme is twice as ...\n\n6\n\nYou have two algorithms, $A$ and $B$, that claim to compute two (essentially) injective, hard-to-invert and costly-to-compute functions $F$ and $G$. Your fear is that either of the algorithms instead compute functions $F'$ and $G'$, that may be neither injective, hard-to-invert, nor costly-to-compute. This may happen because of programming mistakes or (these ...\n\n6\n\nDo I really weaken the password? To some degree, yes. The function is considered public, and the attacker can test random passwords with it and check the output and compare it to your key. Then he finds the correct password, even if he actually just guessed one of those permutations you defined. In your example: Actual password is carphagen The key is: ...\n\n6\n\nThe combined strength of two key stretching algorithms is not greater than the sum of its parts. It is at best equal to the sum of its parts. If you budget $x$ amount of CPU time to password stretching then you have to decide, do you give 100% of $x$ to scrypt? 100% to bcrypt? 50-50? You can't give both 100% of $x$ to both scrypt and bcrypt because that's ...\n\n5\n\nPoints 3 and 4 are a secure way of storing the input to bcrypt (with appropriate choice of parameters for bcrypt). Points 1 and 2 aren't necessary but don't harm: they would add a small amount of extra computation for an attacker is possession of the password database that wants to do a dictionary attack; the attacker wouldn't be able to straight-out use a ...\n\n5\n\nInstead of that home-grown scheme, I would use PBKDF2 instead if you simply are sold on the idea of iterated hash schemes. It uses an such a scheme, although not exactly the one you have described, and is well-studied and considered secure. However, PBKDF2 doesn't offer many advantages over bcrypt, as PBKDF2 is still vulnerable to GPU and FPGA\/ASIC brute-...\n\n5\n\nWhat I did in one of my password generators is that given a secret key $K$, public data $\\text{Pub}$, I first generate a solid \"master key\" $K_m$ via key-stretching the secret key using PBKDF2 (any other key derivation function would work, I just happened to have that lying around): $$K_m = PBKDF2(K, \\text{salt, iterations, } \\cdots)$$ And then derive ...\n\n5\n\nLucas Kauffman is correct that the more recent algorithms were either too new to be proven, or not available at all, when bcrypt was designed. But this immediately brings up the question of whether a replacement for bcrypt could profitably make use of these more recent algorithms. For password-hashing purposes, Blowfish has one great advantage over more ...\n\n5\n\nCurrent best practice does include bcrypt, which is the same as PHP's built in password_hash() function. Future best practice will probably be Argon2. Other widely used secure KDF options include PBKDF2 with SHA512 or SHA256 as the hash function, and scrypt. scrypt and bcrypt differ from PBKDF2 in that they can use large amounts of memory, and thus resist ...\n\n4\n\nThe scrypt function is specifically designed to hinder such attempts by raising the resource demands of the algorithm. Specifically, the algorithm is designed to use a large amount of memory compared to other password-based KDFs, making the size and the cost of a hardware implementation much more expensive, and therefore limiting the amount of paralleling an ...\n\n4\n\nBCrypt is considered more secure The theoretical security of bcrypt has received less scrutiny than that of PBKDF2, SHA2 and HMAC. PBKDF2 is thus widely standardised (e.g. in NIST SP800-132 and PKCS #5) while bcrypt is not. In practice the security (resistance to brute force attack or dictionary attack) of bcrypt and PBKDF2-HMAC-SHA512 can be controlled ...\n\n4\n\nIs it bad to use this method to store passwords? Yes. It is bad. Why? It's bad because you're rolling your own crypto, which is generally considered a bad choice. It's bad because SHA-3 is slow in software (e.g. on servers and consumer PCs) and fast in hardware (e.g. FPGAs, ASICs) and hence attackers can relatively fast try out many passwords. So the ...\n\n4\n\nAlthough your scheme is secure - especially with a random key of 32 bytes or higher - it won't offer any benefit over HMAC. It's therefore not recommended to use such a scheme. Also note that `bcrypt has been designed for key stretching which is deliberately not efficient. You have ample entropy in your key so there is no need for key stretching.\n\n4\n\nBecause bcrypt uses Blowfish as a component inside an irreversible algorithm. This is very common\u2014many variable-input length cryptographic algorithms are built from smaller, fixed-input-length components that may or may not be reversible. One example is the SHA-3 hash function, which is designed following an algorithm known as the sponge construction, ...\n\nOnly top voted, non community-wiki answers of a minimum length are eligible","date":"2020-12-06 01:39:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.23987236618995667, \"perplexity\": 1906.4856659521683}, \"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-2020-50\/segments\/1606141753148.92\/warc\/CC-MAIN-20201206002041-20201206032041-00425.warc.gz\"}"}
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{"url":"https:\/\/www.physicsforums.com\/threads\/how-do-we-know-values-for-a-true-vacuum.100538\/","text":"# How do we know values for a true vacuum?\n\n1. Nov 18, 2005\n\n### Lucretius\n\nThis isn't a homework question or anything, it's just been bothering me as to how we know values for a true vacuum. From my understanding, free space is another term for a true vacuum. If this is correct, how were we able to attain values for the permittivity and permeability of free space if it is unattainable in a laboratory?\n\n2. Nov 19, 2005\n\n### rbj\n\nto start with, at the present time, in SI, the permeability of free space, $\\mu_0$, and the speed of E&M propagation (otherwise known as \"the speed of light\"), $c$ are defined. consequently the permittivity of free space $\\epsilon_0$ and characteristic impedance of free space $Z_0$ (that depend solely on $\\mu_0$ and $c$) are defined. while it hasn't always been the case that the speed of light has been defined (the meter and second were defined independently of each other then) now the meter is defined to be the length of the path travelled by light in vacuum during a time interval of 1\/299792458 of a second. (doesn't get to your vacuum question, hold on a bit.)\n\nhowever the permeability of free space has always been defined to be $\\mu_0 = 4 \\pi \\times 10^{-7}$ because the unit of electical current, the ampere was defined to be such a current that, \"if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to $2 \\times 10^{-7}$ newton per meter of length.\" because of that definition of the ampere, and from the pre-existing definition of the second, the unit of charge, the ampere-second or coulomb was defined. that unit of current or of charge happens to be defined just so that the permeability is $\\mu_0 = 4 \\pi \\times 10^{-7}$.\n\nyou might want to check out the definitions, \"right from the horse's mouth\": http:\/\/physics.nist.gov\/cuu\/ there's some nice history of the SI units there, too.\n\nthe relationship of these four constants are:\n\n$$c^2 = \\frac{1}{\\mu_0 \\epsilon_0}$$\n\nand\n\n$$Z_0^2 = \\frac{\\mu_0}{ \\epsilon_0}$$\n\nso you can see once $\\mu_0$ and $c$ are defined, so also is $\\epsilon_0$ and $Z_0$.\n\nnow at one time (before the 60s) the meter was defined independently from the second and from $c$. in fact, they didn't know $c$ precisely and had to measure it, with their predefined meters and seconds. Albert Michaelson did a famous experiment (about a century ago) with a rotating mirror system and a mirror mounted on a mountain 22 miles away to do that measurement. but that was $c$ in air, not a vacuum.\n\nbut you can set up an interference experiment with light of a known color (or wavelength) where light in air is interfering with light passing through a vacuum chamber. because even though the distance traveled by both rays of light is the same, the ray through a vacuum arrives before the ray in air, and there is some wave mismatch and light and dark interference patterns show up because of \"destructive\" and \"constructive\" interference. as air is slowly let into the vacuum chamber, the interference pattern moves and one can count how many ridges of intereference pass by and from that, they can measure the number of wavelengths the \"fast\" light was ahead of the \"slow\" light and from that determine the ratio of the two speeds of light and from the speed of light in air (Michaelson) you can compute a speed of light in a vacuum. i dunno how they did it on the earth otherwise, but in space, they could have measured it directly.\n\nhowever, eventually they redefined the meter so that $c$ must always be 299792458 m\/s.\n\n3. Nov 19, 2005\n\n### Lucretius\n\nThanks for that lengthy and informational post! So, is the speed of light given now that of a TRUE vacuum, or one of a near vacuum? I'm thinking true vacuum.\n\n4. Nov 19, 2005\n\n### GENIERE\n\nYour question might have had an answer in the past but if quantum physics is correct (most believe it to be), then a true vacuum' cannot exist. You may want to familiarize yourself with zero point energy (ZPE), the Casimer Effect, and the accelerating expansion of the universe.\n\n5. Nov 19, 2005\n\n### Lucretius\n\nOh yes, I am aware that a vacuum cannot be truly empty due to the presence of ZPE (virtual particles and such). I was just wondering, putting aside effects like that, would we have found values for a true vacuum state?\n\n6. Nov 20, 2005\n\n### GENIERE\n\nI understand your question and will try to respond intelligently with the caveat that I enjoy reading about physics but I have very limited knowledge.\n\nWe will need to consider the propagation velocity of an individual photon to avoid getting into a phase and group velocity discussion. We will need to imagine a region in space wherein gravity fields are somehow nulled out or small enough to be ignored. We will have to assume certain quantum effects do not occur during our measurement period; for instance the photon will not propagate as a positron-electron pair and thus travel briefly below C. We will need our region of space to have less density than normal\u2019 space to reduce the probability of interaction with virtual particles.\n\nThe last requirement I think can be obtained by having the proton propagate between two conductive planes i.e., use the Casimer effect to decrease the energy density or increase negative energy. To obtain a true vacuum, the distance between the plates must be reduced to the Plank limit wherein our `laws\u2019 no longer apply. To avoid that conflict, we will keep our gap at a femtometer or so.\n\nIn that environment, I think the photon will have a higher velocity than it will in the vacuum of normal space.\n\nI think above violates SR as it establishes an impossible reference plane. I think your question cannot be answered and I have only demonstrated my lack of knowledge by trying.","date":"2017-08-21 18:37:30","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\": 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\": 0.7216986417770386, \"perplexity\": 429.8628123723204}, \"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-2017-34\/segments\/1502886109470.15\/warc\/CC-MAIN-20170821172333-20170821192333-00569.warc.gz\"}"}
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Q: How to set marquee behaviour in android to alternate programatically This is the code I am using but the behaviour of the marquee is that is scrolls. How to make it to alternate i.e. it moves from right to left and then left to right.
public void setMarquee(TextView textView) {
textView.setEllipsize(TextUtils.TruncateAt.MARQUEE);
textView.setMarqueeRepeatLimit(-1);
textView.setHorizontallyScrolling(true);
textView.setSelected(true);
textView.requestFocus();
}
A: Step1
create folder called anim in res directory
step 2
create slide_left.xml
slide_left.xml
<translate
android:duration="3000"
android:fromXDelta="100%"
android:toXDelta="0" />
</set>
step 3
in main_activity.class
LinearLayout mlayout =
(LinearLayout)findViewById(R.id.mlayout); // the view u want to animate
Animation slide_left_anim;
slide_left_anim=
AnimationUtils.loadAnimation(getActivity().getApplicationContext(),
R.anim.slide_left);
slide_left_anim.setRepeatCount(Animation.INFINITE);
mlayout.startAnimation(slide_left_anim);
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featured Inclusion
How not to report: Chronicle Herald erases prisoners from story on prison conditions
By RobertDevet - April 6, 2017
KJIPUKTUK (Halifax) – The Chronicle Herald, now that its real reporters are walking the picket line, isn't known for high journalistic standards.
Sometimes the results are funny, and people on Twitter and Facebook get a laugh out of the scab paper's silly headlines, sloppy editing and error-ridden reporting.
And sometimes it's not funny at all.
A story the Herald ran earlier this month about a petition prisoners initiated, demanding that something be done about high long distance charges collected by a corporation from Texas is an example of something very definitely not funny.
The anonymous Herald reporter simply quoted several paragraphs from the online petition and a few comments, and then allowed the spokesperson for the department of Justice to systematically deny and dismantle all the prisoners' complaints unchallenged.
Prisoners were not asked about their experiences and they were not given a chance to validate doubtful assertions by the Department of Justice spokesperson. Nor were they asked if they even wanted the Herald to tackle the story.
Spoken word poet and prisoners advocate El Jones has supported the efforts of the inmates of the North East Nova Scotia Correctional Facility to get the petition up and running. She is not happy about the Chronicle Herald's reporting.
"In the petition the prisoners mention how they need the issue addressed from the outside because 'their voices only reach as far as these confined walls,' and then the reporter doesn't even bother talking to them," says Jones.
According to Jones, who has talked with the prisoners since the Herald article was published, the Department of Justice response that prisoners get two free five-minute calls a week is not something inmates are aware of.
And contrary to what the Department of Justice says, prisoners have seen no evidence that fees paid by the Texas company are used for things such as "winter clothes for prisoners about to be released."
"They didn't talk to any prisoners, not even to advocates, they could so easily have talked to the Elizabeth Fry Society, they could have spoken to some of the prisoners' families, they could talk to me," says Jones. "I know how much they pay for calls. To say calls are not expensive, that's a lie."
Even just coming in and quoting their words in the petition without the prisoners' permission is wrong, says Jones, and potentially dangerous.
"I don't do anything without asking the people in prison what they want done. It takes incredible courage to put this petition out there. If people find out who wrote this they can be put in solitary for this," says Jones. "So I would always make that decision with them."
And then there is the little matter of the strike. "Prisoners were not allowed to make the decision whether they want to break a picket line. It's their petition that was being quoted," Jones says.
We submitted several questions to the Chronicle Herald this afternoon, we have not yet received a response.
Sign the petition here.
If you can, please support the Nova Scotia Advocate so that it can continue to cover issues such as poverty, racism, exclusion, workers' rights and the environment in Nova Scotia. A pay wall is not an option, since it would exclude many readers who don't have any disposable income at all. We rely entirely on one-time donations and a group of 25 or so dedicated monthly sustainers.
Tags: #Chronicle Herald #Department of Justice #El Jones #Journalism in Nova Scotia #Media #Prison #Synergy Inmate Phones
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,187
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Ensworth is seeking a dynamic and intellectually engaging teacher to join the faculty of the Math Department. The ideal candidate will value relationships, collaboration, a love for teaching high school students, and joy in learning. Essential to this position is the ability to align teaching and learning to Ensworth's Core Skills Framework, flexibility in teaching most of the courses within the department, and the capacity to adapt to new technology. The ideal candidate will have earned a B.A. in Mathematics or a related field. A master's degree and three years or more of teaching experience at either the high school or college level is preferred, but not required. The primary professional responsibility of a faculty member is to conduct the school's curricular program; however, this instructor will also have extracurricular, complementary, and professional responsibilities as articulated in the Ensworth Employee Handbook.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 2,133
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Emir Dzafič (born 8 September 1972) is a Slovenian former professional footballer who played as a midfielder.
References
External links
1972 births
Living people
Slovenian footballers
Association football midfielders
Slovenian expatriate footballers
Slovenian expatriate sportspeople in Croatia
Expatriate footballers in Croatia
Slovenian expatriate sportspeople in Germany
Expatriate footballers in Germany
NK Celje players
NK Rudar Velenje players
NK Mura players
VfL Bochum players
NK Samobor players
Bundesliga players
Expatriate footballers in Malaysia
Slovenian expatriate sportspeople in Malaysia
Slovenian PrvaLiga players
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,087
|
Q: Newbie: ATmega32u2 USB-powered - how to ground? In ATmega32u2's reference manual, there's a diagram for USB-powered application like shown below.
Should I, or should I not, connect the GROUND to VSS/UVSS line? And why? If not, then what to do, just connect GROUNDs together?
A: Yes, connect ground to UVSS. The ground symbol is used to indicate a common zero voltage reference point. Because you are powering the MCU via USB, this common zero voltage should be the same as the supply and therefore connected to the 0V (UVSS) line.
A: The VSS notation is apparently commonly used in modern digital circuits as alternative notation to GND (references: [1], [2], [3]).
I've also noted, that on the ATmega32u2 pinout (manual, Fig.1-1 on p.2), there's neither VSS nor UVSS mentioned, but there's both GND and UGND, which supports this interpretation.
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 543
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Darren Sawatzky (born February 22, 1973 in Seattle, Washington) is an American soccer coach and former player who is currently the head coach of the Richmond Kickers in USL League One. He spent four seasons in Major League Soccer, one season in the Major Indoor Soccer League, one in USISL and five in the United Soccer Leagues. He currently holds several coaching positions at the high school, collegiate and professional levels and was the Director of Youth Development for Seattle Sounders FC of Major League Soccer. In January 2015, he was named head coach of the Tacoma Stars of the Major Arena Soccer League.
Player
High school and college
Sawatzky grew up in the Seattle area, playing for the Highline club as a youth. He attended Thomas Jefferson High School in Federal Way, Washington. After graduating from high school, Sawatzky entered the University of Portland. He played for the University of Portland Pilots soccer team from 1991 to 1994, finishing his career tenth on the career scoring list. He graduated from Portland with a bachelor's degree in organizational communication.
Professional
In 1995, Sawatzky signed with the expansion Oregon Surge in USISL. He also had trials with Mexican clubs UNAM Pumas and Leon in 1995, but did not earn a contract with either team. In 1996, he went on trial with Leicester City, but was not signed. In February 1996, the New England Revolution of Major League Soccer (MLS) selected Sawatzky in the eighth round (75th overall) in the Inaugural MLS Draft. He played nineteen games, scoring four goals that season. In 1997, his playing time dropped to five games as the Revolution loaned him to both the Connecticut Wolves and Worcester Wildfire of the USISL A-League. The Revolution released Sawatzky on November 10, 1997. In 1998, the Dallas Burn of MLS selected Sawatzky in the third round (thirty-fourth overall) of the 1998 Supplemental Draft. However, he played only a total of three minutes for the Burn as they loaned him out first to the New Orleans Storm then the Hershey Wildcats before releasing him. Sawatzky then signed with the Charleston Battery, playing nineteen games in the 1998 season. In 1999, the Colorado Rapids of MLS took Sawatzky in the first round (eighth overall) of the 1999 Supplemental Draft. He played fourteen games for the Rapids in 1999, then was waived on November 24, 1999. In April 2000, the Seattle Sounders of the United Soccer Leagues (USL). He tied for third in the league with sixteen goals, earning first team All Star recognition. In 2001, he played a single season with the expansion Portland Timbers. On December 20, 2001, the Timbers released Sawatzky. He then moved to the Kansas City Comets of Major Indoor Soccer League. In February 2002, he rejoined the Sounders as a free agent. He saw declining minutes with the Sounders over the next two seasons and on July 23, 2004, he announced his intentions to retire at the end of the season to devote himself full-time to coaching.
Coach
Sawatzky began coaching in 1991 with the Tualatin Hills Soccer Club. Over the years, he continued to coach with various youth clubs as his playing career allowed. In 2001, he became an assistant coach with Central Catholic High School in Portland, Oregon while playing with the Timbers. When he moved to Seattle in 2002, he became the head coach at his alma mater, Jefferson High School. In 2005, he took Jefferson to the 4A Washington State Championship. In 2004, he became an assistant coach with the University of Washington. On February 21, 2007, Sawatzky joined the Seattle Sounders as an assistant coach. He also serves as the Director of Coaching for HPFC, a youth club in Washington State. He coached and helped almost every team for the HPFC boys and girls club teams, including HPFC Boys 94 blue and HPFC Girls 95 Blue.
Since 2015, Sawatzky has coached the indoor Tacoma Stars.
On August 31, 2016, Sawatzky was hired as the interim head coach of the Guam national football team.
On December 12, 2018, Sawatzky was named the head coach of FC Tucson in USL League One.
On November 6, 2019, he was named as head coach and sporting director of the Richmond Kickers.
References
External links
Charleston Battery profile
University of Washington Coach's profile
New England Revolution profile
1973 births
Living people
American soccer players
American soccer coaches
Soccer players from Portland, Oregon
Cascade Surge players
Charleston Battery players
Colorado Rapids players
Connecticut Wolves players
FC Dallas players
Hershey Wildcats players
Kansas City Comets (2001–2005 MISL) players
Major Indoor Soccer League (2001–2008) players
Major League Soccer players
MLS Pro-40 players
New England Revolution players
New Orleans Riverboat Gamblers players
Sportspeople from Portland, Oregon
Portland Pilots men's soccer players
Portland Timbers (2001–2010) players
Seattle Sounders (1994–2008) players
University of Portland alumni
A-League (1995–2004) players
USL First Division coaches
Worcester Wildfire players
People from Federal Way, Washington
USISL players
FC Dallas draft picks
Colorado Rapids draft picks
Guam national football team managers
Association football forwards
USL League One coaches
Association football midfielders
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 169
|
var evalUtils = require('./evalUtils');
var EvalImage = function (style, color) {
// x/y location in pixel space of object's center
this.x_ = 200;
this.y_ = 200;
this.rotation_ = 0;
this.scaleX_ = 1.0;
this.scaleY = 1.0;
this.style_ = style;
this.color_ = color;
};
module.exports = EvalImage;
EvalImage.prototype.updatePosition = function (x, y) {
this.x_ = x;
this.y_ = y;
};
EvalImage.prototype.draw = function (parentElement) {
if (this.style_ && this.color_) {
this.element_.setAttribute('fill', evalUtils.getFill(this.style_, this.color_));
this.element_.setAttribute('stroke', evalUtils.getStroke(this.style_, this.color_));
this.element_.setAttribute('opacity', evalUtils.getOpacity(this.style_, this.color_));
}
var transform = "";
transform += " translate(" + this.x_ + " " + this.y_ + ")";
if (this.scaleX_ !== 1.0 || this.scaleY !== 1.0) {
transform += " scale(" + this.scaleX_ + " " + this.scaleY_ + ")";
}
if (this.rotation_ !== 0) {
transform += " rotate(" + this.rotation_ + ")";
}
if (transform === "") {
this.element_.removeAttribute("transform");
} else {
this.element_.setAttribute("transform", transform);
}
};
EvalImage.prototype.place = function (x, y) {
this.x_ = x;
this.y_ = y;
};
EvalImage.prototype.rotate = function (degrees) {
this.rotation_ += degrees;
};
EvalImage.prototype.scale = function (scaleX, scaleY) {
this.scaleX_ = scaleX;
this.scaleY_ = scaleY;
};
/**
* Get child EvalObjects. overridden by children
*/
EvalImage.prototype.getChildren = function () {
return [];
};
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 6,443
|
This is a real time chat app just to get started with `socket.io`
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 8,619
|
{"url":"http:\/\/eprint.iacr.org\/2007\/106","text":"## Cryptology ePrint Archive: Report 2007\/106\n\nA generalization of Secret Sharing Scheme on the Basis of Recovering Algorithm, K-RA\n\nMasao KASAHARA\n\nAbstract: Extensive studies have been made of the Secret Sharing Scheme(SSS). In this paper new classes of SSS, referred to as K-SSS, $\\rm{K_I}$-SSS, $\\rm{K_{I\\hspace{-.1em}I}}$-SSS and $\\tilde{{\\rm K}}$-SSS are presented on the basis of recovering algorithm, K-RA. As an application, we shall also present a method for the recovering of secret informations learned only by heart, based on a particular class of K-SSS, $\\rm{K_I}$-SSS.\n\nCategory \/ Keywords: cryptographic protocols \/ secret sharing scheme, Reed-Solomon code, recovering algorithm","date":"2016-02-13 21:28:11","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\": 0.46690499782562256, \"perplexity\": 3111.7510183899876}, \"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-2016-07\/segments\/1454701168011.94\/warc\/CC-MAIN-20160205193928-00152-ip-10-236-182-209.ec2.internal.warc.gz\"}"}
| null | null |
Facebook's Long, Psychological Journey To Reactions
Augmenting the Like
By Dave Gershgorn | Published Feb 24, 2016 6:00 PM
Facebook's new Reactions make the Like more robust. Facebook
Facebook Reactions are here, and they've been a long time coming.
Since at least 2012, Facebook has been searching for ways to make its service more expressive. In the minds of product developers and managers at the social media company, there shouldn't be an emotion that you can't express on Facebook. The group's quest brought them all the way back to Charles Darwin, with pitstops at Berkeley University and Pixar Labs.
The Reactions rolled out today are meant to be a quick way to express a flash of emotion, like amazement, a laugh, anger, a pang of sadness, or the feeling of love. Facebook has taken these emotions and assigned them animated emoticons with bits of text: Love, Haha, Wow, Sad, and Angry. These don't replace the Like button, but are meant to be used alongside it.
Facebook's new Reactions make the Like more robust. Facebook
Really like something? Pop a Love on it. See an awesome photo of a double rainbow? Drop some Wows.
This is huge. The Like button is iconic and monolithic, and the last remaining binary (on or off) feature that Facebook has. Businesses hang "Like Us On Facebook" on their doors, and the Like has pretty much been copied by every other social media platform since Facebook. It works. And now Facebook is messing with the recipe.
Facebook's first attempt at a more expressive platform was in the instant messaging tool. This was done through "stickers," little animated emoticons users could send back and forth. They called on researcher Dacher Keltner, a professor of psychology at UC Berkeley, and he worked with Pixar designer Matt Jones to make a set of stickers starring a character called Finch.
Finch is a little yellow ball with facial expressions that harken to Darwin's original sketches. (You can still find Finch by searching Stickers in Facebook Messenger.) In Darwin's 1872 book, The Expression of the Emotions in Man and Animals, he outlined more than 50 universal emotions. Keltner gave Facebook about 40 emotions with sketches from Jones, all tested at his lab for readability. The would show dozens or hundreds of people the emotions, and simply see if they could recognize each one. For Finch, Facebook pared it down to about 16, and refined the ideas internally. These launched in 2013, and Facebook saw them as a success, keeping a team around to make more new stickers.
Finch served as a jumping-off point for Facebook's new Reactions. About a year ago, Facebook reached out to Keltner again, this time to talk about which emotions might accompany the Like button. He worked with his team to send 43 ideas, and from that list Facebook picked, refined, and launched four, in addition to the "Love" Reaction.
Original sketches of the first proposed Reactions. Matt Jones
The list was created partially from Darwinian emotions, and partially from the work of fellow UC Berkeley professor Paul Ekman, a psychologist whose research in the 1970s informed most of what we know today about facial expressions.
"Reactions, I believe, come straight out of Darwin," Keltner told Popular Science. "The artistic rendering process that led to Finch and had great influence on Reactions is very much rooted in science and anatomy."
But as attuned to our psychology as Reactions are, there are limits.
Every emotion that Facebook chose had to be extremely easily recognizable. Keltner says that he's urged Facebook to add like voices or vocal inflections to the emoticons. He's also advocated for giving the Reactions and Stickers arms or bodies in certain situations, saying that it's easier to read body language than the face sometimes.
Prior to launch, Facebook's Reaction team has been testing in seven countries, including Ireland and Spain. The Reactions will be translated into all of the 70+ languages that Facebook supports, which posed a huge challenge to Facebook's sticker team.
For instance, the team was originally going to launch a "Yay" reaction, but it wasn't being used in some countries so the team decided to launch without it, says Sammi Krug, who led the Reactions team.
The set of emotions are the same right now across the whole world, and the translations are all as close as they can be, too.
However, the Reactions team is looking to make changes if necessary. Seven countries don't speak for the entire world, and despite their efforts of bringing native speakers onto the team, there's always more data to be had.
"We're going to continue, after we've launched the entire world, to get so many data points back, and the team will learn and iterate," Krug says.
Facebook Reactions are rolling out today, and you can access them by either hovering over the Like button with your mouse on a computer, or pressing and holding the Like button on mobile.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 6,434
|
Q: Multivariate Grouped Operation with pandas I'm trying to make the switch from R's dplyr to pandas in Python. I've gone through several tutorials to learn the basics but I'm stuck on one task. I'd like to use the agg method in groupby to perform operations on more than one column. This is a trivial task in R as the example below illustrates:
library(dplyr)
DF <- data.frame('ID'=c(1, 1, 1, 2, 2, 2),
'A'=c(1, 2, 3, 4, 5, 6),
'B'=c(2, 4, 6, 8, 10, 12))
IDgp <- group_by(DF, ID) %>%
summarise(C = prod(B) / sum(A))
### # Output:
###
### > DF
### ID A B
### 1 1 1 2
### 2 1 2 4
### 3 1 3 6
### 4 2 4 8
### 5 2 5 10
### 6 2 6 12
###
### > IDgp
### # A tibble: 2 x 2
### ID C
### <dbl> <dbl>
### 1 1 8
### 2 2 64
In this example, I'm grouping on the ID column in DF and creating an arbitrary new variable based on both columns A and B. Is there a straightforward way to convert this example to Python using pandas?
A: You can use GroupBy.apply:
df = df.groupby('ID').apply(lambda x: x['B'].prod() / x['A'].sum()).reset_index(name='C')
print (df)
ID C
0 1 8.0
1 2 64.0
Another solution with GroupBy.prod and GroupBy.sum, divide by Series.div:
g = df.groupby('ID')
df = g['B'].prod().div(g['A'].sum()).reset_index(name='C')
print (df)
ID C
0 1 8.0
1 2 64.0
is same as:
df = df.groupby('ID')['B'].prod().div(df.groupby('ID')['A'].sum()).reset_index(name='C')
print (df)
ID C
0 1 8.0
1 2 64.0
A: apply method as mentioned by jezrael is the way to go.
Alternatively, if you want to store intermediate results and assing new values by chaining, you could use .agg and .assign.
In [251]: df.groupby('ID').agg({'A': 'sum', 'B': 'prod'}).assign(C=lambda x: x.B/x.A)
Out[251]:
A B C
ID
1 6 48 8.0
2 15 960 64.0
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 1,147
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Carriera
Professionista dal 1993 al 1999, vanta anche due partecipazioni al Giro d'Italia (1995 e 1997) e quattro al Tour de France (1995, 1996, 1997, 1998). Alla Batik/Gewiss lavorò come gregario per ciclisti come Evgenij Berzin, Pëtr Ugrumov, Moreno Argentin, al Team Deutsche Telekom per Jan Ullrich, Bjarne Riis ed Erik Zabel.
Palmarès
1991 (dilettanti)
Milano-Rapallo
1995
Rund um den Henninger-Turm
3ª tappa Setmana Catalana
Classifica generale Setmana Catalana
5ª tappa Bicicletta Basca
1996
4ª tappa Vuelta al País Vasco
Piazzamenti
Grandi Giri
Giro d'Italia
1995: 29º
1997: 71º
Tour de France
1995: 77º
1996: 100º
1997: non partito (14ª tappa)
1998: 93º
Altri progetti
Collegamenti esterni
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 6,111
|
#import <Foundation/Foundation.h>
@class SendBuffer;
@interface DDTcpClientManager : NSObject<NSStreamDelegate>
{
@private
NSInputStream *_inStream;
NSOutputStream *_outStream;
NSLock *_receiveLock;
NSMutableData *_receiveBuffer;
NSLock *_sendLock;
NSMutableArray *_sendBuffers;
SendBuffer *_lastSendBuffer;
BOOL _noDataSent;
int32_t cDataLen;
}
+ (instancetype)instance;
-(void)connect:(NSString *)ipAdr port:(NSInteger)port status:(NSInteger)status;
-(void)disconnect;
-(void)writeToSocket:(NSMutableData *)data;
@end
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 2,903
|
{"url":"https:\/\/fangquant.com\/t\/755","text":"FangQuant \u203a Daily Morning\n\n### Daily Market Review on Specified Futures Products 2020.04.02\n\nsubmitted 2020-04-02 10:08:28\n\nCrude oil\n\nCrude oil inventories and exports of Saudi Arabia increase significantly. According to Kpler schedule data, OPEC crude oil exports remained stable in March, but Saudi Arabia increased its export volume to 9.64 million barrels per day in the last week of March, while the average export volume in the first three weeks was 7 million barrels per day. Saudi Arabia is realizing its decision to increase supply, and its exports to Egypt and Japan have increased significantly. In addition, its domestic inventory has also increased from 66 million barrels to 77.3 million barrels. In addition, Iraq and the UAE will also significantly increase exports in April. We believe that April will be the darkest moment of the crude oil market. It is expected that onshore and offshore inventories will continue to increase significantly. At present, the spot price of crude oil is extremely weak, and the actual price of some crude oil has fallen to single digits, but we believe that as more refineries reduce processing capacity and Saudi Arabia increases supply, some spot oil prices may fall to near zero, and once the global tank capacity is approaching the limit, crude oil futures prices will also be under pressure again. In terms of futures operation, it is advised to maintain the short strategy; reverse cash and carry arbitrage strategy to long the back-month contract and short the near-month contract is recommended for Brent oil. Guard against risks that epidemic was under control and OPEC reopens agreement to cut output.\n\nRaw materials of Polyester\n\nThe trends of domestic PTA and MEG showed a certain differentiation yesterday, the former fell under pressure and the latter fluctuated. From the demand side, the cancellation or extension of foreign trade orders caused by overseas epidemics has begun to increase. This week, polyester companies began to continuously reduce prices and stimulate terminal procurement. As far as PTA is concerned, due to the restart of the device shutdown early, under the condition that the existing processing fee remains at a high level, the operating load of the enterprise has increased significantly, and the pressure from the supply side has been significant. In contrast, although the profit of naphtha-based MEG is still acceptable, coal-based enterprises began large-scale shutdowns yesterday, and the starting load may be reduced to around 50%, which may ease some of the supply pressure. Overall, PTA and MEG will continue to oscillate, but MEG may be slightly stronger than PTA.\n\nIron ore\n\nYesterday, the iron ore finally broke down with the related futures varieties. The market sentiment on the iron ore became more objective and the spot transactions in the port also dropped significantly. The current spot price of golden bubba powder at the port is equivalent to \u00a5679 per ton. Fundamentally, the inventory at 7 foreign ports has rebounded. It is expected that domestic shipments will increase in the later stage. As the demand for terminal steel declines, the demand side will gradually fall, and the drag on iron elements will begin to show. The pressure on spot is expected to increase from the end of April to May, and the medium- and long-term trend continues to be bearish on iron ore. In the short term, we still need to pay attention to the uncertainty caused by the epidemic in Brazil and the excessive discount. It is recommended to control the position and focus on back month contracts.\n\nNatural Rubber\n\nOverseas rubber went down weakly. The main force contract of TF06 fell by 3.2 or 2.98% to 104.3. The main force contract of JRU08 fell by 2.1 or 1.50% to 138.0. The SHFE rubber went weak. The main force contract of RU09 fell by 200 or 2.07% and closed at 9,480, and the main force contract of NR05 fell by 145 or 1.87% and closed at 7,620. The quoted price for Qingdao rubber in USD fell by $20 to$30 per ton with general inquiries. The quoted price of RSS3 was $1,420 per ton. The spot price or CIF of STR20 was$1,060 to $1,080 per ton. The CIF of SMR20 in August was$1,110 per ton. The CIF of mixed rubber from Thailand in August was \\$1,130 per ton.\n\nA brief analysis by the 315i Network: According to data released by the Thai Customs, Thailand\u2019s natural rubber (including composite and mixed rubber) exports in February were about 452,100 tons, which increased by 3.55% month-on-month and 1.89% year-on-ear. Among them, the export volume of natural rubber (excluding composite rubber) was about 278,600 tons, down month-on-month and year-on-year; the composite rubber realized a both month-on-month and year-on-year increase. Due to the impact of the Spring Festival holiday in China, the replenishment sentiment in the market was high, and the cargo arrived at the port after the Spring Festival.\n\nToday is the Vietnamese King's Day, and the local market is closed. As for latex, the main upstream producing countries are in the off-season, and the processing enthusiasm for plants is not active. The transaction prices of some brands fell below \u00a51,000 per ton. Domestic demand is slowly recovering, and internal and external prices are still reverse. The downstream replacement tire market ushered in a small peak of resumption of work, and the delivery of goods was acceptable. Distributors' inventory of finished products declined, but their enthusiasm for replenishment was not high.\n\nFutures Operation Advice: The main RU09 contract fluctuated weakly, and it is advised to pay attention to the suppress at the previous high level at 9,660 above.\n\n(For reference only)","date":"2021-12-04 07:05:51","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\": 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\": 0.2011151909828186, \"perplexity\": 4477.624338079016}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964362952.24\/warc\/CC-MAIN-20211204063651-20211204093651-00383.warc.gz\"}"}
| null | null |
Veteran NFL Running Back Was Released On Saturday
By Ajay Pandit
Iage Credit - Google.com
Fifth-year running back Sony Michel has been released by the Los Angeles Chargers.
In order to make room on the roster for standout pass rusher Joey Bosa,
who was reinstated from the injured reserve ahead of this weekend's game against the Rams,
the organisation made this move.
This season, Michel played in 10 games for the Chargers, rushing 36 times for just 106 yards and no touchdowns.
His NFL career's current campaign has been his least fruitful.
The Rams' first-round draught selection racked up 845 yards and four touchdowns in 2021.
In the Chargers' depth chart, Michel was listed third, behind Austin Ekeler and Joshua Kelley.
Along with rookie fourth-round pick Isaiah Spiller, he shared touches.
On Sunday, the Chargers and Rams will play in Week 17, with the winner securing a spot in the postseason.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,130
|
\section{Introduction}
\label{sec:intro}
The new era of artificial intelligence and robotics has an ever-increasing interest in multi-robot systems. \color{black} The causality of this trend is outlined in the following three points. First, the recent \textit{advances \color{black} in hardware and communications} allow the cooperative deployment of many affordable robots. Second, the use of multiple robots introduces \textit{redundancy}, which can be translated into mission speed-up and/or fault-tolerant characteristics (e.g., in cases when one or more robots faces a malfunction). Third, the utilization of multi-robot teams may tackle \textit{problems that cannot be solved with a single robot} (e.g., continuous monitoring/guarding a large area). Robot missions in which the multi-robot configuration can be more appealing include surveillance in hostile environments (e.g., areas contaminated with biological, chemical, or even nuclear wastes), law enforcement missions (e.g., border patrol), agriculture activities (e.g., soil sampling), and cleaning missions (e.g., cleaning up an oil spill).
\subsection{Related work}
\label{subsec:related}
Unfortunately, many of the multi robot tasks have been proven to be extremely difficult. For example, the online generation of robot trajectories so as to maximize SLAM accuracy and efficiency is NP-hard \cite[]{singh2009efficient, kollar2008efficient}. Moreover, the offline design of multi-robot trajectories in order to cover a known area of interest in minimum time/energy has been proven NP-complete \cite[]{zheng2005multi}, etc.
To alleviate the above problem, many multi-robot approaches attempt to solve a simplified version of the original problem. In such a way, it is possible to construct a computationally feasible solution, utilizing \textit{optimal control or dynamic programming} techniques, at the expense, of course, of sacrificing global optimality. For instance, to render the decision-making scheme computationally feasible, many methodologies \cite[]{seyboth2015robust, le2009trajectory, de2008dynamic} assumed relaxed or linearized versions of the multi-robot problem. A usual assumption is that the robots operate in a discrete space where their actions and measurements can also take values from a finite discrete set of values \cite[]{matignon2012coordinated, spaan2005perseus}. The exploitation of the above assumption can lead to remarkable results in the context of multi-robot tasks, presenting many real-life applications (e.g., \cite{capitan2013decentralized}). Unfortunately, these strategies cannot be fully informed by the (usually occurring) continuous field measurements, whereas they can be computationally intractable for large state systems, e.g., a single mobile robot operating in the real world often has millions of possible states \cite[]{roy1999coastal}. Other multi-robot approaches that fall into this class adapt the assumption of perfect or sufficient knowledge of the dynamics of the overall multi-robot system, i.e., the dynamics of each and every robot along with their interactions with the other robots and the external environment \cite[]{wang2016multi, zhou2011multirobot}. In such cases, the multi-robot problem can be seen to be equivalent to a standard optimization problem, where the robots' decision values are generated according to, e.g., a gradient-descent or gradient-descent-like algorithm \cite[]{nesterov2007gradient}. However, the requirement for perfect or sufficient knowledge of the overall dynamics renders the overall control design practically infeasible in many multi-robot applications, as they typically involve a large number of controllable variables with highly complex and uncertain dynamics \cite[]{morgan2016swarm, chen2015occlusion, gomes2013evolution}.
Another well-investigated class of multi-robot approaches is the \textit{optimal one-step-ahead} methodologies. In this family of approaches, the next robots' decision variables are chosen greedily, so as to optimize an appropriately defined cost function that is related to the problem in hand. For instance, in the domain of multi-robot exploration, a common practice is to choose the next robots' positions that maximize the expected information gain \cite[]{rooker2007multi, burgard2005coordinated, stachniss2003exploring} or minimize the trace of the extended Kalman filter (EKF) error covariance matrix \cite[]{cui2016mutual, bourgault2002information}. Although, many of these approaches have been successfully evaluated in real-life multi-robot platforms, the majority of them suffer from the following drawbacks. First and foremost, the nonlinearities may give rise to undesirable divergence (such as in cases where the noise does not follow the additive white Gaussian noise (AWGN) model). For example, it is usually considered that a robot can accurately estimate the position of an object or a point in the environment (landmark/cell) as soon as it perceives it. In most of the existing \textit{optimal-one-step-ahead} approaches, this assumption allows in each timestamp the a priori calculation of the cost function, as well as the robots' decision variables that greedily optimize such a cost function. Moreover, such an assumption is crucial for overcoming deadlocks (local minima), which are frequently encountered when greedy approaches are employed \cite[]{palacios2016distributed,rathnam2013distributed}. Finally, the selection of an adequate cost function that provides an efficient solution to the multi-robot problem is not always trivial.
On the other side of the spectrum are the \textit{simulation-based} multi-robot methodologies \cite[]{kapoutsis2015noptilus, kollar2008trajectory, kohl2004policy}. The idea behind these approaches is as follows. First a parameterized decision-making mechanism is devised for generating the robot decisions online, with different choices for its parameters, leading to different decision-making mechanisms. Then, realistic simulations or similar tools are used in order to optimize the parameters of the decision-making mechanism. Thus, conceptually, many of the optimization computations that otherwise would take place on the real devices are ``moved'' offline. The drawbacks of such approaches are as follows: first, the simulations need to cover a wide range of different realistic scenarios (and, thus, they may become ``expensive'') and second, because the dimensionality of the optimization problem is quite high, a large number of parameters is needed in order to come up with an efficient decision-making mechanism.
We close this subsection by mentioning that for most of the centralized approaches, in all three classes, it is not clear how they can be extended to have a distributed nature. Furthermore, the majority of the distributed multi-robot algorithms [e.g., \cite{palacios2016distributed, morgan2016swarm, rathnam2013distributed}] exploit application-specific dynamics, therefore their solutions cannot be generalized to a broader context. In other words, if the problem objectives or the dynamics are changed, most of the existing approaches must be redesigned from scratch to adequately tackle the altered problem.
\subsection{Contributions}
To overcome the aforementioned problems, we propose a new resource optimization algorithm, specifically tailored to the context of multi-robot applications, that extends the cognitive-based adaptive optimization (CAO) algorithm \cite[]{kosmatopoulos2009adaptive}. CAO was originally developed and analyzed for the optimization of functions for which an explicit form is unknown but their measurements are available, as well as for the adaptive fine-tuning of large-scale nonlinear control systems \cite[]{kouvelas2011adaptive, kosmatopoulos2009large}.
In a nutshell, an update cycle on decision variables of the proposed algorithm consists of the following steps. Initially, the robots' measurements are gathered in a central node (robot or base station) where the calculation of the global objective function takes place. In the following, each robot's contribution to the cost function is approximated and forwarded to the corresponding robot. In a fully distributed fashion, each robot constructs a linear-in-the-parameters (LIP) estimator to approximate the (unknown, problem-dependent) evolution of its subcost function. Then, each robot generates random (or pseudo-random) perturbations around its current state and neglects those that violate the operational constraints (if any). Finally, the next robot's action is the one valid perturbation that achieves the best score on the previously constructed estimator.
The proposed algorithm deviates from the original version of CAO in its distributed nature. More precisely, although each robot does not know explicitly either the decision variables of the other robots nor of their measurements, it is able to update its own decision variables effectively in a way to cooperatively achieve the team objectives. The latter can be achieved through a cost function that is exclusive to each robot, designed so as to encapsulate not only the mission objectives but also the other robots' dynamics (``data-driven gradient descent'' approach: for more details see Section \ref{sec:proposedAlg}). Rigorous arguments establish that despite the fact that the dynamics that govern the multi-robot system are unknown, the proposed methodology shares the same convergence characteristics as those of block coordinate descent algorithms \cite[]{wright2015coordinate}. As exhibited in the presented applications, the distributed nature of the proposed algorithm also allows rapid convergence, especially in cases with many robots.
The contributions with respect to the multi-robot approaches as presented in the previous subsection are as follows.
\begin{itemize}
\item[(i)] The problem is formulated in a continuous domain without the need to either know all the states and measurements beforehand, or to perform a relaxation on the original multi-robot problem (\textit{optimal control} and \textit{dynamic programming} approaches). The ability to cope with unknown dynamics (robots--environment) and unknown cost functions imparts a generality to the proposed algorithm, regarding the spectrum of applications that can be utilized.
\item[(ii)] However, the main advantage of the proposed algorithm is that it does not require either a priori calculation of the cost function (\textit{optimal one-step-ahead} approaches) or the analytical form of the system to be optimized to be explicitly known (\textit{optimal control} and \textit{dynamic programming} approaches). Instead, the proposed algorithm can cope with cost functions whose calculation can only be achieved by actually performing the corresponding course of actions. Along the same lines, the proposed algorithm does not require evaluation of the decision variables in the vicinity of their current values for calculating their corresponding updates. Instead, the proposed algorithm is able to find the (locally) optimal configuration for the decision variables by using only noise-corrupted measurements collected from the robots' sensors.
\item[(iii)] Furthermore, instead of relying on exhaustive, computationally intensive simulations (\textit{simulation-based} approaches), the proposed scheme is able to online learn the problem-specific characteristics that affect the user-defined objectives. By doing so, the proposed algorithm does not need any elaborate model in order to learn its decision-making mechanism.
\end{itemize}
It must be emphasized that apart from rendering the optimization problem practically solvable, the proposed approach preserves additional features that make it particularly tractable:
\begin{itemize}
\item[(i)] its complexity is low, allowing \textit{real-time implementations};
\item[(ii)] it can handle a variety of \textit{physical constraints};
\item[(iii)] it has \textit{fault-tolerant characteristics}, i.e., online redesign in case one or more robots being added or removed, an extra task being added to the set of objectives, etc.;
\item[(iv)] it is able to adapt its behavior even in cases where a \textit{time-varying objective function} is employed\endnote{The rate of change in the objective function should be smaller than the learning capabilities of the algorithm (see Section \ref{sec:problemForm})}.
\end{itemize}
\subsection{Simulation testbeds}\color{black}
The proposed control strategy is evaluated on \textit{three different simulation set-ups} under multiple scenarios, against both general-purpose and problem-specific algorithms. All the simulation set-ups have been chosen so that: i) the objective of the multi-robot mission can be expressed as a cost function, and ii) the evaluation of which cannot be performed beforehand.
In the first simulation set-up, the objective is to spread out the robots over a 2D environment while aggregating in areas of high sensory interest. An important aspect of the set-up is that the robots are not aware beforehand of the sensory areas of interest - instead, they learn this information online via sensor measurements from their current positions. The proposed algorithm is evaluated together with the approach proposed by \cite{schwager2009decentralized} for the problem in hand.
In the second simulation set-up, the trajectories of the robots should be designed in real-time having a twofold objective (which forms a trade-off). On the one hand, the part of the 3D terrain that is monitored (i.e., visible) by the robots has to be maximized and, on the other hand, for each one of these visible points in the terrain, the closest robot has to be as close as possible to that point. This problem along with a centralized CAO-based methodology has been proposed by \cite{renzaglia2012multi}, therefore a detailed analysis regarding the performance of both algorithms, in different scenarios, is presented.
Last but not least, the proposed methodology is evaluated in the task of persistent coverage. The objective of this application is to maintain a user-defined level of coverage in an unknown environment \cite[]{palacios2016distributed}. This is a quite challenging task as the mission objectives constantly change, whereas the unknown morphology of the environment does not allow the prior calculation of the improvement in the coverage task.
Conclusively, if it is possible to define a cost function which encapsulates the mission objectives and can be calculated through the robots' measurements for every decision variables configuration, the proposed methodology will be directly applicable to the corresponding problem.
\subsection{Paper structure}\color{black}
The remainder of the paper is structured as follows. Section \ref{sec:problemForm} presents the translation of a general-purpose multi-robot framework to a constrained optimization problem, highlighting the difficulties and the obstacles of the general problem. The description of the proposed algorithm, which tackles such a problem, is presented in Section \ref{sec:proposedAlg}. Sections \ref{sec:2dCoverage}, \ref{sec:3Dcoverage}, and \ref{sec:persistent} present three indicative multi-robot applications: \textit{adaptive coverage of unknown 2D environment}, \textit{3D surveillance of unmapped terrains}, and\textit{ persistent coverage of unknown 2D environments}, respectively. In all these sections, we perform a series of simulations in different scenarios to adequately analyze the performance of the proposed algorithm. The overall conclusions of the paper are drawn in Section \ref{sec:conclusions}.
\section{Problem formulation}
\label{sec:problemForm}
Consider a team (swarm) that consists of $N$ robots interacting with each other, towards achieving a global set of objectives. Let us assume the following augmented decision vector
\begin{equation}
\label{eq:stataSpace}
\textbf{x}(k) \equiv \left[x_1^\tau(k), x_2^\tau(k),\dots,x_N^\tau(k) \right]^\tau
\end{equation}
where $x_i(k) \in \mathbb{R}^n$ denotes the decision variables of the $i$th robot at the $k$ th iteration. These decision variables represent the controllable parameters of the available robots (e.g., position, motors, propellers, thrusters, rotation of the cameras, etc.). Furthermore, the augmented vector which contains the available exteroceptive measurements takes the form
\begin{equation}
\label{eq:measurements}
\textbf{y}(k) \equiv \left[y_1^\tau(k), y_2^\tau(k),\dots,y_N^\tau(k) \right]^\tau
\end{equation}
where $y_i(k) \in \mathbb{R}^m$ denotes the measurement vector of the $i$th robot at the $k$ th iteration and its evolution can be represented as
\begin{equation}
\label{eq:measurmentsUpdate}
y_i(k) \equiv h_i(k,x_i(k))
\end{equation}
where $h_i(\cdot)$ denotes an unknown, nonlinear function that depends on both $x_i(k)$ and the specific problem characteristics.
The accomplishment of the multi-robot system's objectives (e.g., mapping, surveillance, etc.) can be translated into the minimization (or maximization)\endnote{Without loss of generality, in the rest of the paper we assume a minimization problem.} of a specifically defined global cost function $\jmath_k$, i.e.,
\begin{equation}
\label{eq:globalCFx}
\jmath_k \equiv {\cal J} \bigg(x_1(k), x_2(k),\dots,x_N(k) \bigg)
\end{equation}
where ${\cal J}(\cdot)$ is a non-negative, nonlinear, scalar function that depends, apart from the robots decision variables, on the particular dynamics of the problem (e.g., the environment where the robots operate). Owing to the dependence of the function ${\cal J}$ on the particular problem characteristics, the \textit{explicit form of the function ${\cal J}$ is not known} in practical scenarios; as a result, standard optimization algorithms (e.g., gradient descent with an a priori model) are not applicable. However, in most practical cases, the current value of the objective function can be approximated from the robots' measurements,
\begin{equation}
\label{eq:globalCFy}
{\cal J} \bigg(x_1(k),\dots,x_N(k) \bigg) = \mbox{J} \bigg(y_1(k), \dots,y_N(k) \bigg) + \xi_k
\end{equation}
where $\xi_k$ denotes the noise introduced in the estimation of $\jmath_k$, owing to the presence of noise in the robots sensors.\endnote{Note that, although it is natural to assume that the noise sequence $\xi_k$, is a stochastic zero-mean signal, it is not realistic to assume that it satisfies the typical AWNG property, even if the robots sensors do; as ${\cal J}$ is a nonlinear function of the robots decision variables and, thus, of the robots sensor measurements (\ref{eq:measurmentsUpdate}), the AWNG property is typically lost.} It must be emphasized that, in contrast to ${\cal J}$, $\mbox{J}$ can be evaluated ``offline'', if the measurement vector $\textbf{y}(k)$ is available. However, the \textit{acquisition of a new measurement vector} requires an \textit{actual evaluation} of the decision variables on the robotic system (\ref{eq:measurements}) and (\ref{eq:measurmentsUpdate}).
Apart from the problem of dealing with a criterion for which an explicit form is not known, but only its noisy measurements are available at each time, the decision vector $\textbf{x}(k)$ should satisfy a set of constraints that, in general, can be represented as follows:
\begin{equation}
\label{eq:constraints}
{\cal C} \left( \textbf{x}(k) \right) \leq 0
\end{equation}
where ${\cal C}$ is a set of nonlinear functions of the decision variables $\textbf{x}(k)$. As in the case of ${\cal J}$, the constraints function ${\cal C}$ depends on the particular problem characteristics and an explicit form of this function may be not known in many practical set-ups; however, it is natural to assume that the low-level algorithm is provided with information whether a particular selection of decision variables $\textbf{x}(k)$ satisfies or violates the set of constraints (\ref{eq:constraints}).
Given the mathematical description presented above, the problem of choosing the decision variables online for a multi-robot system, so as to accomplish a set of objectives, can be mathematically described as the following constrained optimization problem:
\begin{equation}
\label{eq:OptimizationProblem}
\begin{array}{rl}
\mbox{minimize} & \jmath_{k}\\
\mbox{subject to} & {\cal C}\left(\textbf{x}(k)\right) \leq 0 \,
\end{array}
\end{equation}
As already noted, the difficulty in solving the constrained optimization problem (\ref{eq:OptimizationProblem}) in real-time lies in the fact that explicit forms for the functions ${\cal J}$ and ${\cal C}$ are not available. Although this is not the only problem, jointly optimizing a function over multiple robots ($N$), each of which with multiple decision variables ($n$), can incur excessively high computational cost.
\section{Proposed algorithm}
\label{sec:proposedAlg}
\begin{figure*}[!th]
\centering
\includegraphics[width=0.99\textwidth]{flowchart.png}
\caption{High-level diagram of the proposed algorithm. At each timestamp, all the operational robots first apply their decision commands and acquire the corresponding measurements $\textbf{y}(k)$, in order to be able to calculate the \textit{global cost function} index. Then, the contribution $\Delta_i(k)$ of the each robot to overall accomplishment of mission objectives is calculated and sent to the $i$th robot. In a fully distributed fashion, each robot constructs a linear-in-the-parameters estimator to approximate the (unknown - problem dependent) evolution of its sub-cost function $J_i(k)$, which encapsulates both the mission objectives and the operational capabilities of the multi-robot team. Finally, each robot's next decision vector $x_i(k+1)$ is the one valid perturbation that achieves the best score on the previously constructed estimator.}
\label{fig:highLevelDiagram}
\end{figure*}
Having defined the fundamental aspects that govern a multi-robot application, we proceed to present the proposed algorithm for updating the decision variables $\textbf{x}(k)$ so as to minimize the cost function (\ref{eq:globalCFx}) subject to (\ref{eq:constraints}). A high-level diagram of the proposed algorithm is sketched in Figure \ref{fig:highLevelDiagram}.
\subsection{Global coordination}
\label{subsec:globalCoordination}
\textit{Step 1}. As a first step, and for each iteration $k$, the robots transmit the acquired measurements, after the execution of $\textbf{x}(k)$ decision variables.
It must be emphasized that this step can be performed even in cases where global communication between all robots is not feasible. In such a case, each robot can send and receive measurements to and from peer (adjacent) robots, until all the measurements aggregate to the corresponding processor unit (robot or ground station). The latter can be guaranteed by introducing an extra condition on the constraints set (\ref{eq:constraints}), ensuring the connectivity, if applicable to the problem in hand, among the different robots.
\textit{Step 2}. Thus, the global cost function can be straightforwardly derived from (see (\ref{eq:globalCFx}) and (\ref{eq:globalCFy})):
$$
\jmath_{k} = \mbox{J} \bigg(y_1(k), \dots,y_N(k) \bigg)
$$
In addition, for each $i$ th robot calculate, the following discrepancy:
\begin{equation}
\label{eq:subCF}
\begin{aligned}
&\Delta_i(k) \equiv \jmath_{k} - \\
& \mbox{J} \bigg(y_1(k),\dots,y_{i-1}(k),y_i(k-1),y_{i+1}(k)\dots,y_N(k) \bigg)
\end{aligned}
\end{equation}
In other words, $\Delta_i(k)$ encapsulates the effect of the $x_i(k)$ on the current problem for the $k$th timestamp.
Note that, because the last term of (\ref{eq:subCF}) is analytically available, we can calculate this term, although the resulting value does not necessary correspond to the actual value when the robots have the following decision variables:
$$
\left\lbrace x_1(k),\dots,x_{i-1}(k),x_i(k-1),x_{i+1}(k)\dots,x_N(k)\right\rbrace
$$
Although, there may be a discrepancy between the way we calculate $J(\cdot)$ and its actual value, that does not affect the convergence properties of the proposed algorithm. This discrepancy is application oriented and depicts the effect of other robots' decisions on each robot's measurements. If the measurements acquired from a robot only affects its own decision variables and the problem itself (\ref{eq:measurmentsUpdate}), then there is no discrepancy at all.
\textit{Step 3}. Next, the calculated discrepancy $\Delta_i(k)$ is sent to the i $th$ robot.
After this step all the calculations are performed locally, building a system that i) is resilient to robot failures, ii) does not require any global coordination, and ii) all the decision variables' updates are made in a (parallel) distributed fashion.
\subsection{Distributed decision}
\label{subsec:distributedDecision}
Each $i$th robot, at the same $k$-th iteration, performs the following.
\begin{enumerate}[label=(\alph*)]
\item Calculate the $J_i(k)$ that corresponds to the last executed decision variables $x_i(k)$ as
\begin{equation}
\label{eq:constituentCF}
J_i(k) = J_i(k-1) + \Delta_i(k) , \; \forall k\ge 1, \;J_i(0) = \jmath_0
\end{equation}
Therefore, each robot is responsible to choose the next values for its decision variables $x_i(k+1)$, having as only objective the minimization of its corresponding cost function $J_i(\cdot)$\endnote{In general case: $\sum_{i=1}^{N}J_i(k) \ne \jmath_k$ and $\prod_{i=1}^{N} J_i(k) \ne \jmath_k, \; \forall k$}. Each such sub-problem is a lower-dimensional minimization problem, and thus can typically be solved more easily than the full problem.
\item Construct a LIP estimator of $J_i(k+1)$ as follows:
\begin{equation}
\label{eq:estimatorJ}
J_i(k+1) \approx \hat{J}_i(k+1) = \theta_i^\tau(k)\phi_i\big(x_i(k)\big)
\end{equation}
where $\phi_i$ denotes the nonlinear vector of $L$ \textit{regressor terms}, $\theta_i$ denotes the vector of the \textit{parameter estimates} and $L$ is a positive user-defined integer which denotes the size of the function approximator.
Defining the vector of regressor terms $\phi_i$ as in Section \ref{subsubsec:monomials_construnction}, the estimator vector $\theta_i$ can be calculated using standard least-squares estimator principles, i.e., $\theta_i$ is obtained by solving the following optimization problem:
\begin{equation}
\label{eq:estimatorTH}
\theta_i(k) = \argmin_\vartheta \sum_{\ell = k-T(k)}^{k-1} \bigg( \vartheta^\tau \phi_i\big(x_i(\ell)\big) - J_i(\ell+1)\bigg)^2
\end{equation}
where $T(k)$ denotes the time window over which the least-squares estimation is taking place.
\item Generate (randomly or pseudo-randomly) a set of $M$ valid candidate perturbations: $$\delta x_i^{(1)}(k),\delta x_i^{(2)}(k),\dots,\delta x_i^{(M)}(k)$$
where $\delta x_i^{(j)}(k)$ are vectors of the same dimension as $x_i(k)$ and $M$ is a positive integer that is larger\endnote{See \cite{kosmatopoulos2009adaptive} for more details about the sufficiency of this condition.} than 2n. A candidate perturbation $j$ is considered valid if\endnote{The distributed nature of the algorithm may impose a stricter set of constraints, in comparison with cases where a centralized control is applied.} :
\begin{equation}
\label{eq:Distributedconstraints}
{\cal C} \left( \left[x_1^\tau, \dots, x_{i-1}^\tau, x_i^\tau + \delta x_i^{(j)}, x_{i+1}^\tau, \dots, x_N^\tau \right]^\tau \right) \leq 0
\end{equation}
The random choice for the candidates is essential and crucial for the efficiency of the algorithm, as such a choice guarantees that $\hat{J}_i(k+1)$ is a reliable and accurate estimate for ${J}_i(k+1)$; see \cite{kosmatopoulos2009adaptive} and \cite{kosmatopoulos2009large} for more details.
\item Estimate the effect of each of the candidate perturbations on the current vector $x_i(k)$ by employing the previously constructed estimator (\ref{eq:estimatorJ}) and pick the candidate perturbation with the ``best'' effect, i.e., choose the vector $\delta x_i^{(j^*)}(k)$ that satisfies
$$
\delta x_i^{(j^*)}(k) = \argmin_{j=1,\dots,M} \theta_i^\tau(k)\phi_i\bigg(x_i(k) + \alpha(k)\delta x_i^{(j)}(k)\bigg)
$$
\item Update the $i$ th robot decision variables as
\begin{equation}
\label{eq:updateRule}
x_i(k+1) = x_i(k) + \alpha(k)\delta x_i^{(j^*)}(k)
\end{equation}
where $\alpha(k)$ is a positive function chosen to be either a constant positive function or a time-descending function satisfying $\alpha(k) >0, \sum_{k=0}^\infty \alpha(k) = \infty, \sum_{k=0}^\infty \alpha(k)^2 < \infty$. Furthermore, $\alpha(k) \leq \bar{\alpha} \; \forall k$, where $\bar{\alpha}$ is a problem-specific constant, correlated with the robot's dynamics (e.g., maximum achievable movement in one timestamp) and the objectives of the multi-robot application.
\item Finally, by applying the $x_i(k+1)$ decision vector, the corresponding $y_i(k+1)$ measurements vector will be acquired. This vector, along with all the measurements from the remaining robots, are utilized in order to evaluate the $k+1$ team configuration (see \textit{Step 1} from the previous subsection).
\color{black}
\end{enumerate}
\begin{remark}
\label{rm:1}
\normalfont
The above distributed update of the decision variables (Section \ref{subsec:distributedDecision}) does not need information about what is happening to the other robots. All the necessary information has been ``packed'' to the scalar value $\Delta_i(k)$. At each iteration, each robot attempts to minimize the objective function $J_i(k)$ by assuming that the other robots' decision variables are part of the problem to be solved.
\end{remark}
\begin{remark}
\label{rm:localMinima}
\normalfont
The utilization of random perturbations provides the proposed algorithm with the potential to escape from local minima. In essence, the random perturbations inside the distributed decision mechanism (step (c)), could have a behavior similar to \textit{simulated annealing}, which has been proved that under specific conditions can overcome local minima \cite[]{granville1994simulated} that may arise from the distributed nature of the algorithm.
\end{remark}
\color{black}
\subsection{Estimator implementation}
\label{subsec:estimator_implementation}
This subsection encloses the implementation details of the $i$th robot estimator (\ref{eq:estimatorJ}), as outlined in step (b) of the distributed decision-making scheme.
\subsubsection{$\phi$ monomial construction.}
\label{subsubsec:monomials_construnction}
The vector $\phi_i$ of regressor terms must be chosen so that it satisfies the so-called \textit{Universal Approximation Property} \cite[]{polycarpou1991identification}, i.e., it must be chosen so that the approximation accuracy of the constructed approximator (\ref{eq:estimatorJ}) is an increasing function of the approximator's size $L$. Polynomial approximators, radial basis functions, kernel-based approximators, etc. are known to satisfy such a property \cite[]{polycarpou1991identification}.\color{black}
Experimenting with different types of $\phi_i$, in different multi-robot set-ups (Sections \ref{sec:2dCoverage}--\ref{sec:persistent}, and \cite{chatzichristofis2013autonomous, kapoutsis2015real}), it was found that it is sufficient to construct a polynomial estimator as in Algorithm \ref{alg:regressorVector}.
\begin{algorithm}[h]
\caption{$\phi_i$ construction}
\label{alg:regressorVector}
\begin{algorithmic}[1]
\REQUIRE maxorder, $L_1,L_2,\dots,L_{\text{maxorder}}$, $ x_i$, $ n$
\ENSURE $\phi_i$
\STATE $\phi_i = 1 $
\FOR{$j \in\{1,...,\text{maxorder}\}$}
\FOR{$v \in\{1,...,L_j\}$}
\STATE $g=1$
\FOR {$l \in\{1,...,j\}$}
\STATE Generate $r:=$ random integer $ \in \{1,\dots,n\}$
\STATE $g = g \cdot x_i^{(r)}$
\ENDFOR
\STATE $\phi_i = \left[\phi_i^\tau, g \right]^\tau $
\ENDFOR
\ENDFOR
\end{algorithmic}
\end{algorithm}
The tunable parameters of this procedure are the maximum order of monomials (maxorder) and the corresponding number of monomials per order ($L_1,L_2,\dots,L_{\text{maxorder}}$, where $L_1 + L_2 + \dots + L_{\text{maxorder}} = L-1$ should be hold). Mathematically speaking, the number of different monomials per order is given by the number of possible combinations with repetitions (multiset coefficient):
$$
\multiset{n}{i} = {n + i -1 \choose i} = \frac{n(n+1)(n+2)\cdots(n+i-1)}{i!}
$$
where ${a \choose b}$ denotes the binomial coefficient. However, the summation $L_1 + L_2 + \dots + L_\text{maxoder}$ may exceed the number of available monomials $L-1$. A usual practice is to downscale the number of monomials as follows:
\begin{equation}
\label{eq:monomials}
L_i = \left[ {n + i -1 \choose i}s\right]
\end{equation}
where $[\cdot]$ denotes the nearest integer and $s$ denotes the following scaling factor
$$
s = \frac{L-1}{\sum_{i=1}^{\text{maxorder}} {n + i -1 \choose i}}
$$
\subsubsection{Solving the least-squares problem.} It is worth pointing out that although the $\hat{J}_i(k+1)$ is evolving in a nonlinear fashion with respect to $x_i$, standard linear regression techniques can be utilized to find $\theta_i$, as (\ref{eq:estimatorJ}) is still linear in the parameters' vector. Therefore, the least-squares problem as defined in (\ref{eq:estimatorTH}) can be solved by several algorithms (normal equation, QR decomposition, SVD, etc.). Although, singular value decomposition (SVD) is more computational intensive in comparison to other alternatives, we utilize this approach due to the fact that it is more numerical stable (e.g., when the problem is ill-conditioned) \cite[]{demmel1997applied}.
\color{black}
\subsection{Convergence analysis}
\begin{remark}
\label{rm:2}
\normalfont
As shown in \cite{kosmatopoulos2009adaptive, kosmatopoulos2009large}, the distributed algorithm implemented in each robot (Section \ref{subsec:distributedDecision}) guarantees that
If $M \geq 2 \times \text{dim}\left(x_i\right)$, the vector $\phi$ satisfies the universal approximation property and the functions $J_i$ and $C$ are either continuous or discontinuous with a finite number of discontinuities, then the update rule of $x_i$ (\ref{eq:updateRule}) is equivalent to
$$
x_i(k+1) = x_i(k) - A(k) \nabla_{x_i} J_i + \epsilon(k)
$$
where $A(k)$ is a positive definite matrix that depends on the choice of $\alpha$ (see step (e) of the distributed decision-making scheme) and $\nabla_{x_i} J_i$ denotes the gradient of $J_i$ with respect to the $x_i$ decision variables.
In addition, $\epsilon(k)$ is a term that converges exponentially fast to zero with probability one. In simple words, the analysis of \cite{kosmatopoulos2009adaptive, kosmatopoulos2009large} establishes that the algorithm will converge to a local minimum of $J_i$.
\end{remark}
The following theorem describes the properties of the proposed methodology; as the proof of this theorem is along the same lines as in \cite[Proposition 2.7.1]{bertsekas1999nonlinear}, only a sketch of proof is provided.
\begin{theorem}
\label{th:1}
The local convergence of the proposed algorithm can be guaranteed in the general case where the global cost function ${\cal J}$ and each robot's contribution $J_i$ are non-convex, non-smooth functions.\endnote{Moreover, recent studies imply that BCD methodologies can achieve global convergence even in cases where the global cost function (\ref{eq:globalCFx}) is non-convex but holds some properties. For example, in \cite{xu2013block} the authors established global convergence of the BCD algorithm in the general case where the global cost function ${\cal J}$ and each robot's contribution $J_i$ are non-convex functions, but the so-called Kurdyka-\L{}ojasiewicz (KL) property is satisfied.}
\end{theorem}
\textit{Sketch of the proof:} By using Remark \ref{rm:2} (\textit{projected gradient-descent} on the minimization of $J_i$) and Equations (\ref{eq:subCF})--(\ref{eq:constituentCF}), we can establish that the distributed update on each robot is equivalent to
$$
x_i = \argmin_{w} {\cal J}\left(x_1,\dots,x_{i-1},w,x_{i+1},\dots,x_{N}\right) \\
$$
subject to (\ref{eq:Distributedconstraints}) and therefore, the proposed algorithm approximates the behavior of the block coordinate descent (BCD) \cite[Algorithm 1]{wright2015coordinate} family of approaches. Following the proof described in \cite[Proposition 2.7.1]{bertsekas1999nonlinear}, it is straightforward to see that if the minimum with respect to each block of variables is unique, then any accumulation point of the sequence $\{x(k)\}$ generated by the BCD methodology is also a stationary point.
\subsection{Complexity}
\begin{table}
\centering
\begin{tabular}{ c c c c}
\hline
\textit{STEP} & Complexity & Practical & Comments\\ \hline
\textit{1-3} & $ \mathcal{O}\left( J\left( \textbf{y}\right) \right) $& $\mathcal{O}\left( N^3 m^2\right) $ & Application \\
&&& dependent \\
\textit{4} & $ \mathcal{O}\left( L^{3} \right) $ & $\mathcal{O}(n^3)$ & Least-squares\\
\hline
\end{tabular}
\caption{Complexity analysis}
\label{tbl:complexity}
\end{table}
The computational burden regarding the global coordination (section \ref{subsec:globalCoordination}) is accumulated in the calculation of $\Delta_i(k)$ (\ref{eq:subCF}) for each robot $i$. However, the calculation of J$\left(\cdot \right) $ is problem-dependent, thus, it is not possible to analytically derive bounds regarding its complexity. In the reported cases (cost functions (\ref{eq:slotiveCFj}),(\ref{eq:cf3dcover}),(\ref{eq:cf3dcoverTT}) and (\ref{eq:persistentCF})), as well as in most real-world applications, the computational needs of J$\left(\cdot \right) $ grow, at most, quadratic with the number of robots $\times$ the number of measurements per robot, i.e., $\mathcal{O}\left( N^2 m^2\right) $. Technically, the above threshold expresses the case where an operation is needed per different pair of measurements $\{ y_a^{(i)}, y_b^{(j)} \}$, with $a,b \in \{1, \dots,m\}$ and $i,j \in \{1, \dots, N\}$. Overall, J$\left(\cdot \right) $ is evaluated $N+1$ times, one for each robot and one for the global cost function term (\ref{eq:subCF}); therefore, \textit{Steps 1--3} are expected to have $\mathcal{O}\left( N^3 m^2\right) $.
The computational requirements for the distributed decision (Section \ref{subsec:distributedDecision}), which is computed on each robot, are dominated by the requirement of solving the least-squares problem (\ref{eq:estimatorTH}). According to \cite[Section 5.5.6, Figure 5.5.1]{golub2012matrix}, the best algorithms for least-squares problem using SVD procedure, take time that is proportional to $\mathcal{O}\left(T^2L + L^3 \right) $. In the interest of simplicity, and owing to the fact that $T \simeq L$, we can assume that the complexity for the distributed decision scales as $\mathcal{O}\left(L^3 \right) $. Although, there exist no theoretical results for providing the lower bound $\bar{L}$ for the size of the regressor vector, practical investigations on many different applications [e.g., \cite{korkas2016occupancy, kapoutsis2015real, amanatiadis2013multi}] indicate that it is sufficient enough to choose $L \ge \bar{L} = 2 \times n$, to adequately tackle the local approximation of $J_i$. Therefore, it is expected that the computational requirements will grow with $\mathcal{O}(n^3)$. Although this step is executed on each robot ($N$ times), the distributed nature of the algorithm guarantees that no extra computational needs will be required.
Overall, it is expected that the complexity of computing $N$ times the cost function J$\left(\cdot \right) $ dominates the requirement of solving the least-squares problem for one robot. Table \ref{tbl:complexity} summarizes the complexity bounds discussed in this section.
\begin{remark}
\label{rm:parameters}
\normalfont
We close this section by accumulating the free parameters of the proposed algorithm. The set is composed of the number of perturbations $M$, the total number of utilized monomials $L$ and the time window $T$ over which the least-squares estimation is taking place. According to Remark \ref{rm:2}, the number of perturbations $M$ should be greater than $2 \times n$. Furthermore, the complexity analysis of Section \ref{subsec:distributedDecision} indicates that the estimator (\ref{eq:estimatorJ}) should have at least $\bar{L} = 2 \times n$ number of monomials. Finally, $T$ is a non-negative integer that expresses the desired ``forgetting factor'' for the constructed estimator. In the following experimental set-ups, we set the algorithm's parameters within these bounds. Alternatively, and if required, all parameters mentioned could be manually tuned in order to achieve better, application-dependent, performance.
\end{remark}
\section{Adaptive coverage control utilizing Voronoi partitioning}
\label{sec:2dCoverage}
The first simulation set-up is the well-investigated optimal robots' placement problem \cite[]{schwager2009decentralized,schwager2006distributed,cortes2002coverage}. The objective for the network of robots is to spread out over an environment, while aggregating in areas of high sensory interest. Furthermore, the robots do not know beforehand where the areas of sensory interest are, but they learn this information online from sensor measurements. The aforementioned task can be found in applications such as environmental monitoring and clean-up, automatic surveillance of rooms/buildings/towns, or search and rescue missions.
\subsection{Problem definition}
It is assumed that the operational area is a bounded $Q \subset \mathbb{R}^n$. A point inside this environment is denoted by $q$ and the decision vector $x_i$ for the $i$ th robot contains its position in $Q$. In addition, let $\{V_1,\dots,V_N\}$ be the Voronoi partition of $Q$, for which the robot positions are the generator points:
$$
V_i = \{q\in Q | \left\| q-x_i\right\| \leq \left\| q-x_j\right\|, \forall j \neq i \}
$$
(Henceforth, we use $\left\| \cdot \right\| $ to denote the Euclidean norm $\left\| \cdot \right\|_2 $) Let $\zeta(\cdot)$ to be the unknown sensory function such that $\zeta : Q \rightarrow \mathbb{R}_{>0}$ (where $\mathbb{R}_{>0}$ is the set of strictly positive real numbers). In other words, this function $\zeta(\cdot)$ assigns in each location of the available space $Q$ a weight of importance related to the necessity of being covered.
The global cost function for the problem in hand, admits the following form:
\begin{equation}
\label{eq:slotiveCF}
\mathcal{J}(\textbf{x}(k)) = \sum^N_{i=1} \int_{V_i} \frac{1}{2} \left\|q-x_i\right\|^2 \zeta(q) dq
\end{equation}
Apparently, the above function cannot be calculated in advance owing to the dependence of the unknown sensory function $\zeta$. Without loss of generality, we assume that the sensory function is given by
\begin{equation}
\label{eq:approxPhi}
\zeta(q) = \mathcal{K}(q)^\tau \upsilon + \mathcal{O}(1/W), \; \forall q \in Q
\end{equation}
where $ \mathcal{K}: Q \rightarrow \mathbb{R}_{>0}^W$ denotes a vector of bounded, continuous basis functions (e.g., Gaussians, wavelets, sigmoids, etc.) and $\upsilon \in \mathbb{R}^W$ is the parameter vector. The deviation from the actual value of $\zeta$ is in the order of the number of basis functions $ \mathcal{O}(1/W)$. Although $ \mathcal{K}$ is defined a priori, the mixing parameters vector $\upsilon$ is environment-dependent and generally unknown. However, the value of the sensory function can be measured from the robots' sensors (e.g., temperature/chemical sensor) at their current position's configuration $\textbf{x}(k)$.
\begin{equation}
\label{eq:sensorModelSlotine}
y(x_i) = \zeta(x_i)
\end{equation}
The value of the parameter estimation vector $\hat{\upsilon}$ can be approximated through these measurements, utilizing standard parameter estimation techniques (e.g., least-squares approach (\ref{eq:estimatorTH})). Therefore, after the update on the parameter vector $\hat{\upsilon}$, a new update on the belief regarding the sensory function is also available through the equation
\begin{equation}
\label{eq:sesnoryFunctionUpdate}
\hat{\zeta} = \mathcal{K}^\tau \hat{\upsilon}
\end{equation}
Hence, the value of the unknown cost function can be approximated through the following equation:
\begin{equation}
\label{eq:slotiveCFj}
\mbox{J}(\textbf{y}(k)) = \sum^N_{i=1} \int_{V_i} \frac{1}{2} \left\|q-x_i\right\|^2 \mathcal{K}^\tau(q) \hat{\upsilon} dq
\end{equation}
\subsection{Simulation results}
For implementation reasons, we assume that the operation area consists of $225$ discrete points, uniformly distributed across the plane of $[0, 1]^2$. The sensory function, $\zeta(q)$, was parameterized as a linear combination of 49 Gaussians, i.e., $\mathcal{K}(j) = \frac{1}{2\pi\sigma^2_j} \mbox{exp} - \frac{(q-\mu_j)^2}{2\sigma^2_j}, \; \forall j \in \{1,\dots,49\}$. Each standard deviation is set to be $\sigma_j = 0.02$ and the Gaussians centers $\mu_j$ are chosen so as to be uniformly distributed in the operational area (seven Gaussians in each row and column). The parameter $\upsilon = [\upsilon_1, \upsilon_2, \dots, \upsilon_{49}]^{\tau}$ was chosen so that $\upsilon_i=0.1, \forall i\in\{1,\dots,49\} $, apart from two random integers $a,b \in \{1,\dots,49\}$ whereas $\upsilon_a=\upsilon_b=100$. In other words, for each simulation instance, the sensory function $\zeta(q)$ was dominated by two, randomly selected, Gaussians. \color{black} Finally, the equations are integrated using a fixed step of $\alpha=dt=0.01$ and the initial values for the estimation of parameter vector (robots' knowledge) was chosen to be $\hat{\upsilon}=[0.1, 0.1, \dots, 0.1]^\tau$.
In addition with the proposed approach, we present simulation results from the algorithm as proposed, for the problem in hand, by \cite{schwager2009decentralized}. The weights' selection was undertaken following the authors' instructions in \cite[Section 7.2]{schwager2009decentralized}. To construct comparable simulations instances, we utilize the same learning rule for the parameter vector $\hat{\upsilon}$ \cite[equation 13]{schwager2009decentralized}. In both the evaluated algorithms, the update of parameter vector was performed, by aggregating all the robots' measurements. To evaluate the performance of each approach in each timestamp, we also calculate the real value of the cost function (\ref{eq:slotiveCF}), but none of the evaluated algorithms utilizes this information.
The proposed approach was employed with a constant time-window for the least-squares estimation of $T = 30$ and the number random perturbations was set to be $M=100$. To approximate each robot's cost function evolution, we utilize a third-order monomial estimator with $L = 10$ and using (\ref{eq:monomials}) we calculate the number of monomials per order to be $L_1 = 2, L_2=3 \text{ and } L_3 = 4$.
\subsubsection{Random initial positions scenario.}
In the first simulation scenario, the robots were placed randomly along the x and y axes of the operation area. An example of this simulation set-up is illustrated Figure \ref{fig:RandomScenario}, where Figure \ref{fig:InitialVoronoiRandom} sketches the Voronoi partitioning for the initial robot configuration. Figure \ref{fig:TrajectoriesRandom} illustrates the robots' trajectories from their initial positions (squares) to the final configuration (circles), and, finally, Figure \ref{fig:VoronoiRandom} illustrates the Voronoi partitioning for the final robots' positions. As one can see, the robots gathered around the areas with the highest values of the unknown sensory function $\zeta(\cdot)$. \color{black}
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_random56_initial.png}\label{fig:InitialVoronoiRandom}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_random56_trajectories.png}\label{fig:TrajectoriesRandom}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_random56_final.png}\label{fig:VoronoiRandom}}
\caption{Illustrative example with random initial positions for the robots. (a) Initial Voronoi partitioning. (b) Robots' trajectories on top of the heatmap of the sensory function. The squares and the circles denote the initial and the final positions of the robots, respectively.(c) Voronoi partitioning of the final configuration. In these figures, we sketch how the proposed algorithm drives the available robots so as to completely cover the space and to aggregate around areas with high sensory interest.}
\label{fig:RandomScenario}
\end{figure*}
Figure \ref{fig:SlotineRandomScenario} presents a comparison study between the evaluated algorithms, over different sizes of robot teams. The number of robots was chosen to be 10, 15, 20, and 25 robots, and for each configuration 60 experiments with randomly selected initial robots' placement and sensory function were performed. The average, final achieved cost function (\ref{eq:slotiveCF}) values, along with the corresponding confidence intervals are illustrated in \color{black} Figure \ref{fig:cfRandom}. In addition, we present the summation of the cost function over the course of each simulation pair (Figure \ref{fig:SumRandom}). It must be emphasized that, although the summation of the cost function may be strongly dependent on the initial robots' positions the final achieved value has a small variance around the average value. This feature highlights the ability of the proposed approach to converge to an optimal configuration, independently of the initial conditions.
\begin{figure*}[h]
\centering
\subfigure[]{\includegraphics[width=0.47\textwidth]{CfRandom.png}\label{fig:cfRandom}}
\subfigure[]{\includegraphics[width=0.47\textwidth]{SumRandom.png}\label{fig:SumRandom}}
\caption{Comparison study for the \textit{random initial positions scenario}: proposed algorithm (blue) and approach presented by \cite{schwager2009decentralized} (red). (a) Final achieved value of the cost function. (b) Summation of the cost function over the experiment's horizon.}
\label{fig:SlotineRandomScenario}
\end{figure*}
\subsubsection{Right half-plane scenario.} In the second simulation scenario, the robots' initial positions were constrained inside the right half-plane of the operation area. In general, this scenario has a greater level of difficulty, compared with random initialization, as the robots can easily get stuck in highly suboptimal situations. Figure \ref{fig:RightHalfPlaneScenario} illustrates an instance of such a scenario where the proposed approach was utilized.
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_halfX53_initial.png}\label{fig:TrajectoriesHalfX}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_halfX53_trajectories.png}\label{fig:TrajectoriesHalfX}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{n_10_halfX53_final.png}\label{fig:VoronoiHalfX}}
\caption{Illustrative example where the robots initial positions are constrained inside the right half-plane of the operational environment. The proposed algorithm navigates the robots around the space, utilizing only their measurements on their current positions, to achieve the mission objective. (a) Initial Voronoi partitioning. (b) Robots' trajectories on top of the heatmap of the sensory function. (c) Voronoi partitioning of the final configuration.}
\label{fig:RightHalfPlaneScenario}
\end{figure*}
\begin{figure*}[h]
\centering
\subfigure[]{\includegraphics[width=0.47\textwidth]{CfRightHalfPlane.png}\label{fig:cfHalfX}}
\subfigure[]{\includegraphics[width=0.47\textwidth]{SumRightHalfPlane.png}\label{fig:SumHalfx}}
\caption{Comparison study for the \textit{right half-plane scenario}: proposed algorithm (blue) and approach presented in \cite{schwager2009decentralized} (red). (a) Final achieved value of the cost function. (b) Summation of the cost function over the experiment's horizon.}
\label{fig:SlotineRightHalfPlaneScenario}
\end{figure*}
As in the previous scenario, we present a comparison between the evaluated algorithms for different sizes of robot teams. The results are illustrated in Figure \ref{fig:SlotineRightHalfPlaneScenario}. Again, the proposed approach utilizes all the available team resources in order to achieve optimal robot configurations with small variance around the average values.
\section{Three-dimensional surveillance of unknown areas}
\label{sec:3Dcoverage}
A more elaborate variation of the previously described set-up has been proposed by \cite{renzaglia2012multi} and applied in several domains (e.g., \cite{kapoutsis2015real, scaramuzza2014vision}). Although the problem is again the optimal placement of robots in realtime, the details of the simulation set-up are important. First and foremost, the robots are moving inside a 3D space (e.g., unmanned aerial vehicles). The terrain to be covered is considered an unknown, non-convex, 3D surface the formation of which may form an arbitrary number and shape of obstacles. Furthermore, a realistic model for the robots' sensors is employed and utilized in all the simulation scenarios.
\subsection{Problem definition}
In this simulation testbed, the decision variables (\ref{eq:stataSpace}) represent the positions of the robots in 3D space, i.e., $\textbf{x} = \left[ x_1^\tau,\dots,x_N^\tau\right]^\tau$, where $x_i \in \mathbb{R}^3$. It is assumed that the area to be monitored is constrained within a rectangle in the $(\mbox{x, y})-$coordinates as
$$
{\cal U} = \big\lbrace \mbox{x, y } | \mbox{ x} \in [\mbox{x}_{min},\mbox{x}_{max}], \mbox{y} \in [\mbox{y}_{min},\mbox{y}_{max}] \big\rbrace
$$
where $\mbox{x}_{min},\mbox{x}_{max},\mbox{y}_{min},\mbox{y}_{max}$ are real numbers that define the ``borders'' of the area of interest. Using the definition of ${\cal U}$, the area can be defined as a function that maps each point $(\mbox{x, y}) \in {\cal U}$ to a point $\mbox{z}=z(\mbox{x, y})$ (height of unknown terrain at $(\mbox{x, y})$). A point $q = (\mbox{x, y, z})$ of the terrain is \textit{visible} if there exist at least one robot so that:
\begin{itemize}
\item the robot $x_i$ and the point $q$ are connected by a line-of-sight;
\item $\left\|x_i - q \right\| \leq \mbox{\textit{thres}} $, where \textit{thres} defines the maximum distance the $i$th robot can ``see''.
\end{itemize}
Given the robots configuration $\textbf{x}(k)$ at timestamp $k$, we let ${\cal V}$ to denote the \textit{visible} area of the terrain, i.e., ${\cal V}$ consists of all points $q \in {\cal U}$ that are \textit{visible} from the robots.
Furthermore, the measurements' model for all the robots admits the following form:
\begin{equation}
\label{eq:sensorsNoise}
y_{x_i-q}=\left\{ \begin{array}{ll} \left\|x_i - q \right\| + h_\xi(x_i,q)\xi & \mbox{ if } q \in {\cal V} \\
\mbox{undefined} & \mbox{ otherwise}
\end{array}\right. \; \forall q \
\end{equation}
where $h_\xi(x_i,q)$ is the multiplicative sensor noise term $(e.g., \propto \left\|x_i - q \right\|^2)$ and $\xi$ is a standard Gaussian noise. The above nonlinear noise model is a realistic representation of the noise effect in many real robot systems
\cite[]{salavasidis2016terrain}\cite[Chapter 3-4]{teixeira2007terrain}. For instance, in the case of sonar or cameras, the noise affecting such sensors is proportional to the sensor-to-sensing-point distance, i.e., the larger the robot-to-sensing-point distance, the larger the sensor noise \cite[]{scaramuzza2014vision}.
Having the above formulation in mind, we define the following combined cost function that the team of robots has to minimize
\begin{equation}
\label{eq:cf3dcover}
\mbox{J}(\textbf{y}(k)) = \int_{q \in {\cal V}} \min_{i=1,\dots,N} y_{x_i-q} dq + K \int_{q \in {\cal U}\setminus{\cal V}}dq
\end{equation}
The fist term is equivalent to the cost function considered in many coverage problems for known 2D environments \cite[]{cortes2002coverage, choset2001coverage}. The second term is related to the invisible area in the terrain. The positive constant $K$ serves as a weight for giving less or more priority to one of the objectives.
Moreover, the set of nonlinear constraints (\ref{eq:constraints}), which must be held for each new robots' configuration $\textbf{x}(k)$, include the following:
\begin{itemize}
\item the robots remain within the terrain's limits, i.e., within $[\mbox{x}_{min},\mbox{x}_{max}]$ and $[\mbox{y}_{min},\mbox{y}_{max}]$ in the x- and y-axes, respectively;
\item the robots satisfy a maximum height requirement, while they do not hit the terrain, i.e., they remain within $[\mbox{z}+d_h,\mbox{z}_{max}]$ along the z axis, where $d_h$ denotes the minimum safety distance the robots should always have from the terrain and $\mbox{z}_{max}$ denotes the maximum allowable operational height for the robots;
\item $\left\|x_i - x_j \right\| \geq d_r, \; \forall i,j \in \{1,\dots,N\} \mbox{ and } i \neq j $, i.e., the safety distance between two robots is $d_r$.
\end{itemize}
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.43\textwidth]{surface.png}\label{fig:3d_coverage_1_3dEnviroment}}
\subfigure[]{\includegraphics[width=0.43\textwidth]{initial2d.png}\label{fig:3d_coverage_1_3initPos}}
\subfigure[]{\includegraphics[width=0.43\textwidth]{CAO_3Dview_t_600.png}\label{fig:3d_coverage_1_CAO_2}}
\subfigure[]{\includegraphics[width=0.43\textwidth]{CAOTopView_t_600.png}\label{fig:3d_coverage_1_CAO}}
\subfigure[]{\includegraphics[width=0.43\textwidth]{Proposed3Dview_t_600.png}\label{fig:3d_coverage_1_Proposed_2}}
\subfigure[]{\includegraphics[width=0.43\textwidth]{ProposedTopView_t_600.png}\label{fig:3d_coverage_1_Proposed}}
\subfigure[]{\includegraphics[width=0.83\textwidth]{cf.png}\label{fig:3d_coverage_1_3cf}}
\caption{Surveillance of unknown terrain by a team of robots. The proposed algorithm and the CAO-based approach \cite[]{renzaglia2012multi} are evaluated on the same set-up (environment, robots initial positions, robots sensor capabilities). (a) 3D representation of the surface to be covered; (b) initial positions of the available robots; (c) 3D view, CAO-based approach; (d) top view, CAO-based approach; (e) 3D view, proposed approach; (f) top view, proposed approach; (g) cost function evolution.}
\label{fig:3d_coverage_1}
\end{figure*}
\subsection{Simulation results}
The centralized CAO-based approach that has been proposed for the problem in hand \cite[]{renzaglia2012multi} is utilized for comparison purposes. The proposed approach was parametrized with a time window $T=40$ for the least-squares estimation, with $M=100$ random perturbations, the corresponding approximator was a third-order monomial estimator with $L = 18$, and the number of monomials per order (\ref{eq:monomials}) were $L_1 = 2, L_2=5 \text{ and } L_3 = 10$. Acknowledging the fact that the CAO algorithm performs optimization in a higher-dimensional space (centralized optimization scheme), a different set of parameters was chosen. Evaluating the CAO version for different numbers of random perturbations, we found that after $M=900$ the number of random perturbations does not affect its performance. Furthermore, to cope with the higher-dimensional state space, the time window was set to $T=60$ and the approximator was chosen to be a third-order monomial estimator with $L_1 = 3, L_2=12 \text{ and } L_3 = 40$ (with overall size of $L = 56$). In both algorithms, we utilize $\alpha=0.1$ to update the robot's positions. For the rest of this section, we use these values in all the presented experiments.
To perform simulations in a realistic environment, we utilized the morphology of an area located in Z{\"u}rich, Switzerland (Figure \ref{fig:3d_coverage_1_3dEnviroment}). This map was generated using a state-of-the-art visual-SLAM algorithm \cite[]{doitsidis2012optimal}, which tracks the pose of the camera while, simultaneously and autonomously, building an incremental map of the surrounding environment. The terrain's dimension is $[0, 162]$ m and $[0, 84]$ m for x and y axes, respectively, while the height of the terrain is between $[0, 7.2]$ m and the maximum operational height was set to $25$ m. Following the authors instructions \cite{renzaglia2012multi}, $K$ weight (\ref{eq:cf3dcover}) was chosen to be 30, whereas both the safety distance from the terrain and the minimum allowable distance between two robots were set to be $d_h=d_r=0.5m$. Finally, the duration of each experiment was set to $k_{\text{max}}=600$ timestamps.
Figure \ref{fig:3d_coverage_1} depicts such a simulation instance with six robots. The initial positions of the robots, as it is sketched in Figure \ref{fig:3d_coverage_1_3initPos}, were selected to be ``crowded'' inside a sub-area of the terrain. Figures \ref{fig:3d_coverage_1_CAO_2} and \ref{fig:3d_coverage_1_CAO} illustrate the final robots' configuration, as calculated by the CAO-based algorithm in 3D and 2D representation, respectively. The corresponding final robots' assignment as calculated by the proposed approach is presented in Figures \ref{fig:3d_coverage_1_Proposed_2} and \ref{fig:3d_coverage_1_Proposed}. In both cases, the 3D representation reports which sub-area of the terrain is covered by each \color{black} robot, whereas the 2D representation reveals the exact positions of the robots in $x-y$ plane and the distance between them. Figure \ref{fig:3d_coverage_1_3cf} depicts the evolution of the cost function (\ref{eq:cf3dcover}) for both the evaluated algorithms. Apart from the difference in the convergent state, the proposed approach is able to find this solution from its early steps $(<50)$. The centralized CAO needs more iterations to learn the dynamics of the robots and the unknown terrain, because it performs its optimization scheme in the higher-dimensional space of $\mathbb{R}^{3N}$ ($\mathbb{R}^{18}$ for the six robots). In contrast, the proposed algorithm separately, although cooperatively, solves $N$(=6 robots for this instance) optimization problems of the size of $\mathbb{R}^{3}$.
In the specific problem set-up, the speed of convergence requires extra attention, as a slow convergence rate may lead to instability or loss of convergence at all. More specifically, if a navigation algorithm does not converge fast enough to the optimal configuration, one or more robots may have reached high-altitude positions, from which they cannot acquire useful measurements (out of their sensor capabilities (\ref{eq:sensorsNoise})). This is a non-recoverable situation, as the robots do not have any ``feedback'' from the terrain to properly evaluate their actions.
\subsubsection{Scalability analysis.}
To validate both the efficiency and the effectiveness of the proposed algorithm in the case of larger robot teams, we performed experiments with 5, 10, 15, and 20 robots\endnote{Note that, for the current experiment set-up with the previously defined sensor's capabilities, the utilization of more than 15 robots cannot significantly affect the coverage task.}. For each different size of robotic team, we created 20 experiment instances with randomly chosen initial robots' positions. The aforementioned simulation instances are evaluated on both the proposed approach and the centralized CAO-based approach.
The results of these simulations are summarized in Figure \ref{fig:3DscalabilityAnalysis}. Figure \ref{fig:3d_scalability_cf} displays the average value of the resulting cost function $\mbox{J}(k_{\text{max}})$, along with the corresponding confidence interval, over the different number of robots. In addition, Figure \ref{fig:3d_scalability_SumCF} displays a statistical analysis on the summation of cost function $\sum_0^{k_{\text{max}}}{\mbox{J}}(k)$, to investigate the convergence rate of each pair (scenario--algorithm).
\begin{figure*}[h]
\centering
\subfigure[]{\includegraphics[width=0.47\textwidth]{cf_2.png}\label{fig:3d_scalability_cf}}
\subfigure[]{\includegraphics[width=0.47\textwidth]{SumCF.png}\label{fig:3d_scalability_SumCF}}
\caption{Comparison study over different number of robots: proposed algorithm (blue) and CAO-based approach \cite[]{renzaglia2012multi} (red). (a) Final achieved value of the cost function. (b) Summation of the cost function over the experiment's horizon}
\label{fig:3DscalabilityAnalysis}
\end{figure*}
Overall, the proposed approach achieves an average improvement of $23\%$ on the \textit{final achieved cost function value}, with $55.33\%$ improvement on the deviation around that average value. Moreover, the \textit{summation of cost function} has been improved by $23.84\%$ with a corresponding improvement on the deviation of $65.06\%$, against the centralized CAO-based approach. The proposed approach achieves these performance enhancements mainly due to the two following reasons.
\begin{itemize}
\item [(i)] The proposed algorithm has a better perspective on the change of the overall cost function by evaluating the appropriate combinations of historical measurements on that cost function (\textit{Step 2-3} of the proposed approach).
\item [(ii)] The fast convergence of the proposed approach eliminates the chances for a robot to be found out of its sensors capabilities. Therefore, the proposed approach is able to converge on approximately the same robots' configuration (per different team size), independently on the robots' initial positions. The latter is depicted in the substantial improvements on the corresponding confidence intervals.
\end{itemize}
\subsubsection{Fault-tolerant characteristics.}
In this scenario, we investigate the performance of the proposed algorithm in the case of catastrophic events or hardware failures. More precisely, five robots were initially deployed to perform the aforementioned coverage task, whereas the duration of the experiment was increased to $k_\text{max}=$1,000 timestamps. It is assumed that, at timestamp 330, one robot did not correspond to our control commands and the measurements' flow had been interrupted. Under these new circumstances, the surveillance task has to be undertaken by remaining, properly working robots. After the completion of two-thirds of the available timestamps, we assume that another robot had an equipment malfunction and cannot continue its covering task. Thus, the number of available robots, which are called to cover the area of interest for the $\sim$300 remaining timestamps, has dropped to three.
Figures \ref{fig:3d_coverage_F_3initPos}--\ref{fig:3d_coverage_F_Final} illustrate the evolution of the robots positions during the course of the previously described scenario, utilizing the proposed approach. After both the robots' malfunctions, the algorithm redesigns the remaining robot positions to achieve the best possible coverage. Overall, Figure \ref{fig:3d_coverage_F_3cf} demonstrates the evolution of the objective function for the proposed approach in comparison with the centralized CAO-based approach \cite[]{renzaglia2012multi}.
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_1.png}\label{fig:3d_coverage_F_3initPos}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_330.png}\label{fig:3d_coverage_F_330}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_331.png}\label{fig:3d_coverage_F_331}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_660.png}\label{fig:3d_coverage_F_660}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_661.png}\label{fig:3d_coverage_F_661}}
\subfigure[]{\includegraphics[width=0.45\textwidth]{t_1000.png}\label{fig:3d_coverage_F_Final}}
\subfigure[]{\includegraphics[width=0.93\textwidth]{cf_faultTol.png}\label{fig:3d_coverage_F_3cf}}
\caption{Malfunction scenario: five robots were initially deployed for the surveillance task. At two distinct timestamps, the swarm of robots loses one of its member due to a simulated malfunction. The surveillance task have to be continued with the remaining team resources. (a) Initial positions of the five available robots. (b) Coverage task with all five available robots. (c) One timestamp after the malfunction on the red robot. (d) Coverage task with four robots. (e) One timestamp after the malfunction on the yellow robot. (f)Again, the algorithm redesigns the robots positions to cover the area in the best possible way utilizing the available resources. (g) Cost function evolution.}
\label{fig:3d_coverage_FaultTolerant}
\end{figure*}
It must be emphasized that the proposed algorithm does not need any separately designed, fault-detection mechanism (e.g., failure in establishing communication, operator to detect the malfunction, etc.), as it is able to implicitly derive this kind of information from the changes in the cost function $\mbox{J}$ with respect to the commanded positions. The above feature is of paramount importance in real-life multi-robot applications, because it removes the tedious, and in many applications impossible, task to predict (or identify online) all the possible malfunctions, as well as to design the appropriate course of actions.
\subsubsection{Target monitoring.}
We close this section by investigating the algorithm's capability to process objectives that can be alternated/activated on the fly, without stopping and restarting the mission. To achieve this, simultaneously with the coverage task, we introduce the task of monitoring a target. For the sake of this simulation set-up, it is assumed that, in addition to the sensors which are responsible for the coverage task (\ref{eq:sensorsNoise}), the robots are equipped with exteroceptive sensors (e.g., cameras, sonars, etc.) which are able to estimate the targets' positions, according to the following measurement model:
\begin{equation}
\label{eq:measurmentOfATarget}
y_{x_i-\chi_j}=\left\{ \begin{array}{ll} \left\|x_i - \chi_j \right\| + h_\xi(x_i,\chi_j)\xi & \mbox{ if } \chi_j \mbox{ \textit{has}} \\ & \mbox{ \textit{ been detected}} \\
\mbox{undefined} & \mbox{ otherwise}
\end{array}\right.
\end{equation}
where $\chi_j$ denotes the $j$th target's position in 3D space, $h_\xi(x_i,x_t)$ and $\xi$, similar to equation (\ref{eq:sensorsNoise}), denote the multiplicative sensor noise term and the standard Gaussian noise, respectively. Therefore, an extra term has to be added to the cost function (\ref{eq:cf3dcover}) to appropriately evaluate the progress of targets' monitoring, as follows:
\begin{equation}
\label{eq:cf3dcoverTT}
\begin{aligned}
\mbox{J}(\textbf{y}(k)) = \int_{q \in {\cal V}} \min_{i=1,\dots,N} y_{x_i-q} dq + K \int_{q \in {\cal U}\setminus{\cal V}}dq \\
+ K_t \sum_{j = 1}^{n_t}\min_{i=1,\dots,N} y_{x_i-\chi_j}
\end{aligned}
\end{equation}
where $K_t$ serves as a weight to give more or less priority to the monitoring task in comparison with the coverage. In addition, $n_t$ denotes the number of targets to be monitored.
The experiments were performed in the same terrain, under the previously defined set-up parameters. Figure \ref{fig:3d_coverage_TargetTracking} illustrates four key snapshots, which demonstrate the functionality of the proposed algorithm. Figure \ref{fig:3d_coverage_2_3initPos} depicts the robots' initial positions along with the corresponding coverage on the terrain. After 367 timestamps (figure \ref{fig:3d_coverage_2_300}), the algorithm has converged to the (locally) optimal robots' configuration for the coverage-only problem. At $k=370$ timestamp, it is assumed that a target, which requires closer examination, appears inside the operation area. The proposed algorithm, after the time needed to learn the changed problem dynamics (activation of the third term in (\ref{eq:cf3dcoverTT})), starts to adapt the robots' positions to minimize the updated cost function (\ref{eq:cf3dcoverTT}). More precisely, as illustrated in Figure \ref{fig:3d_coverage_2_target}, the purple robot (which was, at the time, closer to the target) starts to gain height to minimize its distance from the detected target. However, such an action leads to poor coverage on the subarea underneath that robot. To alleviate the above undesirable situation, the proposed algorithm redesigns the remaining robots' positions so as to achieve the best coverage of the terrain with the available resources. The final robots' positions with the corresponding coverage of the terrain is sketched in Figure \ref{fig:3d_coverage_2_Final}. The evolution of the objective function for the proposed approach in comparison with the centralized CAO-based approach is demonstrated in Figure \ref{fig:3d_coverage_2_3cf}. Conclusively, for this simulation scenario, the proposed algorithm:
\begin{itemize}
\item chooses to assign a robot to be as close as possible to the target without any explicit command;
\item adapts the other robots positions so as to ``fill the hole'' in the coverage task; and
\item achieves almost the same level of terrain coverage with the centralized CAO-based approach for five robots (Figure (\ref{fig:3d_coverage_2_3cf}) dashed line), whereas one (out of five) robots is occupied with another task.
\end{itemize}
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.95\textwidth]{init.jpg}\label{fig:3d_coverage_2_3initPos}}
\subfigure[]{\includegraphics[width=0.95\textwidth]{367.jpg}\label{fig:3d_coverage_2_300}}
\subfigure[]{\includegraphics[width=0.95\textwidth]{427.jpg}\label{fig:3d_coverage_2_target}}
\subfigure[]{\includegraphics[width=0.95\textwidth]{end.jpg}\label{fig:3d_coverage_2_Final}}
\caption{Target monitoring scenario. The robots have been deployed with an extra objective (apart from the surveillance task) to get as close as possible to a target. The target appears inside the operation area of the robots in the middle of the mission. (a) Timestamp 1:initial positions of the five available robots. (b) Timestamp 367: coverage task with all five available robots. (c) Timestamp 427: the purple robot starts to gain height to minimize the distance from the target. As a consequence, it cannot cover adequately its underneath surface. (d) Timestamp 1,000: finally, the algorithm redesigns the robots positions so as to cover the area in the best possible way utilizing the available resources.}
\label{fig:3d_coverage_TargetTracking}
\end{figure*}
\begin{figure*}[]
\centering
\includegraphics[width=0.93\textwidth]{cf_TT.png}
\caption{Cost function evolution in target monitoring scenario.}
\label{fig:3d_coverage_2_3cf}
\end{figure*}
\section{Persistent coverage inside unknown environment}
\label{sec:persistent}
In the final application, we focus on the problem of persistent coverage in an area of interest with a team of robots. In this application, it is assumed that the operational robots are equipped with the appropriate sensors that are able to cover a portion of the environment. The objective in a persistent coverage application is to continuously cover an area of interest, assuming that the coverage level follows a time-decaying function. \color{black} The problem along with a specifically designed algorithm has been proposed in \cite{palacios2016distributed}. The authors also established a well-defined, heuristic mechanism to online share the coverage evolution between the robots in a distributed way.
Although the results are remarkable, the proposed decision-making mechanism in \cite{palacios2016distributed} utilizes a model that accurately predicts the improvement in the coverage level with respect to the robots movement \cite[equations (10),(18)-(21)]{palacios2016distributed}. In real-world applications, the above assumption does not always hold, as the increase in coverage level (i) is usually corrupted by nonlinear noise, (ii) can be affected by environmental specific characteristics, such as local morphology, obstacles, other robots' positions, etc., (iii) may follow a time-varying model (e.g., coverage level deteriorates over time). To circumvent these difficulties, we propose a variation of the above problem, where the changes in the level of coverage cannot be accurately predicted before the action. The actual information about the exact covered area is only available after the execution of each corresponding action through the robot's measurements. The above formulation is not only more \textit{realistic}, as it does not require an exact model of the environment or robot's coverage capabilities, but also more \textit{generic}, as it does not need to redesign the approach when robots with different or unknown coverage models are deployed.
\subsection{Problem definition}
It is assumed that the operational area is a bounded $Q \subset \mathbb{R}^2$, which a team of robots has to persistently cover. The decision variables (\ref{eq:stataSpace}) represent the collective vector of all the robots' positions, i.e., $\textbf{x} = \left[ x_1^\tau,\dots,x_N^\tau\right]^\tau$, where $x_i \in Q$.
Inside the environment there are several positions $q \in O \subset Q$ that cannot be traversed by the robots and additionally the presence of these obstacles affects each robot's coverage distribution. Although the exact positions of the obstacles are generally unknown, we assume that the robots are able to sense their presence when they are in close proximity. The above assumption is in line with the most commercial robots which are also equipped with proximity sensors to avoid collisions (e.g., \cite{nieuwenhuisen2014obstacle}). Thus, each robot's new candidate position $x_i^{\text{cand}}$ should verify the following constraint [see equation (\ref{eq:constraints}) of the general problem formulation]:
\begin{equation}
\label{eq:persistentConstraints}
\min_{q \in O}\left( \left\| x_i^{\text{cand}} - q \right\| \right) \ge b
\end{equation}
where $b$ denotes the safety distance. At each timestamp $k$, the overall coverage increase is given by $y(q,k) = \sum_{i \in \{1,\dots,N\}} y_i(q,k),\; \forall q \in Q$, where
\begin{equation}
\label{eq:persistentProduction}
y_i(q,k) =\left\{ \begin{array}{ll}
\gamma_i(q,x_i) & \mbox{ if } \left\|x_i -q \right\| \leq r_i^{\text{cov}} \text{ \& } \\
& \mbox{there is line-of-sight} \\
& \mbox{between } x_i \text{ and } q \\
0 & \mbox{ otherwise}
\end{array}\right.
\end{equation}
and $\gamma_i(q,x_i)$ denotes a nonlinear function that models how the coverage level evolves in the area around the $i$th robot's position. Note, that coverage distribution model $\gamma_i(q,x_i)$ may be different for each robot as it expresses the functionality of its on-board sensors.
The coverage of the operational area can be modeled by a time-varying field and, in general, admits the following form:
\begin{equation}
\label{eq:persistentCoverageModel}
Z(q,k) = d(q)Z(q,k-1)+y(q,k), \; \forall q \in Q
\end{equation}
In other words, the coverage level decreases to a constant decay gain $d(q)$, with $0<d(q)<1$, and increases according to the $y(q,k)$. The objective of the multi-robot team is to maintain a desired coverage level, $Z^*(q)>0,\; \forall q \in Q$.
Having the above formulation in mind, we define the \textit{quadratic coverage error} the robot team has to minimize
\begin{equation}
\label{eq:persistentCF}
\mbox{J}(k) = \int_{Q} \left(Z^*(q) - Z(q,k) \right)^2 dq
\end{equation}
\subsection{Simulation results}
All simulations were performed in a rectangle environment consisting of $100\times150$ units, with uniformly distributed decay rate $d(q)=0.995,\; \forall q \in Q$. The desired coverage level is $Z^*(q)=100,\; \forall q \in Q$. The number of robots was $N=6$, whereas their maximum motion is $u^{\text{max}}=5$. The coverage increase in \textit{open space} (obstacle-free), caused by the robots' movements, can be simulated by:
\begin{equation}
\label{eq:persistentModelCoverageIcrease}
\gamma_i(q,k) = \frac{P}{r_i^{\text{cov}2}}\left(\left\|x_i - q\right\| - r_i^{\text{cov}} \right)^2
\end{equation}
The maximum value is set to $P=17$ and the coverage radius is set to $r_i^{\text{cov}}=10$ units. Please note that this equation is not utilized during the decision-making process, but it is only employed to simulate the increase in the area coverage, with respect to the robot's movement. Finally, the experiments' duration is set to $k_{\text{max}}=900$ timestamps.
To adapt the parameters of the proposed algorithm to the current application, we have to take into consideration that the navigation algorithm has to rapidly change its behavior owing to the time-varying nature of the cost function. Therefore, the time window for the least-squares estimation was only $T=5$ timestamps and the number of perturbations was $M=100$ candidates. To solve the underlying least-squares optimization problem (\ref{eq:estimatorTH}) with such a reduced historical values, we utilize only a second-order monomial estimator with $L_1 = 2 \text{ and } L_2 = 2$ (with overall size of $L = 5$). Finally, following also the problem definition in \cite[Section II.]{palacios2016distributed}, we utilize $\alpha=1$ to update the robot's positions.
\subsubsection{Obstacle-free environment.}
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_1.png}\label{fig:persistentCoverageEx1}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_200.png}\label{fig:persistentCoverageEx2}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_400.png}\label{fig:persistentCoverageEx3}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{MeanCov.png}\label{fig:persistentCoverageExVals1}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{std.png}\label{fig:persistentCoverageExVals2}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{JJ.png}\label{fig:persistentCoverageExVals3}}
\caption{Obstacle-free scenario: the coverage level for three different timestamps ((a) timestamp 1, (b) timestamp 200, and (c)timestamp 400) and the corresponding performance indices ((d) average coverage level, (e) standard deviation of coverage level, and(f) cost function, quadratic coverage error).}
\label{fig:persistentCoverageExample}
\end{figure*}
In the first simulation scenario, we deploy the team of robots in an obstacle-free environment. An indicative simulation run of this scenario is summarized in Figure \ref{fig:persistentCoverageExample}. Figures \ref{fig:persistentCoverageEx1}--\ref{fig:persistentCoverageEx3} present the evolution of the coverage across the environment $Q$, for three different timestamps. In addition, Figures \ref{fig:persistentCoverageExVals1}, \ref{fig:persistentCoverageExVals2}, and \ref{fig:persistentCoverageExVals3} depict the evolution of the \textit{average coverage level}, the corresponding \textit{standard deviation}, and the \textit{quadratic coverage error} for the course of the experiment, respectively. After the experiment execution, the average coverage level in all the operational environment $Q$ was $97$ with a standard deviation of $21.2$ and the corresponding quadratic coverage error was $6.9\times10^6$.
It should be highlighted that, the objective (\ref{eq:persistentCF}) is a time-varying function with high rate of change, i.e., the evaluation of (\ref{eq:persistentCF}) may result in significantly different scores for the same robots positions, even for very close timestamps. However, the proposed scheme is able to appropriately tackle the above problem, by constantly learning these cost function variations with respect to the robots' positions.
Although the proposed algorithm presents an equivalent performance compared with the dedicated one \cite[Section VI.]{palacios2016distributed}, if the problem is defined as in this scenario and the coverage evolution with respect to the robots movement being accurately predicted, a dedicated approach should be preferred to avoid the extra time due to learning (equations (\ref{eq:estimatorJ}) and (\ref{eq:estimatorTH}) of the proposed algorithm). However, the proposed approach has several advantages when it is deployed in a real-world environment, where the evaluation of the coverage increase cannot be performed beforehand. Such a scenario is presented in the following paragraph.
\subsubsection{Unknown cluttered environment.}
\begin{figure*}[!th]
\centering
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_1ob.png}\label{fig:persistentCoverage2Ex1}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_200ob.png}\label{fig:persistentCoverage2Ex2}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{k_400ob.png}\label{fig:persistentCoverage2Ex3}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{MeanCovob.png}\label{fig:persistentCoverage2ExVals1}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{stdob.png}\label{fig:persistentCoverage2ExVals2}}
\subfigure[]{\includegraphics[width=0.32\textwidth]{JJob.png}\label{fig:persistentCoverage2ExVals3}}
\caption{Scenario in an unknown environment with non-convex obstacles: the coverage level for three different timestamps ((a)timestamp 1, (b) timestamp 200, and (c) timestamp 400) and the corresponding performance indices ((d) average coverage level, (e)standard deviation of coverage level, and (f) cost function, quadratic coverage error).}
\label{fig:persistentCoverageExample2}
\end{figure*}
In the final simulation scenario, we investigate the performance of the proposed approach for the persistent coverage task, when it is evaluated on an unknown environment with non-convex obstacles. The obstacles have been created randomly and do not hold any kind of pattern. The minimum distance between the obstacles and any robot (\ref{eq:persistentConstraints}) has been set to $b=2.5$.
Again, an illustrative example is presented in Figure \ref{fig:persistentCoverageExample2}. Following the same presentation policy, Figures \ref{fig:persistentCoverage2Ex1}, \ref{fig:persistentCoverage2Ex2}, and \ref{fig:persistentCoverage2Ex3} illustrate the evolution of the of the coverage across the environment $Q$, for three different timestamps. Figures \ref{fig:persistentCoverage2ExVals1}, \ref{fig:persistentCoverage2ExVals2}, and \ref{fig:persistentCoverage2ExVals3} depict the evolution of the \textit{average coverage level}, the corresponding \textit{standard deviation}, and the \textit{quadratic coverage error} (\ref{eq:persistentCF}), respectively.
The cost function (\ref{eq:persistentCF}) does not need any adaptation to this scenario as the coverage values $Z(q)$ that correspond to obstructed locations $q \in O$ will remain zero, independently of their distance from any robot. In other words, the calculation of (\ref{eq:persistentCF}) does not need the information of the unknown obstacles, as the robots would never send coverage updates (\ref{eq:persistentProduction}) about the obstacles' positions. However, to construct comparable metrics with the previous scenario, we exclude the values that correspond to obstacles' locations from the calculation of the average coverage level (Figure \ref{fig:persistentCoverage2ExVals1}). After the experiment execution, the average coverage level inside $Q$ was $90.7$ with a standard deviation of $32.1$ and the corresponding quadratic coverage error was $6.6\times10^6$.
Comparing the outcomes of two scenarios side by side, we can draw the following observations:
\begin{itemize}
\item In the cluttered environment scenario, the robots can more easily get ``trapped'' in overcovered areas, resulting in a higher standard deviation. In other words, when a robot detects (implicitly from the changes in its corresponding cost function) that its position deteriorates the coverage level, may have only a small subset of possible new positions.
\item During the course of the experiment in the cluttered environment, the obstacles ``blocked'' a portion of the robots' coverage capabilities. Therefore, for the cluttered environment scenario, the robots achieved a smaller average coverage level (excluding the obstacles positions).
\end{itemize}
\section{Conclusions}
\label{sec:conclusions}
A distributed methodology for dealing with multi-robot problems, where the mission objectives can be translated into an optimization of a cost function, has been proposed. In contrast to the majority of the multi-robot approaches, where the objectives are accomplished in a cost function optimization scheme, the proposed approach has been designed for multi-robot problems where the a priori calculation of the cost function is not feasible. In a nutshell, the proposed approach has the following key advantages:
\begin{itemize}
\item it does not require any knowledge of the dynamics of the overall system;
\item it can incorporate any kind of operational constraint or physical limitation;
\item it shares the same convergence characteristics as those of BCD algorithms;
\item it has fault-tolerant characteristics;
\item it can appropriately tackle time-varying cost functions;
\item and it can be realized in embedded systems with limited power resources.
\end{itemize}
Conclusively, we expect that many interesting tasks in mobile robotics can be approached by the proposed scheme. This is basically due to the fact that the proposed approach, instead of explicitly solving a particular problem, which requires prior knowledge of the system dynamics, learns, from the real-time measurements, exactly the features of the system which affect the user-defined objectives. Furthermore, the proposed approach can be appealing in many real-life application owing to its fault-tolerant characteristics, without an explicitly designed fault-detection mechanism. All the above issues are considered of paramount importance in the emerging field of multi-robot applications.
As future directions, we are interested in performing an extensive set of experiments, ideally with a large number of robots (e.g., a large swarm of femtosatellites (100 g class spacecraft) \cite{hadaegh2016development}). In particular, in such a set-up, it is impossible to explicitly program each and every robot to perform a subtask, therefore the goal will be to achieve an abstract set of objectives, which are defined in the form of cost function optimization. The idea behind the above formulation is, by excluding the intermediate steps from the design process, we enrich the multi-robot decision making scheme with autonomy, regarding the ``type'' of converged solutions.
\begin{funding}
This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under grant agreement no 740593 (ROBORDER).
\end{funding}
\theendnotes
\bibliographystyle{SageH}
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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Q: Facebook Real-Time updates: comment on post vs comment on album Status entry comment:
{"object":"page","entry":[{"id":"106182246249179","time":1386582683,"changes":[{"field":"feed","value":{"item":"comment","verb":"add","comment_id":"185457974988272_294727","parent_id":185457974988272,"sender_id":106182246249179,"created_time":1386582683}}]}]}
Album comment:
{"object":"page","entry":[{"id":"106182246249179","time":1386581446,"changes":[{"field":"feed","value":{"item":"comment","verb":"add","comment_id":"185444231656313_190183","parent_id":185444231656313,"sender_id":100006218707108,"created_time":1386581446}}]}]}
They seem impossible to distinguish. However, the first one's real post id is pageid_parentid = 106182246249179_185457974988272. If you try to do the same thing with the album comment to get the feed from the stream FQL table, you won't get anything (or an exception with graph api).
Has anyone found a way to distinguish somehow between the two?
A: Yes.
First you need the object_id
object_id=pageid_parentid
Make this api call with the object id:
GET https://graph.facebook.com/v2.9/{object-id}?fields=type,status_type&access_token=token
The response should look something like this if the parent is a post:
{
"type": "status",
"id": "106182246249179_185457974988272"
}
If it's an album, it will look like this:
{
"type": "photo",
"id": "106182246249179_185457974988272"
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
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\section{Introduction}
\subsection{Representations of numbers by quadratic forms: History}
The general question that motivates this paper is the following one:
\emph{Given a quadratic form Q(X) over some ring $R$, which elements of $R$ are represented by Q?}
This question has historically received a lot of attention, especially over number fields and their maximal orders. Over
$\mathbb{Q}$ and other number fields $K$, the question turns out to be a completely local one. Specifically, we have the following
\begin{thm}[Hasse-Minkowski \cite{O}]
Let $Q(X)$ be a quadratic form over $K$, where $K$ is a number field. Then $Q$ represents an element $\alpha$ over $K$ iff $Q$ represents $\alpha$
over the completion $K_v$ for every valuation $v$ of $K$.
\end{thm}
Over orders in number fields, however, the question becomes more delicate, as the Theorem of Hasse-Minkowski is no longer true. To
remedy this situation, one must introduce the notion of \emph{genus}. From now on we restrict ourselves to $\mathbb{Z}$.
\begin{definition*} Two quadratic forms $Q_1,Q_2$ over $\mathbb{Z}$ belong to the same genus if they are isomorphic over $\mathbb{Z}_p$
for all prime numbers $p$ and over $\mathbb{R}$.
\end{definition*}
With this definition, we have the following analogue of the Hasse-Minkowski Theorem:
\begin{thm}[Minkowski-Siegel \cite{K}]
Let $Q_1,\dots,Q_g$ constitute a genus $G$ of quadratic forms over $\mathbb{Z}$. Then an integer $n$ is representable by some form
in $G$ iff it is representable by some form (and hence all forms) in $G$ over $\mathbb{Z}_p$ for each prime number $p$, as well as
over $\mathbb{R}$.
\end{thm}
Even though the Theorem of Hasse-Minkowski can fail for individual quadratic forms in $3$ or more variables, it turns out that the set of exceptions is small. In particular the set of square-free exceptions is finite. The techniques leading to such results are analytic ones. By developing the circle method, Hardy and Littlewood managed to prove such a theorem for non-degenerate quadratic forms in at least $5$ variables. Kloosterman refined this method, and extended it to non-degenerate diagonal quadratic forms in $4$ variables.
However, the extension to quadratic forms in $3$ variables had to wait for the theory of automorphic forms and L-functions to be developed, and was finally proved by Duke and Schulze Pillot in 1988. More precisely, the theorem is the following:
\begin{thm}[Hardy-Littlewood $n\geq 5$, Kloosterman $n=4$, Duke-S.P. $n=3$ \cite{D-SP}]
Let $Q(x)$ be a non-degenerate integral quadratic form in $n\geq 3$ variables. Then if $m$ is a large enough square-free number, $Q$ represents $m$ over $\mathbb{Z}$ iff it represents $m$ integrally over all completions of $\mathbb{Z}$.
\end{thm}
It is worth noting that all the analytic proofs of the Theorem show that the number of times a number is represented by a quadratic form in fact is asymptotically ``what it should be''. It is also worth noting that the Theorem is ineffective due to a possible Siegel zero.
We now focus on the case of 3 variables and discuss the theory of an ternary integral quadratic form $Q(\vec{x})$. The story for positive definite and indefinite forms is
slightly different, so we assume for now that $Q(\vec{x})$ is positive definite. The theta function attached to $Q(\vec{x})$ is then defined by
\begin{equation}\label{thetaQ}
\Theta_Q(z) = \displaystyle\sum_{\vec{x}\in\mathbb{Z}^3}e(Q(\vec{x})z)
\end{equation}
$\Theta_Q(z)$ is absolutely convergent and defines a holomorphic function in the upper half-plane. Moreover, if we let $r_Q(m)$ be
the number of solutions to $Q(\vec{x})=m $, then we have the equality:
$$\Theta_Q(z) = 1+\displaystyle\sum_{m>0} r_Q(m)e(mz)$$
We can therefore read off the number of representations of an integer $m$ by $Q$ from the
Fourier coefficients of $\Theta_Q$! Moreover, using Poisson summation, we can see that
$\Theta_Q(z)$ is a modular form of weight $ {3/2}$ for a congruence group $\Gamma_0(N)$ of $SL_2(\mathbb{Z})$ for $N=4\text{disc}(Q)$. These observations are the foundation of this approach to studying $r_Q(m)$.
Although the theta function $\Theta_Q$ contains all the information about the number of representations, it is hard to analyze directly. The way to proceed is to define another theta function for the genus
$G$ of $Q$. For each form $Q'\in G,$ define $n_{Q'}$ to be the order of the group of automorphisms of $Q'$ over $\mathbb{Z}$, so that $n(Q')=|SO_{Q'}(\mathbb{Z})|.$ We note that since $Q'$ is definite, $n_{Q'}$ is finite. Define $n_G=\sum_{Q'\in G}\frac{1}{n_{Q'}}$ and
\begin{equation}\label{thetaG}
\Theta_G(z)=\frac{1}{n_G}\sum_{Q'\in G} \frac{\Theta_{Q'}(z)}{n_{Q'}}
\end{equation}
First, notice that $\Theta_G$ is also a modular form of weight {3/2} for $\Gamma_0(N)$. More importantly, the coefficients $r_G(m)$
of $\Theta_G$ correspond to the number of representations of numbers by the whole genus $G$, and are therefore very well understood
by Siegel's mass formula to be products of local densities. The idea is to show that the coefficients of $\Theta_Q$ and
$\Theta_G$ aren't very different. The key identity is the following:
\begin{lemma}[Siegel]
$\Theta_G(z)-\Theta_Q(z)$ is a cusp form.
\end{lemma}
We give a proof of this in the function field case when $Q$ is anisotropic in section \ref{sectiongauss} (c.f. \S \ref{SiegelsTheorem}).
All that is left to prove the Theorem is to show that cusp forms have relatively small Fourier coefficients compared to the mass in Siegel's formula. It turns out there
are 2 types of cusp forms of weight ${3/2}$. The first kind are theta series associated to one dimensional lattices; these are easy
to deal with in our case since their coefficients are supported on finitely many square-classes, and so contain only finitely many
non-zero square-free coefficients. The second kind are the cusp forms orthogonal to these, and these are all obtained by the Shimura
correspondence from weight 2 cusp forms on the upper half plane. The main task is to bound the Fourier coefficients of
these.
To get a sense for the kind of bound we need, observe that by Siegel's mass formula and his lower bound\footnote{Note that this bound is ineffective over $\mathbb{Q}$.} on quadratic $L$-functions\footnote{See Theorem \ref{largegenusrepresentations}.} either there are no representations of a squarefree
integer $m$ by a form in the genus $G$, or else $m^{{1/2}-\epsilon}\ll r_G(m)\ll m^{{1/2}+\epsilon}$. The kind of bound we are
looking for on the Fourier coefficients of cusp forms is $a(m)\ll m^{{1/2}-\delta}$ for some $\delta >0$. As it happens, the bound
$a(m)\ll m^{{1/2}+\epsilon}$ is easy to prove and any kind of improvement would be sufficient for
our purposes. There are two possible ways to proceed in this case:
The first (and this is the method developed by Iwaniec and Duke) is to develop a Kuznetzov formula, and then proceed to bound
sums of Sali\'e sums. This approach is arguably quicker and more direct, since it never goes through Waldspurger's formula.
The second approach is to use Waldspurger's formula. This is a formula which relates the Fourier coefficients of a half-integral weight
modular form to the central value of a certain L-function associated with its Shimura lift. In this way, the problem becomes a
subconvexity problem. There is by now a great deal of machinery to deal with subconvexity problems, and so one can get better
bounds this way. This also has the advantage that the optimal bound for the central value of an L-function follows from the Riemann
hypothesis for that L-function combined with the knowledge of the distribution of its zeroes, and in the function field case the Riemann hypothesis is known. This is mainly why we follow this
approach. We would also like to emphasize that the metaplectic Ramanujan conjecture is not a spectral statement, in that it is not a consequence of the underlying local representations being tempered. As such, although the Riemann hypothesis is essential for bounding the central value of the L-function, the statement of purity alone is insufficient for our purposes.
We now focus on the state of affairs for function fields. Once and for all, we fix a function field $k=\mathbb{F}_p(T)$, where $p$ is a prime such that $p\equiv 1\pmod{4}$ for convenience. In this setting, the story for rational forms, that is quadratic forms defined over $k$, is the same as for number fields
in that the Hasse-Minkowski Theorem still holds.
\begin{thm}[Hasse-Minkowski \cite{O}]
Let $Q(X)$ be a quadratic form over $k$. Then $Q$ represents an element $\alpha$ over $K$ iff $Q$ represents $\alpha$
over the completion $k_v$ for every valuation $v$ of $k$.
\end{thm}
The completions of $k$ have a slightly different nature than that of $\mathbb{Q}$ in that there are no archimedean places. Indeed, there is one completion $k_P$
for each monic irreducible polynomial $P,$ as well as the completion ``at infinity", $k_{\infty}=\mathbb{F}_p((T^{-1})).$ It should be emphasized that while we
single out $k_{\infty}$ as a fixed place over which to work, it is really no different than any other completion of $k,$ and everything that follows would
work equally well at any completion. The analogue of an integral quadratic form in the function field case is a quadratic form $Q$ over an $\mathbb{F}_p[T]$-lattice $L$ and the question of interest is which polynomials $Q$ represents. It is important here to distinguish 2 cases. We define $Q$ to be \emph{isotropic} over a field if it represents 0
over that field non-trivially, and \emph{anisotropic} otherwise. If $Q$ is isotropic than it often represents a polynomial infinitely many times, so it is natural to
count in ``boxes", that is, we fix a coordinate system $x_1,x_2,\dots,x_n$ for $L$ and bound the degrees of each coordinate. A coordinate-free way of doing this is to fix an $\mathbb{F}_p[[T^{-1}]]$-lattice $\mathcal{O}_V$ in $V=L\otimes_{\mathbb{F}_p[T]}k_{\infty}$ and define the restricted
representation numbers $$r(D;L,\mathcal{O}_V,m) = \#(v\in L\cap T^m\mathcal{O}_V\mid Q(v)=D).$$ Note that these numbers are always finite since $L\cap\mathcal{O}_V$ is finite.
In the anisotropic case, however, the representation numbers $r(L,D)=\#(v\in L\mid Q(v)=D)$ are always finite, and no restriction is necessary. The reason is
that in this case the orthogonal group $SO_Q(k_{\infty})$ is compact, while the lattice $L$ is discrete in $V.$ Another immediate consequence of this compactness
in the anisotropic case is the finiteness of the integral stabilizer group, $SO_Q(\mathbb{F}_p[T]).$
Merrill-Walling \cite{MW} and later Hoffstein-Merrill-Walling \cite{HMW} studied the case of representations of polynomials by sums of $n$-squares, which in our
notation corresponds to $L=\mathbb{F}_q[T]^n,\: Q(x_1,\dots,x_n)=x_1^2+\cdots+x_n^2,\:\mathcal{O}_V=\left\{(x_1,\dots,x_n)\in k_{\infty}^n\mid \deg(x_i)\leq 0\right\}$
and $D$ and $m$ vary. They get an asymptotic for $r(D,m)$, the number of representatios of $D$ as a sum of $n$ squares of degree $\leq m$ as long as $n\geq 3,$ and show that these numbers are non-zero for sufficiently large $D$
subject to the necessary condition $m\geq \deg(D)/2.$ Their method develops the spectral theory on the space
$SL_2(\mathbb{F}_q[T])\backslash SL_2(k_{\infty})/SL_2(\mathbb{F}_q[[T^{-1}]])$
and then expresses an appropriate theta function in terms of the Eisenstein spectrum. They note that this only possible because on this space there are no cusp forms. A phenomenon which does not persist when one adds level and in particular when one considers more general forms.
In \cite{Car}, Car developed the circle method and the Kloosterman refinement of the circle method for diagonal forms
$Q(x_1,x_2,\dots,x_n)= A_1x_1^2+\cdots+A_n x_n^2$ in at least 4 variables where for every $j,$ $A_j\in\mathbb{F}_p[T]$. As a result, she proves an asymptotic for the number of representations
of $D$ even under the strictest degree conditions, namely $$\deg(x_i)\leq \frac12(\deg(D)-\deg(A_i) +1)$$ It turns out that for anisotropic diagonal forms
every representation of a polynomial satisfies the strictest degree conditions, so an immediate consequence of Car's work is an asymptotic for representation
numbers of diagonal anisotropic forms in $\geq 4$ variables.
We now describe our results, focusing primarily on the anisotropic case. Let $Q$ be a quadratic form on a 3-dimensional $\mathbb{F}_q[T]$-lattice $L$, such that $Q$ is
anisotropic over $k_{\infty},$ that is, $Q$ does not represent $0$ non-trivially over $V=L\otimes_{\mathbb{F}_p[T]}k_{\infty}.$ The theta function for $Q$
is then defined by
\[\Theta_Q\left(\left(\left(\begin{smallmatrix} \sqrt{v} & u/\sqrt{v}\\ 0 & 1/\sqrt{v}\end{smallmatrix}\right),1\right)\right)=|v|^{3/4}(\sqrt{v},\varpi_{\infty})_{\infty}^{\frac{v_{\infty}(v)}{2}}\sum_{l\in L}e(Q(l)T^2u)\chi_{\mathcal{O}_\infty}(Q(l)v) \]
\[= |v|^{3/4}(\sqrt{v},\varpi_{\infty})_{\infty}^{\frac{v_{\infty}(v)}{2}}\sum_{D\in \mathbb{F}_p[T]}r_Q(D)e(DT^2u)\chi_{\mathcal{O}_{\infty}}(Dv)\]
Where $\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}\\0&1/\sqrt{v}\end{smallmatrix}\right),1\right)\in \widetilde{SL}_2(k_\infty)$, $e(x)$ is an additive character, $(\cdot\,,\cdot)_{\infty}$ denotes the Hilbert symbol at the completion $k_{\infty}$ (for a precise definition of these see \S\ref{not11} and \S\ref{metgp}), $|v|=|v|_{\infty}$, $\mathcal{O}_{\infty} = \mathbb{F}_p[[T^{-1}]]$ and $\chi_{\mathcal{O}_{\infty}}$ is the characteristic function of $\mathcal{O}_{\infty}$. We form the genus theta function $\Theta_G$ as in the number field case and prove that $\Theta_G-\Theta_Q$ is a cusp form. This reduces the question of representation
numbers to understanding the Fourier coefficients of $\Theta_G$ and bounding the Fourier coefficients of cusp forms. The Fourier coefficients of $\Theta_G$ are
readily read off from the Siegel mass formula. To bound the Fourier coefficients of cusp forms we follow \cite{KS} and \cite{B} to prove a Waldspurger type formula.
A nice feature of the function field case is that since the Riemann hypothesis is known, we can both prove what is essentially the optimal bound for Fourier coefficients of cusp
forms, and give an \emph{effective} lower bound on the Fourier coefficients of $\Theta_G$ coming from the main term. This is primarily because the Riemann hypothesis
rules out Siegel zeroes. This being said we also remark that unlike in the number field case, the necessary estimates \emph{do not} immediately follow from the Riemann hypothesis, cf. \S\ref{sectiondrinfeld}.
Before describing our main results we need to introduce some notation and terminology; this will be explained in detail in \S\ref{sectionfunctionfields}. Let $\widetilde{SL}_2(k_{\infty})$ be the metaplectic cover of $SL_2(k_{\infty})$ given by the explicit cocycle described in \S\ref{metgp}. We write elements of $\widetilde{SL}_2(k_{\infty})$ as $(g;\delta)$ where $g\in SL_2(k_{\infty})$ and $\delta\in\{\pm1\}$. Let $\varpi_{\infty}=T^{-1}$ be a generator for the maximal ideal of the ring of integers $\mathcal{O}_{\infty}$ of $k_{\infty}$. For $N\in\mathbb{F}_p[T]$ and $n\in\mathbb{N}$, let $\widetilde{\Gamma}_0(N)$ and $\iota(\widetilde{K}_{0}(\varpi_{\infty}^n))$ denote the following subgroups of $\widetilde{SL}_2(k_{\infty})$:
\[\widetilde{\Gamma}_0(N)=\setdef{\eta\left(\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)\right)}{\left(\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}\right)\in SL_2(\mathbb{F}_p[T]),\,\,c\equiv0\;\text{mod}\,{N}}\subset\widetilde{SL}_2(k_{\infty})\]
\[\iota(\widetilde{K}_0(\varpi_{\infty}^n))=\setdef{\iota\left(\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)\right)}{\left(\begin{smallmatrix}a&b\\ c&d\end{smallmatrix}\right)\in SL_2(\mathcal{O}_{\infty}),\,\,c\equiv0\; \text{mod}\, \varpi_{\infty}^n}\subset \widetilde{SL}_2(k_{\infty})\]
Where $\eta:SL_2(\mathbb{F}_p[T])\rightarrow \widetilde{SL}_2(k_{\infty})$ and $\iota: SL_2(\mathcal{O}_{\infty})\rightarrow \widetilde{SL}_2(k_{\infty})$ are as defined in \S\ref{metgp}. We call functions, $F$, on the space $\widetilde{\Gamma}_0(N)\backslash\widetilde{SL}_2(k_{\infty})\slash \iota(\widetilde{K}_0(\varpi_{\infty}^n))$ that satisfy $F((I_2,-1))=-F((I_2,1))$, where $I_2$ stands for the $s\times2$ identity matrix, metaplectic functions of level $N$, depth $n$. We note that the latter condition is to ensure that the functions $F$ does not factor through $SL_2$. We denote the space of level $N$ depth $n$ metaplectic functions by $\widetilde{M}_n(\widetilde{\Gamma}_0(N))$.
At this point we want to take a step back momentarily and explain some of the technical and philosophical points of the paper. First of all we will (as much as possible) be working with the singled out place $k_{\infty}$ and local group $\widetilde{SL}_2(k_{\infty})$. The reason (for us choosing such an approach) is mainly the application to quadratic forms we described above. We want to keep the analogy with the corresponding representability problem over number fields as close as possible and the classical language serves this purpose better.
We should, however, note the appearance of the subgroups $\iota(\widetilde{K}_0(\varpi_{\infty}^n))$. As is well known in the number field case, the weight of a modular form is dictated by the action of the maximal compact subgroup of $SL_2(\mathbb{R})$ on the associated representation. In the case of a function field a similar phenomenon occurs. The difference, however, is that the maximal compact subgroup (which is the circle group $S^1$ in the classical picture) is now $\iota(SL_2(\mathcal{O}_{\infty}))\times (I_2,\pm1)$. In particular it is nonabelian and hence has a much richer representation theory\footnote{This feature is already present in the number field case when one works over an imaginary quadratic field and the group $SL_2(\mathbb{C})$ where the maximal compact subgroup is $SU(2)$.}. The theta functions, which are functions on the group $\widetilde{SL}_2(k_{\infty})$, transform under a representation $\rho$ of the maximal compact. This representation being smooth implies that there exists a number $n\in \mathbb{N}$ such that $\rho$ has a fixed vector under the congruence subgroup $\iota(\widetilde{K}_0(\varpi_{\infty}^n))$. In accordance with Moy-Prasad \cite{MP} we call the minimal such $n$ the \emph{depth}. In this paper we will be considering metaplectic forms of depth $0$ or $1$ and arbitrary level. Theta functions associated to anisotropic ternary quadratic forms turn out to be of depth $1$ and hence this depth restriction is enough for the application we have in mind. We also note that all of the above can be treated in a completely uniform manner (as is done in \S \ref{sectiongauss}) by the Weil representation on $\widetilde{SL}_2(\mathbb{A}_k)$ where $\mathbb{A}_{k}$ is the adele ring of $k$. We should further mention that the half-integral weight Ramanujan conjecture can also be expressed in a uniform adelic language and the methods of this paper are capable of establishing this in the most general case without any depth restrictions. One can also replace $\mathbb{F}_p(T)$ with an arbitrary function field $k$ over a finite field. This is the subject of the upcoming paper \cite{AJ}.
With the remarks of the preceding paragraph we now restrict to the depth $n\leq1$ case. A metaplectic function, $F\in \widetilde{M}_n(\widetilde{\Gamma}_0(N))$ is called \emph{cuspidal} if the constant Fourier coefficient of $F$ vanishes at each cusp (see equation (\ref{cuspidal})). The space of cuspidal metaplectic functions of level $N$ and depth $n$ are denoted by $\widetilde{S}_n(\widetilde{\Gamma}_0(N))$. We will be considering cuspidal metaplectic functions that are eigenfunctions of certain operators that fill the role of the Laplacian in the archimedean picture. These are explained in detail in \S\ref{halfintegralwhittakerun} and \S\ref{halfintegralwhittakerram}. Let $\widetilde{\Delta}$ denote right convolution with the characteristic function of the double coset $\iota(SL_2(\mathcal{O}_{\infty}))\backslash \left(\left(\begin{smallmatrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right),1\right)/\iota(SL_2(\mathcal{O}_{\infty}))$. For any polynomial $N$, $\widetilde{\Delta}$ acts on the space, $\widetilde{S}_0(\widetilde{\Gamma}_0(N))$, of cuspidal metaplectic functions of level $N$, depth $0$. An $F\in \widetilde{S}_0(\widetilde{\Gamma}_0(N))$ that is an eigenfunction of $\widetilde{\Delta}$ will be called \emph{a cuspidal metaplectic form} of level $N$, depth $0$. For cuspidal metaplectic functions of depth $1$ the operator $\widetilde{\Delta}$ gets replaced by $\widetilde{W}_{\infty}$, which is defined to be right convolution by the characteristic function of the double coset $\iota(\widetilde{K}_0(\varpi_{\infty}))\backslash\left(\left(\begin{smallmatrix}0&-\varpi_{\infty}^{-1}\\ \varpi_{\infty}&0\end{smallmatrix}\right),1\right)/\iota(\widetilde{K}_0(\varpi_{\infty}))$. For any polynomial $N$, $\widetilde{W}_{\infty}$ acts on the space ($\widetilde{S}_1(\widetilde{\Gamma}_0(N))$) of cuspidal metaplectic functions of level $N$, depth $1$. We will call an $F\in \widetilde{S}_1(\widetilde{\Gamma}_0(N))$ that is an eigenfunction of $\widetilde{W}_{\infty}$, \emph{a cuspidal metaplectic form} of level $N$, depth $1$.
On the other hand, at each finite place $P\nmid N$ we have the usual Hecke operators $\widetilde{T}_{P^2}$ acting on the metaplectic functions of level $N$, depth $n$, $n\leq1$. We will call a cuspidal metaplectic form $F$ of level $N$, depth $n$, that is an eigenfunction of all Hecke operators $\widetilde{T}_{P^2}$ for $P\nmid N$, \emph{a cuspidal metaplectic Hecke eigenform} of level $N$, depth $n$.
A cuspidal metaplectic form $F\in \widetilde{S}_0(\widetilde{\Gamma}_0(N))$ has a Fourier-Whittaker expansion at the standard cusp as
\[F(w)=\sum_{D\in\mathbb{F}_p[T]}\lambda_{F}(D)(D,\sqrt{v})_{\infty}e(T^2Du)\widetilde{W}_{n,i\theta}(Dv)\]
where $w=\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}\\0&1/\sqrt{v}\end{smallmatrix}\right),1\right)$, $(\cdot\,,\cdot)_{\infty}$ denotes the Hilbert symbol at the place $\infty$ as usual, and the Whittaker functions $\widetilde{W}_{n,i\theta}$ are as defined in \S\ref{halfintegralwhittakerun} and \S\ref{halfintegralwhittakerram} respectively. With these definitions in hand we can now state the main result of the paper, which gives an optimally sharp estimation for the Fourier-Whittaker coefficients of metaplectic forms.\\
\begin{thm}[Metaplectic Ramanujan conjecture]\label{ramanujan}
Let $F(w)$ be a cuspidal metaplectic form of level $N$ and depth $0$ or $1$. If $D$ is a square-free polynomial of even degree that is relatively prime to $N$, the Fourier-Whittaker coefficients
$\lambda_F(D)$ of $F$
satisfy the bound $$|\lambda_F(D)|\leq C_{F,\epsilon}\;|D|^{-\frac12+\epsilon}$$
where $|D|=p^{deg(D)}$ and $C_{F,\epsilon}$ is an effective constant depending only on $F$ and $\epsilon.$
\end{thm}
The main application of Theorem \ref{ramanujan} to the representation of polynomials by quadratic forms is the following assertion:\\
\begin{thm}\label{representationTheorem}
Let $Q$ be a ternary quadratic form over $\mathbb{F}_p[T]$ that is anisotropic over $k_{\infty}$. For $D\in \mathbb{F}_p[T]$ such that $\deg(D)$ has the same parity as $\deg(\text{disc}(Q))$ and $(D,\text{disc}(Q))=1$, let $r_Q(D)$ denote the number of times $Q$ represents the polynomial $D$ and $r_G(D)$ the number of times $D$ is represented by the genus of $Q$. Then
$$r_Q(D)=r_{G}(D)+O_{Q,\epsilon}(|D|^{1/4 +\epsilon}).$$
where the implied constant is effective and depends only on $Q$ and $\epsilon$.
\end{thm}
The following local to global principle now follows immediately from Theorem \ref{representationTheorem}.\\
\begin{cor}\label{representationCor} For $Q$ as above there exists an effective constant $A_{Q}$ such that every square-free $D\in\mathbb{F}_p[T]$ with $\deg(D)$ of the same parity as $\deg(\text{disc}(Q))$, satisfying $(D,\text{disc}(Q))=1$ and $|D|>A_Q$ is represented by $Q$ as long as there are no local obstructions.
\end{cor}
The paper is structured as follows: In \S\ref{sectionfunctionfields} we introduce and develop the basic notions over function fields including quadratic
forms, cuspidal automorphic and metaplectic forms, their Fourier expansions, Hecke operators, Whittaker functions and L-functions attached to cuspidal automorphic functions. For each of these notions we first give a treatment for depth $0$ functions and then describe the relevant changes for depth $1$ functions.
In \S\ref{sectiondrinfeld} we identify precise conditions under which the Riemann Hypothesis implies the Lindel\"of Hypothesis for a family of zeta functions in the function field setting. In \S\ref{sectionshimura} we study the Shimura and Maass-Shintani lifts and derive explicit normalisations. To clarify the technical proofs we first give detailed proofs for the full level and depth $0$ case and then point out the differences in the case of arbitrary level and depth $1$. \S\ref{sectionwaldspurger} applies
the results of \S\ref{sectionshimura} to prove a Waldspurger type formula and the metaplectic Ramanujan conjecture. \S\ref{sectionquadratic} gives the promised application to
representing polynomials by quadratic forms, and in \S\ref{Example} we provide a concrete example to the type of representability question we answer in the paper. Finally \S{A} develops the Weil representation, uses it to define theta functions, and proves their transformation
properties.Though it is fundamental and referred to throughout the paper, \S{A} is quite technical and can be skipped on a first reading.
\section{Automorphic Forms Over Function Fields}\label{sectionfunctionfields}
\subsection{Notation}\label{not11}
We will fix some notation which will be used throughout the paper. Let $\mathbb{F}_p$ denote the finite field with $p$ elements. For convenience, throughout the
paper we will be assuming that $p\equiv1\pmod{4}$. Let $R$ denote the ring $\mathbb{F}_p[T]$, and $k$ the field $\mathbb{F}_p(T)$. We also fix the prime at ``infinity'' which corresponds to the
valuation $v_{\infty}$ such that $v_{\infty}(S_1(T)/S_2(T))=\deg{S_2}-\deg{S_1}$, for $S_1,S_2\in\mathbb{F}_p[T]$. The completion of $k$ with respect to this valuation is isomorphic to $\mathbb{F}_p((T^{-1}))=k_{\infty}$, and the ring of integers of $k_{\infty}$ is $\mathcal{O}_{\infty}$. We will denote the uniformizer $T^{-1}$ of $\mathcal{O}_{\infty}$ by $\varpi_{\infty}$ and use them interchangably. We denote the norm induced by $v_{\infty}$ by $|\cdot|_{\infty}$, i.e. For $x\in k_{\infty}$, $|x|_{\infty}=p^{-v_{\infty}(x)}$. For any set $A$ we will use the notation, $\chi_{A}$, to denote the characteristic function of $A$. Once and for all we fix an additive character, $e(x)$, on $k_{\infty}$ defined as follows. Let $x=\sum_{j=-\infty}^{k}a_jT^j\in k_{\infty}$ where $a_j\in\mathbb{F}_p$. Choose a lift $a_1^*$ of $a_1$ to $\mathbb{Z}$, and define $e(x):=e^{2\pi ia_1^*/p}$. Since $e(x)$ is independent of the choice of the lift $a_1^*$, we will simply write $e(x)=e^{2\pi i a_1/p}$. We also note that the conductor of $e(x)$ is $\mathcal{O}_{\infty}$, i.e. $e(x)=1$ for all $x\in\mathcal{O}_{\infty}$ and $e(x)$ is non-trivial on $\varpi_{\infty}\mathcal{O}_{\infty}$.
The norm of an element $S\in\mathbb{F}_p[T]$ will be denoted by $|S|=|S|_{\infty}=p^{\deg{S}}$. The finite valuations of $k$ can be identified with the monic irreducible polynomials $P\in\mathbb{F}_p[T]$ by setting $k_P$ to be the fraction field of the completion of $R$ with respect to $P$. Abusing notation, for a valuation $v$ corresponding to $P$ and an element $c\in R$ we sometimes write $v\mid c$ to denote $P\mid c$.
Define the function field analogues of the classical gamma and zeta functions by
\[\Gamma_k(s)=\frac{1}{1-p^{-s}}\]
\[\zeta_k(s)=\sum_{a\in R}\frac{1}{|a|^s}\]
Note that because the valuations of $k$ are indexed by \emph{monic} irreducible polynomials, the Euler product for $\zeta$ is $\zeta_k(s)=(p-1)\prod_P(1-|P|^{-s})^{-1}$, where the product is over all monic irreducible polynomials $P\in R$.
\subsubsection{Hilbert Symbols and Quadratic Reciprocity}
Recall that we are assuming $p\equiv1 \bmod 4$. For $c\in R\backslash\{0\}$ such that the ideal generated by $c$ is prime in $R$ (i.e. $c$ is an irreducible and we do not care about the leading coefficient), and for $d\in R$ we will define the Legendre symbol mod $c$ by $$\left(\frac{d}{c}\right):=\begin{cases}0&\text{if $\gcd(c,d)\neq1$}\\ 1 & \textrm{$\gcd(c,d)=1$ and $d$ is a square modulo $c$}\\ -1 & \textrm{otherwise}\end{cases}.$$
Where we use $\gcd(c,d)$ to mean that the ideal generated by $c$ and $d$ is the whole ring $R$. We then extend this definition multiplicatively in the $c$ variable. Now let $v$ be a valuation of $k$ and let $k_v$ be the completion of $k$, $\mathcal{O}_v\subset k_v$ the ring of integers of $k_v$, and $\varpi_v$ a uniformizer at $v$.
For $\alpha,\beta\in k_v^{\times}$ we denote the Hilbert symbol at the place $v$ by $(\alpha,\beta)_v$. By definition
$$(\alpha,\beta)_v=\begin{cases}1 & \textrm{if there is a non-zero solution to $z^2=\alpha x^2 +\beta y^2$ with $(x,y,z)\in k_v^3$}\\-1 & \text{otherwise}\end{cases}$$ Recall that the Hilbert symbol is multiplicative in each variable. Moreover, since we are
working over $\mathbb{F}_p$ with $p\equiv 1\mod{4}$ it can easily be checked that the $(-1)^{(\cdot,\cdot)_v}$ is the unique symplectic form on $(k_v)^{\times}/((k_v)^{\times})^2\times(k_v)^{\times}/((k_v)^{\times})^2$.
Explicitly, for $v=\infty$, and $\varpi_{\infty}=T^{-1}$, we have $$(x,y)_{\infty} = \left(\frac{x_0}{T}\right)^m\left(\frac{y_0}{T}\right)^n$$ where $x=x_0\varpi_{\infty}^n,y=y_0\varpi_{\infty}^m$ and $x_0,y_0\in\mathcal{O}_{\infty}^{\times}$.\\
The most important property of the Hilbert symbol is the product formula (cf. \cite{Hasse}), $\prod_{v}(\alpha,\beta)_v=1$, where the product is now over all valuations (including valuation at infinity).\\
\begin{lemma}\label{hilquad}
For $\alpha,\beta\in R\backslash\{0\}$ relatively prime we have $$\left(\frac{\alpha}{\beta}\right)=\prod_{v|\beta}(\alpha,\beta)_v$$
\end{lemma}
\begin{proof}
By the product formula,$$\prod_{v|\beta}(\alpha,\beta)_v=\prod_{v\nmid\beta}(\alpha,\beta)_v=(\alpha,\beta)_{\infty}\prod_{v|\alpha}(\alpha,\beta)_v$$ which shows that both sides are defined multiplicatively in $\beta$. Hence it is enough to consider the case when $\beta$ is a prime and denote the valuation corresponding to $\beta$ by $\mathfrak{b}$. Let $k_{\mathfrak{b}}$ be the completion of $k$ at $\mathfrak{b}$. Then we have the following equalities
\[\prod_{v\mid \beta}(\alpha,\beta)_v=\left(\alpha,\beta\right)_{\mathfrak{b}}= \left(\frac{\alpha}{\beta}\right)\]
\end{proof}
The product formula implies, in particular, the following quadratic reciprocity formula for $k=\mathbb{F}_p(T)$:\\
\begin{lemma}\label{quadrec}
For $\alpha,\beta\in R\backslash\{0\}$ relatively prime we have $$\left(\frac{\alpha}{\beta}\right)\cdot\left(\frac{\beta}{\alpha}\right)=(\alpha,\beta)_{\infty}.$$
\end{lemma}
\begin{proof}
Using the fact that if $v$ doesn't divide $\alpha$ or $\beta$ we have $(\alpha,\beta)_v=1$ together with lemma \ref{hilquad} we have
$$\left(\frac{\alpha}{\beta}\right)\cdot\left(\frac{\beta}{\alpha}\right)=\prod_{v\neq\infty}(\alpha,\beta)_v=(\alpha,\beta)_{\infty}$$ as desired.
\end{proof}
\subsection{The Metaplectic group}\label{metgp}
Following the treatment by Gelbart given in \cite{G}, we define the metaplectic group, $\widetilde{SL}_2(k_{\infty})$, to be the double cover of $SL_2(k_{\infty})$ defined by the following cocycle: For a matrix $g\in SL_2(k_{\infty})$ define $$X(g):=\begin{cases} c& c\neq 0\\ d & \textrm{otherwise}\end{cases}$$ and $$\epsilon(g_1,g_2):=(X(g_1),X(g_2))_{\infty}(X(g_2),X(g_3))_{\infty}(X(g_1),X(g_3))_{\infty}$$ where $g_3=g_1g_2$. That this is actually a cocycle is the main result of \cite{Ku}. Thus elements of $\widetilde{SL}_2(k_{\infty})$ can be written as $(g,\delta)$ where $g\in SL_2(k_{\infty}),\delta=\pm 1$ and the multiplication is
$(g_1,\delta_1)(g_2,\delta_2)=(g_1g_2,\delta_1\delta_2\epsilon(g_1,g_2)$.
In what follows, we will be interested in various operators (for instance Hecke operators), whose definition will depend on splitting properties of $\epsilon$ over various subgroups of $k_{\infty}$. First consider the subgroup $SL_2(\mathcal{O}_{\infty})$. By Lemma 2.9 of \cite{G} we have the following splitting of $\widetilde{SL}_2(k_{\infty})$ over $SL_2(\mathcal{O}_{\infty})$: For $g\in SL_2(\mathcal{O}_{\infty})$ define $$\kappa(g):=\begin{cases}(c,d)_{\infty}&\text{if $c\neq 0$ and $c\notin\mathcal{O}_{\infty}^{\times}$} \\ 1&\text{otherwise}\end{cases}$$ Then the map $\iota:SL_2(\mathcal{O}_{\infty})\rightarrow\widetilde{SL}_2(k_{\infty})$ given by $\iota(g)=(g,\kappa(g))$ is a
group homomorphism. We mention that while Gelbart only works over fields of characteristic 0 an inspection of the proof shows that it carries over verbatim for local fields of odd residual characteristic.
The other subgroup we would like to consider is $SL_2(R)$. Let $\eta$ be the map of sets $\eta:SL_2(R)\rightarrow \widetilde{SL}_2(k_{\infty})$ given by $\eta(g)=(g,\left(\frac{d}{c}\right))$ for $g=\left(\begin{smallmatrix} a&b\\ c&d\end{smallmatrix}\right)$. Then,\\
\begin{lemma}
$\eta$ is a group homomorphism.
\end{lemma}
\begin{proof}
This is a consequence of the product formula for the Hilbert symbol. Consider $g_i=\left(\begin{smallmatrix} a_i&b_i\\ c_i&d_i\end{smallmatrix}\right)\in SL_2(R)$ for $i=1,2,3$ with $g_1g_2=g_3$. We assume for simplicity that $c_1,c_2,c_3$ are all non-zero though the other cases can be handled similiarly. Then by the product formula we have
\begin{align*}
\epsilon(g_1,g_2)&=(c_1,c_2)_{\infty}(c_1,c_3)_{\infty}(c_2,c_3)_{\infty}\\
&= \prod_{v\neq\infty}\left((c_1,c_2)_v(c_1,c_3)_v(c_2,c_3)_v\right)\\
&= \prod_{i=1}^3\prod_{v|c_i} (c_i,d_i)\\
&= \prod_{i=1}^3\left(\frac{d_i}{c_i}\right)\\
\end{align*}
as desired.
\end{proof}
\subsection{Quadratic forms over function fields}
We begin with a review of quadratic forms over function fields. Let $Q(\vec{x})$ be a quadratic form in n-variables,
$\vec{x}=(x_1,x_2,\dots,x_n)$. $Q$ is said to be non-degenerate if its associated bilinear form
$$B(\vec{x},\vec{y})=\frac{1}{2}\left(Q(\vec{x}+\vec{y})-Q(\vec{x})-Q(\vec{y})\right)$$ is non-degenerate.
We also say that a form is \emph{anisotropic} over a field $k$ if it does not represent 0 non-trivially over that field. We remark that
over the field $\mathbb{R}$ of real numbers, the anisotropic forms are precisely the definite ones.
We shall be considering also quadratic forms $Q$ over rings $S$ instead of fields. Given such a ring $S$,a free $S$-lattice $L$, and a quadratic form $Q$ on $L$, we can represent $Q$
as a symmetric matrix $A_Q$ by picking a basis $l_1,l_2,\dots,l_n$ for $L$ over $S$, and writing $A_Q=[Q(l_i,l_j)\cdot\frac{1+\delta_{ij}}{2})]_{\{i,j\}}$ so that
$$Q(\sum_{i=1}^n \alpha_i l_i) = \vec{\alpha}\cdot A_Q\cdot \vec{\alpha}^t$$ where $\vec{\alpha}=(\alpha_1,\alpha_2,\dots,\alpha_n)$ and $\vec{\alpha}^t$ denotes the transpose vector. Changing bases by an element of $g\in GL_n(S)$ amounts to changing $A_Q$ to $gA_Qg^t$. Thus we can define the discriminant $\text{disc}(Q)$ to be the determinant of $A_Q$, and this is a well
defiend element of $S/(S^{\times})^2.$ In particular, note that the ideal $(\text{disc}(Q))$ is well defined in $S$.
\begin{lemma}\label{inverselattice}
Let $Q(x,y,z)$ be an anistropic quadratic form over $k_{\infty}$. Then for all $m\in\mathbb{Z}$, $Q^{-1}(\varpi_{\infty}^m\mathcal{O}_{\infty})$ is an $\mathcal{O}_{\infty}$ lattice in $k_{\infty}^3$.
\end{lemma}
\begin{proof}
First note that since we are not over a field of even characteristic, we can diagonalize the form $Q$, so we can assume it is of the form $Q(x,y,z)=ax^2+by^2+cz^2$. Only the square-class of $a,b,c$ is relevant, so each of $a,b,c$ can be assumed to be one of $1,u,T,uT$, for $u$ a quadratic non-residue in
$\mathbb{F}_p$. Moreover, we can scale to assume that $a=1$. Note that the operations of changing basis and scaling done so far do not affect the statement of
the lemma.
Next, for $Q$ to be anisotropic, we can not have both $b$ and $c$ be elements of $\mathbb{F}_p$. Going through the cases, we see that by scaling (we note that scaling does not effect the statement of the lemma) and changing
basis we can turn every ternary anisotropic form into $Q_0(x,y,z)=x^2+uy^2+Tz^2$. Now, it is easily seen that $v_{\infty}(x^2+uy^2+Tz^2)=\max\{v_{\infty}(x^2),v_{\infty}(uy^2),v_{\infty}(Tz^2)\}$ and so $Q_0^{-1}(\mathcal{O}_{\infty}) = \{(x,y,z)\mid x,y\in\mathcal{O}_{\infty},z\in\varpi_{\infty}\mathcal{O}_{\infty}\}.$
\end{proof}
\subsection{Background on symmetric spaces}\label{backgr}
We denote by $\mathbb{H}$ the ``upper half plane" $$\mathbb{H} = PGL_2(k_{\infty})\slash PGL_2(\mathcal{O}_{\infty})$$ A complete set of coset
representatives for $\mathbb{H}$ is
$$\mathbb{H}=\setdef{
\left(\begin{smallmatrix}
y & x \\
0 & 1
\end{smallmatrix}\right)}{y\in k_{\infty}^{\times}\slash \mathcal{O}_{\infty}^{\times},\; x\in k_{\infty}\slash y\mathcal{O}_{\infty}}$$
Note that $\{T^m\mid m\in\mathbb{Z}\}$ forms a complete set of representatives for $y$. The space $\mathbb{H}$ carries a measure invariant under the action of $PGL_2(k_{\infty})$, which, in the $(x,y)$ coordinates, is given by $$\frac{dx\,dy}{|y|^2}$$ where $dx$ and $dy$ are normalized to give $\mathcal{O}_{\infty}$ measure 1.
\begin{subsubsection}{Metaplectic spaces}\label{metsp}
Recall from \S\ref{metgp} that we have a group homomorphism $\iota:SL_2(\mathcal{O}_{\infty})\rightarrow\widetilde{SL}_2(k_{\infty})$ given by $g\rightarrow (g,\kappa(g))$.
We will also be interested in functions on the space $$\widetilde{\mathbb{H}}=\widetilde{SL}_2(k_{\infty})/\iota(SL_2(\mathcal{O}_{\infty})).$$
A complete set of representatives for $\widetilde{\mathbb{H}}$ is given by
$$\widetilde{\mathbb{H}} = \setdef{\left(\left(\begin{smallmatrix}
\sqrt{v} & u/\sqrt{v} \\
0 & 1/\sqrt{v} \\
\end{smallmatrix}\right),\pm1\right)}{ v\in (k_{\infty}^{\times})^2/(\mathcal{O}^{\times})^2,\; u\in k_{\infty}\slash v\mathcal{O}_{\infty}}$$
Note that a function $F:\widetilde{SL}_2(k_{\infty})\rightarrow \mathbb{C}$ which is invariant under the central element $(Id,-1)\in \widetilde{SL}_2(k_{\infty})$ descends to function on $SL_2(k_{\infty})$. We would like to disregard these functions which are not ``really'' metaplectic. We thus insist on our functions $f$ to satisfy $F((Id,-1)\cdot g)=-F(g)$.
If $F$ is a function on $\widetilde{\mathbb{H}}$ and $g\in SL_2(k_{\infty})$ we often write $F(g)$ to mean $F((g,1))$ by abuse of notation.
The arithmetic of the metaplectic group enters when we ask study functions on $\widetilde{SL}_2(k_{\infty})$ which are left invariant under $\eta(SL_2(R))$. We also note that the metaplectic group is considered from the adelic viewpoint in \S\ref{sectiongauss}.
\end{subsubsection}
\subsubsection{Depth $1$}
For the application to anisotropic quadratic forms, we shall also need to talk about automorphic forms with certain ramification type at the place ``$\infty$''. More precisely, for each integer $n\geq0$ we introduce the subgroups $K_0(\varpi_{\infty}^n)$ and $\widetilde{K}_0(\varpi_{\infty}^n)$,
\[K_0(\varpi_{\infty}^n)=\begin{setdef}{\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)\in PGL_2(\mathcal{O}_{\infty})}{c\equiv0\mod{\varpi_{\infty}^n}}\end{setdef}\]
\[\widetilde{K}_0(\varpi_{\infty}^n)=\begin{setdef}{\left(\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right)\in SL_2(\mathcal{O}_{\infty})}{c\equiv0\mod{\varpi_{\infty}^n}}\end{setdef}\]
and denote $PGL_2(k_{\infty})\slash K_0(\varpi_{\infty})\textrm{ and } \widetilde{SL}_2(k_{\infty})\slash \iota(\widetilde{K}_0(\varpi_{\infty}))$ by $\mathbb{H}_1$ and $\widetilde{\mathbb{H}}_1$, respectively.
$\mathbb{H}_1$ can be decomposed into two ``components" with natural coordinate systems, which we will denote by $\mathbb{H}_1^u$ and $\mathbb{H}_1^l$ and refer to as the `\emph{upper}' and `\emph{lower}' components respectively. A set of representatives
for the upper component $\mathbb{H}_1^u$ is
\begin{equation}\label{measu}
\mathbb{H}^u_1=\setdef{\left(\begin{smallmatrix}
y & x \\
0 & 1
\end{smallmatrix}\right)}{y\in k_{\infty}^{\times}\slash \mathcal{O}_{\infty}^{\times},\; x\in k_{\infty}\slash y\mathcal{O}_{\infty}}
\end{equation}
and a set of representatives for the lower part $\mathbb{H}_1^l$ is given by
\begin{equation}\label{measl}
\mathbb{H}^l_1=\setdef{\left(\begin{smallmatrix}
x & y \\
1 & 0
\end{smallmatrix}\right)}{y\in k_{\infty}^{\times}\slash \mathcal{O}_{\infty}^{\times},\; x\in k_{\infty}\slash y\varpi_{\infty}\mathcal{O}_{\infty}}
\end{equation}
The space $\mathbb{H}_1$ has a measure invariant under left multiplication by $PGL_2(k_{\infty})$ exactly as we did before. We will normalize our measure so that it is compatible with the measure on $\mathbb{H}$ under the projection map $\mathbb{H}_1\rightarrow \mathbb{H}$. Each point $z\in\mathbb{H}$ has $p+1$ pre-images in $\mathbb{H}_1$, and in our coordinate system we have
\[pr^{-1}\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right)=\left\{\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right)\right\}\cup\begin{setdef}{\left(\begin{smallmatrix}x+jy&y\\1&0\end{smallmatrix}\right)}{j\in \mathbb{F}_p}\end{setdef}\]
The measure normalization we will use on the upper and lower components will be different because of the compatibility with the measure on $\mathbb{H}$. More precisely, for a fixed $y$, the point $\left(\begin{smallmatrix}y&x\\ 0&1\end{smallmatrix}\right)\in\mathbb{H}_1^u$ and the point $\left(\begin{smallmatrix}x&y\\1&0\end{smallmatrix}\right)\in \mathbb{H}_1^l$ have different measures, with respect to the measure $\mu$, when considered as an equivalence class. This is because $x$ is defined $\bmod\, y\mathcal{O}_{\infty}$ on $\mathbb{H}_1^u$, which gives the equivalence class of $\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right)$ mass $1$, whereas since $x$ is defined $\bmod\, y\varpi_{\infty}\mathcal{O}_{\infty}$ on $\mathbb{H}_1^l$, the equivalence class of $\left(\begin{smallmatrix}x&y\\1&0\end{smallmatrix}\right)$ gets mass $p^{-1}$. We will normalize our measure to compensate for the power of $p$. Thus, the invariant measure which pushes forward to $dxdy$ on $\mathbb{H}$ is
\[\mathbb{H}_1^u\longmapsto\frac{1}{p+1}\frac{dx\:dy}{|y|^2}\]
\[\mathbb{H}_1^l\longmapsto\frac{p}{p+1}\frac{dx\:dy}{|y|^2}\]
and this is the measure we will be using.
Likewise, $\widetilde{\mathbb{H}}$ has two ``components", $\widetilde{\mathbb{H}}^{u}_1$ and $\widetilde{\mathbb{H}}^{l}_1$. A set of representatives for $\widetilde{\mathbb{H}}_1^{u}$ is $$\widetilde{\mathbb{H}}_1^u=\setdef{
\left(\left(\begin{smallmatrix}
v^{1/2} & u/v^{1/2} \\
0 & 1/v^{1/2} \\
\end{smallmatrix}\right),\pm1\right)}{ v\in (k_{\infty}^{\times})^2/(\mathcal{O}^{\times})^2,\; u\in k_{\infty}\slash v\mathcal{O}_{\infty}}$$
and a representative set for $\widetilde{\mathbb{H}}^{l}_1$ is $$\widetilde{\mathbb{H}}_1^l=\setdef{
\left(\left(\begin{smallmatrix}
u/v^{1/2} & v^{1/2}\\
1/v^{1/2} & 0\\
\end{smallmatrix}\right),\pm1\right)}{v\in (k_{\infty}^{\times})^2/(\mathcal{O}^{\times})^2,\; u\in k_{\infty}\slash v\varpi_{\infty}\mathcal{O}_{\infty}}$$
Reasoning as above we get the invariant measures on the upper and lower components:
\[\widetilde{\mathbb{H}}_1^u\longmapsto\frac{1}{p+1}\frac{du\:dv}{|v|^2}\]
\[\widetilde{\mathbb{H}}_1^l\longmapsto\frac{p}{p+1}\frac{du\:dv}{|v|^2}\]
\subsection{Automorphic and metaplectic functions}
\subsubsection{Automorphic Functions} We denote $PGL_2(R)$ by $\Gamma,$ and for $N\in R$, we define $\Gamma_0(N)\subset\Gamma$ to be
$$\Gamma_0(N) = \setdef{\left(\begin{smallmatrix} a& b\\ c & d\end{smallmatrix}\right)\in PGL_2(R)}{c\equiv0\mod N}$$
We define the space of automorphic functions of level $N$, depth $0$,
to be the space of complex valued function on $\Gamma_0(N)\backslash\mathbb{H}.$
$$M_0(\Gamma_0(N))=\{\phi:\Gamma_0(N)\backslash\mathbb{H}\rightarrow\mathbb{C}\}$$
Such a $\phi$ is moreover called \emph{cuspidal} if for any unipotent subgroup $U$ of $PGL_2(k_{\infty})$ such that $U\cap\Gamma_0(N)\neq 1$, the following
identity holds:
\begin{equation}\label{cuspidal}
\int_{\Gamma_0(N)\cap U\backslash U} \phi(nz) dn= 0,\textrm{ }\forall z\in \mathbb{H}
\end{equation}
We denote the space of cuspidal automorphic functions of level $N$, depth 0, by $S_0(\Gamma_0(N))$. If we take $U$ to be the upper-triangular matrix group
$U_{\infty} = \left\{\left(\begin{smallmatrix} 1& x\\ 0 & 1\end{smallmatrix}\right)\mid x\in k_{\infty}\right\}$
then (\ref{cuspidal}) says that the constant term in the Fourier expansion of $\phi\left(\begin{smallmatrix} y& x\\ 0 & 1\end{smallmatrix}\right)$ with respect to $x,$ vanishes. Cuspidality means that this is true for all the cusps of $\Gamma_0(N)\backslash\mathbb{H}$. It is well-known (cf. Corollary 1.2.3 of \cite{Ha}) that
the functions in $S_0(\Gamma_0(N))$ are supported on finitely many points and thus $S_0(\Gamma_0(N))$ is finite dimensional.
