text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
class Sns::LoginController < ApplicationController
include Sns::BaseFilter
skip_filter :logged_in?, only: [:login]
navi_view nil
private
def get_params
params.require(:item).permit(:email, :password, :ref)
end
public
def login
@item = SS::User.new
@item.email = params[:email]
@item.password = params[:password]
return if !request.post?
@item.attributes = get_params
user = SS::User.where(email: @item.email, password: SS::Crypt.crypt(@item.password)).first
return if !user
if params[:ref].blank? || [sns_login_path, sns_mypage_path].index(params[:ref])
return set_user user, session: true, redirect: true
end
set_user user, session: true
render action: :redirect
end
def logout
put_history_log
unset_user redirect: true
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,384 |
Mentorloop: The mentoring software platform helping organisations develop more engaged, skilled and sustainable workforces
Rapidly growing company announces oversubscribed raising from three leading venture funds
helloquence via unsplash
Mentoring can be extremely valuable within an organisation, with estimates that a mentoring program can boost retention rates as much as 69 per cent for mentors and 72 per cent for mentees.
Australia's leading mentoring software platform is Mentorloop, which enables organisations to build effective mentoring programs, match their people into productive mentorships at any scale, and measure real program outcomes – saving days of admin work and thousands in people costs.
Uptake of Mentorloop's platform has been swift with the company's revenue growing by 500% in 2017. The software is already being used by 28 clients across four continents with Australian clients including RACV, Institute of Public Accountants, TAL Insurance, the Australian Olympic Committee and Monash University.
"We are very excited about partnering with Mentorloop and being able to bring the benefits of mentoring to our members and the broader accounting community in a scalable and manageable way," CEO of Institute of Public Accountant Andrew Conway commented.
Mentorloop recently announced the closure of a $725,000 oversubscribed seed round from Blackbird Ventures, rampersand and Tempus Partners, bringing total funds raised to $1 million.
Organisations spend an average of $1208 per person per year on learning and development. Using Mentorloop, these organisations can connect their people into hugely beneficial mentorships for just $25 per employee per year; $25 per year to improve development, leadership, retention, and performance, which is then compounded over hundreds or thousands of individuals.
Launched in 2016 by Melbourne-based Lucy Lloyd and Heidi Holmes, Mentorloop has been used by organisations in Australia, the U.S., the U.K., Canada, and Asia to start, run, and measure mentoring programs for their people.
"For too long effective mentoring programs have been impossible to run with spreadsheets and email, and viewed by organisations as a 'nice to have'. We now know from decades of research that mentoring is critical for organisational success," co-founder and CEO Lucy Lloyd says.
"Mentorloop's software enables organisations to uncover their latent talent and knowledge on the sidelines. Well-run mentoring programs discover new leaders, uncover new ideas and better harness the depth of knowledge and experience lying dormant in your team. That's where the real productivity gains are," Ms Lloyd says.
The latest capital infusion will go towards the continued development of Mentorloop's software platform as well as growing the team (currently nine people), which will allow the company to deliver even better mentoring experiences to its growing client list.
"Mentorloop is helping organisations develop more engaged, skilled and sustainable workforces, and we're backing a founding team that has the talent to turn this big opportunity into a great company" said Tempus Partners partner Alister Coleman.
Mentorloop Lucy Lloyd Heidi Holmes Blackbird Ventures rampersand Tempus Partners | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 259 |
package com.taobao.weex.ui.component;
import android.view.ViewGroup;
import com.taobao.weex.WXSDKInstance;
import com.taobao.weex.common.Component;
import com.taobao.weex.dom.WXDomObject;
/**
* Created by sospartan on 7/5/16.
*/
public interface Scrollable {
public void bindStickStyle(WXComponent component);
public void unbindStickStyle(WXComponent component);
public void bindAppearEvent(WXComponent component);
public void bindDisappearEvent(WXComponent component);
public void unbindAppearEvent(WXComponent component);
public void unbindDisappearEvent(WXComponent component);
public ViewGroup getView();
public void scrollTo(WXComponent component,int offset);
public String getRef();
public int getScrollY();
public int getScrollX();
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,981 |
{"url":"https:\/\/www.physicsoverflow.org\/43416\/puzzling-graph-for-irreducible-represntation","text":"# \"Puzzling\" Graph for irreducible Represntation\n\n+ 2 like - 0 dislike\n39 views\n\nFrom reading this very short note at p.12 and p.13, I see a strange convention to obtain the product of representations.\n\nThere are two derivations. Each derivation has four equalities\/identities.\n\nFor both two derivations, I can follow all the equalities, except the 3rd equalities\/identities between the left and right hand side.\n\nCan some one focus on explaining what is going on very precisely?\n\nTo make sure this works, can one derive that\n\n$$3\/2 \\otimes 1=?$$ based on this convention? Thanks.\n\nThis post imported from StackExchange Physics at 2020-10-29 20:03 (UTC), posted by SE-user annie marie heart\n\n+ 2 like - 0 dislike\n\nIn case of $SU(2)$, this convention is really not that useful, since there's already a generic formula for tensoring $SU(2)$ irreps: $$j_1 \\otimes j_2 = \\left| j_1 - j_2 \\right| \\oplus \\dots \\oplus \\left( j_1 + j_2 \\right).$$\n\nBut I'll describe the generic algorithm anyway, since the same convention also applies to $SU(3)$ where it is actually very useful.\n\nNote that I'm giving a general overview and thus all of what follows is mathematically imprecise.\n\n1. For every complex simple Lie algebra, there's a maximal Abelian subalgebra called the Cartan subalgebra. The dimensionality of the Cartan subalgebra is called the rank of the Lie algebra. The rank of $\\mathfrak{su}_2$ is $1$, and the Cartan subalgebra is conventionally chosen as $\\mathfrak{c} = \\text{Span}(J_z)$ (a linear span of the $J_z$ generator of $\\mathfrak{su}_2$. The rank of $\\mathfrak{su}_3$ is 2, and the Cartan subalgebra is conventionally chosen as $\\mathfrak{c} = \\text{Span}(\\lambda_3, \\lambda_8)$ (with $\\lambda_1 \\dots \\lambda_8$ the Gell-Mann matrices). Observe that $\\lambda_3$ and $\\lambda_8$ indeed commute.\n\n2. A specially interesting basis in the Lie algebra is given by the Cartan-Weyl basis, consisting of:\n\n\u2022 A basis in the Cartan subalgebra called $c_{\\alpha}$. Let $n$ be the rank of the Lie algebra, then $\\alpha$ runs from $1$ to $n$.\n\u2022 A basis consisting of the eigenvectors of the adjoint action of $c_{\\alpha}$ on the Lie algebra. These are called roots and denoted $r_e$ with $\\vec{e}$ a vector in the $n$-dimensional root space. By definition, $$\\left[ c_{\\alpha}, r_e \\right] = e_{\\alpha} r_e,$$ where $e_{\\alpha}$ are the components of the vector $\\vec{e}$ in the root space. This formula just says that $r_e$ is an eigenvector of the adjoint action of $c_{\\alpha}$ with eigenvalues $e_{\\alpha}$.\n3. Clearly, the Lie algebra decomposes into Cartan generators and roots. Roots form the root diagram of the Lie algebra. Finite-dimensional irreps of the Lie algebra can be classified by weight diagrams, which are symmetric patterns in the root space consisting of points, with root vectors connecting the neighboring points. Note that root diagram is also a weight diagram, for the adjoint representation. There's two extremely important facts about weight diagrams:\n\n\u2022 Coordiates of the weight (a point in the pattern) represent the eigenvalues of the weight with respect to Cartan subalgebra generators (the same goes for roots and the adjoint action).\n\u2022 Vector addition of the root vector and the radius-vector of the weight represents the action of the Lie algebra element on the element of the representation.\n\nFor $SU(2)$, $n = 1$ and weight diagrams are 1-dimensional. The roots are $J_1 \\pm i J_2$ and their root vectors are $-1$ and $1$ (remember that they are 1-dimensional). The number of weights in the diagram classifies irreps completely (it is naturally the dimension of the irrep and is related to spin by $\\text{dim}(j) = 2j + 1$).\n\nFor $SU(3)$, $n = 2$ and weight diagrams are 2-dimensional. They form pretty triangular patterns described in the end of the presentation that you are interested in.\n\nNow to the algorithm of tensoring the irreps.\n\nYou start with two irreps, represented by two weight diagrams. Now imagine a small weight diagram for irrep $B$ instead of the point for every weight of the weight diagram of $A$. You now expand the size of the weight diagram until the neighboring points meet.\n\nNow try to identify parts of the result as weight diagrams belonging to the irreps $c_i$ and scrape them off your drawing. This will give you\n\n$$a \\otimes b = c_1 \\oplus \\dots \\oplus c_k.$$\n\nI hope I described the process clearly enough, as I don't like drawing things (sorry about that).\n\nAs to your example, which is $3\/2 \\otimes 1$, try doing what I just described with the $3\/2$ weight diagram (4 points connected by 3 lines) and $1$ diagram (3 points with 2 lines), you will get something like this (apologies for the poor artwork):\n\nHere I started with the (black) $3\/2$ weight diagram and for each weight drew a (green) $1$ weight diagram in its place.\n\nThen I looked at the resulting mess and decomposed it into three weight diagrams for irreps $5\/2$, $3\/2$ and $1\/2$, which means that\n\n$$3\/2 \\otimes 1 = 1\/2 \\oplus 3\/2 \\oplus 5\/2,$$\n\nin agreement with the first formula in my answer :)\n\nHope this helps, and please let me know if you need any clarifications.\n\nThis post imported from StackExchange Physics at 2020-10-29 20:03 (UTC), posted by SE-user Prof. Legolasov\nanswered Sep 30, 2017 by (20 points)\n\n Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the \"link\" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)\u00a0\u00a0 Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\\varnothing$ in the following word:p$\\hbar$ysicsOverfl$\\varnothing$wThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.","date":"2021-06-13 08:24:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.8670660257339478, \"perplexity\": 440.5726321472983}, \"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-2021-25\/segments\/1623487607143.30\/warc\/CC-MAIN-20210613071347-20210613101347-00126.warc.gz\"}"} | null | null |
{"url":"https:\/\/scriptinghelpers.org\/questions\/70444\/randomnew-or-mathrandom-which-is-superior","text":"Still have questions? Join our Discord server and get real time help.\nLog in to vote\n1\n\n# Random.new or math.random, which is superior?\n\nAsked by 8 months ago\n\n## Which is better for constructing random object from a seed?\n\nLately, I have seen a brief discussion on the discord server about which is the best random number generator available on roblox. One person advised someone to use math.randomseed(tick()) and then do math.random(). However, another user said that Random.new() should be used instead of math.randomseed(). So, after I did a quick search on the wiki, I couldn't really discern the difference between math.randomseed and Random.new().\n\n## Any differences between :NextInteger(min,max) and math.Random(min,max)?\n\nSo after researching Random.new, Random:NextInteger, and Random:NextNumber for a bit I am still confused about why, if both methods provide psuedo-random numbers, why have two ways to perform the same task. For example, the following two bits of code should generate psuedo-random integers between 0 and 200\n\nlocal random = Random.new(tick())\nwhile true do\nprint(random:NextInteger(0,200))\nwait(2)\nend\n\n\nand\n\nmath.randomseed(tick())\nwhile true do\nprint(math.random(0,200))\nwait(2)\nend\n\n\nThese two pieces of code should, essentially do the same thing, that being generating a psuedo-random number between 0 and 200. But that still raises the question of why, why have two different ways to accomplish the same thing?\n\nSo, if anyone has any idea of what the rationale behind having two ways of essentially doing the same thing, and if there is a different, which of the two methods is better, or \"Random-er\" than the other, that would be appreciated.\n\n0\nmath.random follows the same algorithm as Random.new now, but Random has its own benefits nonetheless. User#19524 106 \u2014 8mo\n1\nBiggest benefit of Random as far as I'm concerned - Random datatype includes the seed in its creation. If we set math.randomseed(tick()) - then throughout the whole script this will be the seed for math.random; however, with Random - we can do a = Random.new(seed1) AND b = Random.new(seed2) -- if we needed two separate pseudorandom number gens for whatever reason. SummerEquinox 623 \u2014 8mo\n\n### 1 answer\n\nLog in to vote\n1\nAnswered by 8 months ago\n\nThe TLDR is that Random.new() is better, and there is no reason to use math.random() ever, as it has no benefits and a significant drawback if you're trying to do something with a repeatable, deterministic random sequence.\n\nInternally, math.random() used to use good old C rand(). Which was not actually good, in any way, and the generator was shared by everything running in the Roblox client or Studio: your code, Roblox's Lua code, Studio C++ code... so seeding the thing was completely and utterly pointless.\n\nNow, math.random() just internally calls the PRNG implemented by the new Random class. This was done to retroactively improve the statistical randomness of math.random() for the benefit of games that are already using it. This does not mean you should use it for new work. This re-implementation of math.random() using Random does not address the other major shortcoming which is the single shared generator. If you use math.random(), all your code that calls it is still pulling from the same stream, so it's very difficult to get repeatable results even if you seed it with the same number. Any variation in the order with which scripts or coroutines call math.random() can make the behavior change from run to run. It only takes one extra or one out of order call to get a completely divergent behavior from that point on.\n\nThe other thing that Random.new() has over math.random() is that math.random() now has conditional logic overhead to redirect to Random's functions. You can call math.random() with no arguments, one argument, or two, and the behavior is different. On the C++ side, it's counting the arguments and doing if-then-else branching to decide which function of Random to call. This overhead is very tiny, almost negligible, but it's there, and when you have two options to use that get you the same values, why would you knowingly call the less efficient one?","date":"2019-07-18 13:17:41","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\": 0.2951781153678894, \"perplexity\": 1321.9134490215083}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-30\/segments\/1563195525634.13\/warc\/CC-MAIN-20190718125048-20190718151048-00491.warc.gz\"}"} | null | null |
Earn $1.46 in Rewards credit (146 points) What's This?
Simple and effective, the BR-6403 Brakes Shoes make a great replacement for any Shimano-style road caliper. Non-replaceable pads. Sold in pairs.
While they are not exact replacents for ultegra calipers they are a good set to carry with you incase of a mishap or if someone is in trouble along the road. Good stopping power.
Lasted 300 miles in Oregons fall weather. | {
"redpajama_set_name": "RedPajamaC4"
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namespace {
constexpr char kExtensionMessageType[] = "test-echo";
}
namespace remoting {
TestEchoExtensionSession::TestEchoExtensionSession() = default;
TestEchoExtensionSession::~TestEchoExtensionSession() = default;
bool TestEchoExtensionSession::OnExtensionMessage(
ClientSessionDetails* client_session_details,
protocol::ClientStub* client_stub,
const protocol::ExtensionMessage& message) {
DCHECK(client_stub);
if (message.type() != kExtensionMessageType) {
return false;
}
protocol::ExtensionMessage reply;
reply.set_type("test-echo-reply");
if (message.has_data()) {
reply.set_data(message.data().substr(0, 16));
}
client_stub->DeliverHostMessage(reply);
return true;
}
} // namespace remoting
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,304 |
Tour de France 2010, v pořadí 97. ročník nejslavnějšího cyklistického etapového závodu světa, proběhl mezi 3. a 25. červencem 2010. Odstartoval úvodní časovkou v nizozemském Rotterdamu a skončil tradičně pod pařížským Vítězným obloukem. V závodě sice zvítězil španělský jezdec stáje Astana Alberto Contador, později mu však byl titul kvůli dopingovému trestu odebrán.
Trasa závodu
Závod Tour de France začal popáté na území Nizozemska. Zajímavostí je že to byl třetí start závodu Velké trojky v Nizozemsku v řadě, po startu Vuelty 2009 v Assenu a Giro d'Italia 2010 v Amsterodamu. První byl prolog v Rotterdamu, jehož trasa vedla i přes známý most Erasmusbrug. Další tři etapy byly ve stylu jarních klasik, přejezd Arden v 2. etapě a 13,2 km úsek kostkovaných cest ve 3. etapě.
Průběh závodu
Původní počet přihlášených závodníků byl 198 z 31 zemí a z 22 týmů. K úvodnímu prologu ale nenastoupil Španěl Xavier Florencio, který použil lék obsahující zakázanou látku bez vědomí svého týmu Cervélo TestTeam. Prolog poznamenaný deštěm a mokrým povrchem absolvovalo 197 cyklistů a vyhrál ho Švýcar Fabian Cancellara. Získal tím do držení žlutý trikot vedoucího jezdce závodu a zelený trikot nejlepšího v bodovací soutěži. První etapu z Rotterdamu do Bruselu poznamenanou častými pády a hromadným pádem necelý kilometr před cílem vyhrál Ital Alessandro Petacchi. Druhou etapu s cílem ve Spa, částečně vedoucí po jarní klasice Liége - Bastogne - Liége vyhrál po samostatném úniku Sylvain Chavanel a oblékl se do žlutého trikotu. Zbytek etapy byl neutralizován z důvodu pádu většiny pelotonu ve sjezdu z Col de Stockeu. Ve třetí etapě závodníci zavítali na pět úseků pavé slavného Paříž - Roubaix, bylo k vidění velké množství pádů a jeden z favoritů Frank Schleck musel odstoupit ze závodu se zlomenou klíční kostí, na pádu Franka vydělal jeho bratr Andy, když si připsal přes minutu k dobru na Alberta Contadora. Etapu vyhrál Thor Hushovd a do žlutého se znovu oblékl Fabian Cancellara. Následující etapu do Reims si připsal již letos podruhé Alessandro Petacchi. Poté začal znovu úřadovat fantom loňské tour Mark Cavendish a zvítězil v hromadných dojezdech v Montargis a v Gueugnonu. Osmá etapa znamenala tragédii pro Lance Armstronga, který celkem třikrát spadl a ztratil jakékoliv naděje na finální vítězství. V jinak první horské etapě začali úřadovat specialisté vrchaři, vyhrál Andy Schleck a do žlutého trikotu se oblékl Cadel Evans. Devátá etapa obsahovala stoupání na Col de la Madeleine, ve kterém útočili Andy Schleck a Alberto Contador, kvůli vzájemnému taktizování je dojela skupina pronásledovatelů, z nichž zvítězil Sandy Casar. Po této etapě se poprvé se do puntíkovaného trikotu oblékl Anthony Charteau a do žlutého Andy Schleck, jelikož zraněný Cadel Evans dojel se značnou ztrátou. 11. etapa znamenala nejen třetí etapové vítězství pro Marka Cavendishe, ale i diskvalifikaci jeho týmového kolegy Marka Renshawa. Ten byl vyloučen za údery hlavou do soupeře Juliana Deana při závěrečném spurtu. Další dvě etapy se dojížděly po únicích a vítězství si připsali Joaquim Rodríguez a Alexandr Vinokurov. Ve 14. etapě zavítal peloton do Pyrenejí, kde se jely celkem 4 etapy. První z nich do Ax-3 Domaines vyhrál Christophe Riblon po dlouhém sólovém úniku. Další etapa znamenala změnu ve žlutém trikotu, ovšem poněkud kontroverzním způsobem. Při stoupání na Port de Bales Andy Schleck nastoupil Contadorovi, ale po chvíli mu spadl řetěz. Contador na útok odpověděl a Schleckovi ujel. Tento útok na muže ve žlutém trikotu při jeho technických problémech vyvolal nesouhlas mezi diváky i částí pelotonu. Alberto Contador se pak za tento čin omluvil. 16. etapa označována jako královská pyrenejská - obsahovala 2 horské prémie 1. kategorie a dvě prémie HC - přivedla peloton poprvé na legendární Col du Tourmalet. Do cíle v Pau dorazil první Pierrick Fédrigo. 17. etapa se opět vracela na Col du Tourmalet, kde tentokrát měla svůj cíl. Andy Schleck se snažil útočit, ale Alberto Contador se ho celou etapu udržel a oba dva společně dojeli do cíle, kde zvítězil Andy Schleck. Další změnu v celkovém pořadí již nepřinesla ani časovka jednotlivců, kterou Alberto Contador zahajoval s 8sekundovým náskokem na Schlecka, který navýšil až na finálních 39 sekund. V časovce, stejně jako v prologu, zvítězil Fabian Cancellara. Poslední etapu, prestižní dojezd na Champs-Elysées, vyhrál v hromadném spurtu Mark Cavendish.
Seznam etap
Trikoty jednotlivých klasifikací
Celkové výsledky
Celková klasifikace
Sprinterská klasifikace
Vrchařská klasifikace
Klasifikace mladých jezdců
Týmová klasifikace
Držení trikotů
Dopingový skandál
Contadorovo vítězství bylo několik měsíců po skončení závodu závažně zpochybněno poté, co vyšlo najevo podezření z dopingu. Ve vzorcích jeho moči bylo nalezeno stopové množství anabolika clenbuterolu, látky, kterou sportovci za žádných okolností nesmějí používat. Dne 6.2.2012 Sportovní arbitrážní soud (CAS) ve švýcarském městě Lausanne potrestal vítěze Tour de France 2010 španělského cyklistu Alberta Contadora za užití anabolika clenbuterolu dvouletým zákazem startu a odebráním vítězství na Tour de France 2010.
Startovní listina
Startovní listina Tour de France 2010
Reference
Externí odkazy
Oficiální stránky závodu (EN/FR)
Přehled etap na oficiálních stránkách závodu
Tour de France
Cyklistika v roce 2010 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 267 |
namespace stp
{
namespace detail
{
template <typename ElementType>
struct contains_type
{
contains_type(const ElementType &val) : val_(val) {}
template
<
typename SequenceType,
typename ValueType = typename SequenceType::value_type,
typename = typename std::enable_if<std::is_convertible<ElementType, ValueType>::value>::type
>
bool operator()(const SequenceType &sequence) const
{
auto begin = std::begin(sequence);
auto end = std::end(sequence);
return std::find(begin, end, val_) != end;
}
ElementType val_;
};
}
template <typename ElementType>
detail::contains_type<ElementType> contains(const ElementType &val)
{
return detail::contains_type<ElementType>(val);
}
}
#endif | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,167 |
LISCO poly-cap and EZ Pro Poly-cap fence toppers add safety and aesthetics to your ball field. They are constructed from weather resistant and UV treated 4 1/2" diameter polyethylene. Separate color matched 18" ties are recommended. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,087 |
{"url":"https:\/\/www.maths.ox.ac.uk\/events\/past\/658?page=12","text":"Forthcoming events in this series\n\nThu, 23 Oct 2008\n\n11:00\u00a0- 12:00\nSR1\n\n### Model completeness results for certain Pfaffian structures\n\nGareth Jones\n(Manchester)\nAbstract\nI show that the expansion of the real field by a total Pfaffian chain is model complete in a language with symbols for the functions in the chain, the exponential and all real constants. In particular, the expansion of the reals by all total Pfaffian functions is model complete.\nThu, 16 Oct 2008\n\n17:00\u00a0- 18:00\nL3\n\n### Definably compact, connected groups are elementarily equivalent to compact real Lie groups\n\nKobi Peterzil\n(Haifa)\nAbstract\n\n(joint work with E. Hrushovski and A. Pillay)\n\nIf G is a definably compact, connected group definable in an o-minimal structure then, as is known, G\/Z(G) is semisimple (no infinite normal abelian subgroup).\n\nWe show, that in every o-minimal expansion of an ordered group:\n\nIf G is a definably connected central extension of a semisimple group then it is bi-intepretable, over parameters, with the two-sorted structure (G\/Z(G), Z(G)). Many corollaries follow for definably connected, definably compact G.\nHere are two:\n\n1. (G,.) is elementarily equivalent to a compact, connected real Lie group of the same dimension.\n\n2. G can be written as an almost direct product of Z(G) and [G,G], and this last group is definable as well (note that in general [G,G] is a countable union of definable sets, thus not necessarily definable).\n\nThu, 09 Oct 2008\n17:00\nL3\n\n### On Intersection with Tori\n\n(Universit\u00e9 Lyon I)\nAbstract\nIn 2006, a bad field was constructed (together with Baudisch, Hils and Wagner) collapsing Poizat's green fields. In this talk, we will not concentrate on the general methodology for collapsing specific structures, but more on a specific result in algebraic geometry, a weaker version of the Conjecture on Intersection with Tori (CIT). We will present a model theoretical proof of this result as well as discuss the possible generalizations to positive characteristic. We will try to make the talk\u00a0 self-contained and aimed for an audience with a basic acquaintance with Model Theory.\n\nWed, 23 Jul 2008\n\n14:30\u00a0- 15:30\nSR1\n\n### Isomorphism Types of Maximal Cofinitary Groups\n\nBart Kastermans\n(Wisconsin)\nAbstract\nCofinitary groups are subgroups of the symmetric group on the natural numbers\n\n(elements are bijections from the natural numbers to the natural numbers, and\n\nthe operation is composition) in which all elements other than the identity\n\nhave at most finitely many fixed points. We will give a motivation for the\n\nquestion of which isomorphism types are possible for maximal cofinitary\n\ngroups. And explain some of the results we achieved so far.\n\nWed, 09 Jul 2008\n\n10:30\u00a0- 17:00\nL3\n\n### Dependent fields have no Artin-Schrier extensions\n\nItay Kaplan\n(Lyon 1 and Jerusalem)\nTue, 24 Jun 2008\n\n14:30\u00a0- 15:30\nL3\n\nJohn Baldwin\n(UIC)\nFri, 13 Jun 2008\n15:15\nL3\n\n### Representations of positive real polynomials\n\nAlex Prestel\n(Konstanz)\nAbstract\nWe consider finite sequences $h = (h_1, . . . h_s)$ of real polynomials in $X_1, . . . ,X_n$ and assume that\n\nthe semi-algebraic subset $S(h)$ of $R^n$ defined by $h1(a1, . . . , an) \\leq 0$, . . . , $hs(a1, . . . , an) \\leq 0$ is\n\nbounded. We call $h$ (quadratically) archimedean if every real polynomial $f$, strictly positive on\n\n$S(h)$, admits a representation\n\n$f = \\sigma_0 + h_1\\sigma_1 + \\cdots + h_s\\sigma_s$\n\nwith each $\\sigma_i$ being a sum of squares of real polynomials.\n\nIf every $h_i$ is linear, the sequence h is archimedean. In general, h need not be archimedean.\n\nThere exists an abstract valuation theoretic criterion for h to be archimedean. We are, however,\n\ninterested in an effective procedure to decide whether h is archimedean or not.\n\nIn dimension n = 2, E. Cabral has given an effective geometric procedure for this decision\n\nproblem. Recently, S. Wagner has proved decidability for all dimensions using among others\n\nmodel theoretic tools like the Ax-Kochen-Ershov Theorem.\n\nThu, 12 Jun 2008\n16:00\nL3\n\n### Characterizing Z in Q with a universal-existential formula\n\nBjorn Poonen\n(Berkeley)\nAbstract\nRefining Julia Robinson's 1949 work on the undecidability of the first order theory of Q, we prove that Z is definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that is surjective on rational points.\nFri, 06 Jun 2008\n\n15:15\u00a0- 16:15\nL3\n\n### Fixed-Point Logics and Inductive Definitions\n\nStephan Kreutzer\n(Oxford Comlab)\nAbstract\nFixed-point logics are a class of logics designed for formalising\n\nrecursive or inductive definitions. Being initially studied in\n\ngeneralised recursion theory by Moschovakis and others, they have later\n\nfound numerous applications in computer science, in areas\n\nsuch as database theory, finite model theory, and verification.\n\nA common feature of most fixed-point logics is that they extend a basic\n\nlogical formalism such as first-order or modal logic by explicit\n\nconstructs to form fixed points of definable operators. The type of\n\nfixed points that can be formed as well as the underlying logic\n\ndetermine the expressive power and complexity of the resulting logics.\n\nIn this talk we will give a brief introduction to the various extensions\n\nof first-order logic by fixed-point constructs and give some examples\n\nfor properties definable in the different logics. In the main part of\n\nthe talk we will concentrate on extensions of first-order\n\nlogic by least and inflationary fixed points. In particular, we\n\ncompare the expressive power and complexity of the resulting logics.\n\nThe main result will be to show that while the two logics have rather\n\ndifferent properties, they are equivalent in expressive power on the\n\nclass of all structures.\n\nFri, 23 May 2008\n\n15:15\u00a0- 16:15\nL3\n\n### The real field with an irrational power function and a dense multiplicative subgroup\n\nPhilipp Heironymi\n(Oxford)\nFri, 16 May 2008\n15:15\nL3\n\n### Schanuel\u2019s Conjecture and free E-rings in o-minimal structures\n\nGiuseppina Terzo\nAbstract\nIn recent years Schanuel\u2019s Conjecture (SC) has played a fundamental role\n\nin the Theory of Transcendental Numbers and in decidability issues.\n\nMacintyre and Wilkie proved the decidability of the real exponential field,\n\nmodulo (SC), solving in this way a problem left open by A. Tarski.\n\nMoreover, Macintyre proved that the exponential subring of R generated\n\nby 1 is free on no generators. In this line of research we obtained that in\n\nthe exponential ring $(\\mathbb{C}, ex)$, there are no further relations except $i^2 = \u22121$\n\nand $e^{i\\pi} = \u22121$ modulo SC. Assuming Schanuel\u2019s Conjecture we proved that\n\nthe E-subring of $\\mathbb{R}$ generated by $\\pi$ is isomorphic to the free E-ring on $\\pi$.\n\nThese results have consequences in decidability issues both on $(\\mathbb{C}, ex)$ and\n\n$(\\mathbb{R}, ex)$. Moreover, we generalize the previous results obtaining, without\n\nassuming Schanuel\u2019s conjecture, that the E-subring generated by a real\n\nnumber not definable in the real exponential field is freely generated. We\n\nalso obtain a similar result for the complex exponential field.\n\nFri, 09 May 2008\n\n15:15\u00a0- 16:15\nL3\n\n### Slim Fields\n\nJochen Koenigsmann\n(Oxford)\nFri, 02 May 2008\n15:15\nL3\n\n### Definability in differential Hasse fields and related geometric questions\n\nFranck Benoist\n(University of Leeds)\nAbstract\nI will give a few model theoretic properties for fields with a Hasse derivation which are existentially closed. I will explain how some type-definable sets allow us to understand properties of some algebraic varieties, mainly concerning their field of definition.\nFri, 07 Mar 2008\n14:15\nL3\n\n### Strong theories, weight, and the independence property\n\n(Leeds)\nAbstract\nI will explain the connection between Shelah's recent notion of strongly dependent theories and finite weight in simple theories. The connecting notion of a strong theory is new, but implicit in Shelah's book. It is related to absence of the tree property of the second kind in a similar way as supersimplicity is related to simplicity and strong dependence to NIP.\nThu, 06 Mar 2008\n10:00\nSR1\n\nNina Frohn\n(Freiburg)\nFri, 29 Feb 2008\n14:15\nL3\n\n### Arithmetic in groups of piece-wise affine permutations of an interval\n\nAlexey Muranov\n(Lyon)\nAbstract\nBardakov and Tolstykh have recently shown that Richard Thompson's group\n\n$F$ interprets the Arithmetic $(\\mathbb Z,+,\\times)$ with parameters. We\n\nconsider a class of infinite groups of piecewise affine permutations of\n\nan interval which contains all the three groups of Thompson and some\n\nclassical families of finitely presented infinite simple groups. We have\n\ninterpreted the Arithmetic in all the groups of this class. In particular\n\nwe have obtained that the elementary theories of all these groups are\n\nundecidable. Additionally, we have interpreted the Arithmetic in $F$ and\n\nsome of its generalizations without parameters.\n\nThis is a joint work with Tuna Alt\u0131nel.\n\nThu, 28 Feb 2008\n10:00\nL3\n\n### Zariski reducts of o-minimal structures\n\nPiotr Kowalski\n(Wroclaw)\nAbstract\nThis is joint work with Assaf Hasson. We consider non-locally modular strongly minimal reducts of o-minimal expansions of reals. Under additional assumptions we show they have a Zariski structure.\nFri, 22 Feb 2008\n14:15\nL3\n\n### Non Archimedian Geometry and Model Theory\n\nFrancois Loeser\n(ENS)\nAbstract\nWe shall present work in progress in collaboration with E. Hrushovski on the geometry of spaces of stably dominated types in connection with non archimedean geometry \\`a la Berkovich\nFri, 15 Feb 2008\n14:15\nL3\n\n### Small subgroups of the circle group\n\nAyhan Gunaydin\n(Oxford)\nAbstract\nThere is a well-behaving class of dense ordered abelian groups called \"regularly dense ordered abelian groups\". This first order property of ordered abelian groups is introduced by Robinson and Zakon as a generalization of being an archimedean ordered group. Every dense subgroup of the additive group of reals is regularly dense. In this talk we consider subgroups of the multiplicative group, S, of all complex numbers of modulus 1. Such groups are not ordered, however they have an \"orientation\" on them: this is a certain ternary relation on them that is invariant under multiplication. We have a natural correspondence between oriented abelian groups, on one side, and ordered abelian groups satisfying a cofinality condition with respect to a distinguished positive element 1, on the other side. This correspondence preserves model-theoretic relations like elementary equivalence. Then we shall introduce a first-order notion of \"regularly dense\" oriented abelian group; all infinite subgroups of S are regularly dense in their induced orientation. Finally we shall consider the model theoretic structure (R,Gamma), where R is the field of real numbers, and Gamma is dense subgroup of S satisfying the Mann property, interpreted as a subset of R^2. We shall determine the elementary theory of this structure.\nFri, 08 Feb 2008\n14:15\nL3\n\nAlex Wilkie\n(Manchester)\nFri, 01 Feb 2008\n14:15\nL3\n\nTBC\nFri, 25 Jan 2008\n14:15\nL3\n\nRobin Knight\n(Oxford)\nFri, 18 Jan 2008\n14:15\nL3\n\n### Randomised structures and theories\n\nItai Ben Yaacov\n(Lyon)\nAbstract\nH. Jerome Keisler suggested to associate to each classical structure M a family of \"random\" structures consisting of random variables with values in M . Viewing the random structures as structures in continuous logic one is able to prove preservation results of various \"good\" model theoretic properties e.g., stability and dependence, from the original structure to its randomisation. On the other hand, simplicity is not preserved by this construction. The work discussed is mostly due to H.\n\nJerome Keisler and myself (given enough time I might discuss some applications obtains in joint work with Alex Usvyatsov).\n\nFri, 30 Nov 2007\n14:15\nSR2\n\nMarcus Tressl\n(University of Manchester)\nThu, 22 Nov 2007\n10:00\nSR1\n\n### Minimal definable sets in difference fields.\n\nAlice Medvedev\n(UIC)\nAbstract\nI will speak about the Zilber trichotomy for weakly minimal difference varieties, and the definable structure on them.\n\nA difference field is a field with a distinguished automorphism $\\sigma$. Solution sets of systems of polynomial difference equations like\n\n$3 x \\sigma(x) +4x +\\sigma^2(x) +17 =0$ are the quantifier-free definable subsets of difference fields. These \\emph{difference varieties} are similar to varieties in algebraic geometry, except uglier, both from an algebraic and from a model-theoretic point of view.\n\nACFA, the model-companion of the theory of difference fields, is a supersimple theory whose minimal (i.e. U-rank $1$) types satisfy the Zilber's Trichotomy Conjecture that any non-trivial definable structure on the set of realizations of a minimal type $p$ must come from a definable one-based group or from a definable field. Every minimal type $p$ in ACFA contains a (weakly) minimal quantifier-free formula $\\phi_p$, and often the difference variety defined by $\\phi_p$ determines which case of the Zilber Trichotomy $p$ belongs to.","date":"2022-08-17 02:26:32","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\": 0.7886520624160767, \"perplexity\": 1176.850441157284}, \"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-2022-33\/segments\/1659882572833.78\/warc\/CC-MAIN-20220817001643-20220817031643-00666.warc.gz\"}"} | null | null |
Q: Ruby: When defining a class is "initialize" for convenience? I'm new to programming and am trying to figure out the purpose of "initialize" in creating a class.
Here's an example:
class Person
def initialize(name)
@name = name
@pet = nil
@home = 'NYC'
end
end
So initializing is to create a bunch of attributes that I can pull out directly by saying Person.name and Person.pet and Person.home right? Is "initialize" just to compact a bunch of variables into one place? Would I accomplish the same thing doing this:
class Person
pet = nil
home = 'NYC'
#not so sure how to replicate the @name here.
end
Wouldn't I be able to access the values with Person.pet and Person.home the same way as I would in the first code?
A: This is a little tricky in Ruby (as opposed to, say, Java) since both classes and instances of classes are actual objects at runtime. As such, a class has its own set of variables, and each instance of that class also gets its own set of variables (distinct from the class's variables).
When you say
class Person
pet = nil
end
You're setting a variable, pet, which is local only to the class object called Person.
The way to manipulate the variables of an instance of a class is to use the variables in methods:
class Person
def initialize
pet = nil
end
end
Here, pet refers to a local variable of a given instance of Person. Of course, this pet variable is pretty useless as defined, since it's just a local variable that goes away after the initialize function completes. The way to make this variable persist for the lifetime of the instance is to make it an instance variable, which you accomplish by prefixing it with a @. And thus we arrive at your first initialize:
class Person
def initialize
@pet = nil
# And so on
end
end
So, as to why you need initialize. Since the only way to set the instance variables of instances of Person is within methods of Person, this initialization needs to be in some method. initialize is just the convenient name for a method which is automatically called when your instance is first created.
A: Initialize is a method usually referred as an object constructor. It is used when you call Person.new("Bob") and it will give you an instance of that Person object. The @ symbol you see before the variables in the initialize makes the variable an instance variable meaning that variable will only be accessed once you have an instance of that object and it will stay there for the lifetime of that instance.
For example
person = Person.new("Bob")
person.name #Will output Bob
person.home #Will output NYC
Classes are objects and doing this:
class Person
pet = nil
home = 'NYC'
end
is just creating local variables pet and home and will be outside of the scope of the class. This means calling Person.pet and Person.home will just give you an error. I would suggest do a little reading on Object Oriented Programming (OOP) and if you have any more questions throw them in stackoverflow :D
| {
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package com.webcohesion.ofx4j.domain.data.signup;
import com.webcohesion.ofx4j.domain.data.TransactionWrappedRequestMessage;
import com.webcohesion.ofx4j.meta.ChildAggregate;
import com.webcohesion.ofx4j.meta.Aggregate;
/**
* @author Ryan Heaton
*/
@Aggregate ( "ACCTINFOTRNRQ" )
public class AccountInfoRequestTransaction extends TransactionWrappedRequestMessage<AccountInfoRequest> {
private AccountInfoRequest message;
/**
* The wrapped message.
*
* @return The wrapped message.
*/
@ChildAggregate ( required = true, order = 30 )
public AccountInfoRequest getMessage() {
return message;
}
/**
* The wrapped message.
*
* @param message The wrapped message.
*/
public void setMessage(AccountInfoRequest message) {
this.message = message;
}
// Inherited.
public void setWrappedMessage(AccountInfoRequest message) {
setMessage(message);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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Marjorie Browne (1910–1990) was a British musical theatre actress who made occasional films.
Her West End appearances included the original productions of Cole Porter's Wake Up and Dream at the London Pavilion in 1929; Stanley Lupino's musical Sporting Love at the Gaiety in 1934; and as Marjanah in the revival of Chu Chin Chow at the Palace in 1940.
Filmography
Lassie from Lancashire (1938)
Laugh It Off (1940)
I Didn't Do It (1945)
References
External links
1910 births
1990 deaths
British stage actresses
British film actresses
English musical theatre actresses
20th-century British actresses
20th-century English women
20th-century English people | {
"redpajama_set_name": "RedPajamaWikipedia"
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package com.twitterclient.fragments;
import static com.twitterclient.utils.Constants.SCREEN_NAME;
import android.os.Bundle;
import android.support.annotation.Nullable;
import com.twitterclient.network.NetworkUtils;
import com.twitterclient.network.TwitterClientApplication;
public class FollowersFragment extends FollowListFragment {
public static FollowersFragment newInstance(String screenName) {
FollowersFragment fragment = new FollowersFragment();
Bundle args = new Bundle();
args.putString(SCREEN_NAME, screenName);
fragment.setArguments(args);
return fragment;
}
@Override
public void onCreate(@Nullable Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
if(NetworkUtils.isNetworkAvailable(getActivity()) && NetworkUtils.isOnline()) {
populateFollowList();
}
}
/**
* Function populates the followers list
*/
private void populateFollowList() {
String screenName = getArguments().getString(SCREEN_NAME);
TwitterClientApplication.getTwitterClient().getFollowers(screenName, getHandler());
}
}
| {
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{"url":"https:\/\/math.stackexchange.com\/questions\/2582674\/how-to-understand-logical-implication-in-set-theory","text":"# How to understand logical implication in Set theory?\n\nI am reading about the wiki page of material conditional (a.k.a logical implication).\n\nIn the diagram in that page (which is also pasted here), it draws an Venne Diagram of the truth function of $A \\implies B$\n\nIn the text explanation (in 2nd paragraph), it says $\\ P \\implies Q$ can be symbolized using set theory: $P \\supset Q$\n\nQuestion: The Diagram explanation and text explanation is conflicting. It seems in the diagram, A is not a superset of B. What is the correct way to understand it?\n\n\u2022 Honestly, you don't appear to have read the caption of the image that you took from the linked wikipedia article. It explains that the white area is the set of items for which the material implication is false. Also it doesn't say that it can be symbolized using set theory, it says that the symbol can be used for implication, but also has a meaning in set theory. \u2013\u00a0jgon Dec 28 '17 at 5:51\n\u2022 With the \"horseshoe\" symbol: $\\supset$ he does not mean \"superset\". It is the symbol used sometimes (mainly: beginning XX Century) in place of $\\to$ of $\\Rightarrow$. See The Notation in Principia Mathematica. \u2013\u00a0Mauro ALLEGRANZA Dec 28 '17 at 7:36\n\nUse the fact that $$A \\to B \\equiv \\neg(A \\wedge \\neg B)$$\nNote that $A \\wedge \\neg B$ represents the portion of the set A excluding the area of intersection of $A$ and $B$ (the white portion). The negation gives us the required red area.","date":"2019-08-21 13:21:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.6824727654457092, \"perplexity\": 422.88625765086033}, \"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\/1566027316021.66\/warc\/CC-MAIN-20190821131745-20190821153745-00134.warc.gz\"}"} | null | null |
In this day of instant information, we can get our news so fast that we don't have to wait for the evening news to come on TV anymore. We don't have to wait for the newspaper. We can go out on the Internet and get our news in real time. I think this makes it hard for us to slow down and listen, especially to God.
February 14th we are starting a new series called "Jesus Said." When Jesus speaks he is trying to help us in our daily lives. I don't know about you but I need help handling situations in my life. This new series is going to take some serious problems in our lives and tell us what Jesus said we should do and how to handle them. | {
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In der Frühzeit des Druckens wurden druckfertige Bogen vor Beginn des Auflagendrucks im Freien vor der Druckerei aufgehängt. Dazu wurden die ersten Bogen noch im Druck aus der Maschine entnommen. Interessierte untersuchten diese Bogen und bekamen beim Finden eines Fehlers eine Prämie.
Des Weiteren wurden Aushängebogen aus Werbezwecken an den Verkaufsständen der Buchführer aufgehängt.
Heute sind Aushängebogen gedruckte, gefalzte und geschnittene Bogen, die der Endkontrolle dienen, bevor das Buch gebunden wird.
Literatur
Gutenberg Museum Mainz (Hrsg.): Von Gutenberg zum WorldWideWeb. Wien: Dachs Verlag, 2002.
Hiller, Helmut und Füssel, Stephan: Wörterbuch des Buches. 6. Auflage. Frankfurt am Main: Vittorio Klostermann Verlag, 2002. ISBN 3-465-03220-9
Geschichte des Druckwesens
Probeabzug
Druckweiterverarbeitung | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,094 |
{"url":"https:\/\/www.hepdata.net\/record\/ins505281","text":"\u2022 Browse all\nMeasurement of inclusive $D^{*+-}$ production in two photon collisions at LEP\n\nThe collaboration\nPhys.Lett.B 467 (1999) 137-146, 1999.\n\nAbstract (data abstract)\nCERN-LEP. Measurement of the inclusive production of D*+- mesons in two-photon collisions. Data are given for the differential cross sections for the process e+e- --& gt; e+e- D*+- X at c.m. energy 189 GeV with an integrated luminosity of 176.4 pb-1. The data cover the kinematic region in PT of the D* from 1 to 5 GeV and pseudorapidity & lt;1.4.\n\n\u2022 #### Table 1\n\nData from T 1,F 4\n\n10.17182\/hepdata.28070.v1\/t1\n\nThe measured cross sections, as a function of PT over the bin ranges and the differential cross sections after bin-centre...\n\n\u2022 #### Table 2\n\nData from T 1,F 5\n\n10.17182\/hepdata.28070.v1\/t2\n\nThe measured cross sections, as a function of pseudorapidity over the bin ranges and the differential cross sections after bin-centre...\n\n\u2022 #### Table 3\n\nData from P 145\n\n10.17182\/hepdata.28070.v1\/t3\n\nIntegrated cross section in the visible kinematic region.","date":"2021-01-23 22:56:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 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\": 0.9352925419807434, \"perplexity\": 7478.5824395088675}, \"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-2021-04\/segments\/1610703538741.56\/warc\/CC-MAIN-20210123222657-20210124012657-00395.warc.gz\"}"} | null | null |
Q: Identifying a notion of integration Let $f$: $I\longrightarrow\mathbb{R}$ be a (not necessarily bounded) function on an interval $I\subseteq\mathbb{R}$.
Suppose $f$ admits a function $F$: $I\longrightarrow\mathbb{R}$ such that
(1) $F$ is continuous
(2) $\forall x\in I$: $f$ continuous at $x$ $\Rightarrow$ $F$ differentiable at $x$ with $F'(x)=f(x)$
(3) Up to additive constants, $F$ is unique with the above two properties.
This well-defines a generalized Newton-like integral notion by setting $\int_a^b f:=F(b)-F(a)$
Questions: Which functions are integrable in this sense? Is there an integral notion equivalent to this?
Certainly it is necessary for $f$ to be continuous on a dense set of points.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,658 |
package org.encuestame.utils.enums;
/**
* Gadget Types.
* @author Morales, Diana Paola paolaATencuestame.org
* @since July 29, 2011
*/
public enum GadgetType {
/** **/
ACTIVITY_STREAM,
/** Gadget type for surveys**/
COMMENTS,
/** Gadget type for tweetPolls**/
TWEETPOLLS_VOTES,
/**
* Constructor.
*/
GadgetType(){
};
/**
* Get gadget type by string
* @param gadgetType
* @return
*/
public static GadgetType getGadgetType(final String gadgetType) {
if (null == gadgetType) { return null; }
else if (gadgetType.equalsIgnoreCase("STREAM")) { return ACTIVITY_STREAM; }
else if (gadgetType.equalsIgnoreCase("COMMENTS")) { return COMMENTS; }
else if (gadgetType.equalsIgnoreCase("TWEETPOLLSVOTES")) { return TWEETPOLLS_VOTES; }
else return null;
}
/**
* To String.
*/
public String toString() {
String gadget = "STREAM";
if (this == ACTIVITY_STREAM) { gadget = "STREAM".toLowerCase(); }
else if (this == COMMENTS) { gadget = "COMMENTS".toLowerCase(); }
else if (this == TWEETPOLLS_VOTES) { gadget = "TWEETPOLLSVOTES".toLowerCase(); }
return gadget;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,857 |
Leisure Time Bromine Tablets are designed for hot tub use and works in all types of hot tub bromine feeders. Bromine tablets effectively disinfect hot tub water to keep it clean and odor free.
Before using this product in your hot tub for the first time, add 1/2 ounce of sodium bromide per 100 gallons of water to establish a 30 ppm bromide concentration. Also, add sodium bromide at this dosage whenever the hot tub is drained and refilled. The bromide addition ensures immediate establishment of an all-bromide system, eliminates chlorinous odors and maximizes skin and eye comfort.
Using a suitable feeder adjusted according to the manufacturer's directions, add this product to maintain an active bromine concentration of 2 to 4 ppm in residential spas and 3 - 6 ppm in commercial hot tub. Use a reliable test kit to monitor bromine regularly. This product's usage will typically vary from 0.015 to 0.10 pound for every 300 gallons of hot tub water to maintain the recommended bromine concentration range. The presence of organic debris, high bather use and other factors may require a higher dosage.
Water soluble, non-filerable wastes can accumulate in hot tub water and cause dull or cloudy water and can stimulate algal growth. Superoxidation or superchlorination with a suitable oxidizing shock treatment should be done on a regular basis to remove these wastes and maintaing clear, sparkling water. Suitable oxidizing agents are those based on calcium hypochlorite, lithium hypochlorite, sodium hypochlorite or potassium peroxymonoperfulfate. Do not mix this product in concentrated form with any other chemicals. Do not add other chemicals to the feeding device when using this product.
I ordered O rings for my hot tub filter lid. They fit perfectly. Also, ordered sanitizer. Both came in a timely manner. I will continue to order from hot tub warehouse as their prices and service is excellent.
Fast shipping and the products are great.
I received the shipment but when I opened the individual containers they were broken into small pieces making them difficult to use.
Very happy with the entire process.
Pretty expensive for such a small quantity of Bromine tabs when you add in postage. Local purchase would be equal in cost or cheaper. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,738 |
{"url":"https:\/\/www.r-bloggers.com\/2016\/09\/updated-r-markdown-thesis-template\/","text":"Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.\n\nIn October of 2015, I released an R Markdown senior thesis template R package and discussed it in the blogpost here. It was well-received by students and faculty that worked with it and this past summer I worked on updating it to make it even nicer for students. The big addition is the ability for students to export their senior thesis to a webpage (example here) and also label and cross-reference figures and tables more easily. These additions and future revisions will be in the new thesisdown package in the spirit of the bookdown package developed and released by RStudio in summer 2016.\n\nI encourage you to look over my blog post last year to get an idea of why R Markdown is such a friendly environment to work in. Markdown specifically allows for typesetting of the finished document to be transparent inside the actual document. Down the road, it is my hope that students will be able to write generating R Markdown files that will then export into many formats. These currently include the LaTeX format to produce a PDF following Reed's senior thesis guidelines and the HTML version in gitbook style. Eventually, this will include a Word document following Reed's guidelines and also an ePub (electronic book) version. These last two are available at the moment but are not fully functional.\n\nBy allowing senior theses in a variety of formats, seniors will be more easily able to display their work to potential employers, other students, faculty members, and potential graduate schools. This will allow them to get the word out about their studies and research while still encouraging reproducibility in their computations and in their analyses.\n\n### Install the template generating package\n\nTo check out the package yourself, make sure you have RStudio and LaTeX installed and then direct your browser to the GitHub page for the template: http:\/\/github.com\/ismayc\/thesisdown. The README.md file near the bottom of the page below the files gives directions on installing the template package and getting the template running. As you see there, you'll want to install the thesisdown package via the following commands in the RStudio console:\n\ninstall.packages(\"devtools\")\ndevtools::install_github(\"ismayc\/thesisdown\")\n\n\nIf you have any questions, feedback, or would like to report any issues, please email me.\n\n(The generating R Markdown file for this HTML document\u2014saved in the .Rmd extension\u2014is available here.)","date":"2021-09-16 11:50:04","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\": 0.17305515706539154, \"perplexity\": 1952.4394409005054}, \"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-2021-39\/segments\/1631780053493.41\/warc\/CC-MAIN-20210916094919-20210916124919-00642.warc.gz\"}"} | null | null |
Monthly Siren and Emergency Alert Test, Dec. 2 at 11:45 a.m.
December 2, 2019, 5:25 AM HST
* Updated November 30, 8:39 AM
The monthly test of the all-hazard Statewide Outdoor Warning Siren System, coordinated with the test of the Live Audio Broadcast segment of the Emergency Alert System, is scheduled for Monday, Dec. 2, 2019 at 11:45 a.m.
During this monthly test, all Statewide Outdoor Warning Sirens will sound a one-minute Attention Alert Signal (Steady Tone). A simultaneous test of the Live Audio Broadcast segment of the Emergency Alert System is conducted with the monthly siren sounding, in cooperation with Hawai'i's broadcast industry. There will be no exercise or drill accompanying the test.
The all-hazard Outdoor Siren Warning System for Public Safety is one part of Hawai'i's Statewide Alert and Warning System used to notify the public during emergencies.
If you hear this siren tone in circumstances other than a test, follow emergency information and instructions provided by official government channels. This may be in the form of a local radio, television station broadcast, and/or cellular Wireless Emergency Alert.
Wireless Emergency Alert delivers sound-and-text warnings to compatible mobile cellular phones. The Emergency Alert System and Wireless Emergency Alert's notifications are managed by FEMA's Integrated Public Alert and Warning System, the nation's alert and warning infrastructure.
Emergency management and disaster preparedness information is located at the front section of telephone directories in all counties. The public may contact emergency management and county civil defense agencies to report siren operation issues:
City and County of Honolulu (808) 723-8960
Maui County (808) 270-7285
Kaua'i County (808) 241-1800
Hawai'i County (808) 935-0031
Emergency Management Agency Siren, Maui. Photo by Wendy Osher.
Monthly Siren and Emergency Alert System Test, Dec. 1 December 1, 2020
Monthly Siren and Emergency Alert System Test, June 3 June 3, 2019
Monthly Siren and Emergency Alert System Test, March 2 March 2, 2020
Monthly Siren and Emergency Alert System Test, July… July 1, 2020
Monthly Siren and Emergency Alert System Test on… February 1, 2021
Monthly Siren and Test for Emergency Alert System… March 1, 2021 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,876 |
Missa Chrismatis in the Extraordinary Form in the ...
Holy Saturday - The Pontifical Russian College in ...
The Suffering and Death of Christ in 15th century ...
Roman Sacrament Altars, Holy Thursday 2013
Maundy Thursday from the London Oratory
From Tenebrae, Maundy Thursday, Blackfriars, Oxfor...
Victoria's First Lamentation for Maundy Thursday
Palm Sunday, Ave Maria University
Palm Sunday, Chicago (Canons Regular of St. John C...
Progress Report from Jeff Ostrowski on Campion Mis...
Palm Sunday with the Personal Ordinariate of Our L...
Compendium of the 1961 Revision of the Pontificale...
U.K. Ordinariate Chrism Mass
Palm Sunday at the Birmingham Oratory
Palm Sunday, Heilgenkreuz Abbey
The Rebellion Against the Self-Evident (NLM Reprin...
Francis and Benedict
Two Relief Carvings of the Entry into Jerusalem
Contexutalizing "Noble Simplcity" (NLM Reprint)
EF Mass, Georgetown University
Noble Simplicity and the Liturgiologist Edmund Bis...
"Benedict XVI Put Liturgy Front and Center"
Noble Simplicity Revisited - 1
Passion Sunday, Toledo, Spain
Summer courses: Diploma on the Theology of Sacred ...
CNA: "Oriented Toward Gregorian Chant"
Ceremonial Details of Today's Mass of Inauguration...
Live Coverage of the Papal Inaguration
Details: Illuminations from the Book of Kells (NLM...
Early Irish Christian Architecture & Design (NLM R...
Video of Sculptor Andrew Wilson Smith
Some Liturgical Thoughts for the NLM Following the...
Laudamus Te Magazine
The Importance of Reverence within the Sacred Litu...
St. Francis and the Liturgy
Pope Francis and his Choice of Name
Sandro Magister on the New Pope
Election of Pope Francis I
Quarant'Ore, London Oratory
The New Pope and the Room of Tears
The Papal Tailors
Wounded by Beauty
More from Laetare Sunday - In Houston, Texas
LMS Mass in Westminster Cathedral for Election of ...
Laetare Sunday in Genoa, Italy
Speakers for Sixth Fota International Liturgy Conf...
St Mary's University College Offers a Certificate ...
Solemn Vespers for the Intention of the Election o...
New Blog: View from the Choir Loft - Reflections o...
The Feast of St. Thomas Aquinas
Short Documentary on the Life of Pope Benedict XVI...
The Renaissance of the Mass Propers
Revival of Sacred Music and Ad Orientem at Univers...
NLM Exclusive: Bishop Dominique Rey on Sacra Litur...
Dominican Rite Mass for Feast of St. Thomas Aquina...
Seville, Oratorio de la Santa y Venerable Escuela ...
New EF Mass in Charlotte, North Carolina
Study Sacred Music from Your Laptop
The First Minute of the Sede Vacante at St. Peter'...
ROME, March 13, 2013 - By electing as pope at the fourth scrutiny the archbishop of Buenos Aires Jorge Mario Bergoglio, the conclave has made a move as surprising as it is brilliant.
Surprising for those - almost everyone - who had not noticed, during the preceding days, the effective appearance of his name in the conversations among the cardinals. His relatively advanced age, 76 years and three months, led him to be classified more among the great electors than among the possible elect.
In the conclave of 2005 the opposite had happened for him. Bergoglio was one of the most decisive supporters of the appointment of Joseph Ratzinger as pope. And instead he found himself voted for, against his own will, precisely by those who wanted to block the appointment of Benedict XVI.
The fact remains that both one and the other became pope. Bergoglio with the unprecedented name of Francis.
A name that reflects his humble life. Having become archbishop of Buenos Aires 1998, he left empty the sumptuous episcopal residence next to the cathedral. He went to live in an apartment a short distance away, together with another elderly bishop. In the evening he was the one who saw to the cooking. He rarely rode in cars, getting around by bus in the cassock of an ordinary priest.
But he is also a man who knows how to govern. With firmness and against the tide. He is a Jesuit - the first to have become pope - and during the terrible 1970's, when the dictatorship was raging and some of his confrères were ready to embrace the rifle and apply the lessons of Marx, he energetically opposed the tendency as provincial of the Society of Jesus in Argentina.
He has always carefully kept his distance from the Roman curia. It is certain that he will want it to be lean, clean, and loyal.
He is a pastor of sound doctrine and of concrete realism. To the Argentines reduced to hunger he has given much more than bread. He has urged them to pick the catechism back up again. That of the ten commandments and of the beatitudes. "This is the way of Jesus," he would say. And one who follows Jesus understands that "trampling the dignity of a woman, of a man, of a child, of an elderly person is a grave sin that cries out to heaven," and therefore decides to do it no more.
The simplicity of his vision makes itself felt in his holiness of life. With his few and simple first words as pope he immediately won over the crowd packed into St. Peter's Square. He had them pray in silence.
And he also had them pray for his predecessor, Benedict XVI, whom he did not call "pope," but "bishop."
The surprise is only beginning.
Source: Chiesa
Posted Wednesday, March 13, 2013 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,578 |
Compositional Practice and Technique (1)
Instrument-building Firms (1)
[[missing key: search-facet.tree.open-section]] Music and Media (1)
Film, Television, and Video Game Music (1)
Organology (1)
Electronic Instruments (1)
Instrument-building Firms x
Music Business, Institutions and Organizations x
Film, Television, and Video Game Music x
Siemens Synthesizer
Hugh Davies
Electronic composition machine (not a synthesizer in the current sense of the word), developed by Helmut Klein and W. Schaaf at Siemens & Halske in Munich between 1956 and 1959. It was designed for and was the chief component of the Studio für Elektronische Musik in Munich, which Siemens began planning in 1955, initially to produce the soundtrack for a one-hour publicity film; it was linked to all the other equipment in the studio. A second model was installed in 1964. The director of the studio and the composer most closely involved with the Siemens Synthesizer was Josef Anton Riedl; others who used the machine included the composers Mauricio Kagel, Bengt Hambraeus, Milko Kelemen, and Ernst Krenek, and the sound poet Ferdinand Kriwet. The studio was taken over by a foundation in 1963, and its equipment was moved to Ulm in 1967; it was later acquired by the Deutsches Museum in Munich.... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,362 |
{"url":"https:\/\/crypto.stackexchange.com\/questions\/42144\/computational-diffie-hellman-problem","text":"# Computational Diffie-Hellman problem\n\nFrom here,\n\nThe Computational Diffie-Hellman problem: Given $y_1 = g^{x_1}$ and $y_2 = g^{x_2}$ (but not $x_1$ and $x_2$), find $y = g^{x_1\u00b7x_2}$.\n\n1. What happens if I knew one of the $x_1$, would it still be hard?\n2. Considering the CDH, is the problem still hard for $g^{x_1x_2}\/g^{x_1}$ or $g^{x_1x_2}*g^{x_1}$ or even just $zg^{x_1x_2}$ for some integer $z$. (For cases when I don't know $x_1$ and $x_2$ and the other case when I do know one like $x_1$?)\n\nMy intuition for no.1 is that if it would reduce to only needing to solve $y_2 = g^{x_2}$ which is a hard discrete log problem. And we know that if CDH is hard, DL is hard [2].\n\n\u2022 \u2013\u00a0user991 Dec 8 '16 at 2:46\n\nThe hardness of CDH arises from the fact that we do not know how to obtain $x$, given $g^x$, efficiently.\n1) If one knows $x_1$, then one can easily compute $g^{x_1 x_2}$ by computing $y_2^{x_1} = (g^{x_2})^{x_1} = g^{x_1 x_2}$ using Square and Multiply!\n2) For this case, suppose that computing $k = g^{x_1 x_2} \/ g^{x_1}$ wasn't hard. Then one could easily obtain $g^{x_1 x_2} = k \\, y_1 = k \\, g^{x_1}$ and CDH would not be hard which is a contradiction. You can make a similar argument for the other case. And similarly for $z \\, g^{x_1 x_2}$ (assuming I didn't misunderstand what you asked), if we can compute this then multiplying it by $z^{-1}$ (which is easy to compute) will solve CDH.","date":"2020-07-10 01:06:35","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\": 0.9645737409591675, \"perplexity\": 277.75542765710867}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-29\/segments\/1593655902377.71\/warc\/CC-MAIN-20200709224746-20200710014746-00386.warc.gz\"}"} | null | null |
package edu.mayo.mprc.comet;
import com.google.common.base.Joiner;
import edu.mayo.mprc.MprcException;
import edu.mayo.mprc.chem.AminoAcidSet;
import edu.mayo.mprc.swift.params2.*;
import edu.mayo.mprc.swift.params2.mapping.Mappings;
import edu.mayo.mprc.swift.params2.mapping.MockParamsInfo;
import edu.mayo.mprc.swift.params2.mapping.TestMappingContextBase;
import edu.mayo.mprc.unimod.*;
import edu.mayo.mprc.utilities.TestingUtilities;
import org.testng.Assert;
import org.testng.annotations.BeforeMethod;
import org.testng.annotations.Test;
import java.io.StringWriter;
/**
* @author Roman Zenka
*/
public final class TestCometMappings {
private CometMappingFactory factory = new CometMappingFactory();
private Mappings mappings;
private CometContext context;
@BeforeMethod
public void setup() {
mappings = factory.createMapping();
context = new CometContext();
}
private void assertParam(final String param, final String value) {
Assert.assertEquals(mappings.getNativeParam(param), value, "Value for " + param + " does not match");
}
@Test
public void shouldSupportPeptideTolerance() {
mappings.read(mappings.baseSettings());
// 0.3 Da - low precision
{
final Tolerance da = new Tolerance(0.3, MassUnit.Da);
mappings.setPeptideTolerance(context, da);
assertParam("peptide_mass_tolerance", "0.3");
assertParam("peptide_mass_units", "0");
assertParam("precursor_tolerance_type", "0");
assertParam("isotope_error", "0");
}
// 12 ppm - high precision
{
final Tolerance ppm = new Tolerance(12, MassUnit.Ppm);
mappings.setPeptideTolerance(context, ppm);
assertParam("peptide_mass_tolerance", "12.0");
assertParam("peptide_mass_units", "2");
assertParam("precursor_tolerance_type", "1");
assertParam("isotope_error", "1");
}
}
@Test
public void shouldSupportFragmentTolerance() {
context.setExpectWarnings(new String[]{"does not support ppm, using"});
mappings.read(mappings.baseSettings());
{
final Tolerance ppm = new Tolerance(10, MassUnit.Ppm);
mappings.setFragmentTolerance(context, ppm);
assertParam("fragment_bin_tol", "0.01"); // 10 ppm at 1000
assertParam("fragment_bin_offset", "0.0"); // Offset == 0 for anything under 0.8 dalton, otherwise 0.4
assertParam("theoretical_fragment_ions", "0");
assertParam("use_sparse_matrix", "1");
}
{
final Tolerance da = new Tolerance(1, MassUnit.Da);
mappings.setFragmentTolerance(context, da);
assertParam("fragment_bin_tol", "1.0"); // 1 dalton bin
assertParam("fragment_bin_offset", "0.4"); // Offset is 0.4 (for no particular reason)
assertParam("theoretical_fragment_ions", "1");
assertParam("use_sparse_matrix", "0");
}
}
@Test
public void shouldSupportFixedMods() {
mappings.read(mappings.baseSettings());
{
final ModSet fixedMods = new ModSet();
mappings.setFixedMods(context, fixedMods);
assertParam("add_C_cysteine", "0.0");
}
{
final ModSet fixedMods = new ModSet();
fixedMods.add(getCarbC());
mappings.setFixedMods(context, fixedMods);
assertParam("add_C_cysteine", "57.021464");
}
{
// Return back to zero
final ModSet fixedMods = new ModSet();
mappings.setFixedMods(context, fixedMods);
assertParam("add_C_cysteine", "0.0");
}
{
final ModSet fixedMods = new ModSet();
fixedMods.add(acetylAnyAcidProteinNTerm());
mappings.setFixedMods(context, fixedMods);
assertParam("add_Nterm_protein", "42.010565");
}
{
final ModSet fixedMods = new ModSet();
fixedMods.add(getAcetylAnyPeptideCTerm());
mappings.setFixedMods(context, fixedMods);
assertParam("add_Cterm_peptide", "42.010565");
}
{
final ModSet fixedMods = new ModSet();
// Protein N-term mod + specific site - G - should not be supported
context.setExpectWarnings(new String[]{"Comet does not support fixed mod 'Acetyl (Protein N-term G)' - skipping"});
fixedMods.add(getNtermAcetyl());
mappings.setFixedMods(context, fixedMods);
context.failIfNoWarnings();
}
{
final ModSet fixedMods = new ModSet();
// Stacked mods
context.setExpectWarnings(null);
fixedMods.add(getAcetylG());
fixedMods.add(getSpecialMod());
mappings.setFixedMods(context, fixedMods);
assertParam("add_G_glycine", "52.010565");
}
}
@Test
public void shouldSupportVariableMods() {
mappings.read(mappings.baseSettings());
{
final ModSet variableMods = new ModSet();
mappings.setVariableMods(context, variableMods);
assertParam("variable_mod1", "0.0 X 0 3");
assertParam("variable_mod2", "0.0 X 0 3");
assertParam("variable_mod3", "0.0 X 0 3");
assertParam("variable_mod4", "0.0 X 0 3");
assertParam("variable_mod5", "0.0 X 0 3");
assertParam("variable_mod6", "0.0 X 0 3");
assertParam("max_variable_mods_in_peptide", "3");
}
{
final ModSet variableMods = new ModSet();
variableMods.add(getCarbC());
variableMods.add(getAcetylG());
mappings.setVariableMods(context, variableMods);
assertParam("variable_mod1", "42.010565 G 0 3");
assertParam("variable_mod2", "57.021464 C 0 3");
}
{
final ModSet variableMods = new ModSet();
variableMods.add(getNtermAcetyl());
context.setExpectWarnings(new String[]{"replaced"});
mappings.setVariableMods(context, variableMods);
context.failIfNoWarnings();
assertParam("variable_mod1", "42.010565 G 0 3");
}
{
final ModSet variableMods = new ModSet();
variableMods.add(getAebs());
context.setExpectWarnings(new String[]{"skipped unsupported N-term"});
mappings.setVariableMods(context, variableMods);
context.failIfNoWarnings();
assertParam("variable_mod1", "0.0 X 0 3");
}
{
final ModSet variableMods = new ModSet();
variableMods.add(getAcetylAnyPeptideCTerm());
context.setExpectWarnings(new String[]{"skipped unsupported C-term mod 'Acetyl (C-term)'"});
mappings.setVariableMods(context, variableMods);
context.failIfNoWarnings();
assertParam("variable_mod1", "0.0 X 0 3");
}
}
@Test
public void shouldSupportInstrument() {
mappings.read(mappings.baseSettings());
{
final Instrument instrument = Instrument.ORBITRAP;
mappings.setInstrument(context, instrument);
assertParam("use_A_ions", "0");
assertParam("use_B_ions", "1");
assertParam("use_C_ions", "0");
assertParam("use_X_ions", "0");
assertParam("use_Y_ions", "1");
assertParam("use_Z_ions", "0");
}
{
final Instrument instrument = Instrument.MALDI_TOF_TOF;
context.setExpectWarnings(new String[]{"does not support ion series 'd', 'v', 'w'"});
mappings.setInstrument(context, instrument);
context.failIfNoWarnings();
assertParam("use_A_ions", "1");
assertParam("use_B_ions", "1");
assertParam("use_C_ions", "0");
assertParam("use_X_ions", "0");
assertParam("use_Y_ions", "1");
assertParam("use_Z_ions", "0");
}
}
@Test
public void shouldSupportMinTerminiCleavages() {
mappings.read(mappings.baseSettings());
mappings.setMinTerminiCleavages(context, 1);
assertParam("num_enzyme_termini", "1");
mappings.setMinTerminiCleavages(context, 2);
assertParam("num_enzyme_termini", "2");
context.setExpectWarnings(new String[]{"not support"});
mappings.setMinTerminiCleavages(context, 0);
context.failIfNoWarnings();
}
@Test
public void shouldSupportMissedCleavages() {
mappings.read(mappings.baseSettings());
{
mappings.setMissedCleavages(context, 5);
assertParam("allowed_missed_cleavage", "5");
}
{
context.setExpectWarnings(new String[]{"not support > 5 missed cleavages"});
mappings.setMissedCleavages(context, 6);
context.failIfNoWarnings();
assertParam("allowed_missed_cleavage", "5");
}
}
@Test
public void shouldConvertProteases() {
Assert.assertEquals(CometMappings.proteaseToCometString("2", Protease.getTrypsinAllowP()),
"2. Trypsin_(allow_P) 1 KR -");
Assert.assertEquals(CometMappings.proteaseToCometString("6", aspN()),
"6. Asp_N 0 D -");
}
@Test
public void shouldSupportProtease() {
mappings.read(mappings.baseSettings());
{
final Protease protease = Protease.getTrypsinAllowP();
mappings.setProtease(context, protease);
assertParam("search_enzyme_number", "2");
assertParam("sample_enzyme_number", "2");
}
{
final Protease protease = new Protease("Trypsin", "KR", "!P");
mappings.setProtease(context, protease);
assertParam("search_enzyme_number", "1");
assertParam("sample_enzyme_number", "1");
}
{
final Protease protease = aspN();
mappings.setProtease(context, protease);
assertParam("search_enzyme_number", "6");
assertParam("sample_enzyme_number", "6");
}
{
final Protease protease = new Protease("Asp N", "", "BD");
mappings.setProtease(context, protease);
assertParam("search_enzyme_number", "11");
assertParam("sample_enzyme_number", "11");
final StringWriter writer = new StringWriter(1000);
mappings.write(mappings.baseSettings(), writer);
Assert.assertEquals(writer.toString(), TestingUtilities.resourceToString("edu/mayo/mprc/comet/customEnzyme.params"));
}
}
private Protease aspN() {
return new Protease("Asp_N", "", "D");
}
@Test
public void shouldSupportSequenceDatabase() {
mappings.read(mappings.baseSettings());
{
// We pass the database directly from command line
// Ignore the config file contents
final String databaseName = "hello";
mappings.setSequenceDatabase(context, databaseName);
assertParam("database_name", "pass_from_command_line");
}
}
/**
* Fail if anything unusual happens.
*/
private static final class CometContext extends TestMappingContextBase {
private String[] expectWarnings;
private boolean warningsFound;
/**
* Create basic context with mocked parameter info.
*/
CometContext() {
super(new MockParamsInfo());
}
public void setExpectWarnings(final String[] expectWarnings) {
this.expectWarnings = expectWarnings;
warningsFound = false;
}
public void failIfNoWarnings() {
if (!warningsFound) {
throw new MprcException("The expected warnings were not given: [" + Joiner.on("], [").join(expectWarnings) + "]");
}
}
@Override
public void reportError(final String message, final Throwable t, final ParamName paramName) {
Assert.fail(message, t);
}
@Override
public void reportWarning(final String message, final ParamName paramName) {
if (expectWarnings != null) {
for (final String warning : expectWarnings) {
if (message.contains(warning)) {
warningsFound = true;
return;
}
}
Assert.fail("Warning message does not contain [" + Joiner.on(", ").join(expectWarnings) + "]: " + message);
} else {
Assert.fail(message);
}
}
}
private ModSpecificity getNtermAcetyl() {
final SpecificityBuilder b;
final Mod mod;
b = new SpecificityBuilder(AminoAcidSet.DEFAULT.getForSingleLetterCode("G"), Terminus.Nterm, true, false, "", 0);
mod = new Mod("Acetyl", "Acetylation", 2, 42.010565, 42.0367, "H(2) C(2) O", null, b);
return b.build(mod);
}
private ModSpecificity acetylAnyAcidProteinNTerm() {
final SpecificityBuilder b;
final Mod mod;
b = new SpecificityBuilder(null, Terminus.Nterm, true, false, "", 0);
mod = new Mod("Acetyl", "Acetylation", 2, 42.010565, 42.0367, "H(2) C(2) O", null, b);
return b.build(mod);
}
private ModSpecificity getAcetylG() {
final SpecificityBuilder b;
final Mod mod;
b = new SpecificityBuilder(AminoAcidSet.DEFAULT.getForSingleLetterCode("G"), Terminus.Anywhere, true, false, "", 0);
mod = new Mod("Acetyl", "Acetylation", 2, 42.010565, 42.0367, "H(2) C(2) O", null, b);
return b.build(mod);
}
private ModSpecificity getCarbC() {
final SpecificityBuilder b = new SpecificityBuilder(AminoAcidSet.DEFAULT.getForSingleLetterCode("C"), Terminus.Anywhere, false, false, "", 0);
final Mod mod = new Mod("Carbamidomethyl", "Iodoacetamide derivative", 1, 57.021464, 57.0513, "H(3) C(2) N O", null, b);
return b.build(mod);
}
private ModSpecificity getAebs() {
final SpecificityBuilder b = new SpecificityBuilder(null, Terminus.Nterm, true, false, "", 0);
final Mod mod = new Mod("AEBS", "Aminoethylbenzensulfonylation", 1, 183.034399, 183.2276, "H(9) C(8) N O(2) S", null, b);
return b.build(mod);
}
private ModSpecificity getSpecialMod() {
final SpecificityBuilder b2 = new SpecificityBuilder(AminoAcidSet.DEFAULT.getForSingleLetterCode("G"), Terminus.Anywhere, true, false, "", 0);
final Mod mod2 = new Mod("Special mod", "Specialization", 2, 10.0, 42.0367, "H(10)", null, b2);
return b2.build(mod2);
}
private ModSpecificity getAcetylAnyPeptideCTerm() {
// Peptide C-term mod
final SpecificityBuilder b = new SpecificityBuilder(null, Terminus.Cterm, false, false, "", 0);
final Mod mod = new Mod("Acetyl", "Acetylation", 2, 42.010565, 42.0367, "H(2) C(2) O", null, b);
return b.build(mod);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,955 |
{"url":"http:\/\/openstudy.com\/updates\/556bb3f1e4b0c4e453f99b94","text":"## anonymous one year ago Suppose you have a mean standardized score of 1500 points with a standard deviation of 150 points. This data is normally distributed. What is the z-score of 1600 points? 0.75 0.5 0.67 0.32\n\n1. campbell_st\n\nto find a z score, use the formula $z = \\frac{x - mean}{std.~deviation}$ where x is the score\n\n2. anonymous\n\nBut how do you get the mean in this problem?\n\n3. campbell_st\n\nyou are given the mean.... mean = 1500\n\n4. campbell_st\n\nyou are given the standardeviation = 150","date":"2017-01-19 05:04:24","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\": 0.8829576373100281, \"perplexity\": 1134.0194930582243}, \"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\/1484560280483.83\/warc\/CC-MAIN-20170116095120-00119-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
Unsubscribe from Santa Monica Filtration?
This video shows the new hard plastic magnet protectors that are now installed on the wet sides of all HOG1.3, HOG2, HOG3, HOG3x and HOG3xx models. These protectors, and the extra thick silicone sealant, gives the maximum protection for the magnets. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,432 |
Kelly Middaugh (born August 2, 1999) is a Canadian curler from Victoria Harbour, Ontario. She currently plays lead on Team Laurie St-Georges.
Career
While attending Wilfrid Laurier University, Middaugh competed in two U Sports/Curling Canada University Curling Championships. In 2018, as second for the team skipped by Kaitlin Jewer, they finished with a 3–4 round robin record, failing to advance to the playoffs. At the 2020 U Sports/Curling Canada University Curling Championships, the team, led by Isabelle Ladouceur, finished in sixth place with a 2–5 record.
During the 2018–19 season, Middaugh played lead for the Emma Wallingford rink. The team competed in one women's event, the Royal LePage Women's Fall Classic, where they were able to find success. After dropping their first two games, the team won four straight sudden death games to qualify for the playoffs. They were then defeated by Isabella Wranå in the quarterfinals. At the 2018 Ontario U-21 Curling Championships, the team qualified for the playoffs with a 4–3 record. They then lost to the eventual champions Thea Coburn 7–6 in the semifinals.
For the 2019–20 season, Middaugh joined the Isabelle Ladouceur rink at lead. At the Ontario junior championship, they failed to reach the playoffs after a 3–4 round robin record. The following season, the team competed in and won the Bally Haly Cash Spiel, posting an undefeated 6–0 record throughout the event. They also competed in The Curling Store Cashspiel and the Lakeshore U21 Junior Women's Spiel, losing in the semifinals of both events to Christina Black and Celia Evans respectively.
After two seasons playing for Team Ladouceur, Middaugh was added to the Jacqueline Harrison rink for the 2021–22 season as their alternate. The team also included third Allison Flaxey, second Lynn Kreviazuk and lead Laura Hickey. The team had a strong start to the season, beginning with a semifinal loss at the 2021 Oakville Fall Classic to Suzanne Birt. They then lost two straight quarterfinal games at the 2021 Oakville Labour Day Classic and Stu Sells Toronto Tankard, both to Hollie Duncan. With their successful results over the season, Team Harrison had enough points to qualify for the 2021 Canadian Olympic Curling Pre-Trials. There, they posted a 5–1 record through the round robin, qualifying for the playoffs. They then beat Suzanne Birt in the A event semifinal before dropping the first final 9–6 to Krista McCarville. They rebounded with a 9–2 victory over Corryn Brown to earn the ninth and final spot in the 2021 Canadian Olympic Curling Trials. Middaugh did not compete in the trials with the team.
Personal life
Middaugh is currently an outdoor adventure naturalist program student at Algonquin College She previously attended Wilfrid Laurier University. She is engaged to Kenny Malcolmson. Her parents Wayne and Sherry are also accomplished curlers.
Teams
References
External links
1999 births
Canadian women curlers
Living people
20th-century Canadian women
21st-century Canadian women
Wilfrid Laurier University alumni
Algonquin College alumni
Curlers from Simcoe County
People from Midland, Ontario | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,233 |
Moro Mandjouf Sidibé né le à Conakry, est un médecin et personnalité politique guinéen.
Il est le candidat de l'Alliance des forces du changement (AFC) aux élections présidentielles du 2020 en Guinée.
Biographie et études
Parcours professionnel
Il commence son parcours à l'hôpital préfectoral de Fria puis au CHU Ignace Deen avant de s'exiler en France en 1982.
Après 10 ans d'exercice en France, il retourne en Guinée en 1998.
Entre 2006 et 2010, il est directeur général de l'entreprise VIENTOSUR, cumulativement à partir de 2009 ambassadeur itinérant prêt du président de la république de Guinée jusqu'en 2010.
Il est conseiller chargé de mission à la force africaine en attente d'Addis-Abeba de 2012 en 2014 et cumulativement CEO de l'entreprise Winkon Trade Automobile (WTA) de 2011 à nos jours.
Parcours politique
Il a été designer président de UDIR le pour les élections présidentielle du 18 octobre 2020.
Vie privée
Il est marié et père de six enfants.
Bibliographie
.
.
.
.
Notes et références
Personnalité politique guinéenne
Naissance en mai 1951
Naissance à Conakry | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,190 |
"""
This module lets your server send Web Push Notifications to your clients.
(Please, visit https://github.com/sergioburdisso/solidwebpush for more info).
----
"""
from __future__ import print_function
from sqlite3 import connect as db_connect
from multiprocessing import Pool
from py_vapid import Vapid
import os
import re
import json
import time
import base64
import requests
import http_ece
import pyelliptic
__version__ = '1.2.3'
__license__ = 'MIT'
def __doc_from__(docfunc):
"""A @decorator."""
def __wrapper__(func):
func.__name__ = docfunc.__name__
func.__doc__ = docfunc.__doc__
return func
return __wrapper__
def __database__(func):
"""A @decorator."""
@__doc_from__(func)
def __init_database__(*args, **kwargs):
s = args[0]
if not s.__db_conn__:
s.__db_conn__ = db_connect(s.__db_name__)
s.__db_conn__.row_factory = lambda cursor, row: \
dict((
(col[0], row[idx])
for idx, col
in enumerate(cursor.description)
))
s.__db__ = s.__db_conn__.cursor()
try:
s.__db__.executescript('''
CREATE TABLE subscriptors (
session_id VARCHAR(256) NOT NULL PRIMARY KEY,
subscription VARCHAR(512) NOT NULL,
group_id INT NOT NULL
);
''')
s.__db_conn__.commit()
except:
pass
result = func(*args, **kwargs)
s.__db_conn__.close()
s.__db_conn__ = None
else:
result = func(*args, **kwargs)
return result
__init_database__.__name__ = func.__name__
__init_database__.__doc__ = func.__doc__
return __init_database__
def __is_valid_json__(jstr):
try:
json.loads(jstr)
return True
except:
return False
class SesionIDError(Exception):
""" exception to be thrown when no proper session_id is used """
def __init__(self, message):
Exception.__init__(self, message)
class SubscriptionError(Exception):
""" exception to be thrown when no proper subscription is used """
def __init__(self, msg=''):
Exception.__init__(
self,
"subscription must be a valid JSON str, bytes or bytearray."
)
class Pusher:
"""
Pusher objects allows you to integrate Web Push Notifications
into your project.
Instantiate this class to integrate Web Push Notifications
into your server. Objects of this class will create your public
and private key, track your subscriptions, notify your clients,
and do all the required work for you.
e.g.
>>> from solidwebpush import Pusher
>>>
>>> pusher = Pusher()
>>>
>>> #what's my base64-encoded public key?
>>> print pusher.getB64PublicKey()
>>>
>>> subscription = "{Alice's serviceWorker subscription object}"
>>>
>>> #notify Alice
>>> pusher.sendNotification(subscription, "Hello World!")
>>>
>>> #or
>>> #permanently subscribe Alice
>>> pusher.newSubscription(alice_session_id, subscription)
>>>
>>> #so that, from now on we can notify her by
>>> pusher.notify(alice_session_id, "Hello World")
>>>
>>> #or notify all the permanently subscribed clients
>>> pusher.notifyAll("Hello World")
(for more "toy" examples visit
https://github.com/sergioburdisso/solidwebpush/tree/master/examples)
"""
__vapid__ = None
__verbose__ = False
__db_name__ = None
__db_conn__ = None
__db__ = None
__pool__ = None
__RE_URL__ = r"(https?://(?:[\w-]+\.)*[\w-]+(?::\d+)?)(?:/.*)?"
def __init__(self, db_name="subscriptors.db", verbose=False):
"""
Class constructor.
:param db_name: The [optional] name ("subscriptors.db" by default) of
the file in which subscriptions will be stored in.
This is only required if methods like
``newSubscription`` will be used.
:type db_name: str
:param verbose: An optional value, to enabled or disabled the "verbose
mode" (False by default)
:type verbose: bool
"""
self.__verbose__ = verbose
self.__db_name__ = db_name
if not os.path.exists('private_key.pem'):
self.__print__("No private_key.pem file found")
Vapid().save_key('private_key.pem')
self.__print__("private_key.pem file created")
self.__vapid__ = Vapid('private_key.pem')
if not os.path.exists('public_key.pem'):
self.__print__("No public_key.pem file found")
self.__vapid__.save_public_key('public_key.pem')
self.__print__("public_key.pem file created")
if verbose:
self.__print__("PublicKey: %s" % self.getB64PublicKey())
def __getstate__(self):
"""Class state getter."""
self_dict = self.__dict__.copy()
try:
del self_dict['__pool__']
del self_dict['__db_conn__']
del self_dict['__db__']
except KeyError:
pass
return self_dict
def __call__(self, subscription, data):
"""Class instances callable."""
self.__send__(subscription, data)
def __print__(self, msg):
"""Verbose print wrapper."""
print("[ SolidWebPush ] %s" % msg)
def __b64rpad__(self, b64str):
"""Base64 right (=)padding."""
return b64str + b"===="[:len(b64str) % 4]
def __encrypt__(self, user_publickey, user_auth, payload):
"""Encrypt the given payload."""
user_publickey = user_publickey.encode("utf8")
raw_user_publickey = base64.urlsafe_b64decode(
self.__b64rpad__(user_publickey)
)
user_auth = user_auth.encode("utf8")
raw_user_auth = base64.urlsafe_b64decode(self.__b64rpad__(user_auth))
salt = os.urandom(16)
curve = pyelliptic.ECC(curve="prime256v1")
curve_id = base64.urlsafe_b64encode(curve.get_pubkey()[1:])
http_ece.keys[curve_id] = curve
http_ece.labels[curve_id] = "P-256"
encrypted = http_ece.encrypt(
payload.encode('utf8'),
keyid=curve_id,
dh=raw_user_publickey,
salt=salt,
authSecret=raw_user_auth,
version="aesgcm"
)
return {
'dh': base64.urlsafe_b64encode(
curve.get_pubkey()
).strip(b'=').decode("utf-8"),
'salt': base64.urlsafe_b64encode(
salt
).strip(b'=').decode("utf-8"),
'body': encrypted
}
def __send__(self, subscription, data):
"""Encrypt and send the data to the Message Server."""
if __is_valid_json__(subscription):
subscription = json.loads(subscription)
else:
raise SubscriptionError()
if type(data) == dict:
data = json.dumps(data)
base_url = re.search(
self.__RE_URL__,
subscription["endpoint"]
).group(1)
encrypted = self.__encrypt__(
subscription["keys"]["p256dh"],
subscription["keys"]["auth"],
data
)
jwt_payload = {
"aud": base_url,
"exp": str(int(time.time()) + 60 * 60 * 12),
"sub": "mailto:admin@mail.com"
}
headers = self.__vapid__.sign(jwt_payload)
headers["TTL"] = str(43200)
headers["Content-Type"] = "application/octet-stream"
headers['Content-Encoding'] = "aesgcm"
headers['Encryption'] = "salt=%s" % encrypted["salt"]
headers["Crypto-Key"] = "dh=%s;p256ecdsa=%s" % (
encrypted["dh"],
self.getUrlB64PublicKey()
)
r = requests.post(
subscription["endpoint"],
data=encrypted["body"],
headers=headers
)
if self.__verbose__:
self.__print__(
"Message Server response was: \nStatus: %d\nBody: %s"
%
(r.status_code, r.text)
)
def setVerbose(self, value):
"""
Verbose mode.
Enable and disable the verbose mode (disabled by default).
When verbose mode is active, some internal messages are going
to be displayed, as well as the responses from the Message Server.
:param value: True to enable or False to disable
:type value: bool
"""
self.__verbose__ = value
def getPublicKey(self):
"""
Raw public key getter.
:returns: the raw public key
:rtype: str
"""
return b"\x04" + self.__vapid__.public_key.to_string()
def getPrivateKey(self):
"""
Raw private key getter.
(probably you won't care about private key at all)
:returns: the raw private key
:rtype: str
"""
return self.__vapid__.private_key.to_string()
def getB64PublicKey(self):
"""
Base64 public key getter.
Returns the string you're going to use when subscribing your
serviceWorker.
(as long as you're planning to decode it using JavaScript's
``atob`` function)
:returns: Base64-encoded version of the public key
:rtype: str
"""
return base64.b64encode(self.getPublicKey()).decode("utf-8")
def getB64PrivateKey(self):
"""
Base64 private key getter.
(probably you won't care about private key at all)
:returns: Base64-encoded version of the private key
:rtype: str
"""
return base64.b64encode(self.getPrivateKey()).decode("utf-8")
def getUrlB64PublicKey(self):
"""
Url-Safe Base64 public key getter.
This is the string you're going to use when subscribing your
serviceWorker.
(so long as you're planning to decode it using a function like
``urlB64ToUint8Array`` from
https://developers.google.com/web/fundamentals/getting-started/codelabs/push-notifications/)
:returns: URLSafe-Base64-encoded version of the public key
:rtype: str
"""
return base64.urlsafe_b64encode(
self.getPublicKey()
).strip(b"=").decode("utf-8")
def getUrlB64PrivateKey(self):
"""
Url-Safe Base64 private key getter.
(probably you won't care about private key at all)
:returns: URLSafe-Base64-encoded version of the private key
:rtype: str
"""
return base64.urlsafe_b64encode(
self.getPrivateKey()
).strip(b"=").decode("utf-8")
def sendNotification(self, subscription, data, nonblocking=False):
"""
Send the data to the Message Server.
Pushes a notification carrying ``data`` to
the client associated with the ``subscription`` object.
If ``nonblocking`` is True, the program won't block waiting
for the message to be completely sent. The ``wait()`` method
should be used instead. (see ``wait()`` for more details)
:param subscription: the client's subscription JSON object
:type subscription: str
:param data: A string or a dict object to be sent.
The dict will be automatically converted into a JSON
string before being sent.
An example of a dict object would be:
``{"title": "hey Bob!", "body": "you rock"}``
:type data: str or dict
:param nonblocking: Whether to block the caller until this method
finishes running or not.
:type nonblocking: bool
"""
self.sendNotificationToAll(
[subscription],
data,
nonblocking=nonblocking,
processes=1
)
def sendNotificationToAll(
self, subscriptions, data, nonblocking=False, processes=None):
"""
Send the data to the Message Server.
Pushes a notification carrying ``data`` to
each of the clients associated with the list of ``subscriptions``.
If ``nonblocking`` is True, the program won't block waiting
for all the messages to be completely sent. The ``wait()`` method
should be used instead. (see ``wait()`` for more details)
:param subscriptions: The list of client's subscription JSON object
:type subscriptions: list
:param data: A string or a dict object to be sent.
The dict will be automatically converted into a JSON
string before being sent.
An example of a dict object would be:
``{"title": "hey Bob!", "body": "you rock"}``
:type data: str or dict
:param processes: The [optional] number of worker processes to use.
If processes is not given then the number returned by
os.cpu_count() is used.
:type processes: int
:param nonblocking: Whether to block the caller until this method
finishes running or not.
:type nonblocking: bool
"""
if not self.__pool__:
self.__pool__ = Pool(processes)
if nonblocking:
pool_apply = self.__pool__.apply_async
else:
pool_apply = self.__pool__.apply
for subscription in subscriptions:
pool_apply(self, args=(subscription, data))
if not nonblocking:
self.__pool__.close()
self.__pool__.join()
self.__pool__ = None
def wait(self):
"""
Wait for all the messages to be completely sent.
Block the program and wait for all the notifications to be sent,
before continuing.
This only works if there exist a previous call to a method
with the ``nonblocking`` parameter set to ``True``,
as shown in the following example:
>>> pusher.sendNotificationToAll(
listOfsubscriptions,
"Hello World",
nonblocking=True
)
>>> # Maybe some other useful computation here
>>> pusher.wait()
"""
self.__pool__.close()
self.__pool__.join()
self.__pool__ = None
@__database__
def newSubscription(self, session_id, subscription, group_id=0):
"""
newSubscription(session_id, subscription, group_id=0)
Permanently subscribe a client.
Subscribes the client by permanently storing its ``subscription`` and
group id (``group_id``).
This will allow you to push notifications using the
client id (``session_id``) instead of its ``subscription`` object.
Groups help you organize subscribers. For instance, suppose you
want to notify Bob by sending a notification to all of his devices.
If you previously subscribed each one of his devices to the same group
let's say 13, then calling notifyAll with 13 will push notifications to
all of them:
>>> BobsGroup = 13
>>> ...
>>> pusher.newSubscription(
BobsTabletSessionId,
subscription0,
BobsGroup
)
>>> ...
>>> pusher.newSubscription(
BobsLaptopSessionId,
subscription1,
BobsGroup
)
>>> ...
>>> pusher.newSubscription(
BobsMobileSessionId,
subscription2,
BobsGroup
)
>>> ...
>>> pusher.notifyAll(BobsGroup)
:param session_id: The client's identification
(e.g. a cookie or other session token)
:type session_id: str
:param subscription: The client's subscription JSON object
:type subscription: str
:param group_id: an optional Group ID value (0 by default)
:type group_id: int
"""
if not __is_valid_json__(subscription):
raise SubscriptionError()
if not session_id and session_id != 0:
raise SesionIDError("session_id cannot be empty")
if not self.getSubscription(session_id):
old_session_id = self.getIdSession(subscription)
if old_session_id:
self.removeSubscription(old_session_id)
self.__db__.execute(
"INSERT INTO subscriptors (session_id, subscription, group_id)"
" VALUES (?,?,?)",
(session_id, subscription, group_id)
)
else:
self.__db__.execute(
"UPDATE subscriptors SET subscription=?, group_id=? WHERE"
" session_id=?",
(subscription, group_id, session_id,)
)
self.__db_conn__.commit()
@__database__
def removeSubscription(self, session_id):
"""
removeSubscription(session_id)
Permanently unsubscribes a client.
Unsubscribes the client by permanently removing its ``subscription``
and group id.
:param session_id: The client's identification (e.g. a cookie or other
session token)
:type session_id: str
"""
self.__db__.execute(
"DELETE FROM subscriptors WHERE session_id = ?",
(session_id,)
)
self.__db_conn__.commit()
@__database__
def notify(self, session_id, data, nonblocking=False):
"""
notify(session_id, data, nonblocking=False)
Notify a given client.
Pushes a notification carrying ``data`` to the client associated with
the ``session_id``.
``session_id`` is the value passed to the ``newSubscription`` method
when storing the client's subscription object.
:param session_id: The client's identification (e.g. a cookie or other
session token)
:type session_id: str
:param data: A string or a dict object to be sent.
The dict will be automatically converted into a JSON
string before being sent.
An example of a dict object would be:
``{"title": "hey Bob!", "body": "you rock"}``
:type data: str or dict
:param nonblocking: Whether to block the caller until this method
finishes running or not.
:type nonblocking: bool
"""
if self.getSubscription(session_id):
self.sendNotification(
self.getSubscription(session_id),
data,
nonblocking=nonblocking
)
else:
raise SesionIDError(
"the given session_id '%s' does not exist "
"(it has not been subscribed yet)." % session_id
)
@__database__
def notifyAll(self, data, group_id=None, exceptions=[], nonblocking=False):
"""
notifyAll(data, group_id=None, exceptions=[], nonblocking=False)
Notify a group of clients.
When no ``group_id`` is given, notify all subscribers (except for those
in ``exceptions``). Otherwise, it only notifies all members of the
``group_id`` group (except for those in ``exceptions``).
:param data: A string or a dict object to be sent.
The dict will be automatically converted into a JSON
string before being sent.
An example of a dict object would be:
``{"title": "hey Bob!", "body": "you rock"}``
:type data: str or dict
:param group_id: an optional Group ID value (0 by default)
:type group_id: int
:param exceptions: The list of sessions ids to be excluded.
:type exceptions: list
:param nonblocking: Whether to block the caller until this method
finishes running or not.
:type nonblocking: bool
"""
if group_id is not None:
condition = " WHERE group_id=" + group_id
else:
condition = ""
self.sendNotificationToAll(
[
row["subscription"]
for row in self.__db__.execute(
"SELECT * FROM subscriptors" + condition
).fetchall()
if row["session_id"] not in exceptions
],
data,
nonblocking=nonblocking
)
@__database__
def getIdSession(self, subscription):
"""
getIdSession(subscription)
Given a subscription object returns the session id associated with it.
:param subscription: The client's subscription JSON object
:type subscription: str
:returns: the session id associated with subscription
:rtype: str
"""
res = self.__db__.execute(
"SELECT session_id FROM subscriptors WHERE subscription=?",
(subscription,)
).fetchone()
return list(res.values())[0] if res else None
@__database__
def getSubscription(self, session_id):
"""
getSubscription(session_id)
Given a session id returns the subscription object associated with it.
:param session_id: A session id
:type session_id: str
:returns: The client's subscription JSON object associated with
the session id.
:rtype: str
"""
res = self.__db__.execute(
"SELECT subscription FROM subscriptors WHERE session_id=?",
(session_id,)
).fetchone()
return list(res.values())[0] if res else None
@__database__
def getGroupId(self, session_id):
"""
getGroupId(session_id)
Given a session id returns the group id it belongs to.
:param session_id: A session id
:type session_id: str
:returns: a group id value
:rtype: int
"""
res = self.__db__.execute(
"SELECT group_id FROM subscriptors WHERE session_id=?",
(session_id,)
).fetchone()
return list(res.values())[0] if res else None
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,566 |
namespace net {
const char WebSocketEncoder::kClientExtensions[] =
"Sec-WebSocket-Extensions: permessage-deflate; client_max_window_bits";
namespace {
const int kInflaterChunkSize = 16 * 1024;
// Constants for hybi-10 frame format.
typedef int OpCode;
const OpCode kOpCodeContinuation = 0x0;
const OpCode kOpCodeText = 0x1;
const OpCode kOpCodeBinary = 0x2;
const OpCode kOpCodeClose = 0x8;
const OpCode kOpCodePing = 0x9;
const OpCode kOpCodePong = 0xA;
const unsigned char kFinalBit = 0x80;
const unsigned char kReserved1Bit = 0x40;
const unsigned char kReserved2Bit = 0x20;
const unsigned char kReserved3Bit = 0x10;
const unsigned char kOpCodeMask = 0xF;
const unsigned char kMaskBit = 0x80;
const unsigned char kPayloadLengthMask = 0x7F;
const size_t kMaxSingleBytePayloadLength = 125;
const size_t kTwoBytePayloadLengthField = 126;
const size_t kEightBytePayloadLengthField = 127;
const size_t kMaskingKeyWidthInBytes = 4;
WebSocket::ParseResult DecodeFrameHybi17(const base::StringPiece& frame,
bool client_frame,
int* bytes_consumed,
std::string* output,
bool* compressed) {
size_t data_length = frame.length();
if (data_length < 2)
return WebSocket::FRAME_INCOMPLETE;
const char* buffer_begin = const_cast<char*>(frame.data());
const char* p = buffer_begin;
const char* buffer_end = p + data_length;
unsigned char first_byte = *p++;
unsigned char second_byte = *p++;
bool final = (first_byte & kFinalBit) != 0;
bool reserved1 = (first_byte & kReserved1Bit) != 0;
bool reserved2 = (first_byte & kReserved2Bit) != 0;
bool reserved3 = (first_byte & kReserved3Bit) != 0;
int op_code = first_byte & kOpCodeMask;
bool masked = (second_byte & kMaskBit) != 0;
*compressed = reserved1;
if (!final || reserved2 || reserved3)
return WebSocket::FRAME_ERROR; // Only compression extension is supported.
bool closed = false;
switch (op_code) {
case kOpCodeClose:
closed = true;
break;
case kOpCodeText:
break;
case kOpCodeBinary: // We don't support binary frames yet.
case kOpCodeContinuation: // We don't support binary frames yet.
case kOpCodePing: // We don't support binary frames yet.
case kOpCodePong: // We don't support binary frames yet.
default:
return WebSocket::FRAME_ERROR;
}
if (client_frame && !masked) // In Hybi-17 spec client MUST mask its frame.
return WebSocket::FRAME_ERROR;
uint64_t payload_length64 = second_byte & kPayloadLengthMask;
if (payload_length64 > kMaxSingleBytePayloadLength) {
int extended_payload_length_size;
if (payload_length64 == kTwoBytePayloadLengthField)
extended_payload_length_size = 2;
else {
DCHECK(payload_length64 == kEightBytePayloadLengthField);
extended_payload_length_size = 8;
}
if (buffer_end - p < extended_payload_length_size)
return WebSocket::FRAME_INCOMPLETE;
payload_length64 = 0;
for (int i = 0; i < extended_payload_length_size; ++i) {
payload_length64 <<= 8;
payload_length64 |= static_cast<unsigned char>(*p++);
}
}
size_t actual_masking_key_length = masked ? kMaskingKeyWidthInBytes : 0;
static const uint64_t max_payload_length = 0x7FFFFFFFFFFFFFFFull;
static size_t max_length = std::numeric_limits<size_t>::max();
if (payload_length64 > max_payload_length ||
payload_length64 + actual_masking_key_length > max_length) {
// WebSocket frame length too large.
return WebSocket::FRAME_ERROR;
}
size_t payload_length = static_cast<size_t>(payload_length64);
size_t total_length = actual_masking_key_length + payload_length;
if (static_cast<size_t>(buffer_end - p) < total_length)
return WebSocket::FRAME_INCOMPLETE;
if (masked) {
output->resize(payload_length);
const char* masking_key = p;
char* payload = const_cast<char*>(p + kMaskingKeyWidthInBytes);
for (size_t i = 0; i < payload_length; ++i) // Unmask the payload.
(*output)[i] = payload[i] ^ masking_key[i % kMaskingKeyWidthInBytes];
} else {
output->assign(p, p + payload_length);
}
size_t pos = p + actual_masking_key_length + payload_length - buffer_begin;
*bytes_consumed = pos;
return closed ? WebSocket::FRAME_CLOSE : WebSocket::FRAME_OK;
}
void EncodeFrameHybi17(const std::string& message,
int masking_key,
bool compressed,
std::string* output) {
std::vector<char> frame;
OpCode op_code = kOpCodeText;
size_t data_length = message.length();
int reserved1 = compressed ? kReserved1Bit : 0;
frame.push_back(kFinalBit | op_code | reserved1);
char mask_key_bit = masking_key != 0 ? kMaskBit : 0;
if (data_length <= kMaxSingleBytePayloadLength) {
frame.push_back(static_cast<char>(data_length) | mask_key_bit);
} else if (data_length <= 0xFFFF) {
frame.push_back(kTwoBytePayloadLengthField | mask_key_bit);
frame.push_back((data_length & 0xFF00) >> 8);
frame.push_back(data_length & 0xFF);
} else {
frame.push_back(kEightBytePayloadLengthField | mask_key_bit);
char extended_payload_length[8];
size_t remaining = data_length;
// Fill the length into extended_payload_length in the network byte order.
for (int i = 0; i < 8; ++i) {
extended_payload_length[7 - i] = remaining & 0xFF;
remaining >>= 8;
}
frame.insert(frame.end(), extended_payload_length,
extended_payload_length + 8);
DCHECK(!remaining);
}
const char* data = const_cast<char*>(message.data());
if (masking_key != 0) {
const char* mask_bytes = reinterpret_cast<char*>(&masking_key);
frame.insert(frame.end(), mask_bytes, mask_bytes + 4);
for (size_t i = 0; i < data_length; ++i) // Mask the payload.
frame.push_back(data[i] ^ mask_bytes[i % kMaskingKeyWidthInBytes]);
} else {
frame.insert(frame.end(), data, data + data_length);
}
*output = std::string(&frame[0], frame.size());
}
} // anonymous namespace
// static
scoped_ptr<WebSocketEncoder> WebSocketEncoder::CreateServer() {
return make_scoped_ptr(new WebSocketEncoder(FOR_SERVER, nullptr, nullptr));
}
// static
scoped_ptr<WebSocketEncoder> WebSocketEncoder::CreateServer(
const std::string& extensions,
WebSocketDeflateParameters* deflate_parameters) {
WebSocketExtensionParser parser;
if (!parser.Parse(extensions)) {
// Failed to parse Sec-WebSocket-Extensions header. We MUST fail the
// connection.
return nullptr;
}
for (const auto& extension : parser.extensions()) {
std::string failure_message;
WebSocketDeflateParameters offer;
if (!offer.Initialize(extension, &failure_message) ||
!offer.IsValidAsRequest(&failure_message)) {
// We decline unknown / malformed extensions.
continue;
}
WebSocketDeflateParameters response = offer;
if (offer.is_client_max_window_bits_specified() &&
!offer.has_client_max_window_bits_value()) {
// We need to choose one value for the response.
response.SetClientMaxWindowBits(15);
}
DCHECK(response.IsValidAsResponse());
DCHECK(offer.IsCompatibleWith(response));
auto deflater = make_scoped_ptr(
new WebSocketDeflater(response.server_context_take_over_mode()));
auto inflater = make_scoped_ptr(
new WebSocketInflater(kInflaterChunkSize, kInflaterChunkSize));
if (!deflater->Initialize(response.PermissiveServerMaxWindowBits()) ||
!inflater->Initialize(response.PermissiveClientMaxWindowBits())) {
// For some reason we cannot accept the parameters.
continue;
}
*deflate_parameters = response;
return make_scoped_ptr(new WebSocketEncoder(FOR_SERVER, std::move(deflater),
std::move(inflater)));
}
// We cannot find an acceptable offer.
return make_scoped_ptr(new WebSocketEncoder(FOR_SERVER, nullptr, nullptr));
}
// static
scoped_ptr<WebSocketEncoder> WebSocketEncoder::CreateClient(
const std::string& response_extensions) {
// TODO(yhirano): Add a way to return an error.
WebSocketExtensionParser parser;
if (!parser.Parse(response_extensions)) {
// Parse error. Note that there are two cases here.
// 1) There is no Sec-WebSocket-Extensions header.
// 2) There is a malformed Sec-WebSocketExtensions header.
// We should return a deflate-disabled encoder for the former case and
// fail the connection for the latter case.
return make_scoped_ptr(new WebSocketEncoder(FOR_CLIENT, nullptr, nullptr));
}
if (parser.extensions().size() != 1) {
// Only permessage-deflate extension is supported.
// TODO (yhirano): Fail the connection.
return make_scoped_ptr(new WebSocketEncoder(FOR_CLIENT, nullptr, nullptr));
}
const auto& extension = parser.extensions()[0];
WebSocketDeflateParameters params;
std::string failure_message;
if (!params.Initialize(extension, &failure_message) ||
!params.IsValidAsResponse(&failure_message)) {
// TODO (yhirano): Fail the connection.
return make_scoped_ptr(new WebSocketEncoder(FOR_CLIENT, nullptr, nullptr));
}
auto deflater = make_scoped_ptr(
new WebSocketDeflater(params.client_context_take_over_mode()));
auto inflater = make_scoped_ptr(
new WebSocketInflater(kInflaterChunkSize, kInflaterChunkSize));
if (!deflater->Initialize(params.PermissiveClientMaxWindowBits()) ||
!inflater->Initialize(params.PermissiveServerMaxWindowBits())) {
// TODO (yhirano): Fail the connection.
return make_scoped_ptr(new WebSocketEncoder(FOR_CLIENT, nullptr, nullptr));
}
return make_scoped_ptr(new WebSocketEncoder(FOR_CLIENT, std::move(deflater),
std::move(inflater)));
}
WebSocketEncoder::WebSocketEncoder(Type type,
scoped_ptr<WebSocketDeflater> deflater,
scoped_ptr<WebSocketInflater> inflater)
: type_(type),
deflater_(std::move(deflater)),
inflater_(std::move(inflater)) {}
WebSocketEncoder::~WebSocketEncoder() {}
WebSocket::ParseResult WebSocketEncoder::DecodeFrame(
const base::StringPiece& frame,
int* bytes_consumed,
std::string* output) {
bool compressed;
WebSocket::ParseResult result = DecodeFrameHybi17(
frame, type_ == FOR_SERVER, bytes_consumed, output, &compressed);
if (result == WebSocket::FRAME_OK && compressed) {
if (!Inflate(output))
result = WebSocket::FRAME_ERROR;
}
return result;
}
void WebSocketEncoder::EncodeFrame(const std::string& frame,
int masking_key,
std::string* output) {
std::string compressed;
if (Deflate(frame, &compressed))
EncodeFrameHybi17(compressed, masking_key, true, output);
else
EncodeFrameHybi17(frame, masking_key, false, output);
}
bool WebSocketEncoder::Inflate(std::string* message) {
if (!inflater_)
return false;
if (!inflater_->AddBytes(message->data(), message->length()))
return false;
if (!inflater_->Finish())
return false;
std::vector<char> output;
while (inflater_->CurrentOutputSize() > 0) {
scoped_refptr<IOBufferWithSize> chunk =
inflater_->GetOutput(inflater_->CurrentOutputSize());
if (!chunk.get())
return false;
output.insert(output.end(), chunk->data(), chunk->data() + chunk->size());
}
*message =
output.size() ? std::string(&output[0], output.size()) : std::string();
return true;
}
bool WebSocketEncoder::Deflate(const std::string& message,
std::string* output) {
if (!deflater_)
return false;
if (!deflater_->AddBytes(message.data(), message.length())) {
deflater_->Finish();
return false;
}
if (!deflater_->Finish())
return false;
scoped_refptr<IOBufferWithSize> buffer =
deflater_->GetOutput(deflater_->CurrentOutputSize());
if (!buffer.get())
return false;
*output = std::string(buffer->data(), buffer->size());
return true;
}
} // namespace net
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,187 |
26 Thanksgiving Bible Verses - Top Inspiring Scriptures for Gratitude!
Bible Verses for Thanksgiving - Be encouraged with Scripture on why we should give thanks and how to express our gratitude. It's so easy during the holiday season (or any time of the year!) to be overwhelmed with all the tasks and activities to do that we forget to stop and reflect on why we should be celebrating. Take a minute to stop and read these Bible verses as you meditate on all the ways God has blessed you!
Download a Personal Copy of Thanksgiving Bible Verses!
19 From them will come songs of thanksgiving and the sound of rejoicing. I will add to their numbers, and they will not be decreased; I will bring them honor, and they will not be disdained.
46 For long ago, in the days of David and Asaph, there had been directors for the musicians and for the songs of praise and thanksgiving to God. 47 So in the days of Zerubbabel and of Nehemiah, all Israel contributed the daily portions for the musicians and the gatekeepers. They also set aside the portion for the other Levites, and the Levites set aside the portion for the descendants of Aaron.
1 I will give thanks to you, LORD, with all my heart; I will tell of all your wonderful deeds.
16 Let the message of Christ dwell among you richly as you teach and admonish one another with all wisdom through psalms, hymns, and songs from the Spirit, singing to God with gratitude in your hearts. 17 And whatever you do, whether in word or deed, do it all in the name of the Lord Jesus, giving thanks to God the Father through him.
2 Let us come before him with thanksgiving and extol him with music and song. 3 For the LORD is the great God, the great King above all gods.
15 For this reason, ever since I heard about your faith in the Lord Jesus and your love for all God's people, 16 I have not stopped giving thanks for you, remembering you in my prayers.
17 I will give thanks to the LORD because of his righteousness; I will sing the praises of the name of the LORD Most High.
1 Praise the LORD.Give thanks to the LORD, for he is good; his love endures forever.
4 In that day you will say: "Give praise to the LORD, proclaim his name; make known among the nations what he has done, and proclaim that his name is exalted.
11 the sounds of joy and gladness, the voices of bride and bridegroom, and the voices of those who bring thank offerings to the house of the LORD, saying, "Give thanks to the LORD Almighty, for the LORD is good; his love endures forever." For I will restore the fortunes of the land as they were before,' says the LORD. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,508 |
ANIMALADIES
**ANIMALADIES**
**Gender, Animals, and Madness**
**Edited by**
**Lori Gruen and Fiona Probyn-Rapsey**
CONTENTS
List of Figures
Notes on Contributors
Acknowledgments
DISTILLATIONS
Lori Gruen and Fiona Probyn-Rapsey
Part I
DISMEMBER
Chapter 1
JUST SAY NO TO LOBOTOMY
Lori Gruen
Chapter 2
MAKING AND UNMAKING MAMMALIAN BODIES: SCULPTURAL PRACTICE AS TRAUMATIC TESTIMONY
lynn mowson
Chapter 3
THERE'S SOMETHING ABOUT THE BLOOD... : TACTICS OF EVASION WITHIN NARRATIVES OF VIOLENCE
Nekeisha Alayna Alexis
Chapter 4
ERUPT THE SILENCE
Hayley Singer
Chapter 5
THE LONELINESS AND MADNESS OF WITNESSING: REFLECTIONS FROM A VEGAN FEMINIST KILLJOY
Kathryn Gillespie
Part II
DISABILITY
Chapter 6
ABLEISM, SPECIESISM, ANIMALS, AND AUTISM: THE DEVALUATION OF INTERSPECIES FRIENDSHIPS
Hannah Monroe
Chapter 7
METAPHORS AND MALADIES: AGAINST PSYCHOLOGIZING SPECIESISM
Guy Scotton
Chapter 8
THE HORRIFIC HISTORY OF COMPARISONS BETWEEN COGNITIVE DISABILITY AND ANIMALITY (AND HOW TO MOVE PAST IT)
Alice Crary
Chapter 9
THE PERSONAL IS POLITICAL: ORTHOREXIA NERVOSA, THE PATHOGENIZATION OF VEGANISM, AND GRIEF AS A POLITICAL ACT
Vasile Stanescu and James Stanescu
Chapter 10
WOMEN, ANXIETY, AND COMPANION ANIMALS: TOWARD A FEMINIST ANIMAL STUDIES OF INTERSPECIES CARE AND SOLIDARITY
Heather Fraser and Nik Taylor
Part III
DYSFUNCTION
Chapter 11
THE "CRAZY CAT LADY"
Fiona Probyn-Rapsey
Chapter 12
THE ROLE OF DAMNED AND DAMMED DESIRE IN ANIMAL EXPLOITATION AND LIBERATION
pattrice jones and Cheryl Wylie
Chapter 13
_DUCK LAKE PROJECT_ : ART MEETS ACTIVISM IN AN ANTI-HIDE, ANTI-BLOKE, ANTIDOTE TO DUCK SHOOTING
Yvette Watt
Chapter 14
ON OUTCAST WOMEN, DOG LOVE, AND ABJECTION BETWEEN SPECIES
Liz Bowen
DISCUSSION BY CAROL J. ADAMS
Index
FIGURES
2.1 lynn mowson, _fleshlump_ , 2012–2013 (detail of installation in _beautiful little dead things_ , 2014), microcrystalline wax and pigment. Photo: lynn mowson
2.2 lynn mowson, _fleshlump_ , 2012–2013 (detail of installation in _beautiful little dead things,_ 2014), microcrystalline wax and pigment. Photo: Kerry Leonard
2.3 lynn mowson, _slink_ ( _babyform_ ), 2012, latex, tissue, and string. Photo: lynn mowson
2.4 lynn mowson, _slink_ , 2012–2014 (detail of installation in _beautiful little dead things_ , 2014), latex, tissue, and string. Photo: Kerry Leonard
2.5 lynn mowson, _slink_ ( _sac_ ), 2012, latex, tissue, and string. Photo: lynn mowson
2.6 lynn mowson, _fleshlump_ , 2011–2013 (detail of installation in _beautiful little dead things,_ 2014), microcrystalline wax and pigment. Photo: Kerry Leonard
2.7 lynn mowson, _boobscape_ , 2016–2017 (image used for Animaladies postcard collection, 2016), latex, tissue, and string. Photo: lynn mowson
2.8 lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Mary C. Holmes
2.9 lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Kerry Leonard
2.10 lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Kerry Leonard
13.1 In 2008 Catherine Silcock (far left) devised these innovative wind socks, which proved to be highly effective in deterring ducks away from the shooters' guns. One of the hunters' hides is on the left-hand side. Photo: Yvette Watt
13.2 Dancers in Moulting lagoon. Photo: Michelle Powell
13.3 Photo: Michelle Powell
NOTES ON CONTRIBUTORS
**Nekeisha Alayna Alexis** is an independent scholar with wide-ranging interests connected to human and other animal oppression and liberation. She received her Bachelor of Arts degree from New York University, New York, and her Masters of Arts: Theological Studies degree from Anabaptist Mennonite Biblical Seminary (AMBS), Elkhart, Indiana. She is currently the Intercultural Competence and Undoing Racism coordinator at AMBS, where she assists the institution in its strategic goals in this area, as well as works on the Communication team as a graphic designer and website specialist. Nekeisha has presented and published extensively in both theological and religious settings on a number of topics such as animal liberation, veganism, and Christian peacemaking; the interconnected nature of human violence toward other animals and violence among human selves; intersecting oppressions of race, gender, and/or species; and anarchist politics and alternative Christian faith and ethics. Her most recent writings include "But Isn't All of Creation Violent?" in _A Faith Encompassing All of Creation: Addressing Commonly Asked Questions about Christian Care of the Environment_ (Cascade Books, 2014) and "Table Talk: The Violence of Grace and Gratitude" ( _The Mennonite_ , September 2016). She is motivated by the hope and trust that her intellectual efforts around compassion will inspire others to transform their relationships to other creatures. She dedicates her work toward that end to her loved ones, Mocha and Cairo.
**Liz Bowen** is a Ph.D. candidate in English and comparative literature at Columbia University, where she works at the intersections of 20th and 21st century American literature, disability studies, and critical animal studies. Her dissertation, "Animal Abilities: Disability, Species Difference, and Aesthetic Innovation in the Long 20th Century," traces the intertwined deployments of disability, animality, and cognitive otherness as sites for literary experimentation, from Faulkner to the Harlem Renaissance to contemporary poetics. Liz has been the graduate organizer for Columbia's University Seminar on Disability, Culture, and Society for the past three years, and recently taught her first course on literary animal studies. She is also a widely published poet and critic, whose work has appeared or is forthcoming in _Boston Review, Lit Hub, The New Inquiry, the Journal of Literary and Cultural Disability Studies, and Humanimalia: A Journal of Human/Animal Interface Studies_.
**Alice Crary** is Professor of Philosophy in the Graduate Faculty and Co-Chair of the Gender and Sexuality Studies program of The New School for Social Research (NSSR) in New York City. She is well known for her numerous scholarly works on the moral dimension of language, as well as edited collections on Wittgenstein, Cora Diamond, and Stanley Cavell. Crary is the author of two monographs on ethics, _Beyond Moral Judgment_ (Harvard, 2007) and _Inside Ethics: On the Demands of Moral Thought_ (Harvard, 2016).
**Heather Fraser** is Associate Professor in Social Science in the School of Public Health and Social Work, Health Faculty, QUT, Brisbane (<http://staff.qut.edu.au/staff/fraserh2/>). Heather teaches units relating to critical social work, helping alliances and 'addictions'. With (A/Prof.) Nik Taylor she authored the (2016) book _Neoliberalization, Universities and the Public Intellectual: Species, Gender and Class and the Production of Knowledge_ (Palgrave, London).
**Kathryn Gillespie** earned her Ph.D. in Geography from the University of Washington (UW) in 2014. From 2016 to 2018 she was a postdoctoral fellow in Animal Studies at Wesleyan University. Her current research sits at the nexus of critical race theory (especially black feminisms), postcolonial studies, and critical animal studies, focusing on gendered human–animal relations and racialized histories of coloniality at the Louisiana State Penitentiary farm and rodeo at Angola. Her dissertation research examined the gendered commodification of the lives and bodies of animals in the dairy industry in the Pacific Northwestern United States. This work became _The Cow with Ear Tag #1389_ , University of Chicago Press, 2018. She has published in scholarly journals, such as _Hypatia_ and _Gender, Place, and Culture_ , and has coedited two books, _Critical Animal Geographies: Politics, Intersections and Hierarchies in a Multispecies World_ (Routledge 2015, with Rosemary-Claire Collard) and _Economies of Death: Economic Logics of Killable Life and Grievable Death_ (Routledge 2015, with Patricia J. Lopez).
**Lori Gruen** is the William Griffin Professor of Philosophy at Wesleyan University. She is also Professor of Feminist, Gender, and Sexuality Studies and Coordinator of Wesleyan Animal Studies. She is the author and editor of ten books, including _Ethics and Animals: An Introduction_ (Cambridge, 2011), _Reflecting on Nature: Readings in Environmental Philosophy and Ethics_ (Oxford, 2012), _Ethics of Captivity_ (Oxford, 2014), _Entangled Empathy_ (Lantern, 2015), and _Critical Terms for Animal Studies_ (University of Chicago, 2018). Her work in practical ethics focuses on issues that impact those often overlooked in traditional ethical investigations, for example women, people of color, incarcerated people, and nonhuman animals. She is a former editor of _Hypatia: A Journal of Feminist Philosophy_ , is Fellow of the Hastings Center for Bioethics, is Faculty Fellow at Tufts' Cummings School of Veterinary Medicine's Center for Animals and Public Policy, was the Spring 2018 Laurance S. Rockefeller Visiting Professor for Distinguished Teaching at Princeton University, and was the first chair of the Faculty Advisory Committee of the Center for Prison Education at Wesleyan.
**pattrice jones** cofounded VINE Sanctuary, an LGBTQ-run farmed animal sanctuary that operates within an understanding of the intersection of oppressions. She is the author of _Aftershock: Confronting Trauma in a Violent World: A Guide for Activists and Their Allies_ (Lantern, 2007) and _The Oxen at the Intersection_ (Lantern, 2014), and many chapters and essays.
**Hannah Monroe** holds a Master of Arts in Critical Sociology from Brock University, where her thesis research focused on the experiences of autistic people, employing post-structural analysis. She currently supports and mentors autistic children. She plans to complete a Master of Social Work in order to become a therapist, with the goal of empowering neurodiverse young people. Her other publications include a chapter titled "Post-Structural Analyses of Conformity and Oppression: A Discussion of Critical Animal Studies and Neurodiversity" in _Animals, Disability and the End of Capitalism: Voices from the Eco-ability Movement_ , edited by Anthony J. Nocella, John Lupinacci, and Amber E. George. She has spoken on the intersections between neurodiversity and critical animal studies at the Decolonizing Critical Animal Studies, Cripping Critical Animal Studies conference in June 2016, and at the third Annual Eco-Ability Conference in December 2015.
**lynn mowson** is a practicing sculptor and animal advocate. Her practice-led Ph.D., entitled " _beautiful little dead things: empathy, witnessing, trauma and animals' suffering_ ," was completed at VCA, The University of Melbourne, in 2015. Her sculptural research is featured in the book _The Art of the Animal_ (Lantern Press, 2015) and the exhibition 'SPOM: The Sexual Politics of Meat' at The Animal Museum, Los Angeles, held in February 2017. lynn is Research Assistant for the Human Rights and Animal Ethics Research Network (HRAE), University of Melbourne, is on the committee for HRAE, is Vice-Chair of the Australasian Animal Studies Association, and is Associate for the New Zealand Centre for Human Animal Studies. Website: <https://lynnmowson.com/>
**Fiona Probyn-Rapsey** is Professor in the School of Humanities and Social Inquiry at the University of Wollongong, Australia. She is the author and coeditor of three books, including _Made to Matter_ (Sydney University Press, 2013), _Animal Death_ (Sydney University Press, 2013), and _Animals in the Anthropocene: Critical Perspectives on Non-human Futures_ (SUP, 2015). Fiona is also Series Editor (with Melissa Boyde) of the Animal Publics book series through Sydney University Press (<http://sydney.edu.au/sup/about/animal_publics.html>).
**Guy Scotton** is an independent researcher, currently exploring the role of emotions and virtues in theories of interspecies justice. He is an editor of the open access journal _Politics and Animals_ (www.politicsandanimals.org/).
**Hayley Singer** received her Ph.D. in Creative Writing from the University of Melbourne, where she teaches in the School of Culture and Communication. Her creative and scholarly writing practices engage with eco/feminism's intersectional politics and poetics. Her fiction, nonfiction, poetry, and book reviews have been published in Australian journals and anthologies, including _Meanjin, Page Seventeen, Writing from Below, Press: 100 Love Letters,_ and _Animal Studies Journal_.
**James Stanescu** is Assistant Professor of Communication Studies at Mercer University, in Macon, Georgia. He is the editor, with Kevin Cummings, of _The Ethics and Rhetoric of Invasion Ecology_ (Lexington, 2016). Stanescu publishes frequently on issues surrounding animal and environmental philosophy, and is finishing a monograph on the genealogy of the factory farm. You can also find his occasional writings at his blog, _Critical Animal_.
**Vasile Stanescu** received his Ph.D. in the interdisciplinary program of Modern Thought and Literature (MTL) at Stanford University. He currently serves as Assistant Professor and Director of the Program in Speech and Debate at Mercer University. Stanescu is the co-senior editor of the _Critical Animal Studies_ book series. He is currently working on his forthcoming book project, _Happy Meals: Animals, Affect, and the Myth of Consent_.
**Nik Taylor** is Associate Professor of Sociology in the Department of Human Services and Social Work at the University of Canterbury, New Zealand. She is an award-winning author who has published four books, including _Humans, Animals and Society_ (Lantern, 2012), and over fifty journal articles and book chapters on the human–pet bond; treatment of animals and animal welfare; links between human aggression and animal cruelty; slaughterhouses; meat-eating; and animal shelter work.
**Yvette Watt** is a Lecturer at the School of Creative Arts, University of Tasmania and Lead Researcher of the UTAS College of Arts and Law Animal Studies Theme Area (ASTA). Watt was a founding member of the Australasian Animal Studies Association and is a current committee member of Minding Animals International.
Watt's art practice spans 30 years and includes numerous solo and group exhibitions. She has been actively involved in animal advocacy since the mid 1980s, and her artwork is heavily informed by her activism. Her work is held in numerous public and private collections in Australia including Parliament House, Canberra, Artbank and the Art Gallery of Western Australia. Watt is a co-editor of and contributor to _Considering Animals: Contemporary Studies in Human-Animal Relations_ (Ashgate, 2011). Other publications include "Down on the Farm: Why do Artists Avoid Farm Animals as Subject Matter?", in _Meat Cultures_ , Annie Potts (ed), Brill (2016); 'Animal Factories: Exposing Sites of Capture', in _Captured: Animals Within Culture_ , Melissa Boyd, ed, (Palgrave McMillan, 2014) and 'Artists, Animals and Ethics', in _Antennae: the journal of nature in culture_ , (issue 19, 2011).
**Cheryl Wylie** coordinates animal care at VINE sanctuary, an LGBTQ-led farmed animal refuge that was the first sanctuary to devise a method of rehabilitating roosters used in cockfighting. She is a veterinary technician who participated in 4-H and FFA as a child.
ACKNOWLEDGMENTS
We would like to begin by thanking all the courageous people who work to bring compassion to our mad world with all its animaladies.
We would like to thank HARN: Human Animal Research Network at the University of Sydney (especially Dinesh Wadiwel and Agata Mrva-Montoya, Charlie Jackson-Martin and Indi) for their help with the first Animaladies conference held there in 2016, where Lori Gruen was a keynote speaker. Colleagues from AASA: Australasian Animal Studies Association, Melissa Boyde, Madeleine Boyd, and Yvette Watt did an amazing job on the first Animaladies Exhibition held at Verge Gallery (Glebe), where we all got to see lynn mowson's incredible piece _boobscapes_ in the flesh. Seeing it there "for real" inspired us to ask her if we could use an image of that piece for the front cover of this book. We're delighted that she agreed. Yvette Watt's work on _Duck Lake Project_ also inspired so many of us during 2016 and 2017, and we are delighted to present part of her work in this volume. Brian Rapsey did a fantastic job (as always) filming and photographing the event and was also instrumental in our road trip to Val Plumwood's home at Plumwood Mountain, where we were warmly welcomed by Anne Edwards and Tash Fjin. Thanks are also due to Sunday and Olive and Brian who were squished in the back of the car and patiently indulged Lori and Fiona's never ending conversations on our road trip.
Fiona would also like to acknowledge the support and assistance of the School of Humanities and Social Inquiry at the University of Wollongong which is proving itself to be a great place to do Animal Studies work, especially with terrific colleagues like Melissa Boyde, Alison Moore, Denise Russell, Colin Salter, Esther Alloun, and Kathy Varvaro, who all just happen to be on the committee for the next Animaladies conference and members of the ASRN: Animal Studies Research Network. Lori would like to acknowledge the support of Wesleyan Animal Studies and especially thank pattrice jones for taking care of Taz and Zinnie while I was away in Australia.
We would like to thank all the contributors to this book, who all worked tirelessly incorporating suggestions from our reviewers (thanks to them also), as well as helping to make the idea of "animaladies" come to life in original and insightful ways. Sue Pyke did a brilliant job pulling the final manuscript together. Thanks to Carol J. Adams for her support for the project and for agreeing to write a postscript/discussion for us. We'd also like to thank Haaris Naqvi and Katherine De Chant at Bloomsbury, both of whom have been a pleasure to work with.
Working and writing and laughing together, both in person and across the world, has been a joy for us. Fiona would like to thank Lori for her generosity over the years, both as scholar and as a friend. I have come to appreciate her philosopher's eye, her feminist work ethic, and her ethic of care even more acutely in the process. Lori wants to express her deepest appreciation for Fiona's brilliance and good humor, only Fi could come up with "animaladies" and the energy and passion to initiate and sustain this critical conversation.
LG and FPR
March 1, 2018
DISTILLATIONS
Lori Gruen and Fiona Probyn-Rapsey
I felt a Funeral, in my Brain,
And Mourners to and fro
Kept treading—treading—till it seemed
That Sense was breaking through—
—Dickinson, 1896
"Animaladies" conjoins two words, "animal" and "maladies" or, looked at another way, "animal" and "ladies." Whichever two words you see when you look at it, it is always three: "animal," "malady," and "ladies," a triangulation within Animal Studies that draws gender, animals, and maladies together. Fiona originally coined the term to describe the dis-ease of current human–animal relationships, and the idea that acknowledging these maladies was a necessary catalyst for positive change (Probyn-Rapsey 2014, 4). In 2016, "Animaladies" became an interdisciplinary conference held at the University of Sydney, with Lori Gruen as the keynote speaker. The conference called for papers that interrogated the connections between gender, madness, and animality, bringing together a feminist archive on histories of madness and the flourishing field of Animal Studies.
We were blown away by the excitement that the call for papers for the conference and this volume generated. The term resonates with writers, scholars, activists, and artists whose various engagements with other animals and with Animal Studies are shaped in one way or another by animaladies. Defined broadly, animaladies are sites of tension produced by acknowledging how our relationships with other animals are damaged. These relationships are damaged in a variety of ways, both by common attitudes of human superiority and by the violent and disturbing implications of these attitudes. Naming these damaged relationships as animaladies helps us to see how we might reframe both our attitudes and their consequences within various social contexts. How we imagine the damage and what we do with that damage is a genuine question. The power of animaladies is that they usually resist attempts to disrupt them. Often those who try to escape the damage by reframing it are themselves identified as mad, _as_ damaged, much like Sara Ahmed's "feminist killjoy" (2017). In this volume the authors attempt to disentangle these damaged relations, in order to highlight possible escape routes.
Animaladies also express political and psychological discontent, familiar from feminist theorizing about violent systems of power. Animaladies highlight how pathologizing human–animal relationships blocks empathy toward animals because the characterization of animal advocacy as mad, "crazy," and feminized, distracts attention from broader social disorder regarding human exploitation of animal life. Understanding how the "madness" of our relationships with animals intersects with the "madness" of taking animals seriously is another major aim of this book. The volume will not attempt to show where madness truly lies, but rather illuminates how it is distributed; how it is made purposeful; how it is disguised; how it is made to work for social change or against it; and how it is shaped as an insult, embraced as a zone of quarantine or left as an undefined fear.
The concept of animaladies also builds on a long-standing feminist archive on the topic of women and madness. Elaine Showalter's _The Female Malady_ (1985) deserves special mention. Showalter's early work situates madness as a specifically "female malady," enshrined by a patriarchal psychiatric tradition that creates a double bind for women—damned if they do conform to femininity and damned if they don't. As many feminists have argued (Chesler 1972; Ussher 1991; Russell 1995; Gilbert and Gubar 2000), if being a woman also approximates a maladjustment to patriarchal norms, then it is little surprise that women are more likely to experience "madness" and be seen as "mad." For Showalter, it is not only that more women are diagnosed with mental health problems (which they are still today), and that the psychiatric profession is male dominated (which it still is), but that the condition of madness is itself gendered, coded, as a _female_ malady. Showalter identifies a Victorian fascination with three cultural icons of the "madwoman"—Ophelia, Crazy Jane, and Lucia—each of whom worked to establish "female sexuality and feminine nature as the source of the female malady" and each "stood for a different interpretation of woman's madness and man's relationship to it" (10). Linked to sexuality (excessive or frigid), reason (too much or not enough), obedience (too much or not enough), feminist work on madness emphasizes how cultural icons of the madwoman persist in different forms and preempt assumptions about (and the psychiatric and therapeutic treatment of) "mad" women. The hystericizing of women and the reclaiming of hysteria as a form of feminist resistance has never gone away. It helps us understand how animal advocates, whose objections extend to anthropocentrism, are also hystericized and pathologized as singular damaged individuals. This focus draws our attention away from normalized (and most often non-pathologized) racial and colonial violence that is also linked to gender and the exploitation of animals.
Pathologization is a mechanism for discriminating between acceptable and unacceptable behaviors, identities, and beliefs. In her historical analysis of the animal rights movement in the United States, Diane Beers shows that pathologization of animal advocacy was a key mechanism for disciplining the movement and, more specifically, the white women who constituted the majority of members. Beers writes that "several late nineteenth-century physicians concocted a diagnosable form of mental illness" called "zoophilpsychosis," an invention that she describes as the "most vicious of all" (2006, 109). According to the primary proponent of this diagnosis, physician Charles Dana, zoophilpsychosis was a condition produced by "fine feelings gone wrong" and "overgrown sentimentality" (1909, 382). He presents one case of a man who "worried so much" about horses and another case of a woman who was "victim of a cat obsession." The gender differences between the "cures" are telling—the man's feelings for horses have "gone wrong" and are fixed after three years of therapy while the woman is advised to have "gynecological treatment" to deal with her "perversion of instinct." Because the animal movement was (and still is) dominated by women, "doctors further concluded that the weaker sex was particularly susceptible to the malady." Beers points out that though the condition of zoophilpsychosis was eventually dropped, adversaries of the animal movement retained distinct archetypes of the animal rights "bogeyman" who was framed as a fanatic, antihuman, a national traitor, anti-progress, and/or mentally ill. These "bogeymen" kept being deployed because they were politically useful and curtailed the effectiveness of critique, as Beers writes, they worked with "the entrenched belief systems that subjugated other species to humans and women to men" (2006, 25).
The bogeymen and mad women stereotypes did not simply revolve around gender but also racialized assumptions about civilization and ideas of progress. Supposed zoophilists became bogeymen because they were out of step with "civilized communities," according to Dana (382). This view supposed that "civilized" communities had made improvements on past practices. Here Dana's depiction of the wrongness of advocates' feelings worked to establish the rightness of contemporary practices. In other words, the zoophilists suffered not only disproportionate feelings but also feelings that were anachronistic (out of date) and also out of place (outside of civilized communities). Other versions of this ploy persist. Animaladies may be acknowledged in one context (the past, or other cultures/races/communities), while being refused in the present or in our own communities. We see this in the reassurances offered by animal welfare approaches in animal agriculture; improvements made to address a dysfunction (in care, in housing, in pain management) are likely to be acknowledged retrospectively and only with the caveat of perpetual improvement. Nekeisha Alexis' chapter comparing pro-slavery writings and humane farming narratives also shows that such apologia relies on racist and anthropocentric illusions of progress. We see this when animal advocates fixate on the activities of specific communities and their animal practices, while not acknowledging the ways that such a focus works through an optic of racism (Kim 2015). Animaladies are therefore not the same across all contexts; indeed, the identification of them as animaladies depends very much on the social and political contexts in which they occur.
Animaladies are racialized, gendered, and class-specific, and they can be repeated uncritically by animal advocates and scholars too. Traditional theorists of the animal rights movement also, though perhaps unwittingly, drew on animaladies as excessively gendered and overly emotional—they emphatically denied any connection to sentimental, little old ladies in tennis shoes. In Peter Singer's preface to the 1975 edition of _Animal Liberation_ he is at pains to show that his thinking was motivated by reason: "We didn't 'love' animals. We simply wanted them treated as independent sentient beings that they are, and not as a means to human ends" (1990, 2). Tom Regan also stresses the rationality of _The Case for Animal Rights_ by arguing that he intended it to "give the lie, once and for all, to all those opponents of animal rights who picture everyone in the movement as strange, silly, overly emotional, irrational, uninformed, and illogical" (1983, 94). Instead, Regan argues, those who believe that about the movement are themselves "strange, silly, overly emotional, irrational, uninformed and illogical" (1983).
Feminists by and large could not reject their critics in the same way that Regan does, with a repudiation that affirms rather than undoes the insult. A feminist approach to the imbrication of emotions and reason, the irresistible entanglement of rationality with feeling (see Gruen's (2015) entangled empathy and her chapter here), sees such separation as patriarchal, illusory, and undesirable to maintain. To separate emotion from reason once and for all is, from a feminist ethics of care perspective, akin to reinstating a mind/body dualism, a false dichotomy that underscores not only the masculine/feminine binary but also the human/animal one (see Adams 1990). The risk of being seen as emotional, and being seen to be emotional about _animals_ , poses a particular kind of risk that is both gendered and species-specific. And even women who do write with their animals in mind are, as Susan McHugh explains, frequently doing so _apologetically_ , apologizing for taking their cross-species friendships seriously (2012).
Animal Studies scholarship is frequently marked by the same sorts of anxieties over legitimacy. In part this might relate to resistance to alliance with other political movements. Kymlicka and Donaldson have pointed out that progressive social movements have largely failed to recognize animal rights as a social justice issue, making the animal movement an "orphan of the left." They argue that these other movements fear that focusing on animals will "erode the moral seriousness with which human injustices are treated" (2013, 4), and they identify the fear of displacement, trivialization, and the "depth of our cultural inheritance" as major reasons for resistance to the animal movement as a whole. But there is also another possible element at work here, which is the fear that thinking about animals not only trivializes human injustices, but that it is fundamentally unreasonable, "crazy." Instead of being the "orphan of the left," animal advocates are perhaps more readily identifiable as the left's "crazy aunt," given the predominance of women in the animal movement (Munro: 2001). We might say that Animal Studies has, so far, done all the right things according to "proper" academic inquiry, but perhaps we have neglected to take the matter of madness itself more seriously.
When Donna Haraway writes about having "gone to the dogs" (2003, 5) she too is acknowledging the risk of being seen as having degraded her work, losing a form of respectability associated with "proper" (read: human oriented) academic work. She is also indicating her allegiance to the dogs and signaling a familiar feminist trajectory: redefining an insult as a compliment, reclaiming what is repudiated as a badge of pride. This tactic is familiar, appearing recently in the "pussyhat project" in the United States (to protest Donald Trump's sexism), the group Mad Pride (Lewis 2010) protesting the medicalization of mental difference, the "mad fucking witches" in Australia, and in a similar vein, Yvette Watt's _Duck Lake Project_ (discussed in Chapter 13): all are political campaigns that return the gaze and resituate an animalady as an act of defiance. Reclaiming the "crazy" is an important tactic, as Brittany Cooper describes in _Eloquent Rage_ : "Talking crazy" is either a "compliment or indictment" and indicates a "flirtation with ideas that skirted the line between being profound and absolutely nonsensical" (2018,11). "Crazy" projects reclaim a label, reverse the gaze, and make a great deal of sense, but they are risky. None of them are in any simple way a celebration or trivialization of the distress that "madness" or "craziness" may involve. Rather they are attuned to the risk associated with being seen as mad and as angry, as unable to adjust to injustice, like the character of Yeong-hye in Han Kang's _The Vegetarian_ , described by Hayley Singer in her chapter, as unable to "go docilely into quarantine" nor able to be "re-adjusted to fit a carnist perspective of life."
Animal activists and scholars often readily accept the risk of being derided as misanthropes who have become incomprehensible: neither properly gendered nor properly human. From twentieth-century "zoophilpsychosis" to twenty-first-century "species identity disorder" and "orthorexia" (discussed in Chapter 9), the disciplining of relations between humans and animals in terms of norms pertaining to gender, race, and "humanness" persists.
We've divided the chapters that follow into three interrelated themes: _dismember, disability,_ and _dysfunction._ We'll leave the pleasures of discovery and interpretation to you, but we do want to say a bit about our decisions.
One of the many ways that animaladies function is to alienate, to divide, to, in a word, _dismember_. Of course, animals are routinely, literally dismembered for food and after (and sometimes during) laboratory experiments. Animals are also dis/membered when they have their infants removed from them or when their social groups are altered by human choices and actions. Scholars and activists who are working to reveal the implications of these harms face particular kinds of dangers, including the psychological distress and trauma brought on by witnessing the violence enacted on animals in slaughterhouses, hunting grounds, or laboratories. These scholars/activists allow themselves to be moved by the knowledge generated in painful relationships, to hold on to the violation they are attending to while holding off the cultural and political mechanisms that seek to sanitize and normalize dismemberment. The mechanization and distribution of the process of killing through many hands produces a "double dysjunction," as Noele Vialles describes it, where "we are left without any 'real' killing at all" (1994, 159). If these dismemberments cannot be attributed to any one actor, it starts to seem like they do not happen, and the emotions and knowledge these nonhappenings evoke have no place either. The scholar in the slaughterhouse or in the laboratory and the activist at the hunting ground or at the stockyard witness events that "do not happen" for audiences who may not care to know (Probyn-Rapsey 2013), and thus their grief is "misdirected" or beyond sensibility (see Chapter 5). Cloaking emotion is another way to maintain the reason/emotion, mind/body divide. Allowing the sadness, the anguish, the pain to be seen and heard and felt, although risky in various ways, helps us to re-member. Through art, the discomfort of dismemberment can become real again, as we see in lynn mowson's work on the cover of this volume and in the chapter she has written for this volume.
When it comes to the animaladies associated with the framing of _disability_ , Sunaura Taylor's book _Beasts of Burden_ is central (2017). Taylor explores the shared histories of animalization that have affected those with bodies and minds seen as "lacking" or deficient: animals (other than human) and those humans with physical or cognitive disabilities. Taylor resists the impulse to see the comparison between animal and disabled person as pejorative, instead thinking of it as a preface to an alliance, a potentiality that has been strained by those within animal advocacy as much as outside of it. In her book, Taylor sharply focuses on Peter Singer's dismissal of severely cognitively disabled humans, as does Alice Crary in her chapter in this volume. Some Animal Studies scholars have used mental illness and cognitive disabilities as a rhetorical weapon in their criticisms of speciesism. Guy Scotton outlines how Animal Studies scholars have been guilty of labeling opponents "mad" and "crazy" too, perpetuating the problem of stigmatizing mental illness and cognitive difference. Physical disabilities, cognitive disability, and psychological disorders are a particularly important set of animaladies to consider as potential sites for alliance, as Hannah Monroe's chapter on autism and interspecies friendship shows and Nik Taylor and Heather Fraser's analysis of women, companion species, and anxieties highlights.
_Animaladies_ cautions against an exclusive emphasis on the socially constructed nature of madness; to be seen as "mad" is one thing, but to experience madness as profound psychological distress is quite another, and not one that is likely remedied only by attributing it to the discontents of social life in general. As Jane Ussher reminds us in relation to the "mad woman," we must also listen to what she has to say rather than speak for her as an emblem of heroic feminist resistance. As Nik Taylor and Heather Fraser's chapter shows, the psychological needs and distress of participants in their study of human–animal comfort are palpable and resistant to generalization. The same applies to the animals—alleviating their distress brought about by violence on factory farms and cruelty in laboratories is not only a matter of identifying the architecture of power that imprisons them but must also consider the actual lives they lead as individuals, the freedoms and pleasures they deserve after the horrible pains they endure. As many of the chapters in this book argue, we cannot in any simple way embrace "madness" wholeheartedly, whatever that might look like. But we can, perhaps more modestly, understand how it is used to preemptively frame animal advocacy and Animal Studies as far from the norm while also stigmatizing dis-ease, mental difference, neurodiversity, discontent, and disability.
The chapters in the section called _dysfunction_ draw on the myriad ways in which relations between animals and humans are made dysfunctional or depicted as such. Another "dis" or "dys" word, it describes behaviors or functions that are broken, disturbed, disrupted. Again, our focus here is not on labeling the good as opposed to the bad, but in examining how easy it is for some behaviors (but not others) to be depicted as "the problem" (like the "crazy cat lady," the "hysterical" vegan, or "crazy" activist) while letting other damaging relations (such as in factory farming, humane farming, duck shooting) off the hook. Those who bear the brunt of these damaging relations are also demonized, or outcast with their animals as Liz Bowen's discussion of precarious outcasts shows, and pattrice jones and Cheryl Wylie's play on dammed and damned feelings illuminates. These emotions are a source of strength too, as Katie Gillespie asks at the end of her chapter, "Who would we be without this madness, this feeling, these politicized manifestations of witnessing and care?" Together, these three sections and the three words—"dismember," "disability," and "dysfunction"—account for the various formations of animaladies: those damaged relations that feminist Animal Studies acknowledges, some to be reclaimed in the spirit of defiance and others disclaimed as acts of violence that need to end.
References
Adams, C. J. (1990), _The Sexual Politics of Meat: A Feminist-Vegetarian Critical Theory_ , New York: Continuum.
Ahmed, S. (2017), _Living a Feminist Life_ , Durham: Duke University Press.
Beers, D. (2006), _For the Prevention of Cruelty: The History and Legacy of Animal Rights Activism in the United States_ , Athens: Swallow Press.
Chesler, P. (1972), _Women and Madness_ , New York: Doubleday.
Cooper, B. (2018), _Eloquent Rage: A Black Feminist Shares Her Rage_ , New York: St Martin's Press.
Dana, C. (1909), "The Zoophilpsychosis: A Modern Malady with Illustrative Cases," _Medical Record: A Weekly Journal of Medicine and Surgery_ , 75: 10.
Dickinson, E. ([1896] 1996), "I felt a funeral in my Brain," _The Essential Emily Dickinson_ , Selected by Joyce Carol Oates, New York: HarperCollins, 12–13.
Donaldson, S. and Kymlicka, W. (2013), _Zoopolis: A Political Theory of Animal Rights_ , New York: Oxford University Press.
Gilbert, S. M. and Gubar, S. (2000), _The Madwoman in the Attic: The Woman Writer and the Nineteenth-Century Literary Imagination_. New Haven, CT: Yale University Press.
Gruen, L. (2015), _Entangled Empathy_ , New York: Lantern Press.
Haraway, D. (2003), _Companion Species Manifesto: Dogs, People and Significant Otherness_ , Chicago: Prickly Paradigm Press.
Kim, C. (2015), _Dangerous Crossing: Race, Species and Nature in a Multicultural Age_ , New York: Cambridge University Press.
Lewis, B. (2010), "A Mad Fight: Psychiatry and Disability Activism," in L. J. Davis (ed.), _The Disability Studies Reader_ , 339–352, New York, Routledge.
McHugh, S. (2012), "Bitch, Bitch, Bitch: Personal Criticism, Feminist Theory and Dog-Writing," _Hypatia_ 273: 616–635.
Munro, L. (2001), "Caring about Blood, Flesh, and Pain: Women's Standing in the Animal Protection Movement," _Society and Animals_ 9 (1): 43–61.
Probyn-Rapsey, F. (2013), "Stunning Australia," _Humanimalia: A Journal of Human/Animal Interface Studies_ 4 (2): 84–100. Available online, (accessed March 2, 2018).
Probyn-Rapsey, F. (2014), "Multispecies Mourning: Thom van Dooren's Flight Ways: Life and Loss at the Edge of Extinction," _Animal Studies Journal_ 3 (2): 4–16. Available online: http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1116&context=asj (accessed March 2, 2018).
Regan, T. (1983), _The Case for Animal Rights_ , Berkeley, CA: University of California Press.
Russell, D. (1995), _Women, Madness, and Medicine_ , Cambridge: Polity Press.
Showalter, E. (1985), _The Female Malady: Women, Madness, and English Culture, 1830–1980_ , New York: Pantheon.
Singer, P. (1990), _Animal Liberation_ , New York: Avon Books.
Taylor, S. (2017), _Beasts of Burden: Animal and Disability Liberation_ , New York: New Press.
Ussher, J. (1991), _Women's Madness: Misogyny or Mental Illness?_ Amherst: University of Massachusetts Press.
Vialles, N. (1994), _Animal to Edible_ , Cambridge: Cambridge University Press.
Part I
DISMEMBER
Chapter 1
JUST SAY NO TO LOBOTOMY
Lori Gruen
The case of lobotomy, despite its extremity, provides a poignant illustration of the precarity or threat of affect (or emotion or sentiment or care) in our relationships with each other and other animals. In this chapter, I will explore the ways "affect" has been understood, the way it has been feminized, rejected, and policed, and interrogate attempts to have it removed from our discourse and theory, from our activism, even from our brains! These efforts are inevitably unsuccessful, but the impact of the rejection of affect has nonetheless been intense and I think it has hindered collective efforts at making the world better for animals, or at least less horrible. Indeed, we are not able to fully be in meaningful relationships when a big part of our cognitive/affective capacity is cut off, even if it's not technically "cut out."
I will first discuss this scientific malady of remarkable proportions, the lobotomy, and then I will turn to an analysis of the rejection of affect, and finally I will revisit the sort of affect I have been advocating, what I call entangled empathy (Gruen 2015), which resists the division between reason and emotion and seeks to not just enhance our pursuit of justice but provide us with meaningful, caring "crazy"—in the sense of counter-normative, excessive ways to enrich our relationships in that pursuit.
Lobotomies
Walter Freeman was an "overzealous" showman who traveled the United States performing and promoting lobotomies. He is reported to have performed over 2,500 lobotomies on patients from twenty-three states. His first patient, in 1936, was a housewife from Kansas, the first of many more housewives who had parts of their brains ablated. Another housewife, a 29-year-old, was the first to receive the transorbital lobotomy. His last lobotomy was performed on another housewife, Helen Mortensen, who was subjected to her third lobotomy and died from a brain hemorrhage. That was in February 1967 and it was after her death that Freeman was banned from operating.
In 2005, National Public Radio in the United States did a story on one of the youngest people to have a lobotomy, Howard Dully, who was just twelve years old (NPR 2005). The story is shocking, and Dully (with Charles Fleming) wrote a riveting memoir about his experience (2008). The NPR story included a few oral histories, one was from a housewife, Patricia, who seemed glad to have had a lobotomy as she was suffering from depression. Her husband had arranged for her to have the lobotomy and apparently this interview was the first they had talked about it (the lobotomy was in 1962—forty-three years earlier). In that interview Patricia says she doesn't remember anything at all about it and Glenn says, "We were coming back from San Jose, following the operation, and Pat informed me that she couldn't wait to get home because she wanted to go down and file for divorce." Patricia responds, "Hmmm... Don't remember that at all. I don't think I said it." Glenn says, "I think I just went on driving and ignored the situation and began to wonder to myself, 'How much good did this operation accomplish?' Really, I can see no changes in most areas except she's much easier to get along with." Pat says, "I was a more free person after I'd had it. Just not to be so concerned about things... I just, I went home and started living, I guess is the best I can say—just started living again and was able to get back into taking care of things and cooking and shopping and that kind of thing."
The idea of altering the brain in order to facilitate social compliance and eliminate undesirable behavior has an interesting history. Surgical interventions reached their heyday in the 1940s as mental asylums were brimming over with cases after the Second World War. In that decade alone, more than 18,000 lobotomies were performed in the United States and tens of thousands more in other countries.
In "Psychosurgery: Intelligence, Emotion and Social Behavior Following Prefrontal Lobotomy for Mental Disorders," Freeman wrote:
[T]he frontal lobes are essential for satisfactory social adaptation... certain individuals may suffer from perverted activity of these areas and may become capable of better adaptation when these lobes are partially inactivated... Partial separation of the frontal lobes from the rest of the brain resulted in reduction of disagreeable self-consciousness, abolition of obsessive thinking, and satisfaction with performance, even though the performance is inferior in quality. The emotional nucleus of the psychosis is removed, the sting of the disorder, is drawn. (1942, vii)
He goes on to describe the history of surgical intervention in mental disorder, since female genitalia were often thought to be the site of the disorder. He noted that
surgeons began searching about here and there for offending organs that were supposed to be causing mental disorder. The first attack... was upon the internal genitalia, particularly the ovaries, because of the notion that functional nervous disorders were produced by the wanderings of the uterus into various parts of the body... After several years of experimentation and the sacrifice of many thousands of ovaries, the conclusion was reached that castration in the female, while sometimes exercising a temporarily beneficial effect, was not the solution to the problem of mental disorder. On the contrary, it frequently brought in its wake a train of undesirable symptoms that increased the discontent and often the misbehavior of the sufferer. (1942, 5)
In the early days of medicine, when all sorts of different theories were floated about the causes of illness, it was not uncommon to think that they were due, in some way, to "a depraved state of the humors" which was usually the fault of the sufferer. Thomas Sydenham, a well-known seventeenth-century British physician, noted that female hysteria was the second most common disease, just behind fevers. He attributed the malady to "irregular motions of the animal spirits," which were caused by "some great commotion of mind, occasioned by some sudden fit, either of anger, grief, terror or like passions."
Two hundred years later, it's only slightly surprising that women were the most common patients—and even today, women suffer more mental disturbances than men. A short piece in _Psychology Today_ reports that even though it may be simple to attribute the "epidemic of mental illness among women" to hormones, or the idea that women are more emotional, "The truth, though, is that psychiatrists aren't really sure why mental illness is more common among women" (Young 2015). Perhaps the reason this remains mysterious is because there still are more men than women asking the question.
One male psychiatrist, Gottlieb Burckhardt, was the first person on record to perform a surgical procedure to relieve the commotion of the mind. Burckhardt was a superintendent at a small Swiss mental hospital, and in 1888 he was the first to experiment with removing or destroying parts of the brain to address "perverted" problems of the mind. He experimented on six people. His work was later criticized because he was unaware of brain functionality and, in fact, was not trained as a surgeon. One of the patients died five days after the operation from epileptic convulsions, one "improved" but later committed suicide, another two showed no change, and the last two patients became "quieter."
About fifty years later, brain surgery for behavioral maladies got going again after a paper presented at a neurological conference in London renewed excitement about surgical intervention for mental disorder. At that conference, John Fulton and his graduate student Carlyle Jacobsen from Yale reported on an experiment they performed on two young chimpanzees, Lucy and Becky. The use of chimpanzees in the history of lobotomies is often overlooked, but when it is mentioned, it is usually just these two chimpanzees that are noted. The full impact of Fulton's research on chimpanzees is largely absent. Indeed, at the conference, Fulton and Jacobsen only mentioned the two young chimpanzees who survived the procedure. Ross, another young chimpanzee, died of dysentery while in Fulton's lab. Infant chimpanzee Lu died from meningitis following frontal lobe extirpation. She was involved, with Lucy, Becky, and another chimpanzee, Jerry, in Fulton's laboratory where they were trying "to create a group or colony of experimental defectives" (R.M.Yerkes Papers). Jerry died following an experimental operation, Lucy was killed and her brain prepared for study. An annual report from the lab in 1937 states that "Becky will be sacrificed within a few months" (R.M. Yerkes Papers).
At the London Conference, in their report to the attendees, Fulton and Jacobsen describe the behavioral change that occurred after they ablated the frontal lobes of Lucy and Becky's brains. It is a small sample, just two chimpanzees since the others didn't survive, and importantly, the behaviors they reported were opposite one another. One became more agitated about things she didn't care much about before, the other less agitated about things she did care about. This should not have led anyone to the conclusion that this procedure be attempted on humans, and Fulton allegedly thought as much (although he continued with his lobotomy work on chimpanzees). In addition, in the 1930s, very little was actually understood about chimpanzee behavior, so what the experimenters report they believed about behavior must be viewed with skepticism. The first infant bred and born in a laboratory, Alpha, was in 1930 in part to begin to understand chimpanzee development and behavior. Altering the developing brain of infant and young chimpanzees, without understanding their species' typical behaviors and their individual personalities, could not lead to any respectable conclusions. Sadly, this sort of scientific rationality was a large part of early biomedical research, and in the case of chimpanzees, at least, this "foolishness" continued for another fifty years.
At the conference, two important figures in the development of human lobotomies were in the audience, Egas Moniz and Freeman, who within months developed techniques and began performing lobotomies on humans. The desire to destroy unwanted emotion actually overtook reasoned assessment ironically in the name of scientific rationality. Lobotomy's reputation once ran so high that the Nobel Committee awarded the prize in Medicine and Physiology to Moniz in 1949. But within the next decade, lobotomy fell out of favor and its memory increasingly was vilified.
The operation's descent into disgrace had many causes. For one thing, lobotomy never had a scientific basis and animal work wasn't thought to be useful as a foundation for the procedure because researchers couldn't admit that animal models of mental illness existed. That was a barrier that the infamous Harry Harlow most notably sought to break with his psychological experiments on infant monkeys (Gluck 2016). Similar experiments on sensory and maternal deprivation were also being performed on chimpanzees at that time in an attempt to create animal models for despair, depression, schizophrenia, anxiety, addiction, and the like (R.M. Yerkes Papers). Of course, the advent of psycho-pharmaceuticals also played a role in ending the lobotomy. In the history of medicine, the lobotomy is one of the rare examples in which those within the biomedical community themselves share the negative assessment.
In 2005, Dr. Nuland, for example, began a discussion of the history of lobotomies noting:
Major steps in scientific progress are sometimes followed closely by outbursts of foolishness. New discoveries have a way of exciting the imagination of the well-meaning and misguided, who see theoretical potentialities in new knowledge that may prove impossible to attain. On occasion, the seemingly imminent is later shown to be far further off than originally thought, yet still possible to achieve. More frequently, the apparent prospect is revealed to be the result of unrealistic hypotheses based more on wishful thinking than on fact. In no branch of human thought have erroneous leaps of this kind been more prevalent than in that peculiar mix of science and art that goes by the name of medicine. (2005)
Nuland had a personal interest in the case of lobotomies, as someone who suffered from depression he was hospitalized and almost had a lobotomy, but a young physician recommended electric shock therapy instead. He ended up having a long notable career. Of this sorry chapter in medical history, Nuland writes: "Freeman's foolishness influenced an entire generation of psychiatrists, neurologists, and neurosurgeons and devastated the lives of tens of thousands of patients and their families." This tragic path "can serve as a cautionary tale about those who come to believe that they are beyond the restraints of judicious professional behavior."
Despite the demise of the surgical lobotomy and the scientific maladies that followed, there is a more ideological sort of lobotomy—a cutting off of feeling or affect that has been much more successful, indeed entrenched, and it is to this sort of cognitive alienation that I now turn.
Affect
In the United States in recent years, due in large part to the wide availability of social media, the murder of black people by police officers has come to wider attention. One of those killings, of Philando Castile, was live streamed on Facebook by his partner Diamond Reynolds, whose four-year-old was also in the car. The video showed the police officer with his gun drawn on Castile who is in the driver's seat bleeding out.
Many people who watched the video commented on Reynold's composure. She was calm and appeared quite rational. For both black and white commentators, her composure seemed a sign of her trustworthiness as a witness. Of course, she and her young daughter needed to make it out alive, so there was good reason for her to be calm in the face of a panicked cop with a gun. But as Melvin Rogers notes, there is something else going on here:
We would never expect others to display such composure in the face of such traumatic circumstances. We would not penalize their failure of self-control by tying it to untrustworthiness. In fact, we think, and rightly, that emotional eruptions at precisely this moment are appropriate... It makes perfect sense to come undone in that moment... And yet, we find ourselves holding Reynolds and other black folks, often women, to a higher standard as a prerequisite to be considered trustworthy, capable of accurately recounting the injustice that has just been committed against them. In doing so, we commit another form of violence, the reverberations of which most assuredly affects the mental health of black folks, reminding us, yet again, that what is expected of Black Americans is not expected of whites. It is demanded that we hold in and contain what should rightly be released: screams and tears. In short, pain. (2016)
I don't know if it's true that "we" don't hold "others" to this standard, but that is not really the point. This is certainly violence, what Dinesh Wadiwel (2015) and others have called epistemic violence. In particular, what Rogers is decrying is a type of testimonial injustice that denies an individual credibility in virtue of prejudice on the part of the hearer. Most women and people of color suffer from this form of injustice and thus experience all manner of credibility deficits. When exposed to long-term epistemic injustice, many will alter their/our mind-sets and behaviors in an attempt to conform to the epistemic norms, even though their/our attempts will seldom succeed. Most of us are familiar with the experience of having our perfectly reasonable claims dismissed because of who we are (perhaps in addition to a disagreement with what is said as well as how it is said). There is a growing and important literature on the ways these injustices further distort our relations with one another, and I think it is particularly important to be mindful of these credibility deficits in Animal Studies when we encounter scholars who express skepticism about what we might be claiming about what we know of other animals' experiences, for example. There is a cognitive alienation—a type of lobotomy—at work here.
So-called experts have been quick to diagnose Reynold's calm response. Jim Hopper, a psychology instructor at Harvard Medical School, said her behavior was consistent with a dissociative state. "In the immediate aftermath of horrific violence, he said, victims don't always sob." "People are literally not feeling in their body what's going on," Hopper said. "That circuitry can basically shut down" (2016).
This shutdown is emotional distancing—cutting off one's affect—and it is to some extent a "flight" reflex in the face of extreme horror, but I also think it is important to explore the social/political ramifications of the view that emotion must be cut off in an attempt to muster some credibility resources. In Reynold's case, she at least had good reason to believe that her chance of surviving would be greater if she did not display emotion. I see this as a coerced affect lobotomy, and it is much more widespread than the surgical lobotomies I discussed earlier.
There has been a lot of interesting, and conflicting, work on affect theory over the last decade. Some understand affect as the automatic, reflective phenomena that can be explained through forms of scientific reductionism reinvented as "embodiment." Others see the affective turn as a measured response to the rejection of sentiment, particularly when in literature it is deployed to alienate and subordinate. As Colin Dayan recounts:
[T]he language of sentiment animates subordination. A slave, a piece of property, a black cat—once loved in the proper domestic setting, they arouse a surfeit of devotion, bonds of dependence that slavery apologists claimed could never be felt by equal... Narratives of humane care are always conducted by the free in the name of the bound, their emotive impulse turning away from political action and toward... the neoliberal "performance of pathos." (2015)
Against this take, the affective turn is an intervention in political/literary invocations of domination. In philosophy, affect or sentiment has stood in opposition to reason, in judgments of value as well as in perceptions of good and bad, right and wrong.
This opposition between reason and emotion is at the heart of why animal ethicists, like Singer, make arguments based on our capacities to reason about similarities. It is in virtue of other animals being like us in "morally relevant" ways that we owe them consideration. We come to this through reason not sentiment. Recently, J.M. Coetzee, in a lecture about animals, echoed an early sentiment expressed by Singer, exclaiming, "I am not an animal lover... Animals don't need my love... I don't care about love. I care about justice."
I've been asking why not both? Coetzee is admitting he cares—just not about love? Why? The answer, of course, is political and gendered and I think it is based on a misperception of the structure of our cognition.
Singer, Coetzee, and so many others are in love with a liberal fiction that our relationships of care are "private," beyond the scope of ethical reason, and optional. Of course, most people don't want the State too intimately involved in their lives, but the continued reliance on a strict public/private division is not only a faulty notion, but it also perpetuates gendered power dynamics. White men have a sense of themselves that is shaped by imagining themselves primarily as thinkers and actors, something they admittedly learn in relationships with others, but their ethical/political identity kicks in once they are beyond those relationships, and they imagine themselves as post-relational.
According to this post-relational fiction, care, love, and sentiment are private, feminine experiences; justice on the other hand is seen as masculine and unsentimental. Of course, this binary thinking not only builds on stereotypical gender roles that preclude the idea that men are caring and obscures gender-queer expression, but it also ignores the particularity of caring relationships, which are informed by racial, economic, ethnic, cultural, and differently gendered experiences, that are fundamentally about justice or, more precisely, injustice. Perhaps most importantly, those of us who are not under the illusion that one can ever be post-relational and who find that fiction undesirable to start with are further marginalized when we reveal that this view is untenable. We are denied credibility, brushed off—we are subject to testimonial injustices.
Justice and love aren't at odds because they can't be disentangled in any meaningful way; they are mutually informing. Any compelling moral or political theory has to attend to the interconnections between cognition/reason and affect/emotion. Rather than generating distance between us and them, justice and love, in other words, to avoid this sort of lobotomy, we need courage, even while being marginalized, to bridge perceived gaps between reason/emotion and self/other by recognizing the ways that each side informs the other without collapsing into it.
Entangled Empathy
I've been thinking about building a bridge for many years and have developed the notion of entangled empathy with the hope that it will be strong enough to span these perceived gaps. It is a view that involves refining one's perception to more accurately see the concerns of particular, situated others; to recognize the ways we are in relationships that entail responsibilities to ourselves and others; and to do our best to make these relationships go better. Entangled empathy is a type of caring or loving perception that inevitably blends emotion and cognition.
While entangled empathy is part of the feminist ethics of care tradition in animal ethics, I was also inspired by the work of Iris Murdoch (1970). Murdoch is critical of what I'm calling this post-relational moral agent who is conceived as someone who already has a handle on any given situation, who knows what he is doing, whose thoughts and intentions are "directed towards definite overt issues," and whose responsibility is a function of impersonal knowledge. I love the irony in Murdoch's comparison of this sort of moral action with shopping, which is usually feminized—the agent enters the shop "in a condition of totally responsible freedom" and surveys the products and chooses to purchase one product or another. Shopping is public, and one understands the shopper through his choices and actions, much as the modern economist understands the preference satisfaction of economic man through his choices and actions. The inner life of the shopper, of economic man, and of the moral agent understood through modern moral theory is "parasitic" on his outward behaviors. But there really is only so much that one sees of that "inner life" through outer behavior, it is an anemic view of our inner lives, if it provides anything at all. Indeed that we perform behaviors that are meant to project meaning very different from what we internally experience is a good part of what therapy and other efforts at self-reflection start with. These outward behaviors become the focal point of ethical choice and action, and the inner life of the agent remains mysterious or, when accessible, thought to be beside the point of ethics.
Entangled empathy is, in part, trying to solve that mystery and make the embedded and embodied process of moral perception more accessible. I've argued that entangled empathy involves movement from the first personal to the third personal points of views. To meaningfully attend to the particularities of another being's interests, desires, vulnerabilities, etc., as they occur in particular contexts, under certain norms, within social relations of all sorts, and to avoid projecting one's own state of mind on others, this movement from me to you and back, through these shifting perspectives, is key. This process allows one to check oneself to avoid projection and to correct misperception.
Entangled empathy isn't simply a form of ethical attention but a particular form of caring or loving attention, attention that is directed toward another's flourishing. And, of course, people flourish in different ways. Through entangled empathy we see not only who we ought to attend to and what their situation evokes but also whether and how we should respond in ways that help to preserve and promote their well-being.
We can and do go wrong. One might err when they fail to grasp cultural understandings of the values and disvalues that are presupposed by empathetic experience. Evaluating those presuppositions is one of the tasks for getting empathy right. An empathetic agent's evaluations, deliberations, and choices are shaped, at least in part, by the social context in which he or she lives. Various social institutions and norms affect expectations. Empathetic engagement will often involve examining the conditions under which both the empathizer and the one with whom she is empathizing form their desires and come to appreciate their particularity. Entangled empathizers will be attuned to the distribution, both just and unjust, of hermeneutical resources that have an impact on desire and action. An astute empathizer will thus try to answer a host of questions, informed by the particular situation they are in, including: What predispositions do I have, and does she have, and how do they affect our different levels of confidence in formulating our desires and acting on them? How do cultural understandings of value impact our sense of our worth? Were certain paths (emotional, deliberative, and/or material) closed to me or to her by familial, educational, social, political, racial, gendered, economic, or religious barriers or prohibitions? Will my empathic success or failure depend on the social position I occupy? The social position she occupies? Do people like me culturally or historically have less chance of empathically succeeding and of "making a difference"? Are there any resources available or that I can cultivate to more successfully empathize?
I imagine a slightly different set of questions when the relationship is with nonhuman animals. What were the early rearing conditions this animal experienced and did that shape her current experiences? Chimpanzees who were singly housed and nursery reared have very different ways of being than those who had more socially appropriate upbringings. What sort of species-typical behaviors does this kind of being usually engage in and does she have opportunities to engage in those behaviors? For example, is there enough space to do what they normally would do? What sorts of social relationships are important, whether they be with conspecifics or animals from other species, including humans? Is this animal able to be alone, if she chooses? Is she able to make choices about who to spend time with, where to be, what and when to eat? Are these the sort of choices that are meaningful to this particular animal?
Answers to these questions, and others, will require us to develop better skills at perceiving and noticing the complexity of moral experiences in the world allowing us to navigate the "values round about us" as richly and fully as we can. It is a very different set of choices that we are considering than those enacted through typical transactional experiences, alluded to by Murdoch, in which mature actors are thought to be rational economic agents, expressing value through choices.
These "rational" actors, those who are lobotomized, are not able to engage empathetically and that means that so many are not attending to the sorry state of emergency that we live in. Of course, most of us are busy and absorbed in our own problems, projects, and plans, and many of us also have the luxury of not thinking about the significant problems that, for example, black people in the United States, Indigenous people in Australia, most people around the globe, and the majority of other animals are confronted with, in one form or another, almost every day. Those of us with relative privilege do not need to worry about being arrested, assaulted, profiled, starved, or shot in the streets. But we can pay attention and empathize with all those who are disregarded and do something to stop it, even though it is difficult, often painful, and we may be ostracized, ridiculed, or pathologized in our solidarity with others. This is necessary and possible, since the empathetic, caring, side of our cognitive architecture has not, fortunately, been surgically removed.
Some theorists are suggesting that we ought to remain figuratively lobotomized, although not in those words, and that empathy is a problem. Paul Bloom is probably the most vocal critic of empathy. He worries that we will end up caring about the wrong things, the wrong people, we'll be too parochial, we'll be subject to all sorts of biases (2014, 2016). I have written a bit about this, but I think these worries amount to a fairly standard worry about emotion being unhinged and unchanging.
There are different ways to understand what emotions are, and while Bloom seems to be thinking of emotion as simple sensations or feelings, emotions can be explained by the reasons that give rise to them and can be altered in light of those reasons. Emotional states can also alter reasons. Emotions are the sorts of things that we can be taught or conditioned to feel or not feel and reasons can be changed based on our affect. But, importantly, entangled empathy is not itself an emotion, but a _process_ or _method_ of moral perception.
I want to end by clarifying what I have in mind by the entanglement part of entangled empathy. I have a relational conception of the self and argue that our agency is co-constituted by our social and material entanglements. Social entanglements often extend beyond the human and far beyond our geographical location. By material entanglements, I have in mind the sense of materialism that is linked to our socioeconomic opportunities and limitations. I am also thinking about the new sense of materialism, which would include our entanglement with the food we have access to, the safety of our physical environment (e.g., water, air, particulate matter, toxic exposure), and the nature of our microbiome. These entanglements are quite complex and include our relations to the child slaves who harvest cocoa for chocolate; the orangutans who are on the brink of extinction due to our consumption of palm oil and palm products; those working in sweatshops who provide cheap clothing; our greenhouse gas emitting choices for food that are creating climate refugees. All of these actions, in part, constitute who we are.
Our identities are not simply "socially constructed," rather we are who we are at any particular time as an expression of entanglements in multiple relations across space, species, and substance. I am here inspired by the notion of entanglement from feminist philosopher of physics Karen Barad, who suggests that:
Matters of fact, matters of concern, and matters of care are shot through with one another... Ethics is therefore not about right responses to a radically exteriorized other, but about responsibility and accountability for the lively relationalities of becoming, of which we are a part. Ethics is about mattering, about taking account of the entangled materializations of which we are part, including new configurations, new subjectivities, new possibilities. (Barad 2012)
We should care about others because they are fundamentally part of our own agency. My failure to respond to others is not just a failure of my reasoning and my affect, but I may come to see it as a weakness in who I am or an error in my sense of agency.
Of course, it would be arrogant or naïve to think even though we co-constitute each other's agency that we can really ever, truly understand another. Sometimes, especially when it comes to animals, those of us in particularly intimate relations think we do really know. I would caution more humility here. But I worry that too often we take the possibility that we can't fully understand as an excuse to not to even try to take the perspective of another. The clearest case of this lately is that white people in a culture of anti-black racism cannot understand the full weight of years that burden those who experience racism, as well as the feelings of invisibility, rejection, extrajudicial violence, and disrespect that result from it. For some this has meant that white people need to step away from the world; for others it has meant that we need to work to develop and deepen our empathy.
Entangled empathetic moral attention involves working through complicated processes of understanding one another and other animals in situations of differential social, political, and species-based power. Usually what we "get" is just a glimpse. That we never really "know" cannot be an excuse to opt out of working at it. I take this to be a failure of both imagination and agency. To avoid this failure, we need to _say no to lobotomy_ and deepen our care for each other, for other animals, as well as for ourselves.
Acknowledgments
I would like to thank Fiona Probyn-Rapsey for conceiving and planning the wonderful conference at which an early version of this chapter was presented and to Dinesh Wadiwel and HARN for bringing me to Sydney. The audience at Animaladies was terrifically receptive and I am grateful for and was inspired by that. pattrice jones helped me come up with the title of this chapter. My deepest gratitude is to Njeri Thande. Without her, I don't think this chapter would be here.
Notes
The term "crazy" is often thought to be ableist and many have been arguing that we should be more specific when we use the term. I agree. Because the term often refers to a particularly racialized and gendered notion of defying normative expectations, I have an urge to reclaim it, but it's not really my place, so I'm looking forward to being in solidarity with disability rights scholars and activists in the project of reclaiming the crazy!
There are multiple books and articles written about Freeman, a particularly interesting and accessible story is Michael M. Philip's _Wall Street Journal_ series (2013).
As cited in Brown, p. 447.
See my history of chimpanzee research (Gruen, First 100 Chimps, 2006).
The week before I gave my presentation at Animaladies in Sydney, Australia (July 2016), two tragically senseless murders of black men by cops had occurred, one in New Orleans, one in Minneapolis, and these were followed by the sniper killing five police officers in Dallas.
As reported by Danielle Paquette in the _Washington Post_ Wonkblog, July 7, 2016. Available online: <https://www.washingtonpost.com/news/wonk/wp/2016/07/07/the-incredible-calm-of-diamond-lavish-reynolds/?utm_term=.89f0376ddaf6> (accessed February 20, 2018).
As reported in the _Daily Mail_ , June 30, 2016. <http://www.dailymail.co.uk/wires/afp/article-3669253/Nobel-laureate-J-M-Coetzee-speaks-against-animal-cruelty.html>
As Murdoch (1970) puts it, "Both as act and reason, shopping is public. Will does not bear upon reason, so the 'inner life' is not to be thought of as a moral sphere. Reason deals in neutral descriptions and aims at being the frequently mentioned ideal observer. Value terminally will be the prerogative of the will; but since will is pure choice, pure movement, and not thought or vision, will really requires only action words such as 'good' or 'right'" (page 8).
References
Barad, K. (2012), "Matter Feels, Converses, Suffers, Desires, Yearns and Remembers," in R. Dolphijn and I. Van Der Tuin (eds.), _New Materialism: Interviews and Cartographies_ , Ann Arbor, MI: Open Humanities Press.
Bloom, P. (2014), "Against Empathy," _Boston Review_ , September 10.
Bloom, P. (2016), _Against Empathy_ , New York: Ecco.
Brown, T. H. (1993), "Mental Diseases," in W. F. Bynum and R. Porter (eds.), _Companion Encyclopedia of the History of Medicine_ V. 1, London: Routledge.
Dayan, C. (2015), "Feeling into Action," _Boston Review_ , September 28.
Dully, C. and Fleming, C. (2008), _My Lobotomy_ , New York: Random House.
Freeman, W. and Watts, J. W. (1942), _Psychosurgery: Intelligence, Emotion and Social Behavior Following Prefrontal Lobotomy for Mental Disorders_ , Springfield, IL: Charles C. Thomas.
Gluck, J. (2016), _Voracious Science and Vulnerable Animals_ , Chicago: University of Chicago Press.
Gruen, L. (2006), First 100 Chimps. Available online: First100Chimps.wesleyan.edu (accessed January 28, 2018).
Gruen, L. (2015), _Entangled Empathy_ , New York: Lantern Press.
Murdoch, I. (1970), _The Sovereignty of the Good_ , London: Routledge.
NPR (2005), " 'My Lobotomy': Howard Dully's Journey" Available online: <https://www.npr.org/2005/11/16/5014080/my-lobotomy-howard-dullys-journey> (accessed January 28, 2018).
Nuland, S. (2005), "Killing Cures," _New York Review of Books_ , August 11, V. 52 #13.
Philip, M. M. (2013), "The Lobotomy Files," _Wall Street Journal_ , December 14. Available online: <http://projects.wsj.com/lobotomyfiles/> (accessed February 8, 2018).
Rogers, M. (2016), "On Diamond Reynolds after Dallas," July 8. Available online: <http://www.publicseminar.org/2016/07/on-diamond-reynolds-after-dallas/> (accessed January 28, 2018).
Wadiwel, D. (2015), _The War against Animals_. Koninklijke: Brill.
Yerkes, R. M. Papers. Manuscripts and Archives, Yale University Library, Group 569, Series II, Box 107.
Young, J. (2015), "Women and Mental Illness," _Psychology Today,_ April 22, 2015. Available online: <https://www.psychologytoday.com/blog/when-your-adult-child-breaks-your-heart/201504/women-and-mental-illness> (accessed February 24, 2018).
Chapter 2
MAKING AND UNMAKING MAMMALIAN BODIES: SCULPTURAL PRACTICE AS TRAUMATIC TESTIMONY
lynn mowson
Prolonged exposure to animal activism and self-enforced witnessing of atrocities committed upon agricultural animals had left me hypersensitive to images of suffering. My research into the dairy industry, and in particular the slaughter of pregnant cows and the treatment of unborn calves in abattoirs, included not only undercover activist descriptions, audio and video footage but also agricultural industry reports and agricultural codes of conduct and regulations—strange dissociative accounts of barbarity. Engaging with this material produced recurrent nightmares filled with the sounds and sights of animal suffering. The constant witnessing of animal death all around me was shattering. Like an undertow, the traumatic knowledge of the lives and deaths of these agricultural animals dragged my sculptural practice into uncharted waters.
At the time I was working on full-scale sculptures of humans, bodies gesturing toward suffering and martyrdom, and I was focused on the particularities of empathic interactions with figurative sculpture.
Enmeshed within my research was an attempt to untangle art historical debates on wholeness and fragmentation of the body, and contemporary art theories that prioritized sculptural body fragmentation and aligned depictions of the whole body with idealism or the saccharine. My sculptural bodies determinedly navigated a visual wholeness and avoided fragmentation with a purpose I would not understand until much later (see Figures 2.1 and 2.2). In retrospect my avoidance of fragmentation and investigation of empathy were driven by my desire to answer other questions about our ethical and exploitative relationships with the nonhuman animal.
**Figure 2.1** lynn mowson, _fleshlump_ , 2012–2013 (detail of installation in _beautiful little dead things_ , 2014), microcrystalline wax and pigment. Photo: lynn mowson.
Concurrently, my own pregnancy created situations where I needed to justify my decision to raise a vegan child with medical staff and the "concerned"; people become philosophers, nutritionists, and evolutionists around a vegan parent, and accusations of brainwashing my, as-yet unborn, child were not uncommon. Research into vegan nutrition segued into researching the treatment of dairy cows. It was the first time I had become fully cognizant of the enormous numbers of cows going to slaughter pregnant and there were some horrific statistics; at that time, in the United Kingdom 150,000 pregnant cows were sent to slaughter annually with approximately 40,000 of these in late-stage pregnancy. In a survey in the 1990s, also from the United Kingdom, one slaughterhouse revealed that 23.5 percent of cows were pregnant at the time of slaughter with 26.9 percent of those in their final trimester (Singleton and Dobson 1995). More recent agricultural studies indicate that the numbers of productive and pregnant cows killed worldwide are much higher (Fayemi and Muchenje 2013). Regulations around the slaughter of pregnant cows are applicable only to those cows in the last tenth of their pregnancy (OIE World Organisation for Animal Health 2017). In the last few weeks of fetal development the death these calves experience is mostly dependent on whether by-products are required and gathered from their bodies. For many calves there are no regulations for how they should die. I thought I knew about animal mistreatment, but the sheer numbers caused a visceral response. Beyond the statistics quoted in industry reports there was the personal testimony of witnesses such as Gabriele Meurer, a former official veterinary surgeon in UK abattoirs, who stated:
What is happening right now in British slaughterhouses is quite simply a scandal. Sometimes when these creatures are hanging on the line bleeding to death, you can see the unborn calves kicking inside their mothers' wombs. I, as a vet, am not supposed to do anything about this. Unborn calves do not exist according to the regulations. I just had to watch, do nothing and keep quiet. It broke my heart. I felt like a criminal. I left the Meat Hygiene Service... completely disillusioned and full of disgust. (Viva! 2014)
My inability to do anything meaningful in response to this knowledge was experienced as an overwhelming trauma, a trauma that returned when I saw people eating cheese or drinking milk around me, building pressure, becoming a silent scream of futility in the face of the enormous normality of animal production and consumption. In the studio, while attempting to avoid the incursions of this knowledge, I simultaneously modified my sculptural figures; they became pregnant and indications of multispecies entanglements such as hair in the wrong places and extra nipples (teats) started to appear (see Figure 2.2).
**Figure 2.2** lynn mowson, _fleshlump_ , 2012–2013 (detail of installation in _beautiful little dead things_ , 2014), microcrystalline wax and pigment. Photo: Kerry Leonard.
I laid bare these nonhuman animal clues; the teats were just too perky or were hidden inside out. These were awkward self-conscious attempts to sidestep potentially reductive readings of my work as an iteration of "becoming animal," or of exhibiting an anthropocentric hybridity that flourished in the artworld and that jarred with my perspective of already "being animal" and my concern with the actual political, ethical, and sociocultural issues at stake when considering agricultural animals.
As a sculptor, the operation of empathy between humans and figurative sculpture has held a prolonged fascination and became increasingly important in my artistic approach. There is a lineage from aesthetic empathy developed in the nineteenth century (Vischer [1874] 1994 and Lipps 1965) through to the phenomenological intersubjective empathy developed in the twentieth century to account for the way in which we understand others to be subjects. The phenomenological empathy articulated by Edith Stein, at the beginning of the twentieth century, is an account of an empathy by which our own somatic and embodied awareness provides the understanding that there are other bodies in the world; it is how we know that there are other subjects (Stein [1916] 1989). We encounter others through the embodied empathic encounter, an encounter that is a conscious and directed attentiveness to an other. Additionally, it is an ethical encounter that creates an awareness of the absolute alterity of the other, and as such avoids many of the theoretical problems of the models of empathy that depict the process as an unconscious mirroring of the other, a colonizing of the other, or as an unstoppable contagion of the self. This phenomenological empathy is a process: a contingent and precarious encounter, and as such there is always a decision whether to respond and engage with an other (Lipps, 408). Obversely, and just as importantly, a lack of empathy or empathic indifference to others can be an indication of cultural and societal forces that have normalized the withdrawal of empathy toward certain subjects, such as agricultural animals. In this context a withdrawal of empathy is an act of violent erasure of the other.
Lori Gruen's _Entangled Empathy_ argues that empathy can have a strong ethical and active role in our relations with animals (2015). Empathy can provide an important pre-linguistic and embodied space of encounter that informs our moral perceptions. As part of the feminist ethics of care tradition, entangled empathy is a process that is based on attending to and responding to animals as subjects with their own lives and needs within our complex economic and cultural systems. My sculptural change in direction was informed by this underlying concern with empathy and an empathic witnessing of the lives and deaths of agricultural animals. By sculpturally blurring the boundaries between the human and nonhuman animal, I tentatively explored and gestured toward our shared mammalian experiences—in particular birth, motherhood, and death. Further, it seemed that I could work toward simultaneously bringing empathic attention to the other while also revealing the violence done to it.
Material changes occurred in my works. I started using latex because it is ephemeral, fragile, and transitory. Latex ages, thins, and eventually decays like our own bodies. I took multiple latex casts from the whole bodies I had made and developed a method to fabricate the latex skins to resemble worn vellum and membranes, dried and treated animal skins devoid of hair. A process of making and unmaking bodies commenced—creating bodies and disassembling them. These adult bodies were subsequently accompanied by a series of _babyforms_ and sacs. The _babyforms_ were made from the all-in-one baby-suits that my son was outgrowing (see Figure 2.3).
**Figure 2.3** lynn mowson, _slink_ ( _babyform_ ), 2012, detail, latex, tissue, and string. Photo: lynn mowson.
I cast the _babyforms_ in multiples, ensuring individuality in each cast, reflecting my desire to bring attention to the subject, the individual within the mass. They became part of the series I eventually entitled _slink_ (see Figure 2.4).
**Figure 2.4** lynn mowson, _slink_ , 2012–2014 (detail of installation in _beautiful little dead things,_ 2014), latex, tissue, and string. Photo: Kerry Leonard.
"Slink" is a wonderful word meaning lurking, prowling, slithering, skittering, skulking around. Slink leather is a highly valued luxury item, most often used in expensive gloves, religious scrolls, and vellum and it is desirable because it is soft and unblemished. Slink means intrauterine skin; slinks are the skins of animals born prematurely, although calves used for slink leather are not born, but rather left to die in their mother's body or worse. One witness described how an "almost-full-term calf struggled inside and against the mother's body, kicking in desperation, dying a horrible death inside the womb" (Ernst 2013).
The multiple bag-like _sacforms_ that complete the _slink_ series emerged as a response to the regulations for the slaughter of fetal calves (see Figure 2.5).
**Figure 2.5** lynn mowson, _slink_ ( _sac_ ), 2012, latex, tissue, and string. Photo: lynn mowson.
Fetal calves can survive their mother's death, and slaughterhouses are advised, if possible, to leave the calves in the uterus for more than five minutes after the mother's throat has been cut: "A foetal heartbeat will usually still be present and foetal movements may occur at this stage, but these are only a cause for concern if the exposed foetus successfully breathes air" (Australian Veterinary Association 2006). These procedures are based on the assumption that the first breath, which oxygenates the brain, produces the ability to perceive pain, and therefore measures should be taken to avoid the calf taking a breath (OIE World Organisation for Animal Health 2017 and van der Valk et al. 2004). When the slaughterhouse collects fetal-bovine serum there becomes a delicate balance of holding the calf in a pre-living stasis while their blood is drained from their beating heart. The Regulatory Code describes how the worker should hold the amniotic sac over the head of a calf to prevent them from taking their first breath:
Any living fetus removed from the uterus must be prevented from inflating its lungs with air and breathing. This can be done by keeping its head inside the amniotic sac, by clamping its windpipe, or perhaps less satisfactorily, by simulating the amniotic sac by immersing its head in a water-filled plastic bag. These methods would ensure that such fetuses would remain unaware and therefore would not suffer when exposed to noxious stimuli such as insertion of a 12–16 gauge syringe needle between the fourth and fifth ribs into the fetal heart to allow blood to be collected. (Mellor 2003)
These welfare procedures are not always employed. Timothy Pachirat, in _Every Twelve Seconds,_ describes the collection of fetal-bovine serum:
Sometimes out of the pipe in the wall an oblong gray mass shoots that is not a lung, kidney, windpipe or liver... the white-helmeted worker walks over, picks up the object... cuts into the grey mass. There will be a fetus inside, with smooth, slick skin, and clearly marked hide patterns. Raising the fetus up by the neck and hind legs, the man swivels... and pushes the fetus's mouth onto one of the protruding hooks... he uses two hands to stick another hook into the fetus's anus. The fetus now hangs suspended by its mouth and anus, and the worker makes an incision in the neck area, bringing a bottle with a straw... to the incision. (2011, 79–80)
Calves are kept on the brink of life and death in order to collect blood, a balance between animal welfare and production necessity. Research has indicated that fetal calves are likely to be exposed to discomfort and pain; studies on fetal resistance to suffocation reveal that pain can be experienced until brain damage occurs due to lack of oxygen. In fact bovine fetuses are considered able to feel pain from about a third of the way into their gestation, when the neural tube develops into a functioning brain, and some studies suggest that due to the way the brain is developing they might actually feel pain more extremely (Jochems et al. 2002). My latex _sacforms_ evoke the meaty nourishing placenta, the emptied caul, and the amniotic sac put to the most brutal use in the slaughterhouse. Fetal calves exist in a liminal space, between life and death, between waste by-products and useful resource, between disregard and regulation, creatures whose first breath must be smothered while they are kept alive and their blood is drained and later their skins are collected.
Through the witnessing of this traumatic knowledge, the work _slink_ emerged. It was not consciously directed, and often resisted, propelled from an unconscious material working through and regurgitation of my garbled and somewhat hysterical traumatic thoughts: a mass of assimilated and unassimilated, compressed and compounded scraps of images both seen and imagined; the fetal calf kicking as he/she was cut from his/her bled-out mother, her body hanging upside down, and the cold emotionless descriptions of horrific procedures and processes that reemerged as detailed nightmares and flashbacks.
The changes that occurred through this traumatic working practice often surprised me, for example the violence I enacted on my sculptures proved to be something of a shock. Removing the latex from the mold was a rough and violent task that involved cutting, tearing, and pulling the skins from the little baby forms. To me this process of violent skinning echoed the disassembling of animal subject that occurs both literally and linguistically, and I found it a challenge to undertake, as my studio notes attest:
Skinning days. The bodies are taken down from their hanging position, and rubbed with talc, rubbing into the crevices, the pits, the groin. A sharp scalpel makes a cut through the skin, and then the process of skinning commences, pulling and rubbing down, pulling, stretching, releasing, it is an ugly task, on par with creating meat lumps from the creatures. I'm sometimes callous with my little objects. Sometimes their grip on me is too strong, their tenderness, fragility and exposure is too painful to bear. I become meat worker, butcher, in order to do this work, and I make amends [regrettably useless] with small objects. I counterbalance the butchering with the endless work of reparation. (Studio notes)
Concurrent with the development of _slink_ I had started to violently dismember my whole wax bodies and animal portraits ( _creatures_ ), butchering them into fleshy meaty lumps. While many of these _fleshlumps_ were pushed beyond recognition, others bear traces of their origin—a nostril here, a teat there (see Figure 2.6).
**Figure 2.6** lynn mowson, _fleshlump_ , 2011–2013 (detail of installation in _beautiful little dead things,_ 2014), microcrystalline wax and pigment. Photo: Kerry Leonard.
I questioned the impact of this unmaking of the body; was it an act of violent erasure, was it a reduction of a subject to an object? Had I deliberately excluded the possibility of an empathic encounter with these objects or did the remaining traces of the body create empathic opportunities? I followed the violence of skinning _slink_ and dismembering the _fleshlumps_ with a phase of care and reparation: either carefully resurfacing the waxes or gently washing and then sewing the latex forms together. Sewing was a small intimate practice of care, a futile and impossible reparation task, as if attempting to atone for brutality in my work and the world beyond. The disassembling of my whole sculptural bodies from presence into absence led to a radical reevaluation of my processes and practice, and a consideration of the affect of trauma on my works.
Trauma affecting animals' advocates is complex and has only in recent years gained attention as an issue for animal activism. As an activist it was, and in some cases still is, inadvisable to mention one's own trauma in relation to vastness of animal suffering, and one feels compelled to continue to endlessly bear witness to acts of cruelty, to avoid looking away. Rational argument not emotion is lauded, although these rational arguments have not stopped the inexorable expansion and industrialization of animal agriculture. Nor have they conquered the seemingly subjectively embodied collaborators in cruelty, taste and pleasure.
Sometimes I stand at the edge of butchers' shops, normally I rush by, their smell envelops me, covers me in a layer of flesh and fatty tissue, the thick smell of cold death. I wonder at how normal this all seems to people, these lumps of bodies laid out, creatures that had lives given and taken from them for a meal. How invisible yet visible the atrocity is. This atrocity that is invited into our homes and our mouths. (Studio notes)
As late as the 1990s, trauma was considered to be an event outside the range of normal human experience and most commonly used to describe the symptoms of Holocaust or war survivors. The definition of trauma was amended by the American Psychiatric Association in 1994 to become any event "involving 'actual or threatened death or serious injury, or a threat to the physical integrity of self or others'" (Bryant 2006, 94). Animal activists experience a threat to the physical integrity of an other when they witness the suffering of animals through audio-visual or other methods (95–96). Activist and writer pattrice jones states: "even the stringent diagnostic criteria for PTSD acknowledge that witnessing death, injury, or the threat thereof to another can be a traumatic experience. In fact, some researchers have found that witnessing—and being helpless to stop or prevent—harm to another can have a greater traumatic effect than being a victim of violence oneself" (2007, 93).
Traumatic affects include experiences of anguish, guilt associated with not having prevented harm or death, and "sadness, grief, depression, anxiety, dread, horror, fear, rage, and shame; intrusive imagery in nightmares, flash backs, and images; numbing and avoidance phenomena; cognitive shifts in viewing the world and oneself, such as suspiciousness, cynicism, and poor self-esteem" (Valent 2002, 19). Those affected can have "intrusive thoughts about the violence; hypersensitivity to triggers of thoughts and memories of the violence; volatile personal relationships; persistent and involuntary emotional numbing or unregulated emotional extremes of outbursts and low affect; severe mistrust of others" (Bryant, 102). Trauma can also cause hypermnesia, which is a strong recall or vivid recall of memories, as well as those memories being "garbled" because of the difficulty of processing traumatic memories into everyday life.
jones coined the term "aftershock" to describe the aftereffect of a traumatic event and observed post-traumatic stress disorder in animal advocates as basically a normal reaction to extraordinary experiences (75–76). _Aftershock_ focuses on recovery; however, jones notes that while general trauma therapy focuses on coming to terms with and integrating trauma into one's worldview, this is almost impossible for the animals' advocate. It is the 'reality' of everyday life, jones contends, that continues to inflict trauma on the animal advocate; "everyday life can be similarly nightmarish for those who have undone the socialization that leads us to see cadavers as 'meat'" because "vegans, unlike flesh-eaters, never stop noticing the violence inherent in meat" (90, 149). We are surrounded in day-to-day life by the constant reminders of what I call the ag-trocities (atrocities caused by the animal agricultural industry) against animals. For the affected witness, meat, dairy, and leather products are no longer food and clothing products: they are flesh products, bodies and parts of once living beings. Animals are co-opted in advertising into promoting their own fleshy bodies to be consumed. Supermarket shelves are filled with parts of animal bodies, and friends and family eat these foods in front of you: "vegans are constant witnesses to the horrors of carnism, [and] must live in a world that daily offends their deepest sensibilities" (Joy 2012).
Advertisements and children's books and toys depict unrealistic pictures of farms: happy cows in the fields, pigs smiling, and chickens roaming free. In children's books animals, particularly agricultural animals, start as empathic fellow creatures and playmates, and then are gradually moved away from us, moved onto the farm and turned into product machines. Raising a vegan child meant that I was hyperaware of the normalizing narrative processes of carnism, and the gradual disassociation of empathy articulated so well in Jane Legge's _Learning to Be a Dutiful Carnivore_ (1969):
Eat the flesh from "filthy hogs"
But never be unkind to dogs.
Grow up into double-think—
...
They only come on earth to die,
So eat your meat, and don't ask why.
Fiona Probyn-Rapsey recently articulated the term "animalady" to "gesture at a state of profound disease in the face of destructive human–animal relationships but with the view that such disorders can provoke positive transformations" (2014, 16). In this concept of "animalady" both trauma and the transformative possibilities of traumatic affects can coexist; in this context my trauma resulted in the production of the new works: _slink_ and _fleshlumps._ Both of these series are a transformation of my traumatic knowledge into what I consider to be a form of sculptural testimony. Testimony transforms traumatic knowledge into words/sound/text/object. It is essentially outwardly directed toward another, offered to another, and ideally reaches a responsive audience with a shared communicative language: visual, verbal, or textual. However, my sculptural testimony is often experienced across the experiential abyss between the vegan and the carnist, across a seemingly impassable divide.
As traumatic testimony, my material working through was overstretched to encompass the traumatic memories of the abuses in the slaughterhouses and factory farms; it was further burdened with the weight of the whole sociocultural processes by which these events are normalized—carnism. In facing the overwhelming sociocultural mechanisms of carnism my work became somewhat contradictory and hysterical as I fought also to suppress the incursion of agricultural animal lives and deaths into my work. In trying to discuss the underlying tensions in my work I found myself positioned as the "radical vegan freak," the "vegan killjoy" (Twine 2014), the "out-there irrational-nutty-screw-loose-mushy-softy-weirdo-bunny-hugger-animal-lover." Moreover, the reception of my sculptural testimony was never clear-cut, sometimes animal advocates rejected my work: the message is not clear enough, the works are too meaty, they look too much like real skin. Similarly, I too questioned the aesthetics of my representations of animal skin and flesh, my representation of skinned bodies and fleshy lumps. To continue this traumatic making and unmaking of bodies, this sculptural testimony, I needed to surrender to the possibilities of communicative mistakes, failures, misreadings, and misunderstandings.
While the emergence of traumatic knowledge in my practice had been initially undesirable, it focused my attention on how to align my animal advocacy with my art, since it had become very clear that one would not leave the other alone. So while _slink_ and _fleshlumps_ emerged somewhat unbidden from trauma, with my series _boobscape_ (2016–2017) I determined from the outset to utilize the productive force of "animalady." My focus on dairy cows continued, but moved from the slaughterhouse to the conditions of their lives, and the exploitation of their motherhood for the production and consumption of milk. For me there is no surprise that the word "milk" has been used to describe exploitation for profit for centuries; to milk is to tap, exploit, bleed, drain, extort, extract, suck dry, wring, elicit, empty, exhaust, fleece, press, pump, siphon, use, draw off, impose on, let out, take advantage of, take out.
The horrors of the dairy industry are so extensive that here I outline only a few of the elements that fomented _boobscape_ (see Figures 2.7 to 2.10).
**Figure 2.7** lynn mowson, _boobscape_ , 2016–2017 (image used for Animaladies postcard collection, 2016), latex, tissue, and string. Photo: lynn mowson.
Traditional dairy farms are decreasing; dairying is big business, but only for those who farm intensively. Some mega-dairies can house over 15,000 cows. Cows are kept indoors with their feed manipulated and zero-grazing opportunities causing lameness, hoof problems, teat tramp, and mastitis. Intensive farming leaks into the environments millions of liters of slurry need to be disposed of, often poorly, causing water and air pollution and wildlife diseases.
While the average life span of a wild cow is around twenty to thirty years, commercial dairy cows go to slaughter around their fifth to eighth year, worn out. Milk making is physically hard work and dairy cows are expected to produce milk for up to ten months of the year. This depletes the body of minerals and nutrients, meaning contemporary dairy cows are in a constant state of metabolic hunger. They get a break from milk production only during the last fifty to sixty days of pregnancy—the "drying off" period to allow the udder to recover and for the treatment of mammary infections.
Selective breeding has increased production of milk; a calf would normally drink around eight times daily, keeping the production of milk stable, and the udders and teats in good condition. Mastitis is one of the leading causes of antibiotic use in dairy farming and for the culling of pregnant cows (Food and Agricultural Organization of the United Nations, 1989). Mastitis is an inflammation of the mammary gland, with a high economic cost due to decreased milk quantity and quality, and fever and depression in cows (Jones 2009). Milking machines transmit the mastitis pathogens to other members of the herds, and they also frequently damage teats. And as cows age their propensity for mastitis increases. Controls for mastitis include tail docking, injections of antibiotics into the teats in the dry phase, and the burning of udder hair—known as flame clipping. Flame clipping is increasingly replacing other more labor-intensive forms of hair removal, as hairy udders are thought to gather more dirt and require more cleaning, and they impair robot efficiency, but error rates can be high, and farmers report "flare ups" requiring dousing (Gamroth et al. 2000). Mastitis not only affects the udder internally but also causes ulcerations on the flesh, and teat sores and cracks.
**Figure 2.8** lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Mary C Holmes.
The repetitive exhausting pregnancies, the limping lameness, the extended, overburdened ulcerated diseased udders, the memory of the cow's foot stamping as the flame goes over their udders and lingers a little too long, and the endless removal of calves were the starting point for _boobscape._ The exploitation of motherhood in the dairy industry emerged in the studio as multiple mammary glands of humans, bovines, and other fellow-creatures, these multispecies mammaries indicating the ongoing embodied and empathic approach of my work. Single udders became multibreasted and nipples elongated into teats. The breast skin is dry and aged, weathered and sore, veins bulging and ulcerated skin peeling, there are sore breasts, dried out empty breasts, worn nipples, leaky lactating breasts, breasts blurring between species, multiple breasts indicating the endless cows and the endless reproduction in the dairy industry. The surrounding skin is papery thin and soft like membranes and dried fleshless skins, like unprocessed slink skins as a material testimony for those little lives lost in the dairy industry (see Figure 2.9).
**Figure 2.9** lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Kerry Leonard.
_boobscape_ makes possible embodied and empathic connections by obscuring the boundaries and the spaces between the mammary glands shared between mammalian species, increasing the potentiality for a viewer to experience an embodied empathy mediated through sculpture. I hope that one might, on encountering these mammary forms, clasp one's hand to one's breast, and think "ouch." That one might imagine the swollen bruised hot breasts, veins bulging, the awful searing pain of mastitis, the feel of nipples raw to touch, skin flaking. That one might empathically respond to the materiality and form, and in doing so recognize those things we share with our fellow creatures, our entangled embodiment and potentially shared physical memories of childbirth and breast-feeding. No longer do I tentatively place teats on human forms, now I muddy the boundaries between species, when teats become nipples and breasts become udders, I evoke our entangled nurturing and exploitative relations with other creatures and I nod to visual lineage of humans suckling animals and animals suckling humans. I witness a history that has human–animal suckling closely entwined, although these are no utopian spaces, human needs surmount animal needs.
_boobscape_ alludes to possible monstrous milking machines, animals reduced to mammaries, the multiplicity of the herd, multibreasted goddesses, boundary crossings and infringements between human and nonhuman animals, to the potent abject and transgressive possibilities of milk and motherhood. There are breasts that bud and form and mutate; there are supernumerary teats, prepubescent nipples.
Calves can be born with an extra teat, a supernumerary teat, a sprig or a web teat; these are removed because they can interfere with future milk collection practices. They can be cut off with scissors, the codes recommend but do not enforce pain relief. Teats are unwanted elements in leather production, the waste by-products of the animal body. Thus my process of sculptural testimony continues to strive to include all this traumatic knowledge and more.
**Figure 2.10** lynn mowson, _boobscape_ , 2016–2017, latex, tissue, and string. Photo: Kerry Leonard.
_boobscape_ lingers discordantly between beauty and horror, attempting a balance between empathy and erasure through making and unmaking mammalian bodies (Figure 2.10). While I hope my sculptural offering opens the possibility of an empathic encounter, my struggle with the misunderstandings and misreadings of my sculptural testimonial continues. As often as not, I find myself standing at the edge of that abyss of incomprehension—that yawning gap between the ubiquity of a glass of milk and my anger and bewilderment at the horrors of the dairy industry, mumbling: "That is not it at all, That is not what I meant, at all" (Elliot 1963, 17).
Acknowledgment
Special thanks go to creative writers and collaborators Hayley Singer and Sue Pyke, whose ruminations in my studio were influential on the development of boobscape. I would like to thank Melissa Boyde, Maddi Boyd and Yvette Watt for including me in the Animaladies exhibition. Fiona Probyn-Rapsey for her ongoing enthusiasm and encouragement of artists working in this field. Curators Kathryn Eddy, Janell O'Rourke and L.A. Watson for including slink and boobscape in the exhibition SPOM: The Sexual Politics of Meat at The Animal Museum, LA, and of course Carol J. Adams whose work inspired the exhibition.
Notes
Two influential studies subsequently consolidated information on the lives of dairy cows (Butler 2014, Gellatley 2014). See also _The Life of the Dairy Cow: A Report on the Australian Dairy Industry_ (Voiceless 2015).
"The death of nonhumans not only violates specific nonhuman animals, it is a violation of the humane desire for the good and the just. The death of nonhumans is always on hand for animal rights activists. _This is traumatic knowledge_ " (Adams 2004, my emphasis).
These studies are produced because of the perceived economic waste of late-stage calves.
The Code advises against transportation and slaughter for late-stage pregnancy. However, in the event that late-stage slaughter occurs the following rules apply: "Foetuses should not be removed from the uterus sooner than 5 minutes after the maternal neck or chest cut, to ensure absence of consciousness" (OIE World Organization for Animal Health 2017). Otherwise they advise leaving the fetus in the body until dead.
Gabriel Meurer's (2007) undercover video footage of the slaughter of pregnant cows is available on YouTube.
The concept of "becoming animal" had a significant impact in the visual arts (see Thompson 2005). As an example of the anthropocentrism I find problematic, I quote the overview for the book, which states: "In an age when scientists say they can no longer specify the exact difference between human and animal, living and dead, many contemporary artists have chosen to use animals in their work—as the ultimate 'other,' _as metaphor, as reflection_ " (The MIT Press 2018, my emphasis).
These important conversions around the interpretations of "becoming animal" and the post-human are out of the scope of this chapter; for an example of the issues raised, see Iveson (2013).
The theoretical debates around the term "empathy" are complex; however, it is important that Stein's intersubjective empathy be distinguished from the instinctual or automatic mirroring as considered by proponents of mirror-neuron empathy (see Rizzolatti et al. 1992 and Gallese et al. 1996).
See Dean for a discussion of empathic indifference as an act of cruelty and a "violent erasure" (2004, 104).
Slink is also made from lambskin sourced from the bodies of newly born and deceased lambs, although this is less desirable for vellum due to size.
Stephanie Ernst provides this textual account from Meurer's video of the slaughter of a pregnant cow (2013).
I write personal notes while working in my studio. Short extracts are included in this chapter.
For a discussion of these works in terms of absence, see mowson (2015).
This is indicated by the emergence of new terms to describe the trauma affecting animal advocates. Psychologist Melanie Joy uses the term "carnism-induced trauma": "it is our assertion that carnism, like other atrocities, causes mass traumatization of not only the primary victims (farmed animals) but of secondary victims (humans) as well. For clarity and accuracy, we describe the traumatization resulting from carnism as carnism-induced trauma" (2012). Recently, the term "Vystopia" has been coined by psychologist Clare Mann: "1. Existential crisis experienced by vegans, arising out of an awareness of the trance-like collusion with a dystopian world. 2. Awareness of the greed, ubiquitous animal exploitation, and speciesism in a modern dystopia" (2017).
Ben Grossblatt refers to "any depiction of animals that act as though they wish to be consumed" as "suicide food" (2011).
The issue of trauma and language and the failures of language to communicate that are amplified by trauma are beyond the scope of this chapter. For accounts on testimony, see Derrida (2000), Caruth (1995), LaCapra (2001), and Trezise (2013).
Special thanks go to Richard Twine for articulating the political agency and positive disruptive role of the vegan killjoy (2014).
For example, my series _fleshlumps_ created hunger for one carnist friend and revulsion in a vegan colleague, neither of which responses were my intention.
This has been widely reported and monitored by government agencies and industry bodies (see United States Environmental Protection Agency 2001; Dairy Australia 2008; Dairy Industry Profile Agriculture Victoria 2014; and other state-based departments responsible for environment and primary industries in Australia).
I use this term in line with Cora Diamond's concept of nonhuman animals as fellow creatures. Animals, Diamond contends, are our "fellows in mortality"; we share fear and pain; birth and death; social and emotional bonds with animals (Diamond 1978).
"While calf rearing practices are basically the same for conventional or robotic milking, removal of extra teats and disbudding are more important for calves that will be milked automatically because extra teats can slow down robotic cup attachment" (Kerrisk 2015).
The RSPCA recommends this procedure is done prior to three months old and with anesthetic (2009). In the United Kingdom, a calf is protected once they reach three months old (Department for Environment, Food and Rural Affairs, 2003).
References
Adams, C. J. (2004), "Home Demos and Traumatic Knowledge," _SATYA_. Available online: <http://www.satyamag.com/mar04/adams.html> (accessed August 1, 2014).
Agriculture Victoria (2014), "Dairy Industry Profile," Available online: <http://agriculture.vic.gov.au/agriculture/dairy> (accessed February 1, 2017).
Australian Veterinary Association (2006), _Policy 85: Fetal Bovine Serum Collection_. Available online: <http://www.ava.com.au/policy/85-fetal-bovine-serum-collection> (accessed June 1, 2012).
Bryant, T. L. (2006), "Trauma, Law, and Advocacy for Animals," _Journal of Animal Law and Ethics_ , 1 (63): 63–138.
Butler, J. (2014), _White Lies, A Viva! Health Report_ , J. Gellatley (ed.), Viva! Health: Bristol.
Caruth, C. (ed.) (1995), _Trauma: Explorations in Memory_ , Baltimore and London: The Johns Hopkins University Press.
Dairy Australia (2008), "Effluent and Manure Management Database for the Australian Dairy Industry." Dairy Australia. Available online: <http://www.dairyaustralia.com.au/Environment-and-resources/Soils-nutrients-and-effluent.aspx> (accessed February 1, 2017).
Dead Unborn Calves (2007) [Video]. Dir. G. Meurer. Available online: <https://www.youtube.com/watch?v=Zytvvi4Q-aw> (accessed January 1, 2012).
Dean, C. J. (2004), _The Fragility of Empathy after the Holocaust_ , Ithaca; London: Cornell University Press.
Department for Environment, Food and Rural Affairs (2003), _Code of Recommendations for the Welfare of Livestock: Cattle_ , PB7949. United Kingdom.
Derrida, J. (2000), " 'A Self-Unsealing Poetic Text': Poetics and Politics of Witnessing," in M. P. Clark (ed.), R. Bowlby (trans.), _Revenge of the Aesthetic: The Place of Literature in Theory Today_ , 180–207, Berkeley: University of California Press.
Diamond, C. (1978), "Eating Meat and Eating People," _Philosophy_ 53 (206): 465–479.
Elliot, T. S. (1963), "The Love Song of J. Alfred Prufrock," _Collected Poems 1909–1962_ , London: Faber and Faber.
Ernst, S. (2013), "Pregnancy at Slaughter: What Happens to the Calves?" Available online: <http://www.all-creatures.org/articles/ar-pregnancy.html> (accessed June 1, 2013).
Fayemi, P. O. and Muchenje, V. (2013), "Maternal Slaughter at Abattoirs: History, Causes, Cases and the Meat Industry," _SpringerPlus_ 2 (125): 1–7.
Gallese, V., Fadiga, L., Fogassi, L., and Rizzolatti, G. (1996), "Action Recognition in the Premotor Cortex," _Brain_ 119 (2): 593–609.
Gamroth, M., Downing, T., and Peters Ruddell, A. (2000), _Flame-clipping Udders on Dairy Cows_ , EM 8755, Oregon State University Extension Service.
Gellatley, J. (ed.) (2014), _The Dark Side of Dairy, A Viva! Report_ , Viva! Health: Bristol.
Grossblatt, B. (2011), "Five Years: An Announcement," _suicidefood_. Available online: suicidefood.blogspot.com (accessed June 1, 2016).
Gruen, L. (2015), _Entangled Empathy_ , New York: Lantern Books.
Iveson, R. (2013), "Deeply Ecological Deleuze and Guattari: Humanism's Becoming-Animal," _Humanimalia: A Journal of Human/Animal Interface Studies_ 4 (2): 20–40.
Jochems, C. E., Van Der Valk, J. B., Stafleu, F. R. and Baumans, V. (2002), "The Use of Fetal Bovine Serum: Ethical or Scientific Problem?" _Alternatives to Laboratory Animals_ 30: 219–227.
Jones, G. M. (2009), _Guidelines to Culling Cows with Mastitis_ , Virginia Cooperative Extension Publications, Publication no. 404-204: 1–3. Available online: <http://pubs.ext.vt.edu/404/404-204/404-204.html> (accessed January 1, 2016).
Jones, P. (2007), _Aftershock: Confronting Trauma in a Violent World, a Guide for Activists and Their Allies_ , New York: Lantern Books.
Joy, M. (2012), "Carnism-Induced Trauma: How to Avoid Burning Out as an Animal Rights Activist," republished in All-Creatures. Available online: <http://www.all-creatures.org/articles/act-ab-carnism-induced-trauma.html> (accessed June 1, 2016).
Kerrisk, K. (2015), "Raising Cows for AMS," _Future Dairy_. Available online: <http://futuredairy.com.au/raising-cows-for-ams/> (accessed June 1, 2016).
LaCapra, D. (2001), _Writing History, Writing Trauma_ , Baltimore: Johns Hopkins University Press.
Legge, J. (1969), "Learning to Be a Dutiful Carnivore." Available online: <http://www.all-creatures.org/poetry/ar-learning.html> (accessed June 1, 2014).
Lipps, T. (1965), "Empathy and Aesthetic Pleasure," in K. Aschenbrenner (ed.), _Aesthetic Theories: Studies in the Philosophy of Art_ , 403–412, Englewood Cliffs: Prentice-Hall.
Mann, C. (2017), "Vystopia." Available online: <http://vystopia.com/index.html> (accessed December 1, 2017).
Mellor, D. J. (2003), "Guidelines for the Humane Slaughter of the Fetuses of Pregnant Ruminants," _Surveillance_ 30 (3): 26–28.
Mowson, l. (2015), "beautiful little dead things," in K. Eddy, L. A. Watson, and J. O'Rourke (eds.), _The Art of the Animal: Fourteen Women Artists Explore the Sexual Politics of Meat_ , 107–116, Brooklyn: Lantern Books.
OIE World Organisation for Animal Health (2017), _Terrestrial Animal Health Code_. Available online: <http://www.oie.int/international-standard-setting/terrestrial-code/access-online/> (accessed June 1, 2017).
Pachirat, T. (2011), _Every Twelve Seconds: Industrialised Slaughter and the Politics of Sight_ , New Haven, CT: Yale University Press.
Probyn-Rapsey, F. (2014), Review Article: "Multispecies Mourning: Thom van Dooren's Flight Ways," A _nimal Studies Journal_ 3 (2): 4–16. Available online: <http://ro.uow.edu.au/asj/vol3/iss2/3> (accessed June 1, 2016).
Rizzolatti, G., Di Pellegrino, G., Fadiga, L., Fogassi, L., and Gallese, V. (1992), "Understanding Motor Events: A Neurophysical Study," _Experimental Brain Research_ 91: 176–180.
RSPCA (2009), "Invasive Farm Animal Husbandry Procedures," _Position Paper B4_. Available online: <http://kb.rspca.org.au/files/2/> (accessed June 1, 2016).
Singleton, G. H., and Dobson, H. (1995), "A Survey of the Reasons for Culling Pregnant Cows," _The Veterinary Record_ 136 (7): 162–165.
Stein, E. ([1916] 1989), _On the Problem of Empathy_ , W. Stein (trans.), Washington: ICS Publications.
The MIT Press (2018), "Becoming Animal: Overview." Available online: <https://mitpress.mit.edu/books/becoming-animal> (accessed June 1, 2016).
Thompson, N. (ed.) (2005), _Becoming Animal: Contemporary Art in the Animal Kingdom_ , Cambridge; London: MIT Press.
Trezise, T. (2013), _Witnessing Witnessing: On the Reception of Holocaust Survivor Testimony_ , New York: Fordham University Press.
Twine, R. (2014), "Vegan Killjoys at the Table—Contesting Happiness and Negotiating Relationships with Food Practices," _Societies_ 4 (4): 623–639.
United States Environmental Protection Agency (2001), "Notes from Underground," _EPA Region 9 Water and Underground Pollution Newsletter_. Available online: <https://nepis.epa.gov/>. Department of Primary Industries (accessed June 1, 2016).
Valent, P. (2002), "Diagnosis and Treatment of Helper Stresses, Traumas, and Illnesses," in C. R. Figley (ed.), _Treating Compassion Fatigue_ , 1–17, New York: Taylor and Francis.
Van Der Valk, J., Mellor, D., Brands, R., Fischer, R., Gruber, F., Gstraunthaler, G., Hellebrekers, L., Hyllner, J., Jonker, F. H., Prieto, P., Thalen, M., and Baumans, V. (2004), "The Humane Collection of Fetal Bovine Serum and Possibilities for Serum-Free Cell and Tissue Culture," Workshop Report _Toxicology in Vitro_ 18, 1–12.
Vischer, R. ([1874] 1994), "On the Optical Sense of Form: A Contribution to Aesthetics 1873," in H. F. Mallgrave and E. Ikonomou (eds.), _Empathy, Form, and Space: Problems in German_ Aesthetics, _1873–1893_ , 89–124 Texts & Documents. Santa Monica: University of Chicago Press.
Viva! (2014), "Throwaway Lives: Stop the Massacre of Pregnant Animals," _Briefing Notes_. Available online: <http://www.viva.org.uk/what-we-do/pregnant-cow-massacre/briefing-notes> (accessed 2014).
Voiceless (2015), _The Life of the Dairy Cow: A Report on the Australian Dairy Industry_ , Voiceless, The Animal Protection Institute.
Chapter 3
THERE'S SOMETHING ABOUT THE BLOOD... : TACTICS OF EVASION WITHIN NARRATIVES OF VIOLENCE
Nekeisha Alayna Alexis
Ours in such circumstances, are kindly cared for, and are never considered a burden; our laws are, generally speaking, humane and faithfully administered. We have enactments which not only protect their lives, but which compel their owners to be moderate in working them, and to ensure them proper care as regards their food.
—Eastman (1852, 70–71)
They were happy chickens. They had the run of the yard, and they took advantage of it. They grazed on the lawn and lolled about in the breeze under the treehouse. When we worked in the garden, our chickens were right beside us, companions raking the earth. We treated those birds right...
—Roth (2016, 25)
Narratives of violence about conscientiously consuming ethically raised farmed animals are perplexing. On one hand, those who advocate humane farming and do-it-yourself slaughter testify to a host of positive outcomes such as cultivating reverential eating habits, increasing compassion toward other animals, and restoring human relationships in a broken agricultural system. Yet proponents of knowing and killing your dinner as "a strong corrective to dislocation and alienation in our industrial food system" (Kaminer 2010, MB1) often leave unexamined the substantial contradictions inherent within this action. The unwillingness to grapple with the tensions in this ritual are especially curious since the intent of slitting a sow's throat or dismembering a hen's body is to unflinchingly face the bloodshed that converts an individual into food. The oversight is also strange since this form of conscious omnivorism has gained visibility amid and in response to increased mainstream and liberationist vegan agitation against using other animals as food.
Interestingly, this practice of redirecting questions of power and violence toward other tangential considerations is not unique to do-it-yourself slaughter writings. On the contrary, the effort to reframe the grotesque as benign is also present in at least one other narrative of violence: that of plantation romances. In these nineteenth-century works of fiction, authors used various "polemical strategies" to reassert the legitimacy of slavery in the face of abolitionist pressures (Railton n.d.[a]). Although plantation romances and conscious omnivore narratives are dissimilar in significant ways, these seemingly disparate genres rely on common storytelling devices to make their case. In this chapter, I identify their overlapping tactics of evasion and interrogate how they work to make palatable again destabilized systems of domination.
To begin, I review a handful of do-it-yourself slaughter reflections and humane farming accounts with a focus on short articles published for popular audiences. Here, I describe some of the techniques that divert attention from the discrepancies within humane agriculture and agribusiness. I then outline how these tactics function in two plantation romances, specifically the anti-Tom novels _Aunt Phyllis's Cabin; or, Southern Life As It Is_ (1852) and _The Planter's Northern Bride_ (1854). In examining these texts together, I make evident some of the ill-logics dominant groups employ to justify subjugating other persons. By extension, I challenge the idea of conscious omnivorism as an antidote to exploitative relationships with other animals and highlight the insidious nature of its arguments.
Before proceeding, I want to clarify my interest is not in comparing the conditions facing humanely farmed animals in the present with those slaves endured throughout the sixteenth and seventeenth centuries in the United States. Nor am I suggesting that these, or other conscious omnivores, are drawing on inspiration from plantation romances or advocating for the enslavement of black people. Instead, I am fascinated by the mechanics of simultaneously writing _and not writing about_ power within acts of interpersonal and systemic violence, especially when the validity of those behaviors is upset. Reading humane farming accounts and do-it-yourself slaughter reflections alongside plantation romances is one way I seek to untangle and understand this dynamic.
The narrative terrain: Liberationist veganism and conscious omnivorism
In recent years, a narrative contest has emerged between vegans and conscious omnivores as both movements respond to the crises caused by industrial farming. In general, vegans criticize factory farming for its deplorable treatment of other animals and its devastating effects on the environment and human health, and, at minimum, choose a plant-based diet to lessen those conditions. However, a particular wing I refer to as liberationist vegans also see these calamities as resulting from the prevailing views that humans are superior to and separate from other animals; that other animals are destined or designed for human use; and that the legal, economic, political, and social constructs emerge from and perpetuate these perspectives. By refusing to eat other animals, advocating for plant-based diets, and working to end factory farming among other activism, liberationist vegans resist a larger paradigm that reduces other animals to human instruments, denies them equitable ethical consideration, and provides license to kill them. For liberationists, an overarching goal is dismantling the confused categories of "human" and "animal" such that other animals can, as much as possible, be self-determining individuals in and for their communities, and people's use and abuse of other creatures is no longer normalized.
As mainstream and liberationist vegans have exposed gratuitous violence against animals and workers, and ecological irresponsibility across major flesh-food industries, they have also troubled the landscape around animal agriculture and agribusiness. Undercover investigations have led to slaughterhouse closings and legislation against some of the most egregious farming techniques. Meanwhile, vegan campaigns have contributed to a rise in plant-based alternatives and eating (Strom 2017), reduced milk sales resulting in billions of lost dollars (Yu+ 2017), and a decade-long dip in beef and other meat consumption. At the time of writing, 6 percent of US consumers identify as vegan—a 5 percent gain in that foodway in only three years (GlobalData 2017). Additionally, leading meat producers like Tyson Foods and Maple Leaf Foods have begun investing in plant-based companies; ninety-year-old Elmhurst Dairy has switched to an all plant-based production, and there are more reports of small-scale animal farms converting to vegetable operations and sanctuaries.
Although meat production in the United States is bouncing back (Sawyer 2016), the case against flesh-foods remains strong. The World Health Organization's report on the potential carcinogenicity of processed meats (Bouvard et al. 2015) and UN reports that reduced meat consumption can stave off climate change (IPCC 2015) have challenged the industry. Documentaries like _Cowspiracy_ and _What the Health?_ and the film _Okja_ are also popularizing plant-based eating. Although the dent made by animal advocates is tiny compared to the billions of cows, sows, hens, and others still exploited and killed annually in the United States alone, debates about the validity and viability of animal agriculture are more commonplace. It is in this context of actual and perceived upset, when "the social norm of meat-eating seems to be losing its rigidity" (Gutjahr 2013, 380), that humane farming and do-it-yourself slaughter have gained traction.
Unlike most consumers, conscious omnivores see farmed animals as unique individuals with distinct personalities, desires, and needs, and condemn standard flesh-food production for its abuses. They also "question the normality of the consumption, or high consumption of meat" and criticize other meat, egg, and dairy eaters for ignoring the consequences of current food practices (Gutjahr 2013, 381). Essential to their approach is acknowledging that living, thinking, feeling animals die to accommodate their diet and moderating their intake in light of that awareness. Adherents insist on compassionate treatment of animals from birth through death, including appropriate living conditions and careful slaughter, and either provide those things for their animals or patronize farmers who do. For conscious omnivores, the problems with our disastrous system lie not in eating other animals, their status as property, nor the belief that other animals exist for us in some way, but in the _how_ of animals becoming edible. Animal agriculture and agribusiness are legitimate, _so long as they are done correctly_.
In _The Ethical Meat Handbook_ , butcher, homesteader, and chef Meredith Leigh articulates four principles of proper killing and eating, including "the animal enjoyed a good life... was afforded a good death... is butchered properly... is cooked or preserved properly" (Leigh 2015, 1). For Joel Salatin of Polyface Farms, ethical flesh-food involves letting his chickens, cows, and pigs live in a free-range, low-tech, complementary, pastoral system (Wirzba 2007, 9). While some conscious omnivores are content to purchase items produced with these standards, others take the extra step of personally killing an animal. For this sub-movement, do-it-yourself slaughter is not only advisable; it is a crucial, if not necessary, act of individual transformation and resistance to the dominant model. Yet the idea that bleeding rightly raised animals with our own hands creates more honest flesh-food eating excludes a major consideration: the matter of power.
Core to liberationist vegan objections to industrial and humane farms alike is the use of power against vulnerable subjects who are predestined for legitimized subjugation and premeditated violence. In his critique of ethical meat, Justin Van Kleeck recalls that:
What humans have done over thousands of years is create a situation, a system in which domesticated animals are victims by design, from birth... humans _always_ have the power, along with free reign to enact violence (of all kinds) on innocent bodies. The indelible reality of this power dynamic, which results in the killing of non-consenting individuals, also belies any notion of "ethical meat." (2017)
Animal agriculture and agribusiness, including farms with the least cruelty, depend on repressive measures. They require reproductive tyranny such as control over sexual partnerships; forced mating and insemination; extensive monitoring of fertility; and restraints against childrearing, all of which disproportionately exploits female bodies, especially mothers. Many humane farmers also employ the same techniques as industrial operations, from castration and tail docking to "grinding up male chickens at birth, using animals who have been selectively bred into shapes which cause disease, suffering and early death; forced and repeated pregnancies; separating family members for profit; and killing the animals in the exact same slaughterhouses and identically 'inhumane' conditions" (Stanescu 2013, 103).
In some humane flesh-food operations, farmers manage their soil with blood, bone, or feather meal, and fish emulsion from industrially raised animals killed in conventional slaughterhouses (Veganic Agriculture Network 2008). These practices undermine the idea of happy flesh-foods.
In addition to these dissonant practices, the conceptual framework behind ethical meat is also flawed. How does one love an individual while purposely breeding her for premature annihilation? How does one appreciate the intrinsic value of another being while reducing her to consumable and sellable parts? What does it mean to honor someone while denying her desire to live? In this discourse, ideas like respect are "removed from the context of human society" and "adapted to the hierarchical human-animal relationship" (Gutjahr 2013, 382). For this reason, liberationist vegans attend to the extreme violence and suffering in animal agriculture _and_ to the everyday force needed to harmonize irreconcilable interests between farmers and the farmed. Conscious omnivore storytelling minimizes the latter concern.
Tactics of evasion in conscious omnivore storytelling
Intimate, lethal violence against other animals is an act of power within a system of power. Yet in a curious twist, conscious omnivore stories make power immaterial. This erasure takes place through a variety of literary and interpretive measures that reimagine bloodshed including emphasizing affect, selective comparing and contrasting, representing victims as partners, and reframing coercion and domination.
Emphasizing affect
I look at the blood streaming down the corrugated metal and soaking into the sawdust on the ground. _The life is in the blood._ Then I look up at Montgomery.
"How are you doing, Mav?" he asks. I grimace...
"It's disturbing"
"It's supposed to be," he says. "We're not supposed to take a life and then say, Well whatever." (Mavrich 2013, 58)
On the surface, conscious omnivore storytelling is about flesh-food eaters' thoughtful, unwavering encounters with the farmed animals they consume. However, a closer read reveals these animals to be vehicles for justifying human supremacy. One tactic that hides this characteristic is preoccupation with the killer's disposition. By emphasizing affect, humane farming accounts and do-it-yourself slaughter reflections redirect questions away from the appropriateness of overpowering a vulnerable creature for profit or preference toward the appropriate feelings killers should have about such overpowering.
For example, early in _Raising Chickens for Meat_ , Gwen Roland distinguishes herself as a "chicken lover" unlike those who "eat store-bought chicken" (2009, 73). Yet she does not address how she reconciles her love with choosing to buy hens who are "Genetically programmed for less than a two-month life span" or killing the hen who affectionately sat on her lap (Roland 2009, 74, 78). Similarly, in her account of beheading a humanely raised Bourbon Red turkey, journalist Ariel Kaminer admits being "Scared that I would fail—that at the moment of truth I would hesitate, and thereby hurt the bird, and scared that I would succeed and end up with blood on my hands, literally and figuratively" (2010). Yet her fears about causing harm do not prompt a change of heart, despite having a host of ethically produced, plant-based foods at her disposal.
This fixation on the killer's experience functions as a "moral catharsis" (Gutjahr 2013, 382) with the visceral response to bloodshed serving as absolution. It also arbitrarily positions conscious omnivores as exceptional killers without considering how industrial laborers feel about their actions. As a tactic of evasion, emphasizing affect also masks how conscious omnivores perpetuate the dominant human–animal binary. The result is a circular ill-logic in which killers are allowed or encouraged to kill so long as they are troubled by their killing.
Selective comparing and contrasting
In a commercial operation, Ramona Huff says, an old cow like Frances already would have been crammed in a trailer, slaughtered, and turned into a hamburger. "That's not the deal I make with my cows." (Sinclair 2010)
Another strategy for avoiding issues of power in conscious omnivore storytelling is contrasting "compassionate" bloodshed with egregious violence. This tactic of evasion hinges also on overlooking the repressive techniques within humane operations and avoiding comparisons with more liberated spaces. For example, Huff speaks highly about letting sixteen-year-old Frances live the rest of her days, as compared to factory farms that slaughter young cows for cheap fast food. Interviewer Melissa Scott Sinclair also situates Huff between sentimental pet lovers and partakers of "shrink-wrapped steaks." The animals' "idyllic existence" and Huff's decision to spare Frances, Banana Puddin' the sow, and Pinky the "friendly as a dog" cow give the appearance that something extraordinary is taking place on the farm (Sinclair 2010). However, other elements of the story suggest otherwise.
Sinclair notes that Frances had ten calves, but does not disclose whether the cow became pregnant through natural intercourse or through a forced breeding program based on Huff's schedule and customer demands. Neither Huff nor Sinclair mention whether Frances raised all her children or if Huff stole, sold, and slaughtered them, nor do they discuss whether Frances' longevity might have as much to do with her productivity, and thus her profitability, as with Huff's "affection" (Sinclair 2010). Perhaps most glaringly, the article does not investigate Huff's rationale for refusing to kill three animals while sentencing others of their kind to die. Sinclair sidesteps this tension with the first tactic of evasion by describing Huff as "not a softie" who "does, however, get attached" (2010).
By comparing humane farming and do-it-yourself slaughter to the worst, most obvious offenders, these narratives make conscious onnivorism seem like a radical alternative to the standard system. Yet, there are other methods of agriculture and agribusiness that meet the movement's ethical concerns— _and_ break with dominant ideologies about humans and other animals. Small, organic permaculture farms where animals live until they die naturally and local, organic, veganic farms that forgo using other animals are more merciful than farms predicated on killing and premature death. Selective comparing and contrasting not only masks important similarities between conventional and humane endeavors; this strategy also confuses animals living relatively unrestricted lives with animals having the freedom to exist for themselves and their communities.
Representing victims as partners
Years later, when I designed a restraint chute for holding cattle for slaughter, I was amazed that the animals would stand still and seldom resist the chute. I found that I could just ease their head and body into position by adjusting the chute... It was my job to hold the animal gently while the rabbi performed the final deed. (Grandin 1999, 161)
Huff's statement about making a deal with Frances hints at a third tactic of evasion, namely portraying animals as agreeable participants in their subjugation and demise. Temple Grandin's observation about the cows' behavior in the chute suggests submission and a willingness to die. However, what has actually transpired is that people have coaxed each cow from her home, taken her to a place she did not choose, led her into a space from which she cannot escape, and restrained her until she meets a violent end she did not anticipate. Roland's statement that her hens "were ready to lay it down by the time we picked a slaughter date" is equally deceptive (2009, 74). Not only does Roland admit that the birds were healthier than those raised in a conventional system; she clearly has total control over their fates (74).
Another method of representing victims as partners occurs when death-dealers speak _for_ farmed animals. In "Would You Kill This Chicken with Your Bare Hands?," Brett Mavrich recalls his encounter with a rooster as he and other men dispatch several hens. In his words, the rooster "bebops" onto the scene, "freezes," then "saunters off as if to say, 'I'm going to pretend I didn't see that'" (2013, 58). Meanwhile, when Kaminer contacts the "next of kin" for advice on cooking her turkey, farmer Hart Perry responds, "'We heritage Bourbon reds are very tasty... and require no seasoning since that would interfere with our inherent deliciousness'" (2010, MB1). These disturbing interpretations about violence toward farmed animals also communicate distressing messages about gendered violence more generally. Mavrich picturing the rooster as a casual passer-by during the grizzly massacre of hens and Perry bizarrely portraying himself as one of the brood while dispensing advice how to cook one of their eviscerated carcasses each makes light of the culture of brutality against female-identified persons.
What appear to be innocuous analogies between killer and cock, farmer and dead hens, reaffirm the patriarchal nature of flesh-food production, including "the end justifies the means, that the objectification of other beings is a necessary part of life, and that violence can and should be masked" (Adams 2002, 24), even when storytellers are boldfaced about their executions. Furthermore, portraits of farmed animals tacitly agreeing to die and colluding with their killers obfuscate the sinister reality that humane farms and do-it-yourself slaughter are not sites of mutual exchange. Cows, sows, and other predominantly female animals are not sacrificing themselves to nourish flesh-food eaters in a cooperative arrangement. What happens to the individuals in Grandin's chute is what happens to all animals destined for death: they are overpowered and their lives taken away, albeit under less harsh conditions. Conscious omnivorism not only supports these violations; it provides a positive framework for their continuance.
Reframing coercion and domination
Everything at the farm, from Montgomery and me to the chicken to the land, has a Creator. And because of this, I hold no ultimate mastery over the bird I have just killed, because it wasn't mine to begin with. The hen was a gift. (Mavrich 2013, 58)
While the third tactic of evasion recreates the victim as a partner, reframing coercion and domination rehabilitates the killer by dispossessing him of his power. Even after cutting two hen's throats, a process he recounts in detail, Mavrich still concludes that he does not rule over the birds. He might have taken "its life," but the responsibility lies with a higher being (2013, 58). This perspective fits a type of Christian theology that sees creation as "an altar on which creatures are offered to each other as an expression of the Creator's self-care and provision for life" (Wirzba 2011, 112). However, it also appears in notions of a natural web of life in which all must die so all can live. The language of "gift" is instrumental here, masking the fact that some death is artificial and unnecessary. For, if animal flesh is God's or nature's offering, then slaughter is only gratitude, taking life is only receiving it, and refusing to kill and eat is sacrilege.
Another form of this fourth strategy is indiscriminately grouping the slaughter of farmed animals with other forms of killing and dying. In "What Does It Mean to Kill Humanely?," Bryan Welch explains, "I kill some of our food animals myself, or I haul them to a slaughterhouse. I sometimes help customers kill the animals they've purchased. Once in a while I put an injured animal out of its misery" (2011, 104). Although there are social, legal, and ethical distinctions between different forms of killing when people are involved, conscious omnivore storytelling categorizes distinct types of animal death as the same. Refusing to distinguish between and make moral judgments about euthanasia or accidental killing, and slaughtering a healthy farmed infant as a matter of preference, positions the latter as inevitable. Using a passive term like "death" instead of more accurate terms like "murder" or "execution" ignores the fact that humane farming and do-it-yourself slaughter are acts of coercive systemic power.
Conscious omnivore storytelling and plantation romances
At first glance, contemporary conscious omnivore storytelling and plantation romances have little to nothing in common. One genre comprises real testimonies of killing actual farmed animals. The other consists of false accounts about slavery. However, at least two factors invite inquiry into their overlapping tactics of evasion. One consideration is the similar function of humane farming accounts and do-it-yourself reflections within the "field of social conflict" (Gutjahr 2013, 381) between liberationist and other vegans, and the role of anti-Tom novels as "a kind of literary damage control" (MacKethan 2004) for pro-slavery advocates refuting abolitionists. Each type of writing serves as defensive literature seeking to reestablish the legitimacy of systemic violence amid intensified scrutiny and charges of cruelty. They are both attempts to regain moral ground for their violent hierarchies.
Plantation romances responded to antislavery agitation with "idealistic portrayals of the master class, embellished with silent slaves, usually in the background" (MacKethan). These stories became especially prevalent after Harriet Beecher Stowe published _Uncle Tom's Cabin_ (1852), selling 10,000 copies in its first week and 300,000 copies in its first year in the United States, and 1.5 million copies in one year in Great Britain (Harriet Beecher Stowe Center [a]). Stowe's two-volume narrative, which drew heavily on other abolitionist writings, dramatically advanced the antislavery cause and intensified public conversation about the institution. _Uncle Tom's Cabin_ sparked numerous favorable and critical book reviews, negative newspaper campaigns and letters to editors, and inspired nationwide theater performances by people on both sides of the issue. A host of memorabilia also flooded the marketplace, including ceramics, board games, wallpapers, song sheets, and other everyday merchandise. In short order, it rapidly touched every area of society and even fanned the flames leading to Civil War (1852). In the wake of the novel's impact, slavery advocates responded with their own writing flurry. By the time union and confederate soldiers began fighting less than a decade after Stowe's publication, they had rereleased or published approximately twenty-nine anti-Tom novels disputing her work (Harriet Beecher Stowe Center [b]).
In her analysis of plantation romances and abolitionist narratives, Lucinda MacKethan describes them as "symbiotic genres" (2004). While fugitive slave narratives nevertheless reflected and sustained Southern culture, plantation romances also drew upon abolitionist themes to make their arguments. Consequently, anti-Tom novels were often "much clearer in expressing the South's anxiety about power and order than in promoting the South's confidence in its 'peculiar institution'" (2004). This dialectic also characterizes the dynamic between conscious omnivore storytelling and vegan criticism. Although humane farming accounts and do-it-yourself slaughter reflections are forms of "carnistic backlash," it is "not despite vegan advocacy, but largely because of it that such defensiveness has made its way into public discourse" (Joy 2012). These new pro-meat arguments take seriously their opponents' concerns even as their assumptions and conclusions reflect the dominant, meat-eating culture's resistance to "truly embracing a vegan ethic" (2012). This attempt to embrace liberationist ethics, while refusing their prohibition against bloodshed, is part of conscious omnivorism's internal instability.
Another reason to explore the shared ill-logics of conscious omnivore storytelling and plantation romances are the ways in which animals and slaves are defined and excluded since the introduction of race as a social construct. As Syl Ko explains, "The domain of the 'human' or 'humanity'... is a _conceptual way to mark the province of European whiteness as the ideal way of being homo sapiens_. This means that the conceptions of 'humanity/human' and 'animality/animal' have been constructed along _racial_ lines" (2017, 23, Ko's italics). Furthermore, what distinguishes the ideal from other homo sapiens is the latter's presumed closeness to the colonial, European invention of _the_ animal, "with 'animals' here being a gross reduction of a vast plurality of species" (67). As the farthest away from the ideal human, animals are the most abject, and thus designated for disposal, based on their usefulness to people—and especially to _the_ human. By extension, "what condemns [Black people] to our inferior status... is not merely our racial category but _that_ our racial category is marked _the most_ by animality" (67). Although it is not possible in this space to fully articulate the mutually reinforcing relationship between blackness and animality, the historical and ongoing connections between these social constructs make it reasonable to cross-examine narratives that target members of these groups.
Shared tactics of evasion in plantation romances
The same tactics that appear in humane farming accounts and do-it-yourself slaughter reflections are present in at least two anti-Tom novels: Mary Henderson Eastman's _Aunt Phillis's Cabin; or Southern Life As It Is_ borrowed from and responded directly to Stowe and was the best-selling book in the genre at between 20,000 and 30,000 copies (Railton n.d.[b]). Meanwhile, Caroline Lee Hentz's _The Planter's Northern Bride_ took a more indirect approach, with a story of a slaveholder whose love interest with abolitionist leanings comes to appreciate plantation life. Her counter to "the dark and horrible pictures drawn of slavery and exhibited to a gazing world" (1854, iv) was republished several times in the nineteenth century.
Emphasizing affect
[Cousin Janet's] heart was full of love to all God's creatures; the servants came to her with their little ailings and grievances, and she had always a soothing remedy—some little specific for a bodily sickness, with a word of advice and kindness. (Eastman 1852, 28)
You do not speak more gently to your little sister than did [Emma Livingston] to her household slaves. I have seen her lavish the tenderest caresses on their little infants. I have seen her hang in anxious watchfulness over their sick-beds. I have seen her weep over their humble graves. (Hentz 1854, 131–132)
The tactic of emphasizing the masters' characters and their attachment to their slaves is widespread in anti-Tom novels. In _Aunt Phillis's Cabin_ , the planters of Exeter are loving and devout Christians who care for their slaves like members of an extended family, and patriarch Mr. Weston is a "southern gentleman" with "a kind and charitable heart" (1852, 27). Similarly, in an aside to her primary drama, Hentz describes the Livingstons as enamored with and attentive to the needs of their slaves. Meanwhile, protagonist and slaveholder Mr. Moreland declares that "next to our own kindred, we look upon our slaves as our best friends" (1852, 24). When characters in the narratives address cruelty in the South, they identify it as an anomaly committed by people who lack good Christian morals, or who are greedy, prone to drunkenness, and mean-spirited. In this way, the good-natured dispositions of the masters are signs of slavery's integrity.
One of the foremost problems with this argument is that it is demonstrably false. Slaveholders did not "make the life of servitude... as much as possible a life of comfort and enjoyment" (Hentz 1854, 82–83) but brutally did the opposite. Yet, even if this fanciful picture of master–slave relationships had any bearing in reality, it would not erase that the institution arose from colonialism and violent removal; systematic denial of language, culture, religion, and other social organization; and extreme restrictions on individual movement and community self-determination. The master's feelings and personality traits did not alter the fact that slaves were buyable, sellable, and inheritable property and legally, socially, and politically subject to their owners' personal and economic interests. This fixation on the emotions, intentions, and manner of those who administered slavery—on the _how_ of bondage—masked the multilayered consequences for those who remained vulnerable to various forms of physical, emotional, and psychological aggression. Here again, a circular ill-logic arises in which slaveholders can be slaveholders as long as they have admirable feelings about slaveholding.
Selective comparing and contrasting
Mrs. Brown's blood was up too, and she struck the poor girl in the face, and her big, hard hand was in an instant covered with blood, which spouted out from Ann's nose
"Well, Mrs. Brown, good evening," said Arthur. "I shall tell them at the South how you Northern people treat your white niggers." (Eastman 1852, 73–74)
"I've got to work for Mistress Grimby all this time... She's kept me on the go ever since the day broke, a scrubbing and scouring on all fours."
Moreland... sympathized, too, with Albert's wounded aristocracy, which had never bled so copiously before.
"My poor boy," said he, smiling at Albert's half-comic, half-rueful look, "you have not been used to such hard usage, I must acknowledge. It is well to have a taste of what the Northern bondwomen have to endure." (Hentz 1854, 90)
Anti-Tom novels also used selective comparing and contrasting with places they fashioned as more callous in order to present slavery as a suitable ethical option. They frequently compared plantation life with extreme images of deplorable labor conditions in the North, including indiscriminate violence toward Irish servants; destitute women workers; and free blacks experiencing greater hardship than they had while enslaved. Hentz also pitted a generous South against an un-Christian "native Africa" that practiced "slavery more galling," human sacrifices and cannibalism (1854, 83–84) to suggest slaves were worse off in their ancestral lands. Anti-Tom novels contrasted scenes of excessive violence and poverty with shackle-free slaves living in pleasant homes; worshipping and fellowshipping with their masters; and lazily dancing, singing, sleeping, and eating. As in conscious omnivore storytelling, these images obscured blatant and intrinsic domination between masters and slaves and foreclosed the idea of liberation elsewhere. However, this tactic did not eliminate the texts' ill-logics.
Hentz describes Mr. Moreland's devoted companion and slave Albert as "a young mulatto... handsome, golden-skinned youth" (1854, 14). In addition, Eastman's Aunt Phillis is "a tall, dignified, bright, mulatto woman" (1852, 102). Neither author clarifies whether Albert's and Phillis' racial identity resulted from consensual sexual relations—a possibility already complicated by the problem of unequal power and agency—or resulted from sexual violence. Other elements of the story also contradict the authors' assertions of peaceful coexistence. In a conversation with Mr. Weston, Aunt Phillis admits to sheltering a runaway slave in her exquisite cabin to which Mr. Weston responds with a gentle reprimand. The scene is intriguing as Eastman tries to balance assertions about Phillis' faithfulness and her master's extraordinary patience within a story of her betrayal and a slave escape. The attempted slave revolt in Hentz's story also interrupts representations of a tranquil South and inadvertently underscores turmoil within the system (MacKethan).
Representing victims as partners
My father has several times brought servants to New York, but they have never run away from him (Eastman 1852, 137).
"You know the people are all free at the North, Albert."
"Yes, master."
"And when you are there, they will very likely try to persuade you that you are free too, and tell you it is your duty to run away from me"
they couldn't come round this boy with that story; I've hearn it often enough already; I ain't afraid of anything they can say and do, to get me away from you. (Hentz 1854, 14–15)
Like conscious omnivore storytelling, plantation romances narrate the worldviews of their victims through the lens of those who wield ultimate, lethal power. In anti-Tom novels, pro-slavery advocates depicted obedient slaves, making them partners in their condition. One way of accomplishing this task was extensive dialogues in which slaves refused opportunities to become free, despite enticements by abolitionists and masters offering to let them go. Another method was to tell stories of slaves who escaped or received their freedom only to return after run-ins with unscrupulous abolitionists and malicious Northern employers. Like Grandin's chute, the victim's refusal to escape in these stories serves as evidence of approval and submission. Moreover, when authors acknowledge the victim's resistance to their condition, they claim it is rare and misguided, which reaffirms the rightness of the institution.
As with Mavrich's rooster and Perry's Bourbon Red turkey, authors of plantation romances co-opted slaves' voices in service of institutional violence and the ideologies that upheld it. Caricatures of cooperative servants detracted from the historical, legal, political, and social circumstances that made slavery possible and frustrated any real or imagined expressions of acceptance. Slaves came to the plantation through colonialism, kidnapping, and brutal voyages. They were akin to land, horses, and other property, and subject to both transfers of ownership and punishment. They endured patrols, pass systems, and laws that limited their associations and future possibilities. Plantations were not mutually beneficial communities or families, and slaves were not willing participants. Representing them as partners distorts these realities.
Reframing coercion and violence
Why, sir, do you mean to say, that the life of a slave is in the power of a master, and that he is not under the protection of our laws? (Eastman 1852, 136)
Were you to ask me if I justified the slave trade,—that traffic forced upon us, by that very British government which now taunts and upbraids us... I would answer No! but if you mean the involuntary slavery which surrounds me and my brethren of the South, I reply, I can justify it; we had no more to do with its existence than our own. We are not responsible for it, though we are for the duties it involves, the heaviest perhaps ever imposed upon man. (Hentz 1854, 82)
Plantation romances reframed the intrinsic coercion and domination of slavery by locating power and responsibility away from masters. Mr. Moreland blames the British for creating a situation he cannot control and for which he has a "duty" to continue for mercy's sake. Similarly, when Arthur Weston discusses slavery with an abolitionist-minded colleague, he cites the South's "humane" laws as the determining factor for using violence against slaves and suggests that the few strict laws that exist resulted from "meddling, and unprincipled" abolitionists agitating slaves against their masters (Eastman 1852, 136). Arguably, the most prevalent strategy of dispossessing masters of their obvious dominating power was advocates' insistence that slavery was "authorized by God, permitted by Jesus Christ, sanctioned by the apostles, maintained by good men of all ages" (Eastman 1852, 24). That there were slaves to begin with was not the planters' doing, but rather a natural, ordained, and unalterable order. Rejecting the practice amounted to a kind of cosmic disobedience.
Here again, language plays a significant role. Just as words like "gift," "sacrifice," and "death" do not relay the forced elements of humane farms and do-it-yourself slaughter, anti-Tom references to slaves as "servants" and "dependents" reframe domination. In _The Planter's Northern Bride,_ Hentz calls "the negroes of the South... the happiest _labouring class_ " (1854, vi, Hentz's italics). These and other similar terms give the impression that slavery was like other forms of employment with voluntary agreements about time and tasks. However, it was a site of daily subtle and explicit, systemic and personal subjugation, managed by the use and threat of violence and maintained by prevailing ideologies about slaves' perceived animality. While workers of the North could quit, only masters could determine when slaves were free. Even if plantation life was idyllic—and the historical record says otherwise—masters were not good stewards and slaves' lives were never fully their own.
Conclusion
As forms of defensive literature responding to threats against established and assumed systems of violence, plantation romances and conscious omnivore storytelling use a variety of tactics of evasion to paint subjugation with a benevolent, principled veneer. Noticing the overlaps in rationales for their distinct but intersecting forms of violence offers another avenue to think critically about humane farming accounts and do-it-yourself slaughter reflections, especially as they appear to offer a radically different relationship to those who have disproportionate power and uneven ethical standing. Inspecting their reasoning in light of anti-Tom novels makes conscious omnivorism's ill-logics visible. Moreover, and just as importantly, seeing how these ill-logics operate in pro-slavery and conscious omnivore arguments makes clear their danger for other overpowered groups.
Humane farming accounts and do-it-yourself slaughter reflections seem to be telling a new tale: that it is possible to use others against their own interests with compassion; to practice exploitation with love and respect; to deepen our capacity for care with experiments in unnecessary bloodshed; to honor someone's intrinsic value _and_ order their lives as walking dead. However, conscious omnivorism upholds
the mentality of domination and subjugation, of privilege and oppression... that causes us to turn someone into something, to reduce a life to a unit of production, to erase someone's being. It is the might-makes-right mentality, which makes us feel entitled to wield complete control over the lives and deaths of those with less power—just because we can. And to feel justified in our actions, because they're only... savages, women, animals. (Joy 2011)
The ill-logics within these stories have devastating implications—even on the most pleasant of farms—but they also have consequences beyond agricultural spaces. For this reason, those concerned with justice and liberation must recognize these tactics of evasion and confront them wherever they appear. In so doing, we can identify obstacles to appropriate care for every body, humans, and other animals alike.
Acknowledgments
Deep gratitude to Kelly Struthers Montford, Dinesh Wadiwel, and Austin Stonewall; and to Red Oak Community House in Elkhart, Indiana, and Piebird Farm Sanctuary/Vegan Farmstay in Nipissing, Ontario. Thanks also for the Race and Animals Summer Institute at Wesleyan University for creating a space to think together about some of these issues. In remembrance of Mocha and Cairo. In service to all our creaturely kin.
Notes
The term "vegan" is widely used to refer to a dietary choice versus its original meaning of someone who forgoes the use of nonhuman animal bodies and by-products in all areas of life. I use "liberationist vegan" to differentiate between those who adopt a plant-based diet as part of a larger commitment and set of practices toward ending individual and structural domination over other animals, and those who solely adopt a plant-based diet for ecological, health, and/or other non-animal-specific reasons. Although "ethical vegan" is the popular term to make this distinction, it is the case that eating for human health and/or the health of the planet are also forms of ethical eating. Therefore, "ethical vegan" is too vague a descriptor to distinguish it from a liberationist perspective.
The current food system also uses animal remains and waste in the production of vegetables, grains, and other plant-based foods. Growing interest in and development of veganic agriculture is one response to this conundrum.
References
Adams, C. J. (2002), _The Sexual Politics of Meat: A Feminist Vegetarian Critique_ , Tenth Anniversary Edition, New York: Continuum.
Bouvard, V., Loomis, D., Guyton, K. Z, Grosse, Y., El Ghissassi, F., Benbrahim-Tallaa, L., Guha, N., Mattock, H., and Straif, K. (2015), "Carcinogenicity of Consumption of Red and Processed Meat," _The Lancet_ 16 (16): 1599–1600.
Eastman, M. H. (1852), _Aunt Phillis's Cabin; or Southern Life as It Is_ , Philadelphia, Grambo & Co. Available online: <http://utc.iath.virginia.edu/proslav/eastmanhp.html> (accessed September 29, 2017).
Global Data (2017), "Top Trends in Prepared Foods 2017: Exploring Trends in Meat, Fish and Seafood; Pasta, Noodles and Rice; Prepared Meals; Savory Deli Food; Soup; and Meat Substitutes," June. Available online: <https://www.reportbuyer.com/product/4959853/top-trends-in-prepared-foods-2017-exploring-trends-in-meat-fish-and-seafood-pasta-noodles-and-rice-prepared-meals-savory-deli-food-soup-and-meat-substitutes.html> (accessed July 29, 2017).
Grandin, T. (1999), "Slaughtering Can Be Humane," in T. L. Roleff and J. A. Hurley (eds.), _The Rights of Animals_ , 159–162, San Diego: Greenhaven Press.
Gutjahr, J. (2013), "The Reintegration of Animals and Slaughter into Discourses of Meat Eating," in H. Röcklinsberg and P. Sandin (eds.), _The Ethics of Consumption_ , 379–384, Wageningen: Wageningen Academic Publishers.
Harriet Beecher Stowe Center (n.d.[a]), "Her Words Changed the World." Available online: <https://www.harrietbeecherstowecenter.org/harriet-beecher-stowe/her-global-impact> (accessed September 23, 2017).
Harriet Beecher Stowe Center (n.d.[b]), "Stowe's Global Impact." Available online: <https://www.harrietbeecherstowecenter.org/harriet-beecher-stowe/her-global-impact/>(accessed September 23, 2017).
Hentz, C. L. (1854), _The Planter's Northern Bride_. Philadelphia: T. D. Peterson. Available online: <http://utc.iath.virginia.edu/proslav/hentzhp.html> (accessed February 4, 2018).
IPCC (2015), _Meeting Report of the Intergovernmental Panel on Climate Change Expert Meeting on Climate Change, Food, and Agriculture_ , M. D. Mastrandrea, K. J. Mach, V. R. Barros, T. E. Bilir, D. J. Dokken, O. Edenhofer, C. B. Field, T. Hiraishi, S. Kadner, T. Krug, J. C. Minx, R. Pichs-Madruga, G.-K. Plattner, D. Qin, Y. Sokona, T. F. Stocker, M. Tignor (eds.), Geneva: World Meteorological Organization. Available online: <https://www.ipcc.ch/pdf/supporting-material/Food-EM_MeetingReport_FINAL.pdf> (accessed July 31, 2017).
Joy, M. (2011), "Carnism: Why Eating Animals Is a Social Justice Issue," _One Green Planet_ , 3 November. Available online: <http://www.onegreenplanet.org/lifestyle/carnism-why-eating-animals-is-a-social-justice-issue/>(accessed October 11, 2017).
Joy, M. (2012), "Understanding Neocarnism: How Vegan Advocates Can Appreciate and Respond to 'Happy Meat, Locavorism' , and 'Paelo Dieting', " _One Green Planet_ , July 29. Available online: <http://www.onegreenplanet.org/lifestyle/understanding-neocarnism/> (accessed February 19, 2018).
Kaminer, A. (2010), "The Main Course Had an Unhappy Face," _New York Times_ , November 19. Available online: <http://www.nytimes.com/2010/11/21/nyregion/21citycritic.html> (accessed August 27, 2017).
Leigh, M. (2015), _The Ethical Meat Handbook: Complete Home Butchery, Charcuterie and Cooking for the Conscious Omnivore_. Gabriola Island: New Society Publishers.
MacKethan, L. (2004), "Plantation Romances and Slave Narratives: Symbiotic Genres," _Southern Spaces_ , March 4. Available online: <https://southernspaces.org/2004/plantation-romances-and-slave-narratives-symbiotic-genres> (accessed October 12, 2017).
Mavrich, B. (2013), "Would You Kill This Chicken with Your Bare Hands?" _Christianity Today_ , November.
Railton, S. (n.d.[a]), "Anti Uncle Tom Novels." Available online: <http://utc.iath.virginia.edu/proslav/antitoms.html> (accessed March 1, 2018).
Railton, S. (n.d.[b]), "Aunt Phyllis's Cabin." Available online: <http://utc.iath.virginia.edu/proslav/eastmanhp.html> (accessed March 1, 2018).
Roland, G. (2009), "Raising Chickens for Meat," _Mother Earth News_ , June/July: 73–80.
Roth, B. (2016), "Butchering Beatitude," _The Mennonite_ , September.
Sawyer, W. (2016), "Chickens, Cows and Pigs... Oh My!," _Rabobank_ , August. Available online: <https://research.rabobank.com/far/en/sectors/animal-protein/chicken-cows-and-pigs-oh-my.html> (accessed September 20, 2017).
Sinclair, M. S. (2010), 'Facing Your Food," _Style Weekly_ , December 15. Available online: <https://www.styleweekly.com/richmond/facing-your-food/Content?oid=1441931> (accessed August 27, 2017).
Stanescu, V. (2013), "Why 'Loving' Animals Is Not Enough: A Response to Kathy Rudy, Locavorism, and the Marketing of 'Humane' Meat," _Journal of American Culture_ 36 (2): 100–110.
Strom, S. (2017), "Americans Ate 19% Less Beef from '05 to '14, Report Says," _New York Times_ , March 21. Available online: <https://www.nytimes.com/2017/03/21/dining/beef-consumption-emissions.html> (accessed July 29, 2017).
Van Kleeck, J. (2017), "Of Bullies and Butchers: Ethical Meat, Vegan Bullies and the Humane Myth," _Striving with Systems_ , February 19. Available online: <https://strivingwithsystems.com/2017/02/19/%EF%BB%BFof-bullies-and-butchers-ethical-meat-vegan-bullies-and-the-humane-myth/>(accessed September 20, 2017).
Veganic Agriculture Network (2008), "Introduction to Veganics," February 25, 2008. Available online: <http://www.goveganic.net/rubrique16.html> (accessed September 20, 2017).
Welch, B. (2011), "What Does It Mean to Kill Humanely?" _Mother Earth News_ , October/November: 103–105.
Wirzba, N. (2007), "Barnyard Dance," _Christian Century_ , January 23, 2007.
Wirzba, N. (2011), _Food and Faith: A Theology of Eating_ , Cambridge: Cambridge University Press.
Yu+, D. (2017), "US Dairy Milk Sales Expected to Decline until 2020, Mintel Report Shows," _Dairy Reporter_ , March 16. Available online: <http://www.dairyreporter.com/Markets/US-dairy-milk-sales-expected-to-decline-until-2020-report-shows> (accessed July 29, 2017).
Chapter 4
ERUPT THE SILENCE
Hayley Singer
Here is a woman. Her husband describes her as timid, of middling height, plain as a black shoe. She has, he thinks, a "passive personality" (Kang 2007, 3). She exhibits neither "freshness nor charm, or anything especially refined" and is "completely unremarkable in everyway" (2007). One morning, this woman stands in the dim light of her fridge, bare foot and silent as a ghost. And then she empties it. Gone is the beef for shabu-shabu. Gone is the belly of pork and the sides of black beef shin. Gone are the squid, the sliced eel, the frozen dumplings, the eggs, and the milk. Gone, all gone, into a black rubbish bag. Her husband is distressed: is she crazy? All night she has had dreams, painfully vivid visions, "A long bamboo stick strung with great blood-red gashes of meat, blood still dripping down" (12). Strange, horrible, uncanny nightmares that chart the ugly legacies of carnist violence. Soon, she won't be able to sleep for fear of more dreams. "Dreams of murder. Murderer or murdered... hazy distinctions, boundaries wearing thing" (28). Her husband thinks she is self-centered: "So you're saying that from now on, there'll be no meat in this house?" (13). He is yet to abuse her. Her family is worried. Vegetarianism is unnatural. Her father is ashamed. He is yet to abuse her.
The woman, the vegetarian, is not given space to tell her version of the story. Like so many female figures in literary history (think Bertha Rochester, that iconic mad woman in the attic; think Elizabeth Costello, whose transgressions of the generic conventions of the academic humanities leave her words to slide into a kind of obscurity), her story is taken from her. It is denied, censored, refused, put into quarantine. As novelist and essayist Porochista Khakpour writes, it is only through "something approaching a post-language state" (2016, 2) that is used to recount Yeong-hye's dreams can a reader come to know the horror that haunts this woman, the protagonist of Han Kang's novel _The Vegetarian_. But, her silence is not inactive. It is not docile. It shifts cultural dynamics; it creates gender, species, and genre trouble.
She is meat. She. And so speaking meat she lives the silence. Pitch-black. Silence.
Literatures that attend to the intersections of speciesism, racism, classism, sexism, able-bodism, and ageism listen for, and document, silences: their causes and their effects. They do so in order to address exclusion and inclusion, power and powerlessness, voice and voicelessness: who can speak, who is listened to, who listens, who is authorized to speak, and who takes for themselves the authority to speak?
In her essay "A Short History of Silence" (2017), Rebecca Solnit writes that silence, which is a tool of oppression and therefore different from quietude, still needs to be interrogated and annihilated. There is a world of difference, she writes, between quiet and silence. Quiet is something that might be sought after, while silence may be imposed: "Quiet is to noise as silence is to communication" (18). Solnit charts the ways silence precedes, supports, and results from violence. Her essay moves through a nuanced landscape in which different codes and kinds of silence—those forged through shame, politeness, fear, indifference, the legal status of powerlessness, ridicule, ostracism, and trauma—concrete into cultural habitats in which speaking up and calling attention to silence and violence are acts of empathy. She traces the lineage from second- to third-wave feminist literatures, and literary analysis, to understand the way women have turned to silence as (and turned silence into) a serious topic of concern. From Rachel Carson's _Silent Spring_ (1962) to Deborah Levy's _Diary of a Steak_ (1997) and Alexis Wright's _The Swan Book_ (2013), intersectional literatures have shown that liberation from silence is a storytelling process and a fundamental part of articulating the knots of violence in which all earth-bound critters are living and dying. Importantly, these texts also recognize that silence is a politically potent form of poetic expression.
Cartographies of silence have also been traced and tracked in critical ecological, feminist-animal, and vegan-feminist scholarship, including Carol J. Adams' germinal works _The Sexual Politics of Meat_ (1990) and _The Pornography of Meat_ (2003), Val Plumwood's deeply influential study _Feminism and the Mastery of Nature_ (1993), Lori Gruen's _Entangled Empathy: An Alternative Ethic for Our Relationships with Animals_ (2015), and studies like Susan Fraiman's 'Pussy Panic versus Liking Animals: Tracking Gender in Animal Studies' (2012). There are so many kinds of silence to contemplate in these texts: the silence of the "absent referent" (Adams 1990, 5–6); silences produced by Western philosophy's discourse of rationalism (Plumwood 1993); silences created by philosophical abstraction, individualism, and impartiality (Gruen 2015); and the bibliographic silences produced by overlooking the rich bodies of work written by women within the fields of critical ecological and animal studies (Fraiman).
In carnist systems of knowledge there is a strong desire for anti-carnist silence. Silence remains the persistent (enforced) condition of most animals in contemporary culture. As Elizabeth Costello (the protagonist of J. M. Coetzee's (2004) highly influential novel of the same name) notes, "Animals have only silence left with which to confront us" (70). Silence, in this context, might be understood as critiquing, condemning, bearing witness to, and acting as testimony to the experience of erasure that colonizes the lives and deaths of so many animals.
The thing that hurts is my. All those remnants. I don't know why. Sticks in the chest. That lump.
How to work with silence as a form of poetic expression? Can silence be used as a storytelling technique? As a writer, I wonder how I can conspire with silence to read it as a disruptive narrative tactic. Can it offer new forms of imagining, resisting, revolting, living, dying, and telling stories of the myriad lives and deaths that make up this damaged planet? What if silence is not docile but citational—pointing to something that is purposefully kept off the cultural scene? Can silence, as a citational practice, act as a form of resistance—one that teaches something about the characteristics of the stories given cultural primacy? Can silence help stories unfurl the ongoing destruction of carnism and its interconnected systems of violence?
For Rebecca Solnit, having a voice and being heard is part of living as "a human being with full membership" (24). But, what if a person does not want to be folded into the field of humanity? What if, as Carol J. Adams wonders, one is invested in exploring what it means for humans to recognize themselves more fully as "animal beings" (2006, 120)? And what if a person has more vegetal desires—desires to phytomorphize? What kinds of stories will they need to tell?
"A free person tells her own story," Rebecca Solnit writes (2017, 19). But I want to think about those who are not freed by this act. Those people who are rendered socially unintelligible, inaudible, dysfunctional, untrustworthy, and even indigestible because of the stories they need to tell. That is the story of Yeong-hye.
Originally published in South Korea as three novellas— _The Vegetarian, The Mongolian Mark,_ and _Flaming Trees_ — _The Vegetarian_ burrows into the social, cultural, and political fibers of carnist violence. As the novel opens, the reader is confronted with Yeong-hye as a young suburban woman who has had a sudden experience of disgust in relation to meat. She has had dreams, particularly visceral dreams of slit flesh, pools of blood, butchered bodies, screams, breathlessness, and darkness. These dreams have formed a council of images that haunt her; they are the specters of all the animals she has eaten in her life.
In her attempts to step away from carnist frameworks of thought and action, Yeong-hye renounces human and nonhuman animal characteristics. She feels her body transform into a vegetal being. She responds to light and shadow with phytomorphic desires, she feels roots grow from her hands and flowers emerge from her vulva. Coming to exist within root networks that link veins to vines, birthmarks to blooms, and blood to chlorophyll, Yeong-hye shrugs "off flesh like a snake shedding its skin" (170). Within the novel this botanical turn poses significant challenges to carnist and humanist identities. It allows Han Kang to complicate ideas of embodiment, communication, kinship, nourishment, life, death, and time.
Four juddering legs. The rope. The blood. Its dead eyes. I remember. I did scoop up a mouthful.
In an interview published in the online journal _Lit Hub_ (Patrick 2016), Han Kang says that _The Vegetarian_ questions the relentlessness of human violence and the (im)possibilities of innocence from this condition of violence. The drama of _The Vegetarian_ emerges as the novel traces the "undoing" of Yeong-hye, a woman who cannot be anything but the antithesis of the self that is demanded by carnism. At a family lunch, Yeong-hye refuses the family law that demands she eat meat.
My mother-in-law brought in dishes of stir-fried beef, sweet and sour pork, steamed chicken, and octopus noodles arranging them on the table in front of my wife.
"This whole vegetarian business stops right now," she said. "This one, and this, and this—hurry up and eat them. How could you have got into this wretched state when there's not a thing in the world you can't eat?" (Kang 2007, 36)
In this passage, and those that follow below, Yeong-hye lands the force of a disobedient vegan silence into a world where what is audible/intelligible is authored in the image of carnivorous humanity. "The children were staring wide-eyed at my wife. She turned her blank gaze on her family, as if she couldn't fathom the reason for all the sudden fuss" (Kang 36).
Yeong-hye's gaze is not so blank, it acts as a spectator of the spectral, she holds her eyes firmly on what, in the contemporary carnist moment, is occluded and occulted: the ghosts of animals turned into meat. Those ghosts are gathered up into Yeong-hye's silent stare and she brings them with her to the family table. Bringing occulted others to the table, being _cum panis_ with the ghosts of industrial slaughter, threatens the ordinary carnist subject with "invasion" or "contamination" by these dead others. Her silence becomes an expression, and an enactment, of trouble. The living infects the dead. Yeong-hye feels herself to be infected with the dead. She is full-up with death and can eat no more. As Yeong-hye's husband narrates, "This time, my mother-in-law picked up some sweet and sour pork with her chopsticks and thrust it right up in front of my wife's mouth, saying, 'Here. Come on, hurry up and eat.' Mouth closed, my wife stared at her mother as though entirely ignorant of the rules of etiquette" (37).
For Solnit making new stories means breaking silences, but as Han Kang shows in _The Vegetarian_ , silence can be a powerful tool in breaking old stories. French psychoanalyst and literary theorist Luce Irigaray (1980) once wrote, "If we keep on speaking the same language together, we're going to reproduce the same history. Begin the same old stories all over again. Don't you think so?" (205). Yes, of course. To say what remains unsaid, to chart what is politically and culturally different, is to wander into the dark spots of one's era.
In his essay "What Is Contemporary" (2009), Italian philosopher Giorgio Agamben asks what it means to look into the dark spots of one's era, to perceive the "special darkness" of one's time, to catch sight of the obscure things (the things kept off the cultural scene) and never cease to engage them (44). Such a task is, he writes, an imaginative and a physical act: one's eyes must be "struck by the beam of darkness that comes from his own time" (45). Agamben's thinking holds important threads for my own contemplation of silence in _The Vegetarian_ , of silence as an act of vegan disobedience not a lapse into madness. Agamben recognizes that those who let their eyes latch onto the darkness of their times will, simultaneously, be taken up by that darkness: submerged, subsumed, engulfed, overwhelmed, inundated, swamped. While Agamben's thinking is focused on the practice of certain writers, his argument holds true for the work of Han Kang and her character, Yeong-hye. Yeong-hye is held by the nightmares that she holds in her mind. She touches the ghosts that reach out to touch her. This reciprocity leaves deep traces in her identity. They trace the outline of a story she will no longer uphold.
"Open your mouth right now. You don't like it? Well, try this instead then." She tried the same thing with stir-fried beef, and when my wife kept her mouth shut just as before, set the beef down and picked up some dressed oysters. "Haven't you liked these since you were little? You used to want to eat them all the time." (Kang, 37)
Yeong-hye's silence breaks with the familiarity of her family's carnist narratives. In so many ways, breaking with carnist narratives makes space for breaking bread with other "companion species of terra" (Haraway 2016, 55). Breaking, failing, refusing, ignoring, wilfully forgetting to follow pathways of thought, speech, and action: these are some of the ways to unmake carnist narratives. I take these as modes of thinking, knowing, and writing that might allow for an understanding, and further development, of anti-carnist ways of being in the world. These might be ways to stray from the bounds of carnist knowledge, while keeping in touch with the ways animals live, how they die, and why they haunt.
Wilfully forgetting carnist rules of etiquette becomes a form of embodied resistance. Silent resistance turns Yeong-hye's body into outlaw, a pirate. This kind of resistance is interruptive of "normal" modes of functioning. It is also citational as it points to what is kept off the cultural scene. This kind of embodied resistance is a practice of forgetting. Yeong-hye forgets the customs that uphold carnist manners and patterns of thought, patterns that snuff out potentials for new knowledge formations. Her resistance pokes holes in carnism's toxic discourses, predictable and instituted stories—stories that function in carceral ways because they attempt to shut up the wild possibilities for ways of living and dying that may be offered by anti-carnist imaginings.
My father-in-law took up a pair of chopsticks. He used them to pick up a piece of sweet and sour pork and stood tall in front of my wife, who turned away.
...
"Eat it! Listen to what your father's telling you and eat. Everything I say is for your own good. So why act like this if it makes you ill?" (Kang, 38)
To forget is to break with lineage. To break with lineage is to shift the dynamics of times-yet-to-come by refusing to enact what is expected to come next. The carnist mentality that presides over _The Vegetarian_ situates "the vegan" (Yong-hye) as an incomprehensible, irrational, and even an impossible identity because she does not live out carnist expectations.
With one hand my wife pushed away his chopsticks, which were shaking silently in empty space.
"Father, I don't eat meat."
In an instant, his flat palm cleaved the empty space. My wife cupped her cheek in her hand.... I approached my wife hesitantly. He'd hit her so hard that the blood showed through the skin of her cheek. Her breathing was ragged, and it seemed that her composure had finally been shattered. (Kang, 38–39)
In the moments that follow, Yeong-hye grabs a little fruit knife and cuts open one of her wrists. Why are some traditions more important than some lives?
In these quoted scenes, carnist patriarchy and carnist nationalism patronize: they argue, they bully, they hit. Carnism (that nasty little tyrant) has powerful tantrums.
Throughout _The Vegetarian_ , Yeong-hye's silence "outs" two of carnism's most significant pathological symptoms: (1) the utter conviction in the right and "rationality" of using all animals and ecologies for one's own gains, desires, and luxuries; and (2) the hysterical focus on meat as a singularly exceptional source of sustenance and identity. By doing this, _The Vegetarian_ uses silence as a narrative strategy to lay bare (and amplify) the mechanisms by which carnism relentlessly attempts to fix women, vegans, animals, and plants in the place of absolute Others, by projecting onto them an incomprehensibility and unintelligibility constituted as the refuse of human, masculine, and carnist "rationality."
The first red is blood. The dream is flesh. Bury the dream. But first. Erupt the silence.
How to distinguish between different kinds of silence: remembrance, stealth, protest, (self) censorship, guilt, obedience, complicity, support, or the slack-jawed void of ignorance? Is Yeong-hey's silence a kind of revolutionary (to turn, to roll back) silence in that it unravels the way carnist discourses twist the realities of mass slaughter into narratives of health care?
"You waste away after months without meat, it seems," says Yeong-hye's mother to Yeong-hye's husband, "so... eat this together, the two of you. It's black goat.... Try feeding it to Yeong-hye, just tell her it's herbal medicine. I put a load of medicinal stuff in it to mask the smell." (Kang, 45)
In Tillie Olsen's essay "Silences in Literature," published in _Silences_ (1978), Olsen writes that the history of literature is riddled with natural and unnatural silences. Unnatural silences include deletions, omissions, abandonments, and refutation of subject matter. Unnatural silences are present everywhere in carnist systems of representation and reality. As Adams has written in her deeply influential book _The Sexual Politics of Meat_ (1990), there is the silence of the "absent-referent"—those animals who have been "cut off" from their own bodies through slaughter (21). Then there are those smothered bodies, smothered lives, smothered deaths, and smothered stories that James Stanescu narrates in his article, "Species Trouble: Judith Butler, Mourning and the Precarious Lives of Animals" (2012). Try mourning those "'nameless and faceless deaths' that come to constitute our world" (579) and you will find yourself neck deep in a political practice that opens you up to the possibility of losing your social intelligibility, credibility, and legibility. Lose intelligibility, Stanescu writes, and you become spectacle, spectral, and a spectee. These three conditions converge within Yeong-hye's body as she stops eating meat, then stops eating altogether. As her body begins to eat itself her anti-carnist narrative is twisted into a discourse of madness: schizophrenia, catatonia, anorexia. Thinking with these familiar narratives the medical staff caring for Yeong-hye subject her to the kind of treatment in which the forceful preservation of a certain kind of life takes precedence over asking the question (and then listening for an answer!): What do anti-carnists want? Yeong-hye's doctor explains to her sister: "But we're still not sure why exactly it is that Kim Yeong-hye is refusing to eat, and none of the medicines we've given her seem to have had any effect" (141).
Schizophrenia, catatonia, anorexia: these three conditions used by family and doctors to colonize Yeong-hye's silent story, which continues (nonetheless) to gather human-animal-plant bodies up into the drama of living and dying together. In doing this, Yeong-hye's silence breathes with (conspires) gender, genre, and species trouble. Neither her body, nor her silence will go docilely into quarantine, nor will they be readjusted to fit a carnist perspective of life. Her silence is not a narrative wasteland/dead zone/vacuum but a position of poise—a narrative position that remains alert to the possibility that there are myriad ways to live outside the single-minded, and ultimately deadly, narrative of carnism.
One time. I want to shout. Just one time. To pitch. To yell. To howl. Yes, perhaps that could work.
_The Vegetarian_ explores enmeshments of the more-than-human with the inhuman, human-as-humus, human-as-animal, human-as-meat, human-as-vegetal, human-as-spectee, and human-as-fiction. When, in the latter parts of the novel, Yeong-hye feels herself transforming into a plant, it comes as her final (and most extreme) attempt to renounce all kinds of carnist violence. As she mentally metamorphoses, Yeong-hye's desires to live a plant-based and plant-bound life are interpreted as signifiers of delusion.
This novel can be read as a tale for what Donna Haraway calls the Chthulucene. Like Haraway's cyborg from "A Cyborg Manifesto" (1991), the Chthulucene is a figure for thinking with, a way to frame narratives of life and death. In her recent book _Staying with the Trouble: Making Kin in the Chthulucene_ , Haraway describes the Chthulucene as a figure of reality and of imagining, of science and of fiction. The concept of the Chthulucene is taken from, but not rooted in, H.P. Lovecraft's "misogynist racial nightmare monster Cthulhu" (101). Rather, the Chthulucene describes an era that stands within and alongside (while challenging) the Anthropocene, Capitalocene, and Plantationocene. It is an era that acknowledges the "myriad intra-active entities-in-assemblages" (1991) that constitute life on earth. The Chthulucene is an age that thrives on stories, on speculation, speculative feminisms, and speculative fabulation.
Haraway's figure of the Chthulucene functions in a practical way for writers and other kinds of thinkers and activists, because it invites us to reframe the stories we tell so that we might learn the art of staying with complex (and often troubling) questions of multispecies justice in intersectional ways.
To tell stories in and of the Chthulucene is to tell stories rooted in the soil, in the earth's humus. It is to tell stories of earthly presence and entanglement. Yeong-hye's silence contains, and even speaks, the precarious, unfinished, and deadly conditions in which animals caught in the systems of industrial animal agriculture are forced to live. Yeong-hye's body is at stake to sheep and lambs and cows and chickens and fish. Her silence speaks the madness of not taking the lives and deaths of animals born into industrial agriculture seriously. Haunted by meat, she turns to cellulose in search of a new narrative frame, another mode of being. The roots that Yeong-hye imagines to be growing out of her hands act as feelers and, as Haraway points out, the Latin word for "feeler" is _tentaculum_ , from which the word _tentacle_ emerges (31).
Using imaginative finger-roots to feel her way beyond carnism, Yeong-hye threads herself to a network of stories in which women and animals witness oppression, alienation, and disfiguration with poetic and politically potent forms of silence.
Kang's complex, poetic use of silence leads me to read Yeong-hye's character as one rooted in the historic figure of the "snaky Medusa," a figure Haraway takes as one of her many "chthonic ones" (71). Chthonic ones embody the Chthulucene as their stories, and their concerns are rooted in the earth. They are critters with many legs, critters who spin webs and stories. They are those like "Naga, Gaia, Tangaroa, Terra, Haniyasu-hime, Spider Woman, Pachamama, Oya, Gorgo, Raven, A'akuluujjusi, and many more" (Haraway 1991). They are those who "romp in multicritter humus but have no truck with sky-gazing Homo" (2). They are immunized to human exceptionalism. They act as speakers for the dead and because of this they are available for multispecies storytelling.
Just like Yeong-hye, chthonic ones take risks in how they live, what they imagine, whose stories they hear, and whose points of view they hold alongside their own. It is my reading that Yeong-hye's dreams of meat and murder, as well as her phytomorphic desires, make her a chthonic one. In this way, Yeong-hye can be read as a literary affiliate of the Medusa whose stare petrifies because it conveys all the horrors of disfigurement.
The Italian philosopher and feminist thinker Adriana Cavarero unpicks the etymology of horror to discover its links with repugnance and the physiological state of paralysis. In her book _Horrorism: Naming Contemporary Violence_ (2009), Cavarero ties the power of the mythical Medusa's silent stare to this etymological nexus. For Caverero, Medusa's stare petrifies because it speaks of the kinds of violence not merely content to kill but driven to "destroy the uniqueness of the body, tearing at its constitutive vulnerability" (8). Yeong-hye's silent stare speaks of the destruction of uniqueness that is just one of the dictates organizing the logic of the abattoir. So it is that I take Medusa and Yeong-hye as literary oddkin. They are, to use a phrase from queer-trans-feminist-literary scholar Jack Halberstam, "fugitive knowers" (2011, 8)—ones who unleash forms of knowing, valuing, and mourning that are predominantly ignored, lost, or forgotten. Yeong-hye's silent stare looks directly at connections that are feared. And she catches herself in the silent stare of the animals who haunt her. Yeong-hye is horrified, but she cannot look away. Rather, she turns from the narratives, identities, and actions that produce, legitimate, normalize, and maintain such horrors: carnism. Yeong-hye no longer wants to know the world through the narrative of carnism. For her, carnism has become utterly unthinkable.
In her introduction to a collection of essays _Mourning Animals_ (2016), Margo DeMello writes that while today there are "countless options for dealing with the death of a companion animal" (xvii) there are fewer ways to publicly acknowledge and mourn the vast numbers of animals killed in processes of industrial meat, dairy and egg production, scientific testing, or as a result of the unpredictable and "slow violence" (Nixon 2013, 2) produced by environmental catastrophes of climate change, toxic drifts, oil spills, deforestation, and the environmental aftermaths of war. Tracing the "animal fragments" in Butler's work, Stanescu says that to ignore the deaths of those millions of "nameless and faceless" animals, whose exploitation is woven into the fabric of everyday life, is to ignore the death of part of ourselves (569). Precisely, we lose that part of ourselves that is made up of the myriad connections we have with those others. "To disavow the death of another achieves two kinds of isolation," he writes: "it cedes others into social unintelligibility as well as making one unintelligible to themselves" (569). For Stanescu, the practice of creating "species trouble" draws on and remains intimate with gender trouble. In _Precarious Life: The Powers of Mourning and Violence_ (2004), Butler writes, "I propose to consider a dimension of political life that has to do with our exposure to violence and our complicity in it, with our vulnerability to loss and the task of mourning that follows, and with finding a basis for community in these conditions" (19). Stanescu applies this idea to the practice of publicly mourning animals. Continuing to show connections between gender and species trouble, Stanescu describes the way rituals of public grief can take deaths that are "invisibilized" and amplify them in order to allow them the weight, reality, and voice they deserve (578–579). The first step in this practice of mourning is to risk coherency. To make gender trouble, to make species trouble, is to make genre trouble. Yeong-hye does handstands in the muddle of all this trouble.
Yeong-hye's silence never loses touch with questions of ethics, justice, or response-ability. It opens up, and speaks of, the gaps between how things are and how they might be. Silence in _The Vegetarian_ calls me to uncomfortable sensibilities because it is, at once, a tool of oppression _and_ a mode of poetic expression. It is a force of annihilation just as it can be used to critique oppression and act as a practice of liberation. Silence can erupt from indifference _and_ from care shocked into stupefaction. Silence offers space to hear murmurings, muted cries, and mutterings. Silence provides space for ghosts to talk and be heard. Across _The Vegetarian_ Yeong-hye's silence turns haptic, it unravels into/across/beneath carnist structures and identities. Attempting to discipline Yeong-hye's silence is the drama that consumes the narrative. Her silence has voice; it is a kind of rhetoric. It erupts, disrupts, speaks up, and reveals. In doing so, it makes space for a new narrative world.
Notes
As Rachel Carson has shown in no uncertain terms, silence is just one of the many effects that result from the introduction of poisons (used as herbicides and pesticides) into ecosystems, which result in the unintended killing of numerous insects, birds, fish, cows, sheep, and even some people.
I take this term from Donna J. Haraway who uses it to describe companion species meeting, being, and eating at table together. See chapter 2 "Tentacular Thinking: Anthropocene, Capitalocene, Chthulucene" in _Staying with the Trouble: Making Kin in the Chthulucene_ , 55.
In the essay "The Everyday Resistance of Vegetarianism," which comes from the edited collection _Embodied Resistance_ (2011), Samantha Kwan and Louise Marie Roth theorize the way acting out certain bodily practices, and abstaining from "normalizing" bodily practices, can form modes of resistance to and interruption of institutional power. Here, I draw on their ideas of "counter-hegemonic embodiment" and use it to describe the bodily resistance that comes from acting out veganism.
References
Adams, C. J. (1990), _The Sexual Politics of Meat: A Feminist-Vegetarian Critical Theory_ , New York: Continuum.
Adams, C. J. (2006), "An Animal Manifesto: Gender, Identity, and Vegan-Feminism in the Twenty-First Century," _Parallax_ 38: 120–128.
Agamben, G. (2009), "What Is Contemporary?" in D. Kishik and S. Pedatella (trans.), _What Is an Apparatus? And Other Essays_ , 39–54, Stanford, CA: Stanford University Press.
Butler, J. (2004), _Precarious Life: The Powers of Mourning and Violence_ , New York: Verso.
Carson, R. (1962), _Silent Spring_ , Boston: Houghton Mifflin.
Cavarero, A. (2009), _Horrorism: Naming Contemporary Violence_ , New York: Columbia University Press.
Coetzee, J. M. (2004), _Elizabeth Costello_ , London: Vintage Books.
DeMello, M. (2016), "'Who Goes to the Rainbow Bridge?' Conceptions of the Afterlife for Non-Human Animals," in M. DeMello (ed.), _Mourning Animals: Rituals and Practices Surrounding Animal Death_ , xvii–xxvi, East Lansing: Michigan State University Press.
Gruen, L. (2015), _Entangled Empathy: An Alternative Ethic for Our Relationships with Animals_ , Brooklyn: Lantern Books.
Halberstam, J. (2011), "Shadow Feminisms: Queer Negativity and Radical Passivity," in _The Queer Art of Failure_ , 123–146, Durham: Duke University Press.
Haraway, D. J. (2016), _Staying with the Trouble: Making Kin in the Chthulucene_ , Durham: Duke University Press.
Irigaray, L. (1980), "When Our Lips Speak Together," in C. Burke (trans.), _This Sex Which Is Not One_ , 205–218. New York: Cornell University.
Kang, H. (2007), _The Vegetarian_ , London: Portobello books.
Khakpour, P. (2016), " _The Vegetarian_ by Han Kang," _The New York Times,_ February 2. Available online: <https://www.nytimes.com/2016/02/07/books/review/the-vegetarian-by-han-kang.html> (accessed August 5, 2016).
Kwan, S. and Roth, L. M. (2011), "The Everyday Resistance of Vegetarianism," in C. Bobel and S. Kwan (eds.), _Embodied Resistance: Challenging the Norms, Breaking the Rules_ , 186–196, Nashville: Vanderblit University Press.
Levy, D. (1997), _Diary of a Steak_ , London: Book Works.
Nixon, R. (2013), _Slow Violence and the Environmentalism of the Poor_ , Cambridge: Harvard University Press.
Olsen, T. (1978), "Silences in Literature," in S. Fisher Finkin (ed.), _Silences_ , New York: The Feminist Press at CUNY.
Patrick, B. (2016), "Han Kang on Violence, Beauty, and the (Im)possibility of Innocence," February 12. Available online: <http://lithub.com/han-kang-on-violence-beauty-and-the-impossibility-of-innocence/> (accessed August 5, 2016).
Plumwood, V. (1993), _Feminism and the Mastery of Nature_ , London: Routledge.
Stanescu, J. (2012), "Species Trouble: Judith Butler, Mourning, and the Precarious Lives of Animals," _Hypatia: A Journal of Feminist Philosophy_ 27 (3): 567–582.
Wright, A. (2013), _The Swan Book_ , Artarmon: Giramondo.
Chapter 5
THE LONELINESS AND MADNESS OF WITNESSING: REFLECTIONS FROM A VEGAN FEMINIST KILLJOY
Kathryn Gillespie
"How do you cope?" One of the students asked, intently—searchingly.
I froze. It was a reasonable question. Especially so, considering I had been invited into this space—a student-led undergraduate course on self-care and trauma in social justice-oriented work—to talk about my own experiences related to the theme for the week: _What to do when people don't care about what you care about._ My mind raced: _They're asking for strategies. What strategies for coping or self-care do I have? What can I offer?_ And then my mind went blank, panicking. I felt a quiver move through my body. I felt my chin begin to tremble. _How do I cope? Is that what I'm doing? Coping?_ I felt my face start to flush.
_How do I cope? How do I cope?_ Everyone in the room was looking at me, waiting. I wondered what coping looks like and if that's what it looked like I was doing. I wondered if looking like I was coping was why I had been asked to come in to talk to the class. _I'm not coping,_ I thought. _I haven't been coping for a long time._ I felt my vision go blurry as my eyes filled with tears. _Oh no_ , I thought frantically. _Don't cry. Not here. Not now. Get it together, Gillespie!_ I looked up and they were still waiting.
Tears catching in my throat, "I'm not coping," I said. "I haven't been coping for a long time." And then I broke down, mortified, but without any control over the full-bodied, undignified sobs that cut through the silent room.
"Oh god! Oh my god!" one of the students blurted out, too loudly for the space. "Are you OK? Are you OK? Oh my god!" and then, to her classmates: "What do we do? What should we do? Oh god!"
Haley Bosco Doyle, who was facilitating the class and who had invited me to attend, turned to the other student and said, "It's OK. Let her be." Then Haley turned to me and put her hand on my shoulder gently and waited. They all waited while I covered my face with my hands and sobbed.
When I had finally gathered myself together, we talked about how out-of-place tears can feel in an academic classroom. How classrooms, and academic spaces more generally, are framed as spaces of intellectual engagement and not emotional outpourings. I talked to them about my mortification at crying in front of them, and about how it might be useful to try to reframe how I was thinking about those tears. What if they weren't something to be ashamed of; what if, instead, we could think about crying— _a teacher crying_ —as a subversive act: a rejection of masculinist, rationalist notions of the academy as an unemotional space, or academics as unemotional beings. I left the classroom that day, emotionally undone.
I'd like to say that this undoing in front of a roomful of students was a breaking point or a turning point of some kind, but it wasn't. It is a memorable moment of rupture, a moment where the damage done by my experiences witnessing violence bubbled up to the surface to remind me that I was not OK. That in witnessing, studying, teaching, and writing about violence against animals, I will probably, in some ways, never be OK again.
This was early 2016. Four years earlier, in 2012, I had completed the fieldwork for my dissertation on the lives of cows in the Pacific Northwestern United States dairy industry. My intention was to document as best I could the embodied experiences of animals—cows, bulls, calves—raised for dairy production. This work involved entering spaces where the visceral experience of suffering and, often, dying animals was made mundane and routine through the abstracting effects of the commodification process (Gillespie 2016, Gillespie 2018). Farmed animal auction yards were one of my primary research sites. In these spaces, I witnessed countless instances of animal suffering and violence not typically viewed as violence: cows collapsing and dying in the rear holding pens and in the auction rings; animals being jabbed with electric prods, leaping forward to avoid the shocks; cows and calves sold apart from one another as they bellowed for each other from across the auction yard; cows crammed into pens so tightly they couldn't turn around; day-old calves with their umbilical cords still attached selling for as little as $15, or lying crumpled and weak in the holding pens. There were cows in all stages of physical health: some were robust and still viable as commodity producers; many others were emaciated and barely able to walk; many limped severely, their hides covered with open wounds and udders red with infection. Intentionally witnessing the trauma animals experience in farming is, for the witness, a psychically overwhelming onslaught of visceral suffering—an exposure to secondary trauma.
At the same time, the speed, efficiency, and everydayness with which animals are sold through the auction ring has the effect of obscuring or making mundane the violence experienced by each singular cow passing through the ring. To repeatedly reject this abstracting effect and focus in on each body, each life, and each face requires you to become the witness, the killjoy. Witnessing the suffering of animals in spaces of routine animal use is an act of embodying and inhabiting what Sara Ahmed has identified as _the feminist killjoy_. Ahmed writes, "When we make violence manifest, a violence that is reproduced by not being made manifest, we will be assigned as killjoys. It is because of what she reveals that a killjoy becomes a killjoy in the first place" (Ahmed 2017, 256). The killjoy is a witness. The killjoy bears witness to acts of violence and injustice and documents them as such—in memory, in speech, in writing, in the acts of recollection that mark and politicize this violence.
I have written elsewhere about my feelings of grief and mourning in my role witnessing the suffering experienced by cows in the auction yard (Gillespie 2016). And these experiences and moments of seeing this violence _as violence_ were, indeed, overwhelmed by lasting grief and sadness, but they were also marked by profound loneliness and by feelings of madness. To intentionally focus on each individual suffering being—to remind myself again and again that _this is the cost of commodifying life_ —made me feel like witnessing this violence for another second would push me "over the edge" into a kind of abyss, a place of being unhinged, inconsolable, and permanently changed.
And yet, I found myself moving forward. I didn't witness this violence for just another second, but for too many more seconds to count—too many animal lives to count or remember or grieve. And in order to witness, I found a way to contain these feelings of madness—not eliminate them, but contain them, and push them down, in order to survive. Ahmed tells us that "[the feminist killjoy] comes to exist as a figure, a way of containing damage, because she speaks about damage." I watched as these animals passed by and I contained these feelings of grief and feelings of being driven to the edge of sanity. I felt anger and disbelief and shame and desperation and I contained those, too. I moved on to the next field site. I wrote my fieldnotes. I finished my fieldwork. I taught courses on violence against animals. I prepared to write my dissertation. I defended the dissertation and finished the Ph.D. I rewrote the research in book form, all the while working hard to contain the damage, because it _was_ damage—layers of damage: the internalization of the damage humans cause to the animals they farm and the damage to the witness of this damage as a result of witnessing.
Witnessing can easily drive you to madness or exacerbate mental health issues already there. It can carve out new psychological and emotional wounds. And it can open old ones, worrying at the tender scars until suddenly what you thought was healed, or at least contained, is open again, raw, festering, and exposed to the world. For me, the act of witnessing has done both. Witnessing animal suffering, for me, has exacerbated these familiar affective specters of madness, deepening them and fleshing out their contours. But they have also cut new wounds, laying bare new realities of violence, suffering, and apathy.
There are layers of damage in witnessing. There is the act of witnessing that, in spaces of animal agriculture like the auction yard, left me with overwhelming feelings of despair, rage, shame, and grief. There's something about the scale of animal agriculture—the 50 billion land animals killed each year for food—that is incomprehensible. You try to comprehend it, to contain it—you witness one animal suffering and dying before your eyes and you know that that one is billions—but the scale of it is uncontainable. You can't grieve for 50 billion animals at once and contain that grief. You try. You fail. Your mind works hard to abstract from the animals before you—to blur your vision with tears, to set a ringing in your ears to obscure the sounds of the suffering—to protect itself and to protect your heart. You don't see or remember the next few animals passing before you. You feel shame that you can't focus on and remember each one. You try harder. You find yourself abstracting again. You exhaust yourself with the effort.
And then you notice that no one around you is having this experience: they are laughing, bidding, snacking, chatting with friends and family. This pushes these feelings of madness further. You return to your life—changed, undone—to find that most people don't know about, care about, think about the suffering of animals at all. And this is another layering of the madness of witnessing. You've just witnessed this violence and you stand, outside of (and always within) spaces of violence against animals, always a witness, a killjoy, a reminder that this violence is happening all the time. You find yourself alone. Ahmed writes:
A killjoy might first recognize herself in that feeling of loneliness: of being cut off from others, from how they assemble around happiness. She knows, because she has been there: to be unseated by the tables of happiness can be to find yourself in that shadowy place, to find yourself alone, on your own... The costs of killing joy are high; this figure herself is a cost (not to agree with someone as killing the joy of something). (Ahmed 2017, 259)
I am lucky to have a close handful of family, friends, and colleagues who understand or who have been willing to try to understand violence against nonhuman animals _as violence._ Some of these people already cared about violence against animals and others have come to care about it because it is something I care about. Within this circle, I am also lucky to have a partner who is enormously supportive and has engaged in this journey of learning about violence against animals with me, and a close friend and colleague who has accompanied me into some of these spaces and engaged in endless conversations about this work (see Lopez and Gillespie 2016).
Still, most people don't understand nor do they bother to try to understand what animals experience—indeed, many people take offense at the thought that farmed animals' lives and experiences matter in any consequential way. Or, others think the matter of caring about animals is cute or laughable or merely a manifestation of privilege. Working on and caring about violence against animals frequently renders one socially unintelligible. Social unintelligibility, as James Stanescu writes, is "a failure of recognition by others, a failure to code as reality what you know reality to be. It is an erasure of existence, an erasure of sense, and an erasure of relations. To have your grief for one you care about rendered unintelligible does not invite simple ridicule; it invites melancholia and madness" (Stanescu 2012, 579). And so, sometimes it is easier—less painful—to try to cope, or to pretend to cope. At least in trying to cope, it is only the pain of what you have witnessed that you must carry. To expose yourself as not coping, to try to talk about the pain of what you have witnessed with people who don't see it as intelligible adds a layer of isolation and a feeling of going mad that only works to amplify the damage.