\subsubsection{Metaplectic Functions} We denote $\eta(SL_2(R))$ by $\widetilde{\Gamma},$ and for $N\in R$ we define $\widetilde{\Gamma}_0(N)\in\widetilde{\Gamma}$ to be
$$\widetilde{\Gamma}_0(N) = \setdef{\eta\left(\left(\begin{smallmatrix} a& b\\ c & d\end{smallmatrix}\right)\right)\in \widetilde{\Gamma}}{ c\equiv0\mod N}$$
We define the space of metaplectic functions of level $N$ and depth $0$, $\widetilde{M}_0(\widetilde{\Gamma}_0(N))$ as follows.
$$\widetilde{M}_0(\widetilde{\Gamma}_0(N))=\begin{setdef}{F:\widetilde{\mathbb{H}}\rightarrow\mathbb{C}}{F(\gamma w) = F(w)=-F(w\cdot(Id,-1)) ,\textrm{ }\forall \gamma\in \widetilde{\Gamma}_0(N)}\end{setdef}.$$
Such an $F$ is moreover called \emph{cuspidal} if it satisfies
\begin{equation}\label{mcuspidal}
\int_{\Gamma_0(N)\cap U\backslash U} \phi(\eta(n)w) dn= 0,\textrm{ }\forall w\in \widetilde{\mathbb{H}}
\end{equation} for every unipotent subgroup $U$ of $SL_2(k_{\infty})$. We denote the space of cuspidal metaplectic functions of level $N$, and depth $0$ by $\widetilde{S}_0(\widetilde{\Gamma}_0(N)).$ As before (cf. \cite{Ha}, in particular Lemma 1.2.2, which works equally well over the metaplectic group), the functions in $\widetilde{S}_0(\widetilde{\Gamma}_0(N))$ are supported on finitely many $\widetilde{\Gamma}_0(N)$-orbits, and so
$\dim\left(\widetilde{S}_0(\widetilde{\Gamma}_0(N))\right)<\infty.$ \\
\subsubsection{Depth $1$}
If a function $\phi$ (resp. $F$) on $PGL_2(k_{\infty})$ (resp. $\widetilde{SL}_2(k_{\infty})$) satisfies all the conditions of being automorphic, with respect to the congruence subgroup $\Gamma_0(N)$ for some $N$ (resp. metaplectic) with respect to $\widetilde{\Gamma}_0(N)$), but with the condition of right invariance under $PGL_2(\mathcal{O}_{\infty})$ (resp. $\iota(SL_2(\mathcal{O}_{\infty}))$) weakened
to right invariance under $K_0(\varpi_{\infty})$ (resp. $\iota(\widetilde{K}_0(\varpi_{\infty}))$), then $\phi$ (resp. $F$) is called an automorphic function of level $N$, depth $1$. (resp. metaplectic function of level $N$, depth $1$) Denote the space of all automorphic functions of level $N$, depth $1$, by $M_1(\Gamma_0(N)).$ Define the spaces $S_1(\Gamma_0(N)), \widetilde{M}_1(\widetilde{\Gamma}_0(N)),\textrm{ and }\widetilde{S}_1(\widetilde{\Gamma}_0(N))$ analogously.
\subsubsection{Fourier expansions}\label{Fourierexpand}
Let $\phi(z)$, on $\mathbb{H}$, and $F(w)$, on $\widetilde{\mathbb{H}}$, be an automorphic and a metaplectic function of depth $0$ respectively. Since $\phi(z)$ and $F(w)$ are left invariant under the upper triangular groups
$\left\{\left(\begin{smallmatrix} 1 & a\\ 0 & 1\end{smallmatrix}\right)| a\in R\right\},$ and$\left\{\left(\left(\begin{smallmatrix} 1 & a\\ 0 & 1\end{smallmatrix}\right),1\right)| a\in R\right\} $ we can Fourier expand $\phi(z)$ and $F(w)$ for $z=\left(\begin{smallmatrix} y & x\\ 0 & 1\end{smallmatrix}\right)$ and $w=\left(\left(\begin{smallmatrix} \sqrt{v}& u/\sqrt{v}\\ 0 & 1/\sqrt{v}\end{smallmatrix}\right),1\right)$, as follows:
$$\phi(z)=\sum_{a\in R}e(T^2a x)\phi_a(y)$$
\[F(w)=\sum_{a\in R}e(T^2au)F_a(v)\]
(Note that the introduction of the $T^2$ factor is because under our normalization of the character $e(x)$, the orthogonal complement of the ring $R$ is $T^2R$.) Since $x$ is only defined up to addition by $y\mathcal{O}_{\infty}$, and $u$ is defined modulo $v\mathcal{O}_{\infty}$, we must have $\phi_a(y) = 0$ unless $v_{\infty}(ay)>1$, and respectively $F_a(v)=0$ unless $v_{\infty}(av)>1$. Moreover, if $\phi(z)$ (or $F(w)$) is a cusp form, then
$\phi_0(y) = 0$ (and $F_0(v)=0$ respectively). By convention, we write $\phi_a(y)=0$ (respectively $F_a(v)=0$) when $a\notin R.$
\subsubsection{Depth $1$}\label{Fourierexpandinfty}
Let $z = \left(\begin{smallmatrix} y & x\\ 0 &1 \end{smallmatrix}\right)$ (or $z=\left(\begin{smallmatrix}x&y\\1&0\end{smallmatrix}\right)$ depending on whether we are on $\mathbb{H}_1^u$ or $\mathbb{H}_1^l$ respectively), and
$w=\left(\left(\begin{smallmatrix} \sqrt{v}& u/\sqrt{v}\\ 0& 1/\sqrt{v}\end{smallmatrix}\right),1\right)$ (or $w=\left(\left(\begin{smallmatrix} u/\sqrt{v} & \sqrt{v}\\ 1/\sqrt{v} & 0\end{smallmatrix}\right),1\right)$ depending on whether we are on $\widetilde{\mathbb{H}}_1^u$ or $\widetilde{\mathbb{H}}_1^l$ respectively) denote our chosen coordinates as before, and let $\phi(z)$ be an automorphic function of depth $1$ on $\mathbb{H}_1$, and $F(w)$ a metaplectic function of depth 1 on $\widetilde{\mathbb{H}}_1$. Then reasoning as above, for both $\phi$ and $F$ we have two Fourier expansions, for the upper and lower components, as follows:
For $z\in\mathbb{H}_1^u$ and $w\in\widetilde{\mathbb{H}}_1^u$ we have;
$$\phi(z)=\sum_{a\in R}e(T^2ax)\phi^u_a(y)$$
\[F(w)=\sum_{a\in R}e(T^2au)F_a^u(v)\]
For $z\in\mathbb{H}_1^l$ and $w\in\widetilde{\mathbb{H}}_1^l$ we have;
$$\phi(w)=\sum_{a\in R}e(T^2ax)\phi^l_a(y)$$
\[F(w)=\sum_{a\in R}e(T^2au)F_a^l(v)\]
We reason as before that $\phi^u_a(y)$ and $F_a^u(v)$ are $0$ unless $v_{\infty}(ay)>1$ and $v_{\infty}(av)>1$ respectively, and $\phi^l_a(y)$ and $F_a^l(v)$ are $0$ unless $v_{\infty}(ay)>0$ and $v_{\infty}(av)>0$ respectively. Moreover, if $\phi(z)$, or $F(x)$, is cuspidal then $\phi^l_0(y)=\phi^u_0(y)=0$, and $F_0^u(w)=F_0^l(w)=0$.
\subsection{Petersson inner product}
Given automorphic functions $\phi_1,\phi_2$ of level $N$ and depth $0$, we define the Petersson inner product of $\phi_1$ and $\phi_2$ to be
$$\langle \phi_1,\phi_2\rangle = [\Gamma:\Gamma_0(N)]^{-1}\int_{\Gamma_0(N)\backslash\mathbb{H}} \phi_1(z)\overline{\phi_2(z)}d\mu(z)$$ where $d\mu(z)$ is the left invariant measure as defined in \S\ref{backgr}.
As in the number field case, this is a positive definite inner product with respect to which all the Hecke operators $T_P$ (defined in the next section) for $(P,N)=1$ are self-adjoint. We define the Petersson inner product for the other spaces of functions that we have introduced analogously, and note that because of the measure normalizations on $\mathbb{H}_1$, the norm of a automorphic (or metaplectic) function is independent of its realization in $\mathbb{H}$ or in $\mathbb{H}_1$, as an old vector (similarly for the metaplectic functions).
\subsection{Whittaker Functions and Hecke Operators}
\subsubsection{Whittaker Functions on $\mathbb{H}$} In this section we define the analogue of the Laplacian on the space $\mathbb{H}$. As there is no
differential structure, we will define it as a convolution operator (the Hecke operator at $\infty$). Specifically, we shall define $\Delta$ to be right convolution with the double coset
$$PGL_2(\mathcal{O}_{\infty})\left(\begin{smallmatrix} \varpi_{\infty} & 0\\ 0 & 1\end{smallmatrix}\right) PGL_2(\mathcal{O}_{\infty})$$
and we normalize it (as in the classical Hecke operators, where weight is taken to be $0$) by dividing by $p$. Given an automorphic function $\phi(z)$ on $\mathbb{H}$ we can Fourier expand it as in \S\ref{Fourierexpand}:
$$\phi(z)=\sum_{a\in R}e(T^2ax)\phi_a(y)$$
Then the action of the Laplacian operator $\Delta$ on $\phi$ is realized by
\begin{equation}\label{Laplacianaction}
\Delta(\phi)(z)=p^{-1}\sum_{a\in R}e(T^2ax)\phi_a(yT)+p^{-1}\sum_{a\in R}\sum_{j\in\mathbb{F}_p}e(T^2a(x+jy))\phi_a\left(yT^{-1}\right)
\end{equation}
We will call automorphic functions $\phi$ that are eigenfunctions of $\Delta$, \emph{automorphic forms}. Now let $\phi$ be an automorphic form with Laplacian eigenvalue $\lambda_{\infty,\phi}$. We are interested in the relation between
the Fourier coefficients of $\phi$ and the Fourier coefficients of $\Delta(\phi)$. \\
\begin{lemma}\label{Laplacianrelation}Let $\chi_{\mathcal{O}_{\infty}}$ denote the characteristic function of $\mathcal{O}_{\infty}$. Then,
\[\lambda_{\infty,\phi}\:\phi_a(y)=p^{-1}\phi_a(yT)+\chi_{\mathcal{O}_{\infty}}(ayT^2)\phi_a(yT^{-1})\]
\end{lemma}
\begin{proof}
By (\ref{Fourierexpand}) we know that $\phi_a(yT^{-1}) = 0$ unless $v_{\infty}(ay)>0$, and in this case the character sum over $j$ in (\ref{Laplacianaction}) vanishes iff $v_{\infty}(ay)=1.$ The statement now follows directly from (\ref{Laplacianaction}).
\end{proof}
Since, for fixed $a\in R$, $\phi_a(y)$ depends only on $v_{\infty}(y),$ we can determine $\phi_a(y)$ up to a constant using Lemma \ref{Laplacianrelation}.
We denote $\phi_1(T^{-n})$ by $c(n)$. Then the $c(n)$'s satisfy the recursion
\[\lambda_{\infty,\phi}\:c(n)=\frac{1}{p}c(n-1)+\delta_{n\geq 2}c(n+1)\]
and by \S\ref{Fourierexpand}, $c(n)=\phi_1(T^{-n})=0$ when $v_{\infty}(T^{-n})\leq 1$, i.e. for $n<2$. We write $\lambda_{\infty,\phi}$ as
$$\lambda_{\infty,\phi}\:p^{1/2}=e^{i\theta} + e^{-i\theta}$$
where\footnote{It will turn out that $\theta\in\mathbb{R}$ but we do not use it here.} $e^{i\theta}\in\mathbb{C}$. We solve the 2-step recursion to get the following
\begin{lemma}\label{wh} For $n\geq2$
\[c(n)=\frac{p^{\frac{1}{2}}}{e^{i\theta}-e^{-i\theta}}\left[\left(\frac{e^{i\theta}}{p^{\frac{1}{2}}}\right)^{n-1}-\left(\frac{e^{-i\theta}}{p^{\frac{1}{2}}}\right)^{n-1}\right]c(2)\]
and $c(n)=0$ for $n<2$.
\end{lemma}
Before we go on, we shall take a moment to motivate the definitions of Whittaker functions to come. Recall that in the classical theory of automorphic forms one asks for automorphic forms to be eigenfunctions of certain differential operators (Hecke operators at $\infty$ so to speak), which in the case of $GL(2)$ reduces to the Laplacian on the hyperbolic plane. This condition (together with the invariance under the unipotent group) imposes the $\phi_a(y)$'s to satisfy a certain differential equations in the $y$-variable (Bessel's differential equation in the case of $GL(2)$) whose solutions are the Whittaker functions, and we expand our automorphic forms in terms of these. In the case of a function field the role of the Laplacian is ``replaced" (in a sense it was always the ``Hecke operator" that we were interested in) by the Hecke operator defined above (in terms of the underlying graph this is the classical discrete Laplacian, which is averaging over nearest neighbors of vertices), and this operator gives rise to difference equations instead of differential equations, whose solutions, given in Lemma \ref{wh}, are (going to be) the Whittaker functions we will use to expand our automorphic functions. Note that while in the number field case the differential equation we get has two solutions and growth conditions at the cusp separate one solution out, in the function field case we are invariant under a much bigger group (more precisely the initial condition that $c(n)=0$ for $n<2$, described in \S\ref{Fourierexpand}, reduces the space of solutions by one dimension) on the right and so the growth conditions on the solutions follow for free.
By the above paragraph, we define our Whittaker functions (of depth $0$) by
\begin{equation}\label{integralWhittaker}
W_{0,i\theta}(y) = \begin{cases} 0 & \text{ if } v_{\infty}(y) < 2\\
\frac{p^{\frac{1}{2}}}{e^{i\theta}-e^{-i\theta}}\left[\left(\frac{e^{i\theta}}{p^{\frac{1}{2}}}\right)^{n-1}-\left(\frac{e^{-i\theta}}
{p^{\frac{1}{2}}}\right)^{n-1}\right]& \text{ $ n=v_{\infty}(y)\geq2$}\end{cases}
\end{equation}
The above analysis shows that there are constants $\lambda_{\phi}(a)$ such that
$$\phi(z) = \sum_{a\in R} \lambda_\phi(a)e(aT^2x)W_{0,i\theta}(ay)$$
We call $\lambda_{\phi}(a)$ the Fourier-Whittaker coefficients of $\phi.$
\subsubsection{Depth $1$} {\label{whittakerwithdepth}}
To get a nice theory of Whittaker functions on $\mathbb{H}_1$, we first have to restrict to those automorphic functions that are first appear in depth 1.
There are two injections $\pi_1,\pi_2$ from $S_0(\Gamma_0(N))$ into $S_1(\Gamma_0(N))$ given by
$$\pi_1(\phi)(z) := \phi(z),\,\,\, \pi_2(\phi)(z) := \phi\left(z\left(\begin{smallmatrix} T & 0\\0 & 1\end{smallmatrix}\right)\right)$$ where we Define $S_1^{old}(\Gamma_0(N))$ to be the space
spanned by the image of both $\pi_1$ and $\pi_2$. We define the space of `new' cuspidal functions, $S_1^{new}(\Gamma_0(N))$, to be the orthogonal complement to
$S_1^{old}(\Gamma_0(N))$ with respect to the Petersson inner product. We mention that in the language of representation theory, these correspond to the representations
of depth 1 at the infinite place.
We also have a trace operator (which corresponds to summing over the fibers of the covering map $\mathbb{H}_1\xrightarrow{\rho} \mathbb{H}$) given by $$\tr: S_1(\Gamma_0(N))\rightarrow
S_0(\Gamma_0(N))$$
$$\tr(\phi)(z_0):=\sum_{\substack{z\in\mathbb{H}_1\\\rho(z)=z_0}}\phi(z) $$
The trace operator is the adjoint to the inclusion $\pi_1$ and therefore annihilates $S_1^{new}(\Gamma_0(N))$. The inverse image of
$\left(\begin{smallmatrix} y & x\\ 0 & 1 \end{smallmatrix}\right)\in\mathbb{H}$ under the restriction map is
$$\left\{\left(\begin{smallmatrix} y & x\\ 0 & 1 \end{smallmatrix}\right)\right\}\cup\begin{setdef}{\left(\begin{smallmatrix} x+jy & y\\ 1 & 0 \end{smallmatrix}\right)}{j\in\mathbb{F}_p}\end{setdef}$$
Then since $\phi\in S_1^{new}(\Gamma_0(N))\Rightarrow\tr(\phi)=0$, we get the following relation between the ``upper" and ``lower" Fourier coefficients of an automorphic function $\phi(z)\in S_1^{new}(\Gamma_0(N))$;
\begin{equation}\label{genuineupperlower}
\phi_a^u(y)=-p\phi_a^l(y)\chi_{\mathcal{O}_{\infty}}(aT^2y)\,\,\,\,\,\,\,\,\forall a\in R,\,y\in k_{\infty}^{\times}/\mathcal{O}_{\infty}^{\times}
\end{equation}
Taking the place of the Laplacian in this context is the Atkin-Lehner involution at infinity $W_{\infty}$, which we define to be
$$W_{\infty}(\phi)(z) := \phi\left(z\left(\begin{smallmatrix} 0 & 1\\ T^{-1} & 0\end{smallmatrix}\right)\right).$$
Note that $K_0(\varpi_{\infty})\left(z\left(\begin{smallmatrix} 0 & 1\\ T^{-1} & 0\end{smallmatrix}\right)\right)K_0(\varpi_{\infty})=\left(z\left(\begin{smallmatrix} 0 & 1\\ T^{-1} & 0\end{smallmatrix}\right)\right)K_0(\varpi_{\infty})$ so that $W_{\infty}$ can still be considered as convolution with a double coset.
Since $\left(\begin{smallmatrix} 0 & 1\\ T^{-1} & 0\end{smallmatrix}\right)^2$ is the identity, $W_{\infty}$ is indeed an involution. Moreover,
$\pi_1W_{\infty}=W_{\infty}\pi_2$ and $W_{\infty}$ is self-adjoint for the Petersson inner product, so $W_{\infty}$ preserves $S_1^{new}(\Gamma_0(N))$. We define a cuspidal form of depth 1 and level $N$ to be a new cuspidal function of level $N$ which is furthermore an eigenfunction of $W_{\infty}$.
Consider an automorphic form $\phi(z)$ of depth 1 with eigenvalue $w_{\phi,\infty}\in\{\pm1\}$ under $W_{\infty}$. By considering Fourier expansions we deduce
that $$w_{\infty,\phi}\phi_a^l(Ty)=\phi^u_a(y)$$ Combining this with (\ref{genuineupperlower}) we can solve the recursion for $\phi_a^u(y)$ and get
$$\phi_a^u(y)=\chi_{\mathcal{O}_{\infty}}(aT^2y)\phi_a^u(T^{-2})(\lambda_{\infty,\phi})^{v_{\infty}(y)-2}$$ where $\lambda_{\infty,\phi}=-\frac{w_{\infty,\phi}}{p}$.
We thus define our Whittaker functions of depth $1$ by
\begin{equation}\label{integralWhittakerinfty}
W_{1,\lambda_{\infty,\phi}}(y) = \delta_{v_{\infty}(y)>1}\cdot\lambda_{\infty,\phi}^{v_{\infty}(y)-2}
\end{equation}
By the above analysis, we see that there are constants $\lambda^u_{\phi}(a)$ such that for $z\in\mathbb{H}_1^u$,
$$\phi(z) = \displaystyle\sum_{a\in R}\lambda^u_{\phi}(a)e(T^2ax)W_{1,\lambda_{\infty,\phi}}(ay)$$
As in the previous section we will refer to the $\lambda^u_{\phi}(a)$ as the Fourier-Whittaker coefficients of $\phi.$
\subsubsection{Hecke Operators on $\mathbb{H}$} Given a monic polynomial $P\in R$ such that $P$ and $N$ are relatively prime, we associate to it a Hecke
operator $T_P$ that acts on $S_0(\Gamma_0(N))$ by the following formula
\[T_{P}(\phi)(z)=|P|^{-1}\sum_{\substack{GH=P\\J \bmod{H}}}\phi\left(\left(\begin{smallmatrix}G & J\\ 0 & H\end{smallmatrix}\right)\left(\begin{smallmatrix}y & x\\ 0 & 1\end{smallmatrix}\right)\right)\]
where $G,H$ are monic, and $z=\left(\begin{smallmatrix}y & x\\ 0 & 1\end{smallmatrix}\right)$ as usual.
As in the number field case these operators constitute a commuting family of normal operators, so they can be simultaneously diagonalised.
We will be interested in automorphic forms that are common eigenfunctions of all the Hecke operators. An automorphic form $\phi\in S_0(\Gamma_0(N))$ that is a common eigenfunction of all Hecke operators $T_P$ with $(P,N)=1$ will be called a cuspidal \emph{Hecke eigenform}.
Let $\phi$ be a Hecke eigenform and $P\in R$ a monic irreducible polynomial. Denote the
eigenvalue of $T_P$ on $\phi$ by $\lambda_{P,\phi}$. Then we have
\[\lambda_{P,\phi}\phi(z)=T_P(\phi)(z)=|P|^{-1}\sum_{\gamma} \phi(\gamma z)\]
where the summation is over $\gamma\in\left\{\left(\begin{smallmatrix}P & 0\\ 0 & 1\end{smallmatrix}\right),\left(\begin{smallmatrix}1 & H\\ 0
& P\end{smallmatrix}\right)\right\}$ with $H\in R/PR$, and $z=\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right)$. Plugging this formula in the Fourier expansion of $\phi$ gives
\begin{equation}\label{integralHeckeaction}
|P|\lambda_{P,\phi}\sum_{a\in R}e(T^2ax)\phi_a(y)=\sum_{\substack{a\in
R\\H\bmod P}}e\left(T^2a\left(\frac{x+H}{P}\right)\right)\phi_a\left(\frac{y}{P}\right)+\sum_{a\in R}e(T^2aPx)\phi_a(Py)
\end{equation}
Note that when $a\notin PR$ in the first sum on the right hand side of the equality in (\ref{integralHeckeaction}), the coefficient for $a$ vanishes, since in that case $e(\cdot T^2H/P)$ is a \emph{non-trivial} character. Taking this into account and equating the $e(T^2ax)-$Fourier coefficients in (\ref{integralHeckeaction}) we end up with
\begin{equation}\label{integralHeckerelation}
\lambda_{P,\phi}\phi_a(y)=\phi_{aP}\left(\frac{y}{P}\right)+|P|^{-1}\phi_{\frac{a}{P}}(Py)
\end{equation}
Note that specializing to $a=1$, this relation implies that $\phi_P(y)=\lambda_{P,\phi}\phi_1(yP)$. Note also that for a Hecke eigenform $\phi$ of level $N$, depth $0$, for $a\in R$ if we denote the $a$'th Fourier-Whittaker coefficient of $\phi$ by $\lambda_{\phi}(a)$ then for any $P$ relatively prime to $aN$, relation (\ref{integralHeckerelation}) implies that $\lambda_{\phi}(aP)=\lambda_{P,\phi}\lambda_{\phi}(a)$.
\subsubsection{Depth $1$}\label{integralheckedepth1}
Now suppose that $\phi(z)\in S_1(\Gamma_0(N))$ for some $N\in R$. Then we define the Hecke operators $T_P$ in the same way as before:
\[T_{P}(\phi)(g)=|P|^{-1}\sum_{\substack{GH=P\\Q\bmod H}}\phi\left(\left(\begin{smallmatrix}G & Q\\ 0 & H\end{smallmatrix}\right)g\right)\]
where $G,H$ are monic. If $\phi(z)$ is an eigenfunction of $T_p$ with eigenvalue $\lambda_{P,\phi},$ then in the notation of \S\ref{Fourierexpandinfty} this translates to:
\[\lambda_{P,\phi}\phi^u_a(y)=\phi^u_{aP}\left(\frac{y}{P}\right)+|P|^{-1}\phi^u_{\frac{a}{P}}(Py)\]
and
\[\lambda_{P,\phi}\phi^l_a(y)=\phi^l_{aP}\left(\frac{y}{P}\right)+|P|^{-1}\phi^l_{\frac{a}{P}}(Py)\]
Specializing to $a=1$ we again get $\phi_P^{\cdot}(y)=\lambda_{P,\phi}^{\cdot}\phi_1^{\cdot}(Py)$, for $\cdot=u$ or $l$. As in the previous section an automorphic form $\phi\in S_1(\Gamma_0(N))$ that is a common eigenfunction of all the Hecke operators $T_P$ with $(P,N)=1$ will be called a cuspidal Hecke eigenform of depth $1$.
\subsubsection{Whittaker functions on $\widetilde{\mathbb{H}}$}\label{halfintegralwhittakerun}
For an $F$ that is a metaplectic function of level $N$, depth $0$, we define the Laplacian $\widetilde{\Delta}$ on $\widetilde{M}_{0}(\widetilde{\Gamma}_0(N))$ to be right convolution of $F$ with the characteristic function of
the double coset $\iota\left({SL}_2(\mathcal{O}_{\infty})\right)\left(\left(\begin{smallmatrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right),1\right)\iota\left(SL_2(\mathcal{O}_{\infty})\right).$ A set of right coset representatives can be
computed to be
$$\begin{cases}
\alpha_b = \left(\left(\begin{smallmatrix}\varpi_{\infty}&\varpi_{\infty}^{-1}b\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right),1\right) & b\in \mathcal{O}_{\infty}/\varpi_{\infty}^2\mathcal{O}_{\infty}\\
\beta_h = \left(\left(\begin{smallmatrix}1&\varpi_{\infty}^{-1}h\\0&1\end{smallmatrix}\right), (h,\varpi_{\infty})_{\infty}\right) & h\in (\mathcal{O}_{\infty}/\varpi_{\infty}\mathcal{O}_{\infty})^{\times}\\
\sigma = \left(\left(\begin{smallmatrix}\varpi_{\infty}^{-1}&0\\0&\varpi_{\infty}\end{smallmatrix}\right), 1\right)
\end{cases}$$
To see the above, note that $$\alpha_b = \iota\left(\left(\begin{matrix}1&b\\0&1\end{matrix}\right)\right)\cdot\left(\left(\begin{matrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{matrix}\right),1\right),$$
$$\sigma = \iota\left(\left(\begin{smallmatrix}0&1\\-1&0\end{smallmatrix}\right)\right)\cdot\left(\left(\begin{smallmatrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right),1\right)\cdot
\iota\left(\left(\begin{smallmatrix}0&-1\\1&0\end{smallmatrix}\right)\right),$$ and
$$ \beta_h = \iota\left(\left(\begin{smallmatrix}0&h\\-h^{-1}&\varpi_{\infty}\end{smallmatrix}\right)\right)\cdot
\left(\left(\begin{smallmatrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right),1\right)
\cdot\iota\left(\left(\begin{smallmatrix}1&0\\h^{-1}\varpi_{\infty}&1\end{smallmatrix}\right)\right).$$
The sign in $\beta_h$ comes from the fact that
\begin{align*}
\epsilon\left(\left(\begin{smallmatrix}0&h\\-h^{-1}&\varpi_{\infty}\end{smallmatrix}\right),\left(\begin{smallmatrix}\varpi_{\infty}&0\\0&\varpi_{\infty}^{-1}\end{smallmatrix}\right)\right)
&=(-h^{-1}\varpi_{\infty},\varpi_{\infty}^{-1})_{\infty}(-h^{-1},-h^{-1}\varpi_{\infty})_{\infty}(-h^{-1},\varpi_{\infty}^{-1})_{\infty}\\
&=(h,\varpi_{\infty})_{\infty}
\end{align*}
Let $F\in \widetilde{M}(\widetilde{\Gamma}_0(N))$. Carrying out the convolution we compute the action on the Fourier expansion of $F$ to be
\begin{align*}
\widetilde{\Delta}(F)(w)&=(\varpi_{\infty},\sqrt{v})_{\infty}\sum_{b\in \mathcal{O}_{\infty}/T^{-2}\mathcal{O}_{\infty}}\sum_{a\in R}e(T^2a(u+vb))F_a(T^{-2}v)\\
&+\sum_{h\in (\mathcal{O}_{\infty}/T^{-1}\mathcal{O}_{\infty})^{\times}}\sum_{a\in R}(h,\varpi_{\infty})_{\infty}e(T^2a(u+hTv))F_a(v)\\
&+(\varpi_{\infty},\sqrt{v})_{\infty}\sum_{a\in R}e(T^2au)F_a(T^2v)\\
\end{align*}
A metaplectic function $F$ that is an eigenfunction of $\widetilde{\Delta}$ is called a \emph{metaplectic form}. Now suppose $F$ is a metaplectic form with eigenvalue $\lambda_{\infty,F}.$ In computing the Fourier coefficient of $e(T^2au)$ the second sum on the RHS of \eqref{halfweightLaplacianaction} gives the sum
\begin{equation}\label{fouriergauss}
\sum_{h\in (\mathcal{O}_{\infty}/T^{-1}\mathcal{O}_{\infty})^{\times}} (h,\varpi_{\infty})_{\infty}e(h\cdot T^3av)F_a(v)
\end{equation}
$F_a(v)$ vanishes unless $v_{\infty}(av)\geq 2$, and if $v_{\infty}(av)>2$ then the character $e(h\cdot T^3av)$ vanishes and hence we're left with $\sum_{h\in (\mathcal{O}_{\infty}/T^{-1}\mathcal{O}_{\infty})^{\times}} (h,\varpi_{\infty})_{\infty}=0$. If $v_{\infty}(av)=2$ then \eqref{fouriergauss} becomes a Gauss sum which determined by the square class of $av$. Since $v\in (k_{\infty}^{\times})^2$ this is the same as the square class of $a$. Hence \eqref{fouriergauss} gives $F_a(v)\cdot p^{1/2}\delta_{v_{\infty}(av)=2}\cdot(a,\varpi_{\infty})_{\infty}$.
Equating Fourier coefficients we arrive at
\begin{equation}\label{halfweightLaplacianrelation}
\lambda_{\infty,F}F_a(v) = (\varpi_{\infty},\sqrt{v})_{\infty}p^2F_{a}(T^{-2}v)\chi_{\mathcal{O}_{\infty}}(T^2av) + p^{1/2}F_a(v)\delta_{v_{\infty}(av)=2}(a,\varpi_{\infty})_{\infty} + (\varpi_{\infty},\sqrt{v})_{\infty}F_a(T^2v)
\end{equation}
Let $e^{i\gamma}$ be a complex number such that
$$e^{i\gamma} + e^{-i\gamma} = p^{-1}\lambda_{\infty,F}$$ Taking $\xi\in\{1,\epsilon,T^{-1},\epsilon T^{-1}\}$, where $\epsilon\in\mathbb{F}_p$ is a non-square, we define the metaplectic Whittaker function (of depth $0$) $\widetilde{W}_{0,i\gamma}(\xi v)$ to be:
\begin{multline*}\label{halfweightWhittaker}
\widetilde{W}_{0,i\gamma}(\xi v)=\\
\begin{cases}
\frac{p(\varpi_{\infty},\sqrt{v})_{\infty}^n}{e^{i\gamma}-e^{-i\gamma}}\left[\left(1-\frac{\delta_{v_{\infty}(\xi)=0}(\xi,\varpi_{\infty})_{\infty}e^{-i\gamma}}{\sqrt{p}}\right)\left(e^{i\gamma}p^{-1}\right)^n-
\left(1-\frac{\delta_{v_{\infty}(\xi)=0}(\xi,\varpi_{\infty})_{\infty}e^{i\gamma}}{\sqrt{p}}\right)\left(e^{-i\gamma}p^{-1}\right)^n\right] & v_{\infty}(\sqrt{v})=n\geq 1\\
0 & \textrm{else}
\end{cases}
\end{multline*}
Solving the recursion \eqref{halfweightLaplacianrelation} starting from the fact that $F_a(v)=0$ if $v_{\infty}(av)<2$, we see that there are constants $\lambda_F(a)$ such that $F_a(v) =
\widetilde{W}_{0,i\gamma}(av)(a,v^{1/2})_{\infty}\lambda_F(a).$ We call these the Fourier-Whittaker coefficients of $F.$
\subsubsection{Depth $1$}\label{halfintegralwhittakerram}
We begin by defining the analogue of the Laplacian in this context. Let $\widetilde{W}_{\infty}$ be right convolution with the characteristic function of the double coset
\[\iota(\widetilde{K}_0(\varpi_{\infty}))\left(\left(\begin{smallmatrix}0&-\varpi_{\infty}^{-1}\\\varpi_{\infty}&0\end{smallmatrix}\right),1\right)\iota(\widetilde{K}_0(\varpi_{\infty}))\]
A set of right coset representatives for the above is given by
\[\begin{setdef}{\left(\left(\begin{smallmatrix}0&-\varpi_{\infty}^{-1}\\ \varpi_{\infty}&i\end{smallmatrix}\right),1\right)}{i\in\mathbb{F}_p}\end{setdef}\]
The effect of $\widetilde{W}_{\infty}$ on the upper and lower coordinates is given by
\[\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}\\0&1/\sqrt{v}\end{smallmatrix}\right),1\right)\longrightarrow
\begin{cases}\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}-\sqrt{v}\varpi_{\infty}^{-1}i^{-1}\\0&\frac{1}{\sqrt{v}}\end{smallmatrix}\right),\left(\frac{i}{T}\right)\right)&\text{if $i\neq0$}\\ \left(\left(\begin{smallmatrix}u\varpi_{\infty}/\sqrt{v}&-\varpi_{\infty}^{-1}\sqrt{v}\\ \varpi_{\infty}/\sqrt{v}&0\end{smallmatrix}\right),(\varpi_{\infty},\sqrt{v})_{\infty}\right)&\text{if $i=0$}\end{cases}\]
\[\left(\left(\begin{smallmatrix}u/\sqrt{v}&\sqrt{v}\\ -1/\sqrt{v}&0\end{smallmatrix}\right),1\right)\longrightarrow\left(\left(\begin{smallmatrix}\varpi_{\infty}\sqrt{v}&-u\varpi_{\infty}^{-1}/\sqrt{v}+i\sqrt{v}\\0&\varpi_{\infty}^{-1}/\sqrt{v}\end{smallmatrix}\right),
(\varpi_{\infty},\sqrt{v})_{\infty}\right)\]
If $F$ is an eigenfunction of $\widetilde{W}_{\infty}$ with eigenvalue $\widetilde{w}_{\infty,F}$ we see that
\begin{equation}
\widetilde{w}_{\infty,F}F_a^l(v)=(\varpi_{\infty},\sqrt{v})_{\infty}\sum_{i\in\mathbb{F}_p}e(Taiv)F_a^u(T^{-2}v)
\end{equation}
and
\begin{equation}\label{laplacianeq}
\widetilde{w}_{\infty,F}F_a^u(v)=\sum_{i\in\mathbb{F}_p^{\times}}\left(\frac{i}{p}\right)F_a^u(v)e(T^3aiv)+(\varpi_{\infty},\sqrt{v})_{\infty}F_a^l(T^2v)
\end{equation}
Note that by section \ref{Fourierexpandinfty} we know that $F_a^u(v)=0$ for $v_{\infty}(av)<2$ and $F^l_a(v)=0$ for $v_{\infty}(av)<1$. Using these and the relations above we find that the eigenvalue $
\widetilde{w}_{\infty,F}$ satisfies
\begin{equation}\label{laplacian}
\widetilde{w}_{\infty,F}^2=p
\end{equation}
Using these representatives it is an easy check to see that $\widetilde{W}_{\infty}$ is self adjoint for the Petersson inner product. As before, there is an inclusion $$\pi_1:\widetilde{S}_0(\widetilde{\Gamma}_0(N),1)\rightarrow \widetilde{S}_1(\widetilde{\Gamma}_0(N),1)$$ given by $\pi(F)(g):=F(g)$.
We define $\widetilde{S}^{old}_1(\widetilde{\Gamma}_0(N))\subset \widetilde{S}_1(\widetilde{\Gamma}_0(N))$ to be the space spanned by the image of $\pi_1$ and $\widetilde{W}_{\infty}\circ\pi_1$. We denote the orthogonal complement of $\widetilde{S}^{old}_1(\widetilde{\Gamma}_0(N))$ by $\widetilde{S}_1^{new}(\widetilde{\Gamma}_0(N))$. Each element of $\widetilde{S}_1^{new}(\widetilde{\Gamma}_0(N))$ is called a new cuspidal metaplectic function of level $N$. Since $\widetilde{W}_{\infty}$ is self adjoint,
it preserves the space of new cuspidal metaplectic functions of level $N$.
We call a function $F(z)\in \widetilde{S}^{new}_1(\widetilde{\Gamma}_0(N))$ which is an eigenfunction
of $\widetilde{W}_{\infty}$ a new metaplectic form of level $N$ . As before, we have the trace operator $\tr$ which is adjoint to $\pi_1$, which annihilates
$\widetilde{S}^{new}_1(\widetilde{\Gamma}_0(N))$, and thus for a new cuspidal metaplectic form $F(z)$ we have $$F_a^u(v)=-p\:F_a^l(v)\chi_{\mathcal{O}_{\infty}}(aT^2v).$$
Combining this with equation (\ref{laplacianeq}) we deduce that $$-\frac{\widetilde{w}_{\infty,F}}{p^2}F_a^u(T^2v)=(\varpi_{\infty},\sqrt{v})_{\infty}\chi_{\mathcal{O}_{\infty}}(av)F_a^u(v)$$
For $\xi\in\{1,\epsilon,T^{-1},\epsilon T^{-1}\}$, where $\epsilon\in\mathbb{F}_p$ is a non-square, we define Whittaker functions of depth $1$ by
$$\widetilde{W}_{1,\lambda_{\infty,F}}(\xi v)=\chi_{\mathcal{O}_{\infty}}(T^2\xi v)\lambda_{\infty,F}^{v_{\infty}(T v^{1/2})}(\varpi_{\infty},\sqrt{v})_{\infty}^{v_{\infty}(v^{1/2})}$$ where $\lambda_{\infty,F}=-\frac{\widetilde{w}_{\infty,F}}{p^2}$.
We define the Fourier-Whittaker coefficients $\lambda_F(a)$ to be such that $F^u_a(v)=\lambda_F(a)(a,v^{1/2})_{\infty} \widetilde{W}_{1,\lambda_{\infty,F}}(av)$.
\subsubsection{Hecke operators on $\widetilde{\mathbb{H}}$}
Recall the embedding $\eta:SL_2(R)\hookrightarrow\widetilde{SL}_2(k)$ given by
$$\eta\left(\left(\begin{smallmatrix} a&b\\c&d\end{smallmatrix}\right)\right) = \left(\left(\begin{smallmatrix} a&b\\c&d\end{smallmatrix}\right),\left(\tfrac{d}{c}\right)\right).$$
Let $P$ be a monic irreducible polynomial that
is relatively prime to $ND.$ We define the $P^2-$ metaplectic Hecke operator, $\widetilde{T}_{P^2}$, to be the \emph{left convolution} of $F$ with the characteristic function of the double coset
$$\eta(\Gamma_0(N))\left(\left(\begin{smallmatrix}P^{-1}&0\\0&P\end{smallmatrix}\right);1\right)\eta(\Gamma_0(N)).$$
A set of left coset representatives for the double coset is given by:
\[\begin{cases}
\alpha_b = \left(\left(\begin{smallmatrix}P^{-1}&P^{-1}b\\0&P\end{smallmatrix}\right),1\right) & b\in R/P^2R\\
\beta_h = \left(\left(\begin{smallmatrix}1&P^{-1}h\\0&1\end{smallmatrix}\right), \left(\frac{h}{P}\right)\right) & h\in (R/PR)^{\times}\\
\sigma = \left(\left(\begin{smallmatrix}P&0\\0&P^{-1}\end{smallmatrix}\right), 1\right)
\end{cases}\]
We indicate the hardest case, $\beta_h$: Pick $d,\bar{h}\in R$ such $Pd-h\bar{h}=1$ and $N|h$. Then:
$$ \beta_h = \eta\left(\left(\begin{smallmatrix}1&0\\-P\bar{h}&1\end{smallmatrix}\right)\right)\cdot\left(\left(\begin{smallmatrix}P^{-1}&0\\0&P\end{smallmatrix}\right),1\right)
\cdot\eta\left(\left(\begin{smallmatrix}P&h\\\bar{h}&d\end{smallmatrix}\right)\right).$$
Carrying out the product using the cocycle we get that the sign of $\beta_h$ is $(h,P)_{\infty}\cdot\left(\frac{P}{h}\right)$ which is $\left(\frac{h}{P}\right)$ by lemma \ref{quadrec}.
The effect of $\widetilde{T}_{P^2}$ on the Fourier coefficients of a metaplectic form $F$ of level $N$, depth $0$ is:
\begin{align*}\label{halfweightHeckeaction}
\widetilde{T}_{P^2}(F)(w)&=(P,\sqrt{v})_{\infty}\sum_{b\in R/P^2R}\sum_{a\in R}e(T^2a(P^{-2}u+bP^{-2}))F_a(P^{-2}v)\\
&+\sum_{h\in (R/PR)^{\times}}\sum_{a\in R}\left(\frac{h}{P}\right)e(T^2a(u+hP^{-1}))F_a(v)\\
&+(P,\sqrt{v})_{\infty}\sum_{a\in R}e(T^2aP^2u))F_a(P^{2}v)\\
\end{align*}
In evaluating the above we come up against the following Gauss sum modulo $P$:
\[G_a(P)= \sum_{h\in R}\left(\frac{h}{P}\right)e\left(\frac{haT^2}{P}\right)\]
If $P|a$ then $G_a(P)=\sum_{h\in R}\left(\frac{h}{P}\right) = 0$. Else, $G_a(P)$ is a Gauss sum and depends on $a$ through the quadratic character $\left(\frac{a}{P}\right)$.
Thus we can write $G_a(P)=\delta_{P\nmid a}\left(\frac{a}{P}\right)G_1(P)$.
We will call a metaplectic form $F\in \widetilde{M}_0(\widetilde{\Gamma}_0(N))$ that is an eigenfunction of all the metaplectic Hecke operaors $\widetilde{T}_{P^2}$ for $(P,N)=1$, a \emph{metaplectic Hecke eigenform}. Now suppose $F$ is an eigenfunction of $\widetilde{T}_{P^2}$ with eigenvalue $\lambda_{P^2,F}.$ Equating Fourier coefficients, we get
\begin{equation}\label{halfweightHeckerelation}
\lambda_{P^2,F}F_a(v) = (P,\sqrt{v})_{\infty}|P|^2F_{aP^2}(P^{-2}v) + G_1(P)\delta_{P\nmid a}\left(\frac{a}{P}\right)F_a(v) + (P,\sqrt{v})_{\infty}F_{aP^{-2}}(P^2v)
\end{equation}
Observe that if $a$ is relatively prime to $P$ then $$\lambda_{P^2,F}F_a(v) = (P,\sqrt{v})_{\infty}|P|^2F_{aP^2}(P^{-2}v) + G_1(P)\left(\frac{a}{P}\right)F_a(v)$$
\subsubsection{Depth $1$} We add this section for completeness as everything works the same as \S\ref{integralheckedepth1}. Hecke operators are defined in the same way as above and their action is now calculated on the ``upper" and ``lower" Fourier coefficients separately. For $F\in\widetilde{M}_1(\widetilde{\Gamma}_0(N))$ that is an eigenfunction of $\widetilde{T}_{P^2}$ with eigenvalue $\lambda_{P^2,F}$, the formula reads
\[\lambda_{P^2,F}F^u_a(v) = (P,\sqrt{v})_{\infty}|P|^2F^u_{aP^2}(P^{-2}v) + G_1(P)\delta_{P\nmid a}\left(\frac{a}{P}\right)F^u_a(v) + F^u_{aP^{-2}}(P^2v)\]
and
\[\lambda_{P^2,F}F^l_a(v) = (P,\sqrt{v})_{\infty}P|^2F^l_{aP^2}(P^{-2}v) + G_1(P)\delta_{P\nmid a}\left(\frac{a}{P}\right) + F^l_{aP^{-2}}(P^2v)\]
As in depth $0$ case, a metaplectic form $F\in\widetilde{M}_1(\widetilde{\Gamma}_0(N),1)$ that is a common eigenfunction of all the metaplectic Hecke operators $\widetilde{T}_{P^2}$ for $(P,N)=1$ will be called a metaplectic Hecke eigenform of depth $1$.
\subsection{Non-monic Fourier Coefficients}\label{dnotsquare}
We would like to only deal with Fourier coefficients $\lambda_F(D)$ where $D$ is a \emph{monic} polynomial. Every $D\in R$ can be decomposed as
$D=u_D D_0$ where $D_0$ is monic and $u_D\in\mathbb{F}_p$. If $u_D = \alpha^2$ for some $\alpha\in\mathbb{F}_p^{\times}$, then since
$$\left(\left(\begin{smallmatrix}\alpha&0\\0&\alpha^{-1}\end{smallmatrix}\right),1\right)\left(\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right),1\right)\left(\left(\begin{smallmatrix}\alpha^{-1}&0\\0&\alpha\end{smallmatrix}\right),1\right)=
\left(\left(\begin{smallmatrix}y&u_Dx\\0&1\end{smallmatrix}\right),1\right)$$
$\lambda_{F}(D)=\lambda_{F}(D_0)$. Now, let $u_D\in\mathbb{F}_p$ be a non-square. We can extend our cocycle $\epsilon(g,h)$ to $g,h\in GL_2(k_{\infty})$ by making the following definitions (See \cite{G},pp 15-16).
\begin{enumerate}
\item $p(g):= \left(\begin{smallmatrix} 1 & 0\\ 0 & det(g)\end{smallmatrix} \right) \cdot g$
\item For $y\in k_{\infty},\, g\in GL_2(k_{\infty}), g^y:=\left(\begin{smallmatrix} 1 & 0\\ 0 & \det(g)\end{smallmatrix} \right)^{-1}g\left(\begin{smallmatrix} 1 & 0\\ 0 & \det(g)\end{smallmatrix} \right)$.
\item For $y\in k_{\infty},g=\left(\begin{smallmatrix} a & b\\ c & d\end{smallmatrix} \right)\in GL_2(k_{\infty})$ define $v(y,g):=\begin{cases} 1 & c\neq 0\\ (y,d)_{\infty} & else\end{cases}$.
\item For $g,h\in GL_2(k_{\infty})$ we extend $\epsilon$ by $$\epsilon(g,h):=\epsilon(p(g)^{Q(h)},p(h))\cdot v(Q(h),g).$$
\end{enumerate}
Moreover, the cocycle has splittings over $GL_2(\mathcal{O}_V)$ and $GL_2(R)$, extending $\iota$ and $\eta$, defined as follows: For $g=\left(\begin{smallmatrix} a & b\\ c & d\end{smallmatrix} \right)$, we set
$$\iota(g)=\begin{cases} 1 & c=0\textrm{ or } c\in\mathcal{O}_{\infty}^{\times}\\ (c,d\cdot \det(g))_{\infty} & \textrm{else} \end{cases}$$
and for $g\in GL_2(R)$, $$\eta(g)=\prod_{v|c} (c,d\cdot \det(g))_v = \left(\frac{d\cdot \det(g)}{c}\right).$$
Define $d_{u_D}:=(\left(\begin{smallmatrix} 1 & 0\\ 0& u_D\end{smallmatrix} \right)$. For an element $\tilde{g}\in\widetilde{SL}_2(k_{\infty})$ define $\tilde{g}_{u_D}:= d_{u_D}gd_{u_D}^{-1}$. Given an element $F\in\widetilde{M}_1(\widetilde{\Gamma}_0(N))$ we define $F_{u_D}$ via
$$F_{u_D}(\tilde{g}) := F(\tilde{g}_{u_D}).$$ Since $d_{u_D}\in \iota(GL_2(k_{\infty}))$ it follows that $F_{u_D}$ is $\iota(SL_2(\mathcal{O}_{\infty}))$ invariant on the right, and since $d_{u_D}\in\eta(GL_2(R))$ it follows that $F_{u_D}$ is $\eta(SL_2(R))$ invariant on the left. Thus, we have the following\\
\begin{lemma}\label{nonsquarecoef}
$F_{u_D}\in\widetilde{M}_1(\widetilde{\Gamma}_0(N))$.
\end{lemma}
Computing products as defined above, it is easy to verify that if $\tilde{g}=\left(\left(\begin{smallmatrix} \sqrt{v} & u/\sqrt{v}\\ 0& 1/\sqrt{v}\end{smallmatrix}\right),1\right)$ then
$\tilde{g}_{u_D}=\tilde{g}\cdot(1,(-1)^{v_{\infty}(v)/2}).$
Since the map $F\rightarrow F_{\epsilon}$ anti-commutes with $\Delta_{\infty}$, it is easy to see that if $F$ is a cuspidal metaplectic form then so is $F_{u_D}$, and moreover $\lambda_F(D) = (-1)^{\lfloor deg(a)/2\rfloor}\lambda_{F_{u_D}}(u_D D)$. We can therefore restrict ourselves to studying monic Fourier coefficients.
\subsection{Atkin-Lehner Operators}
\subsubsection{Atkin-Lehner Operators on $\mathbb{H}$} Let $\phi$ be a Hecke eigenform in $M_0(\Gamma_0(N))$. For $\ell^{\alpha}||N$, in analogy with the number field case we define the Atkin-Lehner involution $W_{\ell^{\alpha}}$ to be the following matrix
\[W_{\ell^{\alpha}}=\left(\begin{smallmatrix}\ell^{\alpha}&a\\N&b\ell^{\alpha}\end{smallmatrix}\right)\]
Where $a,b\in R$ and $\ell^{2\alpha}b-aN=\ell^{\alpha}$. Then $W_{\ell^{\alpha}}\Gamma_0(N)W_{\ell^{\alpha}}=\Gamma_0(N)$ and $W_{\ell^{\alpha}}^2\in\Gamma_0(N)$. An important property of these operators it that $W_{\ell^{\alpha}}$ commutes with Hecke operators $T_P$ for $(P,N)=1$. Therefore if $\phi$ is also an eigenfunction of $W_{\ell^{\alpha}}$, then denoting the eigenvalue of $\phi$ by $w_{\ell^{\alpha},\phi}$ we have
\[\phi(W_{\ell^{\alpha}}z)=w_{\ell^{\alpha},\phi}\:\phi(z)\]
with $w_{\ell^{\alpha},\phi}\:\phi(z)=\pm1$.
\subsection{L-functions of cuspidal automorphic forms}
Let $\phi\in S_0(\Gamma_0(N))$ be a Hecke eigenform with the Laplacian eigenvalue $\lambda_{\infty,\phi}=
p^{-1/2}(e^{i\theta}+e^{-i\theta}).$ We define the L-function of $\phi$ by
$$L(s,\phi) = \sum_{a\in R\backslash\{0\}} \frac{\lambda_{\phi}(a)}{|a|^s}.$$
As the $\lambda_{\phi}(a)$ are the fourier coefficients of $\phi$ , and $\phi$ is bounded above as it is supported on finitely many $\Gamma_0(N)$ orbits, we have that
$\lambda_{\phi}(a)$ is bounded above independently of $a$. Hence, $L(s,\phi)$ converges absolutely in the region $Re(s)>1$.
As in the number field case, the L-function attached to $\phi$ is, up to an explicit factor, the Mellin transform of $\phi$. The purpose of this section is
to explicitly derive this relation over function fields. Following \cite{HMW} we define the Mellin transform of $\phi$ to be
\[M\phi(s)=\int_{k_{\infty}^{\times}}\phi\left(\left(\begin{smallmatrix} y & 0\\ 0 & 1\end{smallmatrix}\right)\right)|y|^sd^{\times}y\]
where the multiplicative measure is normalized so that $\int_{\mathcal{O}_{\infty}^{\times}}d^{\times}y=1$. Note that since $\phi$ is cuspidal the integral is supported only on
finitely many points, and thus $M\phi(s)$ is a polynomial function of $p^{-s}$.
Plugging in the Fourier expansion of $\phi$ we have
\[M\phi(s)=\int_{k_{\infty}^{\times}}\sum_{a\in R}\phi_a(y)|y|^sd^{\times}y.\]
For $Re(s)>2$ the sum and integral converge absolutely. Interchanging the sum and integral and using the Hecke relations (see end of section 2.4.1) gives
\begin{align*}M\phi(s)&=\sum_{a\in R}\int_{k_{\infty}^{\times}}\lambda_{\phi}(a)W_{0,i\theta}(ay)|y|^sd^{\times}y\\
&=\sum_{a\in R}\frac{\lambda_{\phi}(a)}{|a|^{s}}\int_{k_{\infty}^{\times}}W_{0,i\theta}(y))|y|^sd^{\times}y
\end{align*}
So we are left with the integral
\[I=\int_{k_{\infty}^{\times}}W_{0,i\theta}(y)|y|^sd^{\times}y\]
Now using (\ref{integralWhittaker})
\begin{align*}
I&=\frac{\sqrt{p}}{e^{i\theta}-e^{-i\theta}}\sum_{n=2}^{\infty}\left(\frac{e^{i(n-1)\theta}}{p^{(n-1)/2}}-\frac{e^{-i(n-1)\theta}}{p^{(n-1)/2}}\right)p^{-ns}\\
&=p^{-2s}\Gamma_k(s+1/2+i\gamma)\Gamma_k(s+1/2-i\gamma)
\end{align*}
Where $\gamma$ is such that $e^{i\theta}=p^{i\gamma}$. Hence the Mellin transform is
\begin{equation}
M\phi(s)=p^{-2s}\Gamma_k(s+1/2+i\gamma)\Gamma_k(s+1/2-i\gamma)L(s,\phi).
\end{equation}
It follows in particular that $L(s,\phi)$ is a polynomial function of $p^{s}$.
\subsubsection{Depth $1$}
We now describe the Mellin transform of a $\phi\in S_1(\Gamma_0(N))$ which is a Hecke eigenform with the Laplacian eigenvalue $\lambda_{\infty,\phi}.$ We define the L-function of $\phi$ to be
$$L(s,\phi) = \sum_{a\in R\backslash\{0\}}\frac{\lambda^u_{\phi}(a)}{|a|^s}$$
Define the Mellin transform of $f(z)$ by
\[M\phi(s) = \int_{k_{\infty}^{\times}}\phi\left(\left(\begin{smallmatrix} y & 0\\ 0 & 1\end{smallmatrix}\right)\right))|y|^sd^{\times}y\]
Plugging in the Fourier expansion and proceeding as above, we arrive at
\[M\phi(s) = \sum_{a\in R}\frac{\lambda^u_{\phi}(a)}{|a|^{s}}\int_{k_{\infty}^{\times}}W_{1,\lambda_{\infty,\phi}}(y)|y|^sd^{\times}y\]
Evaluating the integral yields
\begin{equation}
M\phi(s)= \frac{p^{-2s}}{1-\lambda_{\infty,\phi}\:p^{-s}}\cdot L(s,\phi)
\end{equation}
\section{Lindel\"of Hypothesis for Families of L-functions}\label{sectiondrinfeld}
In this section we clarify the role that the generalised Riemann hypothesis and Drinfeld's work play in obtaining the relevant L-function bounds for proving the metaplectic Ramanujan conjecture. We start with a smooth, projective, geometrically irreducible curve $X$ over $\mathbb{F}_p$ of genus $g$. The zeta function attached to $X$ is defined as follows: \[\zeta(t,X)=\prod_{w\in X}\left(1-t^{\deg(w)}\right)^{-1}\]
where $w$ runs over closed points of $X$. This product converges and defines a holomorphic function on the open unit disc $|t|<\frac1p$. Furthermore by the Riemann-Roch theorem there exists a degree $2g$ polynomial $P(t,X)$ such that
\[\zeta(t,X)=\frac{P(t,X)}{(1-t)(1-pt)}\]
By the work of Weil on the Riemann hypothesis for curves we know that the zeroes of $P(t,X)$ all lie on the circle $S=\{t\mid |t|=p^{-1/2}\}$. We see by the Riemann-Roch theorem again that $\zeta(t,X)$ satisfies a functional equation relating it to $\zeta(\tfrac{1}{pt},X)$. Translated to $P(t,X)$, this functional equation reads $$P\left(\frac{1}{pt},X\right)=C(X)t^{-2g}P(t,X).$$
Where $C(X)$ is the conductor of $X$ and it related to the genus of the curve by $C(X)=p^g$.
We will be considering the size of the polynomial $P(t,X)$ on the circle $S$ when $X$ is varying in a family $\mathcal{F}$ of smooth projective curves over $\mathbb{F}_p$ with increasing genus. We start with defining a special class of families of such curves.
\begin{definition*} A family $\mathcal{F}$ of curves with increasing genus is called \emph{Lindel\"of} if for $\epsilon>0$
\[M(X):=\max\left\{ |P(t,X)|\mid t\in S\right\}\] satisfies \[M(X)=O_{\epsilon}(C(X)^{\epsilon})\]
as $X$ varies in $\mathcal{F}$.
\end{definition*}
The asymptotic behavior of $M(X)$ depends heavily on the chosen family, and especially on the distribution of the zeroes of $P(t,X)$.
In particular we have the following Theorem:\\
\begin{thm}\label{lindelofcondition} A family $\mathcal{F}$ is Lindel\"of if and only if the zeros of $P(t,X)$ become equidistributed with respect to the Haar
measure on $S$ as genus goes to infinity.
\end{thm}
\begin{proof} Let $\mathcal{F}$ be a family of curves. For each curve $X$ we have a \emph{Weil measure} on the unit circle given by
$\mu_X=\frac1{2g(X)}\displaystyle\sum_{i=1}^{2g(X)}\delta_{\alpha_i}$ where $p^{-\frac12}\alpha_i$ are the roots of $P(t,X)$. Note that the set of roots
is closed under complex conjugation, and hence $$\{\alpha_i, 1\leq i\leq 2g\} = \{\alpha_i^{-1},1\leq i\leq2g\}.$$ As in \cite{TV} we can pick a sequence $X_j\subset\mathcal{F}$ of curves with genera $g_j$ such that the sequence $\mu_j=\mu_{X_j}$ converges to a measure $\mu$ in the weak-* topology.
Next, we observe that for $t\in S$,
\[\frac{1}{2g_j}\log(P(t,X_j))=\frac{1}{2g_j}\sum_{i=1}^{2g_j}\log(1-p^{1/2}\alpha_{j,i}t)=\int_{S^1}\log(1-wz)d\mu_j(z)\] where we set $w=p^{1/2}t$ and $S^1$ is the unit circle. We thus deduce that the family $\mathcal{F}$ is Lindel\"of iff
\begin{equation}\label{integraloflog1}
\limsup_{j}\left\{\max_{w\in S^1}\int_{S^1}\log(1-wz)d\mu_j(z)\right\}\leq 0
\end{equation}
We would now like to apply the outer limit to the measures $\mu_j(z)$, but there is a slight technical annoyance coming from the fact that $\log(1-e^{i\theta})$ is singular at $\theta=1$. This can be addressed by a smoothing argument: For $\epsilon>0$ define
$$L_{\epsilon,w}(z)=\int_{\theta=0}^{\epsilon}\log(1-we^{i\theta}z)d\theta.$$
Then by equation \eqref{integraloflog1} it follows that for the family $\mathcal{F}$ to be Lindel\"of we must have
\begin{equation}
\limsup_j\int_{S^1}L_{\epsilon,w}(z)d\mu_j(z)\leq 0.
\end{equation}
As $L_{\epsilon,w}(z)$ is continuous, we may now exchange the limit and integral to arrive at
\begin{equation}\label{intermint}
\int_{S^1}L_{\epsilon,w}(z)d\mu(z)\leq 0.
\end{equation}
By \cite{TV} the measure $\mu$ can be written as $F(\theta)d\theta$ where $z=e^{i\theta}$ and $F(\theta)$ is a non-negative \emph{continuous} probability function. It follows from this that the singularity of $\log(1-z)$ at $z=1$ is integrable with respect to $\mu$. Since equation \eqref{intermint} holds for all $\epsilon>0$
we deduce that for $\mathcal{F}$ to be Lindel\"of we must have
\begin{equation}\label{integraloflog}
\int_{S^1}\log(1-wz)d\mu(z) \leq 0
\end{equation}
Since $$\limsup_j\int_{S^1}\log(1-wz)d\mu_j(z)\leq \int_{S^1}\log(1-wz)d\mu(z)$$ equation \ref{integraloflog} is actually equivalent to $\mathcal{F}$ being a
Lindel\"of family.
Since $\displaystyle\int_{|w|=p^{1/2}}\log(1-wz) |dw|=0$, equation (\ref{integraloflog}) is actually equivalent to the stronger statement
\begin{equation}\label{logiszero}
\int_{S^1}\log(1-wz)d\mu=0
\end{equation}
for all $w\in S^1.$ Now, since $F(z)$ is continuous it is also in $L^2(S^1)$ and thus has a Fourier expansion $F(z)=\sum_{m\in\mathbb{Z}}F_me^{mz}$ for $\{F_m\}\in l^2(\mathbb{Z})$.
Since $\log(1-z)$ is also in $L^2(S^1)$ we can write
\begin{align*}
\int_{S^1}\log(1-wz)d\mu_X &=\int_{S^1}\log(1-wz)F(z)d|z|\\
&=\displaystyle\sum_{m\neq 0} \frac{F_mw^m}{m}\\
\end{align*}
Since $\frac{F_m}{m}\in l^1(\mathbb{Z})$, for $\displaystyle\sum_{m\neq 0} \frac{F_mw^m}{m}$ to be identically zero we must have $F_m=0$ for $m\neq 0$, or equivalently that $d\mu$ is the usual Haar measure on $S^1$. This completes the proof.
\end{proof}
The following Lemma shows that not every family of curves is Lindel\"of, and thus being Lindel\"of is not a formal consequence of the Riemann hypothesis.
We call the \emph{universal family} the family consisting of \emph{all} curves.\\
\begin{cor} The universal family is \emph{not} Lindel\"of.
\end{cor}
\begin{proof}
This follows from the work of Tsafman and Vladut and Serre \cite{Ser} who showed that the family of modular curves $X_0(N)$ over $\mathbb{F}_p$ has Weil measures converging to
the p-adic Plancherel measure $\mu_p,$ and thus is not Lindel\"of.
\end{proof}
The distribution of zeroes for a curve $X$ is related to the number of rational points of $X$ by
$$|X(\mathbb{F}_{p^r})|=p^r+1-p^{r/2}\displaystyle\sum_{i=1}^{2g(X)}\alpha_{X,i}^r$$
As all the Weil measures are invariant under $z\rightarrow\bar{z}$ the above relation combined with Theorem \ref{lindelofcondition} implies
that for a family to be Lindel\"of, it is neccessary and sufficient that
the number of rational points grows slower than the genus, i.e. $\forall r\in\mathbb{N}, |X(\mathbb{F}_{p^r})|=o_r(g(X))$. \\
\begin{definition*} The \emph{gonality}, $G(X)$, of a curve $X$ is the minimal degree of a morphism from $X$ to $\mathbb{P}^1_{/\mathbb{F}_p}.$
\end{definition*}
Because of the inequality $|X(\mathbb{F}_{p^r})|\leq G(X)(p^r+1)$, we immediately deduce the following theorem.\\
\begin{thm} A family $\mathcal{F}$ is Lindel\"of if we have $G(X)=o(g(X))$ as $X$ varies over $\mathcal{F}$.
\end{thm}
The authors have been noted that this result has also appeared in (\cite{F}, proposition 5.1) for the case of hyperelliptic curves, and in \cite{Shp} in the general case.
We now specialize to the case of hyperelliptic curves $X_D$, which are by definition those algebraic curves with gonality 2. These are obtained by adjoining $\sqrt{D}$ to the function field $\mathbb{F}_p(T)$ for a square-free
polynomial $D$. Define the L-function $L(s,\chi_D)$ as follows:
$$L(s,\chi_D) = \sum_{a\in R}\left(\frac{D}{a}\right)p^{-\deg(a)s}.$$ Then we have the identity
$$P(p^{-s},X_D) = L(s,\chi_D).$$ As hyperelliptic curves have gonality 2, the family is Lindel\"of, but we can actually
do better for this family of curves. The following explicit bound is the analogue of a result of Littlewood \cite{L} in the number field case, and we follow very closely a simplified proof of Soundararajan, \cite{S}.\\
\begin{thm}\label{lindelofhyper}
Let $D$ be a polynomial of degree $2g$ or $2g+1$.
Then \[|L(1/2,\chi_D)|\leq e^{\frac{2g}{\log_p(g)} + 4p^{\frac12}g^{\frac12}}.\]
\end{thm}
\begin{proof}
We begin with some notation. Let $g=g_D$ be the genus of the curve $X_D,$ so that depending on the parity of $\deg(D)$, $|D|=p^{2g}$ or $p^{2g+1}$. We also define $p^{-1/2}\alpha_i, 1\leq i \leq 2g$ to be the roots of $P(t,X_D)$. By the Riemann hypothesis for curves we know that $|\alpha_i|=1$, and since
$L(s,\chi_D)$ is real on the real line, the set of $\alpha_i$ is closed under inversion. Taking the logarithmic derivative of $L(s,\chi_D)$ gives
\[\frac{L'}{L}(s,\chi_D) = \log(p)\left(-2g+\sum_{i=1}^{2g}\frac{1}{1-\alpha_i p^{\frac{1}{2}-s}}\right)\]
Define $$F(s)=\sum_{i=1}^{2g}\Re\left(\frac{1}{1-\alpha_ip^{-s}}-\frac{1}{2}\right),$$ so that
\begin{equation}\label{logd}
\frac{L'}{L}(s,\chi_D) = \log(p)\left(-g+F(s)\right).
\end{equation}
Let $s_0$ be a real number such that $s_0>\frac12$. Integrating the above from $\frac{1}{2}$ to $s_0$ and taking real parts gives
\begin{equation}\label{Lfun1}
\log|L(1/2,\chi_D)|-\log\left|L\left(s_0,\chi_D\right)\right| = g\log(p)\left(s_0-\frac12\right)-\log(p)\sum_{i=1}^{2g}\int_{\frac12}^{s_0}\Re\left(\frac{1}{1-\alpha_i p^{\frac{1}{2}-s}}-\frac12\right)ds.
\end{equation}
To control the second term on the right hand side, we have the following lemma:
\begin{lemma}\label{hardineq}
Let $\theta, 0<t<1$ be real numbers. Then \[\int_0^t\Re\left(\frac{1}{1-e^{-s-i\theta}}-\frac12\right)ds\geq 2\cdot\frac{1+e^{-t}}{1-e^{-t}}\cdot \Re\left(\frac{1}{1-e^{-t-i\theta}}-\frac12\right)\]
\end{lemma}
\begin{proof}
Computing the integral on the left hand side, we arrive at \[\frac{t}{2}+\Re\log\left(\frac{1-e^{-t-i\theta}}{1-e^{-i\theta}}\right).\]
Using that $\Re(\log(z))=\log|z|$, we see the expression above equals:
\begin{align*}
\frac{t}{2}+\frac{1}{2}\cdot\log\left|\frac{1-2\cos(\theta)e^{-t}+e^{-2t}}{2-2\cos(\theta)}\right|&=
\frac{1}{2}\cdot\log\left|\frac{e^t-2\cos(\theta)+e^{-t}}{2-2\cos(\theta)}\right|\\
&=\log\left|1+\frac{e^t+e^{-t}-2}{2-2\cos(\theta)}\right|.\\
\end{align*}
Now using the inequality $\log(1+x)\geq \frac{x}{x+1}$ for $x>0$, we have that
\begin{align*}
\log\left|1+\frac{e^t+e^{-t}-2}{2-2\cos(\theta)}\right|&\geq \frac{1-2e^{-t}+e^{-2t}}{1-2e^{-t}\cos(\theta)+e^{-2t}}\\
&=\frac{1-e^{-t}}{1+e^{-t}}\cdot\left(\frac{1-e^{-2t}}{1-2e^{-t}\cos(\theta)+e^{-2t}}\right)\\
&=2\cdot\frac{1-e^{-t}}{1+e^{-t}}\cdot\left(\Re\left(\frac{1}{1-e^{-t-i\theta}}\right)-\frac{1}{2}\right)\\
\end{align*}
\end{proof}
Using equation \eqref{Lfun1} and lemma \ref{hardineq} gives
\begin{equation}\label{firstsoundformula}
\log\left|L\left(\frac12,\chi_D\right)\right|-\log\left|L\left(s_0,\chi_D\right)\right|\leq g\log(p)\left(s_0-\frac12\right) -2\cdot\frac{1+p^{\frac12-s_0}}{1-p^{\frac12-s_0}}\cdot F(s_0)
\end{equation}
Define $h=\lceil\log_p(g)\rceil.$
Next, for $\Re(s)>0$ we compute $$\frac{1}{2\pi i}\displaystyle\int_{2}^{2+\frac{2\pi i}{\log(p)}}-\frac{L'}{L}(s+w,\chi_D)\frac{p^{hw}p^{-w}}{(1-p^{-w})^2}dw$$ in two different ways:
First by
expanding into $$\frac{L'}{L}(s,\chi_D) = \sum_{n\in\mathbb{N}}\frac{\lambda_D(n)}{p^{ns}}$$ and integrating term by term, and second by analytically continuing to the left
and picking up the residues. Note that there are double poles at $w=0$, as well as single poles at the values of $w$ for which $p^{s+w}=\alpha_ip^{\frac12}$. We end up with the relation
$$-\log(p)^{-2}\sum_{0\leq n\leq h}\frac{\lambda_D(n)\log(p^{h-n})}{p^{ns}} =
h\log^{-1}(p)\frac{L'}{L}(s,\chi_D)+\log^{-2}(p)\left(\frac{L'}{L}(s,\chi_D)\right)'+\sum_{i=1}^{2g}\frac{(\alpha_i p^{\frac12-s})^h\alpha_i^{-1}p^{s-\frac12}}{(1-\alpha_i^{-1}p^{s-\frac12})^2}$$
We integrate the above from $s_0$ to $\infty$ , take real parts and multiply by $\log(p)^2$ to get
\begin{align*}
h\log(p)\log|L(s_0,\chi_D)| &= -\frac{L'}{L}(s_0,\chi_D) +\log(p)^{-1}\sum_{0\leq n\leq h}\frac{\lambda_D(n)\log(p^{h-n})}{np^{ns_0}}\\
&+\log(p)^2\sum_{i=1}^{2g}\int_{s_0}^{\infty}\Re\left(\frac{(\alpha_i p^{\frac12-s})^h\alpha_i^{-1}p^{s-\frac12}}{(1-\alpha_i^{-1}p^{s-\frac12})^2}\right)ds
\end{align*}
\begin{lemma}\label{calcineq}
For $s>s_0>\frac12$ we have the inequality
\begin{align*}
\log(p)\left|\frac{\alpha_i^{-1}p^{s-\frac12}}{(1-\alpha_i^{-1}p^{s-\frac12})^2}\right|&\leq\left(s-\frac12\right)^{-1}\Re\left(\frac1{1-\alpha_ip^{\frac12-s}}\right)\\
&\leq\left(s_0-\frac12\right)^{-1}\Re\left(\frac1{
1-\alpha_ip^{\frac12-s_0}}\right)
\end{align*}
\end{lemma}
\begin{proof}
We first prove the first inequality: set $y=p^{s-\frac12}$ and $\alpha_i=e^{\theta_i}$. Using
$\Re(\frac1z)=\frac{z+\overline{z}}{2|z|^2}$ the inequality in the lemma rearranges to
\[\left|\frac{y}{(1-\alpha_i^{-1}y)^2}\right|\leq\frac{y}{\log(y)}\cdot\frac{y-\cos(\theta_i)}{\left|1-\alpha_i^{-1}y\right|^2}\]
which is true since
\[\log(y)\leq y-1\leq y-\cos(\theta_i)\] for $y>1$.
To see the second inequality, set $y = \Re\alpha_i$ so that $|y|<1$ and set $F(x)=x^{-1}\cdot\frac{1-ye^{-x}}{1-2ye^{-x}+e^{-2x}}$. Then setting $x=\log(p)\cdot(s-\frac12)$ the claim amounts to proving
that $F(x)$ is decreasing in the range $x>0$. Taking the derivative, we see $$F'(x) = -\frac{e^-t(e^{3t}+ e^t(1+2s^2-2t)+e^{2t}(-3s+st)+s(-1+t))}{4t^2(s-\cosh(t))^2}.$$
We need to show that $F'(x)<0$, or equivalently that $W_s(t):=e^-t(e^{3t}+ e^t(1+2s^2-2t)+e^{2t}(-3s+st)+s(-1+t))>$ is positive. Differentiating with respect to $t$ we see that
$W_s'(t)=e^{-t} (-1 + e^{2t}) (2e^t + s (-2 + t))$ which is clearly positive as $t>0$ and $s<1$. Finally, $W_s(0)=2(s-1)^2>0$. This completes the proof.
\end{proof}
The above lemma implies
\begin{align*}
\int_{s_0}^{\infty}\Re\left(\frac{(\alpha_i p^{\frac12-s})^h\alpha_i^{-1}p^{s-\frac12}}{(1-\alpha_i^{-1}p^{\frac12-s})^2}\right)ds&\leq \int_{s_0}^{\infty}\left|\frac{(\alpha_i p^{\frac12-s})^h\alpha_i^{-1}p^{s-\frac12}}{(1-\alpha_i^{-1}p^{\frac12-s})^2}\right|ds\\
&\leq\log(p)^{-1}\left(s_0-\frac12\right)^{-1}\Re\left(\frac1{1-\alpha_ip^{-s_0}}\right)\int_{s_0}^{\infty}|p^{h(1/2 -s)}|ds
\end{align*}
so that
\begin{align*}
\log|L(s_0,\chi_D)|&\leq -h^{-1}\log(p)^{-1}\frac{L'}{L}(s_0)+h^{-1}\log(p)^{-2}\sum_{0 < n\leq h}\frac{\lambda_D(n)\log(p^{h-n})}{np^{ns_0}}\\
&+ h^{-2}\log(p)^{-1}\left(s_0-\frac{1}{2}\right)^{-1}F(s_0)p^{h(1/2-s_0)}
\end{align*}
Adding this to (\ref{firstsoundformula}) and using (\ref{logd}) we get
\begin{align*}
\log|L(1/2,\chi_D)|&\leq g\left(\log(p)\left(s_0-\frac12\right)+h^{-1}\right)+\\ &+ F(s_0)\left(\frac{\left(s_0-\frac12 \right)^{-1}p^{h(1/2-s_0)}}{h^2\log(p)}-2\cdot\frac{1+p^{\frac12-s_0}}{1-p^{\frac12-s_0}}-\frac{1}{h}\right)\\
&+ h^{-1}\log(p)^{-2}\sum_{0 < n\leq h}\frac{\lambda_D(n)\log(p^{h-n})}{np^{ns_0}}
\end{align*}
Taking $s_0=\frac{1}{2}+\frac{1}{h\log(p)}$ ensures the coefficient of $F(s_0)$ is negative. Since $F(s_0)>0$, we arrive at
\begin{equation}\label{mainineqlindelof}
\log|L(1/2,\chi_D)|\leq \frac{2g}{h} +h^{-1}\log(p)^{-2}\sum_{0 < n\leq h}\frac{\lambda_D(n)\log(p^{h-n})}{np^{ns_0}}
\end{equation}
We need to estimate $|\lambda_D(n)|$. We have the product formula \[L(s,\chi_D)=(p-1)\prod_{P}\frac{1}{1-\chi_D(P)p^{-\deg(P)s}}\]
where the product is over all monic irreducible polynomials $P\in\mathbb{F}_p[T]$. Therefore
\[\frac{L'}{L}(s,\chi_D)=\sum_{P}\sum_{n\geq 1} \chi_D^n(P)p^{-n\deg(P)s}.\]
Thus $$\lambda_D(n)=\sum_{d|n}\sum_{\deg(P)=d}\chi_D^n(P)\leq n\#\{P\mid\deg(P)=n\}\leq np^n.$$
Using this and $s_0>\frac12$ we arrive at
$$\log|L(1/2,\chi_D)|\leq \frac{2g}{h} + 4p^{\frac{h}{2}}\leq\frac{2g}{\log_p(g)} + 4p^{\frac12}g^{\frac12}.$$
Exponentiating implies the result.
\end{proof}
We will also bound $L(1,\chi_D)$ as it will come up for us as a normalizing coefficient in the Siegel mass formula. We point out that in the number field case, the ineffectivity of Theorem \ref{representationTheorem} is due to the ineffectivity of the bound on $L(1,\chi_D)$ that is caused by a possible Siegel zero. Since in the function field setting Riemann hypothesis eliminates all the possible Siegel zeroes we get an effective bound. The following is the analogue of a result of Littlewood over $\mathbb{Q}$.\\
\begin{lemma}\label{classnumber}
Let $D$ be a square-free polynomial of degree $2g$ or $2g+1$. Then
$$(\log_p(g))^{-3}\ll_p|L(1,\chi_D)|\ll_p (\log_p(g))^3$$
\end{lemma}
\begin{proof}
We start with the identity $$\log(L(1,\chi_D))=-\sum_{r\in\mathbb{N}}\frac{1}{rp^{\frac{r}2}}\sum_{i=1}^{2g}\alpha_i^r$$ where
$p^{-\frac{1}{2}}\alpha_i$ are the roots of $L(s,\chi_D)$ as above.
Since $|\alpha_i|=1$ we have the bound $\left|\sum_{i=1}^{2g}\alpha_i^r\right|\leq 2g$. Also, since the hyperelliptic family under consideration has gonality 2,
we know that \[2(p^r+1)=2\mathbb{P}^1(\mathbb{F}_{p^r})\geq |X_D(\mathbb{F}_{p^r})| = p^r + 1 -p^{\frac{r}{2}}\sum_{i=1}^{2g}\alpha_i^r\] so we have the bound $\left|\sum_{i=1}^{2g}\alpha_i^r\right|\leq 3(p^{\frac{r}{2}}+p^{-\frac{r}{2}}).$ We can thus write
$$|\log(L(1,\chi_D))|\leq O(1)+\displaystyle\sum_{1\leq r\leq 2\log_p(g)}\frac3r + 2g\sum_{2\log_p(g)<r}p^{-r/2}\leq O_p(1) + 3\log\log_p(g)$$
The Lemma then follows by exponentiating the above.
\end{proof}
We will also need to study the degree $2$ L-functions
$$L(s,\phi\times\chi_D)=\displaystyle\sum_{\substack{a\in\mathbb{F}_p[T]\\(a,D)=1}}\lambda_{\phi}(a)\chi_D(a)|a|^{-s}$$
where $\phi$ is an automorphic Hecke eigenform of level $N.$ By Drinfeld's work \cite{Dr} on the Langlands conjectures for $GL(2)$ and Deligne's proof of the Weil conjectures \cite{Del}, this is a polynomial of degree
at most $DN$ in $p^{-s}$ which only has roots on the line $\frac{1}{2}$. It also follows that $|\lambda_{\phi}(P)|\leq 2|P|^{\frac{1}{2}}$ for every monic irreducible
polynomial $P$. Define $\beta_{\phi,D}$ by expanding the logarithmic derivative $$-\frac{L'}{L}(s,\phi\times\chi_D)=\sum_{n\in\mathbb{N}} \frac{\beta_{\phi,D}(n)}{p^{ns}}.$$
Using the product formula we have the bound $|\beta_{\phi,D}(n)|\leq 2np^n\log(p)$. Then repeating the proof of Theorem \ref{lindelofhyper} we arrive at the following analogue:\\
\begin{thm}\label{lindelofhyper2}
Let $D$ be a polynomial of degree $2g$ or $2g+1$. Then
\[|L(1/2,\phi\times\chi_D)| \ll e^{\frac{2g}{\log_p(g)} + 8p^{\frac12}g^{\frac12}}\]
\end{thm}
We conclude this section by mentioning that the above is not limited to the specific family of $GL_2$ forms that we are considering. In particular, let $\mathcal{F}_{aut}$ denote the family of unitary cuspidal automorphic representations of $GL(n)$ for a \emph{fixed} $n$. Now consider the family of \emph{standard} L-functions, $\mathcal{F}:=\begin{setdef}{L(s,\pi)}{\pi\in \mathcal{F}_{aut}}\end{setdef}$ attached to each member of $\mathcal{F}_{aut}$. We sketch an analytic argument proving that the family $\mathcal{F}$ is Lindel\"of.
Let $L(s,\pi)\in\mathcal{F}$ be given by
\[L(s,\pi)=\sum_a\frac{\lambda_{\pi}(a)}{|a|^s}\]
The L-function $L(s,\pi)$ also factors as $L(s,\pi)=\prod_{v}L_v(s,\pi)$ where each local factor is given by
$$L_v(s,\pi) = \prod_{i=1}^n \left(1-\frac{\beta_{\pi,i}(v)}{|v|^s}\right)^{-1}$$ where some of the $\beta_{\pi,i}(v)$ could vanish if $\pi$ is ramified at $v$.
Since we are fixing the dimension of the underlying group, $n$, and considering only the standard $L$-functions, by the unitarity of $\pi$'s there is a $t>0$ such that the $L$-functions $L(s,\pi)$ all converge for $\Re(s)>t$. Then we see that each eigenvalue uniformly satisfies the upper bound $|\beta_{\pi,i}(v)|\leq |v|^t$. Hence the coefficients $\lambda_{\pi}(a)$ satisfy
\begin{equation}\label{rankbound}
|\lambda_{\pi}(a)|\leq n|a|^t
\end{equation}
We now follow the argument in the proof of Theorem \ref{lindelofhyper}. By the work of Lafforgue and
Deligne \cite{La}, the zeroes of $L(s,\pi)$ are all on the critical line $\Re(s)=\frac12$. The non-zero moments of the zeroes are
controlled by the coefficients $\lambda_{\pi}(a)$ and are thus bounded by (\ref{rankbound}). The zeroes are therefore equidistributed, and the Lindel\"of bound follows as before.
\section{Shimura Correspondence and Niwa's Lemma}\label{sectionshimura}
The goal of this and the following section is to prove a ``Waldspurger type formula" relating the Fourier-Whittaker coefficients of a metaplectic form to the central values of the
twisted L-function of its Shimura lift. Our method of proof will follow Katok-Sarnak \cite{KS}.
\subsection{Siegel Theta Functions for function fields}
In this section we will define the theta functions that will be used to define the theta lifts. We start with some notation. Let $V$ be the three dimensional vector space $(h_1,h_2,h_3)$ over $k_{\infty}$, $Q$ the quadratic form
$Q(\vec{h}) = h_2^2 - 4h_1h_3$, and $B(\cdot,\cdot)$ its associated billinear form. Define $\mathcal{O}_V$ to be the $\mathcal{O}_{\infty}$ lattice
$\{h_1,h_2,h_3\}\in \mathcal{O}_{\infty}^3$, and $L$ to be the $R$ lattice $\{h_1,h_2,h_3\}\in (TR)^3$. Recall that we write $w$ symbolically for the element $\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}\\0&1/\sqrt{v}\end{smallmatrix}\right),1\right)$. We also note that throughout this section, we will use the symmetric space coordinates $z$ on $\mathbb{H}$ (or on $\mathbb{H}_1$) and the group variable $g\in PGL_2(k_{\infty})$ interchangeably. Finally, as in the number field case, we let $PGL_2(k_{\infty})$ act on $V$ via the isomorphism with the orthogonal group. Namely,
$$g\left(\left(\begin{smallmatrix} 2h_3 & h_2\\ h_2 & 2h_1\end{smallmatrix}\right)\right) =
\det(g)^{-1}\cdot g\left(\begin{smallmatrix} 2h_3 & h_2\\ h_2 & 2h_1\end{smallmatrix}\right)g^t.$$
For convenience, we defie the function $\tau:k_{\infty}^{\times}\rightarrow\pm \{1\}$ by $\tau(x)=(\varpi_{\infty},x)_{\infty}^{v_{\infty}(x)}.$
We define the Siegel theta function of level $0$, depth $0$, to be
$$ \Theta(w;g) = \tau(\sqrt{v})|v|^{3/4}\displaystyle\sum_{\vec{h}\in L} e(Q(\vec{h})u)\chi_{\mathcal{O}_V}(\sqrt{v}g^{-1}(\vec{h}))$$
where $w\in \widetilde{\mathbb{H}}$ and $g\in PGL_2(k_{\infty})$. As $\mathcal{O}_V$ is invariant under the action of $PGL_2(\mathcal{O}_{\infty})$, $\Theta(w;g)$ descends to a function on $\widetilde{\mathbb{H}}\times \mathbb{H}$. Also, in the $g$-variable $\Theta$ is evidently left invariant under the action of the full modular group $PGL_2(R)$. In the $w$-variable it is
an element of $\widetilde{M}_0(\widetilde{\Gamma})$ by Lemma \ref{invariance}.
We will need more general classes of theta functions to get our lifts. To define them, first let $D$ be a square-free polynomial of even degree, such that $D\in \left(k_{\infty}^{\times}\right)^2$. For a quadratic form $Q$ over $R$ such that $D\mid\text{disc}(Q)$, define $W_D(Q)$, as in
Kohnen \cite{Ko} as follows:\\
\begin{definition*}\label{kohnen}
If for all $v\in \mathcal{O}_V$, $Q(v)$ is not relatively prime to $D$ then $W_D(Q) = 0.$ Else, pick a vector $v_0$ such that $(Q(v_0),D)=1,$ and define
$W_D(Q) = \left(\frac{Q(v_0)}{D}\right).$ Note that this definition is independent of $v_0.$
\end{definition*}
Identifying $\vec{h}$ with the quadratic form $h_1X^2+h_2XY+h_3Y^2$, we can speak meaningfully of $W_D(\vec{h})$.
We then define
$$\Theta_D(w;g) = \tau(\sqrt{v})|v|^{3/4}\displaystyle\sum_{\substack{\vec{h}\in L\\ D\mid Q(h)}}W_D(\vec{h})e(Q(\vec{h})u/D)\chi_{\mathcal{O}_V}(\sqrt{v}g^{-1}(h)/\sqrt{D})$$
As before, it is clear $\Theta_D$ descends to a function on $\widetilde{\mathbb{H}}\times \mathbb{H}$ and is invariant under the action of the full modular group in the $g$-variable. The fact
that $\Theta_D(w;g)$ is an element of $\widetilde{M}_0(\widetilde{\Gamma})$ in the $w$-variable follows from Lemma \ref{invariance}.
As we will be working over a general congruence subgroup $\Gamma_0(N),$ we will need the analogue of $\Theta_D(w;g)$ for arbitrary level $N$ that is relatively prime to $D$. Let $N\in R$ such that $\gcd(N,R)=1$, and define the Siegel theta function of level $N$, depth $0$, to be:
\[\Theta^N_D(w;g) = \tau(\sqrt{v})|v|^{3/4}\displaystyle\sum_{\substack{\vec{h}\in L,\, h_1\in TNR\\ D\mid\det(\vec{h})}}W_D(\vec{h})e((h_2^2 - 4h_1h_3)u/D)\chi_{\mathcal{O}_V}(\sqrt{v}g^{-1}(h)/\sqrt{D})\]
As before $\Theta_D^N$ defines a function on $\widetilde{\mathbb{H}}\times \mathbb{H}$. Note that $\Theta_D^N$ is invariant under the congruence subgroup $\Gamma_0(N)$ in the $g$-variable. The same argument in Lemma \ref{invariance} and an appropriate choice of functions at various completions yield $\Theta^N_D(w;g)\in \widetilde{M}_{0}(\widetilde{\Gamma}_0(N))$ in the $w$-variable. More specifically, in the notation of \S\ref{classicaltheta}, one chooses $\phi_w$ for all $w$ such that $v_w(N)>0$ to be
$$\phi_w(h_1,h_2,h_3) =\chi_{L_w}(N^{-1}h_1,h_2,h_3)$$ where $L_w:=L\otimes_{R}\mathcal{O}_w$ and $\chi_{L_w}$ denotes the characteristic function of $L_w$.
\subsubsection{Depth $1$}
We shall also need a Siegel theta function to transfer depth $1$ forms. Taking our cue from the adelic description, define $\mathcal{O}_{V,1}$ to be the lattice $\mathcal{O}_{V,1}:=\begin{setdef}{\vec{h}=(h_1,h_2,h_3)}{(Th_1,h_2,h_3)\in\mathcal{O}_{\infty}^3}\end{setdef}.$ We then pick $\phi_{\infty}(v) = \chi_{\mathcal{O}_{V,1}}(v).$ This yields
\[\Theta^{N}_{D,1}(w;g) = \tau(\sqrt{v})|v|^{3/4}\displaystyle\sum_{\substack{\vec{h}\in L,\, D\mid\det(\vec{h})\\ h_1\in NTR}}W_D(\vec{h})
e((h_2^2 - 4h_1h_3)u/D)\chi_{O_{V,1}}(\sqrt{v}g^{-1}(h)/\sqrt{D})\]
Then $\Theta_{D,1}^N$ descends to a function on $\widetilde{\mathbb{H}}_1\times \mathbb{H}_1$, that it is invariant under $\Gamma_0(N)$ in the $g$-variable, and once again using the same arguments in Lemma \ref{invariance} we see that it is an element of
$\widetilde{M}_{1}(\widetilde{\Gamma}_0(N))$ in the $w$-variable. Note that the above Fourier expansion in the $w$-variable is valid only on $\widetilde{\mathbb{H}}^u_{1}\times\mathbb{H}_1.$
\subsection{Maass-Shintani lift}
Let $D,N\in R$, $\gcd(D,N)=1$ be as above. We will use $\Theta^N_D(w;g)$ as a kernel against which we integrate cuspidal automorphic forms and cuspidal metaplectic forms to go from one space to the other. As in \cite{KS}, for a given cuspidal automorphic form $\phi(g)\in S(\Gamma_0(N))$, we define its $D$'th Maass-Shintani lift $F^{[D]}(w)$ to be the metaplectic function given by $$F^{[D]}(w) = \int_{\Gamma_0(N)\backslash \mathbb{H}} \phi(g)\,\Theta^N_D(w;g)dg.$$
Similarly, if $\phi(g)\in S_1(\Gamma_0(N)$ we define its $D$'th Maass-Shintani lift $F^{[D]}(w)$ to be the metaplectic function given by $$F^{[D]}(w) = \int_{\Gamma_0(N)\backslash \mathbb{H}} \phi(g)\,\Theta^N_{D,1}(w;g)dg.$$
Our main result for this section is:\\
\begin{thm}\label{shintanilift}
Let $\phi(g)$ be a cuspidal automorphic form of level $N$, depth $0$ or $1$, and for $D\in R$, $\gcd(D,N)=1$, $F^{[D]}(w)$ be its D'th Maass-Shintani lift. Then $F^{[D]}$ is a cuspidal metaplectic
form, and we have the following identity:
$$\lambda_{F^{[D]}}(D)=\begin{cases}C_{\phi}G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right)&\text{if $\phi$ is of depth $0$}\\ C_{\phi}G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right)(1+w_{\infty,\phi})&\text{if $\phi$ is of depth $1$}\end{cases}$$
Where $N=\prod_{i=1}^m l_i^{\alpha_i}$ is the prime factorization of $N$, $w_{l_i^{\alpha_i},\phi}$ are the eigenvalues of $\phi$ under the Atkin-Lehner
involutions, and $$C_{\phi} = \begin{cases}
\frac{p^{-3/2}}{\left(1-\frac{e^{-i\theta}}{\sqrt{p}}\right)\left(1-\frac{e^{i\theta}}{\sqrt{p}}\right)}& \textrm{ depth 0}\\
\frac{-pw_{\infty,\phi}}{p+w_{\infty,\phi}} & \textrm{depth 1 case}\end{cases}$$ where $\lambda_{\infty,\phi}=p^{-1/2}(e^{i\theta}+e^{-i\theta})$ is the Laplacian eigenvalue of $\phi$ in the depth $0$ case, and $w_{\infty,\phi}$ is the eigenvalue of $\phi$ under the Atkin-Lehner involution $W_{\infty}$ in the depth 1 case.
\end{thm}
\begin{proof} The cuspidality follows Corollary 15.6 of \cite{G-P-S}. For the statement of the lemma we only need the $D$'th Fourier coefficient of $F^{[D]}$. For simplicity,
we first do the case of $N=1.$ Since $F^{[D]}$ is left-invariant under $\widetilde{\Gamma}_{\infty}=\begin{setdef}{\left(\begin{smallmatrix}1&a\\0&1\end{smallmatrix}\right)}{a\in R}\end{setdef}$, we can recover its Fourier coefficients as follows:
\begin{align*} \label{quadraticformssum}
F^{[D]}_{D}(v) &=\mu(T^{-1}\mathcal{O}_{\infty})^{-1}\int_{T^{-1}\mathcal{O}_{\infty}}F^{[D]}(w)e(-DT^2u)du \\
&=\tau(v)|v|^{3/4}\int_{\Gamma\backslash \mathbb{H}} \phi(g)\sum_{\vec{h}\in T^{-1}L, Q(\vec{h})=D^2}W_D(\vec{h})\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h})/\sqrt{D})dg \\
&=\tau(v)|v|^{3/4}\sum_j W_D(\vec{h_j})\int_{\mathbb{H}} \phi(g)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h_j})/\sqrt{D})dg
\end{align*}
Where the last step is obtained by unfolding the integral, and $\vec{h_j}$ is a set of representatives for the action of $PGL_2(R)$ on vectors
with norm $D^2$. A complete such set of representatives is $\left\{\vec{h_j} = (0,D,j)\mid j\in R/DR\right\}$.
Note $W_D(h_j) = \left(\frac{j}{D}\right)$. We define $g_j$ to be the element $\left(\begin{smallmatrix}
1 & \frac{j}{D} \\
0 & 1 \\
\end{smallmatrix}
\right)$, so that $g_j^{-1}(\vec{h_j})=\vec{h_0}$. Denoting the summand in the above sum corresponding to $h_j$ by $I_j$ and making a change of
coordinates we have
$$I_j = \tau(v)|v|^{3/4}\left(\frac{j}{D}\right)\int_{\mathbb{H}}\phi(g_jg)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h_0})/\sqrt{D})dg$$
For $g=\left(\begin{smallmatrix} y & x\\ 0 & 1\end{smallmatrix}\right)$, we have $g^{-1}(\vec{h_0}) = (0,D,-Dx/y)$, so
we
can rewrite the integral as follows
\begin{align*}
I_j &= \tau(v)|v|^{3/4}\left(\frac{j}{D}\right)\int_{\mathbb{H}}\phi(g_jg)\chi_{\mathcal{O}_{\infty}}(Tx\sqrt{vD}/y)\chi_{\mathcal{O}_{\infty}}(T\sqrt{vD})dx\frac{d^{\times}y}{y} \\
&=\tau(v)|v|^{3/4}\chi_{\mathcal{O}_{\infty}}(T\sqrt{vD})\left(\frac{j}{D}\right)\int_{\mathbb{H}}\sum_{a\in R}e(T^2aj/D)\lambda_{\phi}(a)W_{0,i\theta}(ay)e(aT^2x)\chi_{\mathcal{O}_{\infty}}(Tx\sqrt{vD}/y))dx\frac{d^{\times}y}{y} \\
&=p^{-1}\tau(v)|D|^{-1/2}\chi_{\mathcal{O}_{\infty}}(T^2vD)\left(\frac{j}{D}\right)|v|^{1/4}
\int_{k_{\infty}^{\times}}\sum_{a\in R}e(T^2aj/D)\lambda_{\phi}(a)W_{0,i\theta}(ay)\chi_{\mathcal{O}_{\infty}}(Tay/\sqrt{vD})d^\times y\\
&=p^{-1}\tau(v)|D|^{-1/2}\chi_{\mathcal{O}_{\infty}}(T^2vD)\left(\frac{j}{D}\right)|v|^{1/4}
\int_{k_{\infty}^{\times}}\sum_{a\in R}e(T^2aj/D)\lambda_{\phi}(a)W_{0,i\theta}(y)\chi_{\mathcal{O}_{\infty}}(Ty/\sqrt{vD})d^\times y\\
\end{align*}
where the third equality follows by evaluating the integral over $x$, and the fourth equality is the change of variables $y\rightarrow\frac{y}{a}.$
We now want to interchange the sum and integral signs, but unfortunately the sum is not absolutely convergent in the 4th equation. To get around this problem, we introduce the complex variable $s$ and define
$$I_j(s) :=\tau(v)p^{-1}|D|^{-1/2}\chi_{\mathcal{O}_{\infty}}(T^2vD)\left(\frac{j}{D}\right)|v|^{1/4}
\int_{k_{\infty}^{\times}}\sum_{a\in R}e(T^2aj/D)\frac{\lambda_{\phi}(a)}{|a|^s}W_{0,i\theta}(ay)\chi_{\mathcal{O}_{\infty}}(Tay/\sqrt{vD}) d^\times y$$
Note that $I_j(0)=I_j$, and $I_j(s)$ is analytic in $s.$ Now, for $Re(s)>>0,$ the sum is absolutely convergent, so we can write:
$$I_j(s)=\tau(v)p^{-1}|D|^{-1/2}\chi_{\mathcal{O}_{\infty}}(T^2vD)\left(\frac{j}{D}\right)|v|^{1/4}
\sum_{a\in R}e(T^2aj/D)\frac{\lambda_{\phi}(a)}{|a|^s}\int_{k_{\infty}^{\times}}W_{0,i\theta}(y)\chi_{\mathcal{O}_{\infty}}(Ty/\sqrt{vD}) d^\times y$$
Since $\chi_{\mathcal{O}_{\infty}}(T^2vD)$ vanishes for $v_{\infty}(vD)<2$, we restrict to $v$ such that $v_{\infty}(vD)\geq2$. It follows that $v_{\infty}(Ty/\sqrt{vD})\leq v_{\infty}(y)-2$, so that $\chi_{\mathcal{O}_{\infty}}(Ty/\sqrt{vD})\neq0$ only if $v_{\infty}(y)\geq2$. Since by equation (\ref{integralWhittaker}) $W_{0,i\theta}(y)\neq0$ only if $v_{\infty}(y)\geq2$, we get
\[\int_{k_{\infty}^{\times}}W_{0,i\theta}(y)\chi_{\mathcal{O}_{\infty}}(Ty/\sqrt{vD})d^{\times}y=\sum_{n=v_{\infty}(\sqrt{vD})+1}^{\infty}W_{0,i\theta}(T^{-n})\]
Evaluating the sum yields
\[\frac{p^{\frac{2-M}{2}}}{e^{i\theta}-e^{-i\theta}}\left(\frac{e^{iM\theta}}{\sqrt{p}-e^{i\theta}}-\frac{e^{-iM\theta}}{\sqrt{p}-e^{-i\theta}}\right)\]
where $M=v_{\infty}(\sqrt{vD})$. This multiplied by $\chi_{\mathcal{O}_{\infty}}(T^2vD)|v|^{1/4}$ is easily seen to be $|D|^{-1/4}C_{\phi}\widetilde{W}_{0,i\theta}(Dv)$. Adding up the $I_j$
and using the fact that
$$\sum_{j\mod{D}} \left(\frac{j}{D}\right)e(T^2aj/D)=G_1(D)\left(\frac{a}{D}\right),$$ we arrive at
$$\sum_j I_j(s) = G_1(D)|D|^{-3/4}L(1/2+s,\phi\times\chi_D)\widetilde{W}_{0,i\theta}(Dv)C_{\phi}.$$
Continuing analytically to $s=0,$ we get
$$\lambda_{F^{[D]}}(D)\widetilde{W}_{0,i\theta}(Dv)=F^{[D]}_D(v)=G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)\widetilde{W}_{0,i\theta}(Dv)C_{\phi}$$
and so $$\lambda_{F^{[D]}}(D)=C_{\phi}G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)$$ as desired.
We now say a few words about the case of general level $N.$ Repeating the above calculation, we arrive at
$$F^{[D]}(v)=\tau(v)|v|^{3/4}\sum_{j,\; t} W_D(\vec{h^t_j})\int_{\mathbb{H}} \phi(g)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h^t_j})/\sqrt{D})dg$$
Where now $\vec{h^t_i}$ is a set of representatives for the action of $\Gamma_0(N)$ on vectors $h_1,h_2,h_3$ with determinant $D^2$ such that $N|h_1.$ The set of
such forms is given by
$$\newline\left\{\vec{h^t_j} = W_t\vec{h_j}\mid \vec{h_j} = (0,D,j), j \in R/DR\right\}$$ and $W_t$ varies over the Atkin-Lehner
involutions of $\Gamma_0(N).$ A
proof of this can be found in \cite{B} pg.29 (Biro proves the statment for $\mathbb{Z}$ and the proof carries through verbatim to our setting.). It is easily seen that
$W_D(\vec{h^t_j}) = \left(\frac{t}{D}\right)W_D(\vec{h_j}),$ and so
\begin{align*}
F^{[D]}(v)&=\tau(v)|v|^{3/4}\sum_{j,\; t} W_D(\vec{h^t_j})\int_{\mathbb{H}} \phi(g)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h^t_j})/\sqrt{D})dg\\
&=\tau(v)|v|^{3/4}\sum_j W_D(h_j)\sum_t \left(\frac{t}{D}\right)\int_\mathbb{H}\phi(W_tg)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h_j})/\sqrt{D})dg\\
&=\tau(v)|v|^{3/4}\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right) \sum_j W_D(h_j)\int_\mathbb{H}\phi(g)\chi_{\mathcal{O}_V}(T\sqrt{v}g^{-1}(\vec{h_j})/\sqrt{D})dg\\
\end{align*}
the calculation then proceeds as before and the main result follows. \end{proof}
\subsubsection{Depth $1$}
For $\phi(g)\in S_1 (\Gamma_0(N))$ a cuspidal automorphic form of level $N$, depth $1$, we proceed as above to get
\begin{align*}
F^{[D],u}_D(v) &=\mu(T^{-1}\mathcal{O}_{\infty})^{-1}\int_{T^{-1}\mathcal{O}_{\infty}}F^{[D],u}(w)e(-DT^2u)du\\
&=\int_{\Gamma_0(N)\backslash \mathbb{H}_1} \phi(g)\sum_{\vec{h}\in R^3, \det(\vec{h})=D^2}W_D(\vec{h})\chi_{O_{V,1}}(T\sqrt{v}g^{-1}(\vec{h})/\sqrt{D})dg\\
&=\sum_{j,\; t} W_D(\vec{h^t_j})\int_{\mathbb{H}_1} \phi(g)\chi_{O_{V,1}}(T\sqrt{v}g^{-1}(\vec{h_j})/\sqrt{D})dg\\
\end{align*}
where the $h^t_j$ are as before. Now, since the Atkin Lehner involution $W_{\infty}$ preserves $O_{V,1},$ we can restrict to the integral over the upper component $\mathbb{H}^u_1:$
\begin{equation}
F^{[D],u}_D(v)=(1+w_{\infty,\phi})\sum_{j,\; t} W_D(\vec{h^t_j})\int_{\mathbb{H}_1^u} \phi(g)\chi_{O_{V,\infty}}(T\sqrt{v}g^{-1}(\vec{h_j})/\sqrt{D})dg\\
\end{equation}
We can now proceed as before except that the Whittaker function is different. The result follows as before from the following identity, which amounts to evaluating a geometric series as before:
\begin{align*}
&(\varpi_{\infty},v)^{deg(v)/2}|Dv|^{1/4}\chi_{\mathcal{O}_{\infty}}(T^2vD)\int_{k_{\infty}^{\times}}W_{1,\lambda_{\infty,\phi}}(y)\chi_{\mathcal{O}_{\infty}}(Ty/\sqrt{vD})d^{\times}y=\\
&\frac{-p^2w_{\infty,\phi}}{w_{\infty,\phi}+p} \widetilde{W}_{1,\lambda_{\infty,F}}(vD)
\end{align*}
where $\lambda_{\infty,F} = -w_{\infty,\phi}p^{3/2}$.
\subsection{Niwa's Lemma}
In \cite{Shim} it is shown how to construct a holomorphic modular form of integral weight starting from a holomorphic modular form of half integral weight. The
method that Shimura uses to show that the resulting function is a modular form is the converse Theorem of Weil. Later after Shintani's \cite{Sh} proof
of the ``reverse'' correspondence (which was studied earlier by Maass \cite{M} in certain specific cases), Niwa \cite{Niwa} gave a more direct proof of Shimura's result by using theta functions. In \cite{KS} the result is generalized to the non-holomorphic case following the methods of Niwa. In this section, we generalize this approach to the function field setting.
For $F$ a cuspidal metaplectic form (of depth $0$ or $1$), let the Fourier-Whittaker expansion of $F$ be given by
\[F(w)=\begin{cases}\sum_{l\in R}\lambda_F(l)\widetilde{W}_{0,\lambda_{\infty,F}}(v)e(T^2lu)&\text{if $F$ is of depth $0$}\\ \sum_{l\in R}\lambda^u_F(l)\widetilde{W}_{1,\lambda_{\infty,F}}(v)e(T^2lu)&\text{if $F$ is of depth $1$} \end{cases}\]
Now suppose $F$ is of level $N$ and let $D\in R$ be a square-free polynomial that is relatively prime to $N$. We define the L-function $L(s,F,D)$ by
\[L(s,F,D)=\begin{cases}\sum_{l\in R}\frac{\lambda_F(Dl^2)}{|l|^s}&\text{if $F$ is of depth $0$}\\ \sum_{l\in R}\frac{\lambda^u_F(Dl^2)}{|l|^s}&\text{if $F$ is of depth $1$}\end{cases}\]
For such a $D$, we define the $D$'th Shimura lift of $F$ as follows:\\
\begin{definition*}[$D'th$ Shimura lift] Let $F(w)$ be a cuspidal metaplectic form of level $N$ (and of depth $0$ or $1$) and $D\in R$ a square-free polynomial. Define the $D'th$ Shimura lift $\phi(g)$ of $F$ by:\\
\[\phi(g) = \begin{cases}\displaystyle\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}} F(w)\overline{\Theta^N_D(w;g)}dw& \text{if $F$ is of depth $0$}\\ \displaystyle\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}_1} F(w)\overline{\Theta^{N}_{D,1}(w;g)}dw& \text{if $F$ is of depth $1$}\end{cases} \]
\end{definition*}
The main result of this section is the following theorem.\\
\begin{thm}\label{Niwa}
Let $F(w)\in \widetilde{S}_0^{new}(\Gamma_0(N))$ or $\widetilde{S}_1^{new}(\Gamma_0(N))$ be a cupidal metaplectic form and $D$ a square-free polynomial which is relatively prime to $N.$ Let $\phi(g)$ be the $D'th$ Shimura lift of $F(w)$. Then we have the following equalities of L-functions:
$$L(s,\phi) =\begin{cases} p^{-1/2}L^N(1+s,\chi_D)|D|^{3/4}L(s-1/2,F,D)&\text{if $F$ is of depth $0$}\\ \frac{\lambda_{\infty,F}p^{-1/2}}{p+1}L^N(1+s,\chi_D)|D|^{3/4}L(s-1/2,F,D)&\text{if $F$ is of depth $1$}\end{cases}$$
Where $L^N(s,\chi_D) = \displaystyle\prod_{P\nmid N}\left(1-\frac{\left(\tfrac{P}{D}\right)}{|P|^{s}}\right)$.
\end{thm}
For clarity of exposition and convenience of the reader, we will first prove Niwa's Lemma for the case $N=1$ and forms unramified at infinity, and then outline the necessary modifications for the general level and ramification.
\begin{proof}
During the proof unless otherwise stated we will use (as usual)
\begin{align*}
w&=(u,v)=\left(\left(\begin{smallmatrix}\sqrt{v}&u/\sqrt{v}\\0&1/\sqrt{v}\end{smallmatrix}\right),1\right)\in\widetilde{\mathbb{H}}\\
z&=(x,y)=\left(\begin{smallmatrix}y&x\\0&1\end{smallmatrix}\right)
\in \mathbb{H}.
\end{align*}
\textbf{Case of N=D=1, depth 0}
We will calculate the Mellin transform of $\phi$ and show that it is the Mellin transform of the form in the Theorem.
\[M\phi(s)=\int_{k_{\infty}^{\times}}\phi(0,y)|y|^sd^{\times}y\]
\[=\int_{k_{\infty}^{\times}}\left(\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}} F(w)\overline{\Theta(w,(0,y))}\frac{du\,dv}{|v|^2}\right)|y|^sd^{\times}y\]
The theta function factors as:
\[\Theta(w,(0,y))=\tau(v)|v|^{1/4}\sum_{h_2\in TR}e(uh_2^2)\chi_{\mathcal{O}_{\infty}}(vh_2^2)\;\;\times|v|^{1 /2}\sum_{h_1,h_3\in TR}e(-4h_1h_3u)\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}}{y}h_3\right)\chi_{\mathcal{O}_{\infty}}(\sqrt{v}y h_1)\]
\[=\Theta(w)\theta_2(w,y)\]
We now use Poisson summation in the $h_3$ variable in order to separate the $h_1$ and $h_3$ variables in $\theta_2$. Define
\[f(\alpha)=\sum_{h_1\in TR}e(-4h_1u\alpha)\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}}{y}\alpha\right)\chi_{\mathcal{O}_{\infty}}(\sqrt{v}y h_1)\]
The Fourier transform of $f$ is
\begin{align*}
\hat{f}(\beta)&=\int_{k_{\infty}}f(\alpha)e(\beta \alpha)d\alpha\\
&=\sum_{h_1\in TR}\chi_{\mathcal{O}_{\infty}}\left(\sqrt{v}yh_1\right)
\int_{k_{\infty}}e(-4h_1u\alpha+\alpha\beta)\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}}{y} \alpha\right)d\alpha\\
&=\sum_{h_1\in TR}\chi_{\mathcal{O}_{\infty}}\left(\sqrt{v}yh_1\right)\int_{\mathcal{O}_{\infty}}e\left(\frac{y(-4h_1u+\beta)\alpha}{\sqrt{v}}\right)\frac{|y|d\alpha}{|\sqrt{v}|}\\
&=\frac{|y|}{|\sqrt{v}|}\sum_{h_1\in TR}\chi_{\mathcal{O}_{\infty}}(\sqrt{v}{y}h_1)\chi_{\mathcal{O}_{\infty}}\left(\frac{y(-4h_1u+\beta)}{\sqrt{v}}\right)
\end{align*}
By Poisson summation we get
\[\theta_2(w,y)=|y|\sum_{h_1,h_3\in TR}\chi_{\mathcal{O}_{\infty}}(\sqrt{v}{y}h_1)\chi_{\mathcal{O}_{\infty}}\left(\frac{y(-4h_1u+h_3)}{\sqrt{v}}\right)\]
Define $I=\int_{k_{\infty}^{\times}}\overline{\theta_2(w,y)}|y|^sd^{\times}y.$ Then
\[ I=\sum_{h_1,h_3\in TR}\int_{k_{\infty}^{\times}}\chi_{\mathcal{O}_{\infty}}(\sqrt{v}h_1y)\chi_{\mathcal{O}_{\infty}}\left(\frac{(4h_1u-h_3)y}{\sqrt{v}}\right)|y|^{s+1}d^{\times}y\]
Let $\alpha=\frac{(4h_1u-h_3)y}{\sqrt{v}}$, then
\[I=\sum_{h_1,h_3\in TR}\frac{|v|^{(s+1)/2}}{|4h_1u-h_3|^{s+1}}\int_{k_{\infty}^{\times}}\chi_{\mathcal{O}_{\infty}}\left(\frac{vh_1\alpha}{4h_1u-h_3}\right)\chi_{\mathcal{O}_{\infty}}(\alpha)|\alpha|^{s+1}d^{\times}\alpha\]
\[=\sum_{h_1,h_3\in TR}\frac{|v|^{(s+1)/2}}{|4h_1u-h_3|^{s+1}}\int_{\mathcal{O}_{\infty}\backslash\{0\}}\chi_{\mathcal{O}_{\infty}}\left(\frac{vh_1\alpha}{4h_1u-h_3}\right)|\alpha|^{s+1}d^{\times}\alpha\]
Let $v_{\infty}\left(\frac{vh_1}{4h_1u-h_3}\right)=A$, then
\[\int_{\mathcal{O}_{\infty}\backslash\{0\}}\chi_{\mathcal{O}_{\infty}}\left(\frac{vh_1\alpha}{4h_1u-h_3}\right)|\alpha|^{s+1}d^{\times}\alpha=\sum_{j=\max\{-A,0\}}^{\infty}\int_{\mathcal{O}_{\infty}^{\times}}p^{-j(s+1)}d^{\times}\alpha\]
\[=\Gamma_k(s+1)p^{\min\{A,0\}(s+1)}\]
So we get
\begin{align*}
I&=\Gamma_k(s+1)\sum_{h_1,h_3\in TR}\frac{|v|^{(s+1)/2}}{|4h_1u-h_3|^{s+1}}p^{(s+1)\min\{v_{\infty}\left(\frac{vh_1}{4h_1u-h_3}\right),0\}}\\
&=\Gamma_k(s+1)\sum_{h_1,h_3\in TR}\frac{|v|^{(s+1)/2}}{|4h_1u-h_3|^{s+1}}\min\left\{\frac{|4h_1u-h_3|^{s+1}}{|vh_1|^{s+1}},1\right\}\\
&=\Gamma_k(s+1)\sum_{h_1,h_3\in TR}\frac{|v|^{(s+1)/2}}{\max\{|vh_1|,|h_1u+h_3|\}^{s+1}}\\
&=\frac{\Gamma_k(s+1)\zeta_k(s+1)}{p^{s+1}}E(w,(s+1)/2)
\end{align*}
Where the Eisenstein series is defined as in the usual way
\[E(w,s)=\sum_{\gamma\in\widetilde{\Gamma}_{\infty}\backslash\widetilde{\Gamma}}Im(\gamma w)^s=
\sum_{\substack{c,d\in R\\ (c,d)=1}}\frac{|v|^s}{\max\{|cv|,|cu+d|\}^{2s}}.\] This is absolutely convergent for $Re(s)>1$ and evidently left-invariant by $\widetilde{\Gamma}$.
Putting things together we have
\begin{equation}\label{mellin}
M\phi(s)=\frac{\Gamma_k(s+1)\zeta_k(s+1)}{p^{s+1}}\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}}F(w)\overline{\Theta(w)}E(w,(s+1)/2)\frac{du\,dv}{|v|^2}\end{equation}
Define $J =\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}}F(w)\overline{\Theta(w)}E(w,(s+1)/2)\frac{du\,dv}{|v|^2}.$ Then
\begin{align*}
J&=\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}}F(w)\overline{\Theta(w)}E(w,(s+1)/2)\frac{du\,dv}{|v|^2}\\
&=\int_{\widetilde{\Gamma}_{\infty}\backslash\widetilde{\mathbb{H}}}F(w)\overline{\Theta(w)}|v|^{(s+1)/2}\frac{du\,dv}{|v|^2}
\end{align*}
where the second equality is obtained by unfolding the Eisenstein series..
\begin{align*}
J&=\int_{\widetilde{\Gamma}_{\infty}\backslash\widetilde{\mathbb{H}}}F(w)\overline{\Theta(w)}|v|^{(s+1)/2}\frac{du\,dv}{|v|^2}\\
&=2\iint\limits_{\substack{v\in k_{\infty}^{\times} \\ u\in T^{-1}\mathcal{O}_{\infty}}}\tau(v)|v|^{s/2-5/4}\left(\sum_{a\in R}F_a(v)e(T^2au)\right)\overline{\left(\sum_{l\in R}e(T^2l^2u)\chi_{\mathcal{O}_{\infty}}(l^2v)\right)}du\,dv
\end{align*}
The inner integral over $u$ vanishes unless $a=l^2,$ so we get
\begin{align*}
J&=\sum_{l\in R}\frac{\lambda_F(l^2)}{|l|^{s-1/2}}\int_{v\in k_{\infty}^{\times}}|v|^{s/2-1/4}\widetilde{W}_{0,i\gamma}(v)d^{\times}v\\
&=p^{-s+1/2}\Gamma_k(s-1/2+i\xi)\Gamma_k(s-1/2-i\xi)\Gamma^{-1}(1+s)L(s-1/2,F)
\end{align*}
Where $p^{i\xi}=e^{i\gamma}$.
Plugging $J$ back in we get,
\[M\phi(s) = p^{-2s-1/2}\zeta_k(s+1)\Gamma_k(s-1/2+i\xi)\Gamma_k(s-1/2-i\xi)L(s-1/2,F)\]
which completes the proof in the case $N=D=1$ and depth $0.$\\
\textbf{Case of N=D=1, depth 1}
We first introduce the following modified Eisenstein series on $\widetilde{\mathbb{H}}_1$:
$$E_1(w,s) :=\sum_{\gamma\in\widetilde{\Gamma}_{\infty}\backslash\widetilde{\Gamma}}Im\left(\gamma w\left(\begin{smallmatrix} \varpi_{\infty}^{-1} & 0\\0 & 1 \end{smallmatrix}\right)\right)^s $$
(We note that since $\left(\begin{smallmatrix}\varpi_{\infty}^{-1} & 0\\0 & 1\end{smallmatrix}\right)^{-1}\widetilde{K}_0(\varpi_{\infty})\left(\begin{smallmatrix}\varpi_{\infty}^{-1}& 0\\0 & 1\end{smallmatrix}\right)\subset SL_2(\mathcal{O}_{\infty})$ we see that $E_1(w,s)$ is well defined and of depth 1.)
Let $F(w)$ be a newform of depth 1, and define $\phi(z)$ to be its Shimura lift. Then following the above computations replacing $\Theta(w;g)$ by
$\Theta_1(w;g)$ we arrive at the following analogue of (\ref{mellin}):
\begin{equation}\label{meldep}
M\phi(s)=\frac{\Gamma_k(s+1)\zeta_k(s+1)}{p^{s+1}}p^{-\frac{s+1}{2}}\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}_1}F(w)\overline{\Theta(w)}E_1(w,(s+1)/2)\frac{du\,dv}{|v|^2}
\end{equation}
Define $J =\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}_1}F(w)\overline{\Theta(w)}E_1(w,(s+1)/2)\frac{du\,dv}{|v|^2}.$ Then
\begin{align*}
J&=\int_{\widetilde{\Gamma}\backslash\widetilde{\mathbb{H}}_1}F(w)\overline{\Theta(w)}E_1(w,(s+1)/2)\frac{du\,dv}{|v|^2}\\
&=\frac{1}{p+1}\int_{\widetilde{\Gamma}_{\infty}\backslash\widetilde{\mathbb{H}}^u_1}F(w)\overline{\Theta(w)}p^{(s+1)/2}|v|^{(s+1)/2}\frac{du\,dv}{|v|^2}\\
&+\frac{p}{p+1}\int_{\widetilde{\Gamma}_{\infty}\backslash\widetilde{\mathbb{H}}^l_1}F(w)\overline{\Theta(w)}p^{-(s+1)/2}|v|^{(s+1)/2}\frac{du\,dv}{|v|^2}
\end{align*}
Using the fact that $F_a^l(v)=-\frac{F_a^u(v)}{p}$, we Fourier expand as before and get the following:
\begin{align*}
J &=\frac{1}{p+1} (p^{\frac{s+1}{2}} - p^{-\frac{1+s}{2}})\sum_{l\in R}\frac{\lambda_F(l^2)}{|l|^{s-1/2}}\int_{v\in T^{-1}\mathcal{O}_{\infty}\backslash \{ 0 \} }|v|^{s/2-1/4}
\widetilde{W}_{1,\lambda_{\infty,F}}(v)d^{\times}v\\
&= \frac{1}{p+1}p^{\frac{1+s}{2}}\Gamma_k^{-1}(1+s)L(s-\frac{1}{2},F)\frac{\lambda_{\infty,F}\:p^{1/2-s}}{1-\lambda_{\infty,F}\:p^{1/2-s}}\\
\end{align*}
Plugging this expression back into (\ref{meldep}), we get
\[M\phi(s)=\frac{\lambda_{\infty,F}\:p^{-1/2}}{p+1}L(s-\frac{1}{2},F)\zeta_k(s+1)\frac{p^{-2s}}{1-\lambda_{\infty,F}\:p^{1/2-s}}\]
as desired.\\
\textbf{General case, depth 0}
We now do the above computations but with the general theta function $\Theta^N_D(w;g).$
As before, we shall compute the Mellin transform \[M\phi(s)=\int_{k_{\infty}^{\times}} \phi(0,y)|y|^{s} d^{\times}y. \]
We shall need the theta functions $$\theta(D,w,h) = \tau(v)\displaystyle\sum_{\substack{m\in TR,\\ m\equiv h\;\text{mod $D$}}} e\left(\frac{um^2}{D}\right)\chi_{\mathcal{O}_{\infty}}\left(\frac{vm^2}{D}\right)$$
where $h\in R/DR.$ We begin by writing:
\[\Theta^N_D(w;g) = \tau(v)\displaystyle\sum_{\substack{\vec{h}\in L,\;N|h_1\\ D\mid Q(\vec{h})}}W_D(\vec{h})e((h_2^2 - 4h_1h_3)u/D)\chi_{O_V}(\sqrt{v}g^{-1}(h)/\sqrt{D})\]
Splitting over representatives $\vec{r}$ defined modulo $D$ we get
\begin{multline*}
\Theta^N_D(w;(0,y)) = \tau(v)|v|^{3/4}\sum_{\substack{\vec{r}\in TR^3/DTR^3\\ r_2^2-4r_1r_3\equiv 0\:(D)}}W_D(\vec{r})\theta(D,w,r_2)\\
\times\sum_{\substack{h_1\equiv r_1\;(D)\\h_3\equiv r_3\;(D) \\NT|h_1\\T|h_3}}e\left(\frac{-4h_1h_3u}{D}\right)\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}h_3}{y\sqrt{D}}\right)
\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}y h_1}{\sqrt{D}}\right)
\end{multline*}
Applying Poisson summation over $h_3$, we get (we denote the dual variable by $s_3$ which should not be confused with the exponent $s$ of the Mellin transform)
\begin{multline*}
\Theta^N_D(w;(0,y)) = \frac{\tau(v)|y||v|^{3/4}}{|\sqrt{vD}|}\sum_{\substack{\vec{r}\in TR^3/DTR^3\\ r_2^2-4r_1r_3\equiv 0\:(D)}}W_D(\vec{r})\theta(D,w,r_2)\\
\times\sum_{\substack{h_1\equiv r_1\;(D)\\ NT|h_1\\T|s_3}}e\left(\frac{-s_3r_3}{D}\right)\chi_{\mathcal{O}_{\infty}}\left(\frac{\sqrt{v}yh_1}{\sqrt{D}}\right)
\chi_{\mathcal{O}_{\infty}}\left(\frac{y(-4h_1u+s_3)}{\sqrt{vD}}\right)
\end{multline*}
So that
\begin{multline*}
\int_{k^{\times}_{\infty}}\Theta^N_D(w;(0,y))|y|^s d^{\times}y = \Gamma_k(1+s)|D|^{s/2}\tau(v)|v|^{1/4}
\sum_{\substack{\vec{r}\in TR^3/DTR^3\\ r_2^2-4r_1r_3 \equiv 0\:(D)}}W_D(\vec{r})\theta(D,w,r_2)\\
\times\sum_{\substack{h_1\equiv r_1\;(D)\\ NT|h_1\\T|s_3}}e\left(\frac{-s_3r_3}{D}\right)\frac{|v|^{\frac{1+s}{2}}}{\max\{|vh_1|,|-4h_1u+s_3|\}^{1+s}}
\end{multline*}
Define $G_{N,D,r_2}(w,s)$ by
$$G_{N,D,r_2}(w,s)=\sum_{\substack{r_1,r_3\in R/DR\\4r_1r_3\equiv r_2^2\;(D)}}W_D(\vec{r})\sum_{\substack{h_1\equiv r_1\:(D)\\ NT|h_1\\T|s_3}}\left(\frac{-s_3r_3}{D}\right)\frac{|v|^{\frac{1+s}{2}}}{\max\{|vh_1|,|-4h_1u+s_3|\}^{1+s}}$$
We now express $G_{N,D,r_2}(w,s)$ in terms of Eisenstein series. Specifically, we define the following congruence subgroups of $\eta(SL_2(R)):$
$$\widetilde{\Gamma}_1(D)=\left\{\eta(\gamma)\in \eta(SL_2(R))\;\left|\;\gamma \equiv \begin{pmatrix} 1 & *\\ 0 & 1\end{pmatrix}\mod D\right.\right\}$$ and $\widetilde{\Gamma}_{N,D}=\widetilde{\Gamma}_0(N)\cap\widetilde{\Gamma}_1(D).$
Now define the Eisenstein series via $$E_{N,D}(w,s) = \sum_{\gamma\in\widetilde{\Gamma}_{\infty}\backslash\widetilde{\Gamma}_{N,D}}Im(\Gamma_k(w))^s $$
Then for $\gamma_{c_0,d_0}=\eta\left(\left(\begin{smallmatrix} * & *\\ c_0 & d_0 \end{smallmatrix}\right)\right)\in SL_2(R),$ we readily compute
$$E_{N,D}(\gamma_{c_0,d_0}(w),(1+s)/2) = \sum_{\substack{c\equiv c_0\;\text{mod $D$}\\ d\equiv d_0\;\text{mod $D$}\\ (c,d)=1}} \frac{|v|^{\frac{1+s}{2}}}{\max\{|vc|,|cu+d|\}^{1+s}}$$
Though $E_{N,D}(w,s)$ looks similiar to $G_{N,D,r_2}(w,s),$ we have to deal with the fact that $h_1$ and $s_3$ might not be relatively prime. In order to separate the gcd from the sum we define the following function
\[\tilde{G}_{N,D,r_2}(w,s)=\sum_{\substack{r_1,r_3\in R/DR\\r_1r_3\equiv r_2^2\;(D)}}W_D(\vec{r})\sum_{\substack{h_1\equiv r_1\:(D)\\ NT|h_1\\(s_3,N)=1\\T|s_3}}e\left(\frac{-s_3r_3}{D}\right)\frac{|v|^{\frac{1+s}{2}}}{\max\{|vh_1|,|-4h_1u+s_3|\}^{1+s}}\]
The following Lemma separates the factors of $DN$ from the sum.
\begin{lemma}\label{sieve}
\[G_{N,D,r_2}(w,s)=\sum_{\substack{r_1,r_3\in R/DR\\r_1r_3\equiv r_2^2\;(D)}}W_D(\vec{r})\sum_{\substack{h_1\equiv r_1\:(D)\\ NT|h_1\\((r_1,s_3),D)=1\\T|s_3}}e\left(\frac{-s_3r_3}{D}\right)\frac{|v|^{\frac{1+s}{2}}}{\max\{|vh_1|,|-4h_1u+s_3|\}^{1+s}}\]
and
\[G_{N,D,r_2}(w,s)=\sum_{d\mid N}d^{-s-1}\left(\frac{d}{D}\right)\tilde{G}_{\tfrac{N}{d},D,r_2}(w,s)\]
\end{lemma}
\begin{proof} Let $((h_1,s_3),D)=b$. Since $D$ is square-free, $D$ and $D/b$ are relatively prime. Hence by the Chinese Remainder Theorem we have $$R/DR=R/bR\oplus R/(D/b)R.$$ Using this decomposition we separate the $r_3$ sum into $r_3\;\text{mod $b$}$ and $r_3\;\text{mod $(D/b)$}$, and $W_D$ splits accordingly as $W_D=W_{(D/b)}W_b$. Since $b\mid s_3$ the character $e(-s_3r_3/D)$ is constant on $R/bR$ and the sum over $r_3\;\text{mod $b$}$ becomes
\[\sum_{r_3\; (b)}W_b(r_3)=\sum_{r_3}\left(\frac{b}{r_3}\right)=0\]
This establishes the first statement.
For the second statement let $c=(s_3,N)$. The substitution $\{h_1\rightarrow \tfrac{h_1}{c},\;s_3\rightarrow
\tfrac{s_3}{c},\; r_1\rightarrow \tfrac{r_1}{c},\; r_3\rightarrow cr_3\}$ leaves the character $e(-r_3s_3/D)$ invariant. Note that with the flip, $W_D$ changes
by the quadratic character: $$W_D((r_1,r_2,r_3))\rightarrow W_D((r_1/b,r_2,br_3))=\left(\tfrac{b}{D}\right)W_D((r_1,r_2,r_3).$$
Summing over all such $c$ gives
\[\tilde{G}_{N,D,r_2}(w,s)=\sum_{d\mid N}\mu(d)d^{-s-1}\left(\frac{d}{D}\right)G_{\tfrac{N}{d},D,r_2}(w,s)\] as desired.
\end{proof}
Now for $((h_1,s_3),ND)=c\neq 1$ the same substitution $\{h_1\rightarrow \tfrac{h_1}{c},\;s_3\rightarrow
\tfrac{s_3}{c},\; r_1\rightarrow \tfrac{r_1}{c},\; r_3\rightarrow cr_3\}$ as in the proof above gives
\begin{multline*}
\tilde{G}_{N,D,r_2}(w,s)=\prod_{P\nmid DN}\left(1-\frac{\left(\tfrac{P}{D}\right)}{|P|^{1+s}}\right)\\ \times\sum_{\substack{r_1,r_3\in R/DR\\
r_1r_3\equiv r_2^2\;(D)}}W_D(\vec{r})\sum_{\substack{h_1\equiv r_1\:(D)\\ NT|h_1 \\ (h_1,s_3)=T}}e\left(\frac{-s_3r_3}{D}\right)\frac{|v|^{\frac{1+s}{2}}}{\max\
{|vh_1|,|-4h_1u+s_3|\}^{1+s}}}
\end{multline*}
Note that the first factor is $L^N(s+1,\chi_D) = \displaystyle\prod_{P\nmid N}\left(1-\frac{\left(\tfrac{P}{D}\right)}{|P|^{1+s}}\right)$, and so the above simplifies to
\begin{equation}\label{eisensteinappears}
\tilde{G}_{N,D,r_2}(w,s)=L^N(1+s,\chi_D)\sum_{\substack{r_1,r_3\in R/DR\\
r_1r_3\equiv r_2^2\;(D)}}W_D(\vec{r})\sum_{s_3\in R/DR} p^{-(1+s)}E_{N,D}(\gamma_{r_1,s_3}(w),(1+s)/2)e\left(\frac{-s_3r_3}{D}\right)
\end{equation}
We now compute the Mellin transform of $\phi((0,y))$ as intended.
\begin{align*}
\overline{M\phi(\overline{s})} &= p^{-(1+s)}\int_{k_{\infty}^{\times}}\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}}\overline{F(w)} \Theta_D^N(w;(0,y))|y|^s dwdy\\
&=p^{-(1+s)} \Gamma_k(1+s)|D|^{s/2}\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\sum_{r_2}\theta(D,w,r_2)G_{N,D,r_2}(s)dw\\
&= p^{-(1+s)}\Gamma_k(1+s)|D|^{s/2}\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\sum_{r_2}\theta(D,w,r_2)\sum_{d\mid N}d^{-s-1}\left(\frac{d}{D}\right)\tilde{G}_{\tfrac{N}{d},D,r_2}(s)dw\\
\end{align*}
Now, for $d\neq 1, d|N $, $\theta(D,w,r_2)E_{\frac{N}{d},D}(w,s)$ is invariant under $\widetilde{\Gamma}(D)\cap\widetilde{\Gamma}(\frac{N}{d})$ which is not contained inside $\widetilde{\Gamma}_0(N)$. However, $F(w)$ is a newform for $\widetilde{\Gamma}_0(N)$ and so is orthogonal to any function invariant by a bigger group
as it would then be in the old space. Thus the above integral vanishes unless $d=1.$ So
\begin{align*}
\overline{M\phi(\overline{s})} &= p^{-(1+s)}\Gamma_k(1+s)|D|^{s/2}\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\sum_{r_2\in(R/DR)}\theta(D,w,r_2)\tilde{G}_{N,D,r_2}(s)dw\\
&= p^{-(1+s)}\Gamma_k(1+s)|D|^{s/2}\int_{\widetilde{\Gamma}_0(N)\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\sum_{\vec{r}\in(R/DR)^3}W_D(\vec{r})\theta(D,w,r_2)L^N(1+s,\chi_D)\\
&\times\sum_{s_3\in R/DR} E_{N,D}(\gamma_{r_1,s_3}(w),(1+s)/2)e\left(\frac{-s_3r_3}{D}\right)dw\\
&=p^{-(1+s)}\Gamma_k(1+s)|D|^{s/2}[\widetilde{\Gamma}_0(N):\widetilde{\Gamma}_{N,D}]^{-1}\\
&\times\int_{\widetilde{\Gamma}_{N,D}\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\sum_{\substack{\vec{r}\in(R/DR)^3\\r_2^2-4r_1r_3=0}}W_D(\vec{r})\theta(D,w,r_2)L^N(1+s,\chi_D)\\
&\times\sum_{s_3\in R/DR} E_{N,D}(\gamma_{r_1,s_3}(w),(1+s)/2)e\left(\frac{-s_3r_3}{D}\right)dw\\
\end{align*}
Since $(N,D)=1$, we can pick representatives for $r_1,s_3$ such that $\gamma_{r_1,s_3}\in\widetilde{\Gamma}_0(N).$ Then $F(w)$ is invariant under the change of variables
$w\rightarrow\gamma_{r_1,s_3}^{-1}(w).$ As in \cite{Shim} we have the following transformation property:
$$\theta(D,\gamma^{-1}_{r_1,s_3}(w),r_2) = |D|^{-1/2}i(u/d)\sum_{\nu\in R/DR} C_{r_2,\nu}\theta(D,w,\nu)$$
where $C_{r_2,\nu}$ are constants and $C_{r_2,0} = \left(\frac{r_1}{D}\right)e\left(\frac{s_3(4r_1)^{-1}r_2^2}{D}\right) = W_D(\vec{r})e\left(\frac{s_3r_3}{D}\right).$ Now, since $E_{N,D}(w,s)$ and $F(w)$ are both invariant under $w\rightarrow w+1,$ and $\theta(D,w+1,a)=e(\frac{a^2}{D})\theta(D,w,a),$ everything but the $\theta(D,w,0)$ contribution vanishes. Therefore, we are left with
\begin{align*}
\overline{M\phi(\overline{s})} &=p^{-(1+s)}\Gamma_k(1+s) L^N(1+s,\chi_D)|D|^{\frac{s+1}{2}}[\Gamma_0(N):\Gamma_{N,D}]^{-1}\kappa(D)\\
&\times\int_{\widetilde{\Gamma}_{N,D}\backslash\widetilde{\mathbb{H}}}|v|^{1/4}\overline{F(w)}\theta(D,w,0)
E_{N,D}(w,(1+s)/2)dw\\
\end{align*}
where $\kappa(D)=\#\{\vec{r}\mid W_D(\vec{r})\neq 0\}$. A simple computation yields
\[[\widetilde{\Gamma}_0(N):\widetilde{\Gamma}_{N,D}]^{-1}\kappa(D) = 1.\]
Unfolding the Eisenstein series, we get
\[\overline{M\phi(\overline{s})} =p^{-(1+s)}\Gamma_k(1+s)L^N(1+s,\chi_D)|D|^{\frac{1+s}{2}}\int_{\widetilde{\Gamma}_{\infty}\backslash\widetilde{\mathbb{H}}}\overline{F(w)}\theta(D,w,0)|v|^{s/2+3/4}\frac{du\,dv}{|v|^2}\]
Unfolding as before leads to
\[M\phi(s) =p^{-2s-1/2}L^N(1+s,\chi_D)|D|^{3/4}\Gamma_k(s+1/2-i\xi)\Gamma_k(s+1/2+i\xi)L_D(s-1/2,F)\]
from which the result follows. \\
\textbf{General Case, depth 1}
The above calculations go through, except $$E_{N,D}(w,s) = \sum_{\gamma\in\widetilde{\Gamma}_{\infty}\backslash\widetilde{\Gamma}_{N,D}}Im(\gamma(w))^s $$
is replaced by $$E_{1,N,D}(w,s) = \sum_{\gamma\in\widetilde{\Gamma}_{\infty}\backslash\widetilde{\Gamma}_{N,D}}Im\left(\gamma(w)\left(\begin{smallmatrix} \varpi_{\infty}^{-1} & 0\\ 0 & 1\end{smallmatrix}\right)\right)^s$$ as in the case where $N=D=1$.
As before, $E_{1,N,D}(w,s)$ is a depth 1 function. Following the above calculations gives the result.
\end{proof}
\section{A Waldspurger type formula}\label{sectionwaldspurger}
\subsection{Qualitative facts about the Shimura correspondence}\label{qualwalds}
We will need two general facts about the correspondences that we have defined: that they preserve cuspidality and Hecke eigenspaces. To establish these we use the fact that locally, the correspondences that we defined (for any $D\in\mathbb{F}_p[T]$ that we are considering) are instances of a general
correspondence known as the \emph{local Howe correspondence}. To define the correspondence we start with two closed subgroups $H$ and $G$ of a symplectic group that are maximal commutants of each other. (Such pairs of groups are called \emph{dual reductive pairs}.) Denote their inverse image in the metaplectic cover of the symplectic cover by $\widetilde{H}$ and $\widetilde{G}$ respectively. Then a representation $\pi_{\widetilde{H}}$ of $\tilde{H}$ is said to correspond to a representation $\pi_{\widetilde{G}}$ of $\widetilde{G}$ if the tensor product $\pi_{\widetilde{H}}\otimes\pi_{\widetilde{G}}$ can be realized as a quotient of the Weil representation of the symplectic group that $H$ and $G$ sit in. Howe's conjectures (proved for archimedean local fields by Howe \cite{H} and for nonarchimedean local fields of characteristic not $2$ by Waldspurger \cite{Wa}) roughly states that for any representation $\pi_{\widetilde{G}}$ of $\widetilde{G}$ there is at most one irreducible representation $\pi_{\widetilde{H}}=\theta(\pi_{\widetilde{G}})$ of $\widetilde{H}$ that it corresponds to, and if $\theta(\pi_{\widetilde{G}})\neq0$ and $\theta(\pi_{\widetilde{G}})\cong\theta(\pi_{\widetilde{G}}')$ then $\pi_{\widetilde{G}}\cong\pi_{\widetilde{G}}'$. We will only need the first part of the statement which gives a local multiplicity one result. The case that is pertinent here is that of $H=PGL(2)$ and
$G=\widetilde{SL}(2)$. Translated to the language of the present paper, the Howe correspondence, combined with the strong multiplicity one theorem for $PGL(2)$, says that if $F$ is a Hecke eigenform on $\widetilde{SL}(2)$, than so is its Shimura lift $\phi$. So the Shimura lift
preserves Hecke eigenspaces.
In \cite{G-P-S}, Gelbart and Piatetski-Shapiro proved cuspidality results for general theta lifts (cf. Theorem 15.1 and Corollary 15.6), which in our case gives:
\begin{itemize}
\item[(i)] If $F$ is a cuspidal Hecke eigenform on $\widetilde{SL}(2)$ that is not a theta function of 1-variable, then its ($D$'th) Shimura lift is also cuspidal.
\item[(ii)] If $\phi$ is a cuspidal Hecke eigenform on $PGL(2)$, then its ($D$'th) Maass-Shintani lift is also cuspidal.
\end{itemize}
In what follows we shall also use these two facts.
\subsection{Waldspurger's formula}
We are now ready to deduce Waldspurger's formula. We start with the depth 0 case. Pick an Hecke-eigenbasis for $\widetilde{S}_0(\widetilde{\Gamma}_0(N))$: $\{F_1,F_2,..,F_r\}$, which
is orthonormal for the Petterson inner product. Let $N=\prod_{i=1}^m l_i^{\alpha_i}$ be the decomposition of $N$ into irreducible prime powers. Let $\phi(z)$ be an
automorphic Hecke eigenform of depth 0 of level $N$, with first Fourier-Whittaker coefficient $\lambda_{\phi}(1)$ equal to 1. Let $F^{[D]}(w)$ be the $D$'th Maass-Shintani lift of $\phi$. We are going to write the $D$-th Fourier-Whittaker coefficient $\lambda_{F^{[D]}}(D)$
of $F$ in 2 different ways. On the one hand by Theorem \ref{shintanilift} we have
\[ \lambda_{F^{[D]}}(D) = C_{\phi}G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right)(1+w_{\infty,\phi})\]
On the other hand, since we know that $F^{[D]}$ is cuspidal, we can expand it as
\[F^{[D]}(w)=\sum_j\langle F^{[D]},F_j\rangle\; F_j(w)\]
We also have by definition
\begin{multline*}
\langle F^{[D]},F_j\rangle=\int_{\widetilde{\Gamma}_0(N)\backslash \widetilde{\mathbb{H}}}F^{[D]}(w)\overline{F}_j(w)dw=\int_{\widetilde{\Gamma}_0(N)\backslash \widetilde{\mathbb{H}}}\int_{\Gamma_0(N)\backslash \mathbb{H}}\Theta_D^N(w;z)\phi(z)\overline{F}_j(w)dzdw\\ =\int_{\Gamma_0(N)\backslash \mathbb{H}}\phi(z)\overline{\phi}_j(z)dz=\langle \phi,\phi_j\rangle
\end{multline*}
where $\phi_j$ is the $D$'th Shimura lift of $F_j$. Since $\phi_j$ is a Hecke eigenform, by strong multiplicity one it is either a constant multiple of $\phi$ or orthogonal to it. If it is a constant multiple $M_j$ of $\phi$, then $$\langle\phi_j,\phi\rangle = M_j\langle\phi,\phi\rangle,$$ and thus
\begin{align*}
C_{\phi}G_1(D)|D|^{-3/4}L(1/2,\phi\times\chi_D)\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right)(1+w_{\infty,\phi})&=\lambda_F(D)\\
&=\sum_j \langle F,F_j\rangle\lambda_{F_j}(D)\\
&=\sum_j\overline{M}_j\langle\phi,\phi\rangle\lambda_{F_j}(D)\\
\end{align*}
where $C_{\phi} = \frac{p^{-3/2}}{\left(1-\frac{e^{-i\theta}}{\sqrt{p}}\right)\left(1-\frac{e^{i\theta}}{\sqrt{p}}\right)}$.
By Niwa's Lemma, if $\lambda_{F_j}(D)\neq 0,$ then $M_j=p^{-1/2}|D|^{3/4}\lambda_{F_j}(D)/\lambda_{\phi}(1)$. Putting this together, we arrive at:\\
\begin{thm}[Waldspurger's formula for depth 0]
Let $\phi\in S_0(\Gamma_0(N))$ with $D$ coprime to $N$, squarefree and $D\in k_{\infty}^2$. Then we have the following identity:
$$\frac{1}{\langle\phi,\phi\rangle} p^{1/2}C_{\phi}G_1(D)|D|^{-3/2}L(1/2,\phi\times\chi_D)\prod_{i=1}^m \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right) = \sum_{\textrm{ Shim}(F_j) = \phi} |\lambda_{F_j}(D)|^2$$ where $C_{\phi} = \frac{p^{-3/2}}{\left(1-\frac{e^{-i\theta}}{\sqrt{p}}\right)\left(1-\frac{e^{i\theta}}{\sqrt{p}}\right)}.$
\end{thm}
For the depth 1 case, we pick an orthonormal Hecke eigenbasis for $\widetilde{S}^{new}_0(\widetilde{\Gamma}_0(N),1)$. Now repeating the argument
above,we arrive at:\\
\begin{thm}[Waldspurger's formula for depth 1]
Let $\phi\in S^{new}_1(\Gamma_0(N))$ with $D$ coprime to $N$, square-free, and $D\in k_{\infty}^2$. Then we have the following identity:
$$\frac{1}{\langle\phi,\phi\rangle}\frac{(p+1)}{p+w_{\infty,\phi}}G_1(D)|D|^{-3/2}L(1/2,\phi\times\chi_D)\prod_{i=1}^R \left(1+\left(\frac{l_i^{\alpha_i}}{D}\right)w_{l_i^{\alpha_i},\phi}\right)(1+w_{\infty,\phi}) = \sum_{\textrm{ Shim}(F_j) = \phi} |\lambda_{F_j}(D)|^2$$ where
$C_{\phi} = \frac{-pw_{\infty,\phi}}{p+w_{\infty,\phi}}.$
\end{thm}
By Drinfeld's \cite{Dr} and Deligne's \cite{Del} works, $L(1/2,\phi\times\chi_D)$ satisfies the Riemann hypothesis. Hence by Theorem \ref{lindelofhyper2} we know that it satisfies the Lindel\"of Hypothesis. Therefore we get\\ \\
\begin{thm}[Metaplectic Ramanajun conjecture]\label{metramcon}
Let $F$ be a fixed cuspdial meteplectic form of level $N$, depth $0$ or a newform of depth $1$. Then for $D\in R$ square-free of even degree and relatively prime to $N$ we have the following bound
\[\begin{array}{cc}
|\lambda_F(D)|^2\ll_F |D|^{-1/2+o(1)}\,,&\text{as }|D|\rightarrow\infty
\end{array}\]
\end{thm}
\begin{proof}
Without loss of generality we can assume that $F$ is a Hecke eigenform. If $F$ is a 1-variable theta function then the Fourier-Whittaker coefficients $\lambda_F(D)$ are supported only on one square class, and the theorem follows tautologically.
Else, consider the $D$'th Shimura lift, $\phi$, of $F$. By the discussion in \S\ref{qualwalds}, $\phi$ will is a cuspidal Hecke eigenform itself. Then Waldspurger's formula combined with the fact that $|G_1(D)|=|D|^{1/2}$ gives us
\begin{equation}\label{ineqram}
|\lambda_{F}(D)|^2\leq \sum_{Shim(F_j)=\phi}|\lambda_{F_j}(D)|^2\ll_F\frac{L(1/2,\phi\times\chi_D)}{\langle\phi,\phi\rangle}|D|^{-1}\ll_F L(1/2,\phi\times \chi_D)|D|^{-1}
\end{equation}
Where the implied constant in the last inequality is \emph{independent} of $D$ (Note that the Shimura lifts depended on $D$). This is because the space $S_0(\Gamma_0(N))$ is finite dimensional, so we have $\langle\phi,\phi\rangle\geq \min\{\langle\phi_1,\phi_1\rangle,\cdots,\langle\phi_n,\phi_n\rangle\}$ independently of $D$, where $\{\phi_j\}_{j=1}^n$ is a Hecke eigenbasis for $S_{0}(\Gamma_0(N))$ (and similarly $S_1(\Gamma_0(N))$).
Then \eqref{ineqram} combined with Theorem \ref{lindelofhyper2} and gives the result for $D\in k_{\infty}^2$. For $D$ of even degree and not in $k_{\infty}^2$, take $\epsilon\in\mathbb{F}_p$ not a square so that we have $\epsilon D\in k_{\infty}^2$. We appeal to section \ref{dnotsquare} to see that $|\lambda_F(D)|=|\lambda_{F_{\epsilon}}(\epsilon D)|$ and the result follows.
\end{proof}
Note that the implied constants in $\ll_F$ notation are \emph{effective} and the stronger bound in Theorem \ref{lindelofhyper2} applies.
\section{Proof of Theorem \ref{representationTheorem}}\label{sectionquadratic}
We are now ready to finish the proof of Theorem \ref{representationTheorem}. Let $Q$ be an anisotropic ternary quadratic form, which is rationally equivalent over $k_{\infty}$
to $T\epsilon x^2 + Ty^2 +\epsilon z^2$, where $\epsilon\in \mathbb{F}_p\backslash \mathbb{F}_p^2$. Define $\Theta_Q(z)$ and $\Theta_G(z)$ as in equations \ref{thetaG} and \ref{thetaQ}. Then by Siegel's Theorem (Theorem (\ref{SiegelsTheorem})) we can expand it as a sum of cuspidal Hecke eigenforms of type 1, depth 1 and level $\text{disc}(Q)$ as
$$ \Theta_Q(z) = \Theta_G(z) + \displaystyle\sum_j F_j(z)$$
Recall that the sum on the right hand side is a finite sum.
Take $D\in R$ to be of even degree, square-free and relatively prime to $\text{disc}(Q).$ By looking at the $D$'th Fourier-Whittaker coefficients of the above equality we get
$$ |v|^{3/4}r_Q(D)\chi_{\mathcal{O}_\infty}(Dv) = |v|^{3/4}r_G(D)\chi_{\mathcal{O}_\infty}(Dv) + \displaystyle\sum_j \lambda_{F_j}(D)\widetilde{W}_{F_j}(Dv)$$
where $\widetilde{W}_{F_j}$ is the appropriate Whittaker function, depending on which of the spaces
$\widetilde{S}_1^{new}(\widetilde{\Gamma}_0(N))$ and $\widetilde{S}_0(\widetilde{\Gamma}_0(N))$ contains
$F_j$.
By theorem \ref{metramcon} we have $|\lambda_{F_j}(D)|\ll_j |D|^{-1/2+\epsilon}$. Also by Siegel's mass formula \ref{Siegelmassformula} we have $r_G(D)\backsim L(q,\chi_D)|D|^{1/2}$. This, combined with Lemma \ref{classnumber} shows that $r_G(D)\gg_Q|D|^{1/2}/\log_p\log_p|D|$. (See \S\ref{Siegelmassformula}.) We conclude that, for $\epsilon>0$
\[r_Q(D) = r_G(D) + O_{\epsilon}(|D|^{\frac{1}{4}+\epsilon})\]
as desired. Note that the effectivity of Lemma \ref{classnumber} implies that the above is effective. In particular for a given form $Q$ we can actually write down all the even degree polynomials $D\in\mathbb{F}_p[T]$ that it represents.
\section{An Example}\label{Example}
In order to give a flavor of the kind of representability questions to which the methods developed in this paper applies to, we give the following example. Let $p=5$, $k=\mathbb{F}_5(T)$, $\epsilon\in\mathbb{F}_{5}$ a non-square, and $Q_1,\; Q_2$ be the anisotropic quadratic forms given by
\[Q_1(X,Y,Z)=X^2+(T^3+T+1)Y^2+\epsilon Z^2\]
\[Q_2(X,Y,Z)=(T^2-T-1)X^2+(T+1)XY+TY^2+\epsilon Z^2\]
First note that the two forms have the same discriminant $$\text{disc}(Q_1)=\text{disc}{(Q_2)}=\epsilon(T^3+T+1)=N$$ which is square-free over $\mathbb{F}_{5}$. \\
\begin{lemma}
$Q_1$ and $Q_2$ belong to the same genus.
\end{lemma}
\begin{proof}
In order to check the equivalence of these forms at each completion we check the equivalence of the Kohnen symbol for each form. Note that for $w\nmid N$ the two forms are diagonalizable over $\mathcal{O}_w$ and since they have the same determinant (which is a unit in $\mathcal{O}_w$) they are equivalent and we only need to check $w$ dividing $N$. We start with $Q_1$. $Q_1$ represents $1$ hence the Kohnen symbol is $1$. The second form represents $T^2-T-1$. The Kohnen symbol is
\[\left(\frac{T^3+T+1}{T^2-T-1}\right)=1\]
Hence the forms belong to the same genus.
\end{proof}
Now, Taking $X=0,Y=1,Z=0$ we see that $Q_2$ represents $T$, while it easy to see by degree considerations that $Q_1$ does not represent any degree 1 polynomial.
Therefore there is no local to global principle in this case. However, our Corollary \ref{representationCor} implies that for all sufficiently large odd degrees,
$Q_1$ and $Q_2$ will represent the same polynomials.
The authors would like to thank Peter Sarnak for originally suggesting the problem under consideration and for many helpful discussions. We would also like to thank Benjamin Bakker and Bhargav Bhatt for related conversations. We would also like to thank the referee for a careful read of the first draft of the paper and pointing out to numerous inaccuracies in the exposition.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 1,768
|
Naheed Farid is an Afghan politician. She was the youngest member of the Afghan parliament. Fearing for her life, she fled Afghanistan after the Afghan government fell and the Taliban seized control.
References
Living people
1984 births
Afghan feminists
21st-century Afghan women politicians
21st-century Afghan politicians
Members of the House of the People (Afghanistan)
|
{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 1,783
|
1964 AD Thai Communist Forces sent some natives to <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" />Huaminh City in Communism Republic of Vietnam to train in political and military tactics to become the leaders of the operation in Northern Thailand especially in Chiang Rai province.
In 1966 the first gun blasted as the beginning of full form military operations at Ban Nam Pan , Na rai Luang sub district , Tungchang district in Nan province as for the February 26th is called "The Blasted Day" . The fought increased its scale to become the war and on May 10th , 1967 , the battle at Ban Huai Chompu in Theong district was the first fight in the area of Doi Yao – Doi Phamon.
In 1978 , Thailand Communist Forces achieved their 5 settlements in the North while their most important base was on Doi Yao – Doi Phamon, Chiang Rai province called "Chiang Rai Chamber of Committees" , divided in to 4 areas of action, which were the 52nd , 9th , 7th and 8th forces.
Doi Yao –Doi Phamon was in the area of acton of the 8th forces of Theong district and Chiangkong district in Chiang Rai province included also with Wieng Kaen and Khun Tan district. There vere about 600 , well trained and armed forces mainly from Hmong tribe acted in the area tobether with roughly about 2300 non-military supporters. Their objective was to sabotage buildings, roads and other infrastructures to obstruct the establishment of Government's area for security.
In 1981 , the 473th Army Battalion led by Lieutenant Colonel Wirote Thongmit gain a great victory by took over hill 1188 on Doi Phayapipak in the area of Doi Yao- Doi Phamon became the remembrance battle of Phraya Pipak. Thus on February 27th , 1982 , His Majesty the King Bhumibol together with Her Majesty the Queen Sirikit , Her Royal Highness Princess Maha Chakri Sirindhorn , and Her Royal Highness Princess Somsawalee visited the army base and his populace on Doi Phayapipak Mountain, Theong district. Never before and never once more up to now, was it a great appreciation for all of His Majesty's subjects who had and audience the day that the king graciously leaved his footprint for the soldiers in the camp to be a cherished possession and a great memorial of his royal visit.
Nowadays the footprint enshirine inside the royal footprint pavilion "Sala Roi Phra Bata " inside 3rd Battalion of Infantry , 17th Infantry Regiment of Her Royal Highness the Princess Mother, MengRaiMaharath Military Camp in Muang district ChiangRai province and open daily for people to have a visit.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 6,055
|
<?php
namespace Site\Factory\Action;
use Core\Action\ViewActionResult;
use Core\Service\MotFrontendIdentityProviderInterface;
use Dvsa\Mot\Frontend\PersonModule\View\ContextProvider;
use DvsaClient\MapperFactory;
use DvsaCommon\Csv\MotTestLogCsvGenerator;
use Interop\Container\ContainerInterface;
use Zend\Mvc\Router\Http\RouteMatch;
use Zend\ServiceManager\FactoryInterface;
use Site\Action\MotTestLog\IndexAction as SiteIndexAction;
use Site\Action\MotTestLog\CsvAction as SiteCsvAction;
use Zend\ServiceManager\ServiceLocatorInterface;
class MotTestLogActionFactory implements FactoryInterface
{
/**
* @param ServiceLocatorInterface $serviceLocator
*/
public function createService(ServiceLocatorInterface $serviceLocator)
{
return $this($serviceLocator, MotTestLogActionFactory::class);
}
public function __invoke(ContainerInterface $container, $requestedName, array $options = null)
{
/** @var RouteMatch $routeMatch */
$routeMatch = $container->get('Application')->getMvcEvent()->getRouteMatch();
$action = $routeMatch->getParam('action');
if ($action === 'downloadCsv') {
return new SiteCsvAction(
$container->get('Request'),
$container->get(MapperFactory::class),
$container->get(ContextProvider::class),
new MotTestLogCsvGenerator()
);
}
return new SiteIndexAction(
$container->get(MotFrontendIdentityProviderInterface::class),
$container->get('Request'),
$container->get(MapperFactory::class),
$container->get(ContextProvider::class),
new ViewActionResult(),
$container->get('AuthorisationService')
);
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 4,480
|
package org.bpmscript.loanbroker;
import java.io.Serializable;
/**
* Credit score dto for the loanbroaker
*/
public class CreditScore implements Serializable {
private int score;
private int hlength;
public CreditScore() {
}
public CreditScore(int score, int hlength) {
super();
this.score = score;
this.hlength = hlength;
}
public int getScore() {
return score;
}
public void setScore(int score) {
this.score = score;
}
public int getHlength() {
return hlength;
}
public void setHlength(int hlength) {
this.hlength = hlength;
}
}
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 106
|
Studio Lab
Teen Choreo Lab
For Artists & Educators
Building Cultures of Dance
With Schools & Organizations
Teachers Creating Change
lunadance
Rosemary Hannon
Rosemary first encountered Luna through founder Patricia Reedy when they were introduced at a Bay Area arts education providers' meeting in the early 2000s. At the time Rosemary was already a well-seasoned teaching artist, having taught music and dance in public schools through the arts education non-profit Young Imaginations since 1996. Luna's child-centered approach to creative dance education inspired her own teaching practice, and she found that the practical and theoretical training she received through Luna's Professional Learning workshops complemented her degree in arts-integrated teaching. Rosemary is woven into Luna's history and continuing legacy as a past faculty member 2005-07, as a Summer Institute alumna, and now as a colleague and fellow expert in the field.
A prolific artist and committed educator, Rosemary addresses her own creative identity by becoming actively involved in many facets of the Bay Area dance scene. From organizing dance events that build community, to cultivating much needed East Bay arts spaces through studio management, Rosemary, like many dancers, does a little bit of everything. But she has been most lauded for her choreography – her piece Gallus Gallus Domesticus was nominated for an Isadora Duncan Dance Award in 2013 – and for her teaching – she was recognized as an Outstanding Educator for Berkeley Unified School District in 2014.
Since 2007 she has been teaching standards-based dance at Berkeley's Cragmont Elementary, where she also collaborates with classroom teachers to support the integration of dance into other core subject areas. Selected as one of Luna's Leadership Cohort in 2015, Rosemary focused her inquiry on articulating dance goals to build a more comprehensive district-wide dance program in Berkeley Unified. She is a well-known local Contact Improvisation and Axis Syllabus teacher-candidate and the somatic inquiry of both practices inspires her investment in anatomy, biomechanics and physics. She continues "to be curious about the intersection of creative process and somatic inquiry" and how that manifests through technical training. She credits Luna for how she organizes her dance lessons and units. "The arc generally follows creative process cycles – exploration, improvisation, composition, performance, reflection."
Rosemary's long term impact on her students is clear from this story: Last year I was inspired by a student I had worked with who entered a grade level that I wasn't teaching. He loved dancing so much he started choreographing a dance for his whole class. His teacher followed his lead and helped the class practice so that they were able to perform his dance at one of our school assemblies.
In 25 years, Luna has worked with hundreds of teachers who we're now proud to say are teaching all around the globe.
From Emily Blossom to Jakey Toor, our past Professional Learning colleagues are collectively and cumulatively teaching tens of thousands of children. We're sharing their stories, about how they continue to positively impact the dance education field, the future, the world.
administrator@lunadanceinstitute.org
Site Credit: SQUARE M
Drawings: Valentina Alexander
Videos: Heather Stockton, Youth Uprising, Luna staff
Photos: Kreate Photography, Lauren Forbus, Michael Ertem, Lanny Weingrod, Marshall Berman, Luna staff & board
Copyright © 2020 Luna Dance Institute
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
| 5,130
|
{"url":"https:\/\/www.assignmentexpert.com\/homework-answers\/chemistry\/general-chemistry\/question-184524","text":"106 251\nAssignments Done\n97.5%\nSuccessfully Done\nIn May 2022\n\n# Answer to Question #184524 in General Chemistry for bubbles\n\nQuestion #184524\n\nGlauber\u2019s salt is a form of hydrated sodium sulfate, Na2SO4\u1427 xH2O(s), that is used medicinally as a mild laxative. Chemical analysis of this hydrate shows that it is 44.1% sodium sulfate. Determine the FORMULA and the NAME of this hydrate.\n\n1\n2021-04-25T23:11:43-0400\n\nQ184524\n\nGlauber\u2019s salt is a form of hydrated sodium sulfate,\u00a0Na2SO4\u1427\u00a0xH2O(s), that is used medicinally as a mild laxative. Chemical analysis of this hydrate shows that it is\u00a044.1% sodium sulfate. Determine the\u00a0FORMULA\u00a0and the\u00a0NAME\u00a0of this hydrate.\n\nSolution :\n\nIf there is 44.1 % of sodium sulfate in the salt,\n\nthen the remaining (100 - 44.1 ) = 55.9 % will be H2O.\n\nLet us consider that there are 100 grams of hydrated sodium sulfate.\n\nSince there is 44.1 % sodium sulfate, so 100 grams of hydrated sodium sulfate will contain\n\n44.1 grams of sodium sulfate and 55.9 grams of H2O.\n\nStep 1: To find moles of Na2SO4 and H2O present in 100 grams of hydrated salt.\n\nConvert 44.1 grams of Na2SO4 and 55.9 grams of H2O to moles by using their molar mass.\n\nMolar mass of Na2SO4 = 142.041 g\/mol\n\nMolar mass of H2O = 18.0148 g\/mol\n\n\"moles \\\\ of \\\\ Na_2SO_4 = 44.1 \\\\ \\\\bcancel{g \\\\ Na_2SO_4 } * \\\\frac{1 \\\\ mol \\\\ Na_2SO_4 }{142.041 \\\\bcancel{g \\\\ Na_2SO_4 }}\"\n\n\"= 0.3105 \\\\ mol \\\\ of \\\\ Na_ 2SO_4\"\n\n\"moles \\\\ of \\\\ H_2O= 55.9 \\\\ \\\\bcancel{g \\\\ H_2O } * \\\\frac{1 \\\\ mol \\\\ H_2O}{18.0148 \\\\bcancel{g \\\\ H_2O }}\"\n\n\"= 3.1030 \\\\ mol \\\\ of \\\\ H_2O\"\n\nFor finding the number 'x' . We will divide moles of both by the one with the least number of moles.\n\nHere Na2SO4 has least number of moles.\n\n\"For Na_2SO_4 , \\\\ \\\\ \\\\ \\\\ \\\\ \\\\frac{0.3105 \\\\ mol }{0.3105 \\\\ mol } = 1\"\n\n\"For H_2O , \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\frac{3.1030 \\\\ mol }{0.3105 \\\\ mol } = 9.994 \\\\ \\u2248 \\\\ 10\"\n\nSo for each mole of Na2SO4, there is 10 mole of H2O.\n\nSo x = 10.\n\n### The formula of the hydrated salt will be Na2SO4.10 H2O.\n\nThere are 10 water molecules in this formula. For denoting the number of hydrated water molecules we will use the prefix ' deca' .\n\n10 means deca.\n\nSo the name of the compound will be\n\n### Sodium sulfate decahydrate.\n\nNeed a fast expert's response?\n\nSubmit order\n\nand get a quick answer at the best price\n\nfor any assignment or question with DETAILED EXPLANATIONS!","date":"2022-05-23 11:46:11","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\": 1.0000100135803223, \"perplexity\": 8668.005749029393}, \"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-2022-21\/segments\/1652662558015.52\/warc\/CC-MAIN-20220523101705-20220523131705-00253.warc.gz\"}"}
| null | null |
\section{Introduction}
The discovery of graphene is intimately related to the first
measurements of the integer quantum Hall effect in this material
system.\cite{Novos2005,Zhang2005} It was observed as early as 2005
that the integer quantum Hall effect shows an anomalous sequence of
Hall plateaus in the Hall conductivity $\sigma_{xy} = 4(k+1/2)\,e^2/h$
due to the graphene-specific Berry phase that finds its origin in the
bipartiteness of the honeycomb lattice. This is a crucial difference
from quantum Hall effect measurements in more established material
systems such as two-dimensional electron gases (2DEGs) in
semiconductor heterostructures.
A second distinction between the quantum Hall effect in graphene and
that in ordinary 2DEGs is suggested by two terminal conductance studies on
narrow ribbons, \cite{PhysRevLett.107.086601,Schmidmeier} where
conductance quantization was interpreted in quantum Hall terms,
even though the ribbons are narrower than the typical separation
between edge states in a 2DEG. To confirm the validity of this
interpretation, we have fabricated a 60-nm-wide graphene Hall bar,
allowing for proper four terminal measurement of $R_{xy}$ and
confirming that quantum Hall edge states do survive even in such
narrow devices in graphene.
In order to reconcile these observations with the conventional picture
of edge-state separation, we need to recall the physics of edge states in ordinary 2DEGs. The first detailed description of
edge-state transport in the quantum Hall regime was provided by
Halperin \cite{Halperin} using a noninteracting electron
picture. While this model is useful in describing much of the relevant
physics, it was subsequently found that such a picture does not in
general properly account for the position of the edge states. A more
exact description emerges when considering the influence of
electrostatic interactions between the electrons that form the quantum
Hall state and the surrounding electrons in the substrate and the
nearby metallic gates. In ordinary 2DEGs, it is well established that
these electrostatic interactions lead to the formation of compressible
and incompressible strips.\cite{Chklovskii:1992vg,Chklovskii:1993cw} Indeed, the effect of
electrostatic interactions is of such importance that, in many cases,
the single-particle picture fails to provide even a qualitative
description of experiment. The situation is different in narrow
graphene structures, where, as our zero-free-parameter model shows,
the relevant length scale for the single-particle picture --- the
magnetic length $l_B=\sqrt{\hbar/eB}$ --- is similar to the width of
the compressible and incompressible strips.
\section{Experimental part}
A scanning electron micrograph (SEM) of our sample is shown in
Fig.~\ref{fig:SEM}. It is made from single-layer graphene flakes
exfoliated from an HOPG block onto a highly p-doped Si substrate
having a $285$\,nm thick SiO$_2$ cap layer. After contacting Ti$/$Au electrodes, these flakes are etched in an Ar$/$O$_2$ plasma to
obtain narrow Hall bars with six terminals. To reduce residual
contaminations, the etched structure is annealed at $200\,^\circ$C in
forming gas for about 2 h. The sample is studied at the base
temperature of a dilution refrigerator using standard low-noise ac
measurement techniques.
\begin{figure}
\centering
\includegraphics{SEM.eps}
\caption{(Color online) SEM image of a plasma patterned six-terminal graphene
Hall bar with $w=60$\,nm and $l=250$\,nm.}
\label{fig:SEM}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{sigmaxy.eps}
\caption{(Color online) Hall conductivity $\sigma_{xy}$ as a function of gate voltage $V_g$ and Landau level filling factor $\nu= h/(e^2 B) C_g(V_g-V_g^D)$ at $B=11$\,T and $30$\,mK. (Figure adapted from Ref. \onlinecite{Duerr2012}.)}
\label{fig:sigmaxy}
\end{figure}
Preliminary characterization of the sample is done at $4.2$\,K, where,
as typical for ribbons of width below $100$\,nm, the conductance $G$
of the sample is strongly suppressed in the vicinity of the charge
neutrality point, which is at $V_g^D\approx7.5$\,V. At high electron
and hole concentrations, the field-effect mobility of the charge
carriers is $\mu=\frac{l}{2a_rC_g} \frac{dG}{dV_g} \approx
1500$\,cm$^2/$Vs, where the effective gate capacitance
$C_g\approx210$\,$\mu$F$/$m$^2$ is determined from Hall measurements
at various gate voltages $V_g$. This corresponds to a diffusion
constant of $D\simeq 0.01$\,m$^2/$s and a mean free path of $l_m
\simeq 20$\,nm. Such small values are typical for plasma-etched
graphene nanoribbon devices and are a consequence of the great amount
of edge disorder in these systems.\cite{Molitor:2011gz}
We recently observed the quantum Hall effect in very narrow graphene wires.\cite{Duerr2012} A representative example of such a measurement is shown in Fig.~\ref{fig:sigmaxy}, where we plot the measured Hall conductivity
$\sigma_{xy}$ as a function of the back-gate voltage $V_g$ and filling
factor $\nu=\pm4(k+1/2)$ at $B=11$\,T. The occurrence of conductance
plateaus at $k= 0$, $1$, and $2$ is typical for Dirac fermions and
clearly confirms that our sample is mono layer graphene. In general,
$\sigma_{xy}$ plateaus are well developed if the energy spacing
between the corresponding Landau levels is much larger than their
broadening $\Gamma$. In graphene the former, given by
Eq.~\eqref{eq:8}, decreases with increasing filling (i.e., the index
$k$), whereas the broadening $\Gamma=\hbar v_F/l_m\simeq 30$\,meV is
constant. This explains why only the $k=0$, $1$, and $2$ plateaus are
visible up to $B=11$\,T, with the $k=0$ plateaus being most pronounced. We found this observation remarkable in view of previous experience with (Al,Ga)As--based structures. Therefore, we decided to investigate the electrostatics of the edge channels in more detail, which is presented in the next sections.
\section{Theoretical part}
From a theoretical point of view, the essence of our device is an
etched graphene ribbon separated from a metallic back gate by an
insulating SiO$_2$ layer. We note that the thickness, of the gate
insulator is a significant parameter because, for very thin thicknesses
tunneling becomes as important as electrostatic effects. Our geometry
is therefore fundamentally different from the one used in recent STM
studies of the spacial extent of edge channels in graphene resting
directly on graphite, where the thickness of the gate insulator is
basically 0 (i.e., the distance between the graphene and the graphite
substrate).\cite{Guohong}
We now examine the consequences of our geometry on the accepted models
by Chklovskii, Shklovskii, and Glazman (CSG) \cite{Chklovskii:1992vg}
as well as Chklovskii, Matveev, and Shklovskii (CMS).\cite{Chklovskii:1993cw} In the electrostatic theories of CSG and
CMS, a 2DEG is laterally confined by electric fields originating from
gate electrodes which are in plane with the 2DEG. In the absence of
magnetic fields, the electrostatic solution of such a two-dimensional
problem was provided by Larkin and Shikin.\cite{Larkin:1990wr} They
find a charge density distribution which reduces from its bulk value
to 0 at the boundary of the electron gas. Although the confinement
of mobile electrons in these models is generated by gates, the authors
of Refs.~\onlinecite{Chklovskii:1993cw,Chklovskii:1992vg} argue that their
results also apply to etched structures of conventional
heterostructures. This is justified by surface states which lead to
Fermi level pinning and negative charges accumulate at the edges.
Inner electrons are repelled, yielding the same depletion effect as
split gates. However, as shown by Silvestrov and Efetov (SE),
\cite{Silvestrov:2008bk} the situation is substantially different in
the case of a graphene nanoribbon. Since the edges of this
two-dimensional
material end abruptly, they act as hard- instead of
soft-wall boundaries. Assuming a constant electrostatic potential in a
ribbon positioned in the $xz$ plane, such that in the transverse
$x$ direction no electric force acts on its excess electrons, SE
derived an expression for the charge density. If the ribbon width
$2a_r$ is smaller than the gate dielectric thickness $b$, the electron density
across the ribbon is, to a good approximation, given by
\cite{Silvestrov:2008bk}
\begin{equation}
\label{eq:1}
\rho(x,y) = \frac{\sigma}{\pi}\frac{\delta(y)}{\sqrt{a_r^2-x^2}}\left\{1-C_2\left(\frac{a_r}{b}\right)^2\left(\frac{2x^2}{a_r^2}-1\right)\right\}\,,
\end{equation}
where $ C_2 \equiv \sum_{n=1}^{\infty}
\frac{\epsilon}{1-\epsilon}\,\left(\frac{1-\epsilon}{1+\epsilon}\right)^n\frac{1}{4n^2}$ is
a numerical constant \cite{Note1}
that, for a dielectric constant $\epsilon \simeq 3.9$ as in the case of ${\rm SiO}_2$, has a value of 0.175. The charge per unit length
$\sigma$ is linearly related
to the back-gate potential $V_g$,\cite{Silvestrov:2008bk}
\begin{equation}
\label{eq:3}
V_g =\frac{4\sigma}{\epsilon+1}\left\{
\ln{\frac{4b}{a_r}} + C_0+\left(\frac{a_r}{b}\right)^2\,C_2\right\}\,,
\end{equation}
with
$ C_0 \equiv
\sum_{n=2}^{\infty}\frac{2\epsilon}{1-\epsilon}\left(\frac{1-\epsilon}{1+\epsilon}\right)^n\ln
n$.
The inverse-square-root edge singularity in Eq.~\eqref{eq:1} is in stark contrast to the soft density profiles
($\rho\sim\sqrt{x}$) predicted at the edges of conventional
heterostructures.\cite{Chklovskii:1993cw,Chklovskii:1992vg,Larkin:1990wr} In the
following, we analyze the impact of this diverging density
distribution on the formation of compressible and incompressible
strips in graphene.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]
{Filling.eps}
\caption{(Color online) Schematic of the compressible and incompressible strips in graphene, showing the
electron density $\propto n(x)$ and the Landau levels with their
local fillings. In (a) the ribbon is in a C state with a
compressible strip at its center whereas in (b) it is in an I state with
an incompressible strip in the middle. The regions near the edges of the ribbon where the Landau levels
increase very sharply due to hard-wall confinement are not shown.
In these regions of size $\sim l_B$ away from the edges, the
electrostatic analysis is no longer applicable.\cite{Note2}
}
\label{fig:C-I-state}
\end{figure*}
The formulas above are valid for any metallic strip with a hard-wall
boundary. The graphene-specific physics comes into play with quantum
effects. Evidently, the Pauli principle prevents the excess electrons
from all being in the same state. When the Fermi wavelength varies
slowly on the considered length scale (here the width of the ribbon),
one can divide the system into many elements of sizes where
equilibrium thermodynamics is still applicable. By using this
Thomas-Fermi approximation, SE defined a local Fermi momentum for each
element and derived a relation between the inhomogeneous charge
density given by Eq.~\eqref{eq:1} and the potential felt by an
individual electron. At zero temperature and in the limit of rather
narrow ribbons ($a_r \ll b$), the curly bracket in Eq.~\eqref{eq:1}
reduces to $1$, and the potential has the form
\begin{equation}
\label{eq:5}
U(x) =
-\hbar\,v_F\,\sqrt{\sigma/e}\left(\frac{1}{a_r^2-x^2}\right)^{1/4}\,,
\end{equation}
with $v_F$ the Fermi velocity in graphene. The derived expression is
valid at distances $\delta x \gtrsim
a_r^{1/3}\left(\frac{e}{\sigma}\right)^{2/3}$ from the strip edges, where the Thomas-Fermi approximation is applicable. This
potential should be viewed as a quantum correction to the electrostatic
potential and describes locally the energy difference between the
constant Fermi energy and the Dirac point.
Knowing the electron distribution and the potential in a graphene
ribbon, we can now adapt the CMS formalism to graphene. Making use of
the semiclassical electrostatic picture described above, we expect,
for a finite magnetic field, the
scenario sketched in Fig.~\ref{fig:C-I-state}. As in the case of the
2DEG in Ref.~\onlinecite{Chklovskii:1993cw}, the electron density $\sim
n(x)$ in our graphene ribbon is divided into alternating compressible
and incompressible strips. The latter are characterized by filled
Landau levels and describe local unscreened regions in which electrons
have no possibility to reorder. This is due to the large energy gap
they must overcome in order to find unoccupied states in one of the
nearby empty levels. On the other hand, compressible strips are
characterized by partially filled Landau levels residing at the Fermi
level. The many unoccupied states allow for the electrons to
rearrange and minimize their energy such that the electric field is
locally screened. In general, two situations are possible. In
Fig.~\ref{fig:C-I-state}(a), we show a C state
that describes a central compressible strip in the $k$-th Landau
level which is partially filled near $x=0$. Upon decreasing the magnetic
field strength or increasing the density of excess charges, the $k$-th
Landau level gets filled and the ribbon is driven into an I state with
an incompressible strip at the center [cf.~Fig.~\ref{fig:C-I-state}(b)].
\begin{table}[b]
\caption{\label{tab:1} Experimental parameters used in the modeling.}
\begin{center}
\begin{tabular}{l|r}
\hline
Quantity & Value \\
\hline
Magnetic field $B$ & $11\,\mathrm{T}$ \\
Insulator dielectric constant $\epsilon$ & $3.9$, $\mathrm{SiO}_2$ \\
Thickness of insulator $b$ & $0.3\,\mu\mathrm{m}$ \\
Half-width of graphene ribbon $a_r$ & $30\,\mathrm{nm}$\\
Back-gate potential $V_g$ & $-20$ to $35$ V\\
\hline
\end{tabular}
\end{center}
\end{table}
\section{Results}
The basic formalism used in Ref.~\onlinecite{Chklovskii:1993cw} to determine the widths and
positions of the compressible and incompressible strips in a gate
confined 2DEG is also valid in
graphene nanoribbons. Imposing the same requirements on the
electrostatic boundary conditions as within the framework of the CMS
model, and solving for our geometry leads to the following set of equations:
\begin{align}
\label{eq:1a}
\left[\nu(0)-4(k+1/2)\right]n_L+n''(0)\frac{a^2+a'^2}{4} &= 0\,,
\end{align}
\begin{multline}
-\frac{2\,\pi\, e\, n''(0)\,
a}{3(\epsilon+1)}\left\{(a^2+a'^2)E\left[\sqrt{1-(a'/a)^2}\right]-\right.\\\left.-2(a')^2K\left[\sqrt{1-(a'/a)^2}\right]\right\}
= -\mu_k\,,\label{eq:1b}
\end{multline}
\begin{align}
\nu(0)-\nu_B(0) &= -\frac{n''(0)(a-a')^2}{4n_L}\nonumber\\ &= \frac{(a-a')^2}{a^2+a'^2}\left[\nu(0)-4(k+1/2)\right]\,.\label{eq:1c}
\end{align}
Here, $E$ and $K$ are elliptic integrals, and the quantities $a$ and
$a'$ determine the positions and widths of the compressible and
incompressible strips next to $x=0$. The
energy difference,
\begin{equation}
\mu_k\equiv
\frac{\hbar v_F}{l_B}\left(\sqrt{2(k+1)}-\sqrt{2k}\right)\,,\label{eq:8}
\end{equation}
is that of adjacent Landau levels (see Fig.~\ref{fig:C-I-state}) and
depends on the index $k$, the Fermi velocity $v_F$, and the magnetic
length $l_B=\sqrt{\hbar/eB}$. The occupation number of these levels is
defined by $\nu_B(0) \equiv n_B(x=0)/n_L$, with $n_B(0)$ the electron
concentration at magnetic field strength $B$ in the center of the
ribbon, and $n_L \equiv 1/2\pi l_B^2$ the Landau level degeneracy.
Furthermore, we define $\nu(0) \equiv n(x=0)/n_L$, with $n(x)$ the
electron concentration in the absence of a magnetic field, which can be
extracted from $\rho(x,y) = e\,n(x)\, \delta(y)$ via Eq.~\eqref{eq:1}.
\begin{figure}[t]
\centering
\includegraphics[width=0.43\textwidth]{PlateauWidth.eps}
\caption{(Color online) Top: Two-terminal conductance plateau
corresponding to Landau level index $k=0$, plotted over the back-gate
voltage $V_g$. The charge neutrality point is at $V_g^D$, and the
dashed line indicates $G_0$. Bottom: The position and width of the
compressible and incompressible strips are plotted, which, in
Fig.~\ref{fig:C-I-state}, correspond to the occupation level
$4(k+1/2)\,n_L$ with $k=0$. The dashed-dotted line shows $a$, the
outer edge position; the solid line shows $a'$, the inner edge
position of the incompressible strips. In the upper graph the
suppressed contribution of distant incompressible strips to the conductance
at the I-C transition is incorporated, whereas in the lower
graph it is neglected, resulting in a slight mismatch in width of the
shaded areas.
}
\label{fig:plateau}
\end{figure}
Taken together, Eqs.~\eqref{eq:1a}, \eqref{eq:1b}, and \eqref{eq:1c}
represent a complete system from which the quantities $a$, $a'$, and
$\nu_B(0)$ can be derived. The latter is linearly related to the two-terminal conductance \cite{Chklovskii:1993cw} via
\begin{equation}
\label{eq:7}
G = \frac{e^2}{h}\nu_B(0)\,.
\end{equation}
In order to analyze the results provided by this model, we use the experimental parameters listed in
Table~\ref{tab:1}, and solve for $a$, $a'$, and $\nu_B$.
Since Eqs.~\eqref{eq:1a}, \eqref{eq:1b}, and \eqref{eq:1c} are
derived under the assumption that $n(x) \simeq n(0)+\frac{1}{2}n''(0)\,x^2$, we are
limited to a parameter range where this
approximation is valid. This is ensured when $a$ and $a'$ are
small compared to $a_r$ which is the case at the transition from a C
to an I state caused by increasing the doping or decreasing the
magnetic field. In the upper graph in Fig.~\ref{fig:plateau}, we show the
conductance plateau which corresponds to the Landau level with index
$k=0$. From the electrostatic point of view, incompressible strips
next to $x=0$, characterized by local regions with an additional
charge accumulation, are described by dipolar strips.\cite{Chklovskii:1992vg} Although the calculated charge density
distribution, Eq.~\eqref{eq:1}, is not altered on a rough scale at any
reasonable magnetic field, the formation of such strips leads to a
small enhancement in charge concentration at $x=0$. Thus, it is reasonable that the conductance,
given by Eq.~\eqref{eq:7}, lies above the dashed line, which indicates
$G_0\equiv\frac{e^2}{h}\nu(0)$. From the lower graph in Fig.~\ref{fig:plateau}, we can read
off the positions and widths of the compressible and incompressible
strips which correspond to the occupation level $4(k+1/2)\,n_L$ with
$k=0$. In the C state, before the formation of the conductance
plateau, the incompressible strips next to the central compressible
one have a width of $\sim 9\text{ nm ... }14\text{ nm}$. This, however,
contradicts a crucial assumption of the electrostatic model,\cite{Chklovskii:1993cw}
\begin{equation}
\label{eq:9}
l_B\sqrt{k} \ll (a-a')\,.
\end{equation}
For the quasi classical electrostatic treatment above to be
justified, the size of the electron wave function determined by the
magnetic length should be much smaller than the length scales provided
by the widths of the compressible and incompressible strips. Since
$l_{B=11T} \sim 8$ nm, our experiment is in the crossover regime
to the conventional single-particle picture of ballistic transport.\cite{1990PhRvB..41.7906B} The latter is mandatory at high quantum
numbers $k$ where condition \eqref{eq:9} is strongly violated. For the
first several plateaus, however, the electrostatic model which results
in Eqs.~\eqref{eq:1a}, \eqref{eq:1b}, and \eqref{eq:1c} is still relevant, as Eq.~(\ref{eq:9}) is approximately valid. Also note that the widths of incompressible strips
located at $x_k$
scale as $\sim1/\sqrt{n'(x_k)}$.\cite{Chklovskii:1992vg} Thus, for narrow
ribbons with large $n'(x_k)$ and therefore small $a-a'$, condition
\eqref{eq:9} is violated much earlier as for wide ribbons with
expanded incompressible strips. Furthermore, since $n'(x_k)$ increases
as we approach the edges, the spatial extent of the edge states within
the electrostatic picture is much narrower in our graphene ribbon
compared to $l_B$. Hence, we show that the CSM picture of
transport in the quantum Hall regime breaks down here and the simpler single-particle
picture not only suffices but, indeed, is essential to correctly describe the physics.
\section{Comparison of theory and experiment}
Comparing the data on the $k=0$ plateau, corresponding to filling
factor $\nu=2$ in Fig.~\ref{fig:sigmaxy}, with the theoretical result
given in Fig.~\ref{fig:plateau}, we find discrepancies in width and
location, both measured in units of the back-gate voltage. Our
electrostatic model leads to very
narrow plateaus occurring at gate voltages which are too small by a
factor of $\sim3$ to $4$. This disagreement is consistent with theory overestimating the gate capacitance, which is a commonly observed discrepancy in graphene nanoribbons.\cite{Lian2010}
The narrowness of the theoretically derived plateaus compared to their experimental widths
can be explained by disorder, which is certainly present in the device, but
neglected in our model. As realized in
Refs.~\onlinecite{Chklovskii:1993cw,Chklovskii:1992vg}, disorder leads to
localization in a compressible liquid a low small enough density, such
that at the I to C state transition there is a range of voltage
where Landau levels which locally (in the vicinity of $x=0$) start to
fill up cannot contribute to the conductance.
\section{Conclusions}
We have performed four terminal transport measurements on
a 60-nm-wide Hall bar of graphene. Our results validate the interpretation that the
Hall effect is responsible for the quantized conductance in narrow
ribbons. A quantitative study of the electrostatics of graphene
nanoribbons, and its implication for the spatial extent of edge states in such devices,
confirms that, indeed, the formation of compressible and incompressible
strips which dominate the physics of traditional 2DEG devices is
of minor importance here. Instead, the single-particle picture is more
appropriate.
\acknowledgements
B.T. would like to thank Misha
Fogler for interesting discussions at the KITP in Santa Barbara. This work was supported by the DFG in the framework of the strategic Japanese-German cooperative program and the European Science Foundation (ESF) under the EUROCORES Program EuroGRAPHENE.
\providecommand{\href}[2]{#2}
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{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,878
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Q: Probability. Solving equation with distribution function Distribution function is given
$$D(x)= \begin{cases}0, \text{ if } x<0 \\ \frac{x}{5}+\frac{1}{5} \text{ if } 0 \leq x <3 \\ 1, \text{ if } x \geq 3 \end{cases}$$
We need to find $D_1$ - discrete distribution function and $D_2$ - continuous distribution function that equation $$D=p D_1+(1-p)D_2$$ will be correct with chosen $p\in(0,1).$
So I think continuous distribution function should be found $D_2= D'(x)$, but how to find discrete distribution function and find p?
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 3,963
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Paulig eller Oy Gustav Paulig Ab er en finsk fødevarekoncern. Virksomheden er specialiseret indenfor import af kolonialvarer som kaffe, te, kakao og krydderier. I 2012 var Pauligs omsætning på 858 mio. Euro og der var 1.846 ansatte. Hovedkvarteret ligger i Helsinki. Der satses primært på markedet i Norden og Nordeuropa.
Historie
Grundlæggeren konsul Gustav Paulig (1850–1907) stammede fra Lübeck. Hans søn Eduard Paulig (1889–1953) udviklede ristningsteknikkerne og etablerede direkte kontakter i de kaffeproducerende lande. Dennes søn Henrik Paulig (1915–1982), som var i spidsen for virksomheden fra 1947 til 1973, udvidede aktiviteterne betydeligt.
Paulig fremstiller kaffeprodukter, is, te og krydderier. Paulig var først i Finland med et industrielt kafferisteri (1904) og i 1942 grundlagde de Nordens første fryseanlæg til dybfrost af fødevarer. Denne forretning var man ene om i Finland frem til 1987. Under 2. verdenskrig blev kaffeimporten sat helt i bero.
I 1971 afstod virksomheden sin handel med kolonialvarer og investerede i stedet for i rederivirksomhed.
Siden 1989 har Paulig markedsført Santa Maria krydderier i Finland og de ejer Lihel Oy, som i Esbo fremstiller krydderier til industrien. I 2005 opkøbte Paulig en norsk krydderifabrik. Virksomheden har en krydderifabrik i Danmark og en andel i et et kafferisteri i Norge.
Ekstern henvisning
Pauligs website
Fødevarevirksomheder fra Finland
Virksomheder i Helsinki
Etableret i 1876
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{
"redpajama_set_name": "RedPajamaWikipedia"
}
| 5,362
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Q: c# httpclient - disable ntlm I'm using this code to connect to a third party server.
using (HttpClientHandler httpClientHandler = new HttpClientHandler())
{
httpClientHandler.AllowAutoRedirect = false;
httpClientHandler.Credentials = new NetworkCredential(login, password);
using (HttpClient authClient = new HttpClient(httpClientHandler))
{
response = await authClient.GetAsync(authenticationUrl).ConfigureAwait(false);
... response processing here
}
}
The third party server is an appliance, and they've turned on NTLM recently. Starting with the turning on of NTLM, my request now gets an HTTP 500 error error like this:
type Exception report message NTLM specified. Downgraded to Basic
Auth (and/or SSL) but downgrade not supported. description The server
encountered an internal error that prevented it from fulfilling this
request. exception java.lang.UnsupportedOperationException: NTLM
specified. Downgraded to Basic Auth (and/or SSL) but downgrade not
supported.
net.sourceforge.spnego.SpnegoProvider.negotiate(SpnegoProvider.java:146)
net.sourceforge.spnego.SpnegoAuthenticator.authenticate(SpnegoAuthenticator.java:271)
net.sourceforge.spnego.SpnegoHttpFilter.doFilter(SpnegoHttpFilter.java:229)
I'm assuming my httpclient sees that the server now supports NTLM and tries to do NTLM. Is there any way to tell my httpclient to don't even bother with NTLM?
A: To disable NTLM try this:
var modules = AuthenticationManager.RegisteredModules;
while (modules.MoveNext())
{
var module = (IAuthenticationModule) modules.Current;
if (module.AuthenticationType == "NTLM")
{
AuthenticationManager.Unregister(module);
break;
}
}
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{
"redpajama_set_name": "RedPajamaStackExchange"
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| 1,056
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Missouri Ozarks commercial property for sale in West Plains, Missouri. (BUSINESS IS NOT FOR SALE, PROPERTY ONLY) This 3.42 acres includes Railroad Spur and Switch and a 24,260 square foot warehouse with offices, storage areas, and meeting rooms with parking.Major visibility with Business 63 Road Frontage as well as Howell and College Ave. This property is located in an industrial area of West Plains, MO and offers city water and sewer. Easy access to Hwy 63. This location can be purchased with all above or mainly vacant ground with 2.33 acres with Business 63 Frontage for only $799,900.Prefect for Industrial, Warehouse, Retail, Multi Family and More!
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{
"redpajama_set_name": "RedPajamaC4"
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| 9,521
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Greg Brkich (né le ) est un homme politique provincial canadien de la Saskatchewan. Il représente la circonscription de Arm River à titre de député du Parti saskatchewanais depuis 1999.
Biographie
Né à Bladworth en Saskatchewan, Brkich entame sa carrière politique en remportant les élections de 1999 dans Arm River, réélu dans Arm River-Watrous en 2003, 2007 et en 2011, il est à nouveau en 2016 dans la nouvelle circonscription de Arm River.
Il est leader du gouvernement à l'Assemblée législative de la Saskatchewan d'août 2017 à août 2019.
Résultats électoraux
Références
Liens externes
Naissance en décembre 1958
Député du Parti saskatchewanais
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{"url":"https:\/\/research.wmz.ninja\/articles\/2017\/03\/crbs-in-classical-doa-estimation-problems.html","text":"# Mianzhi Wang\n\nPh.D. in Electrical Engineering\n\n# Cram\u00e9r-Rao Bounds in Classical Direction of Arrival Estimation Problems\n\nThe problem of direction-of-arrival (DOA) estimation is to find the directions of impinging far-field narrow-band signals using a sensor array (either acoustic or electromagnetic), as illustrated in the figure below. It is a classical problem in the field of array signal processing. For a comprehensive understanding of this field, it is recommended to check Dr. Van Trees's book Optimum Array Processing[1].\n\nFor a linear array, the time-domain snapshot model can be written as\n\n$\\mathbf{y}(t) = \\mathbf{A}(\\mathbf{\\theta})\\mathbf{s}(t) + \\mathbf{n}(t), t = 1,2,\\ldots,T,$\n(1)\n\nwhere $\\mathbf{\\theta} = [\\theta_1, \\theta_2, \\cdots, \\theta_K]^T$ denotes the DOAs, $\\mathbf{y}(t) \\in \\mathbb{C}^M$ denotes the snapshot vector, $\\mathbf{A}(\\mathbf{\\theta}) \\in \\mathbb{C}^{M\\times K}$ denotes the array steering vector, $\\mathbf{s}(t) \\in \\mathbb{C}^K$ denotes the source signal, and $\\mathbf{n}(t) \\in \\mathbb{C}^M$ denotes the additive measurement noise. For a linear array whose sensors are located at $\\mathcal{D}=\\{d_1, d_2, \\ldots, d_M\\}$, the steering matrix can be written as\n\n$\\mathbf{A}(\\mathbf{\\theta}) = [\\mathbf{a}(\\theta_1), \\mathbf{a}(\\theta_2), \\cdots, \\mathbf{a}(\\theta_K)],$\n\nwhere\n\n$\\mathbf{a}(\\theta_k) = \\Big[\\exp\\Big(-j\\frac{2\\pi}{\\lambda}d_1 \\sin\\theta_k\\Big), \\exp\\Big(-j\\frac{2\\pi}{\\lambda}d_2 \\sin\\theta_k\\Big), \\cdots, \\exp\\Big(-j\\frac{2\\pi}{\\lambda}d_M \\sin\\theta_k\\Big)\\Big]^T,$\n\nand $\\lambda$ denote the wavelength of the narrow-band signals.\n\nExample: For a uniform linear array (ULA), the sensor locations are given by $\\mathcal{D}=\\{0, d_0, \\ldots, (M-1)d_0\\}$, where $d_0$ is usually chosen to be $\\lambda\/2$ to avoid grating lobes.\n\nGiven the measurement model (1) and further assumptions on the statistics of $\\mathbf{s}(t)$ and $\\mathbf{n}(t)$, the problem of finding the DOAs becomes a parameter estimation problem. One straight-forward approach is to use the maximum likelihood estimator (MLE). There also exists many other DOA estimation algorithms. Classical ones include beamforming, MUltiple SIgnal Classification (MUSIC)[2], Estimation of Signal Parameters via Rotational Invariance (ESPRIT)[3]. Recent developed ones include sparsity based algorithms and super resolution based algorithms[4].\n\nIn parameter estimation problems, one of the important concepts is the Cram\u00e9r-Rao Bound (CRB), which gives the lower bound of the variance of unbiased estimators. The CRB can be very useful in performance analysis, as well as in assessing the statistical efficiency of unbiased estimators. Compact expressions of the CRBs for the classical DOA estimation problem based on (1) were first derived and analyzed by P. Stoica and A. Nehorai[5][6][7]. We will review these classical results as follows.\n\nConcerning (1), there are two commonly used data model[7]:\n\n1. Conditional\/deterministic model: the source signals $\\mathbf{s}(t)$ are assumed to be nonrandom, and deterministic unknown.\n2. Unconditional\/stochastic model: the source signals $\\mathbf{s}(t)$ are assumed to be random and unknown.\n\nWe further make the following assumptions:\n\n1. The $K$ DOAs are distinct.\n2. The additive noise is white circularly symmetric complex Gaussian noise, and temporarily uncorrelated.\n3. The source signal sequence $\\mathbf{s}(t)$ are temporarily uncorrelated.\n4. The source signals and the additive noise are spatially and temporarily uncorrelated.\n\nFor the unconditional model, we further assume that $\\mathbf{s}(t)$ follows the circularly symmetric complex Gaussian distribution with zero mean and non-singular covariance matrix $\\mathbf{P}$.\n\nFor the conditional model,\n\n$\\mathbf{y}(t) \\sim \\mathcal{CN}(\\mathbf{A}\\mathbf{x}(t), \\sigma^2\\mathbf{I}).$\n(2)\n\nThe unknown parameters are\n\n$\\mathbf{\\eta}_\\mathrm{C} = [\\theta_1, \\cdots, \\theta_K, \\Re(x(1)), \\Im(x(1)), \\cdots, \\Re(x(T)), \\Im(x(T)), \\sigma^2] \\in \\mathbb{R}^{K+2T+1}.$\n(3)\n\nTheorem 1. Under the aforementioned assumptions, the CRB of the DOAs for the conditional model is given by[5]:\n\n$\\mathrm{CRB}_\\mathbf{\\theta}^\\mathrm{C} = \\frac{\\sigma^2}{2T} \\big\\{\\Re[\\mathbf{H} \\circ \\hat{\\mathbf{P}}^T]\\big\\}^{-1},$\n(4)\n\nwhere $\\circ$ denotes the Hadamard product, and\n\n\\begin{aligned} \\mathbf{H} &= \\dot{\\mathbf{A}}^H [\\mathbf{I} - \\mathbf{A}(\\mathbf{A}^H\\mathbf{A})^{-1}\\mathbf{A}^H]\\dot{\\mathbf{A}}, \\\\ \\dot{\\mathbf{A}} &= \\begin{bmatrix} \\frac{\\partial\\mathbf{a(\\theta_1)}}{\\partial\\theta_1} & \\frac{\\partial\\mathbf{a(\\theta_2)}}{\\partial\\theta_2} & \\cdots & \\frac{\\partial\\mathbf{a(\\theta_K)}}{\\partial\\theta_K} \\end{bmatrix}, \\\\ \\hat{\\mathbf{P}} &= \\frac{1}{T}\\sum_{t=1}^T \\mathbf{x}(t)\\mathbf{x}^H(t). \\end{aligned}\n\nFor the unconditional model,\n\n$\\mathbf{y}(t) \\sim \\mathcal{CN}(\\mathbf{0}, \\mathbf{A}\\mathbf{P}\\mathbf{A}^H + \\sigma^2\\mathbf{I})$\n(5)\n\nThe unknown parameters are\n\n$\\mathbf{\\eta}_\\mathrm{U} = [\\theta_1, \\cdots, \\theta_K, \\cdots, \\Re(P_{ij}), \\Im(P_{ij}), \\cdots, \\sigma^2] \\in \\mathbb{R}^{K+K^2+1}.$\n(6)\n\nTheorem 2. Under the aforementioned assumptions, the CRB of the DOAs for the unconditional model is given by[7]:\n\n$\\mathrm{CRB}_\\mathbf{\\theta}^\\mathrm{U} = \\frac{\\sigma^2}{2T} \\big\\{\\Re[\\mathbf{H} \\circ (\\mathbf{P}\\mathbf{A}^H\\mathbf{R}^{-1}\\mathbf{A}\\mathbf{P})^T]\\big\\}^{-1},$\n(7)\n\nwhere $\\mathbf{R}=\\mathbf{A}\\mathbf{P}\\mathbf{A}^H + \\sigma^2\\mathbf{I}$, and $\\mathbf{H}$ follows the same definition as in Theorem 1.\n\nNote: In the original paper, (7) is obtained from the asymptotic ($T\\gg 0$) covariance matrix of the unconditional MLE. P. Stoica et. al. also gave a textbook derivation later on[8].\n\nRecently, there is a renewed interest in sparse linear arrays (thinned ULAs, such as minimum redundancy linear arrays[9][10]) with the development of nested arrays[11] and co-prime arrays[12]. When the sources are uncorrelated, these arrays have the capability of identifying more sources than the the number of physical sensors ($K > M$) under the unconditional model. However, careful inspection of (7) reveals that $\\mathrm{CRB}^\\mathrm{U}_\\mathbf{\\theta}$ does not exist when $K > M$ because $\\mathbf{A}^H\\mathbf{A}$ becomes singular. Hence, we cannot use (7) to characterize the performance of these sparse linear arrays when $K > M$. Note that the derivation of (7) assumes a general source covariance matrix $\\mathbf{P}$ and does not make use of the prior knowledge that the sources are uncorrelated. If we further assume the sources are uncorrelated in the unconditional model, the unknown parameters become:\n\n$\\mathbf{\\eta}_\\mathrm{UU} = [\\theta_1, \\cdots, \\theta_K, p_1, \\cdots, p_K, \\sigma^2] \\in \\mathbb{R}^{2K+1},$\n(8)\n\nwhere $p_1, \\ldots, p_K$ are the diagonal elements of $\\mathbf{P}$. The corresponding CRB is summarized in Theorem 3.\n\nTheorem 3. Under the aforementioned assumptions, plus the prior knowledge of uncorrelated sources, the CRB of the DOAs for the unconditional model is given by[1][13][14][15]:\n\n$\\mathrm{CRB}_{\\mathbf{\\theta}}^\\mathrm{UU} = \\frac{1}{T} (\\mathbf{M}_{\\mathbf{\\theta}}^H \\Pi^\\perp_{\\mathbf{M}_{\\mathbf{p}}} \\mathbf{M}_{\\mathbf{\\theta}})^{-1},$\n(9)\n\nwhere\n\n\\begin{aligned} \\Pi^\\perp_{\\mathbf{M}_\\mathbf{p}} &= \\mathbf{I} - \\mathbf{M}_\\mathbf{p}(\\mathbf{M}_\\mathbf{p}^H \\mathbf{M}_\\mathbf{p}) \\mathbf{M}_\\mathbf{p}^H, \\\\ \\mathbf{M}_\\mathbf{\\theta} &= (\\mathbf{R}^T \\otimes \\mathbf{R})^{-1\/2} \\dot{\\mathbf{A}}_\\mathrm{d} \\mathbf{P}, \\\\ \\mathbf{M}_\\mathbf{p} &= (\\mathbf{R}^T \\otimes \\mathbf{R})^{-1\/2} [\\mathbf{A}_\\mathrm{d}\\ \\mathrm{vec}(\\mathbf{I}_M)], \\\\ \\mathbf{A}_\\mathrm{d} &= \\mathbf{A}^* \\odot \\mathbf{A}, \\\\ \\dot{\\mathbf{A}}_\\mathrm{d} &= \\dot{\\mathbf{A}}^* \\odot \\mathbf{A} + \\mathbf{A}^* \\odot \\dot{\\mathbf{A}}. \\end{aligned}\n\nHere $\\mathrm{vec}(\\mathbf{X})$ denotes the vectorization of $\\mathbf{X}$ (i.e., stacking the columns of $\\mathbf{X}$ into a long vector), $\\dot{\\mathbf{A}}$ follows the same definition as in Theorem 1, $\\otimes$ denotes the Kronecker product, and $\\otimes$ denotes the Khatri-Rao product (i.e., the column-wise Kronecker product).\n\nRemark 1. The corresponding Fisher information matrix of (9) is given by[1]\n\n$\\mathbf{J} = T\\begin{bmatrix} \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{\\theta}} & \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{p}} & \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{\\sigma^2}} \\\\ \\mathbf{J}_{\\mathbf{p}\\mathbf{\\theta}} & \\mathbf{J}_{\\mathbf{p}\\mathbf{p}} & \\mathbf{J}_{\\mathbf{p}\\mathbf{\\sigma^2}} \\\\ \\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{\\theta}} & \\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{p}} & \\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{\\sigma^2}} \\end{bmatrix},$\n(10)\n\nwhere\n\n\\begin{aligned} \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{\\theta}} &= 2\\Re[(\\dot{\\mathbf{A}}^H \\mathbf{R}^{-1} \\dot{\\mathbf{A}})^* \\circ (\\mathbf{P} \\mathbf{A}^H \\mathbf{R}^{-1} \\mathbf{A} \\mathbf{P}) + (\\dot{\\mathbf{A}}^H \\mathbf{R}^{-1} \\mathbf{A})^* \\circ (\\mathbf{P} \\mathbf{A}^H \\mathbf{R}^{-1} \\dot{\\mathbf{A}} \\mathbf{P})],\\\\ \\mathbf{J}_{\\mathbf{p}\\mathbf{p}} &= (\\mathbf{A}^H \\mathbf{R}^{-1} \\mathbf{A})^* \\circ (\\mathbf{A}^H \\mathbf{R}^{-1} \\mathbf{A}),\\\\ \\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{\\sigma^2}} &= \\mathrm{tr}(\\mathbf{R}^{-2}),\\\\ \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{p}} &= 2\\Re[(\\dot{\\mathbf{A}}^H \\mathbf{R}^{-1} \\mathbf{A})^* \\circ (\\mathbf{P} \\mathbf{A}^H \\mathbf{R}^{-1} \\mathbf{A})],\\\\ \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{\\sigma^2}} &= 2\\Re[\\mathrm{diag}(\\mathbf{P} \\dot{\\mathbf{A}}^H \\mathbf{R}^{-2} \\mathbf{A})],\\\\ \\mathbf{J}_{\\mathbf{p}\\mathbf{\\sigma^2}} &= \\mathrm{diag}(\\mathbf{A}^H \\mathbf{R}^{-2} \\mathbf{A}), \\end{aligned}\n(11)\n\nand $\\mathbf{J}_{\\mathbf{p}\\mathbf{\\theta}} = \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{p}}^H$, $\\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{\\theta}} = \\mathbf{J}_{\\mathbf{\\theta}\\mathbf{\\sigma^2}}^H$, $\\mathbf{J}_{\\mathbf{\\sigma^2}\\mathbf{p}} = \\mathbf{J}_{\\mathbf{p}\\mathbf{\\sigma^2}}^H$.\n\n$\\mathrm{CRB}_{\\mathbf{\\theta}}^\\mathrm{UU}$ can still be valid even if $K > M$, and can be used to evaluate the performance of sparse linear arrays in cases when $K > M$. This is because the invertibility of the Fisher information matrix actually depends of the \"difference coarray\" steering matrix $\\mathbf{A}_\\mathrm{d}$, which may still be full-rank when $K > M$[13]. For certain sparse linear arrays, $\\mathrm{CRB}_{\\mathbf{\\theta}}^\\mathrm{UU}$ remains valid for up to $\\mathcal{O}(M^2)$ sources[14][15].\n\nTheorem 1-3 summarizes three CRBs in the classical DOA estimation problem. These three CRBs are commonly used in the literature for performance comparison. It should be noted that in the field of array signal processing, there exists many other signal models equipped with difference statistical assumptions. Hence there exists many other CRBs for DOA estimation, and this article only covers a small corner.\n\nCode: the MATLAB code for evaluating the above three CRBs are available on my GitHub. There is also an example that compares the three CRBs numerically.\n\n1. H. L. Van Trees, Optimum array processing. New York: Wiley, 2002.\n\n2. R. Schmidt, \"Multiple emitter location and signal parameter estimation,\" IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276\u2013280, Mar. 1986.\n\n3. R. Roy and T. Kailath, \"ESPRIT-estimation of signal parameters via rotational invariance techniques,\" IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no. 7, pp. 984\u2013995, Jul. 1989.\n\n4. Z. Tan, Y. C. Eldar, and A. Nehorai, \"Direction of arrival estimation using co-prime arrays: a super resolution viewpoint,\" IEEE Transactions on Signal Processing, vol. 62, no. 21, pp. 5565\u20135576, Nov. 2014.\n\n5. P. Stoica and A. Nehorai, \"MUSIC, maximum likelihood, and Cramer-Rao bound,\" IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no. 5, pp. 720\u2013741, May 1989.\n\n6. P. Stoica and A. Nehorai, \"MUSIC, maximum likelihood, and Cramer-Rao bound: further results and comparisons,\" IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 12, pp. 2140\u20132150, Dec. 1990.\n\n7. P. Stoica and A. Nehorai, \"Performance study of conditional and unconditional direction-of-arrival estimation,\" IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 10, pp. 1783\u20131795, Oct. 1990.\n\n8. P. Stoica, E. G. Larsson, and A. B. Gershman, \"The stochastic CRB for array processing: a textbook derivation,\" IEEE Signal Processing Letters, vol. 8, no. 5, pp. 148\u2013150, May 2001.\n\n9. M. Ishiguro, \"Minimum redundancy linear arrays for a large number of antennas,\" Radio Sci., vol. 15, no. 6, pp. 1163\u20131170, Nov. 1980.\n\n10. A. Moffet, \"Minimum-redundancy linear arrays,\" IEEE Transactions on Antennas and Propagation, vol. 16, no. 2, pp. 172\u2013175, Mar. 1968.\n\n11. P. Pal and P. P. Vaidyanathan, \"Nested arrays: a novel approach to array processing with enhanced degrees of freedom,\" IEEE Transactions on Signal Processing, vol. 58, no. 8, pp. 4167\u20134181, Aug. 2010.\n\n12. P. Pal and P. P. Vaidyanathan, \"Coprime sampling and the MUSIC algorithm,\" in 2011 IEEE Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop (DSP\/SPE), 2011, pp. 289\u2013294.\n\n13. M. Wang and A. Nehorai, \"Coarrays, MUSIC, and the Cram\u00e9r-Rao bound,\" IEEE Transactions on Signal Processing, vol. 65, no. 4, pp. 933\u2013946, Feb. 2017.\n\n14. C.-L. Liu and P. P. Vaidyanathan, \"Cram\u00e9r\u2013Rao bounds for coprime and other sparse arrays, which find more sources than sensors,\" Digital Signal Processing, vol. 61, pp. 43\u201361, Feb. 2017.\n\n15. A. Koochakzadeh and P. Pal, \"Cram\u00e9r-Rao bounds for underdetermined source localization,\" IEEE Signal Processing Letters, vol. 23, no. 7, pp. 919\u2013923, Jul. 2016.","date":"2018-12-17 08:34:58","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 61, \"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\": 0.992672324180603, \"perplexity\": 1478.5588433800922}, \"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-2018-51\/segments\/1544376828448.76\/warc\/CC-MAIN-20181217065106-20181217091106-00166.warc.gz\"}"}
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{"url":"https:\/\/www.vedantu.com\/question-answer\/starch-is-composed-of-two-polysaccharides-namely-class-12-chemistry-cbse-5fd838b2d7db7b0995b0f821","text":"# Starch is composed of two polysaccharides namely:\u00a0A) Amylopectin and glycogen.\u00a0B) Amylose and glycogen.\u00a0C) Amylose and Amylopectin.\u00a0D) Amylose and Amylopectin and glycogen.\n\nVerified\n119.7k+ views\nHint: Starch is a colorless and odorless polysaccharide that is found in plants as stored carbohydrates. It is a polymer of glucose monomers that are linked with each other to form polysaccharide; it is a glucose polymer in which glucopyranose units are bonded by alpha-linkages.\n\nAmylose - Amylose consists of a linear chain of several hundred glucose molecules. It is a polysaccharide made of $\\alpha - D - glucose$ units, bonded to each other through $\\alpha - \\left( {1,4} \\right){\\text{ }}glycosidic$ bonds. When iodine is added to starch, the colour changes to dark blue or black due to the presence of Amylose present in the starch. Amylose is soluble in water and can be hydrolyzed into glucose units by the enzymes $\\alpha - {\\text{ }}amylase$ and $\\beta - amylase$.\nAmylopectin - Amylopectin is a polymer of several $D - glucose$ molecules. 80% of amylopectin is present in starch. Amylopectin molecules are linked by $\\alpha - 1,4 - glycosidic$ bonds and $\\alpha - 1,6 - glycosidic$ bonds. Amylopectin is a water-soluble polysaccharide and highly branched polymer of \u03b1-glucose units found in plants. When iodine is added to starch, it gives reddish-brown appearance due to the presence of amylopectin. It readily dissolves in hot water. On cooling, it forms a starch paste or starch gel.\nNote: Starches are insoluble in water. They can be digested by hydrolysis, catalyzed by enzymes called amylases, which can break the $\\alpha$-linkages (glycosidic bonds).","date":"2022-01-29 04:56:18","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\": 0.2962700426578522, \"perplexity\": 6512.656964151348}, \"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\/1642320299927.25\/warc\/CC-MAIN-20220129032406-20220129062406-00371.warc.gz\"}"}
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{"url":"https:\/\/math.stackexchange.com\/questions\/1146757\/what-can-we-conclude-if-mathcaln-is-an-elementary-extension-of-mathcalm","text":"# What can we conclude if $\\mathcal{N}$ is an elementary extension of $\\mathcal{M}$?\n\nIn particular, if $\\mathcal{N}$ is an elementary extension of $\\mathcal{M}$, can we immediately conclude that if $\\mathcal{M} \\models T$, then $\\mathcal{N} \\models T$? Why or why not?\n\nMy line of reasoning\n\nWe have for all $\\mathcal{L}$-formula $\\phi$, $\\forall \\bar{a} \\in \\mathbb{M}$ and its interpretation in $\\mathcal{N}$ $\\pmb{k}(\\bar{a})$: $$\\mathcal{M} \\models \\phi(\\bar{a}) \\Leftrightarrow \\mathcal{N} \\models\\phi(\\pmb{k}(\\bar{a})).$$\n\nLet $T$ be comprised of such $\\phi$'s, then we have $\\mathcal{N} \\models T$ as desired.\n\nUpdate\n\nMy question is a more general version of this question, which gives more context about what $T$ is.\n\nSuppose $T$ has $\\forall\\exists$-axiomatization, $(\\mathbb{I},<)$ is a linear order, and $(\\mathcal{M}_i : i \\in \\mathbb{I})$ is a chain of models of $T$. We show that $\\bigcup \\mathcal{M}_i$ is a model of $T$.\n\n\u2022 @RobArthan I reasoned this is immediate as well, but as a novice I don't trust anything I think. \u2013\u00a0chibro2 Feb 13 '15 at 16:50\n\u2022 Excuse me! The comment I just deleted wasn't helpful. What is $T$? \u2013\u00a0Rob Arthan Feb 13 '15 at 17:08\n\u2022 Yeah that's exactly my problem, I updated the question with my proof, stating what $T$ is. Please check to make sure it's sound? \u2013\u00a0chibro2 Feb 13 '15 at 17:09\n\u2022 The question doesn't seem to have changed. \u2013\u00a0Rob Arthan Feb 13 '15 at 17:10\n\u2022 @RobArthan sorry didn't know you'd respond so quickly! \u2013\u00a0chibro2 Feb 13 '15 at 17:12","date":"2019-08-25 17:39:37","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\": 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\": 0.8394521474838257, \"perplexity\": 381.93232247264314}, \"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-2019-35\/segments\/1566027330786.8\/warc\/CC-MAIN-20190825173827-20190825195827-00088.warc.gz\"}"}
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{"url":"http:\/\/openstudy.com\/updates\/5605815ce4b06b2f42187e99","text":"## dan815 one year ago $|V > =\\frac{1+\\sqrt{6}}{2\\sqrt{6}}|00> + \\frac{1-\\sqrt{6}}{2\\sqrt{6}}|01>+\\frac{\\sqrt{2}-\\sqrt{3}}{2\\sqrt{6}}|10>+\\frac{\\sqrt{2}-\\sqrt{3}}{2\\sqrt{6}}|11>$ http:\/\/prntscr.com\/8kds95\n\n1. dan815\n\n@Empty\n\n2. Empty\n\ncool\n\n3. Empty\n\npellet why did I speak it breaks this terrible site's latex :'(\n\n4. Empty\n\nMaybe we should go to the superior Peer Answer\n\n5. dan815\n\nlol\n\n6. Empty\n\n$|V > =\\frac{1+\\sqrt{6}}{2\\sqrt{6}}|00> + \\frac{1-\\sqrt{6}}{2\\sqrt{6}}|01>+\\frac{\\sqrt{2}-\\sqrt{3}}{2\\sqrt{6}}|10>+\\frac{\\sqrt{2}-\\sqrt{3}}{2\\sqrt{6}}|11>$ http:\/\/prntscr.com\/8kds95\n\n7. Empty\n\nWhat would we do without wio's add on to make this site less trash? Like literally users are fixing the site haha.\n\n8. dan815\n\n9. Empty\n\nI'll ban him idgaf\n\n10. Empty\n\nok so what do you wanna do with this shiz son? This is a matrix basically. I'll write it out too one sec.\n\n11. dan815\n\nthis tensor product |ij> = |i> * |j>, 1<=i,j<=2 whats that about\n\n12. dan815\n\ndoes this first mean that i and j are 2 by 2 matrces and we take tensor product of these 2 matrices?\n\n13. dan815\n\nor are they 2 vectors of dimension 2\n\n14. dan815\n\n|dw:1443201862130:dw|\n\n15. dan815\n\nlike that?\n\n16. Empty\n\nNah not quite.\n\n17. Empty\n\n$|ij \\rangle = |i \\rangle \\otimes |j \\rangle$ i and j can each take on 0 or 1 to give you entries of a matrix. It might be easier to imagine taking the product of two vectors to make a matrix: $A_{ij} = x_iy_j^\\dagger$ Notice that this is like the dot product but flipped backwards so that it creates a matrix. This is called the outer product as opposed to the dot product which is an inner product. :P\n\n18. dan815\n\nwait an outer product always produces an operator right\n\n19. dan815\n\n|dw:1443202519738:dw|\n\n20. Empty\n\nYeah, all you're doing is this: |dw:1443202706547:dw|\n\n21. dan815\n\nok i gotcha\n\n22. dan815\n\nwould that thing you did there be the tensor product of the 2 vectors i and j defined above\n\n23. dan815\n\nwhere that matrix can be rewritten as ac|11> + ad|12>+bc|21> +bd |22>\n\n24. dan815\n\ni dont think that matrix can be rewritten like this nevermind\n\n25. dan815\n\nse this would be like one of those column vectors they keep using for 4 states\n\n26. dan815\n\nokay so basically a tensor product is just this diract notation for a matrix\n\n27. Empty\n\nwell ok so really all this does is take the hermitian conjugate: $|i \\rangle^\\dagger = \\langle i|$ Also I realize that this stuff is pretty confusing since it has a lot of overlap of notation for stuff. Here we're looking at: $| ij \\rangle = \\left[\\begin{matrix}a & b \\\\ c & d\\end{matrix}\\right] = a|00\\rangle + b |01 \\rangle +c |10 \\rangle + d | 11 \\rangle$\n\n28. Empty\n\nAt least I think so, I might be mixing the notation up possibly.\n\n29. dan815\n\nya im looking through the book they are reseving this tensor product strictly for like a matrix and that way of writing http:\/\/prntscr.com\/8ke94r for like your column matrices only like if u look at page 25 example 2.2.4\n\n30. dan815\n31. dan815\n\nwait okay before that question so supppose i just write it out like this 2 by 2 matrix\n\n32. dan815\n\n|dw:1443204170570:dw|\n\n33. dan815\n34. dan815\n\ni better go eat","date":"2017-01-24 09:25:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.8685460090637207, \"perplexity\": 2374.059397026597}, \"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\/1484560284376.37\/warc\/CC-MAIN-20170116095124-00242-ip-10-171-10-70.ec2.internal.warc.gz\"}"}
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{"url":"https:\/\/thirdspacelearning.com\/gcse-maths\/statistics\/frequency-density-formula\/","text":"GCSE Maths Statistics Histograms\n\nFrequency Density Formula\n\n# Frequency Density Formula\n\nHere we will learn about the frequency density formula, including rearranging it and using it to find missing values.\n\nThere is also a histogram worksheet based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you\u2019re still stuck.\n\n## What is the frequency density formula?\n\nThe frequency density formula is a calculation that involves dividing the frequency by the class width.\n\nWe use frequency density to plot histograms which show frequency distribution. The larger the area of the bar on a histogram, the higher the frequency.\n\nWe can calculate the frequency density by using the formula\n\n\\text{Frequency density }=\\frac{\\text{frequency}}{\\text{class width}} .\n\nGiven that\n\n\u2022 D represents frequency density\n\u2022 F represents the frequency (number of values) of a class interval\n\u2022 And W is the class width of the class interval\n\nThe formula abbreviates to\n\nD=\\frac{F}{W} .\n\nFor example,\n\nIf a class interval has a frequency of F=8 and a class width of W=10 , these values can be substituted into the frequency density formula to find the frequency density.\n\n\\begin{aligned} D&=\\frac{F}{W}\\\\\\\\ &=\\frac{8}{10}\\\\\\\\ &=0.8 \\end{aligned}\n\nThe formula can also be rearranged to find a missing frequency or a missing class width,\n\n\\text{Frequency }=\\text{frequency density } x \\text{ class width}\n\n\\text{Class width}=\\frac{\\text{frequency}}{\\text{frequency density}}\n\n## How to use the frequency density formula\n\nIn order to use the frequency density formula:\n\n1. Write down the frequency density formula.\n2. Substitute any known values into the formula.\n3. Calculate the unknown value, rearranging the formula where necessary.\n\n## Related lessons on histograms\n\nFrequency density is part of our series of lessons to support revision on histograms. You may find it helpful to start with the main histograms lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:\n\n## Frequency density formula examples\n\n### Example 1: calculating the frequency density using the formula\n\nA class interval has a frequency of 12 and a class width of 5.\n\nCalculate the frequency density.\n\n1. Write down the frequency density formula.\n\n\\text{Frequency density} =\\frac{\\text { frequency }}{\\text { class width }}\n\n2Substitute any known values into the formula.\n\n\\text{Frequency density } =\\frac{12}{5}\n\n3Calculate the unknown value, rearranging the formula where necessary.\n\n\\begin{aligned} \\text { Frequency density } &=\\frac{12}{5} \\\\\\\\ &=2.4 \\end{aligned}\n\n### Example 2: calculating the frequency using the frequency density formula\n\nA data set is recorded for the number of times the baseball is thrown in a season of matches. A class interval has a frequency density of 1.8 and a class width of 5.\n\nFind the frequency of the class.\n\n\\text { Frequency density }=\\frac{\\text { frequency }}{\\text { class width }}\n\n1.8=\\frac{\\text { frequency }}{5}\n\nTo find the frequency we need to rearrange the formula. We do this by multiplying both sides by 5 to get\n\nFrequency = 1.8 \\times 5 = 9 .\n\n### Example 3: calculating the class width using the frequency density formula\n\nA class interval has a frequency density of 3.4 and a frequency of 51.\n\nCalculate the class width.\n\n\\text { Frequency density }=\\frac{\\text { frequency }}{\\text { class width }}\n\n3.4=\\frac{51}{\\text { class width }}\n\nTo find the class width we need to rearrange the formula. Multiplying both sides by the class width we get\n\n3.4 \\times \\text{ class width }=51 .\n\nDividing both sides by 3.4, we get\n\n\\text { Class } \\text { width }=\\frac{51}{3.4}=15 .\n\n### Example 4: calculating the frequency density from a table\n\nBelow is the grouped frequency table for the number of minutes 30 customers wait on hold on the phone to an energy company.\n\nComplete the table.\n\n\\text { Frequency density }=\\frac{\\text { frequency }}{\\text { class width }}\n\nAs we are completing the table, we need to apply this formula to the first row of data.\n\nThe first row has the class interval 0 \\leq m < 5. Subtracting the lowest value in the range from the highest value, we get\n\n\\text{Class width }=5-0=5.\n\nAs the frequency is 17 we can substitute these into the formula to get\n\n\\text { Frequency density }=\\frac{17}{5} .\n\n\\text { Frequency density }=\\frac{17}{5}=3.4\n\n### Example 5: calculating the frequency from a table\n\nBelow is the grouped frequency table for the height of trees in a woodland, measured in centimetres.\n\nComplete the table.\n\n\\text { Frequency density }=\\frac{\\text { frequency }}{\\text { class width }}\n\nAs we are completing the table, we need to apply this formula to the second row of data.\n\nThe second row has the class interval 50 \\leq x < 100. Subtracting the lowest value in the range from the highest value, we get\n\n\\text{Class width }=100-50=50.\n\nAs the frequency density is 5.7 we can substitute these into the formula to get\n\n5.7=\\frac{\\text { frequency }}{50} .\n\nMultiplying both sides of the equation by 50, we can calculate the value for the frequency to be\n\n\\text { Frequency }=5.7 \\times 50=285 .\n\n### Example 6: calculating the frequency from a histogram\n\nBelow is a histogram showing the length of time it took students to complete a maths question.\n\nCalculate the frequency of students who took between 10 and 15 seconds to solve the puzzle.\n\n\\text { Frequency density }=\\frac{\\text { frequency }}{\\text { class width }}\n\nAs we are looking for the number of students who took between 10 and 15 seconds, we need to get the data from the third bar in the histogram.\n\nThe remaining groups are not required for this solution.\n\nThe class width is the width of the bar. This is found using the horizontal axis (the x -axis). The class width is equal to\n\n\\text{Class width }15-10=5.\n\nThe frequency density is the height of the bar. Using the vertical axis (the y -axis), the height of the bar is 3 as the bars all start from a frequency density of 0 and so D=3.\n\nWe can now substitute these into the formula to get\n\n3=\\frac{\\text { frequency }}{5} .\n\nMultiplying both sides of the equation by 5, we can calculate the value for the frequency to be\n\n\\text { Frequency }=3 \\times 5=15 .\n\nNote: the total area of the bar is the frequency. Each bar is a\u00a0 rectangle, and so to calculate the frequency, we multiply the height (the frequency density) by the width (the class width) of the bar.\n\n### Common misconceptions\n\n\u2022 Frequency density formula incorrectly rearranged\n\nIt is important that the frequency density formula is rearranged correctly when trying to calculate an unknown class width or frequency.\n\nThe correct rearrangements are\n\n\\text{Frequency }=\\text{frequency density } x \\text{ class width}\n\n\\text{Class width}=\\frac{\\text{frequency}}{\\text{frequency density}}\n\nIt is also worth remembering that in a histogram, the frequency represents the area of the bar.\n\n\u2022 Incorrect class width\n\nThe class width is the range of the class. When the class width is written as an interval, such as 0 \\leq x < 5, we accept that the largest value in the range is 5, and not 4.9. This makes calculating the class width much easier!\n\n\u2022 The vertical axis of a histogram is mislabelled \u2018frequency\u2019\n\nThe vertical axis of a histogram represents the frequency density for the class. It can sometimes be incorrectly labelled as \u2018frequency\u2019 due to prior knowledge of drawing a bar chart where the frequency is always the vertical axis label.\n\n\u2022 Mixing up histograms with other diagrams\n\nHistograms use frequency density, which should not be confused with adding up the frequencies for cumulative frequency or using the midpoints to plot a frequency polygon.\n\n### Practice frequency density formula questions\n\n1. Which is not an equivalent frequency density formula?\n\n\\text{Frequency }=\\text{frequency density }\\times\\text{class width}\n\n\\text{Class width}=\\frac{\\text{frequency}}{\\text{frequency density}}\n\n\\text{Frequency density}=\\frac{\\text{frequency}}{\\text{class width}}\n\n\\text{Frequency}=\\frac{\\text{frequency density}}{\\text{class width}}\n\nTo make the frequency the subject of the formula we must multiply both sides of the formula by the frequency density.\n\n2. A class interval has a frequency of 16 and a class width of 5. Calculate the frequency density. Write your answer as a decimal.\n\n3.2\n\n0.3125\n\n80\n\n0.32\n\\text{Frequency density}=\\frac{\\text{frequency}}{\\text{class width}}=\\frac{16}{5}=3.2\n\n3. A class interval has a width of 20 and a frequency of 7.\nCalculate the frequency density.\n\n3.5\n\n0.35\n\n2.86 \\ (1dp)\n\n140\nD=\\frac{F}{W}=\\frac{7}{20}=0.35\n\n4. A class interval has a frequency of 18 and a frequency density of 1.2. Calculate the class width.\n\n21.6\n\n12\n\n15\n\n10\nW=\\frac{F}{D}=\\frac{18}{1.2}=15\n\n5. The table below shows the results of a survey where commuters were asked about the number of hours per week they read non-fiction books.\n\nCalculate the frequency of commuters who read between 2 and 6 hours of non-fiction books per week.\n\n0.75\n\n1.3\n\n12\n\n24\nF=W\\times{D}=4\\times{3}=12\n\n6. Below is a histogram showing the number of spelling mistakes per paper, made in 30 academic papers.\n\n18\n\n23\n\n14\n\n42\n\nThe first bar has a width W=10 and frequency density D=1.8.\n\nThe frequency of the first bar is therefore\n\nF=W\\times{D}=10\\times{1.8}=18 .\n\nThe second bar has a width W=4 and frequency density D=1.25.\n\nThe frequency of the second bar is therefore\n\nF=W\\times{D}=4\\times{1.25}=5 .\n\nThere are no values between 14 and 15 spelling mistakes per paper as there is no bar.\n\nThe total frequency of these two classes is 18+5=23.\n\n### Frequency density formula GCSE questions\n\n1. The grouped frequency table below shows the number of items of stationery in 120 pencil cases. Calculate the frequency density, D , for the class 10 \\leq x < 25.\n\n(2 marks)\n\n48 \\div 15\n\n(1)\n\n3.2\n\n(1)\n\n2. A grouped frequency table has a class interval with a frequency of 36 and a frequency density of 1.8.\n\nWhich of the following could have been that class interval?\n\n(1 mark)\n\n35 < x \\leq 55\n\n(1)\n\n3. Higher only: Below is a histogram showing the density of 22 common substances.\n\nEstimate the number of substances that have a density in the range 0.5 \\leq x < 1.5 \\ g\/cm^3.\n\n(3 marks)\n\n\\begin{aligned} &0.5 \\leq x < 1 \\\\\\\\ &(1-0.5) \\times 11=5.5 \\end{aligned}\n\n(1)\n\n\\begin{aligned} &1 \\leq x < 1.5 \\\\\\\\ &(1.5-1) \\times 3=1.5 \\end{aligned}\n\n(1)\n\n5.5+1.5=7\n\n(1)\n\n## Learning checklist\n\nYou have now learned how to:\n\n\u2022 Understand and use standard mathematical formulae; rearrange formulae to change the subject\n\u2022 Substitute numerical values into formulae\n\n## Still stuck?\n\nPrepare your KS4 students for maths GCSEs success with Third Space Learning. Weekly online one to one GCSE maths revision lessons delivered by expert maths tutors.\n\nFind out more about our GCSE maths revision programme.","date":"2023-03-20 15:00:30","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\": 0.9398375153541565, \"perplexity\": 1751.8300460724383}, \"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-2023-14\/segments\/1679296943484.34\/warc\/CC-MAIN-20230320144934-20230320174934-00663.warc.gz\"}"}
| null | null |
Q: Issue in C language using 'fgets' after 'printf' as 'fgets' runs before 'printf'
Possible Duplicate:
Why does printf not flush after the call unless a newline is in the format string? (in C)
I am getting a problem using printf and fgets as in my code printf is written earlier then fget but it does not run, it runs after fgets runs.
enum { max_string = 127 };
static char string[max_string+1] = "";
int main( int argc, char ** argv ) {
printf("Type a String: ");
fgets(string, max_string, stdin);
printf("The String is %s\n", string);
return 0;
}
A: do a flush of the stdout
fflush(stdout);
before fgets(...)
printf("Type a String: ");
fflush(stdout);
fgets(string, max_string, stdin);
A: The point is not that printf runs after fgets, but instead that its output is displayed after it.
This happens because standard output (the file descriptor you're writing on with printf) is line-buffered, i.e. the standard library defers prints after a newline character (\n) has been received for printing.
From man stdout:
The stream stdout is line-buffered when it points to a terminal.
Partial lines will not appear until fflush(3) or exit(3) is called, or
a newline is printed.
To investigate different results, edit your example to use fflush, or print on standard error using fprintf(stderr, ... .
A: put a \n in printf statement. This might be the problem as in C buffers are line terminated.
A: Neel is right. If you want to just write something down without having to put that '\n' you can use the function write();
#include <stdio.h>
#include <unistd.h>
#include <string.h>
enum { max_string = 127 };
static char string[max_string+1] = "";
my_putstr(char *str)
{
write(1, str, strlen(str));
}
int main( int argc, char ** argv ) {
my_putstr("Type a String: ");
fgets(string, max_string, stdin);
printf("The String is %s\n", string);
return 0;
}
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 7,068
|
{"url":"https:\/\/support.bioconductor.org\/p\/102543\/","text":"Search\nQuestion: Using name parameter in DESeq2-results function\n0\n8 months ago by\nmuratcokol0 wrote:\n\nHi. I am trying to make sense of a previously written DESeq analysis which uses the \u201cname\u201d parameter to obtain results. A sample code is below, the first two lines are straightforward - making the Input file and running DESeq. My question is what does the results function return when the name parameter points to only a single condition. What is the comparison that is made? Thanks in advance for the input and I will also appreciate if you can point out the documentation regarding this usage.\n\nddsInput <- DESeqDataSetFromMatrix(countdata, coldata, ~ condition)\n\ndds <- DESeq(ddsInput, betaPrior=TRUE, modelMatrixType=\"expanded\")\n\nmyresults <- results(dds, name = \u201ccondition1\u201d)\n\nmodified 8 months ago \u2022 written 8 months ago by muratcokol0\n\nHi Michael, thank you very much for your input, it was extremely helpful.\n\nI have a follow-up question on this thread. I implemented the behavior of \u201cname\u201d according to your description as shown below, where I do a contrast of one condition to all other conditions.\n\nexpnames <- unique(coldata)\nexpnow <- \"1\"\notherexps <- str_c(\u201ccondition\u201d, setdiff(expnames, expnow))\n\nnewresults <- results(\ndds, contrast=list(\"condition1\u201d), otherexps))\n\nI give the results for two versions below. As you will see, basemean-stat-pvalue-padj replicates perfectly; \u00a0but the log2FoldChange is exactly double in the new results compared to old results. Would you have an explanation as to why this is the case?\n\nmyresults\n\nbaseMean log2FoldChange \u00a0 \u00a0 lfcSE \u00a0 \u00a0 \u00a0 \u00a0stat \u00a0 \u00a0 \u00a0 pvalue \u00a0 \u00a0 \u00a0 \u00a0 padj\ngene__A \u00a0 \u00a00.2054465 \u00a0 \u00a0 0.11371753 0.1943700 \u00a00.58505706 \u00a0 0.55850935 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 NA\ngene__B \u00a0 \u00a06.4477539 \u00a0 \u00a0 0.45373690 0.3068560 \u00a01.47866394 \u00a0 0.13923015 \u00a0 0.23173656\n\nnewresults\n\nbaseMean log2FoldChange \u00a0 \u00a0 lfcSE \u00a0 \u00a0 \u00a0 \u00a0stat \u00a0 \u00a0 \u00a0 pvalue \u00a0 \u00a0 \u00a0 \u00a0 padj\ngene__A \u00a0 \u00a00.2054465 \u00a0 \u00a0 0.22743636 0.3887400 \u00a00.58506039 \u00a0 0.55850711 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 NA\ngene__B \u00a0 \u00a06.4477539 \u00a0 \u00a0 0.90747168 0.6137120 \u00a01.47866052 \u00a0 0.13923107 \u00a0 0.23173510\n\n(note, the question here is specific to old settings for running DESeq2, which are not the defaults since v1.14)\n\nA few differences, using a list, you need to set listValues.\n\nIt still won\u2019t be the same because the list approach is comparing X vs the rest, while name is comparing X vs all (including X).\n\nHi Michael, if the difference between \u201cname\u201d and \u201ccontrast\u201d approaches is the inclusion of X, wouldn\u2019t all results metrics be different? Now some are exactly same, some are exactly double.\n\nAlso, does this mean I cannot replicate the \u201cname\u201d approach by using \u201ccontrast\u201d? Because if I write:\n\nallexps <- str_c(\u201ccondition\u201d, expnames)\nnewresults2 <- results(dds, contrast=list(\"condition1\u201d), allexps)\n\nthen DESeq outputs the following error message:\n\n\u201cError in checkContrast(contrast, resNames) :\nelements in the contrast list should only appear in the numerator (first element of contrast list) or the denominator (second element of contrast list), but not both\n\nLet me take a step back. True of all versions of DESeq2: \u2018name\u2019 and \u2018contrast\u2019 arguments are simply ways to add and subtract coefficients. The names of coefficients is given by resultsNames(dds). You can read about how to specify these in ?results\n\nIf after reading that section, do you have remaining questions?\n\nI had read the ?results page before starting this thread and was unable to find some specifications. In your previous answer, for example, you said that when \u201cname\u201d parameter is called without a comparison, DESeq compares to the \u201cmean\u201d of all samples. As far as I can see, the ?results page does not specify this usage.\n\nAfter reading ?results again, my previous question remains: in the examples I gave above, why does the log2foldchange in newresults is exactly double of myresults, while p-values are exactly same. How should one interpret this outcome?\n\nMy reply about using \u2018name\u2019 giving a level compared to a middle point is advice specific to the old settings, which aren\u2019t used anymore. The main reason for moving away was that it was difficult for users to interpret.\n\nThere is still the description of the meaning of coefficients in an expanded model matrix in all the documentation, though we moved away from this approach. When you use \u2018name\u2019 you pull out a single coefficient.\n\nIn your example above you are taking one coefficient and subtracting two other coefficients. If you want to average over those levels you\u2019d have to use listValues, here you would put (1,-1\/2) to take the numerator coefficient and the average of the denominator coefficients.\n\nIf you want a single coefficient you would use \u2018name\u2019.\n\nIs this a copy paste issue or is this how you have it in your code?\n\nnewresults <- results(dds, contrast=list(\"condition1\u201d), otherexps))\n\nDid you mean to finish the list after \"condition1\"?\n\nMy apologies - it is a copy paste mistake. It should have read:\n\nnewresults <- results(dds, contrast=list(\"condition1\", otherexps))\n\nSo the 'name' version is the correct one, and below is a sketch as to why you are getting double that when you use contrast and a list and you don't specify 'listValues' to average over the other conditions (so you are summing over all the other conditions):\n\n(The following only applies to the old settings, which aren't default in DESeq2 in the past two releases)\n\nSuppose you're looking on the log scale at the mean counts for each condition, and we'll write that as x_1, ..., x_n for n conditions.\n\nUsing 'name' is giving you something like:\n\nx_1 - mean_i x_i\n\nUsing the 'list' that you have above is giving you:\n\n(x_1 - mean_i x_i) - sum_{i != 1} [x_i - mean_j x_j]\n\n=\u00a0(x_1 -\u00a0mean_i x_i)\u00a0- (sum_{i} [x_i -\u00a0mean_j x_j] -\u00a0(x_1 -\u00a0mean_i x_i))\n\n= 2 * (x_1 -\u00a0mean_i x_i)\u00a0- sum_{i} [x_i -\u00a0mean_j x_j]\n\n= 2 * (x_1 -\u00a0mean_i x_i)\n\nHi Michael, thank you for this elegant explanation.\n\nThere is one question I asked above which didn\u2019t get an answer yet, perhaps you could help in this as well - Is it possible to use \u201ccontrast\u201d to get the same result as \u201cname\u201d?\n\nYes, but only trivially, like so:\n\nresults(dds, name=x)\n\nresults(dds, contrast=list(x))\n\nAwesome. Thanks once again for your help and patience with all the questions.\n\n0\n8 months ago by\nMichael Love18k\nUnited States\nMichael Love18k wrote:\n\nFirst I will note that we've moved away from these settings. Now betaPrior=FALSE is the default in the past two releases. But the documentation is still there, and it's in the DESeq2 publication. The interpretation of name=\"condition1\" for these older settings, is the LFC from condition1 samples compared to the \"mean\" of the samples from all conditions. It's better to say, the middle point, as it moves from the geometric to arithmetic mean depending on the amount of shrinkage.\n\nExpanded model matrices are described in the DESeq2 publication in the Methods.\n\nIt's described here in the vignette:\n\nhttps:\/\/bioconductor.org\/packages\/release\/bioc\/vignettes\/DESeq2\/inst\/doc\/DESeq2.html#expanded-model-matrices\n\nAnd there's a bit of information under 'modelMatrixType' in ?DESeq and in the Details section of ?nbinomWaldTest.","date":"2018-07-18 22:23:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.5421040654182434, \"perplexity\": 2912.5291539934}, \"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\/1531676590329.62\/warc\/CC-MAIN-20180718213135-20180718233135-00612.warc.gz\"}"}
| null | null |
\section{Introduction}
The study of exclusive diffractive $ep$ reactions at HERA has shown
that when $Q^2$ (photon virtuality) or the mass scale involved is
large, the cross section increases with energy faster than expected
for soft processes~\cite{jim,abramowicz-caldwell}.
The rise is consistent with predictions from models based on perturbative
QCD (pQCD) in which $Q^2$ and mass are used as the perturbative scale.
It is expected that, for diffractive
vector-meson photoproduction, the four-momentum transfer squared, $t$,
between the photon and the final-state vector meson may also serve as a hard
scale, provided $-t$ is large~\cite{large-t}.
In the present paper, this hypothesis is studied by
measuring diffractive vector-meson photoproduction as a function of $t$
and by confronting the data with the predictions of models based on pQCD,
which should be applicable in the presence of a hard scale. In addition,
the data at lower $-t$ are compared to predictions of
models expected to be valid for soft
processes. This provides a means to study the transition between the
soft, non-perturbative, and the hard, perturbative, regimes of
QCD~\cite{halfms}.
A detailed study of the onset of the pQCD regime should give
important insight into the structure of strong interactions at hard scales
as well as improve our understanding of soft phenomena in QCD.
Vector mesons can be diffractively photoproduced via two
processes. In one of them, the target proton
remains intact and the reaction is called exclusive (or elastic),
\begin{equation}
\gamma p \to V p.
\label{eq:el}
\end{equation}
In the other process, the proton dissociates into a higher mass
nucleonic state $N$ and the reaction is called proton-dissociative,
\begin{equation}
\gamma p \to V N.
\label{eq:pd}
\end{equation}
Reaction~(\ref{eq:el}) is called elastic in the framework of the
vector-dominance model (VDM)~\cite{vdm}, in which the photon
fluctuates into a virtual vector meson which in turn scatters
elastically from the target proton~\cite{bauer}. This reaction has
been studied over a wide range of $\gamma p$ center-of-mass energies
$W<200$~GeV~\cite{jim,bauer}. The proton-dissociative
reaction~(\ref{eq:pd}) has been studied at low energies~\cite{chapin}
and information at high $W$ has been obtained recently~\cite{zrho-94}.
In this study, reactions~(\ref{eq:el})
and~(\ref{eq:pd}) are investigated with the ZEUS detector at HERA
by measuring the processes $ e p \to e V p$ and
$e p \to e V N$,
where $V = \rho^0, \phi$ or $J/\psi$, and $N$ is a system with
mass~$\le 7$~GeV.
The scattered positron was
detected in an electromagnetic calorimeter close to the beamline
at a distance of 44~m from the interaction point in the direction
of the outgoing positron. This ensured that the virtuality of the exchanged
photon is very small ($Q^2 \le$ 0.01 GeV$^2$)
and that $-t$ can be well approximated by the transverse momentum
squared of the vector meson.
In the present paper, the pQCD
\cite{bfgms,ryskin,bartels,ivanov,czerniak,ginzburg}
and Regge \cite{collins} based approaches to
vector-meson production are described. Then the measurements of
elastic and proton-dissociative photoproduction of the
$\rho^0, \phi$ and $J/\psi$ mesons are presented. Finally, the results
are compared with models and a summary of the conclusions is given.
\section{Models}
\subsection{The pQCD approach -- hard scale models}
In models based on pQCD~\cite{bfgms,ryskin,bartels,ivanov,czerniak,ginzburg},
the diffractive
photoproduction of a vector meson from a proton
can be viewed
in the proton rest frame
as a three-step process:
the photon fluctuates into a {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} state; the {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} pair
scatters on the proton target; and the scattered {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} pair becomes
a vector meson. The {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} fluctuation is described in terms of
the photon wave-function derived from QCD. The
interaction of the {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} pair with the proton is mediated in the
lowest order by the exchange of two gluons in a color-singlet state.
In the leading logarithmic approximation (LLA), the process can also
be described
by the exchange of a gluon ladder \cite{ryskin,bartels,ivanov}.
To be calculable in pQCD, the interaction has to involve a hard
scale or, in other words, has to involve small transverse distances.
The transition of a {\mbox{$\mathrm{q}\bar{\mathrm{q}}$}} pair into a meson is, however,
a non-perturbative phenomenon and can only be described in terms of the
meson wave-function derived from lattice calculations and
sum rules \cite{czerniak}.
The expected signatures of the perturbative regime in
diffractive meson production are:
\begin{itemize}
\item a fast rise of the diffractive cross sections with $W$,
the available center-of-mass energy, due
to the fast increase with decreasing $x$ (Bjorken scaling variable)
of the gluon density in the proton \cite{bfgms,ryskin};
\item no variation with $W$ of the $t$-dependence of the cross section,
i.e. no $shrinkage$ of the diffractive peak \cite{bartels};
\item approximate restoration of flavor-independent production, which is
expected when the photon couples directly to the
constituent quarks in the meson \cite{halfms};
\item production of light vector
mesons in a helicity-zero state, independent of the
initial photon helicity~\cite{ivanov,ginzburg}, in the asymptotic limit
of very large $-t$ ($W^2\gg -t \gg \Lambda_{\rm{QCD}}^2$) .
\end{itemize}
\subsection{The Regge approach -- modeling the soft interactions}
Regge phenomenology~\cite{collins} has been successful in describing soft hadron-hadron
interactions. In this approach, the interactions are described in terms of
$t$-channel exchanges of Regge trajectories. In particular, diffractive
processes are assumed to proceed through the exchange of the Pomeron
trajectory.
\subsubsection{Regge factorization}
Regge factorization~\cite{collins} is the assumption that Regge pole residues
factorize into a contribution from each vertex. In other
words, for diffractive vector-meson photoproduction,
the properties of the interaction at the Pomeron-proton
vertex should not depend on the properties of the Pomeron-vector-meson vertex.
This hypothesis implies that
the ratio of elastic to proton-dissociative vector-meson photoproduction,
$\dst (\gamma p \to V p)/\dst (\gamma p \to V N)$, should be the same for
the three vector mesons under study in this paper.
In the framework of VDM, these ratios should have the same
values as in hadron-proton reactions.
\subsubsection{The Pomeron trajectory}
In general, the differential cross section for a two-body hadronic
process, \dsdt , can be expressed at high energies as
\begin{equation}
\frac{d\sigma}{dt} = F(t) (W^2)^{[2\alphapom(t)-2]},
\label{eq:regge}
\end{equation}
where $F(t)$ is a function of $t$ only and $\alphapom(t)$ is the
Pomeron trajectory. At lower $W$ values, the exchange of a Reggeon trajectory
should also be taken into account.
By studying the $W$ dependence of \dsdt\ at fixed $t$, $\alphapom(t)$
can be determined directly. Usually, the trajectory is assumed to be
linear, $\alphapom(t) = \alphapom(0) + \alphappom t$, but its form is
not predicted by Regge theory. The early determinations of the
Pomeron trajectory according to this procedure used data from $p p$
elastic scattering~\cite{jl-slope,collins-slope}.
Under the assumption that \dsdt\
decreases exponentially (i.e. $\dsdt\sim\exp(bt)$), $\alphappom$
can also be determined from a study of the energy behavior
of the exponential slope $b$. This method, however, is less direct
and also depends on the $t$ range over which
the exponent is fitted. Determinations of $\alphappom$ based on this
procedure~\cite{giacomelli,burq-slope} from $ p p, K p$ and $\pi p$ elastic
scattering yielded values in the range of 0.14--0.28
GeV$^{-2}$. However, the high precision $p p$ ISR data at small $-t$
showed that $\alphappom$ has a value 0.25 GeV$^{-2}$ with a small
uncertainty~\cite{dl-slope}. The same analysis gave
$\alphapom(0)=1.08$.
Studies of the elastic photoproduction of \rhoz\ and \phiz\ mesons
have shown~\cite{jim} that these processes can be well described by the Regge
phenomenology developed for soft hadron-hadron collisions.
The steep energy behavior of the elastic $J/\psi$ photoproduction cross
section at HERA, however, cannot be described in the Regge picture
by a Pomeron trajectory with an intercept of 1.08 but
requires a larger intercept. In addition, a direct
determination of the Pomeron trajectory in a way similar to that
described above has shown that the slope $\alphappom$ from elastic
photoproduction of $J/\psi$ is smaller than 0.25
GeV$^{-2}$~\cite{noshrink}. These observations suggest
that the Pomeron trajectory is not universal when a large
scale, like a large mass, is involved.
It is thus of interest to see whether the
universality notion can be kept in soft interactions. Earlier attempts
to determine the Pomeron trajectory from the elastic photoproduction
of $\phi$ mesons~\cite{gl,barber-83} were not precise enough owing to the small
span in the energy available. The present measurements at HERA,
together with the existing lower-energy data, enable a more precise
determination of the Pomeron trajectory
and thus make it possible to test its universality.
In this paper the Pomeron trajectory will be determined
from the \rhoz\ and \phiz\ vector-meson data. The \jpsi\ measurement of this
analysis does not add significant information to the analysis done in
\cite{noshrink} and therefore will not be considered here.
\section{Experiment}
\label{setup}
The data used in the present analysis were collected with the ZEUS
detector at HERA in 1995, when HERA collided positrons of energy $E_e
= 27.5$ GeV with protons of energy $E_p =820$ GeV. The data sample used
in this analysis corresponds to an integrated luminosity of 1.98
pb$^{-1}$.
A detailed description of the ZEUS detector can be found
elsewhere~\cite{detector}. A brief outline of the components
which are most relevant for this analysis is given below.
Charged particles are tracked by the central tracking detector (CTD),
which operates in a magnetic field of 1.43 T provided by a thin
superconducting coil. The CTD consists of 72 cylindrical drift chamber
layers, organized in 9 superlayers covering the polar
angle\footnote{The ZEUS coordinates form a right-handed system
with positive-$Z$ in the proton beam direction
and a horizontal $X$-axis pointing towards the center of HERA.
The nominal interaction point is at $X=Y=Z=0$.
The polar angle $\theta$ is defined with respect to the $Z$
direction.} region \mbox{$15^\circ < \theta < 164^\circ$.}
The transverse momentum
resolution for
full-length tracks
is
$\sigma(p_t)/p_t=0.0058p_t\oplus 0.0065 \oplus 0.0014/p_t$,
with $p_t$ in GeV~\cite{ctd}.
The high resolution uranium-scintillator calorimeter (CAL) \cite{CAL}
consists of three parts: the forward (FCAL), the rear (RCAL) and the
barrel (BCAL) calorimeters. Each part is subdivided transversely into
towers and longitudinally into one electromagnetic section (EMC) and
either one (in RCAL) or two (in BCAL and FCAL) hadronic sections (HAC).
The smallest subdivision of the calorimeter is called a cell.
The CAL energy resolutions, as measured under
test beam conditions, are $\sigma(E)/E=0.18/\sqrt{E}$ for electrons and
$\sigma(E)/E=0.35/\sqrt{E}$ for hadrons ($E$ in GeV).
The proton-remnant tagger (PRT1) is used to tag events
in which the proton dissociates. It consists of two layers of scintillation
counters perpendicular to the beam at $Z=5.15$~m.
The two layers are separated by a 2~mm thick lead absorber.
Each layer is split into two halves along the $Y$--axis and each half
is independently read out by a photomultiplier tube. The counters
have an active area of $30\times 26$~cm$^2$
with a hole of $6.0\times 4.5$~cm$^2$ at the center to
accommodate the HERA beampipe. The pseudorapidity range covered by
the PRT1 is \mbox{$4.3<\eta<5.8$}.
The photoproduction tagger (PT) is a small
electromagnetic calorimeter located at \mbox{$Z=-44$}~m,
sensitive to 22--26~GeV positrons scattered under very small angles
(less than a few mrad). The HERA positron beampipe has a
14~mm deep and 60~cm long indentation on the side facing the ring
center (Fig.~\ref{fig:tagger}). The calorimeter is installed behind a
1~mm thick copper window in the beampipe.
During beam injection
and acceleration, a movable 10~cm thick lead shield is inserted
in front of the PT. The detector consists of twelve
$70\times90\times7~\rm{mm}^3$ tungsten
plates interleaved with 3~mm thick scintillator layers. The
light from the scintillator is read out from the bottom by a
wavelength-shifter plate coupled through a plastic light-guide
to a photomultiplier tube with a quartz window (Philips XP1911).
The detector sensitive edge is about 28~mm from the positron
beam.
Additional scintillator strips are installed,
after each of the first three tungsten plates, at depths corresponding
to 2, 4 and 6 radiation lengths.
These 8~mm wide vertical
strips are connected to plastic light-guides
coupled to three miniature photomultipliers (Hamamatsu R5600).
Signals from the strips can be used to apply fiducial cuts and select
well-contained electromagnetic showers.
Test beam measurements demonstrated that for 1--5 GeV electrons
hitting the calorimeter centrally, the energy resolution is
$\sigma(E)/E = 0.25/\sqrt{E({\rm GeV})}$,
and the calorimeter linearity is better than 1\%.
The energy measurement is used only at the trigger
level for tagging photoproduction events.
The tagger issues a trigger for events with an energy
deposition above approximately 1~GeV. The low threshold ensures
that the tagging efficiency is determined mainly by the
geometric acceptance.
\begin{figure}[htb]
\begin{center}
\epsfig{file=setup44.eps,width=0.75\textwidth}
\end{center}
\vspace*{-0.5cm}
\caption{Sketch of the layout of the photoproduction tagging detector.}
\label{fig:tagger}
\end{figure}
The luminosity is determined from the rate of the Bethe-Heitler
bremsstrahlung process, $ep \rightarrow e \gamma p$, where the photon is
measured with a calorimeter (LUMI) located in the HERA tunnel downstream of
the interaction point in the direction of the outgoing positron~\cite{lumi}.
The acceptance of the LUMI calorimeter for Bethe-Heitler events is
greater than 98\%.
\section{Kinematics and cross sections}
\label{Sect:Kinem}
The kinematics of the inclusive scattering of unpolarized
positrons and protons are described by the squared positron-proton
center-of-mass energy, $s$,
and any two of the following variables:
\begin{itemize}
\item $Q^2$, the negative square
of the exchanged photon's four-momentum;
\item $y$, the fraction of the positron energy
transferred to the hadronic final state in the rest frame of the
initial-state proton;
\item $W^2 = ys +M_p^2(1-y) - Q^2$, the squared
center-of-mass energy of the photon-proton system (where
$M_p$ is the proton mass); $ W^2 \approx ys$ in the case of
photoproduction.
\end{itemize}
For the exclusive reaction $e p \rightarrow e V p$ ($V\rightarrow$
two charged particles) and the proton-dissociative process
$e p \rightarrow e V N$, $t$ and the following additional variables
are used (see Fig.~\ref{fig:hel_ang}):
\begin{itemize}
\item the angle, $\Phi$, between the $V$ production plane (which contains
the momentum vectors of the virtual photon and the vector meson)
and the positron scattering plane;
\item the polar and azimuthal angles, $\theta_h$ and $\varphi_h$, of
the positively-charged decay particle in the $V$
helicity frame. The polar angle, $\theta_h$,
is defined as the angle between the direction opposite to that of
the outgoing proton and
the direction of the positively-charged decay particle.
The azimuthal angle, $\varphi_h$, is the angle between
the decay plane and the $V$ production plane;
\item the mass, $M_N$,
of the diffractively-produced state $N$ in the proton-dissociative
reaction.
In the present analysis, however, it was not possible to measure this
quantity directly and the $M_N$ range covered was obtained from
Monte Carlo simulations (see Sect.~\ref{acc_corr}).
\end{itemize}
\begin{figure}[htb]
\begin{center}
\vspace*{-0.5cm}
\epsfig{file=hel_ang.eps,width=0.75\textwidth}
\put(-268,11){$\Phi$}
\put(-90,172){$\varphi_h$}
\put(-47,115){$\theta_h$}
\end{center}
\vspace*{-0.7cm}
\caption{Illustration of the angles used to analyze the helicity
states of the vector meson (for a decay into two particles, $V\rightarrow
\mbox{q}^+\mbox{q}^-$).}
\label{fig:hel_ang}
\end{figure}
Only the three-momenta of the decay particles were
measured. Neither the momentum of the scattered positron, nor
the $\Phi$ angle, were measured. In such tagged
photoproduction events, $Q^2$ ranges from the kinematic
minimum, $Q^2_{\rm{min}} \approx M^2_e y^2/(1-y) \approx
10^{-9}~\rm{GeV^2}$, where
$M_e$ is the electron mass, to a maximum value limited by the angular
acceptance of the PT,
$Q^2_{\rm{max}} \approx
4E_eE_{e'}\sin^2(\theta_{\rm{max}}/2)\approx0.01~\rm{GeV^2}$, where
$\theta_{\rm{max}}$ is the maximum scattering angle, and $E_e$ and $E_{e'}$
are the energies of the initial- and final-state positrons.
The energy of the scattered positron is determined by the PT
acceptance. Since the typical $Q^2$ is very small (the median $Q^2$ is
approximately $7 \times 10^{-6}~{\rm GeV^2}$), it can be
neglected in the reconstruction of the other kinematic variables.
The photon-proton center-of-mass energy is given by
\begin{equation}
W^2 \approx 2 E_p (E - p_Z),
\label{Eq:W2Def}
\end{equation}
where $E_p$ is the incoming proton energy, and $E$ and
$p_Z$ are the energy and longitudinal momentum in the laboratory frame
of the produced meson $V$, respectively; in this approximation,
$M_N$, the meson mass, $M_V$, and its transverse momentum,
$p_T$, are assumed to be much smaller than $W$.
The four-momentum transfer squared is given by
\begin{equation}
t = (M_N^2-M_p^2-Q^2-M_V^2)^2/4W^2-(p_{\gamma}^*-p^*)^2 -4
p_{\gamma}^*p^*\sin^2(\theta^*/2) =
t_0-4 p_{\gamma}^*p^*\sin^2(\theta^*/2),
\label{Eq:tDef}
\end{equation}
where $p_{\gamma}^*$, $p^*$ are the magnitudes of the
photon and meson momenta and $\theta^*$ is the angle between them. The
starred quantities are defined in the
photon-proton center-of-mass system and $t_0$ is the
maximum $t(\theta^*=0)$ value. For $Q^2\ll -t,p_T^2,M_V^2,M_N^2 \ll
W^2$, $t$ and $t_0$ are given by
\begin{equation}
t \approx t_0 - p_T^2 \approx -M_V^2(M_N^2-M_p^2)/W^2 - p_T^2.
\label{Eq:ptrel}
\end{equation}
Since the maximum $-t_0$ value in the kinematic range covered by this
analysis is small ($-t_0 \mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} 7\times 10^{-3}~{\rm
GeV^2}$ for $V=\rhoz,\phiz$ and $-t_0 \mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} 6\times 10^{-2}~{\rm
GeV^2}$ for $V=\jpsi$) compared to the $-t$ value, it can be neglected.
The four-momentum transfer squared is then given by
\begin{equation}
t \approx - p_T^2
\label{Eq:ptapr}
\end{equation}
The differential and integrated photoproduction cross sections for the
processes $\gamma p \rightarrow V p (N)$ were obtained from the
cross sections measured for the reactions $ep \rightarrow e V p
(N)$. The cross sections are related by
\begin{eqnarray}
\frac{d^2 \sigma_{ep}}{dydQ^2} &=& \frac{\alpha}{2\pi Q^2}
\left[ \frac{1+(1-y)^2}{y} - \frac{2(1-y)}{y}
\frac{Q_{min}^2}{Q^2}\right]~
\sigma_{\gamma p}(W) \nonumber \\
&=&\varphi(y,Q^2)~\sigma_{\gamma p}(W),
\label{bornc}
\end{eqnarray}
where $\alpha$ is the fine structure constant and
$\varphi(y,Q^2)$ is the effective photon flux.
A measured $ep$ cross section can thus be transformed into a
$\gamma p$ cross section,
\begin{equation}
\sigma_{\gamma p}= \frac{\sigma_{ep}}{\int \int
\varphi(y,Q^2)\rm{d}\it{y}\rm{d}\it{Q^{\rm{2}}}}
= \frac{\sigma_{ep}}{\Phi_\gamma},
\label{gp_cros}
\end{equation}
if $\sigma_{\gamma p}$ is independent of $W$ (or $y$) in the
studied region (where $\Phi_\gamma$ is the integrated effective photon flux).
\section{Event selection}
\label{event_selection}
Vector mesons were observed in the two-body decay channels \rhotopp,
\phitokk, \jpsitoee,
and \jpsitomm\
via the reconstruction of two oppositely-charged tracks in
the CTD. The scattered positron was detected in the PT
and the proton or its fragments escaped undetected or were
tagged in either the FCAL or the PRT1.
\subsection{Trigger}
\label{trigger}
ZEUS uses a three-level trigger system. At the first level, a
coincidence between signals in the PT and a track candidate in the CTD
was required. Additionally, it was required that the energy deposition
in any of the FCAL towers closest to the beampipe should not exceed
1.25~GeV in order to suppress proton beam-related backgrounds. An
upper limit of 1~GeV on the energy deposited in the LUMI was also
imposed; this requirement suppressed events having a random
coincidence with bremsstrahlung. The second and the third trigger
levels were mainly used to reject non-diffractive backgrounds by
requiring exactly two tracks pointing to the same vertex with a
$Z$-coordinate compatible with that of the nominal position of the
interaction point, $|V_{Z}| <\ 60$~cm.
The trigger efficiency was studied using
data samples selected by two independent triggers
and was found to be about 90\% for the elastic events used in this
analysis and flat in all relevant kinematic variables. The
efficiency for the proton-dissociative events was significantly lower,
of the order of 10\%, due to the FCAL energy requirement.
This requirement restricts the mass of the dissociative
system to $M_N\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$} 7$~GeV.
\subsection{Offline requirements}
\label{offline}
In the offline event selection the following conditions were imposed:
\begin{itemize}
\item exactly two oppositely-charged tracks from a common vertex;
\item each track with $p_t > 0.15 $~GeV and
$|\eta| < 2.2$;
\item the vertex coordinates in the range
$V_R\equiv\sqrt{V_X^2 + V_Y^2} < 0.7$ cm and $|V_Z| < 40$ cm;
\item $85 < W < 105 \ \Gev $, thereby selecting a region of high
and well understood tagging efficiency;
\item a maximum energy of $200$ MeV (RCAL) and $250$ MeV (BCAL)
deposited in any
calorimeter cell, with the exception of those matched to tracks;
\item energy deposition in any of the 8 FCAL towers closest to the
beampipe less than 1.20 GeV.
\vspace*{-0.2cm}
\end{itemize}
The number of events thus selected was 25446.
The final identification of the vector-meson candidates was performed
using cuts on the invariant mass of the track pairs measured in the CTD.
The pion, kaon and electron masses were in turn assigned to the
tracks, leading to the selection of 22823 \rhoz\
($ 0.55 < \Mpp < 1.20 \ \Gev, \Mkk > 1.075 \ \Gev $), 366
\phiz\ ($ 0.99 < \Mkk < 1.06 \ \Gev $), and 120
\jpsi\ ($ 2.98 < \Mee < 3.13 \ \Gev $) meson candidates.
The invariant mass resolution varies from 5 to 60~MeV depending on
the meson type and the values of $t$ and $W$.
\vspace*{-0.3cm}
\section{Acceptance corrections}
\label{acc_corr}
\subsection{Monte Carlo generators}
The exclusive reaction $e p \rightarrow e V p$ was modeled using
the DIPSI~\cite{dipsi} Monte Carlo (MC) program.
For the simulation of the reaction $ep \rightarrow e V N$,
the EPSOFT Monte Carlo generator~\cite{epsoft} was used. The $M_N$
distribution at fixed $t$ was reweighted to the dependence
\begin{equation}
\frac{\rm{d}\sigma_{\gamma p \rightarrow VN}}{\rm{d} \it{M_{N}}^2} \propto
\frac{1}{M_N^{\beta(t)}}.
\label{e:beta}
\end{equation}
For \rhoz\ and \phiz\ production, the function
$\beta(t)=1.12e^{0.6t+0.3t^2+0.04t^3}+1.08e^{0.85t+0.11t^2}$ was
used;
this function was found by parameterizing the ISR \cite{chlm}
data on $\frac{\rm{d}\sigma}{\rm{d} \it{M_{N}^2}}$
in $pp$ single diffraction at large $-t$ and $M_N^2<0.1W^2$~\cite{LA_thesis}.
For \jpsi\ production the average between the above $\beta(t)$ and
$\beta(t)=2.35$ (expected in Regge phenomenology for constant
$\alphapom(t) = 1.175$~\cite{jpsi_intercept}) was used.
The $t$ (and $M_{\pi\pi}$ for $V$=\rhoz ) distribution was reweighted
in both generators so
as to reproduce the measured distribution after reconstruction;
the polar and azimuthal angular distributions of the decay
particles in the helicity frame were also reweighted.
\subsection{Photoproduction tagging acceptance}
The geometric acceptance of the PT was simulated by a program which uses
the HERA beam-transport matrices to track the positron through the HERA
beamline. This program was tuned so as to reproduce the measured tagging
efficiency, $A_{B}$, using Bethe-Heitler events,
$e p \rightarrow e \gamma p$. $A_{B}$ was defined
as the fraction of bremsstrahlung events with a photon measured
in the LUMI photon detector when the PT
fired the trigger.
In Fig.~\ref{fig:tagger_acc}a, $A_{B}$ is shown as a
function of the measured photon energy, $E_\gamma$, in the LUMI;
the MC prediction is in reasonable agreement with the data.
The acceptance for photoproduction events was determined using the
geometric acceptance of the tagger and events generated according to
the equivalent-photon approximation for positron scattering angles up
to 3~mrad (for larger angles the acceptance is negligible); for these
events, the positron was tracked through the HERA beamline. The
photoproduction tagging efficiency, $A_t$, was calculated as a
function of the positron energy, $E_{e^\prime}$, (see
Fig.~\ref{fig:tagger_acc}b). For the kinematic range used in this
analysis, the average (cross-section weighted) PT acceptance was 70\%.
The systematic error was evaluated by changing the data sets used to
tune the MC and by varying the photon energy scale and the position of
the positron exit window in MC within their systematic uncertainties.
\begin{figure}[htb]
\vspace*{-1.cm}
\begin{center}
\epsfig{file=tageff_func.eps,width=0.8\textwidth}
\put(-330,220){\bf \large a)}
\put(-160,220){\bf \large b)}
\end{center}
\vspace*{-1.0cm}
\caption{a) The measured bremsstrahlung tagging efficiency (dots),
$A_B$, as a
function of the measured photon energy, $E_\gamma$, compared to the MC
expectation (solid line). (b) Photoproduction tagging efficiency $A_t$
as a function of
the energy of the scattered positron $E_e'$; the shaded band
represents the systematic uncertainty.}
\label{fig:tagger_acc}
\end{figure}
\subsection{Overall acceptance}
The generated events were processed through the same chain
of selection and reconstruction procedures as the data, thereby accounting
for trigger as well as detector efficiencies (except for that of the PT)
and smearing effects in the ZEUS detector. The reconstructed
Monte Carlo events were then weighted with the function
$A_t(E_{e^\prime})$ in order to account for the PT acceptance and efficiency.
All measured
distributions are well described by the Monte Carlo simulations. Some
examples are displayed in Fig.~\ref{fig:compmc}.
The overall acceptance in a
given bin was then determined as the ratio of the number of accepted
Monte Carlo events (weighted by $A_t$)
to the number generated in the selected kinematic
range. The acceptance, calculated in this manner, accounts for the
geometric acceptance, the detector and reconstruction efficiencies,
the detector resolution and the trigger efficiency.
\begin{figure}[htb]
\vspace*{-.3cm}
\begin{center}
\epsfig{file=mc_data.eps,width=0.9\textwidth}
\end{center}
\vspace*{-1.6cm}
\caption{Comparison between the data and MC distributions of
$\eta$ and $p_t$ of the positively charged track, and $W$,
$\cos\theta_h$, $\phi_h$ and the meson pseudorapidity
$\eta_{V}$. The three columns refer to the sum of the elastic and
proton-dissociative \rhoz, \phiz\ and \jpsi\ samples, respectively.}
\label{fig:compmc}
\end{figure}
Figure~\ref{fig:acceptance} shows the overall acceptance for elastic
events as a function of $t$, $\varphi_h$ and $\cos{\theta_h}$.
Inefficiencies at small $-t$, as well as the strong variation of the
acceptance with $\varphi_h$ for \rhoz\ and \phiz\ mesons, are mainly due to
the relatively small opening angle between the decay particles, resulting
in many very backward tracks (as can be deduced from the
pseudorapidity distributions of
tracks in Fig.~\ref{fig:compmc}) outside the
geometric acceptance of the CTD.
The average acceptances are of the order of 30\% for
elastic and 5\% for proton dissociative events, respectively. The much lower
acceptance for the proton dissociative events is mainly due to the
FCAL energy requirement imposed in the trigger.
\begin{figure}[htb]
\begin{center}
\vspace*{+.5cm}
\epsfig{file=accept.eps,width=0.9\textwidth}
\end{center}
\caption{Overall acceptance for elastically produced
\rhoz, \phiz\ and \jpsi\ mesons as
a function of $-t$ and the helicity variables $\phi_h$ and $\cos\theta_h$.}
\label{fig:acceptance}
\end{figure}
\section{Backgrounds}
The dominant background sources are non-resonant $\pi^+\pi^-$ production
for the \rhoz\ analysis, \rhoz\ production for the \phiz\ analysis, and
Bethe-Heitler $\gamma\gamma\rightarrow e^+e^-/\mu^+\mu^-$
production for the \jpsi\ case.
These backgrounds were statistically subtracted using
the fits to invariant-mass distributions as described
in Sect.~\ref{sec:results}.
The background due to inclusive photon diffractive dissociation,
$\gamma p\rightarrow Xp$, was studied using Monte Carlo simulations
and minimum-bias data samples. It was found to be about 1-2\% and was
also subtracted in the fitting procedure.
In the \rhoz\ analysis, the backgrounds due to decays of
$\omega$ and $\phi$ mesons were found from MC studies to be negligible.
The background due to non-diffractive events was also small and
was neglected.
On average, 10\% of the diffractive events were rejected by the trigger
due to accidental coincidences with bremsstrahlung events in the LUMI
calorimeter. A correction was applied to account for this effect.
A small fraction of events, below 1\%, was selected due to fake
photoproduction tagging from bremsstrahlung overlays
(when the meson decay particles were measured by the CTD and the scattered
positron was undetected, while the PT was hit instead by a
bremsstrahlung positron); this effect was neglected.
\section{Separation of elastic and proton-dissociative processes}
\label{sec:sep}
The selected samples of diffractively-produced vector mesons are
mixtures of elastic and proton-dissociative events. These two processes
have been separated as a function of $t$ on a statistical
basis using the MC simulation.
Proton-dissociative events were tagged by requiring a signal
in one of the PRT1 counters above a threshold corresponding to the
signal of a minimum ionizing particle. Alternatively, for systematic checks,
energy depositions in the FCAL towers close to the beampipe were also used
for tagging the proton-dissociative events.
Since the non-diffractive backgrounds were negligible, the following
relation was assumed:
$$\frac{N^T_{pd,data}}{N_{pd,data}} = \frac{N_{pd,MC}^T}{N_{pd,MC}},$$
where $N_{pd,data}$ and $N_{pd,MC}$ are the numbers of all
accepted (but not necessarily tagged)
proton-dissociative events, whereas $N_{pd,data}^T$ and $N_{pd,MC}^T$
are the numbers of tagged proton-dissociative events,
in the data and proton-dissociative EPSOFT samples, respectively.
Therefore, the fraction, $C_D$, of proton-dissociative events in
the data was calculated from
$$ C_D=\frac{N_{pd,data}}{N_{data}}=\frac{N^T_{pd,data}}{N_{data}}/
\frac{N_{pd,MC}^T}{N_{pd,MC}},$$
where $N_{data}$ is the number of all observed events (elastic and
proton-dissociative) in a given $t$ bin in the data.
In Fig.~\ref{fig:sep} the observed fraction of PRT1 tags, $R_{D}$,
in the data and in the proton-dissociative MC,
as well as the estimated fraction of proton-dissociative events,
$C_D$, are displayed separately for the
$\rho^0$, $\phi$ and $J/\psi$ samples.
For the low $-t$ region, the
elastic process contributes a large fraction of the selected
diffractive events. For $-t>1.0$ GeV$^2$, the contribution from the
proton-dissociative process exceeds that from the elastic
channel.
\begin{figure}[htb]
\begin{center}
\epsfig{file=separation.eps,width=\textwidth}
\end{center}
\caption{Observed fraction of PRT1 tags, $R_{D}$, in the data (triangles
with statistical error bars) and in the proton-dissociative MC
(histogram), and the estimated fraction of
proton-dissociative events in data, $C_{D}$, for the
\rhoz \ (a,b), \phiz \ (c,d) and \jpsi \ (e,f) samples as
a function of $-t$. The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties added in
quadrature. The shaded bands in b), d) and f) represent the size of the
correlated errors due to modeling of the proton dissociation in the
Monte Carlo.}
\label{fig:sep}
\end{figure}
\clearpage
\section{Systematic uncertainties}
The systematic uncertainties were subdivided
into those related to the selection procedure and the
detector simulation, and those reflecting
the uncertainty in the model used for
the Monte Carlo generator.
The effects of the following changes in the
selection procedure were checked:
\renewcommand{\theenumi}{\arabic{enumi}}
\renewcommand{\labelenumi}{\theenumi)}
\begin{enumerate}
\item
the FCAL (instead of PRT1) was used to tag the
proton-dissociative events;
\item
the matching procedure between the tracks and energy depositions in CAL was
varied by changing the matching distance between the track and CAL cluster and
the energy requirement used to define the CAL cluster;
\item
the minimum value of the track transverse momentum was
varied between 100 and 200 MeV;
\item
the limit on the track $|\eta|$ was varied between 2.1 and 2.3;
\item the requirements on the vertex position were varied by amount
corresponding approximately to the resolution, i.e. $\pm$ 5 cm in $Z$
and $\pm$ 0.25 cm in the radial direction;
\item
the selected invariant mass region was changed by widening and narrowing it
by amounts corresponding to approximately the appropriate mass resolution;
\item
the threshold values of all
PRT1 counters were increased by 100\%.
\end{enumerate}
The first check resulted in 5--20\% changes of the measured cross sections.
Checks 2--5 resulted in 3--5\% changes, and the last two checks had
negligible effect.
In the MC simulation, the positions of some beamline elements (eg. the
position of the
synchrotron collimator jaws) were varied within their uncertainties,
resulting in a 5--15\% change in the cross section.
In order to estimate the systematic uncertainty from the uncertainties in
the parameters assumed in the EPSOFT generator, the following
modifications were made:
\begin{itemize}
\item
the shape of $\beta(t)$ was varied within the uncertainties of its
measurement~\cite{LA_thesis};
for \rhoz\ and \phiz\ production, this corresponds to
$\beta(t)=2.24e^{0.6t+0.3t^2+0.04t^3}$ and
$\beta(t)=2.16e^{0.85t+0.11t^2}$; for \jpsi\ production,
to
$\beta(t)=1.12e^{0.6t+0.3t^2+0.04t^3}+1.08e^{0.85t+0.11t^2}$
and $\beta(t)=2.35$. These variations significantly changed
the acceptance corrections, by up to 10\% at low $-t$ and up to 70\% for
the proton-dissociative sample at the highest $-t$;
\item
multiplicity distributions of the decay particles of the
dissociative system $N$ were varied within the uncertainties
of their measurement~\cite{cool}. This resulted in cross section
variations of $<5\%$.
\end{itemize}
Additionally, the re-weighting of other MC distributions (of the decay
particle angles or invariant masses, for example) was performed
in the range allowed by maintaining satisfactory agreement between data
and Monte Carlo. The effect on the cross sections was $<3\%$.
In the determination of the \rhoz\ spin-density matrix elements,
the difference between the nominal method (see Sect. \ref{sec:hel}) and the
method of moments was taken as an additional uncertainty.
The overall normalization error due to the photoproduction
tagging uncertainty was $\pm15$\%.
\section{Results}
\label{sec:results}
The differential cross sections \dsdt\ for elastic and
proton-dissociative photoproduction of $V$
were evaluated in each bin of $t$ as:
\begin{equation}
\label{e:dsdt_el}
\frac{\rm{d}\sigma_{\gamma p \ra V p}}{\rm{d}\it{t}} =
\frac{N\cdot (1-C_{D})\cdot C_{res}}
{A\cdot {\cal L}\cdot \Phi_\gamma \cdot \Delta t \cdot C_{br}},
\end{equation}
\begin{equation}
\label{e:dsdt_pd}
\frac{\rm{d}\sigma_{\gamma p \ra V N}}{\rm{d}\it{t}} = \frac{N\cdot C_{D}\cdot
C_{res}}{A\cdot {\cal L}\cdot \Phi_\gamma \cdot \Delta t \cdot C_{br}},
\end{equation}
where $N$ is the number of observed vector-meson candidates in bin
$\Delta t$ after all selection cuts, $C_{D}$ is the estimated fraction
of the proton-dissociative events in the bin, $C_{res}$ is the resonant
contribution in the bin, $C_{br}$ is the branching ratio of the
vector-meson decay mode considered, $A$ is the overall acceptance in the
bin, ${\cal L}$ the integrated luminosity, and $\Phi_\gamma$ is the integrated
effective photon flux (see Eq.~\ref{gp_cros}). In the kinematic region
$Q^2 < (E_e\theta_{max})^2(1-y)$, where $\theta_{max}=$~3~mrad
(see Sect. 6.2), and $85< W < 105$~GeV, $\Phi_\gamma=0.0121$.
The branching ratios for the \rhotopp,
\phitokk, \jpsitoee\ or \jpsitomm\ decay modes
were taken as $ 1,\ 0.5$ and $0.12$, respectively.
Effects due to QED radiation,
estimated to be smaller than 2\%~\cite{kurek}, were neglected.
A similar procedure was used to evaluate the differential cross section
$\rm{d}\sigma/\rm{d}\Mpp$.
For the proton-dissociative reaction, cross sections are extrapolated to
$M_N^2=0.1W^2$ using the EPSOFT MC, as modified by Eq.~\ref{e:beta}.
\subsection{$\rho^0$ photoproduction }
\subsubsection{Resonance mass shape}
\label{sec:mass}
The differential cross sections $d\sigma/d\Mpp$ were fitted using a
parameterization inspired by the S\"oding model~\cite{soding},
where the p-wave relativistic Breit-Wigner (BW) shape is distorted
by the interference with non-resonant $\pi\pi$ production:
\begin{equation}
\frac{d\sigma}{d\Mpp} = A^2 \left[
\left | \frac{ \sqrt{\Mpp \Mrho \Grho}}{\Mppsq-
\Mrhosq+i\Mrho\Grho}+B/A \right | ^2 + f \right],
\label{soding}
\end{equation}
where \Mrho \ is the \rhoz \ mass, \Grho \ is the momentum-dependent
width
\begin{equation}
\Grho(\Mpp) = \Gz\left( \frac{q}{q_0} \right)^3 \frac{\Mrho}{\Mpp},
\label{width}
\end{equation}
\Gz \ is the width of the \rhoz , $q$ is the $\pi$ momentum in
the $\pi\pi$ rest frame and $q_0$ is the value of $q$ at $M_{\pi\pi}
= M_{\rho}$. The non-resonant amplitude (taken to be
$M_{\pi\pi}$-independent) is
denoted by $B$, and $A$ is the normalization factor of the resonant
amplitude. Additionally, another term, $f$, was introduced to account for
the background from reactions with photon diffractive
dissociation. The~term $f$ was assumed to be linear in $M_{\pi\pi}$,
$f\propto(1+1.5M_{\pi\pi})$~\cite{zrho-94} with $M_{\pi\pi}$ in GeV.
Alternatively the following parameterization, proposed by Ross and
Stodolsky~\cite{rs}, was used:
\begin{equation}
\frac{d\sigma}{d\Mpp} = A\left[
\frac{ \Mpp \Mrho \Grho}{(\Mppsq-
\Mrhosq)^2+\Mrhosq\Grhosq} \left(\frac{\Mrho}{\Mpp} \right)^{n} + f \right] ,
\label{ross}
\end{equation}
where \Grho \ is given by Eq.~\ref{width} and $f$ has the same
form as described above.
The $\chi^2/NDF$ for all the fits is satisfactory. The fitted
values of \Mrho,
\Gz \ and $f$ do not depend on the prescription used to parameterize
the mass distribution. The mass, \Mrho, and width, \Gz, for all $t$
values are
compatible with the values of the Particle Data Group (PDG)\cite{ref:pdg}.
The level of background under the \rhoz \ peak, as given by the
integral of the function $f$, is about 1--2\%. The mass
distributions for elastic and proton-dissociative \rhoz \ production
are shown in Fig.~\ref{fig:rho_mas_t}
together with the results of
the fits using Eq.~\ref{soding}. The mass resolution varies
between 20 and 60~MeV for \Mpp\ between 0.5 and 1.2 GeV,
respectively.
\begin{figure}[htb]
\vspace*{-0.5cm}
\begin{center}
\epsfig{file=rho_mas_t.eps,width=0.8\textwidth}
\end{center}
\vspace*{-1cm}
\caption{The differential cross sections $d\sigma/d\Mpp$ for
several $t$ ranges. The
points represent the data and the curves indicate the result of the fits
with Eq.~\ref{soding}. The dashed curves represent the
resonant contribution, the dotted curves the non-resonant contribution and
the dot-dashed curves the contribution from the interference term. The
solid curves are the sum. Only the statistical errors are shown. The
circles and squares correspond to the elastic and the
proton-dissociative samples, respectively.}
\label{fig:rho_mas_t}
\end{figure}
The fits to the mass distributions were repeated with
\Mrho \ and \Gz \ fixed to the PDG values.
The results for $B/A$ and $n$ are shown as a function of $-t$ in
Fig.~\ref{fig:mas_res}; they match with our earlier
measurement for the low $-t$ region at
$\langle W\rangle=70$~GeV~\cite{zrho-94}.
Both $B/A$ and $n$ decrease with $-t$, indicating
that the resonance shape distortion decreases.
This decrease is much faster
with $-t$ than that with $Q^2$~\cite{zvm95}.
The dependence of the ratio $B/A$ on $t$ was parameterized as
\begin{equation}
B/A = k e^{b_{S}t}.
\label{n_t}
\end{equation}
The fit to the data yields $k = -0.86\pm
0.52$~(stat.)~GeV$^{-1/2}$ and $b_{S} = 1.6 \pm 0.9$~
(stat.)~GeV$^{-2}$ for the elastic reaction, and $k = -0.71 \pm 0.21$~
(stat.)~GeV$^{-1/2}$ and $b_{S} = 0.9 \pm 0.4$~(stat.)~GeV$^{-2}$ for
the proton-dissociative process. The similar magnitudes
and $t$ dependences of the
$B/A$ ratio for the elastic and the proton-dissociative processes
indicate that the data are consistent with the hypothesis of
factorization of the diffractive vertices.
The \rhoz\ production cross section was evaluated in the mass
range $2M_\pi<\Mpp<M_\rho+5\Gamma_0$. The extrapolation from
the measured range $0.55<\Mpp<1.2~\Gev$ was made using the
results of the fit to Eq.~\ref{soding}.
\begin{figure}[htb]
\begin{center}
\epsfig{file=mas_res_new.eps,width=0.9\textwidth}
\put(-320,275){\boldmath $\gamma p \ra \pi^+ \pi^- p$}
\put(-115,275){\boldmath $\gamma p \ra \pi^+ \pi^- N$}
\end{center}
\vspace*{-.2cm}
\caption{The ratio $B/A$ from Eq.~\ref{soding} and the
parameter $n$ from Eq.~\ref{ross}, as a function of $-t$.
The inner error
bars indicate the statistical errors, the outer ones the statistical and
systematic uncertainties added in quadrature. The solid circles and
squares correspond to the elastic and the
proton-dissociative samples, respectively. The
open circles correspond to the low $-t$ ZEUS results \cite{zrho-94}.
The solid curves are fits of the form $k e^{b_{S}t}$ (see text).}
\label{fig:mas_res}
\end{figure}
\subsubsection{$t-$distributions}
The differential cross sections, $\dsdt$, for elastic and
proton-dissociative (for $M^2_N<0.1W^2$)
$\rho^0$ photoproduction are plotted in
Fig.~\ref{fig:dsdt-rho}a. Both samples exhibit an exponential
drop with increasing $-t$, with the cross section for the elastic
process falling off more steeply than that for
the proton-dissociative process. A fit with the function
$A\exp(bt)$ in the range $0.4<-t<1.2$~GeV$^2$ for the elastic process
gives $b_{el}$ = 6.0 $\pm 0.3~(\mbox{stat.})~^{+0.6}_{-0.3}~(\mbox{sys.})
\pm 0.4~(\mbox{mod.})$~GeV$^{-2}$ and
$b_{pd}$ = 2.4 $\pm 0.2~(\mbox{stat.})~^{+0.2}_{-0.1}~(\mbox{sys.})\pm
0.3~(\mbox{mod.})$ GeV$^{-2}$ for the proton-dissociative sample,
where (mod.) represents the uncertainty due to the modeling
of the proton dissociation in the EPSOFT Monte Carlo.
The ratio of the elastic to the
proton-dissociative cross sections, $\rm{d}\sigma(\gamma p \to \rho^0
p)/ \rm{d}\sigma(\gamma p\to \rho^0 N)$, in a given $t$ interval is
shown in Fig.~\ref{fig:dsdt-rho}b.
This ratio falls off rapidly with $-t$ from about unity at $-t\approx$
0.4 GeV$^2$ to about $10^{-2}$ for $-t\ge$ 1 GeV$^2$. By comparison,
this ratio has the value 2.0 $\pm$ 0.2~(stat.) $\pm$ 0.7~(syst.) for
$-t<$ 0.5 GeV$^2$ at $W$ = 70 GeV \cite{zrho-94}. An exponential fit
to the ratio gives a value for the slope $\Delta b=3.4
\pm0.3$~(stat.)~$^{+1.5}_{-0.3}$~(sys.)~ $\pm 0.2$~(mod.)~GeV$^{-2}$,
which is similar to that found previously \cite{zrho-94}.
\begin{figure}[htb]
\vspace*{-1.0cm}
\begin{center}
\epsfig{file=rho.eps,width=0.81\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{a) The differential cross sections \dsdt for elastic
(circles) and proton-dissociative (squares) \rhoz \
photoproduction.
The solid lines represent the results of the fit with the
function $Ae^{bt}$. The normalization error of 15\% is not shown.
b) The ratio of the elastic to the proton-dissociative cross
sections shown in a). The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties added in
quadrature.
The shaded bands represent the size of the correlated errors due
to the modeling of the proton dissociation in the
Monte Carlo.
}
\label{fig:dsdt-rho}
\end{figure}
Figure~\ref{fig:dsdt-rho-el} shows the differential cross
section for the elastic reaction together with results obtained
in our earlier studies of the
low $-t$ region~\cite{zrho-94,zrho-lps}.
The data at low $-t$
were measured at a somewhat lower $W$ ($\langle W\rangle=70$ GeV) and have been
rescaled to the average $W$ of the present analysis
($\langle W\rangle=94$~GeV),
assuming the Pomeron trajectory as measured in this analysis
(see Sect.~\ref{trajectory}).
The large $-t$ data match well with the low $-t$ results.
The data in Fig.~\ref{fig:dsdt-rho-el} cannot be described
by the expression $A\exp(bt)$
over the whole $t$ range. The slope $b_{el}$
(of about $10~\Gev^2$~\cite{zrho-94})
in the low $-t$ region is larger than that in the
large $-t$ region, in contrast to the case for $\Delta b$,
which is the same within errors
in both $t$ regions, as well as at higher $Q^2$~\cite{h1-rho-deltab}.
\begin{figure}[htb]
\begin{center}
\epsfig{file=dirk_lps.eps,width=0.95\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{The differential cross sections, \dsdt, for elastic
\rhoz \ photoproduction. The solid circles are those shown in
Fig.~\ref{fig:dsdt-rho}; the open circles and crosses are from
earlier ZEUS data~\cite{zrho-94,zrho-lps}.
The shaded band represents the size of the correlated errors due
to the modeling of the
proton dissociation in the Monte Carlo. The normalization error of
15\% is not shown.
}
\label{fig:dsdt-rho-el}
\end{figure}
\subsubsection{Decay angular distributions}
\label{sec:hel}
The angular distributions of the decay pions were used to determine
some of the $\rho^0$ spin-density matrix elements using the invariant
mass selection $0.55<\Mpp<1.2~\Gev$. The direction of the virtual
photon was approximated by that of the incoming positron. In this
measurement, the three-dimensional angular distribution has been
averaged over the azimuthal angle between the positron scattering
plane and the $\rho^0$ production plane, $\Phi$, and thus no longer
distinguishes the photon helicity states $\pm$ 1. The normalized
two-dimensional decay angular distribution can be written as
\cite{wolf}
\begin{eqnarray}
W(\cos{\Thel},\fhel) = & \frac{3}{4\pi} \left\{ \frac{1}{2}(1-\rzfzz)+
\frac{1}{2}(3\rzfzz - 1)\cos^{2}{\Thel} \right. \nonumber \\
& - \sqrt{2} \mbox{Re}[\rzfpz]\sin{2\Thel}\cos{\fhel}
\left. - \rzfpm\sin^{2}{\Thel}\cos{2\fhel} \right\} ,
\label{hel_2d_dis}
\end{eqnarray}
where the spin-density matrix element \rzfzz \ represents the probability
that the produced \rhoz \ has helicity $0$; the element \rzfpz \ is
related to the interference between the helicity non-flip and single-flip
amplitudes;
\rzfpm \ is related to the interference between the non-flip and
double-flip amplitudes. If $s$-channel helicity conservation
(SCHC)~\cite{schc}
holds, \rzfzz, \rzfpm \ and $\mbox{Re}[\rzfpz]$ \ should be zero.
The parameters \rzfzz, \rzfpm \ and Re$[\rzfpz]$ were obtained by
minimizing the difference between the two-dimensional ($\cos{\Thel},
\fhel$) angular distributions of the data and those of the simulated
events, which were re-weighted according to Eq.~\ref{hel_2d_dis}.
A binned $\chi^2$-method was used.
The three spin-density matrix elements are shown in
Fig.~\ref{fig:ang_res_2d}, separately for elastic and
proton-dissociative \rhoz\ production as a function of $-t$.
In the $t$ range of this analysis,
Re$[\rzfpz]$ tends to be non-zero and positive,
while \rzfpm\ tends to be non-zero and negative. This is an
indication for small deviations from SCHC giving rise to non-zero
helicity single-flip and double-flip amplitudes.
The element \rzfzz\ is measured to be zero within errors.
The present results are
not corrected for the non-resonant $\pi^+\pi^-$ production. Hence, strictly
speaking, they only apply to the reaction $\gamma
p(N)\to\pi^+\pi^-p(N)$
within the quoted \Mpp\ range.
However, in the previous section it was shown that the non-resonant
contribution is small and decreases rapidly with $-t$.
In order to assess the sensitivity of the data to changes in the
selected \Mpp\ range, the events with $\Mpp<M_\rho$ and $\Mpp>M_\rho$
were analyzed separately. No statistically significant effect was
observed. Data at lower $-t$ ($<-t> \approx $0.1 GeV$^2$) from
ZEUS~\cite{zrho-94} show no evidence for a violation of SCHC.
However, lower energy ($<W> \approx 4.3$ GeV) elastic photoproduction
data~\cite{ballam-73}, while showing no SCHC violation for $-t < 0.2$
GeV$^2$, yield positive values for Re$[\rzfpz]$ and negative values
for \rzfpm\ for $-t> 0.2$ GeV$^2$. Recent HERA measurements, both at low
$Q^2$ (0.25--0.85 GeV$^2$)~\cite{zbpc} and higher $Q^2$ (greater than
1 GeV$^2$)~\cite{zbpc,h1schc}, also report similar values, at $<-t>
\approx$ 0.1--0.2 GeV$^2$, although only the low $Q^2$ results are
significantly non-zero.
\begin{figure}[htb]
\vspace*{-.5cm}
\begin{center}
\epsfig{file=ang_res_2d.eps,width=0.8\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{The spin-density matrix elements \rzfzz,
Re$[\rzfpz]$
and \rzfpm \
as a function of $-t$ obtained by fitting Eq.~\ref{hel_2d_dis}
to the data. The squares correspond to the
proton-dissociative sample and the solid
circles to the elastic sample.
The inner error bars indicate the statistical errors,
the outer bars the statistical and
systematic uncertainties added in quadrature. }
\label{fig:ang_res_2d}
\end{figure}
\subsection{$\phi$ photoproduction}
\subsubsection{Mass distribution}
The invariant mass of the two charged decay products of the $\phi$ is
displayed in Fig.~\ref{fig:phi_mas_t} for different $-t$
ranges for two samples of data: for all events and for those that
have a signal in PRT1 (proton dissociation).
The invariant mass was computed assuming that the two charged
particles were kaons. The lines are fits to a Breit-Wigner
function, convoluted with a Gaussian resolution function, and a
function describing the background. The background, due mainly to
diffractive $\rho^0$ events for which the two pions are assigned the kaon
mass, was assumed to have the form $\sim (M_{KK} - 2M_K)^\Delta$, where
$\Delta$ is a parameter determined by the fit. For the determination of
the background contribution in each $t$ region, the mass and width
of the $\phi$ were fixed to the PDG values.
The fit was performed over
a broad mass range $0.99 < M_{KK} < 1.13 $ GeV to give a better
estimate of the background. A narrower mass range $0.99 < M_{KK} < 1.06 $
GeV was then used to select \phiz\ candidates and the background
contribution in this range was subtracted. The mass resolution is about
10~MeV, consistent with the Monte Carlo simulations.
The background contribution decreases with $-t$,
from about 23\% at $-t=0.5~ \Gev^2$ to 10\% above $-t=1.2~\Gev^2$.
\begin{figure}[htb]
\vspace*{-0.5cm}
\begin{center}
\epsfig{file=phi_mas_t.eps,width=0.85\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{The \Mkk \ distributions in four $-t$ bins. The left-hand plots
are for all events, while the right-hand plots are for PRT1-tagged events.
The points represent the data and the solid
curves indicate the result of the {f}it discussed in the text. The
dashed curves represent the background contribution. Only the
statistical errors are shown.}
\label{fig:phi_mas_t}
\end{figure}
\subsubsection{$t-$distributions}
The differential cross sections $\dsdt$ for the reactions $\gamma p
\to \phi p$ and $\gamma p \to \phi N$ ($M^2_N<0.1W^2$) were
determined following the separation procedure described in
Sect.~\ref{sec:sep}; the results are shown in
Fig.~\ref{fig:dsdt-phi}a. As in
the $\rho^0$ case, both differential cross sections decrease
exponentially with increasing $-t$. A fit with a function of the form
$\dsdt = A\exp(bt)$ in the range $0.4<-t<1.2$~GeV$^2$ yields
$b_{el}$ = 6.3 $\pm
0.7$~(stat.)$\pm 0.6$~(sys.)$\pm 0.3$~(mod.)~GeV$^{-2}$ and
$b_{pd}$ = 2.1 $\pm
0.5$~(stat.)$\pm 0.3$~(sys.)$\pm 0.4$~(mod.) GeV$^{-2}$. These
values are the same within errors as those obtained for the
$\rho^0$. Note that while $b_{el}^\rho > b_{el}^\phi$ in the region
$-t<$ 0.3 GeV$^2$~\cite{zphi-94}, $b_{el}^\rho \approx b_{el}^\phi$
in the region
0.4 $<-t<$ 1.5 GeV$^2$. There are no data at low $-t$ to make a similar
comparison in the case of the proton-dissociative process,
but for the larger $-t$ range, $b_{pd}^\rho \approx
b_{pd}^\phi$. This indicates that the mass difference between the
$\rho^0$ and the $\phi$ is not important in the large $-t$ \ region.
\begin{figure}[htb]
\vspace*{-0.5cm}
\begin{center}
\epsfig{file=phi.eps,width=0.87\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{a) The differential cross sections $\dsdt$ for elastic
(circles) and proton-dissociative (squares) \phiz \
photoproduction. The solid lines represent the results of the fit with the
function $Ae^{bt}$. The normalization error of 15\% is not shown.
b) The ratio of the elastic to proton-dissociative cross
sections. The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties added
in quadrature.
The shaded bands represent the size of the
correlated errors due to the modeling of the proton dissociation in the
Monte Carlo.
}
\label{fig:dsdt-phi}
\end{figure}
Fig.~\ref{fig:dsdt-phi}b shows the ratio of the cross sections for
the elastic and the proton-dissociative processes in a given $t$ interval
as function of $-t$.
The ratio decreases rapidly from unity
at $-t\approx$ 0.5 GeV$^2$ to $\approx 10^{-2}$ at
$-t\approx$ 1.3 GeV$^2$, as in the $\rho^0$ case.
A fit to the
ratio gives $\Delta b=3.0 \pm
0.8$ (stat.)~$^{+0.5}_{-0.9}$~(sys.)~$^{+0.3}_{-0.5}$~(mod.)~GeV$^{-2}$.
This value is the same within errors as that obtained for the
$\rho^0$,
and is thus independent of the
type of the vector meson produced at the photon vertex (see
Sect.~\ref{sec:ff}).
In Fig.~\ref{fig:dsdt-phi-el} the results for $\dsdt$ for
elastic $\phi$ photoproduction are displayed, together with ZEUS
measurements at small $-t$~\cite{zphi-94}. The low $-t$ data have
been rescaled to the present $W$ value by assuming the Pomeron trajectory
as measured in this analysis (see Sect.~\ref{trajectory});
both data sets are plotted
with statistical errors only. The results are consistent.
\begin{figure}[htb]
\begin{center}
\epsfig{file=proskur.eps,width=\textwidth}
\end{center}
\caption{The differential cross sections $\dsdt $ for elastic
\phiz \ photoproduction. The solid circles correspond to the data of
this analysis and
the open circles are from an earlier ZEUS result~\cite{zphi-94}.
The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties
added in quadrature.
The shaded band represents the size of the correlated errors due
to the modeling of the proton dissociation in the
Monte Carlo. The normalization error of 15\% is not shown. }
\label{fig:dsdt-phi-el}
\end{figure}
\clearpage
\subsection{$J/\psi$ photoproduction}
\subsubsection{Mass distribution}
Figure~\ref{fig:jpsi-mass} shows the two body
invariant mass distribution in the region 2.4--3.6 GeV, for the whole
sample in two $-t$ ranges and for the PRT1-tagged sample in one $-t$ bin.
No lepton identification was performed for this sample.
Although the events therefore
represent a sum of $e^+e^-$ and $\mu^+\mu^-$ final
states
the electron mass was always assumed for each of the two charged
particles\footnote{Assuming the muon mass
does not change any of the results.}.
A narrow peak is observed around 3.1 GeV. Fits were made
to the invariant mass distribution using the sum of a Gaussian
(for the $\mu$ case), a Gaussian (modified by the energy loss spectra
due to bremsstrahlung in dead material before the CTD for the $e$ case),
and a background which linearly decreases with mass. Equal numbers of $e$
pairs and $\mu$ pairs were assumed.
The fitted $J/\psi$ mass is in good agreement with the PDG value.
The background in the $J/\psi$ mass
region (2.87--3.13 GeV) is (20 $\pm$ 5)\%, independent of
$t$ in the range under study ($-t<$ 3 GeV$^2$).
\begin{figure}[htb]
\vspace*{-1.0cm}
\begin{center}
\epsfig{file=psi_mas_t.eps,width=0.85\textwidth}
\end{center}
\vspace*{-1.2cm}
\caption{The \Mee \ distributions in two $-t$ bins for the whole
sample (a,b) and in one bin for the PRT1 tagged events (c).
The points represents the data and the curves indicate
the result of the fit discussed in the text. The dashed curve represents the
background contribution. }
\label{fig:jpsi-mass}
\end{figure}
$\ $
\vspace*{0.1cm}
$\ $
\subsubsection{$t-$distributions}
The differential cross sections $\dsdt$ for the elastic and the
proton-dissociative $J/\psi$ photoproduction reactions are shown in
Fig.~\ref{fig:dsdt-jpsi}a.
In contrast to the $\rho^0$ and $\phi$ cases, the high mass of the
$J/\psi$ and the resulting large opening angle of the decay particles
result in significant acceptance in the low $-t$ region.
However, in the case of the proton-dissociative process, the
effect of the minimum kinematically allowed $-t$, $-t_0\approx
0.06~{\rm GeV^2}$ (see Eq.~\ref{Eq:ptrel}), prevents
the measurement of \dsdt\ in the low $-t$ bins. The elastic
differential cross section falls exponentially, with
$b_{el}^{J/\psi}$ = 4.0 $\pm
1.2$(stat.)$^{+0.7}_{-1.1}$(sys.)$^{+0.4}_{-0.6}$(mod.)~GeV$^{-2}$, while
for the proton-dissociative reaction $b_{pd}^{J/\psi}$
= 0.7 $\pm 0.4$(stat.)$\pm 0.2$~(sys.)$^{+0.5}_{-0.3}$(mod.)~GeV$^{-2}$.
The slope
$\Delta b$ agrees, within errors, with the values for the
$\rho^0$ and $\phi$.
Fig.~\ref{fig:dsdt-jpsi}b shows the ratio of the elastic
to the proton-dissociative differential cross sections. This ratio also
falls from a value of about 1 at low $-t$ to a value of about 0.1
for $-t>$ 1 GeV$^2$, similar to the $\rho^0$ and the $\phi$
cases.
\begin{figure}[htb]
\vspace*{-0.5cm}
\begin{center}
\epsfig{file=psi.eps,width=0.8\textwidth}
\end{center}
\vspace*{-1.0cm}
\caption{a) The differential cross sections $\dsdt $ for elastic
(circles) and proton-dissociative (squares) \jpsi \
photoproduction.
The solid lines represent the results of the fit with the function
$Ae^{bt}$. The normalization error of
15\% is not shown.
b) The ratio of the elastic to the proton-dissociative cross
sections. The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties
added in quadrature.
The shaded bands represent correlated errors due
to the modeling of the proton dissociation in the Monte Carlo.
}
\label{fig:dsdt-jpsi}
\end{figure}
The present measurements of $\dsdt$ for the reaction $\gamma p \to
J/\psi p$ are shown in Fig.~\ref{fig:dsdt-jpsi-zeus-h1}, together with
our earlier untagged (i.e.\ $Q^2 \sim 0$)
photoproduction data~\cite{zjpsi-94} ($\langle
W\rangle = 90$ GeV). The data sets agree within errors.
\begin{figure}[htb]
\vspace*{-0.3cm}
\begin{center}
\epsfig{file=unknown.eps,width=0.9\textwidth}
\end{center}
\vspace*{-.2cm}
\caption{The differential cross section $\dsdt $ for elastic
$J/\psi$ \ photoproduction. The solid circles correspond to the present
measurement, the open circles to the published ZEUS untagged
photoproduction results
\cite{zjpsi-94}.
The shaded band represents correlated errors due to the modeling of the
proton dissociation in the Monte Carlo. The normalization error of
15\% is not shown.
}
\label{fig:dsdt-jpsi-zeus-h1}
\end{figure}
\section{Comparisons of data to models}
\subsection{Cross section comparisons with the pQCD-based models}
In order to compare the data to pQCD predictions for light
\cite{ginzburg} and heavy \cite{bartels} mesons, the cross sections
were redetermined in the region of validity of the model calculation,
{\it viz.} $M_N^2<0.01W^2$, using the EPSOFT MC simulation. The
measured proton-dissociative cross sections for the three vector
mesons are shown in Fig.~\ref{fig:pqcd}.
The calculations \cite{ginzburg} for the production of the
\rhoz\ and \phiz\ mesons
were performed at lowest order in $\alpha_S$. Only helicity non-flip
and single-flip amplitudes were taken into account.
The non-perturbative effects
were simulated by introducing
effective quark masses. In Fig.~\ref{fig:pqcd}a and \ref{fig:pqcd}b, the solid
(dotted) curves represent results for a quark mass of 300 (200)~MeV.
For the calculation of the \rhoz\ cross-section, the
sub-asymptotic \rhoz\ wave-function was used, whereas for
the \phiz\ production the asymptotic one
\cite{ginzburg,ivanov} was employed.
The contribution of the perturbative cross section,
represented by the dashed lines in Fig.~\ref{fig:pqcd}a and \ref{fig:pqcd}b,
is well below the \rhoz\ and $\phi$ data.
This observation, together with the helicity analysis (see Sect.~\ref{sec:hel})
in which no significant production of \rhoz\ mesons with helicity 0
is observed, implies that these perturbative calculations are not
applicable in this regime.
The situation is different in the $J/\psi$ case. The perturbative
QCD prediction in the LLA \cite{bartels} expansion in terms of
$\ln{(W^2/W_0^2)}$ (equivalent to $\ln{1/x}$)
compares satisfactorily with the data (solid line in Fig.~\ref{fig:pqcd}c).
A value of $\alpha_S$=0.2 and an energy scale $W_0=1$~GeV
have been used in this calculation.
It should be
noted, however, that the
uncertainties due to the choice of $\alpha_S$ ($\pm10\%$ -- dotted
lines) and the $W_0$ scale ($0.2<W_0^2<5$~GeV$^2$ -- dashed-dotted
lines) are significant.
\begin{figure}[htb]
\vspace{-0.3cm}
\begin{center}
\epsfig{file=cross_all.eps,width=0.75\textwidth}
\end{center}
\vspace{-1.2cm}
\caption{Comparison of the measured differential cross sections
\dsdt for proton-dissociative vector-meson production for
$M_N^2<0.01W^2$ with the pQCD-based models for a)~\rhoz\ ,
b)~\phiz\ ~\cite{ivanov} and c) $J/\psi$ ~\cite{bartels}.
The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties
added in quadrature. The shaded bands represent correlated errors due
to the modeling of the proton dissociation in the Monte Carlo. The
normalization error of 15\% is not shown. For the description of the
curves see text. }
\label{fig:pqcd}
\end{figure}
\subsection{Ratios of cross sections for vector-meson photoproduction}
\label{sec:ratios}
Flavor independence predicts that the ratio of the
production cross sections of $\phi$:$\rho^0$ should be 2:9 and that of
$J/\psi$:$\rho^0$ should be 8:9. These predictions are in striking
disagreement with the previously published low-$Q^2$
data: at $W$=70 GeV, the ratios
$\phi$:$\rho^0=0.065 \pm 0.013$~\cite{zphi/rho}
and \linebreak
$J/\psi$:$\rho^0=0.00294\pm0.00074$~\cite{zjpsi-94}
were measured.
In contrast, in the DIS
kinematic region, for $Q^2\approx$ 12 GeV$^2$,
the ratios
$\phi$:$\rho^0$=0.18$\pm$0.05~\cite{zphi/rho}
and
0.19$\pm$0.04~\cite{h1phi/rho}
were obtained at $W \approx$ 100 GeV. This analysis gives
the ratio $J/\psi$:$\rho^0 0.64\pm 0.35$ for $Q^2$ = 10 GeV$^2$
and 1.3$\pm$0.5 for $Q^2$ = 20 GeV$^2$~\cite{h1jpsi/rho} at $W
\approx$ 100 GeV. These results suggest that flavor independence
may hold at large $Q^2$.
The ratios $\phi:\rhoz$ and $J/\psi:\rhoz$ of the differential cross sections
for elastic reactions from this analysis
are plotted in Fig.~\ref{fig:rVtorho}a and \ref{fig:rVtorho}c
as a function of $-t$.
For both ratios, the point at $t=0$ was obtained by using
the ratios of values of the total
elastic cross section and rescaling them by the ratios
of the corresponding slopes, $b$, of the differential cross sections,
using the relation $\dsdt(t=0)=b\sigma$. An increase of the $\phi:\rhoz$
ratio up to $-t \approx$ 1 GeV$^2$ is observed, approaching the
expected 2:9 ratio. Although the
$J/\psi:\rhoz$ ratio increases quickly up
to $-t \approx $ 0.5 GeV$^2$, it remains more than an order of
magnitude smaller than the 8:9 expectation. A non-perturbative QCD
model \cite{ref:isabelle}
successfully describes the ratios for the elastic production at
$-t>$ 0.3 GeV$^2$.
The ratios for the proton-dissociative reactions are shown in
Fig.~\ref{fig:rVtorho}b and \ref{fig:rVtorho}d.
There are no data at $t$ = 0 for this
process. Both ratios are consistent with the corresponding elastic results.
At $-t\approx 2.2$~GeV$^2$, the $J/\psi:\rhoz$ ratio is still well
below the 8:9 expectation.
\begin{figure}[htb]
\vspace{-0.5cm}
\begin{center}
\epsfig{file=ratio.eps,width=0.73\textwidth}
\end{center}
\vspace{-1.0cm}
\caption{The ratios of the cross sections \dsdt\ for
\phiz \ to \rhoz \ (a and c) and \jpsi \ to \rhoz \ (b
and d)
for elastic and proton-dissociative
photoproduction.
The inner error bars indicate the statistical errors,
the outer bars the statistical and systematic uncertainties
added in quadrature.
The ratios at $t=0$ were obtained from the
data\cite{zphi/rho,zjpsi-94} as
explained in the text.
The solid curves represent
predictions of a non-perturbative QCD model \cite{ref:isabelle} for
elastic
photoproduction.
The dashed lines correspond to the expectations of flavor independence.}
\label{fig:rVtorho}
\end{figure}
\subsection{Test of Regge factorization hypothesis}
\label{sec:ff}
The hypothesis of Regge
factorization~\cite{gribov-fact} implies that the ratio of the
elastic to proton-dissociative differential cross sections should
be independent of the type of vector meson produced at the photon
vertex. Furthermore, this ratio should be the same as for
hadron-proton elastic and proton-dissociative processes.
Several results discussed in previous sections are consistent with
this hypothesis: the decrease in the $\pi\pi$ resonance-shape
distortion with increasing $-t$ is the same for the elastic and
proton-dissociation channels; the $\rho^0$ spin-density matrix
elements for both channels agree; and the difference ($\Delta
b$) between the slopes of the $t$-distributions for elastic and
proton-dissociation processes is independent of the type of vector
meson ($\rho^0, \phi, J/\psi$) produced at the photon vertex.
To test this hypothesis further, the ratios
$\frac{d\sigma}{dt}(\gamma p \to V p)/\frac{d\sigma}{dt}(\gamma p \to
V N)$ for the three vector mesons $V = \rho^0, \phi, J/\psi$
are shown in Fig.~\ref{fig:ff}. As can
be seen, the ratio agrees within errors for each of the three
vector mesons. In the same
figure, the ratio $\frac{d\sigma}{dt}(p p \to p
p)/\frac{d\sigma}{dt}(p p \to p N)$ at center of mass energies of
$\sqrt{s}$ = 23.4 and 38.3 GeV~\cite{chlm} is also shown. The $p p$
proton-dissociative reaction is defined for $M_N^2 \le 0.05 s$. The
ratios for the $p p$ reactions are in agreement with those of
the vector-meson photoproduction. These observations
confirm the factorization hypothesis.
\begin{figure}[htb]
\vspace{-0.5cm}
\begin{center}
\epsfig{file=ff-bw.eps,width=0.71\textwidth}
\end{center}
\vspace{-1.0cm}
\caption{The ratio of the elastic to proton-dissociative differential
cross sections as a function of $-t$ for vector-meson photoproduction,
together with data from $p p$ reactions~\cite{chlm} at
$\sqrt{s}$ = 23.4 and 38.3 GeV. The curve is the result of a combined fit
to all the data as explained in the text.}
\label{fig:ff}
\end{figure}
In a naive additive quark
model~\cite{kokkedee}, the ratio shown in Fig.~\ref{fig:ff} measures
the proton form factor. In such a model, the differential cross
sections can be related to the form factor of the hadrons involved in
the scattering process. In the framework of the VDM, this
relation can also be used for the vector-meson photoproduction reactions
discussed above. The elastic and proton-dissociative processes can be
expressed as
\begin{eqnarray}
\left(\frac{d\sigma}{dt}\right)_{el}
\sim F_p^2\ F_V^2\ |\cal{A}|^{\rm 2}, \nonumber \\
\left(\frac{d\sigma}{dt}\right)_{pd} \sim \ F_V^2\ |\cal{A}|^{\rm 2},
\end{eqnarray}
where $\cal{A}$ is the amplitude describing the constituent
interaction, the form factor of the proton is indicated by $F_p$ and that
of the vector meson by $F_V$. Thus, the ratio of the elastic and the
proton-dissociative cross sections gives the proton form factor:
\begin{equation}
\frac{\frac{d\sigma}{dt}(\gamma p \to V p)}
{\frac{d\sigma}{dt}(\gamma p \to V N)} = F_p^2 =
\frac{D}{(1-t/m^2)^4},
\label{eq:ff}
\end{equation}
where the electromagnetic dipole expression for the
proton form factor has been used and $D$ and $m$ are free parameters.
Equation~\ref{eq:ff} was fitted to both the
photoproduction and $pp$ data and the result is shown
as the curve in Fig.~\ref{fig:ff}.
The best
fit yielded the parameters $D$ = 7.7 $\pm$ 0.4 and $m^2$ = 0.47
$\pm$ 0.01 GeV$^2$, and gives a fair description of the data.
Note that the
mass scale parameter obtained by this fit is smaller than the value of
0.71 GeV$^2$ measured from electron--proton elastic scattering..
Fitting only to the ZEUS photoproduction data yields $D=11.2\pm8.0 $ and
$m^2=0.43\pm0.13~\Gev^2$.
\subsection{Determination of the Pomeron trajectory}
\label{trajectory}
The measurement of the variation of the energy dependence of the
elastic cross section with momentum transfer $t$ yields a direct
determination of the Pomeron trajectory, as shown in
Eq.~\ref{eq:regge}.
Such an analysis is presented for elastic \rhoz\ and \phiz\ photoproduction.
Since the reaction $\gamma p \to \rho^0 p$ is dominated by Pomeron
exchange only at high energies, \dsdt\ measurements at very low $W$ cannot
be used in this analysis. Therefore, the only
fixed target experiment that can be used is the OMEGA experiment
(WA4)~\cite{omega}, which measured elastic photoproduction at $W$ =
8.2 and 10.1 GeV in the $t$ range $0.06<-t<1$ GeV$^2$.
The measurement of the H1 collaboration~\cite{h1rho-94} at $W$=55
GeV, the earlier measurements of the ZEUS collaboration at $W$=71.2
GeV~\cite{zrho-94} and at $W$=73 GeV~\cite{zrho-lps}, and the present
data at $W$=94 GeV are also used.
The $\dsdt$ data used in the determination of $\alphapom(t)$ are
presented in Fig.~\ref{fig:dsdtw-rho} in 12 $t$ bins in the range $0
\le -t \le 0.95$ GeV$^2$. The errors are the statistical and
systematic uncertainties combined in quadrature. The line in each $t$ bin
is the result of a fit of the form $W^n$, where $n = 4\alphapom(t) - 4$.
The resulting values of $\alphapom(t)$ are plotted in
Fig.~\ref{fig:alpha-rho} as a function of $t$. A linear fit to the
data yields
\begin{equation}
\alphapom(t) = (1.096 \pm 0.021) + (0.125 \pm 0.038) t,
\label{eq:rho_trajectory}
\end{equation}
and is plotted as a full line in the figure. The quality of these fits
is acceptable.
The dashed line is the
Pomeron trajectory 1.0808 + 0.25 $t$, as determined by Donnachie and
Landshoff (DL)~\cite{dl}. The resulting intercept, $\alphapom(0)$, is in
excellent agreement with that of DL; however, the slope, $\alphappom$,
is smaller in the present determination.
\vspace{0.5cm}
\begin{figure}[htb]
\begin{center}
\epsfig{file=dsdtrho-bw.eps,width=0.84\textwidth}
\end{center}
\caption{Cross sections for exclusive \rhoz\ production from ZEUS, H1 and
OMEGA~\cite{zrho-94,zrho-lps,h1rho-94,omega} at fixed $-t$
values as a function of $W$.
The error bars show the statistical and systematic uncertainties added in
quadrature. The lines correspond to the results of the fits to
d$\sigma/$d$t\propto (W^2)^{2\alphapom(t)-2}$.
}
\label{fig:dsdtw-rho}
\end{figure}
\begin{figure}[htb]
\begin{center}
\epsfig{file=a-rho-bw.eps,width=0.9\textwidth}
\end{center}
\caption{
Determination of the Pomeron trajectory from the reaction $\gamma p \to
\rho^0 p$. The dots are the values of the trajectory at a given $-t$ as
determined from Fig.~\ref{fig:dsdtw-rho} and the solid line is the result
of a linear fit to these values.
The Pomeron trajectory as determined by
DL~\cite{dl} is shown for comparison as a dashed line.
}
\label{fig:alpha-rho}
\end{figure}
\clearpage
The elastic photoproduction of $\phi$ mesons is a good reaction with
which to study the
properties of the Pomeron, since this is the only trajectory that can be
exchanged~\cite{fruend}, assuming
the $\phi$ to be a pure $s\bar{s}$ state. This
allows the use of data at very low $W$.
The $\dsdt$ data used for the trajectory determination include
the following: $W$=2.64--3.60 GeV~\cite{behrend-78},
$W$=2.8~\cite{barber-83}, $W$=2.81--4.28 GeV~\cite{ballam-73},
$W$=3.59--4.21 GeV~\cite{mcclellan-71}, $W$=4.73--5.85
GeV~\cite{anderson-70}, $W$=12.89 GeV~\cite{busenitz-89}, $W$=70
GeV~\cite{zphi-94} and the present measurement at $W$=94 GeV. These
data points are displayed in Fig.~\ref{fig:dsdtw-phi} for 11 $t$
values in the range $0 \le -t \le 1.4$ GeV$^2$.
The lines are the
results of fits of the function $W^n$ to the data.
\begin{figure}[htb]
\vspace{-0.3cm}
\begin{center}
\epsfig{file=dsdtphi-bw.eps,width=0.84\textwidth}
\end{center}
\vspace{-0.6cm}
\caption{Cross sections for exclusive \phiz\ production from ZEUS and
low energy measurements~\cite{zphi-94,behrend-78,barber-83,ballam-73,
mcclellan-71,anderson-70,busenitz-89} at fixed $-t$
values as a function of $W$.
The error bars show the statistical and systematic uncertainties added in
quadrature. The lines correspond to the results of the fits to
d$\sigma/$d$t\propto (W^2)^{2\alphapom(t)-2}$.
}
\label{fig:dsdtw-phi}
\end{figure}
\clearpage
The resulting values of the trajectory $\alphapom(t)$ are shown in
Fig.~\ref{fig:alpha-phi} as a function of $t$. Assuming a linear
trajectory,
\begin{equation}
\alphapom(t) = (1.081 \pm 0.010) + (0.158 \pm 0.028) t
\label{eq:phi_trajectory}
\end{equation}
is obtained. Again the quality of the fits is generally acceptable.
This trajectory is shown as a solid line in the figure and compared
with the DL trajectory, which is plotted as a dashed line.
\begin{figure}[htb]
\vspace{-0.5cm}
\begin{center}
\epsfig{file=a-phi-bw.eps,width=0.78\textwidth}
\end{center}
\vspace{-0.5cm}
\caption{
Determination of the Pomeron trajectory from the reaction $\gamma p \to
\phi p$. The dots are the values of the trajectory at a given $-t$ as
determined from Fig.~\ref{fig:dsdtw-phi} and the full line is the result
of a linear fit to these values.
The Pomeron trajectory as determined by
DL~\cite{dl} is shown for comparison as a dashed line.
}
\label{fig:alpha-phi}
\end{figure}
\clearpage
As can be seen from (\ref{eq:rho_trajectory}) and (\ref{eq:phi_trajectory}),
the intercepts and slopes from this determination are in good
agreement with each other.
Whereas the intercepts agree very well with DL, the slopes of the
present measurement are clearly smaller than that of the DL trajectory,
which was determined from $pp$ elastic scattering data. It would therefore
seem that this simple Pomeron trajectory is not universal.
\section{Summary}
Elastic and proton-dissociative photoproduction of \rhoz, \phiz\ and \jpsi\
mesons have been investigated at an average photon-proton
center-of-mass energy of 94 GeV and for values of $-t$ up to 3~GeV$^2$.
The proton-dissociative event sample was limited to values for the
mass of the dissociated proton system below 7 GeV.
The differential cross section \dsdt, for each of the vector
mesons in each of these two processes, has been measured.
The following features are common to these reactions:
\begin{itemize}
\item
the ratio of the differential cross sections for the elastic and
proton-dissociative reactions drops rapidly
from a value of about 1 at $-t$ = 0.4 GeV$^2$ to a value $\le$~0.1 for
$-t>$ 1 GeV$^2$;
\item
parameterization of the differential cross section as a single
exponential, $\dsdt \propto \exp{(bt)}$, for values of $-t$ exceeding
0.5~GeV$^2$, yields a difference in the exponential slopes, $b$, for the
elastic and proton-dissociative reactions of about 3.5~GeV$^{-2}$
for each of the vector mesons;
\item
the measured ratio of the elastic and proton-dissociative
differential cross sections is similar to that measured in
$pp$ elastic and single-dissociative scattering and
is consistent with the hypothesis of
Regge factorization.
\end{itemize}
The analysis of the decay-angle distributions for pion-pair
photoproduction
in the $\rho^0$ mass region indicates a small deviation from SCHC
giving non-zero single- and double-flip amplitudes.
A comparison of the measured differential cross sections, $d\sigma/dt$,
for the process $\gamma p \to V N$ with QCD models shows that the
perturbative part of the calculations
for \rhoz\ and \phiz\ production~\cite{ginzburg}
at the $-t$ values covered in this analysis is well below the data.
However, the perturbative QCD prediction~\cite{bartels} compares
satisfactorily to the \jpsi\ data for values of $-t$ as low as 1~GeV$^2$.
The ratio $\phi$ : $\rho^0$ of the elastic cross sections increases
with $-t$ and approaches 2 : 9 at $-t\approx 1$~GeV$^2$. The ratio
$J/\psi$ : $\rho^0$ of the proton-dissociative cross sections
increases with $-t$, but even at $-t =$ 2.2 GeV$^2$ is still
much lower than the value of 8 : 9 expected for a flavor-independent
production mechanism.
The Pomeron trajectory was determined using elastic production of
$\phi$ and $\rho^0$ mesons
by studying the $W$ dependence of $\dsdt$ at fixed $t$
values, together with lower $W$ data from
other experiments. The resulting trajectories are:
\begin{itemize}
\item
$\gamma p \to \rho^0 p$ : \ \ \ $\alphapom(t)=(1.096\pm 0.021)+(0.125\pm
0.038)t$;
\item
$\gamma p \to \phi p$ : \ \ \ $\alphapom(t)=(1.081\pm 0.010)+(0.158\pm
0.028)t$.
\end{itemize}
The values obtained for $\alphapom(0)$ are in good agreement with
those of DL~\cite{dl}. However, the slopes, $\alphappom$, are
significantly lower than the value found in $p p$ elastic scattering.
In conclusion, the results presented in this analysis suggest that
even for the highest $-t$ values studied here ($-t \sim$ 2--3
GeV$^2$), the variable $t$ cannot be consistently treated as a hard
scale in perturbative QCD.
\section*{Acknowledgments}
We thank the DESY Directorate for their strong support and
encouragement. The remarkable achievements of the HERA machine group
were essential for the successful completion of this work and are
gratefully appreciated. We are grateful to
J.R. Cudell, D.Yu. Ivanov and M. W\"usthoff
for providing the theoretical calculations.
It is also a pleasure to thank L. Frankfurt
and M. Strikman for useful discussions.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
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|
Q: LARAVEL - set multiple rule on gate So i wanna return id_level 1,2, and 3 that able to access view-inv but turns out it just the first one return $user->id_level === 1; that work, any possible way to do this?
public function boot()
{
$this->registerPolicies();
Gate::define('view-inv', function($user){
return $user->id_level === 1;
return $user->id_level === 2;
return $user->id_level === 3;
});
}
my controller
public function index()
{
if (Gate::allows('view-inv')) {
$inventaris = Inventaris::all();
return view('index', compact('inventaris'));
}elseif (Gate::denies('view-inv')) {
return view('/home');
} else {
return view('/home');
}
}
A: you can't return more than once from function, so basically you can check if $user->id_level is "in array" with permission
Gate::define('view-inv', function($user){
return in_array($user->id_level, [1, 2, 3]);
});
you can define the array as constant, or just hardcode it as in example
function says, if id_level has value is the equal with some value in array return true, otherwise return false
|
{
"redpajama_set_name": "RedPajamaStackExchange"
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Q: How does the phase plot of Fourier transform of sine wave look like? I found that transform of Sin(t) look like THIS
If its amplitude look like THIS
How does its phase look like?
I have found one question on stack which is similar to my question but does not properly answer my question: fft phase plot of pure sine function, why so messy?
A: The Fourier transform of $\sin(\omega_0 t)$ is
$$
\mathcal{F}\left[\sin(\omega_0 t)\right] = -\frac{i}{2}\delta(\omega -\omega_0) + \frac{i}{2}\delta(\omega + \omega_0)
$$
where $\delta$ is the Dirac delta function. This is seen in your first image. The magnitude of this function is
$$
|\mathcal{F}\left[\sin(\omega_0 t)\right]| = \frac{1}{2}\delta(\omega -\omega_0) + \frac{1}{2}\delta(\omega + \omega_0)
$$
as seen in your second image. So then what about the phase? Well, the delta function is zero everywhere except where its argument is zero. That means that for all $\omega \ne \pm \omega_0$, $\mathcal{F}\left[\sin(\omega_0 t)\right](\omega) = 0$. What's the phase of zero? It's undefined. So your phase plot won't be much of a plot.
The reason the plot in the linked question is so noisy is that numerical error is causing the values of $\mathcal{F}\left[\sin(\omega_0 t)\right]$ to not compute to exactly zero. Instead it computes to an extremely small magnitude complex number whose phase is essentially random.
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\section{Alternative scenario}
As we have seen in the preceding sections, actually users have typically an high level of privacy on the payload level, but a lower one on the network level. In other words, ISPs can only know if, when, and how many times an user have visited a particular website, without having access of what activity the user have performed on it. How to conciliate the need of privacy for the user, with the technical (i.e. QoS) and commercial needs for the ISPs?
In the alternative scenario that we propose, users can voluntarily permit their ISP to access the payload of their communications. In exchange the users can enjoy globally a better service, thanks to Quality of Service (QoS): typically, we have different expectations on the waiting time to access a resource, based on the type of content we are accessing; for example, waiting some (not too much) time to access a textual web page is not a big deal, whilst having a video stream that stops constantly for buffering can be really annoying. Using QoS, ISPs can fine tune the bandwidth given to the users, in function of the accessed resources.
Users can also have economic benefits: they can share the revenues that the ISP obtained by selling their data, in terms of a reduction of their monthly fee for Internet connection. This can be also a big boost in giving access to Internet in the growing countries, and for the most disadvantaged people in first world countries: lowering the fee for accessing Internet, more people can gain access to it, thus giving more data to the ISP for them to sell, creating a virtuous cycle.
However the depicted alternative poses issues from an ethical point of view. In particular, it must be ensured that users must not be forced to ``sell'' their data to the ISPs. The risk is that ISP increase the fee to the users that do not want to give their data to them, thus making the choice practically obligatory for almost everyone. This could be avoided only by a strict control of the fees by the government regulatory agencies, thus this could be a problem in some countries, where this could be seen as an unacceptable intervention of the government in the private economy sector or even a means for political control. The ISPs can also force users to give access to their data by using the QoS, slowing Internet access to users not willing to ``sell'' their data. This behavior by ISP, although avoidable from the legal point of view (i.e. Service Level Agreement), can be hardly traceable, thus creating an ``informal'' threat to the users liberty.
Concluding, we can say that the alternative scenario proposed is feasible, but it should be deployed with great attention for the users rights, and with great scrutiny regarding the ISPs behavior.
\section{Ethical issues}
Given what has been depicted so far in this work, we can identify a set of
ethical issues.
Hereafter we will discuss these issues from two main points of view:
the user one and the ISP one.
From the ISP point of view we can summarize the issue with the question:
``is it right to access the data exchanged by a user?''.
It is not so easy to give an answer to this question: in fact, one could instinctively
be tempted to respond: ``no, it is wrong at all'' because of the user's privacy, but there are
some other aspects that must be considered.
In fact, it seems obvious that when a user relies on an ISP to access the global network
he should also trust the ISP and assume that his data will be shipped without any inspection.
On the other side, if an ISP could inspect user traffic, at least to apply some quality of service
policy or just some internal routing optimizations, it would be able to improve the user network experience.
Given that, the ISP could be justified to inspect the users traffic but where is the boundary located?
Where the ISP should stop in the inspection?
These questions comes out from the fact that the current digital world
most advantageous activity is represented by big data analysis and users profiling \cite{chen2012business}.
Then, if an entity can access a lot of information from a large number of users it might be temped to
sell these data to the highest bidder, that is exactly the case of an ISP.
It seems useful to try to define a limit at which the inspection is deep enough for the ISP optimizations
and not too intrusive for users privacy.
It is not evident in which way the traffic payload inspection could be interesting for routing
optimization purposes and then a solution could be to force ISPs to inspect only
transport information (e.g. IP addresses, TCP/UDP ports):
nevertheless, TCP and DNS analysis are enough to assess websites a client is visiting.
The payload inspection, on the other hand, could be useful to prevent malicious intents or illegal
communications.
As each ISP provides the network access point for its end-users, that are typically a significant amount,
it could be the best point to detect criminal activity, identify involved parties and prevent them.
This fact seems to justify a deeper traffic inspection by the ISPs but, in order to protect users privacy,
the inspection activity could be delegated to a trusted third party such as police or governments
institutions\footnote{
In that case, it should also be discussed the trustworthiness of that entities and identified a
boundary between public security and a big brother effect
}.
It is clear how the decision varies considering different aspects of the topic and how difficult
could be to take a decision about it.
On the other hand, from the final user's point of view the issue is mainly a matter of privacy and personal
information disclosure.
In this case, we identified one main question: ``the user's privacy must be managed only by the user himself?''
In other words, must the end-user care about his privacy while considering all the rest of the world as untrusted
or there should be some privacy level guaranteed by the ISPs?
In this case we believe that truth lies somewhere in the middle: ISPs should implement their services in order to
not disclose users information and end-users should take care of their personal data when sent
on the network.
Currently, personal data protection involves data encryption that is a crucial ethical and legal point of discussion.
Recent events have underlined how encryption can cause problems in case of investigation against criminal acts, e.g.
phones used by terrorists that are totally ciphered and that the authorities cannot access (that is what they publicly said)
\cite{vice2016iphone}.
The ethical discussion about data ciphering can be very hard because it could be impossible to decide what is right among for
main possible decisions. Anyway the ethical discussion about encryption of out of the scope of this work.
We expect a great debate about this topic in the near future, where the role of network will take second place,
as major Content Providers will be involved; \emph{Whatsapp} decision to encipher all messages and hiding them from
inspection of anyone is a good example and will certainly have many consequences \cite{ieee2016whatsapp}.
For the ISP case, data ciphering is a crucial point for an additional point: as we described in Section~\ref{use_cases}
data anonymization could limit the ISP information about the user traffic but the sensitive data can also be accessed from
the payload (which often is not obfuscated at all).
Then, it is clear that the user has to care of his data by ciphering payload when it is needed for privacy means but it is not
clear how to address the social security problem tied to ciphered data.
Moreover, we claim that even when having encrypted connections (i.e. HTTPs) some information is still assessable (e.g., websites history).
In conclusion, ethical issues of the ISPs in the modern web can be placed in the current digital world ethical discussion:
it is about finding a trade-off between personal privacy an public security.
\section{Stakeholders Network}\label{stakeholders}
The scenario described in the previous section depicts a very tangled and complex situation. Since many actors are involved, in this section we provide an in-depth analysis of the \emph{stakeholders} acting in this system. In Fig.\ref{fig:stakeholders} we report the stakeholders network showing involved actors and the respective interactions.
The main involved actors are without any doubt the \emph{users} of broadband Internet Access.
They are the producers of huge information used by other stakeholders, and in many case they are doing it without awareness.
Thus, ISPs' customers are not the clients but the products; personal information is a good normally sold between companies.
Users employ an \emph{Internet Service Provider} to access services across the Internet:
they expect the ISP to carries their data without looking inside the communication respecting their \emph{privacy}.
It is clear that there is a relationship of \emph{trust} between them,
and an ISP is strongly aware that the lack of trust can affect its success or bankruptcy \cite{chiou2004antecedents};
a user not trusting his provider will likely change it and that is the reason of the great effort ISPs put in loyalizing clients.
On the other hand, Internet Access is just a means for user to enjoy some kind of service.
Who offers a service on the Internet is called a \emph{content provider}: social networks, e-commerce portals and search-engines are content providers.
Few of them hold the majority of clients since the modern web is nowadays an oligopoly of few \emph{big players} \cite{anderson2010web}.
For example the social network field converged on two big content providers, namely \emph{Facebook} and \emph{Twitter},
while search engines are dominated by the \emph{Google} giant.
E-commerce sees few giants such as \emph{Amazon}, \emph{Ebay} and \emph{Alibaba},
whereas the first is also the owner of the biggest cloud infrastructure in the Internet.
Although the relationship between users and contents providers is evident
and well-known to the majority, ISPs and content providers are strictly connected
by often conflicting interests.
A crucial voice of cost for an ISP is represented by the traffic outgoing
from its network and, thus, it wishes to cache as much content as possible within its infrastructure.
On the other hand, content providers want to have full and exclusive visibility
on the behavior of their users, using more and more HTTPs (encrypted) instead of HTTP,
not cacheable by its nature.
For example, \emph{Facebook} since April 2013 serves its content by means of encrypted connections:
whereas it is a significant improvement from the privacy point of view,
ISPs were certainly not happy for such decision.
Also \emph{Youtube} in January 2014 started to serve its content by means of encrypted connections,
increasing significantly the amount of traffic not cacheable within ISPs
(\emph{Youtube} traffic is more than 25\% of total).
To save part of outgoing traffic, the last trend consists in ISPs hosting within their infrastructure a Content Delivery Network (CDN) node.
A CDN is a company owning a set of cache servers across a geographical region, that Content Providers rent to serve their contents and offer their services.
Whereas an ISP can benefit from hosting a CDN node, few disadvantages are noticeable: the cache node must be powered,
and especially must be filled with content coming from outside. ISP has no control on the amount of content retrieved
and whether only its broadband clients are using that cache;
moreover, often CDNs serve the content with encryption, giving the ISP no visibility on users behavior.
Nevertheless, there are a lot of works proposing collaboration between ISPs and CDNs
\cite{frank2013pushing}, \cite{lee2012isp}.
Again, modern fashion in content delivering is certainly less appreciated by ISPs,
but decreases the actors routing and handling with users information if compared to old-fashion cache systems owned by ISPs.
The last stakeholders involved are the consumers of network traffic information.
Several actors can benefit from information coming from the network;
for an ISP it is important to know its clients to properly engineer its infrastructure:
knowing which services are important for users allows to better configure the network to carry such traffic.
Thus, obvious questions arise:
\begin{itemize}
\item should an ISP \emph{know} which websites are clients visiting to improve their Quality of Experience?
\item can nowadays an ISP \emph{understand} which websites are clients visiting, the amount of mail they exchange and the videos they prefer?
\item is there the risk of incurring in severe \emph{privacy} issues (e.g., can an ISP read the content of email)?
\end{itemize}
In the next section we focus our attention on such questions, keeping in mind that today's web is totally different from 10 years ago.
Collecting network measurement is getting harder due to encryption and Cloud/CDN infrastructure and privacy is an increasingly popular topic.
Nevertheless, what happens on the network is a rich source of information for ISPs, researchers and marketing enterprises:
many companies have as core business the collection of personal information to sell high detailed customers profile to other companies.
This kind of business concerns marketing, advertising and economy in general;
the monetary turnover of such marketplace is exponentially increasing in last years as well as users' awareness
of privacy related issues \cite{conger2013personal}.
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.75\textwidth]{figs/stakeholders.eps}
\caption{Involved stakeholders.}
\label{fig:stakeholders}
\end{center}
\end{figure}
\section{Scenario}\label{use_cases}
Passive measurement is one of the most practical ways to measure real behavior of the user and performance analysis at network or application layer. The collected data contains information about the users, services that they are using and possibly exposes content or user's credential. The latter case is related to the connections type, it is encrypted or do users use clear text credentials, etc. Basically, there are several ethical issues related to the passive measurement, e.g., which kind of data are visible at probe? What can be extract from the user's flow records? How they should store the extracted data? Who has the right to access the collected data? etc.
\newline
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.75\textwidth]{figs/access_network.eps}
\caption{Typical network probe deployment in ISP.}
\label{fig:access_network}
\end{center}
\end{figure}
Fig.~\ref*{fig:access_network} shows the scenario in which the probe seats at ISP level, for example in a Point of Presence (PoP) where traffic of households is aggregated. All the users' connections behind the probe can be possibly captured and analysed by the ISP. Moreover, nowadays probes can filter connections or packets based on their protocol or their content. The question is, what can be seen at the ISP level, how much can be captured or stored by the probes. The storage security and accessibility of the collected data are out of scope of this work since several, generic and well-known techniques exist. However, we deal with possible ethical issues, about extracted data from users.
The probe at network layer captures traffic, such as, the IP and port of source and destination of the flows and fine grained information about the time, duration, byte transfer by each sides which provides a useful information for performance analysis for network administrators and service providers. ISPs know the personal information about the user when they apply for the service and are responsible to manage and assign clients' IP addresses. However, the mentioned data give information about where you contacted (from the IP address) and at which time and order you contacted them. The server IP address provides information about the location and possibly which service is provided by it. In particular when facing Content Delivery Networks (CDN) a single server IP address can host different services and web pages based on user geographic location and more sophisticated traffic engineering rules.
Nevertheless many techniques exist to infer the actual service used by a client in CDNs scenarios based on DNS and SSL \cite{bermudez2012dns}, allowing the ISP to an insight even on encrypted traffic going to CDN nodes which is nowadays a consistent share
\cite{trevisan_towards_2016}.
Client IP is certainly the field carrying more sensible information, helping the identification of users.
There are several techniques for IP address anonymization like \cite{crypto_pan} which is a cryptography-based sanitization tool, however the drawbacks of IP address anonymization investigated on the measurement society like \cite{anonymize_problem,anonymity}.
Transport layer related data also are distinguishable by the probe, but in this work we specifically focus on the application layer data in the modern web.
\newline
\begin{figure}[h]
\begin{center}
\input{figs/traffic_share/http_https.tex}
\caption{Share of HTTP and HTTPs over last 3 years as measeured on a PoP aggregating about 10,000 households from a popular italian ISP.}
\label{fig:http_https}
\end{center}
\end{figure}
As depicted from the Fig.~\ref*{fig:http_https}, the portion of encrypted data on the web from 2013 to 2016 are less than 10\% and around 40\% respectively, it shows 4 times increment on 3 years. It illustrates that the service providers and users care about privacy and security to avoid readability of contents. In either HTTP and HTTPS the Domain Name System (DNS) query for resolving the name can be capture by the probe and reveal the services which users requested.
Thus, the probe can see which service the user requested \cite{bermudez2012dns}.
This data indeed represent precious information for advertisement company, service providers and market.
Naylor et al. \cite{naylor2014cost} profoundly investigate the advantage and disadvantage of the HTTPS with respect to the HTTP. Although, HTTP traffic still have 40\% of the whole traffic share. It arises the point about how much HTTP traffic can affect users privacy? The probe sees the server IP, HTTP request and response, Uniform Resource Locator (URL) requested by client, HTTP header (cookie, referrer, ...) and User-Agent. In particular URL can carry personal information since many servers
encode in the URL web page parameters unveiling user actions (e.g., what he is buying on an e-commerce website).
Thus, for web services not employing encryption may lead to, consistent information exposure to the network.
Many works investigate about the ethical arguments in the modern web; in particular Zevenbergen et al.~\cite{ethical_guideline} discuss the ethical issues related to traffic measurement.
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Seinfeld Gets an Unofficial Reunion in the Style of Twin Peaks: The Return
By Garrett Martin | January 11, 2021 | 2:48pm
Comedy News Seinfeld
While a true Seinfeld reunion will probably never happen, its stars have toyed around with the idea many times. There was that Super Bowl ad where George and Jerry returned to the diner, episodes of Comedians in Cars Getting Coffee with each main cast member and Larry David, and that entire season of Curb Your Enthusiasm that mocked the idea of a revival. That's probably the closest the world will ever get to more Seinfeld.
That's not good enough for Dominick Nero. The Esquire video editor and culture writer has spend the last year assembling a new season of Seinfeld, but with a startling, daring new vision inspired by Twin Peaks: The Return.
Get ready for Seinfeld: The Return. (And yes: you really should start with part 1.)
hi new followers i'm going to pin this tweet for now. here's where you can find all the parts of my "Seinfeld: The Return" video series trailer: https://t.co/uXpUFK15Rfpt 1: https://t.co/njgWynf6uYpt 2: https://t.co/jCbSabP3fGpt 3: https://t.co/KSsq19ZVK9more to come! pic.twitter.com/2PEgojUOFl
— dom nero (@dominicknero) January 4, 2021
i am beginning to lose my mind making these, but here we go, here's Part 4 of Seinfeld: The Return, my series where i imagine a modern Seinfeld revival in the style of Twin Peaks. i think this one is particularly deranged. final two episodes coming soon https://t.co/QoLZGeCyDOpic.twitter.com/cqOO5tGBKe
As far as mashups go, this is a hilarious premise, and Nero obviously put a lot of time into making it work. The amount of footage he's cobbled together is surprising, and the way he's put it together to reference both the elliptical storytelling of Twin Peaks: The Return and the personalities and story beats of Seinfeld's characters is ingenious. The editing, the music, the dialogue: it all perfectly fits the vision of David Lynch and Mark Frost's 2017 miniseries, only with George Costanza and Kramer instead of Dale Cooper.
It's not hard to see where Nero found some of his footage. Seinfeld, Comedians in Cars Getting Coffee, and Veep are all plundered, as well as Jason Alexander's infamous Criminal Minds episode. When asked about where he found his footage and how his episodes come together, Nero gives an answer as cryptic as Twin Peaks:
"To maintain the grand mystery and spectacle of this bizarre creation, all ill say is this: I don't really plan these episodes. When I sit down to edit them, something enters my mind and i go into a strange semi conscious state and then a few hours later there's another episode on my hard drive. Part of the magic of doing this is, as you search and search and search for footage, sometimes perfect little things present themselves to you and you just have to let them take hold. In terms of the source of this footage…it all comes from a place both wonderful and strange…."
Nero plans on releasing two more episodes through Twitter, before releasing the whole video on his YouTube channel in late January or early February. Via Twitter DM, Nero reveals what we can expect with the final two installments. "For the next two parts, fans should look forward to catching up with a few more of the peripheral characters from Seinfeld and a lot more of the main four, and (hopefully) some conclusion with the George doppelganger storyline," he writes.
Although Seinfeld fans will probably dig it, Seinfeld: The Return works best if you're familiar with Twin Peaks: The Return, one of the most obtuse, most entrancing, and most entertaining TV shows in recent memory. It's startling how well these two vastly different shows line up, though—and a testament to Nero's inspiration and editing skills that he's able to make it work so well.
Senior editor Garrett Martin writes about videogames, comedy, music, travel, theme parks, wrestling, and anything else that gets in his way. He's on Twitter @grmartin.
seinfeld: the return
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In the 60s, segregation and discrimination were no less a part of Aboriginal life than of the lives of black people in the Deep South. We needed a civil rights movement . . . and in Charlie Perkins and company, we got one. This book tells with verve the story of the Freedom Rides and the conscience-searing triumph they were. The characters are skilfully conjured in all their youth and idealism. Ann Curthoys tells the story with an insider's eye and the passion of a true believer—and there is no other way to recount this moral victory and the lasting change it helped edge into being.
Bob Carr, Premier of NSW
In the early 1960s, most Australians could affect ignorance or feel comfortable about the racism, discrimination and poverty affecting Aboriginal Australians. The Freedom Ride of 1965 marked the time when those who had been comfortable with what was happening were confronted with reality. It forced other Australians to look at the darker side of the past and the present. It helped develop a new generation of Aboriginal leaders.
Jack Waterford, Editor-in-chief, _The Canberra Times_
The record of the students' Freedom Ride in New South Wales is profound. Ann Curthoys has recounted the brave action of the students' determination to break the barriers that divided black and white Australia. Meticulously researched, the author has provided a compelling work.
Faith Bandler
This book is a revealing window into the courage, humanity and commitment of the participants. It again focuses the nation on the continuing need for organised political action to secure social justice and a just reconciliation.
Robert Tickner, Minister for Aboriginal and
Torres Strait Islander Affairs 1990–96
For my mother
Barbara Lindsay Curthoys
1924–2000
**ANN CURTHOYS**
**FREEDOM RIDE **
a freedom rider remembers
First published in 2002
Copyright © Ann Curthoys 2002
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without prior permission in writing from the publisher. The _Australian Copyright Act 1968_ (the Act) allows a maximum of one chapter or 10 per cent of this book, whichever is the greater, to be photocopied by any educational institution for its educational purposes provided that the educational institution (or body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act.
Every effort has been made to contact the copyright holders of the photographs produced in this book. In the event where these efforts were unsuccessful, the copyright holders are asked to contact the publisher directly.
Aboriginal readers are warned that this book contains the names and images of some Aboriginal people who have since died.
Allen & Unwin
83 Alexander Street
Crows Nest NSW 2065
Australia
Phone: (61 2) 8425 0100
Fax: (61 2) 9906 2218
Email: info@allenandunwin.com
Web: www.allenandunwin.com
National Library of Australia
Cataloguing-in-Publication entry:
Curthoys, Ann.
Freedom ride : a freedom rider remembers.
ISBN 1 86448 922 7.
1. Curthoys, Ann, – Journeys. 2. Australia – History. I. Title.
994
Set in 10.5 pt Schneidler by Midland Typesetters Pty Ltd
Maryborough, Victoria
Printed in Australia by McPherson's Printing Group
10 9 8 7 6 5 4 3 2 1
Contents
List of illustrations
Dramatis personae
Names
Acknowledgements
1. Let's have a Freedom Ride
2. Getting ready
3. On the way to Walgett
4. High noon at Walgett
5. Moree: Australia's Little Rock?
6. Clash at Moree
7. 'Stirring up trouble': The coastal towns
8. Impact
9. More Freedom Rides
10. Memory and meaning
Epilogue: Whatever happened to . . .?