But there's also a profound loneliness to looking like you're coping when you're not. Thinking back to the theme of that day's class— _what to do when people don't care about what you care about_ —there's a profound loneliness to caring about things that other people don't care about. There's a profound loneliness when people don't care about what you care about. Sometimes the impacts of people not caring about what I care about are so much that there have been times I've wished desperately that I could just not be the killjoy doing the work of killing joy for even a few moments or a day.
These moments of disavowal have occurred in my personal life in many different contexts and they regularly happen in my academic life. For instance, I have had many of these moments while on the academic job market, which for the killjoy can be its own kind of mental health nightmare. For any academic, the experience of going on the job market is fraught, stressful, and sometimes traumatizing. Ann Cvetokovich describes the experience:
Huge uncertainties about the future—Is my intellectual work any good? Will I get a job? Where will I be living? Is this really what I want to do?—coalesce around an endless array of tiny tasks and decisions about everything from which font to use on a CV to how to describe one's dissertation, which represents years of work, in a single paragraph that will capture the attention of an unknown reader. (Cvetkovich 2012, 30–31)
This is compounded by the stress of waiting to hear (often waiting for a rejection that hiring committees might never even bother to send), the stress of interviewing and campus visits (if you're among the very few who land one), the unsettling reality of uprooting your life and moving to a new place, making new friends and colleagues, and so on. Any academic who's been on the job market in recent years will have their own set of stories from their own personal hell of trying to get an academic job.
All of this is magnified and transfigured for the killjoy. For the killjoy whose witnessing work is also about killing joy, the job market is a field of emotional and psychological political landmines. On one side, you're tasked with selling your research over and over again in neatly curated descriptions, all the while pretending that this research hasn't driven you to madness. You try to write about it in applications or talk about it in interviews in ways that don't betray that you have been completely undone by it, that just thinking about it makes you want to close yourself into a dark closet and cry.
On the other, you have to package your research just right—so that it is not too political, not too obviously killing joy, to get in the door. And this process is made even worse if your work is about killing joy in relation to people's everyday practices of consumption (like uncovering the violence of dairy production). When confronted with my first campus visit for a feminist geography job, I was advised to frame my work through its explicit contributions to feminist theory; I developed a job talk that highlighted these contributions. Still, my dissertation was about violence against cows in routine practices of agricultural production; there was no getting around or concealing this fact, and this violence was framed as a distinctly feminist issue. As everyone settled into their seats and I began my talk, I watched with a sinking feeling as a platter of cheese and crackers was passed through the audience. _Oh no._ I thought. _I'm fucked._ As the roomful of academics (many of whom were self-described feminists) nibbled on their cheese, I detailed the gendered violence experienced by cows raised for that cheese. Ahmed writes:
Sometimes, when [the killjoy] appears on the horizon of our consciousness, it can be a moment of despair. You don't always want her to appear even when you see yourself in her appearance. You might say to her: not here, not now... You might think, you might feel: I can't afford to be her right now. You might think, you might feel: she would cost me too much right now. (Ahmed 2017, 171–172)
_Why did it have to be cheese?_ I thought. _I just want a job. Can't I just not be the killjoy for once?_ The committee didn't bother to notify me of my rejection for that job.
Colleagues regularly remind me that rejection on the job market is not personal, but when your work is about witnessing and making legible routinely obscured forms of violence, it is nearly impossible to not take it personally insofar as I regularly feel that I failed the animals whose lives and deaths populate my research. It is not that these animals would care whether or not I had gotten a job; rather, rejection represents a feeling that I didn't do enough to communicate the urgency and importance of attending to violence against them. And this is part of being the killjoy more generally—the way killing joy, witnessing, making political becomes so thoroughly entangled with the killjoy's own life that sometimes I think, at my very core, I have been reconfigured and defined by these forms of violence and others' responses to them. Internalizing this violence and its social unintelligibility marks the body and mind in profound ways and I am still working to understand how this occurs.
The first time I read Johanna Hedva's "Sick Woman Theory," I felt a part of the loneliness I was feeling shatter: she was speaking about the damage done by encountering, being exposed to, being haunted by normalized forms of violence. She wasn't talking about violence against animals, but this didn't matter; her words validated and authenticated the psychic and embodied effects of being the killjoy, the misfit, the outcast, trying to love and care and live in this world. She writes: "the body and mind are sensitive and reactive to regimes of oppression—particularly our current regime of neoliberal, white-supremacist, imperial-capitalist, cis-hetero-patriarchy. It is that all of our bodies and minds carry the historical trauma of this, that it is _the world itself_ that is making and keeping us sick" (Hedva 2016).
Because of the privileged space I inhabit in the world (white, physically able-bodied, cis-gender, born in the United States, human), I am in many ways insulated from feeling the full effects of many direct forms of structural violence. And yet, if we take Hedva's words seriously—that "it is that all of our bodies and minds carry the historical trauma" of our current and historically embedded regimes, then the damage caused by intentional (and sometimes unintentional) witnessing of violence (against animals and others) refracts the echoes of these traumas and violences and animates them anew.
Whether we identify as the killjoy, the witness, or not, the impacts of the violent regimes we live in take their toll—and this occurs radically differentially and unequally depending on levels of vulnerability and precarity. But becoming the killjoy is also another kind of taking-on of damage and committing to disrupt, communicate, and (hopefully) transform, through the act of taking on that damage and refusing to obscure it.
Reading Hedva's work alongside Ahmed's exploration of containment and damage in the killjoy's reality, I understand us all to be containers of damage. "To be a container of damage is to be a damaged container; a leaky container. The feminist killjoy is a leaky container. She is right there; there she is, all teary, what a mess" (Ahmed 2017, 171). If " _the world itself_ " (Hedva 2016) causes us all damage, then we all become containers of damage and damaged containers, absorbing the damage caused by the current and historical violent regimes we inhabit. To be considered _normal, healthy_ , and _happy_ —and to make others feel comfortable and happy—it is expected that we be good at making it look like the damage isn't there. Feeling blue or under the weather are acceptable temporary states of being in response to certain stimuli (a sad or tragic event, a virulent cold virus), but to remain in these states of revealing the damage (the clinically depressed, the chronically ill, the neuro-atypical, the perpetual witness) is to become Ahmed's leaky container; it is to become the killjoy ( _"there she is, all teary, what a mess_ "); it is to become the figure that ruptures the fiction that everyone (no, _any_ one) can be healthy or happy when the world is so thoroughly imbricated with these regimes of oppression that take shape and form in our bodies and minds.
It is in this realization that I am learning, in an unexpected way, to celebrate the killjoy in all her teary, leaky, witnessing mess and to find gratitude in the damage she contains and expels—I've come to find a strange sense of warmth and familiarity in the feelings of madness that are called forth and energized by her presence. Because I see these experiences of witnessing violence against animals as a memorable point of rupture—a place of springing a leak in the container—I sometimes wonder what it would be like to go back to before I chose to expose myself (through witnessing, writing, and teaching) to the ubiquitous world of violence against animals. Becoming the killjoy is painful. It adds an additional psychic burden to the deeply buried wounds that may already be there. In these flickers of thinking about the past, I feel nostalgic for a time when these wounds were not so numerous and when those that were already there were more deeply buried. I feel nostalgic for a time when I was not so actively and relentlessly the leaky container of the killjoy. But this seductive nostalgia is hard to sustain because I wouldn't choose to not have witnessed these things and I wouldn't choose to not be changed by them.
More than that, though, even if I wanted to engage in this undoing of damage, I couldn't. I was already a container of damage, only, perhaps, I was a little less leaky. The surfacing and layering on of the damage of witnessing has shaped and continues to shape who I am in my body and mind and heart. Eli Clare, writing on the politics of cure and pushing back against ableist notions of normative forms of embodiment and neurotypicality, asks: "Can any of us move our bodies back in time, undo the lessons learned, the knowledge gained, the scars acquired? The desire for restoration, the return to a bodily past—whether shaped by actual history, imagination, or the vice grip of _normal_ and _natural_ —is complex" (Clare 2014, 211). In much of his work, Clare refers to the body-mind as a rejection of the mind–body dualism and as an acknowledgment that who we are is a complex and inextricably entangled fusion of embodiment, thought, and feeling. Moving our body-minds back in the temporal arc of our lives is an impossibility. We are shaped so thoroughly and "brilliantly imperfectly" (Clare 2017) by how we arrive in the world, by how our experiences reorient and transform and undo and remake our body-minds. Who would we be without this madness, this feeling, these politicized manifestations of witnessing and care?
Acknowledgments
Many thanks to Lori Gruen and Fiona Probyn-Rapsey for their encouragement and editorial oversight and curating such an interesting and important project as _Animaladies_. Special thanks also to Haley Bosco Doyle for creating such a warm, thoughtful, and inclusive space for so many activists and academics to think through the emotional and psychic tolls of doing this work. To Eric Haberman, my ongoing gratitude for all of the support, love, and understanding given so freely and generously. Finally, the writing of this chapter was made possible by the wonderful time and space provided by the Wesleyan Animal Studies Postdoctoral Fellowship.
References
Ahmed, S. (2017), _Living a Feminist Life_ , Durham, NC: Duke University Press.
Clare, E. (2014), "Meditations on Natural Worlds, Disabled Bodies, and a Politics of Cure," in S. Iovino and S. Oppermann (eds.), _Material Ecocriticism_ , 204–218, Bloomington: Indiana University Press.
Clare, E. (2017), _Brilliant Imperfection: Grappling with Cure_ , Durham, NC: Duke University Press.
Cvetkovich, A. (2012), _Depression: A Public Feeling_ , Durham, NC: Duke University Press.
Gillespie, K. (2016), "Witnessing Animal Others: Bearing Witness, Grief, and the Political Function of Emotion," _Hypatia_ 31 (3): 572–588.
Gillespie, K. (2018), _The Cow with Ear Tag #1389_ , Chicago: University of Chicago Press.
Hedva, J. (2016), "Sick Woman Theory," _Mask Magazine_ , January. Available online: <http://maskmagazine.com/not-again/struggle/sick-woman-theory> (accessed May 2, 2017).
Lopez, P. J. and Gillespie, K. (2016), "A Love Story: For 'Buddy System' Research in the Academy," _Gender, Place, and Culture_ 23 (12): 1689–1700.
Stanescu, J. (2012), "Species Trouble: Judith Butler, Mourning, and the Precarious Lives of Animals," _Hypatia_ 27 (3): 567–582.
Part II
DISABILITY
Chapter 6
ABLEISM, SPECIESISM, ANIMALS, AND AUTISM: THE DEVALUATION OF INTERSPECIES FRIENDSHIPS
Hannah Monroe
Closeness with nonhuman animals is an often discussed aspect of autistic people's experiences. It is present in autobiographies by autistic people and has been written about in research into autistic people's experiences (Solomon 2015). The prevalence of this topic is especially significant given that autistic people are often thought of as not being able to relate to others; but their closeness with animals disrupts this view (Bergenmar et al. 2015; Solomon 2015). Preconceptions and stereotypes surrounding gender, autism, and empathy further complicate understanding the experiences of autistic women in particular. I am connected to this research and the autistic community as both a scholar and an activist for neurodiversity, as part of a movement that questions the construction of autism as pathology within medicalizing discourse. For my master's thesis I interviewed four autistic young adults about their experiences of being autistic in discursive contexts, and I will draw on my research for a part of this chapter.
In this chapter I explore ideas of interspecies closeness between autistic people and nonhuman animals. I will first give an overview of connected oppressions between nonhuman animals and autistic people, including the wider community of disabled people. Then I will discuss notions of empathy as they are connected to gender and autism, and the impact these ideas may have on autistic women. Next, I will explore the ways connections with nonhuman animals are experienced. It is important to avoid generalizing aspects of people's experiences, so I want to address the level to which stereotypes about autistic people complicate the experience of connection to animals, as well as nature, in the lives of many autistic people. Not all autistic people experience these connections to animals and nature. Nonhuman animals and autistic people can be allies for each other, and these connections can be a site of solidarity in working against speciesist and ableist oppression. Relatedly, I will discuss how feeling closer to nonhuman animals than others of one's own species is pathologized as a symptom of autism and show how this distorts an important connection and the solidarity found in it. Lastly, through a discussion of Temple Grandin's approach, I will explore how this feeling of closeness can sometimes be harmful for nonhuman animals.
Connected oppressions
Disability scholars critique the overly rationalist way in which animals are discussed in animal rights discourse, noting that these kinds of arguments are rooted in ableist and speciesist thinking and ultimately do not help animals. These traditional animal rights arguments privilege "rationality" as a basis for beings deserving rights, seemingly leaving out nonhuman animals and people who think and behave in non-normative, non-neurotypical, and non-conforming ways. As Taylor asks, "isn't it ableist to devalue animals because of what abilities they do or do not have?" (2017, 57). Furthermore, this argument upholds dualist binaries of rational and irrational that perpetuate ableist and speciesist oppression.
Taylor suggests that speciesism is supported and constructed by ableism, which justifies viewing abilities associated with neurotypical humans as more valuable than those associated with nonhuman animals (58–59). Gruen also problematizes the argument for caring about and respecting animals because they "share many of the qualities that we admire in ourselves and to which we attach moral significance" (2015, 17). This argument, perhaps unwittingly, promotes anthropocentrism, ignoring the existence of important traits outside of "typical" human experience (24–25).
Salomon argues that privileging the ability to reason is connected to the oppression of autistic people, because neurotypical ways of thinking are held as a standard for others to be measured against. He calls the privileging of these ways of thinking "neurotypicalism" and notes that "this privileging of vermal reasoning over other forms of reasoning not only invalidates and makes suspect autist insights, but neurotypicalism also invalidates and makes suspect animal intelligence" (2010, 48–49). Vermal reasoning is "reasoning that relies heavily on the brain's vermis" (48). He categorizes nonhuman animals as also non-neurotypical (50). Because autistic people and nonhuman animals both may be nonconforming to neurotypical ways of thinking, privileging vermal reasoning is speciesist and ableist.
Taylor asserts that the reasons nonhuman animals are regarded as so different from humans, and thus denied personhood, are deeply rooted in ableism. Nonhuman animals are often regarded as different for not aligning with neurotypical norms of intelligence. Thus the denial of personhood to nonhuman animals is connected to ableism. She asserts "ableism allows us to view human abilities as unquestionably superior to animal abilities" (2017, 58–59). Similarly, Bergenmar et al. argue that the concept "human" is constructed in such a way that we have to meet certain criteria to reach it (2015, 203). They argue that those regarded as not fitting these criteria are animalized or medicalized, and they seek to explore these criteria for "humanness" in regard to norms of emotion and social interaction (204). They draw on Davidson and Smith's work on the connections with nonhuman animals described by autistic people's autobiographies, and focus on how these autobiographies address the constructed "qualifications for obtaining 'humanness'" (207–208). By writing about interspecies experiences, and talking about ways they actually feel like nonhuman animals, autistic authors "question the concept of being 'human'" and in the process disrupt binary dualisms of human and nonhuman animals (208, 210). For example, one author cited by Bergenmar et al., Johansson, describes viewing nonhuman animals, the natural world, and humans all as equal (211). Another author, Prince-Hughes, wrote that she "grew to understand and identify with the gorillas, the way other human people did _not_ identify with them" (209). In these authors' feelings of connection to nonhuman animals and the natural world, they disrupt normative constructions of personhood.
One of the central ideas in disability theory is that our mental and physical abilities are not what make us valuable and deserving of dignity and respect (Taylor 2017, 57). Disability activism urges us to see different ways of being in the world as valuable and positive, and Taylor and Salomon argue that this view is essential for animal advocacy as well (Taylor 2017, 60; Salomon 2010, 47–49). The devaluation of autistic people's ways of living and thinking is an example of a prejudice that needs to be overcome. Instead of determining value based on how close abilities are to those of able-bodied and neurotypical humans, we should value each other's ways of being in the world as valuable in and of themselves. Taylor asserts, "disability activists do not argue that disabled individuals are valuable _despite_ our disabilities; rather, value lies in the very variation of embodiment, cognition, and experience that disability encompasses" (60). We need diversity of expressions and experiences because, as we are interdependent, we all contribute to helping each other in different ways. Furthermore, constructed norms represent few people's actual experiences. Embracing and valuing different ways of being can create a more equitable society for all.
Empathy, gender, and autism
The clinical view of autism describes autistic people as lacking the ability to empathize, not being able to see how someone else might be feeling and respond to that state appropriately (Davidson and Smith 2012, 262; Bergenmar et al. 2015, 204–205). Davidson and Smith draw from evidence of autistic people's close bonds with nonhuman animals and nature to question whether this is really because autistic people lack empathy or whether they just have difficulty interacting socially with other people (2012, 262). In autobiographies and narratives, autistic people express that they experience "difficulties in communicating or understanding emotions" (267). They have trouble communicating emotionally with other people, but this does not affect their empathy. In fact, autistic people describe experiencing emotions to an extreme intensity, called "hyper-emotionality," which is one reason why connecting with other people can be so difficult (Davidson and Smith, 268; Bergenmar et al., 206). Experiencing emotions from connecting with other people can be overwhelming, while those experiences in nature or with nonhuman animals are less intense (Davidson and Smith, 268).
Assumptions about empathy and autism are rooted in normative ideas about gender. Solomon describes Baron-Cohen's claim that autistic people have mental traits more stereotypically associated with "males." Solomon challenges this view, writing "such a dichotomously gendered view, however, may obscure the experiential complexity of affective experiences in ASD" (2015, 339). Solomon notes that autistic boys have been found to be social and empathetic with nonhuman animals as well. She also describes how this stereotypical view of autism is changing, with recognition of the diversity in autistic people's experiences and abilities taking its place (339).
Baron-Cohen also claims that women are more empathetic than men, but Jordynn Jack points out how the evidence for this is based on studies that were biased due to problems in their methodology, where researchers did not account for participants' knowledge of the study: when women participated in studies that they knew were about empathy, they would often demonstrate greater empathy than men, but this has to do with gender norms and women feeling pressure to be more empathetic. Studies that avoided this problem did not find gender differences in empathic responses (2014, 136). It is significant that women do feel such pressure to be empathetic, especially as autistic people are stereotyped as having less empathy. This places autistic women between two contrasting stereotypes. They may experience social pressures to be more empathetic in accordance with gender norms while also being assumed to have less empathy because they are labeled as autistic.
These converging expectations and stereotypes demonstrate the need for an awareness of diversity and intersecting identities, such as race, gender, and sexuality, in clinical ideas around autism. The assumption that autistic people experience less empathy than neurotypical people, and particularly its reliance on gendered stereotypes, is demonstrative of the widely held belief that autism is more common among men than women. Gendered stereotypes about autism render autistic women and their experiences invisible. Feeling that one's identity is invisible in both cultural and clinical views of autism surely affects autistic women's sense of selves. These gendered and ableist stereotypes about autistic women and empathy are disrupted by the close connections some autistic people have with nonhuman animals.
Emotional connections
Close connections with nonhuman animals, as well as nature, play a significant role in autobiographies of autistic authors and are often described as having the emotional depth and closeness of human friendships. Such connections disrupt the idea that autistic people do not have these emotional experiences (Davidson and Smith, 260). Solomon also explains that as autism "has been conceptualized as a disorder of affect, it casts doubt upon the very ability of people with ASD to experience attachment, care, and the intersubjective understandings of others" (327). But the level of connection in autistic people's interactions with nonhuman animals challenges this idea about autism (327). It becomes clear that this idea about autistic people's social and communicative abilities is more complicated than is predominantly thought. One child in Solomon's research, for example, Kid, is described as not getting along well with other children, but as loving nonhuman animals. Solomon explores the way Kid shows care and empathy for animals, disrupting the assumption that autistic people do not experience emotional connections (333).
Davidson and Smith also bring up the idea of "a person who claims to _feel more like_ an animal, or even a place, than they feel like other people" (266–277, 271). Bergenmar et al. describe the narrative of a Swedish autistic person, Brändemo, who says he is like his pet rabbit because they share traits associated with his autism. He and the rabbit share similar sensory and social experiences (209). It is particularly interesting that he expresses this connection in terms of feeling that he is like the rabbit, rather than as a sense of merely feeling understood. This contrasts other accounts of connections with animals written by autistic people, in which they emphasize feeling better understood by animals in comparison to other humans and the relative ease of reading and understanding animals' emotions (Davidson and Smith, 270, 272).
In my research, I asked four participants who they felt understood by, and if this included nonhuman animals. Participants did not describe feeling understood by animals, but some instead talked about feeling like or relating to animals. Perhaps feeling like a nonhuman animal is another kind of emotional connection that is helpful for autistic people and nonhuman animals in a similar way. For example, Mikkel says, "I don't know if they understand me, but I feel like very related to cats. I feel I understand cats better... People, they say they're mysterious animals. And then don't really get them. But I just see them as kind of independent animals. And I kind of like that." He does not feel like cats understand him, but seems to see parts of his own identity in cats and feels like he understands them while other people do not. This connection to cats could still be affirming for him, even if he does not feel understood by them.
I found others expressed relating to nonhuman animals, but not feeling understood or liked by them, while some did not feel this kind of connection but still expressed a fondness for animals and had pets. For example, Grace feels understood by animals because they communicate in ways she can understand. However, she does not feel that any animal she has interacted with has really liked her. This is another distinction, where being able to communicate is not the same as being liked. Being able to communicate with and understand animals in some ways is not the same as having a close emotional bond. This is interesting in that it provides a different narrative, demonstrating diversity in autistic people's experiences. Now I will explore the ways these connections, for the people who do experience them, can be a source of alliance and solidarity.
Possibilities for alliance and solidarity
There are concrete ways that autistic people and nonhuman animals can be allies for each other and be in solidarity. Taylor argues that acknowledging interdependence is critical to disability and animal justice. However, for disabled people and nonhuman animals, being cared for has often been paradoxically linked with oppression. For disabled people the experience of being cared for often means having less independence and agency, and for nonhuman animals it is often connected to their violent exploitation (205–206). In our culture, being dependent is also constructed as negative, with disabled people and domesticated nonhuman animals being viewed as burdensome.
Disrupting this idea, Taylor argues that all of us are dependent on each other in many ways (209–210). Everyone in our society relies on others in all aspects of our lives, such as people who build and maintain infrastructure in our neighborhoods, schools, and cities. We rely on medical professionals to help take care of our health. As we go about our day, we are reliant on people who grow food for us as well as those who serve us in restaurants and cafes. Interdependence is deeply embedded in culture and society. Referencing the feminist ethic of care and Gruen's work on empathy, Taylor argues interdependence should require that we care for each other in non-oppressive ways, and that would include listening to those we care about to understand how to care for them and what they want. She says we need to "start listening to what those who need care are communicating about their own lives, feelings, and the care they are receiving" (218). She calls for a need to recognize the ways we are interdependent with nonhuman animals, including how we can help and benefit each other in ways that do not undermine agency and rights (218). An example of this would be an autistic person gaining validation and emotional support from a nonhuman animal they live with and caring for their companion animal in return. Taylor shares Gruen's account of entangled empathy that stresses the need to be aware of the ways we are both the same and different. Though we are interconnected and interdependent, we also have our own selves. Gruen argues that "value dualisms" in which we see one as superior to another are harmful, but this does not mean we have to disregard differences between ourselves and others. Importantly, Gruen explains that for marginalized people having a "self-identity" is something they have had to claim for themselves in the face of oppression, and thus can be empowering (Gruen in Taylor 2017, 62). This is crucial in reference to autism and identity.
Davidson and Smith describe how connections with nonhuman animals and nature can offer "respite from the disruptive, intrusive, and communicatively overburdened social world" (261). In a social world outside of human interaction, these individuals find connections that are more accommodating of their communication styles (269). For example, in Brändemo's experience as well as that of Prince-Hughes', it is easier to be social with nonhuman animals as their ways of living and communicating are more accommodating of autistic differences (Bergenmar et al., 209). Brändemo and Prince-Hughes describe actually learning and speaking the language of the animals they felt connected to, gorillas for Prince-Hughes and rabbits for Brändemo. In this way, they could communicate with nonhuman animals even though it bothered humans when they made their communicative noises (213).
The nonhuman animals provide a kind of protection and relief from problems that autistic people face in human society, and this "protected time" is often among nature and nonhuman animals. Autistic people do not avoid connection in this safe space, but rather want to connect with different species and the natural world (Davidson and Smith, 269). Davidson and Smith express the sense of refuge autistic people can find in nature and among nonhuman animals, describing that this provides a space for "ASD authors to simply be and feel themselves, comfortably and even pleasurably, however divergent from the norm their feelings are taken to be by clinicians" (269). This really describes how liberatory these connections can be. One of the authors Bergenmar et al. write about, Johansson, says it is easier to relate to nonhuman animals and the natural world because they do not expect anything of her, whereas humans do and often what they expect is harmful for her (211). Solomon suggests a reason the autistic children in her research find it easier to be social with nonhuman animals could be that they have more agency in these interactions, as human contexts for autistic children are very controlled (338). In addition, "the animal gaze can be felt to affirm rather than weaken a sense of self and self-worth" and provide "gentle recognition and (almost unconditional) acceptance" (Davidson and Smith, 274). This description of the interactions between nonhuman animals and autistic people reveals how these connections help with navigating an ableist society. Autistic people's identities and ways of being are oppressed to the point of being detrimental to self-worth. For this reason especially, finding other beings who will be accepting and affirming is critically important.
Expanding this discussion to disabled people's experiences more broadly, I would like to mention Taylor's story about her service dog, Bailey, who is also disabled both physically and mentally, having experienced trauma prior to being adopted (220, 223). Her description of how Bailey helps her is significant, especially in connection to descriptions of the ways nonhuman animals help autistic people in social ways. She describes how as a physically disabled person, being in social spaces is difficult for her because of the ableist ways people interact with her. Taylor writes, "One of the most powerful services animals can provide is a certain kind of social ease, mediating between their human companions and an ableist world" (221). In this way Bailey has been an ally for her in coping with ableist oppression. As Bailey became physically disabled, Taylor recognized that he is her service animal, especially in social ways, and simultaneously she is his service human, helping accommodate his physical and mental disabilities. In this way, she shows us an example of liberating interdependence and interspecies solidarity. While these connections are clearly affirming and empowering for many people, they are also frequently pathologized and devalued through a combination of speciesism and ableism.
Pathologizing of interspecies connections
The devaluation of connections autistic people experience with nonhuman animals shows how they are seen as less socially significant than others of our own species. I believe this is an example of speciesism and objectification, as nonhuman animals are not recognized as social beings in community with us. Within the dominant discourse, animals are constituted as objects and therefore friendships with them are only seen as a substitution, and not as real or meaningful. The objectification of nonhuman animals and the construction of them as inferior to humans is closely connected to the ableist dismissal of the social connections some autistic people may have with nonhuman animals.
One can see from autistic people's narratives about communicating and emotionally connecting with nonhuman animals that these experiences are significant for them. Bergenmar et al. assert that even though these narratives disrupt the clinical view that autistic people cannot experience emotional connection with others, these experiences are often overlooked because they exist outside of neurotypical norms of communication and empathy (214). In this way the meaningful social bonds autistic people form with nonhuman animals are made invisible and subsequently devalued.
Salomon describes how "neurotypical society is suspicious of and threatened by the special relationship autists have with nonhuman animals" and argues this demonstrates the speciesism within our culture (63). Davidson and Smith describe narrative experiences of feeling very close to nonhuman animals, in this case cats, and how the individuals wanted to be friends with cats, but were discouraged by their parents who wanted them to socialize with other children instead (270). This effort of parents to push children toward human friendships rather than interspecies ones demonstrates the pathologizing of these friendships as a symptom of autism and developmentally "abnormal." This is not how parents want their children to behave and socialize.
It seems that in a culture that so devalues and oppresses nonhuman animals, caring about them and feeling close to them is seen as abnormal. The construction of caring about animals as mental illness was more direct in the late 1800s when doctors labeled animal rights activists with "zoophilpsychosis," a constructed mental illness that supposedly made people care too much about animals. Women were diagnosed with this more often (Davidson and Smith, 151). This is addressed by Fraser and Taylor in this volume. The construction of a mental illness to pathologize caring about animals is interesting to think about from a post-structural disability studies and neurodiversity perspective, as this highlights social justice issues rooted in diagnostic labels and who receives them.
While autistic people's close connections with nonhuman animals are often pathologized, these connections are at other times seen as a way for autistic people to become more social with other humans. Davidson and Smith assert that social understanding and feeling comfortable around nonhuman animals can help autistic people develop the same feelings toward other humans (275). Similarly, Solomon asserts these connections with nonhuman animals are important to autistic people's being "social and inter-subjective" (325). She compares two situations that autistic children are involved in, one child is in a psychological interview and the other is participating in an activity with a therapy animal as well as interacting with other animals (325). Referring to autistic and neurotypical children, she writes, "in families with pets in the United States, parents overwhelmingly agree that the animal is beneficial to the children's development" (327). Nonhuman animals are viewed as helping children develop social skills, such as having empathy, which they can then bring to their relationships with other people (327).
Describing the empathetic interactions one child, Kid, has with nonhuman animals, Solomon asserts "sociality may be less a quality of the individual and more a capacity realized through certain kinds of social interactions that are unremarkable and ordinary only within certain interactional substrates, and entirely invisible and unrealizable in others" (336). As mentioned earlier, Solomon demonstrates the way the sociality and intersubjectivity of the children in her research are overlooked, particularly because their connections to nonhuman animals are ignored. She also describes nonhuman animals helping these children develop the "capacity" for this (Jack 2014). However, Solomon does not imply as strongly as Davidson and Smith that this capacity could and should transfer over to interactions and sociality with other humans, as she focuses on the importance of recognizing how autistic children may experience sociality differently around nonhuman animals (229).
I would question what this argument implies about how we view nonhuman animals. It seems that animals may be thought of as a means to an end in attempts to encourage autistic people to be social in ways they may not want to be. Even though these authors describe connections to nonhuman animals that are not pathologized outright, they are still viewed as specifically related to the individuals' autism, and as being positive in their usefulness for potentially changing autistic people's behavior. Wolfe calls this "seeing the non-human animal as merely a prop or tool for allowing the disabled to be mainstreamed into liberal society and its values" (2008, 122). Instead Wolfe suggests a model for supporting and helping each other similar to Taylor's previously mentioned views about interspecies solidarity and interdependence. Aside from the ways autistic people's understanding and connections with nonhuman animals are pathologized, the cultural assumptions about autistic people's ability to do this can also be harmful by perpetuating speciesist oppression.
For example, in discussions of autistic people's feelings of closeness with nonhuman animals, Temple Grandin's narratives are frequently mentioned. As I have talked about how the connections autistic people may have with nonhuman animals can be places for solidarity and alliance, it is important to address Grandin's harmful empathy, given that her form of connection leads to harm and death. She talks about her ability to understand nonhuman animals, even saying "that she feels more _like_ these animals—not simply that she likes or feels more _for_ them—than people" (Grandin in Davidson and Smith, 271). Grandin's description of how she experiences empathy connects to Gruen's discussion of entangled empathy and critique of Grandin. Gruen describes entangled empathy as being able to understand how another being feels in a situation and being inspired to come to their aid. Her description of empathy and how it leads people to ethical actions questions whether approaches to empathy such as Grandin's should truly be considered empathetic (2018). Davidson and Smith suggest that it may actually be because of her statements and discussions of empathy with nonhuman animals in her work that Grandin is seen as an "expert" in designing slaughterhouses (273). Lion points out that as Grandin describes having a connection to nonhuman animals to the extent that she can communicate with them, she has become viewed as a spokesperson for them. This constructs the death of animals in the slaughterhouses she designs as positive for them, because she is seen as having a unique knowledge of their perspectives and wants (2016). Davidson and Smith rightly state "that this might seem a strange mode of employment for someone claiming to empathetically understand how cattle 'feel'" (273). I find it especially problematic that Grandin uses what could be a site of alliance with nonhuman animals as a way to prove her ability to design ways to kill them.
In referencing how nonhuman animals and disabled people can be allies as discussed by Taylor, it is important here to reiterate that this means a reciprocal relationship where nonhuman animals and disabled people can help each other. In Grandin's case, animals help her feel understood, but her work contributes to their violent oppression. Welfarist animal activists would argue she is making their deaths more humane, but as Lion asserts, by promoting a narrative of killing animals in a supposedly empathetic and understanding way, she is only supporting the idea of humane meat, which helps the industry far more than the animals being exploited.
Through discussing notions of closeness between autistic people and nonhuman animals, in this chapter, I have attempted to highlight solidarity while also acknowledging potential issues of ableism, speciesism, and gendered stereotypes. It is important to acknowledge the complexity of this topic while looking at the potential for alliance between autistic people and nonhuman animals.
Notes
I use the term "autistic people," which is called identity-first language, and is preferred by most autistic people. This term affirms that autism is part of a person's identity instead of an illness.
For autobiographies, see Bergenmar et al. (2015); Davidson and Smith (2012); and Wolfe (2008).
See Salomon (2010) and Taylor (2017).
Part of my thesis research for my Master of Arts in Critical Sociology at Brock University.
All participant names are pseudonyms.
For example, see Davidson and Smith (2012) and Wolfe (2008).
References
Bergenmar, J., Bertilsdotter-Rosqvist, H., and Lönngren, A. S. (2015), "Autism and the Question of the Human," _Literature and Medicine_ 33 (1): 202–221.
Davidson, J. and Smith, M. (2012), "Autistic Autobiographies and More-than-Human Emotional Geographies," in D. Spencer, K. Walby, and A. Hunt (eds.), _Emotions Matter: A Relational Approach to Emotions_ , 260–279, Toronto: University of Toronto Press.
Fraser, H. and Taylor, N. (2019), "If It Weren't for... Women Having Their Anxiety Soothed through Companion Animal Connections," in L. Gruen and F. Probyn-Rapsey (eds.), _Animaladies_ , New York: Bloomsbury.
Gruen, L. (2015), _Entangled Empathy: An Alternative Ethic for Our Relationships with Animals_ , Brooklyn: Lantern Books.
Gruen, L. (2018), "Empathy," in L. Gruen (ed.), _Critical Terms for Animal Studies_ , Chicago: University of Chicago Press.
Jack, J. (2014), _Autism and Gender: From Refrigerator Mothers to Computer Geeks_ , Chicago: University of Illinois Press.
Lion, V. (2016), "Disrupting Temple Grandin: Resisting a 'Humane' Face for Autistic and Animal Oppression" at _Decolonizing Critical Animal Studies_ , _Cripping Critical Animal Studies_ , Edmonton, AB, June 21–23.
Salomon, D. (2010), "From Marginal Cases to Linked Oppressions: Reframing the Conflict between the Autistic Pride and Animal Rights Movements," _Journal for Critical Animal Studies_ 8 (1/2): 47–72.
Solomon, O. (2015), "'But-He'll Fall!': Children with Autism, Interspecies Intersubjectivity, and the Problem of 'Being Social,'" _Culture, Medicine and Psychiatry_ 39: 323–344.
Taylor, S. (2017), _Beasts of Burden: Animal and Disability Liberation_ , New York: The New Press.
Wolfe, C. (2008), "Learning from Temple Grandin, or, Animal Studies, Disability Studies, and Who Comes after the Subject," _New Formations_ 64: 110–123.
Chapter 7
METAPHORS AND MALADIES: AGAINST PSYCHOLOGIZING SPECIESISM
Guy Scotton
Introduction
Just what sort of a malady is speciesism? For analytic animal ethics, it is a conceptual error—"the unjustified disadvantageous consideration or treatment of those who are not classified as belonging to one or more particular species," to take Oscar Horta's definition (2010, 245)—amenable to logical exposition and rebuttal. However, in societies already structured on speciesist principles, scholars and activists—including, of course, analytic animal ethicists—find themselves in the midst of speciesism as an ideology with a particular cultural history and political economy or, as Weitzenfeld and Joy gloss it, "a complex of institutions, discourses, and affects" (2014, 20). In the struggle to develop a tractable _gestalt_ of what I will call "actually existing speciesism" in the midst of the moral emergency of industrial animal exploitation, the animal liberation movement has mobilized a host of overlapping models and metaphors to capture its shifting parameters.
One persistent set of metaphors, with its own ableist connotations, equates moral attention with sight and conceives of speciesism as a wall, barrier, or fence that inhibits or "blinds" the broader public to their "natural" sentiments of concern and respect for nonhuman animals. (For a critical discussion of the "politics of sight" conjured by such metaphors, see Pachirat 2011, chap. 9.) And then there are those metaphors that appropriate concepts of mental illness and disability as pejorative figures for human social relations with other animals.
What I am concerned with here are not claims that particular psychological patterns are reliably associated with speciesist beliefs, attitudes, and actions, but rather claims that speciesism constitutes an overarching disorder, one that shapes both institutions and their participants in ways that are fundamentally pathological, threatening mental and social coherence at one and the same time. Sometimes these associations are concrete and explicit, as when Ingrid Newkirk posits that trophy hunters and serial killers share "the same twisted psychology," pronouncing trophy hunting "the pastime of psychopaths" (2015). In other cases, the associations are more evocative, edging forward the notion that harmfully incoherent or contradictory beliefs are the province of "madness." Judith Butler, reflecting on the paradoxical exceptions generated around the category of "the human" by the interplay between racist and anthropocentric discourses, puts the point suggestively: "This is the kind of thinking that drives people mad, of course, and that seems right" (2015, 35–36).
In this chapter, I argue that this array of metaphors constitutes a diagnostic tendency in animal liberation theory and advocacy—a tendency to construe struggles over medical frames of reference as a battle to be won rather than a paradigm to be challenged in its own right. In their content analysis of major newspapers and activist blogs, Wrenn et al. propose that the medicalization of animal liberation discourse can be understood as a case of "frame contestation," in which social movements and countermovements make their appeals by reconfiguring the culturally available meanings and associations of the issue in question (2015). Because activists and scholars must press their claims in (and otherwise function socially within) terms that are resonant with the dominant culture, it is not surprising to find some advocates struggling for possession, rather than subversion or dissolution, of the authority to call others mad. This "ableism in the ranks" (Wrenn et al. 2015, 1313) has an inward function as well, projecting (if tacitly) regulatory ideals of ability and sanity upon the movement's working definitions of identity and cohesion.
I suggest that engaging critically with this diagnostic tendency in animal liberation theory and advocacy offers a renewed approach to actually existing speciesism, better integrating work in sociology and social psychology with normative ethics and political theory. This critical project also presents an opportunity to rethink the spectrum of abilities within and between species as the grounds for interspecies community. This approach challenges both the premises and aspirations of interspecies justice, opening new possibilities for coalition with disability theory and advocacy.
My chapter is organized as follows. In the first section, I survey some indicative associations made between speciesism and mental pathology in animal rights discourse, ranging from flippant metaphors to analogies and models making substantive psychological claims. Invoking first critiques made by disabilities studies scholars and then the recent emergence of theories of disability from within critical animal studies, I highlight the harms and hazards that this mode of discourse perpetuates. In the second section, I offer two resources that might help animal liberation discourse to move beyond this diagnostic frame. One is a new critical agenda, extending Charles Mills' research program for a naturalized epistemology of (racist) ignorance to speciesism as domination. The other is a proposal for an explicitly interspecies conception of neurodiversity. I conclude the third section with some clarifying remarks and a call for a renewed rhetoric of animal liberation.
Against speciesism as madness
Vivid images can have a long afterlife in academic prose no less than in other forms of literature. In a venerable passage, Ted Benton characterized Marx's depiction of human social relations to nature as "a quite fantastic species-narcissism" (1990, 248). With this phrase, Benton established within animal ethics a trope with a long standing: after all, Freud had considered the Darwinian revolution the second of "two great outrages" against humanity's "naïve self-love," a blow that "rebuked [man] with his descent from the animal kingdom, and his ineradicable animal nature" (1920, 246–247). Benton's phrase continues to echo in the literature as a précis of human–nonhuman relations more generally. Kymlicka and Donaldson, for instance, apply Benton's phrase not to Marx but to the collective "sense of entitlement" and "moral blindness" embodied by societies that condone industrial animal exploitation (Kymlicka and Donaldson 2016, 692).
Gary Francione established another notorious psychological trope within animal ethics, pronouncing the fundamental inconsistencies and contradictions in the benefits and protections human communities offer some animals, versus the harms they systematically inflict on others, a form of "moral schizophrenia" (1996, i). In response to ongoing criticism for his use of the term, Francione has only bolstered his claim: "Some critics argue that it is sufficient to say that our moral views about nonhuman animals are contradictory or confused. No, it's not sufficient. When it comes to nonhuman animals, our views are profoundly delusional and I am using that term literally as indicative of what might be called a social form of schizophrenia" (2009).
In _Rattling the Cage_ , Steven Wise builds his case for consciousness in the other great apes in part through a developmental comparison between his (putatively neurotypical) daughter and an autistic child (2000, 152–154). He concludes his book by way of a grand analogy between speciesism and autism, musing: "Perhaps we are an autistic species, biologically incapable of recognizing that nonhumans have minds. Pathologically self-absorbed, we relate to them as if they were machines" (263). Yet for Wise speciesism is an entrenched but permeable moral–religious–juridical belief system, fortified but not determined by humans' general cognitive propensities to interpret other entities and events as serving human purposes: "All this suggests that while our animal mindblindness may be a tendency, even a strong one, it is not irresistible" (264).
Paul Waldau repeatedly employs the trope of autism in a similar way, diagnosing dominant traditions in law, politics, and religion as "almost autistic" (Waldau 2013a, 30), "virtually autistic" (2006, 41; 2010, 81; 2013b, 109), or "truly autistic" (2016, 21; cf. 26) in their regard for nonhuman animals. For Waldau, this "autistic" legacy seems to consist of a particular sort of "self-inflicted ignorance" (2006, 52), involving interpretive distortions not only of the lived realities and individual capacities of nonhuman animals but also of the different social ontologies and modes of relating to other species as communities that are contained within these traditions.
Elisa Aaltola's use of these tropes is instructive, because here they function rhetorically to invert specific forms of philosophical and scientific skepticism about other species' abilities. Thus, for Aaltola, an insistence on mechanical explanations for animal behavior within the personhood debate itself calls the robustness of _human_ personhood into question, insofar as personhood is grounded intersubjectively in intercourse with other minds: "Perhaps not recognising animal experiences, and ultimately animal personhood, consists of 'human-autism', which leads to questioning our own capacity for personhood" (2008, 19). The potential social consequences are stark: "Does skepticism [about animal suffering] not push us toward behaving in a psychopathic, narcissistic fashion in our dealings with other animals?" (Aaltola 2013, 463; cf. 2015, 45) Many of the other examples collected here are, in part, tacit or explicit attempts to leverage a similar dynamic, rhetorically 'turning the tables' on those (whether other scholars or society at large) who would deny or diminish the capacities of other animals.
The point of these examples is not to derive a list of proscribed metaphors or modes of thinking about speciesism, but to illustrate a "diagnostic tendency" within animal liberation discourse centered on abject associations with psychological concepts. However, because even the most stringently conceptual language tends toward (and often benefits from or requires) the figurative, and because a full-fledged account of actually existing speciesism must involve some appeal to human moral psychology, I acknowledge that this critique will only be constructive up to a point that is not, in itself, easily delineated. Other theorists, such as Martha Nussbaum and Zipporah Weisberg, offer more thoughtful quasi-psychological models of human exceptionalism that do not depend on specific derogatory analogies, drawing instead from evocative tropes such as denial and repression, and their meanings in psychoanalysis and critical theory. Considering these models at the outset will help to stake out some of the limits of my own diagnosis.
Frans de Waal coined the term "anthropodenial"—"a blindness to the human-like characteristics of animals, or the animal like characteristics of ourselves" (1999, 258)—as a corollary, and corrective, to ethology's perennial worries about anthropomorphism. Nussbaum, extending and modifying de Waal's term, argues that "[h]uman compassion is diseased" (2010, 203), ruptured by a powerful tendency to deny our human creatureliness, and by "the misogyny that is all too often a concomitant of that denial, since women have repeatedly been portrayed as somehow more bodily than men" (206). By "diseased," Nussbaum means not just that human compassion is fatefully limited, subject to partiality and proximity—a limitation that all species share to various degrees. Rather, humans are impelled, via shame and disgust, to profound internal contradictions that manifest in "moral deformity" (203) and, ultimately, pathological violence.
Uniquely deformed, human compassion is in unique need of therapeutic intervention which, as Nussbaum's broader philosophical project details, means cultivating moral attention, including the right moral emotions, to the vulnerability and neediness that unites us as embodied animals. Nussbaum also asserts here that she "mistrust[s] all reductive monocausal accounts of human depravity," but that without further inquiry into anthropodenial as such, "we have little hope of coming up with an adequate account of gendered violence, or of the aspects of violence in general that are implicitly gendered, involving a repudiation of the filth, stickiness, and non-hardness that are the lot of all human beings" (207, 222)—indeed, of all animals.
Weisberg (2011) argues in more expansively critical terms that the psychological dimension of speciesism is best understood as a pathological repression of humans' own animality. Like Nussbaum, Weisberg takes up Freud, but reads him via the early Frankfurt School's account of repression as concomitant with the technical domination of the more-than-human world: "Animal repression can result in or is even constitutive of an unconscious sense of loss, melancholia, ambivalence, guilt, and a host of other neuroses, on both an individual and a societal level" (178). According to Weisberg, this repression manifests not in apathy _simpliciter_ but in "neurotic ambivalence": warring senses of love and hatred for animal others, investing our encounters with other animals and their images alternately with yearning and contempt; deep guilt over the incessant enactment of this ambivalence in the mechanized violence of slaughter; and "hysterical indifference" to, and alienation within, systems of industrial animal exploitation (181–183).
This is a specifically patriarchal psychology, in which women (are expected to) embody the uneasy reconciliation of beastly subordination in the category of "domestication" (Weisberg 2011, 183–184). Only through practical reconciliation with animal others, cultivating the relationships and practices of care that are coded as feminine and derided by the patriarchal order of speciesism, can human communities "begin reversing the impact of a repression–oppression complex that is literally suicidal, zoocidal, and ecocidal" (193).
Informed by overlapping critical traditions, both Nussbaum's and Weisberg's depictions of speciesism as psychological malady are resistant to the charge that they denigrate particular psychological categories or disabled identities. Both accounts advance the crucial notion that animal ethics needs a moral psychology that can name speciesism and patriarchy as deeply comorbid conditions. However, insofar as the terms of repression and denial are still liable to construe the logic of disease and contamination in sickness/wellness dichotomies, these accounts too could benefit from explicit attention to critical disability theory in general and to the proposal for a conception of interspecies neurodiversity I make further below.
I return now to the rhetorical stable of schizophrenia, autism, narcissism, and psychopathy. Tenuous and derogatory as many of these psychological tropes may be individually, the first point to observe is that they are all shaped by, and contribute to, complex social histories of abjection and appropriation at which I can only gesture here. A 2003 study of US newspaper articles found that 28 percent of references to schizophrenia were metaphorical, compared to 1.3 percent of references to cancer (Duckworth et al. 2003); similar studies of the metaphorical use of schizophrenia have been conducted in several other countries, with a low of 11 percent in UK newspapers (Chopra and Doody 2007) and a staggering 73.7 percent in the Italian press (Magliano et al. 2011). Illnesses and disabilities are themselves interpreted through metaphors that echo and collide: the concept of "mindblindness," for example, as referenced by Wise (2000) above, originates in and pervades the clinical literature on autism. The term purports to capture the difficulties autistic people face in inferring the mental states of others from standard behavioral cues. However, as Dinishak points out, not only does this metaphor of perceptual deficit further stigmatize blindness as such, it collapses the inherently social context of communicative and interpretive problems: indeed, "non-autistic individuals can also have considerable difficulty understanding the mental lives of autistic individuals" (2013, 75). Waldau's portrayal of autism as a self-consumed, self-serving deficit of human institutions such as economic discourse and public policy recalls the self-described "post-autistic economics" movement that began in France in 2000 as a rebuke to the brittle axioms and shallow models of human behavior espoused by neoclassical economics (Fullbrook 2002).
Disability theorists have criticized extensively the unreflective use of terminology pertaining to mental disabilities and disorders within animal rights discourse, arguing that this indicates a broader disengagement of animal rights theory and activism from the lived experiences and perspectives of those with mental disabilities. With a particular focus on the "argument from marginal cases," these critics have concentrated on the representation of humans with disabilities as providing standards or normative fulcrums by which to extend moral consideration to nonhuman animals, who are taken to meet or surpass the "bar" set by severely cognitively disabled humans as regards morally relevant cognitive faculties (e.g., Salomon 2010; Lewiecki-Wilson 2011).
Another array of critiques—along with new political aspirations and identities—comes from the emerging intersection of critical animal studies with disability studies. Only a few years after Sunaura Taylor "challenge[d] the fields of disability studies and animal rights to take _each other_ seriously" (2011, 219; emphasis in original), work in this area has proliferated, with collections offering frames such as "eco-ability" (Nocella II et al. 2017) and "eco-crip theory" (Ray and Sibara 2017), and Taylor's own synthesis of animal and disability liberation (2017). These works demonstrate that when disability is understood as more than a burden or deficit, it can enrich and pluralize cornerstone concepts of political association such as solidarity, interdependence, resistance, and individual and collective agency (Taylor 2017)—insights of profound significance to animal liberation theory and advocacy, if dialogue and cooperation along these lines of inquiry can be sustained.
In light of these developments, could the animal movement nonetheless make strategic and subversive associations between speciesism and madness? After all, as May and Ferri observe, the full force of ableist rhetoric has been wielded "[o]ver the last 200 years" to render feminists and "a wide array of change agents unintelligible, irrational, and unreasonable" (2005, 120). Women's leadership over the past two centuries of animal advocacy has been derided by just such a fusion of misogyny and ableism. Should terms like "madness" and "hysteria" be reclaimed, inverted against an order named specifically as speciesist, ableist, and patriarchal?
The trouble with such inversions, May and Ferri argue, is that they tend to treat the paradigm of disability itself as a fixed point of leverage: wielded as a diagnostic category, "[d]isability is rarely conceptualized as a constructed outcome of power, nor is it regarded as a political identity forged in and through systems of domination" (121). Moreover, abject metaphors evoke complementary images of emancipation: when "metaphors of madness, crippling, and more... characterize and locate objects of remediation, in this case dominant ideologies, practices, and politics," this often launches a corresponding "use of ableist notions of mobility and movement to define and imagine liberation, resistance, and transformation" (122).
Such a dichotomy between speciesist pathology and vegan praxis threatens to occlude the diversity of moral experiences of those with mental illnesses and disabilities, as well as to construe vegan praxis as a determinate, oppositional state of "wellness" or "sanity." Consider, for example, the dichotomy of dissociation and integration presented by Melanie Joy in her introduction to carnism (2011). Joy posits carnism as the ideological subsystem of speciesism involved in legitimating some animals as objects for human consumption, maintained by an essentially defensive psychological schema. Joy proposes that "[d]issociation is the core defense of carnism, the heart of psychic numbing" (140), and that the forms of "mass dissociation" that sustain carnism are on a psychological "continuum" with the term's clinical manifestations:
Most of us... don't dissociate to the degree necessary to kill others; we simply dissociate enough to support the killing that is carried out by others.... It should come as no surprise that the animals we eat aren't the only ones who pay the price of our dissociation. Dissociation limits our self-awareness and thus presents an obstacle to our personal growth. (141)
Conversely, she concludes, bearing witness to nonhuman animals' suffering—and to our own modes of resistance to such witnessing—"dispels dissociation and leads to a more integrated society" (142).
Distinct from the sheer derogatory association of speciesism with specific psychological and neurodevelopmental traits, the hazard here is that the animal liberation movement, conceived as a movement toward perspectival "integration," will thereby fail to incorporate the perspectives of actual people with (for example) schizophrenia and autism in two senses. First, it may fail to solicit and engage with the distinct perspectives and sensibilities that they might contribute to the critique of speciesism and the praxis of animal liberation; second, it may inadequately account for people's diverse needs for, and ways of, living well within a just interspecies community. Just as vegan advocacy becomes exclusionary—and empirically strained—when it insinuates a necessary or typical harmony between interspecies justice and (some normative conception of) physical health in the form of a vegan diet, so too a notion of emancipatory "wellness," defined in opposition to speciesist pathology, obscures the patent complexities of the mental lives of vegans and carnists alike.
From cognitive and affective domination to neurodiverse emancipation
Does the case I have made so far against metaphors and models of systemic pathology mean that critical animal scholarship should retreat to a psychologically thin conception of speciesism? On the contrary, I propose that the framing of speciesism as pathological is best complicated through finer-grained sociological and social psychological work on the psychological intricacies of speciesist institutions. Whereas derogatory invocations of madness, schizophrenia, autism, or psychopathy should be renounced by animal liberation discourse, concepts such as ignorance, denial, and repression suggest more sophisticated paradigms that might be approached as interdisciplinary research programs.
One way of framing this agenda could be adapted from Charles Mills' _The Racial Contract_ (1997), a work that—like Carole Pateman's _The Sexual Contract_ (1988), with which Mills' book is in important conversation—so far has received no concerted attention in critical animal studies. This is somewhat surprising, given the field's commitments to, and extensions of, many of the key insights of feminist and critical race theories. In _The Racial Contract_ , Mills conceives white supremacy as a racial contract covertly underwriting institutions of racial domination (contract theory itself, and the mainstream of moral and political philosophy in general, notwithstanding): "On matters related to race, the Racial Contract prescribes for its signatories an inverted epistemology, an epistemology of ignorance, a particular pattern of localized and global cognitive dysfunctions ( _which are psychologically and socially functional_ ), producing the ironic outcome that whites will in general be unable to understand the world they themselves have made" (1997, 18; my emphasis).
While Mills speaks broadly in terms of cognitive dysfunction in a way that could fall back into a metaphor of mental disorder, and indeed is prone to talk of "blindnesses" (19) and "cognitive handicap" (2007, 15), he asserts here that the malady of white supremacy is, in some important sense, psychologically and socially functional. Moreover, this epistemology of ignorance is not just cognitive but somatic and material, as the Racial Contract normalizes and racializes space and the human body (1997, 41–62). This specifically "white moral cognitive dysfunction," Mills suggests, "can potentially be studied by the new research program of cognitive science" (95). Elaborating on this construct in his essay on "white ignorance," Mills proposes a research agenda for a _naturalized_ epistemology of ignorance, one that would investigate these cognitive processes of denial and avoidance non-reductively. White supremacy avails itself of what we might regard as forms of extended mind, as Mills elaborates: the simultaneous affirmation of racial norms and their denial as such is scaffolded by social processes such as the public "management of memory" in discourses and artifacts of education, commemoration, and celebration (2007, 28–30).
Grounded in a normative analysis of actually existing speciesism as constituting the systematic oppression of nonhuman animals (e.g., Gruen 2009), it is possible to imagine a complementary epistemology of speciesist ignorance. This project could offer a frame and normative impetus for detailed research into the psychology of speciesist domination that does not rely on problematic analogies to discourses of mental disorder, taking a concerted stance on interspecies justice that disciplines like social psychology and cognitive science typically evade. The resources for such a project have already begun to take shape for critical animal studies. There is now a steady stream of empirical research on human beliefs, moral attitudes, and identities regarding other animals, often organized around the paradigm case of meat consumption (for the most comprehensive review of and prospectus for the field to date, see Amiot and Bastian, 2015). Meanwhile, scholars such as Wicks (2011), Cole and Morgan (2011), and Acampora (2016) have introduced key works in ignorance studies and the sociology of denial to critical animal studies. A naturalized epistemology of speciesism, sociologically thick and non-reductive yet conversant with developments in social psychology and cognitive science, could help to build important conceptual bridges for theories of animal liberation.
Of course, such a framework is still vulnerable to its own ambitions to contribute to a _gestalt_ of speciesism, carrying a risk (among others) that it will conceive of "domination" and its epistemology of ignorance as monolithic. One check on this tendency should take the form of an explicit commitment that this research agenda also be reflexive: What patterns of cognition and affect, what flows of ignorance and avoidance shape the animal liberation movement, and how do these interact with other axes of domination? How, for example, does the mainstream of vegan culture propagate white, middle-class "epistemologies of consumption" by promoting dietary "choices" without an adequate account of how access to food and health resources is differentially structured (Harper 2012, 172)? To what extent might characterizations of speciesism as madness and vegan praxis as wellness reflect pervasive cognitive biases and patterns of motivated reasoning of their own, such as "just world" constructs: the expectation, for instance, that wrongdoing is discrete, culpable, and tends to bring about its own punishment?
In criticizing the framing of speciesism as pathology, I have suggested that the emancipatory concepts of "wellness" and "integration" these metaphors evoke in response should also be complicated. The ideal of interspecies justice is in need of concepts and figures that incorporate the experiences and perspectives of people with different psychological profiles into its model of flourishing. One way of framing this contribution would be to develop a conception of _interspecies neurodiversity_. A paradigm forged by the autistic community, neurodiversity signals the diverse goods that a range of differences in mental functioning contributes to, and requires of, the community, if some such range is accepted as a "normal" aspect of human variation rather than a problem to be controlled. This precept illuminates a dimension of justice sensitive to these goods: the prospect of "neuro-equality" (Fenton and Krahn 2009). Neurodiversity has begun to receive concerted attention in ethics and political theory (see, e.g., Herrera and Perry 2013), although many questions and controversies remain regarding the scope and political implications of such diversity.
The idea of interspecies neurodiversity draws a corollary to ideas that have been germinating in the works of neurodiverse scholars for some time: in Salomon's claim, for instance, for recognition of an "autist animal ethics" based on the distinct moral experiences and sensibilities of those with neurodevelopmental differences characteristic of the autism spectrum (2010, 56). Picking up from Salomon, Taylor makes frequent reference to the limits of neurotypical discourse and notes that scholars within neurodiverse communities are now "actively engaging with controversial questions about the relationship between animal and neurodiverse minds" (2017, 114). In this spirit, I want to add a more explicit claim—perhaps too obvious to have merited much discussion—that nonhuman animals are part of the spectrum of neurological diversity. Accordingly, I suggest, the diversity of mental life within and between species should inform aspirations for "neuro-equality," while the concept of neurodiversity should inform conceptions of interspecies justice.
An obvious step through this corollary might now be within the disability/critical animal studies literature, the notion that morally significant interests and capacities are static, discoverable properties that track species membership in terms of "species-typical functioning" holds sway in much of animal ethics. Thus, Clare Palmer suggests in response that "[nonhuman] animals' capacities have some human relational elements to them. We are not just responding to 'what animals are like' in terms of their capacities; we are actually in part _creating_ 'what animals are like'" (2010, 47; emphasis in original). And, I suggest, vice versa: the spectrum of human abilities gains new context and new relational possibilities when arrayed within an interspecies paradigm of neurodiverse ability and difference.
As Sunaura Taylor (2017) details, stigmatic conceptions of disability and animality intertwine to shape what people with disabilities "are like" through scientific, medical, and philosophical discourses that seek to classify and contain disability as deviance from the human prototype. Simultaneously, the institutions and discourses underwriting animal exploitation are both literally and symbolically debilitating for nonhuman animals; a fuller reckoning with "what animals are like," then, must involve understanding nonhuman animals as subjects of, not just objects or figures for, discourses of disability: "Naming animals as crips is a way of challenging us to question our ideas about how bodies move, think, and feel and what makes a body valuable, exploitable, useful, or disposable" (2017, 43). Although Waldau is inclined to portray human abilities as a distinct and coherent profile—we are "creatures of vision embedded in the land" (2006, 44)—he nicely illustrates the interplay between ability understood as a set of individual faculties and the ability to make collective meaning of, and with, those faculties in an interspecies context:
Crucially, each person's particular heritage of ideas—whatever it is—is no less constraining than the obvious limits conferred on each of us by our limited sensory abilities. Just as we can't hear humpback whales' ever-changing communications in the sea while on a terrestrial path, our forebears didn't tell us about those "songs" because our species had no detailed knowledge of these complex communications' existence in any detail until the last half of the twentieth century. (2006, 44)
This is just the sort of challenge that a critical disability lens sharpens for the moral imagination of animal liberation: "What kinds of experiences and understandings of the world develop for a creature who perceives it through smell or who communicates through bioluminescence? What sort of intelligence is needed to accomplish extremely complex migrations or to survive in the depths of the oceans?" (Taylor 2017, 79). This ongoing project of meaning-making, pushing beyond paradigms of inclusion and accommodation, should inform the conception of flourishing appropriate to a just interspecies society, away from unitary constructs of social and individual "wellness" and toward a neurodiverse politics of living well together.
Toward a renewed rhetoric of animal liberation
I have argued that an inverted critique of speciesism as pathology—and its corollary, tacit or explicit, in understanding vegan praxis as psychic "wellness"—is harmful to humans and other animals with disabilities, impedes solidarity with disability advocacy (and is likely strategically inopportune regarding the broader public), and is internally limiting for animal liberation theory and advocacy. This argument should not be taken to obscure or minimize the fact that speciesist institutions, practices, and attitudes are the systematic _cause_ of intense mental distress and illness for both nonhuman animals and humans. I have claimed rather that the social life of speciesism should not itself be conceived on the model of mental illness or disability, precisely because this tends to reinforce a diagnostic frame of disability that occludes the psychological experiences and identities of those—human and nonhuman—who live within regimes of actually existing speciesism.
I have sketched two approaches that might be constructive in moving beyond this diagnostic frame. First, I have argued that resisting this turn to pathology does not involve a retreat from psychological explanation. On the contrary, it affords critical animal studies a richer integration with research agendas in the sociology of ignorance and denial, and in the social psychology of interspecies relations. Such a project need not lose any critical force by dispensing with metaphors of pathology. I have suggested that consolidating the links made to the sociology of denial and ignorance studies, under the auspices of a research program adapted from Charles Mills' account of the epistemology of ignorance enforcing white supremacy, offers one way forward for critical animal studies.
Second, I have suggested that resisting the current of infatuation with the "madness" of speciesism that courses through these metaphors presents an opportunity for a renewed conception of interspecies justice as intricately minded and embodied. By attending to the lived experiences of mental diversity within and between species, critical scholars of speciesism can avail themselves of new theoretical resources and new moral perspectives. In this way, accounts of speciesism might better promote the task of reconstructing moral relations with other animals, in line with the positive commitments staked out by Weisberg and Nussbaum. Informed by the emerging nexus of disability theory and critical animal studies, I have proposed that such accounts of flourishing should incorporate an interspecies conception of neurodiversity.
Finally, although I have focused in this chapter on the ways in which one set of metaphors may denigrate and exclude those with disabilities as well as hamper the analysis of both speciesism and ableism, I do not mean to imply that animal rights theory and advocacy can or should dispense with metaphors or with passionate rhetoric; I agree with Barry Eidlin's declaration that "movements need metaphors" (2013). If, as Michele Moody-Adams argues, conceptual and practical moral progress is necessarily local to some particular domain, gestating within the very cognitive–affective system of situational meanings it aspires to change, then moral growth in some domains might well "require supplying a new metaphor, or some other imaginative structure, in an attempt to reshape our conception of a particular phenomenon" (1999, 175).
The structure of metaphor as such—the pressing together of two apparently unlike things, surprising us with new meaning—itself intimates a figure for neurodiverse interspecies solidarity. Indeed, the conceptual history of solidarity has been shaped by a procession of metaphors—political communities as bodies, families, friends, and teams—whose constraints and ambiguities we may only be able to think through with "the elaboration and introduction of new metaphors" (Honohan 2008, 81). As large as such figures of speech loom in Western political thought, it has often fallen to feminist theory to champion the world-making power of stories, metaphors, and symbols in moral theory, and in the conceptions of political order developed by political theory (see, e.g., Nussbaum 2002, 496–499). One of the tasks that lies ahead for the incipient "political turn" in animal ethics, then, is to return to the critiques of abstract rationality furnished by feminist animal ethicists, and to develop a positive account of how commitments to interspecies justice are shaped and sustained by political rituals, rhetoric, and emotions. Rather than defining itself against specters of speciesism as madness or disorder, a reinvigorated political rhetoric of animal liberation might begin from a sense of the vital and passionate diversity—including neurodiversity—that should be both its ground and its aspiration.
Notes
I offer this phrase by analogy to the venerable notions of "actually existing capitalism" and "actually existing socialism," concepts that gesture to the ways in which a society's ideological prescriptions and self-understandings diverge from, and often serve to obscure, the history and functions of its core political–economic institutions.
This is despite the fact that Francione begins the essay in which he first employs the term by stating: "Social attitudes about animals are hopelessly confused" (1996, i).
Following Weitzenfeld and Joy, "vegan praxis" can be understood here as "a counternarrative and practice in which nonhuman beings are not viewed or treated as appropriate for human consumption" (2014, 21). This involves not just a dietary commitment but the cultivation of morally attentive habits, dispositions, and relationships: "an ever-changing way of understanding and relating to oneself and _all_ other beings based on empathy, authenticity, reciprocity, justice, and integrity" (2014, 25). Compare this conception, situated amid the critical animal studies literature cited in Weitzenfeld and Joy's chapter, to Joy's account of "integration" as discussed above.
Joy's book, intended for a wider audience, mentions "speciesism" only once in the discussion guide appended to the reprinted edition (2011, 151). Weitzenfeld and Joy situate carnism as "a sub-ideology of speciesism" (2014, 21).
In these works, as in much of the related work in sociology and political economy, a different metaphoric regime prevails: as I alluded to in my introduction, talk of visibility/invisibility and blindness/sight abounds. Here, too, scholars should be mindful of the limitations and hazards of their metaphors, even as they examine the particular processes of concealment and revelation that undoubtedly shape our encounters with other animals. Likewise for rhetoric positioning nonhuman animals as "voiceless" and human moral inattention as "deafness," as Sunaura Taylor discusses (2017, 61–67).
"Growth" here seems to me a better general figure for moral developments than Moody-Adams' retention of "progress" for a phenomenon that is, on her account, nonlinear and multidimensional. I note, however, that "growth," like "development" and "progress," also belongs to stultifying metaphoric regimes in economic, business, and policy discourses. These are frames that might be contested via creative links to other biophysical metaphors: for example, those that help to illustrate growth as interdependent maturation (Princen 2010, 64–65).
I owe this point to Cooke (2017), who cites Moody-Adams' claim about metaphor in his welcome call for (primarily liberal) animal rights theories to attend in earnest to the moral imagination.
References
Aaltola, E. (2008), "Personhood and Animals," _Environmental Ethics_ 30 (2): 175–193.
Aaltola, E. (2013), "Skepticism, Empathy, and Animal Suffering," _Bioethical Inquiry_ 10 (4): 457–467.
Aaltola, E. (2015), "Politico-Moral Apathy and Omnivore's _Akrasia_ : Views from the Rationalist Tradition," _Politics and Animals_ 1 (1): 35–49.
Acampora, R. (2016), "Epistemology of Ignorance and Human Privilege," _Animal Studies Journal_ 5 (2): 1–20.
Amiot, C. E. and Bastian B. (2015), "Toward a Psychology of Human–Animal Relations," _Psychological Bulletin_ 141 (1): 6–47.
Benton, T. (1990), "Humanism=Speciesism? Marx on Humans and Animals," in S. Sayers and P. Osborne (eds.), _Socialism, Feminism, and Philosophy: A Radical Philosophy Reader_ , 237–276, London: Routledge.
Butler, J. (2015), _Notes Toward a Performative Theory of Assembly_ , Cambridge, MA: Harvard University Press.
Chopra, A. K. and Doody G. A. (2007), "Schizophrenia, an Illness and a Metaphor: Analysis of the Use of the Term 'Schizophrenia' in the UK National Newspapers," _Journal of the Royal Society of Medicine_ 100: 423–426.
Cole, M. and Morgan, K. (2011), "Veganism Contra Speciesism: Beyond Debate," _The Brock Review_ 12 (1): 144–163.
Cooke, S. (2017). "Imagined Utopias: Animal Rights and the Moral Imagination," _The Journal of Political Philosophy_ 25 (4): e1–e18.
De Waal, F. B. M. (1999), "Anthropomorphism and Anthropodenial: Consistency in Our Thinking about Humans and Other Animals," _Philosophical Topics_ 27 (1): 255–280.
Dinishak, J. (2013), "Mindblindness: A Troubling Metaphor?" in C. D. Herrera and A. Perry (eds.), _Ethics and Neurodiversity_ , 67–85, Newcastle upon Tyne: Cambridge Scholars Publishing.
Duckworth, K., Halpern, J. H., Schutt, R. K., and Gillespie, C. (2003), "Use of Schizophrenia as a Metaphor in U.S. Newspapers," _Psychiatric Services_ 54 (10): 1402–1404.
Eidlin, B. (2013), "The Metaphors of Movements," _Against the Current_ 163. Available online: <https://www.solidarity-us.org/node/3822> (accessed October 4, 2017).
Fenton, A. and Krahn, T. (2009), "Autism, Neurodiversity and Equality beyond the 'Normal,' " _Journal of Ethics in Mental Health_ 2 (2): 1–6.
Francione, G. (1996), "Animals as Property," _Animal Law_ 2: i–vi.
Francione, G. (2009), "A Note on Moral Schizophrenia." Available online: <http://www.abolitionistapproach.com/a-note-on-moral-schizophrenia/> (accessed October 4, 2017).
Freud, S. (1920), _A General Introduction to Psychoanalysis_ , Hall, G. S. (trans.), New York: Boni and Liveright.
Fullbrook, E. (2002), "The Post-Autistic Economics Movement: A Brief History," _The Journal of Australian Political Economy_ 50: 14–23.
Gruen, L. (2009), "The Faces of Animal Oppression," in Ferguson, A. and Nagel, M. (eds.), _Dancing with Iris: The Philosophy of Iris Marion Young_ , 161–172, Oxford: Oxford University Press.
Harper, A. B. (2012), "Going beyond the Normative White 'Post-Racial' Vegan Epistemology," in P. W.Forson and C. Counihan (eds.), _Taking Food Public: Redefining Foodways in a Changing World_ , 155–174, New York: Routledge.
Herrera, C. D. and Perry, A. (eds.) (2013), _Ethics and Neurodiversity_ , Newcastle upon Tyne: Cambridge Scholars Publishing.
Honohan, I. (2008). "Metaphors of Solidarity," in T.Carver and J.Pikalo (eds.), _Political Language and Metaphor: Interpreting_ and _Changing the World_ , 69–82, London: Routledge.
Horta, O. (2010), "What Is Speciesism?" _Journal of Agricultural and Environmental Ethics_ 23: 243–266.
Joy, M. (2011), _Why We Love Dogs, Eat Pigs, and Wear Cows: An Introduction to Carnism_ , reprint, San Francisco, CA: Conari Press.
Kymlicka, W. and Donaldson, S. (2016), "Locating Animals in Political Philosophy," _Philosophy Compass_ 11 (11): 692–701.
Lewiecki-Wilson, C. (2011), "Ableist Rhetorics, Nevertheless: Disability and Animal Rights in the Work of Peter Singer and Martha Nussbaum," _JAC_ 31 (1): 71–101.
Magliano, L., Read, J., and Marassi, R. (2011), "Metaphoric and Non-Metaphoric Use of the Term 'Schizophrenia' in Italian Newspapers," _Social Psychiatry and Psychiatric Epidemiology_ 46 (10): 1019–1025.
May, V. M. and Ferri, B. A. (2005), "Fixated on Ability: Questioning Ableist Metaphors in Feminist Theories of Resistance," _Prose Studies_ 27 (1–2): 120–140.
Mills, C. (1997), _The Racial Contract_ , Ithaca: Cornell University Press.
Mills, C. (2007), "White Ignorance," in S.Sullivan and N.Tuana (eds.), _Race and Epistemologies of Ignorance_ , 11–38, Albany, NY: State University of New York Press.
Moody-Adams, M. (1999), "The Idea of Moral Progress," _Metaphilosophy_ 30 (3): 168–185.
Newkirk, I. (2015), "The Pastime of Psychopaths." Available online: <https://www.huffingtonpost.com/ingrid-newkirk/the-pastime-of-psychopath_b_8084410.html> (accessed January 19, 2018).
Nocella II, Anthony J., George, Amber E., and Schatz, J. L. (2017), _The Intersectionality of Critical Animal Studies, Disability Studies and the Environment_ , London: Lexington Books.
Nussbaum, M. (2002), "Rawls and Feminism," in S.Freeman (ed.), _The Cambridge Companion to Rawls_ , 488–520, Cambridge: Cambridge University Press.
Nussbaum, M. (2010), "Compassion: Human and Animal," in N. A.Davis, R.Keshen, and J.McMahan (eds.), _Ethics and Humanity: Themes from the Philosophy of Jonathan Glover_ , 202–228, Oxford: Oxford University Press.
Pachirat, T. (2011), _Every Twelve Seconds: Industrialized Slaughter and the Politics of Sight_ , New Haven, CT: Yale University Press.
Palmer, C. (2010), _Animal Ethics in Context_ , New York: Columbia University Press.
Pateman, C. (1988), _The Sexual Contract_ , Stanford, CA: Stanford University Press.
Princen, T. (2010), "Speaking of Sustainability: The Potential of Metaphor," _Sustainability: Science, Practice and Policy_ 6 (2): 60–65.
Ray, S. and Sibara, J. (eds.) (2017), _Disability Studies and the Environmental Humanities: Toward an Eco-Crip Theory_ , Lincoln, Nebraska: University of Nebraska Press.
Salomon, D. (2010), "From Marginal Cases to Linked Oppressions: Reframing the Conflict between the Autistic Pride and Animal Rights Movements," _Journal of Critical Animal Studies_ 8 (1–2): 47–72.
Taylor, S. (2011), "Beasts of Burden: Disability Studies and Animal Rights," _Qui Parle_ 19 (2): 191–222.
Taylor, S. (2017), _Beasts of Burden: Animal and Disability Liberation_ , New York: The Free Press.
Waldau, P. (2006), "Seeing the Terrain We Walk: Features of the Contemporary Landscape of 'Religion and Animals,'" in P.Waldau and K.Patton (eds.), _A Communion of Subjects: Animals in Religion, Science, and Ethics_ , 40–61, New York: Columbia University Press.
Waldau, P. (2010), "Law and Other Animals," in M.DeMello (ed.), _Teaching the Animal: Human–Animal Studies across the Disciplines_ , 75–110, New York: Lantern Books.
Waldau, P. (2013a), "Venturing beyond the Tyranny of Small Differences: The Animal Protection Movement, Conservation, and Environmental Education," in M.Bekoff (ed.), _Ignoring Nature No More: The Case for Compassionate Conservation_ , 27–44, Chicago: The University of Chicago Press.
Waldau, P. (2013b), _Animal Studies: An Introduction_ , Oxford: Oxford University Press.
Waldau, P. (2016), "Second Wave Animal Law and the Arrival of Animal Studies," in D.Cao and S.White (eds.), _Animal Law and Welfare–International Perspectives_ , 11–44, New York: Springer.
Weisberg, Z. (2011), "Animal Repression: Speciesism as Pathology," in J.Sanbonmatsu (ed.), _Critical Theory and Animal Liberation_ , 177–194, Plymouth: Rowman & Littlefield.
Weitzenfeld, A. and Joy, M. (2014), "An Overview of Anthropocentrism, Humanism, and Speciesism in Critical Animal Theory," in A. J.Nocella II, J.Sorenson, K.Socha, and A.Matsuoka (eds.), _Defining Critical Animal Studies: An Intersectional Social Justice Approach for Liberation_ , 3–27, New York: Peter Lang.
Wicks, D. (2011), "Silence and Denial in Everyday Life—The Case of Animal Suffering," _Animals_ 1 (1): 186–199.
Wise, S. (2000), _Rattling the Cage: Toward Legal Rights for Animals_ , New York: Perseus Books.
Wrenn, C. L., Clark, J., Judge, M., Gilchrist, K. A., Woodlock, D., Dotson, K., Spanos, R., and Wrenn, J. (2015), "The Medicalization of Nonhuman Animal Rights: Frame Contestation and the Exploitation of Disability," _Disability & Society_ 30 (9): 1307–1327.
Chapter 8
THE HORRIFIC HISTORY OF COMPARISONS BETWEEN COGNITIVE DISABILITY AND ANIMALITY (AND HOW TO MOVE PAST IT)
Alice Crary
What are we to make of the horrific history of the use of animal comparisons in rhetoric urging the marginalization, abuse, and killing of cognitively disabled human beings? Are there appropriate responses to this history that equip us to insist on the equal moral value of the lives of cognitively disabled human beings without simply reinscribing the denigration of animals in our moral and political discourse? Is it possible to combine an image of animals as in themselves morally significant beings with a commitment to human moral equality? This chapter offers an affirmative answer to this last question, and it proceeds by commenting on a conversation that took place at a 2008 conference, in the Philosophy Department of New York State's Stony Brook University, on challenges that the lives of cognitively disabled human beings pose to widely held philosophical beliefs. The most intense public conversations at the event had to do with what some of the speakers saw as the rebuke cognitive disability represents to the classic idea of the equal dignity of all human life or, more succinctly, to the idea of "basic human equality" (Waldron 2017, 4). These speakers defended views to the effect that severely cognitively disabled human beings merit less solicitude and concern in virtue of their disabilities and, further, that reflection on their lives therefore brings into question traditional egalitarian ideals (see esp. McMahan 2010 and Singer 2010). Some of the conference's other speakers responded with expressions of outrage, protesting that this antiegalitarian stance is not only morally offensive and politically pernicious but also philosophically indefensible (see the account of the conference in Kittay 2010).
A key issue at stake between those who set out to question the idea of human moral equality and those who sought to defend it was the appropriate role of animal comparisons in thinking about the lives of human beings with cognitive disabilities. The original impetus for the—at times very heated—discussion of this particular topic was a lecture given by the high-profile moral philosopher and bioethicist Peter Singer. At Stony Brook, Singer methodically presented a case against the idea of human moral equality, specifically by arguing that some seriously cognitively disabled human beings merit less consideration than their cognitively better endowed human fellows. This is a view that Singer was at the time already well known for championing, and it was already characteristic of his strategy for advocating for the view to make use of comparisons between animals and the cognitively disabled (see, e.g., Singer 1994, 159–163). What distinguished Singer's Stony Brook remarks was, above all, the extent to which he foregrounded such comparisons.
Singer's standard line about the moral standing of severely cognitively disabled human beings rests on the premise that the plain fact of being human is morally indifferent. Singer takes it for granted that no consideration a creature merits can be a direct reflection of membership in a life-form or group like "humans" and that any such consideration must be justified by what some ethical theory enables us to recognize as _grounds_ for it. He himself defends a strain of utilitarian theory on which any solicitude that beings warrant is a function of certain individual capacities, in particular, those for pain and pleasure, and he believes that consistency obliges us to allow that any capacities that are morally pertinent in human beings are equally so in animals. _This_ is the moment in his thought about cognitive disability at which Singer generally turns to comparisons with animals. He finds it natural at this point to ask whether some humans and some animals are similarly endowed with morally relevant capacities, and he answers his own question in the affirmative. He presents what he sees as evidence for thinking that some human beings who (say, as a result of a congenital condition) are severely cognitively disabled are no better equipped than some animals with "morally significant capacities," and—in a famous flourish—he concludes that a willingness to assign value to the mere fact that a being is human is _speciesist_ in the sense of involving unwarranted prejudice in favor of our own species (Singer 2009, 18–23).
At Stony Brook, Singer presented these ideas with particular attention to studies of great apes, dogs, and grey parrots that, he claimed, revealed animals of these types to have cognitive capacities superior to those of human beings with, as he put it in the published version of his conference paper, "profound mental retardation" (Singer 2010, 332–333). Singer is and was an outspoken advocate of animal protectionism (see, e.g., Singer 2009), and one of his aims in appealing to these sorts of animal studies—not only at the conference but quite generally—is to show that some animals merit significantly greater solicitude than they typically receive. Yet, insofar as he addresses questions about ethics and severely cognitively disabled humans, as he did at Stony Brook, his ambition in employing animal comparisons is to show that the cognitively disabled have diminished moral standing and that reflection on their lives speaks against affirming an unqualified claim about human moral equality.
The use of animal comparisons in theorizing about cognitive disability is intensely controversial. Some theorists object to such comparisons even when they are not used, as Singer and a fair number of other contemporary theorists use them (see, e.g., Dombrowski 1997; McMahan 2005, 2008, 2009; Rachels 1990), to raise questions about the moral standing of cognitively disabled human beings. (For a representative set of the relevant objections, see Drake 2010; Kulick and Rydström 2015, 273; Price 2011, 133; and Spicker 1990.) The objections reflect awareness of a long history of the employment of animal comparisons in rhetoric urging the marginalization, abuse, and killing of these individuals. Discussions of the relevant history often focus on the place of animals in the rhetoric that the Nazis employed in trying to rationalize the wartime mass murder of patients in psychiatric institutions, and it is certainly reasonable to use these atrocities as a reference point. But the employment of denigrating comparisons of cognitively disabled human beings with animals does not begin in Nazi Germany. There is, for instance, evidence that the use of these comparisons was, at various places in late Renaissance Europe, associated with the mistreatment of cognitively disabled human beings (e.g., by housing them in facilities resembling modern zoos and exposing them to extreme temperatures) (Wolfensberger 1972, 17–23). Moreover, even if our main goal is to better understand the logic of the Nazi use of animal analogies, it is helpful to see how some harmful patterns of thought that bring animals together with cognitively disabled human beings, and that wind up informing Nazi propaganda, originate in nineteenth-century European conversations.
The most notable of these patterns are connected to lines of reasoning that receive a decisive formulation in Darwin's _Descent of Man_ (1871] 1909). Darwin repeatedly likens cognitively disabled human beings to animals, and he does so with an eye to accounting for the "missing link" between human beings and their closest evolutionary antecedents (see Gelb 2008). Although Darwin cannot provide evidence of whole life-forms between "civilized" human beings and apes, he thinks he can demonstrate kinship between what he regards as the most sophisticated nonhuman animals and the least developed human beings (see, e.g., Darwin [1871] 1909, 98–100; for Darwin's general concern with "the imperfection of the geological record" in confronting us with an "absence of intermediate varieties," see Darwin 2006, esp. [chapter 9). Darwin's outlook here is monogenistic, positing a common origin for all human beings, and there is good evidence that he defended monogeny because he abhorred slavery and wanted to resist the polygenistic defenses of it that were common at the time (see 2009, esp., 24 and 1008 and 1009). Yet he gives his overarching project an explicitly racist inflection insofar as he favors the idea of a linear human scale on which some "races," though members of one human family, are yet "lower" and more "savage" than others, and insofar as he picks out as the "lowest" or most "savage" human cases groups of human beings, identified as "nonwhite," such as "the negro and the Australian [aboriginal]" (Darwin [1871] 1909, 241–242; see also 40–43, 141–142, 156, 169–171 and 180–183; see also Desmond and Moore 2009, 977–982). At the same time, echoing the views of prominent contemporaneous anthropologists (see Gelb 2008), he situates the human beings he calls "idiots" or "imbeciles" outside the human family altogether, depicting them as throwbacks to stages on the evolutionary path to human beings (Darwin [1871] 1909, 21–23 and 53). For Darwin "idiots" are most closely related to nonhuman animals (Darwin [1871] 1909, 53, 102–103, and 131–132) and are as such evidence of losses internal to the workings of natural selection.
There is a nuance to Darwin's own views about the appropriate treatment of "idiots." Darwin holds that we have an indirect duty to care for these individuals, since, as he sees it, to do otherwise would risk "deterioration in the noblest part of our nature" (Darwin [1871] 1909, 205–206). Yet he also warns that allowing "idiots," or their "nonwhite" "savage" human cousins, to "propagate their kind" will lead to "degeneration" of the human species (Darwin [1871] 1909, 206). So, there is a sense in which he himself sets the stage for some of the racist and ableist eugenic fervor of late nineteenth and early twentieth-century Europe (see also Darwin [1859] 2006, 208–209 and 217–220).
One characteristic expression of this fervor can be found in the writings of Ernst Haeckel, a German zoologist and popularizer of Darwin who gives his decidedly racist strain of Darwinianism a recognizable "social" turn insofar as he champions, with regard to the human case, "the idea that one can] steer the process of natural selection" (Burleigh 1994, 13; for Haeckel's calls for such "steering," see, e.g., Haeckel 1914, [chapters 7 and ). Many of Haeckel's colleagues interpret this "steering" to include the sterilization and isolation of the cognitively disabled, and Haeckel himself endorses killing in some cases (Burleigh 1994, 13). Although there are many conditions contributing to a cultural environment in which it seems reasonable to thinkers like Haeckel to entertain policies for the murder of their cognitively disabled fellows—including the post–First World War rise of "an economically driven quest for enhanced efficiency and rationalization" (Burleigh 1994, 33)—Darwinian tropes about these individuals as subhuman animals play a significant role. Nor is it only in Germany and other European countries that, in the decades before the Second World War, social Darwinist conversations linking cognitive disability to subhuman animality add to the social vulnerability of the cognitively disabled. In the United States, a notable inheritor of late nineteenth-century European eugenic ideas, there were new programs for "managing natural selection" through the mass sterilization of people with cognitive disabilities and the imposing of marriage prohibitions, as well as through immigration restrictions and targeted deportations (see Baynton 2001, 45–46, Gallagher 1995, 84 and 78–80, Gill 2015, 14, and Simplican 2015, 58). Like their European counterparts, these calls for control of individuals with cognitive disabilities seamlessly integrate animal comparisons with racist ideas of hierarchies of human groups (Samuels 2014, 176–178). This is also true in Britain where in the 1880s the physician John Langdon Down classified individuals with what we now—since the 1960s—call Down syndrome as "Mongoloid idiots," depicting them as recursions to what he regarded as an "inferior" race (Baynton 2001, 36, and Simplican 2015, 58 and 63).
Granted these ideological tendencies, we can represent what was done to those with cognitive disabilities in Nazi Germany as an "application" of already widely accepted "principles of Social Darwinism and the budding science of eugenics" (Gallagher 1995, 5). The most horrific application is the wartime program "T4"—named after the Berlin address of its administrative home ( _Tiergartenstraße 4_ )—under the rubric of which 200,000 people were killed between 1939 and 1945. In the years running up to this period, German asylums were deprived of resources to such an extent that their inhabitants often struck visitors like animals or "beasts" confined in squalid cages (Burleigh 1994, 44), and in memoranda circulated during the planning of T4, prospective grounds for killing "people suffering from serious congenital mental or physical 'malformation' included that they are 'situated at the 'lowest' animal level' (Burleigh 1994, 98) and that to expend resources on them would therefore be to ['sin'] against the 'law of natural selection'" (Burleigh 1994, 195). The Nazis also publicly used animal tropes to sell the murderous T4 policies, for instance, in a series of propaganda films made between 1936 and 1941. Here individuals with intellectual disabilities or chronic psychiatric conditions were often, in the words of historian Michael Burleigh, "explicitly situated below the level occupied by animals, who are invariably depicted with greater affection and sensitivity" (Burleigh 1994, 194). In the 1936 film _Hereditarily Ill_ [ _Erbkrank_ ], "a shaven-headed youth is shown eating handfuls of grass" (Burleigh 1994, 194), and in the 1941 _I Accuse_ [ _Ich Klage an_ ] a crude social Darwinism is deployed to clear the way for the idea that the involuntary euthanasia of "useless" members of society is as innocuous as putting down a suffering pet (Burleigh 1994, 206–207). A second version of _I Accuse_ , which adopts the same basic strategy, includes this bit of dialogue: "Gentlemen, when we foresters have shot an animal and it continues to be in pain, then we give it the _coup de grâce_ " (Burleigh 1994, 201; for a remark on this analogy to putting down pets, see also Gallagher 1995, 18). Moreover, in developing their animal-themed and fundamentally social Darwinist approach to T4, the Nazis increasingly lumped race and various forms of perceived social and sexual deviancy together with cognitive disability, treating all as markers of lack of social "fitness" (see, e.g., Gallagher 1995, 77).
The kinds of animal-cognitive disability comparisons that function in nineteenth-century eugenic and social Darwinist thought, as well as in its later Nazi versions, have a distinctive logic. They don't simply involve, on the one hand, associations of cognitively disabled human beings with a specific kind of animal and, on the other, associations of animals of that kind with some significantly negative characteristic. Cognitively disabled human beings are sometimes denigrated by association with traits that are precisely valued in the animals who possess them. We find a similar structure in animal comparisons the Nazis used to denigrate Jews (see, e.g., Raffles 2007, 525). Thus, as one scholar puts it, "the Nazis were deeply attached to their dogs... [but] that did not keep them from calling Jews 'Hunde'" (Kittay 2010, 399; see also Gallagher 1995, 255–260, and Kittay 2005, 125, for remarks on Nazi laws for the protection of animals). We can understand the apparent paradox here by referring it back to aspects of Darwin's reasoning. The author of _The Descent of Man_ is happy to dehumanize "idiots"—and the racialized "savages" he takes as their close kin—for resembling animals like monkeys whom he praises for their human-like qualities (Darwin 2006, 404–405). This stance makes sense if we take the hierarchy of life-forms internal to evolutionary theory, and also the role of variation in creating it, to be endowed with normative significance (see, e.g., Gelb 2008). Now individual animals of "lower" kinds can be seen as exemplary and laudatory individuals insofar as they possess particular human-like traits that, as it were, "raise" them above their station, while at the same time individual cognitively disabled humans who are taken to possess similar traits—traits that seem to "lower" their station—can be looked down on as evidence of the waste of natural selection.
While the second half of the twentieth century witnessed a large-scale cultural abandonment of social Darwinist beliefs, it's not implausible to think that some of the eugenic practices once associated with social Darwinism (e.g., the forcible control of the sexuality of the cognitively disabled [see Gill 2015], the directing of social resources toward what are perceived as "worthier lives" [see Bodey 2017], and the allocation of medical resources in particular [see Kittay 1999, 164–165]) have outlived these beliefs. Setting aside an investigation into whether, or to what extent, the eugenicist ideas internal to classic comparisons between animals and the cognitively disabled are enjoying a real-world afterlife, it remains important to find ways—not haunted by these ideas—for bringing cognitively disabled human beings into moral thought. Indeed, the appropriate standard for moral thought about the cognitively disabled is higher than this. Such thought should be not only undistorted by these and other forms of prejudice but also informed by the sorts of faithful images of the worldly lives of cognitively disabled human beings that are relevant to ethics.
Singer expresses confidence that his own thinking about cognitive disability meets this high standard. It is not merely that he presents himself as free of pernicious prejudices, such as the "racist viewpoint" that led the Nazis to the "murder of people considered unworthy of living" (Singer 1991, 7; see also Singer 1992, 86). Singer is also sanguine that he is working with accurate empirical descriptions of aspects of the lives of the cognitively disabled. His assurance here is in large part a function of his preferred image of how the mind makes contact with the world. Singer helps himself to a philosophical account of the demands of getting the world in focus—an account that, in its basic outlines, is enormously influential within Anglo-American analytic circles—on which our culturally and ethically local perspectives have an essential tendency to interfere with our view of how things stand, and on which we hence approach a less distorted vision of things by progressively sloughing these perspectives off. Bearing in mind that this account represents movement toward ethical neutrality as essentially tending in the direction of a less obstructed view of the world, we might refer to it as a _neutral conception of reason_ (for a detailed discussion of the relevant rendering of world-directed thought, see Crary forthcoming[a]). Insofar as this neutral conception suggests that we approach a more accurate image of empirical reality by stepping back from our ethical attitudes, it implies that nothing in the empirical world can, qua observable, merit such attitudes and accordingly that nothing in the empirical world can, qua observable, be ethically significant.
Singer only occasionally flags his reliance on the neutral conception, but it structures his thought throughout his career. This is true even though his core philosophical contentions have undergone a notable change over the past twenty years. Whereas early on Singer advocates a type of ethical non-cognitivism (i.e., an outlook on which there are no moral properties and on which moral statements aren't exercises of predicating properties) in reference to which he straightforwardly rejects the idea of objective ethical values, more recently he has shifted toward favoring a rational intuitionist stance that qualifies as a form of cognitivism (or objectivism) about values insofar as it allows that some objective "ethical" truths reveal themselves to intuition (De Lazari-Radek and Singer 2014; see also Singer's own commentary on his development in Singer 1999a and 1999b). Singer now allows that the world contains ethical truths in the form of normatively loaded precepts that speak for particular modes of conduct. This does not, however, represent a retreat from the neutral conception of reason. Singer is not suggesting that the precepts he takes to be intuitable only show up in terms of, or are internally related to, specific attitudes. He construes our mental access to these precepts in neutral terms, and, as a result, he regards our grasp of them as lacking the motivational significance that would by itself explain our acting (De Lazari-Radek and Singer 2014, 197–199). So, Singer continues to abide by the constraints of the neutral conception of reason. Moreover, since the only objective "ethical" truths he recognizes are practical precepts, and since, unlike ethical values as they are standardly conceived, these truths are motivationally inert, he effectively retains the view that nothing in the empirical world is, qua observable, in itself ethically significant (for a fuller treatment of these aspects of Singer's work, see Crary 2016, 19–25).
These philosophical commitments are what underlie Singer's claim that the plain fact of being human, taken (as he in fact takes it) as an observable or theoretically available circumstance, is morally indifferent. At the same time, they are part of the motivation for his insistence that, if we are to represent human beings as in themselves meriting respect and attention, we need to find theory-leveraged grounds for human moral status (e.g., according to the kind of utilitarianism Singer favors, individual human beings' capacities for pleasure and suffering). Further, the neutral conception is the source of his faith in the empirical accuracy of things he says about the cognitively disabled. Because he relies on such a conception, he thinks he goes a long way toward ensuring that he is doing justice to any features of the world that interest him in ethics—including the various features of the worldly lives of cognitively disabled human beings that he discusses—simply by thinking and talking about his subject matter in a manner free from noxious forms of prejudice. _This_ is why Singer thinks his use of comparisons between human beings with cognitive disabilities and animals is unobjectionable. Since the terms in the comparisons are capacities possessed by individual human beings and animals, and since Singer believes that his preferred ethically neutral methods suffice for bringing such capacities, together with likenesses among them, into focus in ethics, it appears to him that his use of the comparisons is philosophically unimpeachable. To be sure, there is a further pragmatic question about whether in thus effectively dealing in analogues of the sorts of animal comparisons that were once integrated into murderously ableist and racist Nazi policies, Singer—despite his personal abhorrence for the policies—risks contributing to a political climate more welcoming of them. But Singer is relatively dismissive of the idea that his views "could erode respect for human life and so lead to a return of the mentality that made Nazi atrocities possible" (Singer 1990, 42; for a similar observation about Singer's attitude toward the risks here, see Kittay 2017, 32). He takes himself to be justified in concluding that his use of animal comparisons is morally unproblematic as well as philosophically sound.
Is Singer's favorable assessment of his own animal-indexed theorizing about cognitively disabled human beings too charitable? The assessment depends for its apparent plausibility on the neutral conception of reason with which Singer operates, and some of Singer's most outspoken critics attack this conception (see, e.g., Crary 2016, chapter 4; Diamond 1978 and 1991; and Mulhall 2009, chapter 9). Indeed, the credentials of the conception were what was at stake in a striking exchange that Singer had with Eva Feder Kittay, a prominent moral philosopher, feminist theorist, and advocate for the cognitively disabled, during the question-and-answer session after Singer's talk at the 2008 Stony Brook conference. Kittay, one of the conference organizers, was at the time already well known as a thinker who became interested in issues affecting the cognitively disabled while advocating for social support and recognition for her daughter Sesha, who has cerebral palsy and who, in adulthood, doesn't speak and isn't capable of even minimal self-care. Writing after the conference, Kittay declares that "for a mother of a severely cognitively impaired child" it is "devastating" to "read texts in which one's child is compared, in all seriousness and with philosophical authority, to a dog, pig, rat, and, most flatteringly, a chimp" (Kittay 2010, 397). Kittay attributes Singer's willingness to deal in animal comparisons in the way he does to limitations in his grasp of the empirical lives of cognitively disabled human individuals like Sesha. But her philosophical image of what it is to do justice to the empirical world is very different from his.
Kittay inherits from and participates in traditions of feminist theorizing that resist the idea—distinctive of the neutral conception—that neutrality is a regulative ideal for all world-directed thought. Antipathy to this idea is sometimes associated with skepticism about objectivity, and it is certainly true that many post-structuralists, including some who are self-identified feminists, move seamlessly from repudiating an aspiration to neutral modes of criticism to embracing such skepticism. But this post-structuralist stance threatens to be politically disempowering, stripping us of any license to claim genuine authority for our critical claims (see Lovibond 1989). There is also a sense in which the stance rehearses the logic of the very neutral conception from which it supposed to free us, and in which it is thus philosophically less radical than it may at first appear. In taking the forfeiture of the ideal of neutrality as equivalent to the loss of an unqualified claim to objectivity, it effectively appeals to the very neutral conception of reason that it is alleged to be disavowing, albeit while also treating the ideal of neutral mental contact with the world internal to the conception as forever beyond reach (see Crary 2018).
Kittay herself works with notable strands of second- and post-second-wave feminist thought that adopt a more antagonistic attitude toward the neutral conception. Here the conception is taken to be philosophically bankrupt and hence incapable of leveraging an attack on the cognitive credentials of particular modes of thought simply because they are ethically non-neutral. The upshot is that it appears wrong to insist that the features of the empirical world that are relevant to this or that bit of feminist or other ethical reflection must reveal themselves to an ethically neutral gaze (for discussion of the relevant feminist literature, see Crary 2001, 2002, and Crary 2018). This is the basic philosophical outlook that Kittay is presupposing in talking about shortcomings in Singer's understanding of the empirical lives of cognitively disabled human beings like her daughter. She is presupposing that specific modes of affective response—of sorts that might be inculcated, for example, by actual experience interacting with cognitively disabled people—are necessary prerequisites for bringing these aspects into focus (Kittay 2010, 406–407; see also Kittay 1999, chapter 2).
At the time of the Stony Brook conference, Kittay was aware that the Princeton, NJ-based Singer had brought some of his students to a local neonatal intensive care unit in New Brunswick, New Jersey, to look at cognitively disabled newborns. She proposed that the next time he take students on a field trip, he bring them to visit the community of small group homes in which Sesha lives. When Singer demurred, saying that this would be "a little further than New Brunswick," Kittay replied that "she would be happy to personally arrange it" and that she wanted him to "see some of these people that [he was] talking about" (quoted in Kittay 2010, 405). Singer then issued the following challenge to Kittay. "I would like you to tell me—just in terms of the argument that I presented—what it is that I would see there that would challenge the argument" (Kittay 2010, 405).
Singer's challenge was in part a demand that Kittay supply him with an advance on the kind of illumination that her proposed excursion would bring with it. This demand seems reasonable if we insist, in accordance with the neutral conception of reason he himself accepts, that any new aspects of the lives of Sesha and her friends must be accessible to us in a manner that doesn't depend on the sorts of capacities for emotional responsiveness that we might develop, say, by spending time with them. Further, insofar as the demand thus appears justified, the reply Kittay gave Singer is bound to seem quite inadequate. What she said to Singer was in essence that "how much you see is... what you bring to the situation" and that therefore she was not "sure what [he'd] see" (Kittay 2010, 405). This struck Singer as mere evasive hand waving, and, when his public debate with her continued in the conference's last session, he told her peremptorily that she had to "put up or stop saying that [he doesn't have the empirical stuff right]" (Kittay 2010, 408). Singer's exasperation reflected his thought that he was justified in insisting not only that she tell him what he would see if he visited her daughter's home but also that she do so "in terms of the argument" he presented. This further requirement also seems reasonable if we impose on ourselves the constraints of the neutral conception of reason. Granted these constraints, it seems reasonable to accept two of the main premises of Singer's argument, namely, that the sheer fact of being human (insofar as that is considered to be an observable circumstance) is not in itself morally significant and that we therefore need to find grounds for human moral status. Now it seems fair to demand that Kittay specify not only what Singer will see if he visits Sesha but also how _that_ —whatever it is—serves to ground a claim about Sesha's moral standing.
But the logical dynamic of the conversation between Singer and Kittay shifts if, in accordance with the feminist traditions in which Kittay is working, we reject the neutral conception of reason. To be sure, it matters what we identify as an alternative to this conception. Any successful case for an alternative needs to start from an attack on the view that undistorted thought about the world is beholden to an ideal of ethical neutrality, and it is possible to mount a plausible challenge of this sort (see Crary 2016, section 2.1, and Crary forthcoming[a]). But, once we establish that empirical thinking is not as such regulated by an ideal of neutrality, we still need to determine which aspects of the world are such that we need ethical resources to get them in view. Within classic Anglo-American philosophy of the social sciences, there are arguments for thinking that _social phenomena_ , taken to be composed of actions that are themselves understood as expressions of practical rationality, are not as such available to thought except through the lens of ethical considerations (see, e.g., Winch 1990, esp. 98–99; for a detailed commentary on relevant portions of the Winch, see Crary 2018e). Such arguments do not, however, suffice for Kittay's purposes. For what distinguishes her position is the thought that ethical resources are required to bring into focus not only the conduct of rational individuals but also aspects of the lives of humans—like Sesha—who never reach rational maturity.
Although Kittay herself doesn't pursue this line of inquiry, it is possible to find considerations that are adequate for a defense of this thought in a view of mind that is sometimes associated with the later philosophy of Wittgenstein. At issue is a view on which our categories for thinking about _all_ aspects of mind, whether or not they are expressive of rationality, are ethically inflected categories that resist meaningful translation to neutral terms, and on which these categories are also essentially matters of sensitivity to how things empirically are. Ian Hacking comes very close to making a case for this sort of Wittgensteinian view, arguing—in a series of articles on autism—that the practical adjustments and responses we typically acquire in the course of early socialization contribute internally to our ability to non-inferentially perceive the psychological significance of the real expressions and conduct of others, without regard to whether they have humanly typical or atypical mental capacities (Hacking 2009a, b and 2010). It is possible to elaborate the sort of approach to mind Hacking defends so that it becomes one on which we require the relevant sorts of practical adjustments and responses in order to pick out the psychological character of the expressive behavior of those adult human beings who are atypical specifically in that they to a greater or lesser degree lack mature capacities of reason (see Crary 2016, sections 2.1–2.3). There is, moreover, an additional element of Hacking's work that deserves mention here. Drawing on his preferred Wittgensteinian view of mind, Hacking advocates what he regards as the further Wittgensteinian idea that the modes of practical response internal to psychological understanding encode a sense of what is humanly important. His thought is not merely that we need ethical resources to do justice in ethics to typical or atypical psychological aspects of human existence but also that in order to get these aspects empirically into focus, we need to look at individuals through the lens of an ethical conception of human life. Once again, it is possible to extend Hacking's reasoning, showing that this thought of his (namely, that we need a gaze saturated by a sense of what matters in human life in order to do justice to the psychological expressions of typical or atypical others) holds in connection with our efforts to pick out aspects of the minds of others who are atypical in the specific sense of being nonrational (see Crary 2016, section 4.2).
Suppose we bring this slightly extended version of Hacking's Wittgensteinian reflections to bear on the case of Kittay's daughter Sesha. Part of the idea would be that in order to capture Sesha's worldly circumstances in a manner relevant for ethics, we need to see her in the light of a morally charged image of human existence. Relatedly, we cannot exclude the possibility that there are aspects of Sesha's circumstances that we will fail to register unless we further develop our current ethical image. There is an open-ended number of ways in which we might go about refining this image: by interacting with people with or without cognitive disabilities or, alternately, by engaging with literature, memoirs, journalism, films, or other works of art that shape our attitudes about the lives of people with cognitive disabilities or about human life more generally (see Kittay 2010, 408). We might turn, for instance, to work that the journalist Katherine Boo did for the _Washington Post_ in the 1990s, exposing fatal forms of abuse and medical neglect of cognitively disabled individuals in a network of private homes in the D.C. area (Boo 1999). Part of what gives Boo's work interest here is that she takes her commitment to writing about urgent social and political matters like these to be consistent with "experimenting with form" in order to engage readers and expand their conceptions of human importance (this last reference is to remarks of Boo's at the Princeton University Center for Human Values, November 8, 2017). Not that every bit of writing or other oeuvre that aims to enrich our sense of what matters in human life will, insofar as it grabs us, directly inform our ability to do justice in ethics to the worldly existence of others. Any particular work may turn out to be sensationalistic, sentimental, or distorting in some further way. The point of—the extended version of—Hacking's Wittgensteinian reflections is simply that the engaged task of investigating different conceptions of human flourishing is internal to world-directed thought about human beings in ethics without regard to the nature or level of their cognitive abilities. So, we must be working with such conceptions if we are to be in a position to recognize whether, say, a given expression of Sesha's is one of anxiety or affection, whether a given activity with her is exploitative or engaging, or whether a given institutional setting for her represents enrichment or an abusive form of confinement. This is the backdrop against which Kittay invited Singer on an excursion on which he would interact with Sesha and her friends and—as Kittay hoped—thereby develop new modes of responsiveness to light up otherwise inaccessible aspects of their lives.
Now it should be clear that Kittay was right not to accede to Singer's request to confine her response to him to the terms of his argument. What emerges from the line of thought just traced out is that it is only from perspectives afforded by an ethically charged conception of human life that it is possible to make sense of psychological aspects of the worldly existence of human beings, whatever the level or nature of their individual cognitive capacities. Seeing the expressions of a human being is, according to this line of thought, inseparable from seeing the person in question as an individual for whom, simply in virtue of her humanity, certain kinds of things matter. This means that human beings, however well or poorly endowed cognitively, figure in legitimate, world-guided moral thought as beings who merit specific forms of attention just as the kinds of beings they are. So, there is no reason to follow Singer in taking as an argumentative premise the idea that the plain fact of being human is morally unimportant. Additionally, there is no reason to follow him in searching for grounds that some ethical theory enables us to recognize as endowing human beings with moral standing. And, lastly, since there is no reason to search for such grounds, there is a fortiori no reason to accept the terms of an argument, like Singer's, that urges us to look for such grounds in individual human capacities that seem to invite comparison with the individual capacities of other animals.
This last reflection is worth underlining. It's not merely that there is no room in responsible moral thought about human beings with cognitive disabilities for Singer-style animal comparisons. The entire Singerian exercise of appealing to animal comparisons—and a fair number of thinkers have followed Singer in attempting this questionable exercise (see, e.g., Dombrowski 1997; McMahan 2005, 2006 and 2009; and Rachels 1990)—is not so much a contribution to the search for the value in human life as a reflection of the failure to see this value where it is.
Granted that human beings enter moral thought as meriting respect and solicitude just as the sorts of being they are, does it follow that we are obliged to regard animals as "lesser" creatures and, by the same token, to reject _all_ human–animal comparisons in ethics as necessarily insidious? Here it is helpful to recall that a key element of the account of the value of bare humanity just presented is a philosophically unorthodox—Wittgensteinian-Hackingian—view of mind. At the heart of this view is the idea that our concepts for aspects of mind, irrespective of whether these are expressive of rationality, are irredeemably ethical and, at the same time, essentially revelatory of how things are. A good case can be made for elaborating a version of this view not only in reference to human minds but also in reference to animal minds (see Crary 2016, chapter 3, and Gaita 2002). Hacking suggests, as we saw, that an exploration of the view in connection with human beings reveals that if we are to do empirical justice in ethics to psychological features of human life, we need to look at individual human beings in the light of an image of what matters in human life. It would be possible to show that an investigation of the view in connection with animals yields an analogous result. The idea would be that if we are to do empirical justice in ethics to the minds of animals of a particular kind, we need to look at individual animals of that kind in the light of an image of what matters in their lives. This would mean that seeing the expressions of an animal of a given kind is inseparable from seeing the creature at issue as an individual for whom, simply in virtue of being an animal of that kind, certain sorts of things matter. It would mean that animals of different kinds enter into sound moral reflections as beings who call for specific forms of attention not as "lesser" beings but just as the kinds of beings they are.
This view of the moral standing of animals, like its counterpart view of human moral standing, has significant implications for how we conceive the demands of moral thought about animals. It implies that investigating different conceptions of flourishing for animals of a given kind is internal to world-directed thought about animals of that kind (see Crary 2016, section 4.3, and Crary 2018). Just as we may move toward a more just understanding of the worldly lives of human beings with cognitive disabilities by immersing ourselves in memoirs, journalism, literature, or other works of art that shape our sense of what matters in human life, we may move toward a more just understanding of the worldly lives of animals of different kinds by immersing ourselves in work that shapes our sense of what matters in the lives of animals of particular kinds. We may progress toward a better understanding here, say, by turning to some of Tolstoy's nonfictional writings on vegetarianism or to Jonathan Safran Foer's work on eating animals. What makes the work of these particular authors especially salient here is that they self-consciously go beyond presenting plain facts of slaughter and try to engage us in ways that will enable us to appreciate the momentousness of the killing of animals (see Crary 2016, sections 6.2 and 7.1, and Crary forthcoming[b]).
Setting aside these methodological issues for other occasions, it is worth noting that the introduction of the above account of the moral standing of animals of different kinds eliminates a hierarchy or normative ordering of life-forms of the sort that informs social Darwinist thought. Now animals of particular kinds show up for us as mattering just as the kinds of creatures they are. So—as far as ethics is concerned—there is no reason to speak, in normatively drenched, pseudo-evolutionary terms, of "lower" and "higher" animals. The point is not merely that we should jettison the type of hierarchy of life-forms found in social Darwinist enterprises. There is an unacceptable hierarchizing of life-forms in the medieval _scala naturae_ , and there is a likewise untenable hierarchizing of life-forms in Singer's thought. Despite his hostility to speciesism, Singer presents us with a human-headed ranking of life-forms insofar as he ties creatures' moral status to their individual capacities. For it is platitudinous that those capacities will typically be those that are typical for whatever species is in question, with members of the human species typically receiving the biggest "morally relevant" portion (see Wolfe 2008, 118, for a version of this same idea about Singer's project). The larger point is that there is no room for any normative pecking order, whether a medieval one, a social Darwinist one, a Singerian one, or one of some other kind.
It would be wrong to protest that we _need_ an ethically laden hierarchy of life-forms to defend the idea of basic human equality. It is true that classic strategies for exalting humanity involve assigning us a station above that of animals (see, e.g., Maritain 1944] 2012, 66 and 101–2), and, despite the intensity of attacks over the last half century on the sorts of hierarchy of life-forms presupposed by these strategies, it is also true that it remains common today for thinkers to attempt to demonstrate the value of humanity by suggesting that all human beings are superior to animals (e.g., Kateb 2011, 3–4 and 22–24, and Anderson 2014, 494–496). The persistence of this trend is perhaps unsurprising given that many social justice movements—including, among others, the US disability rights movement (for commentary, see Taylor 2017, [chapter 2)—demand respect for the oppressed by insisting that they are not animals. It is, however, wrong to think that we can't combat ableism or other forms of oppression without trampling on animals (see, e.g., Taylor 2016, chapter 2). It's not merely that, as the line of thought developed here shows, we can represent all human beings as in themselves valuable without denigrating animals. More significantly, we undermine our own human-centered liberating efforts if we don't do this. Without even following up on empirical evidence indicating that "the more sharply people distinguish between humans and animals, the more likely they are to dehumanize other humans" (Kymlicka 2017, 13), we can say that, in a cultural context like ours, in which the belief that human beings are the end products of a process of natural selection is widespread, the idea of a normative ordering of life-forms is hazardously likely to get associated with the idea of evolutionary stages and, by the same token, hazardously likely to get associated with the idea that some individual human beings or groups of human beings are "lower" than others.
If we abandon a normative ordering of life-forms, we open the door for non-demeaning comparisons between aspects of human life, on the one hand, and aspects of animal life, on the other. Admittedly, Singer's writings about these matters notwithstanding, there are very good pragmatic reasons to be cautious in the use of such comparisons. Given that the notion of ethically charged distinctions between "lower" and "higher" animals is in fact still rampant in our culture, and given that this notion has historically been, and still is, integral to rhetoric that contributes to the subjugation of socially vulnerable groups of people—including, not only the cognitively disabled but also the physically disabled, people identified as nonwhite, women, the gender-non-conforming, the very old, etc.—we need to be especially careful in tracing out lines of filiation between the lives of animals and the lives of members of human groups who confront systematic forms of bias. But we can say all of this without implying that animal likenesses have no place in ethical thought. Indeed, we can say it all without implying that these likenesses have no place in ethical thought that touches on the lives of cognitively disabled human beings.
This is a possibility that Kittay seems to overlook, though, admittedly, her views about the moral standing of animals aren't well developed. In one recent essay, she does say that she sympathizes with challenges to "the claim of [human] superiority [over animals] and its concomitant right to dominate [them]" (Kittay 2017, 31). But elsewhere she seems to at least implicitly operate with the sort of ethically saturated notion of "higher" and "lower" life-forms that would render animal comparisons not merely contingently but inherently demeaning (see, e.g., Kittay 2010, 397; see also Kittay 2017, 25). We can shed a little light on why Kittay hasn't arrived at a settled view of animals and ethics by considering the following, somewhat confusing juncture in her thought. Kittay is clearly committed to the idea that we require moral categories with an essential reference to a conception of what is humanly important in order to bring the worldly life of any human being, however cognitively endowed, into view in ethics (see the text above and also Kittay 2010, 408, and 2017, 28). This commitment ought to have freed her up from the project, decisive for Singer and many others, of providing a theoretical account of the _grounds_ of human moral standing, and, as we have seen, she sometimes insists forcefully that she isn't obliged to supply Singer with such grounds. Yet Kittay now says she needs to confront Singer and others with "an alternative" theoretical account of what undergirds the moral standing of human beings, and she appeals in this connection to what she calls "relational properties" of human beings (Kittay 2017, 36). It doesn't seem unreasonable to connect Kittay's new interest in theorizing about these properties with the fact that she doesn't fully explore the philosophically radical aspects of her view that speak against the very idea that we need to theorize about grounds of human moral status. Kittay never specifically asks _why_ —as she herself maintains—we require moral categories to get worldly human existence into focus in ethics. Perhaps if she had asked this question, she would have inquired whether we also require moral categories to bring the worldly lives of animals into view in ethics. Perhaps then she would have inquired whether, just as—in her view—humans figure in moral thought as creatures who matter just as the kinds of beings they are, animals of different kinds figure in moral thought as creatures who matter just as the kinds of beings they are. If she had addressed these questions, she would have been more advantageously placed to argue—as she now seems to want to—that we are obliged to jettison the idea of an ethical ranking of life-forms and that, far from being a circumstance we should lament, this better equips us to defend basic human equality.
Abstracting from these involved interpretative issues having to do with Kittay's work, it _is_ possible to identify appropriate roles for references to animals in ethical thought about cognitive disability. But this is an indefinitely large topic. One way to approach it would be to investigate the work of people who identify as neuro-atypical and who claim that their particular forms of atypicality give them unusual insight into the lives of animals of specific kinds (see, e.g., Grandin 1995 and Prince-Hughes 2004). Another approach might start from a consideration of the account, laid out above, of how human beings and animals enter moral thought. Encoded in this account is the idea that we require a certain emotional responsiveness or sensibility in order to recognize modes of human and animal expression. This epistemological idea has implications for how in ethics we conceive of the human condition. At issue is a point about how our affective endowments are internal to our rational capacities or, alternately, a point about how certain endowments we have specifically as embodied, fleshly beings are internal to reason. Drawing on this point, we can give a distinctive spin to the now widespread idea that our standing as beings of a rational kind does not exempt us from the contingencies of animal life. We can, that is, give distinctive expression to the idea that—and this is a theme sounded in the work of many great contemporary literary and other artists—as beings of a reasoning kind we are in the condition of animals. To acknowledge this condition is to recognize that there is an ineliminable element of chance both to whether we develop the capacity to reason and to whether we retain it. A sound and illuminating bit of moral thinking might urge us to live in a way that reflects respect for the glorious and terrifying vulnerability that thus binds our lives to the lives of animals—and to at least in this regard accept a role for animal comparisons in ethical thought that touches on questions of cognitive disability.
Acknowledgments
I presented early versions of this chapter at the Disability—Perspectives, Challenges and Aspiration conference sponsored by the Philosophy Department of the University of Tennessee, at the School of Social Science seminar at the Institute for Advanced Study in Princeton, New Jersey, at the Department of Comparative Thought and Literature at Johns Hopkins University, and at the Philosophy Institute at the Freie Universität in Berlin. I also circulated an early version for discussion at a meeting of the Ira W. DeCamp Bioethics Seminar at Princeton University's University Center for Human Values. I am grateful for the helpful feedback I received on these occasions. I owe particular debts, for their constructive comments, to Susan Brison, Cora Diamond, Jacob Dlamini, Didier Fassin, Lori Gruen, Nathaniel Hupert, Eva Feder Kittay, Nick Langlitz, Paola Marrati, Ally Peabody, Fiona Probyn-Rapsey, Silvia Sebastiani, Peter Singer, and Michael Williams.
Notes
There is no suggestion here that animal comparisons _necessarily_ degrade human beings. The claim is that certain classic animal comparisons were _in fact_ intended to degrade specific groups of human beings. I am grateful to this collection's editors for mentioning the importance of underlining this point.
The well-represented position outlined in this paragraph is consistent with holding that an open-ended number of empirical things are in themselves ethically significant. The point is that their ethical significance has to be established by elements of ethical theory or, alternately, by exercises of a strictly practical faculty of reason, and not by exercises of a faculty of reason that, even if partly practical, has an essentially theoretical or world-guided dimension.
This is perhaps the right place to acknowledge that some moral thinkers agree with Singer in accepting the constraints of the neutral conception of reason while also insisting on the moral importance of the sheer fact of being human. A stance of this sort is characteristic of Kantian moral philosophers. For relevant discussion of the work of such moral philosophers, see Crary (2018b).
References
Anderson, E. (2014), "Human Dignity as a Concept for the Economy," in M. Duwell et al. (eds.), _Cambridge Handbook of Human Dignity_ , 492–497, Cambridge: Cambridge University Press.
Baynton, D. (2001), "Disability and the Justification of Inequality in American History," in P. K. Longmore and L. Umansky (eds.), _The New Disability History: American Perspectives_ , 33–57, New York: New York University Press.
Bodey, S. (2017), "My Son Has Autism. Discrimination Almost Cost Him His Life," _Washington Post_ , August 30.
Boo, K. (1999), "Forest Haven Is Gone: But the Agony Remains" _Washington Post_ , March 14, 1999. Available online: <http://www.washingtonpost.com/wp-srv/local/daily/march99/grouphome14.htm> (accessed May 22, 2018).
Burleigh, M. (1994), _Death and Deliverance: 'Euthanasia' in Germany c. 1900-1945_ , Cambridge: Cambridge University Press.
Crary, A. (2001), "A Question of Silence: Feminist Theory and Women's Voices," _Philosophy_ 76: 371–395.
Crary, A. (2002), "What Do Feminists Want in an Epistemology?" in P. O'Connor and M. Scheman (eds.), _Re-Reading the Canon: Feminist Interpretations of Wittgenstein_ , 97–118, University Park: Penn State Press.
Crary, A. (2016), _Inside Ethics: On the Demands of Moral Thought_ , Cambridge: Harvard University Press.
Crary, A. (2018a), "Ethics," in L. Gruen (ed.), _Critical Terms in Animal Studies_ , Chicago: University of Chicago Press.
Crary, A. (2018b), "Cognitive Disability and Moral Status," in A. Cureton and D. Wasserman (eds.), _Oxford Handbook of Philosophy and Disability_ , Oxford: Oxford University Press.
Crary, A. (2018c), "The Methodological Is Political," _Radical Philosophy_ , 202.
Crary, A. (forthcoming[a]), "Objectivity," in J. Conant and S. Greves (eds.), _Wittgenstein: Basic Concepts_ , Cambridge: Cambridge University Press.
Crary, A. (forthcoming[b]), "Seeing Animal Suffering: A Lesson from Tolstoy," in A. Linzey (ed.), _Animal Theologians_.
Darwin, C. ([1871] 1909), _The Descent of Man_ , London: John Murray.
Darwin, C. ([1859] 2006), _On the Origin of Species by Means of Natural Selection_ , London: Dover.
De Lazari-Radek, K. and Singer, P. (2014), _The Point of View of the Universe: Sidgwick and Contemporary Ethics_ , Oxford: Oxford University Press.
Desmond, A. and Moore. J. (2009), _Darwin's Sacred Cause: Race, Slavery and the Quest for Human Origins_ , London: Allen Lane.
Diamond, C. (1978), "Eating Meat and Eating People," _Philosophy_ 53 (206): 465–479.
Diamond, C. (1991), "The Importance of Being Human," in D. Cockburn (ed.), _Human Beings_ , 35–62, Cambridge: Cambridge University Press.
Dombrowski, D. (1997), _Babies and Beasts: The Argument from Marginal Cases_ , Chicago: University of Illinois Press.
Drake, S. (2010), "Connecting Disability Rights and Animal Rights—A Really Bad Idea," October 11. Available online: <http://notdeadyet.org/2010/10/connecting-disability-rights-and-animal.html> (accessed September 15, 2017).
Gaita, R. (2002), _The Philosopher's Dog_ , Melbourne: Text Publishing.
Gallagher, H. (1995), _By Trust Betrayed: Patients, Physicians and the License to Kill in the Third Reich_ , St. Petersburg: Vandamere Press.
Gelb, S. A. (2008), "Darwin's Use of Intellectual Disability in _The Descent of Man_ ," _Disability Studies Quarterly_ 28 (2).
Gill, M. (2015), " _Already Doing It: Intellectual Disability and Sexual Agency_ ," Minneapolis: University of Minnesota Press.
Grandin, T. (1995), _Thinking in Pictures: My Life with Autism_ , New York: Vintage Books.
Hacking, I. (2009a), "Autistic Autobiography," _Philosophical Transactions of the Royal Society_ 364: 1467–1473.
Hacking, I. (2009b), "Humans, Aliens and Autism," _Daedalus_ 138 (3): 44–59.
Hacking, I. (2010), "How We Have Been Learning to Talk about Autism: A Role for Stories," in L. Carlson and E. F. Kittay (eds.), _Cognitive Disability and Its Challenge to Moral Philosophy_ , 261–278, Oxford: Blackwell Publishing Ltd.
Haeckel, E. (1914), _The History of Creation, or the Development of the Earth and Its Inhabitants by the Action of Natural Cause Volume Two_ , 6th edition, New York: D. Appleton & Company.
Kateb, G. (2011), _Human Dignity_ , Cambridge: Harvard University Press.
Kittay, E. F. (1999), _Love's Labor: Essays on Women, Equality and Dependency_ , London: Routledge.
Kittay, E. F. (2005), "At the Margins of Moral Personhood," _Ethics_ 116: 100–131.
Kittay, E. F. (2010), "The Personal Is Political Is Philosophical: A Philosopher and Mother of a Cognitively Disabled Person Sends Notes from the Battlefield," in L. Carlson and E. F. Kittay (eds.), _Cognitive Disability and Its Challenge to Moral Philosophy_ , 393–413, Oxford: Blackwell.
Kittay, E. F. (2017), "The Moral Significance of Being Human," January 6, Presidential Address, Eastern Division Meeting, American Philosophical Association, Baltimore.
Kulick, D. and Rydström, J. (2015), _Loneliness and Its Opposite: Sex, Disability and the Ethics of Engagement_ , Durham: Duke University Press.
Kymlicka, W. (2017), "Human Rights without Human Supremacism," _Canadian Journal of Philosophy_. Available online: DOI: 10.1080/00455091.2017.1386481 (accessed November 17, 2017).
Lovibond, S. (1989), "Feminism and Postmodernism," _New Left Review_ 78: 5–28.
Maritain, J. ([1944] 2012), _Christianity and Democracy_ , San Francisco: Ignatius Press.
McMahan, J. (2005), "Our Fellow Creatures," _The Journal of Ethics_ 9: 353–380.
McMahan, J. (2008), "Challenges to Human Equality," _The Journal of Ethics_ 12: 81–104.
McMahan, J. (2009), "Radical Cognitive Limitation," in B. Kimberly and A. Cureton (eds.), _Disability and Disadvantage_ , 240–259, Oxford: Oxford University Press.
McMahan, J. (2010), "Cognitive Disability and Cognitive Enhancement," in L. Carlson and E. F. Kittay (eds.), _Cognitive Disability and Its Challenge to Moral Philosophy_ , 345–367, Oxford: Blackwell.
Mulhall, S. (2009), _The Wounded Animal: J. M. Coetzee and the Difficulty of Reality in Literature and Philosophy_ , Princeton, NJ: Princeton University Press.
Price, M. (2011), _Mad at School: Rhetorics of Mental Disability and Academic Life_ , Ann Arbor: University of Michigan Press.
Prince-Hughes, D. (2004), _Songs of the Gorilla Nation: My Journey through Autism_ , New York: Harmony Books.
Rachels, J. (1990), _Created from Animals: The Moral Implications of Darwinism_ , Oxford: Oxford University Press.
Raffles, H. (2007), "Jews, Lice, and History," _Public Culture_ 19 (3): 521–566.
Samuels, E. (2014), _Fantasies of Identification: Disability, Gender, Race_ , New York: New York University Press.
Simplican, S. (2015), _The Ability Contract: Intellectual Disability and the Question of Citizenship_ , Minneapolis: University of Minnesota Press.
Singer, P. (1990), "Bioethics and Academic Freedom," _Bioethics_ 4 (1): 33–44.
Singer, P. (1991), "On Being Silenced in Germany," _The New York Review of Books_ , 1–8.
Singer, P. (1992), "A German Attack on Applied Ethics: A Statement by Peter Singer," _Journal of Applied Ethics_ 9 (1): 85–91.
Singer, P. (1994), _Rethinking Life and Death: The Collapse of Our Traditional Ethics_ , New York: St. Martin's Griffin.
Singer, P. (1999a), "Reply to Michael Huemer," in D. Jamieson (ed.), _Singer and His Critics_ , 391–392, Oxford: Blackwell.
Singer, P. (1999b), "A Response," in D. Jamieson (ed.), _Singer and His Critics_ , 269–335, Oxford: Blackwell.
Singer, P. (2009), _Animal Liberation_ , New York: HarperCollins.
Singer, P. (2010), "Speciesism and Moral Status," in L. Carlson and E. F. Kittay (eds.), _Cognitive Disability and Its Challenge to Moral Philosophy_ , 331–344, Oxford: Blackwell.
Spicker, P. (1990), "Mental Handicap and Citizenship," _Journal of Applied Philosophy_ 70 (2): 139–151.
Taylor, S. (2017), _Beasts of Burden: Animal and Disability Liberation_ , New York: The New Press.
Waldron, J. (2017), _One Another's Equals: The Basis of Human Equality_ , Cambridge: Harvard University Press.
Winch, P. (1990), _The Idea of a Social Science and Its Relation to Philosophy_ , London: Routledge & Kegan Paul.
Wolfe, C. (2008), "Learning from Temple Grandin, or, Animal Studies, Disability Studies, and Who Comes after the Subject," _New Formations_ 64: 110–123.
Wolfensberger, W. (1972), _The Principle of Normalization in Human Services_ , Ontario: G Allan Roeher Inst Kinsman.
Chapter 9
THE PERSONAL IS POLITICAL: ORTHOREXIA NERVOSA, THE PATHOGENIZATION OF VEGANISM, AND GRIEF AS A POLITICAL ACT
Vasile Stanescu and James Stanescu
The invention of a new "disease"
"Orthorexia nervosa" is a term that means "fixation on righteous eating" (Bratman 1997). Dr. Steve Bratman, a medical doctor who focuses on holistic treatments, coined the term in the October 1997 issue of the _Yoga Journal_. The _Yoga Journal—_ despite having the term "Journal" in the name _—_ is not an academic journal nor does it provide peer-review. However, despite the absence of any peer-reviewed or academic studies on the topic, Bratman subsequently began to diagnose his patients with what, he had determined, was a newly discovered eating disorder. Orthorexia nervosa is not recognized by the American Psychiatric Association, is not included in the _DSM-5_ ( _Diagnostic and Statistical Manual of Mental Disorders_ ) or any other medical manual (American Psychiatric Association 2017), and to this day, has few credible peer-reviewed studies to substantiate its existence; it does not represent an actual medical diagnosis. However, it has caught on in the wider popular culture including multiple magazine articles, blog post, books, and television news (Kaplan 2015). For example, largely favorable articles about the condition have appeared in virtually every newspaper in the United States one can think of, including _The New York Times_ (Ellin 2009), _The New Yorker_ , (Specter 2014), the _Washington Post_ (Kaplan 2015), _Newsweek_ (Reynolds 2015), and the _Wall Street Journal_ (Reddy 2014). Beyond the United States, the phenomenon of orthorexia nervosa also appeared (in just one year) in _The Australian_ (2016), on SBS (Verghis 2017), in the _Queensland Times_ (Norton 2016), _PerthNow_ (Jurewicz 2016), and _Huffington Australia_ (Blatchford 2016). Therefore, while not an actual diagnosis, unofficially the "diagnosis" has come to represent a large and growing body of popular knowledge and cultural belief. While the exact criteria are still in flux, overarching indicators of orthorexia supposedly include practices such as: "Violation of self-imposed dietary rules causes exaggerated fear of disease, sense of personal impurity and/or negative physical sensations, accompanied by anxiety and shame" and "Dietary restrictions escalate over time, and may come to include elimination of entire food groups" (Bratman 2017a).
While in theory orthorexia is open to any type of dietary preference, a critical reading of the literature suggests that, in reality, it is primarily focused on pathologizing vegetarianism and veganism as a type of eating "disorder." For example, Bratman was a strict vegan before diagnosing himself with orthorexia (Bratman 1997). Likewise, in the original essay in which Bratman coined the term, while including some other dietary practices, he focused primarily on examples of vegetarian and vegan practices, such as vegetarians who refused to eat vegetables cooked in the same pots as meat, a recovering alcoholic who was made to feel guilty for drinking milk, as well as Bratman's personal examples of relearning to eat Kraft cheese and enjoying a triple scoop of ice cream (Bratman 1997). Bratman recently wrote the foreword to a book entitled _Breaking Vegan,_ a memoir from Jordan Younger, a former vegan blogger who diagnosed herself with orthorexia and, as the title suggests, "broke" from her veganism. As far as we can tell, Bratman cites only diets that have at least some type of vegetarian or vegan component, such as a macrobiotic or a raw vegan diet, as dangerous, while explicitly sanctioning as not dangerous other highly restrictive diets that possess a meat-centered component, for example the paleo diet (Bratman 2017a). Such an omission seems odd, since the paleo diets require the complete elimination of food groups such as all cereal grains, all legumes (including peanuts), and even potatoes (Vandyken 2016). In other words, it seems that—at least for Bratman—only diets that eliminate meat, eggs, or dairy run the risk of ever developing into orthorexia.
To be fair, Bratman reassures his readers that it is at least theoretically possible to be a vegan and not suffer from orthorexia. However, it is not clear how that would be possible since, by definition, every vegan would meet several of the Bratman's published criteria for orthorexia, such as elimination of entire food groups, as well as such warning signs as "distress or disgust when in proximity to prohibited foods" or "moral judgment of others based on dietary choices" (Bratman 2017a). In other words, as far as we can tell, the only way anyone could be a vegan and not suffer from orthorexia, under Bratman's interpretation, would be if the person occasionally still consumed meat, diary, or eggs; did not find meat unpleasant to be around; did not criticize or judge the meat-eating practices of others; and did not mind attending social events in which animal products were the only food available. While a person who was occasionally vegan for, say, minor weight loss or health reasons might manage to not to be classified as suffering from orthorexia; it seems likely that every ethical vegan would.
It is important to note the manner in which Bratman mixes his diagnosis of orthorexia, which—as earlier noted—is not actually a disease, with anorexia, a very real and serious medical condition. The similarity begins in the name itself—"orthorexia nervosa" was clearly chosen to sound like anorexia nervosa. Furthermore, the term seems to reclassify the decision to become vegetarian and vegan from an ethical decision—particularly when conducted by young women—to suffering from a dangerous eating disorder paralleled to anorexia. For example, on his website Bratman has a link to a story about Kate Finn who—while medically diagnosed as suffering from anorexia—died, Bratman tells us, because she suffered from orthorexia (Bratman 2003). This account is featured on a website called Beyond Veg, which attempts to convince people not to be vegetarian or vegan, as they see it as inherently unhealthy (Beyond Vegetarianism n.d.). However, they do promote the "paleo diet" that, as earlier mentioned, would seem to meet all of the same criteria of orthorexia (exclusion of entire food groups, etc.). Likewise, it seems clear that Jordan Younger, the ex-vegan blogger discussed earlier, actually suffered from anorexia, a point she herself has admitted, explaining: "I developed obsessions and anxiety around food. It wasn't about veganism. I had restrictions on top of veganism" (James 2015). Indeed, in both of these cases (Jordan Younger and Kate Finn), the health question seems less to do with veganism and far more to do with their desire to eat exclusively raw foods and attempts to engage in—extremely—long juice fasts (Pfeffer 2014), neither of which are standard practices that are part of ethical veganism. Unfortunately, this distinction between ethical veganism on the one hand and not consuming enough calories to maintain health on the other hand is a distinction that not only does Bratman not make clear but, in fact, frequently blurs. For example, on his blog Bratman explains:
A high percentage of the personal communications I receive on this blog involve such young women and their distressed parents. At the fragile physical onset of puberty, these girls are following "healthy food diets" that amount to starvation. A frequent entry point for orthorexia in this group is ethical veganism. This is a philosophy with much to admire and naturally appeals to any idealistic person. Unfortunately, in a young woman this noble impulse can combine with others that are less benign to create an eating disorder. (Bratman 2015)
Anorexia is a real and serious disease, which is caused—in part—by our thin-obsessed and fat-shaming culture. Certain aspects of the animal rights community—for example books such as _Skinny Bitch_ (Freedman 2009)—are, therefore, particularly problematic in their use of fat-shaming as a form of vegan promotion. Likewise, it is possible that some people with a preexisting eating disorder—such as anorexia—might claim to be "vegan" in order to hide their eating disorder. And, finally, it is entirely possible that a new or young vegan may not have the necessary information to make wise nutritional decisions. Vegans and animal rights proponents may need to do more to make sure that everyone makes wise nutritional decisions if they transition into a vegan diet. However, none of these are the arguments that Bratman is making. Instead, he is interviewing fears of concerned parents over their daughters' desire to become ethical vegans and linking this decision with preexisting—but unrelated—worries parents may have of their daughters becoming anorexic. Moreover, we are troubled by the way Bratman uses this diagnosis to discount any reasons that a young woman could choose to become an ethical vegan—such as massive animal abuse or environmental degradation—and instead suggests (as he seems to throughout this writing) that the only reason would be a desire for "purity" or an exercise in "control" (Bratman 2015). For example, he explains that young women's "real" desire for going vegan is not ethics—or, indeed, animals at all—but instead the desire to control "the messiness of being human" and to "escape the horrible complexities of life" (Bratman 2015). In any case, Bratman assures us the young female vegan has "practically no idea what she is truly feeling" (Bratman 2015). Indeed, even if a female vegan claims to know why she is choosing veganism, these insights would be irrelevant since she is, in essence, hysterical: according to Bratman, "her brain is malnourished and not working properly" (Bratman 2015).
As Laura Wright writes on this move to pathologize (as anorexia) the ethical reasons behind women's desire to transition to veganism:
Including animal rights in the discussion about why women choose to become vegetarian or vegan certainly will not alleviate the negative discourse about veganism that pervades both the mainstream media and scientific studies of the links between non-normative diet and eating disorders, but it would certainly allow for more honest analysis, and it might empower instead of pathologize such a choice as having less to do with restricting female diet and more to do with making productive connections between health, feminism, and animal welfare. (Wright 2012)
It is one thing to argue that a concerned parent or society as a whole may wish to make sure that anyone transitioning to veganism has adequate information and support to make informed and healthy nutritional decisions. It is quite another to repeat the preexisting cultural trope that women should simply not be listened to at all because they are hysterical, crazy, diseased, weight-obsessed, and irrational.
Fellowship of the table
Our critique of Bratman's work—as well as the basic idea of orthorexia—is based primarily on the idea of statistical normalization. In other words, under a theory of orthorexia, the main problem with becoming vegan is that it violates established social norms that, in turn, could lead to social isolation. For example, here is the way in which Bratman discusses, in his original article from 1997, how he came to realize that he suffered from orthorexia:
I pursued wellness through healthy eating for years, but gradually I began to sense that something was going wrong. The poetry of my life was disappearing. My ability to carry on normal conversations was hindered by intrusive thoughts of food. The need to obtain meals free of meat, fat, and artificial chemicals had put nearly all social forms of eating beyond my reach. I was lonely and obsessed. (Bratman 1997)
Vasile Stanescu's research, over the last several years, has focused on the rise of so-called "humane meat" and "locavore" eating movements. What is revealing is the striking similarity between the way in which locavores and proponents of humane meat discount veganism and the way in which Bratman discusses his view of orthorexia. We view this diagnosis of orthorexia as part of a larger discourse that what is wrong with veganism and animal rights is our refusal to "break bread" with others and to socially "outcast" ourselves. In both cases, the argument is that veganism will make one a "social outcast" and the claim that veganism itself is based on a supposed desire for "purity." For example, notice the similarities in the way that Michael Pollan, the most famous advocate for locavorism, describes why he chooses not to give up his own brief experiment with vegetarianism: "[E]ating meat is... also more sociable, at least in a society where vegetarians still represent a relatively tiny minority... What troubles me most about my vegetarianism is the subtle way it alienates me from other people and, odd as this might sound, from a whole dimension of human experience" (Pollan 2006).
Both Bratman and Pollan reject their experiment with vegetarian or veganism because, in their view, it makes them abnormal, statistically strange, that it takes them away from other people, isolates them. Likewise, both of them romanticize eating meat or dairy as "the poetry of my life" in Bratman's case and as "a whole dimension of human experience" for Pollan (Bratman 1997, Pollan 2006). So, too, both argue that what underlies this definable loss of the human experience is a type of infantilism, a type of running away from the messiness of life and fear of our own mortality. In fact, Pollan goes so far as to assert that animal rights represent a new type of "Puritanism" (Pollan 2006).
Nor are these arguments limited to Pollan alone, in fact, they appear—universally—throughout every argument or memoir for "humane" or "local" meat that we have ever read. For example, Catherine Friend, a humane farmer who has published two memoirs, assures her readers that she still eats factory-farmed meat for 25 percent of all of her meals because it would not be compassionate enough for her, or her readers, to become too fanatical even about their "compassionate carnivorism" (Friend 2008, 240). Likewise, Donna Haraway—an important writer in the fields of both feminism and animal studies—claims that vegans fail to understand the messiness and complexities of life, are primarily motivated by a desire for purity, and, therefore, refuse to "break bread" with those who eat meat (Haraway 2007, 294–295). But by far our favorite example is Kathy Rudy who in her text _Loving Animals_ asserts that veganism is the same as lesbian separatism—a position she critiques. As she writes: "Veganism is a radical lifestyle change that most of society will never embrace. It's too much like the kind of lesbian separatism that circulated in the 1970's, a radical ideology that felt the world would be a better place without any men in it at all" (Rudy 2013, 104). Perhaps only veganism could manage to be simultaneous compared to both "puritanism" and "lesbian separatism."
Overall, it is odd to hear such appeals to magical surrealism (e.g., "the poetry of life" or "a whole dimension of human experience") in conversations about mental health and ethical decision-making. How exactly is one supposed to argue with logic like that? Do vegans not possess a "fellowship of the table" when we eat together? If fellowship of the table is of such extreme importance, why not simply always serve vegan meals for company, since everyone can always eat vegan? Is a firm commitment to social justice not a desirable part of "the human experience" or the "poetry of life"? What is the most fascinating in all of these magical assertions is that the vegan and animal rights activists are in fact somehow "insane" for being too rational or too logical. Such an assertion represents a fascinating reversal of the stereotype of feminine hysteria. The argument is not that we are crazy because we are too emotional (or—to be exact—not only because we are too emotional), we are pathologized because we have become _too logical_. For example, some of these theorists, such as Rudy, intentionally reference the feminist care ethics tradition of Josephine Donovan and Carol Adams (Donovan 2007), not to argue for animal rights, but, instead, to argue against utilitarian arguments for veganism as being, in her words, "too cold," "clinical," and "sterile" (Rudy 2013, 104). "In other words," she claims, "it lacks heart" (104). Nor is this the only permanent double bind or false choice that vegans find themselves in. If we are not strict enough, we are accused of hypocrisy. If we are, instead, too strict (by whoever's standard) we become insane, fanatical, and obsessed with purity. For example, what we most appreciate about Rudy's comparison to lesbian separatism is the manner in which—on literally the exact opposite page of her book—she indicts vegans for not being pure enough (Rudy 2013, 105). Vegans are, somehow, both too pure and yet never quite pure enough. What exact level of rationality, emotion, or ethical commitment to veganism is acceptable always remains unclear; what is clear is that whatever choices we make or tactics we choose, the vegan—somehow—always gets it wrong.
The vegan as "pervert"
In his College de France lecture _Abnormal,_ Michel Foucault charts the manner in which the view of statistical norms become the basis of all forms of madness or insanity (Foucault 2004). Specifically, he lays out how earlier classical ideas of "the natural monster" (which, Foucault suggests, focused primarily on persons who were viewed as transgressive against the "natural laws" of gender and species) become transformed into the "moral monster" who transgresses against the social contract and, finally, transformed into the "abnormal monster" or—as Foucault phrases it—"the pervert." For Foucault, the "pervert" represents someone who fails to match statistical models of normalcy or, one might say, one who violates what might be viewed as "statistical law." As Foucault phrases it: "Psychiatry introduced something that until then was partly foreign to it: the norm understood as a rule of conduct, informal law, and principle of conformity opposed to irregularity, disorder, strangeness, eccentricity, unevenness and deviation... the norm as functional regularity, as the principal of an appropriate and adjusted function: the 'normal' as opposed to the pathological, morbid, disorganized, and dysfunctional" (162). While Foucault's main focus is on issues related specifically to sex—such as fears over homosexuality and childhood masturbation—in providing his genealogy of the way in which all views and beliefs could become pathologized, he mentions of the manner in which even animal rights, when it was first introduced in the nineteenth century, was also pathologized as a type of statistical "disorder." As Foucault writes:
When, for example, a society for the protection of animals conducts a campaign against vivisection, Magnan, one of the big names in psychiatry at the end of the nineteenth century, discovers a syndrome: the antivivisectionist syndrome. I want to emphasize that, as you can see, there is nothing here that is the symptom of an illness: it is a syndrome, that is to say, a partial and stable configuration referring to a general condition of abnormality. (311)
For Foucault, this reference has the quality of an aside to simply demonstrate the absurd degree that that level of statistical pathologization might reach; however, we wish to take his claims of the pathologization of animal rights quite seriously. For Foucault's overarching argument is to chart that way that the "natural monster," the "moral monster," and the "statistical monster"—far from breaking from one another—build upon one another. For example, Foucault's project, in part, is to chart a genealogy of how the so-called sexual natural monster of gender blending becomes viewed as the moral monster of the sexual criminal, until, ultimately, it becomes solidified into the nineteenth-century discovered disease of "homosexuality." So too, we believe that we can witness a similar continuity in the modern blending of supposed natural, moral, and statistical norms in order to produce the current idea of the morally transgressive vegan who now suffers from the newly discovered "disease" of orthorexia and has become a social pariah (we are told) who disrupts the sacred fellowship of the table. Indeed, the essence of Pollan's argument about how and why veganism is so disruptive invokes, repeatedly, this same type of "natural law" critiqued by Foucault. As Pollan phrases it:
Aristotle speaks of each creature's "characteristic form of life". For domesticated species, the good life, if we can call it that, cannot be achieved apart from humans—apart from our farms and, therefore, our meat eating. This, it seems to me, is where animal rightists betray a profound ignorance about the workings of nature. To think of domestication as a form of enslavement or even exploitation is to misconstrue the whole relationship, to project a human idea of power onto what is, in fact, an instance of mutualism between species. Domestication is an evolutionary, rather than a political, development. (Pollan 2006, 320)
There is far too much to unpack in this paragraph here; however, the essential point we want to take away is the idea that animal rights betray a profound ignorance of the "workings of nature" (i.e., natural law) and, likewise, a profound ignorance of a type of "species contract," (i.e., social contract) leading to a criticism based on statistical irregularity (i.e., veganism becomes "unnatural" only because it is uncommon). We see in Pollan and Bratman, via Foucault, the same leitmotif of the vegan, and in particular, the animal rights activist as a natural, moral, and statistical "monster." Much like Foucault's insight of causes of the pathogenization of homosexuality, what disturbs Pollan so much in the move toward veganism is its perversion of what he views as "natural law" and arrangement of species hierarchy and the "social contract" between humans and domesticated animals. In other words, for Pollan, the vegan is a "pervert." They have perverted the natural rule of man over animal, the moral rule of the social contract between human and other species, and perverted the statistical—yet still sacred—fellowship of table and, therefore, perverted the very essence of the "human experience." If one hears in such claims a certain similarity to arguments for the "sacredness of marriage" or a panic against transfolk using a restroom, we should view such similar refrains as far from purely coincidental. In all such cases, there is a conflation of the natural and moral with the merely statistical, tied to a fear of perversion coupled with a desire for "social quarantine." Utilizing Foucault's insights, we must see these statistical claims of social isolation in relation to fears of contagion of social perversion and fears of a transgressive "monster." By which we mean, the seeming objective claims that vegans are a statistical rarity is, in fact, the way both Pollan and Bratman seem to believe that the vegan should be treated and indeed "cured." Not only that we are socially stigmatized and ostracized but in fact that we should be. And thus via Foucault, we can begin to answer back our earlier hypothetical question of why it is that both Pollan and Bratman—in their discussion of madness—utilize such metaphysical language as "the poetry of life" and "a whole dimension of the human experience." And why they seem incapable of imagining a pleasure of eating together, either between vegans themselves or with omnivores, in which everyone is consuming food free of animal products. Such a sociality is unthinkable for either Pollan or Bratman because it fails the necessary quarantine of veganism; such sociality might even represent a further expansion of the perversion of veganism they wished to domesticate in the first place. And hence also this peculiar emphasis that the "cure" of veganism or orthorexia is a speech act; as Foucault makes clear throughout _Abnormal_ , the cure for insanity was always the model of the confessional, that speech act that disavowed all the different forms of insanity. Since what was at stake was the pervasion of the social order, what mattered were not the private beliefs as much as the public speech act. Hence, too, we can begin to answer our earlier question of how Bratman believes that a vegan could still eat a vegan diet and yet, somehow, not suffer from orthorexia, even as all criteria would suggest that they must. The solution would seem to be that it is acceptable—in Bratman's view—for someone to refrain from eating animal products as long as they refuse to engage in the speech acts identifying as veganism. What is pathologized is less the reality of the diet—whatever it might be—than the speech act itself of identifying as vegan that "isolates" one. In other words, one can refrain from eating animals only as long as no one knows, as long as one repeatedly disavowals any identity or judgment. Judith Butler has written on the unique nature of the "Don't Ask, Don't Tell" compromise in the US military, where it was not the action, not even the desire, but the speech act of identifying as queer that uniquely criminalized and regulated (Butler 1997, 82). So, too, we want to see an attempt in both locavores and orthorexia to pathologize not the eating of meat—one way or another—but the speech act of identifying as ethically vegan.
To provide a concrete example, while in graduate school, Vasile met a prominent environmental researcher who, through his research, had determined that the consumption of animal flesh was a leading cause of climate change and preventable harm against the environment. And so, he was strictly vegan, except for a single meal of meat he had one day a year. We have long wondered about the utility of that single meal of flesh: if he felt that eating meat possessed some unique nutrient, a single meal a year would be irrelevant. Even in terms of pleasure the connection seems unclear: What possible pleasure could one derive from a single meal a year, particularly when his body had, in all likelihood, lost the ability to even fully digest animal flesh? We finally determined that the decision entirely came down to one of identity. When Vasile first congratulated the researcher on being vegan, he stated that he was not and mentioned his one meal a year as his proof. For him, it seemed, that single meal was how he still proved his "virile" and carnivorous identity; his one meal a year proved that he was, by definition, still not a vegan. In other words, he was not a pervert; he was still socially acceptable at the fellowship of the table. So, too, we have discovered the same tendency in all forms of locavorism and so-called "compassionate" or "humane" meat. Since less than 1 percent of animal products are even marketed as humane meat, many advocates for humane meat, such as Catherine Friend, simply eat factory-farmed meat as a large part of their diet. However some, such as Pollan, regularly insist that since humane meat is so hard to locate, they, in reality, eat almost no meat at all. If what they are telling is true, we must ask what is behind these extremely small and rare bites of so-called "humane" meat that they do eat? As Pollan himself writes: "[W]hy am I working so hard to justify a dinner menu?" (Pollan 2006). If they are, as they claim, "basically" vegetarian already, what is at stake for them in not becoming _actually_ vegetarian? We believe the issue is entirely one of identity, no matter how little or how rare their consumption of animals has become. As long as they still eat some meat, any meat, they're not perverted, they're not crazy, and, most importantly for someone such as Pollan, they have not disrupted the natural or moral order, and, arguably, they should still be welcomed at the table of fellowship of (straight?) men. As Chloë Taylor has argued on this same connection:
I will argue that alimentary appetites, like sexual appetites, continue to be sites of normalization, or that how we eat is a target of what Foucault calls disciplinary power. Moreover... just as the sexual and alimentary monsters were frequently fused in the late eighteenth- and early nineteenth-century popular imaginary, so today the abnormalities of eating and sex are often conflated, with male vegetarians in particular suspected of being—queer. The normalization of sex and eating are thus not only analogous but inter-related and mutually reinforced. (Taylor 2012, 132)
Before you decide that we are making too much of this connection between Pollan's hostility to veganism and sex, it is the exact analogy that Pollan himself makes in the same section where he discusses veganism as "a loss of the humane experience." As he phrases it: "We should at least acknowledge that the human desire to eat meat is not, as the animal rightists would have it, a trivial matter, a mere gastronomic preference. By the same token we might call sex—also now technically unnecessary for reproduction—a mere recreational preference. Rather, our meat eating is something very deep indeed" (Pollan 2006).
Grief as political act
There is in fact a feeling of insanity in our experience of being vegan, but it is not the insanity of orthorexia; it is instead the insanity that comes from the feeling of being surrounded by a "banality of evil." As J.M. Coetzee writes via the character of Elizabeth Costello:
I seem to move around perfectly easily among people, to have perfectly normal relations with them. Is it possible, I ask myself, that all of them are participating in a crime of stupefying proportions? Am I fantasizing it all? I must be mad! Yet every day I see the evidence. The very people I suspect produce the evidence, exhibit it, offer it to me. Corpses. Fragments of corpses that they have bought for money. (Coetzee 1999, 69)
Or, as James Stanescu has written in a similar vein:
To tear up, or to have trouble functioning, to feel that moment of utter suffocation of being in a hall of death [the meat aisle in the grocery store] is something rendered completely socially unintelligible. Most people's response is that we need therapy, or that we can't be sincere. So most of us work hard not to mourn. We refuse mourning in order to function, to get by. But that means most of us, even those of us who are absolutely committed to fight for animals, regularly have to engage in disavowal. (Stanescu, J. 2012a, 568)
As Dinesh Wadiwel has recently argued, the correct analogy we should use for our understanding of the mistreatment of animals is not individual cruelty, but instead that of war (Wadiwel 2015). For the simple truth is that to torture and kill 70 billion animals each and every year is not the act of one or two individuals of human cruelty, no matter how depraved; it is the work of millions and millions of humans all working in concert. It is a collective action requiring a collective solution. In such a system, to be an ethical vegan is to violate the deepest held, if unspoken, dictate of our entire society. It is to become a conscientious objector—indeed a traitor—to a global war effort toward human supremacy. This is why, we have always felt, we see the constant invocation of the "analogy" to the holocaust throughout animal rights and critical animal studies literature by Coetzee (1999)—even Jacques Derrida (2008)—and so many others (see Adorno 2005, Dujack 2003, Kupfer-Koberwitz n.d., Netz 2004, Patterson 2002, and Singer 1980). Not that any of them are making moral comparisons between incomparable instances, but because it is the only framework they have to invoke that feeling they possess of fighting against a massively organized system of a "banality of evil" (Arendt 2006, 276) that only they seem able to even see.
If Wadiwel is correct and violence against animals is a collective action, requiring a collective solution, what we must learn to do is to transform these individual moments of grief into political acts of resistance. To refuse food when offered by our family members or to grieve the dead bodies that surround us in the meat aisle of a grocery store or a restaurant is, in our current society, to be "crazy," too feminine, and "hysterical," regardless of the gender of the person grieving. But what if it were not so? We believe that Foucault, via Wadiwel's rereading of him, offers us a way to affectively respond to this pathologization of veganism. If what is occurring is war, we must learn to demonstrate that our individual grief represents a collective political action. We see as the best example of this transformation of what was previously viewed as a purely personal grief into a political action is the work of ACT UP. ACT UP represents a direct action advocacy group that through public actions, such as "die-ins," sought to transform the personal grief of AIDS victims and their loved ones (primarily found within the LGBTQAAI+ community) into public and political project. We see in the actions of vegan activists' recent move to host a funeral within the isles of grocery stores as a movement toward highlighting the banality of evil that surround us at all times, as a way to reject actions of personal disavowal, and as a way to transform our own individual moment of grief into effective calls for political change and action. As Lori Gruen has convincingly argued in this same context: "Creating communal possibilities for mourning our companions whom we have loved and lost as well as all of the animals for whom we grieve can take grief out of the closet, out of the realm of the comic or crazy, and make the lives and deaths of animals visible and meaningful" (Gruen 2014).
Carol Hanisch wrote in her essay "The Personal Is Political" (1970) on the tendency to view women's consciousness raising as a type of therapy:
The very word "therapy" is obviously a misnomer if carried to its logical conclusion. Therapy assumes that someone is sick and that there is a cure, e.g., a personal solution. I am greatly offended that I or any other woman is thought to need therapy in the first place. Women are messed over, not messed up! We need to change the objective conditions, not adjust to them. Therapy is adjusting to your bad personal alternative. (Hanisch, 76)
A view that leads to her conclusion that "One of the first things we discover in these groups is that personal problems are political problems. There are no personal solutions at this time. There is only collective action for a collective solution" (76). The same is true, we would suggest, for our feeling of grief as a vegan and the current attempts to pathologize our political resistance as a new type of personal hysteria requiring therapy. We, too, need to change the objective conditions, not adjust to them. We, too, must come to see that there are no personal solutions to the exploitation of animal suffering—not even personally going vegan alone; there is and can only be our collective action for animal rights in order to achieve a collective solution to our species' war against all other nonhuman animals. Like the feminist, queer, and other social justice movements before us, what animal rights activist need is not therapy, but _change._
Acknowledgments
We would like to acknowledge Chloë Taylor who first suggested the idea of writing about _orthorexia nervosa_ to us and whose work directly helped inspire this chapter.
Notes
This chapter was conceived as a partnership with James Stanescu, whose work directly inspired it. Because of starting a new tenure track, James Stanescu was not able to cowrite the chapter, and he felt it was, therefore, wrong to be listed as a coauthor. However, I disagree. Please read everything as coauthored with James Stanescu, as many of the ideas—if not the actual words—came directly from him.
For example, the _Journal_ includes the claim—directly alongside Dr. Bratman's article, "Reality Check: What Is Everything a Part of and Yet Not Part of Anything? The Source of All Energies! Science Calls It Tachyon." Advanced Tachyon Technologies, "Reality Check," _Yoga Journal_ 1997. September/October: 49. While not entirely clear, I think this might be an advertisement (as it includes an "800" telephone number and an offer of a "free catalogue"). It is possible that the _Yoga Journal_ holds its articles to a different standard than its advertisements. However, it is clearly not an academic or peer-reviewed journal.
See also Kaplan (2015).
Since 1997, a small number of peer-reviewed studies on the disease have been published; however, a meta-analysis found "methodological problems in these studies, such as the use of non-validated assessment instruments, small sample size and sample characteristics, which make generalization of the results impossible" (Varga et al. 2013, 103). Likewise, in her dissertation specifically on the question of whether orthorexia should be considered as a valid diagnosis, Erin Michelle Mcinerney-Ernst found "The vast majority of ON [Orthorexia nervosa] research has been focused on very limited samples, such as homogeneous groups of medical students, nutritional students, or performance artists, and lacks experimental rigor" (Mcinerney-Ernst 2011, 26).
"The main entree was always vegetarian. However, a small but vocal group insisted on an optional serving of meat. Since many vegetarians would not eat from pots and pans contaminated by fleshly vibrations, this meat had to be cooked in a separate kitchen. The cooks also had to satisfy the Lacto-ovo-vegetarians, or Vegans, who eschewed all milk and egg products" (Bratman 1997).
The memoir is a particularly clear example of the way the discourse around orthorexia circulates, as the title was not "Breaking Orthorexia" but instead "Breaking Vegan" (Younger 2016). See also Bratman (n.d.).
Note: Other media outlets have used orthorexia to discuss non-vegetarian-type diets (e.g., avoiding gluten) and some have even criticized the paleo diet; these comments are specific to Bratman.
See Stanescu 2017, 2016, 2013, 2009, and Jenkins 2014.
"A deep current of Puritanism runs through the writing of the animal philosophers, an abiding discomfort not just with our animality, but with the animals' animality too. They would like nothing better than to airlift us out from nature's 'intrinsic evil'—and then take the animals with us. You begin to wonder if their quarrel isn't really with nature itself" (Pollan 2006, 322). See also Stanescu (2012b).
See also Stanescu (2014).
In _When Species Meet_ , Haraway writes a replicate of the arguments made by both Bratman and Pollan about the social isolation of veganism and her view on the possible dangers of extremism. For example, in justifying her decision to eat a feral pig, Haraway explains: "There is a third and last parting bite necessary to explore how to proceed when species meet. No community works without food, without eating _together._.. This is a deeply unsettling fact if one wants a pure diet... There is no way to eat and not to kill, no way to eat and not to become with other mortal being to whom we are accountable, no way to pretend innocence and transcendence or a final peace... Further, one must actively cast oneself with some ways of life and not those who eat differently to a subclass of vermin, the underprivileged. Or the unenlightened; and giving up on knowing more, including scientifically, and feeling more, including scientifically, about how to eat well—together" (Haraway 2007, 295).
"There are aspects of care theory that deeply resonate with the kind of 'connection' I call for in this book. While to some extent I quarrel with both the foundations of care theory (briefly that women are essentially more caring creatures) and with the outcome of care theory (that animals are not ours to use), the impulse behind feminist care ethics is very attractive because it places the weight of social change in the affective, emotive register (rather than in rationality). I hope to revisit these questions in my next project... Utilitarian can be cold, clinical, and sterile. In other words, it lacks heart" (Rudy 2013, 104).
To what degree vegetarians lose the ability to digest meat is a widely debated issue. The overall consensus is that vegetarians do lose the ability to fully digest meat in the short run; however, this ability returns in the long term if vegetarians continue to eat meat. As such, someone who only ate meat once a year would—in all likelihood—experience physical discomfort. For a fuller discussion on the topics, see Lane (2007) and Santillano (n.d.).
As Farm Forward, an organization that actually works to support "humane" farms, admits: "[T]he reality of meat is unambiguous. And at Farm Forward we don't pull any punches when we face inconvenient realities: Most of the animals raised and killed for food (more than 99 percent, to be precise) come from unsustainable and cruel factory farms or, in the case of sea animals, other industrial operations.... Every person who adopts a vegetarian diet reduces suffering and environmental degradation _and_ helps stretch the small supply of non-factory meat, dairy, and eggs currently available for those who choose to eat meat. As long as the demand for non-factory animal products exceeds the supply to this degree, it is best to avoid even these products. But whatever our approach to eating ethically, the important point to remember is that withdrawing our financial support from factory farming reduces the greatest barrier to a humane, sustainable agriculture: the wealth and power that the factory farm industry draws from the money we funnel to it daily" (Food Choices 2011).
We mean banality of evil in the way it was originally framed by Hannah Arendt, as a system whereby it is hard to know your actions are even evil anymore. As she explained, "The trouble with Eichmann was precisely that so many were like him, and that the many were neither perverted nor sadistic, that they were and still are, terribly and terrifyingly normal. From the viewpoint of our legal institutions and of our moral standards of judgment this normality was much more terrifying than all the atrocities put together for it implied... that this new type of criminal, who is in actual act _hostis generis humani_ , commits his crime—under circumstances that make it well-nigh impossible for him to know or to feel that he is doing wrong" (Arendt 2006, 276).
ACT UP quotes on its website this explanation of how personal grief motived Charles Clifton, executive director of Test Positive Aware Network in Chicago, into his work for ACT UP: "I'm tired of grieving. I'm tired of remembering. I'm tired of wondering. I'm tired that I still grieve the death of Antonio, who died 15 years ago on October 8th. I'm tired of marking the anniversary of his death. I'm tired of wondering of what might have been. I'm tired of hoping. I'm tired of coping. I'm tired of dates that always remind me of how tired I am. I'm tired of wondering what's next, who's next. I'm tired of this road" (Clifton 2001).
References
Adorno, T. (2005), _Minima Moralia: Reflections on a Damaged Life_ , New York: Verso.
American Psychiatric Association (2017), _Diagnostic and Statistical Manual of Mental Disorders_ , 5th edition, Arlington, VA: American Psychiatric Publishing.
Arendt, H. (2006), _Eichmann in Jerusalem: A Report on the Banality of Evil_ , New York: Penguin.
Beyond Vegetarianism (n.d.), "Beyond Vegetarianism." Available online: <http://www.beyondveg.com/> (accessed February 21, 2018).
Blatchford, E. (2016), "Orthorexia Nervosa: The Darker Side of Clean Eating," _HuffPost Australia_ , January 3. Available online: <http://www.huffingtonpost.com.au/2016/03/01/orthorexia-nervosa_n_9344844.html> (accessed February 21, 2018).
Bratman, S. (1997), "Health Food Junkie," _Yoga Journal_ (September/October), pp. 42–50.
Bratman, S. (2003), "Fatal Orthorexia." Available online: <http://www.orthorexia.com/original-orthorexia-essay/fatal-orthorexia/> (accessed February 21, 2018).
Bratman, S. (2015), "Adolescent Girls and Orthorexia," July 19. Available online: <http://www.orthorexia.com/adolescent-girls-and-orthorexia/> (accessed February 21, 2018).
Bratman, S. (2017a), "Healthy Eating vs. Orthorexia," March 26. Available online: <http://www.orthorexia.com/healthy-eating-vs-orthorexia/> (accessed February 21, 2018).
Bratman, S. (2017b), "The Authorized Bratman Orthorexia Self-Test," June 8. Available online: <http://www.orthorexia.com/> (accessed February 21, 2018).
Bratman, S. (n.d.), "Foreword to Breaking Vegan." Available online: <http://www.orthorexia.com/foreward-to-breaking-vegan/> (accessed February 21, 2018).
Butler, J. (1997), _The Psychic Life of Power: Theories in Subjection_ , Stanford, CA: Stanford University Press.
Clifton, C. (2001), "I'm Tired of Grieving; I'm Tired of Remembering; Tired of Wondering," _Positively Aware_ , November/December. Available online: <http://www.actupny.org/> (accessed February 21, 2018).
Coetzee, J. M. (1999), _The Lives of Animals_ , A. Gutmann (ed.), Princeton, NJ: Princeton University Press.
Derrida, J. (2008), _The Animal That Therefore I Am_ , M. L.Mallet (ed.), Wills, D. (trans.), New York: Fordham University Press.
Donovan, J. A. (2007), _The Feminist Care Tradition in Animal Ethics: A Reader_ , New York: Columbia University Press.
Dujack, S. R. (2003), "Animals Suffer a Perpetual 'Holocaust,'" _The Los Angeles Times_ , April 21. Available online: <http://articles.latimes.com/2003/apr/21/opinion/oe-dujack21> (accessed February 21, 2018).
Ellin, A. (2009), "What's Eating Our Kids? Fears about 'Bad' Foods," _New York Times_ , February 25. Available online: <http://www.nytimes.com/2009/02/26/health/nutrition/26food.html> (accessed February 21, 2018).
Farm Forward (2011), "Food Choices," _Farm Forward_ , May 17. Available online: <http://www.farmforward.com/farming-forward/food-choices> (accessed February 21, 2018).
Foucault, M. V. (2004), _Abnormal: Lectures at the Collège De France, 1974–1975_ , New York: Picador.
Freedman, R. K. (2009), _Skinny Bitch; Skinny Bitch in the Kitch_ , Old Saybrook: Tantor Media.
Friend, C. (2008), _The Compassionate Carnivore, or, How to Keep Animals Happy, Save Old MacDonald's Farm, Reduce Your Hoofprint, and Still Eat Meat_ , Philadelphia, PA: Da Capo Lifelong.
Gruen, L. (2014), "Facing Death and Practicing Grief," in C. J. Adams (ed.), _Ecofeminism: Feminist Intersections with Other Animals and the Earth_ , New York: Bloomsbury Publishing.
Hanisch, C. (1970), "The Personal Is Political," in S. F.Koedt (ed.), _Notes from the Second Year: Women's Liberation_ , 76–83, New York: Radical Feminism.
Haraway, D. J. (2007), _When Species Meet_ , Minneapolis: University of Minnesota Press.
"Hard to Swallow: Is Clean Eating Really Good for You, or a Damaging Obsession?" (2016), _The Australian_ , June 10. Available online: <https://www.theaustralian.com.au/life/weekend-australian-magazine/clean-eating-and-orthorexia--the-perils-of-maca-root-cacao-nibs-spirulina-chia-seeds-and-other-healthy-food/news-story/02a1094bbe4e6eb22b60a4d1e0e47a4a> (accessed February 21, 2018).
James, S. D. (2015), "Blogger Jordan Younger Reveals How Extreme 'Clean Eating' Almost Killed Her," _Today_ , November 11. Available online: <https://www.today.com/health/breaking-vegan-author-jordan-younger-confesses-dirty-secrets-clean-eating-t55086> (accessed February 21, 2018).
Jenkins, V. S. (2014), "'One Struggle' in Defining Critical Animal Studies," in A. J. Nocella II, J. Sorenson, K. Socha, and A. Matsuoka (eds.), _Counterpoints: Studies in the Postmodern Theory of Education_ , 74–89, New York: Peter Lang Publishing.
Jurewicz, J. (2016), "Orthorexia: Why the Too Clean Diet Spread by Social Media Is Pure Hell," _PerthNow_ , May 1. Available online: <https://www.perthnow.com.au/lifestyle/stm/orthorexia-why-the-too-clean-diet-spread-by-social-media-is-pure-hell-ng-0c7e5bc3ca2ea7970a882e09220646d0> (accessed February 21, 2018).
Kaplan, S. (2015), "Psychiatry Doesn't Recognize "Orthorexia"—An Obsession with Healthy Eating. But the Internet Does," _Washington Post_ , November 5. Available online: <https://www.washingtonpost.com/news/morning-mix/wp/2015/11/05/psychiatry-doesnt-recognize-orthorexia-an-obsession-with-healthy-eating-but-the-internet-does/?utm_term=.3d32e90d09f4> (accessed February 21, 2018).
Kupfer-Koberwitz, E. (n.d.), _Dachau Diaries_ , Chicago: University of Chicago Library.
Lane, A. (2007), "Do Vegetarians Lose the Ability to Digest Meat?" _Chowhound_ , November 28. Available online: <https://www.chowhound.com/food-news/54220/do-vegetarians-lose-the-ability-to-digest-meat/> (accessed February 21, 2018).
Mcinerney-Ernst, E. M. (2011), "Orthorexia Nervosa: Real Construct or Newest Social Trend: A Dissertation in Psychology," Ph.D. diss., University of Missouri-Kansas City, Kansas City.
Netz, R. (2004), _Barbed Wire: An Ecology of Modernity_ , Middletown: Wesleyan University Press.
Patterson, C. (2002), _Eternal Treblinka: Our Treatment of Animals and the Holocaust_ , New York: Lantern Books.
Pfeffer, S. E. (2014), "Popular Food Blogger–the Blonde Vegan–Admits to Eating Disorder," _People_ , July 15. Available online: <http://www.people.com/article/blonde-vegan-jordan-younger-blogger-eating-disorder-orthorexia> (accessed February 21, 2018).
Pollan, M. (2006), _The Omnivore's Dilemma: A Natural History of Four Meals_ , New York: Penguin Press.
Reddy, S. (2014), "When Healthy Eating Calls for Treatment," _The Wall Street Journal_ , November 10. Available online: <https://www.wsj.com/articles/when-healthy-eating-calls-for-treatment-1415654737> (accessed February 21, 2018).
Reynolds, R. C. (2015), "When Eating Healthily Becomes a Fixation," _Newsweek_ , April 4. Available online: <http://www.newsweek.com/when-eating-healthily-becomes-fixation-319453> (accessed February 21, 2018).
Rudy, K. (2013), _Loving Animals: Toward a New Animal Advocacy_ , Minnesota: University of Minnesota Press.
Santillano, V. (n.d.), "Can Eating Meat Really Make Vegetarians Sick?" _More Lifestyle_. Available online: <http://www.more.com/lifestyle/exercise-health/can-eating-meat-really-make-vegetarians-sick> (accessed February 21, 2018).
Singer, I. B. (1980), _The Seance and Other Stories_ , New York: Farrar, Straus and Giroux.
Specter, M. (2014), "Against the Grain: Should You Go Gluten-Free?" _New Yorker_ , November 3. Available online: <https://www.newyorker.com/magazine/2014/11/03/grain> (accessed February 21, 2018).
Stanescu, J. (2012a), "Species Trouble: Judith Butler, Mourning, and the Precarious Lives of Animals," _Hypatia_ 27 (3): 567–582.
Stanescu, J. (2012b), "Towards a Dark Animal Studies: On Vegetarian Vampires, Beautiful Souls, and Becoming-Vegan," _The Journal of Critical Animal Studies_ 10 (3): 26–50.
Stanescu, V. (2009), "Green Eggs and Ham: Michael Pollan, Locavores, and the Myth of Environmentally Sustainable Meat," _The Journal of Critical Animal Studies_ 3, 18–55.
Stanescu, V. (2013), "Why 'Loving' Animals Is Not Enough: A Response to Kathy Rudy, Locavorism, and the Marketing of 'Humane' Meat," _The Journal of American Culture_ 36, 100–110.
Stanescu, V. (2014), "Crocodile Tears: Compassionate Carnivores and the Marketing of 'Happy Meat'," in John Sorenson (ed.), _Critical Animal Studies: Thinking the Unthinkable_ , 216–233, Toronto: Canadian Scholars Press.
Stanescu, V. (2016), "Beyond Happy Meat," in Donaldson, B. and Carter, C. (eds.), _The Future of Meat without Animals_ , 133–154. Lanham, MD: Rowman and Littlefield.
Stanescu, V. (2017), "New Weapons: 'Humane Farming,' Biopolitics, and the Commodity Fetish," in David Nibert (ed.), _Animal Oppression and Capitalism_ , 209–228, Santa Barbara: Praeger.
Taylor, C. (2012), "Abnormal Appetites: Foucault, Atwood, and the Normalization of an Animal Based Diet," _Journal for Critical Animal Studies_ 10 (4), 130–148.
Vandyken, P. (2016), "What to Eat on the Paleo Diet," _Paleo_ , October 12. Available online: <http://www.paleo.com> (accessed February 21, 2018).
Varga, M., Dukay-Szabó, S., Túry, F., and Furth Eric, F. (2013), "Evidence and Gaps in the Literature on Orthorexia Nervosa," _Eating and Weight Disorders–Studies on Anorexia, Bulimia and Obesity_ 18 (2): 103–111.
Verghis, S. (2017), "Orthorexia: When Your Desire for 'Clean Eating' Turns Obsessive," _Special Broadcasting Service_ , April 13. Available online: <https://www.sbs.com.au/topics/life/health/article/2017/04/13/orthorexia-when-your-desire-clean-eating-turns-obsessive> (accessed February 21, 2018).
Wadiwel, D. (2015), _The War against Animals_ , Boston, Brill/Rodopi.
Wright, L. (2012), "The Vegetarian/Vegan Anorexia Connection," _The Vegan Body Project_ , September 12. Available online: <http://veganbodyproject.blogspot.com/2012/09/the-vegetarianvegan-anorexia-connection.html> (accessed February 21, 2018).
Younger, J. (2016), _Breaking Vegan: One Woman's Journey from Veganism, Extreme Dieting, and Orthorexia to a More Balanced Life_ , Beverly, MA: Fair Winds.
Chapter 10
WOMEN, ANXIETY, AND COMPANION ANIMALS: TOWARD A FEMINIST ANIMAL STUDIES OF INTERSPECIES CARE AND SOLIDARITY
Heather Fraser and Nik Taylor
This is Pip, our 4 year old English Staffy. I cannot put into words how much we love her. She is constantly making us laugh—online respondent.
—Fraser and Taylor, 2015–16
This chapter focuses on two projects where participants were invited to represent their connections to animals through photos, art, poetry, or prose. The first was an online visual project, _Whatisitaboutanimals.com,_ and the second project, called _In Good Company,_ involved three focus groups where participants talked about their connections to companion animals and shared photographs of them. As elaborated later, both projects were open to all adults; however, it was women who chose to participate. According to the women, such relationships provided love, support, and friendship, and for many, allowed them to experience themselves in more positive and expansive ways. An important subtheme included companion animals soothing women's anxiety. On face value, these findings fit with the burgeoning growth of stories about the benefits diverse groups of humans enjoy from "keeping pets" (also see Taylor et al. 2017). However, from a more critical perspective, what might the women's stories about companion animals mean?
As this chapter explains, a different light is cast over the women's reports of human–animal relationships if read through a feminist animal studies perspective. Pointed questions are raised about power, privilege, and oppression, not just for women differentially located across class, sex, sexuality, race/ethnicity, ability, and age but also for companion animals. A critique of speciesism shines a different light over discussions of "pet-keeping"—a term that assumes humans can rightfully keep animals (captive) as their playthings. It acknowledges that elements of control are evident in human relations with animal companions. Despite this, the chapter ends with a discussion of whether servitude is an inevitable feature of all human–companion animal relationships, considering the possibility of interspecies alliances, specifically alliances of care and solidarity.
_The projects: (1)_ In Good Company _and (2)_ Whatisitaboutanimals.com _?_
Three focus groups were conducted for the _In Good Company: Women and Animal Companions_ project, with a total of twenty-five women participants; two groups were held on a university campus and one in a local community organization. For the online "What Is It about Animals?" an open and very broad invitation was made to people over the age of sixteen to post images, video, poems, stories, and other texts to a dedicated website about what their animals meant to them. Curious about what a call would bring, we made no mention of anxiety, depression, or well-being, instead simply telling participants that "we want to know how you experience animals you consider important; how you describe and feel about these relationships." We also made no mention of animal rights other than implicitly, through the instructions for participants to only submit "respectful posts," giving them the power to interpret what that might mean. With 200,000 views from 28,000 unique visitors, we ended up with a total of ninety-four image posts, sixty-eight of which also included text—almost all from women. Some excerpts are outlined in the discussion below.
In both projects the call for participants was open, across gender, class, role, and rank (for the focus groups conducted at the university and for the group held in a community organization). That women overwhelmingly stepped forward for both projects is a wider reflection of women's greater ease, interest in, and openness to talking about animals—particularly companion animals—in public settings, a discussion returned to later in the chapter.
During the _In Good Company_ focus groups, we witnessed women not just talking to each other about animals, but bonding with each other (and us) over companion-animal talk. Within each hour of the group discussions, so many emotions were expressed, and among many who had never previously met. Laughter, joy, and shared discussions of funny, poignant, sad, sometimes gut-wrenching stories were narrated. Little was needed from (us) the facilitators, to keep the discussions moving. In each of the three focus groups, women who did not know each other before the groups seemed to talk as easily as those who did, flashing photos of their (animal) loved ones via their phones and in one case, a large iPad, brought in without prompting. For all their differences in age, ethnicity, and class (including role and rank), the women in all three focus groups shared the view that "pets" were not objects or property to be dominated, but family members and cherished friends requiring respectful and sensitive treatment. The same can be said for the tenor of the messages posted online for the _Whatisitaboutanimals.com_ project.
Fun, love, and acceptance
Whether online or through the focus groups, participants kept reiterating how much fun, love, and friendship they felt toward their companion animals. Without being directed, they talked about how their companion animals so attentively listened to and comforted them; how they accepted them without judgment or criticism; and how they provided an anchor in hard times.
This is Millie [dog]. I hate being away from her even if it is for a short amount of time, and I know that feeling is mutual... She puts my mind at ease and calms me in just about any situation—focus group respondent. (Fraser and Taylor 2015–16)
For someone that has had a trying life, my Winky [cat] was my one and only reliable constant. Our relationship constantly surprises people as it is clear that we both care about each other conditionally. I would be lost without her in my life—she is my rock!—focus group respondent. (Fraser and Taylor 2017)
Bessie [dog] very recently passed away... She had her own Facebook page and was loved by people all around the world... so lost without her in my life—focus group respondent. (Fraser and Taylor 2017)
I love her with all my heart, and without her my life wouldn't be the same. I can have the worst day at work, coming home to my Daisy [dog], who is always full of love, hugs and big licks makes everything okay, and instantly better—focus group respondent. (Fraser and Taylor 2017)
Heartfelt accolades continued for the individually named and described companion animals the women participants spoke about, in both our focus groups and online projects. Over and again participants stressed the power of the physical affection shown by companion animals, as well as their acceptance without regard to human preoccupations, such as beauty, status, and money.
I love that animals are so unselfconscious, so uncontrived, yet sentient and affectionate. They just "are"!—focus group or online respondent. (Fraser and Taylor 2015–16)
Louis [dog] has been my best friend from the moment I got him. I moved to a new place far from any family or friends. And that's when I adopted Louis... Even though he's cheeky sometimes, he still gets me through the hard days, and for that I am so thankful.—online respondent. (Fraser and Taylor 2015–16)
Time and again respondents told of how their companion animals got them through "hard times," offering unconditional regard and love, positive reinforcement, and a shoulder to lean on, "I feel blessed having my furry companion (dog) by my side every day, where-ever I go he goes usually. I suffer with a little anxiety and stress out but I'm always less stressed when he's around. No words needed, yet I have the best relationship with my dog" (Fraser and Taylor 2015–16).
Repeated references were made to how companion animals soothed their anxiety and depression, with a few women disclosing their experiences of psychiatric ill-health:
I look after pets for a living and my life couldn't be better because of it. I have struggled with depression and anxiety, I owe my recovery to my pets.—online respondent. (Fraser and Taylor 2015–16)
I suffer from a psychiatric illness. I am a dog lover and have a Labrador-cross called Pogo. He is my best friend and has been my rock and support for many years now. I cannot thank my loyal companion enough for the unconditional love and support he has provided me over the years. When I'm unwell, he stands by me and does not judge. The importance of friendship, love and companionship that my dog provides is beyond words.—online respondent. (Fraser and Taylor 2015–16)
The women who participated in our studies did not speak of the animals as second class or inferior to humans, but as family members that gave their lives meaning. A few participants noticed the potential for "animal lovers" to be dismissed and trivialized. Some women embraced being "gushy" or overly sentimental.
I know I am lucky to have had our time together and can rely on what I know was a real bond to get me through the eye-rolling and eyebrow-lifting other non-animal-lovers give me when I gush about my bestest friend... Love you to infinity Nora-G Xxxoxxxo—online respondent. (Fraser and Taylor 2015–16)
I'm like other animal crazies (as I fondly refer to them) in that I've been owned by several family pets, the most recent of which being my eleven-year-old dog, Sally—focus group respondent. (Fraser and Taylor 2015–16)
In both studies participants shared mostly happy, uplifting, and joyous images and stories about companion animals, perhaps reflecting the wider popular preoccupation with "pets," especially on social media. Yet, questions may be asked about the wisdom of emphasizing women's proximity to, and fondness for, domesticated animals. Eyebrows might also be raised at the apparent lack of critical content, particularly in relation to basic animal rights. No agreement was reached, or discussed at any length, about the love of animals needing to translate into political actions, such as the adoption of rescue animals, the support for animal sanctuaries, resistance to agribusiness and veganism. Without a critical analysis, studies such as ours might be read as exacerbating the potential exploitation and oppression of animals through the construction of them as "pets" for humans, reinscribing (even unwittingly) speciesist, dominant–submissive relationships. It is to this political analysis that we now turn, starting with the historical tendency to pair women with emotions and nervous maladies.
Women, anxiety, and animals
In contemporary society, anxiety is a problem for many whose health is affected by overwhelming, intrusive negative thoughts and feelings, and an impending sense of doom (Shekhar et al. 2005). Historically, women have been closely associated with nervous maladies and disparaged for being prone to hysteria and other nervous ailments (see, e.g., Bernheimer and Kahane 1990; Marcellus 2008; Weeks 2014). Today, anxiety is a problem that still disproportionately affects women. Current estimates of diagnosed anxiety disorders in the United States, for instance, show women outnumber men (2:1); however, it is difficult to determine whether this is due to more women than men presenting for treatment (Armstrong and Khawaja 2002).
The eight main types of medically diagnosed anxiety include (1) separation anxiety, or intense fears of being separated from love attachments; (2) generalized anxiety (disorder), which literally refers to anxiety generalized to all parts of life; (3) social phobia, or social anxiety (disorder), which refers to anxiety in social situations, especially anxiety about the likelihood of humiliation; (4) specific phobias, such as excessive fear of an animal, object, or process (such as air travel); (5) agoraphobia, such as fear of being in public places, leaving home and not having an easy exit if panic attacks occur; (6) post-traumatic stress (disorder), common to many trauma survivors, including those returning from war; (7) panic (disorder), often characterized by intense physical symptoms, such as dizziness and being short of breath; and (8) obsessive-compulsive disorder, involving repetitive rituals, such as frequent hand-washing (American Psychiatric Association 2017).
Medical diagnoses applied to mental health conditions, such as those described above, appear to be stable, certain, and universally applied classifications. These diagnoses can feel comforting and can help people make sense of experiences that can be overwhelming and intensely difficult to manage. For some, anxiety-related diagnoses provide a shorthanded way of expressing to the self and others, the mental health challenges being faced. For many anxiety sufferers, medical diagnoses and often accompanying prescription of medication influence, if not redefine, identities. What is so often forgotten is that both medical diagnoses, particularly those in mental health, and the experience of intense emotions (such as anxiety) are bounded by history, culture, and politics (see Conrad 2005). As with other emotions and psychological states (such as rage, terror, or catatonia), anxiety is not just an individual experience but also a collective, sociocultural one. Anxiety is not always experienced as or best understood to be a classifiable pathology. Nor is it always wise to "treat" it as if it is an individual experience, unrelated to social location (such as class, gender, ethnicity, and age) or the influence of the pharmaceutical industry, which, as Conrad argues, plays a major role with doctors constructing, defining, and prescribing drug treatment for a variety of anxiety-related conditions. As discussed below, rather than disaggregate anxiety from sociocultural contexts, we need to pay attention to living conditions productive of anxiety.
Anxiety and inequality
Anxiety is not confined to individual human psyches but intersects privilege and oppression (based on gender, class, race/ethnicity, age, and ability). Inequality produces anxiety, especially for oppressed groups experiencing discrimination and disadvantage. For many oppressed groups, social problems such as poverty, homelessness, and unemployment generate high levels of anxiety. To quote Haushofer and Fehr, "poverty correlates with unhappiness, depression, anxiety, and cortisol levels... [and that] results from randomized controlled trials that show that cash transfers [to the poor] reduce distress and depression scores" (2014, 864). Goldsmith et al. (1996) noted the negative impact of unemployment on self-esteem, not just on anxiety and depression but also on the experience of alienation.
Rising social inequality and poverty rates for women (Fraser and Taylor 2016) and women's burden of disease risks associated with domestic violence, sexual assault, and legacy of child abuse (see Williams and Mickelson 2004) influence women's experiences of anxiety. Williams and Mickelson show that when women experience poverty and domestic violence, their resilience to anxiety is usually compromised. Stigma, shame, and victim blaming often exacerbate anxiety. Anxiety-producing gendered patterns of work—paid and unpaid—also play a role in the lives of many women, especially for women trapped in casual, underpaid work, performing the double shift and unpaid work in the family (Pease 2010).
Feminists have criticized the biomedical tendency to pathologize women for suffering anxiety, noting that contextual reasons for women's propensity for nervous ailments are usually ignored, "Gender differences between men and women in pay, social status, political power, burdens of domestic care and mothering, relationship inequalities and rates of domestic violence... [and] or gendered ideals about parenthood and care responsibilities... [explain] women's increased likelihood of experiencing mental health problems" (Malson and Nasser 2007, 10).
Gendered expectations of normative anxiety are evident, with women stereotypically portrayed as those who should worry and fret over others, through their assumed roles as wives, mothers, and homemakers. In other words, anxiety is not just the feelings, thoughts, and actions associated with worry, threats, fear, stress, and tension but also the codified expectations, or conventions, for socially sanctioned causes and expressions of anxiety.
High anxiety may distort experience, but it can also be a manifestation of life-threatening situations, such as seeking asylum (see Lindert et al. 2017). This is not a reference to the status anxiety of wealthy humans, but the gritty, collective angst of low-income groups trying to survive (Jetten et al. 2017). For some groups, especially oppressed groups, anxiety—or the impending sense of doom—is not just imagined but an eventuality.
Animals caught up in agribusiness are excellent (nonhuman) examples of structural oppression, and of how anxiety and an impending sense of doom becomes a reality, not just a fear. Irrespective of the position taken with regard to the legitimacy of agribusiness, the anxiety and terror experienced by "livestock" especially during slaughter can no longer be denied (Pachirat 2011). Dominant social and cultural conventions still converge through human carnistic defenses, justifying the incarceration of animals for reproductive products and use of body parts post-slaughter (Taylor and Fraser 2017). However, a large body of research is now available showing the negative impact of forced reproduction and milking for cows, sheep, goats, and camels, and the analogous ways in which lactating women and other animals may be commodified (see Cohen 2015), and the sexual politics of meat (see Wright 2015, referencing Carol Adams).
Abundant feminist critiques are available of the historical inclination to associate emotion with women and reason with men, divorcing emotion from reason and tying emotion to supposedly fragile, brittle forms of femininity (Jaggar and Bordo 1989). Feminists have documented how discourses of madness have been used to control women, just as they have pointed out that women's perceived closeness to nature that has led to their being designated emotional (cf. rational) and in need of seclusion from the public sphere, or control while operating in it (Marcellus 2008). As Malson makes clear, this is often achieved through the animalization of women, particularly focusing on reproduction which is, arguably, the site of the most control of the female body: "The 'maternal body', like 'the body' of dualist discourse, is constructed as the antithesis of the mind, will or spirit. It is animal-like—cow-like—uncontrolled, and excessive" (1997, 237). Those women who fail or refuse to reproduce are still liable to be constructed as lesser women (Letherby 2002).
"Old maids" and "crazy cat ladies"
Single women and women who choose not to have children have long been viewed with suspicion, especially if their single status spans more than a few years (Fraser 2003). To quote Gordon, "The old maid stereotype is related to a perception of single women as lacking something, being incomplete, deviating from the norm and the normal" (1994, 129). Graham and Rich describe the pro-natalist discourses still in circulation in Australian media—media that produces an array of messages that pity childless women and reprimand those who decide not to have children (2012). Bay-Cheng and Goodkind note that "Conventional gender roles and rules for young women center on their relationships to men" but add that these conventions interface with neoliberal imperatives on different socio-demographic groups of women, toward "self-focused striving," exemplified by staying single so as to "stay on track" and "get ahead" (in education or work terms) (2016, 193). Blackstone describes how increasing numbers of Western women are creating families that do not include children, noting that they are often overlooked or treated with ambivalence (2014). Focusing on human–dog relationships in multispecies households, Charles refers to them as post-human families (2016), as does Irvine and Laurent (2017). However, several heteronormative stereotypes still apply to single women, especially as they age and if they live in close company with animals (McKeithen 2017).
Throughout Western history this denigration of, and suspicion about, women who have close relationships with other species has held ground. For instance, at the turn of the twentieth century, and with the rise of women's antivivisectionism, American neurologist Charles Loomis Dana created a new medical condition in 1909 called "zoophilpsychosis," which referred to those with a heightened concern for animals as afflicted with a mental illness (Buettinger 1993, 277). To some extent this notion lives on. Take, for instance, the "crazy cat lady" that implies there's something wrong with women who love cats "too much" (McKeithen 2017, 127). Stereotypically, "crazy cat ladies" are those women who place the needs of cats above humans, a move that is to be scorned and mocked. Some so-called "crazy cat ladies" keep multiple cats, sometimes to the point of hoarding. "Hoarding can be thought of as pathological over-attachment to animals, and has been considered to be a manifestation of several forms of psychopathology" (Herzog 2007, 11). Hoarding animals can be a serious problem for companion animals, especially if they are overcrowded, underfed, or otherwise neglected. However, questions need to be asked about who gets to attribute such labels (see Probyn-Rapsey chapter in this volume).
The kind of reductive thinking that assumes women who have empathy for other animals are somehow "faulty," and/or that their inability to maintain productive (in both senses of the word) relationships with other humans closes down alternate ways of seeing, experiencing, and thinking about the world. In terms of our relationships with other animals, it ensures that emotion and empathy are relegated to "unscientific" ideas about other animals and rationalist critiques of anthropomorphism (Gruen 2015). As Davies points out, "the language of Western science—the reigning construct of male hegemony—precludes the ability to express the experiential realities it talks about" (1995, 208).
A feminist animal studies
We are not alone in our argument that a distinctly feminist animal studies is needed (see, e.g., the special edition of _Hypatia_ , Gruen and Weil 2012). With Gruen and Weil, we are in agreement:
One clear commonality is the need to maintain feminist, ethical, and political commitments within animal studies—commitments to reflexivity, responsibility, engagement with the experiences of other animals, and sensitivity to the intersectional contexts in which we encounter them. Such commitments are at the core of a second, related area of concern, that of the relationship between theory and practice. Animal bodies, we can all agree, must not be "absent referents" in animal studies. (2012, 493)
Feminism also needs animal studies. Mohanty (2003) refers to "feminism without borders" and while she stops short of acknowledging species as a border, her work can be fruitfully extended:
Feminism without borders... acknowledges the fault lines, conflicts, differences, fears, and containment that borders represent. It acknowledges that there is no one sense of a border, that the lines between and through nations, races, classes, sexualities, religions, and disabilities [and species] are real—and that a feminism without borders must envision change and social justice work across these lines of demarcation and division. I want to speak of feminism without silences and exclusions in order to draw attention to the tension between the simultaneous plurality and narrowness of borders and the emancipatory potential of crossing through, with, and over these borders in our everyday lives. (2)
In _Speaking Up for Animals_ , Kemmerer puts it plainly, "Women who seek equality must not support the oppression of nonhuman animals... if women are ever to achieve equality we must topple hierarchy in total" (2012, 5). Maintaining a commitment to anti-oppressive practice is difficult, if not impossible, without recognizing species oppression, given all oppressions share similar structural expression and mechanisms. As Jenkins points out, feminists need to take species seriously because:
[F]eminism is perhaps best positioned to take on questions of the animal. This is manifest in feminist theory's commitment to the materiality of the body, to attending to those bodies most vulnerable to abuse, to exposing the logic of exclusion and the politics of abjection, and perhaps most important... In its commitment to thinking about, and critiquing its own participation in, the ethics of representation and "speaking for" others. (2012, 517)
Brown (2016) explains that liberation discourses must not separate the oppression of animals from humans, noting that domestication has affected many women and animals negatively, with both groups liable to be cast as mindless and rightful subjects of men's servitude.
Feminism and animal studies share the injunction to praxis. A key part of praxis is alliance building. A feminist approach to alliance building recognizes similar structures of oppression but allows room for difference. As Gruen points out, "The feminist care tradition in animal ethics urges us to attend to other animals in all of their difference including differences of power within systems of human dominance in which other animals are seen and used as resources or tools" (2015, 36).
Useful ideas come from feminist work on forming and maintaining alliances across difference. This work stresses, as one might expect from feminist work, that the personal is the political and turns on recognizing the similarity behind different structures of oppression. To paraphrase Ann Bishop (2002), we cannot try to end our oppression by ignoring the oppression of others, or subordinating others, as each form of oppression interacts in a self-perpetuating system of domination. In turn, a feminist critique of individual competition is also required, with attention given to how competition can unhelpfully divide us and position some as superior and others as inferior, "The whole thing rests on a world-view that says we must constantly strive to be better than someone else. Competition assumes that we are separate beings—separate from each other, from other species, from the earth" (Bishop 2002, 19).
This chapter stands as a corrective to this kind of hierarchical thinking by considering how women express emotional connections to other animals, and by doing so in a non-pathologizing way that takes the interspecies relationships considered as "normal," "functional," and positive. The very act of allowing those expressions and seeing this allowance itself is a political act: "establishing the legitimacy of outcast experiences is precisely the political cultural work that needs to be carried out in real life for the sake of all beings disenfranchised by sanctioned value systems" (Scholtmeijer 1995, 231).
Caregiving across species
When we speak of care we are referring to both caring for and caring about others (Fraser et al. 2018). To qualify as care, it needs to be undertaken with kindness and without duress. Far from being easy, mundane, or routine, "quality" care is personalized and thoughtful (Fraser et al. 2018). Feminist sociologist Arlie Hochschild (1979, 1990, 2002) helped us understand the work and complexities involved in caring, especially the emotional labor. Hochschild defines emotion work as "the act of trying to change in degree or quality an emotion or feeling... it refers to the effort—the act of trying—and not to the outcome, which may or may not be successful... [it differs from] emotion 'control' or 'suppression'" (1979, 561).
Hochschild (1979, 1990, 2002) showed how emotions, not just behaviors, are subject to social rules productive of expectations of how emotional management should be undertaken and by whom. This is particularly relevant to women and companion animals in private domestic settings, where caregiving is often taken for granted or assumed to reflect their inherent nurturing capacities.
When speaking of connections to "their" animals, participants of the projects, _In Good Company_ and _Whatisitaboutanimals_ , often expressed taken-for-granted notions of caring relationships, based on reciprocity, particularly mutual understanding (also see Donovan [1990] 1996). The reciprocal nature of their relationships was a key component to seeing their animal companions as part of the family: as agentic, interactive, and emotionally attuned beings.
I think she can understand me... If I'm you know anxious or anything, she will stay really close to me and if I'm a little bit sad, she will kind of just look at me and come up to me and she thinks she is a lapdog, but she is 23 kilos and she gets her whole body like onto me up here and she knows what is going on.—focus group respondent. (Fraser and Taylor 2017)
Many women in our studies noticed the significant forms of emotional labor performed by their companion animals, evident in expressions such as "the dog would know I was always crying and she would come up and make sure I was OK" (focus group respondent in Fraser and Taylor 2017). Many of the animals were understood by participants to have offered themselves as therapists, nurses, and confidantes:
He [dog] slept for hours and hours... and this little puppy actually wedged herself at the top of his pillow just on the top of his head against the bed and just stayed there. She didn't have to get up or anything. She just knew he wasn't right or she thought he needed her somehow and she just stayed there and it was amazing.—focus group respondent. (Fraser and Taylor 2017)
Several participants expressed how important it was to them to care for abused and neglected animals, and in one instance spelt out how much pleasure could come from watching empathy shown across species, from one abused or abandoned animal to another:
I love this face [dog]. I can't get enough of it! Stussy is the naughtiest of dogs but also the most giving. She knows when I am sick or sad. She knows when I'm cold and need a furry spoon. She has been an amazing foster sibling and done so much to help the damaged, abused and neglected dogs who have come in to our care. It's easy to forgive her for all the doonas [bed quilt] and pillows she has eaten.— online respondent. (Fraser and Taylor 2015–16)
Interspecies care, alliance building, and solidarity
Feminist animal studies refuse to pathologize women's deep emotional connections with other animals but instead makes room for an empathic understanding of them. From this perspective, the work that animals perform for humans is noticed and valued, such as attending to emotional needs, soothing anxiety, and providing support that can be therapeutic and healing. Recognizing the care work animals do for humans is crucial if we are to avoid simply taking this work for granted and/or to avoid positing them as tools whose main or only purpose is to help improve human well-being. As Coulter notes, when an animal-centric approach is taken, one that refuses the idea of animals as objects and/or as subordinate to humans, we "see" stories of animal–human cooperation and relationships differently: "The local-global evidence about animals' lives contains inspiring and novel examples of... how people and animals work together with respect and kindness, of animals' diverse and even surprising contributions, and of laudable, moving expressions of compassion within and across species" (2016, 139–140).
Interspecies alliances are tied to the recognition of respectful, mutually beneficial and life-sustaining relationships that can occur across species, human and otherwise (also see von Essen and Allen 2017). Admittedly, becoming allies with other animals is complicated by species differences, particularly communication styles. However, there are other powerful, non-deliberative (not talk-based) ways of building alliances, for instance through the preparedness of allies to perform emotional labor with each other. The challenge is to notice the work that allies do to sustain good relations.
While the broader concept of alliances is underdeveloped in human–animal studies literature, initial searches of mainstream scientific studies show mostly primate studies, apes and monkeys as the subjects (e.g., Cheney and Seyfarth 1986; Harcourt and de Waal 1992), although some bottle-nosed dolphin studies also show intragroup alliances (e.g., Connor et al. 1999). In these accounts, alliances are built on collaboration and teamwork, for many reasons, such as mating, protecting each other, solving problems, play and socialization, food finding, and the rearing of young (Cheney and Seyfarth 1986; Harcourt and de Waal 1992; Connor et al. 1999). However, it should be noted that similar to the concept of "animal lovers," interspecies alliances do not escape the problem of selecting some species, or representatives from selected species to love, without regard for the needs and rights of other species or concern over their maltreatment—for instance, loving dogs but eating cows and drinking their milk. This is why we are emphasizing the need for alliances of both care and solidarity.
According to Bayertz (1999, 3), solidarity "today stands, largely unexplained in relation to complementary terms such as 'community spirit' or 'mutual attachment', 'social cooperation' or 'charity', and—from time to time—'brotherly love' or 'love of mankind'. However, we need to think about solidarity beyond men and humans." To quote Rock and Degeling (2015, 4), " more-than-human solidarity builds on two existing concepts: 'environmental health justice' and 'multi-species flourishing.'" Herzog (2017, 3) reminds us that "People who felt high solidarity with animals were more concerned with animal welfare and more apt to think of themselves as part of the natural world."
Building on the idea of alliances with other species, versus the ownership of them, Coulter proposes "interspecies solidarity," which she describes as "an idea, a goal, a process, an ethical commitment, and a political project" (2016, 3). In keeping with her feminist analysis, she notes that key ideas from the feminist ethic of care for other animals are necessary to the idea of interspecies solidarity: "The concept of solidarity is underscored by ideas of empathy" (150). Key to this idea of caring is that "individual acts of solidarity matter, and they can disrupt dominant perceptions and power relations. They can also set a domino effect in motion which propels a broader set of processes. Moreover, solidarity can prompt and inform larger, collective forms of political work. Caring can be and can become political" (152).
Perhaps it is interspecies alliances of care and solidarity that some of the participants meant through their images, meanings that we did not pick up at first. Consider, for instance, the submission of a photograph online entitled "Me and Dizzy," which depicts a close-up image of a paw in a handshake with a human. An excerpt of the accompanying text submitted with this image included, "Dizzy [dog] has been that confidante, who always calmly listens and offers a comforting, thoughtful and understanding. Unspoken. But nonetheless, shared" (Fraser and Taylor 2015–16).
Our position is that if interspecies care and empathy is shown, the life of a companion animal does not have to be inevitably bounded by servitude. Interspecies alliances of care and solidarity are possible, across and in between humans and companion animals (Rock and Degeling 2015). However, there is a caveat: to meet our criteria for alliances of care and solidarity, there cannot be relationships of human domination and animal subordination. Strict hierarchical arrangements are an anathema to the alliances of care and solidarity. In strict hierarchical arrangements, generosity may be expressed but only through philanthropy and benevolence. It is not a question of allies needing to be the same in rank or similar to each other in personal characteristics. Diversity is, and has been, crucial to alliance building, across borders, classifications, and social movements (Bishop 2002). Interspecies alliances are inherently diverse and must operate with regard to all parties' health and well-being.
The intensely personal experience of anxiety should not be allowed to eclipse the sociocultural contexts that give rise to anxiety in the first place. Biomedical and neoliberal approaches to health, including experiences of anxiety, are approached with caution for their tendency to pathologize and hyper-individualize experiences, especially women's experiences. Because anxiety shapes the way the self and others are experienced culturally, socially, and politically, it is crucial to recognize the interplay of anxiety and gender politics.
From a feminist animal studies perspective, women—including women reporting high levels of anxiety—are believed and respected, rather than teased or mocked, for forming close emotional ties with animals. We have argued for feminism and animal studies to work in simpatico, rather than against each other, to allow for the many cross-species connections in experiences of oppression and to open up possible alliances. Our aim has been to dignify interspecies relationships and recognize the valuable work that companion animals perform for humans. This includes emotional labor, such as soothing anxiety, which for both women and other animals cannot be disaggregated from social, cultural, and political contexts.
References
American Psychiatric Association (2017), "What Are Anxiety Disorders?" Available online: <https://www.psychiatry.org/patients-families/anxiety-disorders/what-are-anxiety-disorders> (accessed February 22, 2018).
Armstrong, K. A. and Khawaja, Nigar G. (2002), "Gender Differences in Anxiety: An Investigation of the Feb Symptoms, Cognitions, and Sensitivity towards Anxiety in a Nonclinical Population," _Behavioural and Cognitive Psychotherapy_ 30: 227–231.
Bay-Cheng, L. Y. and Goodkind, S. A. (2016), "Sex and the Single (Neoliberal) Girl: Perspectives on Being Single among Socioeconomically Diverse Young Women," _Sex Roles_ 74 (5–6): 181–194.
Bayertz, K. (1999), "Four Uses of 'Solidarity,'" in K. Bayertz (ed.), _Solidarity_ , 3–28, Dordrecht: Springer.
Bernheimer, C. and Kahane, C. (1990), _In Dora's Case: Freud—Hysteria—Feminism_ , New York: Columbia University Press.
Bishop, A. (2002), _Becoming an Ally: Breaking the Cycle of Oppression in People_ , 2nd edition, New York: Zed Books.
Blackstone, A. (2014), "Doing Family without Having Kids," _Sociology Compass_ 8 (1): 52–62.
Brown, K. (2016), "A Feminist Analysis of Human and Animal Oppression: Intersectionality among Species" [Departmental Presentation]. Available online: <http://cedar.wwu.edu/scholwk/Departmental_Presentations/Women_Gender_Sexuality_Studies/2/> (accessed February 22, 2018).
Buettinger, C. (1993), "Antivivisection and the Charge of Zoophil-Psychosis in the Early Twentieth Century," _Historian_ 55 (2): 277–288.
Charles, N. (2016), "Post-Human Families? Dog-Human Relations in the Domestic Sphere," _Sociological Research Online_ 21 (3): 1–12.
Cheney, D. L. and Seyfarth, R. M. (1986), "The Recognition of Social Alliances by Vervet Monkeys," _Animal Behaviour_ 34 (6): 1722–1731.
Cohen, M. (2015), "Regulating Milk: Women and Cows in France and the United States," _American Journal of Comparative Law_ 65: 469–526.
Connor, R. C., Heithaus, M. R., and Barre, L. M. (1999), "Superalliance of Bottlenose Dolphins," _Nature_ 397 (6720): 571.
Conrad, P. (2005), "The Shifting Engines of Medicalization," _Journal of Health and Social Behavior_ 46 (1): 3–14.
Coulter, K. (2016), _Animals, Work and the Promise of Interspecies Solidarity_ , London: Palgrave.
Davies, K. (1995), "Thinking like a Chicken: Farm Animals and the Feminine Connection," in C. Adams and J. Donovan (eds.), _Animals and Women: Feminist Theoretical Explorations_ , 192–212, Durham and London: Duke University Press.
Donovan, J. ([1990] 1996), "Animal Rights and Feminist Theory," in J. Donovan and C. Adams (eds.), _Beyond Animal Rights: A Feminist Caring Ethic for the Treatment of Animals_ , 34–59, New York: Continuum.
Fraser, H. (2003), "Narrating Love and Abuse in Intimate Relationships," _British Journal of Social Work_ 3: 273–290.
Fraser, H. and Taylor, N. (2015–16), "What Is It about Animals?" Available online: www.whatisitaboutanimals.com (accessed September 27, 2017).
Fraser, H. and Taylor, N. (2016), _Neoliberalization, Universities and the Public Intellectual: Species, Gender and Class and the Production of Knowledge_ , London: Palgrave.
Fraser, H. and Taylor, N. (2017), "In Good Company: Women, Companion Animals and Social Work," _Society & Animals_ 25 (4): 341–361.
Fraser, H., Taylor, N., and Morley, M. (2018), "An Intersectional Perspective on Ethics, Principles and Practices," in B. Pease, A. Vreugdenhil and S. Stanford (eds.), _Critical Ethics of Care in Social Work: Transforming the Politics and Practices of Caring_ , 229–240, London: Routledge.
Goldsmith, A. H., Veum, J. R., and William, D. (1996), "The Impact of Labor Force History on Self-Esteem and Its Component Parts, Anxiety, Alienation and Depression," _Journal of Economic Psychology_ 17 (2): 183–220.
Gordon, T. (1994), _Single Women: On the Margins?_ New York: New York University Press.
Graham, M. and Rich, S. (2014), "Representations of Childless Women in the Australian Print Media," _Feminist Media Studies_ 14 (3): 500–518.
Gruen, L. (2015), _Entangled Empathy: An Alternative Ethic for Our Relationships with Other Animals_. New York: Lantern Books.
Gruen, L. and Weil, K. (2012), "Invited Symposium: Feminists Encountering Animals," _Hypatia_ 27 (3): 492–526.
Harcourt, A. H., and De Waal F. B. M. (eds.) (1992), _Coalitions and Alliances in Humans and Other Animals_ , Oxford: Oxford University Press.
Haushofer, J. and Fehr, E. (2014), "On the Psychology of Poverty," _Science_ 344 (6186): 862–867.
Herzog, H. (2007), "Gender Differences in Human–Animal Interactions: A Review," _Anthrozoös_ 20 (1): 7–21.
Herzog, H. (2017), "How Much Solidarity Do You Feel with Animals?" _The Animal Studies Repository_ , 1–5. Available online: <http://animalstudiesrepository.org/aniubpos/33/> (accessed February 22, 2018).
Hochschild, A. R. (1979), "Emotion Work, Feeling Rules, and Social Structure," _American Journal of Sociology_ 85 (3): 551–575.
Hochschild, A. R. (1990), "Ideology and Emotion Management: A Perspective and Path for Future Research," in T. D. Kemper (ed.), _Research Agendas in the Sociology of Emotions_ , 117–142, Albany, NY: SUNY Press.
Hochschild, A. R. (2002), "'Emotional Labour,'" in S. Jackson and S. Scott (eds.), _Gender: A Sociological Reader_ , 192–196. London: Routledge.
Irvine, L. and Laurent, C. (2017), "More‐than‐Human Families: Pets, People, and Practices in Multispecies Households," _Sociology Compass_ 11 (2). Available online: <http://onlinelibrary.wiley.com/doi/10.1111/soc4.12455/full> (accessed February 22, 2018).
Jaggar, A. M. and Bordo, S. (eds.) (1989), _Gender/Body/Knowledge: Feminist Reconstructions of Being and Knowing_ , New Brunswick, Rutgers University Press.
Jenkins, S. (2012), "Returning the Ethical and Political to Animal Studies," _Hypatia_ 27 (3): 504–510.
Jetten, J., Mols, F., Healy, N., and Spears, R. (2017), "'Fear of Falling': Economic Instability Enhances Collective Angst among Societies' Wealthy Class," _Journal of Social Issues_ 73 (1): 61–79.
Kemmerer, L. (ed.) (2012), _Speaking Up for Animals: An Anthology of Women's Voices_. London: Routledge.
Letherby, G. (2002), "Childless and Bereft? Stereotypes and Realities in Relation to 'Voluntary' and 'Involuntary' Childlessness and Womanhood," _Sociological Inquiry_ 72 (1): 7–20.
Lindert, J., Von Ehrenstein, O. S., Wehrwein, A., Brahler, E., and Schäfer, I. (2017), "Anxiety, Depression and Posttraumatic Stress Disorder in Refugees—A Systematic Review," _Psychotherapie, Psychosomatik, Medizinische Psychologie_ 68 (1): 22–29.
Malson, H. (1997), "Anorexic Bodies and the Discursive Production of Feminine Excess," in J.Ussher (ed.), _Body Talk: The Material and Discursive Regulation of Sexuality and Madness and Reproduction_ , 223–245, London; New York. Routledge.
Malson, H. and Nasser, M. (2007), "At Risk by Reason of Gender," in M. Nasser, K. Baistow, and J. Treasure (eds.), _The Female Body in Mind: The Interface between the Female Body and Mental Health_ , 3–16, London: Routledge.
Marcellus, J. (2008), "Nervous Women and Noble Savages: The Romanticized 'Other' in Nineteenth‐Century US Patent Medicine Advertising," _The Journal of Popular Culture_ 41 (5): 784–808.
McKeithen, W. (2017), "Queer Ecologies of Home: Heteronormativity, Speciesism, and the Strange Intimacies of Crazy Cat Ladies," _Gender, Place & Culture_ 24 (1): 122–134.
Mohanty, C. (2003), _Feminism without Borders: Decolonising Theory, Practicing Solidarity_ , Durham and London: Duke University Press.
Pachirat, T. (2011), _Every Twelve Seconds: Industrialized Slaughter and the Politics of Sight_ , New Haven, CT: Yale University Press.
Pease, B. (2010), _Undoing Privilege: Unearned Advantage in a Divided World_ , London: Zed Books.
Rock, M. J. and Degeling, C. (2015), "Public Health Ethics and More-than-Human Solidarity," _Social Science & Medicine_ 129: 61–67.
Scholtmeijer, M. (1995), "The Power of Otherness: Animals in Women's Fiction," in C. Adams and J. Donovan (eds.), _Animals and Women: Feminist Theoretical Explorations_ , 231–262, Durham and London: Duke University Press.
Shekhar, A., Truitt, T., Rainnie, D., and Sajdyk, R. (2005), "Role of Stress, Corticotrophin Releasing Factor (CRF) and Amygdala Plasticity in Chronic Anxiety," _Stress_ 8 (4): 209–219.
Taylor, N. and Fraser, H. (2017), "Slaughterhouses: The Language of Life, the Discourse of Death," in J. Maher, H. Pierpoint, and P. Beirne (eds.), _The Palgrave International Handbook of Animal Abuse Studies_ , 179–199, London: Palgrave.
Taylor, N., Fraser, H., and Riggs, D. W. (2017), "Domestic Violence and Companion Animals in the Context of LGBT People's Relationships," _Sexualities_ , 1–15. Available online: <http://journals.sagepub.com/doi/full/10.1177/1363460716681476> (accessed March 15, 2018).
Von Essen, E., and Allen, M. P. (2017), "Solidarity between Human and Non-Human Animals: Representing Animal Voices in Policy Deliberations," _Environmental Communication_ 11 (5): 641–653.
Weeks, J. (2014), _Sex, Politics and Society: The Regulations of Sexuality since 1800_ , London: Routledge.
Williams, S. L. and Mickelson, K. D. (2004), "The Nexus of Domestic Violence and Poverty: Resilience in Women's Anxiety," _Violence against Women_ 10 (3): 283–293.
Wright, L. (2015), _The Vegan Studies Project: Food, Animals, and Gender in the Age of Terror_ , Georgia: University of Georgia Press.
Part III
DYSFUNCTION
Chapter 11
THE "CRAZY CAT LADY"
Fiona Probyn-Rapsey
If you ever work on a project about "crazy cat ladies," you can expect some smiles of the wry, knowing kind, followed up by a flurry of "crazy cat lady" (CCL) memes, mugs, socks, and links to various CCL products. Many of them are pretty funny, especially the picture of the box of kittens labeled "Crazy cat lady start up kit" and the socks emblazoned with "you say 'crazy cat lady' like it's a bad thing." These jokes attest to a level of sympathy for and fascination with crazy cat ladies within popular culture. I've long been fascinated by the "crazy cat lady" as a cultural trope, a sort of "folk devil" whose appearance plays on broader anxieties attached to femininity and animality. Putting the memes, socks, mugs, pyjamas, fridge magnets aside for a moment, this chapter takes a more critical look at the CCL. I explore the current popularity of the CCL in three connected ways. Firstly, as a _gendered_ cultural trope that is mobilized in both negative and positive ways to exemplify the feminization of concern for human–animal relations. Secondly, I examine how the CCL gets tangled up with the animal hoarder: someone who "hoards" or collects animals and keeps them as their self-declared "rescuer," often to protect them from some other terrible fate (neglect and cruelty) that then becomes realized in her own hands. The research on animal hoarding is fascinating in this regard, because it essentially plays chicken and egg with the "crazy cat lady," replicating gender stereotypes in its discussion of the disorder it attempts to outline. While animal hoarding literature situates the CCL as a dangerous obstacle to proper diagnosis and understanding of animal hoarding cases, I then take this idea one step further and discuss whether or not the CCL might be not just a "cute face" of the animal hoarder but also the "folk devil" for the industrial scale hoarding of animals that persists in factory farming situations. The three elements—"crazy cat lady," animal hoarder, and factory farmer—are connected, I suggest, by a broader phenomenon of the intensification of animal keeping in Western modernity, a period in which animals are simultaneously more numerous, less visible but more intensively "kept" (Harrison 1964; Vialles 1994; O'Sullivan 2015; Pachirat 2015). In this chapter, I'll pull on the thread of the crazy cat lady trope and see how she leads us to industrialized hoarding in the form of factory farming.
A popular history of the CCL
When Eleanor Abernathy arrived on the scenes of _The Simpsons_ in 1998, the madness of her rants and raves, accompanied by cats, made her perhaps the most recognizable and transportable first "crazy cat lady" of popular culture. She pops up from time to time throughout the show and reveals in one episode that she has a law degree from Yale and a medical degree from Harvard, a highly accomplished "mad" woman. As a figure of derision, and of dysfunctional and misdirected talent, she exemplifies the fine line between the CCL and the animal hoarder, the latter being the former's much less "funny" companion. Also walking a fine line between humor and loathing is J. K. Rowling's character Dolores Jane Umbridge, whose militancy, empathy failures, and dictatorial style while headmistress of Hogwarts goes hand in hand with her pink outfits, girlish giggle, and her vast collection of kittens framed on her office walls (2003). As a "crazy cat lady" (without any actual cats), Umbridge is also a figure of gendered dysfunction whose "love" for cats is indicative of her contempt for the "real" lives of others (see also McKeithen 2017). Going back to 1975, the documentary film _Grey Gardens_ follows the decline of an American aristocratic mother and daughter and shows the Beales' living conditions shifting from ancestral privilege (they are related to Jaqueline Bouvier Onassis) to one of squalor, where the mother and daughter share their once grand house with raccoons and many cats whom they claim to breed. Their exposure within the film parallels that of other animal hoarding documentaries, where the hoarder's life is exposed by camera and crew, and we, the audience, asked implicitly to recoil and then reinscribe a "line" between animal and human, cleanliness and squalor, civility and barbarism, domestic and feral (Krasner 2017).
While we might situate these popular culture CCLs as a modern and also Western phenomenon, the association between single (often older) women living in the company of cats goes much further back into the archives: women as witches with their "familiars," unhinged from human society, living at odds with the rest of the community and seeking instead the company of animal Others. The CCL gains mobility and meaning because it is a reminder of the historical, cultural association between mature women, animals, and the irrational; that not only are our relations with animals sentimental (read "trivial") but they are also made possible by having a shared status of mindless irrationality and animality. As Adams and Donovan show in their introduction to _Animals and Women_ (1995), women and particularly feminists have historically put a great deal of effort into attempting to show that women are _not_ animals. "Crazy cat ladies" illustrate just why that might be the case, as well as the importance of reclaiming the association in different, more positive terms.
In a recent positive review of the mainstreaming of the CCL, Linda Rodriguez McRobbie suggests that the "crazy cat lady" is actually losing its potency as a stigma and she puts this down to three things. One is that women no longer feel threatened by the spinster image that women with cats seems to conjure up (marriage is on the decline). Secondly, she suggests that pet culture and capitalism encourages grand displays of affection for animals, and that, thirdly, love for cats is made visible and therefore more "normal" by social media. The article also highlights how celebrities (like Taylor Swift) are taking up the moniker of CCL, changing the image of the CCL from Eleanor Abernathy, who throws cats at people, to someone who seeks out photo-opportunities with them. No longer, "crazy," McRobbie's story concludes that the "cat lady" is now "chic, she's young, she's got a good job, she's not always a lady, and it doesn't matter if she's not married... being a cat lady is no longer so taboo" (2017).
This shift away from the "taboo" is also seen most readily in feminist animal studies. For example, in her prescient and insightful essay "Bitch, Bitch, Bitch: Personal Criticism, Feminist Theory, and Dog Writing," Susan McHugh suggests that women who elect to "share their lives with female canines... become targets of criticism as 'indulgent' for focusing on their dogs" (2012, 616). But she goes on to say that women who take the risk are rewarded by the fact that becoming "down with the bitches... offers a way of recalibrating centers beyond the abstract model of the lone 'authoritative' human individual, and thereby of rethinking feminist politics as intra-active, even trans-species, from the ground up" (632). This may well be what is at the heart of the embrace of the CCL image too: a desire to rethink feminist politics in the company of dogs/cats/other animals. But not too far from this desire is also the backlash that McHugh signals, or an undercurrent of sexism and animalization that situates women and animals as forming a dangerous alliance: dangerous to her precarious grip on humanness and its psychic corollaries (reason, rationality, transcendence). At the heart of the "joke" about the CCL is that she has gone too far, "gone to the dogs"/cats, that her love of cats is fundamentally misanthropic.
It's important to bear in mind that when it comes to the animals that she might be "keeping," none of this is particularly funny either for her or for the animals who might have to be rescued from their "rescuers." CCL as a cultural archetype is implicated in animal hoarding—where the "cat lady" becomes the "crazy cat lady" and her care becomes toxic for the animals she "rescues." Just what that toxic care looks like for the animals is frequently overlooked, to the detriment of the animals who suffer profoundly, and are often euthanized as a result (see Pollak et al. 2014; Morrow et al. 2016; and Joffe et al. 2014). According to the literature on animal hoarding, it is predominantly women who are responsible for these cruelty cases, leading more than one expert to comment that the "crazy cat lady" is indeed a stereotype and yet "there is some truth to it" (Arluke and Killeen 2009, 167). However, this is where we need a more complex picture of how gender plays its part in the discussion of animal hoarding. Given her apparent ubiquity in popular culture, it is something of a surprise to find that the evidence for the crazy cat lady (as animal hoarder) is still rather patchy.
Animal hoarding studies
American sociologists have been studying animal hoarding since the late 1990s. A leading expert on animal hoarding is US sociologist Gary Patronek, who in 1999 published a study that concluded that most hoarders were women (76 percent), aged sixty or over (46 percent), single, and living alone. This early study is at the center of multiple studies that follow, and its statistics are cited repeatedly, but often without Patronek's own original equivocations or caveats about the reliability and accuracy of the data. Patronek's study was based on fifty-four case reports sent to him from ten animal control agencies and humane societies across the United States. Three problems with the original mapping of animal hoarders emerge. The data set is very small, and yet the reporting in terms of percentages gets repeated in a way that provides an illusion of bulk. The source for the data (animal control agencies) is also not without problems. It is difficult for Patronek's study to account for the possibility of interpretive bias—an expectation from agents, neighbors, or councilors—that women with multiple pets are deranged and deviant and more likely to be suspected of, and ultimately reported for, hoarding-related offenses. It seems that men do not carry the same cultural baggage when it comes to "keeping" animals. We get a hint of this gender bias in favor of reporting women for hoarding when Patronek notes that agencies found it difficult to prosecute men for animal hoarding offenses because the men did not fit the image of the hoarder, an image that precedes the ascendancy of the condition or crime. If a judge can't see a man as an animal hoarder, then it's likely that neighbors will also overlook them; they are, after all, sharing the same cultural landscape that depicts women and men as having specifically gendered relations to animals and animality. Although studies since then stress that animal hoarding stretches across multiple demographics, they keep returning to this idea that most animal hoarders are female, without all the caveats in place. Consequently, the prevalence of women as animal hoarders gets repeated uncritically throughout the literature.
Most research on the prevalence and demographics of animal hoarders assert an awareness of the stereotype of the cat lady and admit that it may skew reporting, while also suggesting, rather unconvincingly, that the facts remain somehow untouched by the influence of that very stereotype. In other words, the literature on animal hoarding seems to want to have it both ways, which is precisely how stereotypes operate. As literary theorist Homi Bhabha writes, a stereotype "is a form of knowledge and identification that vacillates between what is always 'in place', already known, and something that must be anxiously repeated" (1994, 66). It is this "anxious repeating" that signals its precarious relationship to reality:
Animal hoarders come from varied backgrounds, despite the stereotype of the neighbourhood "cat lady" who is an older, single female, living alone. As with many stereotypes, there is an element of truth to this image. In one study (Worth and Beck 1991) just 70% of the sample were unmarried women who had cats, while in another study (Patronek 1999), 76% of the sample were women, 46% were over sixty years of age, most were single, divorced, widowed and cats were most commonly involved. (Arluke and Killeen 2009, 167)
Urban legends tend to be fairly resistant to "objective" fact-finding. That is, they can work to structure reality while also being self-reflexively repudiated. In the case of women who are animal hoarders, this ambivalence about how to "read" her activities persists. One example of this can be seen in Svanberg and Arluke's reading of the "Swan Lady," which recounts the case of a Swedish woman, convicted for animal cruelty, who rescued and kept a large number of swans in her apartment. The authors argue that there was confusion in the media about whether to classify the offender as an animal lover or a criminal. Svanberg and Arluke suggest that instead "the Swan Lady became a kind of heroine, or rather anti-heroine, at least according to some—not because she had rescued swans per se but because she took these birds into her apartment... the epithet 'Swan Lady' added to the media's spin on this case as a charming, albeit ill-informed, behaviour" (2016, 65). They point out that while there was no fitting term for animal hoarding in Sweden, the community would have been familiar with the "crazy cat lady" through American television, especially Eleanor Abernathy from _The Simpsons_. This encouraged a view of the woman's activities as more akin to an "absurd anti-heroine" than a case of animal cruelty. Their reading suggests the global reach of such a stereotype (via _The Simpsons_ ) and its capacity not only to move between borders and languages but also to influence, construct, and reinforce the social norms it appeals to. For the authors, the emphasis on the "Swan Lady" as "absurd anti-heroine" served to "excuse" the cruelty that was felt by the animals she claimed to care for and exemplified how the reporting of such cases is very often anthropocentric. It is also an example of something pointed to earlier, which is that the "Swan Lady," like the CCL or woman who is an animal hoarder is likely to be partly "excused" on the basis of gender (it is _merely_ caring gone wrong). But she is also likely to be _singled out_ because of her gender.
This ambiguity is perhaps what makes the CCL and woman animal hoarder such an attractive media story. The framing of animal hoarding cases is often not just anthropocentric but also misogynistic. When misogyny combines with anthropocentrism it works to scapegoat women and also confine the issue to the "madness" of women, that is, to a symptom of gender rather than a broader issue of human arrogance. This effectively brackets a broader issue of animal cruelty to aberrant individuals, bad "apples," and their specific gender. Indeed, the media focus on the "Swan Lady," which focused largely on this "quaint" story of care gone wrong (but good intentions maintained), is consistent with the ways that animal cruelty cases involving agriculture also get picked up, as individual aberrations within an otherwise healthy and rational system.
Peter Chen makes the point that media coverage of animal welfare issues tends to be "episodic" rather than "thematic." An episodic framing would treat an animal hoarding issue as an individualized event, a blemish in an otherwise healthy social body, a bad day in an otherwise healthy calendar. Such a framing leaves the structural and broader social explanations (gender and violence against animals) and context largely untouched: "the individualized focus can be engaging but not necessarily productive" (95). So too in the case of the CCL and the "Swan Lady"—these are media events that do not help to either draw attention to the plight of the animals prior to their "rescue" by the hoarder, nor to the conditions under which so many animals live and die as part of a larger social system that defines itself in part by its capacity to maintain institutionalized violence "cleanly" and "rationally" and away from urban spaces, as in the case of factory farms or concentrated animal feeding organizations (CAFOs).
CCLs and CAFOs: The intensification of animal keeping
In this final section, I consider the "crazy cat ladies" appearance as a cultural trope alongside the intensification of farming practices, specifically in the form of factory farms and CAFOs. Animal hoarding, "crazy cat ladies," and CAFOs are connected in key ways but principally as examples of the intensification of animal keeping within Western modernity, and by animal keeping I mean agriculture as well as the breeding of animals designated "pets." Factory farms and CAFOs are institutions that routinely demonstrate the gulf between animal welfare standards, good intentions, and a good life for animals. The CCL who is a potential animal hoarder exemplifies the gulf between declarations of animal care and actual outcomes for animals at an individual level, and the factory farm or CAFO exemplifies it at the structural or institutional level. Thus we rarely see depictions of the latter as media stories, but a great deal of the former in media and popular culture. "Animaladies" of the hoarding variety are therefore not all equal, with some more clearly marked by gender, marking some bodies and behaviors as public exemplars of wrongdoing, while others are made invisible through normalization.
The fascination with CCLs _and_ animal hoarding cases is in itself rather fascinating. It is not only the CCL products that palliate and obscure the dark side of the CCL (her animal hoarding relations) but also the documentaries and texts that want to take us "inside" their homes and minds are remarkable. Animal Planet produced three seasons (thirty episodes) of _Confessions: Animal Hoarders_ (2010–2012), which exposed the lives of hoarders and the animals. They maintained a fairly consistent narrative framing, starting with concern about animal cruelty, fascination with the state of mind of the hoarder, attention to the domestic scene, and then rescue (including euthanasia) of the animals. As well as TV shows and documentaries like _Grey Gardens_ , there are also texts such as _Inside Animal Hoarding: The Case of Barbara Erickson and Her 552 Dogs_ , which promises to take us "inside" but begins by showing that the media got there first. As Celeste Killeen explains:
I first met Barbara and Bob Erickson from a distance, watching the shocking television reports that describe the rescue of their surviving dogs. For several days after the dramatic police action, the evening news was filled with images of wild eyed, filthy animals, some too weak and sick to move, others seemingly trapped in a frenzy of barking and clawing... Reporters bit into the story, holding on like a dog to its bone... They ran the chaotic video clips day after day, changing only their voiceovers. In time, they reported the decision to prosecute the dog owners. But no one talked to Barbara Erickson. (2009, 6)
While sympathetic to the need to consider the perspective of Barbara Erickson, the focus on her also reinforces the ways that interest in these cases is already gendered. Her husband Bob was also charged (and pleaded guilty to charges) of animal neglect and abuse. But the state of the house, the living room, the domestic squalor, and their claims to have "loved" their "babies" (the dogs), situates this story as already about the specific failures of femininity and feminized domains: the domestic sphere, the family, and care. The access to this space is also significant. It was not just that Killeen wanted to get "inside" the mind of her subject, but so did all the reporters and, they presume, their audiences, looking into the state of the living room with a morbid and horrible fascination for such a scene of chaos and suffering. These scenes are repeated in a number of "documentaries" about hoarders, where an audience get to see "inside" the domestic spaces, implicitly enjoying the opportunity to repudiate the "madness" of those whose domestic spaces have become unruly, toxic, and pathological. To some extent, the perverse pleasure associated with repudiating such a neighbor helps to reinforce correct animal care practices and also reinforce the sense that such things should never be seen (but we must look!) in the first place.
The TV footage also works as an uncanny reminder of animal activist footage that seeks to get "inside" the factory farms to expose "hidden truths" about what animal welfare standards actually mean for animals subjected to intensive farming practices. The difference between what we see in the animal hoarder's home and what we see in the factory farm is one of degree rather than kind: the animals suffer conditions of overcrowding, confinement, in ammonia-filled air, surrounded by manure, and unable to escape the company of others or express natural behaviors. But these videos rarely make it onto mainstream television. Nor are the corporate owners and operators of factory farms subjected to the speculation of writers or media commentators about their state of mind, their peculiar biographies, or their personal traumas that may have led them to bring such a horrible site of animal suffering, like the factory farm or CAFO, into being.
Agribusinesses that rely on CAFOs are defined partly by their capacity to prevent such videos or biographies, or pathologizing and individualizing language, from becoming mainstream, with the deliberate obfuscation of public awareness about factory farming a central marketing feature. Take, for example, the packaging of animal products, described by Peter Chen as routinely depicting "pastoral scenes, with farms commonly signified by barns or old fashioned windmills... idealized or archaic portrayals, rather than the realistic representations of modern production facilities" (2017, 115). These "realistic" representations would not be unlike some of the videos on Animal Planet that expose animal hoarders in domestic urban spaces. Neither factory farm nor animal hoarder's house is structured with the animal in mind, though both may well make that claim.
Consumers of televisual and textual material on animal hoarders are given enough data to repudiate the hoarder and also sympathize with the animals. Would they also then repudiate the CAFO operator if they could also see inside? Timothy Pachirat's work on this assumption (that visibility leads to political transformation) would suggest not, especially given that "seeing" it is not the same as caring to know or acknowledging the costs for animals in the long term. Chen makes the point that consumers and voters are not presented with enough data and accurate information to make informed decisions about ethical food practices or animal welfare. He goes on to point out that the ignorance that is perpetuated by sanitized representations of intensive farming (or industrial hoarding) means that the public can become easily "shocked and angry" when confronted with such images but these come in the form of exceptional events, not structures, and that this rarely lasts long because it is not backed up by either a strong base of knowledge or consistent policy changes. This is an argument made in detail by Siobhan O'Sullivan in her book _Animals, Equality, Democracy_ , which also points out that democratic principles of informed debate and discussion are thwarted by a largely secretive and invisible process of food production in Australia, as well as a strong marketing emphasis on "happy" animals on idyllic pastoral settings (2015). Carnists are not told what they are buying into and as such the cultural practices or beliefs about animal welfare suggest not an expression of their assent, or a product of democratic decision-making, but a form of consumption that is conducted largely through concealment, obfuscation, and propaganda.
What is significant about the scale of this silence around the actual conditions under which livestock in Australia live and die is that it stands in contrast to the exposure of the animal hoarder, whose mistreatment of animals is broadcast across borders and depicted in newspapers, in close and personal detail in ways that are so intense and intrusive that they might be described as verging on the violation of individual privacy and ethical duties toward the vulnerable mentally ill. Given the contrast between these two kinds of seeing—not seeing into factory farms and seeing too much into the homes of the animal hoarder—it is likely that the public has had more access to the insides of an animal hoarder's house than they have had access to the factory farm from which she or he buys her eggs, pigs, chicken, and dairy products. And from this exposure to the animal hoarder rather than CAFO operator, consumers may well be more inclined to worry about the neighbor who has too many animals in their house or yard than those high-rise sheds on the edge of town where thousands of animals are kept in windowless sheds. Given the media scrutiny of one form of intensive animal keeping over another, it is not too far-fetched to speculate that this might also skew our attention (and the attention of animal welfare officers) as to what counts as events to be alarmed about and those that may provoke disgust but not accusations of dysfunction. The difference in the quality of interest and the display of the "madness" of the animal hoarder (woman, CCL), but not factory farmer (faceless CAFO), attest to the deeply held social norms around animal agriculture that determine that it is acceptable to confine, restrict, and forcibly breed large numbers of animals that are designated livestock, but not acceptable to confine or restrict large numbers of animals designated "pets."
When the lines between domestic pets and agricultural livestock become blurred, as in the case of puppy farming, the norms by which we measure what counts as acceptable are exposed as largely arbitrary cultural formations. Public outrage that comes with puppy farming scandals attests to the idea that it is simply not acceptable to treat dogs in a way that pigs routinely are. Along with the pigs, we may well object to this arbitrary structural distinction. The arbitrariness does not translate into "easy to change," rather it means that they are prone to the sort of constant "reiteration," reinforcement, and mobility that stereotypes require. The depiction of animal hoarding cases and puppy farm scandals _as scandals_ assists in putting the arbitrariness to one side momentarily, because they draw attention back to the cultural line drawn between domestic and livestock animals. Putting it another way, it's as if outrage on behalf of the puppies comes at the expense of the pigs. The CCL might be said to work in a similar way: interest in her might come at the expense of our interest in factory farmers. Distracted by her behaviors, we may fail to notice how she has come to stand in for, stand in front of, the normalization of intensive animal keeping—which (whether it be described as hoarding or not) is rarely predicated on what is the best for animals.
It is also possible that we are seeing more mainstream depictions of the CCL, this "absurd anti-heroine," at the same time that factory farming, though still largely invisible, is responding to an "increased concern for the welfare of animals" (Chen 2017, 84). This is partly the result of animal protection organizations such as Animals Australia, an organization whose support base is overwhelmingly made up of mature women, much like the demographic described for animal hoarders. The dominance of women in animal protection organizations (something observed also by Munro 2001) alerts us also to the ways in which the "crazy cat lady" may well serve to trivialize and dismiss the work and political commitments of animal advocates in advance, by stigmatizing their interests in animals as potentially pathological.
Despite the benefits of the animal turn for feminist politics, and the apparent acceptance of women's independence as signaled by cat-love rather than human marriage, the persistence of the CCL as a stereotype with which to deride women's care of animals remains, especially those who are animal advocates pushed to the margins of what the mainstream counts as rational political behavior. The "crazy cat lady" has become such a key figure or symptom in exposing the gulf between care and cruelty precisely because these elements persist in much wider and institutionalized forms through intensive factory farming. The CCL is a woman of many talents: she declares her allegiance to cats; she makes a joke of and also points to both animal hoarding and women's advocacy on behalf of animals; she provides an opportunity for good intentions to obscure cruelty; and she operates as a scapegoat who can be repudiated publically while intensive animal keeping such as what we see (or don't see) in CAFOs or factory farms gets off the hook. She serves a much broader purpose as a cultural trope for a variety of "animaladies."
Acknowledgments
I would like to acknowledge Anne Fawcett's expertise and help, pointing me toward the literature on animal suffering caused by animal hoarding cases. The chapter benefited greatly from her insights into veterinary scholarship on hoarding. I thank the audience and organizers (Melissa Boyde and Alison Moore) of the "Beyond the Human" Symposium held at the University of Wollongong in 2015, where I presented an earlier draft. I would also like to thank Annie Potts for the socks, she knows why.
Note
Peter Chen notes that a survey of individual Animals Australia members in 2000 found 74 percent women with a mean age of 51 (Chen 2017, 179).
References
Adams C. and Donovan J. (1995), _Animals and Women: Feminist Theoretical Explorations_ , Durham: Duke University Press.
Arluke, A. and Killeen, C. (2009), _Inside Animal Hoarding: The Case of Barbara Erickson and Her 552 Dogs_ , Indiana: Purdue University Press.
Bhabha, H. (1994), "The Other Question: Stereotype, Discrimination and the Discourse of Colonialism," _The Location of Culture_ , London: Routledge.
Chen, P. (2017), _Animal Welfare in Australia_ , Sydney: Sydney University Press.
"Confessions: Animal Hoarders," _Animal Planet_ (USA TV) 2010–2012.
Harrison, R. (1964), _Animal Machines_ , London, Vincent Stuart Publishers.
Joffe, M., O'Shannessy, D., Dhand, N. K., Westman, M., and Fawcett, A. (2014), "Characteristics of Persons Convicted for Offences Relating to Animal Hoarding in New South Wales," _Australian Veterinary Journal_ 92: 369–375.
Krasner J. (2017), "Cat Food in Camelot: Animal Hoarding, Reality Media, and Grey Gardens," _Journal of Film and Video_ 69: 44–53.
McHugh, S. (2012), "Bitch, Bitch, Bitch: Personal Criticism, Feminist Theory and Dog-Writing," _Hypatia_ 273: 616–635.
McKeithen, W. (2017), "Queer Ecologies of Home: Heteronormativity, Speciesism, and the Strange Intimacies of Crazy Cat Ladies," _Gender, Place & Culture_ 24 (1): 122–134.
McRobbie, L. R. (2017), "The Crazy History of the Cat Lady," _Boston Globe_ , May 21. Available online: <https://www.bostonglobe.com/ideas/2017/05/20/the-crazy-history-cat-lady/5DJaZf5QW0KPv8KTYBBGPO/story.html> (accessed May November 1, 2017).
Morrow, B. L., McNatt, R., Joyce, L., et al. (2016), "Highly Pathogenic Beta-Hemolytic Streptococcal Infections in Cats from an Institutionalized Hoarding Facility and a Multi-Species Comparison," _Journal of Feline Medicine and Surgery_ 18: 318–327.
Munro, L. (2001), "Caring about Blood, Flesh, and Pain: Women's Standing in the Animal Protection Movement," _Society and Animals_ 9 (1): 43–61.
O'Sullivan, S. (2015), _Animals, Equality, Democracy_ , Palgrave: London.
Pachirat, T. (2015), _Every Twelve Seconds_ , New Haven, CT: Yale University Press.
Patronek, G. J. (1999), "Hoarding of Animals: An Under-Recognized Public Health Problem in a Difficult-to-Study Population," _Public Health Reports_ 114: 81–87.
Polak, K. C., Levy, J. K., Crawford, P. C., Leutenegger, C. M., and Moriello, K. A. (2014), "Infectious Diseases in Large-Scale Cat Hoarding Investigations," _Veterinary Journal_ 201: 189–195.
Svanberg, I. and Arluke, A. (2016), "The Swedish Swan Lady Reaction to an Apparent Animal Hoarding Case," _Society & Animals_ 24: 63–77.
Vialles, N. (1994), _Animal to Edible_ , Cambridge: Cambridge University Press.
Chapter 12
THE ROLE OF DAMNED AND DAMMED DESIRE IN ANIMAL EXPLOITATION AND LIBERATION
pattrice jones and Cheryl Wylie
A girl's story
I started in 4-H when I was eight years old. By the time the county fair arrived, I had just turned nine and was caught up in the excitement of packing the camper and show supplies for the animals. I was taking my beloved rabbits to the fair along with my first steer, Buddy. I remember standing by as my dad and older brother got my steer to the weight scales the first day. I remember watching everyone getting him ready for the show ring that Tuesday. I remember the nervousness of being in the show ring and the excitement of being chosen for a trophy. All of those first memories will always be there, but none will overwrite the memories of Friday, which was sale day.
We lined up in the order determined by our placements in the show ring. One by one, we walked in the small sale ring with the steers we had taken care of for the past seven to ten months. The auctioneer was loud; everything else is a blur. The instructions I'd been given rang in my head: Keep moving and smile. I was supposed to smile, but all the while tears were streaming down my face. The time seemed to crawl, but I know it was just minutes before the auctioneer banged the gavel and announced "Sold!" along with the buyer's name.
I walked through the final two chutes and watched as one of the men took off Buddy's halter and handed it to me. Buddy walked through the last gate and was gone, loaded into the truck with so many others. I was supposed to find my mother to find out who the buyer was and where they were sitting, so that we could thank them and ask if they needed anything to eat or drink. After that, I headed back to the barn to empty the buckets and pack up all the supplies into the show box for the trip home on Saturday.
This repeated itself year after year—with steers, sheep, and pigs—for nine years. I cried in every sale ring, from that first one at age nine until the last time just after I graduated high school. In some respects, I think the girls had it easier than the boys. No one other than my older brother ever told me not to cry. The men working the sale always came and walked through the last gate for me. They clearly understood the sorrow, but we all still came back the next year and did it all again.
Loving them to death
Desires for close relationships with other-than-human animals are both damned and dammed. Paradoxically, people who want to be close to animals may be more likely than others to pursue careers and hobbies that hurt animals. If we can understand how people who love animals become invested in recreations and occupations that hurt animals, we may become better able to craft apt interventions. To that end, we will examine this phenomenon through three case examples (cockfighting, backyard hen keeping, and youth programs such as 4-H and Future Farmers of America), attending to both desire and identity in each case, before turning to the question of interventions. We will argue that animal advocates will succeed in altering human relationships with other animals only insofar as we acknowledge and tap into desire in all of its queerness, urgency, and gendered complexity.
We write from the mountainous terrain of a farmed animal sanctuary that offers refuge to survivors of all three of these ways that animals are hurt by people who love them, and more. In addition to survivors of cockfighting, backyard hen keeping, and 4-H programs, VINE Sanctuary has welcomed refugees from petting zoos and pigeon racing as well as from ostensibly humane farms where "beloved" cows, goats, or sheep were allowed to starve or otherwise suffer. One of us (Cheryl) participated in 4-H and FFA programs as a child, and one of us (pattrice) devised a method of rehabilitating roosters used in cockfighting—a feat that has repeatedly brought the sanctuary to the attention of voluble participants in that blood sport. We both have had extensive conversations with women engaged in backyard hen keeping. Our reflections and recommendations are rooted in such encounters with the phenomenon of "loving them to death."
Damned and dammed desire
Some desires are damned, considered by the dominant culture to be bad and wrong. In some cases, that disapproval is warranted. The ability of a community to dampen truly destructive desires is useful, and this probably explains why social disapproval can create palpable unease. As social animals, we are hard-wired to respond to expressions of disapprobation and also to internalize the values of the group. All of this goes awry when the damned desire is a harmless wish and is particularly injurious when the yearning in question is in any way vital to well-being or sense of self. The harms done to individuals by cultural or religious antipathy to homosexual desire are well known. As one of us has discussed elsewhere, suppression of same-sex eros also leads to social and environmental ills (jones 2014a).
Most people consider kindness to animals a virtue. However, in cultures founded in the speciesist notion of an absolute and hierarchical divide between humans and other animals, over-familiarity with other-than-human animals transgresses an essential border and is therefore proscribed. Whether persecuted as witches or mocked as insufficiently sane, people seen as being in unseemly communion with animals face a range of negative social consequences.
"Human" is more than a species—it's a _status_. Preservation of that status, that identity, requires constant policing of the imagined boundary between humans and all other animals. For example, humans are imagined to be more rational and less emotional than other animals. Therefore, people censured for being "too close" to animals may be told that they are insufficiently rational or overly sentimental.
Those are charges frequently leveled at women more generally. Like damnation of homosexual desire, disapproval of the wish for authentic and egalitarian relationships with other-than-human animals tends to be gendered. Girls and women are allowed and even expected to feel affection for animals, but may moderate their sympathies for fear of being seen as excessively emotional and therefore inferior to allegedly more rational males. The social psychological phenomenon known as _stereotype threat_ (Inzlicht and Schmader 2011), in which members of disadvantaged groups are anxiously aware of pejorative stereotypes and sometimes alter their behavior in order to avoid seeming to embody them, may motivate girls and women to dampen or underplay their sympathy for animals.
Boys and men are even less free to express affection for animals, both because tender feelings of any kind may be construed as weakness and because the social role of "man" includes dominion over animals. Human males are supposed to want to hunt, kill, eat, and display control over members of other species. All of these activities can be used to demonstrate masculinity, and distaste for any of them may be read as femininity. Men are permitted to dote on a favored dog or horse but only so long as they maintain the position of "master" over an animal conceived as a devoted servant rather than a peer. Such motivations may redirect friendly feelings for animals into more suitably masculine efforts to control animals. When a boy who loves and wants to spend all his time with horses grows up to be a jockey who whips horses or a cowboy who "breaks" horses, we would consider this to be a case of dammed desire.
4-H and FFA
For many rural youth in the United States, participation in a 4-H or FFA club represents a kind of rite of passage. Both founded in the early 1900s in conjunction with governmental rural development efforts; 4-H and FFA teach vocational and life skills with a heavy emphasis on agriculture. 4-H members pledge to devote hands, head, heart, and health to club, community, and country. Children as young as eight can join their local 4-H club. Some clubs have a specific focus like sewing while others allow members to take any available project. Projects include skills like cooking, woodworking, photography, and gardening, but 4-H is best known for the projects in which children care for animals who are then shown, and often sold, at county fairs. All projects are designed to give the child a base of knowledge that can be built on with increasingly difficult challenges in successive years. Projects are judged either at or just before the county fair, with the results being announced during the fair for all to hear. Club members earn a few dollars for each completed project.
Cheryl recalls:
Animal projects varied greatly. Some, like rabbits, focused on proper care and nutrition for the first years. Others were "market projects" from the outset. I took my first steer to the fair at nine years old. I spent hours, first on the weekends and then daily once school let out, teaching calves to walk while haltered and learning how to position them in the show ring. I learned to groom them, and I taught them not to fear water hoses, fly spray, or the sounds of cars. I spent hours and hours teaching them to trust me, and they did.
Days at the fair started early. Rabbits had to be cleaned, fed, and watered. Steers had to be walked, rinsed, fed, and back in the barn with their stalls cleaned before the fair opened. On show day, the steers had to have a full bath. Then it was into a grooming chute to be trimmed, clipped, and combed to make them look as appealing as possible for the judge. As the assigned class for my steer approached, I was sent off to get cleaned up and changed into dress clothes. I remember being anxious as I awaited my turn in the ring. Once I entered, a thousand thoughts ran through my head, all the while I hoped that the steer wouldn't panic and bolt. There was a strange amount of pressure to do well, even though the show had nothing to do with us as kids. The placements were subjective, but I remember feeling like it meant so much.
The days between the show and sale days at our fair felt like a vacation. After everyone was fed and watered, I could run amok on the fairgrounds. The days were filled with rides, junk food, and picking up free pens in the exhibit hall. So long as I checked the animals' water and checked in for dinner, I was free. That made me look forward to fair week all year.
The last days of the fair were sale days. The times were posted, sale orders announced, and one by one the barns would be emptied. Those last two days every year were always the worst. I think that every person who cares about non-human animals has cringed to see the animal transport trucks on the road. Every year for nine years, I put my friends on one of those trucks. Then, I had to go find my mom who was watching the sale to find out who the buyer was and thank them. In nine years, I don't think I ever did it without tears in my eyes and a lump in my throat.
Originally called Future Farmers of America, FFA began as a vocational program for high school students but now can be joined by children as young as twelve. As with 4-H, club members pursue a variety of projects including but not limited to animal agriculture. Coursework might include learning about the different breeds of farmed animals but might also include woodworking or basic welding. FFA also sponsors public speaking contests, parliamentary procedure teams, and competitions judging everything from soil quality to dairy products. As with 4-H, participants take projects to the county fair, where they might win awards. Projects include horticulture, woodworking, and so-called "production projects" involving sheep, pigs, steers, or veal calves.
Cheryl recalls:
When I made out my schedule for high school, joining FFA and taking the associated class, Vocational Agricultural Education, seemed like a given. For incoming freshmen, it was a popular class, not only for its reputation of being an "easy A," but also because it was worth more credit hours than any other course. In my freshman year about half of the class took some sort of animal project to the fair. Those of us still participating in 4-H clubs had to decide early in the year not only which animals we would take but also which club each animal would fall under. Often the decision was based on which group had the earliest show times or the least competition per class. Every decision that we made during that time was based upon getting "the best return on our investment"—a goal encouraged by advisors and parents alike.
During my four years in the FFA I participated in the "breeding ewe" project in which students each take a pair of pregnant ewes, caring for them for the duration of their pregnancies and monitoring them through the birth of their lambs. Often the sheep would have multiple lambs, and I often found myself stumbling out to the barn at 2am in January to bottle-feed the lambs. Our advisor would come out within a few days of the birth to dock tails and castrate the lambs by banding. The students were responsible for making sure infection didn't set in and that the sites healed properly.
After weaning, the FFA advisor came and collected the ewes as well as one lamb per sheep. We were left with the remaining lambs to raise for the fair. I literally raised these lambs from birth, cared for them for seven months, and then sold them at auction to the highest bidder. For ten years, I cried every time I was in a sale ring. It never got easier, and no one around me ever seemed to understand that fact. The guys never seemed to cry, probably because they would be mocked if they did. Even many of the girls never seemed to shed a tear. More than once, I was accused of "faking it" in an attempt to get sympathy and a higher price from the buyers. My classmates seemed to become more callous every year. Looking back, it seems to me that we were being taught to be little sociopaths who felt nothing while betraying those we had taught to trust us.
Fair week was notorious for reckless behavior among my fellow FFA members. Despite ours being a "dry" fairgrounds, alcohol was never in short supply. Drinking was a recreational activity in the evenings and seemed to intensify year after year. The deputies assigned to patrol looked the other way unless one of us did something dangerous or the barns were loud after midnight. The final night, after the last of the sales had concluded and many of the barns were empty, it became a free-for-all of unsupervised high school students. For me, that raucous last night was an escape from the knowledge that I would go home the next day to an empty barn.
4-H and FFA shape rural youth. In addition to valuable skills like sewing, welding, horticulture, or woodworking, participants learn the value of community service. They develop the habit of seeing projects through to completion and may also develop leadership skills such as public speaking or how to chair meetings. Awards and degrees boost confidence that helps participants navigate the difficulties of adolescence. Club participation can bring the sense of belonging that is so vital to young social animals. And yet, at the same time, children who love and want to spend time with other animals are traumatized anew each year by the experience of sending beloved friends to slaughter. Over time, many of them develop emotional callouses that then allow them to become the next generation of beef farmers or pork producers.
This dispassion may foster a more widespread malaise. Cheryl recalls a dampening or blunting of all emotions, not just the sadness, as well as an unspoken ban on talking about any of the doubt, guilt, or other feelings children might feel upon sending their friends to be killed. When she says "we didn't talk about it," she means not only that her own family didn't talk about it but also that children didn't talk about it among themselves and none of the adults involved helped them to process the feelings flooding their bodies. They were dammed.
Cheryl's own recollections of these childhood experiences have many of the hallmarks of traumatic memory, with all of its nightmarish fragmentation and distortion, as if she were always walking around that show ring, trying unsuccessfully not to cry, as the auctioneer's voice blared. When she tries to open the door to more memories, it's as if something is physically blocking her from doing so. This is not surprising. Being forced to participate in killing loved ones is a kind of torture that leaves people feeling damned. Cheryl has found a way, by devoting her life to caring for animals, to assuage the lingering guilt and shame. But many survivors of this culturally approved form of child abuse repeat the pattern by subjecting their own children to it. The accumulated callousness and defensiveness may help to explain not only the perpetuation of animal agriculture but also many of the other cruelties for which the US "heartland" is internationally infamous.
Cockfighting
In a typical cockfight, men thrust two aroused roosters into unnaturally close proximity. Prevented from flight, they fight. Surrounded by shouting apes and flooded by adrenaline, each rooster concludes correctly that the only way out of this emergency is to attack. In between rounds, their handlers care for them tenderly, sometimes sucking bloody mucus from their beaks with their own mouths, even though it was they who put the birds into this mortal danger. The fight concludes only when one bird dies, at which point his handler mourns while the handler of the battered victor crows as if he himself has prevailed in battle and the gamblers begin to place their bets on the next fight.
As a pastime dating back to antiquity and spanning the globe, cockfighting has proved to be both persistent and culturally meaningful in a wide variety of settings. Here in the United States, cockfighting is illegal in all fifty states and a felony in forty of them. Unlike many other animal cruelty laws, the ban on cockfighting is actively enforced, mostly because fights are also sites of illegal gambling and associated violence. Every year, hundreds and sometimes thousands of birds are seized by authorities enforcing anti-cockfighting statutes, their numbers evidence of the continued vitality of whatever impulse leads men to abuse birds in this way.
While non-participating attendees of cockfights may be drawn by the drama of violence or the thrill of gambling, men who spend much of their own time and money raising roosters and transporting them to fights despite the risk of fines, jail time, and the social penalties of a felony conviction must be vested in the endeavor for deeper reasons. Chief among these is masculinity, but we believe that the wish for relationships also animates men who might demonstrate their virility by any number of legal and less costly ways.
In his essay entitled "Gallus as Phallus," Alan Dundes cites and summarizes numerous studies that demonstrate the association between cockfighting and masculinity within particular cultural settings, arguing that "it is always a mistake to study data from one particular culture as if it were peculiar to that culture if comparable, if not cognate, data exist in other cultures" (2007, 293). We agree that the cumulative scholarship on cockfights does suggest that they are what one of us has called "spectacles of stylized masculinity" (Jones 2010, 191) wherever they appear and even when participants insist that the activity is primarily an expression of national or ethnic identity. (Since maleness tends to be an implicit element of full citizenship, a focus on masculinity does not contradict such claims.)
Our sanctuary was the first to devise a protocol for rehabilitating roosters formerly used in cockfighting, so that they can be integrated into flocks rather than euthanized. Periodically, this fact finds its way into a television or newspaper story, at which point we begin to receive calls and messages from men who proudly participate in cockfighting and want us to know how wrong we are. The ensuing dialog tend to follow a pattern: The man begins in (1) a patronizing tone, in which he (2) presumes to know more than we, often on the basis of far less experience with roosters, and then (3) informs us that it is impossible to do what we have, in fact, done. If we contradict this in any way, then (4) the tone becomes surly and overtly sexist. There may be unappeasable demands for proof or charges of fakery, but inevitably (5) we are accused of abusing the roosters by robbing them of the opportunity to express their naturally combative personalities.
In the context of the current inquiry, the degree to which these men who abuse roosters describe themselves as _protectors_ of roosters whose right to self-expression might be violated by emasculators like us is particularly telling. On the surface, this seems like a simple displacement in line with the use of roosters as avatars of masculine identity: they feel threatened by feminists, and so it feels to them like roosters are threatened by the ecofeminist animal sanctuary. At the same time, these men do seem to sincerely see themselves as caretakers rather than abusers of roosters. They will go on at great length about the specialized diets and other amenities provided to birds in their possession. They will insist that it breaks their hearts to see a rooster die in combat but that they know this was what the bird himself wanted. They seem sincerely not to understand, and not to be able to take in if the facts are explained, that their own interventions—which always include raising roosters apart from flocks in which they could learn the social skills necessary to resolve conflicts without bloodshed and which also sometimes include injecting birds with testosterone or amphetamines—produce the aggressive behavior they see in the cockfighting ring. They feel certain that they are not hurting birds and that, indeed, nobody loves roosters more than they do.
All of this is entirely consistent with the reports of anthropologists and other researchers who have spent time in communities of cockfighting enthusiasts (e.g., Geertz 1972, Maunula 2007). Men who raise roosters for fighting often spend vast amounts of time with the birds, expend significant sums on their care, and really do grieve when they die in the ring. Many develop close relationships with favored roosters, who they sometimes treat as companion animals. Thus, we can speculate that in communities where cockfighting is prevalent, this hobby might offer an appropriately "masculine" outlet for boys and men who like birds, or animals more broadly, and want to have relationships with them. We also notice how much care-taking goes into cockfighting and the degree to which cockfighters seem to enjoy tasks that would, in other contexts, be classified as feminine.
Backyard hen keeping
In the United States in the past decade, the project of keeping backyard hens for eggs has grown from a quirky hobby to a full-fledged fad complete with specialty publications such as _Backyard Poultry Magazine_. While this may seem to be a fairly benign form of animal exploitation, particularly in comparison to confinement of hens in egg factories, the hens themselves often suffer and there are several negative knock-on effects.
Backyard hen keepers usually start with chicks purchased from hatcheries. Mechanically hatched chicks come into the world looking for mothers who will never appear. The incessant peeps that seem so adorable to people are actually distress calls of youngsters crying to be sheltered under parental wings. This is only the beginning of their anguish. Whether shipped in bulk to farm stores or mailed in boxes to individuals, chicks endure terror and disorientation, potentially injurious jostling, and life-threatening dehydration en route to consumers who may have no idea how to care for healthy chicks much less be equipped to care for those disabled in transit. After landing in their new location, the chicks face an uncertain fate. Will their captors provide appropriate food and enough fresh water? Will their coop provide adequate shelter in all weather? Will they have sufficient outdoor space to maintain healthy bodies and social relations? Will they be handled roughly or kindly? What will happen if they don't lay enough eggs? What if they don't lay any eggs at all? What if they turn out to be roosters?
For every chick sexed female and sent off to become an egg producer, a hatchery kills one chick sexed as male. Hatcheries dispatch "worthless" males as quickly and cheaply as possible. After a sorting process that is itself traumatic, male chicks may be gassed, dropped into a wood chipper, or simply tossed on top of one another in a trash receptacle and left to smother or die of dehydration.
Sexing chicks is an inexact process, especially when endeavored at speed. Inevitably, some of the chicks shipped out as hens turn out to be roosters. This may not be clear to their naive keepers until they begin crowing, at which point a literally life-threatening emergency may arise. Some backyard hen enthusiasts will not tolerate roosters. In other cases, neighbors complain. Many residential areas ban roosters. Some hen keepers execute unwanted roosters, either directly or by passing them along to a farmer or family member willing to kill. Others seek to place them at a shelter or sanctuary.
As a sanctuary nationally known for our work with roosters, we have received hundreds of calls, email messages, and social media inquiries—at least one each week for more than ten years—from women seeking to divest themselves of roosters inadvertently obtained in the course of keeping hens for eggs. Here is what we have learned about and from these women:
1. They _are_ women.
Apart from the occasional husband calling on behalf of his wife, virtually all of the backyard hen keepers who contact us are women. This is consistent with the long history of the exploitation of chickens for their eggs—perhaps the only process of "domestication" primarily implemented by women—as well as with traditional rural gender roles assigning the labor of hen keeping and egg collection to women and children.
2. Their motivations tend to be other than economic.
Factor in the costs of a coop, fencing, hatchlings, bedding, and feed, and it's easy to see that this adds up to more than an average household would spend on eggs. While we have sometimes heard from women who keep enough hens to make some money by selling eggs, most backyard hen keepers are paying much more for the pleasure of doing so than they save by not buying eggs.
3. Both desire and identity seem to be factors in their attraction to hen keeping.
Most backyard hen keepers seem to genuinely enjoy and value their relationships with chickens, so much so that it seems safe to infer that some wish for such relationships motivated the choice to begin keeping hens. Some subset of backyard hen keepers state that they began to keep hens in order to be able to consume eggs without being complicit in cruelties such as battery cages. This suggests both care for chickens and the wish to be a "humane" person. A smaller subset express satisfaction at producing their own food or engaging in animal husbandry, even sometimes going so far as to refer to their homes as "homesteads." Members of this subset also sometimes boast of being humane in comparison to the egg industry, but here the greater emotional investment seems to be in the identity of self-sufficient homesteader.
4. Their attachments to the birds in their care sometimes seem shallow or conflicted.
Most women engaged in backyard hen keeping express affection for the hens they call "girls" and do seem to feel attached even to the roosters they are trying to place at the sanctuary. At the same time, they will sometimes joke about "the soup pot" or otherwise make light of the fate awaiting most unwanted roosters. Expressions of affection tend to be sentimental or patronizing rather than indicative of empathic fellow feeling, as though the birds are indulged children rather than respected friends. In both the callous jokes and the treacly expressions of fondness, we discern a distancing consistent with maintaining the elevated identity of human.
5. They tend to display displacement.
Women hoping to place roosters with us often become defensive or even hostile when told that their hobby is the reason no shelter or sanctuary has room for more roosters. Most reject the recommendation that if they want to help roosters, they should stop buying chicks. Some tell us that we are rude for suggesting such a thing. Many rebuke us or sanctuaries in general for our failure to meet the demand for refuge that they themselves have created. We cannot count the number of times a backyard hen keeper calling or writing about a rooster has said that she doesn't want him to "end up" as dinner or be "sent to slaughter," as though she herself would not be the person responsible for that outcome. (We are not here talking about instances where there really is a husband or neighbor threatening to kill the birds.) This doesn't seem to be a conscious maneuver. Like men engaged in cockfighting, these women seem sincere in their feeling that they are protectors of birds without awareness that they are the cause of the menace.
Lessons from LGBTQ liberation
Recent years have brought what seems to be a sea change in public opinion concerning LGBTQ people. In many parts of the world, a goal that once seemed well beyond the reach of what could be hoped for—same-sex marriage—is now the law of the land. This remarkable story of rapid social change may be interpreted in many ways. Since we are interested in the motive power of eros (jones 2014a), we will focus on that aspect of the trajectory from sexual outlaws to wedding cake figurines.
Some LGBTQ people, despite sometimes literally lethal repression, openly and unashamedly proclaimed their romantic and sexual same-sex relationships. These visibly queer folk, along with the friends and family who expressed solidarity with them, collectively created an alternative source of social approval for LGBTQ people whose urgent desire for such approval (itself a kind of relationship) had dammed their longings for same-sex partnerships. Over time, this self-perpetuating process brought more and more LGBTQ people, and the friends and family members who continued to love them, into view. Importantly, this brought more and more LGBTQ people for whom social approval is an urgent wish into the fold of those openly agitating for LGBTQ rights. Marriage represents precisely the kind of social approval desired by those whose same-sex desires had been dammed by social disapproval and therefore became a focus of LGBTQ activism despite its relative unimportance to many of the nonconformists whose early insistence on expressing LGBTQ desire _despite_ social disapproval set the process going.
But what about the desires of the non-LGBTQ "public" whose opinion seems to have so rapidly shifted? Some and perhaps most people always have felt affectionately toward their LGBTQ kin. Mothers have always loved their gay sons. Fathers who have felt bound by the demands of masculinity to disown such sons have felt extreme anguish while doing so. Siblings have felt torn between devotion to a parent and love for a peer. The LGBTQ movement has offered liberation for them too, both by offering that alternative source of social approval and by giving them something to _do_ with their love for the LGBTQ people in their lives. This, too, may help to explain the rapidity with which marriage equality became real. Working for that goal was something specific and understandable that straight "allies" (many of them married) could do.
The wish for close relationships with other-than-human animals is like same-sex desire in that it is both damned and dammed. But people who love animals are also like the friends and family members of LGBTQ people, in that this is an affection for members of a subordinated class and may be the cause of some conflict. This may be one more reason to "queer" animal liberation.
Queering animal liberation
Since 2002, our sanctuary has been among a small but growing number of organizations "queering" animal liberation by drawing attention to intersections between speciesism and anti-LGBTQ bias, by promoting veganism and animal rights within LGBTQ communities, and by drawing inspiration from LGBTQ liberation movements. From our own cheeky efforts to encourage people to "eat the rainbow" (of fruits and vegetables) to a splashy queer kiss-in staged by Collectively Free to protest a fast-food chain known for both homophobia and animal abuse, these efforts have spanned the spectrum of activist tactics. To be true comrades in a shared struggle, we seek to enlist queer eros in the cause of animal liberation.
To do that, we need to do more than explain intersections or promote veganism in LGBTQ communities, although those are both essential things to do. We need to do more than swipe tactics like kiss-ins from LGBTQ activist history, although that is also something that it will be sometimes very useful and appropriate to do. To truly tap into the spirit of LGBTQ activism for the purpose of animal liberation, we will need to tune into desire and attune our interventions so that they work with rather than against the heartfelt wishes and felt identities of the people whose behavior we hope to change, most of whom were once children who loved animals and many of whom continue to claim to love animals today.
Backyard hen keepers bristle at the very idea that their hobby hurts birds because they see themselves as kind people. They reject the suggestion that they stop buying chicks because they want to be in relationship with birds. We are more likely to succeed if we work with rather than against their desires and self-identifications. Instead of telling women currently engaged in hen-keeping to _stop_ buying chicks, what if we encouraged them to _start_ rescuing older hens? Backyard bird keepers might even be willing to stop eating eggs altogether if offered the attractive alternative of running a "micro-sanctuary" and consequently being seen as an especially humane person. Since people tend to become vested in their projects, we may have even more success by making nonexploitive activities more attractive to would-be backyard hen keepers _before_ they buy their first batch of chicks. From setting up a backyard refuge for wild birds to becoming a wild bird rehabilitator, there are so many things a woman who wants to be close to birds could do! Animal rights groups could join with organizations devoted to wild birds to advertise such activities. Similarly, organizations that already publicize the deliciousness and cost-effectiveness of veganism might also market the sensory and economic pleasures of planting, tending, and harvesting fruit and vegetable crops. Women drawn to the "homesteader" identity might respond well to a challenge to get the most food out of every square foot via veganic gardening.
As a semi-underground activity practiced by boys and men who often see it as a cultural legacy, cockfighting is a special case, but the principle of offering other ways to satisfy damned desires still applies. Here, alternatives will need to be region-specific and offered by trusted entities within the concerned communities. We cannot guess what the most attractive alternatives might be, but we can trust that there are people in those communities who hate cockfighting and would be happy to help boys who love birds discover more wholesome activities. Finding and funding those people, rather than devoting more resources to the failed law enforcement approach, ought to be a strategy of national organizations devoted to ending cockfighting. Within regions and communities where cockfighting persists, local animal protection agencies could make common cause with local organizations involved in any way with the project of defining masculinity less violently. In the absence of such resources, local animal shelters and the like could make a special effort to create volunteer opportunities and youth projects that offer boys and men the opportunity to truly become protectors and caretakers of roosters and other animals.
Concerning youth programs like 4-H and FFA, the task is easier yet harder. As noted above, those programs already offer children and teens a wealth of opportunities to learn while growing. However, because those programs were created with the specific purpose of creating the next generation of farmers, their animal-oriented projects tend to teach callousness to children who want to be friends with animals. Since rural, regional, and even racial identity can be bound up with the continuation of particular farming practices (jones 2014b), parents may be particularly vested in such projects. Nonetheless, animal shelters and sanctuaries in rural regions could partner with local 4-H and FFA clubs to offer alternatives. For example, instead of raising bunnies, children and their families could foster litters of rescued puppies or kittens. Older participants could learn how to train dogs to help them become adoptable, with a successful adoption rather than a sale being the pinnacle of the project.
For children and teens who do intend to become farmers and are motivated by that hoped-for identity, "production" projects need not involve animals and can be designed to stimulate creativity in service of sustainability. 4-H and FFA already offer some projects involving crops. These could be expanded to focus on unusual or uncommonly high-yielding crops, with an emphasis on challenging future farmers to drawn upon the exuberance of plant varieties to feed the world in a changing climate. Similarly, as demand for plant-based meat, milks, and cheeses grows, 4-H and FFA participants can be challenged to exercise their creativity in that direction. Or, they could be challenged to emulate George Washington Carver (who devised so many uses for peanuts) by coming up with new uses for traditional crops like peas.
Regardless of whether they partner with 4-H or FFA, animal sanctuaries in rural regions have an important role to play in offering alternative not only to those programs but also to rural recreations such as hunting and fishing. The longing to get out into the woods, the pleasure of searching and finding, the flush of victory after succeeding in an arduous outdoor endeavor—all of those wishes and more can be met by on-site activities such as rock hunting, bird watching, insect identification, and forestry. Volunteer programs for youth can offer children opportunities to care for and get to know farmed animals who can remain their friends, because they will never be trucked away.
Cautions and questions
Every year in New York City, proud vegans stage a Veggie Pride Parade. Organizers of the event probably imagine that they are justly and unproblematically joining the numerous celebrations of ethnic identity or LGBTQ pride. In some ways they are right. Because of the cultural association of masculinity and meat-eating, male vegetarians and vegans really are frequently called pejorative names suggesting that they are gay. The wish for close and equitable relationships with other-than-human animals really is a damned desire in a way that really is related to homophobia. And it certainly is true that many people consider "vegan" to be a central element of their identities.
At the same time, there's no dearth of pride among vegans, so we probably don't need a parade. As we queer animal liberation, we will need to be careful not to adopt the trappings of LGBTQ activism without tapping into the motive power of desire. Parading vegetables _is_ a charming spectacle. Parading fruits (pun intended) might be even more so. How might we use such spectacles to highlight the _fun_ of being friends with animals rather than evoking the stereotype of the prideful vegan? And what about the prideful vegans? Like it or not, "vegan" as identity rather than practice is here to stay. In theory, visibly vegan people can collectively create an alternative source of social approval for the damned desire to be in better relationships with animals. In practice, the off-putting behavior of some of the most visibly vegan people sometimes has had the opposite effect. While there may be some short-term utility in efforts to rescue the word, "vegan" identity cannot help but center the human. We would like to see animal advocacy recenter itself on relationships.
Solidarity for every buddy
Lori Gruen (2015) rightly stresses the potential role of empathy in animal advocacy. While gendered notions about feminine care versus masculine efficiency can create an illusion of opposition, we believe that empathy can lead to greater efficacy, particularly in cases where people who say that they love animals participate in activities that harm animals. We struggle to maintain empathy with people in such situations, yet we cannot help to rehabilitate their own empathy for animals unless we understand the processes by which they learned to be callous upon entering into a project motivated by sympathy for animals. Luckily, empathy is a hallmark of healthy relationships, and so efforts to promote empathy will necessarily promote healthy relationships between human and other animals and vice versa.
Imagination is an essential element of empathy. Here too, we are in luck. People who love animals may pursue socially acceptable recreations and occupations that hurt animals because they cannot imagine other ways of being close to animals. Therefore, anything we can do to stimulate imaginative capacities will tend to both increase empathy and lessen rote participation in injurious activities. Not coincidentally, virtually every social problem we currently confront also calls out for more empathy and more imagination, so any success we might have in fostering those capabilities will help people as well as other-than-human animals.
Everybody wants to be happy, and so does every Buddy. Mutually affectionate and respectful relationships with other-than-human animals happily blur the all-important boundary that segregates and elevates "humanity." That divisive social construct—"human"—also fosters intraspecies inequalities such as ableism, racism, and sexism (Wynter 2003; Ko and Ko 2017). Therefore, sabotaging speciesism by fostering closer and more egalitarian cross-species relationships may have a more broadly salutary effect by undermining ideologies of social injustice.
Another girl's story
VINE's Pasture Pals program offers rural youth opportunities to visit and volunteer at the sanctuary. In each session, children and their caregivers receive a humane education lesson on a topic such as respect for differences followed by time spent visiting with sanctuary residents while helping with age-appropriate chores. In 2017, Willie the turkey and Domino the alpaca appointed themselves the official Teacher's Aides of the program, greeting and guiding program participants. Sadly, Willie died of a heart attack shortly before Thanksgiving, a US holiday sometimes jokingly called "Turkey Day" because of the tradition of consuming turkeys on that day. One Pasture Pals participant was so distressed to hear of his death that she prepared a poster presentation on turkeys, including a section entitled "Why I Loved Willie," as a school project. And so, instead of the usual jokes about eating turkeys, her classmates heard about the amazing capabilities of turkeys, saw pictures of several named individuals at the sanctuary, and—most importantly—learned that their own valued friend considered a turkey to be her valued friend. They mourned with her, and no one told her not to cry.
Acknowledgments
This chapter is dedicated to the memory of young Cheryl's first steer, Buddy, and of every buddy any child has been forced to kill or surrender for sale.
References
Dundes, A. (2007), "Gallus as Phallus: A Psychoanalytic Cross-Cultural Consideration of the Cockfight as Fowl Play," in S. J. Bronner (ed.), _The Analytical Essays of Alan Dundes_ , 285–316, Louisville, CO: University Press of Colorado.
Geertz, C. (1972), "Deep Play: Notes on the Balinese Cockfight," _Daedalus_ 101 (1): 1–37.
Gruen, L. (2015), _Entangled Empathy: An Alternative Ethic for Our Relationships with Animals_. New York: Lantern Books.
Inzlicht, M. and Schmader T. (eds.) (2011), _Stereotype Threat: Theory, Process, and Application_ , Oxford, GBR: Oxford University Press.
Jones, p. (2010), "Harbingers of (Silent) Spring: Avian Archetypes in Myth and Reality," _Spring: A Journal of Archetype and Culture_ 83: 185–212.
Jones, p. (2014a), "Eros and the Mechanisms of Eco-Defense," in Carol J. Adams and Lori Gruen (eds.), _Ecofeminism: Feminist Intersections with Other Animals and the Earth_ , 91–106, New York: Bloomsbury.
Jones, p. (2014b), _The Oxen at the Intersection: A Collision_ , New York: Lantern Books.
Ko, A. and Ko, S. (2017), _Aphro-Ism: Essays on Pop Culture, Feminism, and Black Veganism from Two Sisters_ , New York: Lantern Books.
Maunula, M. (2007), "Of Chickens and Men: Cockfighting and Equality in the South," _Southern Cultures_ 13 (4): 76–85.
Wynter, S. (2003), "Unsettling the Coloniality of Being/Power/Truth/Freedom: Towards the Human, After Man, Its Overrepresentation—An Argument," _The New Centennial Review_ 3 (3): 257–337.
Chapter 13
_DUCK LAKE PROJECT_ : ART MEETS ACTIVISM IN AN ANTI-HIDE, ANTI-BLOKE, ANTIDOTE TO DUCK SHOOTING
Yvette Watt
An activist is someone who cannot help but fight for something. That person is not usually motivated by a need for power or money or fame, but in fact is driven slightly mad by some injustice, some cruelty, some unfairness, so much so that he or she is compelled by some internal moral engine to act to make it better.
—Eve Ensler (2013, ix)
Introduction
On March 5, 2016, just before sunrise, an event unfolded in a remote location on the east coast of Tasmania, Australia. In the planning for nine months, it was something of a mix between Werner Herzog's _Fitzcaraldo_ in production and Stephan Elliott's _Priscilla Queen of the Desert_ in form. The scene involved a troupe of dancers in hot-pink, sparkly tutus and pink leggings performing a specially choreographed routine to music from _Swan Lake_ , on a stage floating on a wide lagoon (see Figures 13.2 and 13.3). Meanwhile, a team of hot-pink camo-clad people with pink sparkly flags made their way across the lagoon, some on foot, others in kayaks towing hot-pink ducks behind them. It was an incredibly still, warm morning, and the lagoon was like a mirror. There was a buzz of excitement that the long-awaited morning had arrived, and a delight that there were media there to record it. But there was also a strong undercurrent of anxiety and anger tied to the very reason that we were all there: the opening of duck shooting season in one of the last places in Australia where recreational duck shooting is still legal.
Since 2003 I have been going to Moulting Lagoon on the east coast of Tasmania for the opening of duck shooting season, as a member of the duck rescue team. According to Tasmania Parks and Wildlife Service, Moulting Lagoon is home to "the largest concentration of black swans in Tasmania, with an average of between 8,000 and 10,000 swans living in the lagoon" (2016, 1). The lagoon gets its name from the swans' flight feathers that accumulate along the shoreline during their annual molt. Despite being a Ramsar listed wetland of international conservation significance, this site is open to duck shooters for three months between March and June each year, and the shooters' hides are there all year round. This site has been the focus of the campaign to end duck shooting in Tasmania for at least two decades now as it is the main public wetland accessible to shooters, with duck shooting commonly taking place on private property (for one strategy to prevent hunting see Figure 13.1).
**Figure 13.1** In 2008 Catherine Silcock (far left) devised these innovative windsocks, which proved to be highly effective in deterring ducks away from the shooters' guns. One of the hunters' hides is on the left-hand side. Photo: Yvette Watt.
Tasmania is one of three Australian states that still allow recreational duck shooting, with permanent bans in place in Western Australia (since 1990), New South Wales (1995), and Queensland (2005). Recreational duck shooting has never been allowed in the Australian Capital Territory. Those states that have banned recreational duck shooting have done so primarily on animal welfare grounds, due to the high wounding rate that is an inevitable result of firing shot into a flock of birds. 1,178 registered duck shooters in Tasmania are estimated to have killed 58,298 ducks in the 2017 season (Tasmanian Government Department of Primary Industries, Parks, Water and Environment Wildlife Management Branch, 16), and the RSPCA Australia estimates that wounding rates quite possibly equal kill rates (n.d.). The shooting of protected and endangered species is also a concern. There are five listed species of ducks that can be legally shot during the Tasmanian recreational duck shooting season, with all other species protected. However, even at a public site such as Moulting Lagoon, protected species, including black swans, have been found shot.
This vast estuarine lagoon is for the most part very deep, but it has three shallow banks where the shooters build their hides. Our strategy as duck rescuers is to spread ourselves around the lagoon, either on foot or in kayaks, paying particular attention to occupied hides. We deter the ducks from the shooters' guns by waving brightly colored flags, as the ducks are highly sensitive to unusual movement and also see a broader range of colors and with more intensity than the human eye—hence the need for hides (Anderson et al. n.d.). Our strategy is simple but effective as the ducks tend to fly high to avoid the unusual color and movement, and, move, we hope, out of the forty to fifty meter range of the shotguns. We also try to rescue injured ducks that have been abandoned by shooters, but the expanse of the lagoon and the fact that wounded ducks often dive underwater in an attempt to escape mean that rescuing injured birds is difficult and those that are rescued rarely survive. So our main aim is to stop the ducks from being shot in the first place. We also aim to get media coverage each year to bring the issue to the attention of the general public, in the hope that this will result in pressure on the Tasmanian government to ban recreational duck shooting in line with other states. But the remoteness of the location, the lack of suitable footage or photographs, and the increasingly tight budgets of media outlets have made getting coverage more and more difficult to achieve. The number of duck rescuers has also started to dwindle over the years. I hadn't been able to attend the opening weekend rescue for three years running and when I returned in 2015, I was shocked to find that there were only about five of us. It seemed the anti-duck-shooting campaign had lost momentum, for the activists, for the media, and for the general public.
Despite the drop in the numbers of duck rescuers in recent years, the sustained campaign at Moulting Lagoon has also seen a drop in shooter numbers. A number of hides have been burned down over the years (no one is owning up to how that happened) and a good number of these have not been replaced. The shooters, who are almost always white men, embody the kind of masculinity embodied in the Australian "bloke." While there is a degree of affection attached to this term at times (you might hear someone referred to as "a good bloke"), it also refers to the type of white male masculinity with a strong rural base and a rough and at times violent manner–this is exemplified in the pejorative name of "wife-beater" that is given to the blue singlet, which is often associated with the "Aussie bloke." This type of man also has a liking for cars and guns. As Marti Kheel has observed, "The association between hunting and masculine self-identity has been a recurring theme throughout history" (Kheel 1996, 38).
_Duck Lake Project_ takes flight
I came away from the opening weekend in 2015 with the feeling that something more needed be done to address what I had increasingly come to think of as the profound "blokey-ness" of duck shooting, the antidote for which might be something like people in tutus on a floating stage, performing to the music from _Swan Lake_. My initial thought was that the "over the top" macho culture of duck shooting would be highlighted by the disruptive and opposing presence of a similarly "over the top" feminine display of pink tutus, ballet, and classical music. I spent a few weeks considering what it would take to turn such a crazy idea into a reality. In working out how to make the project happen, I was also recognizing that this would require a new mode of working for me as an artist and would blur the lines between art and activism beyond what my work had done before. The possibilities were exciting, but also daunting.
In late March I emailed an artist and filmmaker friend, and told him of my plan, asking if he would be prepared to help me document it. His extremely enthusiastic response helped seal the deal—I felt I had now committed myself to bringing this "crazy" idea to fruition. Nonetheless, I spent a lot of the time somewhat terrified at what I had taken on, and not at all sure I could bring it off. Artist Rick Lowe discusses this in relation to his _Project Row Houses_ work: "Oftentimes as an artist you're trespassing into different zones... Oftentimes... I know nothing. I have to force myself and find courage to trespass... Artists can license ourselves to explore in any way imaginable. The challenge is having the courage to carry it through" (Thompson 2012, 93).
Ultimately, I just had to have faith that in some form it would happen, though it was only on the day that I had any sense of exactly how it would all come together.
From the outset I was truly amazed at the enthusiasm and commitment shown by the people I asked to be involved. Where previous artworks of mine have required only a passive engagement (a "looking") from the viewer, _Duck Lake Project_ involved a large group of people actively engaging in a whole performance; the line between artist and audience was blurred from the outset; not only were there many artistic collaborators, the rescuers, the shooters, and even the police and Parks and Wildlife officers were in a sense both participants and audience. This was a truly a participatory art project—I had, in the words of artist Jeremy Deller, gone from "being an artist that makes things, to an artist that makes things happen" (Thompson 2012, 32). In order to make _Duck Lake Project_ happen, a large group of volunteers was required, including a choreographer, a team of dancers (all of them amateurs), costume and prop makers, people to assist with the crowdfunding campaign and design work, people to assist with catering for the event, people to bring the portable toilets, a team to document the event itself and its development over the preceding nine months, a stage designer/builder, and a large team of duck rescuers and general helpers to be there on the opening weekend. Significantly, the project also received enthusiastic support from the Tasmanian arts community, with more than sixty artists volunteering their time and talents to decorate a "decoy" as part of the crowdfunding campaign. I was overwhelmed at the unequivocal support in this regard from the vast majority of artists who I approached, with artists from around Australia emailing me to ask to be involved, and a number of artists expressing disappointment that I hadn't asked them! It was thanks in no small part to these artists that the crowdfunding campaign was so successful, raising a total of $10,000 for the project. As the day of the event drew near, however, one of the key aspects of the performance—that it would be on a floating stage on the lagoon—was suddenly placed in doubt.
Some five or six weeks prior to the event I was contacted by officials from the Tasmania Parks and Wildlife Service who had heard of our plan. In a discussion over the phone they expressed various concerns such as the possibility of causing damage to the foreshore where the stage was to be located. I explained that the stage would be on the water, not on the foreshore. They indicated that I would need to get approvals from Marine Safety Tasmania if the stage was to be floating. I checked and needed no such approval. As requested, I sent them a detailed outline of the plan for their assessment, addressing all the concerns they had raised. Eventually, just four days prior to the event, when everything was ready to go (and after two emails from me asking for a response to the outline I had sent), I was advised that we would not be granted permission to place the stage on the water and would only be issued with a permit to place the stage in a day-use car park near the lagoon. To say we were disappointed would be an understatement.
On Friday March 4, we arrived at the lagoon, set up camp, and set up the stage in the car park as required—there seemed to be no other option without risking the whole event being shut down by Parks and Wildlife officers and police. Last rehearsals took place, before we all retired to camp for an early dinner and an early night, ready to be up before dawn (shooters are allowed to start shooting an hour before sunrise and an hour after sunset). I woke early and got the coffee on to warm people up before they headed to the lagoon, and it was only then I learned that overnight, some of the activists had taken it upon themselves to move the stage onto the water. My delight at this news turned to a concern that we would be shut down before the media had a chance to film the performance. The morning was warm and still as we walked down to the lagoon in the dark. The stage had a portable floodlight at its edge, and the hot-pink of the dancers' costumes were reflected in the mirror-like surface of the lagoon. It was a stunning sight and I was extremely relieved when the media arrived before Parks and Wildlife officers did. We began the performance in the dark, the sound of the music from _Swan Lake_ filling the air, while the dancers began their performance.
**Figure 13.2** Dancers in Moulting lagoon. Photo: Michelle Powell.
The dancers—Judy Blackwood, Kim O'Sullivan, Debbie Lustig, Kate Mascall, Madeleine Southey, Adam Christ, and Sophie Bullock—were seven amazing women ranging in age from their mid-twenties to mid-fifties. A mix of activists and artists, all were both nervous and excited. Debbie, a veteran duck rescuer from Melbourne, was so excited at what _Duck Lake Project_ was trying to achieve that she had been flying in and out of Melbourne for the rehearsals. The special routine they had been working on for weeks with choreographer Glenn Murray, a past member of the Australian Ballet and Sydney Dance Company, was to finally be performed on location, in front of the media, and with the risk that Parks and Wildlife officers would order them off the stage when they arrived. While Kim, Debbie, and Adam had done some amateur dance training in the past, all the others were complete novices—in fact when Judy volunteered to help with _Duck Lake Project_ she anticipated doing something like making sandwiches! While Debbie was terribly anxious, poor Sophie's nerves got the better of her and she couldn't bring herself to perform until much later in the morning. The rest of the troupe walked through the shallow water and climbed the stage, feeling it rock as they did, with us all wondering how stable it would be. As they took their places on the stage you could see the mood of determination take over. I pressed play and as the first strains of music drifted across the lagoon, these seven wonderful women began the routine.
The media were delighted and filmed over some time as the dancers repeated the six-minute routine. Meanwhile the large team of rescuers began to make their way onto the lagoon, as shooters made their way out to their hides. A short time later Parks and Wildlife officers arrived, but rather than stopping us, they seemed equally delighted at the scene. It all came together almost exactly as I had imagined, and I still feel emotional when I recall this scene and think of the incredible team of people who made it happen.
Art and activism
_Duck Lake Project_ provides a useful platform to reflect on the relationship between art and activism; gender, violence, and resistance; and the nature of academic life in the context of animal advocacy. It has been close to a decade now since I was actively engaged with an animal advocacy group, but my commitment to the animal rights–based principles I first embraced thirty years ago has not wavered. My artwork has remained engaged with the ethical and political dimensions that are such a big part of the interactions between human and nonhuman animals. I have significantly less time for my art practice now, due to the demands of an academic position, but this has not dimmed my determination to use my work to promote a consideration of the treatment of animals by humans. If anything, I have had to actively blur the "line" between art and activism over the years. _Duck Lake Project_ manifests a new art territory for me, opening up a world of possibilities that emerge when activism and art become entangled.
The sort of practice that _Duck Lake Project_ signifies might be described as "relational aesthetics," "socially engaged art" (Pasternak in Thompson 2012, 8), "performative democracy," or "artivism" (Weibel 2013, 23). Artworks that operate within this model are generally collaborative, participatory, event-based and foreground social issues and political activism. I fell into this accidentally—I didn't even stop to consider that I was working within this mode until after the fact. But having acknowledged that _Duck Lake Project_ fits within the definitions of socially engaged, participatory model of art practice I have taken an interest in the artists and writers who deal with this way of working. What is interesting about this practice is that despite the obvious potential for socially engaged art to provide a productive platform for drawing attention to issues concerning the effects of human exceptionalism of nonhuman animals, key texts and websites on this mode of practice contain few or no such examples. For example, Nato Thompson's 2012 book _Living as Form: Socially Engaged Art from 1991–2011_ contains not one project that is concerned with the fate of animals at the hands of humans, despite detailing a total of 104 projects. He even lists "seminal pedagogic social movements of the last 100 years... include[ing] AIDS activism, the women's movement, the anti-Apartheid movement, Perestroika, the civil rights movement, Paris '68, the Algerian Wars" (21). This is particularly curious given that Thompson curated the exhibition _Becoming Animal_ at MassMOCA in 2005. Further evidence of the paucity of coverage for art and animal activism can be found in the 700+ page book _Global Activism: Art and Conflict in the 21st Century,_ published to accompany the exhibition _Global aCtIVSsm_ at the ZKM Center for Art and Media in Karlsruhe, Germany, in 2013. There is a passing mention on animal rights (58), but of over 120 featured projects/events/artists/organizations, just two feature animals. However, only one of these is actually advocating for animals: the work of artist collective NEOZOON whose powerful work interrogates the complexities of human–animal relations. The other work, by Moroccan artist Mohammed Laouli, is a video work that shows an abandoned gray horse with its front hooves tied together in a square of a poor neighborhood of Rabat. Laouli has adorned the horse with wings, but rather than intending to draw attention to the suffering of animals, or even the plight of this particular horse, the horse in this work "represents a form of otherness, which, from the perspective of a different social class, is also characteristic of the people living in this neighbourhood" (Weibel, 616).
One might suppose that the lack of coverage of animal activist artists and events in such books is based on a lack of suitable examples. If so, then I would encourage artists and activists to work to remedy this. However, given the broad scope of _Global Activism_ , it is curious that the many performative protests of organizations such as PETA, Anonymous for Animals, and Igualidad Animal (Spain) are given no coverage despite their alignment with the forms of "performative democracy" and "artivism" included in this book and exhibition. Further, that animal-artists with well-established credentials and reputations such as Snaebjornsdottir/Wilson, who have worked in this mode for many years, fail to rate a mention in the literature suggests that animal-themed artworks simply get less attention than those focused on human social-justice issues. This is not meant as a criticism of the many wonderful socially engaged art projects on human social justice issues that are given good coverage. But the lack of attention given to animal-themed socially engaged art projects may be yet more evidence of the animal rights movement being seen as "the orphan of the left" (Kymlicka 2014, citing Canadian author Blaire French), or the orphan of the art world, as the case may be. Kymlicka elaborated on the position of animal rights advocates being the "orphan of the left" by suggesting that the left is concerned that animal advocacy displaces human-centered social justice, that it trivializes the latter and is incompatible with movements that gain power by distancing themselves from forms of "animalization" (2014). As W. J. T. Mitchell has stated, "The question of animal rights produces a combination of resistance and anxiety because to claim rights for animals entails a revolution so profound it would shake the foundations of human society" (Wolfe, x). An artist who engages with these issues faces real challenges due to this anxiety and resistance from those who feel threatened by having their foundations (strategies, priorities, and claims for justice) shaken. While posts to Tasmanian hunter Facebook groups suggest that those who felt most threatened by _Duck Lake Project_ may have been the hunters, the resistance to any challenge of the broader consequences of human exceptionalism is of course widespread. However, this should not stop us from shaking things up, but we also need to consider that if we want to engage people rather than simply upset them, the best form of shaking may be firm and gentle rather than aggressive, engaging rather than confronting.
A questioning of old modes of protest is growing, with Micah White, co-creator of the Occupy Wall Street movement, making strident calls for a change to the way activists work, paying particular attention to the ineffectiveness of street protest in achieving change. Artist and "Godmother of craftivism" (craft+activism), Betsey Greer's Craftivism website reflects White's allegation, stating "people have grown tired of so-called traditional ways of activism... They are looking for a way to connect and deepen their understanding of things. Yelling doesn't change things, but dialogue does" (n.d.). White advocates for a form of activism that uses the electoral system via the formation of political parties as a key strategy. My views align with Greer's in believing that that the visual arts can play an instrumental role in crafting change. As Edelman notes:
Although art is no more a bastion of democracy than elections and lobbying are, it does strengthen democracy in some respects. Because it excites minds and feelings as everyday experiences ordinarily do not, it is a provocation, an incentive to mental and emotional alertness. Its creation of new realities means that it can intrude upon passive acceptance of conventional ideas and banal responses to political clichés. For that reason art can help foster a reflective public that is less inclined to think and act in a herd spirit or according to the cues and dictates provided by a privileged oligarchy. (1995, 143–144)
In general, the strategies I employ in my artwork aim to encourage in the audience a consideration of the issues at hand rather than berate them with an anger-driven polemic. The tone varies, and can at times be quite somber, but until now I have avoided the use of graphic images of animal suffering, believing it is important to engage rather than repel the viewer. _Duck Lake Project_ seeks to engage a broad range of people, using a form of "soft power" to influence opinion, engaging humor as a key strategy to bring home a serious point. But in deflecting the shock of animal suffering by using humor am I softening the blow to the point that it is barely hitting home? I would argue not. In an article posted on his _Striking at the Roots_ blog titled "How Do Graphic Images Affect Animal Advocacy," Mark Hawthorne looked at two studies on the differing effects on viewers of imagery of animals that varied from graphic to fairly mild. One was conducted by the not-for-profit group Farm Animal Rights Movement using still photographs and the other by the Humane Research Council using videos. Interestingly, where the former study found that the least graphic images had the most affect, the latter showed the opposite. Through speaking with various other activists Hawthorne suggests that both strategies can be effective depending on the person, the timing, and the context, a matter supported by reader comments.
At the heart of the work of the activist artist is a hope that in some way their artwork may assist in enacting social change. While it may be a large claim to suggest that art can be the instigator of such change in and of itself, I do believe it has an important role to play in engaging people's imaginations and provoking consideration of the issues at hand. Thompson speaks of this when discussing the powerful work _Palas Por Pistolas_ (Spades for Pistols), which saw the artist Pedro Reyes melt down 1,527 guns and turn them into spades, which were used to dig the soil to plant 1,527 trees. He says: "Pedro Reyes did remove 1,527 guns from the streets of Culiacan. But given the actual extent of the gun violence there, his gesture seems more symbolic than practical. And yet, symbolic gestures can be powerful and effective methods for change" (2012, 18).
The issues around communicating a message and enacting change provide significant challenges for the activist artist. In blurring the boundaries between art and activism there is the quandary of how to negotiate what Thompson refers to as the "Spectrum of Legibility" (2015, 34). As he points out:
For many involved in the arts, an artwork must remain opaque enough to invite a proper amount of speculation and guesswork... In activism, though, clarity is celebrated, and a cogent message can reach a wide audience and can serve as a weapon. The two ends of this dynamic, which I refer to as the ambiguous and the didactic, have long proven irreconcilable. (34)
Finding ways to counter the resistance to pro-animal work (for want of a better phrase) has informed my artwork for many years, but as an academic with a tenured university position, this comes with added complexities. Initially I had intended to undertake _Duck Lake Project_ as a research project within my academic role. I soon realized, though, that in the current institutional climate of caution and risk aversion this would be fraught, if not impossible. Combine an unspecified and changing team of volunteers, with guns, water, and potential hypothermia, and a politically driven project aiming to bring about legislative change, and it is clear that I would struggle to get such a project through institutional ethics approval and workplace health and safety risk assessment processes, not to mention that it may have resulted in potentially unwelcome media attention for the university. Given that I was eventually charged by the Tasmania Parks and Wildlife Service with not complying with a permit, resulting in a court appearance, it was a wise move to undertake this endeavor as a tutu-wearing regular citizen rather than as an academic with ethics approval. While the boundaries between academic work and activism have never been secure either (feminist, queer, indigenous scholarship routinely promotes the necessity of doing both simultaneously), the violence that is at the core of _Duck Lake Project_ 's object—men with guns shooting at birds—meant that it could not be conducted as a "safe" academic exercise.
Safe in the sense of keeping participants from being in danger, and also "safe" in the sense of staying within expected norms and activities (such as writing book chapters!) for academic work. The project had to blur a number of lines in order to exist: the line between artist and audience, between art, activism, and academia, and between doing "sensible" political work of advocacy in suits and being "ridiculous" in a pink tutu. It is in these different senses that I see this as a somewhat renegade project—one that pushes at a variety of boundaries, testing their permeability while risking the consequences of breaking through.
Our intention was to pressure the state government to pursue legislative change, and use the media to turn attention back to this issue that had for a while now been receding in the public's consciousness. It aimed to get the media there: and it did. The media coverage was both thorough and resoundingly positive, airing on all three Tasmanian TV news bulletins as well as on the Australian Broadcasting Commission's Victorian TV news bulletin. Press coverage was similarly thorough, with the story and accompanying image syndicated via Murdoch Press throughout Australia. Images from the performance were also used by the media for the 2017 duck shooting season, as well in coverage of the resulting court case several months later. The project successfully reignited an interest in the campaign in terms of both getting some forty-five or more people up to the lagoon for opening weekend who for the most part experienced the opening of duck shooting season for the first time, and gaining a great deal of interest from nonparticipants via social media and the crowdfunding campaign. It also aimed to counter the hypermasculinity of duck shooting, a matter that was taken up in the report by the Australian Broadcasting Commission TV and online news bulletins, while the response from blogger Matt Hayden suggests it also struck a nerve for him in his post titled "Tasmanian Frightbats Dance _Swan Lake_ to Subvert Patriarchal Duck Hunting" (2016). _Duck Lake Project_ was a high-camp, kitsch spectacle that aimed to challenge the gendered, dominant view of the lagoon as a place for men to kill birds and was underpinned by a general concern over the domination of nonhuman animals by humans. As Jacques Ranciere writes, "In its most general formula, critical art intends to raise consciousness of the mechanisms of domination in order to turn the spectator into a conscious agent in the transformation of the world" (Bishop 2006, 83). While it is impossible to quantify precisely who the audience is in all the forms it has taken for this widely disseminated project, it would include the participants, police and Parks and Wildlife staff, and even the hunters. Whoever the audience is, their reaction and whether I can convince them of the need to end recreational duck shooting in Tasmania is really the end game, if not the swan song.
**Figure 13.3** Photo: Michelle Powell.
Conclusion
_Duck Lake Project_ is a peculiar hybrid beast of a project—part artwork, part strategy to prevent ducks from being shot, part media stunt. But the project is also more than just the event itself, having an afterlife as a two-channel video artwork, as a publicly available documentary summary on YouTube, in being spoken about by me in various academic and nonacademic presentations, and more recently being featured in the revised version of of Carol J. Adams 1994 book, _Neither Man Nor Beast: Feminism and the Defense of Animals_ (2018).
The incongruous scene of dancers in hot-pink tutus, performing a routine based on bird movements to the music from _Swan Lake_ , on a floating stage in a remote lagoon, came about due to my firm belief in the power of art to capture the imagination and to engage emotions, and that art that does this has the potential to challenge the status quo and assist with achieving legislative change. But, has _Duck Lake Project_ resulted in any change? Well, it hasn't led to the government banning duck shooting in Tasmania, but this "mad" project has had the kind of immediate and quantifiable impact that no other project I have undertaken to date has had. But perhaps the most important result of _Duck Lake Project_ is that it stopped a good number of ducks from being killed and that, in my opinion, can be claimed as a real success.
Acknowledgments
The list of acknowledgments for _Duck Lake Project_ is incredibly long—too long to list here. But I must acknowledge the following people who were instrumental in the event's success: my dear friend, artist and key collaborator: Christina Scott; choreographer: Glen Murray; dancers: Judy Blackwood, Sophie Bullock, Adam Christ, Debbie Lustig, Kate Mascall, Kim O'Sullivan, Madeleine Southey; stage design and construction: Jed McNeill; documentary film team: Raef Sawford and Rummin Predictions; photographer: Michelle Powell; and the vast team of people who were involved in one way or another. The generosity of the people who helped, donated, or both was something truly special.
I would also like to acknowledge the artists who produced artworks for the crowdfunding campaign here (in no particular order): Justy Phillips, Margaret Woodward, Phoebe Adams, Leigh Hobba, Ros Meeker, Michael Nay, Lorraine Biggs, Amanda Davies, Ben Booth, Matt Warren, Tricky Walsh, Mike Singe, Mary Scott, Carolyn Wigston, Mat Ward, Penny Burnett, Christine Scott, Karen Cooper, Brigita Ozolins, Ben Kluss (Jamin), Mish Meijers, Pat Brassington, Meg Walch, Tony Richardson, David Edgar, Charles Murdock, Jan Hogan, Neil Haddon, Colin Langridge, Sally Rees, Keven Francis, Cath Robinson, Katy Woodroffe, Lucy Bleach, David Keeling & Helen Wright, Annalise Rees, Joel Crosswell, Kate de Salis, Sue Lovegrove, Julie Gough, Ian Bonde, Patrick Hall, Di Allison, Wayne Brookes, Tom O'Hern, Lucy Hawthorne, Steven Carson, Bill Hart, Nicole Robson, Pip de Salis, Louise Josephs, Antonia Aitken, Kim O'Sullivan, Tor Maclean, Yvonne Rees-Pagh, Meg Keating, Martin Walch, Erin Amor, Lucia Usmiani, and Marion Marison.
Notes
The Ramsar Convention on Wetlands is of international importance especially as Waterfowl Habitat is an international treaty for the conservation and sustainable use of wetlands. It is named after the city of Ramsar in Iran, where the convention was signed in 1971.
We don't compete with shooters to claim a duck. Not only does this risk us being charged with theft, but the shooters have a daily bag limit, so if we allow the shooter to keep a duck that is dead or likely to die this will be one less duck he can shoot before reaching his limit.
A "bloke" is an Australian/British slang term for a man. In Australian usage, it tends to refer to a particularly masculine archetype.
Interestingly, a now-retired colleague did indeed produce an artwork based on his experience of the opening of duck shooting season at Moulting Lagoon in the early 1990s, and a local artist recalls as an undergraduate being taken by this colleague on a field trip there during the duck shooting season for his video class at around the same time. It is notable that this colleague had his tires slashed, presumably by an angry duck hunter. This was almost a decade after virtually the entire art school staff went en masse in a bus to protest at the damming of the Franklin River. Times have well and truly changed.
The case was dismissed in early June 2017 after Tasmania Parks and Wildlife Service failed to provide any evidence to support the charge.
A "frightbat" is a term coined by Australian journalist Tim Blair, who since 2014 via an opinion column in the _Daily Telegraph_ titled "Crown Our Crazy Queen" asks readers to vote for "Australia's craziest left-wing frightbat" (2017).
An eight-minute video documentary of the project is available ( _The Duck Lake Project,_ 2016). Available online: <https://www.youtube.com/watch?v=CDIlURup9Ok>
References
ABC News (2016), "Protesters against Duck Shooting Don Pink Tutus for _Swan Lake_ Performance at Moulting Lagoon Season Opener," March 5. Available online: <http://www.abc.net.au/news/2016-03-05/duck-shooting-protesters-don-pink-tutus-at-moulting-lagoon-seas/7223350> (accessed September 11, 2017).
Adams, C. J. (2018), _Neither Man Nor Beast: Feminism and the Defense of Animals_ , New York: Bloomsbury Revelations.
Anderson, K. A., Unghire, J. M., and Coluccy, J. (n.d.), "A Bird's-Eye View." Available online: <http://www.ducks.org/conservation/waterfowl-research-science/a-birds-eye-view> (accessed May 22, 2018).
"An In-depth Look at the Amazing Visual Abilities of Waterfowl" (n.d.), Available online: <http://www.ducks.org/conservation/waterfowl-research-science/a-birds-eye-view> (accessed September 8, 2017).
Bishop, C. (ed.) (2006), _Participation_ , London: Whitechapel/MIT Press.
Blair, T. (2014), "Crown Our Crazy Queen," _The Daily Telegraph_ , June 24, 2017. Available online: <https://www.dailytelegraph.com.au/blogs/tim-blair/crown-our-crazy-queen-in-2017/news-story/75e28dd921ccf37129fb2b18d4b84459> (accessed February 25, 2017).
_Craftivism:_ Craft + Activism = Craftivism (n.d.), "Craftivism." Available online: <http://craftivism.com/> (accessed September 12, 2017).
Edelman, M. (1995), _From Art to Politics: How Artistic Creations Shape Political Conceptions_ , Chicago: University of Chicago Press.
Ensler, E. (2013), "Foreword," in J. Williams (ed.), _My Name Is Jody Williams: A Vermont Girl's Winding Path to the Nobel Peace Prize_ , i–xi, Berkeley: University of California Press.
French, B. (1988), _The Ticking Tenure Clock_ , New York: Suny Press.
Hawthorne, M. (2012), "How Do Graphic Images Affect Animal Advocacy?" _Striking at the Roots_ , November 1. Available online: <https://strikingattheroots.wordpress.com/2012/11/01/how-do-graphic-images-affect-animal-advocacy/> (accessed September 11, 2017).
Hayden, M. (2016), "Tasmanian Frightbats Dance to Swan Lake," March 5, 2016. Available online: <http://www.matthaydenblog.com/2016/03/tasmanian-frightbats-dance-swan-lake-to.html?m=1> (accessed September 11, 2017).
Kheel, M. (1996), "The Killing Game: An Ecofeminist Critique of Hunting," _Journal of the Philosophy of Sport_ 23: 30–44.
Kymlicka, W. (2014), "Public Lecture: 'Towards a Multicultural Zoopolis: Animals Rights, Race and the Left,'" August 11, 2014, Faculty of the Arts, University of Tasmania.
RSPCA Australia (n.d.), "What Are the Wounding Rates Associated with Duck Hunting?" Available online: <http://kb.rspca.org.au/What-are-the-wounding-rates-associated-with-duck-hunting_529.html> (accessed September 8, 2017).
Tasmanian Government Department of Primary Industries, Parks, Water and Environment Wildlife Management Branch (2018), _Game Tracks_ 23. Available online: <http://dpipwe.tas.gov.au/Documents/Game-tracks.pdf> (accessed February 25, 2018).
Tasmanian Parks and Wildlife Service (2016), "Moulting Lagoon Game Reserve" (Ramsar Site). Available online: <http://www.parks.tas.gov.au/file.aspx?id=19222> (accessed June 30, 2016).
_The Duck Lake Project_ (2016) Film]. Rummin Productions. Available online: [https://www.youtube.com/watch?v=CDIlURup9Ok&feature=youtu.be (accessed September 11, 2017).
Thompson, N. (2012), _Living as Form_ , Hayward: MIT Press.
Thompson, N. (2015), _Seeing Power: Art and Activism in the 21st Century_ , Brooklyn: Melville House Publishing.
Weibel, P. (ed.) (2013), _Global Activism: Art and Conflict in the 21st Century_ , Karlsruhe: ZKM Center for Art and Media.
White, M. (2017), "Occupy and Black Lives Matter Failed. We Can Either Win Wars or Win Elections," _Guardian Australia_ , August 29. Available online: <https://www.theguardian.com/commentisfree/2017/aug/29/why-are-our-protests-failing-and-how-can-we-achieve-social-change-today> (accessed September 12, 2017).
Wolfe, C. (2003), _Animal Rites: American Culture, the Discourse of Species and Posthumanist Culture_ , Chicago: University of Chicago Press.
Chapter 14
ON OUTCAST WOMEN, DOG LOVE, AND ABJECTION BETWEEN SPECIES
Liz Bowen
[O]ne of the gifts of genderqueer family making—and animal loving—is the revelation of caretaking as detachable from—and attachable to—any gender, any sentient being.
—Nelson (2015, 72)
I never understood dog people before I became one, the intense love you can feel for an animal, a gross love that can be without boundaries.
—Zambreno (2015, 102)
Recently, I have been captivated by an emerging thread in contemporary feminist and queer literature: the suggestion that human relationships with domesticated and conventional pets pose a challenge to normative formulations of love and desire. In the epigraph above, for instance, Maggie Nelson reflects on how A.L. Steiner's photo exhibition _Puppies and Babies_ represents dogs as sites of interspecies pleasure akin to mother–child intimacies bordering on the taboo. Likewise, in her essay "Notes on a New Tenderness," Kate Zambreno figures human–pet relationships in the base bodily terms they demand but rarely fully engender—think dirt, think saliva, think oral–anal exchange. At the 2017 Carolee Schneemann retrospective at MoMA PS1 in New York, the presence of the artist's cat Kitch is inescapable; the erotic video _Fuses_ (1969) appears to adopt the cat's point of view as its human companions have sex. Meanwhile, in popular culture and even outside the mainstream, dogs and cats are regularly deployed as symbols of familial security, figures for nostalgic childhoods, or signals of commitment within socially sanctioned relationships—not terribly energizing conceptual realms. But the alternative possibilities are genuinely invigorating: as anyone who has ever loved a pet knows on some level, _of course_ human relationships with pets are gross and intense, and gross in their intensity. Still, these filthy connections have been sanitized in popular discourse, rendered unthreatening to our understandings of species boundedness. The transgressive resonances that Nelson and others locate between human–animal love and queer desire are useful for thinking about human–animal relationality beyond traditional models of ownership, anthropomorphism, and the "unconditional" love we expect from dogs in particular. I can love a dog, and she can love me, but those loves are not identical, unchanging, fully reciprocal, or fully knowable. Not unlike human relationships, companionship between species involves a desirous, delirious, in some ways delusional drive to know one another, in spite of unbridgeable difference. Donna Haraway, another champion of the radical potential of domestic dogs, describes this love as both gross and kind of miraculous: "Significantly other to each other, in specific difference, we signify in the flesh a nasty developmental infection called love. This love is an historical aberration and a naturecultural legacy" (2003, 3).
But dogs aren't simply interesting because they can bring a certain kind of perversity to spheres of heteronormativity and normality, as Nelson suggests. They also bring something complicated to their relationships with humans who are already marginal in other ways. This is visible, for instance, in the love that leads some humans without homes to sleep outside with their dogs even when space is available in a shelter, rather than comply with shelter rules against pets. The interplay of vulnerability and safety is profoundly complex in such a situation, as sticking together exposes both human and dog to violence and the elements at the same time that it provides them with mutual vigilance and protection. To name another example: people with "too many" pets, or the wrong kinds of pets, are typically perceived as perverse or pathological, and their animal attachments may be identified as symptoms of an underlying, stigmatized mental illness. Often, discourses used to denigrate animal lovers are screens for disdain toward other identity categories; stereotypes about people who have too many pets tend to be aimed at figures whose gender, sexuality, age, race, mental health status, and/or class already position them as marginal (e.g., "crazy" old ladies/lesbians or poor people in rural areas).
As a literary scholar, I believe that narrative not only reflects how humans conceptualize their relationships with nonhuman animals but also shapes the form those relationships take—for better and for worse. Thus, to get a better sense of how outsiders and animals relate in human society, I am interested in tracking literary representations of unconventional human–canine love and in exploring the double-edged nature of these literary affinities. In the very same narratives in which these bonds provide enriching affective connections between socially othered humans and dogs, unconfined by heteronormative sentimentality or sanitized domesticity, these relationships can also make their participants vulnerable to violence. Such violence, ostensibly aimed at the human, can be compounded by the additional abjection of the animal, and people seeking to harm humans often end up doing so by harming animals connected with them. Pain, suffering, and precarity are therefore as much a part of these nurturing companionships as pleasure is. In _With Dogs at the Edge of Life,_ for instance, Colin Dayan demonstrates how anti-pit bull legislation has been leveraged as a means of policing and oppressing black and low-income white communities in the Southern United States, where both pits and their human companions are judged to be pathologically aggressive (2016, 3–9). It's clear that perceptions of madness and abjection can slip, or be transmitted, between humans and their companion species, often with the result of the animal being subjected to more harm than it would be likely to encounter on its own. So what is at stake, then, when we view these companionships as liberatory? Is there a danger of eliding pain and precarity, akin to the way feminist reclamations of the "madwoman" obscure actual experiences (and difficulties) of mental illness? What might become invisible when we celebrate the transgressive potential of interspecies love? In asking these questions, I do not wish to evacuate the radical potential offered by against-the-grain readings of human–animal love, but to offer a fuller account of their risks _and_ possibilities.
I will do so with the help of two narratives that dramatize unusual affiliations between socially outcast humans and their dogs: _Disgrace_ by J.M. Coetzee (1999) and Alice Notley's _Culture of One_ (2011), described by the publisher as a "novel in poems." Both texts tell a story of a woman living at the outer edges of society, arguably in closer relationship to dogs than to other humans, in ways that others deem mad, irrational, and/or queer. Both also depict violence against these women as closely bound with violence against their dogs, as the characters are forced to witness the murder of their animal companions as punishment for their own social transgressions. In _Culture of One,_ the central character Marie, who lives on a landfill with her dogs in the American Southwest, endures a series of humiliations at the hands of people more powerful than she is: her shack is burned down by a male sexual partner, killing her infant daughter, and a group of acrimonious teenage girls murder her beloved coyote-mutt Tawny. Meanwhile, Coetzee's Lucy Lurie, a white South African lesbian who prefers a rural life boarding dogs to the more urban proclivities of her young-adult generation, both solidifies and complicates the connection between dogs and social exclusion. While Lucy's queerness and passion for animals render her an outcast and thus a particularly visible target for violence, this outsider status also makes her a conspicuous representative of the history of white domination in her community. Specifically, the tradition of white South Africans training dogs to attack black people is suggested to be at least one part of what makes Lucy a target in the recently post-apartheid moment of the narrative. Although there are important differences between Marie and Lucy and between their attackers, both texts foreground human–animal love as a marker of outcast status, as a site of both nurturing and traumatic encounters, and as a justification for certain kinds of animals—human and nonhuman—being rendered repellant, disposable, and unworthy of compassion.
This transference of abjection from woman to animal destabilizes some of the taxonomies of animal life that we have come to take for granted in animal studies, such as the distinction Cary Wolfe makes between killable-but-not-murderable livestock and domestic animals like dogs—which, as members of communities, are supposedly considered murderable and grievable. But if dogs are members of the wrong communities, these narratives suggest, they become simultaneously killable and murderable: killable to those who kill them and murderable to the humans left to grieve them. This is a devastating outcome, more in line with Derrida's characterization of the nonhuman as that which is always left open to sacrifice, or a "noncriminal putting to death" (1991, 112). However, I will argue that these novels' formal preoccupations with how to narrate experiences of trauma, depression, and grief, which resist incorporation into conventional or realist narrative forms (i.e., linearity, univocality, closure), allow readers to hold together their depictions of the tragic and redemptive possibilities of human–canine affiliations. Moreover, these texts' interpolation of violence against animals into systems of human oppression illuminates how ethical and political questions typically assumed to be limited to the human realm—that is, race, class, ability, and gender—are founded on a privileged concept of the human whose limits put both humans and nonhumans at risk. In other words, to quote Judith Butler, "nonhuman life is also precarious life and... precariousness links human and non-human life in ethically significant ways" (Antonello and Farneti 2009, n. p.). Without minimizing the loss of animal life or sentimentalizing its moral import, these novels allow us to imagine futures that could emerge out of experiences at the edges of normative rationality and the human, in which a kind of becoming-doglike must be the condition for ethical action.
_Disgrace_
They are not going to lead me to a higher life, and the reason is, there is no higher life. This is the only life there is. Which we share with animals. —Lucy Lurie (Coetzee 1999, 74)
When Professor David Lurie, the unsympathetic protagonist in J.M. Coetzee's _Disgrace_ , arrives at his daughter Lucy's rural home, he is none too pleased with her secluded lifestyle and atypical gender expression, but he does not find it his place to tell her so. David, whose recent affair with—and rape of—a student has landed him in the midst of a career-ending public scandal, arrives at Lucy's farm grumbling to himself about her choice to defect from her former human community to live among the dogs she shelters. These animals are "watchdogs," which Marianne DeKoven notes is code for "temporarily out-of-service guard dogs: agents of the enforcement of apartheid whose services are now only sporadically required" (2009, 850). While Lucy's harboring of these animals signals her racial privilege and her complicity in white supremacy in South Africa, it also illuminates her vulnerability as a queer woman living far away from any queer community. However, though the novel's free indirect style sticks closely to David's condescending point of view, it quickly becomes clear to the reader that Lucy has cultivated an existence that is satisfying to her in its austerity and alterity, and that this satisfaction is predicated on her love for dogs. Even David sees how her animal love fits into a constellation of subject-forming affinities: "Now, in her middle twenties, she had begun to separate. The dogs, the gardening, the astrology books, the asexual clothes: in each [David] recognizes a statement of independence, considered, purposeful. The turn away from men too. Making her own life" (89). While David interprets Lucy's non-normative interests as a _separation_ from the status quo, her affection for animals encourages us to read these signs as indicative of a deeply _relational_ existence—that of a social outcast who nonetheless recognizes potential for affiliations "outside the bounds of civil life" (Dayan 2011, 232). When David remarks glibly on his romantic life, "desire is a burden we could well do without," Lucy responds in earnest, "I must say... that is a view I incline toward myself" (Coetzee 1999, 90). And yet it is clear that her desire for relationships with nonhuman animals is expansive and expanding: since David's last visit, she has increased her kennel capacity fivefold and has plans to begin taking in cats. Lucy's impulse to share her world with animals is ethical and visceral, as well as unbounded by the notions of ownership and unconditional love that Haraway so acerbically names "the neurosis of caninophiliac narcissism" (2003, 33).
But this is not where the story ends. In a jarring turn nearly halfway through the novel, a group of robbers force their way into Lucy's home, rape her, and massacre the dogs in the kennel. In the aftermath of this attack, Lucy experiences a major depressive episode defined by silence and passivity, which bewilders and frustrates her father. She never explicitly articulates her reasons for choosing not to narrate her rape to authorities, and so David fixates on the racial identity of her attackers, assuming that since they were a group of black Africans, Lucy is forgoing justice for herself to atone for South Africa's history of racist violence. David misreads Lucy's behavior in much the same way that, earlier in the novel, he misreads her compassion for animals as a matter of guilt or "fear of retribution" (74). Her earlier professed desire not to "come back in another existence as a dog or a pig and have to live as dogs or pigs live under us" (74) is not a matter of guilt, but of sympathetic identification; she can imagine the life-world of domesticated animals and wishes to build a less traumatic alternative. When viewed in the context of her actual relationship to the dogs, then, her depressive reticence following her own traumatic event becomes more comprehensible than David makes it out to be: Lucy responds to the violence committed against her as a dog would. As Dayan so beautifully observes, dogs who die at the hands of human violence appear to exhibit a similar sort of detached passivity: "When dogs find themselves in the wrong place at the wrong time, belonging to the wrong kinds of people or protecting too earnestly the homes of their human companions, they gather themselves up in their flesh, and in a state of prescience and acceptance, they prepare for the time when life stops, as they slip away toward stillness" (2016, 315). This is precisely how Coetzee depicts the deaths of Lucy's dogs while they witness the killing of their kennelmates. As the gunman picks off the animals with his rifle, a dog with a "gaping throat-wound" "sits down heavily, flattens its ears, following with its gaze the movements of this being who does not even bother to administer a _coup de grâce_ " (95). Then, a "hush falls," and the few dogs left alive retreat to the back of their pen until they, too, are killed (96). For a person committed to living with and learning from dogs, Lucy's resignation as she declares "I am a dead person" to her father is more than just a representation of her own mental distress; it is an expression of an interspecies, doglike disposition in the face of human violence (161). While Lucy's turn away from society and toward identification with her politically incorrect dogs is certainly suspect in a post-apartheid economy of social engagement and reconstruction, it is important to note that the dogs, too, are political subjects. They have been conscripted agents of the apartheid regime, relegated to a life of confinement, occasional work, and vengeful death. Thus, when Lucy responds to her attackers' violence _like a dog_ —adopting a state of inanimacy that, to mainstream society (as represented by her father), seems irrational and nonhuman—Lucy takes on the affect of the only characters in the novel who face mortal consequences for their complicity in that regime.
Though much has been written about the importance of sympathetic imagination in _Disgrace_ , this turn in the novel also suggests an ethics beyond just imagining oneself in an other's position. After the attack, as David Lurie comes to grips with the fact that he cannot access his daughter's traumatic experience from his position of logic and reason, he develops a number of close relationships with animals. As Laura Wright has written, "[David's] sensibility with regard to the lives of animals is greatly altered after Lucy is raped, and this change in perception results from a respect for the being of animals regardless of whether or not David can access the animal's interiority" (2007, 92). Simply valuing others' lives without being able to identify or imagine one's way into them is not itself a radical political stance—let's not forget, white supremacists could love their attack dogs, too—but the capacity to do so, which David Lurie surely does not possess at the beginning of the novel, is a necessary basis for any ethical action on the part of a dominant group. The passivity of Lucy's depression and retreat from narrative language, both of which are wholly inaccessible to her father, are what bring him to a place where he might cease reproducing the violence he has wrought in the past precisely by seeking total access to others' lives and bodies.
We might ask, however, if this is where a story of dog love like Lucy's has to end up: death and devastation in service of the questionable ethical development of the white male rapist who remains at the story's center. This outcome is frustrating, to say the very least. Still, I maintain that the outcast status of women in this text puts crucial pressure on David's centrality to the novel. This is evident in the character of Bev Shaw, a friend of Lucy's whom David finds utterly repulsive. He remarks repeatedly on her unkempt, unshapely appearance and overweight body, and when he enters her home, he is "repelled by the odours of cat urine and dog mange and Jeyes Fluid" (72). Bev takes a moralistic view toward her job euthanizing dogs at the local clinic, suggesting that if someone has to do it, it's better that it be someone who is deeply bothered by it. With Lucy's story in mind, we might read her philosophy as a self-defense against the tragedy and vulnerability that human–dog love makes possible. Bev recognizes that she lives in a society that slaughters animals due to their proximity to humans, and rather than open herself up to that same unpredictable vulnerability, she short-circuits it by undertaking the killing herself. Lucy's response enacts a different kind of ethics to respond to the same problem of animals' entanglement in human sociopolitical systems. In living with depression visibly and unapologetically, becoming abject, and responding to violence like a dog, she refuses the values of human superiority wholesale, a refusal she suggests is necessary to combat all kinds of human-perpetrated violence. Cast against these women, David, who only at the end of the novel has begun to ponder whether a dog might have a place in the human tragedy of the opera he is writing, ends up looking rather like an oblivious footnote to the theory of interspecies oppression that the outcast minor characters have been putting into practice throughout.
_Abjection_
Why don't you know how to talk to people? I talk to the dog-masks of the dogs... Your eye is mild in the swirls of your dog-mask, its gentle fibers: your eye is mild. Your mask is used to remove the taboo against two species connecting with each other.— Marie (Notley 2011, 25)
Alice Notley's _Culture of One_ is, like _Disgrace_ , a brutal endeavor. Its central character is rendered inhumanly abject on a routine basis; as an antisocial, aging woman who lives on a landfill at the outskirts of a desert town, she is regularly tormented by hate-spewing teenagers and abused by the few people she maintains relationships with. Her distance from human society is suggested to be partly voluntary, which earns her a reputation for being "crazy"—a madwoman whose love for her dogs is so intense she is rumored to eat them. Like Lucy, Marie does not tend to express dissatisfaction with her isolation from humans, but rather satisfaction with her sense of belonging among dogs. Reflecting on a group of "cruel chicks" that shows up at the dump to taunt her, Marie casts them as inferior to her dogs: "I'm trying to remember; the girls were like my dogs. They liked/suddenly to growl: you have the wrong mask you won't be loved./... I hate you the girl says. You're not like my dogs I say,/you're constructed: glued-on hair and fangs and pulpy genitals" (17). She suggests that although these girls' doglike behaviors show their potential for interspecies connection, they are impoverished in their inability to recognize their own animality the way she can. Their aggressive behavior does not animalize them, but rather exposes their cruelty as a mask, a construction that renders them ontologically subordinate to animals: "just humans; they don't even look/alike, like iguanas, or pallid bats, or pack rats—perfect/animals" (97).
Importantly, though, both Marie and the poems themselves refuse a simple dichotomy in which animals equal natural and good, and the human is cultural, constructed, and therefore corrupted. The "culture of one" to which the book's title refers is, in fact, the "new/way of living" that Marie constructs for herself and her dogs in the dump, hoarding thrown-away scraps to build her home and an impressive portfolio of artworks (60). She spends her days working on a project called the codex, an elaborate alphabet book created out of found objects and media from the dump, encoding each page with associations and materials particular to her experience. The pages' meanings are esoteric—clear only to her, the narrator, and sometimes the reader (e.g., D stands for dog, R for the name of the man who killed her child). But as one of the text's primary narrators—a mysterious goddess of Mercy loosely based on the Tibetan Bodhisattva Tara—tells us, culture "comes from the materials you do it with" (10). Marie's pursuit of an individual culture is both a repudiation of mass culture and a reimagining of its possibilities, participating in it at the level of its discarded materials. She also considers the dogs' vivacity an affirming force for her aesthetic vision and work, noting that their embodied traces constitute the very materials of her project:
The dogs tell me it could be worse: I could be eaten by oversubtlety rather than bold red or blue letters howling. HOWLING! That word again. The dogs open their mouths to word me.
Have you ever dreamed you didn't have a master. We dreamed we ran down the gully to the river, but not without you; we couldn't leave you... Everything's covered with dog hairs; shake them off the illuminated pages, no they're painted on, ocher, gold, and black filaments. (88)
Marie's cultural products are not really "of one"—they are an archive of a life lived among stray animals that, like her work's other materials, are considered extraneous to the town's domestic and economic systems. Marie is, however, what we might call an outsider artist: self-taught, unengaged with the genealogy and traditions of "high art," and excluded from the capital-driven, star-powered art world. The "outsider" genre label has come under well-deserved scrutiny for its encouragement of ableist assumptions that non-neurotypical people lack cultural influences, its presumptive interpretations of artworks as literal representations of the artist's "inner world," and its reification of marginalized artists' status as socially and economically other. Still, there is one commonly cited aspect of outsider art that seems germane to Marie's role as an artist: a presiding interest in process rather than product. Like the sculptor Simon Rodia, who spent thirty years constructing a complex of large-scale structures and then permanently walked away from them, or Henry Darger, who wrote a 15,000-page illustrated epic and then told his neighbor to throw it all away, Marie is devoid of sentimental attachment or preciousness about the products of her labor. When it comes to the precarity of her artworks, she echoes outsider artist The Pope of Montreal, who, when his massive installation of hats was destroyed in a fire, said only, "Well, that's sad, but I will do it again" (Boxer 2013). Note Marie's almost identical response to losing her work in a fire: when "Every once in a while a kid burned down her shack.... She'd start again. She always remembered how to do it" (10). When asked, "What are you going to do when they burn up your shack?" Marie replies, "I don't care, it'll still be great here" (10). What makes Marie's home great is not that it houses her work, but that it provides the materials for its creation and recreation. The process of repurposing the detritus of a culture that considers Marie and her dogs to be waste constitutes a practice of resistance against the toxic systems of production, consumption, and valuation that locate them there.
Though Marie is not diagnosed with any disability, it is clear that she is alienated from artistic and intellectual discourse, including the poetics of the text that narrates her life. The novel-in-poems repeatedly notes that it is using words to describe Marie that she would not know herself, including the word "culture." In this way, to borrow a term from disability studies scholar James Berger, Marie is disarticulate(d) not just from her fictional community but also from the narrative voice and aesthetic sensibility that constructs her. Berger defines the disarticulate as "the figure at the boundary of the social-symbolic order, or who is imagined to be there, and at that liminal place, there is no adequate terminology. One cannot even quite determine whether he is an object of desire or revulsion" (2014, 1). Like this figure, Marie is rendered abject by her status as a linguistic other, making her an unstable body that both fascinates and repels the people around her—as well as the text itself, which attempts to represent her at the same time it avows its failure to do so. While the cruel chicks find Marie repellant to the point of incredible violence, Notley's narrative voice claims that a lifelong fascination with Marie has led her to write a book that betrays her: "I mean _everyone_ lies about Marie. I'm lying about her right now,/in order to pay my respects," she says (21). Notley's commentary on her own betrayal signals an uneasy affiliation with Marie's antagonists. The cruel chicks and the narrator, though seemingly opposed in their attitudes, represent an interplay of desire and revulsion that renders Marie both heroic and degraded, or "beside herself," as Julia Kristeva describes the state of abjection (1982, 1). Whether Marie is portrayed as beside herself as a literary figure—an idealized misrepresentation of an actual person outside the socio-symbolic order—or whether she's beside herself with grief as a result of other characters' violence against her, she is placed in an abject position both by the traumatic events of the novel and by her very existence as a figure within it. Unlike Marie's artwork, the aesthetic tools available to Notley's linguistic medium can only approximate and appropriate Marie's experience, with self-consciously uncertain ethical implications.
Still, the text's attempt to capture in language Marie's eccentric and extralinguistic modes of communication with her dogs enables the reader to imagine what Marie's codex, which she repeatedly claims is her brain and her world, might look and feel like. Though the codex is an alphabet book, Marie's artmaking process is depicted as less akin to writing than to howling, an opening of the body "to word" without or beyond language (i.e., "red and blue letters howling... The dogs open their mouths/to word me"). The letters in her alphabet do not follow a conventional order, but rather correspond to Marie's emotions and experiences at the moment she creates them. Though the letters do sometimes stand for meaningful words in Marie's life, they also often become figures in their own right, defined more by color, materials, or affective charge than by any correspondence to language. The red and blue letters howl not with the "oversubtlety" of poetry, after all, but with the memory and materials of the dump. It is no accident that this process of constructing a text that does not conform to standardized lexicons is figured in animalized terms, since membership in a linguistic community is one of the primary abilities that supposedly separates humans from other animals. As Sunaura Taylor has pointed out, this is misconception that relies on ableist assumptions about human communication, and both humans and nonhuman animals voice their discontent and suffering in forms that proceed and exceed language (2017, 43). Like the pained lowing of a dairy cow whose calves have been taken away by farmers, howling for Marie has a communicative function, if not always a semiotic one. The codex, in its perpetual state of reconstruction, is its own traumatic return, a materialization of the unspeakable experience of being tortured, or being stripped to bare animality in the face of human cruelty. Elaine Scarry writes that witnessing a person in great pain transition from prelingual cries and groans to fragmented verbal expressions is "almost to have been permitted to be present at the birth of language itself" (1985, 6). Marie's reconstitution of the alphabet in extralinguistic form might well be understood to occupy just such a state of creation.
The world that Marie builds in the codex not only disregards conventional syntactical and semiotic forms, but even reaches further than the rather experimental poetic form in which Notley tells Marie's story. In true Notleyan fashion, the voice of _Culture of One_ is never just one voice, as the narratorial position slips between the Goddess of Mercy, Marie, and a Southwestern expat living in Paris who represents Notley herself. While all those voices are quite similar syntactically and stylistically—are all, in a sense, Notley's voice—they are all centered around the codex, intent on including its strange alphabet despite its communicative otherness. As the Notley character agonizes over the cultural embeddedness of her own language, which she wryly bemoans as "Popup thoughts for scholars," the alphabet of Marie's codex builds a language utterly estranged from human community and interpretability, in symbols quite literally made up of dog DNA ("everything's covered with dog hairs... they're painted on") (129, 88). The codex constructs a grammar of abjection that can accommodate Marie as a nomad to society and language. This is quite different from Lucy Lurie's linguistic otherness, which is defined by depressive silence and refusal, the near opposite of Marie's "crazy" howling and hoarding (26). Nonetheless, both are able to imagine and instantiate new worlds through linguistic practices traditionally deemed subhuman or pathological.
The problem for Marie and her dogs, though, is that very sense of shared and shifting territory that empowers her to be an artist on the outer edges of culture: in running down the gully to the river together, untethered and unashamed, she and her dogs provoke the disdain of the nearby community. Others can't bear to see her claim territory _outside_ , whether outside their standards for what constitutes a human life (a life neatly distinguished from nonhuman life) or outside their human standards of living (a life at a sane and sanitary distance from the dump). The diagnosis of insanity based on transgressed boundaries, whether they are city limits or the number of dogs a person should own, are precisely the kinds of territorial disputes that Rosi Braidotti argues form the foundations of human–animal relationality. In _Nomad Theory,_ she writes that becoming-animal requires a becoming "radically immanent" to one's environment, and Marie's willingness to incorporate and be incorporated into her extrahuman culture is what makes both her and those with whom she shares that culture a threat (2012, 94).
Much like Lucy Lurie, Marie finds that her nonnormative life with dogs exposes both her and the dogs to gender-based violence, which is ostensibly directed at the human but ultimately fatal for the dogs. The poem's speaker tells us: "Marie is the truth. Treating her badly—an older/woman—is the world's delight. Her search for a new way/to live, her determination to create a cell of beauty/and meaning around her—despite being in a dump... /We hate her: she's a witch" (139). While Marie is demonstrably traumatized by each act of violence against her, she also seems convinced of the inescapability of that violence, as if it is an uncontrollable element of her habitat. After a group of teenage girls feeds broken glass to Tawny, who dies in Marie's arms, Marie displays rage more visibly than Lucy Lurie, and yet registers the futility of her grief-fueled animacy. While berating the girls, she repeatedly reflects on how "banal" and ineffectual her response is: "Marie turns and says, You're/just anyone, and that's the worst thing I can say. I'm/being so banal, she thinks, without thinking the word./Because, people hurt you and make you confront them—/so banal" (109). Tawny's death is, it seems, the logical, even inevitable consequence of a world in which people hurt people like Marie, so-called crazy women who build their homes at the edges of the human. And yet, still, she carries on with her life among dogs: caring for them, running with them, spending whatever money she has on them—and, yes, sometimes, burying them.
_Affiliation_
Again, I find myself asking: Is this how these stories have to end? Is it the case that dogs are so already-abject that we can only imagine their association with vulnerable humans ending in their deaths? If so, are we obscuring animals' pain by celebrating interspecies connections as sites of desirous potential, aesthetic innovation and alternative subject formation? Are these meaningful, affectively vibrant, and theoretically challenging relationships worth the risk they pose to animals' lives (as well as to the humans who must mourn them)?
These are difficult questions, and in the world outside novels, the interplay of enriching companionship and shared precarity in human–dog partnerships is contingent on the specific circumstances of particular humans and their animals. In the context of fiction, though, I would suggest that there is more room for reparative potential when it comes to the deaths of companion species. The representation of dogs' dual status as "[b]earing the brunt of the most extreme denigration and at the same time enjoying the greatest affection" encourages reflection on how ostensibly human structures of oppression have ethical consequences beyond the human (Dayan 2011, 231). Narratives like _Disgrace_ and _Culture of One_ demonstrate how human relationships to another species never can be unconditional; the dog's status as denigrated or beloved is entirely dependent upon their position within social hierarchies of race, gender, class, sexuality, and ability/normality. By dramatizing this duality, these narratives demand a reinterrogation of "the human" as a privileged and bounded category.
In the meantime, they suggest, there is perhaps no better option for beings on society's margins than affiliation, even as it might render both humans and animals more vulnerable. Take, for instance, the following passages from the ends of our two texts:
(Lucy to her father, after deciding to bear a child conceived during her rape:)
"Yes, I agree, it is humiliating. But perhaps that is a good point to start from again. Perhaps that is what I must learn to accept. To start at ground level. With nothing. Not with nothing but. With nothing. No cards, no weapons, no property, no rights, no dignity."
"Like a dog."
"Yes, like a dog." (Coetzee, 205)
(Notley's narrator:)
Mercy left her concept in place; perhaps
I'll tear it down. Who deserves Mercy except for Tawny,
Marie, or Leroy, or the Satanist girl or maybe Eve?
I deserved it last year. Because this book is _my_ world,
and Mercy still knows my friends. My friends at the dump. (Notley, 121)
Whereas the kind of human–animal brutality depicted in these narratives may leave room for little but trauma in the real world, the imaginative capaciousness of the novel allows us to conceive of more merciful futures that emerge from trauma but are not confined to it. _Disgrace_ is in many ways a pessimistic novel, but I argue that Lucy's becoming-doglike suggests the possibility of undermining a social and narrative order defined by the brutality of human hierarchy. As Dayan asks, "In a country wracked by economic collapse, ingrained racism, and political paralysis, where else is there to go, except into the eyes of dogs?" (Dayan 2015, 121). That is, in a society where an end to humans' legacy of racial disgrace based on dehumanization cannot be easily imagined, a radical deprivileging of the human may be the only hope for escape. Meanwhile, Notley envisions the murder of Tawny as an invocation to mercy for her abject and irrational subjects, a mercy she is only able to generate through narration. Mercy, a disenchanted goddess who has gone into retirement rather than continue to witness "mercy" being wielded by sovereigns and dictators, is called back into action by Tawny's death: "Mercy despised her job: But the agony of a half-coyote/dog with glass in her guts hurts like hell.... We must redefine mercy now, [she says]; it can't/belong as a concept to leaders and exploiters" (107–121). By constructing a world in which mercy is granted _primarily_ to beings like Marie and her dogs, Notley both renders such a world imaginable and demands its materialization. Despite the cruelty of their plots, these are narratives that love dogs and the women who love them too much—not in the sentimentalized modes of pet ownership, but with clear-eyed concern for the ways animals' intimacies with and differences from humans put them at risk. When love between dogs and humans can be so meaningful, so full of potential for new imaginings, it is unlikely that these interspecies affiliations will cease. And so, these novels suggest, in a world where such exquisite encounters are swallowed by the machinations of human power and violence, perhaps the best way forward is to become more like dogs.
Notes
For more on how love between domesticated animals and humans "transcend[s] the boundaries of their bodies and their species," see Kathy Rudy (2011, xii).
Donna Haraway also rightly criticizes this "unconditional love" (2003, 38).
Marianne Scholtmeijer makes this point about outsiders and animals in "The Power of Otherness: Animals in Women's Fiction" (1995, 233).
Dayan notes that while both humans and dogs are harmed by breed bans, it is ultimately the animals whose lives are at stake due to compulsory euthanasia (2006, 10).
See Elizabeth Donaldson (2002, 11–31).
Cary Wolfe writes, "[M]any animals flourish... because they are felt to be members of our families and our communities, regardless of their species. And yet, at the very same moment, billions of animals in factory farms.... Clearly, then, the question here is not simply of the 'animal' as the abjected other of the 'human' tout court" (2012, 53).
For more on the political stakes of this misreading, see Rosemary Jolly (2007, 164).
While this is certainly an anthropomorphic reading, much critical animal studies scholarship admits a certain level of practical anthropomorphizing in service of developing a human–animal ethics. See Vinciane Despret (2004, 111–134); Cora Diamond (1978, 465–479); Jane Bennett (2010); and Tom Tyler (2003, 267–281).
The concept of inanimacy is borrowed from Mel Y. Chen's engagement with animacy as a linguistic and cultural construct. See Chen (2012, 1–20).
For more on Coetzee's interest in the sympathetic imagination, see Sam Durrant (2006, 118–134); and Michael Marais (2006, 75–93).
Derek Attridge puts it another way: "If Lucy and Petrus are for David Lurie others whom he struggles to know, if [his victim] Melanie is an other whom he wrongs by not attempting to know, animals are others whom he cannot begin to know" (2000, 113).
See David Mclagan (2009, 35–41) and Benjamin Fraser (2010, 513).
It is important to note the major difference between the acts of violence in these two books, which is that there is no racial aspect of _Culture of One_ akin to the post-apartheid race relations that play a role in Lucy's rape. The class-based violence against Marie is not analogous to the racial tensions in _Disgrace_. For more on the danger of making such analogies, see Stefanie Boese (2016, 249).
For more on its pessimism, see Mark Sanders (2011, 363–373).
References
Antonello, P. and Farneti, R. (2009), "Antigone's Claim: A Conversation with Judith Butler," _Theory & Event_ 12 (1). Available online: <https://muse.jhu.edu/article/263144> (accessed December 13, 2015).
Attridge, D. (2000), "Age of Bronze, State of Grace: Music and Dogs in Coetzee's _Disgrace_ ," _NOVEL: A Forum on Fiction_ 34 (1): 98–121.
Bennett, J. (2010), _Vibrant Matter: A Political Ecology of Things_ , Durham: Duke University Press.
Berger, J. (2014), _The Disarticulate: Language, Disability, and the Narratives of Modernity_ , New York: New York University Pres.
Boese, S. (2016), "J.M. Coetzee's _Disgrace_ and the Temporality of Injury," _Critique: Studies in Contemporary Fiction_ 58 (3): 248–257.
Boxer, S. (2013), "The Rise of Self-Taught Artists: Out Is the New In," _The Atlantic_ , September. Available online: <https://www.theatlantic.com/magazine/archive/2013/09/out-is-the-new-in/309428/> (accessed July 8, 2017).
Braidotti, R. (2012), _Nomadic Theory_ , New York: Columbia University Press.
Chen, M. Y. (2012), _Animacies: Biopolitics, Racial Mattering, and Queer Affect_ , Durham: Duke University Press.
Coetzee, J. M. (1999), _Disgrace_ , New York: Penguin.
Dayan, C. (2011), _The Law Is a White Dog: How Legal Rituals Make and Unmake Persons_ , Princeton, NJ: Princeton University Press.
Dayan, C. (2015), _With Dogs at the Edge of Life_ , New York: Columbia University Press.
DeKoven, M. (2009), "Going to the Dogs in _Disgrace_ ," _ELH_ 76 (4): 847–875.
Derrida, J. (1991), "Eating Well, or the Calculation of the Subject: An Interview with Jacques Derrida," in E. Cadava, P. Connor, and J.-L. Nancy (eds.), _Who Comes after the Subject?_ 96–119, New York: Routledge.
Despret, V. (2004), "The Body We Care For: Figures of Anthropo-Zoo-Genesis," _Body & Society_ 10 (2–3): 111–134.
Diamond, C. (1978), "Eating Meat and Eating People," _Philosophy_ 53 (206): 465–479.
Donaldson, E. (2002), "The Corpus of the Madwoman: Toward a Feminist Disability Studies Theory of Embodiment and Mental Illness," in D. Bolt, J. Miele Rodas, and E. Donaldson (eds.), _The Madwoman and the Blindman: Jane Eyre, Discourse, and Disability_ , 11–31, Columbus: Ohio State University Press.
Durrant, S. (2006), "J. M. Coetzee, Elizabeth Costello, and the Limits of the Sympathetic Imagination," in J. Poyner (ed.), _J. M. Coetzee and the Idea of the Public Intellectual_ , 118–134. Athens: Ohio University Press.
Fraser, B. (2010), "The Work of (Creating) Art: Judith Scott's Fiber Art, Lola Barrera and Iñaki Peñafiel's _Qué tienes debajo del sombrero?_ (2006) and the Challenges Faced by People with Developmental Disabilities," _Cultural Studies_ 24 (4): 508–532.
Haraway, D. (2003), _The Companion Species Manifesto: Dogs, People, and Significant Otherness_ , Chicago: Prickly Paradigm Press.
Jolly, R. (2007), "Going to the Dogs: Humanity in J. M. Coetzee's _Disgrace, The Lives of Animals_ , and South Africa's Truth and Reconciliation Commission," in J. Poyner (ed.), _J. M. Coetzee and the Idea of the Public Intellectual_ , 148–171, Athens: Ohio University Press.
Kristeva, J. (1982), _Powers of Horror_ , New York: Columbia University Press.
Marais, M. (2006), "J.M. Coetzee's _Disgrace_ and the Task of the Imagination," _Journal of Modern Literature_ 29 (2): 75–93.
Mclagan, D. (2009), _Outsider Art: From the Margins to the Marketplace_ , London: Reaktion Books.
Nelson, M. (2015), _The Argonauts_ , Minneapolis: Graywolf.
Notley, A. (2011), _Culture of One_ , New York: Penguin.
Rudy, K. (2011), _Loving Animals: Toward a New Animal Advocacy_ , Minneapolis: University of Minnesota Press.
Sanders, M. (2011), "Disgrace," _Interventions: International Journal of Postcolonial Studies_ 4 (3): 363–373.
Scarry, E. (1985), _The Body in Pain: The Making and Unmaking of the World_ , Oxford: Oxford University Press.
Scholtmeijer, M. (1995), "The Power of Otherness: Animals in Women's Fiction," in C. Adams and J. Donovan (eds.), _Animals and Women: Feminist Theoretical Explorations_ , 231–262, Durham: Duke University Press.
Taylor, S. (2017), _Beasts of Burden: Animal and Disability Liberation_ , New York: The New Press.
Tyler, T. (2003), "If Horses Had Hands...," _Society & Animals_ 11 (3): 267–281.
Wolfe, C. (2012), _Before the Law: Humans and Other Animals in a Biopolitical Frame_ , Chicago: University of Chicago Press.
Wright, L. (2007), "'Does He Have It in Him to Be the Woman?': The Performance of Displacement in J.M. Coetzee's _Disgrace_ ," _Ariel_ 37 (4): 83–102.
Zambreno, K. (2015), "Notes on a New Tenderness," _Animal Shelter_ 4: 101–111.
DISCUSSION BY CAROL J. ADAMS
Oh animaladies— _Animaladies,_ the book and _animal-ladies,_ the authors—how I do love you! How you open up and restore ways of being. My love comes with sadness, grief, a sense of so much that has been lost, of damage done, of opportunities missed. All the possibilities of beingness that have been lost to us—constrained and labeled and killed. Over and over again, the pathologizing of interspecies connections, especially those that women have made.
Disturbance
Can I say it is a mad love? You have aroused my anger. Do I rage? Yes I rage. I think about Linda Nochlin, the great feminist art critic, writing about rage: "It seems to me, then, important to examine not merely how rage might be said to get into painting or sculpture but also how it gets into women" (2002, 51). She considers gendered rage in writing about Joan Mitchell, an abstract expressionist painter, and quotes from a letter Mitchell sent to her in the late 1980s,
I have lots of real reasons to hate... and somehow I can't ever get to hatred unless someone is kicking my dog Marion (true story)... [ _sic_ ] or destroying Gisèlle [a friend] etc. and then I'll bite—(I can't get to killing—my 'dead' shrink kept trying to get me there—I have never made it—my how I loved her). (52)
How much _animaladies_ that excerpt contains.
When Nochlin goes on to write about how "meaning and emotional intensity are produced structurally" (55), I think of lynn mowson's _boobscapes_ and _slink_. I rage about the slaughter of pregnant cows, and am grateful for lynn and Katie Gillespie for finding receptacles by which to mediate such rage—reflections for Katie, sculptures for lynn.
lynn refers to my own use of the term "traumatic knowledge." I learned that term from feminist historian Bonnie Smith's _The Gender of History_. Smith describes how amateur history (the history associated with women) consists of "the writing of multiple traumas" (2000, 19). She identifies the traumas that women historians of the early nineteenth century would have experienced: They were aware that their rights were eroding in the midst of a time when universal rights were being (supposedly) championed. They or family members had survived revolutions and wars, and at a personal level had experienced the threat or actuality of rape, poverty, violence, abuse. I applied this concept to the experience of those who care about animals and the knowledge we acquire about their experiences.
An important part of our response is to share and reveal; we seek ways to be creative. We write. Traumatic knowledge often leads to empathic witnessing, but I sense there is rage too.
Distraction
My love is mad, angry, destabilizing.
This morning I have been remarkably efficient in anything that took me away from this book—looking up a recipe for creamy vegan grits (searching five cookbooks for the best one). Thinking of the fact that _two_ of my great aunts (eight times removed) were killed as witches in Salem, Massachusetts, in the 1690s. This matters. I stood in front of my books on witchcraft ("mad" women) and pulled out Keith Thomas. Many witches were said to have "witches' familiars," that is, companion animals said to be equally bewitched (especially European women accused of being witches).
As Keith Thomas describes it:
But whether these domestic pets or uninvited animal companions were seen as magical is another matter. These creatures may have been the only friend these lonely old women possessed, and the names they gave them suggest an affectionate relationship. Matthew Hopkin's victims in Essex included Mary Hockett, who was accused of entertaining "three evil spirits each in the likeness of a mouse, called 'Littleman,' 'Prettyman' and 'Daynty,'" and Bridget Mayers, who entertained "an evil spirit in the likeness of a mouse called 'Prickeares.' More recently the novelist J. R. Ackerley has written of his mother that: "One of her last friends, when she was losing her faculties, was a fly, which I never saw but which she talked about a good deal and also talked to. With large melancholy yellow eyes and long lashes it inhabited the bathroom; she made a little joke of it but was serious enough to take in crumbs of bread every morning to feed it, scattering them along the wooden rim of the bath as she lay in it." (1971, 525)
It is a good world when a fly is fed.
Discomfort
It is hard to encounter these essays; they ask a lot of us and we discover that we have that much to give.
I needed comfort food; that explains my search for a good recipe for grits.
These essays offer us a way of understanding. Giving us liberation into _being._ Liberation into grief (Thank you Vas and James Stanescu).
For comfort food, I tried slow cooked lima beans (already made) as a substitute for the grits (which were unmade).
Disembodied
If only embodiment were sufficient. We know of the rationalized definitions that defined "human" by disregarding the body, even though thinking is a bodily function.
How we are supposed to survive, if we practice disembodiment? The _bodied_ iment that Katie encounters is important, as is her witnessing—truly an act of embodying, of being painfully embodied. Yet how much of embodiment is unintelligible to others and their disembodiment is normalized. I like lynn's thought: "that one might empathically respond to the materiality and form, and in doing so recognize these things we share with our fellow creatures, our entangled embodiment." And I recall Hannah Monroe and her reminder of the overly rationalist way of discussing animal liberation that has privileged mind over body.
Disaffection
Disembodiment is connected to dis/affection: the way affection and emotion in general have been stigmatized, misunderstood, dismissed. Lori Gruen asks how can we be fully in meaningful relationships when an important part of our cognitive/affective capacity is cut off? How is the definition of human already a dis/abling discourse? Hannah reminds us, "Autistic people are constructed by medical discourse as being unable to empathize and yet empathy is constructed as solely a feminine trait." Who bears the burden and liberation of caring too much (who says "too much"?) and wrong kinds of caring (again, who says?). Heather Fraser and Nik Taylor explore how the "nervous disposition" (and the stereotypes it bears) manages anxiety with the help of animal companions, but how this understanding pathologizes women's emotions for animals.
Fiona Probyn-Rapsey looks at "caring gone wrong" and how it too pathologizes individual acts of collecting animals but ignores the issue of whether factory farmers aren't themselves hoarders. Who is a hoarder? Why are women pathologized, but not factory farms? What is "too far" and according to whom? Is it because an individual hoarder is involved in a process but factory farms are committed to a product? Sexist distortions become alibis for failure to care. I'm right behind Fiona and asking with her, Why aren't corporate owners and operators of factory farms subjected to the speculation of writers or media commentators about their state of mind, their peculiar biographies, their personal traumas that led them to bring such a horrible site of animal suffering like the factory farm into being?
How do we intervene if we don't understand "damned and dammed desire"? pattrice jones and Cheryl Wylie teach us how to attend to desire and identity, for instance as they function in 4-H programs and backyard hen keeping, so that we can intervene appropriately.
Lori reminds us that this affective turn is an intervening in and against political and literal invocations of domination. Out of disaffection comes an affective and effective turn.
Displace
Where do we place ourselves? How often do we feel displaced? Katie placing herself at auctions, for instance, out of place and in place simultaneously. Yvette Watt chose to create a performance art piece as a specific place to displace the functioning of hunters with guns, to displace the ducks so that they could be safe.
She needed a literal platform to do so—creating space where there wasn't to provide a platform for undermining hunting. In this collaborative, participatory, event-based placement she foregrounded social issues and political activism. She brought people to a space and created protest in this space.
There is a ground to our work.
Conversely, what are places characterized by lack of safety?
Displacement often occurs at the outer edge of society as Liz Bowen explains. What happens there when there are intersections of different kinds of boundaries/loss of boundaries for women and animals?
Discourse
Discourses frame and limit. Discourses don't just interpret, but shape how relationships can and should occur. Liz reminds us that "discourses used to denigrate animal lovers are screens for disdain toward other identity categories." The discourse of personhood that denies animals their claim to personhood is ableist. "Humane" farming narratives create a discourse in which animal victims become seen as partners who collude in their own deaths. Nekeisha Alexis reminds us how conveniently this discourse dispossesses the killer of power.
Alice Crary tackles Peter Singer's discourse on cognitively disabled human beings, while reminding us that even though classic animal comparisons intend to degrade specific human beings, animal comparisons do not necessarily degrade human beings. Is it not time to say that the harm Singer continues to cause by maintaining the importance for his argument of the diminished moral standing of the cognitively impaired shows how he puts a philosophical approach, utilitarianism, before the materiality of any of us? As Alice indicates, Singer is sanguine that he is working with accurate empirical descriptions of the lives of the cognitively disabled. But he should not be. Here is analytic philosophical discourse at its most self-satisfied in its failure to be self-critical.
Silence is both a tool of oppression and a mode of poetic expression, as Hayley Singer suggests. Let us ask of any discourse, who is silent? Who is speaking? Liberation from silence is a storytelling process. But silence can also be a "politically potent form of poetic expression."
Let us pursue ways of co-constructing discourses to balance silence and speaking, to avoid being the "voices for the voiceless" and privileging voice.
Distort
Distortion is everywhere: Ableist metaphors to interpret the existence of speciesism, like equating moral attention with sight and moral inattention with "blindness." Or that humans who don't respond to animal concerns are deaf. Using stereotypes about autism to explain speciesism and then pathologizing the stereotype of autistic people being closer to animals. Saying speciesists are schizophrenic (and then defending it and persisting in it). I was startled to realize how widespread this practice is in anti-speciesist writings. Guy Scotton calls it the "diagnostic impulse to frame speciesism." We also have at work neurotypical people distorting and misunderstanding neurodiversity. One of the results, as this anthology makes clear, is that this keeps us from understanding how definitions of the human are distorted. We are not just responding to "what animals are like"; we are actually in part _creating_ "what animals are like" (Scotton quoting Palmer). As Guy puts it, "This array of metaphors constitutes a diagnostic tendency in animal liberation theory and advocacy—a tendency to construe struggles over medical frames of references as a battle to be won rather than a paradigm to be challenged in its own right."
Our task is clear: to call out every new or continuing reference that uses autism, schizophrenia, blindness to explain speciesism and embrace an interspecies concept of neurodiversity.
Distress and disavowal
I am not okay. As Katie says, "I will probably, in some ways, never be OK again." How do we live after being no longer okay? She continued to write her dissertation. She discovered public tears. We must be those who embrace those who are not okay. We must be those who understand we are not okay. It is okay not be okay. The distortion would be to make peace with a world that is not okay.
Former vegans disavow veganism by pathologizing it. Mislabeling veganism with a non-disease concocted out of free-associating it with "anorexia." What's going on there? Thankfully the Stanescu brothers bring us up to speed: "one can refrain from eating animals only as long as no one knows, as long as one repeatedly disavowals any identity or judgment." Individual grief is part of a larger context—collective political action. It is our avowal that helps us survive the grief that accompanies our knowledge. Our avowal about bodies.
Distress and disorientation
Reading this manuscript during late January and early February 2018 helped me recognize the animaladies situation for survivors of sexual harassment and exploitation in the animal rights movement in the United States. Stories of several women who had been sexually harassed over many years began surfacing publicly in a number of papers. These revelations often left those who had already suffered exposed again. I listened to a number of their stories and they felt vulnerable, they didn't know who to trust. Several survivors expressed deep panic about retaliation. They felt exposed.
Then came the disorienting experience—we needed to forgive the men. All the good they had done for animals! The exploiters' apologists wanted to skip the accountability stage. _Their_ discomfort with holding abusers accountable meant it was time to "move on." They never discussed the safety of the survivors. #ARMeToo and #TimesUpAR were being pathologized, not the decision of abusive men to endanger women and their organizations' work for animals by exploiting their position of power. _We_ —survivors and their advocates–were the problem; according to one prominent funder _we_ were engaged in cyber bullying. _We_ caused people to be afraid to speak up. What of the women who had been silenced for years by slander suits by abusers against their victims; human resources departments that did not act on their reports of sexual exploitation and hostile workplaces; nondisclosure agreements and threats that they would find no place to work in the animal movement? Women had literally disappeared from the animal rights movement because of what had happened to them. A process of accountability for the perpetrators' actions had only begun (if it had begun at all), but still the survivors were told they needed to "move on." And what of the fact that perpetrators took advantage of women who cared about animals? Their bodies—and their caring—had been exploited.
Distraught
You want to cry for all that has been suffered and you want to scream because it was so much worse than all that you had heard over the years and you want to do something—you want to do _everything._ You don't want despair to take over and you want to congratulate the brave women and you mourn the women who left and you think, "how might the movement have looked if for a quarter of century women weren't told to be quiet, or lost their jobs, or left with disgust, and so weren't part of shaping the movement?"
And how do you explain what feels like a certain instability in your being and the inability to focus and the grasping for something solid and it keeps disappearing? And you realize that you are in the midst of an _animaladies_ experience. _This_ book is what explains it.
Distribution
I'd love to see this book used in study groups of activists—feminist, disability, and especially animal activists. We have to find ways to take care as we encounter this exciting and challenging material. But we need to make sure it finds its audience. If we care about animals in this patriarchal ableist world, is it not inevitable that each one of us will experience an _animaladies_ moment—if not many?
Dis/closure
We are overthrowing so much. We aren't seeking a cure, not according to a patriarchal, speciesist, ableist world. And we aren't going to have closure. Nothing will easily be tied up together; no narrative will find its "finis." But together we can work for transformations.
References
Nochlin, L. (2002), "Joan Mitchell: A Rage to Paint," in J. Livingston, L. Nochlin, and Y. Lee (eds.), _The Paintings of Joan Mitchell_ , Berkeley: University of California Press.
Smith, B. G. (2000), _The Gender of History: Men, Women, and Historical Practice_ , Cambridge: Harvard University Press.
Thomas, K. (1971), _Religion and the Decline of Magic: Studies in Popular Beliefs in Sixteenth and Seventeenth Century England_ , London: Weidenfeld and Nicolson.
INDEX
Aaltola, Elisa here
Abernathy, Eleanor here, here, here
abjection
perceptions of here–here
state of here
transference of here–here
ableism here–here
_Abnormal_ (Foucault) here, here
"absurd anti-heroine" here
Acampora, Ralph here
acceptance, of companion animals here–here
Ackerley, J. R. here
Adams, Carol J. here, here, here, here, here, here
affect here–here
"aftershock" here
against speciesism here–here
as madness here–here
overview here–here
Agamben, Giorgio here
agoraphobia here
Ahmed, Sara here–here, here, here, here
Alexis, Nekeisha Alayna here–here
alliance
autism and possibilities for here–here
building here–here
concept of here
interspecies here, here
"almost autistic" here
American Psychiatric Association here, here
animaladies
Animal Studies scholarship here–here
concept here–here
definition here–here
pathologization here–here
women and madness here
"animalady" here–here
"animal beings" here
animal exploitation
backyard hen keeping here–here
cautions and questions here
cockfighting here–here
girl's story here, here–here
4-H and FFA programs here–here
loving them to death here
sexing chicks here
animal hoarding studies here–here
animal liberation. _See also_ liberationist veganism
damned and dammed desire in here–here
lessons from LGBTQ liberation here–here
movement here
queering animal liberation here–here
renewed rhetoric of here–here
solidarity for every buddy here–here
theory here, here, here
animality here, here
cognitive disability _vs._ here–here
slaves' perceived here
stigmatic conceptions of here
_Animal Liberation_ (Singer) here
Animal Planet here
animal rights movement here–here
_Animals, Equality, Democracy_ (O'Sullivan) here
_Animals and Women_ here
Animal Studies here–here, here
Anonymous for Animals here
anorexia nervosa here, here–here
anthropocentrism here, here, here
"anthropodenial" here
anti-carnist silence here
anti-Tom novels here, here, here–here, here, here
anxiety
and inequality here–here
normative, gendered expectations of here
types of here
in women here–here
Arluke, A. here
_Aunt Phillis's Cabin; or Southern Life As It Is_ (Eastman) here, here, here
autism here–here
connected oppressions and here–here
emotional connections with nonhuman animals here–here
empathy and here–here
gendered stereotypes about here
pathologizing of interspecies connections here–here
possibilities for alliance and solidarity here–here
_babyforms_ (mowson) here. _See also slinks_
backyard hen keeping here–here
_Backyard Poultry Magazine_ here
Barad, Karen here
"basic human equality" here, here
Bay-Cheng, L. Y. here
Bayertz, K. here
_Beasts of Burden_ (Taylor) here
_Becoming Animal_ here
Beers, Diane here
"being animal" here
Benton, Ted here
Bergenmar, J. here, here, here, here, here
Berger, James here
Beyond Veg here
Bhabha, Homi here
Bishop, Ann here
Blackstone, A. here
Bloom, Paul here
Boo, Katherine here–here
_boobscape_ (mowson) here–here
Bowen, Liz here, here–here, here
Braidotti, Rosi here
Bratman, Steve here, here–here, here–here
_Breaking Vegan_ (Younger) here
Burckhardt, Gottleib here
Burleigh, Michael here
Butler, Judith here, here
CAFO. _See_ concentrated animal feeding organization
camels, impact of forced reproduction and milking here
caregiving, across species here–here
carnism here, here, here–here
as ideological subsystem of speciesism here
carnist narratives here
carnist systems of knowledge here–here
carnist violence here
Carson, Rachel here
_Case for Animal Rights, The_ (Regan) here
Castile, Philando here
catatonia here
cats here
crazy cat lady here–here, here–here
friendships here
Cavarero, Adriana here
Chen, Peter here, here
chickens here, here, here
in advertisements and children's books here
backyard hen keeping here–here
care for here
chimpanzees here
use in lobotomies here–here
"chthonic ones" here
Chthulucene here–here
civilized communities here
Clare, Eli here
closeness here–here
cockfighting here–here
Coetzee, J. M. here, here, here, here, here
cognitive alienation here
cognitive disability here
moral standing and here
in Nazi Germany here–here
use of animal comparisons here–here
_vs._ animality here–here
cognitive dysfunction here–here
Cole, M. here
"compassionate carnivorism" here
concentrated animal feeding organization (CAFO) here–here
agribusinesses rely on here
_Confessions: Animal Hoarders_ here
connected oppressions here–here
Conrad, P. here
conscious omnivore storytelling
emphasizing affect here–here
and plantation romances here–here
reframing coercion and domination here–here
representing victims as partners here–here
selective comparing and contrasting here–here
tactics of evasion in here
conscious omnivorism here, here–here, here
Cooper, Brittany here
Costello, Elizabeth here
Coulter, K. here, here
cows here, here, here, here, here, here
impact of forced reproduction and milking here
life span of here–here
in mega-dairies here–here
in Pacific Northwestern United States dairy industry here–here
pregnant, slaughtering of here–here
selective breeding of here
violence against here
_Cowspiracy_ here
Crary, Alice here, here–here, here
"crazy" here
"crazy cat lady" (CCL) here–here, here–here
animal hoarding studies here–here
and concentrated animal feeding organizations here–here
fascination with here–here
overview here
popular culture here
popular history of here–here
and woman animal hoarder here–here
_Culture of One_ (Notley) here, here–here, here
cum panis here
Cvetokovich, Ann here
dairy industry, horrors of here–here
antibiotic use here
flame clipping here
mastitis here
repetitive exhausting pregnancies here–here
selective breeding here
traditional dairy farms, decreasing here
dammed desire here–here
damned here–here
Dana, Charles here, here
Darwin, Charles here–here, here
Davidson, J. here, here, here, here, here, here
Dayan, Colin here, here, here, here
Degeling, C. here
DeMello, Margo here
Derrida, Jacques here
_Descent of Man_ (Darwin) here
De Waal, Frans here
"diagnostic tendency" here
_Diary of a Steak_ (Levy) here
Dinishak, J. here
disability here–here
activism here
stigmatic conceptions of here
theory here
disaffection here–here
dis/closure here
discomfort here
discontent here
discourse here–here
dis-ease here
disembodied here
_Disgrace_ (Coetzee) here, here–here, here
dismember here–here
displace here
distort here
distraction here
distraught here
distress
and disavowal here–here
and disorientation here
distribution here
disturbance here–here
dog love here–here
case study here–here
heteronormativity and normality here
human–canine affiliations here–here
unconditional here
unconventional here
dogs here, here, here, here, here
Nazis and here–here
puppy farming here
relationship with here–here
service here
unconditional love from. _See_ dog love
do-it-yourself slaughter here, here, here, here, here, here, here
"domestication" here
domination
affective here–here
cognitive here–here
conscious omnivore storytelling and reframing of here–here
Donaldson, Sue here
Donovan, Josephine here, here
double dysjunction here
Down, John Langdon here
Down syndrome here
Doyle, Haley Bosco here
_DSM-_ _5_ _(Diagnostic and Statistical Manual of Mental Disorders)_ here
Duck Lake Project here–here
art and activism here–here
counter resistance to pro-animal work here
dancers and rescuers role here–here
initiation of here–here
media coverage of here–here
Moulting Lagoon here
old modes of protest here–here
overview here–here
participants, safety of here
protests of organizations here
recreational duck shooting here–here
ducks here
Duck Lake Project to rescue here–here
recreational shooting in Australia here–here
Dully, Howard here–here
Dundes, Alan here
dysfunction here
cognitive here–here
Eastman, Mary Henderson here, here, here
"eco-ability" here
"eco-crip theory" here
Edelman, M. here
Eidlin, Barry here
Elliott, Stephan here
Elmhurst Dairy here
_Eloquent Rage_ (Cooper) here
emancipation, neurodiverse here–here
emotion here
reason and here–here, here–here
emotional connections, with nonhuman animals here–here
emotional distancing here–here
empathetic engagement here
empathic encounter here
empathy
and autism here–here
entangled here–here
between humans and figurative sculpture here–here
imagination and here
phenomenological here
entangled empathy here–here
_Entangled Empathy: An Alternative Ethic for Our Relationships with Animals_ (Gruen) here, here
entanglement, notion of here
epistemic violence here
epistemology of ignorance here, here, here
Erickson, Barbara here
ethical meat here–here
_Ethical Meat Handbook, The_ here
Facebook here
Farm Animal Rights Movement here
Fehr, E. here
fellowship of table here–here
female malady here
_Female Malady, The_ (Showalter) here
_Feminism and the Mastery of Nature_ (Plumwood) here
feminism without borders here
feminist animal studies here–here
feminist killjoy here–here
FFA. _See_ Future Farmers of America
Finn, Kate here
_Fitzcaraldo_ (Herzog) here
flame clipping here
_Flaming Trees_ here
_fleshlump_ (mowson) here, here, here
Foer, Jonathan Safran here
Foucault, Michel here–here, here, here
Fraiman, Susan here
"frame contestation" here
Francione, Gary here
Fraser, Heather here, here–here, here
Freeman, Walter here
Freud, Sigmund here, here
Friend, Catherine here, here
Fulton, John here–here
fun, with companion animals here–here
_Fuses_ here
Future Farmers of America (FFA) here–here, here
gender, and autism here–here
_Gender of History, The_ (Smith) here
gender roles here–here
generalized anxiety here
_gestalt_ here, here
Gillespie, Katie here, here–here, here, here
_Global Activism: Art and Conflict in the_ _21_ _st Century_ (Thompson) here, here
_Global aCtIVSsm_ here
goats here
impact of forced reproduction and milking here
Goldsmith, A. H. here
Goodkind, S. A. here
Gordon, T. here
Graham, M. here
Grandin, Temple here, here–here, here
_Grey Gardens_ here, here
grief
as political act here–here
public here
witnessing feelings of here
Gruen, Lori here, here–here, here, here, here, here, here–here, here, here, here
Hacking's Wittgensteinian reflections here–here
Haeckel, Ernst here
Halberstam, Jack here
Hanisch, Carol here
Haraway, Donna here, here, here, here–here, here, here
Harlow, Harry here
Haushofer, J. here
Hawthorne, Mark here
Hayden, Matt here
Hedva, Johanna here–here
Hentz, Caroline Lee here–here
_Hereditarily Ill_ here
Herzog, Hal here
Herzog, Werner here
Hochschild, Arlie here
"homosexuality" here
Hopper, Jim here
_Horrorism: Naming Contemporary Violence_ (Cavarero) here
Horta, Oscar here
4-H program here, here, here–here
Huff, Ramona here–here
_Huffington Australia_ here
human–animal relationality here
humane farming here, here, here, here, here, here, here
Humane Research Council here
"humanness" here
"hyper-emotionality" here–here
hypermnesia here
hysteria here
hysterical traumatic thoughts here
_I Accuse_ here
Igualidad Animal here
inequality, anxiety and here–here
infantilism here
_In Good Company: Women and Animal Companions_ project here, here
alliance building here–here
caregiving across species here–here
feminist animal studies here–here
interspecies care here–here
solidarity here–here
_Inside Animal Hoarding: The Case of Barbara Erickson and Her_ 552 _Dogs_ here
interspecies care here–here
interspecies connections, pathologizing of here–here
interspecies neurodiversity here
Irigaray, Luce here
Irvine, Leslie here
Jack, Jordynn here
Jacobsen, Carlyle here–here
jones, pattrice here–here
Joy, Melanie here
Kaminer, Ariel here
Kang, Han here, here, here, here, here
Kemmerer, Lisa here
Khakpour, Porochista here
Kheel, Marti here
Killeen, Celeste here
Kittay, Eva here–here, here–here
Kleeck, Justin Van here
Ko, Syl here
Kristeva, Julia here
Kymlicka, Will here, here, here
lambs here, here
Laouli, Mohammed here
_Learning to Be a Dutiful Carnivore_ (Legge) here
Legge, Jane here
Leigh, Meredith here
lesbian separatism here
Levy, Deborah here
liberationist veganism here–here
life-forms
higher here
human-headed ranking of here
lower here
normative ordering of here, here–here
_Lit Hub_ here
_Living as Form: Socially Engaged Art from_ _1991–2011_ (Thompson) here
lobotomy here–here
brain surgery here–here
case studies here–here
history of here–here
London Conference here–here
loneliness
profound here, here
of witnessing here–here
love, with companion animals here–here
Lovecraft, H. P. here
_Loving Animals_ here
loving them to death here
Lurie, David here
Lurie, Lucy here, here
MacKethan, Lucinda here
Mad Fucking Witches, Australia here
madness here
feminist perspective here, here
socially constructed nature of here–here
of speciesism here
against speciesism as here–here
of witnessing here–here
Mad Pride, USA here
Maple Leaf Foods here
"mass dissociation" here
mastitis here
material entanglements here
Mavrich, Brett here–here
McHugh, Susan here, here
McRobbie, Linda Rodriguez here–here
mental difference here
mental disorder, surgical intervention in here–here
Meurer, Gabriele here
Mickelson, K. D. here
Mills, Charles here–here, here
"mindblindness" here
mind–body dualism here
Mitchell, Joan here
Mitchell, W. J. T. here
Mohanty, C. here
_Mongolian Mark, The_ here
"Mongoloid idiots" here
Moniz, Egas here
Monroe, Hannah here, here–here, here
Moody-Adams, Michele here
"moral catharsis" here
"moral deformity" here
morally transgressive vegan here
"moral monster" here
moral standing of animals here–here, here
Morgan, K. here
Mortensen, Helen here
_Mourning Animals_ here
mowson, lynn here–here, here
Murdoch, Iris here
"natural monster" here
_Neither Man Nor Beast: Feminism and the Defense of Animals_ (Adams) here
Nelson, Maggie here, here
neurodiverse emancipation here–here
neurodiversity here, here
"neuro-equality" here
"neurotic ambivalence" here
neurotypicalism here
neutral conception, of reason here–here
Newkirk, Ingrid here
_New Yorker, The_ here
_New York Times, The_ here
Nochlin, Linda here
_Nomad Theory_ here
Notley, Alice here, here, here–here, here
Nuland, S. here
Nussbaum, Martha here–here, here
obsessive-compulsive disorder here
_Okja_ here
"old maids" here–here
Olsen, Tillie here
oppressions, connected here–here
orthorexia here
orthorexia nervosa
criteria for here
diagnosis of here–here
indicators of here
in theory here
O'Sullivan, Siobhan here
Pachirat, Timothy here
_Palas Por Pistolas_ here
"paleo diet" here
Palmer, Clare here
panic disorder here
Pateman, Carole here
pathologization here–here
patriarchal psychology here
Patricia here
Patronek, Gary here
Perry, Hart here–here
_PerthNow_ here
PETA here
phenomenological empathy here
physical disabilities here
pigs here, here, here, here, here
in advertisements and children's books here
production projects here
plantation romances here
analysis of here
conscious omnivore storytelling and here–here
emphasizing affect here–here
reframing coercion and violence here
representing victims as partners here–here
selective comparing and contrasting here–here
shared tactics of evasion in here–here
_Planter's Northern Bride, The_ (Hentz) here, here, here
Plumwood, Val here
Pollan, Michael here, here–here
Polyface Farms here
_Pornography of Meat, The_ (Adams) here
"post-autistic economics" movement here
post-traumatic stress disorder here
in animal here
_Precarious Life: The Powers of Mourning and Violence_ here
Prince-Hughes, Dawn here, here
_Priscilla Queen of the Desert_ (Elliott) here
Probyn-Rapsey, Fiona here, here–here, here–here
profound loneliness here, here
"profound mental retardation" here
_Project Row Houses_ here
psychological disorders here
_Psychology Today_ here
"Psychosurgery" (Freeman) here
public grief here
_Puppies and Babies_ here
"Puritanism" here
pussyhat project here
_Queensland Times_ here
queering animal liberation here–here
_Racial Contract, The_ (Mills) here
racialized conceptions here, here
_Raising Chickens for Meat_ (Roland) here
Ranciere, Jacques here
_Rattling the Cage_ (Wise) here
Regan, Tom here
reproductive tyranny here
Reyes, Pedro here
Reynolds, Diamond here, here
Rich, S. here
Rock, M. J. here
Rogers, Melvin here
Roland, Gwen here
Rowling, J. K. here
Rudy, Kathy here
Salatin, Joel here
Salomon, D. here, here, here, here
Scarry, Elaine here
schizophrenia here, here
social form of here
Schneemann, Carolee here
Scotton, Guy here, here–here, here
sculptural body fragmentation, by mowson here
_babyforms_ here
_boobscape_ here–here
_fleshlumps_ here, here, here–here, here
_slinks_ here–here, here
traumatic knowledge, emergence of here
unmaking of body here–here
Second World War here
separation anxiety here
_Sexual Contract The_ (Pateman) here
_Sexual Politics of Meat, The_ (Adams) here, here
sheep here, here, here, here
impact of forced reproduction and milking here
production projects here
Showalter, Elaine here
shutdown, emotional here–here
Silcock, Catherine here
silence here–here
of "absent-referent" here
cartographies of here
kinds of here, here
quiet _vs._ here
unnatural here
as vegan disobedience here
_Silences_ here
silent resistance here–here
_Silent Spring_ (Carson) here
_Simpsons, The_ (Abernathy) here, here
Sinclair, Melissa Scott here–here
Singer, Hayley here, here–here, here
Singer, Peter here, here, here–here, here–here, here, here, here, here–here
skepticism here, here, here–here
_Skinny Bitch_ (Freedman) here
slaughter, pregnant cow, in the United Kingdom here–here
slaveholder here–here
_slinks_ (mowson) here–here, here
"slow violence" here
Smith, Bonnie here–here
Smith, M. here, here, here, here, here, here
social anxiety here
"social contract" here
social Darwinism here–here, here
social entanglements here
social media here
social phenomena here
social phobia here
social unintelligibility here
solidarity here–here
in autistic people and nonhuman animals here–here
interdependence here
interspecies here
Solnit, Rebecca here, here, here
_Speaking Up for Animals_ here
"special darkness" here
"species contract" here
species identity disorder here
speciesism here, here, here, here, here
associations with mental pathology here
carnism as ideological subsystem of here
madness of here
normative analysis of here
as pathology, criticizing framing of here
as psychological malady here
speciesist here
specific phobias here
Stanescu, James here, here, here, here–here
Stanescu, Vasile here–here
"statistical monster" here
_Staying with the Trouble: Making Kin in the Chthulucene_ here
Stein, Edith here
Steiner, A. L. here
stereotype threat here
Stowe, Harriet Beecher here–here, here
_Striking at the Roots_ here
surrealism, magical here
Svanberg, I. here
_Swan Book, The_ (Wright) here
_Swan Lake_ here, here, here, here
Sydenham, Thomas here
"symbiotic genres" here
Taylor, Chloë here
Taylor, Nik here, here–here, here
Taylor, Sunaura here, here, here, here, here, here, here
Thomas, Keith here
Thompson, Nato here, here–here
trauma
affecting animals here–here
cause hypermnesia here
definition of here
historical here
witnessed in farming here
traumatic knowledge here, here–here
emergence of here
testimony transforms here
witnessing of here
traumatic memories here, here
traumatic working practice here–here
"truly autistic" here
Trump, Donald here
"Turkey Day" here
Tyson Foods here
_Uncle Tom's Cabin_ (Stowe) here
unnatural silence here
Ussher, Jane here
vegan disobedience here
veganism
ethical here, here
pathogenization of here–here
social isolation here–here
speech acts identifying as here
transitioning to here
vegans
ethical here
fellowship of table here–here
morally transgressive here
as pervert here–here
_Vegetarian, The_ (Kang) here, here, here–here
Vialles, Noele here
violence
against animals here, here–here
carnist here
epistemic here
slow here
"virtually autistic" here
Wadiwel, Dinesh here, here
Waldau, Paul here, here, here
_Wall Street Journal_ here
_Washington Post_ here
Watt, Yvette here, here–here, here
Weil, Kari here–here
Weisberg, Zipporah here–here, here
Welch, Bryan here
Weston, Arthur here
_Whatisitaboutanimals.com_ project here, here
_What the Health?_ here
White, Micah here
Williams, S. L. here
Wise, Steven here
_With Dogs at the Edge of Life_ (Colin) here
witnessing here–here
feelings of grief and mourning here
layers of damage in here–here
madness of here–here
suffering of animals here
Wolfe, Cary here, here
women
anxiety in here–here
companion animals here–here
and madness here
Wright, Alexis here
Wright, Laura here
Wylie, Cheryl here, here–here, here–here, here
_Yoga Journal_ here
Younger, Jordan here
Zambreno, Kate here
zoophilpsychosis here, here
BLOOMSBURY ACADEMIC
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BLOOMSBURY, BLOOMSBURY ACADEMIC and the Diana logo are trademarks of Bloomsbury Publishing Plc
First published in the United States of America 2019
Copyright © Lori Gruen, Fiona Probyn-Rapsey, and Contributors, 2019
For legal purposes the Acknowledgments on p.xiii constitute an extension of this copyright page.
Cover design: Eleanor Rose
Cover image: lynn mowson, _boobscape 2016–18_ , latex, tissue and string, (detail). Documentation: Kerry Leonard
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Bloomsbury Publishing Inc does not have any control over, or responsibility for, any third-party websites referred to or in this book. All internet addresses given in this book were correct at the time of going to press. The author and publisher regret any inconvenience caused if addresses have changed or sites have ceased to exist, but can accept no responsibility for any such changes.
Library of Congress Cataloging-in-Publication Data
Names: Gruen, Lori, editor. | Probyn-Rapsey, Fiona, editor.
Title: Animaladies : gender, animals and madness / edited by Lori Gruen and Fiona Probyn-Rapsey.
Description: New York, NY : Bloomsbury, [2018] | Includes bibliographical references and index.
Identifiers: LCCN 2018018008 (print) | LCCN 2018029477 (ebook) | ISBN 9781501342172 (ePDF) | ISBN 9781501342165 (ePUB) | ISBN 9781501342158 (hardback : alk. paper)
Subjects: LCSH: Human-animal relationships | Women and animals. | Animals–Social aspects. | Zoophilia. Classification: LCC QL85 (ebook) | LCC QL85 .A5213 2018 (print) | DDC 591.5–dc23
LC record available at <https://lccn.loc.gov/2018018008>
ISBN: HB: 978-1-5013-4215-8
ePDF: 978-1-5013-4217-2
eBook: 978-1-5013-4216-5
Typeset by Integra Software Services Pvt. Ltd.
To find out more about our authors and books visit www.bloomsbury.com and sign up for our newsletters.
| {
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Unter Stoffwechselstörung, auch Stoffwechselanomalie genannt, versteht man medizinisch die pathologischen Abweichungen der Stoffwechselvorgänge. Diese werden häufig durch genetisch bedingten Enzymmangel verursacht, können aber auch erworben sein.
Pathogenetisch werden die Stoffwechselstörungen gekennzeichnet durch:
Erhöhung von Stoffwechselzwischenprodukten (wie Alkaptonurie, Methylmalonazidurie, Phenylketonurie, Porphyrie)
Defekte des Transports von Substanzen (z. B. Hartnup-Krankheit, Cystinurie)
Produktion von ungewöhnlichen Metaboliten (wie Phenylbrenztraubensäure bei Phenylketonurie, Dicarbonsäuren bei Fettsäureoxidationsstörungen)
Speicherung von Stoffwechselprodukten (Thesaurismosen)
Es können Störungen im Fettstoffwechsel (z. B. Hyperlipoproteinämien, also eine Erhöhung der Blutfette), im Aminosäuren- bzw. Eiweißstoffwechsel (z. B. Porphyrie, eine Störung der Bildung des Hämoglobins), im Kohlenhydratstoffwechsel (z. B. bestimmte Formen der Zuckerkrankheit) und im Mineralstoffwechsel (z. B. Phosphatmangel) auftreten.
Grundprinzip einer Stoffwechselstörung
physiologische Reaktion
pathologische Reaktion, Enzymdefekt
pathologische Reaktion, überaktives Enzym
Das Konzept der angeborenen Stoffwechselstörung wurde zu Beginn des 20. Jahrhunderts von dem englischen Internisten Archibald Garrod entdeckt. Bei seinen Untersuchungen zur Alkaptonurie ging er davon aus, dass für jeden Stoffwechselschritt ein bestimmtes Enzym zuständig ist. Auf dieser Grundlage postulierte er den Enzymdefekt als Ursache einer Stoffwechselstörung. Durch einen Enzymdefekt kommt es zu einer krankhaften Anhäufung des entsprechenden Substrates und Mangel an Stoffwechselprodukten, was zu den klinischen Symptomen einer Stoffwechselerkrankung führt. Eine Anhäufung der Substrate kann zu Intoxikationen, Enzyminhibition, Akkumulation und Aktivierung alternativer Stoffwechselwege führen. Der Mangel an Produkt führt zu Stoffwechseldefiziten.
Liste der Stoffwechselstörungen und Stoffwechselerkrankungen (Auswahl)
3-Methylglutaconazidurie
Adrenogenitales Syndrom
Alkaptonurie
Alpha-1-Antitrypsinmangel
Diabetes mellitus (Zuckerkrankheit)
Dorfman-Chanarin-Syndrom
Erythropoetische Protoporphyrie (Erkrankung aus der Gruppe der Porphyrien)
Galaktosämie
Gicht
Glutarazidurie
Glykogenose
Harnstoffzyklusdefekt
Hashimoto-Thyreoiditis
Hereditärer Adenosindesaminase-Mangel
Hereditäres Zinkmangelsyndrom
Hypertriglyceridämie
Hypophosphatasie (Rathbuin-Syndrom)
Hypothyreose (Schilddrüsenunterfunktion)
Ketoazidose
Ketose (Acetonämie, Acetonurie)
Kombinierte Malon- und Methylmalonazidurie (CMAMMA)
LCAT-Mangel
Lesch-Nyhan-Syndrom (Hyperurikämie-Syndrom oder Hyperurikose)
Lipidose
Maroteaux-Lamy-Syndrom
Methylmalonazidurie (MMA)
Morbus Addison (Hypadrenokortizismus)
Morbus Conn (Hyperaldosteronismus)
Morbus Cushing
Morbus Fabry
Morbus Gaucher
Morbus Hunter (Mukopolysaccharidose Typ II)
Morbus Morquio
Morbus Sanfilippo (MPS Typ III)
Mukoviszidose (zystische Fibrose)
Myoadenylatdeaminase-Mangel (MADD)
Polyzystisches Ovar-Syndrom (PCOS)
Phenylketonurie
Porphyrien
Thesaurismose (Speicherkrankheit)
Literatur | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,682 |
namespace Snippets4.Serialization
{
using NServiceBus;
public class BinarySerialization
{
public void Simple()
{
#region BinarySerialization
Configure.Serialization.Binary();
#endregion
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
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{"url":"https:\/\/www.vedantu.com\/question-answer\/evaluate-the-given-integral-intsec-xtan-xdx-class-12-maths-cbse-5eec87f101f9bf4836e48489","text":"Question\n\nEvaluate the given integral, $\\int{\\sec x\\tan xdx}$\n\nHint: We know that integration of anything is the reverse process of differentiation. In this question, we will solve this by using some basic integration and basic differentiation. You can start your solution by writing sec x is equal to $\\dfrac{1}{\\cos x}$ and tan x is equal to $\\dfrac{\\sin x}{\\cos \\ x}$.\n\nIt is given in the question that to integrate sec x. tan x\n$\\int{\\tan x.\\sec xdx........................\\left( i \\right)}$\nHere, in equation (i) we can write tan x as $\\dfrac{\\sin x}{\\cos \\ x}$ and sec x as $\\dfrac{1}{\\cos x}$.\n\\begin{align} & =\\int{\\dfrac{1}{\\cos x}.\\dfrac{\\sin x}{\\cos x}}dx \\\\ & =\\int{\\dfrac{\\sin x}{{{\\left( \\cos x \\right)}^{2}}}dx.........................\\left( ii \\right)} \\\\ \\end{align}\n\nLet us assume that u = cos x.\n\nThen differentiating u = cos x with respect to x; we get,\n$\\dfrac{du}{dx}=-\\sin x$\n\nWe can write du = -sin x . dx\n\nSo, putting -du in place of sin x dx and ${{\\left( u \\right)}^{2}}$ in place of ${{\\left( \\cos x \\right)}^{2}}$ in equation (ii), we get;\n$=-\\int{\\dfrac{du}{{{\\left( u \\right)}^{2}}}.................\\left( iii \\right)}$\nWe can write $\\dfrac{1}{{{\\left( u \\right)}^{2}}}\\ as{{\\left( u \\right)}^{-2}}$ in equation (iii) we get,\n$=-\\int{{{\\left( u \\right)}^{-2}}du}$\n\nNow, we have to integrate $-{{\\left( u \\right)}^{-2}}$ with respect to u and we know the basic integration formula;\n$\\int{{{x}^{n}}dn}=\\dfrac{{{x}^{n+1}}}{n+1}+c$\nSo, on integrating $-{{\\left( u \\right)}^{-2}}$with respect to u we get;\n\\begin{align} & =\\dfrac{-{{\\left( u \\right)}^{-2+1}}}{-2+1}+c \\\\ & =\\dfrac{-{{u}^{-1}}}{-1}+c \\\\ & ={{u}^{-1}}+c \\\\ & =\\dfrac{1}{u}+c....................\\left( iv \\right) \\\\ \\end{align}\n\nAlso, we had assumed earlier that u = cos x. So, putting the value of u = cos x in equation (iv), we get;\n$=\\dfrac{1}{\\cos x}+c.............\\left( v \\right)$\n\nWe know that $\\dfrac{1}{\\cos x}=\\sec x$so, writing $\\dfrac{1}{\\cos x}\\ as\\ \\sec x$ in equation (v), we get = sec x + c.\n\nThus, we get $\\int{\\sec x.\\tan x=\\sec x+c.}$\n\nNote: Integration of anything is the reverse of the process of differentiation of something. So if you know the correct answer but if you have any confusion in it then you can solve this question by this alternative method.\n\nAs in this question, we have to find $\\int{\\tan x.\\sec x}$ with respect to x. So, we will differentiate sec x with respect to x to get $\\int{\\tan x.\\sec x}$.\n\nSo, we have;\n$u=\\sec x\\ or\\ u=\\dfrac{1}{\\cos x}$ on differentiating with respect to x, we get;\n\\begin{align} & \\dfrac{du}{dx}=-\\dfrac{1.\\left( -\\sin x \\right)}{{{\\cos }^{2}}x} \\\\ & \\dfrac{du}{dx}=\\dfrac{\\sin x}{{{\\cos }^{2}}x} \\\\ & \\dfrac{du}{dx}=\\dfrac{1}{\\cos x}.\\dfrac{\\sin x}{\\cos x} \\\\ & \\dfrac{du}{dx}=\\sec x.\\tan x \\\\ & du=\\sec x.\\tan x.dx \\\\ & \\dfrac{d\\left( \\sec x \\right)}{dx}=\\sec x.\\tan x \\\\ & or \\\\ & \\int{\\sec x\\tan x.dx=\\sec x}. \\\\ \\end{align}","date":"2020-10-20 03:33:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 3, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000094175338745, \"perplexity\": 1086.018580139169}, \"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-2020-45\/segments\/1603107869785.9\/warc\/CC-MAIN-20201020021700-20201020051700-00027.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.cableizer.com\/documentation\/T_4y\/","text":"Effective transient thermal resistance in the earth for yearly load:\n\nFor deeply buried cables and for tunnels, the yearly load variations play a significant role because of the very long constants at great depths.\n\nFor more information, refer to the transient thermal resistance $T_4et$..\n\nSymbol\n$T_{\\mathrm{4y}}$\nUnit\nK.m\/W\nFormulae\n$\\frac{\\rho_{\\mathrm{4}}}{2 \\pi} \\ln{\\left (\\frac{D_{\\mathrm{x_{\\mathrm{y}}}}}{Do_{\\mathrm{d}}} \\right )}$\nRelated\n$D_{\\mathrm{x_{\\mathrm{y}}}}$\n$Do_{\\mathrm{d}}$\n$\\pi$\n$\\rho_{\\mathrm{4}}$\n$T_{\\mathrm{4et}}$\nUsed in\n$T_{\\mathrm{4\\mu}}$","date":"2019-01-17 01:33:46","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\": 0.5721375942230225, \"perplexity\": 2559.3520244509923}, \"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-2019-04\/segments\/1547583658662.31\/warc\/CC-MAIN-20190117000104-20190117022104-00386.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.studyadda.com\/solved-papers\/10th-class\/science\/solved-paper-science-2016-outside-delhi-set-iii\/567","text":"# Solved papers for 10th Class Science Solved Paper - Science-2016 Outside Delhi Set-III\n\n### done Solved Paper - Science-2016 Outside Delhi Set-III\n\n\u2022 question_answer1) Write the name and structure of an aldehyde with four carbon atoms in its molecule.\n\n\u2022 question_answer2) List two functions of ovary of human female reproductive system.\n\n\u2022 question_answer3) In a food chain of frog, grass, insect and snake, assign trophic level to frog.\n\n\u2022 question_answer4) The refractive indices of glass and water with respect to air are 3\/2 and 4\/3 respectively. If speed of light in glass is $2\\times {{10}^{8}}\\,m\/s,$ find the speed of light in water.\n\n\u2022 question_answer5) List four stakeholders which may be helpful in the conservation of forests.\n\n\u2022 question_answer6) The construction of large dams leads to social and environmental problems. List two problems of each category.\n\n The position of eight elements in the Modern Periodic Table is given below where atomic numbers of elements are given in the parenthesis. Period No. 2 Li (3) Be (4) 3 Na (11) Mg (12) 4 K (19) Ca (20) 5 Rb (37) Sr (38) (i) Write the electronic configuration of Ca. (ii) Predict the number of valence electrons in Rb. (iii) What is the number of shells in Sr? (iv) Predict whether K is a metal or a non-metal. (v) Which one of these elements has the largest atom in size? (vi) Arrange Be, Ca, Mg and Rb in the increasing order of the size of their respective atoms.\n\n\u2022 question_answer8) Write three different chemical reactions showing the conversion of ethanoic acid to sodium ethanoate. Write balanced chemical equation in each case. Write the name of the reactants and the products other than ethanoic acid and sodium ethanoate in each case.\n\n An element 'X' belong to 3rd period and group 13 of the Modern Periodic Table. (a) Determine the valence electrons and the valency of 'X'. (b) Molecular formula of the compound formed when 'X' reacts with an element 'Y' (atomic number = 8). (c) Write the name and formula of the compound formed when 'X' combines with \u00a0\u00a0\u00a0 chlorine.\n\n\u2022 question_answer10) The image formed by a spherical mirror is real, inverted and is of magnification -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.\n\n (a) Define focal length of a divergent lens. (b) A divergent lens of focal length 30 cm forms the image of an object of size 6 cm on the same side as the object at a distance of 15 cm from its optical centre. Use lens formula to determine the distance of the object from the lens and the size of the image formed. (c) Draw a ray diagram to show the formation of image in the above situation.\n\n#### Study Package\n\n##### 15 10\n\nLIMITED OFFER HURRY UP! OFFER AVAILABLE ON ALL MATERIAL TILL TODAY ONLY!\n\nYou need to login to perform this action.\nYou will be redirected in 3 sec","date":"2019-07-15 21:57:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.41065263748168945, \"perplexity\": 1454.5526747432043}, \"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-2019-30\/segments\/1563195524254.28\/warc\/CC-MAIN-20190715215144-20190716001144-00146.warc.gz\"}"} | null | null |
All site GEO Programs
Dialogue of Civilizations
Global Co-op
Global Quest
N.U.in
NU Network
Visa & Travel Information
Professor Daniel Aldrich Awarded Grant for Disasters and Recovery Dialogue
April 16, 2019 • from Intern
BOSTON, Massachusetts, Tuesday, April 16, 2019 (Northeastern University Global Experience Office)----- GEO would like to extend our warmest congratulations to Northeastern faculty member and Dialogue of Civilizations leader, Daniel Aldrich!
Professor Aldrich has been selected to receive a grant from the Center for Global Partnership in association with the Japan Foundation which will help to fund his Disasters and Recovery Dialogue to Japan this summer. The funds from this grant come to support grassroots and intellectual exchanges between the US and Japan and will help reduce the overall cost of the Dialogue for participating students.
For students, this funding will help to make the program more accessible for a wider number of students by providing some financial relief. In an email interview, Aldrich noted "all of the money is going to reduce student fees for our trip," something which can be a barrier to access for some students.
"The Japan Foundation has sought to expose more North Americans to Japanese culture," said Aldrich, "they indicated that our Dialogue of Civilizations [program] was a way to bring more students into contact with residents, NGOs, and decision makers in Japan."
Disasters and Recovery aims to educate college students based in North America the ways in which societies encounter shocks, and then are able to use resources to recover. "[The students] speak with survivors of [various] events in Japanese history," Aldrich added on how they would be able to expose the students to real-life examples.
These discussions will give students real-life examples of how a society is able to recover through first-hand accounts from survivors, "including [survivors of] the 1945 Hiroshima atomic bombing, the 1995 Kobe earthquake, and the 2011 triple disasters."
Disasters and Recovery is a month-long experience through a non-traditional "classroom in the field." Students will travel with a Northeastern University faculty member, in this case Professor Aldrich, as well as graduate student program assistants, to learn about these phenomena through literature as well as real-world experience.
"Through visits to the sites of disasters and crises and conversations with individuals who survived and helped respond to [these crises], the trip provides an experiential learning [opportunity] that is impossible to mimic in the classroom."
Read the original story
140 Cullinane Hall
617.373.5276 • geo@northeastern.edu
San Francisco | Bay Area
360 Huntington Ave., Boston, Massachusetts 02115 | 617.373.2000 | TTY 617.373.3768 | Emergency Information
© 2018 Northeastern University | MyNortheastern | {
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Q: Date doesnt update when I add $inc operator to update data in node, mongodb application The date attached to a data doesn't update/show current date when the data is updated.
I'e tried this but only the data is updated
findByIdAndUpdate(req.params.id,
{$inc: {quantity: req.body.quantity, sold: req.body.sold}},
{$set: {created_at: new Date()}},
(callback)=>{})
});
And when i try to put the the code for date before the $inc operator code i.e -
findByIdAndUpdate(req.params.id,
{$set: {created_at: new Date()}},
{$inc: {quantity: req.body.quantity, sold: req.body.sold}},
(callback)=>{})`
it works/show updated time but the $inc code doesnt work. Seems like i can only have one of them present in in update route and i need both to work
Here's the code
router.put('/stocks/:id', (req, res)=>{
Stocks.findByIdAndUpdate(req.params.id,
{$inc: {quantity: req.body.quantity, sold: req.body.sold}},
{$set: {created_at: new Date()}},
(err, updatedStock)=>{
if(err){
res.redirect('/stocks');
}
else{
res.redirect('/stocks'); // + req.params.id
}
})
});
I expect the the data along with the date and time to update
A: The third parameter in mongoose Model.findByIdAndUpdate() is used for options.
You would need to modify your call to something like this:
router.put('/stocks/:id', (req, res)=>{
Stocks.findByIdAndUpdate(req.params.id,
{
$inc: {quantity: req.body.quantity, sold: req.body.sold},
$set: {created_at: new Date()}
},
(err, updatedStock)=>{
if(err){
res.redirect('/stocks');
}
else{
res.redirect('/stocks'); // + req.params.id
}
})
});
Hope this helps :)
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This season is always the time to let loose and go a little crazier than normal. Blame it on summer activities that require us to get off our behinds and be a little more active and sociable. But while it's always fun, it usually leaves us feeling less than fresh. But at least there are small things we can do to help us smell like it.
No matter what perfume you wear, it will always die away with the day. So if you're staying out for long hours, we suggest to stick your scent to your fabrics. Use a fragrant fabric softener so that your chosen smell will linger in your clothes as you go about your summer activities.
Another trick to keep you smelling fresh is to just stick to one scent. If you want to smell like lavender, then make sure your shampoo, body lotion and even shower gel all follow the theme. This will help ensure that the smell will stay with you longer.
Using sunblock—even when you aren't at the beach—is essential. But if you don't want to have that sunblock smell on you the entire day, cheat it by mixing in some oils. But make sure not to mix smells if you're not sure; use this trick for non-scented sunblock.
We mean this literally; stick that bottle in the refrigerator. This will preserve the perfume's strength and quality, but it will also help it last longer when applied. And let's be honest, it would be amazingly refreshing to spritz on.
This is really a no-brainer, but it really is serious stuff. There probably isn't a more effective way to smelling and feeling fresh than taking constant showers. Whoever said you shouldn't wash your hair everyday did not live in a tropical country. | {
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Norrbäck is a settlement in the historical province of Uppland, Västmanland County, Sweden. Located in the Sala Municipality, it is about southeast of the city of Sala, and about northwest of Stockholm, the country's capital city.
Norrbäck's postal code (or postnummer) is 733 92. Its telephone dialing prefix is 46 and its area code is 22.
Amenities
There are no amenities in Norrbäck itself; the nearest are found in Sala.
The nearest church is Norrby kyrka, about to the north-west.
The few school-age children that live in Norrbäck attend school in nearby Varmsätra, to the southeast.
The nearest golf course is Sala-Heby Golfklubb on the northern side of riksvägen (highways) 72/56. (Heby is actually in Uppsala County but the golf club is open to residents of both Västmanland County and Uppsala County.)
Transportation
Road
Norrbäck is accessible from the northwest (via Norrby and Öja) from the combined highways 72 and 56 (Uppsalavägen), then länsväg (county road) 794; from the northeast on an unpaved road (via Isätra) by the same means; from the south (via Sörbäck) on highway 70; and from the east (indirectly) by Littersbovägen in Uppsala County.
Rail
Travel duration by train from Stockholm Central Station to Norrbäck's nearest station, Sala, varies by departure time and the tier of SJ train used. There are three high-speed services (SJ Snabbtåg) throughout the day: 03:36 (one change), 11:14 and 16:46. These take about 1 hour, 20 minutes. Similar-length SJ InterCity journeys depart at 06:14, 07:47, 09:44, 13:44, 15:47, 17:44 and 19:44.
Additionally, there are 23 SJ Regionaltåg and one SJ Tåg i Bergslagen options throughout the day. They each take around one hour and forty minutes (except the 11:40 and 21:12, which take about two hours and ten minutes, because the connecting mode of transport is a bus). They each make one stop — at either Uppsala Central Station or Västerås Central Station — except for the 22:14 SJ Tåg i Bergslagen, which is direct to Sala.
Bus
The number 66 bus, part of the Silverlinjen (Silver Line) run by VL, makes four daily (except Sunday) stops at Södra Kumlaby, which is a 15-minute walk from Norrbäck. The times are 07:10, 08:10, 12:10, 14:10 and 16:10. Boarding at Sala station, the eight stops (fifteen minutes) before Södra Kumlaby are Fiskartorget, Ekebygatan, Fredstorget, Fabriksgatan, Norrby Prästgård, Sörby (Varmsätra), Öja and Norra Kumlaby (Varmsätra).
References
External links
Travelling west along highway 72, through Boda, Isätra and Sala - YouTube user "WirWollen EuchNicht"
Norrbäck at Eniro.se
Uppland
Populated places in Västmanland County
Populated places in Sala Municipality | {
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Sedgewood off hwy 153! Beautiful 3/4 BR, 2 full bath one level home with an Open Floor plan, natural light and lots of updates. Tongue and groove Vautled ceilings in the Great Room with stone Fireplace from floor to ceiling. Office, Bedroom or Living Room off entry foyer. Breakfast room & Dining Room with picture window and sparkling white kitchen with new granite countertops & appliances. Hardwood & Tile flooring. New carpet, paint, hardware & lighting. Master Bedroom Suite with walk in closet and remodeled Bath freaturing 2 sinks, Tiled shower and separate tub. Fenced in backyard, storage building and relaxing deck. Private cul de sac location minutes from I-85, 15 minutes to Anderson and 10 mintues to downtown Greenville.
New two-story construction. Open floor plan with 9" ceilings on main level. Hardwoods throughout main level. Covered 12x16 porch and 4'x12' grilling deck. Crawlspace. Full sod. Vaulted master with spacious master bath and walk-in closet. | {
"redpajama_set_name": "RedPajamaC4"
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This cheesecake was one of the first things I learned how to make. It is an easy winner and I still bring it out today. It requires no oven too, just a fridge!
Crush the biscuits into a fine powder and add 150 grams of melted butter, combine until crumbly. Using your hands, press down the mixture into a 30cm round cake tin. There will be left over mixture to refrigerate and use again next time you make this fantastic cake. After you do this, set aside in the fridge.
For the filling combine 2 packets of Philadelphia cheese, cream, castor sugar, lemon juice and zest and 3 teaspoons of gelatin into a mixing bowl and using a beat mixer mix them until the mixtures is smooth.
Pour the mixture into the cake tin on top of the biscuit base.
Cut the strawberries into halves and arrange them on top of the cheesecake starting from the center and going around.
When you say three teaspoons of gelatin, what exactly do you mean? I thought you had to soak gelatin leaves in cold water? | {
"redpajama_set_name": "RedPajamaC4"
} | 9,809 |
class RegistrationsController < Devise::RegistrationsController
include JSONApiRender
def create
respond_to do |format|
format.json do
create_from_json
end
format.html do
super
end
end
end
def update
respond_to do |format|
format.json { update_from_json }
format.html { super }
end
end
def destroy
if current_user.valid_password?(params[:user][:current_password])
UserInfoScrubber.scrub_personal_info!(current_user)
Activation.disable_instances!([current_user])
Devise.sign_out_all_scopes ? sign_out : sign_out(resource_name)
set_flash_message! :notice, :destroyed
respond_with_navigational(resource){ redirect_to after_sign_out_path_for(resource_name) }
else
flash[:delete_alert] = "Incorrect password"
render action: :edit
end
end
private
def create_from_json
build_resource(sign_up_params)
resource_saved = resource.save
yield resource if block_given?
status, content = registrations_response(resource_saved)
clean_up_passwords resource
render status: status, json_api: content
end
def update_from_json
self.resource = resource_class.to_adapter.get!(send(:"current_#{resource_name}").to_key)
if resource.update_with_password(account_update_params)
UserInfoChangedMailerWorker.perform_async(resource.id, "password")
render json: {}, status: :no_content
else
render json: {errors: [{message: "Current password was incorrect, or new passwords did not match"}]}, status: :unprocessable_entity
end
rescue ActionController::UnpermittedParameters => e
render json: {errors: [{message: e.message}]}, status: :unprocessable_entity
end
def build_resource(sign_up_params={})
super(sign_up_params)
resource.display_name = resource.login if resource.display_name.blank?
resource.project_email_communication = resource.global_email_communication
resource.build_identity_group
end
def registrations_response(resource_saved)
if resource_saved
sign_in resource, event: :authentication
resource_scope = resource.class.where(id: resource.id)
[ :created, UserSerializer.resource({}, resource_scope, { include_private: true }) ]
else
response_body = {}
if resource && !resource.valid?
response_body.merge!({ errors: [ message: resource.errors ] })
end
[ :unprocessable_entity, response_body ]
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,758 |
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The root namespace for the entire #Journeta library. See..
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Preston Lee <preston.lee@prestonlee.com>
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,026 |
\section{Introduction and summary}
In a holographic correspondence, a quantum gravitational
system is exactly equivalent to a non-gravitational theory
on a lower dimensional space.
In known examples \cite{Maldacena:1997re,Gopakumar:1998ki}
the non-gravitational systems are gauge theories.
Gauge invariant observables are mapped
to non-normalizable deformations of the gravitational background.
Following progress in understanding the gravity duals of
local operators in a gauge theory, the recent years have seen further
extension of the dictionary to the realm of non-local gauge invariant operators.
The picture that has emerged is strikingly universal for all local and non-local
operators.
Consider operators of the form ${\rm Tr}_R(...)$, where the trace is
evaluated in a representation $R$
of $SU(N)$.
We will often use the symbol $R$ to denote the associated
Young diagram as well.
For different representations $R$, the operators are best described by
different objects on the gravity side.
The fundamental representation $R=\yng(1)$
corresponds to a fundamental string.
A high-rank symmetric representation corresponds to a D-brane, while an
anti-symmetric representation is given by another type of D-brane.
Finally, an operator with a large rectangular Young diagram is dual
to a smooth bubbling geometry with a flux supported on a new cycle.
A general Young diagram corresponds to a combination of these objects.
This pattern, summarized in Figure \ref{young-trans}, has been demonstrated for
local operators \cite{McGreevy:2000cw,Hashimoto:2000zp,
Balasubramanian:2001nh,Corley:2001zk,Lin:2004nb}
and Wilson loops \cite{Maldacena:1998im,Rey:1998ik,Drukker:2005kx,
Gomis:2006sb,
Yamaguchi:2006tq,
Hartnoll:2006is,Yamaguchi:2006te,
Gomis:2006im,
Lunin:2006xr,D'Hoker:2007fq} in ${\mathcal N}=4$ Yang-Mills,
as well as for Wilson loops in Chern-Simons theory
\cite{Gopakumar:1998ki, Gomis:2006mv,Gomis:2007kz,Okuda:2007ai}.
Higher dimensional non-local operators \cite{Gukov:2006jk,Gomis:2007fi,
Karch:2000gx,Lunin:2006xr,Gomis:2006cu,Lunin:2007ab}
in gauge theories
have descriptions in terms of branes and bubbling geometries.
\begin{figure}[ht]
\centering
\psfrag{a}{
\begin{tabular}{c}
Fundamental\\
string
\end{tabular}}
\psfrag{b}{
\begin{tabular}{c}
D3-brane on \\
$S^2\subset AdS_5$
\end{tabular}}
\psfrag{c}{
\begin{tabular}{c}
D5-brane on\\
$S^4\subset S^5$
\end{tabular} }
\psfrag{d}{\hspace{1.5mm}Bubbling geometry}
\includegraphics[scale=.45]{young-trans3.eps}
\caption{Gravity duals of Wilson loops in ${\mathcal N}=4$ Yang-Mills.
A string corresponds to the fundamental representation,
a D3-brane to a symmetric representation,
a D5-brane to an anti-symmetric representation,
and a bubbling geometry to the representation specified
by a rectangular Young diagram.
(D3-brane ..., D5-brane ...) in the figure should be replaced by (D3-brane wrapping $S^3\subset AdS_5$, D3-brane
wrapping $S^3\subset S^5$)
for local operators in ${\mathcal N}=4$ Yang-Mills, and by (D-brane, anti-D-brane)
for Wilson loops in Chern-Simons theory.
}
\label{young-trans}
\end{figure}
The identification of the operators and their dual bubbling geometries
has been made on the basis of symmetries and charges.
An interesting test of the identification, and AdS/CFT itself,
would be to compare the expectation value of an operator
with the on-shell supergravity action evaluated on the bubbling geometry.
For most operators, however, the test is trivial.
the expectation value vanishes for local operators,
and does not depend on the coupling for the straight Wilson line.
Even if the expectation value does not vanish, the computation
in the gauge theory is usually done only in weak coupling.
It is then hard to make comparison with the strong coupling
computation performed on the gravity side.
In this paper we make a non-trivial prediction for the bubbling geometries
dual to particular Wilson loops in ${\mathcal N}=4$ Yang-Mills,
by computing the vevs of the operators on the gauge theory side
{\it in the strong coupling regime}.
The operators are the circular supersymmetric Wilson loops
defined as
\ba
W_R\equiv
{\rm Tr}_R P \exp \oint (A+\theta^i \Phi^i ds). \label{Wilson-loop}
\end{eqnarray}
Here $A=A_\mu dx^\mu$ is the gauge field,
$\Phi^i$ ($i=1,...,6$) are the real scalars,
$s$ is a parameter for a circle in Euclidean ${\rm R}^4$ such that
$||dx/ds||=1$,
and $(\theta^i)$ is a constant unit vector in ${\rm R}^6$.
A smooth bubbling geometry is expected to be dual to a circular Wilson loop
whose Young diagram has long edges.
More precisely, if we parametrize the diagram as
in Figure \ref{parametrization},
$n_I$ for $I=1,...,g+1$ and $k_I$ for $I=1,...,g$ all have to be of order $N$ for the
geometry to be smooth.
The circular Wilson loop is very special
in that such strong coupling computation from gauge theory is possible,
due to the conjecture \cite{Drukker:2000rr} that
the Gaussian matrix model captures the circular Wilson loops
to all orders in $1/N$ and the 't Hooft coupling $\lambda=g_{YM}^2 N$.
\begin{figure}[htbb]
\begin{center}
\psfrag{n1}{$n_1$}
\psfrag{k1}{$k_1$}
\psfrag{n2}{$n_2$}
\psfrag{kg-1}{$k_{g-1}$}
\psfrag{ng}{$n_g$}
\psfrag{kg}{$k_g$}
\psfrag{ng+1}{$n_{g+1}$}
\includegraphics[width=80mm]{maya-R3.eps}
\caption{The Young diagram $R$, shown rotated and inverted,
is specified by the lengths $n_I$ and $k_I$ of the
edges.
Equivalently, $n_I$ and $k_I$ denote the lengths
of the black and white regions in
the Maya diagram.
$n_{g+1}$ is defined by $\sum_{I=1}^{g+1} n_I=N$.
}
\label{parametrization}
\end{center}
\end{figure}
Relegating the computations to later sections,
let us simply summarize the main result:
in the limit $N\ra\infty$ with $n_I/N$ and $k_I/N$ kept finite,
and for the large finite 't Hooft coupling $\lambda$,
the vev of the circular Wilson loop in the Yang-Mills
with gauge group $SU(N)$ is given by
\ba
\langle W_R\rangle
&=&
\exp\left( \frac{\lambda}{8N} \sum_{I=1}^{g+1} n_I (K_I-|R|/N)^2
+{\mathcal O}(N^2\log \lambda)\right).
\label{the-results}
\end{eqnarray}
Here $|R|$ is the n-ality, i.e., the number of boxes in $R$.
We have also defined $K_{I}=k_{I}+k_{I+1}+...+k_{g}$
for $1\leq I\leq g$ and $K_{g+1}=0$.
An important check of the result is
that it is invariant under
complex conjugation $R\ra \bar R$ of the representation,
or in terms of the parameters, under
\ba
n_I \ra n_{g+2-I},~~
k_{I}\ra k_{g+1-I}.
\end{eqnarray}
We expect that the Wilson loop vev is related to the on-shell supergravity
action $S_{\rm sugra}$ as
\ba
\langle W_R\rangle \sim e^{-S_{\rm sugra}}.
\end{eqnarray}
Note that $\langle W_R\rangle =e^{{\mathcal O} ( N^2 \lambda)}$ in our regime.
The quadratic dependence on $N$ of the exponent is
what is expected from the supergravity action
$S_{\rm sugra}=(1/2\kappa^2)\int \sqrt{g}R+...$
with $\kappa^2\sim g_s^2\alpha'^4$, to be evaluated
on the dual geometry.
This result is obtained
by studying the Gaussian matrix model
that captures the correlation functions
of circular Wilson loops.
In fact we turn the Gaussian matrix model
with operator insertions into
multi-matrix models whose partition functions
are the Wilson loop vevs.
We perform the saddle point analysis
and propose the eigenvalue distributions.
Based on this proposal, we are able to calculate
the Wilson loop vevs with the result (\ref{the-results}).
The circular Wilson loops in Euclidean ${\rm R}^4$
can also be thought of as operators in
the ${\mathcal N}=4$ Yang-Mills defined on $S^4$ \cite{Drukker:2000rr}.
The loop is now the equator of $S^4$, and
the $SO(2)\times SO(3)$ subgroup
of the $SO(5)$ isometry group is preserved.
The $SO(2)$ is part of the preserved
subgroup $SU(1,1)$ of the conformal group $SO(1,5)$.
The operator (\ref{Wilson-loop}) also preserves
an $SO(5)$ subgroup of the $SO(6)$ R-symmetry group.
Thus the bubbling geometry duals of the Wilson loops
must solve the BPS equations of the type IIB supergravity
with the $EAdS_2 \times S^2 \times S^4$ ansatz.
Note that we need to work with Euclidean signatures
since the matrix model captures the circular loop
in Euclidean ${\rm R}^4$ only.
The resulting geometries should be the Euclidean continuation of the
solutions recently found in \cite{D'Hoker:2007fq}.
Given the result of the present paper,
the challenge is to use the dual geometries to reproduce the
prediction (\ref{the-results}) by computing the on-shell
supergravity action \cite{bub}.
One would need to deal with such subtle issues as
volume regularization, counter terms, and ambiguity of the action
due to self-duality of the 5-form flux.\footnote{
The parallel problem of matching the Wilson loop vev and the
closed string partition function has been solved
for the Chern-Simons/conifold duality to all orders
in genus expansion \cite{Gomis:2006mv}.
The matching of the Wilson loop vevs and the dual on-shell
D-brane actions
has also been demonstrated \cite{Drukker:2005kx,Yamaguchi:2006tq,
Hartnoll:2006is} for ${\mathcal N}=4$ Yang-Mills.
}
Though the analysis of
the matrix models for ${\mathcal N}=4$ Yang-Mills
is in principle sufficient,
much confidence in the results and the proposed eigenvalue distributions
comes from the study of surprisingly analogous
matrix models that describe the Wilson loops
in Chern-Simons theory \cite{Marino:2002fk,Aganagic:2002wv,cs-mat}.
For these matrix models, the resolvents and the spectral curves
can be computed exactly in the limit $N\ra\infty$,
with $n_I/N$ and $k_I/N$ kept finite,
without the assumption that the 't Hooft coupling is large.
The eigenvalue distributions turn out to be
qualitatively the same for the ${\mathcal N}=4$
Yang-Mills and Chern-Simons theory.
The paper is organized as follows.
In section \ref{matrix-wilson}, we review
the correspondence between the circular
Wilson loops in ${\mathcal N}=4$ Yang-Mills and
the observables in the Gaussian matrix model.
In section \ref{rectangle} we analyze
the Wilson loop with a rectangular
Young diagram.
Section \ref{general} deals with the Wilson loops
in general representations that admit
smooth dual bubbling geometries.
\section{Gaussian matrix model for circular Wilson loops}
\label{matrix-wilson}
It is believed \cite{Drukker:2000rr,Erickson:2000af}
that the correlation functions of circular
loops in ${\mathcal N}=4$ Yang-Mills are
captured by the Gaussian matrix model.
The precise correspondence states
in particular that
\ba
\left\langle {\rm Tr}_R P \exp \oint (A+\theta^i X^i ds)\right\rangle_{U(N)}
=
\frac{1} Z \int dM \exp\left({-\frac{2N}\lambda {\rm Tr} M^2}\right)
{\rm Tr}_R e^M. \label{mat-wil-U}
\end{eqnarray}
The left-hand side is the normalized expectation value
in the Yang-Mills with gauge group $U(N)$.
The right-hand side is normalized by using
the partition function $Z$ which is
the integral without the insertion of ${\rm Tr}_R e^M$.
$dM$ is the standard hermitian matrix measure.
In the absence of operator insertions, the eigenvalues
are distributed according to the Wigner semi-circle law
in the large $N$ limit.
The eigenvalue density $\rho(m)$, normalized so that $\int \rho(m) dm=1$,
is given by
\ba
\rho(m)=\frac{2}{\pi\lambda}\sqrt{\lambda-m^2}.
\end{eqnarray}
We are also interested in the $SU(N)$ Yang-Mills theory,
for which the conjecture in \cite{Drukker:2000rr} states that
\ba
\left\langle {\rm Tr}_R P \exp \oint (A+\theta^i X^i ds)\right\rangle_{SU(N)}
=
\frac{1} Z \int dM \exp
\left(-\frac{2N}\lambda {\rm Tr} M^2\right)
{\rm Tr}_R \hspace{.4mm} e^{M'}. \label{mat-wil-SU}
\end{eqnarray}
Note that on the right-hand side we need the traceless part
\ba
M':=M-\frac{1}{N}{\rm Tr} M\cdot 1_N \label{Mprime}
\end{eqnarray}
of the matrix $M$ so that $e^{M'}\in SU(N)$.
The relation
\ba
{\rm Tr}_R\hspace{.4mm} e^{M'}= (\det e^M)^{-|R|/N} {\rm Tr}_R e^M \label{TrM'}
\end{eqnarray}
will be useful later.
Matrix integrals
have been studied intensively in the past,
partly motivated by non-critical string theory
\cite{Ginsparg:1993is, Francesco:1993nw}
and relation to supersymmetric gauge theories
\cite{Dijkgraaf:2002fc,Dijkgraaf:2002dh}.
In these contexts one does not encounter operators of the form
${\rm Tr}_R e^M$ with the Young diagram $R$ that is large
both in the row and column directions,
and it appears that there is no study of them in the literature.\footnote{
I thank E. Martinec for a discussion on this point.}
\section{Rectangular Young diagram}\label{rectangle}
In this section, we formulate
2-matrix models whose partition functions
are the vev of the Wilson loop
with a rectangular Young diagram shown in Figure \ref{rectan}.
We will have two such matrix models.
The first captures the geometric transition
of D5-branes wrapping $S^4\subset S^5$ in $AdS_5\times S^5$.
The second is similarly interpreted in terms of
D3-branes wrapping $S^2\subset AdS_5$.
The techniques we introduce here are a generalization
of the methods used in \cite{Hartnoll:2006is}.
The pictures that emerge are similar to those of
\cite{Yamaguchi:2006tq,Yamaguchi:2007ps}.
\begin{figure}[htbb]
\begin{center}
\psfrag{l}{$k$}
\psfrag{n}{$n$}
\includegraphics[width=50mm]{rectan1.eps}
\caption{A rectangular Young diagram with $n$ rows and $k$ columns.
}
\label{rectan}
\end{center}
\end{figure}
\subsection{Eigenvalues as D5-branes} \label{rec-D5}
We begin with the Yang-Mills with gauge group $U(N)$.
Let $U$ be a unitary matrix
and consider a sum over all the Young diagrams for which
the summand is non-vanishing:
\ba
\sum_R
{\rm Tr}_R e^M
{\rm Tr}_{R^T} U
=
\det(1+
e^M\otimes U).\label{RRT-det}
\end{eqnarray}
Here $R^T$ is the transpose of $R$.
This identity, expressed in terms of Schur polynomials
as
\ba\sum_R s_R(x)s_{R^T}(y)=\prod_{i,j}(1+x_iy_j)
~~\hbox{ for } x=(x_i) \hbox{ and } y=(y_j),
\end{eqnarray}
is well-known \cite{Macdonald}.
The relation can be inverted:
\ba
{\rm Tr}_R e^M=\int dU \det(1+e^M\otimes U^\mo){\rm Tr}_{R^T}U. \label{inversion}
\end{eqnarray}
Here $dU$ is the Haar measure on the unitary group normalized
so that $\int dU=1$.
We now specialize to the rectangular Young diagram
$R$ with $n$ rows and $k$ columns.
We choose $U$ to be a $k\times k$ unitary matrix.
This choice has a considerable advantage.
Let us recall the character formula \cite{Fulton}
\ba
{\rm Tr}_R X=\frac{\det(x_b{}^{n-a+R_a})}{\det(x_b{}^{n-a})}~~
\hbox{for $X={\rm diag}(x_1,...,x_k)$ and arbitrary $R$},\label{character}
\end{eqnarray}
where $R_a$ is the number of boxes in the $a$-th row of $R$.
It implies that
\ba
{\rm Tr}_{R^T} U=(\det U)^n \label{tr-det}
\end{eqnarray}
for the rectangular diagram $R$ and {\it for
the $k\times k$ matrix} $U$.\footnote{
This can also be understood as follows.
A column of length $k$ gives the rank-$k$ anti-symmetric
representation $A_k$.
The rectangular diagram $R$ is obtained
by symmetrizing $n$ copies of $A_k$.
The representation $A_k$ for $U(k)$ is one dimensional
and the trace in $A_k$ is the determinant.
Thus ${\rm Tr}_{R^T} U={\rm Tr}_{{\rm Sym}^n (A_k)} U
={\rm Tr}_{A_k{}^{\otimes n}}U=(\det U)^n$.
}
By substituting (\ref{inversion}) and (\ref{tr-det})
into (\ref{mat-wil-U}), we conclude that
\ba
\langle W_R\rangle_{U(N)}&=&\frac{1} Z \int dM dU \exp\left(
-\frac{2N}{\lambda}{\rm Tr} M^2\right)
\det(1+ e^M\otimes U^\mo)
(\det U)^n.
\end{eqnarray}
By diagonalizing the matrices as
\ba
M={\rm diag} (m_i)_{i=1}^N,~U={\rm diag} (e^{u_a})_{a=1}^k,
\end{eqnarray}
and redefining $U\ra - U$,
the vev can be written as
\ba
\langle W_R\rangle_{U(N)}&\propto&
\int \prod_a du_a\prod_i dm_i
\exp\Bigg[ -\frac{2N}{\lambda}\sum_{i=1}^N
m_i^2+\sum_{i<j}\log(m_i-m_j)^2+n\sum_{a=1}^k u_a\nonumber\\
&&~~~+ \sum_{a<b}\log\left( 2\sinh\frac{u_a-u_b}{2}\right)^2
+\sum_{a,i} \log(1- e^{m_i-u_a} )\Bigg].
\label{vev1}
\end{eqnarray}
The constant of proportionality is independent of $k$ and $n$,
is negligible in the precision we work with, and is thus dropped.
Since the integrand is analytic, the contours of integration
may be deformed.
Each $u_a$ is integrated over a period $2\pi i$.
The leading behavior of the Wilson loop vev in the large $N$ limit can be
computed in the saddle point approximation.
Note that all the terms in the exponent in (\ref{vev1}) are of order $N^2$.
We thus expect a back-reaction of the $m$-eigenvalue
distributions to the $u$-eigenvalues.
This is in contrast to the case with a single row or column
\cite{Hartnoll:2006is}.
The saddle point equations are
\ba
-\frac{4N}\lambda m_i+2\sum_{j\neq i}\frac{1}{m_i-m_j}-\sum_a\frac{1}{e^{u_a-m_i}-1}=0, \label{m-EOM1}
\\
n+\sum_{b\neq a}\coth\frac{u_a-u_b}2 +\sum_i \frac{1}{e^{u_a-m_i}-1}=0. \label{u-EOM1}
\end{eqnarray}
One can get useful intuitions by interpreting
these equations as force balance conditions.
The first term in (\ref{m-EOM1}) is a restorative force on $m_i$.
The first term in (\ref{u-EOM1}) represents a constant force applied to
each $u_a$.
These are the external forces acting on the system of eigenvalues.
The other terms are mutual repulsive forces among $m_i$'s and $u_a$'s.
In the absence of $u$-eigenvalues, the $m$-eigenvalues
obey Wigner's semicircle law
and spread over an interval of width $2\sqrt\lambda$.
This motivates us to assume that the $m$- and $u$-eigenvalues spread
over regions of length scale $\sqrt\lambda$.
Under this assumption that will be justified a posteriori,
for large values of $\lambda$,
we can approximate various expressions as follows:
\ba
\frac{1}{e^{u_a-m_i}-1}&=&
\Bigg\{
\begin{array}{cc}
-1& \hbox{~if~} u_a<m_i \\
0 & \hbox{~if~} m_i<u_a
\end{array},\label{u-m-simplify}
\\
\coth{\frac{u_a-u_b}2}
&=&
\Bigg\{
\begin{array}{cc}
-1& \hbox{~if~} u_a<u_b \\
+1 & \hbox{~if~}u_b<u_a
\end{array}.\label{u-u-simplify}
\end{eqnarray}
We now propose an eigenvalue distribution
that solves the saddle point equations.
Suppose that the eigenvalues $m_i$ split into
the first group $\{m^{(1)}_i|i=1,...,n\}$ on the right
and the second one $\{m^{(2)}_i|i=1,...,N-n\}$ on the left.
All the $u_a$'s are between them.
We also assume that the two groups are far enough from each other
so that $1/(m^{(1)}_i-m^{(2)}_j)$ can be ignored.
After we apply (\ref{u-m-simplify}) and (\ref{u-u-simplify}),
(\ref{m-EOM1}) becomes
\ba
-\frac{4N}\lambda m^{(1)}_i+2 \sum_{j\neq i}\frac{1}{m^{(1)}_i-m^{(1)}_j}+k=0,
\label{EOM-m(1)}\\
-\frac{4N}\lambda m^{(2)}_i+2 \sum_{j\neq i}\frac{1}{m^{(2)}_i-m^{(2)}_j}=0.
\label{EOM-m(2)}
\end{eqnarray}
Then the two groups individually
obey Wigner's semi-circle law.
The first group is spread over an interval of width
$2\sqrt{g_s n}={\mathcal O}(\sqrt{\lambda})$
centered at $k\lambda/4N $.
For the second group the interval is centered at the origin
with width $2\sqrt{g_s(N-n)}={\mathcal O}(\sqrt\lambda)$.
(\ref{u-EOM1}) simplifies to
\ba
\sum_{b\neq a}\coth\frac{u_a-u_b}2=0.
\end{eqnarray}
This equation is solved by $u_a$'s uniformly distributed along a line
in the imaginary direction.
The precise location of the line cannot be determined in this approximation.
See Figure \ref{D5eigenvalues-rec}.
\begin{figure}[btp]
\begin{center}
\psfrag{N-n}{$N-n$}
\psfrag{l}{$k$}
\psfrag{n}{$n$}
\includegraphics[width=60mm]{D5eigenvalues-rec2.eps}
\caption{
The eigenvalue distributions in the rectangular case.
The $m$-eigenvalues shown as black lines
split into two groups, $\{m_i^{(1)}\}$
on the right and $\{m_i^{(2)}\}$ on the left.
The $u$-eigenvalues
are distributed uniformly along the red line in the
imaginary direction.
}
\label{D5eigenvalues-rec}
\end{center}
\end{figure}
The parallel matrix model problem in the Chern-Simons case
admits an exact solution for the finite 't Hooft parameter \cite{cs-mat}.
It exhibits an essentially identical distribution of eigenvalues.
This gives us confidence in our proposal of the distribution.
We now use the eigenvalue distribution to
evaluate the Wilson loop vev.
The exponent in (\ref{vev1}) can be evaluated,
with the help of (\ref{u-m-simplify}) and (\ref{u-u-simplify}),
as
\ba
&&
-\frac{2N}\lambda \sum_i (m^{(1)}_i)^2+k\sum_i m^{(1)}_i
+\sum_{i<j}\log (m^{(1)}_i-m^{(1)}_j)^2
-\frac{2N}\lambda \sum_i ({m^{(2)}_i})^2
\nonumber\\
&&+\sum_{i<j}\log (m^{(2)}_i-m^{(2)}_j)^2
+{\mathcal O}(N^2\log \lambda)\nonumber\\
&=&
\frac{ n k^2\lambda}{8N}+{\mathcal O}(N^2\log \lambda).
\label{exponent1}
\end{eqnarray}
The last term arises from completion of squares:
\ba
-(2N/\lambda)( m_i^{(1)})^2
+k m^{(1)}_i=
-(2N/\lambda) (m_i^{(1)}-k\lambda/4N)^2 + k^2\lambda/8N.
\nonumber
\end{eqnarray}
We thus conclude that
\ba
\langle W_R\rangle_{U(N)}=\exp\left(\frac{nk^2\lambda}{8N}+{\mathcal O} (N^2\log\lambda)\right).
\end{eqnarray}
In the $SU(N)$ case,
we need to work with $M'$ defined in (\ref{Mprime}).
Because of (\ref{TrM'}), the Wilson loop vev is given by
\ba
\langle W_R\rangle_{SU(N)}
=\frac{1} Z \int dM dU
e^{-\frac{2N}{\lambda}{\rm Tr} M^2}
\left(\det e^M\right)^{-\frac{kn}N}
\det(1+ e^M\otimes U^\mo)
(\det U)^n.
\end{eqnarray}
(\ref{exponent1}) is replaced by
\ba
-\frac{2N}\lambda \sum_i ({m^{(1)}_i})^2+k\sum_i m^{(1)}_i
-\frac{kn}N \sum_i m^{(1)}_i
+\sum_{i<j}\log (m^{(1)}_i-m^{(1)}_j)^2
\nonumber\\
-\frac{2N}\lambda \sum_i ({m^{(2)}_i})^2
+\sum_{i<j}\log (m^{(2)}_i-m^{(2)}_j)^2
-\frac{kn}N \sum_i m^{(2)}_i.
\label{exponent2}
\end{eqnarray}
The leading parts in $\lambda$ comes from
completion of squares:
\begin{equation}
-\frac{2N}\lambda (m^{(1)}_i)^2+k m^{(1)}_i-\frac{kn}N m^{(1)}_i
=-\frac{2N}\lambda \left(m^{(1)}_i-\frac{\lambda}{4N}k\left(1-\frac{n}N\right)\right)^2
+ \frac{\lambda k^2}{8N}\left(1-\frac{n}N\right)^2,\nonumber
\end{equation}
\begin{equation}
-\frac{2N}\lambda (m^{(1)}_i)^2-\frac{kn}N m^{(1)}_i
=-\frac{2N}\lambda \left(m^{(1)}_i+\frac{\lambda}{4N}k\frac{n}N\right)^2
+ \frac{\lambda k^2}{8N}\left(\frac{n}N\right)^2.\nonumber
\end{equation}
We find that
\ba
\langle W_R\rangle_{SU(N)}&=&
\exp \left(
n\frac{\lambda k^2}{8N}\left(1-\frac{n}N\right)^2
+(N-n)\frac{\lambda k^2}{8N}\left(\frac{n}N\right)^2
+{\mathcal O}(N^2\log\lambda)
\right)
\nonumber\\
&=&\exp\left(
\frac{\lambda k^2}{8N^2}n(N-n)+{\mathcal O}(N^2\log\lambda)\right).
\end{eqnarray}
This is the special case of (\ref{the-results}),
and is invariant under $R\ra\bar R$ or $n\rightarrow N-n$ as it should be.
Recall that each column in $R$ represents a D5-brane.
Since we have as many $u$-eigenvalues as columns,
we identify the eigenvalues with D5-branes.
The back-reaction of the $m$-eigenvalues to the existence of $u$-eigenvalues
then represents the back-reaction of the geometry to the branes,
i.e., geometric transition.
Without operator insertions, there is a single black region
representing $AdS_5\times S^5$.
The hole in the region, which was identified with D5-branes
in \cite{Yamaguchi:2006te}, is created by the repulsion
of $m_i$ and $u_a$ in the present formulation.
This is the Wilson loop analog of giant graviton branes
represented by a hole in the fermion droplet \cite{Lin:2004nb}.
In the topological and non-critical string literature
\cite{Aganagic:2003qj,Maldacena:2004sn},
it is well-known that the insertion of a determinant operator
similar to $\det(1+e^M\otimes U)$ represents non-compact D-branes.
In those cases the eigenvalues of $U$ are the moduli of branes.
Here there is a difference: the eigenvalues are first integrated over
and are fixed only by saddle point equations.
\subsection{Eigenvalue bound states as D3-branes}
If we make use of the identity \cite{Macdonald,Fulton}
\ba
\sum_R {\rm Tr}_R V{\rm Tr}_R e^M=\frac{1}{\det(1-V\otimes e^M)} \label{RR-det}
\end{eqnarray}
instead of (\ref{RRT-det}), we have another expression for ${\rm Tr}_R e^M$:
\ba
{\rm Tr}_R e^M=\int dV \frac{1}{\det(1-V^\mo \otimes e^M)}{\rm Tr}_R V.
\end{eqnarray}
$dV$ is the Haar measure on the unitary group.
More precisely, the contours need to be deformed so
that the eigenvalues of $V$ are
larger than those of $e^M$ in magnitude.
We choose $V$ to be an $n\times n$ unitary matrix,
so that
\ba
{\rm Tr}_R V=(\det V)^k
\end{eqnarray}
for the rectangular Young diagram $R$.
We find that the Wilson loop vev is given by another 2-matrix model
\ba
\langle W_R\rangle_{U(N)}&=&
\frac{1} Z\int dM dV \exp\left(-\frac{2N}{\lambda}{\rm Tr} M^2\right)
\frac{1}{\det(1-V^\mo\otimes e^M)}
(\det V)^k.
\end{eqnarray}
By diagonalizing the matrices, we get
\ba
\langle W_R\rangle_{U(N)}&\propto
&\int \prod_a dv_a\prod_i dm_i
\exp\Bigg[ -\frac{2N}{\lambda}\sum_{i=1}^N
m_i^2+\sum_{i<j}\log(m_i-m_j)^2+k\sum_{a=1}^n v_a\nonumber\\
&&~~~+ \sum_{a<b}\log\left( 2\sinh\frac{v_a-v_b}{2}\right)^2
-\sum_{a,i} \log(1- e^{m_i-v_a} )\Bigg].
\label{vev}
\end{eqnarray}
Let us now analyze this model in the limit $N\ra \infty$
with $\lambda, n/N$, and $k/N$ finite.
The saddle point equations are
\ba
-\frac{4N}\lambda m_i+2\sum_{j\neq i}\frac{1}{m_i-m_j}+\sum_a\frac{1}{e^{v_a-m_i}-1}=0, \label{m-EOM2}
\end{eqnarray}
and
\ba
k+\sum_{b\neq a}\coth\frac{v_a-v_b}2 -\sum_i \frac{1}{e^{v_a-m_i}-1}=0. \label{v-EOM2}
\end{eqnarray}
Again these equations can be interpreted as
force balance conditions for the eigenvalues.
The difference from the previous subsection
is that the interaction between $m_i$ and $v_a$ is {\it attractive}.
Let us study the eigenvalue distribution for finite but large $\lambda$.
The $v$-eigenvalues as a whole are pulled to the right
by a force of magnitude $kn$.
Unlike in the previous subsection,
we cannot apply (\ref{u-m-simplify}) and (\ref{u-u-simplify})
to the terms involving $m_i$ and $v_a$.
If we did, $v_a$ would only be pulled to the right by $m_i$,
and the force balance would not be achieved.
This suggests that each $v_a$ must be very close to $m_i$.
Each $v$-eigenvalue is pulled to the right by a force
of magnitude $k$.
To balance this, we assume that the $v$-eigenvalue and
an $m$-eigenvalue sit very close to each other.
We also assume, as will be justified a posteriori,
that this distance is much smaller than
all other length scales in the problem.
There are $n$ $v$-eigenvalues and they are paired up with
as many $m$-eigenvalues $m^{(1)}_i$ ($i=1,...,n$),
forming $n$ {\it bound states}.
The bound states are
denoted by ($m$-$v$)${}_a$,~$a=1,...,n$.
If we order the eigenvalues so that
$m^{(1)}_1\lesssim v_1<m^{(1)}_2\lesssim v_2<...<m^{(1)}_n\lesssim v_n$,
$v_a$ is pushed to the right by $v_1,...,v_{a-1}$.\footnote{
Strictly speaking, for $b$ such that $0<a-b\lesssim N/\sqrt\lambda$
(\ref{u-u-simplify}) cannot be applied.
The error from ignoring the effects, however,
is cancelled by the error from ignoring the forces
from $v_b$ with $0<b-a\lesssim N/\sqrt\lambda$.
}
It is also pushed to the left by $v_{a+1},...,v_n$,
but these forces are cancelled by the pull of $m^{(1)}_{a+1},...,m^{(1)}_n$.
Thus (\ref{v-EOM2}) in the approximation (\ref{u-u-simplify}) becomes
\ba
k+a-\frac{1}{v_a-m^{(1)}_a}+{\mathcal O}(N/\sqrt\lambda)=0.
\end{eqnarray}
The size of the $a$-th bound state is thus $1/(k+a)$.
Assuming that the group of bound states and the group of
remaining $m$-eigenvalues $\{m^{(2)}_i|i=1,...,N-n\}$
are far enough from each other,
we can replace
(\ref{m-EOM2}) by
(\ref{EOM-m(1)}) and (\ref{EOM-m(2)}).
Since the $m$-eigenvalues are governed by the same equations
as in the previous subsection, their distribution is the same.
The distribution of the $v$-eigenvalues is identical
to the distribution of $m^{(1)}_i$ on the macroscopic scale.
This then justifies the assumptions made in the argument.
The computation of the Wilson loop vev is also identical.
Each row in the Young diagram represents a D3-brane \cite{Gomis:2006sb,
Gomis:2006im}.
The rectangular diagram $R$ then corresponds to $n$ D3-branes.
Since we have the same number of bound states,
it is natural to identify each bound state with a D3-brane.
This is the analog of an extra droplet in \cite{Lin:2004nb}
where it was interpreted as dual giant graviton branes
wrapping $S^3$ in $AdS_5$ .
\begin{figure}[tb]
\begin{center}
\psfrag{dist1}{$\sim 1/(k+a)$}
\psfrag{dist2}{$\sim {\mathcal O}(\sqrt\lambda/N)$}
\psfrag{m}{$m^{(1)}_a$}
\psfrag{v}{$v_a$}
\psfrag{m2}{$m^{(1)}_{a+1}$}
\psfrag{v2}{$v_{a+1}$}
\includegraphics[width=120mm]{moleculesA2.eps}
\caption{
The eigenvalue bound states ($m$-$v$)${}_a$.
The distance between the two eigenvalues
in the $a$-th bound state from the left is $1/(k+a)$.
The distance between neighboring bound states is
much larger and is of the order $\sqrt\lambda/N$.
}
\label{moleculesA}
\end{center}
\end{figure}
\begin{figure}[bt]
\begin{center}
\psfrag{N-n}{$N-n$}
\psfrag{n}{$n$}
\psfrag{m1}{$\{ (m\hbox{-}v)_a\}$}
\psfrag{m2}{$\{m_i^{(2)}\}$}
\includegraphics[width=120mm]{D3eigenvalues-rec2.eps}
\caption{
The eigenvalue distributions for $M={\rm diag}(m_i)_{i=1}^N$
and $V={\rm diag}(e^{v_a})_{a=1}^n.$
$\{m_i\}$ split into two groups $\{m_i^{(1)}\}$
and $\{m_i^{(2)}\}$.
The $n$ $v_a$'s are paired with as many $m_i^{(1)}$'s
to form $n$ bound states $(m\hbox{-}v)_a$.
These bound states are distributed according to Wigner's
semicircle law, as represented by the coincident
black and red lines on the right.
The distribution of the remaining $N-n$ $m_i^{(2)}$'s
independently obeys the semicircle law and is shown on the left.
}
\label{D3-eigenvalues-rec}
\end{center}
\end{figure}
\section{General Young diagram}\label{general}
This section deals with a general Young diagram of the form shown
in Figure \ref{parametrization}, with edge lengths
$n_I$ and $k_I$ all of order $N$.
We will obtain two multi-matrix models
whose partition functions are the Wilson loop vev.
\subsection{Eigenvalue bound states as D5-branes}
\begin{figure}[htbb]
\begin{center}
\psfrag{R}{$R\equiv R^{(1)}$}
\psfrag{R1}{$R^{(2)}$}
\psfrag{Rm-1}{$R^{(g-1)}$}
\psfrag{Rm}{$R^{(g)}$}
\psfrag{K1}{$K_1$}
\psfrag{K2}{$K_2$}
\psfrag{Km-1}{$K_{g-1}$}
\psfrag{Km}{$K_{g}$}
\includegraphics[width=120mm]{D5Young-split5.eps}
\caption{
A shrinking sequence of Young diagrams
$R\equiv R^{(1)}\supset R^{(2)}\supset...\supset R^{(g)}$.
}
\label{D5Young-split}
\end{center}
\end{figure}
Let us first see how to generalize the trick that led to 2-matrix models
in the rectangle case.
We begin with the expression
\ba
{\rm Tr}_{R} e^M
=\int dU^{(1)} \det(1+e^M\otimes U^{(1)\mo}){\rm Tr}_{R^T} U_1.
\end{eqnarray}
Here $U^{(1)}\in U(K_1)$.
Recall that $K_I\equiv \sum_{J=I}^g k_J$.
(\ref{character}) in this case allows us to write
\ba
{\rm Tr}_{R^T} U^{(1)}=(\det U^{(1)})^{n_1}{\rm Tr}_{R^{(2)}{}^T} U^{(1)}.
\end{eqnarray}
Here $R^{(2)}$ is obtained by removing the first $n_1$ rows from $R$.
See Figure \ref{D5Young-split}.
Similarly,
\ba
{\rm Tr}_{R^{(2)}{}^T} U^{(1)}
&=&\int dU^{(2)}
\frac{1}{\det(1-U^{(1)}\otimes U^{(2)}{}^\mo)}{\rm Tr}_{R^{(2)}{}^T} U^{(2)},
\end{eqnarray}
with $U^{(2)}$ in $U(K_2)$.
To be more precise, to avoid singularities
the integral is performed along
the contours such that the eigenvalues of $U^{(2)}$ are
larger than those of $U^{(1)}$ in magnitude.
This time we have the relation
\ba
{\rm Tr}_{R^{(2)}{}^T} U^{(2)}=(\det U^{(2)})^{n_2}{\rm Tr}_{R^{(3)}{}^T} U^{(2)}.
\end{eqnarray}
By removing the first $n_2$ rows from $R^{(2)}$
one obtains $R^{(3)}$.
We now repeat the procedure as many times as we can.
This yields
\ba
&&{\rm Tr}_{R} e^M\nonumber\\
&=&
\hspace{-3mm}
\int
\hspace{-1mm}
dU^{(1)}
\det(1+e^M\otimes U^{(1)}{}^\mo)(\det U^{(1)})^{n_1}
\hspace{-2mm}
\int
\hspace{-1mm}
dU^{(2)}
\frac{1}{\det(1-U^{(1)}\otimes U^{(2)}{}^\mo)}
(\det U^{(2)})^{n_2}\nonumber\\
&&~~...\int dU^{(g)}
\frac{1}{\det(1-U^{(g-1)}\otimes U^{(g)}{}^\mo)}
(\det U^{(g)})^{n_g}.
\end{eqnarray}
Here $U^{(I)}\in U(K_I)$,
and the integration contours are deformed so that
the eigenvalues of $U^{(I)}$ have larger absolute values
than those of $U^{(I-1)}$.
We thus have
\ba
&&
\left\langle
W_R\right\rangle_{U(N)}
=
\frac{1} Z\int dM dU^{(1)} dU^{(2)}... dU^{(g)}
e^{-\frac{2N}{\lambda}{\rm Tr} M^2}
(\det U^{(1)})^{n_1}(\det U^{(2)})^{n_2}...(\det U^{(g)})^{n_g}
\nonumber\\
&&~~~~~
\times\det(1+e^M\otimes U^{(1)}{}^\mo)
\frac{1}{\det(1-U^{(1)}\otimes U^{(2)}{}^\mo)}
...
\frac{1}{\det(1-U^{(g-1)}\otimes U^{(g)}{}^\mo)}.
\end{eqnarray}
After redefining $U^{(I)}\ra -U^{(I)}$ and
diagonalizing the matrices as $M={\rm diag}(m_i)_{i=1}^N$,
$U^{(I)}={\rm diag}(e^{u_a^{(I)}})_{a=1}^{K_I}$, this becomes
\ba
\langle W_R\rangle &\propto&
\int \prod dm_i
\prod du^{(I)}_a
\exp\Bigg[
-\frac{2N}{\lambda}\sum_{i=1}^N m_i^2+\sum_{I=1}^g \sum_{a=1}^{K_I} n_I u^{(I)}_a
\nonumber\\
&&~~+\sum_{i<j}\log(m_i-m_j)^2
+\sum_I \sum_{a<b} \log\left( 2\sinh \frac{u^{(I)}_a-u^{(I)}_b}2\right)^2
\nonumber\\
&&
~~+
\sum_{i,a}\log(1-e^{m_i-u^{(1)}_a})
-
\sum_I\sum_{a,b} \log(1-e^{u^{(I-1)}_a-u^{(I)}_b})
\Bigg]. \label{vev-D5-eigen-general}
\end{eqnarray}
Our aim is to understand the behavior in the limit $N\ra \infty$
with $\lambda, n_I/N, k_I/N$ finite, for large values of $\lambda$.
The saddle point equations following from the action are
\ba
&&-\frac{4N}{\lambda}m_i+\sum_{j\neq i}\frac{2}{m_i-m_j}
-\sum_{a=1}^{K_1} \frac{1}{e^{u^{(1)}_a-m_i}-1}=0 \hbox{~for~}i=1,...,N,
\\
&&n_1+\sum_{b\neq a}\coth\frac{u^{(1)}_a-u^{(1)}_b}2
+\sum_{i=1}^N \frac{1}{e^{u^{(1)}_a-m_i}-1}
+\sum_{b=1}^{K_2} \frac{1}{e^{u^{(2)}_b-u^{(1)}_a}-1}=0
\nonumber\\
&&
\hspace{8cm}
\hbox{~for~}a=1,...,K_1,\\
&&
n_{I}+\sum_{b\neq a}\coth\frac{u^{(I)}_a-u^{(I)}_b}2
-\sum_{b=1}^{K_{I-1}} \frac{1}{e^{u^{(I)}_a-u^{(I-1)}_b}-1}
+\sum_{b=1}^{K_{I+1}} \frac{1}{e^{u^{(I+1)}_b-u^{(I)}_a}-1}=0
\nonumber\\
&&
\hspace{6cm}
\hbox{~for~}I=2,...,g-1 \hbox{~and~}a=1,...,K_I,
\end{eqnarray}
and
\ba
&&n_{g}+\sum_{b\neq a}\coth\frac{u^{(g)}_a-u^{(g)}_b}2
-\sum_{b=1}^{K_{g-1}} \frac{1}{e^{u^{(g)}_a-u^{(g-1)}_b}-1}
=0
\hbox{~for~} a=1,...,K_g.
\end{eqnarray}
All the terms can be interpreted as forces on eigenvalues.
Note that the interaction between $m_i$ and $u_a^{(1)}$ is repulsive,
while the one between $u_a^{(I)}$ and $u_b^{(I+1)}$ is attractive.
This suggests that some eigenvalues form bound states.
\begin{figure}[htbb]
\begin{center}
\psfrag{u1}{$u^{(1)}$}
\psfrag{u2}{$u^{(2)}$}
\psfrag{ug-1}{$u^{(g-1)}$}
\psfrag{ug}{$u^{(g)}$}
\includegraphics[width=150mm]{moleculesB4.eps}
\caption{
There are $g$ types of bound states
($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$),
$I=1,...,g$.
}
\label{moleculesB}
\end{center}
\end{figure}
Let us work in the $\lambda\ra \infty$ approximation.
The following distribution of eigenvalues solves the
saddle point equations.
It involves $g$ types of bound states.\footnote{
Though it is convenient to talk about bound states,
the size of a bound state is in fact
of the same order ${\mathcal O}(1/N)$ as the distance
to the neighboring bound state.
}
The $I$-th type of bound state, which we denote by
($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$),
contains a single $u^{(J)}$-eigenvalue
for $1\leq J\leq I$, as shown in Figure \ref{moleculesB}.
The $m$-eigenvalues split into $g+1$ groups $\{m^{(I)}_i|i=1,..,n_I\}$.
The $k_I$ ($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$)-bound states
are distributed along a line in the imaginary direction,
and separate $\{m^{(I)}_i\}$ from $\{m^{(I+1)}_i\}$.
See Figure \ref{D5eigenvalues-general}.
For interactions between two bound states or between a bound state
and an $m$-eigenvalue, we can apply (\ref{u-m-simplify})
and (\ref{u-u-simplify}).
The ($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$)-bound state
is pulled to the right by an external force of magnitude $n_1+n_2+...+n_I$,
and pushed back to the left by $n_1+n_2+...+n_I$ $m$-eigenvalues
from $\{m^{(J)}_i\}$ for $1\leq J\leq I$.
Bound states of different kinds
do not interact with each other: forces
cancel out among constituent eigenvalues.
The saddle point equations are satisfied if the bound states
are uniformly distributed along vertical lines.
Calculation of relative positions of constituent eigenvalues
in a bound state is straightforward.
In the bound state ($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$),
the distance between the $u^{(J)}$- and $u^{(J+1)}$-eigenvalues
is $1/(\sum_{K=J+1}^I n_K +\sum_{K=J}^{I-1} k_K)={\mathcal O}(1/N)$
for $1\leq J\leq I-1$.
\begin{figure}[htbb]
\begin{center}
\psfrag{l1}{$n_1$}
\psfrag{l3}{$n_2$}
\psfrag{l2m-3}{$n_{g-1}$}
\psfrag{l2m-1}{$n_{g}$}
\psfrag{l2m+1}{$n_{g+1}$}
\includegraphics[width=150mm]{D5eigenvalues3.eps}
\caption{
The eigenvalue distributions for
$M$,
\color{red}$U^{(1)}$\color{black},
\color{green}$U^{(2)}$\color{black},...,
\color{blue}$U^{(g-1)}$\color{black}, and
\color{magenta}$U^{(g)}$\color{black}.
The $N$ $m$-eigenvalues split into $g+1$ groups
$\{m_i^{(I)}|i=1,...,n_I\}$,~$I=1,...,g+1$.
The $k_I$ ($u^{(1)}$-$u^{(2)}$-...-$u^{(I)}$)-bound states
are distributed uniformly between $\{m_i^{(I)}\}$
and $\{m_i^{(I+1)}\}$,
and are represented by $I$ coincident colored lines
in the imaginary direction.
}
\label{D5eigenvalues-general}
\end{center}
\end{figure}
It seems reasonable to believe, based on the analogy with \cite{cs-mat},
that the proposed eigenvalue distribution is the leading saddle point.
Let us calculate the Wilson loop vev by using the proposed distribution.
The exponent of (\ref{vev-D5-eigen-general}) becomes
\ba
&&-\frac{2N}{\lambda}\sum_{I=1}^{g+1} \sum_{i=1}^{n_I} (m_i^{(I)})^2
+\sum_{I=1}^g \sum_{i=1}^{n_I} K_I m^{(I)}_i
+\sum_{I=1}^{g+1} \sum_{i<j}\log(m_i^{(I)}-m_j^{(I)})^2
+{\mathcal O}(N^2\log\lambda)
\nonumber\\
&=&\sum_{I=1}^g \frac{\lambda}{8N}n_I K_I^2+{\mathcal O}(N^2\log\lambda).
\label{exponent3}
\end{eqnarray}
We get the final result for the $U(N)$ Yang-Mills:
\ba
\left\langle W_R\right\rangle_{U(N)}
=
\exp\left(
\sum_{I=1}^g \frac{\lambda}{8N}n_I K_I^2+{\mathcal O}(N^2\log\lambda)
\right).
\end{eqnarray}
In the $SU(N)$ case, (\ref{TrM'}) allows us to write
\ba
\left\langle
W_R\right\rangle_{SU(N)}
&=&
\frac{1} Z\int dM dU^{(1)} dU^{(2)}... dU^{(g)}
e^{-\frac{2N}{\lambda}{\rm Tr} M^2}
(\det e^M)^{-|R|/N}
\nonumber\\
&&
~~\times
(\det U^{(1)})^{n_1}(\det U^{(2)})^{n_2}...(\det U^{(g)})^{n_g}
\det(1+e^M\otimes U^{(1)}{}^\mo)
\nonumber\\
&&
~~\times
\frac{1}{\det(1-U^{(1)}\otimes U^{(2)}{}^\mo)}
...
\frac{1}{\det(1-U^{(g-1)}\otimes U^{(g)}{}^\mo)}.
\end{eqnarray}
(\ref{exponent3}) is replaced by
\ba
&&-\frac{2N}{\lambda}\sum_{I=1}^{g+1} \sum_i (m_i^{(I)})^2
+\sum_{I=1}^{g+1} \sum_i (K_I-|R|/N) m^{(I)}_i
\nonumber\\
&&
~~~
+\sum_{I=1}^{g+1} \sum_{i<j}\log(m_i^{(I)}-m_j^{(I)})^2
+{\mathcal O}(N^2\log\lambda)
\nonumber\\
&=&\sum_{I=1}^{g+1} \frac{\lambda}{8N}n_I (K_I-|R|/N)^2+{\mathcal O}(N^2\log\lambda).
\end{eqnarray}
Recall that $K_{g+1}\equiv 0$.
This is the result (\ref{the-results}) presented in the introduction.
\subsection{Eigenvalue bound states as D3-branes}
\begin{figure}[htbb]
\begin{center}
\psfrag{R}{$R\equiv Q^{(1)}$}
\psfrag{Q2}{$Q^{(2)}$}
\psfrag{Qm-1}{$Q^{(g-1)}$}
\psfrag{Qm}{$Q^{(g)}$}
\psfrag{N1}{$N_1$}
\psfrag{N2}{$N_2$}
\psfrag{Nm-1}{$N_{g-1}$}
\psfrag{Nm}{$N_{g}$}
\includegraphics[width=120mm]{D3Young-split5.eps}
\caption{
Another shrinking sequence of Young diagrams
$R\equiv Q^{(1)}\supset Q^{(2)}\supset...\supset Q^{(g)}$.
}
\label{D3Young-split}
\end{center}
\end{figure}
Another matrix model can be obtained by starting with
the formula
\ba
{\rm Tr}_{R} e^M
=\int dV^{(1)} \frac{1}{\det(1-e^M\otimes V^{(1)}{}^\mo)}{\rm Tr}_{R} V^{(1)}.
\end{eqnarray}
Here $V^{(1)}\in U(N_1)$ and $dV^{(1)}$ is the
Haar measure.
We have defined $N_I:=\sum_{J=1}^{g+1-I} n_J$.
Note that
\ba
{\rm Tr}_{R} V^{(1)}=(\det V^{(1)})^{k_g}{\rm Tr}_{Q^{(2)}} V^{(1)}.
\end{eqnarray}
Here $Q^{(2)}$ is obtained by removing the first $k_{g}$ rows from $R$.
See Figure \ref{D3Young-split}.
Similarly,
\ba
{\rm Tr}_{Q^{(2)}} V^{(1)}
&=&\int dV^{(2)}
\frac{1}{\det(1-V^{(1)}\otimes V^{(2)}{}^\mo)}{\rm Tr}_{Q^{(2)}} V^{(2)},
\end{eqnarray}
with $V^{(2)}$ essentially in $U(N_2)$.
To avoid singularities
the integral is performed along
appropriate contours.
We repeat the same procedure as many times as possible.
This gives
\ba
{\rm Tr}_{R} e^M&=&\int dV^{(1)}
\frac{1}{\det(1-e^M\otimes V^{(1)}{}^\mo)}(\det V^{(1)})^{k_{g}}
\int dV^{(2)} \frac{1}{\det(1-V^{(1)}\otimes V^{(2)}{}^\mo)}
\nonumber\\
&&~
\times
(\det V^{(2)})^{k_{g-1}}...\int dV^{(g)}
\frac{1}{\det(1-V^{(g-1)}\otimes V^{(g)}{}^\mo)}
(\det V^{(g)})^{k_{1}}.
\end{eqnarray}
Here $V^{(I)}\in U(N_I)$,
and the integration contours are deformed so that
the eigenvalues of $V^{(I)}$ have larger absolute values
than $V^{(I-1)}$.
We thus have
\ba
\langle W_R\rangle
\hspace{-1mm}
=
\hspace{-1mm}
\frac{1} Z
\hspace{-1mm}
\int
\hspace{-1mm}
dM dV^{(1)} dV^{(2)}... dV^{(g)}
e^{-\frac{2N}{\lambda}{\rm Tr} M^2}
(\det V^{(1)})^{k_{g}}(\det V^{(2)})^{k_{g-1}}
...(\det V^{(g)})^{k_{1}}
\nonumber\\
\times \frac{1}{\det(1-e^M\otimes V^{(1)}{}^\mo)}
\frac{1}{\det(1-V^{(1)}\otimes V^{(2)}{}^\mo)}
...
\frac{1}{\det(1-V^{(g-1)}\otimes V^{(g)}{}^\mo)}.
\end{eqnarray}
In terms of the eigenvalues, the Wilson loop is given by
\ba
\langle W_R\rangle&\propto&
\int \prod dm_i
\prod dv^{(I)}_a
\exp\Bigg[
-\frac{2N}{\lambda}\sum_{i=1}^N m_i^2+\sum_{I=1}^g \sum_{a=1}^{N_I}
k_{g+1-I}v^{(I)}_a
\nonumber\\
&&~~+\sum_{i<j}\log(m_i-m_j)^2
+\sum_I \sum_{a<b} \log\left( 2\sinh \frac{v^{(I)}_a-v^{(I)}_b}2\right)^2
\nonumber\\
&&~~-\sum_{i,a}\log(1-e^{m_i-v^{(1)}_a})
-\sum_I\sum_{a,b} \log(1-e^{v^{(I-1)}_a-v^{(I)}_b})
\Bigg].
\end{eqnarray}
Let us study this model in the large $N$ limit
with $n_I/N$ and $k_I/N$ fixed.
The saddle point equations are
\ba
&&-\frac{4N}{\lambda}m_i+\sum_{j\neq i}\frac{2}{m_i-m_j}
+\sum_{a=1}^{N_1} \frac{1}{e^{v^{(1)}_a-m_i}-1}=0 \hbox{~for~}i=1,...,N,\\
&&k_{g}+\sum_{b\neq a}\coth\frac{v^{(1)}_a-v^{(1)}_b}2
-\sum_{i=1}^N \frac{1}{e^{v^{(1)}_a-m_i}-1}
+\sum_{b=1}^{N_2} \frac{1}{e^{v^{(2)}_b-v^{(1)}_a}-1}=0
\nonumber\\
&&
\hspace{8cm}
\hbox{~for~}
a=1,..., N_1,
\\
&&k_{g+1-I}+\sum_{b\neq a}\coth\frac{v^{(I)}_a-v^{(I)}_b}2
-\sum_{b=1}^{N_{I-1}} \frac{1}{e^{v^{(I)}_a-v^{(I-1)}_b}-1}
+\sum_{b=1}^{N_{I+1}} \frac{1}{e^{v^{(I+1)}_b-v^{(I)}_a}-1}=0
\nonumber\\
&&
\hspace{6cm}
\hbox{~for~}I=2,...,g-1 \hbox{~and~}a=1,...,N_I,
\end{eqnarray}
and
\ba
&&k_{1}+\sum_{b\neq a}\coth\frac{v^{(g)}_a-v^{(g)}_b}2
-\sum_{b=1}^{N_{g-1}} \frac{1}{e^{v^{(g)}_a-v^{(g-1)}_b}-1}
=0
\hbox{~for~} a=1,...,N_g,
\end{eqnarray}
The forces between $m_i$ and $v^{(1)}_a$
as well as between $v^{(I)}_a$ and $v^{(I+1)}_b$
are attractive.
\begin{figure}[htbb]
\begin{center}
\psfrag{m}{$m$}
\psfrag{v1}{$v^{(1)}$}
\psfrag{v2}{$v^{(2)}$}
\psfrag{vI}{$v^{(g-1)}$}
\includegraphics[width=150mm]{moleculesC2.eps}
\caption{
There are $g+1$ types of bound states
($m$-$v^{(1)}$-...-$v^{(I)}$),
$I=0,1,...,g$.
}
\label{moleculesC}
\end{center}
\end{figure}
Our proposed distribution of the eigenvalues
for large $\lambda$
is as follows.
There are $g$ types of bound states denoted by
($m$-$v^{(1)}$-...-$v^{(I)}$) for $I=0,1,...,g$.
Each bound state of the $I$-th type
has a single $m$-eigenvalue
as well as a single $v^{(J)}$-eigenvalue for $1\leq J\leq I$.
The size of a bound state
is of the order $1/N$, and is much smaller
than the distance between two neighboring bound states.
The $n_{g+1-I}$ ($m$-$v^{(1)}$-...-$v^{(I)}$)-bound states
are distributed according to the semi-circle law
centered at $\lambda K_I /4N$.
Using (\ref{u-m-simplify}) and (\ref{u-u-simplify}),
one can confirm that the force balance among bound states
is achieved.
It is straightforward to calculate the
distance between eigenvalues in a bound state.
In the $a$-th ($m$-$v^{(1)}$-...-$v^{(I)}$)
bound state,
the distance between the $v^{(J)}$- and $v^{(J+1)}$-eigenvalues turns out to be
$1/((I-J)a+\sum_{K=J}^I k_{g+1-K})={\mathcal O}(1/N)$ for $0\leq J\leq I-1$.
Here $v^{(0)}\equiv m$ and $k_{g+1}\equiv 0$.
This configuration solves the saddle point equations.
The distribution of the $m$-eigenvalues is identical
to the one in the previous subsection,
and leads to the same results for the Wilson loop vev.
\begin{figure}[htbb]
\begin{center}
\psfrag{l1}{$n_1$}
\psfrag{l3}{$n_2$}
\psfrag{l2m-3}{$n_{g-1}$}
\psfrag{l2m-1}{$n_{g}$}
\psfrag{l2m+1}{$n_{g+1}$}
\includegraphics[width=120mm]{D3eigenvalues4.eps}
\caption{
The eigenvalue distributions for
$M$,
\color{red}$V^{(1)}$\color{black},
\color{green}$V^{(2)}$\color{black},...,
\color{blue}$V^{(g-1)}$\color{black},
\color{magenta}$V^{(g)}$\color{black}.
The $n_{g+1-I}$
($m$-$v^{(1)}$-...-$v^{(I)}$)-bound states
are distributed according to Wigner's semi-circle law.
}
\label{D3eigenvalues}
\end{center}
\end{figure}
\section*{Acknowledgments}
I thank Jaume Gomis and Kentaroh Yoshida for helpful conversations.
I am especially grateful to
Sean Hartnoll for many useful discussions, and
Nick Halmagyi for collaboration on a
related project \cite{cs-mat}.
I also acknowledge the hospitality of the Simons Workshop at Stony Brook,
where this work was completed.
My research is supported in part by the NSF grants PHY-05-51164 and PHY-04-56556.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,138 |
Q: How to change the first charcater of every new line in a file using python I have a file which looks like this:
1 1:10 2:10 3:40
2 1:30 3:40 4:20
1 1:20 4:40 3:30
I would like to change the first character, say 1 or 2 or 1 to -1, 1 and -1 respectively.
I had written the following python code
with open('filename') as f:
lines = f.readlines()
for line in lines:
if line[0] == '1':
print(line)
line = line.split();
line[0] = "-1"
line = "".join(line)
else:
line = line.split("");
line[0] = "1"
The space character is removed the by split and I don't think can write this into an output file. my output should ultimately look like this
-1 1:10 2:10 3:40
1 1:30 3:40 4:20
-1 1:20 4:40 3:30
The code to write the modified file is
with open('changed_file', 'w') as fout:
for line in lines:
fout.write(line)
A: have you consider something like this?
line = "1 1:10 2:10 3:40"
map = {'1': '-1', '2': '1'}
print map[line[0]] + line[1:-1]
#-1 1:10 2:10 3:4
You can also set a default value to the map dict.
Best,
Alvaro.
A: The problem is that after changing your lines, you're joining them by an empty space, when it should be joined with an interval.
for idx, line in enumerate(lines):
split_line = line.split()
if split_line[0] == '1':
split_line[0] = "-1"
else:
split_line[0] = "1"
lines[idx] = " ".join(split_line)
A: This reads in all of the lines, and changes the lines that start with 1 or 2 as you said, then proceeds to rewrite the file with the edited lines.
with open('<file_name>', 'r+') as f:
lines = f.readlines()
f.seek(0) # moves cursor back to the beginning of the file
for line in lines:
if line.startswith('1'): line = '-1' + line[1::]
elif line.startswith('2'): line = '1' + line[1::]
f.write(line)
New file contents:
-1 1:10 2:10 3:40
1 1:30 3:40 4:20
-1 1:20 4:40 3:30
A: This code should work:
with open('filename') as f:
lines = f.readlines()
with open('output', 'w') as output:
for line in lines:
if line[0] == '1':
line = "-1" + line[1:]
else:
line = "1" + line[1:]
print(line, file=output, end="")
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,199 |
HAMILTON is the story of America's Founding Father Alexander Hamilton, an immigrant from the West Indies who became George Washington's right-hand man during the Revolutionary War and helped shape the very foundations of the America we know today. The score blends hip-hop, jazz, blues, rap, R&B and Broadway - the story of America then, as told by America now.
HAMILTON has book, music and lyrics by Lin-Manuel Miranda, is directed by Thomas Kail, with choreography by Andy Blankenbuehler and musical supervision and orchestrations by Alex Lacamoire and is based on Ron Chernow's biography of Alexander Hamilton.
Please note: Since HAMILTON contains some strong language, the show is appropriate for ages 10+. Children under 4 are not permitted into the theatre. Children under 16 years old must be accompanied by an adult. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,864 |
\section{Introduction}\label{sec:intro}
For two polytopes $P, Q \subset \R^d$ their \emph{Minkowski sum} is the
(innocent--looking) convex polytope
\[
P + Q = \{ p + q : p \in P,\, q \in Q \} \subset \R^d.
\]
Minkowski sums have starred in applied areas, such as robot motion
planning \cite{latombe} and computer aided design
\cite{DBLP:journals/cad/ElberK99}, as well as in fields of pure mathematics,
among them commutative algebra and tropical geometry \cite{stu02}. In
applications it is essential to understand the facial structure of $P + Q$.
But, even with quite detailed knowledge of $P$ and $Q$, it is in general
difficult to determine the combinatorics of $P+Q$. Even for {\it special
cases}, the knowledge of complete face lattices is meager. The best understood
Minkowski sums are zonotopes \cite{zie95} and sums of perfectly centered
polytopes with their polar duals \cite{fuk06}.
So it is natural (and vital) to investigate the combinatorial structure of
Minkowski sums.
From the standpoint of combinatorial geometry, a less ambitious goal one can
settle for is the question of $f$-vector shapes. This includes different kinds
of upper and lower bounds for the $f$-vector entries with respect to the
corresponding entries of the summands. Starting with the first entry of an
$f$-vector, the number of vertices, Fukuda \& Weibel \cite{fuk06} studied the
maximal number of vertices of a Minkowski sum. Their starting point was the
following upper bound on the number of vertices.
\begin{prop}[Trivial Upper Bound; cf.\ \cite{fuk06}]\label{prop:triv_bound}
Let $P_1,\dots,P_r \subset \R^d$ be polytopes. Then
\[
f_0(P_1 + \cdots + P_r) \ \ \le \ \ \prod_{i=1}^r f_0(P_i).
\]
\end{prop}
Fukuda and Weibel gave a construction that showed that the trivial upper bound
can be attained independent of the dimension but with a restricted number of
summands.
\begin{thm}[Fukuda \& Weibel \cite{fuk06}]
For every $r < d$ there are $d$-polytopes $P_1,\dots,P_r \subset \R^d$,
each with arbitrarily large number of vertices, such that the Minkowski
sum $P_1 + \cdots + P_r$ attains the trivial upper bound on the number of
vertices.
\end{thm}
This result was our point of departure. In this paper, we set out to prove
the following result that asserts that the restriction to the number of
summands is best possible.
\begin{thm}\label{thm:main}
Let $r \ge d$ and let $P_1,\dots,P_r \subset \R^d$ be polytopes with
$f_0(P_i) \ge d+1$ vertices for all $i = 1,\dots, r$. Then
\[
f_0(P_1 + \cdots + P_r) \ \le\ \left( 1 -
\frac{1}{(d+1)^r}\right)\prod_{i=1}^r f_0(P_i).
\]
\end{thm}
However, based on a preliminary version of this paper, C.\ Weibel (personal
communication) noted that Theorem \ref{thm:main} is not optimal with respect
to the number of vertices of the summands.
The paper is organized in the following manner: In Section
\ref{sec:problem_reductions} we gather some observations that will reduce the
statement to one special case (per dimension) whose validity has to be
checked. In particular, we give a reformulation of the problem that casts it
into a stronger question concerning projections of polytopes. The very
structure of the problem at hand allows for the utilization of the tools
devised in R\"{o}rig, Sanyal \& Ziegler \cite{rsz07}. In Section
\ref{sec:proj_properties} we give a review to the terminology and techniques.
The punchline will be that a realization of a polytope with certain properties
under projection gives rise to, first, a polytope associated to the projection
and, secondly, to a simplicial complex that is embedded in the boundary of
this polytope. To prove the non-existence of a certain realization it will
suffice to show that this complex is not embeddable into a sphere of the
prescribed dimension. To show the reader that we did not deal one difficult
problem for another one, we give, in Section \ref{sec:embeddability}, a short
account of Matou\v{s}ek's book \cite{MatousekBZ:BU}, in which he presents
means for dealing with embeddability questions in a combinatorial fashion. In
Section \ref{sec:compl_complex}, we finally put together the pieces gathered
to prove a stronger version of Theorem \ref{thm:main} and we close with some
remarks in Section \ref{sec:remarks}.
{\bf Acknowledgements}.
We would like to express our gratitude to Christian Haase, Thilo R\"orig, and
G\"unter M. Ziegler for stimulating discussions and valuable insights. We
also would like to thank Bernd Sturmfels for helpful comments on the exposition.
\section{The problem, some reductions \& a reformulation}
\label{sec:problem_reductions}
Forming Minkowski sums is not a purely combinatorial construction, i.e.\ in
contrast to basic polytope constructions such as products, direct sums, joins,
etc.\ the resulting face lattice is not determined by the face lattices of the
polytopes involved. For a sum $P +Q$ of two polytopes $P$ and $Q$ it is easy
to see that if $F \subseteq P + Q$ is a proper face, then $F$ is of the form
$F = G + H$ with $G \subseteq P$ and $H \subseteq Q$ being faces. This, in
particular, sheds new light on the ``Trivial Upper Bound'' in the last
section: It states that the set of vertices of a Minkowski sum is a subset of
the pairwise sums of vertices of the polytopes involved.
As a guiding example let us consider the first non-trivial case: Are there two
triangles $P$ and $Q$ in the plane whose sum is a $9$-gon?
An \emph{ad-hoc} argument for this case, that uses notation and terminology
presented in \cite{zie95}, is the following: Clearly, the polytope $P+Q$ is a
$9$-gon if its normal fan $\nc(P+Q)$ has nine extremal rays. The normal fan
$\nc(P+Q)$ equals $\nc(P) \wedge \nc(Q)$, the common refinement of the fans
$\nc(P)$ and $\nc(Q)$. Thus, the cones in $\nc(P+Q)$ are pairwise
intersections of cones of $\nc(P)$ and $\nc(Q)$. It follows that the extremal
rays, i.e.\ the $1$-dimensional cones, of $\nc(P+Q)$ are just the extremal
rays of $P$ and of $Q$. If $P$ and $Q$ are triangles, then each one has only
three extremal rays. Therefore, $\nc(P+Q)$ has at most six extremal rays and
falls short of being a $9$-gon. The same reasoning yields the following
result.
\begin{prop}
Let $P$ and $Q$ be two polygons in the plane. Then
\[
f_0(P+Q) \le f_0(P) + f_0(Q).
\]
\end{prop}
However, this elementary geometrical reasoning fails in higher dimensions and
we will employ topological machinery for the general case. But for now let us
give some observations that will simplify the general case.
The first observation concerns the dimensions of the polytopes involved in the
sum.
\begin{obs}[Dimension of summands]
Let $P_1, P_2, \dots,P_r \subset \R^d$ be polytopes each having at least
$d+1$ vertices. Then there are \emph{full-dimensional} polytopes
$P^\prime_1,P^\prime_2, \dots,P^\prime_r$ with $f_0(P^\prime_i) =
f_0(P_i)$ and $f_0(P^\prime_1 + P^\prime_2 + \cdots + P^\prime_r) \ge
f_0(P_1 + P_2 + \cdots + P_r)$
\end{obs}
Clearly, if one of the summands, say $P_1$, is not full-dimensional, then the
number of vertices prevents $P_1$ from being a lower dimensional simplex.
Choosing a vertex $v$ of $P_1$ that is not a cone point and pulling $v$ in a
direction perpendicular to its affine hull yields a polytope $P^\prime_1$ with
$f_0(P_1) = f_0(P^\prime_1)$ with $\dim P^\prime_1 = \dim P + 1$. Exchanging
$P_1$ for $P^\prime_1$ possibly increases the number of vertices of the
Minkowski sum.
\begin{obs}[Number of summands]
Let $P_1, P_2,\dots,P_r \subset \R^d$ be $d$-polytopes such that $P_1 +
P_2 + \cdots + P_r$ attains the trivial upper bound, then so does every
subsum $P_{i_1} + P_{i_2} + \cdots + P_{i_k}$ with $\{ i_1, \dots i_k \}
\subseteq [r]$.
\end{obs}
Thus we can restrict to the situation of sums with $d$ summands. The next
observation turns out to be even more valuable. It states that we can even
assume that every summand is a simplex.
\begin{obs}[Combinatorial type of summands]
Let $P_1, P_2,\dots,P_r \subset \R^d$ be $d$-polytopes such that $P_1 +
P_2 + \cdots + P_r$ attains the trivial upper bound. For every $i \in [r]$
let $P^\prime_i \subset P_i$ be a vertex induced, full-dimensional
subpolytope, then $P^\prime_1 + P^\prime_2 + \cdots + P^\prime_r$ attains
the trivial upper bound.
\end{obs}
The last observation casts the problem into the realm of polytope projections.
\begin{obs}
The Minkowski sum $P + Q$ is the projection of the product $P \times Q$
under the map $\pi: \R^d \times \R^d \rightarrow \R^d$ with $ \pi(x,y) = x
+ y$.
\end{obs}
We will derive Theorem \ref{thm:main} from the following stronger statement.
\begin{thm} \label{thm:main_stronger}
Let $P$ be a polytope combinatorially equivalent to a $d$-fold product of
$d$-simplices and let $\pi : P \rightarrow \R^d$ be a linear projection.
Then
\[
f_0(\pi P) \le f_0(P) - 1 = (d+1)^d - 1.
\]
\end{thm}
Before we give a proof of Theorem \ref{thm:main} let us remark on a few things
concerning the previous theorem.
Special emphasis should be put on the phrase ``combinatorially equivalent to a
product.'' The \emph{standard} product $P \times Q$ of two polytopes
$P\subset \R^d$ and $Q\subset \R^e$ is obtained by taking the Cartesian
product of $P$ and $Q$, that is taking the convex hull of $\V P \times \V Q
\subset \R^{d+e}$. One feature of this construction is that if $P^\prime
\subset P$ and $Q^\prime \subset Q$ are vertex induced subpolytopes, then
$P\times Q$ contains $P^\prime \times Q^\prime$ again as a vertex induced
subpolytope. This no longer holds for \emph{combinatorial products}: The
\emph{Goldfarb cube} $G_4$ is a $4$-polytope combinatorially equivalent to a
$4$-cube with the property that a projection to $2$-space retains all $16$
vertices (cf.\ \cite{Goldfarb2,am98}). The $4$-cube itself is combinatorially
equivalent to a product of two quadrilaterals which, in the standard product,
contains a vertex induced product of two triangles. The subpolytope on the
corresponding vertices of $G_4$ is not a combinatorial product of two
triangles; indeed, this would contradict Theorem \ref{thm:main_stronger} for
$d=2$.
The bound of Theorem \ref{thm:main_stronger} seems to be tight: In Section
\ref{sec:remarks} we give a realization of a product of two triangles such
that a projection to $2$-space has $8$ vertices. Therefore, the bound given in
Theorem \ref{thm:main} is \emph{not} tight for $d = 2$: The sum of two
triangles in the plane has at most $6$ vertices.
Theorem \ref{thm:main_stronger} touches upon properties of the realization
space of products of simplices. While, in general, realization spaces are
rather delicate objects, the statement at hand is on par with the fact that
positively spanning vector configurations with prescribed sign patterns of
linear dependencies do not exist. Methods for treating such problems were
developed in \cite{rsz07}; the next two sections give a made-to-measure
introduction.
\begin{proof}[Proof of Theorem \ref{thm:main}]
We can assume that all polytopes $P_i$ have their vertices $V_i$ in
general position. For every choice $V^\prime_i \subseteq V_i$ of $d+1$
vertices from each $P_i$ the polytopes $P^\prime_i = \conv V^\prime_i$ are
$d$-simplices. The Minkowski sum $P^\prime_1+ P^\prime_2+\cdots
+P^\prime_r$ is a projection of a product of $r \ge d$ simplices and, by
Theorem \ref{thm:main_stronger}, does not attain the trivial upper bound.
There are exactly $\prod_{i=1}^r \tbinom{f_0(P_i)}{d+1}$ choices for the
$P^\prime_i$. On the other hand, every sum of vertices
$v_1+v_2+\cdots+v_r$ occurs in only $\prod_{i=1}^r\tbinom{f_0(P_i)-1}{d}$
different subsums. Thus, by the pigeonhole principle, there are at least
\[
\prod_{i=1}^r \frac{\tbinom{f_0(P_i)}{d+1}}{\tbinom{f_0(P_i)-1}{d}} =
\prod_{i=1}^r \frac{f_0(P_i)}{d+1}
\]
sums of vertices that fail to be a vertex in at least one subsum.
\end{proof}
\section{Geometric and Combinatorial Properties of Projections}
\label{sec:proj_properties}
In polytope projections faces can collapse or get mapped to the interior.
Therefore, it is difficult to predict the (combinatorial) outcome of a
projection. There is, however, a class of faces that behave nicely under
projection and whose properties we will exploit in the following.
\begin{dfn}[Strictly preserved faces, cf. \cite{zie04}]
Let $P$ be a polytope, $F \subseteq P$ a proper face and $\pi: P
\rightarrow \pi(P)$ a linear projection of polytopes. The face $F$ is
\emph{strictly preserved} under $\pi$ if
\begin{enumerate}
\item[ i)] $H = \pi(F)$ is a face of $\pi(P)$,
\item[ ii)] $F$ and $H$ are combinatorially isomorphic, and
\item[iii)] $\pi^{-1}(H)$ is equal to $F$.
\end{enumerate}
\end{dfn}
The first two conditions should trigger an agreeing nod since they model the
intuition behind ``preserved faces.'' The third condition is a little less
clear. In order to talk about \emph{distinct} faces of a projection we have to
rule out that two preserved faces come to lie on top of each other and this
situation is dealt with in condition iii). Figure \ref{fig:faces} shows
instances of non-preserved, preserved, and strictly preserved faces. We will
generally drop the ``strictly'' whenever we talk about strictly preserved
faces.
\begin{figure}[ht]
\centering
\psfrag{p}[bl]{$\scriptstyle \pi$}
\psfrag{q}[cc]{$\scriptstyle q^*$}
\psfrag{v1}[bl]{$\scriptstyle v_1$}
\psfrag{v2}[tl]{$\scriptstyle v_2$}
\psfrag{v3}[cr]{$\scriptstyle v_3$}
\psfrag{v4}[br]{$\scriptstyle v_4$}
\psfrag{v5}[bl]{$\scriptstyle v_5$}
\psfrag{pv1}[cc]{$\scriptstyle \pi(v_1)$}
\psfrag{pv2}[cc]{$\scriptstyle \pi(v_2)=\pi(v_5)$}
\psfrag{pv3}[cc]{$\scriptstyle \pi(v_3)=\pi(v_4)$}
\psfrag{dv1}[cl]{$\scriptstyle v_1^\fdual$}
\psfrag{dv2}[cb]{$\scriptstyle v_2^\fdual$}
\psfrag{dv3}[cb]{$\scriptstyle v_3^\fdual$}
\psfrag{qv1}[tr]{$\scriptstyle q^*(v_1^\fdual)$}
\psfrag{qv2}[cr]{$\scriptstyle q^*(v_2^\fdual)$}
\psfrag{qv3}[cr]{$\scriptstyle q^*(v_3^\fdual)$}
\includegraphics[height=6cm]{projection}
\caption{\label{fig:faces}Projection of pentagon to the real line: $v_1$
is strictly preserved, $v_2$ is not preserved, and $v_3$ is preserved but
not strictly. In accordance with the Projection Lemma: $q^*(v_1^\fdual)$
contains $0$ in interior, $q^*(v_2^\fdual)$ does not, and $q^*(v_3^\fdual)$
has $0$ in its boundary.}
\end{figure}
What makes strictly preserved faces so nice is the fact that the above
conditions can be checked prior to the projection by purely (linear) algebraic
means. The key to that is the Projection Lemma (cf. \cite[Proposition
3.2]{zie04}). We will give a variant of it which requires a few more notions.
Let $P \subset \R^n$ be a full-dimensional polytope with $0$ in the interior.
The dual polytope is
\[
P^\dual \ =\ \{ \ell \in \Rd{n} : \ell(x) \leq 1\,\, \textrm{ for all } x
\in P \} = \conv \{ \ell_1, \dots, \ell_m \} \ \subset\ \Rd{n}
\]
and for every face $F\subseteq P$ we denote by $F^\fdual = \{ \ell \in P^\dual : \ell|_F = 1 \}$ the corresponding face
of $P^\dual$. Furthermore, we define
$I : \{\text{faces of } P\} \rightarrow 2^{[m]}$ to be the map satisfying
\[
\conv \{ \ell_i : i \in I(F) \} = F^\fdual
\]
for every face $F \subseteq P$. Let $\pi : \R^n \rightarrow \R^d$ be a
linear projection and let $q$ be a map fitting into the short exact sequence
\[
0 \longrightarrow \R^{n-d} \stackrel{q}{\longrightarrow} \R^n
\stackrel{\pi}{\longrightarrow} \R^d \longrightarrow 0.
\]
Dualizing gives rise to a (dual) exact sequence
\[
0 \longleftarrow \Rd{n-d} \stackrel{q^*}{\longleftarrow} \Rd{n}
\stackrel{\pi^*}{\longleftarrow} \Rd{d} \longleftarrow 0.
\]
The characterization of strictly preserved faces will be in terms of the dual
map $q^*$ and the dual to the face under consideration.
\begin{lem}[Projection Lemma]
Let $P$ be a polytope and $F\subset P$ a face. Then $F$ is strictly
preserved iff $0 \in \int q^*(F^\fdual) = \int \conv\{ q^*(\ell_i) : i \in
I(F)\}$.
\end{lem}
We first sort out the situation for (non-strictly) preserved faces.
\begin{prop}\label{prop:proj_is_face}
Let $F \subset P$ be a face. Then $\pi(F)$ is a face of $Q = \pi(P)$ iff
$0 \in q^*(F^\fdual)$.
\end{prop}
\begin{proof}
$p(F)$ is a face of $Q$ iff there is an $\ell \in \Rd{d}$ such that
\[
\begin{array}{rl}
\ell\circ \pi(x) < 1 & \text{for all } x \in P \backslash F\text{
and} \\
\ell\circ \pi(x) = 1 & \text{for all } x \in F \\
\end{array}
\]
This is the case iff $\pi^*(\ell) \in F^\fdual$ which in turn holds iff $0 =
q^* \circ \pi^* (\ell) \in q^*(F^\fdual)$.
\end{proof}
\begin{prop}\label{prop:proj_is_comb_equiv}
Let $F\subset P$ be a face. Then $\pi(F)$ is combinatorially equivalent to
$F$ iff $q^*(F^\fdual)$ is full-dimensional.
\end{prop}
\begin{proof}
Let $\aff F = x_0 + L$ with $L$ being a linear space. Then $\aff F^\fdual =
\ell_0 + L^0$ with $L^0 = \ker( \Rd{n} \rightarrow L^*)$. The result
follows if we show that $\pi$ is injective on $L$ iff $q^*$ restricted to
$L^0$ is surjective. Now $\pi|_L$ is injective iff $\im q \cap L = 0$.
This holds iff $q^*$ is surjective when restricted to $L^0 = (\R^n/L)^*$.
\end{proof}
\begin{proof}[Proof of Projection Lemma]
Let $F \subset P$ be a preserved face, i.e.\ $\pi(F)$ is a face of $Q =
\pi(P)$ combinatorially equivalent to $F$, and let $G = \pi^{-1}(\pi(F))$.
Clearly, $G$ is a face of $P$ and $F \subseteq G$.
The inclusion is strict iff $G^\fdual$ is a proper face of $F^\fdual$. Now,
$\pi(G)$ is a face iff $0 \in q^*(G^\fdual)$ by Proposition
\ref{prop:proj_is_face}. This, in turn, is the case iff $0 \not\in \int
q^*(F^\fdual)$.
\end{proof}
\subsection*{The geometric side}
We made use of the fact that $q^*(F^\fdual) = \conv\{ q^*(w) : w \in \V
F^\fdual\}$ and for later reference we denote by $G = \{ g_i = q^*(\ell_i) : i
= 1,\dots,m\}$ the projection of the vertices of $P^\dual$. Note that we will
not treat $G$ as the set of vertices of a polytope (especially since not all
would be vertices) but as a configuration of vectors. In case that all
vertices survive the projection, this vector configuration has some strong
properties: it is a \emph{Gale transform}. Gale transforms are a well-known
notion from discrete geometry; we refer the reader to Matou\v{s}ek
\cite{mat02} and Ziegler \cite{zie95} for full treatments (from different
perspectives) and McMullen \cite{mcm79} for an extensive survey.
A set of vectors $W = \{ w_1, \dots, w_k \} \subset \R^d$ is \emph{positively
spanning} if every point in $\R^d$ is a non-negative combination of the
vectors $w_i$, that is, if $\cone W = \R^d$. Equivalently, $U$ is positively
spanning if $\conv W$ is a full dimensional polytope with $0$ in its interior.
We also need the weaker notion of \emph{positively dependent} which holds if
$0 \in \mathsf{relint}\, \conv W$.
\begin{dfn}[Gale transform]
A finite vector configuration $G = \{g_1,\dots,g_m\}$
is a \emph{Gale transform} if for every $i = 1,\dots,m$ the
subconfiguration $G\backslash g_i$ is positively spanning.
\end{dfn}
The main reason why Gale transforms are useful is that they are yet another
way to represent polytopes.
\begin{thm}[Gale duality]\label{thm:gale_duality}
Let $G = \{g_1,\dots,g_m\}$ be a Gale transform in $(m-d-1)$-dimensional
space, then there is a $d$-polytope $Q$ with vertices $V =
\{v_1,\dots,v_m\}$ such that for every $I \subset [m]$
\[
\conv\{v_i : i \in [m]\backslash I\} \text{ is a face of $Q$} \ \Longleftrightarrow\
\{g_j : j \in I \} \text{ are positively dependent}.
\]
Furthermore, $Q$ is unique up to affine isomorphisms.
\end{thm}
The condition given by the Projection Lemma can be rephrased in terms of
positive spans. The key observation is that the set $G$ is actually a Gale
transform if all vertices survive the projection.
\begin{prop}\label{prop:is_gale}
Let $P \subset \R^n$ be a $n$-polytope with $m$ facets and $\pi: \R^n
\rightarrow \R^d$ a linear projection. The set $G$ is a Gale transform if
all vertices of $P$ are strictly preserved under $\pi$.
\end{prop}
\begin{proof}
Since $P$ is full dimensional for every $i \in [m]$ there is a vertex $v
\in \V P$ such that $i \not\in I(v)$. Since $v$ is preserved under
projection the set $\{g_j : j \in I(v) \} \subset G\backslash g_i$ is
positively spanning.
\end{proof}
Thus, by Theorem \ref{thm:gale_duality}, there is a combinatorially unique
polytope $\A(P,\pi)$ associated to $(P,\pi)$ which we simply call the
\emph{associated polytope}. So far, the main property of $\A(P,\pi)$ is that
it sort of witnesses the survival of the vertices.
For the case that interests us, namely $P$ being a product of simplices, we
can even assume that $\A(P,\pi)$ is a simplicial polytope, the reason being
the following: If $P^\Delta$ is simplicial we can wiggle the vertices without
changing the combinatorial type. For strictly preserved faces of $P$, the
condition as dictated by the Projection Lemma is \emph{open}, i.e.\ stable
under small perturbations. Thus perturbing the bounding hyperplanes of $P$
does neither alter the type nor the fact that all vertices survive the
projection. The effect on the Gale transform $G$ is that the vectors are in
general position with respect to hyperplanes containing the origin. On the
other hand, this is yet another characterization of the fact that $\A(P,\pi)$
is a polytope with vertices in general positions and hence simplicial.
Summing up so far, we have the following.
\begin{cor} \label{cor:associated_to_simplex_product}
Let $P \subset \R^{d^2}$ be a polytope combinatorially equivalent to a
$d$-fold product of $d$-simplices such that a projection to $d$-space
preserves all the vertices. Then there is a $(2d-1)$-dimensional,
simplicial polytope $\A(P,\pi)$ with $d(d+1)$ vertices associated to the
projection.
\end{cor}
\subsection*{The combinatorial side}
Given that all vertices of a polytope $P$ survive the projection we obtain an
associated polytope $\A = \A(P,\pi)$. Furthermore, for every vertex $v \in P$
the polytope $q^*(v^\fdual)$ has zero in its interior which, in particular,
implies that its vertices are positively dependent. By Gale duality (Theorem
\ref{thm:gale_duality}), this induces a face in $\A$. The collection of all
the induced faces is a polytopal complex in the boundary of $\A$. If $P$ is a
simple polytope, we argued that $\A$ can be assumed to be simplicial. Thus,
the polytopal complex is a simplicial complex whose combinatorics is
determined by the sole knowledge of the combinatorics of $P$. We give a rather
general description of this complex since it seems that it is the first
occurrence in the literature. For background on simplicial complexes as well as
notation, we refer to the first chapter of \cite{MatousekBZ:BU}.
\begin{dfn}[Complement complex]
Let $\K \subseteq 2^V$ be a simplicial complex on vertices $V$. The
\emph{complement complex} $\cc{\K}$ of $\K$ is the closure of
\[
\{ V \backslash \tau : \tau \in \K, \ \tau \text{ a facet}\}.
\]
\end{dfn}
From the bare definition of the complement complex we deduce the following
simple properties whose proofs we omit.
\begin{prop}
Let $\K$ and $\Ll$ be simplicial complexes. Then the following statements
hold
\begin{enumerate}
\item[\rm 1.] $\cc{(\cc{\K})} = \K$
\item[\rm 2.] $\dim \cc{\K} = n - \dim\K - 1$.
\item[\rm 3.] $\cc{(\K * \Ll)} = \cc{\K} * \cc{\Ll}$.
\end{enumerate}
\end{prop}
In particular, the first property states that no information is lost in the
passage from $\K$ to its complement complex. To the best of our knowledge
there has been no work on this construction of simplicial complexes. A
possible reason for that is the lack of topological plausibility. For a
simplicial complex $\K$ there seem to be no obvious relation between $\K$ and
$\cc{\K}$ concerning homotopy type and/or (co)homology. For a complex being a
\emph{matroid}, the complement complex is just the matroid dual which is well
understood combinatorially and topologically. But matroids are rare among
simplicial complexes.
For a simplicial polytope $P^\dual$ we denote by $\bd(P^\dual)$ the simplicial
complex of all proper faces of $P^\dual$. For a fixed numbering of the facets
of $P$, the vertex set of $\bd(P^\dual)$ can be identified with $[m] = \{1,
\dots, m \}$.
\begin{thm}
Let $P$ be a simple polytope whose vertices are preserved under $\pi$.
Then the complex $\cc{\bd(P^\dual)}$ is realized in the
boundary of the associated polytope $\A(P,\pi)$.
\end{thm}
\begin{proof}
Since $P$ is simple, the associated polytope $\A(P,\pi)$ is simplicial.
Therefore, it is sufficient to show that all facets of $\cc{\bd(P^\dual)}$
are part of the boundary. For now, let $q_1,\dots,q_m$ be the vertices of
$\A(P,\pi)$ labelled in accordance with the elements of its Gale
transform.
A facet of $\cc{\bd(P^\dual)}$ is of the form
$[m] \backslash I(v)$ for some vertex $v \in \V P$. Since
$\pi(v)$ is a vertex of the projection, we have $0 \in \int \conv \{ g_i :
i \in I(v)\}$ by the Projection Lemma. By Gale duality, this corresponds
to the fact that $\conv\{q_i : i \in [m]\backslash I(v)\}$ is a face of
$\A(P,\pi)$.
\end{proof}
For a full-dimensional polytope $P \times Q$ with $0$ in its interior the
polar dual is $P^\dual \oplus Q^\dual$ whose proper faces are the joins of
proper faces of $P^\dual$ and of $Q^\dual$. Thus for the complement of the
boundary complex we have
\[
\cc{\bd\left( (P \times Q)^\dual \right)} = \cc{\bd(P^\dual)} *
\cc{\bd(Q^\dual)}.
\]
Focusing again on the polytopes in question, we want to consider the
complement complex for the dual of a $d$-fold product of simplices. Since a
simplex is self-dual, we have that $\bd(\Delta_d) \cong \tbinom{ [d+1]}{\le
d}$. Thus, for a $d$-fold product of $d$-simplices the corresponding
complement complex is equivalent to
\[
\tbinom{[d+1]}{ \le 1}^{*d},
\]
that is, the $d$-fold join of a complex consisting of $d+1$ isolated points.
\begin{cor}\label{cor:bla}
If there is a realization of a $d$-fold product of $d$-simplices such that
a projection to $d$-space retains all vertices, then the complex
$\tbinom{[d+1]}{\le 1}^{*d}$ is embeddable into a sphere of dimension
$2d-2$.
\end{cor}
This will be our punchline: We will show that the embedding claimed by
Corollary \ref{cor:bla} does not exist. Let us rest for a moment and
reconsider the example from Section \ref{sec:problem_reductions}.
Let $P$ be a realization of a product of two triangles such that a projection
$\pi$ to the plane preserves all (nine) vertices. By Corollary
\ref{cor:associated_to_simplex_product}, the associated polytope $\A(P,\pi)$
is a $3$-dimensional simplicial polytope with $6$ vertices. The complement
complex is $\tbinom{[3]}{\le 1}^{*2}$, can be thought of as $\K_{3,3}$, the
complete bipartite graph on 6 vertices. By Corollary \ref{cor:bla}, this
complex is embedded in the boundary of $\A(P,\pi)$, which is a $2$-sphere.
This, however, is impossible: Graphs embeddable into the $2$-sphere are planar
while the $\K_{3,3}$ is minimal non-planar.
For a $3$-fold product of $3$-simplices the boundary of the associated
polytope is a $4$-sphere and the complement complex is $2$-dimensional. So,
again, there is no (obvious) elementary reasoning neither are there
off-the-shelf results showing non-embeddability. We therefore have to resort
to more sophisticated machinery, as presented in the following section.
\section{Interlude: Embeddability of simplicial complexes}
\label{sec:embeddability}
We only give an \emph{executive summary} of the techniques and results
needed for the following; see \cite{MatousekBZ:BU}.
The category of free $\Zt$-spaces consists of topological spaces $X$ together
with a free action of the group $\Zt$, i.e.\ a fixed point free involution on
$X$. Morphisms in this category are continuous maps that commute with the
respective $\Zt$-actions. The foremost examples of $\Zt$-spaces are spheres
$\S^d$ with the antipodal action. For a $\Zt$-space $X$ a numerical invariant
is the \emph{$\Zt$-index} $\ind X$ which is the smallest integer $d$ such that
there is a $\Zt$-equivariant map $X \Ztmap \S^d$. For example $\ind \S^d =
d$, which is a statement equivalent to the Borsuk--Ulam theorem.
For a simplicial complex $\K$ we define the \emph{deleted join} of $\K$ to be
the complex
\[
\djn{\K} = \{ \sigma \uplus \tau : \sigma, \tau \in \K, \sigma \cap \tau =
\emptyset \}
\]
The deleted join turns an arbitrary simplicial complex into a free
$\Zt$-complex by means of $\sigma \uplus \tau \mapsto \tau \uplus \sigma$.
\begin{thm}[\cite{MatousekBZ:BU}, Theorem 5.5.5]\label{thm:Z2_embedd}
Let $\K$ be a simplicial complex. If
\[
\ind \djn{\K} > d,
\]
then $\K$ is not embeddable into the $d$-sphere.
\end{thm}
The $\Zt$-index is rather difficult to calculate for general spaces. Luckily,
for the situation in which we will apply Theorem \ref{thm:Z2_embedd} there is
a beautiful theorem due to Karanbir Sarkaria (see \cite{MatousekBZ:BU}). In
order to state it properly we need some more definitions.
{\bf Minimal non-faces.} Let $\K \subset 2^V$ be a simplicial complex. A set
$F \subset V$ is called a \emph{non-face} if $F \not\in \K$ and its a
\emph{minimal non-face} if every proper subset of $F$ is in $\K$. We will
denote by $\nf(\K)$ the set of minimal non-faces.
{\bf Generalized Kneser graphs.} For a collection of sets $\nf = \{ F_1,
\dots, F_k\}$ we denote by $\KG(\nf)$ the (abstract) graph with vertex set
$\nf$. Two vertices $F_i, F_j$ share an edge iff $F_i \cap F_j = \emptyset$.
Such a graph is called a \emph{generalized Kneser graph}.
Finally, for a graph $G$ we denote by $\chi(G)$ its \emph{chromatic number},
i.e.\ the minimal number of colors to properly color the graph.
\begin{thm}[Sarkaria's coloring/embedding theorem]\label{thm:sarkaria}
Let $\K$ be a simplicial complex with $n$ vertices and let $\nf = \nf(\K)$
be the set of minimal non-faces. Then
\[
\ind \djn{\K} \ge n - \chi(\KG(\nf)) - 1.
\]
\end{thm}
Taking up the example of triangle times triangle for the last time, let us
use Theorem \ref{thm:sarkaria} to show that $\K = \tbinom{[3]}{\le 1 }^{*2}$
does not embed into the $2$-sphere. This complex has $6$ vertices and, for
reasons we will give in the next section, the Kneser graph of its non-faces
is, again, the complete bipartite graph $\K_{3,3}$. Thus, using Sarkaria's
theorem, we get
\[
\ind \djn{\K} \ge 6 - 2 - 1 = 3,
\]
which shows that $\K_{3,3}$ is not planar.
\section{Analysis of the complement complex}
\label{sec:compl_complex}
Although determining upper bounds on the chromatic number of graphs is easier
than finding equivariant maps, it is, in general, still hard enough. The key
property that enables us to calculate chromatic numbers for the Kneser graphs
we will encounter is that the complexes are made up of (possibly) simpler
ones, that is they are joins of complexes. The following results will show
that this continues to hold if we pass from complexes to non-faces and then to
Kneser graphs.
\begin{lem}\label{lem:nf_of_join}
Let $\K$ and $\Ll$ be simplicial complexes. Then
\[
\nf(\K * \Ll) = \{ F \uplus \emptyset : F \in \nf(\K) \} \cup
\{ \emptyset \uplus G : G \in \nf(\Ll) \}.
\]
\end{lem}
\begin{proof}
Let $F \uplus G \in \nf(\K * \Ll)$ and $i \in F$ and $j \in G$. Since $F
\uplus G$ is a minimal non-face, it follows that $F\backslash i \uplus G$
and $F \uplus G\backslash j$ are both in $\K*\Ll$. This, however, implies
that $F \in \K$ and $G \in \Ll$.
\end{proof}
On the level of Kneser graphs this fact results in a \emph{bipartite sum} of
the respective Kneser graphs. Let $G$ and $H$ be graphs with disjoint vertex
sets $U$ and $V$. The bipartite sum of $G$ and $H$ is the graph $G \bowtie H$
with vertex set $U \cup V$ and edges $E(G) \cup E(H) \cup (U \times V)$.
\begin{prop} \label{prop:chi_sum}
Let $G$ and $H$ be graphs. Then
\[
\chi(G \bowtie H) = \chi(G) + \chi(H).
\]
\end{prop}
\begin{proof}
The edges $U \times V \subset E(G \bowtie H)$ force the set of colors on
$U$ and $V$ to be disjoint. Thus a coloring on $G \bowtie H$ is minimal
iff it is minimal on the subgraphs $G$ and $H$.
\end{proof}
The complex to which we want to apply the result is $\K = \Ll^{*d}$ with $\Ll =
\tbinom{[d+1]}{\le 1}$. We will analyze the chromatic number of $\KG(\nf)$ for
$\nf = \nf(\Ll)$ and use Proposition \ref{prop:chi_sum} to get an obstruction
to the embeddability of $\K$ into some sphere.
From the definition of $\Ll$ we see that the minimal non-faces are exactly the
two element subsets of $[d+1]$, that is $\nf = \tbinom{[d+1]}{2}$. The
resulting Kneser graph $\KG(\nf)$ is an instance of a famous family of graphs,
the {\it ordinary} Kneser graphs $\KG_{n,k} := \KG\tbinom{[n]}{k}$. The
determination of their chromatic numbers is one of the first success stories
of topological combinatorics.
\begin{thm}[Lov\'{a}sz--Kneser theorem \cite{lov78}]
For $0 < 2k - 1 \le n$ the chromatic number of the Kneser graph
$\KG_{n,k}$ is $\chi(\KG_{n,k}) = n - 2k + 2$.
\end{thm}
With that last bit of information we can finally complete the proof of Theorem
\ref{thm:main_stronger}.
\begin{proof}[Proof of Theorem \ref{thm:main_stronger}]
Assume that there is a realization of a $d$-fold product of $d$-simplices
whose projection to $d$-space preserves all the vertices. This implies, by
Corollary \ref{cor:bla}, that the complex $\K = \tbinom{[d+1]}{\le 1
}^{*d}$ is embeddable into a $(2d-2)$-sphere.
Let $\Ll = \tbinom{[d+1]}{\le 1}$ and let $\nf(\Ll) = \tbinom{[d+1]}{2}$ be
the minimal non-faces of $\Ll$. For the associated Kneser graph
$\KG(\nf(\Ll)) = \KG_{d+1,2}$ we have $\chi(\KG_{d+1,2}) = d-1$.
By Lemma \ref{lem:nf_of_join} and Proposition \ref{prop:chi_sum} we have for
$\nf = \nf(\K)$
\[
\ind \djn{\K} \ge d(d+1) - \chi( \KG(\nf)) - 1 =
d(d+1) - d \chi(\KG_{d+1},2) - 1 = 2d -1 > 2d -2
\]
By Theorem \ref{thm:Z2_embedd}, this contradicts the claim that $\K$ is
embeddable into a $(2d-2)$-sphere.
\end{proof}
It is true that any upper bound on the chromatic number of $\KG_{d+1,2}$ would
have sufficed and it was thus unnecessary to invoke the Lov\'{a}sz--Kneser
theorem. We, nevertheless, wish to argue that the application of the
Lov\'{a}sz--Kneser is justified. Sarkaria's theorem can be used with any upper
bound on the chromatic number of the Kneser graph. This, however, results in a
weaker bound on the $\Zt$-index of $\djn{\K}$. Using the actual chromatic
number shows that Theorem \ref{thm:main_stronger} is sharp concerning the
number of factors, i.e. there are no topological obstruction for a product of
less than $d$ simplices. On the other hand, by Proposition 5.3.2 in \cite[p.
96]{MatousekBZ:BU}, we have that $2d-1 \ge \ind \djn{\K}$ and, therefore, the
calculation in the preceding proof gives the actual $\Zt$-index. Thus, Theorem
\ref{thm:main_stronger} is also sharp with respect to the dimension of the
target space, i.e.\ projecting to a space of dimension $\ge d$. This, in
particular, stands in favor for the result of Fukuda \& Weibel.
\section{Remarks}\label{sec:remarks}
At the Oberwolfach-Workshop ``Geometric and Topological Combinatorics'' in
January 2007 Rade \v{Z}ivaljevi\'{c} suggested a different argument involving
Lov\'{a}sz' \emph{colored Helly theorem}.
\begin{thm}[Colored Helly Theorem; cf.\ \cite{lov74}]
Let $\C_1,\dots,\C_r$ be collections of convex sets in $\R^d$ with $r \ge
d+1$. If $\cap_{i=1}^r C_i \not= \emptyset$ for every choice $C_i \in
\C_i$ then there is a $j \in [r] $ such that $\cap_{C \in \C_j} C \not=
\emptyset$.
\end{thm}
The following proof was supplied by Imre B\'{a}r\'{a}ny (personal
communication): Let $P_1,\dots,P_r \subset \R^d$ be $d$-polytopes and let
$\C_i = \{C_v \subset \Rd{d} : v \in \V P_i\}$. The $C_v$ are defined by the
condition that $\ell \in C_v$ if and only if $\ell$ attains its unique maximum
over $P_i$ in $v$. It is clear that the $C_v$ are pairwise disjoint. Now, if
$P_1 + \cdots + P_r$ attains the trivial upper bound then for every choice of
vertices $v_i \in \V P_i$ the intersection $C_{v_1} \cap \cdots \cap C_{v_r}$
is non-empty and, thus, contradicts the colored Helly theorem.
In the colored Helly theorem the bound $r \ge d+1$ is tight and, thus, yields
Theorem \ref{thm:main} in a slightly weaker version with at least $d+1$
summands.
In Section \ref{sec:problem_reductions} we claimed the existence of a
combinatorial product of two triangles that projects to a plane $8$-gon.
Consider the polytope $P \subset \R^4$ given as the set of solutions to the
following system of inequalities
\[
\begin{array}{r}
\scriptstyle 1 \\
\scriptstyle 2 \\
\scriptstyle 3 \\
\scriptstyle 4 \\
\scriptstyle 5 \\
\scriptstyle 6 \\
\end{array}
\left(
\begin{array}{rrrr}
1 & 1 & & \\
-1 & 1 & & \\
0 & -1 & -\eps & \\
& -\eps & -1 & 0 \\
& & 1 & 1 \\
& & 1 & -1 \\
\end{array}\right) \mathbf{x} \le
\left( \begin{array}{r}
1 \\ 1 \\ 1 \\ 1 \\ 1 \\ 1 \\
\end{array}\right)
\]
The numbers to the left label the facets of $P$. For $\eps = 0$ this is just
a Cartesian product of two triangles and, since this is a simple polytope, we
can choose $\eps > 0$ sufficiently small without changing the combinatorial
type. Taking $\pi : \R^4 \rightarrow \R^2$ to be the projection to the first
and last coordinate and identifying $\Rd{4}$ with $\R^4$ via the standard
scalar product we get the ordered set
\[
G = q^*(\V P^\dual) = \left(
\begin{array}{rrrrrr}
1 & 1 & -1 & -\eps & & \\
& & -\eps & -1 & 1 & 1 \\
\end{array}\right)
\]
For $0 < \eps \le 1$ the set $G$ is the Gale transform of a polytope $\A$
combinatorially equivalent to an octahedron (e.g.\ set $\eps = 1$ and observe
that $G$ is a Gale transform of a regular octahedron.) As intersections of
facets the set of vertices is given by $S = \{ [6] \backslash \{i,j\} :
\{i,j\} \in \K \}$ where the complement complex $\K$ is the complete
bipartite graph on the partition $\{1,2,3\}$ and $\{4,5,6\}$.
We show that the only vertex $v_0$ that fails to
survive the projection is given by the intersection of the facets $[6]
\backslash \{1,4\}$. By the Projection Lemma and Gale duality this is case if
and only if $\K - \{1,4\}$ is a subcomplex of the $1$-skeleton of
$\A$. Figure \ref{fig:octahedron} shows $\A$ and the embedding of $\K -
\{1,4\}$, thus finishing the proof.
The missing edge between the vertices $1$ and $4$ shows that $v_0$ fails
short of being a vertex of $\pi(P)$.
\begin{figure}[ht]
\centering
\includegraphics[height=8cm]{octahedron}\\
\caption{The polytope $\A$ associated to $P$. The marked edges correspond
to the embedding of $\K - \{1,4\}$, that is
$\K_{3,3}$ minus an edge.} \label{fig:octahedron}
\end{figure}
\bibliographystyle{siam}
\begin{small}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,851 |
Q: Find the top value of each row I have a data.frame :
cities <- c("Nantes", "Paris", "London", "Munchen")
variable1 <- c(100, 20, 5, 30)
variable2 <- c(10, 13, 2, 30)
variable3 <- c(10, 200, 5, 300)
df <- data.frame(cities, variable1, variable2, variable3)
My result :
cities variable1 variable2 variable3
1 Nantes 100 10 10
2 Paris 20 13 200
3 London 5 2 5
4 Munchen 30 30 300
What I want :
variable1 | Nantes
variable2 | Munchen
variable3 | Munchen
A: You can use which.max in sapplyto get the index of max per column.
df[sapply(df[-1], which.max), 1]
#[1] "Nantes" "Munchen" "Munchen"
And to get also the colnames:
cbind(colnames(df)[-1], df[sapply(df[-1], which.max), 1])
# [,1] [,2]
#[1,] "variable1" "Nantes"
#[2,] "variable2" "Munchen"
#[3,] "variable3" "Munchen"
A: similar to GKi's answer but with labled output
apply(df[,-1], 2, function(x) df[which.max(x),1])
variable1 variable2 variable3
Nantes Munchen Munchen
A: An option with tidyverse
library(dplyr)
library(tidyr)
df %>%
summarise_if(is.numeric, which.max) %>%
pivot_longer(everything()) %>%
mutate(value = df$cities[value])
# A tibble: 3 x 2
# name value
# <chr> <chr>
#1 variable1 Nantes
#2 variable2 Munchen
#3 variable3 Munchen
A: idx <- sapply(df[-1], which.max)
data.frame(vars = names(idx), cities = df[1][idx])
# vars cities
# 1 variable1 Nantes
# 2 variable2 Munchen
# 3 variable3 Munchen
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,029 |
\section{Introduction}\label{s1}
It is generally believed that the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase appears in a superconductor when the pairing between different fermion species is under the circumstances of mismatched Fermi surfaces~\cite{LO1964,FF1964,Casalbuoni2004}. The mismatched Fermi surfaces are normally induced by the Zeeman energy splitting $2\delta\mu$ in a magnetic field~\cite{CC1962}. Early studies of the LOFF phase were restricted to 1D structures, which include the Fulde-Ferrell (FF) state~\cite{FF1964} with a plane-wave order parameter $\Delta(z)=\Delta e^{2iqz}$ and the Larkin-Ovhinnikov (LO) state~\cite{LO1964} with an antipodal-wave order parameter $\Delta(z)=2\Delta \cos(2qz)$. For $s$-wave pairing at weak coupling, it is known that the FF or LO state exists in a narrow window $\delta\mu_1<\delta\mu<\delta\mu_2$, where the lower critical field $\delta\mu_1=0.707\Delta_0$ and the upper critical field $\delta\mu_2=0.754\Delta_0$~\cite{LO1964,FF1964} with $\Delta_0$ being the pairing gap at vanishing mismatch. However, since the thermodynamic critical field is much lower than $\delta\mu_1$ due to strong orbit effect, it is rather hard to observe the LOFF state in ordinary superconductors \cite{CC1962}. In recent years, experimental evidences for the LOFF state in some superconducting materials have been
reported~\cite{Heavyfermion,HighTc,Organic,FeSe}.
The studies of color superconductivity in dense quark matter promoted new interests in the LOFF state
\cite{Alford2001,Bowers2002,Shovkovy2003,Alford2004,EFG2004,Huang2004,Casalbuoni2005,Fukushima2005,Ren2005,Gorbar2006,Three-flavor,He2007, Anglani2014}.
Color superconductivity in dense quark matter appears due to the attractive interactions in certain diquark channels ~\cite{CSC01,CSC02,CSC03,CSC04,CSCreview}. Under the compact star constraints, different quark flavors ($u$, $d$, and $s$) acquire mismatched Fermi surfaces because of the Beta equilibrium and the electric charge neutrality. On the other hand, recent experiments on ultracold atomic Fermi gases provided a controllable way to study the fermion superfluidity with population imbalance~\cite{Atomexp,Sheehy2006}. Quark color superconductors under compact star constraints as well as atomic Fermi gases with population imbalance are rather clean systems to realize the long-sought LOFF phase.
In addition to the simple FF and LO states, there exist a variety of crystal structures. The general form of the crystal structure of the order parameter can be expressed as~\cite{Casalbuoni2004}
\begin{eqnarray}\label{crystal}
\Delta({\bf r})=\sum_{k=1}^P\Delta e^{2iq\hat{\bf n}_k\cdot{\bf r}}.
\end{eqnarray}
A specific crystal structure corresponds to a multi-wave configuration determined by the $P$ unit vectors ${\bf n}_{k}$ ($k=1,2,...,P$). Around the tricritical point in the temperature-mismatch phase diagram, the LOFF phase can be studied rigorously by using the Ginzburg-Laudau (GL) analysis since both the gap parameter $\Delta$ and the pair momentum $q$ are vanishingly small \cite{Casalbuoni2004}. It was found that the LO state is preferred near the tricritical point~\cite{Buzdin1997,Combescot2002,Ye2007}. However, the real ground state of the LOFF phase is still not quite clear due to the limited theoretical approaches at zero temperature. Various theoretical approaches suggested that the LOFF state has a complicated crystal structure near its phase transition to the normal state~\cite{Bowers2002,EFG2004,Combescot2004,Combescot2005,Buballa2009,Cao2015}. A recent self-consistent treatment of the 1D modulation showed that a solitonic lattice structure is preferred near the phase transition to the BCS state~\cite{Buballa2009}.
The GL free energy is important for us to understand the nature of the phase transition to the normal state and to search for the most preferred crystal structure near the phase transition point. In a pioneer work, Bowers and Rajagopal investigated 23 crystal structures at weak coupling by using the GL approach~\cite{Bowers2002}. They evaluated the GL free energy up to the sixth order in $\Delta$,
\begin{eqnarray}
\frac{\Omega_{\rm GL}(\Delta)}{N_0}= P\alpha\Delta^2+\frac{1}{2}\beta\Delta^4+\frac{1}{3}\gamma\Delta^6+{\cal O}(\Delta^8),
\end{eqnarray}
where $N_0$ is the density of state at the Fermi surface. The coefficient $\alpha$ is universal for all crystal structures and is given by~\cite{Bowers2002}
\begin{eqnarray}\label{alpha}
\alpha(\delta\mu,q)=-1+\frac{\delta\mu}{2q}\ln\left(\frac{q+\delta\mu}{q-\delta\mu}\right)
-\frac{1}{2}\ln\left[\frac{\Delta_0^2}{4(q^2-\delta\mu^2)}\right].
\end{eqnarray}
Near the conventional second-order phase transition point $\delta\mu=\delta\mu_2$ with the optimal pair momentum
$q=1.1997\delta\mu$, we have $\alpha\simeq(\delta\mu-\delta\mu_2)/\delta\mu_2$. The GL approach is meaningful if the phase transition is of second order or weak first order.
The GL coefficients $\beta$ and $\gamma$ for 23 crystal structures were evaluated in~\cite{Bowers2002}. For most of the structures, we find $\beta<0$, which leads to first-order phase transitions. Among the structures with $\gamma>0$, the favored one seems to be the body-centered cubic (BCC) structure with $P=6$. The order parameter can be expressed as
\begin{equation}
\Delta({\bf r})=2\Delta\left[\cos(2qx)+\cos(2qy)+\cos(2qz)\right].
\end{equation}
Further, it was \emph{conjectured} that the face-centered cubic (FCC) structure with $P=8$ is the most preferred structure since both $\beta$ and $\gamma$ are negative and their absolute values are the largest~\cite{Bowers2002}. The order parameter can be expressed as
\begin{eqnarray}
\Delta({\bf r})=8\Delta\cos\left(\frac{2qx}{\sqrt{3}}\right)\cos\left(\frac{2qy}{\sqrt{3}}\right)\cos\left(\frac{2qz}{\sqrt{3}}\right).
\end{eqnarray}
For the BCC structure, the GL free energy up to the sixth order in $\Delta$ predicts a \emph{strong first-order} phase transition at $\delta\mu=\delta\mu_*\simeq3.6\Delta_0$ with a large gap parameter $\Delta\simeq0.8\Delta_0$ at $\delta\mu\lesssim\delta\mu_*$~\cite{Bowers2002}. The prediction of a strong first-order phase transition indicates that the GL approach is not valid or the higher-order terms in $\Delta$ are important. For the FCC structure, the GL free energy up to the sixth order in $\Delta$ actually gives \emph{no prediction} because both $\beta$ and $\gamma$ are negative.
On the other hand, there exist some other approaches that do not use the GL approximation. Combescot and Mora employed Eilenberger's quasiclassical equation with a Fourier expansion for the order parameter~\cite{Combescot2004,Combescot2005}. This approach predicted that the BCC-normal phase transition is of \emph{rather weak first order}: The upper critical field $\delta\mu_*$ is only $3.7\%$ higher than $\delta\mu_2$ and $\Delta\simeq0.1\Delta_0$ at $\delta\mu\lesssim\delta\mu_*$~\cite{Combescot2005}. For the FCC structure, it was found that its upper critical field is only $1.6\%$ higher than $\delta\mu_2$ and hence it is less favored than BCC. Another study employed a solid-state-like approach which calculated the free energy of the BCC structure by directly diagonalizing the Hamiltonian matrix in the Bloch space~\cite{Cao2015}. This approach also predicted that the BCC-normal phase transition is of weak first order and the upper critical field of BCC is slightly higher than $\delta\mu_2$.
The contradiction between the predictions from the above approaches and from the GL approach indicates that the higher-order terms in the GL free energy are rather important for a quantitative prediction. Actually, for a first-order phase transition, the higher-order expansions are crucial to determine whether the first-order transition is weak or strong. For an intuitive understanding, let us add the eighth-order term in the GL free energy for the BCC structure. We have
\begin{eqnarray}
\frac{\Omega_{\rm GL}(\Delta)}{N_0}= P\alpha\Delta^2+\frac{1}{2}\beta\Delta^4+\frac{1}{3}\gamma\Delta^6+\frac{1}{4}\eta\Delta^8
+{\cal O}(\Delta^{10}).
\end{eqnarray}
As a naive example, we assume $\eta\geq0$. For $\eta=0$, we obtain a strong first-order phase transition. However, the first-order phase transition becomes weaker and weaker if we increase the value of $\eta$. For $\eta\rightarrow+\infty$, the phase transition approaches second order and $\delta\mu_*\rightarrow\delta\mu_2$. On the other hand, if $\eta$ is small or even negative, the higher-order terms such as
${\cal O}(\Delta^{10})$ may become important. Therefore, to give more precise predictions within the GL approach we need to evaluate the GL free energy to a sufficiently high order in $\Delta$. Actually, if we can evaluate the GL free energy to arbitrary order and determine the convergence properties of the GL series, we may even treat the strong first-order phase transition within the GL approach.
The higher-order GL coefficients can be evaluated by using the diagrammatic approach used in~\cite{Bowers2002}. In this approach, to evaluate the $2k$-th order GL coefficient one needs to sum all possible configurations that satisfy the momentum constraint
\begin{equation}\label{Mconstraint}
\sum_{i=1}^{2k}(-1)^{i+1}{\bf q}_i={\bf 0}
\end{equation}
for a set of $2k$ wave vectors $\{{\bf q}_1{\bf q}_2...{\bf q}_{2k}\}$ with ${\bf q}_i=q\hat{\bf n}_i$. For large $k$, the number of the configurations becomes very large for the crystal structures with large number of waves $P$. Moreover, one needs to introduce $2k$ Feynman parameters to evaluate the integrals. Therefore, the calculation of the higher-order terms is tedious and complicated in this formalism.
In this work, we introduce a new derivation of the GL free energy based on a solid-state physics approach to the crystal structures. This derivation provides a simple matrix formalism for the GL coefficients without any momentum constraint. We find that the formalism used in~\cite{Bowers2002} and our formalism can be attributed to two different \emph{representations} of the fermion field: The diagrammatic approach~\cite{Bowers2002} employs the
usual continuous momentum representation, while our derivation uses the discrete Bloch representation. Since the matrix operations can be easily realized by using a computer, this new formalism may enable us to calculate the GL free energy to arbitrary order in $\Delta$.
The paper is organized as follows. In Sec. \ref{s2} we briefly review the diagrammatic approach to the GL free energy. In Sec. \ref{s3} we present
our new derivation of the GL free energy by using the solid-state physics approach. The explicit matrix formalism of the GL coefficients for some crystal structures are presented in Sec. \ref{s4}. We summarize in Sec. \ref{s5}. The natural units $\hbar=k_{\rm B}=1$ will be used throughout.
\section{Continuous momentum representation}\label{s2}
We focus on the general two-flavor pairing at high density, low temperature, and weak coupling. In this case, the antiparticle degrees of freedom play no role. Therefore, we can start from a general effective Lagrangian for two-flavor pairing at high density. The Lagrangian density is
given by~\cite{Casalbuoni2004}
\begin{eqnarray}
{\cal L}_{\rm eff}=\psi^\dagger\left[i\partial_t-\varepsilon(\hat{\bf p})+\hat{\mu}\right]
\psi+\frac{g}{4}(\psi^\dagger\sigma_2\psi^*)(\psi^{\rm T}\sigma_2\psi),
\end{eqnarray}
where $\psi=(\psi_{\rm u},\psi_{\rm d})^{\rm T}$ denotes the two-flavor fermion field, $\varepsilon(\hat{\bf p})$ is the fermion dispersion with
$\hat{\bf p}=-i\mbox{\boldmath{$\nabla$}}$, $g$ is a contact coupling which represents the attractive interaction, and $\sigma_2$ is the second Pauli matrix in the flavor space. We shall neglect all other internal degrees of freedom, such as color and spin. These degrees of freedom contribute a simple degenerate factor and can be absorbed into the definition of the density of state $N_0$ at the Fermi surface. The fermion chemical potentials are specified by the diagonal matrix $\hat{\mu}={\rm diag}(\mu_{\rm u},\mu_{\rm d})$ in the flavor space, where
\begin{eqnarray}
\mu_{\rm u}=\mu+\delta\mu,\ \ \ \ \ \ \ \ \ \ \ \ \mu_{\rm d}=\mu-\delta\mu.
\end{eqnarray}
Here $\delta\mu$ plays the role of the mismatch between the Fermi surfaces. For ultra-relativistic fermion systems such as dense quark matter we take $\varepsilon(\bf p)=|{\bf p}|$. The model also works for nonrelativistic fermion systems such as cold atomic Fermi gases. In this case we take $\varepsilon({\bf p})={\bf p}^2$ (we set the fermion mass $M=1/2$ with proper units). Weak coupling requires that the pairing gap $\Delta_0$ at $\delta\mu=0$ is much smaller than the Fermi energy $\varepsilon_{\rm F}\simeq\mu$. At weak coupling, the physical results should be universal if we properly scale the physical quantities by using the pairing gap $\Delta_0$ and the density of states $N_0$ at the Fermi surface.
To evaluate the GL free energy, we start from the partition function ${\cal Z}$ of the system. In the imaginary time formalism, it is given by
\begin{eqnarray}
{\cal Z}=\int [d\psi][d\psi^\dagger]e^{-{\cal S}_{\rm eff}}
\end{eqnarray}
with the Euclidean action
\begin{eqnarray}
{\cal S}_{\rm eff}=-\int_0^{1/T}d\tau\int_Vd^3{\bf r}{\cal L}_{\rm eff}.
\end{eqnarray}
Here $\tau=it$ is the imaginary time and $T$ is the temperature. Once the partition function ${\cal Z}$ is evaluated, the free energy density is given by
\begin{eqnarray}
\Omega=-\frac{T}{V}\ln{\cal Z}.
\end{eqnarray}
Fermionic superconductivity is characterized by a nonzero expectation value of the difermion fields
\begin{eqnarray}
\varphi(\tau,{\bf r})=-g\psi_{\rm u}(\tau,{\bf r})\psi_{\rm d}(\tau,{\bf r})
\end{eqnarray}
The order parameter $\Delta({\bf r})=\langle\varphi(\tau,{\bf r})\rangle$ is static but inhomogeneous in the LOFF state.
At weak coupling and at low temperature, the order parameter fluctuation becomes negligible and we can employ the mean-field approach.
With the help of the Nambu-Gor'kov (NG) spinor
\begin{equation}
\Psi(\tau,{\bf r})=\left(\begin{array}{cc} \psi_{\rm u}^{\phantom{*}}(\tau,{\bf r}) \\ \psi_{\rm d}^*(\tau,{\bf r})\end{array}\right),
\end{equation}
the mean-field Lagrangian can be expressed as
\begin{eqnarray}
{\cal L}_{\rm{MF}}=\Psi^\dagger(\tau,{\bf r})(-\partial_\tau-{\cal H}_{\rm MF})\Psi(\tau,{\bf r})-\frac{|\Delta({\bf r})|^2}{g},
\end{eqnarray}
where the Hamiltonian operator is given by
\begin{eqnarray}
{\cal H}_{\rm MF}=\left(\begin{array}{cc} \varepsilon(\hat{\bf p})-\mu-\delta\mu & \Delta({\bf r})\\
\Delta^*({\bf r})& -\varepsilon(\hat{\bf p})+\mu-\delta\mu \end{array}\right).
\end{eqnarray}
For convenience we first consider a finite system in a cubic box defined as $x,y,z\in [-L/2,L/2]$ and then set $L\rightarrow\infty$. Imposing the periodic boundary condition, the fermion momentum becomes discrete and is given by
\begin{eqnarray}\label{dmomentum}
{\bf p}=\frac{2\pi}{L}\left(l{\bf e}_x+m{\bf e}_y+n{\bf e}_z\right),\ \ \ l,m,n\in \mathbb{Z}.
\end{eqnarray}
To convert to the momentum space, we use the Fourier transformation for the fermion fields
\begin{eqnarray}\label{momentum-rep}
\Psi(\tau,{\bf r})&=&\frac{1}{\sqrt{V}}\sum_{{\bf p}}\sum_{\omega_n}\tilde{\Psi}(i\omega_n,{\bf p})
e^{-i\omega_n\tau+i{\bf p}\cdot{\bf r}},\nonumber\\
\Psi^\dagger(\tau,{\bf r})&=&\frac{1}{\sqrt{V}}\sum_{{\bf p}}\sum_{\omega_n}\tilde{\Psi}^\dagger(i\omega_n,{\bf p})
e^{i\omega_n\tau-i{\bf p}\cdot{\bf r}},
\end{eqnarray}
where $V=L^3$ is the system volume and $\omega_n=(2n+1)\pi T$ $(n\in \mathbb{Z})$ is the fermion Matsubara frequency.
For the general crystal structure of the order parameter given by (\ref{crystal}), the mean-field action in the momentum space can
be evaluated as
\begin{widetext}
\begin{eqnarray}
{\cal S}_{\rm{MF}}=\frac{V}{T}\frac{P\Delta^2}{g}-\frac{1}{T}\sum_{\omega_n,\omega_{n^\prime}}
\sum_{{\bf p},{\bf p}^\prime}\tilde{\Psi}^\dagger(i\omega_n,{\bf p})\left(i\omega_n\delta_{\omega_n,\omega_{n^\prime}}
\delta_{{\bf p},{\bf p}^\prime}-\delta_{\omega_n,\omega_{n^\prime}}{\cal H}_{{\bf p},{\bf p}^\prime}\right)
\tilde{\Psi}(i\omega_{n^\prime},{\bf p}^\prime),
\end{eqnarray}
\end{widetext}
where ${\bf p},{\bf p}^\prime$ are the discrete momenta given by (\ref{dmomentum}) and the Hamiltonian matrix ${\cal H}_{{\bf p},{\bf p}^\prime}$ reads
\begin{eqnarray}
{\cal H}_{{\bf p},{\bf p}^\prime}=\left(\begin{array}{cc} (\xi_{\bf p}-\delta\mu)\delta_{{\bf p},{\bf p}^\prime}
& \Delta (F_+)_{{\bf p},{\bf p}^\prime}\\ \Delta (F_-)_{{\bf p},{\bf p}^\prime}
& (-\xi_{\bf p}-\delta\mu)\delta_{{\bf p},{\bf p}^\prime} \end{array}\right).
\end{eqnarray}
Here and in the following $\xi_{\bf p}=\varepsilon({\bf p})-\mu$. The matrices $F_\pm$ that characterizes the crystal structure are given by
\begin{eqnarray}
(F_\pm)_{{\bf p},{\bf p}^\prime}=\sum_{k=1}^P\delta_{{\bf p}-{\bf p}^\prime,\pm{\bf q}_k},
\end{eqnarray}
where ${\bf q}_k=q{\bf n}_k$.
The partition function in the mean-field approximation can be evaluated in the momentum representation. We have
\begin{eqnarray}
{\cal Z}_{\rm MF}=\int [d\tilde{\Psi}][d\tilde{\Psi}^\dagger]e^{-{\cal S}_{\rm MF}}.
\end{eqnarray}
Completing the Gaussian integral, we obtain the free energy
\begin{eqnarray}
\Omega=\frac{P}{g}\Delta^2-\frac{T}{V}\sum_{\omega_n}{\rm Trln}\left[\frac{(S^{-1})_{{\bf p},{\bf p}^\prime}}{T}\right],
\end{eqnarray}
where the Trln acts in the momentum space and the NG space. The inverse fermion propagator $S^{-1}$ defined in these spaces is given by
\begin{eqnarray}
(S^{-1})_{{\bf p},{\bf p}^\prime}(i\omega_n)=i\omega_n\delta_{{\bf p},{\bf p}^\prime}-{\cal H}_{{\bf p},{\bf p}^\prime}.
\end{eqnarray}
The free energy can be evaluated if we can diagonalize the Hamiltonian matrix ${\cal H}_{{\bf p},{\bf p}^\prime}$. However, this is infeasible because the momenta ${\bf p}$ and ${\bf p}^\prime$ become continuous in the large volume limit. We therefore turn to the GL expansion of the free energy. The standard field theoretical approach is to use the derivative expansion. First, we separate the``BCS" self-energy $\Sigma_\Delta$ and write
\begin{eqnarray}
(S^{-1})_{{\bf p},{\bf p}^\prime}=(S_0^{-1})_{{\bf p},{\bf p}^\prime}-(\Sigma_\Delta)_{{\bf p},{\bf p}^\prime},
\end{eqnarray}
where the inverse of the free fermion propagator reads
\begin{eqnarray}
(S_0^{-1})_{{\bf p},{\bf p}^\prime}=\left(\begin{array}{cc} (S_+^{-1})_{{\bf p},{\bf p}^\prime} & 0 \\ 0
& (S_{-}^{-1})_{{\bf p},{\bf p}^\prime} \end{array}\right),
\end{eqnarray}
with the matrix elements given by
\begin{eqnarray}
(S_\pm^{-1})_{{\bf p},{\bf p}^\prime}=(i\omega_n+\delta\mu\mp\xi_{\bf p})\delta_{{\bf p},{\bf p}^\prime}.
\end{eqnarray}
The self-energy term $\Sigma_\Delta$ is given by
\begin{eqnarray}
(\Sigma_\Delta)_{{\bf p},{\bf p}^\prime}=\Delta F_{{\bf p},{\bf p}^\prime},
\end{eqnarray}
where the matrix $F$ reads
\begin{eqnarray}
F_{{\bf p},{\bf p}^\prime}=\left(\begin{array}{cc} 0 & (F_+)_{{\bf p},{\bf p}^\prime} \\ (F_-)_{{\bf p},{\bf p}^\prime}
& 0 \end{array}\right).
\end{eqnarray}
Using the derivative expansion, we obtain
\begin{eqnarray}
\Omega=\Omega_{\rm N}+\frac{P}{g}\Delta^2+\frac{T}{V}\sum_{\omega_n}
\sum_{l=1}^\infty\frac{\Delta^l}{l}{\rm Tr} \left[(S_0F)^l\right],
\end{eqnarray}
where $\Omega_{\rm N}$ is the free energy of the normal state,
\begin{eqnarray}\label{Normal}
\Omega_{\rm N}=-\frac{T}{V}\sum_{\omega_n}{\rm Trln}\left[\frac{(S_0^{-1})_{{\bf p},{\bf p}^\prime}}{T}\right].
\end{eqnarray}
To obtain the GL free energy, we first complete the trace in the NG space. It is easy to show the trace vanishes for odd $l$. After some manipulation, we obtain the GL free energy
\begin{eqnarray}
\Omega_{\rm GL}(\Delta)=\alpha_2\Delta^2+\sum_{k=2}^\infty\frac{\alpha_{2k}}{k}\Delta^{2k}.
\end{eqnarray}
The second-order GL coefficient $\alpha_2$ is given by
\begin{eqnarray}
\alpha_2=\frac{P}{g}+\frac{T}{V}\sum_{\omega_n}{\rm Tr} \left[S_+F_+S_-F_-\right].
\end{eqnarray}
The higher-order GL coefficients with $k\geq2$ are given by
\begin{eqnarray}
\alpha_{2k}=\frac{T}{V}\sum_{\omega_n}{\rm Tr} \left[(S_+F_+S_-F_-)^k\right].
\end{eqnarray}
Note that the trace is now taken only in the momentum space.
Next we complete the trace in the momentum space and obtain the integral expressions of the GL coefficients. For the second order, we have
\begin{widetext}
\begin{eqnarray}
{\rm Tr} \left[S_+F_+S_-F_-\right]&=&\sum_{a=1}^P\sum_{b=1}^P\sum_{\bf p}\sum_{{\bf p}_1,{\bf p}_2,{\bf p}_3}
\frac{\delta_{{\bf p},{\bf p}_1}}{i\omega_n+\delta\mu-\xi_{\bf p}}\delta_{{\bf p}_1-{\bf p}_2,2{\bf q}_a}
\frac{\delta_{{\bf p}_2,{\bf p}_3}}{i\omega_n+\delta\mu+\xi_{{\bf p}_2}}\delta_{{\bf p}_3-{\bf p},-2{\bf q}_b}\nonumber\\
&=&\sum_{a=1}^P\sum_{b=1}^P\sum_{\bf p}\sum_{{\bf p}^\prime}
\frac{1}{i\omega_n+\delta\mu-\xi_{\bf p}}\delta_{{\bf p}-{\bf p}^\prime,2{\bf q}_a}
\frac{1}{i\omega_n+\delta\mu+\xi_{{\bf p}^\prime}}\delta_{{\bf p}^\prime-{\bf p},-2{\bf q}_b}\nonumber\\
&=&\sum_{a=1}^P\sum_{\bf p}\frac{1}{i\omega_n+\delta\mu-\xi_{\bf p}}
\frac{1}{i\omega_n+\delta\mu+\xi_{{\bf p}-2{\bf q}_a}}.
\end{eqnarray}
Therefore, at zero temperature the second-order GL coefficient $\alpha_2$ can be expressed as
\begin{eqnarray}
\frac{\alpha_2}{P}=\frac{1}{g}+\int_{-\infty}^\infty\frac{dE}{2\pi}\int\frac{d^3{\bf p}}{(2\pi)^3}
\frac{1}{iE+\delta\mu-\xi_{\bf p}}\frac{1}{iE+\delta\mu+\xi_{{\bf p}-2{\bf q}}}.
\end{eqnarray}
We notice that $\alpha_2/P$ is universal for all crystal structures. The above integral suffers from ultraviolet (UV) divergence. In the weak coupling limit, the pairing and hence the momentum integral is dominated near the Fermi surface. It is convenient to use the regularization scheme that the momentum integral is restricted near the Fermi surface; i.e., $-\Lambda<|{\bf p}|-\mu<\Lambda$.
Using the fact that $\delta\mu, q\ll\Lambda\ll \mu$, we can express $\alpha_2$ as $\alpha_2=PN_0\alpha(\delta\mu,q)$, where
\begin{eqnarray}
\alpha(\delta\mu,q)=\frac{1}{gN_0}+\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{-\Lambda}^\Lambda d\xi\int\frac{d\hat{\bf p}}{4\pi}
\frac{1}{iE+\delta\mu-\xi}\frac{1}{iE+\delta\mu+\xi-2\hat{\bf p}\cdot{\bf q}}
\end{eqnarray}
with $N_0=\mu^2/(2\pi^2)$ being the density of state at the Fermi surface and $\hat{\bf p}$ denoting the solid angle. The integrals can now be analytically worked out and the cutoff dependence can be removed by using the pairing gap at vanishing mismatch,
$\Delta_0=2\Lambda e^{-1/(gN_0)}$. We finally obtain the analytical expression given by (\ref{alpha}).
For higher orders ($k\geq2$), the procedure is similar but becomes tedious. For example, for the fourth order ($k=2$), we have
\begin{eqnarray}
{\rm Tr} \left[(S_+F_+S_-F_-)^2\right]&=&\sum_{a=1}^P\sum_{b=1}^P\sum_{c=1}^P\sum_{d=1}^P\sum_{\bf p}\sum_{{\bf p}_1,{\bf p}_2,\ldots,{\bf p}_7}
\Bigg(\frac{\delta_{{\bf p},{\bf p}_1}}{i\omega_n+\delta\mu-\xi_{\bf p}}\delta_{{\bf p}_1-{\bf p}_2,2{\bf q}_a}
\frac{\delta_{{\bf p}_2,{\bf p}_3}}{i\omega_n+\delta\mu+\xi_{{\bf p}_2}}\delta_{{\bf p}_3-{\bf p}_4,-2{\bf q}_b}\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\frac{\delta_{{\bf p}_4,{\bf p}_5}}{i\omega_n+\delta\mu-\xi_{{\bf p}_4}}\delta_{{\bf p}_5-{\bf p}_6,2{\bf q}_c}
\frac{\delta_{{\bf p}_6,{\bf p}_7}}{i\omega_n+\delta\mu+\xi_{{\bf p}_6}}\delta_{{\bf p}_7-{\bf p},-2{\bf q}_d}\Bigg)
\nonumber\\
&=&\sum_{a=1}^P\sum_{b=1}^P\sum_{c=1}^P\sum_{d=1}^P\delta_{{\bf q}_a-{\bf q}_b+{\bf q}_c-{\bf q}_d,{\bf 0}}\sum_{\bf p}
\Bigg(\frac{1}{i\omega_n+\delta\mu-\xi_{\bf p}}\frac{1}{i\omega_n+\delta\mu+\xi_{{\bf p}-2{\bf q}_a}}\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\frac{1}{i\omega_n+\delta\mu-\xi_{{\bf p}-2{\bf q}_a+2{\bf q}_b}}
\frac{1}{i\omega_n+\delta\mu+\xi_{{\bf p}-2{\bf q}_a+2{\bf q}_b-2{\bf q}_c}}\Bigg).
\end{eqnarray}
At weak coupling, the $2k$-th order GL coefficient ($k\geq2$) can be generally expressed as
\begin{eqnarray}
\alpha_{2k}=N_0\sum_{{\bf q}_1,{\bf q}_2,\ldots,{\bf q}_{2k}}J_{2k}({\bf q}_1{\bf q}_2\ldots{\bf q}_{2k})\delta_{{\bf q}_s,{\bf 0}},\ \ \ \ \ \
{\bf q}_s=\sum_{i=1}^{2k}(-1)^{i+1}{\bf q}_i.
\end{eqnarray}
Here the summation over each ${\bf q}_i$ means the summation over all $P$ wave vectors ${\bf q}_a$ ($a=1,2,...,P$). The quantity
$J_{2k}({\bf q}_1{\bf q}_2\ldots{\bf q}_{2k})$ for general $k$ can be expressed in a compact form,
\begin{eqnarray}
J_{2k}({\bf q}_1{\bf q}_2\ldots{\bf q}_{2k})=\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{-\infty}^\infty d\xi\int\frac{d\hat{\bf p}}{4\pi}
\prod_{i=1}^k\frac{1}{iE+\delta\mu-\xi+2\hat{\bf p}\cdot {\bf k}_i}\frac{1}{iE+\delta\mu+\xi-2\hat{\bf p}\cdot{\bf l}_i},
\end{eqnarray}
\end{widetext}
where the momenta ${\bf k}_i$ and ${\bf l}_i$ are given by (we define ${\bf q}_0={\bf 0}$ for convenience)
\begin{eqnarray}
{\bf k}_i=\sum_{n=0}^{2i-2}(-1)^{n+1}{\bf q}_n,\ \ \ \ \ \ \ \ {\bf l}_i=\sum_{n=0}^{2i-1}(-1)^{n+1}{\bf q}_n.
\end{eqnarray}
Note that we have set $\Lambda\rightarrow\infty$ since the integral over $\xi$ is free from UV divergence for $k\geq2$.
The above formalism is completely the same as that obtained by using the diagrammatic approach~\cite{Bowers2002}. For the nonrelativistic case, the results can be obtained
by replacing the pair momentum $q$ with $v_{\rm F}q$ where $v_{\rm F}=2\sqrt{\mu}$ is the Fermi velocity. The density of state $N_0$ at the Fermi surface is replaced by $N_0=\sqrt{\mu}/(4\pi^2)$. Therefore, at weak coupling, the GL free energy is universal for both the relativistic case and the nonrelativistic case once we properly express the free energy in terms of the density of state $N_0$ at the Fermi surface, the pairing gap $\Delta_0$ at vanishing mismatch, and the quantity $v_{\rm F}q$ ($v_{\rm F}=1$ for the ultra-relativistic case).
The GL coefficients up to the sixth order ($k\leq3$) for 23 crystal structures have been evaluated numerically by Bowers and Rajagopal~\cite{Bowers2002}. They introduced Feynman parameters to evaluate the integral $J_{2k}({\bf q}_1{\bf q}_2\ldots{\bf q}_{2k})$. The advantage of the above formalism obtained by using the continuous momentum representation is that one can directly approach the weak coupling limit by using the momentum cutoff scheme $-\Lambda<|{\bf p}|-\mu<\Lambda$. However, for higher-order coefficients with large $k$, the calculation becomes complicated and tedious. First, for general $k$, one needs to introduce $2k$ Feynman parameters $x_1,x_2,...,x_k$ and $y_1,y_2,...,y_k$. At large $k$, the integral over the Feynman parameters becomes complicated. Second, to obtain the GL coefficients, one needs to sum over all possible configurations that satisfy the constraint $\sum_{i=1}^{2k}(-1)^{i+1}{\bf q}_i={\bf 0}$. At large $k$, the number of these configurations becomes also large, which makes the calculation tedious. To the best of our knowledge, no results of the higher-order GL coefficients ($k\geq4$) have been reported so far.
\section{Solid-State Physics Approach: Discrete representation}\label{s3}
In this section, we turn to a discrete representation inspired by solid-state physics. For a specific crystal structure given by (\ref{crystal}), it is periodic in coordinate space. The order parameter can be alternatively expressed as
\begin{eqnarray}
\Delta({\bf r})=\Delta f({\bf r}),
\end{eqnarray}
where
\begin{equation}
f({\bf r})=\sum_{k=1}^Pe^{2iq\hat{\bf n}_k\cdot{\bf r}}
\end{equation}
is a periodic function. Here we assume that the function $f({\bf r})$ corresponds to a 3D lattice structure. The derivation of the GL free energy can be easily generalized to 1D and 2D lattice structures. For a 3D lattice structure, the unit cell is generated by three linearly independent vectors ${\bf a}_1$, ${\bf a}_2$, and ${\bf a}_3$. We can accordingly define the reciprocal space generated by three linearly independent vectors
${\bf b}_1$, ${\bf b}_2$, and ${\bf b}_3$ with ${\bf b}_i$ obtained by the relation ${\bf a}_i\cdot{\bf b}_j=2\pi\delta_{ij}$. The periodicity of the order parameter means $f({\bf r})=f({\bf r}+{\bf a}_i)$. Therefore, the function $f({\bf r})$ can be decomposed into a discrete set of Fourier components. We have
\begin{eqnarray}\label{Fourier}
f({\bf r})&=&\sum_{{\bf G}}f_{\bf G}e^{i{\bf G}\cdot {\bf r}}=\sum_{l,m,n=-\infty}^\infty f_{lmn}e^{i{\bf G}_{lmn}\cdot {\bf r}},\nonumber\\
f^*({\bf r})&=&\sum_{{\bf G}}f_{\bf G}^*e^{-i{\bf G}\cdot {\bf r}}=\sum_{l,m,n=-\infty}^\infty f_{lmn}^*e^{-i{\bf G}_{lmn}\cdot {\bf r}},
\end{eqnarray}
where the reciprocal lattice vector ${\bf G}$ is given by
\begin{eqnarray}
{\bf G}={\bf G}_{lmn}=l{\bf b}_1+m{\bf b}_2+n{\bf b}_3,\ \ \ l,m,n\in \mathbb{Z}.
\end{eqnarray}
The Fourier components $f_{\bf G}$ and $f^*_{\bf G}$ are given by
\begin{eqnarray}
f_{\bf G}&=&\frac{1}{V_c}\int_c d^3{\bf r}f({\bf r})e^{-i{\bf G}\cdot{\bf r}},\nonumber\\
f_{\bf G}^*&=&\frac{1}{V_c}\int_c d^3{\bf r}f^*({\bf r})e^{i{\bf G}\cdot{\bf r}},
\end{eqnarray}
where $V_c$ is the volume of the unit cell and the integration is restricted in the cell volume. It is easy to show that
\begin{equation}
\sum_{\bf G}|f_{\bf G}|^2=P.
\end{equation}
Since the order parameter or pair potential $\Delta({\bf r})$ is periodic, the eigenvalue equation for the fermionic excitation spectrum, which is known as the Bogoliubov-de Gennes (BdG) equation, is analogous to the Schr\"{o}dinger equation of a quantum particle moving in a periodic potential. The BdG equation for the present system can be expressed as
\begin{eqnarray}
\left(\begin{array}{cc} \varepsilon(\hat{\bf p})-\mu-\delta\mu & \Delta({\bf r})\\
\Delta^*({\bf r})& -\varepsilon(\hat{\bf p})+\mu-\delta\mu \end{array}\right)\phi_\lambda({\bf r})
=E_\lambda\phi_\lambda({\bf r}).
\end{eqnarray}
According to the Bloch theorem, the eigenfunction $\phi_\lambda({\bf r})$ takes the form of the Bloch function; i.e.,
\begin{eqnarray}
\phi_\lambda({\bf r})=e^{i{\bf k}\cdot{\bf r}}\phi_{\lambda{\bf k}}({\bf r}),
\end{eqnarray}
where the lattice momentum ${\bf k}$ is restricted in the Brillouin zone (BZ) and the function $\phi_{\lambda{\bf k}}({\bf r})$ has the same periodicity as the order parameter $\Delta({\bf r})$. We therefore have
the similar Fourier expansion
\begin{eqnarray}
\phi_{\lambda{\bf k}}({\bf r})=\sum_{\bf G}\phi_{\bf G}e^{i{\bf G}\cdot {\bf r}}
=\sum_{l,m,n=-\infty}^\infty \phi_{lmn}e^{i{\bf G}_{lmn}\cdot {\bf r}}.
\end{eqnarray}
Substituting this expansion into the BdG equation, we finally obtain a matrix equation in the ${\bf G}$-space,
\begin{eqnarray}\label{matrixEq}
\sum_{{\bf G}^\prime}{\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})\phi_{{\bf G}^\prime}=E_\lambda({\bf k}) \phi_{\bf G},
\end{eqnarray}
where the Hamiltonian matrix ${\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})$ is given by
\begin{eqnarray}\label{Hmatrix}
{\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})=\left(\begin{array}{cc} (\xi_{{\bf k}+{\bf G}}-\delta\mu)\delta_{{\bf G},{\bf G}^\prime}
& \Delta f_{{\bf G}-{\bf G}^\prime} \\ \Delta f^*_{{\bf G}^\prime-{\bf G}}
& (-\xi_{{\bf k}+{\bf G}}-\delta\mu)\delta_{{\bf G},{\bf G}^\prime} \end{array}\right).
\end{eqnarray}
For a given momentum ${\bf k}$ in the BZ, we can solve the eigenvalues $E_{\lambda}({\bf k})$ by diagonalizing the above
matrix in the discrete ${\bf G}$-space. This means that the fermionic excitation spectrum forms a band structure, in analogy to
the energy spectrum of a quantum particle moving in a periodic potential.
Now we turn to the field theory. We consider a finite system spanned by three vectors $N_1{\bf a}_1$, $N_2{\bf a}_2$, and $N_3{\bf a}_3$ and assume periodic boundary condition. Then the system contains $N_1N_2N_3$ unit cells and the thermodynamic limit can be reached by setting $N_i\rightarrow\infty$. In accordance with the Fourier expansion (\ref{Fourier}) and the matrix equation (\ref{matrixEq}), we expand the
fermion field $\Psi(\tau,{\bf r})$ in terms of the Bloch function rather than using the usual momentum representation (\ref{momentum-rep}).
We write
\begin{widetext}
\begin{eqnarray}
\Psi(\tau,{\bf r})&=&\frac{1}{\sqrt{V}}\sum_{{\bf k}\in{\rm BZ}}e^{i{\bf k}\cdot{\bf r}}\sum_{\omega_n}\sum_{{\bf G}}
\tilde{\Psi}(i\omega_n,{\bf k},{\bf G})e^{-i\omega_n\tau+i{\bf G}\cdot{\bf r}},\nonumber\\
\Psi^\dagger(\tau,{\bf r})&=&\frac{1}{\sqrt{V}}\sum_{{\bf k}\in{\rm BZ}}e^{-i{\bf k}\cdot{\bf r}}\sum_{\omega_n}\sum_{{\bf G}}
\tilde{\Psi}^\dagger(i\omega_n,{\bf k},{\bf G})e^{i\omega_n\tau-i{\bf G}\cdot{\bf r}}.
\end{eqnarray}
One can recover the usual momentum representation (\ref{momentum-rep}) by using the fact that ${\bf k}+{\bf G}$ can generate all possible momentum ${\bf p}$ in the momentum space. This expansion defines a new representation with two different quantum numbers ${\bf k}$ and ${\bf G}$. We call this Bloch representation. In the Bloch representation, the mean-field action can be evaluated as
\begin{eqnarray}
{\cal S}_{\rm{MF}}=\frac{V}{T}\frac{\Delta^2}{g}\sum_{\bf G}|f_{\bf G}|^2-\frac{1}{T}\sum_{\omega_n,\omega_{n^\prime}}
\sum_{{\bf k},{\bf k}^\prime\in{\rm BZ}}\sum_{{\bf G},{\bf G}^\prime}\tilde{\Psi}^\dagger(i\omega_n,{\bf k},{\bf G})
\left[i\omega_n\delta_{\omega_n,\omega_{n^\prime}}\delta_{{\bf k},{\bf k}^\prime}\delta_{{\bf G},{\bf G}^\prime}
-\delta_{\omega_n,\omega_{n^\prime}}\delta_{{\bf k},{\bf k}^\prime}{\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})\right]
\tilde{\Psi}(i\omega_{n^\prime},{\bf k}^\prime,{\bf G}^\prime),
\end{eqnarray}
\end{widetext}
where the Hamiltonian matrix ${\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})$ is given by (\ref{Hmatrix}). In mathematics, the Bloch representation corresponds to a similarity transformation of the usual momentum representation, which makes the Hamiltonian matrix
${\cal H}_{{\bf p},{\bf p}^\prime}$ block diagonal with the blocks characterized by the lattice momentum ${\bf k}$. The functional path integral can be worked out by performing integrals over $\tilde{\Psi}^\dagger(i\omega_n,{\bf k},{\bf G})$ and $\tilde{\Psi}(i\omega_{n^\prime},{\bf k}^\prime,{\bf G}^\prime)$ for all possible values of $\{i\omega_n,{\bf k},{\bf G}\}$ and $\{i\omega_{n^\prime},{\bf k}^\prime,{\bf G}^\prime\}$. Since the inverse fermion propagator is diagonal in the frequency space and the ${\bf k}$-space, the free energy can be expressed as
\begin{eqnarray}\label{free-energy-G}
\Omega=\frac{P}{g}\Delta^2-\frac{T}{V}\sum_{\omega_n}\sum_{{\bf k}\in{\rm BZ}}
{\rm Trln}\left[\frac{(S^{-1})_{{\bf G},{\bf G}^\prime}}{T}\right],
\end{eqnarray}
where the Trln acts in the ${\bf G}$-space and the NG space. The inverse fermion propagator $S^{-1}$ defined
in the ${\bf G}$-space and the NG space is given by
\begin{eqnarray}
(S^{-1})_{{\bf G},{\bf G}^\prime}(i\omega_n,{\bf k})=i\omega_n\delta_{{\bf G},{\bf G}^\prime}-{\cal H}_{{\bf G},{\bf G}^\prime}({\bf k}).
\end{eqnarray}
The free energy can be evaluated if we can diagonalize the Hamiltonian matrix ${\cal H}_{{\bf G},{\bf G}^\prime}({\bf k})$ to obtain
all the eigenvalues or the band spectrum $\{E_{\lambda}({\bf k})\}$. This is in principle feasible because the ${\bf G}$-space is discrete.
Since the matrix has infinite dimensions, we should make a truncation $-D\leq l,m,n\leq D$ ($D\in \mathbb{Z}^+$) to perform the diagonalization. The size of the matrix we need to diagonalize is $2(2D+1)^3$. To achieve convergence to the limit $D\rightarrow\infty$ we normally need a large cutoff $D$, which leads to a large computing cost~\cite{Cao2015}.
Then we turn to the GL expansion based on the expression (\ref{free-energy-G}) of the free energy. The procedure is the same as we used in Sec. II. First, for the inverse fermion propagator $S^{-1}$, we separate the BCS self-energy and obtain
\begin{eqnarray}
(S^{-1})_{{\bf G},{\bf G}^\prime}=(S_0^{-1})_{{\bf G},{\bf G}^\prime}-(\Sigma_\Delta)_{{\bf G},{\bf G}^\prime}.
\end{eqnarray}
Here the inverse of the free fermion propagator reads
\begin{eqnarray}
(S_0^{-1})_{{\bf G},{\bf G}^\prime}=\left(\begin{array}{cc} (S_+^{-1})_{{\bf G},{\bf G}^\prime} & 0 \\ 0
& (S_{-}^{-1})_{{\bf G},{\bf G}^\prime} \end{array}\right)
\end{eqnarray}
with the matrix elements given by
\begin{eqnarray}
(S_\pm^{-1})_{{\bf G},{\bf G}^\prime}=(i\omega_n+\delta\mu\mp\xi_{{\bf k}+{\bf G}})\delta_{{\bf G},{\bf G}^\prime}.
\end{eqnarray}
The self-energy term $\Sigma_\Delta$ can be expressed as
\begin{equation}
(\Sigma_\Delta)_{{\bf G},{\bf G}^\prime}=\Delta F_{{\bf G},{\bf G}^\prime},
\end{equation}
where the matrix $F$ is defined as
\begin{eqnarray}
F_{{\bf G},{\bf G}^\prime}=\left(\begin{array}{cc} 0 & (F_+)_{{\bf G},{\bf G}^\prime} \\ (F_-)_{{\bf G},{\bf G}^\prime}
& 0 \end{array}\right).
\end{eqnarray}
Here the blocks $F_\pm$ defined in the ${\bf G}$-space are given by
\begin{eqnarray}
(F_+)_{{\bf G},{\bf G}^\prime}=f_{{\bf G}-{\bf G}^\prime},\ \ \ \ \ \ (F_-)_{{\bf G},{\bf G}^\prime}=f^*_{{\bf G}^\prime-{\bf G}}.
\end{eqnarray}
Using the derivative expansion, we obtain
\begin{eqnarray}
\Omega=\Omega_{\rm N}+\frac{P}{g}\Delta^2+\frac{T}{V}\sum_{\omega_n}\sum_{{\bf k}\in{\rm BZ}}
\sum_{l=1}^\infty\frac{\Delta^l}{l}{\rm Tr}\left[(S_0F)^l\right],
\end{eqnarray}
where $\Omega_{\rm N}$ is the free energy of the normal state,
\begin{eqnarray}
\Omega_{\rm N}=-\frac{T}{V}\sum_{\omega_n}\sum_{{\bf k}\in{\rm BZ}}{\rm Trln}\left[\frac{(S_0^{-1})_{{\bf G},{\bf G}^\prime}}{T}\right].
\end{eqnarray}
Using the fact that $S_0^{-1}$ is diagonal and ${\bf k}+{\bf G}$ generates all continuum momenta ${\bf p}$, we recover the usual expression (\ref{Normal}).
Completing the trace in the NG space, we find that the trace vanishes for odd $l$. Then the GL free energy can be expressed as
\begin{eqnarray}
\Omega_{\rm GL}=\alpha_2\Delta^2+\sum_{k=2}^\infty\frac{\alpha_{2k}}{k}\Delta^{2k}.
\end{eqnarray}
The second-order GL coefficient is given by
\begin{eqnarray}
\alpha_2=\frac{P}{g}+\frac{T}{V}\sum_{\omega_n}\sum_{{\bf k}\in{\rm BZ}}{\rm Tr}(S_+F_+S_-F_-).
\end{eqnarray}
The higher-order GL coefficients $\alpha_{2k}$ ($k\geq2$) read
\begin{eqnarray}
\alpha_{2k}=\frac{T}{V}\sum_{\omega_n}\sum_{{\bf k}\in{\rm BZ}}{\rm Tr}\left[(S_+F_+S_-F_-)^k\right].
\end{eqnarray}
Note that the trace is now taken only in the ${\bf G}$-space. At zero temperature and in the large volume limit, we obtain
\begin{eqnarray}
\alpha_2=\frac{P}{g}+\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{\rm BZ}\frac{d^3{\bf k}}{(2\pi)^3}{\cal A}_2(iE,{\bf k}).
\end{eqnarray}
and
\begin{eqnarray}
\alpha_{2k}=\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{\rm BZ}\frac{d^3{\bf k}}{(2\pi)^3}{\cal A}_{2k}(iE,{\bf k}).
\end{eqnarray}
for $k\geq2$. Here the quantity ${\cal A}_{2k}(iE,{\bf k})$ is defined as
\begin{eqnarray}
{\cal A}_{2k}(iE,{\bf k})={\rm Tr}\ \Big\{\left[S_+(iE,{\bf k})F_+S_-(iE,{\bf k})F_-\right]^k\Big\}
\end{eqnarray}
with
\begin{eqnarray}
(S_\pm)_{{\bf G},{\bf G}^\prime}(iE,{\bf k})=\frac{\delta_{{\bf G},{\bf G}^\prime}}{iE+\delta\mu\mp\xi_{{\bf k}+{\bf G}}}.
\end{eqnarray}
The GL coefficients should be independent of the representation. Therefore, $\alpha_2/P$ is still universal for all crystal structure. We can evaluate it from the FF state. We have
\begin{equation}
\alpha_2=P\alpha_2^{\rm FF}.
\end{equation}
For the FF state we have $f({\bf r})=f(z)=e^{2iqz}$, which can be regarded as a 1D crystal structure with periodicity $a=\pi/q$. We have the Fourier transformations
\begin{eqnarray}
f(z)=\sum_{n=-\infty}^\infty f_ne^{i\frac{2\pi n}{a}z},\ \ \ \ \ f^*(z)=\sum_{n=-\infty}^\infty f_n^*e^{-i\frac{2\pi n}{a}z},
\end{eqnarray}
where the Fourier components $f_n$ and $f_n^*$ are given by
\begin{eqnarray}
f_n=f_n^*=\delta_{n,1}.
\end{eqnarray}
Therefore, the matrices $F_\pm$ read
\begin{eqnarray}
(F_+)_{n,n^\prime}=\delta_{n-n^\prime,1},\ \ \ \ (F_-)_{n,n^\prime}=\delta_{n^\prime-n,1}.
\end{eqnarray}
The GL coefficient $\alpha_2^{\rm FF}$ can be expressed as
\begin{eqnarray}
\alpha_2^{\rm FF}=\frac{1}{g}+\int_{-\infty}^\infty\frac{dE}{2\pi}\int_0^\infty\frac{k_\perp dk_\perp}{2\pi}
\int_{-q}^q\frac{dk_z}{2\pi}{\cal A}_{2}(iE,k_\perp,k_z).
\end{eqnarray}
The trace in ${\cal A}_2$ can be worked out analytically. We have
\begin{eqnarray}
&&{\cal A}_{2}(iE,k_\perp,k_z)={\rm Tr} \left[S_+F_+S_-F_-\right]\nonumber\\
&=&\sum_{n}\sum_{n_1,n_2,n_3}
\frac{\delta_{n,n_1}}{iE+\delta\mu-\xi_{n}}\delta_{n_1-n_2,1}
\frac{\delta_{n_2,n_3}}{iE+\delta\mu+\xi_{n_2}}\delta_{n-n_3,1}\nonumber\\
&=&\sum_{n}\frac{1}{iE+\delta\mu-\xi_n}
\frac{1}{iE+\delta\mu+\xi_{n-1}},
\end{eqnarray}
where $\xi_n$ is defined as
\begin{eqnarray}
\xi_n(k_\perp,k_z)=\left[k_\perp^2+(k_z+2nq)^2\right]^\nu-\mu.
\end{eqnarray}
Here $\nu=1/2$ for the ultra-relativistic case and $\nu=1$ for the nonrelativistic case. Since $k_z+2nq$ generates all continuous momenta in the
$z$ direction, the final result for $\alpha_2$ can be expressed as (36).
For higher-order GL coefficients $\alpha_{2k}$ ($k\geq2$), the trace in the quantity ${\cal A}_{2k}(iE,{\bf k})$ becomes tedious.
However, because the ${\bf G}$-space is discrete, this procedure can be realized by using a computer with a proper code. Since the ${\bf G}$-space has infinite dimensions, we first make a truncation $-D\leq l,m,n\leq D$ to perform the matrix operations. Precise results can be approached by using a sufficiently large $D$. Some of the GL coefficients may suffer from UV divergence and a proper regularization scheme should be implemented. For ultra-relativistic dispersion $\varepsilon({\bf p})=|{\bf p}|$, $\alpha_2$ and $\alpha_4$ are divergent. For non-relativistic case with $\varepsilon({\bf p})=|{\bf p}|^2$, only $\alpha_2$ is divergent. The GL free energy can be expressed as
\begin{eqnarray}
\frac{\Omega_{\rm GL}(\Delta)}{N_0\delta\mu^2}=P\bar{\alpha}\left(\frac{\Delta}{\delta\mu}\right)^2+
\sum_{k=2}^\infty\frac{\bar{\alpha}_{2k}}{k}\left(\frac{\Delta}{\delta\mu}\right)^{2k},
\end{eqnarray}
where the GL coefficients become dimensionless. We have
\begin{equation}
\bar{\alpha}_{2k}=\frac{\delta\mu^{2k-2}}{N_0}\alpha_{2k}.
\end{equation}
These dimensionless GL coefficients are \emph{universal} in the weak coupling limit. Therefore, we can evaluate them by using the non-relativistic dispersion because all the coefficients $\alpha_{2k}$ ($k\geq2$) are free from UV divergence. On the other hand, in this matrix formalism, we need to treat the momenta ${\bf k}$ and ${\bf G}$ separately. Therefore, the usual momentum cutoff scheme $-\Lambda<\xi_{\bf p}<\Lambda$ is not proper to achieve the weak coupling limit. The dependence on the chemical potential $\mu$ becomes explicit in the matrix formalism. Weak coupling corresponds to the case $\mu\simeq\varepsilon_{\rm F}\gg\delta\mu$. In practice, we can vary the value of $\mu/\delta\mu$ and approach the weak coupling limit.
\section{Formalism for some crystal structures}\label{s4}
In the final part of this paper, we consider some crystal structures of which the order parameters $\Delta({\bf r})$ are real. We have $f_{\bf G}^*=f_{-{\bf G}}^{\phantom{*}}$ and hence
\begin{eqnarray}
(F_+)_{{\bf G},{\bf G}^\prime}=(F_-)_{{\bf G},{\bf G}^\prime}\equiv F_{{\bf G},{\bf G}^\prime}=f_{{\bf G}-{\bf G}^\prime}.
\end{eqnarray}
In the following, we list the explicit forms of the matrix $F$, the propagators $S_\pm$, and the GL coefficients $\alpha_{2k}$ ($k\geq2$). As we pointed out in Sec. \ref{s3}, we shall use the nonrelativistic dispersion $\varepsilon({\bf p})={\bf p}^2$. In practice, this leads to faster convergence and hence is better for numerical calculations.
\subsection{LO}
The LO state is a superposition of two antipodal plane waves ($P=2$) with
\begin{equation}
\hat{\bf n}_1=(0,0,1),\ \ \ \ \hat{\bf n}_2=(0,0,-1).
\end{equation}
The function $f({\bf r})$ can be expressed as
\begin{eqnarray}
f({\bf r})=f(z)=2\cos(2qz),
\end{eqnarray}
which forms a 1D crystal structure with periodicity $a=\pi/q$. The Fourier decomposition is given by
\begin{eqnarray}
f(z)=\sum_{n=-\infty}^\infty f_ne^{2niqz},
\end{eqnarray}
where the Fourier component $f_n$ reads
\begin{eqnarray}
f_n=\delta_{n,1}+\delta_{n,-1}.
\end{eqnarray}
The matrix form of the BdG equation is given by
\begin{eqnarray}
\sum_{n^\prime}{\cal H}_{n,n^\prime}({\bf k})\phi_{n^\prime}({\bf k})=E_\lambda({\bf k}) \phi_{n}({\bf k}),
\end{eqnarray}
where the Hamiltonian matrix ${\cal H}_{n,n^\prime}({\bf k})$ reads
\begin{eqnarray}
\left(\begin{array}{cc} (\xi_n-\delta\mu)\delta_{n,n^\prime} &
\Delta f_{n-n^\prime} \\ \Delta f_{n-n^\prime}
& (-\xi_n-\delta\mu)\delta_{n,n^\prime} \end{array}\right)
\end{eqnarray}
with
\begin{eqnarray}
\xi_n(k_\perp,k_z)=k_\perp^2+(k_z+2nq)^2-\mu.
\end{eqnarray}
The BZ can be defined as $k_z\in[-q,q]$. The GL coefficients $\alpha_{2k}$ ($k\geq2$) can be expressed as
\begin{eqnarray}
\alpha_{2k}=\int_{-\infty}^\infty\frac{dE}{2\pi}\int_0^\infty\frac{k_\perp dk_\perp}{2\pi}
\int_{-q}^q\frac{dk_z}{2\pi}{\rm Tr}_{[n]}\left[(S_+FS_-F)^k\right].
\end{eqnarray}
The matrix elements of $S_\pm$ and $F$ are given by
\begin{eqnarray}
&&(S_\pm)_{n,n^\prime}=\frac{\delta_{n,n^\prime}}{iE+\delta\mu\mp\xi_n},\nonumber\\
&&F_{n,n^\prime}=\delta_{n,n^\prime+1}+\delta_{n,n^\prime-1}.
\end{eqnarray}
\subsection{Square}
The Square state is a superposition of four plane waves ($P=4$) with
\begin{eqnarray}
&&\hat{\bf n}_1=(1,0,0),\ \ \ \ \hat{\bf n}_2=(-1,0,0),\nonumber\\
&&\hat{\bf n}_3=(0,1,0),\ \ \ \ \hat{\bf n}_4=(0,-1,0).
\end{eqnarray}
The function $f({\bf r})$ can be expressed as
\begin{eqnarray}
f({\bf r})=f(x,y)=2\left[\cos(2qx)+\cos(2qy)\right],
\end{eqnarray}
which forms a 2D crystal structure. The unit cell is generated by two linearly independent vectors ${\bf a}_1=a{\bf e}_x$ and ${\bf a}_2=a{\bf e}_y$ with the lattice spacing $a=\pi/q$. The Fourier decomposition is given by
\begin{eqnarray}
f(x,y)=\sum_{l,m=-\infty}^\infty f_{lm}e^{i\frac{2\pi}{a}(lx+my)},
\end{eqnarray}
where the Fourier component $f_{lm}$ reads
\begin{eqnarray}
f_{lm}=(\delta_{l,1}+\delta_{l,-1})\delta_{m,0}+\delta_{l,0}(\delta_{m,1}+\delta_{m,-1}).
\end{eqnarray}
The matrix form of the BdG equation is given by
\begin{eqnarray}
\sum_{l^\prime m^\prime}{\cal H}_{[lm],[l^\prime m^\prime]}({\bf k})\phi_{[l^\prime m^\prime]}({\bf k})=E_\lambda({\bf k}) \phi_{[lm]}({\bf k}),
\end{eqnarray}
where the Hamiltonian matrix ${\cal H}_{[lm],[l^\prime m^\prime]}({\bf k})$ reads
\begin{eqnarray}
\left(\begin{array}{cc} (\xi_{lm}-\delta\mu)\delta_{l,l^\prime}\delta_{m,m^\prime} &
\Delta f_{l-l^\prime,m-m^\prime} \\ \Delta f_{l-l^\prime,m-m^\prime}
& (-\xi_{lm}-\delta\mu)\delta_{l,l^\prime}\delta_{m,m^\prime} \end{array}\right)
\end{eqnarray}
with
\begin{eqnarray}
\xi_{lm}(k_x,k_y,k_z)=(k_x+2lq)^2+(k_y+2mq)^2+k_z^2-\mu.
\end{eqnarray}
The BZ can be defined as $k_x,k_y\in[-q,q]$. The GL coefficients $\alpha_{2k}$ ($k\geq2$) are given by
\begin{eqnarray}
\alpha_{2k}&=&\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{-q}^q\frac{dk_x}{2\pi}\int_{-q}^q\frac{dk_y}{2\pi}
\int_{-\infty}^\infty\frac{dk_z}{2\pi}\nonumber\\
&&{\rm Tr}_{[lm]} \left[(S_+FS_-F)^k\right].
\end{eqnarray}
The matrix elements of $S_\pm$ and $F$ read
\begin{eqnarray}
&&(S_\pm)_{[lm],[l^\prime m^\prime]}=\frac{\delta_{l,l^\prime}\delta_{m,m^\prime}}{iE+\delta\mu\mp\xi_{lm}},\nonumber\\
&&F_{[lm],[l^\prime m^\prime]}=(\delta_{l,l^\prime+1}+\delta_{l,l^\prime-1})\delta_{m,m^\prime}\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \delta_{l,l^\prime}(\delta_{m,m^\prime+1}+\delta_{m,m^\prime-1}).
\end{eqnarray}
\subsection{BCC}
The BCC state is a superposition of six plane waves ($P=6$) with
\begin{eqnarray}
&&\hat{\bf n}_1=(1,0,0),\ \ \ \ \hat{\bf n}_2=(-1,0,0),\nonumber\\
&&\hat{\bf n}_3=(0,1,0),\ \ \ \ \hat{\bf n}_4=(0,-1,0),\nonumber\\
&&\hat{\bf n}_5=(0,0,1),\ \ \ \ \hat{\bf n}_6=(0,0,-1),
\end{eqnarray}
The function $f({\bf r})$ can be expressed as
\begin{eqnarray}
f({\bf r})=2\left[\cos(2qx)+\cos(2qy)+\cos(2qz)\right],
\end{eqnarray}
which forms a 3D crystal structure. The unit cell is generated by three linearly independent vectors ${\bf a}_1=a{\bf e}_x$, ${\bf a}_2=a{\bf e}_y$, and ${\bf a}_3=a{\bf e}_z$ with the lattice spacing $a=\pi/q$. The Fourier decomposition is given by
\begin{eqnarray}
f({\bf r})=\sum_{l,m,n=-\infty}^\infty f_{lmn}e^{2iq(lx+my+nz)},
\end{eqnarray}
where the Fourier component $f_{lmn}$ reads
\begin{eqnarray}
f_{lmn}&=&\left(\delta_{l,1}+\delta_{l,-1}\right)\delta_{m,0}\delta_{n,0}
+\delta_{l,0}\left(\delta_{m,1}+\delta_{m,-1}\right)\delta_{n,0}\nonumber\\
&&\ +\ \delta_{l,0}\delta_{m,0}\left(\delta_{n,1}+\delta_{n,-1}\right).
\end{eqnarray}
The matrix form of the BdG equation is given by
\begin{eqnarray}
\sum_{l^\prime m^\prime n^\prime}{\cal H}_{[lmn],[l^\prime m^\prime n^\prime]}({\bf k})\phi_{[l^\prime m^\prime n^\prime]}({\bf k})
=E_\lambda({\bf k}) \phi_{[lmn]}({\bf k}),
\end{eqnarray}
where the Hamiltonian matrix ${\cal H}_{[lmn],[l^\prime m^\prime n^\prime]}({\bf k})$ reads
\begin{eqnarray}
\left(\begin{array}{cc} (\xi_{lmn}-\delta\mu)\delta_{l,l^\prime}\delta_{m,m^\prime}\delta_{n,n^\prime} &
\Delta f_{l-l^\prime,m-m^\prime,n-n^\prime} \\ \Delta f_{l-l^\prime,m-m^\prime,n-n^\prime}
& (-\xi_{lm}-\delta\mu)\delta_{l,l^\prime}\delta_{m,m^\prime}\delta_{n,n^\prime} \end{array}\right)
\end{eqnarray}
with
\begin{eqnarray}
\xi_{lmn}=(k_x+2lq)^2+(k_y+2mq)^2+(k_z+2nq)^2-\mu.
\end{eqnarray}
The BZ can be defined as $k_x,k_y,k_z\in[-q,q]$. The GL coefficients $\alpha_{2k}$ ($k\geq2$) are given by
\begin{eqnarray}
\alpha_{2k}&=&\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{-q}^q\frac{dk_x}{2\pi}\int_{-q}^q\frac{dk_y}{2\pi}\int_{-q}^q\frac{dk_z}{2\pi}\nonumber\\
&&{\rm Tr}_{[lmn]}\left[(S_+FS_-F)^k\right].
\end{eqnarray}
The matrix elements of $S_\pm$ and $F$ read
\begin{eqnarray}
&&(S_\pm)_{[lmn],[l^\prime m^\prime n^\prime]}=\frac{\delta_{l,l^\prime}\delta_{m,m^\prime}\delta_{n,n^\prime}}{iE+\delta\mu\mp\xi_{lmn}},\nonumber\\
&&F_{[lmn],[l^\prime m^\prime n^\prime]}=(\delta_{l,l^\prime+1}+\delta_{l,l^\prime-1})\delta_{m,m^\prime}\delta_{n,n^\prime}\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \delta_{l,l^\prime}(\delta_{m,m^\prime+1}+\delta_{m,m^\prime-1})\delta_{n,n^\prime}\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +\ \delta_{l,l^\prime}\delta_{m,m^\prime}(\delta_{n,n^\prime+1}+\delta_{n,n^\prime-1}).
\end{eqnarray}
\subsection{FCC}
The FCC state is a superposition of eight plane waves ($P=8$) with
\begin{eqnarray}
&&\hat{\bf n}_1=\frac{1}{\sqrt{3}}(1,1,1),\ \ \ \ \hat{\bf n}_2=\frac{1}{\sqrt{3}}(-1,-1,-1),\nonumber\\
&&\hat{\bf n}_3=\frac{1}{\sqrt{3}}(1,-1,1),\ \ \ \ \hat{\bf n}_4=\frac{1}{\sqrt{3}}(-1,1,-1),\nonumber\\
&&\hat{\bf n}_5=\frac{1}{\sqrt{3}}(1,-1,-1),\ \ \ \ \hat{\bf n}_6=\frac{1}{\sqrt{3}}(-1,1,1),\nonumber\\
&&\hat{\bf n}_7=\frac{1}{\sqrt{3}}(1,1,-1),\ \ \ \ \hat{\bf n}_8=\frac{1}{\sqrt{3}}(-1,-1,1).
\end{eqnarray}
The function $f({\bf r})$ can be expressed as
\begin{eqnarray}
f({\bf r})=8\cos\left(\frac{2qx}{\sqrt{3}}\right)\cos\left(\frac{2qy}{\sqrt{3}}\right)\cos\left(\frac{2qz}{\sqrt{3}}\right),
\end{eqnarray}
which forms a 3D crystal structure. The unit cell is generated by three linearly independent vectors ${\bf a}_1=a{\bf e}_x$, ${\bf a}_2=a{\bf e}_y$, and ${\bf a}_3=a{\bf e}_z$ with the lattice spacing $a=\sqrt{3}\pi/q$. The Fourier decomposition is given by
\begin{eqnarray}
f({\bf r})=\sum_{l,m,n=-\infty}^\infty f_{lmn}e^{\frac{2i}{\sqrt{3}}q(lx+my+nz)},
\end{eqnarray}
where the Fourier component $f_{lmn}$ reads
\begin{eqnarray}
f_{lmn}=\left(\delta_{l,1}+\delta_{l,-1}\right)\left(\delta_{m,1}+\delta_{m,-1}\right)\left(\delta_{n,1}+\delta_{n,-1}\right).
\end{eqnarray}
The matrix form of the BdG equation and the Hamiltonian matrix ${\cal H}_{[lmn],[l^\prime m^\prime n^\prime]}({\bf k})$ take the same forms
as (104) and (105) but with $\xi_{lmn}$ given by
\begin{eqnarray}
\xi_{lmn}=\left(k_x+\frac{2lq}{\sqrt{3}}\right)^2+\left(k_y+\frac{2mq}{\sqrt{3}}\right)^2+\left(k_z+\frac{2nq}{\sqrt{3}}\right)^2-\mu.
\end{eqnarray}
The BZ can be defined as $k_x,k_y,k_z\in[-\frac{q}{\sqrt{3}},\frac{q}{\sqrt{3}}]$. The GL coefficients $\alpha_{2k}$ ($k\geq2$) are given by
\begin{eqnarray}
\alpha_{2k}&=&\int_{-\infty}^\infty\frac{dE}{2\pi}\int_{-\frac{q}{\sqrt{3}}}^\frac{q}{\sqrt{3}}\frac{dk_x}{2\pi}
\int_{-\frac{q}{\sqrt{3}}}^\frac{q}{\sqrt{3}}\frac{dk_y}{2\pi}\int_{-\frac{q}{\sqrt{3}}}^\frac{q}{\sqrt{3}}\frac{dk_z}{2\pi}\nonumber\\
&&{\rm Tr}_{[lmn]}\left[(S_+FS_-F)^k\right].
\end{eqnarray}
The matrix elements of $S_\pm$ and $F$ can be expressed as
\begin{eqnarray}
&&(S_\pm)_{[lmn],[l^\prime m^\prime n^\prime]}=\frac{\delta_{l,l^\prime}\delta_{m,m^\prime}\delta_{n,n^\prime}}{iE+\delta\mu\mp\xi_{lmn}},\nonumber\\
&&F_{[lmn],[l^\prime m^\prime n^\prime]}=(\delta_{l,l^\prime+1}+\delta_{l,l^\prime-1})(\delta_{m,m^\prime+1}+\delta_{m,m^\prime-1})\nonumber\\
&&\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \times\ (\delta_{n,n^\prime+1}+\delta_{n,n^\prime-1}).
\end{eqnarray}
\section{Summary}\label{s5}
In this work, we presented a new derivation of the GL free energy of crystalline (color) superconductors and compared it with the conventional diagrammatic derivation~\cite{Bowers2002}. The diagrammatic derivation and our derivation can be attributed to the use of two different representations of the fermion field: The diagrammatic derivation employs the usual continuous momentum representation, while our derivation
uses the discrete Bloch representation. In either formalism, we need to evaluate the trace of the form ${\rm Tr}
\left[(S_+F_+S_-F_-)^k\right]$. In the usual momentum representation, taking this trace leads to a summation of all possible configurations that satisfy the momentum constraint (\ref{Mconstraint}). For large $k$, the number of these configurations becomes also large, which makes the calculation tedious. In our formalism, this trace is taken in the discrete Bloch space. Therefore, the calculation of the GL coefficients can be computerized: One can generate the matrices $F_\pm$ and $S_\pm$ and perform the matrix operations by using a computer with a proper code. Once the
computerization is realized, we may be able to evaluate the GL free energy to arbitrary order in $\Delta$. With the information of the higher-order terms in the GL free energy, we can give more reliable predictions for the phase transitions.
\emph{Acknowledgments} --- The work of G. C. was supported by the NSFC under Grant No. 11335005 and the MOST under Grant Nos. 2013CB922000 and 2014CB845400. The work of L. H. was supported by the US Department of Energy Topical Collaboration ``Neutrinos and Nucleosynthesis in Hot and Dense Matter". L. H. also acknowledges the support from Frankfurt Institute for Advanced Studies in the early stage of this work.
| {
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} | 5,070 |
Oșești este o comună în județul Vaslui, Moldova, România, formată din satele Buda, Oșești (reședința), Pădureni și Vâlcele.
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Conform recensământului efectuat în 2011, populația comunei Oșești se ridică la de locuitori, în scădere față de recensământul anterior din 2002, când se înregistraseră de locuitori. Majoritatea locuitorilor sunt români (93,79%), cu o minoritate de romi (1,74%). Pentru 4,43% din populație, apartenența etnică nu este cunoscută.
Din punct de vedere confesional, majoritatea locuitorilor sunt ortodocși (91,51%), cu o minoritate de penticostali (3,2%). Pentru 4,47% din populație, nu este cunoscută apartenența confesională.
Politică și administrație
Comuna Oșești este administrată de un primar și un consiliu local compus din 13 consilieri. Primarul, , de la , este în funcție din . Începând cu alegerile locale din 2020, consiliul local are următoarea componență pe partide politice:
Note
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} | 4,248 |
Q: Trigger Google Cloud SQL export within VM tl;dr: Cannot trigger an export with gcloud sql export sql ... on VM which always leads into a PERMISSION_DENIED even though I think that I have set all permissions for its Service Account.
The whole problem actually sounds relatively simple. I want to trigger an export of my Cloud SQL database in my Google Cloud Compute VM at certain times.
What I did so far:
*
*Added the Cloud SQL Admin (just for the sake of testing) permission to the VMs service account in the IAM section.
*Created and downloaded the service account key and used gcloud auth activate-service-account --key-file cert.json
*Ran the following command:
gcloud sql export sql "${SQL_INSTANCE}" "gs://${BUCKET}/${FILENAME}" -d "${DATABASE}"
(this works without a problem with my own, personal account)
The command resulted in the following error:
ERROR: (gcloud.sql.export.sql) PERMISSION_DENIED: Request had insufficient authentication scopes.
What else I tried
I found this article from Google and used the Compute Service Account instead of creating a Cloud Function Service Account. The result is sadly the same.
A: You do not have the roles assigned to the service account that you think you have.
You need one of the following roles assigned to the service account:
*
*roles/owner (Not recommended)
*roles/viewer (Not recommended)
*roles/cloudsql.admin (Not recommended unless required for other SQL operations)
*roles/cloudsql.editor (Not recommended unless required for other SQL operations)
*roles/cloudsql.viewer (Recommended)
Go to the Google Cloud Console -> Compute Engine.
Click on your VM instance. Scroll down and find the service account assigned to your VM instance. Copy the service account email address.
Run the following command (replace \ with ^ for Windows in the following command and specify your PROJECT ID (not PROJECT NAME) and the service account email address):
gcloud projects get-iam-policy <PROJECT_ID> \
--flatten="bindings[].members" \
--format="table(bindings.role)" \
--filter="bindings.members:<COMPUTE_ENGINE_SERVICE_ACCOUNT>"
Double-check that the roles you require are present in the output.
To list your projects to obtain the PROJECT ID:
gcloud projects list
Note: Do not assign permissions directly to the service account. Assign permissions to the project granting the required role to the service account IAM member.
gcloud projects add-iam-policy-binding <PROJECT_ID> \
--member serviceAccount:<COMPUTE_ENGINE_SERVICE_ACCOUNT> \
--role roles/cloudsql.viewer
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,434 |
Q: CSS table: How to position action buttons left to each row I've this default responsive Bootstrap table:
<div class="table-responsive">
<table class="table table-bordered">
<thead>
<tr>
<th>#</th>
<th>First Name</th>
<th>Last Name</th>
<th>Username</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo</td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat</td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter</td>
</tr>
</tbody>
</table>
</div>
How can I add a div or container to the right of each row showing some action buttons, like delete row, updating icon etc.? They should be hidden by default. When I mouse over a row, it should be displayed right to the row. Not inside the table, but the top and bottom should be aligned with the position and height of the given table row.
How can I solve this? If it cannot be done using CSS alone, a solution using jQuery/JavaScript or like could be okay.
A: you may use hover and absolute to allow also tab crawling from a link to another :
td,th {
border:1px solid;
}
table {
margin:1em;
}
tr> :last-child {
width:1em;
vertical-align:top;
border:none;
}
:last-child a {
text-align:center;
position:absolute;
left:-9999px;
display:inline-block;
width:1em;
color:white;
text-decoration:none;
background:red;
}
tr:hover td:last-child a,td a:focus {
left:auto;
}
<div class="table-responsive">
<table class="table table-bordered">
<thead>
<tr>
<th>#</th>
<th>First Name</th>
<th>Last Name</th>
<th>Username</th>
<th></th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo</td>
<td><a href>X</a></td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat</td>
<td><a href>X</a></td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter</td>
<td><a href>X</a></td>
</tr>
</tbody>
</table>
</div>
A: Since you need complete width for the table and it should be responsive, you can keep the delete button inside last td(Username) and position it by getting few values from the hovered row using jQuery.
$('.table-bordered-custom tr')
.on('mouseenter', function () {
var offset = $(this).offset();
var top = offset.top;
var width = parseInt($('.table-responsive').css('width'),10);
var elem = $(this).find('span.delete');
var parent_padding_left = parseInt($('.table-responsive').parent().css('padding-left'),10)
elem.css({
"top": top + "px",
"left": (width + parent_padding_left) - 1 + "px",
"display": "inline"
});
})
.on('mouseleave', function () {
$('span.delete').css({
"display": "none"
})
});
span.delete {
display: none;
position: absolute;
background: crimson;
color: #fff;
cursor: pointer;
padding: 9px 12px;
}
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" rel="stylesheet"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="container">
<section id="content">
<div class="col-xs-8 col-xs-offset-2">
<div class="table-responsive">
<table class="table table-bordered table-bordered-custom">
<thead>
<tr>
<th>#</th>
<th>First Name</th>
<th>Last Name</th>
<th>Username</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo<span class="delete">x</span>
</td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat<span class="delete">x</span>
</td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter<span class="delete">x</span>
</td>
</tr>
</tbody>
</table>
</div>
</div>
</section>
</div>
A: imho so many difficult answers, I would do it with an easy aproach.
In this JSFIDDLE I just add a display:none cell to each row with whatever buttom you want to show inside and with no borders so it won't look at all as inside the table, then :
tr:hover .buttom {display:table-cell;}
may do the trick.
and no idea why I have the feeling this may not be what you want (bounty question so many javascript answers and such)... but as much as I reread the question this is it.
Excuse my poor english
Edited: Btw, if you really want the buttoms outside the "responsive" table so you have your border around, it's easily done with absolute positioned, but you shoudn't really do it. Once the table goes 100% of the window width, then those buttoms you want won't be visible for the user.
Edited: When the "buttom" cell is displayed as none, it won't take the fixed 40px width we need (or whatever future width you need once you have all buttoms inside) so I set the width to .X0 insteed becuase this element is there (but with no border, style or content) and will make all the column the same width.
Then I just overwrite some bootstrap styles that were messing with the table. (Please notice that something like:
.table-responsive {border:0; padding:2px;}
.table-bordered {border:0;}
may affect all your project so be sure you just overwrite the styles in this table and non others. Use something like:
.container-of-the-table-with-buttoms .table-responsive {border:0; padding:2px;}
Fiddle has been updated
A: Try the following code
$('tbody tr').hover(function(){
$(this).find('td:last').show();
},function(){
$(this).find('td:last').hide();
});
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" rel="stylesheet"/>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<style>
.table-bordered-custom{
border:0px;
border-top:initial;
}
.table-bordered-custom thead th {
border-top:1px solid #ddd !important;
}
.table-bordered-custom tbody td:last-child {
border:0 !important;
display:none;
}
</style>
<table style="margin:10px" class="table table-bordered table-bordered-custom">
<thead>
<tr>
<th width="10%">#</th>
<th width="25%">First Name</th>
<th width="25%">Last Name</th>
<th width="25%">Username</th>
<th style="border:0 !important" ></th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo</td>
<td ><input type="button" value="X"> <input type="button" value="Edit"></td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat</td>
<td ><input type="button" value="X"> <input type="button" value="Edit"></td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter</td>
<td ><input type="button" value="X"> <input type="button" value="Edit"></td>
</tr>
</tbody>
</table>
A: I quickly wrote some code that might help you get started :
HTML
<div class="table-responsive">
<table class="table table-bordered">
<thead>
<tr>
<th>#</th>
<th>First Name</th>
<th>Last Name</th>
<th>Username</th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo</td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat</td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter</td>
</tr>
</tbody>
</table>
</div>
<div class="actionbuttons"></div>
CSS
.actionbuttons
{
position:absolute;
width: 150px;
height: 30px;
background: #f00;
display:none;
}
jQuery code
$('tbody tr').on('mouseover',function(){
var rowPosition = $(this).position();
var targetPosition = {
top: rowPosition.top,
left: rowPosition.left + $(this).width()
}
$('.actionbuttons').css(targetPosition);
$('.actionbuttons').show();
});
$('tr').on('mouseout',function(){
$('.actionbuttons').hide();
});
The fiddle
A: try adding an onmouseover and an onmouseout attribute to each row of the table. Use each to make the button visible and invisible.
<tr onmouseover="
*insert code to make button for this row visible*
" onmouseout="
*insert code to make button for this row invisible*
">
*insert table data for this row*
</tr>
A: You can also play a little with CSS3 transform, transition and eventually FontAwesome to obtain a:
Pure CSS3 solution ( NO JavaScript, NO images )
td {
background: white;
}
th.buttons {
display: none;
}
td.buttons {
border: none !important;
padding: 0px !important;
z-index: -1;
transform: translateX(-100%);
transition: transform .5s ease 0s, z-index .1s ease 0s;
}
tr:hover td.buttons {
transform: translateX(0%);
z-index: 1;
transition: transform .5s ease 0s, z-index .01s ease .5s;
}
.buttons ul {
text-align: left;
margin: 0;
padding: 0;
}
.buttons ul li {
display: inline-block;
min-height: 100%;
text-align: center;
}
.buttons a {
border-radius: 2px;
color: red;
display: block;
font-size: 16px;
line-height: 100%;
min-width: 5em;
text-decoration: none !important;
transition: background 0.3s ease 0s;
}
.buttons i {
display: block;
font-size: 1.5em;
}
.buttons span {
font-family: sans-serif;
font-size: 0.625em;
text-transform: uppercase;
}
li:hover a {
background: red;
color: white;
z-index: 1;
}
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap-theme.min.css" rel="stylesheet" />
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap.min.css" rel="stylesheet" />
<link href="http://maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" rel="stylesheet" />
<div class="table-responsive">
<table class="table table-bordered">
<thead>
<tr>
<th>#</th>
<th>First Name</th>
<th>Last Name</th>
<th>Username</th>
<th class="buttons"></th>
</tr>
</thead>
<tbody>
<tr>
<th scope="row">1</th>
<td>Mark</td>
<td>Otto</td>
<td>@mdo</td>
<td class="buttons">
<ul>
<li><a href="javascript:alert('update row...');"><i class="fa fa-pencil-square-o"></i><span>update</span></a>
</li><!--
--><li><a href="javascript:alert('delete row...');"><i class="fa fa-times"></i><span>delete</span></a>
</li>
</ul>
</td>
</tr>
<tr>
<th scope="row">2</th>
<td>Jacob</td>
<td>Thornton</td>
<td>@fat</td>
<td class="buttons">
<ul>
<li><a href="javascript:alert('update row...');"><i class="fa fa-pencil-square-o"></i><span>update</span></a>
</li><!--
--><li><a href="javascript:alert('delete row...');"><i class="fa fa-times"></i><span>delete</span></a>
</li>
</ul>
</td>
</tr>
<tr>
<th scope="row">3</th>
<td>Larry</td>
<td>the Bird</td>
<td>@twitter</td>
<td class="buttons">
<ul>
<li><a href="javascript:alert('update row...');"><i class="fa fa-pencil-square-o"></i><span>update</span></a>
</li><!--
--><li><a href="javascript:alert('delete row...');"><i class="fa fa-times"></i><span>delete</span></a>
</li>
</ul>
</td>
</tr>
</tbody>
</table>
</div>
Note: the <li> are connected by HTML comments (<!-- -->) to prevent the inline-block spacing problem.