Select bibliography
A note on sources
Illustrations
Burning an imitation KKK cross at a student demonstration for US civil rights, Sydney, 6 May 1964 ( _Daily Telegraph_ , 7 May 1964).
A female student is arrested at a civil rights demonstration ( _Daily Telegraph_ , 7 May 1964).
Gary Williams and Charles Perkins on their first day as students at the University of Sydney, March 1963.
Students demonstrate for Aboriginal rights during National Aborigines Week at Hyde Park and Parliament House, Sydney, 7 July 1964. Photographer: Michael Elton.
John Powles, Charles Perkins, Pat Healy and Jim Spigelman plan the Freedom Ride ( _Sydney Morning Herald_ , 17 June 2000).
Publicity notice for folk concert to raise money for the Freedom Ride, 21 January 1965.
Machteld Hali draws the placard: 'Good enough for Tobruk. Why not Walgett?'
Helen Gray, Machteld Hali, Norm McKay and Ann Curthoys hold banners outside Walgett RSL, 15 February 1965.
Students demonstrate outside the Walgett RSL holding their banner, 'Student Action for Aborigines' and RSL worker offers drinks to the students (Sydney Morning Herald, 17 February 1965).
'Nonsense! Of course you want a drink'. Cartoon by Molnar, _Sydney Morning Herald_ , 17 February 1965.
Bob Brown, Freedom Ride supporter, standing outside his electrical goods store, Moree.
Ann Curthoys and Louise Higham interview Aboriginal residents at the Aborigines Welfare Board Station, Moree, 17 February 1965.
The students demonstrate outside the council chambers in Balo Street, Moree ( _Tribune_ , 24 February 1965).
Charles Perkins waits with children to enter the swimming pool, Moree, 17 February 1965 ( _Sydney Morning Herald_ , 24 February 1965).
Charles Perkins with children in the Moree pool on Wednesday 17 February 1965 ( _Australian_ , 19 February 1965).
The bus stands outside the Hotel Boggabilla, where students rested before interviewing people at the Aboriginal Station.
Students greet Charles Perkins at Inverell airport.
Charles waits with children outside the Moree pool, 20 February 1965 ( _Daily Mirror_ , 22 February 1965).
Police attempt to keep the crowd away from the students at the Moree pool.
Charles Perkins is led away from the pool. ( _Daily Mirror_ , 22 February 1965).
Bob Gallagher is hit on the head with an egg at Moree ( _Australian_ , 22 February 1965).
The _Daily Mirror_ 's full-page coverage of the demonstration at Moree pool, 22 February 1965.
Cartoonist Martin Sharp makes a harsh comment on the citizens of Moree ( _Australian_ , 22 February 1965).
'It's not too cold for me—it's too hot.' Cartoon by Eyre Jnr, _Sydney Morning Herald_ , 22 February 1965, satirising the Chief Secretary's lack of response to the Freedom Ride.
Charles Perkins, Gerry Mason, John Powles and Brian Aarons wait in Grafton for the replacement bus driver to arrive, Monday 22 February 1965 ( _Daily Examiner_ , 23 February 1965).
The students hold a watermelon eating competition while waiting in Grafton.
Clarrie Combo, chairman of directors of the Aboriginal Cooperative at Cabbage Tree Island, discusses problems with the sugar cane crop with Mr H. Jeffery, manager of the Cabbage Tree Island Reserve, Tuesday 23 February ( _Sydney Morning Herald_ , 24 February 1965).
Bruce Petty cartoon of the bus leaving Moree ( _Australian_ , 25 February 1965).
George Bracken, Aboriginal former lightweight boxing champion, criticises the Freedom Ride ( _Daily Mirror_ , 22 February 1965).
The students arrive in Bowraville.
Brian Aarons and Gary Williams drink together in Bowraville Hotel ( _Sydney Morning Herald_ , 25 Feb 1965).
Charles Perkins is barred from taking a child into the McElhone olympic swimming pool, Kempsey (Sydney Morning Herald, 26 February 1965)., 26 February 1965).
Students outside Kempsey swimming pool hold placards protesting against exclusion of Aboriginal people from the pool ( _Macleay Argus_ , 27 February 1965).
Wendy Golding's photo of the students posed outside the bus.
'He does not drink, hates crowded pools, likes to sit in front at the pictures. How can we desegregate him?' Cartoon by Molnar ( _Sydney Morning Herald_ , 26 February 1965).
Ted Noffs welcomes back Charles Perkins at the University of Sydney on 26 February 1965. The Freedom Ride is over ( _Sydney_ _Morning Herald_ , 27 February 1965).
The Student Action for Aborigines stall during the University of Sydney Orientation Week.
Students hold 100-hour vigil outside the NSW Liberal Party and Labor Party headquarters. Photographer: Bruce Adams.
Members of SAFA visit Walgett in May and August 1965.
Harry Hall's place and members of Harry Hall's family with two SAFA students, Walgett, 1965.
The Luxury Theatre, Walgett, 1965.
Marie Peters, Pattie Hall and Lorna Hall, participants in the demonstration to desegregate the Walgett Luxury Theatre on 7 August 1965.
Harry Hall, Pattie Hall and Lorna Hall ( _Tribune_ , 18 August 1965).
Ted Fields buys his ticket to the dress circle at the Luxury Theatre, Walgett, Saturday 14 August 1965 ( _Tribune_ , 18 August 1965).
Walgett community members and students pose together for a group photo in August 1965.
A young Aboriginal man addresses a meeting near the Aboriginal reserve, Bowraville, 12 March 1966, while police watch.
Sue Johnston burns copies of the _Aborigines Protection Act_ outside Parliament House, 13 July 1966 (, 20 July 1966) _Honi Soit_ , 20 July 1966).
Note: Every effort has been made to contact the copyright holders of the photographs and illustrations produced. As these efforts were unsuccessful, the copyright holders are asked to contact the publisher directly.
Dramatis personae
The students
_Note:_ Ages are sometimes approximate, and both age and enrolment in university courses are for February 1965.
Charles Perkins, 29, third-year Arts, Arrernte man, born in Alice Springs, former soccer player, Aboriginal activist
Gary Williams, 19, third-year Arts, Gumbaynggir man from Nambucca Heads
Aidan Foy, 19, third-year Medicine, member of the ALP Club
Alan Outhred, 19, third-year Science, member of the Labour Club
Alex Mills, 25, third-year Theology, member of the Liberal Club
Ann Curthoys, 19, third-year Arts, member of the Labour Club
Barry Corr, 18, second-year Arts
Beth Hansen, 19, third-year Arts, member of the Humanist Society
Bob Gallagher, 19, third-year Engineering, member of the Labour Club
Brian Aarons, 19, third-year Science, member of the Labour Club
Chris Page, 19, third-year Medicine
Colin Bradford, 19, third-year Science, member of the Labour Club
Darce Cassidy, 22, part-time third-year Arts, also ABC radio producer
David Pepper, 18, second-year Arts
Derek Molloy, 19, third-year Arts
Hall Greenland, 19, third-year Arts, member of the ALP Club
Helen Gray, 19, second-year Arts
Jim Spigelman, 19, third-year Arts, leader of the Fabian Society, breakaway group from the ALP Club
John Butterworth, 20, third-year Science
John Gowdie, University of New England, son of Presbyterian minister from Dubbo
John Powles, 22, fifth-year Medicine, founder of the Sydney University Humanist Society, involved in Campaign for Nuclear Disarmament
Judith Rich, 20, third-year Arts
Louise Higham, 18, second-year Medicine, member of the Labour Club.
Machteld Hali, 18, second-year Arts, born in Holland, raised in Indonesia
Norm Mackay, 19, third-year Science, member of the Labour Club
Paddy Dawson, 19, third-year Arts, member of the ALP Club
Pat Healy, 20, third-year Arts, member of the Labour Club
Ray Leppik, 22, postgraduate Science
Rick Collins, 19, third-year Arts
Robyn Iredale, 20, fourth-year Arts, in Geography Honours
Sue Johnston, 20, fourth-year Arts, in History Honours
Sue Reeves, 19, third-year Arts, member of Abschol
Warwick Richards, 19, third-year Arts, member of the Student Christian Movement
Wendy Golding, 17, second-year Arts
Also on the bus
Gerry Mason, an older Aboriginal friend of Charles Perkins from Gerard government reserve in South Australia
Bill Pakenham, from Punchbowl, driver of the bus until Grafton
Ernie Albrecht, from Lugarno, driver of the bus from Grafton onwards
Students on the follow-up trips
Sue-Ann Loftus
Owen Westcott, 18, second-year Arts
Christine Jones
Aboriginal rights organisations and leaders
AAF Aboriginal-Australian Fellowship, a mixed-race organisation for Aboriginal rights founded by Pearl Gibbs and Faith Bandler in 1956.
APA Aborigines Progressive Association, a largely Aboriginal organisation for Aboriginal rights, founded in January 1964, with Bert Groves, formerly president of the AAF, as president. The name had also been used by an earlier organisation in the 1930s.
The Foundation The Foundation for Aboriginal Affairs, founded in 1964 to provide support for Sydney's growing Aboriginal population.
SAFA Student Action for Aborigines. Formed in 1964 at the University of Sydney to organise the Freedom Ride. Lasted until 1967.
Abschol Organisation under the leadership of NUAUS, founded to raise funds for scholarships for Aboriginal university students; from 1965, supported political campaigns such as the Referendum.
FCAA Federal Council for Aboriginal Advancement, founded in 1958. Changed its name in April 1964 to FCAATSI—Federal Council for the Advancement of Aborigines and Torres Strait Islanders.
Aboriginal leaders based in Sydney
Bert Groves, an Aboriginal man from the northwest of New South Wales, president of the AAF 1957–58, and of the APA 1964–?
Charles (Chicka) Dixon, active in the APA and the Foundation
Ray Peckham, Aboriginal man from northwestern New South Wales, now active in APA and the Waterside Workers' Federation
Non-Aboriginal activists
Faith Bandler, founder and secretary of the Aboriginal-Australian Fellowship
Allan Duncan, lecturer in Aboriginal adult education, member of the Aboriginal-Australian Fellowship, and chairman of the Foundation's Education Committee
Jack Horner, secretary of the Aboriginal-Australian Fellowship
At the University of Sydney
Michael Kirby, 25, Law, president of the SRC, student representative on the University Senate
Ken Buckley, senior lecturer in Economic History, secretary of the Council for Civil Liberties
Peter Westerway, executive producer of the investigative Channel 7 television program _Seven Days_ , occasional lecturer in Government
Tom Roper, 19, third-year Arts, member of SAFA, later director of Abschol
David Ellyard, 19, Science, member of SAFA
Eric Doldissen, 20, treasurer of SAFA
At the University of New South Wales
Bill Ford, lecturer in the School of Economics, former Fulbright scholar in the United States, observer of Freedom Rides in Jackson, Mississippi in 1961
Walgett people Aboriginal
Harry Hall, Gamilaraay, ex-shearer, worker at Walgett garage, leader of Aboriginal people in Walgett
George Rose, Yuwaaliyaay, from Brewarrina, sergeant in army during World War II, shearer and member of the AWU, settled in Walgett in 1949, leading figure in Walgett APA
Gladys Lake, leading figure in Walgett APA
Ted Fields, leading figure in Walgett APA
Pat Walford, woman in her twenties, outspoken resident
Marie Peters, 18, resident
Pattie Hall, daughter of Harry Hall
Lorna Hall, niece of Harry Hall
Non-Aboriginal
Alex Trevallion, Town Clerk
Athol White, manager, Oasis Hotel-Motel
Tom Hogan, manager, Walgett RSL Club
James Conomos, owner, Luxury Theatre
Moree people
Aboriginal
Lyall Munro Snr, shearer and local Aboriginal leader
Lyall Munro Jnr, 14, living on Mehi mission
Zona Craigie, 8, resident of Thompson's Row
Non-Aboriginal
Alf Sadlier, Mayor in 1955 when resolution banning Aborigines from the local pool was passed
William Tait, Deputy Mayor in 1955
Bill Lloyd, Mayor in 1965
Bob Brown, 29, owner/manager of an electrical business
Aboriginal people in other towns
Ann Holten, 16, high school student, Bowraville
Pastor Frank Roberts Jnr, Bundjalung leader, Lismore
The clergy
Ted Noffs, Methodist pastor supportive of Aboriginal people, associate minister of the Central Methodist Mission in Sydney, co-founder of the Foundation for Aboriginal Affairs
Reverend Peter Dowe, the vicar at St Peter's Church of England in Walgett Ted Ryan, Methodist minister, Moree
The journalists
Bruce Maxwell, cadet reporter for the _Sydney Morning Herald_ , travelled with the students
Gerald Stone, migrated from the United States to Australia in 1962, reporter for the _Daily Mirror_ and the _Sunday Mirror_ , travelled with the students from Moree onwards
Judith Rich, reporter for the _Daily Telegraph_ from Moree onwards, also a student at the University of Sydney
Peter Martin, reporter for _Seven Days_ , Channel 7
Politicians and bureaucrats
A.G. Kingsmill, chair of the Aborigines Welfare Board H.J. Green, Superintendent of the Aborigines Welfare Board
Gus Kelly, Chief Secretary, responsible for Aboriginal welfare until 1 May 1965
Jack Renshaw, Premier of New South Wales until 1 May 1965, member for Castlereagh, the electorate in which Walgett was situated
Eric Willis, Chief Secretary of New South Wales, 13 May 1965 to 19 June 1972
Bill Rigby, Labor MLA for Hurstville, one-time member of the AAF, one of the few supporters of Aboriginal rights in the New South Wales Parliament
Names
_Aboriginal people_ a general term for the Indigenous people of Australia. The term 'Aborigines' was most commonly used in the 1960s, but is now less preferred.
_Indigenous_ the indigenous people of Australia and the Torres Strait Islands. Increasingly the preferred term by those whom it designates.
_Murris_ the term derived from local languages, meaning 'our people' or 'us', for Aboriginal people in southern Queensland and the central section of northern New South Wales.
_Kooris_ the equivalent term for Indigenous people in southern and eastern New South Wales.
_Kamilaraay_ a large language group in northern New South Wales; Walgett, Moree and Boggabilla lie in Kamilaraay country.
_Wiradjuri_ a large language group in western and southern New South Wales; Wellington is in Wiradjuri country.
_Bundjalung_ a large language group in far northeastern New South Wales; Lismore is in Bundjalung country.
_Gumbaynggirr_ the people of the east coast region near present-day Bowraville.
_Dhan-gadi_ , _Ngaku_ and _Ngumbar_ the people of the Macleay Valley, at the mouth of which lies Kempsey.
Acknowledgments
From the moment I started writing a diary as a student on the Freedom Ride in February 1965, there was a possibility I might write this book.
I did not, however, form a definite intention to write it until some time in 1988, the year in which Indigenous political protest so effectively deflected the Bicentennial celebrations towards a more reflective reconsideration of the meaning of Australian history. Perhaps I was moved to write it by Peter Read, who interviewed me in 1987 about the Freedom Ride for a chapter in his biography of Charles Perkins. In 1989 I applied for funding for the research from the Australian Research Council, stating in my application that the Freedom Ride was a 'key event' in the history of the relations between Aboriginal and other Australians. My book, I said, would assist the development of 'a clearer understanding of the historical processes through which a strong Aboriginal political movement emerged in the 1960s'. I saw the Freedom Ride then—and still do—as 'a jumping-off point' for investigating some large themes in the history of relations between Indigenous and non-Indigenous people in Australia. When the grant was awarded, I began serious work on the project in 1990, with the wonderful Kathy Moffatt as my research assistant.
My original plan was to write the book during study leave in 1991. In April that year, John Docker and I retraced the itinerary of the Freedom Ride, interviewing many people and looking at the places that had witnessed these significant events two-and-a-half decades earlier. We travelled through the towns of Orange, Wellington, Dubbo, Gulargambone, Walgett, Moree, Lismore, Bowraville and Kempsey, and interviewed people, both Indigenous and non-Indigenous, who had been involved. My having been a Freedom Rider led many Aboriginal people to speak to me who may not have done so otherwise, though most of those interviewed did not wish to speak into a tape-recorder. So I took extensive notes while we talked and then typed up my diary each evening. Later that year I wrote my first academic paper on the Freedom Ride project, and delivered it at the Sir Robert Menzies Centre for Australian Studies in London, and at the History Workshop conference in Oxford.
What I learnt during 1991 was that the project had still a long way to go. I seemed to be endlessly diverted by the many and diverse activities of a busy senior academic in the 1990s—undergraduate teaching, graduate supervision, academic administration, consultancies, conferences, prize and grant committees, endless selection committees, committees of review, advisory committees, indeed academic committees of every imaginable kind. And there were still many intellectual lessons to learn. I found that I had to circle around my material before I could get directly to it. Through the 1990s I had a burst of writing activity on a wide range of issues, including national identity, the anti-war movement, the history of journalism, historical representation, second-wave feminism, Australian historiography, and colonialism and gender.
But delaying me most of all was the realisation that I had still a great deal of research and thinking to do. I especially needed to interview the Freedom Riders themselves. After interviewing one of them, Beth Hansen, during my 'retracing tour' in 1991, I realised that I could not be the interviewer of the rest. Beth was, naturally, too aware that I had been there too, finding it difficult to tell me about things she thought I would already know, and feeling wrong-footed if I asked about details of events that I remembered or knew about and she didn't. With the aid of a grant from the University of Technology, Sydney in 1993, I hired Inara Walden to do the oral history interviews for me. As a much younger person—Inara had not been born at the time of the Freedom Ride, to the amusement of many of her interviewees—I correctly judged that the Freedom Riders would feel bound to explain things to her that they would find odd telling me. In the interviews, we concentrated on asking about the Freedom Riders' strongest impressions, and eliciting a lot more about who they were, their background, how they got involved, and what they had been doing since. I did a great deal of other research as well, especially at the Australian Institute of Aboriginal and Torres Strait Islander Studies library; I also placed a letter in the _Sydney Morning Herald_ (which yielded few, but valuable, replies), and one way and another collected vast quantities of material.
Early in 1995 I moved from UTS in Sydney to the Australian National University in Canberra. This meant more academic administration and new, very demanding, teaching commitments, so my work on this book was seriously interrupted for several years. In the long run, however, the change proved to be valuable, bringing me into intellectual contact with a new group of Indigenous and non-Indigenous people who were also engaged in rethinking Australian history. I taught units on Australian Aboriginal history for the first time, working with Indigenous teachers where I could, and forcing myself to gain a wider understanding of the history to which I was attempting to contribute, submitting my ideas to the unblinking stare and close scrutiny only undergraduates can give. With additional small ARC grants, I was able to hire Lani Russell and Ann Genovese to help with the final phases of research, in the National Library, the Australian Archives, the Mitchell Library and the New South Wales State Records Office. I gave papers on the progress of my research to the 'Gender and National Identity' symposium organised by the journal _Gender and History_ at the Rockefeller Centre at Bellagio, Italy, and the conference 'Suffrage and Beyond' in Wellington, New Zealand. Closer to home, I spoke to the Royal Australian Historical Society and the Australian Historical Association conference in Perth in 1994, presented a seminar on Indigenous Citizenship under the auspices of the Reshaping Australian Institutions Project at ANU in 1996, spoke to the Australian Oral History Association conference in Alice Springs in 1997, and presented papers to the History Division seminar at the Research School of Social Sciences at ANU in 1997 and 2001 and at Macquarie University in 1998 and 2001.
After such a long gestation, I have many people to thank. I sincerely thank the funding bodies that supported me—the Australian Research Council, the University of Technology, Sydney and the Australian National University. I especially thank the four research assistants who worked on this project at various times—Kathy Moffatt, Inara Walden, Ann Genovese and Lani Russell. All were brilliant researchers and wonderful to work with. Many of the Freedom Riders helped by consenting to interview, and by donating to me documentary material; particular thanks must go to Aidan Foy, Barry Corr, Bob Gallagher, Brian Aarons, Charles Perkins, Darce Cassidy, Jim Spigelman, Louise Higham, Patricia Healy, Warwick Richards and Wendy Watson-Ekstein. Indeed, I thank all those—Freedom Riders and others—listed in the note on sources, who gave Inara or me their time in interviews. I also thank Frances Peters-Little for reading and correcting the Walgett chapters, and drawing for me an illuminating if eccentric map of the town.
Others who over the years lent me material, passed on ideas and contacts, or discussed my ideas with me, and whom I wish to thank, include Andrew Markus, Barry Higman, Bert Castellari, Carol Johnson, Catherine Hall, David McKnight, Fiona Paisley, Georgine Clarsens, Gordon Briscoe, Heather Goodall, Jack Horner, John Murphy, Judith Keene, Kate Evans, Ken Buckley, Lyndall Ryan, Marilyn Lake, Nic Peterson, Paula Hamilton, Peter Read, Susan Magarey, Terry Fox, Tim Rowse, Tom Griffiths and Vicki Grieves. Special thanks to Brian Aarons and Pat Healy for reading the whole manuscript, correcting errors and discussing ideas, and also to Bain Attwood for reading and commenting on the first half of the book.
Above all I thank the people in the Freedom Ride towns who gave so unstintingly of their time when I visited them in 1991, especially Harry Hall, Phillip Hall, George Rose and Gladys Lake in Walgett; Lyall Munro Snr in Moree; Tess and Vic Brill in Lismore; Bob Perry in Bowraville; and Bob Brown (formerly of Moree) in Port Macquarie.
I have tried out my ideas for this project a number of times, and wish to thank the organisers and audiences at those events. I also thank my students in my Australian Aboriginal history classes at ANU and my Writing History classes at UTS and ANU, and the Grade 6 class at Lyneham Primary School (1998) whose interest and challenging questions spurred me on.
I wish to thank my publisher John Iremonger, for giving me that extra push when it started to seem as if this project would never be finished, and for supporting this book so wholeheartedly, even through his own serious illness. Warm thanks are also due to my production editor at Allen & Unwin, Alexandra Nahlous, for her efficiency and support.
'Aboriginal Charter of Rights', by Oodgeroo of the Noonuccal tribe from _My People_ , third edition, The Jacaranda Press, 1990, is reproduced by permission of John Wiley & Sons, Australia.
I thank Bruce Petty, Martin Sharp, Gary Williams, Darce Cassidy, Wendy Watson-Ekstein, the Search Foundation, the State Library of New South Wales, the _Daily Examiner_ , the _Macleay Argus_ , _Honi Soit_ , the Fairfax Photo Library and News Limited for permission to reproduce cartoons and photographs.
Finally, a special thank you to my late mother, Barbara Curthoys, who first interested me in Aboriginal rights and gave me valuable documentary material. I also thank my son, Ned Curthoys, and father, Geoff Curthoys, for being so interested and reading the entire manuscript and my husband, John Docker, for making detailed comments on the entire manuscript and whose continuing intellectual and personal support is incalculable.
_Ch_ _apter_
'Let's have a Freedom Ride'
You can always start earlier in the writing of history, but I begin this story with a student demonstration for civil rights in the centre of Sydney on 6 May 1964. Held just nine months before the Freedom Riders set out on their remarkable journey from the University of Sydney's graceful neo-Oxfordian quadrangle to the race-inflected towns of northern New South Wales, this demonstration—surprisingly, perhaps—supported the civil rights not of Indigenous Australians, but of African Americans.
Perhaps it wasn't so surprising. In their concern for racism overseas, the students' actions were not unusual. Eminent anthropologist Bill Stanner had written a letter to the _Sydney Morning Herald_ only four days earlier referring to that 'mountainous fact of Australian mentality: that we are angered only by very distant racial wrongs'. Racial inequality was often understood more easily elsewhere than at home—at least in the imagination.
Opposition to South African apartheid, for example, was growing rapidly at this time. After some large campus meetings, and a demonstration of thousands of students in Martin Place in Sydney in reaction to the shootings in Sharpeville in March 1960, there had been a lull in activity, though the Students Representative Council at the University of Sydney held remembrances of the event each year. Unlike British Prime Minister Harold Macmillan, who saw the Sharpeville shootings as 'the turning point in the history of race relations', and who recognised a 'wind of change' blowing through Africa, Prime Minister Menzies refused to protest officially against apartheid to the South African government. His refusal was taken to indicate tacit support and was roundly condemned by the Labor opposition. An anti-apartheid movement slowly developed which sought to pressure the Australian government into a stronger stand. Leading white anti-apartheid campaigner John Brink arrived from Pretoria in 1961, and became the focus of anti-apartheid activity in Sydney. In 1963, students at Melbourne and Monash Universities protested against apartheid in front of the South African stand at the International Trade Fair in Melbourne, while Queensland university students demonstrated against the gaoling without trial of black activists in South Africa. The cricket tour by the South Africans in the southern summer of 1963–64 was greeted by demonstrations of students, trade unionists and others at airports and cricket grounds during Test matches, though these were tiny compared with the massive demonstrations that greeted the South African (Springbok) footballers eight years later. As knowledge of apartheid grew, students began to campaign in earnest. The trial of Nelson Mandela and others in Pretoria was sympathetically covered in student newspapers. Their national body, the National Union of Australian University Students (NUAUS), agreed in February 1964 to institute an anti-apartheid campaign. It would seek cooperation with churches and trade unions to pressure the federal government into a stronger stand against South Africa in the United Nations, and to implement a boycott of South African goods.
The May demonstration that I've taken as the beginning of my story was, however, advocating racial equality not in South Africa but in the United States. Australian interest in and knowledge of US civil rights had been greatly increased a year earlier by reports of police violence against thousands of African Americans conducting peaceful demonstrations in Birmingham, Alabama. On 12 April 1963, Martin Luther King and Reverend Ralph Abernathy had been gaoled for marching in Birmingham in support of civil rights. Four days later, King wrote his 'Letter from Birmingham Jail', a profound statement on the goals and tactics of the civil rights movement; it was to become something of a manifesto for the Australian Freedom Ride less than two years later. Once King was released, the civil rights campaign was stepped up, and now involved teenagers and even younger children on a large scale. In response, Birmingham's Public Safety Commissioner, T. Eugene 'Bull' Connor—a white supremacist who routinely used physical force against civil rights activists—attempted to stop the marches on 3 May using police dogs and fire hoses at high pressure. As historian Robert Weisbrot tells it:
Using fire hoses at a pressure set to take off tree bark, they blasted adults and children, the jet streams ripping their clothes and leaving them bloodied on the ground. Police swung nightsticks into skulls indiscriminately, and attack dogs set loose among the panicked crowd sank their fangs into three fleeing children.
In America, graphic images had not accompanied earlier protests; now newspapers carried photographs of huge, snarling dogs lunging at black women and children. The images of dogs biting peaceful protesters, and of fire hoses, batons and fists being used against people seeking equal treatment in schools, restaurants, theatres and other public places shocked many and led to an outpouring of support for the civil rights movement.
The Australian urban press, especially the afternoon and Sunday tabloids, carried similar images. Brian Aarons, who was to become one of the Australian Freedom Riders, remembered the images and their importance many years later:
I can remember that in the US, when the Civil Rights Movement was being built up, led by Martin Luther King, there was a particular incident . . . where a police chief called Bull Connor had loosed the police dogs onto civil rights demonstrators and there were dramatic photographs on the front page of the Sunday papers . . . And there was a policeman with a dog—an Alsatian or German Shepherd—on a leash and the dog is biting or going for a black demonstrator.
Brian had a good memory. _The Sun_ , a Sydney afternoon tabloid, carried on its front page on 4 May a graphic photo of a dog, held on a leash by a policeman, biting a young black activist. It accompanied a story headed 'Wild Dogs Turned on Negroes. Many children among victims'. Other papers, like the _Sun-Herald_ on 5 May, carried similar images and stories. The _Daily Mirror_ sent a journalist to the United States specifically to cover the riots and their aftermath. 'What an affront to human dignity,' it editorialised, 'that the Negro demonstrations should be met with such brutalities as turning fierce Alsatian dogs on children, knocking men, women and children off their feet with water from fire hoses, and charging demonstrators with batons.' Brian Aarons and some others in the Eureka Youth League bought about 100 copies of the _Sun-Herald_ , and used the front page as a poster to call a protest meeting.
The Birmingham events, involving over a hundred thousand protesters and nearly fifteen thousand arrests, finally convinced the US President, John Kennedy, that the federal administration needed to intervene. He introduced a Civil Rights Bill to make it illegal to discriminate against black people in employment and places of public accommodation, enabling the US federal government to compel local school districts to desegregate, and affirming the right to vote in national elections. Soon afterwards, the massive March on Washington, on 28 August 1963, attracted up to a quarter of a million people, providing the occasion for King's moving 'I have a Dream' speech, followed by the memorable singing together of the movement's anthem, 'We Shall Overcome'. The civil rights movement was clearly gaining strength.
Australians knew about the growing American movement not only from extensive press coverage, but also from television. Two years earlier, _Four Corners_ had pioneered a new style of documentary on Australian television, and the ABC carried reports from the BBC as well. Robert Raymond, who had just arrived at Channel 9 from the ABC's _Four Corners_ , produced as one of his first programs for Nine 'The Negro Revolution', to coincide with the March on Washington. According to his memoirs, _Out of_ _the Box_ , he assembled from the United States Information Service library 'a visual history of black America, going back to slavery and the Civil War'. It used interviews with notable black and white Americans and the Bob Dylan song 'Blowin' in the Wind', sung by a new folk group, Peter, Paul and Mary, for its musical theme. The program, Raymond accurately recalled, went to air in prime time (9.35 p.m.), only a few hours after the March on Washington took place.
After President Kennedy was assassinated on 22 November 1963, his replacement, President Lyndon Johnson—to the surprise of many—took up the cause and sought to push the Bill through Congress. It was always going to be tough getting it through the race-conservative Senate. For several months, Southern Senators tried to defeat the Bill by filibuster. It needed a two-thirds majority to close the debate; once the Bill was put, it would require only a simple majority. There was to be a crucial vote on procedure on 6 May.
May 6 happened also to be Commem Day at the University of Sydney, an annual university holiday commemorating the founding of the university in 1850, and marked since 1896 by a procession through city streets and collection of money for good causes. That year the good cause was the 'South African Committee for Higher Education', an expression of growing student anti-apartheid sentiment. Commem Day was also traditionally a time for student pranks. In 1963, for example, a group of students had 'invaded' one of Sydney Harbour's islands, Pinchgut, so named for the hungry convicts who had been kept in isolation there over a century earlier. One of them, Darce Cassidy, was dressed as Fidel Castro. Soon to become one of the Freedom Riders, Darce was from a wealthy North Shore background, and by this time was a member of the left-leaning Sydney University ALP (Australian Labor Party) Club. Now, in 1964, Darce and the others in the ALP Club decided Commem Day provided an excellent opportunity for a more serious action: a student demonstration outside the US Consulate in support of American civil rights. A leaflet was distributed in the morning, urging students to join the demonstration that afternoon. It began: 'Would you like to be jabbed by an electric cattle prod? To be set upon by an Alsatian police dog?' and went on to ask whether its readers would like to be 'clubbed, imprisoned, lynched, castrated or burnt? You wouldn't? Then you're lucky you're not black. These are the methods used by the white supremacists in the American Deep South.' Today, 6 May, the leaflet went on, was the last day the Civil Rights Bill could be passed. All over the United States, 'people are demonstrating in support of the Bill, and we should support them'.
The ALP Club's plan proved successful. The usual Commem Day procession took place without incident in the late morning, on a mild autumn day, with student floats passing through the city and students collecting about £2000 for the South African Committee for Higher Education. But this was to prove no typical Commem Day; a new spirit of rebellion and political awareness was in the air. At around 1.30 p.m., a large crowd (the press estimated it at 2000) gathered outside the US Consulate. Some were robed as Ku Klux Klansmen and set fire to a 10-foot (3-metre) wooden cross they had erected in the centre of the roadway. Darce Cassidy had brought the cross: 'I had the cross (an old wooden clothes line wrapped in cloth and soaked in petrol) in the back of my car. We took it to Wynyard Street, sat it upright in a garbage can weighed down with bricks, and set it alight.' About 50 students sat down on the roadway in a peaceful protest, while the rest watched. I was there, a second-year student, one of the watchers—a little apprehensive, as I remember. I would have preferred us not to challenge the police in this way. The students chanted: 'We want the Consul.' Police began arresting those sitting down, while other students tried to free them. The tussle developed, as the _Daily Telegraph_ put it the next day, 'into an all-in brawl' between police and students. Twice police called for reinforcements, and with vastly increased numbers order was restored by about 2.30 p.m. Around 50 students and a Channel 7 cameraman, Richard McNicoll, were arrested; later, those aged under 17 were allowed to go.
Students set alight a mock Ku Klux Klan cross outside the US Consulate in Wynyard, Sydney, to symbolise white racist opposition to the Civil Rights Bill before the US Congress. _Daily Telegraph_ , 7 May 1964.
Newspaper coverage tended to focus especially on the young women being manhandled by police. One of them was Arts student Pat Healy, later to be one of the Freedom Riders. When interviewed in 1994, she recalled that this had been a key moment in her involvement with left-wing student politics. Although she had come from a well-known political family, her grandfather being Jim Healy, the former communist leader of the powerful Waterside Workers' Federation, until this moment she had not been politically inclined. She recalled:
I just thought it was a good idea. Despite the fact that I hadn't been involved politically I guess my ideas had been very much formed by my family. And I'd gone along and unfortunately I got arrested . . . I just happened to be on the edge when the police were sort of pushing things through and I think I turned around and said to a big burly copper 'Don't push me', being a very sort of brash type. And he sort of grabbed me and I struggled and subsequently got charged with assaulting said policeman which was really pretty ridiculous because at that stage I was about a size 8 in clothes, I was very very small, and this copper was about 6 ft tall [2 metres] and made about three of me.
The next day, hundreds of students gathered at Central Court to hear the charges. Twenty-five students were formally charged, and all but one pleaded not guilty to their various charges of offensive behaviour, resisting arrest, using insulting words and obstructing police. Among them was another student who was later to join the Freedom Ride: John Powles, a fourth-year medical student. John was already a seasoned political activist, having helped establish the Humanist Society on campus, become a member of the Council of the New South Wales Humanist Society, and been involved in the university anti-nuclear movement.
[A female student is arrested.
_Daily Telegraph_ , 7 May 1964. ](chap7_9781741150575_epub_part7.html#d41151541)
At the court, the ALP Club distributed a leaflet in support of the arrested students, saying 'it is tragic that Australian students seeking to support the civil rights of others should have their own civil rights brutally abused'. The leaflet called on the unions to demand that the charges be withdrawn. The university's Students Representative Council swung into action. Its president, Michael Kirby, also the student representative on the University Senate and later to become a High Court judge, called a meeting of all those arrested and anyone who had witnessed or photographed the arrests to assist with legal representation. Ken Buckley, a senior lecturer in Economic History at the University of Sydney, and secretary of the recently formed Council for Civil Liberties, stressed the right of students to protest and not be pushed around by police. A few days later, Richard Walsh, better known for his editing of the controversial _Oz Magazine_ at this time, edited a special supplement of the University of Sydney student newspaper _Honi Soit_ on the arrests and the subsequent campaign in the students' defence. The defence campaign was highly successful: of those whose charges were proceeded with, ten were acquitted outright, five had the offence proved but the charge dismissed under the First Offenders' section of the _Crimes_ _Act_ , and just six were fined, of whom at least two had their appeals upheld. Meanwhile, in the United States itself, students were pleased to learn, the Senate voted on 10 June to close off the Southern filibuster, thus making way for the passing of the Bill a week later and its presidential signature on 2 July.
The Commem Day protest raised not only the issue of the rights of protesters, but also some other very disturbing questions. Why, many people began to ask, were university students so prepared to demonstrate for civil rights in the United States, when they should be campaigning against racism in Australia itself? Brian Aarons remembers that 'the point was made, both in private conversations I recall and also publicly, that all this was done for the rights of black people in America but nothing had been done about . . . you know, what were we doing about Aboriginal rights'. This was especially true of overseas newspaper comment, which was directed both at the notorious 'White Australia' immigration policy and the question of Aboriginal rights. The _Ceylon Observer_ carried a commentary on 10 June headed 'Strange Reactions', which thought the students' demonstration for US civil rights 'must surely have brought guffaws and giggles from any who gave these reports a second glance'. It continued:
For this is the one country into which no human being is permitted if the pigment of his skin has acquired even the slightest shade of colour—be it brown, yellow or black. We 'coloured' folk in Ceylon can even go to the U.S. and make it our home and be discriminated against, if we so choose. But Australia? Very definitely NO . . . These demonstrators . . . would have done well to look around their own homeland and probe the complete LACK of coloured neighbours. If these demonstrators cared to look a little further and deeper, they would have come across as nauseating a form of social hypocrisy in their own backyards as that they were demonstrating against. I refer to the treatment of the Australian Aborigines.
There was also commentary in the United States itself. The demonstration had been covered in the American press, the _New York Times_ reporting on it on 7 May under the heading 'Sydney Students Riot Against US: Battle Police at Consulate in Protest on Segregation'. The American _Life_ magazine commented: 'Students in Sydney have just rioted against racial prejudice—in the US! Conveniently overlooking the fact that Australia herself possesses some of the most stringent racial exclusion laws in the world.' _Honi Soit_ reprinted the _Life_ comment, sent to it with a letter from Charlie Pyatt III, an African American in San Francisco. His letter, also published in _Honi Soit_ , first thanked the students for their support: 'News of your sympathy demonstration reaching our shores caused America to look with silent embarrassment (including Negroes)', then mentioned the _Life_ magazine comment, and went on to ask: 'If you cannot deny this, and if your concern was sincere, profound and genuine, I ask you most humbly, most appreciatively, can you find the sympathy in your hearts and consciences to conduct PEACEFUL demonstrations against these laws in your own country?'
Within Australia, many people also commented that the students should have been protesting for the rights of Aboriginal people. One letter published in the _Sydney Morning Herald_ on 11 May, from Mrs R. Schodde, was particularly telling. After noting that students had also held demonstrations against the visiting South African cricketers when they were on tour, she wrote:
The motives behind these demonstrations may be admirable, but in the midst of their righteous indignation these students seem to have completely forgotten the plight of the Australian aboriginal. It is a relatively simple thing to join a crowd shouting slogans condemning discrimination in other countries and deluding themselves that they are championing the cause of coloured people. It is quite another thing to help our underprivileged aborigines in a constructive way . . . How many of Tuesday's demonstrators have ever mixed with an aboriginal socially? How many would invite an aboriginal to their homes? Or how many of those students would contemplate marrying an Australian of coloured blood? Only when all Australians stop treating the aboriginal as a second-class citizen and accept him into the white society without reservation can our student groups protest against racial discrimination in other countries without seeming hypocritical.
Criticisms like these hit home. What, indeed, _had_ the students been doing in support of the campaign for Aboriginal civil rights? For, though there was truth in the claim that white Australians were more likely to deplore racism abroad than at home, there was in fact an active Aboriginal rights campaign in existence. Politically diverse and multi-racial, it sought full citizenship for Aboriginal people, taking up a range of issues from around the country as they came to light, often in the less 'settled' regions of northern and western Australia. Key figures in these organisations were frequently Christians, anthropologists, or from the Left. Leading Christians in the Aboriginal movement included Charles Duguid, a Presbyterian minister in Adelaide known for his writing and activism on behalf of Aboriginal people, the Reverend Frank Engel, the secretary of Division of Mission of the Australian Council of Churches, and Barrie Pittock, a Quaker. Duguid's book _No Dying Race_ , published in 1964, became a key text for the growing Aboriginal movement. Both Engel and Pittock were becoming prominent advocates of Aboriginal land rights, influenced by travels and knowledge of the situation in the United States and New Zealand. Anthropologists like T.G.H. Strehlow, Donald Thompson and A.P. Elkin were also influential, in various ways given their very divergent politics. T.G.H. Strehlow's book _White and Dark Australians_ , his printed lecture 'Assimilation Problems: The Aboriginal Viewpoint', and Elkin's books such as _The Australian Aborigines: How to Understand Them_ (1938) and _Aborigines and Citizenship_ (1960) were all part of the reading of concerned citizens in these years. Also important were the voices of a growing number of Left-liberal intellectuals, including historians like Brian Fitzpatrick, who included a chapter, 'Disinherited Australians', in his _The Australian Commonwealth_ (1956), and Ken Inglis, who wrote a book on the case of Max Stuart (an Aboriginal man unfairly tried for murder) in 1962. In January 1962, Aboriginal Affairs, an independent and voluntary association to stimulate thoughts on subjects concerned with Aboriginal welfare and advancement, was established in Melbourne. From April that year, it published a bi-monthly news-sheet, _On Aboriginal Affairs_ , edited by Ian Spalding, which provided in-depth information and analysis on a regular basis.
The Communist Party of Australia (CPA) was especially active on Aboriginal rights, its influence so great that it was beginning to cause concern in some circles. The Party had taken Aboriginal issues seriously since its inception in the early 1920s, and continued to do so through the succeeding decades. Before World War II, the communists had seen Aboriginal issues through the framework provided by the international communist body, the Comintern. This rested on a distinction between tribalised peoples, who were seen to have the rights of national minorities, and detribalised people, for whom equal citizenship rights were appropriate. This view was restated at its sixteenth congress in August 1951, under the heading 'Safeguard the Native Races'. From 1954, however, influenced by a change in international communist policy, the CPA more or less abandoned its former distinction between tribal and detribalised peoples, and took up the Aboriginal cause with a new intensity. Communist policy now emphasised the exploitation of Aboriginal people as workers, and sought to establish the unity of all Aboriginal people in different parts of the country in a common struggle for full citizenship. Aboriginal matters were given high priority, with leader Sam Aarons calling for CPA members' commitment in the _Tribune_ , the party's newspaper, on 19 January 1955. From then on, the communist press consistently gave a great deal of publicity to Aboriginal issues, publicising examples of prejudice, drawing attention to Aboriginal activism such as strikes and anti-eviction protests, and encouraging Aboriginal membership.
The priority given to Aboriginal rights by the CPA flowed into the various organisations over which it had influence. One was the Union of Australian Women, a nationwide communist-led women's organisation which from 1958 adopted and actively pursued the CPA interest in Aboriginal rights. It sought to include Aboriginal women in its own ranks, and had succeeded in doing so for some years, with prominent Aboriginal members including Pearl Gibbs and Dulcie Flower in Sydney, Gladys O'Shane in Townsville and Gladys Elphick in Adelaide, until it became clear that Aboriginal women preferred to form their own organisations. In unions with Communist Party leadership, support for Aboriginal rights stepped up from the mid-1950s, notably in the Waterside Workers' Federation, which attracted a number of Aboriginal members, the Sheetmetal Workers Union, led by long-time pro-Aboriginal campaigner Tom Wright, and the two building workers' unions, which also had some Aboriginal members.
New organisations developed in the 1950s focusing specifically on Aboriginal rights—or, as it was more commonly put at the time, advancement. In New South Wales, Aboriginal activism had a long history of opposition to the surveillance of the Aborigines Welfare Board and its predecessors. The Aboriginal-Australian Fellowship was formed in 1956 by Pearl Gibbs and Faith Bandler, and had a mixed Aboriginal and non-Aboriginal membership, many of its members being close to the Communist Party. One of its Aboriginal leaders, Bert Groves, left in 1958 and in January 1964 he was one of those who formed a new group, the Aborigines Progressive Association (APA), a title reviving that of an earlier organisation of the late 1930s. Unlike the Fellowship, the APA's constitution ensured the dominance of Aboriginal people in the organisation (unless married to an Aboriginal person, others could only join if nominated by an Aboriginal person and accepted by a majority of members at a general meeting). There were mixed-race organisations also in other states and territories, notably the Coolbaroo League in Western Australia, the Council for Aboriginal Rights in Victoria, the Aborigines Advancement League in South Australia, and the Northern Territory Council for Aboriginal Rights.
These organisations frequently drew attention to the situation of Aboriginal people by pointing out how far Australian practice diverged from the principles enunciated in the United Nations Declaration on Human Rights of 1948, which Australia had signed. A decade after the Declaration, Aboriginal rights remained extremely limited everywhere, with restrictions on freedom of movement, control of property and freedom of association with Europeans. Only if one had an 'exemption certificate' could equal rights be granted. In Queensland and Western Australia, there were government controls over marriage and Aboriginal people did not have the right to vote in elections. There were restrictions on the right to drink alcohol in all states except Victoria. Throughout the country, town councils and businesses practised various forms of exclusion of Aboriginal people from town amenities, and employment inequality was rife. Aboriginal people were moved on and off reserves without reference to their basic right to freedom of movement. More starkly, in the outback regions of the country, Aboriginal people were exploited—sometimes brutally. In most parts of the country, authorities removed Aboriginal children from their families, from a strange mixture of genocidal intent (by which I mean a desire to ensure that Aboriginal identity was extinguished) and welfarist concern for neglected children. In 1957, veteran campaigner Mary Bennett's book, _Human Rights for_ _Australian Aborigines_ , drew attention to these practices, and to how different they were from the UN principles which Australia itself had supported.
Yet international censure and opprobium did not matter a great deal to state governments, whose focus was far more local. Aboriginal rights activists had been arguing since the 1930s that there would only be substantial gains when the Commonwealth government, more susceptible than state governments to international opinion, took responsibility. Commonwealth governments, however, left Aboriginal affairs largely to the states, and responded to pressure to take action by arguing that their hands were tied by the Constitution. There were two relevant clauses. Section 51 provided that the Parliament had the power to make laws with respect to 'the people of any race, other than the aboriginal race in any State', and section 127 excluded Aboriginal people from the census. When Jessie Street, well-known Australian feminist and supporter of human rights now living in London, returned to Australia in 1956–57 to investigate the situation for the British-based Anti-Slavery Society, she found governments citing the Constitution as the reason for Commonwealth inaction. She concluded that the Constitution must be changed to establish Commonwealth control, which she saw as essential for the framing of an appropriate national response to the UN Declaration, and to facilitate meeting Australia's local and international obligations generally. Faith Bandler and others in the Aboriginal-Australian Fellowship took up the idea, and a campaign for a Referendum for constitutional change began in earnest.
Leaders of the state-based Aboriginal rights organisations around the country began to move for a national body to coordinate their campaign for constitutional change and for a new national government policy. The Federal Council for Aboriginal Advancement (FCAA) was accordingly formed in February 1958, and campaigned energetically on a wide range of issues.
Accompanying the growing campaign domestically was an increased level of criticism internationally, just as the Aboriginal rights campaigners hoped and Australian governments feared. Australia was deeply concerned by attacks by Soviet leader Krushchev in the United Nations on its Aboriginal record. The meeting of the UN General Assembly on 13 October 1960 is often remembered as the occasion on which Krushchev pounded his desk with his fists and brandished a shoe to emphasise his objections to the rulings of the UN president. Yet it was also the occasion when the Assembly supported Krushchev's motion to debate a declaration of independence for colonial peoples. Accusing Australia of having exterminated her Aboriginal population, Krushchev said: 'Everyone knows in what way the aboriginal population of Australia was exterminated.'
With racial discrimination becoming an embarrassment internationally, the Commonwealth was forced to take some action, despite its supposed lack of relevant powers. In fact, the Commonwealth government had been attempting to develop some common policies and approaches through meetings of Commonwealth and state Ministers of Aboriginal Affairs, with a landmark meeting in 1937, followed by another in 1951. These did not provide for the citizenship rights and freedoms that many activists in the 1930s had wanted, but they did progressively develop policies of inclusion and assimilation rather than exclusion and segregation. A Commonwealth Parliamentary Select Committee to Enquire into Aboriginal Voting Rights was established in 1961; one of its members, Kim Beazley Snr, was to be profoundly influenced by its deliberations and remained a strong parliamentary voice for Aboriginal rights thereafter. As a result of the Select Committee's report presented on 19 October 1961, the Commonwealth government removed discriminatory features from its own legislation—for example, extending the franchise to Aboriginal people in the Northern Territory in 1962, a move followed by both Queensland and Western Australia.
Through all this, there was concern about communist influence in the expanding Aboriginal movement. The growing emphasis in the movement on autonomy rather than assimilation was interpreted in a detailed ASIO report in 1962 as the result of communist influence, in line as it was with international communist policy for minorities. At a meeting of the Trusteeship Council of the United Nations in June 1963, the Soviet delegate confronted the Australian delegate with section 127 of the Constitution as evidence of discrimination against Aborigines. Yet unwelcome scrutiny was coming not only from the communist world. International pressure greatly intensified with the adoption on 20 November 1963 of the UN Declaration on the Elimination of All Forms of Racial Discrimination. It not only reaffirmed the principles contained in the UN Charter and the UN Universal Declaration of Human Rights, but also affirmed the necessity of 'speedily eliminating such discrimination, in any form, throughout the world and of adopting national and international measures to that end'. Henceforth, governments were not only urged by the United Nations to cease all practice of racial discrimination themselves, but they were also expected to work to eliminate it from their society altogether. Senior public servants serving on an Inter-Departmental Committee on Racial Discrimination, formed in response to the changing UN situation, secretly agreed in March 1964 that 'there was an urgent need to remove, as far as practicable, instances of racial discrimination in Australia in order to ensure that Australia's international reputation and influence are not to be seriously endangered'.
Equally troubling for the Australian government was increased pressure from the International Labour Organisation (ILO). The payment of lower wages to Aboriginal pastoral workers was directly in contravention of ILO Convention 107 on the employment of Indigenous people, passed in 1957. The FCAA took this issue very seriously, with one of its leaders, a white Communist Party member named Shirley Andrews, compiling for its 1962 annual conference a detailed report revealing the widespread payment of low wages, especially in the pastoral industry in the Northern Territory, Queensland and Western Australia, and the restricted employment opportunities in Victoria and New South Wales. When the Australian delegation to an ILO conference in 1963 realised that the Aboriginal wages question might receive critical ILO scrutiny, the Australian Council of Trade Unions was galvanised into action, passing a resolution in favour of equal pay for Aboriginal pastoral workers at its Congress in September 1963. Soon after, the Equal Wages for Aborigines Committee of the FCAA headed by Andrews conducted a public campaign on the matter, widely distributing a pamphlet, _The Facts on Wage_ _Discrimination Against Aborigines_. Kim Beazley Snr proposed in Parliament on 8 April 1964 that Aboriginal workers in the Northern Territory cattle industry be paid award (equal) wages, and a long and well-publicised debate ensued.
The Referendum campaign was rapidly gaining ground. Beazley initiated an urgency debate in the House of Representatives on 30 August 1962, calling for a Referendum on section 51. A public meeting in Sydney a few weeks later, on 6 October, launched a national petition, eventually taken with 40 000 signatures by an Aboriginal delegation to the Prime Minister.57 The Labor Party continued to campaign on the issue, with Arthur Calwell, the leader of the Labor opposition, moving unsuccessfully in the House of Representatives on 15 April 1964 for a Referendum to remove both racially discriminatory clauses from the constitution.
Students were not quite yet part of this growing public protest and debate. When they protested publicly about racial policies within Australia itself, they had nearly always been concerned with immigration rather than Aboriginal policy. Several developments made them keenly aware of overseas opposition to the 'White Australia' policy. Student organisers attending overseas conferences found Australia's reputation as a racist society deeply embarrassing. More importantly, on campuses around the country—especially at the universities of Melbourne, Sydney and Queensland—the considerable number of Asian students entering the universities under the Colombo Plan or privately put paid to older ideas about Asian intellectual inferiority, and facilitated feelings of friendship towards Asian people generally. At the newly opened Monash University, the first student demonstration in October 1961 was a picket, along with students from the University of Melbourne, of the West End Private Hotel in Melbourne for refusing board to three Nauruan women 'simply on the grounds of colour'. Students carried placards reading 'Ban the White Australia Policy' and 'Racial discrimination is immoral'. Shortly afterwards, a meeting of about 800 students at the University of Melbourne formed Student Action, which mobilised hundreds of students in protest against the 'White Australia' policy during the federal election campaign of November 1961. Both Menzies and Calwell made angry attacks on the students, and Student Action became front-page news, attracting generally negative newspaper reports and editorial comment.
Over the next two years, the student campaign against the 'White Australia' policy continued. Student Action groups appeared in Sydney and Brisbane in 1962. Sydney University students demonstrated outside the Immigration Department in Sydney in January that year in support of three Portuguese seamen threatened with deportation by the Menzies government; the day before, students from the University of Queensland had staged a similar demonstration outside the Immigration Department offices in Brisbane. In April, more than 250 students at Melbourne and Monash Universities and at the Royal Melbourne Institute of Technology marched in protest at the action of the Immigration Department in deporting Mr Willie Wong; by September, Queensland students were picketing a hotel for its refusal to serve beer to an Indian and two African students. A key figure in the New South Wales branch of the Association for Immigration Reform was Ken Rivett, a lecturer at the University of New South Wales. The School of Economics at Rivett's university had several active members of the association, including Bill Ford, soon to become a key figure in the Freedom Ride story. Darce Cassidy joined the committee of the association and began to write articles and speak to meetings about the need to abolish the 'White Australia' policy. The Students Representative Council at the University of Melbourne put pressure on the National Union of Australian University Students (NUAUS) to adopt a policy of clear opposition to the 'White Australia' policy. NUAUS agreed, after its own survey in 1963 of a random sample of its members in all ten universities and the university colleges in Townsville and Newcastle showed that almost 70 per cent of students nationwide favoured liberalisation of immigration policy, with Monash students being most in favour at 84 per cent and Townsville University College students least so, at 52 per cent.
Very slowly, student interest in Aboriginal issues did develop, though less among the political radicals than among students simply interested in helping fund scholarships for Aboriginal people to attend university. In 1950 and again in 1951, NUAUS had urged the state governments that 'greater educational facilities be made available for Aboriginals'. In 1952 it agreed to sponsor a scholarship scheme for Aboriginal students, providing an establishment grant of £1300 and requesting the Students Representative Councils in each university to set up local appeal committees, with Melbourne acting as a central organising committee. Jennifer Crew, director of the scheme in 1955, presented a complete report and wanted to broaden NUAUS's Aboriginal policy beyond scholarships, but it refused. Plans for a scholarship scheme gradually became a reality: in 1957 Melbourne University agreed to act as trustee and the first two scholarships were awarded, though neither student graduated with a Bachelor's degree. Abschol committees at a number of universities were formed, and raised funds through appeals to schools and private industry, button days, film showings and concerts. The University of Sydney made Abschol its charity for its annual Commem Day collection in 1961. By August 1964, there were Abschol committees or directors in most universities, including the University of Sydney. Students in the Abschol branch at the University of Sydney raised money through an annual collection, and also through lunch-hour entertainment shows featuring artists such as Jimmy Little and Tony Morrison. In May 1964, at the time students were being criticised for doing so little for Aboriginal rights, Abschol was sponsoring a visit to the university of 42 Aboriginal children from the Sydney area.
Abschol had little involvement in public political debate on the broader questions of Aboriginal rights. In 1963, however, with Margaret Valadian (an Aboriginal university student at the University of Queensland) as director, it persuaded NUAUS to agree to a motion requesting the state governments to take action to deal with problems preventing 'Aborigines as a group from participating in or gaining benefit from education'. The following year, NUAUS passed a motion urging the Commonwealth government to call a Referendum to change the Constitution. These were still small steps, and on the whole NUAUS and Abschol remained aloof from the growing Aboriginal rights movement. Abschol was, however, starting to achieve its aims of assisting Aboriginal students to attend university. In 1963, scholarships were awarded to students of Aboriginal descent, at the Universities of Sydney (going to Charles Perkins and Gary Williams, both of whom enrolled in Arts) and Queensland (Margaret Valadian and Betty Anderson, both in Social Studies). It held a national conference in May 1963, and by mid-1964 its national funds exceeded £11 000.
Charles and Gary's presence at the University of Sydney was to change both them and the university forever. Gary, born in Mullumbimby in Bundjalung country (his father's country), grew up in Nambucca Heads, in Gumbaynggirr country (his mother's country). His family, he told me in interview, had a history of resisting white authority, having opposed segregation of the picture theatre in the town, and fighting hard against children being taken away (and if they were taken and then made their way back, making sure they were not taken again). His schooling had been at the Aboriginal school on the reserve, then a convent school, from which he won a bursary to attend Woodlawn College in Lismore. After he completed the Leaving Certificate in 1962, he was welcomed at the start of the university year in 1963 at St John's College, having just turned 17. Sydney for him was a much wider world than he had ever known, and through his uncle, Clive Williams, he met the growing network of Aboriginal activists.
[Gary Williams, left, and Charles Perkins, right, at the University of Sydney on their first day as students, March 1963.
(Photo courtesy of Gary Williams)](chap7_9781741150575_epub_part7.html#d41151591)
Charles Perkins, by contrast, was already an experienced political leader. His story has been told in detail a number of times, including his autobiography, _A Bastard Like Me_. This book is notable not only for the story it tells but also because, appearing in 1975, it was one of the first of a long line of such autobiographies, one of the main means by which Aboriginal people have communicated their individual and community experiences to a wider non-Aboriginal audience. Peter Read's _Charles_ _Perkins: A Biography_ also tells his story well. Born in Alice Springs in the Northern Territory in 1936, of Arrernte and Kalkadoon descent, he had gone to school in Adelaide ('I failed seven out of eight subjects in the final year at Technical School in Adelaide, so I was no academic giant' he told me), played soccer for several English teams in 1957–59, and then became a noted public speaker for Aboriginal rights in Adelaide, being elected vice-president of the FCAA in 1961.
Charles came to Sydney in late 1961 or early 1962, where he played soccer for the Pan-Hellenic team, met a range of Aboriginal and non-Aboriginal activists, and in particular struck up a friendship with Methodist minister Ted Noffs. Noffs' first posting in 1951 had been as a Methodist pastor at the Far West mission at Wilcannia, where he had become close friends with many Aboriginal people, observed the dire conditions under which they lived, and developed respect for their spiritual beliefs. He had spent time in the late 1950s in Chicago, doing his Master's degree in Theology, and had been influenced by racial politics there. On his return to Australia, he became associate minister of the Central Methodist Mission (CMM) in Sydney, and used its welfare agencies to assist the growing urban Aboriginal population in inner Sydney. He wrote in _The Methodist_ at this time: 'One of the most explosive social questions facing Western society today is that of race.' He outlined its importance in South Africa, the Deep South of the United States and in London, and reflected on the future of European relationships with the Aboriginal people of Australia. 'Have we,' he asked, 'reached a point of no return so far as the building of a bridge between the cultures is concerned?' His answer was no, given the emergence of Aboriginal–European committees throughout the nation 'aimed at building new and better relations'. There was also, he thought, 'a growing recognition throughout the country of the significance of the culture that the aborigine people represent'. He drew his readers' attention to a new factor in Aboriginal affairs—the large numbers of Aboriginal people forsaking the fringe dwellings and reserves in country towns for the cities. The time had come, he said, to offer assistance, though 'aid must never again be given patronisingly or in the form of welfare handouts'.
Ted Noffs now arranged for Charles to speak at public meetings under the auspices of the CMM, and one of these speeches at the Lyceum Theatre was so successful that Noffs realised a new Aboriginal leader was emerging. He was also important in supporting Charles's desire to go to university, encouraging him to study for his matriculation through the Metropolitan Business College. Charles did, and finally arrived at university in 1963 at the age of 27. Although he was not the only Aboriginal student, Gary Williams having started at the same time, he was to become the most visible on campus. When my research assistant, Inara Walden, interviewed Charles in November 1994, he told her:
I was very pleased when I walked through the gates of Sydney University, and I thought 'This is it'. I knew that something was going to happen as a consequence of me going through there, personally and in Aboriginal Affairs, because the fire in the belly was well and truly alight by then . . . and things were going to happen. I was going to make them happen. And I was very determined but I didn't know what to do really, but the subjects I chose were really tuned into what I wanted to do later on, for example Anthropology I, II and III, Political Science I, II and III, the other two were Psychology and Social Theory or Sociology. So I was training for the future.
In May 1964, Charles's political activity was still more off campus than on. He was closely involved in plans to provide some kind of welfare and social support for the growing number of Aboriginal people in Sydney, who had migrated to the city in search of work. By this time there were about 6000 Aboriginal people in Sydney, and public discussion of their needs was growing. The year before, on 3 May, the Labor Lord Mayor, Harry Jensen, had chaired a well-attended public meeting from which had emerged the Aboriginal Affairs Association, aiming to assist Sydney's Aboriginal population. Its committee included Noffs as chair, Perkins and Ken Brindle (an influential Aboriginal Sydney man) as vice-chairmen, and Bill Geddes, Professor of Anthropology at the University of Sydney, as treasurer. Geddes was a New Zealander who hoped to achieve some of the same closeness between the university and Indigenous students that he had witnessed in Auckland, and readily made the Department of Anthropology's facilities available for the early meetings of the association. Just five weeks before the students' May demonstration for US civil rights, a well-publicised general meeting of the association had been held in the Anthropology lecture room. The committee undertook fund-raising, found a property in lower George Street which would be suitable as a cultural, social and welfare assistance centre, and at a meeting on 1 July changed the name of the society to the Foundation for Aboriginal Affairs and agreed to purchase the building.
Student protest meetings on Aboriginal issues were still rare. One of the first was at the University of Melbourne in mid-1963, when its ALP Club held a meeting on the proposals to disperse the Aboriginal community at Lake Tyers, the last remaining Aboriginal reserve in Victoria. Gordon Bryant, president of the Victorian Aborigines Advancement League, drew students' attention to a range of injustices, such as the fact that Aborigines on the reserve could not be visited without the permission of the Aboriginal Welfare Board. Clyde Holding described the slum conditions, the low wages and the forcing of families away from the settlement. Pastor Doug Nichols, a Victorian man of Djadjawurung and Yorta Yorta descent, a preacher in the Church of Christ and noted Aboriginal political leader, also spoke, asking that Lake Tyers be retained.
The national student body, NUAUS, began to take a much stronger and more openly political position on Aboriginal issues when Robert McDonald, who had been one of the leaders of Student Action in Sydney, became its president. At its Annual General Meeting in March 1964, just two months before the Wynyard demonstration, McDonald publicly criticised the federal government's refusal to guarantee its support for the rights of Northern Territory Aborigines, and 'its unwillingness to take adequate steps towards elimination of discriminatory practices'.
Noting the principles established by the United Nations, he urged the government to 'make an immediate and unequivocal declaration of its support for what are basic human rights'. The meeting supported the ongoing campaign to eliminate the two discriminatory clauses in the Constitution, and 'laid down a comprehensive program for student action on aboriginal affairs in 1964'. NUAUS sent two observers to the FCAA annual Easter conference in Canberra, to consider affiliation and to learn more about Aboriginal organisations and issues generally. Although NUAUS decided not to affiliate at this stage, the basis had been laid for new lines of communication between students and off-campus organisations for Aboriginal rights.
Perhaps goaded into action by the criticisms of the May demonstration, members of the Labour Club at the University of Sydney urged the national conference of the Australian Student Labour Federation, the umbrella body for the Labour and ALP Clubs around the country, to organise a protest on 'the treatment of Aborigines' on National Aborigines Day in July 1964. This was a day that had begun in 1957 as a government attempt to publicise its assimilation policies, but had gradually been taken up as a focus for campaigning by Aboriginal rights organisations. By 1964, the day had extended to a National Aborigines Week. A fairly small demonstration was held in Melbourne, when about 200 students displayed placards and distributed leaflets headed 'Australia's Disgrace', first in a march around a large city block and then on the steps of Parliament House. They moved to nearby gardens for a rally, addressed by the state leader of the opposition Mr Stoneham and Clyde Holding, the state ALP spokesman on Aboriginal affairs.
A much larger demonstration was held at the same time at the University of Sydney. In June 1964, several students formed a committee called the 'Sydney University Organising Committee for Action on Aboriginal Rights' to organise action around National Aborigines Day on 8 July. The committee consisted of three students who were later to join the Freedom Ride—John Powles, Hall Greenland and myself (as treasurer)—plus the student and folk singer Jeannie Lewis and another student, Christopher Sweeney, who was active in the Civil Liberties Association; both Jeannie and Christopher had been arrested in the May demonstration at Wynyard. Hall Greenland was a second-year Arts student and a member of the university's ALP Club, while I, another second-year Arts student, was a member of the communist-influenced Labour Club. Louise Higham, a first-year medical student who was soon to become one of the Freedom Riders, was also involved in organising the demonstration as a member of the Labour Club. She wrote to the Aboriginal-Australian Fellowship, letting them know about the proposed demonstration on 8 July, and seeking information about reading material 'we could sell on the bookstall the Labour Club will be opening in the near future'. This committee organised a public meeting and concert in Hyde Park, in the centre of the city, with substantial student support. Jeannie Lewis helped arrange the folk singers, Hall Greenland wrote on behalf of the ALP Club to the trade unions to raise funds for financial support, while I wrote on behalf of the committee to the university's clubs and societies with the same request.
I remember helping to write and produce the leaflet, a copy of which I still have. It was signed by the committee, and supported by a range of clubs and societies including Abschol, the ALP Club, the Anglican Society, the Civil Liberties Association, the Education Society, the Humanist Society, the Jewish Students Union, the Labour Club, the Newman Society, the Students' Christian Movement, and the Students Representative Council. It was headed 'Mass meeting today—Demonstration tomorrow', and then 'Poor bloody Abos!' (What, quite, _were_ we thinking?!) It went on:
150 years of persecution, extermination, indifference, prejudice, discrimination, paternalist 'welfare' policies and sheer neglect have left the original Australians as a depressed racial minority. This abhorent [ _sic_ ] situation is ignored by a complacent society. The community's conscience MUST be awakened by protest action. This has succeeded in the USA—it could do so here.
The leaflet advertised a meeting at the university that day, 7 July, with speakers Senator Lionel Murphy, Ron Hancock (of the BWIU, a director of Tranby College and a former member of the FCAA) and the Reverend Alf Clint. Murphy, who nine years later became Attorney-General in the Whitlam Labor government of the 1970s, spoke of the Queensland Act that restricted Aboriginal people's freedoms—in, for example, handling their own money, choice of marriage partner, and deciding where to live. He drew attention to the discriminatory clause in the Constitution that meant Aborigines were not counted in the census, and the fact that the government had recently rejected Arthur Calwell's attempt to have the offending clause removed. Ron Hancock outlined trade union support for Aboriginal people, mentioned the ACTU taking up the issue of Aboriginal wages the previous year, and drew attention to a recent incident in Walgett where two 9-year-old children had been locked up over night for taking two table tennis bats, two balls and a packet of crayons, an incident we return to in detail later in this story. The Reverend Alf Clint, an Anglican priest with strong socialist convictions who had first developed cooperative enterprises in Papua New Guinea and subsequently persuaded the Australian Board of Missions to support the development of cooperatives in Aboriginal communities, spoke about the success of the cooperative movement.
The leaflet also advertised a peaceful demonstration for the following day at Parliament House. Students were urged to 'make your placards (or "police-proof " smocks) tonight'. The themes were to be:
**Equal Rights here * End Legal and Social Discrimination** **now * Equal Opportunities for Aborigines * Education** **for Aborigines**
Students responded, with about 500 attending the rally-cum-concert in Hyde Park and the demonstration outside Parliament House, designed to give publicity to the legal and social discriminations against Aborigines. At the Hyde Park event, Gary Shearston sang a number of freedom songs from America, as well as songs written by the Aboriginal poet Kath Walker, later to be known as Oodgeroo. One song, I remember, was a musical rendition of her poem 'Aboriginal Charter of Rights', first presented to the 5th Annual General Meeting of FCAA in Adelaide held over Easter 1962. It went:
We want hope, not racialism,
Brotherhood, not ostracism,
Black advance, not white ascendance:
Make us equals, not dependents.
We need help, not exploitation,
We want freedom, not frustration;
Not control, but self-reliance,
Independence, not compliance,
Not rebuff, but education,
Self-respect, not resignation.
Free us from a mean subjection,
From a bureaucrat Protection.
Let's forget the old-time slavers:
Give us fellowship, not favours;
Encouragement, not prohibitions,
Homes, not settlements and missions.
We need love, not overlordship,
Grip of hand, not whip-hand wardship;
Opportunity that places
White and black on equal basis.
You dishearten, not defend us,
Circumscribe, who should befriend us.
Give us welcome, not aversion,
Give us choice, not cold coercion,
Status, not discrimination,
Human rights, not segregation.
You the law, like Roman Pontius,
Make us proud, not colour-conscious;
Give the deal you still deny us,
Give goodwill, not bigot bias;
Give ambition, not prevention,
Confidence, not condescension;
Give incentive, not restriction,
Give us Christ, not crucifixion.
Though baptized and blessed and Bibled
We are still tabooed and libelled
You devout Salvation-sellers,
Make us neighbours, not fringe-dwellers;
Make us mates, not poor relations,
Citizens, not serfs on stations.
Must we native Old Australians
In our land rank as aliens?
Banish bans and conquer caste,
Then we'll win our own at last.
Oodgeroo of the tribe Noonuccal
Delegates from an International Student Seminar held the week before at the University of New South Wales attended. The seminar had been organised after Australia was rejected as a venue for the International Student Conference (ISC) because of its racist immigration and Aboriginal policies, with New Zealand chosen instead. Some of the ISC delegates were invited to Australia after the conference. From Malaysia, the United Arab Republic, Israel, Hong Kong and India, they spoke in support of any move to end racial discrimination in Australia. Charles Perkins also spoke, outlining numerous discriminations against Aborigines, including the fact that they were not counted in the census. 'We rightly protest against the racial discrimination in South Africa and the USA,' he said, 'but we also have the same problem in Australia. We don't want charity, just give us the freedom and opportunity to lift ourselves.' Gary Williams again drew attention to the gaoling of the two 9-year-old Aboriginal boys at Walgett. As _Honi Soit_ reported of the speeches by Charles and Gary: 'Both speakers said Aborigines wanted to integrate into society, but not to be completely assimilated. They said that their people wanted to retain their culture etc. but to still live as ordinary citizens without discrimination.'
[Students demonstrate for Aboriginal rights outside Parliament House, Macquarie Street, Sydney, 7 July 1964.
(Photo by Michael Elton and reproduced with permission of the Australian Photographic Agency collection, State Library of New South Wales)](chap7_9781741150575_epub_part7.html#d41151611)
After the rally, the students moved from Hyde Park along Macquarie Street to state Parliament. They chanted slogans and sang songs, holding placards and banners depicting such themes as 'End Discrimination Now', 'Civil Rights Now', 'Civil Rights for all Australians', 'Education for Aborigines' and 'You're right if you're white'. They distributed a pamphlet headed 'Are You a Racialist?' asking 'Do you condone the existing discrimination against Aborigines?' and drawing attention to the discriminatory clauses in the Constitution, the gross denial of civil rights in Western Australia and Queensland, and the fact that Aborigines had no land rights on their reserves. Even in New South Wales, where there was less legal discrimination, the pamphlet pointed out that there were examples of discrimination, including the locking up of the two Walgett children and the exclusion of Aborigines from the artesian baths and swimming pool— a popular tourist attraction—in Moree. The pamphlet concluded with the demand that:
1. The Commonwealth government remove Section 127 and the discriminatory words in Section 51 by holding a referendum at an early date.
2. The State governments abolish legal discrimination in their respective states.
3. The people of Australia do all they possibly can to end discrimination against Aborigines.
The protest was notable for the lack of a police presence, its peaceful nature, and generally positive publicity. SRC president Michael Kirby said the demonstration aimed to draw parliamentary backbenchers' attention to discriminatory clauses in the Australian Constitution, and to get the state government to support scholarships for Aboriginal students. After the meeting, I (as treasurer) wrote to various clubs and societies seeking financial contributions to offset the costs of the demonstration.
Having achieved its immediate objective, this committee faded away, and a new organisation with a new leadership developed in its place. Although very active in the July demonstration, I was not involved in the developments and events of the next few months that I now relate. I've pondered possible reasons—personal, political, my studies—but in the end, I simply cannot remember why I vanish from this story until February 1965.
After the National Aborigines Day demonstration, and the establishment of the foundation, Charles was beginning to look for a new way of organising student action for Aborigines. In later years, he was well aware of the importance of his presence to the development of Aboriginal politics on campus: 'I played my part in terms of bringing the Aboriginal element into it.' He met with several others to discuss the foundation of a more permanent student organisation for Aboriginal rights. One was Labour Club student Brian Aarons. It was a combination that might seem surprising, given Charles's suspicion of communist influence in the Aboriginal movement, and Brian's role as a communist student. It could not have happened at the University of Melbourne, where the communist students had been excluded from Student Action. Charles in fact seems to have been unaware of Brian's communist connections, and the two got on very well; they joined up with several other students and staff to call a meeting at the university for 20 July to discuss what forms of action students could take in support of Aboriginal campaigns for equality.
Also involved in calling the 20 July meeting were two of the academics at the University of Sydney. One was lecturer and Council for Civil Liberties secretary Ken Buckley; another was Peter Westerway, a lecturer in Government. Peter had a particular interest in politics and the media, and was much influenced in this by Henry Mayer, a pioneer of Australian media studies whose foundational text _The Press in Australia_ appeared that same year. Although he had recently moved to the position of executive producer of the investigative Channel 7 television program _Seven Days_ , Peter still maintained a teaching role at the university. He had a clear interest in covering Aboriginal issues on _Seven Days_ , having aired a program called 'The Australian Aboriginal and his Future' on 9 July, during National Aborigines Week. This covered the issues and activities of Aboriginal people in Sydney, and also on Palm Island in Queensland. It explored the formation of the Foundation for Aboriginal Affairs, and included a panel discussion featuring Bill Geddes, Charles Perkins, Michael Sawtell—an 80-year-old former bushman who had been involved in Aboriginal rights organisations and the Aborigines Welfare Board—and Allan Duncan, an adult education teacher much involved with Aboriginal education. The other two names on the list of those calling the meeting were Peter Martin, a reporter on _Seven Days_ , and Kevin Martin from the Students Representative Council.
These six collectively distributed a leaflet to 29 clubs and societies on campus. They explicitly addressed the troubling issues raised by the Commem Day demonstration: 'This was fine as far as it went, but what now? How can we show our sympathy and support for our own coloured minority, the Aborigines?' They asked all clubs and societies to 'appoint two representatives of your club to attend a meeting in Gosper rooms 1 and 2, at 1 pm, to consider the matter'. At this point, the leaflet said, there was a range of options to consider:
a) more demonstrations in the city; b) collections, voluntary labour, e.g. Abschol or the new Foundation for Aboriginal Affairs centre at Central; c) a long vac demonstration continued over 2–3 weeks, e.g. 'freedom rider' buses in northern NSW and Queensland, and d)??? suggestions welcomed.
The contact person was Peter Westerway.
This was the first mention of a possible Freedom Ride in print. The idea of demonstrations or voluntary assistance was by now familiar, but how did the idea of 'freedom rider' buses get on to this list? It seems that Charles first pondered the idea of an Australian Freedom Ride after a conversation with Peter Westerway. Peter remembers his contact with Charles Perkins when he delivered a lecture in mid-1964 to a Government class at which Charles was present:
It was in the Old Geology lecture theatre, one of those cantilevered lecture halls, and I was talking about politics and the media. I remember that the major point that I was making was that television was critical, and radio was now less important than it had been, and that if you wanted to do anything about television you had to be talking in terms of pictures. Without pictures it didn't work.
And that's all I remember having said. The reason I remember it is that after the lecture was finished Charlie stayed behind and said to me what could he do about publicising the Aboriginal cause. And I remember we were sitting in the body of the lecture hall, not down at the lecture podium, and I repeated this stuff about pictures and said, 'Look, television's all about short grabs, you have to be able to see interesting pictures or they won't use it. They only use things which they have pictures to illustrate. Talking heads are dead on television.' And we began to talk and I think I suggested about the Freedom Rides in the United States and the way in which that had been done. And as I was talking it occurred to me that there was no reason why you couldn't do something similar in Australia and I said to him, 'If you get together a group of people who will go on a bus ride around what has come to be called the Deep North of New South Wales, I suppose I'll send a camera crew with you. And we'll do a documentary and put it on _Seven Days_.'
The US Freedom Rides to which Peter Westerway drew Charles's attention had occurred three years earlier, in the northern summer of 1961. Indeed, the term Freedom Ride is even older—having been used, for example, in Jamaica in 1957 to refer to a procession of 4000 city cyclists who rode miles through city streets and lanes in 'joyful celebration', as _Public Opinion_ , the local newspaper, put it, of the removal of a tax on their bicycles. One cyclist carried a banner saying 'freedom ride', and the newspaper reporter, Jervis Anderson, took the word 'freedom' seriously:
Like the cyclist whose bicycle was appropriately bannered, they were on a real 'Freedom ride', for like many of our forefathers who were born in shackles, many hundreds of them for the first time in their lives were going to be allowed to ride throughout Jamaica without having to pay for it.
It seems likely that the term was around even earlier.
The aim of the US Freedom Riders in 1961 had been very specific: to challenge segregation on interstate buses and in interstate bus terminals. The original thirteen Freedom Riders, seven black and six white, had gone in two buses from Washington to New Orleans via Alabama, and more buses had travelled soon after from Birmingham to New Orleans via Jackson, Mississippi. When they encountered racist violence at Anniston and Montgomery, Alabama, and at Jackson, Mississippi, the Congress of Racial Equality (CORE) had organised buses of Freedom Riders from different parts of the country to converge on Jackson. More than 300 Freedom Riders had been arrested, and their cases were heard from August onwards. The Freedom Rides had provided dramatic headlines in several ways: the joint action of black and white students; the racist violence they encountered; and their success in achieving their immediate aims. After the Freedom Rides, the Interstate Commerce Commission issued a regulation prohibiting segregated bus facilities. The commitment to a Civil Rights Bill, though, would have to await the shocking events in Alabama two years later.
Australians knew of these Freedom Rides through the mass media— press, radio and television. The attacks in Anniston and Montgomery, Alabama and the violence and gaoling of Freedom Riders in Jackson were well covered. Newspaper reports emphasised the hostility of the whites, the _Sydney Morning Herald_ reporting on 26 May 1961: 'Highway patrolmen, troops in helicopters, National Guardsmen with fixed bayonets, and local police with savage dogs on leashes kept angry white crowds away from the "freedom riders" when they arrived from Alabama.' Although the coverage was overwhelmed by the much more extensive coverage at the same time of one of Australia's great murder mysteries—the Bogle– Chandler deaths on New Year's Eve in 1960, and the inquest through May 1961—Australians did know about the US Freedom Riders and the violence they had encountered. They related the term Freedom Ride less to the specific idea of desegregating transport facilities than to the more general notion of a racially mixed group of students travelling by bus, confronting and drawing attention to segregationist practices so publicly that these practices had to end.
The 20 July meeting attracted a dozen people, those present signing their names on a list. They were: Charles Perkins, Jim Spigelman, Brian Aarons, Colin Bradford, Robert Gallagher, John Powles, Beth Hansen, Eric Doldissen, Brian Jardine, Judith Mahony, John Russell and Bill Ford. The first seven of these later became Freedom Riders. We've already met Charles, Brian and John Powles. Jim Spigelman was an especially significant addition to the gradually forming group. The surviving written records reveal just how important his organising role was soon to become. He was a second-year student enrolled in Arts/Law, a member of the Labor Party and the university's ALP Club. Beth Hansen, an Arts student, was a member of the Humanist Society and came along with her boyfriend John Powles; she was to become very important to the new organisation. Colin Bradford and Bob Gallagher were both friends of Brian's in the Labour Club.
The meeting canvassed several options for action, but it was soon clear that a Freedom Ride on the American model was becoming the favoured plan. Bill Ford, a lecturer in the School of Economics at the University of New South Wales, spoke to the group about his experiences with Freedom Rides in the United States. He had won a Fulbright scholarship in the late 1950s and studied at the University of Illinois. Later, at the University of California in Los Angeles, where he worked as a research assistant at the Institute of Industrial Relations, he developed a close friendship with Bob Singleton, an African American who was a local leader of CORE and led the Freedom Ride from Los Angeles to Jackson, Mississippi in the summer of 1961. Bill remembers that 'when they went off in the summer of '61 and were gaoled, I flew to Jackson, to be with my friends at their arraignment. It was an incredible experience attending the mass meeting, the courtroom drama.'
Now he spoke to the meeting about the Freedom Rides in the United States, ideas of non-violent protest, and the possibility of doing something similar here. Ford had a history of interest in Aboriginal issues, having met Charles Duguid in Adelaide before he went to the United States. Beth Hansen says of this meeting: 'The start of it for me was Bill Ford, and some blonde woman that was with him . . . She and or him had been to the States and had some connection with the Freedom Ride there, and they came out and gave a talk at one of the lunchtime meetings. That is my memory of where the idea started.'
A committee was formed, consisting of Charles Perkins, Jim Spigelman, Beth Hansen and Eric Doldissen (who did not, in the end, go on the Freedom Ride). Attracted to the idea of a Freedom Ride, and hoping for a larger attendance, the group called another meeting in the MacCallum Room for Friday, 31 July. Clubs and societies were again urged to send representatives. The group produced a leaflet reporting on the idea of a Freedom Ride, and the importance of publicity about discrimination against Aborigines: 'While our initial impact on the country towns and aboriginal settlements is likely to be short lived and therefore possibly ineffective, it is hoped that student action of this kind will draw public attention to the problem.' Publicity was the main focus, and the leaflet also announced that 'Peter Westerway will be leaving the University soon to become Director of Public Affairs at ATN Channel 7. He would like to send a camera crew along with the bus to film a documentary for ATN.'
The meeting on 31 July was much larger. It seems to have been moved from the MacCallum Room to the much bigger Old Geology lecture theatre. Again Bill Ford spoke about the American Freedom Rides and the possibility of doing something similar in Australia. Warwick Richards, a politically interested student in the Students' Christian Movement, and later to become one of the Freedom Riders, remembers the meeting well. He was struck by the breadth of political views represented there:
There was an intention to form an organisation that would be broadly representative of the different religious, political and philosophical points of view at the university. So each of the religious groups was invited to participate, all the political factions, sects and parties and a number of them did. Obviously the right wasn't directly involved but the communists, the Labour Club, the various Trotskyite factions . . . there were a number of Jewish students who were involved, there were Christians . . . It was intended to unite students and essentially to combat racism and to right social wrongs.
Pat Healy remembers it too:
The things I remember were a large meeting in one of the large lecture theatres at Sydney U, that Bill Ford, who had been in the USA on— might have been a Fulbright scholarship or something like that—and he had been involved in the civil rights struggles. And he got very enthusiastic and very involved and he gave a talk about it. And I know that after that a lot of people were sort of saying: 'We should do something like that in Australia.'
Brian Aarons remembers that:
There was this very big meeting, it would have been probably 300, where a guy called Bill Ford who had recently come back from America . . . he spoke at this meeting and very sharply raised the question about—'Well, you're doing these things for the black movement in America, what about here?' . . . I think he'd been deliberately invited by the organisers of the meeting to talk about how the civil rights movement worked, and out of that came the idea for a Freedom Ride. Charlie Perkins used to say to me for years afterward that just after that meeting—I think it was the same afternoon, or it may have been a day or two later—he and I and a fellow called Barry Corr were talking about what had come up at the meeting and as I recall it Charlie said: 'Well, are we going to organise a Freedom Ride? ' and we all said: 'Well, yes we are, that's what we're going to do.'
The decision had been made. There would be a Freedom Ride.
_Ch_ _apter_
**_2_**
Getting ready
On the evening of Friday, 12 February 1965 a white touring bus stood at the front of the University of Sydney's historic main building. Begun in 1855 and completed in 1862, the large two-storey sandstone building had a good view over the city. Well-kept lawns swept down to busy Parramatta Road, the main artery to the suburbs of the west and beyond. Twenty-nine students waited with their bags and suitcases and rolled-up sleeping bags to get on board and start their journey. Second-year medical student Aidan Foy remembers that 'there was some sort of banner at the front or along the side', and photographs and film footage show a large banner inscribed 'Student Action for Aborigines' along the side of the bus. It did not say 'Freedom Ride', a term the students had come to see as somewhat patronising. They called it simply the 'SAFA bus tour'. Only one of the students—Charles Perkins— was Aboriginal; a second, Gary Williams, would join later. There was also on the bus another Aboriginal man, Gerald (or Gerry) Mason, a lay preacher and an older friend of Perkins's from Gerard government reserve in South Australia, one of the better-funded reserves in the country. Gerry was a gentle and rather conservative man who, it later emerged, had had no idea this bus tour had a political purpose. The composition of the group would change slightly as the tour went on, with five students joining later, one changing her status on the trip from 'student' to 'journalist', and three leaving before the end for a mixture of personal, work-related and political reasons. The students ranged in age from 18 to 29, with most about 19 years old. Of the 34, eleven—or about a third—were women, a gender ratio roughly reflecting that of the student population at the university as a whole at that time.
There was a short farewell ceremony. Beth Hansen remembers the 'send off, with Ted Noffs's blessings, from the university grounds, Noffs on the steps of the bus'. I remember this too. Darce Cassidy, on tour not only as a student but also as a reporter for ABC radio, recorded the farewell. From this point until the major conflict in Moree, he recorded everything indefatigably. A program he made from the tapes still survives, providing us now with a remarkable record of the voices, ideas and people associated with the Freedom Ride. We can still hear Reverend Ted Noffs' travellers' prayer:
Almighty God we thank thee that thou hast given us life and liberty in this great land Australia, and we ask now that thy blessing will rest upon these Australians as they journey out as they endeavour to bring reconciliation and healing among people who have been divided because of the colour of their skin . . . Give them travelling mercies and give them, we pray, that word that will be a word not only to the people of Australia, but perhaps a word to the people of the world of our concern and of our love for people no matter what the colour of their skin may be. So go with these young people we pray and bless them in all that they seek to do. And these things we ask in the name of Jesus Christ Our Lord. Amen.
In retrospect, Noffs's mention of 'reconciliation' and 'healing' is remarkable for prefiguring much subsequent politics on Aboriginal issues. Yet it is worth noting that, while the students appreciated this blessing and support, probably less than half were Christians; the rest were a mix of atheists, agnostics and Jews. As one of the atheists, I remember feeling distinctly uncomfortable. Aidan Foy, whose family was 'traditional Irish, Labour, Catholic', remembers that he'd 'never actually heard a Protestant praying in public before, I remember that'. Then, on a quite different note, a group of visiting Black American folk song and dance performers from the 'Go Tell it on the Mountain' stage company sang songs in farewell. They were by no means the first African Americans to support the Aboriginal cause. Forty years earlier, a group of visiting Black American seamen had attended the Australian Aborigines Protection Association conference in Sydney, and only four years before the Freedom Ride, in November 1960, Paul Robeson had visited Australia for an eight-week tour of Darwin, Brisbane, Melbourne, Adelaide, Perth and Sydney, as well as towns in New Zealand. His four concerts in the Sydney Town Hall, where he sang 'folk songs of many countries, Negro Spirituals, popular songs', had made a considerable impact, and he became— famously—the first performer at the half-built Sydney Opera House, singing to the building workers. He had supported the Aboriginal cause at a reception in his honour at Paddington Town Hall organised by the New South Wales Peace Committee and the Aboriginal-Australian Fellowship; it was attended by 1500 people, of whom about 30 were Aboriginal.
Listening to the recording today, it is hard not to be moved by these African American voices singing on a February summer evening in support of a Freedom Ride in Australia:
We shall overcome, we shall overcome
We shall overcome some day.
Oh deep in my heart, I do believe
That we shall overcome some day.
And with that, soon after midnight, the bus with its load of students drove off into the night.
It had been a hectic six months between the decision and the setting out. A new organisation had been formed, a constitution drawn up, publicity arranged, an itinerary worked out, and over 30 students attracted to and prepared for the trip. It was a remarkable feat for a group of people who were mostly still too young to vote. Yet they had a confidence distinctive to their generation—a sense of innovation and adventure. Only a few weeks before, the Rolling Stones had visited Sydney, and seven months earlier the Beatles had made their historic visit, rapturously received by youth all over the country. The music somehow expressed the mood of the age group and the time. This was a generation that produced a New Left beyond earlier Cold War certainties of either the self-congratulation of the 'free world' or the rigid authoritarianism of communism, interested in challenging consciousness as well as social structures and institutions, and as concerned with issues of 'race' (and within a few years 'gender') as those of class. In the process of forming itself, this generation both inherited many loyalties, political and religious, from their parents, yet in the end had a curious lack of respect for the authority or wisdom of their elders. They—we—were no longer to be dutiful sons and daughters.
The large meeting on 31 July which resulted in the decision to hold a Freedom Ride had occurred shortly before the end of second term, and there was a lull in SAFA activity during the four-week vacation. In that time, however, student action on Aboriginal issues was greatly enhanced when NUAUS held an Aboriginal Affairs conference on 17, 18 and 19 August, using the broader term 'Aboriginal Affairs' to denote a new extension of its interest beyond the traditional concern with providing scholarships. Three of the scholarship students—Charles, Margaret Valadian and Betty Anderson—attended, along with 21 other students. Papers were delivered by three people experienced in Aboriginal activism—Alan Duncan on education, Shirley Andrews on legislation and Barry Christophers (another communist activist in the Aboriginal movement) on wages and employment. Over 100 motions were passed, including a suggestion for a tutorial scheme for Aboriginal students (such schemes became widespread in the 1980s and 1990s), the holding of work camps to build facilities or provide services requested by Aboriginal people themselves (these work camps became popular during the mid-1960s and later), support for the FCAATSI Referendum campaign to remove discriminatory clauses from the Constitution, more local control in Aboriginal communities, making Aboriginal people 'aware of their rights as regards copyrighting of arts and artifacts, Aboriginal ritual and cultural activities in general', and many other issues. Student interest in Aboriginal issues was rapidly rising.
When third term started on 7 September, plans for a Freedom Ride went ahead. The name of the new organisation was settled—it would be Student Action for Aborigines (SAFA)—and a constitution was adopted at a meeting in the first week of the new term. The name was a clear derivation from the Student Action groups that had opposed the 'White Australia' policy a few years earlier. The objectives of Student Action for Aborigines, as stated in the constitution, were quite modest, and well within the equal rights perspective of the existing Aboriginal movement. They were:
1. to arouse public attention, especially within the University, to fundamental Aboriginal problems in health, education, housing, etc;
2. to break down social discrimination barriers to the extent possible by student action; and
3. to stimulate the interest of Aborigines in improving their situation within society.
Office bearers were elected. Some continued from the meeting at the end of second term: Charles Perkins as chair; Jim Spigelman and Beth Hansen as co-secretaries; and Eric Doldissen as treasurer. Jim rapidly became a key figure in the organisation. Born in Sosnowiec, Poland on New Year's Day in 1946, he had come to Australia with his family in 1949, and by this time his father owned a jewellery shop at Circular Quay. At Sydney Boys' High School he had been disturbed by the lack of support for the Asian Colombo Plan students in contrast to that for an American exchange student, and had complained to the headmaster ('that's because of my Jewish background more than anything else . . . I'm sure it came from my Jewish background that racism had a very high salience').
To these four main office bearers were now added John Powles as vice-president and Pat Healy as publicity officer. A committee of six was formed, with Colin Bradford, who had been at the initial meeting, one of its members. Colin had migrated from England with his parents—his father was a bricklayer and his mother a typist—when he was three years old, and he was now a second-year Science student, active in the Labour Club. Another member, Chris Page, would also go on the Freedom Ride. The son of a left-wing North Shore doctor, Chris was now a second-year medical student. Four members of the committee did not go on the Freedom Ride, including Margaret Hall and Anglican Society student David Sloper. One of the other committee members was David Ellyard, another Anglican and chair of the Students' Camp Association, sponsored by the New South Wales Christian Youth Council, which had just organised the second annual camp for Aboriginal and European high school students in Lane Cove, Sydney. He was an important figure in SAFA, though he did not join the Freedom Ride.
Now, with its name, constitution and structure in place, the new organisation went into full swing. SAFA's first task was to agree that the Freedom Ride would indeed be a bus trip to racially discriminatory towns. Warwick Richards remembers 'a number of meetings at the university that were planning it and there was a lot of discussion: "Should it be a bus or should we take cars?" and there were a number of people who had various views about how that ought to be done.' Its next task was to gather together enough students. Jim Spigelman wrote an article for _Honi_ _Soit_ on 24 September, describing the new organisation, its aims and its decision to conduct a 'Freedom Ride' in order to attract publicity, and asking any student sincerely interested in participating to give his or her name and address to SAFA.
Publicity became a major activity of the new group, partly because that was a main aim of SAFA and partly to raise enough funds to hire a bus. In a leaflet distributed to the media on 14 September, SAFA announced its aim of arousing public attention to Aboriginal disadvantage, and its chosen method of a bus tour around country towns in northern New South Wales during February. In addition, the leaflet announced, students would undertake a social survey to back their protest with statistical information on housing, wages and so forth. While it is not clear just when and how the idea of a survey arose, it is likely that Pam Beasley, an anthropologist who conducted a survey of Sydney Aboriginal people for the Foundation, may have had an influence. The survey was strongly supported by Ted Noffs and the Christian clubs on campus, who were concerned that there was insufficient knowledge of actual conditions in country towns; Noffs may also have been a little apprehensive that radical action might have negative effects on the Aboriginal people in the targeted towns. The survey, the leaflet announced, would cover housing, education, health, employment, social welfare and racial attitudes among both Aborigines and whites.
SAFA's media release was effective. Three days later, the Sydney _Sun_ carried a story, 'A Bus Ride to Freedom', which featured a photograph of Charles Perkins and reported that students 'will go in mixed parties to hotels, picture shows, milk bars and swimming pools which, they believe, discriminate against aborigines. The Freedom Riders will then buy tickets, call for drinks or order meals for the whole party, aborigines as well as whites. Their plan is strictly non-violent.' The Sydney _Daily Mirror_ , the _Australian_ and the _Sunday Telegraph_ all picked up the story, while Eric Baume interviewed Charles Perkins on radio. There was some mixed response in letters to these newspapers, with one letter to the _Sunday_ _Telegraph_ suggesting that 'Aboriginal people are quite happy with things as they are, the Freedom Ride would just stir up trouble'.
As a result of this media coverage, Charles Perkins received supportive letters and some donations from individuals, like Dorothy May, who said, 'I am with you all the way, though financially I cannot help much (encl. 10/-) I will help in any other way that I can . . . Here's luck to your campaign.' Mr T. Frawley congratulated SAFA for 'taking the initiative in this very just and much needed movement and to wish you every success in your aims'. One letter from Boronia, Victoria, offered best wishes: 'This action has long been needed to highlight the fact that we have racists in our country, who by intention or ignorance, are hampering the integration of Aborigines.' The story was picked up interstate—for example, in the _Hobart Mercury_ —leading Eleanor Brinton to write approvingly to Charles: 'It is quite time somebody did something about race relations in this country. We do not have the problem in Tasmania as the first white settlers apparently shot most of the original inhabitants or drove them into the cold part of the country where they could not survive.'
Some of those already involved in Aboriginal rights issues were a little concerned at the announcement of a Freedom Ride. Ian Spalding, editor of _On Aboriginal Affairs_ , sent a telegram to Jack Horner of the AAF on 18 September: 'Please consider prevailing upon Charles Perkins have Freedom Riders survey discrimination scene before seeking notoriety and alternative deterrent stop force entrench difficulties some localities. Ian.' He followed this with a letter on 30 September, saying that when he first heard of the move he was worried about it, since there was no way of knowing from the newspaper reports 'how well considered the whole project was'. He applauded student interest in social discrimination, but was concerned that 'the repercussions could be so great, damaging, and even ineffective unless made to fit the needs'. His own view was that discriminatory practices could be removed 'by quite short and rational negotiation which leaves no bad odour'.
Media stories of Aboriginal disadvantage and lack of basic civil and human rights continued to appear. The _Australian_ on 30 September carried a feature story by Jock Marshall headed 'Color Bar!' which emphasised Australian governments' poor record in Aboriginal affairs. A week later, the _Australian_ published a letter from Jim in response to this story, which told its readers about the Freedom Ride, the survey, the interest television stations had expressed in covering the trip, and the fact that SAFA had received several donations in response to the _Australian_ 's earlier article. The students were hoping, he said, for more donations towards the cost of chartering a bus. Jim's letter generated another group of letters and donations. Jean Culley, from Port Melbourne, wrote in support saying 'to my mind this is a tremendously important task you have all set yourselves, and from my rather limited experiences of racial intolerance will need a good deal of courage and level headedness', and enclosing a cheque for £5, a substantial sum. Marion Hellier wrote from Surfers' Paradise, saying: 'Such a "fresh" approach should do much towards awakening a lethargic public. The several worthwhile organizations who have been working to assist the Aborigines do not gain the all important publicity which this "freedom ride" should do. I wish your mission success and am enclosing a small donation.' Margaret Langford wrote from Belfield, in Sydney, enclosing a cheque and expressing her doubts about the assimilation policy:
I feel that the Aboriginals might be happier if they could evolve a way of life to suit themselves . . . I feel that they should be assisted to work out their own salvation independently of the white community. In the process, we might even learn to work out ours! I hope that your 'freedom Ride' will be successful: problems cannot be tackled until their precise nature and extent are revealed. Above all, I hope that the Aboriginals themselves will form an organisation to look after their own interests.
The ideas behind the Freedom Ride continued to develop as the months of preparation went by. The common political philosophy binding this diverse group of students together was the idea of nonviolent direct action, its inspiration in a very direct sense the US civil rights movement. The SAFA publicity leaflet had been quite explicit: 'Such student action has worked well in the USA, we have to make it work here.' In his article in _Honi Soit_ that same month, Jim Spigelman had said: 'We intend to adopt appropriate methods of passive resistance.' The notion of non-violent direct action, he explained, was modelled on the Student Non-Violent Co-ordinating Committee in the United States, which had 'achieved so much in the Negro struggle for civil rights'. Another leaflet printed just before the bus set off said: 'The team has been largely patterned on the concept of the Freedom Riders who were involved in programmes of integration in the United States.'
And indeed the tactic of non-violent action had good claims to effectiveness. Since the students' demonstration in May, Congress had passed the _Civil Rights Act_. It had not, however, ensured the right to vote, and in the months just passed—May to July—nearly one thousand volunteers had gone to Mississippi to participate in the 'Freedom Summer', designed to register blacks to vote and establish 'Freedom Schools' for black Americans.
It is little wonder, then, that the Australian students were impressed by the idea of non-violent direct action as a means of pursuing a campaign for racial equality. It seemed to be working. Of all the American civil rights literature, the most influential by far on the Australian students was that written by Martin Luther King. SAFA was especially interested in his letter from Birmingham City Jail, and reprinted a condensed version from an American journal, _The New Leader_ , which had published it in full on 24 June 1963. In the reprint, it became 'Our Struggle', and anyone going on the Freedom Ride was encouraged to read it. Aidan Foy remembers that 'we all had a pamphlet, in advance, of Martin Luther King's speech "Our Struggle"'. The organisers also encouraged the Freedom Riders to read the full text and 'a vivid description of the events surrounding it' in Martin Luther King's latest book, _Why We Can't Wait_ , available from the Pocket Bookshop in Sydney. It would make 'ideal light after-exam reading'.
'Our Struggle' makes fascinating reading today. Written on scraps of paper with a pen smuggled into King's cell in Birmingham City Jail in Alabama in 1963, it was an impassioned response to criticism from churchmen who accused him of creating tension between blacks and whites. In this letter, King argues against gradualism and for immediate, direct, non-violent action. The purpose of direct action, he writes, is 'to create a situation so crisis-packed that it will inevitably open the door to negotiation'. King goes on to say, in reply to clerical critics who said the time was not yet ripe for such radical action, that:
Freedom is never voluntarily given by the oppressor; it must be demanded by the oppressed. Frankly I have never yet engaged in a direct action movement that was 'well timed', according to the timetable of those who have not suffered unduly from the disease of segregation. For years now I have heard the word 'Wait'. It rings in the ear of every Negro with a piercing familiarity. This 'wait' has almost always meant 'never' . . . I have almost reached the regrettable conclusion that the Negroes' great stumbling block in the stride towards freedom is not (the White Citizens' 'Counciler' or) the Ku Klux Klanner, but the white moderate who is more devoted to 'order' than to justice; who prefers a negative peace which is the absence of tension to a positive peace which is the presence of justice; who constantly says 'I agree with you in the goal you seek, but I can't agree with your methods of direct action'; who paternalistically feels that he can set the timetable for another man's freedom.
Beth Hansen also remembered this pamphlet, and it made a lasting impression:
There was the quote about how what was worse than the Ku Klux Klan sort of people were the white middle class, the ones who set a timetable on other people's freedom. It's just a quote that's hung in there forever . . . the other Martin Luther King quote was 'creating a constructive crisis'.
King concluded his letter with these words:
We will reach the goal of freedom in Birmingham and all over the nation, because the goal of America is freedom. Abused and scorned though we may be, our destiny is tied up with the destiny of America. One day the south will know that when these disinherited children of God sat down at lunch counters they were in reality standing up for the best in the American dream and the most sacred values in our Judeo–Christian heritage, and thus carrying our whole nation back to great wells of democracy which were dug deep by the founding fathers in the formulation of the Constitution and the Declaration of Independence.
No black Australian—or indeed white Australian—had ever written quite like that, nor believed that the goal of Australia was freedom. Yet the sense of a contrast between conventional Australian notions of democracy, equality and fair play on the one hand and the continuing reality of racism on the other was sufficient for King's oratory and ideas to have resonance in a country very different from his own.
Jim Spigelman wanted to learn more about the US Freedom Rides of 1961—how they had been conducted, and what lessons the Australians might learn from them. In December he wrote to the US Consulate in Sydney seeking the addresses of several American civil rights organisations— the National Association for the Advancement of Colored People, the Congress of Racial Equality (CORE), the Southern Christian Leadership Conference (SCLC), and the Student Non-Violent Coordinating Committee (SNCC). The consulate wrote back several days later with the first three addresses, but was unable to trace the address of SNCC. Jim wrote to all three, and received a reply from Bobbie Knable, the community relations officer for CORE, who replied rather briefly:
The Freedom Rides in the southern part of the United States were made on public buses. The riders were _both_ Negro and white. Their purpose was to show, by example, to what extent violence and intimidation were used to enforce local segregation laws.
Somehow, Jim also found SNCC's address, and received a reply on 16 January 1965, which was not especially helpful: 'We do not have the specific kind of information available which you need.' The SNCC people, however, did suggest that Jim read Jim Peck's _Freedom Ride_ , an eyewitness account, and that he look at some of the American periodicals of the time; they also enclosed a copy of their publication _The Student Voice_. I don't know if Jim or the others did get hold of a copy of Peck's _Freedom Ride_ (it would not have been easy, as this was an American book and Australian book distribution was then closely tied to Britain), but if they had they would have read an exciting narrative of the quite dangerous 1961 Freedom Rides. Peck was one of the white Riders, who was subject to vicious attacks by white supremacists in Birmingham when a group of black and white students attempted to enter a whites-only waiting room at the bus station. A photo of his bandaged head appeared in newspapers and on television screens around the world, including in the Australian papers. His story was a warning, both that white desegregationists could be hated even more than their black counterparts, and that non-violence could be met with violence.
SAFA also had access to some more direct information about the US Freedom Rides and civil rights movement. At the end of the year, it again invited Bill Ford to address it, as well as Sondra Silverman, a radical American then studying at the Australian National University for a doctoral thesis on political movements, comparing the US civil rights movement, the British anti-nuclear movement and the Australian labour movement. The SAFA newsletter explained that 'they were involved in the "Freedom Rides" in the USA and we look forward to further cooperation with them'. Bill and Sondra told the students about non-violent protest techniques, and gave them some American publications. While there is no record of what Sondra said that day, the thesis on which she was working distinguishes between 'non-violent direct action' and 'passive resistance'. The former derived its ideas from Gandhi, and its essential element was its 'refusal to sanction cooperation with what is regarded as evil'. It was more than a political tactic; it was a way of life— the continual pursuit of truth by non-violent means, having permanent regard for both ends and means. 'Passive resistance', on the other hand, derived from the early twentieth century British suffragettes, _was_ purely a tactical weapon. In civil rights discourse, both in the United States and Australia, the terms were generally used interchangeably, and what was intended seems to have been something in between—that is, an ethically sustainable political tactic.
In 1998, Bill Ford remembered very clearly a meeting at the Foundation before the Freedom Riders left, when 'I was sharing my experiences with the group and _The Bulletin_ wrote it up as a major feature'. It did indeed. Sam Lipski's article 'The Freedom Riders' came out in _The Bulletin_ on 20 February, when the Freedom Ride was in progress, but he had been researching the article for some weeks before. Lipski recorded Bill Ford as saying:
Don't any of you go into this tour with preconceived ideas about what you're going to face. When the first Freedom Riders came down from California to the Deep South there were 3000 police and troops ready to greet them when the 13 of them got there. Now this isn't going to happen here. Passive resistance works in some kinds of situations, but it doesn't in others. Obviously it wouldn't have done the Jews very much good against the Nazis. But it did work with Gandhi in India and it is working with students and Negroes in the Deep South.
Bill Ford's advice was very precise, and very much within the philosophy of 'non-violent direct action' and 'passive resistance'. He told the SAFA group:
If you find a segregated swimming pool just go and stand out in front of it. Just stand there. Don't go climbing over fences or trying to force your way in. The real key to this whole thing is to get some visual image across, to make certain that when you do something the Press, radio and television know about it. But if you go into a segregated bar and someone pushes someone else aside and a brawl starts—well, you've lost everything. You've got to have discipline. Don't dissipate your energy demonstrating all over the place. Pick out one or two key centres and make sure you've got the camera on you. Remember a passive demonstration is the most effective. Any violence and you've defeated our own purpose.
One of those at this meeting was Alex Mills, soon to be one of the Freedom Riders. He remembers that 'that night there was a zing click click . . . I could see there was something valuable in this thing—the conditions for Aboriginal people were bad and this was an effective way of doing something about it.' Alex was rather different from most of the other students. For one thing, he was from a country town, whereas most of the others were Sydney born and bred. He had gone to Orange High School, his father a carpenter and his mother a domestic worker before her marriage. Later, he became the leader of the Presbyterian Fellowship in Orange, and was at university studying Theology in order to become a Presbyterian minister. For another, he was a member of the Country Party, which meant his politics were more conservative than those of most of the other Freedom Riders. He had, however, got to know some of the others— Charles and Warwick Richards—the previous year when they had shared the same Social Theory I class. These three had formed a critical minority in the class. As Warwick, who joined SAFA early on, remembers it:
I guess we were all there under the misapprehension from the student handbook that it had to do with, you know, political and social theories, but it was really social work for social workers . . . The main text was a dreadful book by Ben and Peters called _Social Theory of_ _the Democratic State_ , which was taught laboriously through most of the year, and this was an extremely conservative text with all the sort of welfarist implications. A small group of us including Charles and myself, we would sort of argue from one side of the room with the class and the lecturers about that.
Little preparation was done during October and November, the examination period, but once exams were over, planning became intense. A newsletter, _SAFA Talkabout_ , was devised to keep SAFA members informed and to call meetings. The first edition, in early December, reported that SAFA badges had been printed, called a committee meeting at Charles's home in Forest Lodge on 14 December, and contained a slip at the bottom that asked students to indicate whether they intended to go on the trip. A letter signed by Charles, John Powles, Gary Williams, Paul Cohen and Ken Buckley was sent with explanatory material to academic staff members in the faculties of Arts, Law and Economics. A meeting on 21 December at the Foundation, which had opened at its premises at 812 George Street near Central Railway just a few days before, heard the Aboriginal leader of the Aborigines Progressive Association, Bert Groves, speak on the Aboriginal view of the trip, though what he said is not recorded. John Butterworth, a second-year Science student who was to become one of the Freedom Riders, agreed (along with another student, Des Moore) to seek further information from the Teachers' Federation about education facilities in the towns to be visited. That very day, in fact, the federation had published its report on a survey it had conducted of Aboriginal pupils in New South Wales secondary schools, revealing serious educational disparity—not so much from differential education provision as from the deprived social and economic conditions in which pupils lived. The solutions were seen to be in Aboriginal employment, housing and special assistance. This report was widely disseminated and discussed, even reaching an international audience via the _New York Times_ , to the consternation of officials in the Department of External Affairs.
It was also agreed at this same SAFA meeting that the students needed to inform themselves as well as they could about conditions in rural New South Wales. Alan Duncan, Australia's first full-time tutor for adult Aboriginal people after many years as a teacher in country schools, a member of the Aboriginal-Australian Fellowship and also chairman of the Foundation's Education Committee, explained to the students about the location of Aborigines in settlements, reserves, towns and so on, while Pam Beasley spoke on the 'anthropological aspects'. Intending Freedom Riders were asked to look at two articles just published on 'assimilation versus integration' in the _Sydney Morning Herald_ on 14 and 16 December. Signed simply 'a Staff Correspondent', these articles noted the growing critique of assimilationist policies in many quarters. The second article said assimilation meant nothing less than 'the complete absorption of the aboriginal race by the white community', and went on: 'The aim, as it was in the ruthless days of exploitation, is that eventually the aborigines as a race will disappear.' In support of this critique, it quoted Alan Duncan: 'Aborigines are a proud people. They don't want to lose their identity, become just like us. We're kidding ourselves if we think we can change them, make them adopt our ways. For instance, aborigines have a very strong community feeling; they share everything . . . They don't accept the individualism of white people.' These articles prompted a correspondence to the _Herald_ , leading it to comment in an editorial on 26 December that 'there is a new and lively interest in New South Wales in aboriginal welfare. It seems to be a questing, deep-seated interest, concerned . . . with a systematic rethinking of policy.' The editorial suggested that present assimilation policy should be abandoned for one of integration, which would mean the survival of Aborigines as a 'separate and distinct segment of the Australian people'.
[From left to right: John Powles, Charles Perkins, Pat Healy and Jim Spigelman plan the Freedom Ride.
(Photo courtesy of Fairfax Photo Library)](chap7_9781741150575_epub_part7.html#d41151631)
Then there was the question of where to go. All indications were that the towns in the north of New South Wales had the most blatant discrimination, and SAFA had settled on this region as its focus back in September. The meeting of 21 December agreed on an itinerary: the bus would go, as Jim Spigelman wrote to Jack Horner of the Aboriginal-Australian Fellowship three days later, 'from here to Dubbo, then north to Walgett, Moree, etc. then touching the Queensland border on our way to the coast and through Lismore, Kempsie [ _sic_ ] etc'. Wellington, Gul-argambone, Boggabilla, Tabulam, Bowraville and Taree had yet to be included.
The students tried hard to learn as much as they could about conditions in the targeted towns. None of them, including Charles, had direct first-hand experience, for Charles was from central Australia and had now been living in cities for some years. He did, though, gain a good understanding of conditions generally from the Aboriginal people he met through his work at the Foundation for Aboriginal Affairs. Charles was exceptionally busy working at the Foundation during the summer vacation: Sam Lipski reported that, in his first eight weeks, 'Perkins has had nearly 1000 interviews with job-seekers, with evicted families, abandoned children, people seeking information about social services, about education and many who come because they have nothing else to do'. An excellent opportunity to research the situation further in at least some of the towns—Walgett, Moree and Kempsey—came when Charles was invited to join an 1800-mile (2900-kilometre) light-plane tour through New South Wales in early January in the company of Ted Noffs, the _Australian_ journalist Graham Williams and photographer Aubrey McCarthy. The group visited the southern town of Nowra, the western towns of Cowra and Wilcannia, the northwestern towns of Walgett, Moree and Armidale and the east coast town of Kempsey. The four newspaper stories by Williams were scathing in their condemnation of the racial inequality endemic in country towns. The first, on 4 January, focused on Aboriginal poverty in Wilcannia, and the second on racial discrimination in pools, hotels and cinemas in places like Moree, Walgett and Kempsey, concluding: 'Racial discrimination is the result of deep-rooted prejudice.' The third focused on schooling conditions in Cowra, and the final article in the series discussed the assimilation and advancement leagues in Armidale, Kempsey and Nowra.
Charles gave a talk about this trip to a general SAFA meeting on 13 January. This meeting also confirmed the timing of the Freedom Ride—the two weeks before Orientation Week, that is, the second half of February—and that the itinerary would be through the towns previously listed, adding Taree. There was a major discussion about whether the tour would focus only on the survey, or on demonstrations as well. The notice for the meeting had said: 'This general meeting is most critical and all members and others are requested to attend', and indeed it _was_ critical. The issue had become the nature of the tour itself. As Jim later wrote, the survey became for a while a 'bone of contention' between those who had come from the Christian societies—who favoured it—and those from the ALP Club—who accepted it 'somewhat begrudgingly'. Colin Bradford remembers that 'in the planning stages there was a real argument about whether we should be demonstrating at all, or whether we should be just getting factual information then coming back and doing something about it'. So great had this disagreement become that at one stage Jim wrote: 'It was suggested that no demonstration should occur during the vacation and that only a social survey should be carried out.' Colin remembered David Ellyard, in particular, 'arguing that we should just have a fact-finding mission and not be demonstrating as well'. Charles himself seems to have briefly favoured the survey over the demonstrations, announcing in _SAFA Talkabout_ (No. 3) in early January that at the General Meeting on 13 January he would 'explain reasons why emphasis is now on the Social Survey aspect more so than the integrating of cafés, pool, etc'. The motion to focus only on the survey and to abandon demonstrations was, however, 'overwhelmingly defeated' by the General Meeting, and a compromise was reached. The Freedom Ride would give equal emphasis to both. Indeed, this was the view of a number of students in any case—especially those in the Labour Club who, as we shall see, were active in preparing the survey. In the end, Ted Noffs agreed to organise and direct the survey, and to oversee the processing of the results.
The survey idea impressed the media. Sam Lipski, for example, noted that 'they are obviously on the tour with a different expectation than American students. They are not going so much to right a social injustice, the form of which is clear and known, as to find out what form the problem takes.' The _Australian_ carried a story on 20 January which emphasised the survey and the role of Ted Noffs. Yet by and large the students seem to have constructed the survey themselves. It eventually had six parts, with a one-page sheet of questions for each. They were: Aboriginal Attitudes; European Attitudes; Living Conditions; Health; Occupations and Incomes; and Schooling and Education. Bob Gallagher remembers that a lot of time was spent in the committee meetings on preparing the questionnaires. So too does Alan Outhred, who recalls that, on Colin's suggestion, he had 'participated in various working groups, for example, designing the surveys that we were going to do'. Alan, Bob and Colin were all friends. Bob was in the Labour Club; he was an Engineering student who had grown up in Ryde, his father an official in the Federated Engine Drivers' and Firemen's Association, and his mother a self-employed dressmaker and occasional factory worker. Alan was another doctor's son, his father at that time Chief Medical Officer for the Joint Coal Board with fairly radical political views. His mother was a strong supporter of Aboriginal rights and later a member of the Save Our Sons movement in opposition to Australia's involvement in the war in Vietnam.
The students sought assistance from academics in devising the questionnaires, with Jim Spigelman contacting several departments within the university. Tom Brennan, the head of the Social Work Department, gave a talk on doing a sociological survey, and how to interview people. Wendy remembers getting help in developing the questionnaire on 'European Attitudes':
I was involved in that, being a Psych student and being interested in that, and there was a book, _The Roots of Prejudice_ or something—from which I gained a lot about the dynamics behind prejudice and I remember going to—I think it was—the School of Clinical Psychology, there was somebody there who helped me put the questionnaire together . . . the questionnaires had to be written in a non-loaded fashion, so that we weren't actually leading people to give an answer in one direction or another.
Aidan Foy and John Powles devised the survey on Health, while Bob Gallagher rather ingeniously devised the one on Living Conditions which mainly focused on housing:
As I say, I was the engineer and so there were a number of these survey questionnaires assembled and I constructed the one on the housing conditions, the condition of the houses. I got the . . . standard council planning regulations about light and ventilation, water, sewerage, electricity and sort of constructed a questionnaire around that.
The survey not only received praise from the media, but it also assisted SAFA in its approach to the Aborigines Welfare Board for permission to enter the Aboriginal stations and reserves it controlled. The board by this time had been in existence for 25 years. It was the successor to the earlier Aborigines Protection Board, which had been established in 1883 when it became clear that the Aboriginal population would not disappear as had been generally thought during the 'frontier' period, and new policies of protection, surveillance and 'improvement' were put in place. The Protection Board had established a number of reserves throughout the colony specifically for Aboriginal use, and under the _Aborigines Protection Act 1909_ acquired much-increased powers over the Aboriginal peoples it controlled. For example, the board now had the power to break up those reserves where white farmers wanted the land, to concentrate large populations in others, and to move the people on and off reserves at will. It also intensified its program of removing Aboriginal children from their parents and placing them in institutions that trained them to become useful as labourers and domestic servants. After Aboriginal discontent rose to a peak in the late 1930s, and the system of surveillance and control seemed to be coming unstuck, the Aborigines Protection Board was abolished in 1939 and replaced by the Aborigines Welfare Board the following year.
The new board was charged with the task of implementing the policy of assimilation, which meant trying to persuade and educate Aborigines to take their place as individuals or small families in white society. Its entire assimilation project was in direct conflict with the wishes of the vast majority of white townsfolk, who wanted Aboriginal people kept out of town, and opposed Aboriginal access to schools, clubs, picture theatres and swimming pools. They were especially opposed to the central plank in board policy: the relocation of individual Aboriginal families to houses in town, and many town councils refused the board permission to acquire land for this purpose within town boundaries. The result was that in 1965 few Aboriginal people actually lived in houses in town, and some of those who did had ceased to identify as Aboriginal. With a fast-growing Aboriginal population, the closure of some reserves and the inability to rent houses in town, an increasing number of Aboriginal people lived in unofficial shanty towns on unauthorised land, often now-disused common land on the edge of town, or along riverbanks. These shanty towns were usually without a clean water supply, proper sanitation, any form of electricity, proper roads, rubbish collection or other town services. On the other hand, the people there were more or less beyond board control, and often regarded themselves as having more autonomy and independence than those on the stations and reserves.
Almost 7000 people did live on the stations and reserves run by the board. In these years, Aboriginal people often had to make a direct tradeoff between reasonable living conditions and freedom from surveillance and petty interference. Housing over 2600 people between them, the sixteen stations run by the board in 1964 usually had basic weatherboard houses, and facilities like a school, a recreation hall or a rudimentary medical centre. Each station had full-time white resident supervision, usually with a married couple in charge as manager and matron. The residents were employed in outside occupations, yet direct supervision of the people remained extensive. These sixteen stations were often referred to somewhat confusingly as 'missions', which they were not; they were government run and managed enclosed communities. Between the stations and the shanty towns, along the scale of Aboriginal options, lay the reserves, 42 of them, housing over 4000 people. These were also under board control, but were distinguished from the stations in not having a resident white manager. Their inhabitants were, however, supervised to some degree by a range of people—perhaps the teacher at the reserve school where there was one, or the local off-site board welfare officer, or—most frequently—the local police. The reserves also had a much lower level of housing and facilities than the stations. While they had some homes built by the board, they consisted mainly of makeshift homes built by the Aboriginal residents themselves from discarded materials.
The Freedom Riders could visit the shanty towns and the town-dwellers relatively easily, but they needed board permission to visit those who lived on stations and reserves. Requests for permission had to go to full meetings of the board, held once a month. In mid-January, Charles and Jim went to see the chair of the board, Mr A.G. Kingsmill, and soon afterwards, on 18 January, Charles wrote him a formal letter seeking permission to enter 'all reserves, plus missions, and town homes of Aboriginal people' on the planned route through Wellington, Dubbo, Walgett, Moree, the Queensland border, Lismore, and back to Sydney. The main object of the tour, he wrote, was the 'comprehensive survey of Aboriginal life in the main towns visited', under the direction of 'the Rev. T.D. Noffs who did a similar survey in America'. He also mentioned the more political purpose of the tour: 'SAFA proposes also to integrate certain theatres, swimming pools, etc. which discriminate against Aboriginal people', and pointed out that the 'tactics will follow the pattern set by the Rev. Martin Luther King. It is passive non-violent action.' He enclosed a copy of 'Our Struggle'. Charles went on to reassure Kingsmill that the students 'do not intend to create confusion or disturbances that will lead to violent action'. The board replied that it would consider his application at its next meeting on 16 February, three days after the tour had begun, and instructed its managers not to grant permission to the students to enter the stations and reserves until then. It also promised that as soon as the decision was made, telegrams would be sent to all the board's officers en route. This meant the students would have to leave Sydney without the all-important permission, something which must have caused some concern to Charles, Jim and the others. However, they decided to go right ahead and hope for the best.
The background research went on. Jim received a valuable letter from Jack Horner, the non-Aboriginal secretary of the Aboriginal-Australian Fellowship for eight years from 1958. Horner had written to SAFA in September when the original Freedom Ride publicity went out, offering to supply information and contacts if the students wanted it. Now, on 24 December, Jim took up the offer. After reading the fellowship's _Monthly_ _Bulletin_ , he wrote to Horner 'that you could be of great importance to our tour'. He outlined the itinerary and requested information on 'instances of discrimination in this approximate area', as well as names and addresses of people to contact in the towns. Horner's reply on 19 January was long and informative. 'I think,' he wrote, 'you will find that discrimination and prejudice are greatest where there are large concentrations of Aborigines, e.g. Kempsey district, Walgett, Woodenbong, and least where there are only small groups, e.g. Yamba, MacLean, Casino.' He outlined some specific instances, as follows:
_Kempsey_ —Baths and Public halls. Kinchella Boys' Home, from which many boys have absconded lately. We understand there is no longer an 'Aboriginal ward' at the hospital—but are Aborigines treated in exactly the same way as Europeans, or put on verandahs, etc.? Is Green Hills School (nominally a Public School) still used solely by aborigines, other parents preferring to pay bus fares to send their children into town?
_Moree_ —We have heard that the school bus picks up Aboriginal children from the Station after it has delivered other children to school, and takes them home before school finishes, so that they lose up to an hour a day. Moree has a very bad name for discrimination generally— a sort of hard-core attitude, which should yield you a lot of material.
_Walgett_ —no doubt you have all the material on this town. We had correspondence with the manager (Mr White) of the Oasis Hotel-Motel, in which he admitted putting up a notice 'Aborigines by invitation only' . . . There are many issues worth taking up in places like Walgett, but it is essential to pick the unassailable ones, and to check carefully the facts given.
Horner also enclosed a list of stations and reserves, with numbers of people living on each one, and people to contact in each town—school teachers, ministers of religion, Aboriginal leaders like Pearl Gibbs in Dubbo and Frank Roberts in Lismore, and other interested individuals. Horner's letter went on to outline the AAF approach. It sought, he said, 'to give Aborigines some say in their own affairs'. The Welfare Board, he wrote:
gives no opportunity to assume responsibility, with stations under the control of a manager, who has wide powers, and the need to get his permission even to visit their families. There is no provision for a committee of residents to make their own decisions. There is little education, and most adult Aborigines are barely literate. The Board is so unpopular with Aborigines that they decline to get involved in its policies. Although Aborigines in NSW are eligible to vote in state and Federal elections, only a minority do so.
His letter concluded with warm wishes: 'We are convinced that this will be very valuable, and we wish you very well indeed.' Jim replied gratefully five days later, seeking further information, which Horner helpfully supplied.
Despite all their preparations, the students had in fact relatively little direct contact with Aboriginal people living in the towns to be visited. Charles was still seen by the Aboriginal people there as an outsider. Alan Duncan, who had very extensive contacts with people in these towns, recalled in 1994:
There was a little bit of a negative attitude, I suppose more apprehension than anything else, because [through] my work with Aboriginal communities, they as far as I'm aware, were not consulted very much at all. Now that's not a criticism, it's just a fact. And some of the older people there, Ella Simons for example at Taree, who was a matriarch there; I'm trying to remember Mary Dureaux at Kempsey, her attitude, I think it wasn't quite as negative in a way as say Ella— but a lot of the older people on the Aboriginal stations were very apprehensive about what would happen (a) when the students arrived and (b) after they'd gone. This was really what the worry was, what was going to be the effect on the local community about people busting in, you know, stirring up a hornet's nest and shooting off again, so that was the worry.
At the same time as the students were researching the trip, they were also working hard to raise enough money to hire a bus. Beth Hansen organised the tenders, choosing Saint's Bus Company (which still exists), which charged £460 after a £77 concession. The earlier publicity had attracted some donations, but they were nowhere near this amount. There were other ways of raising money, like the sale of Christmas cards with an Aboriginal motif, organised by Chris Page, which brought in £30. Several lunchtime folk concerts were held at the university during term time, raising £62, and a public folk concert, organised almost single-handedly by Pat Healy, netted £72. This concert was held in Paddington Town Hall on Thursday, 21 January, with non-Aboriginal folk singers Gary Shearston, Jeannie Lewis and Declan Affley and others, and Aboriginal singers Jenny Bush and Alan Moarywaalla. A good deal of the money for the bus tour in the end came from the students themselves. Student members of SAFA paid 2 shillings membership, and those going on the Freedom Ride had each to pay £10 to contribute to the cost of the bus and food. In the end, the £460 needed for the bus came from the funds raised by all these means, and additional SAFA subscriptions levied after the bus returned.
Publicity notice for folk concert to raise money for the Freedom Ride.
The main approach, though, was to keep costs down. SAFA looked for free accommodation in church halls and country showgrounds. Warwick Richards remembers that, because Charles had contacts with the Methodist church through Ted Noffs, he hoped that the Methodists 'would provide a sort of a network of support'; this, he says, 'was a bit controversial obviously'. Alex Mills remembers that he wanted the Presbyterians to be involved. When people at one SAFA meeting asked 'How are we going to do the washing?' and 'How are we going to eat on this trip around?', he thought:
Well, why not do things like contacting a few of the Presbyterian churches around and ask some people to cook a bit of food for us, get a few things organised like that. That just sort of seemed a fairly reasonable thing to do, and I guess I was a few years older than a few other people who hadn't had those experiences. So I somehow seemed to get involved in it as the quarter master or words to that effect . . . I know I ended up having a bit of an office—a phone and an office there in the Foundation for Aboriginal Affairs for the last few weeks doing something about organising.
Pat Healy and Beth Hansen actually bought the food, though. Pat remembers going to 'one of the big bulk food stores down in the Dixon St, Haymarket area'.
In addition to Alex's efforts with the Presbyterians, Jim Spigelman wrote many letters to churches, councils and agricultural societies. Show-grounds were offered at Lismore and Kempsey, and a National Fitness Hut in Warwick. Church halls were made available in many towns, and some of the letters of permission survive. In two of the most important towns, Walgett and Moree, church halls were made available for free. Reverend P.J. Dowe, the vicar at St Peter's Church of England in Walgett, who will reappear in our story, wrote saying the students could stay in the hall on 14 and 15 February. Ted Ryan, of the Methodist parsonage in Moree, also wrote, saying 'the Church hall would be available for your group as a dormitory'. He mentioned also that: 'I wrote to Charles Perkins and volunteered to help in any way I could if he would let me know exactly what the team intends to do here and how I might assist. I have not received any information. Be assured of our cooperation.'
Jim also wrote to a number of unions seeking support and information. Though generally pro-Aboriginal at this time, especially after the ACTU policy of 1963, the unions contacted were not as enthusiastic as SAFA might have wished, largely because they seem to have feared that SAFA's militant tactics might disturb their own longer-term strategies in support of Aboriginal demands. The Teachers' Federation is an interesting example. It was to be expected that the federation would be helpful and supportive, given its strong commitment to the cause of Aboriginal education. Gloria Phelan, its research officer, replied to Jim's letter offering her personal support and referring his request to the federation executive. However, when the letter finally came on 28 October from I.G. Lancaster, the general secretary, it was not the support SAFA expected:
While the Federation agrees with the need to publicise cases of discrimination, it suggests that this type of action is premature at this moment, and may have an undesirable aftermath as far as the Aboriginal people themselves are concerned. You will appreciate, therefore, that the Federation cannot accede to your request at this juncture.
The Australian Workers' Union, New South Wales branch, wrote a fairly formal letter, advising Jim that 'there are no legal discriminations concerning the employment of Aborigines in the State of NSW, all awards and acts of parliament give them equal rights', and seeking information on any breaches of the law.
Jim also wrote to the Liquor and Allied Trades Union, seeking support for SAFA's plan to desegregate clubs and hotels. Aboriginal people had been barred by law for a century from drinking or buying alcohol (unless they had an exemption certificate); this did not actually prevent drinking, but it did make it more clandestine and expensive, and served to exclude Aboriginal people from public bars, clubs and other forms of sociality. After a campaign led by the Aboriginal-Australian Fellowship, the relevant section of the _Aborigines Protection Act_ had been repealed in March 1963. There was now no legal basis for any refusal to serve liquor to Aborigines on the grounds of their race, though there was also no legislation as yet making it _illegal_ to discriminate on the basis of race. Some publicans still refused to serve Aboriginal customers at all, or served them only in designated parts of their hotel. One challenge to this practice occurred with demonstrations in January 1964 of six Aboriginal people, along with representatives of the Aboriginal-Australian Fellowship, the New South Wales Council for Civil Liberties, a _Mirror_ journalist, two Members of Parliament and Channel 7 at the Clifton Hotel in Redfern, fast becoming an area in which many Aboriginal people lived. The hotel had finally agreed to serve Aboriginal people on the same basis as others. Yet some city and many country hotels continued to segregate their customers. The union replied to Jim on 9 February rather cautiously: 'We are prepared . . . to examine the merits of any particular instance and take any action deemed to be appropriate.'
Still searching for more information, Jim Spigelman also wrote in late January to church bodies which had had significant contact with Aboriginal people in the towns. Noel Flint, the pastor at the Church of Christ, Gilgandra, wrote suggesting the students visit the schools and dwellings in Gilgandra. He already knew something of the students' plans, having met two of the students, one of them Chris Page, on a preliminary tour a week or two earlier. While little record of this trip remains, we do know that they visited Gilgandra, that their tour cost £13, and that they arrived back in Sydney only a few days before the bus left. The Reverend Flint now told Jim that 'there is not much discrimination' in Gilgandra, though 'the Western Stores and Nelson's timber yard require a guarantor before allowing credit'. He added the information that in nearby Gulargambone 'they may go to the counter and be served but cannot sit at the table in the restaurant and there is a separate section in the theatre'. Gulargam-bone was added to the itinerary very late, and this letter may well have been the catalyst.
At the end of January, the fourth edition of _SAFA Talkabout_ informed everyone that an itinerary had been fixed and called a General Meeting for 4 February. This was the deadline for those intending to go to pay their £4 deposit. An itinerary was printed, showing that the bus would visit and survey ten towns—Wellington, Gulargambone, Walgett, Moree, Boggabilla, Tabulam, Lismore, Bowraville, Kempsey and Taree—with some other towns on the way as stopovers. The trip would cover a total distance of 1390 miles (over 2300 kilometres).
Finally, everything had been done. On Friday, 12 February, the bus, the 29 students, some parents and well-wishers gathered at the university. I returned from my family home in Newcastle and joined the group of students waiting to leave. It was after midnight when we finally all boarded the bus and waved goodbye. Aidan Foy remembers us 'all driving off in the dark'. As the white bus slowly went down the hill and then out along Parramatta Road through Sydney's western suburbs and along the Great Western Highway to the towns of the west and north, our thoughts began to turn to the unknown and possibly dangerous situation we were about to enter. Each of us had our own thoughts on the opportunities, pleasures, dangers and perils that might lie ahead. The American Freedom Rides had been attended by violence. Could anything similar occur in country Australia? Despite all the preparation, few of us had any real idea of what lay ahead.
_Ch_ _apter_
_3_
On the way to Walgett
While the students are chatting and gradually falling asleep on the bus in the early hours of the morning, let's pause and learn more about those we've already met, and meet the rest. What did they have in common, and how did they differ? What were their family and class backgrounds, their political and religious beliefs, and their fields of study?
For most of the journey, Charles Perkins was the only Aboriginal student. Gary Williams, though involved in SAFA, felt wary of going to places outside his own country. He joined the tour when it reached Bowraville. This nearly all-white composition marked the Australian Freedom Ride off from the American Rides that had inspired it. As Sam Lipski noted, on the American Freedom Rides, 'the dynamism for the freedom riders was supplied largely by Negro university students themselves'. There are some other interesting features of the group. About two-thirds were from one faculty, the Faculty of Arts, and the rest were divided between Science (six undergraduates and one graduate), Medicine (four undergraduates) and Engineering (one). All but six were entering just their second or third year of university study. All but one—John Gowdie, whom we'll meet shortly—were from the University of Sydney. There had been some talk in the preparation phase of students joining from universities in Tasmania, Victoria, Queensland and South Australia, but this idea seems to have faded.
The class backgrounds of the students were extremely diverse. They ranged from wealthy (Darce Cassidy) to solidly middle class (most of the others) to working class (Colin, Bob, Brian and Pat). Most were from Sydney, but several had grown up in country towns, including Alex in Orange, John Powles in Deniliquin and John Butterworth partly in Moree, while I had grown up in Broken Hill and Newcastle.
Just over one-third of the students were from the organised Left. The largest group came from the Labour Club, some of whose members were in the Communist Party, or its youth organisation, the Eureka Youth League (EYL). Brian, Pat, Colin, Bob and Alan, who had been involved in the planning and preparation, were all in the Labour Club. Three more joined at this point. One was Norm Mackay, a second-year Science student along with Brian, Colin and Alan, and a close friend of Brian's. His parents were both teachers and Communist Party members living near the Aarons family in Fairfield in the western suburbs of Sydney. Another was Louise Higham, a good friend of mine. Her father, like Alan's and Chris Page's, was a left-wing doctor and her mother a nurse and receptionist for the home-based practice. Both parents were Labor voters and atheists, with wide cultural interests. She was just about to enter her second year of Medicine, which she abandoned later and transferred to Arts. She was a member of the Folk Music Club, where she 'received the powerful "Jim Crow must go" message of many of the songs in the concerts at the Wallace theatre'.
I was the last in this group. I was about to enter the third year of an Arts degree, specialising in Modern History. My father was an academic scientist, a senior lecturer in Chemistry at the University of Newcastle, while my mother had just gone to the same university as a mature-age student to do an Arts degree, and was to become a psychologist on graduation. Both were committed communists, but it was my mother who introduced me to Aboriginal politics. She was involved not only through the Union of Australian Women, which strongly supported Aboriginal rights, but also in 1961 established, along with several others, the Newcastle Trades Hall Aboriginal Advancement Committee. This committee campaigned in support of a rent strike by the people at Purfleet mission station near Taree, a protest against the appalling state of housing and an incipient demand for land rights. As a result of my mother's activism, Aboriginal people from Purfleet came to our home in Newcastle from time to time, and I gained in my teenage years some idea of Aboriginal conditions and political activism.
Shortly before the Freedom Ride started, I had written an article, 'The Fight for Aboriginal Rights', for _Left Forum_ , the extremely transient journal of the Labour Club. It indicates the strong influence of the Communist Party's position on Aboriginal issues on my own thinking, namely the need for equality, and the importance of black and white people organising together for Aboriginal rights. It also reads now like the work of a History student. It began:
Ever since the first European settlement of Australia in 1788 the Australian white population has degraded the Aboriginal population, originally by methods of shooting, poisoning, starvation, brutal seizure of land and destruction of the aboriginal social organisation, and later by the more 'progressive' policy of 'Protection'.
It went on to discuss the destruction of the population, and the limitations on Aboriginal people's basic freedoms: 'Innumerable instances of social discrimination exist all over Australia, whether in a place of leisure such as a hotel bar or a swimming pool, a place of work, or a place of social welfare such as a hospital or school.' This history of destruction and discrimination existed, I argued, because the Aboriginal population 'by its very existence constituted a threat to the European acquisition of the land'. In addition, 'the new Australian settler, like his counterparts in Africa, Asia and America, used aborigines as a source of cheap labour'. I concluded with a call for racial equality and an end to legal and economic discrimination: 'This can only be done through the development of a strong integration movement consisting of aboriginal and white Australians, which must aim firstly to secure those formal rights which are still not held by aborigines, and secondly to attack and destroy the discrimination and hostile racial attitudes now existing.'
With a quarter of the students connected to the Labour Club, the Eureka Youth League or the Communist Party, it is understandable that Charles and Jim were both concerned about the fact and the appearance of too many communists on the trip. _The Bulletin_ had reported on the impending Freedom Ride several weeks earlier, offering cautious support but also warning of the dangers of communist influence. Whatever the number of communist students actually on the trip, there was always the danger that the Freedom Ride could be written off as a communist plot, given the general tendency to associate any radical cause with communist influence and the strong actual association of communists with Aboriginal organisations at the time. As Sam Lipski accurately put it: 'The Communist Party's interest in Aborigines dates back to the party's inception, and has changed as the international Communist line has changed. But at no time in its history has CPA interest in and work amongst Aborigines been more active than it is today.' To counter charges of communist influence, Charles and Jim announced publicly that they would not allow a communist 'stacking' of the tour, and that they had discouraged members of the Eureka Youth League from enrolling. Whether the latter was literally true or not (and there is no evidence that it was), this announcement did effectively remove the question of communist influence from most coverage of the tour. In all its publicity, SAFA played down the fact that up to a quarter of the students were indeed associated either with the CPA, the EYL or the Labour Club. The students concerned also kept their political allegiances muted, for that was the approach of the time. The question was to reappear, though, as we shall see.
There was a group of three students from the ALP Club, to become four when Hall Greenland joined the bus in Walgett. There would have been five, had not Jim Spigelman at the end of 1964 led a breakaway group which soon became the more centrist Fabian Society. The four had been involved in either the May 1964 demonstration for US civil rights, or the July rally and demonstration in Hyde Park, or in SAFA itself. Aidan Foy had been deeply involved in the organising phase, and now joined the Freedom Ride. He had arrived in Australia with his mother as an assisted immigrant from northern England in May 1962 ('Australia being as far as my mother could possibly get from my father at the time'). His mother eventually became a schoolteacher 'so that she could get a job to keep us because my father didn't'. In his Labor-voting family, 'people who voted for any other party were nearly as bad as Protestants but not quite as bad'. Aidan remembers that initially some of the students in the ALP Club had described SAFA as 'a middle-class guilt, condescending organisation, we thought there were more important things at that stage. And then the bus tour idea started and suddenly everybody wanted to be part of it.' At this point, Darce Cassidy, Paddy Dawson and Hall Greenland decided to come. Three of the four—Hall, Aidan and Darce—leant towards the Trotskyists in their political position, while Paddy, the son of a noteworthy academic at the university, Madge Dawson, was probably more anarchist and libertarian in his politics than the rest of the group. Darce Cassidy's position was a little unusual. As a full-time ABC employee and part-time student, he needed to get time off to join the Freedom Ride:
I heard about the Freedom Ride on the grapevine, and asked the ABC for permission to cover it. Initially they said no. I had not been there long enough to have any annual leave, but had accrued three days off in lieu of overtime. Finally they agreed to let me have two days on duty, and three days' leave. Together with the two weekends, this would give me nine days . . . My role became a bit ambiguous. I was still a student at Sydney University, and a financial member of SAFA. I was also an ABC journalist.
The remaining students were from a wide variety of backgrounds, and had quite different reasons for joining in. Two, John Powles and Beth Hansen, came from the Humanist Society. Warwick Richards was in the Students' Christian Movement. 'I was the first member of the family to have gone to university. My parents left school at the age of 15 in both cases. My father was a bank officer and my mother was basically a house person who had various part-time jobs but never had a career of any sort.' Sue Johnston, a History Honours student as I was, came from the very middle-class suburb of Beecroft, and was to become an important figure in SAFA during and after the tour. Her father was a solicitor with the NSW State Railways, dealing with workers' compensation. Sue had become interested in Aboriginal issues through hearing Paul Robeson sing in Sydney four years earlier and through her university study of race relations in American history.
Jim Spigelman was not the only student on the tour born overseas. Machteld Hali was born in Holland and grew up in Indonesia, before arriving in Australia to attend university. Wendy Golding was a second-year Arts student whose Jewish parents had left Vienna after Hitler annexed Austria, going first to New Zealand and then in 1952 to Australia, with 5-year-old New Zealand-born Wendy. They came, she recalled, from a 'very middle-class cosmopolitan rather sophisticated background', and were 'very small "l" liberal in their thinking'. She said later that 'because I was very aware of the persecution of the Jews I guess I was very aware of injustice to any peoples anywhere on the basis of creed, colour, race, religion—whatever it may be. So that's probably what gave me a sensitivity to the Aboriginal issue.' Two months after the Freedom Ride, she wrote in _The Bridge_ , a Jewish magazine, that she had for a long time 'shuddered at stories of Hitler's regime and shaken my head about the American Negro situation'. The Freedom Ride offered her 'the opportunity to put my fine words into action'. Judith Rich, who knew Charles from their Anthropology class, had a similar background to Wendy's, though she was born in Australia. Her Jewish parents had also left Vienna in 1938 or 1939, and fled as refugees to Australia, where they met and married. She, too, had grown up with an interest in questions of race and racism.
Some of the students, such as Alex Mills, came from politically conservative backgrounds. Robyn Iredale joined up because she was about to do an Honours thesis in Geography on rural–urban migration of Aborigines and her lecturer, Diana Howlett, had recommended she join the bus: 'I was a bit apprehensive because I didn't know any of the people.' Robyn was from a large, conservative, religious family in West Ryde, her father an accountant at the Water Board for 43 years, her mother the organist at the Methodist church. She was, she says, 'basically brought up anti-Aborigine, anti-anybody who was different, and we were even brought up anti-Catholic, because that's what Methodists were like . . . I went off to university and that changed me.' Another, Derek Molloy, was an Arts student studying Anthropology who had been invited along by his friend, Alex Mills, just four days before the tour. From an Anglican background, his father was a lawyer who had earlier been involved in the Australian administration of Papua New Guinea, and his mother a nurse. He thought the Freedom Ride was to be a survey only, and was taken aback to find it also involved demonstrations against racial discrimination.
There are nine students still to introduce. Four of them (John Gowdie, Hall Greenland, Barry Corr and David Pepper) joined later; we will meet them as they join the bus. Five of them, two women and three men, I have not been able to trace for this book. The women were Sue Reeves, a third-year Arts student involved in Abschol; and Helen Gray, a second-year Arts student. The men were John Butterworth, a third-year Science student; Ray Leppik, a graduate Science student; and Rick Collins, a third-year Arts student.
The bus travelled through Sydney's western suburbs, past Penrith and on to the Great Western Highway as it left the coastal plain and wound up through the Great Dividing Range. After passing through the cool mountain towns of Katoomba and Mt Victoria, the student bus travelled down the slopes to Lithgow and Bathurst, and then on to the Mitchell Highway to the inland town of Orange. A distance of 170 miles, or 280 kilometres, the trip probably took around five hours.
The bus arrived at its first stop, Orange, before dawn on Saturday, 13 February. 'I seem to remember we arrived at Orange in darkness,' says Bob Gallagher. We went at 8.00 a.m. to the Presbyterian Church of St John's, a very fine old church with a church hall next door, for breakfast. Pat Healy recalls: 'Alex had arranged for us all to have breakfast in this large hall. That's about all I remember. Staggering off the bus to have this wonderful breakfast that was all organised by these country ladies.' Alex provides some more detail:
I'd organised some people in the Presbyterian Church of St John's there that I'd grown up in to get breakfast for the students, and organised for the Mayor of the town, who happened to be the president of the Labor Party, and the Deputy Mayor to come along and meet up with me. . . We probably had the [local] TV [station] along. I can't remember, but anyway we got a little bit of hype there. And then I went off to see my cousin and came back late, held the bus up from making a start, so they went crook on me in Orange, which was right—they're all rearing to go and here's Millsie off visiting his cousin.
At around 9.30 a.m. the bus left Orange, and went on to Wellington, arriving two hours later. Wellington, a pretty town at the junction of the Bell and Macquarie Rivers, had an interesting history. The Aboriginal people in the region were Wiradjuri, one of the most populous Aboriginal groups in New South Wales, who had first encountered Europeans in 1817. Europeans established sheep and cattle farming soon after, with the usual devastating effects on traditional sources of food supply. A prison farm was set up in 1823; when the soldiers and convicts left in 1830, the military buildings were given to the Church Missionary Society. With government funds, a mission was established under the leadership of the Reverend William Watson. The mission emphasised the education and segregation of children away from their parents, and agriculture as the basis of civilisation. Aboriginal people were employed on the mission as shepherds, threshers, gardeners, ploughmen and draymen, and some had built and settled into huts. The whole enterprise, wrote social scientist Charles Rowley in _The Destruction of Aboriginal Society_ , resembled a workhouse rather than a place of conversion to Christianity. The missionaries' efforts were undermined by the contradictions their society presented to the people: 'The gospel of love was being preached while white men were flogging each other and shooting black men.' After the closure of the mission in 1843, the Aboriginal people in the Wellington region worked for pastoralists and other employers, and camped on the properties or on the edge of town. Gradually, they came more directly under the purview of the colonial and then state governments of New South Wales.
By 1965, Wellington had both a board-managed station known as the Nanima reserve with its own school just out of town, and an Aboriginal shanty town on Crown land near the river. We could not visit the former, as the board had not yet met to consider our application to enter, and had in the interim instructed the manager to keep us out. When we arrived, the police warned us not to go there. Warwick Richards remembers the 'circling policemen, who were sort of walking suspiciously around the bus'.
Of necessity, therefore, our focus had to be the shanty town and the town itself, though there was no sign of Aboriginal families in town. We split up into a number of smaller groups, and I was in one of the groups that went to the shanty town. The idea was that we would conduct our survey, investigate claims of racial discrimination and, if we found any, make some kind of demonstration against them. We had little idea of what to expect. There were few if any contacts between the local Aboriginal community and us students, including Charles. As Rick Collins later remarked: 'No one who was brought up in the city could've known what was going on out there, and we were just a bunch of green kids.' In that situation, the survey could serve to emphasise, as Brian put it, that 'we weren't white students breezing in and kicking up a fuss about Aboriginal rights, we were going to try and talk to Aboriginal people and get their own version of their actual conditions'. Some of the students, however, were not very interested in the survey and thought we should focus on non-violent protests. Darce remembers:
I think there had been a good deal of debate on the bus, and before, about what we should be doing. Some were pushing the survey, saying that the important thing was gathering the facts. Others were saying that in a broad sense we knew the facts from investigations already carried out. We had a fair knowledge of what the world was like; our task was now to change it through some kind of confrontation. At Wellington, it seemed to me, the survey faction still held the upper hand.
Only a few months earlier, Charles Rowley had investigated the situation in Wellington, along with many other towns, as part of his research into the status of Aboriginal people across Australia for the Social Science Research Council. The results of his research were not yet available, and were later published in _Outcasts in White Australia_ , part of his influential trilogy that did so much in the 1970s to inspire non-Aboriginal people's desire to understand. He had written to Mr H.S. Kitching, the Area Welfare Officer in Dubbo, who provided considerable information about the shanty town. Kitching told Rowley that there were 40 adults and 67 children, living in fourteen dwellings made mainly of scrap iron, and provided a list of the dwellings and their inhabitants, with a column denoting the 'caste' of each family—H.C. (half-caste), Q.C. (quarter-caste), L.C. (lesser-caste, i.e. less than quarter-caste)—with L.C. the most commonly noted. He also pointed out the local council neither provided services (there was no water or sanitation service) nor control of the settlement, so the people were 'free to live without restriction as to social standards or social behaviour'.
That Saturday afternoon, we got out our survey forms, walked up to the tin shacks on the settlement, introduced ourselves to their residents and asked our questions. Looking back, there is something a little touching about this strange cross-cultural encounter. We were finally about to meet the people whose cause we hoped we understood and wanted to publicise. Would the questionnaires, so carefully prepared in Sydney, be useful or entirely inappropriate?
The survey form I had that day was probably the one headed 'Aboriginal Questionnaire' and had a total of 29 questions. Some of these sought to elicit the ideas of Aboriginal people about their treatment ('Are the white people giving the Aborigines a fair chance?'), their sense of worth ('Are the Aboriginal people as good as the white people in every way? '), ideas about committees to 'deal with Aboriginal assimilation', the Aborigines Welfare Board, experience in getting jobs, accessing health services, whether their situation had improved at all over the last twenty years, and their views about not being counted in the census. It also asked for opinions about not being accepted for the recently instituted national military service, an issue that had received some media attention during January 1965. One question was 'Do you think that Aboriginal people are happier than white people?', while others sought to elicit views on whether Aborigines should be on reserves or in towns, whether 'the Aborigines should stand up for their rights or just accept the situation as it is?', whether they should 'preserve some of the old customs or adopt all the new ones?', how Aboriginal people were discriminated against, and how 'the Aboriginal situation could be helped'.
Now, either totally or largely untrained as interviewers, we students walked around the settlement just outside Wellington, looking for Aboriginal people to interview. We got a tremendous shock. We really had no idea until this moment what it was we were protesting about. Here it was, the utmost poverty in our well-off First World industrialised country. Pat Healy remembers: 'Wellington. Dry, dusty. And that's where we first started to see the living conditions for Aboriginal people. I have a visual memory of Wellington more than anything else. I can just visualise these hot, dusty shacks. I don't particularly remember what we did there.' Soon after the Freedom Ride, she told an interviewer that her first reaction had been 'complete numbness and shock. You know roughly before you go what you are going to face, but you simply don't realise until you get there and see for yourself. Take the houses they live in. I could hardly believe it when I first saw it.' I still remember Wellington clearly, for the poverty, and the feeling of trespass.
That evening, perhaps realising that this was getting to be something serious and disturbing, I started to write a diary. The diary was written in a Croxley spiral notebook, and I have kept it all these years, through fifteen house moves. I remember writing it each night from then on, sometimes in rather poor light. I deliberately wrote it in a very matter-of-fact way, careful not to say anything that was embarrassing, should it be found and read by another student. There was no privacy on the bus, and the chances of having a diary read were potentially high. It does provide, however, a reminder of many of the details of the bus tour, and some idea of my own experience of it at the time. My first entry concerns our stay in Wellington:
Interviewed about ten tin shacks of people. Most of us found the questionnaires unsuitable. Houses of tin, mud floors, very overcrowded, kids had eye diseases, had to cart water (very unhealthy) from river. People fairly easy to talk to, kids quite friendly. General picture of extreme poverty but not a great deal of social discrimination. Got seven interviews on the settlement just outside the reserve, and two in the town. General picture of scarcity of jobs. Mainly garden work, which is very seasonal. Average of three months of year out of work. Some working on a dam nearby. Some did shearing jobs. Did not encounter or hear of any women with jobs at all. Did not seem to know much about social services.
Thirteen of the completed survey forms for the 'Aboriginal Questionnaire' in Wellington survive, nine from women and four from men. Two of the women were named Ah See, possibly descendants of one of the Chinese families that had arrived in the region in the nineteenth century looking for gold, and owned and managed stores and market gardens for decades afterwards. It is difficult, now, to know what to make of these answers, and hard to tell what the students and the Aboriginal people of the settlement understood what each wanted of the other, or thought the other could do. While the respondents varied in their answers to the question 'Are the white people giving the Aborigines a fair chance?', all agreed 'the Aborigines should stand up for their rights' rather than 'accept the situation as it is'. Only two thought Aboriginal people should 'preserve some of the old customs'; the others agreed they should 'adopt all the new ones'. All said Aboriginal people should live in the towns rather than on reserves. Clearly, the question of acquiring houses in town was uppermost in these answers; when asked how they thought 'the Aboriginal situation could be helped' or how the health standards of Aboriginal people could be raised, answers ranged from 'better housing', 'build more homes', 'nice homes with water, etc.' to 'do away with missions and put Aborigines in towns, mixing' and 'put them in town'. When asked for examples of discrimination, the answers included 'up to twelve months ago not allowed in pubs', 'Courthouse Hotel', 'hotels, shops', 'employment', 'putting them out of town' and 'won't let them live in town even if can afford [it]'.
While we had been interviewing people at the settlement, Jim and Charles and some of the others had been in town. They asked some local Aboriginal people about which pubs discriminated against them, and went to the one named 'The Courthouse', which some Aboriginal people said refused to serve them. Jim started capturing the events of the Freedom Ride on super-8 film, to which he added a commentary in 1987. His film shows Darce interviewing an Aboriginal man, whom we then see outside the Courthouse Hotel, talking to Darce and Charles. It seems from my diary that this man was allowed in, but only because he was with the students: 'The publican said he only prevented Aborigines from coming in "if they were disorderly".' Charles then went into the same hotel, and there was some discussion between the barmaid and the publican before they served him. When Darce interviewed him outside the hotel, Charles reported:
Oh well the lady, the barmaid, asked me what I wanted and then went over, very reluctantly went over to the tap to serve me and then stopped serving, pouring out the beer, and went and asked the manager. The manager came over and had a conference and they both looked at me very slyly and then decided that I was a possibility, a doubtful case and so they decided to give me a glass of beer. Very reluctantly, after asking me twice, the manager himself that is.
This meant that the students did not have direct evidence of racial discrimination in the hotel, making it difficult to demonstrate about the matter.
Darce also interviewed the local Salvation Army officer, who said there was no discrimination in Wellington's hotels, as did one of the drinkers he interviewed. He went with a team administering the 'European Questionnaire'. This form asked people to agree or disagree with a range of questions, such as 'The Aborigines are just as honest and public-spirited citizens as the Europeans. Do you agree?', 'The Aborigines are morally inferior to most other people. Do you agree?', and 'Does it worry you that the Aboriginal population is increasing at a rate about twice as fast as that of the European population?' And so on, for seventeen questions, followed by four questions where respondents were to choose between two alternatives—for example, 'Would you prefer Aborigines to live on the reserves or in the town?' Finally, there were two open-ended questions, one asking 'What sort of qualities would a "good" Aborigine have?' and the other asking about the qualities of a 'bad' Aborigine.
While these filled-in survey forms have not apparently survived, Darce did record an interview with some of the local white townsfolk. The theme in their comments was that Aboriginal people did not know the value of houses, money or education—though also, in one case, that 'if they had the same chance as the whites, nobody really knows'. Darce also went with a group who spoke with the Anglican minister, Archdeacon Graham. He saw only one problem, that of 'educating the Aboriginal so that they can be integrated into our community . . . They know so little about employer–employee relationships, about landlord and tenant relationships, and to my mind about personal hygiene. They need to be educated on those matters so they can take their place in the community.' A child told Darce that Aboriginal children were her friends, though her mother would not allow Aboriginal children to play at her house, as 'they make a mess of me dolls and that'.
Aidan Foy and John Powles, meanwhile, had investigated the hospital. They probably took with them the Health survey that they had devised, of which no copy seems to have survived. Aidan remembers going to the tiny hospital 'and the matron showing me the little black babies in the hospital, obviously keen to tell me how well they looked after them'. He also remembers interviewing a general practitioner. 'The medical people interviewed by and large welcomed us. I think they thought they'd get some more resources if there was a bit of a fuss . . . We just marched in and asked matron to please answer some questions, and in every case that I can recall she did.'
There were three other questionnaires prepared by the students, which may have been used that day. In addition to those on attitudes and health, there was an 'Occupations and Incomes' survey, with ten questions about employment, including the nature of the employment, wages, training, locality, union membership and discrimination on the job, and seven questions about unemployment, concerning its duration, nature of the unemployed person's training, union membership, social and unemployment benefits, and reasons for unemployment. The fifth questionnaire in the survey was on living conditions, and again, I have no copy. In view of the centrality of housing issues in Aboriginal politics at the time, this is rather a shame. The sixth, also seemingly lost, focused on schooling and education, and was designed to be put to school principals in each town. It asked about the number of Aboriginal students who completed primary school, the numbers in each class in high school, non-attendance, the nature of and reasons for success and failure in exams, ideas about mixed versus segregated schools, curriculum, standards of homework, levels of acceptance and thoughts about employing Aboriginal teachers.
Later in the afternoon, the students compared notes. They agreed that, although there was some evidence of racial discrimination, especially in the Courthouse Hotel, there was nothing substantial enough to justify a demonstration. Although Wellington may have had an assimilation organisation in the early 1960s (the board report said it did), there was no sign of it in 1965, and if there was one, it may have been largely or entirely white. In any case, the students had not made contact with politically active locals, and this was a major barrier to any further action. Many years later, Charles recalled that the students hadn't been able to take the matter further partly because he, Charles, had in fact been served in the hotel and partly because:
There weren't enough Aboriginal people around to support us, and we wanted to get Aboriginal people to support the things we did. So after a while we decided to leave it at that and go on. We went on to the next town. There _was_ discrimination in the pubs there, but it was more sophisticated, it wasn't so blatant, and we wanted a clear-cut case of discrimination.
And with that, at around 5.30 p.m., the bus left town for the nearby large town of Dubbo. We had been in Wellington for a total of five, perhaps six, hours. We were learning a lot, and indeed it could be argued that it was in Wellington that we started to become a group. Jim Spigelman later said: 'At the outset we were not yet a unit—and didn't become one till Wellington.'
The bus arrived in Dubbo an hour later. We all had dinner, went for a swim in the local council pool, and then walked to the Dubbo Hotel, where we noticed a sign above the doorway: 'Aborigines not allowed in the Lounge without the Licensee's permission.' This same hotel had a large Aboriginal clientele in the public bar—in part because, as Charles Rowley later wrote, 'that was where Aborigines had got their supplies when it was illegal to sell to them'. We didn't do anything about it, but instead went to the Methodist church where we were to stay. Alex Mills remembers that the Methodist minister, John Mason, welcomed us, and that he was 'the guy who later became the leader of the Liberal Party'. That evening, Alex visited Jack Gowdie, the Presbyterian minister in Dubbo, and told him, his wife and his son John about the bus ride, and what it was about, as Alex understood it. John, a first-year student at the University of New England (UNE) in Armidale, and involved in its Society for Aboriginal Advancement, decided to join us. Gowdie had gone to school with Aboriginal children, and at UNE helped with a school support scheme for Aboriginal children. He had also been influenced by reading Charles Duguid's _No Dying Race_ , which began with a quote from John Ruskin he still remembered pretty accurately 30 years later:
I saw an injustice done, and tried to remedy it. I heard a falsehood told, and was compelled to deny it. Nothing else was possible for me. I knew not what would come of my actions, or whether I was fit for them, but here was a lie, full set in front of me, and there was no way round it but over it.
For us, Dubbo was simply an overnight stop, but in fact it was a place of some significance in Aboriginal Australian history. It had traditionally been an important camping area before European settlement, and continued as a centre of religious activity, with the Aborigines Inland Mission located there, and large religious gatherings being held there from time to time. It had been a centre of Aboriginal protest in 1938–39, when William Ferguson and Pearl Gibbs led one arm of the all-Aboriginal Aborigines Progressive Association (APA) seeking equal rights (the other arm of the organisation was based in Sydney, and led by Jack Patten). The all-Aboriginal political movement of the late 1930s is probably now best remembered for the 'Day of Mourning' it held on Australia Day, 26 January 1938, in protest at the triumphal sesquicentennial celebrations, emphasising that for Aboriginal people white settlement was not something to commemorate and celebrate. In rural New South Wales, the target of protest was the Aborigines Protection Board; Gibbs and Ferguson wanted nothing less than its abolition. In December 1938, a meeting of the APA at Talbragar, the riverside Aboriginal reserve 5 miles (8 kilometres) out of town, called for support for the agricultural development of Talbragar, Nanima and Burra Bee Dee reserve at Coonabarabran. The following year, the APA mounted a major campaign against the board for moving people around against their will, providing poor schooling, denying social welfare benefits and removing children. A major conference of the APA in Dubbo over Easter 1939, with 60 Murris attending, criticised not only the board, but also the white towns for segregating schools and hospitals. The APA faded away during the war years.
On Sunday, 14 February 1965, we were up by 6.30 a.m., and left with our new recruit, John Gowdie, on board at 9.15 a.m. There was as yet no newspaper or television coverage of the Freedom Ride, but someone must have had a radio, for we heard there was some local radio publicity about our presence in the area.
The next stop was Gulargambone, not far from the Castlereagh River, in what had once been Kawambarai land, just north of Wiradjuri country. Just 30 miles (48 kilometres) from the slightly larger town of Gilgandra, it was—and remains—a very small town indeed. It had one hotel, one café, one grocery store and several hundred permanent residents. The white residents lived on one side of the Castlereagh River, and the Aboriginal people on the other. About 120 people lived on the reserve, less than a third of its population of five years before, and it was to halve its population again within three years of our visit. It was no wonder people were leaving: the reserve consisted of several shacks, with very few amenities such as electricity or sewerage, and had a rubbish tip and a sanitary depot about 150 metres from the houses. Three months later, Mrs Baxter, one of the residents, explained to a television reporter how the shacks were made:
They buy their own tin; they buy their own piece of timber from the mill. Sometimes they make one-room places, sometimes they make two-room places, but they can never get enough tin or timber to make verandahs and bathrooms, or a washhouse or anything like that because the tin's too dear for them and they're only just working men.
As in Wellington, Charles and the other Freedom Riders had little or no contact with the local Aboriginal people, so it was again a matter of conducting the survey. We had permission to visit the reserve, though only for an hour. Visiting the Gulargambone reserve was a sobering experience. Darce recorded an interview with Jim, who commented on the lack of normal facilities, the poor conditions of the houses and the proximity of the sewerage to the reserve. Jim's film of Gulargambone shows an unidentified Aboriginal man standing outside one of the houses, the camera panning to emphasise the makeshift corrugated iron roof. Charles told _The Methodist_ a month later: 'We found a reserve about 2 miles [3 kilometres] out of town. It was in a deplorable condition— sub-standard houses surrounded by barbed-wire fencing, not much water, no electricity. Fifty yards [metres] from the reserve was an open sewage pit the stench and flies from which came across the reserve causing a lot of diarrhoea, eye sore, skin sores, etc. among the people in the reserve.' Jim later remembered it 'mainly because the Aboriginal community was the other side of the town rubbish dump'. He was shocked by the conditions there:
It was well out of the town, and it was very depressed, I mean just appalling conditions, and that would have been my first experience personally. I mean I'd heard and they'd sent pictures, but my first experience of Aboriginal living standards directly. That's why I remember Gulargambone; I can't remember what happened there.
Everyone interviewed remembered it in much the same way. Not that everyone _did_ remember Gulargambone—Charles, for instance, said to Inara in 1994: 'I have no memories of Gulargambone', and Norm McKay commented: 'Gulargambone has sort of terrible memories for some reason but I can't quite remember why.' Many of the others, though, recall how shocked they were by what they saw. Warwick, for instance, said Gulargambone was the first place where the situation of Aboriginal people was really brought home to him:
I remember—pretty sure it was Gulargambone—going to a mission. Some of the experiences that stand out from the Freedom Ride—a lot of it obviously at that distance of time is a series of impressions that meld together—but what was fairly striking was the stark images of deprivation that one got first hand in going into living conditions where there were, you know, houses with no doors and with no windows and cars with no wheels and no sanitation and no water, flies, rubbish, people cooking over fires, children obviously ill with running noses and flies in their eyes and all of those sort of things . . . I think the thing that struck me most were just those sort of very stark conditions that made quite an impact in terms of the very abstract ideas of racism and deprivation that we had before we headed out.
Alan Outhred has similar memories of recognising that the situation was far worse than we knew how to imagine: 'Certainly, we knew we were going to strike conditions that were rough for the Aboriginal people we were visiting . . . but on the other hand to actually come and see—it certainly increased my understanding.' For Pat Healy, it was 'very hot . . . very hot and dry . . . There's this sort of procession in my mind of huts and fibro houses and tin sheds and hot, dusty, flat, isolated living areas, with very primitive facilities. Blocks of toilets and showers and taps. Kids running around in the hot dust.' Robyn Iredale says: 'Well I'd never seen that sort of life before so I suppose I was shocked. But I'd read about it, I knew about it, but, yeah, I found it pretty disgusting that people lived like that. But it was taken for granted—I mean, nobody really questioned it too much in those days, you know, that was just the way Aborigines lived.'
I too remember a feeling of shock. My diary reminds me that I 'spoke to Mr and Mrs Baxter—very old and very interesting'. I now have before me the form noting my interview with Mr Baxter that day. He agreed that Aboriginal people were as good as the white people in every way and should have more say in their affairs, and disagreed that the Welfare Board was doing a good job. He thought Aborigines should be on reserves, not in towns, and that they should stand up for their rights. I also noted in my diary that 'Welfare board and police very much disliked'. Warwick remembers the people's hatred of the police well:
One thing that struck me when we were interviewing Aborigines on the trip, I think at Gulargambone . . . four Aborigines who were telling us about the police, and they were recently out of gaol and they told us that they were staying out of the town on the reserve, which was essentially controlled by the police. And the police would simply roll in, come through the door or the window, at any hour of the night. If there's any kind of disturbance out there, the police would roll out and would know who the troublemakers were and would simply go and arrest people. So they could be in bed with their wife and the police would come and drag them out and thump them. And they got so sick of this that, even though they knew the consequences, every now and again when they'd had a few drinks they'd decide they'd had enough, they'd wait behind the door until the police arrived and then they'd thump the Christ out of the police and go to gaol for six months after being beaten up in the police station. And they said it was worthwhile.
The message Robyn Iredale received was the people's hatred of the board. She spoke to another Mrs Baxter on the Gulargambone reserve (there were several Baxter families, and several Carrs), who said the 'people on the Welfare Board [were there] to better [their] own ends'. Their conversation then turned—perhaps surprisingly, given the totally secular nature of our questions and concerns—to spirit beings. Robyn noted on the back of her survey form:
_Belief in Spirits_.
Little woman—see her dressed grey, or hear her—walks up flat. Once a week or once a month. See her come up to flat land to the fence— never hear her go . . . Mrs Baxter thinks it is the daughter she lost—same size. Son thinks it was a ghost.
Robyn remembers this interview well:
I've got a really interesting slide that I think is Gulargambone, where we went out to a reservation, and I remember talking to these Aboriginal people about spirits and the spirits of ancestors and so on, and I asked them could I take a photo of them standing in front of their little tin shed before I left. And when I got the photo developed, there looks like there's another person there, and to me this was really strange because I'd had this conversation and then the photo comes back with an almost mystical other person in it.
In the afternoon, we conducted our surveys in the town. Beth remembers Gulargambone as an 'isolated one-horse town, three shops in the main street . . . The dryness and the dust.' She remarked: 'Don't remember any connection with the Aboriginal people there. I remember eating in a café, and the high school, some connection there.' For Aidan: 'Gulargambone was sort of a novel experience. It was a funny little town. I'd never been in a place quite as wild as that.' He also remembers going to the hospital: 'I went to see the babies . . . and I think they were on the verandah off the one ward. There would have only been a tiny hospital there with a few beds.'
To put on a demonstration, we needed firm evidence of discrimination and support from the local Aboriginal community. It was soon clear we had the first. We quickly confirmed that only certain Aborigines were allowed in the hotel, none could get served in the one and only café, and blacks and whites sat separately in the picture theatre. One of the survey respondents reported that, in the café, Aboriginal people were 'not allowed to sit down and have a meal', and that they could not stay and drink in the hotel. Charles later told an interviewer that 'in the café aborigines can stand up but they can't sit down for any meals. The proprietor said that when he first came to the town he did allow aborigines to sit down for meals but the white people complained and wouldn't do business with him. So now he won't allow aborigines to sit down for meals.' Another survey respondent, an 18-year-old, said the local constable 'picked on' the young men. Noreen Carr said that in the picture theatre you 'can mix, but because of attitudes of whites don't feel right so sit separately'. She also reported discrimination at 'dances, work and school'; in the long run, she wanted homes in town. Darce recorded an interview with an Aboriginal man that confirmed these accounts:
_Cassidy:_ Can you go into the picture show in Gulargambone any time you want to?
_Man:_ Yes I can.
_Cassidy:_ And you sit anywhere you like?
_Man:_ Ah . . . no.
_Cassidy:_ Why's that? Where do you have to sit?
_Man:_ Well it's not so much that you're made to, but there is a separate spot in the picture hall for the dark people . . .
_Cassidy:_ Now we've heard some stories about the café here. What goes on there, can you get a meal there?
_Man:_ Ah, no, you can't get a meal there, but you can get anything else that you want there.
It was crystal clear that racial discrimination was rife in Gulargam-bone, yet the leaders of the Freedom Ride agreed that this was not the place for a demonstration. We didn't have local support and, perhaps even more importantly, we didn't have any media coverage or interest at this point. We would have been demonstrating with hardly an audience. We had to go to a bigger town. So, at around 4.00 p.m. we left Gulargambone and drove on to Walgett, arriving three hours later. Hopefully, in Walgett, we would meet up with the local Aboriginal people, confirm the existence of racial discrimination and, at last, demonstrate against it. We were itching for some action.
_Ch_ _apter_
_4_
High noon at Walgett
The students desperately wanted media attention, and knew something more striking than an amateur survey was needed to get it. Walgett seemed especially promising for our purposes, given its reputation for racial discrimination and the presence of Aboriginal people who had already proven they were willing to speak out. The town seemed to be waiting for us, to test our mettle. The question was, were we up to the task?
The Walgett township lies at the junction of the Barwon and Namoi Rivers, the natural boundaries for two traditional language groups—the Gamilaraay (in older texts rendered as Kamilaroi) and Yuwaaliyaay (Uralarai); other nearby groups included the Wayilwan (Wailwan). All are known as Murri, the name for Aboriginal people in a large region covering Queensland and northern and central New South Wales. Amongst the first Europeans to visit the area were Thomas Mitchell and his party in 1831. Frontier violence was rife in the 1830s and 1840s, reaching its peak in 1843 after the manager of the Gingie station on the Barwon River was killed. Pastoralists continued to press into the district, and direct conflict seems to have been over by 1855. The numbers of Aboriginal people in the district dropped rapidly in the wake of white settlement, partly as the result of violent conflict, but mostly from starvation and disease.
Once direct conflict was over, the various Murri groups wanted to stay on their own land. Many began working on the pastoral stations, which were originally mainly cattle but later predominantly sheep. Heather Goodall, in her book _Invasion to Embassy_ , and John Ferry, in _Walgett Before the Motor Car_ , tell some of the story of these survivors and fighters. Permanent camps were established at several sites near the town of Walgett itself, the most popular being at Namoi Bend, with many smaller camps on the stations. In 1895, the Aborigines Protection Board established a reserve at Gingie station 6 miles (10 kilometres) out of town in order to keep people away from Walgett and under board control. The people, however, refused to go there for several decades; Gingie station only became a reality when the board forcibly removed people from the Namoi Bend settlement to it in 1925. The camp at the Bend continued, however, and its population grew after 1936, when the board closed down the Angledool station, 60 miles (100 kilometres) to the north. Angledool had by this time become a problem station, with the demand for pastoral labour declining, poor housing and epidemic trachoma. On 26 May 1936, over 100 people were taken away by truck to Brewarrina, but over the next few months and years, many went on to Walgett and other towns. Angledool remains important in the memory of many Walgett people. As Frances Peters-Little, whose mother's family is from Walgett, points out, many Walgett people have continued to identify with the Angledool mission, right up to the present. 'Proclaiming Angledool as their site of Aboriginal heritage and culture,' she writes, 'their links to Angledool were perhaps strengthened by the terrifying events surrounding the night it was abandoned at midnight during winter in 1936 when families were split and forced on to the back of cattle trucks and transported to unknown destinations.'
Soon after the growth in its Aboriginal population as a result of the forced removal from Angledool, the Aboriginal political movement of the late 1930s came to Walgett. A public meeting in Walgett chaired by the Mayor, held on 20 February 1939, heard Bill Ferguson and Jack Kinchela of the Aborigines Progressive Association speak about the need for change, and passed a motion asking for Aboriginal representatives on the proposed new Welfare Board (a request which was granted). The Welfare Board carried on the plans of its predecessor for more control over the growing Aboriginal population at Walgett. The Gingie reserve was upgraded to a station, with a manager appointed in 1941, and became known as the Gingie mission. Despite somewhat better facilities than at the campsites, many people refused to move there, and continued to camp at the Bend. They could afford to do so: the war meant employment. When Marie Reay studied Aboriginal society in Walgett during World War II (one of the first anthropologists to study a 'part-Aboriginal' community), she found the Murris there much engaged in shearing and cutting scrub. Reay also found sharp racial segregation; racial intermixing was not possible, and any white people mixing with Aboriginal people were regarded as Aborigines, not whites. Most whites did not know Aboriginal people personally, and saw them in town brawling and drinking, regarding them as 'unclean'. She reported that, though they failed to keep Murris out of town, the whites did keep places of entertainment segregated.