A: Use this:
$('tr').hover(function(){
$('div').removeClass('hide');
$('div').addClass('open');
})
CSS:
.open {
background: yellow;
height: 300px;
position: absolute;
top: 0;
left: -500px;
width: 500px;
opacity: 1;
-webkit-transition: all 0.7s ease-out;
-moz-transition: all 0.7s ease-out;
-ms-transition: all 0.7s ease-out;
-o-transition: all 0.7s ease-out;
transition: all 0.7s ease-out;
}
.close {
background: yellow;
height: 300px;
position: absolute;
top: 0;
left: -500px;
width: 500px;
opacity: 1;
-webkit-transition: all 0.7s ease-in;
-moz-transition: all 0.7s ease-in;
-ms-transition: all 0.7s ease-in;
-o-transition: all 0.7s ease-in;
transition: all 0.7s ease-in;
}
Hope it Works!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,554 |
This could be the only web page dedicated to explaining the meaning of MMO (MMO acronym/abbreviation/slang word).
Ever wondered what MMO means? Or any of the other 9127 slang words, abbreviations and acronyms listed here at Internet Slang? Your resource for web acronyms, web abbreviations and netspeak.
MMO is "Short for MMORPG"
The definition of MMO is "Short for MMORPG"
MMO means "Short for MMORPG"
So now you know - MMO means "Short for MMORPG" - don't thank us. YW!
What does MMO mean? MMO is an acronym, abbreviation or slang word that is explained above where the MMO definition is given. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,145 |
Bolivia Prepares Literacy Programs in 36 Indigenous Languages
LATIN AMERICA & THE CARIBBEAN, 12 Sep 2016
teleSUR – TRANSCEND Media Service
Since Evo Morales took office illiteracy has been reduced from 13.3 percent to 2.9 percent, the lowest rate in the history of Bolivia.
Bolivia's constitution states that the official languages are Spanish and all 36 languages spoken by the country's Indigenous nations. | Photo: teleSUR
10 Sep 2016 – Next year Bolivia plans to kick off literacy programs in the 36 native languages recognized and spoken in the South American nation, the education ministry announced on Friday.
Bolivia's President Evo Morales Ready to Step Down in 2020
"It's very clear that the issue of literacy needs to be diversified and strengthened. We have already started to work with some of them," the head of the illiteracy campaign, Ramiro Tolaba said to teleSUR.
Tolaba also considers it necessary to create methodologies for teaching literacy to people with hearing and visual disabilities. "We need to make much more progress in this regard and the challenge is huge, but this is what the country needs," he added.
During the past decade and under the government of President Evo Morales, illiteracy was reduced from 13.3 percent to 2.9, the lowest rate in the history of Bolivia.
President Morales, who is the country's first Indigenous president, has advanced Inidigenous rights in the country. Bolivia's Indigenous peoples constitute approximately 62 percent of the country's population of over 10 million. In 2008 he adopted the U.N. Declaration on the Rights of Indigenous Peoples.
Bolivia Has Cut Extreme Poverty in Half Since 2006
Bolivia's constitution states that the official languages are Spanish and all 36 languages spoken by the country's Indigenous nations. It also states that universities must implement programs for the recovery, preservation, development, and dissemination of learning these different languages.
Go to Original – telesurtv.net | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,426 |
The Carolingian World
At its height, the Carolingian empire spanned a million square kilometres of western Europe – from the English Channel to central Italy and northern Spain, and from the Atlantic to the fringes of modern Hungary, Poland and the Czech Republic. As the largest political unit for centuries, the empire dominated the region and left an enduring legacy for European culture. This comprehensive survey traces this great empire's history, from its origins around 700, with the rise to dominance of the Carolingian dynasty, through its expansion by ruthless military conquest and political manoeuvring in the eighth century, to the struggle to hold the empire together in the ninth. It places the complex political narrative in context, giving equal consideration to vital themes such as beliefs, peasant society, aristocratic culture, and the economy. Accessibly written and authoritative, this book offers distinctive perspectives on a formative period in European history.
MARIOS COSTAMBEYS is Senior Lecturer in the School of History at the University of Liverpool. His previous publications include _Power and Patronage in Early Medieval Italy: Local Society, Italian Politics and the Abbey of Farfa, c.700–900_ (Cambridge, 2007).
MATTHEW INNES is Professor of History at Birkbeck, University of London. His previous publications include _State and Society in the Early Middle Ages: The Middle Rhine Valley, 400–1000_ (Cambridge, 2000).
SIMON MACLEAN is Senior Lecturer in the School of History at the University of St Andrews. His previous publications include _Kingship and Politics in the Late Ninth Century: Charles the Fat and the End of the Carolingian Empire_ (Cambridge, 2003).
Cambridge Medieval Textbooks
This is a series of introductions to important topics in medieval history aimed primarily at advanced students and faculty, and is designed to complement the monograph series _Cambridge Studies in Medieval Life and Thought_. It includes both chronological and thematic approaches and addresses both British and European topics.
For a list of titles in the series, see
www.cambridge.org/medievaltextbooks
# THE CAROLINGIAN WORLD
MARIOS COSTAMBEYS
_University of Liverpool_
MATTHEW INNES
_Birkbeck, University of London_
SIMON MACLEAN
_University of St Andrews_
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521563666
© Marios Costambeys, Matthew Innes and Simon MacLean 2011
This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.
First published 2011
3rd printing 2012
Printed and bound at MPG Books Group, UK
_A catalogue record for this publication is available from the British Library_
_Library of Congress Cataloguing in Publication data_
Costambeys, Marios.
The Carolingian world / Marios Costambeys, Matthew Innes, Simon MacLean.
p. cm. – (Cambridge medieval textbooks)
Includes bibliographical references and index.
ISBN 978-0-521-56366-6 (hardback)
1. Carolingians – History. 2. France – History – To 987. 3. France – Civilization. 4. Europe, Western – History. 5. Europe, Western – Civilization. 6. Europe – History – 476–1492. 7. Civilization, Medieval. I. Innes, Matthew. II. MacLean, Simon.
III. Title. IV. Series.
DC70.C67 2011
944'.014 – dc22 2010054602
ISBN 978-0-521-56366-6 Hardback
ISBN 978-0-521-56494-6 Paperback
* * *
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
* * *
For Rosamond McKitterick and Jinty Nelson
## CONTENTS
_List of illustrations_
_List of maps_
_Acknowledgements_
_List of abbreviations_
_The Carolingian family (simplified)_
_The children and grandchildren of Charlemagne_
1. Introduction
The dawn of the Carolingian age
Was there a Carolingian world?
The sources for the Carolingian world
2. The creation of Carolingian kingship to 800
Replacing the ruling dynasty
The Merovingian world and Carolingian origins
Charles Martel and the extension of Carolingian power
Securing Carolingian hegemony: Pippin III
Charlemagne as king
3. Belief and culture
The problem of Christianisation
The problem of sin
Christian leadership and learning
4. Inventing the Carolingian empire: politics and government, 800–840
Introduction
The imperial coronation
Governing the empire
Dynastic politics, _c_.806–827
Kingship and 'subkingship'
Revolt and recovery: dynastic politics 827–840
5. Villages and villagers, land and landowners
Introduction: interpreting Carolingian society
Villages
Landowning and landowners
Community and mobility
Landlords and manors
The problem of economic growth
The powerful and the poor: social conflict in the Carolingian countryside
Conclusion: community and conflict
6. Elite society
Introduction
Aristocratic identity: vocabulary, appearance and lifestyle
Aristocratic behaviour: upbringing, morality and culture
Aristocratic families
Aristocratic resources and relationships: _honores_ , benefices and lordship
7. Exchange and trade: the Carolingian economy
Introduction: interpreting the Carolingian economy
Mechanisms of exchange
The North Sea economy
The transformation of the emporia: the ninth century
The Vikings and the Frankish economy
Italy and the Mediterranean economy
Conclusion: was there a Carolingian economy?
8. Sustaining the Carolingian empire: politics and government, 840–888
Introduction: fraternal rivalry, 840–843
Fraternal love, 843–877
Government and resources
The end of the empire, 877–888
9. Epilogue
_Bibliography_
_Index_
## ILLUSTRATIONS
1. A charter from St Gallen. Stiftsarchiv St Gallen, I 51 ( _Chartae Latinae antiquiores_ 1, no. 76)
2. The altar of Ratchis (ara di Duca Ratchis). Museo Cristiano del Duomo, Cividale del Friuli, Italy. Reproduced by kind permission of Dr Neil Christie, University of Leicester
3. The Tassilo chalice. The Art Archive / Kremsmünster Stiftsbibliothek / HarperCollins Publishers
4a. Abbey of Lorsch, Germany, gatehouse. © 2010. DeAgostini Picture Library / Scala, Florence
4b. Abbey of Korvey, Germany, _Westwerk_. Scala © 2010. Photo Scala, Florence
5. The Stuttgart Psalter, 'Anima'. Stuttgart, Württembergische Landesbibliothek, Biblia Fol. MS 23, fol. 55r
6. Mosaic, apse of the chapel at Germigny-des- Prés, France. The Art Archive / Gianni Dagli Orti
7. Plan of St Gallen. St Gallen, Stiftsbibliothek, MS 1092
8. Mosaic of Charlemagne and Pope Leo III, Rome. akg-images / Andrea Jemolo
9. Aristocratic assembly from the Utrecht Psalter. Utrecht, Universiteitsbibliotheek, MS 32, fol. 83r. Reproduced by kind permission of the Utrecht University Library
10a. Plan of Aachen palace and chapel. After K. J. Conant, _Carolingian and Romanesque Architecture 800–1200_ (4th edn, New Haven, CT, 1978), p. 47
10b. Reconstruction of palace at Ingelheim. Kaiserpfalz Ingelheim – ArchimediX
11. Portrait of Louis the Pious from Hraban Maur's _De laudibus sanctae crucis_. Rome, Biblioteca Apostolica Vaticana, Reg. lat 124, fol. 4v
12. Reconstruction of a hilltop settlement ( _curtis_ ) at Miranduolo, Tuscany. Reproduced with kind permission of Professor Marco Valenti, Dipartimento di Archeologia e Storia delle Arti, Universitaà degli Studi di Siena
13. King as lawgiver, from the _Golden Psalter_ of St Gallen. St Gallen, Stiftsbibliothek, MS 22, fol. 39
14. A nobleman, fresco in church of San Benedetto, Malles Venosta, South Tyrol. The Art Archive
15. The earliest Confraternity Book of St Gallen. St Gallen Stiftsarchiv, C3 B55, p. 22
16. Silver _denarius_ minted at Dorestad. Reproduced by permission of the Syndics of The Fitzwilliam Museum, Cambridge
17. Portrait of Charles the Bald from the _Codex_ _aureus_ of St Emmeram. Munich, Bayerische Staatsbibliothek, Cod. lat. 1400, fol. 5v
## MAPS
1. Europe (relief)
2. Places mentioned in Chapter 2: 'The creation of Carolingian kingship to 800'
3. The expansion of the Carolingian empire. After map by T. S. Brown, from D. Ditchburn, S. MacLean and A. Mackay (eds.), _The Atlas of Medieval Europe_ (2nd edn, London, 2007), p. 18
4. Cultural centres in Carolingian Europe
5. Places mentioned in Chapter 4: 'Inventing the Carolingian empire: politics and government, 800–840'
6. Places on Charlemagne's itineraries, 768–814. Source: R. McKitterick, _Charlemagne_ (Cambridge, 2008), p. 181
7. Places mentioned in Chapter 5: 'Villages and villagers, land and landowners'
8. Places mentioned in Chapter 6: 'Elite society'
9. Landholdings of Hraban Maur's family. Source: M. Innes, _State and Society in the Early Middle Ages_ (Cambridge, 2000), p. 64
10. The lands in the will of Eberhard and Gisela of Friuli. After map in D. Ditchburn, S. MacLean and A. Mackay (eds.), _The Atlas of Medieval Europe_ (2nd edn, London, 2007), p. 48
11. Exchange and trade: the North Sea and the Baltic Sea
12. Dorestad. After Fig. 2 in W. A. van Es, 'Dorestad centred', in J. C. Besteman, J. M. Bos and H. A. Heidinga (eds.), _Medieval Archaeology in the Netherlands_ (Assen and Maastricht, 1990)
13. Exchange and trade: the Mediterranean Sea
14. Places mentioned in Chapter 8: 'Sustaining the Carolingian empire: politics and government, 840–888'
15. Viking raids, _c_.835 to 863
16a. Ninth-century divisions: The partition of Verdun, 843
16b. Ninth-century divisions: The Carolingian kingdoms in 855
16c. Ninth-century divisions: The partition of Meersen, 870. After maps in R. McKitterick, _Frankish Kingdoms under the Carolingians_ , _751–987_ (London and New York, 1983), pp. 381, 382, 383
17. Viking raids, 863–77
18. Viking raids, 879–91
19. Places on the itineraries of Charles the Fat (876–88)
## ACKNOWLEDGEMENTS
Our initial thanks are due to Rosamond McKitterick and to Jinty Nelson, for first presenting each of us with the challenge of teaching the history of the early Middle Ages. As many of the references in this book testify, the work of these two scholars has fundamentally influenced the development of this field over the last few decades, and during our PhD research and since we have also been privileged to learn from them in person. We also owe warm thanks to Elina Screen. Her contribution extends well beyond the formal aspects to which we initially asked her to pay attention; both form and content would have been much the poorer without her diligent work. We would like too to thank Sally Lamb, on whose work Maps 15, and are based, and all those who read parts of the book in draft, or discussed particular problems or issues with us. All offered useful comments, though of course none is responsible for the views we have expressed. From the start we envisaged that undergraduates would form an important part of our readership, and indeed the idea for this book first arose when two of the authors covered some of Rosamond McKitterick's lecturing duties at the University of Cambridge during a period of research leave. Teaching and writing history are genuinely interconnected activities, and we are grateful to our friends and students at the Universities of Liverpool, Birkbeck London and St Andrews not just for road-testing drafts of some chapters, but also for helping us form and clarify our ideas. We are also indebted to successive commissioning editors at CUP for their encouragement, efficiency and patience: Bill Davies, Simon Whitmore, Michael Watson and Liz Friend-Smith. Our most profound gratitude goes, of course, to our families, for support, encouragement, and welcome distraction: to Greg and Joe, and Naomi and Evan, and to Charlotte, Jayne and Claire.
## ABBREVIATIONS
_AB_ | _Annales Bertiniani_ Annals of St Bertin], ed. F. Grat, J. Vielliard, S. Clémencet and L. Levillain ([Paris, 1964), trans. J. L. Nelson, _The Annals of Saint-Bertin_ (Manchester, 1991)
---|---
_AF_ | _Annales Fuldenses_ Annals of Fulda], ed. F. Kurze, _MGH SRG in usum scholarum separatim editi_ IX ([Hanover, 1891), trans. T. Reuter, _The Annals of Fulda_ (Manchester, 1992)
_AL_ | _Annales Laureshamenses_ Annals of Lorsch], ed. G. H. Pertz, _MGH SS_ I ([Hanover, 1826), pp. 22–39
_AMP_ | _Annales Mettenses priores_ Earlier Annals of Metz], ed. B. von Simson, _MGH SRG in usum scholarum separatim editi_ X ([Hanover and Leipzig, 1905)
_Annales HSS_ | _Annales. Histoire, Sciences Sociales_
_ARF_ | _Annales regni francorum_ Royal Frankish Annals], ed. F. Kurze, _MGH SRG in usum scholarum separatim editi_ VI ([Hanover, 1895), trans. B. Scholz, _Carolingian Chronicles_ (Ann Arbor, MI, 1970)
_AV_ | _Annales Vedastini_ Annals of St Vaast], ed. B. von Simson, _Annales Xantenses et Annales Vedastini_ , _MGH SRG in usum scholarum separatim editi_ XII ([Hanover and Leipzig, 1909); extract (a.844–62) trans. P. E. Dutton (ed.), _Carolingian Civilization: a Reader_ , 2nd edn (Peterborough, ON, 2004), pp. 347–50
_AX_ | _Annales Xantenses_ Annals of Xanten], ed. B. von Simson, _Annales Xantenses et Annales Vedastini, MGH SRG in usum scholarum separatim editi_ XII ([Hanover and Leipzig, 1909); extract (a.882–6) trans. Dutton (ed.), _Carolingian Civilization_ , pp. 507–12
Bede, _HE_ | Bede, _Historia Ecclesiastica_
_Capit_. I, II | A. Boretius and V. Krause (eds.), _Capitularia regum francorum, MGH Leges sectio_ III, 2 vols. (Hanover, 1883–97)
_CC_ | _Codex epistolaris Carolinus_ , ed. W. Gundlach, _MGH Epp_. III ( _Epistolae merovingici et karolini aevi_ I) (Berlin, 1892), pp. 476–657
_CCCM_ | _Corpus Christianorum, continuatio medievalis_
_CCM_ | _Corpus consuetudinum monasticarum_ (Siegburg, 1963–)
_CCSL_ | _Corpus Christianorum, series Latina_
_CDL_ | L. Schiaparelli, C. Brühl and H. Zielinski (eds.), _Codice diplomatico longobardo_. 5 vols. Fonti per la storia d'ltalia 62–6 (Rome, 1929–86)
_Chron. Moiss_. | _Chronicon Moissiacense_ Moissac Chronicle], ed. G. Pertz, _MGH SS_ I ([Hanover, 1829), pp. 282–313; extracts trans. in P. D. King, _Charlemagne: Translated Sources_ (Kendal, 1987), pp. 145–9
_CL_ | K. Glockner (ed.), _Codex Laureshamensis_ , Arbeiten der historischen Kommission für den Volksstaat Hessen 3. 3 vols. (Darmstadt, 1929–36)
_Conc_. I, II | A. Werminghoff (ed.), _Concilia aevi Karolini_ 11.1 and 11.2 (Hanover, 1906–8)
_DA_ | _Deutsches Archiv für Erforschung des Mittelalters_
Dipl. | Diplomata
_Dipl. Kar_. I | E. Mühlbacher _et al_. (eds.), _Die Urkunden der Karolinger_ I: _Die Urkunden Pippins, Karlmanns und Karls des Groβen. MGH Diplomata Karolinorum_ I (Hanover, 1906)
_Dipl_. _LG_ | P. Kehr (ed.), _Die Urkunden Ludwigs des Deutschen, Karlmanns und Ludwigs des Jüngeren. MGH Diplomata Regum Germanie ex stirpe Karolinorum_ I (Berlin, 1934)
_Dipl. Loth_ II | T. Schieffer (ed.), _Die Urkunden Lothars I und Lothars II. MGH Diplomata Karolinorum_ III (Berlin, 1966)
_DNB_ | H. C. G. Matthew, B. H. Harrison, L. Goldman (eds.), _Oxford Dictionary of National Biography_ (Oxford, 2004)
_EHD_ | D. Whitelock (ed.), _English Historical Documents_ , 2nd edn (London and New York, 1979) I: _c.500–1042_
_EHR_ | _English Historical Review_
Einhard, _VK_ | Einhard, _Vita Karoli_ Life of Charlemagne], ed. O. Holder-Egger, _MGH SRG_ XXV ([Hanover, 1911), trans. P. Dutton, _Charlemagne's Courtier: The Complete Einhard_ (Peterborough, ON, 1998), and D. Ganz, _Two Lives of Charlemagne_ (Harmondsworth, 2008)
_EME_ | _Early Medieval Europe_
_Ep., Epp_. | _Epistola, Epistolae_ [Letter(s)]
Fred., _Cont_. | Fredegar, _Continuations_ , ed. and trans. J. M. Wallace-Hadrill, _The Fourth Book of the Chronicle of Fredegar with its Continuations_ (London, 1960)
_HL_ | Paul the Deacon, _Historia langobardorum_ History of the Lombards], ed. L. Bethmann and G. Waitz, _MGH SRL_ ([Hanover, 1878), pp. 12–187
_HZ_ | _Historische Zeitschrift_
_LHF_ | _Liber historiae francorum_ Book of the History of the Franks], ed. B. Krusch, _MGH SRM_ II ([Hanover, 1888), pp. 215–328
_LP_ I, II | _Liber pontificalis_ Book of the Popes], ed. L. Duchesne, _Le Liber pontificalis. Texte, introduction et commentaire_ , 2 vols. ([Paris, 1886 and 1892); amplified 3 vol. edn ed. C. Vogel (Paris, 1955–7), trans. in three books by R. Davis, _The Book of Pontiffs_ (Liber Pontificalis), revised edition (Liverpool, 2000); _The Lives of the Eighth-Century Popes_ (Liber Pontificalis) (Liverpool, 1992); The Lives of the Ninth-Century Popes (Liber Pontificalis) (Liverpool, 1995)
McKitterick, | R. McKitterick, _History and Memory in the_
_History and Memory_ | _Carolingian World_ (Cambridge, 2004)
_MGH_ | _Monumenta Germaniae historica_
MIÖG | Mitteilungen des Instituts für Österreichische Geschichtsforschung
n.s. | new series
_NCMH_ II | R. McKitterick (ed.), _The New Cambridge Medieval History_ II: _c.700-c.900_ (Cambridge, 1995)
Notker, _Gesta_ | Notker Balbulus, _Gesta Karoli magni imperatoris_ , ed. H. F. Haefele, _MGH SRG_ , n.s. 12 (Berlin, 1959), trans. D. Ganz, _Two Lives of Charlemagne_ (Harmondsworth, 2008)
_P &P_ | _Past and Present_
_PBA_ | _Proceedings of the British Academy_
_PBSR_ | _Papers of the British School at Rome_
PL | Patrologia Latina: _Patrologia Cursus Completus, Series Latina_ , ed. J.-P. Migne, 221 vols. (Paris, 1841–66)
_Poet_. | _Poetae_
_QFIAB_ | _Quellen und Forschungen aus italienischen Archiven und Bibliotheken_
Regino,
_Chronicle_ | Regino of Prüm, _Chronicon_ , ed. F. Kurze, _MGH SRG_ L (Hanover, 1890), trans. S. MacLean, _History and Politics in Late Carolingian and Ottonian Europe: the Chronicle of Regino of Prüm and Adalbert of Magdeburg_ (Manchester, 2009)
_s. a_. | _sub anno_
_s.n_. | _sub nomine_
_SRG_ | _Scriptores rerum Germanicarum_
_SRL_ | _Scriptores rerum Langobardicarum_
_SRM_ | _Scriptores rerum Merovingicarum_
_SS_ | _Scriptores_
Story (ed.),
_Charlemagne_ | J. Story (ed.), _Charlemagne: Empire and Society_ (Manchester and New York, 2005)
_TRHS_ | _Transactions of the Royal Historical Society_
_UBF_ | E. E. Stengel (ed.), _Urkundenbuch des Klosters Fulda_. Veröffentlichungen der historischen Kommission für Hessen und Waldeck 19 (Marburg, 1936)
_UBMR_ | H. Beyer, L. Eltester and A. Goerz (eds.), _Urkundenbuch zur Geschichte der jetzt die Preuβischen regierungsbezirke Coblenz und Trier bildenden mittelrheinischen Territorien_ I: _Von den ältesten Zeiten bis zum Jahre 1169_ (Koblenz, 1860)
VMPIG | Veröffentlichungen des Max-Planck-Instituts für Geschichte
The Carolingian family (simplified)
The children and grandchildren of Charlemagne
**Map 1.** Europe (relief)
## I
### INTRODUCTION
#### THE DAWN OF THE CAROLINGIAN AGE
Late in the year 753, Pippin, king of the Franks, heard news that the pope had left Rome and was coming to visit him. This journey – the first time a pope had ever crossed the Alps – presented the king with both a problem and an opportunity. On the one hand, he may have known that what Pope Stephen II wanted was military protection, with all the risk and expense that that entailed, against an opponent in Italy, the king of the Lombards, whose predecessor had been Pippin's own godfather. On the other hand, the pope was just the kind of politically neutral and prestigious figure from whom Pippin could seek endorsement for the radical move he had made two years earlier, when he had usurped the throne of the Franks from the Merovingian dynasty that had held it for the previous two and a half centuries.
Neither Pippin nor Stephen quite appeciated the impact that their actions that winter would have but, in a process that typifies the problems faced by historians of this period, political significance was quickly heaped onto their meeting and within a few years the circumstances surrounding it were being intensively rewritten. Thus Stephen II's biographer, a clerk in the papal bureaucracy, reports that Pippin sent his young son Charles to meet the pope 100 miles from his destination and to escort him to the king, who knelt in homage before him. A Frankish source, on the other hand, has the pope and his attendant clergy kneeling before the king. Other Frankish sources assert that Pippin had already sought the approval of Stephen's predecessor for his usurpation; a claim apparently unknown to papal writers. It was certainly true that each could help the other. Frankish and papal sources concur that the pope anointed Pippin and his family. Pippin then secured the approval of the Frankish aristocracy and despatched campaigns in successive years which forced the Lombard king Aistulf to sue for peace. Returning home, Stephen reinforced his attachment to the Franks by granting buildings near St Peter's in Rome to the Parisian monastery of St Denis, the Frankish royal saint under whose auspices he had secured his alliance with Pippin.
In the short term the effects of this alliance were not decisive for either party. The popes remained relatively weak and for the next two decades the Lombards continued to menace their interests in and around Rome, while the Franks were generally reluctant to fulfil their newly acquired obligation to protect the papacy by committing themselves to military action hundreds of miles away across the Alps. In a longer perspective, however, these events represent what has long been interpreted by historians as an epochal turning point in the history of western Europe. For some historians of the first half of the twentieth century the change of ruling dynasty was regarded as 'the most momentous act of the entire Middle Ages', either because it inaugurated the pope's involvement in the legitimation of kingship, or because of the break it signalled between Rome and the surviving 'Roman' empire in the east – the Byzantine empire that covered the Balkans and Asia Minor. These views were crystallised in the 1920s in the work of the famous Belgian historian Henri Pirenne, who saw this break as only one component of a structural shift in the political and economic geography of Europe, as the lands of the western Mediterranean separated decisively from the eastern empire and struck up a more intense relationship with the kingdoms of the north, thus permanently fixing the shape of a new, specifically western, European civilisation.
Pippin did not see himself as standard bearer of a new age in these terms. Indeed, he was motivated above all by a sense of his own vulnerability. As we shall see in greater detail in Chapter 2, by having himself proclaimed king in 751 in place of the reigning king Childeric III, Pippin had defied a strong sense among the Franks that the aura of legitimacy rested upon Childeric's family, the Merovingians. Pippin's need to legitimise his action and to undermine the opposition of those hostile to his new royal status, including some members of his own family, lay behind his acquisition of papal blessing not only for himself but for his wife and sons as well. Nonetheless, the novelty of these rituals did reflect a self-conscious attempt to mark off and announce the beginning of a new political era. It was successful in ways that those present in 753–4 could not have foreseen: Pippin was born an aristocrat; his descendants would be kings and emperors of western Europe.
Thanks to their monopoly on royal power in the Frankish realms between 751 and 888, the Carolingians ('the family of Charles' (Latin: _Carolus_ ) – named for Pippin's father Charles Martel) are remembered as one of European history's great dynasties. The first phase of their tenure witnessed a breath-taking territorial expansion. Seeking to consolidate their tenuous position, Pippin and his sons embarked on a spectacularly successful series of campaigns pursued in equal measure through extreme violence and ruthless political manoeuvring. Within fifty years of Stephen's visit to Paris, they had doubled their territory and accumulated an empire spanning approximately one million square kilometres, stretching south from the English Channel to central Italy and northern Spain, and east from the Atlantic to the fringes of modern Hungary, Poland and the Czech Republic: easily the largest European political unit for many centuries. On Christmas Day 800 Pippin's son Charles 'the Great' (or Charlemagne as he is known to posterity, the same boy who as a five-year-old had reportedly been sent to receive Pope Stephen in 753) was crowned emperor in Rome, the first man to bear this title in the West since the deposition of the last Roman emperor in 476. Five of his immediate successors were to be emperors and many more ruled as kings as generations of Carolingians maintained and dominated this huge empire through most of the ninth century, during which the territory was often formally divided between members of the family, but always remained a dynastic unit. The territorial integrity of the empire was definitively ended only in 888, hastened by a succession crisis within the family.
Imperial aggrandisement was the basis, but not the end, of the dynasty's achievement. Inspired by court circles filled with scholars and spiritual advisers of international repute, the Carolingians also declared their aspiration to reform the social and moral behaviour of the peoples under their dominion. They sought to achieve this imaginative goal by exploiting to their limits the technologies of government available in the early Middle Ages. Pippin and his successors constructed a hierarchical political system which could allow the word of the king to penetrate to the furthest reaches of his realms; and they managed to do so in large part because of advances in the production, dissemination and preservation of knowledge. To some extent these advances were down to royal initiative. The foundation or revival by Carolingian rulers and aristocrats of institutions for which the written word was a central raison d'être – particularly, but not exclusively, the institutions of the Church – is a cardinal fact of the age. This is of the utmost importance for historians because those institutions' ability to copy existing works, to produce new ones, and to preserve both, has fundamentally shaped the record not just of the Carolingian period but of every preceding century back to the dawn of western history. We owe a good proportion of what we know of every century before 900 to the hands of Carolingian scribes. Their work attests a fusion of economic vitality (manuscripts were very expensive), political will and intellectual ambition which confirms that the Carolingians were distinctive for much more than the novelty of their relationship with the popes.
The Carolingians thus left an indelible mark on the historical record, but they also bequeathed an ideological legacy which dominated the imaginations of their successors. The heroes of the dynasty did not take long to pass into the realm of mythology, and posterity quickly canonised Pippin's family as a benchmark for dynastic prestige. It was this aura which, in 1000, drew the German emperor Otto III to Charlemagne's palace chapel at Aachen where, as an act of piety and political theatre, he exhumed and re-interred the great emperor's body, eyewitnesses reporting that apart from overlong fingernails and a touch of decay on the nose he remained bodily incorrupt and upright on his throne. In the twelfth century Suger, abbot of St Denis, built a new church to house the bodies of his patrons alongside the Carolingians already buried there, and thus to create a sense of dynastic continuity that flattered the great Capetian dynasty of his own day. Meanwhile, the German emperor Frederick I 'Barbarossa' sought to outdo the Capetians, and assert unmediated control of the Carolingian past, by translating Charlemagne's remains to a new casket in 1165, and having him recognised as a saint. Post-medieval imperialists have also looked to the eighth and ninth centuries to anchor their sense of themselves: the memory of the Carolingians was appropriated, for instance, by Napoleon, who visited Charlemagne's tomb to contemplate the great emperor prior to his own coronation in 1804. He has also found a place in the ideologies of modern regimes of various hues including those of the Nazis (whose army contained a unit named after Charlemagne) and the European Union (which sponsors a prize for European unity named after him).
It is, then, not surprising that modern historians, whose work is never uncontaminated by the wider ideological atmosphere in which it is written, continue to reinvent the contemporary relevance of the Carolingians by casting them in the role of 'a family who forged Europe', and seeing in their empire 'the scaffolding of the Middle Ages'. Some of the most prominent debates about the origins of modern Europe have revolved around the significance of key events in Carolingian history. The defeat by Pippin's father Charles Martel of a Muslim army near Tours was traditionally seen as decisive in halting the northward spread of Islam; Charlemagne's imperial coronation in 800 was, centuries later, recast as the founding event of the 'Holy Roman Empire'; the Treaty of Verdun in 843, by which the empire was divided into three parts, two of which corresponded roughly to France and Germany, has been seen as 'the birth certificate of Europe'; and the end of the empire in 888 was the focus for an intensely ideological debate about the origins of the kingdom of Germany coloured by a barely concealed mid-twentieth-century political agenda. The modern baggage loaded on to these distant moments hints at how the period has been quarried as a source of material for highly charged controversies about modern national identities, particularly those of France and Germany. To some extent this way of thinking was hard-wired into the field from the start: sustained critical study of the period was inaugurated in 1819 by the founding of the _Monumenta Germaniae historica_ (Historic Monuments of Germany), an institution whose purpose was explicitly framed as a patriotic attempt to raise German national consciousness through the publication of all texts relating to the medieval history of a country that was at that point still over fifty years from emerging as a full nation-state. Conversely, mid-twentieth-century French historians like Louis Halphen, haunted by the cataclysm of World War II, wrote the Carolingian story as a great tragedy of failed European unity; while some more recent authors have sketched a very different narrative arc by explicitly claiming the empire as a foreshadowing of contemporary Europe, united in diversity. All these views find support in the sources because the empire was always united (as an ideal) and often divided (in reality): contemporaries saw themselves as simultaneously members of regional or national groupings and of an imperial community, emphasising one or the other depending on who they were talking to or about. Because contemporary Franks argued about their identity in recognisable terms, the contested history of the Carolingian empire is useful for writing any one of a number of modern stories about the past.
It is not the aim of this book to take issue with or propound any one of these possible narratives. Rather, its writing has been prompted by the fact that the most recent general surveys of Carolingian history published in English are now over twenty-five years old, and since they were written there has been a dramatic surge in research that has subjected many aspects of the field to new levels of scrutiny. As is proper, this work has not led to the incremental formation of consensus on all topics, but has opened up new questions by identifying the parameters and paradoxes within which debate about eighth-and ninth-century society can be framed. Thus this often appears to be a world very alien to our own, one in which the ruling class was simultaneously pious and violent (with no sense of dissonance between the two); in which officials fulfilled functions we call 'governmental' and yet had little concept of the state; in which peasants, though legally free, could be bound by complex obligations to landlords and rulers; and in which increasing efforts to define and prescribe Christian belief were made against a background of enormously varied religious practices. The last twenty-five years have witnessed huge advances in historical comprehension of most of these areas, stimulated in part by increasing interest in the Carolingian period in the Anglophone scholarly world. Our aim is therefore not only to introduce the main features of the period to readers who may not be well acquainted with it, but also to synthesise and engage with the issues debated in the latest research. Working out how to fit all this together involves making difficult decisions, especially in a book aimed primarily at newcomers to the period. Political narrative is an essential framework for modern readers, as it was for contemporary authors. However, one of our aims in this book is to suggest that developments in social structures, rural and elite society, economic forces, religious beliefs and aspects of culture were inextricably tied up with political events, and with each other, in a complex multilateral relationship. One way we have chosen to emphasise this (since writing three-dimensional 'total history' is impossible) is by playing down the political narrative that dominates most textbooks and weaving it throughout the book, mainly restricted to chapters at the beginning, middle and end. Nevertheless, the interleaved thematic chapters do broadly follow a chronological arc so that, for example, it makes sense to know about Charlemagne's wars of conquest before discussing the establishment of structures of religious belief during his reign; but it is also sensible to analyse the main features of elite society before turning to the role of the aristocracy in the years leading up to the end of the empire. We hope that the book therefore not only serves to synthesise the recent flourishing of Carolingian studies, but also reflects scholars' increasing awareness of the complex interrelationships between political, social and economic phenomena that are often regarded as discrete.
At the same time, we have had to decide what to leave out. By focussing on broad themes such as belief, communications, village society and elite culture, we draw on examples that come from a range of geographical areas. Naturally, we are drawn more regularly to some areas than others – those for which sources survive most abundantly, and those that we know best. An inevitable consequence of this is that some important areas are under-represented in this book, for instance northern Spain, southern Gaul and the eastern frontiers. Other very important topics have receded into the background because comprehensive introductory accounts are readily available elsewhere. In this category we might place art, literature and other high cultural aspects of the Carolingian reform; the role of law and law-making; and warfare. Still others which could have been placed centre-stage, such as the political role of women, the structures of the institutional Church and the workings of government, we have tried to fold into our thematic discussions. We cannot claim comprehensiveness, and the bibliography at the end of the book should be used by readers wishing to learn more about particular subjects.
#### WAS THERE A CAROLINGIAN WORLD?
Listing some of the topics that do not appear in this book means that we are obliged to try to justify the coherence of those that do. Self-evidently, the book rests on the proposition that the 'Carolingian world' in the eighth and ninth centuries constitutes a discrete historical time and place that deserves analysis; and in doing so it could be seen as privileging a narrative of European history defined by the deeds of a single powerful family that focusses disproportionately on the geographical areas where they owned their greatest estates (in particular the Seine basin, the Rhineland and the Po valley). An important critique along these lines was published in 1989 by the American historian Richard Sullivan, who argued that by underplaying the importance of regionalism and screening out underlying continuities, historians were guilty of overemphasising the distinctiveness and significance of the Carolingian empire and era. He was certainly correct to stress the significance of regionalism in the eighth and ninth centuries. The geographical coherence of the empire is artificially enhanced by modern cartography, which can create the illusion of political boundaries as firm and uncontested lines. Contemporary thought did have a place for precisely defined borders – Carolingian kings thought they could impose restrictions on the passage across their frontiers of some commodities, particularly weapons and coins, which suggests a significant level of confidence in their ability to fix and police borders, as does Charlemagne's imposition of a trade embargo in a dispute with King Offa of Mercia around 790. However, the varying degree of royal control in different parts of the Frankish realms means that our maps' sharp edges begin to look frayed under close inspection. Some areas were at times nominally part of the empire but in practice not fully integrated, such as northern Spain, central Italy and Brittany. Other parts of Europe, including the kingdoms of Anglo-Saxon England, were clearly beyond the frontier but through regular contact and cultural pressure absorbed many of the characteristics of Carolingian political culture. Nor was the empire cleanly defined against outsiders as a religious entity: while Charlemagne's campaigns against the pagan Saxons are talked about in some sources in terms that suggest religious justifications were used, he also fought Christians in Brittany and Aquitaine, and his attacks on Muslim Spain were initiated not against an enemy defined by its different religion, but on behalf of one faction within the Caliphate against another. By the same token, Frankish Christian elites in the ninth century often pursued internal political and military interests by allying with non-Christian Scandinavians and Slavs. Concepts of religious difference overlapped with, and could be superseded by, a different set of assumptions concerning the cultural difference or similarity of the Franks' neighbours.
Since the Carolingians found it impossible to impose or adhere to rigid geographical boundaries in their world, we have not sought to do so in this book. Our coverage is of course partly dictated by that of the primary sources, which survive more thickly from some areas than from others. Even the focus of many of the narrative sources on the Carolingians themselves lends little geographical consistency to the picture, both because rulers were itinerant and because, after 840, the division of the realm produced multiple simultaneous foci. It is certainly possible to distinguish regions such as the Rhineland or the Po valley, but what can be said about them varies according to the concerns of the source material. Overall, the reader will find that most of the evidence discussed in the following chapters is drawn from the core Frankish realm – modern France, Belgium, Luxembourg, Switzerland, the Rhineland and southwestern Germany – and from northern and central Italy, where the Carolingians became dominant after 774. But other areas will come into focus when the book turns to topics on which their material makes especially significant contributions: the English and Irish in the discussion of Christianisation; Brittany when we turn to village life; Scandinavia and the Arab world in relation to long-distance exchange. Most of these experienced the strength of Carolingian political power only slightly, if at all. But they all made vital contributions to the shaping of the Carolingian world, and were themselves directly or indirectly influenced by it.
Carolingian influence fluctuated in intensity within the empire's borders as well as beyond them. Despite the rhetoric of unity persistently transmitted by Carolingian rulers and their religious advisers, we have to be constantly aware of the empire's great regional diversity in social and cultural terms. The huge and powerful monasteries of the middle Rhine or western Gaul, for instance, dominated landscapes defined by very different social, political and religious conditions from those surrounding the rather more impoverished churches of newly conquered Saxony. Similarly, not only did many peoples in the regions of the empire have their own lawcodes, but close study of how law operated in particular local societies has sharpened our appreciation of how different were the experiences of people who lived in a place like Catalonia from those of their, say, Bavarian contemporaries. Linguistic variety was almost equally kaleidoscopic. Acknowledging this variety does not, though, lead inevitably to the conclusion that the idea of a coherent Carolingian world is an illusion concocted to satisfy the fantasies of nineteenth-century nationalists or late-twentieth-century Europeanists; or that the persistence of internal differences is simply a sign that the Carolingian drive for unity and hierarchy should be judged a failure. Unity and diversity are not mutually exclusive – indeed, outside the totalitarian and absolutist states of the more recent past, large polities had to be built precisely through the acknowledgement of local identities by the central authority. The Carolingian empire was not like the British empire with a clearly defined centre-to-periphery political economy, nor a centralised state on the model of the Roman empire, but rather an agglomeration of regions with their own identities and greater or lesser degrees of autonomy. In writing this book we have tried to keep in mind as much as possible the fact that there were many Carolingian worlds, each of which adapted in different ways to being part of a larger political entity, and readers should keep this in mind before reaching general conclusions.
The chronological limits we have chosen to define the book are those which constitute the period during which the empire was united through rule by members of the same family, but these dates are also potentially porous. It is possible that political structures conventionally associated with the Carolingian takeover of the mideighth century are actually continuations of older phenomena for which we simply lack the sources. The ideological novelty of Pippin's anointing in 754 can certainly be played down using this sort of argument. At the other end of the period, despite the territorial disintegration of the empire in 888, members of the dynasty intermittently held royal status in parts of west Francia and Italy for another century. The Carolingian period neither began nor ended with a social revolution. Most historians would agree that most forms of change during the period were significant but gradual, governed by slow transformation rather than abrupt shifts or collapses that might have created the clean edges useful to those interested in defining historical eras. On the other hand, the step change in the number of surviving written sources (which we will consider more fully in the next section) from around the time of Pippin's usurpation could be seen as a significant historical fact in itself. It might indicate a shift in contemporary consciousness as people and institutions responded to the new political circumstances – in this case by taking up writing with new enthusiasm. It would be possible to explain the jump in the number of surviving documents recording donations to monasteries in, for instance, the Rhineland, Alsace and Bavaria in the reigns of Pippin and Charlemagne, by casting these institutions as prominent markers of shifts in the organisation of local society prompted by the rise of the Carolingians. Yet this point itself indicates that the change of dynasty cannot be given sole responsibility for every major development. Donations to monasteries also survive in increasing numbers from areas beyond the Carolingians' writ (at least initially), like Lombard Italy. What is more, the proliferation of monasteries at around this time itself affected the historical record. While it is an open question whether monastic houses were better at producing written texts than were previous groups of scribes, it is certain that they were better at producing texts that would last, and better at preserving both their own and earlier texts, partly because they themselves proved durable as institutions. The relationship between patterns of source survival and changes in the social and political world they reveal is, in other words, something of a chicken-and-egg problem.
What defined the Carolingian world above all was the ruling dynasty itself. The dynasty thought of itself as such even when (as after 840) the territories of the empire were divided between multiple and competing kings: responding to a belittling jibe from the Byzantine emperor Basil I in 871, who had patronisingly observed that being ruler of Italy alone did not make him much of an emperor, Louis II fumed that the western empire was exactly that because of the common blood shared by all of its Carolingian rulers. This was not just ideological froth. The dynasty's identity was not an incidental feature of the period; their longevity rested in part on their success in creating and imposing ways of thinking that self-consciously redefined the Frankish world _as_ Carolingian. The rewriting of the past that became, as we shall see, such a feature of the cultural output of the age was shot through with a concern to locate the Carolingians in history. Contemporary intellectuals sought both to write the history of the Franks in terms of the deeds of Carolingian (and proto-Carolingian) rulers, and to find a place for the 'Carolingian' era itself in the schemes provided by established models of long-term historical development – and ultimately, therefore, to make the empire's rise seem inevitable and its continued existence natural. Thus, writing in the middle of the 880s, Notker of St Gallen conceived of Charlemagne's Frankish empire as a divinely ordained successor to the great empires of the past: a new, discrete and coherent entity ready to be loaded with religious and political significance.
Texts like this could influence the thought-processes of the Frankish elite, but could not control them. Fragments of alternative discourses allow us to glimpse contemporaries imagining the possibility of a world not dominated by Carolingians. Yet even authors writing away from court in the ninth century were usually party to the same assumptions and modes of thought as those who enjoyed more regular contact with the king. By the time of Charlemagne's grandsons, and certainly by Notker's day, the court's cultural and reform agendas had been internalised by provincial bishops and monks. Such ways of thinking could filter down to ordinary lay people in a variety of ways: through the courts of the counts regularly convened in the king's name; through daily use of coins bearing his name and image; through the prayers said for his soul in church on Sunday. An idea of the political implications of this can be gleaned from the fact that, of the many rebellions in the period between 785 and 888, only one was led by an outsider against the dynasty – that of Boso of Vienne – while the rest sought only to replace one Carolingian with another. Little wonder, then, that contemporary authors commenting on the dynastic crisis of 888 perceived it as the end of an era: with the accession of non-Carolingian kings and the consequent territorial division of the empire between different dynasties, something had very definitely finished.We can, in other words, describe this world as Carolingian because that is how contemporaries perceived it.
#### THE SOURCES FOR THE CAROLINGIAN WORLD
The most striking aspect of the historian's evidence for the Carolingian world is simply its quantity: as we have already noted, far more texts survive from this era than from earlier ones. Only 1,800 manuscript books or fragments of books survive that were written in the continental west before ad 800, and many of those were copied in the eighth century. From the same part of the world, we possess over 9,000 manuscript books or fragments produced by scribes in the century from 800 to 900. These dramatic figures require some explanation. Only a minority of the 9,000 ninth-century manuscripts contained works composed in that century. Mostly they were copies of texts that had been written many years earlier: Latin classics like Virgil, early Christian literature, or books of the Bible. We are dealing here with an increase in copying, quite as much as a rise in literary creativity. But is the increase itself a real one, or an accident of survival? Does it signify a genuine quantum leap in the rate of production of written texts? A number of developments of the Carolingian age may inadvertently have affected the rate of survival. This period saw the development of a new script in which most books came to be written. Caroline (or Carolingian) minuscule is easily legible to us – indeed, it is the forerunner of the font in which this book is printed. This standardisation was evidently important in a contemporary context, though it is far from certain that its familiarity to modern eyes favoured the survival of books using the new script. More importantly, the Carolingian age benefited from long-term changes in the construction and materials of books that made them easier to preserve. Where in the ancient world the main writing material was papyrus, made from reeds, and books were scrolls of sheets of papyrus stitched together, by the Carolingian period writing was generally done on parchment, made from the skins of sheep, cows and goats and therefore far more durable than papyrus. Parchment leaves were stacked in quires and stitched together between hard or soft covers to form a codex – or what we would recognise as a book. Where papyrus scrolls were apt to rip and rot, parchment books could last for centuries – and have.
These changes in the technology of the written word themselves suggest that the Carolingian age placed new emphasis on knowledge and its dissemination. Scribes before that time may not have been quite as scarce as the paltry survivals of their work suggest, but they were working in contexts and with techniques that had changed since the Roman period only in the dwindling amount of resources devoted to them. The growth of Carolingian literate culture was largely the product of patronage directed at new institutions – principally monasteries – that were especially concerned to foster writing and learning. It is these which produced and preserved the very large documentary residue of the Carolingian world, including the original compositions of the time: histories, laws, land transactions and a host of other textual genres. Overall, we possess many more sources about the Carolingian period than about any previous era of comparable length.
One area where the Carolingian impact on culture can be observed very easily is in the production of historical writing. In the eighth and ninth centuries, remembrance of the past was a matter both of _memoria_ – the commemoration of the dead, especially in books of the names of the deceased whose souls were the subject of prayer ( _Libri vitae, libri memoriales_ ) – and of _historia_ – the relating of past deeds, and the form of the latter was changing as the annals, which started as by-products of liturgy, evolved into free-standing literature. Annals were one part of the outpouring of history, which sought (as mentioned earlier) to explicate the present and the recent past with reference to more distant times. Historical works written after 800 reveal constant debate about the place of the Carolingians in relation to past empires and the place of the empire in God's plans for the future as hinted at in the Bible. Contemporary historians and annalists tacked accounts of their own times on to versions of the more distant past that modelled the present variously as a continuation of the Roman past, a reinvention of it, a Christian empire that was distinct from the Roman, or the final age of the world in the eschatological scheme popularised by St Augustine. Often they did so by rewriting or suppressing uncomfortable memories of the more recent Merovingian past, anxious to mask the sour taste of usurpation and resistance. The fact that this debate existed at all suggests that whichever model they chose, contemporaries regarded the Carolingian period as a distinct historical era. The spill-over of this concern into continuous histories of the present makes even more obvious the role of numerous contemporary annalists and chroniclers in the 'Carolingianising' of the Frankish world. An initial model was established by the authors of the _Royal Frankish Annals_ , which presented an account of history between 741 and 829 that defined the history of the Frankish people in terms of the deeds of Carolingian kings: their wars, assemblies, and itineraries were the scaffolding used to construct a narrative of the times. This way of thinking was obviously part of the court's ideological armoury, but it also had a wider impact. The _Royal Frankish Annals_ were copied, excerpted and reused many times during the ninth century to the extent that they became part of a canon that influenced both subsequent writers and the consciousness of the Frankish elite.
The extent to which Carolingian political success had itself shaped the historical record becomes clear when we consider the contrast between the material produced before and after around 750. The only contemporary narrative history from the late seventh and early eighth centuries is the _Liber historiae francorum_ ('Book of [the] History of the Franks': hereafter referred to as the _LHF_ ). Completed in 727, probably in Soissons and perhaps by a woman, the _LHF_ traces the history of the Franks from their legendary beginnings, drawing on and summarising earlier sources until the last of them, the fourth book of the _Chronicle_ of Fredegar, ends in 642, from which point it provides an original, if rudimentary, account of events up to 721, seen from the perspective of the Neustrian – that is, the west Frankish – aristocracy. There are, in addition, a number of saints' lives that have been mined for the snippets of information that they give on political events and personalities, especially when those lives related events within the living memory of their intended audiences. Such matters were not their main concern, however: when approached with due regard to their original purpose, they allow us to glimpse the complexity of Merovingian culture and belief and to sample the mood prevalent in aristocratic society.
Although they depend on the _LHF_ , the two other major narratives of the period from 687 to 721 post-date Pippin III's takeover of the Frankish kingship in 751. Continuations of the _Chronicle_ of Fredegar were most likely added after Pippin's death in 768. Comparison with other sources reveals the tendency of these continuators, and especially the first, to garble events that had occurred only a generation earlier. This indicates the extent to which they were writing with their eyes on the present, and sought precedents for their current situation in the relatively recent past. In this case we know that the continuations to Fredegar's chronicle were written under the auspices of Pippin III's uncle Childebrand, and of the latter's son Nibelung. The way in which the continuators reworked the text of the _LHF_ is very evident. Reporting the death of the Merovingian Childebert III (694–711), the _LHF_ states 'then the famous and just lord King Childebert of good memory, passed away unto the Lord'. The first continuator of Fredegar is significantly more laconic at this point: 'it was now that King Childebert died'.
Equally rooted in their time of composition are the _Annales Mettenses priores_ (Earlier Annals of Metz), a set of annals first put together in a surviving version in 805. This work seeks, from its beginning at 688, to portray the history of the late seventh and eighth centuries as the history of the Carolingians. Its demonstrable use of an earlier source at least for events up to 751 might only reinforce the view that its account is unreliably 'pro-Carolingian'. Nevertheless, that earlier source, in so far as it can be discerned, can be set alongside other sources – letters written outside Francia, charters and coins – which seem to attest considerable power in the hands of earlier Carolingians, Pippin II and Charles Martel, before the 750s. Historians still debate the extent to which that power was exaggerated by later authors like those of the _Annales Mettenses priores_. The most succinct example of the latter's perspective is in the biography of Charlemagne by his courtier Einhard, who claimed that the last Merovingians possessed no more than a single estate, and travelled in an ox-cart. Annals of a more conventional kind were written at various centres in Francia throughout the eighth and ninth centuries. Relating events to a particular year is a practice that dates back to antiquity, but it was given a new context by the organisation of time that the Christian Church gradually imposed. The production of Easter tables, necrologies and martyrologies encouraged the recording of events annually, and this was made easier by the adoption from the beginning of the eighth century of dating by the incarnation of Christ. These yearly entries appear in eight early Carolingian annals. Interrelated, with often identical entries, and becoming ever fuller through the eighth century and into the ninth, they pursue a 'pro-Carolingian' agenda by relating only the deeds of the Carolingians, especially their military victories. They therefore sometimes transmit unique snippets of information that are less difficult to interpret than the narratives of the continuations of Fredegar and the _Annales Mettenses priores_.
As a form of writing about the past, annals were taken up energetically in some areas beyond Francia, not least in the British Isles, where the later ninth century saw court-centred annalistic works take shape in several Anglo-Saxon kingdoms (the origins of the later _Anglo-Saxon Chronicle_ ) and in Wales (the _Annales Cambriae_ ). Other regions preferred different historiographical forms. In Italy, just before Charlemagne's imperial coronation, Paul the Deacon completed a history of his own people, the Lombards, that proved to be an important foundation for subsequent Italian historians. Nonetheless, it can be read as using the Lombard past as a vehicle for comment on what was for Italy by the 790s a Frankish present.
The images of the past that Paul wrote into his _History of the Lombards_ seem to have been aimed principally at a circle of courtiers, either those of Duke Arichis of Benevento or those of Charlemagne's son Pippin, king of Italy under his father from 781. Many of the other writings about the past in this period seem similarly to have been intended, at least initially, for a fairly exclusive audience, whether courtiers of a ruler, an aristocratic entourage, or a monastic community ( _familia_ ). Many may never have permeated beyond these immediate audiences. Nevertheless, in conveying messages to powerful social groups these writers had the opportunity to influence opinion and attitudes among the political community.
The decade after Charlemagne's death in 814 seems to witness a change in the historical perspective of Frankish writers. Their concern was now not merely to offer 'Carolingianised' views of the past, but also to comment on recent events in ways charged with the language of contemporary controversies. Thus both of the extant biographies of Louis 'the Pious' give voice to opinions on Louis's sons' revolt against their father in 833–4: in Thegan's _Life_ , written in 836, we can detect the views of the circle of Rhenish aristocrats who were his chief contacts; while the author known to us only as 'the Astronomer' (because of his interest in celestial objects) wrote just after 840 from the perspective of the court itself, and probably making use of its archive. After 843, with the formal division of the empire, the multiplication of royal courts and the frequency of conflict between kingdoms gave a further boost to the writing of contemporary history, most notably in the _Annals of Fulda_ from the east Frankish realm, and the _Annals of St Bertin_ from the West. We can get an impression of how such works might have been read by looking at the manuscripts which contained them. The biographies of Louis, for example, circulated principally alongside Einhard's _Life of Charlemagne_ and often with versions of the _Royal Frankish Annals_ , and were edited and amalgamated to produce composite works of Frankish history with a distinctly Carolingian flavour. The texts of many annals, however, circulated piecemeal, meaning that they could be used as a form of news and comment, and might be tinged with traces of local colour. The _Annals of Lorsch_ , for example, preserved its very particular, east Frankish, memory of the revolt against Charlemagne by members of that region's aristocracy under Hardrad.
Historical writing is only one index of an increasing attention to literature in the decades following the accession of Charlemagne in 768. The emergence at that time of a group of men of letters, working initially at the royal court, has seemed one of the best indications that Charlemagne's age witnessed a renaissance of learning: a return to classical standards of intellectual life after a slump in the later sixth, seventh and earlier eighth centuries. The apparent void may, however, be due in part to the vagaries of manuscript loss, and in any case the standard of work of the great literary figures of the late eighth and early ninth centuries must owe something to a pre-existing tradition of Latin letters. These men employed a variety of genres, but one with which they evidently liked to play was poetry: the 'final phase of a thorough education' at the time. The sheer quantity of poetry preserved, as well as the number of surviving manuscripts including verse, shows that contemporaries saw poetry as neither unusual nor arcane as a medium for all sorts of ideas and sentiments. Slender threads of the Latin poetic tradition can be traced through the late seventh century and into the eighth, especially in Italy, where its range of uses – from theology to civic identity to commemoration – serves as a warning not to underestimate how important a literary form it was to contemporaries. If it was partly the influx of Italians into the royal court, alongside other scholars from beyond Francia, that turned it into the centre of intellectual activity in Charlemagne's kingdom, it is the surviving poetry that stands testimony to their conversations. In the Carolingian age, Latin verse was a vehicle not only for the dedications and epitaphs for which it would remain popular throughout the Middle Ages, but for reflections on the lives and relationships of the poets, their nicknames, their friendships and their flytings. The surviving poems seem to have been very immediate in their aims. As Mary Garrison has noted: 'apparently verse was intended to address and entertain contemporaries, not posterity'. Most prominently, the verses of these new poets were aimed at the king himself. Numerous lines of often extravagant praise were addressed to Charlemagne in particular. Epic set-pieces such as the so-called _Paderborn Epic_ , purporting to depict the king's encounter with Pope Leo III at that town in 799, present Charlemagne as the terrible scourge of his pagan enemies, aswell as the generous patron of the pope. Poems of this sort mirrored the classical form of the praise poem or panegyric, albeit with new tones and emphases. Imitation of the classics continued as an ideal in later generations, growing in ambition as authors sought consciously to echo the epics and elegies of Roman poets like Virgil and Ovid. But such works were not merely imitative: they served all the various purposes that historians have identified in the works of Carolingian cultural protagonists.
While the writing of _historia_ , recording the deeds of the past, whether distant or very immediate, responded to the needs of discrete, often elite, groups, the culture of _memoria_ had a wider impact. As we shall see in Chapter 3, memorialisation of the dead came to be bound up with patronage of churches and monasteries, and that patronage was generally enacted by or recorded in legal documents. Indeed, so great was the number of such documents, and so good were churches and monasteries at preserving them, that for some regions there is an impression that ecclesiastical patronage was the _only_ reason to produce documents. This was clearly not the case, but it does point to the need to bear in mind that the documentary legacy of the early Middle Ages has been shaped by the way in which documents have been transmitted down the centuries; and that process has been dominated, until the modern era, by the Church. The early medieval legal documents that we now possess survive in clusters associated with particular archives across the Carolingian world, mostly those of monasteries and episcopal churches. Some of them – those which embody the pronouncements of rulers – fit quite well into the 'Carolingianising' of the record that we have noted in narrative histories: legal decrees divided into chapters ( _capitulae_ , and hence known as capitularies) provided the framework for the actions of those to whom power was delegated in the localities, while collections of them transmitted this fundamentally Carolingian structure to successive generations. In simple numerical terms, however, the great majority of surviving legal documents are charters, the single sheets of papyrus or (more usually) parchment with which business of all sorts was conducted (see for example Figure 1). We possess these in sufficient numbers to see that their subject matter extended well beyond the interests of particular church institutions, and down to the most small-scale and mundane activities: not only conveyances of property through gift, sale and exchange, but also testaments, judicial and extra-judicial dispute settlements, leases, inventories and many others.
**Figure 1.** A charter from the abbey of St Gallen, modern Switzerland, which retains 750 original charters and contemporary copies written between the eighth century and 920. This example, issued on 2 May 775 by one Sighiharius, was written by the abbey's deacon, and later abbot, Waldo, who made a note on the dorse (reverse), summarising its contents: one of the first signs of systematic record management at St Gallen.
The Carolingian period witnessed changes in society's awareness of these documents. Charters survive in increasing numbers from about the middle of the seventh century, giving some insight into literate culture and patterns of production, landholding and power in a few localities, and providing the skeleton of a political chronology. In many of the lands that came to form the Carolingian realm, the number of survivals increases markedly through the eighth century. This cannot be ascribed to a dramatically higher level of their production: those that do survive from the Merovingian period concerned business that was just as routine as the Carolingian examples, and as legal documents in the late Roman period. But in that earlier time, there had been reliable ways not only to preserve documents, but also to validate, re-affirm and re-record the legal business they contained. The network of Roman public legal offices – _gesta municipalia_ – may not have been quite so extensive, elaborate or reliable as has sometimes been maintained, but it did ensure that documents were a crucial part of the framework of social regulation. The continued appearance of references to parts of this framework – to the _gesta_ as public centres of legal validation and record, with attendant officials – in the Merovingian and early Carolingian periods indicates two things. First, that at least in some regions the framework persisted after the end of Roman rule, and second, that it had disappeared by the mid-eighth century, while some of its functions had been taken up by those institutions – overwhelmingly, it would seem, churches and monasteries – capable of the regular production and, perhaps, the retention of relatively standardised documents. Legal recordkeeping no longer depended on organs of government in the way that it had done. Moreover, attitudes to archiving were changing. Those institutions that could preserve records – not just of their own legal business but of those who had entrusted documents to them – began to sift and shape their archives to help construct their institutional memory. Often, in fact, what was in their archives (and also, therefore, what had been lost) dictated the way they viewed their own past. Thus, monasteries not only produced cartularies into which their scribes laboriously copied the sheaves of documents in their archives, but also cartulary chronicles, in which selected documents formed a framework for a narrative history of their institution – and in particular a very partial (in both senses) account of its acquisition of its properties.
Careful consideration of the ways in which our record was created allows us to glimpse beyond it a world of document-users, both lay and clerical. Even as it stands, the record includes evidence for substantial engagement with documents by the laity: dossiers of documents involving only lay men and women were preserved in a number of monastic archives in the eighth and ninth centuries, such as those of St Gallen in Alemannia and Monte Amiata in Tuscany. That their protagonists possessed widely varying social statuses, and often also appear alongside churchmen conducting similar legal affairs, indicates both that document use by the laity was in many areas absolutely routine and that in any case a strict demarcation between lay people and clerics in this context is not really necessary. Although preserving documents for long periods may gradually have become the preserve of ecclesiastics, the use of documents at the time was certainly not.
Charters offer insights well beyond levels of engagement with writing, or the bald mechanics of the landholdings that are the principal subjects of the majority of the survivals. Because they were redacted at assemblies of local people, some of whom attested them as witnesses, and because they often describe not only the extent of landed properties, but their agricultural uses and the names and, often, conditions of the people living on them, these documents constitute invaluable witnesses to many aspects of the everyday life of the mass of the population. These emerge best when a number of charters from a particular locality and a relatively restricted period can be studied together, as is increasingly possible thanks to a steady increase inmodern editions. Cumulatively these bodies of documents reveal the composition, and some of the dynamics, of groups of local people, sometimes extending quite far down the social hierarchy. For these reasons, the charter evidence forms much of the basis of the observations on rural life and social structure in Chapters 5 and .
While today's historian theoretically enjoys a quantity of written sources for the Carolingian world barely higher than that available to previous generations, in practice he or she has readier access to much of it and is better able to appreciate the implications of its transmission, and so to place it in an appropriate context. Moreover, written sources can be set alongside a growing volume of material data, revealing hitherto hidden features of eighth and ninth-century existence. The sustained attention that archaeologists have paid to the early Middle Ages over the last thirty years or so has produced a rising tide of data on aspects of life that our written sources mention only tangentially, if at all. Archaeology can give a much more threedimensional view of the physical realities of early medieval life – not only of such things as dwellings, implements, ornaments and diet, but also of the physical condition of the people themselves. Such evidence is not a simple complement to the written sources; often, it challenges historians' long-standing interpretations of their texts. Thus, the charters' terminology for settlements, such as _villa_ or _fundus_ , in many areas remained relatively constant, while archaeology reveals dramatic changes taking place in the actual shape of human communities, such as the emergence of nucleated villages in many parts of Europe between the sixth and eighth centuries. New techniques of investigating the past also take us beyond material culture to movements of people themselves. Both recovered ancient DNA and samples taken from modern populations can be analysed to determine the movements, and the coming together, of biologically distinguishable populations in the past. The problem of mapping this data on to the historical sources is difficult: medieval ethnic and cultural labels cannot be applied straightforwardly to genetic profiles.Nonetheless, this new and rapidly developing science holds out the possibility of a much better understanding of human migrations, a crucial issue for our period, flanked as it is by the 'barbarian' migrations of the fifth and sixth centuries and the Viking settlements of the late ninth and tenth.
The growth in archaeological and biological data has been rapid, and their integration into the written history of the early Middle Ages is a significant preoccupation of students of the period. This drawing together of diverse and often fresh sources holds out the possibility that what has hitherto been frustratingly obscure or at least opaque might become clearer in the future. This is perhaps especially the case with aspects of everyday life – diet, for instance, or housing – that are only glancing concerns for the major genres of written text. Our more complex and subtle appreciation of the meanings in these latter sources is a necessary corollary of the effort to read them alongside the new stories related by material culture and biology. As a result, at the start of the twenty-first century, the Carolingian world has never appeared with sharper definition, and greater scope for understanding.
* * *
See _LP_ I, c. 25, p. 447, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 62, and _Chron. Moiss., s.a_. 741, pp. 292–3.
McKitterick, _History and Memory_ , pp. 137–8.
_LP_ I, c. 27, p. 448, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 63; Fred., _Cont._ , c. 33.
As even the papal biographer in the _Liber pontificalis_ tells us: _LP_ ii, c. 29, p. 448; Davis, _Lives of the Eighth-Century Popes_ , p. 64.
M. Costambeys and C. Leyser, 'To be the neighbour of St Stephen: patronage, martyr cult and Roman monasteries, _c_.600–900', in K. Cooper and J. Hillner (eds.), _Religion, Dynasty and Patronage in Early Christian Rome, 300–900_ (Cambridge, 2007), pp. 262–87, at pp. 273–4.
See R. Schieffer, '"Die folgenschwerste Tat des ganzen Mittelalters"? Aspekte des wissenschaftlichen Urteils über den Dynastiewechsel von 751', in M. Becher and J. Jarnut (eds.), _Der Dynastiewechsel von 751. Vorgeschichte, Legitimationsstrategien und Erinnerung_ (Münster, 2004), pp. 1–14.
See Chapter 7 below, pp. 326–8, and H. Pirenne, _Mahomet et Charlemagne_ (Brussels, 1937), trans. as _Mohammed and Charlemagne_ (London, 1939).
See P. Fouracre, 'The long shadow of the Merovingians', in Story (ed.), _Charlemagne_ , pp. 5–21; Becher and Jarnut (eds.), _Der Dynastiewechsel von 751;_ McKitterick, _History and Memory_ , pp. 133–55; M. J. Enright, _Iona, Tara, and Soissons: The Origin of the Royal Anointing Ritual_ (Berlin and New York, 1985).
Generally, capital-C 'Church' refers to the institution, while small-c 'church' refers to the building: thus we can write of the Anglo-Saxon (or Roman or Catholic) Church, but the church of St Peter's, cathedral church at Tours, etc.
Respectively, see: G. Althoff, _Otto III_ (University Park, PA, 2003); L. Grant, _Abbot Suger of St-Denis: Church and State in Early Twelfth-Century France_ (London, 1998); J. Petersohn, 'Saint-Denis – Westminster – Aachen. Die Karls-Translatio von 1165 und ihre Vorbilder', _Deutsches Archiv für Erforschung des Mittelalters_ 31 (1975), pp. 420–54. In general see M. Gabriele and J. Stuckey (eds.), _The Legend of Charlemagne in the Middle Ages. Power, Faith and Crusade_ (New York, 2008).
R. J. Morrissey, _Charlemagne and France: A Thousand Years of Mythology_ (Notre Dame, IN, 2003); J. Story, 'Introduction: Charlemagne's reputation', in Story (ed.), _Charlemagne_ , pp. 1–4; R. D. McKitterick, _Charlemagne: The Formation of a European Identity_ (Cambridge, 2008), pp. 1–3.
The quotations are from P. Riché, _The Carolingians: A Family who Forged Europe_ , trans. M. I. Allen (Philadelphia, PA, 1993) and Pirenne, _Mohammed and Charlemagne_ , p. 235.
P. Fouracre, _The Age of Charles Martel_ (Harlow, 2000), pp. 86–7; I. Wood, _The Merovingian Kingdoms, 450–751_ (London, 1994), p. 283.
Riché, _The Carolingians_ , p. 168.
C. Brühl, _Deutschland-Frankreich. Die Geburt zweier Volker_ , 2nd edn (Cologne and Vienna, 1995), pp. 7–17.
P. Geary, _The Myth of Nations_ (Princeton, NJ, 2002), esp. pp. 1–14.
D. Knowles, _Great Historical Enterprises_ (London, 1963), pp. 65–97.
L. Halphen, _Charlemagne and the Carolingian Empire_ (Amsterdam, 1977); J. L. Nelson, _The Frankish World, 750–900_ (London, 1996), pp. xiii–xiv; A. Barbero, _Charlemagne: Father of a Continent_ (Berkeley, 2004). On the writing of European history across specific periods, see S. Woolf, 'Europe and its historians', _Contemporary European History_ 12 (2003), pp. 323–37.
K. Leyser, 'Concepts of Europe in the early and high middle ages', _P &P_ 137, pp. 25–47, repr. in Leyser, _Communications and Power in Medieval Europe: The Carolingian and Ottonian Centuries_ (London, 1994), pp. 1–18.
The most recent English-language surveys of a specifically defined Carolingian period are Rosamond McKitterick's _The Frankish Kingdoms under the Carolingians, 751–987_ (London and New York, 1983) and Riché, _The Carolingians_ , which also first appeared in 1983.
Both McKitterick, _Frankish Kingdoms_ and Riché, _The Carolingians_ have very good discussions of culture; see also R. McKitterick (ed.), _Carolingian Culture: Emulation and Innovation_ (Cambridge, 1994); on law see P. Wormald, _The Making of English Law: King Alfred to the Twelfth Century_ i: _Legislation and its Limits_ (Oxford, 1999) (which despite the title contains much on continental history); on warfare, G. Halsall, _Warfare and Society in the Barbarian West_ (London and New York, 2003). On all these areas, see _NCMH_ II.
R. Sullivan, 'The Carolingian age: Reflections on its place in the history of the Middle Ages', _Speculum_ 64 (1989), pp. 267–306.
On frontiers, see W. Pohl, I. Wood and H. Reimitz (eds.), _The Transformation of Frontiers from Late Antiquity to the Carolingians_ (Leiden, Boston and Cologne, 2001) and W. Pohl and H. Reimitz (eds.), _Grenze und Differenz im frühen Mittelalter_ (Vienna, 2000). On Charlemagne and Offa, see Alcuin, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. IV ( _Epp. Karolini aevi_ II) (Berlin, 1895), pp. 1–493, no. 7, trans. S. Allott, _Alcuin of York: his Life and Letters_ (York, 1974), no. 31; J. Story, _Carolingian Connections: Anglo-Saxon England and Carolingian Francia, c.750–870_ (Aldershot, 2003), p. 186.
See respectively R. Collins, _Early Medieval Spain: Unity in Diversity, 400–1000_ (2nd edn, Basingstoke, 1995); M. Costambeys, _Power and Patronage in Early Medieval Italy_ (Cambridge, 2007), Chapters 7 and ; J. M. H. Smith, _Province and Empire. Brittany and the Carolingians_ (Cambridge, 1992).
J. Story, 'Charlemagne and the Anglo-Saxons', in Story (ed.), _Charlemagne_ , pp. 195–210; Story, _Carolingian Connections_.
I. Wood, 'Missionaries and the Christian frontier', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_ , pp. 209–18.
See respectively M. Innes, _State and Society in the Early Middle Ages: The Middle Rhine Valley, 400–1000_ (Cambridge, 2000) and C. J. Carroll, 'The bishoprics of Saxony in the first century after Christianization', _EME_ 8 (1999), pp. 219–45.
On Bavaria, see W. Brown, _Unjust Seizure: Conflict, Interest and Authority in an Early Medieval Society_ (Ithaca, NY, 2001); on Catalonia, see C. J. Chandler, 'Between court and counts: Carolingian Catalonia and the aprisio grant, 778–897', _EME_ 11/1 (2002), pp. 19–44; see also the essays in W. Davies and P. Fouracre (eds.), _The Settlement of Disputes in Early Medieval Europe_ (Cambridge, 1986), for discussion of regions including Brittany, Spain and Italy.
On language see M. Banniard, 'Language and communication in Carolingian Europe', in _NCMH_ ii, pp. 695–708 and P. Kershaw, 'Laughter after Babel's fall: misunderstanding and miscommunication in the ninth-centurywest', in G. Halsall (ed.), _Humour, History and Politics in Late Antiquity and the Early Middle Ages_ (Cambridge, 2002), pp. 179–202.
See R. McKitterick, 'Unity and diversity in the Carolingian church', in R. Swanson (ed.), _Unity and Diversity in the Church_ , Studies in Church History 32 (1996), pp. 59–82; M. Innes, 'Danelaw identities: ethnicity, regionalism and political allegiance', in D. M. Hadley and J. D. Richards (eds.), _Cultures in Contact: Scandinavian Settlement in England in the Ninth and Tenth Centuries_ (Turnhout, 2000), pp. 65–88.
On typologies of polity, see the essays by W. Pohl, 'Staat und Herrschaft im Frühmittelalter: Überlegungen zur Forschungsstand', H.-W. Goetz, 'Die Wahrnehmung von "Staat" und "Herrschaft" im frühen Mittelalter', M. de Jong, _'Ecclesia_ and the early medieval polity' and P. Wormald, 'Premodern "State" and "Nation": definite or indefinite?', all in S. Airlie, W. Pohl and H. Reimitz (eds.), _Staat im frühen Mittelalter_ , Forschungen zur Geschichte des Mittelalters 11 (Vienna, 2006), respectively pp. 9–38, 39–58, 113–32 and 179–89.
See P. Fouracre, 'Conflict, power and legitimation in Francia in the late seventh and early eighth centuries', in I. Alfonso, H. Kennedy and J. Escalona (eds.), _Building Legitimacy: Political Discourses and Forms of Legitimacy in Medieval Societies_ , The Medieval Mediterranean: Peoples, Economies and Cultures 400–1500 53 (Leiden, 2004), pp. 3–26.
See Y. Hen, 'The Christianisation of kingship', in Becher and Jarnut (eds.), _Der Dynastiewechsel von_ 751, pp. 163–77; R. Le Jan, 'Die Sakralität der Merowinger oder: Mehrdeutigkeiten der Geschichtsschreibung', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 73–92. The notion that Pippin's usurpation in 751 included his anointing by bishops has been called into question by the reconsideration of the sources by R. McKitterick, 'Kingship and the writing of history', in _History and Memory_ , pp. 133–55.
On these regions, see respectively Innes, _State and Society;_ H. Hummer, _Politics and Power in Early Medieval Europe: Alsace and the Frankish Realm, 600–1000_ (Cambridge, 2005); Brown, _Unjust Seizure_.
See M. Costambeys, 'The laity, the clergy, the scribes and their archives: the documentary record of eighth-and ninth-century Italy', in W. Brown, M. Costambeys, M. Innes and A. Kosto (eds.), _Documentary Culture and the Laity in the Early Middle Ages_ (forthcoming).
See the introduction to Brown, _et al_. (eds.), _Documentary Culture_.
For the following, see above all S. Airlie, _Carolingian Politics_ (Oxford, forthcoming).
_Epistola ad Basilium_ I., ed. W. Henze, _MGH Epp_. VII ( _Epp. Karolini aevi_ V) (Berlin, 1928), pp. 386–94; S. Fanning, 'Imperial diplomacy between Francia and Byzantium: the letter of Louis II to Basil I in 871', _Cithara_ 34 (1994), pp. 3–15. For western attitudes to Byzantium more generally, see C. Wickham, 'Ninth-century Byzantium through western eyes', in L. Brubaker (ed.), _Byzantium in the Ninth Century: Dead or Alive?_ (Aldershot, 1998), pp. 245–56. For the context, see below, Chapter 8.
Notker, _Gesta_ , 1.1, trans. Ganz, p. 55.
See S. Airlie, ' _Semper fideles?_ Loyauté envers les carolingiens comme constituant de l'identité aristocratique', in Le Jan (ed.), _La Royauté et les élites_ , pp. 129–43; K. Brunner, _Oppositionelle Gruppen im Karolingerreich_ (Vienna, 1979); and M. Innes, 'Kings, monks and patrons: political identities and the abbey of Lorsch', in Le Jan (ed.), _La Royauté et les élites_ , pp. 301–24, on St Nazarius.
See S. Airlie 'The aristocracy in the service of the state in the Carolingian period', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 93–111; R. Collins, 'Charlemagne's imperial coronation and the Annals of Lorsch', in Story (ed.), _Charlemagne_ , pp. 52–70; H. Reimitz, 'The art of truth. Historiography and identity in the Frankish world', in R. Corradini _et al_. (eds.), _Texts and Identities in the Early Middle Ages_ (Vienna, 2006), pp. 87–104.
See Hummer, _Politics and Power_ , pp. 130–54; J. L. Nelson, 'Charles le Chauve et les utilisations du savoir', in D. Iogna-Prat, C. Jeudy and G. Lobrichon (eds.), _L'École carolingienne d'Auxerre_ (Paris, 1991), pp. 37–54, repr. as no. VII in J. L. Nelson, _Rulers and Ruling Families in Early Medieval Europe: Alfred, Charles the Bald and Others_ (Aldershot, 1999).
Patzold, 'Die Bischöfe im karolingischen Staat. Praktisches Wissen über die politische Ordnung im Frankenreich des 9. Jahrhunderts', in S. Airlie, W. Pohl and H. Reimitz (eds.), _Staat im frühen Mittelalter_ (Vienna, 2006), pp. 133–62'; I. Garipzanov, _The Symbolic Language of Authority in the Carolingian World (c.751–877_ ) (Leiden and Boston, 2008).
See Airlie, ' _Semper fideles?_ '; S. Airlie, 'Charlemagne and the aristocracy: captains and kings' in Story (ed.), _Charlemagne_ , pp. 90–102.
AF, _s.a_. 888 and Regino, _Chronicle, s.a_. 888; for discussion see S. Airlie, '"Sad stories of the deaths of kings": narrative patterns and structures of authority in Regino of Prüms _Chronicle_ ', in E. M. Tyler and R. Balzaretti (eds.), _Narrative and History in the Early Medieval West_ (Turnhout, 2006), pp. 105–31.
This calculation has been cited, with minor differences, by J. R. Davis and M. McCormick, 'The early Middle Ages: Europe's long morning', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 1–10, at p. 2; D. Ganz, 'Book production in the Carolingian empire and the spread of Carolingian minuscule', in _NCMH_ ii, pp. 786–808, at p. 786; G. Brown, 'Introduction: the Carolingian Renaissance', in McKitterick (ed.), _Carolingian Culture_ , pp. 1–51, at p. 34; and R. McKitterick, _The Carolingians and the Written Word_ (Cambridge, 1989), pp. 163–4. See also B. Bischoff, _Latin Palaeography. Antiquity and the Middle Ages_ , trans. D. Ó Cróinín and D. Ganz (Cambridge, 1990), p. 208.
On book production and the development of scripts, see Bischoff, _Latin Palaeography_. On the factors involved in the preservation of books, see P. J. Geary, _Phantoms of Remembrance: Memory and Oblivion at the End of the First Millennium_ (Princeton, NJ, 1994).
Davis and McCormick, 'Europe's long morning', pp. 1–5.
J. Raaijmakers, 'Memory and identity: the _Annales necrologici_ of Fulda', in Corradini, _et al_. (eds.), _Texts and Identities_ , pp. 303–22.
For an influential early medieval definition of _historia_ , see Isidore of Seville, _Etymologiae_ , I.41, ed. and trans. S. A. Barney, _et al., The Etymologies of Isidore of Seville_ (Cambridge, 2006), p. 67.
M. Innes and R. McKitterick, 'The writing of history', in McKitterick (ed.), _Carolingian Culture_ , pp. 193–220; I. H. Garipzanov, 'The Carolingian abbreviation of Bede's World Chronicle and Carolingian imperial "genealogy"', _Hortus Artium Medievalium_ (2005), pp. 291–7; McKitterick, _History and Memory_ , esp. pp. 218–64; see also the studies in Y. Hen and M. Innes (eds.), _The Uses of the Past in the Early Middle Ages_ (Cambridge, 2000).
Fouracre, 'Long shadow', pp. 5–21.
Cf. P. Magdalino, 'The distance of the past in early medieval Byzantium (VII–X centuries)', in _Ideologie e pratiche del reimpiego nell'alto medioevo_ , Settimane 46 (Spoleto, 1999) 1, pp. 115–46.
McKitterick, _History and Memory_ , pp. 120–32; Reimitz, 'Art of truth'.
_LHF_ , ed. B. Krusch, _MGH SRM_ II (Hanover, 1888), pp. 215–328; commentary and Eng. trans. of cc. 43–53 (covering 638–726) in P. Fouracre and R. Gerberding, _Late Merovingian France. History and Hagiography 640–720_ (Manchester and New York, 1996), pp. 79–96, and of cc. 1–4 and 43–53 in R. Gerberding, _The Rise of the Carolingians and the_ Liber historiae francorum (Oxford, 1987); for a complete translation, see B. S. Bachrach, _Liber historiae francorum_ (Lawrence, KS, 1973).
Gerberding, _Rise of the Carolingians_ , pp. 146–72; for the suggestion of female authorship, see J. L. Nelson, 'Gender and genre in women historians', in J.– P Genet (ed.), _L'Historiographie médiévale en Éurope_ , Editions du CNRS (Paris, 1991), pp. 149–63, repr. in Nelson, _Frankish World_ , pp. 183–97, at pp. 194–5. On Fredegar see J. M. Wallace-Hadrill (ed. and trans.), _The Fourth Book of the Chronicle of Fredegar with its Continuations_ (London, 1960); R. Collins, _Fredegar_ , Authors of the Middle Ages 13 (Aldershot, 1996).
For insights into the value to the historian of Merovingian hagiography, see P. Fouracre, 'The origins of the Carolingian attempt to regulate the cult of saints', in J. Howard-Johnston and P. A. Hayward (eds.), _The Cult of Saints in Late Antiquity and the Middle Ages. Essays on the Contribution of Peter Brown_ (Oxford, 1999), pp. 143–66; P. Fouracre., 'Merovingian history and Merovingian hagiography', _P &P_ 127 (1990), pp. 3–38; Fouracre and Gerberding, _Late Merovingian France_ , pp. 37–52.
Cf. R. Collins, 'Deception and misrepresentation in early eighth-century Frankish historiography: two case studies', in J. Jarnut, U. Nonn and M. Richter (eds.), _Karl Martell in seiner Zeit_ , Beihefte der Francia 37 (Sigmaringen, 1994), pp. 227–47, esp. pp. 241–6; McKitterick, _History and Memory_ , pp. 138–9.
_LHF_ , c. 50, trans. Fouracre and Gerberding, _Late Merovingian France_ , p. 94.
Fred., _Cont._ , c. 7, p. 86, trans. (rather freely) Wallace-Hadrill, p. 86.
_AMP_ , ed. B. von Simson, _MGH SRG in usum scholarum separatim editi_ x (Hanover and Leipzig, 1905); Eng. trans. of Section 1 (to 725) with commentary in Fouracre and Gerberding, _Late Merovingian France_ , pp. 330–70; see also McKitterick, _Charlemagne_ , pp. 52–3, 60–2.
Wood, _Merovingian Kingdoms_ , pp. 257–9.
R. Collins, 'Pippin III as mayor of the palace: the evidence', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 75–91. Compare R. McKitterick, 'Political ideology in Carolingian historiography', and Y. Hen, 'The Annals of Metz and the Merovingian past', in Hen and M. Innes (eds.), _Uses of the Past_ , pp. 162–74 and 175–90 respectively.
Einhard, _VK_ , c. 1, and trans. Dutton, _Charlemagne's Courtier_ , pp. 16–17.
On this form of writing in the Carolingian age, see R. McKitterick, 'Constructing the past in the early Middle Ages: the case of the Royal Frankish Annals', _TRHS_ 6th ser. 7 (1997), pp. 101–29, and Innes and McKitterick, 'The writing of history', esp. pp. 199–202.
_Annales Sancti Amandi_ , _Annales Tiliani_ , _Annales Laubacenses_ , _Annales Petaviani_ , _Annales Laureshamenses, Annales Alamannici, Annales Guelferbytani, Annales Nazariani_ , all ed. G. H. Pertz, _MGH SS_ 1 (Hanover, 1826), pp. 6–12, 22–60.
See P. Stafford, 'The Anglo-Saxon Chronicles, identity and the making of England', _Haskins Society Journal_ 19 (2008), pp. 28–50; M. Miller, 'Final stages in the construction of the Harleian _Annales Cambriae_ ', _Journal of Celtic Studies_ 4 (2004), pp. 205–11; _Annales Cambriae_ , ed. and trans. D. N. Dumville, _Annales Cambriae_ , ad _682–954, texts A–C in parallel_ (Cambridge, 2002).
On Paul the Deacon see above all W. Pohl, 'Paulus Diaconus und die "Historia langobardorum": Text und Tradition', in A. Scharer and G. Scheibelreiter (eds.), _Historiographie im frühen Mittelalter_ , Veröffentlichungen des Instituts für Österreichische Geschichtsforschung 32 (Vienna and Munich, 1994), pp. 375–405; P. Chiesa (ed.), _Paolo Diacono. Uno scrittore fra tradizione longobarda e rinnovamento carolingio_ (Università di Udine, 2000); on Paul's continuators, including Andreas of Bergamo, see J. Ferry and M. Costambeys, _Historians of Ninth-Century Italy_ (Liverpool, forthcoming), and A. Berto, _Testi storici e poetici dell'Italia carolingia_ (Padua, 2002).
R. McKitterick, 'Paul the Deacon and the Franks', _EME_ 8 (1999), pp. 319–39; A. Plassmann, 'Mittelalterliche _origines gentium_. Paulus Diaconus als Beispiel', _QFIAB_ 87 (2007), pp. 1–35.
Innes and McKitterick, 'The writing of history', pp. 209–10; on the revolt of 833–5 and subsequent events, see below, pp. 218–22.
R. McKitterick, _Perceptions of the Past in the Early Middle Ages_ (Notre Dame, IN, 2006), pp. 68–81.
M. Garrison, 'The emergence of Carolingian Latin literature and the court of Charlemagne (780–814)', in McKitterick (ed.), _Carolingian Culture_ , pp. 111–40 at p. 114.
On poetry in inscriptions from Lombard Italy, see N. Everett, _Literacy in Lombard Italy, c.568–774_ (Cambridge, 2003), pp. 244–7.
Garrison, 'The emergence of Carolingian Latin literature', p. 128.
A partial translation of the _Paderborn Epic_ is in P. Godman, _Poetry of the Carolingian Renaissance_ (London, 1985), pp. 197–207; original text, _Karolus magnus et Leo papa_ , ed. E. Dümmler, _MGH Poet_. I (Berlin, 1881), pp. 366–79.
P. Godman, _Poets and emperors: Frankish Politics and Carolingian Poetry_ (Oxford, 1987), p. 184.
For more on capitularies, see Chapter 4.
See below, Chapter 4. Original surviving charters dating before 800 are published in _Chartae Latinae Antiquiores_ , ed. A. Bruckner, R. Marichal, _et al_. (Zurich, 1954–1998), and those dating to the ninth century are in the course of publication in _Chartae Latinae Antiquiores_ , 2nd ser., ed. G. Cavallo, G. Nicolaj, _et al_. (Olten and Lausanne, 1997–); principal among the many editions, which also include texts not surviving as originals, are T. Kölzer with M. Hartmann and A. Stieldorf (eds.), _Die Urkunden der Merowinger_ , 2 vols. (Hanover, 2001) and J. M. Pardessus, _Diplomata, chartae, epistolae, leges ad res Gallo-Francicas spectantia_ , 2 vols. (Paris, 1843–9; repr. Aalen 1969); for comment, see Fouracre and Gerberding, _Late Merovingian France_ , pp. 28–9 and 36.
D. Ganz and W. Goffart, 'Charters earlier than 800 from French collections', _Speculum_ 65 (1990), pp. 906–32.
W. Brown, 'Lay people and documents in the Frankish formula collections', and Brown, 'On the _Gesta municipalia_ and the public validation of documents in Frankish Europe', both in Brown, _et al_. (eds.), _Documentary Culture_ (forthcoming); A. Rio, _The Formularies of Angers and Marculf: Two Merovingian Legal Handbooks_ (Liverpool, 2008), pp. 255–8.
Geary, _Phantoms of Remembrance_ , pp. 81–133; A. Sennis, 'The power of time: looking at the past in medieval monasteries', in A. Müller and K. Stöber (eds.), _Self-Representation of Medieval Religious Communities: the British Isles in Context_ , Vita Regularis, Abhandlungen 40 (Münster, 2009), pp. 307–26.
For full discussion, see Chapter 5.
For introductions to the application to early medieval history of techniques drawn from the biosciences, and especially from genetics, see M. McCormick, 'Molecular Middle Ages: early medieval economic history in the 21st century', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 83–98; M. McCormick, 'Toward a molecular history of the Justinianic pandemic', in L. K. Little (ed.), _Plague and the End of Antiquity. The Pandemic of 541–750_ (Cambridge, 2007), pp. 290–312. For a cautionary note see G. Halsall, _Barbarian Migrations and the Roman West, 376–568_ (Cambridge, 2007), pp. 451–2.
## 2
### THE CREATION OF CAROLINGIAN KINGSHIP TO 800
#### REPLACING THE RULING DYNASTY
We began Chapter 1 with the elevation of the Carolingian Pippin, generally known as Pippin III, or Pippin 'the Short', to the kingship of the Franks. Almost everything about this event is uncertain. The best evidence for Pippin's accession comes from his charters – the single-sheet documents through which legal business like property transactions were habitually enacted. A charter of 20 June 751 was issued in the name of 'the illustrious man Pippin, mayor of the palace'. By the time of another court case on 1 March 752, Pippin was styled 'king of the Franks' ( _rex francorum_ ). At some point between these dates, therefore, Pippin had replaced Childeric III, last king of the Merovingian family that had ruled the Franks for over 250 years. That Pippin and his brother Carloman, jointly mayors of the palace (the most senior non-royal office in the Frankish kingdom) had themselves established Childeric as king just four years earlier gives some indication of the strong position from which Pippin could launch this bid for the throne. But the precise mechanics of the takeover are entirely unknown. Although our texts are often difficult to date precisely, the strongest likelihood is that, the charters apart, all our Frankish sources for the events of 751 were written after 768, when Pippin died and his sons succeeded to the kingship. In other words, these texts probably formed part of a deliberate and retrospective attempt to establish the ease and propriety of Pippin's succession in order to make that of his sons (who were, after all, not Merovingians but children of a usurper) seem routine.
A cluster of texts containing one or other version of a narrative about Pippin's acquisition of the kingship were written in a context in which the Carolingians were already dominant. The most famous rendition of the story is that of Einhard in his _Vita Karoli_ (Life of Charlemagne), probably written around 817, who claims that by 751 the Merovingian family 'had in fact been without any vitality for a long time and had demonstrated that there was not any worth in it except the empty name of king'. But Einhard was simply echoing the various sets of annals compiled in the last years of the eighth, and first decades of the ninth, century. The most influential, and probably the earliest, of these are the so-called _Annales regni francorum_ (Royal Frankish Annals), according to which legates (they are named as Bishop Burchard of Würzburg and Fulrad the chaplain) were sent to Rome to gain Pope Zacharias's sanction for the replacement of Childeric III with Pippin. This the pope duly gave, commenting, in the words of the annalist, that 'it was better to call him king who actually possessed royal power'. Pippin was therefore anointed king (the annalist says that this was performed by the renowned English missionary Boniface) and Childeric III was tonsured and sent to a monastery. Reports along these lines also appear, with less detail, in the Continuations to the _Chronicle_ of Fredegar, and in a text known as the _Clausula de unctione Pippini regis_ (the clause on the anointing of King Pippin). Each of these has periodically been dated as roughly contemporary with the events of 751, but the argument for a later date is stronger in both cases: the Continuations were most likely added to the _Chronicle_ of Fredegar in the period 768–86, while the _Clausula_ looks certain to have been written in the ninth century. Their composition after the kingship had been passed successfully to a second generation of Carolingians makes it highly unlikely that they could have presented an objective record of 751, even if one could be recalled. Moreover, their partisanship looks all the more striking if we compare them to texts written in Rome, which are the only ones, apart from the charters, that may be roughly contemporary. Despite the growing general interest of papal biographers in the papacy's contacts with Francia, the _Life_ of Pope Zacharias, part of the collection of papal biographies known as the _Liber pontificalis_ , breaks off its narrative in 749, while the collection of letters between the popes and the Carolingians, the _Codex Carolinus_ , includes no letter between 747 and 753. It may be that the Roman authors placed no great importance on Pippin's elevation; alternatively, these apparent oversights may point to a deliberate attempt to restrict or manipulate the memory of 751. Either way, the silence from Rome casts doubt on the later version of events contained in Frankish sources, and in particular on the notion that Pippin's seizure of the kingship was sanctioned beforehand by the pope.
As we saw in Chapter 1, papal backing for Pippin's elevation came not before the event, but after it, and involved not Pope Zacharias but his successor Stephen II. It is significant that texts mostly written in the reign of Pippin's son Charlemagne still felt the need to justify Pippin's takeover by supposing prior papal approval. This suggests very strongly that what actually took place was, and was recognised as, a usurpation whose controversial nature required special explanation. It has implications for the pope too: in so far as he came to be recognised as possessing the kind of authority that could be used to legitimise secular kings – which had not previously been the case – it was because he had become involved in the effort to justify Pippin's usurpation. In other words, it was an authority with which he was invested by Carolingian apologists, and not something already regarded as a natural part of his remit. The texts written by these apologists also retrospectively inflated the power of members of the Carolingian family in the era before they attained formal kingship, while diminishing that of the Merovingian kings, and especially the later scions of the dynasty in the seventh and early eighth centuries. They thus painted a picture of Merovingian ineptitude, incapacity and obsolescence that has proved very durable.
#### THE MEROVINGIAN WORLD AND CAROLINGIAN ORIGINS
If we mentally take ourselves back to the later seventh century itself, the Merovingian kings look far less vulnerable than they do in later texts, and Carolingian success very far from inevitable. The Carolingians originated in the eastern part of the Frankish realm and first emerge into the historical record as one of a number of aristocratic families who figure in sources describing the many succession crises of the Merovingian dynasty in the seventh century. Pippin I had been mayor of the palace – the premier aristocratic office under the king – in the eastern Frankish sub-kingdom of Austrasia in the 620s and 630s. Pippin's son Grimoald seems to have risen to even greater power there, to the extent that his son Childebert was 'adopted' by the Merovingian king of Austrasia Sigibert III, and succeeded him as king, even though Sigibert had a son of his own, Dagobert. None of this was accomplished without opposition from other factions within the Austrasian, and wider Frankish, aristocracy, however, and in 657 or 661/2 this 'Pippinid' (an alternative name for the earlier Carolingians) King Childebert was ousted from the Austrasian throne and replaced by Childeric II, a Merovingian from the western sub-kingdom of Neustria.
This narrative immediately reveals the highly fragmented nature of Merovingian Francia. There was, first, a distinction between the kings and aristocrats of the different Frankish sub-kingdoms ( _regna_ in Latin). The basic structure of the Frankish realm had been established by the 530s, with the conquest of the lands of the Alemans (c.506) and of the Burgundians (534) and the cession by the Ostrogoths of most of Provence (536) (see Map 2). Thereafter, it encompassed all of modern France, with the exception of Septimania (between the Rhône delta and the Pyrenees), held by the Visigoths until the early eighth century, and it also included most of modern Switzerland, central and southwestern Germany, the Rhineland and the Low Countries as far north as the lower Rhine. It has even been argued that at this time the Franks exercised some sort of rule over southern England, although the evidence for this is circumstantial, at best. England apart, the shape of this vast area enjoyed remarkable stability for nearly four centuries, partly because other peoples buffered it from potential invaders from the east and south (though not from the north, as we shall see). This stability is all the more remarkable because the whole realm was united under one ruler for less than half of this period, and intermittently at that. Almost from its inception, the Frankish realm had been divided among different members of the Merovingian dynasty. The kingdom's effective creator, Clovis ( _d_.511), reportedly set the precedent by providing for its division between his four sons on his death, although his reasons for doing so and the precise nature of the division are hard to see clearly through our highly political sources. Because the rules of inheritance were at no time well defined, rivalries within the Merovingian family, exacerbated by the uxoriousness of most of its male members in the sixth century, ensured that no simple pattern was ever established to govern the royal succession. The repeated divisions of the realm gradually encouraged the coalescence of three kingdoms within it: Neustria in the northwest, Austrasia in the east and Burgundy in the centre and south. Frequently these kingdoms were ruled over by different Merovingian kings, though by the mid-seventh century Neustria and Burgundy usually had the same king. Aquitaine, in the southwest, was in the seventh century generally carved up between the different kings, but by the early eighth century its elite was increasingly independent of any Merovingian control.
**Map 2.** Places mentioned in Chapter 2: 'The creation of Carolingian kingship to 800'
Some measure of the fractures in the Merovingian world at this time can be taken from the account of the travels of the Anglo-Saxon ecclesiastic Wilfrid by his biographer, Stephen of Ripon. Travelling through Austrasia in 680 on his way back to England from Rome, Wilfrid was waylaid by a bishop 'with a great army', who berated, and nearly killed, him for having sent back to Austrasia the Dagobert who had been ousted by Grimoald and Childebert 'the Adopted' back in 656. The rule of this Dagobert (II) had proved oppressive, according to the bishop, and he had been murdered. This story reveals something of the factionalism of the Frankish aristocracy at this time. According to Stephen of Ripon, a group of Frankish, presumably Austrasian, aristocrats had asked Wilfrid to arrange for the return of Dagobert II from exile in Ireland. On his outward journey to Rome in 679 Wilfrid had therefore been warmly welcomed by Dagobert and offered the bishopric of Strasbourg (an offer perhaps also prompted by his connections within the Burgundian aristocracy). But only a year later, as the wheel of Austrasian factional fortune turned against the king, these same connections were what placed Wilfrid's life in danger. Fortunately for him, Wilfrid was a formidable operator and he managed to talk his way out of trouble. Nonetheless, the episode highlights the highly partisan and volatile nature of Merovingian politics.
Dagobert II's short reign in fact exemplifies a period of particular instability that followed the murder in 675 of Childeric II, the king who had supplanted the Pippinid Childebert 'the Adopted' on the throne of Austrasia. Childeric had assumed the kingship of Neustria and Burgundy as well as Austrasia in 673, but was killed by a faction of Neustro-Burgundian aristocrats who apparently thought his government tyrannical. It may be that he had been over-dependent on the support of Austrasian aristocrats. The murder split the aristocracies of both sub-kingdoms. The dominant faction in the years following 675 was one that drew support from both Neustria–Burgundy and Austrasia, and was headed by the mayor of the Neustrian palace Ebroin. This faction was opposed by others in both sub-kingdoms. A Neustro-Burgundian faction led by Bishop Leudegar of Autun was dealt with by Ebroin in a bloody series of killings culminating in that of the bishop himself – his death would later be painted as a martyrdom. In Austrasia, there may in fact have been a number of factions. A group of aristocrats opposed to Ebroin had sought Wilfrid's help in bringing the exiled Dagobert II back to the throne; it was a group aligned with Ebroin who, in their turn, killed him three years later. Some power also resided in the hands of a third group, who supported neither the murdered king nor Ebroin, and were led by the ancestor of the Carolingians, the mayor of the Austrasian palace Pippin II. This Pippin's origins are not entirely clear, since the association between his father Ansegisel, and the earlier 'Pippinids', Pippin I and Grimoald, is attested only in later sources, but a faction under his co-leadership came to blows with that of Ebroin in 679 at a battle at Bois-du-Fays (also known as 'Lucofao'), from which Ebroin emerged the victor. Nevertheless, he was himself murdered in the following year, and, after further in-fighting, a peace was brokered between Pippin and a new dominant group in Neustria. This faction in turn splintered in 686–7, and a part of it sided with Pippin, who won a victory with its support at Tertry in 687.
These episodes clearly demonstrate the centrality in Frankish aristocratic society of warfare, albeit often on a limited scale. Nevertheless, victory at Tertry did not bring Pippin immediate control of Neustria: non-military factors like marriage and court intrigue were also important in building political support. The mayor of the Neustrian palace, Berchar, survived the battle, only to be assassinated shortly afterwards at the behest of his mother-in-law, Ansfled. She represented a Neustrian faction that was prepared to ally with the Pippinid family, an alliance sealed by the marriage of Ansfled's daughter (Berchar's widow) to Pippin's son Drogo. This allowed Pippin to take over the office of mayor of the Neustrian palace. But he could not yet exercise power there in the same way as in Austrasia. The best evidence for Pippinid power in Austrasia comes from contemporary charters preserved in the archives of monasteries. This material suggests a precocious association with or control of monasteries as a significant element in early Carolingian power. That said, we must remember that monastic documents are more likely to survive than other sources, and that even then we do not have them in great numbers. What's more, most of the individuals that appear in these charters are not otherwise known. The considerable efforts made by historians to reconstruct from this evidence the composition of contemporary factions thus remains highly speculative, especially when it is dependent on such questionable methods as assuming a family relationship between two individuals simply because they had similar names.
Despite these problems, it is possible to see that Pippin's power in Austrasia was centred on two principal areas: the valley of the Sambre (in present-day Belgium), where there were a number of Pippinid-controlled monasteries; and the area around Cologne and in the valleys of the Moselle and Meuse, where the family of Pippin's wife Plectrude had extensive lands. The main monastic house in this area was Echternach, founded in 697/8 and taken under Pippin's protection in 706. As Austrasian mayor of the palace Pippin also seems to have been able to acquire fiscal (i.e. royal) lands in the turmoil surrounding Dagobert II's death: another important resource for winning support from his peers. Pippin's power in Austrasia was effectively sovereign, as shown by grants of immunity he made to the church of St Arnulf in Metz and to the monastery of Stablo- Malmédy. These actions reflect the potency of the office of mayor of the palace: participation in, if not power over, the exercise of royal rights like the issuing of diplomas stemmed from the mayor's traditional role in controlling access to the king. The mayoralty of Neustria had been the most important non-royal position in the Frankish kingdoms throughout the seventh century, especially after 675 when the sole remaining Merovingian king seems to have been permanently based in that kingdom.
It is thus significant that, having gained the mayoralty of Neustria through his alliance with Ansfled, Pippin II relinquished it almost immediately to a certain Nordebert. Although Nordebert was a follower, and although Pippin's son Grimoald took over the office on Nordebert's death, probably in 696, this act suggests that Pippinid power in Neustria was as yet limited. True, Pippin did exercise some control in the region of Rouen, where he was able to install supporters as bishop of Rouen and as abbot of the important monastery of St Wandrille; and about the same time, his son Drogo was made duke in Champagne on the frontier between Neustria and Austrasia. But charters from the reign of Childebert III (694–711) show the king's court upholding the rights of monasteries, including the Merovingians' principal abbey of St Denis, against the encroachments of Drogo and Grimoald; and reveal that his court still attracted magnates from across the Merovingian realm, including some (like Antenor, _patricius_ of Provence, and Savaric, bishop of Orléans) who would be remembered as opponents of the Pippinids. Evidently, Pippin's power was restricted in Neustria, and resisted especially in the Seine–Oise region where King Childebert himself was based, and where St Denis lay. We should therefore take seriously our only contemporary Neustrian narrative, the _Liber historiae francorum_ , when it describes Childebert as 'the famous and just lord... of good memory', and conclude that the battle of Tertry was not the decisive turning point it was claimed to be by later Carolingian apologists like the compiler of the _Annales Mettenses priores_.
After Childebert's death, though, there are signs that the core Frankish elite was beginning to disintegrate. It was probably at this point that Antenor rebelled in Provence, and Savaric built up his independent power base in the region of Orléans and Auxerre. And already before that, outlying regions that had once fallen under Merovingian hegemony were responding to the centrifugal pull generated by the turmoil within that core aristocracy from 675 onwards. A ninth-century source asserts that the duke of the Alemans stopped obeying the Franks because he was 'no longer able to serve the Merovingian kings as [he] had been accustomed to do before'. Though written a century after the events it describes, this statement may reflect a real shrinking, starting even before Childebert's accession, in the scope of the king's personal effectiveness. For all that he could not call the shots unhindered in Neustria, in the kingdom writ large it was now Pippin who led Frankish armies against peoples traditionally tributary to the Merovingians. He responded against the Alemans with annual campaigns between 709 and 712, and took the army to Frisia, also independent of the Franks by the 670s, in 690 and 695, when he seems to have seized territory as far north as Utrecht, thus bringing under Frankish control the important trading centre of Dorestad. Ultimately, Pippin was able to make peace with the Frisian leader Radbod, whose daughter married Pippin's son Grimoald some time after 711. In the meantime, these wars show Pippin directing the Frankish military machine even while Childebert III was on the throne. Leadership in war – that most powerful attracter of political support – had passed out of the hands of the Merovingians. But there was as yet no thought of doing without them: even if he no longer played general to his aristocratic warriors, Childebert III was still an effective political force, as were his successors in the decade following his death.
If the political balance, which had been maintained to good effect while he was alive, tilted slightly away from the Merovingians on Childebert III's death (as indicated by the revolts of Antenor and Savaric), the death of Pippin in December 714 reset the political agenda by tipping the Frankish heartlands into civil war. Within a year the Pippinids had come close to extinction. Pippin's two sons with Plectrude had died – Drogo in 707 and Grimoald just a few months before his father in 714 – leaving Grimoald's young son Theudoald as nominal mayor in Neustria. After Pippin's death, the Neustrians rebelled, defeated Theudoald's forces at Compiègne and drove him from the kingdom. At the same time, Pippin's only surviving adult son, Charles, had been imprisoned by his stepmother Plectrude. The absence of any sign that this Charles, who had acquired the nickname 'Martel' ('the Hammer') by the ninth century, featured in his father's plans up to this point makes it ironic that it was to be he who rescued Pippin's legacy. The lack of continuity from father to son – with the eventual eradication of what historians have tended to regard as the 'legitimate' Pippinid line of Drogo and Grimoald – is the main reason why from this point on posterity knows the family not after Pippin but after Charles. The Pippinids were becoming the Carolingians.
But in late 715 the prospects did not look bright for either branch of the family. With the expulsion of Theudoald, the Neustrians appointed their own mayor, Ragamfred, and made an alliance with the Frisian leader Radbod. The Merovingian king Dagobert III now died, and Ragamfred replaced him with a monk called Daniel, a son of Childeric II, who was crowned with the name Chilperic (II). Charles Martel, having managed to escape from Plectrude's custody, tried to stop Radbod's attack on Austrasia but was beaten, and the Neustrians and Frisians forced Plectrude to pay them off with a good deal of Pippin's treasure. When Ragamfred and Chilperic II were returning to Neustria in April 716, however, Charles Martel met and defeated them at Amblève. Quite how this table-turning victory was achieved is not known. Our sources for all these events are decidedly sparse, consisting principally of the _Liber historiae francorum_ and deductions about dates made from the few surviving charters. The elaborations made by later, Carolingian-era, narratives, are less than reliable. However, it seems fair to suggest that many Austrasians would have supported Charles Martel simply because they were in a very tight spot – beset not only by the Neustrians and Frisians but from the north-east by the Saxons – and he was the only surviving adult male representative of the Pippinid family. His victory is nonetheless remarkable, and began a sequence that bears out the _Liber historiae francorum_ 's comment that he was 'effective in battle'. By the following spring Charles had attracted enough support to be able to attack and beat the Neustrians at Vinchy near Cambrai. This was not, however, a decisive defeat; nor should we imagine the political conflict in terms of a simple Neustria–Austrasia split. Charters of Chilperic II dating from after the battle demonstrate his continued, and very far-flung, power, and the willingness of at least some of the Austrasian aristocracy to associate with him. Charles Martel remained excluded from the Merovingian palace – still in theory the fount of sovereign authority – and turned instead to securing his position in his heartland by travelling to Cologne where he forced Plectrude to surrender the rest of his father's treasure. That he also at this time established another Merovingian, Chlothar IV, in rivalry to Chilperic II demonstrates the continued necessity of having a Merovingian stamp on the exercise of power, even in Austrasia. Ragamfred and Chilperic now allied with the duke of the Aquitanians, Eudo, and their army met that of Charles in battle at Soissons in the spring of 718. This seems to have been a more decisive encounter than Vinchy: Charles won, and pursued his enemies across Neustria until they took refuge in Orléans. He was now able to take control in Neustria. Over the next few years, we find a number of his supporters, including laymen, in possession of many of the bishoprics of that kingdom. Most prominent among them was Charles's nephew Hugo, a product of that marriage of Drogo that had first introduced Pippinid power into Neustria. Quite contrary to canon law, Hugo was simultaneously abbot of the prominent Neustrian abbeys of St Wandrille and Jumièges, as well as bishop of no fewer than five different sees, including Paris and Rouen. Chlothar IV having died in 718, by about 720 Charles had come to terms with Eudo and secured the return of Chilperic II, along with his treasure. Chilperic died in 721 and was replaced by Theuderic IV, now truly merely a cipher. Theuderic reigned, but it was now Charles who ruled over the core of the old Merovingian realm, a power amply demonstrated by his imprisonment in 723 of the two surviving sons of Drogo (one of whom died). The Pippinid branch of the family had now decisively given way to the Carolingians.
The reasons for Charles Martel's astonishing success between 715 and 723 must ultimately have lain in his ability to attract the support of his fellow aristocrats. This was presumably achieved through a combination of material inducements in the form of treasure and land, but it also reflects the centrality of participation in warfare to the identity of the ruling class. Whether Charles started off with enough moveable and landed wealth to attract the following needed to secure his first victories, or whether it was those successes, perhaps especially at Amblève and Vinchy, that enabled him to offer rewards to his followers, is an ultimately unanswerable chicken-and-egg question. But his own prowess as a warrior must have some bearing on the answer, and the rest of his career leaves the strong impression that this was a man who was most at home, and most successful, when at the head of an army. This was fortunate for the Franks, because if the intermittent turmoil of the previous fifty years had fractured the old Merovingian hegemony, the civil warfare of the previous nine, 714–23, threatened to split it wide open.
#### CHARLES MARTEL AND THE EXTENSION OF CAROLINGIAN POWER
Merovingian rule was a hegemony, so had not operated in the same way everywhere. This means that we need to distinguish different levels of relationship between the Frankish heartland and the different areas in which Charles and his sons had to fight. Some places that were essentially part of that heartland had broken off under independent rulership during the civil war of 714–19: Orléans, Auxerre and the surrounding region under Savaric, and Angers, where Ragamfred took refuge after his defeat at Soissons. These had been brought under Charles's control by 721 (though Ragamfred made a final abortive bid to assert himself in 724). There were also regions more geographically distant from the centre, but where the aristocracy was closely bound by family and social ties to the ruling class in Neustria and Austrasia. This was especially true of central-southern Burgundy and Provence. The former area is very hard to see through the confused source material, most of it written long after the event. Our most reliable source reports that Charles began in the early 730s to establish within Burgundy trustworthy and able men as a counterweight to the rebellious and unfaithful. He handed over the Lyonnais to his followers, and made written legal agreements to shore up his rule there.
That there was a major upheaval in the area in the later 730s is evident too in the sources for Provence. We have seen that the _patricius_ there, Antenor, who was connected to northern aristocratic families, had rebelled after Pippin II's death. His dominance in Provence seems to have extended well into the period of Charles Martel's rule in Francia, during which time he despoiled the lands of local monasteries. We do not know the precise state of Provence when Charles invaded in 735 following his successful campaign in Burgundy, but we do know that he found there both friends and enemies. He was opposed by a certain Maurontus, titled _dux_ ('duke', but literally 'leader'), who may have been a member of a recently ousted Burgundian aristocratic family. Contemporary chronicles assert that Maurontus enlisted the help of Muslim contingents based in Septimania. Charles had to send another army in 736, headed by his half-brother Childebrand, to deal with this threat, following it up himself. The combined Muslim and Provençal enemy seems finally to have been subdued after a further campaign in 739. That Charles also drew on local support in this effort is clear from a document drawn up in that latter year, the will of Abbo, who was by then _patricius_ of Provence. Earlier in his career in 726 we can see him as _rector_ (roughly, administrator) of the crucial Susa-Maurienne region that straddled the main Alpine pass into Italy. Abbo's will reveals that he had subsequently benefited from gifts by Charles (and, so the document says, King Theuderic IV: evidently the veneer of Merovingian rule was still necessary) of land confiscated from rebels. The patriciate must have been the crowning reward for support in an area where Charles badly needed it. Abbo's will also suggests the severity of the long series of wars in Provence: it tells of Abbo's dependants having been 'dispersed by necessity' because of the depredations of the Muslims. The evident decline of the formerly important port of Marseille, and of trade in the western Mediterranean in general, in this period must also be in part connected with political disorder in the south.
On a different, more distant, level of detachment from the Frankish heartland were the duchies of Alemannia and Bavaria, whose rulers (usually termed _duces_ in our sources) had traditionally owed allegiance to the Merovingians. The _Laws of the Alemans_ reissued by Duke Lantfrid in the 720s even stressed the ultimate authority of the (Frankish) king. But as the Frankish mayor's power increased, so also did the enmity of the Aleman duke towards him. Charles first waged war in Alemannia in 730, and in 734 expelled Lantfrid's successor as _dux_. Of more direct impact on the Carolingian family were his dealings with Bavaria, where the dukes were intent on increasing their power. In 716, for instance, Duke Theodo exploited his connections with Italy, where the Lombard kings were members of the same, extensive Agilolfing clan (as indeed were the dukes of the Alemans), to seek papal help in restructuring the Bavarian Church. The strong suggestion in the sources that at this time Theodo married a sister of Plectrude reflects equally the increasing prominence of both the Agilolfing and Pippinid families. The stakes were high, then, when on Theodo's death in 717 or 718 conflict broke out between his son Grimoald and grandson Hugbert. In 725, after Grimoald was murdered, Charles Martel invaded Bavaria in support of Hugbert. He strengthened the new Bavarian duke's dependence on him by marrying one of his relatives, Swanahild. Bavaria remained quiescent even after Hugbert's death in 735 or 736, which brought the direct line of Agilolfing dukes to an end. The new duke, Odilo, from the Aleman ducal family, was chosen with Charles's permission, according to one Carolingian annalist. When Odilo was expelled from Bavaria in 740, for reasons which can only be guessed at, he took refuge at the Frankish court, where he formed a relationship with Charles's daughter Chiltrudis, who followed him back to Bavaria when he was restored in the following year. Charles's involvement in Bavaria therefore produced two children who, as we shall see, were to prove deeply troublesome to his successors over the next two generations: Grifo (his own son with Swanahild), and Tassilo (the son of Odilo and Chiltrudis).
Aquitaine was another of the duchies traditionally subordinate to the Merovingians. Very little is known about this area before the second decade of the eighth century. It seems to have been governed in the later seventh century by dukes: we know the names of Felix in the 660s and Lupus in the 670s. How far its aristocracy was independent of those in Neustria, Austrasia and Burgundy is a matter of debate among historians. We can say little more than that northern monasteries had lands in Aquitaine. For how long and by what means Eudo had been duke before his first appearance in the sources is impossible to know. That first appearance, as we have seen, was in 718, when he allied with Chilperic II and Ragamfred against Charles Martel. By 720, however, he had concluded a treaty with Charles. By this time, the Muslims who had conquered Visigothic Spain with lightning speed from 711 were raiding north of the Pyrenees. Eudo defeated a contingent near Toulouse in 720 or 721, and the sources suggest that by this time he was both militarily successful and prestigious. He was certainly sufficiently strong for Charles Martel to put off campaigning in Aquitaine until two raids in 731. Eudo may at this time have been increasingly distracted by Muslim pressure. The claim of our main Frankish source, the Continuations of the _Chronicle_ of Fredegar, that Eudo invited the Muslims into Aquitaine after Charles's attacks, has been recognised as a fabrication by a highly partisan pro-Carolingian writer – Eudo was in fact attacked and defeated by the Muslim leader 'Abd ar-Rahman before he called on Charles for aid.
The result of this appeal was what history generally knows as the battle of Poitiers, 732 (which in fact took place nearer Tours, and probably in 733). This victory has come to define Charles's posthumous reputation: it regularly features in lists of history's most significant battles, and gained the mayor a heroic place in numerous romantic paintings. Yet this reputation is based more on the epigrammatic but misplaced judgements of Enlightenment historians like Edward Gibbon (who thought the battle was all that prevented Europe falling completely to Islam) than on contemporary sources. Although the combined forces of Charles and Eudo were victorious, and 'Abd ar-Rahman was killed, the Muslim army was a raiding party rather than the vanguard of a religiously motivated invasion from Spain. And while further attacks by the Muslims on Aquitaine were deterred, they simply turned their attention to Provence instead, as we have seen. Charles does not seem to have gained any permanent influence in Aquitaine from the victory. Though he raided there again just after Eudo's death in 735, and may have exerted some control of the succession of the latter's son Hunoald to the duchy, he is recorded as fighting 'the sons of Eudo' in the following year, and Hunoald was certainly among the sternest opponents of Charles's sons after his death.
Some peoples on the edges of the Frankish realm had only been occasionally tributary to the Merovingians, and remained distinct in both their leadership and culture: in particular, they resisted straightforward Christianisation. This was the case with the Frisians, who were an important influence on Frankish politics in the 710s, as we have already seen. Though Pippin II had gained some measure of control as far north as Utrecht in the 690s, and had allied with the Frisian ruler Radbod through Grimoald's marriage to the latter's daughter, on his death Radbod had attacked Austrasia in synchrony with the Neustrians, and had given a distinctly hostile reception to incoming Anglo-Saxon missionaries who were supported by Pippin. Only after Radbod's death in 719 was Charles able to resume some sort of influence. But a new Frisian leader, Bubo, had arisen by the 730s, and Charles campaigned against him in 734. The fact that this was at least partly a naval campaign indicates two points: first, what the Franks really coveted in that region was unquestionably the trade that ran through the important emporia of Dorestad and Domburg; secondly, the terrain of fens, dunes and coastal islands was extremely hard to penetrate. After 734 Frankish rule theoretically extended as far north as the river Lauwers (in the modern province of Groningen); in practice, as the murder of the missionary Boniface at Dokkum in 754 suggests, it remained very hard to impose.
Most distinctively and steadfastly pagan of the Franks' neighbours to their north and east were the Saxons, whose apparently expansionist activity was disturbing the whole region in the early eighth century. It may be for this reason that Charles had found time even in 718 to campaign against them, and waged war in Saxony again in 720, 724, 728 and 738. These were not, apparently, wars of conquest: at least, if that had been their object, they were entirely unsuccessful, though Fredegar's Continuator does report that in 738 Charles ordered the Saxons in the region of the river Lippe to pay tribute. These Frankish claims to tribute from the Saxons dated back at least a century to the high Merovingian era and were to continue to feature in Carloman's and Pippin III's campaigns against them. By consistently couching Saxon activity in terms of rebellion and infidelity, Frankish sources suggest that throughout this period the Franks retained some sense of hegemony over the Saxons, and from Carloman's time, at least, this was accompanied by the ambition to convert them to Christianity. Before the reign of Charlemagne, however, these efforts made little headway.
Charles Martel's campaigns allowed the coagulative quality of aristocratic warfare in the early Middle Ages to have its full effect, bringing on to his side the aristocracy of the Frankish heartland. For them the prospect of victory held the promise of plunder, office and land. Crucial to his success at the time, this patronage has also contributed to Charles's traditional reputation, both positive and negative. Earlier historians credited Charles not only with saving Christendom from Islam, but also with inventing a new type of cavalry warfare which, because of its expense, was funded with church property seized to reward his followers. In fact, none of these points really stands up. Not only is the significance of 'Poitiers' much overrated (as we saw), but there is no good contemporary evidence that Frankish military success was based on mastery of cavalry. Horses were indeed used by the Franks, but so they were also by their opponents, and in truth success in warfare depended on a variety of strategies and tactics. Meanwhile, Charles's reputation as an oppressor of churches was largely a retrospective invention of ninth-century hagiographers. While we do have charters recording temporary grants of church lands ('precarial grants') to his lay followers, this was not an unusual practice – especially given the disputes over ownership created by the turbulence of the times – and it cannot be seen as a co-ordinated programme. What Charles definitely achieved was the attraction of a significant following among the Frankish aristocracy, so much so that after the death of Theuderic IV in 737 he felt no immediate need to put another Merovingian on the throne, though he did not, on the other hand, raise himself to the kingship. Among those who now permanently attached themselves to the Carolingians we can identify the family of Rotbert, _dux_ in the Hesbaye region (in modern Belgium), who seems to have been given some power in the county of Sées in Neustria: he may in fact have been a distant relative of the Carolingians. The loyalty of such men reveals the strength of Carolingian power in the Franks' Neustrian and Austrasian heartland. We see no real rivals to them there after the end of the civil war in which Charles had come to power.
Links could arise, however, between potential opponents further afield and those closer to home. The principalities on the periphery of that heartland – Thuringia, Alemannia, Bavaria, Provence, Aquitaine – had never been part of the core Frankish realm, and were bound into Frankish politics first and foremost by loyal attachment to the Merovingian dynasty. It is perhaps a sign of their sense of superiority to the rulers of these principalities that the Merovingians never allied themselves to them through marriage. The Pippinids, by contrast, had not been so remote. The family of Pippin II's wife Plectrude seems to have been connected by marriage to the family that provided the dukes of both Alemannia and Bavaria, the Agilolfings. This relationship with Charles's rivals within the Pippinid family, added to the Agilolfings' loyalty to the Merovingians, meant that the latter were a powerful potential enemy for Charles. It may have been a need to neutralise this threat that had led to his marrying Swanahild. This marriage proved of great significance in the years following the death of Theuderic IV in 737, not least because it produced a son, Grifo. The lateness of our sources means that historians have had to work hard to discern not just Grifo's true role, but also the general course of events at this time. The succession to Charles was far from assured in his last years: Grifo was still a minor in 737, and of Charles's two legitimate sons with his first wife, only the elder, Carloman, had a son; Pippin was still unmarried. Our main narrative of events comes from a continuator of the _Chronicle_ of Fredegar, who reports that in 740 Charles provided for the division of the kingdom between Carloman and Pippin, implicitly excluding Grifo. But this source, remember, was written with hindsight after Pippin had become king. There are in fact indications that Charles intended to make, or even did make, provision for Grifo alongside his other sons in a geographical division of responsibility of the Frankish realm. Squinting at this complex picture of alliances and relationships, we can see that the defining feature of Frankish politics, gradually obscuring the role of the Merovingians and subsuming relations with the frontier principalities, was now the competition for power between members of the Carolingian family.
#### SECURING CAROLINGIAN HEGEMONY: PIPPIN III
That Charles could hope to make such a division between his sons illustrates how crucial the mayor's own prestige and personality had become to holding together the Frankish hegemony; and what happened on his death shows how fragile a construction such power was. In the years that followed, his two eldest legitimate sons, Carloman and Pippin, worked closely together to win for themselves as much of Charles's legacy as they could. Moving quickly after Charles's death in October 741, they had Theudoald, the last descendant of Pippin II and Plectrude, killed, made Grifo captive, and confined his mother Swanahild to a nunnery. The latter is held responsible by a continuator of Fredegar's _Chronicle_ for encouraging their sister Chiltrudis to marry her lover Odilo, the duke of Bavaria, a match that we are told Carloman and Pippin strongly opposed. In the following year, 742, Carloman and Pippin struck a deal to divide up the Frankish realm between them. Having first dealt with their rivals within the family, their over-riding challenge became the opposition that now made itself fully evident throughout the principalities on the periphery of the Frankish core. Although a ninth-century source identifies Odilo of Bavaria as ring-leader, it was against Duke Hunoald in Aquitaine that the brothers turned first, in 742. That same year they fought the Alemans, and in 743 raised a new Merovingian, Childeric III, from obscurity to the kingship – a measure that points up their insecurity at this time. In that year they also attacked Odilo, whose marriage to Chiltrudis had obvious potential to prejudice Carloman and Pippin's position because it united the Carolingian line with the Agilolfings. In the following year, Carloman fought the Saxons and Pippin the Alemans. In 745 they campaigned together in Aquitaine. It was the turn of the Alemans again in 746 in a battle at Cannstatt (modern Stuttgart) where Carloman's army inflicted slaughter on the Aleman aristocracy. Along with this came wholesale expropriation: in the next generation, a high proportion of the known property in Alemannia was in the hands of Franks (see Map 3).
**Map 3.** The expansion of the Carolingian empire. Although the arrows suggest a primarily military expansion, many of the regions incorporated into the empire were taken without fighting.
In the midst of this campaigning, both brothers held councils of bishops to promulgate rules on religious matters: Carloman in 742, 743 and (probably) 747, and Pippin in 744. The staging by each brother of councils in his own part of the realm shows their overlapping preoccupations: to consolidate a sense of identity in their new sub-kingdoms, and to reinforce the ecclesiastical structure, with better-organised personnel and tighter rules, to cement their kingdoms' common Frankish, Christian culture. That the need was greater in Carloman's sub-kingdom, which, being more easterly, bordered yet unchristianised lands, is explanation enough for his greater involvement in such activity at this time: we need not take it as a sign that Pippin was any less devout than his brother. Letters both from the English missionary Boniface and from Pope Zacharias refer to the two brothers acting together to restructure the Church, and Pippin also requested that the pope send to Francia copies of canons (ecclesiastical laws) from earlier councils. It was from texts like these that Pippin later drew phrases that appear in his charters, about the moral responsibilities of the Christian ruler. These were not mere formulae. The moral exhortations of the councils found practical reflection in the efforts of the Englishman Boniface, alongside many others, to bring the full apparatus of the Christian Church, with church buildings, priests, monasteries, monks and the regular round of liturgical practices, to areas east of the Rhine where it had previously been known only very imperfectly, if at all. We shall examine this development in greater detail in Chapter 3; here we need only say that little could have been achieved without the direct and material support of the Frankish upper class, and in particular of the Carolingians themselves. The effort to Christianise in the east was a telling practical result of very genuine Christian belief among powerful lay people. Another instance, of more immediate and dramatic significance for the Carolingians, occurred in the year after Cannstatt, 747, when Carloman abdicated his position and went off to Rome. It is not known if this was simply a pilgrimage, or whether from the start he intended it as the first step on a path towards the monastic habit in which he ended up, but he was certainly not the only such figure to become a monk in this period: others include the brothers' erstwhile opponent Hunoald, duke of the Aquitanians, as well as several Anglo-Saxon kings.
It looks certain that on his abdication Carloman intended and expected his part of the Frankish realm to be given over to his son Drogo. At first, in fact, this is precisely what happened: there is some evidence that Drogo was able to enjoy his father's inheritance for a short time. Pippin had delayed marrying until three years after his father's death, and had then taken as his wife Bertrada, member of a family who were prominent landowners in Carloman's part of the kingdom. By 747 Bertrada had still borne no children, so Drogo remained the only direct heir of both Carloman and Pippin. Initially, therefore, Carloman's abdication meant for Pippin not greater power, but more uncertainty. Very unusually, the Frankish army does not seem to have assembled in 747, and in that year too Pippin's half-brother Grifo was released, or escaped, from his captivity, and travelled to Bavaria. As the product of a union between the Carolingians, in the person of Charles Martel, and the Agilolfings, in the person of Swanahild, he presented a powerful alternative focus of loyalty for the aristocracy, with potentially wider reach than Pippin. Duke Odilo having recently died, Grifo was able to make himself duke in Bavaria in 748, but Pippin managed to recapture him, restored Odilo's son Tassilo as duke and gave Grifo twelve counties in Neustria as recompense. This was evidently not enough to satisfy his ambition, and he fled again, this time to Aquitaine.
In the meantime, Pippin's situation changed fundamentally when, in April 748, Bertrada finally gave birth to his son, Charles (the future Charlemagne). It may have been this that prompted Pippin now single-mindedly to aim at hegemony for himself and his bloodline. Exterminating, rather than accommodating, Grifo was part of this. His other rival, Carloman's son Drogo, had now probably reached maturity. Concern for his son may lie behind Carloman's departure from his monastery to intervene again in Frankish politics, though one source says that rather than supporting his son Drogo, he delivered 'words of concord and peace' to Pippin and their half-brother Grifo. If there is uncertainty whether Pippin considered as his chief opponent his half-brother or his nephew, it is at least clear that by the late 740s both were regarded as rivals rather than potential co-rulers.
Carloman's intervention shifts the focus to Italy, the affairs of which now impacted directly and momentously on Francia. The fact that it was the natural destination for Carloman following his abdication illustrates the attractive influence that Italy, and especially its cultural and religious connotations, exerted not just on the Franks, but on all western Christian peoples. Rome may have held particular fascination: by the end of the eighth century, it accommodated hostels specifically designated for Lombard, Frankish, Frisian and 'Saxon' (that is, Anglo-Saxon) pilgrims. But Frankish relations had for generations also been cordial with the Lombards, who ruled most of the north and centre of Italy. This is attested most clearly by the adoption in 737 of Charles Martel's son Pippin by the Lombard king Liutprand, an act which forged a strong personal bond between the two families. The fact that Charles chose to secure it through his second son Pippin suggests that marriage with a daughter of Liutprand may have been mooted. Nothing came of this, but it might also be argued that the adoption of a Carolingian as a king's son was the first step towards the family's adoption of the kingship itself. This kind of venture into Italian politics was never straightforward, however, as Pope Gregory III's response on this occasion indicates: he twice wrote to Charles seeking help against precisely the Lombard king to whom the Frank had so recently become related. Conflict between the Lombards and the Byzantines, still then in control of large parts of central Italy, including Rome, had been a feature of Italian politics for generations. In the early eighth century, with the emperor making heavy fiscal demands on his Italian subjects, but with Byzantine strength in Italy simultaneously looking increasingly uncertain, indigenous Romans, and specifically the pope (their bishop), were prompted to explore other sources of help against Lombard pressure. The Franks were the obvious choice, and Gregory III's reported gifts to Charles, the keys to St Peter's tomb and a link from his chains, were certainly valuable. Charles, though, resisted the pope's blandishments. Given the choice, he preferred the ability to treat with the Lombards as equals to an unpredictable entanglement with a new ally – the kudos arising from Liutprand's adoptive paternity over Pippin should not be underestimated.
Gregory III's failure did not discourage his successor, Pope Zacharias, from continuing to pursue closer relations with the Franks. The exchange of a string of letters with Boniface shows that Zacharias appreciated the opportunity that the Englishman's activities in northern Europe presented for extending papal authority among Christians there. But what really brought the papacy, and Italian affairs, into the secular politics of the Franks was Carloman's arrival in Italy following his abdication. Zacharias proved very adept at negotiating his way between interests and opinions in both the Frankish and the Lombard kingdoms. He handled Carloman carefully, giving him his monastic tonsure and apparently also bestowing on him the monastery on Monte Soracte, where he seems to have spent some time between 747 and 750 before entering the recently restored abbey of Monte Cassino, but he did not or could not prevent Carloman from continuing his interest in Frankish politics with the intervention that we have just noted. Whether Carloman's journey back to Francia indicates that Zacharias had had him tonsured against his will is a much-debated, but ultimately unanswerable, question. The suggestion may underestimate the extent to which continued engagement with the secular world was possible in a cosmopolitan institution like Monte Cassino, for all its ascetic ideals. Carloman could return there, probably in 751, only to embark on a second mission north a few years later, as we shall see. Zacharias's dealings with the Lombards were equally astute. He was able to agree peaceful settlements with successive kings – Liutprand (712–44) and Ratchis (744–9) – even if on each occasion part of the price was a loss of Byzantine territory. (See Figure 2 for the altar that Ratchis had made when he was duke of Friuli.) Among the Lombards themselves there were conflicting tendencies, aspiring on the one side towards peaceful co-existence with Byzantine territories in Italy, and on the other towards their conquest. While there were some Lombard aristocrats who were unwilling to risk themselves in war, there must certainly have been others who coveted the wealth, in both land and moveables, of the Byzantine lands. It may have been this tension that lay behind the ousting in 749 of Ratchis, who was himself then sent to Monte Cassino, and his replacement by his brother Aistulf.
**Figure 2.** The altar of Duke Ratchis, commissioned 734–7 before he became king of the Lombards (744–9), is now in the Museo Cristiano del Duomo in Cividale del Friuli. While incompetence is one possible explanation for its obvious disproportions, it may be that the figures are abstractions, emphasising what were considered the most spiritual parts of the body – the head and hands – and so focussing attention on Christ's divinity.
The campaigns that Aistulf launched against the Byzantine territories in central Italy were certainly not unprecedented – Zacharias's desperate diplomacy with his predecessors Liutprand and Ratchis would hardly have been necessary if they had not been exerting similar pressure – but what made them significant was simply their success. By the summer of 751 he had conquered the whole of the Byzantine exarchate of Ravenna and the duchy of the Pentapolis, attacked Istria, and made a separate peace with Venice. In central Italy only Rome and its surrounding duchy remained outside his control. These powerful actions provoked strong reactions in our key sources, though close analysis shows that they do not wholly justify the poor reputation from which the Lombard king has suffered in subsequent history. The ninth-century Ravennate chronicler Agnellus, for instance, certainly portrayed Aistulf as an oppressor, but overall he leaves the impression that he preferred Lombard to papal domination. Our principal contemporary sources for these years, papal letters and the _Liber pontificalis_ biography of Pope Stephen, heap abuse onto Aistulf's head: in one letter this Catholic king is even called 'a devourer of the blood of Christians'. Amid the hyperbole, though, Pope Stephen's biographer cannot avoid admitting that Aistulf actually renewed the peace treaty that Liutprand had made with the Romans, and indeed extended it to forty years. And while he says that Aistulf tried to exact 'tribute' from the Romans, his emphasis on the pope's frequent diplomatic overtures, gifts and promises of peace to Aistulf, on the consent of the Romans for the pope's actions, and on divine favour, reads very much like a retrospective justification for Stephen's approach to Pippin, perhaps in reaction to direct criticism of the pope's actions, either within Rome or further afield. Yet on the ideological, if not the political, level, there was no question that the king and the pope were contesting control of the same ground. Aistulf's statement, in the prologue to his first set of laws, that the Roman people had been 'given to us by the Lord', precisely conflicts with the papal claim to represent the whole of Byzantine Italy, advanced first categorically in Stephen II's pontificate: in 752 Stephen approached Aistulf 'for the entire exarchate of Ravenna and for the people of the whole of this province of Italy'. The pope, that is, was asserting that he was representative of these 'Roman' people: not just the citizens of the city, but all those who still, in some way, regarded themselves as subjects of the 'Roman' (that is, Byzantine) emperor in Constantinople. Although this was a role apparently assigned to him by that emperor, the pope knew that, with the Byzantines looking increasingly unable to give practical help, he needed to turn elsewhere for a strong military ally. It was in this context that Stephen decided to leave Rome in October 753 and to head north, to the kingdom of the Franks.
While Aistulf was winning territory in Italy, Pippin had become king of the Franks. At the start of this chapter we looked at the difficulties in establishing precisely how this came about, difficulties which show that it was controversial – indeed, we have references to disloyalty among the aristocracy which suggest that the coup of 751 had not sealed the Carolingian victory. Pippin therefore seized the opportunity presented by Pope Stephen's arrival in the winter of 753 to gain some endorsement for his takeover. The _Royal Frankish Annals_ report that 'Pope Stephen confirmed Pippin as king by holy anointing and with him he anointed as kings his two sons, the Lords Charles and Carloman.' The _quid pro quo_ was not straightforward, however, because in seeking his support Pope Stephen was asking Pippin – and the Frankish aristocracy – to abandon a generationslong alliance with the Lombards, one which, as we have seen, in Pippin's case extended to his own spiritual paternity. It was a radical departure for the papacy too. Stephen's biographer works hard to present precedents for the alliance, but in reality no contemporary report before 753 gives the Franks any role in papal political diplomacy. Named Frankish envoys to Rome appear in our sources only after Pope Stephen's initial soundings with Pippin. The anointing of 753–4 carried enormous ideological implications for the future, since, as we have seen, apologists for the dynasty later celebrated papal endorsement as a crucial element in legitimising Carolingian kingship, and backdated it to coincide with the coup itself. But it also had immediate consequences for the last of Pippin's family rivals, who now found themselves marginalised even further. Not coincidentally, it was in 753 that Grifo was finally caught and killed by two of Pippin's counts while en route from Aquitaine to Italy – that this was a fully fledged battle indicates that he had retained substantial support to the last. What's more, around the same time Carloman's sons (Drogo and an unnamed brother) were sent to a monastery. It was probably on their behalf that their father left his monastic retreat for a second time and travelled to Francia, but, whatever he thought he could achieve, he was swiftly detained and died soon after. One may suspect, indeed, that Pippin's decision to risk all by seizing the throne, and by breaking the Lombard alliance in search of papal endorsement two years later, was prompted less by a desire to underline Carolingian superiority over the Merovingians than by a pressing need to make a decisive move in the fight for dominance within his own family: the birth of his first son Charles in 748 had given him an urgent incentive to push Drogo, Grifo and his other male relatives out of the picture for good. Thirteen years after the death of Charles Martel, the junior branch of the Carolingians had established itself as unchallenged rulers of the Franks.
The papal anointing went hand in hand with Pippin's effort to convince the Frankish aristocracy to launch war against the Lombards. But persuading the warrior class to attack their erstwhile allies may have taken some time, even after the anointing: it was probably not until 755 that the Frankish army set out for the Alpine passes into Italy. Defeating the Lombards there, Pippin then besieged Aistulf in his capital of Pavia, and forced him into an accommodation which essentially acknowledged his subordination to the Franks. Yet this seems simply to have encouraged the Lombard king to go to the brink, and he besieged Rome early in 756. This in turn provoked a second Frankish campaign, a second siege of Pavia, and a second peace treaty. Once again the Franks had shown their military superiority over a neighbour. But almost since the day itself doubts have circulated about the settlement that Pippin was thereby able to impose. It looks certain that he deputed Fulrad of St Denis to oversee Aistulf's relinquishing of a roster of cities in central Italy. These, it seems, were to be transferred to St Peter, or rather to his representative, the pope. But whether by this Pippin intended the establishment of a papally governed 'state' seems more doubtful. This was an age in which such matters were thought of in terms not of territorial sovereignty, but of rights, about the definition of which our evidence is very vague. Whatever Pippin tried to stipulate in 756, however, neither Aistulf nor his successor Desiderius (king from 757) did much to fulfil their part of the settlement, and control of central Italy was once more contested in the reign of Charlemagne, as we shall see.
After a hiatus under the later Merovingians, the ruler of the Franks came back into the reckoning of other powerful rulers following Pippin's intervention in Italy. His contacts with the Byzantine emperor Constantine V underline how uncertain the settlement of Italy still was. It was shortly after his second successful Italian campaign – in 756 or 757 – that Pippin exchanged embassies with Constantine V, and, according to the Continuator of Fredegar's _Chronicle_ , 'through their representatives each swore friendship and fidelity to the other'. Other sources tell us that Pippin and Pope Paul I sent a joint embassy to Constantinople in 763, which returned three years later with a reciprocal legation from the emperor. Among the subjects of discussion were certainly the theological innovations introduced by Constantine V in Byzantium, reinterpreting the Trinity and denying the validity of images of Christ and the saints in worship, and Pippin attended a debate between the Byzantine envoys and Greek-speaking Romans at Gentilly just outside Paris in 767. But other points of contact were more amicable: it was proposed that Pippin's daughter Gisela might marry Constantine V's son, the future emperor Leo IV (reigned 775–80). And the fact that Frankish envoys in turn accompanied the Byzantine legation back to Constantinople indicates that both sides saw the value of continued negotiation. All this shows how Pippin's military success was bringing him into contact with more distant rulers. He also despatched envoys to Baghdad in 763 or 764 and received a return embassy from the caliph in 767–8. Though our sources do not reveal it, the amicable nature of the contacts – gifts were exchanged and the Muslim envoys were escorted back as far as Marseille – and the strategic situation at the time suggest that one major subject of discussion would have been the situation in Spain and Aquitaine. In these regions too things were changing: the Carolingians were not the only new (usurping) dynasty on the scene in the mid-eighth century. In the Muslim world the Abbasids had seized the caliphate from the Umayyad dynasty, one of whose last representatives had, however, managed to take power in Muslimcontrolled Spain. Thus the Abbasid caliph al-Mansur faced in Spain a similar danger to that confronting Pippin in neighbouring Aquitaine; and thus, perhaps, the tentative contacts between the two.
Aquitaine was in fact the overriding military concern of Pippin's reign as king. Although he also campaigned against the defiant Saxons in 753 and 758, a sustained Frankish effort there had to wait. As we have seen, it was the Aquitanian duke Hunoald who was the first regional leader against whom Pippin and Carloman had had to fight after their father's death, and while their campaigns in Aquitaine in 742 and 745 succeeded in pacifying the region temporarily, Pippin was called back there in 759 and thereafter had to make war against Hunoald's son Waifar in every year but one until 768. The annalistic record of these campaigns reveals that they were destructive affairs, a matter of small-scale raiding and counter-raiding, of the systematic ravaging of territory and, occasionally, of siege warfare. By 768 Duke Waifar was a hunted man, and while on the run from his Frankish pursuers he was assassinated by his own men. Despite his death, Aquitanian resistance continued under Hunoald II, probably his son. But Pippin's own son, the twenty-year-old Charles, was now well placed to batter down the doors his father had cracked open.
#### CHARLEMAGNE AS KING
When Pippin died in September 768, therefore, the Aquitanians' continuing rebellion was the first problem confronting his sons Carloman and Charles (hereafter to be known by the name he has borne through subsequent history: Charlemagne – Charles 'the Great'). The brothers marched into Aquitaine together in 769, but for some reason, perhaps a quarrel over the division of the duchy between them, Carloman soon returned home, and it was left to Charles to chase down Hunoald. His capture marked the end of Aquitanian resistance. The wars there from 759 to 769 demonstrate how solid was the Carolingians' control now of the resources and manpower of their heartlands. In the end the Aquitanians were ground down by relentless, year-after-year campaigning. The ability to do this allowed the Carolingians to inflict a new level of defeat on their enemies. They used the same technique in Saxony, as we shall see, and it must be significant that, once subdued, neither the Saxons nor the Aquitanians seriously challenged Carolingian rule thereafter.
The falling out of Charlemagne and Carloman in 769 was the first sign of difficulties between the two brothers that played themselves out over the next two years, chiefly in the context of continued uncertainty in Italy. The brothers were made fully aware of papal anxieties in a letter from Pope Stephen III (768–72) in 770, urging them to help the pope to secure what he saw as his rights. At about that time, their mother Bertrada travelled to Italy with a rather different object in mind: the marriage of her elder son Charlemagne to the daughter of the Lombard king Desiderius, who was probably named Gerperga. There was some strategic sense in this: Desiderius was in a strong position, having married other daughters to the rulers of Bavaria and Benevento – a significant proportion of the 'independent' Christian rulers in continental western Europe. Nonetheless, it seems clear that Bertrada's initiative was an act beneficial to one son (Charlemagne) and prejudicial to the other (Carloman). Charlemagne's marriage meant that Carloman was encircled, by his brother, by King Desiderius, and by Tassilo, duke of the Bavarians and husband of another of the Lombard king's daughters.
The political logic changed utterly, however, with Carloman's premature death in December 771. Charlemagne's priority now was to weld his brother's sub-kingdom, and especially its aristocracy, to his own. The need to create unity within the Frankish realm necessitated a change of stance toward those beyond it. Thus Charlemagne now sought in marriage Hildegard, a descendant of the ducal house of Alemannia, in order to secure that part of Carloman's former kingdom. This, of course, meant the repudiation of the Lombard princess and, inevitably, the enmity of her father. At the same time, in Rome, Pope Stephen III, who had been in favour of the Franco-Lombard alliance (it at least helped him get the disputed towns that he wanted), died and was replaced by Hadrian I, who was far more inimical towards the Lombards. With Charlemagne intent on taking over his late brother's kingdom, and members of the latter's following deserting to his side – among them Fulrad, the abbot of St Denis, and his eventual successor Maginarius – Carloman's wife and children fled for refuge to Desiderius. The Lombard king now reversed his policy and once more began to threaten Rome. This prompted an appeal for help from Pope Hadrian to Charlemagne. The latter initially offered Desiderius money if he would restore captured towns, but he refused. So, very late in the campaigning season in 773, Charlemagne launched a two-pronged attack on Italy, over the Mont Cenis and Great St Bernard Passes. Desiderius, perhaps thinking that the Franks would return home at the end of the season as Pippin had done in 755 and 756, took refuge behind the walls of his capital, Pavia. However, in another sign of the step change in Frankish military capability under the Carolingians, Charlemagne kept his army before the walls of Pavia throughout the winter of 773–4. The siege was sufficiently secure for Charles to be able to travel to Rome to celebrate Easter in 774. By June, Desiderius was ready to surrender. He was taken into exile in Francia, his son Adelchis having fled to Constantinople. Carloman's children, meanwhile, vanished from history: once more, there is a suspicion that the outward expansion of Carolingian power was driven partly by a need to eliminate the threat represented by members of the dynasty itself.
Charlemagne's assumption of the title 'King of the Lombards' ( _rex langobardorum_ ) in the summer of 774 was an act without parallel. No west European king had taken another's kingdom and title by force for over 200 years. The relative ease with which Charlemagne accomplished the transfer indicates two things. First, it suggests that the bulk of the Lombard aristocracy submitted to Charlemagne's rule in the first half of 774: certainly, he was initially willing to let them keep their offices. And secondly, it points to a radically more ambitious attitude on the part of the Frankish king. The aim now was not merely to pacify or to dominate through the exaction of tribute, but to rule. This shows the degree to which Charlemagne now felt secure in his government of the Frankish kingdom proper. In northern Italy, Lombard resistance to the Carolingian takeover was a piecemeal and half-hearted affair. Charlemagne had to return to Italy in 776 to suppress a rebellion launched the previous year by the dukes of Friuli and Treviso. Although the rebels may have harboured the aspiration that other Lombard dukes would join them, there is no evidence that any did so, and the revolt ended with the killing of Duke Hrodgaud of Friuli. Frankish counts now replaced Lombard dukes in those cities that had resisted. Charlemagne returned to Italy twice in the next ten years. A trip to Rome in 780–1 saw the anointing and crowning by the pope of his two younger sons, Pippin and Louis. Charles clearly already had an eye on the future: Pippin was to be king of the Lombards, Louis of the Aquitanians (both nominal appointments at first, since the boys were children); we must assume that he intended his elder son Charles to succeed to the Frankish kingdom proper. In 786 Charlemagne entered Italy with the express purpose of bringing to heel the Lombard duchy of Benevento, which covered most of southern Italy and had always been a separate entity from the Lombard kingdom in the north. After the deposition of Desiderius, Arichis II, the duke of Benevento, had begun to style himself 'prince'. Charlemagne was rapidly successful, receiving hostages, including Arichis's younger son Grimoald, and oaths from both the prince and his leading men, though he did not attempt to rule Benevento directly.
The Frankish conquest of northern Italy and, in particular, Pope Hadrian's decisive commitment to a Frankish alliance, radically affected relations with the dominant power in the east, the Byzantine empire. The city of Rome itself was the key to this change, for Byzantium was simply the continuation of the eastern portion of the old Roman empire, and as long as it held Rome – however nominally – that continuity was real. Once the city had fallen under Frankish 'protection' (which in practical terms meant military and political domination), Byzantium was a Roman empire without Rome. Yet Byzantine weakness, which had caused the popes to look to the Franks as alternative protectors in the first place, meant that Constantinople harboured few realistic hopes of military action to recover Italian lands. Their attitude to the Franks was therefore ambivalent. They could entertain, as they did in the 780s, secret negotiations with Prince Arichis of Benevento, while at the same time pursuing a plan hatched in 781 for the marriage of the young emperor Constantine VI to Charlemagne's daughter, Rotrud. That this potentially momentous match did not come about seems to have been due to reluctance on the part of Charlemagne, who refused to send Rotrud to Constantinople. In 788 he allowed his Beneventan hostage Grimoald to return to the principality, to become a ruler with what he hoped would be a pro-Frankish stance. As a result, the Byzantines sent an army to southern Italy. It is significant, however, that this was opposed, and heavily defeated, by Grimoald of Benevento and Duke Hildeprand of Spoleto, both still nominally independent Lombard rulers. This did not, however, indicate complete Carolingian domination of Benevento, which had to wait until after 800. In the meantime, Byzantine policy towards the Frankish kingdom remained changeable. The Byzantine dowager empress and regent Irene may have pleased the pope by her attempts to undo the previous emperors' religious policy of iconoclasm, particularly at the Synod of Nicaea in 787, but among north European theologians (using a faulty translation of that synod) it prompted only further condemnation of Byzantine practices as now constituting the veneration of images. It did not help relations that Constantine VI then lost a violent power struggle with his mother Irene, who blinded him (causing wounds from which he subsequently died). Following this, it could be considered by the Franks that the imperial throne in Constantinople, occupied by a woman, was effectively vacant.
The successful conclusion of the Beneventan campaign in 787 allowed Charlemagne to deal with the last of the quasi-independent duchies bordering Francia itself – Bavaria. Much mystery surrounds the background to the fate of Bavaria. Its duke, Tassilo, had been in exile at the Frankish court until his reinstallation in 748, as we have seen. According to the _Royal Frankish Annals_ , Tassilo not only owed the recovery of his duchy to Pippin, but went on to swear formal loyalty to the Frankish kings in 757 and 781. Then, in the later 780s, Charlemagne took a series of increasingly stringent measures with the clear object of eradicating the Bavarian duchy's independence: a disagreement between Charlemagne and Pope Hadrian on one side, and Bavarian envoys on the other, led in 787 to a threepronged Frankish invasion of Bavaria, which the duke fended off only by swearing further oaths of loyalty and handing over hostages. The following year Tassilo attended an assembly at Charlemagne's palace of Ingelheim, was accused of disloyalty (some of the charges relating to events almost three decades in the past) and apparently helplessly submitted. He was tonsured and sent to a monastery, in what the Carolingian sources claim, with jaw-dropping cynicism, was an act of mercy (the original sentence having been death).
Not surprisingly, we have to take this account with a strong pinch of salt. The first section of the _Royal Frankish Annals_ is thought to have been compiled around this very time (late 780s), and it is therefore hardly surprising to find that it presents a carefully manufactured retrospective argument against Tassilo. The details of this account have been exposed as extremely tendentious, and in places demonstrably inaccurate – indeed, the text itself has to be seen as part of the process mobilised against Tassilo, rather than a detached description of it. All this gives the strong impression that Charlemagne had already made up his mind that he wanted to be rid of the duke, and that the annexation of Bavaria was unprovoked. That he succeeded may seem inevitable with hindsight, but in truth it was anything but: Tassilo was a powerful and independent ruler and the scion of a long-established ducal dynasty. (See Figure 3 for the Tassilo Chalice, the inscription of which shows the Bavarian duke's desire to assert his own leadership credentials, in the face of the growing power of his Carolingian neighbours.) He was also considerably older and more experienced than the Frankish king – his downfall, engineered without significant bloodshed, testifies to Charlemagne's astonishing political sagacity as well as his overwhelming military resources. When considering Charlemagne's motives, we should recall that Tassilo was a grandson of Charles Martel and therefore a member of the Carolingian family; and that the duke's son was also taken into Frankish custody and tonsured. Once more, we have to ask whether territorial expansion was conceived with one eye on the family tree. Bavaria was carved up into counties on the Frankish model and entrusted to the overall supervision of Charlemagne's brother-in-law, Count Gerold.
**Figure 3.** The Tassilo Chalice was given by Tassilo III, duke of the Bavarians (748–88) and his wife, the Lombard princess Liutperga (here 'Liutpirc'), to the monastery of Kremsmünster, probably at the time when Tassilo founded it in 777. Cast in bronze, and depicting Christ and saints, its inscription reads 'TASSILO DVX FORTIS + LIVTPIRC VIRGA REGALIS' (brave Duke Tassilo + Liutperga royal scion).
The principal charge against Tassilo in 788 was that he had been plotting with the Avars. The latter were an originally nomadic, Asiatic people who had in the sixth century taken control of a huge swathe of land along the middle Danube and its tributaries. From there they posed a perennial threat to north-eastern Italy, and thus became a concern for Charlemagne after his invasion across the Alps in 774. One of the first recorded clashes between Franks and Avars took place in northern Italy in 788; the two sides also came to blows in Bavaria at the same time. There then seem to have been some diplomatic contacts, apparently concerning the frontier between the territories of Charlemagne and the Avar ruler, the _khagan_. Then, at an assembly in Regensburg in 791, Charlemagne organised a two-pronged attack on the Avar lands, with an army including Saxon and Frisian contingents. Accounts of this campaign reveal a strong religious element: the army spent three days in penitential fasting and prayer before entering the territory of the pagan Avars. The Avars' response to this attack was far more feeble than their fearsome reputation had promised, and Charlemagne's armies returned home having ravaged the western part of their lands with impunity. For the next few years he was occupied with fighting elsewhere, but the Avars proved quite capable of damaging their cause for themselves, as the evidence points to the outbreak of a civil war among them. It fell to Eric, duke of the north-east Italian frontier region of Friuli, to take advantage of this. In 796 he launched an expedition that attacked and successfully plundered the Avars' _Hringum_ or 'Ring', their main royal residence and collection point for the tribute and treasure that they had accumulated over many generations. Charlemagne's son Pippin, king of Italy, launched a second expedition in the same year to complete the destruction. The weakness of the Avars in the face of these attacks suggests that, however militarily powerful the Franks may have been, the Avar confederation was collapsing in any case, and the Franks were simply fortunate enough to be in the right position to benefit from its fall. The extent of that benefit is clear from the evidence that Charlemagne sought, successfully, to enhance Carolingian prestige by lavishly distributing gifts from the Avar treasure hoards to his neighbours, such as King Offa of Mercia, and to the Church. Some of the Avar leaders seem to have accepted baptism before their defeat in 796 (indeed, this may have contributed to fractures in the confederacy and hence to the Carolingian victory), but in its wake were sent missionaries directed by Arno, bishop of Salzburg. The next phase of the history of that region was to be that of Christianisation, but it is a story that belongs to the ninth century, and does not really feature the Avars, who disappear from the record within a generation of the Frankish victory: their last appearance comes in 822, when they are recorded as having sent gifts and envoys to Louis the Pious.
Warfare and religion were far from inseparable: after all, the Franks sometimes fought other Christians, and habitually conducted peaceful relations with non-Christian neighbours. Yet they merged nowhere more clearly, more protractedly and more bloodily than in the Frankish campaigns against the Saxons. Their sheer duration, lasting thirty years, makes them the most prolonged and, probably, most costly of Charlemagne's military activities. It is unlikely, however, that he anticipated their importance from the start. After all, the Franks had fought intermittent campaigns against the Saxons for the previous 250 years – Charlemagne's father and grandfather had done so, as we have seen – without ever getting bogged down. Several reasons conjoined in Charlemagne's reign to make the Saxons a more difficult problem. First, they seem unquestionably to have been expanding their territory south from the Lippe valley where Carloman and Pippin had tried to limit it in their campaigns of the 740s. Secondly, the tendency of Frankish sources to describe Saxon aggression in terms of 'rebellion' and 'infidelity' was not mere rhetoric. For while successful campaigns normally concluded with the soldiers of the losing side swearing oaths _en masse_ to respect agreed peace terms, in the case of the pagan Saxons, their difference in religion with Christian Franks meant that their oaths were insecure. Already, therefore, Carloman in 744 and Pippin in 747 had made efforts to Christianise the Saxons, baptising those whom they captured. Christianisation was plainly one motivation behind Charlemagne's initial campaign too. In 772, having captured the fortress of Eresburg, his army proceeded to destroy the Irminsul, an idol or shrine that was clearly a place of religious significance to Saxon paganism. Retaliation by the Saxons in 773 was followed, in the winter of 774 and still more in 775, by concerted Frankish efforts to subdue them. These were successful in extracting formal submissions and hostages from some of the major sub-groups into which the Saxons were divided. Frankish suspicions about the value of such deals were confirmed in the following year, however. While Charlemagne was suppressing Hrodgaud's revolt in Italy, the Saxons attacked Frankish-held fortresses. Marching north late in 776, Charlemagne now for the first time forced one group to be baptised. Significantly, he held the Franks' annual assembly the next year at the new fortress that he had established in Saxony, Paderborn. But not all were subdued: a Saxon leader called Widukind remained in revolt and fled to the north at this time. Any thoughts of Saxon submission once again proved temporary, for in the next year the Saxons raided the Frankish Rhineland, provoking, in 779 and 780, renewed Frankish campaigns and further mass baptisms. The indecisiveness of all this warfare reflects not just the insecurity of oaths and treaties due to religious differences, but also the lack of a shared political culture between the antagonists: the Saxons, most importantly, had no king, and decisions were apparently made at gatherings of lesser leaders. Would-be invaders therefore faced a many-headed hydra, and could not hope for a decisive victory by capturing an identifiable political centre.
In 782 Charlemagne issued what is known as the First Saxon Capitulary, outlining thirty-four new laws to be applied to the Saxons, many of them of Christianising intent, from the prohibition of human sacrifice to the death penalty for eating meat during Lent. These provisions were unprecedented – the Franks had never before tried to impose Christianity on a conquered population in so systematic a way. Most significant was the imposition of tithe (a payment of a tenth of the moveable wealth and produce of all free men for the support of the Church), which shows that 'Christianisation' implied not just strictures about religious belief, but involved forced adjustment of social structures, ways of life, and even economic behaviour. Such measures provoked hostility not just from the Saxons themselves but also from Charlemagne's own advisers. The Northumbrian Alcuin, a leading scholar at Charlemagne's court, wrote to Arno of Salzburg and to Charlemagne, declaring tithes to be an impediment to Christianisation: how could new converts be genuinely brought to God through such oppression? This kind of stringency on the part of the Franks must have contributed to the almost immediate, and serious, uprising of the Saxons. A contingent of Franks was heavily defeated in the Süntel mountains, provoking dramatic retribution from Charlemagne: according to one annalist, 4,500 Saxons were summarily executed. Yet even this did not bring an end to what had become a general rebellion, and the Franks had to fight intensively in Saxony in the next few years, even campaigning through the winter of 784–5. This seemed to have achieved its objective when Widukind surrendered and received baptism, with Charlemagne standing as godfather. But peace was not to last long. In 793, perhaps attempting to capitalise on Pippin 'the Hunchback's' revolt against Charlemagne, the Saxons once more rebelled. The king retaliated in 794, and the next few years saw tit-for-tat rebellions and punitive campaigns. In contrast to the wars of the 770s and 780s, fighting is now reported to have taken place mostly in northern Saxony, and the Franks enlisted the support of the Saxons' neighbours to the east, the Abodrite Slavs. Despite a further setback in 798 when a number of Frankish nobles are reported as having been killed, the Saxons' gradual subjugation was brought about by a combination of the Abodrite alliance, constant campaigning (Charlemagne wintered in Saxony again in 797–8) and increasingly repressive measures against recalcitrants. The latter included mass deportations, recorded in 799 and, more extensively, in 804. The Chronicle of Moissac reports that 'the emperor sent his _scarae_ [armies]... into Wihmodia [part of northern Saxony]... to take the people there away, out of their homeland; and he also removed the Saxons beyond the Elbe from their homes, and he dispersed them within his kingdom where he saw fit'.
Charlemagne's campaigns against the Lombards, Avars and Saxons were essentially wars of expansion that took the Frankish empire beyond its traditional frontiers. The reconstruction by military means of the old Merovingian hegemony had really been completed slightly earlier with the defeat of the duke of Aquitaine. This achievement, in 769, saw the end of nearly a century of faction-fighting and fractioning of kingdoms that had begun, as we have seen, in 675. A mere glance at this history, which was being written up so busily in the later eighth century by the continuators of Fredegar's _Chronicle_ and the compilers of the _Royal Frankish Annals_ , made palpably clear to Pippin III and Charlemagne what were the keenest dangers to their rule: on the one hand competition for dominance within the Carolingian dynasty, and on the other the centrifugal tendencies among the ruling class which continually encouraged the pursuit by individuals, families and factions of goals that were detrimental to Carolingian kingship. The political history of this century is thus a story not just about 'the rise of the Carolingians', but equally one about the rise of some Carolingians at the expense of others – and the two stories are inextricably linked. Following them has taken us on a body-strewn path through late-seventh- and eighth-century history, at whose end we find the triumphant figure of Charlemagne. Yet while he was unquestionably more powerful than any of his predecessors, his position would not have been possible without their efforts. Nor was that position ever totally secure: he had to keep running just to stand still. Once the 'peripheral' provinces of Alemannia, Bavaria and Aquitaine had been conquered, their elites had to be tied into a new, king-centred, system. How, in the eighth century, was this to be achieved?
The first, earliest and principal means was, as we have already pointed out, to wage war. The eighth century was a century of aggressive warfare; much more so, as far as the Franks and their neighbours were concerned, than the seventh (and especially the second half of the seventh). To our annalists, it was a surprise when a year passed without a campaign. And as the eighth century progressed, that aggression was increasingly, and then routinely, led by the king. It can hardly be coincidental, then, that the seventh century witnessed the gradual diminution of royal power, while the eighth saw it steadily increase. In order to fight alongside the king (or, initially, the mayor of the palace) one had to pledge loyalty to him, and back up that pledge with action; in return, one qualified for the king's gratitude, usually by sharing in the resources or position of his vanquished foes. This links to the second means of binding together the potentially fractious aristocracy: the distribution by the ruler of office, or what in the early Middle Ages were called _honores_. In most places government seems to have continued at a local level through the upheavals of the earlier eighth century. The Carolingians were fortunate that the old Merovingian structure of counts and bishops had survived. These offices were still valued; they still bestowed real advantages on their holders. Reconnecting them to the kingship meant providing, or reinvigorating, central places that allowed physical access to, and personal contact with, the king, as well as with other officeholders. Thus in Pippin III's reign, and still more in Charlemagne's, we see a renewed emphasis on the court as a forum for aristocratic activity. As under the Merovingians, this court was at first itinerant, travelling between a number of royal villas spread out across the heartland. The choice of a particular estate at any given time was determined by the resources available there and by political or military necessity. The Avar campaign thus necessitated a protracted stay for Charlemagne at Regensburg from the winter of 791 to the spring of 793. Yet at this very period we can also see a desire for greater stability, as work began on a more permanent palace complex at Aachen, which became Charlemagne's principal, though still not his only, residence from 796. Excavation has revealed something of the plan of this site, as also at Ingelheim, where he stayed in 787 and 788, and which became a favourite of Louis the Pious. Perhaps the most prominent building in both was the chapel – that at Aachen still surviving as part of the later cathedral. It was here that, throughout the Carolingian era, the king's most ritualised acts were performed. Less formal, but of equal importance, was the personal contact that took place between the king and his aristocracy, contact that reaffirmed the bonds of the battlefield through communal activities like hunting and feasting and reinforced loyalty through conspicuous generosity of lands, material goods and offices. Among those who benefited from such activity we can mention Gairefred and Gairhard, who were successively counts of Paris, an office that their family held consistently from 753, if not earlier, to 858. Their example shows the constant tension between this society's strong propensity towards heritability, and the ideal of _ministerium_ – service in an office for which one had to show oneself worthy. Families like that of Gairhard sought to pass their _honores_ down through the family because they were secure from the vagaries of partible inheritance. The strong competition for position that this situation created was perfectly manageable while the realm was expanding and the kings were stern enough occasionally to replace the incompetent and the disloyal. Thus in Pippin III's and Charlemagne's reigns, the traffic in _honores_ maintained a low hum that denoted the operation of healthy, king-centred government.
Yet there remained tension not far below the surface. Even the strongly pro-Carolingian sources cannot hide from us a major rebellion east of the Rhine in 785–6 which expressed outright opposition to the dynasty's authority – the rebels said they wanted to kill the king. Charlemagne prevailed, but only by mutilating and murdering the ringleaders – an extreme penalty that smacks uncomfortably of royal insecurity. The peoples incorporated into the Frankish empire did not necessarily take it lying down. Be that as it may, dissent within the Carolingian family itself remained a more serious threat to the ruler. Since his marriage to the Lombard princess in 770, Charlemagne had increasingly marginalised his eldest son with Himiltrude, Pippin (known, on the basis of a report by Einhard, as 'the Hunchback'). That he did not figure in his father's plans for the future must have been plain when the king had his second son with Hildegard, hitherto called Carloman, renamed Pippin after his baptism by the pope. Little wonder, perhaps, that Pippin 'the Hunchback' eventually instigated a conspiracy against Charlemagne. The plot was uncovered by a Lombard called Fardulf (later made abbot of St Denis for his trouble), and Pippin was packed off to the monastery of Prüm. His co-conspirators were executed. The fact that Pippin seemingly attracted substantial support – that his plot was not confined within the family – points to the dangers and responsibilities that had been thrust upon Charlemagne as king. Even his virtually boundless success could not give satisfaction to every aristocrat in his expanding realm. By rewarding some he was automatically denying opportunity to others, who might find in disenchanted members of the royal family a convenient focus for their resentments.
What is more, the principal response to these two conspiracies, a royal capitulary (edict) issued at Regensburg in 789, indicates that those who acquired office did not always use it as the king might wish. Men had complained, it says, that 'they do not have their law maintained'. The king was forced to affirm that if anyone had suffered anything contrary to their law, it was certainly not by his command: 'indeed, if a count or _missus_ or any man has done this, let it be reported to the lord king, for he wishes to set such matters most fully to rights'. The law, then, did not reside with the king: it belonged to each man, and it was the king's responsibility to uphold it. But how effectively he could do so – how effective Carolingian government ultimately was – depended in large part on his agents: on their debt to, and loyalty to, the king. Through their own actions, or lack thereof, royal agents could make enemies for the king. They, as much as Charlemagne, could provide ammunition for hostility among other aristocrats, and there might be little to balance this out. After all, as the rebels of 785–6 had pointed out when questioned, they had sworn no oath of fidelity to the king. Hence the major provision of that same 789 capitulary was to require the king's envoys to ensure that all the more important of Charlemagne's subjects swore an oath of loyalty to him. But the king required a _quid pro quo_. Stipulations about the oath are followed by a requirement from the elite of something even more crucial: participation in the army. In this capitulary, then, the oath was the preliminary, if not the prerequisite, for service in the army, that most significant badge of aristocratic identity. The first step on the road to elite status could now not be made without sworn loyalty to Charlemagne.
* * *
Pippin I (d.640), an Austrasian Frankish magnate, had a daughter named Begga. Her marriage to one Ansegisel is not well attested, but they are nevertheless generally held to have been the parents of Pippin II (d.714), the father of Charles Martel (d.741), whose second eldest legitimate son is therefore counted as Pippin 'III' (d.768).
Respectively, _Die Urkunden der Arnulfinger_ , ed. I. Heidrich (Bad Münstereifel, 2001), no. 22, and _Dipl. Kar_. I, no. 1, pp. 3–4. In _Die Urkunden der Arnulfinger_ , nos. 23 (which, on the basis of the properties it lists, probably dates from before 20 June 751) and 24 (which has no formal date clause, but is assigned by Heidrich to '741–751'), Pippin was still styled _maior domus_ (mayor of the palace).
Einhard, _VK_ , c. I, trans. Dutton, _Charlemagne's Courtier_ , p. 16. The _Vita_ has been dated variously between 814 and 830. For arguments in favour of an early date see Innes and McKitterick, 'The writing of history', pp. 203–8; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 7–30. For a date in the later 820s see M. Tischler, _Einharts Vita Karoli. Studien zur Entstehung, Überlieferung und Rezeption, MGH Schriften_ XLVIII, 2 vols. (Hanover, 2001), esp. pp. 163–4, 587–9.
_ARF, s.a_. 749 and 750, trans. Scholz, _Carolingian Chronicles_ , p. 39. For discussion of the annals as a genre, see McKitterick, _History and Memory_ , pp. 84–119 (esp. pp. 101–19, together with 141–2, for the _Annales regni francorum_ ); McKitterick, _Perceptions of the Past_ , pp. 65–8.
_Clausula de unctione Pippini Regis_ , ed. B. Krusch, _MGH SRM_ i (Hanover, 1885), trans. B. Pullan, _Sources for the History of Medieval Europe from the Mid-Eighth to the Mid-Thirteenth Century_ (Oxford, 1966), pp. 7–8; repr. in Dutton, _Carolingian Civilization_ , pp. 13–14. The dates given here are those proposed – to our minds convincingly – by McKitterick, _History and Memory_ , pp. 137–42; see also McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 7–20. Many alternatives have been put forward for both: for the _Continuations_ of Fredegar see in particular Collins, _Fredegar_. The _Clausula's_ attribution of regnal dates to his sons Charles (Charlemagne) and Carloman before Pippin's death in 768 argue strongly against its contemporaneity.
The last narrative chapter of Zacharias's _Life_ is c. 23, _LP_ I, pp. 433–4, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 47–8. The only letter from Zacharias to Pippin dates from 747: CC, no. 3; the next ones in sequence are CC, nos. 4 and 5, which can be dated to 753 by reference to _LP_ I, pp. 433–4, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 59.
See e.g. Hen, 'Annals of Metz'; E. Peters, _The Shadow King_. Rex inutilis _in Medieval Law and Literature, 751–1327_ (New Haven, CT, 1970), pp. 8–14.
Wood, _Merovingian Kingdoms_ , pp. 51–4.
I. N. Wood, _The Merovingian North Sea_ (Alingsås, 1983), pp. 12–13. Bishops from Kent attended the council held by King Chlothar II at Paris in 614: _Concilia Galliae a.511–695_ , ed. C. de Clercq, _CCSL_ 148a (Turnhout, 1963).
These were 558–61 (Chlothar I), 613–23 (Chlothar II), 629–32 (Dagobert I), 656–7 (Clovis II), 673–5 (Childeric II), 687–91 (Theuderic III), 691–741 (the last Merovingians and Charles Martel), 748–68 (Pippin III after the 'retirement' of Carloman), 771–840 (Charlemagne and Louis the Pious) and 884–8 (Charles the Fat): a total of 166 of the 377 years from 511 to 888, of which only thirty-nine fell before 700. These figures can only be a rough guide since the precise nature of some divisions is open to debate.
M. Widdowson, 'Merovingian partitions: a genealogical charter?', _EME_ 17 (2009), pp. 1–22.
Stephen of Ripon, _Vita Wilfridi_ , c. 33, ed. and trans. B. Colgrave, _The Life of Bishop Wilfrid by Eddius Stephanus_ (Cambridge, 1927; repr. 1985), pp. 68–9.
The term 'faction' (Latin _factio_ ) is used in contemporary sources: e.g. Fredegar, _Chronicle_ , ed. and trans. J. M. Wallace-Hadrill, _The Fourth Book of the Chronicle of Fredegar with its Continuations_ (London, 1960) IV, c. 40.
Stephen of Ripon, _Vita Wilfridi_ , cc. 4, 6 and 28.
See Fouracre, _Charles Martel_ , pp. 33–40, and n. I above.
Fouracre, _Charles Martel_ , pp. 41–8.
Further on this, see Fouracre, _Charles Martel_ , pp. 41–5.
For the minimalist and maximalist views of Pippinid lands and connections around the time of Tertry, see Fouracre, _Charles Martel_ , pp. 41–54.
Fouracre, _Charles Martel_ , p. 47.
Kölzer (ed.), _Urkunden der Merowinger_ , no. 7 (Metz) and no. 125 (Stablo-Malmédy), and see Gerberding, _Rise of the Carolingians_ , p. 100, n. 55.
_LHF_ , cc. 48, 49.
Wood, _Merovingian Kingdoms_ , p. 264.
Kölzer (ed.), _Urkunden der Merowinger_ , nos. 149, 156, 157.
_LHF_ , c. 50. On the _LHF_ and the _AMP_ , see above, Chapter 1, pp. 19–21.
Fouracre, _Charles Martel_ , p. 66.
Erchanbert, _Breviarium regum francorum annis 715–827_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), p. 328.
On Dorestad, see below, Chapter 7.
The only reference to him before this point might suggest that he was well educated: this, at least, is one meaning of the adjective _elegans_ , which the _LHF_ attaches to him in its first mention of him: _LHF_ , c. 49.
_LHF_ , c. 49; for Charles's possible supporters at this time, see Fouracre, _Charles Martel_ , pp. 61–3.
Fouracre, _Charles Martel_ , pp. 64–6.
Fouracre, _Charles Martel_ , pp. 74–5.
Reviewed fully by Fouracre, _Charles Martel_ , pp. 89–93.
We are reliant here on Fred., _Cont_., cc. 14 and 18, the Latin of which is not entirely clear: see Fouracre, _Charles Martel_ , p. 92, for the most likely interpretation.
The following account draws heavily on P. Geary, _Aristocracy in Provence. The Rhône Basin at the Dawn of the Carolingian Age_ (Stuttgart, 1985).
S. Loseby, 'Marseille and the Pirenne thesis II: "ville morte"', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 167–94. See also below, Chapter 7.
Fred., _Cont_. 12; Fouracre, _Charles Martel_ , pp. 108–9; J. Jarnut, 'Untersuchungen zur Herkunft Swanahilds, der Gattin Karl Martells', _Zeitschrift für bayerische Landesgeschichte_ 40 (1977), pp. 254–9.
_AMP_ , p. 33.
See in general K. L. R. Pearson, _Conflicting Loyalties in Early Medieval Bavaria: a View of Socio-Political Interaction, 680–900_ (Aldershot, 1999); C. I. Hammer, _From_ Ducatus _to_ Regnum: _Ruling Bavaria under the Merovingians and Early Carolingians_ (Turnhout, 2007).
Compare, for instance, Fouracre, _Charles Martel_ , pp. 81–9 and Wood, _Merovingian Kingdoms_ , pp. 281–4.
Note the account of his defeat on the Garonne by the _Chron. Moiss_., p. 291.
Collins, 'Deception and misrepresentation', pp. 35–41.
Fouracre, _Charles Martel_ , pp. 86–7; Wood, _Merovingian Kingdoms_ , p. 283.
_LHF_ , c. 52; Alcuin, _Vita Willibrordi_ , ed. W. Levison, _MGH SRM_ vii (Hanover, 1920), pp. 81–141, trans. C. H. Talbot, _Anglo-Saxon Missionaries in Germany_ (London, 1954), pp. 9–10. See further Chapter 3 below.
Fred., _Cont_., c. 17.
See below, Chapter 7, pp. 349–51.
For Boniface, see below, Chapter 3, pp. 102–4.
Fred., _Cont_., c. 19. For Martel's Saxon campaigns in general see Fouracre, _Charles_ _Martel_ , pp. 117–18.
See below, pp. 52, 64.
B. Bachrach, 'Charles Martel, mounted shock combat, the stirrup and feudalism', _Studies in Medieval and Renaissance History_ 7 (1970), pp. 49–75; see also Halsall, _Warfare and Society_ , pp. 185–6.
See Fouracre, _Charles Martel_ , pp. 137–45; Halsall, _Warfare and Society_ , pp. 72–7.
Fouracre, _Charles Martel_ , pp. 72–3; Innes, _State and Society_ , pp. 178–9.
See above, pp. 46–7.
See S. Airlie, 'Towards a Carolingian aristocracy', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 109–28.
M. Becher, 'Drogo und die Königserhebung Pippins', _Frühmittelalterliche Studien_ 23 (1989), pp. 131–53.
Fred., _Cont_., c. 23.
Collins, 'Pippin III as mayor of the palace', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 75–91, esp. pp. 84–5; Fouracre, _Charles Martel_ , pp. 161–5.
As argued by Airlie, 'Towards a Carolingian aristocracy'.
Fred., _Cont_., c. 25.
_AMP, s.a_. 742; Fred. _Cont_., c. 25. For a more equivocal reconstruction, see Collins, 'Pippin III as mayor of the palace', p. 79.
Fred., _Cont_., c. 26.
Fred., _Cont_., c. 27.
Fred., _Cont_., c. 28.
T. Reuter, _Germany in the Early Middle Ages 800–1056_ (London and New York, 1991), pp. 59–60.
For details, see below, Chapter 3.
_Contra_ H. Schüssler, 'Die fränkische Reichsteilung von Vieux-Poitiers (742) und die Reform der Kirche in den Teilreichen Karlmanns und Pippins', _Francia_ 13 (1985), pp. 45–111; see also Collins, 'Pippin III as mayor of the palace', p. 91.
In Boniface, _Epistolae, Ep_. 57 (ed. M. Tangl, _Die Briefe des Heiligen Bonifatius und Lullus, MGH Epp. selectae_ I (Berlin, 1916), pp. 102–5, trans. E. Emerton, _The Letters of Saint Boniface_ (New York, 1940), no. xlv, pp. 72–4), Boniface praised the support he had received from both Carloman and Pippin. _Ep_. 58 (pp. 105–8) refers to a letter from both brothers asking the pope for _pallia_ (symbols of office) for the archbishops of Sens, Rheims and Soissons – two of which were in Pippin's territory; _Ep_. 60 (pp. 120–5; Emerton, no. xlviii, pp. 85–9, at p. 86) refers to a recent synod held 'through the mediation' of both brothers; _Ep_. 61 (pp. 125–7; Emerton, xlix, pp. 89–91), a general letter from the pope to the Frankish clergy and laity, was distributed with the agreement of both brothers.
Boniface, _Epistolae, Ep_. 77, ed. Tangl, pp. 159–61, trans. Emerton, no. lxi, pp. 112–13.
See e.g. Pippin's charter for Prüm, _Dipl. Kar_. I, no. 16.
C. Stancliffe, 'Kings who opted out', in P. Wormald, D. Bullough and R. Collins (eds.), _Ideal and Reality in Frankish and Anglo-Saxon Society_ (Oxford, 1983), pp. 154–76; for Hunoald, see _AMP_ , p. 36. One set of annals suggests that Carloman took up the religious life in remorse for the slaughter at Cannstatt: _Annales Petaviani, s.a_. 746, ed. Pertz, _MGH SS_ I, p. II.
Since it was written after Pippin was firmly established as king, the report of Fred., _Cont_., c. 30 that on abdication Carloman 'handed over his rule together with his son Drogo' to Pippin has been widely and rightly mistrusted: e.g. Collins, 'Pippin III as mayor of the palace', p. 86.
Boniface, _Epistolae, Ep_. 79, ed. Tangl, pp. 171–2, trans. Emerton, no. LXIII, pp. 119–20; Becher, 'Drogo und die Königserhebung Pippins'.
J. L. Nelson, 'Bertrada', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 93–108.
We are dependent for the news of Grifo's release on a later source: _AMP_ , _s.a_. 747, pp. 39–40, which credits it to Pippin, 'moved by mercy'; see also Airlie, 'Towards a Carolingian aristocracy', pp. 116–17, and Fouracre, _Charles Martel_ , pp. 172–3.
_ARF, s.a_. 748, trans. Scholz, p. 39.
M. Becher, 'Neue Überlieferungen zum Geburtsdatum Karls des Großen', _Francia_ 19 (1992), pp. 37–60.
_Epistolae aevi Merowingici collectae_ , no. 18, ed. W. Gundlach, _MGH Epp_. III ( _Epp_. Merovingici et Karolini aevi I) (Berlin, 1892), p. 467.
On the _scholae peregrinorum_ (pilgrim hostels), see R. Schieffer, 'Charlemagne and Rome', in J. M. H. Smith (ed.), _Early Medieval Rome and the Christian West_ (Leiden, 2000), pp. 279–95, at pp. 291–3.
Paul the Deacon, _HL_ VI, c. 53; see also next note.
J. Jarnut, 'Die Adoption Pippins durch König Liutprand', in J. Jarnut, U. Nonn and M. Richter (eds.), _Karl Martell in seiner Zeit_ (Sigmaringen, 1994), pp. 217-26; see also B. Kasten, _Königssöhne und Königsherrschaft. Untersuchungen zur Teilhabe am Reich in der Merowinger- und Karolingerzeit, MGH_ Schriften 44 (Hanover, 1997), esp. p. III.
CC, nos. 1 and 2, pp. 476–8.
Fred., _Cont_., c. 22.
Boniface, _Epistolae, Epp_. 50, 51, 52, 53, 57, 58, 59, 60, 61, 68, 77, 80, 82, 83, 86, 87, trans. Emerton, nos. XL, XLI, XLII, XLIII (pp. 56–69); XLV–XLIX (pp. 72–91); LIV (pp. 100–1); LXI (pp. 112–13); LXIV (pp. 120–7); LXVI–LXVII (pp. 128–32); LXX–LXXI (pp. 135–42).
For Carloman at Monte Soracte, see CC, no. 23, pp. 526–7, though note that the date of this letter is highly uncertain. For Carloman's monachisation and entry into Monte Cassino, see _LP_ I, p. 433, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 46–7.
W. Pohl, 'Das Papsttum und die Langobarden', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 145–61, at pp. 148–51.
For apparent reluctance among some Lombard aristocrats, see _CDL_ I 114, _CDL_ v 52; for wavering loyalty towards the kings on the part of some Lombard bishops, Pohl, 'Das Papsttum und die Langobarden', p. 155; S. Gasparri, 'Roma e i longobardi', in _Roma nell'alto medioevo_ , Settimane di Studio del Centro italiano di studi sull'alto medioevo 48 (Spoleto, 2001), pp. 219–53, at pp. 246–7.
_Pauli continuatio cassinese_ , c. 4, ed. G. Waitz, _MGH SRL_ (Hanover, 1878).
Agnellus, _Liber pontificalis ecclesiae Ravennatis_ , ed. D. M. Deliyannis, _CCCM_ 199 (Turnhout, 2006), _Vita Sergii_ , cc. 155–6, trans. D. M. Deliyannis, _Agnellus of Ravenna. The Book of Pontiffs of the Church of Ravenna_ (Washington, DC, 2004), pp. 279–80; for discussion of Agnellus, see J. M. Pizarro, _Writing Ravenna. The_ Liber pontificalis _of Andreas Agnellus_ (Ann Arbor, MI, 1995).
CC, no. II ('devorator sanguinum Christianorum').
_LP_ I, pp. 441–2, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 54–5.
'... traditum nobis a Domino': _Leges Ahistulfi_ [Laws of Aistulf], prologue, ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ (Weimar, 1947; repr. Witzenhausen, 1962), p. 194; the translation by Fischer-Drew, _The Lombard Laws_ , p. 227, is unfortunately and misleadingly wide of the mark here.
_LP_ I, c. 15, p. 444, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 58 ('pro universo exarchato Ravennae atque cunctae istius italiae provinciae populo...'); see further Pohl, 'Das Papsttum und die Langobarden', p. 157. That this statement is roughly contemporary seems confirmed by similar claims made in papal letters: see _CC_ nos. 10 and 11 (probably dating from 756 and 757 respectively).
_CC_ no. 5.
_ARF, s. a_. 754, trans. B. Scholz, _Carolingian Chronicles_ , p. 40.
Pohl, 'Das Papsttum und die Langobarden', p. 160: which is not to say that there had been no _contacts_ between the Franks and the popes, just that they had not operated on the level of political negotiation.
Abbot Droctegang was the first such envoy, with Bishop Chrodegang, Abbot Fulrad, and the dukes Autchar and Rothard subsequently involved: see _LP_ I, c. 16, p. 444, c. 18, 20, p. 445, c. 24, p. 447, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 59–62 ( _Vita Stephani II_ , cc. 16, 18, 20, 24).
Fred., _Cont_., c. 35.
Compare _ARF, s. a_. 753 with the revised version of the same annal (trans. Scholz, p. 40), and _LP_ I, c. 30, pp. 448–9. The _LP_ says that Carloman was put into a monastery in Francia by Pippin and Pope Stephen, where he died after a few days; see further M. de Jong, 'Monastic prisoners or opting out? Political coercion and honour in the Frankish kingdoms', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 291–328.
Becher, 'Drogo und die Königserhebung Pippins'; Fouracre, _Charles Martel_ , pp. 171–4.
Charter evidence for the summoning of the Lombard army in 754 has been taken to indicate that Pippin's campaign took place in that year; but this is not necessarily the case, and the sum of the evidence is consistent with a date for the first campaign of 755, as argued by T. F. X. Noble, _The Republic of St Peter. The Birth of the Papal State, 680–825_ (Philadelphia, PA, 1984), p. 88, n. 113.
This is often called the First Peace of Pavia, the terms of which are reported variously by Stephen's biographer and Frankish annalists: see _LP_ I, p. 451, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 67–8; ARF, _s.a_. 755; _AMP, s.a_. 754, pp. 46–7; _Pauli continuatio tertia_ , c. 39, ed. G. Waitz, _MGH SRL_ (Hanover, 1878), p. 210.
_LP_ I, pp. 452–4, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 70–2.
Fred., _Cont_., c. 40.
For the despatch of the embassy in 763, CC, nos. 28 and 29; for the debate at Gentilly, _CC_ , nos. 36 and 37, convincingly interpreted by M. McCormick, 'Textes, images et iconoclasme dans le cadre des relations entre Byzance et l'occident', _Testo e immagine nell'alto medioevo_ , Settimane di Studio del Centro italiano di studi sull'alto medioevo 41 (Spoleto, 1994), pp. 95–162.
For the diplomatic to and fro of these years, see McCormick, _Origins of the European Economy. Communications and Commerce ad 600–900_ (Cambridge, 2001), pp. 873–4; for the marriage proposal, ARF, _s.a_. 767.
Fred., _Cont_., c. 51.
For this line of argument, see M. McCormick, 'Pippin III, the embassy of Caliph al Mansur, and the Mediterranean World', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 221–41.
Halsall, _Warfare and Society_ , pp. 136–8. For a sustained narrative, see McKitterick, _Frankish Kingdoms_ , pp. 50–3.
CC, no. 44.
The only others being the king of Asturias (then Silo), and the duke of the Bretons.
On this marriage, see J. L. Nelson, 'Making a difference in eighth-century politics: the daughters of Desiderius', in A. C. Murray (ed.), _After Rome's Fall: Narrators and Sources of Early Medieval History. Essays presented to Walter Goffart_ (Toronto, 1998), pp. 171–90, at pp. 178–84; on the name Gerperga, p. 183.
For the events of this paragraph, see Noble, _Republic of St Peter_ , pp. 99–137; R. Collins, _Charlemagne_ (Basingstoke, 1998), pp. 38–9; Costambeys, _Power and Patronage_ , Chapter 8; J. Jarnut, 'Ein Bruderkampf und seine Folgen: die Krise des Frankenreiches (768–771)', in G. Jenal and S. Haarländer (eds.), _Herrschaft, Kirche, Kultur: Beiträge zur Geschichte des Mittelalters. Festschrift für Friedrich Prinz zu seinem 65. Geburtstag_ (Stuttgart, 1993), pp. 165–76.
See Collins, _Charlemagne_ , p. 62. The point applies only to kings: note that both Merovingians and Carolingians had at times replaced lesser rulers, in, for example, Aquitaine and Alemannia.
The only evidence of the aspiration is a letter of Pope Hadrian, who had an interest in talking up the hostility of some Lombard dukes to Frankish rule: CC, no. 57, pp. 582–3.
J. L. Nelson, 'Charlemagne – Pater Optimus?', in P. Godman, J. Jarnut and P. Johanek (eds.), _Am Vorabend der Kaiserkrönung: das Epos "Karolus Magnus et Leo papa" und der Papstbesuch in Paderborn 799_ (Berlin, 2002), pp. 271–83.
See T. F. X. Noble, _Images, Iconoclasm and the Carolingians_ (Philadelphia, PA, 2009); and below, Chapter 3.
See above, pp. 55–6.
M. Becher, _Eid und Herrschaft. Untersuchungen zum Herrscherethos Karls des Großen_ (Sigmaringen, 1993); S. Airlie, 'Narratives of triumph and rituals of submission: Charlemagne's mastering of Bavaria', _TRHS_ 6th ser. 9 (1999), pp. 93–119.
ARF, _s.a_. 788.
ARF, _s.a_. 791.
For the gift to Offa, see Alcuin, _Ep_. 100, trans. Loyn and Percival, _Reign of Charlemagne_ , no. 28, trans. King, _Charlemagne: Translated Sources_ , pp. 312–14. For the general impact of the treasure: Einhard, _VK_ , c. 13.
ARF, _s.a_. 822.
Fred., _Cont_., cc. 27 and 31.
_ARF, s.a_. 772. For a full narrative of the Saxon wars, Collins, _Charlemagne_ , pp. 47–56, and see ARF, _s.a_. 772–802.
D. H. Green and F. Siegmund (eds.), _The Continental Saxons from the Migration Period to the Tenth Century: an Ethnographic Perspective_ (Woodbridge, 2003).
Alcuin, _Ep_. 107 (to Arno) and 110, 174 (to Charlemagne); P. E. Dutton (ed.), _Carolingian Civilization: a Reader_ , 2nd edn (Peterborough, ON, 2004), pp. 125–7.
ARF, _s.a_. 782.
_Chron. Moiss., s.a_. 802, pp. 306–7, trans. King, p. 146.
E.g. _ARF_ , _s.a_. 792.
J. L. Nelson, 'The Lord's anointed and the people's choice: Carolingian royal ritual', in D. Cannadine and S. Price (eds.), _Rituals of Royalty_ (Cambridge, 1987), pp. 137–80; repr. in Nelson, _Frankish World_ , pp. 99–131.
R Hennebicque-Le Jan, 'Prosopographica neustrica. Les Agents du roi en Neustrie de 639 à 840', in H. Atsma (ed.), _La Neustrie: les pays au nord de la Loire de 650 à 850_ , Beihefte der Francia 16, 2 vols. (Sigmaringen, 1989), I, pp. 231–69, at pp. 236–7; also Fouracre, _Charles Martel_ , pp. 163–4.
For more on these themes see below, Chapter 4.
For this paragraph see J. L. Nelson, _Opposition to Charlemagne_ (German Historical Institute, London, 2008).
Nelson, 'Pater optimus' discusses the shifting succession arrangements.
Capitularies are discussed more fully in Chapter 4.
_Capit_. I, no. 25, trans. King, _Charlemagne_ , p. 223.
_Capit_. I, no. 25, c. 6, trans. King, _Charlemagne_ , p. 223.
## 3
### BELIEF AND CULTURE
In the first two chapters we have made regular references to the Christian character of the Frankish court, which acted as a powerful patron associated with the founding of monasteries, the patronage of holy men and intellectuals, and the production and standardisation of religious texts. Well before the end of the eighth century, where we left Charlemagne demanding comprehensive oaths of loyalty from his elite male subjects, and indeed before the anointing of 753–4, kingship itself was conceived as an office with religious responsibilities. Christianity was part of the very identity of elite Franks, who increasingly came to see themselves as a people chosen by God, and thus to define themselves in distinction to the nonand imperfectly Christian peoples that surrounded them. These ideologies played a part in the Franks' justifications to each other and to themselves of their conquests. As victorious Carolingian armies withdrew they were often – as we have seen – replaced by missionaries, charged with winning the hearts and souls of the conquered, and with establishing their obedience to the Frankish Church (and, therefore, empire). Even if we find it to be outlandish or distasteful, we should not be surprised that Frankish kings thought themselves to have a moral responsibility to save the souls of those under their dominion, nor should we write this off as moral posturing designed to justify territorial expansion – after all, given the long decades of virtually unblemished military success, how could they not believe they were doing God's work? These themes represent central aspects of Carolingian politics and society which have been touched on earlier in this book, but which take centre stage in this chapter – here we hope to explain the mentalities and intellectual attitudes that informed the actions of those involved in the high politics of the previous chapter.
Yet placing Carolingian Christianity under the spotlight complicates matters more than one might expect. The closer we look at the concepts of religion, paganism, the Church, and Christianity itself, as they operated in early medieval Europe, the more they start to fall apart under our gaze. By placing Carolingian Christianity in a broad context, the chapter is therefore intended to shake the foundations of some commonly held modern assumptions about the early Middle Ages, as well as to offer some reorientation. The discussion is divided into three main sections: the problem of Christianisation; the problem of sin; and the role in society of Christian kingship and learning. But to understand the place of these phenomena in eighth- and ninth-century Europe, we must first define our terms of reference, and ask what we mean when we talk about paganism, Christianity and the Church. We can begin exploring these questions by visiting the Carolingian court itself.
#### THE PROBLEM OF CHRISTIANISATION
#### _Defining Christianity_
When, towards 860, Lothar II, king of the Franks, wanted to get divorced, some of his bishops wrote to Archbishop Hincmar of Rheims to ask him whether 'it can be true, as many men say, that there are women who can create with their evil-doing irreconcilable hatred between man and wife, or join together a man and woman with uncontrollable love'. The archbishop's reply comprised a long and vivid enumeration of the demonic powers that he detected at work in Lothar's court:
there are magi, who are commonly called evil-doers because of the enormity of their sins... there are necromancers, whose incantations seem to understand the dead as if revived and to reply to their questions... there are soothsayers, who utter evil prayers and offer sacrifices to the dead around the altars of idols... there are augurs who observe the flights and songs of birds...
and many others besides. But it opened with more pointed observations, including that 'certain men are debilitated by witches or by feminine wiles, and certain women are found to have committed sexual intercourse with harpies in the guise of men, with whom they fall in love'. The bishops would not have mistaken Hincmar's intended target. Lothar was seeking the dissolution of his union with his wife Theutberga so that he could marry his long-standing mistress Waldrada. Witchcraft and devilry, Hincmar was hinting, lay behind the latter's hold over the king.
Hincmar's depiction of a Carolingian court beset by soothsayers, sorcerers and witches is a troubling one on a number of levels. At first sight, it seems to reveal a society that was incompletely Christian, even at the very top. Five and a half centuries after the conversion to Christianity of the Roman emperor Constantine, and some three hundred years after that of the first Christian Frankish king Clovis, Hincmar depicts a Frankish Church in daily battle with distinctly unchristian beliefs and practices that apparently held sway even among the elite. This is surprising not least because most other indications, and the accounts historians have built from them, tell of the complete Christianisation of the Franks by this time. The eighth century in particular was in fact, according to the traditional view, the period when the Franks sponsored missions aimed at converting to Christianity other peoples living to their immediate north and east: Frisians, Saxons, Hessians and Thuringians. The missionisers themselves, in a neat and often-noticed progression, were drawn from among the Anglo-Saxons so recently Christianised themselves by a mission sent by a pope from Rome. According to this view, when that pope's successors consecrated English 'missionary bishops', and when those bishops allied with the Franks' rulers both to extend Christianity and to reform it within the kingdom, Rome-rooted mission had come full circle. This section, then, will re-assess the idea of the extension of Christian belief in this period, while subsequently we will look at the condition of Christianity itself, and the development of the Christian Church.
The difficulty of this task is immediately evident from a second level of disquiet about our source: Hincmar was not a neutral observer but a partisan of a king, Charles the Bald, who had a vested interest in ensuring his nephew Lothar's childlessness for the leverage it gave him in inter-kingdom politics. What is more, Hincmar's long description of the various kinds of magic-makers and malefactors is actually taken, almost verbatim, from a much earlier work, the _Etymologies_ , a kind of encyclopedia written by Bishop Isidore of Seville in the seventh century. It looks as if Hincmar wanted to project a particular picture of Lothar's court, for political reasons, by reproducing recognisable images of unacceptable practices. The one passage from this section of the work that does not parrot an earlier text is precisely the one about wanton, bewitched and bewitching women which was aimed, undoubtedly, at the 'adulterous' Waldrada. That said, Hincmar's description must have 'rung true' to himself and his intended audience (most immediately, the bishops of Lothar's kingdom who had prompted his letter in the first place). It would have had little impact if it had amounted entirely to fantasy. So even if Hincmar and his colleagues did not think that dark spiritual forces _were_ at work at Lothar's court, they admitted the possibility that they _could_ be.
It is not immediately clear where such forces stood in relation to Christianity. Some historians have suggested that these demons were the distinctive residue of a pre-Christian world of magic and superstition that survived uncleansed despite centuries of attentive opposition by Christian activists; that, in other words, such texts offer direct evidence for non-Christian belief. It is very probable, however, that Hincmar himself would have thought nonsensical the very notion of 'pre-Christian', since Christ was Alpha as well as Omega, and that in his mind these forces were understood in very Christian terms, as earthly representatives of the Biblical devil, the perennial tempter, and foe, of the aspirant Christian. As such, they were coded symbols for the human moral corruption which was the root of Lothar's personal crisis. Hincmarmay simply have been noting that the Carolingian elite languished in the same sinful condition as every human since Adam's fall from grace. In this sense Hincmar's reply to the bishops, like many early medieval Christian texts, is more useful for telling us what Christianity was not – that is, for revealing what those who called themselves Christians thought were the _wrong_ beliefs and practices – than for enumerating the correct doctrines and actions that we could put in a pigeonhole marked 'Christian'.
Prejudiced and derivative, then, Hincmar's letter illustrates how difficult it is for us to access belief in this period. By foregrounding actions like chanting and sacrificing, it is one among many texts that have encouraged the view that in the earlier Middle Ages belief was largely a matter of external practices rather than of internal mentality – that what mattered was what one did, not what one thought or felt – and that these practices were generally communal rather than individual or personal. But we need to remember that the kinds of sources we have condition our view of early medieval beliefs. After the end of the period covered by this book, a number of texts began to emphasise individual rather than collective piety, to an extent that has sometimes been seen as marking a radical break with early medieval practice; but the change may reflect the adoption of new genres and styles of writing at least as much as actual or generalised shifts in what people believed. It would be wrong, and unfair, to deny to the inhabitants of early medieval Europe the capability of reflective belief, just because they articulated it in different ways from their later medieval counterparts, ways perhaps no longer recoverable.
It has been crucial to the long-term success of Christian doctrine that it is very flexible, the result of its origins among Greek-speakers in the Roman empire steeped in the philosophical tradition of the eastern Mediterranean. In these first generations, what came to be called Christianity amalgamated the cult of a Jewish prophet with the concerns of Hellenistic philosophy. In particular, the latter's interest in the nature of God and the divine relationship with the physical universe became central issues of emerging Christian doctrine, and arguments in early councils of bishops duly focussed on Jesus's relationship with God (Christology) and on the idea of salvation for humans through him (soteriology). From the mid-fifth century, however, Christian apparatchiks – the priests, bishops and monks of the Church hierarchy – began to seek, and to gain, access to aspects of life of only tangential interest to earlier Christian leaders, and into which the priests of pagan Roman cults had never even dreamt of intruding: sexual relations, for instance, and marriage. In speculative theology, there is no mistaking the decline in an interest in the precise _nature_ of the divine, and a stress instead on the _presence_ of the divine in this world, and on the practical steps believers might take to touch it, in both the here-and-now and the hereafter.
The spread of this attitude signalled a reorientation of the way in which people viewed their relationship with an institution, the Church. ('The Church' in this sense is a problematic concept in itself, since it is questionable whether at this period the community of Christians was organised into any kind of institution sufficiently coherent to deserve the title; as we shall see, the argument in favour of its existence is stronger towards the end of the period we are covering than at the beginning.) Crucially for us, it also involved a radical change in the way in which people discussed that relationship. Emerging genres of writing, such as hagiography, stressed that belief was revealed through practice: actions displayed the heart and mind of the actor. Such texts make it as hard to arrive at any detailed definition of Christianity as it is to get a clear view of non-Christianity. At the start of our period, around 700, self-professed Christians would very probably accept the possibility of eternal life after death for those who believed that God had become man in the person of Jesus. Many might further have accepted that public profession of this belief should be made through the initiation ritual of baptism. Beyond that, though, all was variety. Holy writ – the Bible – was by no means universally known, and there were in any case numerous interpretations of it. In short, there was not one Christianity, but many Christianities, not one Church, but many churches. It is instructive to compare this definition with that implicit in Hincmar's condemnation of Lothar's court, which, as we have noted, is really a list of what Christianity was not. It excludes a whole raft of practices and beliefs which some earlier writers had slated as 'rustic', most of which go back not just to Isidore of Seville in the seventh century, but to the writings of the sixth-century bishops Caesarius of Arles and Martin of Braga. But it also assumes a more rigid definition of what Christianity actually was. By Hincmar's time, Christianity in the eyes of churchmen was increasingly thought of as constituting the rules of an institution as much as a code of moral practice. These uncertainties about the very nature of Christianity, and the emergence of increasingly confident definitions in the ninth century, are important to keep in mind.
#### _Defining non-Christianity_
If Christianity in the early Middle Ages is difficult to define, then so too are other concepts that are habitually used when discussing beliefs. Terms such as 'paganism', 'religion', 'magic' and 'superstition' imply to the modern ear concepts that were recognisable and well-defined in practice. What is more, ancient and medieval writers were just as seduced by them as modern authors: in the early fifth century, for instance, St Augustine of Hippo optimistically declared that superstitions were merely the tenuously surviving beliefs that Christianity would abolish. The problem is that none could agree on which practices belonged in which category, and therefore on which were unacceptable and which tolerable. In practice, concepts like 'religion', 'superstition' and 'magic', as well as 'paganism', can be defined only in relation to each other: that is, what might constitute 'religion' to one person might look like 'magic' to another, and 'superstition' to a third. Those who sought to foretell the future might be demonic to Hincmar, but it is hard to see what really separated them from the Christian heroes who were praised for their prophetic powers. The difficulty is evident in the _Indiculus superstitionum et paganiarum_ , a brief list of (presumably proscribed) practices produced in the context of the Church councils in the east Frankish kingdom instigated by St Boniface in the 740s, of which there will be more to say shortly. The _Indiculus_ was clearly composed for a society familiar with Christianity: it mentions 'sacrilegious acts in churches', 'sacrifice which is made to any of the saints', 'the improper places which they [the unnamed religious miscreants] tend for the saints'. Yet its authors were happy to lump these practices – which really come under the heading of 'bad Christianity' – together with 'amulets', 'incantations', 'sacred rites of woods', 'sacred rites of Mercury and Jupiter', 'auguries using either the dung or utterances of birds, horses or cattle', and 'the pagan dance which they call "yrias", with torn cloaks or shoes', among others. In part, these evidently belong to the same tradition as Hincmar's litany of sorceries; both authors were drawing on that series of common models of 'wrong' religious behaviour, some of them quite venerable, that we have already identified. It is surely this that accounts for the reference to Mercury and Jupiter, rather than the Roman re-casting of Germanic gods that we shall examine shortly, still less a centurieslong continuity of cult from antiquity.
Moreover, while modern definitions sometimes try to distinguish 'magic' (categorised as the attempt to bend nature to one's will), from 'religion' (defined as appealing to a higher power), the _Indiculus_ prefers to blur such categories. Amulets (which might constitute 'magic') and idols (which are more straightforwardly 'religious') are equally condemned, and thrown together with some fairly rustic superstitions, like shouting 'triumph, moon!' ('vince, luna!') during an eclipse. Charlemagne's close adviser Alcuin, writing in the heyday of Carolingian Church formation, combined these elements when he described the whittling down of the company of his fellow Englishman St Willibrord, as a pagan king selected victims by lot in punishment for their violation of an island dedicated to the god Fosite, with its temples, spring and sacred cattle. 'Religion', 'magic' and 'superstition' are not, in fact, neatly distinct, and neither Alcuin nor the writers of the _Indiculus_ tried to make them so.
Things might be clearer if we had writings left by non-Christians about their beliefs, but since none survive we have to look at this lost world from the hostile and often clichéd perspectives of contemporary learned Christians. But these Christian authors were not primarily concerned with drawing a boundary between religious and non-religious belief – they were looking at themselves, using non-Christian practices to help develop a new, narrow and rigorist definition of 'true' Christianity. This has to be borne in mind even when we are reading letters, or the reports of church councils. These texts' purposes were not so much to report the real practices of lay people as to define them in relation to the emerging Christian Church. When, for example, Pope Gregory III exhorted peoples in Germany to 'reject absolutely all divination, fortune-telling, sacrifices to the dead, prophecies in groves or by fountains, amulets, incantations, sorcery (that is, witchcraft) and all those sacrilegious practices', he was echoing late antique canon law, replicated in turn in the acts of the councils that Boniface organised, as well as, in its fullest form, in the _Indiculus_. Whether or not people in Germany actually did those things, by the eighth century the traditions of the Church said that they _might_. The authors of the _Indiculus_ were therefore drawing on the same traditions as Hincmar, and with the same result: an increasingly rigid definition of Christianity among the learned elite, pointing towards the condemnation of anything else as unbelief and, ultimately, heresy. Not for nothing was the term _correctio_ often used to describe these currents of thought.
The fact that contemporaries were arguing intensely about where to fix the boundaries between Christianity and non-Christianity makes it more difficult for us to decide where the lines actually were – the reality is hard to see through their discourse. The tenets and practices that each community held before its profession of Christianity differed from region to region. In lands with direct cultural continuity from Rome, we sometimes find references to the Greco-Roman gods – Jupiter, Mercury and the rest of the Olympian pantheon. It is difficult to know, however, whether these attest real continuity, or simply authors using the _interpretatio romana_ – the drawing of parallels between Roman and non-Roman gods, and attributing to the latter the names of the former – which dates back to classical Roman writers. Since, as we shall see, such references are found well into Germany, in lands that never fell into the Roman empire, it is in fact impossible to draw a neat line between areas where beliefs and practices had been essentially Roman, and those areas where they were something else. The term 'religion' itself is problematic here, because earlier sets of beliefs and practices did not have a number of features that we find in Christianity and other monotheistic faiths: sacred texts, a prophetic or historical tradition, abstract theology. There was a consciousness that Christianity had a more substantial identity – perhaps it was this that led Louis the Pious's moneyers to strike coins with the legend _Christiana religio_. The search for the 'old gods' in different parts of northern and western Europe is also hampered by the dating of the available evidence. A good deal is said about supposedly pre-Christian deities and their veneration in much later literature, but its distance in time from the genuinely pre- Christian era makes irrecoverable the real beliefs of that earlier era, which are transformed, through layers of accretion, into something more like folklore.
The religious tenets and practices that preceded Christianity in many of the more northerly parts of the Carolingian world, and are generally labelled 'Germanic', are a good example of this bleeding of religion into mythology. The most elaborate accounts of those beliefs survive only in the writings of authors in twelfth- and thirteenthcentury Iceland, creating their distant past through the filter of the Christianity which had been adopted there over two hundred years earlier. In any case, it is very difficult to say what the religion of the Icelanders' tenth-century ancestors shared with that of eighth-century Saxons, or seventh-century Frisians. Their languages, and therefore their names for gods, were related (thus, in Old English, Old High German and Old Norse respectively, Woden/Wodan/Odin, and Thunor/Donar/Thorr), but this does not mean they shared common religious beliefs: the 'Germanic' culture of the period is a modern invention. In general, eighth- and ninth-century north European sources provide far more information about practices than they do about beliefs. For example, burial practices, both cremation and inhumation, might evince belief in an after-life – and burial with a means of transport, whether a horse or the Sutton Hoo ship, seems to indicate the notion of a journey towards it – but we can say nothing about how it was imagined, or how it was thought attainable. Similarly, while there is evidence for the celebration of non-Christian festivals and even cattle sacrifice, it is less often clear what they signified. Some people east of the Rhine in the eighth century may even have practised human sacrifice, if Pope Gregory III's complaint to Boniface about Christians who sold their slaves to pagans for sacrifice was at all well informed; and we have evidence of ritual drownings taking place in Frisia at around the same time. But what any of this effusion of blood was for, or to whom the deaths were offered, is far from clear.
Pre-Christian gods feature as weakly in our evidence as does their capacity to withstand Christianity. Boniface's mentor, Bishop Daniel of Winchester, knew that they could be demystified simply by pointing to their supposed genealogies, and therefore to their very biological, non-divine, need for procreation. It is straightforward to put names to some of these gods, since they occur in the days of the week (in both medieval and modern languages, and in both England and Germany): Tîw, Woden, Thunor, Freya. They appear also in place names (especially in England), and in some contemporary written sources: a baptismal formula apparently used for converting Saxons required them to renounce Donar, Woden, and Saxnot, and one of the intriguing Old High German charms refers to Woden and Freya. By referring also to gods that are not otherwise known, several texts reveal the patchiness of our knowledge: the _Lives_ of Willibrord and Liudger show both saints encountering the cult of the otherwise obscure Fosite; and an Anglo-Saxon spell refers to an 'earth mother' named Erce, not attested anywhere else. As to cult places themselves, our sources for continental Germany point to the importance not of religious buildings, firm evidence for which is entirely lacking, but to natural sites: as we have seen, Fosite was culted especially at a sacred spring, while Boniface chopped down an oak at Geismar in Hesse which evidently served as an idol. The attribution of spiritual power to places connects with a belief in the existence of animate spirits, which might also take physical form. This is most apparent in the evidence from Anglo-Saxon literature for dragons, giants, elves and dwarves, who intruded mischievously or menacingly into human affairs. The monsters in the Anglo-Saxon poem _Beowulf_ – Grendel, Grendel's mother, and the dragon that was the hero's nemesis – are only the most famous of these. Nonetheless, it is worth repeating, these creatures are known to us almost entirely in stories written in Christian contexts. Grendel's genealogy in _Beowulf_ leads back not to some pagan figure but to the Old Testament's aboriginal fratricide Cain. The persistence of these figures troubled some churchmen – 'what has Ingeld to do with Christ?' complained the Anglo-Saxon scholar Alcuin, referring to a figure we know only from an oblique reference in _Beowulf;_ but others, evidently, saw no incompatibility between their Christianity and belief in such beings. It is decidedly moot whether many of them should be labelled 'pagan' at all. All pre-Enlightenment cultures (including Christianity) developed explanations of the world around them that involve what we would call the supernatural. It would be wrong then, as some of the more optimistic readings of these texts have done, to see references to such phenomena as tip-of-the-iceberg evidence for a fully coherent pagan religion.
#### _Extending the Church_
By suggesting that non-Christian religion was insubstantial and adaptable we are also undermining the traditional notion of conversion to Christianity (from something else, equally well defined) as a result of 'mission'. Contemporary narratives made much play of the idea of missions to the pagans, thus presenting the development of Christianity as a black-and-white conflict. Until recently modern histories have followed suit, to the extent that they often tell the story of the Christian Church's spread through the lives of a series of Christian heroes – missionaries – whose triumphant struggle was aimed at winning large numbers of direct, pagan-to-Christian, converts. These heroes' efforts to extend Christianity are seen as working in parallel with the drive to define it more closely. This narrative portrays conversion not just as the adoption of a faith, but as induction into an institution, with definite administrative and geo-political boundaries: the Church. As we have already noted, though, it was only in our period that the Church began to emerge with any kind of solid institutional profile, and much diversity persisted. The Church has looked most concrete and tangible in the acts of church councils (meetings of bishops), which gradually built up into a formidable body of canon law, applying in theory not only to churchmen but to anyone involved in issues that the Church claimed as its own, like marriage. Accumulating into a body of legal rules, these have tended to encourage the notion of a unified Church, since the series begins with the acts of the universal or 'ecumenical' councils of the fourth century. But before the eighth century, councils in the former western empire had generally been restricted to, at best, single realms, Frankish, Visigothic or Lombard, with no aspiration to apply beyond that particular kingdom. The mistaken complaint that even these had not been held in Francia for more than eighty years by the 740s is a sign that when new councils were summoned at that time, it was at the initiative of Christian leaders of a different stripe. These were Anglo-Saxons with their unique, rigorous and expansionist vision of the institutional Church, and the new Carolingian dynasty, eager for an ideology to underpin their rulership. The writ of these councils ran as far as that of the Carolingians themselves, traversing the old political boundaries. At the same time, the identity of the western Church was firming up in relation to that of the east. This is already evident in the acts of the council of Pavia, held under the auspices of the Lombard king Cunincpert in 698, which presented a specifically Lombard, and therefore western, solution to the Three Chapters dispute, an argument over eastern ideas that had split the north Italian churches.
The traditional narrative, then, tends to see the religious history of these centuries in terms of the extension to new peoples of the institution governed by the rules of canon law, membership of which was acquired primarily through submitting to the initiation ritual of baptism. At the opening of our period, the community of Christians so defined extended no further than the writ of the rulers who had formally accepted Christianity: the kings of the Lombards, Franks and Visigoths, the dukes of the Bretons, Alemans and Bavarians, and the various rulers of the British Isles. In the latter, the last Anglo-Saxon people formally to accept Christianity – those on the Isle of Wight – had done so only in the years after 686, while most of Visigothic Spain would pass into the hands of Muslims very suddenly in 711. 'Christendom' (a later concept of strictly limited applicability here) was restricted, even embattled. By 900, however, Christianity had been accepted in some sense in the Germanic-speaking lands as far east as the Elbe and as far north as the North Sea and the Jutland peninsula. The first sustained attempts at evangelisation in Scandinavia were made in the ninth century, though they put down no long-term roots at that time. By the end of that century too, concerted efforts at Christianisation were being aimed at the Slavic-speaking peoples, both those immediately to the east of Frankish territory – the Carantanians, Bohemians and Moravians – and those to the north of the Byzantine empire, principally the Bulgarians.
Mapping onto this geography, it has been the growth of the Church's institutional profile – its buildings, its personnel, their organisation – that has most often captured the attention of historians. Our period was one in which this aspect of Christianity became far more complex and concrete. While it needs to be noted that these aspects of the Church are of course very imperfect means of measuring Christianisation – they tell us little of the social impact of Christianity, let alone of changes in actual belief – they do indicate the spread of the institution of the Church. It was generally this, rather than the more intellectual and psychological features of 'mission', like preaching, that was the first concern when trying to extend Christianity geographically. In particular, it was important to set up bishops with cathedral seats and delineated dioceses. From the conversion of the emperor Constantine in the early fourth century, the late Roman period had seen this skeletal structure of bishops and dioceses established across most, if not all, of the western empire. Subsequently the hiatus of imperial collapse and the establishment of 'barbarian' kings seems to have erased this network in some places, especially Britain and northern Gaul. In most provinces, though, there was a good deal of continuity. It was a bishop seated as far north as Rheims, Remigius, who, around 500, persuaded the first great Frankish king Clovis of the benefits of Christian baptism. Even in the heart of the empire, in Italy, where the written records for Christianity are very sparse in the years of turmoil between the mid-fifth and the mid-sixth century, the archaeology of some episcopal centres shows disruption, hiatus and retrenchment. Yet Christianity never disappeared. Its presence had been felt among barbarian groups even before they entered the empire, when many adopted the Arian form of the faith at a time when it was coming to be regarded by leaders of the Church within the empire as heretical: this was itself a sign that religious discussion in the later Roman empire was already coming to take place entirely in Christian terms. The prevalence of Christianity in the empire's successor states is affirmed for the historian by evidence from the late sixth, and above all from the seventh, century which reveals the level of veneration of Christian saints by this time. While Gregory, the late-sixth-century bishop of Tours, could write of the numerous, already venerable (and distinctly legendary) martyrs and confessors of the Gaul of two or more hundred years previously, seventh-century Frankish writers turned to the task of sanctifying the Christian leaders of their own day in pristine hagiographies. These leaders were saints, according to such texts, because they had demonstrated their supernatural power through the unimpeachably Christian method of performing miracles, usually those which improved the human condition, for example by healing. The point of writing about them was to reveal their holiness, and it was in that context that apparently Christianising activities should be read. His anonymous hagiographer could write of St Audoin that
strengthened in the practice of his faith, with the Lord as protector, he turned the most savage ferocity of the Franks into gentleness, and from the holy font he so tempered them with the sweetness of honey, and so consecrated his parishes with the divine practice, that they abandoned the rite of the heathen and voluntarily placed themselves under the yoke of Christ and their necks under his service.
But he tells us this immediately after relating Audoin's consecration as bishop of Rouen. Seen in the light of Gregory of Tours's descriptions, from a hundred years previously, of a highly Christianised Merovingian Gaul, we are forced to read this passage as describing what its author thought a bishop – especially the ideal, or the best, bishop – _ought_ to do.
Audoin's position as a bishop in fact indicates where the priorities of historians diverge from those of hagiographers. Audoin was a particularly important bishop less because of his miracles than because he had been a prominent, high-born and powerful aristocrat before he became a cleric. His career neatly demonstrates the extent to which the history of Christianity throughout western Europe in the seventh century can be sketched as the history of bishops and their dioceses: the delineation of their extent, and their powers. Audoin's elevation to the see of Rouen was a reward for royal service and a mark of his membership of the Frankish ruling class at least as much as a sign of his holiness, although in his case it was probably also that. These earlier associations with the kingship and aristocracy may have lain behind his foundation of no fewer than four important monasteries, but the fact that when he moved across into the clerical profession it was more or less immediately into a bishopric nonetheless indicates the dominance of that office within the clerical hierarchy, as well as the importance of this institutional aspect of the wider Christian community. It is perhaps not surprising, given the relatively systematic nature of the Anglo-Saxons' Christianisation, that the episcopal office and diocesan structure were among their chief concerns, as they gradually turned in the seventh century to a Christianity that was partly inherited from their British predecessors, but received more concretely, and more or less simultaneously, from the Irish, Roman and Frankish churches. Differences between the organisation of these latter explains the century-long controversy in England over Christian structures and the powers of bishops, which reached its culmination with the career of the argumentative bishop Wilfrid of York, whose power provoked opposition from both kings and fellow bishops. Wilfrid's mistake, it has been argued, was to aspire to be, and to behave like, a bishop of Frankish Gaul. That is, he was an extensive landowner who aspired to control every aspect of Christian life in his diocese (the extent of which was, in any case, a major cause of dispute): in particular, he combined his episcopal role with being head of monastic communities at Ripon and Hexham. In fact, the complexion of Wilfrid's Christian leadership, while it found some parallels in the kingdom of the Franks, was coloured even more intensely by the special circumstances of the early Anglo-Saxon Church, which left him the only bishop in the Northumbrian kingdom, a prominent monastic leader, and a significant influence elsewhere. Wilfrid lacked the local saints – earlier bishops and martyrs – whose cults were an important adjunct of Frankish bishops' power. He himself became such a figure after his death, though for centuries his cult was strictly limited, especially to his foundations at Ripon and Oundle. Rather, he had to channel his episcopal power through imported relics, and his biographer stresses the care he took on his visits to Rome to collect the remains of martyrs, and notes his particular devotion to the apostle Andrew, venerated at important sites in Rome. This is one witness among many of the significance widely attached to the tradition of Rome as a centre of early martyrdom.
Rome was more than a source of relics for Wilfrid; it was also the seat of the bishop of Rome – the pope – and Wilfrid's journeys there were above all quests for a source of authority as his unprecedented power as an ecclesiastical leader meant that he crossed swords with secular rulers. Deposed from his see of York in 678 by King Ecgfrith of Northumbria, Wilfrid appealed for reinstatement to the pope. It is hard to imagine a Frankish bishop doing the same. Although the pope's judgement in favour of Wilfrid was pointedly ignored by King Ecgfrith, the fact that it was thought worth making at all illustrates how the convergence of differently originating trends served to build up both the ideological and the administrative structures of the western Church. Pre-existing reverence for Rome as a centre of early Christianity in the west; recognition of the succession of its bishops from St Peter, the prince of the apostles (in an as yet loosely defined way); the Roman and papal roots of one of the currents that evangelised the Anglo-Saxons; the increasing emergence of ecclesiastical leaders on a par with each other and hesitating to submit to single secular authorities – as we shall see, all these circumstances led to more frequent recourse to the papacy as arbiter, the firming up of an administration built around bishops, and better-defined lines of authority.
#### _Creating Christians in northern Europe_
Wilfrid has traditionally been seen as a pioneer in 'mission' to the pagans. But behind this rhetorical status, it looks to have been his particular configuration of episcopal power, and his insistence on lines of authority culminating in St Peter, that were his most important contributions to future generations of Christianisers. His 'mission' was really a chance by-product of his first journey to Rome. According to his biographer Stephen of Ripon, political circumstances forced him away from the shortest route across the Channel, and towards the land of the Frisians instead. There he 'preached the word of God daily to the people', so that 'with a few exceptions all the chiefs were baptised by him in the name of the Lord, as well as many thousands of the common people'. In a slightly later account, Bede is if anything even keener to stress this aspect of Wilfrid's activity. But these tales clash rather abruptly with stories of continued, and quite strongly held, paganism among the Frisians in the next generation. Wilfrid's impromptu 'mission' turned out to be the first of many attempts by Anglo-Saxons to make new Christians on the continent, and as such looks to have been rather less deliberate or successful than writers with their own missionising agendas would suggest.
Reports of active paganism among the Frisians arise in connection with the figure of Willibrord, himself formerly a member of Wilfrid's monastery at Ripon. On Wilfrid's fall in 678 Willibrord had gone to Ireland, to a monastery established by another Englishman, Ecgberht, who, according to Bede, wished to travel to the continent to try to convert peoples from whom he knew that the Anglo-Saxons derived their origin. Prevented from doing this himself, and after false starts by others, he sent Willibrord, who first won the support of the Frankish mayor of the palace Pippin II, and then went to Rome 'in order to begin the missionary task he wished to undertake with the pope's permission and approval'. Willibrord's mission to the Frisians encountered some serious obstacles, to judge by the account of his biographer Alcuin, writing some hundred years later. Alcuin was evidently keen to create an impression of obdurate Frisian pagans, who proved ultimately unmoved by Willibrord's teaching. This image of strong Frisian paganism is painted too in another hagiography, the _Life_ of Bishop Wulfram of Sens, written in response to Alcuin's _Life_ of Willibrord and set in the same period as the latter's career. It describes contemporary Frankish efforts to Christianise in Frisia, directed from the monastery of St Wandrille, and stresses that their success depended not, as in Alcuin's narrative, on a preaching 'mission', but on miracles. These, it suggests, were a more reliable method of counter-acting non-Christian religious feeling which, while not as coherent as Christianity, may have become more solid under threat from it. It seems likely, in fact, that the first Frisians to adopt Christianity did so in Francia, and Willibrord certainly enjoyed more success where the writ of the Frankish rulers ran. There 'many began in their zeal for the faith to make over to the man of God their hereditary properties'. Among them were Pippin himself, and members of his own family, one of whom founded the monastery of Echternach, and gave it over to Willibrord as its first abbot. With this secure base well within the Frankish heartland, Willibrord attracted patronage from far afield, including from landowners who may have been inimical to, or at best neutral towards, the Pippinids. He did so because he was able to act as an honest broker, a figure who rose above the petty and competing interests in orbit around late Merovingian kingship.
The notion among some Anglo-Saxons of 'mission' to pagans on the continent cannot simply be dismissed as a chimaera, however, especially in the light of what we know about the man usually seen as Willibrord's successor in his 'mission field', Boniface. Originally called Wynfreth, he journeyed first from Wessex to Frisia in 716, but found himself in the middle of a war between Charles Martel and the Frisian leader Radbod and quickly returned home. He set off for a second time in 718 and this time went to Rome, where he was given the name Boniface (Latin: _Bonifatius_ ) and commissioned by the pope to 'go forth with His [i.e. God's] guidance to those peoples who are still in the bonds of infidelity'. The pope specifically mentioned 'the work of beneficial preaching'. At first this was undertaken alongside Willibrord, who had been given the former Roman fortress at Utrecht as his see by Pippin II, and consecrated archbishop of the Frisians by Pope Sergius I. But Boniface felt called to strike out on his own and in 721 went to Hesse, where, according to his biographer Willibald, he encountered the local rulers, 'two twin brothers named Dettic and Devrulf, whom he converted from the sacrilegious worship of idols which was practised under the cloak of Christianity'. Though these words suggest syncretism (the juxtaposition of different or opposing religious practices), Willibald is also happy to call their religion straightforward 'paganism'; he credits Boniface with much success in turning these people to Christianity. In 722 Boniface returned to Rome to receive consecration as a bishop, with no fixed see: the pope's letter of introduction mentions vaguely 'some peoples in the regions of Germany and on the eastern side of the Rhine'.
Willibald goes on to credit Boniface with successful evangelisation further into Hesse – where he felled a great oak dedicated, in an apparent example of _interpretatio romana_ , to Jupiter – and in Thuringia. Throughout this region Boniface, from 732 invested with the authority to consecrate other bishops, also founded monasteries at Ohrdruf, Fritzlar, Tauberbischofsheim, Ochsenfurt and Kitzingen. Fleeting military success by Charles Martel against the Saxons even raised in him the hope, attested in his letters, that he might extend his mission into their lands. But the tide of war flowed back in the Saxons' favour and he journeyed instead to Bavaria, to whose Christian community Willibald credits him with bringing both organisation and doctrinal orthodoxy. Returning to Hesse, in 742 Boniface was able to establish what proved to be his most important monastic foundation, at Fulda, thanks to a gift from Charles Martel's son Carloman. In that year also he could write to Pope Zacharias to announce his creation of three new dioceses in central Germany, at Würzburg, Erfurt (soon transferred to Eichstätt) and Buraburg. Finally receiving a settled see at Mainz in 746, he used it to lay claim to the legacy of Willibrord: he appointed a bishop to the see of Utrecht, and made plans himself to take a campaign of preaching far into northern Frisia. There, on 5 June 754, his party was attacked and Boniface killed along with many companions.
The reaction to Boniface's death, which quickly came to be treated as a martyrdom, demonstrates the breadth of his influence. It was soon commemorated far and wide: in annals in Northumbria, and in the prayers of the monks of Monte Cassino in southern Italy (joined in confraternity with the monks of Fulda). But his impact continued to be felt most deeply in and around his mission field, through the band of enthusiastic architects of an organised Church among his disciples. His designated successor was Lull, who became archbishop of Mainz. Others of his followers succeeded to the abbacy of Fulda and the bishopric of Utrecht. Each furthered Boniface's work in their own area, but this inevitable fragmentation of his legacy also led to tensions, not least over his own remains. Hagiographical texts written some years later point to disagreement over where the saint should be laid to rest. Mainz, Fulda and Utrecht each had good reason to want to be the centre of the cult of the immediately sainted missionary hero, not least because of the patronage it might bring for their institution. But the contest also partly reflected the differing priorities of some of Boniface's heirs. While Lull was concerned with his place, as archbishop, in the emerging Church hierarchy, and so was seeking to bolster his archiepiscopal church at Mainz, at Fulda the priority was to build the most successful monastic community east of the Rhine. Boniface was therefore portrayed there as first and foremost a monk and monastic founder: missionising was not high on the agenda at Fulda.
England continued to provide personnel and materials to support the new continental churches. In letters to English contacts both Boniface and Lull requested books. People, too, continued to come. Like Willibrord before him, from Northumbria came Willehad, who about 770 began to work among the Frisians. It was here, more than anywhere else, that the earlier English churchmen's sense of mission – of deliberately seeking the conversion of non-Christians – would be taken forward by their successors. This is especially evident in the career of Liudger, himself from a family of Frisian converts to Christianity, who was sent to reinforce the Christian Church first in eastern Frisia and then, by Charlemagne himself, across the river Lauwers in Saxon Westphalia, where his work inevitably became entangled in the Frankish–Saxon contest. Though forced to withdraw by Saxon attacks in the late 770s, he eventually established in that territory both a bishopric, at Münster, and a monastery, at Werden. Dependence on Frankish military power was constantly evident: when Liudger ventured from his Frisian base at Deventer to smash pagan shrines, he gave two-thirds of their treasure to Charlemagne: this, surely, was the _quid pro quo_ for the force, or threat of it, that allowed Liudger so brusquely to overturn traditional Frisian religion. Hagiographers wove into their stories of Christian heroism the Frankish campaigns against the Saxons that began in 772: another English evangeliser, Leofwine (known as Lebuin), stepped boldly into an assembly of Saxons to warn them that if they were unwilling to accept Christianity 'there is a king in a neighbouring country who will invade your land, who will despoil and lay waste, will tire you out with his campaigns, scatter you in exile, dispossess or kill you... ' Writing in the mid-ninth century, the _Life_ 's author knew perfectly well how accurate this prophecy would prove. In between the Franks' military activities among the Saxons and their legal attempts to impose Christianity, the job of evangelisers was less that of winning hearts and minds and more of building in bricks and mortar. Liudger built a monastery and episcopal seat at Münster, Willehad a cathedral at Bremen, Charlemagne himself one at Paderborn. These were the foundations for a Christianity in Saxony, which by the tenth century was among the most vibrant in Europe.
As we have seen, however, our sources for this apparently triumphant progress have their shortcomings. Where their descriptions of organised paganism turn out to be unreliable, or their references to real preaching missions frustratingly scant, we can question the black-and-white narrative of Christian victory over paganism. These texts were not, after all, of a kind intended to give an objective view of religious life in western Europe. They were predominantly hagiographies, meant to vindicate the claims to sanctity of their subjects. Willibrord's slaughtering of the sacred cattle of Fosite and Boniface's felling of the oak of Jupiter are portrayed as miraculous, and the miracle lay in the fact that they were allowed to get away with such deeds in what their hagiographers were keen to stress were viperous nests of pagans. But these interpretative problems are not limited to saints' _Lives_. Letters in the Boniface collection could misrepresent the situation in Germany, exaggerating the robustness of paganism, or other difficulties faced: Fulda was not, as Boniface claimed in a letter to Pope Zacharias, 'in the midst of a vast wilderness'. A related point is that the Anglo-Saxon 'missionaries' belonged to a limited network of prominent religious. As Alcuin said himself, he was in fact related to Willibrord, as was the man for whom he wrote his biography, Willibrord's successor-but-one as abbot of Echternach, Beornrad. Boniface received close support not only from his blood relative Leoba, who became abbess of Tauberbischofsheim, but from others with whom he corresponded: his old diocesan bishop Daniel of Winchester; a Mercian network that included his successor Lull and the bishop of Würzburg Burchard; and a number of abbesses and nuns in England. These interconnections remind us that early medieval societies worked and interacted most often on personal levels. They also suggest that the rhetoric of 'mission' was not the only, or even the dominant, motivation for travel to the continent. It often looks more like a social and family enterprise, which reinforces the impression that expectations of bold encounters with inveterate pagans quickly gave way to the more prosaic business of the assimilation of immigrants: 'far more had been achieved by the Frankish clergy than Boniface and his compatriots realised when they set out'. The notion of 'mission' was at least as much about the English as about the continental situation, for it was born out of the very particular circumstances of the English conversion: the deliberate 'mission', we might almost say 'embassy', despatched to King Æthelberht by Pope Gregory, and its subsequent spread in like manner to other kings. Subsequent generations owe this reconstruction in particular to one man, Bede. Writing while Willibrord was still alive, and Boniface was at his most active, Bede saw these enterprises through the intellectual prism he had constructed, using materials above all from Canterbury, over a lifetime's work at the monastery at Jarrow which he never left as an adult.
We need also to take account of the evidence for what we might call the background noise of religious life in the seventh to ninth centuries. Some of it points to paganism, avowed as such, present in the heart of the Frankish kingdom: in the Merovingian era St Amandus cured a woman of blindness by making her cut down the tree where she had venerated an idol. On the other hand, there was the behaviour of which Boniface complained in letters to the pope, of fornicators and drunkards among the Frankish priesthood, and even among the bishops, of prelates who hunted, and entered into bloodfeuds, and of pagan revelries practised (and here, it seems, his tact wholly deserted him) even in the heart of Rome, 'in the neighbourhood of St Peter's'. Somewhere between the apparently pagan practices which his biographer has Amandus combat in the Frankish heartland of the 640s, and the earthily secular behaviour of the Frankish bishops of the mid-eighth century condemned by Boniface, there was room for practices that were neither transparently non-Christian nor obviously contrary to the ancient rules of the institutional Church. Rather, they arose through interpreting Christian precepts in singular, unconventional ways. We know, for example, that in parts of England in the eighth century people were taking their communion wine not from a special, ecclesiastically sanctioned vessel, but from an ordinary drinking-horn: an English Church council condemned them for doing so. Similarly, Charlemagne complained that many had adopted the Christian practice of lifting a child from the baptismal font, without having the basic Christian knowledge – of the Lord's Prayer, for example, and the Creed – that was expected of properly Christian godparents. What these examples indicate is that Christianisation constituted a spectrum of activities. Combating a 'pagan' religion might be one of them, though there are question marks against even our most detailed depictions of these (such as in the _Life_ of Willibrord). Very often, though, the Church must have been filling a vacuum, where nothing nearly as sophisticated, in spiritual and theological terms, had existed before its arrival. Indeed, where no organised, institutionalised pagan religion existed, Church promoters may have felt the need to invent the appearance of one, in comparison with which Christianity would look a more coherent spiritual proposition.
The problem appears especially starkly in the case of the Frankish encounters with the Avars and the Saxons. In Charlemagne's reign these were, as we have seen, decidedly violent. But both peoples had in fact had long contact with the Franks and experience of their Christian religion: archaeology reveals thriving Frankish–Saxon commerce, for instance. Frankish churchmen worried not that Christianity was entirely alien to their foes, but that they understood it incompletely, or practised it poorly. Hence, the conquest of the Avar kingdom in 796 was the occasion for an exceptional meeting of Frankish bishops on the banks of the Danube, where correct practices, and baptism in particular, dominated discussion; and Alcuin, in letters to his friend Arno, bishop of Salzburg, and to Charlemagne, argued in favour of preaching and baptism as the right way to deal with both the Avars and the Saxons. Revolts of both peoples were due to 'negligence' on the Franks' part. However, these recommendations, which recognised the complexities of belief on and across the Frankish frontier, had minimal practical effect on Frankish activity there, where the concern was above all military subjugation. Carolingian reports of these wars tend to by-pass the conciliatory concerns of the leading ecclesiastics, detailing slaughter by the Franks, and equating the Saxons' stubbornness directly with their paganism. After another 'revolt' – or continued resistance to conquest – even Alcuin questioned the point of 'toiling over the accursed tribe of the Saxons'. As we have seen, the baptismal formula that the Franks imposed on the Saxons stressed renunciation of the old gods. But the suspicion remains that this image of paganism attests a Frankish desire for self-justification as much as a real, deep-rooted, non-Christian religion.
The repeated injunctions of kings and ecclesiastics against them are sufficient testimony that across the Carolingian world practices unsanctioned by the ecclesiastical hierarchy never disappeared. To counteract them, the process of Christianisation put stress on outward activities, on the rituals and symbols that made religious change visible. We should not think that this emphasis detracted from or excluded deepening inward understanding of the Christian message. Moreover, both ritual and word may often have been less important in the process of initial conversion than social and political bonds, but both worked in harness, miracle and message together, in deepening the Christian experience thereafter. Nevertheless, the concern to define, interpret and standardise rituals, which we will see most pertinently in the case of the eucharist, related problematically to the fundamental message that the more sophisticated Christian thinkers wanted to project: that Christian belief involved not simply the performance of ritual practices, but wholesale self-improvement. The goal was certainty of salvation, reached through moral 'perfection'. The right rituals might help, but the target remained dauntingly challenging, and naturally gave rise to the language of negativity and complaint about the moral state of this world that we have seen in Archbishop Hincmar's letter. Some in this world were so imperfect that they could be characterised as 'non-Christians'; others, selfprofessed Christians, were still nothing like perfect enough. What stood in the way of perfection in this world, and so guaranteed continuing pessimism about it, was, in a word, sin.
#### THE PROBLEM OF SIN
Hincmar's apparent anxiety about non-Christian practices among Carolingian courtiers masks his deeper concern for the sins of particular individuals: the incestuous sodomy, resulting in abortion ( _sic_ ), of which Lothar II's queen Theutberga was accused, and the adultery of the king himself. Theutberga's enemies could point both to her sins themselves and to the penance required for her absolution – her confinement to a nunnery – as making her unfit to be a wife and queen, while the other side could allege that Lothar had transgressed the morality required of a Christian king. Paganism existed in Hincmar's world less as a reality than as an image in which to cast a preoccupation with the human moral failings which stood between the believer and heaven. This concern was a vital pulse, impeccably Christian, yet so basic and insistent as to be almost subconscious among Christians of Hincmar's generation. Christianity's central teaching was to tackle sins in this world by appealing to the next: Jesus had taken the sins of humanity to the cross, and in his resurrection offered the prospect of redemption for them, in a life of bliss after death. This message therefore focussed the attention of Christians on sin and death together.
#### _Christian death and giving to the Church_
By 700, Christianity was already beginning to influence the treatment of the dead. Between c.400 and c.700, many across western Europe deposited in their burials goods ranging from pots to swords alongside the corpses of their dead, earning the gratitude of modern archaeologists for the invaluable insights into their society's material culture that they thus provided. The gradual disappearance of this practice from c.700 cannot be taken as direct evidence for the Christianisation of the act of burial, however: Christian writers had not complained about the practice, and some excavated graves contain distinctly Christian artefacts (for example, votive crosses), while other furnished burials are found in churches. Rather, it is a sign of a change in a variety of social actions that accompanied death. In some places, old strictures about the location of burials broke down as families began to bring clergymen into the burial process. Everywhere, lavish deposition rituals which had affirmed the status and wealth of the deceased clashed against an increasing recognition of the need to help the inevitably sinful souls of the dead after death. Families continued to spend publicly on their dead, but rather than displaying their wealth at the point of inhumation by ostentatiously furnishing graves, they were encouraged to sponsor the rituals that Christian belief increasingly emphasised as effective remedies for the soul's sinful condition Chief among these was the mass – the reenactment, enjoined apparently by Christ himself, of the Last Supper, which immediately became a commemoration of his sacrifice. The mass would gradually acquire a great weight of meaning, as it came to be regarded as a miracle, a daily instance of divine power working in the world, and we will see shortly how and when this came about. Its development in the early Christian centuries was evidently a response to the centrality of sacrifice in some sense to nearly all religions at that time. But it also developed as part of a wider body of liturgical practices, in particular of prayers, which emerged as the Church deepened its involvement with everyday society. Eloquent testimony to the importance of these practices in the Christianising societies of the post-Roman west is provided by some of the many hundreds of single-sheet documents (charters) on which much legal business, especially transactions of all kinds, was set down. The ones that survive mostly concern ecclesiastical institutions, because they themselves lasted often through many generations, and so were best able to preserve documents down the centuries.
One such institution was the monastery of St Bartholomew, built in Pistoia in Lombard northern Tuscany in the early eighth century, and the recipient of a smaller monastery of Sts Peter, Paul and Anastasius from the latter's founder, Ratpert. He had established it with an endowment of half of his property in a charter of 748. In this document we can detect the voice of Ratpert himself, standing at the scribe's shoulder, instructing the monastery's abbot
to pray day and night to almighty God and to Mary, the mother of the same almighty God, and to the most blessed saints Peter, Paul and Anastasius, in whose honour the church is founded, for my soul and for the heavy burden of my sins, so that I, a great sinner, may be worthy to break the chains of my punishments...
Ratpert's evident anxiety arose in part from the grave illness from which he was then suffering. In his case, endowing ecclesiastical institutions was relatively uncomplicated because he had no sons, and even required that his female relatives – mother, wife, sister and daughter – take up a monastic life in the new foundation or forfeit any right to enjoy the family property. When male heirs existed account had to be taken of their rights to inherit – and when our charters record disputes in this period, they very often involved lay heirs trying to vindicate claims to properties that churches and monasteries had or claimed through gifts of their owners. But such problems did not deter patronage of the Church: we have only to look at St Bartholomew's itself for an example of a patron transmitting property to an institution in addition to, rather than instead of, a bequest to his son. It had been established by the long-standing royal doctor Gaidoald, who even stipulated that his son and later heirs should defend the monastery in any dispute and ensure that its property was not diminished; property which, it is worth underlining, would have passed to the son himself had the monastery not been established. Gaidoald, it seems, was engaging in a common practice, 'using the end of life as a pretext for arranging relations during life'.
Gaidoald, like Ratpert, was endowing monks 'who by their works offer alms and do not cease to pray to the Lord day and night for our sins'. Theirs were acts and attitudes by no means confined to Lombard Italy, but found across the Christianising west. Charters from the mid-eighth century like these represent the culmination of important stages in the development of a distinctively Christian and distinctly post-Roman western culture. Spreading from the British Isles was the notion that individual sins could be atoned for by precisely calibrated penances usually in the form of periods of prayer and fasting. Sins and their requisite penances were set out in detailed tariffs – penitentials – that first emerged in Ireland in the sixth century. From there in the seventh century they spread along with peregrine Irish monks to England and to Francia. In the latter in particular, these individual or 'secret' penances, as they were sometimes called, sat comfortably next to the liturgical practices of communities of monks, who were seen as specialist purveyors of activities for purging the soul – their monasteries were 'powerhouses of prayer', in Peter Brown's vivid phrase. Everywhere, establishing these institutions chimed with a culture routinely animated by donation and counter-donation. Making over one's property to communities of monks and nuns prompted the reciprocal gift of their expertise for atonement, honed for themselves, but offered also to others – to material patrons, to distant kings, to 'ordinary' lay associates. By the ninth century, many monasteries had 'books of commemoration' ( _libri memoriales_ ) recording the names of those for whom the monks prayed, which they could not recite individually since they now ran into thousands. Individual penance, monastic prayer and patronage of the Church had been coalescing throughout the post-Roman period in the west. By the eighth century they had integrated to produce a culture in which pious gifts were commonplace.
In his charter, the ailing Ratpert makes clear enough his pressing concern with 'the heavy burden of my sins' and suggests a belief that prayer could help to wash it away. But behind that concept lay a number of tensions, the resolution of which remained at the centre of debate among Christians for centuries – up to, and indeed beyond, the Reformation. One of these is evident if we look at particular passages in charters like that of Ratpert just quoted (a passage called a proem or _arenga_ , which set down the motives for the legal act embodied in the charter). While some express a certainty that a pious gift would result in definite benefits to the soul, others acknowledge the need to have in addition the mercy or grace of God: 'certainty' faded into 'hope'. This ambiguity, still at the heart of Christian doctrine, can be traced back at least to the pre-eminent western theologian of earlier centuries, St Augustine, bishop of Hippo, who in the early fifth century taught that human sin was ultimately ineradicable because of Adam and Eve's original sin in Eden, but affirmed nonetheless that penances were a necessary part of human life, so that what he called the 'minor' sins ( _peccata levia_ ) of an individual could and should be atoned for through such daily penances as prayer and almsgiving. The tension between this view and the rather less nuanced idea behind 'tariffed' penances that were thought to wash away carefully enumerated sins was not one on which early medieval Christians generally chose to dwell, however. Augustine had focussed their attention rather on the notion that the process of cleansing the stain of minor sins crossed the threshold of death; 'the geography of the hereafter' became of central concern to Christians as they continued to atone for sin beyond the grave. With hindsight, this is an idea that points directly to purgatory, although the absence of the term itself until the twelfth century has made it hard to trace its development as a coherent doctrine. Before the seventh century, in the works of figures like Augustine, the emphasis was on intercession on behalf of believers' souls by an emperor-like God mercifully disposed to amnesty, or by the great heroes of Christianity who had direct access to him – the saints. But in the seventh century there developed a more practical, hands-on approach to individual salvation, which happened in conjunction with the first signs of interest in what the after-life might actually look like. In tales that began to be told of the soul's voyage after death, souls eternally damned and those temporally purged mingled in the same space: in his terrifying Vision, the flames of an unpurged sinner burnt the cheek of the Irishman Fursa, while in a similar text angels and demons contested the soul of the Frankish aristocrat Barontus.
As Christian belief absorbed and disseminated these terrible possibilities, Christians were increasingly prompted to make provision in their lifetime for the good of their own souls, and of those of their families, encouraged by the idea that sins could still be purged, and divine mercy appealed to, even after death. Hence in the seventh, and increasingly through the eighth, century, a rising tide of gifts to churches and monasteries – property, people and possessions, intended to sponsor the prayers of priests, monks and nuns – effected a massive transfer of wealth to Church institutions. Later in the Middle Ages, the salvific benefit of such prayers would be quantified on an individual basis, each 'unit' of intercession measuring with scholastic determination a specific subtraction from the soul's spell in purgatory. But at this stage the sponsorship of prayer was neither so organised nor so institutionalised. Family and monastery were not distinct entities, and indeed overlapped to the point of identity in cases such as Ratpert's own foundation in Pistoia. In larger monastic houses, monks and nuns were drawn from numbers of different sponsoring families, but the gifts of each were made less for the discrete benefit of a specific individual than to bind each family to a community whose penitential activities benefited their entire collection of patrons – their _familia_ , in the contemporary Latin.
The complications of the relationship between families and the monasteries they sponsored are evident in the case of the abbey of Lorsch, founded by Cancor under the influence of his kinsman Chrodegang, his era's most creative shaper of the religious life (see Figure 4a). By 772, its ownership was the subject of a dispute, submitted to Charlemagne's judgement in Easter of that year, between Cancor's son Heimerich and his kinsman, the then abbot Guntland. Cancor's death late in 771 had provoked the tussle, but what provided Guntland with the opportunity to win it was the death around the same time of Carloman, who until that time had divided rule over the Frankish realm with his brother Charlemagne. At this particular juncture, the dispute over Lorsch offered Charlemagne the opportunity to assert his authority over a religious institution, and by extension over a family that had formerly maintained a careful equidistance between himself and his brother; equally, Guntland's success depended on his ability to make real the prospect of Charlemagne's control. It is no surprise, then, that when Charlemagne duly ruled in Guntland's favour and against Heimerich, the abbot immediately placed Lorsch under royal protection, turning it into what Carolingian historians tend to call a 'royal monastery'. We are fortunate that the details of this case have survived, because it demonstrates how a family's beliefs were made concrete by the establishment and patronage of an institution, and how that institution was inescapably bound to the world that had created it.
**Figure 4a.** Abbey of Lorsch, Germany, gatehouse. Lorsch was patronised by several kings, and two – Louis the German (d.876) and his son Louis the Younger (d.882) – were buried there. The gatehouse was probably built in the time of the latter.
#### _The objects of patronage: masses, priests and monks_
This connection between abbey and aristocracy demonstrates an essential paradox at the heart of the monastic enterprise. Monasticism had arisen out of the belief, not unique to Christianity, which identified virtue, and ultimately the purification or perfection of the soul, with the rejection of all things associated with 'the world': material wealth, power over fellow men, the concupiscence of the flesh. For Christians, who drew on the New Testament's repeated emphasis on self-denial, to pursue the ascetic ideal of renunciation was to seek to imitate in some way the sacrificial life of Christ. Monasticism was the conduct of such asceticism communally (as that of the disciples in Jerusalem after the resurrection), rather than as a hermit. But since monks and nuns were themselves drawn from 'the world' and depended upon it for sustenance, and since that world recognised, and wanted to harness, the spiritual power of these ascetics, they could never break entirely free from it. Monastic practitioners therefore faced the inescapable problem of what degree of compromise with the material world was acceptable. The battle to keep the world out of the monastery required that monks and nuns keep in mind constantly the need for reform: both on a personal level – reform of the individual's lifestyle and soul – and on that of the institution – reform of the practices of the monastery and of its personnel. And what was good for monasticism was good for the Christian Church generally: the ever-present nagging fear of compromise engendered pressure for reform; and though ever-present, in historical terms that pressure for reform has ebbed and flowed.
Enthusiasm for reforming religious life drew on the basic notion that the activities that were most effective for the good of the soul were those performed by the purest actors, least blemished by the world of sin. Attention to the activities of the clergy, monastic and secular, grew only slowly, and the eighth century was still a period in which the prayers that they offered took many forms. In the charters quoted above, neither Ratpert nor Gaidoald was especially precise about the form of the prayers they were sponsoring. Prayers were of course incorporated into the service of the mass, and many donations similar to those of these Italian benefactors were made 'for the mass and for lights' ( _pro missa et luminaria):_ the expense of illuminating churches was a central concern of patronage. Already in the Merovingian period in Francia, the mass, as high point of the liturgy, was also becoming the convergence point for the ideas of commemoration and of gift that we have just noted. What had once been seen as a ritual re-enactment of the Last Supper was therefore itself coming to be thought of as a gift to God, or even as a sacrifice, if in symbolic form: it was a particularly privileged form of that mediation between man and God that was the common concern of Augustine, Fursa, Barontus and Ratpert. As such, and as writers of the ninth century emphasised, it reaffirmed the identity of every Christian within the community of the faithful.
By the ninth century, the centrality of the mass to the efficacy of Christian practice, the daily experience of it by legions of priests and monks, and the increased production of liturgical texts that this necessitated, led many scholars to explore what the mystery of the eucharist signified, and what exactly was the nature of the 'miracle' that it enacted. The abbey of Corbie in northern Neustria emerged as a centre of the lively debates that sometimes ensued. (Although nothing from this era survives at Corbie, Figure 4b shows the Carolingian _Westwerk_ of its daughter house of Korvey in Germany.) There at the end of the eighth century an anonymous monk had set down an apparently straightforward perception of the mass:
For what reasons is the mass celebrated? For many reasons. First so that they may frequently address the Lord. Second, so that God may receive prayers and offerings. Third, for offerants and for the dead. Fourth, for the kiss of peace. Fifth, so that the offering may be sanctified. Sixth, so that the offering may be confirmed through the Holy Spirit in the body and blood of Christ. Seventh, so that the Our Father may be sung...
But this sixth reason, in particular, proved in fact to be very problematic: the question of the 'real presence' in the eucharist – that is, in what sense the bread and wine are, or become, or represent, the body and blood of Jesus – has been in contention in Christianity ever since; but a heightened concern for it in the eighth and ninth centuries must be seen as a direct response to the mass's emerging importance at the centre of Christian ritual. Thus in 844 Corbie's then abbot, Paschasius Radbertus, stepped into the debate by sending to Charles the Bald a detailed work in which he averred that in the eucharist 'Christ's real flesh and blood is truly created'. His claims were countered by a monk of his own monastery, Ratramnus, who argued that he had taken too literal an interpretation of the Last Supper. Ratramnus preferred to see the sacraments as visible words, distinct from the matter that they signified. Similar arguments unfolded at Lyon in response to the ideas of Amalarius of Metz. Amalarius had put forward detailed allegorical explanations for every part of the liturgy, including the eucharist, and attempted to implement his resulting scheme for new liturgical practice in the episcopal church at Lyon when, between 835 and 837, he replaced the exiled archbishop Agobard. Agobard and his deacon Florus both responded with vigorously critical works, and Amalarius was hauled before a synod at Quierzy in 838 and his opinions condemned as heretical.
**Figure 4b.** Abbey of Korvey, Germany, _Westwerk_.
Anxiety in the Amalarius affair focussed around the effect his ideas might have on the priesthood. Most priests were not members of the highly educated circle among whom texts like Amalarius's circulated. Growing emphasis on the mass cast steadily more insistent attention on the office of priest, for only he could dispense the sacraments. This task, it was increasingly felt, demanded a certain moral purity on the part of the celebrant, and this only added to a list of requirements for priests that lengthened through our period as the Church became better defined as an institution. It is very hard to discover much about the range of Christian and Christianising activities that come under the heading of 'pastoral care' in the years around 700: we know very little about who precisely dispensed communion, administered baptisms and officiated at funerals in the early eighth century – and, with exceptions, about where they did so. Rural churches and their accompanying priests do appear sometimes in donations of landed estates to monasteries. In Italy, for instance, where Christianity was relatively deeply embedded, the abbey of Farfa received in this manner at least sixteen churches during the eighth century. This at least indicates that alongside the existence of proprietary monasteries ( _Eigenklöster_ ) we need to posit that of proprietary churches ( _Eigenkirche_ ) – in other words, institutions effectively owned by powerful churches or aristocrats. But it is not clear whether these ever extended their functions much beyond those of family chapel and/or the commemoration of a saint's cult.
Although texts relating to priests gradually increase through our period, they were mostly produced by their superiors. The Carolingian kings' capitulary legislation envisaged that the collectivity of priests within a diocese would be formally subordinate to the bishop, and slightly later indicated to bishops their responsibility for educating priests in their duty of care over their flock. Structurally, though, the Church was still rudimentary. In the Carolingian empire the only definite units of ecclesiastical administration were the 180 episcopal sees, which nearly all followed boundaries of the now long-departed Roman secular administrative structure. These were being grouped into metropolitan archbishoprics following the pattern established for the English Church and brought to the continent by English evangelisers. A formal structure of parishes did not appear until the tenth century or, mostly, even later. Priests themselves were very far from a uniform group. Some might be rural representatives of the communities of canons that came into being around many episcopal cathedrals in the eighth and ninth centuries. Priestly office could also be held by professed monks, either inmates of the great houses that large-scale patronage had created, or from the many small _cella_ – some of them, as we have seen, essentially family owned – that dotted parts of western Europe. The latter were mostly in the same position as the priests of the proprietary churches ( _Eigenkirche_ ) that we have already noted, beholden to their lords and receiving from them, perhaps, only a portion of the income that their church received through the tithe. The involvement of lay lords and great abbots meant that leadership of this motley group was still contested. Those who asserted it most explicitly were the bishops, who at the same time set out the ideals to which they hoped priests would aspire, in _capitula episcoporum_ – directives sent by bishops to the clergy of their dioceses. Priests worthy of the 'blessed people' of the Franks should have clean hands when they administered the sacraments, unpolluted by sex and violence; they should be distinguished, socially and hierarchically, from their flock and, as a corollary, freed from economic dependence on any secular lord; and they should be literate, and in possession of the texts needed to do their job. Although it took centuries for the western Church's priesthood even to come close to fulfilling the first of these requirements, its persistence is striking. The insistence on clerical celibacy was one sign among many that the preoccupations of the monastery – of personal holiness, of living according to a Christian code of morality – were invading the world of secular priests. Who those priests were is not easy to discern, but efforts to ensure their economic self-sufficiency were an early preoccupation of the Carolingians, with Pippin III's measures to enforce the payment of tithe for the upkeep of priests. As for the literate capabilities of the priesthood, two surviving manuscript codices that were evidently used as handbooks by rural priests give an encouraging picture of a priesthood that both knew and regularly used canon law and the standard liturgies, though both seem to have originated in the Carolingian heartland, where we might expect closest conformity to the ideal. Manuscript illustrations, too, may have been designed partly with the education of priests in mind. (See Figure 5.)
The prescriptiveness of so much of our evidence for priests generates a certain tension in the way we interpret it. When bishops set down in their _capitula_ the detailed canonical rules that they wanted priests to follow, does this indicate, as our two handbooks suggest, that those orders flowed out through a widespread network of educated, responsive Christian ministers? Or was it a case, more often, of a rarefied learned elite trying to impose its agenda on a haphazard patchwork of grudging and independent priests? Although the question has sometimes been posed in this starkly oppositional way, it should be pointed out that in a realm of the size that the Carolingians' had attained by the early ninth century, both scenarios, and most points on the spectrum between them, may have co-existed. Tension of a similar intensity is present too when we try to interpret the development of penance in this period. As we have seen, individual or 'secret' penance – the performance of specific numbers of fasts or prayers to atone for specific sins – grew on the continent in parallel with the sponsorship of intercessory prayers and masses. As with the mass, penance involved the priesthood materially, for only they could hear the confession and prescribe the correct penitential action. The evidence of penitential books, liturgies, and episcopal statutes, while ambiguous about the involvement of ordinary priests in the administration of penance, at least before the tenth century, does show a consistent aspiration to control it on the part of bishops. How far they actually did so, however, is moot: when we have bishops complaining about priests accepting money from those seeking to avoid penances, this could indicate that lay people either had fully absorbed the ideas behind penance, and were trying to manipulate them, or that they still found such rules alien and elitist. The ninth century's new concern to distinguish these more everyday 'secret' penitential activities from penances that were performed in public for sins committed in public certainly reveals how the notion was elaborated among the powerful. Louis the Pious experienced both the benefits and drawbacks of this development. As will be seen in Chapter 4, his penance in 822 was a means of reconciling discontents from a position of strength, casting himself in the role of a late Roman emperor, whereas that which he was forced to perform at Soissons in 833 risked endangering the entire political order, so severely did it humble the emperor. Royal penance, a subset of the penitential mentality that lasted throughout the Middle Ages, would never again threaten kingly status itself.
**Figure 5.** The Stuttgart Psalter, now Stuttgart, Württembergische Landesbibliothek, Bibl. fol. 23, but probably produced at the monastery of St-Germain-des-Prés _c_.820–30, includes on fol. 55r this illustration for Psalm 43:5: 'Why art thou cast down, O my soul?' David plays a cithara, a biblical instrument, while 'Anima' (soul) is personified on a hilltop, reflecting Carolingian Christianity's emphasis on measures that Christians could take to benefit their souls.
Uncertainties within the hierarchy of the secular clergy about their responsibilities and capabilities were mirrored in monastic communities. Here the main root of anxiety was the entanglement of monasteries and their patron families that we noted earlier.
In early-eighth-century Northumbria, Bede complained of 'laymen in charge of monks', founding so-called monasteries where they lived with their families like secular lords. Changes in the practice of monasticism in the course of the eighth century might be seen as in some measure responses to these worries. It is in this era that we get the first signs of a concern physically to segregate monks from secular society: in Lombard Italy, the duke of Spoleto specifically forbade women from walking near or approaching the abbey of Farfa; and monastic buildings increasingly included a _claustrum_ (cloister) – a secluded inner space accessible only to members of the community, and to a few privileged guests. In addition, greater attention began to be paid to the way of life of monks: their prayers would be effective only if they were rigorous in their pursuit of holiness for themselves. Moreover, increasing focus on the mass meant that growing numbers of monks sought ordination as priests: no prayer was more powerful than a votive mass, and the monks' asceticism was some sort of guarantee of the purity of the celebrant. This did not entirely disadvantage nunneries, whose virgin inmates retained a prized spiritual status. Another response was the institution of canons: clerics organised into a community, usually around a cathedral. The first rule for such canons was composed in 742 by Chrodegang, bishop of Metz and co-founder of Lorsch.
Gauging the motivation behind the patronage of monasteries is not as straightforward as the pious declarations of surviving charters suggest. We need to note, first, that these documents survive precisely because they benefited monasteries: only there would they be preserved down the centuries. So we are ignorant, for the most part, of how far this culture of gift-giving extended to other targets, and even to the non-religious. The earliest charters preserved by the monastery of Echternach were often addressed not to the institution, but to its abbot, Willibrord, who was also bishop of Utrecht. Evidently, patronage did not _have_ to be directed at a monastic institution. Secondly, these gifts very often had consequences other than the purely spiritual. Through such patronage, Lorsch became the most extensive landowner in the middle Rhine; Echternach was made the vehicle for drawing an entire local elite – that of Toxandria, the hazy, low-lying frontier zone between Franks and Frisians – into the Frankish orbit; Reichenau and St Gallen came to play pivotal roles in the extension of Carolingian power into Alemannia; and Farfa attained a crucial mediating position between the secular rulers of northern Italy and formerly Byzantine Rome. All these monasteries had been established at the end of the seventh or in the first decades of the eighth century, and all were by 800 more or less securely under Carolingian control. Many others found themselves in similarly politically and socially influential positions. (See Figure 6.) Landed patronage had turned them into powerful corporations, with substantial disposable wealth: lands that could be leased to secular lords, and had the potential to provide significant military retinues. The ability of the Carolingians yearly to collect an effective military force was based partly on their granting to military men as 'benefices' lands attached to monasteries under their control. What was good for the kings was good for the rest of the aristocracy, and even abbots themselves could be found granting monastic land in order to build a military retinue. Abbeys thus offered practical, military support as well as prayers for the soul as return gifts to their royal patrons: Louis the Pious had a list drawn up of these gifts, of all kinds.
**Figure 6.** Mosaic, apse of the chapel at Germigny-des-Prés, France, commissioned c.793 by Theodulf, bishop of Orléans, reflects both his response to Byzantine image veneration in his _Opus Caroli regis_ , and his beliefs about the eucharist. Angels gesture towards an empty ark of the covenant – no longer housing for the divine or exemplar of religious imagery – and below it, to the altar, where Christ was present in the eucharist.
**Figure 7.** Plan of St Gallen.
The political, economic, and cultural status of monasteries in the Carolingian age is underlined by the remarkable 'Plan of St Gallen'. (See Figure 7.) Now in the Monastic Library of St Gallen (Switzerland), the Plan was actually created at the monastery of Reichenau (in modern southern Germany) at some point between 819 and 826. It is drawn on five pieces of parchment stitched together, measuring 112 cm cm × 77.5 cm, and depicts the ground plan of a monastic complex, including scriptorium, dormitory, privy, laundry, refectory, kitchen, bake and brew houses, guest house, abbot's residence, and an infirmary. We cannot be certain why it was created, but the monastery's actual main church, built in the 830s, does not closely follow the design on the Plan; and in any case the Plan's overall complex could not have fitted into the actual site of St Gallen. We should therefore see the Plan not as a practical blueprint but as a generic image of the ideal monastery, at a time when monasteries' wealth made them sources of valuable economic and military, as well as spiritual, power.
How far such a position was desired or planned for on the part of the monasteries' lay benefactors is questionable. But it meant that control over them became a political issue of great significance. Many of these seventh- and eighth-century foundations, even if they had originally been established by a single aristocratic family, soon began to attract donations from others. In some cases these were families, perhaps of lower status or wealth, keen to associate themselves with the founding family, as seems to have been the case, for example, at Hornbach. In others, power relations between the various donors are far less clear. Monasteries could be used to pool the resources of local elites, or they could broker contests over wealth and influence between different families. They could also mediate between such elites and kings. Indeed, rulers had in their gift legal privileges, grants of immunity, that helped to strengthen many monasteries' institutional identity and in some cases to move them decisively away from the control of one family or faction. Beginning with the seventh-century Merovingians, kings could grant to an abbey freedom from tolls on its goods – like that which survives exempting St Denis, near Paris, from levies on the oil that was transported up from the south to light the church. They could go further and exclude their own officials from any jurisdiction over the buildings and lands of the monastery. Bishops too could be excluded, or could exclude themselves, from interference in the monastery's affairs. This untouchability sometimes had a paradoxical effect: while monasteries enhanced their holiness by thus distancing themselves from the sullying influence of worldly government, they thereby became all the more attractive as nodes of peculiar status, both to elites looking to by-pass royal power structures, and to rulers looking to enhance them. The acts by which Pippin II, ancestor of the Carolingians, took Echternach under his protection before giving himself the right to confirm its abbot and requiring that the latter remain loyal to his family, reveal that there was a short distance between exempting a monastery from old impositions and exacting new ones. By the time he took these measures, in 706, Pippin was effective ruler of the region in which Echternach lay; over the next fifty years, he and his descendants would use control of monasteries as an important weapon in the extension of their power. We have seen how Charlemagne used the dispute over its ownership to take over Lorsch. His action was one in a series by which the Carolingians overrode the rights of bishops to control monasteries, bringing significant numbers under their own protection.
#### CHRISTIAN LEADERSHIP AND LEARNING
#### _Regulating Christianity under the Carolingians_
Royal moves to control monasteries highlight a feature of Carolingian religious culture that we can also see behind the letter of Hincmar with which we began. Asking whether Lothar II's marriage was lawful, or whether he should be allowed a divorce, and on what grounds such a decision could be made, were components of a much broader quest for more authoritative rules and more secure structures in belief and practice that preoccupied western religious culture in the eighth and ninth centuries. The new emphases of the period – on gifts to churches and monasteries, on the spiritual benefits of masses and prayers, on the moral distinctiveness of priests, monks and nuns – all contributed to the growth and strengthening of the Church as an institution. This was one of the great religious developments of the age. But it would be wrong to think that the emergence of the Church opened up a gap between the ecclesiastical and the secular. One of the most striking features of this period – remarkable because it goes against traditional distinctions between ecclesiastical and lay, Church and state – is that the more robust the Church's hierarchy became, the more prominent its buildings in the landscape, the better defined its hierarchy, and the more explicit its rules, then the more intertwined it became with the dominant culture among the laity. This meant that moral questions, which in much later centuries the Church would claim for its own, were in this period decided by clerical and lay elites together.
This symbiosis of the secular and the ecclesiastical is clear in the case of Lothar II's divorce. His marital situation was unexceptional in the context of the traditional attitude to sexual relationships. Both Roman and post-Roman law allowed for a variety of types of marriage, varying according to the requirements for the consent of the parties and their families, the payments between the parties at the point of marriage, the legal status of the wife, the inheritance rights of the children, and the ease of dissolubility. They allowed for sexual relationships outside marriage – chiefly when a high-born man took a lower-status woman as a concubine – and the possibility of multiple simultaneous partnerships of different levels. Already in the Merovingian period we can perceive a growing distance between such arrangements and developing Christian thinking on marriage. Church doctrine in the later Roman period may have been based on secular Roman law – and therefore recognised concubinage – but Christian thinkers had from the beginning a fairly rigorous approach to human sexual relations. In passages later inspirational to the ascetic movement, though of questionable representativeness of his own views, St Paul suggested a strict list of moral priority: 'It is well for a man not to touch a woman. But because of cases of sexual immorality, each man should have his own wife and each woman her own husband.' As asceticism crystallised, so the attitudes of some towards sex and marriage in lay society hardened: Columbanus pointedly denied the legitimacy of the Merovingian Theuderic II's children by his concubines, and in his vision the danger to Barontus's soul was prompted by his multiple marriages and adulteries. Beginning with a synod in Rome in 721, successive church councils sought to refine the definition of marriage. Non-biological kinship acquired at the baptismal font had already achieved a significant status, proving very useful in Christianising societies in promoting and strengthening Christian identity within groups of families, and bishops were keen to close the gap between biological and spiritual kin further by bringing the latter into the group within which marriage would constitute incest. There were even moves to extend the definition of prohibited, consanguineous relations from the traditional four generations to seven (i.e. prohibiting marriage to any descendant of one's great-great-great-great-great grandfather). It was also stipulated that weddings be public, that Christian marriage was indissoluble, and that simultaneous sexual relationships should be avoided. Yet, although he may have found it harder than did the Merovingians to pursue relationships with both his queen and his concubine simultaneously, it was not really these developments of which Lothar II was the victim. What necessitated his divorce was rather his desire to make his concubine his queen, a desire born not of dynastic or religious considerations, but of love. Early medieval sources are frustratingly silent on the subject of love and, though the argument once put forward that romantic love did not even exist before the twelfth century is easily disproved, such emotional attachments are rarely explicit, and more often have to be inferred, as in the evidence for Lothar's divorce. Lothar's case at least shows that when it came to love and marriage, in the early Middle Ages you could have one without the other.
What made Lothar's divorce so difficult was that it was proposed at a time when authority was particularly hotly contested, between factions comprising both laymen and ecclesiastics, and between essentially secular powers and ecclesiastical institutions. Among the latter was especially the pope, Nicholas I, who intervened to invalidate the divorce in 863. Though this did not make the case a straightforward contest between Church and state, as some conflicts between pope and emperor later in the Middle Ages might better be described, it does indicate that the central problem was competing claims to authority over moral issues. Lothar's case was judged by various bodies: a secular court, employing trial by ordeal (which he lost); a council of bishops, hearing the evidence of a new witness (favourable to Lothar); and the pope, who as we have seen ruled against the king. Lothar was accorded no authority to adjudicate his own case. Paradoxically, it had been weakened by his own plea, which showed him to be vulnerable either to his own passions or, as we have seen Hincmar hint at the outset of this chapter, to others' unholy malefactions. As king, Lothar II was in fact almost uniquely vulnerable in the ninth century to the evolving Christian agenda for marriage, which took centuries to impose itself on wider society. But it was precisely the ideology developing around kingship that increased the attention on the Carolingians' moral rectitude.
The entire Frankish elite, lay and ecclesiastical, approved and supported each new king, who in return offered leadership and office. The duties of office, from the king downwards, were conceived of as a _ministerium_ (literally, ministry), which encompassed leadership not only in worldly affairs, but also in spiritual ones. Part of the responsibility of _ministerium_ , then, was leadership of a Christian people to salvation, and on none did this responsibility fall more heavily than on the king. This notion that the ruler should lead both secular polity and Christian institution naturally looked back to Constantine and his successors as late Roman Christian emperors, but followed the lead also of barbarian kings who had presided over synods – Chlothar II (614), the Visigoth Sisenand (633), the Bernician Oswiu (664) – as well as drawing on the model of Christian leadership by a _rector_ propounded by Pope Gregory I (590–604). Thus, throughout our period, by far the strongest role in legislating on religious as well as on secular matters was taken by the king. And this was not only true of the Carolingians: the emergence of a culture of religious patronage in the eighth century is a feature of Lombard Italy as much as of Francia, and the Lombard king Liutprand legislated in response to it. The close attention Liutprand paid to regularly promulgating and disseminating written laws finds an echo in the activity of the Carolingian kings after 754. But unlike in the Lombard kingdom, Carolingian legislation was bound up with ecclesiastical authority from the very first.
#### _Sources of authority: kings, popes and bishops_
The Franco-papal alliance that came about in the fraught circumstances of 753–4 has traditionally been viewed as politically expedient for both parties. Each side made attempts to put its own slant on the meeting between Pope Stephen II and Pippin III. Papal sources, for instance, agree that on Pope Stephen's arrival in Francia Pippin prostrated himself before the pontiff; in Frankish texts, it was the pope who was on his knees before the king. What this episode, and especially the anointing of Pippin and his sons, certainly achieved was to bind the new regime to the bishops of Rome in an unprecedented way. The Carolingians' fortunes were from then on entangled with events in Italy: a point fully appreciated by Charlemagne, and which must go some way to explaining his own decision to invade the Lombard kingdom in the autumn of 773. But if he entered the Lombard kingdom as a conqueror, Charlemagne came to Rome principally as a pilgrim. Our picture of the Rome that he visited is shaped fundamentally by the papal biographies, kept up apparently by papal clerks intermittently through each pope's lifetime and collected in a work known to posterity as the _Liber pontificalis_. The long lists of papal building projects included in these _Lives_ portray a Rome in the process of transformation by successive popes in the later eighth century. But, extensive though they are, we can tell from other sources that these omit many instances of construction and other material patronage, by no means all of which were papal. Literal readings of the _Liber pontificalis_ give a one-sided impression of Rome, and this is true too when we try to see how the implications of the Franco-papal alliance were worked out in the pontificate of Hadrian, both in his _Life_ in the _Liber pontificalis_ and in his correspondence, as preserved in the so-called _Codex Carolinus_. The latter in particular, however, clearly lifts phrases from earlier letters, suggesting that its authors were very deliberately drawing on the papal bureaucracy's literary traditions to build a case for the maximum possible freedom of manoeuvre for the papacy, addressed to Charlemagne's 'Italian experts': the handful of prominent Frankish magnates and ecclesiastics who dominated his dealings there in the first generation after 774. Other evidence shows how different was those experts' perspective from that of papal authors. In Rome, the Franks found what Anglo-Saxon missionaries had already discovered: a city of martyrs that stood as a new pinnacle to their hierarchy of holiness, and a source of relics, the bones of the martyrs, which would be taken north to bring new sanctity into the heart of their realm. For northern Christian peoples, therefore, the city of Rome's authority derived from its past associations, not from any current power. The Carolingians knew that contemporary Rome was 'incessantly poisoned by feuds'. What attracted them to it was precisely what the Romans were themselves beginning to emphasise as they redefined their own identity, falling back on the indigenous as they cut loose the ties to Constantinople: that is, the traditions peculiar to the city itself, built above all around the magnetism of Rome's martyrs and pre-eminently around St Peter.
For the Carolingian elite this authority was transmitted through particular texts in various genres. Pope Zacharias had already sent to Pippin III a small collection of canon law in around 747; when Charlemagne celebrated Easter at Rome in 774, while his army besieged Desiderius in Pavia, Pope Hadrian presented him with a revised version of the famous compilation of canon law made by Dionysius Exiguus in the sixth century (and so generally called the _Dionysio-Hadriana_ ). Large parts of this were then formally promulgated across his kingdom by Charlemagne in the _Admonitio generalis_ of 789, and passages from it were read aloud at the synod of Aachen in 802. Rome's ability to supply authoritative texts may have encouraged the request for a copy of the service-book, or sacramentary, thought by the Franks to have been composed by Pope Gregory the Great. Knowledge that no such thing existed did not deter Pope Hadrian from despatching a mass-book known as the _Hadrianum_ , containing a text with Gregorian associations that was no longer followed in Rome itself. Further, in 787, Charlemagne sought the set of monastic regulations known as the _Rule of St Benedict_ , which was coming to be seen as the most authoritative such collection of rules, and asked for a copy from the manuscript thought to be Benedict's autograph, which had been preserved at Rome and then taken to Benedict's abbey of Monte Cassino after its refoundation c.717. This demand for authoritative texts which might set a uniform standard arose both because of the desire for points of authority – whether at the Frankish court or the papal palace – and as a reaction, conscious or not, to what we can now see was a situation of great diversity. There had been no single _Rule of St Benedict_ , but instead, within a few decades of the great monastic saint's death around 550, many lists of rules bearing his name, each more or less different in wording from the next. Similarly, we can see that much of the liturgy that supposedly originated in Rome, and especially the sacramentary attached to Pope Gregory's name, was concocted from texts produced in many of the post-Roman kingdoms, including the Frankish. The true, complex, origins of these texts – canon law, liturgy, monastic Rule – mattered less than the image that they helped to create of a single authority under the Roman brand. The texts themselves were often adapted to suit Frankish requirements – thus Benedict of Aniane had to write a long supplement to the _Hadrianum_ , to cover the diverse liturgical needs across the Frankish empire.
Responding to holiness in the way most familiar to them, what the northern ecclesiastical aristocrats whom Charlemagne sent south to pursue his interests sought to acquire in Rome was not mere tourist souvenirs but actual ownership of holy sites. The popes' perspective, though founded on the same emphasis on Rome's traditional Christian aura, was rather different: only in papally produced texts – the letters they sent north, the biographies that their clerks produced of them – is there any durable sense that the spiritual aura of Rome's past imbued its present bishop with an authority that was not simply doctrinal or ecclesiastical, but secular and political; that is, that by dint of the city's past, its bishop could be a secular ruler. There are signs of uncertainty in the Frankish elite's response to the wave of ideological implications that followed their military success, especially over the Lombards. There was, as we shall see in Chapter 4, lively debate over the meaning, and even the desirability, of Charlemagne's coronation as emperor by the pope on Christmas Day 800. To some extent there still is, though it has proved impossible reliably to recover contemporary intentions on either side. On the one hand, 800 has been claimed as a defining point in the establishment of a separate polity centred on Rome and headed by the pope. On the other, Frankish writers even at the time were pretty consistent in their belief that Rome was part of Charlemagne's empire. On the level of ideology, Alcuin argued that the king not only had to defend the Church, but also had to act to strengthen the faith within the Christian community: the pope's role was simply to pray for the king's victory. Lothar I, sub-king in Italy under his father Louis the Pious, enshrined this attitude in his definition of the political position of the city of Rome in 824, known as the _Constitutio romana_ , which among other things required that the emperor approve papal elections. Only when the imperial office was weakened by political divisions later in the ninth century did the fractiousness of Rome's local aristocracy make the _Constitutio_ 's written provisions less viable in practice.
Another crucial component in the Franco-papal relationship was the establishment of close ties with the figures who were taking control of, and building to new strength, the Church in Francia. First among these was Boniface, who as we have seen found that east of the Rhine there was at least as often weak or incomplete Christianity as there was outright paganism. He himself had a striking conviction in the rightness of his own conception of Christianity, such as could come only from a society but freshly Christianised itself. But he needed the authority to put that conception into practice, and here the popes could certainly help him. This explains his frequent visits to Rome, and the stress placed by him and others on the innovative titles and offices awarded to him by successive popes, themselves stepping unsurely into an unfamiliar world of Churchbuilding. Gregory II referred to Boniface's _ministerium_ , and appointed him a bishop 'consecrated to the duty of preaching'; Gregory III made him an archbishop with metropolitan powers 'to ordain bishops where the multitude of the faithful has become very great'; and Zacharias finally allowed him a fixed see to go with his metropolitan status, first intended to be Cologne but ultimately established at Mainz. These offices, each in response to requests or hints from Boniface, were innovations, because the pope had not previously played any part in the appointment of Frankish bishops. They drew, rather, on the example of the Gregorian mission to England. Nor was there any necessary conflict between the pope as a source of authority and the other power on which Boniface relied, the Carolingian mayors and kings. It was Carloman who instigated the first of a series of church councils organised by Boniface and usually seen as the first chapters in a programme of church reform under Carolingian rule. The first, called simply the _Concilium germanicum_ because its place of meeting is unknown, set the tone. Its concern above all was the moral fitness and correct behaviour of the clergy: all clerics were forbidden to carry arms or to hunt; priests had to wear distinctive clerical dress, and be subject to their bishop, rendering to him an annual account of their activities, and penances were prescribed of flogging and imprisonment for transgressors; bishops should make the rounds of their diocese, taking particular care, 'with the help of the count', to prevent pagan practices. Reference to the latter, we have already seen, was a stylised literary convention as well as, or as much as, an indication of real opposition to Christianity. Either way, it was the strengthening of the Church, especially through improvements in its personnel, that was the key priority. A council in the following year at Les Estinnes reiterated these points, as well as trying to regulate the leasing of Church land for military purposes, and including the first of many rulings forbidding adultery and incestuous marriage. Subsequent councils – at Soissons in 744, an unknown location in 747, Ver in 755, Verberie in 756, Compiègne in 757 and Attigny in 762 – continued to reflect these concerns. The meeting at Soissons was the first to be held under the auspices of Carloman's brother Pippin, king from 751, and this and subsequent councils cannot be separated from other efforts to bolster his rule after his usurpation of the Merovingians' crown: in them we see 'a new king affirming his control of the sacred by creating clear hierarchical structures'.
The council of Soissons is the first to give us a precise idea of the difficulties facing those seeking a stricter definition of the Christian Church. The bishops there condemned for heresy a certain Aldebert, who claimed to possess a letter from heaven and had had written a saint's life of himself. He was sent to Rome and there stripped of his priesthood and anathematised, as was an Irish priest named Clemens who denied the teachings of the Church Fathers. Opposing such men was a relatively straightforward task since all within the Church hierarchy could agree on the unsoundness of their doctrine; indeed, Aldebert may even have proved useful, as a negative image of sanctity (claimed, arrogantly, by himself) to set against the positive image of the humble saint (recognised as such by others, through his works). Once the Frankish rulers were on side, Boniface also found that he could persuade them to take measures against contemporary bishops who he felt were too prone to typical aristocratic behaviour, such as hunting: we find, for instance, a certain Bishop Gewilib dashing off to Rome to contest (unsuccessfully) his deposition from the see of Mainz. A more difficult opponent was Virgilius, probably originally Ferghil, abbot of Aghaboe in Ireland, who had established himself at Salzburg where he incurred Boniface's displeasure by, apparently, holding the unorthodox view that there was 'another world and other men, and also a sun and moon' below the earth. The pair also came into conflict when Virgilius challenged Boniface's insistence on rebaptising those baptised by an illiterate priest. Pope Zacharias was inclined to leniency towards this minor transgression, and was rather more concerned that Boniface's rebaptism of the people in question was itself heretical. Virgilius proved, in fact, at least as successful a promoter of the Church as Boniface. His career shows that we should not over-concentrate on the figure who left the most prominent legacy to posterity.
The dependence of churchmen and women like Boniface and his followers on the Carolingians, as a source of authority as well as of effective power, only increased after Pippin III's seizure of the Frankish throne. Lacking the legitimacy bestowed by blood or tradition, Pippin turned to Christian ideology to sanction his rule. His anointing by the pope was of critical significance, and, as we have seen, helps to explain his dramatic interventions in Italy in 755 and 756. The next decades saw the crystallisation of an ideology portraying the king as 'rector of the kingdom of the Franks and devout defender and humble adjuvant of the holy Church'. This heightening of the king's responsibility for the spiritual welfare of his people led to yet further emphasis on correct clerical practice: as noted already, masses would be most effective where those who conducted them were most correct. There was therefore a more concerted attempt both to define the correct liturgy, and to ensure its performance throughout the kingdom. Texts were sought from Rome, and schools of chant established. This stress on correct liturgy continued under Charlemagne. The key theme of the capitulary known as the _Admonitio generalis_ (General Admonition), issued in 789, was the conduct of the episcopate and priesthood. They were to introduce no innovations into the liturgy. Rather, the emphasis was on preaching according to a strictly defined programme of doctrine and moral exhortation. The message was repeated in further capitularies and letters throughout the reign, and finds its natural reflection in the _capitula episcoporum_ mentioned earlier, with their concern for episcopal oversight of priestly behaviour. The aim was nothing less than control over the moral conduct of the laity. The _Admonitio_ was the first great expression of this unprecedented ambition, though it had been adumbrated in Carloman's councils, which explicitly delegated royal authority by assigning to the bishops responsibility for 'moral' crimes like adultery and incest. The theme became a keynote of ninth-century royal legislation: in 846, for example, Lothar I outlined bishops' responsibility to investigate and punish 'public shameful acts', including homicide and theft, as well as incest, adultery, and the ravishing of nuns. But bishops were not alone in this moral duty: other capitularies required the royal _missi_ – secular and ecclesiastical officials – to safeguard correct ways of life so that 'all are to live in perfect charity and peace one with another'.
#### _Christian rulership and the promotion of culture_
That such measures were the natural results of a Christian ideology of kingship became properly apparent in legislation issued by Charlemagne. The impetus began with a concern for what was happening in church. In the _Epistola de litteris colendis_ ('Letter on the cultivation of letters'), addressed by Charlemagne to Baugulf, abbot of Boniface's foundation of Fulda, ecclesiastical communities were instructed to teach literacy, 'so that those who seek to please God by right living may not neglect to please Him also by right speaking'. This view was elaborated in the _Admonitio generalis_. Its logic was straightforward. The king had responsibility for the salvation of his people: he had to follow the example of the biblical king Josiah, who 'strove to recall the kingdom which God had given him to the worship of the true God'. This was to be achieved by trying to ensure that moral and religious conduct was both correct and uniform. To establish correctness required authoritative texts, above all. As we have seen, the majority of the _Admonitio_ consists of canons copied from the collection that Charlemagne had recently received from Rome. These, the traditional rules of the Church, were only one of a set of texts of which authoritative copies were needed. Selection, edition and dissemination were paramount. Thus in Chapter 72 of the _Admonitio_ , Charlemagne required that monasteries and cathedral churches should set up schools to teach the psalms, musical notation, singing, computation and grammar: the skills required to save the souls of his people through prayer. 'Correct properly the catholic books', he exhorted, 'for often, while people want to pray to God in proper fashion, they yet pray improperly because of uncorrected books'.
The focus of Charlemagne and his advisers, then, was on books. The period also produced frescoes, church architecture, sculpture and jewellery, examples of all of which survive, if in small quantities. But the main artistic medium – for pictorial as well as literary art – was the parchment of the book. By this time the codex had fully replaced the scroll, and it was inscribed with the new script developed in this period, Carolingian minuscule. What a Christian kingdom needed above all, of course, was Bibles. Scriptoria often only copied sections of the Bible – the gospels, or the psalter – rather than the whole book, depending on what was required, although two of the intellectual luminaries of Charlemagne's court, Alcuin and Theodulf, both produced editions of the full Bible (pandects). A fair proportion of the other books produced in this period were also those necessary for Christian worship. Sacramentaries set down the order of the mass, antiphonaries contained its music, and the requirement for correct preaching led Charlemagne to commission from the Italian scholar Paul the Deacon a new homiliary – a book of approved sermons, taken from the writings of the Church Fathers – which was disseminated along with a covering letter in or just after 786. Although the primary concern of Carolingian copyists was what was read and said in churches and monasteries, they also copied works on more secular subjects, notably an approved collection of the laws of post-Roman rulers, together with a digest of Roman law, produced by a designated scriptorium.
Historians have dubbed this efflorescence of learning 'the Carolingian Renaissance'. How apt is this tag? The term 'renaissance' implies a marked improvement in cultural quality – an estimation that is ultimately rather subjective. As we said in Chapter 1, many more sources survive from the Carolingian than from the earlier Merovingian period, but that contrast may or may not reflect fundamental cultural change. It is also the case that cultural activities in the Carolingian period have been fundamentally influential on modern culture, not only by preserving the culture of antiquity for posterity, but also because the script forms developed then form the basis for those in use today. What is more, as the examples of the _Admonitio generalis_ and the _De litteris colendis_ demonstrate, writings emanating from the Carolingian court consistently promoted the dynasty as cultural improvers, combining the ideas of renewal ( _renovatio_ ) and correction ( _correctio_ ).
How seriously can we take this rhetoric? There is certainly better evidence for direct _royal_ involvement in culture under the Carolingians than under the later Merovingians. But there were nevertheless ample precedents for this kind of royal patronage, both historical and contemporary. Earlier Merovingians like Chilperic and Dagobert I had shown their interest in culture, as had sixth-century rulers like the Byzantine emperor Justinian or the Ostrogothic king Theoderic, and the Carolingians' contemporaries – the Lombard kings Liutprand and Desiderius, the Byzantine emperor Theophilus, or the English kings Offa and Alfred – all sponsored cultural production of a high order. If there is no sign of such a concern among the later Merovingians, this might be accounted for partly by their relative emasculation, and by the youth at accession and early deaths of many of them. What is unquestionable is the increase in the sheer number of texts that survive from the Carolingian era compared with the Merovingian. We have already seen the bald figures: while only 1,800 books or fragments survive from the entire period to 800, there are 9,000 from the ninth century alone. It is overwhelmingly Carolingian scribes whom we have to thank for copying and transmitting the writings of classical antiquity: in the period between 750 and 900 the earliest copies were made of most of the classical works that we know today, of some seventy authors. Some of the authors thus transmitted were pagan, but many more were Christian: the early Fathers of the Christian Church were as, if not more, important to the readership of these books than authors like Virgil and Ovid, whose paganism was problematic for Christian readers. That works such as the latter came to be defined as 'the classics' at all, distinct from other categories of literature, resulted from a movement for Christian reform that nonetheless allowed room for scholarship, even if its dangers were appreciated: Ermenric of Ellwangen told the story of his haunting by the ghost of Virgil because of his love for the pagan classics.
The sheer volume of copying indicates a sincere desire in the Carolingian age to preserve and transmit Christian texts and the learning of the past. The original compositions of the period have, in general, been less easily esteemed. Yet the eighth and ninth centuries saw the writing of numbers of important new works not only in what seem to have been the most popular genres (at least among the monastic scribes who wrote most of them), like Biblical commentary or poetry, but also in grammar, spelling, philosophy and theology. Perhaps most strikingly, writers of the Carolingian period explored new genres, including (as we saw in Chapter 1) innovative ways of writing about the past, not least in annals and royal biography. Some new types of text reflect the concerns of the monasteries in which they were, for the most part, produced: confraternity books that recorded the names of the many thousands of patrons and associates for whom the monks prayed; and cartularies into which were copied the documents by which some of those patrons donated their wealth, mostly lands, for the support of the monks. But there were also, as we have seen, handbooks for ordinary priests to guide them in their pastoral work.
Many of the most authoritative texts – sacramentary, canon law, monastic rule – came from Italy. Travelling in the same direction was a movement of scholars to the king's court in the wake of Charlemagne's conquest of the Lombard kingdom. The poet and grammarian Paulinus, later patriarch of Aquileia, was followed by Peter of Pisa, who according to Einhard taught grammar to Charlemagne himself, and the all-round intellectual Paul the Deacon, to whose work as historian, poet and liturgist we have already referred. Signalling that the royal court would be the focus of intellectual and cultural achievement in the Frankish kingdom for that generation, these men were joined by scholars from all over western Europe. The most prominent of them for posterity was Alcuin, the Anglo-Saxon monk and scholar (and relative of Willibrord), who came to Francia at Charlemagne's invitation in 782 and whose hand has been detected behind many of the king's pronouncements on cultural and religious activity. From England also came Beornrad, who became abbot of Echternach and archbishop of Sens, Cathwulf, who wrote a letter of advice to Charlemagne in 775, the theologian Hwita, known as Candidus, the nickname that Alcuin, as was his custom, bestowed on him, and Fridugisus (or Frithugils, in Old English), another theological writer who became close to the royal family, witnessed Charlemagne's will in 811 and was archchancellor to Louis the Pious from 819 to 833. From Ireland there came the deacon Joseph, a poet who was employed by the king as one of his Italian envoys, the philosopher Dúngal, and Dícuil, who wrote on astronomy and computus (the reckoning of time, involved especially in the calculation of the date of Easter). Another Irishman, known as Cadac-Andreas, was a writer of exegesis (commentary on the Bible) so pedantic as to arouse the ire of this scholarly circle's great poetic eulogist, Theodulf, who had come to the court from the last vestige of Visigothic Spain. The latter was a poet and theologian, who composed the _Opus Caroli regis_ (also known as the _Libri Carolini_ ), an extensive and learned discussion of the place of art in Christian worship (see Figure 6 above). This was intended as a riposte to the Byzantine rejection of images of Christ and the saints in worship ('iconoclasm'), though it seems to misunderstand the acts of the Byzantines' second council of Nicaea of 787, which were in fact intended to restore the use of images. After his appointment to the bishopric of Orléans in 800 Theodulf became assiduous in his concern for the education of the local clergy. From the 790s the so-called 'court school' dispersed to such posts around the kingdom, spreading their ideas wherever they went. Alcuin became abbot of St Martin's in Tours in 796 and continued to be pivotal as the teacher of many of the next generation of Carolingian scholars.
The cultural effort was therefore continued under Charlemagne's successors, though subtle differences emerged. Only after Charlemagne's death was literature used as a vehicle for political criticism, however guarded. Only from that time, too, were attempts made to demarcate the education of the monastic and the secular clergy, the synod of Aachen of 817 restricting entry into monastic schools to oblates. This is symptomatic of a wider shift in emphasis, for as the institutional Church became an ever more secure and widespread presence, so attention moved from the foundational work of Charlemagne's reign, with its emphasis on basic authoritative texts, to a more managerial concern with running a large and supremely important institution. Education was beginning to aid social mobility – both the scholar Walahfrid Strabo and the archbishop of Rheims Ebo came from humble backgrounds – and the proliferating clergy in general needed to be properly directed. Hence the need for the handbook for trainee clerics ( _De institutione clericorum_ ) composed by Hraban Maur (c.780–856), whose _On the Nature of Things_ ( _De rerum naturis_ ), a kind of encyclopedia, is the epitome of the high Carolingian urge to classify and to organise. Hence too demarcation became a major preoccupation of Hincmar of Rheims. In several works he tried to define the responsibilities of the different grades of the clergy, while his 'On the Governance of the Palace' sought to idealise a similar level of organisation at the heart of the secular world. Indicative of the same institutional context are Hincmar's efforts, involving appeals to the authority of the pope, to depose bishops consecrated by his rebellious predecessor Ebo, or later to impose his superiority on his own nephew, Hincmar, bishop of Laon.
With the fading of the generation after Boniface, there was also a change in the way in which the Christian Church conceived of its heroes. In the eighth century it was still possible for Christians to revere as saints the only recently dead among their leaders. This was precisely what had happened to Boniface, in fact: we have already noted the rather unseemly struggle for possession of his recently dead corpse between his episcopal foundations of Utrecht and Mainz and his monastery at Fulda. But even this contest might be taken as a sign of the increasing stress being laid on corporeal relics as the centre of devotion. The holy man was now not a living role model, but a dead saint. The ninth century produced no new saints. Rather, increasing effort was directed at identifying, translating and venerating the bodies of those whom tradition revered. The process is epitomised by the transfer from the suburban catacombs of Rome into the city's churches of the bones of long-dead 'martyrs', which began under Pope Paul I (757–67), and the subsequent removal of many of them to churches in Francia. Both Hraban and Hincmar exemplify the centrality of the cult of relics to the structure of the Carolingian Church: the former arranging the procurement of the bones of Roman martyrs for his abbey of Fulda, the latter devoting considerable energy to promoting the cult, and ultimately composing the hagiography, of his fifth-century predecessor at Rheims, St Remigius.
This kind of activity demonstrates the reach of the Christian culture that grew to fit into the Carolingian empire: traffic between Rome and Germany was normal; the single rulership of Charlemagne and Louis the Pious giving the appearance of unity as much to the Church as to the empire. But we should resist the temptation to read into the break-up of this empire a deterioration also in the Church, and in the culture that had grown in parallel with it. The later ninth century has often seemed a time of fragmentation, and not only in politics. Culturally, what has been seen as an exclusive commitment of resources to Christian uses in the heyday of the Carolingian renaissance looks diluted when we observe in the later ninth century the growth of a lay vernacular culture exemplified by the Old High German poem _Ludwigslied_ , whose tale of a Frankish king battling the Vikings seems to characterise the age. But vernacular poems and stories never really stood in opposition to Latinate, Christian culture. The _Ludwigslied_ is a resolutely Christian text, a praise-poem for a ruler in a long tradition with both Germanic and Latin exemplars. What happened to Carolingian culture as Louis the Pious's rule gave way to that of his sons was less fragmentation than diversification.
**Map 4.** Cultural centres in Carolingian Europe
The cultural artefacts of the later ninth century were in general just as diverse as they had been earlier: law, history, hagiography, poetry, theology, grammar, computus. What changed was that the forces motivating their production, which had previously come first and foremost from the royal court and palace, became more numerous, as more than one royal court existed at the same time, and as monasteries, bishoprics and aristocrats more often stepped forward as cultural patrons in their own right. The process had begun, as we have seen, in Charlemagne's day, as the learned figures of the initial court school distributed themselves around the kingdom. Their pupils, and their pupils' pupils, gradually spread out to form a dense network of cultural centres across the empire (see Map 4). What we can see of it now is attested by the books which survive from that era, copies both of classics and of original compositions. Library catalogues are extant from a number of centres, and reveal important facets of the organisation of knowledge at the time. Since, in common with much else, we lack catalogues or inventories from the Merovingian period, it is hard to see the immediate precedents for Carolingian practice, but by the first decades of the ninth century the surviving catalogues reveal the emergence of a roughly defined canon of intellectual literature, and display a certain consistency in their organisation, listing first works for use in church (especially the Bible or parts of it), then works of wider relevance to the institutional Church (monastic rules, canon law, hagiographies), and finally school books (grammar, rhetoric, history). Among the remnants of early medieval libraries, very few have remained together (the best example is the collection of manuscripts at the monastery of St Gallen in modern Switzerland). Mostly, the books of a particular early medieval institution have to be identified among manuscripts scattered through modern libraries, usually on the basis of palaeographical and codicological characteristics. In this way, for example, we can piece together the surviving books of the library of the important monastery of St Amand in northern Francia. This continued to be a thriving intellectual centre throughout the ninth century, producing figures like Hucbald, whose works of poetry, music, logic, computus and hagiography encompass a polymathic output which, like those of Hraban Maur and Hincmar of Rheims in previous generations, shows that although Carolingian intellectuals took pains to arrange material according to genres, they did not find them restrictive. Hucbald's work reaches across the end of this book's period – he died in 930 – throughout which time St Amand remained a major producer of books. Nearly half of the books in its own library were copied there, a relatively high proportion, but it also demonstrably exported its work: it was a major source of gospel books and sacramentaries for other centres. This kind of production necessitated consistent cooperation between intellectual centres, a traffic in books and a workforce of competent copyists to sustain Carolingian culture. The figure of Lupus of Ferrières (805–c.862) exemplifies this empirewide network. Trained initially at Ferrieres and then at Fulda, where he compiled a corpus of secular law and a hagiography, his correspondence with many of the major intellectuals of the ninth century is peppered with requests for books to copy, and a number of these, bearing Lupus's own hand, are extant.
One of St Amand's most notable products takes us back to Lothar II, and in doing so demonstrates that although this cultural activity was dispersed across the realm and remained resolutely intellectual, it was never detached from the nitty-gritty of Frankish political life. Lothar never did manage to get his divorce from Theutberga formalised, and so when he died in 869 he lacked a legitimate heir. Immediately, one of his uncles, Charles the Bald, made a grab for his 'middle' kingdom, and had himself crowned as its king that September in Metz. It was almost certainly for that occasion that the scribes of St Amand produced a carefully chosen compilation of writings on Frankish history, rounded off with a three-page summary of the codex's narrative that portrayed Carolingian rulers fitting seamlessly into a continuous line of succession over the west Frankish lands – Charles the Bald's original kingdom – stretching back to the seventhcentury Merovingians (and from there ultimately back to the legendary Priam, king of Troy, whence, one legend said, the Franks had originally come). The book would have made an elegantly apt addition to Charles the Bald's already substantial court library which, together with other surviving books dedicated to him, reveal him to have been a notable patron of book production and literate culture.
The projection from the king or emperor of a deliberate programme for fostering education and culture is an aspect of Carolingian rule that is often emphasised, and seems to set the dynasty apart from both its predecessors and its successors. The systematic approach to cultural and intellectual patronage, the specific attention to schools, the use of the court as a magnet for talent, and the dissemination from it of approved texts are all distinctive features of Carolingian kingship. The reasons for this have already been mentioned: at root, the promotion of learning was seen as a necessity for the proper Christianisation of the people and the purging of sin from the realm and, therefore, an obligation on the king. Two further points need to be made about this extraordinary effort. The first is that, despite the emphasis in much of the rhetoric on uniformity of texts and doctrines, it is striking how much variety there still was in the cultural and scholarly products of the age. Partly this was itself due to the variety in the sources and models that writers and artists of the period used, drawn from previous post-Roman kingdoms, late antique Christianity and the pagan classical tradition. One of the results, and this is the second point, was that the Carolingian cultural effort did not eradicate disagreement. Controversies still occurred, for instance over baptism or, as we saw earlier, over the eucharist; they would break out with new vigour in succeeding periods. But what the Carolingians bequeathed to the future was a sense that rulers _should_ concern themselves with such matters; that they had a duty to sponsor art and foster learning. This was done through the medium of the book, which found its essential form in this period; and it was done to bring about reform of society in the direction of Christian ideals. This was a need felt too in successive ages – through the Ottonian tenth, the reform movement of the eleventh, and the renaissance of the twelfth century – and contemporaries responded to it by recourse to the means that the Carolingians had given them.
* * *
Hincmar of Rheims, _De divortio Lotharii regis et Theutbergae reginae_ , ed. L. Böhringer, _MGH Concilia_ IV, supp. I (Hanover, 1992), p. 205.
_Ibid._ , p. 207.
_Ibid._ , p. 206.
The best detailed account along these relatively traditional lines is still W. Levison, _England and the Continent in the Eighth Century_ (Oxford, 1946), the poignancy of which book might be detected in Levison's understated preface, pp. v–vii.
On the possible motivations behind Hincmar's polemic, see S. Airlie, 'Private bodies and the body politic in the divorce case of Lothar II', _P &P_ 161 (1998), pp. 3–38; and for context see below, Chapter 8.
Hincmar, _De divortio_ , p. 207, n. 14, identifying Isidore, _Etymologiae_ VIII.9.9–29. As first pointed out by W. Boudriot, _Die altgermanische Religion_ (Bonn, 1928), Hincmar was not the only ninth-century writer to borrow descriptions of unChristian practices from earlier authors – not only Isidore but, in particular, Caesarius, bishop of Arles (c.470–542). All ultimately go back to Biblical texts, e.g. Deuteronomy 18:10–11.
V. Flint, _The Rise of Magic in Early Medieval Europe_ (Oxford, 1991), pp. 155–7.
This characterisation draws on G. Vermes, _Jesus the Jew. A Historian's Reading of the Gospels_ , 5th edn (London, 1994); _Jesus and the World of Judaism_ (Philadelphia, PA, 1984); _The Changing Faces of Jesus_ (London, 2001).
On the 'eclipse of theology', see A. Angenendt, _Das Frühmittelalter. Die abendländische Christenheit von 400 bis 900_ (Stuttgart, 1990), p. 155; also P. Brown, 'Vers la naissance de purgatoire. Amnistie et penitence dans le christianisme occidental de l'Antiquité tardive au Haut Moyen Âge', _Annales HSS_ 6 (1997), pp. 1247–61 at pp. 1260–1.
G. Macy, 'Was there a "Church" in the Middle Ages?', in R. Swanson (ed.), _Unity and Diversity in the Church_ , Studies in Church History 52 (Oxford, 1996), pp. 107–16.
See J. Arnold, _Belief and Unbelief in Medieval Europe_ (London, 2005), pp. 1–26 and 143–90.
Peter Brown has characterised Christianity's development up to the seventh century as the emergence of a series of 'Micro-Christendoms': P. Brown, _The Rise of Western Christendom_ , second edn (Oxford, 2003), pp. 355–79.
Caesarius of Arles, _Sermones_ , ed. G. Morin, 2 vols., _CCSL_ 103–4 (Turnhout, 1953) (e.g. nos. 13, 15, 62); Martin of Braga, _On the correction of the rustics_ ( _De correctione rusticorum_ ), ed. and trans. C.W. Barlow, _Iberian Fathers_ i: _Martin of Braga, Paschasius of Dumium, Leander of Seville_ (Washington, DC, 1969) (e.g. cc. 8, 9).
Y. Hen, _Culture and Religion in Merovingian Gaul_ (Leiden, 1995), pp. 158–9, esp. n. 25.
For a definition of 'magic' that subsumes many of the characteristics of 'superstition', see Flint, _Rise of Magic_ , esp. p. 3.
As was, for example, St Cuthbert: Bede, _Vita Cuthberti_ , trans. B. Colgrave, _Two Lives of Saint Cuthbert. A Life by an Anonymous Monk of Lindisfarne and Bede's Prose Life_ (Cambridge, 1940), pp. 142–307; see also C. Stancliffe, 'Cuthbert and the polarity between pastor and solitary', in G. Bonner, D. Rollason and C. Stancliffe (eds.), _St Cuthbert, his Cult and his Community to ad 1200_ (Woodbridge, 1989), pp. 21–44.
_Indiculus superstitionum et paganiarum_ , ed. R. Rau, _Briefe des Bonifatius; Willibalds Leben des Bonifatius_ (Darmstadt, 1968), pp. 444–8, nos. 5, 9, 18, trans. J. T. McNeill and H. A. Gamer (eds.), _Medieval Handbooks of Penance_ (New York, 1990), pp. 419–21, and repr. in Dutton (ed.), _Carolingian Civilization_ , pp. 3–4 (from which the translation given here differs slightly).
_Indiculus superstitionum et paganiarum_ , nos. 6, 8, 10, 12, 13, 24. The full list runs to thirty clauses.
See now J. Palmer, 'Defining paganism in the Carolingian world', _EME_ 15 (2007), pp. 402–25.
See e.g. A. Meaney, 'Magic', in M. Lapidge, _et al_. (eds.), _The Blackwell Encyclopedia of Anglo-Saxon England_ (Oxford, 1999), pp. 298–9, and, in general, Flint, _Rise of Magic_.
_Indiculus superstitionum et paganiarum_ , no. 21; and compare Hrabanus Maurus, _Homilia_ XLII ('Contra eos qui in lunae defectu clamoribus se fatigabant'), PL cx, coll. 78–80.
Alcuin, _Vita Willibrordi_ , trans. Talbot, p. 10.
Boniface, _Epistolae, Ep_. 43, ed. Tangl, pp. 68–9, trans. Emerton, no. XXXIII, pp. 69–71 (from which the translation given here differs slightly). The language seems to be lifted from the canons of the fourth-century Council of Laodicea (PL LXVII, p. 168), replicated in later councils (e.g. Council of Agde 506, _Concilia Galliae a.314–a.506_ , ed. C. Munier, _CCSL_ 148 (Turnhout, 1953)).
R. I. Moore, 'Literacy and the making of heresy _c_.1000– _c_.1150', in P. Biller and A. Hudson (eds.), _Heresy and Literacy, 1000–1530_ (Cambridge, 1994), pp. 19–37, repr. in L. K. Little and B. H. Rosenwein (eds.), _Debating the Middle Ages. Issues and Readings_ (Oxford, 1998), pp. 163–75.
Tacitus, _Germania_ , c. 9, trans. M. Hutton, _Agricola, Germania, Dialogus_ (London, 1970), pp. 143–5.
On definitions of religion and superstition, see Hen, _Culture and Religion_ , pp. 157–61.
See S. Coupland, 'Money and coinage under Louis the Pious', _Francia_ 17/1 (1990), pp. 23–54.
For the apposite example of Ireland in this context, see T. Charles-Edwards, _Early_ _Christian Ireland_ (Cambridge, 2000), pp. 200–2.
See P. Meulengracht Sørensen, 'Religions old and new', in P. Sawyer (ed.), _The Oxford Illustrated History of the Vikings (Oxford, 1997), pp. 202–24_.
For Sutton Hoo, see M. Carver, _Sutton Hoo: Burial Ground of Kings?_ (Philadelphia, PA, 1998).
For festivals accompanied by drinking, see I. Wood, 'Pagan religion and superstitions east of the Rhine from the fifth to the ninth century', in G. Ausenda (ed.), _After Empire_ (Woodbridge, 1995), pp. 253–68, at p. 259. Sacrifice: Alcuin, _Vita Willibrordi_ , trans. Talbot, p. 10; _Pactus legis Salicae_ , ed. K. A. Eckhardt, _MGH Legum sectio_ I, _Leges Nationum Germanicarum_ IV (Hanover, 1962) 2, 16, trans. K. Fischer-Drew, _The Laws of the Salian Franks_ (Philadelphia, PA, 1991).
Boniface, _Epistolae, Ep_. 28, trans. Hillgarth, _Christianity and Paganism_ , p. 175: 'Among other difficulties which you face in those parts, you say that some of the faithful sell their slaves to be sacrificed by the heathen. This, above all, we urge you to forbid, for it is a crime against nature'; see also trans. Emerton, no. xx, pp. 57–9; Altfrid, _Vita Liudgeri_ I.6–7, ed. W. Diekamp, _Die Vitae Sancti Liudgeri_ (Münster, 1881). Christian priests performing pagan sacrifice: Boniface, _Epistolae, Ep_. 80, trans. Emerton, no. LXIV, pp. 142–9.
Boniface, _Epistolae, Ep_. 23, trans. Emerton, no. XV, pp. 48–50.
Saxon baptismal formula: H. D. Schlosser (ed.), _Althochdeutsche Literatur_ (Frankfurt, 1970), pp. 251–60, and W. Lange, _Texte zur Bekehrungsgeschichte_ (Tübingen, 1962), p. 176. Second Merseburg Charm: Knight Bostock, _Handbook on Old High German Literature_ , pp. 26–7, and W. Braune, _et al., Althochdeutsches Lesebuch_ (Tübingen, 1958) XVI, 2, II (p. 86). On both, see C. Edwards, 'German vernacular literature: a survey', in McKitterick (ed.), _Carolingian Culture_ , pp. 141–70.
Alcuin, _Vita Willibrordi_ , trans. Talbot, p. 10; Altfrid, _Vita Liudgeri_ I.22. See further R. Bartlett, 'Reflections on paganism and christianity in medieval Europe', _PBA_ 101 (1998), pp. 55–76.
'Erce, eorðan modor', in _Æcerbot_ , ed. and trans. G. Storms, _Anglo-Saxon Magic_ (The Hague, 1948), no. 8.
Alcuin, _Vita Willibrordi_ , trans. Talbot, p. 10; Willibald, _Vita Bonifatii_ , ed. W. Levison, _MGH SRG in usum scholarum separatim editi_ LVII (Hanover, 1905) c. 6, trans. Talbot, pp. 45–6. There may have been some temples in England, but the Anglo-Saxons may here have been re-using or mimicking the Roman and/or Christian religious buildings that they found there: Wood, 'Pagan religion', p. 261. Some Slav peoples of the later ninth and early tenth centuries certainly had temples: see the description by Thietmar of Merseburg, _Chronicon_ , ed. R. Holtzmann, _MGH SRG, n.s_ IX (Berlin, 1935), VI.23–5, trans. D. Warner, _Ottonian Germany: The_ Chronicon _of Thietmar of Merseburg_ (Manchester, 2001), and L. Słupecki, _Slavonic Pagan Sanctuaries_ (Warsaw, 1994).
For spells or charms, see G. O. Cockayne (ed.), _Leechdoms, Wortcunning, and Starcraft of Early England_ , 3 vols. Rolls Series 35, reprint rev. C. Singer (London, 1961), vol. II. See also _Beowulf_ , ed. E. van K. Dobbie, _Beowulf and Judith_. Anglo-Saxon Poetic Records 4 (New York and London, 1953), ll.111–13, trans. R. M. Liuzza, _Beowulf_ (Peterborough, ON, 2000), p. 56: 'From thence arose all misbegotten things,/trolls and elves and the living dead,/and also the giants...' ('Þanon untydras ealle onwocon,/eotenas ond ylfe ond orcneas,/swylce gigantas...').
On these monsters and their interpretation see, classically, J. R. R. Tolkien, 'Beowulf: the monsters and the critics', _PBA_ 22 (1936), pp. 1–53; repr. in J. R. R. Tolkien, _The Monsters and the Critics and Other Essays_ (London, 1983). As we have it, _Beowulf_ is probably a composition of the late ninth or tenth centuries: best initial guides to the poem are R. E. Bjork and J. D. Niles (eds.), _A Beowulf Handbook_ (Lincoln, NE, 1997), and A. Orchard, _A Critical Companion to 'Beowulf'_ (Woodbridge, 2004).
_Beowulf_ , ll. 104–10, trans. Liuzza, p. 56; Brown, _Rise of Western Christendom_ , pp. 482–5.
Alcuin, _Ep_. 124, ed. Dümmler, p. 183: 'quid Hinieldus cum Christo?', see D. Bullough, 'What has Ingeld to do with Lindisfarne?', _Anglo-Saxon England_ 22 (1993), pp. 93–125, and now M. Garrison, 'Quid Hinieldus cum Christo?', in K. O'Brien O'Keefe and A. Orchard (eds.), _Latin Learning and English Lore: Studies in Anglo-Saxon Literature for Michael Lapidge_ , 2 vols. (Toronto 2005), I, pp. 237–59. Ingeld appears in _Beowulf_ , l. 2064, trans. Liuzza, p. 116.
The notion was dismissed effectively by E. G. Stanley, _The Search for Anglo-Saxon Paganism_ (Cambridge, 1975).
See e.g. R. Fletcher, _The Conversion of Europe: From Paganism to Christianity, 371–1386_ (London, 1997), pp. 271–84.
In Boniface, _Espitolae, Ep_. 50 (trans. Emerton, no. xl, pp. 78–83), datable to 742, Boniface complains that 'the Franks have not held a council for more than eighty years'. In fact, we possess acts of Frankish synods in the Merovingian period up to at least 695.
_Acts of the Council of Pavia_ , ed. G. Waitz, _MGH SRL_ (Hanover, 1878), pp. 189–91; on the Three Chapters (or Tricapitoline) schism, see R. Markus, _Gregory the Great and his World_ (Cambridge, 1997), pp. 125–40; J. Herrin, _The Formation of Christendom_ (Oxford, 1987), pp. 119–27.
Bede, _HE_ IV.16.
I. Wood, _The Missionary Life: Saints and the Evangelisation of Europe, 400–1050_ (Harlow, 2001), pp. 123–41.
_Ibid._ , pp. 168–244; Fletcher, _Conversion of Europe_ , pp. 327–68.
See A. Cameron, _The Later Roman Empire_ (London, 1993), pp. 66–84, esp. pp. 71–4. The exception here may have been parts of Britain, which may have had as few as three bishops during the Roman period: see A. S. Esmonde Cleary, _The Ending of Roman Britain_ (London, 1989), p. 121.
Dating Clovis's baptism has provoked a long debate: see most recently D. Shanzer, 'Dating the baptism of Clovis: the Bishop of Vienne vs the Bishop of Tours', _EME_ 7 (1998), pp. 29–57.
See for example V. Gaffney, H. Patterson and P. Roberts, 'Forum novum (Vescovio): a new study of the town and bishopric', in H. Patterson (ed.), _Bridging the Tiber: Approaches to Regional Archaeology in the Middle Tiber Valley_ (London, 2004), pp. 237–48.
P. Heather and J. Matthews, _The Goths in the Fourth Century_ (Liverpool, 1991), pp. 124–43.
Such thaumaturgical miracles – rooted in, and improving, the physical world – are a hallmark of Merovingian hagiography. Elsewhere, hagiographers sometimes revealed saints' divine powers operating transcendentally, for instance in prophecies. For the categorisation and characterisation of miracles, see Fouracre and Gerberding, _Late Merovingian France_ , pp. 134–5, and Brown, _Rise of Western Christendom_ , pp. 161–3, 214, and their references.
See J. McNamara, 'A legacy of miracles: hagiography and nunneries in Merovingian Gaul', in J. Kirshner and S. Wemple (eds.), _Women of the Medieval World. Essays in Honour of John H. Mundy_ (Oxford, 1985), pp. 36–52, at p. 38: 'Miracles are the whole point of the _vitae_...'
_Vita Audoini episcopi Rotomagensis_ , ed. W. Levison, _MGH SRG_ v (Hanover, 1910), pp. 536–67, c. 4, trans. Fouracre and Gerberding, 'Life of Audoin', _Late Merovingian France_ , p. 156.
Yitzhak Hen has noted how relatively incidental the theme of conversion is in the Merovingian _Lives_ , including that of Audoin, and how it is stressed to a far greater degree in Carolingian, ninth-century, versions of the same hagiographies: _Culture and Religion_ , pp. 189–97. For a slightly different slant on the _Life of Audoin_ from the one taken here, see P. Fouracre, 'The work of Audoenus of Rouen and Eligius of Noyon in extending episcopal influence from the town to the country in seventh-century Neustria', _Studies in Church History_ 16 (1979), pp. 77–91.
Fouracre and Gerberding, _Late Merovingian France_ , pp. 133–52, esp. 147–52.
Early and independent evidence for Audoin's reputation for holiness is provided by Fredegar, _Chronicle_ , iv, c. 78, p. 66, ed. and trans. Wallace-Hadrill.
On Audoin's influence on monasticism, see Fouracre and Gerberding, _Late Merovingian France_ , pp. 147–8.
On the conversion of the Anglo-Saxons, see now J. Blair, _The Church in Anglo-Saxon Society_ (Oxford, 2005), pp. 8–51. On Wilfrid, A. Thacker, 'Wilfrid', _Oxford Dictionary of National Biography, s.n_.
H. Mayr-Harting, _The Coming of Christianity to Anglo-Saxon England_ (3rd edn, London, 1991), pp. 130–9; ecclesiastical magnates of similar scope and power existed also at this time in Ireland: Charles-Edwards, _Early Christian Ireland_ , pp. 416–40. So in the character of his rule as well as in practices like calculating the date of Easter, to label Wilfrid as 'Roman' and to oppose him to an 'Irish' party is too simplistic.
D. P. Kirby (ed.), _Saint Wilfrid at Hexham_ (Newcastle-upon-Tyne, 1974); R. N. Bailey, 'St Wilfrid, Ripon and Hexham', _American Early Medieval Studies_ 1 (1990), pp. 3–25.
Thacker, 'Wilfrid'.
Stephen of Ripon, _Vita Wilfridi_ , cc. 35 and 55, pp. 66–8 and 120 (note that modern scholars agree that the name 'Eddius Stephanus' arises from a misinterpretation: his biographer, a monk of Ripon, was called just 'Stephen'). See also A. Thacker, 'In search of saints: the English Church and the cult of Roman apostles and martyrs in the seventh and eighth centuries', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 247–77 at pp. 258–61. Andrew was dedicatee of a chapel at the Vatican and, most significantly here, of Gregory the Great's monastery on the Caelian hill, home to Augustine and his companions before their mission to England.
J. M. H. Smith, 'Old saints, new cults: Roman relics in Carolingian Francia', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 317–39.
Stephen of Ripon, _Vita Wilfridi_ , c. 24. On this episode see above, Chapter 2, p. 37.
Stephen of Ripon, _Vita Wilfridi_ , c. 26. Bede, _HE_ v.19.
Bede, _HE_ v.9.
Bede, _HE_ V.II. For what follows, see M. Costambeys, 'Willibrord', _Oxford Dictionary of National Biography, s.n_.
Alcuin, _Vita Willibrordi_ , trans. Talbot, pp. 3–22; Wood, _Missionary Life_ , pp. 79–99.
_Vita Vulframni_ , ed. W. Levison, _MGH SRM_ v (Hanover, 1910), pp. 657–73; see Wood, _Missionary Life_ , pp. 92–4 and idem, 'Saint-Wandrille and its hagiography', in I. N. Wood and G. A. Loud (eds.), _Church and Chronicle in the Middle Ages_ (London, 1991), pp. 1–15.
Altfrid, _Vita Liudgeri_ I, cc. 1–3, ed. Diekamp, pp. 6–8.
Alcuin, _Vita Willibrordi_ , trans. Talbot, p. 11.
See above, Chapter 2, and M. Costambeys, 'An aristocratic community on the northern Frankish frontier', _Early Medieval Europe_ 3/1 (1994), pp. 39–62.
See above, Chapter 2.
Boniface, _Epistolae, Ep_. 12, trans. Emerton, no. iv, pp. 32–3. The best short account of Boniface's career is now I. Wood, 'Boniface', _DNB_ , _s.n_.
Boniface, _Epistolae, Ep_. 12: '...in laborem salutiferae praedicationis'; Emerton translates this as 'to missionary work' at p. 33, which assumes a little too much, to my mind.
Costambeys, 'Willibrord'; _LP_ i, p. 376, trans. R. Davis, _The Book of Pontiffs_ (Liber pontificalis), revised edition (Liverpool, 2000), p. 89.
Willibald, _Vita Bonifatii_ , c. VI, trans. Talbot, p. 42.
Boniface, _Epistolae, Ep_. 17, trans. Emerton, no. IX, pp. 42–3 (from which the translation given here differs slightly).
See above, n. 37.
Willibald, _Vita Bonifatii_ , c. VII, trans. Talbot, p. 42.
For Carloman's authority, see above, Chapter 2.
Boniface, _Epistolae, Ep_. 50, trans. Emerton, no. XL, pp. 78–83.
See the _Northern Annals_ , ed. T. Arnold, _Symeonis monachi opera omnia_ , 2 vols., Rolls Series 75 (London, 1882–5), II, pp. 30–66, trans. Whitelock, _EHD_ , no. 3(a), p. 266, and the _Continuation_ of Bede, _Historia Ecclesiastica_ , trans. Whitelock, _EHD_ , no. 5, p. 286, _s.a_. 754; for Monte Cassino, see Boniface, _Epistolae, Ep_. 106.
On Lull, see J. Palmer, 'The "vigorous rule" of Bishop Lull: between Bonifatian mission and Carolingian church control', _EME_ 13/3 (2005), pp. 249–76.
For Boniface's heirs, see Wood, _Missionary Life_ , pp. 57–73.
See e.g. Boniface, _Epistolae, Epp_. 30, 35, 75, 124, 142, trans. Emerton, nos. XXII, XXVI, LIX, pp. 60–1, 64–5 and 132–3 (124 and 142 not translated).
_Vita Willehadi_ , ed. A. Röpke, _Das Leben des heiligen Willehad_ (Bremen, 1982), trans. T. F. X. Noble and T. Head, _Soldiers of Christ_ (University Park, PA, 1995), pp. 279–91.
On Liudger's career, see the summary in Wood, _Missionary Life_ , pp. 100–17.
_Vita Lebuini_ , c. 6, ed. A. Hofmeister, _MGH SS_ XXX.2 (Leipzig, 1934), pp. 789–95, p. 794; translation based on Talbot, p. 232.
Boniface, _Epistolae, Ep_. 86, trans. Emerton, no. LXX, pp. 157–9; Eigil follows the same _topos_ in the _Vita Sturmi_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), pp. 365–77, cc. 5–12: see Wood, _Missionary Life_ , p. 70.
Wood, _Missionary Life_ , p. 91. Beornrad was also archbishop of Sens.
R. McKitterick, _Anglo-Saxon Missionaries in Germany: Personal Connections and Local Influences_ , Vaughan Paper 36 (Brixworth, 1991), repr. in McKitterick, _Books, Scribes and Learning in the Frankish Kingdoms, 6th–9th Centuries_ (Aldershot, 1994), no. IV.
Wood, _Missionary Life_ , p. 92.
On Bede's notion of mission, see Wood, _Missionary Life_ , pp. 44–5.
_Vita Amandi_ , c. 24, ed. B. Krusch, _MGH SRM_ V (Hanover, 1910), p. 448, trans. Hillgarth, _Christianity and Paganism_ , p. 147.
Boniface, _Epistolae, Epp_. 50 and 60, trans. Emerton, nos. XL and XLVIII, pp. 78–83 and 107–11. See also J. M. Wallace-Hadrill, The _Frankish Church_ (Oxford, 1983), p. 137.
As the Council of 786 reported to Pope Hadrian: Alcuin, _Ep_. 3, c. 10, ed. Dümmler, pp. 19–29 at p. 23.
_Capit_. I, no. 122, p. 241; and see J. Lynch, _Godparents and Kinship in Early Medieval Europe_ (Princeton, NJ, 1986), pp. 285–332.
I. Wood, 'Before or after mission. Social relations across the middle and lower Rhine in the seventh and eighth centuries', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 149–66.
_Conventus episcoporum at ripas Danubii_ (a.796), in _Conc_. II/I, no. 20, pp. 172–6; de Jong, 'Charlemagne's Church', in Story (ed.), _Charlemagne_ , pp. 126–7.
Alcuin, _Epp_. nos. 107, 110, 112, 113, trans. Allott, nos. 59, 56, 137. For context on the Avars and Saxons see above, Chapter 2, pp. 70–2, 73–5.
Alcuin, _Ep_. 184, trans. Allott, no. 65.
E.g. Chapter 2.
Alcuin, _Ep_. 184, trans. Allott, no. 65.
See above, p. 91.
For the relationship between miracle and word in a slightly earlier context, see K. Cooper, 'Ventriloquism and the miraculous: conversion, preaching, and the martyr exemplum in late antiquity', in K. Cooper and J. Gregory (eds.), Signs, Wonders, Miracles. Representations of Divine Power in the Life of the Church, _Studies in Church History_ 41 (Woodbridge, 2005), pp. 22–45.
Airlie, 'Private bodies'.
Innes, _State and Society_ , pp. 34–40 with references; G. Halsall, 'Burial ritual and Merovingian society', in J. Hill and M. Swan (eds.), _The Community, the Family and the Saint_ (Turnhout, 1998), pp. 325–38, and G. Halsall, 'Female status and power in early Merovingian central Austrasia: the burial evidence', _Early Medieval Europe_ 5/1 (1996), pp. I–24. In general, see F. S. Paxton, _Christianizing Death: The Creation of a Ritual Process in Early Medieval Europe_ (Ithaca and London, 1990).
M. Costambeys, 'Burial topography and the power of the Church in fifth- and sixth-century Rome', _PBSR_ 69 (2001), pp. 169–89.
C. La Rocca, 'Segni di distinzione. Dai corredi funerari alle donazioni "post obitum" nel regno longobardo', in L. Paroli (ed.), _L'ltalia centro-settentrionale in età longobarda_ (Florence, 1997), pp. 31–54.
See Matt. 26:26–8, Mark 14:22–4, Luke 22:19–20; also I Cor. II:23–7.
_CDL_ I 96: 'pro anima mea grauata ponderibus peccatis meis die noctuque omnipotentem Deum et eiusdem omnipotentis Dei genitrice Maria uel beatissimi sancti Petri et Pauli seu Anastasii, in cuius honore ecclesia est fundata, exorare, ut me nimis peccator de uinculis penarum eripere dignetur'; the passage continues: 'et inter sanctis et electis suis aliqua parte uel societas tribuere iubeas, quia scriptum est per eloquium et minestrationem domini nostri Iesu Christi: "petite et dabitur uobis, querite et invenietis, pulsate et aperietur uobis"' (Matthew 7:7).
_CDL_ II 203; on Gaidoald _medicus_ see C. Wickham, _Framing the Early Middle Ages. Europe and the Mediterranean, 400–800_ (Oxford, 2005), p. 215.
C. La Rocca, 'La legge e la pratica. Potere e rapporti sociali nell'Italia dell' VIII secolo', in C. Bertelli and G. P. Brogiolo (eds.), _Il futuro dei Longobardi. L'Italia e la costruzione dell'Europa di Carlo Magno_ (Brescia, 2000), pp. 45–69 at p. 52.
_CDL_ II 203.
R. Meens, 'The frequency and nature of early medieval penance', in P. Biller and A. Minns (eds.), _Handling Sin: Confession in the Middle Ages_ (Woodbridge, 1998), pp. 35–61.
S. Hamilton, 'The unique favour of penance: the Church and the people _c_.800– _c_.1100', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 229–45, esp. 232–3.
Brown, _Rise of Western Christendom_ , p. 226. On the meaning of such prayers for the dead, see A. Angenendt, 'Theologie und Liturgie der mittelalterlichen Totenmemoria', in K. Schmid and J. Wollasch (eds.), _Memoria. Der geschichtliche Zeugniswert des liturgischen Gedenkens im Mittelalter_ (Munich, 1984), pp. 80–199.
See the controversy between Althoff and Hoffmann, the most recent salvo in which is G. Althoff and J. Wollasch, 'Bleiben die _Libri Memoriales_ stumm? Eine Erwiderung auf H. Hoffmann', _Deutsches Archiv für Erforschung des Mittelalters_ 56 (2000), pp. 33–53, and D. Geuenich, 'A survey of the early medieval confraternity books from the continent', in D. Rollason (ed.), _The Durham Liber Vitae and its Context_ (Woodbridge, 2004), pp. 141–7.
D. MacCulloch, _Reformation. Europe's House Divided, 1490–1700_ (London, 2003), pp. 11–14.
P. Brown, _The End of the Ancient Other World: Death and Afterlife between Late Antiquity and the Early Middle Ages_ , Tanner Lectures (New Haven, CT, 1996), pp. 51–3. It should be noted that the distinction between 'venial' and 'mortal' sins, still current in Catholic theology, comes later.
P. Brown, 'Vers la naissance de purgatoire'.
Compare e.g. Brown, _Rise of Western Christendom_ , pp. 258–65 with C. Watkins, 'Sin, penance and purgatory in the Anglo-Norman realm', _P &P_ 175 (2002), pp. 3–33.
_Visio Fursi_ Vision of Fursa], 16.5, ed. C. Carozzi, _Le Voyage de l'âme dans l'au- delà_ , Collection de l'EFR 189 ([Rome, 1994), p. 691, and see in general pp. 99–186; _Visio Baronti_ , ed. W. Levison, _MGH SRM_ v (Hanover, 1910), pp. 386–94, 12, trans. Hillgarth, _Christianity and Paganism_ , p. 199; see also Y. Hen, 'The structure and aims of the _Visio Baronti'_ , _Journal of Theological Studies_ , n.s. 47 (1996), pp. 477–97; Brown, _Rise of Western Christendom_ , pp. 258–60.
See Watkins, 'Sin, penance and purgatory', pp. 14–15.
M. McLaughlin, _Consorting with Saints: Prayer for the Dead in Early Medieval France_ (Ithaca and London, 1994); P. Geary, 'Exchange and interaction between the living and the dead in early medieval society', in Geary, _Living with the Dead in the Early Middle Ages_ (Ithaca, NY, and London, 1994), pp. 77–94; and D. Iogna- Prat, 'The dead in the celestial bookkeeping of the Cluniac monks', in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 340–62.
Innes, _State and Society_ , pp. 18–19. On Chrodegang: M. Claussen, _The Reform of the Frankish Church. Chrodegang of Metz and the_ Regula canonicorum _in the Eighth Century_ (Cambridge, 2004), pp. 19–57.
_Dipl. Kar_. I, no. 65. For the political background, see above, Chapter 2.
Innes, _State and Society_ , pp. 55–7 and 180–2; Innes, 'Kings, monks and patrons', pp. 308–10.
Acts 2: 44–6.
See initially G. Ladner, _The Idea of Reform: Its Impact on Christian Thought and Action in the Age of the Fathers_ (Cambridge, MA, 1959).
For the diversity of liturgy in Merovingian Francia in this context, see Hen, _Culture and Religion_ , pp. 61–81 and 143–4.
_CDL_ I 54, 59; II 188, 190, 234, 291; on lighting in this context, see P. Fouracre, 'Eternal light and earthly needs: practical aspects of the development of Frankish immunities', in W. Davies and P. Fouracre (eds.), _Property and Power in the Early Middle Ages_ (Cambridge, 1995), pp. 53–81.
In the preface to the _Expositio antiquae liturgiae Gallicanae_ , for example, the mass 'is sung in commemoration of the death of the Lord... that by being offered it may bring about the salvation of the living and the rest of the dead': _Expositio antiquae liturgiae Gallicanae_ , ed. E. Ratcliff, Henry Bradshaw Society 98 (London, 1971), pp. 3–16, here p. 3, trans. Hillgarth, _Christianity and Paganism_ , pp. 186–92, here p. 186. The text is convincingly dated to the Merovingian period by Hen, _Culture and Religion_ , pp. 47–9. Noting this development in the eighth and ninth centuries makes conceptions of the mass in the twelfth century look less original; for the latter, see M. Rubin, _Corpus Christi: the Eucharist in Late Medieval Culture_ (Cambridge, 1991), esp., in this context, pp. 13–14.
R. McKitterick, _The Frankish Church and the Carolingian Reforms, 789–895_ (London, 1977), pp. 115–55; D. Ganz, 'Theology and the organisation of thought', in _NCMH_ II (Cambridge, 1995), pp. 758–85, at pp. 777–80.
Rubin, _Corpus Christi_ , p. 16.
A. Wurnburger (ed.), _Über eine ungedruckte Kanonensammlung aus dem 8. Jahrhundert_ (Munich, 1890), p. 60 (taken from Paris, BN lat. 12444), quoted in McKitterick, _Frankish Church_ , p. 148.
Paschasius Radbertus, _De corpore et sanguine Domini_ , ed. B. Paulus, _CCCM_ 16 (Turnhout, 1969), p. 23.
Ratramnus of Corbie, _De corpore et sanguine Domini_ , PL cxxi, cols. 169–70.
Amalarius of Metz, _De officiis_ , ed. J. Hanssens, _Amalarii opera litúrgica omnia_ II, Studi e Testi 138–40 (Vatican City, 1948–50), pp. 13–543.
Agobard of Lyons, _De Antiphonario_ , ed. L. van Acker, _CCCM_ 52 (Turnhout, 1981), pp. 335–51; Florus of Lyon, _Adversus Amalarium_ , PL 119, cols. 74–6; Synod of Quierzy: _Concilium Carisiacense, Conc_. II/I, pp. 768–82; see further Ganz, 'Theology and the organisation of thought', pp. 777–8.
McKitterick, _Frankish Church_ , pp. 150–5.
Costambeys, _Power and Patronage_ , Chapter 2 (this figure includes, however, four churches in or just outside local towns). On the 'extreme flexibility of religious geography in the early middle ages', see P. Toubert, _Les Structures du Latium médiéval: Le Latium méridional et la Sabine du_ IXee _siècle á la fin du_ XIIe _siècle_ , 2 vols., Bibliothèque des écoles françaises d'Athènes et de Rome 221 (Rome, 1973) II, pp. 855–6.
E.g. _Capit_. i, nos. 138, c. 9, 140, c. 5.
_Admonitio ad omnes regni ordines_ , c. 5, _Capit_. I, p. 304.
On development of the metropolitan structure, see R. Reynolds, 'The organisation, law and liturgy of the western church, 700–900', in _NCMH_ II, pp. 587–621 at pp. 599–600.
For a relatively upbeat assessment of the extent of parish organisation in Francia by the time of Hincmar, see McKitterick, _Frankish Church_ , p. 64; see also C. Treffort, _L'Église carolingienne et la mort_ (Lyon, 1996), p. 188.
C. van Rhijn, _Shepherds of the Lord. Priests and Episcopal Statutes in the Carolingian Period_ (Turnhout, 2007).
Alcuin, _Ep_. 228, trans. Allott, no. 91; see M. Garrison, 'The Franks as the new Israel? Education for an identity from Pippin to Charlemagne', in Hen and Innes, _Uses of the Past_ , pp. 114–61, esp. pp. 159–60 and de Jong, 'Charlemagne's church', p. 113 ('the expression _novus Israel_ was never used').
M. de Jong, 'Religion', in R. McKitterick (ed.), _The Early Middle Ages: Europe 400–1000_ (Oxford, 2001), pp. 131–66, at pp. 155–6.
There is still scope for a detailed study of Carolingian tithe. Pippin III's concern to enforce it seems evident from a letter to Archbishop Lull: Boniface, _Epistolae_ , _Ep_. 118 (not translated in Emerton); see further G. Constable, _Monastic Tithes from their Origins to the Twelfth Century_ (Cambridge, MA, 1964).
Y. Hen, 'Knowledge of canon law among rural priests', _Journal of Theological Studies_ 50 (1999), pp. 117–34.
Hamilton, 'The unique favour of penance', pp. 240–2. See further C. van Rhijn and M. Saan, 'Correcting sinners, correcting texts: a context for the _Paenitentiale pseudo-Theodori_ ', _EME_ 14/1 (2006), pp. 23–40.
Hamilton, 'The unique favour of penance', p. 231.
M. de Jong, 'Power and humility in Carolingian society: the public penance of Louis the Pious', _EME_ I (1992), pp. 29–52; M. de Jong, 'What was public about public penance? _Poenitentia publica_ and justice in the Carolingian world', _La giustitia nell'alto medioevo (secoli IX-XI_), Settimane di Studio del Centro italiano di studi sull'alto medioevo 44 (Spoleto, 1997), pp. 863–902; M. de Jong, 'Transformations of penance', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 184–224; Hamilton, 'The unique favour of penance', pp. 234–5.
Bede, _Epistola ad Egbertum_ , ed. C. Plummer, _Venerabilis Baedae opera historica_ (Oxford, 1896), pp. 405–23, esp. 414–16.
_CDL_ IV/I 8.
On the development of the cloister, see W. Braunfels, _Monasteries of Western Europe. The Architecture of the Orders_ , trans. A. Laing (London, 1972), pp. 27–9. For the cloister at Farfa and, by comparison, at other eighth-century abbeys, see C. McClendon, _The Imperial Abbey of Farfa_ (New Haven, CT, 1987), pp. 8, 64–6, 70–4, 116.
Claussen, _The Reform of the Frankish Church_ , pp. 19–57.
Innes, _State and Society_ , pp. 51–9.
Costambeys, 'An aristocratic community'.
McKitterick, _The Carolingians and the Written Word_ , pp. 83–4, 178–85; _Frankish Kingdoms_ , pp. 42–4.
Costambeys, _Power and Patronage_ , pp. 250–352.
Halsall, _Warfare and Society_ , pp. 72–6; J. L. Nelson, 'The Church's military service in the ninth century: a contemporary comparative view?', in W. J. Shiels (ed.), _The Church and War_ , Studies in Church History 20 (1983), pp. 15–30, repr. Nelson, _Politics and Ritual_ (1986), pp. 117–32; Innes, _State and Society_ , pp. 13–34; Fouracre, _Charles Martel_ , pp. 137–45.
_Notitia de servitio monasteriorum_ (a.819), ed. P. Becker, _CCM_ I (Siegburg, 1963), pp. 493–9.
A. Doll, 'Das Pirminskloster Hornbach. Gründung und Verfassungsentwicklung bis Anfang des 12. Jahrhunderts', _Archiv für mittelrheinische Kirchengeschichte_ 5 (1953), pp. 108–42.
See Fouracre, 'Eternal light', pp. 70–1.
B. Rosenwein, _Negotiating Space: Power, Restraint and Privileges of Immunity in Early Medieval Europe_ (Manchester, 1999), esp. pp. 74–96.
C. Wampach (ed.), _Geschichte der Grundherrschaft Echternach im Frühmittelalter_ 1.2: _Quellenband_ (Luxemburg, 1930), nos. 14 and 15.
M. de Jong, 'Carolingian monasticism: the power of prayer', in _NCMH_ II, pp. 623–7.
De Jong, 'Charlemagne's Church', p. 106.
I Corinthians 7:1–2 (NRSV). For comment, see P. Brown, _Body and Society. Men, Women and Sexual Renunciation in Early Christianity_ (New York, 1988), pp. 53–5 ('Paul left a fatal legacy to future ages').
Jonas, _Vita Columbani_ , i.19, ed. B. Krusch, _MGH SRM_ IV, p. 87, trans. E. Peters, _Monks, Bishops and Pagans_ (Philadelphia, PA, 1975), p. 94; see J. L. Nelson, 'Queens as Jezebels: Brunhild and Balthild in Merovingian history', in D. Baker (ed.), _Medieval Women: Essays Dedicated and Presented to Professor Rosalind M. T. Hill_ , Studies in Church History: Subsidia I (Oxford, 1978), pp. 31–77 at p. 29, repr. in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 219–53, and in J. L. Nelson, _Politics and Ritual in Early Medieval Europe_ (London, 1986), pp. 1–48. _Visio Baronti_ , c. 12, ed. Levison, p. 386, trans. Hillgarth, _Christianity and Paganism_ , p. 199.
Lynch, _Godparents and Kinship_.
M. de Jong, 'To the limits of kinship: anti-incest legislation in the early medieval west (500–900)', in J. Bremmer (ed.), _From Sappho to De Sade: Moments in the History of Sexuality_ (London and New York, 1989), pp. 36–59.
P. Toubert, 'The Carolingian moment (eighth–tenth century)', in A. Burguiere, _et al_. (eds.), _A History of the Family_ (Cambridge, 1996), pp. 379–406, at 396–406.
On the elusiveness of early medieval love, on which further study is certainly needed, see C. Larrington, 'The psychology of emotion and study of the medieval period', _EME_ 10/2 (2001), pp. 251–6.
The progress of the case is summarised in Airlie, 'Private bodies', pp. 8–9. For a similar marital problem also accessible to us through Archbishop Hincmar's writings, see Smith, _Europe after Rome: A New Cultural History_ (Oxford, 2005), pp. 131–3.
Airlie, 'Private bodies', pp. 29–33.
Markus, _Gregory the Great_ , pp. 28–9.
E.g. _Leges Liutprandi_ 6, ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ (Weimar, 1947; repr. Witzenhausen, 1962), pp. 99–182, trans. Fischer-Drew, _The Lombard Laws_ , p. 146. On Liutprand's legislating, see La Rocca, 'La legge e la pratica'.
Different manuscripts of collections of papal biographies transmit different texts of Stephen II's _Life_ , among which two contrasting versions have been identified (one more and one less 'pro-Frankish' or 'anti-Lombard'): see Davis, _The Lives of the Eighth-Century Popes_ , pp. 51–2; but all versions agree that Pippin was at the pope's feet, not _vice versa_.
_LP_ I, pp. 447, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 63.
E.g. _Chron. Moiss._ , p. 293.
De Jong, 'Charlemagne's Church', p. 116.
Translated in three books by R. Davis, _The Book of Pontiffs_ (Liber Pontificalis), rev. edn (Liverpool, 2000); _Lives of the Eighth-Century Popes; The Lives of the Ninth-Century Popes_ (Liber pontificalis) (Liverpool, 1995).
T. F. X. Noble, 'Paradoxes and possibilities in the sources for Roman society in the early middle ages' in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 55–83, at pp. 58–73 (construction) and pp. 73–83 (other gifts); see also C. Goodson, _The Rome of Pope Paschal I. Papal Power, Urban Renovation, Church Rebuilding and Relic Translation, 817–824_ (Cambridge, 2010).
R. Coates-Stephens, 'Byzantine building patronage in post-Reconquest Rome', in M. Ghilardi, _et al_. (eds.), _Les Citès de l'Italie tardo-antique ( IVe–VIe siécle_) (Rome), pp. 149–66.
Alcuin, _Ep_. 245, ed. Dümmler, pp. 393–8, trans. Dutton, _Carolingian Civilization_ , p. 131, trans. Allott, no. 114.
CC, no. 3.
See above, Chapter 2, pp. 66–7.
Y. Hen, _The Royal Patronage of Liturgy in Frankish Gaul to the death of Charles the Bald (877)_ , Henry Bradshaw Society Subsidia 3 (London, 2001), pp. 65–95. (1989), pp. 112–30.
Theodemar of Monte Cassino, _Letter to Charlemagne_ , ed. K. Hallinger and M. Wegener, _CCM_ I (Siegburg, 1963), pp. 157–75, and _MGH Epp_. IV ( _Epp. Karolini aevi_ II), ed. E. Dümmler (Berlin, 1895), no. 13, pp. 509–14. According to Paul the Deacon, the autograph copy of the _Rule of St Benedict_ had been taken from Monte Cassino to Rome when the former was sacked by the Lombards in the 570s ( _HL_ IV.17), and returned by Pope Zacharias in the 740s following Petronax's refoundation of the abbey ( _HL_ vi.40).
K. Zelzer, 'Von Benedikt zu Hildemar. Zu Textgestalt und Textgeschichte der _Regula Benedicti_ auf ihrem Weg zur Alleingeltung', _Frühmittelalterliche Studien_ 23 (1989), pp 112–30.
Hen, _Royal Patronage of Liturgy_ , pp. 72–8.
Hen, _Royal Patronage of Liturgy_ , pp. 75–6.
Costambeys and Leyser, 'Neighbour of St Stephen'.
Alcuin, _Ep_. 93.
Boniface, _Epistolae, Ep_. 19, ed. Tangl, p. 33 ('Ministerio quoque praesentis fratris karissimi Bonifatii, quem ad vos episcopum consecratum in sorte praedicationis distinavimus...'), trans. Emerton, no. XI, pp. 44–5. The translation given here differs slightly from Emerton's.
Boniface, _Epistolae, Ep_. 28, p. 50, trans. Emerton, no. XX, pp. 57–9.
Boniface, _Epistolae, Epp_. 60 and 80, trans. Emerton, nos. XLVIII and LXIV, pp. 107–11 and 142–9.
Boniface, _Epistolae, Ep_. 51, trans. Emerton, no. XLI, pp. 83–8, a letter from Zacharias to Boniface of I April 743, brings out Carloman's role.
Boniface, _Epistolae, Ep_. 56, trans. Emerton, no. XLIV, pp. 91–4; 'Karlmanni principis capitulare', _Capit_. I, pp. 24–7.
'Capitulare Liptinense', _Capit_. I, pp. 27–9.
De Jong, 'Charlemagne's Church', p. 111.
Boniface, _Epistolae, Ep_. 59, trans. Emerton, no. XLVII, pp. 98–107; see further N. Zeddies, 'Bonifatius und die zwei nützliche Rebellen: die Häretiker Adelbert und Clemens', _Ordnung und Aufruhr im Mittelalter: historische und juristische Studien zur Rebellion_ , Ius Commune. Sonderheft 70 (Frankfurt, 1995), pp. 217–63.
This seems to be the implication of Pope Zacharias's decision to keep Aldebert's unholy documents: Boniface, _Epistolae, Ep_. 60, trans. Emerton, no. XLVIII, pp. 107–11.
Boniface, _Epistolae, Ep_. 60, trans. Emerton, no. XLVIII, pp. 107–11.
Boniface, _Epistolae, Ep_. 80, trans. Emerton, no. LXIV, pp. 143–9, at p. 147.
Boniface, _Epistolae, Ep_. 68, trans. Emerton, no. LIV, pp. 122–3. The ignorant Bavarian priest had apparently said 'Baptizo te in nomine patria et filia et spiritus sancti' (I baptise you in the name fatherland and daughter and holy spirit), instead of 'Baptizo te in nomine patris et filii et spiritus sancti'.
_Admonitio generalis_ , preface, _Capit_. I, no. 22, p. 53, trans. King, _Charlemagne: Translated Sources_ , p. 209.
Perhaps not coincidentally, the one letter of Charlemagne to dwell on the preaching of the priesthood was addressed to Bishop Gerbald of Liége, also closely associated with surviving examples of the _capitula episcoporum:_ the letter is _Capit_. 1, no. 122.
_Capit_. 11, no. 203, c. 6, p. 66.
_Capitulare missorum generale_ a.802, _Capit_. 1, nos. 33–4, pp. 91–102, trans. King, _Charlemagne: Translated Sources_ , pp. 233–42.
_Epistola de litteris colendis, Capit_. 1, no. 29, pp. 78–9, trans. King, _Charlemagne: Translated Sources_ , pp. 232–3.
II Kings 22, 23: cited in _Admonitio generalis_ , prologue, _Capit_. i, no. 22, pp. 52–62 at 54, trans. King, _Charlemagne: Translated Sources_ , p. 214.
_Admonitio generalis_ , c. 72, _Capit_. i, no. 22, pp. 52–62 at 60, trans. King, _Charlemagne: Translated Sources_ , p. 217.
For a good introduction to the visual art and architecture of the period, see D. Bullough, _The Age of Charlemagne_ (London, 1965), pp. 131–59.
R. McKitterick, 'Script and book production', in McKitterick (ed.), _Carolingian Culture_ , pp. 221–47. See also above, Chapter 1, p. 17.
_Epistola generalis, Capit_. i, no. 30, pp. 80–1, trans. King, _Charlemagne: Translated Sources_ , p. 208.
R. McKitterick, 'Some Carolingian law-books and their function', in B. Tierney and P. Linehan (eds.), _Authority and Power. Studies in Medieval Law and Government Presented to Walter Ullman_ (Cambridge, 1984), pp. 13–27, and McKitterick, 'Carolingian book production: some problems', _The Library_ , 6th ser., 12 (1990), pp. 1–33; both repr. in her _Books, Scribes and Learning in the Frankish Kingdoms_ (Aldershot, 1994).
See above, Chapter 1, pp. 16–17.
See above, Chapter 1.
For this calculation, see Chapter 1.
Ermenric of Ellwangen, _Epistola ad Grimaldum Abbatem_ , ed. E. Dümmler, _MGH_ _Epp_. v ( _Epp. karolini aevi_ III) (Berlin, 1899), pp. 561–2.
See above, Chapter 1, pp. 18–23.
For the Italian scholars, see D. Bullough, _'Aula renovata:_ the Carolingian court before the Aachen palace', _PBA_ 71 (1985), pp. 267–301, repr. in Bullough, _Carolingian Renewal_ , pp. 123–60.
L. Wallach, _Alcuin and Charlemagne_ , 2nd edn (Ithaca, NY, 1968), pp. 198–226; Bullough, _'Aula renovata'_ , p. 284.
See now J. Story, 'Cathwulf, kingship and the royal abbey of Saint-Denis', _Speculum_ 74 (1999), pp. 1-21.
J. Marenbon, 'Candidus', _Oxford DNB, s.n_.
M. Garrison, 'Fridugisus', _Oxford DNB, s.n_.
M. Garrison, 'Joseph Scottus', _Oxford DNB, s.n_. (for most of the Middle Ages, the epithet 'Scottus' meant 'Irishman').
D. Ganz, 'Dúngal', _Oxford DNB, s.n_.
J. J. Contreni, 'Dícuil', _Oxford DNB, s.n_.
See Godman, _Poetry of the Carolingian Renaissance_ , no. 15, ll. 213–33 (with trans.), for Theodulf's verses against Cadac-Andreas, and pp. 6, 10–16 on Theodulf's poetry and rivalry with Cadac-Andreas, with references. _Opus Caroli regis contra synodum_ ( _Libri Carolini_ ), ed. A. Freeman with P. Meyvaert, _MGH Conc_. II (Hanover, 1998); on this text see T. F. X. Noble, _Images, Iconoclasm and the Carolingians_ , esp. pp. 158–206. The usual term for the struggle over images in the Byzantine empire – 'iconoclasm' (literally, 'image-breaking') – is misleading because there is very little evidence for the actual destruction of images. On the whole issue, see J. Haldon and L. Brubaker, _Byzantium in the Iconoclast Era, c.680–850_ (Cambridge, 2010).
D. Bullough, 'Alcuin', _Oxford DNB, s.n_.
P. E. Dutton, _The Politics of Dreaming in the Carolingian Empire_ (Lincoln, NE, 1994).
Aachen, 817, c. 5, _CCM_ I (Siegburg, 1963), p. 474.
Hrabanus Maurus, _De institutione clericorum libri tres. Studien und Edition_ , ed. D. Zimpel (Frankfurt, 1996), and Hrabanus Maurus, _De rerum naturis_ , PL 111, cols. 9–614.
Hincmar of Rheims, _Collectio de ecclesiis et capellis_ , ed. M. Stratmann, _MGH Fontes iuris germanici antiqui_ XIV (Hanover, 1990); also _Capitula quibus de rebus magistri et decani singulas ecclesias inquirire_ , PL cxxv, cols. 777–92.
Hincmar of Rheims, _De ordine palatii_ , ed. T. Gross and R. Schieffer, _MGH Fontes iuris germanici antiqui_ III (Hanover, 1980), trans. D. Herlihy, _A History of Feudalism_ (London, 1970), pp. 209–27; see J. L. Nelson, 'Kingship, law and liturgy in the political thought of Hincmar of Rheims', _EHR_ 92 (1977), pp. 241–79.
P. McKeon, _Hincmar of Laon and Carolingian Politics_ (Urbana, IL, 1978).
Wood, _Missionary Life_ , pp. 57–73.
Smith, 'Old saints, new cults'; Hincmar of Rheims, _Vita Remigii episcopi Remensis_ , ed. B. Krusch, _MGH SRM_ III (Hanover, 1896), pp. 239–349, trans. D. Herlihy, _A History of Feudalism_ (London, 1970), pp. 122–4.
P. Fouracre, 'The context of the OHG _Ludwigslied_ ', _Medium Aevum_ 54 (1985), pp. 97–103.
McKitterick, _The Carolingians and the Written Word_ , pp. 182–5.
For Hucbald of St Amand, see initially J. M. H. Smith, 'A hagiographer at work: Hucbald and the library at Saint-Amand', _Revue bénédictine_ 106 (1996), pp. 151–71.
McKitterick, _Frankish Kingdoms_ , pp. 207–10.
On Lupus, see T. F. X. Noble, 'Lupus of Ferriéres in his Carolingian context', in A. C. Murray (ed.), _Rome's Fall and after. Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 232–50.
H. Reimitz, 'Ein fränkisches Geschichtsbuch aus Saint-Amand und der Codex Vindobonensis palat. 473', in C. Egger and H. Weigl (eds.), _Text-Schrift-Codex. Quellenkundliche Arbeiten aus dem Institut für Österreichische Geschichtsforschung_ , MIÖG Ergänzungsband 35 (Vienna and Munich, 2000), pp. 34–90; Reimitz, 'Art of truth'.
R. McKitterick, 'The Carolingian renaissance of culture and learning', in Story (ed.), _Charlemagne_ , pp. 151–66.
See above, pp. 119–21.
## 4
### INVENTING THE CAROLINGIAN EMPIRE: POLITICS AND GOVERNMENT, 800–840
#### INTRODUCTION
Very early in the year 814, having endured a winter of fevers and pains in his side, Charlemagne took to his deathbed. Abstaining from food, as he was accustomed to do when sick, the sixty-five-year-old ruler tried to fight off his illness armed with 'nothing more than an occasional drink'. A week later, on 28 January at 9 o'clock in the morning, he died. Charlemagne's friend and biographer Einhard tells us that without delay, the emperor's body was washed and prepared for burial. Later that same day he was placed in a late antique imperial sarcophagus obtained from Italy and interred under the west entrance of the church in his principal palace at Aachen while all present wept. To judge by a lavish lament written shortly afterwards by a monk from the Italian monastery of Bobbio, their tears were shared by mourners across the empire: 'Francia has endured awful wounds / But never has suffered such great sorrow as now / Alas for miserable me.'
The hyperbole used to describe his people's grief should probably be taken with a pinch of salt, and serves as an index of how quickly after his death Charlemagne passed into the realms of mythical greatness. Nonetheless, people taking stock of his final achievements in the immediate aftermath of his death would probably have been inclined to dwell on three major landmarks. One was Charlemagne's most famous act, his coronation as emperor on Christmas Day 800 in Rome. This resonant event seems in retrospect to represent the highpoint of his reign, setting the seal on the territory he had acquired, reinforcing his alliance with the papacy and opening a new imperial epoch in European history. Another was the winding down of the wars of expansion in the early years of the ninth century, drawing to a successful close the annual cycles of war and aggression that had characterised Frankish politics since the age of Charles Martel. Thirdly and finally, shortly before his final illness Charlemagne bequeathed the Frankish empire, secured, stabilised and ennobled by the lustre of Rome, to his last surviving son Louis ('the Pious') with the consent of all the leading men.
According to the trajectory of this rosy narrative, Louis could hardly have taken over the reins of the empire in a better position. Nevertheless, in the view of posterity, he blew it. If Charlemagne is the archetypally heroic medieval emperor, Louis is the hapless failure from central casting. He has long been seen as a pale reflection of his magnificent predecessor, as weak and feckless a ruler as his father was great. The story of his lengthy reign (814–40) is usually written as a tragic tale of disaster and crisis in which the emperor is cast as a weak cipher, dominated by his churchmen and his wife, aloof and uninterested in worldly affairs, and overdependent on particular favourites. Writing in 837 one of his two biographers, Thegan of Trier, sketched a Louis who was detached and imperious and 'never even allowed his white teeth to be bared in laughter'. The other, an anonymous author known as the Astronomer, wrote shortly after Louis's death that he had had the fault of being 'all too mild'; and that at times he had considered abandoning secular responsibility to enter a monastery. Both biographies were attempts to grapple with the causes and consequences of the great events of the reign, in particular the massive rebellions raised against the emperor by his three eldest sons in 830 and 833–4, which attracted considerable aristocratic support and for a time achieved his deposition. The success of the rebellions was unprecedented in living memory and their deeply unsettling consequences reverberated through Carolingian politics for decades: even forty years later they were still invading the dreams of the emperor's son King Louis the German, who saw a troubling vision of his father in hell and ordered all the churches in his kingdom to organise prayers for his soul's redemption. Modern historians have been similarly shocked by the turmoil of the early 830s, sometimes defining it as the first chime of the empire's slow decline. As a result, accounts of Louis's reign are often compressed into a search for clues as to the personal and political flaws that lay at the root of the disintegration.
These two caricatures (Charles as Great, Louis as Weak) form a diptych which until recently structured almost all accounts of Frankish politics in the first half of the ninth century. Since the 1990s, however, there have been significant attempts to write more nuanced accounts of Louis's reign which rehabilitate his personal capabilities. The most common mitigating plea is that Charlemagne's last years, far from being the glorious culmination described in our opening paragraphs, in fact witnessed a phase of decline and disintegration, and that some of Louis's problems were therefore inherited from his frail father. Images of age suffuse early-ninth-century descriptions of Charlemagne's imperial years, during the final four of which he was ill. Compare the flickering images of the bellicose and perpetually moving eighth-century Charlemagne provided by Einhard and the _Royal Frankish Annals_ , a ruler unable even to sleep through the night without getting up to deal with affairs of state, with the poet Ermold the Black's stately tableau of the old emperor on his throne in 813, white hair flowing over his pale neck and quavering that 'my war-like right hand, once famous throughout the world, now shakes as my blood grows cold'. In the months before he died, omens symbolising the decay of the aged emperor were reported. The word _princeps_ (ruler) faded from the inscription identifying him as the builder of the church at Aachen: the emperor's personal decline was seen as connected to the dwindling of what he had created. Historians have also detected the frustrations of an old man in the exasperated tone of some of Charlemagne's governmental decrees from late in the reign, which rage about the shortcomings of various royal agents. These hints of underlying political decline have suggested to some historians that the last decade of Charlemagne's reign should be seen as a political twilight, and that the slow fade of this once-great conqueror rendered him unable to construct an impersonal governmental apparatus that could survive without his own unique personality – that, in effect, his failure left his successor running to stand still.
These issues – Louis's weakness, and the extent to which he inherited a malaise incubated during his father's dotage – are central to traditional versions of Carolingian history written as 'magnificent tragedy'. But before accepting the terms of this debate we should pause to acknowledge the problematic assumptions inherent in their foregrounding of great or inadequate personalities as major historical forces. Arguing about the relative personal qualities of individual rulers requires us to engage in a kind of retrospective psychoanalysis for which the sources are much less useful than they may seem. In an era when the personal was highly political, the gestures, expressions and comportment of kings could be seen as profoundly symbolic. Louis's reported monastic inclinations and refusal to smile, therefore, have to be read as pointed literary constructions that tell us more about contemporary discussions of political ideas than about the emperor's sense of humour or dedication to secular affairs. The nickname _pius_ represented a positive attribute that did not carry with it modern overtones of other-worldliness. Care is also needed with the Astronomer's rueful reflection on the emperor's excessive mildness, which is undermined several times by his own account, in which for example Louis decides to blind an opponent whom the author himself considered 'worthy of mercy'. Although the personalities of early medieval kings could be very important in shaping their reigns, contemporary texts rarely open transparent windows onto their inner feelings or defining characteristics – much more often they have to be read as carefully crafted polemical presentations which were constructed to suit the agendas of their authors and audiences, and offer only an indirect view of the public image adopted by the ruler at court.
Instead of distilling the political history of this period into a story of kingly strength and weakness, of rise and decline, this chapter will try to show the underlying complexities of the political situation by focussing on the two main problems facing Charlemagne and his son after 800: the management of power within the royal/imperial dynasty; and the need to establish a pattern of politics that would tie the regional elites of the empire to the political centre. We will see that, ironically, the very success of the strategies developed to meet these challenges helped create the preconditions for the crises of the early 830s. These twin problems were perennial conundrums for early medieval dynasts (they featured prominently, after all, in Chapter 2), but they loomed over the early-ninth-century empire with particular immediacy owing to the end of territorial expansion. Eighth-century soldier-kingship was structured around an annual cycle of assemblies, campaigns and redistribution of booty which bound the Frankish elite to their Carolingian leaders and created a political culture with the war-trail at its centre. The tailing-off of the wars of conquest in the 790s, and their cessation in the very early 800s, catalysed a dramatic shift in this culture which meant the roles of every member of the elite from the royal family downwards had to be redefined. The elites of regions recently incorporated by force had to be persuaded to become willing participants in the new political order. The empire had been cobbled together, now it had to be made to fuse: in other words, it had to be invented in the imaginations and mentalities of its elites.
#### THE IMPERIAL CORONATION
At first sight, it seems natural to assume that the imperial coronation of Charlemagne in Rome on Christmas Day 800 must have played a major part in this process, by setting a seal on the spectacular conquests of the preceding decades and creating the idea of the empire as a single entity. The revival of the imperial title was a novelty: there had been no emperor in the west since the deposition in 476 of the last Roman to hold the title. Despite the breathtaking audacity of the move, hindsight has made it look almost inevitable, a natural sequel to the Franco-papal alliance established in the 750s. European rulers looked back to the event centuries later and identified it as the founding moment of the 'Holy Roman Empire'. Oppressed by our inability to ignore the knowledge of what happened later, it is easy to forget that Charlemagne was not a prophetic architect of the European future. When we look at the contemporary circumstances in detail, it becomes clear that the coronation itself was the result of a period of serious political conflict, rather than the culmination of a smooth and assured rise to imperial power, and that it may have had a much more limited significance to contemporaries than it did to the ideologues of later centuries.
The immediate context was a dispute within the city of Rome. Long-simmering tensions surrounding the pontificate of Leo III (795–816) came to a head on 25 April 799 when the pope was attacked during a public procession by enemies including senior members of the papal entourage and relatives of his predecessor. He was charged with perjury, simony (the buying of ecclesiastical office) and sexual impropriety, and an attempt was made to incapacitate him by cutting out his eyes and tongue (successful but miraculously reversed, according to papal sources). After undergoing what may have been formal deposition proceedings, Leo came to meet Charlemagne in the autumn at the palace of Paderborn where the king had been campaigning against the Saxons. Having heard representations from the pope and (again, according to papal sources) his enemies, the king sent Leo back to Rome accompanied by royal legates under instructions to investigate further and to reinstate him. That, for the time being, seemed to be the end of the matter. Charles's itinerary over the subsequent year (see Maps 5 and ) gives few obvious clues that he was gearing up for a journey to the eternal city, being taken up largely by tours of the northern coastline, apparently to oversee the construction of a fleet against the Danes, and visits to the holy shrines of Neustria. However, in August 800 the king announced his departure for Italy and at the end of his journey was received by Leo at Mentana, at the twelfth milestone from Rome. Entering the city itself at the end of November, he 'made it clear to all why he had come to Rome'. At the same time, an assembly was staged at which Leo swore that he was innocent of all that had been alleged against him in the previous year. Finally, Charles was acclaimed and crowned as emperor on Christmas Day.
Although this basic outline of events is relatively clear, their meaning and precise contours are frustratingly opaque, which has given rise to a veritable historical cottage industry dedicated to the issue. Our sources are relatively plentiful but very partial, and almost all of them were written several years later – they deceive us in appearing to provide clear journalistic windows onto the events of 799–800. Their information should be inspected as the fossilised remains of an after-the-fact and politically charged debate about the significance of what had happened; these texts were subtly argumentative, and were written as part of a contemporary struggle to control interpretation of the encounter between Charles and Leo. This means that we should resist the temptation to create a composite account of events that draws apparently complementary details from different sources, and undermines our attempts to discover what really happened. Firstly, there is an obvious difference of emphasis between the Frankish and papal sources as to the relationship between the main protagonists. The author of this section of the _Royal Frankish Annals_ , working around 807, depicts Charles as a saviour riding into Rome to save the pope from his enemies, while Leo's biographer (writing after the pope's death in 816) downplays his problems and places him in the driving seat.
**Map 5.** Places mentioned in Chapter 4: 'Inventing the Carolingian empire: politics and government, 800–840'
**Map 6.** Places on Charlemagne's itineraries, 768–814. Plotting the places known to have been visited by Charlemagne shows how far he travelled, but not how many times he stayed in one place, nor for how long. In fact, his most frequent stops almost all lie in the area between the Seine and the Rhine, and visits to Saxony, Italy and Bavaria were connected with exceptional military or political expeditions.
The _Royal Frankish Annals_ projects an image of Charlemagne claiming his rightful place at the head of the world order, confirmed by propitious omens and exotic gifts sent by respectful eastern rulers (including the Patriarch of Jerusalem, who reportedly sent him the keys to the Holy Sepulchre). A mosaic installed in the Lateran Palace by the pope conveys a rather different set of messages. (See Figure 8.) It shows Leo and Charlemagne kneeling together at the feet of St Peter, and the identifying inscriptions above or next to each figure reveal the work to have been dedicated by the pope to the king: 'St Peter, the most holy lord pope Leo, to the lord king Charles'. St Peter sits with the keys to the kingdom of heaven in his lap, indicating his power over the fate of every human soul (Matt. 16:19). To Pope Leo he gives a pallium, symbol of the jurisdictional rights of the bishop; to Charlemagne, a banner, indicating his responsibility to protect the Church; and this message is reinforced by the inscription below the figures: 'Blessed Peter give life to Pope Leo; give victory to King Charles.' The image was mirrored on the left of the apse by a mosaic in which Christ gives the keys to heaven to an unknown pope (Peter or Sylvester), and a banner to Constantine, the first Christian Roman emperor (r.306–37). In the apse itself, Christ exhorts the apostles, in the words of the so-called Great Commission (Matt. 28:19–20): 'Go ye therefore, and teach all nations, baptising them in the name of the Father and of the Son and of the Holy Spirit.' Although the mosaic (now on an exterior wall) that the modern visitor to Rome sees is a reconstruction, the original decorated an interior wall of the so-called _triclinium maius_ , the greater of two banqueting and reception halls begun by Pope Leo III in 797 or 798, and demolished in the 1580s. The mosaic was certainly completed before Charlemagne's coronation as emperor on 25 December 800, since the Frankish ruler is there still styled 'king'. The decorative scheme conveyed several linked messages: it stressed the role of the Church, and particularly the papacy, in Frankish military victory, especially over pagans like the Saxons, whom Charlemagne was fighting at that time, and the Avars, whom he had recently defeated; it linked that victory with Christianisation; it implied an association between Charlemagne's rule and that of the Roman emperors of antiquity; and it promoted the idea that legitimate Carolingian rulership depended on St Peter, and therefore on the pope. The gist of papal claims around this time is also reflected in the _Donation of Constantine_ , an influential text which claims (falsely) that the powers and resources of the western empire had been handed over to the papacy by the eponymous emperor in the fourth century.
**Figure 8.** Mosaic of Charlemagne and Pope Leo III, Rome.
Secondly, the respective biases of the sources make the balance between planning and opportunism difficult to establish. For example, Einhard's famous assertion, written down at least seventeen years after the fact, that Charles had no idea what was going to happen on Christmas Day in St Peter's before he entered the church, is sometimes taken at face value but must surely be read as a literary attempt to highlight the emperor's virtuous humility. Conversely, on the basis of references to the realm as the _imperium christianum_ in letters written by his close adviser Alcuin, it has been argued that members of Charlemagne's circle were already thinking in imperial terms in 798–9; but we must also acknowledge that the concepts to which this terminology referred were as much eschatological as political. While Einhard's claim seems implausible, and Alcuin's dangerously ambiguous, the important thing is to understand why authors made such claims at all: in the end, we probably have to be satisfied with trying to understand the ways contemporaries argued about the coronation rather than hoping to excavate the precise details of its stage-management from the mass of rhetoric under which they are buried.
This is not, however, to say that we can know nothing. When we tighten our perspective to the sources written closest in time to events, the role of another party to this argument suddenly swims into focus. A manuscript from Cologne apparently written in 798 refers obliquely to an occasion 'when messengers came from Greece to hand over the empire to Charles]'. Discussions with the Byzantines, who considered their empire to be an uninterrupted continuation of the Romans', may have been thought by Charlemagne more important than those with Leo, whose authority after all was weak even in Rome. As with the events of 753–4 discussed in [Chapters 1 and 2, we should not let the novelty of the papacy's involvement in the making of secular rulers, nor its ability to make its views stick in the historical record, mislead us into overestimating its contemporary influence. When Charles met the pope at Paderborn in 799, there were probably Byzantine legates in attendance too. The weight given by the Franks to the position of Byzantium is confirmed in backhanded fashion by the account in the _Annals of Lorsch_ , which justified the coronation with reference to the fact that the Byzantines were ruled by a woman (the dowager empress Irene), and argued that the position of emperor was therefore implicitly vacant. This is almost certainly the earliest of our narrative sources, and probably represents a version of the official line developed by the court upon Charlemagne's return from Italy.
Acknowledging the importance to the Franks of Byzantine sensibilities may also help us get closer to the contemporary meanings of the coronation. It has been argued that Charlemagne's imperial status was devised as a way of making his rule acceptable to the Saxons, whose pre-conquest society had no kings, but since Saxony had not been in the Roman empire it is hard to see on what basis an emperor would have been any more welcomed. In parts of Italy, on the other hand, the imperial title had more immediate resonance. Southern and central Italy (including Rome itself) were long accustomed to an imperial presence either directly or mediated through the Byzantine exarchates, so the gradual retreat of Byzantine power from the peninsula during the eighth century may have created something approaching a crisis of authority for its elites. Charlemagne's bid to acquire imperial status may have been designed in large part to answer that crisis by appealing to Italian models of authority; and hence to bolster his claims to govern parts of that realm which had hitherto remained beyond his reach. In this context it is significant that a Sicilian embassy visited Aachen in 799, that an official from the island is known to have defected to Charlemagne in 800 and that, according to the Byzantine chronicler Theophanes, Constantinople's greatest worry about the Frankish king's trip to Rome was that he intended to take over Sicily and the south. The events of 800 may thus be viewed in part as the result of a fortuitous alignment of Charlemagne's desire to justify his Italian ambitions through appropriation of a traditional and appropriate form of authority, Leo's need to prop up his position in Rome by making powerful friends and recasting himself as a maker of monarchs, and the Byzantines' inability to maintain active influence over their far-off Italian possessions. In the era of Charles's grandsons and for centuries after that, the title of emperor became a _de facto_ adjunct to the kingship of Italy – and as already a primarily Italian affair is perhaps the best way to interpret the dynamics that led to the events of Christmas Day 800.
This does not mean that the emperor's new status could not also have had wider resonances. There are some hints that the coronation coincided with a shift in the way that he expressed his authority. In the last twenty years of Charlemagne's reign, a new palace at Aachen was erected and gradually became the centre of a more sedentary style of Frankish rulership that could be described as imperial. Charlemagne's visit to Italy in 800–1 afforded him the opportunity to collect antique adornments for the palace which enhanced its symbolic references to the classical past: one contemporary source even refers to Aachen as a 'new Rome', and another reveals that part of the complex was known as 'the Lateran'. The seriousness with which Charlemagne regarded the title is also demonstrated by the valuable territorial concessions he was prepared to make in 812 to acquire renewed Byzantine recognition of his status – only after this was secured did he put the title on his coins. Being emperor clearly mattered to him. In other respects, Charles wore his new status lightly. It is important to remember that contemporary Rome was a religious and not a political centre, a place of pilgrimage rather than a source of jurisdiction. The coronation endowed the emperor not with a new set of constitutional powers, but rather an enhanced prestige, the nature of which drew on the powerful religious and classical–imperial resonances of the city but remained ill defined: ancient Rome was not a direct template for Alcuin's _imperium christianum_. After 801 Charlemagne declined to intervene directly in Rome's affairs, and the fact that he never went back there hints that his relationship with the pope was rather tense – although his subordinates took an interest in the city and its relics, their activities did not require them to pay much heed to papal claims to power there. The imperial dignity became part of his titulature, but did not supersede its other parts. Charles retained his traditional status as 'king of the Franks and Lombards' and continued to comport himself as a Frankish king rather than as a neo-Roman emperor – and, tellingly, the wording of the additional title he adopted (the rather lukewarm 'governing the Roman empire') owed more to the terms of Italian charter formulas than it did to the conventions of ancient Rome or contemporary Byzantium. The coronation did not change the character of the empire as a territorial unit. Nobody tried to pretend that internal regnal boundaries had been erased, and the empire remained an agglomeration of smaller units each with its own laws and customs. 'Kingdom' and 'empire' were not distinct constitutional concepts, and the Latin words _regnum_ and _imperium_ are much more ambiguous than their English counterparts (hence their general interchangeability in this book).
If the title did not radically change the way Charlemagne ruled, or the nature of what he ruled, nor did it transform the character of his dynasty. In a plan made in 806 for a posthumous division of the realm between his three sons, Charlemagne made no mention of the imperial title, though he implied that Rome was a special place outwith the main territory of the empire and was to be protected corporately by all the Frankish kings. When in 813, after the deaths of his two elder adult sons, he eventually did crown the third, Louis, as emperor, he staged the ceremony in Aachen and without reference to the pope. It is significant that Einhard, however sceptically we view the details of his account, felt able tacitly to claim that this event was _more_ important than the coronation of 800. After 800, triumphal histories of the Carolingian dynasty such as the _Earlier Annals of Metz_ (c.806) did not reconfigure their heroes as proto-emperors, but continued to root their narratives in the Merovingian Frankish past, starting with Pippin II and eulogising him and his successors as great conquerors and defenders of the Church. Twenty years later, even after Louis the Pious had been re-crowned by another pope, the poet Ermold the Black listed the predecessors of Louis's son Pippin of Aquitaine in exactly the same terms and sequence as had the Metz annalist – traditional ways of characterising the dynasty were not effaced. Empire and _Romanitas_ were resonant concepts, ringing with echoes of Rome's great secular past and its current identity as a holy city. Yet these concepts were slippery and contemporary observers clearly disagreed about their significance – they meant different things to different audiences. To Charles himself, as far as we can tell, being emperor was an extremely important badge of prestige, but perhaps no more than that. To all intents and purposes he already ruled an empire, and it remained more or less what it already was: neither a reinstitution of ancient Rome nor a newly minted 'Holy Roman Empire', but something all of its own – an 'empire of the Franks'.
#### GOVERNING THE EMPIRE
A nearly simultaneous but unrelated development of the early ninth century had a far more profound influence on the politics of the empire than did events in Rome at Christmas 800 – namely, the end of Frankish military expansion. After the defeat of the Avars in the mid-790s, thirty years of Franco-Saxon conflict finally ground to a halt in 804 with the forced immigration to Francia of the people beyond the river Elbe. The decision to bring to an end nearly a century of territorial aggrandisement seems to have been made consciously and was presumably based on a combination of factors including geography, limitations on resources and the extension of the empire to the traditional limits of Frankish influence. Military activity by no means stopped completely. The last few years of Charlemagne's reign, for example, saw the Franks assert themselves as an influential naval power in the Mediterranean, scoring victories over Byzantines and Arabs alike in Corsica, the Balearics and elsewhere. However, the establishment at this time of 'marks' ( _marca_ ), military commands designed to control the frontiers in the east and south, illustrates the conscious shift away from expansionary warfare in favour of a more regularised frontier structure.
These arrangements were not purely defensive, but also served as platforms for attempts to impose tributary status on the Slavs to the east and Danes to the north. Frankish interference in these regions had a variety of unintended consequences which could affect patterns of cross-border interaction, as exemplified by the case of the Abodrites. This grouping of Slavs, found to the east of the Elbe river, had become allies of the Franks during the Saxon campaigns, and by dealing with and bolstering sympathetic elements within the Abodrite elite Charlemagne encouraged the formation of a much clearer political hierarchy with a single leader, where previously there had been several. In the case of the Abodrites and other Slavic peoples, this form of pervasive cultural and political pressure created an impulse to social change which was hard to resist and which allowed the regularisation of relations with neighbouring peoples without the need for territorial incorporation or even persistent evangelisation. The effects of these dynamics were not always benevolent for the Franks – for example, the destabilising pressure placed on the Danes by Charlemagne's conquest of Saxony played a material role in creating the preconditions for the Viking raids of the ninth century. The consolidation of the frontiers nevertheless clearly symbolises a fundamental shift in the orientation and temperament of the Frankish polity.
The metronomic listing of conquests and frontiers in ninth-century descriptions of the empire suggests that the memory of the Franks' past victories lived on in their imaginations and constituted a central pillar of the elite's political identity. At the same time, the end of expansion had potentially negative implications for the Frankish aristocracy, which was by nature geared for war and for its reward, booty. Charlemagne's attempt to ease his aristocracy into a new 'peacetime' mentality is visible in a series of decrees from the first decade of the ninth century which aimed to redefine the military obligations of the nobility. Whereas previously, leading members of the secular aristocracy would have turned up every year at the start of the campaigning season together with their warrior followings, ready to fight in the king's army and share in the prestige and proceeds of war, the lessening of the opportunities for expansionary campaigning meant that the emperor now had to regularise and limit their duty to serve – only in the case of invasion from without were all expected to take up arms and defend the _patria_. The sheer size which the empire had now attained also had profound implications for how it was ruled. After the conquest of Saxony the total area of Frankish dominion extended to some one million square kilometres, a huge and rapid increase from the days of Pippin III. Einhard commented that the empire nearly doubled in size during Charlemagne's reign. An informed estimate suggests that there were approximately 600–700 _pagi_ (basic geographical units used to describe administrative or political jurisdiction); 700 royal estates; 150 royal residences, of which twenty-five were major palaces; 180 bishoprics (not counting around forty-five subject directly to Rome); and about 700 monasteries. By any standards, all this would take some governing. In an age before the bureaucratic state and in the absence of mass communications, this meant that the aristocracy, habituated to annual campaigning, now had to be bound into the life of the polity by other means (see Figure 9).
**Figure 9.** The Utrecht Psalter, probably produced in the Rheims area _c_.850, includes this illustration to Psalms 149 and 150, texts about God's glory and inflicting punishment on nations and kings. Although taking such images as reflecting the artist's world is sometimes problematic, it is possible that, for instance, the seated men talking in the structure towards the top left were drawn with a royal assembly in mind.
The Carolingians' response to this imperative is discernible in the gradual institutionalisation of Frankish politics which gained pace after 800. One crucial aspect of this process was the stabilisation of the political centre through the establishment of a system of government structured around palaces. Charlemagne's rule became increasingly sedentary from the 790s, coinciding with the Aachen building project, and palaces on a similar scale were built at other sites including Frankfurt, Ingelheim and Nijmegen. These complexes provided forums for regular assemblies of the great and the good. The practical benefits of such a system are illustrated by the Astronomer's description of the young Louis the Pious rotating his court around four winter palaces in Aquitaine in order to spread the burden of provisioning a large and hungry royal entourage. The regularity and predictability of this circular progress, with the venue for the next assembly announced at the end of the previous, was its central virtue: access to the ruler was made possible for all those who mattered, and the king was made available in different parts of his kingdom at different times. The effects of this on the royal itinerary are clear from the full reign of Louis the Pious, whose movements can be studied in some detail. Louis was a relatively static ruler, able to govern without making endless circuits of the empire. This is not to say he was immobile, but his itinerary was contained within relatively tight borders. He never visited Italy and rarely went west of Paris, south of Chalon-sur-Saône, north of Nijmegen or east of Remiremont or Paderborn. His general assemblies (two or three a year in the period 816–28) were almost always held in the three major palace complexes centred on Aachen, the Seine–Oise region (Ver, Quierzy etc.) and the Middle Rhine (Frankfurt, Mainz and Ingelheim). In other words, Louis ruled effectively from the heartlands of the empire, maintaining political influence in more far-flung regions by bringing the nobles in to court and sending his agents out to regulate their behaviour. Another indication of this style of government is the huge number of royal charters surviving from his reign: around 500, compared with only about twenty for the last twelve years of Charlemagne's reign. Charters, documents recording grants of land and privileges to churches and loyal followers, are the visible remains of royal patronage, clever deployment of which allowed rulers to intervene directly in distant regional politics and create bonds of mutual obligation between granter and recipient, shoring up aristocratic loyalty. The dramatic increase in the number of these documents hints at both the growing geographical centralisation of Louis's regime and the developing need to replace the diminishing flow of war booty with alternative forms of royal patronage.
**Figure 10a.** Plan of Aachen palace and chapel.
**Figure 10b.** Reconstruction of palace at Ingelheim.
These palaces were not simply administrative centres, but served to translate the political capital built up by the successful but ephemeral campaigning of the eighth century into the permanence of stone. The construction of 'public' buildings was an act for which classical and late antique emperors were often praised, and Einhard discusses Aachen, Ingelheim and Nijmegen in this context as indicative of Charlemagne's greatness (see Figures 10a and 10b). The architecture itself also conveyed the prestige of the ruler. The palaces were monumental rather than defensive or strategic, and were usually sited in rural locations not far from major towns (Ingelheim, for instance, was close to Mainz). Their multi-storey frontages rising from the surrounding countryside were intended to inspire awe in those who viewed and visited them, and their complex layouts, with halls, chapels and living quarters linked by walkways surrounding public courtyards and balconies, as at Aachen, provided monumental settings for the pronouncements of the emperor. The paraphernalia of late antique rulership adorned the rooms and open spaces of Aachen: an imperial eagle on the dome of the roof, pillars of rare black stone, and the statue of a mounted ruler believed by contemporaries to be the great sixth-century king Theoderic of the Ostrogoths. An organ received from the Byzantines and an elaborate water-clock from Baghdad represented cutting-edge technology, advertising the regime's modernity and its imperial reach. Game parks and orchards in the grounds were home to exotic peacocks and at least one middle-aged elephant, whose presence was a reminder of Charlemagne's relationship with the Abbasid caliph Harun al-Rashid from whom he had received it. Historians have even detected religiously significant number-symbolism in the dimensions of the chapel, whose octagonal shape also echoed ancient templates in Ravenna. It is debatable whether all this can be read as part of a carefully designed and unified ideological programme encoded into the design of the buildings, or whether it should be seen as a mish-mash of souvenirs and ideas stuffed into sacks as passing Frankish armies looted Ravenna and other Italian cities – but either way, these palaces and their furniture were unmistakable as concrete expressions of Carolingian prestige.
It is important to realise that these buildings were not passive and silent embodiments of imperial status, but were actively used as a way of staging and building up the authority of the ruling dynasty. Ermold the Black provides a famous and detailed description of the paintings on the walls of Ingelheim, which he had visited in the mid-820s. The chapel was lined with images from the Bible, from the Garden of Eden to the Crucifixion, and the hall of the palace was decorated with a picture cycle celebrating the deeds of great kings. Down one side were depicted the exploits of legendary classical kings and Roman emperors, and facing them were the military achievements of the Carolingians: Charles Martel conquering the Frisians, Pippin III bringing law to Aquitaine, and Charlemagne mastering the Saxons. These images of conquest served as the backdrop for magnificent state occasions like the baptism of the Danish king Harald Klak in 826, but also, as Ermold points out, for the more mundane routines of daily government. Regardless of whether contemporaries saw in these images the same nuances as do modern historians, the basic message behind pictures of kings smashing their enemies is hard to mistake: at Ingelheim, memories of the dynasty's triumphs and conquests were kept alive and made permanent, given a place at the culmination of sacred and imperial history. In this way they were domesticated and channelled into the service of a new type of governmental regime through being hard-wired into the perceptions and memories of those who participated in it. Narrative sources written in the late eighth and earlier ninth centuries increasingly refer to royal palaces as special places, at times even employing the reverential expression _sacrum palatium_ (sacred palace). The spectacular return on the symbolic capital invested in their residences by Charlemagne and Louis is indicated in back-handed fashion by a poem written by the courtier and monk Walahfrid Strabo in 829. Seeking to evoke the political tensions and recriminations of that year (to which we shall come shortly), the poet could do no better than to invert the symbolism of Aachen: the statue of Theoderic became a dark and brooding presence, while the Byzantine organ exuded decadence rather than prestige. By 829, the palace system had become so entrenched in the mentality of the Frankish elite that one could drape a critique of the entire political regime over the architecture and furniture of its flagship buildings.
As they rarely ventured outside the northern heartlands of their empire after 800, Charlemagne and Louis needed reliable agents to carry out their will in the provinces. The archetypal secular officials were counts, whose most important local responsibilities included the enforcement of justice and the gathering of those eligible to serve in the army. There were probably around 400 counties north of the Alps, but since they were not cleanly defined territorial units the power enjoyed by different counts could vary considerably – blocks of several counties were sometimes committed to a single man in strategically important areas, especially on the frontiers. Bishops and abbots, drawn from the same aristocratic families as the counts, were also regarded as royal representatives, appointed by the ruler and expected to cooperate with the count and to contribute contingents to the army (as we saw in Chapter 3, the sense of 'the Church' as something separate from 'the state' is anachronistic before the late eleventh century at the very earliest). Local conditions determined the precise roles of these men: whereas the establishment of a network of counties was used by the Carolingians as a key technique of control in annexed kingdoms like Italy, other regions such as Alsace were ruled more through royal monasteries than secular officials. A kaleidoscopic array of lesser figures also flits across the sources, among their number estate managers, gamekeepers, vice-counts and palace officials.
Overseeing all of these people were agents known as _missi_ – literally, 'the sent men'. Before about 800 the term was applied to men sent out from the palace on a variety of _ad hoc_ missions, but from the early ninth century the system became increasingly regularised as pairs of _missi_ (often a bishop and a count) were despatched to check up on the conduct of affairs in carefully defined territories ( _missatica_ ). A document issued by Louis the Pious in 825 gives a sense of what their duties might include, by telling them to hold meetings with local functionaries (counts, abbots and so on) in the middle of May to find out if they were doing their jobs properly, and, if not, to correct them on royal authority and to settle any cases that had been left unresolved through their negligence. Another document, from 802, charges the _missi_ with investigating and rectifying anything that was being done 'against written law' and instructs them to refer difficult cases to the emperor. We should resist the temptation to look at such arrangements simply as an administrative hierarchy governed by formal checks and balances. Almost without exception (except in conquered regions like Italy), counts, bishops and abbots were members of families whose local dominance predated their acquisition of these titles, local bigwigs whose influence was bolstered through their acquisition of official status. The _missi_ were no more impartial. Indeed, the areas designated as _missatica_ in the 825 document were dioceses, and many of the _missi_ appointed were the bishops of those very dioceses. Contemporaries saw no paradox in this – if local officials were to have any clout in the regions where they were assigned influence, they had to have family, friends and contacts in the area already. The ruler could distribute these offices to the people with most integrity and aptitude – the 802 document claims that the _missi_ were chosen on the basis of their superior 'good sense and wisdom' – but the range of candidates in a given locality would be severely limited by the need to spread this form of favour around a restricted group of leading families who expected a share in power.
Beyond such general observations, it is actually quite difficult to define how these royal agents were regulated by the ruler and how they operated in their regions. Our 825 document on the _missi_ is one of few that state explicitly what was expected of local officials – although thousands of sources obliquely testify to a relatively high level of organisation and regulation of early-ninth-century society, contemporaries hardly ever felt the need to write nuts-and-bolts descriptions of how that worked. Historians are now gradually reconstructing the regional impact of Carolingian rule through painstaking analysis of the rich but opaque charter material that survives in quantities from certain monasteries, and we will return to this matter in Chapters 5 and 6. For now, however, we will keep our attention on the political centre and try to catch a flavour, from a fairly large surviving body of legislative material, of how Carolingian government was meant to work. There was no single set of laws for all the peoples of the empire, which was founded on the acknowledgement and even encouragement of ethnic distinctions within its frontiers and not on the ideological imposition of a single uniform identity. Accordingly, the Franks, Bavarians, Saxons, Lombards and other regnal groups had separate and sometimes quite old lawcodes ( _leges_ ) which were systematically revised, and in some cases written down for the first time, during the reign of Charlemagne. These _leges_ (which derived from late Roman provincial law rather than – as was once thought – from the norms of pre-migration barbarian society) contained rules to do with social status, landholding, criminality and other areas in which disputes were likely to arise. On the face of it, they appear to provide a framework for the running of local affairs, but matters are made more complicated by the fact that it is very hard to find clear examples of the written texts being cited or applied in practice. In truth, the small worlds of Carolingian Europe were regulated primarily by bodies of custom transmitted orally and refracted through local power relations. While the resulting norms bore similarities to the written provisions of the _leges_ , they rarely corresponded exactly and the latter are perhaps best seen not as cast-iron rules but as starting points for negotiation in the process of disputes.
For governing the empire, on the other hand, the fundamental royal documents were the legislative texts known as capitularies. Capitularies can be defined in the most general terms as texts which recorded the will of the ruler in consultation with his leading men (though rarely as the direct product of an assembly); which were organised into chapters ( _capitula_ ); and which were intended to be disseminated to, and acted upon by, the counts, bishops and _missi_. Their precise character and legal force are, however, debated by historians, with much discussion about whether they gained legal force through being written down as documents or through oral pronouncement by the ruler. Part of the problem arises from the fact that the texts confidently classified as capitularies by nineteenth-century editors are really quite diverse in both form and content. They cover a wide and ambitious range of topics including the regulation of weights and measures, precise stipulations about the form, timing and nature of military service, amendments to the _leges_ , and instructions to counts and _missi_. Some had very particular regional audiences, while others served as general statements of intent or exhortation on behalf of a ruler. Ideally, therefore, they should be read as individual texts rather than as a coherent genre about which we can safely generalise. But as long as we bear in mind these caveats, for present purposes we need not worry too much about splitting hairs, particularly because Carolingian writers themselves did not hesitate to generalise about royal legislation. _De ordine palatii_ ('On the Governance of the Palace'), written in 882 by Archbishop Hincmar of Rheims but based on an earlier work probably composed during the reign of Charlemagne, and one of the very few Carolingian texts directly concerned with the mechanics of government, contains a detailed description of how reports from the regions were received at court, pondered and processed into capitulary form. Ninth-century commentators like Hincmar, blissfully unencumbered by the intellectual baggage of nineteenth- and twentieth-century scholarship, betray no angst when talking about the capitularies as a specific genre relating to a particular sphere of royal activity.
After the turn of the ninth century there is a marked increase in the number and quality of these documents, which cannot be put down to mere accident of survival. For the first thirty-two years of his reign Charlemagne is known only to have issued twelve capitularies, while between 800 and 814 there are over fifty. The high rate of output continued well into the reign of Louis the Pious. Although statistical analysis is not really possible owing to the nature and quantity of the evidence, there is a clear trend here which appears to indicate a genuine intensification of Charlemagne's ambitious governmental programme. It has been argued that this gear-change was informed in part by Charles's perception of his imperial status as something which gave him an enhanced responsibility for the religious integrity of his realms, and thus demanded of him a redoubled effort in his programme of _renovatio_. But the more important factor was surely the new peace-time footing of the empire and the need to establish more regularised relations between the political centre and the provinces – to give, in short, the warrior aristocracy something else to do now that regular opportunities to demonstrate their power and social status through offensive warfare had been taken away. Historians have, therefore, understandably approached these documents as integral parts of an effort to construct institutions and procedures, and hence to streamline and unify governmental structures.
The problem is that, as with the _leges_ , normative sources tell us much less about what happened than about what was _meant_ to happen, and it is frustratingly difficult to prove that the capitularies' prescriptions were actually followed in practice. Despite the survival of many records of formal courtroom proceedings presided over by Carolingian _missi_ , counts and bishops, not one of them provides a concrete example of a capitulary being consulted or cited. Moreover, their status as an official record of governmental decision-making is open to question. Capitularies were often copied into manuscripts alongside works from disparate genres including history and theology, which suggests that they were not always seen as having practical legal uses. Despite occasional references to a palace archive, there is little evidence for the existence of an authoritative central storehouse of governmental documents: when Abbot Ansegisus of St Wandrille made a collection of capitularies in 827 that was subsequently taken up as a standard reference work, he misattributed several texts and was apparently unable to find many others that are known today. Arguments have therefore been made that the capitularies were actually more ideological than practical, issued principally to conform with the long European tradition that saw law-giving in writing as a characteristically royal or imperial act. All this leaves us with a spectrum of possibilities for understanding the contemporary function of capitularies: as evidence primarily for the Carolingians' ideological preoccupations; as a source for their ambitions and aspirations, but not necessarily their effectiveness; or, most optimistically, as practical governmental tools used in their duties by agents of the king.
We can attempt to weigh up these possibilities by looking at a single example. The so-called 'Programmatic Capitulary' (the title is modern), promulgated by Charlemagne along with a range of other legal codifications upon his return to Aachen from Italy in 802, is one of the most lavish pieces of Carolingian legislation. Its forty articles cover a very wide range of subjects. After an opening statement about the supremacy of justice and the necessity that it be maintained through respect for written law and the correct behaviour of the _missi_ , the text dwells for eight chapters on the nature and implications of the loyalty oath that everyone over the age of twelve was required to swear to the emperor, and then spells out the qualities demanded of different sections of society – the purity of monks, the probity of clerics and the justice of counts. The _missi_ were to be given assistance and not hindered, the exemptions of the poor were to be respected, and the crimes of incest and homicide were condemned. This text encapsulates some of the genre's apparent paradoxes. Although it was seemingly intended as something like a definitive statement of the Carolingian agenda, very little of its content corresponds with what modern observers might expect of governmental legislation, and what there is of that (declarations about criminality, for example) comes towards the end. Hardly any of it is specifically interested in procedural matters and how exactly things should be done. The key sanction was the oath, and personal fidelity was seen as the social glue that would hold the empire together. The universal oath to the ruler had been introduced in something like this form in 789 (as we saw at the end of Chapter 2), but the 802 document expanded it by specifying that it implied acceptance of various obligations beyond remaining faithful, including service in the army, acting honestly in court and respecting the emperor's property. Even passive failure to act against threats to the emperor's interests became an act of treason. This oath, taken solemnly and publicly on holy relics, underwrote a hierarchy in which people had to promise to do more or less whatever they were told. Yet despite the all-encompassing nature of these obligations, the emperor's claims to authority were expressed in quite abstract and rhetorical terms. Instead of the contract jargon familiar from modern managerial government, or indeed from old-fashioned concepts of 'feudal' oaths, Charlemagne's demands are couched in the language of moral exhortation. The moral tone in which obligations and sanctions were set out pervades the text and explains how a document that begins with a statement about the significance of written law ends with an instruction to the _missi_ to check up on the behaviour of other royal officials, 'and above all how each is striving to keep himself in God's holy service'.
It is not hard to see how a text like this might contribute to a view of capitularies as impractical. The rather generalising moral tone might suggest a ruler who had only a slender grasp on the way his representatives actually ruled their localities, and a governmental mentality obsessed with theological posturing and grand statements of majesty. Certainly, the emphasis on moral probity fits with Carolingian understandings of the ruler's role in the 'correction' of his people: to rule (regere) was to correct ( _corrigere_ ). This is why criticisms of royal government in the ninth century lingered less on accusations of inefficiency or mismanagement than on kings' failure to ensure political stability by maintaining the moral integrity of their households and agents. We might well be tempted to interpret this attitude as primarily ideological, telling us a lot about how the ruler and his advisers understood their mission but having little to do with the nuts-and-bolts running of affairs in the empire.
On the other hand, it is also possible to interpret such documents as practical governmental instruments. Although the 'Programmatic Capitulary' itself was preserved in only one manuscript, it has been seen as a kind of statement of intent, meant to instruct those charged with ruling the Italian kingdom under Charlemagne's son Pippin. Other capitularies are known to have been disseminated more widely and although (as noted earlier) their impact on legal proceedings cannot be observed directly, their provisions very occasionally left traces elsewhere. The 802 oath, for example, appears not just in capitularies like the one we have been examining, but quickly turned up in documents written in places as distant as Freising in Bavaria. There was certainly a presumption that capitularies were to be used somehow: the texts cross-reference each other, counts were instructed to keep copies against which their actions could be judged, and kings threatened penalties against royal agents who ignored their 'letters'. Surviving manuscripts containing collections of capitularies suggest that some royal agents obeyed these injunctions by keeping reference books of the king's commands. A legal compendium owned by _marchio_ (margrave) Eberhard of Friuli, one of the era's greatest magnates, shows signs of having been updated and therefore, presumably, used. It may have been with this kind of collection in mind that an exasperated Charlemagne, confronted with a list of detailed questions from a count, snapped back impatiently that he should already know the answers, referring him not just to his capitularies but also to Frankish (Salic) law and to instructions received in person. The existence of letters like this one, combined with the rarity of evidence for the capitularies' direct use, might lead us to the conclusion that capitularies were intended to be followed and that they were widely distributed, but that much to the court's chagrin they were rarely consulted and their injunctions hardly ever acted upon.
The evidence does not, then, tell a single story. One way out is simply to make a choice between the two main interpretations outlined so far, and decide either that these texts were ideological statements of authority or that they were intended to make specific demands on royal agents but that they were often ineffective. However, we can also ask whether these views can be reconciled. A more subtle and comprehensive interpretation is possible if we take seriously the exhortatory rhetoric of the capitularies and think about how it might have served to shape the identities and actions of those for whom it was intended – the king's agents. Despite the scolding administered by the emperor to the hapless character mentioned at the end of the last paragraph, we should not regard his apparent lack of knowledge as the only significant aspect of the exchange. The fact that counts like him made enquiries to the court at all is also interesting, and suggests that some kind of two-way dialogue existed between the ruler and his representatives. The capitularies can be seen as a fragmentary remnant of this dialogue, engagement in which bolstered the local authority of counts and _missi_ by legitimising their claims to act on the ruler's behalf.
If the texts did not always furnish counts and _missi_ with precise procedural instructions, that is probably because they were already expected to know how to administer justice according to local laws and customs. Moral exhortation was not some kind of conceit concocted to cover up an embarrassing lack of power – this rhetoric was itself the language of politics, referring to codes of behaviour that royal agents implicitly understood and were repeatedly reminded of. Capitularies and narrative sources alike are full of the language of 'admonition': Charlemagne's great capitulary, the _Admonitio generalis_ , issued in 789 but distributed widely thereafter, refers to the ruler's role as 'visitation, correction and admonition'. This view of government was inspired by the Bible, but these codes also pervaded the vocabulary of contemporary office-holding. The responsibilities of counts and other office-holders were generically referred to as _honores_ ('honours') or, from the 780s onwards, _ministeria_ ('ministries'). These terms betray the notions of honour and responsibility that coloured contemporary perception of these roles – to be removed from office was not simply to lose one's job but to be literally 'dishonoured'. Such ideas were not, obviously, new, but were insisted upon by the Carolingians with increasing coherence and intensity. By the reign of Louis the Pious at the latest these concepts had been internalised by men like Orendil, a count in Bavaria who described his own position in terms of _ministerium_. The capitularies' vocabulary of honour, justice and moral probity helped to mould the identities of counts like Orendil – to influence the way they saw themselves. They created parameters for such men's activities, defined by the court but acted upon locally, and reinforced regularly by attendance at palace assemblies and interaction with the _missi_.
To evaluate the efficiency of Frankish government by combing the capitularies for evidence of a self-standing institutional structure, and to measure their effectiveness by enumerating hard examples of their practical use, is therefore an enterprise that rests on potentially anachronistic questions. Although they could be very precise in their stipulations, in general they were not definitive lists of rules and regulations so much as guides to how royal agents should behave and conceive of their actions. Men like Eberhard of Friuli and Orendil were powerful not because they held positions delegated by kings, but because of the lands and regional influence held by their families – they and their ilk had to be convinced to see themselves primarily as royal subordinates. The capitularies offer us glimpses of this process of persuasion, and represent one of the means by which it was furthered. They reveal not a pre-existing political hierarchy, but a constant effort on the part of the Carolingians to create one.
This is why the capitularies rarely had much to say on procedure but were obsessed with structure and establishing chains of command. Repeated injunctions to counts and _missi_ to refuse bribes, to hold courts in appropriate settings and not in their vassals' houses, and to refrain from cutting short judicial hearings to go hunting, are back-handed evidence not for corruption but for the Carolingians' drive to persuade their aristocratic followers to consider themselves royal agents and to follow certain codes of behaviour when they were on the king's business. The urgency of these attempts to mark off boundaries between its agents' public functions and their membership of local aristocratic culture shows that Carolingian government was not something that existed external to society, but was rather deeply enmeshed in pre-existing social structures. In the previous generation, these sorts of men would have participated in the political system by bringing their armed followers and dependants to the annual assembly and riding with the king on campaign. In the new post-expansion world the court's need to stabilise and routinise their power into predictable roles became increasingly pressing. This was not just, or even mainly, about satisfying an urge to create administrative efficiency – it was about giving these powerful men a stake in the polity from which they could profit without having to reach for their swords.
None of this should be taken to mean that counts became more just in practice. Far from it – by bolstering the authority of local aristocrats this ideology probably increased rather than diminished the oppressiveness of village and county society. Not everyone was equal before the law. The Carolingians vigorously legislated against the formation of horizontal social bonds (branding them as _coniurationes_ – conspiracies) and insisted on the primacy of vertical bonds of obligation based on sworn fidelity and lordship. While 'men of good family who act[ed] wickedly or unjustly' were to receive the benefits of due process through being tried before the king and could expect a firm request to mend their ways, lesser men were told to put up with anything their lord decided they deserved short of attempted murder, rape, or land-theft – a resounding endorsement of the brutal structures of lordship. The official rhetoric of justice, wisdom and correction cannot hide the fact that _missi_ must often have acted less like chairs of public enquiries than as the ruler's strong-men, and that adjudication and investigation could easily be euphemisms for intimidating and loading local meetings – such was the case in 781 when Charlemagne's _missi_ orchestrated a judgement which removed some strategic land in Thuringia from a local aristocrat and placed it instead in the hands of a trusted royal agent, the abbot of Fulda. But we do not have to approve of strong kingship to recognise it. All this helped to strengthen the idea that authority descended from the king. Occasionally, as in the surviving letters written by Bishop Frothar of Toul (c.813–47), we have a source that lets us glimpse the king's servants responding to specific orders (for example Frothar organised a cull of wolves in his diocese), and therefore acting directly as the ruler's instruments. The dispossessed elements of the Thuringian aristocracy may not have enjoyed their experience of Carolingian rule any more than did the wolves of Toul, but such glimpses at least prove that the moral language of office did map onto relationships of hierarchy, accountability and obligation that actually made things happen.
All these tendencies represented an intensification rather than a complete transformation of politics. All the post-Roman kingdoms including those of the Merovingians and Lombards inherited a language of office-holding that helped shape the way they were governed, and the Merovingians also commanded counts and issued documents resembling capitularies. The distinctiveness of Carolingian government in the earlier ninth century was less of kind than of degree, thrown into sharp focus by contrast with the preceding phase of of military expansion. This intensification could not have been achieved simply by top-down _Diktat_. As we have seen, the evidence suggests that local elites embraced it, sometimes enthusiastically. By accepting a redefinition of their status in terms of delegated office, they bought into a political system that not only opened up to them the prospect of access to the ruler and promotion to a wider imperial stage, but also helped to legitimise and reinforce their existing influence. This calculation of advantage explains why we sometimes see counts actively soliciting royal interference in their affairs: aristocrats wanted strong kings. By the 820s, an ethos of service can be discerned as part of the identity of the more prominent nobles who served as Carolingian _missi_. Through meeting at court and being despatched on missions in royal service, men from divergent family and geographical origins got to know each other, formed common memories of important events, and developed a sense of themselves as a group distinguished in part by their participation in royal government. This oligarchic understanding of government means that we cannot reduce our view of the effectiveness of the king's power to his ability to convince each of his agents to do what they were told. The capitularies' repetitive insistence on particular patterns of 'public' activity for counts and _missi_ helped create a system that was more than the sum of a vast number of individual personal relationships. The establishment of ideas in the minds of counts like Orendil (and, indeed, their ecclesiastical counterparts) about the correct ways to exercise office was central to the project of creating social roles patterned on repetitive and predictable behaviours: the state was the aggregate of these roles and mentalities.
The elusiveness of the sources and the obvious differentness of Carolingian government when set against modern expectations do not, then, mean that it was inefficient or that the rulers lacked power. In the few places where its operation can be discerned in any kind of detail, Carolingian government looks surprisingly effective and intrusive. The ability of the Frankish state to sustain itself by taxing its subjects had dwindled by the seventh century at the latest, but the Carolingians were nevertheless very successful at gathering revenues, influencing the circulation of currency, raising armies and standardising aspects of religious and judicial culture. Close study of monastic charters has revealed the extent to which the emperor's _missi_ succeeded in establishing Frankish understandings of property rights in areas like Alsace and Bavaria, in the process transforming previously dominant local norms and instigating political and social change. The evidence also suggests that the court had a pragmatic governmental mentality, implicit in its obsession with lists. Although only a few survive (of, for example, military obligations owed by monasteries and of people who had sworn the oath of fidelity before an Italian _missus_ ) that is perhaps because such practical texts had little long-term value and were less likely than capitularies to be preserved. We should probably place in the same category the deceptively small number of documents that contain attempts to micro-manage specific situations. Royal authority was a powerful enough agency to send high aristocrats to offices in all corners of the empire, sometimes within the course of a single career. Charlemagne's cousin Wala, for example, started out as a count in Francia, but by the time he died in 836 he had also served as abbot of the important monastery of Corbie and done two stints in Italy as guardian and adviser to Louis the Pious's son Lothar. His brother Adalard, also abbot of Corbie, covered a similarly impressive amount of territory in royal service: from acting as close adviser to Charlemagne in Aachen, he went on to serve as regent in Italy after the death of the emperor's son Pippin in 810, and performed various functions at assemblies in Francia after that. As members of the royal family these two men are unusually well documented, but the trajectory of their careers in royal service was not atypical of the very highest stratum of the aristocracy.
Early medieval government was not like Roman, later medieval or modern government, but it existed and it worked. Its effectiveness depended as much on underlying social structures as on formal institutions: even by the end of our period the idea of a clear distinction between the public and private identities of the king's agents was far from being cut and dried. Nevertheless, contemporaries implicitly understood royal government as an entity in itself. While not using terms that can be easily translated as 'state', and hardly ever devoting direct attention to its operations, they still thought of the political order as a coherent whole, and they had a vocabulary for discussing it in the abstract. The renewal of the state across the generations depended on the continuity of the aristocratic families and elite culture with which it was bound up – these underlying social structures changed too slowly to be fundamentally affected by the frailty and even death of any individual king, however great. Charlemagne complained in a capitulary of 811 that he had heard about too many people misbehaving in the counties, being disobedient to their counts, and 'having more frequent recourse to the _missi_ than was previously the case'. This has been used as prime evidence for corruption, decay and decline at the end of the old emperor's reign. Surely, though, what it actually reveals is the canny manoeuvring of people who had become familiar enough with the hierarchy and functions of royal officials to play the system – and that, therefore, there was some sort of system in place for them to play.
#### DYNASTIC POLITICS, _C_.806–827
The establishment of these governmental routines and structures meant that the political system was not exclusively dependent on the will or personal qualities of any given ruler. The king had a unique role, but no individual king was indispensable. Not even Charlemagne was immune from the plottings of the discontented, as in 792 when his eldest son Pippin ('the Hunchback') felt himself being marginalised and attracted enough support to unsettle the king seriously. Afterwards Charles rewarded those who had _not_ rebelled and had it put about that Pippin was illegitimate and physically imperfect (both questionable claims) in an attempt to 'un-person' him – these measures show how vulnerable Charlemagne had been made to feel. To stop such situations before they arose, early medieval rulers had to manage their families: when disgruntled aristocrats joined forces with a king-worthy member of the royal family, as they had in 792, the possibility of usurpation became real and the stability of the whole realm could start to unravel. Kings' sons were conditioned to expect not only a share in the succession but also a role in the government of the kingdom while their fathers still lived. Because they tried to exclude all but their legitimate sons from these arrangements, the Carolingians were even more interventionist and aggressive than the Merovingians (whose dynastic definitions were more flexible) in their efforts to prune the family tree. As their stakes in the empire were defined and negotiated, the complex dance of competing interests engaged in by kings with their sons, nephews and cousins became the engine driving political events in the early decades of the ninth century.
Charlemagne was a serial monogamist and a prolific parent: his five wives and many concubines bore him around twelve children in total. After the death of his last wife Liutgard in 800 he made a conscious decision not to remarry. With Pippin safely confined to a monastery, the emperor was left with three legitimate sons, all with his third wife Hildegard. Charlemagne seems to have begun thinking seriously about the succession at the latest during his trip to Rome in 800, when he had his eldest son, also Charles, crowned and perhaps anointed as king. Since the others, Louis and (another) Pippin, had been granted this status already in 781, this meant all three of his sons were now kings, and in 806 the emperor set out a division and succession plan to regulate relations between them. Charles the Younger was to receive Francia proper (the land between the Seine and Meuse) as well as various outlying lands in Bavaria, Burgundy, Thuringia, Frisia and Neustria; Pippin was to get Italy, Alemannia and Chur-Rhaetia (the latter covering roughly the easternmost part of modern Switzerland); and for Louis the Pious were earmarked Aquitaine, the Auvergne and other areas in the southwest. The project was about the present as much as the future (it confirmed the two younger sons in possession of some territories that they had in truth controlled for some time), and claimed to place all three heirs on an equal footing. To this end it set out a long series of safeguards to ensure they continued to cooperate, including provisions for what should happen to their kingdoms and children when one of them died, and rules for dealings between uncles and nephews. However, Charles the Younger's share was marginally superior to those of his brothers, containing as it did the Frankish heartlands which were traditionally divided between the ruler's sons. It is quite possible that this inequality of prestige, if not of formal authority, would have led to serious tensions upon Charlemagne's death had he not been predeceased by Pippin of Italy in 810 and Charles the Younger in 811. The loss of his children 'deeply disturbed' the emperor, as one might well imagine, but it made things look politically straightforward for the youngest and only remaining legitimate son, Louis the Pious. On 11 September 813, Charlemagne called a general assembly at Aachen and 'established Louis as the co-ruler of the entire kingdom and the heir to the imperial title'.
The _Royal Frankish Annals_ and Einhard's _Life of Charlemagne_ , both most likely written up some time after the fact, suggest that upon Charlemagne's death in January 814 Louis's succession proceeded straightforwardly 'with the full consent and support of all the Franks'. As with the coronation of 800, however, things may not have been as simple as these authors chose to remember. The historian Nithard, who was Charlemagne's grandson and presumably drew on personal memories, refers darkly to 'those [at Aachen] whose loyalty seemed doubtful'. Even the annals note that the new ruler (who was some distance away) took thirty days to arrive at the palace, long enough for any doubts about the prospect of Louis's rule to harden into discussions about the alternatives. If we bear in mind that Louis was in many ways an outsider at Aachen, the suggestion of opposition is not so surprising. Almost all of his thirty-six years had been spent in Aquitaine and on campaign on the Spanish March, far from the main centres of Frankish power. In contrast, Charles the Younger seems to have been groomed for rule in the Frankish heartlands: although he was given the title of king much later than his brothers, he was given responsibilities that kept him close to his father at the political centre. While Louis was occasionally summoned to his father's court, Charlemagne is said to have snubbed his son when requested to make a return trip to Aquitaine, perhaps hinting at a frosty edge to their relationship. After Charles the Younger's death the really influential people at Aachen were in fact the women of the dynasty: Charlemagne's daughters, for whom the emperor reportedly had such fondness that he refused to let them marry or even leave his side, and other female members of court. It may well have been his daughters who made the decision to bury Charlemagne at Aachen on the same day as his death, thus over-riding the emperor's own earlier plans to be interred at St Denis next to Pippin III and other great Frankish kings of past ages. By making an instant pitch to be seen as the custodians of the dead ruler's last wishes they asserted their control of the palace during the transitional period and staked a claim to have a say in his succession.
Could Charlemagne's daughters have orchestrated an attempt to have someone other than Louis take the throne in January 814? There were certainly other candidates close at hand. Wala, Charlemagne's cousin, was 'greatly feared' at Aachen in this period according to the Astronomer, his tongue loosened by Louis's own death: 'it was thought that he might plot something sinister against the new emperor'. Wala's sisters had been close to Charlemagne, and his position was therefore strong – he was listed first among the secular magnates in the emperor's will. Pippin of Italy's son Bernard was another contender: his sisters had also been living in Aachen since their father's death in 810, and a list of names entered in the confraternity book of the monastery of St Gallen c.812 shows that Bernard had extensive networks of kin and contacts north of the Alps as well as south, and particularly in Alemannia. Little wonder that pro-Louis authors went out of their way to minimise Bernard's claim by insinuating that he was illegitimate (when in fact he may have inherited Carolingian blood, legitimately, from both parents); and that he had been made king of Italy in 813 only as a kind of subordinate to Louis (when in fact he had been an independent king since 812, before Louis was designated emperor – a decision which, according to the _Annals of Lobbes_ , had been approved by both Louis and Charles the Younger). The multiplicity of serious candidates and the potential for conflict between them may have been what lay behind the appeals for peace and unity in the face of an anticipated but unspecified threat to the stability of the realm that featured in a major series of Church councils held under imperial patronage in 813. These exhortations uncover Charlemagne's own concerns about the fragility of the political situation, which were disguised by subsequent authors anxious to minimise the memory of opposition to the new regime. Potential crisis was an ever-present consideration in early medieval dynastic politics, even in the reign of a powerful ruler like Charlemagne, and successful rulership was about managing and containing it. In this context the manipulation of historical memory was one way that sympathisers like Einhard sought to erase political tension in the present.
As we saw at the beginning of this chapter, Louis the Pious has traditionally been seen as the archetype of an unsuccessful king, the antithesis of his war-like and powerful father. Historians often portray him as unsmiling, puritanical and dominated by his episcopal advisers, in stark contrast to the all-action war-leader Charlemagne. There is good reason, however, to cast serious doubt on the validity of this polarised comparison between Louis and his father. Louis's public political piety was not unusual, and only came to be seen as a mark of weakness when placed in the value systems of eighteenth-and nineteenth-century historians (the nickname which eventually stuck was only one of a number of imperial virtues applied to him by contemporaries). When we read between the lines, we see fundamental continuities between Charlemagne's and Louis's practice of rulership. Charlemagne was just as ardent a reformer of religious practice and social morality as his son, and pursued these ends with palpable urgency and energy: 'are we really Christians?' he anxiously pondered in one of his later capitularies which ordered a seminar on a Biblical text that he believed would reveal some eternal verities about how to govern. By the same token, Louis was just as much a traditional Frankish ruler as was his father: both his biographers stress his love of hunting, an archetypally masculine elite activity. Louis's imperial postures as expressed in iconography and texts looked to the same sorts of political models as had his father's: not only Biblical rulers like David and Solomon, but also Frankish kings like Clovis and Roman emperors such as Constantine and Theodosius (see Figure 11). To dismiss Louis's personality and political style as pale shadows of his father's is to be misled by the foreknowledge that he was to suffer serious rebellions in the 830s. His reputation for severe religiosity does not explain the outcome of his reign, nor why those rebellions happened.
**Figure 11.** Portrait of Louis the Pious, from 'On praising the Holy Cross' by Hraban Maur. The letters form a dedicatory epistle, with subsidiary verses made up of just the letters within the cross, the halo, the shield, and Louis's body. These blend Roman and Christian influences in praising Louis as both a warrior (dressed in Roman war-gear) and a 'soldier of Christ'.
In fact, we get closer to the truth if we invert this proposition: it is the politics of the reign which help us understand Louis's image. Louis the puritan reformer was a political persona consciously created by the emperor in the first few months of his reign. In early 814, the new emperor set out to establish himself in control of the palace by banishing his sisters from court and placing them in nunneries. He also expelled Wala and his brother Adalard, and replaced many of his father's advisers with his own. To justify this palace revolution, Louis denounced Aachen as a den of sexual permissiveness and corruption and presented himself as a righteous and pious reformer, riding into town to cleanse the court and the empire of impurity. The houses of officials and their servants were to be searched for hidden 'whores' and 'men', who once discovered were to be publicly flogged. Removing his actual or potential opponents from the palace was an obviously political move, but we cannot rule out the possibility that Louis did actually disapprove of his unmarried sisters' sexual conduct, especially in view of his closeness to a group of Aquitanian monastic reformers. The king's household and the palace already had religious associations, encouraged by Charlemagne's stance as a moral reformer – as mentioned earlier, texts from the 790s onwards sometimes referred to it as the _sacrum palatium_ (sacred palace). Louis developed this identity into a more concrete and explicit form of political ideology. In 817, after ordering an enquiry into the monasteries of the empire with a view to establishing the Benedictine Rule as the standard regime for all monks, the emperor constructed a model monastery at Inden, only three miles from Aachen, to provide a base near the palace for his spiritual adviser Benedict of Aniane and a place of retreat for himself. This close association between secular palace and holy monastic site illustrates Louis's institutionalisation of the notion that the palace was a place of purity and probity that represented the moral centre of the realm.
These ideologies and accusations took shape in a very particular political context. Louis's presentation of himself as a moral paragon was directed against not just his sisters, but also his father. Louis's open criticism of Charlemagne in the early years of his reign was intended to distance his regime from that of his father, and to give it a distinct personality. In 814 _missi_ were sent throughout the empire, and with much fanfare announced that they had discovered oppression and corruption wherever they looked. Though there is no consensus on the dating, it was arguably around this time that a new version of the _Royal Frankish Annals_ was compiled, in which were included accounts of Charlemagne's military defeats which had been left judiciously unmentioned while the old emperor was alive. Meanwhile, accusations of sexual licentiousness at Charles's court (implicitly aimed at the unmarried state of both the emperor and his daughters) found expression in highly political vision texts dating from the first decade after his death, one of which depicted the late emperor in purgatory having his genitals gnawed at by a beast. The irony of all this was that the man most responsible for establishing the political significance of the ruler's moral conduct had been none other than Charlemagne himself – Louis was not as different from his father as he perhaps liked to believe.
One reason that Louis felt the need to legitimise his rule so aggressively was that, even after he had purged the palace and got his feet under the table, there were still other Carolingians around with both a justifiable claim to power and a solid constituency of support. Chief among them was his nephew Bernard, king of Italy, who retained an independent power-base: some Italian charters from 814 refer to Bernard as king without making any mention of Louis. Bernard was also an obstacle to Louis's own ambitions – the Astronomer hints that the emperor was disappointed not to have inherited direct control of Italy for himself. Initially Louis kept his nephew close to him, having him appear at Aachen and perform other errands in the summers of 814, 815 and 816. Relations seem to have become distinctly frostier, however, in the aftermath of the emperor's recoronation by the pope at Rheims in October 816. Louis's wife Irmingard was also crowned on this occasion: a message was thus sent out about the exclusivity of the dynastic line directly descended from the emperor and his wife. Louis may also have regarded this coronation as providing him with a new mandate that freed him from any obligations imposed on him by his father in 813. This had serious implications for Bernard, who was steadily being shunted into the role of outsider. Whether or not the 816 coronation started alarm bells ringing at the Italian court, the division plan which Louis proclaimed in 817 must have set off the red alert. This declaration, known as the _Ordinatio imperii_ ('Ordering of the empire'), set forth a division of the empire between Louis's three sons. The youngest, Louis ('the German') was to receive a kingdom based on Bavaria and the middle son, Pippin, one focussed on Aquitaine. Lothar, the eldest, was to occupy a position of clear superiority in the Frankish heartlands and Italy, and also inherited the imperial title. The document contained a series of clauses on marriages, military campaigns and other political matters on which the brothers were to cooperate, with the eldest to have the final say. This was Louis's definitive statement on the shape of the family tree, its finality advertised with much beseeching of God's approval. King Bernard of Italy was not mentioned.
Because it envisaged Lothar as supervisor of the entire empire, in contrast to the traditional Frankish practice of equal division of power and territory between sons, the _Ordinatio_ is often seen as evidence for the victory of a court party ideologically committed to the unity of the empire over another which argued for its division. However, the existence of such parties is not explicitly described in the sources, and in truth this perceived ideological dichotomy derives more from the preoccupations of historians living in an age of European fragmentation, the twentieth century, than from those of contemporaries. The practice of regnal division was a more or less uncontested norm which always coexisted in Frankish politics with a rhetoric of unity, whose broad Christian connotations cannot be reduced to a debate about the distribution of territory. While the _Ordinatio_ was innovative in its attempt formally to define the superiority of the eldest brother in terms of office as well as family, it differs in degree more than kind from Charlemagne's division plan of 806, which had granted, albeit less ostentatiously, a superior kingdom to Charles the Younger. There may also have been a similar, now lost, written plan promulgated in 813 to regulate relations between Louis the Pious and Bernard. The _Ordinatio's_ novelties were driven less by ideology than by Louis's need to confront an age-old problem: how to forestall the almost inevitable outbreak of conflict among the ruler's ambitious adult sons. Such plans were not only for the future, but also affected political configurations at the time in which they were issued. By spelling out the disposition of the realm, Louis hoped to reassure his sons in their roles and to remove grounds for resentment and rebellion. But in this context, the most significant aspect of the _Ordinatio_ was what it did not mention: the silence surrounding Bernard's status is deafening. His position as king of Italy, guaranteed by Charlemagne, was now suddenly and deliberately erased. Read as _Realpolitik_ , one could interpret the imperial-unity language of the division not just as a projection for the next generation but as part of Louis's attempt to establish the idea of the empire as a single unit in the here and now – with him, and not his potential rival Bernard, as its ruler.
Bernard's response, as Louis must have expected, was to cross the Alps to negotiate, a move which the emperor readily interpreted as an act of rebellion. Bernard was seized at Chalon, put on trial, condemned and blinded. Blinding was a Byzantine punishment reserved for usurpers, and in theory offered rulers a way of neutralising their enemies without risking the dishonour of killing them. Unfortunately, if unsurprisingly, Bernard died of his injuries two days after having his eyes put out. Taking the opportunity to reel in the circle of potential heirs and tie it off even more tightly, Louis now also sent his young illegitimate brothers to monasteries. The restriction of royal power to legitimate male Carolingians born in the main line of descent was not a simply accepted rule: it had to be asserted and enforced constantly, often using violence or the threat of violence.
Bernard's 'rebellion' was arguably the result of Louis's aggression and insecurity. It was the culmination of an extended period of rivalry and manoeuvring within the ruling dynasty which went back to the deaths of Charlemagne's elder sons in 810–11. Such jostling for position at the political centre always had reverberations away from court as well, because royal figures built their power by winning the allegiance of aristocratic elites within their regional spheres of influence. Bernard was supported not only by magnates in Italy whose relationship with him gave them a vested interest in the continuation of his regime; but also by men as geographically distant as Bishop Theodulf of Orléans, one of Charlemagne's former advisers, who had been marginalised by Louis and therefore saw the rebellion as an opportunity for settling old scores. Unfortunately for Theodulf and the other rebels, it was Louis the Pious who was doing most of the settling: Bernard's supporters all ended up either blinded or confined to monasteries. These dynastic machinations took place in parallel with the new ruler's continuation and intensification of Charlemagne's reform programme. Along with the standardisation of monastic life instigated by the inquisition of 817, the emperor held a series of councils in 816–17 which ruminated deeply on matters of monastic discipline. That these and subsequent synods were all held at Louis's chief 'sacred palace' of Aachen, in contrast to the 813 councils which Charlemagne had called at points across the realm, is another indication of his desire to centralise the running of imperial affairs.
The events and councils of 817 ended the first chapter of the reign. Louis must have been pleased with how things had worked out. He had removed a variety of actual and potential opponents, established himself as the political and spiritual leader of the empire and set his house in order for the future. However, political events unfolded in unpredictable ways. The death of Bernard was quickly followed by that of the empress Irmingard, an event of major significance. Louis had worked hard to reshape the royal family so that his sons by Irmingard would be regarded as the only Carolingians with a legitimate claim to the throne. Now, before the dust had had a chance to settle on his bloody achievements, the empress's death created the potential for renewed uncertainty in the configuration of the dynasty. A wise choice of new wife could, nevertheless, bring political advantages, at least in the short term. The choice he made, in 819, was a young noblewoman called Judith. The sources dwell on her youth and beauty, and suggest that she was chosen from a lineup at a kind of Miss (Carolingian) World brideshow. These claims may not be trustworthy, since the accounts were written some time later and use Judith's beauty to express a particular set of ideological and exegetical points that may not reflect the events of 819 at all. At least as important to Louis as her physical appearance was Judith's family and their extensive political connections east of the Rhine, particularly in Alemannia. The political organisation and culture of the empire's outlying regions had been gradually Frankified over the preceding few decades, and Louis's marriage to Judith gave him the influence to advance this process. The first appearance of counts in many parts of Alemannia can be dated to the period 817–20, a development which implies an intensive reorganisation of royal resources and political structures. Louis's marriage to Judith and the fall of Bernard (who, remember, had allies in the region) must be seen as instrumental in this process, and it is no surprise that nobles from Alemannia, including the new empress's brothers and other relatives, subsequently became major players at court. Royal intrusiveness was something to be desired by figures such as these, whose regional political careers were thereby catapulted into the big time. The marriage illustrates the interdependence of politics at court and those in the provinces, however great the geographical distance between them. With their networks of kin and contacts, queens could act as one important bridge between the two arenas, which is one reason why Carolingian rulers always married noblewomen from within the empire in preference to foreign princesses.
Judith was to play an increasingly important role at court itself, and because of this was one of the main targets of the rebels who sought to depose Louis in the early 830s. However, there was no warning of the storm to come in the ruling dynasty in the early 820s, when the watchword was reconciliation. Charlemagne's cousins Wala and Adalhard and Louis's illegitimate half-brothers, all of whom had earlier been cast into exile by the anxious emperor, were welcomed back at court and given prominent jobs. The process of reconciliation was capped in 822 at the palace of Attigny, where Louis performed a public penance to atone for his and his father's sins, including the death of Bernard. Past generations of historians regarded this as the pathetic gesture of a weak ruler giving in to the whisperings of religious advisers, but this is not how the contemporary sources presented it. They suggest instead that it was an opportunity for Louis to portray himself as a new Theodosius, the great Roman emperor who had performed penance in 390, and to continue a well-established tradition of emperors organising the collective expiation of their own and their people's sins: if staged correctly, demonstrations of humility could project the ruler as the 'exalted servant' of God, and thus enhance his prestige. If Louis's own sons felt threatened by their father's second marriage and the possibility of further offspring, he took steps to allay their fears: Lothar and Pippin were now granted wives and sent out to rule as kings in their own _regna_ (Italy and Aquitaine, respectively), and the _Ordinatio imperii_ was renewed. The early 820s also saw a rejuvenation of the emperor's circle of advisers after the deaths of many close counsellors in the period 814–22. The birth of a new son, Charles 'the Bald', in 823 was a potential fly in the ointment and has often been seen, with hindsight, as sowing the seeds of conflict in the royal dynasty. However, contemporaries seem not to have regarded the birth as worthy of much comment, and Lothar even agreed to act as the boy's godfather. The fact that Charles was named after his grandfather suggests that the birth was integrated into Louis's programme of reconciliation, an attempt to make peace publicly with the memory of Charlemagne.
Contemporary flatterers like Ermold still knew that the way to praise Louis was to tell him that he was greater than his father. From what we know about Louis's activities during the first half of the 820s, there is little sign that he would have had much cause to disagree. The _Royal Frankish Annals_ for this period is dominated by news of successful campaigns on the Breton, Spanish and Slav frontiers prosecuted by Louis and his sons. Although, as we have seen, he was not interested in extending the empire's territory, the emperor did enhance Frankish influence among the Danes by intervening in a dynastic dispute on the side of King Harald Klak, who accepted baptism before the wall paintings at Ingelheim with his family and followers and allowed Louis to send missionaries among his people. The most ostentatious demonstration of Louis's self-assurance during the earlier 820s is the great capitulary known as the _Admonitio ad omnes regni ordines_ ('Admonition to all orders of the realm') issued at some point in the period 823–5. This document was a grand statement on the nature of rulership which spelled out the roles of all the empire's office-holders and placed them in a clear hierarchy descending from the emperor, while at the same time emphasising their solidarity with him – the ruler and his representatives were characterised as sharing a common responsibility for the good governance of the realm. In its ambitious all-encompassing vision of society and wide definition of the nature of political power, this statement (like the _Admonitio generalis_ of 789 with which it often circulated) epitomised the basic principles of Carolingian government and is manifestly the product of a period of supreme royal confidence.
#### KINGSHIP AND 'SUBKINGSHIP'
Working out how Louis got from this point to the crisis of the early 830s is not straightforward because the sources for the 820s are much fewer than for the decades on either side, making it difficult to trace political events in detail. Historians have often compensated by projecting onto the period an image of instability, with factions at court lining up behind different members of the royal family and the emperor increasingly vulnerable to the corrupting influence of the bishops who, in a grotesque inversion of Attigny, would in 833 orchestrate another penance designed to deprive him definitively of his throne. The roots of these processes have been detected in the text of the _Admonitio_ itself. In elaborating his conception of rulership as a shared _ministerium_ , Louis not only expected counts and bishops to check up on each other, but also proffered the possibility that he himself might be held to account for the neglect of public affairs. Here, some scholars have detected the concession of a starry-eyed king selling himself down the river and allowing his powerful monarchy to devolve into an episcopal theocracy. This is a rather too constitutional way of looking at the matter. As we have already seen, the idea of office-holding as a _ministerium_ , that is as a moral responsibility to be shouldered by all those entrusted with bishoprics, abbeys and counties, had been seeping into the consciousness of the Frankish elite for some decades, and in the _Admonitio_ of 823–5 it only reached its fullest and most refined expression. Ultimately, this way of imagining the Carolingian empire does not really help us comprehend how and why some members of the political elite signed up to armed revolt only a few years later. To understand the crucial preconditions for the rebellions, we must instead try to evaluate the positions of the people who led them: the emperor's sons.
As we have already seen, the management of relationships and political expectations within the ruling dynasty was essential to the maintenance of stability within the empire, and to this end rulers sometimes issued formal statements of their children's responsibilities, as in 806 and 817. This created a very precarious tightrope for kings to walk, since they had to empower their sons at the same time as restraining them. They did so by making them kings too. Charlemagne had had his younger sons Pippin and Louis anointed as kings in 781, while they were still infants, and sent (with guardians) to act as rulers in Italy and Aquitaine respectively. Louis the Pious acted equally quickly once he came to power in 814, sending his eldest son Lothar to rule Bavaria and his second, Pippin, to Aquitaine; this was modified in 817 when Lothar was shifted to Italy to make room for Louis the German, the third son, who was eventually despatched to Bavaria in 825. Rulers expected their sons to establish themselves by immersing themselves in the _regna_ assigned to them and building up connections among the indigenous aristocracy. To this end they were usually married to a noblewoman from a locally influential family as quickly as possible (Lothar in 821, Pippin in 822), and they were given lands which they could use to bestow patronage and gain influence. 'Subkings', as they are generally known in the modern literature, also established their own palaces and operated a regional political system on the model of their father's. When Louis the Pious organised his _missatica_ in 825, no _missi_ were assigned to Bavaria, Aquitaine or Italy, the _regna_ where his sons were ruling as subkings. This underlines the sons' relative autonomy, manifest in their ability to raise armies and sometimes to issue charters. At the same time, it reminds us of the regional nature of the empire, which was polycentric in a way that was not the case with centre/periphery empires like, say, the British. Because the _regna_ retained their individual identities within the empire, and because its rulers' influence rippled out in concentric circles from the areas where they spent most of their time, they ruled different parts of the empire in different ways. While regions close to the Carolingian heartlands in northern France and the Rhineland could be controlled directly, _missi_ tended to have a greater role in intermediate zones, and the furthest _regna_ were those most often delegated to subkings, who therefore had a crucial part to play in binding the geographical peripheries of the realm to the political centre.
The ways in which they did so can be partly understood by thinking of them as regional middle-men: thus we have examples of capitularies issued jointly by Lothar and his father for Italy; and we can find plentiful examples in the narrative sources from the reigns of both Charlemagne and Louis the Pious of subkings mounting military campaigns on their fathers' direct orders and reporting back to them on the outcome. However, the modern appellation 'subking' disguises the fact that there was no formal hierarchy of rulers in contemporary thought. A king was a king. Ermold describes the majesty and formality of Pippin of Aquitaine's court, crammed with courtiers prostrating themselves before the throne, in exactly the same terms as he describes Louis the Pious's. The equivalence between them is also implicit in Bishop Jonas of Orléans's handbook on kingship composed for Pippin in the early 830s, which summarised a set of precepts on the same subject concocted for Louis the Pious at Paris in 829. The reason that 'subkings' had to obey their fathers was not because they were a different kind of ruler, but exactly because they were their fathers' sons. The basis of paternal authority was moral and familial, authorised not by constitutional theories but by the Old Testament's fifth commandment: 'honour your father and your mother'. This is why Ermold the Black and the Astronomer do not talk about the young Louis the Pious's relationship with Charlemagne in terms of a king obeying an emperor, but instead repeatedly stress that he was 'Charles's son'; why the sources try to establish the inferiority of Bernard of Italy's position by labelling him as 'Louis's nephew'; and why the _Ordinatio imperii_ , even as it superimposes concepts of formal office onto family relationships, still describes Lothar's superiority over his younger brothers as a kind of pseudo-parenthood.
The moral language of familial seniority was ubiquitous, and for the most part successful in bolstering the distribution of power within the royal family. This distribution was also crucial in 'Carolingianising' the political landscape of the empire. The narrative sources are much less interested in the administrative role of subkings as middle-men than they are in the kingliness of the younger generations. The Astronomer dwells on young Louis's clothing and outward behaviour: above all it was his comportment that marked him out as a king, and Charlemagne was anxious that '[no] outward matters should dishonour him'. To 'dishonour' ( _dehonestare_ ) was a stronger concept than simple embarrassment, and here carried overtones of loss of position or office: Louis's very status evidently depended on the kingliness of his behaviour. It was important that such performances of royalty were seen by the empire's elites. Just as the five-year-old Charles had been sent to represent his dynasty by meeting Pope Stephen in 753, so by propping his three-year-old son Louis on a horse and giving him a sword Charles fast-tracked him to adulthood and sent him to claim distant Aquitaine as a royal territory. Along with the establishment of the palace system and the inculcation of new attitudes towards government in the minds of the ruling class, the despatching of young sons to the provinces was a critical component of the process by which the Frankish kingdom was turned into a Carolingian empire.
All these developments contributed, by the reign of Louis the Pious, to the emergence of new ways of representing rulership. Where eighth-century sources relentlessly stressed Charlemagne's dynamism and activity, the narratives of Louis's reign idealised the emperor as the still centre of the realm, receiving and dismissing subordinates and embassies, hunting in the royal forests after assemblies had finished, and despatching armies to the frontiers under the command of his sons. These steady rhythms also inform the idealisation of politics visible in the _Admonitio_ of 823–5. Nevertheless, this platform of stability concealed a tectonic potential for friction: the more effectively the empire was restructured and defined as a family concern, the more efficiently disputes within the family would be translated into crisis across the empire. Louis's Achilles' heel was the very success of the transformation of Frankish politics engineered by him and his father since the start of the ninth century. In creating an elaborate political hierarchy defined in terms of honour and morality and articulated by oaths, they had made possible the effective government of an enormous continental empire. But by its own logic Louis's sons, as kings in their own right, had the potential to appropriate that same moral language to bid for control of the system for themselves, given the motivation and the right circumstances. Those circumstances presented themselves as a result of a series of events after 827.
#### REVOLT AND RECOVERY: DYNASTIC POLITICS 827–840
The roots of the crisis were found not in the palace, but hundreds of miles away on the southern and eastern frontiers. At an assembly in Aachen in early 828, reports were received of two major setbacks for the Franks. The Bulgars had wreaked havoc on the Pannonian frontier in the southeast, and in the Spanish March a rebellion supported by the Muslims ended with the devastation of the countryside around Barcelona and Girona. For the former embarrassment the fall guy was Baldric, _dux_ of Friuli, who was deprived of his _honores_ for cowardice; for the latter, the patsies were Counts Hugh of Tours and Matfrid of Orléans, accused of delaying tactics when bringing reinforcements to the aid of Bernard of Septimania, count of Barcelona. In attempting to deprive these men of their public roles, Louis put the idea of _honores_ as delegated offices to its first serious test. Hugh and Matfrid were particularly hard targets because, more so than Baldric, they had connections at court. Hugh was the leading member of a highly influential Alsatian family which was accustomed to a leading role in the empire. What's more, his daughter was married to Louis's eldest son Lothar. Matfrid was if anything an even more formidable figure, who for most of the 820s was able to control access to Emperor Louis and was thus widely regarded as the second most influential person in the empire: a letter of Agobard, archbishop of Lyon, describes him in the mid-820s as being 'like a wall' between the king and his people, suggesting that his position was causing a certain amount of discomfort even before 828.
To try to humble men such as these might seem in retrospect an unwise move, but in truth Louis may have had little choice. Barcelona was a resonant city in his own career, ever since he had taken it for the Franks in a glorious campaign in 801. In the 820s this was still remembered as one of his greatest achievements – in his praise-poem to Louis, Ermold effectively collapsed the whole of the emperor's pre-814 career into an account of his siege of Barcelona. His personal stake in the city's history made its fate a point of honour on which the emperor was required to act. By exercising the moral logic of office-holding to deprive the counts of their _honores_ , Louis literally dis-honoured them. According to Thegan, Hugh was taunted as 'the Timid' by his followers, and was shamed into taking refuge in his house. Adding insult to injury, their positions at court and their Neustrian counties were taken by Bernard of Septimania, the wronged hero of Barcelona, who was appointed to the influential position of chamberlain, and by his relatives. Contemporaries clearly regarded these moves as a test of the political system symbolised by the palace: the Astronomer, for example, associated the deposition of the two counts with an earthquake at Aachen that he evidently interpreted as a metaphor for unrest in the empire. In 829, perhaps giddy with confidence after the removal of Hugh and Matfrid, the emperor flexed his muscles again by amending the _Ordinatio imperii_ to provide a portion of the kingdom for Charles the Bald. From this point on, Louis's problems only increased.
Exactly how and why has been a matter of much discussion among historians. In the broadest perspective, the rebellions against Louis the Pious were of a kind endemic in Frankish politics since at least the sixth century, a complex interplay between the ambitions of the ruler's adult sons, regional aristocratic politics, and unpredictable events. The specific dynamics which caused the emperor's bold gestures of 828–9 to flip over into open revolt are, however, less easy to discern. Traditional explanations characterise Louis as a passive figure at the mercy of competing court factions, one orchestrated by the empress Judith which pushed for a new division of the empire to favour her son Charles the Bald, and the other supporting Lothar by standing up for the irrevocability of the _Ordinatio imperii_. The problem with this reconstruction is that it relies too much on the evidence of highly polemical and aggressively gendered post-revolt sources designed to demonise the queen and justify the actions of the rebels. It does not explain, for example, the motives of Pippin of Aquitaine for becoming involved in the revolt, since his territory was not affected by the grant of land to Charles the Bald in 829. Nor does it square with Ermold's comment, written before the crisis, that Judith could be seen at court in the company of Hugh and Matfrid, her supposed enemies.
If anything, the sources suggest that Louis was too aggressive rather than too passive. The royal activity generated by the tensions of 828– 9 is indicated by a flurry of capitularies issued for the _missi_ , who had clearly been sent out in droves. These texts dwell on the need for the _missi_ to check that each count was fulfilling his _ministerium_ , to make sure that obligations to the king were being honoured, and to round up miscreants and bring them to the palace. Strikingly, they were also given licence to tamper with the make-up of the panels which helped decide the outcome of _placita_ (formal dispute hearings). Inquisitions concerning royal lands were not to be decided by the usual witnesses but instead by those locals who were found to be 'better and truer'; _scabini_ (judicial professionals, effectively permanent jurors) found to be dishonourable were to be replaced by people whom the _missi_ regarded as better suited to decide cases; and there were repeated reminders that the ruler himself would hear the cases of those who 'refused to live in peace' and that he would decide in person 'what should be done about such men'. The vagueness and menacing moralism of these prescriptions gives them the sinister ring of the political witch-hunt. It almost looks as if Louis's most trusted agents were being sent out as a pre-emptive strike to pick up those who were likely to oppose his interventionist manoeuvres. The main targets must have been the friends and supporters of Hugh and Matfrid, who had lost influence thanks to the two counts' disgrace. Not content with removing their public offices, Louis now went after them with guns blazing. Hugh's family power-base in Alsace was threatened by an apparent plan to install Charles the Bald as _dux_ of the region. Meanwhile, the _missi_ were specifically instructed to solicit complaints about Matfrid and to invite people to denounce their association with him by revoking grants of land they had made to him. The great power that the count of Orléans had recently enjoyed meant that dismantling the branches of his influence was a major task that could not be accomplished without a concerted effort. A subsequent edition of _De institutione laicali_ , a handbook of advice for lay aristocrats dedicated to Matfrid by Jonas of Orléans, circulated with the count's name excised. Matfrid, like Tassilo of Bavaria and Pippin 'the Hunchback' before him, had to be un-personed, erased from the approved political memory of the empire.
This intrusive activity was instigated against a backdrop of famines and other natural disasters which were readily interpreted as signs of divine displeasure. God's wrath can only have seemed clearer given that the perpetrators of the setbacks on the frontiers in 827 had been non-Christians. The emperor himself shared this interpretation, and convened a series of reform councils in late 828 and early 829 to deliberate over the task of appeasing God. Written records of these discussions were made, but only the proceedings of the great council of Paris survive. These reveal a lot of hand-wringing about the roles of different orders of society, including the ruler, in the correct management of the empire. Louis was a full participant in these deliberations. According to Paschasius Radbertus the emperor himself, together with the nobles, initiated the event as an enquiry into the causes of God's disfavour, and this is corroborated by contemporary letters. He was not being brought to book by his bishops in some sort of proto-constitutional drama, as is often assumed, so much as engaging in an act of self-examination and collective expiation of a type that had been thought appropriate to the ruler of the Frankish empire at least since the reign of Charlemagne.
That said, the glowering mood is hard to ignore. Walahfrid's poem on the court written in 829 captured the atmosphere by, as we have seen, transforming the symbols of Aachen's prestige into gloomy tokens of decay. Louis's court had always had room for a certain amount of 'admonition' aimed in the general direction of the ruler, as long as it was expressed formally and carefully, but there are signs that opinions were now being aired with increasing regularity and frankness. Influential nobles like Einhard and Wala composed booklets explaining where they thought things had gone wrong, and made them known at court. Einhard went so far as to put critical echoes of the 829 synod into the mouth of a destructive demon called Wiggo (which some historians have interpreted as an abbreviated form of Ludwig – the vernacular equivalent of Louis). Dormant recriminations were dredged up. In obliquely mentioning Louis in the same breath as Herod, the Bible's most famous child-killer, Walahfrid nodded slyly to the death of Bernard of Italy over a decade earlier. He also noted that Pippin of Aquitaine was not present at court and voiced a concern that Louis the German's portion of the empire was too small. Louis the Pious had become over-confident in his ability to control the actions and fates of his sons and the leading aristocrats. The problem was that the atmosphere of self-examination and moral recrimination which he had deliberately fostered to justify his own actions early in his reign was sufficiently vague and moralistic to be appropriated in turn by his enemies.
Despite the sources' retrospective insistence that the grant of territory to Charles the Bald in 829 was the spark that lit the fuse of rebellion, this does not seem to have been a major issue at the time. Instead, the contemporary circumstances we have outlined suggest that the outrage of their aristocratic clients and supporters was probably the most important single factor in nudging Louis's sons over into open revolt. Kings could not afford to stand idly by when their most powerful supporters lost face: leaders have to be seen to lead. Hugh must have played a major role in winning his father-in-law Lothar over to the cause, and Pippin was made amenable to the idea through disillusion at his father's heavy-handed interference in Aquitaine. The sons also stood to gain, of course, and the prospect of coming in from the empire's peripheries to stake claims at the political centre must have been very tempting. Open rebellion broke out in Lent 830 as the emperor led an army to the Breton frontier through territories controlled by Matfrid's friends. Amidst a rhetorical attack on the court as riven with sorcery and adultery (a very similar discourse to the one which Louis himself had earlier deployed against his late father's regime), the emperor's two elder sons converged on Aachen. Bernard of Septimania, the deposed counts' nemesis, was picked up and removed from the palace. So too was the empress Judith, accused of illicit sexual relations with Bernard and hence of polluting the palace, the moral centre of the realm.
With the support of his third son Louis the German, who had remained detached from his brothers, Louis managed to out-grit his opponents, negotiate a compromise and make a full return to power. The peace was sealed in early 831 by a new division plan which relegated Lothar to Italy and bought off the other sons with portions of territory in Francia. This document also contained a striking clause by which Louis reserved the right to change his mind about the details of the settlement – a far cry from the divinely inspired finality of 817 – and within months the emperor had upset his children again by forgiving and promoting Lothar. Pippin protested passively by refusing a summons to court, while Louis the German forced his father into military action by trying to take over Alemannia in 832. Louis's next move, the dispossession of Pippin in favour of Charles the Bald, showed how high-handed he had become in his management of his family. Responding to the emperor's capriciousness, the three sons made common cause and in 833 squared up to their father in Alsace – not coincidentally, Hugh's main stamping-ground. The emperor's men, stared out by the opposition, deserted: the place subsequently became known as the 'Field of Lies'. Lothar began calling the shots and forced his father to perform penance at Soissons, a ritual which, in a sinister inversion of the voluntary penance he had undertaken at Attigny in 822, was held by the rebels to disqualify him from holding office – context was everything. Louis resisted intense pressure to enter a monastery for long enough to be saved by renewed dissension among his sons. Lothar, eyes glazed over by memories of the superior role once promised him in the _Ordinatio imperii_ , pushed for too much, triggering his brothers' disagreements and jealousies. After a few months Louis the German again sprang his father from captivity and, rallying the emperor's supporters in the east, restored him to power. In 835 Louis was solemnly re-armed at St Denis in a public ritual intended to reverse his penance. Louis's first act was to depose and disgrace Archbishop Ebo of Rheims, who was accused of having masterminded the Soissons penance in 833. The two men had been childhood friends.
To attempt to depose an emperor permanently in this way was an act of breathtaking audacity. Virtually ever since, the emperor's humiliation at Soissons has been seen as the proof of Louis's weakness as a ruler, and even as the absolute nadir of Carolingian power. Yet the accumulation of armed tension did not really spill over into open violence until 834, when Lothar and his supporters were pushed onto the back foot and had to fight a retreat. The contest turned more on the protagonists' ability to win over a critical mass of elite support through argument, persuasion and intimidation. It is important to stress again that the language used against Louis by his opponents was not constitutional but familial and moral. The idea that a king should rule with equity and justice was a theme which became increasingly formalised through repetition in texts of this period: these were dangerously broad and flexible notions that became available to others to measure the ruler against. The accusations levelled against Louis in 833, recorded in a document that his opponents wished to be regarded as definitive, were couched in exactly this idiom. His crimes included: having broken the _Ordinatio imperii_ by instigating new divisions; having blinded Bernard of Italy; having organised a campaign in Lent; having tried people without due process (perhaps referring to Matfrid, Hugh and the inquisitions of 828–9); and having turned his sons into enemies instead of using paternal authority to keep the peace. Through these unjust actions (especially by changing the shape of the succession so often) he had compelled people to swear contradictory oaths that they could not keep, turning them into perjurers against their wills. They did not just accuse him of having been a bad father to his sons, but also went one better: above all (this was the first item on the charge-sheet), they denounced him as a bad son to his own father for having broken his 813 oath to protect his close relatives. These accusations were improvised attempts to rationalise what had happened. The rebels may have been throwing the book at Louis, but it was one they themselves were composing, spontaneously and conjecturally, not one that appealed to accepted legal justifications for rebellion.
Still, their list of accusations went entirely with the grain of Carolingian politics. Both sides used the same political codes to try to gain the moral high ground and justify their actions: this is why Lothar advertised his assumption of control after the Field of Lies by hunting and receiving ambassadors at the palace; and why Louis tried to undermine him by reminding him that he was his father; and why the emperor's deposition was articulated in the language of penance and sin, which had become the dominant idiom for talking about political responsibility. These codes – the paternal authority of the ruler, the palace as the centre of the realm, the fundamental significance of oaths and the classification of political behaviour in terms of sin and virtue – were absolutely central symbols of the political system that the Carolingians had tried to establish. Louis's own rigorous management of the family tree since the 810s was intended to establish the notion that only his own sons could be regarded as legitimate kings, and it was he who had empowered them by overlaying the territories of the empire with a Carolingian dynastic template. This had worked: the fact that the aggrieved nobles turned to the emperor's sons to lead them is a sign of how much dynastic modes of thought had influenced them – theirs was a rebellion within the system, not against it. The structures of government were not, in other words, disintegrating. The problem was that they had become so refined and coherent that other Carolingians were able to manipulate the dominant political rhetoric to bid to take over the empire as a going concern. In this sense, Louis was a victim of his own success.
Clearly, though, he was a victim. Modern historians have thus generally been unwilling to countenance the possibility that he could ever have genuinely recovered from the political traumas of the early 830s. The absence of capitularies after 834 has been taken as an indication that he was a lame duck, playing out time until his death in 840. Yet, as Janet Nelson has argued, there are compelling reasons for rejecting this interpretation. New appointments were made to restore peace in Neustria (where quarrels over Hugh and Matfrid's _honores_ had turned into open war) and other trouble-spots. At court, Louis dismissed those he felt he could not rely on and then pulled up the drawbridge, giving the most important positions to his half-brothers and other close allies. The coinage retained its value; and the emperor responded to the Danish raids which the rebellions had drawn in by renewing alliances across the frontiers to stabilise the situation. Lothar and his supporters were banished back to Italy, and there they stayed, only coming back in 839 with the emperor's permission. Charles the Bald's inheritance was finally forced through in Aquitaine after Pippin's death in 838. Although there was some opposition to this from Pippin's son, and then from Louis the German, these later rebellions never threatened to coalesce into an uprising as serious as those of the earlier 830s. Charter evidence from east of the Rhine shows that the emperor managed to reassert his authority in the localities very successfully. Louis's restoration of normal service suggests a certain tenacity and must be regarded as a notable success.
On the other hand, the smooth working of the system as it had been thought about in the 820s had been seriously disrupted. The memories of rebellion, and of Louis's high-handed unpredictability in its wake, did not just vanish. The bishops' slanders about the sexual licentiousness of the palace were still hanging in the air in 837, when Thegan felt compelled to counter them by re-erecting Louis's earlier persona as an unsmiling paragon of Christian self-control. The routines of government may have returned to business as usual, but bitter rivalries had been created and hardened through being played out in an atmosphere of open confrontation. Although there had been little actual fighting, the connections between court factions and local elites meant that the royal family's distress had sent fault lines snaking out across the empire in every direction. These cracks in the aristocratic community were papered over but also, as we shall see in Chapter 8, saved up for the future. In view of what had happened, it was perhaps fitting that when Louis the Pious died on an island in the Rhine in June 840, he was once again campaigning against a rebellious son. Ironically, given his reputation for humourlessness, he reportedly died laughing.
* * *
Einhard, _VK_ , c. 30 (who wrongly thought that Charles was seventy-two). On the literary constructions of emperors' deaths see E. Tremp, 'Die letzten Worte des frommen Kaisers Ludwig. Von Sinn und Unsinn heutiger Textedition', _DA_ 48 (1992), pp. 17–36.
Einhard, VK, c. 31. See A. Dierkens, 'Autour de la tombe de Charlemagne: considérations sur les sépultures et les funérailles des souverains carolingiens et des membres de leur famille', _Byzantion_ 61 (1991), pp. 156–80; J. L. Nelson, 'Carolingian royal funerals', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 131–84, at pp. 145–53.
_Planctus de obitu Karoli_ , ed. E. Dümmler, _MGH Poet_. _Latini aevi Karolini_ i, pp. 435–6, trans. Dutton, _Carolingian Civilization_ , pp. 157–9.
Einhard, _VK_ , c. 30; _ARF_ , _s.a_. 813.
For a recent example see I. Gobry, _Histoire des rois de France: Louis Ier, Premier successeur de Charlemagne_ (Paris, 2002); critiqued by C. Booker, 'The demanding drama of Louis the Pious', _Comitatus: A Journal of Medieval and Renaissance Studies_ 34 (2003), pp. 170–5. See also P. Depreux, 'Louis le Pieux reconsidéré? À propos des travaux récents consacrés à l'héritier de Charlemagne et à son régne', _Francia_ 21 (1994), pp. 181–212, and M. de Jong, _The Penitential State: Authority and Atonement in the Age of Louis the Pious, 814–840_ (Cambridge, 2009).
Thegan, _Gesta Hludowici imperatoris_ , ed. E. Tremp, _Die Taten Kaiser Ludwigs, MGH SRG in usum scholarum separatim editi_ LXIV (Hanover, 1995), c. 19, trans. Dutton, _Carolingian Civilization_ , p. 165.
Astronomer, _Vita Hludowici imperatoris_ , ed. E. Tremp, _Astronomus_. _Das Leben Kaiser Ludwigs, MGH SRG in usum scholarum separatim editi_ LXIV (Hanover, 1995), prologue and c. 32.
_AF_ , _s.a_. 874; Flodoard, _Historia Remensis ecclesiae_ , ed. J. Heller and G. Waitz, _MGH_ _SS_ XIII (Hanover, 1881), pp. 405–599,III.20; Dutton, _Politics of Dreaming_ , pp. 219–22. For the enduring memory of the rebellions see also D. Ganz, 'The _Epitaphium Arsenii_ and opposition to Louis the Pious', in P. Godman and R. Collins (eds.), _Charlemagne's Heir: New Perspectives on the Reign of Louis the Pious (814–840_ ) (Oxford, 1990), pp. 537–50.
See now C. Booker, _Past Convictions: the Penance of Louis the Pious and the Decline of the Carolingians_ (Philadelphia, PA, 2009).
Godman and Collins (eds.), _Charlemagne's Heir;_ de Jong, _The Penitential State_. E. Boshof, _Ludwig der Fromme_ (Darmstadt, 1996) is more traditional.
Einhard, VK, c. 22.
Ermold, _In honorem Hludowici imperatoris_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), p. 52, trans. Dutton, _Carolingian Civilization_ , p. 152. On images of age in Carolingian sources see P. E. Dutton, _Charlemagne's Mustache and Other Cultural Clusters of a Dark Age_ (New York, 2004), pp. 151–67.
Einhard, VK, c. 32.
J. L. Nelson, 'The voice of Charlemagne', in R. Gameson and H. Leyser (eds.), _Belief and Culture in the Middle Ages: Studies Presented to Henry Mayr-Harting_ (Oxford, 2001), pp. 76–88.
F. L. Ganshof, 'Louis the Pious reconsidered', 'The last period of Charlemagne's reign: a study in decomposition', and 'Charlemagne's failure', all in Ganshof, _The Carolingians and the Frankish Monarchy_ (London, 1971), pp. 261–72, 240–55, 256–60 respectively. See also J. M. Wallace-Hadrill, _The Barbarian West, 400–1000_ (London, 1952), pp. 87–114. For a recent appraisal see Collins, _Charlemagne_ , pp. 171–4.
J. L. Nelson, 'Rewriting the history of the Franks', in Nelson, _Frankish World_ , p. 170.
T. F. X. Noble, 'The monastic ideal as a model for empire: the case of Louis the Pious', _Revue Bénédictine_ 86 (1976), pp. 235–50; Noble, 'Louis the Pious and his piety reconsidered', _Revue Belge de Philologie et d'Histoire_ 58 (1980), pp. 297–316; M. Innes, '"He never even allowed his white teeth to be bared in laughter": the politics of humour in the Carolingian renaissance', in G. Halsall (ed.), _Humour, History and Politics in Late Antiquity and the Early Middle Ages_ (Cambridge, 2002), pp. 131–56; de Jong, _Penitential State_ , pp. 83–4.
R. Schieffer, 'Ludwig "der Fromme". Zur Entstehung eines karolingischen Herrscherbeinamens', _Frühmittelalterliche Studien_ 16 (1982), pp. 58–73; P. Depreux, 'La _Pietas_ comme principe de gouvernement d'après le _Poème sur Louis le Pieux_ d'Ermold le Noir', in Hill and Swan (eds.), _Community_ , pp. 201–24.
Astronomer, _Vita Hludowici imperatoris_ , c. 21.
For discussion see S. Hamilton, 'Early medieval rulers and their modern biographers', _EME_ 9 (2000), pp. 247–60; D. Ganz, 'Einhard's Charlemagne: the characterization of greatness', and J. L. Nelson, 'Charlemagne the man', both in Story (ed.), _Charlemagne_ , pp. 38–51 and 22–37 respectively; G. Koziol, 'Is Robert I in Hell?', _EME_ 14 (2006), pp. 233–67.
On the shift see above all T. Reuter, 'Plunder and tribute in the Carolingian Empire', _TRHS_ 5th ser. 35 (1985), pp. 75–94; Reuter, 'The end of Carolingian military expansion', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 391–405. Both are repr. in Reuter, _Medieval Polities and Modern Mentalities_.
There are many discussions of the coronation: see for example R. Folz, _The Coronation of Charlemagne, 25 December 800_ (London, 1974); Collins, _Charlemagne_ , pp. 141–59; M. Becher, _Charlemagne_ (New Haven, CT and London, 2003), pp. 7–17.
For what follows the key sources are _ARF, s.a_. 799–801 and _LP_ II, pp. 1–8, trans. Davis, _The Lives of the Eighth-Century Popes_ , pp. 176–89.
J. Fried, 'Papst Leo III. besucht Karl den Großen in Paderborn oder Einhards Schweigen', _HZ_ 272 (2001), pp. 281–326; P. Godman, J. Jarnut and P. Johanek (eds.), _Am Vorabend der Kaiserkrönung: das Epos "Karolus Magnus et Leo papa" und der Papstbesuch in Paderborn 799_ (Berlin, 2002).
_ARF_ , _s.a_. 800.
J. L. Nelson, 'Why are there so many different accounts of Charlemagne's imperial coronation?', in J. L. Nelson, _Courts, Elites and Gendered Power in the Early Middle Ages: Charlemagne and Others_ (Aldershot, 2007), no. XII.
For the mosaic, which has been heavily restored but which was also recorded in an early modern sketch, see Dutton (ed.), _Carolingian Civilization_ , pp. 58–62; M. Becher, 'Die Kaiserkrönung im Jahr 800. Eine Streitfrage zwischen Karl dem Großen und Papst Leo III.', _Rheinische Viertelsjahrblätter_ 66 (2002), pp. 1–38, at pp. 21–2.
See Dutton (ed.), _Carolingian Civilization_ , pp. 14–22.
Einhard, _VK_ , c. 28.
Folz, _Coronation of Charlemagne_ , pp. 118–31;M. Alberi, 'The evolution of Alcuin's concept of the _Imperium Christianum_ ', in Hill and Swan (eds.), _Community_ , pp. 3–17.
Fried, 'Papst Leo III.'; D. Bullough, 'Charlemagne's men of God: Alcuin, Hildebald and Arn', in Story (ed.), _Charlemagne_ , pp. 136–50, at pp. 145–6; Nelson, 'Why are there so many different accounts?', pp. 16–18.
_AL_ , _s.a_. 801; Collins, 'Charlemagne's imperial coronation'.
H. Mayr-Harting, 'Charlemagne, the Saxons and the imperial coronation of 800', _EHR_ III (1996), pp. 1113–33.
_ARF_ , _s.a_. 799, 811; Theophanes, _Chronographia_ , ed. C. de Boor, 2 vols. (Leipzig, 1883–5), a.m. 6293, trans. C. Mango and R. Scott with G. Greatrex, _The Chronicle of Theophanes Confessor. Byzantine and Near Eastern History ad 284–813_ (Oxford, 1997), p. 653.
J. L. Nelson, 'Aachen as a place of power', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 217–41; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 157–70.
Collins, _Charlemagne_ , p. 153; S. Coupland, 'Charlemagne's coinage: ideology and the economy', in Story (ed.), _Charlemagne_ , pp. 211–29, at pp. 223–7.
Schieffer, 'Charlemagne and Rome'; Smith, _Europe after Rome_ , pp. 268–77.
Becher, 'Die Kaiserkrönung'; Costambeys, _Power and Patronage_ , Chapter 8.
On titles see I. H. Garipzanov, 'Communication of authority in Carolingian titles', _Viator_ 36 (2005), pp. 41–82; Garipzanov, _Symbolic Language_.
_Divisio regnorum_ , ed. A. Boretius, _Capit_. I, cc. 3–4 establish the sons' shared access to Italy.
Einhard, _VK_ , c. 30.
Fouracre and Gerberding, _Late Merovingian France_ , pp. 330–70; Hen, 'Annals of Metz'; Fouracre, 'Long shadow'.
Ermold, _Ad eundem Pippinum_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), pp. 228–30.
Garipzanov, _Symbolic Language_ , pp. 277–82.
Einhard, _VK_ , c. 7; I. Wood, 'Beyond satraps and ostriches: political and social structures of the Saxons in the early Carolingian period', in D. H. Green and F. Siegmund (eds.), _The Continental Saxons from the Migration Period to the Tenth Century: An Ethnographic Perspective_ (Rochester, NY, 2003), pp. 271–97.
_ARF_ , _s.a_. 799, 806, 807, 809, 812, 813. See below, Chapter 7, pp. 372–3.
Reuter, 'End of Carolingian military expansion'; H. Wolfram, 'The creation of the Carolingian frontier system, _c_.800', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_.
J. M. H. Smith, ' _Fines imperii_ : the Marches', in _NCMH_ II, pp. 169–89.
_ARF_ , _s.a_. 804, 808, 809; Collins, _Charlemagne_ , p. 164.
P. Heather, 'Frankish imperialism and Slavic society', in P. Urba czyk (ed.), _The Origins of Central Europe_ (Warsaw, 1997), pp. 171–90; M. Innes, 'Franks and Slavs, 700–1000: European expansion before the millennium', _EME_ 6 (1997), pp. 201– 14; P. M. Barford, _The Early Slavs. Culture and Society in Early Medieval Eastern Europe_ (London, 2001), pp. 89–113; T. Reuter, 'Charlemagne and the world beyond the Rhine', in Story (ed.), _Charlemagne_ , pp. 183–94.
For arguments along these lines see B. Myhre, 'The archaeology of the early Viking age in Norway', in H. B. Clarke, M. Ní Mhaonaigh and R. Ó Floinn (eds.), _Ireland and Scandinavia in the Early Viking Age_ (Dublin, 1998), pp. 3–36. See also below, Chapter 7, pp. 355–6.
H. Reimitz, 'Conversion and control: the establishment of liturgical frontiers in Carolingian Pannonia', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_ , pp. 188–207 discusses such lists as a strategy of 'positive affirmation'.
Reuter, 'Plunder and tribute'.
Reuter, 'End of Carolingian military expansion'; T. Reuter, 'Carolingian and Ottonian warfare', in M. Keen (ed.), _Medieval Warfare: A History_ (Oxford, 1999), pp. 13–35. For additional nuances see Innes, _State and Society_ , pp. 143–53; J. France, 'The composition and raising of the armies of Charlemagne', _Journal of Medieval Military History_ 1 (2002), pp. 61–82; Halsall, _Warfare and Society_ , pp. 71–110.
Einhard, _VK_ , c. 15.
K. F. Werner, 'Hludovicus Augustus: gouverner l'empire chrétien – idées et réalités', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 3–123, at pp. 82– 3. Cf. the figures cited by M. Stansbury, 'Early medieval biblical commentaries, their writers and readers', _Frühmittelalterliche Studien_ 33 (1999), pp. 49–82: 312 cathedrals, 1,254 monasteries, 129 palaces.
R. Samson, 'Carolingian palaces and the poverty of ideology,' in M. Locock (ed.), _Meaningful Architecture: Social Interpretations of Buildings_ (Woodbridge, 1994), pp. 99–131; Nelson, 'Aachen as a place of power'; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 157–70.
Astronomer, _Vita Hludowici imperatoris_ , c. 7.
Werner, 'Hludovicus Augustus', p. 8.
On royal and aristocratic landscapes see M. Innes, 'People, places and power in the Carolingian world: a microcosm', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 397–437. On assemblies see S. Airlie, 'Talking heads: assemblies in early medieval Germany', in P. S. Barnwell and M. Mostert (eds.), _Political Assemblies in the Earlier Middle Ages_ (Turnhout, 2003), pp. 29–46.
Werner, 'Hludovicus Augustus', pp. 7–8. Unfortunately, Louis is the only Carolingian whose charters are still not available in a modern critical edition.
Einhard, VK, c. 17.
T. Zotz, 'Carolingian tradition and Ottonian–Salian innovation: comparative observations on Palatine policy in the empire', in A. Duggan (ed.), _Kings and Kingship in Medieval Europe_ (London, 1993), pp. 69–100; U. Lobbedey, 'Carolingian royal palaces: the state of research from an architectural historian's viewpoint', in C. Cubitt (ed.), _Court Culture in the Early Middle Ages_ (Turnhout, 2003), pp. 129–54; Samson, 'Carolingian palaces'.
Nelson, 'Aachen as a place of power'; J. Story, _et al_., 'Charlemagne's black marble: the origins of the epitaph of Pope Hadrian I', _PBSR_ 73 (2005), pp. 157–90.
Ermold, _In honorem Hludowici imperatoris_ , pp. 136–42; Einhard, VK, c. 16; Dutton, _Charlemagne's Mustache_ , pp. 43–68; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 279–91.
J. L. Nelson, 'Charlemagne's church at Aachen', _History Today_ (Jan. 1998), pp. 62–3.
Samson, 'Carolingian palaces', argues against the ideological coherence of palace architecture. See now M. de Jong, 'Charlemagne's balcony: the solarium in ninth-century narratives', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 277–90.
Ermold, _In honorem Hludowici imperatoris_ , pp. 157–65, trans. Godman, _Poetry of the Carolingian Renaissance_ , pp. 250–5; and Dutton, _Carolingian Civilization_ , pp. 252–4.
Ermold, _In honorem Hludowici imperatoris_ , pp. 166–93 on Harald; p. 166 for the reference to governmental business in the hall. Trans. Godman, _Poetry of the_ _Carolingian Renaissance_ , p. 255: 'With these and other deeds that place shines brightly / those who gaze on it take strength from the sight.'
S. Airlie, 'The palace of memory: the Carolingian court as political centre', in S. R. Jones, R. Marks and A. J. Minnis (eds.), _Courts and Regions in Medieval Europe_ (York, 2000), pp. 1–20; see also J. L. Nelson, 'The Lord's anointed'.
M. de Jong, ' _Sacrum palatium et ecclesia_. L'Autorité religieuse royale sous les carolingiens (790–840)', _Annales HSS_ 58 (2003), pp. 1243–69.
M. Herren, 'The _De imagine Tetrici_ of Walafrid Strabo: edition and translation', _The Journal of Medieval Latin_ 1 (1991), pp. 118–39; M. Herren, 'Walafrid Strabo's _De imagine Tetrici:_ an interpretation', in R. North and T. Hofstra (eds.), _Latin Culture and Medieval Germanic Europe_ (Groningen, 1992), pp. 25–41.
Cf. Ermold, _In honorem Hludowici imperatoris_ , p. 192, which dwells on the organ as a symbol of prestige; and de Jong, _Penitential State_ , p. 95 for a different interpretation. Theoderic was an ambiguous figure in the culture of the Frankish court: see F. Thurlemann, 'Die Bedeutung der Aachener Theoderich-Statue für Karl den Großen (801) und bei Walahfried Strabo (829). Materialien zu einer Semiotik visueller Objekte im frühen Mittelalter', _Archiv für Kulturgeschichte_ 59 (1977), pp. 24–65; M. Innes, 'Teutons or Trojans? The Carolingians and the Germanic past', in Hen and Innes (eds.), _Uses of the Past_ , pp. 227–49.
F. L. Ganshof, _Frankish Institutions under Charlemagne_ (Providence, RI, 1968), pp. 26–34; K. F. Werner, 'Missus–marchio–comes: entre l'administration centrale et l'administration locale de l'empire carolingien', in W. Paravicini and K. F. Werner (eds.), _Histoire comparée de l'administration ( IVe–XVIIe siècle_) (Sigmaringen, Munich and Zurich, 1980), pp. 191–239; Innes, _State and Society_ , pp. 118–24; M. Innes, 'Charlemagne's government', in Story (ed.), _Charlemagne_ , pp. 71–89.
Ganshof, _Frankish Institutions_ , p. 28 for the estimate of 400.
De Jong, ' _Ecclesia_ and the early medieval polity', and Patzold, 'Die Bischöfe im karolingischen Staat'.
Hummer, _Politics and Power_ , pp. 56–75.
_Capit_. I, no. 151; cf. no. 152.
_Capit_. I, no. 33, c.I, trans. King, _Charlemagne: Translated Sources_ , pp. 233–4.
J. Hannig, 'Zentralle Kontrolle und regionale Machtbalance. Beobachtungen zum System der karolingischen Königsboten am Beispiel des Mittelrheingebietes', _Archiv für Kulturgeschichte_ 66 (1984), pp. 1–46; J. Hannig, 'Zur Funktion der karolingischen _missi dominici_ in Bayern und in den südöstlichen Grenzgebieten', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Germanistische Abteilung_ 101 (1984), pp. 256–300. The classic demonstration (originally published in 1965) of the antiquity of prominent Carolingian-era noble families is K. F. Werner, 'Important noble families in the kingdom of Charlemagne', in Reuter (ed.), _The Medieval Nobility_ , pp. 137–202, first published in W. Braunfels and P. E. Schramm (eds.), _Karl der Große: Lebenswerk und Nachleben_ , 4 vols. (Düsseldorf, 1967).
J. L. Nelson, 'Dispute settlement in Carolingian west Francia', in Davies and Fouracre (eds.), _Settlement of Disputes_ , pp. 45–64, at pp. 47–8; Fouracre, _Charles Martel_ , pp. 13–15.
Innes, _State and Society;_ Brown, _Unjust Seizure_ ; Hummer, _Politics and Power_ ; Costambeys, _Power and Patronage_.
McKitterick, _The Carolingians and the Written Word_ , pp. 23–75; Wormald, _Making of English Law_ , pp. 45–9.
H. Nehlsen, 'Zur Aktualität und Effektivität germanischer Rechtsaufzeichnungen', in P. Classen (ed.), _Recht und Schrift im Mittelalter_ (Sigmaringen, 1977), pp. 449–502; A. Rio, 'Freedom and unfreedom in early medieval Francia: the evidence of the legal formularies', _P &P_ 193 (2006), pp. 7–40; M. Costambeys, 'Disputes and courts in Lombard and Carolingian central Italy', _EME_ 15 (2007), pp. 265–89; A. Rio, _Legal Practice and the Written Word in the Early Middle Ages: Frankish Formulae, c.500–1000_ (Cambridge, 2009).
For discussion and further references see J. L. Nelson, 'Literacy in Carolingian government', in R. McKitterick (ed.), _The Uses of Literacy in Early Medieval Europe_ (Cambridge, 1990), pp. 258–96; C. Pössel, 'Authors and recipients of Carolingian Capitularies, 779–829', in R. Corradini, R. Meens, C. Pössel and P. Shaw (eds.), _Texts and Identities in the Early Middle Ages_ (Vienna, 2006), pp. 253–74.
Hincmar, _De ordine palatii_ , c. 34. For discussion of the date, see now McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 149–55.
For example F. L. Ganshof, 'Charlemagne's programme of imperial government', in Ganshof, _Carolingians and the Frankish Monarchy_ , pp. 55–85, at p. 70. On _renovatio_ see above, Chapter 3.
The archetype of this approach is usually taken to be the work of the great Belgian historian François Louis Ganshof (1895–1980), whose essays are translated and collected in _The Carolingians and the Frankish Monarchy_ and _Frankish Institutions under Charlemagne_. McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 228–63 offers a new interpretation.
G. Schmitz, 'The capitulary legislation of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 425–36; S. Airlie, '"For it is written in the law": Ansegis and the writing of Carolingian royal authority', in S. Baxter, _et al_. (eds.), _Early Medieval Studies in Memory of Patrick Wormald_ (Aldershot, 2009), pp. 219–36.
P. Wormald, ' _Lex scripta_ and _verbum regis_ : legislation and Germanic kingship from Euric to Cnut', in P. H. Sawyer and I. N. Wood (eds.), _Early Medieval Kingship_ (Leeds, 1977), pp. 105–38, at pp. 107–10.
Text: _Capitulare missorum generale, Capit_. I, no. 33, trans. King, _Charlemagne: Translated Sources_ , pp. 233–42. Context: Einhard, _VK_ , c. 29; _AL_ , _s.a_. 802. Commentary: Ganshof, 'Charlemagne's programme'.
Becher, _Eid und Herrschaft_ , esp. pp. 211–12; Innes, 'Charlemagne's government', pp. 80–2.
See above, Chapter 3.
For example, Paschasius Radbertus, _Epitaphium Arsenii_ (hereafter _Life of Wala_ ), ed. E. Dümmler, _Abhandlungen der kaiserlichen Akademie der Wissenschaften zu Berlin, phil.-hist. Klasse_ (1900), trans. A. Cabaniss, _Charlemagne's Cousins. Contemporary Lives of Adalard and Wala_ (New York, 1967), bk. II, c. 2.
McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 261–2.
T. Bitterauf (ed.), _Die Traditionen des Hochstifts Freising_ i (Munich, 1905), no. 186. For context see now W. Brown, 'The idea of empire in Carolingian Bavaria', in Weiler and MacLean (eds.), _Representations of Power_ , pp. 37–55.
_Capit_. I, no. 85, c. 7; no. 139, c. 16.
R. McKitterick, 'Zur Herstellung von Kapitularien: Die Arbeit des Leges-Skriptoriums', _Mitteilungen des Instituts für Österreichische Geschichtsforschung_ 101 (1993), pp. 3–16; Wormald, _Making of English Law_ , pp. 53–70; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 263–6.
P. Kershaw, 'Eberhard of Friuli, a Carolingian Lay Intellectual', in Wormald and Nelson (eds.), _Lay Intellectuals_ , pp. 77–105 at pp. 85–6.
_Capit_. I, no. 58, cc. 2, 4, 6, trans. King, _Charlemagne: Translated Sources_ , pp. 267–8.
De Jong, _Penitential State_ , pp. 112–47, esp. pp. 131–5.
T. Zotz, 'In Amt und Würden. Zur Eigenart "offizieller" Positionen im früheren Mittelalter', _Tel Aviver Jahrbuch für deutsche Geschichte_ 22 (1993), pp. 1–23. On _honores_ see also below, Chapter 6, pp. 313–20.
Jonas of Orléans, _De institutione regia_ , ed. J. Reviron, _Les Idées politico-religieuses d'un évêque du_ ixe _siècle: Jonas d'Orléans et son_ De institutione regia (Paris, 1930), pp. 119–94, Admonitio line 156 and c. 9.
Bitterauf (ed.), _Traditionen_ , no. 313; Zotz, 'In Amt und Würden', pp. 12–13. On Orendil see also below, Chapter 6, pp. 314–15.
For historiographical discussion of these issues see Innes, _State and Society_ , pp. 1–12.
E.g. _Capit_. I, no. 150, c. 8.
E.g. _Capit_. I, no. 20, c. 1; no. 139, c. 13; no. 189; see also Theodulf of Orléans's characterisation of Carolingian judges: _Carmina_ 28, ed. E. Dümmler, _MGH Poet_. I (Hanover, 1881), pp. 493–517; and the selection trans. Godman, _Poetry of the Carolingian Renaissance_ , pp. 162–6.
P. Fouracre, 'Carolingian justice: the rhetoric of improvement and contexts of abuse', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 42 (Spoleto, 1995), pp. 771–803.
E.g. _Capit_. I, no. 19, c. 31; no. 20, cc. 14, 16; no. 44, c. 10. O. G. Oexle, ' _Coniuratio_ und Gilde im frühen Mittelalter', in B. Schwineköper (ed.), _Gilden und Zünfte: kaufmännische und gewerbliche Genossenschaften im frühen und hohen Mittelalter_ (Sigmaringen, 1985), pp. 151–213; McKitterick, _Perceptions of the Past_ , Chapter 3.
_Capit_. I, no. 77, cc. 12, 16, trans. King, _Charlemagne: Translated Sources_ , p. 245.
Nelson, _Opposition to Charlemagne_ , pp. 18–19.
Frothar of Toul, _Letters_ , ed. K. Hampe, _MGH Ep_. v ( _Epp. Karolini aevi_ III) (Berlin, 1899), pp. 275–98; French trans. M. Parisse and J. Barbier, _La Correspondance d'un_ _évêque carolingien: Frothaire de Toul (ca. 813–847). Avec les lettres de Theuthilde, abbesse_ de Remiremont (Paris, 1998). Airlie, 'The aristocracy in the service of the state', pp. 107–8.
Innes, 'Charlemagne's government', p. 79.
Airlie, 'The aristocracy in the service of the state', esp. pp. 100–9.
Pohl, 'Staat und Herrschaft', p. 35. On episcopal office as _ministerium_ see S. Patzold, 'Redéfinir l'office épiscopal: les évêques francs face à la crise des années 820/30', in F. Bougard, L. Feller and R. Le Jan (eds.), _Les Élites au haut Moyen Âge. Crises et renouvellements_ (Turnhout, 2006), pp. 337–59.
On the significance of the shift from tax to land see Wickham, _Framing the Early Middle Ages_. On coinage see Coupland, 'Charlemagne's coinage'.
Innes, _State and Society_ , pp. 193–5; Brown, _Unjust Seizure_ , pp. 73–123; Hummer, _Politics and Power_ , pp. 76–129.
_Capit_. I, nos. 171, 181. No. 80 demands lists of fiscal estates and benefice holders, among other things. For discussion of one such list see J. L. Nelson, 'Charlemagne and empire', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 223–34.
_Capit_. I, nos. 152, 155.
P. Depreux, _Prosopographie de l'entourage de Louis le Pieux (781–840_ ) (Sigmaringen, 1997), pp. 390–3.
B. Kasten, _Adalhard von Corbie: die Biographie eines karolingischen Politikers und Klostervorstehers_ (Düsseldorf, 1986); Depreux, _Prosopographie_ , pp. 76–9.
H.-W. Goetz, ' _Regnum_ : zum politischen Denken der Karolingerzeit', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Germanistische Abteilung_ 104 (1987), pp. 110–89; de Jong, ' _Ecclesia_ and the early medieval polity'; Airlie, 'The aristocracy in the service of the state', pp. 97–100; Wormald, 'Pre-modern "state" and "nation": definite or indefinite?'. For the view that such a vocabulary was lacking, see J. Fried, 'Der karolingische Herrschaftsverband im 9. Jahrhundert zwischen "Kirche" und "Königshaus"', _HZ_ 235 (1982), pp. 1–43.
_Capit_. I, no. 73, c. 9, trans. King, _Charlemagne: Translated Sources_ , p. 265.
_AL_ , _s.a_. 793. See above, Chapter 2, pp. 78–9.
Airlie, 'Charlemagne and the aristocracy'.
On the general issues see Kasten, _Königssöhne und Königsherrschaft;_ S. Kaschke, _Die karolingischen Reichsteilungen bis 831. Herrschaftspraxis und Normvorstellungen in zeitgenössischer Sicht_ (Hamburg, 2006). On the Merovingian family see I. Wood, 'Deconstructing the Merovingian family', in R. Corradini, M. Diesenberger and H. Reimitz (eds.), _The Construction of Communities in the Early Middle Ages_ (Leiden and Boston, 2003), pp. 149–71.
_LP_ II, pp. 7–8, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 187–8; Alcuin, _Ep_. 217. For the proposition that an earlier succession plan was conceived in the early 780s see W. Goffart, 'Paul the Deacon's _Gesta episcoporum Mettensium_ and the early design for Charlemagne's succession', _Traditio_ 42 (1986), pp. 53–87; and the critique by Nelson, 'Charlemagne the man'. See also P. Classen, 'Karl der Große und die Thronfolge im Frankenreich', in _Festschrift für Hermann Heimpel_ (Göttingen, 1972), III, pp. 109–34.
_Divisio regnorum_.
Einhard, _VK_ , c. 19. Einhard, VK, c. 30; _ARF, s.a_. 813.
_ARF, s.a_. 814.
Nithard, _Historiarum Libri IV_ , ed. P. Lauer, _Histoire des fils de Louis le Pieux_ (Paris, 1926), I.2.
M. Innes, 'Charlemagne's will: piety, politics and the imperial succession', _EHR_ 112 (1997), pp. 833–55, at pp. 841–5; Nelson, 'Pater optimus?'.
Astronomer, _Vita Hludowici imperatoris_ , c. 12.
Einhard, VK, c. 19; J. L. Nelson, 'Women at the court of Charlemagne: a case of Monstrous Regiment?', in J. C. Parsons (ed.), _Medieval Queenship_ (New York, 1993), pp. 43–61, repr. in Nelson, _Frankish World_ , pp. 223–42; J. L. Nelson, 'La Cour impériale de Charlemagne', in R. Le Jan (ed.), _La Royauté et les élites_ , pp.177–91; repr. in Nelson, _Rulers and Ruling Families_.
Nelson, 'Carolingian royal funerals', pp. 145–53.
Astronomer, _Vita Hludowici imperatoris_ , c. 21, trans. A. Cabaniss, _Son of Charlemagne: A Contemporary Life of Louis the Pious_ (Syracuse, NY, 1961), p. 54. On Wala see L. Weinrich, _Wala. Graf Mönch und Rebell. Die Biographie eines Karolingers_ (Lübeck, 1963); H. Mayr-Harting, 'Two abbots in politics: Wala of Corbie and Bernard of Clairvaux', _TRHS_ 5th series 40 (1990), pp. 217–37; Depreux, _Prosopographie_ , pp. 390–3.
Paschasius Radbertus, _Vita Sancti Adalhardi_ , ed. Dom J. Mabillon, PL cxx, 1507–1556c, c. 33; Einhard, VK, c. 33; J. L. Nelson, 'Gendering courts in the early medieval west', in L. Brubaker and J. M. H. Smith (eds.), _Gender in the Early Medieval World. East and West, 300–900_ (Cambridge, 2004), pp. 185–97, at p. 191.
J. Fried, 'Elite und Ideologie, oder die Nachfolgeordnung Karls des Großen vom Jahre 813', in Le Jan (ed.), _La Royauté et les élites_ , pp. 71–109, at pp. 90–5.
P. Depreux, 'Das Königtum Bernhards von Italien und sein Verhältnis zum Kaisertum', _QFIAB_ 72 (1992), pp. 1–25; Fried, 'Elite und Ideologie', p. 84.
_Conc_. II, nos. 34–8; Fried, 'Elite und Ideologie', pp. 71–5.
Schieffer, 'Ludwig "der Fromme"'.
_Capit_. I, no. 71, trans. King, _Charlemagne: Translated Sources_ , pp. 263–4. For discussion see Nelson, 'Voice of Charlemagne', pp. 80–1; and for broader context see de Jong, ' _Sacrum palatium_ '; T. F. X. Noble, 'From brigandage to justice: Charlemagne, 785–794', in C. M. Chazelle (ed.), _Literacy, Politics, and Artistic Innovation in the Early Medieval West_ (Lanham, MD, 1992), pp. 49–76.
Werner, 'Hludovicus augustus', pp. 56–69.
Depreux, _Prosopographie_ , pp. 46–7.
_Capit_. I, no. 145, trans. Nelson, 'Aachen as a place of power', pp. 238–9. See Nelson, 'Women at the court of Charlemagne', repr. in Nelson, _Frankish World_ , pp. 239–41; R. Collins, 'Charlemagne and his critics, 814–29', in Le Jan (ed.), _La Royauté et les élites_ , pp. 193–211, at pp. 204–5.
De Jong, ' _Sacrum palatium_ ', esp. pp. 1247–51; M. de Jong, 'Charlemagne's Church', pp. 103–35.
Ermold, _In honorem Hludowici_ , pp. 93–7; Ardo, _Vita Sancti Benedicti abbatis Anianensis_ Life of Benedict], ed. G. Waitz and W. Wattenbach, _MGHSS_ XV ([Hanover, 1888), c. 35; selections trans. Dutton (ed.), _Carolingian Civilization_ , pp. 176–98.
_ARF, s.a_. 814; Thegan, _Gesta Hludowici imperatoris_ , c. 13.
R. Collins, 'The reviser revisited: another look at the alternative version of the _Annales regni francorum_ ', in A. Murray (ed.), _After Rome's Fall. Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 191–213;McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 27–31.
D. Traill (ed. and trans.), _Walahfrid Strabo's Visio Wettini: Text, Translation and Commentary_ (Frankfurt, 1974); Dutton, _Politics of Dreaming_ , pp. 63–5; D. Ganz, 'Charlemagne in Hell', _Florilegium_ 17 (2002 for 2000), pp. 175–94. Einhard, _VK_ , c. 19 refers to allegations of sexual misdemeanour at court.
Depreux, 'Das Königtum', p. 12. Bernard's position was also boosted by marriage in _c_.810– _c_.814.
Astronomer, _Vita Hludowici imperatoris_ , c. 20; Depreux, 'Das Königtum', pp. 8–9.
Astronomer, _Vita Hludowici imperatoris_ , cc. 23, 25, 26.
Werner, 'Hludovicus augustus', pp. 38–40.
_Ordinatio imperii, Capit_. I, cc. 4–8, 12–16.
Kaschke, _Die karolingischen Reichsteilungen_ , pp. 324–53; S. Patzold, 'Eine "loyale Palastrebellion" der "Reichseinheitspartei"? Zur "Divisio imperii" von 817 und zu den Ursachen des Aufstands gegen Ludwig den Frommen im Jahre 830', _Frühmittelalterliche Studien_ 40 (2006), pp. 43–77. See also F.-R. Erkens, ' _Divisio legitima_ und _unitas imperii_ : Teilungspraxis und Einheitsstreben bei der Thronfolge im Frankenreich', _DA_ 52 (1996), pp. 423–85; K. H. Krüger, 'Herrschaftsnachfolge als Vater-Sohn-Konflikt', _Frühmittelalterliche Studien_ 36 (2002), pp. 225–40.
Fried, 'Elite und Ideologie', pp. 82–8.
T. F. X. Noble, 'The revolt of King Bernard of Italy in 817: its causes and consequences', _Studi Medievali_ 15 (1974), pp. 315–26; McKitterick, _History and Memory_ , pp. 265–83.
G. Bührer-Thierry, '"Just Anger" or "Vengeful Anger"? The punishment of blinding in the early medieval west', in B. Rosenwein (ed.), _Anger's Past. The Social Uses of an Emotion in the Middle Ages_ (Ithaca, NY, 1998), pp. 75–91.
J. L. Nelson, 'The Frankish kingdoms, 814–898: the west', in _NCMH_ 11, pp. 110–41, at pp. 113–15.
_Conc_. II, nos. 39–40; McKitterick, _Frankish Kingdoms_ , pp. 112–17.
De Jong, 'Charlemagne's Church', p. 129.
M. de Jong, 'Brideshows revisited: praise, slander and exegesis in the reign of the empress Judith', in L. Brubaker and J. M. H. Smith (eds.), _Gender in the Early Medieval World. East and West, 300–900_ (Cambridge, 2004), pp. 257–77.
M. Borgolte, _Geschichte der Grafschaften Alemanniens in fränkischer Zeit_ (Sigmaringen, 1984).
For the significance of Bernard's fall for Louis's control of Alemannia see M. Borgolte, 'Die Alaholfingerurkunden. Zeugnisse vom Selbstverständnis einer adligen Verwandtengemeinschaft des frühen Mittelalters', in M. Borgolte, D. Geuenich and K. Schmid (eds.), _Subsidia Sangallensia_ I. _Materialien und Untersuchungen zu den Verbrüderüngsbuchern und zu den älteren Urkunden des Stiftsarchivs St. Gallen_ (St. Gallen, 1986), pp. 287–322.
In this respect they were different from most other early medieval dynasties. See for example S. Hellmann, 'Die Heiraten der Karolinger', in S. Hellmann, _Ausgewählte Abhandlungen zur Historiographie und Geistesgeschichte des Mittelalters_ , ed. by H. Beumann (Darmstadt, 1961), pp. 293–391; P. Stafford, _Queens, Concubines and Dowagers: the King's Wife in the Early Middle Ages_ (London, 1983); S. MacLean, 'Queenship, nunneries and royal widowhood in Carolingian Europe', _P &P_ 178 (2003), pp. 3–38.
Astronomer, _Vita Hludowici imperatoris_ , c. 35; _ARF_ , _s.a_. 822.
De Jong, 'Power and humility'; R. Deshman, 'The exalted servant: the ruler theology of the prayerbook of Charles the Bald', _Viator_ II (1980), pp. 385–417; de Jong, _Penitential State_ , pp. 122–31.
Depreux, _Prosopographie_ , pp. 48–9.
K. H. Krüger, 'Neue Beobachtungen zur Datierung von Einhards Karlsvita', _Frühmittelalterliche Studien_ 32 (1998), pp. 124–45 argues that the composition of Einhard's _Life of Charlemagne_ should also be placed in this context. For the debate on the dating of Einhard's work, the following are important starting points: Innes and McKitterick, 'The writing of history', in McKitterick (ed.), _Carolingian Culture_ , pp. 193–220; Tischler, _Einharts Vita Karoli_ ; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 11–14.
Ermold, _In honorem Hludowici_ , pp. 62–6.
S. Coupland, 'From poachers to gamekeepers: Scandinavian warlords and Carolingian kings', _EME_ 7 (1998), pp. 85–114;Wood, _Missionary Life_ , pp. 123–41; J. Palmer, 'Rimbert's _Vita Anskarii_ and Scandinavian mission in the ninth century', _Journal of Ecclesiastical History_ 55 (2004), pp. 235–56.
_Capit_. I, no. 150; O. Guillot, 'Une "ordinatio" méconnue. Le Capitulaire de 823–825', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 455–86.
_Capit_. I, no. 150, c. 15; Guillot, 'Une "ordinatio" méconnue', pp. 481–2.
The characterisation is that of de Jong, ' _Sacrum palatium_ ', p. 1246.
Astronomer, _Vita Hludowici imperatoris_ , cc. 24, 29.
Astronomer, _Vita Hludowici imperatoris_ , cc. 6, 17 for lands held by Louis the Pious as subking. E. J. Goldberg, _Struggle for Empire. Kingship and Conflict under Louis the German, 817–876_ (Ithaca, NY, and London, 2006), pp. 75–85 elucidates the techniques used by Louis the German to increase his entourage in the 830s.
On subkings see J. Jarnut, 'Ludwig der Fromme, Lothar I und das Regnum Italiae', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 349–62; R. Collins, 'Pippin I and the kingdom of Aquitaine', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 363–89; Kasten, _Königssöhne und Königsherrschaft_.
_Capit_. I, no. 151.
Werner, 'Missus–marchio–comes' is a classic discussion of these zones.
Astronomer, _Vita Hludowici imperatoris_ , cc. 6, 36, 38, 40; Ermold, _In honorem Hludowici_ , pp. 46–50; Kasten, _Königssohne und Königsherrschaft_ , pp. 272–377; M. Geiselhart, _Die Kapitulariengesetzgebung Lothars I. in Italien_ (Frankfurt, 2002), pp. 7–16, 247–50.
Ermold, _Ad Pippinum regem_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), pp. 220–32.
Jonas, _De institutione regia_ ; _Conc_. II, no. 50.
Exodus 20:2–17; Deuteronomy 5:6–21.
Ermold, _In honorem Hludowici_ , pp. 21, 32; Astronomer, _Vita Hludowici imperatoris_ , cc. 12, 14, 23, 29; _Ordinatio imperii_ , _Capit_. I, c. 10; Paschasius, _Life of Wala_ , II.17.1.
For this expression, and the ideas behind this paragraph, see S. Airlie, _Carolingian Politics_ (Oxford, forthcoming).
Astronomer, _Vita Hludowici imperatoris_ , c. 6, trans. Cabaniss, _Son of Charlemagne_ , p. 38.
Astronomer, _Vita Hludowici imperatoris_ , c. 4.
_ARF_ , _s.a_. 827, 828. Depreux, _Prosopographie_ , pp. 262–4.
Depreux, _Prosopographie_ , pp. 329–31; P. Depreux, 'Le Comte Matfrid d'Orléans (avant 815 – + 836)', _Bibliothèque de l'École des Chartes_ 152 (1994), pp. 331–74; de Jong, _Penitential State_ , pp. 143–4.
Ermold, _In honorem Hludowici_ , pp. 26–50.
Thegan, _Gesta Hludowici imperatoris_ , cc. 28, 55.
Astronomer, _Vita Hludowici imperatoris_ , c. 43.
Thegan, _Gesta Hludowici imperatoris_ , c. 35; _AX_ , _s.a_. 829.
Boshof, Ludwig, pp. 129–34, 173–7, 182–91; B. Bigott, _Ludwig der Deutsche und die Reichskirche im ostfränkischen Reich (826–876_ ) (Husum, 2002), pp. 60–77, 116–18.
E. Ward, 'Caesar's wife: the career of the empress Judith, 819–29', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 205–27; E. Ward, 'Agobard of Lyons and Paschasius Radbertus as critics of the empress Judith', _Studies in Church History_ 27 (1990), pp. 15–25; de Jong, 'Brideshows revisited'; Patzold, 'Eine "loyale Palastrebellion"'.
Collins, 'Pippin I', p. 377. Ermold, _In honorem Hludowici_ , p. 176.
_Capit_. II, nos. 184–93. _Capit_. II, no. 188, c. 2; no. 192, cc. 2, 7.
Hummer, _Politics and Power_ , pp. 157–65. _Capit_. II, no. 188, c. 3.
I. Schröder, 'Zur Überlieferung von _De institutione laicali_ des Jonas von Orleans', _DA_ 44 (1988), pp. 83–97 at pp. 89–92.
On Tassilo and Pippin see above, Chapter 2, pp. 69–70, 78–9.
_Conc_. II, no. 50.
Paschasius, _Life of Wala_ II.1; de Jong, _Penitential State_ , pp. 170–6.
_Capit_. II, no. 185; de Jong, ' _Ecclesia_ and the early medieval polity', pp. 129–31; de Jong, _Penitential State_ , esp. pp. 176–84.
See above, p. 178.
Paschasius, _Life of Wala_ I.2–3; Einhard, _Translatio et miracula sanctorum Marcellini et Petri_ _Translation and Miracles of Saints Marcellinus and Peter_ ], ed. G. Waitz, _MGH SS_ XV.I ([Hanover, 1888), pp. 239–64, III.13, trans. Dutton, _Charlemagne's Courtier_ , pp. 69–130.
Einhard, _Translation and Miracles_ , III.14. De Jong, _Penitential State_ , pp. 161–3 rightly doubts the direct equation of Wiggo and Louis, though the choice of name is still striking.
Fried, 'Elite und Ideologie', pp. 102–3.
Thegan, _Gesta Hludowici imperatoris_ , c. 35. Collins, 'Pippin I', pp. 378–9.
_AB_ , _s.a_. 830. For detailed accounts of the rebellions see Boshof, _Ludwig_ , pp. 192–210; Goldberg, _Struggle for Empire_ , pp. 59–77; de Jong, _Penitential State_.
_Capit_. II, no. 194.
Thegan, _Gesta Hludowici imperatoris_ , c. 42.
De Jong, 'Power and humility'; de Jong, _Penitential State_ , pp. 228–41.
Nithard, _Historiarum Libri IV_ , 1.4. Booker, _Past Convictions_.
AB, s.a. 834; Thegan, _Gesta Hludowici imperatoris_ , c. 52.
_Capit_. II, no. 197; de Jong, _Penitential State_ , pp. 234–41 (and pp. 271–7 for a translation).
Astronomer, _Vita Hludowici imperatoris_ , cc. 45, 48, 49.
J. L. Nelson, 'The last years of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 147–59.
Depreux, _Prosopographie_ , pp. 52–3.
J. L. Nelson, _Charles the Bald_ (London and New York, 1992), pp. 92–101; Goldberg, _Struggle for Empire_ , pp. 87–94.
Innes, _State and Society_ , pp. 202–7.
See above, pp. 155–6.
Astronomer, _Vita Hludowici imperatoris_ , c. 64. On the authorial agendas at play in this anecdote see Tremp, 'Die letzten Worte'.
## 5
### VILLAGES AND VILLAGERS, LAND AND LANDOWNERS
#### INTRODUCTION: INTERPRETING CAROLINGIAN SOCIETY
Afraid of meeting 'dog–headed men' on his travels in Scandinavia, the missionary Rimbert, some time in the middle of the ninth century, was moved to enquire of Abbot Ratramnus of Corbie whether such monstrous perversions of humanity had souls that could be saved. Ratramnus – a theological authority whose monastery had longstanding links with the Frankish mission in the north – replied that all the available information on contemporary Scandinavian societies pointed to familiar patterns of agrarian life: did not the Danes and Swedes follow laws, live in villages, farm the land, domesticate animals and indeed wear clothes similar to the Franks'? They therefore had souls; Rimbert's job was to save them for the true, Christian, God. Ratramnus's exchange with Rimbert belongs in a long tradition of Roman and Frankish ethnographic fantasies about their northern neighbours which were intended to assert the normality of home society by vividly defining distant and not-so-distant neighbours as 'others'. But rather than identifying, as was customary, monstrous peoples as agents of God's wrath or actors in Biblical prophecies, here Ratramnus described the familiarity of the way of life of rural Scandinavia, regardless of the shape of its inhabitants' heads. These rural communities resembled those whose labours sustained Ratramnus and his monks in Francia, and so were ripe for conversion under the aegis of a Christian empire.
As so often, in imagining others distant from home Ratramnus and Rimbert reveal social assumptions that would have been much harder to voice in a discussion of their own society. Indeed, direct commentary on the structure of Frankish society by the spokespeople of the ruling elites of Church and court is rare. When such commentary did occur, it was theological in nature and ecclesiological in aim, designed to explicate the proper harmonious relationship between the different orders that made up Christian society. The first decades of the ninth century saw a series of attempts to apply to Carolingian society the theory of 'three orders of man' developed by Augustine and elaborated by other late antique churchmen. At Aachen in 802, for example, the three orders of clergy, laity and monks were each encouraged to meditate on their roles, as reflected in authoritative texts from canon law, secular law and the monastic rule. A few decades later the monastic scholar Heiric of Auxerre, influenced by classical texts, inaugurated what was to become the dominant social theory of the Middle Ages by classifying society as made up of those who fight, those who pray and those who work. Fascinating though it is, such theorising is primarily a part of intellectual history: early medieval social theories do not aim at the kind of understanding sought by modern historians.
The lack of recognisable social analysis in Carolingian sources has had important historiographical ramifications. Firstly, without useable contemporary comment as a starting point for debate, modern historians have tended to draw on chronologies and trajectories inherited from political history, and to equate periods of royal weakness with 'rising violence' or 'social breakdown'. These ideas are based on contemporary legislation, which exhibits a recurrent concern with protection for the poor, widows and orphans. But individual snippets of legislation should not be divorced from the context in which they were issued and taken as proof of more generalised 'abuses'. The complaints we find are standard, indeed stereotyped, with long precedents in Christian thought right across the late antique and early medieval worlds; they also tended to be voiced in times of political instability precisely because political instability was seen by the intellectual elite as a worrying manifestation of divine displeasure, and as such was likely to encourage social critique. Such concerns indicate, therefore, a louder volume of ideological conversation within the ruling class rather than actual social changes. One of the primary intentions of legislators was the inculcation of a distinctly Christian ethos amongst the 'powerful', to use their term for those who ruled. When legislation referred to the poor, it was to remind the powerful of their duty of protection in the context of a harmonious Christian social order – this was ideological posturing, not social analysis. This is not to deny that kings could play a role in social change, particularly by destabilising local societies in which they intervened (as witnessed by the kind of tensions visible in the _Stellinga_ revolt in Saxony in the 840s or, in a different form, by the century of endemic land litigation set in train by the Carolingian conquest of Alemannia). But these developments were neither deliberately sought, nor had any direct connection with the aspirations declared in our more ideological texts.
A second, related, consequence of the lack of contemporary social analysis in our sources has been the tendency to slot the eighth and ninth centuries into existing grand narratives by importing models from either the Roman world or the high Middle Ages against which Carolingian developments can be measured. Interpretations of social history often debate where to place the Carolingian world in a linear development 'from antiquity to feudalism'. Thus for two early-twentieth-century pioneers, Alfons Dopsch and Henri Pirenne, in different ways the Carolingian period witnessed the end of an ancient economy and society and the beginning of the medieval. For Dopsch, impressed by the evidence for rural organisation and the development of estates, the Carolingian period created the social and economic foundations of the medieval countryside, on which later growth was built; for his near contemporary Pirenne, the Carolingian empire could be characterised as agrarian and land-locked, and its genesis seen as a direct result of the contraction of commerce and urban life. Although their conclusions directly clashed, it is noteworthy that for both the central concern was to place the Carolingian era in a millennium-long transformation, not to understand its peculiarities and specificities on their own terms. Today it remains commonplace for studies of Carolingian and post-Carolingian Europe to be framed in terms of a debate over 'continuity' and 'change' that presumes that what we are really looking for is a point in history which marked the end of an 'ancient' social order and the beginning of the 'medieval'.
One consequence of these historiographical problems is that potentially anachronistic categories of analysis are often imported into the eighth and ninth centuries from outside. Were, for example, Carolingian peasants 'slaves' or 'serfs'? Were Carolingian estates closer to their Roman forebears or to the medieval 'seigneurie'? Did Carolingian rural settlements resemble the Roman pattern or the villages of the high Middle Ages? Questions such as these can be useful if we are seeking to describe very long-term processes of change. But they are not the only questions, nor even the most fruitful. Classifying Carolingian practices either as fossilised hangovers from antiquity or as embryonic versions of high medieval phenomena obscures their contemporary function and meaning, risks ignoring the human agents of change, and discounts the very likely possibility that society transformed not in a straight line but in a complex and discontinuous series of changes spanning half a millennium. It also rules out the possibility that the social structures of the fourth to tenth centuries might have had their own defining characteristics distinct from those of the preceding and succeeding periods.
Another consequence is that there is no real consensus amongst historians on the social and economic dynamics of the Carolingian centuries. Those looking through high-medieval spectacles tend to talk about the ninth century as a time of relative stasis, with the end of the empire as the catalyst for massive and sudden change (the 'feudal revolution') in the tenth century that generated social structures familiar from the eleventh and twelfth. Meanwhile, those interested in continuity with late antiquity normally focus on formal, institutional aspects (royal legislation, for example) rather than the inner workings of society. Neither view is much interested in analysing how Carolingian society functioned. Yet this state of affairs is not the result of any deficiency of evidence. Far from it: the deepening of source material from the Carolingian centuries, discussed in Chapter 1, means that for the very first time in European history it is possible for us to understand in detail the social relationships that animated the villages and hamlets of the eighth- and ninth-century countryside. The written evidence takes two forms: on the one hand charters, legal records mostly of land transfer and title, which survive in sufficient volume from the last decades of the eighth century onwards to allow us to peer into the small worlds of Carolingian villages; and on the other polyptychs, records of estate management, which proliferate in the ninth century. The documentary record, moreover, can be counterpointed with archaeology, in particular the growing body of evidence from excavations of rural settlements (see Figure 12).
**Figure 12.** Reconstruction of the hilltop centre of a manorial estate ( _curtis_ ) at Miranduolo, Tuscany, where lords and peasants lived side by side: common in Italy, far less so elsewhere. In its Carolingian phase Miranduolo was divided between a fortified zone that housed the lord, and a group of peasant huts with an unhierarchical material culture. Food storage huts in the fortified compound indicate the rich diet of the elite.
In marked contrast to the student of earlier centuries (including the Roman period), the Carolingianist is thus in a fortunate position. Rather than wrestling with isolated episodes gleaned from narratives or spectral norms fleetingly glimpsed in law-codes, we have a rich body of evidence for the everyday dynamics of the countryside. The possibilities of this data are only just beginning to be appreciated, but we should also recognise the problems they present. For one thing, the geographical coverage of all three sources is very sporadic. Moreover, charters, polyptychs and archaeology by their very nature present radically different views of the countryside, and the relationship between them is not always easy to establish. Polyptychs, surveys in which kings and great churches documented the tenants and dues on their lands, present an image of carefully organised and centrally controlled great estates whose inhabitants were clearly divided into different classes; while the surviving charters, which mostly record transactions in which individual landowners transferred or occasionally disputed rights over land in the presence of their neighbours, show a more complex and fragmented grid of rights. Archaeology, meanwhile, is often integrated imperfectly with written sources. These observations about the sources and about the questions we should ask of them should be kept in mind as we proceed through this chapter. The next section deals with the village, the basic social unit of the Carolingian countryside. The two subsequent sections discuss rural landowners, village communities and their role in the social hierarchy. Next we explain one of the archetypal features of Carolingian economic organisation, namely the 'manorial system' found on the great estates of the king and the Church, and ask what we can learn from it about economic growth and stagnation. Finally we return to the village to look at how all of this fitted together and what it meant for the majority of the population by trying to understand if and how rural communities were able to resist the power of landlords, and how they saw their place in the great political hierarchies of the empire.
#### VILLAGES
Ratramnus's belief in the similarity of Frankish and Scandinavian societies rested on the fact that Scandinavians, like Franks, lived in villages. He used the Latin term _villa_ to refer to these basic social units. The _villa_ of the early Middle Ages differed radically from that of the Roman period, when the term generally refers to the rural residences of landowning elites, elaborate and often luxurious stone-built country houses which were also focal points for the organisation of land and labour. Poorer hamlets and farmsteads, often built of wood, are harder to identify and date, and as a consequence less well understood. It is nonetheless clear that the islands of conspicuous wealth that the _villa_ represented dominated the rural economy and society of western Europe in the Roman era. In terms of administrative geography, _villas_ shaped the estate units into which the countryside was divided. This rural landscape was, however, not to last: hence by the end of the sixth century the hagiographer and historian Gregory of Tours, himself a descendant of the _villa_ -owning class, could use the term _villa_ to denote an agglomeration of rural households – in other words, a village.
The thickening of the documentary record in the course of the eighth century confirms the division of the countryside into a network of units built up of individual households, fields and other appendages. The degree to which habitation and human activity within these units was concentrated differed as a result of a variety of factors, first and foremost local topography. But right across Europe north of the Alps, rural society was divided into a grid of multihousehold settlement units which were taking on an increasingly territorial definition. The degree to which these units had their own formal structures of organisation is inevitably cloudy, given the nature of our evidence, though judicial meetings of local landowners are well attested in the documentary record. Since the evidence gives little explicit sense of how communities were organised internally, and suggests that their layout varied considerably, some historians have seen the emergence of the village as a post-Carolingian phenomenon. But while we should certainly accept that settlements changed over time (the idea of a timeless rural community is misleading), it would be a mistake to see the topographically and organisationally looser settlements of the Carolingian period as fundamentally different from their more tightly structured successors.
North of the Alps, the Latin term _villa_ was well established as the label for these settlement units. Polyptychs show great landowners detailing the dues expected from the rural population _villa_ by _villa_ and the charters, recording the transfer of individual pieces of property, show that landowners likewise conceptualised the countryside as a network of such units. In Frankish Italy, terminology was more varied, but even here the grid of villages formed a basic mental map of the countryside. Where habitation was fairly concentrated, _villa_ could be used in a more restricted sense to refer to the primary area of residence at the core of the settlement. It could then be contrasted with the countryside beyond, the fields worked by the inhabitants and the surrounding landscape exploited more intermittently as pasture or woodland. These outlying areas, though legally and territorially dependent on the _villa_ , were often referred to using a variety of other terms such as 'mark' ( _marca_ ). A series of stories recorded in the _Annals of Fulda_ give a clear sense of how these divisions structured village life in the Rhine valley, an area of nucleated settlement (i.e. containing concentrated villages). When a cattle plague hit the _villa_ of Walahesheim, 'the dead animals were dragged daily from their stalls to the fields, where the village dogs tore up and devoured them' until they mysteriously gathered together and vanished. In the _villa_ of Kempten, an evil spirit was blamed for fomenting bitter disputes among the inhabitants: bored with throwing stones and banging on walls, it spoke openly and spread accusations about theft so as to stir up feelings against one man, even causing houses to catch fire when his victim entered them: 'as a result the man was forced to live outside the _villa_ in the fields with his wife and children, as all his kin feared to take him in'. Just as at Walahesheim the inhabitants dealt with the disaster of dying livestock collectively, and their dogs were identified as belonging to the village, so the Kempten story indicates that the village was the basic unit for collective action: here deep-rooted conflicts divided the community and were discussed and resolved by the village as a collectivity. Territorial boundaries articulated this identity, dividing the countryside into a network of villages. Thus when a flash flood hit Eschborn, not only did it uproot trees and vines, wash away foundations and hurl 'the draught animals and beasts with everything which was in the houses to destruction', it also swept corpses and coffins from their graves and washed them into the bounds of another village.
Eschborn, Kempten and Walahesheim (see Map 7) in all probability lacked the degree of formal internal institutionalisation which was a hallmark of the high Middle Ages, but they had hierarchies and structures, as the ways in which the inhabitants of Kempten dealt with demonic trouble-making make clear. Legal documents show that disputes heard in these communities were debated in public meetings informed by the collective testimony of influential landowners, and where we can sometimes see a particular individual consistently serving as a 'chair', and often being the 'leading witness' for all local property transfers. Very occasionally, charter scribes might give such individuals a formal title – judge ( _iudex_ ) or hundredman ( _centenarius_ ) – but such terms were not used consistently or frequently in the charters, nor were they explicitly linked to a particular locale or village. Capitularies do make catch-all injunctions about 'hundredmen' and others, and constitutionally minded historians have as a result been tempted to see them as a particular class of local official, with consistent duties and reporting lines back to counts. The charter evidence, however, shows a more informal system of local leadership in which counts operated not through institutional links but by seeking to draw local figures into patronage relationships. As we saw in Chapter 4, we should probably regard the capitularies' injunctions for these local leaders to swear oaths of office, hold courts and ensure the administration of justice as attempts to draw those able to exercise informal leadership within the community into the purview of the official hierarchies of the kingdom. It is only very occasionally that we see counts imposing an outsider in such positions, and the result was almost always tension. The Istrian landowners who met Charlemagne's _missi_ (envoys) at Rižana in 804, for example, complained that the Frankish _dux_ John had overturned their ornate local hierarchies by imposing instead 'his hundredmen'. But such situations were exceptional and often, as at Rižana or with the career of the _escultaizo_ Folkwine at Rankweil in the Alps, coincided with moments of political turmoil at strategically important locations. The norm is indicated instead by numerous examples from across the empire of locally pre-eminent men emerging to serve as the key intermediaries between villages and the official structures of rule. Quite how locals referred to their 'headmen' we cannot be sure, although there are hints at vernacular terms (for example, _escultaizo_ or _sculdahis_ , ancestors of the modern German word _Schultheiss_ ). The titles used in capitularies and charters should be seen as generic labels, not formal designations of office, and the precise degree of influence and spheres of activity enjoyed by such men must have varied from area to area, depending on local tradition and political context.
**Map 7.** Places mentioned in Chapter 5: 'Villages and villagers, land and landowners'
A village was not a single unit of residence or agricultural exploitation: it was made up of an agglomeration of homes and other buildings, as our stories make clear. Both charters and polyptychs confirm this. The charters show landowners transferring rights over often tiny parcels of land – individual fields or plots – and also, on occasion, the household from which these parcels were cultivated, which might be called a courtyard ( _curtis_ ) or a farm ( _casalis, casata_ ), and might also include a residence ( _domus_ ). The polyptychs, even though they show landlords organising extensive estates, show peasants living in restricted households – a marital couple, their children and perhaps their parents – and supporting themselves off the attached holding. In the seventh and eighth centuries the vocabulary used to refer to these household-farms begins to show some standardisation, with _mansus_ (manse) and its vernacular equivalents ( _hoba, hufe_ ) increasingly used to refer to the 'standard family farm'. These units were not strictly surveyed assessments of agrarian output, but were based rather on a general sense of the norm that was appropriate for a peasant household. The origins of this nomenclature – and of the notion of a standardised household – probably lie in landlord initiatives: the settling of dependent peasants on planned estates, often 'new builds' on cleared land, a phenomenon we can trace as early as the seventh century and which was increasingly important in Carolingian times. Carolingian efforts to record and standardise the services expected from peasants on such great estates further encouraged its adoption, until _mansus_ and its cognates became generic terms, as in the ninth-century estate inventories of the monastery of Fulda.
The processes by which the early medieval countryside was pressed into this shape remain obscure. The reasons for the transition from late Roman _villa_ units defined by ownership and management to villages defined by collective action and shared territory are particularly shadowy, but the shift was complete north of the Alps by the time of our earliest documents in the seventh century, if not by the time of Gregory of Tours in the sixth; and even in Italy, although change was slower, by 800 at the latest the basic categories of social and economic activity had shifted in a similar direction. The physical reshaping of human settlement in the countryside that took place alongside these changes is apparent from the archaeology. Right across western Europe, Roman _villas_ , even where they had survived the disruption of the fifth century, fell into disuse by the seventh. North of the Alps, the vast majority of excavated rural settlements seem to have originated between the third and seventh centuries and continued developing into the Carolingian period, and often beyond. The archaeological record suggests, in other words, the emergence of a wholly new social order in the countryside in the late- and post-Roman eras. In many areas we cannot detect marked social differentiation between settlements, or indeed hard and fast status distinctions within settlements. In northern Gaul, for example, there are new forms of rural settlement and new building types in wood which suggest that groups of perhaps half a dozen households of roughly equal status were sharing the space. In southern Gaul, Catalonia and parts of Italy, around the shores of the western Mediterranean, different patterns of change are evident. Roman _villas_ persisted into the sixth century, some evolving into more modest centres of agrarian management. Elsewhere, new centres emerge in the settlement hierarchy: fortified centres on hilltops in both southern Gaul and Italy, for example. But most rural settlement in the western Mediterranean remained small-scale and relatively dispersed at the beginning of the Carolingian period, with village structures growing relatively slowly and late.
Excavated sites exhibit a number of important common characteristics that span the entire early medieval period across western Europe. First and foremost was the almost complete dominance of building in wood, other than for high-status structures like churches – not for nothing was the scapegoated man at Kempten accused of arson. There were two basic types of wooden structure. The larger was a rectangular building, characteristically around 10–15 metres long, supported by rows of wooden posts – these 'halls' were the living-place for a household. Auxiliary buildings around them took the form of smaller post-based structures built over a shallow pit, the so-called _Grübenhaus, fonds de cabane_ or 'sunken featured building'. These patterns reflect the social makeup of households based around a marital couple and their immediate dependants, each holding its own property. The alleged troublemaker at Kempten, for example, lived in a household with his wife and children, separately from his other kin in the _villa_ , and tended and harvested his own fields even when he was driven out to live in the mark. On many sites there are clear indications of internal boundaries – fences and the like – dividing rectangular 'halls' and their appendages from each other. Narrative sources, legal evidence, and by the Carolingian period charters, provide clear evidence that these internal boundaries were widely understood as delimitations of private property: as is clear from their role in bounding private and public space in the Kempten story, fences and doorways were culturally significant locations as the points at which household intersected with community. At Kootwijk in the modern Netherlands, indeed, a fence neatly bisected one such plot, marking out an area in which a second rectangular 'hall' and ancillary structures were built, providing concrete evidence that property was subdivided in the way indicated by charters and polyptychs.
Such subdividing reflects the relative ease of erecting new wooden structures, and this also made it possible for village topography to respond to shifts in community life-cycles. As individuals reached maturity, married and started households of their own, prospered or failed, inherited, and eventually died, the relative standing of the households within a village inevitably altered. New building was one way in which family and community could come to terms with the changing distribution of resources and social status. Perhaps related to this necessity of periodic rebuilding was the phenomenon of 'shifting settlement'. This is a particular characteristic of the very earliest, pre-Carolingian, early medieval centuries, and is best attested beyond the former Roman frontier in northern Germany and Scandinavia, where slightly different settlement forms and house types prevailed. The shape of many villages was determined by local topography as they strung along river terraces or beside roads, and as old buildings were abandoned and new constructed the central occupied zone of such villages might slowly – almost imperceptibly – move. One excavated settlement on the outskirts of modern Speyer, for example, worked its way half a kilometre along a terrace beside the Rhine between the fifth and ninth centuries.
The sometimes scattered nature and shifting focus of settlements within a defined area should not be confused with nomadism, an economic strategy built round constant movement to tend herds, which was wholly alien to early medieval Europe west of the Carpathians. Movements of a settlement 'core' within a wider area did, however, reflect a crucial characteristic of the early medieval rural economy: the relatively diverse and unspecialised economic strategies pursued by peasant households. The disappearance of the infrastructure of the Roman state dramatically changed the terms of aristocratic control in the countryside and relieved the pressures on peasant cultivators. This is why skeletal data show the early medieval countryside populated by smaller livestock than had been the case in Roman times. This was not a simple matter of biological or technological regression. The impetus for economic specialisation, which encouraged intensive stockbreeding of the type that had produced huge girths for specific purposes, was gone, and the use of livestock for agricultural work as well as for dairying and eventually slaughter made far more sense. Whereas in the Roman period agriculture often involved intensive concentration on a handful of crops ultimately destined for the tables of landlords or for sale at market to meet tax and rent demands, the early Middle Ages saw a diversification that altered the rural landscape. The margins of cultivation, waste and woods which might be used as pasture, hunting reserve or source of building materials increased in their importance. In other words, as the pressures of intensified production abated in the immediately post-Roman period, cultivators adopted new strategies which involved a different relationship with the landscape, a relationship which began to change again from the seventh and eighth centuries as the impetus for intensification once again began. The mark – the less densely exploited area on the margins of a settlement – thus stood in an economically symbiotic relationship with the houses and fields of the settlement core. Nonetheless, culturally and socially, the mark lay outside the sphere of normal public action and the collective gaze of the community, and so could serve as a wild and uncultivated 'other' against which the normal structure of village society defined itself. Just as Frankish writers could use the frozen north with its monstrous half-human, half-animal inhabitants to affirm the humanity of 'home' society, so for Frankish peasants (like the conflict-torn inhabitants of Kempten) the mark was the place to which to drive trouble-makers whose behaviour could be explained only by demonic possession.
The mobility of settlements remains a little-understood phenomenon. But, though it probably does mean that some villages had not yet acquired a permanent territorial focus, perhaps the most marked feature of Carolingian and post-Carolingian rural settlement was an increased stabilisation and nucleation of sites. Even in Italy, where our data is much patchier, the concentration of peasant habitation into what we would recognise as villages (traditionally thought of as a post-Carolingian development) seems to begin in the late sixth and seventh centuries. The crucial factor in this seems to have been the emergence of a static focal point (often a cemetery and church) around which habitation clustered. At Dommeln in the Netherlands, for example, a number of loosely related farmsteads and two- and three-household hamlets were replaced in the eighth century by a concentrated village with a clear internal hierarchy. At a similar date at Mondeville in Normandy, the creation of a series of wooden structures in the cemetery – at first, 'grave-houses' over a single burial or group of burials – was followed by the building of a chapel associated with the cemetery and the stabilisation of the settlement. Similar examples are known from Bavaria. The building of churches in stone, increasingly common from the Carolingian period, created immovable focal points which helped to fix village identities not just physically, but also in the minds of their inhabitants. Churches and cemeteries were public spaces where meetings were held and legal actions took place, and where acts of community such as wakes for the dead were held. The significance of this public space is also shown by its role in the playing out of conflict: Archbishop Hraban of Mainz, for example, had to deal with the disruption to sacred order caused when long-running feuds boiled over and led to bloody killings in that most public of places, the village church; while his friend Einhard dealt with a succession of convicted poachers, feuding peasants and eloping couples who came to the boundaries of his church at Michelstadt. Whether such places acted as sites of consensus or conflict, these developments testify to the gradual coalescing of village society during the Carolingian age.
The stabilisation of rural settlement coincided with significant economic changes. There is clear archaeological evidence for more intensive arable exploitation and an increase in economic specialisation in the Carolingian period. Skeletal data suggest that livestock, whilst not matching the size of their Roman ancestors, were stock bred to a larger size than in Merovingian times, whilst faunal remains show a greater concentration on large-scale cereal cropping. There is also some evidence for expanded craft production: on the Rhine terrace near Speyer, for example, there were spinning and weaving workshops of a kind associated with 'women's work' in the written sources. All of this implies a raised level of social organisation and a shift back towards the intensification of settlement and production that distinguishes the eighth and ninth centuries from the sixth and seventh. It also led to important shifts in the relationship between the settled 'core' of a territory and its immediate environment.
#### LANDOWNING AND LANDOWNERS
To understand the dynamics behind these changes, we need to examine the effects of aristocratic and royal power at the level of the village. Here we can turn to the charter evidence, which survives in increasing quantities from the eighth and ninth centuries because monastic foundations were acquiring property and documenting their holdings on an unprecedented scale, meaning we have data-bases of dozens – sometimes hundreds – of charters for village societies from Bavaria to Brittany. Although what they reveal varies from region to region because of differences in social custom, landscape and aristocratic power, they share a number of common characteristics. The basic units of agrarian exploitation and property ownership were small and fragmented: the property dealt with in the charter evidence typically consisted of individual fields, plots, or occasionally farmsteads. Carefully used, the charter evidence reveals a social hierarchy with no sharp or sudden discontinuities of status, in which small landowners might scrape together a living from a handful of plots. The brothers Ripwin and Giselhelm, for example, whose careers can be traced in the late-eighth-century charters from Lorsch (a monastery in the middle Rhine valley), owned around half a dozen such parcels. Most of these holdings lay in the village of Bensheim, where the brothers often served as witnesses for their neighbours' transactions, and where they had invested in clearing woodland to bring it under the plough, but they also had individual plots in three other villages all within a day's travel, in a pattern that is absolutely typical.
The rich cache of charter evidence that documents Ripwin and Giselhelm's careers allows us to see them as middling owner-cultivators. The pair had poorer neighbours who owned only a couple of plots, and could not afford to make clearances, and richer contacts who owned a dozen or more land parcels, some of them farmed by unfree dependants. But within this broadly based and inevitably unequal landowning class we do not find any landowners distinguishing themselves from their peers with labels of social distinction or claims of legal privilege of the kind that structured late Roman and high medieval society: the public office of count is the only such distinction consistently advertised by charter scribes, and was open only to a handful able to access and acquire royal patronage. This absence of overt status divisions within the landowning class differentiates the early medieval centuries from the Roman and high medieval worlds, and also from contemporary states elsewhere in Eurasia, where broader distinctions between producers and consumers of rent and tax are far clearer. In the absence of formal criteria of rank, tiny variations on the sliding scale of status within the community of landowners were revealed by precedence in public meetings, as reflected in the witness lists of charters. The modest status of Ripwin and Giselhelm is thus reflected by their regular appearances in witness lists; but the fact that they were not listed in prominent positions, and that they were frequently associated with a small group of higher-status individuals, points to the significance of patronage relationships within the community.
Even for those further up the social hierarchy than Ripwin and Giselhelm, landholding was made up of agglomerations of these small parcels interleaved with their neighbours' holdings. Among the outlying plots held by the brothers was one across the Rhine from their home in Bensheim, in the village of Dienheim. Dienheim was an important regional centre where several major churches had extensive interests; Ripwin and Giselhelm's entry into the patronage networks which centred on such places, clear from Ripwin's purchase of a horse in order to perform military service (a badge of high status, as we saw in earlier chapters), explains their interests here. Count Rupert, a member of the most powerful aristocratic family of the region, can be seen in our evidence levying tolls and sitting in judgement at Dienheim, his official role reinforced by dense networks of patronage evident in over a hundred charters from the years either side of 800. His family holdings here, however, essentially consisted of vineyards and plots little different from those held by Ripwin and Giselhelm, and although we have clear evidence of the scale of his family's wealth (a far-flung scattering of interests from Hesse and the Moselle valley down to the upper Rhine), there are only a handful of locations where more elaborate complexes can be seen. Even very important landowners like Rupert, then, built their influence on control of numerous units of a familiar type, without their being amalgamated into a different form of estate or landownership. Whilst the archaeological and documentary evidence shows increasing concentration of aristocratic wealth in our period, distinguishing it from the immediately post-Roman centuries when landlord domination of peasants was relatively weak, this did not overturn the basic character of early medieval settlement and society.
Charters can also tell us something about how land changed hands. Ecclesiastical archives sometimes preserve dossiers of title deeds handed over by early donors, from which we can get a sense of the frequency and nature of land exchanges. The hundreds of ninth- and tenth-century secular documents which existed in the Cluny archive in early modern times, when they were copied by antiquarians, consist of the fossilised remnants of dozens of such dossiers, typically consisting of bundles of between half a dozen and a dozen related documents, often annotated or physically connected to one another. Around half of these documents concern land sales, roughly evenly split between sales between kin and between neighbours, whilst written dowry agreements were also common. In such material we find not a discrete and defined family plot held in trust by each generation in turn, but land parcels of varying sizes, from farms to fields to tiny plots, some clustered and some scattered, and normally held by an individual. In at least some cases, the transmission and division of property rights must have been affected by relationships within a kin-group as marriage, birth and death changed the demands and size of its constituent parts, and so the language of individual property described the distribution of resources within a family or a household. Certainly individuals transferring land beyond their immediate kin, for example by making a pious gift to the Church for the good of their souls, typically went out of their way to have their kin record their consent to the transaction (a practice endorsed in royal legislation), while a significant number of surviving land-disputes were brought by disinherited kin contesting a relative's decision to donate land. The donations to the west Frankish monastery of Fleury made in the will of the aristocrat Eccard of Mâcon, for example, were contested by kin who after his death seized the land in question 'as if it were inheritance'. In other words, despite the fact that land was understood as individual property, and society as an agglomeration of conjugal households, cultural norms and social expectations to some extent limited individual control over property and made it a matter of family trust.
We should acknowledge that there were regional differences in the character of rural society: in Italy, for example, aristocrats were less wealthy than those north of the Alps, but at the same time enjoyed more formalised precedence over those who fell under their influence. Likewise, political heartlands like the Moselle and Rhine valleys should be distinguished from 'peripheral' areas like Alemannia, Bavaria or Burgundy, which were dominated by regional aristocracies rather than the distant but powerful cliques of the court and so had a shallower social hierarchy. The Paris basin, as we shall see, was home to unusual forms of landholding that provide a notable exception to the norm. But even in royal heartlands like the middle Rhine valley, where the wooden halls of middling owner–cultivators like Ripwin and Giselhem were loomed over by monumental stone palaces and by the inherited interests of leading aristocratic families, and where, if anywhere, we would expect to find concentrations of wealth and formalised social hierarchies, landholding remained fragmented and social status a matter of subtle gradations among the community of free landowners.
That said, quantitative differences in the number of holdings did lead to qualitative differences in lifestyle. There is no evidence that Ripwin and Giselhelm possessed a dependent labour force of unfree peasants. As owner–cultivators, they may have engaged in short-term sub-letting, perhaps occasionally buying in labour at harvest time or even working in collaboration with kin and neighbours, but fundamentally they must have relied on their own labour and that of their kin to work their land. Their patron Count Rupert, on the other hand, dealt with peasant families who were an integral part of his landed properties. Peasant families like this, who worked the land-parcels owned by an aristocratic family, were typically unfree in status; free tenants remained rare even at the end of our period, and were in general rarer the further one travelled from the heartlands of the royal court and the imperial aristocracy in the Paris basin and the valleys of the Meuse, Moselle, Rhine and Po rivers.
But despite the existence of an unfree labour force on the estates of aristocratic families like Rupert's, it would be misleading to talk of a 'slave society' or a 'slave mode of production' in the Carolingian period. To translate the varied and often fuzzy early medieval terminology of unfreedom in terms of our concept of 'slavery' would be to prefer modern ideas and definitions to late antique and early medieval understandings of unfreedom and dependence. Even in the Roman period, the extensive use of slave gangs to exploit large estates – the classic case of a 'slave system' defined in economic terms – was confined to Italy, and in decline after the third century. Nonetheless, legal definitions of personal unfreedom – the possession of one human being by another – continued through late antiquity and into the early Middle Ages, in part because the classical discourse of freedom and slavery fed into the thought world of the early Christian Church. One major problem for historians of early medieval society has been that the supposedly clear division between the legally free and the legally unfree was in practice blurred as varying degrees of subjection acquired their own labels and terminologies. Free and unfree were not absolute categories that related to clearly defined practices or conditions. It therefore makes more sense to think of a continuum of dependencies than a clear-cut divide. For modern historians this continuum creates problems of interpretation, because it does not fit easily into our inherited grand narratives of transition 'from slavery to serfdom'. Faced with such a situation, rather than imposing the straitjacket of totalising categories on the evidence, we need to analyse the texture of rural society in the Carolingian period on its own terms, and try to tease out the complex interactions between legal status, economic function and social standing amongst the peasantry.
#### COMMUNITY AND MOBILITY
The pattern of scattered small-scale property units had important implications for social structure. Clearly, a lifestyle sustained by this type of landholding presupposed rhythms of residence and movement, vividly described in the ninth-century _Life_ of the Saxon noblewoman Liutberga. Einhard's mocking description of the last Merovingians trundling around on an oxcart, even though they barely had estates to trundle between, implies similar expectations. This peripatetic lifestyle should not be seen as an economic necessity for aristocrats: it was not a case of behaving like the very hungry caterpillar, eating all an estate's resources before moving on to the next stop, since renders of food and livestock could easily be transported or stored. Although we lack the data to trace aristocratic itineraries in detail, the indications are that they were determined, like itinerant kingship, by political factors. Staying at a specific residence for winter, or to enjoy the hunting season, or to celebrate festivals like Lent and Easter, allowed links to be reforged with friends and neighbours, kin and clients. For adult male aristocrats at least, the demands of the king and the cares of office were further complicating factors, necessitating presence at the royal court, or on campaign, or involvement in the transmission of royal orders and the dispensation of royal justice.
Structural mobility, however, was not confined to aristocratic elites: the patterns of landowning we have been investigating meant that it was a crucial aspect of social status at a local level too. Pioneering work on the charter evidence preserved at the monastery of Redon in Brittany, for example, has revealed how local landowners also moved around. While the majority of smallholders are generally encountered only in a single settlement and its immediate neighbours, the local standing of some individuals gave them a greater range, as they regularly appear as witnesses, guarantors or legal experts over a wider area. Mobility of this type demonstrated a certain level of economic resource: it was only possible, after all, for those who were not tied into the daily routine of agricultural cultivation. Carolingian legislation, indeed, regulated the duration and frequency of public meetings so as to prevent smallholders who were summoned to them from suffering hardship. Regular travel over these kinds of distances, moreover, presupposed ownership of horses, which were expensive and were therefore crucial badges of status. Indeed, prominent among the complaints of the inhabitants of Istria against their _dux_ in 804 was that he had summoned them to the host, then taken the horses they had brought, given them to his own men and sent the Istrians home on foot, to the ridicule of their neighbours. In other words, entry onto the public stage of courts and meetings through which local society was organised was theoretically open to all, but in practice regular participation in the public business of the locality, crucial for those who sought to become involved in networks of favour and patronage, required a certain amount of modest wealth.
Possession of a horse was also a prerequisite for the performance of military service, the most significant public due demanded by the king and the most prestigious service one might perform on behalf of one's community. Military service was determined by precisely the bonds of patronage and obligation that structured rural society. That it could be viewed as both a duty and a right is clearest from the example of the Lombard kingdom, where the term _arimannus_ and its Latin equivalent _exercitalis_ (both literally mean 'army-man') denoted a free landowner who had the right to participate in the annual assembly of the army, which was at least as much a political gathering as a prelude to campaigning. In the post-Roman centuries, liability for military service had come to imply not only freedom in law and from certain exactions by the state, but also an appreciable political and social status. The Carolingian wars of expansion in the eighth century presented those who were liable with unprecedented opportunities to enhance their wealth and status on the wartrail, so that military service was both a goal for the socially aspiring, and an important element in patronage relationships. The situation changed in the first decade of the ninth century, when (as we saw in Chapter 4) the end of expansion coincided with a spate of legislation placing the raising of the army in the hands of the royal missi. That they were to draw up lists of those liable to serve suggests that participation in war had become less desirable: the opportunities for enrichment were fewer, and had given way to the needs of defence and consolidation. But while _ad hoc_ patronage networks were therefore less reliable recruiters than they had been in the age of expansion, the obligation to participate continued to be based on generalised notions of a man's status and obligations, rather than on any direct relationship between service and landholding. The 'vassal' who held land in return for military service – an important prop in the traditional construction of 'feudalism' – is nowhere to be found in the Carolingian world.
The central fact of the Carolingian countryside was thus the complex interaction between the steepening of the social hierarchy, leading to longer and more formal ties of patronage, on the one hand; and on the other a continued understanding of Frankish society as based on the community of free landowners acting collectively. Tensions between these two models surfaced in royal legislation, which was ostentatiously concerned with protection of the free poor whilst simultaneously attempting to formalise aristocratic power in terms of public office. It is thus hardly surprising that it is from the Carolingian period that we also have the fullest attempts to formalise the public obligations of free landowners, for example the responsibility of all to fight in defence of their country ( _patria_ ), first explicitly stated in ninth-century capitularies. At the same time as their military obligations were more closely defined, peasants who armed themselves outside approved structures of authority were increasingly seen as acting illegitimately. In 859 when the 'common folk' between the Seine and Loire formed a sworn association ( _coniuratio_ ) which 'stoutly resisted' the Vikings, the author of the _Annals of St Bertin_ recorded the actions of their aristocratic overlords – who effortlessly ( _facile_ ) butchered what was seen as an illegal and subversive association – with unhesitating approval. What was at stake here and in similar cases was not the letter of the law, but the sometimes competing ways in which different social classes (the aristocracy and the wider free) defined their identities. Those who had organised themselves to fight the Vikings may have seen themselves as doing nothing other than defending the _patria_ as stipulated by the law; but to the 'more powerful people' who killed them, their self-organisation was an affront to a growing sense of social superiority which was endorsed by the ruling dynasty and which was partly expressed in terms of the right to bear arms and to participate in warfare.
The picture sketched so far, of scattered and small-scale property interests, gradual but steepening social distinctions and considerable geographical mobility, contrasts with a received image of medieval communities as cohesive, inward-looking and tied together by common interests and kinship. This image is simply incompatible with the patterns of public action revealed by our charters. The public meetings at which property transfers were enacted or disputes resolved were not 'village meetings'. Frequently, they took place in the same village as the property concerned, but where our charter evidence is dense enough we can discern public activity clustering around important regional sites which were also markets or administrative centres, and where high-status individuals were likely to be present: in Ripwin and Giselhelm's case, we have already seen their being pulled towards Dienheim, which was just such a centre. And although smallholders might be found witnessing transactions in their own villages more than elsewhere, their names typically appear associated with those of higher-status landowners who witnessed in several places. Moreover, although the Carolingian countryside was divided into a series of geographical units called _pagi_ (singular: _pagus_ ), which had evolved from Roman administrative divisions and had clear territorial boundaries, the patterns of sociability and public action so visible in the charters do not correspond neatly to these units, nor to any visible subdivisions. Public activity which transcended the village was absolutely central to the social life of the Carolingian countryside: village affairs were not closed, but tied into the business of a wider locality. The 'culture of the public', which was a crucial legacy of Carolingian society from the Roman and post-Roman centuries, was defined by and tied up with these patterns of interaction, rather more than with the 'state' as a formal institution.
None of this means that villages did not matter as formal structures: as we have seen, they (and not the _pagi_ ) were the basic units of society, in which fields and houses were located, to which demons and dogs belonged, and with which resident landowners were identified. Identification with a particular village emerges most clearly in our sources where we see villagers acting together, such as when collective testimony was needed on some matter of local knowledge, or where the village's boundaries needed defining. The increasing demands of king and God at a local level in the Carolingian period, indeed, encouraged these collectively expressed identities. The levying of tithe and the performance of 'public services' by the free population were organised on a village-by-village basis; similarly court cases show obligations towards landlords and rulers being resisted through such collective identities. This indicates that we can see the village as the most basic of a series of interlocking tiers of public action. But just because villagers saw themselves as a community in some contexts, they did not always present a united front or act in the interests of all. At Kempten, as we saw, conflict and petty jealousies threatened to spiral out of control when one man and his wife were driven out of their home in the village core and forced to live in the fields. They had kin in the village, but these were afraid to take the scapegoated couple into their households because of the anger of the community as a whole and the family's need to continue social intercourse with their neighbours. This story shows how our ideas about social consensus, community identity and kin loyalty are ideals which in practice were compromised by circumstance and which were often in competition with each other. Kinship was a compelling bond so far as it overlapped with interests in property, but when the harvest had to be gathered and stored, it was no match for the urgent demands of community. And community, as the couple cast into the fields beyond Kempten and their family inside the village could surely remind us were we able to ask them, can also be a euphemism for a small world of suspicion, discord and oppression.
#### LANDLORDS AND MANORS
Scattered smallholdings remained the dominant form of landholding right through our period, even for aristocrats. Nonetheless, in the course of the eighth and ninth centuries a new form of organisation becomes evident in the countryside: the manor. Sometimes termed 'bipartite estates', manors rested on a twofold division of the land: most was divided into individual plots of a familiar type, from which dependent peasant households supported themselves in return for rent, but a central area was set aside, its produce directly bound for the landlord. This 'demesne' or reserve was worked by the dependent peasantry, who performed fixed labour services or corvées (such as working in the lord's field a certain number of days a week, or performing other 'higher status' duties such as transporting goods, running errands or meeting public obligations on his behalf). The spread of this system on royal and ecclesiastical land is documented in the polyptychs – written documents (of which over two dozen survive from the ninth century) recording in minute detail the rent and service owed by peasants on ecclesiastical and royal estates.
The origin of the polyptychs is intimately tied up with the origins of this more intensive system of rural exploitation as a whole. Polyptychs, as records of estate management, help us trace the emergence of manorial organisation on royal land in the heartlands of the Merovingian kingdom in the Paris basin in the seventh century, and its slow export in the eighth and ninth as an aspect of the political and social expansion of the Frankish world under the Carolingians. But in origin they are linked to the activities of rulers, and in reading them we have to remind ourselves that the distinction between public obligations and private estate management was far from clear cut, not least as the polyptychs recorded practice on royal and ecclesiastical domains which were political creations, and were treated by the Carolingians as state resources.
The term 'polyptych' was used to refer to lists of dues and obligations owed to the state in the Roman and immediately post-Roman periods. A series of documents from the sixth and seventh centuries, dealing with payments made to bishops, reveals the complex evolution that had taken place by the Carolingian era. While landlords had always played a central role in collecting such dues from the peasantry before passing them on to the state, royal grants of immunity received by great churches turned them into islands of fiscal and jurisdictional independence and allowed them to hold on to these revenues in return for other services to the king and kingdom. Documentary practices once associated with public tax collection thus survived through the seventh century, when actual royal tax collection disappeared, on the estates of large churches and other privileged landowners. The likely existence of a continuous documentary tradition connecting Roman practices of land-registration and tax-assessment to the Carolingian polyptychs does not, therefore, mean that the two forms of documentation had identical functions. Indeed, the polyptychs' detailed surveying of agricultural resources, household by household, and their recording of the specific rents and services owed by dependent peasants to a landowner, would have had no place in the tax-lists documenting dues to Roman rulers and their immediate barbarian successors. By the same token, the compilers of these Carolingian surveys detailed the public dues and services owed by the dependent peasantry simply because such demands were by now thoroughly integrated into practices of estate management, often as fossilised custom.
From the time of Pippin III on, as the Carolingians sought to utilise 'excess' church land, estate surveys of a fairly rudimentary type, listing the extent of ecclesiastical holdings, were compiled. It was on these practices that the Carolingian court drew when, in the years around 800, it began to insist on the systematic surveying of royal estates so as to ensure that they were exploited to their maximum potential; this example was subsequently adopted by the great churches of the empire as they sought to meet their dues to God and king. The distribution of the surviving polyptychs – all ninth century or later, all documenting royal or major ecclesiastical estates – is thus scarcely an accident. The production of polyptychs was a response to royal initiatives, and polpytychs closely followed templates promoted by the court, for example in _De villis_ ('Concerning estates'), a capitulary outlining the duties of the steward of a model royal estate, and the closely related _Brevium exempla_ ('Brief examples'), which consisted of actual surveys of specific estates produced to demonstrate the application of the template in practice. As _De villis_ made clear, this surveying activity was designed to ensure that estate-stewards operated with the interests of their royal masters in mind; its rapid application to ecclesiastical estates, again encouraged by the court, underlines the extent to which church land was understood as a public resource whose proper use was a responsibility of kings as well as the churchmen who administered it.
The manors which dominated the polyptychs of major churches such as the abbeys of St-Germain-des-Prés or Prüm rested on two central developments: the creation of a 'home farm' or demesne for the lord, and the imposition of corvées on the dependent peasantry to cultivate this reserve. Neither can be seen as standing in direct continuity with Roman forms of estate management. The emergence in the seventh-century Paris basin of these new forms of estate on the lands of the Merovingian kings and their favoured churches should thus be seen as a conscious initiative, undertaken to support a new political system centred for the first time on a single, sedentary, court establishment. It was an initiative which was possible only because its authors enjoyed political control and could lay claim to public rights inherited from the late Roman state, in particular to force the peasantry to labour on public works, and the title to large blocks of land from which demesnes could be created. A product of specific circumstances, this form of organisation was therefore neither natural nor 'normal'. The subsequent spread of the system from the Paris basin to a few other political heartlands, primarily in the north-east of the Frankish world, was likewise a reflection of expanding royal power under the Carolingians.
The generally fragmented patterns of landholding we have been discussing meant that the combination of factors necessary for the creation of manorial estates was difficult to realise, which explains why they did not become widespread very quickly. The investment of considerable resources in the clearance of wood or uncultivated land on a substantial scale was often necessary to create the discrete blocks of uninterrupted property necessary for manorialisation. Here, king and Church enjoyed a key strategic advantage, in that land of this kind – not only wooded land – was defined legally as _forestum_ (forest), title to which lay ultimately in the hands of the king; and vast swathes of forest were subsequently granted to favoured churches under the Carolingians. These fairly abstract rights over large tracts of land might be transformed into manorial 'new build', particularly by churches which as large-scale institutional landowners had the resources to support the necessary investment, but also by the top tier of aristocratic families. A trend towards the foundation of separate aristocratic residences, centred on a hall or a church-and-hall complex and often distant from the hustle and bustle of village life, is visible in both archaeological and documentary sources of the seventh and eighth centuries, and encouraged the creation of discrete complexes of family property: it is typically at such sites that manorial structures are most clearly visible on aristocratic land. Remarkable excavations in an area where we have good charter evidence have helped us see just such a process in the Dommeln region of the modern Netherlands. Here, in the first half of the eighth century, local elites aligning themselves with Charles Martel were able to transform the landscape through the systematic creation of new estate centres on cleared lands.
The impact of these changes on peasant society remains little understood, partly because, as we saw at the beginning of this chapter, debate about Carolingian society has been conducted with reference to the serfdom of the twelfth century, and has therefore been overly concerned with whether or not manors hastened the transition from free to unfree by blurring the line between one and the other. But as we have already noted, these categories were never as clear-cut as is sometimes made out. In fact, we cannot assume that manorialisation significantly altered the texture of peasant society. The Prüm polyptych, for example, contains clear indications of regional or local customs: horizontal bonds of community among the peasantry were arguably as important as monastic lordship in shaping the manorial economy and society here. In the rare documents that allow a glimpse of the peasantry on manorial estates, we see familiar structures of local testimony and public meetings being deployed to process co-operation and competition within the community. For example, in the case of the scapegoated man at Kempten the community of tenant peasants dealt collectively with allegations of theft and wrongdoing before staging legal and religious rituals (an ordeal of hot iron and an exorcism); similarly, in 857 a complex dispute over possession of land within the immunity of St Martin's at Tours was resolved through a series of public meetings at which the testimony of local 'good men' ( _boni homines_ ) and dependent peasants ( _coloni_ ) was used to decide between conflicting written documents; and around 900 jurors ( _scabini_ ) and a judge drawn from the peasant _familia_ of an estate owned by the monastery of Gorze watched two of their fellows undertake the ordeal of hot iron in an attempt to prove that a particular holding was family 'inheritance' rather than a part of the abbey's reserve or demesne. Landlords are visible primarily as a possible source of discipline where things were not resolved through these local agencies. Charlemagne's biographer Einhard, for example, intervened in a number of cases where local conflict escalated into violent feud, and the landlord's representative, rather than aggrieved kin, were to exercise rights of vengeance and impose physical punishment. It is probably mistaken, therefore, to draw too strong a contrast between the workings of the 'public courts' used by free landowners and 'private justice' of the great estates. Dependent peasants could, indeed, bring certain cases against their landlords before public courts, especially those that concerned landownership or personal freedom. Free tenants enjoyed access to public courts and meetings, and the prestigious services frequently expected from them – notably military service – placed them side by side with free landowners of good standing in the performance of public dues. On occasion, there are hints at the kind of bonds that could arise: a court case of _c_.820, for example, shows a free landowner called into the royal host entrusting his property to a dependent peasant on a nearby royal estate.
Horizontal links of this kind were common precisely because bonds of association and kinship among the peasantry crossed tenurial boundaries, giving the lie to a view of manorial estates as discrete blocks controlling huge tracts of the countryside. In fact, where we have relatively full transmission of the charter evidence alongside the polyptychs, these estates begin to look much less solid. Estate surveys from Prüm in the Ardennes and Wissembourg in Alsace suggest that some estates – particularly those which rested on large-scale campaigns of clearance in marginal areas such as the Ardennes – were huge contiguous blocks of property, but in the more densely populated and intensively cultivated Moselle and Rhine valleys the abbeys' estates nestled alongside those of other landowners. In the immediate vicinity of the palace of Trebur in the Rhine valley, the rich charter evidence shows no private property or peasant-proprietors, but beyond this area dependent peasants whose dues are listed in the surviving polyptych lived in villages where there was extensive private landholding, and were interleaved with free peasant proprietors and aristocratic estates.
Manors are often seen as the real motors of social and economic change in the Carolingian countryside. Yet manorialisation was not an all-encompassing process sweeping all else aside and creating a new rural landscape, but a strategy that was viable only where the creation of a significant demesne and the provision of a labourforce was possible. The presence of manors was the major difference between the countryside of the seventh and the ninth centuries, but their distribution was uneven, and they tended to cluster in those political heartlands where the Carolingian kings and their favoured churches enjoyed extensive landholdings, and which were also the homelands to the top tiers of the aristocracy. Geographically and socially, manors were anything but closed worlds, and their impact on the economies and societies of the Carolingian world must be understood in terms of their interaction with existing social forms.
#### THE PROBLEM OF ECONOMIC GROWTH
All of these issues also play a role in debates about whether the Carolingian period witnessed economic growth or stagnation. Thanks to the impression of systematic organisation gained from the Polyptychs, some historians have seen the manor as a model of economic efficiency and so a motor of economic development. For their opponents, however, big was not necessarily beautiful: manorial structures were conservative, shackling rural producers to the demands of landlords and limiting their ability to participate in networks of exchange. But, as is the case with most set-pieces, the contours of this debate may tell us less about historical realities than the ideological and intellectual predilections of modern academics, here working in the last third of the twentieth century when ideological controversy raged over the relative merits of direct economic management by state elites and small-scale private enterprise.
There certainly are clear indications within the polyptychs that the systems of production pursued on the estates of the great churches succeeded not only in meeting the imperatives of generosity imposed on abbatial and episcopal tables by the Carolingian political system, but also in generating significant surpluses that were actively marketed. Careful study of the services demanded from the dependent peasantry on the estates of St Germain and Prüm, for example, has shown a complex system whereby certain privileged groups were required to oversee the transport of local surpluses by boat or cart, some to central points within the abbeys' holdings where it could be redistributed to feed the monks and their guests, but some to major markets for sale. A series of royal privileges allowing the foundation of markets at central points within ecclesiastical estates, climaxing in the middle decades of the ninth century in west Francia and the tenth century in the east, illustrate how the infrastructure created by these systems of redistribution could stimulate exchange. Perhaps more significantly still, the granting of formal privileges to license specialised 'markets' perhaps indicates a step change. We know that before the ninth century there were some seasonal fairs at major centres such as St Denis, which were the visible peaks of 'market-type' activity in a countryside where most exchange remained embedded within wider patterns of social interaction, buying and selling going on at regular public meetings which had a wide range of functions ranging from legal hearings to feasts and hunts. Such a state of affairs is typical of a world in which the economy was not yet understood as a separate sphere of activity with its own rules and processes; and against such a backdrop the creation of recognised and recognisable markets more distinct from the generality of social intercourse constitutes an important shift.
Royal demands also played an important role in this process. Those free peasants who oversaw the transport of surpluses typically had relatively light obligations in respect of corvée labour on the lord's reserve, but were responsible for meeting many of the public obligations owed by their lord to the king, carrying goods or messages at the king's command or taking customary gifts of produce to royal palaces. On the estates of the abbey of Wissembourg, for example, certain groups of free peasants were required to carry stone and building materials for the upkeep of specific royal estates, and it was at these centres that regional markets developed. Systems of redistribution within estates, the need to meet the demands of kings for produce and services from those estates, and the emergence of broader exchange networks were thus thoroughly intertwined.
We will explain all this in more detail in Chapter 7. But for now it is important to underline that these developments were not the result of a conscious economic policy aimed at encouraging exchange: the primary aim of ecclesiastical and royal estate-management was the creation of a stable and predictable flow of goods and rent, not at what we would recognise as economic growth. Indeed, the economics of ecclesiastical and royal estates may have been far less centralised than is implied by the polyptychs and capitularies, with real agency resting in the hands of the bailiffs and stewards who were responsible for individual estate-complexes. Whilst the great polyptychs of ecclesiastical institutions like St Germain (in Paris) or Prüm (in the Ardennes) might encourage us to think of abbots and bishops hatching economic masterplans, the practical impact of estate surveys was at a more local level, and it is on this local level that we can see documents used in practice. Record keeping of this kind, of course, was a way of preventing estate managers enriching themselves at their lords' expense, and the documentary and literary evidence repeatedly hints at the influence of such figures, and the fuzzy boundaries between the interests of landlord and steward. But not all local agency should be seen in terms of corruption. Stewards and bailiffs, where we can identify them, were drawn from influential landowning families and therefore had the contacts and knowledge to react to threats and opportunities far more effectively than distant landowners. Indeed, they were encouraged to show initiative: in _De villis_ , for example, it was the steward who was responsible for the marketing of any produce that remained once the immediate needs of his estate and the demands of his royal lord had been met. Above all, though, we should remember that those lordly demands were seen as more significant than the money raised through selling surplus. After all, ecclesiastical and royal estates were the primary sources of funding for both Carolingian kingship and the Carolingian renaissance: huge resources were consumed by the building and provisioning of palaces and churches, the production of luxury manuscripts, and the dispensing of patronage.
But for all that production for the market was not the primary aim of manorial economies, such initiatives were only possible because manors were producing considerable surpluses. Economies of scale played a part in this. Improvements in agricultural technology – the diffusion of iron ploughs or water mills – depended not on a heroic history of new inventions, but on the slow diffusion of practices which required significant investment. Similarly, the adoption of field rotations and new crops was far easier to effect on a carefully managed and extensive demesne than it was on scattered smallholdings, reflected in archaeological evidence for greater concentration on large-scale cereal cultivation on some Carolingian sites. But some eighth- and ninth-century developments worked equally to the benefit of smaller landowners, such as the slow move towards some specialised cultivation. This should not be seen as a sweeping change from subsistence to cash-cropping: peasants and landowners continued to pursue a mixed agrarian strategy aimed at supplying their own households, cultivating a variety of crops, and raising livestock which supplied labour and non-food produce (wool, candles, leather) rather than being specially bred for meat. But in the eighth and particularly the ninth centuries, there is increasing evidence for specialised production for the market: the cultivation of vineyards, or olive groves, or chestnuts. Female labour might be especially important, too, engaging in the small-time baking of bread or weaving of cloth to serve nearby towns and their markets. Such practices were suited to owner-cultivators, requiring as they did the careful tending of relatively small-scale units of land, and the making of small adjustments to the household economy; indeed, this kind of 'market gardening' was particularly suited to land not under the plough.
Manorial estates, then, were not closed systems, and formed an integral part of the world we have been describing, providing opportunities for all sectors of local society. The fact that _De villis_ enjoined that dependent peasants not 'waste time' at the markets which they visited on behalf of their landlords shows the interlinking of these ostensibly different parts of the rural economy. Yet this was not just a world of growing opportunities. Even in an agrarian economy, the higher level of economic complexity implied by this evidence for specialisation and exchange involves a higher level of potential risk. The economic changes we have been discussing therefore help us understand why in our narrative sources we repeatedly read of dearth, famine and harvest failures. Even allowing for the occasionally overblown Biblical rhetoric of these reports, their frequency is striking: over the ninth century as a whole it has been calculated that we find a report of a famine or food shortage for one year in four, a much higher incidence than for the immediately preceding and succeeding periods.
We should not rush to generalise these into a picture of widespread crisis. Most shortages were local in their geographical impact, and differentiated in their social impact. When in 806, for example, we find Charlemagne ordering counts and other holders of royal estates to use their surplus food to feed those affected by shortages, and to urge others to follow their example, leading a programme of almsgiving, fasting and prayer designed to appease an angry God, we realise that shortages were a product of social organisation as much as of natural disaster. These were not the inevitable crises of a subsistence economy where hunger was endemic, but the consequence of a particular system of production. The creation of a landscape in which the pockets of habitation were more densely peopled, and elites sustained more lavish tables, involved the creation of more complex systems of exchange and redistribution involving manors and markets. These changes were sustained without any significant technological breakthrough, in an agrarian landscape still exploited by the labour of man and beast. They therefore benefited the ruling class, and left the peasantry increasingly exposed to relatively small climatic variations and meteorological misfortunes.
#### THE POWERFUL AND THE POOR: SOCIAL CONFLICT IN THE CAROLINGIAN COUNTRYSIDE
The vivid impression left by the reports of these recurrent crises has deeply influenced modern perceptions of social change in the ninth-century countryside: accounts of agrarian crisis have encouraged some historians to see the Carolingian countryside as undergoing a fundamental social transformation, with a hard-pressed peasantry forced into ever-greater dependence on aristocratic and ecclesiastical landlords. Yet the idea that the ninth century saw the 'decline of the free peasantry' does not necessarily stand up to sustained examination. Much of the evidence for peasant impoverishment comes from capitularies and church councils, which contain a range of injunctions intended to prevent oppression of 'the poor'. The practices condemned range from price-fixing in times of scarcity to manipulation of the processes of the law, for example ruining peasants by legal filibustering that necessitated their attendance at distant and expensive court-hearings and prevented them cultivating their land. But as we saw in the introduction to this chapter, these repeated exhortations were more ideological than descriptive: protection of the poor had long been established in Christian thought as a crucial duty of the powerful, and much Carolingian legislation of this ilk has an almost timeless quality. The practices condemned can therefore be seen not as new problems, but rather as age-old practices becoming more visible because of a more assertive royal power issuing more legislation (see Figure 13).
Historians, therefore, may have been too ready to read legislation offering protection to 'the poor' ( _pauperes_ ) as a direct response to the changing status of peasant–proprietors. In Carolingian usage, 'poverty' was defined not in economic, but in social terms: the 'poor' were the opposite of the 'powerful'. Hence, royal protection of the poor cannot be seen as a matter of 'social welfare': kings were attempting to educate their ruling elite in the proper exercise of Christian power. Ritual performances ostentatiously demonstrating care of the poor thus became an inextricable aspect of the exercise of power: alms-giving could be understood as giving justice, while the capitularies asked judges to hear the cases of the poor first rather than making them wait. Honouring the poor here was meant to demonstrate that those exercising power did so legitimately, and shows the powerful responding to royal exhortations to see their position as a God-given ministry, rooted in charity. What this actually meant for individual 'paupers' is very hard to pin down: the poor almost always appear in our sources as an anonymous mass. But those paupers we do meet are typically indigent cousins or country priests having to juggle their pastoral responsibilities with the necessity of farming if they are to eat, figures dangling precariously at the end of those hierarchies of patronage and obligation which radiated from aristocratic elites. Indeed, the discourse of alms-giving and protecting the poor could even be used to describe the care shown by aristocrats for their retinues, patrons for their clients, and the influential for their less powerful kin. In the context of a political system which allowed a favoured few to make and lose fortunes with dizzying speed, this discourse insisted on the essential social solidarity of the stars of court politics with those kin and neighbours who had not been so fortunate, but whose continuing support was vital. The charter evidence suggests a similar picture, with a greater concentration of landowning in the hands of the great churches and a handful of favoured aristocratic families steepening the gradient between the poor and the powerful, but not sweeping aside the basic structures of landownership. Even in the last decades of the ninth century and the first of the tenth, patterns of charter witnessing and court hearings continued to conform to familiar patterns, resting on the participation of a community of free landowners in public meetings which might be dominated by a local elite but were open to all. Even well-to-do peasants were still able to maintain a foothold in the world of public courts, and so attempt to mobilise the patronage through which local politics was effected; they may appear to us as a passive and manipulated audience, but they were still on the stage witnessing and swearing on oath.
**Figure 13.** King as lawgiver, from the _Golden Psalter_ of St Gallen, completed at the monastery of St Gallen in the 880s. Illustrating Psalm 17, King David is portrayed as a Carolingian king sitting in judgement, looking towards the hand of God, and pointing with his staff at vanquished foes, and with his finger at the righteous.
Nonetheless, a series of court cases from diverse regions does show increasing pressure on the very lowest strata of the free peasantry, especially where they became implicated in great estates increasingly organised on manorial lines. In 828, for example, peasants ( _coloni_ ) from the villa of Antoigné made a 70-km trip to the royal palace of Chasseneuil to complain about the demands made by the advocate responsible for running the villa, only for their landlord, the abbey of Cormery, to produce an estate survey confirming the validity of the demands being made; whilst in 861 free peasants from the villa of Mitry travelled 60 km along with wives and children to the royal palace of Compiègne to defend their free status against the monk Deodatus, who managed this estate for their landlord, the abbey of St Denis, and had been demanding onerous 'inferior services' normally expected from the unfree. In Italy a complex parchment trail preserved by the cathedral church of San Ambrogio in Milan shows the ways in which an ecclesiastical landlord might use its power and control of the written record to outmanoeuvre dependent peasants on its estates over successive generations. That the surviving documents tend to show peasants losing and ecclesiastical landlords winning is no surprise: after all, their preservation is dependent on ecclesiastical archives. Aristocratic landowners kept careful records too, as is demonstrated by a remarkable dossier preserved at the estate of Perrecy in Burgundy, which shows the local agents who managed Perrecy and two other local estates on behalf of their aristocratic lords pursuing individual peasants and utilising the public courts of Autun and its hinterland to establish documentary proofs of their unfree status. Yet this documentary haul also shows that peasants on aristocratic and ecclesiastical estates continued to enjoy access to public courts. And it would be wrong to assume that landlord pressure on the peasantry in these and other ninth-century documents, backed up by public documentation and local courts, was a wholly new development: the chronological horizons of our documentary evidence are determined by processes of transmission and preservation which mean that we simply have no comparable documentation from an earlier period.
These cases may help us understand the central plank of Carolingian legislation regarding the _pauperes_ , the free but powerless: the insistence of rulers that their access to public courts should not be impeded. Capitularies, indeed, not only guaranteed this access to public justice, but also reserved cases of personal freedom or property ownership to counts' courts. Once there, we should not assume that peasants always and automatically lost: in fact, imperial judgements from the reign of Louis the Pious show that when and where it was possible to appeal to the king, the depredations of landlords might be resisted or reversed. Even where peasants did not win in local courts, the pressure of public opinion and factional politics might force landlords to make concessions. For example, in 856 a dispute over the status of one Uadaruft was settled through a carefully choreographed though opaque compromise in which Uadaruft publicly acknowledged he was unfree, only for Abbot Grimald of St Gallen immediately to free him in return for a gift of land. In the end, the surviving cases, which show both predatory landlord power and the continuing ability of peasants to defend their rights at public meetings, reveal pressure on the margins of free landowning society rather than structural transformation. Carolingian peasants still had chances to put their case, for even the most powerful of landlords still had to work through publicly acceptable norms, and the factional politics of locality and kingdom meant that the powerful never quite had local courts wholly in their pockets. It was the establishment of formal seigneurial rights, some economic and some jurisdictional, that entrapped the free peasantry in a new world of servitude, and this was a process of the post-Carolingian centuries; we should not read it back into the Carolingian world.
#### CONCLUSION: COMMUNITY AND CONFLICT
The Carolingian countryside was, as we have seen, a complex patchwork of properties, villages and scattered interests. In most respects it does not conform to the stereotypical image of the medieval lord dominating the peasants living in the shadow of their stone residences and subjecting them to punitive and capricious demands. In fact, elite residences were typically sited away from the primary agglomerations of rural settlement: powerful aristocrats distanced themselves from the hustle and bustle of village life and the demands of agrarian cultivation, and did not intervene directly in rural settlements, nor dirty their hands with the nitty-gritty of estate management. Aristocratic influence on village life was generally indirect, as they increasingly invested in gifts to churches which, as we saw earlier, could help give focus to rural settlements and made landlords' power visible but absent. Villages were tied into the patronage networks that made the empire tick via well-connected local priests and estate managers who were, as we have seen, members of rural communities themselves rather than agents imposed from outside. The ability of such figures to connect indirectly with earthly and heavenly courts offered aid and protection for villagers in their struggle with the exigencies of rural life. Yet that struggle did not mean that the peasantry could not sometimes organise themselves, resist landlord pressure and access public courts. Despite the growing gap between rich and poor in the Carolingian world, even the 'powerless' could sometimes still act with a degree of autonomy.
But the growing role of churches and churchyards in the Carolingian period symbolises the changes that were taking place in the texture of rural society. The propagation of church 'reform' helped to tie these small worlds into the great religious and political hierarchies of the empire by reclaiming local churches as constituent cells of an overarching imperial Church. A final visit to the conflict-ridden settlement of Kempten demonstrates exactly how these connections worked. At Kempten, the misfortunes affecting the community as a whole were believed to be a punishment meted out by God for the wrongdoings of one individual, and so it was resolved that he should be put to death. At this point, 'priests and deacons with relics and crosses' were despatched by the bishop to bring peace and to drive out the wicked spirit that had stirred up trouble. As mediators between the village and wider Christian society, the representatives of the imperial Church here sought to reshape community justice so that it might fit more easily with contemporary ideologies of 'peace, unity and concord among the Christian people'. But the attempted exorcism was only a partial success: while the priests were reciting the litany and sprinkling holy water in the house where the demon had been most active, he 'threw stones at men coming there from the _villa_ and wounded them', and once they had left he claimed that one of the priests had slept with the daughter of the steward of the villa. The demon, hiding under the robes of the corrupt priest whom he now controlled, had thus been protected from the holy rites designed to drive him out, and continued to spread mischief and arson for three years, bringing disaster to the inhabitants and leading to the abandonment of the settlement.
Here we see a clear sense of the village as not just a social, but a spiritual community, afflicted by common misfortunes and dealt with by God, by demons, and by the institutional Church, as a moral unit. Social relationships between villagers were tied up with this sense of spiritual solidarity and shared responsibility. But this community domain of social action was neither self-sufficient nor wholly controlled by villagers; it was also the forum through which the village as a collectivity negotiated with the agencies of imperial rule. Thus the initial attempt to deal with the activities of the demon through secular self-help, when it threatened to escalate into a scandalous offence against the moral and social order through the killing of the demon's victim, was ended by the intervention of the church hierarchy in the person of the local bishop. However, this second, external and ecclesiastical, attempt to purify the social life of the village also failed. It failed because – according to the demon – those individuals who were the intermediaries between village society and the world of aristocrats and bishops, the priest and the bailiff, were the ultimate cause of the village's misfortune: it was the corrupt priest who had inflicted demonic disorder on the villagers, his double-dealing encapsulated by his illicit sexual activity with the bailiff's daughter which delivered him into the demon's power.
Narratives like the Kempten story were carefully crafted and consciously deployed by their authors. But within this narrative it is difficult not to hear the dim echo of class conflict articulated in village gossip about the double-dealings and improper conduct of the representatives of aristocratic and ecclesiastical authorities, and ultimately of imperial rule, within the village. As told in the _Annals of Fulda_ this is a tale designed to underline the importance of the strict standards inculcated by Carolingian reformers if local priests were to live up to their ministry. The Carolingian reform in both Church and kingdom encouraged such claims. Defining aristocratic and ecclesiastical rule in terms of hierarchies of devolved ministry meant that those individuals who did not conduct themselves as the agents of a Christian empire ought to be brought to book: hence the repetition of this village gossip by the compiler of our annals. In this tale, then, we see the village as a community, and one whose definition was tightened by villagers' shared experience of dealing with those figures who connected them to the hierarchy of Church and court. It turns on a series of complex interactions between horizontal bonds among villagers, and the vertical ties binding the village to the aristocratic and ecclesiastical rulers of the Christian empire. In voicing the ambivalences and tensions that arose from these interactions between community and hierarchy, it takes us to the heart of Carolingian society.
* * *
Ratramnus of Corbie, _Epistolae_ , ed. E. Perels, _MGH Epp_. vi ( _Epp. Karolini aevi_ iv) (Berlin, 1925), _Ep_. 12, pp. 155–7, and see Wood, _Missionary Life_ , pp. 251–3.
See I. Wood, 'Christians and pagans in ninth-century Scandinavia', in B. Sawyer, P. H. Sawyer and I. N. Wood (eds.), _The Christianization of Scandinavia_ (Alingsås, 1987), pp. 36–67; Palmer, 'Defining paganism', at pp. 422–5; Dutton, _Charlemagne's Mustache_ , pp. 46–7.
AL, _s.a_. 802.
O. G. Oexle, 'Tria genera hominum. Zur Geschichte eines Deutungsschemas der sozialen Wirklichkeit in Antike und Mittelalter', in L. Fenske, _et al_. (eds.), _Institutionen, Gesellschaft und Kultur im Mittelalter. Festschrift Josef Fleckenstein_ (Sigmaringen, 1984), pp. 483–99; D. Iogna-Prat, 'Le "Baptême" du schéma des trois ordres fonctionnels: l'apport de l'école d' Auxerre dans la seconde moitié du IXe siècle', _Annales ESC_ 41/1 (1986), pp. 101–26. The classic discussion of post-Carolingian three orders theory is G. Duby, _The Three Orders: Feudal Society Imagined_ (Chicago, 1982).
On legislation as a genre of political communication, see Pössel, 'Authors and recipients'.
_Stellinga_ : E. Goldberg, 'Popular revolt, dynastic politics and aristocratic factionalism in the early middle ages: the Saxon Stellinga reconsidered', _Speculum_ 70 (1995), pp. 467–501; Alemannia: M. Innes, 'Property, politics and the problem of the Carolingian state', in W. Pohl and V. Wieser (eds.), _Staat im frühen Mittelalter_ (Vienna, 2009), pp. 299–313.
C. Wickham, 'The other transition: from the ancient world to feudalism', _P &P_ 113 (1984), pp. 3–36, repr. in Wickham, _Land and Power_ , pp. 7–42; Wickham, _Framing the Early Middle Ages_. For recent responses to Wickham's work, see the special issue of the _Journal of Agrarian Change_ 9 (2009), edited by P. Sarris and J. Banaji: _Aristocrats, Peasants and the Transformation of Rural Society c.400–800_.
A. Dopsch, _Economic and Social Foundations of European Civilisation_ (New York and London, 1937; English trans. of 1923 German original); H. Pirenne, _Mohammed and Charlemagne_ (London, 1939; English trans. of 1937 French original, published posthumously). See also below, Chapter 7.
See for example C. Lauranson-Rosaz, _L'Auvergne et ses marges du VIIIe aux XIe siècles: La Fin du monde antique?_ (Le Puy en Velay, 1987). For historiographical discussion and further references see Innes, 'Economies and societies in the early medieval west, in E. English and C. Lansing (eds.), _Companion to the Middle Ages_ (Oxford, 2009), pp. 9–37.
Innes, 'Economies and societies' argues for the distinctiveness of the early medieval west.
G. Duby, _The Early Growth of the European Economy: Warriors and Peasants from the Seventh to the Twelfth Century_ (Ithaca, NY, and London, 1974) (translation by H. B. Clarke of French original of 1973); T. N. Bisson, 'The "feudal" revolution', _P &P_ 142 (1994), pp. 6–42, with subsequent debate in _P &P_ 152 (1996), pp. 197–223, 155 (1997), pp. 177–225.
For excellent recent syntheses see J.-P. Devroey, _Économie rurale et société dans_ l _'Europe franque ( VI–IX siècles_) (Paris, 2003); Devroey, _Puissants et misérables: Système social et monde paysan dans l'Europe des Francs ( VI–IX siècles_) (Brussels, 2006); P. Depreux, _Les Sociétés occidentales du milieu du VIe à la fin du ixe siècle_ (Rennes, 2002); Wickham, _Framing the Early Middle Ages_ ; Innes, 'Economies and societies'; and Wickham, _The Inheritance of Rome: A History of Europe, 400–1000_ (London, 2009).
The standard work is J. Percival, _The Roman Villa_ (London, 1976). Note that contemporary nomenclature was far more varied: _villa_ has become a modern shorthand.
M. Heinzelman, 'Villa d'après l'oeuvre de Grégoire de Tours', in E. Magnou-Nortier (ed.), _Aux sources de la gestion publique_ I: _Enquête lexicographique sur fundus, villa, domus, mansus_ (Lille, 1993) I, pp. 45–70; G. Halsall, _Settlement and Social Organisation: the Merovingian Region of Metz_ (Cambridge, 1995).
J. Chapelot and R. Fossier, _The Village and the House in the Middle Ages_ (London, 1985). For some early medievalists' responses see the discussion on R. Fossier's paper ('Les Tendances de l'économie: stagnation ou croissance?') in _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 27 (Spoleto, 1981), pp. 261–74, discussion at pp. 275–90.
Wickham, _Framing the Early Middle Ages_ , pp. 280–93, 400–6, 465–514 synthesises material from across Europe.
Costambeys, _Power and Patronage_ , pp. 184–208; M. Costambeys, 'Settlement, taxation and the condition of the peasantry in post-Roman central Italy', _Journal of Agrarian Change_ 9 (2009), pp. 92–119.
AF, _s.a_. 878, 858. M. Innes is preparing an extended discussion of the Kempten story.
_AF, s.a_. 875.
For an overview, see W. Davies, 'Local participation and legal ritual in early medieval law courts', in P. Coss (ed.), _The Moral World of the Law_ (Cambridge, 2000), pp. 61–89.
See Innes, _State and Society_ , pp. 94–140.
For example, Ganshof, _Frankish Institutions_ ; A. C. Murray, 'From Roman to Frankish Gaul: _centenae_ and _centenarii_ in the administration of the Merovingian kingdom', _Traditio_ 44 (1988), pp. 59–100.
C. Manaresi (ed.), _I placiti del regnum Italiae_ I (Rome, 1955), no. 17. For full context, see H. Krahwinkler, _Friaul im Frühmittelalter. Geschichte einer Region vom Ende des fünften bis zum Ende des zehnten Jahrhunderts_ (Vienna, 1992), pp. 199–243.
For cases studies see Innes, _State and Society_ , pp. 94–140; M. Innes, 'Practices of property in the Carolingian empire', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 247–66; F. Bougard, 'Pierre de Niviano, dit le Spoletin, sculdassius, et le gouvernement du comté de Plaisance à l'époque carolingienne', _Journal des Savants_ (1996), pp. 291–337. Istria: M. Innes, 'Framing the Carolingian economy', _Journal of Agrarian Change_ 9 (2009), pp. 42–58, at pp. 42–6. Folkwine: P. Erhart and J. Kleindienst (eds.), _Urkundenlandschaft Rätiens_ (Vienna, 2004), esp. pp. 83–90; M. Innes, 'Dossiers and archives: documents, landowners and power in Frankish society', in W. Brown _et al_. (eds.), _Documentary Culture_.
F. Schwind, 'Beobachtungen zur inneren Struktur des Dorfes in karolingischer Zeit', in H. Jankuhn, _et al_. (eds.), _Das Dorf der Eisenzeit und des frühen Mittelalters_ (Göttingen, 1977), pp. 444–93; D. Claude, 'Haus und Hof im Merowingerreich nach den erzählenden und urkundlichen Quellen', in H. Beck and H. Steuer (eds.), _Haus und Hof in ur- und frühgeschichtlichen Zeit_ (Göttingen, 1997), pp. 321–34.
D. Herlihy, _Medieval Households_ (London, 1985), pp. 56–78; J. Bessmerny, 'Les Structures de la famille paysanne dans les villages de la Francie au IXe siècle', _Le Moyen Âge_ 90 (1984), pp. 165–93.
D. Herlihy, 'The Carolingian mansus', _EHR_ 13 (1960), pp. 69–79; C.-E. Perrin, 'Observations sur la manse dans la region parisienne au début du IXe siècle', _Annales_ 8 (1945), pp. 39–51; W. Schlesinger, 'Vorstudien zu einer Untersuchungen über die Hufe', 'Hufe und mansus im liber donationem des Klosters Weissenburgs', and 'Die Hufe im Frankenreich', in H. Patze and F. Schwind (eds.), _Ausgewählte Aufsätze von_ W _Schlesinger 1965–1979_ (Sigmaringen, 1987), pp. 458– 541, 543–85, 587–614. On seventh-century origins see now J. Banaji, 'Aristocracies, peasantries and the framing of the early middle ages', _Journal of Agrarian Change_ 9 (2009), pp. 59–91, esp. 66–78; for Fulda see U. Weidinger, _Untersuchungen zur Wirtschaftsstruktur des Kloster Fulda in der Karolingerzeit_ (Stuttgart, 1991), esp. pp. 23–54.
G. Ripoll and J. Arce, 'The transformation and end of Roman _villae_ in the west (fourth–seventh centuries): problems and perspectives', in G. P. Brogiolo, N. Gautier and N. Christie (eds.), _Towns and their Territories from Late Antiquity to the Early Middle Ages_ (Leiden, 2000), pp. 63–114; T. Lewit, '"Vanishing villas": what happened to elite rural habitation in the west in the fifth–sixth centuries?', _Journal of Roman Archaeology_ 16 (2003), pp. 26–74; N. Christie (ed.), _Landscapes of Change: Rural Evolution in Late Antiquity_ (Aldershot, 2004).
P. Périn, 'The origins of the village in early medieval Gaul', in Christie (ed.), _Landscapes of Change_ , pp. 255–78; Halsall, _Settlement and Social Organisation_.
R. Francovich and R. Hodges, _Villa to Village_ (London, 2003);Wickham, _Framing the Early Middle Ages_ , pp. 481–95; Costambeys, 'Settlement, taxation and the condition of the peasantry'; F. L. Cheyette, 'The disappearance of the ancient landscape and the climatic anomaly of the early Middle Ages: a question to be pursued', _EME_ 16 (2008), pp. 127–65.
The best archaeological discussion is H. Hamerow, _Early Medieval Settlements: the Archaeology of Rural Communities in North-West Europe, 400–900_ (Oxford, 2002), pp. 12–50.
Hamerow, _Early Medieval Settlements_ , pp. 52–99; H. A. Heidinga, _Medieval Settlement and Economy North of the Lower Rhine_ (Assen, 1987).
H. Bernhard, 'Die frühmittelalterliche Siedlung von Speyer "Vogelgesang"', _Offa_ 39 (1982), pp. 217–33.
For this point and what follows see C. Wickham, 'Pastoralism and underdevelopment in the early middle ages', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 31 (Spoleto, 1983), pp. 401–55, repr. in Wickham, _Land and Power_ , pp. 121–54.
For a sense of just how fundamentally fiscal demands as mediated by landlords and local elites structured the Roman countryside, see T. Lewit, _Agricultural Production in the Roman Economy ad 200–400_ , British Archaeological Reports International Series 568 (Oxford, 1991); J. Banaji, _Agrarian Change in Late Antiquity_ (Oxford, 2001).
Wickham, 'Pastoralism and underdevelopment'; C. Wickham, 'European forests in the early middle ages: landscape and land clearance', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 37 (Spoleto, 1989), pp. 479–548, repr. in Wickham, _Land and Power_ , pp. 155–99. For skeletal data on livestock see B. Ward-Perkins, _The Fall of Rome and the End of Civilisation_ (Oxford, 2005) p. 145, using it as evidence for 'decline'; cf. Hamerow, _Early Medieval Settlements_ , pp. 146–7.
M. Whittow, 'Decline and fall? Studying long term change in the east', in W. Bowden and L. Lavan (eds.), _Theory and Practice in Late Antique Archaeology_ (Leiden, 2004), pp. 404–23; T. Lewit, 'Pigs, presses and pastoralism: farming in the fifth to seventh centuries', _EME_ 17 (2009), pp. 77–91; R. Faith, 'Forces and relations of production in early medieval England', _Journal of Agrarian Change_ 9 (2009), pp. 23–41.
Hamerow, _Early Medieval Settlements_ , pp. 52–124, and for a regional survey Halsall, _Settlement and Social Organisation_.
R. Francovich, 'The beginnings of hilltop villages in early medieval Tuscany', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 55–82; R. Francovich, 'Changing structures of settlement', in C. La Rocca (ed.), _Italy in the Early Middle Ages_ (Oxford, 2002), pp. 144–67.
F. Theuws, 'Landed property and manorial organisation in northern Austrasia: some considerations and a case study', in F. Theuws and N. Roymans (eds.), _Images of the Past. Studies on Ancient Societies in Northwestern Europe_ (Amsterdam, 1991), pp. 299–407; Heidinga, _Medieval Settlement and Economy_.
C. Lorren, 'Le Village de Saint-Martin de Mondeville de l'antiquité au haut moyen âge', in H. Atsma (ed.), _La Neustrie. Le Pays au nord de la Loire de 650 à 850_ , Beihefte der Francia 16, 2 vols. (Sigmaringen, 1989), II, pp. 439–66.
I. Stork, 'Zum Fortgang der Untersuchungen im frühmittelalterlichen Gräberfeld, Adelshof und Hofgrablege bei Lauchheim, Ostalbkreis', _Archäologische Ausgrabungen in Baden-Württemberg 1992_ , pp. 231–9; F. Damminger, 'Dwellings, settlements and settlement patterns in Merovingian southwestern Germany and adjacent areas', in I. Wood (ed.), _Franks and Alamanni in the Merovingian Period_ (Woodbridge, 1998), pp. 33–106; H. Dannheimer, 'Die frühmittelalterliche Siedlung bei Kirchheim', _Germania_ 51 (1973), pp. 152–69.
See M. Lauwers, 'Le Cimetière dans le Moyen Âge latin: Lieu sacré, saint et religieux', _Annales HSS_ 54 (1999), pp. 1047–72, and pp. 110–11 above.
Hrabanus Maurus, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. v (Berlin, 1898–9), pp. 380–533; Einhard, _Epistolae_ , ed. K Hampe, _MGH Epp_. v ( _Epp. Karolini aevi_ III) (Berlin, 1898–9), pp. 105–42; nos. 16, 18, 25.
Hamerow, _Early Medieval Settlements_ , esp. pp. 125–90; Bernhard, 'Die frühmittelalterliche Siedlung'.
C. Sonnlechner, 'The establishment of new units of production in Carolingian times: making early medieval sources relevant for environmental history', _Viator_ 35 (2004), pp. 21–58.
The pioneering case study was W. Davies, _Small Worlds: The Village Community in Early Medieval Brittany_ (London, 1988). See now C. Wickham, 'Rural society in Carolingian Europe', in _NCMH_ II, pp. 431–50; Wickham, _Framing the Early Middle Ages_ , esp. pp. 388–406.
For this pair see Innes, _State and Society_ , pp. 108, 147–52.
Innes, _State and Society_ , pp. 61–5 and _passim_.
M. Innes, 'On the material culture of legal documents: charters and their preservation in the Cluny archive (9th–11th centuries)', in Brown, _et al_. (eds.), _Documentary Culture_. This kind of evidence is most common south of the Alps and Pyrenees: see e.g. A. Kosto, 'Laymen, clerics and documentary practices in the early middle ages: the example of Catalonia', _Speculum_ 80 (2005), pp. 44–74; S. Gasparri and C. La Rocca (eds.), _Carte di famiglia. Strategie, rappresentazione e memoria del gruppo familiare di Totone di Campione, 721–877_ (Rome, 2005); L. Feller, A. Gramain and F. Weber, _La Fortune de Karol. Marché de la terre et liens personnels dans les Abruzzes au haut moyen âge_ , Collection de l'EFR 347 (Rome, 2005).
M. Prou and A. Vidier (eds.), _Recueil des chartes de l'abbaye de Saint-Benoît-sur-Loire (Fleury_ ), 2 vols. (Orleans and Paris, 1900–24), no. 25.
C. Wickham, 'Aristocratic power in eighth-century Lombard Italy', in A. C. Murray (ed.), _After Rome's Fall: Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 153–70; S. Gasparri, 'The aristocracy', in La Rocca (ed.), _Italy in the Early Middle Ages_ , pp. 59–84.
For the continuity of unfreedom in its socio-legal definition, see C. R. Whittaker, 'Circe's pigs: from slavery to serfdom in the Roman world', _Slavery and Abolition_ 8 (1987), pp. 88–122 and on the discourse of slavery P. Garnsey, _Ideas of Slavery from Aristotle to Augustine_ (Cambridge, 1996).
See Rio, 'Freedom and unfreedom'.
_Vita Liutbergae Life of Liutberga]_ , ed. G. H. Pertz, _MGH SS_ iv, pp. 158–64, trans. F. S. Paxton, Anchoress and Abbess in Ninth-Century Saxony: the Lives of Liutbirga of Wendhausen and Hathumoda of Gandersheim ([Washington, DC, 2009).
See below, Chapter 6.
Davies, _Small Worlds_.
For a survey see R. Hennebicque, '"Pauperes" et "paupertas" dans l'occident carolingien aux IXe et xe siècles', _Revue du Nord_ 50 (1968), pp. 167–87.
See S. Gasparri, 'Strutture militari e legami di dipendenza in Italia in età longobarda e carolingia', _Rivista storica italiana_ 98 (1986), pp. 664–726.
M. Innes, 'Land, freedom and the making of the early medieval west', _TRHS_ 16 (2006), pp. 39–73.
Cf. Innes, _State and Society, pp_. 143–53, and Halsall, _Warfare and Society, pp_. 71–110.
See e.g. _Capit_. I, no. 48, cc. 1–2; no. 49, c. 3; no. 50, cc. 1, 9; no. 141, c. 27; Reuter, 'End of Carolingian military expansion'. See also above, Chapter 4, p. 170.
See Susan Reynolds, _Fiefs and Vassals: the Medieval Evidence Reconsidered_ (Oxford, 1996).
See above, Chapter 4, pp. 182–93.
See Reuter, 'End of Carolingian military expansion'.
AB, _s.a_. 859. Innes, 'Economies and societies', pp. 27–9, comments on legitimate and illegitimate violence.
See also below, Chapter 6.
For the genesis and legacy of models of the unchanging village community see J. Burrow, 'The "village community" and the uses of history in late nineteenth-century England', in N. McKendrick (ed.), _Historical Perspectives: Studies in English Thought and Society in Honour of Sir J H Plumb_ (Cambridge, 1974), pp. 255–84; R. Smith, 'Modernisation and the corporate village community: some sceptical reflections', in A. Baker and D. Gregory (eds.), _Explorations in Historical Geography_ (Cambridge, 1984), pp. 140–79; S. Reynolds, _Kingdoms and Communities in Western Europe, 900–1300_ (Oxford, 1997). For similar issues in a different historiographical tradition, F. Staab, 'A reconsideration of the ancestry of modern political liberty: the problem of the so-called King's Freemen ( _Königsfreie)', Viator_ II (1980), pp. 51–70.
For the 'culture of the public' see Wickham, _Inheritance of Rome_ , esp. Chapter 23; for its definition in our centuries see Innes, _State and Society_ , pp. 94–111; Innes, 'Dossiers and archives.
See e.g. Innes, _State and Society_ , pp. 94–140, and for legal resistance Nelson, 'Dispute settlement.
See e.g. Devroey, _Puissants et misérables_ ; A. Verhulst, _The Carolingian Economy_ (Cambridge, 2002); A. Verhulst, _Rural and Urban Aspects of Early Medieval Northwest Europe_ (Aldershot, 1992); J.-P. Devroey, _Études sur le grand domaine carolingien_ (Aldershot, 1993); Y. Morimoto, _Etudes sur l'konomie rurale du haut moyen âge: historiographie, régime domanial, polyptyques carolingiens_ (Paris, 2008).
For a reading of the polyptychs that sees them too unproblematically as evidence for the direct continuity into the early Middle Ages of some of the apparatus of Roman government see J. Durliat, _Les Finances publiques de Dioclétien aux Carolingiens (284–889_ ). Beihefte der Francia 21 (Sigmaringen, 1990); but note the convincing criticisms of C. Wickham, 'The fall of Rome will not take place', in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 45–57.
W. Goffart, 'Merovingian polyptychs: reflections on two recent publications', _Francia_ 9 (1982), pp. 55–77, esp. pp. 65–8; repr. in W. Goffart, _Rome's Fall and After_ (London, 1989), pp. 233–53; S. Sato, 'The Merovingian accounting documents of Tours: form and function', _EME_ 9/2 (2003), pp. 143–61.
On immunities, see Fouracre, 'Eternal light'; Rosenwein, _Negotiating Space_.
_Capitulare de villis, Capit_. I, no. 32, pp. 82–91; _Brevium exempla, Capit_. I, no. 128, pp. 250–6; both trans. Loyn and Percival, _Reign of Charlemagne_ , pp. 65–73 and 98–105 respectively. W. Metz, _Das Karolingische Reichsgut_ (Berlin, 1960) remains the fundamental analysis of this material; see now McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 149–54.
Cf. Banaji, 'Aristocracies, peasantries', and P. Sarris, 'The origins of the manorial economy: new insights from Late Antiquity', _EHR_ 119 (2004), pp. 279–311.
On aristocratic residences see also below, Chapter 6.
See Theuws, 'Landed property'; Costambeys, 'An aristocratic community'.
For useful analysis and a variety of views see H.-W. Goetz, 'Serfdom and the beginnings of a "seigneurial system" in Carolingian Europe', _EME_ 2 (1993), pp. 29–51; W. Davies, 'On servile status in the early Middle Ages', in M. Bush (ed.), _Serfdom and Slavery_ (London, 1996), pp. 225–46; P. Bonnassie, _From Slavery to Feudalism in Southwest Europe_ , trans. J. Birrell (Cambridge, 1991); P. Freedman, _The Origins of Peasant Servitude in Medieval Catalonia_ (Cambridge, 1991).
This is the basic thesis of L. Kuchenbuch, _Bäuerliche Gesellschaft und Klosterherrschaft im 9. Jht. Studien zur Sozialstruktur der Familia der Abtei Prüm_ (Wiesbaden, 1978).
See Nelson, 'Dispute settlement', at pp. 56–9 (and pp. 248–50 for the Latin text); A. d'Herbomez (ed.), _Cartulaire de l'abbaye de Gorze_. Mettensia 2 (Paris, 1898), no. 78 (whose date is probably either 896 or 916).
Einhard, _Epp_. 16, 25, 48. On legislation and lordship see also above, Chapter 4, p. 190.
See for example the run of west Frankish cases discussed by Nelson, 'Dispute settlement', and Innes, 'Dossiers and archives' on the remarkable Perrecy dossier.
_UBMR_ , no. 53.
See _Das Prümer Urbar_ , ed. I. Schwab (Düsseldorf, 1983) with L. Kuchenbuch, _Bäuerliche Gesellschaft und Klosterherrschaft im 9. Jht. Studien zur Sozialstruktur der Familia der Abtei Prüm_. Vierteljahrsschrift für Sozial- und Wirtschaftgeschichte Beihefte 66 (Wiesbaden, 1978); _Liber possessionum Wizenburgensis_ , ed. C. Dette (Mainz, 1987); and for the royal estates around Trebur, M. Gockel, _Karolingische Königshöfe am Mittelrhein_ (Göttingen, 1970).
For a range of views see G. Duby, _Rural Economy and Country Life in the Medieval West_ (Los Angeles, CA, 1968); Fossier, 'Les Tendances de l'économie: stagnation ou croissance?'; Verhulst, _Carolingian Economy_. See also below, Chapter 7.
J.-P. Devroey, 'Les Services de transport à l'abbaye de Prüm au IXe siècle', _Revue du Nord_ 61 (1979), pp. 543–69; Devroey, 'Un monastère dans l'économie d'échanges: les services de transport à l'abbaye de St-Germain-des-Prés au IXe siècle', _Annales ESC_ 39 (1984), pp. 570–89; both repr. in his _Études sur le grand domaine carolingien_.
F. Hardt-Friedrichs, 'Markt, Münze und Zoll im ostfränkischen Reich bis zum Ende der Ottonen', _Blätter für deutsche Landesgeschichte_ 116 (1980), pp. 1–32; W. Bleiber, 'Grundherrschaft und Markt zwischen Loire und Rhein während des 9. Jahrhunderts: Untersuchungen zu ihrem wechselseitigen Verhältnis', _Jahrbuchfur Wirtschaftgeschichte_ 3 (1982), pp. 105–35.
See below, Chapter 7.
Innes, 'Framing the Carolingian economy', and below, Chapter 7.
_Capitulare de villis_ ; on personnel see Metz, _Das Karolingische Reichsgut_.
See Hamerow, _Early Medieval Settlements_ , pp. 125–90, on the archaeological evidence for greater concentration on heavy cereal cropping.
Vineyards: F. Staab, 'Agrarwissenschaft und Grundherrschaft. Zum Weinbau der Klöster im Frühmittelalter', in A. Gerlich (ed.), _Weinbau, Weinhandel und Weinkultur_. Geschichtliche Landeskunde, 40 (Stuttgart, 1993), pp. 1–48. Chestnuts: C. J. Wickham, _The Mountains and the City: the Tuscan Appennines in the Early Middle Ages_ (Oxford, 1988); see also the papers in _Olio e Vino in Alto Medioevo, Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 54 (Spoleto, 2007).
_AF, s.a_. 873.
F. Curschmann, _Hungersnote im Mittelalter_ (Leipzig, 1900); Dutton, _Charlemagne's Mustache_ , pp. 169–88; Dutton, 'Observations on early medieval weather in general, bloody rain in particular', in Davies and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 167–80.
See A. Verhulst, 'Karolingische Agrarpolitik. Das _Capitulare de Villis_ und die Hungersnöte von 792/93 und 805/06', _Zeitschrift für Agrargeschichte und Agrarsoziologie_ 13 (1965), pp. 175–89, repr. in Verhulst, _Rural and Urban Aspects_.
For climatic issues see now M. McCormick, P. Dutton and J. Mayewski, 'Volcanoes and the climate forcing of Carolingian Europe AD 750–950', _Speculum_ 82 (2007), pp. 865–96.
See above, pp. 224–5. See also E. Müller-Mertens, _Karl der Große, Ludwig der Fromme und die Freien. Wer waren die_ liberi homines _der karolingischen Kapitularien (742/3–832)? Ein Beitrag zur Sozialgeschichte und Sozialpolitik des Frankenreiches_. Forschungen zur mittelalterlichen Geschichte 10 (Berlin, 1963); W. Ullman, 'Public welfare and social legislation in the early medieval councils', _Studies in Church History_ 7 (1971), pp. 1–39; C. Humfress, 'Poverty and Roman law', in R. Osborne and M. Atkins (eds.), _Poverty in the Roman World_ (Cambridge, 2006), pp. 183–203.
K. Bosl, _'Potens_ und _pauper_. Begriffsgeschichtliche Studien zur gesellschaftlichen Differenzierung im frühen Mittelalter und zur "Pauperismus" des Hochmittelalters', in K. Bosl, _Frühformen der Gesellschaft in mittelalterlichen Welt_ (Munich and Vienna, 1964), pp. 106–34.
J. Wollasch, 'Gemeinschaftsbewußtsein und soziale Leistung im Mittelalter', _Frühmittelalterliche Studien_ 9 (1975), pp. 61–77.
See e.g. Dhuoda, _Liber manualis_ , ed. and trans. M. Thiébaux, _Dhuoda: Handbook for her Warrior Son_ (Cambridge, 1998); also trans. C. Neel, _Handbook for William: a Carolingian Woman's Counsel for her Son_ (London, NE, 1991), III. 10 and IV.9 and Einhard, _Epistolae_ , which also make liberal use of the language of poverty to mobilise patronage. See also Innes, 'Practices of property', pp. 259–62.
See the discussion of Nelson, 'Dispute settlement'; for the documents B. Guérard (ed.), _Polyptyque de l'Abbé Irminon_ (Paris, 1844), 2 vols., II, appendix 9, and G. Tessier, _et al_. (eds.), _Recueil des actes de Charles II le Chauve_ , 3 vols. (Paris, 1943–55) II, no. 228.
R. Balzaretti, 'The monastery of Sant'Ambrogio and dispute settlement in early medieval Milan', _EME_ 3 (1994), pp. 1–18.
Prou and Vidier (eds.), _Recueil...Saint-Benoît-sur-Loire_ , nos. 9–13, 16–17; Innes, 'Practices of property', pp. 252–6.
See above, Chapter 1, pp. 16–17, 26–9.
On the legislation see Müller-Mertens, _Karl der Große, Ludwig der Fromme und die Freien_ ; Hennebicque, '"Pauperes" et "paupertas"'.
See _Formulae imperiales_ , ed. K. Zeumer, _MGH Formulae Merovingici et Karolini Aevi_ (Hanover, 1886), pp. 285–328, nos. 9, 51.
H. Wartmann (ed.), _Urkundenbuch der Abtei St. Gallen_ II (Zürich, 1866), no. 446.
See especially Freedman, _Origins of Peasant Servitude_ , pp. 1–25.
See above, p. 240.
_AF, s.a_. 858.
## 6
### ELITE SOCIETY
#### INTRODUCTION
We saw in the previous chapter that it is possible to say a surprising amount about the nature and dynamics of peasant life and rural society in the Carolingian age. Yet social class is relative, and it is not possible to study the poor and the powerless without discussing their relationship with the social elite. This is especially so when dealing with a world where power depended ultimately on control over land (see Map 8), and where much of what we know about the lower orders comes to us in texts written by and for members of a landed aristocracy. Although they made up only a very small percentage of the population, wealthy aristocrats' ability to leave a lasting mark on the written record means that they loom disproportionately large in our sources. Yet their impact on contemporary politics and society was also disproportionate, meaning that the study of elite society opens up to us a wide window onto various important aspects of the Carolingian world.
While the existence of an elite grouping that we can call aristocratic is clear from even the most perfunctory reading of the Carolingian sources, attempts to understand the workings of aristocratic society and the nature of aristocratic power have consistently proved controversial. For much of the nineteenth and twentieth centuries, historical research concentrated on the formal identification of this elite, focussing on questions of its origins, continuity, and definition, and as a result anxiously debating the appropriateness or not of the terminology of 'nobility' and 'aristocracy'. Such scholarship privileged certain questions: what was the relationship between early medieval elites and their predecessors, the ruling classes of the Roman empire and its barbarian neighbours? What effect did the rise and then fall of the Carolingians have on the great families of the Frankish world? To what extent did these families form a closed, separate caste, possessing a special legal status and even rights to rule which were in origin independent of kings? And to what extent did they survive the demise of the Carolingians with their social position intact? These issues made sense in a Europe where the fabric of the _ancien régime_ , with its formal structures of noble privilege, was still fresh in the memory.