After the war, the high demand for Aboriginal labour initially continued, with Welfare Board annual reports indicating 96 per cent male employment. From the 1950s, however, pastoral employment gradually decreased, and as a result the station camps gradually disappeared. The residents from nearby Dungalear pastoral camp, for example, moved into Walgett, though some people continued to work on the property during the 1950s. With the station camps disappearing, the population of Walgett continued to grow, with men living in or near town and working in a range of occupations on the nearby properties—as shearers, drovers, musterers and labourers. Others worked in blue-collar jobs for the council, the Department of Main Roads or on the railways.
By the mid-1950s, the Walgett white townspeople were becoming alarmed at the rise in the Murri population, alleging that public drunkenness was driving whites out of the town. One of them, businessman Mr John Cooper, was quoted in the _Sunday Telegraph_ on 25 August 1957 as saying the Aboriginal people in Walgett were drunken and lawless: 'I'll be packing up unless the Government does something about the aboriginal problem.' Cooper told the _Telegraph_ that the Aboriginal population had increased by 30 per cent in the last eighteen months, so that the numbers of Aborigines and whites were almost equal: 'They seem to think they can come to Walgett, do as they like, and have no fear of reprisals.' Cooper was quoted as saying the women would 'make a play for any white man who looks as if he can afford to amuse them'. Cooper's suggested solution was to appoint a welfare officer who could keep the people in check. In response to the _Telegraph_ 's story, the Aboriginal-Australian Fellowship sent a delegation consisting of its secretary, Irene McIlwraith, and Mrs Garland, wife of John Garland of the Amalgamated Engineering Union, a fellowship affiliated union, to Walgett to investigate. They stayed for four days, from 6–10 September, and talked to many people. As McIlwraith, a refugee from Nazi Germany in the late 1930s, wrote to John Garland soon afterwards, they had walked 'the length and width of Walgett on foot from dawn to dusk'.
Their report provides an unusually detailed glimpse of race relations in a country town in the 1950s. On their return to Sydney, McIlwraith described rigorous segregation—separate church services, separate playgrounds at school, exclusion from hotels, separate seating in the picture theatre and separate living areas. The Anglican vicar, Reverend Hadlow, had tried to have mixed congregations, and had been prevented from doing so by the local whites. Living conditions were appalling: the Gingie mission still had no water supply other than the river, and no decent road into town, while the Namoi camp also had no water supply, no sanitation and no electricity. At Gingie, the station manager visited houses once a week, a much-resented imposition on people's privacy. The local doctor was unsympathetic; McIlwraith's report quoted him as saying that 'they do not want to mix with us and I think the best would be if we had special towns for them, run by themselves, where they would not bother us and we would not bother them'.
Walgett Aboriginal people, however, were not to be moved. They had retained something of their political radicalism from the pre-war period and wanted a better deal in town. As Mrs McIlwraith later wrote: 'All the Aborigines we spoke to [in] Walgett said that what they wanted most was full citizenship rights.' The two women called a meeting in the church hall on the Saturday evening, which about 40 Aboriginal people attended. They showed a film about the treatment of Aborigines at the Warburton reserve in Western Australia, and played a recorded speech by Bert Groves, a well-known figure in the region. They explained why they had come, and that the fellowship wanted the people of Walgett to know they had outside support. The Reverend Hadlow and Alec Trevallion, the Town Clerk, also spoke, and George Hill spoke on behalf of the Aboriginal people. He said: 'I live on the Mission and I am an Aborigine. After serving six years with the Australian Army overseas, I came back to Walgett. When I went into the local hotel for a drink, I was rudely ordered out.' Twenty-two Aboriginal people, along with Trevallion, Hadlow and John Cooper (now eager to distance himself from the comments attributed to him by the _Telegraph_ ), signed the fellowship petition requesting a change to the Constitution. When she returned, Irene McIlwraith did everything she could to alert Sydneysiders to the state of affairs in Walgett. Her letter in the _Sydney Morning Herald_ on 2 November drew readers' attention to the 'appalling conditions in Walgett', with 400 people living in shanties on the riverbank, without electricity, gas or water, and Aboriginal women kept in a separate ward in the hospital, and men on one side of the male ward.
The solution, many whites thought in the 1950s, was to house more Aboriginal people on the board's stations. That way, they would be under surveillance, and cause less trouble in the towns. Their living conditions would also be better. A _Herald_ editorial two days after McIlwraith's letter recommended doubling the spending on Aboriginal housing, so that more Aboriginal people could be accommodated on the stations. Yet the funding for Aboriginal housing remained low, and towns like Walgett continued to witness a struggle by the whites to keep the Murris out of town. In 1958, young anthropologist Jeremy Beckett wrote in the Sydney-based discussion magazine, _The Observer_ , that the Aboriginal population was growing and the problem of poor Aboriginal housing and social marginality could only get worse. Aboriginal people wanted to stay together; government policies meant the price they had to pay to do so was shocking housing conditions, and racial dislike and hostility from the whites. He ended his article with the prescient remark: 'In a few years the country towns of the North and West are going to have a very ugly race problem on their hands.'
Walgett returned to the attention of the Sydney papers in 1960, as part of a _Sydney Morning Herald_ series of feature articles called 'Survey of Aboriginal Life'. The report on Walgett on 27 October emphasised the large number of Aboriginal child deaths in the area, and quoted the local Presbyterian minister, Reverend A.R. Ewin, who said 'apathetic Government authorities and the public had shut their eyes to the tragedy'. The Town Clerk, Alec Trevallion, told the _Herald_ 'the commonwealth government will have to finance local authorities to handle the situation', for example by funding the employment of 'male and female social workers to teach the aborigines hygiene'. Some time after this, the riverbank settlement on the north side of the river was declared the Namoi reserve, in an attempt by the board to exert some control over conditions there. (Although gazetting new reserves was by this time against board policy— which was to locate people in houses in town—the refusal of councils to allow Aboriginal housing in town forced the board to create a number of reserves around this time, usually—like this one—comparatively small and close to town.) The settlement on the south side, closer to town, had become known as Montkeila Bend.
In Walgett, the council-owned swimming pool was open to all at the insistence of Trevallion, who seems to have been relatively sympathetic to Aboriginal people, at least by the standards of the time. But private enterprises like hotels, shops, cafés, cinemas and private clubs were another matter. After its 1957 visit, the Aboriginal-Australian Fellowship continued to keep a watch on Walgett. One of its members, Barbara Gibbons, wrote to Jack Horner after her visit there in May 1964: 'In Walgett, George and I noticed something I would like to draw the Fellowship's attention to. The bar lounge of the "Oasis Hotel-Motel" had a notice on the door in very fancy lettering and incorrect spelling "Aborigines admitted only by invertation".' Horner showed the letter to David Tribe, a member of the fellowship who had been the schoolteacher at the Gingie mission school for some years until December 1963. Tribe confirmed the story, and told Horner of other instances of racial discrimination: the refusal of the Returned Servicemen's League (RSL) Younger Set to admit Aboriginal people, and the exclusion of Aboriginal people from upstairs in the picture theatre.
Horner hoped to set up an organising committee of the fellowship in Walgett itself. Meanwhile, he tried to act on the matter of discrimination through a flurry of letters. On 22 June he sent one to Athol White, the manager of the Oasis Hotel-Motel, asking him why the motel had a notice saying Aborigines could enter only by invitation, and another to several Aboriginal residents at the Gingie station, asking whether they wanted any action taken. There is no record of a reply from the latter, but White replied at length: 'The policy of my hotel,' he told Horner, 'is to be of service to the majority of the people of the district, and to maintain a good standard of facilities for their enjoyment.' Aborigines who behaved decently and who were dressed tidily 'would be most welcome to enjoy these facilities'. However, the number of Aborigines answering this description 'is very minute'. The notice, he said, 'was to save embarrassment to the Aborigines, and also to ourselves, as having to constantly eject them because of their general behaviour and disgusting language is embarrassing to us, our patrons and must also be to them'.
Yet, in the end, it was not the appalling housing conditions or racial discrimination in the hotel and the picture theatre that dramatically brought Walgett into public notice the year before the students arrived. It was the police and the courts. In June 1964, as the students had learned from speeches made at their meeting and rally in July, two 9-year-old Aboriginal boys were gaoled for two days and two nights in a police cell in Walgett for stealing from the Anglican church hall two table tennis bats and balls and crayons, together worth a total of 30 shillings ($3). The Sydney _Sun_ featured the case as a page 1 story written within the tabloid tradition of 'exposure journalism', calling for sympathy with the boys and outrage at the authorities who had put them there. It also drew attention to the poor conditions under which Walgett's Aboriginal population lived. The _Sun_ story began: 'Two weeping nine-year-old aboriginal children have been locked up for two days and nights in a police cell at Walgett. They cried continually during the night, prisoners who were in an adjoining cell told me yesterday.' It went on to report that one white citizen had written to the editor saying: 'I am ashamed of the society I live in. Townspeople can see the children in gaol with their little arms hanging through the bars.' The two boys were Roy Hickey and Fred Morgan, who lived on the reserve on the outskirts of Walgett. During discussion with the magistrate the next day, one of the mothers agreed it would be better for the boys to be taken to a boys' home: 'We are desperately poor—it is so hard for coloured people to get work around here . . . Fred has no future around Walgett and that's why I thought he would have a better chance in life if he went to a home for boys. But when I found out he was put in the town lockup I nearly collapsed.'
Jack Horner wrote directly about the matter to the Reverend P.J. Dowe, minister at St Peter's Church of England, from which the bats and balls had been stolen. Dowe wrote a long letter in reply, worth quoting because he was soon to play an important role in the Freedom Ride story. He had agreed, you may remember, to accommodate the students in this same hall. Dowe had little sympathy for the two boys who had been gaoled for stealing toys from his church hall; indeed, it seems possible that complaints from the church had led to police involvement. He had even less for their mothers, commenting that the mother of one 'has no concern for the boys at all'. He objected to Horner's assumption that Aboriginal people in Walgett had a hard time:
The dark people here have been well treated in this district (with some exceptions). That is why so many have come to this town. They are accepted by most of the whites (again with some exceptions). They have the same opportunities as whites. There is no shortage of work. They are paid as well [as] or better than the whites. There appears to be plenty of money among them.
The problems lay not with white racism, but with the Aboriginal people themselves: 'We still have to tackle the basic problem of how to develop a sense of responsibility and the urge to take the possibilities before them, e.g. to develop skills and to use their money properly.' Dowe went on: 'They have had no end of gifts and "hand outs" and they are quite content to take all these, but it has only encouraged them to sit back and take things easy . . . There is a complete apathy and lack of concern to help themselves.'
Yet, if the Reverend Dowe had little sympathy for the boys, many others were moved by this story. Letters poured into the _Sun_ , Charles Leon writing on behalf of the Aboriginal-Australian Fellowship, saying 'most people will share the indignation of the people of Walgett at the callousness that left two small Aboriginal boys in a police cell for two days and two nights, as part of their punishment for stealing some toys and crayons. The rest of their punishment is to be removed from their families and placed in a children's home'. Several unions took up the case, writing to government agencies. In early July, a delegation of five men representing three unions visited the town to investigate the gaoling. Two of the five were Aboriginal—Alan Woods (from the Builders' Labourers Federation (BLF), and also a member of the Aboriginal-Australian Fellowship), and Jack Hassen (from the Waterside Workers' Federation (WWF), and also former boxer—indeed, lightweight champion of Australia). The other three were Dick Prendergast (BLF), Jim Hill (Building Workers' Industrial Union) and Jack Hartley (WWF). The visit was well publicised, with television and radio reports preceding the arrival of the delegation.
The unionists met on 3 July with some local Murri activists who facilitated meetings with the two mothers and liaised between the delegation and the Aboriginal community. Two members of the community are especially important to our story. One was Harry Hall, a Gamilaraay man who in the 1960s lived at Montkeila Bend and was one of the town Aboriginal residents most accepted by white society in Walgett. He had been a shearer, then worked at the Walgett garage, and later for the Department of Main Roads. Another was George Rose, one of the few remaining Yuwaaliyaay speakers, who had grown up in Brewarrina, joined the army late in the war, and settled in Walgett in 1949. In the army, where he had been a sergeant, he had experienced and enjoyed racial equality. His wife, Mavis, was also a strong community activist. Like Harry, George was a shearer and a member of the Australian Workers' Union, and at this point, he was also a member of the Communist Party.
The report written as a result of this visit went far beyond the original gaoling incident. It described the tin shanties, and reported first-hand accounts of the brutality and sadism of one particular policeman. Most importantly for our story, the delegation learnt of the exclusion of returned Aboriginal Diggers from the RSL Club, except sometimes on Anzac Day, and the sign 'Aboriginals by invertation only' at the Oasis Hotel-Motel. Two of their members interviewed the manager of the RSL Club, Tom Hogan, and an official, T. Quinlan, who agreed that returned Aboriginal Diggers were only admitted to the club on Anzac Day. 'They denied,' said the report, 'that this was racial discrimination and said that they were only following past practices.' The delegation also reported that 'perhaps the most important event of our trip was a meeting of 100 Aborigines on the Sunday, who, after listening to our delegation, elected a committee to protect their interests'. This became the Walgett Aborigines Progressive Association (APA), loosely connected to the Aborigines Progressive Association formed by Bert Groves and others in Sydney some months earlier. It involved Harry Hall and George and Mavis Rose, and also Gladys Lake and Ted Fields. Harry Hall now became president of the newly formed APA, and remained so until 1973. There were also, Harry told me in 1991, some white people in the APA, especially Mrs Collins, who was a member for years, and whose son owned the garage that Harry used to work in.
Back in Sydney, the New South Wales Labor Council adopted the trade union delegation's recommendation that it seek a government investigation into the gaoling and the situation in Walgett more generally. A Labor government was in power, led by Jack Renshaw whose own electorate of Castlereagh included Walgett, but this by no means guaranteed government sympathy with the children and their families or a sympathetic hearing of the Labor Council delegation. While the Labor Council waited for an appointment with the Minister for Child Welfare, the Children's Court in Sydney declared the children wards of the state and decided they should go to a foster home. Delegates from the unions and the Labor Council finally met the Minister for Child Welfare in September, and another delegation from the Newcastle Trades Hall Council met him soon afterwards. The request to return the children to their parents was refused, the reason given being 'bad housing'.
The housing situation in Walgett was at crisis point by this time, with the Aboriginal population in Walgett nearing the 1000 mark, many of them living in the shanty town settlements along both sides of the Namoi River. There were different schools of thought on how to deal with the crisis. The Aborigines Welfare Board wanted to build 'transitional housing'—that is, cheap, low-standard houses—on the Namoi reserve, in order to stretch its budget to supply the need. The shire council, which had been pressed by the Aboriginal-Australian Fellowship on the question of housing in mid-1964, strongly opposed the concept, wanting increased government funding for proper housing. Only four days before the students arrived, the council agreed to improve the housing, sanitation, drainage and access road for the Namoi reserve.
Aware of only a fraction of this history and these debates, the students arrived in town just before 7.00 p.m. on a hot summer evening on 14 February. They settled into the St Peter's hall and some went to the service that evening. Alex Mills remembers: 'I did go to church in the Anglican church on the Sunday night and we actually sang the hymn . . . "Lord Jesus, There is No Room in My Heart for You".' Just across from the hall were the basketball courts, and some of the other students had a few games with the local Murri team, the Anglican Fellowship Basketball Team. One of its members was Phillip Hall, Harry's son, and another was Bob Morgan, later to become a leading figure in Aboriginal education, but then a 14-year-old in Walgett. Bob recalls: 'We were intrigued, I remember, about why would white fellas be coming—I remember as kids we had games of basketball.'
It must have been that evening, or perhaps it was on the bus trip into Walgett, that we agreed our target would be the RSL Club. A decision-making structure was emerging. Decisions over whether to demonstrate or not were made democratically by the whole group. There was also a tour 'executive', consisting of Charles, Jim and Pat, which represented the students to outside bodies, and which also was in charge of 'discipline'— that is, ensuring that students who acted violently would be expelled from the tour. We also agreed that Charles would make all official press statements, and in his absence either Jim or Pat would do so. The RSL, the whole group now agreed, was an ideal target for news-making. In a society where ex-servicemen were held in high esteem, and seen as embodying nationhood and national identity, racial discrimination against an ex-serviceman was easily ridiculed and attacked. Charles thought it was important that we had chosen an RSL Club, as he later recalled:
To demonstrate outside the RSL, the great sacred cow at that time, you know, nobody criticises the RSL, they can do whatever they like . . . we decided that that would be the prime objective, to fly in the face of the most cherished institution in Australia, because they were very racist, and they were not only that they were arrogant, and they were self-centred and very discriminating and opinionated and everything else.
Though the exclusion of Aboriginal ex-servicemen from the Walgett RSL Club was perhaps a small matter compared with the massive problems in housing, health and education confronting Aboriginal people at the time, it had great symbolic importance. For it was in the commemoration of war that Australian popular culture found its most profound sense of nationhood. This was as true in Walgett as everywhere else. From the 1920s, war memorials were erected in practically every country town; in Walgett, the war memorial was at the centre of the town, at the intersection of its two main streets, and the location of practically everything in town could be marked by its relation to the monument. Nationally, the RSL found itself in a contradictory situation in respect to Aboriginal ex-servicemen. On the one hand, it regarded the status of returned soldier as transcending all others, and had successfully pressed for Aboriginal ex-servicemen to be given the right to vote (granted in March 1949 by the Commonwealth Labor government for federal elections). On the other hand, it was a conservative organisation, and remained aloof from campaigns for full citizenship rights for Aboriginal people. It had no policy specifically _preventing_ its clubs from excluding Aboriginal ex-servicemen from membership, leaving it to local clubs to determine their own policies. The Walgett club was thus free to exclude Aboriginal ex-servicemen from membership and use of the club, though local Murri activists like Harry Hall, George Rose and Ted Fields had been protesting about its exclusionary practices (and much else) for some years.
_Monday, 15 February 1965:_ My diary records that the next morning we were up at 7.00 a.m. and **'** heard announcement over radio that we intended to picket RSL at 12.00. All surprised that news had got out.' The Reverend Dowe was not pleased at what he heard, and told us we couldn't stay in the church hall if we carried out our plans to demonstrate. What should we do? We held a long and serious meeting. Here was the first chance to put the ideals of passive resistance into action, yet if we demonstrated where would we stay? After much discussion, we decided to go ahead anyway.
_Diary_ : Had meeting and decided to acquiesce in police demands only to point where acquiescence would break up demo. Then would passively resist. Also decided that anyone acting violently would be suspended immediately, and later subjected to general meeting at which it would be decided to send the person home or not.
In deciding to go ahead, we had also, it seemed, called Dowe's bluff. Seeing we had nowhere else to stay, Dowe reluctantly agreed that we could remain in the church hall. The _Australian_ reported that 'plans were being made for them to sleep in abandoned tram cars when they learned they would be allowed in the hall again'. Mr Dowe told the _Australian_ he was strongly opposed to the picket of the club: 'It is only stirring up racial feelings which don't exist in the town . . . I thought they were coming to Walgett purely to study Aboriginal conditions.'
Quite a lot of time had been lost in discussion, and the demonstration was to begin at noon. We made placards, a process Jim Spigelman recorded on film. Aidan Foy remembers: 'Wherever we stayed there was enough space to make all the placards because I do remember doing that.' At this point, another student joined the bus, bringing our number up to 30—Hall Greenland, a member of the ALP Club, educated first at Fort Street Boys' High School, now about to enter his third year in an Arts degree at Sydney University. He had been away on holidays on the north coast and caught a train down to join the bus. He later described himself as 'a scholarship boy from a middle-class background': his father was a plasterer, his mother a clerk. Some years before, his father had left, and 'so we were a single-parent family . . . a working mother and three kids. We lived at Summer Hill and I suppose my mother classified herself as a revolutionary, libertarian, non-Stalinist socialist.' Hall had already had some experience of Aboriginal shanty towns, when he visited Dareton, outside Griffith on the Murray River in the south of the state, in the summer of 1962–63 just before starting university. He told me:
[Machteld Hali draws the placard asking, 'Good enough for Tobruk. Why not Walgett?'.
(Photo courtesy of the _Tribune_ /Search Foundation)](chap7_9781741150575_epub_part7.html#d41151701)
Being a good left-winger and occasionally seeing Aboriginals when I was on holidays up and down the coast, I knew that there was a certain amount of poverty and degradation about the way they lived. But then when I saw them living in this shanty town outside Griffith—with a single tap and of course their humpies—it did actually really shock me and brought home to me, the two or three months I lived in a country town, what their actual living conditions were like. I can remember going to a public meeting there about the fluoridation of water, and moving an amendment to the resolution at the public meeting in favour of fluoridation, that it be delayed until proper piped water and septic tanks and so on had been installed in the Aboriginal camp. That the municipal money that was going to be spent on fluoridation be redirected to that. And it was like a bloody lynch mob.
When asked why he joined the bus, he said he had 'twin objectives': 'I was, I suppose, as much interested in the politics of it as in one of the women who was actually going on the bus. So I thought this was a good chance to actually meet her and get close to this particular woman.' What most of the other students didn't know was that Hall at the time had a 'foster brother I suppose—for about five or six years at this time', an Aboriginal youth from the Northern Territory named Maynard Burmester, who had been living at the factory where Hall's mother worked, and then became part of the household.
After the meeting, we separated out into groups and conducted our survey. Jack Horner's letter to Jim Spigelman just weeks before the Freedom Ride left Sydney had summarised the housing situation in Walgett tersely and accurately: 'Walgett: 1. Reserve six miles out of town, Board houses. 2. Riverbank two miles out of town, bad conditions. 3. Camping grounds in town, shocking conditions.' We did not have permission to visit the first of these, the Gingie mission with its board manager, where about 150 people lived, as the board still had to meet to consider our application. So one group went to the Namoi reserve while others went into town. I went to the reserve, where over 260 people lived, and we interviewed people for several hours.
_Diary_ : Most of the people I spoke to very shy and diffident, and said they were quite happy. Conditions very bad—had to use filthy water, tin shacks with mud floors, overcrowded.
Eighteen of the survey forms filled in that day survive. One woman refused to answer questions because, as one of the students noted on the back of the form, 'previous surveys had humiliated them through newspapers, radio, TV reports . . . and [they] did not see any results from surveys anyway'. This was possibly a reference to the intense media coverage of the previous year. From the others—mainly from women— some consistent themes came through: the desire for houses, perhaps in town, for a better water supply, and better medical services. Mrs Kennedy said Aboriginal people could not buy blocks of land, and mentioned the need for 'better water instead of river water', and proper sanitary arrangements. The people consistently reported on examples of racial discrimination in the town—exclusion from the Walgett RSL, the frock shop (Sheen's, according to Phillip Hall 36 years later), upstairs in the cinema, and the Oasis Hotel-Motel lounge. Mrs Fernando mentioned that, at the doctor's, Aboriginal people were not treated until the Europeans had been seen to. One 16-year-old girl said Aboriginal people could not get jobs, the frock shop barred Aboriginal people, and the police were rough and tough, often putting the young men in gaol.
Another group of students interviewed people in the town, both European and Aboriginal. Some Aboriginal people worked there, and some families—like the Peters family—now lived there. Aidan went to the local hospital, and also interviewed the town doctor, 'who was disappointed because he'd hoped he'd be interviewed by an attractive female medical student and he was upset being confronted with me'. Alex Mills interviewed a young Murri man who worked as an assistant storeman at the shire council. He was willing, he said, to have his name submitted to the Walgett RSL together with other suitable Aboriginal applicants. Alex wrote on the back of the form that his neighbour reported that 'he and his family are good neighbours'.
Wherever we went, the story of racial discrimination was the same. Again and again we heard about the Oasis lounge, the frock shop and the cinema.
_Diary_ : Obviously considerable discrimination in the town . . . Aborigines not accepted socially by white community.
We checked out the RSL situation for ourselves. Several students interviewed Tom Hogan, the club manager, who told them unequivocally that no Aborigines were members of the club and that if any were nominated for membership, the club would not accept them. A student, probably Jim Spigelman, says on Darce Cassidy's tape:
We had a 20-minute interview with the vice-president and the secretary-manager of the RSL Club. The vice-president, who is on the committee that reads the nominations and decides whether this person who's sponsored becomes a member, said categorically that he would never agree to have an Aboriginal, even though sponsored, to join the club.
We had done our research, and everything tallied. There was plenty of racial discrimination, the RSL most definitely included.
[Helen Gray, Machteld Hali, Norm McKay and Ann Curthoys (far right), holding banners outside Walgett RSL, 15 February 1965.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41151761)
The demonstration began, as planned, at noon. Most of the students were there, though Alex Mills wandered off to search out his contacts in the Presbyterian church 'to see what the situation was as far as they were concerned'; he had lunch with their 'senior layperson'. Derek Molloy and John Gowdie refused to join in, saying they opposed demonstrations. Everyone else participated.
_Diary_ : About 12.00 we began to demonstrate outside the RSL. We just stood in a long line outside the RSL holding placards like 'Acceptance, Not Segregation' 'End Colour Bar' 'Bullets did not Discriminate' 'Walgett—Australia's Disgrace' 'Why Whites Only' 'Educate the Whites' and so on.
Darce Cassidy's tapes and the _Sydney Morning Herald_ report also mention Machteld's placard, 'Good enough for Tobruk—why not Walgett RSL? '. Jim's film shows us all standing there, in the hot sun. When the students fanned out in front of the club, we were met at first by a moment's silence, and then the heckling began. One bystander called out: 'Who the hell do you think you are?' My diary continues:
[Above: Students outside Walgett RSL holding banners
(Photo courtesy of the Fairfax Photo Library) and below: RSL worker offering drinks, 15 February 1965](chap7_9781741150575_epub_part7.html#d41151791).
People gathered round, many jeering, many just watching. The RSL characters offered us cold drinks, but we refused them. At lunchtime many heated discussions broke out. Charlie Perkins spoke terrifically and I think most people listened very attentively.
Pat Healy recalls that 'Charlie spoke, very well I thought, contrasting the treatment of the black servicemen who weren't allowed to use or be members of the Walgett RSL'. On Darce's tape, Charles says:
Well as everybody knows in Walgett and all the Aboriginal people do know, and I think most people throughout New South Wales know, the Walgett RSL does discriminate against Aboriginal people on the basis of colour alone, that's the criteria used, and we just want to show them we object to this on principle, we don't think this is a good thing, and we're doing it in a very passive way.
The speeches turned into a public street debate. The report in the _Tribune_ (the CPA newspaper) said: 'In the beginning, the white people in the crowd were laughing, but they then joined in a long mass discussion on discrimination, with many Aborigines also taking part.' Colin remembers 'getting into arguments with townspeople, discussing the rights and wrongs of what we were doing, or the rights and wrongs of Aboriginals going into the hotels'. As time went on, according to my diary, 'more and more Aborigines joined in the discussions'. Aidan remembers that, in addition to Charles's speech, some local men spoke too: 'I'm sure Harry made a speech and George Rose made a speech, I'm fairly sure, just talking about the segregation of the Club.' Darce recorded one man saying: 'I reckon if I'm good enough to fight for the country here, save other people's lives, why shouldn't I walk in there?' It seems that it was the Aborigines living in town and on the reserve who were mainly involved; those on the mission were less affected.
The RSL was picketed continuously from noon until almost 7.00 p.m. The _Tribune_ estimated the crowd at about 350. Halfway through the afternoon, some of the students went along to the frock shop and held a demonstration there, again captured on Jim's film and also observed by police. Helen Gray asked to see a frock and, when shown it, called on an Aboriginal woman with her to try it on. The shop manager said she would not, as the police report put it, 'permit the aborigines to try on the frock because white women would not touch it once it had been handled by blacks. She could buy it and take it away if she so desired, but she would not permit the aborigine woman to put it on and then refuse to buy it.' The woman managing the shop drew the blinds, locked up and went home, and the students returned to the RSL Club.
_Diary_ : After five a lot more people came to argue with us and it seemed as if half the town was there.
Towards evening, the white community became increasingly hostile, and there was a good deal of verbal abuse directed against the students. For Pat Healy, this was the first occasion on which she 'realised how heated the white country people were about our presence, and about our image'. She pointed to an important element of this confrontation when she said:
I think in a way our image was as enraging as what we were doing. The boys all had long hair and the girls all wore miniskirts or tight jeans. I mean we were just normal—what we regarded as fairly sort of conservatively dressed—certainly more conservatively dressed than we would have been at university. But clearly our whole presence, what we looked like and what we were doing was a great affront. I've often thought subsequently that part of the being affronted was that—here were we, relatively privileged university students, who had the wherewithal and the money to sort of take off on a bus trip around New South Wales, and we were aligning ourselves with the blacks in the community.
Darce recorded some of these angry townsfolk, who did indeed express the resentment against students and city folk that Pat recognised:
Your trouble is, you're a little small group come up from, you know nothing about it for a start . . .
In my opinion they oughta take 'em over to the Imperial Hotel for about three hours, lock 'em in with the Aboriginals, and then when they come out see what they think of them then.
I don't think it's the aborigines we gotta worry about, I think it's that motley looking crowd over there we've got to worry about . . . You can't disguise the boys from the girls. There's one long-haired bloke there . . .
Look at 'em. The brains of Australia! God help you if you ever end up under 'em. Have a look at 'em.
Our training and advice from Bill Ford onwards had emphasised not resisting the police. In fact, there was not much police presence, and those who were there did not trouble us. Walgett's four police were joined by two from Bourke, Inspector Chalker and Sergeant Glendenning, with Chalker speaking directly to Charles about what the students were doing. The police reported to their superior at Dubbo that the students had behaved well and no complaints had been made.
After the demonstration ended around 7.00 p.m., some of the students again went to play basketball against two local teams, matches that were, the police reported, 'well attended by both black and white residents of Walgett'. Some of the others went for a swim in the Barwon River. Colin remembers a group of about five or six going for a swim with some local shearers. Brian remembers it too:
There were these shearers who'd picked us up and I still suspect that they had their eyes on some of the young women. But they took us out to a local swimming hole, whatever the river is that runs through Walgett, it was actually quite a big swimming hole . . . And they had this big utility truck . . . and they took us back to town. They were trying to hang around us, I remember that.
Around this time, two white men, Paul Evans and Joey Marshall, were drinking at the Oasis and were overheard making remarks that alerted some Aboriginal people that there might be trouble.
While the students were relaxing and unwinding with the locals, the Reverend Dowe unexpectedly contacted the police station and requested police attendance at the Church of England hall, as the students had stayed there the previous night and he did not want them to stay again. At 9.00 p.m. the students, who had by this time largely returned to the church hall, got a shock. Reverend Dowe arrived with three churchwardens and spoke to Jim and Charles, ordering the students to leave the hall within two hours. The reasons given were not the demonstration, but that the students had been noisy, both sexes were sleeping in the same hall, and cans of beer had been found inside.
_Diary_ : He reckoned that he didn't know we were a mixed group (which he did—he saw us when we first arrived), that we had left beer cans in the hall (which was true) and that we had antagonised people. Charlie had a real go at him because he obviously disliked us because we demonstrated.
Dowe's hostility to the actions of the Freedom Riders was expressed in a letter published in _The Anglican_ the following month. He wrote that 'the students came under the guise of conducting a survey on Aboriginal conditions, but, in fact, they made no attempt to understand the position in Walgett—even if that were possible in two or three hours'. The students, he said, took no account at all of the moves that have been made in the town to help Aborigines. There was plenty of work for Aboriginal people, and the baths were open to all. He then made his own position quite clear, in terms very similar to those in his letter to Jack Horner the previous year:
Our dark friends are just not like Europeans . . . Anyone who has lived among the coloured people in these towns knows the biggest problem is not the lack of means to improve, but the lack of desire to improve. There is not a shortage of money, but the money is wasted. Most do not want to work. They are content to sit back and live on a white man's 'hand-outs' and the returns of those friends who do work . . . Fortunately, in fact most of the ill-feeling on the part of white and dark has been towards the students and not towards the other race.
Dowe was fully aware that the students had made themselves unpopular and were therefore vulnerable to at least some sections of the town. He and his churchwardens now turned them out into the night. The bus driver, Bill Pakenham, was called from his hotel bed, the students packed up their gear, and the bus prepared to leave town. The police stood by while the students put their belongings on the bus. They were joined by Bruce Maxwell, a cadet reporter for the _Sydney Morning Herald_ who had been roaming outback New South Wales, and was now on the spot for a big story. With the students' permission, he boarded the bus, paying £10 like each of the students for the privilege. Alex Mills could not be found: he had gone visiting the Presbyterians again.
It was now after 10.00 p.m. While we were getting ready to leave town, Phillip Hall and some of his friends, sitting on the steps outside the bank opposite the Oasis, saw Paul Evans and Joey Marshall driving around looking for the bus. Suspecting trouble, they thought a convoy of cars to see the bus out of town might be a good idea, and began organising people and cars to follow us.
_Diary_ : About 200 aborigines and some whites came to see us off. We went off quickly, leaving Alex Mills behind because it was obvious there was considerable hostility in the ranks of the pub leavers.
Darce recorded the Aboriginal people singing 'So long, it's been good to know you'. As the bus left Walgett, a long line of cars—nearly all friendly, part of the convoy to protect the bus—followed it. Warwick remembers that the police on motorbikes accompanied the bus out of town for some miles, and then turned back. Jim Spigelman's film, taken from the rear of the bus, shows the car lights in the darkness, an eerie sight. We students, however, had no idea who was following—friend or enemy. Brian recalls this line of cars following the bus, and thought one could have been the shearers, and perhaps some were just caught in the line, while others were unfriendly. About 3 miles (5 kilometres) out of town, we learnt definitely that not all those following were sympathetic. A light green truck driven (as we later learned) by Joey Marshall, the son of a grazier from a large sheep property 40 miles (65 kilometres) from Walgett, pulled out of the line of cars and began to overtake us. John Powles describes what happened then:
We went out of town on the bus and we had one friendly truck with Aborigines and so on behind us, and then there was another truck with hostile people behind them. And as we were going out of town, the friendly truck was weaving all over the road to try and stop the hostile truck getting out to sort of do something to the bus . . . finally this hostile vehicle got around the friendly vehicle trying to shepherd them off, and it came hurtling up the side of the bus.
Warwick picks up the story:
Out of the cars came a big pick-up truck that then proceeded to butt the bus and push us off the road . . . That went on for quite some time with the pick-up going by in front, stopping, braking.
Darce reported:
After waiting at the side of the road, the truck overtook again and swerved suddenly in front of us. But the driver managed to keep the now speeding bus on the road. On the third attempt the truck struck the bus near the driver's cabin forcing the bus off the elevated road.
Warwick:
Finally the bus was forced off the road going quite fast, about 60 miles an hour I guess . . . and went down a levee bank and the driver miraculously stopped it from rolling as it went into the scrub.
In fact, Bill's presence of mind in driving the bus off the road at this point saved it from rolling over. Darce remembers:
Food and suitcases were thrown all over the bus. But, although shaken, no one was hurt. When the bus came to rest we could see that we were surrounded, four or five sets of headlights pointing at the bus from all directions. It seemed that we were trapped, alone with four or five carloads of hoodlums on a country road. But there were 30 of us on the bus and it looked like the numbers were just about even.
At the front of the bus Charles shouted 'girls to the back, girls to the back'. Pat recalls that:
I and a number of other women said, 'Get stuffed! What are you talking about?' I think they thought there was going to be rape and mayhem. Which none of us really knew—who all these lights were because all we could see was all these car lights, and if it had been a group of rough neck whites come to beat us up we wouldn't have had much hope.
Some of the students looked for beer bottles to defend themselves, Darce reporting that 'near me someone was crawling round the floor saying, "Quick, get bottles, get bottles"'. The police reported the event more soberly: 'About 8 miles east of Walgett the vehicle was forced off the roadway by a green Dodge lorry driven by Joseph James Marshall, 22 years of Boorooma Station, Walgett.'
There was no need to defend ourselves. It turned out that the cars surrounding the bus belonged to Aboriginal people checking we were OK. The truck that had hit the bus had driven on. Darce interviewed Charles and the driver, Bill, as soon as the bus stopped and it was clear there was no further danger:
_Cassidy:_ What happened, what'd he do?
_Perkins:_ In front of us, he nearly killed us. He would've killed the whole 30 if there was a ditch here. Isn't that right, Bill?
_Bill (driver):_ Three times this Dodge truck tried to run us off the road. The third time I swerved, I had to run over the bank, otherwise collide severely with the truck. As it is, he slightly damaged us, the bus rolled terrifically as we went over the bank, but no serious damage was done.
_Cassidy:_ Do you reckon you were lucky not to roll?
_Bill:_ Terribly lucky not to roll. As a matter of fact I didn't think I'd be able to straighten the bus up to prevent rolling.
_Cassidy:_ What's the drop like into the ditch?
_Bill:_ Oh, 3 foot 6 on about a 45 degree angle.
We all went back to Walgett. At midnight, the students stood outside the police station while the police took statements from witnesses to the incident—the driver, two students and two other independent witnesses. Many of the students rang their parents to assure them they were unharmed. Bruce Maxwell rang the _Sydney Morning Herald_ with the story. The police noted the green paint marks on the side of the bus and damage to its signalling arm and blinker light, and sent their report to Sydney.
Now it was almost midnight on a very hot, still night. Despite the late hour, it wasn't long before 50 or 60 townspeople were confronting us, and arguments broke out again. Warwick remembers:
On the other side of the road there was a mob—the pubs being closed—of young hoons, who were about 18 or 20, wearing singlets and thongs and shorts and shouting abuse. It was a racist abuse, across the road, at the few Aborigines who were around and at us. And it was an extremely touchy situation I guess.
Brian said: 'What was extraordinary was that this huge debate ensued. And this was in the middle of the night in Walgett, shouting and screaming going on. I can remember Charlie doing a lot of talking and there were whites saying all sorts of things, you know, why you couldn't live with Aboriginals.' As Warwick remembers it, after 'about 15 minutes or so of this abuse, Charles lost his temper completely and he sort of counted these characters on the other side of the road and he said: "Why don't we do them? Why don't we go over there and beat the shit out of them?" But we didn't because he was probably the only one who could fight.' (So much for non-violent direct action!)
Then came one of the defining moments of the tour, described in Charles's biography, _A Bastard Like Me_ , and dramatised in his daughter Rachel's film, _Freedom Ride_ , made in 1993. Some of the Freedom Riders remember it well.
_Aidan:_ Various drunken white men abused us, but some of the Aboriginal women present drew these gentlemen's attention to their own sexual behaviour with Aboriginal women at the time, and that basically was the end of that.
_Brian:_ The most extraordinary thing was this Aboriginal woman who just, you know, came out of nowhere . . . but she really gave 'em heaps and she just—she got very angry and she spoke. And she actually went out with local white guys I gather from something she said. And she really tore strips off them. Again I don't remember the exact words. Just, it'll be forever with me the impression of this woman, this Aboriginal woman dressed . . . I seem to recall a blue dress. And really made this quite emotional, angry speech in the middle of the night in this street in Walgett. I forget her name.
The woman was Pat Walford, a Murri woman in her early twenties. Darce recorded her words on his ever-present tape-recorder. She delivered an angry monologue for about five minutes, pointing to double standards, the secrecy of sexual relations, her attachment to Walgett, and her disgust at the white people in Walgett who were attacking the students. On the tape you can hear constant interjections from male voices, and her angry voice in reply:
I'm black and I'm proud of it and I uphold it too . . . I'm not ashamed to walk around the street and what I do I openly do it . . . There's a lot of white fellas that go looking for gins here at night too. I go with white fellas and I keep on going with white fellas . . . If a white fella didn't want to have anything to do with me when I walked down the street I wouldn't have anything to do with him . . .
She alluded to the segregation at the Oasis Hotel-Motel:
You [white people] wouldn't serve the dark people in the lounge because the white women wouldn't use the toilets after them.
And then to the events that day:
You've been walking past them [the students] all day, criticising your own colour . . . It hurts you white people in Walgett to see the whites from Sydney up here and do that to you, doesn't it? Trouble is it's hurting the whites to see other whites fighting for the blacks . . . Anyhow the colour is only skin deep. Everybody's the same, black and white . . . It's a pity some of the whites wouldn't go and leave the blacks to the town.
They can look at me and talk about me as much as they like but they won't shift me out of Walgett. I intend to die here and I'll stop here just that long to torment the whites.
Charles later recalled:
What was important was the Aboriginal people themselves participated in that and particularly the women, they wanted to be part of it you know, and they began to expose everybody—the relationships in the town that were common at the time, you know, white men sneaking around having relationships with Aboriginal women and making out that those relationships didn't exist and all of that was brought to the surface.
In Rachel's film, the scene goes like this:
_White men to Freedom Riders:_
What are you blokes doing here?
Get back to where you come from.
Piss off.
We don't need your advice here.
You stirrers.
Mongrels.
Our blacks were happy before you lot came here.
A lot of dingoes.
_First Murri woman to white town-dwellers:_ I'm black and I'm proud of it.
Anything I've got to say I show it. And why can't we go into your pub and your pools? We're good enough to sleep with, but we ain't good enough to swim in your pool are we?
_White town-dweller:_ Out of town's that way (points).
_First Murri woman:_ Yeah, you. I seen you down the mission. And you, yeah, hanging around the mission looking for us black gins . . .
_Second Murri woman:_ You want to go and ask your father where he used to spend his Friday nights. Down there at the mission with my mother. That's where he was.
_Charles Perkins's voice-over:_ The white women couldn't believe it and so they turned on their husbands and they all started arguing. The crowd just disintegrated. After about ten minutes they were all gone, but the message was very clear for everybody to hear. After that discussion, Walgett was finished. It had no answer to racial discrimination.
And so, in the middle of the night in Walgett, in an historic moment of confrontational drama, there was a release of the repressed—a naming of behaviours that everyone knew about but no one spoke of. These included sexual contact between white men and Aboriginal women, resulting in mixed-race children living with their mothers, often not acknowledged by their fathers; this was occurring in the same towns as open racism, hostility and widespread segregation. Racism and sexual contact went closely together. The white men who had sexual relations with Aboriginal women were known, in a phrase that now shocks for both its racism and sexism, as 'gin jockeys', a term of mockery and abuse, yet a term that could have been applied to a considerable number of white men living in and around this and any similar town. No wonder the actions of an Aboriginal woman named Pat in Walgett on 15 February 1965, threatening publicly to name the 'gin jockeys', to disclose that which was known but unspeakable, have become legend among Aboriginal people in that region. No wonder the contradiction between racial segregation and high levels of inter-racial sexual contact and procreation made social relations in these small towns so especially bitter. Sexual secrets always just under the surface gave a paranoid psycho-pathological edge to everyday life.
Pat Walford finally finished her tirade, though her words were to be remembered long afterwards. It was now 1.00 a.m. We students all got back on the bus, this time with Alex on board, and went on the road to our next targeted town, Moree, which was 136 miles (217 kilometres) away. Though tired and shaken, we wondered whether there would be any media coverage of our protest.
We had little to worry about on that score. In running the bus off the road, Joey Marshall ensured the Freedom Ride received the publicity it had always wished to attract. Not all of it was favourable; the conservative radio presenter Eric Baume, for example, made hostile comments. But many urban papers presented the story in a light which was favourable to the students and unfavourable to Walgett. _The Bulletin_ scooped everyone with its report by Sam Lipski, written before the bus left Sydney and not covering events in Walgett, but appearing the day after the bus was run off the road and explaining the motivations of Charles and the other students. I have not been able to trace the journalist for the _Australian_ , but there seems to have been someone on the spot. The paper went to press too early for its first Walgett story on the Tuesday morning to cover the bus being run off the road, but it did report the demonstration outside the RSL Club, the opposition of Reverend Dowe to the students' protest, and the jocular hostility of the club vice-president: 'The students all look like beatniks to us.'
The _Sydney Morning Herald_ was lucky to have Bruce Maxwell in town and then on the bus, able to supply some first-hand detailed information, supplemented by other information gathered by a Sydney-based journalist, Bert Castellari. Early editions of the _Herald_ story on 16 February, like that in the _Australian_ , concentrated on the survey and the protests in Walgett during the day, but also included a brief mention of the bus being run off the road. This same report carried a statement made by Premier Renshaw at his Monday press conference that he had been reassured by 'a very reliable person in Walgett who had done more to assist aborigines than anyone else in the northwest' that 'what took place was more or less in the nature of good, light banter between the two groups. Some speeches were made at lunchtime, and subsequently some of the students were playing basketball and some were swimming in the swimming pool.' In later editions, after 'some frank phone calls' from Maxwell, the bus being run off the road came to the front of the story, with Maxwell evoking the danger and describing the fear inside the bus itself. Each edition stressed the incident in increasingly graphic terms, one edition referring to the bus having 'crashed'. Reading one of these _Herald_ accounts the next day, we students liked it very much.
'Nonsense!' Of course you want a drink'. Cartoon by Molnar, _Sydney Morning Herald_ , 17 February 1965.
The _Daily Mirror_ was another positive paper. Under its young 33-year-old Australian–Jewish editor, Zell Rabin, who had spent three years as the paper's New York correspondent, it had taken up a pro-Aboriginal position for some time, and now responded to the Walgett events with an editorial headed 'Dixie comes to NSW', which described racial discrimination as 'an ugly fact of life in northern NSW'. It continued the analogy with the American South when it said: 'The reaction of the hillbilly element of Walgett to the peaceful picketing by the students would not have been out of place in Mississippi. It culminated in an act of hooliganism on the road that could have resulted in serious injury or even loss of life. There should be an immediate inquiry into the accident.' The _Mirror_ defended the students' right to protest, and suggested that it was the Premier's responsibility to ensure that these young people were not molested for the rest of the trip. _The Sun_ 's editorial on 16 February hit a similar note, widening the comparison to include Britain and South Africa. Headed 'Walgett Outrage', it began:
Any Australians who have been feeling smug about happenings in Alabama or the British phobia about having a nigger for a neighbour, should now look honestly at Walgett . . . Little Walgett is on its way to joining the big league, and to rank with Little Rock, Selma, Smeth-wick, Notting Hill Gate and Johannesburg . . . Australia should be shocked at what happened at Walgett yesterday and ashamed of what has been going on there and at places like it for a long time.
In Sydney on Tuesday, 16 February, Premier Renshaw was pressed to comment further on the events in Walgett, in the light of the bus having been run off the road. The _Australian_ on Wednesday quoted him as denying that there was any 'undue discrimination' against Aborigines at Walgett in the north of the state. He said: 'Any well-behaved Aboriginal can go into hotels there or use the local swimming pool. And their children attend the local schools. There is also an extensive housing scheme underway through the Welfare Board to assist in their assimilation into the life of the town.' The _Herald_ on 17 February also reported on Renshaw having said there was no discrimination in Walgett on the ground of colour. It carried a photo of the students standing outside the Walgett RSL in the sun, and another of the RSL Club members carrying cases of soft drink out to the students. The following Tuesday, 22 February, the _Australian_ returned to the Walgett events with an opinion piece by William Olson, strongly critical of the RSL:
I suggest the RSL and the RSL clubs should be out there riding with these students, shouting their indignation to the heavens, tearing down the foul tin shanties on the river banks of the west. I suggest the RSL and the RSL clubs should be in the front-line attacking cant and humbug . . . somewhere the RSL lost the track.
After recounting the brave deeds of Australians in World War II, he asked: 'Is the RSL big enough to recognise something of that spirit in the young students riding through North-Western NSW?'
Yet if the urban papers were strongly for the students, their readers were more mixed in their responses. Some letters were against both Aboriginal people and the students. One in the _Herald_ , from a Walgett resident, said 'there is no racial discrimination in Walgett. There may appear to be some in the eyes of people from the city who, like the university students, know nothing about country towns.' The letter defended the exclusion from the RSL: 'The [Aborigines] cannot "hold" their liquor and to be drunk and swearing is no way for one to enter any home, most of all an RSL hall founded as a mark of respect.' Many similar letters were to be written as the Freedom Ride continued on its way. There were, however, at least as many in support. One in the _Australian_ was from noted poet Bruce Dawe, who thought the hostility that had greeted the students at the RSL Club was 'some indication of the colour prejudice latent in this so-called "egalitarian" land'. He drew attention to the contradictions between Australians' notion of their own egalitarianism and their continuing racism: 'Of course we're democrats—although we draw the line at boorees, boongs, abos, niggers, Chows, Nips, etc.' Another in the Sydney _Sun_ , from Mrs Joy Tyler who described herself as 'the daughter of missionaries' amongst the Aboriginal people of New South Wales and Queensland, expressed admiration for the students, and support for Aboriginal people generally.
Outside Sydney, newspaper coverage of the Walgett events varied. The urban newspapers in other states carried stories syndicated from the Sydney papers. The _Courier-Mail_ editorial thought the students had been provocative. The _West Australian_ on 18 February carried a long and detailed profile of Charles Perkins, mentioning his soccer career, marriage to a white woman from Adelaide, and his enrolment in Arts at the University of Sydney. The New South Wales regional and rural press had a largely unsympathetic coverage. The _Northern Daily Leader_ , based in Tamworth, carried a denial by Walgett police that the students had in fact been run off the road. _The Spectator_ , Walgett's only newspaper, reported in something of an understatement: 'The general feeling towards the visit is one of adverse publicity for Walgett by a group of students whose visit was pointless and only caused dissatisfaction in some circles of the community.'
The students were far from finished with Walgett, several of them returning there for more desegregation battles throughout the year. And Walgett was far from finished with battles over Aboriginal rights. For the moment, though, Walgett had served its purpose of dramatically drawing attention to white racism. Both shaken and excited, the students pressed on to Moree.
_Ch_ _apter_
_5_
Moree: Australia's Little Rock?
Towns like Moree in New South Wales have far too much in common with Little Rock in America.
Reverend Alan Walker, 11 July 1958
If Walgett was tense and dramatic, Moree was confrontational, exciting and threatening. It is the Moree leg of the Freedom Ride which most people now remember, and it was in Moree that so many people now say the Freedom Ride changed race relations forever. It was Moree, too, which attracted international media attention.
Moree was a much larger and more prosperous town than Walgett, lying as it did on a flood plain covered with the broken-down basalt and volcanic black soil brought by the Gwydir River (the Moree section of it is known as the Mehi) from the western slopes of the Great Dividing Range. With such rich soil, this was wealthy sheep, cattle and wheat country. Where Walgett had been on the western edge of Kamilaraay country, Moree was established right in the middle of this large and populous Indigenous people. The Kamilaraay past lives on in many of the place names around Moree—Bundarra, Warialda, Pallamallawa, Mungindi, Narrabri and Terry Hie Hie; Cobbadah, Bingara and Boolooroo; Walan-gulla, Boomi, Collarenebri, Yallaroi, Wongabinda, Boggabilla, and north to Goondiwindi. Because it is further north than Wellington and Walgett, European interest in the area began rather later, starting with Cunningham's overland exploration in 1827–28, and continuing when Sir Thomas Mitchell criss-crossed the region between 1830 and 1832. Mitchell reached the Gwydir not far from the present township of Moree on 10 January 1832, meeting Kamilaraay encampments along the way. The area was declared the Liverpool Plains Pastoral District, and squatting was permitted there from 1836. There was a fierce battle for the land between the squatters and the Kamilaraay from the late 1830s, the most well-known massacre of Aboriginal people in Australian history occurring in June 1838 at Myall Creek, a tributary of the Gwydir about 82 miles (136 kilometres) southeast of Moree.
Fighting between Aboriginal inhabitants and white settlers continued through the 1840s. The settlers urged the government to do more to guarantee their safety. In May 1849, a contingent of Native Police— Aboriginal men hired from distant districts like the Murrumbidgee and thought an effective and cheap way of quelling resistance—arrived led by Commander Walker. By 1852 the area was considered 'pacified'. By the 1860s, a pastoral economy had successfully supplanted the former hunter and gatherer economy, though some traditional food-getting lasted for many decades afterwards. Aboriginal people were now employed as shepherds, drovers and general labourers in the pastoral industry. Eventually, the advent of road transport, railways, steam tractors and irrigation established the conditions for more intensive agricultural production. Pastoral properties were reduced to more manageable sizes, and wheat farming prospered.
The town of Moree started in 1852 with a store on the bank of the Mehi River; a post office opened on 1 May 1853, and the town was surveyed in 1860. Yet, while the district remained one of huge pastoral stations, the town did not grow quickly, reaching a population of only 150 after twenty years. Gradually—and especially with the advent of agriculture and closer settlement—it became the hub of a network of transport and communication in the northwest. Schools, hospitals and churches were all built in the last two decades of the nineteenth century. Early in the twentieth century, professional services developed, along with timber-cutting and brick industries. Moree was a railway junction, and linked with other large towns in every direction. The town was also blessed with a plentiful supply of hot mineral water. An artesian bore was sunk in 1895, and within a year baths were constructed so that people could benefit from the water's medicinal properties. Moree became a tourist town, with several thousand visitors attracted by the hot artesian baths during the winter months each year. More elaborate baths were built in 1913, owned and operated by the Moree Municipal Council.
As Moree grew and prospered, Aboriginal people were generally kept out of town, and lived in camps on the pastoral stations nearby. From 1895, several of these pastoral camps were consolidated at the Aborigines Protection Board station at Terry Hie Hie, 24 miles (38 kilometres) southeast of the town. The station became home to many Kamilaraay Murris, including the survivors of the Myall Creek massacre and their descendants. In 1924, after bitter conflict between the station manager and the residents, and demand for access to the land by settlers, the Terry Hie Hie station was broken up and the land leased to white farmers. As was to happen whenever reserves were broken up in this way, the people drifted to the nearby towns. Many Terry Hie Hie people moved to join their relatives at a camp which had existed for about 30 years, on the bank of the Mehi River, on the Bingara Road stock route just east of Moree itself, dramatically swelling its numbers.
The bitterness of the Terry Hie Hie people at being forced away from their traditional land led them, according to historian Heather Goodall, to 'entrench themselves tenaciously' in their new location. In their desire to stay, they came into conflict with an equally determined white population that wanted them to go. The town council tried throughout the 1920s and early 1930s to drive Kamilaraay people away from the town, resorting to demolishing huts and even gaoling people in an effort to remove them. The struggle, and the gaoling, meant that those living there continued to have a strong emotional attachment to the site for decades afterwards. The council again tried to push them away in 1933 by excluding them from various town services and enforcing a curfew.
None of these strategies worked, and the town authorities found not only that they could not drive the people away, but that more camps sprang up along the river. When Aboriginal people drifted in from Boggabilla in the 1930s, they set up a camp beside the Mehi River on the western side of town which became known as 'Middle Camp'. The original camp became 'Top Camp' (or 'Bingara Road') and there was now also a 'Bottom Camp' on the banks of the Mehi River 2 miles (3 kilometres) west of the town, where in the late 1930s the Aborigines Protection Board built some cottages in an attempt to gain some control of the situation.
By the late 1940s, Moree had become a wealthy, hierarchical, class- conscious town, with several poverty-stricken Aboriginal settlements along the riverbank. Marie Reay and Grace Sitlington, in their anthropological study of the town in 1948, described its class and race relations. Membership of each (white) social class, they said, 'is determined by wealth and other possessions, and whether one's occupation is pastoral, professional, trade or labouring'. Below the working class whites was the Aboriginal population, itself by this time split into a class hierarchy of its own. In the mid-1940s, Aboriginal people could get jobs similar to those of the lower class white community (i.e. labouring occupations). The men could work, in order of status within the Aboriginal community, as railway gangers and fettlers, shearers, Department of Main Roads employees, municipal council employees, station cooks, drovers, station hands, cleaners, gardeners and casual labourers. For the women, possible jobs—also in status order—were taking in washing, hawking, commercial laundry work, general domestic work, hotel laundry and cleaning, and casual domestic work. Women could also work at the McMaster (Abor-ginal) Ward at the Moree hospital as wardsmaids.
Ten years later, Moree had become an even wealthier town, the most important pastoral centre in New South Wales, with a growing Aboriginal population. The white townsfolk made renewed efforts to exclude Aboriginal people from the town altogether and, failing that, from a range of services and entertainments. As the numbers of Aboriginal people in and around the town grew, white attitudes hardened. The Aborigines Welfare Board expanded the 'Bottom Camp' reserve into a station, building an additional 27 houses. Managed by E. Morgan, who appears later in the Freedom Ride story as an Aboriginal Welfare Officer in Lismore, the station—or Mehi mission, as it was often known—opened in 1953. A school was built on the mission especially for Aboriginal children, which helped exclude them from the local school. Aboriginal people were also not allowed to use other town facilities, such as the Memorial Hall built in honour of those who served in war, or the artesian baths and associated Olympic pool.
Tension over these arrangements started when Russell Watson, a young Baptist lay preacher, arrived in Moree from Tamworth in 1952 as the spare parts manager for a Ford dealer. He made friends with some Aboriginal people, read Elkin's _The Australian Aborigines_ , helped form a youth club on the Aboriginal station, and conducted services there on Sunday evenings. In 1955, to the horror of the council and the residents of Moree, he tried to book the supper room of the Memorial Hall for the wedding reception of his Aboriginal friends, Leo Cutmore and Irene Tighe. Moree's white residents were even more worried at the prospect of Aboriginal children using the artesian thermal baths and its adjacent swimming pool. The baths especially represented, in the words of Reay and Sitlington, 'a municipal investment to attract tourists, aid commerce and promote town development'. Thousands of tourists continued to visit the town each winter, and the baths were a key attraction.
To ensure that Aboriginal people did not use either the hall or the baths, the council decided to put into effect a resolution it had passed five years earlier, but never enforced. At the council meeting on 6 June 1955, a motion was passed unanimously by those present, including the Mayor, Alf Sadlier, the Deputy Mayor, William Tait, and Aldermen Robinson (the mover), Doyle (the seconder), Hawkins, Gildersleeve, Bullass and Boland. This was a standing resolution excluding Aboriginal people from the municipal thermal baths and the Memorial Hall. So important is the resolution to the Freedom Ride story that it is worth quoting at length:
No person, being a full-blooded or half-caste aboriginal native of Australia, or being a person apparently having an admixture of abor-ginal blood, shall use, or occupy or be present in or upon, or be allowed or permitted or invited to use or occupy or be present in or upon, the premises of the Council known as the Memorial Hall . . . AND THAT no such person as aforesaid shall use or occupy or be present in or upon or be allowed or permitted to use or occupy or be present in or upon, the premises of the council known as the Bore Baths or in or upon any of the Buildings or places enclosed herewith.
In defending the resolution, Deputy Mayor Tait said the council would 'allow coloured returned soldiers to attend the Anzac Day dinner at the hall', and that 'the preservation of the thermal baths for the exclusive use of white patrons is vital to this town's prosperity'.
Church leaders protested loudly. The _Northwest Champion_ carried several letters condemning the council, including one from the Methodist minister, the Reverend Roy Bedford, who also spoke against the resolution in church. His sermon showed an unusual recognition of the colonial past: 'We are here through invasion and aggression,' he told his congregation. 'We not only took their land, we treated them miserably in doing so. At times they were hunted like animals. They were whipped and mercilessly beaten. Their womenfolk were used to satisfy the lusts of miserable men.' He argued that people had to be judged individually, and whole groups should not be condemned because of the behaviour and habits of some of their members. Canon Ormerod, the vicar of Moree Church of England, also opposed the ban, telling one reporter that 'to keep people out of the memorial hall merely because of the colour of their skin is barbarous', as did the Catholic priest Father Richard Shanahan.
The story was taken up by the Sydney press, especially the _Sun-_ _Herald_ on 12 and 19 June. It reported on Aboriginal people being refused service in cafés and on private buses, on them being expected to occupy the front rows in the cinema, and a separate hospital ward. 'Baths attendants,' it reported, 'have become expert in recognising at a glance the minutest trace of "colour" in patrons.' Bert Groves pointed out that the Moree council's segregationism was in direct conflict with the state government's assimilation policy, and the new manager of the station, Desmond Reynolds, agreed. The council was, said Reynolds, 'encouraging a policy of racial segregation identical with that of South Africa. It is contrary to the policy of our Government and I foresee grave repercussions.' Public interest in the case grew, and when Leo Cutmore and Irene Tighe were married at the All Saints' Church of England in Moree, with Canon Ormerod presiding, he received letters of support from all over the state.
So strong was the clerical outcry that a committee of councillors, doctors and ministers, along with the Superintendent of the Aborigines Welfare Board, the Inspector of Schools and police representatives, was formed to discuss the issue. It met on 26 July, and recommended to the council that it rescind its resolution. The council, however, stood firm on the resolution concerning the pool, though it did agree to allow Aboriginal people to use the Memorial Hall and supper room at the council's discretion. This decision, made at a time when informal segregation was slowly supplanting such formal prohibitions, gave Moree a reputation as a racially segregated town—a reputation which stuck.
Two years later, Allan Ashbolt, a creative and politically radical radio broadcaster, made a devastating radio program about race relations in Moree. Ashbolt had already heard that Moree was 'known as a tough town for Aborigines to live in' from Murris from the area he had met during the war in the North Australia Observer Unit patrolling the far north of the country. He also had Russell Watson, who had recently left the town, as a helpful informant. Ashbolt visited Moree, and interviewed many of the town's leading citizens and some of its more outspoken Aboriginal residents. Broadcast on 18 June 1957, the program, 'A Study in Attitudes', was 45 minutes long, well researched and very hard-hitting.
Moree, said Ashbolt, was 'a rich, fat town'. He went on: 'There's money in Moree, money that the droughts can't dry and the floods can't drown.' It was also a tourist town, for, as Ashbolt said, 'the weather's nearly always dry and fresh, there's shooting on the river flats and swamps, and the artesian bore baths are bubbling even in the wintertime'. Some of this wealth trickled down to the Aboriginal population; the Aborigines, said Ashbolt, 'nearly all earn good money, either as shearers, station hands, railway workers or general labourers'. Yet it was a town marked by racial segregation, which most of the whites Ashbolt interviewed were quite happy to defend. Leo Smith, the president of the Bowling Club, told Ashbolt his club had no Aboriginal members, and the people were happy to be quite separate on the mission station. Mr H.E. Halstead, the president of the Golf Club, asserted to Ashbolt that Aboriginal people shouldn't be allowed amongst white people. 'We wouldn't accept them into the Golf Club, and I don't think any other clubs in town would accept them either. They really are a problem, but you have to live here, and live here for some time to know just what problems they do create.' Like all the other whites Ashbolt interviewed, Halstead saw the solution as segregation on to the mission, except when working. 'They work outside in many fields, especially on the outside in the pastoral area, such as shearing and fencing and that type of thing, and they're very useful in that regard, but when it comes to their private lives, well it's a different matter altogether. Segregate them I would say altogether.' In the same vein, Alf Sadlier, the Mayor, defended the pool resolution passed two years before:
The thing died a natural death and as far as Moree is concerned the thing is forgotten . . . the aboriginal question was a local matter and it had nothing to do with anybody else in this Commonwealth. It was our own affair . . . we had a special meeting and from that special meeting I think everybody was quite happy, and as I said before, the matter has been dropped. It's finished with and it's no good anybody in Australia trying to bring the aboriginal question back in Moree because it's finished with once and for all.
Ashbolt's program demonstrated clearly that, as the Aboriginal population of Moree continued to rise, so white attitudes towards Aboriginal people became more negative. Both the Catholic priest, Father Shanahan, and John Green, the local Aborigines Welfare Officer, told Ashbolt that hostilities had been increasing for some years as more Aboriginal people came into town. (Green later rose to become the Superintendent of Aborigines' Welfare and a member of the Welfare Board, a position he held at the time of the Freedom Ride.) Green drew attention to the exclusion of Aboriginal people from the hotels unless they had an exemption certificate (and the fact that, even then, some hotels would not serve them). In addition, Green told Ashbolt:
Certain cafés won't serve them, either, and certain taxis won't run them. They sit on their own, down in the front stalls at the picture theatre—not because there's a law or regulation or managerial policy that tells them to, but because the community expects them to.
Darce Cassidy had seen this first hand as a teenager:
One of my uncles had practised as the solicitor here in the 1950s, and I had come here several times for holidays. It was here that I had my first experience of racial segregation. It was well before television, and a visit to the cinema on Saturday afternoon was a regular occurrence for most kids. At home I went to Hoyt's at Crows Nest (in Sydney), and my friends and I were allowed ninepence. The cinema cost sixpence downstairs and ninepence upstairs. We all went downstairs and used the remaining threepence for an ice-cream or lollies. When I went to the cinema in Moree with my cousins we went upstairs. When I asked why I was told the Aborigines went downstairs. This annoyed me, not because I was in any way concerned for the Aborigines or opposed to segregation, but because it seemed to be a stupid waste of money. My Moree cousins appeared to have no contact with Aborigines, and I certainly had no contact in the times I stayed there during school holidays.
Green also told Ashbolt:
At the District Hospital, there's a special ward for Aborigines; it's separate from the other wards and there are no trained nurses in attendance—only untrained nursing assistants of their own race.
An Aboriginal interviewee also told Ashbolt about the hospital:
I've lived in Armidale and gone to school there . . . In the hospital, you're in the one hospital right through from upstairs or anywhere, maternity ward—you're in one hospital with the white people and you get good treatment, but down here in Moree, you've just got one separate ward and built away from the white people's ward on your own.
Another told Ashbolt: 'We both hold our Exemption tickets, but then you can't go into the pubs to have a beer or anything. And when you do bring it home there's always the police or someone behind you. You can't even have a decent drink. You can't even give a party.' Segregation continued in the schools, with Aboriginal children confined to the Aboriginal school on the mission. Although one-third of Moree's Aboriginal population was Catholic, none attended the town's Catholic schools. The Catholic church was, however, situated just outside the grounds of the Aboriginal mission so that the 100 or so Catholics there could attend.
Ashbolt's program sparked little immediate press comment, but it drew considerable comment directly to the ABC itself, and it seems to have had a lasting influence on educated urban people's understanding of race relations. Ashbolt received a lot of complimentary mail, especially from academics and anthropologists. Anthropologist Jeremy Beckett described it as 'brilliant', and as having exposed to the nation the 'particularly unpleasant situation in Moree'. He wrote in _The Observer_ , 'the smug complacency of local dignitaries was a particularly nauseating feature'. Two years later, the poet Roland Robinson referred, in a letter to the _Herald_ , to the 'infamous and inhuman statements on the aborigines contained in the ABC radio interviews obtained by Allan Ashbolt a few years ago', and described Moree as 'this centre of Australian "apartheid"'. Years later, Barrie Pittock and Ian Spalding both remembered the program as ground-breaking and ahead of its time.
Within three months of Ashbolt's program going to air, the question of racially segregated towns acquired a dramatic new resonance. In September 1957, the phrase 'Little Rock' became famous and in no time at all towns in New South Wales were being judged for their 'Little Rock' status. Little Rock, a small town in Arkansas in the United States, became a symbol of small-town racism when mobs of white parents and other segregationists stood outside its Central High School in an attempt to prevent African American students entering, as they were legally entitled to do after a Federal Court ordered the public schools in Arkansas to begin desegregation. The state governor, who sent the National Guard to ensure African American students did not enrol at the school, had supported the parents. President Eisenhower responded by ordering the military to Little Rock to ensure that the law was obeyed; at 5.00 a.m. on 24 September, paratroopers encircled the school with bayonets fixed, and several hours later nine black children were able to enter.
With the swimming pool resolution and Ashbolt's program in the public mind, Moree now became number one candidate for the Australian 'Little Rock' title. Reverend Alan Walker, in his National Aborigines Day speech in Sydney on 11 July 1958, spoke strongly of the ways in which Australia was failing Aboriginal people: 'In the past, white Australians pillaged Aborigines' land, organised mass killings of Aborigine people, even crucified them on crude crosses. No recompense can undo the past, but action can redeem the present and the future.' He deplored the fact that the Commonwealth seemed unable to act to ensure a nationwide policy: 'State rights are coming before human rights.' He then said: 'Ugly incidents showing the operation of a colour-bar are all too frequent. The shame of many country towns is the treatment given to the miserably housed Aborigine people on their outskirts.' Then came the crunch line, as far as Moree was concerned: 'Towns like Moree in New South Wales have far too much in common with Little Rock in America.'
Within Moree, there was some pressure to rescind or amend the swimming pool resolution. On the urging of a local teacher, a 21-year-old alderman, Bob Brown, moved two years later that the resolution be amended to let Aboriginal kids in school groups into the baths. There was no seconder. In a long interview in 1991, Bob told me he asked some of the aldermen privately why Aboriginal people couldn't be allowed in the baths. The answer was hygiene; they might spread sexual diseases like syphilis and gonorrhoea. So Bob went to Dr Hollingsworth, the state medical officer, and paid for a consultation to ask if you could get sexual diseases from the baths. Hollingsworth said the baths were a strange place to do the things you needed to do to get gonorrhoea—that is, you could only catch it from sexual contact. So Bob went to the next council meeting and said he had asked about getting sexual diseases from the pool and had found out from the doctor that it wasn't possible. The councillors still weren't convinced. Bob asked what else could go wrong. Someone (it wasn't clear who) said, 'You know how Aboriginal men would love to impregnate white women, well they could ejaculate into the pool and all this semen swimming around would make the women pregnant'. Bob said to us in 1991 that it might sound funny now, but he didn't know anything then, and went back to Dr Hollingsworth to ask if this could happen. Hollingsworth said no it couldn't, and anyway there was chlorine in the swimming pool and the hot baths were sexually segregated. Bob went back to the council and told them there was no worry there either. The councillors were unconvinced, however, and Bob lost his place on the council soon afterwards.
In an attempt to put an end to the baths issue, the town's Apex Club built a 25-metre swimming pool at the Mehi mission in 1960, with materials funded by the Welfare Board, local gifts and the club itself. This was a direct and explicit attempt to ensure Aboriginal children did not use the artesian bore baths. Mr Heffron, the state Labor Premier, who commented that his officiating at the ceremony did not signify his approval of segregation, opened both the pool and the new school. Later that year, an unnamed _Sydney Morning Herald_ journalist visited Moree, and wrote a glowing report on the Mehi mission, describing it as a credit to the board and the local citizens, though he did note that the town garbage dump was only half a mile away. Now, he reported:
Its 33 gaily painted fibro and timber cottages have an average of 10 inhabitants each. Each cottage has three bedrooms, a combined dining room-kitchen, shower recess and a laundry. Most are kept in perfect condition by the tenants and there is evidence of civic pride in the neat lawns and flower gardens surrounding them.
The station also had 'a recreation hall, a school, a sports oval and tennis courts', as well as the new swimming pool. The _Herald_ contrasted the mission favourably with 'Top Camp' and other shanty towns as places where 'many people are living in pig-sty filth'.
The question of racial segregation would not go away. Opponents of the resolution tried again in March 1961. After representations from the local high school headmaster and the Moree council's own Baths Committee to lift the ban on high school children, an amendment was passed allowing Aboriginal children to use the pool for Wednesday afternoon sport or 'on special occasions such as carnivals and training sessions'. Aboriginal adults and unsupervised children were still, however, to be kept away. Two months later there was further trouble—this time over the separate Aboriginal McMaster Ward at the local hospital, and the exclusion of Aboriginal people from other wards. The Minister for Health, W.F. Sheahan, announced that the government intended to ban racial segregation in all public hospitals, and that he had already asked the Moree District Hospital to end its segregationist practices. The chairman of the hospital board said any such order would be ignored, though some integration could occur with Aborigines who were 'good types'. The Mayor of Moree also spoke against the Minister's request, saying Aborigines did not wish to mix with whites, and that everyone was happy with the present state of affairs. The Minister replied: 'If we are to take our place among the nations of the world we have to be prepared to recognise the modern concept of the colour question, particularly in its relation to international obligations and treaties . . . there will be no segregation in hospitals built with public money by the government of this state except on medical grounds.'
This was not the view of most of the citizens of Moree. One former citizen, G.L. Hobson, wrote to the _Herald_ two days later about the segregated hospital: 'What in the world is wrong with this?' Faith Bandler also took the opportunity to liken Moree to Little Rock in the United States; it was disgraceful, she said, that white nurses there did not wish to care for coloured patients. The secretary of the Aboriginal-Australian Fellowship, Jack Horner, wrote to the Australian Trained Nurses' Association seeking its view; the association replied that it did not sanction racial discrimination.
The situation in Moree continued to attract negative comment in the Sydney press. Bert Groves wrote a letter to the _Sun-Herald_ in June 1963 criticising the growth of racial and colour prejudice in 'a flourishing town like Moree, where many children are attending high school'. Moree's racial discrimination was again drawn to urban and national attention with Graham Williams's articles in the _Australian_ in January 1965, the result of his trip with Charles Perkins and Ted Noffs. Williams reported that Moree hospital still had its 'traditional McMaster Ward for Aboriginal patients'. He also reported that the building of a pool on the mission had not eased Aboriginal people's resentment at being excluded from the bore baths—indeed quite the opposite; it symbolised their rejection by the white community. Williams asked the Mayor of Moree, by this time Councillor Bill Lloyd, about the colour bar at the pool. Lloyd was still new at the mayoral job; when the Freedom Ride students conducted their survey in February 1965, one Aboriginal respondent told them that 'the former mayor had not liked "dark people"', but he 'did not yet know what the new one was like'. At this point, Lloyd insisted that the manager had the right to refuse anyone who wasn't clean enough to swim in the pool, but that he couldn't comment further as 'I haven't got the text of the Council resolution before me'. He also told Williams that Moree had too many Aboriginal people: 'Every town can absorb only so many Aboriginals pro rata. Other towns should help share the burden.' And indeed the Aboriginal population at Moree was rising, reaching over 1000 in a total population of 7000 by 1965. The Mehi mission population alone had risen steadily from 283 in 1953 to 434 in 1965.
Six weeks after this story appeared, the Freedom Ride arrived in Moree. On the way from Walgett, we had stopped in the early hours of the morning at Collarenebri and slept for a few hours in the park, illegally. We got up early, at 6.00 a.m., in the hope police wouldn't see us, but later found we had been spotted, and furthermore our presence reported on the radio. We continued on to Moree, over a poor road with long unsealed sections, a distance of 130 miles (217 kilometres).
The students' bus arrived about 8.30 a.m., eight-and-a-half hours ahead of schedule thanks to the Reverend Dowe of the Anglican church in Walgett. We settled in at the Methodist church in Frome Street, where Ted Ryan, who had written supportively to Jim Spigelman in January, was the minister. Some of the students had been to Moree before. Not only had Darce visited in school holidays, but also John Butterworth had lived there for a while and had relatives still in Moree. Most of us, though, had never been there, and we had no Aboriginal or Aboriginal rights organisation contacts. The board report in 1960 mentioned an advancement association at Moree, but no other information about such an organisation survives, and there was certainly no effective organisation when the Freedom Ride arrived. Neville Kelly, who helped form the Moree Association for the Advancement of Aborigines after the Freedom Ride had left, told a parliamentary committee two years later that 'we had been talking about a society for two or three years before the students came here. That was the final thing. That kicked it off. We realised we had to do something.' So, without prior contacts, we would have to get in touch with the local people as best we could. Yet this was not Walgett, with its well-established leadership; in Moree, with its hierarchical and sometimes mutually hostile Aboriginal communities, we were met with suspicion and distrust.
A clue to Aboriginal attitudes in the affected towns can be gained from Isabel Flick's description of the feeling in nearby Collarenebri, where we had camped briefly on our way to Moree. Isabel told Heather Goodall years later:
When the Freedom Riders came out, everybody went quiet, you know. Everyone was scared I guess . . . Some of the women just didn't want to have anything to do with them, they wouldn't even let them go over to the Reserve if they came there, they said . . . Then the white people started saying to us: you fellas don't want to get mixed up with them . . . I remember dad saying to me: Well, you don't know what they are. There's a mob of them. They reckon there's a lot of white people on it. If it was black fellas I'd understand, but it's a lot of white people on there, so that's what's got me mixed up.
After the excitements of Walgett, the students spent the morning cleaning up, writing letters and sending telegrams to possibly anxious parents. Jim Spigelman, for instance, telegrammed his parents at 10.14 a.m., saying 'I am all right collect papers'. Charles Perkins got in touch with Ted Noffs, who reported to the _Herald_ that the trip was quite successful, having carried out surveys in 'Orange, Wellington, Dubbo, Gilgandra and Gulargambone' without any incident. Bill Pakenham, the driver, rang his boss at Saint's bus company and was told, as he later said to a _Herald_ reporter, that 'I was to take every precaution to guard the safety of myself and the bus'.
We then held a general meeting.
_Diary_ , _16 February_ : We discussed just what we were doing, and what to do about Derek Molloy and John Gowdie who . . . didn't really agree with our principles. We decided 27:2 with 1 abstention that everyone on the bus would be bound by majority decisions. This means the two who opposed demonstrations would have to join in them, or leave. They still haven't decided what to do.
In fact, Derek did leave the Freedom Ride at this point, but John stayed. He later wrote:
I had to decide whether to continue with the group or not. I couldn't just be an observer . . . My concern was with what the students were doing. There was no doubt—they were stirring up trouble. I did not question their concern for the Aborigines, which I shared . . . I was far from convinced about the confrontational approach of these city students. It was the most difficult time. I could see both sides. I did not agree with them, but I could understand the hostility of many in the white communities . . . Yet justice demanded and humanity demanded that change had to happen. Discrimination was overt. It was institutionalised. Prejudice was ingrained . . . Someone reminded me that Martin Luther King referred to 'creative tension' as a necessary element in the change process. Was this creative tension? I agonised and I prayed. To stay with the group or to go home . . . I stayed.
We decided to hold a big public meeting in the town the following evening. In the afternoon, the students split into groups to do the survey in the town.
_Diary:_ Sue Reeves and I met Mr Brown and he gave us contacts with the very few aborigines employed in the town.
This was Bob Brown, the young ex-councillor who had opposed the pool resolution some years earlier, and was at this time managing the family electrical business, which sold 'TV, Radio, Home Appliances, Furniture'. Given our lack of contacts in the town, he was something of a godsend, though he had known nothing about us and we nothing of him until we arrived. Here was a local white citizen with no links to any existing organisation, whether political, religious or community based. Bob was an unusual character, both very much of the town and yet so different from most of its white residents.
[Bob Brown, Freedom Ride supporter, standing outside his electrical goods store, Moree.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41151891)
When I visited Bob in 1991 (at Port Macquarie, where he had gone to live some years after, and to some degree because of, the events described in this book), he told me he was born in 1936 and grew up in a house across the river from 'Bottom Camp', later the Mehi mission, and knew Aboriginal kids in his childhood. He played with them and became friends with some of them. He was the son of a magistrate and businessman, who had been notably lenient towards Aboriginal people brought to court for drunkenness. Bob spoke of having come into a business quite young, and always having enough money and a pretty good life. Somehow (probably on the radio) he heard about the students and their bus arriving that morning, went around to the Methodist hall where we were staying and introduced himself to Charles. He told me:
I didn't think the students would actually do or achieve anything; they would just make a few pretty speeches. I thought I'd see. I only met Charlie Perkins two or three times, I hadn't met him before this and I never met him again [he did, though, only a year after this interview, when he appeared in Rachel Perkins's film on the Freedom Ride]. But I was impressed by the way he dressed, he was the first person I ever saw to wear a coat and good shirt with jeans.
With Bob's help, we looked for people to interview. Not surprisingly, given Moree's recent history, the Moree townspeople were reluctant to talk, and we were able to interview only about eight whites and ten Aboriginal people. Charles told reporters that the students had found discrimination at the pool and the school:
Aboriginal children from the mission settlement receive half an hour less schooling each day. This is because the bus that picks them up collects European children first, and delivers them to school before going to the mission. In the afternoons, the Aboriginal children are let out 15 minutes early to get the bus home.
One of the students, the _Australian_ reported, was told by a housewife to 'get to hell out of it', while a shopgirl being interviewed by a student was called away and sent to work in the back of the store by the manager. That night, we felt obliged to attend a film screening put on by the Methodist Youth Fellowship, in whose hall we were staying.
_Diary:_ The minister was very good, but then showed us a film . . . about how lovely life is in South Africa. A few of us walked out after about 5 mins in disgust and later learned that nearly all the SAFA group had walked out. Hall Greenland got up afterwards and made a statement about what apartheid meant. The minister agreed with us.
We had a drink at a hotel, and then went to bed early, about 10.30 p.m.
While we were recovering from our Walgett experiences, and doing our survey, representatives of the media began pouring into the town. The ABC, the _Daily Mirror_ and other media organisations all sent journalists up to Moree to join the tour, and most arrived that Tuesday, or the next day. Journalists and photographers were allowed a place on the bus if they paid £10 per head, and about seven did so. Although they travelled with us, the journalists were banned from most meetings, but were given regular bulletins of decisions. One of the most colourful journalists to arrive that day was Gerald Stone, who had migrated to Australia from the United States three years earlier, and was now working for the sympathetic _Daily Mirror_. One of the students, Judith Rich, at this point changed her status to become a reporter for the _Daily Telegraph_ on the tour. She was to find, though, that the _Telegraph_ 's attitude to the Freedom Ride was much more hostile than her own, and its use of her reports was limited. From this point on, journalists and photographers would accompany every student action, including the survey. Delighted by all the attention, the next morning the students continued their survey at both the Mehi mission and the Bingara Road ('Top Camp') reserve. The day before, the manager of the mission, Mr G.G. Ord, had granted the students permission to visit both, though he refused to say if he had been authorised to do so by the Aborigines Welfare Board. In fact, he had; the board had met that day, Tuesday, 16 February, and agreed that the students be granted permission to visit stations and reserves 'provided the Manager, Supervisor, and/or Welfare Officer is present'. It sent telegrams to the managers and area welfare officers in the towns the students wished to visit.
The contrast between the two communities clearly demonstrated the trade-off people made between material conditions and freedom from intervention in their daily lives.
_Diary:_ The mission had much better housing etc. than we'd seen anywhere, but there was a manager in control who was apparently very disliked and seemed rather unpleasant. The answers we got were very subdued and the fact that the manager and the press were wandering about didn't help. Then we stopped off at the Bingara Rd reserve where the conditions were terrible, same as Wellington, Gulargambone and Walgett. The people there were very friendly and spoke out for themselves. Many of them agreed to come to the big meeting we had planned for the night.
Pat Healy recalls: 'It was while we were at the reserve talking to the Aboriginal people about the swimming pool that the idea of picketing the swimming pool had come to the fore.'
Twenty-one of the survey forms for the 'Aboriginal Questionnaire' from the town, mission and reserve survive. A concern that comes through in many answers and comments on the forms is the lack of a water supply and sanitation services on the Bingara Road reserve. Gloria Tighe said the people would be 'quite happy on reserves if they only had water'. The main source of illness, some said, was the river water. Most said Aboriginal people should be able to get houses in town. Gloria Tighe said the former Mayor had stopped houses being put in town by the Welfare Board, and Nancy Tighe, in answer to the question 'What do you think should be done to help raise the health standards of your people? ', answered 'Get rid of camps.'
[Ann Curthoys and Louise Higham interview unidentified Aboriginal residents at the Aborigines Welfare Board Station, Moree, 17 February 1965.
(Photo courtesy of the _Tribune_ /Search Foundation)](chap7_9781741150575_epub_part7.html#d41151911)
Some of the additional comments related to the issue of social control. One person also reported that the former manager of the mission, Mr Redmond, used to allow parties and dances in the hall at the mission, but he had been removed and sent to Sydney and they now had a new manager who did not. Another respondent commented: 'Manager in reserve now terrible.' There were comments on police harassment. Gloria Tighe told her interviewer that 'they barge in houses without knocking— the men often have had only one or two glasses of beer—then drag them to truck without formally telling them they are being arrested'. The theme of police harassment appears regularly in these survey forms, and it was becoming a major concern for Aboriginal rights groups. Charles Rowley conducted a survey of police treatment of Aboriginal people around this time which showed clearly that arrests and charges of Abor-ginal people were high; Moree was one of the towns investigated. Police treatment of Aboriginal people was not the kind of issue that the Freedom Ride could act on, however, for it provided no clear symbolic case to which we could easily draw attention.
The survey and additional comments also showed evidence of discrimination in employment in town, especially female jobs, with one person mentioning that 'Coles will not employ Aborigines'. Most of the survey respondents reported widespread discrimination in shops, hotels, the picture theatre and the bore baths; the Astoria restaurant was also mentioned several times. The hospital, some reported, used to be segregated but was no longer (the McMaster Ward had recently been closed). Only one respondent advocated some form of political or community action to deal with the situation. When asked how the Aboriginal situation could be helped, Fred (surname illegible) replied: 'Form committee so the Aborigines and the white people can get together and solve problems when they come up . . . on your own you don't do nothing.'
The earlier reports of discrimination were thoroughly confirmed by the survey. The _Herald_ reported: 'The Sydney students, members of the Student Action for Aborigines Council [ _sic_ ], checked council regulations this morning on the use of the swimming pool.' They confirmed the continuing existence of the resolution of 1955, excluding Aboriginal children from the pool except for sports afternoons and school carnivals. John Powles asked five Moree doctors to sign a statement saying that the health standard of Aboriginal people in Moree did not warrant their exclusion from public swimming pools. The Town Clerk, Mr O.J. Jones, confirmed to the press that 'adult aborigines are not allowed into the baths. This has been a council rule for a number of years and I understand it has something to do with hygiene . . . the Aborigines have their own baths at the mission.'
After these visits and interviews, the students went back to the church hall and held a meeting to discuss their plans. There were many competing ideas and suggestions.
_Diary:_ It was a very heated meeting with a lot of dissensions and disagreements. But finally we worked it out to (1) Have 1hr picket outside the Council Chambers protesting against the swimming baths discriminatory clause; (2) Go to baths and take 6 aboriginal children in; (3) Hold big meeting in the night.
The students invited the Mayor to attend their public meeting that evening, and Lloyd at first agreed. The students printed a notice (perhaps with the help of the Methodist minister), which read:
TO THE CITIZENS OF MOREE
THERE WILL BE A PUBLIC MEETING TO DISCUSS THE
ABORIGINAL QUESTION IN MOREE
IN THE MEMORIAL HALL AT 8 PM TONIGHT.
THERE WILL BE TWO SPEAKERS—ALDERMAN LLOYD,
THE MAYOR OF MOREE AND MR CHARLES PERKINS
THE LEADER OF THE STUDENT ACTION FOR
ABORIGINES BUS TOUR.
* * * * * *
_ALL HUMANS ARE BORN FREE AND_
_EQUAL IN DIGNITY AND RIGHTS._
_(ARTICLE 1 OF THE UNIVERSAL DECLARATION OF_
_HUMAN RIGHTS)_
IS THIS SO IN MOREE?
Lloyd's promise to participate was withdrawn after he consulted his fellow aldermen, some of whom he found to be strongly opposed to the idea. He told the _Northern Daily Leader_ that, as a result, 'it was decided that the civic representatives, as a council, would not attend the meeting'. Aldermen, however, could attend as private citizens. Lloyd said 'inferences of racial discrimination at Moree had been grossly exaggerated, and were, in fact, far from correct'. He pointed out that the Moree Services Club (the Moree equivalent of the Walgett RSL Club) did not bar Aboriginal applicants. The hospital was no longer segregated, and a young couple from the mission had only recently had their wedding reception in the Memorial Hall. (Indeed, the local Moree paper, the _North West_ _Champion_ , had only a fortnight before reported this reception.) Aboriginal people frequently attended travelling shows in that very same hall. He acknowledged that there was a resolution discriminating against Aboriginal people in relation to the pool, and said the resolution, 'in his personal opinion, was harsh'.
We then embarked on the first of our three planned protests. We went to the Moree Municipal Council Chambers in Balo Street to protest against racial discrimination at the swimming pool. For about an hour, we carried placards saying 'Hotels and clubs are integrated, but not baths', 'Are you proud of your council?', 'Color is not contagious' and 'Why whites only?' Unlike in Walgett, where we had the element of surprise, our picket did not attract much interest. Jim's film shows that there was no one but us there, other than a policeman on a motorbike waiting nearby.
Moree Council Chambers demonstration, 17 February 1965. (The above photo appeared in the _Tribune_ , 24 February 1965. Both photos courtesy of the _Tribune_ / Search Foundation)
_Diary:_ We did the picket, but nobody much came around, and we all boiled, it was very hot.
The _North West Champion_ reported: 'A few people watched from the shade of the other side of the street, and only a group of children and an occasional adult stopped to discuss their activities with them.'
Next, it was time to go to the baths and take some Aboriginal children with us. Most of the students went with Bob Brown and a group of six children, probably from Thompson's Row, to the pool, while Charles went off to the mission to gather more children. Thompson's Row was a line of seven dwellings in Maud Street, on the fringe of the town, about 300 metres from 'Top Camp'. The houses were old weatherboard cottages that once belonged to the employees of Thompson's soap factory, and the area was sometimes called Soapy Row. One of the Aboriginal women, Granny Duncan, had cleaned for Mr Thompson; as the workers moved out when the factory closed, her extended family moved in. Their standard of living was similar to that of the white labouring class, and they generally sought acceptance in the white community. Most of the women had worked as domestics on pastoral properties.
Those of us at the pool with the Thompson's Row children then tried to enter. On Jim's film you can see Sue Johnston carrying a young Aboriginal child, and the other children waiting to enter. Darce recorded the following exchange at the ticket window:
_Student:_ I've been waiting for half an hour. Will you serve me please?
I want six adults' and eight children's tokens.
_Manager:_ But I'll tell you this. If they haven't got the health regulations, how would they get on? They could bar me from going in if I had sores or anything on me.
_Brian Aarons:_ Yes, but that's not the reason they're barring them. You go and read the council motion: the law of the council says that no Aboriginal, part-Aboriginal, any person who's got Aboriginal blood is allowed in the baths . . .
_Bystander:_ You've come up here, we're living in peace, we're living in peace until you come up.
_Wendy Golding:_ In apathy you mean, in apathy! You just don't do anything about it.
Wendy recalled, when we interviewed her in 1994, that when she heard Darce's program on the ABC many years later:
I remember recognising my own voice on that tape at Moree. And I was screaming furiously, 'You're so apathetic! You just don't care!' Because I think I thought that that was in fact a lot of the root of the problem, that the racism was very passive in many ways. There was no emotion almost attached to it. It was just sort of 'That's the way it was' and there wasn't any evaluation as to the rights and wrongs of it, it was just life in the 1960s in small country towns.
Darce interviewed Bob Brown, who was at the pool:
_Darce:_ Bob, you've lived in Moree all your life. How do you think these people here regard the Aborigines?
_Bob:_ Definitely not favourably, but the biggest problem here is not disapproval, it's plain out and out apathy. The thing that we're trying to fight is that they don't care . . . We have approached people in the street to sign a petition to have the motion on the council books barring Aborigines removed, and from personal experience, the people who would have signed a petition to open up a dogs' home or any sort of charitable institution at all are definitely just against Aborigines.
Darce also interviewed one of the bystanders:
_Darce:_ Do you think everything's right in Moree, or that something needs to be done?
_Bystander:_ I think that the Aborigines will probably be assimilated in time, but at the moment the standards of hygiene and so on are just not good enough to mix with the other people in the town.
_Diary:_ The manager refused to let the six aboriginals in and so we held up our posters and signs.
The _Australian_ reported the manager, Don Ford, as arguing heatedly with the students' leaders for almost an hour. The Mayor, four policemen and Matt Munro, a Waterside Workers' Federation (WWF) organiser up from Sydney, all watched the demonstration, and a crowd of about 100 began to gather at the pool. After some consultation, the Mayor, pool manager and police agreed that the children should be allowed in.
Charles Perkins queues with Aboriginal children at the Moree pool.
[Charles Perkins swims with Aboriginal children in Moree pool on Wednesday 17 February ( _Australian_ , 19 February 1965, p. 4). The original caption read: 'Mr Charles Perkins, the part Aboriginal student leader, frolics with children in the swimming pool he helped desegregate.
(Photo courtesy of Newspix)](chap7_9781741150575_epub_part7.html#d41152031)
At this point, Charles arrived with a busload of over twenty Aboriginal children from the mission, and they too were allowed in. Jim's film shows Aboriginal children diving and swimming in the pool. The photographer from the _Australian_ took photos of Charles and the children in the pool; one photo has been much reprinted since, an enduring image of desegregation in action. The Mayor and pool manager were emphatic in their statements to the press that they would have been allowed in anyway. Mayor Bill Lloyd in particular was concerned at the image of Moree: 'I am afraid, with all this ruckus, our actions may be gravely misconstrued by those living outside Moree.' He went on: 'In recent years, despite the now-outmoded council regulations, I have never refused permission for an aboriginal child to enter this pool, provided the child was clean and healthy.' Charles insisted that this was not the case: the children, he said, would have had 'no chance' of getting in without student help. Charles also spoke to some white children at the pool, whose attitude, according to my diary, was 'rather ambivalent'.
High on our success in having forced the manager to allow the Aboriginal children in the pool, the student bus took the children back to the mission. Darce recorded some of the singing, featuring, somewhat remarkably it seems to me now, a song 'Stomping at Maroubra', with several verses and the chorus:
Stomp, stomp, stomping at Maroubra
Everybody's doing the Maroubra stomp.
On the tape, you can hear everyone joining in.
_Diary:_ A little girl with a fantastic voice led the singing and we sang Beatles songs all the way back. The spirit was tremendous. We all got out of the bus and everyone was running around getting their photo taken, and swapping addresses.
In 1991, I met that little girl again. Zona Craigie (now Moore) had grown up in Thompson's Row, had married a white man and had seven children, and now worked at the Commonwealth Employment Service office. She had done a TAFE course for two years, she told me, so that she could get the kind of job she now had. Zona remembered having been on the bus that day, including the singing, and knew there was a tape around with her on it.
With the pool visit a great success, the students' next action was to hold the meeting at the Memorial Hall in the evening. There were about 300 people there, mainly white. One of the Aboriginal people present was 15-year-old Ernie Crighton, then working as a labourer for the shire council. He remembered the meeting well when I interviewed him in 1991. The council workers, he said, were all told that if they went to the meeting they would be sacked. They went anyway, and in the end they weren't sacked. Jim Spigelman spoke first, explaining (according to my diary) 'who we were and how we came to be there. Then John Powles, on the survey. Then Charles.' The meeting was then thrown open for public discussion. At first the atmosphere was very hostile, with lots of jeering and interjections. Hecklers shouted such questions as: 'Why don't you mind your own business?' Some locals said: 'Aborigines are dirty and lazy people', and the students retorted: 'You are just ignorant and prejudiced.'
_Diary:_ The questions were sometimes antagonistic but there were some very sympathetic ones too.
The meeting calmed down after some people left the hall in anger. Charles quietened the meeting when he said: 'I'd like to paint you black and put you in a tin hut and see how you'd make out.' The atmosphere became quite humorous and friendly, judging from Darce's tape. Ken Swann, an Aboriginal resident of Thompson's Row, spoke, saying his own children had been denied entry to the pool.
One of the main issues for debate was the sincerity of the students. Bill Forrest, an ex-police sergeant, defended them:
I feel very much in sympathy with the reason why these gentlemen have come here today . . . My wife and I have had a lengthy conversation with [two of] them, and I know first hand that there is a vast difference between their purpose and that suspected by quite a lot of people who don't want to understand.
In reply to a question as to whether the students were 'fair dinkum', Charles said:
Now this is a funny sort of question. It's costing us £800 to come up here and do this tour right around for two weeks. Two weeks of hard labour . . . we're sleeping in sleeping bags all the time on hard board floors . . . We're paying for this, we're paying for this with concerts we've had at the University of Sydney, folk concerts etc . . . Nobody's sponsoring us in any way, so you don't have to worry about any outside influence. We're only university students, and that's all we claim to be.
Charles had worked hard to maintain this independence and freedom from outside assistance of any kind. During that day, he had received an offer of help from Matt Munro, the WWF organiser who had arrived by car with Noel Hazzard, the _Tribune_ reporter. Munro had offered Charles a donation of £100 worth of amplification equipment for demonstrations. Anxious to deflect any charges of communist influence, Charles turned down the offer; he told the WWF that the students 'had no wish to become associated with any particular body or organisation'.
At the end of the meeting, Neville Kelly, president of the Moree branch of the ALP and secretary of the Barwon ALP State Electorate Council, moved that the clause in the statute books about segregation in the swimming pool be removed, a motion seconded by Bob Brown. The motion was passed 88 votes to 10, the _North West Champion_ reporting that only about half of those present voted. Alderman Charles Jones was in the audience in a private capacity, and undertook to convey the resolution to the Moree Municipal Council at its next meeting.
_Diary:_ We were all thrilled to bits. Then we invited the people to come to the church hall for tea and coffee, which a lot of people did. That was pretty good. Then a lot of people got into all sorts of discussions.
In an interview, Charles subsequently said that:
Later in a more or less private meeting in a church hall I debated with about 40 young people who wanted to speak to me privately about this whole issue. It was an intense, organised and very good debate on every aspect of the Aboriginal situation in Moree. There was a significant change of attitude among quite a number of them.
We students were on a high. We had 'desegregated' the swimming pool, and had also held a successful public meeting which held out promise of a permanent change in attitude in Moree. Before we left, we arranged that Bob Brown would test the desegregation of the baths by taking another group of children to the pool the next day, this time not only from the mission but also from the Bingara Road shanty town. Charles told the press: 'If we hear that there is any trouble, we will come straight back to Moree. If necessary, we will picket the baths and the council chambers to try to eliminate discrimination against any aboriginal children, no matter where they come from.'
We didn't think a return visit would be necessary, however. Believing we had more than achieved our aims, we set off the next morning for the next town. We had done with Moree . . . or so we thought.
_Ch_ _apter_
_6_
Clash at Moree
The Freedom Ride was growing more interesting to the media each day. The urban press coverage of our two days in Moree was as extensive and as sympathetic as we could have wished. The _Australian_ 's report on Thursday, the day we left town, was headed 'Students Crack Pool Color Bar at Moree'. Its editorial was headed 'Facing Up to Facts', and was concerned primarily about Australia's image abroad. The Freedom Ride, it said, was making it clear that 'there is in Australia widespread discrimination against Aborigines'. This was potentially a matter for some considerable international embarrassment:
It is important for us in Australia to be able to hold up our heads before other nations, showing that we do not have any dirty racial practices which we are trying to keep hidden from the rest of the world, where many nations are having to face racial issues squarely and honestly as part of an attempt to grow up. Australian discrimination against, and generally shabby treatment of, Aborigines is becoming increasingly well known and discussed around the world. Any sensitive traveller can report his own experiences on being closely questioned on this matter.
The _Australian_ followed up the next day with another report on the students' stay in Moree, which included that striking photo of Charles and the children in the pool.
The _Sydney Morning Herald_ featured the Freedom Ride on page 1 on Thursday, 18 February. Its lead story was the survey at the Bingara Road reserve, with a photo of Brian Aarons interviewing an Aboriginal family outside a tin shack. Below that photo was another, of two boys—one white (Gary James) and one black (Richard Brown)—walking to the Moree Public School; it was intended to show that the school, at least, was integrated. When I visited Moree in 1991, Darrell Crighton, who ran a milk bar—one of the very few Aboriginal-run businesses in the town— told me Richard Brown was now a boxer who worked on a property, and Gary James was a member of the council and owned land. That same issue of the _Herald_ also carried an informative story about the demonstration at the baths. The following day, the _Herald_ 's editorial said the residents of Walgett and Moree should welcome, not resent, the Freedom Ride: 'The students' mission is commendable evidence that 35 young Australians care sufficiently about the future of aborigines to forsake Sydney's tempting summer beaches and go into the field in search of answers.' It approved the students' refusal, led by Charles, to 'lend themselves to any log-rolling Left-wing group that seeks to exploit a social problem for its own benefit' (a clear reference to the Waterside Workers' Federation, or the Communist Party). The students were finding segregation in action, and the _Herald_ predicted that 'it will continue, openly or surreptitiously, until a great deal more is done by Governments, local authorities and individuals to diagnose and eradicate the causes and fears which prompt segregation'.
Gerald Stone's first report for the _Daily Mirror_ , on Wednesday, 17 February while we were still in Moree, emphasised the non-violent ethic of the tour, and reported Charles saying that 'any student freedom rider who tried to hit back if assaulted would be sent home immediately . . . Otherwise our whole plan of passive resistance would be a failure'. His second report was headed 'Moree Win to Students'; it covered the public meeting and its vote to end the official ban against Aboriginal people at the baths, and ended with Charles's comment: 'I think we have accomplished quite a great deal in Moree.' Interstate papers also covered the demonstration in Moree, often with front-page stories. There was relatively little immediate rural press coverage, as many papers came out only bi-weekly or tri-weekly. What there was, though, was somewhat hostile. The _Northern Daily Leader_ headed its story 'Racial Discrimination at Moree "Exaggerated"', a quote from its interview with Mayor Bill Lloyd.
The broadcast media were slow to cover the Freedom Ride. The promised _Seven Days_ crew had not arrived, and there were no other television crews from either the ABC or the commercial channels. For this reason, the only film footage of the events to be narrated in this chapter comes from Jim Spigelman's super-8 camera. However, the ABC _Four_ _Corners_ television program contacted the Freedom Riders in Moree and arranged to fly both Charles and the Moree Shire Clerk to Sydney for a televised debate on Friday. And ABC radio, though it had a reporter on the spot in Darce Cassidy, neither used his material nor sent another reporter along. Local radio stations reported the Freedom Ride, though it is difficult now to retrieve any information on their coverage.
Meanwhile, the Freedom Ride was pressing on. We left Moree at 9.30 a.m. on Thursday, arriving at our next stop, the tiny town of Bogga-billa, in time for lunch. It was a straight journey, with no towns on the way, though there were lots of tracks running off from the highway to the stations and properties. It was rich pastoral country all the way.
I remember with unusual clarity the lunch we had that day on the Freedom Ride in a wonderful beer garden shaded by grapevines. Many of the other Freedom Riders recall it too. Pat: 'I remember a pub in Bogga-billa. I was so hot and it had wonderful cold beer, and the beer garden was covered by a grapevine with great huge bunches of grapes hanging down, and here we all were, helping ourselves to the grapes.' And Brian: 'The main thing I remember about Boggabilla was when we arrived it was lunch time and very hot . . . Grapevine over a pergola in the pub, probably the first light relief we'd had . . . I can remember that being a particularly good fun afternoon.'
[The bus stands outside the Hotel Boggabilla, where students rested before interviewing people at the Aboriginal station.
(Photo courtesy of the _Tribune_ /Search Foundation)](chap7_9781741150575_epub_part7.html#d41152081)
I tried to recapture this idyllic moment when I revisited the town in 1991. We found the only pub in town and went in. I wanted to see if it had the grapevines I remembered, or at least the pergola. It had neither. There was an unkempt, unused-looking outdoor beer garden space, guarded by a huge unpleasant black dog. It must have been the same place, but it didn't match my memory at all. We had a beer there, but it was a very unfriendly white outback pub, with only a few old regulars stuck around the bar, watching a motorcycle race on TV.
Back then, after our all-too-brief idyllic moment, we went to the Aborigines Welfare Board station, 9 miles (14 kilometres) out of town, at the junction of the Dumaresq and Macintyre Rivers. We had only the afternoon to spare, as we had to be in Warwick, over the Queensland border, by nightfall. (By travelling interstate, we avoided paying about £250 in road taxes that would have been imposed for a 1400-mile (2240-kilometre) intra-state journey.) The station had been established in 1938 as one of the board's 'model' stations, on 450 acres (180 hectares), with a manager—Norman Clarke—who was, according to Jack Horner, 'friendly, humane, and endowed with humour and common sense'. Its population was drawn from the people on the old Toomelah station nearby and from the small border town of Texas, about 50 miles (80 kilometres) up the river. By 1965, there were 238 people living there, in crowded and dilapidated conditions. There were weatherboard houses, very often without windows and doors, no gas supply and no electricity. There was no clean water laid on, though river water was piped to taps in the yard. A cyclone had damaged many of the houses the previous year, so there were now leaking roofs, broken windows and corroded fireplaces. An estimate of £14 000 for repairs had been held over by the board due to insufficient funds, and it showed.
As in Moree, we now had the media in tow. The manager, a Mr R. Sawtell, appeared to want to use our visit to shame the government into granting the board the held-over funds. After he greeted us, we wandered around and spoke to several people, many of whom invited us into their homes. Warwick Richards recalls the women complaining about the shocking living conditions. Alex remembers: 'We were taken down by the riverbank to see where the water supply had come from.'
_Diary:_ Many of them told us that the manager had told them not to answer our questions, but they intended to do so anyway. The manager and press wandered round authoritatively, making this difficult. Even so the people were the most talkative, cooperative and straightforwardly critical of all the aborigines we've met.
Beth Hansen has especially strong memories of Boggabilla:
Pictures in my mind of the houses at Boggabilla and the manager's house, with this white fence, shrubs, green lawn, sprinkler going. And then everything else there was like a dustbowl. The school, little infant kids going in or coming out of the door. Quite a way out of town, 7 or 8 or 9 miles [11–14 kilometres] out of town. I'm sure I would recognise the manager's house again.
_Diary:_ We heard some terrible stories such as the fact that the police came in the houses without knocking whenever they liked, to find out who had been drinking. Also they 'did what they liked with the women'.
Warwick Richards also remembers women telling us about the police. He recalls: 'Most of the girls become domestics, and according to the ones I spoke to the conditions are terrible. The men are usually shearers. Everyone we spoke to agreed that they would rather live in the town than on the reserve.'
There was not much to do there, apart from the surveys. The completed forms that survive confirm my diary account and Freedom Riders' memories. The pressing issues were felt to be not so much employment or discrimination in shops and hotels as police harassment and the need for better housing, either on the station or in town, and for clean water and sanitation facilities. Yet our main purpose by this time was not so much the survey itself as to take the urban media to a particular settlement and say, 'Look, isn't this awful?' The media obliged, with both the _Herald_ and the _Australian_ reporting the next day that the students had described the Boggabilla station as (in the latter's words) 'the worst Government mission we have seen on our trip'. The 25 mission houses containing 240 Aborigines were reported to be in a disgraceful state. The manager, Sawtell, said: 'I must agree. The houses are badly in need of repair. I made representations to the Aboriginal Welfare Board in Sydney to have the repairs made and as I understand it the request was approved. However, a delay has developed somewhere along the line.'
Warwick recalls: 'At the end we got them all together and Charlie gave a bit of a speech saying we would try to do something about the houses, and that they should write to the Welfare Board. They were very enthusiastic.' The visit over, we got back on the bus, cheered by about 50 Aboriginal people on the station, and drove straight to Warwick, just over the Queensland border. We arrived about 9.30 p.m., ate at an all-night café, and then went to yet another Methodist hall to sleep. Our plan the next day was to visit Tabulam, supposedly a model station in Bundjalung country in the far northeast region of the state, travelling on to stay that evening at nearby Lismore, not far from the coast.
Events in Moree that same day threatened these plans, however. While we were on our way to Boggabilla, the pool manager, Don Ford, announced that the ban on Aboriginal children from the 'up-the-river' shanty town (at Bingara Road) would not be lifted. 'The people live in dirty tin huts,' he said, 'and there are no washing facilities and no proper toilets. There is a good chance some of the people have a disease. That is why nobody from the up-the-river will be admitted to the pool.' The children who had been allowed in on Wednesday were from Thompson's Row and the mission and had been judged clean. But anyone from up the river could not come in, 'no matter what their appearance'.
The stage was set for further confrontation. On Thursday, as arranged, Bob Brown tried to take about six Aboriginal children into the pool. Ford and Bob engaged in a heated argument until finally, at 5.30 p.m., Ford closed the baths early (they usually stayed open until 8.00 p.m.). Bob told television reporter Peter Martin, who arrived with the _Seven Days_ team a few days later:
I took six small Aboriginal children running from 3 to about 14 to the baths with me. They're friends of mine. And we were refused admittance. And we stood in the queue to buy a token and we refused to move from the window until we were sold a token. As they wouldn't sell us a token we wouldn't leave. And that prevented anybody else from buying a token. After half an hour the baths were entirely closed.
At 7.00 p.m. the Mayor arrived, fresh from an emergency meeting of council. He ordered Ford to reopen the baths, and to enforce the 10-year-old segregationist statute. He told the press: 'The council met in extraordinary session and we have now given the baths manager a written statement to guide him.' The baths were then reopened. By this time, Bob had returned with yet more Aboriginal children, all of whom were turned away. A large crowd gathered, several nasty arguments broke out and police had to clear people from the scene.
The next morning, Charles flew from Brisbane to Sydney for the _Four_ _Corners_ television interview; the rest of us travelled on the bus from Warwick to Tabulam. When we arrived in Tenterfield, halfway to Tabulam, we rang Bob Brown and he told us what had happened. We then rang up the Reverend Ryan, who confirmed this news and told us not to come back because we weren't wanted, and Neville Kelly, who also confirmed Brown's story. We rang Don Ford, who passed on the call to Bill Lloyd, at the baths at the time, who told us that we would not help our cause by returning. While this was happening, the press also ascertained from the Mayor himself that the report was true. He told the _Australian_ : 'If the students return they can only cause trouble. It seems the situation in Moree has been set back ten years overnight. I feel we had a very happy community here before the students arrived. Now, families are split on the issue of integration.' He also said that he had invoked the 1955 ordinance 'merely to deal with an unruly situation. The council would still consider rescinding the 1955 regulations.'
So there we were in Tenterfield, without Charles and with a critical decision to make. We held a general meeting to decide whether we should return to Moree. We excluded the press, and feelings were quite heated. Wendy remembers a vigorous debate, with a number of impassioned speeches being made:
I felt really strongly that we should go back, that it was no good to just be these ivory tower university students flitting in to the town and leaving again and basically leaving them to deal with all the problems that we had probably stirred up and created. And I thought the least we could do was go back and give moral support and by going back demonstrate that we really did care and that it was an important issue that should be dealt with. So I remember arguing passionately about going back.
We decided, after much discussion, to return to Moree. Alan remembers: 'We thought, well, we don't have any choice, we have to go back. Otherwise what's the point of the whole thing? We have to make it clear that we'll keep on, which we did . . . We really didn't have any choice, otherwise we would have turned the whole thing into a farce, so we had to go back and take whatever came.' We decided to go straight to Inverell, leaving out Tabulam, and reunite with Charles who could arrive by 9.30 a.m. the next day. From there we would all go straight to Moree and take strong action of some kind, such as a 24-hour picket. The decision, my diary tells me, was unanimous. The driver, Bill Pakenham, again rang Mr Saint, his boss, seeking advice. Saint told him to stick it out as long as he could.
Pat Healy remembers that we didn't want to tell any of the press because we didn't want any publicity about the fact that we were going back to Moree. We wanted to slip in quietly. We pretended until the bus got going that we were still going to Tabulam; the press, Pat remembers, 'were very irate and talked about kidnapping' since they hadn't been told where we were going. They explained we could, and should, have told them what we were doing 'off the record'; it was not necessary to play games. We stopped at Glen Innes for half an hour, where Robyn Iredale left to catch a train to Sydney to attend to her very ill mother. Robyn recalled: 'All I remember was worrying about how I'd get on a train, where would I get on a train, because after the bus incident, that's when I became really concerned that my mother would be really worried about me. I felt that I shouldn't cause her that sort of anxiety in the state she was in, so it'd just be better to go home.'
While we were on our way back on the Friday, another 40 Aboriginal children again attempted to get into the pool. As Bob Brown told Darce the next day: 'They were all refused except for one incident when four girls in the one family went up, and two of the sisters were admitted and two other sisters were rejected.' Mrs R Briggs, from Thompson's Row, told the press: 'Yes, two of my daughters were allowed into the pool and two made to stay outside—they said the eldest were too dark.' Gerald Stone remembered this incident well when interviewed in 1994: 'One of the classic cases I remember from Moree was an Aboriginal woman, part-Aboriginal woman, with four children of different skin tones and the two lighter ones were allowed into the Moree baths and the two darker ones were not. And that was such a blatant act of discrimination.'
The students arrived at Inverell at about 6.30 p.m. On the radio we heard that we were still going to Tabulam, so the news had not yet leaked out. We rang Charles, who was very enthusiastic about our returning to Moree, and apparently Ted Noffs agreed with him. He told us he had been met at Sydney airport by a flood of pressmen, and also by Bill Ford and Ted Noffs who took him to the Channel 2 television station and briefed him on what had been happening in the city since he'd left. That night, we settled down to sleep on the ground in the park behind the Twin Swans Motel in Inverell. John Powles remembers:
getting rather a sense of thrill and excitement because we would listen to the radio and there was this kind of—seemingly no one knew where the bus was—so we were a kind of mystery group travelling through, no one knowing where we were, but there were rumours that we were on our way back. And I remember we slept overnight in a park somewhere and there were just sort of bits on the news of the bus having been sighted here there and everywhere and so on.
As we settled in, the reporters finally had a chance to ring in their story. The stage was set for our biggest confrontation yet.
_Saturday, 20 February 1965_. We began the day in the park at Inverell, waking early, covered in burrs from sleeping on the ground. We knew this would be a big day. Mayor Bill Lloyd issued a warning that the students' return could only cause harm, which we heard on the radio over breakfast. By this time, everyone knew we were on our way back, the newspapers reporting that the students had decided to return to Moree and were due early that day. Our first task was to pick up Charles; Jim's film shows us all meeting him at the airport with our banner. We then travelled on to Moree, debating tactics in the bus on the way. As Darce recalls:
By now these debates had become a feature of the trip, which had become an exercise in travelling direct democracy. The debates happened not only in the towns, but almost continually, including while travelling in the bus using the microphone installed in the bus for the purpose of the driver describing points of interest to tourists, but in our case for continual discussion of objectives and tactics.
Charles Perkins rejoins the Freedom Ride at Inverell Airport after his interview on ABC Television in Sydney. (Unpublished _Mirror_ photograph. Photo courtesy of Newspix)
We knew this was crunch time. As Jim said in this on-bus debate recorded by Darce: 'If we break through here it doesn't matter if it's only one place, it's signalled, it's an example.' So the stakes were high. Yet it was a dangerous situation. Jim said: 'I think we're going to find a lot of hostility on the part of the white people; we're going to find ourselves more and more in this town aligned mainly and largely and almost completely with the Aboriginal people.' There were some difficult questions. How long should we stay in Moree? What should we actually do when we got there? Jim emphasised the importance of staying: 'I'd like to suggest that we don't just run in now and leave six hours later . . . I think we should go for something like a twelve-hour picket or a 24-hour picket of the pool.' This, though, would take us into a Saturday night. Charles warned: 'Saturday night is a very dangerous night in a country town, extremely dangerous, because about midday a lot of people will be pretty drunk and a lot of people will be pretty steamed up.'
We arrived in Moree about 12.30 p.m. and it was already a hot day, with the temperature to rise to 100 Fahrenheit (38 C) during the afternoon. We went first to Thompson's Row, only to find that the people there did not want to support our protest. That morning, Alderman Charles Jones—who was also president of the Moree Swimming Club— had arranged for the Thompson's Row Aboriginal children to be given swimming club tickets, which meant that they could enter the baths at any time. The children from Bingara Road and the mission were not given tickets, and were refused entry. We were disappointed the Thompson's Row people did not want to help.
_Diary:_ The Thompson's Row people obviously felt little or no sympathy for the other aborigines and were not prepared to fight for them. A case of 'divide and rule', as most of us soon realised.
Charles also remarked when interviewed in 1993 that 'some Aboriginal people were against us doing that [protesting] because we were disturbing everything. They were comfortable even in their disadvantaged and second-class position. At least they knew their place, in that sense, and they were happy with that.'
Our next task was to gather children from the mission and the Bingara Road reserve. Bill drove the bus to the mission gate but refused to go any further, so Charles and Beth walked in. Despite their having permission, the manager wouldn't let them stay, so they only had time to ask about four or five of the children at the main gates to come along. Charles told Ord, the manager, what he thought: 'You have,' he said, 'revealed your true nature.' Meanwhile, Bob Brown took Sue Johnston and Chris Page by car to get some children from the Bingara Road shanty town. The rest of us congregated at the shop opposite the baths, at the corner of Anne and Warialda Streets, and very quickly a huge and noisy crowd gathered. Brian remembers us engaged in discussions with the crowd: 'They were angry that we'd come back and they were angry about what we were on about, but they weren't, you know, vicious or threatening physical violence at that stage.' Meanwhile a crowd was gathering at the Victoria Hotel, also across the road from the baths; many of them were shearers in town on a free Saturday afternoon. It was a much bigger crowd than one would normally expect in Moree. When I talked in 1991 to Lyall Munro Snr, he said some of the graziers had given their shearers (both Aboriginal and non-Aboriginal) time off to go to the demonstration, presumably to take part in expressing opposition to the students. He himself had been shearing at Barney Amis's, and came into town for the demonstration. The railway workers, he told me, had also got time off to participate.
We had to wait quite a while for Charles, Beth, Sue, Chris and Bob Brown to arrive. When they did at 2.30 p.m., we all crossed the road and went to the pool. The hotel crowd poured across the road too. According to the Brisbane _Sunday Mail_ , Bob Brown 'was grabbed by local youths when he arrived at the pool. He was carried bodily to the front of the pool and dumped in a gutter.' There were nine children altogether, and when Charles sought tickets for them, they were refused. The baths manager offered to admit Charles himself, but he would not enter without the children. We lined up behind the children, continually requesting permission to enter. Brian remembers that: 'Charlie would say, "I would like to exercise my right as a human being" or whatever the words were "and seek entry to this pool", but was denied permission.' Colin remembers Charles also talking to the crowd to a lot of hissing and booing.
[Charles Perkins waits with children from Moree Aboriginal Station outside Moree swimming pool, shortly before attempting to enter, 20 February 1965. _Daily Mirror_ , 22 February.
(Photo courtesy of Newspix)](chap7_9781741150575_epub_part7.html#d41152121)
Bill Lloyd then arrived. He told me when I interviewed him in 1991 that he had been at the State Emergency Service, talking to the director and some VIPs, when an urgent message came that there was trouble at the baths. He left the function, and went straight to the baths. 'You students,' he told me, 'were doing your passive resistance, obstructing entry to the baths.' When he arrived, the crowd was steadily growing in size and hostility. 'It was a frightening awesome thing,' he remembered, 'a crowd out of control.' Some people in the crowd, he said, were Aboriginal. The crowd continued to build up to about 500, and it was getting ugly. People began shouting 'Get back to Sydney', and calling names.
A call went out for all available police in Moree and the surrounding towns to come to the baths. About 40 arrived, including a superintendent and inspectors. Charles noted in his book, _A Bastard Like Me_ , in 1975:
The police had received instructions by this time from the Labor Party which was in power in New South Wales at that time, to lay off us. 'Don't do anything that will cause any controversy with these people. Go with them as far as you can', seemed to be government advice to the police.
With these instructions, the police refused to move the students away from the pool, telling Lloyd it was his problem. Lloyd later told me that he rang two solicitors in town for advice, but they couldn't help. 'I was on my own . . . I had only a couple of council employees and the baths manager to help me.' It is clear from Jim's film, too, that the police did little, and that it was the Mayor himself, the baths manager and a couple of others who tried to remove the students from the scene.
We students didn't know about this behind-the-scenes conflict at the time, but we did realise that the police were handling us very carefully. Beth remembers that the Mayor and the police 'very politely asked us to leave and we didn't so they escorted us away. The police were there but I think it was the Mayor and the council officials who escorted us away.' And indeed it was. Jim's film clearly shows the baths manager leading Charles, Paddy, Pat, Wendy, Helen and others, and the Mayor himself leading John Powles, Louise, Beth and Pat (again) away from the pool.
_Diary:_ Charlie went to the front of the line and when he refused to move was grabbed and taken away from the line. Then John Powles,
The students and the crowd outside Moree pool. (Taken by _Mirror_ photographer, Neville Whitmarsh)
[Charles Perkins is led away from the pool. _Daily Mirror_ , 22 February 1965.
(Photo courtesy of Newspix)](chap7_9781741150575_epub_part7.html#d41152201)
Lou, Beth, Alex, myself and a couple of others were removed by the mayor first asking us if we would move, us saying no (individually) and then they put their hand on our back and took us away from the line. Chris Page sat down and was carried off by the two council employees. Those of us who had been walked off were prevented from rejoining the line as we had intended.
While this was going on, angry discussion broke out everywhere. Darce recorded some of the abuse:
The only good one's a dead one [referring to Aborigines].
As far as I'm concerned run the lot of them clean out of this swimming pool. Every one of them.
_Darce:_ And the university students?
They're the ones who caused the trouble in this town.
Run them out of town.
Get them out before night.
Get out real quick or get out on a stretcher.
There'll be a blue on for sure if it keeps going.
All the big rockers will be round. They'll hunt them out.
The police, my diary records, 'cleared everyone away from the entrance except us, and during all the mess those of us who had been marched off managed to sneak back. The police obviously didn't know what to do.'
Bill Lloyd left the scene briefly to attend the opening at the courthouse of the Gwydir Valley flood warning radio network. When he returned at about 4.30 p.m., it was clear that the situation was getting worse. Police Inspector Steer told him the students must be got out of town; the hostility was turning from verbal abuse to physical violence. The crowd began to attack the students with eggs and rotten tomatoes. Bill Lloyd told me: 'I saw respected businessmen there, throwing tomatoes, eggs and other things. I learnt then how awful a crowd out of control could be. The whole thing was getting out of hand.' Brian remembers that 'the crowd started to turn nasty and started to throw eggs. I can remember being in this line . . . along the building . . . and looking out along this stretch of grass and these eggs would be flying—you know, they'd be thrown quite high to get over the police . . . They were splattering everywhere.' Beth remembers Bob Gallagher having an egg smashed over his head, and Bob recalls that he 'got on the front page of the _Herald_ [ _sic_ ] I got an egg on the back of my head'.
As the students continued to try to have the children admitted to the pool, some of the students were physically assaulted.
_Diary:_ Jim S was punched and knocked down in the course of an argument. He lay quite dazed on the ground for a few seconds.
Gerald Stone reported in the _Daily Mirror_ that Jim was 'knocked to the ground after being hit in the stomach and on the chin by two youths'. Jim recalled in a 1993 interview being knocked to the ground and said 'you could really feel the aggression, it was a very violent day'. The _Mirror_ also reported that another student, 'Mr John Butterworth, 20, of Turella, had his glasses smashed. Other students, including girls, complained they had been burnt with cigarette butts.' Darce was knocked over, with his tape recorder, and this helps explain why relatively little of this afternoon's events was recorded on his tape. Four men were arrested, one for trying to damage the camera of _Mirror_ photographer Neville Whitmarsh; he was later charged with offensive behaviour.
I wrote in my diary that evening: 'There were a number of arrests and several fights, especially the one between two women.' One of the women was Aboriginal and the other white, and the police stopped the fight. My diary went on: 'The women were particularly hostile and I had several remarks "Who did you sleep with last night?" etc. directed at me.' John Powles remembered the women 'spitting at the female students'. I wrote: 'I have never met such hostile, hate-filled people. The hostility seemed to be directed at us as university student intruders rather than to the aborigines. The aboriginal children told us that they had been called "scabby black —– niggers". One child had been knocked down. The poor kids were very frightened.' Most of the students were scared, too. Alan says: 'I'd have to say that was a pretty scary experience and I think we were all pretty scared, just seeing the hatred of those people.'
The atmosphere was getting more dangerous by the minute. The police warned the students that if they stayed the violence would get much worse. Bill Lloyd told me: 'I remember a male blond student [this would have been Paddy Dawson] arguing with the crowd, and being grabbed by the hair . . . It was when this happened that I really started to get worried. I became very concerned.' The police told the driver to park the bus around the corner from the town baths and to keep it out of sight.
The baths were closed at the suggestion of the police, and Lloyd and the pool manager and employees decided to erect a weldmesh fence to enclose the students. As he explained to me in 1991, 'that meant you were on council property, and the crowd couldn't get at you. The crowd were all on the other side of the fence.' John Powles remembers vividly the 'police putting up fences to separate us from the hostile crowds, and the tension building up'. The _Herald_ reported that 'when council employees used wire to bind a hastily erected barricade, youths in the crowd began shouting "let's string them up"'. Ted Haddock, the District Electrical Engineer with the North West County Council, happened to be there with his 16-mm film camera, and filmed the fence being erected.
Then—breakthrough! The Mayor came up to us and said he would be prepared to sign a motion to rescind the 1955 statute, and would get two other aldermen to co-sign it. The Mayor and three other aldermen— George Mills, Charles Jones and Perry James—then went into the baths and had a private discussion with Charles, Jim and Pat, our tour executive. While they had their discussion we sat outside singing freedom songs— 'We Shall Overcome', 'If You Miss Me at the Back of the Bus', 'I'm So Glad', 'Sinner Man' and so on. Lloyd recalled: 'I had some very serious negotiations with the student leaders, mainly Charlie, but also Jim Spigelman, and the girl Healy; she was the daughter [ _sic_ ] of the communist union leader. I was afraid the crowd would go berserk. I said I would do all I could to get the council to remove the discriminatory resolution. It should never have been there, and was voted by the previous council.'
After twenty minutes of negotiations, Lloyd announced that two of the aldermen had agreed to sign a motion to rescind the resolution. They promised the students they would put notice of motion to the council meeting the following Monday, 22 February, and it would be voted on the following week. They would consider an alternative motion that would have entry based on health criteria only.
_Diary:_ We took a vote on it and unanimously agreed that this meant that we had won. We decided to leave.
It was now 5.30 p.m. and the crowd was becoming very threatening. The police offered to take us through the back gate of the baths, but we refused, so the police escorted us through the crowd to the bus. Lloyd: 'I arranged for the bus to be driven right up to the baths, and for the students to get on, with police assistance.' Bill Pakenham, the bus driver, told Gerald Stone that 'the police told me to pull up in front of the baths, get the students boarded and clear out of town as fast as I could'. Policemen and burly council workers tried to clear a path, but the crowd closed in. Lloyd: 'We did it as quickly as possible, but there were still missiles thrown, and students were hit.' Of necessity, we walked in single file, while the crowd threw eggs, tomatoes and stones, and spat at us. The jeering, said the _Mirror_ , 'rose to a deafening pitch'. John Powles remembers: 'I think when we finally decided to go, or we were escorted on to the bus or something, it was a very tense departure as I recall. And I had the feeling, you know, of very substantial impending violence which never actually really broke out, but one had the feeling there really that the situation was pretty explosive.'
Brian remembers a funnier side:
I still remember Paddy Dawson, who was quite tall and had very long hair, naturally blond hair and somebody threw an egg as he was walking the gauntlet as it were and it landed splat on the top of his head and just sort of went everywhere. And this brought great laughter from the crowd and we all laughed too at it, it was sort of funny in a way. And I seem to remember Paddy thinking it was funny too.
Aidan Foy remembers this too: 'They threw an egg that hit Paddy Dawson on the back of the head. I remember that because he was—poor old Paddy was a good target because he was quite tall and he had . . . shoulder-length blond hair which was quite unacceptable in country town New South Wales, and so of course he copped it.'
The students got on the bus, and the police kept the crowd back.
_Diary:_ We bundled into the bus and closed all the windows. Eggs and tomatoes were still thrown.
Then we all moved off, with a police escort. Some lessons had been learnt from the Walgett experience, and the police stayed with the bus until they were sure it was not being followed. About 30 cars tried to follow, but were turned back by police. 'Those cars,' Gerald Stone later reported, 'were filled with very angry people.' Lloyd recalled that they 'blocked all exits from the town, so no one could attack you students'. Traffic police halted cars at the city limits, and examined the credentials of drivers proceeding towards Inverell. The trouble was, not everyone was on board: Sue Johnston, Gerald Mason and the press were still in Moree. Charles told the driver to turn back to collect the missing passengers but, as Bill told Gerald Stone: 'I refused to turn back . . . there would have been real violence if we had returned to town.' So the police and Charles returned by car to pick up Sue and Gerald and take them to a spot out on the highway to meet the bus.
_Diary:_ About ten miles out of Moree we stopped, to wait for the press, Sue J, Charlie and Gerald Mason. Charlie came back, and made a radio statement while we waited for the others. Finally they all came and we set off again.
Darce was not on the bus; he had had to leave to return to the ABC.
At this point I had to leave the bus. My leave had expired, and despite the fact that this was a front-page story (indeed an international story), and that I was the only ABC person travelling with the bus, the ABC would not extend my leave. The night of the second pool confrontation I jumped on the North West Mail and headed back to Sydney.
Brian remembers:
We were not far out of town—I don't know 5, 10, 15 minutes, when Bill the bus driver came on the microphone, and of course the bus was a touring bus, and he said 'I have to tell you all that I will not be driving this bus any further, in the interests of your safety, and I am responsible for your safety and I do not believe that I can any longer guarantee that after this incident and therefore I will not be taking the bus any further'.
This was an enormous blow, but also brought home to us—and to the public when it became known—how potentially dangerous this bus tour had become.
We stopped at Gravesend, a small town about 30 miles (48 kilometres) east of Moree, for dinner. The town was the site of a reported massacre in 1837, though none of us knew that then. After dinner we continued along the Gwydir Highway, passing within twelve minutes of the site of the Myall Creek massacre, but we did not know that either. We arrived at the Inverell Twin Swans Motel at about 10.30 p.m. Ever-conscious of the media, I wrote in my diary: 'We got first place in the 11 o'clock news.' That same night, and the next, Bob Brown's shop was pelted with refuse. The next day, Sunday, Aboriginal people were again excluded from the baths.
The media response was huge—locally, in Sydney and nationally; there was even international coverage. Moree's own newspaper, the _North_ _West Champion_ , was angry. After a detailed front-page story about the confrontation, its editorial—headed 'Severe Setback on Aboriginal Problem'—referred to the students as 'misguided juveniles'. Rights, it said, must be extended gradually: 'It has been proved that to allow aborigines full rights all of a sudden only brings trouble . . . Since the students left on Thursday, the town's progress in handling its aboriginal problem has been set back years.' The paper urged the council not to rescind the 1955 ordinance. The regional _Northern Daily Leader_ , based in Tamworth—a large town with a much smaller Aboriginal population— took a more pro-Aboriginal and somewhat more pro-student position. Its editorial, after describing the amount of colour discrimination in country towns as 'negligible', said the students 'merit the goodwill of country people', especially as they had bothered to come to country areas and see for themselves, in contrast to 'most of the people associated with movements for the welfare of aborigines'. It described the shanty towns as 'a disgrace', needing greater government funding.
In Sydney, the media coverage was extensive and nearly all sympathetic. Gerald Stone's story in the _Daily Mirror_ was the first to appear, coming out in a late edition that same Saturday afternoon. The _Four_ _Corners_ program Charles had recorded on Friday, in which he had confronted the Town Clerk of Walgett about the exclusion of Aboriginal ex-servicemen from the RSL Club, screened on ABC television that Saturday night after the news of the Moree confrontation, and made a huge impression. The Sunday papers—the _Sunday Truth_ , the _Sunday Telegraph_ , the _Sunday Mirror_ and the _Sunday Sun_ —all carried front-page stories of the violent confrontation at the Moree pool. One of the most detailed was Stone's report in the _Sunday Mirror_ , headed 'Violence Explodes in Racist Town'. The _Sunday Sun_ and the Brisbane _Sunday Mail_ both carried a story on Charles Perkins, 'the man who heads our "freedom riders"', based on separate interviews conducted before the Moree events. Together they signified that in many ways the story was not the Freedom Ride itself, but rather the emergence of an articulate Aboriginal leader.
[The _Daily Mirror_ 's full-page coverage of the demonstration at Moree pool, 22 February 1965.
(Photo courtesy of Newspix)](chap7_9781741150575_epub_part7.html#d41152301)
The _Mirror_ continued its strongly sympathetic coverage on Monday, with a story focusing on the driver's refusal to continue, headed 'Students in Danger: Freedom Driver Quits'. There was another story on the Moree riot headed 'Little Dixie' (the analogy with Dixie seems to have been a _Mirror_ favourite), with photos of Charles, John Powles and Beth Hansen being walked away from the pool, and another of Jim Spigelman over a caption headed 'Victim', mentioning his having been knocked over outside the pool. The next day the _Mirror_ carried a series of comments, with very mixed views, from the 'Under 25s' in answer to the question 'Should they (the students) come home?' The _Sun_ was supportive, with an editorial emphasising the driver's withdrawal, and fiercely critical of the whites in Walgett and Moree. It said: 'This is the kind of thing now going on in the southern United States. We haven't yet reached the Alabama level of violence, but that seems to be on the way up.' It concluded:
If the university students have done nothing else, they have at least focused national attention on the place of the aborigines in Australian society. We must accept the aborigines and accommodate them with decency and freedom in our midst'.
The _Sydney Morning Herald_ also had extensive coverage, its front-page story headed: 'Students in Wild Moree Scenes', which emphasised the violence of the pool incident. In a separate story, the _Herald_ quoted Ted Noffs:
The events in Moree on Saturday, which marked the end of discrimination against aborigines in the local swimming pool, must go down as a milestone in the history of race relations in Australia. The fact that this was accomplished by a small student group must also bring judgment to bear on the complacency and apathy of many adult Australians who have done little despite discrimination against aborigines in Australia. It is to be hoped that at Walgett and Moree committees consisting of equal numbers of aborigines and white people will sit down and work out for themselves ways by which an end can be brought to all social divisions that have persisted for so long.
Another _Herald_ story focused on an interview with Lloyd, and yet another on the driver having abandoned the students. The _Herald_ editorial thought the students had touched a sensitive nerve, and had acted well. They 'seem to have acted in accordance with the best democratic traditions of non-violence, although they have themselves been jostled, punched and pelted with refuse'. It thought the Moree council should not have a racially discriminatory resolution on its books, but suggested the problem could not be entirely laid at the feet of towns such as Moree and Walgett. The problem, it said, lay ultimately with the government.
Not all Sydney's papers were sympathetic. The _Daily Telegraph_ 's editorial on 24 February was headed: 'Wrong way to help our aborigines', and suggested the students had good intentions but the wrong tactics for achieving them. It could not see what good could come from 'stirring up passions in country towns', and then referred to the squalid circumstances in which some Aborigines lived, commenting that it was 'hardly a matter for wonder that there should be some local reluctance to sharing a swimming-pool with this kind of aborigine'. One letter to the _Telegraph_ from a Moree resident, E.J. Lipsham, referred to the paper as 'the only one that appears interested in the truth'. It pointed out that there was a pool at the mission and then, revealing a clear sense of white ownership of the town, asked 'Why would the aboriginal people want to use our pool? '
The Moree events were covered well beyond New South Wales. Nationally, the _Australian_ gave extensive and sympathetic coverage, with the pool confrontation its front-page story on the following Monday, featuring photos of Charles, Beth and John Powles being escorted from the pool by the Mayor, and Bob Gallagher being hit by an egg, together with reports of the decision of the driver to leave the tour, as it was 'too dangerous'. On Wednesday, the _Australian_ editorialised: 'The demonstrations by university students from Sydney over the last week have helped us all to see beyond the complacency and lazy indifference of our attitudes to Australia's indigenous people. Will the students' brave pioneering work become merely another seven days' wonder?' The editorial concluded: 'The great value of the students' demonstrations has been to draw our attention to the plight of these people.'
Interstate papers—in Brisbane, Adelaide, Hobart, Perth and Melbourne— all covered the Moree confrontation with front-page stories and editorials. The _Canberra Times_ editorial was especially supportive, saying the students had 'made everyone think and talk about the way we treat our Aborigines and half-castes'. It continued in strong terms:
The people of Moree and Walgett are especially angry because they know in their hearts that what the students say is true. There is colour prejudice in these towns and in practice a rough and ready kind of apartheid is the rule . . . Racial prejudice shows itself . . . in a general contempt and disinterest, a damning apathy which is content to regard the Aborigines as an incurable disease which should be kept out of sight as far as possible. They are part of the landscape but not quite part of the community, human beings but not citizens . . . There is no friendship, no sympathy and precious little interest.
The _West Australian_ and _The Age_ in Melbourne both thought the students had performed an important public service in ( _The Age_ 's words) 'publicising the shabby treatment that many Aborigines endure'. The Brisbane _Courier-Mail,_ on the other hand _,_ said the Freedom Ride had created bitterness which would probably last a long time; the solution, it said, was not to pour scorn on those white Australians who lived near Aboriginal Australians but for more money to be spent by governments on Aboriginal welfare.
Cartoonist Martin Sharp makes a harsh comment on the citizens of Moree, the _Australian_ , 22 February 1965. (Cartoon courtesy of Martin Sharp)
A major public debate emerged in the letter columns of the newspapers. On Monday, the _Herald_ published a bundle of letters supporting the students, many written in response to a letter from Mrs B. Booth that had appeared the previous Saturday, accusing the students of barnstorming 'quickly through the country causing dissatisfaction, even minor violence, and then scuttl(ing) back to their fine comfortable homes' and leaving 'the country townspeople to cope with the havoc they have caused'. Mrs Booth had also accused the students of knowing nothing about Aboriginal life, and said they should concentrate on providing scholarships for Aboriginal students. Now G.T. Briot replied, defending the students for 'bringing forcibly to public attention that the American "deep south" has a counterpart in NSW'. A university student, Miss K. Stanton, reported that the students had done a great deal of preparation before going on the bus tour, attending 'seminars given by experts on "freedom rides", local government, social sciences, local health situations, anthropology, etc.' Several other letters were equally pro-Freedom Ride.
The next day, a letter was published from Bill Ford, saying Mrs Booth's letter reminded him of letters in the United States in 1961 when students rode in buses and trains into Jackson, Mississippi. He pointed out that the leader of the students, Charles Perkins, had come from an Aboriginal settlement himself, and suggested the students were not 'poor little rich kids who are bored with holidays' but rather people who had worked hard 'to get enough money to pay for the hire of the bus and their living expenses'. Perkins's own support at university, he noted, came from a scholarship whose funding had been raised by Abschol—that is, by university students. This letter itself prompted some personal responses of appreciation sent directly to Ford, and one letter of vituperation from an 84-year-old man who had lived for 30 years in Moree which said, among other things, that 'the colored people are a totally different breed to whites and it is against nature to mix the two breeds'.
The left-wing unions passed motions of support. A stop-work meeting of the Sydney branch of the Seamen's Union expressed support for the students' 'courageous exposure of the oppression and segregation levelled against the aborigines in NSW towns', while a mass meeting at the Chullora Boiler Shop unanimously agreed on Monday to congratulate Charles and the others. Their letter told Charles that they had also appealed to the Premier to let the people in these towns know, through articles in their local papers, of 'the very bad standing they are putting us in, in the eyes of the world through the United Nations'. One letter to the _Australian_ on Wednesday expressed a similar concern. Headed 'The Eyes of Asia are on Developments in Moree', a letter from B.C. Stevens of Toorak expressed the hope 'that Australians realise the importance of these issues abroad'.
In all this public debate, there was a very muted government response. At the local government level, the Lord Mayor of Sydney, Harry Jensen, was alone in supporting the students, saying the tour 'had succeeded in drawing attention to forms of segregation', and that 'those communities which have refused to accept the spirit of the government's desegregation policy deserve to be exposed'. The local MPs in the affected towns, on the other hand, deplored the Freedom Ride. Mr G.R. Crawford, Country Party MLA for Barwon (which included Moree), described the students' tour as 'ill-advised', and said it was 'tragic' that the students should 'stir up trouble on the aboriginal question . . . After stirring up the trouble they will go away and leave it for the local people to solve.' Later, local Members for the towns of Bowraville and Kempsey would make similar comments.
'It's not too cold for me—it's too hot!' Eyre Jnr cartoon in the _Sydney Morning Herald_ , 22 February 1965, satirising the Chief Secretary's lack of response to the Freedom Ride.
The Premier said nothing. The Moree riots led the relevant government minister, Gus Kelly (Chief Secretary and therefore responsible for Aboriginal welfare), finally to comment. He had been reluctant to do so. On Saturday, as we were returning to Moree, the _Herald_ began criticising the government for refusing to comment. Kelly, it said, 'has declined to be interviewed'; Mr A.G. Kingsmill, chair of the Aborigines Welfare Board, had also refused to say anything; and Mr H.J. Green, the Superintendent of Aboriginal Welfare, was 'absent in the country'. The reason for such quietness, the _Herald_ accurately suggested, was the concern 'not to antagonise white voters in country electorates'. A _Herald_ cartoon on Monday, 22 February lampooned Kelly for his silence, showing him standing at the edge of a swimming pool, saying: 'It's not too cold for me—it's too hot!' The _Daily Mirror_ remarked the same day that Kelly 'seems to hope that if he does not mention the Freedom Ride, the problem will go away'. Perhaps stung by media commentary, Kelly made a brief statement on Monday, 22 February. He denied there had been any discrimination by the state government against Aborigines, saying 'they have full rights as citizens of New South Wales under the law'. He refused to say anything further.
The only minister to comment on any of the issues raised by the Freedom Ride was the Minister for Health, Mr W.F. Sheahan, warning against racial discrimination in hospitals. Sheahan had spoken out on 18 February, after the Walgett and first Moree visit, warning local hospitals that he might reduce their government subsidy if they segregated Aborigines from other patients. Sheahan went out of his way to stress the policy twice, first while opening a baby health centre and then while laying the foundations for hospital extensions at Lismore. Sheahan seems to have had quite a long-standing concern for Aboriginal health, having instituted regular health inspections at board settlements in 1963, and telling Parliament on 14 October 1964 that: 'I believe that in Australia we have not given the aborigines enough attention. In fact, to use the democratic term, we have not given them the fair go that they are entitled to . . . We have now reached a position in Australia and throughout the world where colour is no bar to a person receiving the treatment that humanity dictates.'
There was no comment from the Commonwealth government. Yet, if both Commonwealth and state governments were tight-lipped, both were also becoming increasingly worried behind the scenes. Both feared more adverse publicity. The state government had an election coming up, and was sensitive to any criticism of its Aboriginal policies, while the Commonwealth government was deeply concerned about Australia's overseas reputation on racial issues. To the consternation of both, the Freedom Riders seemed to have attracted a lot of favourable publicity at home, and it seemed they were about to attract attention abroad. Both watched rather anxiously as the Freedom Riders now turned eastwards towards the coastal towns to continue their survey and demonstrations.
_Ch_ _apter_
_7_
'Stirring up trouble': The coastal towns
The Freedom Ride resumed its planned itinerary, through the coastal and near-coastal towns of Lismore, Bowraville, Kempsey and Taree, taking almost a week to complete the 2300-mile (3700-kilometre) loop back to Sydney. This second week repeated many elements of the first: surveys, pickets, rural hostility, urban interest. As some of the news photographs from this leg of the tour clearly show, the students were becoming weary. Yet, as the bus drove on relentlessly eastward then southwards, this second week was not simply more of the same. With the depths of white hostility and the transformative possibilities of direct action now both evident, the political ramifications of the Freedom Ride were intensely debated in the media. Charles Perkins, especially, became the object of intense admiration and interest, and some abuse. Both Aboriginal and non-Aboriginal people in the remaining towns anxiously waited to see what would happen when the Freedom Ride came to them. Through all this, the bus tour rolled on.
The first two days—a Sunday and a Monday—following the high drama at Moree were spent in travelling east, and waiting for a replacement driver. Although Bill Pakenham had dramatically announced his intention to withdraw, he drove us on the Sunday through the beautiful green and hilly country from Inverell to Grafton, a journey of 150 miles (240 kilometres) taking about three hours.
Two more students joined the tour at this stage, bringing our number back up to 29. One was Barry Corr, a foundation member of SAFA. By this time there was something of a support organisation in Sydney, run by Ted Noffs, Alan Walker and Bill Ford, which helped keep the Freedom Ride in touch with its supporters, and organised emergency accommodation now that our tour had departed from its itinerary. Ted Noffs was, in fact, in daily contact with Charles throughout the tour. Alan Walker helped Barry—who had been unable to participate to this point as he had had to undertake 'practice teaching'—join the Freedom Ride. Barry had grown up in a devout Christian family in Penrith, then a country town on the western edge of Sydney. Now, having arrived by train on Saturday, he was billeted with a family in Lismore and waited impatiently for the students to arrive. The other to join around this time was David Pepper (he couldn't quite remember exactly where he joined when interviewed in 1994). About to enter the second year of his Arts degree, David was from a middle-class family; with his father a solicitor and his mother a housewife, he had grown up an apolitical 'surfie' by the beach at Dee Why. He had no political involvements, and said in interview that university, for him, was 'girls, drugs, beer, talking'. One of the Freedom Riders, Machteld Hali, had written him a letter suggesting he join the tour, and he went 'to see what was happening with Machteld. And nothing was happening with her.' His interest in the issues soon became much deeper, however. There was, it seems, another addition to the bus for a short while—Ray Tunks, a Salvation Army officer who now allied himself with SAFA.
The Sydney supporters organised for us to stay in yet another Methodist Church hall, this time at South Grafton, on the banks of the Clarence River. After lunch, Charles and Jim investigated getting another bus and managed to hire one at a cost of £240, an extra expense they hoped to meet through a public appeal. The new bus arrived, and we transferred our luggage to it. When Charles rang Mr Saint, owner and manager of our original bus company, Saint told him not to get another bus, as he would find another driver. On hearing we could keep the old bus, we transferred our belongings back again.
Bill Pakenham was furious. He felt the company had not stood by him. In an interview with Gerald Stone, he expressed some of his concerns and frustrations, and defended his decision not to continue. 'I felt that as the driver of a charter bus I was responsible not only for its safety but for the safety of my passengers. What would happen if the bus was wrecked or set on fire in an incident?' He was not against the students, stressing to Stone that they were 'well behaved and courteous' throughout the trip. 'There was no heavy drinking or indecent behaviour. They are nice kids but it was the worst bus trip of my life.' To the _Sydney Morning Herald_ he said: 'The second time at Moree was enough for me—I'm going back to Sydney as fast as I can. They still have at least one more trouble spot to visit and I'm not going to take any chances by being there.'
[Clockwise from bottom left: Charles Perkins, John Powles, Brian Aarons and Gerry Mason wait in Grafton for the replacement bus driver to arrive, Monday 22 February 1965.
(Photo courtesy of the _Daily Examiner_ , Grafton)](chap7_9781741150575_epub_part7.html#d41152451)
We had now to wait in Grafton until the new driver arrived. This could take some time. Press coverage focused, naturally enough, on the drama of one driver leaving and another arriving. As the _Daily Mirror_ reported on Monday: 'Attempts to get a replacement driver ran into trouble last night. None of the bus company's drivers was anxious to face the rest of such a dangerous tour.' As it turned out, the 30-hour wait for the new driver created a small break, and a much-needed rest for the somewhat shaken students. Grafton was not one of our targeted towns, for its Aboriginal population by this time was relatively small. Fearing the taking of their children, the local people had moved away from the board station at Grafton 40 years earlier, and the reserve had been revoked owing to 'loss of population'. We were relieved to learn that the olympic pool was not segregated, and the local paper, the _Daily Examiner,_ carried a report accompanied by a photograph showing the students going to the pool for a swim. Our task in Grafton was to recover and regroup, ready for the rest of the tour.
While waiting in Grafton, we read the reports of the Moree clash in the Sunday and Monday papers, and were gratified by their prominence and frequently sympathetic coverage. We also received many direct expressions of support, and unsolicited donations. Pat remembers receiving bundles of mail addressed simply 'The Freedom Riders' or 'The Student Bus', and they would be delivered to the student bus in Grafton, Lismore and the other towns. Gloria Phelan, of the Teachers' Federation, forwarded 7 pounds and 10 shillings ($15) to Jim Spigelman by telegram. Bruce Dawe wrote to Charles: 'More power to your arm in your struggle for justice for your people! . . . I am pleased to see that not all the lessons we learn from the United States are bad and that, in an age which has exalted the anti-hero, such men as Martin Luther King still think it worthwhile to believe in and fight for things.'
That Sunday evening, I took time to write up my long diary entry on the events in Moree. I also stepped aside from the day-to-day narrative to note some more general aspects of life on the bus, and it seems a good time to do the same here. I wrote:
One thing wonderful about this trip is the wonderful group spirit we've developed after the first few days. Everything is done very democratically—and in fact our meetings are rather funny, with little points being debated at length until we realise how stupid it is. After the first few days we made our meetings much more formal, so as to get everything decided.
Another thing is that the singing has developed as we go along. At first no one was interested in singing but as we've gone along the singing has grown. Today on the bus we made up two songs—one to the tune of 'Green Grow the Rushes—Oh' which goes like this:
I'll sing you one oh
Go where the buses go
What is your one oh?
One for the bus that carried us through
And ever more shall be so.
Two for the Aboriginals on the bus
Upon the freedom ride—oh
Three, three, the aldermen of Moree
Four for the cops who guarded us
Five for the knuckles on his chin
Six for the kids we tried to take in
Seven for the pressmen who came with us
Eight for the eggs upon his head
Nine for the nine lives we all have
Ten for those dumped in the crowd.
We also made up another song, which went something like this, to the tune of 'Waltzing Matilda':
Once a jolly freedom rider
Stood outside a swimming pool
Under the shade of a ten foot cop
And he sang as he combed the eggshell from his hairy mop
Who'll come a desegregating with me
Desegregating . . . etc.
Up came a coloured kid to swim at the swimming pool
Up jumped the students and grabbed him with glee
And so it goes on, I forget the rest.
In interview years later, some of the former Freedom Riders remembered other aspects of life on the bus. Wendy Golding recalls that 'there were often very limited washing facilities and so I remember being in a swimming costume and all there was was a garden tap, and washing ourselves somehow, the bits that you could reach, that weren't covered by the swimming costume'. In fact, while we were in Grafton, I remember going with two of the other women to a local hotel, walking in, taking a shower and leaving, something I would not normally dream of doing, and an indication of our strong desire for a good shower. Pat Healy remembers how we shopped for food:
There was a roster, and everyone had to do the shopping. The money was just kept in this tin. This tin went all over New South Wales with all this money stuffed in it. And in fact it used to sort of roll around the floor of the bus . . . And whoever was to do the shopping used to just grab the tin and go off and get the milk for breakfast and things like that . . . At that stage my consciousness of gender differentiation in terms of who did the work was perhaps not as finely honed as it was some five years later, so I don't really have a large consciousness of the women doing all the work. Maybe they did. I don't remember.
Actually, my diary seems to indicate a good deal of sharing in preparing food, in which everyone, including Gerry Mason, participated. I recorded the following meal roster at the back of my diary:
_Wednesday 17th_
Tea: Richard Collins, John Butterworth, Charles Perkins, Sue Reeves, Colin Bradford
_Thursday 18th_
Breakfast: John Gowdie, Warwick Richards, Wendy Golding, Jim Spigelman, Paddy Dawson
Lunch: Chris Page, Aidan Foy, Beth Hansen, Richard Collins, Brian Aarons
Tea: Bob Gallagher, John Powles, Derek Molloy, Michelle Hall, Sue Johnston
_Friday 19th_
Breakfast: Darce Cassidy, Colin Bradford, Norm McKay, Louise Higham, Ray Leppik
Lunch: Gerry Mason, Helen Gray, Robyn Iredale, John Butterworth, Alan Outhred
Tea: Aidan Foy, Hall Greenland, Chris Page, John Gowdie, Charles Perkins
_Saturday 20th_
Breakfast: Ann Curthoys, Warwick Richards, Paddy Dawson, Richard Collins, Sue Reeves
These two days were a chance to ring home and reassure anxious parents. Hall Greenland remembers his conversations with Maynard, the young Aboriginal man living with his family.
I used to ring home occasionally just to chat to the old girl [his mother], and then Maynard would answer the phone and there would be an uneasy conversation about what was going on because, you know, I was away fighting his battles in a way. It personalised for me what was a rather difficult political dilemma about privileged white kids fighting the battles of the underclass. So that did worry me at a general and a particular level. It was a source of discomfort.
When asked what Maynard's reaction to the Freedom Ride had been, Hall replied: 'Well he seemed to be quite supportive. He thought it was a good thing that I was doing, and he was interested in it.'
On Monday morning, we held a general meeting and discussed SAFA's future policy. It was, my diary records, 'a pretty heated discussion'. Should we concentrate on raising funds for scholarships for Aboriginal students, rather than intervening in the lives of people in country towns? Hall Greenland moved that Student Action for Aborigines _not_ develop its own scholarship scheme, but rather concentrate on political action.
_Diary:_ We rejected the motion which Hall moved, which opposed SAFA scholarships, but all realised that no definitive policy decisions can be made yet.
The rest of the day was spent resting, relaxing, swimming, washing clothes and writing letters, insofar as all this was possible with the media following us everywhere.
_Diary:_ Today became rather a farce—everything we did was photographed, whether it was eating, walking along the street, having a meeting.
We had to clean the residue of eggs and tomatoes from the bus; this was something the television cameras were keen to capture—physical evidence of the violent reaction to us in Moree. My diary continues: 'Then we all went for a swim, getting photographed all the way . . . We organised a watermelon eating competition, each of about nine of us with a quarter of a watermelon. Charlie had more or less challenged the rest of us to it, but he ended up coming second last.'
Finally, at 6.00 p.m. on Monday, 22 February, the new driver arrived. The _Newcastle Morning Herald_ reported that 'the new driver is Mr E. Albrecht, of Lugarno, who said he was a "little nervous but not particularly worried" about making the journey'. Known as Ernie, he was clearly determined to show the students who would be in charge.
Charles Perkins, John Butterworth, Ann Curthoys, Machteld Hali and Rick Collins join in a watermelon-eating competition, while waiting in Grafton for the new driver to arrive.
_Diary:_ He seemed pretty hard to get on with. The first thing he said was 'Take the sign off the bus', the second 'I'm not going into a hornet's nest'.
We took the sign down, and then the bus set off for Lismore, 63 miles (100 kilometres) to the north.
Lismore presented the Freedom Riders with a different experience from that of any other town. Instead of hostility, we now found welcome. Charles was by now a celebrity, and the Freedom Ride had become a media event. It was a somewhat more sophisticated town, though this was well before it became a favourite rural retreat for professional people tired of urban, especially Sydney, life. By this time, the townsfolk knew quite a lot about the Freedom Ride; as Warwick remembered, 'they'd had plenty of information about the bus trip, presumably from the newspapers and they were quite willing to talk to us'. Many wanted to show us that Lismore was not a racist town. In addition, some of the local Aboriginal (Bundjalung) leaders welcomed us. Respected elder Pastor Frank Roberts had, for example, appealed a week earlier for offers of billets for the female students, as the showground accommodation being provided for the men was thought unsuitable.
This generally positive attitude arose in part from specific historical experiences in Lismore. The territory of the Bundjalung people had been the last in New South Wales, about a century earlier, to see the end of frontier conflict and violence. Before World War I, the region was cattle country; the Aboriginal reserves in the area supplied the cattle stations with a cheap labour force—stockmen, labourers and ringbarkers. After the war, the area gradually shifted from cattle to agriculture, and the farmers increasingly used family rather than Aboriginal labour. As in Moree, disputes with reserve managers led a number of families in the 1920s and 1930s to move closer to town. They chose a campsite on a stock route on the border of the Lismore and Gunderimbah Shires. In an attempt to exert some control, the Aborigines Protection Board declared the site, then known as Tuncester, a reserve in the early 1930s. One of the extended families there was led by Pastor Frank Roberts Snr, who led a three-decade long battle to stay on Tuncester, soon reduced in size and renamed Cubawee.
By the 1950s, Cubawee had its own one-teacher school, so that the children would not be brought into the schools in town. Vic Brill was the teacher from 1956 to 1959, and in 1991 he described to me the conditions there then—the shanties, the dirt, the diseases. He conducted a medical session each day, and would dress the children's sores each day before school could start. His teaching concentrated a lot on extending the children's English vocabulary. An active Parents and Citizens Association developed amongst the community to support the school. Some of the children had gone on to secondary education, and one to university. Although the people had fought hard to stay on Cubawee, it had by this time become a rather unhealthy place. There was no electricity, and the houses were mainly tin shacks. The _Courier-Mail_ reported in 1961 that there were about 120 people in thirteen broken-down huts, drawing their water from cattle-polluted streams, with very primitive sanitation.
From the mid-1950s, Lismore saw considerable activity and conflict over Aboriginal land and housing. Under the influence of assimilation policy, the board now wanted to demolish unauthorised shanty towns like Cubawee. An energetic attempt to relocate the people in town came when Eddie Morgan became the Area Director in 1956. He called a public meeting at the Lismore Council Chambers to discuss what should be done about Cubawee, at which Professor A.P. Elkin, anthropologist and a member of the board, spoke about Aboriginal people and their culture, and a year later he encouraged the development of a Lismore Aboriginal Advancement League.
The assimilationists in Lismore found the Bundjalung people in their area tough customers, demanding land rights and freedom from board and other interference. While they faced many of the same problems as groups elsewhere—land loss and segregation—they had the advantage of a continuing relationship with their traditional lands, and strong cultural and language survival. Certain Aboriginal men like Frank Roberts Snr and his son were strong leaders, who were able and prepared to converse with Europeans. Frank Roberts Jnr was ordained as a Church of Christ preacher in the mid-1950s, and he took over the role of communicating between black and white that his father had performed before him.
In 1958 the board tried to buy some blocks of land in town to rehouse the Cubawee group. The council blocked the sale, and a bitter debate raged for several years over the question of Aboriginal housing in town. Bert Groves visited while still president of the Aboriginal-Australian Fellowship, expressing his strong opposition to the idea of assimilation, and arguing that instead the people should have ownership of their land at Cubawee and elsewhere. A local white woman, Tess Brill, made personal contact with the people at Cubawee, and took some of the women to meetings of the newly formed Lismore Aboriginal Advancement League. She also attended, along with Eddie Morgan, the first meeting of FCAA in nearby Armidale. The following year, Frank Roberts Jnr published a statement in the Lismore paper, the _Northern Star_ , demanding that decent services be brought to Cubawee, rather than the people removed from it.
In the early 1960s, several newspaper stories described the shocking conditions at Cubawee, and the campaign to remove the people intensified. One of the functions of the reserve was lost when the school closed in 1961 in response to a Teachers' Federation policy, announced the previous year, of opposition to segregated schools. The Health Department condemned the water there, and the minister, W.F. Sheahan, ordered the board to solve the problem. Dr Hay, Medical Officer of Health in Lismore, described the settlement as unfit for human habitation, while the Lismore Aborigines Advancement League president urged that the Cubawee reserve be abolished and replaced by a new reserve closer to town. Mr Doig, a member of the Legislative Assembly, took an interest in Aboriginal settlements generally and raised the question of Cubawee in the Assembly on 6 September 1962.
Most of the white residents of Lismore were adamant that the Cubawee people be kept out of town, and those who wanted them included were ostracised. To complicate matters, the Cubawee community itself was divided: while its leader, Pastor Frank Roberts Snr, wanted the people to stay there, the women—increasingly concerned about their children dying from the unhygienic conditions—gradually concluded that a move was inevitable. As a compromise, the Lismore and Gunderimbah Shire Councils jointly offered a solution—land would be allocated for a new Aboriginal settlement in Gunderimbah Shire, just outside the Lismore town boundary but close enough for water, electricity and sewerage services to be provided. Realising nothing would be done to improve conditions at Cubawee, the Cubawee people agreed. The houses were completed and occupied in 1964, the Welfare Board's annual report proudly carrying a photo of the new houses, contrasted with a photo below it captioned 'Makeshift Cubawee dwelling which has since been destroyed and replaced with one of the new houses shown at top of page'. Assimilation, it seemed, was proceeding slowly and painfully in Lismore.
Lismore was also only 22 miles (35 kilometres) west of the Cabbage Tree Island cooperative. As Heather Goodall points out, the Robertses, through their 'highly politicised Christianity', had come into contact with the Reverend Alf Clint, who at this time was spreading the cooperative message amongst Aboriginal people. He saw the cooperative movement as a form of practical socialism guided by ideals of collective endeavour and community, which he thought (quite erroneously) correlated with Indigenous notions of community. The Indigenous societies of Australia did not in fact share this secular notion of community, but rather—as Heather Goodall puts it—'organised their social, economic and political life around families and individuals who had their most compelling links not to a secular "community" but to the land, and through it, to a transcendent, supra-human Law'. The cooperative ideal was taken up, for a while, by groups as diverse as the Communist Party and the Aborigines Welfare board—the former supporting its socialistic flavour, the latter seeing it as a way of encouraging independence and hard work. It also appealed to some Aboriginal groups as a way of retaining or gaining access to land, and of staying together without having to put up with a white manager or board interference in their daily lives. In 1958 the board adopted Clint's proposal that cooperatives be established at its Cabbage Tree Island, Woodenbong and Tabulam stations. Cabbage Tree Island seemed ideal, since it was already a successful community, with lively social, sporting, religious and economic activities. A cooperative with a retail store and sugar plantation was launched in August 1960, sponsored by the Australian Board of Missions and assisted by a £2000 government loan. A small reserve, it occupied about 25 acres (10 hectares) of the 140-acre (56-hectare) island in the middle of the Richmond River. For a few years, it was a great success, as the land was fertile and the people already had sugar growing and cutting skills. By 1964, about 150 Aboriginal people lived there. An ABC _Four Corners_ program on the north coast cooperatives broadcast in September 1964 saw them as a working alternative to assimilation in the towns.
All these developments made the Freedom Riders' visit to Lismore distinctive. The students' spokesmen told the press they had heard good things of Lismore. Jim Spigelman said they had heard much of the cooperative, which he described as 'evidently a brighter page in the story of Aborigines–whites cooperation and relations generally', while Charles announced that he did not expect any trouble at Lismore. For their part, both black and white leaders in Lismore made us welcome. The Lismore council and the Advancement Association members were keen to show the Freedom Riders, and through them the media, how much progress had been made in Lismore, and that it was not like the northwestern towns we had just left. When we arrived on Monday night around 9.00 p.m., Pastor Frank Roberts Jnr met the bus and then escorted the male students to the showground. Lou, Pat and I stayed with Vic and Tess Brill.
Clarrie Combo, at left, chairman of directors of the Aboriginal Cooperative at Cabbage Tree Island, discusses problems with the sugar cane crop with Mr H. Jeffery, manager of the Cabbage Tree Island Reserve, Tuesday 23 February. _Sydney Morning Herald_ , 24 February 1965.
_Diary:_ They were extremely interesting and Mrs Brill particularly knew a lot about the Lismore racial problem.
In her diary, Lou noted: 'In Lismore after spending the night at home of Mr and Mrs Brill. Very nice people with wide understanding of Aboriginal situation.' The _Herald_ reported Lou as saying 'sleeping in a nice clean bed for a change seemed like the best rest I'd had in my life'.
The next morning—Tuesday, 23 February—the cooperative at Cabbage Tree Island was our first stop. Pastor Frank Roberts Jnr and others met us at the post office, and then the whole party set off for the co-op. We were now quite a large group, accompanied by two ministers of religion, the Reverends Trigger and Stewart, Tess Brill and reporters from the local papers in Lismore and nearby towns like Grafton and Coffs Harbour, as well as the ABC, the _Sydney Morning Herald_ , the _Sun_ and the _Mirror_. At the co-op, the manager, Mr H.W. Jeffery, welcomed us.
_Diary:_ We got some interesting surveys and talked to a lot of the aborigines there.
I described Cabbage Tree Island in my diary as 'very interesting but the reserve was really very much like any other reserve. The cooperative shop was OK and so were some of the houses, but others did not have water or electricity.' Lou wrote: 'The houses were better than other reserves but still dilapidated.' Jeffery told the students that 25 men had gone to Narrabri for the cotton chipping, while six people had gone to Sydney for a three-week cooperative management course at Tranby. He also expressed his views on assimilation: 'There's no quick solution to the problem of aboriginal assimilation. It will take several more generations.' We didn't like Jeffery much. I noted in my diary that 'the manager seemed to be a real bastard', while Lou wrote more colourfully in hers that 'the administrator looks like a type doing his stretch in the colony and he acts like one. Rev. Stewart called him and his kind "social misfits" and generally unsuited for the job . . . The Rev. said he [the manager] had been trembling in his shoes all evening', presumably knowing that the students, and their now large media entourage, were to visit. In fact, Jeffery seems to have liked the students, and wrote to the board two days later saying we had been 'very courteous'.
The _Sydney Morning Herald_ reported that the cooperative scheme was near financial disaster. It quoted the chairman of the cooperative board of directors, Mr Clarrie Combo, who said: 'I suppose you could say our financial difficulties have been caused by inexperience.' Charles supported the idea of the cooperative, but noted its difficulties and lack of funds. He told the _Daily Telegraph_ that the people there were 'bright and very intelligent. If the cooperative stimulates a sort of personal initiative on the part of the aborigines it is a good thing. But it badly needs more funds.' The _Herald_ also quoted Charles's perceptive comment: 'I was a little disappointed when I saw it. However, the important thing about the scheme is that it keeps aborigines together. My people badly need unity, and the cooperative provides that even if its financial affairs are somewhat haphazard.'
After the visit to the reserve, and a stint of interviewing people in the town, civic leaders gave the students a reception. Aidan Foy remembers 'a big fuss . . . We sort of got a hero's welcome in Lismore, the local Trades Hall Council organised it, a reception and the Mayor and all sorts of things.' The Mayor, Clyde Campbell, welcomed us and expressed his admiration for the tour; Warwick Richards wrote in his diary that he told us 'you can only do good'. This was followed by a free luncheon hosted by the Lismore Workers' Club, for which we had to improve our standard of dress, and swap our sandals for shoes.
It was time, then, to visit the newly opened Gunderimbah settlement, where Pastor Frank Roberts Jnr and his people now lived.
_Diary:_ The houses there were by far better than any others, but still too small and overcrowded.
Beth Hansen, who later came to live in Lismore, remembers 'going out to visit the Gunderimbah houses and being spun this lovely story about how fantastic the Lismore people were, building all these new houses, and then discovering they were just outside the boundary'. She also remembers that, while we were there, 'someone from council spoke, probably lined up by Tess. I remember being very cynical, it being on the outskirts of town, symbolic of the do-gooding stuff. Though better physically, the racism was still there.'
Demonstrations seemed inappropriate. Somehow, we were back to where we had been in Wellington and Gulargambone, reduced to conducting our survey.
_Diary:_ On the whole a lot of us felt the day had been far too loosely organised and we could have done a lot more if we had organised ourselves better.
In a comment that I now find a little mysterious, I also wrote: 'Also the discipline was getting a bit lax, and Charlie got up in the bus and said we ought to tighten up on discipline.' Perhaps students were not all doing the survey, and going off for a drink or a swim. There was some publicity in the local papers, the _Northern Star_ quoting Paddy Dawson that the problem seemed to be economic and social, rather than racial.
Lismore revealed clearly that the methods of the Freedom Ride were effective only when faced by the most explicit racial segregation. When confronted with evidence of halfway 'successful' assimilation policies, the Freedom Riders had little new to offer. In this sense, our visit to Lismore was a non-event, and when interviewed years later, few of the Freedom Riders remembered much about it, many insisting we hadn't been at all or, if we had, we had done nothing there. Aidan Foy: 'I don't recall what we did in Lismore; I don't think there were any demonstrations or anything. We were all a bit battle weary by then.' I, too, find my memory of Lismore very slight; of all the events recounted here, I remember only staying at Tess Brill's welcoming house.
That evening, we left the Gunderimbah settlement and resumed our travels south. Bowraville, our next stop, was to prove the antithesis of our Lismore experience.
By this time, more political reactions to the Freedom Ride were beginning to be evident. Government response added little to Kelly's Monday statement that Aborigines were equal before the law until A.G. Kingsmill, chair of the Aborigines Welfare Board, made a statement, published as a letter in the _Sydney Morning Herald_ and the _Daily Telegraph_ on Wednesday, 24 February, and reported also in other papers. He pointed out that the board had a record of protesting against racial discrimination, and that it was the board's aim to remove the economic and social conditions which gave rise to 'these misgivings on the part of local communities'. He detailed the board's works in progress, mainly the building of homes in towns like Moree, Walgett, Lismore and elsewhere. Kingsmill was quoted in the _Bathurst Advocate_ as saying that he had warned the students (Jim and Charles) personally against 'any ill-advised action . . . which would impair much painstaking effort by the board's welfare staff over many years . . . both assured me they were as anxious as the board to see that this was done. So, where the chief responsibility lies for the events at Moree and anywhere else, only the reports will ultimately establish.' Kingsmill also appealed to both townspeople and the students to avoid 'unseemly disturbances at the remainder of the stopping places on their itinerary'.
Liberal and Country Party politicians remained silent. Concerned about the possible effects of a positive statement on their chances in key rural electorates, and a negative statement in urban ones, they did not attempt to use the Freedom Ride to criticise Labor's record on Aboriginal affairs. Nor did they try to expose the Freedom Ride as a communist plot, even though they knew some communist students were on board. They were probably aware of this in any case, but would have had little doubt on the matter after a telephone conversation between Alex Mills and Jack Beale, a Liberal frontbencher, on 15 February while the Freedom Ride was in Walgett. When Beale asked who some of the students were, Alex says he 'just sort of reeled off Brian Aarons and Pat Healy and a few other people, and not really realising at that stage of the game that, you know, I was mentioning names that were part of the royal family of communism in Australia'. It is especially interesting, then, that Liberal and Country Party politicians did not pick up on the communist connection.
For its part, the Communist Party was delighted by the Freedom Ride, though it had in fact had no direct role in its planning or conduct. That Wednesday, its newspaper—the _Tribune—_ carried a front-page story, and editorialised that this had been a 'historic ride', congratulating the students on their political skill and maturity. It thought the 'resultant wide public discussion in NSW will greatly help the already powerful development of a nation-wide movement for full rights for Aborigines'. It drew attention to the party's own draft program, and concluded that communists would continue to wage 'a firm and consistent fight in support of the basic struggle of the Aboriginal people themselves'.
More generally, public and media debate gathered momentum. One theme of criticism that grew as the days went by was that the students were stirring up trouble and then moving on, leaving the local people with the consequences. In the _Sun_ , Patricia Giffney wrote: 'By dragging a few bewildered "outcast" aborigines into a swimming pool and then moving on, they're leaving a trail of resentment behind them—to be borne, more likely than not, by other aborigines who have already been accepted in the general community of the towns.' In a somewhat similar vein, Bruce Petty's cartoon in the _Australian_ on 25 February depicted a bus speeding away from a 'Municipal Swimming Pool', being waved away by an Aboriginal woman, with small child, at a shanty town.
It is clear that some Aboriginal people in the towns feared the Freedom Ride. Charles Rowley pointed out in _Outcasts in White Australia_ a few years later that it was not surprising that some 'were resentful of having a situation disturbed in what they regard perhaps as a "good town" where there is at least employment, and little tyranny or interference so long as the coloured people "know their place". They feared that the whites would take a harder attitude when the "freedom riders" had gone.' The _Mirror_ carried a story on 24 February headed 'Aboriginal Attacks Students', which quoted George Bracken, a former lightweight boxing champion, asking what would happen to the local Aboriginal people after the Freedom Ride. His answer was that the Aboriginal people would be back where they started, with the additional problem of animosity caused by the students. Bracken also saw Perkins as out for publicity for himself. A week later—the day after the students returned to Sydney— the _North West Champion_ printed a story headed 'Aboriginal Mother Slates Students'. The unnamed woman said: 'Those students are just a load of troublemakers, I think. They haven't got to live in this town. They are only one-day visitors. They needn't come here trying to force us into things we don't want. We are quite capable of handling our own affairs.' She had, the _Champion_ reported, 'been satisfied with the way things were in Moree until the students came along'. A little later, poet Kath Walker (later known as Oodgeroo) said on _Seven_ _Days_ that 'what worries me is what is going to be left behind, what will happen to the Aborigines of Moree, for instance. How will they fare with the town taking sides? I think that they will suffer for this.'