**Map 8.** Places mentioned in Chapter 6: 'Elite society'
In the second half of the twentieth century, the emergence of new research traditions, particularly in Germany, seemed to offer the hope of providing definitive answers to these hitherto almost intractable questions, and of moving the debate forward. Detailed study of the careers and connections of individuals distinguished by their holding of high office and wielding of political power was championed as a potential key to unlocking the structure of early medieval elites. Prosopography, as this approach is known, served to place ties of kinship centre stage. The results tended to suggest that Carolingian elites were organised into broad and extensive 'clans' in which maternal relations were as important as paternal, and that the post-Carolingian period produced more narrowly focussed patrilineal 'lineages', in which succession passed from father to son; questions about the continuity of elites could thus be rephrased, as the issue became one of how families maintained their position by changing their internal structures. In its methodology, however, medieval prosopography tends to privilege kinship as an explanation for events, even as it reveals such ties to be multi-layered and fluid. It must be remembered that the aristocratic clans which populate the Carolingian world as described by modern historians are reconstructions whose names – Rupertiners, Widonids, Conradines and the like – were almost all coined by historians rather than by contemporary medieval writers. Such groups may well have felt the bonds of their kinship keenly, but this needs to be demonstrated from the evidence and not just assumed.
Rather than seeking to join in these venerable debates about family continuity and political change, this chapter echoes more recent approaches by focussing on the mechanisms by which aristocratic power and status were constructed and exercised, and the consequent political role of the aristocracy. It begins by outlining the practices which marked out the Carolingian aristocracy as an identifiable social group in our sources, distinguished by military leadership, hunting, control of high offices, and particular forms of conspicuous consumption. It was through these strategies of distinction that the aristocracy projected and maintained its position as the dominant class within Carolingian society. Aristocratic status came from participation in these forms of collective activity, which together formed a template of proper behaviour. Because this status was a matter of claiming membership of a group, it was rooted in the demonstration of the archetypical characteristics of that group; as a result, contemporaries did not delineate any precise economic or legal boundary for aristocracy, and nor can we. Cultural codes and modes of conduct, patterns of residence and movement, can be analysed as contributing to these characteristic forms of activity. After discussing these features of the early medieval elite we will see how those behaviours related to their mentality and morality, especially the problems presented by a warrior lifestyle to those living in a world of Christian _correctio_. Next we return to kinship and family before concluding with the political role of the aristocracy.
We shall see that, although clearly identifiable, the aristocracy was not a completely closed caste, and social mobility both upwards and downwards was possible. Neither was it monolithic, socially or in its political behaviour. Although this discussion concentrates on the secular elite with some glances at their ecclesiastical cousins, it also emphasises divisions within that elite, stressing the existence of different layers within aristocratic society, and the interaction between horizontal bonds — which might be rooted in regional origin or political participation as well as kinship — and vertical ties of patronage within it. Aristocratic status rested, of course, on control of resources: land and labour, obviously, but also networks of kin, clients and friends who both provided and expected support, through whom power could be exercised and as a result of which high office might be awarded. But it was legitimated by an unquestioned social dominance: there was no way of conceiving of the social hierarchy other than in terms of the markers of descent, office-holding, and participation in feasting, hunting and warfare which declared aristocratic status.
#### ARISTOCRATIC IDENTITY: VOCABULARY, APPEARANCE AND LIFESTYLE
Our sources use a rich and varied vocabulary to refer to those special characteristics which distinguished the elite. 'Noble' ( _nobilis_ ), in origin a Latin term designating those of high social status, could apply to a wide spectrum of people: in its broadest definition, it simply denoted somebody who was not a nobody. It is therefore not quite synonymous with the modern term 'aristocracy' – understood as a ruling elite sustained by the inheritance of land and formally empowered with political command – though it certainly overlapped with it. Nobility tended to refer to something slightly different, involving a person's character. To describe someone as 'noble' – in the sense of morally superior, truthful or of good character – depended on the context: witnesses to a charter might appear as such at the gathering where the document was issued, as the dominant figures in that particular locality, but might not in comparison with the magnates who routinely attended the royal court. As Louis the Pious's biographer Thegan noted, denigrating his contemporary Archbishop Ebo of Rheims, true nobility was ingrained through descent and upbringing: he contrasted it with the distinction between free and unfree that was defined in written law. 'Noble' was not however the commonest term used to describe the politically powerful in a kingdom, for whom our sources tend to use either the titles of office – duke ( _dux_ ), count ( _comes_ ), marcher lord/superior count ( _marchio_ ) – or a looser vocabulary that described the exalted status of a group relative to the rest: the '(more) powerful' ( _potentes, potentiores_ ), the 'illustrious' ( _illustres_ ), the 'best' ( _optimates_ ) or the 'near' ( _proceres_ : near to the king, that is). The latter designation in particular demonstrates the connection in the contemporary mind between this elite and kingship. The _proceres_ exhibited what German historians have termed _Königsnähe:_ a closeness not only to the king but also to the king's court, which was the forum in which kingdom-wide politics were played out.
Three points deserve to be emphasised about this vocabulary. First, as already noted, it was not merely descriptive, but it imbued the powerful with particular qualities, implying moral distinction: 'the best', and so on. Second, it was a matter of subjective claim, not objective judgement: being described as noble or powerful did not rest on fulfilling a checklist of acknowledged criteria, but on social pre-eminence and so participation in high-level politics. As we saw in Chapter 5, the Carolingian aristocracy did not enjoy the formal legal privileges that had gone with membership of the Roman senate, nor did it cultivate the minute but carefully regulated hierarchy of honorifics that defined social status in the Roman world; similar systems, and the sharp definitions they encouraged, were to emerge in later medieval and _ancien régime_ Europe, but not in the early Middle Ages. Third, this was primarily a vocabulary of collective action: we tend to meet aristocrats in groups, designated as the _nobiles_ , _potentes_ , _proceres_ or _optimates:_ it was through acting together that aristocrats defined their social identity and came to perceive themselves as morally better than other social groups. This sense of collective superiority is revealed in the insults that members of the aristocracy used against their enemies. Low birth was just about the most damning thing one could be accused of, for those of low birth could not be trusted to behave honourably: writing in the 840s, the worst insult Nithard could level at his peers who had not kept faith but turned traitor was that they had behaved 'like peasants'. Disruption of the 'correct' social order was abhorrent. Charlemagne claimed, according to a letter written in 796 by his adviser Alcuin to King Offa of Mercia, that someone who killed his lord was 'worse than a pagan'. A century later, the monk Abbo of St-Germain-des-Prés could think of no better way to show his revulsion at the predations of the Vikings than by describing their impact in the Paris area in terms of social inversion: 'serf became free, freeman became serf'.
Social identities were not absolute, but had to be constantly reinforced and maintained. Legal practice recognised the social fact that aristocrats needed to be handled differently, and punished according to different norms, from their inferiors. This superiority could be reinforced with violence – indeed this was only proper in the view of an eighth-century author who stated that someone who had 'acted against his lord' deserved death and even torture. An even more striking incident is recorded in the _Annals of St Bertin_ for 859: 'Some of the common people living between the Seine and the Loire formed a sworn association amongst themselves and fought bravely against the Danes on the Seine. But because their association had been made without due consideration, they were easily slain by our more powerful people'. The actions of these 'more powerful people' had legal sanction: royal capitularies sought to legislate against such horizontal social solidarities, aiming thus to reinforce the vertical obligations of sworn fidelity to a lord. For the Frankish aristocracy, apparently, threatening a lord's authority really was worse than being a pagan, and it could merit punishment by death.
The expression of this sense of aristocratic 'betterness' was therefore not simply confined to the terminology of written sources. However, concerted outbursts of violence against the less powerful such as that in 859 are rare in the written record. On a more everyday level, elite status had to be made visible in the ways that nobles looked and behaved. Although our sources provide very few detailed physical descriptions of Carolingian nobles, it is clear that lay aristocrats carried visual markers that set them apart from the rest of society. Most significant of these was the _cingulum militare_ , the military belt. The importance of this item had its roots in the later Roman empire, when the belt stood for the holding of public office. In the Carolingian period it was equally symbolic, as illustrated by descriptions of kings and nobles who removed their belts. When Louis the Pious was deposed by bishops loyal to his sons in 833, he was made to remove his military belt and place it on the altar of the church in Soissons. The gesture was echoed almost exactly forty years later by his grandson Charles the Fat, who astonished a royal assembly by throwing down his _cingulum_ in a fit of contrition after rebelling against his father: his intention was to show his complete submission, and thus to throw himself on the king's mercy. These rulers' sword belts symbolised their secular status. As usual, examples featuring kings are the best attested. However, in this respect kings were very much part of a common culture with the secular aristocracy: when Lothar wished to exile Count Odo of Orléans during the rebellion of 830, his first move was formally to disarm him. Ninth-century provisions for the undertaking of public penance, a punishment considered appropriate for sins which had caused disruption on the political stage, regularly demanded that the penitent should set aside marriage, public office and the _cingulum_. These three things constituted the essential badges of secular elite status, and the consistency of these regulations suggests that they were thought to define the lay aristocracy as a distinct and visible group.
High social status was also associated with other pieces of equipment that are often met alongside the _cingulum_ in contemporary references to noble gear. The sword was an equally significant item of aristocratic equipment. The kings who cast aside their belts in 833 and 873 did likewise with their weapons. An apocryphal story from the later ninth century relates how Louis the Pious used to make regular gifts to his personal servants of all his clothing except for his sword and belt, and in the very rare ninth-century fresco at Malles Venosta in the Italian Alps, the lay patron of the church is depicted holding a sword (see Figure 14).
The extent to which aristocrats identified with their weapons is underlined by the fact that they frequently gave them names, and sometimes had these names inscribed along with their own on the blades. More broadly, capitularies demanded that men who were to serve in the army should be properly equipped with appropriate weaponry, armour and horses. Weapons were not monopolised by the ruling class and could denote status at multiple social levels: in the mid-eighth century, the Lombard king Aistulf stipulated that each man who held seven or more peasant farms ( _casae massariciae_ ) should have a horse, mail coat, shield and lance, while those without tenante society farms should still be able to furnish themselves with horse, shield and lance, and those who could not afford a horse should possess a shield and bow and arrows. In so legislating, moreover, Aistulf was simply setting minimum standards. Even in the Lombard kingdom, some aristocrats could afford to equip not only themselves but also their retinues in some style; all the more so, then, were the highest ranks of the generally wealthier Carolingian elite able to arm themselves and their men lavishly. The greater the quantity of horses, arms and armour, with all the status these implied, the greater the impact when they were taken away. Charles the Fat knew very well the degree of public humiliation and loss of status that he was inflicting on the noble followers of the illegitimate Carolingian rebel Hugh when in 885 he had them 'stripped of their horses, arms and clothing, and [they] scarcely escaped naked'.
**Figure 14.** A nobleman, fresco in church of San Benedetto, Malles Venosta, South Tyrol. Lying on an important Alpine route, this church contains a set of frescoes generally thought to date from the Carolingian period. This secular nobleman's clothing recalls pictures of aristocrats in manuscripts and underlines the centrality of the sword to their social identity.
Since the early medieval peasantry could also bear arms, it was not the fact of owning weapons that was crucial so much as their quality. Good-quality swords, horses and armour were expensive, and as such they were symbols which actively distinguished rich nobles from members of less powerful social groups. This is illustrated by a story from Paschasius Radbertus's _Epitaphium Arsenii_ (written in the midninth century) which relates an encounter between Charlemagne's cousin Wala and a 'countryman' ( _ruricola_ ). This yokel was wearing a belt and arms which Wala (because he was being tested by the king) offered to exchange for his own superior set. Unsurprisingly, the rustic enthusiastically agreed: the difference in quality between them was obvious. This sort of military gear could help to reinforce social boundaries within the ranks of the nobility, as well as between nobles and non-nobles. Above all, these were secular items. Monks and clergy often came from the same noble families as did the lay elite; these men rubbed shoulders at the great assemblies of the realm, and they shared the same in-bred sense of superiority. But those aristocrats who entered the religious life had their own clothes, implements and identifiers of rank. By the late eighth century, surrendering the sword and belt on the altar was central to the ritual by which young lay aristocrats became monks. According to the Astronomer it was only in the reign of Louis the Pious that bishops and clerics 'gave up belts with golden baldrics and jewelled knives, exquisite garments and boots with spurs. Louis thought it a monstrosity that men of the clerical order should aspire to these items of worldly glory' (though the fact that he claimed this was a new development shows that some clerics at least did not consider their vocation to be inconsistent with packing iron). These were also badges of exclusively male noble status: while Charlemagne made sure his sons learned to use weapons in fighting, riding and hunting, his daughters were schooled in the archetypal feminine occupations of weaving and making textiles. The formal bestowing of sword and belt on adolescents played a role in structuring the life-cycle of the male aristocrat. This was not a new practice in the eighth and ninth centuries, but from the Carolingian period it seems to have become the main rite of passage for boys into adulthood, replacing Merovingian milestones such as hair-cutting or shaving the beard (indeed, beards and well-groomed hair were probably another sign of elite distinction, to judge from contemporary manuscript illuminations). In other words, possession of the _cingulum militare_ and the sword not only distinguished the aristocracy as an elite group, but also served to construct differences of age, status and gender within that group.
The humiliation of Hugh's followers in 885 also highlights the importance of clothing as a symbol of status. Einhard's description of the habits of Charlemagne's Aachen implies that clerical members of the court had a kind of uniform to denote their status, and it may be that lay courtiers' clothing likewise indicated their identity. Easter was a time of renewal in the rituals of the Christian calendar, and scattered references in the sources suggest that the king and the nobles in his entourage marked this with a symbolic bath and a donning of new clothes. Clothing here was used to symbolise spiritual rebirth, and to reinforce aristocratic group identity. What did these men actually wear? Both Einhard and Notker provide descriptions of the everyday clothing of the Franks: shoes with long laces, a linen shirt, cloth leggings or trousers and a cloak which hung long at the back and front, but short at the sides. Aristocratic women, on the other hand, wore wide-sleeved tunics, often held at the waist with belts and covered with a mantle, and elaborate jewels and pendants which attracted comment from court poets. By 'the Franks', Einhard and Notker meant Frankish aristocrats, and it is clear that the clothing of nobles distinguished them from the poor. Theodulf, bishop of Orléans in the reign of Charlemagne, wrote that to disguise oneself as a peasant the requisite items were a hood, a loose garment, a basic linen shirt and leggings made of strips of cloth, as well as a knife (not a sword) at one's side. This was not so different in style from the outfit described by Einhard and Notker, but the difference in quality must have been obvious: Ermold the Black, albeit with some poetic licence, describes the brightly coloured clothing of courtiers as a source of wonder to onlookers.
The dress of the male lay elite varied from region to region. The best-known example is the outfit which the very young Louis the Pious, as king of Aquitaine, is described as wearing on a trip to meet his father: a round mantle, long-sleeved shirt, full trousers and spurred boots were recognised as the attire of the Basques of his sub-kingdom. To the Franks, with their tight trousers and linen shirts, this must have appeared a fairly outlandish get-up. Such differences were not merely a question of fashion, but helped to reinforce perceptions of difference within and between elites: visible cultural differences such as those expressed in clothing could help to buttress regional political identities, a significant fact in the politically fragmented west of the post-Roman period where elite landowning groups emphasised ethnic identity as one means to legitimate their domination of particular regions. Hence the biographer of Pope Hadrian specifically reports of defectors to Rome from the Lombard duchy of Spoleto at the time of Charlemagne's invasion of Italy that they were 'shaved Roman-fashion'. Elites defined themselves not simply against social inferiors, but also against other groups within the aristocracy. The social world experienced by inhabitants of the Carolingian empire was deeply conditioned by all these outward signs of status, identity and distinction. The translation of clothing, weaponry and bearing into a code of social hierarchy was internalised implicitly and unconsciously, if not always unquestioningly.
Status could thus be worn, ridden or carried: but it could also be owned, flaunted and consumed. Wills left by Count Eberhard of Friuli (d.863–4) and his wife Gisela, and by Count Eccard of Autun (d.876), bequeathed to their heirs numerous pieces of armour and weaponry which were clearly of no practical use, including several swords decorated with gold and silver. They were passed on because they 'embodied their owner's social identity', symbolising the status which defined their holders as nobles. Gisela's and Eberhard's children were also given large drinking and serving vessels, which symbolised the role of the noble as a feast-giver, an entertainer to his or her followers. This was so fundamental an aspect of elite culture that it was frequently parodied in the ninth century. Notker of St Gallen lampoons the nobility's desire for exotic foodstuffs and feasting at several points in his idiosyncratic biography of Charlemagne: one memorable tale tells of a bishop who was so consumed by the urge to possess unusual luxuries that he was tricked into paying three pounds of silver for a mouse stuffed with spices, believing it to be an eastern delicacy. Notker wrote with an agenda and a sharp wit, and so we have to doubt the literal accuracy of his anecdotes. But whether or not they could really tell an unusual snack from a spicy rodent, the rich tastes of such people had implications for how their social status was expressed. For one thing, their better diet probably made them taller and healthier than the poor, a conclusion supported by skeletal data. Contemporary observers sometimes lingered on the impressive physical attributes of high-status males, as did Ermold when describing Pippin of Aquitaine, the son of Louis the Pious, and were also capable (like the author of the _Liber historiae francorum_ ) of equating lack of physique with a shortage of intelligence and moral fibre. As we shall see in Chapter 7, the way that elite landowners filled their groaning tables made direct demands on peasant labour, meaning that their social status was underlined not just by the quantity, quality and variety of the food they consumed, but also by the process through which they acquired it.
As far as displays of status are concerned, consumption is rarely more conspicuous than when it is made concrete in buildings. Yet aristocratic residences remain frustratingly poorly understood: we know surprisingly little about where the aristocracy lived, and still less about how houses and households articulated the status of their owners. Our difficulties in finding aristocratic residences both on the ground and in texts is partly a result of looking for the wrong things in the wrong places. A tendency to focus on kinship as the central determinant of aristocratic identity has led historians to imagine the early medieval aristocracy in ways similar to those in which their better-attested high medieval counterparts have been viewed. Thus early medieval aristocratic families are sometimes thought of as having identified themselves with a particular 'seat', which served as a fixed centre of lordship and which gradually became fortified. But these assumptions wrongly set up the aristocracy of the central Middle Ages as some kind of 'ideal form' which its predecessors strove to reach. In fact, not only have attempts to find fortified aristocratic strongholds in the Merovingian and Carolingian sources utterly failed, but there is no sign (as we saw in Chapter 5) that aristocratic residences were the nuclei of early medieval villages. Both Roman and high medieval aristocracies lived in structures that, while very different from each other, are nonetheless instantly recognisable archaeologically as elite dwellings, and were described as such in our written sources. That we can find few references in texts to, and scant archaeological traces of, specifically secular, aristocratic, structures between the sixth and tenth centuries is therefore significant: it must suggest that neither the identity nor the status of aristocratic families in this period depended on association with a stable central place.
Evidence for rural construction in the sixth and seventh centuries shows a marked shift away from late Roman styles of residence, at all levels. The late Roman elite's villas of stone and brick were abandoned in the fifth century in the frontier provinces of northern Gaul, and in the sixth in the western Mediterranean. Rural settlement, whether village or isolated dwelling, became typified instead by rectangular wooden 'halls', which show some variation in length (the norm was 10–15 metres but some reached 25–30 metres) but no surviving signs, at that date, of structural elaboration: in other words, landowning elites lived in bigger, and presumably better decorated, versions of the same dwellings inhabited by the owner– cultivators who were now also their neighbours. The abandonment of stone building traditions must relate to the diminished resources of post-Roman elites. Our texts emphasise not buildings but clothing adorned with treasures as visible demonstrations of status. Improved networks of exchange in the Carolingian period catered for aristocratic demands for exotica such as 'robes made of pheasant-skins surrounded with silk; or of the necks, backs and tails of peacocks in their first plumage'. Presumably the material wealth so evident in our wills was also used to adorn residences with exotic wall-hangings and fabulous tableware, making them fitting backdrops for the necessary conviviality, the bestowing of favour and the disciplining of subordinates that took place when the lord was present. Treasures – heirlooms around which stories collected, giving them a cultural biography, such as swords passed on from generation to generation which commemorated the daring deeds of forebears – also functioned as objects of identity. This preference for investment in forms of consumption which could be worn or carried belonged to a world where being powerful involved regular movement, seeing and being seen by clients and patrons: scattered landholdings, with their vibrant communities of free peasants, could not be ruled as mere adjuncts of aristocratic seats. Conspicuous consumption of a mobile kind rather than huge investment in stone and wood made sense in a world where what mattered were not rights of property or jurisdiction attached to a particular centre, but the presence of the powerful.
Exclusive focus on the countryside, encouraged by a doomed search for aristocratic 'seats' as fixed centres of rural lordship, can distort our understanding of aristocratic lives. The Roman elite had moved periodically between the country and the city, in a lifestyle articulated by the rhetorical opposition between cultivated leisure and public business, _otium_ and _negotium_. Yet post-Roman aristocrats too were clearly active in cities – the charter evidence, for example, shows counts holding public courts there, and where it is thick enough can give an impression of the hustle and bustle of business being done publicly among the local elite. In contrast to the Romans, we know very little about where they stayed when they were in town. Here, again, charters can help: in those from Mainz, we can see the great churchman and scholar Hraban Maur owning an expensive town-house, built in stone and bought with gold and horses, while rights over major city churches like St Lambert's were subdivided between upwards of twenty aristocratic patrons. Townhouses were visible to more people than were rural dwellings and so had an important role in demonstrating status. Hraban's family town house jutted out into the 'public street', and there is archaeological and documentary evidence for its neighbours having imposing stone frontages, while Adrevald of Fleury describes the count of Orléans residing in a two-storey residence. These hints are all that our written sources reveal of the appearance of aristocrats' town-houses: what is lacking is more archaeological data, and here we draw a blank north of the Alps. It is in Italy that we find substantial evidence of a variegated urban architecture, including simple wooden structures, but also buildings in stone, brick and mortar, some of them with multiple rooms, stairs to upper storeys, and frequently reworked facades. Yet even Italian cities include areas that look to have been abandoned, and often given over to agriculture, in the early Middle Ages. So we have to imagine the 'unpacking' of space within cities, with large tracts of open ground and gardens often separating clusters of domestic buildings, sometimes enclosed by fences. It is likely that cities in Francia as well as Italy developed this kind of patchwork urban landscape in the post-Roman centuries. Where these residential clusters included churches, they should be seen as demonstrating not the exclusion of the laity from cities dominated by bishops and their priests, but the engagement of local property owners in the patronage of religious buildings that were associated particularly with their families, and helped to declare their status.
Aristocrats' associations with churches were becoming important in our period in the countryside just as much as in cities. The foundation of rural churches was just beginning in the seventh century, and accelerated in the eighth. They were often staffed by family members, and remained under the influence of their founding family. Even the smallest churches could double as family mausolea, places where past and present fused as ancestors were commemorated in prayer; women often dominated such foundations, since they took the lead in preserving family identity by cultivating the remembrance of their menfolk. Aristocratic church foundation was also an important factor in changing burial patterns. There are a number of examples where small groups of high-status burials were consciously marked out: east of the Rhine by new or reused barrows, presumably serving a family and its clients; more commonly elsewhere by increasingly elaborate structures that might eventually become chapels or churches. These sites, central to the cultivation of family identity, should not be seen as solely ecclesiastical in their rationale. In the seventh and eighth centuries, the distinction between an aristocratic residence and a family monastery remained blurred at best, as members of the founding family enjoyed proprietorial rights which could entitle them to hospitality, especially from the nieces and daughters, widowed mothers and dowager aunts, who often cared for such sites. As a result, these structures could become recognised political centres which, in times of internal strife, were deliberately targeted by rival families with acts of violence.
Foundation of such churches could involve building in stone for the first time since Roman times, or the appropriation of former Roman villa sites, as at a series of places in the Moselle valley, and accordingly had an impact on the rural as well as the urban landscape. Like their urban houses and churches, rural churches, and particularly family monasteries, offered hospitality to kinsmen and women and thus helped to define complex extended kin-groups, whose elite status was associated with these sites of power. But not all monasteries had such an exclusive relationship with a single kinstructure: the largest institutions enjoyed patronage from a wide range of sources. Some were granted royal protection, coupled with new rights of immunity – enriched through royal as well as aristocratic patronage, they grew rapidly, housing hundreds of monks and dwarfing even the most lavish secular households. Their growth could in turn affect smaller-scale monastic enterprises, which, especially in the late eighth and earlier ninth centuries, were sometimes handed over to them by aristocratic families who were anxious to buy into the new level of commemoration and intercession offered by these 'powerhouses of prayer'. This had significant implications for the role of aristocratic women: unable to perform the mass or participate fully in acts of commemorative prayer, their place in the ninth-century church was more marginal than it had been, as nunneries were rarer and less central to the circuits of power, and women's role as guardians of family memory was increasingly tied to their educative responsibilities as wives and mothers. At the same time, although Carolingian insistence on royal protection of the greatest monasteries significantly reduced the opportunities for formal family control of monastic centres, families maintained the informal links expressed through their patronage, in which boys given into divine service as child oblates increasingly came to act as bridges between monastery and family. Ninth-century monasteries thus remained important points in aristocratic itineraries and anchors of family identity, even where they no longer responded exclusively to the concerns of a single family or kin-group.
Given these changes, it is no surprise that new forms of aristocratic residence do begin to emerge in our evidence for the eighth- and particularly the ninth-century countryside. Where previously aristocratic halls had simply been larger versions of the dwellings of the peasantry, from this time we begin to see in the countryside structures that more obviously declare the elite status of their occupiers. The proliferation of 'hall plus church' complexes, or occasionally of isolated halls, physically set apart from villages and other settlements, is striking. At Lauchheim in central Germany, for example, the process of separation was gradual: as the eighth century progressed, one plot in the settlement became increasingly dominant, the hall there rebuilt as part of a bigger compound containing a number of burials, enclosed by fences taking in a large area and increasing the physical distance between this residence and the rest of the settlement. This kind of redevelopment indicates a level of power and resource that could in some cases support the construction of purpose-built residences on new sites, distant from lower-status dwellings: the family of Hraban Maur, for example, were in the second half of the eighth century able to build from scratch a structure of this kind, complete with a small family church, which may have eclipsed their town-house at Mainz as their principal residence. An important intellectual figure in the mid-ninth century, Hraban (abbot of Fulda 822–42, archbishop of Mainz 847–56) belonged to a significant aristocratic family in the middle Rhine region, where Ripwin and Giselhelm (discussed in Chapter 5) also held their estates (see Map 9). As the map suggests, we have fairly comprehensive information about this family's landholdings. Hofheim was the 'family seat', where the church founded by Hraban's father (and dedicated to Boniface, Fulda's patron) became something like a family mausoleum. Yet like other local worthies, the family's holdings were relatively dispersed across the region. As well as the house in Mainz, they had considerable interests west of the Rhine, and were careful to cultivate their relationship with Fulda some distance to the north-east. Through sites such as Hofheim, the physical imprint of aristocratic power on the countryside becomes evident for the first time since Roman times. The scale of investment in these complexes, and their political importance, is clear at Petegem in the Scheldt valley: here an eighth-century compound centred on a church and associated cemetery was redeveloped in stone in the ninth century, newly focussed on a rectangular hall with a tiled roof. Petegem was an important point in local aristocratic networks, where counts and bishops held meetings; hence Charles the Bald lodged there when he was attempting to rally support in the area.
These sites show no signs of fortification, no obvious need to respond to contemporary threats from internal conflict or Viking activity. The driving force behind their development was the display of elite status, not concerns about defensibility. Even at Petegem, where the site was defined by a seven-metre wide ditch, the function of this boundary marker was to demarcate a space that was significant in cultural and legal terms, rather than militarily; these priorities found parallels at royal palaces, which were not built as defensive (or offensive) strongholds. The archaeological evidence argues against the idea of a restructuring of the countryside around aristocratic strongholds: where a clause in Charles the Bald's Edict of Pîtres (864) commands the tearing down of unauthorised fortifications, it is by no means clear that these were residences. References to similar structures in the narrative sources of the later ninth century often make them sound more like field fortifications, put up quickly and temporarily against an imminent threat.
**Map 9.** Landholdings of Hraban Maur's family
The most important influence on the development of aristocratic residences was the example provided by royal buildings. One distinctive feature of the architecture of Carolingian kingship was the second storey, which provided a secluded but still public space for receiving petitioners and taking counsel, functions which complemented those of the great halls at palace sites like Ingelheim, and the open air spaces favoured for royal assemblies; the use of upper-storey space in this manner was a departure from late antique precedents where rulers met their subjects and counsellors in groundfloor chambers. Second storeys are attested both at royal palaces and at centres of royal estates, where kings and their entourages might stay while passing through a locality. They were safer, of course, when constructed in stone: the collapse of wooden porticoes at Aachen while Louis the Pious was processing through them, or in the smaller rural centre at Flammersheim when Louis the German was surrounded by a 'throng' of subjects, threatened the health of king and kingdom. Buildings for royalty might also be constructed by important abbots and bishops as a way of ingratiating themselves with kings: thus Archbishop Leidrad of Lyon built a residence for the use of kings when they visited his city, and a magnificent and still surviving building was added at the gateway to the abbey of Lorsch when, under Louis the German, it became a centre of royal representation. Against this backdrop, the use of two-storeyed residences by aristocrats in the late ninth century – evident in a series of asides in our narrative accounts – should be understood in terms of aristocratic emulation of an originally royal idiom. At Engis in modern Belgium, an early-eighth-century complex was rebuilt in stone in the ninth century, with the reconstructed church facing a lavish hall. These structures are strongly reminiscent of the Lorsch gatehouse and the descriptions of royal estate centres, and a document of 885 shows that this was a royal centre linked with hunting rights in a nearby forest, now granted out to members of a crucial aristocratic network in this highly contested region.
The similarity of royal and aristocratic buildings is not surprising, for, as the Engis case suggests, the two overlapped. Royal estate centres were run by stewards recruited from the ranks of local landed elites, and where their careers can be traced royal estate managers often seem to have worked in areas where they also had family interests: Odo, one of the crucial political figures of the civil wars of the 830s when he served as count of Orléans, began his career running the royal palace at Ingelheim, which adjoined his family estates. Royal estates were visible manifestations of royal power in the landscape, even when kings were not at home; but they were also home to ambitious aristocrats the year round, and provided lodgings for those rushing to and from court on royal business. Hence aristocratic property complexes are often found around the fringes of royal estates, which suggests that aristocrats may have lived near to the residences of kings: Charles the Fat consciously encouraged this in the areas where he spent most of his time, Alemannia and Italy. Bishops and other nobles (including Einhard) are also known to have had town houses in Aachen and Pavia, two of the principal royal centres of Francia and Italy. All this points to a relatively regular proximity of kings and aristocrats, forming an important nodal point which sustained the identity of the aristocratic political community. The treatise 'On the Governance of the Palace', written by Adalhard of Corbie in the early ninth century and revised by Archbishop Hincmar of Rheims in 882, underlines the importance of this link by describing the various forms of interaction between different levels of aristocrat at assemblies and at the palace more generally.
At Aachen, the doorway to the imperial private chambers was where courtiers loitered awaiting a chance to press their cases. From there, a series of walkways and balconies – where the privileged might access the emperor, but which were visible to all – provided linkages to the major ceremonial spaces of the church and audience hall. Meanwhile, in the surrounding buildings less formal codes of sociability held sway: here the great officers of the court maintained their own dwellings to which visitors and the lesser members of the court – styled 'servants' by Hincmar – might be invited, regaled with gossip and honoured with gifts. Aristocratic households would have had similar, if less complex, arrangements of space: the attention paid to external markers – fences and ditches, and at several sites metalled tracks leading to the central building on a site – underlines the extent to which aristocratic power was seen as something exercised publicly, made manifest in visible activity and outdoor meetings. By the ninth century, not only were royal palaces and estates significant elements in aristocratic patterns of residence and movement, they also provided influential models for the conception and spatial organisation of aristocratic authority itself.
#### ARISTOCRATIC BEHAVIOUR: UPBRINGING, MORALITY AND CULTURE
These hierarchies of space mattered because they defined social relationships and social identities. The 'servants' mentioned by Hincmar, for example, were probably not menial workers, but rather young or lesser-ranking nobles who did not yet hold formal offices. This brings us to the importance of the royal court (as well as the households of great nobles) as a forum for the socialisation of junior aristocrats. In its heyday the Merovingian royal court had performed precisely this function, as the letters of Bishop Desiderius of Cahors, raised at the court of King Dagobert, attest. The succession of minorities in the Merovingian royal line in the later seventh and early eighth centuries (discussed in Chapter 2) is likely to have diminished the role of the court in nurturing young nobles. Hincmar refers to these people as the _pueri_ , the lads, and their career paths typically involved being sent to court to attend the king and his entourage in the hope of eventually making a good enough impression to be granted a good marriage, some land, an important office, or all three. The sorts of bonding activities in which they participated also helped to hone their martial abilities. Important among these was hunting, in which the Frankish aristocracy took great pride: Einhard claimed that 'there is hardly a people on earth who can rival the Franks in this skill'. Hunting mattered also because it was something that kings and nobles did together; like feasting, it was a ritual that helped to express trust and consensus. It is not surprising that royal assemblies therefore often ended with a hunt. 'The lads' were clearly also encouraged to engage in even riskier occupations. In 864 Young Charles, the son of Charles the Bald, was 'enjoying some horseplay with other young men of his own age' when one of his friends hit him on the head with a sword and 'penetrated almost as far as the brain, reaching from his left temple to his right cheekbone and jaw'. Play-fighting with real weapons was a dangerous business, and Charles was by no means the only Carolingian to fall foul of such shenanigans. However, this was evidently not thought inappropriate behaviour for princes and budding secular aristocrats who would have to participate in warfare as adults. The abilities that these men acquired were impressive: Nithard describes spectacularly skilful war games organised by Louis the German and Charles the Bald during the civil wars, as part of which horsemen would charge at each other then wheel in feigned retreats, barely avoiding contact.
Such skill could be nurtured by nobles' participation in the rituals and daily rough and tumble of the royal court, but sending off adolescents for 'finishing' in the house of a patron – often a relative or a godparent – remained the widely practised ideal. Thus Einhard's letters show him acting as a guardian and patron for young men serving in his household, and taking an active role in negotiating marriages, securing the consent of both parties' kin and arranging the necessary bequests of property, when his charges moved on to establish households of their own. Moreover, a figure like Einhard was a desirable patron precisely because he offered a point of contact with the royal court. Royal and aristocratic spheres of upbringing necessarily coexisted and overlapped.
Gaining access to the royal presence made it possible to catch the king's eye: one of Notker's stories concerns Isanbard, an aristocrat who had been disgraced and stripped of his offices until his bravery on the hunt, killing a ferocious beast which had wounded Charlemagne, led to his rehabilitation. Aristocratic life, in a world of easily offended and jealously guarded honour, was not a riskfree activity, as Isanbard could attest. But bonds formed in youth, and rooted in royal and aristocratic households, were powerful, and could last for life. The defining feature of these relationships was a kind of masculine honour. Although the son of Charles the Bald who was maimed while playfighting never recovered, and was to die two years after his accident, it is significant that he and his peers tried to protect his assailant from punishment. Conversely, Count Hugh of Tours's failure to bring reinforcements to the imperial army on the Spanish March in 827 prompted opponents to castigate him as cowardly. Thegan's claim that Hugh was too scared to leave his house because of the taunts of his entourage shows how notions of honour were tied up with constructions of domestic and public space: Hugh's standing was undermined by his inability to control his own household, and his dishonour was complete because 'he almost never dared to put his feet out of doors' and cross the boundary from the domestic to the public sphere. The urgency of these concerns reminds us that the categorisation of public offices in the vocabulary of 'honour' and 'dignity', which we discussed in Chapter 4, has to be taken extremely seriously. Shared codes of honour mattered because entourages could be unruly and needed mastering, and the stories of Young Charles and Hugh confirm that the honour-bound aristocratic milieu was face-to-face, aggressive and macho: what one might expect, in fact, from a group which considered itself a warrior elite.
Yet the martial elements of this identity do not tell the whole story. The training of young noblemen was not restricted to networking and male bonding, as shown by a handbook of advice written in the early 840s by the laywoman Dhuoda for her son William as he made his way at Charles the Bald's court. As well as expecting him to make useful contacts, Dhuoda hoped that William would cultivate wisdom and learn other virtues such as humility, patience and sobriety. Self-restraint was itself part of the legitimate exercise of power. More formal aspects of education were also provided at court, as well as in monastic schools. An emphasis on the heavy moral responsibilities that accompanied the ability to rule followed from a political programme which saw all power as derived from God, and its wielders as responsible to God not only for their actions, but also for the souls of those in their care.
Those moral codes of conduct referred to by Dhuoda brought the lay nobility face to face with a potential contradiction in its position. Noble identity was bound up in family and military roles; yet how could sex and violence be squared with the rigours of Christianity? How, in short, could they save their souls? The paradox was still an irritant at the end of the ninth century to Notker of St Gallen, whose attempt to compare the piety of King Louis the German favourably with that of St Ambrose of Milan forced him to make telling caveats: 'Louis closely resembled the saint, except in such points as are necessary to an earthly commonwealth, as for instance marriage and the use of arms.' These were troubling aspects of secular life which had a particular resonance during the violent expansion of the Carolingian empire in the second half of the eighth century, not all of which was directed at pagans. The sin of killing could be satisfied through penance, but that involved a surrender of arms, office and marriage which effectively emasculated and 'dis-nobled' the penitent. This was not, however, a new problem, and a long intellectual tradition was available from which to construct solutions. For the Franks, a deep respect for the Old Testament coupled with the experience of expansionary warfare helped foster the idea that they were a new Israel, the chosen people of God. Their successes thus became a fulfilment of the divine will on earth. This heavenly approval was not simply claimed, but actively canvassed. While on campaign against the Avars in 791, Charlemagne arranged for a three-day fast to be organised across the realm, in order to appease God before battle commenced. In the second half of the ninth century, the problem of Franks fighting against Franks in civil war was even more traumatic. For this reason, Frankish writers were careful to deprive enemy kings of their legitimacy by labelling them as 'tyrants', while churchmen were often to be found with armies, orchestrating blessings, penance and other rituals of collective expiation. Pope John VIII (872–82) was even ready to promise remission of sins to anyone who came to defend Rome against the Muslims.
It would be anachronistic to see this clerical language as a fig leaf to legitimise violence and imperialism. The mentality of the elite involved a genuine dichotomy in the core identities of men who saw themselves as both warriors and true Christians. The deep concern of some laymen for their own salvation is indicated by the genre of instructional literature known as 'mirrors for princes'. These books were composed by churchmen such as Archbishop Paulinus of Aquileia, but they were actively sought by their lay recipients, in Paulinus's case Eric, count of nearby Friuli. These tracts addressed real concerns on the part of their recipients: Paulinus wrote in response to Eric's fears about the dangers of being preoccupied 'in the business of warfare', while in another tract written in the 790s Alcuin aimed to demonstrate to Count Wido that his lay status would not prevent him from getting to heaven. The most ambitious such treatise, written by Bishop Jonas of Orléans for his local count, Matfrid, presented itself as a guide for the 'lay institution', offering a morality specifically tailored to the needs of those 'in the married state'. Jonas was echoing a series of contemporary attempts to define human society in terms suggested four hundred years earlier by St Augustine, as being made up of three orders, each with their special needs: the laity, defined by their married state; and monks and priests, each of whom already had written rules which had recently been approved by imperial authority. The manuscript transmission of works like Jonas's and especially Alcuin's reflects their popularity, and at least some manuscripts were commissioned or owned by lay aristocrats: Eberhard of Friuli, for example, owned a copy of Alcuin's work. That the messages of such tracts hit home is suggested by the writings of Charlemagne's biographer Einhard, a layman, who consistently called himself 'sinner' in his writings, reflecting a tendency to ponder acutely upon his own humility and worthlessness. Later in the ninth century, we encounter a number of lay nobles who found the paradox impossible to live with and even tried to divest themselves of their secular status.
There were limits to all this. Even churchmen like Notker, Alcuin and Jonas evidently recognised that sexual reproduction and warfare were essential to the survival of the Church and kingdom, and thus of God's chosen people. Restraint, not abstinence, was the core message of most handbooks. This was not, then, simply a case of the Church preaching to the laity. Rather, it reflects exchange between them, and a genuine piety which among at least some members of the secular aristocracy might have extended to a tendency to self-examination. Nevertheless, the strengthening of the institutional Church under the Carolingians (discussed in Chapter 3) firmed up the dividing line between ecclesiastical and secular elites. Priests and monks acquired a group identity through the conscious avoidance of the normal markers of aristocracy in lifestyle as well as dress and haircut: they were to avoid the polluting secularity of the hunt, not even riding behind it as spectators with their dogs, and to take care over their involvement in the lewd merriment of aristocratic feasting. Changing patterns of ecclesiastical recruitment reinforced these boundaries. By the ninth century, ecclesiastical leaders were overwhelmingly drawn from monasteries, having been given up by their parents as child oblates; brought up differently from their lay kinsmen, they acquired a distinct professional identity. 'Career changes', when lay officeholders volunteered or were coerced into ecclesiastical roles – as was frequent in Merovingian Francia and was still possible in the reign of Charlemagne – became very rare thereafter.
Carolingian 'reform' may have encouraged the differentiation of ecclesiastical and secular elites, but this did not cut off the aristocracy from cultural developments. Far from it: there is good evidence for avid aristocratic consumption not only of 'self-help' manuals in the approved pieties of their day, but also of literate culture more generally. Stereotypes about a hard-drinking hard-fighting warrior elite are too simplistic. The written works of lay people like Dhuoda, Einhard and Nithard, which are studded with classical and Biblical quotations, demonstrate that scholarly learning and the ability to write stylish Latin were not the exclusive preserve of a clerical elite, but a prized accomplishment of courtiers. Yet quite how many among the aristocracy were literate, and what kind of literacy they exhibited, remain matters open for debate. Modern concepts of literacy encourage us to connect the ability to read with the ability to write. But in the early Middle Ages the latter was seen as a craft for skilled manual workers. Einhard's portrait of Charlemagne keeping wax tablets under his pillow in his attempts to master the tricky art of writing, but eloquent in his Latin speech and ardently listening to Augustine's _City of God_ read aloud over dinner, looks odd to our eyes, but should not lead us to underestimate the extent of the Frankish ruler's interest and involvement in literate culture. Our understanding of literacy privileges a particular kind of reading, silent and individual, whose cultural dominance is a relatively recent historical phenomenon; in the early Middle Ages, this practice was associated with meditation on the hidden messages of a holy text.
Participation in a culture of books and intellectual debate was worth advertising. For example, among all the heavy weaponry and flashy drinking vessels, Eberhard and Gisela also bequeathed to their children several books, while Count Eccard of Mâcon also had a sizeable library, again showing an involvement with the latest debates at centres like Auxerre. The ability to demonstrate eloquence in Latin speech, and to appreciate the theological reading and public debates staged at court, were central accomplishments for any would-be political player. Accomplished speech of this type was, of course, specific to the milieu of the royal court. In fact, there is some evidence that linguistic competence in Latin may have served as an important marker of social status. Certainly linguistic changes meant that by the ninth century the ability to speak Latin – which now required specialised tutoring – marked one out as an aristocrat. Differing degrees of Latinity also reinforced internal divisions within the aristocracy: this explains the famous oaths sworn by the followers of Charles the Bald and Louis the German at Strasbourg in 842, the earliest surviving instance of Old French and one of the earliest Old High German texts too. Here, to affirm their alliance, a solemn Latin oath was drawn up; this was sworn in the 'Roman tongue', that is the Romance vernacular of western Francia, by the east Frankish king Louis the German and his followers, so that its meaning was transparent to their audience, the followers of the western king Charles the Bald; subsequently, Charles and his followers swore the oath in the 'Teutonic tongue' ( _theudisca_ ), the Germanic vernacular of the eastern Franks. The texts of the oaths in both vernaculars survive; they seem to be phonetically inspired and easy-to-pronounce representations, designed for an audience unfamiliar with the sounds and structures of their respective languages. The ceremony constituted a public guarantee by the two kings and their immediate retinues that they would stand by and protect the interests of those lesser aristocrats who had come to fight for their royal lords, men who would face political ruin if their leaders abandoned them. To these lower tiers of aristocratic society gathered at Strasbourg to listen to an alien king who had recently been an enemy, an oath sworn in the familiar language of the homeland, not the difficult and potentially slippery medium of courtly Latin, offered reassurance.
#### ARISTOCRATIC FAMILIES
Although much of what we have discussed so far suggests an image of the aristocracy as a self-conscious class committed to acting in its own interests, we must remember that criss-crossing this class identity were equally important family solidarities. As we mentioned at the beginning of the chapter, a lot of research has been done on the origins and family structures of the Carolingian aristocracy. It used to be thought that the Carolingians effectively created the aristocracy which governed the empire, by empowering the families which had been their allies in seventh- and eighth-century Austrasia and boosting them on to a grander stage as friends of kings. However, through analysis of their naming patterns, it has been possible to show that powerful aristocratic families in the eighth century were often descended from individuals who were influential in the same regions in the immediate post-Roman period, long before the Carolingians became a serious dynastic proposition. In other words, the Carolingians did not create the aristocracy, but emerged from it. This is why, after taking the throne, they had to work constantly to establish and reinforce their royal status. They could not afford to treat influential noble families with impunity; equally, though, individual families needed to work within the Carolingian system to maintain their position in the social hierarchy.
Family identities often look impressively solid in the writings of modern historians, and this impression is only enhanced by these families' sheer size and wealth. The most important could control immense quantities of land spread across great distances. For example, the extent of the lands left to their children by Eberhard and his wife Gisela (a daughter of Louis the Pious) in 863–4 (see Map 10) shows the rewards of royal patronage: a family whose home-base was around the church of Cysoing in Flanders (an equivalent to Hraban's Hofheim) acquired possessions distributed across the empire, entailing associations with multiple kings. As a consequence of this extensive wealth and influence, the identities of families like Eberhard's were not exclusively defined by their relationship to the royal court, but existed independently. One means of expressing this identity was through names which recurred through generations and in a sense became family 'property': the names Charles and Louis, for instance, seem to have been monopolised by the Carolingians. Very occasionally we encounter families which were labelled by a collective name: the kin of the empress Engelberga, wife of Louis II of Italy, were referred to by an early-tenth-century writer corporately as the 'Supponids', after their most prominent male name, although it is far more normal to read of the 'associates' ( _socii, propinqui_ ) of a named individual, a category which might encompass overlapping and mutually reinforcing bonds of kinship, friendship and lordship. Aristocratic kindreds also expressed their sense of themselves by tracing their ancestry back to a single, sometimes mythical, ancestor who was sometimes a saint: in the case of the Carolingians, it was St Arnulf, a seventh-century bishop of Metz. Many of these families thus invested emotionally in something like a cult of themselves.
**Map 10.** The lands in the will of Eberhard and Gisela of Friuli
Naming patterns suggest that the aristocracy enjoyed associations of an even greater range than the extensive landholdings of individual families. The personal links indicated by names have been taken to show the existence of vast kin-groups – extended clans – which have in turn often been seen as the fundamental building blocks of elite society. The largest repositories of names from this period are the _Libri memoriales_ (memorial books), also known as 'Books of Confraternity', which were produced at monasteries across Europe to list the names used in liturgical ceremonies that were thought to benefit the souls of those named. They testify to the enormous size of the networks of prayer that formed around monastic communities. The two Carolingian-age confraternity books from St Gallen, for example, together contain some 14,932 names. The earlier was put together before 817 and includes names of members of thirty-one of the religious communities bound to St Gallen through confraternity agreements, both living and dead: on page 22 (pictured in Figure 15) the left-hand arcade has been labelled 'of the living' ('vivoru(m)'), the right-hand arcade 'of the dead' ('mortuor(um)'), though in both the lists of names have outgrown the arcades. Careful work over the last few decades has identified individual entries or groups of entries, which may then sometimes be tied down to a specific date or context, showing groups of aristocrats united in prayer. Scholars have inferred that those found grouped in such a way, especially those with similar name-elements, were related, and this has led to the further hypothesis that family structure in the eighth and ninth centuries was clan-based, with extensive bilateral ties pulling together individuals spread across the continent.
**Figure 15.** The earliest Confraternity Book of St Gallen.
The idea of the early medieval kin group as an extended network certainly helps to explain some aspects of the Carolingian high aristocracy, not least their extraordinary mobility. Even after the division of the empire in 843, which forced nobles to choose a single king to be their lord, well-connected aristocrats could still switch sides and move across regnal boundaries. A case in point is the career of Count Robert 'the Strong', a noble from the Worms region who was able to acquire important offices in west Francia thanks to his connections with the family of Charles the Bald's first queen, Ermentrude. Robert's son Odo became king of west Francia in 888, and the Capetian dynasty which ruled west of the Rhine for centuries after 987 were his direct descendants: the ancestor figure of the greatest French medieval royal dynasty was therefore a Rhinelander. This highlights the impermanence of the internal frontiers which divide modern maps of the empire in the ninth century: men like Robert continued to perform on an imperial stage. Even after the disintegration of the empire in 888, such connections survived. Guy of Spoleto was able to make a credible, though ultimately unsuccessful, bid to become king of west Francia in 888, despite the fact that he had spent almost his entire political career in central Italy. This mobility was possible partly because, as we have seen in the case of Eberhard, these great men held land scattered across different kingdoms; but extensive family links were also a pre-requisite.
Elite families could certainly conceive of themselves as extended groups for some purposes, therefore, but in other circumstances family identities could narrow quite sharply. In particular, claims to property were often expressed within a much smaller, even nuclear, family. This is illustrated by Dhuoda's handbook for her son which, listing the people William is to pray for, names only the relatives of his father from whom he had inherited property. Property and inheritance were similarly important in Italy in defining the narrower family unit. When an annalist writing in Mainz in 883 wished to criticise the emperor (Charles the Fat) for attempting to dispossess Guy of Spoleto and his allies, the best way he could think of to underline the illegitimacy of this act was in terms of direct father– son inheritance: '[Charles] gave the benefices which they and their fathers and their grandfathers and their great-grandfathers had held to persons of much lower standing.' These examples suggest that family identity could be defined as patrilinear and bound up with the ownership of inherited property.
The existence of these tighter 'practical' bonds within the wider array of 'official kin' points to the multi-layered and sometimes fluid nature of family structures amongst Carolingian elites. Casestudies of the shifting political alignments of particular families suggest that individuals might privilege and play upon those ties of kinship connecting them to a well-placed figure at court in the hope of patronage and preferment, but that as the political situation changed they might realign themselves, stressing a different set of family ties to connect them with a different potential patron. Einhard and Thegan, for example, draw the kinship connections of Charlemagne's wife, Hildegard, differently, in ways which reflect the immediate political circumstances in which they wrote. This fluidity was not based on confusion, but on the efforts of individuals to make the complex web of kin ties work for them. The sheer extent of the Carolingian empire, and its creation of a hierarchy within the aristocracy focussed on the court, worked integrally to shape the family structures of the aristocracy: the extensive and open-ended systems of kinship so evident in our sources was emphasised in a political context which put a premium on precisely those kinds of networks. The commonplace that kinship was the basic social bond in early medieval society is true not because kin-groups were cohesive entities held together by overwhelming mutual obligation, but because ties with potential patrons and helpers could be activated and expressed by identifying and addressing those people as kin.
The fluidity of kinship ties has sometimes made it hard to map them on to patterns of property-owning and inheritance. Although the evidence for inheritance seems to point us in the direction of smaller family groups, as we have seen, the norms that governed these transfers are extremely elusive. Those set out in law codes tend to concern themselves with special classes of property or with exceptional cases, and were in any case of questionable practical application. Documents that do reflect real cases – charters and records of dispute – nowhere explicitly state principles about inheritance. The run of two dozen or so surviving wills from the Frankish kingdoms, for example, continue to utilise the basic forms of the Roman will into the eighth century and invoke the rules of Roman law guaranteeing some heirs a stated minimum share; but they express no other norms. Admittedly, the sample of wills is exceptional: most of those that survive do so because their authors made a favoured church their principal heir. Nonetheless, they do suggest a situation in which there was an expectation that an individual's property would be divided between heirs on their death, but that there was considerable room for negotiation over the nature of that division.
By the ninth century, indeed, even the Roman law structures that had characterised the earlier material disappear, and wills become agreements between an individual and his or her heirs concerning commemoration and charity: they are styled as, say, 'the alms of Eccard', and the beneficiaries and witnesses are bound together in their role as 'Eccard's almsmen', charged with ensuring the well-being of his soul through commemorative prayer. The best examples of this practice are those drawn up for Count Eccard of Mâcon c.863 and for Ercanfrida, the widow of Count Nithard of Trier, c.853. In both cases, the pattern of bequests reflects ongoing associations between particular estates and individuals. Ercanfrida, for example, gave her major estate-complex to the monks at Prüm, who were to hold an annual feast there on her death day for the good of her soul and her husband's, while other estates were to go back to the closest descendants of those who gave them to Ercanfrida. Overall, such agreements present inheritance not as an abstract matter governed by formal rules, but as a practice rooted in personal relationships which generated emotional and moral claims: heirs were expected to link their receipt of a particular property to the commemoration of the ancestor from whom they received it.
These attitudes are not, it is true, directly documented in the records of property transfer that make up the bulk of the charter evidence – we would not expect them to be – but they are implicit in the commonplace acknowledgement of the wishes of previous owners in donation charters, and in the narrative strategies through which claims to property were made in court hearings. 'Inheritance' is then best understood as involving a claim to be acknowledged as kin and so to be included in the commemoration of the deceased and the redistribution of his or her property. Modern research on the charters, moreover, suggests that property was circulated within families not in a once-and-for-all deathbed drama of inheritance, but through a steady flow of grants between kin through the life-cycle: the centre-piece of Ercanfrida's will, indeed – the donation of her dower to Prüm – had already been ensured by a standard donation charter making no mention of her last will and testament. A family's central places, such as its church or churches, also helped to keep family properties concentrated: by granting one's lands to a church or monastery and then receiving them back as lifetime leases, the dangers of ever-increasing division and subdivision through inheritance could be sidestepped. The lands in question would theoretically belong to the institution in perpetuity, and so would always return intact to the control of the proprietary family of the institution as shorter-term arrangements (time-limited leases) ran their course. There is also strong evidence for transferring land through purchase or exchange. In some parts of Europe, these types of transaction were just as common as donations as ways of circulating property within families, and between families and favoured institutions. Karol, son of Liutprand, built up a considerable estate through purchases in the Vico Teatino in central Italy between about 850 and 870, but perhaps over-reached himself, because his sons were forced to sell some of his estate to the monastery of Casauria, and then to lease it back for an annual rent. Too strong a focus on formal division between kin effected at the deathbed of an individual thus misrepresents practices of property which rested on a continuum of exchange.
#### ARISTOCRATIC RESOURCES AND RELATIONSHIPS: _HONORES_ , BENEFICES AND LORDSHIP
Among the most significant indications of the flexibility of inheritance is the strong role played in surviving examples by women. Three of Eberhard and Gisela's daughters received land alongside their brothers, and they are among numbers of women whom we know to have had independent control over property, with all the social power that that implied. The crucial position of women in the process of augmenting and passing on a family's property was to some extent only natural. As brides, they contributed the dower or morning gift that was a part of the legitimate marriage procedure in most west European traditions. As wives and mothers, they produced the children who could legitimately share the family inheritance. As widows, they could often control at least a portion of the family patrimony in their own right. Since they were therefore linchpins in the ownership and transfer of property that was so crucial to a family's power and position, both in the aristocracy and below, it is no surprise that women were also the principal guardians of family identity, cultivating the remembrance of the deceased and transmitting ideas about the family's shape and status to future generations. Dhuoda's manual is a notable example of the latter. Similarly, Richgard, the wife of Charles the Fat, doggedly pursued the commemoration of her close natal kin and sought to restore its landed interests, which had been damaged in the royal scramble for Lotharingia in 869–70, through the control and clever manipulation of a series of nunneries. In Italy too, Lombard law came to recognise female power over property in various circumstances, and the surviving charters not only reveal numbers of women – nuns, widows and mothers in particular – wielding this power, but also hint at the often decisive influence of personal relationships within the family in enhancing the power of women in particular cases. Yet family identity was not the sole determinant of political allegiance. Despite their impressive size and power, noble families in the Carolingian period did not concertedly pursue their interests as indivisible units. Family members could and did fight against each other in the dynastic conflicts of the period. When (as we shall see in Chapter 8) Boso attempted to seize the throne in 879, for example, his brother Richard lined up with the Carolingians who opposed him. Conflict within, as well as between, families was very often what gave rulers like Charlemagne the opportunity to intervene in a locality and impose their power to adjudicate and govern.
One of the reasons that aristocratic movement and lifestyle shaped itself round the royal court is that kings were a key source of patronage. _Honores_ (offices such as that of count) were in the king's gift, and came to be seen as a vital part of a successful aristocratic career. As we saw in Chapter 4, the term itself indicates that office was thought of less in terms of abstract administrative competence than in the language of status rooted in shared codes of honourable behaviour. To gain an honour was quite literally to be honoured: in contemporary usage, it transformed a private individual into a public figure. _Honores_ were also important resources for families, their attraction lying partly in the fact that they were secure: unlike the landed properties on which aristocratic power otherwise depended, they could not be dissipated through the vagaries of inheritance. Offices granted by the king helped members of the nobility to anchor their status: thus the Bavarian count Orendil, granting land to the church of Freising in 814, could ask the bishop to let it out to his son should he in turn come to exercise his father's ministry.
The role of the _honor_ as a crucial intersection in the relationship between aristocracy and king becomes even more important if it is seen as having become heritable in the ninth century. If _honores_ could be passed on from one aristocrat to the next, then they were removed from the king's immediate power of patronage. Viewed in this way, the aristocratic _honor_ has contributed to the idea that the second half of the ninth century saw a progressive weakening of royal power. There are, however, a number of problems with this theory. In the first place, it depends heavily on reading Charles the Bald's Capitulary of Quierzy (877) as recognising formally the heritability of _honores_. But the capitulary's stipulation that if any count died while the king was in Italy, his son was to succeed to his office, was in fact contingent and specific, not general, and was intended only to prevent Charles's son Louis redistributing offices while the king was away. Secondly, the tendency for one or two families to dominate any given _honor_ was not new in the ninth century, but a permanent and long-acknowledged fact of early medieval politics. Nor was it necessarily detrimental to kings: as they well knew, it was precisely possession of local influence and pre-existing family connections that enabled individuals to exercise control of _honores_ effectively. Where their backgrounds can be studied, it is therefore not surprising that many counts and other regional power-brokers in the reign of Charlemagne were in fact local aristocrats from families of long standing. _Honores_ such as countships were not levels in an abstract administrative 'state' hierarchy; rather, they were inseparably intertwined with the family and personal power of the aristocracy. Contemporaries accepted this implicitly. In 882, Hincmar of Rheims remarked nostalgically that the great office-holders of Louis the Pious's day were now all dead, but added: 'However, I do know that sons were born to replace these fathers from their own families... May they seek not to be deficient in morals... thus they may deservedly fill the places and positions of their fathers.'
Nevertheless, the distribution of _honores_ was an important element in royal patronage. Even if many such appointments went _de facto_ to the 'obvious' candidate, the desire for _honores_ was one of the key factors which kept noble ambitions focussed on the royal court throughout the Carolingian period. Families might cultivate hopes like those we have already seen Count Orendil expressing, but inheritance practices provided no firm basis for the formal transmission of an office within the family: a count might have more than one son, and collateral kin could not be excluded from the equation. The kind of case which was advanced to lay claim to property, rooted in an individual's moral and personal ties to the dead, might on occasion be used to make a claim to an _honor_ : Dhuoda thus reminded her son William of his status as the favoured heir of his uncle and godfather, Theodoric, and expressed the hope that he would receive _honores_ from Charles the Bald. But to remind a ruler of a moral claim of this type was not to presume an automatic right. _Honores_ were acknowledged to be in the king's gift. Rulers, indeed, were also capable of revoking _honores_ and removing incumbents when circumstances permitted. When the obvious candidate for an _honor_ was young, this could be relatively straightforward, as in 868 when, a few years after the death of Count Robert 'the Strong' of Angers, Charles the Bald managed to remove his offices from the control of his young son Odo and to hand them instead to another local potentate who had been Robert's rival. Exploitation of such local rivalries was an essential weapon in the royal armoury, and the shunting of a given office between members of two or three regionally powerful families is not an uncommon pattern. But kings could also engage in much more forthright actions when circumstances allowed: witness Louis the German's spectacular purge of leading members of the east Frankish aristocracy in 861.
The power to revoke office also, however, depended in some measure on the ability of individual favourites to help the king remove those who had fallen from grace. A couple of years before his dispossession of Odo, Charles had attempted to revoke the offices of the rebellious Count Bernard by granting them to Robert himself; yet it emerged some time later that Robert had had considerable trouble in forcing Bernard off the turf which was supposedly now his, and so had failed to make good the king's gift. Such 'aspirational' grants of offices or land certainly encouraged conflict between members of the elite, but this was because they were competing _for_ royal favour and _honores:_ such violence was an integral part of the Frankish political system under the Carolingians. It remained worthwhile to fight for royal patronage throughout our period: kings in the later ninth century had no more trouble distributing or revoking _honores_ than had their predecessors. If aristocratic struggles over _honores_ become more visible in our sources as the ninth century progresses, this is because kings intervened more often to revoke them. The late ninth century should not be seen, as it sometimes is, as an era in which public office was 'privatised', so much as one when aristocratic competition for royal favour increased in line with the political turmoil at the top.
Countships were not the only currency of royal patronage: estates could be granted out too, and these grants were likewise seen as _honores_. Grants of land took a variety of forms. The Merovingians, like the other rulers of the post-Roman west, had rewarded loyal aristocrats with outright alienations of land, although, again as elsewhere, such gifts could be revoked by hook or by crook if the recipient or his heirs incurred the king's displeasure. Outright gifts of this kind were, however, avoided by the Carolingians until the 820s, when the practice was revived under Louis the Pious; they were then used sparingly, with a careful eye on the potential benefits and the need to conserve royal resources. Far more common was a new form of gift, introduced under Pippin III, in which an estate was granted out to a favoured follower for his lifetime, but ultimately remained royal property: this was termed granting _in beneficium_ , literally 'as a benefit', hence modern historians refer to the granting of 'benefices'. Based on the practice whereby a church might grant back to the family of a favoured patron rights over land which that patron had donated to it in a 'precarial grant', under the Carolingians grants of royal estates as benefices were a crucial integrative force, tying the many recipients of such royal patronage firmly into the Carolingian system. Indeed, royal grants of this kind were made not only out of fiscal estates, but also from church land, for under the settlement reached between the Frankish episcopate and the Carolingians in the 740s and subsequently renegotiated and reaffirmed, specific pieces of church land – those deemed 'excess' to immediate needs – could be granted out 'on the king's word' in this manner, so long as a token payment were made in recognition of the church's ultimate title: the process of Carolingian takeover characteristically involved the restructuring of familial patronage networks sustained by precarial grants as monasteries and bishoprics were integrated into a wider Frankish Church establishment working in partnership with the king.
Holders of royal benefices have sometimes been thought of as a special group, bound to the king particularly tightly. It has seemed natural, moreover, to link them with those styled _vassi dominici_ ('vassals of the lord [king]'), who are increasingly visible in our sources from the last decades of the eighth century. It is then a small step to suggest that those who stood in such a special relationship with the king owed him a particular duty of military service. Taken together, the assumed linkages of benefice with vassal, and of vassal with military service, have produced a fairly narrow conception of the Carolingian royal vassal as a mainstay of the king's army; this figure has in turn been a major protagonist in arguments between historians over what some have called 'feudalism' (usually defined as a system in which grants of benefices were made with the specific obligation on the beneficiary to perform military service for the grantor). But the sources for the Carolingian period offer little that really sustains this rather artificial construction. There is no firm proof either that those holding benefices were consistently thought of as vassals, or that those styled _vassi_ always held benefices; nor is there any indication that military service was a particular requirement on those called _vassi_. Capitularies certainly required that they, like others enjoying royal favour, turned up on campaign when summoned, but they are also visible in documents, legislation and narratives performing a wide range of other functions for the king.
Moreover, there is no evidence that Carolingian aristocrats were in turn granting out their own land in the form of benefices, or indeed calling their retainers 'vassals', on any meaningful scale. Of course, as we have seen, aristocratic households included bevies of young retainers, and ties of patronage formed within households continued to animate social relationships between landowners; but the documentary evidence shows that inheritance and exchange remained the dominant ways of acquiring land. If the granting of benefices by aristocrats to their followers remained rare, the terminology of aristocratic lordship also remained indistinct: beyond the end of the ninth century, aristocratic followings are said to be made up of _fideles_ (faithful men) and other relatively vague and general terms. There is simply no foundation for the notion that vassalage emerged in this period as a new form of lordship, characterised by tightly linked service and conditional tenure, and rapidly influencing an array of other relationships such as the obligations of bishops or counts to the king, or of peasants to landlords. The word 'vassal' ( _vassus_ ), whatever its origins, simply became a replacement for the range of terms previously used to denote individuals bound into the service of the king. Its usage was spreading around 800, when landowners who might have spent part of their youth as servants or retainers in the royal household but who had subsequently returned to the countryside came systematically to be styled _vassi dominici_ , and to be seen as royal representatives in their localities. This is not to say that all _vassi_ held benefices: one commentator in 802 distinguished the 'poorer _vassi_ from within the palace' from their counterparts who held benefices in the countryside. The emergence of the _vassus_ was ultimately a way to prolong bonds formed in the royal household, and to use them to project a direct relationship between the king and local landowning communities; it thus fits with a series of other developments in these decades.
The high profile of benefices in our sources rests not on a direct link with royal service, but on the appetite of landowning elites for grants of royal and ecclesiastical land. A fragment of a register of royal rights in Rhaetia, high in the Alps, shows tiny bundles of royal land, some no more than large fields, granted out as benefices to well-placed sections of the local gentry, figures far too humble and distant from the world of court politics even to be referred to as _vassi dominici_ , or to owe any special service to the king. Although made in the king's name, these grants must normally have lain in the hands of counts and their subordinates. They helped to integrate landholders on this level into the political system by providing them with a particularly vital resource, because royal land transferred in this way was not passed on, and thereby fragmented, through inheritance. Those with access to the royal ear sought grants of benefices for their clients and retainers, as Einhard's letters, over a quarter of which involve such petitioning, vividly illustrate. The effective lord was one who could access the court to bid for the benefices and favours that helped to sustain his entourage. But in times of political upheaval benefices could be redistributed as a result of effective petitioning by one's enemies: for those on the fringes of aristocratic society, dependent on their relatives' goodwill and on a tiny benefice to keep them distinct from their less well-born neighbours, such changes of fortune could be disastrous. Hence the urgent need felt by families to hang onto benefices, evident in Hincmar of Rheims's account of the desperate struggle of the widow of Count Donatus of Melun to keep hold of a grant at Neuilly, or Einhard's description of an unnamed individual, who had been granted his father's benefice, though not his countship, as a recognition of his family name, but now was ill with gout, unable to do the emperor's bidding, and terrified of losing the estate which maintained his local standing. Disaster could be averted only by the strength of ties of lordship at all levels. The ability to perform loyal service was balanced by the lord's ability to reward loyalty: both were matters of honour; and both worked as much between lesser landowners and their immediate superiors as between the high aristocracy and the king.
At the top of society, the nobility looked to the king for patronage and offices, while kings depended heavily on the support of influential aristocrats to rule effectively. In the absence of formal state structures as we would understand them today, this was inevitable. As we have seen, the power of the secular nobility did not derive from the Carolingian kings, but was rooted in a complex interplay of inherited family status, tenure of land, and possession of royal offices. The importance of the latter warns us not to understand the relationship between aristocrats and kings as mutually antagonistic, engaged in a zero-sum game in which the goal was to wrest as much power from the other as possible. When aristocratic groups did rebel, in the ninth century they almost always sought to replace one member of the Carolingian family with another. Much of the political violence of the period, while it may have destabilised the regime of this or that individual ruler, thus often worked within the system rather than against it.
Aristocratic power was legitimised by association with royal power; and royal power needed that of the nobility to operate effectively. But no one put it like this at the time. Rather, the most widespread metaphor that the Frankish elite used to conceptualise their political role was that of consensus. The Lombard king Liutprand issued his periodic additions and revisions of the Lombard code 'with the common counsel of the people', 'with all the people assisting', and 'after reviewing all the titles of the earlier edicts with the judges and the rest of our Lombard _fideles_ [faithful men]'. Equally, the ideal Frankish king was one who took advice from 'the people' (which meant the males of the high nobility), so images of good kingship from the period highlighted horizontal bonds between ruler and ruling class: Einhard, for example, depicted Charlemagne as sharing baths in the hot springs at Aachen with up to a hundred courtiers and bodyguards at a time. Such apparently informal sociability was symbolic of good rulership: a king who relied too much on one group of advisers was a king who would encourage factionalism, discontent and strife.
This idea of consensus was not mere rhetoric: it was made real through the general assembly – a regular meeting with the king of those who mattered across the empire – supplemented with occasional regional gatherings of nobles with the ruler as he moved around his realm, and by meetings between the king and his inner circle of close advisers, many of whom would have been more or less permanent members of his entourage. This was, of course, very far from being a democratic system of government. However, the pressing need for the ruler to demonstrate that he was open to advice, and to keep on side as many of the powerful groups among the elite as possible, meant that there must have been some level of genuine consultation at these assemblies.
The discourse of consensus formed part of a relatively coherent set of ideas about the nature of the Carolingian political order and the position of the elite within it. An important capitulary issued by Louis the Pious c.825 conceives of the emperor's _ministerium_ , his 'ministry' of rulership over the chosen people entrusted to him by God, as a collaborative venture. The emperor does not delegate power from a position of autocracy, but shares the very substance of his _ministerium_ with the office-holders of the empire, in particular with bishops and counts. This formulation of joint (but still hierarchical) power and responsibility was rooted in scripture, and fed into the Franks' perception of themselves as a new Israel, the chosen people of the Old Testament. Furthermore, while this view of the _ministerium_ came to maturity as a keynote of royal ideology during the reign of Louis the Pious, it was based on ideas stretching back at least to Charlemagne's Admonitio generalis of 789; and it was echoed in later texts such as Charles the Bald's Treaty of Coulaines of 843. What we, looking in from outside, might describe as the mutual reliance of king and aristocracy, was to contemporaries wrapped up seamlessly into an ideology of elite participation in the running of the kingdom.
But we should not mistake this broad group identity as representing the absolute social or political solidarity of the ruling class. As we have seen in this chapter, the secular elite of the empire was by no means monolithic. A shared sense of social identity was important to the nobility, but it was cut across and modified by numerous other factors including gender, age and relative status. Nor did class consciousness ever translate into unity of political action. Even though the Carolingian period witnessed (as we saw in Chapter 5) a gradual increase in the affluence and social superiority of the wealthy, the aristocracy as a whole never acted as a single body in pursuit of distinct political aims. The political agendas of individuals were conditioned by specific and ever-changing circumstances, and animated by complex motives: the pursuit of _honores_ , the desire to save face in the eyes of one's peers and followers, a feeling of having been excluded from royal patronage or from access to the king's inner circle, or indeed opportunism and the quest for personal gain. These imperatives could very well contribute to political instability (as we saw in Chapter 4, the dishonouring of high-powered counts by Louis the Pious was probably what pushed the emperors' sons into rebellion in 830), but they did so not because 'the aristocracy' saw any advantage in encouraging political crisis. Indeed, as shown by the angst-ridden account of the crisis of 840-2 by the lay noble Nithard, quite the opposite.
The complex impact on aristocratic behaviour of the overlapping imperatives of individual ambition and collective identity can be illustrated by turning to a final contemporary scene which encapsulates many of the themes we have discussed in this chapter. A charter from December 839 recording a gift to the church of Freising in Bavaria provides a description of how the donor, Count Ratolt, made the gift in the courtyard of his house before a large entourage, 'while manfully girded with his sword'. The occasion seems to have been a gathering of part of the east Frankish army, participation in which was essential to aristocrats' sense of who they were. The imminent danger of the campaign, coupled with what we have learned about elite lay religiosity in the ninth century, means that we should not doubt the scribe's claim that the count's generosity was motivated by a desire to save his own soul. But in this vivid image we also catch a whiff of the supreme confidence of men like Ratolt in their right to be powerful and to dominate others. His sword, house and entourage distinguished him not just because they were expensive and visually impressive but because, as we have seen, they were symbols that marked him out as a member of the secular ruling class – they represented his 'manliness'. Aristocratic status could not just be assumed, it had to be performed; and the audience on this occasion comprised not just the count's own men, but also the soldiers of the county who were gathered to serve under him, together with other local worthies and indeed the bishop of Freising himself. But such men saw no contradiction between on the one hand considering themselves part of an elite charged with governing the empire, and on the other the pursuit of their own ambitions. The campaign which Ratolt was preparing to join was organised by his lord Louis the German against the emperor, Louis the Pious, and was therefore part of what was generally regarded as a rebellion against the correct political order. By participating in this campaign, Ratolt was endorsing his lord's breaking of solemn oaths which had guaranteed the existing dynastic settlement only months earlier, and gambling that success would lead to his own advancement as the young Louis became increasingly powerful and able to dispense more glittering prizes to those he favoured. But for all his 'manliness', wealth and self-confidence, as Ratolt followed his lord west into rebellion, and even as he looked on while the old emperor fell ill and died, leaving the realm in a state of turmoil, he would most assuredly have regarded himself above all as a servant of kings.
* * *
T. Reuter, 'The medieval nobility in twentieth-century historiography', in M. Bentley (ed.), _Companion to Historiography_ (London, 1997), pp. 177–202.
Cf. R. W. Southern, _The Making of the Middle Ages_ (London, 1953), p. 15.
The essays edited and translated by Reuter (ed.), _The Medieval Nobility_ offer a good taste of this stage of the debate; see T. N. Bisson, 'Nobility and family in France: a review essay', _French Historical Studies_ 16 (1990), pp. 597–613, for a discussion of the distinctive French traditions, rooted in regional history.
See W. Pohl, 'Telling the difference: signs of ethnic identity', in W. Pohl and H. Reimitz (eds.), _Strategies of Distinction. The Construction of Ethnic Communities, 300–800_. Transformation of the Roman World 2 (Leiden, 1998), pp. 17–69.
This insight owes much to recent work by Christina Pössel: C. Pössel, 'Authors and recipients'. _Aristocratic identity_
Reuter (ed.), _The Medieval Nobility_ , pp. 1–16; H.-W. Goetz, '"Nobilis". Der Adel im SelbstverstNndnis der Karolingerzeit', _Vierteljahresschrift für Sozial-und Wirtschaftsgeschichte_ 70 (1983), pp. 153–91; T. Reuter, 'Nobles and others: the social and cultural expression of power relations in the Middle Ages', in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 111–26.
For these relative values, see Innes, _State and Society_ , pp. 83–4.
Thegan, _Gesta Hludovici_ , c. 20, trans. Dutton, _Carolingian Civilization_ , pp. 165–6.
S. Airlie, 'The aristocracy', in _NCMH_ II, pp. 431–50, esp. pp. 448–50 for the different layers within the aristocracy.
P. Garnsey, _Social Status and Legal Privilege in the Roman Empire_ (Oxford, 1970); M. L. Bush, _Rich Noble, Poor Noble_ (Manchester, 1988), pp. 30–42; S. Clark, _State and Status. The Rise of the State and Aristocratic Power in Western Europe_ (Toronto, 1995), pp. 129–54. See also above, Chapter 5, pp. 242–3.
Nithard, _Historiarum Libri IV_ , II.3, trans. Scholz, _Carolingian Chronicles_ , p. 144; see also Thegan, _Gesta Hludowici imperatoris_ , c. 44, pp. 232–8, trans. Dutton, _Carolingian Civilization_ , pp. 170–3, and _AF, s.a_. 887; this point is noted by J. L. Nelson, 'Public _Histories_ and private history in the work of Nithard', _Speculum_ 50 (1985), pp. 251–93, at p. 272, repr. in Nelson, _Politics and Ritual in Early Medieval Europe_ (London, 1986), pp. 195–237.
_EHD_ no. 198; Alcuin, _Ep_. 101, pp. 146–7.
Abbo of St-Germain-des-Prés, _Bella Parisiacae urbis_ , ed. H. Waquet, _Abbon. Le Siège de Paris par les Normands_ (Paris, 1942), pp. 30–1, ll. 184–5: 'Efficitur servus liber, liber quoque servus / Vermaque fit dominus, contra dominos quoque verma.' This text is translated by N. Dass, _Viking Attacks on Paris_ (Dudley, MA, 2007).
See Capitulary for Aachen, 802–3, _Capit_. I, no. 77, c. 12, p. 171, trans. Loyn and Percival, _The Reign of Charlemagne_ , pp. 82–4.
_LHF_ , c. 43, trans. Fouracre and Gerberding, _Late Merovingian France_ , p. 88. The context is royal-aristocratic politics, but the comment is offered as stating a matter of principle.
AB, _s.a_. 859, p. 80, trans. Nelson, p. 89.
De Jong, 'Power and humility'; and see above, Chapter 4, pp. 218–19.
_AB, s.a_. 873, p. 191; on the events of 873, see J. L. Nelson, 'A tale of two princes: politics, text and ideology in a Carolingian annal', _Studies in Medieval and Renaissance History_ 10 (1988), pp. 103–40, repr. in Nelson, _Rulers and Ruling Families in Early Medieval Europe: Alfred, Charles the Bald and Others_ (Aldershot, 1999), and S. MacLean, 'Ritual, misunderstanding and the contest for meaning: representations of the disrupted royal assembly at Frankfurt (873)', in B. Weiler and S. MacLean (eds.), _Representations of Power in Medieval Germany_ (Turnhout, 2006), pp. 97–120.
Astronomer, _Vita Hludowici imperatoris_ , c. 45.
K. Leyser, 'Early medieval canon law and the beginning of knighthood', in K. Leyser (ed. T. Reuter), _Communications and Power in Medieval Europe. The Carolingian and Ottonian Centuries_ (London and Rio Grande, OH, 1984), pp. 51–71; M. de Jong, 'What was public about public penance? _Poenitentia publica_ and justice in the Carolingian world', _La giustizia nell'alto medioevo (secoli ix–xi), Settimane_ 44 (Spoleto, 1997), pp. 863–902.
Notker, _Gesta_ 2.21. For Malles Venosta, see J. Beckwith, _Early Medieval Art_ (London, 1969), p. 26.
_ARF, s.a_. 799, trans. Scholz, _Carolingian Chronicles_ , p. 78; P. Geary, 'Germanic tradition and royal ideology in the ninth century: the _visio Karoli Magni', Frühmittelalterliche Studien_ 21 (1987), pp. 274–94, repr. in Geary, _Living with the Dead in the Early Middle Ages_ (Ithaca, NY, and London, 1994), pp. 49–76, at pp. 67-71.
See e.g. Charlemagne's _Capitulare Aquisgranense_ [Capitulary for Aachen], _a.802–3, Capit_. i, no. 77, c. 9; _Duplex capitulare missorum in Theodonis villa datum_ [Double capitulary of Thionville for the _missi_ ], _a.805, Capit_. i, no. 44, c. 6, both trans. Dutton, _Carolingian Civilization_ , pp. 80, 83.
_Leges Ahistulfi_ , cc. 2–3; see also _Leges Ratchis_ Laws of Ratchis], ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ ([Weimar, 1947; repr. Witzenhausen, 1962), pp. 194–204, c. 4, both trans. Fischer-Drew, _The Lombard Laws_.
AF, _s.a_. 885, p. 98; S. MacLean, _Kingship and Politics in the Late Ninth Century: Charles the Fat and the End of the Carolingian Empire_ (Cambridge, 2003), p. 151; R. Le Jan, 'Frankish giving of arms and rituals of power: continuity and change in the Carolingian period', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 281–309, at pp. 286–7.
Paschasius, _Epitaphium Arsenii Life of Wala]_ , i.6; Leyser, 'Early medieval canon law', p. 57; M. Innes, '"A place of discipline": Carolingian courts and aristocratic youth', in C. Cubitt (ed.), _Court Culture in the Early Middle Ages_ ([Turnhout, 2003), pp. 59–76.
Le Jan, 'Frankish giving of arms', pp. 298–9.
Astronomer, _Vita Hludowici imperatoris_ , c. 6; Leyser, 'Early medieval canon law', p. 56.
Einhard, _VK_ , c. 19, trans. Dutton, _Charlemagne's Courtier_ , p. 28.
Le Jan, 'Frankish giving of arms', pp. 284–5; Dutton, _Charlemagne's Mustache_ , pp. 39–41.
Einhard, VK, c. 26, trans. Dutton, _Charlemagne's Courtier_ , p. 33; J. L. Nelson, 'Was Charlemagne's court a courtly society?', in C. Cubitt (ed.), _Court Culture in the Earlier Middle Ages_ (Turnhout, 2003), pp. 39–57, at p. 47.
J. L. Nelson, 'Ninth-century knighthood: the evidence of Nithard', in C. Harper-Bill, C. Holdsworth and J. L. Nelson (eds.), _Studies in Medieval History Presented to R. Allen Brown_ (Woodbridge, 1989), pp. 255–66, repr. in Nelson, _Frankish World_ , pp. 75–87, pp. 85–7.
Einhard, VK, c. 23, trans. Dutton, _Charlemagne's Courtier_ , p. 31; Notker, _Gesta_ , 1.34, trans. Ganz, p. 84.
P. Riché, _Daily Life in the World of Charlemagne_ , trans. J. A. McNamara (Liverpool, 1978), pp. 162–3.
Theodulf, _Carmina_ 17, ed. Dümmler, p. 472; Riché, _Daily Life_ , pp. 161–2.
Ermold, _In honorem Hludowici_ , p. 212. Cf. Notker, _Gesta_ , 2.14 for kings disapproving of fancy clothing.
Astronomer, _Vita Hludowici imperatoris_ , c. 4.2. See Innes, 'Land, freedom'.
_LP_ i, p. 495, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 137.
For these expressions see R. Fleming, 'Lords and labour', in W. Davies (ed.), _From the Vikings to the Normans_ (Oxford, 2003), pp. 107–37.
P. Schramm and F. Mütherich, _Denkmale der deutschen Könige und Kaiser_ , 2nd edn (Munich, 1981), pp. 93–4 (Eberhard's will); Prou and Vidier (eds.), _Receuil_... _Saint-Benoît-sur-Loire_ i, p. 64 (Eccard's will). C. La Roccaand L. Provero, 'The dead and their gifts. The will of Eberhard, count of Friuli, and his wife Gisela, daughter of Louis the Pious (863–864)', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 225–80, at p. 250.
La Rocca and Provero, 'The dead and their gifts', pp. 251–3; see J. L. Nelson, 'Carolingian royal ritual', in D. Cannadine and S. Price (eds.), _Rituals of Royalty. Power and Ceremonial in Traditional Societies_ (Cambridge, 1987), pp. 137–80, pp. 166–72 on royal feasts, and p. 174 for the food consumed at a royal commemoration at St Denis.
Notker, _Gesta_ , 1.16, trans. Ganz, pp. 66–7.
Reuter, 'Nobles and others', pp. 116–17.
Ermold, _In honorem Hludowici_ , pp. 219–21; _LHF_ , c. 4,8 trans. Fouracre and Gerberding, _Late Merovingian France_ , p. 92.
See below, Chapter 7, pp. 332–6.
On defensibility, R. Samson, 'The Merovingian nobleman's house: castle or villa', _Journal of Medieval History_ 13 (1987), pp. 287–315 is key. On family centres see Airlie, 'The aristocracy' in _NCMH_ II, p. 436.
Notker, _Gesta_ , 2.17, trans. Ganz, pp. 110–11. Wickham, _Framing the Early Middle Ages_ , pp. 201–2, notes that moveables were used to set apart aristocratic households.
M. Hardt, _Gold und Herrschaft: die Schätze europäischer Könige und Fürsten im ersten Jahrtausend_ (Berlin, 2004).
Innes, 'Practices of property', pp. 246–66; Wickham, _Framing the Early Middle Ages_ , pp. 208–13.
_UBF_ 177 (Hraban) and see also _UBF_ 2 (gold and horses) and _CL_ 1966–7, 1969–72, 1974. St Lambert's has been analysed well by M. Gockel, _Karolingische Königshöfe am Mittelrhein_ (Göttingen, 1970), pp. 238–58, and is discussed briefly in Innes 'People, places and power', pp. 397–437, at p. 409.
See L. Falck, _Mainz im frühen und hohen Mittelalter (Mitte 5. Jht. bis 1244_ ) (Düsseldorf, 1972). For Count Raho of Orléans, see Adrevald of Fleury, _Miracula Sancti Benedicti_ , ed. O. Holder-Egger, _MGH SS_ xv, pp. 474–97, at pp. 486–7.
For Italian cities in this period, see Wickham, _Framing the Early Middle Ages_ , pp. 644–56.
Cf. K. Böhner, 'Urban and rural settlement in the Frankish kingdom', in M. W. Barley (ed.), _European Towns: Their Archaeology and Early History_ (London, 1977), pp. 185–207.
S. Wood, _The Proprietary Church in the Early Medieval West_ (Oxford, 2006), pp. 16–32, 67–79. See also above, Chapter 5, pp. 239–41.
R. Le Jan, 'Convents, violence, and competition for power in seventh-century Francia', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 243–69.
K. Böhner, _Das Grab eines fränkischen Herren aus Morken im Rheinland_ (Cologne, 1959); H. W. Böhme, _Germanische Grabfunde des 4. und 5. Jahrhunderts zwischen Elbe und Loire_. 2 vols. (Munich, 1974).
Le Jan, 'Convents, violence, and competition for power'.
K. Bowes, 'Early Christian archaeology: a state of the field', _Religion Compass_ 2/4 (2008), pp. 575–619; E. James, _The Merovingian Archaeology of South-West Gaul_. BAR supplementary series, 25 (Oxford, 1977); G. P. Fehring, _The Archaeology of Medieval Germany: an Introduction_ , trans. R. Samson (London, 1991).
De Jong, 'Carolingian monasticism'; Brown, _Rise of Western Christendom_ , pp. 219– 24.
J. M. H. Smith, 'The problem of female sanctity in Carolingian Europe c.750– 920', _P &P_ 146 (1995), pp. 3–37; M. Innes, 'Keeping it in the family: women and aristocratic memory c.700–1200', in E. van Houts (ed.), _Medieval Memories: Men, Women and the Past 700–1300_ (London, 2001), pp. 17–35.
On oblation, see M. de Jong, _In Samuel's Image. Child Oblation in the Early Medieval West_ (Leiden and New York, 1996).
See Damminger, 'Dwellings, settlements and settlement patterns', pp. 33–88; Stork, 'Zum Fortgang der Untersuchungen'.
Innes, _State and Society_ , p. 67, n. 49.
G. Tessier, _et al_. (eds.), _Recueil des actes_ , no. 274. On Petegem see C. Loveluck, 'Rural settlement hierarchy in the age of Charlemagne', in Story (ed.), _Charlemagne_ , pp. 230–58, at pp. 237–8, 250; D. Callebaut, 'Résidences fortifiées et centres administratifs dans la vallée de l'Escaut (ixe–xie siècle)', in D. Demolon, H. Galinié and F. Verhaeghe (eds.), _Archéologie des villes dans le Nord-Ouest de l'Europe ( VIIe–VIIIe siècle_) (Douai, 1994), pp. 93–112, at pp. 95–7.
See above, Chapter 4, pp. 175–6.
_Edictum Pistense_ [Edict of Pîtres], ed. V. Krause, _Capit_. II, no. 273, p. 328; for the archaeology see Loveluck, 'Rural settlement', pp. 239–40.
E.g. _AF, s.a_. 880, trans. Reuter, p. 90; _AV, s.a_. 885, trans. Dutton, p. 510.
At Petegem, the stone hall complex closely resembles those described in polyptychs serving royal estates, as noted by Loveluck, 'Rural settlement', pp. 237–9.
The following sentences are heavily indebted to de Jong, 'Charlemagne's balcony'.
See e.g. Notker, _Gesta_ , 1.30; _Brevium exempla_ , trans. Dutton, _Carolingian Civilization_ , pp. 85–7.
_ARF, s.a_. 817, trans. Scholz, p. 102, AF, _s.a_. 870, trans. Reuter, p. 62.
For Leidrad of Lyon's royal house, see Leidrad, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. iv ( _Epp. Karolini aevi_ ii) (Berlin, 1895), pp. 542–4, _Epistola ad Carolum_ , no. 30. For the Lorsch gatehouse see W. Jacobsen, 'Die Lorscher Torhalle. Zum Problem ihrer Deutung und Datierung', _Jahrbuch des Zentralinstituts für Kunstgeschichte_ 1 (1985), pp. 9–77; Innes, 'Kings, monks and patrons'. See also Figure 4a in Chapter 3 above.
_Contra_ Innes, 'People, places and power', assuming that it points to protocastles/ fortifications.
Loveluck, 'Rural settlement', p. 238; J. Witwrouw, 'Le Centre domanial du haut moyen âge du Thier d'Olne à Engis/Hermalle-sous-Huy', _Bulletin de Liaison de l'Association Française d'Archéologie Mérovingienne_ 23 (1999), pp. 105–8.
For this and other examples, see S. Airlie, _The Political Behaviour of Secular Magnates in Francia, 829–79_ , unpublished D. Phil. thesis, University of Oxford (1985); Airlie, 'The palace of memory'.
Airlie, 'Palace of memory'; Airlie, 'Bonds of power and bonds of association in the court circle of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 191–204. See Einhard, _Translation and Miracles_ , IV.7, trans. Dutton, _Charlemagne's Courtier_ , pp. 115–17, for an example of a royal official stopping off at a royal villa.
Airlie, _Political Behaviour_ , p. 198; MacLean, _Kingship and Politics_ , pp. 89–90, 94–6.
Nelson, 'Aachen as a place of power'; D. A. Bullough, 'Urban change in early medieval Italy: the example of Pavia', _PBSR_ 34 (1966), pp. 82–130.
Hincmar, _De ordine palatii_ , c. 27, trans. Dutton, _Carolingian Civilization_ , p. 527.
See e.g. Einhard, _Translation and Miracles_ , I.1, trans. Dutton, _Charlemagne's Courtier_ , p. 70.
For this paragraph see Innes, 'A place of discipline'; Le Jan, 'Frankish giving of arms', pp. 282–5.
Desiderius of Cahors, _Epistolae_ , ed. W. Arndt, _MGH Epp_. iii ( _Epistolae Merovingici et Karolini aevi_ i) (Berlin, 1892), pp. 191–214.
Einhard, _VK_ , c. 22, trans. Dutton, _Charlemagne's Courtier_ , p. 30. Note also Hraban Maur's abridgement of the late Roman military manual by Vegetius, and his comments there on the importance of hunting as training for warfare: see Goldberg, _Struggle for Empire_ , pp. 39–42.
Nelson, 'Carolingian royal ritual'.
_AB, s.a_. 864, p. 105, trans. Nelson, pp. 111–12; Regino, _Chronicle, s.a_. 870.
Nithard, _Historiarum Libri IV_ , III.6, trans. Scholz, _Carolingian Chronicles_ , p. 164.
P. Stafford, 'Parents and children in the early middle ages', _EME_ 10 (2001), pp. 257–71.
Einhard, _Ep_. 62, trans. Dutton, _Charlemagne's Courtier_ , p. 159; see also Innes, 'Practices of property', pp. 259–62; cf. T. Charles-Edwards, 'The distinction between land and moveable wealth in Anglo-Saxon England', in P. H. Sawyer (ed.), _Medieval Settlement: Continuity and Change_ (London, 1976), pp. 180–7.
Notker, _Gesta_ , 2.8, trans. Ganz, pp. 93–4; see MacLean, _Kingship and Politics_ , pp. 87–8, 217; M. Innes, 'Memory, orality and literacy in an early medieval society', _P &P_ 158 (1998), pp. 3–36.
Airlie, 'The aristocracy in the service of the state'.
Thegan, _Gesta Hludovici imperatoris_ , cc. 28, 55, trans. Dutton, _Carolingian Civilization_ , pp. 167, 175. On this story see Innes, 'He never even allowed his white teeth to be bared in laughter', at p. 153.
See above, Chapter 4, p. 188.
E. Goldberg, '"More devoted to the equipment of battle than the splendor of banquets": frontier kingship, martial ritual, and early knighthood at the court of Louis the German', _Viator_ 30 (1999), pp. 41–78, esp. pp. 45–50.
Dhuoda, _Liber manualis_ , iii.9, ed. and trans. Thiébaux, pp. 106–9; Innes, 'A place of discipline', p. 68.
Notker, _Gesta_ , 2.10, trans. Ganz, p. 98.
J. M. H. Smith, 'Genderand ideology in the early Middle Ages', in R. N. Swanson (ed.), _Gender and Christian Religion, Studies in Church History_ 14 (Woodbridge, 1998), pp. 51-73, at p. 61.
Garrison, 'The Franks as the new Israel?'.
_Epistolae variorum Karolo regnante_ , ed. E. Dümmler, _MGH Epp_. iv ( _Epp. Karolini aevi_ 11) (Berlin, 1895), no. 20, pp. 528-9, trans. King, _Charlemagne: Translated Sources_ , pp. 309-10. 300 _Elite society_
J. L. Nelson, 'Violence in the Carolingian world and the ritualization of ninthcentury warfare', in G. Halsall (ed.), _Violence and Society in the Early Medieval West_ (Woodbridge, 1998), pp. 90–107; D. S. Bachrach, _Religion and the Conduct of War, c.300–c.1215_ (Woodbridge, 2003).
John VIII, _Epistolae_ , ed. E. Caspar, _MGH Epp_. vii ( _Epp. Karolini aevi_ v) (Berlin, 1928), nos. 41, 217, 246, pp. 39, 194, 214.
See Paulinus of Aquileia, _Liber Exhortationis ad Hericum Comitem_ , PL ic, cols. 197–282. On these tracts, see S. Airlie, 'The anxiety of sanctity: St Gerald of Aurillac and his maker', _Journal of Ecclesiastical History_ 43 (1992), pp. 372–95; Smith, 'Gender and ideology', esp. pp. 60–5; H. H. Anton, _Fürstenspiegel und Herrscherethos in der Karolingerzeit_ , Bonner Historische Forschungen 32 (Bonn, 1968); R. Stone, 'Kings are different: Carolingian mirrors for princes and lay morality', in F. Lachaud and L. Scordia (eds.), _Le Prince au miroir de la litteérature politique de l'Antiquité aux Lumières_ (Rouen, 2007), pp. 69–86; T. F. X. Noble, 'Secular sanctity: forging an ethos for the Carolingian nobility', in Wormald and Nelson (eds.), _Lay Intellectuals_ , pp. 8–36.
Alcuin, _De virtutibus et vitiis liber_ , PL ci, cols. 613–38.
Jonas, _De institutione laicorum_ , PL cvi, cols. 121–278.
On the transmission of Alcuin, see D. Bullough, _Alcuin: Achievement and Reputation_ (Leiden, 2003); P. Szarmach, 'A preliminary handlist of manuscripts containing Alcuin's _Liber de virtutibus et vitiis'_ , _Manuscripta_ 25 (1981), pp. 131–40; on Jonas, see Schröder, 'Überlieferung'. On Eberhard see Kershaw, 'Eberhard of Friuli.
See J. M. H. Smith, 'Einhard: the sinner and the saints', _TRHS_ 6th ser. 13 (2003), pp. 55–77.
J. L. Nelson, 'Monks, secular men and masculinity, c. 900', in D. M. Hadley (ed.), _Masculinity in Medieval Europe_ (London, 1999), pp. 121–42.
De Jong, _In Samuel's Image_.
McKitterick, _The Carolingians and the Written Word_ , pp. 211–70.
Einhard, VK, cc. 24–5, trans. Dutton, _Charlemagne's Courtier_ , pp. 31–2; Dutton, _Charlemagne's Mustache_ , pp. 69–92.
See McKitterick, _The Carolingians and the Written Word_ , pp. 245–50; Kershaw, 'Eberhard of Friuli'.
Garrison, 'The emergence of Carolingian Latin literature'; M. de Jong, 'The empire as _ecclesia:_ Hrabanus Maurus and biblical _historia_ for rulers', in Hen and Innes (eds.), _The Uses of the Past_ , pp. 191–226.
Nithard, _Histories_ , iii, 5, trans. Scholz, pp. 162–3.
See R. Wright, _A Sociophilological Study of Late Latin_ (Turnhout, 2002), pp. 177– 90.
Werner, 'Important noble families'; for problems with the methodology see Airlie, 'The aristocracy', in _NCMH_ ii, pp. 437–8.
Airlie, ' _Semper fideles_?'.
La Rocca and Provero, 'The dead and their gifts', pp. 245–9.
E. Hlawitschka, _Franken, Alemannen, Bayern und Burgunder in Oberitalien (774– 962). Zum Verständnis der fränkischen Königsherrschaft in Italien_ (Freiburg, 1960), pp. 299–309 (on the Supponids); MacLean, 'Queenship, nunneries', pp. 26–32 (on Engelberga and the Supponids).
Thegan, _Gesta Hludovici imperatoris_ , c. 1, p. 174, trans. Dutton, _Carolingian Civilization_ , p. 159; see Fouracre, _Charles Martel_ , pp. 33–4, 41–4.
Reuter, 'Medieval nobility'; Airlie, 'The aristocracy', in _NCMH_ ii, pp. 433–40; G. Constable, 'The _Liber memorialis_ of Remiremont', _Speculum_ 48 (1972), pp. 260–77; H. Fichtenau, _Living in the Tenth Century_ (Chicago, 1991), pp. 85–6.
K. F. Werner, 'Untersuchungen zur Frühzeit des franzözischen Fürstentums', _Die Welt als Geschichte_ 3–4 (1959), pp. 146–93; Nelson, _Charles the Bald_ , pp. 130–1; Airlie, 'The aristocracy', in _NCMH_ 11, p. 435.
_AV, s.a_. 888; S. Airlie, 'Review article: After empire. Recent work on the emergence of post-Carolingian kingdoms', _EME_ 2 (1993), pp. 153–61.
Dhuoda, _Liber manualis_ , viii.14, ed. and trans. Thiébaux, pp. 204–5; Innes, 'Keeping it in the family'. On inheritance see also above, Chapter 5, pp. 243–5.
Costambeys, _Power and Patronage_ , pp. 209–11.
_AF, s.a_. 883, trans. Reuter, p. 95.
This useful distinction comes from P. Bourdieu, _Outline of a Theory of Practice_ , trans. R. Nice (Cambridge, 1977), pp. 33–8.
R. Le Jan, 'Structures familiales et politiques au ixe siècle: un groupe familial de l' aristocratie franque', _Revue historique_ 265 (1981), pp. 289–333; Le Jan, _Famille et pouvoir dans le mondefranc, VIIIe–Xe siècles_ (Paris, 1995), pp. 162–3. See Einhard, VK, c. 18; Thegan, _Gesta Hludowici imperatoris_ , cc. 1–2, trans. Dutton, _Carolingian Civilization_ , pp. 159–60.
A. C. Murray, _'Pax et disciplina_. Roman public law and the Merovingian state', in K. Pennington, S. Chodorow and K. H. Kendall (eds.), _Proceedings of the Tenth International Congress of Medieval Canon Law_ (Vatican City, 2001), pp. 269–85, repr. in T. F. X. Noble (ed.), _From Roman Provinces to Medieval Kingdoms_ (New York and Abingdon, 2006), pp. 376–88.
U. Nonn, 'Merowingische Testamente', _Archiv für Diplomatik_ 18 (1972), pp. 1– 129; Geary, _Aristocracy in Provence_.
Eccard's will: Prou and Vidier (eds.), _Recueil Saint-Benoît-sur-Loire_ I, no. 25, pp. 59–67; Ercanfrida's will: J. L. Nelson, 'The wary widow', in W. Davies and P. Fouracre (eds.), _Property and Power in the Early Middle Ages_ (Cambridge, 1995), pp. 82–113.
For differing interpretations of Karol's family's position, compare Feller, Gramain and Weber, _La Fortune de Karol_ , pp. 93–115, with P. Cammarosano, 'Marché de la terre et mobilité sociale dans les Abruzzes aux IXe–XIe siécles. À propos d'un livre récent', _Revue Historique_ 310/2 (2008), pp. 369–82.
Innes, 'Dossiers and archives'. For the well-documented example of the family of Toto of Campione, see Gasparri and La Rocca (eds.), _Carte di famiglia_.
Geary, _Phantoms of Remembrance_ , pp. 48–80; Innes, 'Keeping it in the family'.
MacLean, 'Queenship, nunneries', pp. 20–6.
M. Costambeys, 'Kinship, gender and property in Lombard Italy', in G. Ausenda, P. Delogu and C. Wickham (eds.), _The Langobards before the Frankish Conquest. An Ethnographic Perspective_ (Woodbridge, 2009), pp. 69–94; see also Smith, _Europe after Rome_ , pp. 121–2, 141–2; C. La Rocca, 'Pouvoirs des femmes, pouvoirs de la loi dans l' Italie lombarde', in S. Lebecq, A. Dierkens, R. Le Jan and J.-M. Sansterre (eds.), _Femmes et pouvoirs des femmes à Byzance et en Occident ( VIIe–XIe siècles_) (Villeneuve-d' Ascq, 1999), pp. 37–50.
Innes, _State and Society_ , pp. 56, 180–2.
Bitterauf (ed.), _Traditionen_ , no. 313.
Nelson, _Charles the Bald_ , pp. 248–9.
Airlie, 'The aristocracy' in _NCMH_ II, p. 444.
Innes, _State and Society_ , pp. 180–95.
Hincmar, _De ordinepalatii_ , c. 37, trans. Dutton, _Carolingian Civilization_ , p. 532.
Dhuoda, _Liber manualis_ , VIII.14–15, trans. Thiébaux, pp. 204–7; on this discourse see Innes, 'Practices of property', p. 252, and note that Nithard, _Historiarum Libri IV_ , iii, 2, trans. Scholz, p. 156, shows William was successful in mobilising this argument.
AB, _s.a_. 868, trans. Nelson, pp. 143–4.
AF, _s.a_. 861; Goldberg, _Struggle for Empire_ , pp. 267–9.
AB, _s.a_. 864, 866, trans. Nelson, pp. 119, 131; see Nelson, _Charles the Bald_ , pp. 211–12.
See AB, _s.a_. 839, trans. Nelson p. 45, for 'honores consisting of benefices'.
Thegan, _Gesta Hludowici imperatoris_ , _c_. 10 notes the resumption, also evident in the charters. F. L. Ganshof, 'Note sur la concession d'alleux à des vassaux sous le règne de Louis le Pieux', in _Storiografia e Storia: Studi in onore di E. Dupré Theseider_ (Rome, 1974), pp. 589–99 and D. Gladiß, 'Die Schenkungen der deutschen Könige zu privaten Eigen (800–1137), _DA_ 1 (1937), pp. 80–136, give lists. This practice and its use also deserve a special study: for a model contextualisation of its effects in one _regnum_ , J. Martindale, 'The kingdom of Aquitaine and the dissolution of the Carolingian fisc', _Francia_ 11 (1985), pp. 131–91.
G. Constable, _'Nona et decima:_ an aspect of the Carolingian economy', _Speculum_ 35 (1960), pp. 224–50, usefully surveys this. On _precaria_ and their fate, see Hummer, _Politics and Power_ , pp. 76–104.
On _vassi_ , see W. Kienast, _Das fränkische Vassalität von den Hausmaiern bis zu Ludwig dem Kind und Karl dem Einfältigen_ (Frankfurt, 1990), though note that the framework is anachronistic.
See Reynolds, _Fiefs and Vassals_.
Le Jan, _Famille et pouvoir_ , pp. 142–3 and 148–9.
AL, _s.a_. 802, trans. King, _Charlemagne: Translated Sources_ , pp. 144–5.
On this see Innes, 'Charlemagne's government', and Chapter 4 above.
E. Mayer-Marthaler and F. Perret (eds.), _Bündner Urkundenbuch_ I (Chur, 1955), Anhang 1, pp. 375–96.
On Neuilly, see Hincmar of Rheims, _De villa Noviliaco_ , ed. H. Mordek, 'Ein exemplarischer Rechtsstreit: Hinkmar von Reims und das Landgut Neuilly-Saint-Front', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Kanonistische_ _Abteilung_ 83 (1997), pp. 86–112 at pp. 100–7; for Einhard, see Einhard, _Epp_. 27–8, trans. Dutton, _Charlemagne's Courtier_ , p. 141; Innes, 'Practices of property', pp. 259–62 for discussion.
_Leges Liutprandi_ , pp. 99–182, prologues to the laws of the First Year, the Eighth Year and the Ninth Year, trans. Fischer-Drew, _The Lombard Laws_ , pp. 146, 150, 153.
Einhard, VK, c. 22, trans. Dutton, _Charlemagne's Courtier_ , p. 31.
Hincmar, _De ordine palatii_ , c. 30, trans. Dutton, _Carolingian Civilization_ , p. 528. See above, Chapter 4, pp. 172–5.
See J. L. Nelson, 'Legislation and consensus in the reign of Charles the Bald', in Wormald, Bullough and Collins (eds.), _Ideal and Reality_ , pp. 202–27 repr. in Nelson, _Politics and Ritual in Early Medieval Europe_ (London, 1985); J. L. Nelson, 'Kingship and empire in the Carolingian world', in McKitterick (ed.), _Carolingian Culture_ , pp. 52–87; Pössel, 'Authors and recipients'; McKitterick, _Charlemagne: The Formation of a European Identity_ , pp. 222–33; de Jong, _Penitential State_ , Chapter 3.
O. Guillot, 'Une "ordinatio" méconnue'. See above, Chapter 4, pp. 187–8.
See Noble, 'From brigandage to justice', pp. 49–75 on the _Admonitio generalis;_ on Coulaines, see J. L. Nelson, 'The intellectual in politics: contexts, content and authorship in the Capitulary of Coulaines, November 843', in L. Smith and B. Ward (eds.), _Intellectual Life in the Middle Ages: Essays Presented to Margaret Gibson_ (London, 1992), pp. 1–14, repr. in Nelson, _Frankish World_ , pp. 155–68; Nelson, _Charles the Bald_ , pp. 138–9.
Nelson, 'Public _Histories_ '.
Bitterauf (ed.), _Die Traditionen_ , no. 634; Goldberg, _Struggle for Empire_ , pp. 92–3 (on whose interpretation this paragraph is based).
## 7
### EXCHANGE AND TRADE: THE CAROLINGIAN ECONOMY
#### INTRODUCTION: INTERPRETING THE CAROLINGIAN ECONOMY
Around 890, a team of scholars at the court of the Anglo-Saxon king Alfred the Great undertook the translation of the fifth-century Latin world history of Orosius into the written version of their vernacular Old English language. Orosius's work, with its story of barbarian invasions and Christian triumph, had an obvious message for readers in Viking-age England, and Alfred's team translated freely: as a result, when they came across Orosius's lengthy geographical descriptions of Europe, they updated his very classical picture of northern and eastern Europe to reflect contemporary realities. The detailed account of the different peoples and groupings of the Baltic and southern Scandinavia led into a series of digressions, recounting the tales told to King Alfred by two travellers in the north, Ohthere and Wulfstan. Ohthere claimed to Alfred that 'he lived the furthest north of all Northmen', and gave an account of his exploration around the modern Norwegian coast as far as Lapland and the White Sea. Ohthere's accounts of various groupings of _Beormas, Cwenas, Finnas_ and _Norðmanna_ distinguish them not in terms of ethnic origin but in terms of their land and their economy. The lands of the _Finnas_ , for example, were described as 'waste', that is lacking agriculture, animal husbandry or permanent settlement: they were seasonal hunters, in contrast to the _Beormas_ , whose territory was 'fully settled'.
But the scribe recording Ohthere's tale-telling was not solely interested in ethnographic and geographical detail: he focussed also on wealth and its exchange. Hence the almost palpable interest of the audience as they heard an account of riches rooted not in property rights over land and labour, but in control of livestock, some tame but most wild, and the collection of tribute: Ohthere told how he was 'a very rich man in those objects which their riches consist of, that is wild deer... he was among the first men of his land, but he had not more than twenty cattle, twenty sheep and twenty pigs, and little that he ploughed with horses'. The wealth of Ohthere's people, we are told, lay 'mostly in the tribute ( _gafol_ ) that the _Finnas_ pay them', which was carefully graded, with each different rank among the _Finnas_ making specific gifts of animal skins, bird feathers and whale bones. These were destined to be exchanged, for Ohthere's account of his wealth and his relations with the neighbouring peoples naturally flowed into an account of a voyage down the Norwegian coast to the trading town ( _port_ ) of Kaupang, and thence to Hedeby at the base of the Jutland peninsula, the nodal point of the trading routes of southern Scandinavia. From Ohthere's account of the trip to Hedeby, the scribe moved seamlessly on to an analogous account of the voyage of Wulfstan east from Hedeby to Truso, a major centre for exchange in the Baltic. Wulfstan's observation of the coastline and islands of the Baltic is enlivened by discussion of the customs of the peoples he encountered: the drinking habits, funeral rites and magical abilities of the _Este_.
Travellers' tales like those of Ohthere and Wulfstan have an obvious attraction and their survival reflects contemporary fascination with difference: by talking about the exotic practices of distant societies in the far north, where wealth could not be measured in familiar terms of landownership, and the dead were commemorated by drinking and games funded from their property, these stories defined the aristocratic Christian culture of the early medieval west against the otherness of its neighbours. But the adventures they describe also yield important insights into mechanisms of exchange. In this respect the accounts' omissions are as striking as the details carefully recounted. Both Ohthere's and Wulfstan's itineraries were situated in regard to Hedeby: the routes joining Hedeby to the coasts of northwestern Europe and England did not need rehearsing, and Hedeby itself required no introduction. Despite their exoticism, Wulfstan's and Ohthere's accounts were therefore predicated on a body of common knowledge and a shared mental geography that implied routine seaborne contact between the societies around the North Sea. Ohthere, indeed, could refer without hesitation to Alfred as his lord ( _hlaford_ ), and knew implicitly what gifts were appropriate to bring to his court.
'Dark Age Argonauts' like Ohthere and Wulfstan are frustratingly rare figures in the surviving record. The backdrop to their expeditions – the networks of exchange and communications around the North Sea glimpsed in the shadows of their accounts – has been fleshed out only in recent decades thanks to a dramatic increase in archaeological data, beginning at Hedeby in the 1930s but flowering in the 1960s and 1970s as the redevelopment of northern Europe's cities unearthed long inaccessible sites. This has revealed a well-established network of contacts between England, Francia and southern Scandinavia, and thus transformed our understanding of the economy of eighth- and ninth-century Europe. As this material first began to be synthesised in the 1980s, inherited views of the early medieval economy underwent the first stages of a sustained revision.
The beginnings of this process of rethinking primarily took the form of a dialogue with the work of the early-twentieth-century Belgian historian Henri Pirenne, and particularly his posthumously published masterpiece, _Mohammed and Charlemagne_. Pirenne argued that the long-distance trade networks which had long bound together the Mediterranean world survived the collapse of Roman power in the fifth-century west, only to fall victim to the rise of Islam, which meant that by the eighth century the Mediterranean was a religious frontier. This, he thought, marked the watershed between the ancient and medieval worlds, with northwestern Europe, lacking cultural and economic contacts, forced to fall back on its own resources, thus precipitating the rise of the Carolingian empire – whence his famous dictum that 'without Mohammed Charlemagne would have been inconceivable'. For Pirenne, the Carolingian world had a rural and land-locked economy and it was the post-Carolingian period which saw the emergence of distinctively medieval trade networks and forms of town life. Pirenne's perspective was resolutely but unconsciously that of a middle-class northwestern European at the height of the region's economic, cultural and political dominance in world affairs – his projection of that dominance into the distant past and his casting of Islam in the role of a rogue outsider destroying ancient civilisation hint at the prejudices of his own environment. Although his view was not unchallenged – the contemporary German historian Alfons Dopsch wrote a monumental account of the social and economic foundations of medieval Europe that stressed the creativity of the Carolingian countryside rather than fluctuations in trade – the 'Pirenne thesis' maintained a dominant hold on understandings of the Carolingian economy throughout the twentieth century.
The general outlines of Pirenne's chronology, with some modifications, still provide a useful starting point – the broad patterns of economic change in the post-Roman west are not at issue. Although different scholars would lay the emphasis in different places, few would dispute an outline chronology that has the systems of exchange that ensured the economic integration of the ancient Mediterranean, after a series of adjustments in the fifth and sixth centuries, finally collapsing at the end of the seventh; new connections around the North Sea emerging in the course of the seventh century, and growing in the late eighth and early ninth centuries, before undergoing a process of reorientation which enabled renewed growth in the tenth; and new networks emerging in the Mediterranean, too, in the late eighth and ninth centuries, which were likewise to lay the foundations for intensified activity thereafter. Yet the terms of the Pirenne thesis are too often taken for granted, partly because it gives a role to urbanism that has provided a convenient framework for the spectacular archaeological finds of recent decades. Consequently, this data is often used to expand and modify, rather than question, Pirenne's model, and the result has been a generally pessimistic view of the actual level and vitality of trade and exchange in the eighth and ninth centuries. Debates about trade and urbanism conducted in these terms tend, moreover, not to leave much room for study of the Carolingian economy in its own right, but rather see it as a transitional phase between the ancient and high medieval worlds.
The underlying argument of this chapter is that the Carolingian evidence should be examined on its own terms rather than viewed only in the light of Pirennian debates about long-term change. The debates that will concern us here deal with different characterisations of the Carolingian economy itself, and with different explanations for change. Broadly speaking, scholarly opinion can be plotted in relation to two central issues. The first concerns the driving motor of economic change: was it the creation of new trade routes and the emergence of trading settlements, or was it the productivity of the countryside and the production of surpluses? The second relates to the agents of change: rulers and elites, or relatively autonomous small and middling landowners? Nobody would disagree that economic change was ultimately conditioned by all of these things – by the interactions between trading networks and systems of agrarian production, and the dialectic between the wishes of kings and elites and the actions of their subjects and dependants. What is at issue is the nature of those interactions, and where we choose to lay the emphasis. Monumental books by Michael McCormick and Chris Wickham have shown just how complex and polyfocal was the early medieval economy of Europe, and revealed the dangers inherent in generalising from any one part to the whole.
In what follows we will argue that the development of systems of exchange ultimately rested on the increased productivity of the Carolingian countryside, and the ability of a relatively broad landowning class to seize on the possibilities created by the increasingly ambitious and extensive systems of redistribution developed by kings and their court elites. The networks of long-distance trade emerging from the archaeology may be spectacular, but even on the most optimistic assessment they can have accounted for only a tiny segment of the economy as a whole. And although many scholars have been tempted to imagine rulers like Charlemagne developing economic initiatives designed to promote urban growth and maximise exchange, such planning was wholly alien to a conservative worldview in which rulers strove to make their realm correspond to a divinely ordained order: we have no hint in our sources of the kind of strategic discussion and mobilisation that such 'policy-making' would have involved, nor even any real sense of the king and his advisers discussing economic exchange as a special form of activity which deserved promoting in its own right. The next section of the chapter develops these general points, explaining how we ought to conceptualise economic activity in the Carolingian era. The third, fourth and fifth sections then outline the rise and transformation of the North Sea trading network, explaining also the role of the Vikings. In the sixth section we turn south to Italy and the Mediterranean, before asking, in conclusion, whether there was such a thing as 'the Carolingian economy'.
#### MECHANISMS OF EXCHANGE
Another look at Ohthere's account of his activities reminds us of the great variety of mechanisms of exchange in the early Middle Ages, and cautions us to resist the instinct to think about the distant past in terms of the market forces familiar from the economics of the modern world. The cargo taken by Ohthere to Kaupang and Hedeby, remember, was made up of the tribute he had received from the _Finnas_ : 'Each pays according to his rank. The highest in rank has to pay fifteen marten skins, five reindeer skins, one bear skin and ten measures of feathers, and a jacket of bearskin or otterskin and two ship-ropes. Each of these must be sixty ells long, one made from whale-hide and the other from seal.' These tributes were not part of a separate system operating alongside, but distinct from, market exchange of a kind familiar to us. Rather, they were part of a single multifaceted system of exchange, without which Ohthere's trading expedition to the markets of the great ports of southern Scandinavia would have been impossible. Ohthere is silent on the basis of his tributary relationship with the _Finnas_ , but it clearly took a form of personal domination – lordship – based at least partly on the need for 'protection': that is, on the threat of force. But even his interactions with the _Finnas_ were multi-stranded: as well as collecting tribute from them, we can also see hints of more straightforwardly 'economic' relations in his boasts about his herd of 600 'unsold' beasts (some of them 'decoy reindeer' used in hunting wild deer). In other words, not only was Ohthere selling onwards in the marketplace tribute acquired by what we would see today as 'extra-economic' mechanisms; he was also harvesting the fauna – by hunting walruses and taming reindeer – and exchanging at least some of the results with the _Finnas_ , in the process helping them to make the next round of tribute payments. Patterns of exchange were wrapped up in social relationships between groups and individuals, from which they cannot be separated, and market transactions that we would see as 'economic' were inextricably connected to 'extra-economic' forms of social obligation and political domination.
The interdependence of what to us look like quite different forms of exchange is underlined later in Ohthere's account. When Ohthere reached the land of the _Beormas_ he stopped at the mouth of a great river: although there were extensive settlements beyond it, he did not dare to venture there. Our scribe explains Ohthere's reluctance with a spare phrase that he clearly expected his audience to understand immediately: going further was impossible 'on account of _unfriÞ'_. The concept of _unfriÞ_ ('non-peace') signified not a state of formal enmity or dangerous hostility so much as, quite literally, an absence of _friÞ_ , that formal state of mutually recognised friendship which rested on public agreements and allowed agreed processes of exchange. The _Beormas_ were strangers, not foes; Ohthere's non-relationship was different from the formal enmity of plundering and raiding which defined relations between other northern peoples, and also from the implicit violence underpinning the tributary subjection of the _Finnas_. Even more neutral and less personal forms of equal exchange – the activities from which our notion of 'trade' emerged – required the public acknowledgement of a state of formal trust, such as was lacking with the _Beormas_. Normally acquired through a visit to the local ruler, such recognition was a common requirement right across early medieval northwestern Europe. The earliest Frankish and Anglo-Saxon laws on merchants, for example, concern royal acknowledgement and the need for these strangers to advertise their special status, whilst the conclusion of peace between erstwhile enemies involved formal undertakings allowing the resumption of equal exchange and the end of plundering; in Carolingian times, these concerns are still evident in the special protection offered by the king to merchants from abroad, and the agreements reached between Franks and Vikings.
Ohthere's account, of course, concerns a very different society from those of Carolingian Francia and Italy that are our primary concern – it would be misleading to develop a model from his testimony and impose it uncritically on the Carolingian evidence. But Ohthere is worth dwelling on because we lack comparable accounts of the systems of redistribution and exchange within the Carolingian world. In part, this absence shows that economic systems – some relatively sophisticated, as we saw in our discussion of rural society – were so deeply embedded within the social structure as to be taken as read. As a result historians of the Carolingian economy have tended to assume that the systems underpinning the circulation of wealth within Francia took forms familiar and natural to us. After all, the raw materials of Carolingian economic history seem to consist of apparently dry and neutral data, whether maps of the archaeological distribution of particular classes of pottery or finds of jewellery and metalwork from trading centres, royal documents relieving favoured churches of tolls and allowing them to establish mints and markets, or lists of dues required from peasants on royal and ecclesiastical land. For all their apparent neutrality, though, we should pause for thought before assuming that such data-sets should be explained solely in terms of phenomena that are familiar from our own experience, as the result of market-orientated economic exchange understood as having an independent logic outside of social relationships.
In fact, within the empire as on its northern fringe, there were a range of complementary and sometimes interlocking mechanisms at work simultaneously. Tim Reuter memorably uncovered the regular flows of plunder and tribute that were such a central facet of Frankish political expansion. Eighth-century Frankish success then fuelled a flow of high-status gifts; kings like Charlemagne were able to control the distribution of the spoils of war, using them to forge bonds with neighbouring rulers such as Offa, but most importantly to reward the aristocrats who had effected conquest and to build up the institutional wealth of the imperial church. The end of expansion, of course, ended this primitive but effective system of redistribution, and in the ninth century both inter-Frankish conflict and more piecemeal patterns of frontier raiding and tribute gathering, notably in central Europe and northern Spain, offered poorer pickings, and encouraged a more intensive exploitation of internal resources. Indeed, one model of political and economic change would see the Carolingians seizing the opportunity granted them by their eighth-century success, and attempting to reorientate their economy towards internal production in the ninth century – a model that would be supported by the evidence (introduced in Chapter 5) for the emergence of markets in the ninth- and tenth-century countryside.
Nonetheless, there is also abundant evidence that redistributive social exchange continued to be a central mechanism of elite consumption; indeed, the thickening of evidence in the ninth century makes their centrality to aristocratic society even more visible for this period than for the age of conquest. Charlemagne's distributions of plunder were merely the visible tip of a far bigger iceberg, a system of exchange which bound together Frankish society. In order to understand the economic dynamics of Carolingian times, we need to look for the interaction between this system on the one hand, and the formal economy of market exchange on the other. The circulation of prized symbols of elite status – high-quality weaponry, lavish buckles and brooches – was probably the motor of the networks of sociable redistribution. Such items were not commodities, that is anonymous objects whose value was standardised, for they had biographies and identities which rubbed off on their owners: swords, for example, had names, sometimes scratched into the blade, which were mnemonics for stories about former owners and daring deeds such as emerge in epic poetry surviving from our period, the 'Lay of Hildebrand' ( _Hildebrandslied_ ) and the story of 'Walter Strongarm' ( _Waltharius_ ). Because of the cultural and social capital invested in this type of 'treasure', it was passed on face-to-face in personalised exchanges: after all, to pass on a weapon with which a forefather had killed countless foes, or a gift with which a king had shown favour to a relative, was to pass on a part of a family's identity. Exchanging such items through the impersonal mechanism of sale was potentially problematical, because their value lay not in the objects themselves but in the relationships they articulated and helped define.
This was not just a closed system of gift exchange which recycled treasure within a narrow elite: the necessity of generosity, and its increasing institutionalisation after the end of eighth-century expansion, meant that expectations about regular giving and receiving determined at least some of the objectives of manorial economies. We have already seen how the royal assembly slowly mutated from the mustering of a war-host for its annual campaign into an organ of formal counsel-taking and decision-making in the second half of the eighth century. One result was that rulers like Charlemagne and Louis the Pious came to insist on being presented with 'annual gifts' from their leading subjects. The loyalties and identities of the top tier of Carolingian society were thus shaped by a regular cycle of giving – and this cycle rested on a two-way flow of gifts, for kings might present robes and favours on such occasions as well as sharing time talking, feasting and hunting with their aristocracies. These imperatives had a direct impact on aristocratic estate management: for example, Einhard's letters apologising for late arrival and non-attendance at the assembly, and advising aristocrats on what to present, are accompanied by others ordering his stewards to have produce and goods ready to support his obligations to his royal master. Indeed, by the middle decades of the ninth century such obligations were so routinised that they might be recorded in the polyptychs alongside other duties and payments levied on the peasantry, whilst the 'gifts' expected from ecclesiastical institutions had been fixed in standardised 'tariffs' which might be renegotiated.
These obligations of giving structured the relationships between kings, churches and aristocrats. Away from royal courts, on a more local level, systems of giving and receiving are harder to trace; nonetheless, there is little room for doubt that it was such mechanisms that allowed aristocrats and ecclesiastical institutions to build networks of support among the landowning classes, and indeed supplied contingents of properly armed and equipped soldiers for royal campaigns. There are, for example, some indications of significant change in the ways high-quality metalwork and weapons were produced between the seventh and ninth centuries: individual smiths, whose activities were earlier shaped by aristocratic, ecclesiastical and royal patronage, seem in the Carolingian period to be overshadowed by workshops embedded within the manorial economy. Although these indications must be carefully handled (since the nature of the surviving evidence shifts in the ninth century), the archaeological and documentary evidence for significant investment in iron production and workshops on many major Carolingian monastic sites, and the fact that certain types of swords were being given 'brand-names' by the end of the ninth century, is suggestive of larger-scale production leading to changes in patterns of distribution. These shifts again suggest that the social imperatives of the 'gift economy' played an increasingly important role in determining the workaday business of estate management and the organisation of production.
The 'economic logic' of Carolingian landowners, then, was not simply a matter of profit-and-loss style calculation about the maximisation of production for the market. Indeed, we have no real evidence that Carolingian estates were run to return a profit, as we would define it; rather, they were social resources used to support their owners in meeting those obligations which came with their rank. As we saw in Chapter 6, demonstrating and maintaining social status, and developing political influence, were possible only through participation in a culture of elite display, hospitality and gift-giving, and estates were managed so as to facilitate these goals. Here more anecdotal sources, such as Einhard's letters, provide an invaluable context for the polyptychs: in them, as we have noted, Einhard instructs stewards to send cartloads of foodstuffs to nominated estates to feed himself, his retinue, and important guests, and chastises those who fail to send produce of adequate quality, while market exchange is wholly marginal.
None of this is to deny that there were markets, and that both agrarian surpluses and the fruits of craft production could be bought and sold in the Carolingian period. But these forms of exchange cannot be automatically seen as the default mechanisms through which demands were met and to which production was geared. Those whose decisions determined the basic patterns of economic activity were motivated by other concerns, and adopted other strategies, than those which seem natural to us: markets had particular functions in a world where the culturally and ideologically dominant mechanisms of exchange were embedded in social relationships. After all, in practical terms large conglomerations of estates such as those revealed in the polyptychs or in Einhard's letters had their own internal mechanisms of redistribution and transportation, as we saw above; the demands of kings for gifts and obligations to attend court, to fight with an armed retinue and to perform other public services interacted with these internal mechanisms, and the resulting patterns of mobility might play an important role in determining the range of economic possibilities. Similarly, as Einhard's writings and letters show, when travelling to or from the king or undertaking official business the powerful might avail themselves of royal estates and their resources, just as _De villis_ envisaged. Carolingian kings, moreover, inherited from their Frankish and Roman predecessors a system of levying tolls on external trade, and on internal markets; and like them they also granted favoured subjects, and in particular great ecclesiastical institutions, privileges, most usually exemptions from the payment of tolls at particular places. Such privileges blurred the boundary between private and public resources: churches, after all, were so treated because they were a central part of the Frankish political system charged with public duties both religious and political, but a monastery or bishopric with the right to move half a dozen ships up and down a major river like the Po or the Seine could profit on the back of its public status. The Carolingian economy was not like that of the Roman empire. The latter had been driven by a regular system of tax assessment and payment to support a standing army which effected large-scale transfers of wealth in state-minted coin and in provisions, and granted state franchises to those shipping vital supplies. By contrast, while Carolingian rulers and their agents might collect specific dues and demand particular services from all free men, there was no regular system of tax assessment or land inventorying, and no standing army or dedicated bureaucracy. Instead, the systems of obligation and privilege which bound together the aristocratic and ecclesiastical elites determined the basic structures of economic activity in our period.
The interaction of different spheres of economic activity and exchange can be illustrated by returning briefly to the capitularies. Carolingian legislation was particularly interested in establishing proper distinctions between the practices of gift-giving and the logic of the market, and policing the boundaries between them, and we need to understand these contemporary categories if we are to interpret the dynamics of social and economic change. Take the capitulary _De villis_ which we introduced in Chapter 5. In its model of the ideal royal estate, markets play a role, with stewards enjoined to use them to ensure that food of a fitting quality was available when the king visited, and that there was sufficient seed and stock – but this role is clearly subsidiary, acting as a 'top up' to internal mechanisms of redistribution. _De villis_ does recognise that stewards might maximise their estates' income by selling surplus produce, requiring that they render account of their sales each Easter, acquiring sufficient silver coin to send the appropriate payment to the palace. Here, not only was the market the destination for what remained after royal orders for the redistribution of produce had been met, and royal agents shown the appropriate hospitality: the payment of accounts in coin was also a mechanism for monitoring the activities of stewards. Market exchange, with its relatively impersonal standards of value, was useful in this context precisely because it removed some transactions from the web of local ties and personal obligations surrounding stewards, washing clean otherwise potentially sticky fingers – but it was not the ultimate goal of estate management. If we are to understand the Carolingian economy we must take note of how these conceptually distinct mechanisms of exchange interlocked and overlapped, and realise that their operation resulted above all from the political interaction of kings, aristocrats and great churches.
#### THE NORTH SEA ECONOMY
The archaeological discoveries of the past half-century leave little room for doubt over the scale of the long-distance exchange that these dynamics facilitated. Best known, because most spectacular, is the emergence by 700 of a network of dedicated economic centres serving the coastlines and estuaries of the North Sea, and its subsequent growth in the course of the eighth century and the first decades of the ninth. Excavations at sites such as Dorestad on the Rhine delta in the modern Netherlands, and Hamwic, the forerunner of Southampton on the south coast of England, have transformed our understanding of networks barely alluded to in our texts. Perhaps the most striking feature of this network is its international nature: sites of an identical type become visible at very similar dates not only in Francia, but also in southern and eastern England and southern Scandinavia. In other words, we are dealing with the emergence of a regular system of shipborne exchange around the North Sea and its hinterland. These sites are sometimes referred to by archaeologists and historians as _wics_ , on the basis of the common suffix shared by many of the Anglo-Saxon examples in particular, such as Hamwic and Ipswich. However, most discussion now uses the term 'emporium' (plural 'emporia') to describe these gateway sites dedicated to long-distance exchange (see Map 11).
Emerging in the decades around 700, the emporia of the North Sea were typically low-lying, serving sandy beaches in the estuaries of major rivers. The functions of these sites were resolutely economic: in addition to long-distance exchange, archaeology has indicated that they were also major centres for craft production and the secondary processing of raw materials from their hinterlands. They also remained noticeably distinct from the seats of cultural, social or political authority, in England and Francia at least. While there is documentary evidence for royal agents at major Frankish sites such as Dorestad and Quentovic, and at the Anglo-Saxon centres, these were not seats of power from which the surrounding countryside was ruled, but specialised sites where the concentration of exchange demanded the presence of officials to ensure that lucrative royal rights to tolls on trade were upheld. Similarly, while the religious needs of their populations were served by churches, they were not the sites of bishoprics. Normally undefended, they remained distinct from the remnants of major Roman centres, even where – as at London – they lay next door. This separation was primarily practical, enabling the creation of warehouses and jetties serving shallow beaches without having to negotiate difficult-to-clear and potentially dangerous Roman remains. But the fact that observers like Bede used a different vocabulary from the inherited Roman terminology to refer to this sort of extra-mural 'industrial estate' points to a consciousness that this network of economic sites was clearly identifiable and had its own distinct logic.
**Map 11.** Exchange and trade: the North Sea and the Baltic Sea (showing places mentioned in Chapter 7)
That said, it would be a mistake to overstate the homogeneity of the North Sea emporia. First, they differed widely in size. The largest sites, the two main Frankish emporia of Quentovic and Dorestad, remain incompletely excavated precisely because they were huge. Dorestad at its height stretched at least three kilometres along the confluence of the Lek and the Kromme Rijn, with habitation clustering in a strip up to half a kilometre wide. Of this, around 30 hectares were excavated between 1967 and 1977. Surveying at Quentovic, whose site was only discovered in 1990, indicates a settlement of comparable size. Compare Hamwic's 45 hectares, or the tiny emporium of just a few hectares founded at Ribe at the base of the Jutland peninsula in Denmark. Second, the differential impact of the Roman past meant that emporia mapped on to very different topographies. Hence emporia fulfilled different functions in Francia, where the network of former Roman cities largely defined the geography of ecclesiastical authority and where continuity of activity and some economic specialisation can be seen on many such sites; England, where Roman cities were more or less wholly abandoned, but were sometimes revived by Romanising churchmen and rulers; and Scandinavia, where the Roman imprint was wholly lacking, meaning that emporia became seats of political power in a way that was impossible further south.
These variations demonstrate that we are not dealing with the linking together of economies of roughly equivalent complexity and intensity. The Frankish 'super-emporia' were conduits for the export of goods whose production was already a matter of specialisation and sophistication, thanks to significant 'home' demand fed through regional networks within the Frankish heartlands. The major Frankish exports – barrels of wine, top-quality pottery manufactured in the Rhineland workshops, millstones fashioned from Mayen quernstone – were thus produced neither initially nor primarily with a view to the potential of long-distance exchange. The best 'guesstimate' suggests that even at its height, the volume of fine tableware handled through Dorestad represented perhaps the cargo of a barge a week coming down the Rhine, or in other words a regular and routine supply but not a bulk trade – this was the selling on of excess products, not export-geared production. The imports thus funded remain archaeologically far less visible. From the Scandinavian end, raw materials destined for Frankish workshops seem to dominate: amber, for example, is found in its raw form in staggering quantities at Dorestad, and we should add the kinds of goods mentioned by Ohthere, with ivory well attested archaeologically but furs inevitably invisible in the material record. Anglo-Saxon exports are harder still to gauge, though textual evidence suggests that finished products rather than raw materials were dominant: cloaks of English and Frisian make were renowned, and fine cloth may have been the primary English export already, as in the later Middle Ages. Slaves, the most elusive commodity of all in the archaeological and documentary record, were also an object of exchange, but the scale and significance here was in all probability limited: these were not, after all, agrarian regimes which rested on gang slavery, and in any case the economy of the wartrail provided a ready supply of unfree labour.
The sheer size of sites like Dorestad must tell us something about the increasing sophistication of internal systems of production and distribution within northern Francia. Most interpretations of North Sea trade, basing themselves on the emporia's likely political and economic benefits, tend to see royal agency behind these developments. This view seems to sit well with sites like Hamwic, whose regular, grid-like street plan is suggestive of planned foundation rather than organic growth, and where there is evidence for the bulk transporting of foodstuffs and other supplies from the surrounding countryside. The clear archaeological horizon of the site _c_.700 fits with a political context in which expansionist kings in Wessex – the Anglo-Saxon kingdom in which Hamwic was situated – would have been interested in developing an outlet into the Channel. The site is later in its history explicitly attested as being royal property. But it would be a mistake to generalise effortlessly from the specific case of Hamwic to the North Sea economy as a whole. After all, Hamwic was founded just as the networks of exchange which bound together the North Sea were taking shape, but a generation or two after their beginning; Dorestad, by contrast, was an important site of long-distance exchange already by the middle of the seventh century. Hamwic may represent a royal foundation, but one designed to give access to a North Sea economy that was already developing apace – this is why it should not be used as a template into which evidence from other sites can be slotted.
The evidence from Dorestad is particularly important in illuminating the process by which the emporia rose to prominence, for it gives us the best window on to the earliest phase of the North Sea network. Here, in the crucial period after the middle of the seventh century, when we have the first archaeological evidence for regular long-distance exchange, and the earliest written hints at the place's importance, Dorestad changed hands several times between the Franks and their pagan Frisian neighbours, with no detriment to the emporium's economic vitality; it was not until the 720s, decades later, that it lay unequivocally in Frankish hands. The coin evidence, likewise, points to a picture of growing exchange that transcended political and religious frontiers. Seventh-century activity at Dorestad resulted in the presence of distinctive silver coins, pennies known to specialists as _sceattas_ , which have a relatively wide distribution across northern Europe, from southern Scandinavia to coastal regions of England, Germany and the Netherlands. Unlike the other post-Roman coinages, the _sceattas_ did not bear the name or device of any ruler, instead carrying symbols, some seemingly representing monsters and mythical figures; their distribution suggests that they were primarily minted to serve those involved in exchange around the coasts of the North Sea, and that most probably they originated in Frisia. The role of the Frisians as middlemen connecting the coasts of the North Sea in the seventh century is well attested in the written sources. Frisia's economic vitality derived from its distinctive ecology and geography, with low-lying coastal marshes, shifting creeks and small islands of solid earth militating against agriculture and nurturing the inhabitants' expertise in navigation. This in turn prompted engagement with the exchanges that were intensifying along the river systems of the Frankish heartlands. Seventh-century Dorestad was no more a creation of Frisian rulers than it was of the Franks. Its importance derived rather from its location on the river system that was both a frontier between two kingdoms and a natural valve between two contrasting but potentially complementary economic systems.
The written sources suggest something approaching a Frisian monopoly on communication and exchange around the North Sea in the later seventh and early eighth centuries. In part, this was because the Frisians were ideally placed to dominate the routes that linked the North Sea coast of continental Europe to southern Scandinavia and eastern England (though we should note that 'Frisian' was sometimes used less as an ethnic label than as shorthand for 'expert sailor from the North Sea coast'). But these connections did not emerge in a vacuum. Archaeology, particularly in the rich evidence provided by the prized status symbols deposited as grave-goods right across sixth-and seventh-century northwestern Europe, suggests that artefacts and ideas travelled long distances around the Merovingian North Sea. The circulation of such objects was not high volume, nor did it necessarily rest on trade as opposed to gift-giving and status emulation between ruling elites, encouraged by the experiences of exile and travel and the exchange of emissaries; seasonal 'beach markets', which have been canvassed as a potential mechanism for this level of exchange, inevitably remain hard to identify archaeologically. By the later seventh century, the appearance of Frisian shipping in our written sources clearly marks a first step change: we read of emissaries, missionaries and pilgrims availing themselves of a nexus of predictable sailings from well-known points of departure, suggesting that by 700 at the latest the 'gift economy' around the North Sea was riding piggy-back on a system of regular communication and exchange.
A second phase rapidly followed, marked by the expansion and planned development of existing nodal points, and also the creation of new sites designed to serve the growing activity around the North Sea. The former phenomenon is best represented by activity in the excavated 'harbour area' at Dorestad, where a series of large wooden warehouses and workshops served by wooden walkways over the beach and jetties leading into the river was constructed _c_.675–725, with a wooden roadway parallel to the course of the river behind them. Beyond that was a zone between 100 and 500 metres deep made up of individual households, wooden 'halls' and their ancillaries constructed in a manner identical to that of any rural site. The latter phenomenon – construction of new sites – is exemplified (as we have seen) by Hamwic. Its logic, however, is most vividly illustrated by Ribe, founded close by the settlement of Danekirke. Danekirke had been inhabited since the second century by a population whose economy was rooted in agriculture, but whose elite inhabitants were increasingly importing lavish status symbols in the sixth and seventh centuries, presumably on a relatively _ad hoc_ basis as travellers and seafarers passed this high-status coastal site. The foundation of Ribe _c_.700 was designed to institutionalise and make routine these connections.
The crucial development shared by both old and new sites was the emergence of widespread craft production; these were no longer simply ports of trade, but also places where raw materials from the immediate hinterland, and from trading partners, were processed to be sold on. A relatively similar array of activities (though with different emphases) is witnessed at all excavated sites – not only manufacturing through metalworking and glassworking, but also secondary services such as basket-weaving, boat-building and textile-working. Although the emporia were thus centres of production, this activity was quite scattered and seems to have been organised on the level of the individual household. The populations attracted by the potential of such activities grew to significant levels relatively rapidly: in their heyday in the late eighth and early ninth century, major emporia supported resident populations of several thousand, which may sound modest to us but puts them on a par with any other contemporary aggregation in western Europe barring Rome. At peak times, these numbers would have swelled, and the need to cope with this seasonal demand probably explains why there is also good evidence for intensive farming at Dorestad, particularly in the outer sectors of residence; estates in the hinterland of major emporia were also engaged in marketing foodstuffs. Increasing knowledge of the range of activities carried out in the emporia, and the infrastructure which supported sizeable artisanal populations, has led some scholars to stress the concentration of production and the reciprocal relationship this created with the surrounding countryside as the basic functions of the emporia. After all, in Francia the continued use of some former Roman sites as seats of authority encouraged similar, if smaller-scale, concentrations of production, as at Cologne, and an environment structured by aristocratic wealth and excellent river connections meant that some aggregations of craft production could even spring up from nothing at nodal points in local patterns of communications, as at Huy or Maastricht. But Dorestad or Quentovic differed from such sites not only quantitatively, but qualitatively: they were not defined by or tied to patterns of ecclesiastical and political power. If we are to account for their significance and size then these local economic interactions must take centre stage, but we cannot forget that a centre like Dorestad could not have grown and prospered without long-distance seaborne trade. It was their role as valves for the import and export of raw materials and manufactures that encouraged the growth there of production and secondary activity in trades such as shipbuilding, woodworking and butchering. Without the network of exchange off which they fed, the emporia would not have been viable settlements on this scale or at these sites. The Frankish emporia were within their kingdoms, but not exactly _of_ their kingdoms – this dual identity, and their simultaneous existence in two overlapping universes, was what made them what they were.
#### THE TRANSFORMATION OF THE EMPORIA:
THE NINTH CENTURY
These processes (of rising elite-driven production in the interior leading to expanding external exchange) underwrote the boom in the emporia revealed by the archaeological record for the second half of the eighth century and the first three decades of the ninth. The real puzzle is explaining why they faltered in the succeeding half-century. For falter they did: by the end of the ninth century, Dorestad, Hamwic and Quentovic were drastically less active as centres of trade or production. Past generations of scholars working primarily from written sources were understandably tempted to explain these economic changes in terms of a generalised stereotype of ninth-century chaos and destruction, and pointed the finger squarely at a combination of aristocratic infighting and Viking raiding. But this view is incompatible with the recent findings of archaeologists. The cataclysmic view places a heavy weight on the mention of Viking raids on Dorestad and Hamwic in the 830s: Dorestad, indeed, was raided four years running from 834 to 837. The archaeology, however, incomplete though it is, lacks 'destruction layers' such as might indicate the effects of burning or ravaging, and points instead to a gradual flattening out of activity slowly tipping into decline in the 830s. This pattern is confirmed by the distribution of coins minted at Dorestad and Quentovic, which both peak _c_.830, and gradually fade away, with no sign of dramatic discontinuity, thereafter. At the height of production, Dorestad was minting far and away the greatest number of the sole denomination in circulation in the Carolingian empire, the _denarius_ , which had a purchasing power, in 794, of twelve two-pound loaves of bread (see Figure 16). By Louis the Pious's reign the Carolingian government was able to exclude foreign coins from circulation, to ensure that new issues were minted to a single design throughout the empire, and to arrange for the swift withdrawal from circulation of demonetized issues.
**Figure 16.** Silver _denarius_ minted at Dorestad (DORESTATVS), 814–18. All examples of this issue have on the obverse a bust of the emperor Louis the Pious crowned with a laurel wreath. On the reverse, other mints depicted a set of city gates: the image of a ship struck at Dorestad and Quentovic underlines the status of those places as important trading centres – emporia – in the North Sea—Channel economic network.
The significance of Quentovic, meanwhile, continued even in the heyday of Viking activity in the Channel – the coins indicate that its plateau came later, around the middle decades of the ninth century, and that it was not extinct even in the tenth. Major churches fought hard to maintain property complexes at Quentovic, through which the surpluses produced on their estates could be sold on: the significance of such arrangements is vividly illustrated by the lobbying undertaken by Abbot Lupus of Ferrières, eager to evict the aristocrats whom Charles the Bald had installed at the small cell at St Josse, close by Quentovic, and return this property into the direct control of his abbey.
These patterns of gradual change must be explained with reference to processes more complex and long-term than political conflict or Viking attack. At Dorestad, the changing face of the excavated harbour on the Kromme Rijn is suggestive (see Map 12). Here, cargoes were loaded and unloaded into a series of 'warehouses' constructed on long thin plots connected to the river by a series of wooden 'tracks' over the sand. These were constructed and repaired throughout the eighth and ninth century; the period of Dorestad's decline in particular saw their elaboration and extension, the longest exceeding 100 metres in length before the site's final abandonment. This hints at environmental change, with changing sea levels and the rapid silting of the river – itself perhaps a result of the intensive human activity along its banks – simply making Dorestad less and less attractive as a port. But it may also point to the changing nature of trade. It still remains unclear whether in Dorestad's heyday boats were normally 'beached' for unloading, or whether the extreme end of the wooden tracks served as something like a jetty, but it is possible that the extension of the wooden tracks was also an attempt to provide platforms for deeper draught vessels more suited to navigating direct across the open sea, and able to carry higher-volume cargo. Our knowledge of early medieval ships remains imperfect, but there are hints that a major development of the North Sea's 'Viking age' was a move away from the earlier reliance on coast-hugging transport, with accompanying changes in ship design.
Whatever the case, it seems clear that the relative importance of the long-distance high-status exchange that the emporia served was declining by the second half of the ninth century, and that new networks better able to handle the regional marketing of bulk goods were becoming the motor driving the economy. Here, in a sense, the emporia were almost victims of their own success: a site like Dorestad stimulated a significant degree of economic specialisation and secondary exchange in its hinterland, thanks to the demand it generated for foodstuffs, wood and other locally accessible raw materials, and its function as a market and centre of craft production. Already in its heyday, its sheer size was such that a number of secondary centres emerged nearby: smaller markets both on the coast (Dorestad was a significant sail of some 70 km up the Rhine delta from the open sea) as on the island of Domburg at the mouth of the Rhine, and inland too at the nodal points for the collection of produce from the countryside. By the end of the ninth century, a series of sites in what had once been Dorestad's hinterland were emerging as new towns in their own right, smaller in scale but part of a dense network of local centres springing up along the major rivers of northwestern Europe, most fortified thanks to their attachment to a major centre of landlords' activity. Ghent, for example, grew up around a major monastery, and Bruges around an aristocratic centre. Even in the late ninth century, long-distance trade had not disappeared, but now it took place in a series of market places that were defined by an increasingly dense pattern of local exchanges. The preceding two generations had seen a shift in the logic of the economy in northwest Europe, as the specialisation and local exchange encouraged by the success of the emporia became able to sustain dedicated centres better suited to the exchange of higher-volume but lower-value goods on a local level.
**Map 12.** Dorestad
In Dorestad's hinterland, these changes must have caused some dislocation, even if only short-lived, which interacted with the disruption to long-distance exchange caused by Viking activity. Elsewhere in the Frankish heartlands, the rise of more deeply rooted regional markets may have been more seamless. Recent finds at Mainz, for example, demonstrate vividly how the early development of the North Sea economy could kickstart productive activity at a site several hundred kilometres down the Rhine, and eventually stimulate development of coherent systems of regional exchange. Mainz was a major Roman military site located at a strategically important point on the middle Rhine and had thus been an important communication nodal point in the fifth and sixth centuries. At some point in the early eighth century, a long section of the former Roman wall along the Rhine was demolished and a metalled 'public street' parallel to the river bank built, with long narrow plots leading off it serving as warehouses and workshops handling goods travelling along the river. Modern redevelopment in this area has unearthed a rich array of finds, indicative of intensive craft-production as well as the shipping onwards of materials from the city's hinterland: the distinctive metalwork produced here in the second half of the eighth century was distributed right across the eastern part of the Frankish world, and even as far as Birka and York. This indicates a step change in the production and exchange of status-enhancing gifts at the site which directly parallels the changes taking place around the North Sea at the same time. This parallelism was no accident, and can indeed be seen as a matter of direct cause and effect: the wine exported through Dorestad was manufactured in the vineyards of the middle Rhine valley around Mainz, and transported downriver in barrels made of wood felled from the forests of the region.
By the time we get to the ninth century we start to find descriptions of activities like the transport of grain on rafts down the Main, indicating the effects that this kind of demand could have on the local economy. An annalist working in the entourage of the archbishop of Mainz was familiar enough with the role of the city as a regional market to retell sermonising stories of the moral dangers into which it was possible to fall by pursuing wealth too single-mindedly: not only was the archbishop an exemplar of holiness for turning over the produce of his estates to the common good in times of dearth, but miraculous punishments showed that using the Sabbath to undertake household-scale commercial work – baking bread to sell in the city – was a sin. The plentiful documentation from the area shows that this activity was driven by landowners, not professional merchants: local landlords with extensive but not intimidating constellations of property are known to have owned warehouses on the Rhine-front, exporting corn and doubtless investing in craft production. Coin finds in Mainz's hinterland, along with references to cash prices in charters and cash rents in polyptychs, indicate that by the ninth century this was a regional economy familiar with the use of coin. The shifting origins of these coins confirm the increasing coherence of these local networks and their gradual eclipsing of long-distance exchange. The relatively high percentage of issues from distant mints along the Rhine, notably Dorestad, in the later eighth and early ninth century gives way to a much more regionally focussed pattern by 900, with Mainz and neighbouring Rhineland mints accounting for over 80% of finds. Although Mainz still had a 'Frisian quarter' of professional long-distance shippers operating up the Rhine, by 900 it was above all a leading regional market, and the connection to the Rhine delta and the North Sea certainly did not define or drive its activity.
Full understanding of these transformations awaits more casestudies which can highlight regional differences: Mainz was, after all, a direct partner of Dorestad on a site central to natural networks of long-distance communication throughout our period, and is therefore not necessarily typical. Nonetheless, wherever we look similar processes can be discerned. Thus in Charles the Bald's west Frankish kingdom the second half of the ninth century saw major ecclesiastical institutions beginning to acquire royal privileges giving them the right to found new regular markets at specific estate-centres, and on occasion canvassing the king for the creation of new mints so as to allow their followers to acquire coin more easily, in a process which was to continue east of the Rhine in the tenth century. A world where major landlords were seeking to establish markets conveniently sited to pass on the surpluses of their manorial economies, and working to secure a regular supply of coin, was a world which had been economically transformed.
#### THE VIKINGS AND THE FRANKISH ECONOMY
Although we have argued that the Vikings should not be seen as the primary reason for these changes, their role cannot be ignored altogether: after all, the new economic nodes of the decades around 900 were, unlike the emporia, typically defended by stone walls and aristocratic entourages. Even Mainz saw the reconstruction of the city walls following the adventures of Godafrid III in the Rhine and Moselle valleys in the 880s, and the dangers of piracy and plundering must have played a role in shifting the balance away from long-distance exchange to local markets. But the economic impact of Viking activity was a far more complex and subtle matter than the stereotype of wanton destruction would allow. Scandinavia was a crucial part of the North Sea economy served by the emporia, and the Scandinavian warlords who led Viking bands operated in a world where control of exchange was critical to the creation of political power. The rapid growth of the North Sea economy in the two or three generations immediately preceding the first references to Viking raiding in our written sources, in the years around 800, is striking, yet the relationship between the development of exchange and the onset of raiding remains little understood. The presence of Scandinavian warbands along the coasts and rivers of northwestern Europe, sometimes as allies and servants of Frankish kings, sometimes as enemies, points to a fundamental transformation of Scandinavian societies prompted by the gravitational pull of their Frankish neighbour.
Assessing the impact of Viking activity on these patterns of change is difficult because the relationship between trading and raiding remains poorly understood. The major problem here has been the polarised nature of Viking studies: until very recently specialists tended to divide into two camps, one investigating long-term economic and political connections and the other emphasising the short-term disruption wrought by ninth-century raiding, but both tending to draw general conclusions that lump together the diverse activities of different groups of Scandinavians. The running and rerunning of somewhat moralistic arguments along these lines ('bad' vs 'not so bad') has become somewhat unhelpful, and it is only recently that new work has begun to help us reach a new understanding of how Frankish authors thought about the raiders, with polemical presentations of the Vikings as agents of God's wrath being selectively deployed as a means of criticising political opponents. These narratives were often highly coloured by Old Testament expectations which (carefully manipulated for maximum effect) cannot be taken at face value. Careful analysis of the careers, connections and motivations of Scandinavian leaders is the way to fuller understanding.
By about 800, Carolingian military success in Saxony, along with the development of the North Sea economy, had brought Scandinavian rulers into increasingly direct contact with the Franks, and they sought to draw on the new opportunities afforded by this contact to stabilise their own positions. Control of systems of exchange, and particularly of the major emporia, was crucial for ambitious rulers anxious to establish royal claims and attract the armed followings that made them powerful: hence the Swedish king Anund seized Birka, driving out his rival, in order to make good his claims to royal status. These patterns of internal conflict might impinge on Frankish interests. The Danish king Godafrid I, who had succeeded in establishing overlordship over much of the Jutland peninsula by 800, raided the emporium of Reric, situated on the Baltic coast in the territory of the Abodrites, precisely because it provided a valve between the Frankish world and the Baltic which bypassed the nearby Danish emporium at Hedeby. At Reric, archaeology helps show the real meaning of activities our sources refer to as 'raiding', revealing the relocation of a significant proportion of craft production previously carried out at Reric to Hedeby, which involved not only the forced removal of the artisan population but also the rerouting of networks of supply and distribution. Godafrid's need to establish control over networks of exchange inevitably brought him into conflict with Charlemagne: not only did his activities harm the Abodrites (who were Frankish allies), but he also attempted to intervene in the networks stretching from Denmark down the coast to the rivers of the Frankish heartlands by mobilising a force of 200 ships and forcing the Frisians to offer him an annual tribute. Although Frisia was politically part of the Frankish realm, ecologically and geographically it was in many ways an extension of the Jutland peninsula to which it was closely tied economically – Godafrid's attempt to reduce it to tributary status was part and parcel of the strategies by which he had built and maintained his overlordship.
The stand-off between Charlemagne and Godafrid ended with the latter's death in 810 and the dissolution of his personal overlordship in the ensuing conflict between rival successors. Subsequent Frankish policy involved offering political support to Danish royal claimants as a means of avoiding potential conflict in the future. After the 820s this policy went hand in hand with attempts to convert Scandinavian rulers and their entourages, with the missionary bishop Anskar and his helpers acting as something like Frankish emissaries in Hedeby and Birka. Frankish involvement seems to have prevented any individual royal recreating the kind of extensive overlordship enjoyed by Godafrid; this may, indeed, have been a conscious aim of Frankish policy. But it also meant acknowledgement of the close ties between the Frisian coast and Denmark, for favoured Scandinavian leaders were not only given military backing when necessary, but were also allowed to have footholds on the Frisian coast as _honores_ from the Frankish emperor, and thus to control the very area that Godafrid had been so keen to reduce to tributary status.
Given the Frankish policy of selective intervention in Danish politics, it is scarcely an accident that the outbreak of open internal rivalry within the Carolingian family in the 830s coincided with the launching of raids by a series of would-be Scandinavian rulers. This was not simply the opportunistic taking of advantage of internal conflict among the Franks – endemic competition for power within southern Scandinavia spilled over as rival members of the royal family sought to acquire Frankish patronage, and by the 840s rival Carolingians were entering into alliances with different Scandinavian warlords. The reports of raids on emporia like Dorestad in the 830s, and on major Frankish political and ecclesiastical centres like Paris in the 840s, reflect responses to the disruption of these alliances caused by turmoil within Francia. Sailing on Dorestad, for example, was a means of attempting to impose tributary status and contest political control in a crucial region which was a real bone of contention between rival Scandinavian rulers and their Carolingian allies, and not (as our sources say) a straightforward matter of wanton destruction.
By the middle decades of the ninth century, Scandinavian warlords were a part of the Frankish system, seeking patronage and employment with which to gain renown, reward followers, and so augment their standing at home. Dorestad, for example, was granted to a succession of Scandinavians through the 840s, 850s and 860s, with only two documented raids, both the result of contests for Frankish patronage. As poachers-turned-gamekeepers such figures were successful, but where Frankish patronage was not forthcoming or was withdrawn, raiding, and with it the ransoming of captives and levying of tribute, was the response. These developments must have had important implications for patterns of exchange. Scandinavian leaders and their followings were now receiving gifts and extracting tribute in Francia itself. Frankish status symbols were popular with Scandinavian warriors, as Notker noted, and are very much evident in the archaeology of ninth-century Scandinavia: their circulation now rested on patterns of gift and raid within Francia, whence they were carried home by returning warbands.
At the same time, Viking activities and demands increased the liquidity of wealth within those areas of Francia where they were most active. The coin evidence from Charles the Bald's west Francia, for example, suggests a high volume of coinage in rapid circulation: major landowners, and particularly the Church, were required by Charles to raise large amounts of silver coin to enable him to pay tributes, and as a result there was significant pressure towards the greater monetisation of the rural economy. What is more, much of the moveable wealth thus accumulated did not find its way back to the Scandinavian homelands, but further stimulated the Frankish economy as Vikings sought to use it to acquire status-enhancing luxury goods. Hence the bewildering swiftness with which Vikings might alternate between plundering, demanding tribute, and buying and selling. In 882, for example, some Franks, seeing their leaders negotiating with a Viking leader, ventured without hesitation into the fortress they were besieging, 'some to trade, some to look around the defences', once the defenders had flung open the gates and raised a shield on high as a sign of peace. Viking activities, then, not only encouraged the shifting of the old networks of long-distance exchange around the North Sea, but were also potent forces for the development of regional exchange within Frankish society.
#### ITALY AND THE MEDITERRANEAN ECONOMY
The emergence of long-distance exchange around the North Sea and the proliferation of rural markets in the Frankish heartlands have encouraged many archaeologists and historians to see northwestern Europe as the real economic dynamo of the Carolingian world. But for all the undoubted importance of the North Sea networks, we should beware generalising from them: unlike the Roman empire at its height, or later European colonial empires, the Carolingians did not sustain a core–periphery system whereby the economy of the heartlands dominated those around it. Even in the North Sea, demand and production in England and Scandinavia were never subordinated to Frankish needs, but drew on the possibilities inherent in long-distance exchange. Furthermore, these networks also remained relatively insulated from the Mediterranean economy. The seventh century had seen the final collapse of the long-distance exchange which had defined the Mediterranean economy in Roman times. Intimately tied to the demands of the state, this was essentially a system of franchises, where shippers who carried the annual convoy of supplies from surplus-producing provinces to the capital received fiscal and legal privileges giving them a crucial competitive advantage in conducting long-distance trade, which as a result rode 'piggy back' on state requisitions. The need to plug into the western end of these exchanges had exercised Merovingian kings in the sixth and early seventh centuries, prompting their recurrent interest in Marseille, the major valve between Frankish elites and the Mediterranean economy. All this was in rapid decline by the second half of the seventh century, following Constantinople's loss of key shipping centres in Egypt and Syria. The final loss to the Muslims of Carthage in 698 seems to have precipitated the ultimate collapse of this trade, cutting off the trickle of communication still crossing diagonally from Constantinople to its most westerly province, and the slow drip of trade connected to this route, indicated by the presence of African amphorae in Rome and the Adriatic, petered out.
The first half of the eighth century saw the nadir of long-distance exchange around the Mediterranean (see Map 13). It is precisely the contrast between this slump and the simultaneous emergence of the North Sea emporia which has encouraged Pirenne-inspired generalisations about a shifting economic balance northwards. Such a generalisation, however, does not take account of the persistence of less spectacular processes of regional exchange. Take, for example, a treaty concluded in 715 between the men of Comacchio, a Byzantine outpost near the mouth of the river Po, and the Lombard king Liutprand: this regulated toll payments made by Comacchese ships as they plied their way up the Po, entering the Lombard kingdom at Mantua, and then if they wished, moving further still into the heart of the north Italian plain. This was not new trade (the treaty is said to confirm 'ancient custom'), nor was it high-volume – the carriers, after all, were referred to as 'soldiers' ( _milites_ ), the standard term for lesser landowners in Byzantine Italy. It rested primarily on the ready market in the cities of the Lombard kingdom for salt harvested from the mouth of the Po, supplemented by olive oil, fish sauce and on occasion pepper, suggesting that goods received from across the sea, presumably when emissaries were sent to and from Constantinople, might also be sold on. This network has left only a faint imprint in the archaeological record – it dealt, after all, with consumables – but the documents give a steady trickle of references to the presence in the interior of ships from Comacchio, trading and paying tolls right through our period. In other words, the development of new long-distance exchange networks, which is such a dramatic feature of the Carolingian period, took place against a backdrop of existing regional connections served by the rivers and roads of the Italian peninsula, even after the remnants of post-Roman international trade had faded. Thus amongst the complaints voiced by the Istrians against their Frankish _dux_ at Rižana in 804, which we looked at in Chapter 5, was his abuse of the requisitioned transport of state goods that they were expected to undertake along the Adriatic coastline and the rivers that connected with the interior.
**Map 13.** Exchange and trade: the Mediterranean Sea (showing places mentioned in Chapter 7)
The archaeological and documentary evidence highlights the resolutely local horizons of northern Italy, where the basic social units were cities and their associated rural hinterlands. These aspects of Italian society are illustrated by the career of the eighth-century landowner Toto, whose archive of two dozen original documents was kept at the church of St Zeno founded by his family at Campione in the city-territory ( _civitas_ ) of Seprio. Toto's profile is fairly typical of the kind of figures evident from the documentary record, whose interests were more or less circumscribed to their home territory and its immediate neighbourhood: Toto dominated a number of villages around Seprio, and was also active in the far bigger and more important nearby city of Milan. These patterns of landholding and public activity, though not tied to just one city, were defined by local networks centred on major urban centres which were close at hand, in Toto's case Milan as well as Seprio. The result was a local economy resting on regular, unremarkable, flows whereby landowners like Toto could dominate the countryside, and consume its wealth, by involvement in local city life. Of course, not all Lombard landowners were of a comparable scale to Toto: there were bigger figures who benefited from royal patronage and were hence able to create more extensive aggregations of land. The Carolingian conquest strengthened this tendency, to such an extent that by the last decades of the ninth century the political class could divide into as few as two cohesive aristocratic constellations, each bound together by strong regional interests. But even then patterns of redistribution based on the city remained the default, and the kind of extensive rural manorial economies which characterised the Frankish heartlands north of the Alps were largely absent. One important result of these different social patterns was that Italian landowning was probably more implicated in local markets throughout our period: it is striking that, for all the apparent paucity of local coinages in the eighth and ninth century, Italian documents are far more conversant with coin as a standard of value and a mechanism of exchange than is the case north of the Alps. One of the documents in Toto's dossier, for example, records a landowner raising one _solidus_ 's worth of gold, necessary to allow him to meet his obligations for the remainder of the year, guaranteed against some land, a transaction of a form more or less unknown north of the Alps. This indicates that liquid wealth was significant and that values were understood and expressed in abstract terms even at a relatively low social level; higher up the social scale, there is good evidence for landowners holding significant reserves of moveable wealth, and paying prices of up to a hundred _solidi_ for land.
Despite significant differences between the north and central and southern Italy, the basic social parameters (a network of cities organically connected to the surrounding countryside) were common to most of the peninsula. Rome, notably, stood at the heart of a farreaching system designed to maintain the city's food supply, resting on a mixture of imperial privileges and papal property claims. The tying of the rich _latifundia_ (estates) of Sicily to the city's needs had long encouraged regional exchange up the western Tyrrhenian coast, and even the papacy's loss of its Sicilian estates in the 720s and 730s did not end these connections. In fact, the turning off of the regular flows of Sicilian surpluses to Rome ultimately encouraged not economic collapse, but the emergence of a series of more distinct and coherent regional economies. The papacy, for example, intensified its management of its properties and prerogatives in its immediate hinterland, Latium, with the development of a series of sites termed _domuscultae_ in the written sources. Newly excavated elite sites within early medieval Rome, such as the aristocratic residence found in the Forum of Nerva, witness a parallel shift, with local commodities like the fine pottery known as Forum Ware compensating for the lack of long-distance trade. This, along with the programmes of building in the city most extensively attested in the biographies written up in the 'Book of Pontiffs' ( _Liber pontificalis_ ), illustrates how Rome stood at the hub of a complex infrastructure allowing investment in the fabric of the city, in part using the surpluses generated by the surrounding region. With the ebbing away of imperial authority in the first decades of the eighth century, Rome became the main arena in which central Italian elites struggled for dominance: the integration of the hinterland and city is shown by the career of another Toto, this one duke of nearby Nepi, who raised a force from his city's rural hinterland, staged an invasion of Rome (staying at his townhouse for the duration), and confirmed his takeover by having his candidate made pope.
These routine systems of redistribution centred on cities and their territories meant that when new long-distance connections did emerge in the later eighth and early ninth centuries, they could immediately plug into coherent and complex local economies. Michael McCormick's innovative study has transformed our understanding of the chronology of these new connections. Assembling a huge range of data for the movement of people and goods around the Mediterranean, McCormick emphasises the limited and intermittent nature of inter-regional contacts in the first half of the eighth century, with some seaborne communication between Constantinople and its remaining Italian provinces, and a regular trickle of Islamic shipping hugging the north African coast. In the later eighth century, not only does the regularity and intensity of visible inter-regional connections increase, but a series of new axes of movement also emerge in both the archaeological and written records. Here, the last two or three decades of the eighth century appear to be particularly crucial. By 800, regular north–south links between Islamic north Africa, Sicily and Italy's Tyrrhenian coast had been established, taking in the islands of the western Mediterranean and reaching the coasts of western Spain and southern Gaul. Similar developments were taking place at the same time along Italy's Adriatic coast, which was increasingly tied into major routes across and around the Mediterranean. By the 860s the increasing activity around the hinterland of the Adriatic, and the connections made with the Danube river system and so with central and eastern Europe, helped stimulate the renewal of regular overland contacts between western Europe and Constantinople through the Balkan peninsula. The growth of communication and exchange here went hand in hand with the spread of Christianity to the Moravians and Bulgarians, and competition between the Franks and Byzantines for ecclesiastical and political influence.
These new connections were based on the revival of long-distance trade, but it was a trade that followed a different logic from the state franchises of late antiquity. There is eye-catching evidence for the presence of oriental luxury goods – above all, silks and spices – in Carolingian Europe. All of these goods were status symbols, and the fashions underpinning their conspicuous consumption by Carolingian elites seem to have spread north from Italy. Thus in the 770s Pope Hadrian I made gifts of silk altar cloths and hangings to the churches of Rome as part of a systematic reshaping of the city, averaging over a hundred such gifts a year. Silk – perhaps redolent of the holy city of Rome in the eyes of Carolingian courtiers – was soon avidly sought by the Carolingian aristocracy: thus in 793 Charlemagne 'repeatedly honoured' those Frankish aristocrats who had not been involved in Pippin the Hunchback's revolt with 'gold and silver and silk and many gifts'. By the end of the ninth century, Notker of St Gallen could send up aristocratic taste for exotic vestments from beyond the sea, imagining Charlemagne celebrating a feast day surrounded by nobles who 'strutted in robes made of pheasant-skins and silk; or of the necks, backs and tails of peacocks in their first plumage. Some were decorated with purple- and lemon-coloured ribbons; some were wrapped round with otter-skins and some in ermine robes.' For Notker, such magnificence was the natural result of shopping in Italian markets – to explain the extravagance he goes on to mock, he adds that the court 'had just come from Pavia, whither the Venetians had carried all the wealth of the east from their territories beyond the sea'. Spices, the other major oriental import, were used not only in the development of status-enhancing cuisine but also as incense to add mystery to liturgical ritual and, judging from the recipes for potions in Carolingian medical tracts, as drugs. These goods were sucked into western Europe by the conspicuous consumption of Frankish elite society, not by the state-regulated commerce sometimes imagined.
European exports are harder to track, in part because our written sources are less likely to discuss them, but the material available consistently points to furs and textiles, arms (especially highly prized Frankish swords) and slaves. It is, inevitably, this last item that has aroused most attention, with McCormick in particular arguing that the selling on of European slaves in return for oriental luxuries was the basic motor driving the Carolingian economy in the Mediterranean and beyond. There are, however, problems with such an emphasis, inevitably given the taciturn nature of our evidence. The eagerness of Islamic raiders and traders to acquire European slaves is clear from a remarkably rich seam of circumstantial evidence, anecdotes and asides in narrative sources and letters. Quite how this demand was routinely met is rather less clear. The best evidence is for slave-taking in central and eastern Europe (the origin of the term 'slave' in most modern European languages is the ethnonym 'Slav'), while the centre most consistently associated with slave exporting in our sources is Venice. Thus the disciples of the Byzantine missionary Methodius, active among the Moravian Slavs and their neighbours in the middle Danube, ended up being captured and taken to Venice, where they were redeemed just in time to prevent their sale as slaves. But although some slaving took place in the Carolingian realms, it is not at all clear that this was a sizeable trade. We certainly cannot see the economies of the Carolingian world as geared to or powered by slaving, nor is there any reason to believe that the Franks' defeated opponents found themselves sold beyond the sea, rather than taken hostage, ransomed or resettled. Frankish participation in these networks was primarily indirect, as the Venetians and their suppliers around the edges of the Carolingian world shipped out the human traffic that allowed the import of oriental luxuries to Italian markets. True, by maintaining a demand for the export of European slaves these networks encouraged some merchants to work in Francia itself, hence the complaints of the Archbishop of Lyon in the 820s about the activities of Jewish merchants trading Christian slaves into Muslim hands. But the major nodes of international trade in the Mediterranean lay on the fringes of Carolingian power, and operated independently of the Frankish kings.
The long-distance connections which made this series of exchanges possible were heroic in scope. The fascination they have inspired among many modern commentators was shared by some contemporaries, and gave rise to travellers' tales which parallel those of Ohthere and Wulfstan. Ibn Khurradadhbih, a high official under the Caliph al Mu'tamid, wrote his _Book of Routes and Kingdoms_ in 885–6, describing the trading routes connecting the Caliphate with its neighbours. In it, he includes a famous discussion of a group of Jewish merchants he calls 'Radhanites' ( _Radhaniyya_ ), who worked a series of long-distance routes transporting furs, swords and slaves from the shores of Francia into the Caliphate and beyond into the Indian Ocean and Asia. Although texts of this type cannot be taken as journalistic travelogues, Ibn Khurradadhbih was not writing fiction, and there is indeed evidence for the presence of Jewish merchants involved in long-distance trade in Francia, where Louis the Pious had taken under his protection a group of Jewish merchants operating out of Lyon. This community probably represented the extremity of the network described by Ibn Khurradadhbih, for Lyon was ideally suited both to connect with the Frankish interior and, down the Rhône, with the Mediterranean. The Lyon merchants' activities also suggest that Ibn Khurradadhbih's description of the Radhanites working a single network and conducting direct transfers from Francia through the Caliphate as far as China should not be taken at face value; instead, we are probably dealing with a series of discrete interlocking segments, each served by a small community working from nodal points such as Lyon, Venice or Damascus.
Complex connections of this type are spectacular, but they should not distract our attention from the 'background noise' of regional exchange networks which they linked together, and without which they ultimately could not have operated. In Italy as in the North Sea zone the establishment of such local networks preceded and stimulated the crystallisation of new long-distance trade in the eighth century. In 750, for example, the Lombard King Aistulf was moved to issue legislation dealing with the military obligations of merchants ( _negotiantes_ ) within his kingdom, who as a group were not only significant enough to elicit such legislation for the first time, but also diverse and numerous enough to be divided into three strata, and in 756 he sought to limit trade to 'legitimate' merchants licensed by the king. This attempt at regulation is a sure sign of growing exchange. Documents from Lucca reveal some of the individuals to whom Aistulf's laws were addressed: here, people labelled as 'merchants' by charter scribes are seen serving as witnesses of local standing and good character in property disputes. Such men were local landowners whose 'merchant' status, judging from the charters, was a subjective recognition that the balance of their activities, and their interest in buying and selling on goods, differed from that of their peers; they were doubtless engaged in the kind of regular expeditions up and down major rivers and roads, or along the coasts, practised by the 'soldiers' of Comacchio at the beginning of the century.
The priority of regional exchange in the development of trading networks is made clear by the history of the most important site in the ninth-century Mediterranean, Venice. Human activity around the lagoons and islands of the Veneto had intensified in late antiquity, but it was during the eighth century, as Constantinople's authority over its remaining Italian possessions waned, that it emerged as a significant centre. The Veneto and its hinterland occupied an ecological and economic niche not unlike Frisia in the north, and by the middle decades of the eighth century Venice had become the Adriatic's major emporium, a southern counterpart to Dorestad. The example of Comacchio shows that Venice was not the only centre performing such a role, but it stood out thanks to its establishment of a near monopoly on the long-distance trade that connected the regional economies of the Adriatic to the Islamic southern shores of the Mediterranean. A series of rich coin hoards and stray finds from sites right across the Veneto, beginning in the second half of the eighth century, helps explain the supply of oriental luxuries that gave Venice a competitive advantage in catering for the tastes of the Carolingian elite. By 862 the toll station at Mantua expected at least fifteen Venetian ships a year, making payments in pepper, cumin and linen as well as cash, and dwarfing Comacchio's trade. Like Dorestad, Venice's initial success lay in bringing together a series of distinct local economies, but its subsequent rapid growth would not have been possible without the creation of a series of long-distance connections. An indication of the sophistication of the networks which sustained this kind of activity is given in the will of the _doge_ ('leader') Justinian, which immediately stands out for its attention to moveable wealth, used as a means to fund trade. Justinian documents the resources currently invested in a voyage, on which he was awaiting a return, and land, unusually for this period, takes second place.
Venice's political situation was also distinctive. Although, like the rest of the imperial possessions in north Italy, it fell under Carolingian rule in the second half of the eighth century, Venice had always been distant from the established centres of political power in the region, and run by Venetians rather than officials sent by any external authority. In the first decades of the ninth century, as Charlemagne was resisting the efforts of the Danish king Godafrid to establish overlordship in Frisia, he was also competing with Constantinople for the allegiance of Venice and its hinterland. Here, however, after inconclusive fighting involving the Byzantine fleet and various local parties allied to the Franks, Charlemagne conceded to Constantinople in return for formal recognition of his imperial title, selling out his allies within Venice in the process. In fact, the authority he ceded was nominal and symbolic, for Venice remained essentially an independent actor from whom Constantinople might request naval help in Italian ventures, but whose assistance was always ultimately a matter of negotiation rather than command. With its umbilical ties to the markets of Italy, Venice remained _de facto_ part of the Frankish system, its relations regulated by a series of treaties but its formal allegiance to Constantinople underlining its freedom from Carolingian political control. That this relationship was agreeable to all parties underlines Venice's exceptional position, as a valve allowing the entry of oriental luxuries into the Carolingian economy. Its political independence underlay its continued success through the ninth century and beyond, allowing it to use the considerable maritime and mercantile resources already evident in the will of Justinian to secure its economic position. For all the structural similarities with Dorestad in its initial phase of growth, this combination of highly sophisticated economic infrastructure and formal political independence made Venice significantly different from anything to be found around the contemporary North Sea.
The growth of exchange on the other side of the Italian peninsula – in the area encompassing Italy's western coast, the major islands of Sicily, Sardinia and Corsica, and the northern African coast, as well as southern Gaul, western Spain and the Balearics – is harder to trace. In part, this is because exchange here did not fit the Venetian pattern of a single port monopolising long-distance routes through shipping, but grew more organically through the expansion of regional economies. Even Naples, the largest trading city on this side of the peninsula and like Venice an effectively independent duchy under nominal Byzantine sovereignty, could not establish an economic dominance to compare to Venice's in the Adriatic. The creation of inter-regional links was closely tied to the process of political stabilisation in the Islamic world under the 'Abbasids, and the demand stimulated by wealthy political elites in Islamic Spain and Africa. Both had been profoundly affected by the conflicts over the nature of true leadership within the Islamic community which had convulsed the Umayyad Caliphate in the decades preceding the 'Abbasid _daw'la_ or revolution of 750, with tensions erupting between the Islamised Berber tribes which had effected the conquest of these provinces in the decades around 700, and the Arab leaders and armies despatched to control and order them. The position stabilised only in the second half of the eighth century: in Africa, the 'Abbasids recognised the dominance of a local dynasty, the Aghlabids, who were allowed to control the provincial governorship in return for an annual payment to the Caliph; in Spain, the Umayyad refugee 'Abd al-Rahman was able to establish an independent political system which he ruled as emir. Umayyad al-Andalus (as Islamic Spain was known) and Aghlabid Ifriqiya both stood on the fringes of the recast Islamic world, cut off from the major political conflicts and the flows of men and revenue that bound together the Middle Eastern heartlands of the Caliphate. The structure of Islamic politics, however, sustained systems for the redistribution of local wealth thanks to the imposition of a head-tax on non-believers, the right of the descendants of all participants in the initial Islamic conquest to an annual dole paid out of tax revenue, and the existence of salaried standing armies. All of these were powerful stimuli for the renewal of city life and the development of markets attuned to the demands of a secure political elite with significant disposable wealth.
Against this backdrop, it is scarcely surprising to hear Theodulf of Orléans, _c_.780, marvelling at the wares of Narbonne: here the locals anxious to win Theodulf's favour offered eastern gems, Arab gold coins, Andalusian silk and Cordoban leatherware. Nor is it unexpected to find Islamic shipping making the short hop from the north African coast to Sicily, and then connecting via Naples, the major port of the Tyrrhenian Sea, to the regional economies of southern and central Italy and eventually the Ligurian coast. It was by this route, north from Africa up the Italian coast, that emissaries of the Caliph Harun al-Rashid reached Pisa and sought out Charlemagne in 801, offering him diplomatic gifts which included an elephant; Charlemagne then organised a convoy from Liguria to collect the gifts. These interactions may imply that sailings from northern Italy south to Africa were less regular than Islamic shipping making the reverse journey: Charlemagne's convoy had to be specially organised and it was also the occasion for the procuring of relics from St Cyprian's shrine at Carthage, an event which implies that travel here was anything but routine. There is little reason to see regular Islamic shipping beyond Naples, perhaps even Sicily: most likely we are dealing with a series of interconnecting regional segments, not a single long-distance route.
The gradual integration of these regional economies, and the determination of Islamic rulers to establish control over them, emerged from a series of conflicts in the first decades of the ninth century. In 798–9 the Franks despatched a naval force to 'aid' the inhabitants of the Balearic Islands, notionally part of Islamic al-Andalus but now under attack from the rebellious governors of a number of coastal cities; the Frankish sources celebrate this successful intervention as a response to 'raiding' by 'Moorish pirates', resulting in the voluntary submission of the islanders. The following decade sees western sources reporting near annual expeditions against Corsica, Sardinia and Sicily from al-Andalus and Africa, clearly aiming at political subjection but also generating a steady flow of tribute and plunder, not to mention saleable captives such as the five hundred Corsicans rescued when a Frankish fleet ambushed 'raiders' returning to Islamic Spain in 813. The language of our sources, presenting Frankish initiatives in the islands as a matter of 'protection', may hide a reality of Frankish and Islamic fleets struggling to establish control over sea-lanes which were carrying a rapidly expanding regional trade: certainly, as the case of the Balearic Islands in 798–9 demonstrates, Frankish 'aid' could be a euphemism for the aggressive establishment of a military presence. The allegiance of these islands was suddenly becoming something which was more than nominal, and which mattered urgently. Whilst the fear of Islamic 'pirates' led to measures to ensure the defence of the coasts of southern Gaul and Italy – Bishop Claudius of Turin bemoaned the distractions of organising long coastal watches designed to provide early warning of raiders – this was certainly not one-way traffic. In 828, for example, the counts of Tuscany were ordered to sail around Corsica and Sardinia to drive out 'pirates'; finding none, they headed south to Sicily and acquired pilots who could navigate them to Africa, where they raided several coastal settlements.
The sudden appearance of 'pirates' and 'raiders' around the shores of the western Mediterranean is striking because it coincides fairly closely with the earliest Viking raiding around the North Sea. We should take care before assuming that such raids were wholly new, rather than being reported in the written sources for the first time: the growing prominence of the western Mediterranean in Frankish sources may simply reflect the novelty of Carolingian political ambitions in the area. There is, nonetheless, good reason for postulating an intensification of such expeditions in the first decades of the ninth century. This was, after all, the period in which a fleet from al-Andalus fought its way across the Mediterranean and, after briefly establishing itself in Alexandria, set about the conquest of Crete, thus creating a lucrative foothold over crucial sea-lanes in the eastern Mediterranean. This kind of predatory activity culminated with the Islamic conquest of Byzantine Sicily, which began with the capture of the island's south-western tip in 827 and continued until the fall of Syracuse, the provincial capital, in 878. This was no more a simplistic 'clash of civilisations' than was Viking activity in the North Sea. The initial campaign of 827, after all, had been aided and abetted by a rebellious former governor, by no means the first Byzantine official to seek support from the nearby Islamic garrisons of the north African coast, whilst the 'Islamic conquest' was carried out by a series of distinct and sometimes competing groups: Aghlabid fleets and garrisons jostling with adventurers and mercenaries from al-Andalus; local garrisons following their own leaders, sometimes in rebellion against their nominal superiors in Africa or their appointees as governors in Sicily itself; and individual groups of soldiers campaigning under their own steam, seeking out opportunities to plunder and raid, some even attempting to carve out dominions of their own on the Italian mainland in the 860s. Although the outcome was the economic integration of southern Sicily into a regional economy centred on north Africa and geared to the demands of the Islamic political elite there, this was not a war of territorial conquest but rather a predatory venture which absorbed the energies of a footloose and fluid Islamic military eager to enrich itself through plunder and tribute. The implicit threats to Byzantine authority over its southern Italian possessions, allied to the increased volume of communication and connection around the Mediterranean, also meant that the ninth century saw an attempted reassertion of Byzantine political power in the region, with a degree of direct military and naval involvement not witnessed since the seventh century.
The ninth-century Mediterranean therefore throws up similar problems of interpretation to the ninth-century North Sea, with the parallel growth of two apparently distinct, indeed conflicting, forms of exchange: trading and raiding. But whilst the narrative sources may dwell on armed conflict, it is clear from both archaeological and written evidence that this took place against a backdrop of rising prosperity and growing trade. The complexity of interactions so typical of the Viking age in the north is paralleled on a smaller scale by the group of Islamic warriors able to establish itself in a mountainous stronghold at Fraxinetum in Provence in the last decades of the ninth century and oscillate between raiding and plundering the vibrant trade of the Rhône valley and participating opportunistically in local political conflict. Ultimately, however, the coastlines of southern Gaul and Italy stood on the edge of a zone of raiding and trading whose epicentre lay further south in Sicily. This reminds us that the differences between north and south are as important as the similarities. Whereas Viking activity in the North Sea was a response of emerging elites on the fringes of the Frankish empire to the gravitational pull exerted by the economy of northwestern Europe, the patterns of conflict in the ninth-century Mediterranean were the result of the efforts of political elites to seize control of rapidly growing regional economies at the point where the interests of three empires coincided, and to shape them to their own ends.
#### CONCLUSION: WAS THERE A CAROLINGIAN ECONOMY?
As we saw in the introduction to this chapter, the Carolingian economy has often been studied less for its own sake than for what it might tell us about the break between antiquity and the Middle Ages. Because of this subordination to debates about periodisation in European history, the Carolingian period tends to be presented in extreme terms, and usually as the proof that the post-Roman west was introverted and backward. Yet as we have seen, studying the evidence on its own terms reveals a much more complex picture. Arguments generalising from the evidence for traded luxuries or subsistence farming produce one-sided models, because elite exchange and marginal peasant production always coexisted (along with a spectrum of intervening possibilities) – the question is how to characterise the balance between them. Most economic activity in the Carolingian era centred on agricultural production of the type described in Chapter 5. However, this was too orchestrated for us to dismiss it as purely subsistence production. For the most part, the resources to organise and benefit from concentrations of this kind of wealth lay with aristocratic landlords and large churches, and it was their activity that prompted growing regional exchange networks in the seventh and eighth centuries. The need to provide for towns, which always remained significant forums for political action, especially but not only in Italy, provided another important stimulus.
These networks created surpluses that stimulated long-distance trade across the oceans; and the effects of that trade in turn encouraged the further development of regional exchange. Nonetheless, in the context of an overwhelmingly agrarian economy, long-distance trade played only a limited role in the overall picture of redistribution and exchange. This is why it is misleading to interpret major social and political shifts with reference to changes in patterns of trade. The argument, for example, that the North Sea economy was vital in funding the Carolingian renaissance, by creating an indirect connection with Middle Eastern gold and silver via the activities of Scandinavian traders travelling along the rivers of Russia, is hard to sustain – the segments that made up this disjointed snake of connections were relatively distinct, and the archaeology does not suggest that valuable resources flowed smoothly from one extreme to the other. Other mechanisms existed for the circulation of wealth: the treasure of Europe was, largely, its own, inherited from antiquity and circulated by plunder, tribute-taking and gift exchange as well as by trade.
These considerations mean that it may even be misleading to write about 'the Carolingian economy' at all. The disjointedness of the trade route leading east from the North Sea was shared by the western Mediterranean and Adriatic networks we have considered in this chapter. These networks were not only internally discontinuous, but were effectively insulated from each other. Even at the level of individual rivers, differences can be found – this chapter has drawn much material from the very well-researched site of Dorestad on the Rhine, but were we to dwell instead on exchanges along the Meuse or Seine, significant differences would appear. Moreover, the flow of goods along these routes, and the local economic landscapes in which they were embedded, were not designed or controlled by any single central authority. The arteries of trade and exchange cut across political frontiers (internal and external) and, in both the North Sea and the Mediterranean, significantly predated the rise of Carolingian power. As these networks became increasingly profitable, rulers tried to profit from them by taking tolls and other dues, but even then there is nothing resembling 'economic policy' in the capitularies or other sources. Rather than thinking about a single 'Carolingian economy', it may therefore be preferable to imagine a series of distinct local and regional networks, overlapping and intersecting to various degrees, but lacking connection to any real central motor driving activity across the whole.
Yet even if we see the production and movement of goods as operating more or less independently of the political developments of the Carolingian period, we should not imagine that they were static. As we have seen, the ninth century witnessed gradual transformations in patterns of trade and exchange which, arguably, set the scene for the improved economic conditions of the central Middle Ages. The nature of those transformations by the end of our period is illustrated by the activities of the Viking leader Godafrid III in the 880s. Godafrid, on condition of accepting baptism, had been granted Frisia (and with it Dorestad) by Emperor Charles the Fat in 882, but in 885 was persuaded to pursue ambitions further inland. Contemporary texts portray him in fairly black-and-white terms as a treacherous rebel, but it is interesting that our best source describes him demanding control of wine-producing imperial estates in the middle Rhine. Wine, rather than grain, was likely the most saleable agricultural product in this area, and played a major role in exchange along the rivers Seine, Meuse and Rhine. Godafrid's Scandinavian predecessors, such as his namesake who had fought Charlemagne for control of Frisia in the first decade of the century, had been primarily concerned with controlling segments of the North Sea network and thus guaranteeing the opportunity to profit from long-distance exchange. Godafrid's ambitions, by contrast, suggest a desire to control not just the export but also the production of profitable goods from these Rhineland estates. This contrast illustrates again the declining significance of emporia like Dorestad and the rising economic importance of inland centres nearer the heartlands of the realm, and highlights the extent to which the North Sea network's centre of gravity had been drawn inland.
Things did not work out well for Godafrid: the emperor did not take kindly to his threats and, after tricking him into a meeting with his agents, had him and his followers murdered. Yet the fact that he tried to work his scam as an insider also indicates the extent to which that network's main players, Scandinavians and Franks, competed together for access to increasingly concentrated resources – not only had the northern trade routes become gradually more coherent, but so had the groups who sought to profit from them. Godafrid's identity was multi-faceted: detractors inevitably decried him as an invader, stressing his Scandinavianness, but he was also a Christian, a sworn follower of the emperor and the husband of a member of the Carolingian dynasty. Without doubt he saw himself as belonging to Frankish elite society, and his attempt to gain a foothold in one of the political and economic heartlands of the empire was probably motivated above all by a desire to cement that belonging. Membership of that society depended in large part on subscription to its social norms and the associated taste for ostentatious feasts, fancy clothes and exotic luxuries. And above all, it was the demands and imperatives of the wealthy landowners who participated in such activities that drove the processes of exchange we have been describing. As the empire expanded and stabilised, drawing conquered (and even, as shown by the case of Godafrid, neighbouring) regional aristocracies into a shared political system, the growing coherence of the Frankish elite lent an increasing coherence to trade and exchange. The empire encouraged multi-regional landholding and fostered the growth of shared codes of conspicuous consumption among members of its ruling class, which in turn gave momentum to the dynamics we have sketched out in this chapter. There was a Carolingian economy, in other words, because there was a Carolingian empire.
* * *
J. M. Bately (ed.), _The Old English Orosius_ (Oxford, 1980), relevant sections repr. and trans. in N. Lund (ed.), _Two Voyagers at the Court of King Alfred_ (York, 1984), and see Bately and A. Englert (eds.), _Ohthere's Voyages_ (Roskilde, 2007). See also M. Townend, _Language and History in Viking Age England: Linguistic Relations between Speakers of Old English and Old Norse_ (Turnhout, 2002), pp. 79–109; F. L. Michelet, _Creation, Migration and Conquest. Imaginary Geography and the Sense of Space in Old English Literature_ (Oxford, 2006), pp. 115–62; S. Gilles, 'Territorial interpolations in the Old English Orosius', in S. Gilles and S. Tomasch (eds.), _Text and Territory: Geographical Imagination in the Middle Ages_ (Philadelphia, PA, 1998), pp. 79–96; M. Godden, 'The Anglo-Saxons and the Goths: rewriting the sack of Rome', _Anglo-Saxon England_ 31 (2002), pp. 47–68.
See D. Pratt, _The Political Thought of King Alfred the Great_ (Cambridge, 2007), pp. 41, 117.
The phrase is coined by R. Hodges, _Dark Age Economics: The Rebirth of Towns and Trade, 600–1000_ (London, 1982).
Pirenne, _Mohammed and Charlemagne_ , p. 234; first published in French in 1937.
On Pirenne, see B. Lyon, _Henri Pirenne: A Biographical and Intellectual Study_ (Ghent, 1974); P. Delogu, 'Reading Pirenne again', in Hodges and Bowden (eds.), _The Sixth Century_ , pp. 15–40.
Dopsch, _Wirtschaftliche und soziale Grundlagen;_ the English translation by Beard and Marshall ( _Economic and Social Foundations of European Civilisation_ ) never achieved the same status as Pirenne's work.
See Hodges, _Dark Age Economics_ , expanded into a neo-Pirennian global model of the early medieval economy by R. Hodges and D. Whitehouse, _Mohammed, Charlemagne and the Origins of Europe_ (London, 1983). See also Hodges, _Light in the Dark Ages: The Rise and Fall of San Vincenzo al Volturno_ (London, 1997).
McCormick, _Origins of the European Economy;_ Wickham, _Framing the Early Middle Ages_.
The classic discussion remains K. Polanyi, 'The economy as instituted process', in Polanyi, C. Arensberg and H. Pearson (eds.), _Trade and Market in Early Empires_ (Glencoe, IL, 1957), pp. 243–69; for subsequent reception, see S. C. Humphreys, 'History, economics, and anthropology: the work of Karl Polanyi', _History and Theory_ 8 (1969), pp. 165–212; and for a medieval model W. I. Miller, 'Gift, sale, payment, raid: case studies in the negotiation and classification of exchange in medieval Iceland', _Speculum_ 61 (1986), pp. 18–50.
Lund (ed.), _Two Voyagers_ , p. 20.
Itinerant pastoralists like the _Finnas_ are, as a rule, not economically self-sufficient but dependent on regular exchange with more settled peoples: see Wickham, 'Pastoralism and underdevelopment'.
C. Fell, _'Unfriþ:_ an approach to a definition', _Saga-Book of the Viking Society for Northern Research_ 21 (1982–3), pp. 85–100; N. Lund, 'Peace and non-peace in the Viking age', in J. E. Knirk (ed.), _Proceedings of the Tenth Viking Congress_ (Oslo, 1987), pp. 255–69.
P. Sawyer, 'Kings and merchants', in P. H. Sawyer and I. N. Wood (eds.), _Early Medieval Kingship_ (Leeds, 1977), pp. 139–58.
The following section summarises an argument developed in Innes, 'Framing the Carolingian economy'.
Reuter, 'Plunder and tribute', on which see J. L. Nelson, 'Charlemagne and the paradoxes of power', _Reuter Lecture_ (University of Southampton, 2006). Reuterwas responding to the plea of Philip Grierson for early medievalists to take seriously non-market systems of exchange: see P. Grierson, 'Commerce in the dark ages: a critique of the evidence', _TRHS_ 9 (1959), pp. 123–40. For the impact of the most spectacular plunder, the Avar treasure, see Einhard, _VK_ , c. 13; Alcuin, _Ep_. 100, trans. _EHD_ , no. 197.
Nelson, _Charles the Bald_ , pp. 19–40; R. Hodges, 'Trade and market origins in the ninth century: an archaeological perspective on Anglo-Carolingian relations', in M. Gibson and J. Nelson (eds.), _Charles the Bald: Court and Kingdom_ (2nd edn, Aldershot, 1990), pp. 213–33.
See Le Jan, 'Frankish giving of arms'; C. Wickham, 'Rethinking the structure of the early medieval economy', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 19–32. For theoretical perspectives see A. Appadurai (ed.), _The Social Life of Things. Commodities in Cultural Perspective_ (Cambridge, 1986); A. Weiner, _Inalienable Possessions. The Paradox of Keeping-while-Giving_ (Berkeley, CA, 1992).
_Hildebrandslied_ and _Waltharius_ , ed. and trans. Knight Bostock, _Handbook on Old High German Literature_ , pp. 44–7 and 259–80. On treasure and identity see M. Hardt, 'Royal treasures and representation in the early Middle Ages', in W. Pohl and H. Reimitz (eds.), _Strategies of Distinction. The Construction of Ethnic Communities, 300–800_ (Leiden, 1998), pp. 255–80. On these texts see Innes, 'Teutons or Trojans?'.
On manorial economies, see above, Chapter 5, pp. 252–8.
See Reuter, 'Plunder and tribute', pp. 85–6; Nelson, 'The Lord's anointed', at p. 166.
For standardised gifts and their renegotiation, see Innes, 'Framing the Carolingian economy', pp. 48–9; Innes, _State and Society_ , pp. 159–62. See also Notker, _Gesta_ , 2.21. On polyptychs see above, Chapter 5, pp. 252–4.
On workshops, see F. Schwind, 'Zu karolingerzeitlichen Klöstern als Wirtschaftsorganismen und Stätten handwerklicher Produktion', in L. Fenske, W. Rösener and T. Zotz (eds.), _Institutionen, Kultur und Gesellschaft im Mittelalter: Festschrift für Josef Fleckenstein zu seinem 65. Geburtstag_ (Sigmaringen, 1984), pp. 101–23; R. Hodges, _San Vincenzo al Volturno 1. The Excavations 1980–1986, part 1_ (London, 1993) and _San Vincenzo al Volturno 2. The Excavations 1980–1986, part 2_ (London, 1995). For Carolingian weaponry, see S. Coupland, 'Carolingian arms and armour in the ninth century', _Viator_ 29 (1990), pp. 29–50.
See e.g. Einhard, Epp., esp. 23, 24, 36, 37, 38, 54; and for discussion see Innes, 'Practices of property'.
Einhard, _Translation and Miracles_ describes his various journeys to and from Aachen. On _De villis_ see above, Chapter 5, p. 254.
For an encyclopaedic discussion of legislation on tolls and trade, see H. Siems, _Handel und Wucher im Spiegel frühmittelalterliche Rechtsquellen_ (Hanover, 1992).
_Capitulare de villis_ , esp. c. 28.
For more discussion of this theme, see Innes, 'Framing the Carolingian economy'; Innes, 'Practices of property'; Wickham, 'Rethinking the structure'; J. Moreland, 'Concepts of the early medieval economy', in Hansen and Wickham (eds.), _The Long Eighth Century, pp. 1–34_.
On these developments, see Hodges, _Dark Age Economics_ ; M. Anderton (ed.), _Anglo-Saxon Trading Centres: Beyond the Emporia_ (Glasgow, 1999); D. Hill and R. Cowie (eds.), _Wics: The Early Medieval Trading Centres of Northern Europe_ (Sheffield, 2001); C. Scull, 'Urban centres in pre-Viking England?', in J. Hines (ed.), _The Anglo-Saxons from the Migration Period to the Eighth Century_ (Woodbridge, 1997), pp. 269–310; H. Clarke and B. Ambrosiani (eds.), _Towns in the Viking Age_ (London, 1995). For Frankish perspectives see R. Hodges, _Towns and Trade in the Age of Charlemagne_ (London, 2000); A. Verhulst, _The Rise of Cities in North-West Europe_ (Cambridge, 1999); Verhulst, _Carolingian Economy_. On cross-Channel connections more generally see Story, _Carolingian Connections_.
_Gesta sanctorum patrum Fontanellensis coenobii_ Acts of the Abbots of St Wandrille], ed. F. Lohierand J. Laporte, Société del'histoire de Normandie ([Rouen and Paris, 1936), XII, 2, trans. _EHD_ , no. 20; S. Kelly, 'Trading privileges from eighth-century England', _EME_ I (1992), pp. 3–28.
Bede, _HE_ II.3.
W. van Es and W. Verwers, _Excavations at Dorestad I. The Harbour, Hoogstraat I_ (Amersfoort, 1980), and the short accessible summary in W. Verwers, 'Dorestad: a Carolingian town?', in B. Hobley and R. Hodges (eds.), _The Rebirth of Towns in the West, AD 700–1050_ (London, 1988), pp. 52–6; on Quentovic, see D. Hill, _et al_., 'Quentovic defined', _Antiquity_ 61 (1990), pp. 51–8.
For Scandinavian proto-towns as seats of royal power, see Rimbert, _Vita Anskarii Life of Anskar]_ , ed. G. Waitz, _MGH SRG in usum scholarum separatim editi_ LV ([Hanover, 1884), cc. 19, 26, 27.
Wickham, _Framing the Early Middle Ages_ , pp. 794–819 emphasises the asymmetry of exchanges around the North Sea.
See Verwers, 'Dorestad'.
Hodges, _Dark Age Economics_ , lists relevant finds.
Alcuin, _Ep_. 100, trans. _EHD_ , no. 197. On Frisian cloaks, see also Notker, _Gesta_ , 1.34. On the famous 'black stones', also discussed in Charlemagne's letter, see now Story, _et al_., 'Charlemagne's black marble', pp. 157–90.
See above, Chapter 5, pp. 245–6; and cf. M. McCormick, 'New light on the "dark ages": how the slave trade fuelled the Carolingian economy', _P &P_ 177 (2002), pp. 17–54.
On Hamwic, see A. D. Morton, _Excavations at Hamwic I_ (London, 1992), pp. 20– 77, or more accessibly M. Brisbane, 'Hamwic (Saxon Southampton): an eighth century port and production centre', in Hodges and Hobley (eds.), _The Rebirth of Towns in the West_ , pp. 101–8; on the political context, see B. Yorke, 'The Jutes of Hampshire and Wight and the origins of Wessex', in S. Bassett (ed.), _The Origins of Anglo-Saxon Kingdoms_ (London and New York, 1989), pp. 84–96.
On Merovingian Dorestad, see Wood, _Merovingian Kingdoms_ , pp. 296–301.
See above, Chapter 2, pp. 48–9.
On _sceattas_ see Wood, _Merovingian Kingdoms_ , pp. 299–303.
On Frisia and the Frisians see S. Lebecq, _Marchands et navigateurs. Frisons du haut moyen âge_ (Lille, 1983); D. Kilmers, 'The Frisian monopoly of coastal transport in the 6th to 8th centuries AD', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 91–2.
Cf I. Wood, 'The Channel from the 4th to the 7th centuries AD', and S. Lebecq, 'On the use of the word Frisian in the 6th to 10th centuries: some interpretations', both in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 93–7 and 85–90 respectively.
J. W. Huggett, 'Imported grave goods and the early Anglo-Saxon economy', _Medieval Archaeology_ 32 (1988), pp. 63–96. The latter term is taken from Wood, _The Merovingian North Sea_.
M. Carver, 'Pre-Viking traffic in the North Sea', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 117–25. For 'beach markets' see Hodges, _Dark Age Economics_ , and for one possible example, certainly in use in the Viking age, see D. Griffiths, R. Philpott and G. Egan (eds.), _Meols. The Archaeology of the North Wirral Coast_ (Oxford, 2007).
On Danekirke, see H. J. Hansen, 'Dankirke: affluence in late Iron Age Denmark', in K. Randsborg (ed.), _The Birth of Europe. Archaeology and Social Development in the First Millennium AD_ (Rome, 1989), pp. 123–8; for context see B. Ambrosiani and H. Clarke (eds.), _Developments around the Baltic and the North Sea in the Viking Age_ (Stockholm, 1994), and for the connections between economics and politics in Denmark in this period U. Näsman, 'Exchange and politics: the eighth—early ninth century in Denmark', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 35–68.
A. Morton, 'Hamwic in its context', in Anderton (ed.), _Anglo-Saxon Trading Centres_ , pp. 48–62.
For example P. Blinkhorn, 'Of cabbages and kings: production, trade, and consumption in Middle-Saxon England', in Anderton (ed.), _Anglo-Saxon Trading Centres_ , pp. 4–23.
See S. Schütte, 'Continuity problems and authority structures in Cologne', in G. Ausenda (ed.), _After Empire: Towards an Ethnology of Europe's Barbarians_ (San Marino, 1995), pp. 163–76; F. Theuws, 'Maastricht as a centre of power in the early Middle Ages', in De Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 155–216, esp. pp. 200–5.
See S. Coupland, 'Trading places: Quentovic and Dorestad reassessed', _EME_ 11 (2002), pp. 209–32; S. Coupland, 'Between the devil and the deep blue sea: hoards in ninth-century Frisia', in B. Cook and G. Williams (eds.), _Coinage and History in the North Sea World c.500–1250. Essays in Honour of Marion Archibald_ (Leiden, 2006), pp. 241–66; Coupland, 'Money and coinage'.
Coupland, 'Trading places' (though with a different interpretation from that presented here); J. C. Moesgaard, 'A survey of coin production and currency in Normandy, 864–945', in J. Graham-Campbell and G. Williams (eds.), _Silver Economy of the Viking Age_ (Walnut Creek, CA, 2007), pp. 99–121.
See S. Lebecq, 'The role of the monasteries in the systems of production and exchange of the Frankish world between the seventh and the beginning of the ninth centuries', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 121–48. On Lupus's struggle to regain St Josse, see Lupus of Ferrières, _Epistolae_ , ed. P. K. Marshall (Leipzig, 1984), nos. 19, 32, 36, 42, 43, 45, 49, 58, 62, 65, 82, 86. See also J. L. Nelson, 'England and the continent in the ninth century: II, Vikings and others', _TRHS_ 6th ser. 13 (2003), pp. 1–28, for Quentovic.
See for example O. Crumlin-Pedersen, _From Viking Ships to Hanseatic Cogs_ (London, 1983). Carver, 'Pre-Viking traffic' points out the methodological problems in identifying sea-routes from this kind of evidence.
W. van Es, 'Dorestad centred', in J. C. Besteman, J. M. Bos and H. A. Heidinga (eds.), _Medieval Archaeology in the Netherlands. Studies Presented to H. H. von Regteren Altena_ (Assen and Maastricht, 1990), pp. 151–82, is an excellent analysis of the emporium's relationship to its hinterland.
See Verhulst, _The Rise of Cities;_ and A. Verhulst, 'The origins of towns in the Low Countries and the Pirenne Thesis', _P &P_ 122 (1989), pp. 3–35.
On the archaeology of Mainz, see E. Wamers, _Die frühmittelalterliche Lesefunde aus der Löhrstraße (Baustelle Hilton II) in Mainz_ (Mainz, 1994). See also Falck, _Mainz im frühen und hohen Mittelalter_.
Van Es and Verwers, _Excavations at Dorestad 1_.
Einhard, _Translation and Miracles_ , III.6.
_AF, s.a_. 870.
For references and discussion see Innes, _State and Society_ , pp. 66–8, 96–8.
For coin finds at Mainz, see Wamers, _Die frühmittelalterliche Lesefunde;_ see also W. Hess, 'Geldwirtschaft am Mittelrhein in karolingischer Zeit', _Blätter für deutsche Landesgeschichte_ 98 (1962), pp. 26–63; M. Blackburn, 'Coin circulation in Germany during the early Middle Ages: the evidence of single-finds', in B. Kluge (ed.), _Fernhandel und Geldwirtschaft_ (Sigmaringen, 1993), pp. 37–54.
For Frisians at Mainz see _AF_ (Mainz continuation), _s.a_. 886.
The best introduction is Nelson, _Charles the Bald_ , pp. 19–40.
Note that the label 'Viking' is a modern term of art rather than a contemporary designation. Godafrid III's exploits are described in _AF, s.a_. 882–5.
The debate was opened by P. H. Sawyer, _The Age of the Vikings_ (London, 1962, 2nd edn London, 1971). See also P. Wormald, 'Viking studies: whence and whither?', in R. T. Farrell (ed.), _The Vikings_ (Chichester, 1982), pp. 128–53; N. Lund, 'Allies of God or man? The Viking expansion in European perspective', _Viator_ 20 (1989), pp. 45–59; Nelson, 'England and the continent'.
See above all S. Coupland, 'The rod of God's wrath or the people of God's wrath? The Carolingian theology of the Viking invasions', _Journal of Ecclesiastical History_ 42 (1991), pp. 535–54.
Rimbert, _Vita Anskarii_ , c. 19.
See ARF, _s.a_. 808, 809; M. Müller-Wille, A. Tummuscheit and L. Hansen, _Frühstädtliche Zentren der Wikingerzeit und ihr Hinterland. Die Beispiele Ribe, Hedeby und Reric_ (Göttingen, 2002).
ARF, _s.a_. 810.
Palmer, 'Rimbert's _Vita Anskarii_ '; Wood, 'Christians and pagans'.
Cf P. Heather, 'State formation in Europe in the first millennium AD', in B. Crawford (ed.), _Scotland in Dark Age Europe_ (St Andrews, 1994), pp. 47–63; K. L. Maund, '"A turmoil of warring princes": political leadership in ninth-century Denmark', _Haskins Society Journal_ 6 (1994), pp. 29–47; I. Garipzanov, 'Frontier identities: Carolingian frontier and _gens Danorum'_ , in I. H. Garipzanov, P. J. Geary and P. Urbanczyk (eds.), _Franks, Northmen, and Slavs: Identities and State Formation in Early Medieval Europe_ (Turnhout, 2008), pp. 113–42.
Coupland, 'From poachers to gamekeepers'.
Coupland, 'From poachers to gamekeepers'; Coupland, 'Between the devil and the deep blue sea'.
Notker, _Gesta_ , 2.19; E. Wamers and M. Brandt (eds.), _Die Macht des Silbers:_ _Karolingische Schätze im Norden_ (Frankfurt, 2005).
M. Metcalf, 'A sketch of the currency in the time of Charles the Bald', in M. T. Gibson and J. L. Nelson (eds.), _Charles the Bald: Court and Kingdom_ (2nd edn, Aldershot, 1990), pp. 65–97; S. Coupland, 'The Frankish tribute payments to the Vikings and their consequences', _Francia_ 26 (1999), pp. 57–75. For debates over the scale of coinage in circulation, see also P. Grierson, 'The volume of the Anglo-Saxon coinage', _Economic Historic Review_ 20 (1967), pp. 153–60; Coupland, 'Money and coinage'.
_AF_ (Mainz continuation), _s.a_. 882.
See S. Loseby, 'Marseille and the Pirenne thesis I: Gregory of Tours, the Merovingian kings, and "un grandport"', in Hodges and Bowden (eds.), _The Sixth Century_ , pp. 203–29.
McCormick, _Origins of the European Economy_ , Part I, for the best overview of the end of the ancient economy, emphasising the sixth-century plague; for Carthage as the final full stop, see M. Innes, _Introduction to Early Medieval Western Europe, 300–900. The Sword, the Plough and the Book_ (London and New York, 2007), pp. 191–3.
For a theoretical framework stressing the primacy of the latter in the pre-modern Mediterranean, see P. Horden and N. Purcell, _The Corrupting Sea: A Study of Mediterranean History_ I (Oxford, 1999); P. Squatriti, 'Mohammed, the early medieval Mediterranean, and Charlemagne', _EME_ II (2003), pp. 263–79.
Liutprand's _pactum_ is edited by L. Hartmann, _Zur Wirtschaftsgeschichte Italiens im frühen Mittelalter_ (Gotha, 1904); and for discussion see McCormick, _Origins of the European Economy_ , pp. 117–18, 631–3, 778–9. On Comacchio, see S. Gelichi, 'The rise of an early medieval emporium and the economy of Italy in the late Longobard age', in _Annales. Series Historia et Sociologia_ 18/2 (2008), pp. 319–36.
See above, Chapter 5, p. 234.
See Wickham, 'Aristocratic power', and for economic aspects R. Balzaretti, 'Cities and markets in early medieval Europe', in G. Ausenda (ed.), _After Empire. Towards an Ethnology of Europe's Barbarians_ (San Marino, 1994), pp. 113–42; R. Balzaretti, 'Monasteries, towns and the countryside: reciprocal relationships in the archdiocese of Milan, 614–814', in G. P. Brogiolo, N. Gauthier and N. Christie (eds.), _Towns and Their Territories: Between Late Antiquity and the Early Middle Ages_ (Leiden, 2000), pp. 235–57; R. Balzaretti, 'Cities, emporia and monasteries: local economies in the Po valley 700–875', in N. Christie and S. Loseby (eds.), _Towns in Transition. Urban Evolution in Late Antiquity and the Early Middle Ages_ (Aldershot, 1996), pp. 213–34.
Gasparri and La Rocca (eds.), _Carte di famiglia_.
Gasparri, 'The aristocracy'.
Most prominent among the exceptions, which did develop manorial estates similar to those in northern Europe, are some of the larger monasteries: for the example of Farfa, see Costambeys, _Power and Patronage_.
S. Gasparri, 'Mercanti o possessori? Profilo di un ceto dominante in un' età di transizione'; for coin and cash in Toto's documents see A. Rovelli, 'Economia monetaria e monete nel dossier di Campione', both in Gasparri and La Rocca (eds.), _Carte di famiglia_ , pp. 157–78 and pp. 117–40 respectively; and for the general problems of coin use in eighth- and ninth-century Italy see A. Rovelli, 'Some considerations on the coinage of Lombard and Carolingian Italy', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 195–223; A. Rovelli, 'Emissione e uso della moneta: le testimonianze scritte e archaeologiche', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 48 (Spoleto, 2001), pp. 821–52; A. Rovelli, 'Coins and trade in early medieval Italy', _EME_ 17 (2009), pp. 45–76.
See M. Costambeys, 'Property, ideology and the territorial power of the papacy in the early Middle Ages', _EME_ 9 (2000), pp. 367–96.
Wickham, _Framing the Early Middle Ages_ , pp. 736–41.
On _domuscultae_ see Francovich, 'Changing structures of settlement', at p. 163 (see also the glossary at p. 229); Costambeys, _Power and Patronage_ , pp. 187–96.
On the recent finds in Rome, see C. Wickham, 'Overview: production, distribution and demand, II', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 345–77, at pp. 361–2. See also D. Whitehouse, '"Things that travelled": the surprising case of raw glass', _EME_ 12 (2003), pp. 301–5 and M. McCormick, 'Complexity, chronology and context in the early medieval economy', _EME_ 12 (2003), pp.307–23, and a number of the articles in Smith (ed.), _Early Medieval Rome and the Christian West_.
For papal building, see T. F. X. Noble, 'Topography, celebration and power: the making of a papal Rome in the eighth and ninth centuries', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 45–92; Noble, 'Paradoxes and possibilities'; Goodson, _The Rome of Pope Paschal I_.
_LP_ I, pp. 468–71, trans. Davis, _Lives of the Eighth-Century Popes_ , pp. 88–92.
McCormick, _Origins of the European Economy_.
For developments in central-eastern Europe see McCormick, _Origins of the European Economy_ , pp. 548–62; and more generally F. Curta, _Southeastern Europe in the_ _Middle Ages, 500–1250_ (Cambridge, 2006).
See for example _LP_ I, p. 505, trans. Davis, _Lives of the Eighth-Century Popes_ , p. 152.
AL, _s.a_. 793.
Notker, _Gesta_ , 2.17, trans. Ganz, pp. 110–11; and see McCormick, _Origins of the European Economy_ , pp. 719–26.
McCormick, _Origins of the European Economy_ , pp. 708–19.
On aristocratic tastes see above, Chapter 6, pp. 284–5.
McCormick, _Origins of the European Economy_ , pp. 729–78.
McCormick, _Origins of the European Economy_ , pp. 761–8; McCormick, 'New light on the "dark ages"'.
McCormick, _Origins of the European Economy_ , pp. 766–7; _The_ Vita _of Constantine and the_ Vita _of Methodius_ , ed. M. Kantor (Ann Arbor, MI, 1976), where Venice's nodal role in communications between Rome, Constantinople and central Europe is made clear.
See e.g. A. J. Kosto, 'Hostages in the Carolingian world', _EME_ 11 (2002), pp. 123–47.
McCormick, _Origins of the European Economy_ , p. 675; Agobard of Lyon's voluminous tracts against the Jews are edited by L. van Acker: _Agobardi Lugdunensis Opera Omnia, CCCM_ 52 (Turnhout, 1981).
Ibn Khurradadhbih, _Book of Routes and Kingdoms_ , ed. M. J. de Goeje, _Bibliotheca geographorum arabicorum_ 6 (Leiden, 1889), trans. R. S. Lopez and I. W. Raymond, _Medieval Trade in the Mediterranean World: Illustrative Documents_ (London and New York, 1955), pp. 30–3; for discussion and bibliography, see McCormick, _Origins of the European Economy_ , pp. 688–93.
_Formulae imperiales_ , no. 31; McCormick, _Origins of the European Economy_ , p. 772.
_Leges Ahistulfi_ , cc. 3, 4, 6.
McCormick, _Origins of the European Economy_ , pp. 630–1; see also Gasparri, 'Mercanti o possessori?', p. 169.
See McCormick, _Origins of the European Economy_ , pp. 361–9.
McCormick, _Origins of the European Economy_ , pp. 633–6.
Justinian, _Testament a.828/9_ , ed. L. Lanfranchi and B. Strina, _Ss. Ilario e Benedetto e Gregorio_ (Venice, 1965), no. 2, p. 24.
The major source for these events is the ARF, _s.a_. 806–11.
The earliest surviving treaty is from 22 February 840, though there may have been precedents.
On Naples see P. Arthur, _Naples from Roman Town to City-state_ (London, 2004).
See P. Crone, _Slaves on Horses: The Evolution of the Islamic Polity_ (Cambridge, 1980); H. Kennedy, _The Prophet and the Age of the Caliphates_ (Harlow, 1986, 2nd edn 2004).
H. Kennedy, 'Military pay and the economy of the early Islamic state', _Historical Research_ 188 (2002), pp. 155–69; for early medieval Islamic cities the key discussion is H. Kennedy, 'From _polis_ to _madina_ : urban change in late antique and early Islamic Syria', _P &P_ 106 (1985), pp. 3–27; for north Africa see M. Carver, 'Transitions to Islam', in N. Christie and S. Loseby (eds.), _Towns in Transition. Urban Evolution in Late Antiquity and the Early Middle Ages_ (Aldershot, 1996), pp. 184–212.
Theodulf, _Carmina_ 28, ed. Dümmler, pp. 493–517, trans. Godman, _Poetry of the Carolingian Renaissance_ , pp. 162–6.
_ARF, s.a_. 801; Florus of Lyon, _Carmina_ , ed. E. Dümmler, _MGH Poet. Latini aevi Karolini_ II (Berlin, 1884), 13–14, pp. 544–6. On the elephant see Dutton, _Charlemagne's Mustache_ , pp. 43–68.
See _ARF, s.a_. 798–9; P. Guichard, 'Les Débuts de la piraterie andalouse en Mediterranée occidentale (798–813)', _Revue de l'Occident musulman_ 35 (1983), pp. 55–76.
_ARF, s.a_. 813, and see in general the year-by-year account in the _ARF_ from 806 onwards.
See M. Gorman, 'The commentary on Genesis of Claudius of Turin and Biblical studies under Louis the Pious', _Speculum_ 72 (1997), pp. 279–329.
_ARF, s.a_. 828; McCormick, _Origins of the European Economy_ , p. 521.
An up-to-date study of ninth-century Sicily is a desideratum: for an uncritical rehearsal of the sources, see A. Ahmed, _A History of Islamic Sicily_ (Edinburgh, 1975).
On the political context, see B. Kreutz, _Before the Normans: Southern Italy in the Ninth and Tenth Centuries_ (Philadelphia, PA, 1996).
P. Sénac, _Musulmans et Sarrasins dans le sud de la Gaule du viiie au XIe siècle_ (Paris, 1980).
See Moreland, 'Concepts of the early medieval economy'.
See S. Bolin, 'Mohammed, Charlemagne and Ruric', _Scandinavian Economic History Review_ 1 (1953), pp. 5–39; Hodges and Whitehouse, _Mohammed, Charlemagne and the Origins of Europe_ , pp. 6–7. For archaeology see J. Callmer, 'Numismatics and archaeology', _Fornvännen_ 75 (1980), pp. 203–12; S. Coupland, 'Carolingian coinage and Scandinavian silver', _Nordisk Numismatisk Årsskrift_ (1985–86), pp. 11–32; Myhre, 'The archaeology of the early Viking age in Norway'.
Regino, _Chronicle_ , _s.a_. 885; see Coupland, 'From poachers to gamekeepers', pp. 108–12.
Wickham, 'Overview', p. 355.
See above, Chapter 6, pp. 278–85.
## 8
### SUSTAINING THE CAROLINGIAN EMPIRE: POLITICS AND GOVERNMENT, 840–888
#### INTRODUCTION: FRATERNAL RIVALRY, 840–843
The deposition of Louis the Pious in 833 was neither, we have seen, the definitive disaster of the emperor's own reign nor of the Carolingian empire writ large. Still, the Frankish political community was unmistakably shocked. The main protagonists harboured anxieties about what they had done: in a letter of 847, the emperor Lothar reflected almost disbelievingly on that time of conflict between him and his brothers as 'the work of the Devil through his agents'. But even the traumas of the early 830s were eclipsed in the Frankish psyche by the three years of bloody civil war which followed the death of Louis the Pious in 840. Once again, his sons were at the heart of the matter. A loose alliance of Charles the Bald and Louis the German teamed up against Lothar and Pippin II of Aquitaine (the three kings' nephew who was hoping to dislodge Charles from the south-west and claim the kingdom of his father Pippin I, who had died in 838). As their armies ceaselessly roamed the empire in a game of armed chess whose top prize was control of the Carolingian heartlands in the north, a long series of armed stand-offs and skirmishes peaked at the bloody battle of Fontenoy in June 841. (See Map 14 for places mentioned in this chapter.) A man called Engelbert, who fought on Lothar's side, later wrote a poem lamenting the extreme violence and horrifying implications of the battle: 'No slaughter was ever worse on any field of war... This battle is not worthy of praise, not fit to be sung.'
**Map 14.** Places mentioned in Chapter 8: 'Sustaining the Carolingian empire: politics and government, 840–888'
Major pitched battles were rare in the early medieval period precisely because so much could hinge on their outcome; and recent history, even the dark days of the early 830s, provided few examples of noble Franks drawing swords in earnest against their comrades. The Franks were thus stunned by the loss of aristocratic life at Fontenoy. Four decades later in a work written for the emperor Charles the Fat, Notker of St Gallen recoiled from even mentioning the name of the battle, so horrified was he that Christian blood had been spilled by Louis the German, Charles's father. A few years before that, Pope John VIII had taunted the same Louis by reminding him of the 'stilldamp fields of Fontenoy that he soaked with human blood in his youth'. All four Carolingians survived the fighting and in this sense the battle was not decisive. However, victory for Charles and Louis gave them the edge and effectively undermined Lothar's prospects of winning the war as a whole. His forays into the western strongholds of Charles, and those of Louis in the east, became less and less convincing and he was forced to negotiate. The final seal was set on the truce in summer 843 by the famous Treaty of Verdun. This carefully planned division split the empire into three vertical strips, with Charles receiving the western portion, Lothar the middle, and Louis the eastern – Pippin II, like Pippin the Hunchback and Bernard of Italy before him, was airbrushed out of the family picture.
Verdun represented an orderly conclusion to what had been a vicious and divisive conflict. This was not solely down to the shocking bloodshed of Fontenoy. The routine intimidation, bribery and betrayal that characterised the civil war are revealed by the detailed account composed by the lay noble Nithard, a disillusioned partisan of Charles the Bald whose mother was one of Charlemagne's daughters. The root cause of the war, and the reason for its atavistic animosity, was fraternal rivalry. Even a casual glance at the Carolingian family tree reveals the extent to which fortune had favoured the dynasty. Since 771 Charles and then Louis had been able to rule the empire unencumbered by brothers to rival them; in 840, for the first time in three generations, more than one royal son survived to fight over their father's inheritance. The civil war of 840–3 resulted from fraternal suspicions and ambitions which had simmered throughout the 830s, and now erupted unrestrained by any consensus on how power should be divided between members of the dynasty. The lack of consensus was not inevitable – brothers, even royal brothers, do sometimes get on with each other – but the preconditions for discord had been created by the actions of the ageing Louis the Pious himself. Driven by Louis's desire to carve out a kingdom for Charles the Bald, as well as his periodic need to punish his other sons for their contumacy by restricting their future share in power and territory, no fewer than five imperial division plans were promulgated between 829 and 839. This bred uncertainty in the minds of regional aristocracies shunted from pillar to post – which Carolingian should they court as their future lord? The charge made against Louis in 833 – that he had caused people to perjure themselves (and thus imperil their souls) by swearing contradictory oaths – reveals the anxiety that this dilemma created. It also opened the way for conflict within the dynasty. In the aftermath of the old emperor's death Lothar was able to pitch a claim to the implementation of the _Ordinatio imperii_ of 817, which gave him a superior status; while partisans of Charles the Bald such as Nithard believed that the most rightful division had been the one made in 839, which endowed Charles with a large swathe of territory, and that Lothar was breaking his oaths by attempting to override it. The division plans of Louis's reign provided each contender with a more or less equal basis for arguing that his position was legitimate and that the use of violence was therefore just.
The tone of most modern accounts of the decades between the death of Louis the Pious and the disintegration of the empire in 888 is set by the fury of this internecine warfare. Historians used to write the story of the post-840 period as an extended and dismal coda to the disasters of Louis's reign, with familial conflict emblematic of the centrifugal forces that are supposed to have spun the empire out of the Carolingians' control. The root cause of the problems was often diagnosed as territorial division itself: the change from a unified empire to a political landscape populated by multiple rulers was regarded as symbolic of a tectonic shift in the underlying political geology of the empire – a shift that led inexorably towards disintegration and collapse. Division and subdivision of territory, escalating internal conflict, ever-weaker leadership in the face of Viking invasion, increasingly autonomous aristocratic power and rising disillusionment with the ruling dynasty are the notes which form the bass line in this version of history. Even the Carolingians' nicknames have been held against them, the idea being that men known as Louis the Stammerer and Charles the Fat must have been laughable figures (despite the fact that most of these nicknames are not contemporary – all we know about Charles the Fat's appearance is that he was tall and blond). Posterity has therefore seen in the years 840–88 not the high period of the Carolingian empire but rather the birth-pangs of nascent kingdom-nations such as France and Germany, ready to burst out of an anachronistic imperial straitjacket on a trajectory towards their modern destinies.
This view of the 'decline and fall of the Carolingian empire' is underpinned by some problematic assumptions that are arguably rooted as much in nineteenth- and twentieth-century ideas about historical processes as in the contemporary sources. Take as an example the Treaty of Verdun, which is still regarded as the founding document of the kingdoms of France and Germany – put succinctly, 'the birth-certificate of Europe'. Regardless of this metaphor's undoubted resonance, we have to query whether it helps us understand history as it was experienced by ninth-century political figures. They did not know how things would eventually turn out, so how can we properly explain their behaviour by reference to what only we know happened in their future? That the treaty would ultimately turn out to seem particularly significant should not be allowed to colour our judgement too much. As far as contemporaries were concerned, the Treaty of Verdun represented neither a disintegration of the empire nor an acknowledgement of proto-national sentiments, because such division had for centuries been the norm in Frankish politics and culture. Even during the anomalous period of unity under Charlemagne and Louis the Pious the empire was more often than not, as we have seen, split into pieces controlled by rulers' sons crowned as kings with full royal authority. The 843 frontiers were planned very precisely to provide an agreeable division of royal resources between the brothers and did not correspond to linguistic or cultural boundaries between Romance- and Germanic-speaking regions. High aristocrats retained interests across the empire. The dominant idiom of political discourse remained Frankishness, rather than French- or German-ness, until the eleventh century at least. Verdun was, moreover, superseded many times before the ninth century was out. By the 870s Provence and parts of Burgundy had become appendages of the kingdom of Italy; while during the 880s west Francia was divided horizontally into northern and southern kingdoms. All these divisions, including Verdun, were effectively provisional: their contemporary significance was not national but dynastic. Louis the German and Charles the Bald may have been retrospectively cast as founders of nations, but in their own minds they were backwards-looking rulers whose ambitions were resolutely imperial. The mental horizons of these kings were defined by their desire to imitate the achievements of Charlemagne, not to create nation-states – their competition to appropriate his mantle was what led them to seek the imperial title (which helps explain why that title was seemingly more important to his descendants than it had been to Charlemagne himself). The aristocratic elite shared this perspective: provincial observers in the realm of Louis the German, for instance, thought of him not as a king of _Germania_ , but (rather optimistically) as an 'emperor'.
If we need to be aware of our own tendency to project modern nations back onto the medieval world, we also have to acknowledge the ambiguity of the sources on which traditional descriptions of decline and fall are based. Ninth-century reflections on the battle of Fontenoy serve to illustrate this point. The last great historian of the Carolingian age, Regino of Prüm, looked back from the early years of the tenth century and identified Fontenoy as one of the factors in the demise of the empire. So many nobles had been killed, he said, that 'thereafter [the Franks] were incapable not only of expanding the kingdom, but also of defending its frontiers'. This clear statement seems to offer a pellucid window onto contemporary realities, all the more reliable since it tallies with the regret about Fontenoy expressed by other writers like Notker. Historians have invoked such reminiscences in support of a narrative of decline in which the battle illustrates the process of the Franks turning against each other to seek spoils of war that were no longer available from conquests beyond the frontiers. Yet Regino also reveals the problem with this interpretation by contradicting himself in his praise for King Karlmann of Bavaria (876–80) who, he says: 'added to and extended the borders of his kingdom with the sword'. Evidently we have to be very careful with such texts, which present us with pointed authorial constructs rather than objectively reliable information. Long before Regino's day, the trauma of Fontenoy had become part of the social memory of the nobility, crystallising into an episode in a story that late-ninth-century Franks were accustomed to tell each other about themselves. The battle brought aristocrats up against a contradiction in their professed values and self-perception as a Christian elite, and the only way to incorporate it into their sense of themselves was through extravagant regret. Major events like battles, won or lost, could play a key role in creating and sustaining a group identity. Late Carolingian reminiscences about Fontenoy give us an insight into the formation of a shared elite mentality, but this does not mean we can take them at face value as sources for the dwindling of the empire's political vitality.
By highlighting these sorts of problems and looking at the sources afresh, historians have begun in recent decades to evaluate later Carolingian history more positively. A first step in this is to realise that the decline-and-fall narrative lacks an appreciation of political short-termism. While the temptation is strong to write history in terms of sweeping cinematic changes and trends, we have to remember that the actions of early medieval kings (like politicians in any era) were more often than not reactive, driven by short-term concerns rather than the long-term processes extrapolated by modern writers. Replacing the sources in their precise contemporary contexts can therefore open up wholly different interpretations from those traditionally offered. The empire did indeed disintegrate in 888, but we cannot let our knowledge of that fact contaminate our understanding of everything that came before – if we chose to finish our narrative only three years earlier in 885, when the whole of Charlemagne's realm was re-unified for the first time since 840, we could write a triumphant story of how the empire was regained rather than a tragedy about how it was lost. As we shall see, the causes of conflict in late-ninth-century politics, including the end of the empire itself, were not macro-historical processes or fundamental structural decay, but rather specific combinations of circumstances and events.
The context in which these events took place was nonetheless defined by Louis the Pious's death and the Treaty of Verdun. Where family rivalries under Charlemagne and Louis had tended to flare up between kings and their sons, after 843 the potential was opened up for conflicts to cut horizontally and diagonally across the family tree as well as vertically. The prospect of uncles allying with disaffected nephews against their fathers added a combustible element to the mix. This also had the effect of encouraging volatility and uncertainty among the aristocracy, marginalised members of which could now look more easily outside their own kingdoms for royal support. Extra dimensions were added by armed encounters with outsiders such as Scandinavians and Slavs. The proliferation of kings in the two generations after Louis the Pious meant that the Frankish empire became polycentric in a way that it had not been for over a century. Yet the political horizons of kings transcended their own kingdoms: it was precisely their enduring sense that the empire as a whole still mattered which brought kings into conflict with each other, not the gradual solidifying of regional or national units which wished to opt out.
These dynamics did not inevitably undermine the power of the Carolingians, but they did confront the dynasty with a new set of challenges. Successful kingship in this context relied on the clever management of aristocratic interests and family rivalries, and the ability to respond imaginatively and effectively to unexpected events. The political history of the empire between 843 and the dismemberment of Carolingian hegemony in 888 is complex, and has no single narrative thread which can be easily followed. In this era of multiple kingdoms and kings, uneasily trying to defend their interests against their relatives, we will see that it was the relationships between rulers that defined the course of political events. By following the shifts in these relationships through the second half of the ninth century we will see in the rest of this chapter that although the political environment of the empire had changed along with its geography, this does not mean that kings were weaker, nor that the decline and fall of the dynasty had become inevitable. Indeed, we shall see that the end of Carolingian hegemony, and of the Frankish empire, was the outcome of a particular set of circumstances that only played out the way they did precisely because the Carolingians had been so successful.
Throughout this analysis we must bear in mind a crucial change in the pattern of the sources. The narratives that help us understand the reigns of Charlemagne and Louis the Pious were almost all written, before 830 at least, by people close to and generally sympathetic to those rulers. After that date, however, fuller narratives begin to appear which are much more likely to be openly critical of Carolingian rulers. This was partly a consequence of the splitting of the empire into kingdoms which developed their own historiographical traditions (the _Annals of Fulda_ cover the politics of the east Frankish kingdom, the _Annals of St Bertin_ the west), and partly down to the effects of the Carolingian _correctio_ , with its particular interest in written history. This multiplying of argumentative narratives is incredibly useful for the historian, but by their very nature these sources tell a less triumphalist story than the text on which they are modelled, namely the _Royal Frankish Annals_. We should not read this change of tone as a straightforward indication of political change. These annals dwell above all on the conflict between the descendants of Louis the Pious, and consequently this period is sometimes written off as chaotic. As we shall see, this is too simple. Although inter-Carolingian conflict was indeed the driving force of politics, it was governed by a series of implicit codes and norms which affected and limited what kings could get away with, and which shaped the events which led to the ultimate disintegration of the empire.
#### FRATERNAL LOVE, 843–877
Although the actual text of the Treaty of Verdun has not survived, we can reconstruct its territorial provisions quite accurately. Despite the fact that it was conceived as a peace-treaty to end a burst of conflict, the division it enshrined proved to be one of the Carolingian era's most enduring and successful settlements. Louis the German and Charles the Bald ruled their portions until their deaths in 876 and 877 respectively; and although Lothar died in 855, his sons Lothar II (d.869) and Emperor Louis II of Italy (d.875) ensured similar continuity in his realms. The shape of the family tree thus suggests, in retrospect, a certain stability. The longevity of this generation was underpinned by a novel mechanism designed to ease the tensions inherent in the new dynastic configuration. Harmony was to be maintained not by the _Ordinatio imperii's_ vision of a superior emperor acting as overlord, but rather through a system of regular summits between rulers to discuss issues of mutual concern and neutralise disputes. About seventy such meetings are known to have taken place between 843 and 887, and the proceedings of a few survive in the form of jointly issued treaties or capitularies.
Some of these documents reveal the practicalities of inter-kingdom diplomacy through their attempts to settle disputes thrown up in the course of events. However, these meetings were not just forums for the micro-management of cross-border relations, but also had the cumulative effect of reinforcing a particular way of thinking about politics. Just as the power of junior Carolingian kings was regulated by a discourse about filial responsibility towards their fathers, so the sons of Louis the Pious established a rhetoric of fraternal love as the basis for the post-Verdun political order. This ideology was repeated consistently in texts like the Treaty of Meersen negotiated by all three kings in 847, which self-consciously echoed landmark definitions of political order including the _Divisio regnorum_ (806) and the Treaty of Coulaines (843). The familial spirit supposedly captured by the meeting at Meersen is encapsulated in its opening statement: 'concerning the peace, concord and harmony of the three brother-kings: that they should be united by true and not false bonds of love'. This was an understandable way of soothing the moral wounds of those who had lived through the civil wars, and it was this way of thinking that must have informed Lothar's regret about family conflict expressed in the letter of 847 with which we began this chapter. The ideology of brotherly love had thus fully matured a long time before its most famous and striking exposition in a letter of 871 from Louis II of Italy to Basil I of Byzantium. In this angry response to various belittling rebukes, Louis took a pot-shot at the youth of his counterpart's dynasty by arguing that the western empire was a unified whole rather than a collection of kingdoms (and that he himself was therefore a proper emperor) precisely because all of its rulers were of common blood. Competition between Frankish kings, in this view, was aimed at transferring power within the political system rather than undermining or transforming the system _per se_. This discourse turned conflict between individual Carolingians into an opportunity for rehearsing the dynastic status of the family as a whole, and it played an important role in shaping the political mentality of the elite in the second half of the ninth century.
Nonetheless, whatever arguments were made about the meaning of conflict, conflict there most certainly was. Even the most rigorous diplomatic procedures and powerful dynastic ideologies were not enough to erase the suspicion engendered by the conflicts of 840–3. Lothar appears not to have given up on his aspiration to turn his imperial title into concrete superiority over his brothers. In an overtly political move in 844 he got Pope Sergius II to appoint his ally (and uncle) Bishop Drogo of Metz as papal vicar north of the Alps with rights to intervene in the Church across all three kingdoms. Although in practice Drogo was never really able to put these powers into effect, Lothar's actions caused Louis and Charles to maintain their alliance, suspicious of their elder brother's intentions. The air of mutual hostility heightened in 846 when Lothar's daughter married one of Charles's vassals without her father's consent, leading to the accusation that she had been kidnapped. Louis and Charles immediately denied all knowledge – which in itself reveals the high political impact of the incident – and a meeting was convened at Meersen in 847 to sort out the problems between the brothers. The text of this treaty reflects contemporary circumstances by condemning 'abductions', and echoes aristocratic anxieties of the 830s and early 840s by stressing the need for nobles to remain faithful to one lord. In the following year Lothar attempted to lure Louis away from Charles with an appeal to their full brotherhood, and in doing so perhaps insinuated that Charles's paternity was suspect: the language of fraternal love could be manipulated to subvert the political _status quo_ as well as to support it.
Meanwhile, the emperor tried to undermine Charles further by supporting the efforts of his nephew Pippin II to assert himself in Aquitaine. Charles's enormous difficulties in the south-west of his kingdom and on the Spanish March interacted with a steady escalation in attacks on the west Frankish realm by Viking raiders, who had been drawn into Frankish politics (often as mercenaries) by the conflicts of Louis the Pious's reign and its aftermath, and had now begun to overwinter on the continent (see Map 15). All early medieval kings were faced with the need to pursue a constant effort to maintain influence in distant regions of their kingdoms, but this was especially true in the immediate aftermath of Verdun, when rulers had to establish themselves in realms which had not previously existed as stand-alone units, and where their influence might be patchy. The presence of armed Scandinavians made this problem even more intractable. Viking bands scored some notable successes in this period, taking advantage of the turmoil caused by the civil war to occupy parts of Brittany and Frisia, but in general were more interested in seizing moveable wealth to bolster their positions back home in Scandinavia than in bringing down Frankish rulers. Indeed, Frankish rulers could benefit from their raids. In 847–8 a Viking siege of Bordeaux, one of Pippin II's strongholds, provided Charles the Bald with an opportunity to demonstrate his kingly credentials to the Aquitanians. By appearing on the scene and attacking the besiegers he appears to have won over the majority of the south-western nobility, who formally submitted to his authority shortly afterwards. The real loser here was Pippin, whose previously effective local regime was fatally undermined – no more charters or coins bear his name after 848. Pippin's perfectly legitimate claim to royal status was finally snuffed out in 852, when he was apprehended and 'un-personed' by being confined to a monastery. The presence of pagan Scandinavians was therefore crucial in enabling Charles the Bald to wrest control of the peripheries of his realm away from his nephew and thus counteract his brother's attempts to undermine him.
The politics of the middle and eastern kingdoms in the later 840s were likewise dominated by events at the fringes of their rulers' power. For all the trouble Charles had in Aquitaine, Lothar endured similar problems in Provence in 845, where he had to put down a major revolt; while Viking raids on Frisia, the trading nexus in the north of his realm, intensified at the same time. Muslim raids on Italy reached a high point with an attack on Rome in 846, which forced Lothar to make a trip (his last) south of the Alps in 847 and made the Romans ever keener for imperial protection. The repercussions of these events left a permanent mark on the topography of Rome, where Pope Leo IV (847–55) effected the construction of the so-called Leonine Walls, partly at Frankish expense, to prevent a repeat. Louis the German, meanwhile, spent much of the first decade after Verdun attempting to reconcile himself with members of the east Frankish nobility who had opposed him during the civil war and trying to enforce client status upon the Slavic peoples across his eastern frontier. These peoples, whose traditional subjection to Frankish rulers had been loosened by the conflict of 840–3, offered a stern military and political test for Louis, especially at times when he was distracted by affairs in the west or south of his kingdom. For all these rulers, taming the peripheries of their realms was a necessity not simply to maintain the stability of the frontiers and to make their kingdoms cohere into rulable wholes, but also to reduce their vulnerability to the intrigues of their relatives while their backs were turned.
**Map 15.** Viking raids, _c_.835 to 863. The earliest attacks were mostly restricted to the Atlantic coastline; those further east were often associated with dynastic conflict within Scandinavia.
The general atmosphere of tension was eased somewhat in 849, when Charles and Lothar publicly recognised each other's positions and resolved to remain at peace. This time the rhetoric of fraternal solidarity was cemented through ostentatious political action, as Charles consulted Lothar over the imprisonment of the latter's old ally Pippin II in 852 and the two kings indulged in some joint campaigning against the Vikings. The year 852 was also one of consolidation for Louis, who reinforced his control of the east Frankish realm by consecrating the new palace chapel at Frankfurt to the Virgin Mary, in imitation of Aachen, and then going on a regal itineration through Saxony. However, it was now Louis's turn to be marginalised by his brothers. This realignment in the Carolingian diplomatic landscape led almost immediately to new patterns of conflict. Louis's strength in east Francia encouraged him to start negotiations with some of the leading men of the middle kingdom, presumably pitching a claim to succeed the ageing Lothar, now approaching the relatively advanced age of sixty. Louis's predatory ambitions in the west also found a receptive audience in Aquitaine, where erstwhile partisans of Pippin II were once more disillusioned with the intrusive presence of Charles the Bald and had sent word that they would be amenable to the prospect of the eastern king taking over from the 'tyrant'. In response, Charles encouraged the Bulgars to make trouble on his brother's eastern flank. Louis was not deterred. After conspicuously absenting himself from a meeting with his brothers in early 854, he sent his nineteen-year-old son Louis the Younger to take over Aquitaine with a large army. The invasion seems to have faltered almost immediately: Louis arrived in Aquitaine to find that only the kin of Gauzbert, a nobleman who had been decapitated for treason by Charles in the previous year, were pleased to see him. He therefore decided the whole thing was 'pointless' and went home. This is, however, reported by an annalist writing with hindsight: the fact that Louis stayed in Aquitaine for about six months suggests that his invasion was a far more serious proposition than the sources let on.
The death of Lothar in 855 upset the balance of power in the empire in a new way. For the first time, the eldest Carolingian and the emperor were not the same person, which undermined one informal point of stability. The old emperor was succeeded by his three sons: the eldest Louis II as emperor and ruler of Italy, where he had been more or less autonomous since 844; Lothar II in Middle Francia (subsequently called Lotharingia, after him); and Charles in Provence and the Rhône valley. Charles of Provence was ill and his regime was neither well established nor long lived – he suffered badly from epilepsy and died in 863. Competition between the other two sons dovetailed naturally with the ongoing stand-off between their uncles, and each sought to further his interests by allying with one or other of them. The combination of proclaimed peaceful confraternity and underlying tension which had characterised the period 843–55 was thus replaced by an even more complex inter-generational version of the same thing.
The first serious disturbance of this uneasy dynastic balance came at the end of 858, when Louis the German again launched an invasion of his brother's west Frankish kingdom. This time, Louis came in person and through an overwhelming display of military force almost made it stick: by early 859 Charles's support was in disarray and he only retained his throne thanks to the steadfast support of his bishops, who resisted pressure to legitimise the invader as king in the west. Charles's recovery from a position of apparent desperation shows no little political skill. At the same time, it has to be noted that Louis had come very close to reuniting a huge swathe of his grandfather's empire. Nonetheless, as usual in Frankish politics, the causes of this confrontation cannot be reduced to an equation balancing the ambitions of inherently antagonistic 'strong' and 'weak' kings. The roots of Louis's invasion are to be found on the western frontier of the realm, where influential nobles led by Count Robert 'the Strong' of Angers (who was originally from the Rhineland) became resentful of the power of Charles's son Louis the Stammerer, who had been made (sub)king of Neustria under the sponsorship of the Breton _dux_ Erispoë. These antagonisms combined with renewed unrest in Aquitaine, increasing Viking pressure on the Seine, and hostility to Charles's aggressive raising of money to pay off the Scandinavians. It was thus not royal weakness which caused the rebellion: if anything, the problem was that Charles, in an attempt to deal with a range of problems at once, had been too interventionist. The combination of dynastic rivalry, cross-frontier politics and the jockeying for position of powerful regional aristocrats that precipitated the crisis of 858 was typical of the chemistry that catalysed much ninth-century dynastic history.
The invasions of 854 and 858 highlight two key features of later Carolingian politics. Firstly, the fact that these annexations were even attempted reminds us of just how much we are still dealing in this period with kings who retained a determinedly imperial political horizon, rather than with rulers of proto-nations either side of the Rhine. Kings like Louis and Charles still wanted to emulate Charlemagne by re-creating the empire, a mode of thought that exacerbated the endemic instability of the multicentric post-843 political landscape, where noble grievances in one area could have a major influence on the ambitions of kings hundreds of miles away. The degree of instability was, however, tempered by the fact that the Aquitanians sought not to displace the ruling dynasty, but merely to replace one Carolingian with another. Such inter-kingdom tensions could threaten the power of individual rulers; yet paradoxically reinforced the hegemony of the dynasty as a whole by translating into action the notion that only an adult male full-born member of the Carolingian family could be a legitimate king. The extent to which the concept of Carolingian dynastic hegemony had been internalised by the Frankish elite of the mid-ninth century is further illustrated by the Lotharingian magnates' asking Louis the German – the empire's senior ruler – to approve the succession of his nephew Lothar II. Secondly, these events grant us another insight into contemporary political norms. Louis's ambition to acquire the traditional family heartlands in west Francia was long standing and well known: only trouble on the eastern frontier had prevented him from taking up another invitation to invade in 856. However, even driving ambition backed with the appropriate means and opportunity could not be pursued by riding roughshod over contemporary expectations about the correct behaviour of rulers. The moral gymnastics performed by Louis to justify his campaign of 858 are recorded in the so-called _Annals of Fulda_ , which detail how he anxiously weighed up the need to liberate the west Franks from their 'tyrant' ruler against the wickedness of attacking his brother and the danger of appearing to his own people as though he were motivated by self-aggrandisement. This public hand-wringing was evidently self-serving and designed to pre-empt potential accusations of tyranny against Louis himself, but it is still worth noting that he thought it necessary at all. Haunted as they were by the terrible memory of Fontenoy, the discourse of family love was taken seriously by Louis the German and by his subjects. Kings could not attack each other without justification. The late-ninth-century political order was threaded with political discourses that had a restraining influence on how the mighty pursued their ambitions – it was not a free-for-all.
Mistrust remained between the two brothers until peace was finally brokered in June 860 with the help of their nephew Lothar II. By now, however, Lothar himself was setting the political agenda by virtue of his divorce case, which dominated the course of dynastic politics throughout the 860s. As a young man, Lothar had had a relationship with a noblewoman called Waldrada who bore him a son named Hugh and two daughters. Then, in late 855, he put Waldrada aside and married Theutberga, an aristocrat whose family connections brought him control of some of the major routes to Italy. The aim was clearly to establish his influence in the south of Lotharingia at the start of his reign. Early in 860, Lothar divorced Theutberga at a synod in Aachen, using against her as justification a now-familiar litany of unlikely sexual accusations including incest, sodomy, conception through witchcraft, and abortion. It is plausible that the king's primary motives were personal; that he did not like Theutberga, and genuinely loved Waldrada. At the same time, the political value of his marriage to Theutberga had decreased as Lothar's relationship with his brother and southern neighbour Louis II of Italy improved. In any case, the responses of Lothar's Carolingian relatives to the divorce quickly elevated the scandal from the royal bedchamber into a matter of empire-wide significance. Ideas about marriage were not yet cast in stone and Lothar sought to manipulate them in order to legitimise his divorce. But Louis the German and Charles the Bald were equally active in their attempts to keep Lothar married to Theutberga, motivated in part by a desire to obstruct the potential for Waldrada's son Hugh to be retrospectively identified as a legitimate heir. In these politically charged circumstances, Lothar's attempt to deploy against his wife the discourse of sexual sin, developed in the reigns of Charlemagne and Louis the Pious and now a well-established political code, backfired. His claim that he was unable to control the ardour of his own youthful body, a strategy intended to position him as a victim, was quickly taken up by his enemies and used against him.
The prominence of the political stage on which these arguments were aired helped to solidify and institutionalise even further the connection between the moral/sexual behaviour of the king's close family and the legitimacy of his power. This link was reflected in a guidebook on rulership by the Irish scholar Sedulius Scottus, probably written for Charles the Bald in 869, which stressed that: 'A pious and wise king fulfils his office of ruling in three ways. First he ought to rule himself... secondly his own wife, his children and his household, and thirdly the people entrusted to him.' Sedulius here unmistakably nodded to the issues of royal self-control raised by Lothar's divorce. The scandal lent force to anxieties about the behaviour of women in particular, and therefore had particular implications for the role of the queen. The bandying-about of slurs about the behaviour of both Waldrada and Theutberga drew on a deep well of stereotypes about the disruptiveness of female sexuality that had been sharpened by the accusations made against Judith in the crisis of Louis the Pious's reign. Female power was traditionally idealised in terms of domesticity. Hincmar's _De ordine palatii_ , for instance, defines the queen's role in terms of controlling the provisioning of the palace, and by extension access to the king. Around the middle of the ninth century this began to change in subtle but important ways: the first ceremonies for the inauguration of queens were written, royal women became increasingly associated with specific forms of political authority associated with the control of nunneries, and royal couples became more careful about clearly establishing the propriety of their marriages. These developments combined to give royal women a more defined political role and to harden expectations about their conduct. The flurries of heated rhetoric generated by Lothar's divorce case did not evaporate into thin air before they had left an enduring imprint on these aspects of dynastic politics.
Lothar, buoyed by the support of his brother the emperor, might have hoped to get his way at the cost of only minor territorial concessions. If so, he reckoned without the intervention of Pope Nicholas I, who sought to flex his muscles by denying the validity of the divorce and excommunicating Waldrada and the Lotharingian archbishops who had supported their king. Nicholas's stance was reactive and opportunist rather than coherent and ideological – he was not constructing a test-case for the clashes between popes and emperors that took place in the very different political landscape of the late eleventh century. Institutionally and politically, the authority of the mid-ninth-century papacy was not much greater than it had been in the days of Stephen II and Leo III. Nonetheless, the pope's position provided an external point of reference that could be used as a moral prop by Lothar's opponents. Bolstered by Nicholas's intervention, relations between Charles the Bald and Louis the German began to hinge on their respective relationships with their troubled nephew. The three kings met together on as many as sixteen occasions between 862 and 868. Although the uncles' specific intentions and positions were constantly shifting in subtle ways according to circumstance, in general Charles supported Theutberga and aggressively opposed Lothar's actions; while Louis tried to win concessions from Lothar through diplomacy and conditional offers of support. The aim of both was to make inroads into the political heartlands of Lotharingia. After about 865 Louis and Charles seem to have found more common ground. In summer 868 they met in Metz and agreed to divide Lotharingia and Italy between them if their nephews should die heirless. That this meeting took place in Lothar's kingdom, but in his absence, underlines just how far his power had been undermined by the consequences of his divorce case. The death of Nicholas I in 867 seemed to offer a ray of hope to Lothar, who travelled to petition Hadrian II, the new pontiff, in 869. Hadrian, swayed in part by the influence of Louis II and the empress Engelberga, gave the king the answer he wanted: his excommunication was lifted, and a council would convene to look again at the marriage. Yet the gods of historical irony did not look favourably on Lothar II. No sooner had he set off home with this victory under his belt than he caught a fever in the sweltering Italian summer and died before he had even made it as far as the Alps. He was buried in Piacenza, aged only thirty-four.
Charles the Bald reacted fastest to the news. Taking advantage of the fact that his brother was ill, he had himself crowned king of Lotharingia on 9 September in Metz. Charles actively exploited the dynastic resonances of the middle kingdom's topography: Metz housed the special dead of the Carolingian dynasty including St Arnulf and Louis the Pious. A compilation of Carolingian texts including Einhard's _Life of Charlemagne_ and the _Royal Frankish Annals_ produced to mark the occasion implicitly constructed the event as the triumphant culmination of dynastic history; the elite circle which produced it was evidently receptive to the ideological claims radiating from Charles's entourage. Charles reinforced his position in the middle kingdom shortly afterwards when, following the death of his first wife, he married Richildis, sister of the powerful Lotharingian aristocrat Boso and niece of Theutberga. However, Louis's return to health early in 870 enabled him to win over important members of the Lotharingian aristocracy and forced Charles to negotiate with him in accordance with the oaths they had made at Metz in 868. The outcome was an east–west split of Lotharingia enshrined in the Treaty of Meersen, which was as meticulously planned as the division of Verdun. Unlike Verdun, though, the build-up to the Meersen agreement had been contained within the norms of dynastic politics (diplomacy, formal negotiation, veiled threats and courting of aristocratic power-brokers) rather than breaking out into open violence.
Meersen handed to Louis and Charles on a plate much of what they had been angling after for the previous decade. But before they had a chance to rest on their laurels, in the early 870s an old problem reappeared with a vengeance: the ambitions of ageing rulers' adult sons. Charles had had six sons in all. The eldest, Louis the Stammerer, had been closely controlled since rebelling against his father in 862 upon reaching the age of majority (fifteen). After this revolt, which was in part driven by the young king's desire to settle old scores in Neustria dating from the unrest of 858, Louis seems to have been kept on a pretty tight leash and caused his father no major trouble, and in 867 he was installed as king in Aquitaine under close supervision. Four of Louis's brothers died in childhood or young adulthood. By the early 870s, therefore, Charles's only other adult son was Carloman, whom he had tonsured into the religious life at the age of five. This was a highly unusual career for a legitimate male Carolingian – Charles's aggressive pruning of the family tree reveals his concern at the potential trouble that his brood of sons could pose him later in life. Until 869 Carloman seems to have been content with his lot, which included control of a series of important and wealthy monasteries. However, Charles the Bald's expansion of his kingdom through the annexation of Lotharingia opened new horizons and reactivated Carloman's secular ambitions. At the same time the king's remarriage threatened to produce more sons and further marginalise Carloman's prospects. For the forgotten prince it was now or never. Carloman instigated a major rebellion in Lotharingia. Although his platform was formed by the ecclesiastical resources bequeathed by his father, the aim was to advertise the casting-aside of his religious status and to establish the validity of his claim to a throne. His rebellion lasted, on and off, until 873, sustained by some very powerful Lotharingian backers. So severe was the threat that Charles finally resorted to an act of breath-taking brutality, blinding his son to snuff out permanently his claim to a throne. Louis the Pious had been criticised heavily for blinding (and killing) his nephew Bernard of Italy in 818. To risk the opprobrium which opponents would attach to the infliction of a similar penalty on his own son shows just how high Charles felt the stakes to be.
One reason for the great threat posed by Carloman's rising was that it threatened to play into the hands of Louis the German, who was a natural ally of the rebels owing to the fraternal suspicion that had been restored by the death of Lothar II. Louis, however, had his own problems. His sons had been active politically since the 840s, and during the 850s were given informal influence within defined areas of the east Frankish kingdom: Karlmann in Bavaria and the south-eastern marches; Louis the Younger in Saxony and Franconia; and Charles the Fat in Alemannia. These arrangements were shored up by arranged marriages with women of the local aristocracy, and sealed with a formal division plan promulgated in 865. (See Maps 16 a, b and c for the ninth-century divisions of the empire.) Just as Charles the Bald had come up with a novel measure to minimise the inherent dangers of dynastic politics (the tonsuring of Carloman), so Louis improvised to prevent rebellions by refusing to crown his sons as kings. Louis and Charles were poachers turned gamekeepers whose memories of the 830s made them wise to the ambitions of their own sons. Unfortunately for them, such constitutional niceties did not carry decisive weight – a century of Carolingian history had taught the sons of kings that they were kings themselves, whether they were given the title formally or not. During the 860s, Louis, like his brother, endured sporadic defiance from his sons, but this coalesced into a more serious rebellion which lasted, in phases, from 871 to 874. The main problem was a suspicion on the part of the two younger sons that the 865 plan was being modified to the benefit of Karlmann, the eldest, who seems to have been their mother's favourite. Again, the potency of the rebels was amplified by their trans-empire horizons: they took advantage of the king's troubles with the Moravians on his eastern frontier by turning west to make common cause with their uncle Charles the Bald. Ultimately the pressure got too much for Charles the Fat, who submitted to his father at an assembly in early 873 with an extravagant display of penitential contrition that astonished the various annalists who recorded it. Louis the Younger was only temporarily cowed by this turn of events, and went on to mount a final rebellion in 874.
**Map 16a.** Ninth-century divisions: The partition of Verdun, 843
**Map 16b.** Ninth-century divisions: The Carolingian kingdoms in 855
**Map 16c.** Ninth-century divisions: The partition of Meersen, 870. These maps of territorial divisions show that each was provisional, because designed around the configuration of the dynasty at that moment. Care was taken to accord kings equivalent shares of rights and resources. Between 870 and the end of the empire in 888 these kingdoms were reconfigured again as one king after another died.
All of these revolts on both sides of the Rhine were driven by exactly the same basic dynamics as the rebellions of the sons of Charlemagne and Louis the Pious decades earlier. Now, as then, princely ambition was fired by aristocratic discontent: Karlmann's rebellion of the early 860s was supported by marginalised factions on the eastern frontier, while the men who underwrote Carloman's bid for power were big fish motivated by the desire to avoid losing influence by being swept into a bigger pond through Charles the Bald's absorption of Lotharingia. As ever, a healthy dose of fraternal rivalry hindered kings' attempts to impose lasting family settlements. Just as Lothar's claims to superiority had raised the hackles on his brothers' necks in the early 830s, so Karlmann's seniority was the sticking point in Louis the German's attempts to keep a lid on relations between his sons. The language of rebellion was also unchanged. In an act that deliberately echoed the atmosphere of 829, Louis the Younger launched his revolt in 874 by insinuating that a series of famines, unusually harsh winters and a plague of locusts were signs of his father having lost God's favour. Contemporaries clearly understood Louis's code: the author of the so-called _Annals of Fulda_ (an anonymous churchman working in the circle of the archbishop of Mainz) explicitly reminisced about the rebellions against Louis the Pious when describing the 874 uprising. More importantly, Louis the German also understood the code and responded accordingly by complementing his mobilisation of force with an ostentatious display of penitential behaviour. By retreating from secular affairs to pray at the monastery of Fulda during Lent and Easter, and by ordering prayers for his father from all the churches of the kingdom, he not only showed that he too was troubled by the suggestion of divine wrath against his regime, but also engaged with the criticism levelled against him by his son and thus sought to undermine the basis of his rebellion. Kings like Louis the German and Louis the Younger participated in the same moral and familial discourses that had been used by Charlemagne and Louis the Pious for negotiating and disputing the distribution of power within the royal family.
It is clear that part of the reason for all these revolts was the acquisition and partitioning of Lotharingia in 870, which laid before the ambitious junior Carolingians the prospect of lands rich in estates, palaces and political resources. For their fathers, Louis the German and Charles the Bald, a crucial safety valve was presented by the situation south of the Alps where the prospect of acquiring the realm of their nephew Louis II of Italy became a real possibility in the years around 870. Louis II had been established as king of Italy by his father around 840, and was crowned emperor by Pope Sergius II in 844. Louis's spirited defence of his imperial status in the face of Byzantine ridicule has already been mentioned. However, the fact that a west Frankish source refers to him as 'emperor _of_ Italy' illustrates how the imperial title had become primarily an honour reserved for the ruler of that kingdom. Although the prestige of the title made it desirable to many ninth-century kings, it had ceased to correspond to any concrete notion of superiority such as that spelled out in the _Ordinatio imperii_ – arguably, the imperial crown had become more important to the political identity of the popes, who held it out as an incentive to win powerful Carolingian backers against their local rivals, than it was to the Carolingians themselves. As in the reign of Charlemagne himself, this was a model of authority with a largely Italian resonance. In the wider world of Frankish politics, the title was simply one reference point among many that could be deployed in the non-stop competition for power.
Louis is much less well studied than his northern relatives, and the absence of major narrative sources for his reign means that the history of Italy in this period is relatively opaque. Nonetheless, he is generally regarded as one of the more stable and successful of the Carolingian rulers. His marriage to Engelberga, the scion of an extremely influential aristocratic family, contributed to a very strong hand in north Italian politics. He inspired little major unrest, responded effectively to Muslim incursions around Rome, and managed to gain influence and territories north of the Alps through judicious diplomatic interventions. He was, however, sonless, which helps account for the absence of rebellions against him. His great ambition, to incorporate the south of the peninsula with its patchwork of Muslim, Lombard and Byzantine interests, ultimately failed, and in 871 led to a period in captivity at the tender mercies of the Lombard duke of Benevento. It seems to have been this crisis, which inspired rumours that he had been killed, that caused Louis to begin negotiating with his uncles over his succession. Louis the German emerged from this bout of diplomacy clutching the ace, securing in return for concessions in Lotharingia a guarantee of the Italian throne for his eldest son Karlmann. However, the length and nature of the negotiations created doubts about Louis the German's entitlement in the minds of some of Italy's most important power-brokers, including Pope John VIII, who was also disillusioned by his handling of the evangelisation of the Moravians. This meant that when Louis II died in 875, Charles the Bald also found an aristocratic constituency that favoured his succession. Reacting quickest to his nephew's death, Charles crossed the Alps with an army, scared off Karlmann and his brother, and persuaded John VIII to accept him as king. This success inaugurated a five-year period of largely absentee kingship within Italy, which saw the aristocracy split between rival east and west Frankish claims. Charles the Bald succeeded in getting himself made emperor before his death in 877, after which Karlmann finally got his hands on the Italian crown for an equally brief period ended by a stroke in 879.
The quarrels between the descendants of Louis the Pious that characterised the period 840–77 were bewilderingly complex and, to modern eyes, seem to have been the defining feature of the era. Yet, as we have seen, these conflicts and rebellions were expressed and executed within commonly understood and consciously fostered discourses of familial and moral obligation. The rulers of this generation cannot be seen simply as land-grabbing despots dragging the empire into terminal political chaos, for they were part of a political order defined by strong codes of personal and political propriety. Because invasions and revolts were justified by loud claims and counter-claims about the protagonists' adherence to these codes, every act of aggression translated the rhetoric of Carolingian family hegemony into public political action in which leading aristocrats also participated. Even as the power of an individual Carolingian was expanded at the expense of another, the exclusive king-worthiness of the dynasty as a whole was reaffirmed. It is significant that of the many rebellions against rulers in this period, not a single one since the 780s had been led by a non-Carolingian – the aim of all these risings was to replace one Carolingian with another. The never-ending sequence of family quarrels in the post-Louis the Pious generation did not, in other words, represent a disintegration of the political order because these quarrels were themselves an integral part _of_ that order. To gain a more rounded sense of its shape, we must now consider the nature of later-ninth-century royal government.
#### GOVERNMENT AND RESOURCES
Despite the fact that the Frankish kingdoms in the second half of the ninth century were fractions of the massive empire governed by Charlemagne and Louis the Pious, the techniques and structures of government remained largely the same. The capitulary tradition was maintained in both Louis II's Italy and Charles the Bald's west Francia at levels comparable to the output of Louis the Pious. _Missi_ were organised in west Francia in a similar way to earlier in the century: in the Capitulary of Servais (853), for example, Charles the Bald defined twelve _missatica_ to be visited by pairs of _missi_ armed with instructions to do justice to the oppressed and to hunt down wrongdoers. Charles's demand that his _missi_ should possess copies of 'the capitularies of our grandfather and father' (probably a reference to Ansegisus's collection) not only highlights continuity in the governmental practice and institutional memory of the political centre, but also shows the central role that written instructions were meant to play in the centre's communication with its regional agents. The undiminished ambition of Carolingian government comes through clearly in Charles the Bald's famous capitularies issued at Pîtres (864) and Quierzy (877), by which he sought to micro-manage manifold aspects of his realm including coinage, administration of estates, weights and measures, military service and the construction of unauthorised fortifications. As ever with this sort of prescriptive material it is very hard to measure effectiveness – but it is at least suggestive that the evidence of coin-finds proves that a coinage reform ordered in 864 was carried out exactly as ordered.
By contrast, no capitularies survive from the east Frankish kingdoms. This absence has favoured an interpretation of the eastern kings as old-fashioned warlords whose power was less sophisticated than that of the literate west Frankish and Italian rulers, being based primarily on the acquisition and redistribution of plunder from the Slavs. Although there is some truth in this, the contrast should not be drawn too starkly. We know that the east Frankish kings and many of their officials could in fact read Latin, and in charters and other documents we meet the full range of court and provincial officials found in the other Carolingian kingdoms. From stray references in the annals, we can also infer that Louis the German and his sons sometimes made pronouncements of exactly the type found in capitularies; but that these were delivered orally, not written down. This was a different political culture, but not necessarily an inferior or less effective one: again, it is revealing that silver pennies minted at Mainz under Louis were manufactured at exactly the weight prescribed by Charlemagne (1.67 grams). This detail illustrates how much the strength of east Frankish kingship was built on Louis's wholesale importation of the full panoply of Carolingian methods and structures of government (including _missi_ , counts and oaths of loyalty) into areas which had little previous experience of them.
The royal palace sat at the fulcrum of these structures, as the focal point of Carolingian efforts to maintain the sense of a political community which would align royal and noble interests and mobilise the regional power of important aristocrats on behalf of the king. The regular itineraries of the later Carolingian kings around their palaces and estates were crucial in establishing the idea of their kingdoms as units. In 852, for example, Louis the German covered nearly 1,000 miles in three months to advertise his authority by holding assemblies and settling disputes in every territory of his realm. This sort of circuit was unusual; royal itineraries were not ceaseless, but were punctuated by stops, often quite long, at favoured palaces and estates. The east Frankish kings actually spent most of their time on the axis between Regensburg and Frankfurt, rarely travelling into the northern regions like Saxony: over 50% of Louis's surviving charters whose place of enactment is recorded were issued at one of these two palaces. Similarly, Italian kings resided for the most part in the estates of the Po valley, while the west Frankish rulers' presence was felt most heavily in the Seine–Oise–Meuse area, and much less so in the northwest or southeast. Each kingdom therefore had a heartland which experienced royal government more intensively than less-visited outlying areas, whose own regulation was often delegated to a junior Carolingian or regional middleman.
At the core of these heartlands stood the rulers' main residences – magnificent embodiments of royal majesty that served as the forum for the enactment of governmental business at regular assemblies, and as permanent reminders of the king's power when he was absent. The centrality of palaces like Aachen and Ingelheim in the political imagination of the Frankish elite had, as we saw in Chapter 4, underpinned the regimes of Charlemagne and Louis the Pious. After 843 these archetypal royal monuments were clustered disproportionately in the middle kingdom of Lothar, so the other Carolingians responded by developing their own versions of them. Charles the Bald (see Figure 17) developed Compiègne on the Oise as his key residence, his 'Carlopolis'. In dedicating the palace chapel to the Virgin Mary in 877, the king dwelt on its similarities to the Mother of God chapel at Aachen and stated that his purpose was 'to imitate the pattern set by [Charlemagne] and by other kings and emperors, namely our predecessors'. Frankfurt – regarded by at least one contemporary as 'the chief seat of the [eastern] kingdom' – performed a similar role as a neo-Aachen in the realm of Louis the German, while Sélestat in Alsace, the design of whose buildings was closely modelled on Aachen, did the same thing for Charles the Fat. Architecturally and ideologically these palaces represented the ongoing renewal and reinvention of the Carolingian order, recalibrated to fit the new political landscape of the post-Verdun era.
**Figure 17.** Portrait of Charles the Bald from the _Codex aureus_ of St Emmeram. One of five surviving portraits of Charles, this illumination is taken from a gospel book composed around 870. Although there are reasons to believe that the image represents what Charles really looked like, the presentation is clearly stylised in order to underline the divine and Biblical sources of legitimacy to which the Carolingians laid claim.
Although the stages on which they operated were somewhat scaled down, the fundamental political rhythms represented by the palace system of government remained basically unchanged from the previous generation. Kings like Louis the German and Charles the Bald usually held at least one general assembly a year, supplemented by smaller meetings with important advisers. As well as opportunities to discuss events and plans, these gatherings served the wider purpose of bringing the political community together in one place and reinforcing a sense of its continuous existence. Communal activities such as hunting and feasting helped to establish this sense of belonging while ceremonial crown-wearings and other ritualised demonstrations of majesty simultaneously emphasised the special separateness of the king from his magnates. The ties established between aristocrats and kings at such gatherings were tended in between times through the distribution of royal patronage. The flow of charters did not abate – where Louis the Pious issued around 500 extant charters, Charles the Bald is known to have distributed about 450; Louis the German 170; and Charles the Fat, in a much shorter reign, approximately the same number. Far from impoverishing the king, patronage was an important means of gaining local influence, helping to strengthen bonds of mutual obligation with the aristocrats on whom the government of the kingdom depended, and thus to overcome the problems of enormous geographical distance. The Carolingian family itself continued to function as a valuable resource for bridging the distance between political centre and periphery. The generation after 840 was well provided for with royal sons to install as subkings in far-off realms – the fact that these sons mounted so many rebellions in the 860s and 870s is backhanded testimony to how successfully they had been integrated into the political landscape and given a direct stake in the Carolingian polity through being able to establish relationships with powerful local aristocrats. Through the deployment of such classic methods of Carolingian government, the rulers of the post-843 realms sought to mould strong kingdoms from collections of _regna_ whose elites were not necessarily used to thinking of themselves as connected. There was nothing new in this. Although it is beguilingly logical to imagine that the Frankish kingdoms had been definitively 'created' by 840, and that they subsequently unravelled, in truth state formation was a never-ending process – all early medieval polities had to be constantly renewed and reinvented in the imaginations of their inhabitants. The fact that one of the most important ninth-century kingdoms, Lotharingia, was a complete novelty with no historical antecedent highlights the Carolingians' success in persuading the ruling class to invest themselves in their definition of the political order.
The basic continuity of regional elite society is attested by shifting patterns of patronage visible in charters issued by the aristocracy for major royal churches such as Lorsch in the Rhineland and Freising in Bavaria. If the burst of giving to these institutions in the reign of Charlemagne reflects the turmoil created by the imposition of a new political regime, the gradual decrease in numbers of charters surviving thereafter suggests the absence of further social disruption on anything like the same scale. At the same time, these documents do reveal a fundamental shift in the shape of Carolingian politics after 843, namely the narrowing of the distance between regional elites and kings. Records of dispute settlement ( _placita_ ) involving Freising under Charlemagne and Louis the Pious demonstrate that the interests of these rulers were almost always represented by trusted _missi_ like Archbishop Arn of Salzburg. In the second half of the ninth century, by contrast, all surviving _placita_ bar three were presided over by a king in person. The contraction of the social and geographical distance between rulers and their noble elites was a feature of the smaller kingdoms of the era, and helped to regularise and cement the political structures that glued them together.
The shrinking of the political stage on which individual rulers operated also presented them with some novel challenges. Resources were inevitably squeezed: in 856 Lothar II complained that the 'diminution of the kingdom' had forced his father to take lands from the Church. Another structural problem resided in the fact that aristocrats often retained landed interests and family connections across more than one kingdom, a phenomenon that blurred internal frontiers and created opportunities, as we have seen, for magnates to court neighbouring kings when disaffected with their own. As kingdoms got smaller and the number of kings increased, more nobles became accustomed to the benefits of _Königsnähe_ (access to the king). This meant that when a realm like Lotharingia was threatened with absorption, as it was in 869–70, its aristocratic elites were all the more prepared to resist the threat to their influence by inciting or joining a rebellion.
The evolving political geography of the empire not only brought kings and aristocrats closer together but also dragged the frontiers of the realm nearer to its political centres. The status of his relationship with the Breton leaders thus became a key consideration for Charles the Bald in his attempts to rule Neustria, as was the situation on the Spanish March for his control of Aquitaine. Breton involvement in the chain of events leading to Louis the German's invasion of west Francia in 858 shows how important management of the frontier was. In the east, the Slavic Moravian polity presented an equally sustained problem. By about 870 it had emerged as a major central European empire with a developed aristocratic culture and military infrastructure. Moravian power was made concrete in a series of major fortifications including the imposing fortress at Mikul ice, whose 24 acres were defended by 10-foot thick stonefaced walls. The formidable nature of the threat they posed forced the east Frankish kings into a series of close-run military campaigns and turned the evangelisation of the Slavs into a pressing issue for Louis the German, who struggled to resist Byzantine attempts to drag the Moravians under the sway of Constantinople. But the influence ran both ways. Although neither the Slav polities nor Brittany were ever formally incorporated into the empire, Frankish pressure nevertheless contributed to their state formation. Cross-frontier relations could be close (as we saw with Erispoë of Brittany's association with the young Louis the Stammerer), and the Frankish kingdoms thus provided political models for neighbouring rulers. Carolingian kings also engaged in active interference, which accelerated the development of aristocratic hierarchies beyond the frontiers and could encourage political centralisation by providing support for particular leaders or factions. For the Franks, particularly the east Franks, the frontiers remained sources of wealth as well as of instability: a document written between 844 and 862 at the court of Louis the German catalogues the fortresses of various Slavic peoples, and was probably intended to help with the calculation of regularised tribute payments to the east Frankish ruler.
The same dynamics can also be seen at work in Denmark and other parts of Scandinavia, and had a role in the beginnings of the Viking raids, as we saw in Chapter 7. We will return to the Vikings here only to outline their impact on later-ninth-century Frankish politics. The danger to Frankish kings from Scandinavian raiders certainly became very significant in the second half of the ninth century. Viking bands began overwintering in Francia during the troubles of the early 840s and the semi-permanent bases they established, combined with their skill in a surprising variety of types of warfare, made them a serious military proposition. Unlike the Bretons or the Slavs, they were able to penetrate deep into the heart of the empire. The Scandinavians were also well informed and had an uncanny ability to turn up at times of political unrest to gain some advantage. The threat was magnified after 879, when the raiding bands returned in huge numbers and displayed a finely honed ability to coordinate their activities with each other. Sources from both sides of the Channel refer to this megaforce as the 'Great Army' and several annalists describe it as wreaking havoc in the years until it was forced to retreat by a famine in 892. Viking atrocity may have been exaggerated by contemporaries, but we should not over-compensate for this – Scandinavian raids had a major impact in late-ninth-century Europe (see Maps 17 and ).
**Map 17.** Viking raids, 863–77. Attacks were fewer in this period, which, not coincidentally, saw intense raiding in England. One reason for the relative peace was the success of the defensive measures implemented by Charles the Bald.
**Map 18.** Viking raids, 879–91. This era saw more intensive raiding than ever before between the Seine and Rhine. Although the Vikings reportedly sacked Carolingian palaces, Frankish leaders nonetheless scored some notable victories of their own.
Nonetheless, the precise nature of that impact cannot be reduced to a drive towards catastrophe. If we look past the hyperbole of the sources, we see that Frankish armies actually won more battles than they lost against the Vikings, giving the lie to the notion that Carolingian military efficiency withered on the vine after the end of expansion. Strategies developed by Charles the Bald (including the paying of ransoms, the baptism and incorporation of Viking leaders into the empire, and the building of fortified bridges) succeeded in effectively removing the Vikings from Francia for over a decade from the mid-860s. Although the sources, written from a theological perspective, portrayed them as alien and monolithic elements in Frankish politics, and above all as agents of God's wrath, Vikings and Slavs alike were frequently utilised as allies by aristocratic rebels, and by one Carolingian against another: at times, bands of Scandinavian mercenaries can be found on both sides of internal Carolingian disputes. This was true even of the 'Great Army', which was altogether less coherent in its aims and organisation than contemporary authors were inclined to admit. The Vikings were less a source of menace than refuge for some, like the Frankish noblewoman Engeltrude who, under pressure from Pope Nicholas I to return to her discarded husband, retorted that she would rather 'go to the Northmen' than comply. These outsiders were thus a complicating factor in Carolingian politics, but their aim was to profit from the Frankish kingdoms, not to bring them down. In their guise as allies of various Frankish kings, Scandinavian warbands became integral to the conduct of politics in the second half of the ninth century.
The geography of the empire after 843 therefore presented the rulers of the new kingdoms with a series of challenges that constantly threatened to undermine their power. The evidence does not, however, suggest that these kings were structurally weaker than Charlemagne or Louis the Pious. Despite the squeeze on resources they were still able to find sources of revenue to underpin their authority. Some of these were new (the taxes raised by Charles the Bald to pay off the Vikings and those extracted by Louis the German from the eastern parts of his kingdom); while others drew on traditional structures to siphon some of the profits of late-ninth-century commerce and agrarian production into royal coffers. The granting of immunity and protection to wealthy monasteries and churches, some of them controlled by members of the ruling dynasty, continued to provide points of interface and influence between the court and regional elites. Such privileges brought with them the expectation that the churches concerned would, as a charter of Louis the German put it, enter the king's 'power and lordship'. Rulers were eminently capable of translating these resources into political power. They raised armies as effectively as had their predecessors, utilising the same structures of aristocratic lordship: in 858, Louis the German was able to put three armies into the field at the same time, and in 886 it was still possible for Charles the Fat to attack the Vikings in Paris with a huge army drawn from all corners of the empire, persuading them to fight far from their homelands. The authority that these rulers wielded over the elites of their kingdoms is also clear from their ability to punish royal agents who had fallen from favour. Charles the Bald did not shirk from executing even powerful aristocrats like Bernard of Septimania (the villain of the first rebellion against Louis the Pious) in 844 and the Aquitanian Gauzbert in 853. Similarly, in 861 Louis the German managed to reconfigure the balance of power among the east Frankish aristocracy by dispossessing a very influential group of nobles centred on Count Ernest, 'the chief among all his leading men'. The Carolingians could not afford to inflict such extreme punishments on powerful men on a regular basis, but kings could evidently still make or break aristocratic careers. In fact, the later Carolingians arguably had a greater ability to remove counts and other agents from their _honores_ than had Charlemagne and Louis the Pious. Whereas (as we saw in Chapter 4) the latter's attempts to dismiss two counts in 828 had led to his own deposition, Louis the German's ejection of Ernest testifies to the increasing efficacy of the Carolingians' claims that their agents could be treated as accountable officials. The ideologies underpinning such claims were, as we saw, still in their infancy in the capitularies of the early ninth century. By its end they had become so ingrained that observers were beginning to claim the king's right to appoint and dismiss officials as fundamental to definitions of royal power itself. The political structures of the empire after 843 were, in short, somewhat altered but not weakened. To understand why it disintegrated, we must look elsewhere, and turn back to the vagaries of political events.
#### THE END OF THE EMPIRE, 877–888
If the fortunes of the Carolingian empire had a turning point, it came neither in 814 nor in 843, but rather in 875. Between 875 and 884 no fewer than eight reigning Carolingians died, an unprecedented rate of loss, at the end of which only one man was left standing. The impact of these deaths was felt well beyond the ruling family itself because any royal succession created tensions within the kingdom as aristocrats and neighbouring rulers jostled to reposition themselves, and eight in nine years was an unheard-of frequency for such flashpoints. Decline from this point was still not inevitable, but this stunning series of body-blows to the dynasty must have led some to wonder whether divine favour had deserted the ruling house. With this in mind the period has aptly been described as the crisis of the Carolingian empire.
Amidst this complex dynastic dance there was one cuckoo in the nest. In 879, Count Boso of Vienne had himself made king by the leading churchmen and aristocrats of Provence, in the hope of ultimately taking over the whole west Frankish realm. Boso was an establishment figure: his usurpation was built on his status as one of the empire's greatest nobles, a man of wide-reaching connections and influence who had held a series of high offices. In dynastic terms, though, Boso was emphatically an outsider, the first non-Carolingian to lead a rebellion since the 780s, and the first successfully to become king since the removal of the last Merovingian in 751. Wisely, Boso attempted to play his hand within the Carolingian system. He was married to the daughter of Louis II and Engelberga, and his sister was Richildis, Charles the Bald's second wife. Boso played up these Carolingian connections in an attempt to demonstrate his legitimacy. In doing so, he paid a backhanded compliment to the enduring vitality of the idea that legitimate kingship meant Carolingian kingship: Boso wanted to be a member of the club, not to shut it down. Nevertheless, he was plainly an outsider according to the rules of succession that the Carolingians had spent over a century trying to establish. His usurpation was therefore sensational, and represented a genuine challenge to the dynastic hegemony.
Boso's motivation was not principle but rather opportunism. After 876, the sons of Louis the German concerned themselves mainly with internal consolidation and renegotiating their father's territorial division. Only in 879, after Karlmann was paralysed by a stroke, did the brothers come into open conflict with each other, as Louis the Younger tried to push his claims to Bavaria. Relations with the west Frankish cousins were more fraught. Karlmann was much occupied with pursuing his claim to Italy against Charles the Bald. Charles's imperial ambitions were not, however, directed exclusively south of the Alps. In 876, on hearing of his brother's death, he mounted a major invasion of east Francia, only to be thwarted in spectacular and decisive manner on the field of battle at Andernach by Louis the Younger. After Fontenoy as before, open battle between Carolingians was rare, so Andernach struck contemporaries as an event of singular importance. Louis's victory guaranteed his possession of crucial resources in Lotharingia, including Aachen, and gave him a platform on which to build one of the more impressive regimes of the ninth century. By about 877, then, the distribution of power in the reconfigured empire had been fought over and more or less settled by the next generation of kings.
The reign of Charles's son Louis the Stammerer (877–9) in west Francia sowed the seeds of further conflict. Louis was not a particularly 'bad' king. In fact, he showed great military and political vigour in dealing with his aristocracy and the papacy, and in mobilising efforts against the Vikings on the Loire. The problem was his rapidly declining health, and the fact that his two sons were still minors. The king roped in Louis the Younger to underwrite their succession, but the uncertainty of the situation meant that the west Frankish political community was already forming into factions ready to push their own agendas when Louis died in April 879 at the age of only thirty-three. In the aftermath of the king's death, the realm broke down into near civil war for several months. One group of aristocrats supported the succession of the eldest son Louis III while another, fearing that this outcome would leave them politically marginalised, tried to force a division of the kingdom between Louis and his brother, Carloman II. To make matters worse, the Vikings based in England heard about the unrest, and returned to the continent in greater numbers than had been seen there for over a decade (the so-called Great Army). This specific set of circumstances meant that west Francia was deprived of clear leadership, and it was this power vacuum which gave Boso the opportunity to pitch his claim.
Out of conflict, however, was born cooperation. The crisis of 879–80 seems to have shocked the Carolingians into action. Louis the Younger, Charles the Fat, Louis III and Carloman II joined forces in 880 to hound Boso out of his stronghold in Provence and southern Burgundy, and his support crumbled instantly. At the same time, recognising the fact that none of them had a legitimate heir, the four swore oaths to guarantee their future successions to each others' kingdoms, and settled an array of territorial disputes which had been thrown up by the rapidly changing political landscape of the previous decade. Accordingly, in marked contrast to the later 870s, the first half of the 880s was a time of effective Carolingian political cooperation. Contemporary authors were full of optimism for the future of the empire and its ruling dynasty. In 881 Notker of St Gallen referred to Louis III and Carloman as 'the hope of Europe', and was not embarrassed to flatter Charles the Fat that he was an even greater ruler than Charlemagne himself. In the period after 880 these four kings scored some significant successes: victories were won over the Vikings, notably by Louis III, and Charles the Fat acquired the imperial title from the pope in 881. But the four men still lacked even a single legitimate heir between them, and fate intervened before any of them had a chance to procreate further. In 882 Louis the Younger and Louis III both died unexpectedly and prematurely: the former through illness, the latter a victim of youthful indiscretion as he chased a girl into a house on horseback and sustained a fatal injury from the doorframe. In 884 the slapstick mortality continued as Carloman fell foul of a freak hunting accident; he and his brother, Notker's 'hope of Europe', had thus both succumbed to death by misadventure before the age of twenty. Even now, with the options dwindling, the powerbrokers of the empire's regions remained locked into a Carolingian mindset: rather than go it alone, the nobles of each of the kingdoms that had lost its ruler summoned Charles the Fat, the only legitimate male Carolingian adult left, to be their king. In 885, the empire of Charlemagne and Louis the Pious was therefore reunited for the first time since 840.
Charles is usually seen as a peculiarly weak king, pushing vainly against a historical tide that was relentlessly sweeping the empire away to make room for the kingdoms of France and Germany. This, however, is a caricature that draws primarily on sources written by the emperor's enemies. In truth he was an energetic, competent and relatively successful ruler. His record against the Vikings was no worse or better than his predecessors', and his ceaseless circuits of the empire to deal with rebellions, shore up noble support, and obtain recognition of his bastard son Bernard as a legitimate heir were enough to convince regional bigwigs to continue regarding themselves as imperial agents. (See Map 19.) His itinerary was partly a matter of necessity: Charles began as king of Alemannia, but gradually acquired other kingdoms. His forays into west Francia and Bavaria testify to a genuine attempt to rule those regions, but even towards the end of his reign his heartlands remained Alemannia and Italy – the place he visited more than any other was Pavia. The contrast with the pattern of Charlemagne's itineraries is clear, and this geographical shift gradually created problems for the emperor. Nevertheless, most contemporary authors did not share modern historians' pessimism about the reunification of the empire. Regino of Prüm's analysis explicitly contrasted the political turmoil of past ages with the relative peace of the 880s, concluding that '[Charles] understood how to take hold of all the kingdoms of the Franks (which his predecessors had acquired not without bloodshed and with great effort) easily, quickly and without conflict or opposition.'
**Map 19.** Places on the itineraries of Charles the Fat (876–88)
Despite Charles's efforts, the reunification lasted less than three years. In November 887, the emperor was deposed in a palace coup by Arnulf of Carinthia, the illegitimate son of his late brother Karlmann. This, the empire's final crisis, was rooted neither in disintegrating political structures nor in the personal weaknesses of the emperor, but rather in the logic of dynastic politics itself. The empire was, and had always been, too big for one man to rule alone. Since 781, every Carolingian ruler had depended on his sons acting as subkings to diffuse access to the dynasty and tie outlying regions into the political centre. Charles's lack of legitimate sons and nephews, and his failure to have Bernard accepted as heir, deprived him of a crucial political resource. Meanwhile, the emperor's age and increasing Viking activity in the west turned the succession into an issue of resolute urgency. A political system focussed on a particular definition of the ruling family inevitably began to unravel when biological happenstance and youthful misadventure rendered that definition no longer sustainable.
The wilting of the family tree mattered also because the ruling family's identity was intimately connected with the political geography of the empire. The proliferation of Carolingians after the 840s meant that this geography became thoroughly overlaid with a dynastic template. Royal courts were established in almost every corner of the empire, and this helped to draw its peripheral regions closer to the political centre. By the 870s regional magnates in all parts of the empire had (as we saw earlier) become accustomed to the nearby presence of a Carolingian king, and kings were therefore able to rule relatively intensively. When this tide of Carolingians washed back out again in the late 870s and early 880s, the picture it left in its wake was inverted. Regional elites were quite suddenly deprived of access to the dynasty as Carolingians started to die in quick succession and royal courts grew ever more distant. The most striking illustration of the political centre's drift to the geographical periphery is the reign of Charles the Fat, who despite his movement and energy mainly ruled the empire from his own power-bases in Alemannia and Italy and never visited Aachen, even having its relic collection relocated to his court. The elites of the empire's traditional heartlands thus began to feel excluded from the centres of power. In a world where the operation of politics depended on personal patronage, on favours and friendship, and on seeing and being seen, this was a very significant development.
This combination of problems left Charles running to stand still. Concerns about the future spiked when he fell ill at the end of 886, and potential successors began to jostle for position. Prominent among them was Arnulf, who was the most powerful and experienced of the illegitimate Carolingians, but who had been systematically ignored by his uncle as a candidate to share in the succession after a rebellion in 883–4. In late 887, Arnulf felt he had no option but to mount a coup, and at an assembly in Tribur he confronted the sick emperor with a display of force and deposed him. His motives were no different from those of numerous Carolingian rebels of decades and centuries past: like Pippin the Hunchback in 792, the sons of Louis the Pious in the 830s, or even Charles the Fat himself in 871–3, Arnulf was the son of a king, an adult with his own power base and an ageing ruler blocking his path to the throne. When men like this felt themselves being marginalised, their pride and need to prove themselves to their followers forced them into action. For Arnulf in 887, as for Bernard of Italy in 817 or Pippin II of Aquitaine in the 840s, honour dictated that the only way was forwards. For Charles the Fat, middle-aged, sick and heirless, it all ended in tears. Deserted by his men, he was sent back to Alemannia and allowed a few estates as a pension by Arnulf. Charles sent his nemesis the relic of the True Cross on which he had once sworn loyalty to him, 'so that he might be reminded of his oaths and not behave so cruelly and barbarously to him. Arnulf is said to have shed tears at the sight.' The permanence of the coup was sealed six weeks later in January 888 when Charles died of natural causes before he had a chance to make a Louis-the-Pious-style comeback.
If Arnulf's motives have to be understood within the traditional framework of inter-generational Frankish dynastic politics, there was nonetheless one crucial factor distinguishing his status: he was illegitimate. The idea that nobody other than a legitimate-born Carolingian male could be a king had been repeatedly asserted throughout the late eighth and ninth centuries, and at times backed up by force and intimidation. Boso's usurpation aside, this ideology had helped sustain the dynastic _status quo_ for over a century, strengthened, not weakened, by the types of political action and discourse that, as we have seen, characterised the history of the empire after 840. In 887–8, however, there were no legitimate adult Carolingians left to turn to. The success of Arnulf' s coup therefore meant that all bets were off. His decision to restrict his ambitions to the east Frankish kingdom allowed female-line, illegitimate and non-Carolingians to push a claim for kingship elsewhere if they had enough backing. The political landscape that emerged from the dust settling on Arnulf's coup was thus populated by a new set of rulers who had made their careers as high aristocrats in the 870s and 880s: Odo, count of Paris became king in west Francia; the _marchiones_ (margraves) Berengar of Friuli and Guy of Spoleto were crowned as rival rulers of Italy; Rudolf became king in Transjurane Burgundy; and Count Ramnulf of Poitiers reportedly made a pitch to rule in Aquitaine. These men were not representatives of a 'rising aristocracy' that had become increasingly powerful at the expense of their kings. They were trusted agents of kings like Charles the Bald and Charles the Fat, who had empowered them as a means of ruling their extensive kingdoms. Their seizure of power in 888 was not a triumphant act of usurpation based on national or class consciousness – rather, it was an attempt to meet the pressing need for leadership in _regna_ where the deposition and death of Charles the Fat had created an intolerable power vacuum. What else could they do?
These men were not related to each other in any meaningful way. They sought to establish their own dynasties in their own kingdoms, and in competition with each other – the sense of corporate family rule that since 843 had helped bind together the various Frankish kingdoms simply vanished. The dynastic monopoly was over. The new kings' support-bases were factional and equivalent, and wearing a crown was not enough to convince all their peers that they had acquired the aura of royal majesty – even more than the Carolingians, they were open to challenges from any political opponent who felt he was strong enough. Little wonder a contemporary annalist labelled them _reguli_ , 'kinglets'. Regino of Prüm offered the most persuasive summary:
After his [Charles the Fat's] death the kingdoms which had obeyed his authority, just as though a legitimate heir were lacking, dissolved into separate parts and, without waiting for their natural lord, each decided to create a king from its own guts. This was the cause of great wars; not because the Franks lacked leaders who by nobility, courage and wisdom were capable of ruling the kingdoms, but rather because the equality of descent, authority and power increased the discord among them; none so outshone the others that the rest deigned to submit to his rule.
Not just in retrospect, but also to contemporaries like Regino, 888 represented an ending. The dynasty had been so successful in Carolingianising the empire that the shattering of its monopoly on kingship was translated instantly onto the political landscape of the Frankish kingdoms – the crisis of the family became the crisis of the empire.
* * *
Leo IV, _Epistolae_ , ed. A. de Hirsch-Gereuth, _MGH Epp_. v ( _Epistolae Karolini aevi_ iii) (Berlin, 1898–9), no. 46.
Engelbert, _Versus de bella quae fuit acta Fontaneto_ , ed. E. Dümmler, _MGH Poet. Latini aevi Karolini_ II (Berlin, 1884), pp. 138–9, trans. Dutton, _Carolingian Civilization_ , pp. 332–3.
For discussion of battles see Halsall, _Warfare and Society_ , pp. 177–214; and the articles in B. Bachrach (ed.), _Journal of Medieval Military History_ 1 (2003).
Notker, _Gesta_ , 2.11.
_Johannes VIII. Papae Epistolae_ , no. 7; E. J. Goldberg, _Struggle for Empire. Kingship and Conflict under Louis the German, 817–876_ (Ithaca, 2006), p. 333 (whence the translation).
On Pippin the Hunchback see above, Chapter 2, pp. 78–9; on Bernard of Italy, Chapter 4, pp. 202–5.
On Nithard see above all Nelson, 'Public Histories'; and now S. Airlie, 'The world, the text and the Carolingian: royal, aristocratic and masculine identities in Nithard's Histories', in Nelson and Wormald (eds.), Lay Intellectuals, pp. 51–76. On the events of the civil war see Nelson, Charles the Bald, pp. 105–31; A. Krah, Die Entstehung der 'potestas regia' im Westfrankenreich während der ersten Regierungsjahre Kaiser Karl II. (840–877) (Berlin, 2000); E. Screen, 'The importance of the emperor: Lothar I and the Frankish civil war, 840–843', EME 12 (2003), pp. 25–51; Goldberg, Struggle for Empire, pp. 86–116.
See above, Chapter 4, pp. 218–19.
Notker, _Gesta_ , 1.34; Goldberg, _Struggle for Empire_ , p. 44.
Riché, _The Carolingians_ , p. 168.
Kaschke, _Die karolingischen Reichsteilungen_.
Brühl, _Deutschland–Frankreich_.
Dipl. LG 66; W. Hartmann, _Ludwig der Deutsche_ (Darmstadt, 2002), p. 121. Louis never actually acquired the imperial title. See also W. Diebold, ' _Nos quoque morem_ _illius imitari cupientes_. Charles the Bald's evocation and imitation of Charlemagne', _Archiv für Kulturgeschichte_ 75 (1993), pp. 271–300; Goldberg, _Struggle for Empire_ , pp. 288–92.
Regino, _Chronicle, s.a_. 841.
Regino, _Chronicle, s.a_. 880. On Regino's narrative strategies see Airlie, 'Sad stories of the deaths of kings'. Louis the German's eldest son is referred to as Karlmann to distinguish him from his namesake, the son of Charles the Bald, who is referred to as Carloman.
On later commemoration of Fontenoy see J. L. Nelson, 'The search for peace in a time of war: the Carolingian _Brüderkrieg_ , 840–843', in J. Fried (ed.), _Träger und Instrumentarien des Friedens im hohen und späten Mittelalter_ (Sigmaringen, 1996), pp. 87–114 at pp. 112–14.
A. Gillett (ed.), _On Barbarian Identity: Critical Approaches to Ethnicity in the Early Middle Ages_ (Turnhout, 2002).
For example:J. Fried, _König Ludwig der Jüngere in seiner Zeit_ (Lorsch, 1984); Nelson, _Charles the Bald;_ MacLean, _Kingship and Politics;_ Goldberg, _Struggle for Empire_.
See also above, Chapter 1, pp. 22–3.
A third son, Charles of Provence, died young in 863.
For these figures see Brühl, _Deutschland-Frankreich_ , pp. 359–61; the classic work on the subject is R. Schneider, _Brüdergemeine und Schwurfreundschaft: der Auflösungsprozess des Karlingerreiches im Spiegel der Caritas-Terminologie in den Verträgen der karlingischen Teilkönige des 9. Jahrhunderts_ (Lübeck, 1964).
On filial duty see above, Chapter 4, pp. 210–11.
Nelson, _Charles the Bald_ , p. 150, n. 81.
_Capit_. II, no. 204, c. 1.
_Epistola ad Basilium_ I., ed. W. Henze, _MGH Epp_. vII ( _Epp. Karolini aevi_ v) (Berlin, 1928), pp. 386–94; Fanning, 'Imperial diplomacy'. Christian unity was also used as a way of minimising the significance of regnal boundaries: see for example Hincmar, _De divortio Lotharii_ , p. 236.
On the aristocracy's internalisation of this discourse see S. Airlie, 'Les Élites en 888 et après, ou comment pense-t-on la crise carolingienne?', in F. Bougard, L. Feller and R. Le Jan (eds.), _Les Élites au haut Moyen Âge. Crises et renouvellements_ (Turnhout, 2006), pp. 425–37.
AF, _s.a_. 846.
_Capit_. II, no. 204; Nelson, _Charles the Bald_ , pp. 149–50.
AF, _s.a_. 848.
On the Vikings see also above, Chapter 7, pp. 353–8.
Nelson, _Charles the Bald_ , pp. 154–5.
AB, _s. a_. 845; AF, _s. a_. 845.
See B. Ward-Perkins, _From Classical Antiquity to the Middle Ages. Urban Public Building in Northern and Central Italy AD 300–850_ (Oxford, 1984), pp. 195–6. On the Muslim raids see also above, Chapter 7, pp. 372–5.
E. J. Goldberg, 'Ludwig der Deutsche und Mähren: Eine Studie zu karolingischen Grenzkriegen im Osten', in W. Hartmann (ed.), _Ludwig der Deutsche und seine Zeit_ (Darmstadt, 2004), pp. 67–94; Goldberg, _Struggle for Empire_ , pp. 119–46.
AB, _s.a_. 852, 853; Nelson, _Charles the Bald_ , p. 162.
AF, _s.a_. 852; Reuter, _Germany in the Early Middle Ages_ , pp. 85–91.
AF, _s.a_. 852.
AB, _s.a_. 853, p. 67; AF, _s.a_. 853; Martindale, 'The kingdom of Aquitaine'.
AB, _s.a_. 853.
AF, _s.a_. 854.
AF, _s.a_. 854.
Goldberg, _Struggle for Empire_ , pp. 234–42.
Nelson, _Charles the Bald_ , p. 180.
AB, _s.a_. 855, 856, 858, 859, 861, 863.
Nelson, _Charles the Bald_ , pp. 181–96; Goldberg, _Struggle for Empire_ , pp. 248–62.
Nelson, _Charles the Bald_ , pp. 181–6; Smith, _Province and Empire_ , pp. 100–6.
AF, _s.a_. 855.
_AB, s.a_. 856.
AF, _s.a_. 858.
For what follows, see Nelson, _Charles the Bald_ , pp. 198–201, 215–20; Airlie, 'Private bodies'; Goldberg, _Struggle for Empire_ , pp. 292–5.
Regino, _Chronicle, s.a_. 864.
Nelson, _Charles the Bald_ , p. 198.
See above, Chapter 3, pp. 81–2.
Sedulius, _Liber de rectoribus Christianis_ , ed. S. Hellman, _Sedulius Scottus_ (Munich, 1906), c. 5, trans. Dutton, _Carolingian Civilization_ , p. 384. On date and audience see especially N. Staubach, _Rex Christianus: Hofkultur und Herrscherpropaganda im Reich Karls des Kahlen II: Die Grundlegung der 'religion royale'_ (Cologne, 1993), pp. 109, 112, 176–81. On Sedulius see now P. J. E. Kershaw, 'English history and Irish readers in the Frankish world', in D. Ganz and P. Fouracre (eds.), _Frankland. The Franks and the World of Early Medieval Europe. Essays in Honour of Dame Jinty Nelson_ (Manchester, 2008), pp. 126–51.
Hincmar, _De ordine palatii_ , c. 22.
J. L. Nelson, 'Early medieval rites of queen-making and the shaping of medieval queenship', in A. J. Duggan (ed.), _Queens and Queenship in Medieval Europe_ (Woodbridge, 1997), pp. 301–15; MacLean, 'Queenship, nunneries'.
Charles: _AB, s.a_. 861, 863, 864, 866. Louis: _AB, s.a_. 860, 862, 863, 867; _AF, s.a_. 863; _Dipl. Loth II_ 34.
_Capit_. II, no. 245.
Reimitz, 'Ein fränkisches Geschichtsbuch'.
AB, _s.a_. 869.
AB, _s.a_. 870.
Nelson, _Charles the Bald_ , pp. 204, 210–11, 231–2.
On Carloman's rebellion see Nelson, 'A tale of two princes'; Nelson, _Charles the Bald_ , pp. 226–31.
AF, _s.a_. 865; Notker Balbulus, _Erchanberti breviarium continuatio_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), pp. 329–30; M. Borgolte, 'Karl III. und Neudingen. Zum Problem der Nachfolgeregelung Ludwigs des Deutschen', _Zeitschrift für die Geschichte des Oberrheins_ 125 (1977), pp. 21–55; Reuter, _Germany in the Early Middle Ages_ , pp. 72–3.
Goldberg, _Struggle for Empire_ , pp. 304–34.
AB, _s.a_. 870; _AF, s.a_. 871.
AB, _s.a_. 873; AF, _s.a_. 873; AX, _s.a_. 873; MacLean, 'Ritual, misunderstanding and the contest for meaning'.
On 829 see above, Chapter 4, pp. 213–18.
_AF, s.a_. 874; Goldberg, _Struggle for Empire_ , pp. 320–1.
See above, p. 389.
AB, _s.a_. 866; H. Zimmermann, _'Imperatores Italiae'_ , in H. Beumann (ed.), _Historische Forschungen für Walter Schlesinger_ (Cologne and Vienna, 1974), pp. 379–99.
See above, Chapter 4, pp. 167–70.
See F. Bougard, 'La Cour et le gouvernement de Louis II (840–875)', in Le Jan (ed.), _La Royauté et les élites_.
C. E. Odegaard, 'The empress Engelberge', _Speculum_ 26 (1951), pp. 77–103.
AB, _s.a_. 871; Regino, _Chronicle, s.a_. 871. See Kreutz, _Before the Normans_.
AB, _s.a_. 875; AF, _s.a_. 875.
On these events see S. MacLean, '"After his death a great tribulation came to Italy..." Dynastic politics and aristocratic factions after the death of Louis II, c.870–c.890', _Millennium Jahrbuch_ 4 (2007), pp. 239–60.
Airlie, ' _Semper fideles_?'.
Nelson, 'Legislation and consensus'.
_Capit_. II, no. 260; Nelson, _Charles the Bald_ , pp. 167–8, 326; Nelson, 'Literacy in Carolingian government'. On Ansegisus see above, Chapter 4, pp. 183–4.
_Capit_. II, nos. 273, 281–2.
Nelson, _Charles the Bald_ , p. 33.
K. F. Morrison, _Carolingian Coinage_ (New York, 1967), pp. 88–9, 124–5, 172; Goldberg, _Struggle for Empire_ , p. 205.
Goldberg, _Struggle for Empire_ , pp. 186–230.
AF, _s.a_. 852; Goldberg, _Struggle for Empire_ , p. 164.
Goldberg, _Struggle for Empire_ , p. 224.
Werner, 'Missus–marchio–comes'. Cf above, Chapter 4, pp. 171–8.
See Chapter 4, pp. 172–8.
Tessier, _et al_. (eds.), _Recueil des actes_ , no. 425, trans. Nelson, _Charles the Bald_ , p. 247. For the term 'Carlopolis' see D. Lohrmann, 'Trois palais royaux de la vallée de l'Oise d'après les travaux des érudits mauristes: Compiègne, Choisy-au-Bac et Quierzy', _Francia_ 4 (1976), pp. 121–40.
Regino, _Chronicle, s.a_. 876; Zotz, 'Carolingian tradition'; MacLean, _Kingship and Politics_ , pp. 187–9; T. Zotz, 'Ludwig der Deutsche und seine Pfalzen: Königliche Herrschaftspraxis in der Formierungsphase des ostfränkischen Reiches', in W. Hartmann (ed.), _Ludwig der Deutsche und seine Zeit_ (Darmstadt, 2004), pp. 27–46.
Nelson, _Charles the Bald_ , pp. 45–50; Goldberg, _Struggle for Empire_ , pp. 226–9.
T. Reuter, 'Assembly politics in western Europe from the eighth century to the twelfth', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 432–50; repr. in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 193–216.
Nelson, 'The Lord's anointed'; Goldberg, _Struggle for Empire_ , pp. 187–200. For salutary methodological caveats see P. Buc, _The Dangers of Ritual_ (Princeton, NJ, 2001).
Innes, _State and Society_ , pp. 42–3; Brown, _Unjust Seizure_ , pp. 186–200.
Brown, _Unjust Seizure_ , pp. 187–8.
_Dipl. Lothar II_ 34.
Smith, _'Fines imperii_ '; and see above, pp. 395–6.
Goldberg, _Struggle for Empire_ , pp. 244–5.
Goldberg, _Struggle for Empire_ , pp. 300–1, 319–20.
Smith, _Province and Empire;_ Heather, 'State formation'; Innes, 'Franks and Slavs'.
Goldberg, _Struggle for Empire_ , pp. 135–7. For a different emphasis see Reuter, 'Plunder and tribute'.
For recent discussion see Nelson, 'England and the continent'.
S. Coupland, 'The Carolingian army and the struggle against the Vikings', _Viator_ 35 (2004), pp. 49–70.
Nelson, _Charles the Bald_ , pp. 206–13.
Nelson, _Charles the Bald_ , pp. 205–7; on the sources see above all Coupland, 'The rod of God's wrath'. In general see P. Sawyer (ed.), _The Oxford Illustrated History of the Vikings_ (Oxford, 1997).
R. Abels, 'Alfred the Great, the _micel hœthen here_ and the Viking threat', in T. Reuter (ed.), _Alfred the Great: Papers from the Eleventh-Centenary Conferences_ (Aldershot, 2003), pp. 265–79.
Hincmar, _De divortio_ , p. 244.
Nelson, _Charles the Bald_ , pp. 19–40; Innes, _State and Society_ , pp. 156–9; Goldberg, _Struggle for Empire_ , pp. 205–6. See also above, Chapter 7.
_Dipl. LG_ 71; Goldberg, _Struggle for Empire_ , p. 215.
S. MacLean, 'Charles the Fat and the Viking Great Army: the military explanation for the end of the Carolingian empire', _War Studies Journal_ 3 (1998), pp. 74–95; MacLean, _Kingship and Politics_ , pp. 55–64.
_AB, s.a_. 844, p. 47; Regino, _Chronicle, s.a_. 860.
_AF, s.a_. 861.
For more examples see Nelson, _Charles the Bald_ , pp. 202, 211–12; A. Krah, _Absetzungsvefahren als Spiegelbild von Konigsmacht. Untersuchungen zum Kräfteverhaltnis_ _zwischen Königtum und Adel im Karolingerreich und seinen Nachfolgestaaten_ (Aalen, 1987).
Regino, _Chronicle, s.a_. 876; Notker, _Gesta_ , 2.11.
Airlie, 'Les Elites en 888', pp. 426–7.
See S. Airlie, 'The nearly men: Boso of Vienne and Arnulf of Bavaria', in A. Duggan (ed.), _Nobles and Nobility in Medieval Europe_ (Woodbridge, 2000), pp. 25–41; S. MacLean, 'The Carolingian response to the revolt of Boso, 879–87', _EME_ 10 (2001), pp. 21–48.
Regino, _Chronicle, s.a_. 877.
AF, _s.a_. 879, 880.
AF, _s.a_. 876; AB, _s.a_. 876; Regino, _Chronicle, s.a_. 876.
Fried, _König Ludwig_.
K. F. Werner, 'Gauzlin von Saint-Denis und die westfränkische Reichsteilung von Amiens (März 880). Ein Beitrag zur Vorgeschichte von Odos Königtum', _DA_ 35 (1979), pp. 395–462; MacLean, 'Carolingian response'.
_AV, s.a_. 879.
MacLean, 'Carolingian response'.
Notker, _Erchanberti breviarium continuatio_ , p. 330.
MacLean, _Kingship and Politics_ , pp. 81–122.
Regino, _Chronicle, s.a_. 888. For a translation of this text see MacLean, _History and Politics_.
On Carolingian politics as a dynastic system see above all Airlie, _Carolingian Politics_.
MacLean, _Kingship and Politics_ , pp. 157–8.
Innes, 'People, places and power'.
_AF_ (Mainz continuation), _s.a_. 887, p. 103. On this and other such episodes see M. Becher, _'Cum lacrimis et gemitu_. Vom Weinen der Sieger und der Besiegten im frühen und hohen Mittelalter', in G. Althoff (ed.), _Formen und Funktionen öffentlicher Kommunikation im Frühund Hochmittelalter_ (Stuttgart, 2001), pp. 25–52.
Louis the Stammerer's posthumously born third son Charles 'the Straightforward' (or 'Simple') had a claim, but was still very young.
_AF_ , _s.a_. 888.
Airlie, 'The nearly men'.
AF, _s.a_. 888, p. 115.
Regino, _Chronicle_ , _s.a_. 888. On Regino as a historian of the end of the empire see Airlie, 'Sad stories of the deaths of kings'; MacLean, _History and Politics_ , pp. 1–60, and S. MacLean, 'Insinuation, censorship and the struggle for late Carolingian Lotharingia in Regino of Prüms _Chronicle_ ', _EHR_ 124 (2009), pp. 1–28.
Airlie, 'Les Élites'; Airlie, _Carolingian Politics_.
## 9
### EPILOGUE
Equipped as we are with perfect hindsight, modern historians are instinctively inclined to look for beginnings and endings. The urge to impose ordered narratives on the disorder of the past is hard to resist, and thus the story of the Carolingian empire is often told (as indeed it is in this book) as one with an identifiable beginning, middle and end. Introducing this book, we justified our selection and definition of a specifically 'Carolingian' period. By way of conclusion, we can return to the place of the Carolingian era in the bigger picture of European history, and remind ourselves of the tension in all historical explanation between the ideas of abrupt change and continuous development.
In the longer narratives of European history from which our ideas about the origins of modern nations are constructed, the Carolingian period is seen above all as an age of beginnings: of the hierarchical social structures often packaged together as 'feudalism'; of medieval concepts of empire; of the political geography and concept of Europe itself. The details of all this are of course contested, but although few historians now would be as confident and categorical in their arguments as were those who identified Charles Martel as the inventor of vassalage and hence feudalism, a Carolingian template still seems to most to form an essential substructure of central medieval political culture. The Carolingian empire may have fallen in 888, but the grand narratives of the present day often assign it a privileged position in the foundation of the future.
There are methodological grounds for distrusting the pursuit of what Marc Bloch sceptically described as 'the idol of origins'. But even if we disregard such doubts, there remain good reasons to be wary of overestimating the significance of the Carolingians in the shaping of European history. As we have seen, the sources that emphasise the novelty and scope of the dynasty's reach were, in the main, themselves written within the ambit of the royal courts. To all intents and purposes, the story of the origins of Carolingian hegemony is a story told by the Carolingians themselves. Contemporary claims about the epoch-making character of the alliance between the new Frankish rulers and the papacy, as we saw at the beginning of this book, were not neutral observations of a page turning in the course of history, but political arguments made in real time, emerging from the controversies and insecurities of the later eighth century. The same can be said of texts discussing events like the battle of Tertry in 687, retrospectively identified by Carolingian sympathisers as the point at which the dynasty's power began to eclipse that of the kings they later displaced. The baggage hung by modern historians on these dates (and on others like 800 and 843) owes much to the repetitious and insistent rhetoric of reform and renewal deployed by writers surrounding the Carolingian rulers. When Einhard depicted the last Merovingians as straggly haired rustics trundling round the countryside in ox-carts, his aim above all was to sharpen his readers' sense of difference between past and present, and hence to mask the continuities between the two eras. The novelty of Carolingian social and political structures was deliberately exaggerated from the start, and amplified further in the echo-chamber of historical tradition. We might even argue, as some have, that the eighth and ninth centuries should be seen more as an age of endings than beginnings, representing the last gasp of the post-Roman age and its increasingly irrelevant ideas about empire and political unity rather than the template for the disjointed European map of the central Middle Ages.
Posterity thus envisages the Carolingian world teetering precariously on the fulcrum between the late antique past and the medieval future, and, based on what they believe about its economy, or its rural life, or its aristocracy, historians are frequently tempted to venture arguments about which way it tilted. In this book we have attempted to avoid these debates about long-term continuity and change, and to ask instead what the contemporary sources can tell us about the Carolingian period on its own terms. This has revealed a great deal of economic and social diversity within the empire, and a distinct lack of the political centralisation looked for by earlier generations of historians. Judged by modern standards, the empire's rulers might seem structurally weak: they did not have the capability to reach efficiently into the households and pockets of local elites, nor even to dictate very effectively the legal norms that held sway in comital courtrooms. As we have seen, power derived ultimately from the land and people controlled by the great and the good of the kingdom rather than from any state machinery or impositions from above. Yet somehow these kings were able to gather large armies, to mount campaigns of conquest, and to hold the resulting empire together for nearly a century and a half. To understand this we have to embrace the unusualness of contemporary discourse. Eighth- and ninth-century kings regarded themselves as propagators of _correctio_ — to rule ( _regere_ ) was to correct ( _corrigere_ ), according to the influential early medieval etymologist Isidore of Seville, who saw an essential truth implicit in the similarity of the words. Kings were persuaders, not dictators. The impact of the 'Carolingian project' resided not so much in the coercive capabilities of its architects as in its attractiveness to regional elites, who saw the opportunities for personal advancement that could come from buying in (a calculation that was probably made more instinctive by the shared cultural assumptions of post-Roman elites across the west). Imperial ideology stressed unity, but also allowed regional identities and local political traditions to survive. Thus it was that the elites of annexed territories such as Italy and Bavaria could be successfully co-opted as allies; and that well before the end of the ninth century, even the Saxons,Charlemagne's most implacable enemies, were commemorating him as a great Christian ruler. The forces that held the Carolingian empire together emanated as much from below as from above – it worked because most of its powerful inhabitants believed that it existed and that it mattered.
When we try to make sense of the dense blizzards of texts produced in the reigns of rulers like Charlemagne, Louis the Pious and Charles the Bald, we should therefore keep in mind that the early Middle Ages was a distinct historical period and avoid anachronistic comparisons with high medieval administrative kingship or the structured power of the Roman state. Instead, our sources make most sense as reflections of a sustained attempt to create and maintain new patterns of elite mentality. This should not be taken to mean that Carolingian rule was only an abstract concept. These patterns of thought demonstrably shaped elite action, and their effects were far from intangible. As we have seen, they underpinned a patronage system that bound local elites and even rural village communities into increasingly hierarchical relationships with the political centre, reinforced the importance of office and royal service to aristocratic careers, strengthened the tradition of corporate episcopal action, and articulated a sprawling political system that encompassed an entire European empire. The world described in this book was not a new social and political order created from nothing, but it can be said at least to have constituted a comprehensive re-imagining of the existing building blocks of early medieval society. This structure lasted for over a century, and aligned the interests of the landed elite with strong kingship – it was the sudden removal of Carolingian rule in the dynastic crisis of the 880s, not the gradual decay of putative institutions, that caused it to unravel at the end of the ninth century.
For all that the dynastic upheavals of 888 created, as we saw at the end of Chapter 8, the sense of an ending in the minds of Carolingian authors, many features of ninth-century society and political culture survived. There was no major disruption in the character of society at the end of the ninth century, just as there had not been in the middle of the eighth. The insidious social changes often held to underpin the supposed fragility of later-ninth-century politics – particularly the concept of a 'rising' aristocracy holding increasingly concentrated properties and exercising ever-firmer control over the inhabitants of their localities – are, contrary to what one might suspect from a casual reading of the secondary literature, almost impossible to identify in the sources. Carolingian hegemony had had an impact on the shape of the political landscape, creating nodal points around rural palaces and favoured rich monasteries, but the essential features of this landscape long outlasted the dynasty and persisted at least until the early eleventh century, when the transformation of Frankish social relations was symbolised by the increasing domination of the castle. Historians have recently expended much ink on debating whether this happened quickly, around the millennium, in a 'feudal revolution', or whether it was the result of a long evolution driven by the dynamics of the post-Carolingian world. This is not the place for a detailed analysis of the debate. However, it does serve to highlight the fact that it is only really with reference to the mid-eleventh century that we can begin to talk confidently about the emergence of a new social landscape that we might call 'high medieval'. Characterised by castles and lords, knights and chivalry, cities and merchants and the rise of administrative kingship, this is the classical Middle Ages familiar from Hollywood and the historical novel, and though all of its features may have had clear Carolingian antecedents, in sum they constituted a new type of society. Underlying the emergence of this new Middle Ages was the economic improvement of the tenth century and the increasingly complex society that evolved as a consequence. In the Carolingian era, social and political power was rooted ultimately in land and patronage, but by the eleventh and twelfth centuries the rising importance of alternative sources of power such as cities, mercantile activity and universities had created a world of smaller, intensively governed polities in which the old-style imperial aristocracy no longer had the field to themselves. This is the fundamental shift that marks the evolution of early medieval Europe into the high Middle Ages – placed in this context, the end of the Carolingian empire in 888 does not seem as significant as we might assume.
Similar conclusions could be drawn from a survey of the highest political level, where the horizons of Europe's rulers remained defined by the old borders of the Frankish empire for generations to come: tenth- and eleventh-century kings still thought of themselves as successors of Charlemagne rather than founders of proto-nationstates. Some of these kings were even _bona fide_ Carolingians. Charles 'the Straightforward' (traditionally, 'the Simple'), Louis the Stammerer's third son who had been too young to pitch a claim in 888, ruled west of the Rhine in the period 898–923, and his descendants did likewise from 936 until 987. In the eastern kingdom, Carolingian kings reigned until 911, and in Italy too descent from Charlemagne proved an effective argument for would-be kings until at least the 950s. Nor was there any fundamental shift in the methods or styles of power at the highest level: all the post-888 rulers, even those unrelated to the Carolingians, attempted to rule using the symbolic idioms, political language and (to a lesser extent) written instruments of their predecessors.
Yet these dynastic changes mattered profoundly because, as we saw at the end of Chapter 8, they were intimately connected with the political geography of the empire. Arnulf's illegitimacy gave licence to powerful magnates across the empire to try to have themselves recognised as kings whether they could claim Carolingian ancestry or not. Possession of Carolingian blood was no longer held out as the exclusive touchstone of royal legitimacy. The decades after 888 were therefore characterised not by conflict within a single dynasty, but by conflicts between (would-be) dynasties. The uncertainty bred by this situation meant that while post-888 kings may have presented themselves as continuing the legacy of Charlemagne and tried to mould themselves to his model, their power was in fact more fragile than their predecessors': powerful rebels, rather than seeking to ally themselves with a relative of the ruler, were now more likely to make a bid to seize the throne themselves. Consequently, while kings can be found fighting other kings in most eras of the early Middle Ages,the political violence of the first generations after 888 had a different character to that of the high Carolingian period. As we saw earlier, the history of the 840s and 850s was one of kings based in traditional royal heartlands struggling to control the peripheries of their kingdoms. A measure of how things had changed is that the story of the 890s is rather one of kings whose power-bases lay at the edges of the Frankish kingdoms struggling to take control of the heartlands, often by force of arms. Kings Berengar of Friuli (888–924) and Guy of Spoleto (888–94) fought for control of the royal estates of the Po valley in northern Italy; King Odo (888–98), whose main power-base was in Neustria and the Breton March, expended much energy trying to assert himself in the east and south of his kingdom; and Arnulf's son King Zwentibald found it almost impossible to take command of the traditional levers of power in Lotharingia, leading to a struggle that eventually provoked his murder. Kings like Charles the Bald and Charles the Fat had ruled by trying to balance the interests and ambitions of various factions and groups among the high nobility; kings like Odo and Berengar were themselves not much more than leaders of individual factions.
In all of the post-888 kingdoms, it therefore took some time for more or less stable dynasties to establish themselves, and where they succeeded they did so on new terms. In Italy Berengar and Guy, important servants of the late Carolingians, both had themselves declared king and spent the early 890s engaged in an armed struggle for supremacy. The lack of consensus on royal legitimacy in Italy meant that kings' regimes were constantly under threat of rebellion and usurpation, and no new dynasty was able to establish itself with lasting success until the invasion of the Saxon king of east Francia, Otto I (936–73), in the 950s. The first Ottonian ruler of east Francia itself, Otto's father Henry I, did not become king until 919, and even then only slowly established his authority through a willingness to recognise the independent power of the regional dukes. Henry was a magnate who acquired the throne after prospering politically during the minority of Arnulf's son Louis the Child (900–11) and the fragile regime of Conrad I (911–19), another aristocrat-turned-king: his success was in helping the other dukes to forget, or to overlook,the fact of their social equality with him and to start to think of his family as royal. In the west, the throne fluctuated between the relatives of Odo and those of Charles the Straightforward. Yet the fact that Odo had been able to integrate the lands of the Carolingian kings in Neustria and Francia with his own family properties meant that the power of the tenth-century Carolingians was heavily compromised. They could still rule, but not in the same way as had their ancestors in the ninth century. Finally, in 987 the throne was taken over definitively by Odo's descendants, known to posterity as the Capetians, and they kept it until 1328. The removal in 888 of the dynastic hegemony that the Carolingians established therefore did have direct and important effects on the way that politics was conducted. The end of the Carolingian empire might not have entailed radical social or structural changes – but it mattered. The Europe that emerged in the tenth century was the same but different. This Europe still thought of itself as Frankish and continued to look backwards to the Carolingians for its sense of itself – but the shape of its politics had subtly and significantly changed.
Ultimately, any attempt to unpick what the Carolingian world bequeathed to the future from what it received from the past must raise as many questions as answers. Seeing in the empire a direct revival of Rome, a prelude to the classical Middle Ages of the high medieval period or a prototype for the European Union does not really do justice to what was specific about the eighth and ninth centuries. Instead we have to acknowledge that the history of the Carolingian world presents us with astonishing ambition, failed experiments and a number of open questions and seeming contradictions. Powerful but fragile, coherent but fragmented, culturally conservative but politically volatile – the paradoxes of the Carolingian empire reveal the distinctive features of the early Middle Ages as a whole.
* * *
See above, Chapter 2, pp. 44–51 on Charles Martel; and for a sophisticated modern interpretation of the Carolingian legacy and the creation of medieval Europe see R. Bartlett, _The Making of Europe: Conquest, Colonization and Cultural Change, 950–1350_ (London, 1993), esp. pp. 269–70, 285–6.
M. Bloch, _The Historian's Craft_ , ed. P. Burke (Manchester, 1992), pp. 24–9.
Sullivan 'The Carolingian age'.
Isidore, _Etymologiae_ ix.3.4, ed. and trans. Barney, _et al_., p. 200.
P. Fouracre, 'Cultural conformity and social conservatism in early medieval Europe', _History Workshop Journal_ 33 (1992), pp. 152–61.
For pertinent comments see now F. Mazel, 'Des familles de l'aristocratie locale en leurs territoires: France de l'ouest, du ixe au xie siècle', in P. Depreux, F. Bougard and R. Le Jan (eds.), _Les Élites et leurs espaces. Mobilité, rayonnement, domination (du vie au xie siècle_ ) (Turnhout, 2007), pp. 361–98; A. Rio, 'High and low: ties of dependence in the Frankish kingdoms', _TRHS_ 6th ser., 18 (2008), pp. 43–68. See above, Chapter 5.
See H. Hummer, 'Reform and lordship in Alsace at the turn of the millennium', in W. C. Brown and P. Górecki (eds.), _Conflict in Medieval Europe: Changing Perspectives on Society and Culture_ (Aldershot, 2003), pp. 69–84; for the Carolingians and monasteries, see Costambeys, _Power and Patronage_ , pp. 52–3.
For an introduction to the issues and further references see S. MacLean, 'Apocalypse and revolution: Europe around the year 1000', _EME_ 15 (2007), pp. 86–106.
See P. Fouracre, 'Marmoutier and its serfs in the eleventh century', TRHS 15 (2005), pp. 29–49; P. Fouracre, 'Space, culture and kingdoms in early medieval Europe', in Linehan and Nelson (eds.), The Medieval World, pp. 366–80.
See above, Chapter 8, pp. 391–5. MacLean, 'After his death'.
G. Sergi, 'The kingdom of Italy', in Reuter (ed.), _The New Cambridge Medieval History III_ , pp. 346–71.
Reuter, _Germany in the Early Middle Ages_ , pp. 137–47.
## BIBLIOGRAPHY
Volumes of charters (and hence also some other series like Capitularia and Concilia) are to be found under the editor's name.
There are separate entries for those individual capitularies which are cited frequently.
#### 1. PRINTED PRIMARY SOURCES
Abbo of St-Germain-des-Prés, _Bella Parisiacae urbis_ , ed. H. Waquet, _Abbon. Le Siège de Paris par les Normands_ (Paris, 1942); extract trans. Dutton (ed.), _Carolingian Civilization_ , pp. 514–16; full trans. N. Dass, _Viking Attacks on Paris_ (Dudley, MA, 2007).
_Acts of the Council of Pavia_ , ed. G. Waitz, _MGH SRL_ (Hanover, 1878), pp. 189–91.
_Actus pontificum Cennomannis in urbe degentium_ , ed. G. Busson and A. Ledru, Archives historiques du Maine 2 (Le Mans, 1902).
_Admonitio generalis_ , ed. A. Boretius, _Capit_. I, no. 22, pp. 52–62; trans. King, _Charlemagne: Translated Sources_ , pp. 209–20.
_Admonitio ad omnes regni ordines_ , ed. A. Boretius, _Capit_. I, no. 150, pp. 303–7.
Adrevald of Fleury, _Miracula Sancti Benedicti_ , ed. O. Holder-Egger, _MGH SS_ xv, pp. 474–97.
_Æcerbot_ , ed. and trans. G. Storms, _Anglo-Saxon Magic_ (The Hague, 1948), pp. 173–4.
Agnellus, _Liber pontificalis ecclesiae Ravennatis_ , ed. D. M. Deliyannis, _CCCM_ , 199 (Turnhout, 2006); trans. D. M. Deliyannis, _Agnellus of Ravenna. The Book of Pontiffs of the Church of Ravenna_ (Washington, DC, 2004).
Agobard of Lyon, _De Antiphonario_ , in _Agobardi Lugdunensis opera omnia_ , ed. L. van Acker, _CCCM_ 52 (Turnhout, 1981), pp. 335–51.
Alcuin, _De virtutibus et vitiis liber, PL_ CI, cols. 613–38.
—, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. IV ( _Epp. Karolini aevi_ II) (Berlin, 1895), pp. 1–493; trans. S. Allott, _Alcuin of York: His Life and Letters_ (York, 1974).
—, _Vita Willibrordi_ , ed. W. Levison, _MGH SRM_ VII (Hanover, 1920), pp. 81–141; trans. Talbot, _Anglo-Saxon Missionaries_ , repr. in Noble and Head, _Soldiers of Christ_ , pp. 189–211.
Altfrid, _Vita Liudgeri_ , ed. W. Diekamp, _Die Vitae Sancti Liudgeri_ (Münster, 1881); selections trans. Whitelock, _EHD_ , no. 160, pp. 787–90.
Amalarius of Metz, _De officiis_ , ed. J. Hanssens, _Amalarii opera liturgica omnia_ II, Studi e Testi 138–40 (Vatican City, 1948–50), pp. 13–543.
_Anglo-Saxon Chronicle_ , trans. Whitelock, _EHD_ , no. 1.
_Annales Alamannici_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 22–60.
_Annales Bertiniani_ [Annals of St Bertin], ed. F. Grat, J. Vielliard, S. Clémencet and L. Levillain (Paris, 1964); trans. J. L. Nelson, _The Annals of Saint-Bertin_ (Manchester, 1991).
_Annales Cambriae_ , ed. and trans. D. N. Dumville, _Annales Cambriae, AD 682–954, texts A–C in parallel_ (Cambridge, 2002).
_Annales Fuldenses_ , ed. B. de Simson, _MGH SRG in usum scholarum separatim editi_ IX (Hanover, 1891); trans. T. Reuter, _The Annals of Fulda_ (Manchester, 1992).
_Annales Guelferbytani_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 23–31, 40–6.
_Annales Laubacenses_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 7–15.
_Annales Laureshamenses_ [Annals of Lorsch], ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 22–39; selections trans. King, _Charlemagne: Translated Sources_ , pp. 137–45.
_Annales Mettenses priores_ , ed. B. von Simson, _MGH SRG in usum scholarum separatim editi_ X (Hanover and Leipzig, 1905); Section I (to 725) trans. P. Fouracre and R. Gerberding, _Late Merovingian France. History and Hagiography 640–720_ (Manchester, 1996), pp. 330–70.
_Annales Nazariani_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 23–31, 40–4.
_Annales Petaviani_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 7–18.
_Annales regni francorum_ [Royal Frankish Annals], ed. F. Kurze, _MGH SRG in usum scholarum separatim editi_ VI (Hanover, 1895), trans. B. Scholz, _Carolingian Chronicles_ (Ann Arbor, MI, 1970).
_Annales Sancti Amandi_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 6–14.
_Annales Tiliani_ , ed. G. H. Pertz, _MGH SS_ I (Hanover, 1826), pp. 6–8, 219–24.
_Annales Vedastini_ [Annals of St Vaast], ed. B. von Simson, _Annales Xantenses et Annales Vedastini, MGH SRG in usum scholarum separatim editi_ XII (Hanover and Leipzig, 1909); extract (a.844–62) trans. Dutton (ed.), _Carolingian Civilization_ , pp. 347–50.
_Annales Xantenses_ [Annals of Xanten], ed. B. von Simson, _Annales Xantenses et Annales Vedastini, MGH SRG in usum scholarum separatim editi_ XII (Hanover and Leipzig, 1909); extract (a.882–6) trans. Dutton (ed.), _Carolingian Civilization_ , pp. 507–12.
Ardo, _Vita Sancti Benedicti abbatis Anianensis_ [Life of Benedict], ed. G. Waitz and W. Wattenbach, _MGH SS_ XV (Hanover, 1888); selections trans. Dutton (ed.), _Carolingian Civilization_ , pp. 176–98.
Astronomer, _Vita Hludowici imperatoris_ , ed. E. Tremp, _Astronomus. Das Leben Kaiser Ludwigs, MGH SRG in usum scholarum separatim editi_ LXIV (Hanover, 1995); trans. A. Cabaniss, _Son of Charlemagne: A Contemporary Life of Louis the Pious_ (Syracuse, NY, 1961).
Barlow, C. W. (ed. and trans.), _Iberian Fathers_ I: _Martin of Braga, Paschasius of Dumium, Leander of Seville_ (Washington, DC, 1969).
Bately, J. M. (ed.), _The Old English Orosius_ (Oxford, 1980), extracts trans. in N. Lund (ed.), _Two Voyagers at the Court of King Alfred_ (York, 1984).
Bede, _Continuation_. See _Continuation_ of Bede.
—, _Epistola ad Egbertum_ [Letter to Egbert], ed. C. Plummer, _Venerabilis Baedae opera historica_ (Oxford, 1896), pp. 405–23; trans. Whitelock, _EHD_ , no. 170, pp. 799–810.
—, _Historia ecclesiastica gentis anglorum_ , ed. C. Plummer, _Venerabilis Baedae opera historica_ (Oxford, 1896); ed. and trans. B. Colgrave and R. A. B. Mynors, _Bede's Ecclesiastical History of the English People_ , Oxford Medieval Texts (Oxford, 1969).
—, _Vita Cuthberti_ , ed. and trans. B. Colgrave, _Two Lives of Saint Cuthbert. A Life by an Anonymous Monk of Lindisfarne and Bede's Prose Life_ (Cambridge, 1940).
Beowulf, ed. E. van K. Dobbie, _Beowulf and Judith_. Anglo-Saxon Poetic Records 4 (New York and London, 1953); trans. R. M. Liuzza, _Beowulf_ (Peterborough, ON, 2000).
Beyer, H., Eltester, L., and Goerz, A. (eds.), _Urkundenbuch zur Geschichte der jetzt die Preußischen regierungsbezirke Coblenz und Trier bildenden mittelrheinischen Territorien_ , I: _Von den ältesten Zeiten bis zum Jahre 1169_ (Koblenz, 1860).
Bitterauf, T. (ed.), _Die Traditionen des Hochstifts Freising_ I (Munich, 1905).
Böhmer, J. F., and Mühlbacher, E., _Regesta imperii_ I, 2nd edn (Innsbruck, 1908).
Boniface, _Epistolae_ , ed. M. Tangl, _Die Briefe des Heiligen Bonifatius und Lullus, MGH Epp. selectae_ I (Berlin, 1916); selected letters trans. E. Emerton, _The Letters of Saint Boniface_ (New York, 1940); Talbot, _Anglo-Saxon Missionaries;_ Hillgarth, _Christianity and Paganism_.
Boretius, A., and Krause, V. (eds.), _Capitularia regum francorum, MGH Leges sectio_ III, 2 vols. (Hanover, 1883–97). Selections trans. in Dutton (ed.), _Carolingian Civilization_ , pp. 65–92, 501–2; D. Herlihy, _A History ofFeudalism_ (London, 1970); King, _Charlemagne: Translated Sources_ , pp. 202–68; Loyn and Percival, _Reign of Charlemagne_ , pp. 46–105.
Bouchard, C. B. (ed.), _The Cartulary of Flavigny, 717–1113_ (Cambridge, MA, 1991).
_Brevium exempla_ , ed. A. Boretius, _Capit_. I, no. 128, pp. 250–6; trans. Loyn and Percival, _Reign of Charlemagne_ , pp. 98–105; Dutton (ed.), _Carolingian Civilization_ , pp. 85–7.
Bruckner, A. (ed.), _Regesta Alsatiae_ , I. _Quellenband_ (Strasbourg, 1949).
Bruckner, A., Marichal, R., _et al_. (eds.), _Chartae latinae antiquiores. Facsimile Edition of the Latin Charters prior to the Ninth Century_ , 49 vols. (Olten and Lausanne, 1954–1998).
Caesarius of Arles, _Sermones_ , ed. G. Morin, 2 vols., _CCSL_ 103–4 (Turnhout, 1953).
_Capitulare Aquisgranense_ [Capitulary for Aachen], _a.802–3_ , ed. A. Boretius, _Capit_. I, no. 77, pp. 170–2; trans. Loyn and Percival, _The Reign of Charlemagne_ , pp. 82–4; part also trans. in Dutton (ed.), _Carolingian Civilization_ , p. 83.
_Capitulare missorum generale_ [Programmatic Capitulary], _a_.802 ed. A. Boretius, _Capit_. I, nos. 33–4, pp. 91–102; trans. King, _Charlemagne: Translated Sources_ , pp. 233–42.
_Capitulare de villis_ , ed. A. Boretius, _Capit_. I, no. 32, pp. 82–91; trans. Loyn and Percival, _Reign of Charlemagne_ , pp. 65–73.
_Capitularia regum francorum_. See Boretius, A., and Krause, V. (eds.).
_Carmen de synodo Ticinensi_ , ed. L. Bethmann, _MGH SRL_ (Hanover, 1878), pp. 189–91.
Cavallo, G., Nicolaj, G., _et al_. (eds.), _Chartae latinae antiquiores. Facsimile Edition of the Latin Charters_ , 2nd ser.: _Ninth Century_ , 63 vols., in progress (Olten and Lausanne, 1997–).
_Chartae latinae antiquiores_. See Bruckner, A., _et al_., and Cavallo, G., _et al_.
Chevrier, G., and Chaume, M. (eds.), _Chartes et documents de St Benigne de Dijon_ (Dijon, 1943).
_Chronicle of Ireland_ , trans. T. Charles-Edwards, _The Chronicle of Ireland_ , 3 vols. (Liverpool, 2006).
_Chronicon Moissiacense_ , ed. G. Pertz, _MGH SS_ I (Hanover, 1829), pp. 282–313; extracts trans. in King, _Charlemagne: Translated Sources_ , pp. 145–9.
_Clausula de unctione Pippini Regis_ , ed. B. Krusch, _MGH SRM_ I (Hanover, 1885); trans. B. Pullan, _Sources for the History of Medieval Europe from the Mid-Eighth to the Mid-Thirteenth Century_ (Oxford, 1966), pp. 7–8; repr. in Dutton, _Carolingian Civilization_ , pp. 13–14.
Cockayne, G. O. (ed.), _Leechdoms, Wortcunning, and Starcraft of Early England_ , 3 vols. Rolls Series 35, reprint rev. C. Singer (London, 1961).
_Codex epistolaris Carolinus_ , ed. W. Gundlach, _MGH Epp_. III ( _Epistolae merovingici et karolini aevi_ I) (Berlin, 1892), pp. 476–657; selections trans. and summarised in King, _Charlemagne: Translated Sources_ , pp. 268–307.
Codice diplomatico longobardo. See Schiaparelli, L., _et al_. (eds.).
Colgrave, B. (trans.), _The Life of Bishop Wilfrid by Eddius Stephanus_ (Cambridge, 1927; repr. 1985).
_Concilia Galliae_ a.314–a.506, ed. C. Munier, _CCSL_ 148 (Turnhout, 1953).
_Concilia Galliae_ a.511–695, ed. C. de Clercq, _CCSL_ 148A (Turnhout, 1963).
_Continuation of_ Bede, _Historia Ecclesiastica_ , ed. and trans. B. Colgrave and R. A. B. Mynors, _Bede's Ecclesiastical History of the English People_ , Oxford Medieval Texts (Oxford, 1969), pp. 572–7; trans. Whitelock, _EHD_ , no. 5, pp. 285–6.
_Conventus episcoporum at ripas Danubii_ (a.796), in _Conc_. II/I, no. 20, pp. 172–6.
Corpus consuetudinum monasticarum (Siegburg, 1963–).
Council of Laodicea, PL LXVII, cols. 165–70.
Desiderius of Cahors, _Epistolae_ , ed. W. Arndt, _MGH Epp_. III ( _Epistolae Merovingici et Karolini aevi_ I) (Berlin, 1892), pp. 191–214.
d'Herbomez, A. (ed.), _Cartulaire de l'abbaye de Gorze. MS 826 de la Bibliothèque de Metz_. Mettensia 2 (Paris, 1898).
Dhuoda, _Liber manualis_ , ed. and trans. M. Thiébaux, _Dhuoda: Handbook for her Warrior Son_ (Cambridge, 1998); also trans. C. Neel, _Handbook for William: a Carolingian Woman's Counsel for her Son_ (London, NE, 1991).
_Diplomata Karolinorum_ I. See Mühlbacher, _et al_. (eds.).
_Divisio regnorum_ , ed. A. Boretius, _Capit_. I, no. 45, pp. 126–30; trans. Loyn and Percival, _Reign of Charlemagne_ , pp. 91–6.
Dumville, D. N. (ed.), _Annales Cambriae_ , AD _682–954, texts A–C in parallel_ (Cambridge, 2002).
Duplex capitulare missorum in Theodonis villa datum [Double capitulary of Thionville for the _missi_ ], _a.805_ , ed. A. Boretius, _Capit_. I, nos. 43–4, pp. 120–6; trans. King, _Charlemagne: Translated Sources_ , pp. 86–90; extract trans. Dutton, _Carolingian Civilization_ , p. 80.
_Edictum Pistense_ [Edict of Pîtres], ed. V. Krause, _Capit_.II, no. 273, pp. 332–7.
Eigil, _Vita Sturmi_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), pp. 365–77; trans. Talbot, _Anglo-Saxon Missionaries_ , repr. in Noble and Head, _Soldiers of Christ_ , pp. 165–87.
Einhard, _Epistolae_ , ed. K. Hampe, _MGH Epp_. v ( _Epp. Karolini aevi_ III) (Berlin, 1898–9), pp. 105–42; trans. Dutton (ed.), _Charlemagne's Courtier_ , pp. 131–63.
—, _Translatio et miracula sanctorum Marcellini et Petri_ [ _Translation and Miracles of Saints Marcellinus and Peter_ ], ed. G. Waitz, _MGH SS_ XV.I (Hanover, 1888), pp. 239–64; trans. Dutton (ed.), _Charlemagne's Courtier_ , pp. 69–130.
—, _Vita Karoli_ , ed. O. Holder-Egger, _MGH SRG_ XXV (Hanover, 1911); trans. Dutton (ed.), _Charlemagne's Courtier_ , and D. Ganz, _Two Lives of Charlemagne_ (Harmondsworth, 2008).
Engelbert, _Versus de bella quae fuit acta Fontaneto_ , ed. E. Dümmler, _MGH Poet. Latini aevi Karolini_ II (Berlin, 1884), pp. 138–9; trans. Dutton, _Carolingian Civilization_ , pp. 332–3.
_English Historical Documents_ ( _EHD_ ). See Whitelock, D. (ed.).
_Epistola ad Basilium I_., ed. W. Henze, _MGH Epp_. VII ( _Epp. Karolini aevi_ v) (Berlin, 1928), pp. 386–94.
_Epistola de litteris colendis_ [On cultivating letters], ed. A. Boretius, _Capit_. I, no. 29, pp. 78–9; trans. King, _Charlemagne: Translated Sources_ , pp. 232–3.
_Epistolae aevi Merowingici collectae_ no. 18, ed. W. Gundlach, _MGH Epp_. III ( _Epp. Merovingici et Karolini aevi_ I) (Berlin, 1892), pp. 434–68.
Epistolae variorum Karolo regnante, ed. E. Dümmler, _MGH Epp_. IV ( _Epp. Karolini aevi_ II) (Berlin, 1895), pp. 494–567.
Erchanbert, _Breviarium regum francorum annis 715–827_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), p. 328.
Erhart, P., and Kleindienst, J. (eds.), _Urkundenlandschaft Rätiens_ (Vienna, 2004).
Ermenric of Ellwangen, _Epistola ad Grimaldum Abbatem_ , ed. E. Dümmler, _MGH Epp_. V ( _Epp. karolini aevi_ III) (Berlin, 1899), pp. 534–79.
Ermold, _Ad eundem Pippinum_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), pp. 202–19.
—, _Ad Pippinum Regem_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), pp. 220–32.
—, _In Honorem Hludowici_ , ed. E. Faral, _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964), pp. 2–201; extracts trans. in Godman, _Poetry of the Carolingian Renaissance_ (London, 1985), pp. 250–7.
_Expositio antiquae liturgiae Gallicanae_ , ed. E. Ratcliff, Henry Bradshaw Society 98 (London, 1971), pp. 3–16, trans. J. N. Hillgarth, _Christianity and Paganism 350–750_ (Philadelphia, PA, 1986), pp. 186–92.
Faral, E. (ed.), _Ermold le Noir. Poème sur Louis le Pieux_ (with French trans.) (Paris, 1964).
Flodoard of Rheims, _Historia Remensis ecclesiae_ , ed. J. Heller and G. Waitz, _MGH SS_ XIII (Hanover, 1881), pp. 405–599; trans. S. Fanning and B. S. Bachrach, _The Annals of Flodoard of Rheims, 991–966_ (Peterborough, ON, 2004).
Florus of Lyon, _Adversus Amalarium_ , PL 119, cols. 71–80.
—, _Carmina_ , ed. E. Dümmler, _MGH Poet. Latini aevi Karolini_ II (Berlin, 1884), pp. 507–66.
_Formulae imperiales_ , ed. K. Zeumer, _MGH Formulae Merovingici et Karolini Aevi_ (Hanover, 1886), pp. 285–328.
Fredegar, _Chronicle_ , ed. and trans. J. M. Wallace-Hadrill, _The Fourth Book of the Chronicle of Fredegar with its Continuations_ (London, 1960).
—, _Continuationes_ , ed. and trans. J. M. Wallace-Hadrill, _The Fourth Book of the Chronicle of Fredegar with its Continuations_ (London, 1960).
Frothar of Toul, _Letters_ , ed. K. Hampe, _MGH Ep_. v ( _Epp. Karolini aevi_ III) (Berlin, 1899), pp. 275–98; French trans. M. Parisse and J. Barbier, _La Correspondance d'un évêque carolingien: Frothaire de Toul (ca. 813–847). Avec les lettres de Theuthilde, abbesse de Remiremont_ (Paris, 1998).
Fulrad of Saint-Denis, _Testament_ , ed. M. Tangl, 'Das Testament Fulrads von Saint-Denis', _Das Mittelalter in Quellenkunde und Diplomatik. Ausgewählte Schriften_ , Forschungen zur mittelalterliche Geschichte 12 (Graz, 1966), pp. 540–81.
_Gesta sanctorum patrum Fontanellensis coenobii_ [Acts of the Abbots of St Wandrille], ed. F. Lohier and J. Laporte, Société de l'histoire de Normandie (Rouen and Paris, 1936).
Glockner, K. (ed.), _Codex Laureshamensis_ , Arbeiten der historischen Kommission für den Volksstaat Hessen 3. 3 vols. (Darmstadt, 1929–36).
Guérard, B. (ed.), _Polyptyque de l'Abbé Irminon_ (Paris, 1844), 2 vols.
Heidrich, I. (ed.), _Die Urkunden der Arnulfinger_ (Bad Münstereifel, 2001).
_Hildebrandslied_ , ed. and trans. Knight Bostock, _Handbook on Old High German Literature_ , pp. 44–7.
Hincmar of Rheims, _Capitula episcoporum_ , ed. R. Pokorny and M. Stratmann, _MGH Capitula episcoporum_ II (Hanover, 1995), pp. 1–89.
—, _Capitula quibus de rebus magistri et decani singulas ecclesias inquirire_ , PL CXXV, cols. 777–92.
—, _Collectio de ecclesiis et capellis_ , ed. M. Stratmann, _MGH Fontes iuris germanici antiqui_ XIV (Hanover, 1990).
—, _De divortio Lotharii regis et Theutbergae reginae_ , ed. L. Böhringer, _MGH Concilia_ IV, supp. I (Hanover, 1992).
—, _De ordine palatii_ [On the Governance of the Palace], ed. T. Gross and R. Schieffer, _MGH Fontes iuris germanici antiqui_ III (Hanover, 1980); trans. D. Herlihy, _A History of Feudalism_ (London, 1970), pp. 209–27 and repr. in Dutton (ed.), _Carolingian Civilization_ , pp. 516–32.
—, _De villa Noviliaco_ , ed. H. Mordek, 'Ein exemplarischer Rechtsstreit: Hinkmar von Reims und das Landgut Neuilly-Saint-Front', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte Kanonistische Abteilung_ 83 (1997), pp. 86–112.
—, _Vita Remigii episcopi Remensis_ , ed. B. Krusch, _MGH SRM_ III (Hanover, 1896), pp. 239–349, trans. D. Herlihy, _A History of Feudalism_ (London, 1970), pp. 122–4.
Hrabanus Maurus, _De institutione clericorum libri tres. Studien und Edition_ , ed. D. Zimpel (Frankfurt, 1996).
—, _De rerum naturis_ , PL III, cols. 9–614.
—, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. V ( _Epp. Karolini aevi_ III) (Berlin, 1898–9), pp. 380–533.
—, _Homiliae_ , PL CX, cols. 9–470.
Ibn Khurradadhbih, _Book of Routes and Kingdoms_ , ed. M. J. de Goeje, _Bibliotheca geographorum arabicorum_ 6 (Leiden, 1889); trans. R. S. Lopez and I. W. Raymond, _Medieval Trade in the Mediterranean World: Illustrative Documents_ (London and New York, 1955), pp. 30–3.
_Indiculus superstitionum et paganiarum_ , ed. R. Rau, _Briefe des Bonifatius; Willibalds Leben des Bonifatius_ (Darmstadt, 1968), pp. 444–8; trans. J. T. McNeill and H. A. Gamer (eds.), _Medieval Handbooks of Penance_ (New York, 1990), pp. 419–21, and repr. in Dutton (ed.), _Carolingian Civilization_ , pp. 3–4.
Ine, _Laws_ , ed. F. Liebermann, _Die Gesetze der Angelsachsen_ , 3 vols. (Halle, 1903–16); trans. F. L. Attenborough, _The Laws of the Earliest English Kings_ (Cambridge, 1922; repr. 2000), pp. 36–61.
Isidore of Seville, _Etymologiae_ , ed. and trans. S. A. Barney, _et al., The Etymologies of Isidore of Seville_ (Cambridge, 2006).
John VIII, _Epistolae_ , ed. E. Caspar, _MGH Epp_. VII ( _Epp. Karolini aevi_ V) (Berlin, 1928), pp. 1–333; no. 7 trans. E. J. Goldberg, _Struggle for Empire. Kingship and Conflict under Louis the German, 817–876_ (Ithaca, NY, and London, 2006), p. 333.
Jonas, _Vita Columbani_ , ed. B. Krusch, _MGH SRM_ IV (Hanover, 1902), pp. 1–152; trans. E. Peters, _Monks, Bishops and Pagans_ (Philadelphia, PA, 1975), pp. 75–113.
Jonas of Orléans, _De institutione laicorum, PL_ CVI, cols. 121–278.
—, _De institutione regia_ , ed. J. Reviron, _Les Idées politico-religieuses d'un évêque du_ IXe _siècle: Jonas d'Orléans et son_ De institutione regia (Paris, 1930), pp. 119–94.
Justinian, _Testament a.828/9_ , ed. L. Lanfranchi and B. Strina, _Ss. Ilario e Benedetto e Gregorio_ (Venice, 1965), no. 2, p. 24.
_Karolus magnus et Leo papa_ [Paderborn Epic], ed. E. Dümmler, _MGH Poet_. I (Berlin, 1881), pp. 366–79; partial trans. in Godman, _Poetry of the Carolingian Renaissance_ , pp. 197–207.
Kehr, P. (ed.), _Die Urkunden Ludwigs des Deutschen, Karlmanns und Ludwigs des Jüngeren. MGH Diplomata Regum Germanie ex stirpe Karolinorum_ I (Berlin, 1934).
Knight Bostock, J., _A Handbook on Old High German Literature_ , 2nd edn rev. K. King and D. McLintock (Oxford, 1976).
Kölzer, T., with Hartmann, M., and Stieldorf, A. (eds.), _Die Urkunden der Merowinger, MGH Diplomata regum francorum e stirpe Merovingica_ , 2 vols. (Hanover, 2001).
Krusch, B., 'Chronologica regum francorum stirpis Merovingicae', _MGH SRM_ VII (Hanover, 1920), pp. 468–516.
_Leges Ahistulfi_ [Laws of Aistulf], ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ (Weimar, 1947; repr. Witzenhausen, 1962), pp. 194–204; trans. Fischer-Drew, _The Lombard Laws_.
_Leges Liutprandi_ , ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ (Weimar, 1947; repr. Witzenhausen, 1962), pp. 99–182; trans. Fischer-Drew, _The Lombard Laws_.
_Leges Ratchis_ [Laws of Ratchis], ed. F. Beyerle, _Leges langobardorum, 643–866. Die Gesetze der Langobarden_ (Weimar, 1947; repr. Witzenhausen, 1962), pp. 183–93; trans. Fischer-Drew, _The Lombard Laws_.
Leidrad, _Epistolae_ , ed. E. Dümmler, _MGH Epp_. IV ( _Epp. Karolini aevi II_) (Berlin, 1895), pp. 539–46.
Leo IV, _Epistolae_ , ed. A. de Hirsch-Gereuth, _MGH Epp_. V ( _Epistolae Karolini aevi_ III) (Berlin, 1898–9), pp. 585–612.
_Liber de episcopis Mettensibus_ ( _Gesta episcoporum Mettensium_ ), PL, 163, cols. 579–614; and ed. G. Pertz, _MGH SS_ II (Hanover, 1829), pp. 260–8.
_Liber historiae francorum_ , ed. B. Krusch, _MGH SRM_ II (Hanover, 1888), pp. 241–328; trans. B. S. Bachrach, _Liber historiae francorum_ (Lawrence, KS, 1973).
_Liber pontificalis_ , ed. L. Duchesne, _Le Liber pontificalis. Texte, introduction et commentaire_ , 2 vols. (Paris, 1886 and 1892); amplified 3 vol. edn ed. C. Vogel (Paris, 1955–7); trans. in three books by R. Davis, _The Book of Pontiffs_ (Liber pontificalis), rev. edn (Liverpool, 2000); _The Lives of the Eighth-Century Popes_ (Liber pontificalis) (Liverpool, 1992); _The Lives of the Ninth-Century Popes_ (Liber pontificalis) (Liverpool, 1995).
_Liber possessionum Wizenburgensis_ , ed. C. Dette (Mainz, 1987).
_Libri Carolini_. See _Opus Caroli regis_.
Liutprand, _Pactum_ , ed. L. Hartmann, _Zur Wirtschaftsgeschichte Italiens im frühen Mittelalter_ (Gotha, 1904).
Lull, _Epistolae_. _See_ Boniface, _Epistolae_.
Lupus of Ferrières, _Epistolae_ , ed. P. K. Marshall (Leipzig, 1984); trans. G. W. Regenos, _The Letters of Lupus of Ferrières_ (The Hague, 1966).
Manaresi, C. (ed.), _I placiti del regnum Italiae_ , 3 vols. (Rome, 1955–60).
Mango, C., and Scott, R., with Greatrex, G. (trans.), _The Chronicle of Theophanes Confessor. Byzantine and Near Eastern History AD 284–813_ (Oxford, 1997).
Martin of Braga, _De correctione rusticorum (On the correction of the rustics_ ), ed.and trans. Barlow, _Iberian Fathers_.
Mayer-Marthaler, E., and Perret, F. (eds.), _Bündner Urkundenbuch_ I (Chur, 1955).
Mühlbacher, E., _et al_. (eds.), _Die Urkunden der Karolinger_ I: _Die Urkunden Pippins, Karlmanns und Karls des Großen. MGH Diplomata Karolinorum_ I (Hanover, 1906).
Nithard, _Historiarum Libri IV_ , ed. P. Lauer, _Histoire des fils de Louis le Pieux_ (Paris, 1926); trans. B. Scholz, _Carolingian Chronicles_ (Ann Arbor, MI, 1970).
Noble, T. F. X., and Head, T., _Soldiers of Christ. Saints and Saints' Lives from Late Antiquity and the Early Middle Ages_ (University Park, PA, 1995).
_Northern Annals_ , ed. T. Arnold, _Symeonis monachi opera omnia_ , 2 vols., Rolls Series 75 (London, 1882–5), II, pp. 30–66; trans Whitelock, _EHD_ , no. 3(a), pp. 264–76.
_Notitia de servitio monasteriorum_ (a.819), ed. P. Becker, _CCM_ I (Siegburg, 1963), pp. 493–9.
Notker Balbulus, _Erchanberti breviarium continuatio_ , ed. G. Pertz, _MGH SS_ II (Hanover, 1829), pp. 329–30.
—, _Gesta Karoli magni imperatoris_ , ed. H. F. Haefele, _MGH SRG_ n.s. 12 (Berlin, 1959); trans. D. Ganz, _Two Lives of Charlemagne_ (Harmondsworth, 2008), and by L. Thorpe, _Einhard and Notker the Stammerer: Two Lives of Charlemagne_ (Harmondsworth, 1969).
_Opus Caroli regis contra synodum (Libri Carolini_ ), ed. A. Freeman with P. Meyvaert, _MGH Concilia_ II, suppl. I (Hanover, 1998).
Ordinatio imperii, ed. A. Boretius, _Capit_. I, no. 136, pp. 270–3; trans. Dutton (ed.), _Carolingian Civilization_ , pp. 199–204.
_Pactus legis Salicae_ , ed. K. A. Eckhardt, _MGH Legum sectio_ I, _Leges Nationum Germanicarum_ IV (Hanover, 1962); trans. K. Fischer-Drew, _The Laws of the Salian Franks_ (Philadelphia, PA, 1991).
_Paderborn Epic_. See _Karolus magnus et Leo papa_.
Pardessus, J. M., _Diplomata, chartae, epistolae, leges ad res Gallo-Francicas spectantia_ , 2 vols. (Paris, 1843–9; repr. Aalen 1969).
Paschasius Radbertus, _De corpore et sanguine Domini_ , ed. B. Paulus, _CCCM_ 16 (Turnhout, 1969); trans. G. E. McCracken, _Early Medieval Theology_ (Philadelphia, PA, 1957), pp. 94–108.
—, _Epitaphium Arsenii_ [ _Life of Wala_ ], ed. E. Dümmler, _Abhandlungen der kaiserlichen Akademie der Wissenschaften zu Berlin, phil.-hist. Klasse_ (1900), trans. A. Cabaniss, _Charlemagne's Cousins. Contemporary Lives of Adalard and Wala_ (New York, 1967).
—, _Vita Sancti Adalhardi_ , ed. Dom. J. Mabillon, _PL_ CXX, 1507–1556c; trans. A. Cabaniss, _Charlemagne's Cousins: Contemporary Lives of Adalard and Wala_ (New York, 1967).
Paul the Deacon, _Historia langobardorum_ , ed. L. Bethmann and G. Waitz, _MGH SRL_ (Hanover, 1878), pp. 12–187; trans. W. D. Foulke, _History of the Langobards by Paul the Deacon_ (Philadelphia, 1907).
_Pauli continuatio cassinese_ , ed. G. Waitz, _MGH SRL_ (Hanover, 1878), pp. 198–200.
_Pauli continuatio tertia_ , ed. G. Waitz, _MGH SRL_ (Hanover, 1878), pp. 203–16.
Paulinus of Aquileia, _Liber Exhortationis ad Hericum Comitem_ , PL IC, cols. 197–282.
_Planctus de obitu Karoli_ , ed. E. Dümmler, _MGH Poet. Latini Aevi Karolini_ I, pp. 435–6; trans. Dutton, _Carolingian Civilization_ , pp. 157–9.
Prou, M., and Vidier, A. (eds.), _Recueil des chartes de l'abbaye de Saint-Benoît-sur-Loire (Fleury_ ), 2 vols. (Orleans and Paris, 1900–24).
_Prümer Urbar, Das_ , ed. I. Schwab (Düsseldorf, 1983).
Ratramnus of Corbie, _De corpore et sanguine Domini, PL_ CXXI, cols. 169–70; trans. G. E. McCracken, _Early Medieval Theology_ (Philadelphia, PA, 1957), pp. 118–47.
—, _Epistolae_ , ed. E. Perels, _MGH Epp_. VI ( _Epp. Karolini aevi_ IV) (Berlin, 1925), _Epistolae variorum_ , nos. 8–13, pp. 149–58; no. 12 trans. Dutton, _Carolingian Civilization_ , pp. 452–5.
Regino of Prüm, _Chronicon_ , ed. F. Kurze, _MGH SRG_ 50 (Hanover, 1890); trans. MacLean, _History and Politics_.
Rimbert, _Vita Anskarii_ , ed. G. Waitz, _MGH SRG in usum scholarum separatim editi_ LV (Hanover, 1884); trans. C. H. Robinson, _Anskar, The Apostle of the North, 801–865_ (London, 1921), repr. in Dutton, _Carolingian Civilization_ , pp. 409–51.
_Sancti Bonifatii et Lulli Epistolae_. See Boniface, _Epistolae_.
Schiaparelli, L., Brühl, C., and Zielinski, H. (eds.), _Codice diplomatico longobardo_. 5 vols. Fonti per la storia d'Italia 62–6 (Rome, 1929–86).
Schieffer, T., _Die Urkunden Lothars I und Lothars II. MGH Diplomata Karolinorum_ III (Berlin, 1966).
Schlosser, H. D. (ed.), _Althochdeutsche Literatur_ (Frankfurt, 1970).
Sedulius, _Liber de rectoribus Christianis_ , ed. S. Hellman, _Sedulius Scottus_ (Munich, 1906); trans. E. G. Doyle, _Sedulius Scottus. On Christian Rulers and the Poems_ (New York, 1983), extracts trans. Dutton, _Carolingian Civilization_ , pp. 374–86.
Stengel, E. E. (ed.), _Urkundenbuch der Kloster Fulda_ , Veröffentlichungen der historischen Kommission für Hessen und Waldeck 19 (Marburg, 1936).
Stephen of Ripon, _Vita Wilfridi_ , ed. and trans. B. Colgrave, _The Life of Bishop Wilfrid by Eddius Stephanus_ (Cambridge, 1927; repr. 1985).
Tacitus, _Germania_ , trans. A. R. Birley, _Agricola and Germany_ (Oxford, 2009); J. B. Rives, _Germania_ (Oxford, 1999); H. W. Benario, _Germany_ (Warminster, 1999); M. Hutton, _Agricola, Germania, Dialogus_ (London, 1970).
Tangl, M. (ed.), 'Das Testament Fulrads von Saint-Denis', _Das Mittelalter in Quellenkunde und Diplomatik. Ausgewählte Schriften_ , Forschungen zur mittelalterliche Geschichte 12 (Graz, 1966), pp. 540–81.
Tessier, G., _et al_. (eds.), _Recueil des actes de Charles II le Chauve_ , 3 vols. (Paris, 1943–55).
Thegan, _Gesta Hludowici imperatoris_ , ed. E. Tremp, _Die Taten Kaiser Ludwigs, MGH SRG in usum scholarum separatim editi_ LXIV (Hanover, 1995); trans. P. Dutton, Thegan, _Life of Louis the Pious_ , in Dutton, _Carolingian Civilization_ , pp. 159–76.
Theodemar of Monte Cassino, _Letter to Charlemagne_ , ed. K. Hallinger and M. Wegener, _CCM_ I (Siegburg, 1963), pp. 157–75; ed. E. Dümmler, _MGH Epp_. IV ( _Epp. Kar. aev_. II), (Berlin, 1895), no. 13, pp. 509–14.
Theodulf, _Carmina_ , ed. E. Dümmler, _MGH Poet_. I ( _Poet. Karolini Aevi I_) (Hanover, 1881), pp. 437–581; selections trans. Godman, _Poetry of the Carolingian Renaissance_ , and Dutton, _Carolingian Civilization_ , pp. 100–6.
Theophanes, _Chronographia_ , ed. C. de Boor, 2 vols. (Leipzig, 1883–5), trans. C. Mango and R. Scott with G. Greatrex, _The Chronicle of Theophanes Confessor. Byzantine and Near Eastern History AD 284–813_ (Oxford, 1997).
Thietmar of Merseburg, _Chronicon_ , ed. R. Holtzmann, _MGH SRG_ , n.s. IX (Berlin, 1935), trans. D. Warner, _Ottonian Germany: The_ Chronicon _of Thietmar of Merseburg_ (Manchester, 2001).
_Visio Baronti_ , ed. W. Levison, _MGH SRM_ V (Hanover, 1910), pp. 386–94, trans. J. Hillgarth, _Christianity and Paganism_ , pp. 195–204.
_Visio Fursei_ [Vision of Fursa], ed. C. Carozzi, _Le Voyage de l'âme dans l'audelà_ , Collection de l'EFR 189 (Rome, 1994), p. 691.
_Vita Amandi_ , ed. B. Krusch, _MGH SRM_ V (Hanover, 1910), pp. 428–49; trans. Hillgarth, _Christianity and Paganism_ , pp. 139–48.
_Vita Audoini episcopi Rotomagensis_ , ed. W. Levison, _MGH SRG_ V (Hanover, 1910), pp. 536–67; trans. P. Fouracre and R. Gerberding, 'Life of Audoin', _Late Merovingian France. History and Hagiography 640–720_ (Manchester, 1996), pp. 133–65.
Vita _of Constantine and the_ Vita _of Methodius_ , _The_ , ed. M. Kantor (Ann Arbor, MI, 1976).
_Vita Eligii_ , ed. B. Krusch, _MGH SRG_ IV (Hanover, 1902), pp. 634–761.
_Vita Lebuini_ , ed. A. Hofmeister, _MGH SS_ xxx.2 (Leipzig, 1934), pp. 789–95; trans. Talbot, _Anglo-Saxon Missionaries_.
_Vita Liutbergae_ [ _Life of Liutberga_ ], ed. G. H. Pertz, _MGH SS_ IV, pp. 158–64, trans. F. S. Paxton, _Anchoress and Abbess in Ninth-Century Saxony: the Lives of Liutbirga of Wendhausen and Hathumoda of Gandersheim_ (Washington, DC, 2009).
_Vita Vulframni_ , ed. W. Levison, _MGH SRM_ V (Hanover, 1910), pp. 657–73.
_Vita Willehadi_ , ed. A. Poncelet, _De sancto Willehado primo Bremensis episcopo et inferioris Saxoniae apostolo_ , Acta Sanctorum (Brussels, 1910), 3 November, pp. 842–6; trans. Noble and Head, _Soldiers of Christ_ , pp. 279–91.
_Vita Willehadi_ , ed. A. Röpke, _Das Leben des heiligen Willehad_ (Bremen, 1982); trans. Noble and Head, _Soldiers of Christ_ , pp. 279–91.
_Waltharius_ , ed. and trans. Knight Bostock, _Handbook on Old High German Literature_ , pp. 259–80.
Wampach, C. (ed.), _Geschichte der Grundherrschaft Echternach im Frühmittelalter_ 1.2: _Quellenband_ (Luxembourg, 1930).
Warner, D. (trans.), _Ottonian Germany: The Chronicon of Thietmar of Merseburg_ (Manchester, 2001).
Wartmann, H. (ed.), _Urkundenbuch der Abtei St. Gallen_ II (Zürich, 1866).
Werminghoff, A. (ed.), _Concilia aevi Karolini_ II.1 and II.2 (Hanover, 1906–8).
Whitelock, D., _English Historical Documents_ , 2nd edn (London and New York, 1979), I: c.500–1042.
Willibald, _Vita Bonifatii_ , ed. W. Levison, _MGH SRG in usum scholarum separatim editi_ LVII (Hanover, 1905); trans. Talbot, _Anglo-Saxon Missionaries_ , repr. in Noble and Head, _Soldiers of Christ_ , pp. 107–40.
#### 2. SECONDARY SOURCES
Abels, R., 'Alfred the Great, the _micel hæthen here_ and the Viking threat', in T. Reuter (ed.), _Alfred the Great: Papers from the Eleventh-Centenary Conferences_ (Aldershot, 2003), pp. 265–79.
Ahmed, A., _A History of Islamic Sicily_ (Edinburgh, 1975).
Airlie, S., 'The anxiety of sanctity: St Gerald of Aurillac and his maker', _Journal of Ecclesiastical History_ 43 (1992), pp. 372–95.
—, 'The aristocracy', in _NCMH_ II, pp. 431–50.
—, 'The aristocracy in the service of the state in the Carolingian period', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 92–111.
—, 'Bonds of power and bonds of association in the court circle of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 191–204.
—, _Carolingian Politics_ (Oxford, forthcoming).
—, 'Charlemagne and the aristocracy: captains and kings', in Story (ed.), _Charlemagne_ , pp. 90–102.
—, 'Les Élites en 888 et après, ou comment pense-t-on la crise carolingienne?', in F. Bougard, L. Feller and R. Le Jan (eds.), _Les Élites au haut Moyen Âge. Crises et renouvellements_ (Turnhout, 2006), pp. 425–37.
—, '"For it is written in the law": Ansegis and the writing of Carolingian royal authority', in S. Baxter, _et al_. (eds.), _Early Medieval Studies in Memory of Patrick Wormald_ (Aldershot, 2009), pp. 219–36.
—, 'Narratives of triumph and rituals of submission: Charlemagne's mastering of Bavaria', _TRHS_ 6th ser. 9 (1999), pp. 93–119.
—, 'The nearly men: Boso of Vienne and Arnulf of Bavaria', in A. Duggan (ed.), _Nobles and Nobility in Medieval Europe_ (Woodbridge, 2000), pp. 25–41.
—, 'The palace of memory: the Carolingian court as political centre', in S. R. Jones, R. Marks and A. J. Minnis (eds.), _Courts and Regions in Medieval Europe_ (York, 2000), pp. 1–20.
—, _The Political Behaviour of Secular Magnates in Francia, 829–79_ , unpublished D. Phil. thesis, University of Oxford (1985).
—, 'Private bodies and the body politic in the divorce case of Lothar II', _P &P_ 161 (1998), pp. 3–38.
—, 'Review article: After empire. Recent work on the emergence of post- Carolingian kingdoms', _EME_ 2 (1993), pp. 153–61.
—, '"Sad stories of the deaths of kings": narrative patterns and structures of authority in Regino of Prüm's _Chronicle'_ , in E. M. Tyler and R. Balzaretti (eds.), _Narrative and History in the Early Medieval West_ (Turnhout, 2006), pp. 105–31.
—, ' _Semper fideles?_ Loyauté envers les carolingiens comme constituant de l'identité aristocratique', in Le Jan (ed.), _La Royauté et les élites_ , pp. 129–43.
—, 'Talking heads: assemblies in early medieval Germany', in P. S. Barnwell and M. Mostert (eds.), _Political Assemblies in the Earlier Middle Ages_ (Turnhout, 2003), pp. 29–46.
—, 'Towards a Carolingian aristocracy', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 109–28.
—, 'The world, the text and the Carolingian: royal, aristocratic and masculine identities in Nithard's _Histories'_ , in Nelson and Wormald (eds.), _Lay Intellectuals_ , pp. 51–76.
Airlie, S., Pohl, W., and Reimitz, H. (eds.), _Staat im frühen Mittelalter. Forschungen zur Geschichte des Mittelalters_ II (Vienna, 2006).
Alberi, M., 'The evolution of Alcuin's concept of the _Imperium Christianum'_ , in Hill and Swan (eds.), _The Community_ , pp. 3–17.
Allott, S., _Alcuin of York – his Life and Letters_ (York, 1974).
Althoff, G., _Otto III_ (Darmstadt, 1996), trans. P. J. Jestice, _Otto III_ (University Park, PA, 2003).
Althoff, G., and Wollasch, J., 'Bleiben die _Libri Memoriales_ stumm? Eine Erwiderung auf H. Hoffmann', _Deutsches Archiv für Erforschung des Mittelalters_ 56 (2000), pp. 33–53.
Ambrosiani, B., and Clarke, H. (eds.), _Developments around the Baltic and the North Sea in the Viking Age_ (Stockholm, 1994).
Anderton, M. (ed.), _Anglo-Saxon Trading Centres: Beyond the Emporia_ (Glasgow, 1999).
Angenendt, A., _Das Frühmittelalter. Die abendländische Christenheit von 400 bis 900_ (Stuttgart, 1990).
—, 'Theologie und Liturgie der mittelalterlichen Totenmemoria', in K. Schmid and J. Wollasch (eds.), _Memoria. Der geschichtliche Zeugniswert des liturgischen Gedenkens im Mittelalter_ (Munich, 1984), pp. 80–199.
Anton, H. H., _Fürstenspiegel und Herrscherethos in der Karolingerzeit_ , Bonner Historische Forschungen 32 (Bonn, 1968).
Appadurai, A. (ed.), _The Social Life of Things. Commodities in Cultural Perspective_ (Cambridge, 1986).
Arnold, J., _Belief and Unbelief in Medieval Europe_ (London, 2005).
Arthur, P., _Naples from Roman Town to City-state_ (London, 2004).
Attenborough, F. L. (trans.), _The Laws of the Earliest English Kings_ (Cambridge, 1922; repr. 2000).
Bachrach, B., 'Charles Martel, mounted shock combat, the stirrup and feudalism', _Studies in Medieval and Renaissance History_ 7 (1970), pp. 49–75.
Bachrach, B. (ed.), _Journal of Medieval Military History_ I (2003).
Bachrach, D. S., _Religion and the Conduct of War, c.300—c.1215_ (Woodbridge, 2003).
Bailey, R. N., 'St Wilfrid, Ripon and Hexham', _American Early Medieval Studies_ 1 (1990), pp. 3–25.
Balzaretti, R., 'Cities, emporia and monasteries: local economies in the Po valley 700–875', in N. Christie and S. Loseby (eds.), _Towns in Transition. Urban Evolution in Late Antiquity and the Early Middle Ages_ (Aldershot, 1996), pp. 213–34.
—, 'Cities and markets in early medieval Europe', in G. Ausenda (ed.), _After Empire. Towards an Ethnology of Europe's Barbarians_ (San Marino, 1994), pp. 113–42.
—, 'Monasteries, towns and the countryside: reciprocal relationships in the archdiocese of Milan, 614–814', in G. P. Brogiolo, N. Gauthier and N. Christie (eds.), _Towns and Their Territories: Between Late Antiquity and the Early Middle Ages_ (Leiden, 2000), pp. 235–57.
—, 'The monastery of Sant'Ambrogio and dispute settlement in early medieval Milan', _EME_ 3 (1994), pp. 1–18.
Banaji, J., _Agrarian Change in Late Antiquity_ (Oxford, 2001).
—, 'Aristocracies, peasantries and the framing of the early middle ages', _Journal of Agrarian Change_ 9 (2009), pp. 59–91.
Banniard, M., 'Language and communication in Carolingian Europe', in _NCMH_ II, pp. 695–708.
Barbero, A., _Charlemagne: Father of a Continent_ (Berkeley, 2004).
Barford, P. M., _The Early Slavs. Culture and Society in Early Medieval Eastern Europe_ (London, 2001).
Barthélemy, D., 'La Chevalerie carolingienne: prélude au XIe siècle', in Le Jan (ed.), _La Royauté et les élites_ , pp. 159–75.
—, 'Debate. The "Feudal Revolution"', _P &P_ 152 (1996), pp. 196–205.
—, 'Modern mythologies of medieval chivalry', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 214–28.
Bartlett, R., _The Making of Europe: Conquest, Colonization and Cultural Change, 950–1350_ (London, 1993).
—, 'Reflections on paganism and christianity in medieval Europe', _PBA_ 101 (1998), pp. 55–76.
Bately, J. M., and A. Englert (eds.), _Ohthere's Voyages_ (Roskilde, 2007).
Becher, M., _Charlemagne_ (New Haven, CT, and London, 2003).
—, _'Cum lacrimis et gemitu_. Vom Weinen der Sieger und der Besiegten im frühen und hohen Mittelalter', in G. Althoff (ed.), _Formen und Funktionen öffentlicher Kommunikation im Früh- und Hochmittelalter_ (Stuttgart, 2001), pp. 25–52.
—, 'Drogo und die Königserhebung Pippins', _Frühmittelalterliche Studien_ 23 (1989), pp. 131–53.
—, _Eid und Herrschaft: Untersuchungen zum Herrscherethos Karls des Großen_ (Sigmaringen, 1993).
—, 'Die Kaiserkrönung im Jahr 800. Eine Streitfrage zwischen Karl dem Großen und Papst Leo III.', _Rheinische Viertelsjahrblätter_ 66 (2002), pp. 1–38
—, 'Neue Überlieferungen zum Geburtsdatum Karls des Großen', _Francia_ 19 (1992), pp. 37–60.
Becher, M., and Jarnut, J. (eds.), _Der Dynastiewechsel von 751. Vorgeschichte, Legitimationsstrategien und Erinnerung_ (Münster, 2004).
Beckwith, J., _Early Medieval Art_ (London, 1969).
Bernhard, H., 'Die frühmittelalterliche Siedlung von Speyer "Vogelgesang"', _Offa_ 39 (1982), pp. 217–33.
Berto, A., _Testi storici e poetici dell'Italia carolingia_ (Padua, 2002).
Bessmerny, J., 'Les structures de la famille paysanne dans les villages de la Francie au IXe siècle', _Le Moyen Âge_ 90 (1984), pp. 165–93.
Bigott, B., _Ludwig der Deutsche und die Reichskirche im ostfränkischen Reich (826–876_ ) (Husum, 2002).
Bischoff, B., _Latin Palaeography. Antiquity and the Middle Ages_ , trans. D. Ó Cróinín and D. Ganz (Cambridge, 1990).
Bisson, T. N., 'The "feudal" revolution', _P &P_ 142 (1994), pp. 6–42; 'Reply', _P &P_ 155 (1997), pp. 208–25.
—, 'Nobility and family in France: a review essay', _French Historical Studies_ 16 (1990), pp. 597–613.
—, 'La Terre et les hommes: a programme fulfilled?', _French History_ 14 (2000), pp. 322–45.
Bjork, R. E., and Niles, J. D. (eds.), _A Beowulf Handbook_ (Lincoln, NE, 1997).
Blackburn, M., 'Coin circulation in Germany during the early Middle Ages: the evidence of single-finds', in B. Kluge (ed.), _Fernhandel und Geldwirtschaft_ (Sigmaringen, 1993), pp. 37–54.
Blair, J., _The Church in Anglo-Saxon Society_ (Oxford, 2005).
Bleiber, W., 'Grundherrschaft und Markt zwischen Loire und Rhein während des 9. Jahrhunderts: Untersuchungen zu ihrem wechselseitigen Verhältnis', _Jahrbuch für Wirtschaftgeschichte_ 3 (1982), pp. 105–35.
Blinkhorn, P., 'Of cabbages and kings: production, trade, and consumption in Middle-Saxon England', in Anderton (ed.), _Anglo-Saxon Trading Centres_ , pp. 4–23.
Bloch, M., _The Historian's Craft_ , ed. P. Burke (Manchester, 1992).
Bloch, M. E., 'The resurrection of the house among the Zafimaniry of Madagascar', in J. Carsten and S. Hugh-Jones (eds.), _About the House: Levi-Strauss and Beyond_ (Cambridge, 1995), pp. 69–83.
Böhme, H.W., _Germanische Grabfunde des 4. und 5. Jahrhunderts zwischen Elbe und Loire_. 2 vols. (Munich, 1974).
Böhner, K., _Das Grab eines fränkischen Herren aus Morken im Rheinland_ (Cologne, 1959).
—, 'Urban and rural settlement in the Frankish kingdom', in M. W. Barley (ed.), _European Towns: Their Archaeology and Early History_ (London, 1977), pp. 185–207.
Bois, G., _The Transformation of the Year 1000: The Village of Lournand from Antiquity to Feudalism_ , trans. J. Birrell (Cambridge, 1992).
Bolin, S., 'Mohammed, Charlemagne and Ruric', _Scandinavian Economic History Review_ I (1953), pp. 5–39.
Bonnassie, P., _From Slavery to Feudalism in Southwest Europe_ , trans. J. Birrell (Cambridge, 1991).
Booker, C., 'The demanding drama of Louis the Pious', _Comitatus: A Journal of Medieval and Renaissance Studies_ 34 (2003), pp. 170–5.
—, _Past Convictions: the Penance of Louis the Pious and the Decline of the Carolingians_ (Philadelphia, PA, 2009).
Borgolte, M., 'Die Alaholfingerurkunden. Zeugnisse vom Selbstverständnis einer adligen Verwandtengemeinschaft des frühen Mittelalters', in M. Borgolte, D. Geuenich and K. Schmid (eds.), _Subsidia Sangallensia I. Materialien und Untersuchungen zu den Verbrüderungsbüchern und zu den älteren Urkunden des Stiftsarchivs St. Gallen_ (St. Gallen, 1986), pp. 287–322.
—, _Geschichte der Grafschaften Alemanniens in fränkischer Zeit_ (Sigmaringen, 1984).
—, 'Karl III. und Neudingen. Zum Problem der Nachfolgeregelung Ludwigs des Deutschen', _Zeitschrift für die Geschichte des Oberrheins_ 125 (1977), pp. 21–55.
Boshof, E., _Ludwig der Fromme_ (Darmstadt, 1996).
Bosl, K., _'Potens_ und _pauper_. Begriffsgeschichtliche Studien zur gesellschaftlichen Differenzierung im frühen Mittelalter und zur "Pauperismus" des Hochmittelalters', in Bosl, _Frühformen der Gesellschaft in mittelalterlichen Welt_ (Munich and Vienna, 1964), pp. 106–34.
Boudriot, W., _Die altgermanische Religion_ (Bonn, 1928).
Bougard, F., 'La Cour et le gouvernement de Louis II (840–875)', in Le Jan (ed.), _La Royauté et les élites_ , pp. 249–67.
—, 'Pierre de Niviano, dit le Spoletin, sculdassius, et le gourvernement du comté de Plaisance à l'époque carolingienne', _Journal des Savants_ (1996), pp. 291–337.
Bourdieu, P., _Distinction: A Social Critique of the Judgement of Taste_ , trans. R. Nice (London, 1984).
—, _Outline of a Theory of Practice_ , trans. R. Nice (Cambridge, 1977).
Bowes, K., 'Early Christian archaeology: a state of the field', _Religion Compass_ 2/4 (2008), pp. 575–619.
Braune, W., _et al., Althochdeutsches Lesebuch_ (Tübingen, 1958).
Braunfels, W., _Monasteries of Western Europe. The Architecture of the Orders_ , trans. A. Laing (London, 1972).
Brisbane, M., 'Hamwic (Saxon Southampton): an eighth century port and production centre', in R. Hodges and B. Hobley (eds.), _The Rebirth of Towns in the West, AD 750–1050_ (London, 1988), pp. 101–8.
Brown, G., 'Introduction: the Carolingian Renaissance', in McKitterick (ed.), _Carolingian Culture_ , pp. 1–51.
Brown, P., _Body and Society. Men, Women and Sexual Renunciation in Early Christianity_ (New York, 1988).
—, _The End of the Ancient Other World: Death and Afterlife between Late Antiquity and the Early Middle Ages_ , Tanner Lectures (New Haven, CT, 1996).
—, _The Rise of Western Christendom_ , 2nd edn (Oxford, 2003).
—, 'Vers la naissance du purgatoire. Amnistie et pénitence dans le christianisme occidental de l'Antiquité tardive au Haut Moyen Âge', _Annales HSS_ 6 (1997), pp. 1247–61.
Brown, W., 'On the _Gesta municipalia_ and the public validation of documents in Frankish Europe', in Brown, _et al_. (eds.), Documentary Culture.
—, 'The idea of empire in Carolingian Bavaria', in Weiler and MacLean (eds.), _Representations of Power_ , pp. 37–55.
—, 'Lay people and documents in the Frankish formula collections', in Brown, _et al_. (eds.), Documentary Culture.
—, _Unjust Seizure: Conflict, Interest and Authority in an Early Medieval Society_ (Ithaca, NY, 2001).
Brown, W., Costambeys, M., Innes, M., and Kosto, A. (eds.), _Documentary Culture and the Laity in the Early Middle Ages_ (forthcoming).
Brubaker, L., and Smith, J. M. H. (eds.), _Gender in the Early Medieval World. East and West, 300–900_ (Cambridge, 2004).
Brühl, C., _Deutschland-Frankreich. Die Geburt zweier Völker_ , 2nd edn (Cologne and Vienna, 1995).
Brunner, K., _Oppositionelle Gruppen im Karolingerreich_ (Vienna, 1979).
Buc, P., _The Dangers of Ritual_ (Princeton, NJ, 2001).
Böhrer-Thierry, G., '"Just Anger" or "Vengeful Anger"? The punishment of blinding in the early medieval west', in B. Rosenwein (ed.), _Anger's Past. The Social Uses of an Emotion in the Middle Ages_ (Ithaca, NY, 1998), pp. 75–91.
Bullimore, K., 'Folcwin of Rankweil: the world of a Carolingian local official', _EME_ 13 (2005), pp. 43–77.
Bullough, D., _The Age of Charlemagne_ (London, 1965).
—, 'Alcuin', DNB, _s.n_.
—, _Alcuin: Achievement and Reputation_ (Leiden, 2003).
—, _'Aula renovata:_ the Carolingian court before the Aachen palace', _PBA_ 71 (1985), pp. 267–301, repr. in Bullough, _Carolingian Renewal_ , pp. 123–60.
—, _Carolingian Renewal: Sources and Heritage_ (Manchester 1991).
—, 'Charlemagne's men of God: Alcuin, Hildebald and Arn', in Story (ed.), _Charlemagne_ , pp. 136–50.
—, 'Urban change in early medieval Italy: the example of Pavia', _PBSR_ 34 (1966), pp. 82–130.
—, 'What has Ingeld to do with Lindisfarne?', _Anglo-Saxon England_ 22 (1993), pp. 93–125.
Burrow, J., 'The "village community" and the uses of history in late nineteenth-century England', in N. McKendrick (ed.), _Historical Perspectives: Studies in English Thought and Society in Honour of Sir J H Plumb_ (Cambridge, 1974), pp. 255–84.
Bush, M. L., _Rich Noble, Poor Noble_ (Manchester, 1988).
Caciola, N., 'Wraiths, revenants and ritual in medieval culture', _P &P_ 152 (1996), pp. 3–45.
Callebaut, D., 'Résidences fortifiées et centres administratifs dans la vallée de l'Escaut (IXe—XIe siècle)', in D. Demolon, H. Galinié and F. Verhaeghe (eds.), _Archéologie des villes dans le Nord-Ouest de l'Europe ( VIIe—VIIIe siècle_), Actes du IVe Congrès d'Archéologie Médiévale (Douai, 1994), pp. 93–112.
Callmer, J., 'Numismatics and archaeology', _Fornvännen_ 75 (1980), pp. 203–12.
Cameron, A., _The Later Roman Empire_ (London, 1993).
Cammarosano, P., 'Marché de la terre et mobilité sociale dans les Abruzzes aux IXe—XIe siècles. À propos d'un livre récent', _Revue Historique_ 310/2 (2008), pp. 369–82.
Carroll, C. J., 'The bishoprics of Saxony in the first century after Christianization', _EME_ 8 (1999), pp. 219–45.
Carsten, J., and Hugh-Jones, S. (eds.), _About the House: Lévi-Strauss and Beyond_ (Cambridge, 1995).
Carver, M., 'Pre-Viking traffic in the North Sea', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 117–25.
—, _Sutton Hoo: Burial Ground of Kings?_ (Philadelphia, PA, 1998).
—, 'Transitions to Islam', in N. Christie and S. Loseby (eds.), _Towns in Transition. Urban Evolution in Late Antiquity and the Early Middle Ages_ (Aldershot, 1996), pp. 184–212.
Castagnetti, A., _L'organizzazione del territorio rurale nel medioevo. Circoscrizioni ecclesiastiche e civile nella 'Langobardia' e nella 'Romania'_ (Turin, 1970).
Chandler, C. J., 'Between court and counts: Carolingian Catalonia and the aprisio grant, 778–897', _EME_ 11/1 (2002), pp. 19–44.
Chapelot, J., and Fossier, R., _The Village and the House in the Middle Ages_ (London, 1985).
Charles-Edwards, T., 'The distinction between land and moveable wealth in Anglo-Saxon England', in P. H. Sawyer (ed.), _Medieval Settlement: Continuity and Change_ (London, 1976), pp. 180–7.
—, _Early Christian Ireland_ (Cambridge, 2000).
Cheyette, F. L., 'The disappearance of the ancient landscape and the climatic anomaly of the early Middle Ages: a question to be pursued', _EME_ 16 (2008), pp. 127–65.
Chiesa, P. (ed.), _Paolo Diacono. Uno scrittore fra tradizione longobarda e rinnovamento carolingio_ (Università di Udine, 2000).
Christie, N. (ed.), _Landscapes of Change: Rural Evolution in Late Antiquity_ (Aldershot, 2004).
Clark, S., _State and Status. The Rise of the State and Aristocratic Power in Western Europe_ (Toronto, 1995).
Clarke, H., and Ambrosiani, B. (eds.), _Towns in the Viking Age_ (London, 1995).
Classen, P., 'Karl der Große und die Thronfolge im Frankenreich', in _Festschrift für Hermann Heimpel_ (Göttingen, 1972), III, pp. 109–34.
Claude, D., 'Haus und Hof im Merowingerreich nach den erzählenden und urkundlichen Quellen', in H. Beck and H. Steuer (eds.), _Haus und Hof in ur- und frühgeschichtlichen Zeit_ (Göttingen, 1997), pp. 321–34.
Claussen, M., _The Reform of the Frankish Church. Chrodegang of Metz and the_ Regula canonicorum _in the Eighth Century_ (Cambridge, 2004).
Coates-Stephens, R., 'Byzantine building patronage in post-Reconquest Rome', in M. Ghilardi, _et al_. (eds.), _Les Cités de l'Italie tardo-antique ( IVe—VIe siècle_) (Rome), pp. 149–66.
—, 'Dark Age Architecture in Rome', _PBSR_ 65 (1997), pp. 177–232.
Collins, R., _Charlemagne_ (Basingstoke, 1998).
—, 'Charlemagne and his critics, 814–29', in Le Jan (ed.), _La Royauté et les élites_ , pp. 193–211.
—, 'Charlemagne's imperial coronation and the Annals of Lorsch', in Story (ed.), _Charlemagne_ , pp. 52–70.
—, 'Deception and misrepresentation in early eighth-century Frankish historiography: two case studies', in J. Jarnut, U. Nonn and M. Richter (eds.), _Karl Martell in seiner Zeit_ , Beihefte der Francia 37 (Sigmaringen, 1994), pp. 227–47.
—, _Early Medieval Spain: Unity in Diversity, 400–1000_ (2nd edn, Basingstoke, 1995).
—, _Fredegar_ , Authors of the Middle Ages 13 (Aldershot, 1996).
—, 'Pippin I and the kingdom of Aquitaine', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 363–89.
—, 'Pippin III as mayor of the palace: the evidence', in Becher and Jarnut (eds.), _Der Dynastiewechsel von_ 751, pp. 75–91.
—, 'The reviser revisited: another look at the alternative version of the _Annales regni francorum'_ , in A. Murray (ed.), _After Rome's Fall. Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 191–213.
—, _Visigothic Spain, 409–711_ (Oxford, 2004).
Constable, G., 'The _Liber memorialis_ of Remiremont', _Speculum_ 48 (1972), pp. 260–77.
—, _Monastic Tithes from their Origins to the Twelfth Century_ (Cambridge, MA, 1964).
—, _'Nona et decima:_ an aspect of the Carolingian economy', _Speculum_ 35 (1960), pp. 224–50.
Contreni, J. J., 'Dícuil', DNB, s.n.
Cooper, K., 'Ventriloquism and the miraculous: conversion, preaching, and the martyr exemplum in late antiquity', in K. Cooper and J. Gregory (eds.), _Signs, Wonders, Miracles. Representations of Divine Power in the Life of the Church_ , Studies in Church History 41 (Woodbridge, 2005), pp. 22–45.
Corradini, R., Diesenberger, M., and Reimitz, H. (eds.), _The Construction of Communities in the Early Middle Ages_ (Leiden and Boston, 2003).
Corradini, R., Meens, R., Pössel, C., and Shaw, P (eds.), _Texts and identities in the Early Middle Ages_ (Vienna, 2006).
Costambeys, M., 'An aristocratic community on the northern Frankish frontier', _EME_ 3/1 (1994), pp. 39–62.
—, 'Burial topography and the power of the Church in fifth- and sixth-century Rome', _PBSR_ 69 (2001), pp. 169–89.
—, 'Disputes and courts in Lombard and Carolingian central Italy', _EME_ 15 (2007), pp. 265–89.
—, 'Kinship, gender and property in Lombard Italy', in G. Ausenda, P. Delogu and C. Wickham (eds.), _The Langobards before the Frankish Conquest. An Ethnographic Perspective_ (Woodbridge, 2009), pp. 69–94.
—, 'The laity, the clergy, the scribes and their archives: the documentary record of eighth- and ninth-century Italy', in Brown, _et al_. (eds.), Documentary Culture.
—, _Power and Patronage in Early Medieval Italy: Local Society, Italian Politics and the Abbey of Farfa, c.700–900_ (Cambridge, 2007).
—, 'Property, ideology and the territorial power of the papacy in the early Middle Ages', _EME_ 9 (2000), pp. 367–96.
—, 'Settlement, taxation and the condition of the peasantry in post-Roman central Italy', _Journal of Agrarian Change_ 9 (2009), pp. 92–119.
—, 'Willibrord', Oxford Dictionary of National Biography, s.n.
Costambeys, M., and Leyser, C., 'To be the neighbour of St Stephen: patronage, martyr cult and Roman monasteries, c.600–900', in K. Cooper and J. Hillner (eds.), _Religion, Dynasty and Patronage in Early Christian Rome, 300–900_ (Cambridge, 2007), pp. 262–87.
Coupland, S., 'Between the devil and the deep blue sea: hoards in ninth-century Frisia', in B. Cook and G. Williams (eds.), _Coinage and History in the North Sea World c.500–1250. Essays in Honour of Marion Archibald_ (Leiden, 2006), pp. 241–66.
—, 'Carolingian arms and armour in the ninth century', _Viator_ 29 (1990), pp. 29–50.
—, 'The Carolingian army and the struggle against the Vikings', _Viator_ 35 (2004), pp. 49–70.
—, 'Carolingian coinage and Scandinavian silver', _Nordisk Numismatisk Årsskrift_ (1985–86), pp. 11–32.
—, 'Charlemagne's coinage: ideology and the economy', in Story (ed.), _Charlemagne_ , pp. 211–29.
—, 'The Frankish tribute payments to the Vikings and their consequences', _Francia_ 26 (1999), pp. 57–75.
—, 'From poachers to gamekeepers: Scandinavian warlords and Carolingian kings', _EME_ 7 (1998), pp. 85–114.
—, 'Money and coinage under Louis the Pious', _Francia_ 17/1 (1990), pp. 23–54.
—, 'The rod of God's wrath or the people of God's wrath? The Carolingian theology of the Viking invasions', _Journal of Ecclesiastical History_ 42 (1991), pp. 535–54.
—, 'Trading places: Quentovic and Dorestad reassessed', _EME_ 11 (2002), pp. 209–32.
Crone, P., _Meccan Trade and the Rise of Islam_ (Princeton, NJ, 1987).
—, _Slaves on Horses: The Evolution of the Islamic Polity_ (Cambridge, 1980).
Crumlin-Pedersen, O., _From Viking Ships to Hanseatic Cogs_ (London, 1983).
Curschmann, F., _Hungersnote im Mittelalter_ (Leipzig, 1900).
Curta, F., _Southeastern Europe in the Middle Ages, 500–1250_ (Cambridge, 2006).
Damminger, F., 'Dwellings, settlements and settlement patterns in Merovingian southwestern Germany and adjacent areas', in I. Wood (ed.), _Franks and Alamanni in the Merovingian Period_ (Woodbridge, 1998), pp. 33–106.
Dannheimer, H., 'Die frühmittelalterliche Siedlung bei Kirchheim', _Germania_ 51 (1973), pp. 152–69.
Davies, W., 'Local participation and legal ritual in early medieval law courts', in P. Coss (ed.), _The Moral World of the Law_ (Cambridge, 2000), pp. 61–89.
—, 'On servile status in the early Middle Ages', in M. Bush (ed.), _Serfdom and Slavery_ (London, 1996), pp. 225–46.
—, _Small Worlds: The Village Community in Early Medieval Brittany_ (London, 1988).
Davies, W., and Fouracre, P. (eds.), _The Settlement of Disputes in Early Medieval Europe_ (Cambridge, 1986).
Davis, J., _Land and Family in Pisticci_ (Cambridge, 1974).
Davis, J. R., and McCormick, M., 'The early Middle Ages: Europe's long morning', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 1–10.
Davis, J. R., and McCormick, M. (eds.), _The Long Morning of Medieval Europe. New Directions in Early Medieval Studies_ (Aldershot, 2008).
Davis, R., _The Book of Pontiffs_ (Liber pontificalis), rev. edn (Liverpool, 2000).
—, _The Lives of the Eighth-Century Popes_ (Liber pontificalis) (Liverpool, 1992).
—, _The Lives of the Ninth-Century Popes_ (Liber pontificalis) (Liverpool, 1995).
Déléage, A., _La Vie économique et sociale de la Bourgogne dans le haut moyen âge_ (Mâcon, 1941).
Delogu, P., 'Reading Pirenne again', in Hodges and Bowden (eds.), _The Sixth Century_ , pp. 15–40.
Depreux, P., 'Le Comte Matfrid d'orléans (avant 815 -+ 836)', _Bibliothèque de l'École des Chartes_ 152 (1994), pp. 331–74.
—, 'Das Königtum Bernhards von Italien und sein Verhältnis zum Kaisertum', _QFIAB_ 72 (1992), pp. 1–25.
—, 'Louis le Pieux reconsidéré? À propos des travaux récents consacrés à l'héritier de Charlemagne et à son règne', _Francia_ 21 (1994), pp. 181–212.
—, 'La _Pietas_ comme principe de gouvernement d'après le _Poème sur Louis le Pieux_ d'Ermold le Noir', in Hill and Swan (eds.), _The Community_ , pp. 201–24.
—, _Prosopographie de l'entourage de Louis le Pieux (781–840_ ) (Sigmaringen, 1997).
—, _Les Sociétés occidentales du milieu du VIe à la fin du IXe siècle_ (Rennes, 2002).
Deshman, R., 'The exalted servant: the ruler theology of the prayerbook of Charles the Bald', _Viator_ II (1980), pp. 385–417.
Devroey, J.-P., _Économie rurale et société dans l'Europe franque ( VI-IX siècles_) (Paris, 2003).
—, _Études sur le grand domaine carolingien_ (Aldershot, 1993).
—, 'Un monastère dans l'économie d'échanges: les services de transport à l'abbaye de St-Germain-des-Prés au ixe siècle', _Annales ESC_ 39 (1984), pp. 570–89, repr. in Devroey, Études sur le grand domaine carolingien.
—, _Puissants et miserables: Systeme social et monde paysan dans l'Europe des Francs ( VI-IX siècles_) (Brussels, 2006).
—, 'Les Services de transport à l'abbaye de Prüm au IXe siècle', _Revue du Nord_ 61 (1979), pp. 543–69, repr. in Devroey, _Études sur le grand domaine carolingien_.
Diebold, W., _'Nos quoque morem illius imitari cupientes_. Charles the Bald's evocation and imitation of Charlemagne', _Archiv für Kulturgeschichte_ 75 (1993), pp. 271–300.
Dierkens, A., 'Autour de la tombe de Charlemagne: considérations sur les sépultures et les funérailles des souverains carolingiens et des membres de leur famille', _Byzantion_ 61 (1991), pp. 156–80.
Doll, A., 'Das Pirminskloster Hornbach. Gründung und Verfassungsentwicklung bis Anfang des 12. Jahrhunderts', _Archiv für mittelrheinische Kirchengeschichte_ 5 (1953), pp. 108–42.
Dopsch, A., _Wirtschaftliche und soziale Grundlagen der europaischen Kulturentwicklung aus der Zeit von Cäsar bis auf Karl den Großen_ (Vienna, 1918–20); 2nd edn (Vienna, 1923–4), trans. M. G. Beard and N. Marshall, _Economic and Social Foundations of European Civilisation_ (New York and London, 1937).
Duby, G., _Guerriers et paysans, VII-XIIe siècle: premier essor de l'économie européenne_ (Paris, 1973), trans. H. B. Clarke, _The Early Growth of the European Economy: Warriors and Peasants from the Seventh to the Twelfth Century_ (Ithaca, NY, and London, 1974).
—, _Rural Economy and Country Life in the Medieval West_ (Los Angeles, CA, 1968).
—, _The Three Orders: Feudal Society Imagined_ (Chicago, 1982).
Durliat, J., _Les Finances publiques de Dioclétien aux Carolingiens (284–889_ ). Beihefte der Francia 21 (Sigmaringen, 1990).
Dutton, P. E., _Charlemagne's Mustache and Other Cultural Clusters of a Dark Age_ (New York, 2004).
—, 'Observations on early medieval weather in general, bloody rain in particular', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 167–80.
—, _The Politics of Dreaming in the Carolingian Empire_ (Lincoln, NE, 1994).
Dutton, P. E. (ed.), _Carolingian Civilization: a Reader_ , 2nd edn (Peterborough, ON, 2004).
—, _Charlemagne's Courtier. The Complete Einhard_ (Peterborough, ON, 1998). Dutton, P., and Kessler, H. L., _The Poetry and Painting of the First Bible of Charles the Bald_ (Ann Arbor, MI, 1997).
Edwards, C., 'German vernacular literature: a survey', in McKitterick (ed.), _Carolingian Culture_ , pp. 141–70.
Effros, B., _Merovingian Mortuary Archaeology and the Making of the Early Middle Ages_ (Berkeley and London, 2003).
Ellmers, D., 'The Frisian monopoly of coastal transport in the 6th to 8th centuries AD', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 91–2.
Endemann, T., _Markturkunde und Markt in Frankreich und Burgund vom 9. bis 11. Jahrhundert_ (Constance, 1964).
Enright, M.J., _Iona, Tara, and Soissons: the Origin of the Royal Anointing Ritual_ (Berlin and New York, 1985).
Erhart, P., and Kleindienst, J. (eds.), _Urkundenlandschaft Rätiens_ (Vienna, 2004).
Erkens, F.-R., _'Divisio legitima_ und _unitas imperii:_ Teilungspraxis und Einheitsstreben bei der Thronfolge im Frankenreich', _DA_ 52 (1996), pp. 423–85.
Es, W. van, 'Dorestad centred', in J. C. Besteman, J. M. Bos and H. A. Heidinga (eds.), _Medieval Archaeology in the Netherlands. Studies presented to H. H. von Regteren Altena_ (Assen and Maastricht, 1990), pp. 151–82. Es, W. van, and Verwers, W., _Excavations at Dorestad I. The Harbour, Hoogstraat I_ (Amersfoort, 1980).
Esmonde Cleary, A. S., _The Ending of Roman Britain_ (London, 1989).
Everett, N., _Literacy in Lombard Italy, c.568–774_ (Cambridge, 2003).
Ewig, E., 'Studien zur merowingischen Dynastie', _Frühmittelalterliche Studien_ 8 (1974), pp. 15–59.
Faith, R., 'Forces and relations of production in early medieval England', _Journal of Agrarian Change_ 9 (2009), pp. 23–41.
Falck, L., _Mainz im frühen und hohen Mittelalter (Mitte 5. Jht. bis 1244_ ) (Düsseldorf, 1972).
Fanning, S., 'Imperial diplomacy between Francia and Byzantium: the letter of Louis II to Basil I in 871', _Cithara_ 34 (1994), pp. 3–15.
Fasoli, G., _I Re d'italia (888–962_ ) (Florence, 1949).
Fehring, G. P., _The Archaeology of Medieval Germany: an Introduction_ , trans. R. Samson (London, 1991).
—, _Die Stadtkirche St. Dionysius in Esslingen a.N.: Archäologie und Baugeschichte_ (Stuttgart, 1995).
Fell, C., _'Unfriþ:_ an approach to a definition', _Saga-Book of the Viking Society for Northern Research_ 21 (1982–3), pp. 85–100.
Feller, L., _Les Abruzzes médieévales. Territoire, économie et société en italie centrale du IXe au XIIe siècle_. Bibliothèque des Écoles Françaises d'Athènes et de Rome 300 (Rome, 1998).
Feller, L., Gramain, A., and Weber, F., _La Fortune de Karol. Marché de la terre et liens personnels dans les Abruzzes au haut moyen âge_ , Collection de l'EFR 347 (Rome, 2005).
Ferry, J., and Costambeys, M., _Historians of Ninth-Century Italy_ (Liverpool, forthcoming).
Fichtenau, H., _Living in the Tenth Century_ (Chicago, 1991).
Fischer-Drew, K., _The Laws of the Salian Franks_ (Philadelphia, PA, 1991).
—, _The Lombard Laws_ (Philadelphia, PA, 1973).
Fleming, R., 'Lords and labour', in W. Davies (ed.), _From the Vikings to the Normans_ (Oxford, 2003), pp. 107–37.
Fletcher, R., _The Conversion of Europe: From Paganism to Christianity, 371–1386_ (London, 1997).
Flint, V., _The Rise of Magic in Early Medieval Europe_ (Oxford, 1991).
Folz, R., _The Coronation of Charlemagne, 25 December 800_ (London, 1974).
Fossier, R., _Enfance de l'Europe_ , 2 vols. (Paris, 1982).
—, 'Les Tendances de l'économie: stagnation ou croissance?', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 27 (Spoleto, 1981), pp. 261–74.
Fouracre, P., _The Age of Charles Martel_ (Harlow, 2000).
—, 'Carolingian justice: the rhetoric of improvement and contexts of abuse', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 42 (Spoleto, 1995), pp. 771–803.
—, 'Conflict, power and legitimation in Francia in the late seventh and early eighth centuries', in I. Alfonso, H. Kennedy and J. Escalona (eds.), _Building Legitimacy: Political Discourses and Forms of Legitimacy in Medieval Societies_ , The Medieval Mediterranean: Peoples, Economies and Cultures 400–1500 53 (Leiden, 2004), pp. 3–26.
—, 'The context of the OHG _Ludwigslied', Medium Aevum_ 54 (1985), pp. 97–103.
—, 'Cultural conformity and social conservatism in early medieval Europe', _History Workshop Journal_ 33 (1992), pp. 152–61.
—, 'Eternal light and earthly needs: practical aspects of the development of Frankish immunities', in W. Davies and P. Fouracre (eds.), _Property and Power in the Early Middle Ages_ (Cambridge, 1995), pp. 53–81.
—, 'The long shadow of the Merovingians', in Story (ed.), _Charlemagne_ , pp. 5–21.
—, 'Marmoutier and its serfs in the eleventh century', _TRHS_ 15 (2005), pp. 29–49.
—, 'Merovingian history and Merovingian hagiography', _P &P_ 127 (1990), pp. 3–38.
—, 'The origins of the Carolingian attempt to regulate the cult of saints', in J. Howard-Johnston and P. A. Hayward (eds.), _The Cult of Saints in Late Antiquity and the Middle Ages. Essays on the Contribution of Peter Brown_ (Oxford, 1999), pp. 143–66.
—, 'Space, culture and kingdoms in early medieval Europe', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 366–80.
—, 'The work of Audoenus of Rouen and Eligius of Noyon in extending episcopal influence from the town to the country in seventh-century Neustria', _Studies in Church History_ 16 (1979), pp. 77–91.
Fouracre, P., and Gerberding, R., _Late Merovingian France: History and Hagiography, 640–720_ (Manchester and New York, 1996).
France, J., 'The composition and raising of the armies of Charlemagne', _Journal of Medieval Military History_ 1 (2002), pp. 61–82.
Francovich, R., 'The beginnings of hilltop villages in early medieval Tuscany', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 55–82.
—, 'Changing structures of settlement', in C. La Rocca (ed.), _Italy in the Early Middle Ages_ (Oxford, 2002), pp. 144–67.
Francovich, R., and Hodges, R., _Villa to Village_ (London, 2003).
Freedman, P., _The Origins of Peasant Servitude in Medieval Catalonia_ (Cambridge, 1991).
Fried, J., 'Elite und Ideologie, oder die Nachfolgeordnung Karls des Großen vom Jahre 813', in Le Jan (ed.), _La Royauté et les élites_ , pp. 71–109.
—, 'Der karolingische Herrschaftsverband im 9. Jahrhundert zwischen "Kirche" und "Königshaus"', _HZ_ 235 (1982), pp. 1–43.
—, _König Ludwig der Jüngere in seiner Zeit_ (Lorsch, 1984).
—, 'Papst Leo III. besucht Karl den Großen in Paderborn oder Einhards Schweigen', _HZ_ 272 (2001), pp. 281–326.
Gabriele, M., and Stuckey, J. (eds.), _The Legend of Charlemagne in the Middle Ages. Power, Faith and Crusade_ (New York, 2008).
Gaffney, V., Patterson, H., and Roberts, P., 'Forum novum (Vescovio): a new study of the town and bishopric', in H. Patterson (ed.), _Bridging the Tiber: Approaches to Regional Archaeology in the Middle Tiber Valley_ (London, 2004), pp. 237–48.
Ganshof, F. L., _The Carolingians and the Frankish Monarchy_ (London, 1971).
—, 'Charlemagne's failure', in Ganshof, _The Carolingians and the Frankish Monarchy_ , pp. 256–60.
—, 'Charlemagne's programme of imperial government', in Ganshof, _The Carolingians and the Frankish Monarchy_ , pp. 55–85.
—, _Frankish Institutions under Charlemagne_ (Providence, RI, 1968).
—, 'The last period of Charlemagne's reign: a study in decomposition', in Ganshof, _The Carolingians and the Frankish Monarchy_ , pp. 240–55.
—, 'Louis the Pious reconsidered', in Ganshof, _The Carolingians and the Frankish Monarchy_ , pp. 261–72.
—, 'Note sur la concession d'alleux à des vassaux sous le règne de Louis le Pieux', in _Storiografia e Storia: Studi in onore di E. Dupré Theseider_ (Rome, 1974), pp. 589–99.
Ganz, D., 'Book production in the Carolingian empire and the spread of Carolingian minuscule', in _NCMH_ II, pp. 786–808.
—, 'Charlemagne in Hell', _Florilegium_ 17 (2002 for 2000), pp. 175–94.
—, 'Dúngal', _DNB, s.n_.
—, _Einhard_ (forthcoming).
—, 'Einhard's Charlemagne: the characterization of greatness', in Story (ed.), _Charlemagne_ , pp. 38–51.
—, 'The _Epitaphium Arsenii_ and opposition to Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 537–50.
—, 'Theology and the organisation of thought', in _NCMH_ II (Cambridge, 1995), pp. 758–85.
—, _Two Lives of Charlemagne_ (Harmondsworth, 2008).
Ganz, D., and Goffart, W., 'Charters earlier than 800 from French collections', _Speculum_ 65 (1990), pp. 906–32.
Garipzanov, I. H., 'The Carolingian abbreviation of Bede's World Chronicle and Carolingian imperial "genealogy"', _Hortus Artium Medievalium_ (2005), pp. 291–7.
—, 'Communication of authority in Carolingian titles', _Viator_ 36 (2005), pp. 41–82.
—, 'Frontier identities: Carolingian frontier and _gens Danorum'_ , in I. H. Garipzanov, P. J. Geary and P. Urbanczyk (eds.), _Franks, Northmen, and Slavs: Identities and State Formation in Early Medieval Europe_ (Turnhout, 2008), pp. 113–42.
—, _The Symbolic Language of Authority in the Carolingian World, c.751–877_ (Leiden and Boston, 2008).
Garnsey, P., _Ideas of Slavery from Aristotle to Augustine_ (Cambridge, 1996).
—, _Social Status and Legal Privilege in the Roman Empire_ (Oxford, 1970).
Garrison, M., 'The emergence of Carolingian Latin literature and the court of Charlemagne (780–814)', in McKitterick (ed.), _Carolingian Culture_ , pp. 111–40.
—, 'The Franks as the new Israel? Education for an identity from Pippin to Charlemagne', in Hen and Innes (eds.), _Uses of the Past_ , pp. 114–61.
—, 'Fridugisus', _DNB, s.n_.
—, 'Joseph Scottus', _DNB, s.n_.
—, 'Quid Hinieldus cum Christo?', in K. O'Brien O'Keefe and A. Orchard (eds.), _Latin Learning and English Lore: Studies in Anglo-Saxon Literature for Michael Lapidge_ , 2 vols. (Toronto, 2005), I, pp. 237–59.
Gasparri, S., 'The aristocracy', in La Rocca (ed.), _Italy in the Early Middle Ages_ (Oxford, 2002), pp. 59–84.
—, 'Mercanti o possessori? Profilo di un ceto dominante in un'età di transizione', in Gasparri and La Rocca (eds.), _Carte di famiglia_ , pp. 157–78.
—, 'Roma e i longobardi', in _Roma nell'alto medioevo, Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 48 (Spoleto, 2001), pp. 219–47.
—, 'Strutture militari e legami di dipendenza in Italia in età longobarda e carolingia', _Rivista storica italiana_ 98 (1986), pp. 664–726.
Gasparri, S., and La Rocca, C. (eds.), _Carte di famiglia. Strategie, rappresentazione e memoria del gruppo familiare di Totone di Campione, 721–877_ (Rome, 2005).
Geary, P., _Aristocracy in Provence. The Rhône Basin at the Dawn of the Carolingian Age_ (Stuttgart, 1985).
—, 'Exchange and interaction between the living and the dead in early medieval society', in Geary, _Living with the Dead in the Early Middle Ages_ (Ithaca, NY, and London, 1994), pp. 77–94.
—, 'Germanic tradition and royal ideology in the ninth century: the _visio Karoli Magni', Frühmittelalterliche Studien_ 21 (1987), pp. 274–94, repr. in Geary, _Living with the Dead in the Early Middle Ages_ (Ithaca, NY, and London, 1994), pp. 49–76.
—, _The Myth of Nations_ (Princeton, NJ, 2002).
—, _Phantoms of Remembrance: Memory and Oblivion at the End of the First Millennium_ (Princeton, NJ, 1994).
Geiselhart, M., _Die Kapitulariengesetzgebung Lothars I. in Italien_ (Frankfurt, 2002).
Gelichi, S., 'The rise of an early medieval emporium and the economy of Italy in the late Longobard age', in _Annales. Series Historia et Sociologia_ 18/2 (2008), pp. 319–36.
Gerberding, R., _The Rise of the Carolingians and the_ Liber historiae francorum (Oxford, 1987).
Geuenich, D., 'A survey of the early medieval confraternity books from the continent', in D. Rollason (ed.), _The Durham_ Liber Vitae _and its Context_ (Woodbridge, 2004), pp. 141–7.
Gilles, S., 'Territorial interpolations in the Old English Orosius', in S. Gilles and S. Tomasch (eds.), _Text and Territory: Geographical Imagination in the Middle Ages_ (Philadelphia, PA, 1998).
Gillett, A. (ed.), _On Barbarian Identity: Critical Approaches to Ethnicity in the Early Middle Ages_ (Turnhout, 2002).
Gladiß, D., 'Die Schenkungen der deutschen Könige zu privaten Eigen (800–1137), _DA_ I (1937), pp. 80–136.
Gobry, I., _Histoire des rois de France: Louis Ier, Premier successeur de Charlemagne_ (Paris, 2002).
Gockel, M., _Karolingische Königshöfe am Mittelrhein_ (Göttingen, 1970).
Godden, M., 'The Anglo-Saxons and the Goths: rewriting the sack of Rome', _Anglo-Saxon England_ 31 (2002), pp. 47–68.
Godman, P., _Poetry of the Carolingian Renaissance_ (London, 1985).
—, _Poets and emperors: Frankish Politics and Carolingian Poetry_ (Oxford, 1987).
Godman, P., and Collins, R. (eds.), _Charlemagne's Heir: New Perspectives on the Reign of Louis the Pious_ (Oxford, 1990).
Godman, P., Jarnut, J., and Johanek, P. (eds.), _Am Vorabend der Kaiserkrönung: das Epos "Karolus Magnus et Leo papa" und der Papstbesuch in Paderborn 799_ (Berlin, 2002).
Goetz, H.-W., '"Nobilis". Der Adel im Selbstverständnis der Karolingerzeit', _Vierteljahresschrift für Sozial- und Wirtschaftsgeschichte_ 70 (1983), pp. 153–91.
—, _'Regnum:_ zum politischen Denken der Karolingerzeit', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Germanistische Abteilung_ 104 (1987), pp. 110–89.
—, 'Serfdom and the beginnings of a "seigneurial system" in Carolingian Europe', _EME_ 2 (1993), pp. 29–51.
—, 'Social and military institutions', in _NCMH_ II, pp. 451–80.
—, 'Die Wahrnehmung von "Staat" und "Herrschaft" im frühen Mittelalter', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 39–58.
Goffart, W., 'The Fredegar problem reconsidered', _Speculum_ 38 (1963), pp. 206–41.
—, 'Merovingian polyptychs: reflections on two recent publications', _Francia_ 9 (1982), pp. 55–77; repr. in Goffart, _Rome's Fall and After_ (London, 1989), pp. 233–53.
—, 'Old and new in Merovingian taxation', in Goffart, _Rome's Fall and After_ (London, 1989), pp. 213–31.
—, 'Paul the Deacon's _Gesta episcoporum Mettensium_ and the early design for Charlemagne's succession', _Traditio_ 42 (1986), pp. 53–87.
Goldberg, E. J., 'Ludwig der Deutsche und Mähren: Eine Studie zu karolingischen Grenzkriegen im Osten', in W. Hartmann (ed.), _Ludwig der Deutsche und seine Zeit_ (Darmstadt, 2004), pp. 67–94.
—, '"More devoted to the equipment of battle than the splendor of banquets": frontier kingship, martial ritual, and early knighthood at the court of Louis the German', _Viator_ 30 (1999), pp. 41–78.
—, 'Popular revolt, dynastic politics and aristocratic factionalism in the early middle ages: the Saxon Stellinga reconsidered', _Speculum_ 70 (1995), pp. 467–501.
—, _Struggle for Empire. Kingship and Conflict under Louis the German, 817–876_ (Ithaca, NY, and London, 2006).
Goodson, C., _The Rome of Pope Paschal I. Papal Power, Urban Renovation, Church Rebuilding and Relic Translation, 817–824_ (Cambridge, 2010).
Gorman, M., 'The commentary on Genesis of Claudius of Turin and Biblical studies under Louis the Pious', _Speculum_ 72 (1997), pp. 279–329.
Grant, L., _Abbot Suger of St-Denis: Church and State in Early Twelfth-Century France_ (London, 1998).
Green, D. H., and Siegmund, F. (eds.), _The Continental Saxons from the Migration Period to the Tenth Century: an Ethnographic Perspective_ (Woodbridge, 2003).
Grierson, P., 'Commerce in the dark ages: a critique of the evidence', _TRHS_ 9 (1959), pp. 123–40.
—, 'The volume of the Anglo-Saxon coinage', _Economic Historic Review_ 20 (1967), pp. 153–60.
Griffiths, D., Philpott, R., and Egan, G. (eds.), _Meols. The Archaeology of the North Wirral Coast_ (Oxford, 2007).
Guichard, P., 'Les Débuts de la piraterie andalouse en Méditerranée occidentale (798–813)', _Revue de l'Occident musulman_ 35 (1983), pp. 55–76.
Guillot, O., 'Une "ordinatio" méconnue. Le Capitulaire de 823–825', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 455–86.
Haldon, J., and Brubaker, L., _Byzantium in the Iconoclast Era, c.680–850_ (Cambridge, 2010).
Halphen, L., _Charlemagne et l'empire carolingien_ (Paris, 1947), trans. G. de Nie, _Charlemagne and the Carolingian Empire_ (Amsterdam, 1977).
Halsall, G., _Barbarian Migrations and the Roman West, 376–568_ (Cambridge, 2007).
—, 'Burial ritual and Merovingian society', in Hill and Swan (eds.), _The Community_ , pp. 325–38.
—, 'Female status and power in early Merovingian central Austrasia: the burial evidence', _Early Medieval Europe_ 5/1 (1996), pp. 1–24.
—, _Settlement and Social Organisation: the Merovingian Region of Metz_ (Cambridge, 1995).
—, _Warfare and Society in the Barbarian West_ (London and New York, 2003).
Halsall, G. (ed.), _Humour, History and Politics in Late Antiquity and the Early Middle Ages_ (Cambridge, 2002).
Hamerow, H., _Early Medieval Settlements: the Archaeology of Rural Communities in North-West Europe, 400–900_ (Oxford, 2002).
Hamilton, S., 'Early medieval rulers and their modern biographers', _EME_ 9 (2000), pp. 247–60.
—, 'The unique favour of penance: the Church and the people c.800–c.1100', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 229–45.
Hammer, C. I., _From_ Ducatus _to_ Regnum: _Ruling Bavaria under the Merovingians and Early Carolingians_ (Turnhout, 2007).
Handley, M. A., _Death, Society and Culture: Inscriptions and Epitaphs in Gaul and Spain, AD 300–750_ (Oxford, 2003).
Hannig, J., 'Zentralle Kontrolle und regionale Machtbalance. Beobachtungen zum System der karolingischen Königsboten am Beispiel des Mittelrheingebietes', _Archiv für Kulturgeschichte_ 66 (1984), pp. 1–46.
—, 'Zur Funktion der karolingischen _missi dominici_ in Bayern und in den südöstlichen Grenzgebieten', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Germanistische Abteilung_ 101 (1984), pp. 256–300.
Hansen, H. J., 'Danekirke: affluence in late Iron Age Denmark', in K. Randsborg (ed.), _The Birth of Europe. Archaeology and Social Development in the First Millennium AD_ (Rome, 1989), pp. 123–8.
Hansen, I. L., and C. J. Wickham (eds.), _The Long Eighth Century. Production, Distribution and Demand_ (Leiden, 2000).
Hardt, M., _Gold und Herrschaft: die Schätze europäischer Könige und Fürsten im ersten Jahrtausend_ (Berlin, 2004).
—, 'Royal treasures and representation in the early Middle Ages', in W. Pohl and H. Reimitz (eds.), _Strategies of Distinction. The Construction of Ethnic Communities, 300–800_ (Leiden, 1998), pp. 255–80.
Hardt-Friedrichs, F., 'Markt, Münze und Zoll im ostfränkischen Reich bis zum Ende der Ottonen', _Blätter für deutsche Landesgeschichte_ 116 (1980), pp. 1–32.
Hartmann, L., _Zur Wirtschaftsgeschichte Italiens im frühen Mittelalter_ (Gotha, 1904).
Hartmann, W., _Ludwig der Deutsche_ (Darmstadt, 2002).
Heather, P., 'Frankish imperialism and Slavic society', in P. Urba czyk (ed.), _The Origins of Central Europe_ (Warsaw, 1997), pp. 171–90.
—, 'State formation in Europe in the first millennium ad', in B. Crawford (ed.), _Scotland in Dark Age Europe_ (St Andrews, 1994), pp. 47–63.
Heather, P., and Matthews, J., _The Goths in the Fourth Century_ (Liverpool, 1991).
Heidinga, H. A., _Medieval Settlement and Economy North of the Lower Rhine_ (Assen, 1987).
Heinzelman, M., 'Villa d'après l'oeuvre de Grégoire de Tours', in E. Magnou-Nortier (ed.), _Aux sources de la gestion publique_ I: _Enquête lexicographique sur fundus, villa, domus, mansus_ (Lille, 1993), pp. 45–70.
Hellmann, S., 'Die Heiraten der Karolinger', in S. Hellmann, _Ausgewählte Abhandlungen zur Historiographie und Geistesgeschichte des Mittelalters_ , ed. by H. Beumann (Darmstadt, 1961), pp. 293–391.
Hemming, J., 'Strong rulers – weak economy? Rome, the Carolingians, and the archaeology of slavery in the first millennium AD', in Davis and McCormick, _The Long Morning of Medieval Europe_ , pp. 33–54.
Hen, Y., 'The Annals of Metz and the Merovingian past', in Hen and Innes (eds.), _Uses of the Past_ , pp. 175–90.
—, 'The Christianisation of kingship', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 163–77.
—, _Culture and Religion in Merovingian Gaul_ (Leiden, 1995).
—, 'Knowledge of canon law among rural priests', _Journal of Theological Studies_ 50 (1999), pp. 117–34.
—, _The Royal Patronage of Liturgy in Frankish Gaul to the Death of Charles the Bald (877_ ), Henry Bradshaw Society Subsidia 3 (London, 2001).
—, 'The structure and aims of the _Visio Baronti'_ , _Journal of Theological Studies_ , n.s. 47 (1996), pp. 477–97.
Hen, Y., and Innes, M. (eds.), _The Uses of the Past in the Early Middle Ages_ (Cambridge, 2000).
Hennebicque, R., '"Pauperes" et "paupertas" dans l'occident carolingien aux IXe et xe siécles', _Revue du Nord_ 50 (1968), pp. 167–87.
Hennebicque-Le Jan, R., 'Prosopographica neustrica. Les Agents du roi en Neustrie de 639 à 840', in H. Atsma (ed.), _La Neustrie: les pays au nord de la Loire de 650 à 850_ , Beihefte der Francia, 16, 2 vols. (Sigmaringen, 1989), I, pp. 231–69.
Herlihy, D., 'The Carolingian mansus', _EHR_ 13 (1960), pp. 69–79.
—, 'Church property on the European continent, 701–1200', _Speculum_ 36 (1961), pp. 81–105.
—, _A History of Feudalism_ (London, 1970).
—, _Medieval Households_ (London, 1985).
Herren, M., 'The _De imagine Tetrici_ of Walafrid Strabo: edition and translation', _The Journal of Medieval Latin_ I (1991), pp. 118–39.
—, 'Walafrid Strabo's _De imagine Tetrici_ : an interpretation', in R. North and T. Hofstra (eds.), _Latin Culture and Medieval Germanic Europe_ (Groningen, 1992), pp. 25–41.
Herrin, J., _The Formation of Christendom_ (Oxford, 1987).
Hess, W., 'Geldwirtschaft am Mittelrhein in karolingischer Zeit', _Blätter für deutsche Landesgeschichte_ 98 (1962), pp. 26–63.
Hill, D., _et al_., 'Quentovic defined', _Antiquity_ 61 (1990), pp. 51–8.
Hill, D., and Cowie, R. (eds.), _Wics: The Early Medieval Trading Centres of Northern Europe_ (Sheffield, 2001).
Hill, J., and Swan, M. (eds.), _The Community, the Family and the Saint: Patterns of Power in Early Medieval Europe: Selected Proceedings of the International Medieval Congress, University of Leeds, 4–7 July 1994, 10–13 July 1995_ (Turnhout, 1998).
Hillgarth, J., _Christianity and Paganism, 350–750. The Conversion of Western Europe_ (Philadelphia, PA, 1986).
Hlawitschka, E., _Franken, Alemannen, Bayern und Burgunder in Oberitalien (774–962). Zum Verständnis der fränkischen Königsherrschaft in Italien_ (Freiburg, 1960).
Hodges, R., _Dark Age Economics: The Rebirth of Towns and Trade, 600–1000_ (London, 1982).
—, _Light in the Dark Ages: The Rise and Fall of San Vincenzo al Volturno_ (London, 1997).
—, _San Vincenzo al Volturno 1. The Excavations 1980–1986, part 1_ (London, 1993).
—, _San Vincenzo al Volturno 2. The Excavations 1980–1986, part 2_ (London, 1995).
—, _Towns and Trade in the Age of Charlemagne_ (London, 2000).
—, 'Trade and market origins in the ninth century: an archaeological perspective on Anglo-Carolingian relations', in M. Gibson and J. Nelson (eds.), _Charles the Bald: Court and Kingdom_ (2nd edn, 1990), pp. 213–33.
Hodges, R., and Bowden, W. (eds.), _The Sixth Century. Production, Distribution and Demand_ (Leiden, 1998).
Hodges, R., and Whitehouse, D., _Mohammed, Charlemagne and the Origins of Europe_ (London, 1983).
Horden, P., and Purcell, N., _The Corrupting Sea: A Study of Mediterranean History_ I (Oxford, 1999).
Huggett, J. W., 'Imported grave goods and the early Anglo-Saxon economy', _Medieval Archaeology_ 32 (1988), pp. 63–96.
Humfress, C., 'Poverty and Roman law', in R. Osborne and M. Atkins (eds.), _Poverty in the Roman World_ (Cambridge, 2006), pp. 183–203.
Hummer, H., _Politics and Power in Early Medieval Europe: Alsace and the Frankish Realm, 600–1000_ (Cambridge, 2005).
—, 'The production and preservation of documents in Francia: the evidence of cartularies', in Brown, _et al_. (eds.), _Documentary Culture_.
—, 'Reform and lordship in Alsace at the turn of the millennium', in W. C. Brown and P. Górecki (eds.), _Conflict in Medieval Europe: Changing Perspectives on Society and Culture_ (Aldershot, 2003), pp. 69–84.
Humphreys, S. C., 'History, economics, and anthropology: the work of Karl Polanyi', _History and Theory_ 8 (1969), pp. 165–212.
Hvass, S., 'Rural settlements in Denmark in the first millennium AD', in K. Randsborg (ed.), _The Birth of Europe_ (Rome, 1989), pp. 91–9.
Innes, M., 'Charlemagne's government', in Story (ed.), _Charlemagne_ , pp. 71–89.
—, 'Charlemagne's will: piety, politics and the imperial succession', _EHR_ 112 (1997), pp. 833–55.
—, 'Danelaw identities: ethnicity, regionalism and political allegiance', in D. M. Hadley and J. D. Richards (eds.), _Cultures in Contact: Scandinavian Settlement in England in the Ninth and Tenth Centuries_ (Turnhout, 2000), pp. 65–88.
—, 'Dossiers and archives: documents, landowners and power in Frankish society', in Brown, _et al_. (eds.), Documentary Culture.
—, 'Economies and societies in the early medieval west', in E. English and C. Lansing (eds.), _Companion to the Middle Ages_ (Oxford, 2009), pp. 9–37.
—, 'Framing the Carolingian economy', _Journal of Agrarian Change_ 9 (2009), pp. 42–58.
—, 'Franks and Slavs, 700–1000: European expansion before the millennium', _EME_ 6 (1997), pp. 201–14.
—, '"He never even allowed his white teeth to be bared in laughter": the politics of humour in the Carolingian renaissance', in Halsall (ed.), _Humour, History and Politics_ , pp. 131–56.
—, _Introduction to Early Medieval Western Europe, 300–900. The Sword, the Plough and the Book_ (London and New York, 2007).
—, 'Keeping it in the family: women and aristocratic memory _c_.700–1200', in E. van Houts (ed.), _Medieval Memories: Men, Women and the Past 700–1300_ (London, 2001), pp. 17–35.
—, 'Kings, monks and patrons: political identities and the abbey of Lorsch', in Le Jan (ed.), _La Royauté et les élites_ , pp. 301–24.
—, 'Land, freedom and the making of the early medieval west', _TRHS_ 16 (2006), pp. 39–73.
—, 'On the material culture of legal documents: charters and their preservation in the Cluny archive (9th–11th centuries)', in Brown, _et al_. (eds.), Documentary Culture.
—, 'Memory, orality and literacy in an early medieval society', _P &P_ 158 (1998), pp. 3–36.
—, 'People, places and power in the Carolingian world: a microcosm', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 397–437.
—, '"A place of discipline": Carolingian courts and aristocratic youth', in C. Cubitt (ed.), _Court Culture in the Early Middle Ages_ (Turnhout, 2003), pp. 59–76.
—, 'Practices of property in the Carolingian empire', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 246–66.
—, 'Property, politics and the problem of the Carolingian state', in W. Pohl and V. Wieser (eds.), _Staat im frühen Mittelalter_ (Vienna, 2009), pp. 299–313.
—, _State and Society in the Early Middle Ages: The Middle Rhine Valley, 400–1000_ (Cambridge, 2000).
—, 'Teutons or Trojans? The Carolingians and the Germanic past', in Hen and Innes (eds.), _Uses of the Past_ , pp. 227–49.
Innes, M., and McKitterick, R., 'The writing of history', in McKitterick (ed.), _Carolingian Culture_ , pp. 193–220.
Iogna-Prat, D, 'Le "Baptême" du schéma des trois ordres fonctionnels: l'apport de l'école d'Auxerre dans la seconde moitié du ixe siécle', _Annales ESC_ 41/1 (1986), pp. 101–26.
—, 'The dead in the celestial bookkeeping of the Cluniac monks', in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 340–62.
Jacobsen, W., 'Die Lorscher Torhalle. Zum Problem ihrer Deutung und Datierung', _Jahrbuch des Zentralinstituts für Kunstgeschichte_ 1 (1985), pp. 9–77.
James, E., _The Merovingian Archaeology of South-West Gaul_. BAR supplementary series 25 (Oxford, 1977).
Jankuhn, H., _et al_. (eds.), _Das Dorf der Eisenzeit und des frühen Mittelalters_ (Göttingen, 1977).
Janssen, W., 'Dorf und Dorfformen des 7.-12. Jhts. im Lichte neuer Ausgrabungen in Mittel- und Nordeuropa', in Jankuhn, _et al_. (eds.), _Das Dorf der Eisenzeit_ , pp. 285–356.
Jarnut, J., 'Die Adoption Pippins durch König Liutprand', in J. Jarnut, U. Nonn and M. Richter (eds.), _Karl Martell in seiner Zeit_ (Sigmaringen, 1994), pp. 217–26.
—, 'Ein Bruderkampf und seine Folgen: die Krise des Frankenreiches (768–771)', in G. Jenal and S. Haarländer (eds.), _Herrschaft, Kirche, Kultur: Beiträge zur Geschichte des Mittelalters. Festschrift für Friedrich Prinz zu seinem 65. Geburtstag_ (Stuttgart, 1993), pp. 165–76.
—, 'Ludwig der Fromme, Lothar I und das Regnum Italiae', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 349–62.
—, 'Untersuchungen zur Herkunft Swanahilds, der Gattin Karl Martells', _Zeitschrift für bayerische Landesgeschichte_ 40 (1977), pp. 254–9.
Jong, M. de, 'Brideshows revisited: praise, slander and exegesis in the reign of the empress Judith', in Brubaker and Smith (eds.), _Gender in the Early Medieval World_ , pp. 257–77.
—, 'Carolingian monasticism: the power of prayer', in _NCMH_ II, pp. 622–53.
—, 'Charlemagne's balcony: the solarium in ninth-century narratives', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 277–90.
—, 'Charlemagne's Church', in Story (ed.), _Charlemagne_ , pp. 103–35.
—, _'Ecclesia_ and the early medieval polity', in Airlie, Pohl and Reimitz (eds.), _Staat im Frühmittelalter_ , pp. 113–32.
—, 'The empire as _ecclesia:_ Hrabanus Maurus and biblical _historia_ for rulers', in Hen and Innes (eds.), _Uses of the Past_ , pp. 191–226.
—, _In Samuel's Image. Child Oblation in the Early Medieval West_ (Leiden and New York, 1996).
—, 'Monastic prisoners or opting out? Political coercion and honour in the Frankish kingdoms', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 291–328.
—, _The Penitential State: Authority and Atonement in the Age of Louis the Pious, 814–840_ (Cambridge, 2009).
—, 'Power and humility in Carolingian society: the public penance of Louis the Pious', _EME_ I (1992), pp. 29–52.
—, 'Religion', in R. McKitterick (ed.), _The Early Middle Ages: Europe 400–1000. The Short Oxford History of Europe_ (Oxford, 2001), pp. 131–66.
—, _'Sacrum palatium et ecclesia_. L'Autorité religieuse royale sous les carolingiens (790–840)', _Annales. HSS_ 58 (2003), pp. 1243–69.
—, 'To the limits of kinship: anti-incest legislation in the early medieval west (500–900)', in J. Bremmer (ed.), _From Sappho to De Sade: Moments in the History of Sexuality_ (London and New York, 1989), pp. 36–59.
—, 'Transformations of penance', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 184–224.
—, 'What was public about public penance? _Poenitentia publica_ and justice in the Carolingian world', _La giustitia nell'alto medioevo (secoli IX–XI_), Settimane di Studio del Centro italiano di studi sull'alto medioevo 44 (Spoleto, 1997), pp. 863–902.
Jong, M. de, and Theuws, F. with Rhijn, C. van (eds.), _Topographies of Power in the Early Middle Ages_ (Leiden, Boston, MA, and Cologne, 2001).
Jorns, W., 'Zullestein. Ein Beitrag zur Kontinuität von Bauwerken', in _Deutsche Königpfalzen: Beiträge zu ihrer historischen und archäologischen Erforschung_ III, Veröffentlichungen des Max-Planck-Institutes für Geschichte II (Göttingen, 1979), pp. 111–35.
Kaschke, S., _Die karolingischen Reichsteilungen bis 831. Herrschaftspraxis und Normvorstellungen in zeitgenössischer Sicht_ (Hamburg, 2006).
Kasten, B., _Adalhard von Corbie: die Biographie eines karolingischen Politikers und Klostervorstehers_ (Düsseldorf, 1986).
—, _Königssohne und Königsherrschaft. Untersuchungen zur Teilhabe am Reich in der Merowinger- und Karolingerzeit, MGH_ Schriften XLIV (Hanover, 1997).
Kelly, S., 'Trading privileges from eighth-century England', _EME_ 1 (1992), pp. 3–28.
Kennedy, H., 'From _polis_ to _madina:_ urban change in late antique and early Islamic Syria', _P &P_ 106 (1985), pp. 3–27.
—, 'Military pay and the economy of the early Islamic state', _Historical Research_ 188 (2002), pp. 155–69.
—, _Muslim Spain and Portugal: A Political History of Al-Andalus_ (London, 1996).
—, _The Prophet and the Age of the Caliphates_ (Harlow, 1986, 2nd edn 2004).
Kershaw, P., 'Eberhard of Friuli, a Carolingian lay Intellectual', in Wormald and Nelson (eds.), _Lay Intellectuals_ , pp. 77–105.
—, 'Laughter after Babel's fall: misunderstanding and miscommunication in the ninth-century west', in Halsall (ed.), _Humour, History and Politics_ , pp. 179–202.
—, 'English history and Irish readers in the Frankish world', in D. Ganz and P. Fouracre (eds.), _Frankland. The Franks and the World of Early Medieval Europe. Essays in Honour of Dame Jinty Nelson_ (Manchester, 2008), pp. 126–51.
Kienast, W., _Das fränkische Vassalität von den Hausmaiern bis zu Ludwig dem Kind und Karl dem Einfältigen_ (Frankfurt, 1990).
King, P. D., _Charlemagne: Translated Sources_ (Kendal, 1987).
Kirby, D. P. (ed.), _Saint Wilfrid at Hexham_ (Newcastle-upon-Tyne, 1974).
Knowles, D., _Great Historical Enterprises_ (London, 1963).
Kosto, A. J., 'Hostages in the Carolingian world', _EME_ 11 (2002), pp. 123–47.
—, 'Laymen, clerics and documentary practices in the early middle ages: the example of Catalonia', _Speculum_ 80 (2005), pp. 44–74.
Koziol, G., 'Is Robert I in Hell?', _EME_ 14 (2006), pp. 233–67.
Krah, A., _Absetzungsverfahren als Spiegelbild von Königsmacht. Untersuchungen zum Kräfteverhältnis zwischen Königtum und Adel im Karolingerreich und seinen Nachfolgestaaten_ (Aalen, 1987).
—, _Die Entstehung der 'potestas regia' im Westfrankenreich während der ersten Regierungsjahre Kaiser Karl II. (840–877_ ) (Berlin, 2000).
Krahwinkler, H., _Friaul im Frühmittelalter. Geschichte einer Region vom Ende des fünften bis zum Ende des zehnten Jahrhunderts_ (Vienna, 1992).
Kreutz, B., _Before the Normans: Southern Italy in the Ninth and Tenth Centuries_ (Philadelphia, PA, 1991).
Krüger, K. H., 'Herrschaftsnachfolge als Vater-Sohn-Konflikt', _Frühmittelalterliche Studien_ 36 (2002), pp. 225–40.
—, 'Neue Beobachtungen zur Datierung von Einhards Karlsvita', _Frühmittelalterliche Studien_ 32 (1998), pp. 124–45.
Kuchenbuch, L., _Bäuerliche Gesellschaft und Klosterherrschaft im 9. Jht. Studien zur Sozialstruktur der Familia der Abtei Prüm_. Vierteljahrsschrift für Sozial- und Wirtschaftsgeschichte Beihefte 66 (Wiesbaden, 1978).
La Rocca, C., 'Le elites, chiese e sepolture familiari tra VIIIe e IXe secolo in Italia settentrionale', in Depreux, Bougard and Le Jan (eds.), _Les Élites et leurs espaces_ , pp. 259–71.
—, 'La legge e la pratica. Potere e rapporti sociali nell'Italia dell' VIII secolo', in C. Bertelli and G. P. Brogiolo (eds.), _Il futuro dei Longobardi. L'Italia e la costruzione dell'Europa di Carlo Magno_ (Brescia, 2000), pp. 45–69.
—, 'Pouvoirs des femmes, pouvoirs de la loi dans l'Italie lombarde', in S. Lebecq, A. Dierkens, R. Le Jan and J.-M. Sansterre (eds.), _Femmes et pouvoirs des femmes à Byzance et en Occident ( VIIe-XIe siècles_) (Villeneuved'Ascq, 1999), pp. 37–50.
—, 'Segni di distinzione. Dai corredi funerari alle donazioni "post obitum" nel regno longobardo', in L. Paroli (ed.), _L'Italia centro-settentrionale in età longobarda_ (Florence, 1997), pp. 31–54.
La Rocca, C. (ed.), _Italy in the Early Middle Ages, 476–1000_. The Short Oxford History of Italy (Oxford, 2002).
La Rocca, C., and Provero, L., 'The dead and their gifts. The will of Eberhard, count of Friuli, and his wife Gisela, daughter of Louis the Pious (863–864)', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 225–80.
Ladner, G., _The Idea of Reform: Its Impact on Christian Thought and Action in the Age of the Fathers_ (Cambridge, MA, 1959).
Lanfranchi, L., and Strina, B., _Ss. Ilario e Benedetto e Gregorio_ (Venice, 1965).
Lange, W., _Texte zur Bekehrungsgeschichte_ (Tübingen, 1962).
Larrington, C., 'The psychology of emotion and study of the medieval period', _EME_ 10/2 (2001), pp. 251–6.
Lauranson-Rosaz, C., _L'Auvergne et ses marges du VIIIe aux XIe siècles: La Fin du monde antique?_ (Le Puy en Velay, 1987).
Lauwers, M., 'Le Cimetière dans le Moyen Âge latin: Lieu sacré, saint et religieux', _Annales HSS_ 54 (1999), pp. 1047–72.
Le Jan, R., 'Convents, violence, and competition for power in seventhcentury Francia', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 243–69.
—, _Famille et pouvoir dans le monde franc, VIIIe-Xe siècles_ (Paris, 1995).
—, 'Frankish giving of arms and rituals of power: continuity and change in the Carolingian period', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 281–309.
—, 'Die Sakralität der Merowinger oder: Mehrdeutigkeiten der Geschichtsschreibung', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 73–92.
—, 'Structures familiales et politiques au IXe siécle: un groupe familial de l'aristocratie franque', _Revue historique_ 265 (1981), pp. 289–333.
Le Jan, R. (ed.), _La Royauté et les élites dans l'Europe carolingienne (du début du IXe siècle aux environs de 920_), Centre de l'Europe du Nord-Ouest 17 (Lille, 1998).
Lebecq, S., _Marchands et navigateurs. Frisons du haut moyen âge_ (Lille, 1983).
—, 'On the use of the word Frisian in the 6th to 10th centuries: some interpretations', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 85–90.
—, 'The role of the monasteries in the systems of production and exchange of the Frankish world between the seventh and the beginning of the ninth centuries', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 121–48.
Levison, W., _England and the Continent in the Eighth Century_ (Oxford, 1946).
Lewit, T., _Agricultural Production in the Roman Economy AD 200–400_, British Archaeological Reports International Series 568 (Oxford, 1991).
—, 'Pigs, presses and pastoralism: farming in the fifth to seventh centuries', _EME_ 17 (2009), pp. 77–91.
—, '"Vanishing villas": what happened to elite rural habitation in the west in the fifth–sixth centuries?', _Journal of Roman Archaeology_ 16 (2003), pp. 26–74.
Leyser, K., 'Concepts of Europe in the early and high middle ages', _P &P_ 137, pp. 25–47, repr. in Leyser, _Communications and Power in Medieval Europe: The Carolingian and Ottonian Centuries_ (London, 1994), pp. 1–18.
—, 'Early medieval canon law and the beginning of knighthood', in K. Leyser (ed. T. Reuter), _Communications and Power in Medieval Europe. The Carolingian and Ottonian Centuries_ (London and Rio Grande, OH, 1984), pp. 51–71, first published in L. Fenske, W. Rösener and T. Zotz (eds.), _Institutionen, Kultur und Gesellschaft im Mittelalter. Festschrift für Josef Fleckenstein zu seinem 65. Geburtstag_ (Sigmaringen, 1984), pp. 549–66.
Linehan, P., and J. L. Nelson (eds.), _The Medieval World_ (London, 2001).
Little, L. K., and Rosenwein, B. H. (eds.), _Debating the Middle Ages. Issues and Readings_ (Oxford, 1998).
Lobbedey, U., 'Carolingian royal palaces: the state of research from an architectural historian's viewpoint', in C. Cubitt (ed.), _Court Culture in the Early Middle Ages_ (Turnhout, 2003), pp. 129–54.
Lohrmann, D., 'Trois palais royaux de la valléxe de l'Oise d'après les travaux des érudits mauristes: Compiégne, Choisy-au-Bac et Quierzy', _Francia_ 4 (1976), pp. 121–40.
Lopez, R. S., and Raymond, I. W., _Medieval Trade in the Mediterranean World: Illustrative Documents_ (London and New York, 1955).
Lorren, C., 'Le Village de Saint-Martin de Mondeville de l'antiquité au haut moyen âge', in H. Atsma (ed.), _La Neustrie. Le Pays au nord de la Loire de 650 à 850_ , Beihefte der Francia 16, 2 vols. (Sigmaringen, 1989), II, pp. 439–66.
Loseby, S., 'Marseille and the Pirenne thesis I: Gregory of Tours, the Merovingian kings, and "un grand port"', in Hodges and Bowden (eds.), _The Sixth Century_ , pp. 203–29.
—, 'Marseille and the Pirenne thesis II: "ville morte"', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 167–94.
Loveluck, C., 'Rural settlement hierarchy in the age of Charlemagne', in Story (ed.), _Charlemagne_ , pp. 230–58.
Loyn, H. R., and Percival, J., _The Reign of Charlemagne: Documents on Carolingian Government and Administration_ (London, 1975).
Lund, N., 'Allies of God or man? The Viking expansion in European perspective', _Viator_ 20 (1989), pp. 45–59.
—, 'Peace and non-peace in the Viking age', in J. E. Knirk (ed.), _Proceedings of the Tenth Viking Congress_ (Oslo, 1987), pp. 255–69.
Lund, N. (ed.), _Two Voyagers at the Court of King Alfred_ (York, 1984).
Lynch, J., _Godparents and Kinship in Early Medieval Europe_ (Princeton, NJ, 1986).
Lyon, B., _Henri Pirenne: A Biographical and Intellectual Study_ (Ghent, 1974).
MacCulloch, D., _Reformation. Europe's House Divided, 1490–1700_ (London, 2003).
MacLean, S., '"After his death a great tribulation came to Italy..." Dynastic politics and aristocratic factions after the death of Louis II, c.870– c.890', _Millennium Jahrbuch_ 4 (2007), pp. 239–60.
—, 'Apocalypse and revolution: Europe around the year 1000', _EME_ 15 (2007), pp. 86–106.
—, 'The Carolingian response to the revolt of Boso, 879–87', _EME_ 10 (2001), pp. 21–48.
—, 'Charles the Fat and the Viking Great Army: the military explanation for the end of the Carolingian empire', _War Studies Journal_ 3 (1998), pp. 74–95.
—, _History and Politics in Late Carolingian and Ottonian Europe: the Chronicle of Regino of Prüm and Adalbert of Magdeburg_ (Manchester, 2009).
—, 'Insinuation, censorship and the struggle for late Carolingian Lotharingia in Regino of Prüm's _Chronicle', EHR_ 124 (2009), pp. 1–28.
—, _Kingship and Politics in the Late Ninth Century: Charles the Fat and the End of the Carolingian Empire_ (Cambridge, 2003).
—, 'Queenship, nunneries and royal widowhood in Carolingian Europe', _P &P_ 178 (2003), pp. 3–38.
—, 'Ritual, misunderstanding and the contest for meaning: representations of the disrupted royal assembly at Frankfurt (873)', in B. Weiler and S. MacLean (eds.), _Representations of Power in Medieval Germany_ (Turnhout, 2006), pp. 97–120.
Macy, G., 'Was there a "Church" in the Middle Ages?', in R. Swanson (ed.), _Unity and Diversity in the Church_ , Studies in Church History 52 (Oxford, 1996), pp. 107–16.
Magdalino, P., 'The distance of the past in early medieval Byzantium (VII-X centuries)', in _Ideologie e pratiche del reimpiego nell'alto medioevo_ , Settimane di Studio del Centro italiano di studi sull'alto medioevo 46 (Spoleto, 1999), I, pp. 115–46.
Manacorda, F., _Ricerche sugli inizii della dominazione dei Carolingi in Italia_ (Rome, 1968).
Marenbon, J., 'Candidus', DNB, s.n.
Markus, R., _Gregory the Great and his World_ (Cambridge, 1997).
Martindale, J., 'The kingdom of Aquitaine and the dissolution of the Carolingian fisc', _Francia_ 11 (1985), pp. 131–91.
Matthew, H. C. G., Harrison, B. H., and Goldman, L., _et al_. (eds.), _Oxford Dictionary of National Biography_ (Oxford, 2004).
Matthews, J. F., _Western Aristocracies and the Imperial Court, 364–425_ (Oxford, 1975).
Maund, K. L., '"A turmoil of warring princes": political leadership in ninth-century Denmark', _Haskins Society Journal_ 6 (1994), pp. 29–47.
Mayr-Harting, H., 'Charlemagne, the Saxons and the imperial coronation of 800', _EHR_ 111 (1996), pp. 1113–33.
—, _The Coming of Christianity to Anglo-Saxon England_ (3rd edn, London, 1991).
—, 'Two abbots in politics: Wala of Corbie and Bernard of Clairvaux', _TRHS_ 5th ser. 40 (1990), pp. 217–37.
Mazel, F., 'Des familles de l'aristocratie locale en leurs territories: France de l'ouest, du ixe au xie siècle', in P. Depreux, F. Bougard and R. Le Jan (eds.), _Les Élites et leurs espaces. Mobilité, rayonnement, domination (du VIe au XIe siècle_) (Turnhout, 2007), pp. 361–98.
McClendon, C., _The Imperial Abbey of Farfa_ (New Haven, CT, 1987).
McCormick, M., 'Complexity, chronology and context in the early medieval economy', _EME_ 12 (2003), pp. 307–23.
—, 'Molecular Middle Ages: early medieval economic history in the 21st century', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 83–98.
—, 'New light on the "dark ages": how the slave trade fuelled the Carolingian economy', _P &P_ 177 (2002), pp. 17–54.
—, _Origins of the European Economy. Communications and Commerce AD 600–900_ (Cambridge, 2001).
—, 'Pippin III, the embassy of Caliph al Mansur, and the Mediterranean World', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 221–41.
—, 'Textes, images et iconoclasme dans le cadre des relations entre Byzance et l'occident', _Testo e immagine nell'alto medioevo_ , Settimane di Studio del Centro italiano di studi sull'alto medioevo 41 (Spoleto, 1994), pp. 95–162.
—, 'Toward a molecular history of the Justinianic pandemic', in L. K. Little (ed.), _Plague and the End of Antiquity. The Pandemic of 541–750_ (Cambridge, 2007), pp. 290–312.
McCormick, M., P. Dutton and J. Mayewski, 'Volcanoes and the climate forcing of Carolingian Europe AD 750–950', _Speculum_ 82 (2007), pp. 865–96.
McGrail, S. (ed.), _Maritime Celts, Frisians and Saxons_ (London, 1990).
McKeon, P., _Hincmar of Laon and Carolingian Politics_ (Urbana, IL, 1978).
McKitterick, R., _Anglo-Saxon Missionaries in Germany: Personal Connections and Local Influences_ , Vaughan Paper 36 (Brixworth, 1991), repr. in McKitterick, _Books, Scribes and Learning in the Frankish Kingdoms, 6th–9th Centuries_ (Aldershot, 1994).
—, 'Carolingian book production: some problems', _The Library_ , 6th ser., 12 (1990), pp. 1–33, repr. in McKitterick, _Books, Scribes and Learning in the Frankish Kingdoms, 6th-9th Centuries_ (Aldershot, 1994).
— (ed.), _Carolingian Culture: Emulation and Innovation_ (Cambridge, 1994).
—, 'The Carolingian renaissance of culture and learning', in Story (ed.), _Charlemagne_ , pp. 151–166.
—, _The Carolingians and the Written Word_ (Cambridge, 1989).
—, _Charlemagne: The Formation of a European Identity_ (Cambridge, 2008).
—, 'Constructing the past in the early Middle Ages: the case of the Royal Frankish Annals', _TRHS_ 6th ser. 7 (1999), pp. 101–29.
—, _The Frankish Church and the Carolingian Reforms, 789–895_ (London, 1977).
—, _The Frankish Kingdoms under the Carolingians, 751–987_ (London and New York, 1983).
—, _History and Memory in the Carolingian World_ (Cambridge, 2004).
—, 'Paul the Deacon and the Franks', _EME_ 8 (1999), pp. 319–39.
—, _Perceptions of the Past in the Early Middle Ages_ (Notre Dame, IN, 2006).
—, 'Political ideology in Carolingian historiography', in Hen and Innes (eds.), _Uses of the Past_ , pp. 162–74.
—, 'Script and book production', in McKitterick (ed.), _Carolingian Culture_ , pp. 221–247.
—, 'Some Carolingian law-books and their function', in B. Tierney and P. Linehan (eds.), _Authority and Power. Studies in Medieval Law and Government Presented to Walter Ullman_ (Cambridge, 1984), pp. 13–27, repr. in McKitterick, _Books, Scribes and Learning in the Frankish Kingdoms, 6th-9th Centuries_ (Aldershot, 1994).
—, 'Unity and diversity in the Carolingian church', in R. Swanson (ed.), _Unity and Diversity in the Church_ , Studies in Church History 32 (Oxford, 1996), pp. 59–82.
—, 'Zur Herstellung von Kapitularien: Die Arbeit des Leges-Skriptoriums', _Mitteilungen des Instituts für Österreichische Geschichtsforschung_ 101 (1993), pp. 3–16.
McKitterick, R. (ed.), _The New Cambridge Medieval History_ , II _c.700–c.900_ (Cambridge, 1995).
McLaughlin, M., _Consorting with Saints: Prayer for the Dead in Early Medieval France_ (Ithaca, NY, and London, 1994).
McNamara, J., 'A legacy of miracles: hagiography and nunneries in Merovingian Gaul', in J. Kirshner and S. Wemple (eds.), _Women of the Medieval World. Essays in Honour of John H. Mundy_ (Oxford, 1985), pp. 36–52.
McNeill, J. T., and Gamer, H. A. (eds.), _Medieval Handbooks of Penance_ (New York, 1990).
Meaney, A., 'Magic', in M. Lapidge, _et al_. (eds.), _The Blackwell Encyclopedia of Anglo-Saxon England_ (Oxford, 1999), pp. 298–9.
Meens, R., 'The frequency and nature of early medieval penance', in P. Biller and A. Minns (eds.), _Handling Sin: Confession in the Middle Ages_ (Woodbridge, 1998), pp. 35–61.
Metcalf, M., 'A sketch of the currency in the time of Charles the Bald', in M. T. Gibson and J. L. Nelson (eds.), _Charles the Bald: Court and Kingdom_ (2nd edn, Aldershot, 1991), pp. 65–97.
Metz, W., _Das Karolingische Reichsgut_ (Berlin, 1960).
Meulengracht Sørensen, P., 'Religions old and new', in Sawyer (ed.), _The Oxford Illustrated History of the Vikings_ , pp. 202–24.
Michelet, F. L., _Creation, Migration and Conquest. Imaginary Geography and the Sense of Space in Old English Literature_ (Oxford, 2006).
Miller, M., 'Final stages in the construction of the Harleian _Annales Cambriae', Journal of Celtic Studies_ 4 (2004), pp. 205–11.
Miller, W. I., 'Gift, sale, payment, raid: case studies in the negotiation and classification of exchange in medieval Iceland', _Speculum_ 61 (1986), pp. 18–50.
Moesgaard, J. C., 'A survey of coin production and currency in Normandy, 864–945', in J. Graham-Campbell and G. Williams (eds.), _Silver Economy of the Viking Age_ (Walnut Creek, CA, 2007), pp. 99–121.
Moore, R. I., 'Literacy and the making of heresy c.1000–c.1150', in P. Biller and A. Hudson (eds.), _Heresy and Literacy, 1000–1530_ (Cambridge, 1994), pp. 19–37, repr. in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 163–75.
Mordek, H., 'Ein exemplarischer Rechtstreit: Hinkmar von Reims und das Landgut Neuilly-Saint-Front', _Zeitschrift der Savigny-Stiftung für Rechtsgeschichte, Kanonistische Abteilung_ 83 (1997), pp. 86–112.
Moreland, J., 'Concepts of the early medieval economy', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 1–34.
Morimoto, Y., _Études sur l'économie rurale du haut moyen âge: historiographie, régime domanial, polyptyques carolingiens_ (Paris, 2008).
Morrison, K. F., _Carolingian Coinage_ (New York, 1967).
Morrissey, R. J., _Charlemagne and France: A Thousand Years of Mythology_ (Notre Dame, IN, 2003).
Morton, A. D., _Excavations at Hamwic_ I (London, 1992).
Morton, A., 'Hamwic in its context', in Anderton (ed.), _Anglo-Saxon Trading Centres_ , pp. 48–62.
Müller-Mertens, E., _Karl der Große, Ludwig der Fromme und die Freien. Wer waren die_ liberi homines _der karolingischen Kapitularien (742/3–832)? Ein Beitrag zur Sozialgeschichte und Sozialpolitik des Frankenreiches_ , Forschungen zur mittelalterlichen Geschichte 10 (Berlin, 1963).
Müller-Wille, M., 'Fremdgut und import östlicher Provenienz in Schleswig-Holstein (9.-12. Jahrhundert)', _Bericht der römischgermanischen Kommission_ 69 (1988), pp. 740–83.
Müller-Wille, M., Tummuscheit. A., and Hansen, L., _Fruhstädtliche Zentren der Wikingerzeit und ihr Hinterland. Die Beispiele Ribe, Hedeby und Reric_ (Göttingen, 2002).
Murray, A. C., 'From Roman to Frankish Gaul: _centenae_ and _centenarii_ in the administration of the Merovingian kingdom', _Traditio_ 44 (1988), pp. 59–100.
—, _'Pax et disciplina_. Roman public law and the Merovingian state', in K. Pennington, S. Chodorow and K. H. Kendall (eds.), _Proceedings of the Tenth International Congress of Medieval Canon Law_ (Vatican City, 2001), pp. 269–85, repr. in T. F. X. Noble (ed.), _From Roman Provinces to Medieval Kingdoms_ (New York and Abingdon, 2006), pp. 376–88.
Myhre, B., 'The archaeology of the early Viking age in Norway', in H. B. Clarke, M. Ní Mhaonaigh and R. Ó Floinn (eds.), _Ireland and Scandinavia in the Early Viking Age_ (Dublin, 1998), pp. 3–36.
Näsman, U., 'Exchange and politics: the eighth–early ninth century in Denmark', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 35–68.
Nehlsen, H., 'Zur Aktualität und Effektivität germanischer Rechtsaufzeichnungen', in P. Classen (ed.), _Recht und Schrift im Mittelalter_ (Sigmaringen, 1977), pp. 449–502.
Nehlsen-von Stryck, K., _Die boni homines des frühen Mittelalters unter besonderer Berücksichtigung der fränkischen Quellen_ , Freiburger Rechtsgeschichtlichen Abhandlungen 2 (Berlin, 1981).
Nelson, J. L., 'Aachen as a place of power', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 217–41.
—, 'Bertrada', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 93–108.
—, 'Carolingian royal funerals', in Theuws and Nelson (eds.), _Rituals of Power_ , pp. 131–84.
—, 'Carolingian royal ritual', in D. Cannadine and S. Price (eds.), _Rituals of Royalty. Power and Ceremonial in Traditional Societies_ (Cambridge, 1987), pp. 137–80.
—, 'Charlemagne's church at Aachen', _History Today_ (Jan. 1998), pp. 62–3.
—, 'Charlemagne and empire', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 223–34.
—, 'Charlemagne the man', in Story (ed.), _Charlemagne_ , pp. 22–37.
—, 'Charlemagne and the paradoxes of power', _Reuter Lecture_ (University of Southampton, 2006).
—, 'Charlemagne: pater optimus?', in Godman, Jarnut and Johanek (eds.), _Am Vorabend der Kaiserkrönung_ , pp. 271–83.
—, _Charles the Bald_ (London and New York, 1992).
—, 'Charles le Chauve et les utilisations du savoir', in D. Iogna-Prat, C. Jeudy and G. Lobrichon (eds.), _L'École carolingienne d'Auxerre_ (Paris, 1991), pp. 37–54, repr. as no. VII in Nelson, _Rulers and Ruling Families_.
— 'The Church's military service in the ninth century: a contemporary comparative view?', in W. J. Shiels (ed.), _The Church and War, Studies in Church History_ 20 (1983), pp. 15–30, repr. in Nelson, _Politics and Ritual_ , pp. 117–32.
—, 'La Cour impériale de Charlemagne', in R. Le Jan (ed.), _La Royauté_ , pp. 177–91; repr. in Nelson, _Rulers and Ruling Families_.
—, 'Dispute settlement in Carolingian west Francia', in Davies and Fouracre (eds.), _Settlement of Disputes_ , pp. 45–64.
—, 'Early medieval rites of queen-making and the shaping of medieval queenship', in Anne J. Duggan (ed.), _Queens and Queenship in Medieval Europe_ (Woodbridge, 1997), pp. 301–15.
—, 'England and the continent in the ninth century: II, Vikings and others', _TRHS_ 6th ser. 13 (2003), pp. 1–28.
—, 'The Frankish kingdoms, 814–898: the west', in _NCMH_ II, pp. 110–41.
—, _The Frankish World, 750–900_ (London, 1996).
—, 'Gender and genre in women historians', in J.-P. Genet (ed.), _L'Historiographie médiévale en Europe_ , Éditions du CNRS (Paris, 1991), pp. 149–63, repr. in Nelson, _Frankish World_ , pp. 183–97.
—, 'Gendering courts in the early medieval west', in Brubaker and Smith (eds.), _Gender in the Early Medieval World_ , pp. 185–97.
—, 'The intellectual in politics: contexts, content and authorship in the Capitulary of Coulaines, November 843', in L. Smith and B. Ward (eds.), _Intellectual Life in the Middle Ages: Essays Presented to Margaret Gibson_ (London, 1992), pp. 1–14, repr. in Nelson, _The Frankish World_ , pp. 155–68.
—, 'Kingship and empire in the Carolingian world', in McKitterick (ed.), _Carolingian Culture_ , pp. 52–87.
—, 'Kingship, law and liturgy in the political thought of Hincmar of Rheims', _EHR_ 92 (1977), pp. 241–79.
—, 'The last years of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 147–59.
—, 'Legislation and consensus in the reign of Charles the Bald', in P. Wormald, D. Bullough and R. Collins (eds.), _Ideal and Reality in Frankish and Anglo-Saxon Society_ (Oxford, 1983), pp. 202–27; repr. in Nelson, _Politics and Ritual_.
—, 'Literacy in Carolingian government', in R. McKitterick (ed.), _The Uses of Literacy in Early Medieval Europe_ (Cambridge, 1990), pp. 258–96.
—, 'The Lord's anointed and the people's choice: Carolingian royal ritual', in D. Cannadine and S. Price (eds.), _Rituals of Royalty_ (Cambridge, 1987), pp. 137–80; repr. in Nelson, _Frankish World_ , pp. 99–131.
—, 'Making a difference in eighth-century politics: the daughters of Desiderius', in A. C. Murray (ed.), _After Rome's Fall: Narrators and Sources of Early Medieval History. Essays presented to Walter Goffart_ (Toronto, 1998), pp. 171–90.
—, 'Monks, secular men and masculinity, c.900', in D. M. Hadley (ed.), _Masculinity in Medieval Europe_ (London, 1999), pp. 121–42.
—, 'Ninth-century knighthood: the evidence of Nithard', in C. Harper-Bill, C. Holdsworth and J. L. Nelson (eds.), _Studies in Medieval History Presented to R. Allen Brown_ (Woodbridge, 1989), pp. 255–66, repr. in Nelson, _Frankish World_ , pp. 75–87.
—, _Opposition to Charlemagne_ (German Historical Institute, London, 2008).
—, _Politics and Ritual in Early Medieval Europe_ (London, 1986).
—, 'Public _Histories_ and private history in the work of Nithard', _Speculum_ 50 (1985), pp. 251–93, repr. in Nelson, _Politics and Ritual_ , pp. 195–237.
—, 'Queens as Jezebels: Brunhild and Balthild in Merovingian history', in D. Baker (ed.), _Medieval Women: Essays Dedicated and Presented to Professor Rosalind M. T. Hill_ , Studies in Church History: Subsidia 1 (Oxford, 1978), pp. 31–77, repr. in Nelson, _Politics and Ritual_ , pp. 1–48, and in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 219–53.
—, 'Rewriting the history of the Franks', in Nelson, _Frankish World_ , pp. 169–83.
—, _Rulers and Ruling Families in Early Medieval Europe: Alfred, Charles the Bald and Others_ (Aldershot, 1999).
—, 'The search for peace in a time of war: the Carolingian _Brüderkrieg_ , 840–843', in J. Fried (ed.), _Träger und Instrumentarien des Friedens im hohen und späten Mittelalter_ (Sigmaringen, 1996), pp. 87–114.
—, 'A tale of two princes: politics, text and ideology in a Carolingian annal', _Studies in Medieval and Renaissance History_ 10 (1988), pp. 103–40; repr. in Nelson, Rulers and Ruling Families.
—, 'Violence in the Carolingian world and the ritualization of ninthcentury warfare', in G. Halsall (ed.), _Violence and Society in the Early Medieval West_ (Woodbridge, 1998), pp. 90–107.
—, 'The voice of Charlemagne', in R. Gameson and H. Leyser (eds.), _Belief and Culture in the Middle Ages: Studies Presented to Henry Mayr-Harting_ (Oxford, 2001), pp. 76–88.
—, 'The wary widow', in W. Davies and P. Fouracre (eds.), _Property and Power in the Early Middle Ages_ (Cambridge, 1995), pp. 82–113.
—, 'Was Charlemagne's court a courtly society?', in C. Cubitt (ed.), _Court Culture in the Earlier Middle Ages_ (Turnhout, 2003), pp. 39–57.
—, 'Why are there so many different accounts of Charlemagne's imperial coronation?', in Nelson, _Courts, Elites and Gendered Power in the Early Middle Ages: Charlemagne and Others_ (Aldershot, 2007), no. XII.
—, 'Women at the court of Charlemagne: a case of Monstrous Regiment?', in J. C. Parsons (ed.), _Medieval Queenship_ (New York, 1993), pp. 43–61, repr. in Nelson, _Frankish World_ , pp. 223–42.
Noble, T. F. X., 'From brigandage to justice: Charlemagne, 785–794', in C. M. Chazelle (ed.), _Literacy, Politics, and Artistic Innovation in the Early Medieval West_ (Lanham, MD, 1992), pp. 49–76.
—, _Images, Iconoclasm and the Carolingians_ (Philadelphia, PA, 2009).
—, 'Louis the Pious and his piety reconsidered', _Revue Belge_ 58 (1980), pp. 297–316.
—, 'Lupus of Ferriéres in his Carolingian context', in A. C. Murray (ed.), _Rome's Fall and after. Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 232–250.
—, 'The monastic ideal as a model for empire: the case of Louis the Pious', _Revue Bénédictine_ 86 (1976), pp. 235–50.
—, 'Paradoxes and possibilities in the sources for Roman society in the early middle ages', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 55–83.
—, _The Republic of St Peter. The Birth of the Papal State, 680–825_ (Philadelphia, PA, 1984).
—, 'The revolt of King Bernard of Italy in 817: its causes and consequences', _Studi Medievali_ 15 (1974), pp. 315–26.
—, 'Secular sanctity: forging an ethos for the Carolingian nobility', in Wormald and Nelson (eds.), _Lay Intellectuals_ , pp. 8–36.
—, 'Topography, celebration and power: the making of a papal Rome in the eighth and ninth centuries', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 45–92.
Nonn, U., 'Merowingische Testamente', _Archiv für Diplomatik_ 18 (1972), pp. 1–129.
Odegaard, C. E., 'The empress Engelberge', _Speculum_ 26 (1951), pp. 77–103.
Oexle, O. G., _'Coniuratio_ und Gilde im frühen Mittelalter', in B. Schwineköper (ed.), _Gilden und Zünfte: kaufmännische und gewerbliche Genossenschaften im frühen und hohen Mittelalter_ (Sigmaringen, 1985), pp. 151–213.
—, 'Tria genera hominum. Zur Geschichte eines Deutungsschemas der sozialen Wirklichkeit in Antike und Mittelalter', in L. Fenske, _et al_. (eds.), _Institutionen, Gesellschaft und Kultur im Mittelalter. Festschrift Josef Fleckenstein_ (Sigmaringen, 1984), pp. 483–99.
_Olio e Vino in Alto Medioevo, Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 54 (Spoleto, 2007).
Orchard, A., _A Critical Companion to 'Beowulf'_ (Woodbridge, 2004).
Palmer, J., 'Defining paganism in the Carolingian world', _EME_ 15 (2007), pp. 402–25.
—, 'Rimbert's _Vita Anskarii_ and Scandinavian mission in the ninth century', _Journal of Ecclesiastical History_ 55 (2004), pp. 235–56.
—, 'The "vigorous rule" of Bishop Lull: between Bonifatian mission and Carolingian church control', _EME_ 13/3 (2005), pp. 249–76.
Patze, H., and Schwind, F. (eds.), _Ausgewählte Aufsätze von W. Schlesinger 1965–1979_ (Sigmaringen, 1987).
Patzold, S., 'Die Bischöfe im karolingischen Staat. Praktisches Wissen über die politische Ordnung im Frankenreich des 9. Jahrhunderts', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 133–62.
—, 'Eine "loyale Palastrebellion" der "Reichseinheitspartei"? Zur "Divisio imperii" von 817 und zu den Ursachen des Aufstands gegen Ludwig den Frommen im Jahre 830', _Frühmittelalterliche Studien_ 40 (2006), pp. 43–77.
—, 'Redéfinir l'office épiscopal: les évêques francs face à la crise des années 820/30', in F. Bougard, L. Feller and R. Le Jan (eds.), _Les Élites au haut Moyen Âge. Crises et renouvellements_ (Turnhout, 2006), pp. 337–59.
Paxton, F. S., _Christianizing Death: The Creation of a Ritual Process in Early Medieval Europe_ (Ithaca and London, 1990).
Pearson, K. L. R., _Conflicting Loyalties in Early Medieval Bavaria: a View of Socio-Political Interaction, 680–900_ (Aldershot, 1999).
Percival, J., _The Roman Villa_ (London, 1976).
Périn, P., 'The origins of the village in early medieval Gaul', in Christie (ed.), _Landscapes of Change_ , pp. 255–78.
Perrin, C.-E., 'Observations sur la manse dans la region parisienne au début du IXe siécle', _Annales_ 8 (1945), pp. 39–51.
Peters, E., _Monks, Bishops and Pagans_ (Philadelphia, PA, 1975).
—, _The Shadow King_. Rex inutilis _in Medieval Law and Literature, 751–1327_ (New Haven, CT, 1970).
Petersohn, J., 'Saint-Denis – Westminster – Aachen. Die Karls-Translatio von 1165 und ihre Vorbilder', _Deutsches Archiv für Erforschung des Mittelalters_ 31 (1975), pp. 420–54.
Pirenne, H., _Mahomet et Charlemagne_ (Brussels, 1937), trans. B. Miall, _Mohammed and Charlemagne_ (London, 1939).
Pizarro, J. M., _Writing Ravenna. The_ Liber pontificalis _of Andreas Agnellus_ (Ann Arbor, MI, 1995).
Plassmann, A., 'Mittelalterliche _origines gentium_. Paulus Diaconus als Beispiel', _QFIAB_ 87 (2007), pp. 1–35.
Pohl, W., 'Paolo Diacono e la costruzione dell'identità longobarda', in P. Chiesa (ed.), _Paolo Diacono. Uno scrittore fra tradizione longobarda e rinnovamento carolingio_ (Udine, 2000), pp. 413–26.
—, 'Das Papsttum und die Langobarden', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 145–61.
—, 'Paulus Diaconus und die "Historia langobardorum": Text und Tradition', in A. Scharer and G. Scheibelreiter (eds.), _Historiographie im frühen Mittelalter_ , Veröffentlichungen des instituts für (Österreichische Geschichtsforschung 32 (Vienna and Munich, 1994), pp. 375–405.
—, 'Staat und Herrschaft im Frühmittelalter: Überlegungen zum Forschungsstand', in S. Airlie, W. Pohl and H. Reimitz (eds.), _Staat im Frühen Mittelalter_ , pp. 9–38.
—, 'Telling the difference: signs of ethnic identity', in W. Pohl and H. Reimitz (eds.), _Strategies of Distinction. The Construction of Ethnic Communities, 300–800_. Transformation of the Roman World 2 (Leiden, 1998), pp. 17–69.
Pohl, W., and Reimitz, H. (eds.), _Grenze und Differenz im frühen Mittelalter_ , Denkschriften ((Österreichische Akademie der Wissenschaften. Philosophisch-Historische Klasse). Forschungen zur Geschichte des Mittelalters 1 (Vienna, 2000).
—, _Strategies of Distinction. The Construction of Ethnic Communities, 300–800_. Transformation of the Roman World 2 (Leiden, 1998).
Pohl, W., Wood, I., and Reimitz, H. (eds.), _The Transformation of Frontiers from Late Antiquity to the Carolingians_ (Leiden, Boston and Cologne, 2001).
Polanyi, K., 'The economy as instituted process', in K. Polanyi, C. Arensberg and H. Pearson (eds.), _Trade and Market in Early Empires_ (Glencoe, IL, 1957), pp. 243–69.
Pössel, C., 'Authors and recipients of Carolingian Capitularies, 779–829', in R. Corradini, R. Meens, C. Pössel and P. Shaw (eds.), _Texts and Identities in the Early Middle Ages_ (Vienna, 2006), pp. 253–74.
Pratt, D., _The Political Thought of King Alfred the Great_ (Cambridge, 2007).
Raaijmakers, J., 'Memory and identity: the _Annales necrologici_ of Fulda', in R. Corradini, R. Meens, C. Pössel and P. Shaw (eds.), _Texts and Identities in the Early Middle Ages_ , Forschungen zur Geschichte des Mittelalters 12 (Vienna, 2006), pp. 303–22.
Reimitz, H., 'The art of truth. Historiography and identity in the Frankish world', in R. Corradini, R. Meens, C. Pössel and P. Shaw (eds.), _Texts and Identities in the Early Middle Ages_ (Vienna, 2006), pp. 87–104.
—, 'Conversion and control: the establishment of liturgical frontiers in Carolingian Pannonia', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_ , pp. 188–207.
—, 'Ein fränkisches Geschichtsbuch aus Saint-Amand und der Codex Vindobonensis palat. 473', in C. Egger and H. Weigl (eds.), _Text-Schrift-Codex. Quellenkundliche Arbeiten aus dem institutfür Österreichische Geschichtsforschung_ , MIÖG Ergänzungsband 35 (Vienna and Munich, 2000), pp. 34–90.
Reuter, T., 'Assembly politics in western Europe from the eighth century to the twelfth', in Linehan and Nelson (eds.), _The Medieval World_ , pp. 432–50; repr. in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 193–216.
—, 'Carolingian and Ottonian warfare', in M. Keen (ed.), _Medieval Warfare: A History_ (Oxford, 1999), pp. 13–35.
—, 'Charlemagne and the world beyond the Rhine', in Story (ed.), _Charlemagne_ , pp. 183–94.
—, 'Debate. The "Feudal Revolution"', _P &P_ 155 (1997), pp. 177–95.
—, 'The end of Carolingian military expansion', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 391–405; repr. in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 251–67.
—, _Germany in the Early Middle Ages 800–1056_ (London and New York, 1991).
—, 'The medieval nobility in twentieth-century historiography', in M. Bentley (ed.), _Companion to Historiography_ (London, 1997), pp. 177–202.
—, _Medieval Polities and Modern Mentalities_ , ed. J. L. Nelson (Cambridge, 2006).
—, 'Nobles and others: the social and cultural expression of power relations in the Middle Ages', in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 111–26.
—, 'Plunder and tribute in the Carolingian empire', _TRHS_ 5th ser. 35 (1985), pp. 75–94; repr. in Reuter, _Medieval Polities and Modern Mentalities_ , pp. 321–50.
Reuter, T. (ed.), _The Medieval Nobility: Studies on the Ruling Classes of France and Germany from the Sixth to the Twelfth Century_ (Amsterdam, 1979).
—, _The New Cambridge Medieval History_ , III: _c.900–c.1024_ (Cambridge, 1999).
Reynolds, R., 'The organisation, law and liturgy of the western church, 700–900', in _NCMH_ II, pp. 587–621.
Reynolds, S., _Fiefs and Vassals: the Medieval Evidence Reconsidered_ (Oxford, 1996).
—, _Kingdoms and Communities in Western Europe, 900–1300_ (Oxford, 1997).
Rhijn, C. van, _Shepherds of the Lord. Priests and Episcopal Statutes in the Carolingian Period_ (Turnhout, 2007).
Rhijn, C. van, and Saan, M., 'Correcting sinners, correcting texts: a context for the _Paenitentiale pseudo-Theodori'_ , _EME_ 14/1 (2006), pp. 23–40.
Riché, P., _Les Carolingiens: une famille qui fit l'Europe_ (Paris, 1983), trans. M. I. Allen, _The Carolingians: A Family who Forged Europe_ (Philadelphia, PA, 1993).
—, _Daily Life in the World of Charlemagne_ , trans. J. A. McNamara (Liverpool, 1978).
Rio, A., _The Formularies of Angers and Marculf: Two Merovingian Legal Handbooks_ (Liverpool, 2008).
— 'Freedom and unfreedom in early medieval Francia: the evidence of the legal formularies', _P &P_ 193 (2006), pp. 7–40.
—, 'High and low: ties of dependence in the Frankish kingdoms', _TRHS_ 6th ser., 18 (2008), pp. 43–68.
—, _Legal Practice and the Written Word in the Early Middle Ages: Frankish Formulae, c.500–1000_ (Cambridge, 2009).
Ripoll, G., and Arce, J., 'The transformation and end of Roman _villae_ in the west (fourth–seventh centuries): problems and perspectives', in G. P. Brogiolo, N. Gautier and N. Christie (eds.), _Towns and their Territories from Late Antiquity to the Early Middle Ages_ (Leiden, 2000), pp. 63–114.
Rösener, W. (ed.), _Strukturen der Grundherrschaft im frühen Mittelalter_ , VMPIG 92 (Göttingen, 1989).
Rosenwein, B. H., 'The family politics of Berengar I, king of Italy (888–924)', _Speculum_ 71 (1996), pp. 247–89.
—, _Negotiating Space: Power, Restraint and Privileges of Immunity in Early Medieval Europe_ (Manchester, 1999).
Rouche, M., 'Géographie rurale du royaume de Charles le Chauve', in J. L. Nelson and M. Gibson, _Charles the Bald: Court and Kingdom_ (2nd edn, Aldershot, 1991), pp. 189–202.
Rovelli, A., 'Coins and trade in early medieval Italy', _EME_ 17 (2009), pp. 45–76.
—, 'Economia monetaria e monete nel dossier di Campione', in Gasparri and La Rocca (eds.), _Carte di famiglia_ , pp. 117–40.
—, 'Emissione e uso della moneta: le testimonianze scritte e archeologiche', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 48 (Spoleto, 2001), pp. 821–52.
—, 'Some considerations on the coinage of Lombard and Carolingian Italy', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 195–223.
Rubin, M., _Corpus Christi: the Eucharist in Late Medieval Culture_ (Cambridge, 1991).
Samson, R., 'Carolingian palaces and the poverty of ideology', in M. Locock (ed.), _Meaningful Architecture: Social Interpretations of Buildings_ (Aldershot, 1994) pp. 99–131.
—, 'The Merovingian nobleman's house: castle or villa', _Journal of Medieval History_ 13 (1987), pp 287–315.
Sarris, P., _Economy and Society in the Age of Justinian_ (Cambridge, 2007).
—, 'The origins of the manorial economy: new insights from Late Antiquity', _EHR_ 119 (2004), pp. 279–311.
Sarris, P., and Banaji, J. (eds.), _Aristocrats, Peasants and the Transformation of Rural Society c.400–800_ , special issue of the _Journal of Agrarian Change_ 9.1 (2009), pp. 1–153.
Sato, S., 'The Merovingian accounting documents of Tours: form and function', _EME_ 9/2 (2003), pp. 143–61.
Sawyer, P. H., _The Age of the Vikings_ (London, 1962, 2nd edn 1971).
—, 'Kings and merchants', in P. H. Sawyer and I. N. Wood (eds.), _Early Medieval Kingship_ (Leeds, 1977), pp. 139–58.
Sawyer, P. (ed.), _The Oxford Illustrated History of the Vikings_ (Oxford, 1997).
Scharf, I., 'Studien zur Smaragdus und Jonas', _Deutsches Archiv für Erforschung des Mittelalters_ 17 (1961), pp. 333–84.
Schieffer, R., 'Charlemagne and Rome', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 279–95.
—, '"Die folgenschwerste Tat des ganzen Mittelalters"? Aspekte des wissenschaftlichen Urteils über den Dynastiewechsel von 751', in Becher and Jarnut (eds.), _Der Dynastiewechsel von 751_ , pp. 1–14.
—, 'Ludwig "der Fromme". Zur Entstehung eines karolingischen Herrscherbeinamens', _Frühmittelalterliche Studien_ 16 (1982), pp. 58–73.
Schlesinger, W., 'Die Hufe im Frankenreich', in Patze and Schwind (eds.), _Ausgewählte Aufsatze von W. Schlesinger_ , pp. 587–614.
—, 'Hufe und mansus im liber donationem des Klosters Weissenburgs', in Patze and Schwind (eds.), _Ausgewählte Aufsätze von W. Schlesinger_ , pp. 543–85.
—, 'Vorstudien zu einer Untersuchungen über die Hufe', in Patze and Schwind (eds.), _Ausgewählte Aufsätze von W. Schlesinger_ , pp. 458–541.
Schmidt-Weigand, R., 'Das Dorf nach den Stammesrechten des Kontinents', in Jankuhn, _et al_. (eds.), _Das Dorf der Eisenzeit_ , pp. 408–43.
Schmitt, J., _Untersuchungen zu den Liberi Homines der Karolingerzeit_ (Frankfurt, 1977).
Schmitz, G., 'The capitulary legislation of Louis the Pious', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 425–36.
Schneider, R., _Brüdergemeine und Schwurfreundschaft: der Auflösungsprozess des Karlingerreiches im Spiegel der Caritas-Terminologie in den Verträgen der karlingischen Teilkönige des 9. Jahrhunderts_ (Lübeck, 1964).
Scholz, B., _Carolingian Chronicles_ (Ann Arbor, MI, 1970).
Schramm, P., and Mütherich, F., _Denkmale der deutschen Könige und Kaiser_ , 2nd edn (Munich, 1981).
Schröder, I., 'Zur Überlieferung von _De institutione laicali_ des Jonas von Orléans', _DA_ 44 (1988), pp. 83–97.
Schüssler, H., 'Die fränkische Reichsteilung von Vieux-Poitiers (742) und die Reform der Kirche in den Teilreichen Karlmanns und Pippins', _Francia_ 13 (1985), pp. 45–111.
Schütte, S., 'Continuity problems and authority structures in Cologne', in G. Ausenda (ed.), _After Empire: Towards an Ethnology of Europe's Barbarians_ (San Marino, 1995), pp. 163–76.
Schwind, F., 'Beobachtungen zur inneren Struktur des Dorfes in karolingischer Zeit', in Jankuhn, _et al_. (eds.), _Das Dorf der Eisenzeit_ , pp. 444–93.
—, 'Zu karolingerzeitlichen Klöstern als Wirtschaftsorganismen und Stätten handwerklicher Produktion', in L. Fenske, W Rösener and T. Zotz (eds.), _institutionen, Kultur und Gesellschaft im Mittelalter: Festschrift für Josef Fleckenstein zu seinem 65. Geburtstag_ (Sigmaringen, 1984), pp. 101–23.
Screen, E., 'The importance of the emperor: Lothar I and the Frankish civil war, 840–843', _EME_ 12 (2003), pp. 25–51.
Scull, C., 'Urban centres in pre-Viking England?', in J. Hines (ed.), _The Anglo-Saxons from the Migration Period to the Eighth Century_ (Woodbridge, 1997), pp. 269–310.
Sénac, P., _Musulmans et Sarrasins dans le sud de la Gaule du VIIIe au XIe siécle_ (Paris, 1980).
Sennis, A., 'The power of time: looking at the past in medieval monasteries', in A. Müller and K. Stöber (eds.), _Self-Representation of MedievalReligious Communities: the British Isles in Context_, Vita Regularis, Abhandlungen 40 (Münster, 2009), pp. 307–26.
Sergi, G., 'The kingdom of Italy', in Reuter (ed.), _The New Cambridge Medieval History_ , III, pp. 346–71.
Shanzer, D., 'Dating the baptism of Clovis: the Bishop of Vienne vs the Bishop of Tours', _EME_ 7 (1998), pp. 29–57.
Siems, H., _Handel und Wucher im Spiegel frühmittelalterliche Rechtsquellen_ (Hanover, 1992).
Słupecki, L., _Slavonic Pagan Sanctuaries_ (Warsaw, 1994).
Smith, J. M. H., 'Einhard: the sinner and the saints', _TRHS_ 6th ser. 13 (2003), pp. 55–77.
—, _Europe after Rome: A New Cultural History_ (Oxford, 2005).
—, _'Fines imperii:_ the Marches', in _NCMH_ II, pp. 169–89.
—, 'Gender and ideology in the early Middle Ages', in R. N. Swanson (ed.), _Gender and Christian Religion_ , Studies in Church History 14 (Woodbridge, 1998), pp. 51–73.
—, 'A hagiographer at work: Hucbald and the library at Saint-Amand', _Revue bénédictine_ 106 (1996), pp. 151–71.
—, 'Old saints, new cults: Roman relics in Carolingian Francia', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 317–39.
—, 'The problem of female sanctity in Carolingian Europe c.750–920', _P &P_ 146 (1995), pp. 3–37.
—, _Province and Empire. Brittany and the Carolingians_ (Cambridge, 1992).
Smith, J. M. H. (ed.), _Early Medieval Rome and the Christian West: Essays in Honour of Donald A. Bullough_ (Leiden and Boston, 2000).
Smith, R., 'Modernisation and the corporate village community: some sceptical reflections', in A. Baker and D. Gregory (eds.), _Explorations in Historical Geography_ (Cambridge, 1984), pp. 140–79.
Sonnlechner, C., 'The establishment of new units of production in Carolingian times: making early medieval sources relevant for environmental history', _Viator_ 35 (2004), pp. 21–58.
Sot, M., 'Le _Liber de episcopis Mettensibus_ dans l'histoire du genre "Gesta episcoporum"', in P. Chiesa (ed.), _Paolo Diacono. Uno scrittore fra tradizione longobarda e rinnovamento carolingio_ (Udine, 2000), pp. 527–50.
Southern, R. W., _The Making of the Middle Ages_ (London, 1953).
Sprandel, R., 'Gerichtsorganisation und Sozialstruktur Mainfrankens im früheren Mittelalter', _Jahrbuch für fräkische Landesforschung_ 38 (1978), pp. 7–38.
Squatriti, P., 'Mohammed, the early medieval Mediterranean, and Charlemagne', _EME_ 11 (2003), pp. 263–79.
Staab, F., 'Agrarwissenschaft und Grundherrschaft. Zum Weinbau der Klöster im Frühmittelalter', in A. Gerlich (ed.), _Weinbau, Weinhandel und Weinkultur_. Geschichtliche Landeskunde 40 (Stuttgart, 1993), pp. 1–48.
—, 'A reconsideration of the ancestry of modern political liberty: the problem of the so-called King's Freemen ( _Königsfreie)', Viator_ 11 (1980), pp. 51–70.
—, _Untersuchungen zur Gesellschaft am Mittelrhein in der Karolingerzeit_ , Geschichtliche Landeskunde 11 (Wiesbaden, 1975).
Stafford, P., 'The Anglo-Saxon Chronicles, identity and the making of England', _Haskins Society Journal_ 19 (2008), pp. 28–50.
—, 'Parents and children in the early middle ages', _EME_ 10 (2001), pp. 257–71.
—, _Queens, Concubines and Dowagers: the King's Wife in the Early Middle Ages_ (London, 1983).
Stancliffe, C., 'Cuthbert and the polarity between pastor and solitary', in G. Bonner, D. Rollason and C. Stancliffe (eds.), _St Cuthbert, his Cult and his Community to AD 1200_ (Woodbridge, 1989), pp. 21–44.
—, 'Kings who opted out', in P. Wormald (ed.), _Ideal and Reality in Frankish and Anglo-Saxon Society_ (Oxford, 1983), pp. 154–76.
Stanley, E. G., _The Search for Anglo-Saxon Paganism_ (Cambridge, 1975).
Stansbury, M., 'Early medieval biblical commentaries, their writers and readers', _Frühmittelalterliche Studien_ 33 (1999), pp. 49–82.
Staubach, N., _Rex Christianus: Hofkultur und Herrscherpropaganda im Reich Karls des Kahlen II: Die Grundlegung der 'religion royale'_ (Cologne, 1993).
Stengel, E. E. (ed.), _Urkundenbuch der Kloster Fulda_ , Veröffentlichungen der historischen Kommission für Hessen und Waldeck 19 (Marburg, 1936).
Stoclet, A., _Autour de Fulrad de Saint-Denis (v.710–784_ ) (Geneva, 1993).
Stone, R., 'Kings are different: Carolingian mirrors for princes and lay morality', in F. Lachaud and L. Scordia (eds.), _Le Prince au miroir de la littérature politique de l'Antiquité aux Lumières_ (Rouen, 2007), pp. 69–86.
Stork, I., 'Zum Fortgang der Untersuchungen im frühmittelalterlichen Gräberfeld, Adelshof und Hofgrablege bei Lauchheim, Ostalbkreis', _Archäologische Ausgrabungen in Baden-Württemberg 1992_ (Stuttgart, 1993), pp. 231–9.
Störmer, W., _Adelsgruppen im früh- und hochmittelalterlichen Bayern_. Studien zur Bayerischen Verfassungs- und Sozialgeschichte 4 (Munich, 1972).
Storms, G., _Anglo-Saxon Magic_ (The Hague, 1948).
Story, J., _Carolingian Connections: Anglo-Saxon England and Carolingian Francia, c.750–870_ (Aldershot, 2003).
—, 'Cathwulf, kingship and the royal abbey of Saint-Denis', _Speculum_ 74 (1999), pp. 1–21.
—, 'Charlemagne and the Anglo-Saxons', in Story (ed.), _Charlemagne_ , pp. 195–210.
—, 'Introduction: Charlemagne's Reputation', in Story (ed.), _Charlemagne_ , pp. 1–4.
Story, J. (ed.), _Charlemagne: Empire and Society_ (Manchester and New York, 2005).
Story, J., _et al_., 'Charlemagne's black marble: the origins of the epitaph of Pope Hadrian I', _PBSR_ 73 (2005), pp. 157–90.
Sullivan, R., 'The Carolingian age: Reflections on its place in the history of the Middle Ages', _Speculum_ 64 (1989), pp. 267–306.
Szarmach, P., 'A preliminary handlist of manuscripts containing Alcuin's _Liber de virtutibus et vitiis', Manuscripta_ 25 (1981), pp. 131–40.
Talbot, C. H., _Anglo-Saxon Missionaries in Germany_ (London, 1954).
Thacker, A., 'In search of saints: the English Church and the cult of Roman apostles and martyrs in the seventh and eighth centuries', in Smith (ed.), _Early Medieval Rome and the Christian West_ , pp. 247–77.
—, 'Wilfrid', _Oxford Dictionary of National Biography_ , s.n.
Theuws, F., 'Landed property and manorial organisation in northern Austrasia: some considerations and a case study', in F. Theuws and N. Roymans (eds.), _Images of the Past. Studies on Ancient Societies in Northwestern Europe_ (Amsterdam, 1991), pp. 299–407.
—, 'Maastricht as a centre of power in the early Middle Ages', in de Jong and Theuws with van Rhijn (eds.), _Topographies of Power_ , pp. 155–216.
Theuws, F., and Nelson, J. L. (eds.), _Rituals of Power: From Late Antiquity to the Early Middle Ages_ (Leiden, 2000).
Thurlemann, F., 'Die Bedeutung der Aachener Theoderich-Statue für Karl den Großen (801) und bei Walahfried Strabo (829). Materialien zu einer Semiotik visueller Objekte im frühen Mittelalter', _Archiv für Kulturgeschichte_ 59 (1977), pp. 24–65.
Tischler, M., _Einharts Vita Karoli. Studien zur Entstehung, Überlieferung und Rezeption, MGH Schriften_ 48, 2 vols. (Hanover, 2001).
Tolkien, J. R. R., 'Beowulf: the monsters and the critics', _PBA_ 22 (1936) 1–53; repr. in J. R. R. Tolkien, _The Monsters and the Critics and Other Essays_ (London, 1983).
Toubert, P., 'The Carolingian moment (eighth–tenth century)', in A. Burguiere, _et al_. (eds.), _A History of the Family_ (Cambridge, 1996), pp. 379–406.
—, _Les Structures du Latium médiéval: Le Latium méridional et la Sabine du ixe siècle à la fin du XIIe siècle_, 2 vols., Bibliothéque des Écoles Françaises d'Athénes et de Rome 221 (Rome, 1973).
Townend, M., _Language and History in Viking Age England: Linguistic Relations between Speakers of Old English and Old Norse_ (Turnhout, 2002).
Traill, D. (ed. and trans.), _Walahfrid Strabo's Visio Wettini: Text, Translation and Commentary_ (Frankfurt, 1974).
Treffort, C., _L'Église carolingienne et la mort_ (Lyon, 1996).
Tremp, E., 'Die letzten Worte des frommen Kaisers Ludwig. Von Sinn und Unsinn heutiger Textedition', _DA_ 48 (1992), pp. 17–36.
Ullman, W., 'Public welfare and social legislation in the early medieval councils', _Studies in Church History_ 7 (1971), pp. 1–39.
Verhulst, A., _The Carolingian Economy_ (Cambridge, 2002).
—, 'La Genése du regime domanial classique en France au haut moyen âge', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 13 (1966), pp. 135–60, repr. in Verhulst, Rural and Urban Aspects.
—, 'Karolingische Agrarpolitik. Das _Capitulare de Villis_ und die Hungersnöte von 792/93 und 805/06', _Zeitschrift für Agrargeschichte und Agrarsoziologie_ 13 (1965), pp. 175–89, repr. in Verhulst, Rural and Urban Aspects.
—, 'The origins of towns in the Low Countries and the Pirenne Thesis', _P &P_ 122 (1989), pp. 3–35.
—, _The Rise of Cities in North-West Europe_ (Cambridge, 1999).
—, _Rural and Urban Aspects of Early Medieval Northwest Europe_ (Aldershot, 1992).
Vermes, G., _The Changing Faces of Jesus_ (London, 2001).
—, _Jesus the Jew. A Historian's Reading of the Gospels_ , 5th edn (London, 1994).
—, _Jesus and the World of Judaism_ (Philadelphia, PA, 1984).
Verwers, W., 'Dorestad: a Carolingian town?', in B. Hobley and R. Hodges (eds.), _The Rebirth of Towns in the West, AD 700–1050_ (London, 1988), pp. 52–6.
Wallace-Hadrill, J. M., _The Barbarian West, 400–1000_ (London, 1952).
—, _The Frankish Church_ (Oxford, 1983).
Wallach, L., _Alcuin and Charlemagne_ , 2nd edn (Ithaca, NY, 1968).
Wamers, E., _Die frühmittelalterliche Lesefunde aus der Löhrstraße (Baustelle Hilton II) in Mainz_ (Mainz, 1994).
Wamers, E., and Brandt, M. (eds.), _Die Macht des Silbers: Karolingische Schätze im Norden_ (Frankfurt, 2005).
Ward, E., 'Agobard of Lyons and Paschasius Radbertus as critics of the empress Judith', _Studies in Church History_ 27 (1990), pp. 15–25.
—, 'Caesar's wife: the career of the empress Judith, 819–29', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 205–27.
Ward-Perkins, B., _The Fall of Rome and the End of Civilization_ (Oxford, 2005).
—, _From Classical Antiquity to the Middle Ages. Urban Public Building in Northern and Central Italy AD 300–850_ (Oxford, 1984).
Watkins, C., 'Sin, penance and purgatory in the Anglo-Norman realm', _P &P_ 175 (2002), pp. 3–33.
Weidinger, U., _Untersuchungen zur Wirtschaftsstruktur des Kloster Fulda in der Karolingerzeit_ (Stuttgart, 1991).
Weiler, B., and MacLean, S. (eds.), _Representations of Power in Medieval Germany, 800–1500_ (Turnhout, 2006).
Weiner, A., _Inalienable Possessions. The Paradox of Keeping-while-Giving_ (Berkeley, CA, 1992).
Weinrich, L., _Wala. Graf, Mönch und Rebell. Die Biographie eines Karolingers_ (Lübeck, 1963).
Werner, K. F., 'Gauzlin von Saint-Denis und die westfränkische Reichsteilung von Amiens (März 880). Ein Beitrag zur Vorgeschichte von Odos Königtum', _DA_ 35 (1979), pp. 395–462.
—, 'Hludovicus Augustus: gouverner l'empire chrétien — idées et réalités', in Godman and Collins (eds.), _Charlemagne's Heir_ , pp. 3–123.
—, 'Important noble families in the kingdom of Charlemagne', trans. in Reuter (ed.), _The Medieval Nobility_ , pp. 137–202, first published in W. Braunfels and P. E. Schramm (eds.), _Karl der Große: Lebenswerk und Nachleben_ , 4 vols. (Düsseldorf, 1967).
—, 'Missus–marchio–comes: entre l'administration centrale et l'administration locale de l'empire carolingien', in W. Paravicini and K. F. Werner (eds.), _Histoire comparée de l'administration ( IVe—XVIIIe siècle_) (Sigmaringen, Munich and Zurich, 1980), pp. 191–239.
—, 'Untersuchungen zur Frühzeit des franzözischen Fürstentums', _Die Welt als Geschichte_ 3–4 (1959), pp. 146–93.
West, C., _Upper Lotharingia and Champagne, c.850–c.1100_ , unpublished PhD thesis (Cambridge, 2007).
White, S. D., 'Debate. The "Feudal Revolution"', _P &P_ 152 (1996), pp. 205–23.
Whitehouse, D., '"Things that travelled": the surprising case of raw glass', _EME_ 12 (2003), pp. 301–5.
Whittaker, C. R., 'Circe's pigs: from slavery to serfdom in the Roman world', _Slavery and Abolition_ 8 (1987), pp. 88–122.
Whittow, M., 'Decline and fall? Studying long term change in the east', in W. Bowden and L. Lavan (eds.), _Theory and Practice in Late Antique Archaeology_ (Leiden, 2004), pp. 404–23.
Wickham, C., 'Aristocratic power in eighth-century Lombard Italy', in A. C. Murray (ed.), _After Rome's Fall: Narrators and Sources of Early Medieval History_ (Toronto, 1998), pp. 153–70.
—, 'Debate: the Feudal Revolution', _P &P_ 155 (1997), pp. 196–207.
—, _Early Medieval Italy. Central Power and Local Society, 400–1000_ (London and Basingstoke, 1981).
—, 'European forests in the early middle ages: landscape and land clearance', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 37 (Spoleto, 1989), pp. 479–548, repr. in Wickham, _Land and Power_ , pp. 155–99.
—, 'The fall of Rome will not take place', in Little and Rosenwein (eds.), _Debating the Middle Ages_ , pp. 45–57, first published as 'La Chute de Rome n'aura pas lieu', _Le Moyen Âge_ 99 (1983), pp. 107–26.
—, 'Le forme del feudalesimo', _Settimane di Studio del Centro Italiano di Studi sull'Alto Medioevo_ 47 (2000), pp. 15–51.
—, _Framing the Early Middle Ages: Europe and the Mediterranean, 400–800_ (Oxford, 2005).
—, _The Inheritance of Rome: A History of Europe, 400–1000_ (London, 2009).
—, _Land and Power. Studies in Italian and European Social History, 400–1200_ (London, 1994).
—, _The Mountains and the City: the Tuscan Appennines in the Early Middle Ages_ (Oxford, 1988).
—, 'Ninth-century Byzantium through western eyes', in L. Brubaker (ed.), _Byzantium in the Ninth Century: Dead or Alive?_ (Aldershot, 1998), pp. 245–56.
—, 'The other transition: from the ancient world to feudalism', _P &P_ 113 (1984), pp. 3–36, repr. in Wickham, _Land and Power_ , pp. 7–42.
—, 'Overview: production, distribution and demand, II', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 345–77.
—, 'Pastoralism and underdevelopment in the early middle ages', _Settimane di Studio del Centro italiano di studi sull'alto medioevo_ 31 (Spoleto, 1983), pp. 401–55, repr. in Wickham, _Land and Power_ , pp. 121–54.
—, 'Rethinking the structure of the early medieval economy', in Davis and McCormick (eds.), _The Long Morning of Medieval Europe_ , pp. 19–32.
—, 'Rural society in Carolingian Europe', in _NCMH_ II, pp. 431–50.
Widdowson, M., 'Merovingian partitions: a genealogical charter?', _EME_ 17 (2009), pp. 1–22.
Witwrouw, J., 'Le Centre domanial du haut moyen âge du Thier d'Olne à Engis/Hermalle-sous-Huy', _Bulletin de Liaison de l'Association Française d'Archéologie Mérovingienne_ 23 (1999), pp. 105–8.
Wolfram, H., 'The creation of the Carolingian frontier system, c.800', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_ , pp. 233–45.
Wollasch, J., 'Gemeinschaftsbewußtsein und soziale Leistung im Mittelalter', _Frühmittelalterliche Studien_ 9 (1975), pp. 61–77.
Wood, I. N., 'Before or after mission. Social relations across the middle and lower Rhine in the seventh and eighth centuries', in Hansen and Wickham (eds.), _The Long Eighth Century_ , pp. 149–66.
—, 'Beyond satraps and ostriches: political and social structures of the Saxons in the early Carolingian period', in D. H. Green and F. Siegmund (eds.), _The Continental Saxons from the Migration Period to the Tenth Century: An Ethnographic Perspective_ (Rochester, NY, 2003), pp. 271–97.
—, 'The bloodfeud of the Franks: a historiographical legend', _Early Medieval Europe_ 14 (2006), pp. 489–504.
—, 'Boniface', _Oxford Dictionary of National Biography, s.n_.
—, 'The Channel from the 4th to the 7th centuries AD', in McGrail (ed.), _Maritime Celts, Frisians and Saxons_ , pp. 93–7.
—, 'Christians and pagans in ninth-century Scandinavia', in B. Sawyer, P. H. Sawyer and I. N. Wood (eds.), _The Christianization of Scandinavia_ (Alingsâs, 1987), pp. 36–67.
—, 'Deconstructing the Merovingian family', in R. Corradini, M. Diesenberger and H. Reimitz (eds.), _The Construction of Communities in the Early Middle Ages_ (Leiden and Boston, 2003), pp. 149–71.
—, 'John Michael Wallace-Hadrill, 1916–85', _Proceedings of the British Academy_ 124 (2004), pp. 333–55.
—, _The Merovingian Kingdoms, 450–751_ (London, 1994).
—, _The Merovingian North Sea_ (Alingsås, 1983).
—, 'Missionaries and the Christian frontier', in Pohl, Wood and Reimitz (eds.), _Transformation of Frontiers_ , pp. 209–18.
—, _The Missionary Life: Saints and the Evangelisation of Europe, 400–1050_ (Harlow, 2001).
—, 'Pagan religion and superstitions east of the Rhine from the fifth to the ninth century', in G. Ausenda (ed.), _After Empire_ (Woodbridge, 1995), pp. 253–68.
—, 'Saint-Wandrille and its hagiography', in I. N. Wood and G. A. Loud (eds.), _Church and Chronicle in the Middle Ages_ (London, 1991), pp. 1–15.
Wood, S., _The Proprietary Church in the Medieval West_ (Oxford, 2006).
Woolf, S., 'Europe and its historians', _Contemporary European History_ 12 (2003), pp. 323–37.
Wormald, P., _'Lex scripta_ and _verbum regis:_ legislation and Germanic kingship from Euric to Cnut', in P. H. Sawyer and I. N. Wood (eds.), _Early Medieval Kingship_ (Leeds, 1977), pp. 105–38.
—, _The Making of English Law: King Alfred to the Twelfth Century_ , i: _Legislation and its Limits_ (Oxford, 1999).
—, 'Pre-modern "state" and "nation": definite or indefinite?', in Airlie, Pohl and Reimitz (eds.), _Staat im frühen Mittelalter_ , pp. 179–89.
—, 'Viking studies: whence and whither?', in R. T. Farrell (ed.), _The Vikings_ (Chichester, 1982), pp. 128–53.
Wormald, P., and Nelson, J. (eds.), _Lay Intellectuals in the Carolingian World_ (Cambridge, 2007).
Wormald, P., Bullough, D., and Collins, R. (eds.), _Ideal and Reality in Frankish and Anglo-Saxon Society_ (Oxford, 1983).
Wright, R., _A Sociophilological Study of Late Latin_ (Turnhout, 2002).
Wurnburger, A. (ed.), _Über eine ungedruckte Kanonensammlung aus dem 8. Jahrhundert_ (Munich, 1890).
Yorke, B., 'The Jutes of Hampshire and Wight and the origins of Wessex', in S. Bassett, _The Origins of Anglo-Saxon Kingdoms_ (London and New York, 1989), pp. 84–96.
Zeddies, N., 'Bonifatius und die zwei nützliche Rebellen: die Häetiker Adelbert und Clemens', _Ordnung und Aufruhr im Mittelalter: historische und juristische Studien zur Rebellion_ , Ius Commune. Sonderheft 70 (Frankfurt, 1995).
Zelzer, K., 'Von Benedikt zu Hildemar. Zu Textgestalt und Textgeschichte der _Regula Benedicti_ auf ihrem Weg zur Alleingeltung', _Frühmittelalterliche Studien_ 23 (1989), pp. 112–30.
Zimmermann, H., _'Imperatores Italiae'_ , in H. Beumann (ed.), _Historische Forschungen für Walter Schlesinger_ (Cologne and Vienna, 1974), pp. 379–99.
Zotz, T., 'In Amt und Würden. Zur Eigenart "offizieller" Positionen im früheren Mittelalter', _Tel Aviver Jahrbuch für deutsche Geschichte_ 22 (1993), pp. 1–23.
—, 'Carolingian tradition and Ottonian–Salian innovation: comparative observations on Palatine policy in the empire', in A. Duggan (ed.), _Kings and Kingship in Medieval Europe_ (London, 1993), pp. 69–100.
—, 'Ludwig der Deutsche und seine Pfalzen: Königliche Herrschaftspraxis in der Formierungsphase des ostfränkischen Reiches', in W. Hartmann (ed.), _Ludwig der Deutsche und seine Zeit_ (Darmstadt, 2004), pp. 27–46.
## INDEX
Aachen
and memory of Charlemagne,
Charlemagne's burial place, ,
palace complex and chapel, , , , , , , , , , , , , , , , , , , , , , , , ,
Abbo of St-Germain-des-Prés: on Viking attack on Paris,
Adalhard, Charlemagne's cousin,
and Hincmar's _De ordine palatii_ [On the Governance of the Palace],
and succession of Louis the Pious,
rehabilitated in 820s,
afterlife: ideas of,
Agnellus of Ravenna,
Agobard of Lyon
controversy with Amalarius of Metz,
criticism of Matfrid's influence,
on Jewish slave traders,
Aistulf, Lombard king, ,
laws on merchants,
military legislation of,
Alcuin
as scholar,
as teacher,
asks 'what has Ingeld to do with Christ?',
at Charlemagne's court,
letter to Offa,
_Life of Willibrord_ , ,
on conversion of Avars and Saxons,
on force and conversion,
on _imperium_ ,
on pope and emperor,
on the virtues and vices,
relationship to Willibrord,
Alemannia. _See also_ Judith, Empress; Charles the Fat
and Carolingian conquest,
and Charles Martel,
and family of Empress Judith,
and opposition to Carolingians, ,
and Pippin III,
conquest under Carloman and Pippin III,
Merovingian conquest,
under Charlemagne,
Amalarius of Metz
on Mass,
annals, ,
and Pippin's seizure of kingship,
production of, ,
_Annals of Fulda_ , , , , ,
_Annals of Lorsch_ , ,
_Annals of Metz_ ,
_Annals of St Bertin_ , , , ,
Ansegisus: capitulary collection, ,
Anskar, Frankish missionary,
Antoigné, estate of monastery of Cormery,
Aquitaine. _See also_ Charles the Bald, and Carolingian politics; Carloman, son of Charles the Bald; Pippin II of Aquitaine; Pippin of Aquitaine
and Charles Martel, , ,
and Merovingians,
and opposition to early Carolingians,
and Pippin III, , , , 64–5
conquest by Charlemagne,
under Louis the Pious,
archaeology. _See also_ Rome; Mainz; Hedeby; Quentovic; Hamwic; Dorestad; Ingelheim; Aachen; residences, aristocratic; towns
and changing views of economy,
and rural society,
importance of,
of rural settlement, 236–41
Arnulf of Carinthia, , 425–7
Astronomer: _Life of Louis the Pious_ , , , , , , , , , ,
Audoin, bishop of Rouen, ,
Austrasia
and early Carolingians,
and rise of Carolingians,
and rise of Charles Martel, ,
in late Merovingian times, ,
Austrasia, subkingdom
and early Carolingians. _See_ Childebert 'the Adopted'
Bavaria. _See also_ Arnulf of Carinthia. Karlmann of Bavaria; Louis the German
and Charles Martel,
and opposition to Carolingians,
and Pippin III, ,
Boniface's reorganisation of Bavarian church,
Charlemagne's seizure of, 69–70
relations with Lombard kingdom,
Benedict of Aniane,
and liturgy,
Benevento. _See also_ Louis II
and Charlemagne,
and military alliance with Byzantium,
and Paul the Deacon's 'History',
relations with Lombard kingdom,
_Beowulf_ ,
Bernard of Italy
and Louis the Pious, , 202–5
Bernard of Septimania
and revolt of 829, ,
as Louis the Pious's chamberlain,
executed by Charles the Bald,
Bertrada, wife of Pippin III, , ,
bishop, office of, , , , ,
and Boniface's opponents, ,
and royal government,
Anglo-Saxon perceptions,
development in pre-Carolingian Europe, 96–7
in late Merovingian Gaul,
Boniface, , , , 102–3, 138–41
and definition of Christianity, . _See alsoIndiculus superstitionum et paganiarum_
and 'paganism', ,
Church councils organised by,
claims to sanctity,
criticisms of Frankish and Roman Christianity,
his network of supporters,
books, book production, 16–18, , , , 145–6
in ninth century, 149–52
Boso of Vienne, , , 419–21
Burgundy
in late Merovingian times, ,
Merovingian conquest,
takeover by Charles Martel,
burial, , . _See also_ cemeteries
Byzantium. _See also_ Venice; Rome; Louis II
and Charlemagne, 68–9
and Charlemagne's imperial coronation,
and Frankish response to 'iconoclasm', ,
and negotiations over recognition of Charlemagne's imperial title,
contesting Carolingian claims to empire,
Pippin III relations with,
possessions in eighth-century Italy, , ,
capitularies, 182–9
absence from east Frankish kingdom,
absence in 830s,
_Admonitio ad omnes regni ordines_ 823–5, , ,
_Admonitio generalis_ of 789, , , , ,
and correction of Church under Charlemagne,
Ansegisus's collection of,
Charlemagne's Saxon capitularies, _Devillis_ , , , , ,
episcopal capitularies,
for _missi_ in 802,
of 811,
of 828–9,
of Charles the Bald,
of Louis II,
on local officials,
Pîres 864, ,
preservation of, 'Programmatic' 802, ,
Quierzy 877, ,
Regensburg 789, ,
Carloman II,
Carloman, King, brother of Charlemagne, ,
anointing by pope in 753,
Carloman, mayor of palace and brother of Pippin III, , , 51–61, ,
and Boniface,
and church councils,
and foundation of Fulda,
Carloman, son of Charles the Bald, ,
Carolingians
distinctive feature of their regime, 9–16
in modern historiography, 2–3, , 6–7,
cemeteries, . _See also_ burial
Charlemagne
and Bavaria, 69–70
and Byzantium, 68–9, 166–8,
and Christianisation,
and Church, , , , , , ,
and Danes, , 355–6
and family, 196–8, ,
and government, 170–94
and Harun al-Rashid,
and Italy, , , 160–8
and Louis the Pious as king of Aquitaine,
and Rome, , , , 160–8, ,
and silk,
and Slavs, , 355–6
and the aristocracy, 75–9
and Venice,
anointing by pope in 753,
as patron of literary culture, , 146–7,
birth, ,
burial at Aachen, , 154–5, :
capitularies,
conquest of Aquitaine,
conquest of Avars, 70–2, ,
conquest of Lombard kingdom, 65–7
conquest of Saxons, 73–5,
conquest of Saxony,
court 76–7, ,
criticised under Louis the Pious, ,
death of, 154–5, 196–8 'economic policy',
frontiers of empire, ,
ideologies of empire, 168–70
imperial coronation of 800, , , , 160–8
itineraries of,
last years of, , ,
meets pope in 753,
memory of, , , , , ,
naval campaigns in western Mediterranean,
On the cultivation of letters,
relations with Carloman, 65–7
rule in Italy, 65–8
succession plans, 194–8
warfare, 75–6, , ,
Charles Martel
as ruler of Frankish kingdoms, 44–51
in later Carolingian propaganda,
papacy and Lombard kingdom,
rise to power, 42–4
victory against Muslims,
Charles of Provence,
Charles the Bald
able to punish aristocrats,
and Breton rulers,
and Carolingian politics 843–77, 388–407
and civil war of 840–3, ,
and Compiègne,
and Danegeld, ,
and destruction of unauthorised fortifications,
and _honores_ , ,
and Quentovic,
and rebellions of 830s, 218–22
and Strasbourg oaths,
and theological debate,
and Treaty of Coulaines 843,
birth of,
charters,
commissioning of historiography,
handling of Vikings,
itineraries of,
Louis the Pious creates a kingdom for in 829,
Charles the Fat, , , , , , , , , , , , , 422–6, ,
and Guy of Spoleto,
and palaces,
humiliates followers of rebel Hugh,
submits to father after rebellion,
svelte appearance,
Charles, son of Charlemagne
and Charlemagne's succession plans, , 194–6
crowned in Rome in 800,
Charles, son of Charles the Bald,
charters,
and religious patronage, 112–13, ,
as evidence for royal government, ,
as evidence for rural society, , , 241–6
of Ratolt 839,
production, preservation and use, 13–14, 25–9
royal charters and government of the kingdom,
Childebert III, Merovingian king, ,
Childebert 'the Adopted', , ,
Chrodegang of Metz: rule for canons,
classics, Latin, , , ,
clothing: as expression of social status, ,
Cluny, monastery of: its archive and Carolingian society,
_Codex Carolinus_ , ,
Comacchio, ,
commemoration, 110–11
and inheritance,
and _Libri memoriales_ ,
and women, 312–13
of the dead, , , 110–17
Compiègne, palace,
Corbie, monastery
and debate on Mass,
councils, Church, ,
Aachen, , , , ,
_Concilium germanicum_ 742,
Les Estinnes 743, ,
of 813, 196–8
of 816–17,
of 828–9,
on marriage,
resumption under Carloman and Pippin III,
Soissons 744,
count, office of, , , , , ,
and capitularies, 182–9
created in Bavaria after Charlemagne's takeover, 69–70
imposed in Lombard kingdom after 776,
residence of count of Orleans,
seen as _ministerium_ ,
and village life,
Danes. _See also_ Godafrid I; Godafrid III; Vikings
and Charlemagne,
and Frankish mission,
and Louis the Pious,
baptism of Harald Klak,
economic and political significance in first half of ninth century,
raiding Frankish coast in 830s,
death: and commemoration, 110–17
Desiderius, Lombard king, , , ,
Dhuoda, , , , ,
Dienheim, village, ,
Dommeln, ,
Dopsch, Alfons, ,
Dorestad, , , , , , , 343–4, , , , , , , , ,
_Earlier Annals of Metz_ ,
Eberhard of Friuli
as book owner,
his lawbook,
landholdings of,
library of,
will, ,
Ebo of Rheims,
attacked for low birth by Thegan,
made fallguy for Louis the Pious's penance of 833,
Eccard of Mâcon
land holdings,
library,
will, ,
Echternach, monastery,
and Pippin II,
foundation of,
patronage of,
Einhard,
as courtier,
as landlord, , , , , , , ,
learning,
piety,
_Vita Karoli_ [Life of Charlemagne], , , , , , , , , , , , , , , , , , ,
empire, ideology of, . _See also_ Charlemagne: imperial coronation of 800
Engelberga, wife of Louis II, , ,
Engis, aristocratic residence,
Ercanfrida, wife of Count Nithard of Trier will,
Ermentrude, wife of Charles the Bald,
Ermold the Black, Poem on Louis the Pious, , , , , , , , ,
Eschborn: village of,
Farfa, monastery
exclusion of women,
political significance,
possessor of rural churches,
Fleury, monastery of,
Folkwine, local official in Alps,
Frankfurt, palace, ,
Fredegar, _Chronicle_ and _Continuations_ , , , , , , , , ,
Freising, cathedral church: charters of,
Frisia
and Charles Martel, ,
and Frankish—Danish conflict,
and North Sea trade, ,
and opposition to Charles Martel,
and opposition to early Carolingians,
Boniface's mission in,
Liudgar's mission in,
nature of'paganism' in, ,
Wilfrid initiates mission,
Willehad's mission,
frontiers, 9–10
and crisis of 828–9,
and end of eighth-century expansion,
Frothar of Toul: as a royal agent,
Fulda, monastery
and learning,
and memory of Boniface,
estate inventories,
foundation of, ,
Giselhelm (small landowner in Rhineland), , ,
Godafrid I, Danish king, ,
Godafrid III, Viking leader, ,
Gregory II, Pope: and Boniface,
Gregory III, Pope,
and Boniface,
on 'paganism' in Germany, ,
Grifo, son of Charles Martel, , , , , ,
Guy of Spoleto, , , ,
Hadrian I, Pope, , , ,
and silk,
Hadrian II, Pope,
hagiography, ,
and late Merovingian Church,
and presentation of mission,
Hamwic, , , , ,
Hedeby, , , , ,
Heiric of Auxerre: on three orders of society,
_Hildebrandslied_ ,
Hildegard, wife of Charlemagne, , , ,
Hincmar of Rheims
and cult of relics,
as bishop,
as scholar,
_De ordine palatii_ [On the Governance of the Palace], , , , ,
on magic and boundaries of Christianity, 81–4
on Neuilly,
on the divorce of Lothar, , , , , ,
historiography, historical writing, , 18–23,
and justification of Pippin's seizure of the kingship in 751, 31–3
used by Charles the Bald in 869,
_honores_ , , ,
acquisition and transmission of, 313–20
granted to Viking allies,
Louis the Pious attempts to revoke,
under later Carolingians,
Hraban Maur, ,
as bishop,
as scholar,
family and land holdings, ,
Hucbald of St Amand,
Hugh of Tours: armed struggle over his _honores_ ,
blamed for Muslim success in 828,
family connections,
influence on Lothar,
ridiculed by opponents,
taunted by his followers,
threatened by installation of Charles the Bald in Alsace in 829,
Ibn Khurradadhbih: _Book of Routes and Kingdoms_ , 367–8
'iconoclasm': Frankish responses to, ,
_Indiculus superstitionum et paganiarum_ , ,
Ingelheim, palace, , , ,
described by Ermold the Black,
John VIII, Pope, , ,
Jonas of Orléans: _De institutione laicali_ , ,
Judith, Empress
chosen as second wife by Louis the Pious,
role in revolt of 828–9,
Karlmann of Bavaria, , , , , ,
Karol, son of Liutprand,
Kempten, village of, , , , , , 268–70
kingship: law on marriage,
kinship
and aristocracy, 304–13
and community,
and household, 237–8
and monastic patronage, 288–90
and prosopographical research on the aristocracy, 273–4
and transmission of land, 244–5
burial and family identity,
Kootwijk: village of,
land, landholding,
and aristocracy, 308–13
and endowment of monasteries,
benefices, 316–20
by aristocratic and peasant landowners, 241–6
church lands and Charles Martel,
of monasteries, 126–30
precarial grants of church land,
Lauchheim, village,
Leo III, Pope
and Charlemagne's imperial coronation, 160–8
Leo IV, Pope
and Leonine walls,
_Liber historiaefrancorum (LHF_ ), ,
_Liber pontificalis_ , , , , ,
literacy. _See_ written word
Liudger, St,
_Liutberga, Life of_ ,
Liutprand, Lombard king, , , , , , ,
Lombards, Lombard kingdom, ,
and Pippin III, 56–61
conquest by Charlemagne, 65–7
cultural influence on Carolingian court,
in Paul the Deacon's 'History',
links to Bavarian duchy,
Pippin III attacks as result of papal alliance, 56–63
rebellion against Charlemagne, ,
Synod of Pavia, ,
trade with Comacchio,
Lorsch, monastery of,
and Louis the German,
patronage of, ,
Lothar
and Carolingian politics, 843–55, 388–94
and civil war of 840–43,
and _Constitutio romana_ ,
and rebellions of 830s, 218–22
and revolt of 829, ,
as king of Italy,
as 'subking' in Italy, 209–13
capitularies,
exiles opponents in rebellion of 830,
godfather of Charles the Bald,
Hugh of Tours's son-in-law,
in _Ordinatio imperii_ of 817,
marriage of,
Lothar II, , 396–9
and royal resources,
divorce from Theutberga, , , , ,
succession supported by Louis the German,
Louis II, , , 405–6
letter to Basil I of Byzantium,
Louis III,
Louis the German
and Carolingian politics 843–76, 388–407
and civil war of 840–3,
and Lorsch,
and Moravia,
and rebellions of 830s, 218–22
and revolt of 829,
and royal resources,
and Strasbourg oaths,
and the Slavs,
as emperor,
charters,
government of east Frankish kingdom,
itinerary of,
made king of Bavaria in _Ordinatio imperii_ of 817,
praised by Notker of St Gallen,
purging of east Frankish aristocracy 861, ,
sees vision of his father in Hell,
supports his father in revolt of 829,
Louis the Pious. _See also_ Astronomer; Ermold the Black; Thegan
and gift of royal land,
and government of the empire, 170–94
and monasteries,
and succession plans of Charlemagne, 194–6
anointed by pope as a boy,
as king of Aquitaine, , , ,
capitularies,
conflicting interpretations of his reign, 155–60
crowned emperor in 813,
gift giving of,
his court as described by Ermold the Black and Walahfrid Strabo,
itinerary of,
opposition to his succession, 196–8
protects Jewish traders in Lyon,
reign of, 198–222
ritual of deposition,
Louis the Stammerer, ,
and Charles the Bald,
as subking of Neustria,
Louis the Younger, , , ,
attempt to seize Aquitaine, ,
_Ludwigslied_ ,
Lull, archbishop of Mainz,
Lupus of Ferrieres,
and cell of St Josse,
magic, 81–4
Mainz: urban development at, , , ,
Malles Venosta, church: fresco of aristocratic patron,
manors, 252–8
and dependent peasantry, 266–8
markets
development of, ,
emergence of, ,
marriage, 131–4
Marseille,
and Mediterranean trade,
mass,
and commemoration,
and religious patronage,
debate on, 119–21
Matfrid of Orléans
armed struggle over his _honores_ ,
blamed for Muslim success in 828,
influence in 820s,
investigated by _missi_ in 829,
name excised from public discourse,
Meersen, Treaty of, , , ,
meetings, public,
access to as index of social status,
and dependent peasantry, , 266–7
and dispute settlement,
and organisation of countryside, 250–2
and 'private justice',
often held in cemeteries,
Merovingians, , , , , , , , 34–44, , , , , , , , , , ,
memory of,
Methodius, missionary: nearly sold as slave,
Michelstadt: Einhard's church,
_missi_ , 179–80, , . _See also_ capitularies
and capitularies, 182–9
of Charles the Bald,
investigation into John of Istria, ,
used by Louis the Pious in 828–9,
mission, missionaries, 93–110. _See also_ Frisia; Saxons Mitry, estate of monastery of St Denis,
monasteries, monasticism, 117–18, 125–30,
and charter evidence,
and priests and pastoral care,
and rise of Carolingians,
and royal government,
and Rule of St Benedict,
as centres of writing and learning,
donations to,
Louis the Pious's reforms of 817,
patronage of, , 112–13, :i, 115–17, , 288–90. _See also_ charters
Mondeville: village of,
Monte Amiata, monastery: charter collection,
Monte Cassino, monastery
and Carloman,
and Ratchis,
and Rule of St Benedict,
Monte Soracte, monastery of: and Carloman,
Muslims
and Mediterranean trade, 364–75
and opposition to Charles Martel in Provence, ,
and Pippin III,
attack on Rome 846,
attack on Spanish March in 828,
defeat by Charles Martel at Poitiers,
in eighth-century Aquitaine,
Neustria
and Charles Martel, , ,
and opposition to Carolingians,
in late Merovingian times, , , , ,
Pippin II and Carolingian influence in, ,
under Pippin III,
Nicholas I, Pope,
and Lothar II's divorce, ,
Nithard, historian, , , , ,
on Louis the Pious's succession,
Notker of St Gallen,
_Gesta Karoli magni imperatoris_ [Deeds of Charlemagne], , , , , , ,
mocks taste for oriental luxury,
oaths
Carolingian legislation on,
of fidelity, , , , ,
Odo of Orleans, ,
Odo, King of West Francia, ,
family origins,
removed from his father's _honores_ ,
Ohthere: voyages of, 324–6, 329–31
ordeal, judicial: and 'private justice',
Paderborn,
and conversion of Saxony,
Pope Leo III visits Charlemagne there in 799,
_Paderborn Epic_ ,
'paganism', 86–93. _See also_ mission, missionaries
and mission, 93–110
palaces, , , 293–4. _See also_ Aachen and aristocratic youths, 296–7
Paschasius Radbertus
on mass,
on Wala's testing by Charlemagne,
pastoral care, 121–5
Paul the Deacon,
as scholar,
_Historia Langobardorum_ [History of the Lombards],
Paulinus of Aquileia: book of advice for Eric of Friuli,
Pavia, ,
Penance, ,
and aristocracy,
as withdrawal from public life,
of Louis the Pious, , 202–5, ,
Perrecy, aristocratic estate,
Petegem, aristocratic residence,
Pippin I, mayor of palace, ,
Pippin II of Aquitaine, , , , ,
Pippin II, mayor of palace, , , , , ,
and Echternach,
and Willibrord's mission,
in later Carolingian propaganda,
Pippin III, , , ,
and church land, ,
and _Continuations_ of Fredegar,
and foundation of Echternach,
and Italy, 56–63
and tithe,
as king, 63–5
as mayor of palace, 51–61
burial at St Denis,
campaigns in Aquitaine, 64–5
Church councils,
in later Carolingian propaganda,
Papal alliance, 1–2, 31–4, 56–63,
relationship with brother Carloman, 51–61
seizure of kingship, 1–2, , 31–4, 61–2
Pippin of Aquitaine, , ,
and rebellions of 830s, 218–22
and revolt of 828–9, ,
as 'subking', 209–13
in _Ordinatio imperii_ of 817,
marriage of,
Pippin of Italy, , , , , , ,
and Paul the Deacon's 'History',
and succession plans of Charlemagne, 194–6
Pippin 'the Hunchback', , , , ,
Pirenne, Henri, , , , ,
Plectrude, wife of Pippin II, , , , ,
Polyptychs, , , , , ,
development of, 252–4
on peasant households and farms,
used as legal evidence for peasant dues,
Popes, papacy, 134–9
alliance with Pippin III, 56–61,
and Charlemagne's conquest of Lombard kingdom,
and Charlemagne's imperial coronation, 160–8
and Frankish alliance,
Anglo-Saxon reverence for,
claims to represent Italy under Stephen II,
landed wealth and supply of Rome,
Priests, 121–5,
Provence
and Charles Martel,
and Merovingians,
and opposition to early Carolingians in late Merovingian times, ,
Prüm, monastery
beneficiary of Ercanfrida's will,
Polyptych, , , ,
Quentovic, , ,
Radbod, Frisian leader, , ,
Radhanites, 367–8
Ratchis, Lombard king,
Ratramnus of Corbie
on conversion of Danes and Swedes,
on mass,
Ravenna: conquered by Lombards,
Redon, monastery of: and Breton society,
Regino of Prüm, , ,
Reichenau, monastery: and Carolingians,
residences, aristocratic, , 285–95
Ribe, ,
Richgard, wife of Charles the Fat,
Richildis, wife of Charles the Bald,
Rimbert, missionary,
Ripwin (small landowner in Rhineland), , ,
Rižana, plea of, , ,
Robert the Strong, ,
and Charles the Bald,
and discontent with Charles the Bald in 850s,
Rome
and Boniface's mission,
and Carolingians, 135–6
and Charlemagne, ,
and Charlemagne's imperial coronation, 160–8
and Lombards, , , ,
and plans for Charlemagne's succession,
and Wilfrid, ,
and Willibrord's mission,
as source of authority, ,
as source of relics,
attacked by Muslims 846,
Charlemagne and sons visit in 780–1,
Charlemagne visits in 774,
cultural and religious significance of,
economy of, ,
Pilgrimage by Carloman, brother of Pippin III,
Pope John VIII and defence against Muslims,
Roman identity in eighth century,
under Frankish 'protection',
_Royal Frankish Annals_ , , , , , , , , , , , , ,
Rupert, count in Rhineland, ,
saints, cult of
and episcopal office,
prevalence in Merovingian Gaul,
Sant'Ambrogio, monastery of: as a landlord,
Saxons, Saxony
and Charlemagne's imperial coronation,
and Charles Martel,
and opposition to Charles Martel,
Boniface hopes to convert,
conquest and Christianisation of, 73–5, ,
Frankish campaigns under Carloman and Pippin,
Liudgar's mission in,
missions to,
_Stellinga_ revolt,
Sedulius Scottus: on kingship,
Sergius II, Pope, ,
slavery
and Mediterranean trade,
in countryside,
Speyer: Carolingian settlement around, ,
St Amand, monastery: library,
St Bartholomew, monastery of,
St Denis, monastery, ,
St Gallen, monastery
charter collection,
library,
St Wandrille, monastery of: and mission in Frisia,
Stephen II, Pope, , , , , ,
Stephen III, Pope, ,
St-Germain-des-pres, monastery: polyptych, ,
Strasbourg oaths,
Tassilo III, duke of Bavaria, , , , 69–70
Thegan
_Life of Louis the Pious_ , , , , , , ,
Theodulf
and rebellion of Bernard,
as bishop,
as poet, ,
as royal official,
as scholar, ,
Toto of Campione, ,
towns
aristocratic interests in, 287–8
development of North Sea emporia, 338–53
Italian, 359–64
Trebur, palace: polyptych,
_vassi dominici_ ,
Venice, , 368–70
as centre of slave trade,
Verdun, Treaty of, , , , , ,
Vikings
Abbo on attack on Paris,
activities in Charles the Bald's kingdom, ,
economic effects of, 347–58
impact on ninth-century politics, 414–17. _See also_ Godafrid III
peasant resistance to in 859, ,
raids on Lothar's kingdom,
raids on west Frankish kingdom after Louis the Stammerer's death,
villages, 229–41
Wala,
and revolt of 829,
and succession of Louis the Pious, ,
rehabilitated in 820s,
testing by Charlemagne,
Walahesheim: village of,
Walahfrid Strabo,
on Louis the Pious's court, ,
warfare
and church land, ,
and east Frankish kingship,
and military service in ninth century,
and rise of Carolingians, ,
and rise of Charles Martel, , ,
as motor of Frankish economy,
attempts to regulate participation in,
fortifications,
military service, , 248–9, , 279–81
ninth-century adjustments to end of expansion,
significance under early Carolingians, 75–6
under Louis the Pious,
weaponry: as expression of social status, ,
Wilfrid, bishop and missionary, , , , , ,
Willibrord,
and religious patronage,
encounters with 'paganism',
mission to Frisians,
Wissembourg, monastery
dues of its peasants,
estate surveys,
written word,
and priests,
and secular aristocracy, 298–303
and social mobility,
increased volume of sources, 13–14, 16–28
law codes, 180–1
Promoted to correct religious practice,
Zacharias, Pope, , , , , , , ,
and Boniface,
and Boniface's foundation of new bishoprics,
| {
"redpajama_set_name": "RedPajamaBook"
} | 971 |
Files for Lab 2 of CMPUT 410
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,623 |
Resolve to become a Jenkintown volunteer…
Resolve to become a Jenkintown volunteer firefighter in 2022
David Litts, John Nungesser, and AJ Sulock after running drills.
New Year's is a time to make resolutions that add purpose to your life. There's no better way to do this than by volunteering for the Jenkintown Fire Department. Volunteers protect their community, help their neighbors on their worst days, and make friends that last a lifetime.
Jenkintown Fire Department is comprised of two stations: Pioneer and Independent Fire Companies, both of which were formed in the 1880s. Together they respond to some 300 calls each year.
Three volunteer firefighters from Independent — two new and one returning — explain how joining the company is transforming their lives.
John Nungesser, 26, the newest volunteer, joined the station in September. "I hate to sound like a cliché, but this has been a dream come true. I've wanted to be a firefighter since I was 3 years old."
Moving from Philadelphia to Jenkintown in September gave him his first chance to volunteer. "I jumped on it. It only took me two weeks to sign up."
Ramon Diaz joined Independent as a junior firefighter when he was 14 years old and has volunteered there ever since. This year he turned 18 and graduated from Jenkintown High School.
In November, Ramon completed the Firefighter 1 course and is excited to take on additional responsibilities on the exterior of burning buildings. "Once I get my hazardous materials certification, I'll be able to help my crew on the inside," explains Diaz.
As a child, Diaz spent time at a family friend's firehouse. Diaz watched in awe as a team of firefighters mobilized in minutes to respond to an alarm.
At that moment, he knew this was what he wanted to do. "They worked so closely together, and they did it to help other people. I'll never forget it," said Diaz.
David Litts comes from a family of firefighters. His grandfather was the chief of the Ogontz Fire Station, and his uncle was a firefighter there. He always wanted to follow in this family tradition.
At 17, Litts became a junior firefighter at the station and served as a firefighter there for 14 years, until he moved to the South. For twenty-two years he worked in emergency and rescue operations. His experience at Independent was so rewarding that he rejoined when he moved back to Jenkintown in 2020 at the age of 54.
All three are emphatic that there's no stronger community than the one at their station. Says Litts, "the volunteers are brothers and sisters. There's nothing like the relationships that build at a firehouse. If someone's in need, hurt, or sick, the volunteers rally around them."
This truth was brought to life for him shortly after returning to Jenkintown. Litts' long-time friend, Beth, had encouraged him to return to Jenkintown, the place he loved, and to firefighting, the work he loved most. Beth died shortly after he underwent abdominal surgery. "Everyone at the station took care of me, checked on me, kept me motivated, and busy. It meant the world to me."
Likewise, Diaz says, starting at the age of 14, I became part of a brother and sisterhood that's family to me. I have another home. It's been a blessing."
"We have a great crew. Everyone is committed to serving the community and being there for each other."
In just three months as a volunteer, John says, "the volunteers have become my family. I respond to as many alarms as I can. The volunteers go out of their way to teach me the ropes." He couldn't be happier.
As Nungesser sees it, "one reason for the closeness is the intense focus on teamwork. It's the most important thing I've learned—how to rely on others and have them rely on me."
The key is communication, he explains. In high pressure situations, "we learn how to talk and listen to each other. It's the only way firefighting works." These skills, he believes, will serve him in all areas of his life.
Nungesser, Diaz, and Litts are thrilled with the education they receive as volunteers both inside and outside of classes. Diaz and Litts just completed the Firefighter 1 national certification course — Litts for the second time since his initial certification expired and the science of firefighting has evolved in the 20 years he was away. Nungesser is excited to begin Firefighter1 in January 2022.
"Our certification courses are intensive, and we conduct lots of exercises and drills at the station. We also have a lot to read on our own to stay abreast of the most current knowledge, which constantly grows," explains Litts.
Diaz wants others considering volunteer firefighting to know that the department is committed to the ongoing education of its volunteers.
He explains, "It means a lot to me that the department will pay for any training and certification classes to make me a better firefighter."
The mentorship and support among volunteers are perhaps the most meaningful form of training. With Litts' experience, young firefighters — or as Litts puts it, "his kids" — turn to him for guidance and mentoring. He treasures his relationships with them.
At the academy, Litts and Diaz were partners. In training and in the field, Litts' experience and Diaz's strength are a perfect match.
Says Litts, "Ramon's a fantastic kid. He has latched on to me and I'm mentoring him. He's so hungry to learn that I meet with him at the station three times a week to do training exercises."
Both Nungesser and Diaz plan to pursue careers as full-time firefighters.
Nungesser, Diaz, and Litts are driven to firefight out of a desire to serve others. When a call comes in, Litts says, "we become completely focused on doing our jobs, helping people in need, there's no time to think about ourselves. Our goals are to save lives and property and restore order out of chaos."
Each of the volunteers at the Jenkintown Fire Department shares this mission. It's the glue that binds them together as a family and pushes them to seek excellence. They share a deep pride in their work.
Says Litts, "it made me so happy to return to the close-knit community of Jenkintown. It's our privilege to serve it."
The Jenkintown Fire Department is always looking for volunteers. Diaz wants those considering it to know that "the department is very diverse and open to everyone. It doesn't matter who you are, where you come from, or what your experience is. We're happy to have you on our team."
If you want to be the neighbor who saves a neighbor, fights fire, protects properties, and forges friendships, Jenkintown Fire Department has a place for you. Along with firefighting, there are many ways to volunteer:
Firefighter: Train to fight fires and respond to traffic accidents, hazardous material (HAZMAT) events, rescues and other dangerous situations.
Fire Police: The fire police are attached to the Pioneer Fire Company. Their primary duty is to ensure the safety of firefighters going to and from the fire scene. They also direct traffic at the scene and provide security and crowd control. The fire police also prevent thieves from accessing a burned building until it can be boarded up.
Contributing Members: Not everyone has to run into a burning building to help. Contributing members are needed for administrative tasks, fundraising or serving on the board. The Jenkintown Fire Department sponsors the annual 4th of July Parade. There's plenty to do besides fighting fires!
Junior Firefighter: Age 14 through 17. Train and learn the skills you need to become a firefighter when you turn 18. While you can't go into a burning building until you are 18, you can help the firefighters at the scene of a fire. And it's a great activity to list on your college resume.
If any of these roles interest you, the New Year is a great time to start. We provide all the training and equipment you need to answer calls, and you will not find anything more rewarding than giving back to your community.
Complete the inquiry form at www.fightjenkintownfires.org and member of the Jenkintown Fire Department will contact you soon.
— Submitted by Communication Solutions for Jenkintown Fire Department | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,073 |
Q: Сложить числа массива пока выполняются условия У меня есть массив который складывает значения - вывод всегда 2х-3х значное число.
нужно написать условие, которе будет получит однозначное число путем сложения чисел из которых состоит 2-х или 3-х значное число
Но где выполняются дополнительные условия,
конечное число x >=1 AND <= 9 OR = 11 OR = 12.
Например: х = 79 - Двухзначное 7+9 = 16 -Двухзначное 16 = 1+6 = 7
(оно больше 1 и меньше 9 и не равно 11 или 12)
x = 134 трехзначное 1+3+4 = 7 (оно больше 1 и меньше 9 и не равно 11
или 12)
<?
$string1 = iconv('UTF-8', 'windows-1251', $number1);
foreach (str_split($string1) as $value1) {
$ov1 = ord($value);
$sum_number1+=$ov1;
}
$string2 = iconv('UTF-8', 'windows-1251', $number2);
foreach (str_split($string2) as $value2) {
$ov2 = ord($value);
$sum_number2+=$ov2;
}
$string3 = iconv('UTF-8', 'windows-1251', $number3);
foreach (str_split($string3) as $value3) {
$ov3 = ord($value3);
$sum_number3+=$ov3;
}
$total_number = $sum_number1 + $sum_number2 + $sum_number1;
$total_number = 'Это и есть число к которому нужно применить условия указанные выше';
?>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,020 |
Ahlan wa Sahlan: Letters and Sounds of the Arabic Language. Mahdi Alosh (Author, Editor), Allen Clark (Editor). Yale University Press; 2 Pap/Cdr/ edition (June 23, 2009).
Although an Arabic-English dictionary is not required, it may be useful as a personal reference for the duration of this course. | {
"redpajama_set_name": "RedPajamaC4"
} | 952 |
<?php
namespace Strider2038\ImgCache\Tests\Unit\Imaging\Storage\Converter;
use PHPUnit\Framework\TestCase;
use Strider2038\ImgCache\Collection\StringList;
use Strider2038\ImgCache\Core\QueryParameterCollection;
use Strider2038\ImgCache\Imaging\Parsing\GeoMap\GeoMapParameters;
use Strider2038\ImgCache\Imaging\Storage\Converter\YandexMapParametersConverter;
use Strider2038\ImgCache\Imaging\Storage\Data\YandexMapParameters;
use Strider2038\ImgCache\Imaging\Storage\Data\YandexMapParametersFactoryInterface;
class YandexMapParametersConverterTest extends TestCase
{
private const LAYERS = ['map', 'sat'];
private const LATITUDE = 60.25;
private const LONGITUDE = -40.123;
private const ZOOM = 9;
private const WIDTH = 400;
private const HEIGHT = 300;
private const SCALE = 2.5;
private const QUERY_LAYERS = ['l' => 'map,sat'];
private const QUERY_LONGITUDE_AND_LATITUDE = ['ll' => '-40.123,60.25'];
private const QUERY_ZOOM = ['z' => self::ZOOM];
private const QUERY_SIZE = ['size' => '400,300'];
private const QUERY_SCALE = ['scale' => self::SCALE];
/** @var YandexMapParametersFactoryInterface */
private $yandexMapParametersFactory;
protected function setUp(): void
{
$this->yandexMapParametersFactory = \Phake::mock(YandexMapParametersFactoryInterface::class);
}
/** @test */
public function convertGeoMapParametersToQuery_givenGeoMapParameters_queryParameterCollectionCreatedAndReturned(): void
{
$converter = new YandexMapParametersConverter($this->yandexMapParametersFactory);
$geoMapParameters = \Phake::mock(GeoMapParameters::class);
$yandexMapParameters = new YandexMapParameters();
$yandexMapParameters->layers = new StringList(self::LAYERS);
$yandexMapParameters->latitude = self::LATITUDE;
$yandexMapParameters->longitude = self::LONGITUDE;
$yandexMapParameters->zoom = self::ZOOM;
$yandexMapParameters->width = self::WIDTH;
$yandexMapParameters->height = self::HEIGHT;
$yandexMapParameters->scale = self::SCALE;
$this->givenYandexMapParametersFactory_createYandexMapParametersFromGeoMapParameters_returnsYandexMapParameters($yandexMapParameters);
$query = $converter->convertGeoMapParametersToQuery($geoMapParameters);
$this->assertInstanceOf(QueryParameterCollection::class, $query);
$this->assertYandexMapParametersFactory_createYandexMapParametersFromGeoMapParameters_isCalledOnceWithGeoMapParameters($geoMapParameters);
$this->assertCount(5, $query);
$queryParameters = $query->toArray();
$this->assertArraySubset(self::QUERY_LAYERS, $queryParameters);
$this->assertArraySubset(self::QUERY_LONGITUDE_AND_LATITUDE, $queryParameters);
$this->assertArraySubset(self::QUERY_ZOOM, $queryParameters);
$this->assertArraySubset(self::QUERY_SIZE, $queryParameters);
$this->assertArraySubset(self::QUERY_SCALE, $queryParameters);
}
private function givenYandexMapParametersFactory_createYandexMapParametersFromGeoMapParameters_returnsYandexMapParameters($yandexMapParameters): void
{
\Phake::when($this->yandexMapParametersFactory)
->createYandexMapParametersFromGeoMapParameters(\Phake::anyParameters())
->thenReturn($yandexMapParameters);
}
private function assertYandexMapParametersFactory_createYandexMapParametersFromGeoMapParameters_isCalledOnceWithGeoMapParameters(
GeoMapParameters $geoMapParameters
): void {
\Phake::verify($this->yandexMapParametersFactory, \Phake::times(1))
->createYandexMapParametersFromGeoMapParameters($geoMapParameters);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,708 |
package org.powlab.jeye.decode.graph
import scala.collection.mutable.Map
class OpcodeTreeMarker(tree: OpcodeTree) {
private val id2Node: Map[String, OpcodeNode] = Map[String, OpcodeNode]()
/** Проверить, является ли узел помеченным */
def isMarked(node: OpcodeNode): Boolean = id2Node.contains(node.id)
/** Пометить узел как пройденный */
def mark(node: OpcodeNode) {
id2Node += node.id -> node
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,369 |
{"url":"https:\/\/zbmath.org\/serials\/?q=se%3A2215","text":"## INFORMS Journal on Computing\n\n Short Title: INFORMS J. Comput. Publisher: Institute for Operations Research and the Management Sciences (INFORMS), Catonsville, MD ISSN: 1091-9856; 1526-5528\/e Online: https:\/\/pubsonline.informs.org\/loi\/ijoc Predecessor: ORSA Journal on Computing Comments: Indexed cover-to-cover\n Documents Indexed: 1,224 Publications (since 1996) References Indexed: 618 Publications with 24,104 References.\nall top 5\n\n### Latest Issues\n\n 34, No. 4 (2022) 34, No. 3 (2022) 34, No. 2 (2022) 34, No. 1 (2022) 33, No. 4 (2021) 33, No. 3 (2021) 33, No. 2 (2021) 33, No. 1 (2021) 32, No. 4 (2020) 32, No. 3 (2020) 32, No. 2 (2020) 32, No. 1 (2020) 31, No. 4 (2019) 31, No. 3 (2019) 31, No. 2 (2019) 31, No. 1 (2019) 30, No. 4 (2018) 30, No. 3 (2018) 30, No. 2 (2018) 30, No. 1 (2018) 29, No. 4 (2017) 29, No. 3 (2017) 29, No. 2 (2017) 29, No. 1 (2017) 28, No. 4 (2016) 28, No. 3 (2016) 28, No. 2 (2016) 28, No. 1 (2016) 27, No. 4 (2015) 27, No. 3 (2015) 27, No. 2 (2015) 27, No. 1 (2015) 26, No. 4 (2014) 26, No. 3 (2014) 26, No. 2 (2014) 26, No. 1 (2014) 24, No. 4 (2012) 24, No. 3 (2012) 24, No. 2 (2012) 24, No. 1 (2012) 23, No. 4 (2011) 23, No. 3 (2011) 23, No. 2 (2011) 23, No. 1 (2011) 22, No. 4 (2010) 22, No. 3 (2010) 22, No. 2 (2010) 22, No. 1 (2010) 21, No. 4 (2009) 21, No. 3 (2009) 21, No. 2 (2009) 21, No. 1 (2009) 20, No. 4 (2008) 20, No. 3 (2008) 20, No. 2 (2008) 20, No. 1 (2008) 19, No. 4 (2007) 19, No. 3 (2007) 19, No. 2 (2007) 19, No. 1 (2007) 18, No. 4 (2006) 18, No. 3 (2006) 18, No. 2 (2006) 18, No. 1 (2006) 17, No. 4 (2005) 17, No. 3 (2005) 17, No. 2 (2005) 17, No. 1 (2005) 16, No. 4 (2004) 16, No. 3 (2004) 16, No. 2 (2004) 16, No. 1 (2004) 15, No. 4 (2003) 15, No. 3 (2003) 15, No. 2 (2003) 15, No. 1 (2003) 14, No. 4 (2002) 14, No. 3 (2002) 14, No. 2 (2002) 14, No. 1 (2002) 13, No. 4 (2001) 13, No. 3 (2001) 13, No. 2 (2001) 13, No. 1 (2001) 12, No. 4 (2000) 12, No. 3 (2000) 12, No. 2 (2000) 12, No. 1 (2000) 11, No. 4 (1999) 11, No. 3 (1999) 11, No. 2 (1999) 11, No. 1 (1999) 10, No. 3 (1998) 10, No. 2 (1998) 9, No. 4 (1997) 9, No. 3 (1997) 9, No. 2 (1997) 9, No. 1 (1997) 8, No. 4 (1996) 8, No. 3 (1996)\nall top 5\n\n### Authors\n\n 16 Savelsbergh, Martin W. P. 13 Nelson, Barry L. 12 Ahmed, Shabbir 12 Boland, Natashia L. 12 Nemhauser, George L. 12 Powell, Warren Buckler 11 den Hertog, Dick 11 Golden, Bruce L. 11 Jacobson, Sheldon H. 11 Laporte, Gilbert 10 Lodi, Andrea 10 Tang, Shaojie 10 Topaloglu, Huseyin 10 Van Hentenryck, Pascal 9 Fu, Michael C. 9 Smith, Alice E. 9 Whitt, Ward 8 Cordeau, Jean-Fran\u00e7ois 8 Glover, Fred W. 8 L\u2019Ecuyer, Pierre 8 Toth, Paolo 8 Zeng, Daniel Dajun 7 Bertsimas, Dimitris John 7 Burke, Edmund Kieran 7 Caprara, Alberto 7 Desaulniers, Guy 7 Iori, Manuel 7 Laguna, Manuel 7 Mart\u00ed, Rafael 7 Pessoa, Artur Alves 7 Prokopyev, Oleg Alexan 7 Raghavan, S. Raghu 7 Sherali, Hanif D. 7 Smith, J. Cole 7 Stuckey, Peter James 6 Averbakh, Igor 6 Beck, J. Christopher 6 Chinneck, John W. 6 Cir\u00e9, Andr\u00e9 Augusto 6 Cook, William John 6 Crainic, Teodor Gabriel 6 Dash, Sanjeeb 6 Denton, Brian T. 6 Fourer, Robert 6 Hong, Liu Jeff 6 Hooker, John N. jun. 6 Jans, Raf 6 Koehler, Gary J. 6 Labb\u00e9, Martine V. 6 Ljubi\u0107, Ivana 6 Peng, Yijie 6 Rousseau, Louis-Martin 6 Schaefer, Andrew J. 6 Shen, Siqian 6 Sotirov, Renata 6 Wasil, Edward A. 5 Bodur, Merve 5 Charkhgard, Hadi 5 Contardo, Claudio 5 Dey, Santanu S. 5 Eckstein, Jonathan 5 Ferris, Michael C. 5 Fukasawa, Ricardo 5 G\u00fcnl\u00fck, Oktay 5 Hoogeveen, Johannes Adzer 5 Hurkens, Cor A. J. 5 Irnich, Stefan 5 Kennington, Jeffery L. 5 Lenstra, Jan Karel 5 Monaci, Michele 5 Pisinger, David 5 Potts, Chris N. 5 Romeijn, H. Edwin 5 Sewell, Edward C. 5 Shen, Zuo-Jun Max 5 Song, Yongjia 5 Spieksma, Frits C. R. 5 Wallace, Stein W. 5 Watson, Jean-Paul 5 Wilson, James R. 4 Adomavicius, Gediminas 4 Ahuja, Ravindra K. 4 Bai, Xue 4 Brill, Percy H. 4 Buchanan, Austin 4 Chaovalitwongse, Wanpracha Art 4 Chen, Chun-Hung 4 Chen, Guoqing 4 Chen, Zhi-Long 4 Cornu\u00e9jols, G\u00e9rard P. 4 Dawande, Milind W. 4 Degraeve, Zeger 4 Drew, John H. 4 Du, Ding-Zhu 4 Fischetti, Matteo 4 Garfinkel, Robert S. 4 Gendreau, Michel 4 Gendron, Bernard 4 Gopal, Ram D. 4 Haouari, Mohamed ...and 2,135 more Authors\nall top 5\n\n### Fields\n\n 1,068 Operations research, mathematical programming\u00a0(90-XX) 151 Computer science\u00a0(68-XX) 73 Game theory, economics, finance, and other social and behavioral sciences\u00a0(91-XX) 70 Statistics\u00a0(62-XX) 67 Numerical analysis\u00a0(65-XX) 61 Probability theory and stochastic processes\u00a0(60-XX) 47 Biology and other natural sciences\u00a0(92-XX) 40 Combinatorics\u00a0(05-XX) 13 Information and communication theory, circuits\u00a0(94-XX) 10 General and overarching topics; collections\u00a0(00-XX) 7 Systems theory; control\u00a0(93-XX) 4 Integral transforms, operational calculus\u00a0(44-XX) 4 Calculus of variations and optimal control; optimization\u00a0(49-XX) 3 History and biography\u00a0(01-XX) 2 Linear and multilinear algebra; matrix theory\u00a0(15-XX) 2 Convex and discrete geometry\u00a0(52-XX) 1 Number theory\u00a0(11-XX) 1 Integral equations\u00a0(45-XX) 1 Geometry\u00a0(51-XX) 1 Geophysics\u00a0(86-XX)\n\n### Citations contained in zbMATH Open\n\n884 Publications have been cited 9,178 times in 6,641 Documents Cited by Year\nA column generation approach for graph coloring.\u00a0Zbl\u00a00884.90144\nMehrotra, Anuj; Trick, Michael A.\n1996\nCombinatorial auctions: a survey.\u00a0Zbl\u00a01238.91003\nDe Vries, Sven; Vohra, Rakesh V.\n2003\nThe granular tabu search and its application to the vehicle-routing problem.\u00a0Zbl\u00a01238.90141\nToth, Paolo; Vigo, Daniele\n2003\nA unified framework for numerically inverting Laplace transforms.\u00a0Zbl\u00a01241.65114\nAbate, Joseph; Whitt, Ward\n2006\nWhen does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)?\u00a0Zbl\u00a01034.90014\nWoeginger, Gerhard J.\n2000\nHeuristic and metaheuristic approaches for a class of two-dimensional bin packing problems.\u00a0Zbl\u00a01034.90500\nLodi, Andrea; Martello, Silvano; Vigo, Daniele\n1999\nA computational study of search strategies for mixed integer programming.\u00a0Zbl\u00a01040.90535\nLinderoth, J. T.; Savelsbergh, M. W. P.\n1999\nAn exact approach to the strip-packing problem.\u00a0Zbl\u00a01238.90116\nMartello, Silvano; Monaci, Michele; Vigo, Daniele\n2003\nSolving the orienteering problem through branch-and-cut.\u00a0Zbl\u00a01034.90523\nFischetti, Matteo; Salazar Gonz\u00e1lez, Juan Jos\u00e9; Toth, Paolo\n1998\nExact solution of the quadratic knapsack problem.\u00a0Zbl\u00a01034.90521\nCaprara, Alberto; Pisinger, David; Toth, Paolo\n1999\nGRASP and path relinking for 2-layer straight line crossing minimization.\u00a0Zbl\u00a01092.90544\nLaguna, Manuel; Mart\u00ed, Rafael\n1999\nOptimization for simulation: theory vs. practice.\u00a0Zbl\u00a01238.90001\nFu, Michael C.\n2002\nAn iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem.\u00a0Zbl\u00a01238.90061\nCongram, Richard K.; Potts, Chris N.; Van De Velde, Steef L.\n2002\nTime-indexed formulations for machine scheduling problems: Column generation.\u00a0Zbl\u00a01034.90004\nvan den Akker, J. M.; Hurkens, C. A. J.; Savelsbergh, M. W. P.\n2000\nSetting the research agenda in automated timetabling: the second international timetabling competition.\u00a0Zbl\u00a01243.90007\nMcCollum, Barry; Schaerf, Andrea; Paechter, Ben; McMullan, Paul; Lewis, Rhyd; Parkes, Andrew J.; Di Gaspero, Luca; Qu, Rong; Burke, Edmund K.\n2010\nUsing decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem.\u00a0Zbl\u00a01241.90118\nPisinger, David; Sigurd, Mikkel\n2007\nThe shortest-path problem with resource constraints and $$k$$-cycle elimination for $$k\\geq 3$$.\u00a0Zbl\u00a01241.90161\nIrnich, Stefan; Villeneuve, Daniel\n2006\nMINLPLib \u2013 a collection of test models for mixed-integer nonlinear programming.\u00a0Zbl\u00a01238.90104\nBussieck, Michael R.; Drud, Arne Stolbjerg; Meeraus, Alexander\n2003\nSolving parallel machine scheduling problems by column generation.\u00a0Zbl\u00a01034.90506\nChen, Zhi-Long; Powell, Warren B.\n1999\nFormulations and branch-and-cut algorithms for multivehicle production and inventory routing problems.\u00a0Zbl\u00a01356.90011\nAdulyasak, Yossiri; Cordeau, Jean-Fran\u00e7ois; Jans, Raf\n2014\nAlgorithms for hybrid MILP\/CP models for a class of optimization problems.\u00a0Zbl\u00a01238.90106\nJain, Vipul; Grossmann, Ignacio E.\n2001\nA reactive variable neighborhood search for the vehicle-routing problem with time windows.\u00a0Zbl\u00a01238.90136\nBr\u00e4ysy, Olli\n2003\nReactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment.\u00a0Zbl\u00a01040.90504\nPrais, Marcelo; Ribeiro, Celso C.\n2000\nGuided local search for the three-dimensional bin-packing problem.\u00a0Zbl\u00a01238.90112\nFaroe, Oluf; Pisinger, David; Zachariasen, Martin\n2003\nJob shop scheduling by local search.\u00a0Zbl\u00a00863.90094\nVaessens, R. J. M.; Aarts, Emile H. L.; Lenstra, Jan Karel\n1996\nAn exact solution approach based on shortest-paths for $$p$$-hub median problems.\u00a0Zbl\u00a01034.90505\nErnst, A. T.; Krishnamoorthy, M.\n1998\nComputing in operations research using Julia.\u00a0Zbl\u00a01331.90001\nLubin, Miles; Dunning, Iain\n2015\nCapacitated network design \u2013 polyhedral structure and computation.\u00a0Zbl\u00a00871.90031\nBienstock, Daniel; G\u00fcnl\u00fck, Oktay\n1996\nExtreme point-based heuristics for three-dimensional bin packing.\u00a0Zbl\u00a01243.90088\nCrainic, Teodor Gabriel; Perboli, Guido; Tadei, Roberto\n2008\nA stochastic radial basis function method for the global optimization of expensive functions.\u00a0Zbl\u00a01241.90192\nRegis, Rommel G.; Shoemaker, Christine A.\n2007\nMathematical programming for data mining: Formulations and challenges.\u00a0Zbl\u00a00973.90096\n1999\nScatter search and local NLP solvers: a multistart framework for global optimization.\u00a0Zbl\u00a01241.90093\nUgray, Zsolt; Lasdon, Leon; Plummer, John; Glover, Fred; Kelly, James; Mart\u00ed, Rafael\n2007\nFilMINT: an outer approximation-based solver for convex mixed-integer nonlinear programs.\u00a0Zbl\u00a01243.90142\nAbhishek, Kumar; Leyffer, Sven; Linderoth, Jeff\n2010\nAccelerating Benders decomposition by local branching.\u00a0Zbl\u00a01243.90122\nRei, Walter; Cordeau, Jean-Fran\u00e7ois; Gendreau, Michel; Soriano, Patrick\n2009\nSALOME: A bidirectional branch-and-bound procedure for assembly line balancing.\u00a0Zbl\u00a00895.90121\nScholl, Armin; Klein, Robert\n1997\nThe knowledge-gradient policy for correlated normal beliefs.\u00a0Zbl\u00a01243.91014\nFrazier, Peter; Powell, Warren; Dayanik, Savas\n2009\nA multiobjective branch-and-bound framework: application to the biobjective spanning tree problem.\u00a0Zbl\u00a01243.90206\nSourd, Francis; Spanjaard, Olivier\n2008\nUsing variable redefinfition for computing lower bounds for minimum spanning and Steiner trees with Hop constraints.\u00a0Zbl\u00a01054.90622\nGouveia, Luis\n1998\nA hybrid heuristic for an inventory routing problem.\u00a0Zbl\u00a01460.90009\nArchetti, Claudia; Bertazzi, Luca; Hertz, Alain; Speranza, M. Grazia\n2012\nA new formulation and resolution method for the $$p$$-center problem.\u00a0Zbl\u00a01239.90103\nElloumi, Sourour; Labb\u00e9, Martine; Pochet, Yves\n2004\nAn ejection chain approach for the generalized assignment problem.\u00a0Zbl\u00a01239.90091\nYagiura, Mutsunori; Ibaraki, Toshihide; Glover, Fred\n2004\nGenetic algorithms for the operations researcher.\u00a0Zbl\u00a00893.90145\nReeves, Colin R.\n1997\nA metaheuristic approach for the vertex coloring problem.\u00a0Zbl\u00a01243.90226\nMalaguti, Enrico; Monaci, Michele; Toth, Paolo\n2008\nA simplex-based tabu search method for capacitated network design.\u00a0Zbl\u00a01040.90506\nCrainic, Teodor Gabriel; Gendreau, Michel; Farvolden, Judith M.\n2000\nThe vehicle routing problem with time windows. II: Genetic search.\u00a0Zbl\u00a00866.90058\nPotvin, Jean-Yves; Bengio, Samy\n1996\nNeural network for combinatorial optimization: a review of more than a decade to research.\u00a0Zbl\u00a01034.90528\nSmith, Kate A.\n1999\nParre\u00f1o, Francisco; Alvarez-Valdes, Ram\u00f3n; Tamarit, Jos\u00e9 Manuel; Oliveira, Jos\u00e9 Fernando\n2008\nChained Lin-Kernighan for large traveling salesman problems.\u00a0Zbl\u00a01238.90125\nApplegate, David; Cook, William; Rohe, Andr\u00e9\n2003\nVariable neighborhood search for the pickup and delivery traveling salesman problem with LIFO loading.\u00a0Zbl\u00a01241.90103\nCarrabs, Francesco; Cordeau, Jean-Fran\u00e7ois; Laporte, Gilbert\n2007\nComputing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes.\u00a0Zbl\u00a01243.90174\nAnjos, Miguel F.; Vannelli, Anthony\n2008\nProgress in linear programming-based algorithms for integer programming: An exposition.\u00a0Zbl\u00a01052.90048\nJohnson, Ellis L.; Nemhauser, George L.; Savelsbergh, Martin W. P.\n2000\nUsing extra dual cuts to accelerate column generation.\u00a0Zbl\u00a01239.90089\nVal\u00e9rio de Carvalho, Jos\u00e9 Manuel\n2005\nA tree search algorithm for solving the container loading problem.\u00a0Zbl\u00a01243.90090\nFanslau, Tobias; Bortfeldt, Andreas\n2010\nAlgorithms for the bin packing problem with conflicts.\u00a0Zbl\u00a01243.90189\nMuritiba, Albert E. Fernandes; Iori, Manuel; Malaguti, Enrico; Toth, Paolo\n2010\nStochastic programming computation and applications.\u00a0Zbl\u00a00885.90087\nBirge, John R.\n1997\nA lifted linear programming branch-and-bound algorithm for mixed-integer conic quadratic programs.\u00a0Zbl\u00a01243.90170\nVielma, Juan Pablo; Ahmed, Shabbir; Nemhauser, George L.\n2008\nAn ant colony system hybridized with a new local search for the sequential ordering problem.\u00a0Zbl\u00a01040.90570\nGambardella, Luca Maria; Dorigo, Marco\n2000\nAn exact algorithm based on cut-and-column generation for the capacitated location-routing problem.\u00a0Zbl\u00a01356.90070\nContardo, Claudio; Cordeau, Jean-Fran\u00e7ois; Gendron, Bernard\n2014\nTour merging via branch-decomposition.\u00a0Zbl\u00a01238.90128\nCook, William; Seymour, Paul\n2003\nPerformance guarantees of local search for multiprocessor scheduling.\u00a0Zbl\u00a01241.90057\nSchuurman, Petra; Vredeveld, Tjark\n2007\nThe vehicle routing problem with time windows. I: Tabu search.\u00a0Zbl\u00a00866.90057\nPotvin, Jean-Yves; Kervahut, Tanguy; Garcia, Bruno-Laurent; Rousseau, Jean-Marc\n1996\nThe multidimensional knapsack problem: structure and algorithms.\u00a0Zbl\u00a01243.90190\nPuchinger, Jakob; Raidl, G\u00fcnther R.; Pferschy, Ulrich\n2010\nImproved constructive multistart strategies for the quadratic assignment problem using adaptive memory.\u00a0Zbl\u00a01040.90541\nFleurent, Charles; Glover, Fred\n1999\nChance-constrained binary packing problems.\u00a0Zbl\u00a01304.90179\nSong, Yongjia; Luedtke, James R.; K\u00fc\u00e7\u00fckyavuz, Simge\n2014\nApproximate dynamic programming for ambulance redeployment.\u00a0Zbl\u00a01243.90109\nMaxwell, Matthew S.; Restrepo, Mateo; Henderson, Shane G.; Topaloglu, Huseyin\n2010\nSolving large $$p$$-median problems with a radius formulation.\u00a0Zbl\u00a01243.90091\nGarc\u00eda, Sergio; Labb\u00e9, Martine; Mar\u00edn, Alfredo\n2011\nImprovement procedures for the undirected rural postman problem.\u00a0Zbl\u00a01034.90525\nHertz, Alain; Laporte, Gilbert; Nanchen Hugo, Pierrette\n1999\nBilevel knapsack with interdiction constraints.\u00a0Zbl\u00a01343.90075\nCaprara, Alberto; Carvalho, Margarida; Lodi, Andrea; Woeginger, Gerhard J.\n2016\nA branch-and-cut procedure for the multimode resource-constrained project-scheduling problem.\u00a0Zbl\u00a01241.90168\nZhu, Guidong; Bard, Jonathan F.; Yu, Gang\n2006\nCombining exact and heuristic approaches for the capacitated fixed-charge network flow problem.\u00a0Zbl\u00a01243.90031\nHewitt, Mike; Nemhauser, George L.; Savelsbergh, Martin W. P.\n2010\nMultistage adjustable robust mixed-integer optimization via iterative splitting of the uncertainty set.\u00a0Zbl\u00a01348.90507\nPostek, Krzysztof; den Hertog, Dick\n2016\nLinear time dynamic-programming algorithms for new classes of restricted TSPs: a computational study.\u00a0Zbl\u00a01238.90126\nBalas, Egon; Simonetti, Neil\n2001\nOperating room pooling and parallel surgery processing under uncertainty.\u00a0Zbl\u00a01243.90102\nBatun, Sakine; Denton, Brian T.; Huschka, Todd R.; Schaefer, Andrew J.\n2011\nDiscrete optimization with decision diagrams.\u00a0Zbl\u00a01338.90260\nBergman, David; Cire, Andre A.; van Hoeve, Willem-Jan; Hooker, J. N.\n2016\nExact solution of graph coloring problems via constraint programming and column generation.\u00a0Zbl\u00a01461.05091\nGualandi, Stefano; Malucelli, Federico\n2012\nA new genetic algorithm for the quadratic assignment problem.\u00a0Zbl\u00a01238.90108\nDrezner, Zvi\n2003\nGRASP with path relinking for three-index assignment.\u00a0Zbl\u00a01239.90087\nAiex, Renata M.; Resende, Mauricio G. C.; Pardalos, Panos M.; Toraldo, Gerardo\n2005\nDynamic-programming approximations for stochastic time-staged integer multicommodity-flow problems.\u00a0Zbl\u00a01241.90172\nTopaloglu, Huseyin; Powell, Warren B.\n2006\nAn evolutionary algorithm for polishing mixed integer programming solutions.\u00a0Zbl\u00a01241.90092\nRothberg, Edward\n2007\nA recursive algorithm for finding all nondominated extreme points in the outcome set of a multiobjective integer programme.\u00a0Zbl\u00a01243.90203\nPrzybylski, Anthony; Gandibleux, Xavier; Ehrgott, Matthias\n2010\nCombination of nonlinear and linear optimization of transient gas networks.\u00a0Zbl\u00a01243.90030\nDomschke, Pia; Gei\u00dfler, Bjorn; Kolb, Oliver; Lang, Jens; Martin, Alexander; Morsi, Antonio\n2011\nA branch, bound, and remember algorithm for the simple assembly line balancing problem.\u00a0Zbl\u00a01462.90112\nSewell, E. C.; Jacobson, S. H.\n2012\nStrengthened benders cuts for stochastic integer programs with continuous recourse.\u00a0Zbl\u00a01364.90220\nBodur, Merve; Dash, Sanjeeb; G\u00fcnl\u00fck, Oktay; Luedtke, James\n2017\nA hybrid GRASP with perturbations for the Steiner problem in graphs.\u00a0Zbl\u00a01238.90117\nRibeiro, Celso C.; Uchoa, Eduardo; Werneck, Renato F.\n2002\nA hybrid exact algorithm for the TSPTW.\u00a0Zbl\u00a01238.90054\nFocacci, Filippo; Lodi, Andrea; Milano, Michela\n2002\nA Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestion.\u00a0Zbl\u00a01243.90043\nElhedhli, Samir; Wu, Huyu\n2010\nA criterion space search algorithm for biobjective integer programming: the balanced box method.\u00a0Zbl\u00a01338.90365\nBoland, Natashia; Charkhgard, Hadi; Savelsbergh, Martin\n2015\nMinmax regret median location on a network under uncertainty.\u00a0Zbl\u00a01034.90007\nAverbakh, Igor; Berman, Oded\n2000\nA bundle type dual-ascent approach to linear multicommodity min-cost flow problems.\u00a0Zbl\u00a01034.90534\nFrangioni, Antonio; Gallo, Giorgio\n1999\nSolving the generalized assignment problem: an optimizing and heuristic approach.\u00a0Zbl\u00a01238.90090\nNauss, Robert M.\n2003\nA set-covering-based heuristic approach for bin-packing problems.\u00a0Zbl\u00a01241.90191\nMonaci, Michele; Toth, Paolo\n2006\nNew exact algorithms for one-machine earliness-tardiness scheduling.\u00a0Zbl\u00a01243.90071\nSourd, Francis\n2009\nThe reliable facility location problem: formulations, heuristics, and approximation algorithms.\u00a0Zbl\u00a01243.90096\nShen, Zuo-Jun Max; Zhan, Roger Lezhou; Zhang, Jiawei\n2011\nAn improved primal simplex algorithm for degenerate linear programs.\u00a0Zbl\u00a01243.90121\nElhallaoui, Issmail; Metrane, Abdelmoutalib; Desaulniers, Guy; Soumis, Fran\u00e7ois\n2011\nA reactive tabu search metaheuristic for the vehicle routing problem with time windows.\u00a0Zbl\u00a00901.90088\nChiang, Wen-Chyuan; Russell, Robert A.\n1997\nBranch and price for large-scale capacitated hub location problems with single assignment.\u00a0Zbl\u00a01243.90087\nContreras, Ivan; D\u00edaz, Juan A.; Fern\u00e1ndez, Elena\n2011\nOn the two-level uncapacitated facility location problem.\u00a0Zbl\u00a00863.90102\nAardal, Karen; Labb\u00e9, Martine; Leung, Janny; Queyranne, Maurice\n1996\nFeature selection via mathematical programming.\u00a0Zbl\u00a01034.90529\nBradley, P. S.; Mangasarian, O. L.; Street, W. N.\n1998\nImproving the integer L-shaped method.\u00a0Zbl\u00a01348.90498\nAngulo, Gustavo; Ahmed, Shabbir; Dey, Santanu S.\n2016\nCovering linear programming with violations.\u00a0Zbl\u00a01304.90139\nQiu, Feng; Ahmed, Shabbir; Dey, Santanu S.; Wolsey, Laurence A.\n2014\nDistributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and Humanitarian logistics.\u00a0Zbl\u00a007551207\nNoyan, Nilay; Rudolf, G\u00e1bor; Lejeune, Miguel\n2022\nAlfonso: Matlab package for nonsymmetric conic optimization.\u00a0Zbl\u00a007549362\nPapp, D\u00e1vid; Y\u0131ld\u0131z, Sercan\n2022\nIntegrated multiresource capacity planning and multitype patient scheduling.\u00a0Zbl\u00a007549369\nZhou, Liping; Geng, Na; Jiang, Zhibin; Jiang, Shan\n2022\nExact and approximation algorithms for the expanding search problem.\u00a0Zbl\u00a007549378\nHermans, Ben; Leus, Roel; Matuschke, Jannik\n2022\nInteger programming, constraint programming, and hybrid decomposition approaches to discretizable distance geometry problems.\u00a0Zbl\u00a007549379\nMacNeil, Moira; Bodur, Merve\n2022\nSolving the type-2 assembly line balancing with setups using logic-based Benders decomposition.\u00a0Zbl\u00a007549380\nZohali, Hassan; Naderi, Bahman; Roshanaei, Vahid\n2022\nThe value of randomized solutions in mixed-integer distributionally robust optimization problems.\u00a0Zbl\u00a007549381\nDelage, Erick; Saif, Ahmed\n2022\nLearning for constrained optimization: identifying optimal active constraint sets.\u00a0Zbl\u00a007549388\nMisra, Sidhant; Roald, Line; Ng, Yeesian\n2022\nBranch-and-bound for biobjective mixed-integer linear programming.\u00a0Zbl\u00a007551217\n2022\nEstimating the size of branch-and-bound trees.\u00a0Zbl\u00a007551218\nHendel, Gregor; Anderson, Daniel; Le Bodic, Pierre; Pfetsch, Marc E.\n2022\nNovel formulations and logic-based Benders decomposition for the integrated parallel machine scheduling and location problem.\u00a0Zbl\u00a007551225\nLi, Yantong; C\u00f4t\u00e9, Jean-Fran\u00e7ois; Callegari-Coelho, Leandro; Wu, Peng\n2022\nAn analytic center cutting plane method to determine complete positivity of a matrix.\u00a0Zbl\u00a007551228\n2022\nA general framework for approximating min sum ordering problems.\u00a0Zbl\u00a007552216\nHappach, Felix; Hellerstein, Lisa; Lidbetter, Thomas\n2022\nA scalable algorithm for sparse portfolio selection.\u00a0Zbl\u00a007552219\nBertsimas, Dimitris; Cory-Wright, Ryan\n2022\nBenders subproblem decomposition for bilevel problems with convex follower.\u00a0Zbl\u00a007552233\nByeon, Geunyeong; van Hentenryck, Pascal\n2022\nSOS-SDP: an exact solver for minimum sum-of-squares clustering.\u00a0Zbl\u00a007587562\nPiccialli, Veronica; Sudoso, Antonio M.; Wiegele, Angelika\n2022\nEnumeration of the nondominated set of multiobjective discrete optimization problems.\u00a0Zbl\u00a007362304\nTamby, Satya; Vanderpooten, Daniel\n2021\nSDDP.jl: a Julia package for stochastic dual dynamic programming.\u00a0Zbl\u00a007362301\nDowson, Oscar; Kapelevich, Lea\n2021\nLogic-based Benders decomposition and binary decision diagram based approaches for stochastic distributed operating room scheduling.\u00a0Zbl\u00a007549350\nGuo, Cheng; Bodur, Merve; Aleman, Dionne M.; Urbach, David R.\n2021\nRobust optimization for electricity generation.\u00a0Zbl\u00a007362319\nYang, Haoxiang; Morton, David P.; Bandi, Chaithanya; Dvijotham, Krishnamurthy\n2021\nA mixed-integer fractional optimization approach to best subset selection.\u00a0Zbl\u00a007362333\nG\u00f3mez, Andr\u00e9s; Prokopyev, Oleg A.\n2021\nStochastic decomposition for two-stage stochastic linear programs with random cost coefficients.\u00a0Zbl\u00a007362303\nGangammanavar, Harsha; Liu, Yifan; Sen, Suvrajeet\n2021\nComplexity results and effective algorithms for worst-case linear optimization under uncertainties.\u00a0Zbl\u00a007362310\nLuo, Hezhi; Ding, Xiaodong; Peng, Jiming; Jiang, Rujun; Li, Duan\n2021\nEfficient sampling allocation procedures for optimal quantile selection.\u00a0Zbl\u00a007362313\nPeng, Yijie; Chen, Chun-Hung; Fu, Michael C.; Hu, Jian-Qiang; Ryzhov, Ilya O.\n2021\nDecision diagram decomposition for quadratically constrained binary optimization.\u00a0Zbl\u00a007362323\nBergman, David; Lozano, Leonardo\n2021\nData-driven preference learning methods for value-driven multiple criteria sorting with interacting criteria.\u00a0Zbl\u00a01466.90041\nLiu, Jiapeng; Kadzi\u0144ski, Mi\u0142osz; Liao, Xiuwu; Mao, Xiaoxin\n2021\nScenario grouping and decomposition algorithms for chance-constrained programs.\u00a0Zbl\u00a007362345\nDeng, Yan; Jia, Huiwen; Ahmed, Shabbir; Lee, Jon; Shen, Siqian\n2021\nA multistage stochastic programming approach to the optimal surveillance and control of the emerald ash borer in cities.\u00a0Zbl\u00a007362348\nK\u0131b\u0131\u015f, Eyy\u00fcb Y.; B\u00fcy\u00fcktahtak\u0131n, \u0130. Esra; Haight, Robert G.; Akhundov, Najmaddin; Knight, Kathleen; Flower, Charles E.\n2021\nThe quadratic multiknapsack problem with conflicts and balance constraints.\u00a0Zbl\u00a007548819\nOlivier, Philippe; Lodi, Andrea; Pesant, Gilles\n2021\nAn augmented Lagrangian decomposition method for chance-constrained optimization problems.\u00a0Zbl\u00a007548825\nBai, Xiaodi; Sun, Jie; Zheng, Xiaojin\n2021\nData-driven optimization of reward-risk ratio measures.\u00a0Zbl\u00a007548829\nJi, Ran; Lejeune, Miguel A.\n2021\nSDP-based bounds for the quadratic cycle cover problem via cutting-plane augmented Lagrangian methods and reinforcement learning.\u00a0Zbl\u00a007549332\nde Meijer, Frank; Sotirov, Renata\n2021\nMultivariable branching: a 0-1 knapsack problem case study.\u00a0Zbl\u00a007549338\nYang, Yu; Boland, Natashia; Savelsbergh, Martin\n2021\nUnifying online and offline preference for social link prediction.\u00a0Zbl\u00a007549341\nZhou, Fan; Zhang, Kunpeng; Wu, Bangying; Yang, Yi; Wang, Harry Jiannan\n2021\nA branch-and-bound algorithm for building optimal data gathering tree in wireless sensor networks.\u00a0Zbl\u00a007549344\nZhu, Xiaojun; Tang, Shaojie\n2021\nRanking and selection with covariates for personalized decision making.\u00a0Zbl\u00a007549347\nShen, Haihui; Hong, L. Jeff; Zhang, Xiaowei\n2021\nRobust capacity planning for project management.\u00a0Zbl\u00a007549349\nConejo, Antonio J.; Hall, Nicholas G.; Long, Daniel Zhuoyu; Zhang, Runhao\n2021\nModeling defender-attacker problems as robust linear programs with mixed-integer uncertainty sets.\u00a0Zbl\u00a007549351\nBorrero, Juan S.; Lozano, Leonardo\n2021\nSong, Guopeng; Kis, Tam\u00e1s; Leus, Roel\n2021\nExploiting the structure of two-stage robust optimization models with exponential scenarios.\u00a0Zbl\u00a007362308\nDoulabi, Hossein Hashemi; Jaillet, Patrick; Pesant, Gilles; Rousseau, Louis-Martin\n2021\nComputing feasible points of bilevel problems with a penalty alternating direction method.\u00a0Zbl\u00a007362311\nKleinert, Thomas; Schmidt, Martin\n2021\nA computational approach to first passage problems of reflected hyperexponential jump diffusion processes.\u00a0Zbl\u00a007362312\nCai, Ning; Yang, Xuewei\n2021\nSparse convex regression.\u00a0Zbl\u00a007362315\nBertsimas, Dimitris; Mundru, Nishanth\n2021\nMultistage stochastic power generation scheduling co-optimizing energy and ancillary services.\u00a0Zbl\u00a01466.90037\nHuang, Jianqiu; Pan, Kai; Guan, Yongpei\n2021\nWorst-case expected shortfall with univariate and bivariate marginals.\u00a0Zbl\u00a007362321\nDhara, Anulekha; Das, Bikramjit; Natarajan, Karthik\n2021\nConflict analysis for MINLP.\u00a0Zbl\u00a007362326\nBerthold, Timo; Witzig, Jakob\n2021\nModeling single-picker routing problems in classical and modern warehouses.\u00a0Zbl\u00a007362327\nGoeke, Dominik; Schneider, Michael\n2021\nVehicle sequencing at transshipment terminals with handover relations.\u00a0Zbl\u00a01466.90006\nBriskorn, Dirk; Fliedner, Malte; Tsch\u00f6ke, Martin\n2021\nReducing simulation input-model risk via input model averaging.\u00a0Zbl\u00a01466.90002\nNelson, Barry L.; Wan, Alan T. K.; Zou, Guohua; Zhang, Xinyu; Jiang, Xi\n2021\nConflict-driven heuristics for mixed integer programming.\u00a0Zbl\u00a007362342\nWitzig, Jakob; Gleixner, Ambros\n2021\nExact multiple sequence alignment by synchronized decision diagrams.\u00a0Zbl\u00a007362343\nHosseininasab, Amin; van Hoeve, Willem-Jan\n2021\nLearning to solve large-scale security-constrained unit commitment problems.\u00a0Zbl\u00a007362344\nXavier, \u00c1linson S.; Qiu, Feng; Ahmed, Shabbir\n2021\nBreaking the $$r_{\\max}$$ barrier: enhanced approximation algorithms for partial set multicover problem.\u00a0Zbl\u00a007362346\nRan, Yingli; Zhang, Zhao; Tang, Shaojie; Du, Ding-Zhu\n2021\nEnhanced pseudo-polynomial formulations for bin packing and cutting stock problems.\u00a0Zbl\u00a007284456\nDelorme, Maxence; Iori, Manuel\n2020\nPresolve reductions in mixed integer programming.\u00a0Zbl\u00a007290858\nAchterberg, Tobias; Bixby, Robert E.; Gu, Zonghao; Rothberg, Edward; Weninger, Dieter\n2020\nGlobally solving nonconvex quadratic programs via linear integer programming techniques.\u00a0Zbl\u00a007284452\nXia, Wei; Vera, Juan C.; Zuluaga, Luis F.\n2020\nA new branch-and-price-and-cut algorithm for one-dimensional bin-packing problems.\u00a0Zbl\u00a007290855\nWei, Lijun; Luo, Zhixing; Baldacci, Roberto; Lim, Andrew\n2020\nThe mothership and drone routing problem.\u00a0Zbl\u00a01451.90020\nPoikonen, Stefan; Golden, Bruce\n2020\nSampling scenario set partition dual bounds for multistage stochastic programs.\u00a0Zbl\u00a007284459\nBakir, Ilke; Boland, Natashia; Dandurand, Brian; Erera, Alan\n2020\nOn solving the quadratic shortest path problem.\u00a0Zbl\u00a01451.90018\nHu, Hao; Sotirov, Renata\n2020\nOn the variance of single-run unbiased stochastic derivative estimators.\u00a0Zbl\u00a007290853\nCui, Zhenyu; Fu, Michael C.; Hu, Jian-Qiang; Liu, Yanchu; Peng, Yijie; Zhu, Lingjiong\n2020\nA criterion space method for biobjective mixed integer programming: the boxed line method.\u00a0Zbl\u00a007284451\nPerini, Tyler; Boland, Natashia; Pecin, Diego; Savelsbergh, Martin\n2020\nBranch and price for chance-constrained bin packing.\u00a0Zbl\u00a007290862\nZhang, Zheng; Denton, Brian T.; Xie, Xiaolan\n2020\nAdvanced tabu search algorithms for bipartite Boolean quadratic programs guided by strategic oscillation and path relinking.\u00a0Zbl\u00a007284454\nWu, Qinghua; Wang, Yang; Glover, Fred\n2020\nProbabilistic analysis of rumor-spreading time.\u00a0Zbl\u00a01451.90030\nMocquard, Yves; Sericola, Bruno; Anceaume, Emmanuelle\n2020\nEstimating the probability that a function observed with noise is convex.\u00a0Zbl\u00a007290852\nJian, Nanjing; Henderson, Shane G.\n2020\nMathematical models and search algorithms for the capacitated $$p$$-center problem.\u00a0Zbl\u00a01451.90087\nKramer, Raphael; Iori, Manuel; Vidal, Thibaut\n2020\nPiecewise linear function fitting via mixed-integer linear programming.\u00a0Zbl\u00a007290859\n2020\nOptimization-driven scenario grouping.\u00a0Zbl\u00a007290877\nRyan, Kevin; Ahmed, Shabbir; Dey, Santanu S.; Rajan, Deepak; Musselman, Amelia; Watson, Jean-Paul\n2020\nAssortment optimization under the multinomial logit model with sequential offerings.\u00a0Zbl\u00a007290879\nLiu, Nan; Ma, Yuhang; Topaloglu, Huseyin\n2020\nOn mixed-integer programming formulations for the unit commitment problem.\u00a0Zbl\u00a007303811\nKnueven, Bernard; Ostrowski, James; Watson, Jean-Paul\n2020\nRobust quadratic programming with mixed-integer uncertainty.\u00a0Zbl\u00a01474.90312\nMittal, Areesh; Gokalp, Can; Hanasusanto, Grani A.\n2020\nMultiobjective integer programming: synergistic parallel approaches.\u00a0Zbl\u00a007290857\n2020\nA branch-price-and-cut procedure for the discrete ordered Median problem.\u00a0Zbl\u00a01451.90085\nDeleplanque, Samuel; Labb\u00e9, Martine; Ponce, Diego; Puerto, Justo\n2020\nRobust optimization of a broad class of heterogeneous vehicle routing problems under demand uncertainty.\u00a0Zbl\u00a01451.90021\nSubramanyam, Anirudh; Repoussis, Panagiotis P.; Gounaris, Chrysanthos E.\n2020\nThe optimal design of low-latency virtual backbones.\u00a0Zbl\u00a01456.90040\nValidi, Hamidreza; Buchanan, Austin\n2020\nCommunication-constrained expansion planning for resilient distribution systems.\u00a0Zbl\u00a01456.90038\nByeon, Geunyeong; Van Hentenryck, Pascal; Bent, Russell; Nagarajan, Harsha\n2020\nProduction and transportation integration for commit-to-delivery mode with general shipping costs.\u00a0Zbl\u00a01456.90032\nLi, Feng; Xu, Zhou; Chen, Zhi-Long\n2020\nAn adaptive heuristic approach to compute upper and lower bounds for the close-enough traveling salesman problem.\u00a0Zbl\u00a007303821\nCarrabs, Francesco; Cerrone, Carmine; Cerulli, Raffaele; Golden, Bruce\n2020\nA core-based exact algorithm for the multidimensional multiple choice knapsack problem.\u00a0Zbl\u00a007303823\nMansini, Renata; Zanotti, Roberto\n2020\nReducing conservatism in robust optimization.\u00a0Zbl\u00a007303826\nRoos, Ernst; den Hertog, Dick\n2020\nFiltering algorithms for biobjective mixed binary linear optimization problems with a multiple-choice constraint.\u00a0Zbl\u00a007284453\n2020\nAn improved branch-cut-and-price algorithm for parallel machine scheduling problems.\u00a0Zbl\u00a01451.90068\nOliveira, Daniel; Pessoa, Artur\n2020\nA flexible, natural formulation for the network design problem with vulnerability constraints.\u00a0Zbl\u00a01451.90024\nArslan, Okan; Jabali, Ola; Laporte, Gilbert\n2020\nConvex optimization for group feature selection in networked data.\u00a0Zbl\u00a01451.90034\nWon, Daehan; Manzour, Hasan; Chaovalitwongse, Wanpracha\n2020\nAn MDD-based Lagrangian approach to the multicommodity pickup-and-delivery TSP.\u00a0Zbl\u00a007290845\nCastro, Margarita P.; Cire, Andre A.; Beck, J. Christopher\n2020\nLeast-cost influence maximization on social networks.\u00a0Zbl\u00a01461.91224\nG\u00fcnne\u00e7, Dilek; Raghavan, S.; Zhang, Rui\n2020\nSuccessive quadratic upper-bounding for discrete mean-risk minimization and network interdiction.\u00a0Zbl\u00a01474.90325\nAtamt\u00fcrk, Alper; Deck, Carlos; Jeon, Hyemin\n2020\nOnline risk monitoring using offline simulation.\u00a0Zbl\u00a007290851\nJiang, Guangxin; Hong, L. Jeff; Nelson, Barry L.\n2020\nRelative robust and adaptive optimization.\u00a0Zbl\u00a007290854\nBertsimas, Dimitris; Dunning, Iain\n2020\nOn the derivation of continuous piecewise linear approximating functions.\u00a0Zbl\u00a007290861\nKong, Lingxun; Maravelias, Christos T.\n2020\nDomination measure: a new metric for solving multiobjective optimization.\u00a0Zbl\u00a007290863\nHale, Joshua Q.; Zhu, Helin; Zhou, Enlu\n2020\nLearning to correlate accounts across online social networks: an embedding-based approach.\u00a0Zbl\u00a01461.91239\nZhou, Fan; Zhang, Kunpeng; Xie, Shuying; Luo, Xucheng\n2020\nBilinear assignment problem: large neighborhoods and experimental analysis of algorithms.\u00a0Zbl\u00a007290872\nSokol, Vladyslav; \u0106usti\u0107, Ante; Punnen, Abraham P.; Bhattacharya, Binay\n2020\nDifferentially private distributed learning.\u00a0Zbl\u00a007290875\nZhou, Yaqin; Tang, Shaojie\n2020\nAn approximation approach for response-adaptive clinical trial design.\u00a0Zbl\u00a007303812\nAhuja, Vishal; Birge, John R.\n2020\nA theoretical framework for learning tumor dose-response uncertainty in individualized spatiobiologically integrated radiotherapy.\u00a0Zbl\u00a007303815\nAjdari, Ali; Saberian, Fatemeh; Ghate, Archis\n2020\nA practical scheme to compute the pessimistic bilevel optimization problem.\u00a0Zbl\u00a007303827\nZeng, Bo\n2020\nProvably near-optimal approximation schemes for implicit stochastic and sample-based dynamic programs.\u00a0Zbl\u00a007303829\nHalman, Nir\n2020\nInterdiction games and monotonicity, with application to knapsack problems.\u00a0Zbl\u00a007281718\nFischetti, Matteo; Ljubi\u0107, Ivana; Monaci, Michele; Sinnl, Markus\n2019\n...and 784 more Documents\nall top 5\n\n### Cited by 9,539 Authors\n\n 55 Laporte, Gilbert 39 Lodi, Andrea 37 Pardalos, Panos M. 35 Gendreau, Michel 35 Lim, Andrew E. B. 33 Crainic, Teodor Gabriel 32 Cordeau, Jean-Fran\u00e7ois 31 Hao, Jin-Kao 31 Iori, Manuel 30 Glover, Fred W. 30 Savelsbergh, Martin W. P. 28 Mart\u00ed, Rafael 28 Resende, Mauricio G. C. 27 Uchoa, Eduardo 25 Archetti, Claudia 25 Powell, Warren Buckler 25 Puerto Albandoz, Justo 24 Gendron, Bernard 24 Gouveia, Luis 23 Bertsimas, Dimitris John 23 Boland, Natashia L. 23 Boysen, Nils 23 Burke, Edmund Kieran 23 Furini, Fabio 23 Irnich, Stefan 22 Hartl, Richard F. 22 Labb\u00e9, Martine V. 22 Mladenovi\u0107, Nenad 21 Ahmed, Shabbir 21 Coelho, Leandro C. 21 Pessoa, Artur Alves 20 Monaci, Michele 19 Frangioni, Antonio 19 Letchford, Adam N. 19 Luedtke, James R. 19 Rodriguez-Chia, Antonio M. 19 Sadykov, Ruslan 19 Schmidt, Martin 18 Berthold, Timo 18 Desaulniers, Guy 18 D\u00f6rner, Karl F. 18 Fischetti, Matteo 18 Haouari, Mohamed 18 Jans, Raf 18 Ljubi\u0107, Ivana 18 Locatelli, Marco 18 Nemhauser, George L. 18 Pisinger, David 18 Prins, Christian 18 Sahinidis, Nikolaos V. 18 Soumis, Fran\u00e7ois 18 Strusevich, Vitaly A. 17 Grossmann, Ignacio E. 17 Malaguti, Enrico 17 Prokopyev, Oleg Alexan 16 Anjos, Miguel F. 16 Ernst, Andreas T. 16 Martello, Silvano 16 Salazar-Gonz\u00e1lez, Juan-Jos\u00e9 16 Smith, J. Cole 16 Vidal, Thibaut 16 Vielma, Juan Pablo 16 Woeginger, Gerhard Johannes 16 Wu, Qinghua 15 Charkhgard, Hadi 15 Cheng, Tai-Chiu Edwin 15 Fern\u00e1ndez, Elena 15 Hanafi, Sa\u00efd 15 Hansen, Pierre 15 Koch, Thorsten 15 Liberti, Leo 15 Pereira, Jordi 15 Scholl, Armin 15 Sherali, Hanif D. 14 Chaudhry, Mohan L. 14 Della Croce, Federico 14 Hooker, John N. jun. 14 Mar\u00edn, Alfredo 14 Martin, Alexander 14 Pfetsch, Marc E. 14 Poss, Michael 14 Schoen, Fabio 14 Sinnl, Markus 14 St\u00fctzle, Thomas G. 14 Wei, Lijun 13 Atamt\u00fcrk, Alper 13 Ceselli, Alberto 13 Cir\u00e9, Andr\u00e9 Augusto 13 Clautiaux, Fran\u00e7ois 13 Dash, Sanjeeb 13 Dey, Santanu S. 13 Drezner, Zvi 13 Duarte, Abraham 13 Fukasawa, Ricardo 13 Golden, Bruce L. 13 Grosso, Andrea 13 G\u00fcnl\u00fck, Oktay 13 Jacobson, Sheldon H. 13 Landete, Mercedes 13 Rousseau, Louis-Martin ...and 9,439 more Authors\nall top 5\n\n### Cited in 353 Journals\n\n 1,295 European Journal of Operational Research 931 Computers & Operations Research 347 INFORMS Journal on Computing 322 Annals of Operations Research 170 Mathematical Programming. Series A. Series B 159 Discrete Applied Mathematics 144 Journal of Global Optimization 130 Operations Research Letters 126 Computational Optimization and Applications 121 Operations Research 95 Discrete Optimization 90 Optimization Letters 87 Mathematical Programming Computation 84 Journal of Combinatorial Optimization 78 Journal of Scheduling 64 Theoretical Computer Science 63 OR Spectrum 60 Networks 59 Optimization Methods & Software 57 Applied Mathematics and Computation 56 Applied Mathematical Modelling 56 International Transactions in Operational Research 56 4OR 52 Top 52 Journal of Heuristics 51 SIAM Journal on Optimization 43 Optimization and Engineering 41 Mathematical Problems in Engineering 41 RAIRO. Operations Research 39 Constraints 36 International Journal of Production Research 36 Algorithmica 34 Information Sciences 34 Journal of Optimization Theory and Applications 33 Mathematical Methods of Operations Research 31 Asia-Pacific Journal of Operational Research 29 EURO Journal on Computational Optimization 27 Journal of Computational and Applied Mathematics 26 CEJOR. Central European Journal of Operations Research 26 Computational Management Science 25 Optimization 24 Information Processing Letters 23 Queueing Systems 23 Journal of Industrial and Management Optimization 22 Mathematics of Operations Research 21 Naval Research Logistics 18 Annals of Mathematics and Artificial Intelligence 18 Networks and Spatial Economics 17 JMMA. Journal of Mathematical Modelling and Algorithms 16 Artificial Intelligence 14 International Journal of Computer Mathematics 14 Methodology and Computing in Applied Probability 13 Journal of Computer and System Sciences 12 Computers & Mathematics with Applications 12 Physica A 12 Mathematics and Computers in Simulation 12 Numerical Algorithms 12 SN Operations Research Forum 11 Journal of Computational Physics 11 Opsearch 11 Discrete Dynamics in Nature and Society 11 Journal of Applied Mathematics 10 Computer Methods in Applied Mechanics and Engineering 10 Linear Algebra and its Applications 10 Computational Statistics and Data Analysis 10 SIAM Journal on Scientific Computing 10 Probability in the Engineering and Informational Sciences 9 Automatica 9 Mathematical and Computer Modelling 9 Machine Learning 9 Communications in Statistics. Theory and Methods 9 Computational and Applied Mathematics 9 Algorithms 9 Advances in Operations Research 9 Journal of the Operations Research Society of China 8 Advances in Applied Probability 8 Journal of Mathematical Biology 8 Mathematical Biosciences 8 Bulletin of Mathematical Biology 8 Communications in Statistics. Simulation and Computation 8 Cybernetics and Systems Analysis 8 International Journal of Systems Science. Principles and Applications of Systems and Integration 7 International Journal of Systems Science 7 Games and Economic Behavior 7 Automation and Remote Control 7 Journal of Statistical Computation and Simulation 7 ACM Transactions on Modeling and Computer Simulation 7 Quantitative Finance 7 Stochastic Models 7 The Annals of Applied Statistics 6 Journal of Fluid Mechanics 6 Journal of Applied Probability 6 SIAM Journal on Computing 6 Insurance Mathematics & Economics 6 SIAM Journal on Discrete Mathematics 6 Computational Geometry 6 Journal of Computer and Systems Sciences International 6 Theory of Computing Systems 6 Soft Computing 6 International Journal of Theoretical and Applied Finance ...and 253 more Journals\nall top 5\n\n### Cited in 50 Fields\n\n 5,747 Operations research, mathematical programming\u00a0(90-XX) 777 Computer science\u00a0(68-XX) 409 Game theory, economics, finance, and other social and behavioral sciences\u00a0(91-XX) 378 Numerical analysis\u00a0(65-XX) 358 Combinatorics\u00a0(05-XX) 275 Statistics\u00a0(62-XX) 231 Probability theory and stochastic processes\u00a0(60-XX) 188 Biology and other natural sciences\u00a0(92-XX) 90 Calculus of variations and optimal control; optimization\u00a0(49-XX) 78 Systems theory; control\u00a0(93-XX) 45 Convex and discrete geometry\u00a0(52-XX) 35 Fluid mechanics\u00a0(76-XX) 32 Information and communication theory, circuits\u00a0(94-XX) 28 Mechanics of deformable solids\u00a0(74-XX) 25 Linear and multilinear algebra; matrix theory\u00a0(15-XX) 18 Number theory\u00a0(11-XX) 18 Integral transforms, operational calculus\u00a0(44-XX) 17 Partial differential equations\u00a0(35-XX) 16 Statistical mechanics, structure of matter\u00a0(82-XX) 14 Operator theory\u00a0(47-XX) 12 Ordinary differential equations\u00a0(34-XX) 8 General and overarching topics; collections\u00a0(00-XX) 8 History and biography\u00a0(01-XX) 8 Mathematical logic and foundations\u00a0(03-XX) 7 Group theory and generalizations\u00a0(20-XX) 7 Geophysics\u00a0(86-XX) 6 Integral equations\u00a0(45-XX) 6 Functional analysis\u00a0(46-XX) 6 Quantum theory\u00a0(81-XX) 5 Order, lattices, ordered algebraic structures\u00a0(06-XX) 5 Dynamical systems and ergodic theory\u00a0(37-XX) 5 Harmonic analysis on Euclidean spaces\u00a0(42-XX) 4 Measure and integration\u00a0(28-XX) 4 Classical thermodynamics, heat transfer\u00a0(80-XX) 3 Algebraic geometry\u00a0(14-XX) 3 Real functions\u00a0(26-XX) 3 Special functions\u00a0(33-XX) 3 Approximations and expansions\u00a0(41-XX) 2 Field theory and polynomials\u00a0(12-XX) 2 Functions of a complex variable\u00a0(30-XX) 2 Global analysis, analysis on manifolds\u00a0(58-XX) 2 Mechanics of particles and systems\u00a0(70-XX) 2 Optics, electromagnetic theory\u00a0(78-XX) 1 Associative rings and algebras\u00a0(16-XX) 1 Several complex variables and analytic spaces\u00a0(32-XX) 1 Sequences, series, summability\u00a0(40-XX) 1 General topology\u00a0(54-XX) 1 Manifolds and cell complexes\u00a0(57-XX) 1 Astronomy and astrophysics\u00a0(85-XX) 1 Mathematics education\u00a0(97-XX)","date":"2022-10-05 09:04:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.47604861855506897, \"perplexity\": 14502.528387234173}, \"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-2022-40\/segments\/1664030337595.1\/warc\/CC-MAIN-20221005073953-20221005103953-00099.warc.gz\"}"} | null | null |
package edu.stanford.nlp.trees;
import java.util.List;
import java.util.regex.Pattern;
import edu.stanford.nlp.trees.tregex.TregexPattern;
import edu.stanford.nlp.trees.tregex.tsurgeon.Tsurgeon;
import edu.stanford.nlp.trees.tregex.tsurgeon.TsurgeonPattern;
import edu.stanford.nlp.util.Generics;
import edu.stanford.nlp.util.Pair;
/**
* Transforms an English structure parse tree in order to get the dependencies right:
* -- put a ROOT node
* -- remove NONE nodes
* -- retain only NP-TMP and NP-ADV tags
*
* (Note [cdm]: A lot of this overlaps other existing functionality in trees.