Bruce Petty cartoon, the _Australian_ , 25 February 1965. (Courtesy of Bruce Petty)
George Bracken, the former lightweight boxing champion of Australia, said this today
Yet there was strong support as well. The Australian Council of Churches sent a telegram to Charles, care of the Presbyterian Manse at Taree, on Wednesday, 24 February. Signed by the general secretary of the council, the Reverend H.L. Perkins, and the secretary of the council's Division of Mission, the Reverend Frank Engel, it read: 'Your survey of the aboriginal situation and action against discrimination of great importance. Hope it stimulates imaginative Government and community action for aboriginal development and education of white community.' Here was an important supporter, for Engel was one of the leading advocates of Aboriginal rights within the churches, and his telegram was given wide publicity. Support also came from Professor Baxter, the Vice Chancellor of the University of New South Wales, who praised the students for avoiding violence, and for disturbing 'the apathy of the people'. No similar comment came from the students' own Vice Chancellor, the historian of white pastoral settlement, Stephen Roberts.
Our overnight stop was at the Scouts' Hall in the beautiful coastal town of Coffs Harbour, where we were belatedly joined by the Channel 7 _Seven_ _Days_ team. On Wednesday morning we drove on south. At Bowraville, the last of the students joined the Freedom Ride. This was Gary Williams, and this was his country. Situated on the banks of the Nambucca River in Gumbaynggirr country, Bowraville had a population of about 900 white and 116 Aboriginal residents, the latter nearly all living on the reserve. The main street was wide with wooden buildings, many of which still had the verandah posts of an earlier era, and a wide median strip.
Arriving around lunchtime, we were met, as we had been in Lismore, by representatives of the local Aborigines Welfare Committee, who told us of the progress they had made. This was, however, an all-white committee, started in 1958 by Mrs T. Henderson, the wife of a dairy farmer about 4 miles (almost 7 kilometres) out of town. The _Herald_ described her as 'a vital energetic woman with firm convictions about discrimination'. Mrs Henderson opposed racial discrimination in the town, and was especially concerned about housing conditions. If there were Aboriginal activists, as there had been in Walgett and Lismore, we did not meet them. In fact, the people on the Bowraville mission had heard about the Freedom Ride, but most were too fearful of the consequences to meet us. Pat Healy thought that 'in Bowraville we found economic conditions so bad that all the progressive Aborigines who might have led the people had gone off to get jobs somewhere else. Unemployment was worse there than anywhere else.' Bowraville was in a timber industry region, but Aboriginal people seem by this time to rarely have been employed as timber getters or cutters.
[The students outside the bus at Bowraville. From left to right: Gerry Mason, Pat Healy, Sue Reeves, Charles Perkins, Ray Leppik, Bob Gallagher, Ann Curthoys, John Butterworth, Norm McKay, Alan Outhred, unknown, Colin Bradford and Louise Higham.
(Photo courtesy of the _Tribune_ /Search Foundation)](chap7_9781741150575_epub_part7.html#d41152671)
We decided to find out about the situation for ourselves, splitting up to do our surveys and looking around the town to see if there were any examples of racial segregation. We soon decided that Bowraville was a seriously racist town. 'The area is simply riddled with discrimination,' Charles Perkins told the _Herald_. If most of the Freedom Riders now have trouble remembering anything about Lismore, the opposite is true of Bowraville. Many of them remember it with unpleasant clarity. There was something nasty and threatening about Bowraville that I and many other students felt at the time, and still remember. Aidan Foy said years later: 'In Bowraville there was a sort of brooding kind of menace that I felt was there. I remember feeling that about that place, it was a nasty place. Brutal place.' Barry Corr commented: 'Bowraville was discrimination from the cradle to the grave. It was a mongrel of a place. I loathed it, hated it.'
The atmosphere of racial division was palpable. Gerald Stone wrote that 'almost everywhere we went on the tour—with the painful exception of Bowraville—there were Aboriginals eating, drinking and working with whites'. Jim would later remember the situation in Bowraville in this way:
When I asked people in other towns which pubs or cafés discriminated, they would say, 'We're not allowed in this place', or 'We're not allowed in that place'. In Bowraville, the Aborigines I asked said, 'We are allowed in such and such a place'. It was a complete reversal of emphasis.
Alex Mills remembers that in Bowraville one white man he spoke to 'made the point to me that if you were friendly with an Aboriginal person you would be looked down upon by other people in the community'.
The group I was in went out to the board unmanaged reserve, about one-and-a-half miles (2.5 kilometres) out of town. One of the smaller reserves, its population had fluctuated between 50 and 80 over the last eight years, though this particular year it had jumped to 116, only to fall back to around 80 the following year. While we interviewed the people there, my diary says the press 'wandered around like flies as usual'.
_Diary_ : The conditions were very bad. The houses were weatherboard, very run down, and hadn't been looked after for 15 years (the houses were 26 years old).
Barry Corr remembers:
The people lived on an old reserve on a hill out the back of the town. And they reported the police regularly just driving around at night with the headlights on. They'd shoot dogs. As they were driving around if there was a stray dog wandering around, they'd shoot it. And all this is happening during the night . . . the people were living in fear. It was a police state, that's all it amounted to.
The students who conducted the survey in town found the racial discrimination there, as my diary put it, 'absolutely shocking—by far the worst we'd encountered'. The local barber, Cecil Brown, told the _Sydney_ _Morning Herald_ he had lost white customers because he cut Aboriginal people's hair: 'Some white locals drive into Macksville for a haircut rather than come here.' Warwick Richards remembers that 'there was a joke in the pub to the effect that when the police wanted wood cut or gardening done they'd arrest a darkie to do a day's hard labour'. _Seven Days_ reported a story of 'Aboriginal members of the football team forced to wait outside the clubhouse while their white team mates were presented with their team blazers'. We also discovered that there were a number of segregated cafés and hotels. At the milk bar, Aboriginal customers were not allowed to drink from the reusable metal milkshake cups. Tom Harris, the manager of the milk bar, told the _Daily Telegraph_ 'the aborigines never get milk shakes here. If I served a milk shake to one of them I would lose the trade of 20 white people.' Mrs Eakin, proprietor of another café, told the press that she did not serve Aborigines meals at the tables, because 'they throw food all over the floor' and tended to leave without paying. One pub had a 'dark room', while another allowed in only a select few Aboriginal drinkers. When some of the students went to the latter, the _Herald_ photographer took a picture of Gary Williams and Brian having a beer.
Brian Aarons and Gary Williams drinking in Bowraville Hotel. _Sydney Morning Herald_ , 25 February 1965.
The most striking example, though, was the racial segregation in the picture theatre, the Bowra Theatre. We learnt that 'there was a partition in the picture theatre separating the aborigines from the whites. The aborigines had to buy their tickets separately and could only enter the theatre after the picture had started.' Pat remembers:
this amazing old theatre in the main street, it sort of stood there in this dusty main street in all its glory. Just like the picture theatre we'd had in my suburb in Newtown where I'd grown up. And the theatre actually had a fence, an actual partition inside, and Aboriginal people had to go in a side entrance and sit in front of this partition. And everyone else went in the main entrance and sat behind the partition.
Several years earlier, the local Aborigines Welfare Committee had tried unsuccessfully to have the partition removed, and had even approached the Chief Secretary, who had said he had no powers over the matter. When Hall Greenland interviewed the theatre manager, Samuel Raymond, he said he would let no Aboriginal people in the back of the theatre, and that included Charles Perkins. Raymond was happy to explain his position to the _Herald_ as follows: 'The partition has been there since 1940 and white residents would not tolerate it to be otherwise.' Gerald Stone's report quoted him saying of Perkins: 'If he's got Abo blood he's got only one place and that with the other darkies. They all smell, are ignorant, and drink too much. People from the outside just don't understand what they're like.' Raymond told Judith Rich that he would lose white customers if he allowed Aboriginal people into the white section: 'All the townspeople agree with what I'm doing.'
_Diary:_ At first we weren't sure where to start—the town was just so bad.
In a revealing comment, I wrote that 'we thought the press could blow up a big story about it, but they refused, obviously instigating us to put on a demonstration'. It seems the journalists were tired of trailing around after us tamely looking at reserves and settlements; they were with us because we could stir up conflict, and that was what they wanted to relay to their audiences. The _Seven Days_ team wanted some action. If the media wanted action, the students were more than happy to provide it. 'We decided we could not leave without protesting,' Charles said.
With so many examples of discrimination to choose from, we decided to start with the Bowra Theatre. This was the first commercial public facility we had picketed, for the RSL was a private organisation (though with significant government support) and the Moree pool had been publicly owned and controlled. Since New South Wales had failed to follow South Australia's lead in passing legislation outlawing racial segregation, Raymond could not be charged with any offence. The Chief Secretary, Mr Kelly, said later that same day that under the _Theatres and_ _Public Halls Act_ 'he had no control over admissions to theatres, nor had he any control over where theatre and hall managements seated people'. This was avoiding the issue; when asked if he would recommend legislation to give him the relevant powers, he said no. W.M. Rigby, Labor MLA for Hurstville, a Sydney electorate, took a much stronger stand. Unusual amongst the Members of Parliament on either side of the House, Rigby had joined the Aboriginal-Australian Fellowship, and spoke up on Aboriginal issues from time to time. The _Theatre and Public Halls Act_ should, he said, be amended to give the government power to discipline racially discriminatory owners, and people who barred Aboriginal people from pools, hotels and cinemas should be treated as lawbreakers. The _Mirror_ reported that, while some other Labor backbenchers agreed with Rigby, they did not wish to speak out and embarrass the government on the eve of an election.
Along with the press photographers, we went again to see Raymond at his home, but he slammed the door on us.
_Diary:_ The press got a photo of him opening the door slightly and shutting it.
Then we went to the hotel, but the manager blatantly denied discrimination. At our meeting, we decided—but not unanimously—to stage a stand-in demonstration in the picture theatre that night, and my diary intriguingly notes that 'this was the first occasion that Charlie had voted with the minority group'.
After a barbecue meal near the house of an Aboriginal family, the Flanders, on the reserve (meat supplied by the Channel 7 crew), we returned to town. As soon as the manager of the picture theatre saw the bus approaching, he cancelled the show and put up a small sign—'No Pictures Tonight'—at the doorway, though in fact the projectionists had already begun preparing for the evening's show. As it started to get dark, we nevertheless began our picket. Beth remembers: 'We were there with our signs, and then slowly being joined by Aborigines, in ones or twos, just on dusk.'
_Diary_ : A crowd gathered round, the aborigines keeping a bit distant and quite separate. The white people weren't on the whole particularly hostile, nothing like Walgett and Moree. They seemed to me interested and even sympathetic, but on the whole a fairly apathetic lot.
Nearly half the population of the town gathered round.
Around 9.00 p.m. the atmosphere changed. Charles announced to the crowd: 'Well, folks, we have finished. You are free to talk to any of the students if you wish.' Many people took advantage of the offer, and many intense conversations ensued. The voices, reported the _Herald_ , could be heard two blocks away. Aidan Foy remembers 'people abusing us and some concern that the police may not have been too keen on helping us if there'd been any real trouble'. He reflected that part of their hostility was the by now significant media presence:
They were outraged that their town had suddenly acquired this notoriety. I don't believe they'd thought twice about the racism. I think they thought theirs was a nice little town that anyone would be proud to come from and a nice country town, you know, with all those Australian outback images. And to have this collection of students to suddenly come up and say, 'No, you're a collection of racists who are no better than the people who live in South Africa or Alabama', they were outraged and shocked and horrified, and a lot of them by that stage were turning quite nasty.
_Diary_ : One 16-year-old aboriginal girl called Ann was wonderful—in the discussions which broke out she stood up to the more aggressive whites very well.
This was Andrea (Ann) Holten, a 16-year-old high school student who had a few years before won a bursary to attend St Ursula's at Armidale. Her high school education, she told me in interview in 2002, had given her confidence. Now back in Bowraville, she ignored the warnings of her elders about getting into trouble, and came looking for the Freedom Riders, bringing 10-year-old Martin Ballangarry with her, who kept saying, 'We'll get a hiding, Annie'. Having found the white townsfolk arguing loudly with the Freedom Riders in the street, she was appalled to hear them denying the racial segregation that permeated the town.
So I found some courage and confidence to start speaking. Everything that had been bottled up for several years came out. I remember yelling out, 'You can't judge a book by its cover'.
Many of the students were struck by the courage of this young woman, younger even than we were, and a few months later Beth recalled the incident in an article, 'Our Freedom Ride', in _Overland_ :
One woman protested at our being in the town and added defensively: 'anyhow, what's wrong with our town? The darkies have been allowed to go to the white school for ages'. We explained that we weren't complaining about the school and were about to bring back the conversation to the partition when a young Aboriginal girl dramatically interrupted us. She stepped forward into the light and walked directly up to the woman who had spoken. There was a hush as everyone strained to hear her soft voice explaining how just a few years ago her aunt had tried to enrol her cousin at the school and had been refused . . . Just one quietly spoken girl had broken through the hidden intensity of feelings.
After half an hour or so of debate on the footpath, we left for Kempsey.
The media made a good deal of Bowraville. Pat Healy remembers the picture theatre with its partition and separate doors as summing up the essence of discrimination, and conjectured that the press must have had a similar view, 'because they certainly publicised this theatre in Bowraville'. The reports in the _Sydney Morning Herald_ , the _Australian_ and other papers were indeed extensive. The local _Guardian Gazette_ , circulating in Macks-ville, Nambucca Heads and Bowraville, was very hostile, saying of the students:
Their juvenile inaccuracies, prejudices against white people, and lack of concern for right or wrong labels them for what they are: a hysterical publicity-seeking band of adolescents, hiding under a guise of false humanitarianism hell-bent on causing trouble and getting out before it descends on them.
The nearby _Macleay Argus_ headed its report 'Best Laugh in Years', a quote from its interview with the Royal Hotel publican Paul Grant, who also described the students as 'a bunch of idiots having a good holiday'.
Despite the extensive media coverage, our efforts in Bowraville had been something of a failure. It is an indication that the Freedom Ride was by this time running out of energy that we did not decide to stay, or return there as we had done at Moree. We had not desegregated the theatre, and we knew it. Raymond, the theatre manager, defiantly told the press the next day that 'it had always been the theatre policy to segregate the white people from the aborigines and he would continue to enforce it'. We had simply put on a demonstration and left. This time, we truly did leave the question to be resolved by the local people. The next day, some of the Aboriginal people in Bowraville decided to try to desegregate the theatre themselves. Ann Holten told the _Newcastle Morning_ _Herald_ that she planned to lead her friends direct to the white sections and demand seats there. 'They can't keep us out of the "white" sections any more,' she said. In an interview a fortnight later with _Seven Days_ , she reported that they still could not enter the picture theatre, and that the local Aboriginal community had decided instead on a boycott. The picture theatre remained segregated and closed later that year.
It was to be another year before some of the students in SAFA returned to Bowraville to continue the fight they had started during the Freedom Ride.
A little dispirited by our Bowraville experience, we arrived in Kempsey around 11.30 p.m., and slept in the showground. This was to be our second-last night, and we were tired. We could not, however, give up yet. We still had this one major town to go and we continued to receive donations (£27 during the last three days of the tour) and messages of support. As it turned out, the Kempsey leg of the tour, though rather nasty and unproductive on the surface, was important in the longer term for its extensive media coverage—locally, nationally and internationally— and for later changes in Kempsey itself. Among the media by now was a BBC team, led by Trevor Philpot, producing a program on Australian race relations for the popular _Tonight_ show. Aidan remembers 'the BBC appearing and being terribly excited because it'd gone international'.
Kempsey had a considerable Aboriginal population of at least 600. There was a board station at Burnt Bridge, which at this point had a population of 162, well down on the population of 270 two years earlier. Greenhill—an unmanaged reserve close to town, with four houses built by the Welfare Board, surrounded by a large number of tin shanties— housed 200 people, well up on the 46 residents of the previous year. Clearly there had been considerable recent movement from Burnt Bridge to Greenhill. Forty miles (65 kilometres) west another 124 people lived at the Bellbrook unmanaged reserve.
Like Moree, Kempsey was at this time well known as a segregationist town. Its council, too, had passed an ordinance excluding Aboriginal children from its swimming pool, except during sports days or carnivals. The Kempsey ordinance had been passed in January 1949 and, like the Moree ordinance seven years later, aroused some opposition at the time. The United Associations of Women, a feminist organisation established by Jessie Street, took up the issue, seeing the segregation of Kempsey's McElhone Memorial Swimming Pool as violating the UN charter, which affirmed 'there shall be no discrimination on account of race, colour, creed or sex'. The ban had come to attention in the urban press again when the nearby town of Wauchope opened a new pool, and invited Aboriginal people to use it. Thus Kempsey—like Moree—had a reputation, and as the student bus drew nearer many in the town became apprehensive. Charles had said while we were still in Grafton that the students expected problems in Kempsey, and the _Sydney Morning Herald_ had said 'more trouble is expected when the students reach Kempsey on the return journey to Sydney. Some members of the group say they have evidence of "blatant discrimination" at Kempsey.'
It was clear from the start that we were not welcome. The day we arrived there was a letter in the local paper, the _Macleay Argus_ , describing the students as 'a busload of half-baked young men and women, probably unparalleled in their own conceit and impudence'. Supporters of Aboriginal advancement in Kempsey were worried, and spoke to local papers about their achievements to date. A letter from the local Aborigines Welfare Committee the day we arrived emphasised that, although there was prejudice in the town, the situation had recently improved, and expressed the hope that the students would take no aggressive action in Kempsey. J.H. Brown, the Country Party MLA for Raleigh, Kempsey's electorate, criticised the students and said 'it is a tragedy that people go around and stir up trouble, then leave it for the local people to solve. My observation as one most interested in the welfare of those of aboriginal descent is that the people of Kempsey and district have done all they could to help the less fortunate in their community. This visit by these ill-advised students can only undo the good work that has been done.' Brown did indeed have some claims as an Aboriginal supporter. Only four months earlier, when the _Macleay Argus_ carried a story about Aboriginal child deaths in the area, he had drawn the matter to the attention of the Legislative Assembly. The source of the problem seemed to be diseases caught from roundworm and hookworm, their prevalence a product of the poor housing and related amenities at Greenhill and the other settlements. Spurred on by the child deaths, the Save the Children Fund organisation in December had initiated a pre-school for Greenhill, and soon afterwards the Aboriginal Welfare Board had begun an eight-home building project, also at Greenhill.
Kempsey differed from Lismore not only in the hostility expressed by white leaders before we, the students, arrived, but also in that there was no organised support from the local Aboriginal community. No Aboriginal leader met us, and it was clear we would have to investigate on our own.
Thursday morning was wet and dismal, the first and only rainy day of the entire trip. Yet again, we split into groups to conduct our survey. I went with the group that talked to the Aboriginal people at the Burnt Bridge station.
_Diary:_ We all had to wear heavy shoes because of the hookworm. The reserve was a few miles out of town, and was in a gully. It was pouring rain (the first rain we'd had all trip) and the gully was terribly wet—that is apparently why there is so much hookworm . . . Well we all spread out and did our survey as usual.
The Welfare Board officer, L.B. Cowley, was under orders from the board to accompany us. 'It was an impossibility to accompany the students around the Station,' he complained to the board a few days later, 'owing to the fact they would split up and go in all directions so as to interview the residents.'
_Diary:_ I went to two houses. The first was a woman whose husband was white, with a job on the railways, and who had three children (small for an aboriginal family). The youngest child had a bursary at school, which was the first instance of this I had come across.
Yet, on the whole, we were not impressed by what we saw.
_Diary:_ The people at the reserve lived in very sub-standard houses as usual—wooden ones, which were generally overcrowded. They had no electricity or gas, I'm not sure whether they had water or not.
Beth Hansen remembers the Burnt Bridge reserve, with its 'incredibly decrepit' houses, as 'even worse than Boggabilla'. There was, she recalled, a 'sense of hopelessness there'. Charles Perkins told the press that living conditions on the reserve were 'deplorable'.
The BBC crew filmed this visit. Barry says:
We were doing the questionnaire with some families and there was this film crew filming us doing the interview and I got angry and just told them to go away because they were very obviously upsetting the family that we were interviewing. They just did not want to be filmed. It was that simple. It was hard enough for them to just do the interview, without being filmed, so I think I spoiled the take for the film crew anyway. I just thought, bugger it, what are we here for? Are we here for an English TV show or are we here to actually do something?
Meanwhile, one group of four, including Charles, interviewed the Mayor, Alderman R.G. Melville, who had thought we were arriving a day earlier, as did some of the local papers, and had waited all day for us to arrive. He had already expressed his hostility publicly, telling reporters he would be happy to answer the students' questions and would ask some of his own, such as where they had got the funds for their trip, and why they were focusing on problems in country towns rather than in Sydney. By the time we got to Kempsey, he was in full confrontational mode. Aidan Foy remembers that 'the Mayor of Kempsey, I've forgotten his name but he was a nasty piece of work, he was a nasty man . . . we got no support at all'. When the students requested Melville to sign a motion rescinding the by-law passed by Kempsey council in 1949 banning Aborigines from the pool, he refused and debated with them for an hour, disagreeing strongly that the by-law was a matter of racial discrimination, and arguing that the ban had been in force purely on the ground of hygiene. It would take, he told the _Australian_ , 'ten years of intensive health and educational efforts before restrictions on Aborigines using public baths could safely be removed'. Yet, as _Seven Days_ reporter Peter Martin pointed out, only the day before there had been a school swimming carnival where Aboriginal children had been allowed into the baths, and then at 3.30 p.m. had had to leave. 'The Cinderellas who once seemed so clean,' went Martin's narration on _Seven Days_ , 'are suddenly transformed into dangerous risks to public health.'
The pool provided us with the clear case of discrimination we needed. When the students rang Jack Lee, manager of the Kempsey picture theatre, to see if he had any objection to their bringing Aboriginal children there, he said he had none. I wrote in my diary: 'The general picture in Kempsey re discrimination was that everything was fair (a café here and a pub there excepted). On the whole a pretty middling sort of set up comparatively.' We all returned to the showground for our usual meeting. We agreed that, as in Moree, the clearest case of discrimination we had found was at the swimming pool. Indeed, as Charles noted, discrimination was even harsher than at Moree. 'Here,' said Charles, 'anybody with aboriginal blood in them is barred from the pool outside school hours. Adult aborigines are not admitted at all.' Indeed, Charles himself had been barred from the pool less than two months earlier, when he went there with Ted Noffs and Graham Williams.
_Diary:_ After some discussion we decided to go to Greenhill shanty town and get some aboriginal children and then to go to the swimming pool.
We took about ten or fifteen children with us to the pool. They weren't allowed in and this time neither were Charles nor Gary. The students stood in line across the entrance in an attempt to stop other people entering the baths until Charles and Gary were sold an entry ticket. Gary waited in vain at the head of the queue. The pool manager, Neville Duke, said he was just enforcing council regulations. My diary records a rather sad little occasion:
We blocked up the entrances as we had done in Moree but there was no one much to block the entrance to. Then we held up signs, and the press madly took photographs etc. There were very few people around and very little discussion provoked. At 5 o'clock (we had got there at 2 o'clock) we packed up and left. Charlie was very emphatic about the success of it because of the publicity, but most of the rest of us thought it an absolute flop because we had failed to force the issue within Kempsey itself. We all realised Kempsey had ignored us, which was precisely what we didn't want. We came back, some of us dejected, others jubilant that the trip was nearly over. Everyone is by now absolutely exhausted and I don't think we put much into our efforts at Kempsey.
Hostile reporting by the _Macleay_ _Argus_ , 27 February 1965.
[Charles Perkins is barred from entering the Kempsey swimming pool, Thursday, 25 February 1965.
(Photo courtesy of the Fairfax Photo Library)](chap7_9781741150575_epub_part7.html#d79191)
[Paddy Dawson, Ann Curthoys, and other students hold placards outside the McElhone Memorial Swimming Pool, Kempsey, on Thursday 25 February 1965.
(Photo courtesy of _Macleay Argus_ )](chap7_9781741150575_epub_part7.html#d41152781)
Things were getting rather ragged by this time. We had lost our energy and spirit, and indeed some of our composure. In retrospect, it seems to me that the delayed effects of the confrontation at the Moree pool, a traumatic event, were starting to set in. One of the _Macleay Argus_ reports was headed 'They Were Rude', which said the belligerent attitude of the Freedom Riders had shocked all who had observed it. They had been rude not only to the Mayor but also to the _Argus_ reporter who had asked what 'after sales service' would they offer to the Aboriginal communities they visited. When the _Argus_ reporter complained of Charles Perkins's rudeness, he offered his apologies, and said that he was 'at the end of his strength'.
This particular journalist had in fact sorely tested Charles and the other students. She had made her antagonism to the students clear early on, and continuously throughout the day. During the pool demonstration, she kept asking the Aboriginal children pointed questions, and in general acted so aggressively that she prodded Charles into asking her to 'stop intimidating his group'. Gary remembers urging the children not to answer her. Colin remembered this particular reporter years later:
The one thing that sticks in my mind at Kempsey is something I'll never forget, because you don't often come against pure hatred, really naked hatred, and it wasn't something you could actually put your finger on and say that's what it was. But it was a woman from the local newspaper [who had] come out to interview us. And there was Brian, Pat Healy and myself and a couple of others, and this woman literally oozed hatred. I've never experienced it like that. Even when we were demonstrating, the people that came up and argued with us and [were] obviously angry, I didn't get that same feeling as with that woman there, just pure hatred. A very strange sensation to face that.
One reason for this particular hatred may have been not only opposition to the students' criticism of Kempsey, but also her discovery that some of the students may have had communist connections. She suspected a connection between Pat Healy and the communist union leader, Jim Healy, and pursued Pat about her political affiliations. She had discovered that Jim Healy's daughter was named Patricia, and wondered if the student Patricia Healy was Healy's daughter. Pat remembers:
Charlie being a bit fussed about all of this and not wanting it known that I was involved—came from a communist family . . . I remember they kept trying to keep me away from this woman. So she'd come and ask for interviews and I'd sort of be spirited to the back somewhere. Finally she grabbed hold of me and sort of put to me the question, she'd obviously done her research and found that when he [Jim Healy] died he'd left three sons and a daughter called Patricia— my aunt—and so she very pompously put to me this question, 'Was Jim Healy your father?', and I said 'No'. That did take the wind out of her sails somewhat. She was silly enough not to ask me any more.
The reporter published an article in the _Macleay Argus_ headed 'The "Ride" was Red-inspired', which announced that 'inquiries made yesterday morning by the _Argus_ point strongly to Communist leadership and support of the Freedom Ride'. A letter signed 'Video' in the same issue also dwelt on the fact that some belonged to the Eureka Youth League. It was the kind of coverage Charles and Jim had worked hard to avoid, and it is interesting that neither the conservative parties nor the urban media picked up the story.
Overall, the local Kempsey response was antagonistic. The _Macleay_ _Argus_ 's coverage could not have been more hostile. In an editorial headed 'They Came, They Saw, They Sickened', it described the survey as 'an absolute farce' and the students as 'a pack of impudent rabble rousers'. Part of the hostility was the publicity; this same editorial referred to the students being accompanied by 'a string of city reporters and photographers who . . . continued to churn out stories and pictures for the world at large'. A local radio station was sharply critical, describing the students as 'just a mob of idiots out for a good time'. The local Aborigines Welfare Officer reported that Aboriginal opinion in Kempsey was unfavourable to the students, and indeed it does seem that the Aboriginal leaders there kept their distance from Charles and the Freedom Ride.
In contrast, the city coverage continued to be largely supportive. Alongside a photo of the pool manager preventing Charles and a young Aboriginal boy from entering the pool, the _Sydney Morning Herald_ report listed the signs we had held—'Rescind colour bar resolution', 'Allowed with school, why not after school?' and 'Equal at school—unequal at pool'. It reported two white girls from Kempsey High School saying most of the pupils were in favour of Aboriginal children being allowed in the pool after school hours. 'We swim with them anyway,' said young Julie Harvey, 'and it's silly that they have to go home after school hours.' The _Australian_ reported the presence of the BBC television team, and quoted Trevor Philpot as saying that discrimination at a swimming pool was a minor problem compared with the generally depressed living conditions of Australian Aborigines. 'But when students stop protesting it is a bad day. I think there is too little protest in Australia.'
Wendy Golding's photo of the students posed outside the bus. (Courtesy of Wendy Watson-Ekstein)
The media coverage continued that evening.
_Diary:_ While tea was being cooked there was another round of publicity, photograph taking etc.—us throwing boomerangs, us posing in front of the bus and so on and so on and so on.
In the end, we were not as isolated from Kempsey Aboriginal opinion as the _Macleay Argus_ wanted its readers to believe. When we left around 8.00 p.m., the Aboriginal families, as Warwick remembers, 'farewelled us all—they all sort of turned out and you know waved and sent us on our way'.
We arrived in Taree quite late at night, intending to stay at the show-ground. Gary had gone home. My diary reveals the sense of getting near the end of the trip by this time. 'As it was the last night quite a few of us were celebrating and getting merry. When we arrived at the Taree show-ground, which smelt awful, there were two huts. The drinkers went in one hut and the sleepers in the other. I was a sleeper, being absolutely exhausted.'
The last day of the trip, Friday, 26 February, began with an early start. Originally, we had been going to visit Taree for almost a full day; its board station, Purfleet, had a history of discrimination, but also an interesting history of resistance to the board through a rent strike. With our return to Moree having thrown out our plans, however, we were now well behind schedule and had little time left. The local paper carried a photograph of students lining up for breakfast (baked beans and fried vegetables) at the showground.
'He does not drink, hates crowded pools, likes to sit in front at the pictures. How can we desegregate him?' Cartoon by Molnar, _Sydney Morning Herald_ , 26 February 1965.
_Diary:_ We stopped at the Purfleet reserve for half an hour, talking to the people there.
The manager of the station, a Mr Robertson, reported this visit to the board. The students, he said, arrived at about 10.15 a.m. and left at 10.45. They walked around the station in small groups, and he as manager addressed the remaining students, including Charles Perkins. Perkins visited one Aboriginal family and the Gillawarra Gift Shop, where he and several others signed the visitors' book. This gift shop was a local success story, having been established three years earlier after a visit from Victorian Aboriginal leaders Bill Onus and Pastor Doug Nicholls. It was now managed by Ella Simon, a local leader of the community, and had become a tourist attraction with visitors from 'most parts of the world'. Alex, who later came to live and work in Taree, remembers:
When we went through Taree we stopped at Purfleet and Charlie got off the bus and talked to this lady there for a bit. I don't think she was very impressed with the student bus ride. And as I understand it later on it was Ella Simon, whom I got to know very well and helped to promote her book _Through My Eyes_.
When we arrived in Newcastle, my father came to say hello. He was not the only person to do so. Alex Mills remembers: 'We pulled into the car park at Newcastle near the beach . . . and who should be there at the time but my former school principal from Orange High School, Danny Blakewell . . . He first sort of wakened me to some interest in Aborigines.' We had lunch and a swim, and then resumed the trip to Sydney. At Hornsby, we stopped to eat and freshen up. The _Sydney_ _Morning Herald_ reported: 'Girl students tried to comb windblown hair and paint cracked fingernails, but the hectic bus trip had taken its toll.'
We were expecting a large press conference on our return, and became somewhat tense in anticipation.
_Diary:_ We had a rule about no drinking, so that we wouldn't turn up to the press conference drunk and smelly.
The Rev. Ted Noffs, of Kings Cross, welcomes back Charles Perkins on Friday night, 26 February 1965. _Sydney Morning_ _Herald_ , 27 February 1965.
When we arrived at the university in the evening, however, there was Ted Noffs, a few press, some parents, a few supporters, and that was all. My diary records rather wistfully: 'No aborigines or other supporters.' We found out later that Ted Noffs had deliberately not told anyone where and when we were arriving. Christopher Day in the _Sun_ reported that 'it was a brief welcome because Mr Noffs had wanted it that way'. Yet if it seemed a let down to us, it was not so to the press. The _Sydney Morning Herald_ recorded our return on its front page the next day, saying 'when the bus pulled up in front of the University Union building waiting parents broke into a spontaneous burst of clapping'.
Even at this point, Charles had a good speech for the press and the parents: 'I am no leader. I am only an Aboriginal lucky enough to be able to do something I think is right for my people. Without the courage and humility of these students we could have done nothing.' He also said:
This small group of students has created a new dawn of hope for my people. They have provided the impetus for a new era of doing things to help Australian Aborigines. There have been critics of our aims, our actions and our achievements. To my mind the most important feature of the trip was that we laid bare the strong prejudice against Aborigines existing in various country towns and showed that there is a hard core of white residents who seek to perpetuate this attitude. In addition we have stimulated both white Australian and Aboriginal thought so that they will now more closely and constructively consider the problems facing aborigines today.
The parents and friends, led by Ted Noffs, gave the students three cheers before they left for home and, as the _Sun_ put it, 'a welcome bed'. Actually we didn't go straight home; some of us went to John Powles's place for a wind-up party. My diary reads: 'About 10.30 pm I left and went home, thoroughly exhausted'. I had exhausted not only myself, but also my wish and capacity to write a diary. This was my last diary entry, and from here on, when reconstructing 'what happened next', I must do without it.
The tour was over. Its reverberations, though, had only just begun.
_Ch_ _apter_
_8_
Impact
The students succeeded beyond their wildest dreams in putting into practice Martin Luther King's idea of 'creative tension'. A lively debate over Aboriginal conditions and rights continued in local, urban, national and even international arenas. Messages of congratulations poured in, alongside growing criticism. Ever since, observers, activists and historians have differed about the impact of the Freedom Ride. For some, it was but a moment, overshadowed by the much larger achievements of the Referendum and the equal wages and land rights campaigns. For others, it was the beginning of a new kind of Aboriginal politics—confident, demanding and instilling in many young Aboriginal people a new belief in the possibility of change. From our twenty-first century vantage point, we can see in it elements of both.
Congratulations came, in editorials, letters to newspapers and directly to the students. Many thought they had shown great courage. Ted Noffs spoke of the students' 'rare courage that was admired even by police in Moree, where the students faced a mob of 1000 people'. Wilma Apps in the _Australian_ on 4 March said 'it takes courage to be laughed at and derided. It is with young people such as these, able and willing to criticise and correct, that the future of Australia lies.' The Teachers' Federation at its council meeting on Saturday, 7 March carried a resolution paying tribute to the students, which read:
We consider that the university students have displayed a high degree of civic responsibility in forcing public recognition of the racial discrimination existing in this State; and we pay tribute to the moral and physical courage they have shown in carrying through this undertaking.
Trade unions, especially, sent supportive letters to Charles or Jim, saying the tour had 'brought hope to the Aborigines and shame to many white occupants of their country', and ensured that 'world attention will be directed against State and Federal Governments both past and present in their failure and criminal neglect to give justice to the Aboriginal people'. The South Coast Labour Council offered its 'sincerest congratulations', and told Charles that the council had written to the Premier protesting against discriminatory practices where public utilities were concerned. Other groups with a record of sympathy on Aboriginal issues also congratulated the students. Some letters came from individuals, who frequently enclosed donations.
Support came from some parts of the Australian Labor Party, though not from the Labor state government. Bill Hartley, secretary of the Victorian ALP, wrote warmly of the Freedom Ride in the _Melbourne Herald_ on 6 March. The students, he said, were to be admired for making the trip. They had put up with 'insults and bitterness', paid their own way, given up their annual leave, and gone into debt. Their proposal for desegregation clauses in relevant Acts and local government by-laws, he predicted (incorrectly, as it turned out), was likely to win a positive response from the Labor government of New South Wales. Six days later, as Hartley wrote to Charles, the Victorian Central Executive endorsed his article and resolved to applaud and congratulate Charles and the students on their actions. In New South Wales, while the right-wing state ALP organisation continued to keep its distance, local ALP branches sometimes expressed their support. The Asquith branch, for example, wrote to Charles on 13 March, sending 'hearty congratulations to you and the Student Action Group for Aborigines for their exposure of the discrimination practised in NSW country towns against coloured residents. We all admire the courage and resourcefulness shown by the Freedom Marchers and wish you well.'
Some of the letters of congratulation came from student councils and labour clubs, and new SAFA branches were formed in several universities. Charles spoke to a meeting at the University of New South Wales, from which a SAFA branch was formed, its members including Warwick Mosman, Paul Brennan, Pauline Stewart, Lyn and Bill McLean, and Lindsay Wood. The ALP Club at the University of Western Australia announced its intention to organise a Freedom Ride in Western Australia, while Helen Moore commissioned from Jim an article for a new student paper at the ANU called _Purge_. Interest was especially strong in Queensland, where a group called Student Aboriginal Survey was formed, which organised a student petition to the Minister for Native Affairs and demonstrated outside Parliament House. Student editor Brian Toohey commissioned from Jim an article in _Semper Floreat_ , the university's student newspaper, which appeared on 1 April.
One undoubted effect of the Freedom Ride was that Charles became one of Sydney's—and indeed Australia's—best-known Aboriginal leaders. He was invited to speak by many organisations, and often did so. He was a good speaker, and knew how to attract attention. His talk on Sunday, 28 February at Ted Noffs's invitation at the Wayside Chapel at King's Cross was the first of many. Newspapers continued to carry endless profiles, and discussed his significance. It was common for a while, both at home and abroad, to compare Charles to Martin Luther King. The _NY_ _Herald Tribune_ said: 'Perkins has been described as the Martin Luther King of Australia but there are certain obvious differences. He is a tough professional soccer player noted for his quick temper on the playing field, and he made it clear more than once in dealing with mobs that passive resistance does not come easily to him.'
More significant than the congratulations was the serious and extended debate that raged over the next few weeks. Much discussed was the question of whether the Freedom Ride had addressed the important issues. One aspect of the media coverage that shocked people most was the Freedom Ride's revelation of appalling housing conditions in the shanty towns, a situation that was not much better on the reserves. Many observers, both sympathetic to and critical of the students, said the real problems facing Aboriginal people in New South Wales were not to do with swimming pools and where they could sit in a cinema, but with housing, education and health. In a curious way, the white townsfolk's repeated response that exclusion of Aborigines from pools and cinemas was a matter of hygiene not race, intended as a defence against charges of racism, served only to highlight the poverty in which many, if not most, Aborigines lived. As the _Sun-Herald_ editorial put it: 'If aborigines are barred from this or that pool, not because of colour, but because they are dirty or disease carrying, it is a damning indictment of the whole State for our failure to sweep away shanty camps and provide adequate medical services.' In a similar vein, the _Bulletin_ on 6 March described Aboriginal issues as constituting 'not a race problem but a slum clearance problem'.
So who was to blame? A common theme was that the state government, rather than the towns themselves, was to be held responsible. The _Sun-Herald_ suggested Aboriginal welfare was not the responsibility only of a few northern towns, but of the whole state, and the current situation would cost a lot of money to put right: 'The problem cannot be solved by a short-lived "crash" program. Resettlement, education, instruction in hygiene and the provision of suitable work opportunities must go hand-in-hand. And we shall have to dig deep into our collective pocket and not count the cost.' An article in _Nation_ on 6 March, entitled 'Well Protected', emphasised the inaction of the New South Wales state government on Aboriginal issues, and another in _The Bulletin_ the same day said what was needed was community and government action to clear up Aboriginal slums. Many in the towns agreed—it was not their fault that Aboriginal people lived in such dire poverty, but rather that of the government. The _Northern Daily Leader_ (at Tamworth) said in its editorial on 4 March that the Freedom Ride had diverted attention to 'the racial issue' rather than the 'social and economic obligations of the people of New South Wales for the welfare of our relatively small residue of aboriginal population'. The problem as a whole, said the _Leader_ , is not to be solved by urban newspaper criticism of country towns like Walgett, Moree and Kempsey; there was a need for 'a fresh look at the whole problem of assimilation at the Parliamentary level'. Though most attention was directed to the state government, sometimes the Commonwealth government was called upon. _The Anglican_ wrote: 'This is the time when the Commonwealth government might well call all State Governments into conference to get a unified vigorous programme moving for the benefit of all coloured Australians.'
Some letter writers thought blame lay ultimately with Aboriginal people themselves. 'Part-Aboriginal people,' wrote B. McCann of Bal-gowlah to the _Sydney Morning Herald_ on 3 March, 'possibly due to the strain of aboriginal blood, find it hard to settle down to the humdrum life of modern civilisation with its emphasis on regular work, conventional standards of living, hygiene, etc.' R.V. Bateman of Bega, an employer of Aboriginal labour and a shire councillor, made a similar point in a long letter in the _Herald_ the same day. Aborigines, he reminded _Herald_ readers, were 'only four generations removed from the Stone Age man'. What it had taken 50 000 years for Europeans to achieve, Aboriginal people were supposed to achieve in one generation. The Aborigine had, he said, 'seized the more attractive aspects of modern civilisation, and rejected those aspects which he finds tedious and laborious'. The results were appalling. Sometimes the Welfare Board and employers did provide modern housing for Aborigines, only to find 'the flooring in the new home burnt for firewood after the first cold night'. Loungeroom fireplaces were used as toilets, children's hair constantly had lice, and unhygienic conditions meant Aborigines carried diseases. Missions and reserves were not built near places of work, 'thus forcing aborigines to construct their humpies on public reserves and roads for easy access to work'. Councils, for humanitarian reasons, did not order the demolition of the resultant shanty towns. The solution, Bateman argued somewhat surprisingly, was a national approach and uniform legislation between the states. This letter was warmly praised in a _Herald_ editorial, which drew the conclusion that what was at fault was not white racism but government inaction at both local and state levels—local councils for shutting their eyes to the unhealthy conditions in the shanty towns, and the state government for failing to insist on Aboriginal education.
Some letter writers thought the task of reform lay not only with government but also with each local community, and many were appalled at the level of racism the tour had apparently exposed. In a letter to the _Australian_ on 18 March, M.H. Pears congratulated the students, and said each community must now 'make determined efforts to help its Aboriginal population. Responsible members of each town and city should bring pressure to bear upon their councils to end segregation and discrimination.' Many townsfolk had been resisting assimilation policies for over a decade; now, after the Freedom Ride, there were many expressions of a desire for assimilation. This usually meant providing housing in town, or a massive program of education in the ways of white society. The _Cooma-Monaro Express_ spoke for many when it said on 24 February that the answer lay in educating Aboriginal people in hygiene, and the way to do this was by taking 'the younger generation of the aborigines and bringing them up into our way of life. They must be taught to be clean, they must be educated beyond their present level, they must be helped to live with us, and above all they must be accepted by us all.'
A few insisted there was no problem at all. A letter to the _Sydney_ _Morning Herald_ from Walgett signed 'Realist' on 3 March said Aboriginal people in Walgett 'mix with the whites on equal terms in all Government and semi-government institutions'. The shops, said the letter, 'serve them on equal terms . . . some intermarry with white people, some live in town beside white people, dark children play with white children'. It was a shame, said 'Realist', that Premier Renshaw's defence of Walgett had not been heard amidst the huge attention given to the students.
The Freedom Ride threw the churches into something of a turmoil, caught between their doctrine of the equality of all human beings in the eyes of God, and the day-to-day reality whereby some clergymen worked with Aboriginal people while others shared the racial attitudes of their white parishioners. The debate was played out in the pages of the journal, _The Anglican_ , during February and March. Given the role of an Anglican minister in putting the students in danger in Walgett, the debate had a particular piquancy, and given the journal's national reach it involved clergymen and laymen from around the country. On 25 February, _The_ _Anglican_ carried a news item on the tour, which said the students 'deserve the thanks of the nation for their initiative and for their perseverance in the face of some local hostility'. The item went on to say there was little difference between 'our treatment of the Aboriginal people and that inflicted in some parts of the United States. The main difference is that our coloured people are much less numerous and that most of them live well away from the cities so that most Australians have no first-hand acquaintance with the problem.' This was flanked by a supportive edi-orial, which took the form of a satire on country people's negative reactions to both students and Aboriginal people. It caught many of these reactions perfectly:
During the past week or so, a collection of mere Sydney University students—irresponsible, overgrown children—have been deliberately stirring up trouble and attempting to overturn the very foundations of society in the North and West of New South Wales . . . These students, like the ivory-tower professors who are supposed to teach them, are a pretty unsavoury crowd, as everyone knows. They all live in ease and idleness for which the taxpayer foots the bill. It is well known that many of them wear long hair and rarely wash.
The chief target of _The Anglican_ 's satire, though, was not so much country views of the students, as of Aborigines:
As everyone in Moree, Walgett and similar cultural centres knows, there is just nothing to be done about Aborigines except make sure they don't go getting ideas above their lowly station in life to which it has pleased the Lord to call them . . . These students, for example, and their airy-fairy professors have the ridiculous notion that you can do something for the Aborigine by treating him as a human being.
Sadly, many letters missed the irony, and indeed it is rather telling that so many readers thought _The Anglican_ could be seriously arguing against the humanity of Aborigines. A letter from Bishop (later Archbishop) Moyes on 4 March, however, did get the irony and concluded: 'Let us thank the students for their adventurous campaign; and do our utmost to remove discrimination not only from local government documents, but from practice in these areas.'
Moyes also explained the doctrinal basis for opposition to racial discrimination:
The basis of the Christian position is the 'new' man created in Christ. This New Testament conception is most profound. It does not just refer to those in the Church but to the whole human race as Christ has claimed it for Himself and has given to each and all a new and equal worth by dying for us all without discrimination. So, in this matter of racial discrimination we Christians can have only one attitude. Any discrimination on the grounds of race or sex or class is not merely bad, but impossible without denying the Gospel itself.
The same issue, however, contained a quite different response to the Freedom Ride from the Reverend A.J. Gerlach in Brisbane. The issues, he suggested, went much deeper than the question of racial discrimination. Aboriginal people were suffering the effects of 'civilisation'. In their native state, Aboriginal people had had a very well organised society, with tribal areas, and in which tribal elders administered the law. The effects of white settlement had been to remove the tribal boundaries, language, and the authority of the elders.
With the disappearance of the tribal religion, personal discipline and morale have come to a very low ebb . . . In handing on our own civilisation we have inadvertently taken from this race not only their former way of life but [also] the religion which regulated it.
The answer, therefore, was to provide a religion to replace the one that had been lost.
The following week saw four more letters on the Freedom Ride, pondering the large and complex question of human unity and diversity, and its implications for Christian behaviour. Two of them stressed that Aboriginal people were different from Europeans. One we have already seen, from the Reverend Dowe; it not only criticised the students but also argued that 'our dark friends are just not like Europeans'. The other, from the Reverend John Parten of Brewarrina, said: 'People forget that Aboriginals are NOT Europeans—they have a completely different outlook on life. They don't want to become Europeans. They are only interested in being what they are.' Dowe's letter drew a response from the Reverend P. McD. Smith, from Kilburn, South Australia: if Aborigines are not like Europeans, he asked, 'Who then are they like? Are they like human beings? '
The most impassioned letter of all came from E.G. Morgan of Cary Bay, south of Newcastle, who introduced the question of a history of colonisation and land-taking into the debate. He accused Dowe of complacency and smugness, and went on: 'No-one in this land who is of European descent can escape his share of the collective guilt.' He argued that Europeans had filched the tribal lands and taken away the Aborigines' religious beliefs. In his own area, Lancelot Threlkeld had come as a missionary, and found that within sixteen years of his arrival the local Awabakal people 'had become completely extinct, thereby achieving that final solution to a racial problem that Hitler failed to achieve with all the advantages of modern gas ovens and machine guns'. He returned to the question of guilt:
The guilt is in our heritage as white Australians and as Christians and Anglicans. Where we have not murdered, we have degraded, and the Church has helped. Ignorance and good intentions cannot erase or excuse the guilt and shame. By what right do we deny these victims of our past their present human rights? In their own native land, their heritage for thousands of years, they are not citizens. They have no voice or vote as their automatic right, as do white Australians . . . They are not free to move about their land as we usurpers are.
The students, he concluded, 'have at least attempted something towards the righting of a national shame'.
With an election imminent, it was easier for most to blame government inaction than either white Australian civilisation itself, or the citizens of towns like Walgett and Moree. And this particular government made a good target. Premier Jack Renshaw and Chief Minister Gus Kelly had both tried to defend the government's record. The only minister not in defensive mode was the Minister for Health, Mr Sheahan, who on 6 March repeated the warning he had first made in Lismore ten days before that hospitals that discriminated against Aborigines might have their subsidies cut or withdrawn. Behind the scenes, though, the Freedom Ride prompted the Aborigines Welfare Board to pay particular attention to the Freedom Ride towns. On 16 February, the day after the students' visit to Walgett, Mr Alf Thomas, the Welfare Board Area Officer based at Moree, came to Walgett for a seven-day inspection tour. Walgett was immediately declared a separate welfare district with its own welfare officer and R. Snooks was appointed to look after both the Walgett station and reserve, and the Collarenebri reserve. At Boggabilla, houses were soon fitted with electricity, concrete floors, shower recesses and closed-in porches.
In an attempt to demonstrate the government's commitment to Aboriginal welfare, and to reply to the growing swell of criticism, Premier Renshaw agreed to debate the issues with Charles Perkins and Jim Spigelman on television for the _Seven Days_ program screened on 8 March 1965. The 45-minute program was a mix of reportage and discussion. Devoted entirely to the Freedom Ride, it gave major sympathetic publicity to the students, reaching a large television audience. After a screening of scenes taken by Jim Spigelman of students being removed from outside the baths in Moree, it showed interviews by reporter Peter Martin with Bill Lloyd and Bob Brown, and covered the Bowraville and Kempsey visits in some detail. It ended with a studio interview with Renshaw, Perkins, H.J. Green of the Aboriginal Welfare Board and Spigelman. Charles spoke about racial discrimination in the picture theatre at Bowraville, and the baths in Moree and Kempsey, and pointed to the shocking conditions in which many Aboriginal people lived. The people lacked housing,
In response, Renshaw demonstrated a good practical knowledge of Aboriginal life in country towns. Not only was he a country man himself, but the Aborigines Welfare Board had also briefed him, after talks with Chief Secretary Gus Kelly about the Freedom Ride on 1 March, three days after the students returned. The board obtained reports from the area officers at Lismore, Kempsey and Taree to complement those it already had, compiled a collection of newspaper clippings, and prepared a report for the Premier on 3 March. The board's report was fair to the students, noting the wide range of clubs and societies represented on the Freedom Ride, and the fact that students had sought and gained permission to visit stations and reserves for the purposes of the survey. The Premier began the interview by speaking highly of the Aboriginal people he knew in the western towns who were 'living in the community'—that is, assimilated into the towns. The shearers, he said, earned good money and some had houses in town. The government assisted those who lived in poverty on the edge of town 'as far as we can', and spent large amounts on housing. But then he said the problems lay largely with Aborigines themselves. When asked why educational standards were so low, Renshaw—like many others in this debate—attributed it to Aboriginal mobility deriving from their past as hunters: 'Generations of instinct have been built into them . . . they moved across the country . . . getting them to settle down after any period of time is a very difficult problem.' He opposed the idea of anti-discrimination laws, saying Aborigines already had equal legal rights. There were, he said, no rules to bar Aboriginal people from belonging to an RSL Club. education and jobs. He advocated an anti-discrimination law, a six- or seven-fold increase in spending, and an investigation of Aboriginal health.
Local debate on Aboriginal issues was coloured by the knowledge that the Freedom Ride had been reported internationally, in the United States, Europe, Africa and Asia. Fears of more adverse international publicity for Australia on race issues were soon realised. The story was covered in the _New Yorker_ , and in the _NY Herald Tribune_ Australian journalist Zell Rabin wrote: 'Church and civil leaders throughout the nation are now calling for immediate action to combat the apparently deep-seated racial prejudice in many walks of Australian life.' The _New York Times_ on 26 February emphasised the opposition encountered by the students who, it reported, 'have been pelted with gravel in their trip from small town to small town, heckled and pushed by white crowds, barred from staying in a church hall, and locked out of a segregated movie house. Their bus has been forced off the road by angry white autoists.' In Britain, _The Times_ on 25 February carried a news item on the Bowraville picket, and two days later a general story on Aboriginal issues headed 'Australians Look at Aborigines' Life', which included a very sympathetic account of the Freedom Ride and stressed the supportive coverage given to it in the Australian press. The tour was also widely covered in European papers. The story was, according to two student members of the Democratic Labor Party, picked up in an international youth and student magazine, subsequently translated into Spanish, and distributed to youth and student organisations throughout the world, including those in Latin America and Africa. The _Cape Argus_ , in Cape Town, South Africa, carried a detailed and sympathetic account of the tour on 6 April, profiling Charles Perkins and outlining the hostility of white townsfolk and the state government's response. 'These incidents,' it said, 'ensured wide publicity for the demonstrating students.' The article concluded that 'if Mr Perkins and other young aborigines do develop as leaders of their people the problems of Australia's aborigines will be much nearer solution'.
There was also some coverage in Asian newspapers. In a detailed story headed 'Discrimination Against Aboriginals in Australia?', _The Working_ _People's Daily_ in Rangoon, Burma noted the surprise with which many had reacted to the revelations of racial discrimination. The _Morning News_ in Karachi on 14 March 1965 emphasised Australian sensitivity to Asian opinion: 'Australians, already deeply conscious of the unfavourable impression their country's "White Australia Policy" has made in recent years throughout Asia, are now painfully awaiting Asian reaction to "this blot on our national character"—as one Canberra newspaperman described the exposure by the "Freedom Riders" of the plight of Australia's 100,000 Aboriginals.' The story ended: 'Some of Australia's diplomats in Asian posts may be feeling more than a little uneasy that the students brought the issue so dramatically out into the open.' And indeed diplomats from around the world were sending press clippings to the Department of External Affairs, warning that Australia's international reputation in the sphere of race relations, already low, had been further harmed.
Both local and overseas reports frequently compared Australia's racial situation with that in the United States. An External Affairs internal memo of 22 February warned that it was important 'that the position of the aborigines or part aborigines in Australia be not associated with that of the Negroes in the USA. No real comparison, in fact, can be made between the treatment of these two coloured people.' By this time, though, the comparison was firmly embedded in public consciousness locally, and was picked up in international reports as well. Indeed, it ensured the newsworthiness of the Freedom Ride both locally and abroad. On 4 March the _Herald_ carried an article by 'John Moses, who last year toured the Deep South', which carried a photograph of the students lined up outside the picture theatre, and made strong comparisons between the Bowraville picture theatre and the picture theatre in Hattiesburg, Mississippi. The _NY Herald Tribune_ story also made the comparison. It read: 'Sydney: Smug Australians who like to believe that the colour bar is something applied exclusively by White Americans against Negroes have received a rude awakening.' The Freedom Ride, it went on, had 'proved it may not be such a long way from Australia to Alabama as some of their countrymen would like to think'. The Freedom Riders, it reported, had 'found repeated examples of what the Press has called "Dixie-style" segregation in country areas'.
At home, meanwhile, public criticism of the Freedom Riders was growing. The _Daily Telegraph_ published at the end of February an article attacking their survey, claiming it contained loaded questions and the student interviewers were biased, reportedly based on information supplied by a disgruntled participant who had left early. Although he was not identified, the students all knew it must have been Derek Molloy. When Helen Seager went to Moree to do a story for _Woman's Day_ , published on 15 March, she came down firmly on the side of the Moree townsfolk and against the students. She interviewed people who said the students had caused trouble, and made much of the fact that the Aboriginal children at Moree had their own pool at the mission. Moree, she said, was 'no Little Rock', and she quoted approvingly Mayor Bill Lloyd's comment that assimilation had been set back ten years.
The critics rarely attacked the Freedom Ride as communist-inspired. Charles always feared they would, for that was the fate at that time of many radical movements. He was right to worry, in the sense that there were some keen observers of communist involvement in Aboriginal affairs. A 'special correspondent' for _The Bulletin_ wrote about the question of communism and Aborigines on 27 March, in terms identical to those in an ASIO report written around this time. In a story headed 'After the Freedom Ride', the correspondent listed communist members of FCAATSI but specifically excluded Charles from any suggestion of communist influence. It warned in more general terms that communists 'saw the Aborigines not as people but as one of a series of steps to power . . . Of all the political parties it alone has a comprehensive programme for Aborigines.' Another reason for Charles to worry was the pressure from student political groups anxious to ensure that communists were excluded from SAFA's activities. Peter Manning, president of the Sydney University DLP Society, and Denis Strangman, federal president of the Australian Young Democratic Labor Association, wrote an open letter to SAFA supporters around this time, enclosing a DLP leaflet on racialist incidents— mainly involving African students—in the Soviet Union and other communist countries, and warning them of communist involvement in Aboriginal politics. These comments seem to have had little effect, as communist students continued to work in SAFA, though in a small minority.
Much more serious was the continuing charge that the students had heightened white antagonism to Aborigines, and then left the latter to deal with a highly charged situation. The _Sunday Mirror_ on 28 February quoted Professor Elkin, well-known anthropologist and member of the Aborigines Welfare Board, saying that the students had aroused hostility amongst the whites in the towns, leaving a legacy of hatred for Aboriginal people in those towns to deal with alone. The Freedom Riders, he said, 'have come home, the Aborigines are still in the towns'. Existing organisations for Aboriginal rights had some similar concerns. Bert Groves of the APA wrote a letter critical of the Freedom Ride which appeared in a number of publications, including _The Dawn_ and the _Northwest Champion_ , in which he defended non-Aboriginal Australians against the charge of racism. Most Europeans, he wrote, were 'fair-minded' people who 'judge individuals on their own merits'. It is the Aborigines 'with the chip on the shoulder who create the false issue and make Europeans dread them'. It was important for Aborigines to lose any feeling of inferiority, and not to 'dwell bitterly on the injustices and blind prejudice we have met. Let us not look at our white neighbours with accusing eyes.' He stressed that these were his own views, and noted that they 'may not be the views of the three associations that I hold executive positions in'. Also a little wary at first was the Aboriginal-Australian Fellowship, which agreed on 3 March to congratulate the students, but also arranged its own visit to the Freedom Ride towns to find out for itself the views of Aboriginal people there about the tour. Peggy and Charles Leon, two of the organisation's Aboriginal members, visited Moree and Walgett only a week after the students returned, and reported back that most local Aboriginal people in both towns were in favour of the SAFA visit. At the fellowship's next monthly meeting, Faith Bandler moved that they welcome the discussion generated by the students' tour, and noted that 'all methods have their place if used wisely'.
Criticism also came from student bodies. The students' own national body, the National Union of Australian University Students, debated the Freedom Ride at length at its February council meeting, and so great was the criticism that in the end it was neither supported nor opposed. NUAUS did decide, however, to strengthen its own Aboriginal policies. Keith Crook, a student at the Australian National University, wrote an article critical of SAFA saying that the tour had 'increased tension in the areas visited and set back the prospects for integration of the aboriginal and white communities'. Crook opposed the notion of creative tension, drew attention to social stratification within Aboriginal communities, and suggested the issues may be social rather than racial.
Abschol, a subsidiary of NUAUS, also reacted cautiously. On their return to Sydney, the students each received—individually—a letter from Warwick Mosman, Abschol's national director, seeking their views on a range of issues. They were asked what they thought about demonstrations and picketing tactics, whether they had 'pre-conceived opinions', and whether they thought their actions had hindered the process of 'integration or assimilation of the aboriginal population'. It also asked the students whether they thought local Aboriginal residents were sincerely in support of SAFA's aims. Mosman analysed the Freedom Riders' responses and wrote a favourable report for NUAUS, saying the tour had encouraged much 'healthy criticism'. At its annual conference in April, Abschol considered its formal response. As Tom Roper later wrote: 'SAFA had gained an invitation to the conference with almost full rights but hostility was widespread. I was SAFA's delegate and for one whole day had to combat completely false views on the Ride.' After a long debate which Roper described as 'one of the bitterest debates in Abschol's history', the following cautiously supportive motion was passed (by nine votes to six):
That this conference, while noting that the effects of the SAFA tour of northern NSW towns were not entirely successful in the achievement of the stated aims of this tour, nevertheless supports the aims of SAFA and congratulates SAFA on its action and on the achievement of those results which were undoubtedly satisfactory.
The critics had a point; there _was_ trouble in the towns. Even before we had arrived back in Sydney, we knew that Bob Brown's shop had been pelted with eggs and his sister-in-law threatened. When I met Bob Brown in 1991, he told me the day after the baths incident the windows of his shop were smashed in. People would abuse him in his shop, custom fell off, and he 'got thumped' in a hotel. Supporting the Aborigines was the 'kiss of death' for business. People would drive up and down outside his house at night, yelling threats. He was barred from the baths for years, and barred from hotels by the publicans. He was also, he told me, excluded from the Moree Golf Club, of which he'd been a member. He was constantly called a 'gin jockey'. Actually, Bob said, he was quite a womaniser in those days, but he never had any contact with Aboriginal girls.
Moree was clearly in a state of high tension. The Monday after the students left town, the Mayor called a meeting of the council to discuss the whole issue. Bill Lloyd told me in 1991:
We met in a second-storey room, near the Wesley chambers, for security reasons. There were various groups meeting in the town, and other people taking their car registration numbers. It was very divided, some people very very bigoted, anti-Aboriginal, and others the opposite. There was much animosity and ill-feeling. Aborigines then were very much victimised and ostracised in general. It was amazing. The Freedom Ride disclosed how much anti-Aboriginal feeling there was.
One of the groups meeting that day was possibly the newly formed Society for the Advancement of Aborigines at Moree. Several whites, including Bill Forrest who had spoken at the public meeting on 17 February called by the students, formed a sub-committee to draw up a constitution, and then called together an all-Aboriginal group.
When the Moree council met on 1 March to discuss the pool resolution it decided to delay the rescission motion for another three weeks. Bill Lloyd said the council needed time to frame an alternative resolution, and announced rather defiantly that 'we will do it in our own good time. We will not be forced or intimidated to take action by an irresponsible, juvenile, immature body of students.' John Butterworth wrote to Lloyd on behalf of SAFA soon afterwards, expressing 'amazement and disappointment' at the delay in putting the motion to council. In a letter to Jim Spigelman, Bob Brown explained that the council members felt they had 'put the students in their place and regard the fact council has not rescinded the motion as some sort of victory'. When the delayed motion came to council three weeks later, on 22 March, it was again deferred on the grounds the council needed to conduct a 'proper' survey of the people of Moree to find out their wishes. Again the Mayor refused to be 'pushed' into giving an earlier decision. A Moree resident named Philip Hayward wrote to me in 1994 that 'the aldermen decided that they would not move at that time, not wanting it to be thought that they were being "railroaded" into a decision. So they deliberately withheld their move for a few months.'
In the face of criticism, and the tense situation in Moree, it was especially important to Charles and the other students to know that many Aboriginal people actually welcomed and supported the Freedom Ride. In his many talks and speeches after his return, Charles emphasised this Aboriginal support, and pointed out that Aboriginal criticism came only from that very small minority of Aboriginal people who had something to lose. This was one of his main themes at a large meeting held by SAFA on 3 March in Orientation Week at the University of Sydney. About 350–400 students, mainly first years, attended, and all the speakers—Jim Spigelman, Ted Noffs and Bill Ford, as well as Charles—were listened to intently. Charles took the opportunity to respond to his Aboriginal critics, saying 'Uncle Toms' in the Aboriginal community still wanted to cling to the few privileges granted them by the white man. Ted Noffs supported Charles's criticisms, saying that 'the students had spoken out for the dispossessed Aborigines, not for the few who had already arrived'. In speeches and interviews from then on, Charles often stressed the high levels of support received from Aboriginal people in the towns—78 per cent, he told _Outlook_ —but also mentioned that there were people who were apprehensive and others who wanted to preserve the status quo, so as to keep the few privileges they had already gained. In an interview in _The Methodist_ , Charles said that 'what we gave aboriginal people in the towns we visited was hope. We stirred their imagination, their desire for human rights, and we have cultivated a feeling of oneness, of unity among the aboriginal people.'
Alan Outhred, Louise Higham, Ann Curthoys and Gerry Mason in the Student Action for Aborigines stall at the University of Sydney during Orientation Week, 3 March 1965.
The same theme emerged in the letters and articles many of the Freedom Riders now wrote about their experiences. Their analyses show how much at least some of them had learnt in a short time. Sue Johnston wrote a letter to the _Herald_ on 8 March answering some of the criticisms made in letters to the editor. She pointed out that the students, far from abandoning Aboriginal people in the towns, had kept in close touch with them since. Sue also pointed out that the students themselves did not use or like the term 'Freedom Riders', and did not argue that Australian and American situations were perfectly parallel. Warwick Richards and four other Christian students wrote a long, articulate letter to _The Anglican_ , in reply to the criticisms of the students made by the Reverend Dowe, assuring _The Anglican_ 's readers that SAFA 'does not see its work as ending on the last night of the bus trip. Contact is being kept with Aboriginal friends made during the trip and the year's programme is being planned to include sustained visits by students to Aboriginal Settlements with the intention of discussing Aboriginal problems and opportunities with the Aborigines.'
Jim Spigelman, Hall Greenland and Alex Mills all wrote articles in _Honi Soit_. Jim argued on 1 March that the Freedom Ride had achieved its aims—arousing public attention, breaking down discrimination and stimulating the interest of Aboriginal people in resisting discrimination. For him, as for many other Freedom Riders, the most important aspect of the tour was the 'enthusiastic reception and gestures of support in towns such as Walgett and Moree'. The task now was to 'keep public debate consistently probing the problems'. SAFA, he thought, had 'created a place of its own, as an activist organisation'. Its continuing task must be to keep the issues in the public eye. Hall Greenland took up the theme of Aboriginal response and action two weeks later. For him, the key issue was the development of Aboriginal militancy, which in the long run must seek stronger and more natural allies than students could provide, and for Hall this was the labour movement. He was critical of aspects of the Freedom Ride, especially the transitory nature of its visits. Perhaps forgetting his own late arrival in Walgett, he pointed out that the students stayed only a day; they held no meeting on the reserve, and they made no attempt to initiate any organisation. There would have to be longer stays in future (as indeed there were, as we shall shortly see). He was critical of the Cabbage Tree Island cooperative, and the students' uninformed support for it. It was, he said, 'a flop', heavily indebted.
The students had clearly returned in an evangelical mood. They wanted to do something more, despite—or perhaps because of—the fact that they had all, as Jim Spigelman put it, 'had an insight into the sheer complexity of the problem'. In the weeks and months following, many students spoke to various groups, especially church organisations and trade unions, on request. I remember going with Warwick Richards to speak to a Christian youth group, and the minister asking why were we trying to get Aborigines into hotels when alcohol was so destructive for them. And there were many others. Louise Higham sent me a copy of her lecture notes for one such talk, which outlined the formation of SAFA, what the students had learned on the tour, Aboriginal reaction and plans for the future (election meetings and continuing pressure). Jim Spigelman was invited to speak on 9 May at a seminar organised by the Australian Institute of Political Science called 'Aborigines in New South Wales'; his topic was 'The Student Point of View'. The left-wing magazine _Outlook_ carried an article, 'The Student Bus', which was in fact the transcript of an interview conducted by Bill Ford with Jim Spigelman, Pat Healy, Paddy Dawson, John Butterworth and Charles Perkins.
Yet most of the students felt they had to do more. They were anxious not to rest on their laurels and wanted to work out a new plan of action. SAFA held its Annual General Meeting on 23 March, at which it endorsed a new constitution and elected a new executive. Charles was elected president, John Powles vice-president, Jim Spigelman secretary, Pat Healy assistant secretary, Eric Doldissen treasurer, and Sue Johnston publicity officer. The committee members had all been on the Freedom Ride— Darce Cassidy, Brian Aarons, Paddy Dawson, Aidan Foy, Beth Hansen and Chris Page, with Alex Mills being coopted later. The meeting canvassed all sorts of plans for further action—study groups, new branches on other campuses, demonstrations at election meetings, visiting Aboriginal reserves, encouraging Aborigines to vote. When the committee met a week later, it discussed the future of SAFA at some length.
Given this earnest consideration of future action, many of the students were very offended by a skit involving Barry Creyton that appeared on 30 March on the satirical TV show, _The Mavis Bramston Show_ , called 'Chug Chug Chug off to Moree'. It took up the idea of spoilt middle-class university students having fun in Moree and forgetting about Aboriginal problems in Sydney.
I usually spend vacations at Surfers with Eddy Schwartz
But this year I went to this rather plush resort
I long for something quiet
That wouldn't cause a fuss
So I joined some friends on an old government bus,
Ha, fun
And we went chug, chug, chugging off to Moree
And many other towns in the State
I took it as a penance
To assist the oldest tenants
Of our island to assimilate
We really started up in every centre
And when the Councils moved in for the kill
I shot my picket in my pocket
And I took off like a rocket
To daddy's little home in Bellevue Hill.
. . .
Hello, oh Charles, how are you?
Charles, another picket.
Well gladly.
You know I'd love to help.
Such fun.
Yes, what's that Charles, where, Redfern,
I'm sorry, Charles, but aren't you forgetting
Redfern is a suburb of Sydney
Well I mean, country towns, yes, but I mean,
Redfern is just a little bit too close to home
Don't you think?
I'm sorry Charles, next year perhaps.
Redfern has it tough today
But it's not quite far enough away
From daddy's little mansion in Bellevue Hill.
By early April, New South Wales was in election mode; the election date had been set for 1 May. After 27 years in power, Labor was in danger of losing. Despite the fact that Aboriginal policy had rarely, if ever, featured as a significant issue in state elections, it did generate some discussion this time. The _Sydney Morning Herald_ in particular used Aboriginal issues against the Labor government, which (as usual) it opposed. It published its own study of racial discrimination in Sydney on 6 April, showing that while Aboriginal people could use Sydney's swimming pools and cinemas, and most hotels and clubs, there remained subtle prejudice in many aspects of life—for example, in RSL Clubs, some hotels, white-collar jobs and some accommodation. Charles told the _Herald_ there were hotels in Sydney which imposed bans irregularly against Aborigines at the whim of the licensee, and pointed out that Aboriginal people were often refused jobs on the basis of their colour. It was not easy, said the _Herald_ , to track down the extent of discrimination since, as Ted Noffs and H.J. Green both pointed out, most Aboriginal people were too proud to draw attention to it.
As the election drew closer, the _Herald_ continued to criticise the continuing inaction of Gus Kelly as the Minister Responsible for Aboriginal Affairs. Its unidentified 'political correspondent' commented on 7 April that Kelly had:
sought to apply his tried and tested formula of sitting tight and saying nothing to the recent controversy on aboriginal rights stirred up by the bus tour of inland centres made by a group of university students . . . Then, when it was revealed that a strict colour bar applied to admission to the theatre at Bowraville, Mr Kelly, who previously had boasted that the law recognised no distinction in NSW between aborigines and whites, said he had no power to prevent segregation of aborigines in public theatres and halls. Yet he is responsible not only for aboriginal welfare but also for licensing cinemas. His political mishandling of such a delicate issue has cost the government friends among those devoted to equal rights for aborigines, and has left an impression that Mr Kelly lacks the intellectual stature to be entrusted with their protection.
Though SAFA was only partially aware of it, the winds of change in Aboriginal affairs were blowing at a national as much as at the state and local levels. The nationwide campaign for constitutional change was gaining momentum. A month after the students returned, Prime Minister Menzies agreed on 1 April to hold a Referendum on whether section 127 of the Constitution (concerning the census) should be repealed, though he refused to do the same for section 51 (concerning Commonwealth ability to legislate specifically for Aborigines). In debate, Kim Beazley Snr argued that the Referendum should also cover section 51. 'We have,' he said, 'almost the worst native policy in the world'; anyone who said the states had been doing a marvellous job was 'either very blind or very complacent'. A campaign to have the Referendum cover both offending clauses raged over the next six weeks. Abschol circulated a petition, presented to Parliament on 20 May (to all tertiary students), asking the Commonwealth government to abolish section 51. Two days earlier, the tide had turned when Billy Wentworth, a Liberal backbencher, spoke in the House of Representatives in support of a Referendum on both sections. A bipartisan policy now seemed likely to emerge.
Although SAFA supported the Referendum campaign and helped to distribute the petition, its focus remained firmly on state issues. During April it campaigned hard to pressure both major parties into adopting a new Aboriginal policy. This was a tough assignment: both major parties supported current assimilation policies, and neither wished to make Aboriginal affairs an election issue. _SAFA Talkabout_ urged members to attend both parties' policy speeches, picket outside and ask questions inside. SAFA produced a leaflet to distribute at election meetings; it was headed 'Aborigines', drawing attention to racial discrimination, Aboriginal people's sub-standard dwellings, and their low levels of education. Picking up on Renshaw's unfortunate phrase after the Walgett visit—'there is no undue discrimination in Walgett'—SAFA now argued that the current state government had done little for Aborigines. 'As for the honourable leader of the Opposition,' SAFA's leaflet continued, 'the usually outspoken Mr Askin has been amazingly silent on this issue.' The leaflet then demanded the government:
• double expenditure;
• call for action to change the Constitution;
• implement civil rights clauses in relevant legislation;
• increase Aboriginal representation on the Welfare Board;
• set up an all-party parliamentary committee; and
• delegate state powers to give the federal government full control of Aboriginal affairs.
SAFA members then attended several election meetings. They stood outside a Liberal Party rally in the Sydney Town Hall on 5 April, holding banners asking 'What is Liberal Party policy on Aboriginal poverty?' and urging people to 'vote for the party that will do something for Aborigines'. Some had gained tickets to the rally inside, and heckled the Prime Minister, Sir Robert Menzies, when he addressed the 2500 Liberal Party supporters in the hall. Another group of about a dozen students, including Alex Mills, drove to Orange that same day to question the leader of the Country Party, Roden Cutler, at his election opening speech. They staged a mild demonstration, distributed leaflets inside and outside the hall, and listened to Cutler's speech quietly in the audience of about 300. When he had finished, they asked the only two questions of the evening. The local newspaper, the _Central Western Daily_ , did not record the questions, but it did report the answers. In answer to the first, Cutler stressed the importance of education, and to the second he said the Country Party would support the establishment of a Select Committee to study the plight of Aborigines.
When Labor launched its campaign on 8 April, SAFA members were probably there, handing out leaflets, though I have not found a newspaper report which mentions them. Renshaw's election speech made no mention of Aboriginal policy, except to indicate plans to create a Ministry of Welfare to include Child Welfare, Social Welfare and Aboriginal Welfare which suggests a strengthening of the existing assimilation policy. In his election advertisement for his own electorate in the Walgett _Spectator_ , however, Renshaw did cite in his list of achievements for the area to date the following: 'Appointed Aborigines Welfare Officer at Walgett. Building 12 homes for Aborigines—£32,000 and has approved £40,000 to further improve Aborigines' housing.'
SAFA was also ready for the launch of the Liberal Party election campaign on 13 April. Earlier in the day, it held an organising meeting to discuss tactics, with well over 60 students present. A motion to demonstrate wearing KKK clothing was lost 34 to 28, and another to interject at the rally and then stage a walkout was carried. Students heckled Robin Askin's policy speech; when he had ten minutes to go, one of them called out, 'Have you got a policy on Aborigines?' Askin replied that he believed Aborigines were entitled to the same rights and privileges as other Australians. Another student yelled 'You're as bad as Renshaw' and the group then filed out of the meeting. After the students had left, Askin promised to set up a Parliamentary Select Committee to investigate Aboriginal conditions.
That same day, 13 April, SAFA held its own public meeting in the Lower Town Hall on 'The Freedom Ride and You'. Faith Bandler, Ted Noffs and Charles Perkins spoke, and the meeting drew a crowd of 300 people. The Aborigines Welfare Board declined the invitation to be represented on the platform. Each of the speakers stressed his or her own particular concerns. As secretary of FCAATSI, Bandler emphasised the need for the amendment of the federal Constitution and the likelihood of a Referendum that year; Noffs said that legislation was not enough and that attitudes had to change; while Charles Perkins hinted somewhat mysteriously at further student action in the next fortnight.
Right in the middle of the election campaign came the Eighth Annual Conference of FCAATSI, always held at Easter, that year on 16–18 April. There were 200 delegates, 70 of them Aborigines and Torres Strait Islanders, representing 56 organisations. Charles was one of four delegates from SAFA. He now had to face his critics from within the Aboriginal movement, and had good reason to be a little apprehensive after receiving a letter from Stan Davey, the non-Aboriginal federal secretary of FCAATSI, which seemed to contain part congratulations, part implicit criticism. It welcomed the attention brought to Aboriginal demands, but was critical of Charles's lack of prior contact with the Aboriginal communities visited and asked him to prepare a statement 'as to the preliminary steps taken by SAFA to set up this action? This would be a useful document to have circulated to Conf delegates before they arrive in Canberra—I would hate people to get the idea that all they have to do is get on a bus and charge into any district in which they have heard there is discrimination.' In particular, Davey wanted Charles to make clear 'the prior contact with local Aboriginal communities, how they were involved, how SAFA made contact and gained their support'. He also asked Charles to clarify whether there had been 'any thought given to the follow up necessary and what support can be given to Aboriginal leaders in the various districts who must of consequence face deepened hostility from the minority who were so active in opposing you? '
After outlining SAFA's aims and achievements in his speech to the conference, Charles said, in reply to Davey's questions, that 'the significant feature of the tour was the support, morally and physically, received from the Aboriginal people. Ninety-nine per cent of the people gave us full support. Wherever we went we consulted them first about the situation and whether they wanted our group there or not. The response of the people was justification for our efforts.' He also returned to Martin Luther King's notion of 'creative tension': 'We realise that tension has been heightened in some towns but this is inevitable and I believe it is "creative tension". The problem is out in the open now and is stark reality whereas before it was suppressed and not considered at all.'
In discussion, Charles received support from Bill Forrest, who spoke about developments in Moree—especially the formation of the local association and its very high Aboriginal participation. 'The protest by Students for Aboriginal Action in February,' he said, 'gave many Moree citizens their _first_ opportunity to grapple with such a situation.' He thought the outside assistance from the students had been essential to get things going. He was critical of 'those who tend to think that the "Freedom Rides" disturbed a rapturous harmony between 1000 Aborigines deprived of the use of all public utilities and 6000 and 7000 Europeans permitted to use them', and who thought the students 'created racial strife where none had existed previously'. Such 'harmony', he said, had existed only because Aboriginal people in Moree had not felt sufficiently adequate to challenge this outrageous inequality—and had been prepared to 'keep their place'. Those in the town who were against the ordinance and discrimination had been able to do little on a purely local basis: 'We want all the assistance, particularly moral assistance, we can get.' Other speakers were also in support of the Freedom Ride. The president of the Armidale Aboriginal Advancement Association reported that the 'awakening of group identity and individual dignity . . . seems to be a general trend throughout the Commonwealth as the action of a student group of the Sydney University has, in particular, emphasised. The most impressive aspect of this awakening is the re-emergence from their own ranks of a national leader of his own people in the person of Charles Perkins.' Charles had thus come through the FCAATSI conference rather well.
[Students hold 100-hour vigil outside Liberal Party and Labor Party NSW headquarters, 27–30 April 1965.
(Photos by Bruce Adams, and reproduced courtesy of the Australian Photographic Agency Collection, State Library of New South Wales)](chap7_9781741150575_epub_part7.html#d41152971)
But SAFA felt it was getting nowhere in the state election campaign. In the last days of the campaign, in protest against the failure of both parties to make 'any constructive reference to plans for aborigines' future', it held a 100-hour vigil outside the headquarters of both the Labor government and the Liberal Party, which ended at 8.00 p.m. on election day. As expected by many, the 1 May election saw Labor lose and a new Liberal–Country Party coalition come to power, with Robin Askin as Premier and Eric Willis as Chief Secretary. The only change they had committed themselves to—and that not very energetically—was a Parliamentary Committee of Inquiry. The situation was not very promising. SAFA had made one useful contact in the new government, however. Carrick, the state secretary of the Liberal Party, was rather impressed with their commitment at their pre-election vigil, staying outside the party's headquarters even in cold weather, and had had a number of casual conversations with the picketers. He suggested, as he later wrote to Eric Willis, that 'they might care to call upon me in the post-election period to put their views. They agreed to do so.'
Change was on its way faster than the students had hoped. Three days after the election, despite the hostile reception given to the students by its Mayor, Kempsey became the first town to change its policies as a result of the Freedom Ride. At a council meeting on 4 May, the government medical officer, Dr S.H. Marsh, told the Kempsey council that no health grounds existed for the ban; even though Aborigines were more liable to have hookworm and roundworm than were others, these could not be transmitted at the baths. The council then resolved to lift the ban on Aboriginal use of the McElhone Memorial Swimming Pool. The Town Clerk of Kempsey wrote personally to Jim Spigelman on 11 May to advise him of the change, which was reported in the Sydney papers, the _Sun_ being especially supportive.
The situation was also at last changing in Moree. On hearing the news of the second deferral of the rescission motion, Ted Noffs told the press that legal advisers of the students were preparing a report on the council's action. In Moree itself, those who supported rescission— including the Mayor—also sought legal advice, which was that the 1955 resolution was invalid and illegal under the _Local Government Act_. This legal opinion seems to have clinched victory in Moree for the opponents of the resolution, and a meeting of council on 3 May agreed that it would be rescinded. On 25 May, Moree council finally removed the offending resolution by a vote of six to one, and replaced it with a 'hygiene' motion. Charles described the results of the Freedom Ride as 'already spectacular'—Moree and Kempsey councils had both lifted their ban on Aboriginal use of their swimming pools.
While the debates in Moree were still in progress, the SAFA committees at the University of Sydney and the University of New South Wales held a joint meeting on 12 May to discuss overall policy and planning in the context of the new government. The meeting agreed that, while SAFA supported the campaign for the Commonwealth government to assume responsibility, state governments had a moral and legal responsibility to legislate for the welfare of Aboriginal people in their state. SAFA's demands on the new state government would include: abolition of reserves and stations; provision by the state's Housing Commission of housing for Aboriginal people; provision by schools of extra study facilities for those children who did not have them at home; and the inclusion of anti-discriminatory clauses in all relevant state Acts. These demands were not only SAFA demands; they were becoming the focal point of Aboriginal politics in New South Wales generally, and were to remain so until the end of the decade. It was also agreed that SAFA's tactics would include working with Sydney activists, visits to country towns and production of a SAFA magazine. A list of fifteen students, including Charles, Pat, Sue Johnston, John Butterworth and Sue Reeves from the Freedom Ride, signed on for the Sydney activities.
The reference to working with Sydney activists is especially interesting. SAFA was nothing if not responsive to criticism. Founded in response to critical comment of a demonstration for African American civil rights, it now tried to respond to criticisms that students had ignored the situation in their own backyard—Sydney. Charles himself was already deeply involved in a new wave of Sydney-based Aboriginal radicalism, centred loosely on the Foundation for Aboriginal Affairs and the Aborigines Progressive Association. He joined a protest organised by Ken Brindle, a leading Redfern figure, at the Burlington Hotel in Haymarket, which did not allow Aborigines into its lounge. On 21 March, three weeks after the students' return to Sydney, up to 40 Aboriginal people walked into the Burlington and staged a sit-in demonstration. As it turned out, they were served without incident, and the _Sun-Herald_ carried a photo of Clarrie Cook, Ken Brindle, Geoff Holton and George Jackson drinking in the lounge.
The other students wanted to get more involved with Sydney issues too. A letter to members from assistant secretary Sue Johnston in mid- March had said SAFA was now 'turning its searching eye on Sydney and aboriginal conditions, specifically the rent situation and the anomalies in the Welfare Board Elections'. A joint SU–UNSW group decided that a good Sydney-based action would be, as Pat Healy later wrote, to 'try to interest an Aborigine in standing for council elections'. This idea was preferred to other suggestions, such as a door-knock campaign to meet Aborigines and inform them of voting rights and social services provisions. Yet SAFA's attempt to do something in Sydney was frustrating. Pat later wrote:
We contacted APA, AAF and the Foundation and had a meeting with delegates from these organisations to discuss the matter. Delegates seemed fairly enthusiastic and agreed to report back to their own organisations and try to find a candidate. This scheme unfortunately lapsed for lack of a suitable candidate . . . Tom [ _sic_ ] Leon offered as candidate but felt he was too old and not suitable.
By May, SAFA was struggling to find new directions, and some of its former energy seemed to be dissipating, or turning elsewhere. There were plans to produce a magazine, called _Sundown_ , but they came to nothing when SAFA realised it didn't have the funds for such a project. Some of the Freedom Riders were becoming deeply involved in the movement opposing Australian participation in the American war in Vietnam, announced on 29 April 1965, the day before the New South Wales election. The Labour Club and ALP Club students in particular were turning to the growing anti-war movement. Some of us attended the Australian Student Labour Federation conference in Canberra on 26–27 May 1965, and while there were arrested in a demonstration against Australian troops being sent to Vietnam. Of the twelve arrested, five—Bob Gallagher, Brian Aarons, Paddy Dawson, Alan Outhred and myself—were SAFA members.
In mid-year, some of the more thoughtful media commentators began to ask, now that some time had passed, what the Freedom Ride had so far achieved. A journalist and a journal editor in different ways attempted to provide some answers. Bruce Maxwell, the _Herald_ journalist who had travelled with the Freedom Ride, did a follow-up story. It was the first in a genre that continued for years afterwards and indeed continues today. In his article 'Following the Freedom Riders', published on 16 June, he investigated what was happening in the towns. His story emphasised the positive effects that had already flowed from the Freedom Ride. First Kempsey and then Moree had lifted their respective bans on Aboriginal use of council swimming pools. The local Aboriginal people were getting organised in Walgett. Houses at the Boggabilla reserve had been renovated, and the board had promised to remove the open sanitary pit beside houses at Gulargambone reserve.
One of the most thoughtful and far-reaching of all the assessments came from Ian Spalding, editor of a newsletter of information and discussion, _On Aboriginal Affairs_. Although, as we've seen, he had originally been a little suspicious of the plans for the Freedom Ride, he had since become very supportive. His analysis of the Freedom Ride appeared as a 'guest editorial' in the Students' Christian Movement journal, _Crux_ , in June–July 1965. He began by noting the wide debate the students had generated. 'Reasonable questions,' he wrote, 'can be asked about the wisdom or efficacy of projecting outsiders into those local situations where social class and colour are tied inextricably. Certainly city students of either the long- or short-haired variety would rarely constitute the ideal group for such a purpose.' Nevertheless, the Freedom Ride constituted 'a stinging challenge to the whole country'; it was 'bigger than those who participated in it'. 'It was a direct and rude blow at the genteel silence that has clothed injustices with respectability, a side-swipe at the self-righteousness that has allowed Australians to warm themselves championing the causes of the Bantu at Sharpeville or the Negro parents at Little Rock.' The students, Spalding wrote, 'rode out headlong to identify with Aboriginal poverty and humiliation, nation wide and generations deep'. He called for a greater understanding of Aboriginal history and the history of colonisation, and gave a considered historical account of first contact, the brutal practices of colonisation and the impact on Aboriginal people. He also drew attention to the fact that it was Aboriginal memory of a deep historical wrong that affected current relationships. Finally, in language that seems to belong more clearly to the 1990s than the 1960s, he wrote: 'Many young Australians seem to be recognising that the representatives of two peoples, not one, are the occupants of this land. The "freedom riders" belong to such a company.'
He called on the churches to change their own attitudes. 'The churches,' he wrote, had 'had less and less to say to the nation.' The Statement on Aboriginal Policy issued by the National Missionary Council of Australia in 1963 had recognised distinct Aboriginal rights, the importance of Aboriginal initiative and consent, and 'that Aborigines have just claims for assistance based upon their prior occupation of this land'. It was time these policies were digested by the Australian Council of Churches. Spalding hoped that one day Christian citizens in congregations across the country would stop talking about assimilation and start talking about the rights of Aboriginal people to justice and compensation.
In retrospect, it seems that the Freedom Ride, limited though the students' understanding of the issues and ideas about the future may have been, placed the question of 'rights' more firmly on the public agenda than it had been before. It created a social tension on Aboriginal issues which had mixed short-term consequences, but which did indeed make possible the emergence of something new. It insisted that Aboriginal conditions and demands raise moral and economic questions which white Australians had, at last, to face. And it stimulated a new kind of Aboriginal politics, with far-reaching consequences.
_Ch_ _apter_
_9_
More Freedom Rides
During the years I was collecting material for this book, I would often come across people who said they had been on the Freedom Ride, or people who said a friend or relative had been on the Freedom Ride, and whom I knew had not. Everyone wants to have been in on the action, I thought. I also noticed that many people referred to the Freedom Rides in the plural. Gradually I realised the importance of the 'follow-up trips' to Walgett, Bowraville and other towns. Many people—Aboriginal activists and non-Aboriginal students—had been involved in these events, and they have a great significance in popular memory. For some, they are more important than the original Freedom Ride. While they did not attract the enormous publicity of that first tour, they did signify the emergence of a new kind of politics. In Walgett especially, SAFA achieved its ideal of cooperating with and supporting the self-directed actions of local Aboriginal people. The story of these later Freedom Rides has not yet really been told, partly because existing historical accounts tend to be focused on Charles Perkins, and Charles was only slightly involved. Other Aboriginal leaders, like Harry Hall and Ted Fields in Walgett, and Chicka Dickson in Sydney, came to the fore. Amongst the students, the initiative gradually shifted from Charles and Jim Spigelman to Darce Cassidy, Aidan Foy, Wendy Golding, Barry Corr, Sue Johnston and others, and to some newer SAFA members like Sue-Ann Loftus.
Charles's April promise to the FCAATSI conference that the students would follow up their action in the towns was formally endorsed at a SAFA meeting in May. Some of the towns the students visited over the next year or two were the original Freedom Ride towns—Wellington, Boggabilla, Bowraville and of course Walgett—while others were new to SAFA, like Bega and Griffith in the south of the state. These visits were SAFA's sustained reply to the charge of having 'stirred up trouble' and then left the local communities to cope with the backlash, and involved cooperation with local and Sydney-based Aboriginal people on a much wider scale than the original Freedom Ride. The relationships which developed between the students and some of these local Aboriginal activists became quite strong—especially in Walgett—as they learnt something about each other's lives through sharing housing, food and conversation. In some cases, they still keep in touch through Christmas cards and the like, and they still remember each other with warmth and affection today.
The follow-up visits began during the May vacation. Charles and Paddy Dawson had moved at a committee meeting on 30 March that the students return shortly to Kempsey, Charles calling for volunteers and Paddy moving they go there by bus the following Sunday. The motion was lost—no one was up to going anywhere just then. However, by early May the mood had changed, with a SAFA meeting on 4 May agreeing on the May vacation visits with the following aims:
• to establish contact with and support organisation amongst the white and Aboriginal people;
• to complete a log of claims and complaints from each town to present to the Aborigines Welfare Board;
• to encourage Aborigines to register as voters.
At another meeting a week later, there were nine people ready to go to various towns over the following two weeks—two to Bega, one to Bogga-billa and six to Walgett. There seems to be no surviving report of Bill Kitchener's visit to Boggabilla, but Howard Foley did write a report on Bega, a town on the far south coast of New South Wales, which gives some idea of the kinds of information the students sought and brought back. There were, he reported, 60–80 Aboriginal people, rising to 200 in the picking season, in a town of 4000 whites. He described the poor housing several miles out of town, and the presence of Aboriginal people on the surrounding farming properties, tolerated by the growers 'because they constitute a pool of picking labour'. Foley also reported on Aboriginal unemployment and reliance on social services, though some worked at the local sawmill and with the Department of Main Roads. He listed those people who might be of some help—a journalist on the local paper, a local Salvation Army man and a woman, Patricia Morlton, who contacted the SAFA delegates and also unsuccessfully urged the Mayor to form an advancement league. The students could find little Aboriginal organisation, and no further visits to Bega seem to have been made.
Walgett presented a very different story. The Aborigines Progressive Association was now very active, with Harry Hall as president and Ted Fields as vice-president. On 19 May, a group of six students arrived, three male and three female, including Aidan Foy, Barry Corr, Sue-Ann Loftus and Wendy Golding. Barry remembers going up to Walgett by train and arriving there at some unearthly hour:
Anyway we camped in a park and someone had this huge—it could have been a tent, or a huge ground sheet. All of this was winter too, so it was freezing cold, so the four of us in our sleeping bags—one, two, three, four—on this ground sheet tent. Anyway the coppers found us around about six in the morning or something like that. Obviously they were looking for us and they wanted to know—so they were, you know, 'Who are you? Where're you from? What are you doing? ' They were just looking for any excuse to bag us, and anyway so it came out that Wendy was still under 18. 'Oh, do your parents know that you're here? Look, I think I'm going to take you down the police station because you're under 18, your parents are not here, you're sleeping with these guys in the park. I'm going to charge you with exposure to moral danger.'
[Members of SAFA (Barry Corr and Wendy Golding) visit Walgett in May and August 1965.
(Photos courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41152991)
No charges were actually laid. The next morning, Barry recalls:
We went off to the post office to collect the voter registration forms. And sitting in the post office going, 'Oh this is what the voter registration form looks like?' And this Aboriginal man was in there. He'd been following us around . . . to find out what we were up to. And like a lot of Aboriginal people they were going to suss us out before they reacted. So he followed us around and we walked out into the bright sunshine of Walgett and said, 'What do we do now?' and he just introduced himself and he took us off to meet people and we ended up staying at Harry Hall's place.
Barry remembers staying with Harry Hall:
[Harry Hall's place.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41153011)
They were on the riverbank at Walgett . . . [Harry's house] was a typical humpy you know, bits of flattened out corrugated iron and earth floor and stuff like that. And just additions, additions, it was a maze of little rooms and stuff like that. But it was so clean, it was so warm and friendly, it blew me away. Funny cultural things. They put us in a room. We were just sleeping in our sleeping bags on the floor and they gave us a Tilly lamp, and I turned it off to go to sleep. They didn't bother explaining to me or any of us how to turn off a Tilly lamp because they knew how to turn off a Tilly lamp because they used it all the time. But what I didn't realise was that you had to turn off the fuel as well as turn off the lamp. So the thing flooded. You know, how dumb. Technology. I'd never used a Tilly lamp, I was used to just flicking off the electric light switch. That hit me.
Members of Harry Hall's family with two SAFA students, Walgett 1965.
(Photo courtesy of Darce Cassidy)
Well, obviously there was no bathroom. But what Harry used to do, he used to take his kids out to a bore. We hopped in his Ute and we went out to this bore. This bore could have been half an hour or an hour out of town or something like that. And the bore was a tank . . . about six-foot square, concrete, flat, bit of scrub. And I remember standing, and it was warm, in this concrete bore having to wash. He used to bring his kids out there every night to wash the kids you know, before—for school. But it just blew me away. And when you talk to Aboriginal families, particularly during that Welfare Board protection era, the drive for cleanliness—because you know you were constantly being watched by white people, and you know you had to be whiter than white, you had to be cleaner than clean. And I don't think white people ever really understood the extent that Aboriginal people went to to ensure that they met white standards, you know, to prevent the criticism. Also, most importantly to prevent the kids being taken away, because the kids were still being taken away at that stage.
To this date the Association had been unable to hire the RSL hall for meetings, but now it was made available. The students twice visited Mr R. Snooks, the Walgett Aborigines Welfare Officer, the day after they arrived, two seeing him at his office and the other four at the reserve. Snooks was quite impressed, as they carried out no demonstrations and spent most of their time inquiring about Aboriginal conditions in the town, on the reserve, at the station and among a small number of white residents. The Town Clerk, Alec Trevallion, took the students to view the 'transitional housing' then under construction on the reserve— what Snooks called 'purely experimental temporary homes'. The board had decided to build 40 cheap 'transitional' houses in Walgett on 16 February, the day after the Freedom Ride had been in town, and Snooks as a board man supported the program while Trevallion for the council opposed it. Though the students seem to have been unaware of it, Snooks feared that Trevallion wanted to get the students involved in the council's campaign against the transitional housing program. If this was indeed Trevallion's aim, he was successful. Barry Corr remembers:
The council took us out to see some houses that were being built— I can't remember where they were exactly in Walgett, but I know they were showing us these tin boxes as examples of what they were doing. You know, 'We are addressing the Aboriginal problem, so don't pick on us' . . . You know they're out there on the bloody river bank, they've got no toilets, they've got no electricity, they've got no water, they couldn't cope with a modern house could they? So we really need a transition for them. So these places really, these places are good because it's a step . . . And they built these things out of what must have been good intention. Two-roomed, corrugated iron roof, I think they were fibro walls, no insulation, cold water, cold-water shower. I think there was a septic toilet out the back. There was a porcelain hand basin for the kitchen, but only a cold-water tap . . . There was electric light, there was cold water, and there was the sewer put on. We were just horrified by these houses, but they were really instructive as to the thought processes.
At an APA meeting in town later that day (20 May), attended by 67 Aboriginal people, opposition was expressed to the board's transitional housing program and it was recommended instead that twelve 'first-class' houses be built in town, their occupants to be chosen by ballot. The APA was developing a strong local agenda; the meeting also passed a motion seeking a bus service to the mission, agreed that Harry Hall should stand as an Aboriginal candidate at the next council elections, and supported the nomination of Eric Thorne for membership of the Walgett RSL Club. For their part, the students addressed the meeting about the need to register as voters, and gave out registration forms.
The students contacted every Aboriginal household in Walgett in a massive voter registration drive. Wendy remembers: 'We basically did the odd door knock, house to house, encouraging people to register so that they could vote at the next election—explaining to them the importance of that. I seem to remember getting a mainly positive attitude.' She also reflected on the particular kind of cultural contact these follow-up trips represented:
It must have seemed so strange to them if I sort of look back retrospectively to see these white rather hippy looking, terribly middle-class, freshly scrubbed university students trying to tell them what to do with their lives. They were remarkably tolerant of us, really . . . There were nights where we sat down and chatted or went in and had cups of tea, and we told them what we were doing and they told us a bit about their lives. Yes . . . I think they were actually very tolerant and welcoming . . . I think they appreciated that we had the best of intentions even if we were a bit naive in our methods.
[The Luxury Theatre, Walgett, 1965.
(Photo courtesy of the _Tribune_ /Search Foundation)](chap7_9781741150575_epub_part7.html#d41153031)
After the students left town, the APA decided that its next move was to break the colour bar in the lounge of the local cinema, the Luxury Theatre. This had been an issue for years, and the students had learned of it during the Freedom Ride. A plan was hatched for another SAFA group to visit later, to help desegregate the cinema. Charles seems to have been in Walgett briefly around this time, and he and Harry talked to James Conomos, who with his brother owned the cinema. Conomos was adamant he would retain the ban on Aboriginal people in the upstairs section. Charles told the _Tribune_ in early June that when he asked Conomos to allow Aboriginal people to sit upstairs, 'he said this would mean he would lose money, but if I liked to compensate him he would lift the ban'. Determined to break the ban, Harry visited Sydney in July and sought another SAFA visit in the August vacation. The students did come back, on 6–7 August, but Charles was not with them. A lot had changed in the ten weeks since their visit in May.
One of the changes was in policy at Commonwealth and state levels. Desperate to deflect international criticism of its racial policies, and beginning to succumb to the pressure for more involvement, the Commonwealth government increasingly sought to coordinate and influence Aboriginal policy. On 22 July, a conference of relevant Commonwealth and state ministers in Adelaide, chaired by the newly elected South Australian Attorney-General and Minister for Aboriginal Affairs, Don Dunstan, reaffirmed the assimilation policy. It also, however, modified the policy to emphasise that assimilation depended on Aboriginal _choice_ 'to attain a similar manner and standard of living to that of other Australians and live as members of a single Australian community—enjoying the same rights and privileges'. The new wording also deleted the phrases referring to Aboriginal people 'observing the same customs and being influenced by the same beliefs as other Australians', in order to remove the implication that assimilation policy sought the destruction of Aboriginal culture.
These changes in Commonwealth thinking were paralleled by developments in Victoria and South Australia. It did not seem at first that New South Wales would follow suit; the new Liberal–Country Party coalition government was conservative, uninterested in following the path being taken in South Australia by Dunstan, who announced in August that he was drafting legislation to make it an offence to practise race discrimination in any sphere. Yet the coalition government wanted to ensure that, on the Aboriginal issue, it did not provide the media with a stick with which to beat it as its Labor predecessors had done. Soon after its election, the government increased the allocation for Aboriginal housing for the 1965/66 financial year by over 60 per cent, from £104000 to £270 000. By August, new houses were being built everywhere, and on 7 September 1965 Chief Secretary Willis was speaking of a 'new deal for the aborigines'.
The government had promised to conduct a Committee of Inquiry into Aboriginal Conditions, and now both the AAF and SAFA pressed it to deliver. SAFA now had something of a personal connection with the state Liberal Party secretary, J.L. Carrick, who had warmed to them during their pre-election vigil outside Liberal Party headquarters. On 7 July, as promised during the vigil, he met a delegation of five SAFA members— Charles, Tom Roper, Beth Hansen, Alex Mills and Warwick Mosman. They had a long and interesting discussion, Carrick later describing the students in a letter to Willis as 'extremely pleasant and eager university students who are seized with a crusading spirit on this matter'. The students emphasised the Liberal Party's promise to set up a committee of inquiry. 'I must confess,' wrote Carrick to Willis, 'that this point had escaped me.' The students presented Carrick with a document they had written headed 'Suggested Terms of Reference for an Enquiry into Aboriginal Conditions in New South Wales'; it was a long and detailed document, remarkable not least because its suggestions were very close to those of the inquiry that was eventually established. It proposed a full investigation of the conditions of life of Aboriginal people, the functioning of the Aborigines Welfare Board, land rights, the role of police, the refusal of town councils to make land in town available for board homes and 'the need to insert civil rights clauses in relevant Acts of Parliament'.
On Carrick's suggestion, and having received the students' suggestions for the inquiry, Willis himself met a formal delegation of five students on 5 August. There was some discussion as to who should chair the Committee, on the need for more trained social workers, and of the importance of greater employment opportunities for Aboriginal people in country towns. Jim and Charles criticised the board for not involving Aboriginal people sufficiently in decision-making, and emphasised the need for sociologists and representatives like Faith Bandler and Jack Horner on the board. The students also raised the question of racial discrimination—for example, in picture theatres. At the end of the meeting, the students had reason to feel pleased that they had presented their case and been heard. This cosy association with government, however, was soon to be disturbed by further events in Walgett.
Another change between May and August influenced the nature of SAFA's August visit to Walgett. Charles was moving on to a wider stage, and becoming less involved in SAFA itself. He was by now involved in a large number of organisations, especially the Foundation for Aboriginal Affairs and the Aborigines Progressive Association, and could give SAFA only limited attention. Some of his activities, however, were still in the name of SAFA. On 5 June, as the president of SAFA, he, Faith Bandler and Jack Horner issued a leaflet entitled 'Is this Good Enough?', which was distributed by twenty or more Aboriginal and other people to Sydney Film Festival viewers, criticising the Commonwealth government's documentary _The Aborigines of Australia_. It was a sign of his changing priorities that he resigned as chair of meetings at a SAFA meeting on 29 June, though not as president of SAFA itself. Charles was now to be seen everywhere speaking for Aboriginal rights. He was involved, as he had been the year before, in the National Aborigines Day ceremony in Martin Place on 8 July, and addressed the Central Methodist Mission Pleasant Sunday Afternoon meeting in the State Theatre on 11 July, at which he angrily criticised the attitude of the churches.
In early August, Charles got involved in a case that highlighted Australia's racist immigration policies. Peter Read describes it well in his biography. Nancy Prasad was a 7-year-old Fijian–Indian girl living with her elder sister and her sister's husband in Australia, after her parents had been deported to Fiji. The sister applied to adopt Nancy but was unsuccessful, and the Immigration Department insisted Nancy herself be deported. Only a few days before, the Labor Party had finally dropped the 'White Australia' policy from its platform, and the Commonwealth Immigration Minister, Hubert Opperman, had said there was no such policy in force. An hour before Nancy's plane was due to leave for Fiji on Friday, 6 August, 100 students (including me) demonstrated at Sydney airport to draw attention to the continued operation of the 'White Australia' policy. Then, in full view of media cameras, Charles snatched Nancy from her brother-in-law, and he and another Freedom Rider (Louise Higham) drove her away. She was soon returned to her family, and deported the following day, but the students' protest had achieved its object—huge media coverage. The 'White Australia' policy had taken a heavy media beating.
Meanwhile, in Walgett, Harry Hall waited anxiously for the student delegation to arrive. The same day as many SAFA students were demonstrating at the airport against Nancy Prasad's deportation, four students arrived in Walgett to help Harry and the others desegregate the picture theatre. To Harry's great disappointment, Charles was not among them. Those who did come were Aidan Foy, David Pepper, Owen Westcott and David's girlfriend, Christine Jones. Aidan and David had been on the Freedom Ride, but Owen and Christine were new, and neither was actually a member of SAFA. Christine came along with David, and Owen, in the second year of his Arts degree, had joined in on Aidan's invitation. He had gone to the same school as Aidan—Christian Brothers at Chatswood—and had recently moved into a house 'divided up into awful little flatettes', occupying the flatette adjoining Aidan's. Owen had the sort of confidence and the insouciance common to many upper-class rebels. His father, he told me, was a lawyer of conservative politics, while his mother was from an upper-class Catholic background, who had 'learnt how to run a household of servants and how to make lace and things like that', but who also encouraged her six children 'to be concerned about issues like social justice and to question the social order that we saw all around us'.
In the late afternoon that Friday, the students and Harry Hall immediately called on Snooks. They told him they had arrived in Walgett for the week and that a further carload of students was due to arrive. (It never did, presumably as a result of the Prasad events back in Sydney.) In return, Snooks told them the Conomos brothers had only the previous day agreed that before the end of the year they would start quietly admitting to the upstairs section of the cinema Aboriginal people of 'good standards and behaviour', two or three families at a time. (Realising there could be trouble if Aboriginal people continued to be excluded from the upstairs of the cinema, Snooks had been gently twisting Jim Conomos's arm behind the scenes.) Jim Conomos, Snooks wrote to the board soon afterwards, spent some time the next day, Saturday, 'looking for an adult daughter to the Peters family [Aboriginal] in Walgett to advise her that henceforward she could go upstairs. He couldn't find her.' Harry and the students were unconvinced by these promises, and decided to go on with the demonstration.
Owen, David, Christine and Aidan stayed with the Halls that evening, as Barry and Wendy had done in May. Owen remembers it in terms very like Barry's:
We lived with the family; we ate with them and shared their life in every way. I mean that was part of the excitement and the interest of it for me and for all of us I think . . . I'd never slept in a house made out of kerosene tins and hessian bags before. So it was a real eye opener. I knew about this stuff but I didn't really know about it. My most vivid memories are just the house, the physical conditions in which the family lived.
The Halls were the leaders of the growing Aboriginal militancy in Walgett. As Owen remarked:
They weren't in any way downtrodden . . . this was a family that was prepared to expose themselves to whatever the consequences were, so they were obviously very courageous. Harry was unusual in a number of ways. He was one of the very few men in the whole camp that had a job . . . and there was some talk of him being able to get a house in town later on. So in a way he had prospects that many of the other families living in that camp didn't have.
Images of life in Walgett have stayed with the students ever since. Aidan remembered games at the levee bank:
One of the things at Walgett was the levee bank around the town. You get about 20 people in a ute, sitting in the back and what you do is you drive over as fast as it will go and it's great fun. As you go over the levee bank, which is like a hump backed bridge, everybody takes off and there's much squealing and giggling and falling over.
While there was time for talk and play, the main task ahead was a political one. It soon became clear that Snooks and Conomos had failed in their attempt to forestall the demonstrations. Harry gathered together a group of young Aboriginal women to go to the cinema with the students—his daughter, Pattie, his niece, Lorna Hall, and 18-year-old Marie Peters (the 'adult daughter' Conomos was looking for). His 10-year-old daughter, Mary, came as well. That Saturday evening, Harry and Ted Fields, together with Pattie, Lorna and Marie, went along with the four students to seek admittance to the white upstairs section of the theatre. The movie was _Solomon and Sheba_ , a 6-year-old Hollywood biblical movie of lust, licentiousness and power starring Yul Brynner and Gina Lollobrigida. Owen remembers that 'we made up a set of couples, black and white couples, so that the three male students all had a black woman to accompany to the theatre and Christine had an Aboriginal man to be her partner'. David Pepper remembers the scene clearly:
[Marie Peters, Pattie Hall and Lorna Hall.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41153051)
[Harry Hall with his daughter Pattie Hall and niece Lorna Hall, Walgett 1965.
(Photo courtesy of the _Tribune/_ Search Foundation)](chap7_9781741150575_epub_part7.html#d41153071)
What was interesting to me was the different cultures in action there. We invited these girls to go to the movies, and here we were scruffy students with our old jeans on and t-shirts and the girls had their hair done, wore fantastic gear, and looked fantastic . . . So the scruffy students were permitted to go in but these girls who were dressed up to the nines and looking fantastic weren't allowed to go in . . . And these people came from the humpies out of town and their dresses were ironed, you know and starched, stuff like that, it was amazing.
The group then went to the ticket window and asked for upstairs tickets. They expected to be refused. As Owen remembers: 'We didn't say, you know, we're going to take four Aboriginal people in with us or anything, but we were all there standing there, so it should have been apparent to the person in the window.' The group was sold the tickets, and started to go upstairs. Jim Conomos then refused to admit them, telling Harry Hall he could not go upstairs even though he had a ticket. When the group insisted on its right to go upstairs, Conomos called the police, Constables Rowe, Gleeson and Marsh—Walgett's entire force on duty that night. Aidan remembers: 'The police told us to move and we refused. Owen waved his ticket and claimed it constituted a contract. The police then began to push us downstairs. We all asked them if we were being arrested. They made no reply.' Owen says the police told them they had to leave the theatre, and 'we sort of argued with them about their rights to make us leave the theatre and our rights to be in the theatre because we had tickets'.
By now it was 8.30 p.m., and the police began making arrests. Owen, not having been through the 'non-violent direct action' training of the original Freedom Ride, resisted. 'I was the first person to be forcibly removed from the theatre. And I resisted being removed; they had to carry me down the stairs and with me making that as difficult as possible for them.' Aidan wrote, probably for the ensuing trial:
When I looked round Owen had fallen against the banister and was being hustled downstairs by constables Marsh and Rowe. At the bottom of the stairs they carried him out and as he went through the door he grabbed hold of the frame. One of the policemen punched his biceps until he let go. He was then dragged into the street.
He was charged with assaulting Constable Robert Marsh, resisting arrest and behaving offensively, and taken into custody at the local gaol.
The rest of the group stayed on the cinema staircase, except for Harry, who left with his 10-year-old daughter, Mary. After an hour, during which they refused to move, Aidan, David, Christine, Ted and Marie were arrested and charged with obstructing James Conomos's free passage on the stairway of the Luxury Theatre. The two Hall girls were kept in gaol for about four hours, but then—being under 18—were released into the custody of their fathers. Marie remembers that she and Christine were held in a cell together. Aidan recalls: 'They charged us with obstruction, and let us go on the next morning. We spent the night in the cells and I think the girls were pretty brave about that because being locked up in the cells was pretty traumatic for them.' The next day Owen returned to Sydney, and approached the Council for Civil Liberties for assistance.
Charles Perkins suggested that this was the first time that Aboriginal people had been arrested for participating in an organised civil rights action and several journalists said the same. The demonstrations were reported locally in the _Sydney Morning Herald_ , interstate and overseas. Then FCAATSI got involved. A meeting of NSW affiliates was held at Charles Perkins's home in Sydney on Monday, 9 August, with Aboriginal representatives including Ray Peckham, Joyce Mercy (APA vice-president and assistant secretary of the fellowship), Isabelle McCallum (secretary of the APA) and Lester Bostock (Tranby College). Paddy Dawson, Alex Mills and several other students, along with representatives from a left-wing immigrant organisation, the New Settlers' Federation, were also there. The cinema demonstration highlighted the lack of anti-discrimination legislation, and the group agreed to send telegrams of protest. Accordingly, telegrams reading 'Protest against racial discrimination in Walgett demand civil rights law' were sent to the Premier from SAFA, the APA and the New Settlers' Federation. The meeting also agreed the group should seek a deputation to the Premier requesting civil rights legislation (this proved unsuccessful). Most importantly, the meeting agreed to send a delegation led by Aboriginal people to Walgett.
The Aboriginal activists in Walgett waited excitedly for this next delegation to arrive. On Tuesday, Inspector Chalker arrived with police reinforcements from Bourke, and seemed to be under instructions to support the APA campaign to desegregate the theatre, consistent as it was with the government's recently reformulated policy of assimilation. However, since there was no relevant legislation, the police tried negotiation. Sergeant Gleeson chaired a meeting on 11 August of Jim Conomos and Walgett APA representatives Ted Fields and George Rose to discuss the situation. The meeting agreed—and the theatre management later issued a statement to this effect—that 1 September would be the deadline after which Aboriginal people would be admitted to all parts of the theatre; in return, Ted Fields and George Rose agreed that there would be no demonstration at the cinema that evening. There was, however, a long list of stipulations for admission, and the manager said he reserved the right to refuse entry to anyone.
Harry Hall had not been at the meeting, and thought the rule excluding Aboriginal people had been completely and immediately dropped. Under this misunderstanding, he went with three Aboriginal young women to the cinema again that evening. He was shocked to find that this time the young women were admitted but he was turned away. For the moment, though, there was to be no demonstration, since this had been agreed. As the _Herald_ reported, 'a crowd of about 200 waited silently outside the theatre, but there was no demonstration'. The next day, Thursday, an APA meeting was held in the RSL hall to discuss what to do next. Aidan Foy spoke, his 'inflammatory language' and 'aggressive pacing and gesticulations' causing consternation to the observing Snooks. We can only imagine, now, what Aidan said.
Driven by long-time white supporter Helen Hambly, the all-Aboriginal delegation arrived in Walgett two days later, on Friday, 13 August. It included Ray Peckham, Eric Woods from the Sydney APA and Louise West from the Union of Australian Women. Harry welcomed them and explained that he and Ted Fields were determined to break the colour bar at the Luxury Theatre. With Harry and Ted, the delegation visited the main Aboriginal localities around Walgett and concluded that the arrests had strengthened the people's determination. Some SAFA students, including Darce Cassidy, Wendy Golding and Paddy Dawson, also went up to Walgett that weekend.
The stage was now set for a major confrontation. On the Saturday night, a crowd of several hundred people and a number of police gathered outside the theatre to see whether Harry and Ted would be admitted to the Theatre Lounge this time, and what would happen if they were not. The excitement in the street was palpable. As the _Tribune_ reported: 'Walgett was a town of tension, Aborigines stood in small groups in the street, some business people stood in shop doorways and watched. Everyone knew that Harry Hall would try to buy a ticket for the "luxury" section of the Luxury Theatre that night and they were all waiting on the outcome.' Sergeant Gleeson announced that if Hall were refused, he would instruct the theatre management to admit him. Hall and Fields approached the cinema. They reached the window, and tendered their money.
[Ted Fields buys his ticket to go upstairs in the Luxury Theatre, 14 August 1965.
(Photo courtesy of the _Tribune_ /Search Foundation) ](chap7_9781741150575_epub_part7.html#d41153131)
This time, both Harry and Ted received their tickets, and defiantly walked up the carpeted stairs to take their seats in the 'whites only' section. The ban had finally been broken. Many other Aboriginal people then queued up for admission; several were sold tickets without incident and joined them, while others were refused for 'various reasons'. The crowd gathered in 'surging groups', vigorously debating the colour bar. As Snooks wrote to his superiors, 'many animated and loud discussions could be heard'. One of the topics of discussion was whether the demonstrations would lead to people losing their jobs, some employers having already warned their workers against any involvement.
Harry Hall addressed the crowd in victory. He thanked the police for their protection and cooperation, the university students for their unfailing efforts to reveal the colour bar to the public, the delegates from Sydney for coming so far to give moral support, and the people in the crowd. Referring to the threats of job loss, he asked: 'Must we and our children live all our lives being told what we can do by our employers? They need our labour as much as we need employment, and for our children's sake, we must change things now.' So lively were things out in the street that at interval the crowd was joined by many theatre patrons 'who considered it more interesting outside than the entertainment inside' (which was, incidentally, the 7-year-old movie _The Vikings_ , starring Kirk Douglas and Tony Curtis as brothers in a feud for both power and love).
The APA leaders called a meeting on Sunday morning, 15 August at George and Mavis Rose's home to review the previous night's events. With the cinema now effectively desegregated, attention shifted to the Oasis and the town's other hotel, the Imperial. Unfazed by Jack Horner's letters of the previous year, the Oasis's licensee, Athol White, still required Aboriginal people, on entering the hotel, to present themselves to White or his wife, who would decide whether they were sufficiently well-attired to enter either the lounge or the bar. In the preceding weeks, Harry Hall had started to challenge this practice, as a matter of principle rather than out of any desire to use the hotel (he was a teetotaller). Throughout the previous day, the visitors had pointedly conducted Aboriginal people to all parts of the hotel. Darce Cassidy saw White refuse service to Harry Hall, though Harry was well dressed and sober. He also saw another Aboriginal man, Arthur Murray, who may have been acting belligerently, physically thrown out. Snooks reported to the board that he had heard that at approximately 10.00 p.m. (closing time), White called out 'All Aborigines outside; whites can go into the lounge'. In an increasingly defiant mood, White instituted a policy of allowing Aboriginal people into any part of the hotel if they signed a statement saying 'there is no discrimination in Walgett' and that 'recent disturbances have been the work of Communists and troublemakers'.
[Walgett community members and students pose together in August 1965. Darce Cassidy is in the front right. In the back row, Harry Hall is third from the right, Tom Lake is fourth from the right and Gladys Lake is fifth from the right.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41153181)
SAFA and the Sydney APA took up the hotel campaign, just as they had the cinema issue. Darce spoke at a meeting of the Aboriginal-Australian Fellowship in Sydney on 18 August, giving what its minute-taker described as 'a vivid account of SAFA activities in Walgett since February last'. At a meeting of the Sydney APA a week later, Harry asked leading Aboriginal people to visit Walgett a second time to assist the local APA to break the hotel colour bar. Accordingly, a second all-Aboriginal delegation was brought together for a trip to Walgett on the weekend of 27–29 August. This time, Charles came as president of SAFA—indeed, it was one of his last SAFA-identified actions. Other members of the delegation were Isabelle McCallum, Erica and Allan Woods, Ray Peckham, Charles (Chicka) Dixon, Jack Hassen, Tony Williams, Kevin Kelly and Harry Jard, the last five from the Waterside Workers' Federation Aboriginal Committee. Some SAFA people went as well—Darce, Paddy and Ray Tunks, a Salvation Army officer who had allied himself with the students.
When this second delegation arrived, many of the same events that had occurred over the cinema were repeated. The delegation contacted Harry and Ted, and then went to see Athol White. They talked with him for about an hour, in the presence of the Police Inspector, two Crown Sergeants and Snooks. Members of the delegation then talked to many people in and around town, including Mr L. Ridgeway, the newly appointed Aboriginal manager of the station (later to become a welfare officer for the board), and many Aboriginal people in the various settlements. Next they visited both the Imperial Hotel and the Oasis. At the Imperial, the licensee refused to serve former Australian lightweight boxing champion Jack Hassen with a glass of beer in the lounge. At the Oasis, a barmaid served Charles and two other Aboriginal people with one glass of beer, but Athol White told them they would get no more and ordered Charles, Harry and Ted from the lounge. When asked why he had refused them, White replied: 'Perkins and Hall don't drink and Fields is a very moderate drinker. They're trying to prove a point, and I'm proving a point that I've got certain rights.'
The Walgett APA and the Sydney delegation called a well-attended public meeting at 3.00 p.m. on Saturday, 28 August at the RSL hall. It was lively, with many interjections. Ted and Harry spoke, then Charles called for all Walgett Aboriginal people to support their APA leaders. Isabelle McCallum spoke on the importance of Aboriginal people uniting to support all efforts towards integration, and Ray Peckham referred to the Walgett and Australian Aboriginal people being part of 'the movement of coloured people throughout the world, demanding equality with all other people'. Not everyone supported the APA; a resolution of no confidence in the APA was moved by an (unidentified) Aboriginal person but gained only four votes. The meeting agreed that the Oasis licensee be told that if he continued to refuse service, legal action would be taken against him. The meeting also agreed to request that the Premier, Mr Askin, introduce civil rights legislation in New South Wales. Afterwards, Charles and Harry went again to the Oasis lounge where, in the presence of a police officer, White again refused them service.
Charles was furious, and he was to refer to this refusal many times later in his life. It was for him the ultimate direct proof of racial discrimination, uncomplicated by any issues of hygiene, dress standards or the like. He told the _Sydney Morning Herald_ he intended to sue, and that it would be the first legal action by an Aboriginal person attempting to break down the colour bar. On his return to Sydney, still very angry, he rang the Chief Minister's office and asked to speak to the minister. He reported that he and two other Aboriginals, 'respectably attired', had been refused a drink in the lounge of the Oasis and requested that the minister 'institute proceedings against the proprietor of this hotel'. Charles was advised to put his complaints in writing, but there is no record of a written complaint and it seems that he never did sue, possibly because by this time he was preparing for his final exams, and soon afterwards took on much greater responsibilities when he became manager of the Foundation.
The excitement at Walgett, however, was far from over. The charges against Joey Marshall, who had driven the students' bus off the road in February, were finally heard. Though the Walgett police had reported Marshall to the Police Traffic Superintendent for dangerous and negligent driving the very next day, almost two months passed before the Commissioner of Police agreed Marshall should be charged, and it was many more months before his case was heard. On 2 September, Marshall was found guilty of driving in a manner dangerous to the public, given a four-month suspended gaol sentence, a fine of £80, a twelve-month good behaviour bond, ordered to pay court and witnesses' costs, and lost his driver's licence for seven days. If this sounds like a defeat for Marshall, it was not seen this way in Walgett amongst the whites. Marshall was something of a hero there by now, and his younger brother—a classmate of young Jack Waterford (years later to become editor of the _Canberra_ _Times_ )—'basked in the glory of his brother's deed'.
Then, the following month, the case against those who had demonstrated at the cinema was heard. The Council for Civil Liberties provided the students and two Aboriginal demonstrators with barristers Gordon Samuels QC and Malcolm Hardwick, instructed by Michael Kirby. As Aidan remembers it: 'Of course, to appear on a charge of obstruction with a barrister was a bit of overkill, but it all was part of stirring the pot . . . The facts were very clear: we had sat on the stairs and they had arrested us and put us in gaol and bailed us the next morning. And we weren't even contesting the facts, in fact; we wanted to be found guilty and we were all prepared to go to gaol.' The magistrate ruled that for all charges, except those against Westcott, there was indeed no case to answer. When Westcott's case was resumed the following year, the magistrate dismissed the charge of offensive behaviour, but found him guilty of the offences of obstruction and resisting arrest. No convictions were recorded.
There was yet another SAFA visit to Walgett later that year, this time to campaign for Harry's election to council at the 4 December elections. Aidan recalls 'the time we went up when Harry Hall ran for council'. In the final count, Harry was unsuccessful, with 78 of a total of 1031 votes in 'C Riding' in the Shire of Walgett. With this visit, SAFA's engagement with Walgett was largely over, though some students did visit again in 1966.
The persistence and sincerity of students like Darce, Wendy, Aidan, Barry, Owen, David, Sue, Paddy and Christine can hardly be doubted. Yet, in the end, it was true that they did not live in Walgett, and it was the people who did who carried out the long fight for change, and who suffered the consequences of heightened white hostilities. The experience had been an ordeal for Marie Peters. As a young woman in one of the very few Aboriginal families in town, she felt the odium of arrest and imprisonment keenly. Her white neighbour turned hostile, telling her she ought to go and live in the camps like the rest of the blacks, leading her mother to tell the neighbour to leave her kids alone. She felt very much alone in the following months, and still feels that her role in the cinema demonstration has not been fully recognised. And indeed it hasn't. As one of the first Aboriginal people to be arrested in a political demonstration, she deserves a great deal of credit.
To my mind, the real heroes of the story told in this chapter are Marie Peters, Pattie and Lorna Hall, Ted Fields, George and Mavis Rose and, above all, Harry Hall—that tenacious home-grown political activist who took on racism where it bites deepest.
The battle in the Walgett microcosm was an indication of the significant changes on the way in the larger context. The government began to move on the Committee of Inquiry, Premier Askin informing SAFA and the APA that it would be established 'as soon as practicable'. The Aborigines Welfare Board was coming under criticism, as the pattern of policy and administration that had been in place for decades began to break up. The board's first discussion of SAFA and the Freedom Ride took place on 21 September, when Snooks reported on the recent activities in Walgett. Although the board decided not to make any public statement on the activities of SAFA, it did, significantly, instruct area officers to bring to its notice instances of recent or long-standing discrimination in hotels, places of public entertainment and swimming pools. A week later, Jim Morgan, its 'full-blood' Aboriginal member, criticised the board publicly, saying it was 'distrusted by Aborigines', helping only the 'better-class Aborigine, the man who has helped himself'. It also, he said, 'keeps a file on every Aborigine in the state and its welfare officers are like secret police agents'. The board later subjected Morgan to what it called a 'brief discussion' and Morgan called a 'third degree method of questioning'. Morgan later said in a letter of protest to the board: 'I am descended from a poor but proud people. I want to be their representative, not a puppet.'
Further attacks on the board came at a conference organised by the Aboriginal-Australian Fellowship on 16–17 October in Sydney, involving about 100 people of whom 70 were Aboriginal. The fellowship had gone to great lengths to assist Aboriginal people in country areas to attend, and those present included many leading Aboriginal activists of the day— Charles Perkins, Harry Hall, Pearl Gibbs, Kath Walker, Charles Leon, Bert Groves, Ken Brindle, Joyce Mercy, Ray Peckham, Lester Bostock, Clarrie Combo and many others. The only SAFA member apart from Charles seems to have been John Powles. The conference called for equal representation of Aboriginal people on the board, to be elected on a regional basis, and sought the establishment of voluntary elected committees of Aboriginal people on every station and reserve, to be trained and developed eventually to manage the stations or reserves themselves. Furthermore, the conference requested that the government honour its election promise to establish a Parliamentary Committee of Inquiry on Aboriginal Conditions, and to include two Aboriginal members.
Eventually a committee was appointed, though it did not have Aboriginal representation. On 8 December, the government announced a Joint Parliamentary Committee to inquire into the conditions of Aboriginal people in New South Wales, and to recommend on 'the legislative or other proposals necessary to assist Aborigines to attain an improved standard of living'.
Here was an opportunity for SAFA to put its by now considerable knowledge of conditions in towns and reserves in New South Wales to good use. A few days after the committee was announced, the students received the February survey material back from Ted Noffs, and were a little taken aback to find that nothing at all had been done by way of analysis. The Annual General Meeting of SAFA on 13 December was told that Professor Brennan would advise on the 'attitudes' surveys (it seems he never did), while the students would process the other elements themselves after their exams. While no survey report as such ever eventuated, and most of the survey forms seem now to have been lost, the results _were_ used in SAFA's submission to the Committee of Inquiry. On 25 January 1966, a SAFA meeting discussed its submission in detail, and students were asked to bring with them full reports of their activities and the conditions in any towns they had visited. It would take the students, principally Sue Johnston and Alex Mills, six months to write the submission.
For most SAFA members, however, their main involvement continued to be visits to country towns. One student visit to a country town at this time—though this was not a formal SAFA visit—was a disaster, Pat Healy describing it in her notes on the history of SAFA as 'a farce'. Owen told the story in detail to Inara, my research assistant. On his return from his visit to Walgett in late August, Owen's car broke down in Coonamble. He caught a train to Sydney, consulted with a car mechanic, and returned a few weeks later, on 11 September, with spare parts and tools to fix and retrieve his car. He met two men on the train, one of them Polish in origin, who were talking about their plans to conduct a demonstration in Coonamble. When they arrived in Coonamble, Owen and the other two men made contact with the Aboriginal people with the aim of desegregating the picture theatre, as had been done in Walgett.
Coonamble was another of these northwestern New South Wales towns with a 'Little Rock' reputation. Here, as in many other towns, the council had continually refused to allow the Welfare Board to purchase land within the town boundaries for Aboriginal housing. The target was the Plaza Cinema. According to Owen, when the demonstrators arrived in the main street, 'the whole town was out. There were cars cruising up and down. There was a crowd congregated outside the theatre and literally there were people hanging out windows.' According to the _Sydney_ _Morning Herald_ , a crowd of more than 300 residents gathered outside to witness the test of strength with the cinema management. The demonstration achieved its ends in the short term: 'About 10 Aborigines were allowed in the upstairs section, where they are not usually admitted, and 30 watched the show from downstairs, their usual position.' Then, on the pavement in full view of the crowd, Owen was assaulted:
I woke up on the pavement covered in blood . . . The Polish guy . . . took me to the local doctor who stitched me up in the most painful way possible and told me that we didn't want your kind around here. My Polish friend put me up for the night in the local flea house. The next morning I went down to retrieve my car—I'd got it all ready and it was fixed and ready to go, and I found it'd been like totally trashed, it'd been demolished with an axe. It was like totally destroyed.
The _Herald_ mentioned the assault, and reported the proprietor of the Plaza, Mr T.L. Wall, as refusing to say whether Aboriginal people would continue to be allowed in the upstairs section in the future. Charles Perkins commented to the _Herald_ that 'he hoped Mr Wall had not allowed Aborigines in the upstairs section of his cinema for one night only'.
Despite the attack on Owen, SAFA remained committed to visiting country towns. A general meeting on 12 October agreed on a series of summer visits, during which the students would research the situation in the town, encourage the formation of Aboriginal organisations and conduct active demonstrations, 'preferably with Aborigines'. By this time contact with Aboriginal organisations was quite considerable; the AAF and the APA provided lists of contacts, and the APA constitution was suggested as a model for other towns. A SAFA newsletter outlined the plans and listed the targeted towns—Bowraville, Wellington, Boggabilla, Collarenebri, Brewarrina, Gulargambone, Narrabri, Lismore—as well as larger regions such as the Riverina and the South Coast. Those leading the visits were Darce, Barry Corr, Alan Outhred, Tom Roper, Warwick Richards, Chris Page, Paddy Dawson, and Lyn and Bill McLean from the UNSW branch of SAFA. Having by this time graduated and become manager of the Foundation, Charles was no longer a member.
These summer trips increased SAFA's knowledge and understanding of conditions in the towns, but received very little publicity. Colin Bradford remembers going with Alan Outhred and Sandra Levy on the trip to the Riverina, to the towns of Griffith and Leeton, and also Gundagai and Brungle: 'We made contact first of all with a family in Griffith; they were a white family and they were active in the church and they were also activists for the Aborigines, trying to do things. And we stayed with them for a couple of days, and just went round to the reserves and talked to people there.' Tom Roper remembers the visit to Wellington with Sue Johnston:
I can remember one very signal interview we had with the school principal, who told us how there were quite a number of Aboriginal kids that were good at sport but none were good at school. I can remember us having an argument with him about that because it did turn out that one of the Aboriginal kids, despite all the difficulties, had done comparatively well, but I mean the stereotype was such that they could run fast but they couldn't do anything else . . . We reported back and that certainly encouraged me and I think encouraged others to get more heavily involved in the education side . . . how they could be assisted through tutoring and through having adequate places to study.
Barry, Darce and Wendy, and perhaps Sue-Ann, did a very long trip during the first week of February through Coonamble, Walgett, Wee Waa, Moree, Narrabri and Bowraville. Barry: 'We also did a lot of driving around and we went to Wee Waa, we went to Narrabri, because we were looking at work and a whole range of issues . . . All these funny images of Imperial, Railway and Telegraph Hotels and Astoria Cafés stick in my mind.'
The most significant town visited that summer was probably Bowra-ville. The Freedom Riders remembered it as a particularly racist town from their first visit, and indeed this impression remained in all subsequent encounters. The group that went there in February 1966 had exactly the same impression. Darce later wrote that there were children on the reserve with chicken pox, the houses were far too small for the large Aboriginal families that lived in them, and the two hotels, the picture show and the cemetery remained racially segregated. Barry Corr:
The discrimination went down to the bloody cemetery. You know, you had the Church of England there, you had the Presbyterians, you had the Catholics, you had the Methodists and down the bottom you had the blackfellas. And so the Aboriginal cemetery was down the bottom. And of course all up the hill with the white people, that was all tombstones and nicely looked after graves, and the Aboriginal graves—I can't forget some of the kids' graves because they had sea shells as a border around them, no grave stones or anything like that. If you didn't know, you wouldn't know . . . But that was bloody Bowraville.
SAFA now decided on a major visit to Bowraville on the weekend of 12–13 March 1966, with the support of the APA, and accompanied by Aboriginal activists from Sydney. Accompanied by _Herald_ and ABC TV reporters, 27 students and three Aboriginal activists—Charles, Harold Jard and Chicka Dickson—went there by car. Their target this time was the hotels; Bowraville had two, the Royal and the Bowra. In Darce Cassidy's words in an article written soon after, the 'Royal, tiled, clean and antiseptic, is patronised by farmers and their surfie sons. The Bowra, large, rambling and grimy, is frequented by workers and rockers—or rather some of the workers and rockers, for about half of Bowraville's working class is barred from this hotel.' Aboriginal people never drank at the Royal, the cockies' hotel, but they had always been able to drink in the 'dark room' at the Bowra. Recently, however, the 'dark room' had been closed by order of the police sergeant, and now Aboriginal people could not drink there either.
The people in Bowraville, having heard that between six and eight carloads of students were due to arrive that Saturday, were out in the main street waiting. Some cafés were closed. The visitors arrived in nearby Macksville at 9.45 a.m., and an hour later the first car set off for Bowra-ville. At 12.45 p.m. the rest of the cars set off, followed, as they got closer to town, by a convoy of police cars almost as large. The visitors split up. When Harold Jard went with Paddy Dawson to the Royal Hotel, they were met with hisses, catcalls and abuse from the crowd in the bar and on the hotel verandah, but being accompanied by reporters they were allowed in. The crowd in the bar parted to let the two enter, where they were served a glass of beer and photographed. Harold and Paddy debated with the other hotel patrons for about an hour. Another group went to the Bowra Hotel to challenge its exclusion of Aboriginal people, but with so much urban press interest the colour bar was 'off ' that day. Then a café was tested: 'A local Aboriginal child was taken to a café where a milkshake was ordered. Service was refused.' One group then went to the reserve, just out of town on the cemetery road, while 'about one hundred teenage and sub-teenage children in George Street' surrounded another group. Charles was 'pinned down by reporters, including those representing Sydney newspapers and ABC TV'. Subsequently, another group of Aboriginal people went to the Royal Hotel, and again all were admitted.
[A young Aboriginal man addresses a meeting near the Aboriginal reserve, Bowraville, 12 March 1966.
(Photo courtesy of Darce Cassidy)](chap7_9781741150575_epub_part7.html#d41153201)
By this time there were 400–500 people in the street—high drama in itself for a population of between 1200 and 1300. The crowd was noisy and somewhat hostile, jeering loudly at the students. The visiting group withdrew for a meeting at the showground, then in the evening held a meeting at the reserve—well, not quite at the reserve; the Aboriginal men, women and children left the reserve, walked across the road and sat on the red clay bank, ready for the meeting, while police lined the side of the road to ensure there was no trouble. Not far off, said the _Guardian News_ , was 'an old Kiparra ground, meeting place for the elders, where once carved trees stood and the sacred rites were performed'. Darce spoke, and then Wendy. One of the students said: 'We will return as often as it is necessary to see you have a fair deal.' It was an angry meeting. David Pepper remembers that 'a lot of young blokes got up and roundly told the sergeant off . . . the big issue was the local sergeant there was controlling the local people by handing out government cheques to people who'd been good. So that if you were in his bad books you wouldn't get your dole payment or whatever.'
Some dissension within the Aboriginal community became evident. When Gerry Walker, a young Aboriginal, said 'I mightn't get a job. They wouldn't trust me because I am black . . . They bag black blokes because they are a blot on the world', 20-year-old Bernadette Ballangarry criticised Aboriginal people like Gerry:
You haven't got to live like this. Through your drinking you are dragging everyone else down. You have only yourselves to blame. If you would wake up to yourselves, it wouldn't be too bad. We are all pulled down because you stagger round the streets. I have been offered a job in town. Gerry has had plenty of jobs but he gets drunk. It's his own fault he is out of work.
The SAFA and APA visit was reported at length and quite sympathetically in the local paper, the _Guardian News_ , and more modestly in other papers. Even the Aborigines Welfare Board took notice. When the local Area Welfare Officer reported to the board that there was no discrimination at Bowraville, the board rejected his advice.
One of the most important challenges made by SAFA to existing regulations was somewhat accidental. Two weeks after the Bowraville demonstration, Darce and Sue-Ann Loftus returned. They were invited by some of the Aboriginal people to the reserve and were standing in front of one of the cottages when two police came by and charged them with entering the reserve without permission. The police pressed the case, even though Green, the board superintendent, had recently made it clear in the board magazine _The Dawn_ that 'Aborigines on Reserves should be allowed to invite friends to their homes, and believed this restriction should be removed'. When the case came to court on 13 July 1966, the Council for Civil Liberties again sponsored the defence. The case was dismissed, not on the principles at issue, but on the technical grounds that since no survey had ever been conducted to establish the boundaries of the reserve, the police could not be certain that the house in question was actually on the reserve. That same day, SAFA members demonstrated outside Parliament House in Sydney, with Sue Johnston (now secretary) burning copies of the _Aborigines_ _Protection Act_.
Despite all this activity, no local organisation seems to have emerged at this time in Bowraville as it did in Walgett.
While these confrontations at Bowraville were going on, the Joint Committee was gathering submissions, interviewing witnesses in Sydney and country towns, and visiting stations and reserves throughout the state. Many of the submissions and interviews were well publicised; the AAF's proposal for land rights for Aboriginal people in New South Wales, for example, merited the headline 'Aborigines ask for land rights' in the _Australian_ on 14 March 1966. The SAFA submission, presented in June 1966, was long and detailed. It covered in its first three sections the same issues as the original Freedom Ride survey—health (using the Health Questionnaires filled in by eight medical practitioners), employment and incomes (using the responses from 58 male and 22 female Aboriginal people surveyed), and education (based on SAFA interviews with a 'small number' of teachers). It recommended increased spending on housing and health, a program of health education, the return of 'land capable of development' to Aboriginal people, housing of Aboriginal people in town, the development of rural cooperatives, and spending on education at all levels. The fourth section, headed 'Education of the Public', gave a history of the positive steps that had been taken to improve community awareness, while the fifth, 'Analysis', was highly critical of the Aborigines Welfare Board, and recommended proper training for the welfare officers hired by the board. It is not quite clear, on my reading, just what the SAFA submission envisaged for the future of the board. There were, however, clear recommendations for a statutory body operating under new legislation to deal with racial discrimination. SAFA advised the committee to investigate legal activity in this area in the United States, Britain and, after Don Dunstan's initiative, South Australia. Charles Perkins submitted on behalf of the Foundation, and made similar recommendations concerning anti-discrimination legislation. He had also led a deputation on 6 May to the Chief Secretary, seeking constitutional change to protect people from racial discrimination.
[Sue Johnston, Secretary of SAFA, burns the _Aborigines Protection Act_ , under which Loftus and Cassidy were charged, outside Parliament House during a protest against the Act on Wednesday 13 July 1966.
(Photo courtesy of _Honi Soit_ ) ](chap7_9781741150575_epub_part7.html#d41153221)
SAFA seemed indefatigable. By August, the students were planning a Freedom Ride in Queensland for February 1967. Three SAFA members— Chris Page, Darce Cassidy and Jenny (Jean) Buckley—went to Queensland to conduct a preliminary investigation. The aim was to concentrate on the northern part of Queensland where discrimination was most thorough, in hotels, a picture theatre and elsewhere. A leaflet headed 'Plans for Action' reported the various ideas under discussion— encouraging voting (Aboriginal people had just won state voting rights) and demonstrations to expose discrimination. The plan was for about 30 students to meet in Townsville, hire a bus and visit various northern towns. They would also look at Palm Island, off Townsville, where about 1000 Aboriginal people and Torres Strait Islanders lived. Palm Island was something of a prison: there were reports of bans on interracial dancing, Aboriginal girls caught with white men being detained in the mission compound, the exclusion of Aboriginal people from the main street, and a roll call at which anyone late had to do free work for the mission.
It was important to get FCAATSI support for the proposed Freedom Ride. Sue Johnston and Chris Page attended a FCAATSI meeting in Glebe on 15–16 October, outlining their plans. Executive members put forward various suggestions, and expressed a willingness to be involved, as long as the local Aboriginal communities were consulted and included and FCAATSI itself kept informed. Faith Bandler and Joe McGinnis, executive members of the council, were appointed as the liaison officers. As the consultations with the Queensland Aboriginal leaders continued, however, the plans gradually came unstuck. Queensland SAFA said February was not the right time for a Freedom Ride in North Queensland; monsoonal weather would prevent a bus travelling on unsealed roads. More time was needed, in any case, to organise the campaign and to do preliminary survey work, so the target date was set back to May. The Indigenous community in North Queensland began to split over the proposal, with some leading community members turning against the idea. Darce remembers that 'both Margaret Valadian and Neville Bonner were against it, and it looked like it would have been painted as outside interference from the south, with little local support'. The _Courier-Mail_ had reported in September that the president of the One People of Australia League, Mr J. Hamilton, had said he would welcome any group prepared to work for the betterment of Aboriginal people, but 'would not welcome anyone concerned with "destructive criticism"'. The local students were not in support either; one of them who was, Elena Bardsley, wrote to Chris Page that the Townsville University Union Council had met on 16 September 1966 and had dissociated itself completely from SAFA and its plans. While there was support from some Aboriginal people like John Newfong, Darce remembers that there was not a lot of other local support. In February 1967 there was another investigative trip to Queensland. But the lack of support from the Queensland organisations meant there never was a Freedom Ride in Queensland.
While the New South Wales Joint Parliamentary Committee was in progress, the national situation changed rapidly. Harold Holt succeeded Menzies as Prime Minister in January 1966, and he was more sympathetic to the proposals for Commonwealth involvement than Menzies had been. A Referendum on section 127 (concerning the census) was agreed to in February 1966 and was originally to be held in May that year, but was then delayed while the question of section 51 (xxvi) was further debated. Parliament finally agreed in February 1967 to a Referendum on both sections. When the referendum was held in May that year, the proposals for change were supported by 90.77 per cent of voters. Public opinion in the cities, especially, had swung round to the assimilationist notion that Aboriginal people should be treated equally, and that a racially discriminatory constitution was unfair and damaging to Australia's international reputation. With that, a whole new set of governing relationships and principles and sources of funding was inaugurated. In the short term, a three-man Council of Aboriginal Affairs was formed to advise the Commonwealth government. Dr H.C. Coombs was appointed director, and Barrie Dexter and Bill Stanner as the other two members. None of these three had worked under the old regime in the states, and they brought a whole new approach to the issues.
By this time, the baton of student Aboriginal politics was passing from SAFA to Abschol. During 1965, Abschol had grown in size and scope, holding a conference at the University of Sydney on 5 June. In 1966 and 1967, many SAFA students drifted into Abschol, bringing to it a much more militant style and radical politics. Tom Roper was one of them. Active in SAFA throughout 1965, he became very active in Abschol during 1966, when we were both completing our History Honours year. Years later he described SAFA as 'one of those organisations that kind of flowered if you like, but rather than dying it changed what various other organisations were doing'. It changed Abschol 'into a different organisation, and a much more active organisation'. The memberships of SAFA and Abschol, he said, 'tended to become more similar and eventually they in fact virtually became the same'. One of the reasons for the shift, Tom suggested, was that Abschol was connected to NUAUS, and therefore had access to continuing funds, which SAFA did not.
The drift of SAFA students and ideas into Abschol had a marked effect on NUAUS Aboriginal policy more broadly. Whereas NUAUS had in March 1965 refused to support or congratulate the Freedom Ride, only a year later it passed resolutions commending Charles Perkins 'for his active leadership in efforts to counter racial and social discrimination in Australia'. It noted the 'efforts of SAFA to follow up their tour of Northern NSW towns', and expressed support for the aims of SAFA and congratulations on its action. Now it was agreed that: 'NUAUS supports in principle the concept of student protest with the aim of improving Aboriginal conditions, but urge[s] that the protesters be confident and assured that their actions are supported by the Aboriginal community involved.' This same meeting approved in principle the appointment of a full-time National Abschol Officer to pull the organisation together, and to organise a campaign favouring a Referendum on section 51. In early 1967, NUAUS agreed to regard Aboriginal affairs as a priority issue, and appointed Tom Roper full-time director in order to strengthen the links between Abschol on various campuses and create a strong national organisation.
There was one last follow-up trip before SAFA finally dissolved, and this time I was involved. On 5 July 1967, SAFA asked for volunteers to go to Dareton on the Murray River on 14–16 July. In Dareton, the SAFA newsletter said, thirteen Aboriginal families lived on the rubbish dump under impossible conditions. They had in fact been living there for almost twenty years, having moved there when the AWB mission at Menindee was moved to Murrin Bridge in 1948. In early 1967, the Senior Welfare Officer of the board undertook a detailed survey at Dareton and recommended two standard townhouses be built 'for the families considered suitable for standard housing' and that 'transitional housing' be built for the others. With the Joint Parliamentary Committee still to report, however, and the board's notion of 'transitional housing' under severe criticism from several quarters, the building plans remained on hold and the shanty town remained at the tip. When Pastor Doug Nicholls visited it in March 1967, he described it as a 'national disgrace'. Now, in July, the aim of a SAFA trip was to find out more about the actual conditions.
Sue Johnston went, along with her boyfriend Kim Sweeney—now a major figure in what remained of SAFA—and doctoral student and later well-known sociologist Bob Connell. Now sharing a house with Sue, I came too. I was by this time doing my Diploma of Education, while she was working on her Master's thesis on the history of New South Wales government policy towards Aboriginal people.
We visited people in the shanty town, and also some Aboriginal people in town. The latter were extremely friendly and helpful, and the former told us they needed houses, decent water and other necessary amenities. This Dareton visit was a defining experience for me. The shanty town dwellers had thought we were able to get something for them, and I felt that we had nothing to offer. I came home feeling that without Aboriginal activists to work with, our own activism could be nothing but the do-gooding of which SAFA had so often been accused. Feeling very uncomfortable, it was some time before I could find a way to support Aboriginal campaigns and actions again.
I was probably wrong, though, in my thinking that our Dareton visit had been useless. It seems to have had more effect than I realised at the time. Soon afterwards a petition was presented to the Legislative Assembly from 1147 university students, requesting an Automobile Tuberculosis Unit be sent to Dareton to prevent the disease from spreading, and that the Aboriginal families there be moved 'from their present situation near this rubbish tip outside Dareton'. In December, the Aborigines Welfare Board approached the Water Conservation and Irrigation Commission to set aside an area on the southern boundary of the Coomealla Irrigation Area for an Aboriginal reserve, and by mid-1968 twelve new cottages were being erected there.
When the Joint Parliamentary Committee's final report was tabled on 13 September 1967, it had some elements that SAFA would have liked, and others it would have strongly opposed. The former included proposals to provide more housing in the towns, and more education at all levels from pre-school upwards. It would probably also have supported the recommendation to abolish the Aborigines Welfare Board, with Aboriginal services henceforth being provided through the existing agencies of the state, such as the Housing Commission, the Department of Child Welfare and the Department of Social Welfare, though coordinated by a Director of Aboriginal Affairs. It would have liked the recommendation for the director to be advised by an elected board made up of Aboriginal people. SAFA would have been less impressed by the report's strongly assimila-tionist tone and purpose, and the committee's decision not to recommend an _Anti-Discrimination Act_.
Adopting an attitude of 'wait and see' in the context of rapid policy change at the Commonwealth level, the New South Wales government took fourteen months to translate the committee's recommendations into legislative form. As the months passed, some Aboriginal organisations in New South Wales became increasingly impatient at the lack of action at the state level. After much discussion and Aboriginal protest, legislation was finally brought forward on 7 November 1968; it was passed in February 1969, and came into effect on 2 June 1969. A new era in policy and administration had begun.
By this time, however, SAFA had disappeared from the political scene and the Freedom Rides were finally over.
_C_ _ha_ _pter_
_10_
Memory and meaning
As in a film or a novel, the only thing harder than the beginning of a history is the end. I could have ended with the last of the SAFA visits to country towns, but this would leave unexplored the Freedom Ride's long-term impact on Australian political culture. The Freedom Ride did not end with the demise of SAFA, but lives on in our memory and continues to inform expectations and debate on Aboriginal issues. So let's explore the changing ways in which the Freedom Ride has been remembered and understood, look at its effects on the subsequent history of the towns, and ponder its significance for the present.
Knowledge of the Freedom Ride has been kept alive first by the prominence of Charles Perkins himself, both in life and in his passing. Charles never tired of telling his Freedom Ride story in speeches and interviews. There were many profiles in print and on television current affairs programs over the years, and many mentioned his role in the Freedom Ride, and briefly explained what it was. Especially important in this process was Charles's own autobiography, _A Bastard Like Me_ , which provided the first extended historical evocation. 'The Freedom Ride,' Charles began, 'was probably the greatest and most exciting event that I have ever been involved in with Aboriginal affairs.' He provided some general description of the preparations for the trip and the confrontation at Walgett, and ended with a telling description of the clash outside the Moree swimming pool.
The Freedom Ride is well remembered in both Walgett and Moree. However, memories have gradually changed over the years. When the Joint Parliamentary Committee reached Moree in May 1966, only fifteen months after the original Freedom Ride, it found that attitudes to it had already softened. Albert Thomas, the Moree Area Welfare Officer, acknowledged that the Freedom Riders had 'certainly brought the baths before the attention of the public, though many Aborigines had not liked their methods'. Neville Kelly told the committee the Moree Association for the Advancement of Aborigines had been formed directly as a result of the Freedom Ride. The students, he said, 'really made some of us think a little deeper than we had previously about this problem hence the establishment of the society for the Advancement of Aborigines in Moree . . . It was a harsh awakening.' When asked about the effects of the Freedom Ride, even the Mayor, Bill Lloyd, replied: 'They undoubtedly did some good, in this respect, that they brought to light this resolution that was on the books of council.'
In Walgett, where there had been more Freedom Rides than anywhere else, their memory sustained and informed a good deal of subsequent political action. The Walgett activists found that persistence was essential. If the pools in Moree and Kempsey had been desegregated relatively quickly, the Walgett RSL Club proved a much tougher nut to crack. Three ex-servicemen—Tom Lake, Sye Morgan and Eric Thorne—made sustained efforts to join, but it was another six years before Aboriginal ex-servicemen were admitted to the Walgett RSL Club. The RSL leadership refused to intervene. FCAATSI took up their case, resolving at its annual conference in April 1969 to condemn RSL branches refusing membership, and urging that the matter be discussed and made public at the RSL Congress. Pressure increased when the National Aborigines Day Organising Committee arranged a march and wreath-laying ceremony by Aboriginal ex-servicemen at the Cenotaph in Sydney on National Aborigines Day two months later, on 11 July 1969. The Walgett RSL Club held out for another two years, but finally succumbed in 1971 when Tom Lake, who had served with the army in the 39/52nd unit in New Guinea, was finally admitted, an event covered by ABC television in a _Four Corners_ program.
The memory and influence of the Freedom Ride was also kept alive in Walgett through a close association with the Foundation for Aboriginal Affairs in Sydney. Walgett activists wanting a community centre on the Sydney model established a branch of the Foundation in September 1968, obtained land, and raised money in a local appeal (backed by a grant from the Sydney-based foundation of $10 for every $1 raised). A few months after Charles moved to Canberra to take up a position as research officer with the newly formed Council for Aboriginal Affairs in April 1969, a high-level team from the council, led by Nugget Coombs, visited Walgett and met with the local Foundation committee. After further financial assistance, work started in February 1971 on the building, which was opened to much fanfare eight months later. The foundation served as an effective community centre under Harry Hall's management for some years, but was eventually forced to close for lack of finances.
All was not lost, however, as the building took on a new and important function. When the foundation closed, the Walgett Aboriginal Legal Service took over. Like the other legal and medical services appearing in country towns during the 1970s, it was a product of the Whitlam government's policy of making funding available for community-based service organisations. These services, too, owed something to the Freedom Ride. Many of the professional lawyers and doctors who staffed them had as students a few years earlier made their first contacts with rural Aboriginal communities during Abschol visits patterned on the Freedom Ride model of survey and practical action.
After the Freedom Ride, the Sydney media maintained an interest in race relations in rural New South Wales. Journalists in all media kept memories of the Freedom Ride alive by the occasional visit to the Freedom Ride towns, to see how they were getting on. These return visits started with Bruce Maxwell's visit in June 1965, and have occurred from time to time ever since. This has happened mainly in Walgett and Moree, and to a lesser extent Bowraville and Kempsey. Wellington, Gulargambone, Boggabilla and Lismore have rarely been remembered in this way. One of these return visits was the subject of a segment of the ABC current affairs program, _This Day Tonight_ , called 'Moree—Racism Now and Ten Years Ago', screened on 12 June 1975. Some idea of its content can be gained from its shot list: 'library footage of freedom riders travelling on bus and commentary and music, voiceover of Bob Brown, shots of Moree and riots, library footage interview with mayor William Lloyd back in 1965, Mayor today speaking, Charles Perkins interview, various shots of Moree—entering and shots of township, library footage of Aboriginal camps, camp today and old mission site'.
Three years later in 1978, Paul Rea, a journalist with the _Newcastle_ _Morning Herald_ , visited the Freedom Ride towns for his four-part series called 'In the Steps of the Freedom Riders'. His article on Moree, published on 4 January 1979, began:
Fifteen years ago the Sydney Sunday Press described Moree as Australia's 'Little Rock', after the race-torn town in the Deep South of the United States. Amongst the whites feelings had changed from amusement to resentment to anger. Inevitably there was a showdown and the students were punched, spat upon, and pelted with fruit and eggs by white residents. The bus left town under police escort but the students had achieved their objective: to expose white racism.
Lyall Munro Snr, a leading figure in Moree's Aboriginal community, told Rea the Freedom Ride had effects that were 'both good and bad'. He went on: 'For a time the visit of the Freedom Riders polarised the black and white communities and resentments ran pretty deep. But on the positive side it made the black people stand up and be counted and do something to help themselves.'
Rea did what many journalists were to do in subsequent years—he visited the reserves and settlements, interviewed a few people and gave his own judgment of Aboriginal living conditions and relations between black and white in the Freedom Ride towns. By the late 1970s, some of the hope evident amongst Aboriginal people in these towns in the early years of the decade had gone, and the tone of these journalists' reports was generally negative. Rea reported that housing conditions in Moree were still poor. Stanley Village, newly built in the years after the Freedom Ride to relocate the people at Bingara Road, was by now in a state of neglect—'wall panels and windows are broken and some fences are down'—while the village is 'badly littered with rubbish and broken bottles'. Conditions at Mehi, said Rea, were no better. The swimming pool 'is abandoned, empty, and vandalised'. Lyall Munro Snr told Rea that, while many Aboriginal people had moved on to the reserves or to town, what had not changed was the 'vicious cycle facing the young Aborigine'—no job prospects, so doesn't do well at school, no education, cannot get a job. While some individuals were able to make good, the Aboriginal people in general 'are still on the bottom of the pile'. He thought the result of assimilation policies had 'been the gradual loss of aboriginal identity and self-assurance'. The result was frustration, which 'often gives rise to violence but rarely against white people. It is usually vented against other blacks, against property, and against themselves. A lot of people, young and old, are killing themselves with grog . . . It is a slow suicide.'
Journalists' stories about Walgett in these years were similar. When journalist Lenore Nicklin of the _Sydney Morning Herald_ visited in June 1978, along with the federal Minister for Aboriginal Affairs, Ian Viner, she described the Gingie reserve as 'grim', and noted that 'children who should be at school play among the rusting cars. There are dogs everywhere.' Nicklin found that there was widespread resentment among the whites at the social service benefits Aborigines received. 'All they spend it on is booze and the TAB,' said the taxi driver. Her account of Boggabilla was very similar. When Paul Rea arrived in Walgett six months later, he interviewed a Walgett Aboriginal man, George Fernando, who said 'the older generation white man did not like talking to the Aborigines but the younger kids mix all right now. They get to know each other.' Overall, though, Rea's report on race relations in Walgett was negative. There were serious health problems in the Aboriginal community, related to poor housing and overcrowding, with more than 60 per cent of the children at Dewhurst camping area and Gingie reserve suffering ear disease and hearing loss. He also found racial hostility alive and well: 'When I asked a group of white men for directions to Gingie reserve they made obscene remarks about black women.' Aboriginal people were still being asked not to drink at a certain bar of one hotel.
Rea moved on to Bowraville. There he learned that, four years earlier, a pre-school had been built, funded by grants from the state and federal governments and from the Van Leer Foundation, and opened to 'joyful celebrations'. The building by 1979 was empty and abandoned, its windows smashed and most of its fixtures removed: 'Built by blacks, it was disfigured by blacks.' John Ballangarry explained to Rea that the people wanted 'a place where aboriginal mothers could take their kids and teach them', but the government 'wanted it to be like white pre-schools and wanted to bring in white teachers from outside to do the teaching'. The people tried for a while to run it without government funding, but gave up. 'Then it got all smashed up because people were having grog sessions up there.' Rea concluded:
In its present condition the pre-school is a tragic monument to lost hopes and very few people I spoke to, white or black, believed that either the State or Federal government would venture money for a second chance. Worse, the state of the building is cited by many whites to vindicate one of the most enduring negative attitudes towards Aborigines: that is, that they are incapable of doing things for themselves.
The drinking problem was huge. While Rea was there, he found 'many were drinking at either the "bottom pub" or in a shed behind the Royal Hotel'. The main meeting place of the children and young Aborigines was a café run by Val Walker. Val told Rea:
Bowraville is still a very racist town. I have tried to organise dances for the kids but when the white parents find out that Aborigines will be there they keep their children away. It's the adults who are racist. I have heard white mothers tell their children not to come into my shop because it is dirty.
From around this time, race relations in Moree were coming under strain, as trouble brewed between black and white young men in Moree's hotels. The young Aboriginal men began to challenge the right of publicans to bar them from entry to hotels for alleged misbehaviour. One of these angry young Aboriginal men was Lyall Munro Jnr, who now worked in the Aboriginal Legal Service of New South Wales, based in Sydney, was active in the land rights campaign, and regularly returned to Moree. There seemed to be a major racial incident starting in the hotels about every two years or so. In 1976 there was an incident called the 'Moree rampage', and in 1978 a hotel was bombed. Two years later, Moree and its race relations were back in the news. On 3 December 1980 there was a major hotel fight between police and Aborigines, and Ben Sandilands went up there to report for the _Sydney Morning Herald_ and the _Sun-Herald_. It was not just a report on events in a country town, but also another opportunity to compare Moree at the time of the Freedom Ride with now. His report for the _Sydney Morning Herald_ began: 'Things have changed in Moree since 1965 when Charles Perkins and his "freedom riders" broke through the racial barriers which kept Aborigines out of the town's mineral baths.' He then reported on the changes—Aborigines using the bars, clubs, baths and stores, and playing a major role in every sporting activity. When a Channel 10 news crew took some Aboriginal people into the Victoria Hotel, they were readily served. In the _Sun-Herald_ , Sandilands reported that people seemed to mix freely across racial barriers, laughing, talking and carrying on 'with a natural friendliness that Sydney hasn't achieved'. He also reported that one of the twelve people charged for the recent pub brawl was Lyall Munro Jnr. For his part in the fighting, Munro was banned from the town for five years.
Sandilands explored some of the more general problems facing Moree. 'The town that burned itself into the Australian conscience in the 'sixties,' he wrote, 'still has problems, including its past history of racial discrimination. Its wheat crop has failed, the drought has ruined its cattlemen, and on the day after the pub fight the local abattoir closed with the loss of 94 jobs—half of them held by Aborigines.' Lyall Munro Snr pointed out the disused and damaged swimming pool at Mehi village: 'I'm really ashamed of that . . . It was built with help from the local Apex club and there were days when black children and white children went there for swimming carnivals. Then . . . there was anger in the village. It got wrecked. Things went wrong. Things don't always go right.' Lyall Munro Jnr stressed the importance of identity. 'More of us,' he said, 'want a right to practise our religion and culture. We want compensation for the lands stolen from us; we want land rights and protection for our reservations and sacred sites.' Sandilands reported 'an almost universal resentment among Moree's whites at the alleged affluence of Aborigines "living on handouts" with pockets "stuffed full of bank notes" while the rest of the town was feeling the economic pinch'.
The visits from Sydney journalists continued. Malcolm Brown, also for the _Sydney Morning Herald_ , went there in November 1982, after incidents at a Moree hotel that ended in a fatal shootout. A young Aboriginal man, Ronald McIntosh, was gunned down by white youths from a car after a brawl between whites and blacks in the Imperial Hotel's Ned Kelly Bar. In the days after the shooting, hundreds of Aboriginal people stormed around the town in a fury. Brown's story mentioned the Freedom Ride and its influence on Lyall Munro Jnr, by now the administrator of the Aboriginal Legal Service of New South Wales and in 1984 to become its chair. Brown attributed the problems of Moree's Aboriginal people to chronic unemployment and low morale. Petty theft was rife; there was also a growing drug problem. He also noticed a proliferation of racist jokes amongst the whites. 'The white community,' said Brown, 'is heartily sick of the Aboriginal problem. They wish it would go away.' Author Roger Millis, in town doing research for his book on the Myall Creek and other massacres, was also struck by the persistence of racial prejudice among the whites. For their part, members of the Aboriginal community were both angry and distressed at the killing, with 1200 mourners turning up for McIntosh's funeral. Father Dick Buchhorn, the Catholic parish priest at Boggabilla, gave a remarkable oration at the graveside, printed in full in Roger Millis's book. He saw the killing as the result of Aboriginal people fighting for their rights, in the tradition of Martin Luther King in Memphis, Hector Peterson in Soweto and Gibber, an Aboriginal leader of the Kamilaraay tribe, on the Macintyre River 133 years before. 'I have a dream,' he said, 'that one day even this town of Moree, a town sweltering in the heat of racial tension, will be transformed into an oasis of freedom and justice.'
Two years further on and yet another journalist, Frank Walker, wrote a piece in the _National Times_ which began: 'With the long summer, social tensions are again rising in Moree, the NSW country town which has become the barometer of race relations in eastern Australia.' Moree was still smarting, he said, from the headlines it had received over the pub brawl and shooting in 1982, and now pub fighting and other incidents such as cars being pelted with stones had in recent weeks broken out again. Lyall Munro Jnr was described by Walker as the _enfant terrible_ of Moree. His ban for the disturbances in 1980 was over, and many saw him as the cause of the present trouble. The state National Party MP, Wal Murray, said the fights were the work of black power activists seeking publicity for land rights. Many whites said Aborigines were treated far more leniently than whites: 'The thinking that the Aborigines are getting something for nothing and then doing nothing with it is very strong.' Many blamed welfare payments: 'We have to go out and work for our money while they just sit there and let it come to them.'
While the urban papers were presenting this pessimistic picture of the Freedom Ride towns, the Freedom Ride was developing quite a different image on ABC radio. Darce Cassidy's tapes, recorded during the Freedom Ride, sat in his bottom drawer for thirteen years, though Malcolm Long used a small excerpt for a program he made in 1972 on Moree, following up on Allan Ashbolt's 1957 radio documentary. By 1978, however, Darce was Supervisor of the Talks Department of the ABC in Melbourne. In the course of an interview for an ABC program, Lyall Munro Jnr heard of Darce's tapes and expressed interest, revealing he had been one of the children at the Moree pool. In response, a program using the tapes was finally broadcast on 20 February 1978, exactly thirteen years after the original clash at the baths. It is a stunning piece of radio, juxtaposing the voices of angry Aboriginal people and whites in the streets of the towns with those of some of the students including Charles himself, all linked together by Darce's calm connecting narrative.
By the late 1980s, references to the Freedom Ride in the media were becoming rare. Charles Perkins was in trouble as the head and then ex-head of the Department of Aboriginal Affairs, and the story of the Freedom Ride was gradually fading from public life. However, John Mulvaney, a historian and archaeologist with a particular interest in heritage, drew timely attention to it in his book, _Encounters in Place_ (1989), which gave the histories of a number of places thought to be important in Australian history and regarded as worth protecting and memorialising in some way. The Moree pool, he suggested, was one such place. He used newspaper sources to provide a brief account of the Freedom Ride at Moree, and argued that, although new brick buildings had replaced the old wooden ones in 1977, the Australian Heritage Commission's Register of the National Estate should include the site of the clash. The buildings had acquired national symbolic significance: 'Through the Freedom Ride incidents they symbolise a positive action in the civil rights struggle for Aborigines; and _by_ Aborigines, for the leader of the bus tour was an Aborigine, and his message got through to other young Aborigines.' Mulvaney's campaign was successful; the baths were registered on 15 May 1990. The Heritage Commission's Statement of Significance reads: 'The Moree Baths have historic and social significance as the focus of the 1965 Freedom Ride, when Charles Perkins successfully challenged racial discrimination in Moree, in particular bans on Aboriginal people using the Spa Baths.'
In 1991, as part of the preparation for this book, I retraced the itinerary of the Freedom Ride towns with my husband, John Docker. I wanted partly to talk to people about the past, and partly to see how the towns were doing now. I did not realise at the time just how much I was one of a long line of people who had made the same trip, asking the same people the same questions.
When we visited Wellington on 31 March, we saw the shanty town, which was still there with tin shacks, washing on the line and people around. It struck me just how beautiful the countryside was, rolling down to the river with willows and other vegetation all along. Its colonial past seemed to hang in the air, just out of sight. When we visited the Wellington Museum, a large and interesting place, we saw a tribute to the white pioneer settlers. A volunteer guide told us that many people, when they saw the display concerning the children at the mission in 1832, said to her that it was wrong for the missionary, Watson, to have taken Aboriginal children from their parents. Personally, she said, she thought the children were lucky and Watson had done his best.
We also visited Gulargambone, though not the old reserve, which we couldn't find. It was still a small and very depressed town, with no new buildings, no tourist office, and few people around except some Aboriginal teenagers and children. There was an Aboriginal arts and crafts shop called Narko Uluru, funded under the Community Development Employment Projects scheme, the only shop open in the town apart from the garage. It had started only two weeks before, and sold t-shirts, framed woodcuts, Aboriginal paintings on board, earrings, brooches, spears, wooden snakes and emu eggs.
In Walgett we met Harry Hall, George Rose, Phillip Hall and Gladys Lake, the activists of the 1960s and since. In 1991, Walgett had two Aboriginal community centres. One was the Barwon Aboriginal Community Centre, run by George Rose, its vice-president, in the old Foundation building. George told me that at first he hadn't supported the Freedom Ride and thought it was the Aboriginal people in the town who did the real work of bringing about change. He showed us around the Aboriginal medical centre, in a new impressive building a few blocks away, proudly emphasising that 20 to 30 per cent of its patients were white. We also visited the other Barwon Aboriginal Community Centre, where Phillip Hall worked, having returned to Walgett only twelve months before after leaving a senior position in the Department of Aboriginal Affairs following Charles's departure. There we met Harry Hall, who came down from Lightning Ridge to meet us. At that time he was aged about 60 to 65 with grey hair; he was a very dignified man, a very impressive person, thoroughly politically committed. He hadn't given up, and I thought he probably never would. He was now in a group called the Independent Aboriginal Council, which was gathering together 21 handpicked people in Dubbo on 14 April of that year.
Harry said the whites led the town by day and the blacks by night. It seemed to us pretty true—the whites had indeed abandoned the streets at night, though Aboriginal people were quite evident in the daytime too. The problem, he said, was alcohol, and the police no longer tried to control it; there could be 200 to 300 Aborigines on the street, and the police would just turn right away from it all. They could no longer do what they used to do—march everyone into the paddy wagon when they got drunk and the situation was out of control. The only solution to the policing problem, Harry thought, was to have mixed police, half white, half black, to handle disturbances. But there were few Aboriginal police in New South Wales at that time, and none in Walgett because an Aboriginal policeman would get too much flak from his own people.
When we arrived in Moree, Bill Lloyd—by this time in his early eighties—gave me quite a different story about Moree from that told by journalists over the years. The emancipation of Aborigines in the town since 1965 had, he told me, been truly remarkable. There were several successful Aboriginal families, like the Jenkinses, the Duncans, the Tighes, the Craigies and the Binns, who were important in sport and in other ways. While Aboriginal employment had suffered with the closing of the abattoirs, the cotton-growing industry employed many Aboriginal people and had, in effect, saved the town. Bob Brown's brother was complaining— quite rightly, Lloyd thought—about the health risks of spraying the cotton. I also had a long conversation with Lyall Munro Snr, who stressed how well things were going ahead in Moree—Aboriginal people owned some businesses, were on the board of the bowling club, owned racehorses, were on the board of directors of the hospital and controlled the Police Boys' Club. Alcohol and drugs were the biggest problem, but this was a problem they shared with the whites in the town.
Lyall recalled a recent conversation in which he and other Murris in Moree had been discussing whether the old days or now were best. On the credit side for the 1960s had been more employment, less alcoholism, more kinship, no vandalism, no drugs, marriages lasted better, good mission schools. On the debit side was the fact that life was so controlled by the managers and the police and the law. The Freedom Ride, he said, had given a lot of people a big shock, an enormous cultural shock. The biggest was that the white supporters of Charles Perkins (the students) were educated people, people who were going to be powerful. After talking to Bill and Lyall, I visited the pool and artesian baths. While the latter were used mainly by middle-aged Europeans, children—both Aboriginal and white—were using the pool. As I swam around, I thought: 'This really has changed, and perhaps these kids are there as a result of the actions we took so long ago.'
In Lismore we met Tess and Vic Brill, who talked about the Aboriginal Advancement League days, and took us to Gunderimbah, which now had new houses and where we met some of the local Aboriginal people. Then we went on to Bowraville, which seemed to have the same intense, brooding, racist flavour it had had in 1965. Yet things had in fact changed. We went to a large concert and barbecue called 'Building the Bridges', organised by a combination of black and white organisations and described by the _Guardian News_ as 'a sincere attempt by both parties to promote greater friendship and understanding between Aboriginal and white people in the Nambucca Valley'. There were Aboriginal people there of all ages, and a lot of counter-cultural middle-class whites. The hall was decorated with red, black and yellow balloons, and everything was very warm and lively. When we went outside after the concert there were people all over the street, including on the centre strip, talking, drinking, having fun. In my diary the next morning, I asked myself: 'Which was the real Bowraville, the tense racist town we had entered that day, or the town hosting the "Building the Bridges" concert that night, where black and white enjoyed themselves together, and where the Aborigines took the initiative and took over the town? '
During the 1990s, while I was researching this book, the Freedom Ride gradually returned to public consciousness. Peter Read's biography of Charles Perkins appeared in 1990, and its lively and detailed account informed a new generation about the events of 1965. Rachel Perkins and Ned Landers' film, 'Freedom Ride', was first screened on SBS in July 1993 and was a revelation for many. Charles's return to public life after the charges of maladministration of the DAA were quashed also helped the fortunes of the Freedom Ride in public memory. Then, on the Freedom Ride's thirtieth anniversary in February 1995, Jim Spigelman and Brian Aarons organised a reunion in Sydney. A barrage of media, including ABC radio, the _7.30 Report_ from ABC television, and teams from _A Current_ _Affair_ and SBS, came along. Charles spoke about the significance of the Freedom Ride—how we couldn't do that particular thing again, but it was important at the time. Phillip Hall spoke, saying it changed his life; after that, Aboriginal people like himself could get into the bureaucracy and try to bring about change. Harry Hall was there, but refused to speak. Media coverage was substantial. ABC Radio broadcast _Speaking Out_ on 26 February 1995, which traced the history of the Freedom Ride and interviewed Charles and George Rose. George said the Freedom Ride was one of the best things that ever happened, but in the end nothing came of it and there was still no consultation with Aboriginal people in Walgett.
There were several more radio programs in the 'retracing' genre that year. One was by Lorena Allam, of Radio National's Indigenous culture program _Awaye_ —the first made by an Aboriginal person, as far as I can tell. She interviewed Lyall Munro Snr, Bob Brown and many other Aboriginal residents of Moree. Lorena suggested that, while racial segregation had gone in Moree and other towns, the social and health problems remained. When Ginny Stein made a program for regional ABC radio that same year on what had happened since the Freedom Ride, she encountered some weariness with the whole subject. George Rose refused to be interviewed, as he was 'sick of being interviewed about things that never changed'. Darce Cassidy's program was re-broadcast by the _Awaye_ program, and was aired again in 1997 to mark the thirtieth anniversary of the Referendum.
The Freedom Ride began to be taught in schools at the upper primary level in 1997, in a unit entitled 'People Power' in the _Discovering Democracy_ series. The unit investigated three popular movements in which citizens' actions had achieved civil rights (the other two were the Eight-hour Day and the Equal Pay for Women campaigns). Placement of civil rights—and especially the Freedom Ride—on the curriculum, in the context of a push to expand the teaching of Civics in senior primary schools, stimulated a new interest in and knowledge of the event. Teachers were looking for accessible material, and I willingly accepted an invitation from Judy Aulich in March 1998 to speak to Grade 6 pupils at the local primary school, Lyneham Public School. I was extremely moved by their interest in what I had to say, and their questions, such as whether I had been scared, and how many girls were on the Freedom Ride. The teacher showed the Rachel Perkins film on video, and I had to point out which one of the students on the bus was me. I also read out sections of my diary.
The entire class wrote letters to me afterwards, telling me how much they had enjoyed the talk and what they had learnt. Common themes were the fact there 'were more boys than girls on the Freedom Ride', 'I never knew that Charles Perkins was a soccer player', 'I learned about Aborigines' rights and everyone has the right to feel safe and go to the pool when they want'. One wrote: 'I reckon that getting the confidence and then going out on a Freedom Ride is a pretty cool thing to do.' Many commented on seeing me on the video. One girl wrote: 'I enjoyed guessing who you were on the video then finding out who you were', and another said: 'I enjoyed seeing who you were on the video. I would have never known that that was you because you look so different to what you look like now.' Many said they enjoyed 'the part when I read the diary'. One girl wrote that she hoped 'anyone who discriminates against Aboriginals gets what is coming to them!' and that the main thing she had learnt was 'that no matter how big the problem it can always be solved by people who care'. I wrote to the class thanking them for their wonderful letters.
Journalists still use the Freedom Ride as a touchstone for reporting Aboriginal conditions in country towns, notably Moree. After a van was turned over and set alight in the southern part of town, and a crowd of about 200 pelted police and firemen with rocks and other missiles in January 1998, Malcolm Brown went there again for the _Sydney Morning_ _Herald_ , as he had done sixteen years earlier, to investigate. Some white residents were saying there had been too much latitude in law enforcement, while others thought 'lawlessness among sections of the Aboriginal community has been stirred up by the aftermath of the _Wik_ and _Mabo_ High Court decisions'. Brown noted:
The Moree spa baths, with water at 41 degrees bubbling from the bowels of the earth, have provoked other bubblings in the past, including an ugly confrontation when the Aboriginal-oriented 'Freedom Riders' came to Moree in early 1965, highlighting issues of racial discrimination in pool use. Now, although Aborigines have long been allowed into the pool, there is still bubbling discontent because so many Aboriginal children have been banned for varying periods from the pool, and move on to far less suitable waters . . . The Abor-ginal children go to the nearby Mehi River, a stream of varying depths littered with rocks, broken glass, abandoned shopping trolleys and tree roots.
Yet there are many in Moree who regard its present and history a little differently. Aboriginal memory in Moree aims to stress both the extent of change and the seriousness of the problems that remain, and there are whites who do retain hope for the future. For example, Dick Estens, a cotton grower who chaired the Gwydir Valley Cotton Growers' Aboriginal Employment Strategy that found many jobs for Aboriginal people in the area, is a member of the board of directors of 'Reconciliation Australia'. The town held a commemoration of the Freedom Ride 35 years later, in February 2000. The Mayor of Moree Plains Shire Council, Mike Montgomery, welcomed Charles Perkins to the celebration, saying: 'Stories can be told today, and we can listen and acknowledge history, the troubled times then and now and accept we've come a long way.' Longtime Aboriginal residents Lyall Munro Snr and Mrs Pearl French also spoke, remembering a time when Aboriginal people were segregated on to missions and reserves on the edge of town, and excluded from the footpaths, shops, cafés, pubs, public toilets, the high school and the whites-only sections of the cinema. One of the Freedom Riders, Rick Collins, was there, joking that he would never forgive Charles for getting him into the Freedom Ride. Bill Ford was invited to the celebrations, and was deeply moved by the whole event.
The former Freedom Riders in later years came to evaluate the Ride's importance in a number of different ways. More than anything, it had drawn attention to the situation of Aborigines. When asked by the Joint Parliamentary Committee in June 1966 about the effects of the Freedom Ride, Charles had replied:
The main objective of the trip was to create or stimulate awareness among the Australian public as to the actual situation concerning aboriginal people, or of the fact that there was discrimination existing in society. We wanted to help stimulate both the aborigine and the Europeans in respective towns to rethink the situation in which they are living. This is our objective, and I think that we did achieve this success . . . it was sensational, and it had its effect.
Nine years later, his book had the same message, and fifteen years further on he told Stuart Rintoul: 'I think it was a major turning-point, a catalyst in black–white relations in this country.'
The other Freedom Riders agree. Gary Williams thought it 'upset the apple-cart' for those who had been in power over Aboriginal people— the police, town councillors, the Welfare Board. Hall Greenland thought 'the political effects were that it helped put race relations in this country on the map . . . What the Freedom Ride did was to remind us that there were problems here as well, and reminded us and reminded the whole society. So it did raise the profile of Aboriginal problems.' Jim Spigelman said: 'I think it was the first time that Aborigines were consistently front-page news ever in Australia. So it did have the effect of dramatising the issues to a wider public. And that was its political effect.' John Powles believed 'it was an enormous publicity success, I mean I think it put Aboriginal affairs and the conditions of fringe dwellers in country towns on the front pages for some days and I recall it did force some kind of political response . . . I think our effort was one of the things that helped to push Aboriginal affairs to the forefront of political debate and discussion.' For Wendy Golding: 'My very strong feeling is that what the Freedom Ride did was put the whole matter—the whole Aboriginal issue—on the agenda. Up until then it just simply wasn't an issue. People did not think about it—it was irrelevant.' As Pat Healy put it: 'Black civil rights in Australia—the Aboriginal people—were not front-page news. The Freedom Ride put it on the front page . . . The message that came across to ordinary suburban Australia was that we had rampant racism in 1965 in country New South Wales—of a form that I think most people didn't realise was there.'
Some felt it had contributed to the success of the 1967 Referendum. Charles pulled no punches, as always, when he said: 'The Referendum in 1967 was successful because of the Freedom Ride. That's what gave the Referendum real meaning and influenced the number of people who voted in a positive way.' John Powles: 'It helped to create the climate that led on to the Referendum.' Jim said: 'I'm not saying there wouldn't have been a Referendum without it, but it was one of the things which created the circumstances in which the Referendum was successful, and that obviously has ongoing effects.' Barry Corr: 'I still think that what we did contributed to the high percentage of the vote in the Referendum. If we did something to change the attitudes of white Anglo-Celtic Australians of that time, I'd be very content.' Colin Bradford drew a similar conclusion: 'The people that were on the Freedom Ride would have also been amongst those actively pushing for the Constitution to be changed and campaigning for that. I know I was and I think most of the others were too, so I guess the fact that we were enthusiastic in our compassion and we were protagonists for the Aboriginals probably influenced other people to do the same, and maybe it had an influence on the way that constitutional reform went.'
Many felt that its main effect was to stimulate Aboriginal political activism. Charles told Stuart Rintoul: 'I think it changed the psychology of Aboriginal people. They realised, hey, we don't have to cop this shit. That was the biggest thing.' Gary Williams thought the Freedom Ride 'gave people a little glimmer of something different. Even if it did frighten some people, it widened things.' Bob Gallagher said: 'I think it has provided a spark and a bit of stimulus and so on so that Aborigines will go and do it for themselves . . . It's got to be their commitment, they have to take it into their own hands, it has to be their reforms . . . So I think myself, that's its place in history.' Hall thought that 'here and there, [it] encouraged local Aboriginal organisers and campaigners to keep going and to keep organising. So I think it was a positive event and a positive initiative that was taken.' Darce Cassidy quoted Lyall Munro Jnr as saying 'it gave hope and encouragement to those engaged in the often lonely daily grind.' Darce went on:
The bus trip itself was largely symbolic, but the follow-up work from SAFA activists, and more particularly from Aboriginal communities throughout the country, made significant advances. While the SAFA organisation fairly quickly faded, the struggle of the Aboriginal people escalated in the following years. The Freedom Ride helped generally in the development of a mature Aboriginal leadership. In 1965 white liberals dominated many organisations, but over the next few years the leadership changed. This of course was the result of a number of factors other than the bus trip, and there were leaders other than Charles developing around this time—both at the local level with people like Harry Hall and Ted Fields in Walgett, Lyall Munro in Moree and Chicka Dixon in Sydney.
Brian Aarons agreed: 'It was an event that wouldn't happen in that way after about 1972, because from then on it was the Aboriginal people themselves acting on their own behalf and whites were very much there as assistants and so forth.'
For several of the Freedom Riders, it was not only Aboriginal activism generally, but the prominence it gave to Charles Perkins in particular, that made the Freedom Ride important. Jim remarked that the Freedom Ride 'was of considerable significance in launching Charles's career in the entire area. That may have been one of the more significant influences. He went on to do all sorts of things with all kinds of hats in the Aboriginal affairs area.' Robyn Iredale retained her very high regard for Charles Perkins: 'I felt very privileged to have been associated with the Ride I suppose afterwards, when I realised what I'd actually been involved in, and I was really pleased to have been able to have come in contact with Charlie and seen what he was like and the sort of things that drove him.'
Darce suggests that the Freedom Ride provided a model for political activism on other issues. He writes:
The concept of a bus trip as a political strategy, and the use of the travelling direct democracy aspect as a way of building unity among a diverse group, and of coming up with appropriate reactions to developing situations was used in a number of other situations. Nine years later the Campaign Against Foreign Military Bases in Australia held the Long March and the Quick March to the US Naval Communications Base at North West Cape in Western Australia.
Political scientist Sean Scalmer develops this argument: 'The Freedom Ride had important consequences for the history of collective action in Australia. It demonstrated to local activists that dramatic actions used overseas—sit-ins, pickets, bus rides, colourful protests—could be equally successful when applied to Australian problems . . . In the aftermath of the SAFA tour, other actors began to take up these new, now less-unfamiliar political techniques.' And indeed the notion of a Freedom Ride remains very much alive in Australian political culture. In protest against the detention of asylum seekers, a Freedom Ride was conducted to the Woomera Detention Centre on 21 September 2001. The leaflet advertising the ensuing public meeting was headed 'FREEDOM RIDE', and the text read in part: 'In the tradition of the Freedom Rides of the 1960s there will be a solidarity tour travelling from Melbourne on September 21 to the Woomera Immigration Detention Centre in South Australia to protest against the imprisonment of refugees and asylum seekers.' Further Freedom Rides to Woomera were held in 2002.
Yet some Freedom Riders felt that the impact was relatively limited. Aidan Foy thought: 'All it did was put it on the agenda. It didn't actually achieve anything lasting in itself.' A number stressed that the effects of the Freedom Ride were, as Colin put it, 'probably in the long term only minimal'. For Norm Mackay, it was a small event indeed. Compared with 'what happened in Montgomery, Alabama . . . our attempt was a bit Mickey Mouse really'. It brought 'no earth-quaking changes'. He went on: 'So as a part of Australian history it should be a comma or a semi-colon, not a chapter. If Ann's getting a book out of this, well she's getting it easy.'
So what do I think? I think a number of things. I think the Freedom Ride was a brief episode in a long history of Aboriginal people fighting for their rights, and there are many profound issues it did not address, though its existence sometimes helped prompt others to do so. These included issues such as land rights, native title, child removal, sovereignty and a treaty, to name a few that have created so much anxiety over recent years. It had no clear position on the rights and wrongs of assimilation, being on the one hand supportive of Aboriginal initiative and freedom of choice, and on the other concentrating its attention on Aboriginal admission to the benefits of white society. It by no means brought an end to the problems facing Aboriginal people; indeed, this retelling of the Freedom Ride story reminds us of their longevity, persistence and depth.
I also think that the Freedom Ride was nevertheless, as Charles suggested, a turning point in race relations in Australia. It was one of those transitional moments in Australian history when one era fades and another takes its place. More clearly than any other event, the Freedom Ride signified the shift from the Cold War to the 'Sixties'. This was the beginning of the end of the Cold War period in Australian political culture, with its predominant certainties about the virtues of Australian society as a member of the 'free world' and its small critical Left operating cautiously and quietly in a hostile environment. With their willingness to confront authorities in mayoral offices, election meetings, swimming pools and elsewhere, the SAFA students were a harbinger of the New Left and the student revolts of the second half of the 1960s. They brought to Australia a sense of politics as informed by folk songs, visual displays and theatricality. There was something very modern and media-savvy about the Freedom Ride, so conscious were the students from the beginning of the power and importance of the mass media. For them the media were not all-powerful, but something to be captured and used for public good. With this media awareness came a self-consciousness about recording their actions; between them, the students produced some enduring film images, recorded sound and written accounts of their own.
The Freedom Ride was both a local and an international event. Some aspects were distinctly Australian. The students' focus on swimming pools in Moree and Kempsey and picture theatres and hotels in Walgett and Bowraville bespoke an interest in the democratic egalitarianism of public leisure spaces, and a genuine immersion in the easy enjoyment of life that such spaces promised. In developing the ideas of non-violent direct action, and adopting ideas of confrontation from the American civil rights movement, the students also brought something new to Australian politics. They listened to and learned from the American civil rights movement, especially Martin Luther King's idea of 'creative tension', and adapted what they found to their specific situation. With their ethic of non-violence and passive resistance, they created a space that was enabling for the women as well as the men, a space that was lost in the following years when so many radical activists came to favour violent confrontation and had then to be regained and enlarged by a revitalised feminism.
Above all, the students' actions—and especially Charles's leadership of those actions—became a symbol of protest for Aboriginal people, and a benchmark against which to measure Aboriginal hopes and realities.
The Freedom Ride held out the promise that nothing could be quite the same again.
Epilogue:
Whatever happened to . . . ?
Without exception, all of us white students, all at that time aged about 19 or 20, learnt an awful lot. I mean it was the sort of thing that I think you can count yourself lucky for having been through, an experience that most people wouldn't have had . . . It's the sort of thing that I think stays with you in a variety of tangible and intangible ways, and sort of affects and influences you.
Brian Aarons, interview 1994
What happened to all these people? How did the Freedom Ride influence them in later life? How did the Aboriginal activists get on and to what extent did the students and their supporters remain interested in the question of Aboriginal rights? Let's have a brief peek into their later lives.
Charles went on to the national stage of Aboriginal politics and policy, and there is space to mention only a few of his achievements here. His story has been well told by Peter Read in _Charles Perkins: A Biography_. After his graduation in 1966, he worked for several years as the manager of the Foundation for Aboriginal Affairs. During this period he turned to the ideas of Black Power, began quoting not so much Martin Luther King as Malcolm X, and warned of the dangers of violence if bodies like the Foundation did not succeed. He also became much more fervently anticommunist than before, and fought what he considered was the undue influence of communists in FCAATSI. In 1969, he left Sydney for a position at the Council of Aboriginal Affairs, and joined the Department of Aboriginal Affairs when it was created in 1973. He became its deputy secretary in 1979, before resigning in 1980 to take up the position of chair of the newly created Aboriginal Development Commission. He returned to the Department in 1984, now as its secretary, the highest-ranking position achieved by an Aboriginal person.
In all these positions, Charles retained the role of public commentator and conscience on Aboriginal issues, and at times got into trouble for publicly criticising superior departmental officers and ministers. A charge of maladministration (later quashed) led to his resignation from the public service in 1988. After this bruising experience, he returned to his birthplace in Central Australia, where he was initiated. He continued to speak publicly on Aboriginal issues, becoming chair of the Arrernte Council of Central Australia (1991–94), and being nominated by the National Aboriginal and Islander Day Observance Committee as Aboriginal of the Year in 1993. He was elected Aboriginal and Torres Strait Islander Commission Commissioner for the Northern Territory–Central in late 1993, and its deputy chair in 1994. He left it in 1995 to become a consultant to the Australian Sports Commission, mentoring Aboriginal athletes, but returned in 1999 as ATSIC Commissioner for Sydney.
During the 1990s Charles became very bitter about many of the people and directions in Aboriginal politics, attacking the federal government's Council for Reconciliation as irrelevant, a 'sell out' and a product of the 'lunatic Left' when it was announced in 1991. His oratorical skills failed him in a television confrontation with Pauline Hanson in September 1996 in which he came over as abusive and unconvincing. His call to Aborigines to protest during the Olympics in 2000, with the words 'burn, baby, burn', was widely condemned, and out of touch with most Aboriginal sentiment, which favoured support for Cathy Freeman and other Aboriginal athletes at the Olympics. When he died on 18 October 2000, after years of ill-health following kidney failure in 1969 and a kidney transplant in 1972, there was a mixture of fulsome praise and some critical comment. The _Australian_ 's editorial, although headed 'Perkins's Fight Enriches Us All' and praising his role in the Freedom Rides, said he had lost much of his political savvy in recent years and lost his status as an Aboriginal leader. It mentioned that 'the most damaging claims involved allegations that he brokered deals with mining companies then took a slice of the resulting Aboriginal profits. Some condemned him for using his position within the Aboriginal community to advance his personal business dealings.' On the whole, though, the praise far outweighed the criticism. A state funeral was held in his honour, a ceremony normally reserved for governors, premiers and ministers.
Charles's death made headlines around the country. The _Sydney_ _Morning Herald_ 's front-page story was headed 'A Freedom Rider's Journey Ends'. Inside was a full-page life history in which the Freedom Ride was prominent. The obituaries and public comments revealed strong appreciation of Charles's originality, dedication and achievement. Many of them focused on the Freedom Ride. Bob Carr, the Premier of New South Wales, said:
When he stood up in country towns in 1965 and said: 'Aboriginal people are being discriminated against', it was a relatively lonely cause . . . let's acknowledge the Charlie Perkins, the young man, the footballer who went to university . . . [who] took a stand for the rights of Australian Aborigines before the cause had gathered much momentum.
Evelyn Scott, chairperson of the Council for Aboriginal Reconciliation, said 'the Freedom Ride changed Australia's comfortable self-image and played a part in building the pressure to hold the historic 1967 Referendum'. Isobelle Coe, of the Aboriginal Tent Embassy in Canberra, said the Freedom Rides were still important to many young Aboriginal people. Some made direct comparisons, as they had always done, with Martin Luther King. Gatjil Djerrkura, former ATSIC chairman, commented: 'His greatest legacy I would see somewhat similar to Martin Luther King, I would say in comparison. Because I think, that what his legacy was all about was a freedom fighter.' John Pilger, in the _Guardian_ in the United Kingdom, drew a different analogy, calling him 'Australia's Mandela'.
The state funeral was held at Sydney Town Hall at 11.00 a.m. on Wednesday, 25 October, a gigantic Aboriginal flag draping the stage. The city's flags flew at half-mast as about 2500 people packed the Town Hall and more than 1000 listened outside. Mourners included, the _Herald_ reported, 'the Governor General, Sir William Deane, two Federal ministers, Senator Herron and Mr Ruddock, the Federal Opposition leader, Mr Beazley, numerous state parliamentarians, eight Federal MPs—and another Aboriginal hero, Cathy Freeman'. Indigenous leaders attending included Geoff Clark, Evelyn Scott, Lowitja O'Donoghue, Tony Mundine and Aden Ridgeway. At least eight of the Freedom Riders attended—Alan Outhred, Alex Mills, Bob Gallagher, Brian Aarons, Hall Greenland, Jim Spigelman, Pat Healy and Warwick Richards. Jim gave a moving tribute, recalling the Freedom Ride and describing it as 'the emergence for the first time in our history of an Aborigine with a clear leadership role'. The Freedom Ride, he said, was the event 'which first brought him to the forefront of national attention, a prominence which by force of his character, capacity and achievements, he would never relinquish. There were numerous occasions on the Freedom Ride when Charlie displayed the intelligence, the debating skill, the determination, the passion and the anger which would mark his life.'
The family invited mourners to join a public walk to a wake to be held at Bennelong Point, and 2000 people did so. Many carried pictures of Charles Perkins as they followed his coffin to the Opera House, and many hands reached out to touch the hearse. I was not there; my mother had died after a heart-wrenching six-month illness less than four weeks before, and an old friend had died suddenly nine days after that. I could not face another funeral just then. But my thoughts were with Charles that day, and his death did lead me to reflect on the Freedom Ride in a new way. I realised how well it was now remembered, and how important it had been for the growth of Aboriginal leadership, initially in the figure of Charles himself, later joined by others. Soon afterwards I wrote an obituary for the journal _Aboriginal History_ , in which I said that 'Charles Perkins had a full and active life fighting for Aboriginal rights, and with his passing we have lost one of the most courageous and forthright Aboriginal activists this country has so far seen. I am glad to have known him, and very sad that he is no longer around to provoke, irritate, and inspire us all.' A year after Charles's death, the first Charles Perkins Memorial Oration was held at the University of Sydney, the speaker Aboriginal lawyer and leader Noel Pearson, who argued for zero tolerance of alcohol and drug abuse in Aboriginal communities and the dismantling of the 'passive welfare paradigm'.
Gary Williams abandoned his studies but not his political activism. He continued to live in Sydney for some years, participating in the Foundation for Aboriginal Affairs, the Aboriginal Legal Service, the Aboriginal Medical Service, and the Tent Embassy. He worked for some years as a judge's tipstaff in Sydney, and in the late seventies as a driver at Papunya in the Northern Territory, and then for the newly formed Central Australian Lands Council. In the 1990s he returned home. 'I realised,' he told me, 'how my thought patterns are still in the Nambucca Valley.' Through the Community Development Employment Project scheme, he teaches the Gumbayggirr language to children and adults. He also helped establish the Goori Broadcasters of Radio Nambucca, and broadcasts a program called _Goori Time_ , which plays music and news for about two hours each Friday. He seems to have found a nice balance between local commitment and involvement, and those connections to a wider world that began when he moved to Sydney as a 17-year-old almost 40 years earlier.
Jim Spigelman became just as well known as Charles. He was Gough Whitlam's principal private secretary when Whitlam was Prime Minister between 1972 and 1975, and then head of the short-lived Department of the Media in 1975. When the Whitlam government fell, he went overseas for several years, and wrote a book jointly with Peter Pringle on nuclear energy, called _The Nuclear Barons_ , published in New York in 1981. He married and returned to the law in 1979. When he became Chief Justice of the Supreme Court of New South Wales in 1998, newspaper profiles of him frequently mentioned his Freedom Ride participation. A later profile by Bernard Lagan on 17 June 2000 did too, also noting that Jim had participated in the walk across the Sydney Harbour Bridge for Aboriginal Reconciliation. Jim told the students at Sydney Grammar School, in an address in 1998, that he still considered his involvement in the Freedom Ride at the age of 19 to be the most important thing he had ever done.
Tom Roper was one of those who remained heavily involved in Aboriginal issues. He was state director of FCAATSI for a while in the late 1960s, and became an adviser to Gordon Bryant as Minister for Aboriginal Affairs in the Whitlam government. In that role, he strongly advocated the introduction of bilingual education in the Northern Territory: 'In that three months we held the first meeting of Aboriginal elders to actually tell the Northern Territory administration what they wanted for their kids, rather than what this very Anglo-Saxon administration wanted . . . We funded for the first time, or first significant time, health and education programs by the states.' Later, he entered politics himself, becoming Aboriginal Affairs Minister in the Victorian Labor government from 1987 until he became Treasurer in 1989. He kept an interest in Aboriginal issues, and as a member of the Labor Party in Victoria tried to persuade the Commonwealth government 'before during and after _Mabo_ that in terms of Aboriginal communities like here, you needed national Aboriginal land rights legislation, that _Mabo_ would not be adequate for the kind of dispossessed communities that we saw in New South Wales in the 1960s and continue to exist all over the country.' Following his retirement, after 21 years in the Victorian Parliament, half as a minister, Tom focused on environmental issues, especially climate change, and lived for several years in Ottawa and London.
Three of the Freedom Riders—Chris Page, Aidan Foy and John Powles—became doctors. Aidan was involved in the establishment of the Aboriginal Medical Service in Newcastle and also gave evidence to an inquest in Wilcannia concerning Aboriginal deaths, and to the Black Deaths in Custody Royal Commission. He became a specialist on alcohol addiction, and director of Drug and Alcohol Services at the Royal Newcastle Hospital. In 1994, he remained both supportive of and concerned by some of the changes in Aboriginal leadership:
There's still reluctance on the part of some Aboriginal leaders to accept responsibility where they need to, and I find that frustrating. I'm probably one of the few people in the country who is expert in the medical management of alcoholism and that is a significant problem for Aboriginal people, but they need to tell me if they want my help what it is they want. If Charlie were to say to me, 'Aidan, we need this and this and this, and we would like you to do this', I would do it. But I'm not hearing that and that upsets me . . . there are groups who hold on to their injustice as if they don't want to let go of it. They're almost addicted to their sense of injustice that they wish to express rather than look at the way we can fix this together. We can.
Aidan thought the positive sides of change since 1965 had outweighed the negative ones. 'There's been some fantastic things happen,' he remarked. The _Mabo_ legislation, he thought in 1994, was 'just light years ahead of the sort of issues we were dealing with 30 years ago'. He also welcomed the fact that 'relations between the two communities, Aboriginal and non-Aboriginal, have actually improved; after all, I've got Aboriginal colleagues now, I didn't have them before and that sort of thing has got much better'. Finally, says Aidan, 'I've gone back to where I started in the sort of Catholic social justice movement. I subscribe to _Eureka Street_. I sort of take a politically radical but socially conservative view of the world, which is probably pretty much as I did at the beginning.'
John Powles, like many of the others, was active in the anti-war movement, protesting against Australian involvement in the American war in Vietnam. 'I remember I was one of the people who disrupted the visit of LBJ to Sydney. I was the person whom the Premier said to: "Drive over the bastard." We ran out on the road between the motorcade— between the motorcycles and the first car, which included the Premier and the police chief. So that was my second arrest for a demonstration.' He finished his degree in Medicine, and then in 1968 when he was a junior resident doctor at Canterbury Memorial District Hospital in the western suburbs of Sydney he was involved in a demonstration against the Soviet invasion of Czechoslovakia. In 1969 he went to the University of New South Wales to study Sociology, and a year later married and went to England, where he lived for four years until he returned to Australia, to teach at the Department of Preventive Medicine at Monash Medical School for the next sixteen years. During the 1980s, when Tom Roper was Minister of Health in the Victorian Labor government, John was his adviser, 'and we did a number of things in the area of food and nutrition policy and general prevention policy'. In 1990, he left Australia again, and took up an academic position at the Institute of Public Health at the University of Cambridge, as well as working in the National Health Service in Britain and also in a European Community-funded project in Bulgaria. Throughout this full and varied career, John continued to care a lot about racial issues. Interviewed in 1994, he said: 'I was very affected by the changes in South Africa this year. That really affected me a lot emotionally.'
Louise Higham dropped out of her medical degree and transferred to Arts. After graduation, she went to England, and then Spain, where she married and had two children. By the late 1990s, she was working as director of arts and literature programs in a cultural organisation in Spain. She now feels rather out of touch with life in Australia. 'Changes in Australia and Spain,' she writes, 'although of different natures, have been equally profound in both countries, but I haven't been there to live through and witness them day by day, so to that degree I am a foreigner. One inevitably pays more attention to what is happening on one's own doorstep—the repairs of the British nuclear submarine in Gibraltar Bay, ETA assassinations and threats and the coming Basque elections—or nearby—Israeli/Palestinian confrontation in the occupied territories— than day-to-day events further away.'
Several of the Freedom Riders were studying to be teachers. Beth Hansen took up her first teaching job at Chester Hill High School, and became involved not only in Vietnam demonstrations, but also in the Teachers' Federation, being elected to its council for a couple of years. She married Eric Earley and travelled through Asia for a year, followed by two years of suburbia in Homebush, 'feeling very lonely and isolated'. In 1974 Beth and Eric went up to Papua New Guinea with two small children. They lived for two years in Goroka, had another baby and then lived for another two years at 'a little isolated rural place called Palmalmal, on East New Britain, about an hour's flight south from Rabaul, no road access'. The school was on an old coconut plantation. 'We had to feed them, clear the jungle, and clear part of the plantation which had all sorts of war debris on it, put in gardens . . . They had a school council that ran that school in Pidgin English. These were bushies, and they knew what education was about, they knew what they wanted for their kids. It was just a fantastic experience, the whole four years, but especially the last two.' When Beth went to live in Lismore in 1979, she became involved in adult education. She regained contact with Aboriginal issues when she was appointed to the council of the Northern Rivers College of Advanced Education in 1981.
Hall Greenland was editor of _Honi Soit_ in 1966, graduated from university, went to Europe and returned to Australia in the late 1960s. He worked as a schoolteacher for six or seven years and on and off as a journalist after that. He remained politically active, becoming involved with the Anti-Vietnam War Movement, and remained in the Labor Party until 1984. He was involved in Green politics for a while, went on land rights support demonstrations for Aborigines, and was especially involved in inner city local politics. He wrote _Red Hot_ , a lively and readable book about one of his mentors, Nick Origlass, in 1998.
We last saw Robyn Iredale leaving the Freedom Ride after Moree, to attend to her very ill mother. Her mother died two months later. She finished her Honours year, writing her Geography thesis on Aboriginal rural–urban migration, and completed her Diploma of Education. Later, she married and taught at Cheltenham Girls' High School where she wrote the first Asian Social Studies syllabus for use in schools in New South Wales. She went overseas, first travelling for a year and then teaching in Canada for three years. Robyn's life underwent a major change when she enrolled in a Master's degree in Population and Development at Macquarie University, separated from her husband and completed her Master's thesis on occupational adjustment of Indo-Chinese in the Australian labour market. 'I'd sort of decided by then that I couldn't work in Aboriginal research because I basically felt you had to be an Aborigine.' She enrolled in a PhD in the School of Economic and Financial Studies, also at Macquarie, and completed a thesis on the recognition of overseas qualifications. She became a policy officer in employment at the New South Wales Ethnic Affairs Commission and later worked on the Human Rights and Equal Opportunity Commission, supervising research projects or policy documents on a variety of issues: 'We did the National Inquiry into Racist Violence while I was there.' Robyn moved to Wollongong in 1990, to take up a research position at the university's Centre for Multicultural Studies.
Another of the Freedom Riders to become a teacher, and one of the few to remain in teaching, was Alex Mills. He abandoned his theological studies, did a Diploma of Education instead and in the middle of 1967 started as a teacher-librarian at Taree High School, where he has been ever since. He married in 1972. 'After a couple of years I started getting involved with the Aboriginal scene in Taree and had an involvement in that for about fifteen to twenty years'. Alex worked with Ella Simon and others in the Purfleet community, for example taking up the issue of in-service courses for teachers and teacher-librarians relating to Aboriginal education. He also worked with a Catholic priest, Barry Tunks, in a group called 'Black and White Unity', which met every month for a while. 'My involvement's just sort of been bits and pieces that crop up along the way,' he said in 1994. '. . . the awareness of it came from that bus ride . . . I haven't really been involved with things for quite a few years now. I've got involved in other things since then, because the Aboriginal people are involved and they're doing things the way they'd like to see things happen.'
Barry Corr taught for two years at Fairfield Boys' High School and for three at Ashcroft High in Green Valley. 'From there I got married, got divorced, went to Strathfield South, left there in '78, went to Bidwell in '79 which is in Mount Druitt.' It was there that he got 're-involved' in Aboriginal issues: 'Aboriginal education was the specific area I got involved in and I've been involved with that ever since.' In 1990, Barry became the Aboriginal education Consultant for the mid-west Region. His role was 'everything to do with Aboriginal education in the mid-west region. It's the education of Aboriginal children and it's also Aboriginal education in the sense of Aboriginal studies and Aboriginal perspectives. So I develop resources for schools, I go to an awful lot of conferences, I'm responsible for the development of teachers—all teachers, I'm responsible for the professional development of Aboriginal staff in the region, and for a committee which advises on Aboriginal education in the region.' Since the Freedom Ride, he reflected in 1994, 'I think this has been, you know, professionally it's been the happiest time of my life, you know, makes me feel I'm doing something. Doing what I want to do, where I belong.'
Colin Bradford was one of several Freedom Riders who became deeply involved in the Anti-Vietnam War Movement, becoming a member of the steering committee of the Vietnam Action Campaign and being one of the first to burn his draft card. When he graduated, he married at the age of 20 and settled down into suburban life with four children. He became a Maths teacher, and has remained one ever since in the Parramatta region of Sydney. The big change in Colin's life was his conversion to Christianity, influenced by his wife Cathy. Cathy died from a heart attack, and he later remarried. Colin told me that 'apart from being involved as a Teachers' Federation representative at my school for a few years, I haven't had any sort of political involvement at all since then . . . I still have a compassion for the Aboriginal people. In fact at the moment I'm organising with a Pastor Bill Bird, who's an Aboriginal pastor, to bring a group of Aboriginals to our church as part of the Reconciliation process.' He reflects that 'what led me into left-wing politics was compassion for people, particularly the underprivileged, the outcasts of society, and that still comes out in my life as a Christian. I go into Parramatta Prison to talk to people there, so I'm still involved at a different level with the outcasts of society . . . I'm still a political activist in a sense, but I don't see it through political parties now but through offering Jesus Christ to people as a way of changing within.'
Warwick Richards took almost the reverse trajectory. He had been involved in the Students' Christian Movement, but after the Freedom Ride his politics turned more to the Left: 'I got called up in 1967 and through that experience I became involved in the anti-war movement, I was a conscientious objector, went to court and involved in a whole lot of anti-war activity.' He joined the Association for International Co-operation and Disarmament, and became a member of its committee for a number of years. After he graduated with a BA DipEd in 1967, he was sent for his first teaching job to Dapto High School, becoming involved in the Teachers' Federation and the Labor Party. After a few years, he gave up teaching, returned to university and studied Government and Economics. He married and became the father of triplets, all girls, and he now manages a small consultancy business from Austinmer near Wollongong.
Machteld Hali became a printmaker. She practised woodblock printing on fabric in the 1960s, and subsequently followed a career as a studio potter, systems analyst, librarian, and teacher of Art, Drama and English. She eventually became a leading printmaker in the vibrant artistic community on the New South Wales south coast, known especially for her use of the collograph process. She has had solo and group exhibitions, locally and overseas, and conducts printmaking classes in her studio as well as popular weekend workshops. In her work, she has been reclaiming both the Indonesian and Dutch parts of her heritage, somewhat subdued in the assimilationist atmosphere in which she grew up.
Owen Westcott did not stay in teaching either. He finished his Bachelor of Arts degree and became an English teacher for a while, until he too developed new interests. He returned to university, gained a Science degree, and worked for ten years in scientific research. In the late 1980s, he 'got involved in the AIDS epidemic, by way of working in a needle exchange' and when interviewed in 1994 was running one of the largest of Sydney's needle exchanges. As he put it, 'the moral fervour is still there. See it's the Catholic effect, you can't get away from it.' The program he managed covered the central Sydney health area, including Redfern, and he was responsible for ensuring that AIDS prevention services like the needle exchange program were readily accessible to Aboriginal residents. 'So personally it means that it's sort of like coming full circle. Well, I'm having much more to do with Aboriginal people than I ever did in those days. My involvement then was you know really very fleeting.' Owen's work led him back into contact with Marie Peters, who had been arrested with him in Walgett at the cinema demonstration in August 1965. As he remembers it, 'one of the agencies that we were dealing with was called the Aboriginal Health Service which is in George St, Redfern'. His name was written on the health service's white board, and was seen by Marie, a teacher's aide working at Redfern Primary School across the road:
She recognised me as the person that she'd gone to the pictures with 25 years previously . . . This was the big lesson for me though. Because of that connection being made, she then told the people there what had happened in 1965 and the sort of cooperation we then got from this agency was totally different from anything we ever got from anyone else . . . one of the lessons I've learnt from working with Aboriginal people and Aboriginal organisations, is that it takes a lot of time to develop that sort of trust and acceptance and of course why wouldn't it be when you think about everything that's happened. This was like an incredible circuit breaker. It brought twenty years of history into our relationship and enabled us to develop something that's turned out since to be very constructive. And I never would have guessed that what I was doing in 1965 was going to help me in 1989.
Pat Healy was yet another Freedom Rider to become involved in health services. She completed her degree, worked in health education, married Brian Aarons and had two children. She also remained a political activist:
I joined the Communist Party not long after I returned from the Freedom Ride. And I think it certainly strengthened my resolve to become politically active, and I've been politically active ever since. Some time after that in the Aboriginal movement, but subsequently in a number of other movements, including the anti-war movement and support for the Gurindji land rights campaign—after the late '60s the women's movement particularly. Then when I had my kids becoming involved in local politics, school politics. You sort of do things closer to home when you've got kids.
She remained in the Communist Party until it ceased to exist in 1991. She has continued to work in the health area—particularly in occupational health and safety and on consumer health issues. In the late 1990s she started a PhD thesis in Sociology at ANU.
After graduation at the end of 1965, Sue Johnston went on to complete an MA in Aboriginal history, one of the first people to do so. Her thesis focused on government policy in New South Wales 1880–1909, and is still valuable today. In the early 1970s, she travelled extensively in Asia, Europe and Africa. On her return to Australia she became involved in Buddhism, 'Tibetans particularly'; she also returned to historical research, becoming the Research Librarian at the Royal Australian Historical Society in Sydney. She wrote a couple of history textbooks, which were in fact collections of historical documents for school and university use, including _We Came to Australia_ in 1980, on immigration, and _Aboriginal_ _Civilisation_ in 1981. From the mid-1980s, she was the Local Studies Librarian at Hornsby Public Library.
The Science students went their different ways too. Alan Outhred became very involved in left-wing politics after the Freedom Ride. He became a leading figure in the Sydney University Vietnam Action Committee, formed in January 1966. He also:
joined the Aboriginal land rights movements, particularly the uprising at Wave Hill with the Gurindjis. We had campaigns around the supermarkets for all the products of Vesteys' various multi-national companies— like going into the supermarket and taking all their things off the shelves and putting them into trolleys and wheeling them up to the checkout and leaving them there, saying, 'I don't actually want any of this thank you very much'. So that created a bit of disturbance, again drawing public attention to the Gurindjis—that what was once their land had been just taken over by this British baron.
He joined the Labor Party for a while and later the Communist Party, 'of which I was a member up until not long before its demise'. Alan completed a PhD in Cosmic Ray Physics at the University of Sydney in 1972. Somewhat disillusioned with the value and objectivity of physics, and feeling that he'd 'spent more than ten years at university and seen all my friends go off on their trips around the world and go and work in other countries and see a bit of the world', he left Australia to do something new. He was appointed a lecturer at the Haile Selassi I University in Addis Ababa in Ethiopia, arriving just as Emperor Haile Selassi I was being overthrown. The university was closed down fifteen months after he arrived, and he returned to Australia. By the 1990s, he was back in the Labor Party, in the Summer Hill branch, though 'I can't say I'm politically active now'. He drifted into the computing arena and at the time of inter- view in 1994 worked for the Southern Sydney Area Health Service as their computer manager.
Norm McKay finished his degree in Biology and he too went on to complete a PhD, in his case in Biology at the University of Sydney. His interests shifted strongly to environmental issues, and he took up a research position looking at heavy metal pollution in fish 'because I'd been appalled by what happened at Mitamata in Japan where people started to suffer mercury poisoning by eating fish polluted with mercury'. He was involved in a battle to save the rainforest at Terania Creek near Lismore, and has remained an interested bystander on Aboriginal issues:
I feel diffident about being involved because I think that what's happened over the last decade or so is that there's been a new generation of young Aboriginal leaders spawned and they're highly skilled orators—as we've seen over _Mabo_ for example. They've been able to articulate what Aboriginal needs are . . . we really have to let Aboriginal people get their own act together and facilitate it by simply voting for or lobbying with politicians who seem to be doing the right sort of thing.
Brian Aarons completed his Honours degree in Physics, taught Physics at university, then switched to Sociology, starting a PhD. He continued to be involved in social movements around Aboriginal rights (including the Save the Gurindji Campaign), environmental issues, and against the Vietnam War, and was active in the Communist Party. He married Pat Healy and travelled with her for eight months through South-East Asia and Europe. Returning to Australia in November 1975 in the midst of 'the Dismissal' events, he was asked to work for the Communist Party during the election campaign. Shortly after, he decided to abandon the PhD and work outside the university as a publicist, writer and organiser for social causes—among other things, writing and editing for _Australian Left Review_ and the Communist Party's weekly paper, the _Tribune_. In the early 1970s Brian became interested in environmental issues, working with Green Bans leader Jack Mundey and getting involved in the Movement Against Uranium Mining of the late 1970s and early 1980s. By then he was arguing that the Left needed new forms of organisation and to rethink its ideas. 'I gave a paper to the CPA Executive in 1981 advocating that the party change its name, which didn't get majority support, I have to say'— though later it did. In 1993 Brian and Pat moved to Canberra where Brian worked as the Communications Director for the Council for Aboriginal Reconciliation until its work ended in December 2000. He continues to work for its successor body, Reconciliation Australia.
Another Freedom Rider to change direction was Bob Gallagher, who graduated in Engineering in 1967. After working for a year in Australia as an engineer, he married Ashley Leyden, whom he'd met through the Labour Club, and in 1969 they went to England, where Bob worked as an engineer for a year or two then completed a Master's degree in Business Administration at City University in London. In 1972 they returned to Australia and joined Ashley's family's business, Peter Leyden Publishing, which they later owned after Peter Leyden died in 1978. Bob explained that it was an educational business specialising in primary school teaching resources. Some of the publications have been in Aboriginal Studies, such as a series of flash cards on 'Aboriginal Australia A to Z', which involved negotiating with Aboriginal advisers on the cultural perspective, who wanted particular things, such as 'I for invasion'.
Wendy Golding finished university, and then travelled overseas and lived in Canada. When she returned she 'got into the advertising industry more or less by accident'. In the early 1990s, she set up a committee on women in advertising, which, she said in 1994, 'will be the first time that women's views will have had a chance to express themselves officially in a formal way through the advertising industry, and looking at issues like portrayal of women in advertising and also the glass ceiling, which is fairly conspicuously present in the advertising industry'. She also set up an informal group of people who were interested in ethics in the advertising industry. She did not continue her involvement with Aboriginal rights, except that she became close friends with Fred Hollows and his family. 'There were always Aborigines at Fred's place. And so we had contact with Aborigines there, I mean just on an ordinary social level, not so much on a political level . . . Gary Foley used to go there regularly . . . Good people, very active.'
Darce Cassidy was transferred to Melbourne by the ABC in September 1966, and enrolled at Monash University in 1967. He became editor of _Print_ , the Monash Labour Club's duplicated newsletter (motto: 'Power grows out of the barrel of a gestetner'). He had some contact with Bruce McGuinness and others at the Aborigines Advancement League, but was most preoccupied with the anti-war movement. After a year in Canberra, he returned to Melbourne, where he became involved in a range of Left and liberal activities, many of them concerned with the media. He was also involved in the Worker–Student Alliance in Victoria in the 1970s and the Campaign Against Foreign Military Bases in the 1980s. After an incident in the 1970s in which he was described in the Senate by Vince Gair and Frank McManus as a 'terrorist' working for the ABC, Darce spent much of the 1970s in 'the ABC version of Siberia'. Following the changes to the ABC board in 1983 he was admitted back into ABC 'polite society', becoming state manager in South Australia between 1989 and 1997. When he turned 55 in 1997, he left the ABC and worked as a consultant on computer communications. Though Darce was one of SAFA's most active members during the two years after the Freedom Ride, he has not remained quite as involved in Aboriginal issues as some of the others. 'Apart from writing a few articles, giving a few papers, and a few guest lectures (I still do one on the Freedom Ride for Rob Foster at the Adelaide University History Department each year),' he wrote to me, 'I have had no further direct involvement in Aboriginal affairs, apart from the normal things of signing the Sorry Book and taking part in some of the Reconciliation walks.'
Judith Rich went on to a career in journalism and public relations. On her return from the Freedom Ride, the _Daily Telegraph_ hired her as a regular reporter. Later, she worked as a journalist in London for five years, before returning to Australia and working as a promotions manager for Harry M. Miller. A spiritual quest led her to the Himalayas and elsewhere in Asia before settling down in the United States for sixteen years. There, in addition to working in journalism and public relations, she became very involved in the Tibetan cause. On her return to Australia, where she worked in public relations for the Australian Tourist Commission, the Film Finance Corporation and Greenpeace, she assisted the Dalai Lama's visits to Australia in 1992 and 1996. She returned to her early interest in Aboriginal issues, this time trying to come to terms with Indigenous spirituality. She has, she says, 'been impressed by what Aboriginal people have had to teach us, and the way they have been opening up their spiritual knowledge to us'.
Some of the Freedom Riders did not retain any particular interest in Aboriginal issues. David Pepper finished university, went travelling, and didn't return to Australia for ten years, until he was in his thirties. He lived in Laos in South-East Asia during the Vietnam War, and when he came back found there had been quite a revolution in ideas and attitudes. He settled down, had a family, and for some years managed a hardware store in Annandale in Sydney. Derek Molloy finished his Arts degree and a Law degree, went overseas for a few years, including to Africa, and then returned to Australia, where he has practised as a lawyer ever since.
And what of some of the other people in this story?
Harry Hall remained president of the Aborigines Progressive Association from 1965 to 1973, and was the first Walgett member of the National Aboriginal Consultative Council. He continued to be a leading figure in Aboriginal activism in the town and region, highly respected by Aboriginal people and others. Lyall Munro Snr became a Regional Chair of ATSIC and continues to be a leading figure in Moree. Lyall Munro Jnr became director of the Metropolitan Lands Council in Sydney. Ted Fields remains in Walgett and has been closely involved in its local language-maintenance program. Chicka Dixon became a leader in Aboriginal politics in Sydney in the late 1960s and early 1970s, was in the forefront of the Tent Embassy of 1972, and became an active and effective chairman of the Aboriginal Arts Board.
Ann Holten, now known as Andrea Douglas, had three children, her first when she was 17, a year or so after the Freedom Ride. She was pleased, she told me in 2002, that when she first held him in her arms, they were in the ordinary part of the hospital, and not confined to the verandah any more. After her marriage she moved to Kempsey, and dedicated her life for some years to her children. The family lived on the mission and she sent her children to the Catholic school, where she worked as a cleaner to help pay the school fees. She taught her children not to feel intimidated, and helped them to build self-esteem. All three have become or are studying to be teachers. She now coordinates the Early Childhood Centre in Kempsey, and as I finish this book is in her final year of a Bachelor of Teaching (Early Childhood) at Macquarie University. She is, she says, 'completing a dream'.
Bill Lloyd became quite friendly with Charles, who came to Moree on DAA business several times. Lloyd told me in 1991: 'When I heard Charlie was very ill with kidney problems, I rang him, and later Charlie thanked me warmly and said he really appreciated it.' A year or two after the Freedom Ride, Bob Brown married, had children and some years later left Moree for Port Macquarie. He never received much credit for his role in the Freedom Ride, until he figured in Rachel Perkins and Ned Landers's film made in 1993, in a memorable scene at the end where he and Charles sit by the pool, and Bob says, 'They even let me in now'. Bill Ford continued as an academic at the University of New South Wales until his retirement. He has remained in contact with his American friend Bob Singleton, the Freedom Rider, ever since. Ted Noffs continued to run the Wayside Chapel, known especially for its support for drug rehabilitation, until he became ill in 1986 (he died in 1995). He remained a friend of Charles's all his life.
Peter Westerway became general secretary of the Labor Party in New South Wales from 1969 to 1974, and then a senior public servant in the Department of the Media. After his retirement, he worked as a consultant for ATSIC on its Aboriginal policy. He also began to investigate his family history, when he learned he had some Aboriginal ancestry of his own. His father, he said, 'had all the normal prejudices of Australian whites about Aborigines although his own mother was I think half Aboriginal. They concealed the fact; they never mentioned he was Aboriginal. It was only after his death that I've discovered that that was the case and that the contemporaries who lived with him in Glen Innes spoke of the family as being Aboriginal. I discovered it by doing a genealogy, tracing it back, finding people.'
Gerald Stone's performance as a journalist covering the Freedom Ride enhanced his reputation. He left the _Daily Mirror_ in 1967 for the ABC, where he became, along with Sam Lipski— _The Bulletin_ 's reporter on the Freedom Ride—a founding reporter on the landmark current affairs program _This Day Tonight_. Stone stayed in television journalism thereafter, and is best known for his years as executive producer of the Australian _Sixty Minutes_ ; in 2000 he became director of Australia's multicultural television service, SBS. David Ellyard, the active SAFA member who did not actually go on the Freedom Ride, went on to become a well-known science communicator. He has written ten books on weather, astronomy and current developments in science and technology, as well as an award-winning biography of Australian physicist Sir Mark Oliphant.
Michael Kirby went on to become a judge in the High Court, known and respected for his involvement in international human rights organisations and his liberal stance on many issues. Gordon Samuels continued his distinguished career, becoming a judge in the Supreme Court of New South Wales, Chancellor of the University of New South Wales, Chair of the New South Wales Law Reform Commission, and Governor of New South Wales. Kevin Martin went on to become a senior public servant, working with Charles at the Office of Aboriginal Affairs in the late 1960s.
As for me, what can I say? After the Freedom Ride, I wrote a PhD on the history of race relations in New South Wales in the mid-nineteenth century, comparing the opposition to Chinese immigration with the attitudes to Aboriginal people at the same time. I became deeply involved in the women's movement from 1970, and for many years my writing revolved around feminist theory and history. Like most of the others, I married, went overseas for a year, travelling through Asia and then living in London, and returned in mid-1974. After the birth of my son in November 1974, I established the Women's Studies program at the Australian National University in 1976, returning to Sydney in 1978 to take up a position at the then New South Wales Institute of Technology. For many years I taught History and Social Theory there, and developed a strong interest in television history, popular culture and the history of journalism. In the mid-1980s I became very interested in the public uses of history, and worked with several others to establish graduate programs in Applied History. In 1988 I became Dean of its Faculty of Humanities and Social Sciences; this was a testing three years, as the Institute acquired university status in 1990 and amalgamated with several other academic institutions to become a large, diverse, modern university, the University of Technology, Sydney. I took up the Chair of History at the Australian National University in 1995, which became the Manning Clark Chair of History a year later. I teach courses in Australian history, including a specialist course on Aboriginal history. Finally, in 2001, I cleared a space in my life to write this book.
And so our journey ends, at least for now.
Select bibliography
Books
Attwood, Bain and Markus, Andrew, _The Struggle for Aboriginal Rights:_ _A documentary history_ , Allen & Unwin, Sydney, 1999
Buckley, Ken, _Offensive and Obscene: A Civil Liberties Casebook_ , Ure Smith, Sydney, 1970
Goodall, Heather, _Invasion to Embassy: Land in Aboriginal Politics in New_ _South Wales, 1770–1992_ , Allen & Unwin, Sydney, 1996
Horner, Jack, _Bill Ferguson: Fighter for Aboriginal Freedom_ , Australia and New Zealand Book Company, Sydney, 1974
Jarratt, Phil, _Ted Noffs: Man of the Cross_ , Macmillan, Sydney, 1997
Lake, Marilyn, _Faith_ , Allen & Unwin, Sydney, 2002
Levy, Peter, _The Civil Rights Movement_ , Greenwood Press, Westport, 1998
Middleton, Hannah, _But Now We Want the Land Back_ , New Age Publishers, Sydney, 1977
Miller, J., _Koori: A Will to Win_ , Angus & Robertson, Sydney, 1985
Millis, Roger, _Waterloo Creek: The Australia Day Massacre of 1838, George_ _Gipps and the British Conquest of New South Wales_ , McPhee-Gribble, Ringwood, 1992
Mulvaney, John, _Encounters in Place: Outsiders and Aboriginal Australians_ _1606–1985_ , University of Queensland Press, St Lucia, 1989
O'Donnell, Penny and Simons, Lynette, _Australians Against Racism: Testimonies_ _from the Anti-Apartheid Movement in Australia_ , Pluto Press, Sydney, 1995
Parbury, N., _Survival: A History of Aboriginal Life in New South Wales_ , Ministry of Aboriginal Affairs (NSW), Sydney, 1986
Peck, Jim, _Freedom Ride_ , Grove Press, New York, 1962
Perkins, Charles, _A Bastard Like Me_ , Ure Smith, Sydney, 1975
Peters-Little, Frances, _The Community Game: Aboriginal Self-Definition at the_ _Local Level_ , AIATSIS Research Discussion Paper no. 10, AIATSIS, Canberra, 2000
Raymond, Robert, _Out of the Box: An Inside View of the Coming of Current_ _Affairs_ , Seaview Press, Adelaide, 1999
Read, Peter, _Charles Perkins: A Biography_ , Penguin, Ringwood, 2001 (first edition 1990)
Rowley, C.D., _Outcasts in White Australia_ , Penguin, Ringwood, 1972 (first edition 1970)
Rowley, C.D., _The Destruction of Aboriginal Society_ , Penguin, Ringwood, 1970
Scalmer, Sean, _Dissent Events: Protest, the Media and the Political Gimmick in_ _Australia_ , UNSW Press, Sydney, 2002
Weisbrot, Robert, _Freedom Bound: A History of America's Civil Rights_ _Movement_ , Norton, New York, 1990
Journal articles and chapters in books
Boughton, Bob, 'The Communist Party of Australia's Involvement in the Struggle for Aboriginal and Torres Strait Islander People's Rights, 1920–1970', in Ray Markey, ed., _Labour and Community: Historical_ _Essays_ , University of Wollongong Press, Wollongong, 2001, pp. 263–94
Clark, Jennifer, 'The Winds of Change', _International History Review_ , vol. XX, no. 1, March 1998, pp. 89–117
Curthoys, Ann, 'The personal is historical', in Ann Curthoys, and Ann McGrath, eds, _Writing Histories: Imagination and Narration_ , Monash Publications, Melbourne, 2000, pp. 75–81
Curthoys, Ann, 'Freedom Ride', in Sylvia Kleinert and Margo Neale, eds, _The Oxford Companion to Aboriginal Art and Culture_ , Oxford University Press, Melbourne, 2000, pp. 589–90
Curthoys, Ann, 'National narratives, war commemoration, and racial exclusion in a settler society: the Australian case', in T.G. Ashplant, Graham Dawson and Michael Roper, eds, _The Politics of War Memory_ _and Commemoration_ , Routledge, London and New York, 2000, pp. 128–44
Curthoys, Ann, 'Sex and Racism: Australia in the 1960s', in Jane Long, Jan Gothard and Helen Brasch, eds, _Forging Identities: Bodies, Gender_ _and Feminist History_ , University of Western Australia Press, Nedlands, 1997, pp. 11–28
Golding, Wendy, 'Freedom Riders in Australia', _The Bridge_ , May 1965, pp. 17–19
Hauser (Hansen), Beth, 'Our Freedom Ride', _Overland_ , no. 32, August 1965 Read, Peter, 'Darce Cassidy's Freedom Ride', _Australian Aboriginal Studies_ , vol. 1, no. 1, 1988, pp. 40–4
Reay, Marie, 'A Half Caste Aboriginal Community in North Western New South Wales', _Oceania_ , vol. 15, no. 3, June 1945
Reay, Marie and Sitlington, Grace, 'Class and Status in a Mixed-blood Community (Moree, NSW)', _Oceania_ , vol. 17, no. 3, March 1948, pp. 179–207
Rootes, C.A., 'The Development of Radical Student Movements and their Sequelae', _Australian Journal of Politics and History_ , vol. 34, 1968, pp. 367–78.
Scalmer, Sean, 'Translating Contention: Culture, History, and the Circulation of Collective Action', _Alternatives_ , no. 25, 2000, pp. 419–514
Spigelman, Jim, 'Reactions to the SAFA Tour', _Dissent_ , no. 14, Winter 1965, pp. 44–9
Spigelman, Jim, 'Student Action for Aborigines', _Vestes_ , vol. 8, no. 2, June 1965, pp. 116–18
Spigelman, Jim, _Honi Soit_ , 1 March 1965
Spigelman, Jim et al., 'The Student Bus', _Outlook_ , April 1965
Unpublished theses
Flack, Kylie, Creative Tension or Creating Trouble? The Student Action for Aborigines (SAFA) 'Freedom Ride', 1965, MA thesis, University of Sydney, 1993
Johnston, Susan, The New South Wales Government Policy Towards Aborigines 1880–1909, MA thesis, University of Sydney, 1970
Russell, Lani, Today the Students, Tomorrow the Workers! Radical Student Politics and the Australian Labour Movement 1960–1972, PhD thesis, University of Technology, Sydney, 1999
Silverman, Sondra, Political Movements: Three Case Studies in Protest, PhD thesis, Australian National University, 1966
Taffe, Sue, Attitudes to Aboriginal Australians: Signs of Change, 1957–1963, MA thesis, Monash University, 1995
Radio and television
Cassidy, Darce, 'Freedom Ride', ABC radio, first broadcast 20 February 1978, rebroadcast several times since
Perkins, Rachel and Landers, Ned, 'Freedom Ride', first screened on SBS, Tuesday, 13 July 1993
A note on sources
This note is a guide to the primary sources used in this book. The (extensive) endnotes are available electronically on the author's home page, at <http://arts.anu.edu.au/history/curthoys>
Interviews
**Interviewed by Inara Walden**
Hall Greenland, 18 October 1993
Pat Healy, 21 November 1993
Norm McKay, 21 November 1993
Brian Aarons, 22 November 1993
Warwick Richards, 24 November 1993
David Pepper, 5 January 1994
Wendy Watson-Ekstein (Golding), 8 January 1994
Bob Gallagher, 25 January 1994
Gerald Stone, 7 February 1994
Barry Corr, 14 March 1994
Owen Westcott, 14 April 1994
Alex Mills, 15 April 1994
Derek Molloy, 28 April 1994
Alan Outhred, 1 May 1994
Aidan Foy, 7 May 1994
Bob Morgan, 10 May 1994
Colin Bradford, 10 May 1994
Robyn Iredale, 12 July 1994
Jim Spigelman, 16 August 1994
Alan Duncan, 4 October 1994
John Powles, 21 October 1994
Charles Perkins, 4 November 1994
Interviewed by Lani Russell
Bill Ford, 23 December 1998
Interviewed by Ann Curthoys
Harry Hall, 3 April 1991
Gladys Lake, 3 April 1991
Phillip Hall, 3 April 1991
Bill Lloyd, 5 April 1991
Lyall Munro Snr, 6 April 1991
Ernie Crighton, 7 April 1991
Zona Moore, 7 April 1991
Beth Hansen, 8 April 1991
Vic Brill, 8 April 1991
Tess Brill, 9 April 1991
Bob Brown, 12 April 1991
Peter Westerway, 11 April 2001
Darce Cassidy, between 2 and 18 May 2001
Louise Higham, mid-October 2001
Marie Cohen (Marie Peters), early November 2001
Andrea Douglas (Ann Holten), 28 March 2002
Judith Rich, 28 March 2002
Gary Williams, 29 March 2002
Newspapers consulted
_Adelaide Advertiser_ , _Australian_ , _Canberra Times_ , _Courier-Mail_ , _Daily Mirror_ , _Daily Telegraph_ , _Macleay Argus_ (Kempsey), _Newcastle Morning Herald_ , _North_ _West Champion_ (Moree), _Northern Daily Leader_ (Tamworth), _Northern Star_ (Lismore), S _ydney Morning Herald_ , _Spectator_ (Walgett), _Sun-Herald_ , _Sun_ (Sydney), _Age_ (Melbourne) and the _West Australian._
Student newspapers and journals
_Honi Soit_ , _Left Forum_ , _Wednesday Commentary_ , _Semper Floreat_ , _Farrago_
Journals and magazines
_Churinga_ , _AAF Bulletin_ , _Comment_ , _Dawn_ , _New Dawn_ , _Dissent_ , _Identity_ , _Outlook_ , _Overland_ , _The Bulletin_ , _The Observer_
Government printed records
Commonwealth Parliamentary Debates, NSW Parliamentary Papers, NSW Parliamentary Debates
Manuscripts and archives
AWB records, New South Wales Record Office; Aboriginal-Australian Fellowship papers, Mitchell Library; Gordon Bryant Papers, NLA; National Archives of Australia; University of Sydney Archives; Communist Party records, Mitchell Library; Charles Rowley files, AIATSIS library; Union and ACTU records, Noel Butlin Archives, ANU
Private papers of Darce Cassidy, Jim Spigelman, Warwick Richards, Pat Healy, Robert Gallagher, Aidan Foy, Louise Higham, Wendy Golding (now Watson-Ekstein) and Ann Curthoys
Diaries used include my own, and diary excerpts from Louise Higham and Warwick Richards
|
{
"redpajama_set_name": "RedPajamaBook"
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| 7,145
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We were approached by the Roostertail to help them revitalize their online presence. The elegant and well established Roostertail was just not that when it came to their website outlook. It lacked engagement, pizzazz and overall it lacked the broad view needed to relay who the Roostertail was (especially when it came to its history).
The Roostertail is Detroit's premier waterfront entertainment facility. Since its inception in 1958 the Roostertail has become an icon in Detroit's social scene and has captured the interest of the "who's who" all around the city and has become "the" place to see and be seen.
Aside from hosting some of Detroit's most memorable parties, the Roostertail has also had its share of fame hosting a number of celebrity performers from the likes of Tony Bennett and Eric Clapton to the Rolling Stones and Aretha Franklin.
These days the Roostertail is devoted to catering private events, one third of all high school proms in the Metro Detroit Area are held at the Roostertail as well handling over 70 weddings a year. Whatever the occasion, it's sure to be a hit.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 5,331
|
Q: Unlist data frame column wihtout losing information from other column I have found a post, which is very similar to my problem.
I have a data.frame with a list of keywords, which are separated by semicolons in one coloumn and the year in another column. I would like to unlist the keywords without losing the information about the year.
I can separate the keywords with strsplit and unlist
keywords <- unlist(strsplit(df$keywords,";"))
l1 <- sapply(df$keywords, length)
Year <- rep(df$Year, l1)
length(Year)
length(keywords)
dfkeywords=data.frame(Year=Year, Keywords=keywords, stringsAsFactors = F)
but I fail to generate a vector of the year that is the same length as the keywords vector.
How do I do that in a smart way?
Best
Pete
A: Calculate the lengths before unlisting the split keywords. So split the keywords
keywords = strsplit(df$keywords,";")
find the lengths (number of key words) in each record
lens = lengths(keywords)
create the data.frame
data.frame(Year=rep(df$Year, lens), Keywords=unlist(keywords),
stringsAsFactors=FALSE)
A: Assuming you have something that looks like this:
df <- data.frame(keywords = c("some;text", "some;other;text", "even;more;text;here"),
Year = c(2025, 2026, 2099))
df
# keywords Year
# 1 some;text 2025
# 2 some;other;text 2026
# 3 even;more;text;here 2099
Then I would suggest that you just consider using cSplit from my "splitstackshape" package.
library(splitstackshape)
cSplit(df, "keywords", ";", "long")
# keywords Year
# 1: some 2025
# 2: text 2025
# 3: some 2026
# 4: other 2026
# 5: text 2026
# 6: even 2099
# 7: more 2099
# 8: text 2099
# 9: here 2099
Other approaches to consider would be:
"dplyr" + "tidyr"
library(dplyr)
library(tidyr)
df %>%
mutate(keywords = strsplit(as.character(keywords), ";")) %>%
unnest(keywords)
"data.table"
library(data.table)
as.data.table(df)[, list(keywords = unlist(strsplit(as.character(keywords), ";"))),
by = Year]
|
{
"redpajama_set_name": "RedPajamaStackExchange"
}
| 6,125
|
I hope I can write clearly what I want to say here; let me know if not.
We had another US government warning day before yesterday -July 11th - of imminent obl linked attacks, from cells the government says are operative within the US. This followed on from the day before's web site internet warning from allegedly one of obl's senior lieutenants. Now that is timing; 300 degrees from Sept 11.
Important to note however, the obl inspired statement prior to that came out on June 24 I believe, again from an obl lieutenant. More on this later, but this one did not fit obl's timing of the 11th and 26/27th of each month.
Once again, the US govt. warning comes right in the midst of when the President and Vice President are under intense pressure from corporate responsibility issues. (The previous US govt. warning came when both were under attack about how much they knew of intelligence warnings prior to the Sept 11, did it not ?) Anybody noticed a pattern here, or am I just being overly cynical. It's becoming a handy excuse for Mr President now n'est-ce pas? And straight after the warning given, another republican jumps up, as will be echoed and called for no doubt elsewhere from some US partners, just how bad the Iraqi dictator is (which is no doubt a reasonable statement) and that the US ought to invade immediately. Ahh the timing.
- refer to the QBE chart. You can see where a short sell was taken. On 18th June QBE makes an announcement that the recent drop in its share price is not warranted, and that the company will meet or better its earnings forecast for the year; up goes the price. 3 things I want to say about that.
1. The announcement purporting to be bullish, was in a downtrend. The day's top ends up being a lower top in the direction of the trend. I received a call from the broker at this point- happens only rarely - at the most serene time of 6am for me here, who relates to me the announcement, and I promptly panic out of my position, without first looking at my charts, which I now never to do. (I do sleep with the charts off these days.) The last time that happened, I swore to myself that I would immediately do the opposite of what the broker was suggesting, and when I hung up I knew immediately I should have shorted more - ah our psychology!
2. Here is a reason why shorting the market can be a little difficult; companies do all they can to support their share price (and also of course to improve it as you have seen via the accounting frauds now coming to light - all done to boost earnings and hence share prices, not to mention the CEO options packages.) We have the added problem in Australia of so many Australian mums and dads continually looking for cheap bargains, and buying stocks going lower, hence you may have noticed the trend on some stocks downwards can be a bit more erratic.
3. And here is the link to obl; things are not always what they seem. The announcement is released with the object of achieving a result. This will not be in line with the result you want or that is in your best interests. Ultimately the market players will make their collective judgement of the QBE announcement, which the chart will reveal; so trade the chart, not what the announcement says. And so it is with recent obl announcements, which are purporting to say that they have re grouped, that obl is alive and well. Can you see why I think this could be false. Like the QBE announcement, they are having to defend something, that if the trend was up, they would not have to do. I hope that makes sense to you. (The timing of these announcements are also important, that if one could study well enough would reveal a lot more about future events, as you see in some charts.) When things are going well, you don't have to come out with statements to say so; the obvious chart trend tells the story for you. But when your statements take on the defensive tone, there is an attachment there to something, that is being hidden.
If obl's group was really operative, they would have struck again heavily by now, and if they were really as undamaged as their releases say they are, they would not need to put out their releases. I could be wrong.
Anyway, that's what I try to remember about announcements, and relate it to what I see in the charts. I learnt this clearly with the Gann study work done by a fellow subscriber and trading of the US stock Priceline some years back, which some of you would have seen discussed in class.
There are some really odd things coming to light now about 9/11 that I am linking from lots of different sources; for example; remember the golfer Payne Stewart's plane that drifted aimlessly in the US skies on autopilot after the plane apparently lost pressurization or something like that and all on board suffocated or passed out, remember too that the US scrambled fighter jets to the side of this stricken plane, which I seem to remember was within 90 seconds of the plane not responding to air traffic control instructions. Yet on Sept 11 as I recall, no fighter jets could be found to do the same, yet they had much longer than 90 seconds to scramble.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 9,902
|
Be warned: it is not cheap. But, if you don't take advantage of your trip to Miami to treat yourself (perhaps more than once), when are you going to do it? This is one of the largest malls in Florida and is distributed over three floors, which are home to more than 200 shops. Some of them are true North American icons, like Macy's. Several parts of the mall are outside.
|
{
"redpajama_set_name": "RedPajamaC4"
}
| 4,767
|
{"url":"https:\/\/byjus.com\/maths\/derivative-function-calculus\/","text":"# Derivative of A Function- Calculus\n\nIf f is a real valued function and \u2018a\u2019 is any point in its domain for which f is defined then f(x) is said to be differentiable at the point x=a if the derivative f'(a) exists at every point in its domain. It is given by\n\n$f'(a) = \\displaystyle{\\lim_{h \\to 0} \\frac{f(a+h)-f(a)}{h}}$\n\nGiven that this limit exists and f\u2019(a) represents the derivative of f(x) at a. This is the first principle of derivative.\nThe domain of f\u2019(a) is defined by the existence of its limits. The derivative is also denoted as $\\frac{d}{dx}, f(x) \\;\\; or \\;\\; D(f(x))$.\nIf y = f(x) then derivative of f(x) is given as $\\frac{\\mathrm{d} }{\\mathrm{d} x}$ or y\u2019.\n\nThis is known as derivative of y with respect to x.\n\nAlso, the derivative of a function f in x at x = a is given as:\n\n$\\frac{\\mathrm{d} }{\\mathrm{d} x} f(x)|_{x = a}$ or $\\frac{\\mathrm{d} f}{\\mathrm{d} x} |_{x = a}$\n\nDerivative of a function f(x) signifies the rate of change of the function f(x) with respect to x at a point lying in its domain. For a function to be differentiable at any point x = a in its domain, it must be continuous at that particular point but vice-versa is necessarily not always true.\n\nThe process of determining the derivative of a function is known as differentiation. It is clearly visible that the basic concept of derivative of a function is closely intertwined with limits. Therefore, it can be expected that the rules of derivatives are similar to that of limits. The following rules are a part of algebra of derivatives:\n\nConsider f and g to be two real valued functions such that the differentiation of these functions is defined in a common domain. Then,\n\n\u2022 Sum of derivatives of the functions f and g is equal to the derivative of their sum, i.e.,\n\n$\\frac{\\mathrm{d} }{\\mathrm{d} x} \\left [ f(x) + g(x) \\right ] = \\frac{\\mathrm{d} }{\\mathrm{d} x} f(x) + \\frac{\\mathrm{d} }{\\mathrm{d} x} g(x)$\n\nLet u = f(x) and v = g(x), then (u + v)\u2019 = u\u2019 + v\u2019\n\n\u2022 Difference of derivatives of the functions f and g is equal to the derivative of difference of these functions, i.e.,\n\n$\\frac{\\mathrm{d} }{\\mathrm{d} x} \\left [ f(x) \u2013 g(x) \\right ] = \\frac{\\mathrm{d} }{\\mathrm{d} x} f(x) \u2013 \\frac{\\mathrm{d} }{\\mathrm{d} x} g(x)$\n\nLet u = f(x) and v = g(x), then (u \u2013 v)\u2019 = u\u2019 \u2013 v\u2019\n\n\u2022 Derivative of the product of two functions f and g is given by the product rule as follows, i.e.,\n\n$\\frac{\\mathrm{d} }{\\mathrm{d} x} \\left [ f(x) . g(x) \\right ] = g(x) \\frac{\\mathrm{d} }{\\mathrm{d} x} f(x) + f(x)\\frac{\\mathrm{d} }{\\mathrm{d} x} g(x)$\n\nLet u = f(x) and v = g(x), then the product rule can be restated as\n\n(uv)\u2019 = u\u2019v + uv\u2019\n\nThis is also known as Leibnitz rule for differentiating the products of functions\n\n\u2022 The derivative of quotient of two functions f and g is given by the quotient rule (provided that the denominator is non- zero), i.e.,\n\n$\\LARGE \\frac{\\mathrm{d} }{\\mathrm{d} x} \\frac{f(x)}{g(x)} = \\frac{g(x). \\frac{\\mathrm{d} f(x)}{\\mathrm{d} x} \u2013 f(x). \\frac{\\mathrm{d} }{\\mathrm{d} x}g(x)}{(g(x))^{2}}$\n\nLet u = f(x) and v = g(x), then the quotient rule can be restated as\n\n$\\large \\left ( \\frac{u}{v} \\right )\u2019 = \\frac{u\u2019v \u2013 vu\u2019}{v^{2}}$\n\nChain Rule:\n\nWhenever a quantity \u2018y\u2019 varies with another quantity \u2018x\u2019 such that y = f(x), then f\u2019(x) indicates the rate of change of y with respect to x (at x = x0). Also, if two variables \u2018x\u2019 and \u2018y\u2019 are varying with respect to a third variable say \u2018t\u2019 then according to the chain rule, we have\n\n$\\large \\left ( \\frac{\\mathrm{d} y}{\\mathrm{d} x} \\right ) = \\frac{\\frac{\\mathrm{d} y}{\\mathrm{d} t}}{\\frac{\\mathrm{d} t}{\\mathrm{d} x}},\\;\\; where \\;\\; \\frac{\\mathrm{d} t}{\\mathrm{d} x}\\neq 0$\n\nLet us look into some examples to have a better insight.\n\n Let\u2019s Work Out- Example: Determine the rate of change of the volume of a sphere with respect to its radius \u2018r\u2019 when r = 3 cm. Solution: We know the Volume of a Sphere is given as $\\frac{4}{3} \\pi r^{3}$. Rate of change of Volume w.r.t. Radius is given as $\\frac{\\mathrm{d} V}{\\mathrm{d} r} = \\frac{\\mathrm{d} }{\\mathrm{d} r}\\left ( \\frac{4}{3} \\pi r^{3} \\right ) = \\frac{4}{3} \\times \\pi (3r^{2})$ $\\frac{\\mathrm{d} V}{\\mathrm{d} r} = 4 \\pi r^{2}$ $\\frac{\\mathrm{d} V}{\\mathrm{d} r} \\mid _{(at\\;\\; r=3)}= 4 \\pi (3)^{2} = 36 \\pi$<","date":"2018-11-22 11:23:50","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\": 0.8693628311157227, \"perplexity\": 211.10450804633265}, \"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-2018-47\/segments\/1542039746205.96\/warc\/CC-MAIN-20181122101520-20181122123520-00375.warc.gz\"}"}
| null | null |
Woman Shot, Killed on Newark Street Months After Ex Tried to Take Kids: Sources
By Jen Maxfield and Brian Thompson • Published at 12:02 pm on February 6, 2018
Tiffany Wilson, 28, was shot dead Tuesday allegedly by her ex-boyfriend, who cops say snatched the couple's kids in December
The suspect, Kareem Dawson, went to confront the mother of his kids in the morning, and she tried to flee when she saw him, sources said
Police chased Dawson all the way from Newark to Summit, where Dawson shot himself in the head; he survived and is at a hospital
A New Jersey man who was ordered to stay away from his ex-girlfriend after he snatched their daughter and tried to abduct their son from day care last December has killed the woman on a Newark street, law enforcement sources say.
Kareem Dawson went to confront the mother of his children Tuesday morning, and she tried to flee when she saw him, sources said. Tiffany Wilson, 28, had just moved to the block on Scheerer Avenue three weeks ago from a domestic violence shelter.
Dawson chased after Wilson and shot and killed her on the street. She was taken to University Hospital where she was pronounced dead, according to police.
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Responding police officers identified the car in which Dawson fled, and a Newark officer spotted the car and tried to pull him over, according to sources.
He took off, and police chased him all the way to Summit, where Dawson shot himself in the head. He is still alive and being treated at an area hospital, authorities say.
He is facing murder charges.
Last December, the 31-year-old Dawson allegedly took his 4-year-old daughter from a location in Inglewood, then drove to his son's day care center in Maplewood, where he attacked Wilson while she was dropping off their son, according to police. Workers there had refused to unlock the door for him because they knew Wilson had a restraining order against him.
He followed her to her car, police said, and pulled her out of the vehicle and slammed her to the ground. Witnesses at the scene said the man had a gun at the time. Afterward, he left with his daughter as Wilson ran back into the day care to get help.
Police tracked him and his daughter down about 18 miles away, in Woodbridge Township, where he surrendered to police. Police found a gun in the man's trunk, and the girl was unharmed when officers got on scene.
The girl was returned to her mother at the time, authorities said.
People who knew Wilson described her as a businesswoman and devoted mother. Hany Yacoub, director of the day care center that her children attended, said, "She cared for her kids a lot and she wanted the best for them."
But Wilson was also petrified of Dawson and told people she feared he was stalking her.
"She said she always takes different routes coming here because she thinks he's following her, and apparently that day he was able to follow her," said Yacoub.
|
{
"redpajama_set_name": "RedPajamaCommonCrawl"
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| 6,749
|
import sys
from setuptools import setup, Command
from init import LIB_PATH, VERSION
# Currently Python 2.7 is supported
PYTHON_VERSION_MAJOR = 2
PYTHON_VERSION_MINOR = 7
if sys.version_info.major != PYTHON_VERSION_MAJOR or sys.version_info.minor != PYTHON_VERSION_MINOR:
print "[ERROR] Only Python %s.%s is supported" % (PYTHON_VERSION_MAJOR, PYTHON_VERSION_MINOR)
sys.exit(1)
# Run only on OS X and Linux
if not (sys.platform.startswith("darwin") or sys.platform.startswith("linux")):
print "[ERROR] Only OS X and Linux are supported"
sys.exit(1)
# Add dependencies to the path
sys.path.insert(1, LIB_PATH)
class IntegrationTestCommand(Command):
description = "Run integration tests"
user_options = []
def initialize_options(self):
pass
def finalize_options(self):
pass
def run(self):
import it
sys.exit(it.main())
setup(
name="queue",
version=VERSION,
description="Improved job scheduler for Apache Spark",
long_description="Improved job scheduler for Apache Spark",
author="Ivan Sadikov",
author_email="ivan.sadikov@github.com",
url="https://github.com/sadikovi/queue",
platforms=["OS X", "Linux"],
license="Apache License 2.0",
test_suite="test",
cmdclass={
"run_it": IntegrationTestCommand
}
)
|
{
"redpajama_set_name": "RedPajamaGithub"
}
| 3,148
|
Jordan Cook, Service Supervisor
Employee Spotlight,
It's no secret that Jordan is the grandson of Jim Cook, CSI founder, and the son of CEO Mark Cook. So, Jordan has really been a part of CSI his entire life, but he didn't officially start his professional career on the team until he turned 16. Similar to most teens freshly licensed to drive, Jordan was looking for more independence and needed a part-time job to provide him with the income for his new-found freedom.
Jordan started his journey at CSI in 2008 sweeping the shop and cleaning trucks part-time — which he did for the next two years. He then transitioned full-time in 2010 as a craftsman where he was responsible for welding and pipe installation. Starting in a role with limited scope, Jordan quickly took on additional responsibilities working in maintenance and then the pump shop. Here he was directly responsible for doing repairs and ensuring their on-time completion.
It was while working on field repairs that Jordan grew to understand how truly special CSI was and how much of an impact the work he was doing truly helped others in the processing industry. It was also during this season that he was forced to learn additional skills and knowledge at a rapid pace. He even commented that there were times he felt like he was thrown into a fire pit, but he welcomed the challenges. He then progressed to quoting, taking on more fiscal responsibility by estimating costs to complete jobs.
While Jordan was working as the Pump and Valve Repair Technician, CSI leadership realized that a change needed to be made to bring a more focused approach to providing additional service and repair options to customers. Michael David, the current manager for service, repair, and pumps, would focus solely on pumps, leaving a need for someone to supervise service and repair. Based on Jordan's years of experience in the service area, he was selected as the new Service Supervisor and stepped into his new role in January of 2019.
His vision is that every end-user facility will utilize a CSI Service plan on an on-going basis.
"It's not uncommon for a customer to neglect servicing their equipment as often or as properly as they should," Jordan said.
This opens them up to issues with their systems. Service now steps in to fill this gap be providing system audits and developing a custom service and repair plan to ensure customer's products perform at an optimum level more consistently.
This symbiotic relationship takes time to develop.
As Jordan mentioned, "we have to build these relationships with people over time to establish ourselves as the service provider for their equipment and work with them to schedule visits throughout the year to do service on their equipment."
Once a plan is in place, a plant can expect reduced downtime, lower maintenance costs, and increase productivity and profits.
Another area of focus for Jordan's team will be providing startup support to customers. Going beyond just servicing CSI products, the team will be able to provide knowledge and support for the entire processing facility.
"We can service their equipment in addition to ours," said Jordan. "We are able to be there from the start to walk them through the entire setup, allowing us to diagnose and troubleshoot problems and answer questions onsite as they come up."
In this new role Jordan is also responsible for working with sales to grow the business from a revenue perspective while maintaining the operational side — taking on 100% responsibility for the department reaching its revenue goals. He's excited for this change; which will continue to bring additional responsibility and challenges for him to continue growing himself and the company.
Central States Industrial Equipment (CSI) is a leader in distribution of hygienic pipe, valves, fittings, pumps, heat exchangers, and MRO supplies for hygienic industrial processors, with four distribution facilities across the U.S. CSI also provides detail design and execution for hygienic process systems in the food, dairy, beverage, pharmaceutical, biotechnology, and personal care industries. Specializing in process piping, system start-ups, and cleaning systems, CSI leverages technology, intellectual property, and industry expertise to deliver solutions to processing problems. More information can be found at www.csidesigns.com.
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Rachael Sawyer is one of four Customer Service Reps that work remotely from a home office across the country.
Repairs: In-House or Outsourced?
Outsourcing can provide cheaper service and repairs with more expertise compared to in-house maintenance.
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{
"redpajama_set_name": "RedPajamaCommonCrawl"
}
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Q: VS Extension which declares a new project template and locate the generated project in a specific location of an imported tree I would like to create a Visual Studio extension.
I installed Visual Studio 2012 and Visual Studio SDK 2012.
Now, I want my extension to create a new project template, and then to enable the user to create a new project of the new generated type. i.e: I would like that once the user will open VS and will click on "add new project", he will have a new project type in the list of the regular templates. The template will be a standard C project, with some additinal dependencies, some changes in the.vcxproj file, in the compiling configurations and more.
In additinal, I want that on the project creation, my extension will import an existiong solution from my computer to be the current VS solution, and that the new project will be added to a specific folder in that solution.
Is there any way to write code which is doing the described above, on the creation of a new project of the new template? Do I have any event/other handler on the template code, or in the package code, which I can use?
I googled tons, but I really don't know what is the best way I can do it...
Thanks a lot!
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{
"redpajama_set_name": "RedPajamaStackExchange"
}
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\section{Introduction}
A classical result due to M\"untz says that, if $0=\lambda_0<\lambda_1<\dots<\lambda_n<\dots$ is an increasing sequence of nonnegative \tcr{real} numbers, then the linear span of $x^{\lambda_n}$ is dense in $C([0,1])$ if and only if $\sum_{n=1}^\infty \frac{1}{\lambda_n}=\infty$. When $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the \tcr{closed linear span of} the monomials $x^{\lambda_n}$ in different Banach spaces that contain them is usually not equal to the whole space; it is therefore interesting to study the new spaces thus obtained. \tcr{In particular, if $1\leq p<+\infty$ and $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, then $M_\Lambda^p\varsubsetneq L^p([0,1])$, where $M_\Lambda^p$ is the closed linear span of the monomial $x^{\lambda_n}$, $n\geq 0$, in $L^p([0,1])$.} The literature concerning this class of spaces of functions defined on
$[0,1]$, called \emph{M\"untz spaces}, is not very extensive. We may
refer principally to the two monographs \cite{be95} and \cite{gl05} and the references within,
as well as to the recent papers \cite{aa09,sp08}.
The starting point of our research is formed by some recent results of
Ihab Al Alam, either published in \cite{aa09} or contained in his
thesis \cite{aathesis}. They deal with properties of weighted composition operators on M\"untz spaces, and it is noted therein that the properties of these operators are connected to embedding of the spaces into Lebesgue spaces.
In the present paper
we have pursued this line of approach systematically. More precisely, we discuss boundedness and compactness properties of the embedding ${M_\Lambda^1}\subset L^1(\mu)$, where $\mu$ is a finite \tcr{positive} Borel measure on the interval $[0,1]$. In general the embedding properties are critically dependent on the nature of the sequence $\Lambda=(\lambda_n)$.
The plan of the paper is the following. Section~2 contains preliminaries as well as general results concerning boundedness of the embedding, while Section~3 discusses compactness of the embedding. In Section~4 we introduce an important class of measures that we call sublinear, and which bear a certain resemblance to Carleson measures defined in the unit disc or half-plane. These allow in Section~5 a rather complete solution of the embedding problem for the class of quasilacunary sequences $\Lambda$. Section~6 discusses through some examples the problems that may appear in the general case, while Section~7 investigates the important sequence $\lambda_n=n^2$. Finally, in Section~8 we show how one can recapture in this context some of Al Alam's results on weighted composition operators.
\section{Embedding measures}
The basic reference for M\"untz spaces is \cite{gl05}; occasionally we will use also some results from \cite{be95}.
We denote by $m$ the Lebesgue measure on $[0,1]$ and by $\Lambda=
(\lambda_n)_{n\ge 1}$ an increasing sequence of positive real numbers
with $\sum_{n\geq 1} \frac{1}{\lambda_n}<\infty$.
The norm in $L^p(m)$ will be denoted simply by $\|\cdot\|_p$ (for $1\le p\le\infty$).
The closed linear span in $L^1(m)$ of the functions $x^{\lambda_n}$ is the M\"untz space ${M_\Lambda^1}$. The functions in ${M_\Lambda^1}$ are continuous in $[0,1)$ and real analytic in~$(0,1)$.
Note that sometimes M\"untz spaces are defined by including the value $\lambda_0=0$ in the family of monomials; but the statements are simpler if we start with $\lambda_1>0$. This is a matter of convenience only: all boundedness and compactness results below remain true if we add the one-dimensional space formed by the constants.
\begin{Def}
\tcr{A positive measure $\mu$ on $[0,1]$ is called \emph{$\Lambda$-embedding} if there is a constant $C>0$ such that \begin{equation}\label{eq:def-plongement}
\|p\|_{L^1(\mu)}\le C\|p\|_1,
\end{equation}
for all polynomials $p$ in $M^1_\Lambda$.}
\end{Def}
It is immediate (by applying the condition to the functions $x^{\lambda_n}$) that if $\mu$ is $\Lambda$-embedding, then $\mu(\{1\})=0$, so we will suppose this condition satisfied for all measures appearing in this paper. If $0<\epsilon<1$, then the interval $[1-\epsilon, 1]$ will be denoted by $J_\epsilon$.
The next lemma is a useful technical tool.
\begin{lemma}\label{le:rho}
Suppose $\rho:{\mathbb R}_+\to{\mathbb R}_+$ is an increasing, $C^1$ function with
$\rho(0)=0$ such that $\mu(J_\epsilon)\le\rho(\epsilon)$ for all $\epsilon\in (0,1]$. Then for any continuous, positive, increasing function $g$ we have
\[
\int_{[0,1]}g\, d\mu \le \int_0^1 g(x)\rho'(1-x)\, dx.
\]
\end{lemma}
\begin{proof}
If $F(x)=\mu([0,x))$, then integration by parts yields
\[
\int_{[0,1]}g\, d\mu =\int_0^1 g(x)\, dF(x)= g(1)F(1)-\int_0^1 F(x)\, dg(x)
\]
(remember $F(0)=0$). Since $\mu(J_\epsilon)\le\rho(\epsilon)$ for all $\epsilon\in
(0,1]$ (and $\mu(\{1\})=0$), it follows that
$F(1)-F(x)\le \rho(1-x)$, or $-F(x)\le \rho(1-x)-F(1)$. Plugging this into the previous equation, integrating again by parts, and using $\rho(0)=0$, we obtain
\[
\begin{split}
\int_{[0,1]}g\, d\mu &\le g(1)F(1)-F(1)(g(1)-g(0))+ \int_0^1 \rho(1-x) \, dg(x)\\
&=F(1)g(0) +\int_0^1 \rho(1-x)\, dg(x)\\
&= F(1)g(0) -\rho(1)g(0)-\int_0^1 g(x)\, d(\rho(1-x))\\
&=g(0) (F(1)-\rho(1)) + \int_0^1 g(x)\rho'(1-x)\, dx.
\end{split}
\]
The proof is finished by noting that $F(1)=\mu([0,1))\le \rho(1)$.
\end{proof}
We intend to investigate necessary and sufficient conditions for a measure $\mu$ to be $\Lambda$-embedding. These conditions depend in general on the sequence $\Lambda$; also, in most cases there is a gap between necessity and sufficiency. The starting point for our approach is the following result from \cite[p.185, E.8.a]{be95}.
\begin{lemma}\label{le:BE}
For all $\epsilon\in (0,1]$ there exists a constant $c_\epsilon>0$ such that for any function $f\in {M_\Lambda^1}$ we have
\begin{equation}\label{eq:BE}
\sup_{0\le t\le 1-\epsilon}|f(t)|\le c_\epsilon \int_{1-\epsilon}^1
|f(x)|dx.\end{equation}
In particular, the supremum in the left-hand side is majorized by
$c_\epsilon \|f\|_1$.
\end{lemma}
\tcr{Formally the inequality \eqref{eq:BE} is stated in \cite{be95} only for polynomials in $M_\Lambda^1$, but a standard argument shows that it can be extended to any function $f\in {M_\Lambda^1}$.}
Lemma~\ref{le:BE} has some immediate consequences for the embedding problem.
\begin{corollary}\label{co:compactsupport}
(i) If, for some $\epsilon>0$, $\mathop{\rm supp} \mu\subset [0,1-\epsilon)$, then $\mu$ is $\Lambda$-embedding for any $\Lambda$, and
\[
\|f\|_{L^1(\mu)}\le c_\epsilon \|\mu\| \|f\|_1
\]
for all $f\in{M_\Lambda^1}$.
(ii) More generally, if for some $\epsilon>0$ the restriction of $\mu$ to the interval $[1-\epsilon, 1]$ is absolutely continuous with respect to \tcr{$m_{|[1-\epsilon,1]}$}, with essentially bounded density, then $\mu$ is $\Lambda$-embedding for any $\Lambda$.
\end{corollary}
\begin{Rem}\label{Rem:rem-plongement}
\tcr{If $\mu$ is $\Lambda$-embedding, then $M_\Lambda^1\subset L^1(\mu)$ and $\|f\|_{L^1(\mu)}\leq c \|f\|_1$ for all $f\in M_\Lambda^1$. Indeed if $f\in M_\Lambda^1$, then there exists a sequence $(p_n)_n$ of polynomials in $M_\Lambda^1$ such that $\|f-p_n\|_1\to 0$, $n\to +\infty$. By~\eqref{eq:def-plongement} $(p_n)_n$ is a Cauchy sequence in $L^1(\mu)$, whence it converges to a function $g$ in $L^1(\mu)$. In particular, there exists a subsequence $(p_{n_k})_k$ which converges almost everywhere (with respect to $\mu$) to $g$. But according to Lemma~\ref{le:BE}, $(p_n)_n$ tends to $f$ uniformly on every compact of $[0,1)$, so $g(t)=f(t)$ for almost every $t\in [0,1)$ with respect to $\mu$; since $\mu(\{1\})=0$, we have $g=f$ in $L^1(\mu)$. Therefore $M_\Lambda^1\subset L^1(\mu)$. Moreover, since $(p_n)_n$ tends to $f$ in $L^1(\mu)$ and also in $L^1(m)$,~\eqref{eq:def-plongement} implies that $\|f\|_{L^1(\mu)}\leq c \|f\|_1$, which proves the claim.}
\tcr{Using standard arguments based on the closed graph theorem, it is easy to see that it is sufficient to have the set inclusion $M_\Lambda^1\subset L^1(\mu)$ in order to obtain that $\mu$ is $\Lambda$-embedding.} For a $\Lambda$-embedding $\mu$ we denote by $\iota_\mu$ the embedding operator $\iota_\mu: M_\Lambda^1\subset L^1(\mu)$.
\end{Rem}
To obtain a more general \tcr{sufficient condition}, note
that the smallest constant that can
appear in the right-hand side of (\ref{eq:BE}) is a positive, decreasing function of $\epsilon$, and thus admits
decreasing and continuous majorants. In the sequel we fix such a
majorant, denoted by $c(\epsilon)$.
Then $\kappa(t):=c(1-t)$ is positive, increasing \tcr{and continuous} on $[0,1)$. Using~\eqref{eq:BE} for any monomial $x^{\lambda_i}$, we see that $\kappa(t)\to\infty$ for $t\to 1$, and the order of increase is at least~$(1-t)^{-1}$.
\begin{theorem}\label{th:generalsufficient}
If $\kappa\in L^1(\mu)$, then $\mu$ is $\Lambda$-embedding and $\|\iota_\mu\|\le\|\kappa\|_{L^1(\mu)}$.
\end{theorem}
\begin{proof} For $k,m\ge 1$,
define the set $E_{m,k}=\{x\in [0,1): \frac{k-1}{2^m}< \kappa(x)\le\frac{k}{2^m}\} $. Since $\kappa$ is increasing and continuous, we have $E_{m,k}=(a^{(m)}_{k-1},a^{(m)}_k]$ for some $a^{(m)}_k\in [0,1)$. If the functions $\kappa_m$ are defined by
\[
\kappa_m(x)=\sum_{k=0}^\infty \kappa(a^{(m)}_k) \chi_{E_{m,k}}(x),
\]
then $\kappa_m$ is a decreasing sequence of functions tending everywhere to $\kappa$. By the monotone convergence theorem, it follows from the hypothesis that
\begin{equation}\label{eq:gensuf1}
\sum_{k=1}^\infty \mu ((a^{(m)}_{k-1},a^{(m)}_k]) \kappa(a^{(m)}_k)\to \|\kappa\|_{L^1(\mu)}<\infty.
\end{equation}
On the other hand, from~\eqref{eq:BE} it follows that, \tcr{for any $f\in M_\Lambda^1$},
\[
\sup_{a^{(m)}_{k-1}<x\le a^{(m)}_k} |f(x)|\le \kappa(a^{(m)}_k)\|f\|_1,
\]
whence (taking into account that $f(0)=0$ and $\mu(\{1\})=0$)
\[
\begin{split}
\int_{[0,1]}|f(x)|\, d\mu(x)& =
\sum_{k=1}^\infty \int_{(a^{(m)}_{k-1},a^{(m)}_k]}| f(x)|\, d\mu(x)\\
&\le \sum_{k=1}^\infty \left(\sup_{a^{(m)}_{k-1}<t\le a^{(m)}_k} |f(x)|\right) \mu((a^{(m)}_{k-1},a^{(m)}_k])\\
&\le \sum_{k=1}^\infty \kappa(a^{(m)}_k)\|f\|_1 \mu((a^{(m)}_{k-1},a^{(m)}_k]).
\end{split}
\]
Letting now $m\to\infty$ and using~\eqref{eq:gensuf1}, it follows that $\mu$ is $\Lambda$-embedding and $\|\iota_\mu\|\le\|\kappa\|_{L^1(\mu)}$.
\end{proof}
Since $\kappa$ is \tcr{continuous,} increasing and $\kappa(t)\to +\infty$ for $t\to 1$, the condition $\kappa\in L^1(\mu)$ is related to the asymptotics of $\mu$ in~1. The next corollary gives a sufficient condition on $\mu$ expressed in terms of $\mu(J_\epsilon)$.
\begin{corollary}\label{co:mu(Jeps)}
Suppose $\rho:{\mathbb R}_+\to{\mathbb R}_+$ is an increasing, $C^1$ function with $\rho(0)=0$ such that $\int_0^1 \kappa(x)\rho'(1-x)\, dx<\infty$. If
$\mu(J_\epsilon)\le\rho(\epsilon)$ for all $\epsilon\in (0,1]$, then $\mu$ is $\Lambda$-embedding.
\end{corollary}
\begin{proof}
The proof follows by applying Lemma~\ref{le:rho} to the case $g=\kappa$.
\end{proof}
In general $\kappa$ has not an explicit formula in terms of the sequence $\Lambda$. We would like to obtain more treatable formulas; this will be done below for some special classes of $\Lambda$.
\section{Compactness and essential norm}
A related problem is that of the compactness of the embedding $\iota_\mu$. Here, the starting point is a result stated as Lemma 4.2.5 in \cite{aathesis}; we will sketch a proof for completeness.
\begin{lemma}\label{le:ihab}
If $(f_m)_m\subset{M_\Lambda^1}$, $\|f_m\|_1\le1$ for all $m$, then there exists a subsequence $(f_{m_k})_k$ which converges uniformly on every compact subset of $[0,1)$.
\end{lemma}
\begin{proof}
For any $\epsilon\in (0,1]$ the restrictions of $f_m$ to $[0,1-\epsilon]$ are
uniformly bounded by Lemma~\ref{le:BE}. To prove the result, it is
enough to consider only functions $f_m$ in the linear span of
$x^{\lambda_n}$ with $\lambda_n\ge 1$; it follows then from a
Bernstein-type inequality proven in \cite[p.178, E.3.d]{be95} that the
restrictions of $f'_m$ to $[0,1-2\epsilon]$ are uniformly bounded. By the
Arzela--Ascoli theorem, \tcr{the sequence ${f_n}_{|[0,1-2\epsilon]}$ contains a subsequence which is uniformly convergent on $[0,1-2\epsilon]$}. Applying this to $\epsilon=1/N$ for all positive integer $N$ and using a diagonal procedure, one obtains a subsequence $f_{m_j}$ that converges uniformly on all compact of \tcr{$[0,1)$} to a function $f$. It is then easy to show that $f\in{M_\Lambda^1}$.
\end{proof}
We may now improve Corollary~\ref{co:compactsupport}.
\begin{proposition}\label{pr:bicompact}
If $\mathop{\rm supp} \mu\subset [0,1-\epsilon]$, then $\iota_\mu$ is compact.
\end{proposition}
\begin{proof}
The proof is an immediate consequence of Lemma~\ref{le:ihab}: if we take a sequence $(f_n)_n$ in the unit ball of ${M_\Lambda^1}$, then the subsequence obtained therein converges uniformly in $[0,1-\epsilon]$, and therefore also in $L^1(\mu)$.
\end{proof}
The following notation will be useful: if $\mu$ is a positive measure
on $[0,1]$, we will denote $\mu_m$ the measure equal to
$\mu$ on $[0, 1-\frac{1}{m})$ and $0$ elsewhere, and $\mu'_m=\mu-\mu_m$ (so $\mu'_m$ is the measure that coincides with $\mu$ on
$J_{\frac{1}{m}}$ and is $0$ elsewhere).
Next comes a general abstract compactness result, related to Corollary~\ref{co:mu(Jeps)}.
\begin{proposition}\label{pr:abstractcompactness}
Let ${M_\Lambda^1}$ be a M\"untz space, and suppose that $\rho:{\mathbb R}_+\to {\mathbb R}_+$ is an increasing continuous function, with $\rho(0)=0$, such that any measure $\mu$ with $\mu(J_\epsilon)\le C\rho(\epsilon)$ is $\Lambda$-embedding, with embedding constant at most $C$. Then, for any measure $\mu$ that satisfies $\lim_{\epsilon\to0}\frac{\mu(J_\epsilon)}{\rho(\epsilon)}= 0$ the embedding $\iota_\mu$ is compact.
\end{proposition}
\begin{proof}
Suppose that $\iota_{\mu_m}$ are the embeddings ${M_\Lambda^1}\subset L^1(\mu_m)$. We may regard $L^1(\mu_m)$ as a subspace of $L^1(\mu)$, and the operators $\iota_{\mu_m}$ as taking values in $L^1(\mu)$.
The hypothesis implies that $\mu'_m=\mu- \mu_m$ is
$\Lambda$-embedding, with embedding constant tending to $0$. Therefore
$\|\iota_\mu-\iota_{\mu_m}\|\to 0$. Since each $\iota_{\mu_m}$ is
compact, by Proposition~\ref{pr:bicompact}, the result follows.
\end{proof}
For a general bounded embedding, one can use the measures $\mu'_m$ to obtain a formula for the essential norm of $\iota_\mu$. We start with an abstract simple lemma that will be used also in Section~\ref{se:compo}.
\begin{lemma}\label{le:abstractessential}
Let $X$ be a Banach space, $(E,\nu)$ a \tcr{measurable} space, $T:X\to L^1(\nu)$ a bounded operator,
$(E_m)_m$ a decreasing sequence of measurable subsets of $E$ such that $\nu(\bigcap_m E_m )=0$. \tcr{Suppose that $(I-P_m)$ is compact for all $m$, where $P_m$ denotes the natural projection of $L^1(\nu)$ onto $L^1(E_m,\nu)$}. Then \tcr{the essential norm of $T$ is given by}
\[
\|T\|_e=\lim_{m\to\infty} \|P_mT\|.
\]
\end{lemma}
\begin{proof} Note that the sequence $(\|P_mT\|)_m$ is decreasing, so the limit exists.
Since $T-P_mT$ is compact for each $m$, it is obvious that
$\|T\|_e\le \lim_{m\to\infty} \|P_mT\|$. To prove the reverse
inequality, let $\epsilon>0$ and $K:X\to L^1(\nu)$ be a compact
operator. Take a sequence $(x_m)_m\subset X$ such that $\|x_m\|=1$ and $\|P_mT x_m\|_{\tcr{L^1(E_m,\nu)}}\ge \|P_mT\|-\epsilon$. Then $(Kx_m)_m$ contains a convergent subsequence, say $Kx_{m_j}\to g\in L^1(\nu)$. We have
\[
\|(T-K)x_{m_j}\|_{\tcr{L^1(\nu)}}\ge \|Tx_{m_j} -g\|_{\tcr{L^1(\nu)}}-\|Kx_{m_j}-g\|_{\tcr{L^1(\nu)}},
\]
whence
\begin{equation}\label{eq:3.0}
\limsup_j \|(T-K)x_{m_j}\|_{\tcr{L^1(\nu)}}\ge\limsup_j\|Tx_{m_j} -g\|_{\tcr{L^1(\nu)}}.
\end{equation}
Since $g\in L^1(\nu)$ and $\nu(\bigcap_m E_m )=0$, there exists a
positive integer $N$ such that
$ \int_{E_m}|g|\,d\nu \le \epsilon$
for all $m\ge N$. Then, if $m_j\ge N$, we have
\[
\begin{split}
\|Tx_{m_j} -g\|_{\tcr{L^1(\nu)}}& =\int_E |Tx_{m_j} -g|\, d\nu
\ge \int_{E_{m_j}} |Tx_{m_j} -g|\, d\nu
\ge \int_{E_{m_j}} |Tx_{m_j}| d\nu-\epsilon\\
&=\|P_{m_j}Tx_{m_j}\|_{\tcr{L^1(E_{m_j},\nu)}}-\epsilon\ge \|P_{m_j}T\|-2\epsilon.
\end{split}
\]
From~\eqref{eq:3.0} it follows then that
\[
\|T-K\| \ge \lim_m \|P_{m}T\|-2\epsilon.
\]
Since this is true for any compact $K$, we have
\[
\|T\|_e\ge \lim_m \|P_{m}T\|-2\epsilon.
\]
Letting $\epsilon\to 0 $ yields the desired inequality.
\end{proof}
\begin{theorem}\label{th:essentialnorm}
Let ${M_\Lambda^1}$ be a M\"untz space, and suppose that $\mu$ is an embedding measure. Then
\begin{equation}\label{eq:essentialnorm}
\|\iota_\mu\|_e = \lim_{n\to\infty} \|\iota_{\mu'_n}\|.
\end{equation}
\end{theorem}
\begin{proof}
We may apply Lemma~\ref{le:abstractessential} to the case $X={M_\Lambda^1}$, $(E,\nu)=([0,1], \mu)$, $T=\iota_\mu$, and $E_m=J_{\frac{1}{m}}$. The compactness condition on \tcr{$(I-P_m)$} follows from Proposition~\ref{pr:bicompact}.
\end{proof}
The \tcr{formula} given in Theorem~\ref{th:essentialnorm} can be made explicit in particular cases. We state an example that will be used in Section~\ref{se:compo}.
\begin{corollary}\label{co:essential-abs-cont-limit}
Let ${M_\Lambda^1}$ be a M\"untz space, and suppose there exists $\delta>0$ such that \tcr{$d\mu_{| J_\delta}= h \,dm_{|J_\delta}$} for some bounded measurable function $h$ with $\lim_{t\to 1} h(t)=a$. Then $\iota_\mu$ is bounded and $\|\iota_\mu\|_e= a$.
\end{corollary}
\begin{proof} The boundedness of $\iota_\mu$ is a consequence of Corollary~\ref{co:compactsupport}~(ii). To obtain the essential norm, according to Theorem~\ref{th:essentialnorm}, we have to prove that $\lim_{m\to\infty} \|\iota_{\mu'_m}\|=a$. First, for any $\epsilon>0$, if $m$ is sufficiently large, then $d\mu'_m\le (a+\epsilon) dm$ on $J_\frac{1}{m}$, which implies $\|\iota_{\mu'_m}\|\le a+\epsilon$; therefore
\[
\lim_{m\to\infty} \|\iota_{\mu'_m}\|\le a.
\]
On the other side, fix again $\epsilon>0$. If $m$ is sufficiently large, then $d\mu'_m\ge (a-\epsilon) dm$ on $J_\frac{1}{m}$. Take the function $g_n(x)=(\lambda_n+1)x^{\lambda_n}$. We have $g_n\in{M_\Lambda^1}$, $\|g_n\|_{M_\Lambda^1}=1$, while
\[
\|\iota_{\mu'_m} g_n \|
=\int_{J_\frac{1}{m}}g_n\, d\mu
\ge (a-\epsilon)\int_{1-\frac{1}{m}}^1 g_n(x)\, dx
=(a-\epsilon)\Big[1-\big(1-\frac{1}{m}\big)^{\lambda_n+1}\Big],
\]
and the last quantity tends to $a-\epsilon$ for $n\to\infty$. Therefore $ \|\iota_{\mu'_m} \|\ge a-\epsilon$ for all $\epsilon>0$. Letting now $\epsilon\to 0$ yields the desired reverse inequality.
\end{proof}
\section{Sublinear measures}
We start with the following simple observation.
\begin{lemma}\label{le:the function}
If $\mu$ is $\Lambda$-embedding, then for any $n$ we have $\mu(J_{\frac{1}{\lambda_n}})\le C \frac{1}{\lambda_n}$.
In particular, $\liminf_{\epsilon\to 0}\frac{\mu(J_\epsilon)}{\epsilon}<\infty$.
\end{lemma}
\begin{proof}
Since
$\lim_{n\to\infty}\left(1-\frac{1}{\lambda_n}\right)^{\lambda_n}=\frac{1}{e}$,
there exists a positive integer $N$ such that, for all $n\geq N$ and for
all $x\in \left[1-\frac{1}{\lambda_n},1\right]$, we have
$x^{\lambda_n}\geq \frac{1}{3}$. It follows that for all $n\geq N$
\[\frac{1}{3}\mu(J_{1/\lambda_n})\leq
\int_{J_{1/\lambda_n}}x^{\lambda_n}d\mu\leq \int_0^1
x^{\lambda_n}d\mu \leq \|\iota_\mu\|\int_0^1
x^{\lambda_n}dx=\frac{\|\iota_\mu\|}{\lambda_n +1}.\]
Therefore, for all $n\geq N$, we have
\[\mu(J_{1/\lambda_n})\leq\frac{3\|\iota_\mu\|}{\lambda_n}.\]
It is now obvious that there exists $C>0$ such that
$\mu(J_{1/\lambda_n})\leq\frac{C}{\lambda_n}$ for all $n$.
\end{proof}
This suggests the following definition.
\begin{Def}
A measure $\mu$ is called \emph{sublinear}
if there is a constant $C>0$ such that for any $0<\epsilon<1$ we have
$\mu(J_\epsilon)\le C \epsilon$; the smallest such $C$ will be denoted by
$\|\mu\|_S$. The measure $\mu$ is called
\emph{vanishing sublinear} if $\lim_{\epsilon\to 0}\frac{\mu(J_\epsilon)}{\epsilon}=0$.
\end{Def}
We can then obtain a necessary condition for $\Lambda$-embedding for a class of sequences $\Lambda$.
\begin{proposition}\label{pr:sublinear} Suppose that there exists $M>0$ such that $\frac{\lambda_{n+1}}{\lambda_n}\le M$. Then any $\Lambda$-embedding measure is sublinear.
\end{proposition}
\begin{proof}
\tcr{Obviously it is sufficient to check the condition of sublinearity for $\epsilon$ sufficiently small. Since $1/\lambda_n$ is a decreasing sequence tending to $0$, we may assume that for some $n$ we have
$\frac{1}{\lambda_{n+1}}\le \epsilon\le \frac{1}{\lambda_n}$.} Then, applying Lemma~\ref{le:the function},
\[
\mu(J_\epsilon)\le \mu(J_{\frac{1}{\lambda_n}} )\le \frac{C}{\lambda_n}
\le \frac{CM}{\lambda_{n+1}}\le CM\epsilon. \qedhere
\]
\end{proof}
It is interesting that sublinearity is also a sufficient condition for $\Lambda$-embedding for the class of quasilacunary sequences $\Lambda$. This will be proved in the next section; now we continue with some elementary facts about sublinear measures.
The next lemma is a consequence of Lemma~\ref{le:rho}, in case $\rho(x)=x$.
\begin{lemma}\label{le:second}
Suppose that $\|\mu\|_S<\infty$. If $g$ is continuous, positive, and increasing, we have
\begin{equation}\label{eq:11}
\int_{[0,1]}g\, d\mu\le \|\mu\|_S \int_{[0,1]}g\, dm.
\end{equation}
\end{lemma}
\begin{corollary}\label{co:first} (i) If $\mu$ is sublinear, then
\[
\sup_{\lambda}\|(\lambda+1)\Pwr{}\|_{L^1(\mu)}\le \|\mu\|_S.
\]
(ii) If $\mu$ is vanishing sublinear, then
\[
\lim_{\lambda\to\infty}\|\lambda\Pwr{}\|_{L^1(\mu)}=0.
\]
\end{corollary}
\begin{proof}
For (i), we apply Lemma~\ref{le:second} to the case $g=\Pwr{}$.
For (ii), fix $\epsilon>0$. By the definition of vanishing sublinear, there is $\delta>0$ such that $\mu(J_{\delta'})\le \epsilon\delta'$ for all $\delta'\le\delta$. If $\lambda$ is large enough, then $\lambda x^\lambda\le \epsilon$ for all $x\le 1-\delta$, and we have
\[
\int_{[0,1]}\lambda\Pwr{}\,d\mu(x)= \int_{[0,1-\delta)}\lambda\Pwr{}\,d\mu(x)+ \int_{[1-\delta,1)}\lambda\Pwr{}\,d\mu(x)
\le \epsilon\|\mu\|+ \int_{[1-\delta,1)}\lambda\Pwr{}\,d\mu(x).
\]
\tcr{Let $\mu_\delta$ be the measure which is equal to $\mu$ on
$J_\delta$ and is $0$ elsewhere. Then applying again
Lemma~\ref{le:second} to the measure
$\mu_{\delta}$ and to the function $g(x)=\lambda\Pwr{}$, we get that} the second term is also bounded by~$\epsilon$.
\end{proof}
\section{Quasilacunary sequences}
\tcr{A sequence $\Lambda$ is \emph{lacunary} if for some $q>1$ we have $\lambda_{n+1}/\lambda_n\geq q$, $n\geq 1$. More generally a sequence $\Lambda$ is \emph{quasilacunary} if for some increasing
sequence $(n_k)$ of integers and some $q>1$ we have $\lambda_{n_{k+1}}/\lambda_{n_k}\ge q$ and $N:=\sup_k(n_{k+1}-n_k)<\infty$. (The first condition of
quasilacunarity is sometimes stated as} $\lambda_{n_k+1}/\lambda_{n_k}\ge q$; it is easy to see that the two are equivalent, of course with a different $q$.) The sequence $\Lambda$ will be fixed in this section.
We need a few results from \cite{gl05}.
\begin{lemma}[{\cite[Corollary 6.1.3]{gl05}}]\label{le:majorize_f}
There exists a constant $d>0$ (depending only on $\Lambda$) such that,
if $f(x)=\sum_{n=1}^m \alpha_n x^{\lambda_n}$, then, for all $x\in[0,1]$,
\[
|f(x)|\le d x^{\lambda_1} \|f\|_\infty.
\]
\end{lemma}
\begin{lemma}[{\cite[Proposition~8.2.2]{gl05}}]\label{le:bernstein}
There is a constant $K>0$ (depending only on $\Lambda$) such that, if $f(x)=\sum_{n=1}^m \alpha_n x^{\lambda_n}$, then
\[
\|f'\|_\infty\le K \left(\sum_{n=1}^m \lambda_n \right)\|f\|_\infty.
\]
\end{lemma}
\begin{lemma}[{\cite[Theorem~9.3.3]{gl05}}]\label{le:quasil1}
If $\Lambda$ is quasilacunary, $F_k=\Span\{x^{\lambda_{n_k+1}},\ldots, x^{\lambda_{n_{k+1}}}\}$, then there is $d_1>0$ such that for any sequence of functions $f_k\in F_k$ we have
\[
d_1 \sum_k \|f_k\|_1 \le \|\sum_k f_k\|_1 \le \sum_k \|f_k\|_1.
\]
\end{lemma}
\tcr{In particular, if $\Lambda$ is lacunary, then there is $d_1>0$ such that
\begin{equation}\label{eq:lacunary}
d_1\sum_n \frac{|a_n|}{\lambda_n}\leq \|p\|_1\leq \sum_n \frac{|a_n|}{\lambda_n},
\end{equation}
for every polynomial $p(x)=\sum_n a_n x^{\lambda_n}$ in $M_\Lambda^1$.}
Let us also note that, in the proof of \cite[Theorem 9.3.3]{gl05}, it is shown that any quasilacunary sequence may be enlarged to one that is still quasilacunary and satisfies $\lambda_{n+1}/\lambda_n\le q^2$ for all $n$. We will suppose this true in the sequel; it follows then that we can assume
\begin{equation}\label{eq:ratio_lambdas}
q\le \frac{\lambda_{n_{k+1}}}{\lambda_{n_k+1}}\le q^{2(N-1)}.
\end{equation}
Finally, we will use also the following elementary lemma.
\begin{lemma}\label{le:elementary}
If $f:[0,1]\to {\mathbb R}$ is a nonconstant differentiable function,
then
\[
\|f\|_1\ge \min\left\{\frac{\|f\|_\infty^2}{2\|f'\|_\infty},
\frac{\|f\|_\infty}{4}\right\}.
\]
\end{lemma}
\begin{proof}
Let $x_0\in [0,1]$ such that $|f(x_0)|=M$, where $M:=\|f\|_\infty>0$.
Replacing $f$ by $-f$ we may assume that $f(x_0)=M$. Obviously
one of the intervals $[x_0-1/2,x_0]$ or $[x_0,x_0+1/2]$ is in $[0,1]$.
Suppose that the first interval is in $[0,1]$. \\
If $\frac{\|f\|_\infty}{4}\leq \frac{\|f\|_\infty^2}{2\|f'\|_\infty}$, i.e.
if $\|f'\|_\infty\leq 2M$, for all $x\in [x_0-1/2,x_0]$,
\begin{equation*}\label{eq:triangle}
f(x)\geq 2M (x- x_0)+M\geq 0.
\end{equation*}
It follows that $\|f \|_1\geq \int_{x_0-1/2}^{x_0}f(x)dx\geq \frac{M}{4}$.\\
If $\|f'\|_\infty >2M$ then $x_0-\frac{M}{\|f'\|_\infty}\in [x_0-1/2,x_0]$
and for all $x\in [x_0-M/\|f'\|_\infty,x_0]$,
\begin{equation*}\label{eq:triangle2}
f(x)\geq \|f'\|_\infty (x- x_0)+M\geq 0.
\end{equation*}
It follows that $\|f \|_1\geq \int_{x_0-M/\|f'\|_\infty}^{x_0}f(x)dx\geq
\frac{M^2}{2\|f'\|_\infty}$.\\
The proof in the case where $[x_0,x_0+1/2]$ is in $[0,1]$ follows along
the same lines.
\end{proof}
We are ready now for the promised extension.
\begin{theorem}\label{th:Sarquasilac2}
If $\Lambda$ is quasilacunary, then any sublinear measure $\mu$ is $\Lambda$-embedding.
\end{theorem}
\begin{proof}
By Lemma~\ref{le:quasil1}, it is enough to show that there is a constant $C>0$ such that for any $k$ and any $f\in F_k$ we have $\|f\|_{L^1(\mu)}\le C\|f\|_1$. Let us then fix $k$ and $f\in F_k$. Applying Lemma~\ref{le:majorize_f} and Corollary~\ref{co:first}, we have
\begin{equation}\label{eq:estimate}
\begin{split}
\|f\|_{L^1(\mu)}&=
\int_0^1 |f(x)|\, d\mu(x)
\le d\|f\|_\infty \int_0^1 x^{\lambda_{n_k+1}}\, d\mu(x)\\
&\le \frac{ d\|\mu\|_S \|f\|_\infty}{\lambda_{n_k+1}} .
\end{split}
\end{equation}
We apply now Lemma~\ref{le:elementary}; there are two possible cases. If $\|f\|_\infty\le 4\|f\|_1$, then it follows immediately from~\eqref{eq:estimate} that
\[
\|f\|_{L^1(\mu)}\le \frac{4 d\|\mu\|_S \|f\|_1}{\lambda_{n_k+1}}.
\]
We obtain thus the desired inequality and the theorem is proved in this case.
If the minimum in Lemma~\ref{le:elementary} is given by the other term, we use Lemma~\ref{le:bernstein}, which yields
\begin{equation}\label{eq:bernstein_here}
\|f'\|_\infty\le K \left(\sum_{n=n_k+1}^{n_{k+1}} \lambda_n \right)\|f\|_\infty \le KN\lambda_{n_{k+1}} \|f\|_\infty.
\end{equation}
Then, by Lemma~\ref{le:elementary},
\[
\|f\|_\infty^2\le 2\|f\|_1\|f'\|_\infty\le 2KN \lambda_{n_{k+1}} \|f\|_1\|f\|_\infty.
\]
We cancel $\|f\|_\infty$ from both sides and plug the resulting inequality into~\eqref{eq:estimate}. With the aid of~\eqref{eq:ratio_lambdas}, one obtains
\[
\|f\|_{L^1(\mu)} \le \frac{2KNd \lambda_{n_{k+1}} \|\mu\|_S \|f\|_\infty }{\lambda_{n_k+1}} \le 2KNd q^{2(N-1)} \|\mu\|_S \|f\|_1,
\]
which finishes the proof.
\end{proof}
Combining Theorem~\ref{th:Sarquasilac2} with Proposition~\ref{pr:sublinear}, we obtain a class of $\Lambda$ for which sublinearity is a necessary and sufficient condition for $\Lambda$-embedding.
\begin{corollary}\label{co:bibounded}
If, for some increasing sequence $(n_k)$ of integers with $\sup_k(n_{k+1}-n_k)<\infty$ we have
\[
1<\inf_k \frac{\lambda_{n_{k+1}}}{\lambda_{n_k}}\le \sup_k \frac{\lambda_{n_{k+1}}}{\lambda_{n_k}} <\infty,
\]
then a measure $\mu$ is $\Lambda$-embedding if and only if it is sublinear.
\end{corollary}
The next corollary follows from Proposition~\ref{pr:abstractcompactness} \tcr{and Theorem~\ref{th:Sarquasilac2}}.
\begin{corollary}\label{co:compactsublinear}
If $\Lambda$ is quasilacunary, then for any vanishing sublinear measure the embedding $\iota_\mu$ is compact.
\end{corollary}
\section{Some examples}
In general the property of being $\Lambda$-embedding depends on the sequence $\Lambda$, as shown by the next example.
\begin{example}\label{ex:twolambdas}
We intend to construct a measure $\mu$ and two lacunary sequences $\Lambda=(\lambda_n)_n$ and $\Lambda'=(\lambda'_n)_n$ such that $\mu$ is $\Lambda$-embedding but not $\Lambda'$-embedding.
For $0<a<1$, consider the function $\lambda\mapsto \lambda a^{\lambda}$. It attains its maximum in $x_a=-\frac{1}{\ln a}$, and the maximum value is between $x_a/2$ and $x_a$; also, the limit for $\lambda\to\infty$ is 0. Since, for $a$ close to 1, $-\ln a$ is of the same order as $1-a$, it follows that $x_a$ is of the same order as $(1-a)^{-1}$.
Take then $\mu=\sum_k c_k \delta_{a_k}$, where $\delta_x$ defines the Dirac measure in $x$, $a_k\uparrow 1$ and $c_k>0$, $\sum_k c_k<\infty$. The values $c_k, a_k, \lambda_k$ will be defined recurrently. We start with $c_0=\lambda_0=1$ and $a_0=0$. Suppose then that they have been defined for $k\ge n$. We choose then $\lambda_{n+1}$ large enough such that $\lambda_{n+1} a_k^{\lambda_{n+1}}\le 1$ for all $k\le n$. Then we take $a_{n+1}$ such that
(i) $1-a_{n+1}\le \frac{1-a_n}{2}$;
(ii) $(n+1)(1-a_{n+1})\le \frac{1}{\lambda_{n+1}}$.\\
Finally, we define $c_{n+1}=(n+1)(1-a_{n+1})$.
Note first that (i) implies $1-a_n\le 2^{-n}$ and therefore
$c:=\sum_k c_k\le \sum_k k 2^{-k}<\infty$. Moreover, using (i), we
have also $c_{n+1}\leq (2/3)c_n$ for all $n\geq 3$. Now, since
$\int x^\lambda \, d\mu=\sum_k c_k a_k^{\lambda}$, it follows that,
for all $n\geq 3$
\[
\begin{split}
\int \lambda_n x^{\lambda_n} \, d\mu &=\sum_k c_k \lambda_n a_k^{\lambda_n}
=\sum_{k<n} c_k \lambda_n a_k^{\lambda_n}+\sum_{k\ge n} c_k \lambda_n a_k^{\lambda_n}\\
&\le \sum_{k< n} c_k +\sum_{k\ge n} c_k \lambda_n
\le c+ \sum_{k\geq n}(2/3)^{n-k}c_n\lambda_n=c+3c_n\lambda_n.
\end{split}
\]
Since (ii) implies that $c_n\lambda_n\leq 1$, it follows that,
for all $n\geq 3$
\[\int \lambda_n x^{\lambda_n} \, d\mu\leq c+3,\]
and therefore, for all $n$, there exists a positive constant $C>0$
such that \[\int \lambda_n x^{\lambda_n} \, d\mu\leq C.\]
Now, if we take an arbitrary function $f$ of the form
$\sum_{n} b_n \lambda_n\Pwr{n}\in M^1_\Lambda$, we obtain
\[
\|f\|_{L^1(\mu)}\le \sum_n |b_n|\ \|\lambda_n\Pwr{n} \|_{L^1(\mu)} \le
C\sum_n |b_n| \le C' \|f\|_1 ,
\]
(the last inequality follows from \eqref{eq:lacunary}). Therefore $\mu$ is $\Lambda$-embedding.
As for $\Lambda'$, we define $\lambda'_n=x_{a_n}$. Then
\[
\begin{split}
\int \lambda'_n x^{\lambda'_n} \, d\mu
&= \sum_k c_k \lambda'_n a_k^{\lambda'_n}\ge c_n \lambda'_n a_n^{\lambda'_n}.
\end{split}
\]
Since the maximum value of $\lambda\to\lambda a^\lambda$ is greater
than $x_a/2$, and since $x_{a_n}$ is of the same order as
$\frac{1}{1-a_n}$ when $n$ tends to $\infty$, there exists a positive
constant $C_1$ such that
\[\int \lambda'_n x^{\lambda'_n} \, d\mu \geq C_1\frac{c_n}{1-a_n}.\]
Then, by definition of $c_n$, it follows that
\[\int \lambda'_n x^{\lambda'_n} \, d\mu \geq C_1n.\]
Since $\| \lambda'_n x^{\lambda'_n}\|_{L^1(m)}\le 1$, $\mu$ is not $\Lambda'$-embedding.
\end{example}
The next example shows that for sequences that are not quasilacunary, the sublinearity of the measure $\mu$ is not in general a sufficient condition for $\Lambda$-embedding.
\begin{example}
Note first that if $\delta_t$ is the Dirac measure in $t\in [0,1)$, then $\|\delta_t\|_S=\frac{1}{1-t}$; therefore $\delta'_t=(1-t)\delta_t$ is a sublinear measure of unit (sublinear) norm.
Let us consider, for all positive integers $p,q$, the function $h_{p,q}(x)=x^p(1-x)^q$. We are interested in some estimates related to this function when $p,q\to\infty$ and $q/p\to 0$.
First, note that the maximum of $(1-x)h_{p,q}(x)$ is attained in $t_{p,q}=\frac{p}{p+q+1}$. If $p,q\to\infty$ and $q/p\to 0$, then this maximum value is of order $\frac{1}{p^{q+1}}$.
Secondly, to estimate $\|h_{p,q}\|_1$, note that it is equal to $B(p+1,q+1)$ (Euler's beta function), and thus (by standard estimates for $B$) we have
\[
\|h_{p,q}\|_1\sim \frac{(p+1)^{p+\frac{1}{2}}(q+1)^{q+\frac{1}{2}}}{(p+q+2)^{p+q+\frac{3}{2}} }.
\]
After some simple computations using the definition of $e$, it follows that
\begin{equation}\label{eq:hpq}
\frac{\int |h_{p,q}| d\delta'_{t_{p,q}} }{ \|h_{p,q}\|_1 } \sim (q+1)^{\frac{1}{2}}.
\end{equation}
Define then the sequence $\Lambda$ by adding together the groups of consecutive integers from $k^7$ to $k^7+k^5$, for all $k\ge 1$. Then
\[
\sum_n \frac{1}{\lambda_n}= \sum_{k=1}^\infty \sum_{j=0}^{k^5} \frac{1}{k^7+j}\le \sum_{k=1}^\infty \frac{k^5+1}{k^7}<\infty.
\]
Since $h_{p,q}$ is a polynomial in $x^p, x^{p+1},\dots, x^{p+q}$, we have $h_{k^7,k^5}\in {M_\Lambda^1}$ for all $k\ge 1$. Define the measure $\mu=\sum_{k\ge 1}\frac{1}{k^2}\delta'_{t_{k^7,k^5}}$. Then $\mu$ is sublinear, with $\|\mu\|_S\le \frac{\pi^2}{6}$.
On the other hand,
by~\eqref{eq:hpq} we have
\[
\int|h_{k^7,k^5}|d\mu\ge\frac{1}{k^2} \int |h_{k^7,k^5}| d\delta'_{t_{k^7,k^5}}
\ge\frac{1}{k^2} (k^5+1)^{\frac{1}{2}}\|h_{k^7,k^5}\|_1,
\]
and therefore
\[
\sup_k \frac{\int|h_{k^7,k^5}|d\mu}{\|h_{k^7,k^5}\|_1}\to \infty.
\]
Thus $\mu$ is not $\Lambda$-embedding.
\end{example}
\section{The sequence $\lambda_n=n^2$}
To show an example of what can be obtained going beyond quasilacunary sequences, we give in this section a more precise estimate for the function $\kappa$ in the case of the sequence $\lambda_n=n^2$. This will be done in several steps, which essentially make explicit the calculations that are involved in the general results, as found, for instance, in \cite[4.2]{be95}. The sequence $n^2$ is a main example of a \emph{standard} sequence, that is, one for which $\lambda_{n+1}/\lambda_n\to1$; it is a test for several unsolved questions in the theory of M\"untz spaces (see~\cite{gl05}). For the rest of this section, we will denote $\Lambda=(n^2)_{n\ge 1}$ and $\tilde\Lambda=(n^2+1)_{n\ge 1}$.
First, if $f(x)=a_\gamma x^\gamma+ \sum_{n=1}^m a_n x^{\gamma_n}$, then by standard euclidian space arguments we have
\begin{equation}\label{eq:gram}
|a_\gamma|\le d^{-1}\|f\|_2,
\end{equation}
where $d$ is the distance in $L^2[0,1]$ from $x^\gamma$ to the span of the functions $x^{\gamma_1}, \dots, x^{\gamma_m}$.
A calculation involving biorthogonal bases and Cauchy determinants
that can be found in \cite[pp. 176--177]{be95} shows that
\[
d=\frac{1}{\sqrt{2\gamma+1}}\prod_{n=1}^m \left| \frac{\gamma-\gamma_n}{\gamma+\gamma_n+1}\right|.
\]
We intend now to apply~\eqref{eq:gram} to the case of the M\"untz space $M_{\tilde\Lambda}^1$. Suppose
$f(x)=\sum_{n\ge 1} \tilde a_n x^{n^2+1}$. According to~\eqref{eq:gram}, we have
\begin{equation}\label{eq:gram2}
|\tilde a_m|\le \sqrt{2m^2+3} \mathop{\prod_{n=1}^\infty}_{n\not=m} \left| \frac{m^2+n^2+3}{m^2-n^2}\right| \|f\|_2.
\end{equation}
We break in three parts the infinite product in the right-hand side. The first two are estimated simply:
\begin{equation}\label{eq:prod1}
\prod_{n=1}^{m-1} \left| \frac{m^2+n^2+3}{m^2-n^2}\right| \le
\prod_{n=1}^{m-1} \frac{(m+n)^2}{m^2-n^2}=\frac{(2m-1)!}{m!(m-1)!}.
\end{equation}
\begin{equation}\label{eq:prod2}
\prod_{n=m+1}^{2m} \left| \frac{m^2+n^2+3}{m^2-n^2}\right| \le
\prod_{n=m+1}^{2m} \frac{(m+n)^2}{n^2-m^2}=\frac{(3m)!}{(2m)!m!}.
\end{equation}
As for the third, we have
\[
\prod_{n=2m+1}^{\infty} \left| \frac{m^2+n^2+3}{m^2-n^2}\right| =
\prod_{n=2m+1}^{\infty} \left(1+\frac{2m^2+3}{n^2-m^2}\right).
\]
Using the inequality $\log(1+x)\le x$, we obtain
\[
\begin{split}
\log \left( \prod_{n=2m+1}^{\infty} \left(1+\frac{2m^2+3}{n^2-m^2}\right) \right)&=\sum_{n=2m+1}^\infty \log \left(1+\frac{2m^2+3}{n^2-m^2}\right)\\
&\le
(2m^2+3) \sum_{n=2m+1}^\infty \frac{1}{n^2-m^2}\le \frac{(\log 3)(2m^2+3)}{2m},
\end{split}
\]
and thus
\begin{equation}\label{eq:prod3}
\prod_{n=2m+1}^{\infty} \left| \frac{m^2+n^2+1}{m^2-n^2}\right|\le 3^{\frac{2m^2+3}{2m}}.
\end{equation}
Remembering now that Stirling's formula says that
\[
\sqrt{2\pi N}\left(\frac{N}{e}\right)^N e^{\frac{1}{12N+1}}\le N!
\le \sqrt{2\pi N}\left(\frac{N}{e}\right)^N e^{\frac{1}{12N}}
\]
we obtain from~\eqref{eq:prod1},~\eqref{eq:prod2}, and~\eqref{eq:prod3}, after some majorizations,
\[
|\tilde a_m|\le m 3^{\frac{8m^2+3}{2m}}\|f\|_2.
\]
Consider now a polynomial $p(x)=\sum_m a_m x^{m^2}\in{M_\Lambda^1}$. If $\tilde p(x)=\int_0^x p(t)\, dt$, then $\tilde p(x)=\sum_m \frac{a_m}{m^2+1} x^{m^2+1}\in M_{\tilde\Lambda}^1$, and we may apply the previous estimate to $\tilde p$, obtaining
\[
|a_m| \le m(m^2+1)3^{\frac{8m^2+3}{2m}}\|\tilde p\|_2
\le m(m^2+1)3^{\frac{8m^2+3}{2m}}\|\tilde p\|_\infty \le 100^m \|p\|_1.
\]
Take $\epsilon>0$. For any $x\in[0, 1-\epsilon)$, we have
\[
|p(x)|\le \sum_m |a_m| (1-\epsilon)^{m^2}\le
\sum_m 100^m (1-\epsilon)^{m^2} \|p\|_1 \le
C_1 e^{\frac{C}{\scriptstyle\epsilon}} \|p\|_1.
\]
The last estimate is obtained from the fact \cite[p 57]{ha71} that, for $a>1$,
\[
\sum_{m\ge1} a^m x^{m^2} \sim e^{-\frac{(\log a)^2}{4\log x}}
\]
when $x\nearrow 1$.
In conclusion, for the sequence $\Lambda=(i^2)_{i\ge1}$ we can use in Theorem~\ref{th:generalsufficient} and Corollary~\ref{co:mu(Jeps)} the function
\[
\kappa(t)=C_1 e^{\frac{C}{\scriptstyle 1-t}}
\]
in order to obtain sufficient conditions for a $\Lambda$-embedding measure $\mu$.
One can see that there is a big gap between these conditions and the necessary sublinearity given by Proposition~\ref{pr:sublinear}.
\section{Applications: weighted composition operators}\label{se:compo}
A starting point for this paper was Section 4.2 from \cite{aathesis}, which studies certain weighted composition operators on ${M_\Lambda^1}$. We show below how the main results therein fit in our general frame. In this section $\Lambda$ is an arbitrary fixed sequence.
Let $\phi,\psi$ be two Borel functions on $[0,1]$, such that $\phi([0,1])\subset [0,1]$. For any Borel function $f$ one can define
\[
C_\phi(f)=f\circ \phi,\qquad \mathcal{T}_\psi(f)=\psi f.
\]
At this level of generality, $C_\phi$ and $\mathcal{T}_\psi$ are linear mappings in the vector space of Borel functions. We are interested in conditions under which the \emph{weighted composition operator} $ \mathcal{T}_\psi\circ C_\phi$ maps ${M_\Lambda^1}$ boundedly into $L^1$; in case this happens, we may want to compute the essential norm.
There is a standard way to view this as an embedding problem. Recall that the \emph{pullback} of a measure $\nu$ by $\phi$ is the measure $\phi^*\nu$ on $[0,1]$ defined by
\[
\phi^*\nu(E)=\nu (\phi^{-1}(E))
\]
for any Borel set $E$. Then the formula
\begin{equation}\label{eq:comp-measure}
\int_0^1 \psi(x) f(\phi(x))\, dx= \int_{[0,1]} f\, d(\phi^*(\psi dm))
\end{equation}
is easily checked on characteristic functions, whence it extends to all Borel functions on~$[0,1]$.
\begin{lemma}\label{le:relation-embedding}
Define the measure $\mu= \phi^*(\psi dm)$. Then
(i) $\mathcal{T}_\psi\circ C_\phi$ is bounded from ${M_\Lambda^1}$ to $L^1$ if and only if $\mu$ is a $\Lambda$-embedding measure.
(ii) $\mathcal{T}_\psi\circ C_\phi$ is compact from ${M_\Lambda^1}$ to $L^1$ if and only if $\iota_\mu$ is compact.
(iii) Suppose that $m(\phi^{-1}(\{1\}))=0$. If $\mu'_n=\mu_{|[1-\frac{1}{n}, 1]}$, then
\[
\|\mathcal{T}_\psi\circ C_\phi\|_e=\|\iota_\mu\|_e=\lim_{n\to\infty}\|\iota_{\mu'_n}\|.
\]
\end{lemma}
\begin{proof}
Formula~\eqref{eq:comp-measure} implies that the map $J$ defined by $J(f)=\psi (f\circ \phi)$ is an isometry from $L^1(\mu)$ into $L^1$. Since we have
\begin{equation}\label{eq:8.0}
\mathcal{T}_\psi\circ C_\phi=J\circ\iota_\mu,
\end{equation}
(i) and (ii) follow immediately.
As for (iii), we will apply Lemma~\ref{le:abstractessential} to the case $X={M_\Lambda^1}$, $(E,\nu)=([0,1], m)$, $T=\mathcal{T}_\psi\circ C_\phi$, and $E_n=\phi^{-1}([1-\frac{1}{n}, 1])$. The hypothesis on $\phi$ implies that
\[
m\left(\bigcap_n \phi^{-1}([1-\frac{1}{n}, 1])\right)=0;
\]
on the other side, since $P_n$ is the natural projection onto $L^1(\phi^{-1}([1-\frac{1}{n}, 1]))$, one verifies easily that
\[
(I-P_n)T=J\circ(\iota_\mu-\iota_{\mu'_n)},
\]
whence $(I-P_n)T$ is compact by Proposition~\ref{pr:bicompact}. It follows then from Lemma~\ref{le:abstractessential} that
\[
\|\mathcal{T}_\psi\circ C_\phi\|_e =\lim_n\|J\circ \iota_{\mu'_n} \|
=\lim_n\| \iota_{\mu'_n} \|. \qedhere
\]
\end{proof}
One can now recapture some of the results in \cite{aathesis}, where a certain regularity is assumed for the functions $\phi$ and $\psi$; in this case we can describe more precisely the measure $\phi^*(\psi\,dm)$, as shown by the following lemma, whose proof is a simple computation.
\begin{lemma}\label{le:density}
Suppose $[a,b]\subset[0,1]$ has the property that $\phi^{-1}([a,b])$ is the union of $p$ intervals $[x_i,y_i]$, which have at most an end point in common, and, for each $i=1,\dots,p$, $\phi_i:=\phi_{|[x_i,y_i]}$ is a function in $C^1([x_i,y_i])$, with $\phi_i'(x)\not=0$. Then the restriction of $\phi^*(\psi\,dm)$ to $[a,b]$ is absolutely continuous, with density
\begin{equation}\label{eq:density}
\rho(x)=\sum_{i=1}^p \frac{\psi(\phi_i^{-1}(x))}{\phi_i'(\phi_i^{-1}(x))}.
\end{equation}
\end{lemma}
The next proposition is Lemma 4.2.8 in \cite{aathesis}.
\begin{proposition}\label{pr:ihab1}
Suppose that $\phi\in C^1$. Then $ C_\phi$ is bounded from ${M_\Lambda^1}$ to $L^1$ if and only if either $\phi([0,1])\subset [0,1)$, or $\phi^{-1}(\{1\})\subset \{0,1\}$ and $\phi(x_0)=\tcr{1} \Longrightarrow \phi'(x_0)\not=0 $.
\end{proposition}
\begin{proof}
If $\phi([0,1])\subset [0,a]$ with $a<1$, then $\phi^*dm$ is supported in $[0,a]$ and thus $\Lambda$-embedding by Corollary~\ref{co:compactsupport}. \tcr{By Lemma~\ref{le:relation-embedding}, we conclude that $C_\phi$ is bounded from ${M_\Lambda^1}$ to $L^1$.}
Suppose now that $x_0\in [0,1]$ satisfies $\phi(x_0)=1$ and $\phi'(x_0)=0$. If $\delta>0$, let $\epsilon>0$ be such that $|\phi'(x)|\le \delta$ for $|x-x_0|<\epsilon$. Then $\phi(x)\ge 1-\delta\epsilon$ for $|x-x_0|<\epsilon$, whence $(\phi^*m)(J_{\delta\epsilon})\ge \epsilon$. Therefore $\frac{(\phi^*m)(J_{\delta\epsilon})}{\delta\epsilon}\ge \delta^{-1}$, which implies by Lemma~\ref{le:the function} that $\phi^*m$ is not $\Lambda$-embedding \tcr{and therefore $C_\phi$ is not bounded from ${M_\Lambda^1}$ to~$L^1$}.
Thus, if \tcr{$C_\phi$ is bounded from ${M_\Lambda^1}$ to $L^1$}, then $\phi(x_0)=1$ implies $\phi'(x_0)\not=0$. This already proves the necessity part of the proposition, since if $x_0\in (0,1)$ and $\phi(x_0)=1$ then $x_0$ is a local maximum for $\phi$ and thus $\phi'(x_0)=0$.
Finally, let us suppose that $\phi^{-1}(\tcr{\{1\}})=\{0,1\}$, $\phi'(0)\not=0$, $\phi'(1)\not=0$ (the other cases are simpler). Then there is $\delta>0$ such that $\phi^{-1}([1-\delta,1])$ is the union of two intervals $[0,a_1]$ and $[a_2,1]$ on which $\phi'$ is not zero. We may apply Lemma~\ref{le:density} to conclude that
$\phi^*m$ restricted to $J_\delta$ is absolutely continuous with respect to Lebesgue measure, with bounded density; it follows then by Corollary~\ref{co:compactsupport} (ii) that $\phi^*m$ is $\Lambda$-embedding, \tcr{that is, $C_\phi$ is bounded}.
\end{proof}
We will now state a definition appearing in~\cite{aathesis}. One says that the measurable function $\phi:[0,1]\to [0,1]$ \emph{satisfies the condition $(\alpha)$} if:
(a) $\phi^{-1}(1)=\{x_1, \dots x_p\}$ is finite;
(b) there exists $\epsilon>0$ such that, for each $i=1,\dots, p$, $\phi\in C^1([x_i-\epsilon,x_i])$ and $\phi\in C^1([x_i,x_i+\epsilon])$;
(c) $\phi'_-(x_i)>0$ and $\phi'_+(x_i)\tcr{<}0$ for all $i$, \tcr{where $\phi'_-(x_i)$ (respectively $\phi'_+(x_i)$) is the left (respectively right) derivative of $\phi$ at $x_i$};
(d) there exists $\alpha<1$ such that, if $x\not\in\bigcup_{i=1}^p (x_i-\epsilon, x_i+\epsilon)$, then $\phi(x)\le \alpha$.
The next result combines Theorems~4.2.11 and~4.2.15 from \cite{aathesis}.
\begin{proposition}\label{pr:ihab2}
Suppose $\phi:[0,1]\to [0,1]$ satisfies the condition $(\alpha)$, while $\psi:[0,1]\to{\mathbb C}$ is continuous. Then $\mathcal{T}_\psi\circ C_\phi$ is bounded, and
\[
\|\mathcal{T}_\psi\circ C_\phi\|_e=\sum_{i=1}^p |\psi(x_i)| L(x_i),
\]
where
\[
L(x_i)=\begin{cases}
\frac{1}{\phi'_-(x_i)} + \frac{1}{|\phi'_+(x_i)|} &\mbox{if } x_i\in(0,1),\\
\frac{1}{\phi'_-(x_i)}&\mbox{if } x_i=1,\\
\frac{1}{|\phi'_+(x_i)|}&\mbox{if } x_i=0.
\end{cases}
\]
\end{proposition}
\begin{proof}
If we define $\mu=\phi^*(\psi\,dm)$, then condition $(\alpha)$ implies that,
for some $\delta>0$, $\phi^{-1}([1-\delta,1])$ is the union of $2p$ intervals $[x_i-\eta_i,x_i]$ and $[x_i,x_i+\eta'_i]$, $i=1,\dots,p$, with $\phi(x_i-\eta_i)=\phi(x_i+\eta'_i)=1-\delta$, and on each of these intervals $\phi'$ is not zero.
Thus the interval $[1-\delta,1]$ satisfies the hypothesis of Lemma~\ref{le:density}. We may then apply Corollary~\ref{co:essential-abs-cont-limit} to $\mu$, and formula~\eqref{eq:density} gives $a=\sum_{i=1}^p |\psi(x_i)| L(x_i)$. Therefore $\iota_\mu$ is bounded and its essential norm is $\sum_{i=1}^p |\psi(x_i)| L(x_i)$. Part (iii) of Lemma~\ref{le:relation-embedding} finishes then the proof.
\end{proof}
One should note that both Propositions~\ref{pr:ihab1}
and~\ref{pr:ihab2} are valid for any $\Lambda$. This is a consequence
of imposing rather strong hypotheses on $\phi$ and $\psi$
(correspondingly, on the measure~$\mu$).\\
\noindent\textbf{Acknowledgment:} The authors wish to thank Pascal Lef\`evre
for helpful discussions on M\"untz spaces, starting point of this work.
|
{
"redpajama_set_name": "RedPajamaArXiv"
}
| 6,920
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\section{Introduction}
We consider the following nonlinear Schrödinger (NLS) system of equations
\begin{equation}\label{sys_NLS}
\begin{cases}
i\partial_t u + \Delta u +(|u|^2+\beta |v|^2) u= 0,\\
i\partial_t v + \Delta v +(|v|^2+\beta |u|^2) v = 0,\\
\end{cases}
\end{equation}
where $u$ and $v$ are complex-valued functions on the variables $(x,t) \in \mathbb{R}^{3} \times \mathbb{R}$, and $\beta>0$ is a coupling constant. From the physical point of view, system \eqref{sys_NLS} appears, for example, in nonlinear optics when higher-order nonlinear effects are included such as stimulated Raman scattering (SRS) and
stimulated Brillouin scattering (SBS).
For instance, if the
peak power of the incident pulse is above a threshold level then both SRS and SBS
may transfer energy from the pulse to a new pulse. The two pulses interact with each other through the Raman or Brillouin gain. A similar situation occurs when two
or more pulses at different wavelengths are incident on the fiber (see \cite{agrawalbook}). The interested reader will find a wide discussion concerning nonlinear optics, for instance, in \cite{agrawalbook} or \cite{boydbook}.
The initial value problem associated with \eqref{sys_NLS} may be studied following the same strategies for the standard cubic NLS equation,
\begin{equation}\label{standardNLS}
i\partial_t u+\Delta u +|u|^2u=0.
\end{equation}
In particular local well-posedness in the usual $L^2$-based Sobolev spaces is well understood. We are interested in considering \eqref{sys_NLS} mainly in the inhomogeneous Sobolev space $H^1(\mathbb R^3)\times H^1(\mathbb R^3)$. Therefore, given an initial data $(u_0,v_0)\in H^1(\mathbb R^3)\times H^1(\mathbb R^3)$, there exist $T_*=T_*(u_0,v_0)\in(0,\infty]$, $T^*=T^*(u_0,v_0)\in(0,\infty]$ and a unique solution of \eqref{sys_NLS} satisfying $(u,v)\in C((-T_*,T^*):H^1(\mathbb R^3)\times H^1(\mathbb R^3))$. In addition, the following blow-up alternative holds: if $T^*<\infty$ then
\[
\lim_{t\to T^*}\|(u(t),v(t))\|_{H^1\times H^1}=\infty.
\]
In this case we say that solution \textit{blows-up in finite positive time}. Similarly, if $T_*<\infty$ then
\[
\lim_{t\to -T_*}\|(u(t),v(t))\|_{H^1\times H^1}=\infty
\]
and we say that the solution \textit{blows-up in finite negative time}. We refer the reader to \cite{Cazenave03}*{Chapter 4} or \cite{LiPo15}*{Chapter 5} for the proofs in the case of the scalar Schr\"odinger equation; but a very similar analysis also establishes the results for system \eqref{sys_NLS}. If both $T_*=\infty$ and $T^*=\infty$ we say that the solution is \textit{global} and \eqref{sys_NLS} is said to be \textit{globally well-posed}.
Note that \eqref{sys_NLS} is invariant by scaling. Namely, if $(u,v)$ is a solution with initial data $(u_0,v_0)$, then \begin{equation}
(u_{\delta}(x,t),v_{\delta}(x,t)) = (\delta u(\delta x, \delta^2 t),\delta v(\delta x, \delta^2 t)), \qquad \delta > 0,
\end{equation}
is also a solution with initial data $(u_\delta(0),v_\delta(0))=(\delta u_0(\delta x),\delta v_0(\delta x))$. Computing the homogeneous $\dot{H}^s(\mathbb R^3)$ norm yields
\begin{equation}
\| (u_{\delta}(0),v_{\delta}(0))\|_{\dot{H}^s\times \dot{H}^s} = \delta^{s-
1/2}\|(u_0,v_0)\|_{\dot{H}^s\times \dot{H}^s}.
\end{equation}
Hence, the scale-invariant Sobolev space is $\dot{H}^{\frac{1}{2}}(\mathbb R^3)\times \dot{H}^{\frac{1}{2}}(\mathbb R^3)$. Such a space is sometimes referred to as the critical Sobolev space. In particular we see that the critical regularity is below that of our target space $H^1(\mathbb R^3)\times H^1(\mathbb R^3)$.
Consequently, in order to prove a global well-posedness result it suffices to guarantee, as usual, an a priori bound of the solution in hand. As for the scalar NLS equation, such a priori bound may be obtained with the help of the available conservation laws. Here we recall that system \eqref{sys_NLS} conserves the \textit{energy}
\begin{equation}
E(u(t),v(t)) := \frac{1}{2} \int \left[ |\nabla u(t)|^2 +|\nabla v(t)|^2\right] -
\frac{1}{4}\int \left[|u|^4+2\beta|uv|^2+|v|^4\right]
\end{equation}
the \textit{mass}
\begin{equation}
M(u(t),v(t)) := \int\left[ |u(t)|^2 + |v(t)|^2 \right]
\end{equation}
and the \textit{momentum}
\begin{equation}
F(u(t),v(t)) := \Im\int \left[ \bar{u}(t)\nabla u(t)+\bar{v}(t)\nabla v(t)\right].
\end{equation}
The dicothomy global well-posedness versus blow-up in finite time was studied in \cite{Pastor}. To give a precise description of the results, recall that a \textit{standing wave} for \eqref{sys_NLS} is a solution of the form
\begin{equation}\label{standing}
{u(x,t) = (e^{i t}\phi(x),e^{i t} \psi(x)) },
\end{equation}
where $\phi$ and $\psi$ are real-valued functions in $H^1(\mathbb R^3)$. By substituting \eqref{standing} in \eqref{sys_NLS} we see that $\phi$ and $\psi$ must be solutions of the following nonlinear elliptic system
\begin{align}\label{sys_def_ground}
\begin{cases}
\Delta \phi - \phi +(|\phi|^2+\beta |\psi|^2)\phi=0,\\
\Delta \psi - \psi +(|\psi|^2+\beta |\phi|^2)\psi = 0.
\end{cases}
\end{align}
A (weak) solution of \eqref{sys_def_ground} is also called a \textit{bound state}. It is easy to see that bound states are critical points of the functional
$$
I(\varphi,\psi)=E(\varphi,\psi)+\frac{1}{2}M(\varphi,\psi).
$$
Among all bound states, the minimizers of $I$ play a fundamental role in the dynamics of \eqref{sys_NLS}. These particular solutions are called \textit{ground states}. We will denote the set of all ground states by $\mathcal{G}$.
Take any $(\phi,\psi) \in \mathcal{G}$ and introduce the quantities
\begin{equation}\label{MKdef}
\mathcal{MK}(f,g):=\dfrac{M(f,g)K(f,g)}{M(\phi,\psi)K(\phi,\psi)} \quad \mbox{and} \quad \mathcal{ME}(f,g):=\dfrac{M(f,g)E(f,g)}{M(\phi,\psi)E(\phi,\psi)},
\end{equation}
where here and throughout the whole paper,
$$
K(f,g)=\int \left[ |\nabla f|^2 +|\nabla g|^2\right].
$$
By using \eqref{sys_def_ground} and integration by parts one can see that $M(\phi,\psi) = M(\tilde{\phi},\tilde{\psi})$, $K(\phi,\psi) = K(\tilde{\phi},\tilde{\psi})$, and $E(\phi,\psi) = E(\tilde{\phi},\tilde{\psi})$ for all $(\phi,\psi), (\tilde{\phi},\tilde{\psi}) \in \mathcal{G}$. In particular the denominators in \eqref{MKdef}
do not depend on the choice of the ground state.
The results established in \cite{Pastor} may be summarized as follows: assume $(u_0,v_0)\in H^1(\mathbb R^3)\times H^1(\mathbb R^3)$ and
\begin{equation}\label{MEcond}
\mathcal{ME}(u_0,v_0)<1.
\end{equation}
If $\mathcal{MK}(u_0,v_0)<1$ then the corresponding solution is global. Also, if $\mathcal{MK}(u_0,v_0)>1$ and $u_0,v_0$ are radial functions (or satisfy $|x|(u_0,v_0)\in L^2(\mathbb R^3)\times L^2(\mathbb R^3))$ then the corresponding solution blows-up in negative and positive finite time. These results were complemented in \cite{FP}, where the authors proved that in the case of a global solution it also scatters forward and backward in time. Recall we say that a global solution $(u(t),v(t))$ of \eqref{sys_NLS} scatters forward in time if there exist $u_0^+,v_0^+\in H^1(\mathbb R^3)$ such that
\begin{equation}\label{defscat}
\lim_{t\to+\infty}\|(u(t),v(t))-(e^{it\Delta}u_0^+,e^{it\Delta}v_0^+)\|_{H^1\times H^1}=0.
\end{equation}
Also, we say that $(u(t),v(t))$ scatters backward in time if there exist $u_0^-,v_0^-\in H^1(\mathbb R^3)$ such that
\begin{equation}\label{defscat-}
\lim_{t\to-\infty}\|(u(t),v(t))-(e^{it\Delta}u_0^-,e^{it\Delta}v_0^-)\|_{H^1\times H^1}=0.
\end{equation}
Here, $e^{it\Delta}f$ stands for the free solution of the scalar Schr\"odinger equation with initial data $f$.
If $(\phi, \psi)$ solves \eqref{sys_def_ground}, then the {standing wave} given in \eqref{standing}
neither blows up in finite time, nor scatters, in any time direction. Hence, it seems that the assumption \eqref{MEcond} is crucial to obtain the above mentioned results. In the present paper we are interested in the dynamics of \eqref{sys_NLS} exactly at the threshold, that is, in the case $\mathcal{ME}(u_0,v_0)=1$.
Before stating our results, let us discuss a little more concerning the ground states of \eqref{sys_def_ground}. It is immediate to check that the pair $((1+\beta)^{-1/2}\,\varphi,(1+\beta)^{-1/2}\,\varphi)$ solves system \eqref{sys_def_ground} if $\varphi$ is a (weak) solution of the scalar equation
\begin{equation}\label{scalar_ground}
\Delta \varphi-\varphi+
|\varphi|^2\varphi=0.
\end{equation}
Such equation is related to the scalar NLS equation \eqref{standardNLS} and it is well known (c.f. \cite{Strauss77}, \cite{BLP81}, \cite{Kwong89},\cite{TaoBook}*{Appendix B}) that it admits a unique radial positive $H^1$ solution (the ground state), which is smooth and decays exponentially. Besides the \textit{trivial solution} $(\phi,\psi) = (0,0)$, system \eqref{sys_def_ground} also exhibits \textit{semi-trivial} solutions of the form $(\varphi,0)$ and $(0,\varphi)$, where $\varphi$ solves the scalar equation \eqref{scalar_ground}.
Therefore, differently from the scalar case, ground states are not necessarily unique up to symmetries. Indeed, the results given in \cite{Mande115}*{Lemma 1 and Lemma 2}, \cite{Maia}*{Corollary 2.6} and \cite{WY_Uniq}*{Theorem 1.3} (see also \cite{STH16} and \cite{Correia16}) show that if $\beta>1$, then there is a unique ground state (up to phase, scaling and translation), and it is given by the fully nontrivial solution $((1+\beta)^{-1/2}\,\varphi,(1+\beta)^{-1/2}\,\varphi)$, where $\varphi$ is the radial positive solution of \eqref{scalar_ground}. On the other hand, if the coupling is weak, i.e., if $0 < \beta < 1$, then the ground states are the semi-trivial solutions $(\varphi,0)$ and $(0,\varphi)$. In view of this, throughout the paper we will assume
\begin{equation}\label{betarange}
\text{either } 0 < \beta < 1 \text{ or } \beta > 1.
\end{equation}
The case $\beta=1$ is degenerated, as there appear infinitely many radial non-negative solutions given by $(\lambda\, \varphi, \sqrt{1-\lambda^2}\, \varphi)$, for any $0 \leq \lambda \leq 1$.
Since there can be more than one ground state, the main challenge here, which has no analogue in the scalar case, is to understand the possible behaviors this situation leads to. The variational characterization of the ground states must take the lack of uniqueness into account, and the approach has to be changed, given the uniqueness assumptions were heavily used in several works (c.f. \cites{DM_Dyn,DR_Thre,higher_thre,CFR_thre}).
Our first result shows that the dynamics of \eqref{sys_NLS} at the threshold is even richer.
\begin{teo}[Special solutions]\label{sub_special}
Assume $\beta$ satisfies \eqref{betarange}. For each ground state $Q = (\phi,\psi) \in \mathcal{G}$ there exist two radial solutions $Q^+=(\phi^+,\psi^+)$ and $Q^-=(\phi^-,\psi^-)$ to \eqref{sys_NLS} in $H^1(\mathbb R^3)\times H^1(\mathbb R^3)$ such that
\begin{itemize}
\item[(i)] $M(Q^\pm) = M(Q)$, $E(Q^\pm) = E(Q)$ , $T^*(Q^\pm)=+\infty$ and there exist $C$, $e_0>0$ such that
\begin{equation}
\|Q^\pm(t) - e^{it}Q\|_{H^1 \times H^1} \leq C e^{-e_0t}\text{ for all } t \geq 0,
\end{equation}
\item[(ii)] $K(Q^+(0)) >K(Q)$ and $T_*(Q^+)<+\infty$
\item[(iii)] $K(Q^-(0))< K(Q)$, $T_*(Q^-)=+\infty$
and $Q^-$ scatters backward in time.
\end{itemize}
\end{teo}
We then show that, besides the behavior already expected below the threshold, the standing waves and the above special solutions essentially cover all possible orbits:
\begin{teo}[Classification of threshold solutions]\label{sub_class_thresh}
Let $(u,v)$ be a solution to \eqref{sys_NLS} such that $\mathcal{ME}(u_0,v_0) = 1$. Then, the following holds.
\begin{itemize}
\item[(i)] If $\mathcal{MK}(u_0,v_0) < 1$, then $(u,v)$ is global. Moreover, either $u$ scatters in both time directions, or there exists a ground state $Q=(\phi,\psi)\in \mathcal{G}$ such that $(u,v) = Q^-$ up to the symmetries of the system.
\item[(ii)] If $\mathcal{MK}(u_0,v_0) = 1$, then there exists a ground state $Q=(\phi,\psi)\in \mathcal{G}$ such that $(u,v) = e^{it}Q$ up to the symmetries of the system.
\item[(iii)] If $\mathcal{MK}(u_0,v_0) > 1$ and $(u_0,v_0)$ is either radial or $(|x|u_0,|x|v_0) \in L^2(\mathbb R^3)\times L^2(\mathbb R^3)$, then either $(u,v)$ blows-up in finite positive and negative time, or there exists a ground state $Q=(\phi,\psi)\in \mathcal{G}$ such that $u = Q^+$ up to the symmetries of the system.
\end{itemize}
\end{teo}
In the above theorem, and throughout the whole paper, by \textit{up to the symmetries} we mean up to scaling, space translation, time translation, phase rotation and time reversal. That is, $(\tilde u,\tilde v) = (u,v)$ up to symmetries if
$$
(\tilde u, \tilde v) = (e^{i\theta_0}u_\delta\left(x+x_0,t+t_0 \right), e^{i\theta_1}v_\delta\left(x+x_0,t+t_0 \right))
$$
or
$$
(\tilde u, \tilde v) =(e^{i\theta_0}\bar{u}_\delta\left(x+x_0,\-t+t_0 \right),e^{i\theta_1}\bar{v}_\delta\left(x+x_0,\-t+t_0 \right)),
$$
with $(\delta,\theta_0, \theta_1, x_0,t_0) \in \mathbb R_+\times \mathbb R/2\pi\mathbb{Z}\times \mathbb R/2\pi\mathbb{Z}\times \mathbb R^N \times \mathbb R$. All these symmetries leave the $\dot{H}^{\frac{1}{2}}\times \dot{H}^{\frac{1}{2}}$ norm invariant.
Threshold problems in the scalar case were studied, for instance, in \cites{DM_Dyn, DR_Thre, higher_thre, CFR_thre}. Even though the general idea of threshold behavior for NLS equations can be considered understood, the main challenge to proving the results above is to deal with the possibility of multiple ground states in system \eqref{sys_NLS}. One has to be careful from the very beginning, since the linearized equation depends on the ground state being considered. The variational characterization given by applying the Sobolev-adapted profile decomposition has to take the multiplicity into account, and the modulational stability proved along the manuscript must be strong enough as to prove that not only the corresponding phase and translation parameters converge as $t \to +\infty$, but that the corresponding ground state (which can be different for different time intervals, as there can be no uniqueness) also converge. Non-degeneracy of the ground states then play an important role here, as well as the spectral properties and coercivity of the linear operator in a suitable subspace.
This paper is structured as follows: In Section \ref{Sec2}, we state the notations used throughout the whole text and recall some basic estimates. In Section \ref{Sec3}, we study the spectral properties of the linearized operator associated to the ground states. Section \ref{Sec4} is devoted to a detailed study of the variational characterization of the ground states, which culminates in a modulation theory developed in Section \ref{Sec5}. We then construct special solutions in Section \ref{Sec6} and prove results about the possible dynamics at the threshold in Section \ref{Sec7}, showing that some of them are associated with exponentially time-decaying solutions to the linearized equation. Finally, Section \ref{Sec8} is devoted to studying such decaying solutions and collecting all of the previous results to close the main results of this paper.
\smallskip
{\bf Acknowledgements.} L. C. was financed by grant \#2020/10185-1, São Paulo Research Foundation (FAPESP). A. P. is partially supported by CNPq grant 303762/2019-5 and FAPESP
grant 2019/02512-5.
\section{Notation and preliminaries}\label{Sec2}
In this section we introduce some notations and give some basic estimates. We use $c$ to denote various constants that may vary line by line. Given two positive numbers $a$ and $b$, the notation $a \lesssim b$ means
that $a \leq cb$, where the constant $c$ is independent of $a$ and $b$. Sometimes we use $a\lesssim_{a_1,\ldots,a_k}b$ to indicate that the implicit constant $c$ depends on the parameters $a_1,\ldots,a_k$. Given a complex number $z$, we use $\Re(z)$ and $\Im(z)$ to denote, respectively, the real and imaginary parts of $z$. To simplify notation, $\int f$ always mean integration over all $\mathbb R^3$. By $\partial_{x_k}$ (or $\partial_k$, for short) we mean differentiation with respect to $x_k$.
By $L^p(\mathbb R^3)$, $1\leq p\leq \infty$, we denote the usual Lebesgue space endowed with the standard norm denoted by $\|\cdot\|_{L^p_x}$ or $\|\cdot\|_{L^p}$. Given a function $f=f(x,t)$, the mixed norm $L^q_tL^r_x$ is defined as $\|f\|_{L^q_tL^r_x}=\|\|f\|_{L^r_x}\|_{L^q_t(\mathbb R)}$. By $\|\cdot\|_{L^q_IL^r_x}$ we mean integration in time over the interval $I\subset\mathbb R$ instead of $\mathbb R$. For any $s\in\mathbb R$, the operators $D^s$ and $J^s$ stand, respectively, for the Fourier
multiplier with symbol $|\xi|^s$ and $\langle \xi \rangle^s = (1+|\xi|)^s$.
Consequently, the norm in the $L^2$-based Sobolev spaces $H^s:=H^s(\mathbb R^3)$ and $\dot{H}^s:=\dot{H}^s(\mathbb R^3)$
are given, respectively, by
\begin{equation*}
\|f\|_{H^s}\equiv \|J^sf\|_{L^2_x}=\|\langle \xi
\rangle^s\hat{f}\|_{L^2_{\xi}}, \qquad \|f\|_{\dot{H}^s}\equiv
\|D^sf\|_{L^2_x}=\||\xi|^s\hat{f}\|_{L^2_{\xi}}.
\end{equation*}
The product space $H^s\times H^s$ is equipped with the norm $\|(f,g)\|^2_{H^s\times H^s}\equiv \|f\|^2_{H^s}+\|g\|^2_{H^s}$. In an analogous way we define the norm in $\dot{H}^s\times \dot{H}^s$. To simplify notation, sometimes we use $(H^s(\mathbb R^3))^k$ for $H^s(\mathbb R^3)\times \ldots\times H^s(\mathbb R^3)$ ($k$ times).
We say that a pair $(q,r)$ is
$\dot{H}^s$ admissible if
$$
\frac{2}{q}+\frac{3}{r}=\frac{3}{2}-s.
$$
In what follows, we set
$$
\|u\|_{S(L^2)}=\sup\left\{\|u\|_{L^q_tL^r_x};\; (q,r)\, {\rm is}\, L^2\; {\rm
admissible},\; 2\leq r\leq6,\; 2\leq q\leq\infty\right\}
$$
and
$$
\|u\|_{S'(L^2)}=\inf\left\{\|u\|_{L^{q'}_tL^{r'}_x};\; (q,r)\,{\rm is}\, L^2\;
{\rm admissible}, \, 2\leq q\leq\infty,\; 2\leq r\leq6\right\}.
$$
If a time interval $I\subset\mathbb R$ is given, we use ${S(L^2;I)}$ and ${S'(L^2;I)}$ to inform
that the integration in time is over $I$. The space $S(L^2)\times S(L^2)$ is endowed with the norm $\|(u,v)\|_{S(L^2)\times S(L^2)}\equiv \|u\|_{S(L^2)}+\|v\|_{S(L^2)}$.
Next, we recall the well-known Strichartz inequalities. For the proofs we refer the reader to \cite{Cazenave03}.
\begin{lemma}\label{strilem}
The following estimates hold:
\begin{itemize}
\item[(i)] (Linear estimates)
$$
\|e^{it\Delta}u_0\|_{S(L^2)}\lesssim\|u_0\|_{L^2}.
$$
\item[(ii)] (Inhomogeneous estimates)
$$
\left\| \int_0^te^{i(t-t')\Delta}f(\cdot,t')dt'\right\|_{S(L^2)}\lesssim\|f\|_{S'(L^2)}.
$$
\end{itemize}
\end{lemma}
As in the scalar case, the ground states of \eqref{sys_def_ground} may also be obtained as minimizers of a vectorial Gagliardo-Nirenberg inequality. In fact, let us introduce the functional
\begin{equation}\label{Pdef}
P(u,v)=\int\left[ |u|^4+2\beta|uv|^2+|v|^4\right].
\end{equation}
The Gagliardo-Nirenberg inequality then reads as follows:
\begin{lemma} \label{gnlemma}
For any $(u,v)\in H^1(\mathbb R^3)\times H^1(\mathbb R^3)$ there holds
\begin{equation}\label{GN}
\begin{split}
P(u,v)\leq c_{GN} M(u,v)^{1/2}K(u,v)^{3/2}.
\end{split}
\end{equation}
In addition, the sharp constant $c_{GN}$ is given by
\begin{equation}\label{sharpc}
c_{GN}=\frac{4}{3M(\phi,\psi)^{1/2}K(\phi,\psi)^{1/2}},
\end{equation}
where $(\phi,\psi)$ is any ground state in $\mathcal{G}$.
\end{lemma}
For the proof, see \cite{FanelliMontefusco}. Note that, using integration by parts and \eqref{sys_def_ground}, we may obtain
the following {\textit{Pohozaev}}-type identities
\begin{align}\label{pohozaev}
K(\phi,\psi)&= 3 M(\phi,\psi) \quad \mbox{and}\quad
P(\phi,\psi) = 4M(\phi,\psi).
\end{align}
In particular, by setting $(u,v)=(\phi,\psi)$ in \eqref{GN} we see that equality holds. Also, using \eqref{pohozaev} it may be easily checked that
\begin{equation}\label{sharpc2}
c_{GN}=\frac{4}{3\sqrt6 M(\phi,\psi)^{1/2}E(\phi,\psi)^{1/2}},
\end{equation}
which gives $c_{GN}$ in terms of the mass and the energy of the ground states.
\section{The linearized equation}\label{Sec3}
In order to prove the main theorems of this paper, we need to carefully study \eqref{sys_NLS} around the ground state.
We identify the pair of complex numbers $(a + bi,c+di)$ with the vector $
(a,c,b,d)^T
$. For a complex-valued function, we write $f_1$ for its real part and $f_2$ for its complex part. We next introduce the following definition.
\begin{de}\label{defilinearop} For any ground state $Q = (\phi,\psi)$, we define
\begin{align}\label{def_op}
L_R &=\begin{pmatrix}1-\Delta-3\phi^2 -\beta \psi^2& -2\beta\phi\psi
\\
-2\beta\phi\psi
& 1-\Delta-3\psi^2-\beta \phi^2 \\
\end{pmatrix},\\
L_I&=\begin{pmatrix}1-\Delta-\phi^2-\beta \psi^2 & 0 \\
0 & 1-\Delta-\psi^2-\beta \phi^2 \\
\end{pmatrix},\\
\mathcal{L} &:= \begin{pmatrix}0 & -L_I \\
L_R & 0 \\
\end{pmatrix},\\
L(h,k) &= \begin{pmatrix}2\phi^2 h + \phi^2 \overline{h}+ \beta \psi^2 h
+\beta \phi \psi k + \beta \phi \psi \overline{k}
\\
2\psi^2 k + \psi^2 \overline{k}+ \beta \phi^2 k
+\beta \phi \psi h + \beta \phi \psi \overline{h}
\end{pmatrix} \\
R(h,k) &= \begin{pmatrix}2\phi|h|^2+\phi h^2+\beta\phi|k|^2+\beta\psi h k +\beta \psi h \overline{k}+|h|^2h+\beta|k|^2h\\
2\psi |k|^2+\psi k^2+\beta\phi|h|^2+\beta\phi h k +\beta \psi \overline{h} k+|k|^2k+\beta|h|^2k \end{pmatrix}.
\end{align}
\end{de}
If $(u,v)$ is a solution to \eqref{sys_NLS}, write $(u,v) = (e^{it}(\phi+h),e^{it}(\psi+k))$. Then $w:= (h,k)$ must satisfy
\begin{equation}\label{linearized_eq}
\partial_t w + \mathcal{L}w = iR(w),
\end{equation}
or, writing it as a Schrödinger equation,
\begin{equation}\label{linearized_eq_2}
i\partial_t w + \Delta w -w +L(w) + R(w) = 0.
\end{equation}
In the next two sections we establish some properties of the operator $\mathcal{L}$.
\subsection{Properties of the linearized operator}
We have, by a direct calculation, for any ground state $Q = (\phi,\psi)$
\begin{align}
L_I(\phi,\psi) &= 0,\\
L_R(\partial_k \phi, \partial_k \psi)&= 0,\quad 1 \leq k \leq 3.
\end{align}
This implies
\begin{equation}
\mathcal{L}(\partial_k\phi,\partial_k \psi)=\mathcal{L}(i\phi,i\psi) = 0,\quad 1 \leq k \leq 3.
\end{equation}
Also, defining $\Lambda f$ as the scaling generator $f +x \cdot \nabla f$, we have
\begin{equation}
L_R(\Lambda \phi,\Lambda\psi) = -2(\phi,\psi).
\end{equation}
Moreover, we define the bilinear form associated to $i\mathcal{L} = \begin{pmatrix}L_R&0\\0&L_I\end{pmatrix}$,
\begin{align}
B((f,g),(\tilde{f},\tilde{g})) &:= \frac{1}{2}(L_R(f_1,g_1),(\tilde{f}_1,\tilde{g}_1))_{L^2}+ \frac{1}{2}(L_I(f_2,g_2),(\tilde{f}_2,\tilde{g}_2))_{L^2},
\end{align}
and the \textit{linearized energy},
\begin{align}
\Phi(f,g) &:= B((f,g),(f,g))
\end{align}
One can check directly that, for any $(f,g)$, $(\tilde f, \tilde g) \in S(\mathbb R^3)\times S(\mathbb R^3)$,
\begin{equation}\label{prop_B}
\begin{gathered}
B((f,g),(\tilde f, \tilde g)) = B((\tilde f,\tilde g),(f,g)),\\
B(\mathcal{L}(f,g),(\tilde f, \tilde g)) = - B((f,g),\mathcal{L}(\tilde f, \tilde g)),\\
\quad B((i\phi,i\psi),(f,g)) = 0,\\
B((\partial_k \phi,\partial_k \psi),(f,g)) = 0, \,1\leq k \leq 3,\\
{B((\Lambda \phi,\Lambda \psi),(f,g)) = -\int (\phi f_1}+\psi g_1).\\
\end{gathered}.
\end{equation}
We prove the following result:
\begin{lemma}[]\label{spectrum_L} For any ground state of \eqref{sys_NLS}, let $\sigma(\mathcal{L})$ be the spectrum of the operator $\mathcal{L}$, defined in $\left(L^2(\mathbb R^3)\right)^4$ with domain $\left(H^2(\mathbb R^3)\right)^4$ and let $\sigma_{ess}(\mathcal{L})$ be its essential spectrum. Then
\begin{equation}
\sigma_{ess}(\mathcal{L}) = \{i y:\,\, y \in \mathbb R, |y| \geq 1\},\quad \sigma \cap \mathbb R = \{-e_0,0,e_0\} \quad \text{with } e_0 >0.
\end{equation}
Moreover, $e_0$ and $-e_0$ are simple eigenvalues of $\mathcal{L}$ with eigenfunctions $
\mathcal{Y}_+
$, $
\mathcal{Y}_-
\in \mathcal{S}(\mathbb{R}^3) \times \mathcal{S}(\mathbb{R}^3)$, respectively. The null space of $\mathcal{L}$ is spanned by $(i\phi,i\psi)$ and $(\partial_k \phi,\partial_k \psi)$, $1 \leq k \leq 3$ in the case $\beta<1$ and by $(i\phi,0)$, $(0,i\psi)$ and $(\partial_k \phi,\partial_k \psi)$, $1 \leq k \leq 3$ in the case $\beta >1$.
\begin{re}\label{re_spectrum}
By Lemma \ref{spectrum_L}, if $
\mathcal{Y}_1
=
\Re(\mathcal{Y}_+)
$ and $
\mathcal{Y}_2
=
\Im(\mathcal{Y}_+)
$, then
\begin{equation}
L_R
\mathcal{Y}_1
= e_0
\mathcal{Y}_2
\quad \text{and } L_I
\mathcal{Y}_2
= -e_0
\mathcal{Y}_1
.
\end{equation}
Furthermore, the null space of $L_R$ is spanned by the vectors $(\partial_k \phi,\partial_k \psi)$, $1 \leq k \leq 3$, and the null space of $L_I$ is spanned by $(\phi,\psi)$ in the case $\beta<1$ and by $(\phi,0)$ and $(0,\psi)$ in the case $\beta > 1$. Moreover, we have
\begin{equation}
\Phi(\mathcal{Y}_+) = \Phi(\mathcal{Y}_-) = 0.\\
\end{equation}
\end{re}
\end{lemma}
\begin{proof}
{
{The proof follows very closely the scalar case (c.f. \cites{DM_Dyn, DR_Thre, CFR_thre}), and we just sketch the main points here.}
We first show that $\mathcal{L}$ is a relatively compact perturbation of $i(1-\Delta)$. Indeed, define $K: (L^2)^4 \to (L^2)^4 $ as to satisfy $(1-\Delta)^{-1/2}i\mathcal{L}(1-\Delta)^{-1/2} = I-K$. We claim that $K$ is compact. It is enough to show that $\chi (1-\Delta)^{-1/2}$ is a compact operator in $(L^2)^4$ if $\chi$ is a radial, positive, non-increasing Schwartz function, which follows from the fact that, for any $f$,
\begin{equation}
\|\chi (1-\Delta)^{-1/2}f\|_{L^2} + \|\nabla(\chi (1-\Delta)^{-1/2}f)\|_{L^2}+\frac{1}{\chi(R)}\|\chi (1-\Delta)^{-1/2}f\|_{L^2(\{|x|\geq R\}}\lesssim \|f\|_{L^2}.
\end{equation}
The assertion about the essential spectrum then follows from Weyl's criterion. We now prove that $\mathcal{L}$ has only one negative eigenvalue (hence, only one positive eigenvalue, by conjugation).
We define the Weinstein functional associated to the corresponding Gagliardo-Nirenberg inequality:
\begin{equation}
J(u,v) = \frac{ M(u,v)^{\frac{1}{2}}K(u,v)^{\frac{3}{2}}}{P(u,v)}.
\end{equation}
Since $(\phi,\psi)$ is a minimizer of $J$ (see Lemma \ref{gnlemma}), we have $\frac{d^2}{d\eta^2}J(\phi+\eta h,\psi+\eta k)_{|\eta = 0} \geq 0$ for all $(h,k) \in H^1 \times H^1$. A direct calculation then shows that if
\begin{equation}
\int h_1 \Delta \phi + k_1 \Delta \psi = 0,
\end{equation}
then
\begin{equation}
\Phi(h,k) \geq 2 \left(\int \phi h_1 + \psi k_1\right)^2.
\end{equation}
We conclude that $L_R$ can have at most one negative direction, and that $L_I$ has none.
Defining
\begin{equation}
Z = \Lambda Q - \frac{(Q,\Lambda Q)_{L^2\times L^2}}{(Q,Q)_{L^2\times L^2}}Q
\end{equation}
and noting that $(L_RZ,Z)_{L^2\times L^2}<0$ and $(Z,Q)_{L^2\times L^2}=0$, we conclude that $\mathcal{L}$ has exactly one negative direction. Finally, the assertions about the kernel for $\beta>1$ follow from the non-degeneracy of $L_R$, shown in \cite{WY_Uniq}*{Corollary 4.4}, together with the explicit form of $L_I$, namely
\begin{equation}
L_I = \begin{pmatrix}1-\Delta-\varphi^2 & 0 \\ 0 & 1-\Delta-\varphi^2 \end{pmatrix},
\end{equation}
since it is known (\cite{W85_stability}*{Proposition 2.8}) that $\ker(1-\Delta-\varphi^2) = \text{span}\{\varphi\}$.
For $0<\beta<1$, we recall that the ground states are the semi-trivial solutions $(\varphi,0)$ and $(0,\varphi)$, where $\varphi$ solves \eqref{scalar_ground}. For $Q = (\varphi,0)$, the operators $L_R$ and $L_I$ reduce to:
\begin{align}
L_R &=\begin{pmatrix}1-\Delta-3\varphi^2 & 0 \\
0 & 1-\Delta-\beta \varphi^2 \\
\end{pmatrix},\\
L_I&=\begin{pmatrix}1-\Delta-\varphi^2 & 0 \\
0 & 1-\Delta-\beta \varphi^2 \\
\end{pmatrix}.
\end{align}
Since the linearized system is now decoupled, we just need to analyze the operator $L_\gamma := 1-\Delta - \gamma \varphi^2$, $\gamma >0$. It is known (\cite{W85_stability}*{Proposition 2.8}) that $L_1\geq 0$ on $H^1(\mathbb R^3)$, from which we conclude, for $0<\beta<1$:
\begin{equation}
L_\beta = \beta L_1 + (1-\beta)(1-\Delta) \geq (1-\beta)(1-\Delta) >0.
\end{equation}
Therefore, $\ker({L_\beta}) =\emptyset$. The same Proposition 2.8 of \cite{W85_stability} gives $\ker(L_1) = \text{span}\{\varphi\}$ and $\ker(L_3) = \text{span}\{\nabla \varphi\}$. The proof for $Q = (0,\varphi)$ is analogous.}
\end{proof}
For any ground state $Q = (\phi,\psi)$, consider the following orthogonality relations
\begin{equation}\label{sub_o1
\int h_2\phi = \int k_2\psi = \int h_1 \partial_j \phi + k_1 \partial_j \psi= 0, \quad 1 \leq j \leq 3,
\end{equation}
\begin{equation}\label{sub_o2
\int h_1 \Delta \phi + k_1 \Delta \psi = 0.
\end{equation}
\begin{equation}\label{sub_o3
B((h,k),\mathcal{Y}_+) = B((h,k),\mathcal{Y_-})=0.
\end{equation}
Denote by $G^\perp$ the set of all $(h,k) \in H^1\times H^1$ satisfying \eqref{sub_o1} and \eqref{sub_o2}, and $\tilde{G}^\perp$ the set of all $(h,k) \in H^1 \times H^1$ satisfying \eqref{sub_o1} and \eqref{sub_o3} (note that either the first or the second member of \eqref{sub_o1} is trivially zero if $\beta < 1$).
By direct calculations, one sees that, for $\beta > 0$,
\begin{equation}
\Phi_{|\text{span}\{(\nabla \phi,\nabla\psi), (i\phi,i\psi)\}} = 0, \text{ if } \beta < 1, \quad
\Phi_{|\text{span}\{(\nabla \phi,\nabla\psi), (i\phi,0), (0,i\psi)\}} = 0, \text{ if } \beta > 1,
\end{equation}
and
\begin{equation}\label{sub_Phi_W_neg}
{\Phi(\phi,\psi) = -2P(\phi,\psi) < 0.}
\end{equation}
Next lemma shows the coercivity property of $\Phi$ on $G^\perp\cup\tilde{G}^\perp$:
\begin{lemma}\label{lem_coerc}
There exists a constant $c > 0$ such that, for any $(f,g) \in G^\perp\cup\tilde{G}^\perp$
\begin{equation}\label{Phi_coerc}
\Phi(f,g) \geq c\|(f,g)\|_{H^1 \times H^1}^2.
\end{equation}
\end{lemma}
\begin{proof}
{{We also give just a sketch of the proof here.} From the proof of Lemma \ref{spectrum_L}, the relative compactness of the operator $K$ implies that the point spectrum of $i\mathcal{L}$ can only accumulate at $1$. Therefore, only a finite number of eigenvalues (counted with multiplicity) lie in the interval, say, $(-\infty,\tfrac{1}{2}]$. The proof also shows that the first eigenvalue of $i\mathcal{L}$ is negative, and that the second one is zero and has multiplicity $4$ in the case $\beta < 1$, corresponding to $(i\phi,i\psi)$ and $(\partial_k\phi, \partial_k \psi)$, $1\leq k \leq 3$, and multiplicity $5$ in the case $\beta > 1$, corresponding to $(i\phi,0)$, $(0,i\psi)$ and $(\partial_k\phi, \partial_k \psi)$, $1\leq k \leq 3$. The third one then must be positive, implying that $\Phi$ is coercive on $G^{\perp}$. The coercivity on $\tilde{G}^{\perp}$ follows from the index being independent of the basis, from $B(\mathcal{Y}_+,\mathcal{Y}_-) \neq 0$ and from a dimensional counting argument. }
\end{proof}
\section{Variational characterization of the ground state}\label{Sec4}
The main goal of this section is to give a variational characterization of the ground states. The results here show which functions can lie at the mass-energy threshold and have kinetic energy close to the one of the ground states. This is an essential step towards the modulation theory developed in the following section. We remark that, differently from the scalar case, the ground state here may fail to be unique, and the statements of the propositions below must account for this multiplicity.
\subsection{Bubble decomposition adapted to Gagliardo-Nirenberg-Sobolev for systems of NLS equations}
We first make use of the following \textit{bubble decomposition}, adapted to systems of equations, as to use the same translation parameter in both coordinates. The proof is analogous to the scalar case, to which we refer the reader to \cites{HK, KV_Clay}. A similar decomposition, although adapted to the linear Schr\"odinger evolution, can be found in \cite{FP}.
\begin{prop}\label{bubble_decomp} Let $(f_n,g_n)$ be a bounded sequence in $H^1 \times H^1$. There there exist $J^* \in \{0,1,2,\cdots \}$ $\cup \{ \infty\}$, $\{\phi^j,\psi^j\}_{j=1}^{J^*} \subset H^1 \times H^1$ and $\{x^j_n\}_{j=1}^{J^*}\subset \mathbb R^N$ so that, along a subsequence in $n$, one can write
\begin{align}
f_n = \sum_{j=1}^{J}\phi^j(x-x_n^j) + r_n^J\\
g_n = \sum_{j=1}^{J}\psi^j(x-x_n^j) + \tilde{r}_n^J,
\end{align}
for all $1 \leq J \leq J^*$, where
\allowdisplaybreaks
\begin{align}
\limsup_{J \to J^*} \limsup_n \left(\|r^J_n\|_{L^4} +\|\tilde{r}^J_n\|_{L^4}\right) = 0,\\
\sup_{J } \limsup_n \left|\|f_n\|^2_{H^1}-\left(\sum_{j=1}^J \|\phi^j\|_{H^1}^2 + \|r_n^J\|_{H^1}^2\right)\right| = 0,\\
\sup_{J } \limsup_n\left|\|g_n\|^2_{H^1}-\left(\sum_{j=1}^J \|\psi^j\|_{H^1}^2 + \|\tilde{r}_n^J\|_{H^1}^2\right)\right| = 0,\\
\limsup_{J \to J^*} \limsup_n\left|\|f_n\|^4_{L^4}-\left(\sum_{j=1}^J \|\phi^j\|_{L^4}^4 \right)\right| = 0,\\
\limsup_{J \to J^*} \limsup_n\left|\|g_n\|^4_{L^4}-\left(\sum_{j=1}^J \|\psi^j\|_{L^4}^4 \right)\right| = 0.
\end{align}
Moreover, if $j \neq k$, then $|x_n^j-x_n^k| \to +\infty$. If $J^*$ is finite, our notation reads $\displaystyle\limsup_{J \to J^*}a_J := a_{J^*}$.
\end{prop}
\begin{re} Note that we have the same translation parameters $x_n^j$ for both $\phi^j$ and $\psi^j$. That implies
\begin{equation}
\limsup_{J \to J^*} \limsup_n\left|P(f_n,g_n) - \sum_{j=1}^J P(\phi^j,\psi^j) \right| = 0.
\end{equation}
\end{re}
We now make use of the decomposition above to establish a variational characterization of the ground states.
\begin{prop}\label{prop_mod_1} Let $(f_n,g_n)$ be a sequence in $H^1 \times H^1$ such that $M(f_n,g_n) = M(\phi,\psi)$ and $E(f_n,g_n) = E(\phi,\psi)$, where $(\phi,\psi)$ is any ground state to \eqref{sys_NLS}. If
\begin{equation}
K(f_n,g_n) \to K(\phi,\psi),
\end{equation}
then, up to a subsequence, there exist $\theta_0, \theta_1 \in \mathbb{R}/2\pi \mathbb{Z}$ and $\{x_n\} \subset \mathbb R^N$ such that
\begin{equation}\label{mod_close_H1}
\min_{(\phi,\psi)\in \mathcal{G}}\left\|\left(e^{i\theta_0}f_n(\cdot-x_n),e^{i\theta_1}g_n(\cdot-x_n)\right) - (\phi,\psi)\right\|_{H^1 \times H^1} \to 0.
\end{equation}
\end{prop}
\begin{proof} If \eqref{mod_close_H1} does not hold for any choice of $\theta_0$ and $\{x_n\}$, passing to a subsequence, if necessary, we apply the bubble decomposition to write, as in Propostion \ref{bubble_decomp},
\begin{align}
f_n = \sum_{j=1}^{J}\phi^j(x-x_n^j) + r_n^J\\
g_n = \sum_{j=1}^{J}\psi^j(x-x_n^j) + \tilde{r}_n^J.
\end{align}
Using the fact that $E(f_n,g_n) = E(\phi,\psi)$, we deduce
\begin{equation}\label{bubble_modulation}
P(f_n,g_n) = 2K(f_n,g_n)-4E(f_n,g_n)\to 2K(\phi,\psi)-4E(\phi,\psi) = P(\phi,\psi).
\end{equation}
By the profile decoupling, this means
\begin{equation}
\sum_{j=1}^{J^*}P(\phi^j,\psi^j) = P(\phi,\psi).
\end{equation}
On the other hand, by the $H^1$ decoupling, for all $J$,
\begin{align}
M(\phi^k,\psi^k) \leq \sum_{j=1}^J M(\phi^j,\psi^j) &\leq M(\phi,\psi), \text{ for } k \leq J,
\end{align}
and
\begin{align}
\sum_{j=1}^J K(\phi^j,\psi^j) &\leq K(\phi,\psi),
\end{align}
which implies
\begin{align}
\sup_{J} M(\phi^k,\psi^k) \leq M(\phi,\psi) \quad \mbox{and} \quad \sum_{j=1}^{J^*} K(\phi^j,\psi^j) \leq K(\phi,\psi).
\end{align}
Therefore, by the sharp Gagliardo-Nirenberg inequality,
\begin{equation}\label{ineq_1}
P(\phi,\psi) = \sum_{j=1}^{J^*}P(\phi^j,\psi^j) \leq c_{GN}\sum_{j=1}^{J^*} M(\phi^j,\psi^j)^{\frac{1}{2}}K(\phi^j, \psi^j)^\frac{3}{2} \leq c_{GN}M(\phi,\psi)^{\frac{1}{2}}\sum_{j=1}^{J^*} K(\phi^j, \psi^j)^\frac{3}{2}.
\end{equation}
Since
\begin{equation}\label{ineq_2}
\sum_{j=1}^{J^*} K(\phi^j, \psi^j)^\frac{3}{2} \leq \left[\sum_{j=1}^{J^*} K(\phi^j, \psi^j)\right]^\frac{3}{2} \leq K(\phi,\psi)^\frac{3}{2},
\end{equation}
the uniqueness up to symmetries of the set of minimizers of the sharp Gagliardo-Nirenberg inequality ensures that all the inequalities in \eqref{ineq_1} and \eqref{ineq_2} are equalities, and also implies that $J^*\leq1$, otherwise the equality in \eqref{ineq_2} cannot hold. The case $J^*=0$ is precluded since $P(\phi,\psi)\neq 0$.
Therefore, up to constant phase and translation, $\phi^1 = \phi$, $\psi^1$ = $\psi$ for some ground state $(\phi,\psi)$. The decoupling in \eqref{bubble_modulation} then ensures $\|(r_n^1,\tilde{r}_n^1)\|_{H^1 \times H^1} \to 0$. We have thus found $\tilde{\theta}_0, \tilde{\theta}_1$ and $\{\tilde{x}_n\}$ such that
\begin{equation}
\min_{(\phi,\psi)\in \mathcal{G}}\left\|\left(e^{i\tilde{\theta}_0}f_n(\cdot-\tilde{x}_n),e^{i\tilde{\theta}_1}g_n(\cdot-\tilde{x}_n)\right) - (\phi,\psi)\right\|_{H^1 \times H^1} \to 0,
\end{equation}
contradicting our first assumption that \eqref{mod_close_H1} does not hold.
\end{proof}
We now define the quantity
\begin{equation}\label{def_delta}
\delta(f,g) = |K(f,g) -K(\phi,\psi)|.
\end{equation}
and note that Proposition \ref{prop_mod_1} gives:
\begin{cor}\label{modulation_quant_1}
If $M(f,g) = M(\phi,\psi)$ and $E(f,g) = E(\phi,\psi)$, then
\begin{equation}
\inf_{\theta_0, \theta_1,y} \min_{(\phi,\psi)\in \mathcal{G}} \left\|\left(e^{i\theta_0}f(\cdot-y),e^{i\theta_1}g(\cdot-y)\right) - (\phi,\psi)\right\|_{H^1 \times H^1} <\varepsilon(\delta(f,g)),
\end{equation}
where $\varepsilon(d) \to 0$ as $d \to 0$.
\end{cor}
\section{Modulation theory}\label{Sec5}
We are now able to construct and refine the modulation theory for the system \eqref{sys_NLS}. Our first result shows that, on connected time intervals, the ground state given by the variational characterization must remain the same.
To abbreviate the notation, if $I \subset \mathbb R$ and $(u,v):I \to H^1\times H^1$, we often write $\delta(t) = \delta(u(t),v(t))$ for $t \in I$. We then have the following time-dependent version of modulation.
\begin{cor}\label{cor:connected_modulation} There exists $\delta_0>0$ such that if $(u,v): I \to H^1 \times H^1$ is a continuous curve on an interval $I = (a,b)$, $M(u(t),v(t)) = M(\phi,\psi)$, $E(u(t),v(t)) = E(\phi,\psi)$ and $\delta(t) <\delta_0$ for all $t \in I$, then there exist $(\phi,\psi)\in\mathcal{G}$, and functions $\theta_0,\theta_1: I \to \mathbb{R}/2\pi\mathbb Z$ and $x_0: I \to \mathbb{R}^3$ such that, for all $t \in I$,
\begin{equation}\label{modulation_param_1}
\left\|\left(e^{i\theta_0(t)}u(\cdot-x_0(t)),e^{i\theta_1(t)}v(\cdot-x_0(t))\right) - (\phi,\psi)\right\|_{H^1 \times H^1} < \varepsilon(\delta(t)),
\end{equation}
where $\varepsilon(d) \to 0$ as $d \to 0$.
\end{cor}
\begin{proof}
We first note that the manifolds generated by the group of symmetries acting on the ground states are at a positive distance from each other, since all the ground states are non-negative and radial. That is,
\begin{equation}
\inf_{\substack{x \in \mathbb R^3\\ \theta_0, \theta_1 \in \mathbb{R}/2\pi\mathbb Z}}\min_{\substack{(\phi,\psi)\in \mathcal{G}\\ (\tilde\phi,\tilde\psi)\in \mathcal{G}\\{(\phi,\psi)\neq (\tilde\phi,\tilde\psi)}}}\left\|\left(e^{i\theta_0}\phi(\cdot-x),e^{i\theta_1}\psi(\cdot-x)\right) - (\tilde \phi,\tilde \psi)\right\|_{H^1 \times H^1} > 0.
\end{equation}
This implies that the choice of ground state in \eqref{modulation_param_1} is unique, if $\delta_0>0$ is chosen sufficiently small. We then apply Corollary \ref{modulation_quant_1} to obtain $\theta_0(t)$, $\theta_1(t)$ and $x_0(t)$ for every $t \in I$.
\end{proof}
\begin{re} In the case $0< \beta < 1$, if $(\phi,\psi) = (\varphi,0)$, one can choose $\theta_1 \equiv 0$, since $v$ itself is small in the $H^1$ norm. The similar choice $\theta_0 \equiv 0$ can be made in the case $(\phi,\psi) = (0,\varphi)$.
\end{re}
We now exploit the coercivity of the linearized operator to modify the modulation parameters in order to get control on their size depending on $\delta(u(t),v(t))$.
\subsection{Modulation with orthogonality}
\begin{prop}\label{prop_mod_ort}
Let $\delta_0 >0$ and $I_0$ be the set
\begin{equation}
I_0 = \{t : \delta(t)< \delta_0\}.
\end{equation}
Then, for every connected interval $J \subset I_0$, there exist $(\phi,\psi)\in \mathcal{G}$, $\theta, \tilde\theta: J \to \mathbb{R}/2\pi\mathbb Z$, $x: J \to \mathbb{R}^3$, $\alpha: J \to \mathbb{R}$ and $(h,k) : J \to H^1 \times H^1 $ such that, for all $t \in J$,
\begin{equation}
\left\|(u(t),v(t))-\left[(1+\alpha(t))\left\{e^{i\theta(t)}\phi(\cdot-x(t)),e^{i\tilde\theta(t)}\psi(\cdot-x(t))\right\}+(h(t),k(t))\right]\right\|_{H^1 \times H^1} < \epsilon(\delta(t)).
\end{equation}
Moreover, in the case $0<\beta<1$, one can choose $\tilde\theta \equiv 0$ if $(\phi, \psi) = (\varphi,0)$ and $\theta \equiv 0$ if $(\phi,\psi)=(0,\varphi)$.
\end{prop}
\begin{proof}
To prove Proposition \ref{prop_mod_ort}, we first make use of the Implicit Function Theorem to modify $\theta_0$ and $x_0$ in order to impose suitable orthogonality conditions. Then, we can use the coercivity of the quadratic form $\Phi$ to obtain bounds on the derivatives of the parameters.
Given a connected component $J \subset I_0$, consider the corresponding $\theta_0$, $\theta_1$, $x_0$ and $(\phi,\psi)$ given by Corollary \ref{cor:connected_modulation}. In the case $0<\beta < 1$, if $(\phi,\psi) = (\varphi, 0)$, define
\begin{align}
\Omega &: H^1 \times \mathbb R/2\pi \mathbb Z \times \mathbb R^3 \to \mathbb R^4,\\
\Omega(u,\theta,x) &= \begin{bmatrix}
\Im (u,e^{i\theta}\varphi(\cdot-x))_{L^2}\\
\Re (u,e^{i\theta}\partial_{x_1}\varphi(\cdot-x))_{L^2 }\\
\Re (u,e^{i\theta}\partial_{x_2}\varphi(\cdot-x))_{L^2 }\\
\Re (u,e^{i\theta}\partial_{x_3}\varphi(\cdot-x))_{L^2 }
\end{bmatrix}.
\end{align}
For all $t \in J$, note that
\begin{equation}
\Omega(e^{i\theta_0(t)}\phi(\cdot-x_0(t)),\theta_0(t),x_0(t)) = 0
\end{equation}
and
\begin{equation}
\det\frac{\partial \Omega}{\partial{(\theta,x)}}\big|_{(e^{i\theta_0(t)}\varphi(\cdot-x_0(t)),\theta_0(t),x_0(t))} = -\left(\int \phi^2\right)\left(\displaystyle\prod_{k=1}^3\int |\partial_{x_k}\varphi|^2\right)\neq 0.
\end{equation}
Note that the right-hand side of the last equations is independent of $t$. Therefore, there exist balls $U_t \subset H^1 $, $V_t\subset \mathbb R/2\pi \mathbb Z \times \mathbb R^3 $ (with diameter bounded below uniformly on $t \in J$) and $\xi_t:U_t \to V_t$ such that for all $t\in J$, $e^{i\theta_0(t)}\varphi(\cdot-x_0(t)) \in U_t$, $(\theta_0(t),x_0(t))\in V_t$, and $\Omega(u,\xi_t(u,v)) = 0$ for all $u \in U_t$. By choosing a smaller $\delta_0>0$, if necessary, Corollary \ref{cor:connected_modulation} ensures $u(t)\in U_t$ for all $t \in J$. Hence, defining $(\theta(t),x(t)) = \xi_t(u(t))$, we have, for all $t$,
\begin{equation}
\begin{bmatrix}
\Im (u(t),e^{i\theta(t)}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_1}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_2}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_3}\varphi(\cdot-x(t)))_{L^2}\\
\end{bmatrix} = 0.
\end{equation}
Now write
\begin{equation}\label{mod_decomposition}
(e^{-i\theta(t)}u(x+x(t),t),v(x,t)) = (1+\alpha(t)) (\varphi,0)+ (h(x,t),k(x,t)),
\end{equation}
where
\begin{equation}
\alpha(t) := \frac{ \Re\displaystyle\int e^{-i\theta(t)}u(x+x(t),t) \Delta\varphi \, dx}{K(\varphi,0)}-1
\end{equation}
is chosen as to make $(h,k) \in G^\perp$. In this case, we can take $\tilde\theta \equiv 0$. The case $(\phi,\psi) = (0,\varphi)$ is handled analogously.
In the case $\beta>1$, we recall that the ground state is given by $((1+\beta)^{-1/2}\varphi,(1+\beta)^{-1/2}\varphi)$. Since we do not have a semi-trivial ground state, we take advantage of both phase symmetries and define
\begin{align}
\Omega &: H^1 \times H^1\times \mathbb R/2\pi \mathbb Z \times \mathbb R/2\pi \mathbb Z \times \mathbb R^3 \to \mathbb R^5,\\
\Omega((u,v),\theta, \tilde\theta,x) &= \begin{bmatrix}
\Im (u,e^{i\theta}\varphi(\cdot-x))_{L^2}\\
\Im (v,e^{i\tilde\theta}\varphi(\cdot-x))_{L^2}\\
\Re (u,e^{i\theta}\partial_{x_1}\varphi(\cdot-x))_{L^2 }+ \Re (v,e^{i\tilde\theta}\partial_{x_1}\varphi(\cdot-x))_{L^2 }\\
\Re (u,e^{i\theta}\partial_{x_2}\varphi(\cdot-x))_{L^2 }+ \Re (v,e^{i\tilde\theta}\partial_{x_2}\varphi(\cdot-x))_{L^2 }\\
\Re (u,e^{i\theta}\partial_{x_3}\varphi(\cdot-x))_{L^2 }+ \Re (v,e^{i\tilde\theta}\partial_{x_3}\varphi(\cdot-x))_{L^2 }\\
\end{bmatrix}.
\end{align}
In the same fashion, since $\det\frac{\partial \Omega}{\partial{(\theta,x)}}\big|_{((e^{i\theta_0(t)}\varphi(\cdot-x_0(t)),e^{i\theta_1(t)}\varphi(\cdot-x_0(t))),\theta_0(t), \theta_1(t),x_0(t))} \neq 0$, we obtain $(\theta(t), \tilde\theta(t),x(t))\in \mathbb R/2\pi \mathbb Z \times \mathbb R/2\pi \mathbb Z \times \mathbb R^3 $ such that
\begin{equation}
\begin{bmatrix}
\Im (u(t),e^{i\theta(t)}\varphi(\cdot-x(t)))_{L^2}\\
\Im (v(t),e^{i\tilde\theta(t)}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_1}\varphi(\cdot-x(t)))_{L^2}+\Re (v(t),e^{i\tilde\theta(t)}\partial_{x_1}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_2}\varphi(\cdot-x(t)))_{L^2}+\Re (v(t),e^{i\tilde\theta(t)}\partial_{x_2}\varphi(\cdot-x(t)))_{L^2}\\
\Re (u(t),e^{i\theta(t)}\partial_{x_3}\varphi(\cdot-x(t)))_{L^2}+\Re (v(t),e^{i\tilde\theta(t)}\partial_{x_3}\varphi(\cdot-x(t)))_{L^2}\\
\end{bmatrix} = 0.
\end{equation}
We then write
\begin{equation}\label{mod_decomposition_2}
(e^{-i\theta(t)}u(x+x(t),t),e^{-i\tilde\theta(t)}v(x+x(t),t)) = (1+\beta)^{-1/2}(1+\alpha(t)) (\varphi,\varphi)+ (h(x,t),k(x,t)),
\end{equation}
where
\begin{equation}
\alpha(t) := \frac{ \Re\displaystyle\int e^{-i\theta(t)}u(x+x(t),t) \Delta\varphi + e^{-i\tilde\theta(t)}v(x+x(t),t) \Delta\varphi \, dx}{K(\varphi,\varphi)}-1.
\end{equation}
\end{proof}
We then have the following bounds on the parameters:
\begin{prop} Let $(u,v)$ be a solution to \eqref{sys_NLS} satisfying $M(u,v) = M(\phi,\psi)$ and $E(u,v) = E(\phi,\psi)$. Then, taking a smaller $\delta_0$, if necessary, one has, for $t \in I_0$:
\begin{equation}\label{mod_approx_small}
|\alpha(t)| \approx \left| \int \phi h_1(t) + \psi k_1(t) \right| \approx \|(h(t),k(t))\|_{H^1 \times H^1} \approx \delta(t).
\end{equation}
One also has
\begin{equation}\label{mod_lesssim_small}
|\alpha'(t)| + |x'(t)| + \|\phi\|_{L^2}^2|\theta'(t)-1|+\|\psi\|_{L^2}^2|\tilde\theta'(t)-1| \lesssim \delta(t).
\end{equation}
\end{prop}
\begin{proof}
Let $\tilde{\delta} = \delta + |\alpha|+ \|(h,k)\|_{H^1 \times H^1}$. The relation $M(\phi + \alpha\phi + h,\psi + \alpha\psi + k) = M(\phi,\psi)$ gives
\begin{equation}\label{mod_small_1}
\left||\alpha|-\frac{1}{M(\phi,\psi)}\left|\int \phi h_1 + \psi k_1\right| \, \right| = O(\tilde{\delta}^2).
\end{equation}
Moreover, the orthogonality condition \eqref{sub_o1} gives
\begin{equation}\label{mod_small_2}
K(\phi + \alpha\phi + h,\psi + \alpha\psi + k)-K(\phi,\psi) = 2\alpha K(\phi,\psi)+\alpha^2 K(\phi,\psi) + K(h,k).
\end{equation}
Thus, by the definition of $\delta$,
\begin{equation}\label{mod_small_3}
\delta \lesssim |\alpha| +\tilde{\delta}^2 \lesssim \delta +\tilde{\delta}^2.
\end{equation}
Note that the orthogonality condition \eqref{sub_o1} gives
\begin{equation}
\int \phi h_1 + \psi k_1 = - \int (\phi^2+\beta \psi^2)\phi h_1 + (\psi^2+\beta \phi^2)\psi k_1.
\end{equation}
Therefore, $B((\phi,\psi),(h_1,k_1)) = - \displaystyle\int \phi h_1 + \psi k_1 $. Now, since the relations $M(\phi + \alpha\phi + h,\psi + \alpha\psi + k) = M(\phi,\psi)$ and $E(\phi+\alpha \phi + h,\psi+\alpha \phi + k) = E(\phi, \psi)$ give
\begin{equation}
\Phi(\alpha \phi +h, \alpha \psi +k) \lesssim |\alpha|^3 + \|(h,k)\|_{H^1\times H^1}^3,
\end{equation}
we have
\begin{equation}\label{mod_small_4}
\alpha^2 \Phi(\phi,\psi) + 2 \alpha B((\phi,\psi),(h_1,k_1))+ \Phi(h,k) = \Phi(\alpha \phi +h, \alpha \psi +k) \lesssim \tilde{\delta}^3,
\end{equation}
or
\begin{equation}
\Phi(h,k) \lesssim |\alpha|^2 + \tilde{\delta}^3.
\end{equation}
Finally, coercivity on $G^\perp$ implies $\Phi(h,k) \approx \|(h,k)\|_{H^1 \times H^1}^2$, showing that
\begin{equation}\label{mod_small_5}
\|(h,k)\|_{H^1 \times H^1} \lesssim |\alpha| + \tilde{\delta}^{\frac{3}{2}}.
\end{equation}
Equations \eqref{mod_small_1}, \eqref{mod_small_2} and \eqref{mod_small_5} give $\tilde{\delta}\lesssim |\alpha|$, which in turn shows that \eqref{mod_small_1}-\eqref{mod_small_5} imply \eqref{mod_approx_small}. We not turn to the proof of \eqref{mod_lesssim_small}.
Let $\delta^* = \delta + |\alpha'|+|x'|+|\theta'-1|+|\tilde\theta'-1|$. We write the equations for $h$ and $k$, given the decomposition \eqref{mod_decomposition}, as
\begin{equation}
\begin{cases}
i \partial_t h + \Delta h +i\alpha' \phi - (\theta'-1) \phi - i \nabla \phi \cdot x' = O( \delta + \delta \delta^*)\\
i \partial_t k + \Delta h +i\alpha' \psi - (\tilde\theta'-1) \psi - i \nabla \psi \cdot x' = O( \delta + \delta \delta^*)
\end{cases}.
\end{equation}
Projecting the pair of equations above against $(\phi,0)$, $(0,\psi)$, $(\partial_j \phi, \partial_j \psi)$, $1 \leq j \leq 3$, $(\Delta \phi, \Delta \psi)$ and integrating by parts yields
\begin{equation}
|\alpha'|+|x'|+\|\phi\|_{L^2}^2|\theta'(t)-1|+\|\psi\|_{L^2}^2|\tilde\theta'(t)-1|\lesssim \delta + \delta \delta^*,
\end{equation}
which implies \eqref{mod_lesssim_small}.
\end{proof}
The following lemma gives a simple criteria to show the convergence of the modulation parameters. It reflects a strong modulational stability around the ground states.
\begin{lemma}\label{const_modul} Let $(u,v)$ be a global solution to \eqref{sys_NLS} such that $M(u,v) = M(\phi,\psi)$ and $E(u,v) = E(\phi,\psi)$. If
\begin{equation}\label{delta_int_exp}
\int_0^\infty \delta(s) \, ds < +\infty,
\end{equation}
then there exist $\theta_0$, $x_0$ and $(\phi_0,\psi_0)$ such that
\begin{equation}\label{const_mod_param}
\|(e^{-i\theta_0}u(x+x_0,t),e^{-i\theta_1}v(x+x_0,t) - (e^{it}\phi_0,e^{it}\psi_0)\|_{H^1 \times H^1} \lesssim \int_t^\infty \delta(s) \, ds.
\end{equation}
In other words, up to constant symmetries of the NLS system \eqref{sys_NLS}, the flow $(u(t),v(t))$ approaches the standing wave $(e^{it}\phi_0,e^{it}\psi_0)$ as $t \to +\infty$.
\begin{proof}
We first show that $|\alpha(t)| \approx\delta(t) \to 0$ as $t \to +\infty$. If not, then there exist $\eta>0$ and two unbounded sequences of times, $\{t_n\}$ and $\{t_n'\}$, such that $t_n < t_n'$ for all $n$, $\delta(t) < \delta_0$ for $t \in [t_n,t_n']$, $\delta(t_n) \to 0$ and $\delta(t_n') = \eta$. For all $n$, $\alpha(t)$ is defined for $t \in [t_n,t_n']$ and, by
\eqref{mod_lesssim_small} and \eqref{delta_int_exp}, it satisfies
\begin{equation}
|\alpha(t_n')-\alpha(t_n)| \leq \int_{t_n}^{t_n'} |\alpha'(t)| \, dt \lesssim \int_{t_n}^{+\infty} \delta(t) \, dt\to 0,
\end{equation}
which contradicts $\delta(t_n) < \eta/2$ and $\delta(t_n') = \eta $ for all $n$.
Therefore, if $t_0>0$ is large enough, then $\delta(t) < \delta_0$ for $t> t_0$, so that the modulation parameters $\alpha(t)$, $\theta(t)$, $\tilde\theta(t)$ and $x(t)$, as well as the corresponding ground state $(\phi_0,\psi_0)$, are (uniquely) defined for any $t>t_0$ and satisfy
\begin{equation}
d(t) \approx |\alpha(t)| \leq \int_t^{+\infty} |\alpha'(s)| \, ds \lesssim \int_t^{+\infty} \delta(s) \, ds,
\end{equation}
and, for $\beta >1$,
\begin{align}
\int_{t_0}^{+\infty}|\theta'(t)-1|+|\tilde\theta'(t)-1| + |x'(t)| \, dt \lesssim \int_{t_0}^{+\infty} \delta(t) \, ds < +\infty.
\end{align}
This means that $\theta(t)-t$, $\tilde\theta(t)-t$ (with the respective changes for $\theta$ or $\tilde\theta$ in the case $0<\beta<1$) and $x(t)$ have limits, say, $\theta_0$, $\theta_1$ and $x_0$ as $t \to +\infty$. By continuity of the flow, we get \eqref{const_mod_param}.
\end{proof}
\end{lemma}
\section{Construction of special solutions}\label{Sec6}
In this section, we prove the existence and uniqueness of special solutions to the NLS system \eqref{sys_NLS} at the mass-energy threshold that exponentially approach the standing waves $(e^{it}\phi,e^{it}\psi)$.
\subsection{Preliminary estimates}
We start with some estimates for the linearized equation.
\begin{lemma}\label{prel_estimates} For any ground state $Q=(\phi,\psi)$ and any time interval $I$ such that $|I|\leq 1$, we have
\begin{itemize}
\item $\|\langle\nabla\rangle L(w)\|_{S'(L^2,I)\times S'(L^2,I)} \lesssim |I|^{\frac{1}{2}}\|\langle\nabla\rangle w\|_{S(L^2,I)\times S(L^2,I)}$,
\item $\|\langle\nabla\rangle (R(v+w)-R(v+\tilde{w}))\|_{S'(L^2,I)\times S'(L^2,I)}$
$\quad\quad\lesssim \left[\|\langle\nabla\rangle v\|_{S(L^2,I)\times S(L^2,I)}
+
\|\langle\nabla\rangle w\|_{S(L^2,I)\times S(L^2,I)}
+
\|\langle\nabla\rangle \tilde{w}\|_{S(L^2,I)\times S(L^2,I)}]\right.$
$
\,\quad\quad+\left.\|\langle\nabla\rangle v\|_{S(L^2,I)\times S(L^2,I)}^2
+
\|\langle\nabla\rangle w\|_{S(L^2,I)\times S(L^2,I)}^2
+
\|\langle\nabla\rangle \tilde{w}\|_{S(L^2,I)\times S(L^2,I)}^2\right]\|\langle\nabla\rangle(w-\tilde{w})\|.
$
\end{itemize}
where $L$ and $R$ were defined in Definition \ref{defilinearop}.
\end{lemma}
\begin{proof} By the explicit forms of $L$ and $R$, the lemma follows immediately from H\"older and Sobolev's inequalities, since, for any $f,g,h$,
\begin{align}
\|fgh\|_{L^2_I L^{\frac{6}{5}}_x} &\lesssim |I|^{\frac{1}{2}}\|\nabla f\|_{L^\infty_I L^{2}_x}
\|\nabla g\|_{L^\infty_I L^{2}_x}
\|h\|_{L^\infty_I L^{2}_x}, \text{ and}\\
\|fgh\|_{L^2_I L^{\frac{6}{5}}_x} &\lesssim \||\nabla|^{\frac{1}{2}} f\|_{L^2_I L^{4}_x}
\||\nabla|^{\frac{1}{2}} g\|_{L^2_I L^{4}_x}
\|h\|_{L^\infty_I L^{2}_x}.
\end{align}
\end{proof}
\subsection{Spectral decay and regularity} Let $(F,G) \in \mathcal{S}(\mathbb R^3) \times \mathcal{S}(\mathbb R^3)$ and $\lambda \in \mathbb R$. If, given a ground state $Q=(\phi,\psi)$, $(f,g) \in H^2(\mathbb{R}^3) \times H^2(\mathbb{R}^3)$ satisfies
\begin{equation}\label{spectral_elliptic}
\mathcal{L}(f,g) - \lambda (f,g) = (F,G),
\end{equation}
then $(f,g) \in \mathcal{S}(\mathbb R^3) \times \mathcal{S}(\mathbb R^3)$.
\begin{proof}
Defining $A$ and $B$ as
\begin{align}
L_R = (1-\Delta)I - A,\\
L_I = (1-\Delta)I - B,
\end{align}
we can rewrite \eqref{spectral_elliptic} more explicitly, obtaining
\begin{align}\label{full_eq_spectral_elliptic}
\left((1-\Delta)^2+\lambda^2\right)\begin{pmatrix}
f_1 \\
g_1
\end{pmatrix}
= B L_R\begin{pmatrix}
f_1 \\
g_1
\end{pmatrix} + L_I\left\{A\begin{pmatrix}
f_1 \\
g_1
\end{pmatrix}\right\}-BA\begin{pmatrix}
f_1 \\
g_1
\end{pmatrix}.
\end{align}
with a similar equation for $(f_2,g_2)$. By induction, it is clear that $f,g \in H^s(\mathbb R^3)$, for any $s \geq 0$. As for the decay, let $\chi \in C^\infty_c(\mathbb{R}^3)$ and $\chi_R (x) = \chi(x/R)$, for $R \geq 1$. Let also $\tilde{\chi}\in C^\infty_c(\mathbb{R}^3)$ be such that $\tilde{\chi} \equiv 1$ on the support of $\chi$. We will show that, for any such $\chi$ and any non-negative integers $s$, $l$, one has
\begin{equation}\label{Hs_decay_ind}
\|\chi_R f\|_{H^s} + \|\chi_R g\|_{H^s} \lesssim_{\chi,s,l} \frac{1}{R^l}.
\end{equation}
It is clear that \eqref{Hs_decay_ind} holds for $(s,l) = (3,0)$. Now, note that
\begin{align}
\|\chi_R f_1\|_{H^{s+1}} + \|\chi_R g_1\|_{H^{s+1}} &\approx \| \left((1-\Delta)^2+\lambda^2\right)\chi_R f_1\|_{H^{s-3}}
+\|\left((1-\Delta)^2+\lambda^2\right)\chi_R g_1\|_{H^{s-3}}
\\&\lesssim
\|\chi_R \left((1-\Delta)^2+\lambda^2\right) \tilde{\chi}_R f_1\|_{H^{s-3}}
+
\|\chi_R \left((1-\Delta)^2+\lambda^2\right) \tilde{\chi}_R g_1\|_{H^{s-3}} \\
&\quad+
\|[ (1-\Delta)^2+\lambda^2;\chi_R] \tilde{\chi}_R f_1\|_{H^{s-3}}
+ \|[ (1-\Delta)^2+\lambda^2;\chi_R] \tilde{\chi}_R g_1\|_{H^{s-3}}.
\end{align}
For the first two terms on the right-hand side, the equation \eqref{full_eq_spectral_elliptic} and the (exponential) decay of the ground state and its derivatives give
\begin{align}
\|\chi_R \hspace{-2pt}\left((1-\Delta)^2+\lambda^2\right)\hspace{-2pt} \tilde{\chi}_R f_1\|_{H^{s-3}}
+
\|\chi_R \hspace{-2pt}\left((1-\Delta)^2+\lambda^2\right) \hspace{-2pt}\tilde{\chi}_R g_1\|_{H^{s-3}}
&\lesssim \frac{1}{R} \|\tilde{\chi}_R f_1\|_{H^{s-1}}
+
\frac{1}{R} \|\tilde{\chi}_R g_1\|_{H^{s-1}} \\
&\lesssim \frac{1}{R}\|\tilde{\chi}_R f_1\|_{H^{s}}
+
\frac{1}{R}\|\tilde{\chi}_R g_1\|_{H^{s}},
\end{align}
whilst the commutator immediately bounds the remaining terms, since an explicit calculation gives
\begin{equation}
\|[ (1-\Delta)^2+\lambda^2;\chi_R]\|_{H^s \to H^{s-3}} \lesssim
\frac{1}{R}.
\end{equation}
Thus, we have just showed that, if \eqref{Hs_decay_ind} holds for $(s,l)$, with $s\geq 3$, then it also holds for $(s+1,l+1)$, which completes the proof for $f_1$ and $g_1$. For $f_2$ and $g_2$, the argument is completely analogous and is ommited.
\end{proof}
\subsection{A family of approximate solutions}
Starting from an eigenfuction of $\mathcal{L}$, we now iteratively construct a family of approximate solutions to the linearized equation.
\begin{prop}\label{family_appr} Let $A \in \mathbb R$ and $Q=(\phi,\psi)$ be any ground state. There exists a sequence ($Z_k^A)_{l \geq 1}$ of functions in $\mathcal{S}(\mathbb R^3) \times \mathcal{S}(\mathbb R^3)$ such that $Z_1^A = A \mathcal{Y}_+$ and, if $l \geq 1$ and $\mathcal{V}_l^A = \sum_{j=1}^l e^{-je_0 t}Z_j^A$, then as $t \to +\infty$ we have
\begin{equation}\label{eq_sol_v}
\partial_t\mathcal{V}_l^A + \mathcal{LV}_l^A = R(\mathcal{V}_l^A)+O\left(e^{-\left(l+1\right)e_0t}\right) \text{ in } \mathcal{S}(\mathbb R^3)\times \mathcal{S}(\mathbb R^3).
\end{equation}
\end{prop}
\begin{proof}
The sequence is constructed inductively. We omit the index $A$ throughout this proof. Define $Z_1 = A\mathcal{Y}_+$ and note that
\begin{equation}
\partial_t \mathcal{V}_1 + \mathcal{LV}_1 -R(\mathcal{V}_1) = -R(\mathcal{V}_1).
\end{equation}
Now, since the entries of $R(f,g)$ are polynomials of degree three on $f, \overline{f},g,\overline{g}$, for any $(f,g)$, and since $\mathcal{Y}_+ \in \mathcal{S}(\mathbb R^3)$, we conclude that
\begin{equation}
\partial_t \mathcal{V}_1 + \mathcal{LV}_1 -R(\mathcal{V}_1) = O(e^{-2e_0t}).
\end{equation}
Suppose now that $\mathcal{V}_1$, $\mathcal{V}_2$, $\cdots,$ $\mathcal{V}_l$ are defined. Write
\begin{equation}\label{def_eps_l}
\epsilon_l = \partial_t \mathcal{V}_l + \mathcal{LV}_l - iR(\mathcal{V}_l)
\end{equation}
and note that
\begin{equation}
\partial_t \mathcal{V}_l = -\sum_{i=1}^l j e_0 e^{-je_0t}Z_j,
\end{equation}
which allows us to write
\begin{equation}\label{epsilon_expansion}
\epsilon_l = \sum_{i=1}^l e^{-je_0t}(-j e_0 Z_j+\mathcal{L}Z_j)-R(\mathcal{V}_l).
\end{equation}
Since $Z_j \in \mathcal{S}(\mathbb R^3)$ for all $j\leq l$, and from the explicit expression of $R$ one can rewrite the last equation as
\begin{equation}
\epsilon_l(x,t) = \sum_{i=1}^{l+1} e^{-je_0t}F_j(x) + O(e^{-e_0(l+2)t}),
\end{equation}
with $F_j \in \mathcal{S}(\mathbb R^3)$ for all $j$. Since $\epsilon_l = O(e^{-(l+1)e_0t})$, by the induction hypothesis, we conclude that $F_j = 0$ for $j \leq k$, allowing us to write
\begin{equation}
\epsilon_l(x,t) = e^{-(l+1)e_0t}F_{l+1}(x) + O(e^{-e_0(l+2)t}).
\end{equation}
Define now $Z_{l+1} = -(\mathcal{L}-(l+1)e_0)^{-1}F_{l+1} \in \mathcal{S}(\mathbb R ^3) \times \mathcal{S}(\mathbb R^3)$, which can be done since $(l+1)e_0$ does not belong to the spectrum of $\mathcal{L}$. It remains to estimate
\begin{equation}
\epsilon_{l+1} = \epsilon_l - e^{-(l+1)e_0}F_{l+1}-i(R(\mathcal{V}_{l+1})-R(\mathcal{V}_l)).
\end{equation}
But this is clear, since $\epsilon_l - e^{-(l+1)e_0}F_{l+1} = O(e^{-(l+2)e_0t})$ and the explicit expression of $R$ gives $R(\mathcal{V}_{l+1})-R(\mathcal{V}_l) = O(e^{-(l+2)e_0t})$.
\end{proof}
\subsection{Fixed-point argument near an approximate solutions}\label{def_l_0}
We now want to find an exact solution to \eqref{linearized_eq} close to $\mathcal{V}_l$. Given a ground state $Q = (\phi,\psi)$ and recalling \eqref{linearized_eq_2} and \eqref{def_eps_l}, we want to solve
\begin{equation}
i\partial_t w + \Delta w - w + L(w) + i[R(\mathcal{V}_l+w)-R(\mathcal{V}_l)]-i\epsilon_l=0.
\end{equation}
We now show:
\begin{prop}\label{sub_exist_UA} Given any ground state $Q=(\phi,\psi)$, there exists $l_0 > 0$ such that for any $l \geq l_0$, there exists $t_l \geq 0$ and a solution $U^A$ to \eqref{sys_NLS} such that for $t \geq t_l$, we have
\begin{equation}\label{sub_bound_UA}
\|\langle\nabla\rangle(U^A-e^{it}Q-e^{it}\mathcal{V}_{l}^A)\|_{S'(L^2,[t,+\infty))} \leq e^{-(l+\frac{1}{2})e_0 t}.
\end{equation}
Furthermore, $U^A$ is the unique solution to the NLS system \eqref{sys_NLS} satisfying \eqref{sub_bound_UA} for large $t$. Finally, $U^A$ is independent of $l$ and satisfies for large $t$,
\begin{equation}\label{sub_bound_UA2}
\|U^A(t) - e^{it}Q - Ae^{-e_0t+it}\mathcal{Y}_+\|_{H^1} \leq e^{-2e_0 t}.
\end{equation}
\end{prop}
\begin{proof}
Given a ground state $Q = (\phi,\psi)$, we define
\begin{equation}
\mathcal{M}(w)(t) = i \int_t^{+\infty} e^{i(t-s)(\Delta-1)}\left\{L(w) + i[R(\mathcal{V}_l+w)-R(\mathcal{V}_l)] + i\epsilon_l \right\} \, ds
\end{equation}
for $w$ in the (complete) metric space $B = B(l,t_l)$ defined as
\begin{align}
B &:= \{ w \in E: \|w\|_E \leq 1\},\\
E &:= \{ w \in S(L^2,[t_l+\infty))\times S(L^2,[t_l+\infty)) : \|w\|_{E}<+\infty\},\\
\|w\|_E &:= \sup_{t \geq t_l} e^{\left(l+\frac{1}{2}\right)t}\|\langle \nabla \rangle w\|_{S(L^2,[t+\infty))\times S(L^2,[t+\infty))},
\end{align}
equipped with the metric
\begin{equation}
\rho(w,\tilde{w}) =
\sup_{t \geq t_l} e^{\left(l+\frac{1}{2}\right)e_0t}
\|w - \tilde{w}\|_E.
\end{equation}
We will show now that $\mathcal{M}$ is a contraction on $B$, if $l$ and $t_l$ are chosen to be large.
Indeed, if $w, \tilde{w} \in B$, by Strichatz's inequality,
\begin{align}
\|\langle \nabla \rangle \mathcal{M}(w)\|_{S(L^2,[t,+\infty))\times S(L^2,[t,+\infty))}
&\lesssim
\|\langle \nabla \rangle L(w)\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))}
\\&\quad+
\|\langle \nabla \rangle (R(\mathcal{V}_l+w)-R(\mathcal{V}_l))\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))}
\\&\quad+
\|\langle \nabla \rangle \epsilon_l\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))} \end{align}
and
\begin{align}
\|\langle \nabla \rangle [\mathcal{M}(w)-\mathcal{M}(\tilde{w})]\|_{S(L^2,[t,+\infty))\times S(L^2,[t,+\infty))}
&\lesssim
\|\langle \nabla \rangle L(w-\tilde{w})\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))}
\\&\hspace{-0.8cm}+
\|\langle \nabla \rangle (R(\mathcal{V}_l+w)-R(\mathcal{V}_l+\tilde{w}))\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))}.
\end{align}
By Lemma \ref{prel_estimates}, for $0< \tau < 1$, if $I^{\tau}_{j}=[t+j\tau,t+(j+1)\tau]$:
\begin{align}
\|\langle \nabla \rangle L(w)\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))}
&\leq \sum_{j=0}^\infty \|\langle \nabla \rangle L(w)\|_{S'(L^2,I^{\tau}_{j})\times S'(L^2,I^{\tau}_{j})}
\\&\lesssim \sum_{j=0}^\infty \tau^{\frac{1}{2}} \| \langle \nabla \rangle w\|_{S(L^2,I^{\tau}_{j})\times S(L^2,I^{\tau}_{j})}\\
&\lesssim \tau^{\frac{1}{2}} \sum_{j=0}^\infty e^{-\left(j+\frac{1}{2}\right)e_0(t+j\tau)}\\
&= \tau^{\frac{1}{2}} \|w\|_E e^{-\left(l+\frac{1}{2}\right)e_0t} \|w\|_E\sum_{j=0}^\infty e^{-j\left(l+\frac{1}{2}\right)e_0\tau}\\
&= e^{-\left(l+\frac{1}{2}\right)e_0t}
\frac{\tau^{\frac{1}{2}}}{1-e^{-\left(l+\frac{1}{2}\right)e_0\tau}}\|w\|_E.
\end{align}
If $l_0 := \frac{\ln 2}{e_0} \frac{1}{\tau}-\frac{1}{2}$, we have, for all $l > l_0(\tau)$,
\begin{equation}
\|\langle \nabla \rangle L(w)\|_{S'(L^2,[t,+\infty))\times S'(L^2,[t,+\infty))} \lesssim \tau^\frac{1}{2} e^{-\left(l+\frac{1}{2}\right)e_0t}\|w\|_E.
\end{equation}
Similarly, abbreviating $S(L^2,I_j^{\tau})\times S(L^2,I_j^{\tau}) = S(L^2,I_j^{\tau})^2$ and $S'(L^2,I_j^{\tau})\times S'(L^2,I_j^{\tau}) = S'(L^2,I_j^{\tau})^2$,
\begin{align}
&\|\langle \nabla \rangle (R(\mathcal{V}_l+w)-R(\mathcal{V}_l+\tilde{w}))\|_{S'(L^2,I_j^{\tau})^2}\\ &\quad\lesssim
\left[\|\langle\nabla\rangle \mathcal{V}_l\|_{S(L^2,I_j^{\tau})^2}
+
\|\langle\nabla\rangle w\|_{S(L^2,I_j^{\tau})^2}
+
\|\langle\nabla\rangle \tilde{w}\|_{S(L^2,I_j^{\tau})^2}\right.\\
&\quad\quad+\left.\|\langle\nabla\rangle \mathcal{V}_l\|_{S(L^2,I_j^{\tau})^2}^2
+
\|\langle\nabla\rangle w\|_{S(L^2,I_j^{\tau})^2}^2
+
\|\langle\nabla\rangle \tilde{w}\|_{S(L^2,I_j^{\tau})^2}^2\right]
\|\langle\nabla\rangle(w-\tilde{w})\|_{S(L^2,I_j^{\tau})^2}\\
&\quad\lesssim_l\left[e^{-e_0t} + e^{-\left(l+\frac{1}{2}\right)e_0t}(\|w\|_E+\|\tilde{w}\|_E) \right]e^{-\left(l+\frac{1}{2}\right)e_0(t+j\tau)}\|w-\tilde{w}\|_E\\
&\quad\lesssim_l e^{-\left(l+1\right)e_0t}\|w-\tilde{w}\|_E \, e^{-j\left(l+\frac{1}{2}\right)\tau},
\end{align}
we have
\begin{equation}
\|\langle \nabla \rangle (R(\mathcal{V}_l+w)-R(\mathcal{V}_l+\tilde{w}))\|_{S'(L^2,[t,+\infty))^2} \lesssim_l e^{-\left(l+1\right)e_0t}\|w-\tilde{w}\|_E.
\end{equation}
Finally, by construction,
\begin{equation}
\|\epsilon_l\|_{S'(L^2,[t,+\infty))^2} \lesssim_l e^{-(l+1)e_0t},
\end{equation}
which proves, for $t \geq t_l$, with $t_l>0$ large enough,
\begin{equation}
\|\mathcal{M}(w)\|_{E} \leq \left[C \tau^{\frac{1}{2}} + C_l e^{-\left(l+\frac{1}{2}\right)e_0 t_l}\right] \leq 1,
\end{equation}
and
\begin{equation}
\|\mathcal{M}(w)-\mathcal{M}(\tilde{w})\|_{E} \leq \left[C \tau^{\frac{1}{2}} + C_l e^{-\left(l+\frac{1}{2}\right)e_0 t_l}\right]\|w-\tilde{w}\|_E \leq \frac{1}{2}\|w-\tilde{w}\|_E.
\end{equation}
(Recall the order of choices: one first chooses a small universal $\tau>0$, then a large $l>l_0(\tau)$ and finally a large $t_l(l)$).
\end{proof}
\begin{re} We remark that the uniqueness condition still holds if, given $l>l_0$, one chooses a larger $\tilde{t}_l > t_l$. Moreover, the function $U_l := e^{it}(Q+ \mathcal{V}_l + w_l)$ is independent of $l$, since given $l'>l>l_0$, $t_{l'} > t_l$ and two solutions $w_l$ and $w_{l'}$, respectively, one has two solutions on $B(l,t_{l'})$, namely $w_l$ restricted to $t \in [t_{l'},+\infty)$ and $\tilde{w}_l := \mathcal{V}_{l'}- \mathcal{V}_{l} + w_{l'}$, which, by uniqueness of \eqref{linearized_eq_2}, must coincide on $[t_l',+\infty)$ and by uniqueness of solutions to \eqref{sys_NLS}, must also coincide on $[t_l,+\infty)$.
\end{re}
\section{Behavior of solutions at the mass-energy threshold}\label{Sec7}
Having shown the existence of different solutions at the threshold level, we classify the possible behaviors in this setting. As in the case $\mathcal{ME}(u_0,v_0)<1$, we have different behaviors depending on whether the mass-kinetic energy is high ($\mathcal{MK}(u_0,v_0)>1)$ or low ($\mathcal{MK}(u_0,v_0)<1$). The case $\mathcal{MK}(u_0,v_0) = 1$ implies that $(u,v)$ is, up to symmetries, the standing wave $(e^{it}\phi,e^{it} \psi)$.
\subsection{High kinetic energy}
We treat the solutions such that $\mathcal{ME}(u_0,v_0)=1$ and $\mathcal{MK}(u_0,v_0)>1$ first. Up to a constant rescaling, we assume $M(u_0,v_0) = M(\phi,\psi)$, $E(u_0,v_0) = E(\phi,\psi)$ and $K(u_0,v_0) > K(\phi,\psi)$. By uniqueness of the flow, this implies $K(u(t),v(t)) > K(\phi,\psi)$ for all $t$ in the maximal interval of existence of $(u,v)$. Recalling the definition of $\delta$ \eqref{def_delta}, in this case we have
\begin{equation}
\delta(t) = K(u(t),v(t))-K(\phi,\psi).
\end{equation}
This section is devoted to proving the following Lemma.
\begin{lemma}\label{conv_ground_high} Let $(u,v)$ be a solution to \eqref{sys_NLS} such that $M(u_0,v_0) = M(\phi,\psi)$, $E(u_0,v_0) = E(\phi,\psi)$ and $K(u_0,v_0)>K(\phi,\psi)$. Assume, in addition, that either $u_0$ is radial or has finite variance. Then either $(u,v)$ blows up in finite positive time, or there exist $x_0 \in \mathbb{R}^3$, $\theta_0 \in \mathbb{R}/2\pi \mathbb{Z}$, $(\phi_0,\psi_0) \in \mathcal{G}$ and $c>0$ such that
\begin{equation}
\|(u(t),v(t)) - (e^{i(\theta_0+t)}\phi_0(\cdot+x_0),e^{i(\theta_0+t)}\psi_0(\cdot+x_0))\|_{H^1 \times H^1} \lesssim e^{-ct}.
\end{equation}
Moreover, $(u,v)$ blows up in finite negative time in $H^1 \times H^1$.
\end{lemma}
\subsubsection{Radial case}
We define $a$ to be a smooth, radial function such that
\begin{equation}
a(x) = \begin{cases}
|x|^2, & |x| < R\\
0, & |x| > 3R
\end{cases}
\end{equation}
and that $\partial^2_r a(x) \leq 2$ for all $x\neq 0$, where $\partial_r a(x) = \frac{x \cdot \nabla a(x)}{|x|}$ is the radial derivative and $R \geq 1$.
We define the virial quantity
\begin{equation}
V_R(t) = \int a \left[|u(t)|^2 + |v(t)|^2\right],
\end{equation}
for which we have the identities
\begin{equation}
V_R'(t) = 2 \Im \int \nabla a \cdot (\nabla u(t) \overline{u}(t)+\nabla v(t) \overline{v}(t))
\end{equation}
and, in the case $E(u_0,v_0) = E(\phi,\psi)$,
\begin{equation}
V_R''(t) = -4\delta(t) + A_R(u(t),v(t)),
\end{equation}
where
\begin{equation}\label{def_AR}
A_R(u,v) = 2\int(\partial_r^2 a -2) \left[|\nabla u|^2+|\nabla v|^2\right] -\int(\Delta^2 a)\left[| u|^2+| v|^2\right] - \int (\Delta a-6)\left[|u|^4 + 2 \beta |uv|^2 + |v|^4\right].
\end{equation}
We now give different bounds for $A_R$, depending on $\delta$. If $\delta\geq \delta_0$, since $\partial_r^2 a -2 \leq 0$, $|\Delta^2 a| \leq \frac{1}{R^2}$ and $|\nabla a -6| \lesssim 1$, one has, by the well known radial Strauss lemma,
\begin{equation}
A_R(u,v) \leq \frac{1}{R^2}M(u,v) + \frac{1}{R^2}M(u,v)^\frac{3}{2}\left[K(\phi,\psi) + \delta\right]^\frac{1}{2} \leq \delta,
\end{equation}
if one chooses $R = R(M(u_0,v_0),\delta_0)$ large. Now, for $\delta<\delta_0$, we recall that $A_R(e^{it}\phi,e^{it}\psi) = 0$, since the corresponding $V_R$ is constant. Therefore, writing $(u,v) = (e^{it}(\phi+h),e^{it}(\psi+k))$,
\begin{align}
|A_R(u(t),v(t))| &= |A_R(h(t)+\phi,k(t)+\psi) - A_R(\phi,\psi)|
\\&\lesssim \int_{|x| \geq R} |\nabla \phi| |\nabla h(t)| +
|\nabla \psi| |\nabla k(t)|
+ |\nabla h(t)|^2 + |\nabla k(t)|^2\\
&\quad+\int_{|x|\geq R} |\phi||h(t)|+|\psi||k(t)|+
|h(t)|^2+|k(t)|^2 \\ &\quad+\int_{|x|\geq R}|\phi|^3|h(t)| + |\psi|^3|k(t)| + |h(t)|^4 + |k(t)|^4 \\
&\lesssim (e^{-R}+\delta_0^\frac{1}{2})\delta(t),
\end{align}
since $(\phi,\psi)$ and their derivatives decay as $e^{-|x|}$. Choosing a possibly larger $R$ (but still independent on time), and a possibly smaller $\delta_0$, we conclude, in any case, that
\begin{equation}
A_R(u(t),v(t)) \leq 2\delta(t).
\end{equation}
Therefore, $V''_R(t) \leq - 2\delta(t)$, if one chooses $R$ large. With this bound on $V_R''$, we are able to show:
\begin{lemma} Let $(u,v)$ be a radial solution to \eqref{sys_NLS} such that $M(u_0,v_0) = M(\phi,\psi)$, $E(u_0,v_0) = E(\phi,\psi)$ and $K(u_0,v_0)>K(\phi,\psi)$. If $(u(t),v(t))$ is defined for all $t>0$, then $(u_0,v_0)$ has finite variance.
\end{lemma}
\begin{proof}
We first recall that $ V_R(t)>0$ and $V_R''(t) \leq -\delta(t) < 0$ for all $t$, for sufficient large $R$. This means that $V'_R$ is decerasing and positive (otherwise $V_R(t)$ would become negative in finite time). Therefore, the limit
\begin{equation}
\lim_{t\to +\infty} V'_R(t)
\end{equation}
exists, and so the integral
\begin{equation}
\int_t^{+\infty} V''_R(s) \,ds
\end{equation}
is convergent, which implies
\begin{equation}
\int_0^{+\infty} \delta(s) \,ds < +\infty.
\end{equation}
This alone allows us to use Lemma \ref{const_modul} to conclude that there exist $\theta_0 \in \mathbb{R}/2\pi \mathbb{Z}$ such that
\begin{equation}\label{slow_bound}
\|(u(t),v(t)) - (e^{i(\theta_0+t)}\phi,e^{i(\theta_0+t)}\psi)\|_{H^1 \times H^1} \to 0,
\end{equation}
as $t \to +\infty$. However, we can also get quantitative bounds, which will be important later. To do this, we first note that \eqref{slow_bound} implies that the variance of $(u,v)$ is always finite, since $V_R$ is non-decreasing and, as $t \to +\infty$,
\begin{equation}
\int_{|x|\leq R} |x|^2 \left[|u_0|^2+|v_0|^2\right] \leq \int a \left[|u(t)|^2+|v(t)|^2\right] \to \int a\left[\phi^2+\psi^2\right]
\end{equation}
for all $R>0$ sufficiently large. Since the variance of $(\phi,\psi)$ is finite, due to the exponential decay, one can make $R\to +\infty$ in the last inequality to conclude that
\begin{equation}
\int |x|^2 \left[|u_0|^2+|v_0|^2\right] \leq \int |x|^2\left[\phi^2+\psi^2\right],
\end{equation}
which gives the desired
\end{proof}
We have then reduced the problem to treating finite-variance solutions, which is done below.
\subsubsection{Finite-variance case}
Here, there is no need to truncate the variance, so we define
\begin{equation}
V(t) = \int |x|^2\left[|u(t)|^2 + |v(t)|^2\right],
\end{equation}
for which we have the identities
\begin{equation}
V'(t) = 4 \Im \int x \cdot (\nabla u(t) \overline{u}(t)+\nabla v(t) \overline{v}(t))
\end{equation}
and, in the case $E(u_0,v_0) = E(\phi,\psi)$,
\begin{equation}
V''(t) = -4\delta(t).
\end{equation}
As in the radial case, we have that $V'$ is positive and decreasing, and again by Lemma \ref{const_mod_param}, $V$ is uniformly bounded above by the ground state variance. Now, to get the desired exponential decay on time, we make use of the following Cauchy-Schwarz-type inequality
\begin{lemma}\label{Banica} Let $a$ be smooth and $(f,g) \in H^1 \times H^1$. If $|\nabla a|f$ and $|\nabla a|g$ belong to $L^2$, and assuming
\begin{equation}
M(f,g) = M(\phi,\psi), \quad E(f,g) = E(\phi,\psi),
\end{equation}
then
\begin{equation}
\left(\Im \int \nabla a \cdot (\nabla f \overline{f}+\nabla g \overline{g}) \right)^2 \lesssim \delta^2(f,g) \int |\nabla a|^2(|f|^2+|g|^2).
\end{equation}
\end{lemma}
\begin{proof}
By using the sharp Gagliardo-Nirenberg inequality on $(e^{i\lambda a}f, e^{i\lambda a}g)$, we get, for all $\lambda \in \mathbb R$,
\begin{equation}
\lambda^2 \int |\nabla a|^2(|f|^2+|g|^2) + 2 \lambda \Im \int \nabla a \cdot (\nabla f \overline{f}+\nabla g \overline{g}) +
K(f,g)-\frac{|P(f,g)|^{\frac{2}{3}}}{c_{GN}^\frac{2}{3}M(f,g)^{\frac{1}{3}}} \geq 0.
\end{equation}
The result then follows by noting that, if $M(f,g) = M(\phi,\psi)$ and $E(f,g) = E(\phi,\psi)$, then
\begin{equation}
K(f,g)-\frac{|P(f,g)|^{\frac{2}{3}}}{c_{GN}^\frac{2}{3}M(f,g)^{\frac{1}{3}}} = K(\phi,\psi)\left[1+\frac{\delta(f,g)}{K(\phi,\psi)}-\left|1+ \frac{3\delta(f,g)}{2K(\phi,\psi)}\right|^{\frac{2}{3}}\right] \lesssim \delta^2(f,g).
\end{equation}
\end{proof}
In particular, choosing $a(x) = |x|^2$, we obtain
\begin{equation}
V'(t) \lesssim \sqrt{V(t)}\, \delta(t)\lesssim - \sqrt{\int |x|^2\left[\phi^2+\psi^2\right]}\, V''(t).
\end{equation}
In other words, there exists $c>0$ such that
\begin{equation}
V''(t) \leq -c V'(t),
\end{equation}
which immediately implies
\begin{equation}
\int_t^{+\infty} \delta(s) \, ds = \frac{1}{2} V'(t) \leq \frac{1}{2}V'(0) e^{-ct}
\end{equation}
In view of Lemma \ref{const_modul}, we have just proved Lemma \ref{conv_ground_high}, up to the blow up in finite negative time. But this is a consequence of $V'(0)>0$, $V''\leq 0$ and the time-reversal symmetry.
\subsection{Low kinetic energy}
We now treat the case $\mathcal{ME}(u_0,v_0) = 1$ and $\mathcal{MK}(u_0,v_0)< 1$. Again, up to scaling, we assume $M(u_0,v_0) = M(\phi,\psi)$, $E(u_0,v_0) = E(\phi,\psi)$ and $K(u_0,v_0) < K(\phi,\psi)$. In this case, $\delta(t)$ is given by
\begin{equation}
\delta(t) = K(\phi,\psi) - K(u(t),v(t)).
\end{equation}
We then prove a result similar to Lemma \ref{conv_ground_high}:
\begin{lemma}\label{conv_ground_low} Let $(u,v)$ be a solution to \eqref{sys_NLS} such that $M(u_0,v_0) = M(\phi,\psi)$, $E(u_0,v_0) = E(\phi,\psi)$ and $K(u_0,v_0)<K(\phi,\psi)$. Then either $(u,v)$ scatters in positive time, or there exist $x_0 \in \mathbb{R}^3$, $\theta_0 \in \mathbb{R}/2\pi \mathbb{Z}$, $(\phi_0,\psi_0) \in \mathcal{G}$ and $c>0$ such that
\begin{equation}
\|(u(t),v(t)) - (e^{i(\theta_0+t)}\phi_0(\cdot+x_0),e^{i(\theta_0+t)}\psi_0(\cdot+x_0))\|_{H^1 \times H^1} \lesssim e^{-ct}.
\end{equation}
Moreover, $(u,v)$ is defined for all $t \in \mathbb R$ and scatters in negative time in $H^1 \times H^1$.
\end{lemma}
The difference here is that we cannot rely on some ``trapping'' given by the variance, but instead rely on compactness, given by the scattering norm being infinite. The following two lemmata are essentially the same as in \cite{DR_Thre}, to where we refer the reader for a proof.
\begin{lemma}\label{compactness_lemma} Let $(u,v)$ be a solution to \eqref{sys_NLS} with $M(u_0,v_0) = M(\phi,\psi)$ and $E(u_0,v_0) = E(\phi,\psi)$, defined for all $t\geq0$ and which does not scatter in positive time. Then, there exists a continuous function $x: [0,+\infty) \to \mathbb R^3$ which coincides with the translation parameter defined in \eqref{mod_decomposition} on the set $\{t \,|\, \delta(t)<\delta_0\}$ and
such that the set
\begin{equation}
\left\{ (u(x-x(t),t),v(x-x(t),t))\,|\, t \in [0,+\infty) \right\}
\end{equation}
is precompact in $H^1\times H^1$. Moreover, if $K(u_0,v_0) < K(\phi,\psi)$, we have
\begin{equation}
\frac{x(t)}{t} \to 0, \quad \text{as } t \to +\infty.
\end{equation}
\end{lemma}
\begin{lemma}\label{control_x} There exists $C_0>0$ such that if {$T_1 \geq T_0+1$ \color{red}}, then
\begin{equation}
|x(T_1)-x(T_0)| \leq C_0 \int_{T_0}^{T_1} \delta(s) \, ds.
\end{equation}
\end{lemma}
Even though we do not have radiality here, we work with a truncated variance to make use of compactness. For $R \geq 1$, let $a$ be a smooth, positive, radial function such that
\begin{equation}
a(x) = \begin{cases}
|x|^2, & |x| < R\\
2, & |x| > 3R
\end{cases}
\end{equation}
and that $|\nabla a|^2 \lesssim a$. As usual, define $V_R(t) = \displaystyle\int a \left[|u|^2+|v|^2\right]$ and note that $|V_R(t)| \lesssim R^2$. We also have, by the virial identities,
\begin{equation}\label{second_virial_below}
V_R''(t) = 2 \delta(t) + A_R(u(t),v(t)),
\end{equation}
where $A_R$ is defined in \eqref{def_AR}.
\begin{lemma}\label{bound_delta_below} There exists $C\geq 1$ such that, for any $0\leq T_0 \leq t \leq T_1$, one has
\begin{align}
|A_R(u(t),v(t))|\leq \delta(t),\label{bound_AR_below}\\
|V'_R(t)|\lesssim R \,\delta(t)\label{bound_FprimeR_below},
\end{align}
where $R = R(T_0,T_1,\eta) = \displaystyle\sup_{T_0\leq t \leq T_1}|x(t)| + C$.
\end{lemma}
\begin{proof}
As in the previous section, we have, for $\delta(t) < \delta_0$, upon writing
\begin{equation}
(u(x,t),v(x,t)) = \left(e^{i\theta(t)}[\phi(x-x(t))+h(x-x(t),t)],e^{i\theta(t)}[\psi(x-x(t))+k(x-x(t),t)]\right).
\end{equation}
we have, for any (fixed) $t \in [a,b]$,
\begin{align}
|A_R(u(t),v(t))| &= |A_{R}(h(\cdot-x(t),t)+\phi,k(\cdot-x(t),t)+\psi) - A_{R}(\phi(\cdot-x(t)),\psi(\cdot-x(t)))|
\\&\lesssim \int_{|x+x(t)| \geq R} |\nabla \phi| |\nabla h(t)| +
|\nabla \psi| |\nabla k(t)|
+ |\nabla h(t)|^2 + |\nabla k(t)|^2\\
&\quad+\int_{|x+x(t)|\geq R} |\phi||h(t)|+|\psi||k(t)|+
|h(t)|^2+|k(t)|^2 \\ &\quad+\int_{|x+x(t)|\geq R}|\phi|^3|h(t)| + |\psi|^3|k(t)| + |h(t)|^4 + |k(t)|^4 \\
&\lesssim (e^{-(R-x(t))}+\delta_0^\frac{1}{2})\delta(t)\\
&\lesssim (e^{-C}+\delta_0^\frac{1}{2})\delta(t).
\end{align}
Choosing a smaller $\delta_0$, if necessary, and a large enough $C\geq 1$, equation \eqref{bound_AR_below} is proved in the case $\delta(t)<\delta_0$. If $\delta(t) \geq \delta_0$ and $t \in [a,b]$, we write
\begin{align}
|A_R(u(t),v(t))| &\lesssim \int_{|x|\geq R } \left[|\nabla u|^2+|\nabla v|^2 +| u|^2+| v|^2 + |u|^4 +|v|^4\right]\\
&\lesssim \int_{|x-x(t)|\geq R-|x(t)| } \left[|\nabla u|^2+|\nabla v|^2 +| u|^2+|u|^4 +|v|^4\right]\\
&\lesssim \int_{|x-x(t)|\geq C } \left[|\nabla u|^2+|\nabla v|^2 +| u|^2+ |u|^4 +|v|^4\right].\\
\end{align}
Thus, by possibly increasing $C\geq 1$, we have, by compactness, $|A_R(u(t),v(t))|\leq \delta_0 \leq \delta(t)$.
To get \eqref{bound_FprimeR_below}, we make use of Lemma \ref{Banica} and the definition of $a$ to write
\begin{equation}
|V_R'(t)| \lesssim \sqrt{V_R(t)} \delta(t) \lesssim R \delta(t),
\end{equation}
which proves the desired.
\end{proof}
\begin{cor}\label{virial_delta} There exists $C_1>0$ such that, for any $0\leq T_0\leq t \leq T_1$, one has
\begin{equation}\label{estimate_virial_delta}
\int_{T_0}^{T_1} \delta(s) \, ds \leq C_1 \left[1+\sup_{T_0\leq t \leq T_1}|x(t)|\right](\delta(T_1)+\delta(T_0)) = \,o_{T_0}(T_1),
\end{equation}
where $o_{T_0}(T_1)/T_1 \to 0$ as $T_1 \to +\infty$ and $T_0$ is fixed. In particular, there exists a sequence $\{t_n\}_{n = 0}^{\infty}$ with $t_{n+1}\geq t_n+1$ and such that $\delta(t_n) \leq \displaystyle\frac{1}{2^{n+2}C_0C_1}$ for all $n$, where $C_0$ is defined in Lemma \ref{control_x}.
\end{cor}
\begin{proof}
By equations \eqref{second_virial_below}, \eqref{bound_AR_below} and \eqref{bound_FprimeR_below}, one has
\begin{equation}
\int_{T_0}^{T_1} \delta(s) \, ds \leq \int_{T_0}^{T_1} V_R''(s) \, ds \leq |V_R'(T_1)|+|V_R'(T_0)| \lesssim \left[1+\sup_{T_0\leq t \leq T_1}|x(t)|\right](\delta(T_1)+\delta(T_0)).
\end{equation}
Recalling that $\delta(t) \leq K(\phi,\psi)$ for all $t$ and that $x(t) = o_1(t)$ (by Lemma \ref{compactness_lemma}), we get \eqref{estimate_virial_delta}. The existence of the sequence $\{t_n\}$ comes from the mean value theorem.
\end{proof}
\begin{cor}\label{x_bounded} We have
\begin{equation}
\sup_{t \in [0,+\infty)}|x(t)| \lesssim 1 + \sup_{t_0\leq s \leq t_1}|x(t)| < +\infty
\end{equation}
\end{cor}
\begin{proof}
Let $t^*_n$ be such that $|x(t^*_n)| = \displaystyle\sup_{t_1 \leq t \leq t_n} |x(t)|$, where $\{t_n\}$ is given in Lemma \ref{virial_delta}. By Lemmas \ref{control_x} and \ref{virial_delta}, we can write
\begin{align}
|x(t^*_n)| &\leq |x(t_0)| + C_0 C_1 \left[1+\sup_{t_0 \leq t \leq t_1}|x(t)|+|x(t^*_n)|\right]\frac{1}{2C_0C_1}\\
&\leq |x(t_0)| + \frac{1+\sup_{t_0 \leq t \leq t_1}|x(t)|}{2} + \frac{|x(t^*_n)|}{2}.
\end{align}
\end{proof}
Summing up all of the results of this section, we get the desired bound on $\delta$, which implies Lemma \ref{conv_ground_low} in view of Lemma \ref{const_modul}, up to the scattering for negative time:
\begin{cor}
\begin{equation}
\int_t^{+\infty}\delta(s) \, ds \lesssim e^{-ct}.
\end{equation}
\end{cor}
\begin{proof}
By Corollaries \ref{virial_delta} and \ref{x_bounded}, we have, for any $t\geq0$,
\begin{equation}
\int_{t}^{t_n} \delta(s)\, ds \lesssim \delta(t)+\delta(t_n).
\end{equation}
The result follows by making $n \to +\infty$ and using Gronwall's lemma.
\end{proof}
The scattering part then follows from the following result.
\begin{cor} $(u,v)$ scatters for negative time in $H^1 \times H^1$
\end{cor}
\begin{proof} The boundedness of the $H^1 \times H^1$ norm implies global existence of the solution. If it does not scatter for negative time, we can apply the results of this section to the time-reversed solution $t\mapsto(\overline u(-t),\overline{v}(-t))$ to conclude that
\begin{equation}
\lim_{t\to \pm \infty}\delta(t) = 0
\end{equation}
and that, for any $t \in \mathbb R$,
\begin{equation}
\int_{-t}^{t}\delta(s)\, ds \lesssim \delta(t)+\delta(-t).
\end{equation}
The last two equations then imply $\delta \equiv 0$.
\end{proof}
\section{Exponentially decaying solutions to the linearized equation}\label{Sec8}
Given any ground state $Q=(\phi,\psi)$, we now study solutions to the equation
\begin{equation}\label{eq_exp_decay}
\partial_t (h,k) + \mathcal{L}(h,k) = g,
\end{equation}
where
\begin{align}\label{eq_exp_decay_2}
\|(h(t),k(t))\|_{H^1 \times H^1} \lesssim e^{-\gamma_1 t} \text{ and } \|g(t)\|_{H^1 \times H^1} \lesssim e^{-\gamma_2 t}\text{ , with }\gamma_2>\gamma_1>0.
\end{align}
We first normalize the functions in the null space of $\mathcal{L}$ by enumerating $\ker(\mathcal{L}) = \{\tilde Q_j\}_{j=1}^{\dim(\ker(\mathcal{L}))}$ and writing for all $j$
\begin{equation}
Q_j = \frac{1}{\|\tilde{Q}_j\|_{L^2 \times L^2}} \tilde Q_j.
\end{equation}
We also renormalize $\mathcal{Y}_{\pm}$, as to satisfy
\begin{equation}
B(\mathcal{Y}_+,\mathcal{Y}_-) = 1.
\end{equation}
Write
\begin{equation}
(h,k) = \alpha_+(t) \mathcal{Y}_+ +\alpha_-(t) \mathcal{Y}_- + \sum_{j} \beta_j(t) Q_j + w(t),
\end{equation}
with $w(t) \in \tilde{G}^\perp$. Note that
\begin{align}
\alpha_+(t) = B((h,k),\mathcal{Y}_-)\\
\alpha_-(t) = B((h,k),\mathcal{Y}_+)\\
{\beta_j(t) = ((h,k),Q_j)}\\
\Phi(h,k) = \Phi(w) + \alpha_+ \alpha_-
\end{align}
In particular, $|\alpha_+(t)|+|\alpha_-(t)| +\sum_j |\beta_j(t)| + \|w(t)\|_{H^1 \times H^1} \lesssim e^{-\gamma_1t}$.
\subsection{Differential equations for the modulation parameters}
The following result follows from direct differentiation.
\begin{prop}
We have
\begin{align}
\frac{d}{dt}(e^{e_0t}\alpha_+) = e^{e_0t}B(g,\mathcal{Y}_-)\\
\frac{d}{dt}(e^{-e_0t}\alpha_-) = e^{-e_0t}B(g,\mathcal{Y}_+)\\
{\frac{d}{dt}\beta_j = (g,Q_j)}, \quad\forall\, j\\
\frac{d}{dt}\Phi(h,k) = 2B(g,(h,k))
\end{align}
In particular,
\begin{align}
\left|\frac{d}{dt}(e^{e_0t}\alpha_+)\right| \lesssim e^{(e_0-\gamma_2)t}\\
\left|\frac{d}{dt}(e^{-e_0t}\alpha_-)\right| \lesssim e^{-(e_0+\gamma_2)t}\\
{\sum_{j}\left|\frac{d}{dt}\beta_j\right| \lesssim e^{-\gamma_2 t}}\\
\left|\frac{d}{dt}\Phi(h,k)\right|| \lesssim e^{-(\gamma_1+\gamma_2)t}.
\end{align}
\end{prop}
\subsection{Self-improving decay}
The decay of $g$ can be used to improve the decay of $(h,k)$.
\begin{lemma}
\begin{align}
|\alpha_-(t)| \lesssim e^{-\gamma_2 t}\\
\sum_{j}|\beta_j(t)| \lesssim e^{-\gamma_2 t}\\
\|w(t)\|_{H^1 \times H^1} \lesssim e^{-\frac{\gamma_1+\gamma_2}{2}}.
\end{align}
\begin{proof}
The bounds follow from direct integration.
\end{proof}
\end{lemma}
\begin{lemma}
There exists $A \in \mathbb{R}$ such that
\begin{equation}
|\alpha_+(t)-Ae^{-e_0t}| \lesssim e^{-\gamma_2^- t}.
\end{equation}
\end{lemma}
\begin{proof}
Write
\begin{equation}
e^{e_0s}\alpha_+(s)-e^{e_0t} \alpha_+(t) = \int_t^s e^{e_0 \tau} B(g(\tau),\mathcal{Y}_-) \, d \tau.
\end{equation}
If $\gamma_2>e_0$, then the last integral converges, wich means $e^{e_0s}\alpha_+(s)$ has a limit $A$ as $s \to +\infty$. That implies
\begin{equation}
|\alpha_+(t)-Ae^{-e_0t}| \lesssim e^{-e_0t}\int_t^{+\infty} e^{(e_0-\gamma_2) \tau} \, d \tau \lesssim e^{-\gamma_2t}.
\end{equation}
If $\gamma_2 \leq e_0$, then
\begin{equation}
|e^{e_0t}\alpha_+(t)| \lesssim |\alpha_+(0)| + e^{(e_0-\gamma_2^-)t},
\end{equation}
which means we can choose $A = 0$.
\end{proof}
Define now $(\tilde h, \tilde k) = (h,k) - Ae^{-e_0t}\mathcal{Y}_+$ and $\tilde{\alpha}_+ = \alpha_+ - Ae^{-e_0t}$. Note that $(\tilde h, \tilde k)$ satisfies the same differential equation as $(h,k)$. We then have
\begin{equation}
\|(\tilde h(t), \tilde k(t))\|_{H^1 \times H^1} \lesssim |\tilde{\alpha}_+(t)| + |\alpha_-(t)| + \sum_{j}|\beta_j(t)| + \|w(t)\|_{H^1 \times H^1} \lesssim e^{-\gamma_2^- t} + e^{-\frac{\gamma_1+\gamma_2}{2}} \lesssim e^{-\frac{\gamma_1+\gamma_2}{2}}.
\end{equation}
In view of the improved decay of $(\tilde h, \tilde k)$, we can replace $\gamma_1$ by $\frac{\gamma_1+\gamma_2}{2}$, and by repeated iteration, we conclude:
\begin{lemma}\label{lemma_improv_decay} If $(u,v)$ satisfies \eqref{eq_exp_decay} and \eqref{eq_exp_decay_2}, then there exists $A \in \mathbb R$ such that
\begin{equation}
(h(t),k(t)) = Ae^{-e_0t}\mathcal{Y}_+ + O(e^{-\gamma_2^-t}) \quad \text{in }H^1 \times H^1.
\end{equation}
\end{lemma}
\subsection{Uniqueness}
\begin{prop}\label{prop_unique_decay}
Let $(u,v)$ be a solution to \eqref{sys_NLS} such that $\|(u(t),v(t)-(e^{it}\phi,e^{it}\psi)\|_{H^1 \times H^1} \lesssim e^{-ct}$ for some ground state $Q=(\phi,\psi)$ and some $c>0$. Then there exists $A \in \mathbb R$ such that $(u,v) = U^A$.
\end{prop}
\begin{proof}
Write $(u,v) = (e^{it}(\phi + h), e^{it}(\psi+k))$ and let $A \in \mathbb{R}$ be given by Lemma \ref{lemma_improv_decay}. Recall that $(h,k)$ satisfies
\begin{equation}
\partial_t (h,k) + \mathcal{L}(h,k) = R(h,k),
\end{equation}
where
\begin{equation}
\|R(h,k)\|_{H^1 \times H^1} \lesssim \|(h,k)\|_{H^1 \times H^1}^2.
\end{equation}
Therefore, by Lemma \ref{lemma_improv_decay}, we have that $\|(h(t),k(t))\|_{H^1 \times H^1} \lesssim e^{-e_0t}$ and $\|R(h(t),k(t))\|_{H^1 \times H^1} \lesssim e^{-2e_0t}$. This lets us bootstrap the decay to conclude
\begin{equation}\label{bound_A_uniq}
\|(h(t),k(t))-Ae^{-e_0t}\mathcal{Y}_+\|_{H^1 \times H^1} \lesssim e^{-2e_0^-t}.
\end{equation}
Consider the corresponding $U^A$ and write $U^A = (e^{it}(\phi + h^A), e^{it}(\psi+k^A))$. Recall that
\begin{equation}
\|(h^A(t),k^A(t)) - Ae^{-e_0t}\mathcal{Y}_+\|_{H^1 \times H^1} \lesssim e^{-2e_0t}.
\end{equation}
Thus,
\begin{equation}
\|(h(t),k(t)) - (h^A(t),k^A(t))\|_{H^1 \times H^1} \lesssim e^{-2e_0^-t}.
\end{equation}
We now note that $z := (h,k)-(h^A,k^A)$ satisfies
\begin{equation}
\partial_t z + \mathcal{L}z = R(h,k)-R(h^A,k^A)
\end{equation}
and that $$\|R(h,k)-R(h^A,k^A)\|_{H^1 \times H^1} \lesssim (\|(h,k)\|_{H^1 \times H^1}+\|(h^A,k^A)\|_{H^1 \times H^1})\|(h,k)-(h^A,k^A)\|_{H^1 \times H^1}.$$
We conclude that, for any $\gamma>0$,
\begin{equation}
\|(h,k)-(h^A,k^A)\|_{H^1 \times H^1}\lesssim_{\gamma}e^{-\gamma t}.
\end{equation}
In particular, choosing $\gamma>(l_0+1)e_0$, (where $l_0$ is defined in Section \ref{def_l_0}),{ and using Strichartz,} the uniqueness of $U^A$ implies $h = h^A$, i.e., $(u,v) = U^A$.
\end{proof}
The above result also allows us to narrow the number of solutions even further down.
\begin{cor} Let $A \in \mathbb R$ and $Q = (\phi,\psi) \in \mathcal{G}$. We define $Q^+ = U^{+1}$ and $Q^- = U^{-1}$. Then, if $A>0$, there exists a time $T_A \in \mathbb R$ such that $U^A = e^{iT_A}Q^+(t-T_A)$. Conversely, if $A<0$, there exists a time $T_A \in \mathbb R$ such that $U^A = e^{iT_A}Q^-(t-T_A)$.
\end{cor}
\begin{proof}
Indeed, given $A>0$, define $T_A = - \frac{1}{e_0}\ln A$. Then
\begin{equation}
e^{-iT_A}U^A(t+T_A) = e^{it}(Q + \mathcal{Y}_+e^{-e_0t})+O(e^{-2e_0t}).
\end{equation}
By using the same argument after \eqref{bound_A_uniq}, we conclude that $e^{-iT_A}U^A(t+T_A) = U^{+1}$. The proof for $A<0$ is completely analogous.
\end{proof}
We then sum the previous results up to obtain the main theorems of this paper:
\begin{proof}[Proof of Theorem \ref{sub_special}]
The existence part follows from Proposition \ref{sub_exist_UA}. The finite-variance and the blow-up part for $Q^+$ come from Lemma \ref{conv_ground_high} and the scattering backwards in time for $Q^-$ comes from Lemma \ref{conv_ground_low}.
\end{proof}
\begin{proof}[Proof of Theorem \ref{sub_class_thresh}] It is a direct consequence of Lemma \ref{conv_ground_high}, in the case $\mathcal{MK}(u_0,v_0)>1$, of the variational characterization of the ground states in the case $\mathcal{MK}(u_0,v_0)=1$ and of Lemma \ref{conv_ground_low} in the case $\mathcal{MK}(u_0)<1$.
\end{proof}
\addtocontents{toc}{\protect\vspace*{\baselineskip}}
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journal={J. Math. Phys.},
volume={56},
number={2},
pages={021507, 18},
url={https://doi.org/10.1063/1.4908555},
review={\MR{3390859}},
}
\bib{Strauss77}{article}{
author={Strauss, Walter~A.},
title={Existence of solitary waves in higher dimensions},
date={1977},
ISSN={0010-3616},
journal={Comm. Math. Phys.},
volume={55},
number={2},
pages={149\ndash 162},
review={\MR{0454365}},
}
\bib{TaoBook}{book}{
author={Tao, Terence},
title={Nonlinear dispersive equations: local and global analysis},
publisher={American Mathematical Soc.},
date={2006},
number={106},
}
\bib{WY_Uniq}{article}{
author={Wei, Juncheng},
author={Yao, Wei},
title={Uniqueness of positive solutions to some coupled nonlinear
schr{\"o}dinger equations},
date={2012},
journal={Communications on Pure \& Applied Analysis},
volume={11},
number={3},
pages={1003},
}
\bib{W85_stability}{article}{
author={Weinstein, Michael~I.},
title={Modulational stability of ground states of nonlinear
{S}chr\"{o}dinger equations},
date={1985},
ISSN={0036-1410},
journal={SIAM J. Math. Anal.},
volume={16},
number={3},
pages={472\ndash 491},
url={https://doi.org/10.1137/0516034},
review={\MR{783974}},
}
\end{biblist}
\end{bibdiv}
\newcommand{\Addresses}{
\bigskip
\footnotesize
L. Campos, \textsc{IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária, 13083-859, Campinas, São Paulo, Brazil.}\par\nopagebreak
\textit{E-mail address:} \texttt{luccasccampos@gmail.com}
\vspace{3mm}
A. Pastor, \textsc{IMECC-UNICAMP, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária, 13083-859, Campinas, São Paulo, Brazil.}\par\nopagebreak
\textit{E-mail address:} \texttt{apastor@ime.unicamp.br}
}}
\setlength{\parskip}{0pt}
\Addresses
\batchmode
\end{document}
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\section{\label{}}
\section{Introduction}
The observed Higgs mass leads to the fact that the Higgs self coupling and its beta function become zero at string/Planck scale depending on the value of the top mass~\cite{flat potential,Hamada:2012bp}.
Further, bare Higgs mass also vanish around this scale~\cite{flat potential,Hamada:2012bp}.
These facts indicate that the Higgs potential is very flat, which is good for the inflation by the Higgs boson~\cite{Bezrukov:2007ep,Hamada:2014iga,critical,Haba:2014zda}.
By introducing the non-minimal coupling between the Higgs field and the Ricci scalar $\xi |H|^2 \mathcal{R}$~\cite{Salopek:1988qh}, the Higgs potential becomes sufficiently flat to realize the successful inflation. For the critical case, only $\xi= O(10)$ is needed~\cite{Hamada:2014iga,critical,Haba:2014zda}, while $\xi=O(10^4)$ is needed for non-critical case.
Furthermore, if the multiple point criticality principle~\cite{Froggatt:1995rt} is satisfied, the Higgs field becomes the seeds of the topological inflation~\cite{Hamada:2014raa}.
This paper is based on our works~\cite{Hamada:2012bp,Hamada:2014raa,Hamada:2014iga,Hamada:2014xka,Hamada:2014ofa,Hamada:2015ria}.
\section{Higgs potential and inflation}
At the scale much larger than the electroweak scale, we can approximate the Standard Model(SM) Higgs potential as
\begin{equation}
V\sim {\lambda(\varphi)\over4} \varphi^4,
\end{equation}
with $\varphi$ being the physical Higgs field.
In Fig.~\ref{SM potential}, we plot the Higgs potential as a function of $h$ with various values of top mass $M_t$.
See e.g. Ref.~\cite{Kawabataa:2014osa} for the current uncertainty of the top mass.
We can see that our vacuum is stable for lighter $M_t$ and is unstable for heavier $M_t$.
Furthermore, if $M_t$ is tuned, there arises the saddle point where the first and the second derivatives of the potential is zero.
In the following, we introduce the Higgs inflation in these three cases.
\begin{figure}[ht]
\centering
\includegraphics[width=80mm]{Fig1.eps}
\caption{The Higgs potential as a function of the Higgs field value $\varphi$ near the SM criticality. Here we take $M_H=125.9$GeV and $\alpha_s=0.1185$ and use the two loop renormalization group equations.} \label{SM potential}
\end{figure}
\subsection{Usual Higgs inflation and the saddle point inflation}
For the small value of $M_t$, the Higgs potential is stable up to the inflation scale and, we can realize successful inflation.
By adding the non-minimal coupling $\xi$, the action becomes
\begin{align}
S=\int \sqrt{-g}\, d^4x
\left(
-M_P^2 \mathcal{R}+\xi \varphi^2 \mathcal{R}+{1\over2}(\partial_\mu \varphi)^2-
{\lambda\over4}\varphi^4
\right).
\end{align}
Here we focus on the Higgs and gravity sectors and neglect other sectors for simplicity.
After the redefinition of the metric,
\begin{align}
&
g_{E\mu\nu}=\Omega^2 g_{\mu\nu},
&
\Omega^2=1+{\xi\varphi^2\over M_P^2},
\end{align}
we obtain the following Einstein frame action,
\begin{align}
S=\int \sqrt{-g_E}\, d^4x
\left(
-M_P^2 \mathcal{R}_E+{1\over2}(\partial_\mu \chi)^2-
{\lambda\over4}{\varphi^4\over(1+\xi \varphi^2/M_P^2)^2}
\right),
\end{align}
where $\chi$ is the canonical field in the Einstein frame, and the relation between $\varphi$ and $\chi$ is
\begin{align}
{d\chi\over d\varphi}=\sqrt{\left(\Omega^2+{6\xi^2\varphi^2\over M_P^2}\right){1\over\Omega^4}}.
\end{align}
The point is that the potential is divided by the factor $\Omega^4$.
This fact leads the flat potential because $\varphi^4/(1+\xi\varphi^2/M_P^2)^2$ becomes constant at the high scale.
For the value of $\lambda=O(0.1)$, $\xi$ is needed to be $O(10^4)$ to fit the COBE normalization.
If the $M_t$ is tunes so that the Higgs potential becomes flat, the required amount of the non-minimal coupling $\xi$ is significantly reduced since the potential is suppressed due to the smallness of $\lambda$.
This corresponds to the green line in Fig.~\ref{SM potential}.
We only need small $\xi=O(10)$ to realize the inflation~\cite{Hamada:2014iga,critical}.
\subsection{topological Higgs inflation}
Let us focus on the case where there are two vacua as in blue line in Fig.~\ref{SM potential}, which is predicted by Froggatt and Nielsen~\cite{Froggatt:1995rt} about twenty years before the Higgs discovery.
See also Refs.~\cite{MEP,Hamada:2014ofa} for another explanation of the SM criticality, and for Refs.~\cite{extension,Hamada:2014xka} for the criticality in the minimal extensions of the SM.
Since the potential has two vacua, the domain wall connecting the our vacuum and the Planck scale one would be formed in general initial condition, see Fig.~\ref{domain wall}.
\begin{figure}[ht]
\centering
\includegraphics[width=80mm]{DW.eps}
\caption{
The schematic picture of the formation of the domain wall in the Higgs potential.
} \label{domain wall}
\end{figure}
In this case, the topological inflation driven by the Higgs field is possible if the thickness of the domain wall is larger than the Hubble horizon case~\cite{Hamada:2014raa}. See also Ref.~\cite{Kitajima:2015nla} for the production of the Higgs domain wall after the inflation.
The thickness of the domain $\delta_\text{DW}$ wall can be estimated as follows.
Let us start from the action,
\begin{align}
S=\int d^4x \left(
(\partial \varphi)^2- V(\varphi)
\right) .
\end{align}
If we consider the the domain wall configuration which we denote $\varphi_\text{DW}$,
the terms in the action should be balanced.
\begin{align}
(\partial \varphi_\text{DW})^2\simeq V(\varphi_\text{DW}).
\end{align}
Naively, $\partial \varphi_\text{DW}\simeq \varphi_\text{DW}/\delta_\text{DW}$,
and we get
\begin{align}
\delta_\text{DW}\simeq {V\over \varphi_\text{DW}^2}\simeq V''(\varphi_\text{DW}).
\end{align}
Practically, we evaluate $V''(\varphi_\text{DW})$ at the local maximum of the Higgs potential.
The condition for the topological Higgs inflation is satisfied by adding small non-minimal coupling $\xi=O(0.1-10)$ or the right handed neutrino~\cite{Hamada:2014raa}.
\section{Higgs potential beyond the Planck scale}
We comment on the implication from string theory.
Higgs potential beyond the Planck scale can not be computed by using field theory.
In order to discuss this, we consider the non-supersymmetric string theory~\cite{SO(16) model}. This is because that the tachyon-free non-supersymmetric vacua is generic in string theory~\cite{fermionic construction} and that
the recent LHC result may indicate that the study of the phenomenology based on non-supersymmetric string~\cite{nonSUSY string, Hamada:2015ria} become important.
The flat potential around the string scale suggests that the Higgs comes from the tree level massless state of string.
The Higgs field generally mixes other moduli above the Planck scale, and
we can argue that at least the one of the direction, radion direction, has runaway vacuum if the ten dimensional cosmological constant is positive using the non-supersymmetric string model.
Taking into account this, we conclude that the topological Higgs inflation is generically realized in string theory~\cite{Hamada:2015ria}.
\section{Summary}
We have considered the Higgs inflation in light of the discovery of the Higgs boson.
Taking into account the small $\lambda$ at high scale, we can realize the Higgs inflation with small non-minimal coupling.
We also have discussed the topological inflation by the Higgs field.
These inflations are compatible with non-supersymmetric string theory.
\begin{acknowledgments}
We thank Hikaru Kawai, Kin-ya Oda, Seong Chan Park and Fuminobu Takahashi for useful discussion and fruitful collaborations.
\end{acknowledgments}
\bigskip
|
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| 1,432
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{"url":"https:\/\/amdis-test.readthedocs.io\/en\/develop\/api\/classAMDiS_1_1cg__solver__type.html","text":"AMDiS \u00a00.1 The Adaptive Multi-Dimensional Simulation Toolbox\ncg_solver_type Class Reference\n\nITL_Solver <cg_solver_type> implementation of conjugate gradient method. More...\n\n#include <ITL_Solver.hpp>\n\nInherits ITL_Solver.\n\n## Public Member Functions\n\ncg_solver_type (std::string const &)\n\ntemplate<class LinOp , class X , class B , class P , class I >\nint\u00a0operator() (LinOp const &A, X &x, B const &b, P const &precon, I &iter)\n\n## Detailed Description\n\nITL_Solver <cg_solver_type> implementation of conjugate gradient method.\n\nSolves a linear system $$Ax=b$$ by the conjugate gradient method (CG) and can be used for symmetric positive definite system matrices. Right preconditioner is ignored.\n\nThe documentation for this class was generated from the following file:","date":"2022-08-10 04:55:48","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\": 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\": 0.23431117832660675, \"perplexity\": 13081.836025906929}, \"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\/1659882571147.84\/warc\/CC-MAIN-20220810040253-20220810070253-00093.warc.gz\"}"}
| null | null |
Q: Iterate through all cells in a column instead of checking all cells individually I have a simple list with labels and values in a Google Spreadsheet. Below, I have some fields in which I would like to get the value when writing the label.
For example, if I write D in a cell, I want the next cell to show 4, the value corresponding to D.
This can of course be done with repetitive IFs inside IFs inside IFs... in cell B8, like this:
=IF(A8=A1;B1; IF(A8=A2;B2; IF(A8=A3;B3; IF(A8=A4;B4; IF(A8=A5;B5;0)))))
This simply checks row by row: If the written value matches the label of row 1, then show the value. If not, then perform a new IF command on the second row. Etc.
With many rows this is quite tedious. Is it possible in Google Spreadsheets to simplify this a bit? For instance, can I in some way collect all cells in a column in one IF statement by doing A1:A5 or something like that? Something along the lines of:
=IF(A8=A1:A5;B1:B5;0)
A: solve it by using simple VLOOKUP:
=VLOOKUP(A8, A1:B5, 2, 0)
|
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| 6,377
|
{"url":"http:\/\/documenta.sagemath.org\/vol-03\/03.html","text":"DOCUMENTA MATHEMATICA, Vol. 3 (1998), 27-133\n\nAnnette Huber, J\u00f6rg Wildeshaus\n\nClassical Motivic Polylogarithm According to Beilinson and Deligne\n\nThe main purpose of this paper is the construction in motivic cohomology of the {\\it cyclotomic}, or {\\it classical polylogarithm} on the projective line minus three points, and the identification of its image under the regulator to absolute (Deligne or $l$-adic) cohomology. By specialization to roots of unity, one obtains a compatibility statement on {\\it cyclotomic elements} in motivic and absolute cohomology of abelian number fields. As shown in \\cite{BK}, this compatibility completes the proof of the Tamagawa number conjecture on special values of the Riemann zeta function.\n\nThe main constructions and ideas are contained in Beilinson's and Deligne's unpublished preprint Motivic Polylogarithm and Zagier Conjecture'' (\\cite{BD}). We work out the details of the proof, setting up the foundational material which was missing from the original source: the paper contains an appendix on absolute Hodge cohomology with coefficients, and its interpretation in terms of Saito's Hodge modules. The second appendix treats $K$-theory and regulators for simplicial schemes.\n\n1991 Mathematics Subject Classification: Primary 19F27; Secondary11R18, 11R34, 11R42, 14D07, 14F99.\n\nKeywords: Polylogarithm, motivic and absolute cohomology, regulators, cyclotomic elements.\n\nCorrection, this volume: 297-299.\nFull text: dvi.gz 164 k, dvi 455 k, ps.gz 310 k, pdf 706 k","date":"2019-04-18 10:21:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9365336298942566, \"perplexity\": 1570.1366119375011}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-18\/segments\/1555578517558.8\/warc\/CC-MAIN-20190418101243-20190418122326-00048.warc.gz\"}"}
| null | null |
University of Denver Stadium and the Field House Arena, between 1968-1972
Identifier: U300.01.0002.00212
Division of Athletics and Recreation Records
Athletics and Recreation Photographs, 1891-2007
Aerial view of the University of Denver Stadium and Field House Arena in Denver, Colorado.
between 1968-1972
Purdie, Richard W. (Photographer, Person)
University of Denver Stadium and the Field House Arena
From the Series: This series contains images (photographic prints, film negatives, slides, and digital images) taken of University of Denver intercollegiate athletics and recreation (club sports, intramurals, and youth sports) events and activities. This series was collected and arranged prior to 2007. For additional University of Denver athletics and recreation images, see Working Files (Series 6).
8 x 10 inches black and white
College buildings
Field House Arena (Denver, Colo.)
Field houses
University of Denver Stadium (Denver, Colo.)
U300.01.0002.00212, University of Denver Stadium and the Field House Arena, between 1968-1972. Division of Athletics and Recreation Records, U300. Special Collections and Archives. https://duarchives.coalliance.org/repositories/2/archival_objects/108999 Accessed January 19, 2020.
|
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|
Sand Creek Massacre
National Historic Site Colorado
Evans' "Proclamation to the Friendly Indians"
Territorial Governor John Evans, circa 1860-1870.
Image courtesy of the Colorado State Archives.
Sand Creek Massacre News Release
Eric Sainio, 719-729-3003
This article is part of a series by the National Park Service concerning the 150th Anniversary of the Sand Creek Massacre.
As rising tensions and several murders contributed to war on the High Plains in the summer of 1864, Colorado Territorial Governor John Evans proclaimed that "the friendly Indians of the Plains" needed to go to outposts like Fort Lyon; there, they would receive "provisions, and [be shown]… a place of safety".
Also serving as Colorado's Superintendant of Indian Affairs, Evans issued his proclamation on June 27, arguing that it intended "to prevent friendly Indians from being killed through mistake… The war on hostile Indians will be continued until they are all effectually subdued." The so-called 1864 Indian War would linger, but Evans intended to isolate the peaceful groups from the warrior bands.
Unfortunately, certain factors made the proclamation ineffective. First, because of the distance involved, news of the offer failed to reach many of the Plains Indians until the middle of July at the earliest, when warrior societies and the U.S. Army had already committed to war. Second, Evans lacked the military authority or funds to feed peaceful Cheyenne and Arapaho that reported to Fort Lyon.
When chiefs like Black Kettle and White Antelope sought peace and complied with this directive in the fall, Colorado Volunteers of the U.S. Army attacked their unsuspecting village on Sand Creek in November. The subsequent massacre proved the ineffectiveness of the June proclamation and drastically affected Cheyenne and Arapaho societies.
To find out more about Territorial Governor Evan's June Proclamation, go to www.nps.gov/sand or visit the Sand Creek Massacre National Historic Site outside of Eads, Colorado.
Last updated: April 4, 2020
1301 Maine Street
Eads , CO 81036-0249
|
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| 8,951
|
{"url":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/JHASS-06-2020-0088\/full\/html","text":"# Population growth and human resource utilization nexus in Nigeria\n\nOluyemi Theophilus Adeosun (Department of Economics, University of Lagos, Lagos, Nigeria)\nOluwaseyi Omowunmi Popogbe (Department of Economics, University of Lagos, Lagos, Nigeria)\n\nISSN: 2632-279X\n\nPublication date: 4 November 2020\n\n## Abstract\n\n### Purpose\n\nPopulation growth has remained a key issue facing developing economies in the world. While developed countries are experiencing diminished or negative population growth, many countries in sub-Saharan Africa including Nigeria are having population growth above the economic growth rate. With the deadline for the sustainable development goals approaching, attention is increasingly being focused on population growth and human capital development. Extant literature focused on population growth, human resource utilization and economic growth but this study aims to examine the effect of population growth on human resource utilization.\n\n### Design\/methodology\/approach\n\nUsing secondary data for the period 1990-2018, the study conducted unit root test and co-integration analyses to determine the stationarity and correlation in the long-run in the variables. The study used the error correction model to ascertain the speed at which shocks can be corrected in the long-run. Granger causality test was also carried out to ascertain the direction of causality among the variables.\n\n### Findings\n\nThe empirical results revealed that population growth has a negative and significant effect on human resource utilization. The study also revealed that unidirectional causality runs from employment rate to population growth rate and a unidirectional causality runs from employment growth rate to expected years of schooling. The Nigerian Government needs to not only control population growth but also focus on the quality of education.\n\n### Originality\/value\n\nThe paper provides insights into the relationship between population growth and human capital utilization in Nigeria focusing on the 1986-2018 period.\n\n## Citation\n\nAdeosun, O.T. and Popogbe, O.O. (2020), \"Population growth and human resource utilization nexus in Nigeria\", Journal of Humanities and Applied Social Sciences, Vol. ahead-of-print No. ahead-of-print. https:\/\/doi.org\/10.1108\/JHASS-06-2020-0088\n\n## Publisher\n\n:\n\nEmerald Publishing Limited\n\n## 1. Introduction\n\nPopulation growth has remained a key issue facing developing economies in the world. While developed countries are experiencing diminished or negative population growth, many countries in sub-Saharan Africa including Nigeria are having population growth above the economic growth rate (Zahonogo, 2016; Saghir and Santoro, 2018). With the deadline for the sustainable development goals (SDGs) fast approaching, attention is increasingly being focused on population growth and human capital development (United Nations, 2015; Swain, 2018). The population growth has its benefits which include:\n\n1. large consumer market for both domestic and foreign products which can lead to an inflow of foreign direct investments (Bell et al., 2015; Erdogan and Unver, 2015; Nauman et al., 2016).\n\n2. Increase in labour force which will increase output and economic growth (Jha and Saritha, 2019; Yakubu et al., 2020). The negative effect of population growth can include:\n\n\u2022 pressure on employment opportunities;\n\n\u2022 pressure on infrastructure, overcrowding and standard of living; and\n\n\u2022 Balance of payment problems as they may depend on imports or need to divert products for the export market for local consumption (Pandya and Sisombat, 2017; Gatawa et al., 2018).\n\nSome countries especially developed nations have challenges with diminishing population growth. They have had to set up a scheme to encourage a certain type of professionals and individuals with certain skill sets to migrate into their country to improve their population growth rate (Turner, 2018; Anson et al., 2019). They are also putting in place incentives to encourage procreation and childbirth. A country such as Spain, for example, has a minister of Sex. Although they are largely capital intensive and technology savvy, they still need a reasonable population for balance (Ahmed, 2017; Chae et al., 2018). Population growth has been of interest to scholars as early as the 19th century. Malthus theory had raised concern about possible famine and the world not being able to support itself based on population growth (Deliu and Ilea, 2018; Hendrixson et al., 2020). Fortunately, industrial advancement in agriculture and other areas did not allow the fears to materialize.\n\nThe argument by scholars on the impact of population growth on development is inconclusive as outcomes from various scholars are at opposing ends. Adewole (2012) found a positive relationship between population and growth in Nigeria on one hand while Onwuka (2006) found a negative relationship between population and growth in Nigeria. In another vein, the dilution effect of population growth was considered in the study by Bucci et al. (2019) and different outcomes were found for both developing and developed countries. Even at that, development is a broad and multidimensional construct and the human capital utilization aspect needs to be further explored. Human resource is a key determinant of firm performance and an economy at large (Adewole, 2012; Ali et al., 2018; Cunningham, 2010; Okoye and Ezejiofor, 2013). It identifies the efficiency of growth and development in the country, in varying sectors; and also reveals advancement in social norms. Nigeria, like most developing nations in the world, has put in place many economic policies in her numerous attempts to use her human resources and provide employment opportunities to enhance economic growth (Isiaka and Oghenekevwe, 2019; Uneke, et al., 2017). It has a very positive effect on economic growth and economic development.\n\nIt is crystal clear that Nigeria is not just blessed with abundant deposit or supply of diverse natural resources but also highly favoured in terms of growing human population size. According to the Nigerian National Population Census conducted in 2006, the population of Nigeria, was about 140,003,542 (National Bureau of Statistics, 2009). Annually, the rate of growth stood at 3.02%, with the population capable of yearly doubling itself in less than a decade time. Again, the United Nations calculation of 2016 put the Nigerian total population at 185,989,600. As such, the country is currently the most populous in Africa (World Bank, 2016). For a country with such a huge population size, it is imperative to incorporate or consider human resources in any feasible economic development plan because the achievement of developmental goals and realization of its objectives highly depends on the effective utilization of qualified and committed human resources as drivers of other resources.\n\nIn spite of the rising population, numerous problems exist which hinder the productivity of human resources in the country. Ineffective human resources utilization in Nigeria results from the inability to organize, sensitize and equip the human resources for the achievement of developmental goals (Adeyemi, 2009; Fapohunda, 2012; Okoye and Ezejiofor, 2013). Although a huge amount of resources has since independence been invested by numerous bodies, government departments and institutions for the purpose of training and enhancing human resources (which by extension, was to lead to poverty alleviation); however, investment has not been commensurate with the development of human resources in Nigeria (Aliyu et al., 2014; Jaiyeoba, 2015). The increasing unemployment situation has been worrisome (5.31% in 2015, 6.03% in 2018) while industrial output has been on the decline (Adeomola and Badiru, 2016; Adelowokan et al., 2019). The quality of university graduates has been called to questioning as employers say they are not workplace ready (Longe, 2017; Aloysius et al., 2018) even as their numbers continue to increase every year. The infrastructure deficiency such as epileptic electricity, bad roads and heavy traffic has furthermore contributed to the productivity and human capital output challenges (Ajide and Ridwan, 2018; Afolayan et al., 2019)\n\nRural-urban migration has also tilted the population growth in favour of urban centres with villages left to an ageing population and short of able-bodied people to farm. This has led to congested city centres and the development of urban slums. The detrimental trend of migration is an addition to the identified problems of human capital utilization in the country. Nyoni and Bonga (2018) asserted that migration may drain away valuable talents, as educated and motivated people are in most cases likely to migrate in search of opportunities. They asserted further that in 2014, about 10.7% of the highly proficient population, trained in the country will be abroad working mostly in Organizations for Economic Cooperation and Development (OECD) nations. Dao (2012) also noted that 64% of Nigerian emigrants (on the average) have attained a tertiary level of education. Summarily, these are powerful indications showing that people who should be involved in enhancing the country have abandoned the nation and used their skills and intellect to aid the development of other countries.\n\nWhile numerous moves have been made by the successive Nigerian Government at various times to tackle these problems, only negligible success has been attained (Adepoju, 2007; Emeh, 2012) and yet, Nigeria continues to experience population growth. Many studies have examined the relationship between population growth and economic growth; and the relationship between human resources and economic growth in Nigeria (Adenola and Saibu, 2017; Tartiyus, Dauda and Peter, 2015; Essien, 2016; Ogunleye-Adetona, 2010; Sankay, Ismail and Shaari, 2010). However, looking at the linkage human resources have with the population of a country, it is paramount at this juncture to examine the impact of population growth on the utilization of human resources in Nigeria and also to investigate the direction of their causality in Nigeria. Our a priori expectation is that an increase in population growth will increase human capital utilization in Nigeria.\n\nThe remainder of this paper proceeds as follows: Section 2 presents the theoretical and empirical review. Section 3 discusses the methodology used while the result discussions are presented in Section 4. Section 5 provides a conclusion and recommendations from the study.\n\n## 2. Literature review\n\n### 2.1 Theoretical literature\n\nA key theory which this study hinges upon is the optimistic theory. The optimistic theory was pioneered by Ester Boserup an economist of Danish descent in 1965. She used an argument on an increase in both population and employment to challenge Malthus theory. Instead of agricultural method determining population as assumed by Malthusians, Boserup argued that population determines the agricultural method. A major theme of her work is that \u201cnecessity begets invention\u201d. Factors that distinguished Bosernp (1965) \u201coptimistic\u201d theory compared to that of Malthusian\u2019s \u201cpessimistic\u201d theory were: causal relationship from population to agricultural productivity and not vice versa; and population growth having the capacity to further trigger the use of more intensive production techniques. Therefore, in the long-run, population growth leads to a productive initiative, which, in turn, increases economic productivity.\n\nIn essence, the optimistic theory concludes that the use of the initiative to create during difficult situations is higher. An example was during the primitive time of hunters and gatherers, which was submerged by an increase in population and led to the emergence of cultivation and agriculture. When that, too, became inadequate, intensive multi-annual cropping was developed. More recently the world experienced what is known as a green revolution which has almost quadrupled world food production since 1950 using just 1% more land and a direct reaction to population pressure (Mahmud, 2015).\n\nIn the same vein, Simon Kuznets followed the optimistic view by opining that \u201can increase in population means, other things being equal, increase in the labour force\u201d (Kuznets et al., 1960). This implies that if the labour force increases at an equal pace with the total population, it will be able to turn out as much or more product per worker. Moreover, when a greater labour force is in place, untouched natural resources will be greater used. This utilization, coupled with a more specialized division of labour will lead to a greater product per worker. In the long-run, an increase in national output will occur. Simon viewed that the population is needed to handle resource scarcity and environmental problems with innovation from both the people and the markets (Mahmud, 2015). Kuznets et al. (1960) also acknowledged that increases the population can lead to the stock of the knowledge base of an economy. This is because population increase further increases the proportion of innovators in an economy and in the long-run, the growth of product per capita.\n\nKuznets et al. (1960), however, opined some structural changes in the economy may imply that the labour force is not directly influenced by the increase in population. Some of these structural changes that lead to \u201cstickiness\u201d in the reaction of the labour force are the mobility of labour and transition to industrialization. Insufficient flows of labour to improving economic opportunities may, therefore, lead to the high cost of labour and output which will further limit economic output from getting to its full capacity.\n\n### 2.2 Empirical literature\n\nMany empirical studies have been carried out to examine the relationship between population growth and human capital utilization with varying findings obtained. With a focus on the Ugandan economy, Klasen and Lawson (2007) examined the impact of population growth on the unemployment rate and poverty. The research was conducted using both cross-section data and panel data. The result of the estimates shows that population increase positively impacted the overall unemployment rate. However, the value is usually less than one, meaning people added are of minimal proportionate impact on unemployment.\n\nIn a different economy, Afzal and Awais (2014) examined the relationship between population growth and employment rate in Pakistan. Using a simple model expressing the relationship between population growth and employment rate, the result found out that the numeric value signifying population is negative and not zero which tells that increase in population, unfavourably affects employment rate. This does not support the view that the rise in population is not a real problem. High population growth has become an important limiting factor for achieving the overall development goals. Afzal and Awais (2014) findings can be seen to imply the same as those of Klasen and Lawson (2007).\n\nTo analyse the relationship between population growth and per capita growth, Emeh, (2012) has developed a model in which technical advancement, human capital and population interrelate endogenously. We find a mixed result in this study. Population growth could have both positive and negative bearings on the advancement of the economy and the outcome would depend on the relative input of the population and human capital to the economy.\n\nFurthermore, Eze and Eze (2014) investigated the effects of an increase in population on growth in the economy. The study used GDP growth per capita in lieu of economic growth. ARDL test to Cointegration was used for the analysis. The study revealed a long-run sustainable equilibrium between economic growth and population growth through the use of the ARDL. The study again revealed a unidirectional causality between the population and the economic growth through the use of the pairwise Granger Causality test technique. This implies a positive relationship between economic growth and population growth in the long-run, contrary to Afzal and Awais (2014); and Klasen and Lawson (2007). From the same research perspective, Adenola and Saibu (2017) examined the impact of population growth on economic growth in the long-run on the Nigerian economy. Unlike Eze and Eze (2014), their study adopted the fully modified ordinary least square method and found that the benefits from the working population had not been fully maximized by the Nigerian economy. They, therefore, recommended the need for the government to spur the populace to engage in productive activities which will further trigger economic growth.\n\nAlong the same research line, Mahmud (2015) focused on the Indian economy to examine the relationship between population growth and economic growth. Using the Johansen cointegration test and VECM, the study found a positive relationship between population and economic growth and also a uni-directional relationship from economic growth to population growth. This causal relationship is in contradiction to the findings of Eze and Eze (2014) in their study carried out in Nigeria. The study recommended the need to invest in human capital and optimize utilization so as to achieve long-run economic growth. Tartiyus et al. (2015) also examined the impact of population on economic growth in Nigeria between 1980 and 2010. In line with findings from Eze and Eze (2014) and Mahmud (2015), the study found a positive relationship between an average increase in population and economic growth in Nigeria. The study recommended that it is important to maintain an average population growth if sustained economic growth will be experienced.\n\nExamining the long-run benefits of population growth, the study by Simon (2019) found similar results with those of Afzal and Awais (2014) and Klasen and Lawson (2007) in the short run. Simon (2019) observed that an increase in population in the short run places a negative impact on the standard of living as a result of diminishing returns and the transient responsibility it places upon society. It, however, comes with a positive impact on standards of living in the long-run due to knowledge advances and economies of scale. Using a simulation design, it was discovered by the studies that in the long-run, (30\u2013100\u2009years later) when juxtaposed with constant-size population, an average increase in population, enhances living conditions in developed and underdeveloped nations. We, thus, see similar results with those of Eze and Eze (2014), Mahmud (2015); Tartiyus et al. (2015) in the long-run analysis. Over the long term, a growing population tends to advance knowledge, which, in turn, increases productivity and output at a higher rate than that of population growth. The study, thus, established advantages of increased population growth with respect to the economic growth of underdeveloped nations.\n\nFollowing an empirical and theoretical path, Bucci et al. (2019) examined the \u201cdilution effect\u201d of population growth on per-capita human capital formation. The dilution effect (discussed in respect of average years of schooling at the individual level and average human capital at the aggregate level) examined the addition of new-borns (who are uneducated) which then reduced both the long-run and short-run level of physical capital per capita. Bucci et al. (2019) showed that the dilution effect was heterogenous and peculiar for each country. The regression analysis revealed that countries with high dilution effects experienced the negative relationship between population growth and economic growth while an \u201cambiguous\u201d relationship (i.e. negative, neutral or positive) existed between population growth and economic growth in countries with low dilution effect. Along with a similar research thought, Furuoka (2016) examined the advantage of high population growth in the Indian economy. Using ARDL, the study also found a negative long-run relationship between population growth and economic growth and recommended that a continued increase in population may be detrimental to the Indian economy. All these results further complement those of Afzal and Awais (2014) and Klasen and Lawson (2007).\n\nFrom another research perspective, Bashir et al. (2012) focused on the period between 1972 and 2010 to examine the cointegrating relationship between education, health and employment. VECM and co-integration examination were carried out. Conclusively, the examination revealed long-run expenses on education, health and rate of population, as prominent means of maintaining the rate of employment in Pakistan. In the end, it is suggested that there should be more spending on education to support enrolment at primary and expert levels by offering scholarships to students. For superior health and education, the government ought to expand expenses on health also. In the development of the level of employment, they are crucial players, they also perform important functions in economic and output growth through the availability of similar opportunities in the health and education sector to every individual of any nation all differences can be removed. A review of this research shows the crucial roles of health and education in minimising the rate of unemployment in the long-run and short-run. The minimum wage has also been seen to be a determining factor in employment decisions. While Zavodny (2000) observed that minimum wage had a significant negative effect on employment; Schmitz (2017) observed that minimum wage increases may lower employment but do not affect working hours.\n\nAnalysing local employment enlargement for the case of West Germany (1977\u20132009) Suedekum, Blien and Wolf (2012) kept the impact of human capital and population growth as independent factors and arrived at reasons why countries with the skilled populace, grow rapidly than countries with the less skilled population. A huge portion of a very skilled workforce reduced the consecutive rise in jobs requiring the skilled workforce. Positive impact observed on total employment growth by an increase in human capital and population growth evaluates that jobs demanding low skills are quick to increase than jobs requiring high skills. This study concludes a significant link between human capital, population growth and employment growth.\n\nAnother line of study attempted to study the importance of human capital utilization and development for sectoral and national growth. Aliyu et al. (2014) examined the role of human resource development plays in the banking sector in Malaysia and Nigeria. Using regression analysis, the study found that there exists a significant positive relationship between human resources development and the performance of banks in the two economies studied. The study, therefore, recommended greater investment in their human resources. In a broader perspective, Jaiyeoba (2015) examined the relationship between investment in human capital and economic growth in Nigeria. Using ordinary least squares, findings show a long-run relationship between human capital development and economic growth in Nigeria. Concluding along the same research line as Aliyu et al. (2014), the study recommended increased investment in education and health, the two major factors that enhance human capital development. This is quite contrary to the propositions of Bucci et al. (2019) and Furuoka (2016).\n\n## 3. Methodology\n\n### 3.1 Model specification\n\nBased on the theoretical underpinning of the work of optimistic theory by Bosernp (1965) which takes into cognizance population growth and human resource utilization; this paper seeks to evaluate the effect of increasing population on human resource utilization in Nigeria. In this study, the employment rate is used as a proxy for human resource utilization. Employment rate was used as the proxy as opposed to measures of human productivity, human resource allocation, availability or levels of human skills due to paucity of data. Following previous studies by Adenola and Saibu (2017), Furuoka (2016), Zavodny (2000) and Schmitz (2017), independent variables to be considered in this study are population growth rate, expected years of schooling and minimum wage. Data was obtained from the World Development Indicator (WDI) and Human Development Report (2019) covering a time span of 1990\u20132018. The time period is adopted due to available data and because it spans through the oil boom, the economic crisis, as well as the post-structural adjustment periods and the global economic recession \u2013 within which population stimulants have undergone different rhythms.\n\nIf the variables are of order I(0) and co-integration has been seen among the variables, then it implies a long-run relationship and there will be a need to apply the vector error correction model (VECM) as specified by Engle and Granger (1987). The VECM does not only involve the explanation of functional relationship but also a good or the best prediction of variation influence of independent factors on the dependent variable.\n\nThe functional model to be estimated in this study is, thus, specified below:\n\n(1) EMP=f\u00a0(PGR,\u00a0LAFR,\u00a0EYS)\nwhere:\n\nEMP = employment rate;\n\nPGR = population growth rate;\n\nEYS = expected years of schooling; and\n\nMW = minimum wage.\n\nThe econometric form of the model is given as:\n\n(2) EMP=\u03b20+\u03b21\u00a0PGR+\u03b22\u00a0EYS+\u03b23\u00a0MW+t\nwhere,\n\nt is a random error term representing all other variables not specified in the model\n\nThe regression equation of the VECM is as follows:\n\n(3) \u0394Yt=\u00a0\u03b11+i=1j\u03b21\u0394Yt-i+i=1j\u03c61i\u0394Xt-i+i=1j\u03c61i\u0394Xt-i+i=1j\u03b31iZt-i\n(4) \u0394Xt=\u00a0\u03b12+i=1j\u03b22\u0394Yt-i+i=1j\u03c62i\u0394Yt-i+i=1j\u03c61i\u0394Xt-i+i=1jY2iZt-i\nwhere:\n\nYt = employment rate;\n\nXt= independent variables;\n\n\u0394 = difference operator;\n\n\u03b11 and \u03b12 = constants;\n\n\u03c61 and \u03c62 = short run coefficients; and\n\nY1 and Y2 = error correction term derived from the long-run cointegrating relationship.\n\n## 4. Empirical results and discussions\n\n### 4.1 Trend analysis\n\nFigure 1 shows the trend of employment rate and population growth rate between 1990 and 2018. Between 1990 and 1992, although there was a drop in population growth rate, the employment rate kept rising. However, beginning in 1992, the employment rate started to drop as the population began to rise. Since the decline in 1992, the employment rate only began to increase in 2004 as the population increased. A further decrease was then experienced in both employment and population growth rate between 2014 and 2016. While there was a continued decline in population growth rate, the employment rate increased between 2016 and 2017 before dropping again in 2018. While the employment growth rate in Nigeria has not been stable over the years, it is saddening to note that it has reduced from 53.8% in 1990 to 51.9% in 2018. The impact of this difference can be seen as drastic with the understanding that the Nigerian population was just 95.27 million in 1990 compared to over 190 million in 2018 (World Bank, 2019).\n\n### 4.2 Descriptive statistics results\n\nTable 1 presents the results of the descriptive statistics of employment rate, population growth rate, estimated years of schooling and minimum wage from 1990 to 2018.\n\nThe descriptive statistics show that the highest employment rate within the period under study was 54% while the lowest stood at 52%. The highest population growth rate was also 2.6% while the lowest stood at 2.5%. There appears to be a significant difference in the minimum wage as the minimum value is N250 (less than $1) while the maximum was N30,000 (about$83) which is currently the minimum wage in the country. Despite this significant increase in the minimum wage, the welfare of the citizens has not been impressive as increased poverty and unemployment are major features of the Nigerian economy (Adelowokan, et al., 2019; Olotu, Salami and Akeremale, 2015). The Jacque bera test shows that the variables are normally distributed with the probabilities not significant at 5%.\n\n### 4.3 Unit root test\n\nLiterature has discovered that many time series factors are not fixed which makes the application of changing factors to the model, result in false regression which will not determine accurate prediction (Gujarati, 2003). Hence, our first step is to examine the order of integration of the series, using the Augmented Dickey-Fuller (Dickey and Fuller, 1979) and Phillips- Perron tests (Phillips and Peron, 1988).\n\nTable 2 shows that the variables are of the same order, thus, we conclude that all the variables have a unit root at I(1). That is, a short-run equilibrium exists between the variables. We then apply the use of Johansen and Juselius (1990) co-integration technique model to predict the availability of a long-run relationship among these variables.\n\n### 4.4 Co-integrating result\n\nTable 3 reveals the cointegration test of the variables used in this study. There are two cointegrating equations which show that there are no spurious correlations and prove the existence of long-run relationship among the variables.\n\n### 4.5 Vector error correction model\n\nAs the factors are co-integrated for a long-run relationship, an Error Correction Model was computed to ascertain the speed at which shocks can be corrected in the long-run; the outcome derived is presented in Table 4.\n\nTable 4 presents the long-run and short-run effect of population growth rate, expected years of schooling and minimum wage on the employment rate. In the short run, there is a positive relationship between population growth rate and employment growth rate; however, in the long-run, the population growth rate shows a negative relationship with the employment growth rate. Expected years of schooling and minimum wage also reveal a positive relationship. In the long-run, a percent increase in population growth rate will reduce the employment growth rate by \u22127.99% which shows a very huge effect; this relationship is, however, positive in the short run. A percent increase in expected years of schooling will, however, increase the employment growth rate by 0.65%. This shows the relevance of education in human resource utilization while increased growth rate may be inimical to the utilization of human resources in the economy. This effect of an increase in the minimum wage is also quite significant in the employment growth rate. Contrary to findings by Zavodny (2000) and Schmitz (2017) where minimum wage negatively impacted employment decisions, this research shows that a percent increase in the minimum wage is capable of increasing the employment growth rate by 3.6%. Our findings, thus, show that an increase in population growth rate may be disadvantageous to human resource utilization (this is also in line with outcomes from Furuoka, 2016 and Simon, 2019) while years of schooling and minimum wage play more important roles in influencing human resource utilization.\n\nThe coefficient of determination of 0.73 indicates that 73% of the total variation in employment rate is explained by the population growth rate, expected years of schooling and minimum wage during the period of this study while other exogenous variables account for about 27% of the variation in the employment rate. This implies that population growth rate, expected years of schooling and minimum wage had a significant implication on employment rate position in Nigeria during the period of this study. Finally, the ECM measures the speed of adjustment of variations due to unexpected shocks. The ECM is negative (\u22120.384569) and significant which indicates a long-run causality from population growth rate, expected years of schooling and minimum wage to the employment growth rate. It also shows that disequilibrium in the previous periods is adjusted at a speed of about 38% annually.\n\n### 4.6 Granger causality test\n\nHaving established that there is a long-run correlation among the variables, the objective of this section is to determine the direction of the causality among the variables during the period 1990 to 2018.\n\nTable 5 reveals that unidirectional causality runs from employment rate to population growth rate and also a unidirectional causality also runs from employment growth rate to expected years of schooling. Also, there is a unidirectional causality relationship from minimum wage to employment growth rate at 10% level of significance. This shows that while the employment rate can cause the population to increase, population growth does not cause employment growth. On the other hand, the minimum wage can cause the employment growth rate to increase but the employment growth rate cannot cause minimum wage.\n\n### 4.7 Impulse response function\n\nFigure 2 reveals the impulse response function showing the responsiveness of employment growth rate to shocks in employment growth rate, population growth rate, expected years of schooling and minimum wage up to period 10. The impulse response function is depicted by the thick lines.\n\nThe response of employment rate to itself shows that shocks in employment rate indicate a positive impact all from the first period to the tenth period, albeit at different degrees. The response of expected years of schooling to employment growth rate, however, showed varying negative impact all through the 10 periods. For the response of population growth rate to employment growth rate, there seems to be a zero-impact from period one to four, after which a positive impact is seen over periods five to ten. The correlations among employment growth rates and identified independent variables can, thus, be seen to be relatively complex.\n\n## 5. Conclusion and recommendations\n\nThe main drifts of this research are to examine the impact of population growth on human resource utilization in Nigeria and also to investigate the direction of causality between them. In a bid to accomplish these objectives, the population growth rate measured in the annual growth rate was instead used for population growth while the employment rate was used as a proxy for human resource utilization. Using a time-series data from 1990 to 2018 sourced from the World Development Index (WDI) and United Nations Report, the Augmented Dickey-Fuller, Philip Perron test and Johansen\u2019s co-integration technique were used to examine the unit root and also for the confirmation of co-integration among the respective factors. The results from the unit root and Johansen co-integrating equation revealed that long-run relationships exist between employment rate, population growth rate, expected years of schooling and minimum wage.\n\nIn a bid to investigate their long-run relationship, this study has used the use of VECM to ascertain the speed at which shocks can be corrected in the long-run. The result from the VECM revealed that the population growth rate has a negative relationship and a significant effect on the employment rate in Nigeria. This implies that an increase in population growth rate in Nigeria does not increase the number of populace used in the labour market. This is because the effect of the supply of labour on unemployment would be the opposite of the request for labour effects. Our findings show that the Optimistic theory does not apply to the Nigerian economy. A number of factors determine the supply of labour in an economy and the chief among them is the level of growth in population. Furthermore, the result from the Granger causality test shows a single-direction course flowing from employment rate to expected years of schooling and from minimum wage to employment in Nigeria. This implies that the employment growth rate has a predictive effect on expected years of schooling in Nigeria and the minimum wage also has the ability to predict the employment rate in Nigeria. There has been a moderate increase in the minimum wage in Nigeria over the years, therefore, employers may not find it difficult to pay the minimum wage to their workers bearing in mind inflation and other macroeconomic factors in the economy. This study has to some extent enhanced our understanding of the relationship between population growth and human capital utilization with the general findings of the study pointing to the fact that population growth in Nigeria may not lead to a rise in the utilization of human resources.\n\nBased on our analysis and research findings, this study, therefore, recommends that Nigeria needs to adopt a skilled-oriented education principle to train skilled and technically strong manpower, so as to build and maintain its critical infrastructure to drive the economy. Following the significant relationship in expected years of schooling and employment rate in Nigeria, an increase in skill-oriented education during the period of formal education in the country will boost employment as graduates need not find white-collar jobs to be used or engaged in productive activities. This will, thus, lead to good utilization of human capital. Furthermore, the notion that population increase in Nigeria is a key to the control of political power and resources should be discarded and proactive approach such as engaging in labour-intensive projects, industrial development projects capable of absorbing a large number of labour, large scale farming to make available food and security for the incessantly rising population should be adopted.\n\nA major limitation of this study is the use of the employment rate as a proxy for human capital utilization. This may be less than desirable; howbeit we are constrained in the absence of any other viable options. Future studies can adopt measures that greater capture human productivity, human resource allocation and levels of human skills; to examine the interactive effect on economic productivity.\n\n## Figures\n\n#### Figure 1.\n\nTrend analysis of employment rate and population growth in Nigeria\n\n#### Figure 2.\n\nImpulse response for the employment growth rate equations\n\n## Table 1.\n\nSummary statistics\n\nEMP PGR EYS MW\nMean 52.90841 2.576448 8.106897 7,956.897\nMedian 52.929 2.579 8 6,000\nMaximum 53.866 2.681 9.7 30,000\nMinimum 51.752 2.489 6.7 250\nStd. dev. 0.523451 0.070998 1.000689 8,410.524\nSkewness \u22120.346032 0.137795 0.031262 0.837697\nKurtosis 3.264361 1.470314 1.817862 2.634859\nJarque-Bera 0.66318 2.9192 1.69331 3.55283\nProbability 0.717782 0.232329 0.428847 0.169244\nSum 1,534.344 74.717 235.1 230750\nSum Sq. dev. 7.672027 0.141141 28.03862 1.98E\u2009+\u200909\nObservations 29 29 29 29\n\nSource: Authors\u2019 computation, 2020\n\n## Table 2.\n\nUnit root test result\n\nVariables ADF statistics Critical values Order of\nintegration\nPP statistics Critical\nvalues\nOrder of\nintegration\nEMP \u22123.3155 \u22122.9763 I(1) *\u22121.8815 \u22121.9534 I(1)\nPGR *\u22121.7341 \u22121.955 1(1) \u22122.0567 \u22121.9539 1(1)\nEYS \u22125.9473 \u22122.9763 I(1) \u22125.9474 \u22122.9763 I(1)\nMW \u22124.2521 \u22122.9763 I(1) \u22124.2521 \u22122.9763 I(1)\n\nSource: Authors\u2019 computation.\n\n*\n\nIndicates statistical significance level at 10%\n\n## Table 3.\n\nJohansen co-integration test\n\nUnrestricted co-integration rank test (trace)\nHypothesized Trace 0.05\nNo. of CE(s) Eigenvalue Statistic Critical value Prob.**\nNone* 0.675031 65.38279 47.85613 0.0005\nAt most 1* 0.600859 35.03409 29.79707 0.0114\nAt most 2 0.315519 10.23622 15.49471 0.263\nAt most 3 2.47E-05 0.000667 3.841466 0.9807\nNotes:\n\nTrace test indicates two cointegrating eqn(s) at the 0.05 level.\n\n*\n\nDenotes rejection of the hypothesis at the 0.05 level.\n\nSource: Authors\u2019 computation\n\n## Table 4.\n\nVECM result\n\nCointegrating eq: CointEq1\nEMP(\u22121) 1\nPGR(\u22121) \u22127.985803 (\u22120.85835)\nEYS(\u22121) 0.646576 (\u22120.06263)\nMW(\u22121) 3.56E\u221205 (\u22127.50E\u221206)\nC \u221237.8422\nError correction: D(EMP) D(PGR) D(EYS) D(MW)\nCointEq1 \u22120.384569 (\u22120.20735) 0.016437 (\u22120.00325) \u22121.114332 (\u22120.69929) 1615.89 (\u22126874.31)\nD(EMP(\u22121)) 0.586824 (\u22120.2312) \u22120.018602 (\u22120.00362) \u22120.388394 (\u22120.77974) 4798.513 (\u22127665.16)\nD(PGR(\u22121)) 16.35335 (\u22125.33388) 1.622397 (\u22120.08353) 26.5987 (\u221217.989) \u2212214993.1 (\u2212176838)\nD(EYS(\u22121)) 0.008181 (\u22120.11752) \u22120.008142 (\u22120.00184) 0.086455 (\u22120.39634) \u22122002.705 (\u22123896.16)\nD(MW(\u22121)) 4.71E\u221206 (\u22121.10E\u221205) \u22122.90E\u221208 (\u22121.80E\u221207) 2.75E\u221206 (\u22123.80E\u221205) \u22120.3811 (\u22120.37304)\nC \u22120.119065 (\u22120.03124) \u22120.000891 (\u22120.00049) 0.089153 (\u22120.10535) 1839.735 (\u22121035.58)\nR2 0.734664 0.991079 0.39607 0.252979\nAdj. R2 0.585413 0.986061 0.056359 \u22120.167221\nSum sq. resids 0.195066 4.78E\u221205 2.218746 2.14E\u2009+\u200908\nS.E. equation 0.110416 0.001729 0.372386 3660.697\nF-statistic 4.922326 197.5103 1.165903 0.602045\nLog-likelihood 26.71027 134.7831 \u22124.897397 \u2212243.9214\nAkaike AIC \u22121.285406 \u22129.598701 1.145954 19.53242\nSchwarz SC \u22120.801522 \u22129.114818 1.629837 20.0163\nMean dependent \u22120.073885 0.0025 0.115385 1144.231\nS.D. dependent 0.171484 0.014646 0.383346 3388.343\nDeterminant resid\n0.042855\nDeterminant resid covariance 0.006146\nLog-likelihood \u221281.37407\nAkaike information criterion 9.64416\nSchwarz criterion 11.77325\nNote:\n\nStandard errors are in ()\n\nSource: Authors\u2019 computation 2020\n\n## Table 5.\n\nGranger causality test result\n\nNull hypothesis: Obs F-statistic Prob.\nPGR does not Granger Cause EMP 27 1.61753 0.2211\nEMP does not Granger Cause PGR 0.19023 0.8281\nEYS does not Granger Cause EMP 27 1.36915 0.2752\nEMP does not Granger Cause EYS 3.75907 0.0394\nMW does not Granger Cause EMP 27 2.71593* 0.0883\nEMP does not Granger Cause MW 2.06588 0.1506\nEYS does not Granger Cause PGR 27 0.44844 0.6443\nPGR does not Granger Cause EYS 0.01255 0.9875\nMW does not Granger Cause PGR 27 0.75543 0.4816\nPGR does not Granger Cause MW 0.23223 0.7947\nMW does not Granger Cause EYS 27 1.14787 0.3356\nEYS does not Granger Cause MW 2.08772 0.1478\nNote:\n\n*Denotes significance at 10%\n\nSource: Authors\u2019 computation, 2020\n\n## References\n\nAdelowokan, O.A., Maku, O.E., Babasanya, A.O. and Adesoye, A.B. 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(2020), \u201cLabour force participation and economic growth in Nigeria\u201d, Advances in Management and Applied Economics, Vol. 10 No. 1, pp. 1-14.\n\nZahonogo, P. (2016), \u201cTrade and economic growth in developing countries: evidence from sub-Saharan Africa\u201d, Journal of African Trade, Vol. 3 Nos 1\/2, pp. 41-56.\n\nZavodny, M. (2000), \u201cThe effect of the minimum wage on employment and hours\u201d, Labour Economics, Vol. 7 No. 6, pp. 729-750, doi: 10.1016\/s0927-5371(00)00021-x.\n\nFox, S., Bloch, R. and Monroy, J. (2018), \u201cUnderstanding the dynamics of nigeria\u2019s urban transition: a refutation of the \u2018stalled urbanisation\u2019 hypothesis\u201d, Urban Studies, Vol. 55 No. 5, pp. 947-964.\n\nHossain, M.Z., Khan, M.O.A. and Ahmed, J.U. (2016), \u201cDeterminants of rural-urban migration in Bangladesh including its consequences for origin households and urban amenities\u201d, Research and Reviews: Journal of Statistics, Vol. 5 No. 2, pp. 47-61.\n\nNational Population Commission (NPC) [Nigeria] (1998), \u201c1991 Population census of the federal republic of Nigeria: analytical report at the national level\u201d, Lagos.\n\n## Acknowledgements\n\nThe authors acknowledge everyone who has and will still contribute to the great success of this research work. Special thanks to Owolabi Kayode for his contribution towards the research.\n\nFunding details: The authors received no direct funding for this research work.\n\nDeclaration of interest statement: The authors declare no conflict of interest.","date":"2021-02-25 05:22:07","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.4490070044994354, \"perplexity\": 3995.638949840933}, \"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-2021-10\/segments\/1614178350717.8\/warc\/CC-MAIN-20210225041034-20210225071034-00101.warc.gz\"}"}
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AMONG THE JANEITES
Book Club Guide
Buy / Share the Book
Other People's Children
ABOUT JANE AUSTEN
Her Life
Her Work
Austen's eyes
By Deborah Yaffe, Mar 16 2017 01:00PM
When the whole world is gobbling down a giant ice cream sundae, it can be hard to come along and insist we all switch to spinach. But such is my task today, as I confront the latest Amazing! Austen! Revelation!
I speak of course of the news – I use that word advisedly – that Jane Austen's eyeglasses show she died of arsenic poisoning.
This alleged new biographical fact came our way courtesy of last week's blog post by British Library curator Sandra Tuppen, who was reporting on a new research project undertaken by library staff: the analysis of the prescription strength of three pairs of spectacles that the library owns and that may have belonged to Austen.
Optometrical analysis concluded that Austen was far-sighted ("long-sighted," in British terminology) and that one of her glasses had a very strong prescription, much stronger than the other two. Cataracts can cause deteriorating eyesight; arsenic exposure can cause cataracts; Regency folk were routinely exposed to arsenic in medication, among other places; and at least one writer has speculated that the symptoms of Austen's final illness suggest arsenic poisoning. Q.E.D.
Well, not quite Q.E.D: to be fair to Tuppen, she concludes only that the analysis of the eyeglasses "may indeed give further credence" to the arsenic-killed-Austen theory. Blame headline writers for cutting the qualifiers to get to the arsenic-sprinkled ice cream sundae of a good story.
By now – after all the real-Mr.-Darcy stories and the this-stately-home-was-the-model-for-Pemberley stories and the newly-discovered-love-of-Jane-Austen's-life stories – it's probably pointless to note the six degrees of plausible-to-wild speculation required to get from A to B on this one. But I'll give it a try nonetheless. I'm a dedicated player of Janeite Whac-a-Mole.
This story requires us to assume that:
1. These eyeglasses belonged to Jane Austen (and not someone else in her family);
2. They were prescribed by a physician who accurately measured Austen's eye strength (and weren't off-the-shelf purchases that might have been too strong);
3. They represent deteriorating eyesight (and not a choice to use stronger lenses for close-up work);
4. The deteriorating eyesight was caused by cataracts (and not just normal aging);
5. The cataracts were caused by arsenic exposure (and not something else);
6. The arsenic exposure was severe enough to kill (and wasn't superseded by some other cause of death).
It all might be true. But we have virtually no evidence for any point except the first. Personally, I like my biographical facts to be, you know, factual. Spinachy, if you will. But hey – have another scoop of ice cream, if you prefer.
As a side note: You also can't blame Tuppen for a further embellishment of this story -- the claim, apparently first made by Austen scholar Deirdre Le Faye in the New York Times account of the brouhaha, that the British Library's post says Austen "must have been almost blind by the end of her life," a point Le Faye disputes by noting that Austen was handwriting letters until six weeks before her death.
In fact, Tuppen's post makes no such claim – the word "blind" doesn't even appear in it. Tuppen says only that Austen complained of "weak" eyes. Still, the blindness claim immediately struck me, because, as it happens, the very strong +5.0 prescription in the right-hand lens in one of the pairs of Austen eyeglasses is the same strength as the prescription in one of my eyes (the better one, believe it or not!) -- although, because I am nearsighted, my prescription is -5.0.
My vision is very bad: without my contact lenses, objects begin to look fuzzy to me at seven or eight inches away, and I can't recognize even close friends at a distance of a couple of yards. Reading is impossible unless the book is practically glued to my nose, and God forbid that I should ever try to drive in that condition.
But I wouldn't say I'm "almost blind" (or, as the Daily Mail describes Austen's state, "almost totally blind.") I can distinguish my surroundings. I don't walk into walls. I don't get lost on my way to the bathroom at night. And more to the point, I always wear my lenses, which correct my vision into reasonable adequacy. If Jane Austen's eyes were anything like mine, I'd bet she, too, could manage just fine.* (And for the record: I don't have cataracts and no one is poisoning me with arsenic. At least as far as I know.)
So Jane Austen wasn't blind, or even close. But did she die of arsenic poisoning? We don't know. We are no closer to knowing than we were before the glasses were tested. We have no direct evidence either way. Eat your spinach.
* Online vision simulators offer a rough sense of what the world looks like with various eye prescriptions. The near-sighted simulator is here and the far-sighted version is here.
Filed under: British Library, Austen, Jane, Le Faye, Deirdre
Mar 25 2017 07:35PM by A. Marie
Well said, as always! (And as far as "very bad" vision is concerned, I'll see your -5.0 and raise it to my -8.0 in one eye and -8.75 in the other. Nevertheless, like both you and JA, I'm managing to make my way around without a white cane, and even to earn a modest wage with the written word.)
Apr 8 2017 08:52PM by dyaffe
Yeah, this whole story struck me as wildly exaggerated. But that's life for us Janeites. . .
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Победа () — деревня в Гафурийском районе Республики Башкортостан Российской Федерации. Входит в состав Табынского сельсовета.
География
Географическое положение
Находится на берегу реки Белой.
Расстояние до:
районного центра (Красноусольский): 28 км,
ближайшей ж/д станции (Белое Озеро): 46 км.
Население
Согласно переписи 2002 года, преобладающая национальность — русские (100 %).
Примечания
Ссылки
Совет муниципальных образований Республики Башкортостан
Населённые пункты Гафурийского района
Населённые пункты на Белой (приток Камы)
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{"url":"https:\/\/keenwiki.shikadi.net\/wiki\/Patch:Sprite_direction","text":"# Patch:Sprite speed\n\n(Redirected from Patch:Sprite direction)\n\nThis page is a tutorial page on patching sprite speeds and jump heights. It contains information on what sprite speed is and how to patch it. A sprite's speed is, unsurprisingly, how fast a sprite is moving. Other sprite variables are discussed briefly in Patch:Galaxy Sprite Parameters.\n\nThere are two directions of speed, vertical and horizontal. Speeds are usually given in pixels (16ths of a tile) with 'positive' speeds ($0000W-$7FFFW) being right or down and 'negative' speeds ($8000W-$FFFFW) being left and right. (But see the section on direction below.)\n\nIt is possible to patch speeds in decimal, like all patches, which may be simpler for newer modders. A speed of +-10 looks better than $000AW\\$FFF6W. However values of 0-256 patch only one byte, which can cause problems. Otherwise patching speeds is quite simple, both action and normal speeds require a simple two byte patch.\n\n## Speeds in Vorticons vs Galaxy\n\nIn Keen Vorticons sprite speeds are set in the sprite code. Most speeds are horizontal speeds, vertical speeds being mainly used to set jump heights. (Though exceptions exist, such as the Scrub. 'Coded' speeds are always 'smooth'; that is the sprite will not jump from one place to another, but smoothly cover all points between. That is a sprite with a speed of ten pixels per second will move one pixel every tenth of a second, giving the impression of smooth gliding movement.\n\nIn Galaxy the situation is more complex; not only are speeds given in spite code, but also in sprite actions. While coded speeds are smooth, 'action speeds' can be jerky, making the sprite move in fits and bursts, or even teleport from one place to another without covering the distance between. This is detailed in Patch:Galaxy Action Parameters.\n\nAs well as these two kinds of speeds there is the variable of sprite direction, detailed in the section below.\n\nKeen Dreams uses the same methods as galaxy.\n\n## Direction\n\nSpeed and direction are two different variables. (Actually four, horizontal and vertical values exist for speed and direction.) Sprite direction can be considered the direction the sprite is facing, is it looking left, right, up or down (Or nowhere)? Direction has one of three values, -1, 0 and 1. (Left, nowhere, right.) If a direction is not set, it is 0.\n\nThis affects two things, firstly it affects the animation used. In Vorticons the horizontal direction controls which sprite animation is displayed whereas in galaxy both the horizontal and vertical direction can influence this (With horizontal taking priority.) If a sprite's direction is 0 it will show the same sprite as if it were facing left.\n\nDirection may also affect action speed. A sprite with a horizontal action speed of 40 pixels will move 40 pixels right if its direction if right (or none) but will move 40 pixels left if the sprite's direction is left.\n\nKeen Vorticons does not have independent sprite direction, a sprite that is moving left is automatically facing left, one moving right is facing right and one sitting still facing right. (In Galaxy and Dreams it is possible for a sprite to be facing left while moving right and so on.)\n\nIt is possible for a sprite's direction OR its' speed to affect other things if that is coded, as well as the action speed (Though this is not done by default.)\n\nSometimes two speeds do not make sense, jump heights can be positive (In theory downwards, not upwards.) and a sprite may use a negative speed to move right. As such the relation between magnitude and direction is a guide only and it is wise to pay attention to the default magnitude.\n\n## Examples\n\nThe following alters Keen 1's Yorp's walking speed. The speed is set when looking for Keen, (but not the direction.) As can be seen, this is a good example of the Vorticons 'two speed' system.\n\n### Keen 1\n\n%patch $1A1C$FFC4W #If right of Keen after searching (Move left)\n%patch $1A14$003CW #If left of Keen after searching (Move right)\n\n\nThis patch illustrates the Keen 4 Dart speeds. There are three types of dart, up, down and left\\right. Notice that both the speed and direction are set here and that in the case of the horizontal darts the direction controls whether they move left or right.\n\n### Dart speeds\n\n#Horizontal darts\n%patch $327FC [$0040W] [$0000W] %patch$3281A [$0040W] [$0000W]\n\n#Up darts\n%patch $32838 [$0000W] [$0040W] %patch$32856 [$0000W] [$0040W]\n\n#Down darts\n%patch $32874 [$0000W] [$0040W] %patch$32892 [$0000W] [$0040W]\n\n\n### Keen 4 dart directions\n\n#Down dart\n%patch $12948$0000W #H\n%patch $1294D$FFFFW #V\n\n#Right Dart\n%patch $12965$0001W #H\n%patch $1296A$0000W #V\n\n#Up Dart\n%patch $12982$0000W #H\n%patch $12987$0001W #V\n\n#Left dart\n%patch $1299F$FFFFW #H\n%patch $129A4$0000W #V","date":"2021-12-01 09:59:53","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\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3552244305610657, \"perplexity\": 4136.424639643132}, \"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-2021-49\/segments\/1637964359976.94\/warc\/CC-MAIN-20211201083001-20211201113001-00314.warc.gz\"}"}
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Calories: When consuming a pint-sized craft beer, the number of calories in that beverage can be pretty high. In general, such beers can range from about 200-400 calories. Obviously ever beer differs and, if you want to know the specific number, you will have to do some research on the individual beer of consumption.
To put that in perspective, it is recommended that you eat somewhere between 2,000-2,500 calories a day to maintain your current weight (the numbers alter for various reasons). If you're eating a 2,000-calorie daily diet, that allows you about 667 calories per meal. If you are drinking a 300 calorie beer, that takes up about half of an entire meal. So, if you are trying to lose or maintain your current weight, be mindful of these numbers. Choose beers that have lower caloric value – typically light, mass-produced beers like a Bud Light (183 calories per pint). Or, if you'd like to treat yourself to an IPA, make sure to keep the calories in your other meals a little smaller to combat that. And, if you drink a craft beer or two one day, and go over your caloric limit, just make sure to give yourself a boozy break the next day.
Promotes Snacking: We've all been there, you head home after a long night of drinking and either make that infamous, drunken taco bell run or hit up Papa John's for their late-night pizza deals. Your stomach is full, but your brain is so buzzed that you stuff your face with all that crap. And I'm not judging, in fact, I'm getting hungry thinking about a Cheesy Potato Burrito and some garlic bread with Papa's famous garlic dip!
The issue is that on topof drinking your calories, you're also adding unhealthy, junk food with a high caloric value to that mess already going on inside your stomach. Even if you ultimately throw everything up, one hour after that food or booze hits your tongue, the calories are already absorbed by your body and that trip to the toilet won't help you much. My advice is to plan ahead. Give yourself some restrictions that don't allow you to add those extra snacks. Only bring a certain amount of cash out with you, so that you won't even be able to afford a late-night burrito. Throw a bag of chips in your purse or pocket so that you'll get your fix of that junk food craving, but won't be able to go overboard. Do whatever works for you – just plan ahead. And, if all else fails and you end up greeting the Papa John's driver when you get home, just go with moderation. Eat one slice of pizza instead of the entire pie (guilty!).
Hangovers: Hangovers are a nasty thing that no one enjoys. Everyone's method of handling or avoiding a hangover will be a bit different – but there are some tips that can definitely ease the hangover or help you avoid it entirely. There is the obvious method of not drinking enough to cause a hangover, but sometimes we want to have a good time and that doesn't always work. If I've had a lot to drink, I make sure to pop some ibuprofen and chug some water before I go to bed. For the most part, it works every time! You can also make sure to hydrate yourself while drinking. Try to do the one water for every beer trick and see if that helps! It may also be good to keep a note, in your phone, of the beers you drank on the nights before you wake up with a bad hangover. See if there is some sort of trend that tends to cause worse hangovers than others.
Having a hangover is not fun, but on top of feeling like crap, it can contribute to a continuation of the bad habits from the previous night. I don't know about you, but when I'm hungover, there's not a chance I'm doing anything productive, working out, or eating healthy for, most likely, the entire day. So, if you're trying to minimize beer's impact on your waistline, try to avoid getting a hangover so that you can get right back on track the morning after your night of drinking.
Regular exercise: I try to workout at least 5 days a week and include a variety of cardio and strength training. Exercise will help you burn off some of the extra calories you may have earned with beer.
No alcohol on weekdays: I try to avoid any alcohol on Mondays-Thursdays to limit my weekly consumption and help keep me on track for my early-morning workouts. It doesn't have to be weekdays, though, just try to make sure there are at least 2-3 days a week where you don't drink at all.
Healthy eating: make sure you are healthy meals as often as possible. This will help you lose weight, promote healthy habits which may curb the desire to drink as often, and, sometimes, leave a little more room for beer if you choose to that day.
DRINK WATER: 'nuff said. You should be drinking half of your body weight, in ounces, each day. Water helps your body in more ways than I can describe in one post. Not to mention, beer is a diuretic – which means that you will become dehydrated from drinking it and water, obviously, helps fight that!
Drink in moderation and find what works for you. The one last point I will make, though, is that, for adults, "moderation" is considered one drink, daily, for women and two drinks, daily, for men. I can't remember the specifics on that, but I do know that men's and women's bodies process alcohol differently, hence the difference in numbers. I do, also, believe those numbers are in reference to light beers, so keep that in mind as well. Beer is an amazing beverage, but sometimes the tastiest things aren't the healthiest. Just keep your gut, liver, and overall health in mind when consuming this beverage and your waistline and future body will thank you!
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BACKGROUND: The Eiroa family has a long and storied history in the cigar industry, dating back to before the Cuban Revolution as tobacco growers and then in Honduras as tobacco growers and cigar producers.
When Christian Eiroa left Camacho to launch Tabacalera Unidas, his first priority was to get the company off the ground and to build a solid footing, but once that was settled he was able to begin the process of creating the cigar that would bear the Eiroa family name. Ultimately, he went back to his roots, finding the perfect Honduran tobaccos to make a cigar that is now called Eiroa.
The Eiroa by Christian Eiroa is being manufactured in the company's brand new El Aladino factory in Honduras. Each exquisitely crafted cigar pays tribute to the Eiroa family, a cigar family with a legacy 100 years in the making.
Martell Cordon Bleu is the cognac for true connoisseurs and has acquired legendary status since its creation by Edouard Martell in 1912. Its distinctive taste, characterized by a predominance of eaux-de-vie from the Borderies growth, and its classy bottle design make it a classic unequalled in the world of cognac.
In the Cordon Bleu, we have a unique cognac in the XO category. The different parts of the blend have been aged for between 10 and 25 years, well beyond the regulatory six.
This review is on the Lou Rodriguez Edición Reserva Bom Bom. I first featured this cigar in Episode 336 of the Stogie Fresh 5 podcast back on Saturday, October 27, 2012. These cigars have been resting for 1 year, 3 months and 9 days and I pulled out my last two samples for this review.
BACKGROUND: For those of you who don't know, Edgar Hoill, he is a renowned photographer who is also known by his moniker, "One Shot, One Kill," or simply, OSOK. This speaks to his uncanny ability to take a perfect photo on the first try.
The EH Cigars inaugural cigar line is available in three unique vitolas and is purportedly a complex and full-bodied blend. The wrapper, binder and filler tobaccos are all from Nicaragua, but the blends vary according to shape and size. Each cigar has a unique taste due to its blending and unusual shape.
Today's cigar is called the Cultura (Culture) and it's a true pyramid. That is, it's widest at the foot and gradually and consistently tapers toward its smallest ring size at the head.
This week's featured stogie is the 4.5" by 54 ring gauge Short Robusto.
Hermitage Brewing Company was established in 2009 and is located in San Jose. California. Along with producing its own label of small batch beers, Hermitage contracts with beer and soda clients to produce their products. Today I'm featuring the Fruit Crate Pumpkin Ale, which is a seasonal ale that utilizes brewery-grown Heritage Pumpkins.
Davidoff Releases 2014 Limited Edition: Year of the Horse.
The Davidoff Colorado Claro series is expanding with the addition of the new Aniversario No. 3.
This review is on the La Palina Classic Robusto. I first featured this cigar in Episode 335 of the Stogie Fresh 5 podcast back on Saturday, October 20, 2012. They have now been resting a total of 1 year, 2 months and 27 days in my humidor prior to this review.
BACKGROUND: In 1988, Davidoff of Geneva was established to bring the world's finest cigars to American soil. To honor this very important milestone, the Master Blenders from Davidoff drew on their stock of extra aged Dominican tobaccos to create what they consider to be a timeless cigar.
Rolled in a stocky Robusto format, the cigar features Davidoff's own Dominican Yamasá wrapper, which was first unveiled on a regular production cigar with the advent of the Puro d'Oro series. The rest of the blend for the 25th anniversary stick also features tobaccos from the Dominican Republic.
This week's featured cigar comes in just a single size and it is the 5-inch by 56 ring gauge Robusto Gordo.
The Macallan estate, called Easter Elchies House, was built in 1700. The estate covers 390 acres, of which some 90 acres are sown in the spring with the Minstrel barley variety to make The Macallan scotch. The Macallan 21-year uses scotch aged in three different barrel-seasoned spirits: American Oak sherry casks, American Oak bourbon casks and Spanish Oak sherry casks.
This review is on the Avo 25th Anniversary Edition Toro. I first featured these cigars in Episode 334 of the Stogie Fresh 5 podcast back on Saturday, October 13, 2012. They have now been aging for a total of 1 year, 2 months and a day and I pulled out two more samples this past week for this review.
BACKGROUND: This week's featured cigar from Casa Fernández is the Miami Reserva Maduro. This cigar is made with binder and filler tobaccos all coming from the Aganorsa farms in Nicaragua. The cigar is then wrapped in a Mexican San Andres Maduro wrapper leaf.
The Miami Reserva Maduro comes in three sizes: a 6" x 54 ring Toro, a 6" x 60 Toro Gordo and the cigar I'm reviewing today, a 5 ¼" x 46 ring gauge Corona Extra.
The Bruery, which is located in Placentia, CA, has as its mission to create beers with character and depth using the simplest and purest of means. They don't filter or pasteurize their beers. The majority of their bottled beers gain carbonation through 100% bottle conditioning, which allows carbonation to naturally occur through a secondary bottle fermentation.
• Afterword about Grand Re-Opening at The Boss Cigars.
I first reviewed the Respect, Hooah Robusto from AKA Cigars back in Episode 333 of the Stogie Fresh 5 podcast back on Saturday, October 6, 2012. These cigars have been resting for a total of 1 year, 3 months and 7 days prior to this review.
|
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| 2,818
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Dhofar, Dofar, Zufar o Dhufar () és la regió més occidental del sultanat d'Oman, fronterera amb el Iemen (amb la regió de Mahra). És un territori d'aspecte diferent de la resta d'Oman.
Història
La ciutat de Zufar a la costa del modern Dhofar, va donar nom a la regió. Una tradició diu que ja existia abans de l'islam però cap prova s'ha trobat en aquest sentit, i el port preislamic per encens era Smhrm/Smrm (Samahram, corresponent al modern Khawr Rawri, a l'est d'al-Balid). De fet Zufar no era un port pròpiament, i correspon avui dia a les ruïnes d'al-Balid, a uns 5 km a l'est de la capital moderna Salala. Se l'esmenta a l'edat mitjana; a l'inici del hi van arribar els manju o mandjawiyyun, després de la decadència de Siraf al . En aquestos dos segles (XI a començament del XIII) hi va haver un sultanat dels mandjàwides, dinastia encapçalada a l'inici del per Muhammad ibn Ahmad al-Mandjawi, que segons l'historiador Abu Makrama (+1540) que pertanyia a un poble anomenat Buluk, i hauria mort vers 1203/1204 acabat la dinastia. Els Buluk (Bulh) segons l'historiador Muhammad al-Kindi (+1892/1893) són un subgrup de la tribu iemenita dels Madhhidj. Aquestos colons haurien construït el port de Mirbat proper a Zufar. Llavors una família hadhrami, els habúdides (de Habuda que podria ser Habuza prop de Shibam) es va apoderar de Zufar; la ciutat fou destruïda pel cap habúdida Ahmad per por que fos ocupada pels aiúbides, i reconstruïda com a nova ciutat amb el nom d'al-Mansura o al-Kahira, si bé el nom de Zufar es va continuar utilitzant de fet. La ciutat fou fortificada, i tenia quatre portes; gaudia de bona aigua i cultius de canya de sucre i plàtans.
El 1278 fou conquerida pels rassúlides que la van atacar per mar (des d'Aden) i per terra (un destacament seguint la costa i un altre baixant pel Wadi Hadramaut). No fou necessària cap batalla: quan les forces rassúlides es van reunir al port de Raysut, els habúdides, el cap dels quals Salim havia mort en un tumulte, es van rendir; els habitants hadhramis foren amnistiats i amb mercaders nouvinguts, la ciutat va passar a ser un centre comercial. El domini rassúlida va durar fins al final del , bé governant directament o per mitjà d'una branca de la família que a vegades era independent i a vegades depenia del govern de Taizz (la capital rassúlida). No hi ha referències sobre el , excepte al final del segle quan la ciutat hauria caigut en mans dels kathiri, grup tribul de la regió que el 1462/1463 es van apoderar d'al-Shihr a la costa i en endavant la seva activitat va tenir per centre l'Hadramaut i no la regió moderna de Dophar.
Dhofar va passar a dependre del soldà de Masqat al final del , quan els otomans ambicionaven establir-se a la regió. El soldà Said ben Taimur (1932-1970) va administrar la regió com un domini privat i hi va residir llargues temporades, concretament a Salalah, la capital, sense aparèixer per Masqat durant molt de temps. La ciutat de Zafar, a uns 5 km de Salala, va portar el nom d'al-Balid
El sultanat de Masqat ocupava la zona de la costa, però a l'interior les tribus obeïen l'imam d'Oman. La guerra entre Masqat i Oman va durar del 1911 al 1955. L'imam mai va reclamar el Dhofar i quan fou derrotat es va establir a l'exili amb els seus partidaris sense cap pretensió sobre Dhofar.
La revolta a Dhofar va començar el 9 de juny de 1965 dirigida pel Dhufar Liberation Front. Aquesta organització es va transformar en Popular Front for the Liberation of the Occupied Arabian Gulf el setembre de 1968, i més tard, a finals del 1971, es va fusionar amb el National Democratic Front Liberation of Oman and Arabian Gulf (que havia iniciat accions armades a la zona central i del nord d'Oman el juny de 1970), fusió de la que va resultar el Popular Front for the Liberation of Oman and the Arab Gulf (PFLOAG). L'organització estava formada inicialment per nacionalistes progressistes i també per separatistes dufarís, i va dirigir la lluita amb un programa d'orientació socialista que va rebre el suport del Iemen del Sud i la Unió Soviètica. Al final del 1971 i el 1972 els rebels controlaven la major part de Dhofar i havien establert un govern regular a les zones alliberades; però aquestes forces no tenien res a veure amb l'imam d'Oman i se li oposaven igual que al soldà de Masqat.
Fou llavors quan es va produir molta confusió, ja que a partir de 1971 van aparèixer sèries de segells de correus de l'Estat d'Oman (és a dir de l'imamat) amb sobrecàrrega (o amb la llegenda modificada) per a un inexistent Estat de Dhofar; aquest segells foren emesos a Beirut i a Síria per Youssef Salim Tadros, agent de l'imam. Era impossible aleshores saber si la província de Dhofar del sultanat d'Oman estava emetent segells propis o aquestos corresponien als territoris dominats pel rebels dofarís, i finalment va resultar ser una actuació especulativa.
El 1974 el PFLOAG va canviar el seu nom que va passar a Popular Front of Liberation of Oman (PFLO).
Els darrers guerrillers foren assetjats el 1975 i es van haver de rendir o van morir en combat.
Banderes
La bandera del Front d'Alliberament de Dhofar el 1965 (que va restar quan va canviar el nom) va agafar els colors àrabs, que també s'utilitzaven llavors pels rebels d'Aràbia del Sud (Aden i Federació d'Aràbia del Sud). El National Democratic Front Liberation of Oman and Arabian Gulf tenia els mateixos colors però a l'inrevés. Les dues organitzacions armades fusionades el 1971 van mantenir els mateixos colors, en l'ordre del grup més antic, i amb una inscripció en negre a la franja central (per la posició de la inscripció la bandera es devia col·locar normalment en vertical). La inscripció al final (1974-1975) era "ALJABHA ALSHA'BIYAH LITAHRIR OMAN".
Bibliografia
Enciclopèdia de l'Islam, XXII, 412 a 413
Geografia d'Oman
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