* Could aim to unify it.)
*
* @author mcdm
*/
public class DependencyTreeTransformer implements TreeTransformer {
private static final Pattern NPTmpPattern = Pattern.compile("NP.*-TMP.*");
private static final Pattern NPAdvPattern = Pattern.compile("NP.*-ADV.*");
protected final TreebankLanguagePack tlp;
public DependencyTreeTransformer() {
tlp = new PennTreebankLanguagePack();
}
public Tree transformTree(Tree t) {
//deal with empty root
t.setValue(cleanUpRoot(t.value()));
//strips tags
stripTag(t);
// strip empty nodes
return stripEmptyNode(t);
}
protected static String cleanUpRoot(String label) {
if (label == null || label.equals("TOP")) {
return "ROOT";
// String constants are always interned
} else {
return label;
}
}
// only leaves NP-TMP and NP-ADV
protected String cleanUpLabel(String label) {
if (label == null) {
return ""; // This shouldn't really happen, but can happen if there are unlabeled nodes further down a tree, as apparently happens in at least the 20100730 era American National Corpus
}
boolean nptemp = NPTmpPattern.matcher(label).matches();
boolean npadv = NPAdvPattern.matcher(label).matches();
label = tlp.basicCategory(label);
if (nptemp) {
label = label + "-TMP";
} else if (npadv) {
label = label + "-ADV";
}
return label;
}
protected void stripTag(Tree t) {
if ( ! t.isLeaf()) {
String label = cleanUpLabel(t.value());
t.setValue(label);
for (Tree child : t.getChildrenAsList()) {
stripTag(child);
}
}
}
private static final TregexPattern matchPattern =
TregexPattern.safeCompile("-NONE-=none", true);
private static final TsurgeonPattern operation =
Tsurgeon.parseOperation("prune none");
protected static Tree stripEmptyNode(Tree t) {
List<Pair<TregexPattern, TsurgeonPattern>> ops = Generics.newArrayList();
ops.add(Generics.newPair(matchPattern, operation));
return Tsurgeon.processPatternsOnTree(ops, t);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
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Семён Афанасьевич Уласевич (2 сентября 1895 — 1 июня 1939) — комбриг РККА (26 ноября 1935), начальник и военный комиссар Татаро-Башкирской военной школы в 1931—1934 годах. Репрессирован и расстрелян в 1939 году по ложному обвинению в военном заговоре.
Биография
Родился 2 сентября 1895 года в деревне Горностайлово (нынешний Копыльский район Минской области). Белорус, из крестьян. Окончил сельскую начальную школу и учительскую семинарию в 1914 году (экстерном). Призван в мае 1915 года в Русскую императорскую армию, окончил учебную команду. Рядовой запасного пехотного батальона 185-го запасного пехотного полка. С весны 1917 года участник Первой мировой войны в составе 727-го Новоселенгинского пехотного полка. Был ранен, лечился в военном госпитале Петрограда. Старший унтер-офицер РИА, в отпуске по болезни с сентября 1917 года.
Член РКП(б) с 1919 года, с апреля того же года в рядах РККА. Учился на Минских и Смоленских пехотных курсах, окончил . Участник Гражданской войны: командир взвода (с ноября 1919), помощник командира роты (с марта 1920) и командир роты 31-х Смоленских командных пехотных курсов (с июля 1920). Адъютант (с сентября 1920), командир роты (с ноября 1920) и командир батальона 46-х командных пехотных курсов (с апреля 1921). В феврале 1922 года назначен помощником начальника учебной части по политчасти на 88-х пехотных командных курсах, занимал также посты командира батальона, начальника курсов и военкома.
В июне 1923 года назначен помощником военкома (позже военком) 23-х командных пехотных курсов. С сентября того же года — помощник начальника 6-х командных пехотных курсов объединенной Белорусской военной школы по политической части. В июле 1926 года был назначен командиром и военным комиссаром 11-го Сычёвского стрелкового полка (4-я Смоленская стрелковая дивизия). Избирался членом ЦКК КП(б)Б в 1930 году и членом ЦИК Татарской АССР в 1932 году. Был начальником и военным комиссаром Татаро-Башкирской военной школы имени ЦИК ТАССР с 1 мая 1931 по 28 февраля 1934 годов. С февраля 1934 года — командир 71-й стрелковой дивизии имени Кузбасского пролетариата Сибирского военного округа, с июля 1937 года — военком этой же дивизии.
5 июля 1938 года был арестован Военной коллегией Верховного суда СССР по обвинению в участии в военном заговоре против Сталина. 10 мая 1939 года признан виновным и приговорён к высшей мере наказания. Приговор приведён в исполнение 1 июня (по другим данным, 2 июня) 1939 года. Реабилитирован 25 февраля 1956 года определением Военной коллегии.
Награды
Орден Красного Знамени (22 февраля 1938)
Орден Красной Звезды (16 августа 1936)
Медаль «XX лет РККА» (22 февраля 1938)
Примечания
Литература
Участники Первой мировой войны (Россия)
Участники Гражданской войны в России (красные)
Начальники Казанского высшего танкового командного училища
Преподаватели Объединённой белорусской военной школы
Члены ЦИК Татарской АССР
Военачальники, репрессированные в СССР
Расстрелянные в СССР
Реабилитированные в СССР | {
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} | 7,580 |
Q: Existing website that requires multiple users to access the same data I have an existing website, that doesn't use any specific framework. This project is much older and is slowly being evolved, which is somewhat of a nightmare really.
Currently, I am trying to implement a better solution to current users to have 'assistants' to their accounts.
The current data resides like this (users & contacts tables):
**users table**
userId, email, password...
1 test@test.com, pa$$word
2 ass@test.com, pa$$word
**contacts table**
contactId, userId, fName, lName...
1, 1, john, doe
I am trying to figure out how to modify my site to enable userId's (1&2), to be able to access this contact.
Instead of starting over, any direction or samples that I could glean from on how to solve this issue of mine? Any help would be greatly appreciated.
A: Remove the userId column from the contacts table and create a new table contacts_users with two columns, contactId and userId.This is called a PIVOT TABLE and allows many-to-many relationships like what you are describing.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,452 |
{"url":"https:\/\/loving-transformation.com\/casino-online-spielen-book-of-ra\/1-x-2-x.php","text":"Review of: 1 X 2 X\n\nReviewed by:\nRating:\n5\nOn 13.03.2020\n\n### Summary:\n\nMit einem Unterschied: Der Einzahlungsbetrag darf sofort wieder ausbezahlt werden.\n\nHi, In meinem Buch steht zu diesem Integral folgendes: int(1\/x^2,x,)= 1\/x+C Ich h\u00e4tte das Integral so gel\u00f6st: int(1\/x^2,x,)= int(x^(-2),x,)= -1\/3*x^(-3)+C Wer l\u00fcgt. Also gilt \u222b1xdx=ln(x)+C. Sieht man einer Funktion f(x)=tan(x). F(x)=\u2212ln|cos(x)|\u200b+C. f(x)=1sin2(x). F(x)=\u2212cot(x)+C. f(x)=1cos2(x). F(x)=tan(x)+C. f(x)=11+x2. Hi x 2 \u2212 1 x \u2212 1 = (x \u2212 1) (x + 1) x \u2212 1 = x + 1 \\frac{x^}{x-1} = \\frac{(x-1)(x+\u200b1)}{x-1} = x+1 x\u22121x2\u22121\u200b=x\u22121(x\u22121)(x+1)\u200b=x+1. Denn der.\n\n## Elementarmathematik Beispiele\n\nDiese Tabelle von Ableitungs- und Stammfunktionen (Integraltafel) gibt eine \u00dcbersicht \u00fcber Ableitungsfunktionen und Stammfunktionen, die in der Differential\u200b- und Integralrechnung ben\u00f6tigt werden. Inhaltsverzeichnis. 1 Tabelle einfacher Ableitungs- und Stammfunktionen (Grundintegrale) 2 Rekursionsformeln f\u00fcr weitere Stammfunktionen; 3 Weblinks. 2 (x \u2013 1) = 3 (x + 1). 2x \u2013 2 = 3x + 3. | \u2013 2x. \u2013 2 = x + 3. | \u20133. \u2013 5 = x. Und nun gibt es neben Binomen noch andere Schwierigkeiten. (Achte auch auf Minuszeichen\u200b. 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Inhaltsverzeichnis. 1 Tabelle einfacher Ableitungs- und Stammfunktionen (Grundintegrale) 2 Rekursionsformeln f\u00fcr weitere Stammfunktionen; 3 Weblinks.\nFor example, finding log 2 5 is hardly possible by just using our simple calculation abilities. Knorr \u00f6sterreich Exact constants Tables Unit circle. Therefore, logarithm is the exponent to which it is necessary to raise a fixed number which is called the baseto get the Maidcafe y.\n\n1 X 2 X\n\n### 3 Kommentare zu \u201e1 X 2 X\u201c\n\n\u2022 16.03.2020 um 05:33","date":"2021-09-17 07:32:19","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\": 0.5485537052154541, \"perplexity\": 3890.428323535614}, \"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-2021-39\/segments\/1631780055601.25\/warc\/CC-MAIN-20210917055515-20210917085515-00016.warc.gz\"}"} | null | null |
Lotus 30/40 Registry – Span Inc.
Registry Feedback – Thank You!
The Lotus 30/40 - The biggest, hairiest Lotus Colin Chapman ever built!
According to the article article "Will 1965 be the Year? The Development History of the Biggest Lotus", Motor, 10 Jun. 1965, 4 Lotus 30s were delivered to Lotus Southwest.
Dan Davis, publisher of Victory Lane magazine, was a co-owner of Lotus Southwest.
A.J Foyt may have bought the last Lotus 40 from Lotus Southwest.
The present whereabouts of all of these cars is unknown, except for 30/L/12 and perhaps 40/L/3.
1965 Lotus Southwest (U.S.A.) ?
This page last updated on 7/06/2015.
Copyright © 2019 www.Lotus30.com. All Rights Reserved. | {
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.. default-role:: code
============
Installation
============
To install PyAutoGUI, install the `pyautogui` package from PyPI by running `pip install pyautogui` (on Windows) or `pip3 install pyautogui` (on macOS and Linux). (On macOS and Linux, `pip` refers to Python 2's pip tool.)
OS-specific instructions are below.
Windows
-------
On Windows, you can use the ``py.exe`` program to run the latest version of Python:
``py -m pip install pyautogui``
If you have multiple versions of Python installed, you can select which one with a command line argument to ``py``. For example, for Python 3.8, run:
``py -3.8 -m pip install pyautogui``
(This is the same as running ``pip install pyautogui``.)
macOS
-----
On macOS and Linux, you need to run ``python3``:
``python3 -m pip install pyautogui``
If you are running El Capitan and have problems installing pyobjc try:
``MACOSX_DEPLOYMENT_TARGET=10.11 pip install pyobjc``
Linux
-----
On macOS and Linux, you need to run ``python3``:
``python3 -m pip install pyautogui``
On Linux, additionally you need to install the ``scrot`` application, as well as Tkinter:
``sudo apt-get install scrot``
``sudo apt-get install python3-tk``
``sudo apt-get install python3-dev``
PyAutoGUI install the modules it depends on, including PyTweening, PyScreeze, PyGetWindow, PymsgBox, and MouseInfo.
| {
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\section{Introduction}
Systems of granular particles (e.g. sands) exhibit many interesting
phenomena \cite{s84,cc90,jn92}. The formations of a spontaneous heap
\cite{er89,ldf89,cdr92,l92} and convection cells
\cite{r76,s88,zs91,t92,gh92} under vibration, and the segregation of
particles \cite{w76,hw86,rsps87,d90,jm92,drc93} are just a few
examples. These phenomena are consequences of unusual, and often
complex, dynamical responses of the system. Considering the complexity
of the dynamics, one is tempted to first have comprehensive
understanding of the dynamics of granular media in relatively simple
geometries, and proceed to more complicated situations. Even for the
simple geometries like shear cells, vertical tubes and hoppers,
granular media still show complex dynamics. For example, granular
particles in a shear cell show not only non-Newtonian behaviors
\cite{b54,ss84,c89,bss90}, but also stick-slip motions \cite{tg91} as well
as density waves \cite{hl90,ss92}. Here, we study the flows of
granular particles through vertical tubes and hoppers, whose
geometries are as simple as shear cells, but are less well studied. In
granular flows through vertical tubes, P\"{o}schel \cite{p92} found
that the particles do not flow uniformly, but form regions of high
density which travel with velocity different from that of the center
of mass. The mechanism for the traveling density pattern or the
density wave is, however, not clearly understood. The density waves
are also found in outflows through hoppers \cite{cp67,bbfj89}.
Especially, Baxter {\it et al} \cite{bbfj89} show that the velocities
of the density waves are dependent on the opening angle of hoppers,
and even their directions can be changed. Furthermore, they find the
density waves only when they mix some amount of rough sands with
smooth sands. In MD simulations of hopper, the density field is found
out to be non-uniform \cite{r92}. Again, the mechanism for the density
wave is not clearly understood.
We first construct equations of motion for quasi one-dimensional
systems. With the Bagnold's law for friction
\cite{b54}, the equations are used to describe the time evolutions of
the density and the velocity fields for narrow tubes and hoppers. The
solutions of the equations can have two types of density waves,
kinetic and dynamic. The dynamic waves are similar to sound waves,
while kinetic waves are due to the kinematics of the equations
\cite{lw55}. For tubes, we can show the existence of kinetic waves, and
obtain the condition for dynamic waves by a linear stability analysis.
We also study the effects of static friction, and find that it changes
the qualitative behaviors of the flows. For hoppers, we obtain the
solutions of the equations up to the first order of the opening angle,
and also show the existence of kinetic waves. Next, we study the
systems using molecular dynamics (MD) simulations. For tubes, we
reproduce density waves, and we find a few strong evidences that the
waves are of kinetic nature, which includes a well defined
flux-density curve and the density dependence of the velocities of the
waves. We also study the existence of dynamic waves by changing the
inelasticity of the particles, and do not find dynamics waves. In MD
simulations of flows in hoppers, we find density waves, which are
believed to be kinetic waves due to the strong correlation between the
density and the velocity fields. For hoppers with periodic boundary
conditions, we find additional density waves, which eventually
dominates. We find a few evidences that the additional waves are of
dynamic nature. We, however, do not find dynamic waves in hopper with
open boundary conditions. The results obtained by these theoretical
and numerical studies are compared with the experiments.
This paper is organized as follows. In Sec.\ \ref{sec:theory}, we
present theoretical results. Detailed discussions on the definitions
and properties of dynamic and kinetic waves are given in Sec.\
\ref{sec:dvsk}. The kinetic and dynamic waves in tubes are discussed
in Sec.\ \ref{sec:thtube} and Sec.\ \ref{sec:dynamic}, respectively.
Also, kinetic waves in hoppers are discussed in Sec.\ \ref{sec:thhop}.
We present the numerical results in Sec.\ \ref{sec:numerical}. First,
we define the interactions between the particles in Sec.\
\ref{sec:inter}. The results for kinetic and dynamic waves in tubes
are given in Sec.\ \ref{sec:nutube}, and the results for hoppers are
discussed in Sec.\ \ref{sec:nuhop}. Brief summary as well as the
limitations of this work are given in Sec.\ \ref{sec:dis}.
\section{Theoretical Approach}
\label{sec:theory}
\subsection{Dynamic and kinetic waves}
\label{sec:dvsk}
Here, we construct equations of motion for flows in one-dimension,
which will later be used to describe the time evolutions of fields in
vertical tubes and hoppers. Let us define $\rho (x,t)$ and $v(x,t)$ be
the density and the velocity at position $x$ and time $t$,
respectively. If we require the mass of the system to be conserved,
\begin{mathletters}
\label{eq:motion}
\begin{equation}
{\partial \over \partial t} \rho + {\partial \over \partial x} (\rho v) = 0.
\label{eq:mass}
\end{equation}
Other equation comes from the momentum conservation,
\begin{equation}
\rho {\partial \over \partial t} v + \rho v {\partial \over \partial x} v = F(x,t),
\label{eq:momentum}
\end{equation}
\end{mathletters}
where $F(x,t)dx$ is the total force acting on the mass within
$[x,x+dx]$ at time $t$.
There are two distinct mechanisms by which density patterns can
travel. One is due to the instability of uniform-density flows to
density fluctuations (``dynamic wave''), and the other is of kinetic
origin (``kinetic wave'') \cite{lw55}. We now discuss both types of
waves in detail, paying particular attention to their differences. In
order to make the discussion more concrete, we use a specific form of
the force
\begin{equation}
\label{eq:force}
F(x,t) = \rho - {\partial \over \partial x} \rho - \rho ^{\nu} v^{\mu},
\end{equation}
where $\mu$ and $\nu$ are constants. The form of Eq.\
(\ref{eq:force}), motivated from a granular flow in a tube, is chosen
such that the discussion becomes more clear. The followings are,
however, applicable for any form of the force.
We first consider the dynamic wave. The equations of motion Eqs.\
(\ref{eq:motion}) with the force given by Eq.\ (\ref{eq:force}) have a
solution of uniform density $\rho _o$,
\begin{eqnarray}
\label{eq:uniform}
\rho (x,t) &&= \rho _o, \cr
v(x,t) &&= \rho _o^{(1-\nu)/\mu}.
\end{eqnarray}
We study the stability of the solution Eq.\ (\ref{eq:uniform}) by a
linear stability analysis. For simplicity, we consider the case of
$\rho _o = 1$. The trial solution for the time evolution of a
perturbation of Eq.\ (\ref{eq:uniform}) is
\begin{eqnarray}
\label{eq:perturbe}
\rho (x,t) &&= 1 + \epsilon _{\rm \rho} \exp [i(kx-\omega t)] \cr
v(x,t) &&= 1 + \epsilon _{\rm v} \exp [i(kx-\omega t)],
\end{eqnarray}
where $\epsilon _{\rm \rho}$ and $\epsilon _{\rm v}$ are constants. We want to
study the time evolution in a linear approximation, where we consider
terms up to the first order of $\epsilon$. The analysis is valid only if a
perturbation term is much smaller than unity. Substituting Eq.\
(\ref{eq:perturbe}) into Eqs.\ (\ref{eq:motion}), and discard terms
higher order than $\epsilon$, we obtain
\begin{eqnarray}
\label{eq:linear}
(\omega - k) \epsilon _{\rm \rho} - k \epsilon _{\rm v} &&= 0 \cr
[k + i(1 - \nu )] \epsilon _{\rm \rho} + [(k - \omega ) - i \mu] \epsilon _{\rm
v} &&= 0,
\end{eqnarray}
whose solution is given by
\begin{equation}
\label{eq:wk}
\omega = {2k - i\mu \pm \sqrt{4k[k+i(1-\nu )] - \mu ^{\rm 2}} \over
2}.
\end{equation}
The density fluctuation travels with velocity $Re(\omega ) / k$, where
$Re(\omega )$ is the real part of $\omega $. If $Im(\omega )$ (the
imaginary part of $\omega $) is positive, the perturbation grows with
time, makes uniform-density flow unstable. This mechanism for creating
density waves, which is based on the instability of the equations, is
called dynamic waves.
We now discuss the mechanism for kinetic waves. For an excellent
introduction to the subject, please see Ref.\ \cite{lw55}. Consider a
case that the system is divided into two uniform-density flow regions
with densities $\rho _a$ and $\rho _b$, and the velocities of each
region is determined by Eq.\ (\ref{eq:uniform}) (Fig.\
\ref{fig:inter}). The equations of motion Eqs.\ (\ref{eq:motion}) imply
that density and velocity field ($\rho (x,t)$ and $v(x,t)$) inside
each domains do not change. The system evolve only by moving the
interface. Let $U$ be the velocity of the interface. We also set the
initial position of the interface to be $0$ without losing generality.
Then, the position of the interface at time $t$ is $Ut$. At a given
time, we choose an interval $[-\epsilon ,\epsilon ]$ which includes the
interface. We then integrate Eq.\ (\ref{eq:mass}) in the interval
\begin{eqnarray}
\label{eq:kvstep}
\int_{-\epsilon}^{\epsilon} {\partial \over \partial t} \rho + {\partial \over \partial x} (\rho v) = && {\partial \over \partial t} [(\epsilon + Ut)\rho
_a + (\epsilon - Ut)\rho _b] + \rho v |_{-\epsilon}^{\epsilon} \cr = && (\rho
a - \rho _b)U + j_b - j_a = 0,
\end{eqnarray}
where the flux $j$ is defined to be $\rho v$. Therefore, the
interface, or any density fluctuations, travels with velocity
\begin{equation}
\label{eq:kvel}
U = {j_a - j_b \over \rho _a - \rho _b}~=~{\Delta j \over \Delta
\rho}.
\end{equation}
Since the above mechanism for the travel of density fluctuations is a
consequence of a kinetic equation (mass conservation, Eq.\
(\ref{eq:mass})), it is called kinetic wave. Unlike dynamics waves,
the fluctuations in kinetic waves can not be amplified, the system can
only reorganize existing fluctuations. The fluctuations are created by
initial conditions or by noises in the dynamics. Furthermore, kinetic
waves, in most cases, decay into uniform flows \cite{lw55}.
In general, flows in $1$-d have both kinetic and dynamic waves. If a
system is stable under density fluctuations, existing dynamic waves
will decay exponentially, and only kinetic waves can survive. On the
other hand, if the system is unstable, the amplitudes of the dynamic
waves will grow, and they eventually dominate over kinetic waves. In
order to illustrate this point, we integrate numerically Eqs.\
(\ref{eq:motion}) to get $\rho (x,t)$ and $v(x,t)$, where the force is
given by Eq.\ (\ref{eq:force}). The integration is done using the
staggered leapfrog method \cite{pftv86} with the time step $0.001$.
We also use a periodic boundary condition. The initial conditions are
that $\rho (x,0)$ is a short pulse of higher density (1 \%) on the top
of background density of unity, and $v(x,0)$ is given by Eq.\
(\ref{eq:uniform}). We first study the case of $\mu = 2, \nu = -1.$
The behavior of the dynamic waves is studied by a linear stability
analysis. Equation (\ref{eq:wk}) gives the dependence of $\omega$ on
$k$ to be $2k, -2i$. There is one marginally stable mode of velocity
$2$, and one stable mode of velocity $0$. On the other hand, the flux
is given as
\begin{equation}
\label{eq:kvel2}
j \equiv \rho v = \rho ^{(\mu-\nu+1)/\mu},
\end{equation}
and the velocity of kinetic wave, determined by Eq.\ (\ref{eq:kvel}),
is approximately $2$. Since the system is not unstable to density
fluctuations, the kinetic waves, not greatly affected by the dynamic
waves, will survive for a long time (Fig.\
\ref{fig:dvsk}(a)). We now study the case of $\mu =-2, \nu = -1$.
Following the same analysis, $\omega (k)$ is determined to be $2k +
2i$ and $0$. One unstable mode of velocity $2$ and one marginally
stable mode of velocity $0$. The velocity of the kinetic wave is
approximately $0$. The dynamic wave of increasing amplitude (that of
the velocity $2$) is dominating over the kinetic wave (Fig.\
\ref{fig:dvsk}(b)).
\subsection{Density waves in vertical tubes}
\subsubsection{Kinetic waves in vertical tubes}
\label{sec:thtube}
We consider vertical tubes of narrow width, which are filled with
granular material. The particles will flow down due to gravity. This
motion will induce the forces between the particles as well as the
friction forces by the inner walls of the tubes. We assume that these
forces follow the Bagnold's law \cite{b54}. The law, first found in a
rapid granular flow, implies that the components of the stress tensor
$\tau _{ij}$ are proportional to the square of the shear rate
$\dot{\gamma }$,
\begin{equation}
\label{eq:bagnold}
\tau _{ij} = \rho _B D^{2} f_{ij}(p) \dot{\gamma }^{2}.
\end{equation}
Here, $\rho _{B}$ is the density of the material which forms the
particles, and $p$ is the volume fraction of the particles. The
density $\rho $ is, therefore, $\rho _{B}$ times $p$. Also, $D$ is
the average diameter of the particles, $f_{ij}(p)$ is a system
dependent function. Bagnold predicted the shear rate dependence in
rapid flows using a simple argument, which later confirmed by more
elaborate calculations as well as experiments
\cite{cc90,jn92,ss84}. In this paper, we will use the law except
the case that the velocities of the particles are considered to be
very small.
Let $x$-axis ($y$-axis) be the direction parallel (perpendicular) to
the tube, where the positive $x$-direction is chosen to be upward. We
consider the forces acting on the granular material contained in
$[x,x+dx]$. Since we study only narrow tubes, we assume the material
is homogeneous along the $y$ direction. There is a gravitational force
given by $-\rho g W dx,$ where $g$ is the gravitational acceleration,
and $W$ the width of the tube. There also is a friction by the wall,
which is $-\tau _{xy} dx$, and pressure by other particles $-d \tau
_{xx} /dx~D dx$. The total force $F(x,t)$ becomes
\begin{eqnarray}
\label{eq:reforce}
F(x,t) = && -\rho _B p g W - sign(v) \rho _B D^{2} f_{xy}(p)
({v \over D})^{2} - D {\partial \over \partial x} [\rho _B D^{2} f_{xx}(p) ({v
\over D})^{2}] \cr = && -\rho _B p g W - sign(v) \rho _B
f_{xy}(p) v^{2} - D {\partial \over \partial x} [\rho _B f_{xx}(p) v^{2}],
\end{eqnarray}
where $sign(v)$ is the sign of $v$, and we assume the width of shear
layer to be of order of $D$.
Having found the force, we now proceed to study kinetic waves in the
system. We first consider the case of {\it no} static friction. The
steady-state velocity $v_{s}(p)$ of a uniform flow is obtained from
the condition that the total force acting on the granular material is
zero. Since we consider uniform density flows, the force free
condition gives
\begin{equation}
\label{eq:terminal}
v_{s}(p) = -\sqrt{pgW/f_{xy}(p)}.
\end{equation}
The flux $j(p)$ is given by $\rho _B p v_{s}(p)$, then the velocity of
a small density fluctuation $U(p)$ becomes
\begin{equation}
\label{eq:rekvel}
U(p) = {\Delta j \over \Delta \rho} \simeq {dj(p) \over d\rho } = {1
\over 2} v_{s}(p) {3f_{xy}(p) - pdf_{xy}(p)/dp \over f_{xy}(p)}.
\end{equation}
Therefore, the form of the force Eq.\ (\ref{eq:reforce}) allows
density fluctuations to travel with velocity $U(p)$. The condition for
the existence of kinetic waves is the balance between the forces, and
the waves are not very sensitively dependent on the exact form of the
forces. Therefore, they are very likely to be seen in the experiments.
We now consider the effects of static friction on the kinetic waves.
By static friction, we mean one has to apply a finite force in order
to break contacts between surfaces. There are two contributions to the
normal stress on the wall. One is a static pressure $P_{s}$, which is
independent of the motion of the particles. The other is due to the
collisions of the particles on the wall $\tau _{yy}$, given by Eq.\
(\ref{eq:bagnold}). The total friction force is the minimum of $\rho g
W - \tau _{xy}$ and $\mu (\tau _{yy}+P_{s})$, where $\mu $ is the
friction coefficient. If the shear force (gravity and friction) is
smaller than $\mu$ times the normal force, the total force on the
particles is zero, and the particles form a stagnant zone of no
movement \cite{zc92}.
Depending on the parameters, there can be two behaviors of the system.
If the gravitational force $\rho g W$ is less than the friction due to
static pressure $\mu P_{s}$, the particles can not move, and the
system remains as a static column. If $\rho g W > \mu P_{s}$, the
particles will start move. The steady-state velocity $v_{s}^{\prime}
(p)$ for given packing fraction $p$ is,
\begin{equation}
\label{eq:rekvelmu}
v_{s}^{\prime} (p) = - \sqrt{ p g W - \mu P_{s} / \rho _{B} \over
f_{xy}(p)},
\end{equation}
which is very similar to Eq.\ (\ref{eq:terminal}). However, we have
additional constraint that the shear force should exceed $\mu$ times
the normal force, which gives
\begin{equation}
\label{eq:static}
\rho g W - \rho _{B} f_{xy}(p) v^{2} > \mu P_{s} + \mu \rho _{B}
f_{yy}(p) v^{2}.
\end{equation}
If we define $v_{c}(p)$ be the velocity that above equation becomes
equality,
\begin{equation}
v_{c}(p) = v_{s}^{\prime} (p) {1 \over 1 + \mu f_{yy}(p) / f_{xy}(p)} <
v_{s}^{\prime} (p).
\end{equation}
Since the inequality Eq.\ (\ref{eq:static}) is not satisfied for $v(p)
> v_{c}(p)$, the particles can not reach their steady state. Instead,
they forms a stagnant zone. If we assume that the particles are
stopped completely in the stagnant zone, the distances between the
zones ${\cal D}(p)$ are constant, which is the distance needed for the
particles to be accelerated to $v_{c}(p)$ from the stopped state. We
can calculate the distance ${\cal D}(p)$ as follows. The velocity of
the particles, obtained by integrating the Newton's equation with the
friction force of Eq.\ (\ref{eq:static}), becomes
\begin{equation}
\label{eq:vtp}
v(t,p) = v_{s}^{\prime} (p) \tanh [v_{s}^{\prime} (p) ( g - {\mu P_{s}
\over
\rho W}) t].
\end{equation}
The distance covered by the particles during the interval $[0, t_{c}]$
becomes ${\cal D}(p)$, where $t_{c}$ is given by $v(t_{c},p) =
v_{c}(p)$. Integrating Eq.\ (\ref{eq:vtp}), we obtain
\begin{equation}
\label{eq:tubesep}
D(p) = -{v_{s}^{\prime 2}(p) \over 2 (g - \mu P_{s} / \rho W)} \ln (1 -
\gamma ^{2}),
\end{equation}
where $\gamma = 1 / (1 + \mu f_{yy}(p) / f_{xy}(p))$. The distance
${\cal D}(p)$ increases as $\mu$ is decreased, and it diverges when
$\mu \to 0$.
We now summerize the results obtained in this section. If static
friction is not present, the particles in vertical tubes form density
waves travels with velocity $U(p)$. When we take into account static
friction, the system forms periodic stagnant zones with their
separations ${\cal D}(p)$.
\subsubsection{Dynamic waves in vertical tubes}
\label{sec:dynamic}
In this section, we study the stability of the uniform-density flows
through vertical tubes under density and velocity fluctuations. We
will follow the analysis presented in Sec.\ \ref{sec:dvsk}. We start
with the equations of motion Eqs.\ (\ref{eq:motion}) with the force
given by Eq.\ (\ref{eq:reforce}). Here, we do not consider static
friction. The uniform-density flow solution with the density $\rho
_{o}$ is
\begin{eqnarray}
\label{eq:tubeuni}
\rho (x,t) &&= \rho _{o} \equiv \rho _{B} p_{o} \cr
v(x,t) &&= v_{o} \equiv - \sqrt{p_{o} g W \over f_{xy} (p_{o})}.
\end{eqnarray}
We study the stability of the solution by studying the time evolution
of the perturbation from the uniform-density flow, given by
\begin{eqnarray}
\label{eq:tubepe}
p (x,t) &&= p _{o} + \epsilon _{p} \exp [i(kx-\omega t)]
\cr
v(x,t) &&= v_{o} + \epsilon _{v} \exp [i(kx-\omega t)].
\end{eqnarray}
Substituting Eqs.\ (\ref{eq:tubepe}) into Eq.\ (\ref{eq:motion}), and
consider only up to the first terms of $\epsilon$, we obtain
\begin{eqnarray}
\label{eq:tubeset}
(k v_{o} - \omega) \epsilon _{p} + p _{o} k \epsilon _{v} &&= 0 \cr [g -
{v_{o}^{2} \over W} ({df_{xx} \over dp} - i k D {df_{xy} \over dp})]
\epsilon _{p} + [i (k v_{o} - \omega ) - {2 v_{o} \over W} (f_{xy} - i k D
f_{xx})] \epsilon _{v} &&= 0.
\end{eqnarray}
Since the two equations in Eq.\ (\ref{eq:tubeset}) are valid for any
values of $\epsilon _{p}$ and $\epsilon _{v}$, the solution is
\begin{equation}
\label{eq:omega}
\Omega ^{2} - i {2 v_{o} \over p_{o} W} (f_{xy} - i k D f_{xx})
\Omega + i k [g - {v_{o}^{2} \over W}({df_{xy} \over dp} - i k D
{df_{xx} \over dp})] = 0,
\end{equation}
where $\Omega \equiv \omega - k v_{o}$. The stability of the uniform
solution is determined by the imaginary part of $\omega$.
Unfortunately, since $\omega$ depends on the exact form of the unknow
function $f_{ij}$, we can not determine the stability of the flow.
Similar stability analysis on shear cells \cite{ss92} and dissipative
gases \cite{gz93} shows that the system is unstable for small
coefficient of restitution $e$. Especially, in \cite{gz93}, this
instability is traced back to the fact that pressure can decrease as
the density is increased. Here, we can show that Eq.\ (\ref{eq:omega})
has an unstable mode if $df_{xx}/dp$ is sufficiently negative (smaller
pressure for larger density), where the exact criterion is a
complicated function of $k, f_{xy}$ and $f_{xx}$. The stability of the
flow is later checked by MD simulations, where we will study the
stability for various degrees of the inelasticity of the particles.
\subsection{Density waves in hoppers}
\label{sec:thhop}
Consider a hopper with the opening angle $2 \theta$, where the width
at position $x$ is given by $W(x) = W_{o} + 2 \tan \theta x$ (Fig.\
\ref{fig:hopper}(a)). Here, we consider only the positive ranges of
$x$. The equations of motion for flows in hoppers are slightly
different from those for tubes. Since the width $W$ is dependent on
$x$, the conservation of mass implies
\begin{equation}
\label{eq:hmass}
W {\partial \over \partial t} \rho + {\partial \over \partial x} (W \rho v) = 0,
\end{equation}
instead of Eq.\ (\ref{eq:mass}). Equation (\ref{eq:momentum}), which
is a consequence of momentum conservation, still holds for hoppers,
with a modified form of friction force. Since the sidewalls are
tilted, the friction per unit length along the walls have two
contributions. One is the component of $\tau _{xy}$ (friction force
for tubes) parallel to the walls $\tau _{xy} \cos \theta$. Forces on
the walls by the internal pressure $\tau _{xx}$ give additional
contribution $\tau _{xx} \sin \theta \cos \theta $, where $\sin
\theta$ is due to the cross-section for the collisions of particles
to the walls. (Fig.\ \ref{fig:hopper}(b)). Therefore, the total force
becomes,
\begin{equation}
\label{eq:hopforce}
F(x,t) = - \rho g + \rho _B v^{2} (f_{xy} \cos \theta + f_{xx} \sin
\theta \cos \theta ) - \rho _{B} D {\partial \over \partial x} (f_{xx} v^{2}).
\end{equation}
Since we assume that the system is homogeneous in the horizontal
direction, we only consider hoppers of narrow width $W$. We also
assume $\theta \ll 1$, and the $\theta$ dependences of physical
quantities (density, velocity) are calculated up to the first order of
$\theta$.
We now study the steady state properties of hoppers. Imposing the
steady state condition on the mass conservation Eq.\ (\ref{eq:hmass})
gives
\begin{mathletters}
\label{eq:hop1}
\begin{equation}
\label{eq:hopmass1}
{\partial \over \partial x} (W p v) = 0.
\end{equation}
Also, the momentum conservation Eq.\ (\ref{eq:momentum}) with the
force Eq.\ (\ref{eq:hopforce}), in a steady state, becomes
\begin{equation}
\label{eq:hopmom1}
p v {\partial \over \partial x} v = - p g + {1 \over W} v^{2} (f_{xy} \cos \theta + f_{xx}
\sin \theta \cos \theta) - {D \over W} {\partial \over \partial x}(f_{xx} v^{2}).
\end{equation}
\end{mathletters}
We want to know the density and velocity fields which satisfies Eq.\
(\ref{eq:hop1}). We start with a trial solution
\begin{eqnarray}
\label{eq:hoptry}
p(x) &&= p_{o} + A(x) \theta \cr
v(x) &&= v_{s} + B(x) \theta,
\end{eqnarray}
where $v_{s} = - \sqrt{p_o g W_{o} / f_{xy}(p_{o})}$, the steady state
velocity for tubes Eq.\ (\ref{eq:terminal}). Substituting Eq.\
(\ref{eq:hoptry}) into Eq.\ (\ref{eq:hop1}), and ignore terms of
higher order than $\theta$,
\begin{eqnarray}
\label{eq:hopsteady}
v_s W_o {dA \over dx} + p_o W_o {dB \over dx} && = - 2 p_o v_s
\cr D v_s^2 {df_{xx} \over dp} {dA \over dx} + (2 D v_s f_{xx} +
p_o v_s W_o) {dB \over dx} + g W_o A - 2 v_s f_{xy} B && = v_s^2
f_{xx} - 2 x g p_o.
\end{eqnarray}
Since $f_{xx}$ and $f_{xy}$ are also functions of $p(x)$, one has to
know the exact form of these functions to find the solutions of the
equation Eq.\ (\ref{eq:hopsteady}). Here, we assume that $f_{xx}(p)$
can be approximated to $f_{xx}^o p^m$ for the range of densities found
in a hopper. Similarly, $f_{xy} \simeq f_{xy}^o p.^m$ Since $\theta
\ll 1$, the changes of $A(x)$ and $B(x)$ to $x$ will be also slow. We
therefore consider variations up to the first order of $x$, that is,
$A(x) = A_o x + A_1$ and $B(x) = B_o x + B_1$. Substituting $f_{xx},
f_{xy}$ and $A(x), B(x)$ into Eq.\ (\ref{eq:hopsteady}), we obtain
\begin{eqnarray}
\label{eq:hopsteady2}
v_s A_o + p_o B_o = &&- 2 {p_o v_s \over W_o} \cr 2 g p_o = && (m
v_s^2 f_{xy}^o p_o^{m-1} - g W_o) A_o + 2 v_w f_{xy}^o p_o^m B_o \cr
v_s p_o W_o B_o = && -g W_o A_1 + v_s^2 p_o^m f_{xx}^o + m f_{xy}^o
v_s^2 p_o^{m-1} A_1 \cr && + 2 f_{xy}^o v_s p_o^m B_1 - D f_{xx}^o v_s
p_o^m (2 B_o + {m v_s A_o \over p_o}).
\end{eqnarray}
There are only three conditions in Eq.\ (\ref{eq:hopsteady2}) for four
unknown variables. The other condition comes from the freedom in
choosing the origin of the $x$ axis. We set the origin so that $B_1 =
0$. Then, the solution of Eq.\ (\ref{eq:hopsteady2}) is
\begin{eqnarray}
\label{eq:hopsol}
B_o &&= {2m \over 3-m} \cdot {v_s \over W_o} \cr A_o &&= - {p_o \over
W_o} \cdot {6 \over 3-m} \cr A_1 &&= {v_s^2 \over (m-2) g W_o} \cdot
[{2m \over 3-m} (p_o - f_{xx}^o p_o ^m {D \over W_o}) - f_{xx}^o
p_o^m].
\end{eqnarray}
Intuitive solutions for hoppers are that the magnitude of the velocity
increases, and the density decreases as $x$ is increased. Although the
solution Eq.\ (\ref{eq:hopsol}) becomes intuitive one for $0 < m < 3$,
it can also have very different behaviors for other ranges of $m$.
Having obtained the steady state for hoppers, we now proceed to study
kinetic waves. The density and velocity fields are described by Eq.\
(\ref{eq:hoptry}) with one free parameter $p_o$. Consider two regions
of density, where $p_o$ is chosen to be $p_1$ and $p_2$, respectively.
The velocity of the interface $U_{h}$ between the regions, which can
be calculated following the way described in Sec.\ \ref{sec:dvsk}, is
\begin{equation}
U_{h} = {\Delta j \over \Delta \rho} = {\Delta [p_i v_s(p_i) +
v_s{p_i} A_1(p_i) \theta + (p_i B_o(p_i) + v_s(p_i) A_o(p_i)) x
\theta ] \over \Delta [p_i v_s(p_i) + (A_o(p_i) + A_1(p_i) x) \theta
]}.
\end{equation}
We consider small fluctuations of density: $p_1 = p$ and $\delta p =
p_2 - p \ll 1$. The velocity, up to the first order of $\theta$, is
\begin{eqnarray}
\label{eq:hopgroup}
U_{h} \simeq {dj \over d\rho } = && {d \over dp} (p v_s(p)) + {d \over
dp} (A_1(p) v_s(p)) \theta \cr + && {d \over dp} (p B_o(p) + v_s(p)
A_o(p)) x \theta - {d \over dp} (p v_s(p)) {d \over dp} (A_o(p) x +
A_1(p)) \theta.
\end{eqnarray}
The above velocity $U_{h}$ is calculated at position $x$. One should
note that the density at the position is not $p$ but $p + (A_o (p) x +
A_1(p)) \theta $. We now compare the velocity of density waves in
hoppers and tubes. The velocity of density waves in tubes $U_{t}$ at
the above density is
\begin{equation}
U_{t} = {d \over dp} (p v_s(p)) + ({d v_s(p) \over dp} + p {d v_s(p)
\over dp} + p {d^2v_s(p) \over dp^2})(A_o(p) x + A_1(p)) \theta,
\end{equation}
which is give by Eq. \ (\ref{eq:rekvel}).
Therefore, density waves also exist in hoppers, and their velocity is
given by $U_{h}(\theta ,p,x) = U_{t} + C(p,x) \theta,$ where $C(p,x)$
is a complicated function of $x$ and $p$.
\section{Molecular dynamics simulations}
\label{sec:numerical}
\subsection{Interactions between particles}
\label{sec:inter}
We discuss the interaction between the particles used in the MD
simulations of granular flows. The force between two particles $i$ and
$j$, in contact with each other, is the following. Let the coordinate
of the center of particle $i$ ($j$) to be $\vec{R}_i$ ($\vec{R}_j$),
and $\vec{r} = \vec{R}_i - \vec{R}_j$. In two dimensions, we use a
new coordinate system defined by the two vectors $\hat{n}$ (normal)
and $\hat{s}$ (shear). Here, $\hat{n} = \vec{r} / {\vert \vec{r}
\vert}$, and $\hat{s}$ is defined as rotating $\hat{n}$ clockwise by
$\pi/2$. The normal component $F_{j \to i}^{n}$ of the force acting
on particle $i$ by $j$ is
\begin{mathletters}
\label{eq:mdforce}
\begin{equation}
\label{eq:fnormal}
F_{j \to i}^{n} = k_n (a_i + a_j - \vert \vec{r} \vert)^{3/2} -
\gamma_n m_e (\vec{v} \cdot \vec{n}),
\end{equation}
where $a_i$ ($a_j$) is the radius of particle $i$ ($j$), $m_i$ ($m_j$)
the mass of particle $i$ ($j$), and $\vec{v} = d\vec{r}/dt.$ The first
term is the Hertzian elastic force, where $k_n$ is the elastic
constant of the material. And, the constant $\gamma_n$ of the second
term is the friction coefficient of a velocity dependent damping term,
$m_e$ is the effective mass, $m_i m_j/(m_i + m_j).$ The shear
component $F_{j \to i}^{s}$ is given by
\begin{equation}
\label{eq:fshear}
F_{j \to i}^{s} = - \gamma_s m_e (\vec {v} \cdot \vec {s}) - {\rm
sign} (\delta s) ~ {\rm min}(k_s \vert \delta s \vert, \mu \vert F_{j
\to i}^n \vert),
$$
\end{equation}
\end{mathletters}
where the first term is a velocity dependent damping term similar to
that of Eq.\ (\ref{eq:fnormal}). The second term is to simulate static
friction, which requires a {\it finite} amount of force ($\mu F_{j \to
i}^{n}$) to break a contact \cite{cs79}. Here, $\mu$ is the friction
coefficient, $\delta s$ the {\it total} shear displacement during a
contact, and $k_s$ the elastic constant of a virtual spring. There are
several studies on granular systems using similar interactions.
However, only a few of them \cite{cs79,bg91,lh93} include static
friction. A particle can also interact with a wall. The force on
particle $i$, in contact with a wall, is given by Eqs.\
(\ref{eq:mdforce}) with $a_j = \infty$ and $m_e = m_i$. A wall is
assumed to be rigid, i.e. it is not affected by the collisions with
particles. Also, the system is under a gravitational field $\vec{g}$.
We do not include the rotation of the particles in present simulation.
A detailed explanation of the interaction is given elsewhere
\cite{lh93}.
\subsection{Density waves in vertical tubes}
\label{sec:nutube}
\subsubsection{Waves without static friction}
We first simulate granular flows without static friction. Thus, we set
$\mu = 0$, and the shear force is only due to the velocity dependent
friction term in Eq.\ (\ref{eq:fshear}). We study the system in two
dimensions. Tubes are modeled by two parallel sidewalls of length $L$,
and separated by distance $W$, between which particles flow (Fig.\
\ref{fig:tubeset}). We use a periodic boundary condition in the
vertical direction. Particles come out of the bottom of the tube are
fed into the top. In order to avoid a haxagonal packing formed by
monodisperse particles, we use polydisperse particles, whose radii are
drawn from the gaussian distribution of mean $0.1$ and width $0.02$.
We initially arrange particles to be equally spaced along the vertical
direction, and calculate the positions and the velocities of the
particles at subsequent steps using a fifth-order predictor-corrector
method.
In Fig.\ \ref{fig:mdtube}, we show the time evolutions of the
densities and the velocities of the particles with $W=1$, $L=15$ and
the number of particles $N = 225$. The density plots are made as
follows. We divide the tube into several regions (bins) of equal
height (typically, $5$ times particle diameter), and count the number
of particles $n_{i}$ in bin $i$. We set the grayscale of each bin to
be proportional to $n_{i}$. We choose white for $n_i = d_l$, and black
for $n_i = d_u$, where $d_l$ ($d_u$) is the lower (upper) bound for
$n_{i}$. If $n_{i}$ is smaller than $d_l$ or larger than $d_u$, the
grayscale is chosen to be white or black, respectively. In Fig.\
\ref{fig:mdtube}(a), we use $d_l = 0$ and $d_u =30$. The density
field at a given time step is plotted as one horizontal line, where
boxes of different grayscale represents bins of the tube. Here, the
leftmost box corresponds to the bin at the bottom of the tube. The
velocity plot is made using the same procedure as above, except the
grayscale is proportional to the average vertical velocity $v_i$ in
bin $i$. In order to enhance the contrast, we subtract the center of
mass velocity from $v_i$. We choose white for $v_l$ and black for
$-v_l$. Here, we set $v_l = 60$. The time step is chosen to be $5.0
\times 10.^{-5}$ The time interval between the successive raws in the
density and velocity plots is $100$ iterations. The parameters for the
simulation are $k_n = 1.0 \times 10^{6},$ $k_s = 1.0 \times 10^{4}$
and $\gamma_n = \gamma_s = 500$ between the particles. Between the
particles and the walls, we use $k_n = 5.0 \times 10^{6}$ in order not
to allow the particles go through the walls, while the other
parameters are kept to be the same.
In Fig.\ \ref{fig:mdtube}, one can see a region of high density is
being formed from the homogeneous system \cite{l93}. Also, a high
density region may be split into two, or two regions may merge to form
one region. However, for the most of time, these density fluctuations
just travel with almost constant velocity. These traveling density
patterns are first observed in simulations by P\"{o}schel \cite{p92}.
Comparing Fig.\ \ref{fig:mdtube}(a) and (b), one can notice
correlations between the density $n_i$ and the velocity $v_i$. The
particles seem to travel slower (faster) in high (low) density
regions, which is very similar to traffic flows. This correlation is
one hint that the density waves may be of kinetic nature. In order to
systematically study the correlation, we measure the density
dependence of the flux in a steady state. We choose a bin, and we
calculate the friction and gravity force acting on the bin. Since we
want to measure the flux in a steady state (the total force is zero),
we require the total force (sum of the friction and the gravity) is
smaller than $r$ times the gravity, and we discard bins if the
requirement is not fulfilled. For bin $i$ in a steady state, we
measure the total flux, defined as $j_i = v_i n_i$. We calculate the
density $n_i$ dependence of the average flux $j_i$ for a system of
fixed total number of particles $N$. Here, the averages are taken over
time. We measure the flux-density curve for several different values
of $r$ ranging from $0.1$ to $\infty$. The results are not very
sensitive to the values of $r$, when we study the systems in a steady
state. We set $r=1.0$ from now on. We also measure the curve for
several values of $N=150, 225, 280, 337$. For large $N$, we have
accurate estimate of $j_i$ for large values of $n_i$, but poor one for
small $n_i$. The situation is opposite for the systems of small $N$.
For the intermediate values of $n_i$, however, all the systems give
good estimates, which agree with each other. In Fig.\
\ref{fig:fdtube}, we show the flux-density curve averaged over the
four values of $N$. The fact that we have a well defined flux-density
curve suggest the system is in a steady state, which implies that
kinetic wave is sufficient for the description of the evolutions of
the system. Furthermore, the curve resembles that of a traffic flow,
which is considered to be one of the typical examples of kinetic waves
\cite{lw55}.
One additional evidence that the density waves are of kinetic nature
is the dependence of the velocity of the waves on the average density.
The velocities of kinetic waves are given by Eq.\ (\ref{eq:kvel}),
which are the slope of the flux-density curve, for small density
fluctuations. From Fig.\ \ref{fig:fdtube}, we expect that the velocity
is a large negative value for a small density, approaches to zero, and
becomes a large positive number as the density is increased. We
directly measure the velocities of the waves from the slopes of high
density regions like the one shown in Fig.\ \ref{fig:mdtube}. In
Table.\ \ref{table:vdense}, we show the average velocities for several
values of $N$, where the average density $< n_{i} >$ is given by $N /
L$. In the table, one note the velocity is negative ($-41$) for small
$N$, and is increased to positive ($113$) for large $N$, which is
exactly the way predicted by the theory of kinetic wave. Furthermore,
the measured velocities are consistent with the local slopes of the
flux-density curve Fig.\ \ref{fig:fdtube}, although the slopes can not
be accurately determined due to the large error bars. Based on the
above evidences, as well as the theoretical argument given in Sec.\
\ref{sec:thtube}, we conclude the above density waves found in
vertical tubes are kinetic waves.
We also want to discuss the origin of fluctuations in the system. As
shown above, density fluctuations (waves) are formed from an uniform
density system. But kinetic waves, as discussed in Sec.
\ref{sec:dvsk}, can not create fluctuations. Also, some of the waves
are split into two waves, which can not be described by the evolutions
of kinetic waves alone. There must be some sources of fluctuations or
``noises'' in the system. Since the system is deterministic, one
might think the system can not have noises. The ``noises'' come from
the fact that the equations of motion Eq.\ (\ref{eq:motion}) as well
as the form of the friction force are relations between {\it averaged}
quantities. The fluctuations around their averaged values, especially
relevant in small scale descriptions of systems, are identified as
``noises''.
\subsubsection{Waves with static friction}
We next study the flows through vertical tubes {\it with} static
friction. As discussed in Sec.\ \ref{sec:thtube}, we expect two types
of behaviors depending on the friction coefficient $\mu$. If $\mu >
\rho g W / P_{s}$, the system can not move, and stays as a static
column. Otherwise, the particles start move, and forms periodic
stagnant zones whose separation ${\cal D}(p)$ is determined by Eq. \
\ref{eq:tubesep}. The setup we used in the MD simulations is exactly
the same as the previous one (Fig.\ \ref{fig:tubeset}), where static
friction is introduced by choosing a non-zero $\mu$. Between the
particles, we use $\mu _{PP} = 0.5$. We also set the shear friction
coefficient $\gamma _{s}$ to be zero. We do simulations with $W=1$ and
$L=15$, starting with $N=225$ particles. All the other parameters are
kept to be the same as above. In the simulations, we find three types
of behaviors depending on the friction coefficient between the walls
and the particles $\mu _{WP}$: (1) If $\mu _{WP} \ge 1.0$, the
particles can move initially, but they eventually form static
column(s). (2) On the other hand, if $\mu _{WP} \le 0.6$, the
particles constantly increase their speeds, and do not go into a
steady state until the end of simulations (50 000 iterations). (3) In
the intermediate regime, $0.6 \le \mu _{WP} \le 1.0$, we find
steady states, where density waves travels with almost constant
velocities. The static structures found in the first regime are
precisely what is expected from the theory. In the second regime,
however, the systems do not reach steady states, in contrast to the
theory. One possibility is that the time needed to reach a steady
state is larger than the simulation time. To check this possibility we
do longer simulations of the system with $\mu _{WP} = 0.6$, which does
not reach a steady state in $50 000$ iterations. We find the system
{\it does} reach a steady state at around $100 000$ iterations.
In the third regime, the simulations with $L = 15$ do not show the
expected periodic stagnant zones but traveling density fluctuations.
For example, we show the density evolutions in a tube of $L = 15$ in
Fig.\ \ref{fig:mdstube}(a), where $\mu _{WP} = 0.9$ and the time
interval between the successive raws are $0.0025$. A region of high
density travels with almost constant velocity of $-86 \pm 13$. There
are few possibilities to understand the discrepancy. First of all,
there can be a problem of commensurability. In general, the length of
the tube $L$ is not an integer multiple of the stagnant zone
separation ${\cal D}(p)$. Thus, the distance between the clogged zone
can not all be ${\cal D}(p)$ due to the periodic boundary condition.
It can be shown, following the argument in Sec.\ \ref{sec:thtube},
that the distances between the stagnant zones are all ${\cal D}(p)$
except one, which is smaller than ${\cal D}(p)$. This configuration,
however, can not be a steady state. The stagnant zone just below the
small separation becomes unstable, since the incoming velocity of the
particles are smaller than $v_c(p)$. These particles travel further
down to reach $v_c(p)$, then form a stagnant zone. In effect, the
stagnant zones travels down, if $L$ is not an integer multiple of
${\cal D}(p)$. There also can be problems of ``noises.'' As discussed
before, there are noises to the continuum description we have been
using. Due to these noises, the separations between the zone are not
all equal, but fluctuate around ${\cal D}(p)$. Furthermore, the noise
also cause the stagnant zones to move around. Considering the above
possibilities, we expect that several stagnant zones in a long tube
drift downwards, whose separations fluctuate around ${\cal D}(p)$. In
order to check the possibilities, we study density waves for several
values of $L$, keeping the average density constant. The evolution of
density field for $L = 30$ is shown in Fig.\ \ref{fig:mdstube}(b). One
can see a region of high density is traveling downwards with the
velocity around $-25$. The results for both $L = 15$ and $L = 30$ are
consistent with the prediction. Since there are only one region of
high density, we expect ${\cal D}(p)$ is larger than $L$. We then
expect the velocities of the density waves are always negative, and
their magnitude decreases as one increases $L$, thereby approaching
${\cal D}(p)$. The situation for $L = 45$ is quite different, as shown
in Fig.\ \ref{fig:mdstube}(c). The high density region seems to travel
upwards, and the velocity seems to fluctuate more. These two features
are also found in a few additional runs we study for $L = 45$. The
fluctuations can be caused by the ``noise,'' but the trend of moving
upwards can not be explained. We also studied the system with $\mu
_{WP}= 0.7$ and $0.8$, and find essentially the same.
\subsubsection{Comparison with the experiments}
We now discuss the results of the experiments with vertical tubes, and
compare them with the theoretical and simulational results obtained
above. We first discuss the experiments. Density waves in vertical
tubes are first found in the experiments by P\"{o}schel \cite{p92}. He
found two types of waves: (1) Regions of large densities occur at
random positions, and they travel with non-zero velocity. (2) The
separations between the regions of large densities seem to be about
the same, and they fluctuate around certain positions \cite{p93}. The
conditions needed to obtain each types of waves are unknown. The flows
are also studied in vacuum, and surprisingly, the density waves
disappear \cite{b93,h93}. It is still not understood {\it how} air
affects the formation of density waves. Here, we discuss one of the
possible mechanisms. The conditions for forming kinetic waves, as
discussed in Sec.\ \ref{sec:thtube}, are fairly simple. One important
condition is that the friction force should balance the driving force,
which in this case, gravity. It is possible that the friction force by
the sidewalls is too small to balance gravity. Consider a block of
particles falling down in a tube. If the density of the block is large
enough, air can not easily pass through the block, and the air
pressure just behind the block can be smaller than that of the front.
The pressure difference gives rise a force to slow down the block,
which acts as an additional friction force. Since the pressure
difference is expect to increase by increasing the density and
increasing the velocity of the block, the friction force by air can
balance gravity at high velocity, and the balance produces kinetic
waves. As one can see, this argument is largely speculative, and
should be checked by careful experiments. Especially, it should be
check whether there is pressure difference between the front and the
behind of a moving granular blocks of high density, and whether the
difference is enough to balance the gravity.
Assuming the above mechanism to be hold, how can one understand the
two types of waves found in the experiments? The two waves are readily
compared with the predicted kinetic waves with and without static
friction. If ${\cal D}(p)$ is larger than the length of the tube, we
do not expect to see any stagnant zone (for open boundary condition).
Therefore, we effectively see the system without static friction,
which produces traveling kinetic waves. However, if ${\cal D}(p)$ is
much smaller than the tube length, we {\it do} see periodic stagnant
zones. The distance ${\cal D}(p)$ is a decreasing function of the
friction (both by the sidewalls and air), and it is possible that the
tube which produces the periodic zones have larger friction than
others. This possibility again is speculative, and should also be
checked by more controlled experiments. For example, the friction can
be changed by using the sidewalls of varying surface roughness. If air
is responsible for an additional friction, one can also change the
friction by controlling the pressure of air.
\subsubsection{Dynamic waves}
We conclude this section by discussing dynamic waves in granular flows
through tubes. As discussed in Sec.\ \ref{sec:dynamic}, we expect the
granular flows become less stable under density fluctuations for
smaller coefficient of restitution $e$. Since $e$ is small for large
normal damping coefficient $\gamma _{n}$, we expect the system to be
less stable for large $\gamma _{n}$. We simulate the system with
several values of $\gamma _{n} = 5 \times 10^{2}, 1 \times 10^{3}, 2
\times 10^{3}$, $3 \times 10^{3}$, and study the stability. In Fig.\
\ref{fig:dtube}, we show the density fields of tube with $L = 15$ and
$N = 225$ for several values of $\gamma _{n}$. Here, the time
intervals between the successive raws are $0.0025$. We do not find any
sign of dynamic waves, even for longer simulations. We also repeat the
simulations with higher density $N = 337$, and find that the results
are essentially the same. The coefficient of restitution $e$ depends
on the relative velocity between the colliding particles for the
Hertzian contact force. Considering the scale of velocities found in
tubes, $e$ is roughly estimated to be $0.1$ for $\gamma _{n} = 3
\times 10.^{3}$ It is possible that the dynamic instability occur at
even larger values of $\gamma _{n}$. The limitation of the constant
timestep type algorithm we are using is that we have to decrease the
timestep to prevent a numerical instability, if we want to increase
$\gamma _{n}$. For example, the timestep is chosen to be $5 \times
10^{-5}$ for $\gamma _{n} = 5 \times 10^{2}$, and $1 \times 10^{-5}$
for $\gamma _{n} = 3 \times 10^{3}$. Therefore, we can not simulate
systems of arbitrarily large $\gamma _{n}$. One have to use event
driven type algorithms (for example, Ref.\ \cite{hl90}) to overcome
this limitation.
\subsection{Density waves in hoppers}
\label{sec:nuhop}
In Sec.\ \ref{sec:thhop}, we presented a theory which predicts the
existence of kinetic waves in granular flows through hoppers. In that
section, the velocity of the kinetic wave in hoppers of opening angle
$2 \theta$ is shown, up to the first order of $\theta$, to be $U
_{h}(\theta ,p,x) = U _{t}(p) + C(p,x) \theta$. Here, $p$ is the
packing fraction and $x$ the position, and $U _{t}(p)$ the velocity of
kinetic waves in tubes, and $C(p,x)$ is a complicated function of $p$
and $x$. We thus expect $U _{h}$ for a hopper of small $\theta $ is
not very different from that of tubes. The conditions for the
existence of dynamic waves are too difficult to be obtained from the
theory.
We study hoppers of length $L = 15$, bottom width $W _{o}= 1.0$, and
several values of the opening angle $2 \theta$. We apply a periodic
boundary condition in the vertical direction. The particles come out
of the bottom are again fed into the top. The boundary condition,
which is not natural for the hopper geometry, can introduce some
artifacts to the system. We later check the results by comparing with
those from the open boundary condition. The main reason for using the
periodic boundary condition is that we can simulate the systems for
longer time, which in effect study the systems of larger sizes without
actually increasing the length $L$ (and the number of particles). We
initially arrange particles as a square lattice in a hopper. The
lattice constant is $0.1$, the average radius of the particles. The
average number of particles per unit area is very close to $25$, the
maximum density allowed for the square packing. The randomness in the
initial configuration is introduced by the polydispersity of the
particles. The interaction parameters are chosen to be exactly the
same as those for tubes.
We first study the system without static friction. The static friction
coefficient $\mu$ is chosen to be $0$, and the velocity dependent
shear friction term $\gamma _s$ to be $500$. In Fig.\ \ref{fig:mdhop},
we show the time evolutions of the density and the velocity fields in
hoppers. The plots are made in the same way as Fig.\ \ref{fig:mdtube}
except the fact that the density is obtained by dividing the number of
particles in a bin by the area of the bin, which is not constant for a
hopper. The grayscales are chosen to show clear contrast between the
low and high density (velocity) regions by controlling $d_l$ and $d_u$
($v_l$).
In Fig.\ \ref{fig:mdhop}(a) and (b), we show the density and the
velocity fields for a tube ($\theta = 0$) in order to serve as a
reference to compare with those for hoppers. The time interval between
the successive lines are $0.005$. In Fig.\ \ref{fig:mdhop}(c) and
(d), the fields for a small angle hopper ($\theta = 1^{\circ}$) are
shown. In the density plot (Fig.\ \ref{fig:mdhop}(c)), there are two
waves in the hopper, one travels upwards and the other downwards.
Comparing with the velocity plot (Fig.\ \ref{fig:mdhop}(d)), the
densities of the upward wave are strongly correlated to the
velocities, while there seems to be no such correlation for the
downward waves. The correlations found in the upward waves are
qualitatively the same as that of kinetic wave, i.e., the particles
travel slow (fast) in the regions of high (low) density. It is quite
possible that the upward wave is of kinetic nature. Also, the
velocities of kinetic waves in hoppers with small opening angle are
expected to be very close to that of tubes. The fact that the
velocity of the upward waves ($113 \pm 4$) are very close to that of
the tube ($93 \pm 10$) is one other support that the wave is kinetic
\cite{note1}. We now consider the waves travel downwards. The waves,
not only show no correlations between the density and the velocity
fields, but also travels in the opposite direction to the kinetic
waves in the tube (Fig.\ \ref{fig:mdhop}(a)), which suggests that the
waves are not probably kinetic. Furthermore, the density contrasts of
the waves are constantly increasing, which is not possible for kinetic
waves. The increments can be more clearly seen in hoppers of larger
opening angle as shown in (e)-(f) ($\theta = 4^{\circ}$). The
downward waves initially coexist with the kinetic waves, but
eventually dominate the system. The above facts are still true for the
largest $\theta =10^{\circ}$ we study. The properties of the downward
waves listed above suggest that the downward waves are of dynamic
nature. According to the argument used for the dynamic waves in tubes,
dynamic waves will be more easily formed using non-elastic particles.
We check this possibility by studying a hopper of $\theta = 1^{\circ}$
for different values of $\gamma _{n}$. In Fig.\ \ref{fig:dhopper}, we
show the density fields for $\gamma _{n} = 1 \times 10^{3}$ and $2
\times 10^{3}$. Comparing with that of $\gamma = 5 \times 10^{2}$
(Fig.\ \ref{fig:mdhop})(c), one can see the waves for larger $\gamma
_{n}$ are indeed formed earlier, and their intensities (density
contrast) are larger. This add one more support that the downward
waves are dynamic. We also measure the velocities of the dynamic waves
for several values of $\theta$. As shown in Table \ref{table:vhop},
the magnitude of the velocity is decreased as $\theta$ is increased.
Following the trend, it is quite possible that the velocity becomes
zero for finite $\theta$, and change its sign.
We now study hoppers with the open boundary condition. In Fig.\
\ref{fig:mdohop}(a) and (b), we show the density and the velocity
fields for a hopper of $\theta = 1^{\circ}$ and $L = 30$. Here, we
turn off static friction ($\mu = 0$), and we set $\gamma _{s} = 5
\times 10^{2}$. One can hardly see any fluctuations in the density
field, but one can see some traveling patterns in the velocity field.
We now turn on static friction. We set $\gamma _{s} = 0$ and $\mu \neq
0$. The density and the velocity fields with $\mu = 0.5$ are shown in
Fig.\ \ref{fig:mdohop}(c) and (d). One can now see upward traveling
density waves. Furthermore, the density field have strong correlations
with the velocity field, suggesting that the waves are kinetic. Even
though kinetic waves are present in the system independent of static
friction, the amplitudes of the waves are too small to be visible
without it. Static friction provides an effective mechanism for
creating large density fluctuations. Also, the density waves are not
present in the hoppers of small $L$. The absence of density waves can
be caused by the fact that the particles need to travel certain
distances to reach a steady state around which the density waves can
only be seen. All these results remain valid for larger values of
$\theta$ we have studied. For example, we show the case of $\theta =
5^{\circ}$ in Fig.\ \ref{fig:mdohop}(e)-(f).
We also search for the dynamic waves in hoppers with the open boundary
condition. We simulate the system with several values of $\gamma
_{n}$, and check the instability of creating dynamic waves. For the
range of $\gamma _{n}$ we have studied ($5 \times 10^{2} \sim 3 \times
10^{3}$), we do not find the instability. Again, the simulations for
larger values of $\gamma _{s}$ are limited due to the algorithm we are
using. Even though we do not rule out dynamic waves in hoppers in
general, the dynamic instability found above seems to be an artifact
of the periodic boundary condition.
We now compare the results with the experiments. Baxter {\it et al}
found density waves in a hopper only if a certain amount of rough
sands is mixed with smooth sands \cite{bbfj89}. The role of the rough
sands is not clearly established. It is possible that the rough sands
forms local ``arches'', thereby increasing density fluctuations. In
that case, the role played by the rough sands is the same as that of
static friction, which provides density fluctuations to maintain
kinetic waves. Also this is consistent with the fact that the
amplitudes of the density waves are a smooth function of the fraction
of the rough sands, which suggests that the density waves in the
experiments are kinetic. The suggestion, of course, has to be checked
by experiments, for example, by measuring the correlations between the
density and the velocity fields.
\section{Discussion}
\label{sec:dis}
We have presented theoretical and numerical evidences that the density
waves found in the simulations of P\"{o}schel is of kinetic nature.
However, the density waves found in the experiments are not fully
understood. The first and foremost problem is to find the form of the
friction force. In the MD simulations, the friction force is generated
by the collisions of particles to the sidewalls. In experiments, the
collisional friction force seems to be too small compared to gravity,
and another friction force related to air gives dominant contribution.
We proposed a mechanism how air can generates a friction force, which
should be checked by experiments. We want to emphasize that since the
existence of kinetic wave is not strongly dependent on the details of
the friction force, the density waves found in the experiments are
very likely to be kinetic waves.
We find conditions for the existence of dynamic waves in tube. The
conditions depend on details of the force, which we do not know. We
numerically search for dynamic waves by increasing $\gamma _{n}$,
since we expect dynamic waves can be more easily created for inelastic
particles. Even for the largest $\gamma _{n}$ we studied, we can not
find the dynamic waves. It is possible that dynamic waves occur for
even larger values of $\gamma _{n}$. We are not able to check the
possibility, since the algorithm we are currently using becomes very
inefficient for larger values of $\gamma _{n}$.
We also have present theoretical and numerical evidences that there
are kinetic waves in hoppers. Especially, the kinetic waves in hoppers
with the open boundary condition are visible {\it only} with static
friction. This can be readily compared with the fact that one need
finite fraction of rough sands to observe the density waves in the
experiments. Here, the role of rough sands can be creating large
density fluctuations to maintain kinetic waves just like static
friction. The suggestion that the density waves in the experiments of
hoppers are kinetic waves should be checked, for example, by studying
the correlation between the density and the velocity fields.
We are not able to do a linear stability analysis for hoppers, due to
the complicated density and velocity fields in the steady state. In
the simulations with the peridic boundary condition, we find another
density waves, which we believe to be dynamic on a few evidences.
Since we do not find the dynamic waves with the open boundary
conditions, we think the above dynamic wave is an artifact of the
boundary condition. However, we do not rule out the dynamic waves in
hoppers, especially for large values of $\gamma _{n}$.
I thank Michael Leibig, Hans Herrmann and Thorsten P\"{o}schel for
many useful discussions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 291 |
\section{Introduction}
Recent advances in the trapping and cooling down to degeneracy
of ultracold Fermi gases have revived interest in the ground state
phases of these systems.\cite{gre03,joc03,zwi03,chi04,reg04,
zwi05,zwi06,par06,sch07,ste08,jor08,jo09,blo08,trento}
In a two-component Fermi system with equal densities attractive
interactions between different species lead to Bardeen-Cooper-Schrieffer
(BCS) pairing in the weak coupling limit and Bose-Einstein condensation
(BEC) in the strong coupling limit.\cite{sademelo}
When the densities are imbalanced more
exotic phases are expected to follow, such as the Sarma
phase\cite{sarma} with zero center-of-mass momentum and
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase\cite{ff,lo} with finite
center-of-mass momentum. There is a growing literature
on the possible phases of two-component Fermi gases with population
and mass imbalance.
\cite{liu03,wu03,bed03,for05,car05,she06,che06,pie06,isk06,pao06,
chi06,gub06,nik07,par07,isk07,pil08,con08,sha08,ber09,he09,
che09,bau09,des09}
The experimental efforts in ultracold
Fermi gases are in their beginning stage and so far only phase
separation between a superfluid and a normal phase has been
observed.\cite{zwi06,par06,shi06,par06b}
Semiconducting electron-hole bilayer systems offer another
realization of a two-component Fermi system with which the exotic
phases can be studied. Formation of excitons between spatially
separated electrons and holes and their subsequent condensation
have long been predicted\cite{lozovik,shevchenko} and arguably observed
nearly 30 years later experimentally.\cite{butov}
The phase diagram of symmetric electron-hole bilayer systems (equal
mass and layer density) is most reliably calculated by quantum Monte
Carlo simulations. \cite{littlewood,senatore}
Recent success in fabricating closely spaced semiconducting
electron-hole bilayer structures\cite{keogh_apl,seamons_apl}
and the ability to control the densities of individual layers
make the investigation of Sarma and FFLO phases very timely.
In fact, experiments supporting evidence of a transition from
the Fermi liquid phase to an excitonic condensate have been
recently reported through Coulomb drag
measurements\cite{croxall_prl,seamons_prl} in such structures.
The BCS-BEC crossover in an electron-hole bilayer system with unequal
electron and hole densities was recently studied in Ref.~\onlinecite{pieri07}
within a BCS mean field approach.
Sarma and FFLO phases were found to be stable in some range of densities; electron-hole
bilayers appear thus promising candidates for the detection of such elusive phases.
In this paper we extend the work of Ref.~\onlinecite{pieri07} by including
the in-plane Coulomb interactions, that were neglected there, as well as
some screening effects.
We find that the effect of intra-layer
Fock energy quantitatively changes the phase diagram moving the
normal-condensed phase boundary to lower densities.
Comparing energy of the condensed phase
with that of the normal phase, we map out the phase diagram in
the average density-population polarization plane. We check the
``local'' stability of the Sarma phase with respect to competing FFLO order
by calculating the superfluid mass density and identify a negative superfluid
mass density with an instability towards an FFLO phase.
We calculate also the compressibility matrix in order to investigate
possible instabilities towards phase separation.
Finally, we consider the effect of gate layer screening,
which proves especially important in the discussion of the local stability of the Sarma phase.
At zero temperature, the simultaneous presence of the singularity in the Coulomb potential and of a
sharp Fermi surface produces in fact a logarithmic divergence in the
momentum dependence of the BCS gap function which makes the Sarma phase always locally stable
against the FFLO phase.
The inclusion of some form of screening removes this peculiar behavior, thus recovering the instability
towards the FFLO phase in some region of the phase diagram.
The intra-layer interactions and
screening effects give therefore rise to a rich phase diagram in the
crossover region between the BCS-like
high density state and the BEC of low density excitons, showing the
possibility to observe exotic superfluid phases as the population
polarization is changed.
The rest of this paper is organized as follows. In the next
section we outline the mean-field theory for electron-hole
bilayers and provide the set of self-consistent equations
for the quasiparticle energies and gap function. In Section
III, after a brief remark about our computational procedure, we
present our results for the quasiparticle properties and phase
diagram of the system. We conclude in Section IV with a summary
and outlook.
\section{Mean-Field Theory\label{mft}}
The Hamiltonian describing electrons and holes in a bilayer system
interacting with the Coulomb potential can be written as
\begin{widetext}
\begin{equation}
\begin{split}
\label{eq:ham}
\op{H}&=
\sum_\bk (\epsilon^a_\bk \ad_\bk a_\bk + \epsilon^b_\bk \bd_\bk b_\bk)
+\frac{1}{2A}\! \sum_{\bk_1\bk_2\bq }\!\! U^{aa}_\bq \ad_{\bk_1+\bq}
\ad_{\bk_2-\bq} a_{\bk_2} a_{\bk_1} \\
&\hfill+\frac{1}{2A} \sum_{\bk_1\bk_2\bq }\!\! U^{bb}_\bq \bd_{\bk_1+\bq}
\bd_{\bk_2-\bq} b_{\bk_2} b_{\bk_1}
+\frac{1}{A} \sum_{\bk_1\bk_2\bq }\!\! U^{ab}_\bq \ad_{\bk_1+\bq}
\bd_{\bk_2-\bq} b_{\bk_2} a_{\bk_1}
\end{split}
\end{equation}
\end{widetext}
The basis
states for electrons and holes are chosen to be plane wave states
labeled by two-dimensional wave vectors $\bk$ as is
conventional for a uniform system.
The operators $a_\bk/\ad_\bk$ ($b_\bk/\bd_\bk$) are
creation/annihilation operators for electrons (holes) respectively.
The single particle energies are denoted by
$\epsilon^a_\bk,\epsilon^b_\bk$ and the matrix element $U_\bq$ with
respect to plane wave states becomes
the Fourier transform of the corresponding two-body Coulomb interaction
$U(\br)$
\begin{equation}
U^{aa}_\bq = U^{bb}_\bq = \frac{2\pi e^2}{\varepsilon q}\, ,
\qquad
U^{ab}_\bq = \frac{2\pi e^2}{\varepsilon q}
\ee^{-qd}
\end{equation}
where $U^{aa}, U^{bb}$, and $U^{ab}$ denote the electron-electron,
hole-hole and electron-hole Coulomb interactions, respectively, $A$
is the area of a layer and $d$ is the inter-layer separation. We disregard
the spin degrees of freedom.
The bilayer system is characterized by the electron and hole densities,
or equivalently by the average density parameter $r_s$ (average
distance between particles in the plane in units of Bohr radius
$a_B$), the population polarization $\alpha$ (characterizing
population imbalance in terms of the ratio of density difference and
total density) defined by
\begin{equation}
n=\frac{1}{2}(n_a+n_b)=\frac{1}{\pi a_B^2 r_s^2} \quad \text{and} \quad
\alpha=\frac{n_a-n_b}{n_a+n_b}
\end{equation}
and the inter-layer separation $d$.
The solution of the mean-field Hamiltonian at zero temperature ($T=0$) is given by
the following coupled integral equations
\begin{eqnarray}
\Delta_\bk &=& - \frac{1}{A} \sum_{\bkp\neq \bk} U^{ab}_{\bk-\bkp}
\frac{\Delta_\bkp}{2E_\bkp} (1-f^+_\bkp-f^-_\bkp)\\
\xi_\bk &=& \epsilon_\bk-\mu-\frac{1}{2A}\sum_{\bkp\neq \bk} U^{aa}_{\bk-\bkp}
[ (1-\xi_\bkp/E_\bkp)\nonumber\\
&&\phantom{aaaaaaa}\times(1-f^+_\bkp-f^-_\bkp)+f^+_\bkp+f^-_\bkp ]\label{csik} \\
E_\bk^2 &=& \xi_\bk^2 + \Delta_\bk^2 \\
f^{\pm}_\bk&=& \left\{
\begin{array}{lll}
1 & \textrm{if} & E^{\pm}_\bk < 0 \\
& \\
0 & \textrm{if} & E^{\pm}_\bk > 0
\end{array}
\right.
\end{eqnarray}
where $\epsilon_\bk=(\epsilon_\bk^a+\epsilon_\bk^b)/2$ (with $\epsilon_\bk^i=\hbar^2 k^2/2m_i$, $i=a,b$),
the mean chemical potential $\mu=(\mu_a+\mu_b)/2$, while
\begin{eqnarray}
E^{\pm}_\bk&=&E_\bk \pm \Delta E_\bk\\
\Delta E_\bk&=&\Delta
\xi_\bk+\frac{1}{2A} \sum_{\bkp\neq \bk} U^{aa}_{\bk-\bkp} (f^-_\bkp-f^+_\bkp)\\
\Delta \xi_\bk&=&\frac{1}{2}(\epsilon_\bk^a-\mu_a-\epsilon_\bk^b+\mu_b) .
\end{eqnarray}
At finite temperature, the occupation functions
$f^\pm_\bk(E^\pm_\bk)$ go from the step function to the Fermi-Dirac
distribution.
Given the electron and hole chemical potentials $\mu_a$ and $\mu_b$,
these equations can be solved numerically to obtain the unknown functions
$\Delta_\bk, \xi_\bk$ and $\Delta E_\bk$.
Physically, $\Delta_\bk$ is the BCS (s-wave) gap function while
$E^\pm_\bk$ are the quasi-particle excitation energies in the superfluid
phase. In the absence of intra-layer interaction $\xi_\bk$ is
just the average of the free electron and hole dispersions
(with respect to the corresponding
chemical potentials). Intra-layer interaction modifies the free
dispersions by the inclusion of the exchange (Fock) interaction,
as explicitly considered in Eq.~(\ref{csik}).
For fixed number of particles the chemical potential values are
adjusted to satisfy the number equations
\begin{equation}
n_a = \frac{1}{2A} \sum_{\bk}
\left[
\left(1+\frac{\xi_\bk}{E_\bk}\right) f^+_\bk +
\left(1-\frac{\xi_\bk}{E_\bk}\right) (1-f^-_\bk) \right]
\end{equation}
and
\begin{equation}
n_b = \frac{1}{2A} \sum_{\bk}
\left[
\left(1+\frac{\xi_\bk}{E_\bk}\right) f^-_\bk +
\left(1-\frac{\xi_\bk}{E_\bk}\right) (1-f^+_\bk) \right] \, .
\end{equation}
In the above mean-field description of the electron-hole
bilayer we have used the bare Coulomb interaction given in
Eq.\,(2).
In realistic systems, the interactions
entering the model hamiltonian of Eq.\,(1) should be modified
to include
many-body effects such as exchange and correlation
and
external potentials. These effects are described by a
screening function which usually decreases the strength of the
bare Coulomb interaction for electrons and holes in the normal
phase. However, the 2D screening due to intra- and inter-layer
interactions is difficult to take into account properly for
the condensed phase.\cite{gortel}
In order to see the qualitative effects of screening we
consider the mechanism of gate screening which can be taken into account
in a simple way. In this mechanism the
Coulomb potential of a point charge is replaced by that of a dipole
consisting of the point charge and its image behind the
metallic gate.
We have approximately modelled the screening by the gate potential
by taking the
intra- and inter-layer interactions to be
\begin{equation}
U^{aa}_\bq = U^{bb}_\bq = \frac{2\pi
e^2}{\varepsilon\sqrt{q^2+\kappa^2}}\, ,
\qquad
U^{ab}_\bq = \frac{2\pi e^2}{\varepsilon\sqrt{q^2+\kappa^2}}
\ee^{-qd}\,
,
\end{equation}
respectively, where the parameter $\kappa$ is a screening
wave number. In recent experiments with metallic gates to
control the charge densities, the separation between the gate
and 2D layer is about $\sim 250$\,nm \cite{seamons_apl,
screening}. Thus, the image charge is $\sim 500$\,nm away from
the real charge and we may assume that for distances larger than
500\,nm, the Coulomb potential will be screened. In
our calculations we take the screening length associated with
gate screening to be $\sim 20 a_B$, i.e.,
$\kappa = 1/20 a_B$. We have also checked other values of
$\kappa$ and found that the results are largely insensitive
in the range $40> 1/(\kappa a_B) >5$.
\section{Results and Discussion\label{results}}
\subsection{Numerical Procedure}
We solve the gap equations by representing the
unknown functions on a grid of $k$-points (after angular integration)
and using a non-linear root finding scheme for the function values
on grid points. For balanced populations an iterative scheme provides a
robust method of solution.
For imbalanced populations we employ a root finding
scheme for the function values on grid points and chemical potential
values. We start with the equal density solution at the same
average density and create imbalance
first at a small finite temperature and then decrease the temperature
(using the solution from the previous step as input) until results do
not change with temperature any more.
The integrals are evaluated using
Gaussian quadrature. The finite temperature is necessary to obtain
smooth functions and gradients for the Newton-Raphson root finding
algorithm. We found it necessary to introduce up to three different
grids for integration to handle "discontinuities" at low temperatures,
when one type of occupation number becomes equal to unity
$f^\lambda_\bk=1$ ($\lambda=+$ or $-$) in a region of $k$-space
(and causing the integrands to vanish there).
The so-called Sarma states
obtained in this way are of the following BCS form
\begin{eqnarray}
\vert \Psi \rangle=\prod_{\bq \in \mathcal{R}} a^\dag_\bq
\prod_{\bk \notin \mathcal{R}} (u_\bk+v_\bk a^\dag_\bk b^\dag_{-\bk})\vert 0 \rangle
\end{eqnarray}
where the resulting wave function has a certain
range of $\bk$ states (the set denoted by $\mathcal{R}$) occupied with
quasi-particles of the BCS theory giving rise to population imbalance.
The region $\mathcal{R}$ is where the quasi-particle energy
$E^\pm_\bk$ becomes negative, i.e. less than that of the ground pair
energy and the corresponding quasi-particle occupation becomes unity.
Incidentally, the quasi-particles of BCS theory are just electron or
hole states at that wave vector $\bk$.
Outside the set $\mathcal{R}$ we have pairs $\bk,-\bk$ of electrons and
holes.\cite{footnote}
Therefore, at $T=0$ there can be one or two Fermi surfaces depending
where the set of $\bk \in \mathcal{R}$
vectors are. These topologically different phases
will be called Sarma-1 (S1) and Sarma-2 (S2). These states have also been
called breached pair states~\cite{for05}
displaying a Fermi surface together with a condensate.
The gap function is non-zero but there are gapless excitations.
\subsection{Quasi-Particle Properties}
In the following we present physical quantities in Rydberg
units, i.e. length is measured in effective (excitonic) Bohr radius
$a_B=\frac{\hbar^2\varepsilon}{me^2}$, momentum in $1/a_B$
and energy in effective Rydberg
(Ryd= $\frac{\hbar^2}{2m a_B^2}=\frac{e^2}{2\varepsilon a_B}$).
The reduced mass $m$ is defined by $1/m=1/m_a+1/m_b$
where $m_a=m_e$ and $m_b=m_h$ are the band mass of the electron and
hole, respectively. In the numerical calculations we specialize
to GaAs system parameters with mass ratio $m_a/m_b=0.07/0.30$ and
background dielectric constant $\varepsilon=12.9$.
Representative solutions with one and two Fermi surfaces at $T=0$ are
illustrated in Fig.~\ref{fig:gap} (bare Coulomb interaction) and
Fig.~\ref{fig:gapscr} (screened interactions) for $d=a_B$. The figures show the gap
function $\Delta_\bk$, the quasi-particle energies $E^\pm_\bk$
and their average $E_\bk$ on the left panels, and the electron and
hole occupation numbers
$n_a(k), n_b(k)$ on the right panels. At $T=0$ in the ground state, the quasi-particle levels
with negative energy are occupied, positive energy levels are empty.
The two different type of excitation branches
are split both due to different electron-hole mass and chemical potential
values. When one of the spectra crosses the zero energy axis, population
imbalance is created.
If the negative energy region includes the origin at $k=0$, the ground
state has one Fermi surface, otherwise it has two. The two cases are
denoted by S1 and S2 respectively.
The top panel in each figure shows an S2 phase and the bottom
panel shows an S1 phase.
Since the quasi-particle energy branch is continuous the system still
has gapless excitations. A close investigation of the gap function
$\Delta_\bk$ in the absence of screening (Fig.~\ref{fig:gap})
shows that it has a cusp at the zero crossings of the quasi-particle energy,
corresponding to a divergence in the derivative of $\Delta_\bk$. This
divergence has important consequences on the stability of the Sarma
phase at $T=0$, as discussed below.
\begin{figure*}[t]
\includegraphics[scale=1.0]{fig1t}
\vspace{0.3cm}
\includegraphics[scale=1.0]{fig1b}
\caption{(color online) Gap function and quasi-particle energies
with bare Coulomb interactions for $m_e/m_h=0.07/0.30$ and $d=a_B$.
The upper panel shows a Sarma-2 phase at $r_s=3$ and $\alpha=-0.3$
with excess holes (heavy majority species).
The lower panel shows a Sarma-1 phase at $r_s=5$ and $\alpha=0.5$
with excess electrons (light majority species).
Occupation numbers are shown on the right.
\label{fig:gap}}
\end{figure*}
\begin{figure*}[t]
\includegraphics[scale=1.0]{fig2t}
\vspace{0.3cm}
\includegraphics[scale=1.0]{fig2b}
\caption{(color online) Gap function and quasi-particle
energies with screened Coulomb interactions for
$m_e/m_h=0.07/0.30$ and $d=a_B$.
The upper panel shows a Sarma-2 phase at $r_s=2.5$ and $\alpha=0.2$
with excess electrons.
The lower panel show a Sarma-1 phase at $r_s=5$ and $\alpha=0.5$
with excess electrons.
Occupation numbers are shown on the right. The gap function has less
variation and the divergence in the derivative at the zero crossings
disappears.
\label{fig:gapscr}}
\end{figure*}
\subsection{Superfluid mass density, compressibility matrix
and the stability of the Sarma phase \label{stability}}
The ``local'' stability of the Sarma phase with respect to phases
of the FFLO type is usually assessed by
calculating the superfluid mass density
(phase stiffness).\cite{pieri07,wu03,isk06} This quantity
should be positive in a stable state and a negative value is
identified with an instability towards an FFLO
phase.\cite{ff,lo,pieri07} Clearly, the positivity of the superfluid mass
density guarantees only that the Sarma phase is a local minumum of the
energy with respect to fluctuations of the gap parameter associated
with pairing of the FFLO type, and does not exclude the possibility that an
FFLO phase with finite pair momentum can be a global mimimum of the energy.
When this happens, the local stability of the Sarma phase actually
corresponds to metastability.
The superfluid mass density is given by~\cite{isk06}
\begin{eqnarray}
&&\rho_s = m_\mathrm{e} n_\mathrm{e} + m_\mathrm{h} n_\mathrm{h}
\nonumber\\
&&-
\frac{\hbar^2 \beta}{8 \pi} \int \dd k k^3
\frac{1}{2} \left[ \frac{1}{\cosh^2(\beta E^+_\bk/2)}
+
\frac{1}{\cosh^2(\beta E^-_\bk/2)}
\right]\phantom{aa}
\end{eqnarray}
where $\beta$ is the inverse temperature. At $T=0$ this expression
can be written as~\cite{pieri07}
\begin{equation}
\rho_{s} \, = \, m_{\mathrm{e}} n_{\mathrm{e}} \, + \,
m_{\mathrm{h}} n_{\mathrm{h}} \, - \, \frac{\hbar^2}{4 \pi} \,
\sum_{j,\lambda} \, \frac{(k_{j}^{\lambda})^{3}}{\left|
\frac{dE^{\lambda}_k}{dk} \right|_{k=k_{j}^{\lambda}}} \, .
\label{superfluid-density}
\end{equation}
where $k_{j}^{\lambda}$ are the roots of $E^{\lambda}_k$ with
$\lambda=\pm$.
At zero temperature the last expression involves the derivative
of $\Delta_k$ (through the derivative of $E_k^\pm$) at the zero
crossings of $E_k^\pm$.
As mentioned above, our calculations are carried out at nonzero but
small temperature.
We have found that this derivative diverges logarithmically as $T\to 0$.
In particular, we have demonstrateed analytically that for the bare
Coulomb interaction one has
\begin{equation}
\left| \frac{ \dd \Delta_\bk}{\dd k} \right|_{k=k^*} \approx
\frac{e^2}{\pi \varepsilon}
\frac{\Delta_{\bk^*}}{2 E_{\bk^*}}
\left|\ln T \right| \quad \textnormal{as} \quad T \to 0
\end{equation}
where $k^*$ is the zero crossing point at $T=0$ as $k \to k^*$
\begin{equation}
\left|\frac{ \dd \Delta_\bk}{\dd k}\right|_{T=0} \approx
\frac{e^2}{\pi \varepsilon}
\frac{\Delta_{\bk^*}}{2 E_{\bk^*}}
\ln \left|k-k^*\right| \quad \textnormal{as} \quad k \to k^*,
\end{equation}
which we have also checked numerically (Fig.~\ref{fig:deldiv}).
This divergence is due to the simultaneous presence of the long range
Coulomb interaction, which is singular at $q=0$, and the
discontinuity of the Fermi function at $T=0$.
Finite temperature and/or screening effects, smear out these
singularities thus removing the divergence.
The presence of this divergence at $T=0$ was overlooked in the
previous mean field study of the
imbalanced electron-hole bilayer system~\cite{pieri07}.
As a matter of fact, making this divergence emerge from the numerical
calculation requires the achievement of very low temperatures in
the calculations and an extreme precision
in the numerical integration.
The presence of this divergence is particularly meaningful
for the analysis of the local stability of the Sarma phase at
strictly $T=0$. The diverging derivative makes in fact the
negative contribution to $\rho_s$ vanish, thus implying
that for the unscreened Coulomb interaction the Sarma phase is
always locally stable at $T=0$.
This result is interesting as a matter of principle, as it
offers an ``extreme'' example, where the argument by
Forbes {\it et al}. \cite{for05}
that mass ratio and momentum structure of the interactions should
favor the stability of Sarma phase is completely effective.
On the other hand we expect it to have few practical consequences,
since the stability of the Sarma phase
induced by this divergence is very fragile with
respect to finite temperature and/or screening effects.
As Fig.~\ref{fig:deldiv} clearly shows, quite small temperatures
suffice to smear out the divergence in the derivative.
Alternatively, the simple screened interaction makes the divergence
to disapper even at $T=0$, as also shown
in Fig.~\ref{fig:deldiv}.
As a result, in the presence of screening, the Sarma phase
will indeed be locally unstable in certain regions of the
$r_s-\alpha$ plane, as discussed in the next subsection.
\begin{figure*}[t]
\begin{center}
\includegraphics[scale=1.00]{fig3}
\caption{The derivative of the gap function $d\Delta_\bk/dk$ as a
function of $k$ at various temperatures with bare interlayer
interactions, or at $T=0$ with gate screening (left). The value
$d\Delta_\bk/dk|_1$ at the zero crossing of $E^+_\bk$ as a function
of temperature $T$ with bare interlayer interactions or with gate
screening (right). In both
panels: $d=a_B,\,r_s=3,\,\alpha=0.3$ and
$m_e/m_h=0.07/0.30$.
\label{fig:deldiv}}
\end{center}
\end{figure*}
The mechanical stability of the system with respect to phase
separation requires the compressibility matrix
$\partial \mu_i/\partial N_j$ to be positive definite.
We have therefore calculated the compressibility matrix
across our phase diagram to check also this
stability. When the intra-layer Coulomb interaction is neglected,
the compressibility matrix develops
negative eigenvalues across most of our phase diagram (restricting
the stable region only to small values of $r_s$) in agreement
with the findings of the recent work by
Yamashita {\it et al.}\cite{ohashi09}.
However, as it was already argued in Ref.~\onlinecite{pieri07},
this apparent dominant instability towards phase separation is
an artifact occurring when the intra-layer Coulomb repulsion
is artificially excluded from the calculation.
It should therefore not be taken seriously.
In particular, we have verified explicitly that in our calculations
{\em with\/} Coulomb intra-layer repulsion,
the Hartree term, which increases linearly with the distance
$d_G$ between the metallic gates and the electron/hole layers, washes out
completely phase separation from our phase diagram of
Fig.~\ref{fig:phased1} already for distances $d_G$ of the order
of 5-10 $a_B$, well below the typical
gate-to-layer distances in current devices.
We thus conclude that, contrary to what happens in cold atom
systems, phase separation is not an issue in
electron-hole bilayer systems.
\subsection{Phase Diagram at $d=a_B$ \label{phasediagram}}
In this section we present the phase diagram resulting from the comparison of
the energies of the Sarma and normal phases and from the stability analysis
discussed in the previous section.
We set the inter-layer separation equal to one effective
(excitonic) Bohr radius $d=a_B$.
To make contact with previous literature, we present in Fig.~\ref{fig:phased1}
the phase diagram for
progressively refined approximations corresponding to the inclusion in the
calculations of: (i) bare inter-layer interactions only, (ii) bare
inter- and intra-layer interactions, (iii) screened inter-layer
interactions only and (iv) screened inter- and intra-layer interactions.
For bare interactions, the superfluid density is always positive and the Sarma
phase is ``locally'' stable, due to the mechanism explained in
Sec. \ref{stability}. Therefore, in the top
panel of Fig.~\ref{fig:phased1} we do not show any FFLO phase, but our
calculations do not rule out the possibility of a first order transition to an
FFLO phase with a finite FFLO modulation momentum ${\bf q}$ as found in
Ref.~\onlinecite{ohashi09}.
Two topologically distinct Sarma phases, Sarma-1 with
one Fermi surface and Sarma-2 with two Fermi surfaces, are present in
the phase diagrams. The effect of the intra-layer repulsive interactions is to
favor the normal phase with respect to the condensed phases, thus shifting
to higher vaues of $r_s$ the boundary between normal and condensed phases
(right panels).
The two bottom panels of Fig.~\ref{fig:phased1} presents the phase diagram when
the gate screening is taken into account. With inter-layer interactions only,
the Sarma phase becomes unstable for a large portion of the phase diagram,
especially with excess holes, i.e. $\alpha<0$. (bottom left panel) There
is no stable S2 phase in this case. Switching on the intra-layer interactions
reduces the space occupied by the FFLO phase in our phase diagram and
restores the S2 phase in some region of the phase diagram.
This result is physically quite sensible, as the FFLO modulations
of the gap parameter should be unavoidably accompanied by some
modulations of the density in real space.
In the presence of the Coulomb intra-layer repulsion such
density modulations are energetically expensive, thus hindering
the FFLO phase with respect to the Sarma phase.\cite{footnote2}
A quite rich phase diagram is therefore obtained when
both intra-layer and screening effects are present. The presence of
locally stable Sarma phases confirms the expectation that isotropic
translationally invariant gapless superfluid states can be stable with
momentum dependent interaction.\cite{for05}
We note in this context that in recent work, Sarma phases were found to be
stable also in two-dimensional, two-band neutral Fermi systems.\cite{he09,des09}
\begin{figure*}[t]
\begin{center}
\includegraphics[scale=1.0]{fig4}
\caption{(color online) Phase diagram for inter-layer separation
$d=a_B$ with progressive refinement of the approximations. Superfluid (S1/S2)-normal (N)
phase boundaries are shown
with red solid lines. A negative
superfluid mass density showing a local instability is assumed to be
towards an FFLO phase. S1, S2 and FFLO boundaries are shown with green
dashed lines. The four panels corresponds to calculations including: bare inter-layer interactions
only (upper left), bare intra- and inter-layer interaction (upper
right), gate screened inter-layer interactions only (lower left) and
gate screened intra- and inter-layer interaction (lower right).
The $\alpha=0$ line is special in the phase diagram and corresponds to the BCS state with
equal populations, which is always stable.
\label{fig:phased1}}
\end{center}
\end{figure*}
\section{Summary\label{summary}}
We have studied a bilayer system of electron and hole
layers spatially separated by an insulating barrier, where
the electron and hole densities can be controlled independently and
have analyzed $s$-wave pairing between electrons and holes as a function of
average density and population difference using mean-field theory.
By solving the
relevant energy gap equations we have compared the energy of the
condensed phase called the Sarma phase with that of the normal state
which is the sum of the electron and hole Fermi liquid energy
described by the Hartree-Fock solution.
We have included both inter- and intra-layer interactions
generalizing earlier work which did not include in-plane
interactions.~\cite{pieri07}
In this way the phase boundary for the ground state is
established in the density-population polarization ($r_s-\alpha$)
plane. The ``local'' stability of the Sarma phase was checked by
calculating the superfluid mass density, whereas the
stability with respect to phase separation was assessed by calculating the
compressibility matrix.
We have found that with bare Coulomb interactions the Sarma
phase is always locally stable due to a peculiar momentum structure of the
gap function originating from the singular infrared behavior of the Coulomb potential, and the simultaneous presence of a sharp Fermi surface at zero temperature.
Employing a simple model of screening which introduces an
infrared cut-off in the Coulomb interaction, we have found
that some regions in the phase space become unstable.
We interpret this as an instability
towards an FFLO phase. Together with intra-layer interactions, the phase
diagram in the crossover regime from the weakly interacting high density
BCS limit to the strongly interacting BEC of dilute excitons has room
for various phases. The topologically different S1 and S2 Sarma phases
and FFLO are present with the inclusion of screening and intra-layer
interactions. On the other hand, without any screening there is no
instability towards FFLO and turning off intra-layer interactions
the phase diagram does not show an S2 state. Currently, the
experimental situation allows these systems to be
realized.~\cite{seamons_prl,croxall_prl,cro09}
Quantitative comparison would require a more realistic model of
screening, accounting for the condensed phase and finite width
of the quantum wells, incorporating the disorder effects,
and inclusion of spin degrees of freedom which may enter non-trivially
when there are spin dependent interactions such as spin-orbit coupling.
With the renewed mean-field phase diagram at hand,
it would also be interesting to perform QMC simulations to
probe the predicted phases.
\acknowledgments{This work is supported by TUBITAK (No. 108T743), TUBA,
European Union 7th Framework project UNAM-REGPOT
(No. 203953), and the Italian MUR under Contract No.
PRIN-2007 ``Ultracold Atoms and Novel Quantum Phases''.
A.\,L.\,S. thanks the hospitality of the Theoretical Physics
Department of the University of Trieste during the time he spent
there at an earlier stage of this work through a
TUBITAK-BAYG scholarship.}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,375 |
Q: Is there a way to implement custom files that work like the 'files' in the /proc file system? I'm looking for something like a persistent named pipe... something that I can cat or grep multiple times, and always get the current state of whatever process is feeding into the pipe.
For example, let's say that I create a named pipe called /tmp/timestamp, and then use date to write to it:
mkfifo /tmp/timestamp
date --iso-8601=seconds > /tmp/timestamp
At this point, the call to date will block, waiting for /tmp/timestamp to be read ...
cat `/tmp/timestamp`
Will un-block date, I'll see something like 2017-03-18T16:11:54-04:00 written to stdout, and date will terminate.
... but what if I want an updated date every time I cat /tmp/timestamp?
I guess that
while :; date --iso-8601=seconds > /tmp/timestamp; done
will work, but I'd like to know if a) there are any non-obvious issues with this approach and b) if there's a way to do it which doesn't require a loop.
I would also like to set this up so that it launches automatically, making the fifo always available.
In terms of why I want this to be in pipes -- the information in question is stored in a database backing a web application. Most of our tech support folks are entirely comfortable logging into the servers via ssh and running queries against the database, but there are certain vital statistics that would be really handy to simply grep from files. Being able to ls the directory containing the named pipes would make all of this discoverable... essentially, I'm not doing this because I have to, I'm doing it because it's a metaphor that I think will work well.
A: Here's a "non-obvious issue" with the loop: if a reading process holds the fifo open (because, say, it blocks on opening another file or is suspended), the write loop will run continuously (until it fills the fifo buffer). There are also issues with multiple concurrent readers, but perhaps you can reasonably eliminate that possibility.
As for a non-loop solution, you can use a socket instead of a fifo, but then you have to write a (trivial) reader program (and use pipes if you want to run something other than cat) since you can't just open those.
A: You could implement a custom filesystem either as a kernel module or by using fuse. Within that custom filesystem you can then have whatever virtual files you want.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 39 |
Alex George Wakely (born 3 November 1988) is an English former cricketer who played for Northamptonshire and was also a former captain of the England under-19s. He is a right-hand batsman, bowls off-breaks and sometimes medium pace bowling. In May 2021, Wakely announced his retirement from all forms of cricket.
Personal life
Born 3 November 1988 in Hammersmith, London, Wakely attended Bedford School. While at the school Wakely was coached by the former England batsman Derek Randall. After his A-levels, Wakely chose to focus on playing cricket professionally, and being a part time pianist.
Career
Domestic
In 2004, Wakely joined the staff of Northamptonshire whilst still in full-time education. He scored 81* on his Northamptonshire Second XI debut aged just 15. In July 2007, he made his first-class debut for Northamptonshire against Somerset. He made scores of 38 and 66, as well as taking two wickets including that of Marcus Trescothick. He played three more first-class matches in 2007 but after scoring 55 against Nottinghamshire he managed only single figure scores in his last five innings. After that poor run of form, he had a spell in the second XI before returning to the first XI in 2009. On 16 June that year, Wakely scored his maiden first-class century against Glamorgan, scoring 113*. For the 2010 season, Wakely was given more of a first team role and began to realise his potential with a century against Middlesex at Lord's.
For the 2013 season, Wakely captained the Northants team in limited overs cricket. This proved to be a successful move; the team finished second in its group in the 40 over league, and won the T20 competition. Wakely played in all of the T20 matches that season and played a key role in the final, scoring 59 from 30 balls.
He missed the whole of the 2014 season because of an Achilles tendon injury that he received during the club's pre-season tour of Barbados.
He returned for the 2015 season recovered, and having been appointed captain in all forms of cricket. He scored two first-class centuries in the season, including a personal highest score of 123 against Leicestershire. Northants once again reached the final of the T20 competition, but this time lost to Lancashire. The next year, Northants returned to Twenty20 finals day with Wakely again captain, and were this time victorious. He was involved in century partnerships in both the semi-final and the final. In the semi, against Notts he and Ben Duckett took Northants from 15/3 to 138/4, himself scoring 53 from 45 balls. The final was versus Durham, and Wakely came in to bat with the score at 9/3, and shared in a partnership of 120 with Josh Cobb.
International
Wakely was picked for the England under-19s tour of Sri Lanka in 2006/07. He scored England's only century of the tri-nation series with 108 from 140 balls against Sri Lanka. In August, he scored a century on his 'Test' debut for England under-19s against Pakistan. On 1 October 2007, he was selected as the England under-19s captain for the 2008 World Cup
References
External links
Player Profile: Alex Wakely from northantscricket.com
1988 births
Living people
English cricketers
English cricket captains
Bedfordshire cricketers
Northamptonshire cricketers
Northamptonshire cricket captains
People from Hammersmith
People educated at Bedford School | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,357 |
Articles and Reviews Comments
Battlefield 2042 CPU Benchmark feat. 128-Player Battles
Thread starter Steve
Phylop
hahahanoobs said:
BF2042 has bigger maps, double the player count, higher polygon count, destruction, physics, explosions with shockwaves, higher quality volumetric smoke, AI etc.
Previous Battlefield titles had all the features you mentioned, except for 128 players. Higher Polygon Count and Volumetric smoke are completely GPU rendered and are barely affected by CPU performance. Even physics are often processed by the GPU, but I'm not sure how Battlefield does it these days. I understand the move to 128 players is going to affect CPU performance more than anything, but even playing on 64 players BF2042 performs a lot worse than BFV and especially BF1 even on lowest settings. I understand that my 5930K is old, but this game shouldn't run as shitty as it does. Even brand new top end CPUs struggle with BF2042, and they should be destroying it.
Philip Pyne said:
(Havok) Physics is software based that runs on CPU.
(Nvidia) PhysX is hardware accelerated that runs on GPU.
You have a very old CPU thinking it shouldn't matter.... It def does.
If you don't know that, how can you be so sure you know what you're talking about?
You're ignoring 90% of what I said so you can defend your argument and try to look smart by nit-picking because I didn't elaborate on physics. I know what PhysX and Havok are. All I said was I don't know exactly how the latest Battlefield implements physics, but that is besides my point. I know that my CPU is old, and I know it matters. Doesn't change the fact that the game runs worse than it should even on brand new top of the line hardware. Look at the benchmarks.
Again, you bring up physics as if that is the only thing you can think of that would have greatest effect on performance. My 5600X and 2070S run the game great at 1440p. Your PC is old and slow. Time to upgrade if you want to play with the least amount of problems. For example I am level 30 something, and haven't had a single crash and the performance is great.
"It was great on BF1, noticed a performance hit with BFV,..."
And you thought the next game being MUCH bigger with more going on would perform - better??? BFV already told you your system wasn't gonna cut it for much longer. You should have listened to what it was telling you.
Could the game use some tweaks? Yes. But you can't expect hardware that was good years ago to last forever. Welcome to PC gaming.
"Again, you bring up physics as if that is the only thing you can think of that would have greatest effect on performance."
The only reason I said anything about physics was because you mentioned it first and I was clarifying you mentioning a bunch of GPU bound workloads when we're talking about CPU performance. I actually didn't say anything about physics performance in the game. What I did mention was 128 players being a big CPU hit, and that is understandable.
"My 5600X and 2070S run the game great at 1440p. Your PC is old and slow. Time to upgrade if you want to play with the least amount of problems. For example I am level 30 something, and haven't had a single crash and the performance is great."
I have a 5930K OC'd to 4.5Ghz, a 2080 Ti FTW3 Ultra, 32GB DDR4-2800, game is installed on a 2TB NVME SSD, and I run the game at 3440x1440. Obviously the CPU is the bottle-neck here, but haven't I made it clear that I realize that?
""It was great on BF1, noticed a performance hit with BFV,..."
And you thought the next game being MUCH bigger with more going on would perform - better??? BFV already told you your system wasn't gonna cut it for much longer. You should have listened to what it was telling you."
No I did not think that BF2042 would perform better than BFV. I was pretty certain it would perform worse and it does, a lot worse, even with just 64 players. Again you misconstrue what I was saying to try and make yourself look smart. What I should have elaborated on is how much of a CPU hog BFV was when compared to BF1. Between BF1 and BFV I don't see much of a reason BFV should be so much harder on the CPU than BF1 is. Now with BF2042, there are legit reasons for the game to be more of a CPU hog, such as 128 players, but I still think it could be optimized a lot better. I'm not saying it should necesarily be optimized well enough to work on my 6 year old CPU, although that would be nice. I'm saying it should be optimized better in general, because it should run a lot better than it does even on a 12900K or 5950X.
"Could the game use some tweaks? Yes. But you can't expect hardware that was good years ago to last forever. Welcome to PC gaming."
I think it could use a lot more than "tweaks." But I'm not trying to split anymore hairs. I don't expect my hardware to last forever, but thanks again for assuming I don't know what I'm talking about. I started building PCs as a kid in the early 90s. Just going by CPUs, here's some of the systems I have built for myself...
The first PC I built was an IBM XT 286 that I threw together with random parts. Eventually moved onto a 486 build, then a Pentium II build, then a Pentium III coppermine build. After that I moved to AMD for a while, had an Athlon XP 2100+ build, upgraded to an Athlon XP Mobile 2500+ since the mobile version overclocked so well and still used a desktop socket. After that had an Athlon X2 4200+, eventually upgraded that to a 5000+. After that I switched back to intel and built a Q6600 based machine which was eventually upgraded to a Q9400. After that I built an i7 930 based machine which lasted me a few years until I built my current machine with the 5930K around 2015. That's just mentioning some of my personal gaming PCs, not mentioning any of my personal servers I've built, or servers I have built for work. I have been working as a Data Center Administrator for more than 11 years and have built thousands of servers.
Anyways... I don't know why I'm even still going on about this.
Reactions: rrwards
"Between BF1 and BFV I don't see much of a reason BFV should be so much harder on the CPU than BF1 is. Now with BF2042, there are legit reasons for the game to be more of a CPU hog, such as 128 players, but I still think it could be optimized a lot better. I'm not saying it should necesarily be optimized well enough to work on my 6 year old CPU, although that would be nice. I'm saying it should be optimized better in general, because it should run a lot better than it does even on a 12900K or 5950X."
Because you replied with novels to say things that were wrong. That's why I'm going on about this. Meanwhile, you're the one writing novels. Will take me 2mins to write this. Your argument is all your opinion. A bad one. Maybe try asking DICE in the forums or on Twitter instead of echoing things where it does no help to the game. I call it game entitlement. It isn't a CPU hog since 60% usage is max I see on my 5600X. You THINK it should run better. That isn't news if that was your whole point. Look anywhere and you'll see people saying the same thing. DICE said don't expect much. So now what? You gonna say DICE doesn't know what they are doing and you do? Neither of us are in game development, so to say, "it should be better" is just insane really. Based on what? BF1 and BFV? You didn't even know what kind of physics BF2042 even used. Not knowing if it was GPU accelerated or not. It's not. Never was.
"It kinda sucks how much of a performance difference there is between these games when BF1 still looks just as good as BFV and BF2042, if not better in a lot of ways and runs a lot smoother."
That started it all. That sentence right there. Because it "looks" the same as old games, it should run the same?
NO! Upgrade your CPU and you'll be gucci.
Noxiious
I play on a PC with a Ryzen 7 5800X OC at 4.2Ghz, Nvidia RTX 3070, 16GB DDR4 3200Mhz CL14, Asus B550-A Gaming, M.2 PNY XLR8 1TB and the game goes very poorly while I play on a 3840x1080 screen in 144hz in high settings without Raytracing, the activation of DLSS does not change anything therefore the game only runs at 80fps and 30-40 in aim mode. So no upgrading your CPU isn't "gucci". This game is poorly optimized, they are aware about it, but "they are working on it".
Reactions: rrwards and Phylop
Noxiious said:
That was meant for the guy with the 6 year old CPU that noticed a perf hit in BFV. It def doesn't help keeping it when you are more likely to have issues on older and slower hardware trying to run the latest software. Bypassing W11 TPM requirements come to mind as an example of that.
I've had no crashes and frame rates are smooth in BF2042. Sadly when performance still isn't good, you'll have to wait for patches. It sucks and wouldn't happen in a perfect world, but whining about it every time like it's an unheard of event gets annoying fast. It then becomes script reading. Upset people just repeating the same things word for word, not offering any actual helpful suggestions. They probably don't report their issues in the proper forums either. I also wonder if how people have their computers (hardware and/or software) configured is what causes some people to have more issues than others.
*Shrugs*
SapientWolf
I think we need 64 player data to test the theory that 128 players are causing the CPU bottlenecking. The map sizes may also play a role.
I've also seen posts from people saying that disabling SMT/hyper threading reduces stutter, and that the game performs better on 6 cores than 12 on a 5900x. That was typically not the case with BFV. Something doesn't smell right when it comes to the game's multithreaded performance.
Reactions: ltkAlpha and Phylop
SapientWolf said:
The game has perf issues. Not an optimization issue. Trying to play this game on old hardware is not wise for starters. If you are running modern hardware then you want to make sure you check Google and BF2042 forums for fixes and or settings you can try. Future patches may fix underlying issues, but if you're getting half the frames you should be, that's not a sign of bad optimization if that's not the majority's experience which it isn't.
The low budget memory, as you said, is single rank, while the rest is dual rank. Maybe this has bigger impact rather than the cl14 vs cl18 and 3000 vs 3200?
kanewang56
Define perf issue vs optimization issue. I am actually a game dev so don't try to fool me with your previous faked shiny cartoons.
You actually just want to bully that guy with an old CPU by flexing your "smooth experience " rtx 3090 oced 5600x stock 3600mhz d4 telling you the experience is not smooth. Think again about your subjective "smooth".
kanewang56 said:
Facts can't be disputed. He revealed he had an inadequate CPU and you have a problem with me telling him that that is an obvious problem? Ok....
Let me explain bugs to you... they don't effect everyone. You're a game developer right? Then you should know this.
You asked that after posting the video that explains it? Um, cool. You know those are the guys that run Techspot, right? If you have a problem with what I'm saying about the performance, then you have a problem with facts.
For a developer you said literally nothing to prove you know anything about game development.
Nicely done re-inventing "facts" "bugs" "performance".
Why would I disturb your ego by proving my dev state when you can just do a search for "rendering" and "glitch" from DICE patch notes?
BATTLEFIELD 2042 UPDATE #3
Addressing further bug fixes, balance changes and quality of life improvements
www.ea.com
"Bug does not effect everyone " basically explained why they stopped wasting time on talking to you who sits on your own "facts" looking for an echo chamber instead of facts. I bet you do not really understand glitch or rendering any way so just believe you are totally right about not answering my original question.
backup321
I posit this game was designed to run well on X box and PlayStation first and foremost. (they have 8 core processors) that is why it likes 8 core pc cpus. it is crushing my 4 core 8 thread 3770. I have 2 xeons in the mail ( E5-2687W and E5-2687W v2) (3.8 GHz and 4.0 GHz clocks) with 8 dedicated cores and 16 threads and will report back when I test on them. ( if it works, I will de clock the xeons until game is unplayable. I am curious how low of a clock speed xeon will play this game smoothly, as there are many cheap xeon workstations with 8 physical cores available refurbished. and if it doesn't work, guess I just have to buy new pc parts to play this terrible game LOL!
"Addressing further bug fixes..."
Battlefield 2042 Benchmarked: 30+ GPUs Tested
riseabove2
DICE's head of design leaves studio in wake of Battlefield 2042's launch
Jrfeimst2
Battlefield 2042 is now one of Steam's worst-rated games of all time
king cleanass | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,910 |
Brazil participated in the 2010 Summer Youth Olympics in Singapore.
The Brazilian squad consisted of 81 athletes competing in 18 sports: aquatics (diving, swimming), athletics, basketball, boxing, canoeing, cycling, equestrian, fencing, gymnastics, handball, judo, modern pentathlon, rowing, sailing, shooting, table tennis, tennis, and triathlon.
Medalists
Athletics
Boys
Track and Road Events
Field Events
Girls
Track and Road Events
Field Events
Basketball
Girls
Boxing
Boys
Canoeing
Boys
Cycling
Cross Country
Time Trial
BMX
Road Race
Overall
Diving
Boys
Girls
Equestrian
Fencing
Group Stage
Knock-Out Stage
Gymnastics
Artistic Gymnastics
Boys
Girls
Trampoline
Handball
Boys
Girls
Judo
Individual
Team
Modern pentathlon
Rowing
Sailing
One Person Dinghy
Windsurfing
Shooting
Pistol
Swimming
Boys
Girls
Mixed
Table tennis
Individual
Team
Tennis
Singles
Doubles
Triathlon
Boys
Mixed
References
External links
Competitors List: Brazil
Youth Olympics
Nations at the 2010 Summer Youth Olympics
Brazil at the Youth Olympics | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,402 |
Q: Silent background push on iOS and Android I am using GCM to deliver notifications to Android and iOS devices.
What I am looking for is to send in the same downstream message a silent push for both platforms.
I have tried with this message
"content_available":true,
"data":
{
//My data here
},
As you can see, no notification key is sended, iOS works fine and we are receiving push in the background but Android shows my app icon at the top bar and it is not calling the GCM receiver.
If I set content_available to false, Android works fine but not in iOS (either background or foreground).
What I supposed to do? Send to my server the OS of each device and send a different message for each system?
I have also tried to set aps dictionary in data payload, but still the same.
Thanks in advance.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,619 |
\section{Introduction}
Radially pulsating variables, and in particular RR Lyrae and Classical Cepheids, play a key role
in modern astrophysics because they are robust primary distance indicators and solid
tracers of old (t$\sim$10--12 Gyr) and young (t$\sim$10--300 Myr) stellar populations,
respectively.
The radially pulsating variables when compared with canonical stellar tracers have the key advantage
of being easily recognized by their characteristic light-curves and to provide firm
constraints on the metallicity gradient and the kinematics of both the thin
disk \citep{pedicelli09, luck11, luck11a, genovali13} and the halo
\citep{kinman12}. The above evidence applies not only to the Galaxy,
but also to nearby resolved stellar systems \citep{minniti03}.
The main drawback in using classical Cepheids is that they have periods ranging from
one day to several tens of days. This means that identifying and characterizing them
is demanding from the observational point of view.
An unprecedented improvement on the number of known radially pulsating
variables was indeed provided by microlensing experiments (MACHO, EROS, OGLE)
as a byproduct of their large-area surveys.
In particular, the ongoing OGLE IV project became a large-scale, long-term, sky-variability survey, and will further increase the variable star identification
in the Galactic Bulge and in the Magellanic Clouds \citep[OGLE IV,][]{sos2012}.
These surveys have been deeply complemented by large experiments aimed at detecting
variable phenomena covering a significant fraction of the Southern Sky, either in the
optical, such as the ASAS Survey \citep{pojmanski02}, the QUEST Survey \citep{vivas04}, the NSVS survey \citep{kinemuchi06}, the LONEOS Survey \citep{miceli08}, the Catalina Real-time Transient survey \citep{drake09}, the SEKBO survey \citep{akhter12} and the LINEAR Survey \citep{palaversa13}; or in the near-infrared (NIR), such as the IRSF \citep{ita04}, the VVV \citep{minniti10}; or in the mid-infrared (MIR) such as the Carnegie RRL Program \citep[CRRLP;][]{freedman12}.
The intrinsic feature of current surveys is that both the identification and the
characterization is performed in optical bands, since the pulsation amplitude is
typically larger in the B--band than in the NIR bands. However, recent theoretical \citep{bono10} and empirical
\citep{storm11a,storm11b,inno13,groe13} evidence indicates that NIR and MIR photometry has several indisputable advantages when compared with optical photometry:
a) it is minimally affected by metallicity dependence \citep{bono10,madore10};
b) it is minimally affected by reddening uncertainties; and
c) the luminosity amplitude is a factor of 3--5 smaller than in optical bands.
This means that NIR observations are not very efficient in identify
new variables, but they play a crucial role in heavily reddened regions
\citep{matsunaga11,matsunaga13}.
Moreover, accurate mean NIR and MIR magnitudes
can be provided even with a limited number of phase points, because of their
reduced luminosity amplitudes in this wavelength regime. However,
NIR and MIR ground--based observations are even more time-consuming than
optical observations, because of sky subtraction. This is the reason why during the past 20 years NIR light-curve templates have been developed for RR Lyrae
\citep{jones96} and classical Cepheids \citep{soszynski05,pejcha12}.
The key advantage of this approach is that variables for which
the pulsation period, the epoch of maximum, and the $B$- and/or the $V$--band
amplitude are available, a single-epoch NIR measurement is enough to provide accurate
estimates of their mean NIR magnitudes, which can then be used to compute their distances.
The most recent Cepheid NIR light-curve template was published by
\citet[][hereinafter S05]{soszynski05}. They used 30 Galactic and
31 Large Magellanic Cloud (LMC) calibrating Cepheids and provided
analytical Fourier fits in the $J$, $H$, and $K$ bands by using
two period bins for Galactic (0.5$< \log P \le$ 1.3 and $\log P > 1.3$)
and LMC (0.5$<\log P \le 1.1$ and $\log P > 1.1$) Cepheids.
We derived new sets of NIR light-curve templates for classical Cepheids
covering the entire period range (0.0 $< \log P \le$ 1.8).
The advantages of the current approach compared with previous
NIR templates available in the literature are the following:
a) Statistics -- We collected optical and NIR accurate photometry
for more than 180 Galactic and 500 Magellanic Cloud Cepheids.
Among these data, we selected the light curves characterized
by full phase coverage and high photometric quality in the
$V$,$J$,$H$ and $K_{\rm{S}}$ bands. We ended up with a sample
of more than 200 calibrating Cepheids.
This sample is a three times larger than the sample
adopted by S05.
The sample size enabled us to split the calibrating Cepheids into
ten period bins ranging from one day to approximately
100 days;
b) Hertzsprung progression -- The sample size allowed us to properly
trace the change in light-curve morphology across the Hertzsprung
Progression (HP). Cepheids in the period range 6$<$ P$<$16 days show
a bump along the light-curves. The HP indicates the relation between
this secondary feature and the pulsation period:
the bump crosses the light-curve from the decreasing branch to the maximum
for periods close to the center of the HP and moves to earlier phases
for longer periods. To properly trace the change in the shape of the light
curve, we adopted a new anchor for the phase zero--point. The classical
approach was to use the phase of maximum light of optical light
curves to phase the NIR light-curves. The use of the phase of maximum light
as zero--point ($\phi$=0) was justified by the fact that the photometry was more
accurate along the brighter pulsation phases.
However, this anchor has an intrinsic limit in dealing with bump Cepheids.
At the center of the HP the optical light-curves are
either flat topped or show a double peak. This means that from an empirical
point of view it is quite difficult to identify the phase of maximum light.
Moreover, the center of the HP is metallicity dependent (see Sect.~2.1).
To overcome this problem, we decided to use the phase of the mean magnitude
along the rising branch. This phase zero--point can be easily estimated
even if the light-curve is not uniformly sampled;
c) First overtones -- We derived for the first time the template for
first overtone Cepheids in the $J$ band;
d) Analytical fit -- Together with the classical analytical fits based
on Fourier series we also provide a new analytical fit based on periodic
Gaussian functions. The key advantage in using the latter functions is
that the precision is quite similar to the canonical fit, but the number of
parameters decreases from fifteen to nine.
The structure of the paper is the following:
In Sect.~2 we discuss in detail the different samples of calibrating
light curves we adopted to derive the template for fundamental (FU)
and first overtone (FO) Cepheids. In particular, in Sect.~2.1 we describe
the new technique adopted for phasing and merge the light-curves.
The preliminary analysis of the calibrating NIR light-curves and
the development of the template is described in Sect.~3, while the
analytical formula are given in Sect.~4. In Sect.~5, we discuss in
detail the NIR--to--optical amplitude ratios that we adopted to apply
the new templates. Sect.~6 describes the application of the templates and
with the error budget associated with the new templates. Finally, in Sect.~7
we summarize the results of this investigation and briefly outline possible
future developments.
\section{Optical and NIR data sets for calibrating Cepheids}
Our analysis is based on the largest available sample of fundamental--mode Cepheids
with well-covered light-curves in the NIR and in optical ($V$,$I$) bands.
This sample covers a very broad period range (1--100 days).
We collected $J$, $H$, and $K_{\rm{S}}$band observations from four different data sets:
\citet[][51]{laney92} and \citet[][131]{monson11} for
Galactic Cepheids, \citet[][92]{persson04} for LMC Cepheids,
and the IRSF survey catalog for $\sim$500 Small Magellanic Cloud (SMC) Cepheids.
\\
The optical ($V$,$I$) light-curves for the galactic Cepheids were collected from the literature
\citep[][and references therein]{laney92, berdnikov04}\footnote{see also \url{www.astronet.ru/db/varstars} and \url{www.astro.utoronto.ca/DDO/research/cepheids}}, while for Magellanic Cloud Cepheids we adopted the data from the OGLE~III Catalog of Variable Stars \citep{sos2008,sos2010}\footnote{\url{www.ogledb.astrouw.edu.pl}}.
When compared with the other microlensing surveys mentioned in the previous section, the OGLE~III Catalog provides very accurate $V$-- and $I$--band light-curves, with the typical photometric error associated with individual measurements $\le$0.008 mag and $\le$ 0.006 mag for $I$ and $V$ bands, respectively. Moreover, the sky coverage of the OGLE~III survey fully matches the coverage by the IRSF survey.\\
\noindent{\it i) Calibrating Cepheids in the IRSF/OGLE Sample (SMC)} \\
\indent During the past few years, the IRSF Survey (Ita et al., 2014, in prep.) collected more than
$\sim$500 complete NIR light-curves (571 $J$, 434 $H$, 219 $K_{\rm{S}}$)
for SMC Cepheids. These Cepheids have optical ($V$,$I$) mean magnitudes,
periods, amplitudes, and positions from the OGLE~III Catalog of Variable Stars
\citep{sos2010}
Typically we have more than 1,000 measurements in the
optical and at least 100 in NIR bands for SMC Cepheids.
This means that phasing optical and NIR light-curves is relatively simple.
The photometric accuracy of the data in the IRSF catalog is $\pm$0.02 mag
for the brightest ($J \approx 13$) and $\pm$0.06 mag for the faintest
($J \approx 17$) Cepheids. To improve the quality of the calibrating
sample, we performed a selection based on the root mean square ($rms$)
between the individual data points and the analytical fit of the
individual light-curves. We adopted a seventh-order Fourier series
and the selection criterion $rms \le \frac{1}{20} A_J$,
where $A_J$ is the pulsation amplitude in the $J$ band
($A_J$=$J_{max}-J_{min}$). The $rms/A_J$ ratio is an indication of how strongly the photometric errors of the individual observations affect the shape of the light-curve.
The threshold we chose allows us to select the most accurate light-curve while keeping a statistically
significant sample for each bin.
However, small changes of the adopted values do not significantly affect our results.
The selection criterion was relaxed to
$rms \le \frac{1}{15} A_{H,K}$ for the $H$-- and $K_{\rm{S}}$--band light-curves,
because the amplitude decreases with increasing wavelength. For Cepheids with shortest period Cepheids (1--3 days) we selected the light-curves with
$rms \le \frac{1}{10} A_{J,H,K}$. The data for these fainter Cepheids are
characterized by larger photometric errors.
The \textit{J,H,K$_{\rm S}$} measurements were transformed into the 2MASS NIR
photometric system following \citet{kato07}.
However, the corrections adopted for the transformations between different
NIR photometric system transformations are smaller than a few hundredths of
magnitude and affect neither the shape nor the amplitude of the light
curves. \\
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=0.90\columnwidth]{f1.pdf}
\caption{Period distribution for the calibrating Cepheids in our sample for the
three different bands $J$ (top), $H$ (middle), and $K_{\rm{S}}$ (bottom).
The color coding indicates different data sets (red: MP sample;
blue: LS sample; green: SMC sample; orange: P04 sample). The total number of
calibrating Cepheids per data set are also labeled. See text for more details.}
\label{f1}
\end{center}
\end{figure}
\noindent{\it ii) Calibrating Cepheids in the Persson et al. 2004 Sample (P04)} \\
\indent This sample is based on the $J$,$H$, and $K$ light-curves
for 92 Cepheids in the LMC published by \citet[][P04]{persson04}
and the $V$ and $I$ photometric data available in the OGLE Catalog for 60 of them.
The photometric precision of the data in the P04 catalog is $\pm$0.02 mag
for the brightest ($J \approx 12$) and $\pm$0.06 mag for the faintest
($J \approx 14$) Cepheids.
We included Cepheids with complete coverage
of the light-curve in the three bands (more than 20 phase points) and with low $rms$
(i.e. $\le$ 0.4 mag in the J band), for a total of $\sim$30 selected Cepheids in the
P04 sample. These Cepheids have periods between 6 and 50 days,
thus increasing the number of calibrating Cepheids ($\gtrsim$50\%) in the long-period regime (see Fig.~\ref{f1}). To transform the NIR measurements from the
original LCO photometric system into the 2MASS photometric system,
we adopted the relations given by \citet{carpenter01}.\\
\noindent{\it iii) Calibrating Cepheids in the Laney \& Stobie Sample (LS)} \\
\indent This sample includes 51 Galactic Cepheids with optical and NIR
light curves with periods ranging from 3 to 69 days
\citep{laney92,laney94}. This is the most accurate photometric
sample for Classical Cepheids available in literature, with intrinsic
errors ranging from about $\pm$0.004 mag for the brightest
($J \approx 3$) to $\pm$0.011 mag for the faintest ($J \approx 8$).
The optical light curves are also highly accurate,
with typical values of the $rms \le \frac{1}{100} A_{V}$.
However, we still performed a selection based on the number of available
phase points (we need at least 15 measurements for the Fourier fit)
in the optical and the NIR light-curves, for a total of $\sim$30
selected Cepheids in the LS sample.
The \textit{J,H,K$_{\rm S}$} measurements in \citet{laney92}
are in the SAAO photometric system.
We have converted them into the 2MASS photometric system
by applying the transformation equations given by \citet{carpenter01}.
\\
\noindent{\it iv) Calibrating Cepheids in the Monson \& Pierce Sample (MP)} \\
\indent This sample is based on NIR photometric measurements for
131 Northern Galactic Cepheids \citep{monson11}.
These Cepheid light-curves are sampled with an average of 22 measurements
per star with an associated photometric error of $\pm$0.015 mag.
However, we selected only the light curves with more than 17 measurements in each
NIR band, for a total of 64, 72, and 93 light-curves in the $J$,$H$, and $K_{\rm{S}}$ bands, respectively.
The original \textit{J,H,K$_{\rm S}$} data were taken in the BIRCAM system
and transformed into the 2MASS photometric system
by applying the equations given by \citet{monson11}.
For all the Cepheids in this sample, $V$ and $I$ light curves were collected
from the literature \citep[][and references therein]{berdnikov04}.
We did not perform any selection on the optical light-curves,
because no high accuracy in the $V$-band data is required by our method.
However, the $rms$ is always better than $\frac{1}{15} A_{V}$ for all the Cepheids in
this sample.
\\
In total, we collected a sample of light-curves that includes more
than 200 calibrating Cepheids and is three times larger
than the sample adopted by S05 (60 Cepheids) to derive the NIR light-curve
templates for classical Cepheids.
To further improve the sampling of the light curve over the entire period
range and to reduce the $rms$ of the light-curve templates, the sample of
Galactic and Magellanic calibrating Cepheids was split into ten period
bins.
Note that the approach we adopted is completely reddening independent.
In particular, the period is the safest diagnostic to bin the calibrating sample, because it
can be easily measured with high accuracy, it does not depend on the wavelength, and it is not affected by reddening.
This means that the binning in period will not introduce any systematic effect
when combining optical and NIR photometric data from different instruments.
Moreover, theoretical predictions \citep{marconi05} clearly show that the light-curve shape changes
with the mass at fixed chemical composition and luminosity and that the period is the best observable to account for this trend.
The adopted period ranges and the number of calibrating Cepheids
per bin are listed in Table~\ref{tab_bins}.
\begin{table}
\caption{Adopted period bins.\label{tab_bins}}
\centering
\begin{tabular}{clccc}
\hline\hline
Bin& Period range [days]& N$_J$ & N$_H$& N$_{Ks}$ \\
\hline
1 & 1--3 &12&3&3\\
2 & 3--5 &40&35&44\\
3 & 5--7 &26&29&29\\
4 & 7--9.5 &18&23&29\\
5 & 9.5--10.5 &11&13&13\\
6 & 10.5--13.5 &19&21&25\\
7 & 13.5--15.5 &24&22&23\\
8 & 15.5--20 &17&19&18\\
9 & 20--30 &14&17&19\\
10 & 30--100 &16&19&17\\
\hline
& 1--100 &197&201&220\\
\hline
\end{tabular}
\end{table}
There are typically twenty Cepheids per period bin
with two exceptions: bin~1 (P$\le$3 days), for which
we have fewer than a dozen objects, and bin~5 (9.5$\ge$ P $<$10),
for which the number of Cepheids ranges from 11 ($J$--band) to
13 ($K_{\rm{S}}$ band).
Fig.~\ref{f1} shows the histograms of the calibrating Cepheids
in $J$ (top), $H$ (middle) and in the $K_{\rm{S}}$ (bottom) band.
Cepheids belonging to different data sets are plotted with
different colors.
A similar selection was also performed for FO Cepheids.
The IRSF monitoring survey collected $\sim$231 complete NIR light-curves for
FO Cepheids (231 $J$, 85 $H$, 10 $K_{\rm{S}}$) with periods
ranging from 0.8 to 4 days. We selected from those the calibrating light curves
by adopting the following criterion: $rms_J \le \frac{1}{10} A_J$.
Again, the threshold was chosen to guarantee the good photometric quality
of the calibrating light curves.
However, because of the limited photometric accuracy of individual measurements
compared with FU light-curves, the final sample of calibrating
FO Cepheids only includes ten $J$-band light curves, with periods ranging from 1.4 to 3.5 days.
We did not apply any binning in period for FO Cepheids, because the
shape of the light-curve in this period range is almost exactly sinusoidal.
\subsection{Phasing the light-curves}
Precise period determinations are required to derive correct phase shifts
between optical and NIR light curves. The constraint is less severe if optical
and NIR time-series data are collected in the same time interval.
The $V$ and $I$ photometric data for Galactic Cepheids cover a time interval that
ranges from several years to more than 20 years. Thus, we adopted the new period
estimate published by \citet[][G13]{groe13} for all the Cepheids
in the LS sample. The G13 sample includes $\sim$130 Galactic Cepheids, and
50\% of them are in common with the MP sample.
The light curves from MP were phased by adopting the
period given in the General Catalog of Variable Stars (GCVS). To check the consistency
of the period listed in GCVS, we compared them with periods estimated by using either
the Lomb-Scargle algorithm \citep{press89} or the PDM2 \citep{stell11}. The difference
between the two sets of periods are about of $10^{-3}$ days, thus we
adopted the GCVS for all the MP Cepheids not included in the G13 catalog.
The phase of the light-curve is usually defined by
\begin{equation}
\phi^{V}_{obs} = \bmod \left( \frac{JD^{V}_{obs}- JD^V_{max}}{P} \right),
\end{equation}
where $JD^{V}_{obs}$ is the epoch of the observation and
$JD^V_{max}$ is the epoch of the maximum in the $V$ band.
The epoch of maximum in the $V$ and $I$ bands for the
LMC and SMC Cepheids is available from the OGLE~III catalog,
while for the Galactic Cepheids in LS and the 50\% in MP
we used the epoch of the maximum estimated by G13.
To estimate the maximum brightness for the Cepheids
for which the epoch of maximum was not available,
we fitted the V--band light-curves with a seventh-order Fourier series.
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=0.90\columnwidth] {f2.pdf}
\caption{$V$--band (left panels) and $J$--band (right panels)
normalized light-curves for Galactic bump Cepheids in the LS sample. The
period increases from bottom to top. For all these light-curves
the phase $\phi$=0 was fixed according to the maximum brightness
in the $V$ band and was marked with the arrow and the red circle.
However, the $J$--band maximum brightness, marked by the arrow,
moves across the light-curves, and occurs at later phases than
the optical maximum. The drift in phase arises because the secondary bump can be brighter than the true
maximum, that corresponds to the phase of minimum radius along
the pulsation cycle. The overplotted orange dots show the
position of the mean magnitude along the rising branch, which
we adopt as the new phase zero--point ($\phi$=0).}
\label{f2}
\end{center}
\end{figure}
The identification of the epoch of maximum in our optical light-curves
is straightforward, because of the very accurate time sampling of $V$- and
$I$-band light-curves of calibrating Cepheids. However, light-curves of
extragalactic Cepheids are covered with a limited number of phase
points, typically fewer than two dozen \citep{sandage06,bono10,madore10}.
The problem becomes even more severe for bump Cepheids, because
the bump moves from the decreasing to the rising
branch in a narrow period range.
As mentioned above, the light-curve at the center of HP
becomes either flat topped or double peaked with the real maximum and
the bump located at close phases.
Fig.~\ref{f2} shows the normalized optical ($V$; left) and NIR
($J$; right) light-curves for three Galactic Cepheids located across the
center of the HP and with periods ranging from 7.02 (U Aql, bottom)
to 9.84 days($\beta$ Dor, top) . If we apply the strict definition of
epoch of maximum the phase shift between the optical and the NIR light-curve
ranges from $\sim$0.1 ($\beta$ Dor) to $\sim$0.8 (U Aql). The red circles
and the red arrows show that the identification of the luminosity maximum
is hampered by photometric errors and by the fact that the bump can be
brighter than the true maximum that corresponds to the phases of maximum
contraction (minimum radius).
The scenario is further complicated because theory
\citep{bono00,marconi05} and observations
\citep{moskalik92,welch97,beaulieu98,moskalik00} indicate that the
center of the HP is anticorrelated with the metal content. It moves
from 9.5 days for Galactic Cepheids to 10.5 and to 11.0 days for LMC
and SMC Cepheids.
For a more quantitative analysis of the physical
mechanism(s) driving the HP refer to
\citet{bono02,marconi05} and refer to \citet{sos2008,sos2010} for a thorough
analysis of the observed light-curves.
To overcome this problem, we decided to use a different zero--point
to phase optical and NIR light-curves. Our phase zero--point
is defined as the phase of the mean magnitude along the rising
branch of the $V$--band light-curve
\begin{equation}
\phi_{obs}^V = \bmod \left( \frac{JD^V_{obs}- JD^V_{mean}}{P}\right),
\end{equation}
We selected this phase point, because the mean magnitudes are more precise
than the maximum brightness in Cepheids with modest phase coverage.
The new phase zero--point allows us to highly improve the
precision of the light-curve template in the period bins located across
the bump (bin~4 to 6). A more detailed discussion of the impact
of the new phase zero--point is given in Sect. 3.1.
The top panel of Fig.~\ref{f3} shows the comparison between the phase lags of $V$ and $J$ light
curves for a sample of SMC Cepheids based on the epoch of the maximum
(Eq.~1, black open circles) and on the epoch of the mean (Eq.~2, orange dots).
The same comparison for the $H$ and $K_{\rm{S}}$--bands are shown
in the middle and bottom panels of the same figure.
Data plotted in this figure clearly show the advantages in using the
epoch of the mean magnitude as the phase zero--point.
\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.90\columnwidth] {f3.pdf}
\caption{Top: Phase lag between the $V$-- and the $J$--band light-curve of
SMC Cepheids. The black open circles are estimated by adopting the epoch of maximum brightness as phase zero--point,
while the orange dots by adopting the new phasing, i.e. the epoch
of the mean--magnitude along the rising branch. The red lines show the linear fit
of the orange data set. The $rms$ (dashed lines) are also overplotted.
The values of the medians and of the $rms$ are labeled in the top of the panel.
Middle: Same as the top, but for the $H$ band.
Bottom: Same as the top, but for the $K_{\rm{S}}$ band.}
\label{f3}
\end{center}
\end{figure}
i) The phase lag anchored to the epoch of the mean can be approximated
by linear relations on a broad period range.
The intercept values of the phase lag are almost zero for all the bands and it slightly
increases from $\sim$0 for the $J$and $H$ bands to 0.011 for the $K_{\rm{S}}$ band.
The slope also systematically increases from 0.05 for the $J$ band,
to 0.08 for the $H$ and 0.09 for the $K_{\rm{S}}$ bands.
Moreover, the standard deviations based on the epoch of the mean magnitude are
at least a factor of two smaller than the standard deviations of the phase lags
based on the epoch of maximum light (0.02 vs 0.11 in the $J$ band).
Thus, using the epoch of the maximum introduces a spurious shift
in the epoch of the maximum of the NIR light-curves of bump Cepheids, and in
turn a systematic error in the estimate of their mean NIR magnitudes.
ii) The zero--point and the slopes of the linear relations to predict the
phase lag between optical and NIR light-curves are
similar for Magellanic and Galactic Cepheids.
iii) The slope of the light-curve's rising branch is steeper than that of the decreasing branch. This means that the error on the estimate of the mean magnitudes propagates into a smaller error in the phase determination. For this reason, the epoch of the mean along the rising branch provides a more accurate phase zero--point than the phase along the decreasing branch. However, the shape of the
light curves changes once again for periods longer than the HP.
The rising branch of Cepheids with periods longer than 15.5 days is shallower
than the decreasing branch. This means that the latter provides a more solid
phase zero--point. However, this problem only affects a minor fraction of our
sample ($\approx$10\%), therefore we adopted the phase of the mean magnitude
along the rising branch.
The phase lags between $V$- and $J$-band FO Cepheid light-curves
are similar to those of the FU Cepheid, with a median value of 0.05.
\begin{figure*}[!t]
\begin{center}
\includegraphics[width=0.8\textwidth, height=0.4\textheight] {f4.pdf}
\caption{Merged light-curves ($T^{bin}$) for the $J$ (left), $H$ (middle) and $K_{\rm{S}}$ bands
(right) for the ten period bins of FU Cepheids (see Eq.~5 and the following text for more details).
The range of periods in days is labeled in the top right corner of the left panel for each bin.
The G3 (green line) and the F7 (red line) templates are also shown.}
\label{f4}
\end{center}
\end{figure*}
To estimate the phase of the mean magnitude for the entire sample of calibrating
Cepheids, we fit the V--band light-curves transformed into intensity with a
seventh-order Fourier series. The mean in intensity was estimated as the
constant term of the analytical fit and eventually transformed into magnitude.
The comparison with the $V$--band mean magnitudes provided by \citet{sos2010}
by using the same definition indicates that the difference is at most of the
order of a few hundredths of magnitude.
The luminosity minimum and the luminosity maximum were estimated as the mean
of the three closest observed point located across the luminosity maximum and
the luminosity minimum of the analytical fit. We adopted this approach because
the analytical fit in the period ranges in which the light-curves show secondary
features (3 $\le$ P $\le$ 5 days; 7 $\le$ P $\le$ 15 days) slightly
underestimate the luminosity amplitude. Moreover, the error associated with the
amplitude estimated by adopting this approach does not depend on the analytical fit,
but is given by the propagation of the photometric error of the observations.
After estimating the epoch of the mean V-band magnitude ($\phi_{mean}^V$) for
FU and FO calibrating Cepheids, the epoch of the mean
magnitude in the NIR bands is given by
\begin{equation}
JD_{mean}^{J,H,Ks}=JD_{mean}^{V}+ P \times \phi_{Lag}^{J,H,Ks},
\end{equation}
where $\phi_{Lag}^{J,H,Ks}$ is a constant for the different bands. Its
value for FU Cepheids with periods shorter than 20 days is 0.03 ($J$),
0.07 ($H$), and 0.13($K_{\rm{S}}$), while for longer periods it is:
0.06 ($J$), 0.14 ($H$), and 0.16($K_{\rm{S}}$). The phase lag in the $J$ band
for FO Cepheids is 0.05.
This equation can also be written in terms of $JD_{max}^{V}$ and $\phi_{mean}^{V}$:
$$JD_{mean}^{J,H,Ks}=JD_{max}^{V}+P \times (\phi_{mean}^{V}+\phi_{Lag}^{J,H,Ks})$$.
Thus, the pulsation phase can also be defined as
\begin{equation}
\phi_{obs}^{V,J,H,Ks} = \bmod \left( \frac{JD_{obs}^{V,J,H,Ks}-JD_{mean}^{V,J,H,Ks}}{P}\right),
\end{equation}
where the symbols have their usual meanings.
The name, the period, the $V$, $J$, $H$, $K_S$ mean magnitudes, the amplitude pulsations, and the
epoch of the mean magnitude along the rising branch for the entire sample of calibrating FU Cepheids are listed in Table~\ref{tab_cat_fu}.
The same parameters for FO calibrating Cepheids are listed in
Table~\ref{tab_cat_fo}.
\section{Merged NIR light-curves of calibrating Cepheids}
To compute the light-curve template for FU Cepheids in the different period bins,
we performed a fit with a seventh-order Fourier series of the $V$,$J$,$H$,$K_{\rm{S}}$
light curves of the calibrating Cepheids.
The analytical fit provides several pulsation parameters:
mean magnitude\footnote{Throughout the paper, mean magnitude means a mean in intensity
transformed into magnitude.}, pulsation amplitude, and the phase of the mean along the
rising branch.
The fit with a seventh-order Fourier series is the most often used for
Classical Cepheid light-curves \citep{laney92,sos2008,sos2010}. Analytical fits
with lower order Fourier series cause an underestimate of FU Cepheid luminosity
amplitudes. On the other hand, higher order analytical fits cause minimal
changes (a few thousandths of magnitude) in the luminosity amplitudes and
in the mean magnitudes.
Following the same approach as adopted by S05, we normalized the
light curves in such a way that the mean magnitude
is equal to zero and the total luminosity amplitude is equal to one.
In particular, for the $J$ band, the normalized light-curve is defined as
\begin{equation}
T_{J,l} = (J_{i,l} - <J>_l)/A_{J,l},
\end{equation}
where $J_i$ are the individual measurements in the $J$ band, $<J>$ is the mean
magnitude and $A_J$ is the luminosity amplitude of the variable in the $J$ band
for the $l$-th light-curve.
This approach allowed us to compute the merged light-curve for each period bin
($T_J^{bin}$). The merged light-curves for
the ten period bins in the $J$ (left), $H$ (middle), and $K_{\rm{S}}$ (right) are shown
in Fig.~\ref{f4}. Data plotted in this figure clearly show that current
NIR data set properly cover the entire pulsation cycle in the three different
bands in the short and the long period range. Moreover, the intrinsic
scatter at fixed pulsation phase is quite small and ranges from $\sim$0.03 to
$\sim$0.05 over the entire data set. This evidence underlines the
photometric precision and homogeneity of the adopted data sets together with
the selection of calibrating Cepheids.
We adopted the same approach for the FO calibrating Cepheids.
To estimate the main physical parameters, we fit the FO light-curves
with a third-order Fourier series, because they have a
sinusoidal shape in the adopted period range (see Fig.~\ref{f5}).
\begin{figure}[!hb]
\begin{center}
\includegraphics[width=0.90\columnwidth, height=0.8\columnwidth] {f5.pdf}
\caption{Merged light-curve for FO Cepheids. The F3 (red line) and G2 (green line)
templates are also shown.}
\label{f5}
\end{center}
\end{figure}
\section{Analytical fits of the merged NIR light-curves of calibrating Cepheids}
The precision of the mean NIR magnitudes based on light-curve templates
depends on the accuracy of the analytical fits in reproducing the shape
of the individual light-curves in the different period bins.
The fit of the merged light-curves was performed by using seventh-order Fourier series
\begin{equation}
{\rm F7(\phi)}= A_0 + \sum_{i=1}^7 A_i \cos (2 \pi i \phi + \Phi_i).
\end{equation}
Fitting the light curves with Fourier series is a very popular approach for
both regular and irregular variables. They have many advantages, but also
several limits. In particular, the F7 templates (red lines) for the bin~1
in the $J$,$H$, and $K_{\rm{S}}$ bands --see top panels of Fig.~4-- show
several spurious ripples along the decreasing branch of the light-curve.
Moreover, the F7 templates for the period bins located across the bump
display a wiggle close to the phases of maximum brightness (bin~5) and
a stiff trend close to the phases of minimum brightness (bin~7).
To provide an independent approach for the analytical modeling of the
light curves, we adopted a fit with multiple periodic Gaussian functions
\begin{equation}
{\rm G3(\phi)}= \sum_{i=1}^3 G_i \exp \left[ \frac{- \sin \pi (\phi- \Gamma_i)}{\tau_i}\right]^2.
\end{equation}
We called these analytical functions PEGASUS, because they provide
PEriodic GAuSsian Uniform and Smooth fits. The key advantage of these functions
is that they follow the features of the light-curves, but the wings remain
stiff. The fits of the calibrating light-curves with the linear combination
of three PEGASUS functions are plotted as green lines in Fig.~\ref{f4} and are very accurate over the entire period range.
The fits based on PEGASUS show two indisputable advantages over the Fourier series: a) the PEGASUS fit (G3) only requires nine parameters,
while the Fourier fit (F7) needs 15 parameters, and b) the G3 fit does not show the ripples in either the short period bins (bins~1 and 2;
see Fig.~\ref{f4}) or across the Hertzsprung progression (bins~4, 6, and 7;
see Fig.~\ref{f6})
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=0.90\columnwidth] {f6.pdf}
\caption{From left to right: residuals of the $J$--band merged light-curves
(silver dots) obtained with the new templates: F7 (red line; top) and
G3 (green line; bottom) for the period bin~4 (7--9.5 days), bin~6 (10.5--13.5 days)
and bin~7 (13.5--15.5 days).
The residuals attain vanishing mean values for the F7 and the G3 templates.}
\label{f6}
\end{center}
\end{figure}
However, the standard deviations of the individual fits and the errors on the
coefficients in G3 and in F7 fits attain similar values. The standard deviations
are on average on the order of a few hundredths of magnitude, wile the errors
of the coefficients are smaller than one thousandth of magnitude. This is the main reason
why we decided to provide the analytical fits for both of them. The coefficients
$A_i$ and $\Phi_i$ for the F7 fits and the $G_i$, $\Gamma_i$ and $\tau_i$ coefficients for the G3 templates are given in Table~\ref{tab_c}.
For the FO light-curve template, we adopted a third-order Fourier (F3) series
and a second-order PEGASUS function (G2) to fit the merged light-curves.
Fig.~\ref{f5} shows the $J$--band template for FO Cepheids together with
the F3 and the G2 best fits.
The $rms$ for the merged light-curve is $\sim$0.07 (F3) and $\sim$0.08 (G2) mag.
The coefficients $A_i$ and $\Phi_i$ for the F3 templates and the exponents
$G_i$, $\Gamma_i$, $\tau_i$ for the G2 templates are listed in Table~\ref{tab_c}
The \textit{IDL} procedure for estimating the mean NIR magnitudes by using the templates is available on the webpage: \url{http://www.laurainno.com/#!idl/c5wp}.
\subsection{Validation of the new phase zero--point: bump Cepheids}
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.80\columnwidth] {f7.pdf}
\caption{Comparison between the merged light-curve T$^{bin~4}_J$ with phasing anchored
on the phase of maximum light (Eq. 1; left) and with the new phasing anchored on
the phase of mean magnitude along the rising branch (Eq. 2; right) for bin~4
Cepheids.}
\label{f7}
\end{center}
\end{figure}
To improve the mean NIR magnitude of bump Cepheids, we adopted (see Sect. 2.1)
a new phase zero--point anchored on the phase of the mean magnitude along the
rising branch. Fig.~\ref{f7} shows the comparison between the merged $J$--band
light curve for the period bin~4 computed by using as phase zero--point both
the phase of maximum light (Eq.~1, left panel) and the phase of mean magnitude
along the rising branch (Eq. 5, right panel).
A glance at the data plotted in this figure show that the $rms$ significantly
decreases in the merged light-curve that was computed using the new phase zero--point,
and the $rms$ decreases by roughly a factor of two (0.06 vs 0.13).
To further constrain the precision of current templates, we also performed
a comparison with the light-curve template provided by
S05\footnote{We applied the S05 templates by using their phase zero--point
--the epoch of the maximum-- and their NIR--to--optical amplitude ratios.}.
The left panel of Fig.~\ref{f8} shows that the $J$--band S05 template
predicts a shape of the normalized light-curve (left panel, blue line)
for Cepheids with period approaching the center of HP (U Aql, P=7.024)
that differs from the observed shape. The difference is quite clear not only
close to the phase of the maximum ($\phi \sim$0.05), but also close to
the phase of the bump ($\phi \sim$0.15), and in particular, along the
decreasing branch. The middle and right panels show the
comparison between our templates (F7, middle; G3, right) and the
observed data.
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=0.80\columnwidth] {f8.pdf}
\caption{From left to right: comparison between the normalized $J$--band light-curve
(black dots) of U Aql and the S05 (blue line; left),
F7 (red line; center) and the G3 (green line; right) templates. The typical error
associated with observations ($\pm$0.01 mag) and rescaled in normalized units is about $\sim$0.001 and is shown in the top left corner of the plot.
The residuals between the data and the templates are plotted in the bottom panels.
The dashed lines indicates the $rms$ of the residuals; it decreases from 0.10 (S05)
to 0.04 (F7, G3).}
\label{f8}
\end{center}
\end{figure}
The residuals for the S05 template plotted in the bottom left panel of the same figure
display a phase delay between the data and the light-curve template
along the rising and the decreasing branch. On the other hand,
the residuals plotted in the middle and right panels
show that the F7 and G3 templates provide a good approximation
of the observed light-curve.
The residuals have an $rms$ (dashed lines) of 0.04 mag, that is a factor of two smaller than
the $rms$ of the S05 template (0.10).
\section{NIR--to-optical amplitude ratios}
\begin{figure*}[!t]
\begin{center}
\includegraphics[width=0.80\textwidth, height=0.4\textheight] {f9.pdf}
\caption{Top left: amplitude ratios -- $A_J/A_V$ -- as a function of the period
for LMC and MW calibrating Cepheids. The dashed vertical lines display the individual
bins in period. The color coding is the same as in Fig.~1: orange dots for the P04
sample, red dots for the MP sample, and blue dots for the LS sample. The black solid
lines are the mean amplitude ratios estimated on the selected period ranges:
$P \le$ 20 days and $P >$20 days. The error bars in the top left corner show
the typical photometric error.
Top right: Same as the left, but for SMC calibrating Cepheids (green dots).
The comparison between the value of the mean ratio in the left and in right panels
shows that amplitude ratios of SMC Cepheids are systematically lower than those of LMC+MW Cepheids.
Middle: Same as the top, but for the $A_H/A_V$ amplitude ratios.
Bottom: Same as the top, but for the $A_{Ks}/A_V$ amplitude ratios.
Note that the period ranges for this band are $P \le$ 15.5 days and $P>$15.5 days.}
\label{f9}
\end{center}
\end{figure*}
The light-curve template allows us to estimate the NIR mean
magnitudes from single-epoch observations if the amplitude
in that specific band is already known. Indeed, Eq.~5 gives
\begin{equation}
<J>_l= J_{i,l}-A_{J,l} \times T_J
\end{equation}
and similar equations for the other NIR bands (see also Eq.~4 in S05).
To estimate the NIR mean magnitudes, the luminosity amplitudes can be
estimated by using the luminosity amplitudes in the
optical bands. We derived new amplitude ratios between optical and NIR
bands by using our calibrating Cepheids. The results are shown
in Fig.~\ref{f9} from top to bottom: $A_J$/$A_V$, $A_H$/$A_V$, and
$A_{Ks}$/$A_V$. We estimated the mean value (black solid line)
over two different period ranges: P $\le$ 20 days and P$>$20 days for
the MW+LMC (left panels) and the SMC calibrating Cepheids
(right panels).
The data plotted in this figure disclose several interesting features
that need to be addressed in more detail, because these ratios
are prone to systematic uncertainties. Classical Cepheids are young objects
and a significant fraction of them are still members of binary systems
\citep{szabados12b}. Their companions are mainly young low--mass stars,
which meant that they mainly affect the $V$--band amplitude. Moreover, recent accurate
optical and NIR interferometric \citep{kervella06}, mid-infrared
\citep{marengo10,barmby11}, and radio \citep{matthews12} measurements indicate
the presence of a circumstellar envelope around several Galactic Cepheids.
This evidence implies that the NIR amplitudes might also be affected
by systematic uncertainties and it accounts for a significant
fraction of the dispersion around the mean values because the photometric
errors are significantly smaller (see the typical error bars in the
top left corners).
Moreover, current theoretical \citep{bono00} and preliminary empirical
evidence \citep{paczy00,szabados12a} indicates that the luminosity amplitudes
depend on the metal content.
The $V$--band amplitudes of SMC Cepheids in the short--period range
(P$\le$ 11 days) are, at fixed period, larger than those of Galactic and LMC
Cepheids. The difference is caused by the HP dependence on the
metallicity (see Sect.~2.1). The trend is opposite in the long--period range.
The difference in the optical amplitude is also clear in the Fourier
amplitude of Magellanic and Galactic Cepheids
\citep[see Fig.~5 and Fig.~2 in][Fig.~2]{sos2008,sos2010,matsunaga13}.
This evidence indicates that solid empirical constraints on the dependence
of the luminosity amplitudes on metallicity requires accurate information on
individual metal abundances. However, \citet{genovali13} did not find, within the errors,
any significant dependence on iron abundance, by adopting
a homogeneous sample of 350 Galactic and 77 Magellanic Cepheids with
precise and homogeneous iron abundances. However, this finding is far
from being definitive, because the number of SMC Cepheids for which accurate iron abundances are
available is quite limited (19).
The data plotted in the top panel of Fig.~\ref{f9} indicate that the NIR--to--optical
amplitude ratios of SMC Cepheids (right panel) are smaller over the entire
period range than the amplitude ratios of MW plus LMC Cepheids
(left panel). This is the reason why we decided to adopt independent values
for the NIR--to--optical amplitude ratios of SMC and MW plus LMC Cepheids.
The high dispersion in the amplitude ratios
is mainly due to the $V$--band amplitude distribution in the Bailey
diagram (amplitude vs period), while the NIR amplitudes show a similar
distribution, but tighter.
Current theoretical and empirical evidence indicates that the amplitude
distribution in the Bailey diagram for Galactic
Cepheids has the typical V shape \citep{vangenderen74,bono00,szabados12a,genovali14}, with
the largest luminosity amplitudes
attained in the short-- ($\log P\le$ 1.0 days) and in the
long--period ($\log P \ge$ 1.2 days) ranges, while the minimum, at fixed chemical composition, is reached at the center of the HP.
This peculiar behavior does not allow a straightforward prediction of the NIR amplitude on the basis of the period.
On the other hand, the NIR--to--optical amplitude ratios are almost constant for a broad range of periods, as shown in Fig.~\ref{f9}. In particular, we find that the mean $A(J)/A(V)$, and $A(H)/A(V)$ amplitude ratios are smaller for periods shorter than P$\le$20 days and larger for periods longer than P$>$20 days. For the SMC mean $A(K)/A(V)$ amplitude ratios we chose a different cut in period: P=15.5 days.
The estimated NIR--to--V amplitude ratios for MW+LMC and SMC calibrating
Cepheids are listed in Table~\ref{tab_amp}.
We also note that the typical dispersion for the NIR--to--optical amplitude ratios
of the MP sample is almost twice as high as that of the LS sample
(MP: $\sigma$=0.05; LS: $\sigma$= 0.03; $J$-band).
The main reason for this is the photometric quality of $V$-band light-curves in the MP sample. As already mentioned in Sect.~2, the optical photometry for these Cepheids
was collected from the literature, with the source data spanning a long time
and coming from different instruments.
Indeed, the typical $rms$ for the MP calibrating $V$-band light-curve is $\sim$0.05 mag,
ten times higher than the typical $rms$ for the LS $V$-band light-curves ($\sim$0.005 mag, see also Sect. 2).
We also performed a test by adopting different mean amplitude ratios for
each period bin and we did not find any significant improvement in the final results.
Similar considerations apply to the use of linear regression to fit the
amplitude ratios as a function of the period. A linear relation
on the entire period range provides a good approximation
for the short-period range, where the ratios are almost
constant, but it underestimates the values in the long-period range.
On the other hand, by adopting two different relations in the two period ranges,
the number of parameters will double without significantly improving the template accuracy compared with the two horizontal lines.
The pulsational amplitudes and Fourier parameters of FO Cepheids also show
a sudden jump for periods close to P=3 days \citep{kienzle99}. This behavior is
associated with the possible presence of a short-period bump along the light-curves
of FO Cepheids with periods between 2 and 3.8 days \citep{bono00}.
Thus, we adopted two different $A(J)/A(V)$ mean values
for the two different regimes of the amplitude before and after
the appearance of this short-period bump.
Fig.~\ref{f10} shows the phase lags (top panel) and the
amplitude ratios (bottom panel) computed for the FO calibrating Cepheids.
The mean values (solid lines) are $A_J$/$A_V$= 0.40
(P$\le$2.8 days) and $A_J$/$A_V$= 0.30 (P$>$2.8 days).
\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.90\columnwidth, height=0.8\columnwidth] {f10.pdf}
\caption{Top: Phase lags in $J$ band for FO Cepheids based on the epoch of the
maximum (black circles) and on the epoch of the mean magnitude along the rising branch
(orange dots). The median (solid lines) and $rms$ (dashed lines) of the ten
calibrating Cepheids are overplotted. The black labels refer to the epoch of maximum,
orange labels to the epoch of the mean magnitude.
Bottom: the amplitude ratio $A(J)/A(V)$ for FO Cepheids. The mean values for the two
adopted bins in period (P$\le$2.8, and P$>$2.8 days) are also labeled
(black solid lines).}
\label{f10}
\end{center}
\end{figure}
\section{Validation of the light-curve templates}
To further evaluate the accuracy of current templates, we performed a
new test by using the complete light-curves of the calibrating Cepheids.
For each period bin, we have several calibrating light-curves (see Fig.~\ref{f1})
for which all the parameters --mean magnitudes, NIR luminosity amplitudes,
period, phase zero--points-- have already been estimated. Therefore, we
randomly selected a phase point from the calibrating light curve
to simulate a single-epoch observation and applied the new templates
to estimate the mean magnitude, which we then compared with the true one.
We define $\delta J$ as the difference in $J$ band between the true mean magnitude
--estimated as the mean along the light-curve-- and the mean magnitude
computed by using the new $J$--band templates.
A similar approach was also adopted for the $H$ and $K_{\rm{S}}$--bands.
Fig.~\ref{f11} shows the $\delta J$ for two period bins: bin~3 (top)
and bin~4 (bottom) by adopting the F7 (red dots, left panels), the G3
(green dots, middle panels) and the S05 (blue dots, right panels)
light-curve templates. The $\delta J$ based on
both F7 and G3 templates give a vanishing mean ($\le 10^{-3}$ mag) and
a small standard deviation $\sim 0.03$ mag. The S05 templates also give
a mean close to zero ($\sim 10^{-3}$ mag) and a slightly larger standard
deviation ($\sim 0.04$ mag). The data plotted in Fig.~\ref{f11} show that the residuals
of the S05 template are not symmetric, therefore we estimated the interquartile range
and found that the difference becomes about 40\% ($\sim$0.06 vs $\sim$0.04 mag).
We also divided the data into ten phase bins
and estimated the mean and standard deviation for each bin.
The values are overplotted in Fig.~\ref{f11} (red dots, F7;
green dots, G3; blue dots, S05). The horizontal error bars display the
range in phase covered by individual bins, while the vertical error bars
display their standard deviations.
\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.99\columnwidth]{f11.pdf}
\caption{Top: $\delta J$ for period bin~3 (5--7 days) by adopting the
F7 (red dots, left panel), the G3 (green dots, central panel), and the S05
templates (blue dots, right panel). The gray dots on the background are the
difference between the mean magnitude estimated by applying the templates
and the true mean magnitude estimate by the individual fits. By binning the
phase in ten different bins, we estimated the mean of the residuals
(dots) and the standard deviation (error bar). The solid black lines show
the mean values, which are $<$10$^{-3}$ mag for the three templates.
Bottom: Same as top, but for period bin~4 (7--9.5 days).}
\label{f11}
\end{center}
\end{figure}
The data plotted in this figure indicate
that the residuals of the F7 and G3 are independent of the phase, while the
residuals of the S05 template show a clear phase dependence for
$\phi\sim$0.5 and $\phi\sim$0.8. In particular, the mean $J$ magnitudes
based on the S05 template are 2$\sigma$ fainter close to
$\phi\sim$0.5 and brighter close to $\phi\sim$0.8. Most of this discrepancy
is due to bump Cepheids for which the phase zero--point anchored on the
epoch of maximum brightness introduces systematic phase shifts in using the template.
Similar trends were also found when estimating the $\delta H$ and
$\delta K_{\rm{S}}$ by applying the F7, G3, and S05 templates.
We also performed the same test for FO Cepheids, and the results are plotted
in Fig.~\ref{f12}. Once again, the residuals for the F7 and the G3 templates
attain vanishing values ($\le 10^{-3}$) and the standard deviations are
smaller than 0.04 mag.
Note that above standard deviations account for the entire error budget,
because they include the photometric error (measurements, absolute calibration)
and the standard deviations of the analytical fits.
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=0.90\columnwidth, height=0.8\columnwidth] {f12.pdf}
\caption{Same as Fig.~11, but for FO calibrating Cepheids.
The $\delta J$ are based on
the F7 (top) and the G2 (bottom) templates. The red (F3) and green (G2) dots indicate
the mean for each of the 20 bins in phase and the standard deviation (error bars).
The mean of the residuals is $\le 0.01$, with a mean $rms$ of 0.04 mag.}
\label{f12}
\end{center}
\end{figure}
\subsection{Test based on single-epoch measurements}
The validation of the light-curve templates performed in the last section
has a limited use, bceause it relies on Cepheids with a good coverage
of the pulsation cycle, and in turn on accurate luminosity amplitudes.
Therefore, we performed an independent validation by using the amplitude
ratios discussed in Sect.~5 and by randomly extracting phase points from
the $J$, $H$, and $K_{\rm{S}}$--band light-curves of the calibrating
SMC Cepheids. This is an acid test, because we are mimicking the typical
use of the light-curve template.
The difference in mean magnitude between the true mean magnitudes and
the mean magnitudes estimated using the new NIR templates are plotted in
Fig.~\ref{f13} as red triangles (F7, left panels), green triangles
(G3, middle panels), and blue triangles (S05, right panels). The red,
green and light blue shadowed areas indicate the standard deviation
$\pm \sigma$, for the $\delta J$ (top), the $\delta H$ (middle) and the $\delta K_{\rm{S}}$
(bottom) estimated with the three different templates.
The mean values for the three bands ($\delta J$, $\delta H$ and
$\delta K_{\rm{S}}$) are lower than a few thousandths in all the cases.
However, the $\sigma$ for the F7 and the G3 $J$ and $H$--band
templates are at least 40\% lower than for the S05 template
(0.03 vs 0.05 mag). The difference for the $K_{\rm{S}}$ band is lower
and of about $\sim$20\% (0.04 vs 0.05 mag).
Moreover, the residuals of the S05 template show a phase dependence
that is not present in the residuals of the F7 and the
G3 templates\footnote{Note that for this test we only adopted calibrating
Cepheids with $\log P \geqslant$0.5, because the S05 template does not include
shorter period Cepheids.}.
The evidence that the new NIR templates do not significantly reduce the
scatter in the $K_{\rm{S}}$ band is a consequence of the fact that the pulsation
amplitude in this band is smaller than in the $J$ and in the $H$ bands. Moreover,
the photometric errors on individual measurements become larger.
We performed the same test for the Galactic calibrating Cepheids, and the
results are given in Fig.~\ref{f14}.
The difference we found for Galactic calibrating Cepheids
from using the new NIR templates is between two ($K_{\rm{S}}$) to three ($J,H$)
times smaller than for the S05 templates. The mean in the three different
bands approaches zero ($\sim10^{-3}$ mag), but the residuals of the
S05 template show a clear phase dependence.
Moreover, data plotted in the right panels show a systematic
overestimate of the mean magnitude for phases close to the rising branch
($\phi\sim$1). The main reason for this discrepancy is once again the
adopted phase zero--point. The use of the maximum brightness to anchor the
phase causes loose constraints along the rising branch, i.e. close to phases
in which the luminosity rapidly increases. The F7 and the G3 templates
do not show evidence of similar systematic effects. However, the former
exhibits a mild phase dependence in the $K_{\rm{S}}$ bands --and probably in the
$H$ bands-- close to $\phi$=0.8.
The difference between the residuals of MW+LMC and SMC calibrating
Cepheids is a consequence of the fact the former sample is characterized
by a better photometric precision over the entire period range.
The mild phase dependence is mainly due to the smaller photometric errors,
and in turn, to the smaller standard deviations (see labeled values).
The key points to explain the above trends are
a) the definition of the phase zero--point: the use of the mean magnitude
along the rising branch (Sect.2.1) instead of the decreasing branch reduces the
precision of the template for periods longer than $13.5$ days;
b) the NIR--to--optical amplitude ratios adopted for the $H$ and $K_{\rm{S}}$:
the $V$--band amplitude of the Galactic calibrating Cepheids shows, at fixed period,
a high dispersion, that propagates into the NIR--to--optical amplitude ratios.
The same test was also applied to the FO calibrating Cepheids.
The residuals plotted in Fig.~\ref{f15} clearly show that the standard
deviation of the $J$--band template decreases by $\sim$50\% when
compared with single-epoch measurements extracted along the light-curves.
Note that the typical pulsation amplitude in the $J$ band
for FO pulsators is $\sim$0.15 mag. This means that the use of single-epoch
measurement as a mean magnitude introduces an error of about
$\sim$0.07 mag. Thus, the new FO NIR templates allow us to reduce the error
budget for FO Cepheids by almost a factor of two. Moreover, the new templates
do not show evidence of a phase dependence.
To fully exploit the impact of the new NIR templates on FU Cepheids,
we also performed a test with the mean Wesenheit magnitudes.
The NIR Wesenheit magnitudes are closely related to apparent magnitudes,
but they are minimally affected by uncertainties on reddening and are
defined as
$$W(JK_{\rm{S}})=K_{\rm{S}}-0.69 \times (J- K_{\rm{S}}),$$
$$W(HK_{\rm{S}})=K_{\rm{S}}-1.92 \times (H- K_{\rm{S}}),$$
$$W(JH)=H-1.63 \times (J- H),$$
where the coefficients of the color terms are based on the reddening law provided
by \citet{cardelli89}, and for the SMC selective absorption coefficient we adopted
$R_V$=3.23. This is an acid test concerning the NIR templates, since the color
coefficients of the Wesenheit relations attain values higher than one for bands
with limited difference in central wavelength. This means that uncertainties
affecting the mean colors are magnified in using Wesenheit relations.
To simulate the effect of non-simultaneous NIR observations, we randomly
extracted for the entire set of SMC calibrating light-curves three different
($J$,$H$,$K_{\rm{S}}$) measurements. The NIR templates were applied to each of
them and we obtained three independent estimates of the mean NIR magnitudes.
Then we computed the three mean Wesenheit magnitudes
--$W(JH)$,$W(HK_{\rm{S}})$, $W(JK_{\rm{S}})$-- by using these relations and
estimated the difference in magnitude with the true mean Wesenheit magnitudes. To properly
sample the luminosity variations along the entire pulsation cycle, the
procedure was repeated ten times per light-curve.
This test was performed with the new (F7, G3) and the S05 templates.
The residuals are plotted in Fig.~\ref{f16}, $W(JK_{\rm{S}})$ (top),
$W(HK_{\rm{S}})$ (middle) and $W(JH)$ (bottom).
A Gaussian fit to the histograms performed to evaluate the mean and the standard deviation is also overplotted. We found that the means
once again vanished.
The $\sigma$ of the mean Wesenheit magnitudes based on the F7 [a) panels] and
on the G3 [b) panels] templates are between 15--30\% lower than the $\sigma$
of the residuals based on the S05 [c) panels] template (see labeled values).
Finally, we also compared the difference between the mean Wesenheit magnitudes
based on the new NIR templates with single-epoch measurements randomly extracted
from the light-curve of the SMC calibrating Cepheids. The gray shaded areas
plotted in the d) panels of Fig.~\ref{f16} show that the standard deviations
of the new NIR templates are a factor of two smaller than those of the
single-epoch measurements.
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.99\columnwidth, height=0.8\columnwidth]{f13.pdf}
\caption{Random-phase extraction test for all the period bins in the different NIR bands
(from top to bottom: $J$, $H$ and $K_{\rm{S}}$) in the SMC sample. The red triangles
show the difference between the mean magnitude predicted by applying the F7 template
to the single-epoch NIR observation (left panel). In the middle panel the green triangles
were evaluated by applying the G3 template, while the blue triangles in the left panel
are evaluated by applying the S05 template. The shadowed areas shows the 2$\sigma$ of
the results (F7: light red; G3: light green; S05: light blue), while the black lines
indicate the zero. The residuals of F7 and G3 template show no dependence on the phase,
and the dispersion is from $\sim$20\% ($K_{\rm{S}}$) to 40\%($J$) lower than the
residuals of the S05 template.}
\label{f13}
\end{center}
\end{figure}
\subsection{Error budget of the analytical fits}
These results clearly show that the application of NIR
light curve templates increases the accuracy on the mean magnitude compared
with single-epoch measurements. However, the templates are affected by several
uncertainties that contribute to the total error budget.
The test discussed in Sect. 6.1 and shown in Fig.~\ref{f13} was also applied
to constrain the impact of the individual uncertainties on the total dispersion
of the $\delta J$, $\delta H$, and $\delta K_{\rm{S}}$ residuals.
{\sl i) Photometric error} -- The photometric error is the main source of error,
and it affects the precision of the template and its application. However, only
the former source should be taken into account when estimating the precision
of current templates. To artificially remove the photometric error on the
measured NIR magnitudes, we extracted the individual measurements from the
Fourier fits of the light-curves. The result of this numerical experiment
shows that 60\% of the total dispersion is due to the photometric error
on the observed magnitudes. This accounts for 0.02 mag in the total error budget.
{\sl ii) Use of the template} -- The use of a template plus a single-epoch
measurement to estimate the mean magnitude accounts for 12\% of the total
dispersion in Fig.~\ref{f13}.
{\sl iii) Merging of the light-curves in period bins} -- Our approach assumes
that all the light-curves inside the same period bin are identical within the errors.
This assumption is verified inside the confidence level given by
the $rms$ of the merged light-curves, typically $\sim$0.03 mag. However, small
differences in shape may occur between the true light-curve of the Cepheid and
the given template. This is a simple consequence of the merging process of
the Cepheid light-curves in a limited number of period bins. We tested the impact
of this approach by using synthetic light-curve based on analytical fits
(F7, G3). We found that 15\% of the total dispersion is due to the process
of merging the light-curves in a modest number of period bins.
{\sl iv) $V$-NIR amplitude ratio} -- The prediction of the pulsation amplitudes
in the $J$, $H$, and $ K_{\rm{S}}$ bands based on the optical amplitude introduces
an uncertainty on the mean magnitude provided by the templates. However, we can quantify this effect
by adopting the true amplitudes measured for the calibrating Cepheids. The error
associated with the use of the $V$-NIR amplitude ratios given in Sect.~5 accounts for
10\% of the total budget.
{\sl v) $V$-NIR phase lags} -- We estimated the epoch of the mean magnitude along the rising
branch by adopting $V$-NIR phase lags (Sect.~2.1). The comparison between the $\delta J$,
$\delta H$, and $\delta K_{\rm{S}}$ residuals estimated with the adopted and the measured
epoch of the mean magnitudes indicates that this assumption accounts for $\sim$3\% of the
error budget.
The error associated with the NIR mean magnitudes estimated by applying the new NIR templates is $\sim$0.015 mag for the $J$ band, 0.017 mag for the $H$ band and 0.019 mag for the $K_{\rm{S}}$ band.
These errors have to be added in quadrature to the photometric error on the single-epoch
measurements to which the template is applied. The use of two or more measurements for the
same Cepheid and the weighted average of the independent mean magnitudes implies a better
precision on the final mean magnitude.
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.99\columnwidth, height=0.8\columnwidth]{f14.pdf}
\caption{Same as Fig.~\ref{f13}, but for Galactic Cepheids (LS, MP). The red triangles
show the difference between the mean magnitude predicted by applying the F7 template
(left panel), the G3 template (central panel, green triangles), and the S05 template
(right panel, blue triangles). The shadowed areas shows the 2$\sigma$ of the results
(F7: light red; G3: light green; S05: light blue), while the black lines indicate the
zero for each data set.}
\label{f14}
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=0.90\columnwidth, height=0.8\columnwidth] {f15.pdf}
\caption{Random-phase extraction for FO calibrating Cepheids in the $J$--band.
The red triangles show the differences between the mean magnitude based on the
F3 template and on single--epoch NIR observations (top panel). The middle panel
shows the residuals (green triangles) based on the G2 template, while the
bottom panel shows the residuals (black triangles) of the single--epoch measurements.
The shadowed areas shows the 2$\sigma$ of the results (F7: light red; G2: light green;
single-epoch: light gray), while the black lines display the mean. }
\label{f15}
\end{center}
\end{figure}
\section{Summary and final remarks}
We developed new NIR $J$, $H$, and $K_{\rm{S}}$ light-curve templates for FU and FO Cepheids.
The new templates compared with those already available in the literature have several
advantages:
{\sl i)} {\bf Period binning} -- We divided the entire period range (1--100 days) into
ten different period bins. The binning was performed to
a) reduce the $rms$ of the merged light-curves,
b) properly trace the change in the shape of the light-curve across the HP, and to
c) minimize the discrepancy in the amplitude ratio and in the phase difference
($R_{l,m}$, $\phi_{l,m}$; Fourier parameters) between templates and individual
light curves. The adopted binning in period allowed us to limit this
difference to less than 15\% of the total error associated with the estimate of
the NIR mean magnitudes.
{\sl ii)} {\bf Phase zero--point} -- The phase zero--point of the mean magnitude was
fixed along the rising branch of the light-curve. The main advantage of this new
definition is that it allow us to estimate the phase lag between optical and
NIR light-curves. Moreover, the identification of the new phase zero--point
is straightforward even for bump cepheids and thus overcomes possible systematic
errors introduced by the secondary bumps along the light curves.
{\sl iii)} {\bf NIR--to--optical amplitude ratios} -- To apply the new templates,
we need to know the luminosity amplitude in an optical band
($V$, $B$) in advance together with the ratio between optical and NIR bands. The optical amplitudes come from the OGLE data set. We provided a new estimate of the
$V$--NIR amplitude ratios for the calibrating Cepheids and found that
a) the ratios for SMC Cepheids are, at fixed period, systematically lower
than the ratios of Galactic and LMC Cepheids;
b) the difference between SMC and MW$+$LMC decreases for periods longer
than the center of the HP. The optical amplitudes of Galactic Cepheids are
smaller than the amplitudes of SMC Cepheids for periods shorter than the center
of the HP.
Therefore, we adopted two different ratios for the short-- and the
long--period regime.
{\sl iv)} {\bf Analytical Functions} -- Together with the popular seventh-order
Fourier series fitting, we also provided a template based on multi-Gaussian
periodic functions. The main advantage in using this new template is that
it provides a solid fit of the light-curves by using fewer
parameters than the Fourier fit. Moreover, it is less sensitive to spurious features that can be introduced in the light-curves by photometric errors and to secondary features (bumps, dips) that can appear along the light-curves.
{\sl v)} {\bf FO pulsators} -- We provide for the first time the $J$-band
template for FO Cepheids, following the same approach as we adopted for
FU Cepheids. The new template reduces the uncertainty
on the mean $J$--band magnitude of FO Cepheids by a factor of two.
The application of the new NIR templates when compared with single-epoch NIR
data provides mean magnitudes that are 80\% more accurate,
and their typical error is smaller than $0.02$ mag.
Cepheids mean magnitudes can be used to estimate
their distances by adopting Period--Luminosity (PL)
and Period--Wesenheit (PW) relations.
The error associated with these distances includes
both the error on the observed mean magnitude
and the uncertainty on the absolute magnitude
estimated by the adopted relation.
This uncertainty is formally derived by the dispersion of the relation,
which is produced by three different error sources:
the photometric errors associated with the measured mean magnitudes
from which the adopted PL or the PW relation is derived,
the line-of-sight depth of the galaxy, and the intrinsic scatter.
This last term is a consequence of the fact that
PL and PW relations do not account for all the physical parameters that contribute
to the stellar luminosity, such as temperature, metallicity, helium-content.
Recent theoretical predictions \citep{bono00,marconi05,fiorentino07}
and empirical results \citep{bono10,inno13}
indicate that the intrinsic dispersion decreases for NIR PW relations.
In particular, \citet{fiorentino07} predicted a dispersion lower than 0.05 mag for
PW$(J,K)$ relation.
This uncertainty of $\sim$ 3\% on individual distances is thus the
precision that intrinsically limits the method we adopted.
The main advantage of the new templates is that
they reach the precision limit,
even with single-epoch NIR observations.
Indeed, for single-epoch measurements with 1\% accuracy or better,
the error on the mean magnitude is lower than 2\%.
Computing the sum in quadrature of all these error sources,
the dominant term is then the intrinsic scatter of the PW
relation.
\begin{figure*}[!ht]
\begin{center}
\includegraphics[width=0.8\textwidth, height=0.4\textheight]{f16.pdf}
\caption{Top: From left to right: histogram of the difference between
the true mean Wesenheit $W(JK_{\rm{S}})$ and the mean Wesenheit magnitude
estimated by using the F7, G3, S05 templates, and the single-epoch data.
The single-epoch data were randomly extracted from the calibrating SMC light-curve
at different phases for the $J$, $H$, and the $K_{\rm{S}}$ bands.
The Gaussian fits from which the labeled standard deviation has been estimated are also overplotted on the histograms.
Middle: Same as top, but for the W($HK_{\rm{S}}$) magnitude.
Bottom: Same as top, but for the W($JH$) magnitude.}
\label{f16}
\end{center}
\end{figure*}
This means that Cepheid distances can be determined
with the highest possible accuracy by using the new templates
and one single-epoch NIR observation.
Compared with the S05 templates, F7 and G3 templates have
the advantage to be minimally affected by problems
in phase dependences, and they provide new NIR mean magnitudes
that are more accurate by 30\%($K_{\rm{S}}$) to 50\% ($J$).
This means that if single-epoch measurements
are available with photometric precision better than 0.03 mag,
the new templates already reduce the total uncertainty
on distances by 20\% with respect to the S05 templates.
For instance, by applying the new templates to the NIR
single-epoch data presented in \citet{inno13} for the SMC Cepheids,
the total dispersion of the optical--NIR
PW relations decreases by up to 30\% (i.e. 0.15 mag vs 0.26 mag, PW$(VJ)$)
when compared to single-epoch data,
and up to 5\% (i.e. 0.15 mag vs 0.16 mag PW$(VJ)$) when compared with the S05 template.
Moreover,the total dispersion for PW$(VJ)$ is 0.15 mag,
indicating that the scatter due to spatial effects is still
significantly larger then the intrinsic dispersion ($\sim$3 times larger).
This means that Cepheid relative distances
can be safely used to derive the three-dimensional structure of the SMC,
with an accuracy limited by the total error estimated above that is $\le$5\%,
which corresponds to the physical limit of the method itself.
If we instead consider all of the Cepheids as a statistical ensemble representing
the stellar distribution in the galaxy, the mean distances to the SMC as derived from different PW relations can be determined with a precision of up to ~0.1\% (0.002 magnitudes, PW$(VJ)$), with the precision scaling as the square root of the number of stars in the ensemble itself ($\gtrsim$2,200 Cepheids).
A more detailed discussion on the application of the new templates
to derive new MC Cepheids relative distances will be given
in a forthcoming paper (Inno et al., in preparation).
Our findings rely on a panoply of Galactic and MC Cepheid light-curves.
The new templates and reddening-free optical--NIR PW relations will provide
accurate absolute and relative distances. The latter appear very promising,
because the intrinsic error is on the order of 1--2 percent. This gives the
opportunity to derive 3D structure of nearby stellar systems by using
single-epoch NIR observations.
In spite of the substantial improvement in the intrinsic accuracy of the
NIR light-curve templates, the observational scenario is far from being
complete. Current NIR light-curves did not allow us to derive accurate $H$- and $K_{\rm{S}}$-band templates for FO Cepheids, because of the limited photometric
accuracy in the short-period regime (faintest Cepheids).
Moreover, we found evidence that the NIR--to--optical
amplitude ratios of SMC Cepheids are lower when compared with MW+LMC
Cepheids. Current data did not allow us to constrain whether a similar difference is present in addition between MW and LMC Cepheids, because of the limited sample of
LMC Cepheids,
The new NIR time series data that are being collected by IRSF for MC Cepheids
appear a very good viaticum to address these open problems.
\begin{acknowledgements}
This work was partially supported by PRIN--INAF 2011 ``Tracing the
formation and evolution of the Galactic halo with VST" (P.I.: M. Marconi)
and by PRIN--MIUR (2010LY5N2T) ``Chemical and dynamical evolution of
the Milky Way and Local Group galaxies" (P.I.: F. Matteucci).
One of us (G.B.) thanks The Carnegie Observatories visitor program
for support as science visitor.
N.M. acknowledges the support by Grants-in-Aid for
Scientific Research (Nos. 23684005 and 26287028)
from the Japan Society for the Promotion of Science (JSPS).
Support from the Polish National Science Center grant
MAESTRO 2012/06/A/ST9/00269 is also acknowledged.
WG gratefully acknowledges support for this work from the BASAL
Centro de Astrof\'{i}sica y Tecnolog\'{i}as Afines (CATA) PFB-06/2007, and
from the Chilean Ministry of Economy, Development and Tourism's
Millenium Science Iniciative through grant IC120009 awarded to the
Millenium Institute of Astrophysics (MAS).\\
We also acknowledge G. Fiorentino for many useful discussions
concerning the theoretical predictions on NIR Period Wesenheit
relations.
It is also a pleasure to thank an anonymous referee for his/her
supportive attitude and insightful suggestions that helped us to improve
the readability of the paper.
\end{acknowledgements}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 510 |
Saman Ediriweera (also known as S. Saman Ediriweera) is the current Chairman of Airport & Aviation Services (Sri Lanka) Limited (AASL).
Early life and education
After receiving his education from Nalanda College, Colombo, Ediriweera entered University of Sri Lanka in 1972 and graduated with a B.Sc in Electronics and Telecommunications Engineering. He is also one of the first batch of engineering students at Moratuwa University.
Professional career
Ediriweera has served Sri Lanka in the capacity of Secretary Ministry of Telecommunications, Chairman of Telecommunication Regulatory Commission (TRC), Secretary Ministry of Tertiary Education and Training, Director Policy Planning at Sri Lanka Telecom and Director of Telecommunications at the Ministry of Posts, Telecommunications and the Media., Chairman of Sri Lanka Rupavahini Corporation, Director General of Sri Lanka Rupavahini Corporation, Director of Sri Lanka Rupavahini Corporation,
General References
Emirate Group Careers
Diploma Awards 2015
Sinhala and Hindu New Year Celebrations at BIA-2016
Sri Lankan Buddhists
Sinhalese engineers
Alumni of Nalanda College, Colombo
Living people
Year of birth missing (living people) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,224 |
Q: How to retrieve the underlier object from a binded Microsoft.Office.Interop.Excel.ListRow? I am binding a BingingList<T> to an excel list object using the VSTO with Visual Studio 2010.
I want to be able to retrieve the object T given a excel ListRow object. The only way I know how is to use ListRow.Range[1,1].ID. It seems to return the index of T in the BindingList. But the index is often not updated on time when the list is altered.
Is there a better way to achieve this?
thanks
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 673 |
\section{Introduction}
\label{sec:introduction}
\gdef\@thefnmark{}\@footnotetext{ \vspace{-0.2in} * indicates equal contribution.}
\vspace{-0.07in}
Deep Reinforcement Learning (RL) is a powerful general-purpose framework for learning behavior policies from high-dimensional interaction data, and has led to a multitude of impressive feats in application areas such as game-playing \citep{Mnih2015HumanlevelCT} and robotics \citep{Levine2018LearningHC, Andrychowicz2020LearningDI}. Through interaction with an unknown environment, RL agents iteratively improve their policy by learning to maximize a reward signal, which has the potential to be used in lieu of hand-crafted control policies. However, the performance of policies learned by RL is found to be highly dependent on the careful specification of task-specific reward functions and, as a result, crafting a good reward function may require significant domain knowledge and technical expertise.
As an alternative to manual design of reward functions, \textit{inverse RL} (IRL) has emerged as a promising paradigm for policy learning. By framing the reward specification as a learning problem, operators can specify a reward function based on video examples. While \textit{imitation learning} typically requires demonstrations from a first-person perspective, IRL can in principle learn a reward function, \textit{i.e.}, a measure of task progression, from \textit{any} perspective, including third-person videos of humans performing a task. This has positive implications for data collection, since it is often far easier for humans to capture demonstrations in third-person.
Although IRL from third-person videos is appealing because of its perceived flexibility, learning a good reward function from raw video data comes with a variety of challenges. This is perhaps unsurprising, considering the visual and functional diversity that such data contains. For example, the task of pushing an object across a table may require different motions depending on the embodiment of the agent. A recent method for cross-embodiment IRL, dubbed XIRL \citep{zakka2022xirl}, learns to capture task progression from videos in a self-supervised manner by enforcing temporal cycle-consistency constraints. While XIRL can in principle consume any video demonstration, we observe that its ability to learn task progression degrades substantially when the visual appearance of the video demonstrations do not match that of the target environment for RL. Therefore, it is natural to ask the question: \textit{can we learn to imitate others from (a limited number of) diverse third-person videos?}
In this work, we demonstrate that it is indeed possible. Our key insight is that, while videos may be of great visual diversity, their underlying scene structure and agent-object interactions can be abstracted via a graph representation. Specifically, instead of directly using images, we extract object bounding boxes from each frame using an off-the-shelf detector, and construct a graph abstraction where each object is represented as a node in the graph. Often -- in robotics tasks -- the spatial location of an object by itself may not convey the full picture of the task at hand. For instance, to understand a task like \textit{Peg in Box} (shown in Figure \ref{fig:teaser}), we need to also take into account how the agent \emph{interacts} with the object. Therefore, we propose to employ \emph{Interaction Networks} \citep{battaglia2016interaction} on our graph representation to explicitly model interactions between entities. To train our model, we follow \citep{zakka2022xirl, dwibedi2019temporal} and apply a temporal cycle consistency loss, which (in our framework) yields task-specific yet embodiment- and domain-agnostic feature representations.
We validate our method empirically on a set of simulated cross-domain cross-embodiment tasks from X-MAGICAL \citep{zakka2022xirl}, as well as three vision-based robotic manipulation tasks. To do so, we collect a diverse set of demonstrations that vary in visual appearance, embodiment, object categories, and scene configuration; X-MAGICAL demonstrations are collected in simulation, whereas our manipulation demonstrations consist of real-world videos of humans performing tasks. We find our method to outperform a set of strong baselines when learning from visually diverse demonstrations, while simultaneously matching their performance in absence of diversity. Further, we demonstrate that vision-based policies trained with our learned reward perform tasks with greater precision than human-designed reward functions, and successfully transfer to a real robot setup with only approximate correspondence to the simulation environment. Thus, our proposed framework completes the cycle of learning rewards from real-world human demonstrations, learning a policy in simulation using learned rewards, and finally deployment of the learned policy on physical hardware.
\vspace{-0.025in}
\section{Related Work}
\label{sec:related_work}
\vspace{-0.1in}
\textbf{Learning from demonstration.} Conventional imitation learning methods require access to expert demonstrations comprised of observations and corresponding ground-truth actions for every time step \citep{pomerleau1988bc, Atkeson1997RobotLF, argall2009lfd, Ravichandar2020Recent}, for which kinesthetic teaching or teleoperation are the primary modes of data collection in robotics. To scale up learning, video demonstrations are recorded with human operating the same gripper that the robot used, which also allows direct behaviro cloning~\cite{song2020grasping,young2020visual}. More recently, researchers have developed methods that instead infer actions from data via a learned forward \citep{Pathak2018ZeroShotVI} or inverse \citep{Torabi2018BehavioralCF, Radosavovic2021StateOnlyIL} dynamics model. However, this approach still makes the implicit assumption that imitator and demonstrator share a common observation and action space, and are therefore not directly applicable to the cross-domain cross-embodiment problem setting that we consider.
\textbf{Inverse RL.} To address the aforementioned limitations, inverse RL has been proposed~\citep{Ng2000,Abbeel2004,ho2016generative,Fu2017,Aytar2018,Torabi2018g} and it has recently emerged as a promising paradigm for cross-embodiment imitation in particular~\citep{schmeckpeper2020reinforcement, jin2020visual, xiong2021learning, lee2021generalizable, chen2021learning, fickinger2021cross, qin2021dexmv, zakka2022xirl, arunachalam2022dexterous}. For example, \citet{schmeckpeper2020reinforcement} proposes a method for integrating video demonstrations without corresponding actions into off-policy RL algorithms via a latent inverse dynamics model and heuristic reward assignment, and \citet{zakka2022xirl} (XIRL) learns a reward function from video demonstrations using temporal cycle-consistency and trains an RL agent to maximize the learned rewards. In practice, however, inverse RL methods such as XIRL are found to require limited visual diversity in demonstrations. Our work extends XIRL to the setting of diverse videos by introducing a graph abstraction that models agent-object and object-object interactions while still enforcing temporal cycle-consistency.
\textbf{Object-centric representations.} have been proposed in many forms at the intersection of computer vision and robotics. For example, object-centric scene graphs can be constructed for integrated task and motion planning \citep{Fainekos2009TemporalLM, srivastava2014combined, zhu2021hierarchical}, navigation \citep{Gupta2019CognitiveMA, Yang2019VisualSN}, relational inference \citep{Xu2017SceneGG, Li2017SceneGG}, dynamics modeling \citep{battaglia2016interaction, watters2017visual, materzynska2020something, ye2019compositional, qi2021learning}, model predictive control~\citep{sanchez2018graph,li2019learning,ye2020object} or visual imitation learning \citep{sieb2020graph}. Similar to our work, \citet{sieb2020graph} propose to abstract video demonstrations as object-centric graphs for the problem of single-video cross-embodiment imitation, and act by minimizing the difference between the demonstration graph and a graph constructed from observations captured at each step. As such, their method is limited to same-domain visual trajectory following, whereas we learn a general alignment function for cross-domain cross-embodiment imitation and leverage \textit{Interaction Networks} \citep{battaglia2016interaction} for modeling graph-abstracted spatial interactions rather than relying on heuristics.
\begin{figure}
\centering
\includegraphics[width=0.95\textwidth]{figures/Corl22_Fig1_final_compressed.pdf}
\vspace{-0.025in}
\caption{\textbf{Overview.} We extract object bounding boxes from video sequences using an off-the-shelf detector, and construct a graph abstraction of the scene. We model graph-abstracted object interactions using \emph{Interaction Networks} \citep{battaglia2016interaction}, and learn a reward function by aligning video embeddings temporally. We then train image-based RL policies using our learned reward function, and deploy on a real robot.}
\label{fig:approach}
\vspace{-0.1in}
\end{figure}
\section{Our Approach}
\label{sec:approach}
\vspace{-0.075in}
In this section, we describe our main contribution, which is a self-supervised method for learning a reward function directly from a set of diverse third-person video demonstrations by applying temporal matching on graph abstractions. Our Graph Inverse Reinforcement Learning (GraphIRL) framework, shown in Figure \ref{fig:approach}, consists of building an object-centric graph abstraction of the video demonstrations and then learn an embedding space that captures task progression by exploiting the temporal cue in the videos. This embedding space is then used to construct a \emph{domain invariant} and \emph{embodiment invariant} reward function which can be used to train any standard reinforcement learning algorithm.
\noindent {\textbf{Problem Formulation.}} Given a task $T$, our approach takes a dataset of video demonstrations $D = \{V_1, V_2, \dots, V_n\}$. Each video consists of image frames $\{I_1^i, I_2^i, \dots, I_k^i\}$ where $i$ denotes the video frame index and $k$ denotes the total number of frames in $V_i$. Given $D$, our goal is to learn a reward function that can be used to solve the task $T$ for any robotic environment. Notably, we do \emph{not} assume access to any action information of the expert demonstrations, and our approach does \emph{not} require objects or embodiments in the target environment to share appearance with demonstrations.
\subsection{Representation Learning}
\label{sec:rep_learning}
\vspace{-0.06in}
To learn task-specific representations in a self-supervised manner, we take inspiration from \citet{dwibedi2019temporal} and employ a temporal cycle consistency loss. However, instead of directly using images, we propose a novel object-centric graph representation, which allows us to learn an embedding space that not only captures task-specific features, but depends \emph{solely} on the spatial configuration of objects and their interactions. We here detail each component of our approach to representation learning.
\noindent {\textbf{Object-Centric Representation.}} Given video frames $\{I_1^i, I_2^i, \dots, I_k^i\}$, we first extract object bounding boxes from each frame using an off-the-shelf detector. Given $N$ bounding boxes for an image, we represent each bounding box as a $4 + m$ dimensional vector $o_j = \{x_1, y_1, x_2, y_2, d_1, d_2, \dots, d_m\}$, where the first $4$ dimensions represent the leftmost and rightmost corners of the bounding box, and the remaining $m$ dimensions encode distances between the centroids of the objects.
For each frame $I^i_j$ we extract an object-centric representation $I'^{i}_j = \{ o_1, o_2, \dots, o_m\}$ such that we can represent our dataset of demonstrations as $D' = \{V'_1, V'_2, \dots, V'_n\}$ where $V'_i$ is the sequence of bounding boxes corresponding to video $V_i$. Subsequent sections describe how we learn representations given $D'$.
\noindent {\textbf{Spatial Interaction Encoder.}} Taking inspiration from recent approaches on modeling physical object dynamics \citep{battaglia2016interaction, watters2017visual}, we propose a \emph{Spatial Interaction Encoder Network} to explicitly model object-object interactions. Specifically, given a sequence $V'_i$ from $D'$, we model each element $I'$ as a graph, $G = (O, R)$, where $O$ is the set of objects $\{o_1, o_2, \dots, o_m\}$, $m$ is the total number of objects in $I'$, and $R$ denotes the relationship between objects (\emph{i.e.}, whether two objects interact with each other). For simplicity, all objects are connected with all other objects in the graph such that $R= \{(i,j) \mid i \ne j \land i \leq m \land j \leq m \}$. We compose an object embedding for each of $o_i \in O$ by combining \emph{self} and \emph{interactional} representations as follows:
\begin{align}
\label{eq:sie_self}
f_{o}(o_i) = \phi_{\text{agg}} (f_{\text{s}} + f_{\text{in}}) \quad\text{with}\quad f_s(o_i) = \phi_s(o)\,, \quad f_{\text{in}}(o_i) = \sum_{j=1}^{m} \phi_{\text{in}}((o_i, o_j)) \mid (i, j) \in \mathbb{R}\,,
\end{align}
where $f_s(o_i)$ represents the \emph{self} or independent representation of an object, $f_{\text{in}}$ represents the \emph{interactional} representation, \emph{i.e.}, how it interacts with other objects in the scene, $f_{o}$ is the final object embedding, and $(,)$ represents concatenation. Here, the encoders $\phi_\text{s}$, $\phi_{\text{in}}$ and $\phi_{\text{agg}}$ denote Multi layer Perceptron (MLP) networks respectively. We emphasize that the expression for $f_\text{in}(\cdot)$ implies that the object embedding $f_o(.)$ depends on \emph{all} other objects in the scene; this term allows us to model relationships of an object with the others. The final output from the spatial interaction encoder $\psi(\cdot)$ for object representation $I'$ is the mean of all object encodings:
\begin{align}
\label{eq:sie_final_eq}
\psi(I') = \frac{1}{m} \sum_i^{m} f(o_i)\,.
\end{align}
\label{approach:sie}
The spatial interaction encoder is then optimized using the temporal alignment loss introduced next.
\noindent {\textbf{Temporal Alignment Loss}}. Taking inspiration from prior works on video representation learning \citep{dwibedi2019temporal, haresh2021learning, liu2021learning, wang2020dynamic, hadji2021representation}, we employ the task of temporal alignment for learning task-specific representations. Given a pair of videos, the task of self-supervised alignment implicitly assumes that there exists true semantic correspondence between the two sequences, \textit{i.e.}, both videos share a common semantic space. These works have shown that optimizing for alignment leads to representations that could be used for tasks that require understanding task progression such as action-classification. This is because in order to solve for alignment, a learning model has to learn features that are (1) common across most videos and (2) exhibit temporal ordering. For a sufficiently large dataset with single task, the most common visual features would be distinct phases of a task that appear in all videos and if the task has small permutations, these distinct features would also exhibit temporal order. In such scenarios, the representations learned by optimizing for alignment are \emph{task-specific} and invariant to changes in viewpoints, appearances and actor embodiments.
In this work, we employ Temporal Cycle Consistency (TCC) \citep{dwibedi2019temporal} loss to learn temporal alignment. TCC optimizes for alignment by learning an embedding space that maximizes one-to-one nearest neighbour mappings between sequences. This is achieved through a loss that maximizes for cycle-consistent nearest neighbours given a pair of video sequences. In our case, the cycle consistency is applied on the \emph{graph abstraction} instead of image features as done in the aforementioned video alignment methods. Specifically, given $D'$, we sample a pair of bounding box sequences $V'_i = \{I'^{i}_1, \dots, I'^{i}_{m_i} \}$ and $V'_j = \{I'{j}_1, \dots, I'^{j}_{m_j} \}$ and extract embeddings by applying the spatial interaction encoder defined in Equation \ref{eq:sie_final_eq}. Thus, we obtain the encoded features $S_i = \{\psi( I'^{i}_1), \dots, \psi (I'^{i}_{m_i})\}$ and $S_j = \{\psi( I'^{j}_1), \dots, \psi (I'^{j}_{m_j})\}$. For the $n$th element in $S_i$, we first compute its nearest neighbour, $\upsilon^n_{ij}$, in $S_j$ and then compute the probability that it cycles-back to the $k$th frame in $S_i$ as:
\begin{align}
\label{eq:tcc_definition}
\beta^k_{ijn} = \frac{e^{-||\upsilon ^n _{ij} - S_i^k ||^2}}{{\sum_k^{m_j} e^ {-|| \upsilon^n_{ij} - S^k_i || ^2}}}\,,
\upsilon^n_{ij} = \sum_k^{m_j} \alpha_k s^k_j\,,
\alpha_k = \frac{e^{-|| S^n_i - S^k_j ||^2}}{{\sum_k^{m_j} e^ {-|| S^n_i - S^k_j || ^2}}}\,.
\end{align}
The cycle consistency loss for $n$th element can be computed as $L_n^{ij} = (\mu^n_{ij} - n)^2$, where $\mu^n_{ij} = \sum^{mi}_k \beta^k_{ijn} k $ is the expected value of frame index $n$ as we cycle back. The overall TCC loss is then defined by summing over all pairs of sequence embeddings $(S_i, S_j)$ in the data, \textit{i.e.}, $L^n_{ij} = \sum_{ijn} L^n_{ij}$.
\subsection{Reinforcement Learning}
\vspace{-0.05in}
We learn a task-specific embedding space by optimizing for temporal alignment. In this section, we define how to go from this embedding space to a reward function that measures task progression. For constructing the reward function, we leverage the insight from \citet{zakka2022xirl} that in a task-specific embedding space, we can use euclidean distance as a notion of task progression, \textit{i.e.}, frames far apart in the embedding space will be far apart in terms of task progression and vice versa. We therefore choose to define our reward function as
\begin{align}
\label{eq:reward_function}
r(o) = -\frac{1}{c} ||\psi(o) - g||^2\,, \quad\text{with}\quad g = \sum_{i=1}^n \psi (I'^{i}_{m_{i}})\,,
\end{align}
where $o$ is the current observation, $\psi$ is the Spatial Interaction Encoder Network from Section \ref{sec:approach}, $g$ is the representative goal frame, $m_i$ is the length of sequence $V'^i$ and $c$ is a scaling factor. The scaling factor \emph{c} is computed as the average distance between the first and final observation of all the training videos in the learned embedding space. Note, that the range of the learned reward is $(-\infty, 0]$. Defining the reward function in this way gives us a dense reward because as the observed state gets closer and closer to the goal, the reward starts going down and approaches zero when the goal and current observation are close in embedding space. After constructing the learned reward, we can use it to train any standard RL algorithm. We note that, unlike previous approaches \citep{schmeckpeper2020reinforcement, zakka2022xirl}, our method does not use \emph{any} environment reward to improve performance, and instead relies \emph{solely} on the learned reward, which our experiments demonstrate is sufficient for solving diverse robotic manipulation tasks.
\section{Experiments}
\label{sec:experiments}
In this section, we demonstrate how our approach uses diverse video demonstrations to learn a reward function that generalizes to unseen domains. In particular, we are interested in answering the questions: (1) How do vision-based methods for IRL perform when learning from demonstrations that exhibit \emph{domain shift}? and (2) is our approach capable of learning a stronger reward signal under this challenging setting? To that end, we first conduct experiments X-MAGICAL benchmark \citep{zakka2022xirl}. We then evaluate our approach on multiple robot manipulation tasks using a diverse set of demonstrations.
\noindent{\textbf{Implementation Details.}} All MLPs defined in Equation \ref{eq:sie_final_eq} have 2 layers followed by a ReLU activation, and the embedding layer outputs features of size $128$ in all experiments. For training, we use ADAM~\citep{kingma2014adam} optimizer with a learning rate of $10^{-5}$. We use Soft Actor-Critic (SAC) \citep{haarnoja2018soft} as backbone RL algorithm for all methods. For experiments on X-MAGICAL, we follow \citet{zakka2022xirl} and learn a state-based policy; RL training is performed for $500$k steps for all embodiments. For robotic manipulation experiments, we learn a multi-view image-based SAC policy \citep{jangir2022look}. We train RL agent for $300$k, $800$k and $700$k steps for \emph{Reach}, \emph{Push} and \emph{Peg in Box} respectively. For fair comparison, we only change the learned reward function across methods and keep the RL setup identical. The success rates presented for all our experiments are averaged over $50$ episodes. Refer to Appendix \ref{sec:implementation_details} for further implementation details.
\textbf{\noindent{\textbf{Baselines.}}} We compare against multiple vision-based approaches that learn rewards in a self-supervised manner: \textbf{(1) {XIRL}}~\citep{zakka2022xirl} that learns a reward function by applying the TCC~\citep{dwibedi2019temporal} loss on demonstration video sequences, \textbf{(2) {TCN}}~\citep{sermanet2018time} which is a self-supervised contrastive method for video representation learning that optimizes for temporally disentangled representations, and \textbf{(3) LIFS}~\citep{gupta2017learning} that learns an invariant feature space using a dynamic time warping-based contrastive loss. Lastly, we also compare against the manually designed \textbf{(4) Environment Rewards} from \citet{jangir2022look}. For vision-based baselines, we use a ResNet-18 encoder pretrained on ImageNet \citep{ILSVRC15} classification. We use the hyperparameters, data augmentation schemes and network architectures provided in \citet{zakka2022xirl} for all vision-based baselines. Please refer to Appendix \ref{sec:env_reward_desc}
for description of environment rewards and \citet{zakka2022xirl} for details on the vision-based baselines.
\input{tables/xmagical/overview-long}
\begin{figure}[t]
\centering
\includegraphics[width=1\textwidth]{figures/xmagical/cross-emb-cross-env/s2d_compressed.pdf}\vspace{0.025in}\\
\includegraphics[width=1\textwidth]{figures/xmagical/cross-emb-cross-env/d2s_compressed.pdf}
\vspace{-0.2in}
\caption{\textbf{Cross-Embodiment Cross-Environment.} Success rates of our method \emph{GraphIRL} and baselines on \textit{(top)} Standard Environment Pretraining $\rightarrow$ Diverse Environment RL and \textit{(bottom)} Diverse Environment Pretraining $\rightarrow$ Standard Environment RL. All reported numbers are averaged over 5 seeds. Our approach performs favorably when compared to other baselines on both settings.}
\label{fig:cross-env-cross-emb-standard2diverse}
\vspace{-0.15in}
\end{figure}
\subsection{Experimental Setup}
\label{sec:setup}
We conduct experiments under two settings: the \emph{Sweep-to-Goal} task from X-MAGICAL \citep{zakka2022xirl}, and robotic manipulation tasks with an xArm robot both in simulation and on a real robot setup. We describe our experimental setup under these two settings in the following.
\noindent \textbf{X-MAGICAL.} We choose to extend X-MAGICAL \citep{zakka2022xirl}, a 2D simulation environment for cross-embodiment imitation learning. On this benchmark, we consider a multi-object sweeping task, where the agent must push three objects towards a static goal region. We utilize two variants of the X-MAGICAL benchmark, which we denote as \textit{\textbf{Standard}} (original) and \textit{\textbf{Diverse}} (ours) environments, shown in Figure \ref{fig:xmagical-variants}. \textit{\textbf{Standard}} only randomizes the position of objects, whereas \textit{\textbf{Diverse}} also randomizes visual appearance. We consider a set of four unique embodiments $\{$\textit{gripper, short-stick, medium-stick, long-stick}$\}$. In particular, we conduct experiments in the \emph{cross-environment} and \emph{cross-embodiment setting} where we learn a reward function in the \textbf{\textit{Standard}} environment on 3 held-out embodiments and do RL in the \textit{\textbf{Diverse}} environment on 1 target embodiment, or vice-versa. This provides an additional layer of difficulty for the RL agent as visual randomizations show the brittleness of vision-based IRL methods. Refer to Appendix \ref{sec:X_Magical_details} for more details on performed randomizations.
\noindent \textbf{Robotic Manipulation.} Figure \ref{fig:teaser} shows initial and success configurations for each of the three task that we consider: \textbf{(1) Reach} in which the agent needs to reach a goal (red disc) with its end-effector, \textbf{(2) Push} in which the goal is to push a cube to a goal position, and \textbf{(3) Peg in Box} where the goal is to put a peg tied to the robot's end-effector inside a box. The last task is particularly difficult because it requires geometric 3D understanding of the objects. Further, a very specific trajectory is required to avoid collision with the box and complete the task. We collect a total of $256$ and $162$ video demonstrations for \emph{Reach} and \emph{Peg in Box}, respectively, and use $198$ videos provided from \citet{schmeckpeper2020reinforcement} for \emph{Push}. The videos consist of human actors performing the same tasks but with a number of diverse objects and goal markers, as well as varied positions of objects. Unlike the data collected by \citet{schmeckpeper2020reinforcement}, we do not fix the goal position in our demonstrations. In order to detect objects in our training demonstrations, we use a trained model from \citet{shan2020understanding}. The model is trained on a large-scale dataset collected from YouTube and can detect hands and objects in an image.; refer to Appendix \ref{sec:xArm_data_details} for more details on data collection. Additionally, we do not require the demonstrations to resemble the robotic environment in terms of appearance or distribution of goal location. We use an xArm robot as our robot platform and capture image observations using a static third-person RGB camera in our real setup; details in Appendix \ref{sec:robot_setup}.
\vspace{-0.05in}
\subsection{Results}
\label{sec:results}
\textbf{X-MAGICAL.} Results for the \emph{cross-embodiment and cross-environment} setting are shown in Figure \ref{fig:cross-env-cross-emb-standard2diverse}. When trained on \textit{Standard}, our method performs significantly better than vision-based baselines (\textit{e.g.}, $0.58$ GraphIRL for gripper vs $0.35$ for XIRL and $0.99$ GraphIRL for longstick vs $0.56$ XIRL). We conjecture that vision-based baselines struggle with visual variations in the environment, which our method is unaffected by due to its graph abstraction. Additionally, when trained on \emph{diverse} environment, GraphIRL outperforms $3$ out of $4$ embodiments.
\begin{figure}[t]
\centering
\includegraphics[width=0.8\textwidth]{figures/xarm/robot_manipulation_compressed.pdf}
\caption{\textbf{Robotic Manipulation.} Success rates of our method \emph{GraphIRL} and baselines on the tasks of \emph{Reach}, \emph{Push} and \emph{Peg in Box}. All results are averaged over 5 seeds. We observe significant gains in performance specially over vision-based baselines due to large \emph{domain-gap}}
\label{fig:xarm-tasks}
\end{figure}
\input{tables/robot-real}
\textbf{Robotic manipulation in simulation.} In this section, we answer the core question of our work: \emph{can we learn to imitate others from diverse third-person videos?} In particular, we collect human demonstrations for manipulation tasks as explained in Section \ref{sec:setup} and learn a reward function as explained in Section \ref{sec:approach}. This is a challenging setting because as shown in Figure \ref{fig:teaser}, the collected data and robotic environments belong to different domains and do not share any appearance characteristics. Further, unlike previous works \citep{schmeckpeper2020reinforcement, zakka2022xirl}, we do not use any environment reward as an additional supervision to the reinforcement learning agent. Figure \ref{fig:xarm-tasks} presents our results. For the \textbf{Reach} task, GraphIRL and environment reward are able to achieve a success rate of $1.0$, while other baseline methods are substantially behind GraphIRL (e.g. $0.477$ XIRL and $0.155$ TCN). The poor performance of vision-based baselines could be attributed to substantial visual domain shift. Due to domain shift, the learned rewards for these baselines produce low rewards for successful episodes, please refer to Appendix \ref{sec:qualitative_analysis} for a more detailed qualitative analysis. In the \textbf{Push} setting, we find that vision-based baseline methods still perform poorly. Similar to \textbf{Reach}, XIRL performs the best out of the vision-based baselines with a success rate of $0.187$, and GraphIRL performs better than environment reward (e.g. $0.832$ GraphIRL vs $0.512$ Environment Reward). This result shows clear advantage of our method as we are able to outperform a hand-designed reward function without using any task specific information. The \textbf{Peg in Box} task is rigorous to solve since it requires 3-d reasoning and a precise reward function. Here, while all vision-based methods fail, our GraphIRL method is able to solve the task with a success rate comparable to that achieved with the hand-designed environment reward. Overall, our GraphIRL method is able to solve 2D and 3D reasoning tasks with a real-robot without a hand-designed reward function or access to 3D scene information.
\textbf{Real robot experiments.} Finally, we deploy the learned policies on a real robot. For each experiment, we conduct $15$ trials per method and report the average success rate. Results are shown in Table \ref{tab:robot_real}. Interestingly, we find that GraphIRL outperforms XIRL in all three tasks on the real robot setup (e.g. $0.26$ XIRL vs $0.86$ GraphIRL on \emph{Reach} and $0.27$ XIRL vs $0.60$ GraphIRL on \emph{Push}), and on \emph{Push}, GraphIRL performs better than the environment reward specifically designed for the task (e.g. $0.47$ Environment Reward vs $0.6$ GraphIRL) which is in line with our findings in simulation.
\input{tables/ablation}
\subsection{Ablations}
\label{sec:ablations}
In this section, we perform ablation study using the \emph{Push} task to validate our design choices in Section \ref{sec:approach}. In the experiments below, we perform RL training for $500$k steps and report the final success rate.
\textbf{Impact of Modelling Spatial Interactions.} We study the impact of modeling object-object spatial interactions using Spatial Interaction Encoder Network described (IN) in Section \ref{sec:rep_learning}. Specifically, we replace our proposed encoder component with an Multi-Layer Perceptron (MLP) by concatenating representations of all objects into a single vector and then feeding it to a 3-layer MLP network. As shown in Table \ref{tab:ablation_interactions}, IN leads to a $20\%$ improvement in the reinforcement learning success rate.
\textbf{Impact of Decreasing Number of Demonstration Videos.}
As shown in Table \ref{tab:ablation_data}, the performance of our approach gradually decreases as we decrease demonstration data. However, we note that GraphIRL achieves $67\%$ success rate with $25$\% of total training videos (49 videos).
This demonstrates that our approach is capable of learning meaningful rewards even with a small number of videos.
\section{Conclusions and Limitations}
\label{sec:conclusion}
We demonstrate the effectiveness of our proposed method, \textit{GraphIRL}, in a number of IRL settings with diverse third-person demonstrations. In particular, we show that our method successfully learns reward functions from human demonstrations with diverse objects and scene configurations, that we are able to train image-based policies in simulation using our learned rewards, and that policies trained with our learned rewards are more successful than both prior work and manually designed reward functions on a real robot. With respect to limitations, while our method relaxes the requirements for human demonstrations, collecting the demonstrations still requires human labor; and although our results indicate that we can learn from relatively few videos, eliminating human labor entirely remains an open problem.
\clearpage
\normalsize{{
| {
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BONG AT HOME VIDEO SERIES
Thuy releases a lovely lyric visualizer for her "111" single
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Cosima unveils an attractive performance video for her "Philly" single
Justy releases a cozy holiday tune, entitled, "Blues on the Crosley"
Zangba Thomson
November 24, 2020 0 2 min read0
Justy (also stylized as J U S T Y) is a Brooklyn-born, Staten Island-raised artist. Not too long ago, she released a cozy holiday tune, entitled, "Blues on the Crosley."
Justy – "Blues on the Crosley" single
"The holidays got a way with putting things into perspective. No surprise, I should expect this. 'Cause when I'm cold, and I'm alone, the vinyl's on, Crosley playing, Nat King Cole and sleigh bells ringing. House ain't a home if you take out the you. I got your heart I'ma fly it to you." – lyrics
'Blues on the Crosley' touches on the longing one experiences when they're apart from the person they love. The emotionally-tinged holiday tune contains a relationship-based narrative, pleasing vocals, and rich harmonies that are sure to pull on your heartstring. Also, the song possesses laidback instrumentation flavored with a warm contemporary R&B aroma. Furthermore, "Blues on the Crosley" follows Justy's most recent releases including "Cool" and "Expectations," which are a part of her forthcoming album due out in 2021.
"House ain't a home if you take out the you."
"This longing is intensified by that 'time of year' when all you want is to be surrounded by love and the warmth of the season. Home becomes less of a place and more of a person/feeling. Sonically, this record feels like your favorite record playing on a vinyl on a late cold night fit for overthinking. 'Blues on the Crosley' is that cozy up by a fire, whiskey-drinking on a cold night kind of song. Sink into its warmth, its sadness, and its comfort." – Justy explained
Justy began writing music at the age of 12. Since then, she has blossomed into a unique and promising force inspired by the works of artists such as J Dilla, Amy Winehouse, NoName, Anderson Paak, and Lauryn Hill. In 2018, her refreshing sound caught the eye of British music powerhead Kwame Kwaten (also of D-Influence). He took on the artist for a two single project which penned her notable tracks, "Try" (2018), and "L8R" (2019). Since then, the self-proclaimed "old soul" has been showcasing her maturity and growth as an independent artist.
"Blues on the Crosley" single
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Zangba Thomson is an award-winning Liberian-American author, journalist, recording artist, and Editor-in-Chief at Bong Mines Entertainment. His creative works have been seen on or talked about in major media outlets such as FOX 5, NBC, Today, Fox & Friends, Kathy Lee & Hoda, ABC, Vibe Magazine, Centric TV, HOT 97, Essence Magazine, and much more. Not too long ago, Thomson received a "Certificate of Special Congressional Recognition" from Congressman Charles B. Rangel for his literary achievements, commitment to strengthening our Nation, and making a difference through volunteering service in urban communities. Show your support by downloading Thomson's award-winning debut novel, entitled, THREE BLACK BOYS, via Amazon.com.
Matt Shi releases a jazzy hip-hop tune, entitled, "Sunnyside View", featuring Justy
March 7, 2019 0 2 min read0
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Saint-Roch-de-l'Achigan est une municipalité du Québec (Canada), située dans la municipalité régionale de comté (MRC) de Montcalm dans la région administrative de Lanaudière. Au début des Basses-Laurentides, elle se trouve à une quarantaine de kilomètres au nord de Montréal, accessible via l'autoroute 25.
Toponymie
Le village doit son nom au seigneur de L'Assomption en 1781, Paul-Roch de Saint-Ours de l'Eschaillon (1747-1814), fils de Pierre-Roch de Saint-Ours (1712-1782).
Géographie
Municipalités limitrophes
Histoire
Saint-Roch-de-l'Achigan faisait autrefois partie de la seigneurie de L'Assomption et par la suite de la paroisse du même nom, est traversé d'ouest en est par la rivière de l'Achigan. Vers 1750, des colons venus surtout de L'Assomption et de Mascouche commencent à s'installer un peu partout sur son territoire.
Entre 1760 et 1770, de nombreuses concessions sont accordées de chaque côté de la rivière de l'Achigan et dans les secteurs du chemin du Ruisseau-Saint-Jean et du rang du Ruisseau-des-Anges par le seigneur Pierre-Roch de Saint-Ours de l'Échaillon. L'arrivée des colons en grand nombre amène le seigneur à vouloir tirer profit du dénivelé de la rivière et à faire construire en 1771 son moulin seigneurial à l'endroit connu aujourd'hui sous le nom de rue Masson.
L'augmentation suffisamment rapide du nombre de colons sur le territoire se traduit inévitablement par le projet d'y fonder une paroisse. Au début des années 1770, Pierre-Roch de Saint-Ours entreprend des démarches en ce sens auprès de l'évêque de Québec. Son fils Paul-Roch les poursuit. Le projet se réalise par l'ouverture des registres de la paroisse en 1787 et la venue d'un curé l'année suivante. Des difficultés reliées au choix de l'emplacement de l'église font qu'il faut attendre en 1803 pour qu'on en entreprenne la construction. Cette église de pierres fut pendant longtemps considérée comme étant l'une des plus belles de la province. Pierre Conefroy, le curé de Boucherville, en a dessiné les plans. La paroisse est érigée canoniquement en 1832. Elle doit son nom à Paul-Roch de Saint-Ours qui était le seigneur des lieux au moment de sa fondation. L'église qui faisait la fierté des paroissiens est malheureusement incendiée le 1er janvier 1958.
La première école ouvre ses portes en 1829. On construit par la suite plusieurs écoles de rangs en plus du collège du village et du couvent. En 1856, la communauté des Clercs de Saint-Viateur accepte de diriger le collège jusqu'en 1894. Dès l'année suivante, celle des Sœurs des Saints Noms de Jésus et de Marie prend charge à son tour du couvent jusqu'en 1969. Aujourd'hui, on retrouve dans la municipalité une école primaire et une école secondaire.
La Municipalité est en premier lieu reconnue civilement en 1842. Elle est abolie en 1847 et fait ensuite partie de la municipalité de comté de Lachenaie. Elle est de nouveau reconnue comme municipalité de paroisse en 1855 sous le nom de Saint-Roch. En raison de la confusion créée par l'existence de plusieurs autres municipalités portant ce nom, elle revient à son appellation d'origine en 1957.
Description
Saint-Roch-de-l'Achigan est une petite paroisse de Lanaudière dont 80 % de son territoire de près de est consacré à l'agriculture.
C'est une municipalité à caractère agricole qui possède des fermes maraîchères, céréalières et d'élevage. À Saint-Roch se trouve une fromagerie très connue, la fromagerie La Suisse normande.
Sa proximité de Montréal et son accès à l'autoroute 25 incitent de plus en plus de citadins à venir y demeurer en permanence. Un parc industriel accueille de nombreuses entreprises depuis plus de trente ans et plusieurs développements résidentiels ont été entrepris au cours des dernières années.
On y trouve une église, la bibliothèque, un bureau postal, des résidences pour personnes âgées, une clinique médicale, un centre sportif, plusieurs garderies et un centre de la petite enfance.
Saint-Roch-de-l'Achigan est connue également pour ses institutions d'enseignement. La première école y a été ouverte au début du et cette localité rassemble aujourd'hui environ dans ses écoles primaire et secondaire, en provenance des municipalités voisines.
Démographie
Administration
Les élections municipales se font en bloc et suivant un découpage de six districts..
Projets
Plusieurs projets de constructions résidentielles et une aire industrielle se développent dans la municipalité.
Parmi les projets domiciliaires, on dénombre les suivants :
Domaine au tournant de la rivière L'Achigan
Les Jardins de l'Achigan
Les Vallons Saint-Roch
La Cité des prés
De plus, Saint-Roch-de-l'Achigan dispose de terrains disponibles d'environ 7 000 000 de pieds carrés dans son parc industriel situé en bordure de l'autoroute 25.
Remarquons que la seule piste de karting homologuée par la FIA en Amérique du Nord, se trouve à Saint-Roch-de-l'Achigan.
De 2018 à 2020, un projet de relocalisation de l'aéroport de Mascouche en bordure ouest de l'autoroute 25 a été rejeté par la population et le gouvernement fédéral.
Éducation
La Commission scolaire des Samares administre les écoles francophones:
École secondaire de l'Achigan
École Notre-Dame
La Commission scolaire Sir Wilfrid Laurier administre les écoles anglophones:
École primaire Joliette à Saint-Charles-Borromée
École secondaire Joliette à Joliette
Liste des écoles
1954: Construction de l'école Notre-Dame (20, rue Vézina)
1972: Construction de l'école de l'Achigan (60, montée Rémi-Henri)
1990: Agrandissement en l'école de l'Achigan
2013: Agrandissement en l'école Notre-Dame
2017: Agrandissement en l'école Notre-Dame (Salle à gymnase)
Personnalités
Bertrand Lamarche (1971-), compositeur et musicien québéco-portugais, est né à Saint-Roch-de-l'Achigan.
Notes et références
Annexes
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Travel InspirationArt + CultureHistory + Culture
By Kayla Stewart
• February 22, 2022
The South Carolina Sea Islands Preserve Gullah Geechee Ingenuity
In South Carolina, stunning sea islands tell a unique story about southern culture.
A canopy of live oaks lines a path at McLeod Plantation Historic Site, which examines the difficult history of sea island cotton.
Photo by Prentiss Findlay/Shutterstock
There's a crisp silence that blows among the trees of South Carolina. Spanish moss drapes the live oaks, as if they can conceal the stories and truths of the region from those who wish to generalize and minimize the great history enacted upon the grounds. Waters traverse humbly, as if to pay respect to the spontaneity of nature in the region. Homes stand guard mere miles from the shoreline, seemingly fighting back against the impact of climate change and unfettered development. Outside of Charleston, a prime travel destination of the American South, the sea islands of South Carolina tell their own tale about southern identity.
South Carolina is home to more than 30 sea islands. These islands, a chain of barrier and tidal islands in the Atlantic Ocean, line the coast of the southeastern United States. They touch South Carolina, Georgia, and Florida and remain the home of numerous Gullah Geechee people: Black Americans who descend from enslaved Africans and who remained on the southeastern shores of the United States. They have their own language and dialect, and their own cultural and cooking traditions, many of which have been conflated with more general southern cooking.
Despite years of racism, private development, and aggressive climate change, about 200,000 Gullah Geechee people reside in the United States; many still live on the stunning sea islands. Those who remain continue to protect and preserve the traditions of their ancestors and elders who crafted Lowcountry cooking, culture, and community.
These traditions, like much in the Black American community, begin on the water. On the coasts where captured Africans were brought to the Americas, Gullah Geechee folks (descendants of some of those very Africans) maintain a relatively peaceful way of life by fishing and shrimping in the area. Sea islands like Edisto Island, St. Helena Island, and Johns Island—the largest sea island in the nation—are rich with lakes, rivers, ponds, and oceanfront that have long produced some of the most important seafood in Gullah Geechee foodways, such as shrimp, oysters, and crab.
Gullah Geechee culinary stalwarts like Emily Meggett, BJ Dennis, and Germaine Jenkins have spent their lives and careers highlighting these culinary traditions, ensuring that dishes like red rice, okra gumbo, and chicken perloo don't get lost or generalized in the southern foodways canon. The Gullah Geechee, and thus African, roots of these Lowcountry meals remain both relevant and essential knowledge when traveling through the region.
The sea islands are connected to the mainland by way of small highways and bridges. Existing on their own, the islands carry their own weight and identity. Unfazed by the shops and bustle of nearby Charleston, they are quiet and quaint and have served as a respite for people looking to indulge in a restorative, yet uniquely southern, experience. Like many off-the-beaten-path locations, the sea islands stand at the crossroads of preservation and development. Kiawah Island, once an oasis for freed enslaved people, is now nearly unrecognizable as largely white tourists have developed private beaches and golf resorts. Johns Island still retains the history of some of its Indigenous and Gullah Geechee heritage, evidenced through the McLeod Plantation, where Gullah Geechee people tell their own stories, but it faces the same challenge: eager developers complicit in cultural erasure.
Sweetgrass basket weaving is a long-practiced Gullah Geechee tradition.
Photo by JHVEPhoto/Shutterstock
And yet, the sea islands, in their own special ways, persist. Edisto Island has managed to keep much of its atmosphere of peace and community intact. It was once home to the venerable Black Kings of Edisto, a group of freed enslaved people who fought for land ownership, voting rights, and general prosperity, and who helped to preserve Edisto Island as one of the premier locations for Gullah Geechee people. Emily Megget, a descendant of one of the kings, James Hutchinson, continues to cook for the community there and is deeply respected as a mother of the island. The Edisto Island Museum shows the complex history of slavery, colonialism, and modern-day living.
Over on Hilton Head, Gullah Heritage Trail Tours allow visitors to learn of the harrowing and heroic history of the storied community. They can watch the still-practiced art of weaving sweetgrass baskets, learn about the distinctive history and language, and see how art and religion take center stage. Importantly, Gullah Geechee people are the primary storytellers—shaping and driving their own narrative.
Many visitors travel to the Lowcountry to see the Angel Oak Tree, a more than 60-foot-tall oak that serves as a centerpiece for Johns Island. The striking tree overlooks centuries of Gullah Geechee history and heritage and is a popular stop along the Gullah-Geechee Corridor, a Federal National Heritage Area that includes Johns Island and stretches all the way to northern Florida.
In the Carolinas, travelers can explore parks and centers important to Gullah Geechee heritage, like the Brookgreen Gardens on Myrtle Beach, Penn Center on St. Helena Island, Mitchelville Freedom Park on Hilton Head Island, and Hilton Head's Gullah Museum. The Caw Caw Interpretive Center on Ravenel is not to be missed. Exhibits show the mastery enslaved people demonstrated in architecture, highlighted by their ability to carve rice fields out of cypress swamps. Afterward, travelers can stop by Gullah-owned Ravenel Seafood, where an order of garlic crabs will lead to a finger-lickin' good meal.
The Gullah Geechee people are a diverse, rich group of Americans who are the foundation of Lowcountry cuisine, culture, and identity. Absorbing their stories, culture, and legacy is imperative to understand South Carolina and to understand the true range of American identity.
Kayla Stewart is a contributor to the forthcoming book, Gullah Geechee Home Cooking, which will be released April 25, 2022.
>> Next: Gullah Geechee Cuisine Is Finally Getting Its Due in Charleston
Kayla Stewart
Kayla Stewart is an award-winning food and travel writer. She is a columnist at The Bittman Project, and her work has been featured in The New York Times, Southern Foodways Alliance, the Wall Street Journal, and others. | {
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{"url":"https:\/\/www.groundai.com\/project\/a-full-multigrid-method-for-semilinear-elliptic-equation\/","text":"A Full Multigrid Method For Semilinear Elliptic Equation1footnote\u00a011footnote 1This work was supported in part by National Natural Science Foundations of China (NSFC 91330202, 11371026, 11001259, 11031006, 2011CB309703) and the National Center for Mathematics and Interdisciplinary Science, CAS.\n\n# A Full Multigrid Method For Semilinear Elliptic Equation111This work was supported in part by National Natural Science Foundations of China (NSFC 91330202, 11371026, 11001259, 11031006, 2011CB309703) and the National Center for Mathematics and Interdisciplinary Science, CAS.\n\nHehu Xie222LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (hhxie@lsec.cc.ac.cn) \u00a0\u00a0and \u00a0Fei Xu333Beijing Institute for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China (xufei@lsec.cc.ac.cn)\n###### Abstract\n\nA full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as the linear solver for solving boundary value problems. The optimality of the computational work is also proved. Compared with the existing multigrid methods which need the bounded second order derivatives of the nonlinear term, the proposed method only needs the Lipschitz continuation in some sense of the nonlinear term.\n\nKeywords. semilinear elliptic problem, full multigrid, multilevel correction, finite element method.\n\nAMS subject classifications. 65N30, 65N25, 65L15, 65B99.\n\n## 1 Introduction\n\nThe purpose of this paper is to study the multigird finite element method for semilinear elliptic problems. As we know, the multigrid and multilevel methods [3, 4, 5, 6, 9, 14, 15, 16, 21] provide optimal order algorithms for solving boundary value problems. The error bounds of the approximate solutions obtained from these efficient numerical algorithms are comparable to the theoretical bounds determined by the finite element discretization. In the past decade years, some researches about multigrid method for nonlinear elliptic problem are studied to improve the efficiency of nonlinear elliptic problem solving, i.e. [16, 22, 23]. The Newton iteration is adopted to linearize the nonlinear equation in these existing multigrid methods and then they need the bounded second order derivatives of the nonlinear terms. For more information, please refer to [10, 16, 22] and the references cited therein.\n\nRecently, a type of multigrid method with optimal efficiency for eigenvalue problems has been proposed in [12, 17, 18, 20]. The aim of this paper is to present a full multigrid method for solving semilinear elliptic problems based on the multilevel correction scheme [17, 18]. The main idea is to design a special low dimensional space to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. For the linearized elliptic problem, it is not necessary to solve the linear boundary value problem exactly in each correction step. Here, we only do some multigrid iteration steps for the linear boundary value problems. In this new version of multigrid method, solving semilinear elliptic problem will not be much more difficult than the multigrid scheme for the corresponding linear boundary value problems. Compared with the existing multigrid methods for the semilinear problem, our method only needs the Lipschitz continuation in some sense of the nonlinear term.\n\nAn outline of the paper goes as follows. In Section 2, we introduce the finite element method for the semilinear elliptic problem. A type of full multigrid method for the semilinear elliptic problem is given in Section 3. In Section 4, some numerical examples are provided to validate the efficiency of the proposed numerical method. Some concluding remarks are given in the last section.\n\n## 2 Discretization by finite element method\n\nIn this paper, the letter (with or without subscripts) is used to denote a constant which may be different at different places. For convenience, the symbols , and mean that , and . Let denote a bounded convex domain with Lipschitz boundary . We use the standard notation for Sobolev spaces and their associated norms and seminorms (see, e.g. [1]). For , we denote and , where is in the sense of trace. For simplicity, we use to denote and to denote in the rest of the paper.\n\nHere, we consider the following type of semilinear elliptic equation:\n\n {\u2212\u2207\u22c5(A\u2207u)+f(x,u)=g,in\u00a0\u03a9,u=0,on\u00a0\u2202\u03a9, (2.1)\n\nwhere is a symmetric positive definite matrix with , is a nonlinear function with respect to the second variable.\n\nThe weak form of the semilinear problem (2.1) can be described as: Find such that\n\n a(u,v)+(f(x,u),v)=(g,v),\u2200v\u2208V, (2.2)\n\nwhere\n\n a(u,v)=(A\u2207u,\u2207v). (2.3)\n\nObviously, is bounded and coercive on , i.e.,\n\n a(u,v)\u2264Ca\u2225u\u22251,\u03a9\u2225v\u22251,\u03a9\u00a0\u00a0\u00a0and\u00a0\u00a0\u00a0ca\u2225u\u222521,\u03a9\u2264a(u,u),\u2200u,v\u2208V. (2.4)\n\nThen we use the norm for any in this paper to replace the standard norm .\n\nIn order to guarantee the existence and uniqueness of the problem (2.2), we assume the nonlinear term satisfy the following assumption.\n\nAssumption A: The nonlinear function satisfies the convex and Lipschitz continuous conditions as follows\n\n {(f(x,w)\u2212f(x,v),w\u2212v)\u22650,\u00a0\u00a0\u00a0\u2200w\u2208V,\u00a0\u2200v\u2208V,(f(x,w)\u2212f(x,v),\u03d5)\u2264Cf\u2225w\u2212v\u22250\u2225\u03d5\u22251,\u00a0\u00a0\u00a0\u2200w\u2208V,\u00a0\u2200v\u2208V,\u00a0\u2200\u03d5\u2208V. (2.5)\n\nNow, we introduce the finite element method for semilinear elliptic problem (2.2). First we generate a shape regular decomposition of the computing domain into triangles or rectangles for , tetrahedrons or hexahedrons for (cf. [7, 8]). The mesh diameter describes the maximum diameter of all cells . Based on the mesh , we construct the finite element space . For simplicity, we set as the linear finite element space which is defined as follows\n\n Vh={vh\u2208C(\u03a9)\u00a0\u2223\u2223\u00a0vh|K\u2208P1,\u00a0\u00a0\u2200K\u2208Th}\u2229H10(\u03a9), (2.6)\n\nwhere denotes the linear function space.\n\nThe standard finite element scheme for semilinear equation (2.2) is: Find such that\n\n a(\u00afuh,vh)+(f(x,\u00afuh),vh)=(g,vh),\u2200vh\u2208Vh. (2.7)\n\nDenote a linearized operator by:\n\n (Lw,v)=(A\u2207w,\u2207v),\u00a0\u00a0\u2200w\u2208V,\u00a0\u2200v\u2208V.\n\nIn order to deduce the global prior error estimates, we introduce as follows:\n\n \u03b7a(Vh)=supf\u2208L2(\u03a9),\u2225f\u22250=1infvh\u2208Vh\u2225L\u22121f\u2212vh\u2225a.\n\nIt is easy to know that as (cf. [7, 8]).\n\nIn order to measure the error for the finite element approximations, we denote\n\n \u03b4h(u)=infvh\u2208Vh\u2225u\u2212vh\u2225a.\n\nFrom [16], we can give the following error estimates.\n\n###### Lemma 2.1.\n\nWhen Assumption A is satisfied, equations (2.2) and (2.7) are uniquely solvable and the following estimates hold\n\n \u2225u\u2212\u00afuh\u2225a \u2264 (1+C\u03b7a(Vh))\u03b4h(u), (2.8) \u2225u\u2212\u00afuh\u22250 \u2272 \u03b7a(Vh)\u2225u\u2212\u00afuh\u2225a. (2.9)\n###### Proof.\n\nFrom Theorem 6.1 in [16], we can know that problems (2.2) and (2.7) are uniquely solvable. Now, it is time to prove the error estimates. For this aim, we define the finite element projection operator by the following equation\n\n a(Phw,vh)=a(w,vh),\u00a0\u00a0\u00a0\u00a0\u2200w\u2208V,\u00a0\u2200vh\u2208Vh.\n\nIt is easy to know that and . Let us define in this proof. From (2.2), (2.5) and (2.7), we have\n\n a(Phu\u2212\u00afuh,wh) \u2264 a(Phu\u2212\u00afuh,wh)+(f(x,Phu)\u2212f(x,\u00afuh),wh) = a(Phu,wh)+(f(x,Phu),wh)\u2212(g,wh) = a(Phu\u2212u,wh)+(f(x,Phu)\u2212f(x,u),wh) = (f(x,Phu)\u2212f(x,u),wh) \u2264 Cf\u2225u\u2212Phu\u22250\u2225wh\u2225a.\n\nThen the following inequalities hold\n\n \u2225Phu\u2212\u00afuh\u2225a\u2264Cf\u2225u\u2212Phu\u22250\u2264Cf\u03b7a(Vh)\u2225u\u2212Phu\u2225a. (2.10)\n\nCombining (2.10) and the triangle inequality leads to the following estimates\n\n \u2225u\u2212\u00afuh\u2225a \u2264 \u2225u\u2212Phu\u2225a+\u2225Phu\u2212\u00afuh\u2225a (2.11) \u2264 \u03b4h(u)+Cf\u03b7a(Vh)\u2225u\u2212Phu\u2225a \u2264 (1+Cf\u03b7a(Vh))\u03b4h(u),\n\nwhich is the desired result (2.8). From (2.10) and the triangle inequality, we have\n\n \u2225u\u2212\u00afuh\u22250 \u2264 \u2225u\u2212Phu\u22250+\u2225Phu\u2212\u00afuh\u22250\u2264\u2225u\u2212Phu\u22250+C\u2225Phu\u2212\u00afuh\u2225a \u2264 C\u03b7a(Vh)\u2225u\u2212Phu\u2225a+Cf\u03b7a(Vh)\u2225u\u2212Phu\u2225a \u2264 (C+Cf)\u03b7a(Vh)\u2225u\u2212Phu\u2225a\u2264(C+Cf)\u03b7a(Vh)\u2225u\u2212\u00afuh\u2225a.\n\nThis is the desired result (2.9) and the proof is complete. \u220e\n\n## 3 Full multigrid method for semilinear elliptic equation\n\nIn this section, a full multigrid method for semilinear problems is proposed based on multilevel correction scheme in [17, 18]. The key point is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. In order to carry out the multigrid method, we first generate a coarse mesh with the mesh size and the linear finite element space is defined on the mesh . Then a sequence of triangulations of is determined as follows. Suppose (produced from by regular refinements) is given and let be obtained from via one regular refinement step (produce subelements) such that\n\n hk=1\u03b2hk\u22121,\u00a0\u00a0\u00a0\u00a0k=2,\u22ef,n, (3.1)\n\nwhere the positive number denotes the refinement index and larger than (always equals ). Based on this sequence of meshes, we construct the corresponding nested linear finite element spaces such that\n\n VH\u2286Vh1\u2282Vh2\u2282\u22ef\u2282Vhn. (3.2)\n\nDue to the convexity of the domain , the sequence of finite element spaces and the finite element space have the following relations of approximation accuracy\n\n \u03b7a(Vhk)\u22481\u03b2\u03b7a(Vhk\u22121),\u00a0\u00a0\u00a0\u00a0\u03b4hk(u)\u22481\u03b2\u03b4hk\u22121(u),\u00a0\u00a0\u00a0k=2,\u22ef,n. (3.3)\n\n### 3.1 One correction step\n\nIn order to design the full multigrid method, first we introduce one correction step in this subsection.\n\nAssume we have obtained an approximate solution . A correction step to improve the accuracy of the given approximation is designed as follows.\n\n###### Algorithm 3.1.\n\nOne Correction Step\n\n1. Define the following auxiliary boundary value problem: Find such that\n\n a(\u02c6u(\u2113+1)hk,vhk)=\u2212(f(x,u(\u2113)hk),vhk)+(g,vhk),\u2200vhk\u2208Vhk. (3.4)\n\nPerform multigrid iteration steps for the second order elliptic equation to obtain an approximate solution with the following error reduction rate\n\n \u2225\u02dcu(\u2113+1)hk\u2212\u02c6u(\u2113+1)hk\u2225a\u2264\u03b8\u2225u(\u2113)hk\u2212\u02c6u(\u2113+1)hk\u2225a, (3.5)\n\nwhere is used as the initial value for the multigrid iteration and is a fixed constant independent from the mesh size .\n\n2. Define a finite element space and solve the following semilinear elliptic equation: Find such that\n\n a(u(\u2113+1)hk,vH,hk)+(f(x,u(\u2113+1)hk),vH,hk)=(g,vH,hk),\u00a0\u2200vH,hk\u2208VH,hk. (3.6)\n\nIn order to simplify the notation and summarize the above two steps, we define\n\n u(\u2113+1)hk=SemilinearMG(VH,u(\u2113)hk,Vhk).\n\nThe error estimate of Algorithm 3.1 is studied in the following theorem.\n\n###### Theorem 3.1.\n\nAssume the given solution has the following estimate\n\n \u2225\u00afuhk\u2212u(\u2113)hk\u22250\u2272\u03b7a(VH)\u2225\u00afuhk\u2212u(\u2113)hk\u2225a. (3.7)\n\nAfter the one correction step defined by Algorithm 3.1, the resultant approximate solution has the following estimates\n\n \u2225\u00afuhk\u2212u(\u2113+1)hk\u2225a \u2264 \u03b3\u2225\u00afuhk\u2212u(\u2113)hk\u2225a, (3.8) \u2225\u00afuhk\u2212u(\u2113+1)hk\u22250 \u2264 C\u03b7a(VH)\u2225\u00afuhk\u2212u(\u2113+1)hk\u2225a, (3.9)\n\nwhere\n\n \u03b3:=(\u03b8+(1+\u03b8)C\u03b7a(VH))(1+C\u03b7a(VH)).\n###### Proof.\n\nFrom (2.5), (2.7) and (3.4), we have\n\n a(\u00afuhk\u2212\u02c6u(\u2113+1)hk,vhk)=(f(x,u(\u2113)hk)\u2212f(x,\u00afuhk),vhk) \u2264Cf\u2225\u00afuhk\u2212u(\u2113)hk\u22250\u2225vhk\u2225a\u2264C\u03b7a(VH)\u2225\u00afuhk\u2212u(\u2113)hk\u2225a\u2225vhk\u2225a,\u00a0\u2200vhk\u2208Vhk. (3.10)\n\nCombing (2.4) and (3.1) leads to\n\n \u2225\u00afuhk\u2212\u02c6u(\u2113+1)hk\u2225a\u2264C\u03b7a(VH)\u2225\u00afuhk\u2212u(\u2113)hk\u2225a. (3.11)\n\nAfter performing multigrid iteration steps, from (3.5) and (3.11), the following estimates hold\n\n \u2225\u02dcu(\u2113+1)hk\u2212\u00afuhk\u2225a \u2264 \u2225\u02dcu(\u2113+1)hk\u2212\u02c6u(\u2113+1)hk\u2225a+\u2225\u02c6u(\u2113+1)hk\u2212\u00afuhk\u2225a (3.12) \u2264 \u03b8\u2225u(\u2113)hk\u2212\u02c6u(\u2113+1)hk\u2225a+\u2225\u02c6u(\u2113+1)hk\u2212\u00afuhk\u2225a \u2264 \u03b8\u2225u(\u2113)hk\u2212\u00afuhk\u2225a+\u03b8\u2225\u02c6u(\u2113+1)hk\u2212\u00afuhk\u2225a+\u2225\u02c6u(\u2113+1)hk\u2212\u00afuhk\u2225a \u2264 (\u03b8+(1+\u03b8)C\u03b7a(VH))\u2225\u00afuhk\u2212u(\u2113)hk\u2225a.\n\nNote that the semilinear elliptic problem (3.6) can be regarded as a finite dimensional approximation of the semilinear elliptic problem (2.7). Let denotes the finite element projection operator which is defined as follows\n\n a(PH,hkw,vH,hk) = a(w,vH,hk),\u00a0\u00a0\u00a0\u00a0\u2200w\u2208V,\u00a0\u2200vH,hk\u2208VH,hk.\n\nSince and , it is obvious that and\n\n \u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a = infvH,hk\u2208VH,hk\u2225\u00afuhk\u2212vH,hk\u2225a (3.13) \u2264 \u2225\u00afuhk\u2212\u02dcu(\u2113+1)hk\u2225a, \u2225\u00afuhk\u2212PH,hk\u00afuhk\u22250 \u2264 C\u03b7a(VH,hk)\u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a (3.14) \u2264 C\u03b7a(VH)\u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a.\n\nLet us define in this proof. Based on problems (2.7) and (3.6), the following estimates hold\n\n a(PH,hk\u00afuhk\u2212u(\u2113+1)hk,whk) (3.15) \u2264 a(PH,hk\u00afuhk\u2212u(\u2113+1)hk,whk)+(f(x,PH,hk\u00afuhk)\u2212f(x,u(\u2113+1)hk),whk) = a(PH,hk\u00afuhk,wh)+(f(x,PH,hk\u00afuhk),whk)\u2212(g,whk) = a(PH,hk\u00afuhk\u2212\u00afuhk,whk)+(f(x,PH,hk\u00afuhk)\u2212f(x,\u00afuhk),whk) = (f(x,PH,hk\u00afuhk)\u2212f(x,\u00afuhk),whk)\u2264Cf\u2225\u00afuhk\u2212PH,hk\u00afuhk\u22250\u2225whk\u2225a.\n\nFrom (3.14) and (3.15), we have\n\n \u2225PH,hk\u00afuhk\u2212u(\u2113+1)hk\u2225a \u2264 Cf\u2225\u00afuhk\u2212PH,hk\u00afuhk\u22250 (3.16) \u2264 C\u03b7a(VH)\u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a.\n\nCombining (3.13), (3.16) and triangle inequality leads to the following inequalities\n\n \u2225\u00afuhk\u2212u(\u2113+1)hk\u2225a \u2264 \u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a+\u2225PH,hk\u00afuhk\u2212u(\u2113+1)hk\u2225a (3.17) \u2264 (1+C\u03b7a(VH))\u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a \u2264 (1+C\u03b7a(VH))\u2225\u00afuhk\u2212\u02dcu(\u2113+1)hk\u2225a.\n\nThis is the desired result (3.8). From (3.15) and the triangle inequality, we have the following estimates\n\n \u2225\u00afuhk\u2212u(\u2113+1)hk\u22250 \u2264 \u2225\u00afuhk\u2212PH,hk\u00afuhk\u22250+\u2225PH,hk\u00afuhk\u2212u(\u2113+1)hk\u22250 (3.18) \u2264 \u2225\u00afuhk\u2212PH,hk\u00afuhk\u22250+C\u2225PH,hk\u00afuhk\u2212u(\u2113+1)hk\u2225a \u2264 C\u03b7a(VH)\u2225\u00afuhk\u2212PH,hk\u00afuhk\u2225a \u2264 C\u03b7a(VH)\u2225\u00afuhk\u2212u(\u2113+1)hk\u2225a,\n\nwhich is the desired result (3.9) and the proof is complete. \u220e\n\n###### Remark 3.1.\n\nThe proof of Theorem 3.1 shows that the structure of the low dimensional space plays the key role for Algorithm 3.1. This special space makes the finite element projection has both the accuracy as in (3.13) and the -norm estimate by duality argument as in (3.14).\n\n### 3.2 Full multigrid method\n\nIn this subsection, a full multigrid method is proposed based on the one correction step defined in Algorithm 3.1. This algorithm can reach the optimal convergence rate with the optimal computational complexity.\n\n###### Algorithm 3.2.\n\nFull Multigrid Scheme\n\n1. Solve the following semilinear problem in : Find such that\n\n a(uh1,vh1)+(f(x,uh1),vh1)=(g,vh1),\u2200vh1\u2208Vh1.\n2. For , do the following iteration:\n\n1. Set .\n\n2. For , do the following iterations\n\n u(\u2113+1)hk=SemilinearMG(VH,u(\u2113)hk,Vhk).\n3. Define .\n\nEnd Do\n\nFinally, we obtain an approximate solution .\n\n###### Theorem 3.2.\n\nAfter implementing Algorithm 3.2, we have the following error estimates for the final approximation\n\n \u2225\u00afuhn\u2212uhn\u2225a \u2264 2\u03b3p\u03b21\u2212\u03b3p\u03b2\u03b4hn(u), (3.19) \u2225\u00afuhn\u2212uhn\u22250 \u2264 C\u03b7a(VH)\u2225\u00afuhn\u2212uhn\u2225a, (3.20)\n\nunder the condition that the coarsest mesh size is small enough such that .\n\n###### Proof.\n\nFrom the first step of Algorithm 3.2, we have . Then from Lemma 2.1 and the proof of Theorem 3.1, the following estimates hold\n\n \u2225\u00afuh2\u2212uh2\u2225a = \u2225\u00afuh2\u2212u(p)h2\u2225a\u2264\u03b3p\u2225\u00afuh2\u2212u(0)h2\u2225a (3.21) = \u03b3p\u2225\u00afuh2\u2212uh1\u2225a=\u03b3p\u2225\u00afuh2\u2212\u00afuh1\u2225a. \u2225\u00af\u00af\u00afuh2\u2212uh2\u22250 \u2264 C\u03b7a(VH)\u2225\u00afuh2\u2212uh2\u2225a. (3.22)\n\nBased on (3.21), (3.22), Theorem 3.1 and recursive argument, the final approximate solution has the following error estimates\n\n \u2225\u00afuhn\u2212uhn\u2225a \u2264 \u03b3p\u2225\u00afuhn\u2212u(0)hn\u2225a=\u03b3p\u2225\u00afuhn\u2212uhn\u22121\u2225a \u2264 \u03b3p(\u2225\u00afuhn\u2212\u00afuhn\u22121\u2225a+\u2225\u00afuhn\u22121\u2212uhn\u22121\u2225a) \u2264 \u03b3p\u2225\u00afuhn\u2212\u00afuhn\u22121\u2225a+\u03b32p(\u2225\u00afuhn\u22121\u2212\u00afuhn\u22122\u2225a+\u2225\u00afuhn\u22122\u2212uhn\u22122\u2225a) \u2264 n\u22121\u2211k=1\u03b3kp\u2225\u00afuhn\u2212k+1\u2212\u00afuhn\u2212k\u2225a \u2264 n\u22121\u2211k=1\u03b3kp(\u2225\u00afuhn\u2212k+1\u2212u\u2225a+\u2225u\u2212\u00afuhn\u2212k\u2225a) \u2264 2n\u22121\u2211k=1\u03b3kp\u03b4hn\u2212k(u)\u22642n\u22121\u2211k=1\u03b3kp\u03b2k\u03b4hn(u)\u22642\u03b3p\u03b21\u2212\u03b3p\u03b2\u03b4hn(u),\n\nwhich is just the desired result (3.19). The second result (3.20) can be proved by the similar argument in the proof of Theorem 3.1 and the proof is complete. \u220e\n\n###### Corollary 3.1.\n\nFor the final approximation obtained by Algorithm 3.2, we have the following estimates\n\n \u2225u\u2212uhn\u2225a \u2272 \u03b4hn(u), (3.23) \u2225u\u2212uhn\u22250 \u2272 \u03b7a(VH)\u03b4hn(u). (3.24)\n###### Proof.\n\nThis is a direct consequence of the combination of Lemma 2.1 and Theorem 3.2. \u220e\n\n### 3.3 Estimate of the computational work\n\nIn this subsection, we turn our attention to the estimate of computational work for the full multigrid method defined in Algorithm 3.2. It will be shown that the full multigrid method makes solving the semilinear elliptic problem almost as cheap as solving the corresponding linear boundary value problems.\n\nFirst, we define the dimension of each level finite element space as . Then we have\n\n Nk\u2248(1\u03b2)d(n\u2212k)Nn,\u00a0\u00a0\u00a0k=1,2,\u22ef,n. (3.25)\n\nThe computational work for the second step in Algorithm 3.2 is different from the linear elliptic problems [4, 14, 15, 16, 21]. In this step, we need to solve a semilinear elliptic problem (3.6). Always, some type of nonlinear iteration method (fixed-point iteration or Newton type iteration) is adopted to solve this low dimensional semilinear elliptic problem. In each nonlinear iteration step, it is required to assemble the matrix on the finite element space () which needs the computational work . Fortunately, the matrix assembling can be carried out by the parallel way easily in the finite element space since it has no data transfer.\n\n###### Theorem 3.3.\n\nAssume we use computing-nodes in Algorithm 3.2, the semilinear elliptic solving in the coarse spaces () and need work and , respectively, and the work of the multigrid iteration for the boundary value problem in each level space is for . Let denote the nonlinear iteration times when we solve the semilinear elliptic problem (3.6). Then in each computational node, the work involved in Algorithm 3.2 has the following estimate\n\n Total\u00a0work = O((1+\u03d6\u03d1)Nn+MHlogNn+Mh1). (3.26)\n###### Proof.\n\nWe use to denote the work involved in each correction step on the -th finite element space . From the definition of Algorithm 3.2, we have the following estimate\n\n Wk = O(Nk+MH+\u03d6Nk\u03d1). (3.27)\n\nBased on the property (3.25), iterating (3.27) leads to\n\n Total work = (3.28) = O(n\u2211k=2(1+\u03d6\u03d1)Nk+(n\u22121)MH+Mh1) = O(n\u2211k=2(1\u03b2)d(n\u2212k)(1+\u03d6\u03d1)Nn+MHlogNn+Mh1) = O((1+\u03d6\u03d1)Nn+MHlogNn+Mh1).\n\nThis is the desired result and we complete the proof. \u220e\n\n###### Remark 3.2.\n\nSince we always have a good enough initial solution in the second step of Algorithm 3.1, then solving the semilinear elliptic problem (3.6) never needs many nonlinear iterations. In this case, the complexity in each computational node will be provided and","date":"2021-01-24 22:54:25","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\": 0.8257136344909668, \"perplexity\": 496.5394967091923}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703557462.87\/warc\/CC-MAIN-20210124204052-20210124234052-00390.warc.gz\"}"} | null | null |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<title>Localization - Germany</title>
<style type="text/css">
/*margin and padding on body element
can introduce errors in determining
element position and are not recommended;
we turn them off as a foundation for YUI
CSS treatments. */
body {
margin:0;
padding:0;
}
</style>
<link rel="stylesheet" type="text/css" href="../../build/fonts/fonts-min.css" />
<link rel="stylesheet" type="text/css" href="../../build/calendar/assets/skins/sam/calendar.css" />
<script type="text/javascript" src="../../build/yahoo-dom-event/yahoo-dom-event.js"></script>
<script type="text/javascript" src="../../build/calendar/calendar-min.js"></script>
<!--there is no custom header content for this example-->
</head>
<body class="yui-skin-sam">
<h1>Localization - Germany</h1>
<div class="exampleIntro">
<p>Calendar provides configuration properties that can be used to change the Calendar's various data labels, when the Calendar is used in different locales. This example shows how to provide locale specific labels for month and weekday names, as well as how to configure the expected format of any date strings passed in to the Calendar. It uses Germany as an example locale</p>
</div>
<!--BEGIN SOURCE CODE FOR EXAMPLE =============================== -->
<div id="cal1Container"></div>
<script type="text/javascript">
YAHOO.namespace("example.calendar");
YAHOO.example.calendar.init = function() {
YAHOO.example.calendar.cal1 = new YAHOO.widget.Calendar("cal1","cal1Container",
{ LOCALE_WEEKDAYS:"short",
START_WEEKDAY: 1,
MULTI_SELECT: true
} );
// Correct formats for Germany: dd.mm.yyyy, dd.mm, mm.yyyy
YAHOO.example.calendar.cal1.cfg.setProperty("DATE_FIELD_DELIMITER", ".");
YAHOO.example.calendar.cal1.cfg.setProperty("MDY_DAY_POSITION", 1);
YAHOO.example.calendar.cal1.cfg.setProperty("MDY_MONTH_POSITION", 2);
YAHOO.example.calendar.cal1.cfg.setProperty("MDY_YEAR_POSITION", 3);
YAHOO.example.calendar.cal1.cfg.setProperty("MD_DAY_POSITION", 1);
YAHOO.example.calendar.cal1.cfg.setProperty("MD_MONTH_POSITION", 2);
// Date labels for German locale
YAHOO.example.calendar.cal1.cfg.setProperty("MONTHS_SHORT", ["Jan", "Feb", "M\u00E4r", "Apr", "Mai", "Jun", "Jul", "Aug", "Sep", "Okt", "Nov", "Dez"]);
YAHOO.example.calendar.cal1.cfg.setProperty("MONTHS_LONG", ["Januar", "Februar", "M\u00E4rz", "April", "Mai", "Juni", "Juli", "August", "September", "Oktober", "November", "Dezember"]);
YAHOO.example.calendar.cal1.cfg.setProperty("WEEKDAYS_1CHAR", ["S", "M", "D", "M", "D", "F", "S"]);
YAHOO.example.calendar.cal1.cfg.setProperty("WEEKDAYS_SHORT", ["So", "Mo", "Di", "Mi", "Do", "Fr", "Sa"]);
YAHOO.example.calendar.cal1.cfg.setProperty("WEEKDAYS_MEDIUM",["Son", "Mon", "Die", "Mit", "Don", "Fre", "Sam"]);
YAHOO.example.calendar.cal1.cfg.setProperty("WEEKDAYS_LONG", ["Sonntag", "Montag", "Dienstag", "Mittwoch", "Donnerstag", "Freitag", "Samstag"]);
YAHOO.example.calendar.cal1.select("1.10.2009-8.10.2009");
YAHOO.example.calendar.cal1.cfg.setProperty("PAGEDATE", "10.2009");
YAHOO.example.calendar.cal1.render();
}
YAHOO.util.Event.onDOMReady(YAHOO.example.calendar.init);
</script>
<div style="clear:both" ></div>
<!--END SOURCE CODE FOR EXAMPLE =============================== -->
</body>
</html>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,030 |
Q: GTM, Event - Click, Target - Links, GA Events - Empty I have the following code:
<body>
<noscript>
<iframe src="//www.googletagmanager.com/ns.html?id=GTM-XXXXXX" height="0" width="0" style="display:none;visibility:hidden"></iframe>
</noscript>
<script>
(function(w,d,s,l,i){
w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);
})
(window,document,'script','dataLayer','GTM-XXXXXX');
</script>
...
<a class="filelink" href="files/Client.zip">Client</a>
...
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.4/jquery.min.js"/>
</body>
I added the following (GTM):
Problem that Events in Google Analystics are empty (including Real-Time). Other functions work correctly.
A: You're very close!
Because you have Wait for Tags checked, you'll need to specify on what pages your want your trigger to fire on e.g. Page URL matches RegEx .* for all pages (if that's what you want to do), and then put your Click URL matches RegEx .(7z|zip)$ as your condition in the "Fire On" step.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,944 |
Handelsmesse (også kaldet messe) er en udstilling, hvor en større gruppe producenter og forhandlere udstiller varer, og indgår handelsaftaler. Messer er typisk begrænset til en bestemt faggruppe, målgruppe eller tema. De afholdes ofte i haller som f.eks. Forum og Øksnehallen i København , eller i deciderede udstillingscentre som Bellacentret, eller som Messecenter Herning, der er Skandinaviens største messe- og udstillingscenter med over 100.000 m² udstillingsareal.
Messer i historisk perspektiv
Begrebet "messe" stammer fra det katolske Kermesse, en festligholdelse af en kirkes indvielsesdag. Ved denne lejlighed strømmede folk til kirken fra nær og fjern – og det benyttede de handlende sig af. De stillede deres boder op omkring kirken og falbød deres varer til kirkegængerne. Byer som Leipzig og Frankfurt i Tyskland fik tidligt særlige privilegier som messebyer. Privilegier, som har holdt ved siden, idet begge byer stadig er vigtige messebyer med meget store haller til messer og udstillinger.
Typer af messer
Der findes flere typer af messer:
Fagmesser. Fagmesser henvender sig til en bestemt faggruppe. Som eksempel kan nævnes Agromek i Herning, der henvender sig til landbruget.
Lukkede fagmesser. Lukkede fagmesser har kun adgang for en bestemt type gæster. Det kan f.eks. være indbudte gæster eller indkøbere inden for en bestemt branche.
Publikumsmesser. Publikumsmesser er rettet imod forbrugerne. Som eksempel kan nævnes messer som feriemesser, biludstillinger samt mindre messer med lokale håndværkere og erhvervsdrivende.
Se også
Champagnemesser
Messe
Massemedier | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,197 |
{"url":"http:\/\/math.stackexchange.com\/questions\/140155\/help-to-find-all-of-the-eigenvalues-of-the-operator-tl20-1-rightarrow-l","text":"# Help to find all of the eigenvalues of the operator $T:L^2([0,1]) \\rightarrow L^2([0,1])$\n\nDefine $K: [0,1] \\times [0,1]\\rightarrow \\mathbb{R}$ by\n\n$$K(x,y) =\\begin{cases} (1-x)y &\\text{if } 0 \\le t \\le x\\\\ (1-y)x& \\text{if }x \\le y \\le 1\\end{cases}$$\n\nAlso, Consider the operator $T: L^2([0,1]) \\rightarrow L^2([0,1])$ defined by $$Tf(x) = \\int_0^1 K(x,y)f(y) \\, dy$$\n\nHow to prove that if $Tf = \\lambda f$ for some $\\lambda \\neq 0$, then $f \\in C^\\infty([0,1])$, $f(0)=f(1)=0$ and $\\lambda f'' = f$? Also, what are the eigenvalues of $T$?\n\n-\n$t=y{}{}{}{}{}$? \u2013\u00a0 Jonas Meyer May 3 '12 at 0:06\nSuggestions for part of the problem: Write out explicitly what $Tf(x)$ is. Observe that $x\\mapsto \\int_a^x g(y)dy$ is continuous when $g$ is integrable. Conclude that $f$ is continuous. Then proceed by induction, using the Fundamental Theorem of Calculus to show that if $f$ is in $C^k$, then it is in $C^{(k+1)}$. (Evaluating $f(0)$ and $f(1)$ is trivial.) (It could probably be made easier by showing that $\\lambda f'' = f$ in 3 steps, and then the fact that $f\\in C^{\\infty}$ would follow easily.) \u2013\u00a0 Jonas Meyer May 3 '12 at 0:19\nYeah, after showing that $f$ is continuous, the Fund. Thm. of Calculus allows $\\lambda f''$ to be computed directly. But maybe I slipped up, because I got $\\lambda f'' = -f$. \u2013\u00a0 Jonas Meyer May 3 '12 at 0:34\nI suggest that you write out explicitly what $Tf(x)$ is, and suppose that $\\lambda f = Tf$. Since functions like $x\\mapsto \\int_a^x g(y)\\,dy$ are continuous when $g$ is integrable, the right hand side of the equation $\\lambda f = Tf$ represents a continuous function. Since $\\lambda\\neq 0$, this means that $f$ is continuous.\nNext you can apply the Fundamental Theorem of Calculus, which says that if $g$ is continuous, then the derivative of $x\\mapsto \\int_a^x g(y)dy$ is $g(x)$. This allows you compute the derivatives of $Tf$. Differentiating the equation $\\lambda f=Tf$ twice yields $\\lambda f'' = -f$. In particular, this makes it straightforward to see that $f$ is in $C^\\infty$.\nIt also allows you to solve a second order homogeneous linear differential equation to find all possibilities for $f$, namely $f(x)=A\\sin(x\/\\sqrt\\lambda)+B\\cos(x\/\\sqrt \\lambda)$ for constants $A$ and $B$. Using the boundary values of $f$ allows you to narrow the possibilities and find all candidates for $\\lambda$.","date":"2014-04-16 04:45:41","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\": 0.963044285774231, \"perplexity\": 76.77169512634737}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-15\/segments\/1397609521512.15\/warc\/CC-MAIN-20140416005201-00574-ip-10-147-4-33.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
\label{sec:introduction}
While it has been established that neutrinos are massive due to the discovery of neutrino oscillations \cite{Fukuda:1998mi,Ahmad:2002jz}, their precise properties, however, are still under active investigation.
An analogous (and even more perplexing) story applies to dark matter (DM) whose nature remains unknown despite the ever-growing evidence for its existence from the astrophysical observables.
An intriguing possibility regarding these mysteries would be to introduce right-handed neutrinos (RHNs), which can address not only the neutrino mass and DM but also their potential roles in the inflation and baryon asymmetry production \cite{seesaw,Asaka:2005an,Fukugita:1986hr,Asaka:2005pn,Canetti:2012kh,Ibe:2015nfa,kk2}.
We, in this article, seek a possibility for a sterile RHN to make up the whole DM in the Universe and, in particular, propose the new production mechanism of sterile RHN DM through the mixing among RHNs.
This is in contrast to the conventional mechanisms requiring the sterile RHN DM to couple to left-handed neutrinos which suffer from the severe tension between the bounds from the X-ray observation and the small-scale structure data \cite{Dodelson:1993je,Shi:1998km,Tremaine:1979we,Boyarsky:2005us,Horiuchi:2013noa,ir2017}. These constraints, however, heavily depend on their production mechanisms and many possibilities have been explored to produce the desired DM abundance in addition to the conventional nonresonant/resonant active-sterile neutrino conversion mechanisms \cite{Asaka:2006ek,Bezrukov:2009th,kenji,Anisimov:2008gg,Adhikari:2016bei,Asaka:2005pn,Canetti:2012kh,Ibe:2015nfa,kk2}.
Our scenario is distinguishable from such alternative scenarios in that it still uses a simple oscillation between the thermal heavy RHN and DM, and yet it demonstrates the totally different features from the Dodelson-Widrow scenario such as the occurrence of the production peak above/around the electroweak which is of great advantage in circumventing the Lyman-$\alpha$ bounds due to the redshifting of DM momentum.
After outlining our setup in Sec. II, we illustrate our scenario in Sec. III for a simple example of two RHNs. Section IV then demonstrates the concrete realization where we introduce a RHN mass matrix whose off-diagonal term can arise from the scalar field vacuum expectation value so that we can explain the light neutrino masses by the seesaw mechanism while avoiding the tight X-ray bounds. Section V is devoted to the discussion/conclusion.
\section{Setup}
\label{sec:setup}
The Lagrangian we study is the standard model (SM) with three Majorana RHNs, given by ${\cal L} = {\cal L}_{\rm SM} + {\cal L}_N$ where ${\cal L}_{\rm SM}$ is the SM Lagrangian and ${\cal L}_N$ reads
\begin{eqnarray}
\overline \nu_R i\slashed{\partial} \nu_R -
\left[
\nu_R^{c}{}^T y_\nu L H - \frac{1}{2}\nu_R^{c}{}^T{\cal M}_N\nu_R^c + {\rm H.c.}
\right], \label{eq:lagrangian}
\end{eqnarray}
where $H, L$, and $\nu_R$ are, respectively, the Higgs doublet, lepton doublet and RHN. For simplicity, we concentrate on the case of three RHNs.
We begin with the field basis where $y_\nu y_\nu^\dagger$ is diagonal, denoted as $y_\nu^{\rm diag}$ so that $y_\nu^{\rm diag} y_\nu^{{\rm diag}\dagger}$ becomes a $3\times 3$ diagonal matrix. ${\cal M}_N$
is, in general, a nondiagonal matrix, which we call the interaction basis.
A familiar seesaw mechanism for the mass of left-handed neutrino $\nu_L$ reads, in terms of its Dirac mass $m_D^{\rm diag} = y_\nu^{\rm diag} v$ with $v=\langle H\rangle$, ${\cal M}_\nu = m_D^{\rm diag} {}^T {\cal M}_N^{-1} m_D^{\rm diag}$ which can be diagonalized as ${\cal M}_\nu^{\rm diag} = U_L^T {\cal M}_\nu U_L$ ($U_L$ is the Pontecorvo-Maki-Nakagawa-Sakata matrix.\footnote{Throughout this article, we take the charged lepton Yukawa coupling to be diagonal.}).
The neutrino mass eigenstates are
\begin{eqnarray}
\left[
\begin{array}{c}
\nu_L\\
\nu_R^c
\end{array}
\right]
&=&
U
\left[
\begin{array}{c}
\nu\\
N^c
\end{array}
\right],
\quad
U \simeq
\left[
\begin{array}{cc}
1 & \theta^\dagger \\
-\theta & 1
\end{array}
\right]
\left[
\begin{array}{cc}
U_L & \\
& U_R^*
\end{array}
\right],
\label{eq:U}
\end{eqnarray}
where $\theta\equiv {\cal M}_N^{-1}m_D^{\rm diag}$ and $U_R$ is a unitary matrix defined to diagonalize ${\cal M}_N$ as ${\cal M}_N^{\rm diag}=U_R^\dagger {\cal M}_N U_R^*$.
By taking the rotation of Eq.~(\ref{eq:U}), the Yukawa coupling $y_\nu$ is in general a nondiagonal matrix while the neutrino masses, ${\cal M}_\nu$ and ${\cal M}_N$, are simultaneously diagonalized. We call this field basis the mass basis.
Thus, we obtain
\begin{eqnarray}
y_\nu^{\rm diag}y_\nu^{\rm diag}{}^\dagger
&=&
v^{-2}
\left[
U_R({\cal M}_N^{\rm diag})^{1/2}R({\cal M}_\nu^{\rm diag})^{1/2}
\right]\nonumber\\
&&\times
\left[
U_R({\cal M}_N^{\rm diag})^{1/2}R({\cal M}_\nu^{\rm diag})^{1/2}
\right]^\dagger,
\label{eq:yuk}
\end{eqnarray}
where $R$ is an arbitrary $3\times 3$ complex orthogonal matrix satisfying $R^TR=1$~\cite{Casas:2001sr}.
The mixing between $\nu_L$ and $N$ is then parametrized by $\Theta=\theta^\dagger U_R^*$, and
\begin{eqnarray}
\Theta^2 &\equiv&
\Theta^\dagger\Theta = ({\cal M}_N^{\rm diag})^{-1/2}R{\cal M}_\nu^{\rm diag}R^\dagger({\cal M}_N^{\rm diag})^{-1/2}.
\label{eq:active-sterile mixing}
\end{eqnarray}
The oscillations among RHNs can take place when their mass and interaction bases differ.
We, in the following discussions, consider three RHNs with their masses ${\cal M}_N^{\rm diag}={\rm diag}\{M_1,M_2,M_3\}$ and take $N_1$ as the lightest one so that it can play the role of DM. For the active neutrino masses, we parametrize ${\cal M}_\nu^{\rm diag} = {\rm diag}\{m_1,m_2,m_3\}$ for the normal hierarchy (NH), where $\Delta m_{21}^2 \equiv m_2^2-m_1^2 = (7.50^{+0.19}_{-0.17})\times 10^{-5}~{\rm eV}^2,
\Delta m_{31}^2 \equiv m_3^2-m_1^2 = (2.457^{+0.047}_{-0.047})\times 10^{-3}~{\rm eV}^2$
\cite{Gonzalez-Garcia:2015qrr}.
For the inverted hierarchy (IH), we take ${\cal M}_\nu^{\rm diag} = {\rm diag}\{m_3,m_1,m_2\}$ and $\Delta m_{32}^2 \equiv m_3^2-m_2^2 = (-2.449^{+0.048}_{-0.047})\times 10^{-3}~{\rm eV}^2$.
The lightest neutrino mass ($m_1$ for the NH case, and $m_3$ for the IH case) is taken as a free parameter.
In our discussions below, whenever it is not necessary to distinguish the mass orderings, $m_1$ refers to the lightest mass for brevity.
\section{DM production through RHN oscillation}
We now check if enough abundance of RHN DM $\nu_{R1}$ can be produced from the RHN oscillations. In our scenario, the heavy RHNs $\nu_{R2}$ and $\nu_{R3}$ explain the left-handed neutrino masses by the seesaw mechanism and they can have sizable neutrino Yukawa couplings to be in the thermal equilibrium at a sufficiently high temperature. $\nu_{R1}$, on the other hand, has a sufficiently small coupling to the SM species, so that its production is dominated by the conversion from heavier RHNs. For clarity of the following quantitative discussion, we focus on the $\nu_{R1}$ abundance produced only from its mixing with $\nu_{R2}$ because $\nu_{R3}$ plays the same role as $\nu_{R2}$ in producing $\nu_{R1}$.
The relevant reactions for the $\nu_{R2}$ thermalization are the scatterings caused by Yukawa interaction, $\nu_{R2} L \leftrightarrow t Q_3,~\nu_{R2} t \leftrightarrow L Q_3,~\nu_{R2} Q_3 \leftrightarrow L t$, those involving the gauge bosons, $\nu_{R2} V \leftrightarrow H L,~\nu_{R2} L \leftrightarrow H V,~\nu_{R2} H \leftrightarrow L V$ and the decay and inverse decay $\nu_{R2}\leftrightarrow LH$ [$Q_3 (t)$ is the left (right) handed top quark, and $V$ represents the $SU(2)_L$ and $U(1)_Y$ gauge bosons].
The Boltzmann equation for $\nu_{R1}$ \cite{Dolgov:2000ew} reads
\begin{eqnarray}
\frac{dn_{\nu_{R1}}}{dt} + 3Hn_{\nu_{R1}} = C_{\nu_{R1}}
\end{eqnarray}
where $C_{\nu_{R1}}$ represents the collision term integrated over the $\nu_{R1}$ momentum given by
\begin{eqnarray}
C_{\nu_{R1}} &\simeq& {\cal P}(\nu_{R2}\to\nu_{R1})(\gamma_{\nu_{R2}}^{\rm col}+\gamma_{\nu_{R2}}^{\rm ID}),\\
\gamma_{\nu_{R2}}^{\rm col} &=& \frac{T}{64\pi^4}\int^\infty_{s_{\rm min}} ds\hat\sigma\sqrt{s}K_1(\sqrt{s}/T),\\
\gamma_{\nu_{R2}}^{\rm ID} &=& \frac{M_2^2T}{\pi^2}\Gamma(\nu_{R2}\to LH)K_1(M_2/T).
\end{eqnarray}
Here ${\cal P}$ is the oscillation probability given by ${\cal P}(\nu_{R2}\to\nu_{R1}) = \frac{1}{2}\sin^22\theta_N$ ($\theta_N$ is the mixing angle between $\nu_{R1}$ and $\nu_{R2}$), $\Gamma(\nu_{R2}\to LH)\simeq (y_\nu y_\nu^\dagger)_{22}M_2/(8\pi)$ is the decay width, and $\hat\sigma$ is the reduced cross section for the $\nu_{R2}$ collisions with the kinematical cut $s_{\rm min}$ of the Mandelstam variable $s$, and $K_1$ is the modified Bessel function of the first kind.
\footnote{A factor 1/2 in ${\cal P}$ comes from averaging out the RHN oscillation because the oscillation timescale is much shorter than the collision timescale involving $\nu_{R2}$. More quantitatively, this averaging is justified for $T\lesssim 10^6$ GeV and/or $\Delta M^2\equiv M_2^2-M_1^2 \gtrsim 1~{\rm GeV}^2$ because $t_{\rm osc}/t_{\rm col} \sim({y_\nu^2}/{10^{-14}})({g^2}/{10^{-2}})({\rm GeV}^2/{\Delta M^2})({T}/{10^6~{\rm GeV}})^2$ where $g$ represents a gauge coupling for a relevant gauge interaction. As we will discuss later, $y_\nu^2$ of order $10^{-14}$ is required for GeV-scale RHN to reach the thermal equilibrium and it is automatically realized by enforcing the seesaw mechanism. The finite temperature effects on the RHN mixing angle $\theta_N$ are suppressed by the neutrino Yukawa couplings in our scenario and we simply consider a constant $\theta_N$ in our estimation. The cases when these approximations are not applicable are left for the future work.}
$\nu_{R1}$ is efficiently produced when the collision terms are large.\footnote{Some of collision terms, such as $\nu_R H\to LV$, possess the infrared divergences, which are regulated by the thermal mass of the propagator in our analysis for $T>T_C$ ($T_C$ is the critical temperature of the electroweak phase transition and we take $T_C = 160$ GeV) \cite{Pilaftsis:2003gt,Besak:2012qm,DOnofrio:2014rug,DOnofrio:2015gop}.}
Figure \ref{fig:rate} shows $\Gamma_i/H$ where $\Gamma_i$ represents the rescaled reaction rates for the process $i$ by taking the neutrino Yukawa coupling as unity (so that the curves can be easily scaled by multiplying the Yukawa coupling of interest).
For illustration purpose, we define the reaction rates $\Gamma_i=\gamma^{\rm col}_{\nu_{R2}}(i)/n_\gamma$, where $n_\gamma=2T^3/\pi^2$ is the radiation number density and $\gamma^{\rm col}_{\nu_{R2}}(i)$ are the collision terms involving the gauge bosons [$\gamma^{\rm col}_{\nu_{R2}}({\rm gauge})$] and the top quarks [$\gamma^{\rm col}_{\nu_{R2}}({\rm top})$]. The inverse decay rate is given by $\Gamma_{\rm ID}=\gamma^{\rm ID}_{\nu_{R2}}/n_\gamma$.
The figure shows the plots for $M_2=1$ GeV (solid) and for $M_2=1$ TeV (dashed), and we note that the inverse decay takes place only for the latter because of the kinematics, namely, the (inverse) decay is available only for $M_2\gtrsim M_h$ with $M_h$ being the Higgs mass. The actual reaction rates can be obtained by multiplying these rescaled reaction rates by $(y_\nu y_\nu^\dagger)_{22}$. We can see, from Fig. \ref{fig:rate}, that $N_2$ can reach the thermal equilibrium ($\Gamma_i/H \gtrsim 1$) when $(y_\nu y_\nu^\dagger)_{22}$ is larger than ${\cal O}(10^{-13})$ for $M_2=1 - 10^3$ GeV, which is also in the desired numerical range to explain the neutrino masses by the seesaw mechanism.
\begin{center}
\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{fig_rate.pdf}
\caption{
The ratios between the rescaled (i.e., divided by the Yukawa couplings) reaction rates and the Hubble parameter are shown (the actual reaction rates are obtained by multiplying the Yukawa couplings). The solid curves are for $M_2=1$ GeV and the dashed curves are for $M_2=1$ TeV.
}
\label{fig:rate}
\end{figure}
\end{center}
\vspace*{-7mm}
The produced $\nu_{R1}$ (interaction state) constitutes the DM $N_1$ (mass eigenstate), \footnote{The produced $\nu_{R1}$ is composed of $N_1$ and $N_2$ which propagate with different velocities. As the $\nu_{R1}$ energy gets redshifted, these two mass states are eventually well separated and thus $\nu_{R1}$ is expected to mostly develop the $N_1$ component as long as $M_1\ll M_2$, although the oscillation property may call for a careful study \cite{Akhmedov:2012uu}.} and the current $N_1$ relic number density can be estimated, in terms of the yield parameter $Y_{N_1}\equiv n_{N_1}/s$ ($s$ is the entropy density), by integrating the Boltzmann equation from $T_{\rm RH}$, the reheating temperature, to the current temperature $T=T_0$
\begin{eqnarray}
Y_{N_1}^0\equiv Y_{N_1}(T=0) = \int^\infty_0dT {\cal P}(\nu_{R2}\to\nu_{R1})\frac{\gamma_{\nu_{R2}}}{sHT},
\end{eqnarray}
where we have taken the limits $T_{\rm RH}\to\infty, T_0\to0$, and $\gamma_{\nu_{R2}}\equiv\gamma_{\nu_{R2}}^{\rm col}+\gamma_{\nu_{R2}}^{\rm ID}$.
The corresponding DM density can then be estimated in terms of the yield parameter
\begin{eqnarray}
\Omega_{N_1}h^2 &\simeq&
0.12
\left[
\frac{\sin^22\theta_N}{8.8\times10^{-3}}
\right]
\left[
\frac{|y_\nu^{\rm diag}|^2_{22}}{10^{-13}}
\right]
\left[
\frac{M_1}{\rm keV}
\right]
\left[
\frac{\tilde Y_{N_1}^0}{10^{12}}
\right],\nonumber\\
\end{eqnarray}
where $\tilde Y^0_{N_1}$ is the rescaled yield parameter, defined by factoring out the oscillation probability and the Yukawa coupling, $\tilde Y^0_{N_1} \equiv Y^0_{N_1}/({\cal P}(\nu_{R2}\to\nu_{R1}) (y_\nu y_\nu^\dagger)_{22})$.
We found the following simple fitting formula to grasp the characteristic features of the DM abundance in our scenario
\begin{eqnarray}
\log_{10} \tilde Y^0_{N_1}
&\simeq&
12.8 \quad (M_2\lesssim M_h)\nonumber\\
&\simeq&
13.3-(1/2)\log_{10}(M_2/M_h) \quad (M_2\gtrsim M_h).\nonumber\\
\end{eqnarray}
This behavior matches our expectation because, as emphasized in referring to Fig. \ref{fig:rate}, the most efficient production occurs when the production rate reaches maximal with respect to the Hubble expansion rate.
$\tilde Y^0_{N_1}$ is hence little dependent on $M_2$ when $M_2$ is smaller than $M_h$, because $N_2$ is dominantly produced via the inverse decay in this case, and thus the temperature at which the production rate becomes maximal is at $T\simeq M_h$.
For $M_2\gtrsim M_h$, on the other hand, the SM particles possess the thermal mass and the production rate becomes maximal around $T\sim M_2$, which leads to some power dependence of the yield parameter on $M_2$.
This is illustrated through a concrete example in the next section.
\section{Benchmark model}
\label{bm}
\begin{center}
\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{fig_BM.pdf}
\caption{
The $N_1$ relic abundance is shown as a function of $M_2$ by varying $M_1$ from 100 keV to 100 MeV. The solid and dashed curves show the NH and IH cases, respectively.
}
\label{fig:BM}
\end{figure}
\end{center}
We here discuss a possible realization of our scenario.
Let us begin with a simple mass matrix given by
\begin{eqnarray}
{\cal M}_N &=&
\left[
\begin{array}{ccc}
M_0&m&\\
m&M_2&\\
&&M_3
\end{array}
\right],
\end{eqnarray}
where $m$ and $M_0$ are taken to be $M_0\lesssim m \ll M_2, M_3$.
${\cal M}_N$ is then diagonalized as ${\cal M}_N^{\rm diag}={\rm diag}\{M_1,M_2,M_3\}$ with $M_1 \simeq M_0-m^2/M_2$ by using $U_R$ which reads
\begin{eqnarray}
U_R^* &\simeq&
\left[
\begin{array}{ccc}
1&\theta_N&\\
-\theta_N&1&\\
&&1
\end{array}
\right]
, \theta_N=m/M_2.
\label{eq:UR1}
\end{eqnarray}
The resultant $N_1$ abundance in the NH case is then given by
\begin{eqnarray}
\Omega_{N_1}h^2 &\simeq&
0.12
\left[
\frac{m_2}{0.01~{\rm eV}}
\right]
\left[
\frac{M_1}{\rm keV}
\right]
\left[
\frac{(m/5~{\rm GeV})^2}{M_2/100~{\rm GeV}}
\right]
\left[
\frac{\tilde Y_{N_1}^0}{10^{13}}
\right],\nonumber\\
\end{eqnarray}
while, in the IH case, $m_2$ should be replaced by $m_1$.
In the case of $M_0 \ll m^2/M_2$, we can take $\theta_N \simeq (M_1/M_2)^{1/2}$ due to $M_1\simeq m^2/M_2$, and thus we obtain
\begin{eqnarray}
\Omega_{N_1}h^2 &\simeq&
0.12
\left[
\frac{m_2}{0.01~{\rm eV}}
\right]
\left[
\frac{M_1}{0.52~{\rm MeV}}
\right]^2
\left[
\frac{\tilde Y_{N_1}^0}{10^{13}}
\right].
\label{eq:Oh2_NH}
\end{eqnarray}
For this simplified case, Fig. \ref{fig:BM} shows $\Omega_{N_1}h^2$ as a function of $M_2$ for various $M_1$ taken from 100 keV to 100 MeV in both the NH and IH cases which are depicted by solid and dashed curves, respectively.
\footnote{It should be noted that, in Fig.~\ref{fig:BM}, $t_{\rm osc}/t_{\rm col} \ll 1$ is achieved for $T\lesssim 10^6\times M_2$ even in the large $M_2$ region, so that a factor 1/2 in ${\cal P}$ by averaging out the RHN oscillation is justified.}
The green band in the figure indicates the observed value of the DM abundance given by $\Omega_{\rm DM}h^2=0.1197\pm0.0022$ \cite{Ade:2015xua}.
On the other hand, since $\Theta^2_{11}$ depends on $\theta_N$ and we need a relatively large $\theta_N$ for our scenario to work, the $N_1$ is subject to the X-ray constraint given by $\Theta^2_{11} \lesssim 10^{-5}({\rm keV}/M_1)^5$ \cite{Boyarsky:2005us}.
One may simply expect that the X-ray bound is easily circumvented because the Yukawa coupling of $\nu_{R1}$ can be negligibly small. We, however, point out that the light RHN can decay into the SM particles through its oscillation to a heavier RHN.
In our current setup, we obtain $\Theta^2_{11} = M_1^{-1} (m_1|R_{11}|^2 + m_2|R_{12}|^2 + m_3|R_{13}|^2),$ where $R_{ij}$ represents the $(i,j)$ entry of the $R$ matrix.
We can now take $R_{13} = 0$, since there is no mixing in this component, and $m_1=0$ is experimentally allowed.
However, since we have $|R_{12}|^2 = 1/(1 + (M_1/M_2)\cot^2\theta_N) \sim 1/2$ in our setup with $M_1 / M_2 \ll 1$, large $M_1$ is not allowed because of the X-ray constraint $\Theta^2_{11} \simeq m_2/(2M_1)\lesssim 10^{-5}({\rm keV}/M_1)^5$, where $m_2\simeq \sqrt{\Delta m^2_{21}}$ in the NH case, and $m_2$ is replaced by $m_1\simeq\sqrt{|\Delta m^2_{32}|}$ in the IH case.
One may naively expect that this decay of light RHN through a heavier RHN is suppressed by the hierarchically large mass ratio $M_1/M_2\ll 1$. If we did not enforce the simple seesaw mechanism to obtain the desirable light neutrino masses, this would be the case and the X-ray bound could be circumvented. We, however, in our model construction stick to the seesaw mechanism to account for the observed neutrino masses, which then inevitably increase $y_2$ if we choose a bigger value of $M_2$ to result in too big an X-ray decay rate. To keep the virtue of explaining the observed neutrino masses by the simple type-I seesaw mechanism and yet not to lose the attractive feature of simple RHN oscillation production, we now discuss a time-dependent RHN mixing to evade the X-ray constraint mentioned above.
Such a time-dependent RHN mixing can be achieved by utilizing the dynamics of a real scalar filed $\phi$.
Let us here consider the two flavor case for simplicity, but the extension to the three flavor system is straightforward.
In the two flavor case, we impose $Z_2$ symmetry under which $\nu_{R2}$ is even, while $\nu_{R1}$ and $\phi$ are odd.
\footnote{
Although our setup is similar to the idea discussed in Ref.~\cite{Berlin:2016bdv}, the DM production scenario is quite different, since our scenario does not rely on the oscillation between active and sterile neutrinos, and thus the temperature at which the production efficiently occurs takes rather a wide range, which can imprint an observable signature on the structure formation.
}
Now the mass matrix ${\cal M}_N$ in Eq. (\ref{eq:lagrangian}) is given by
\begin{eqnarray}
{\cal M}_N(\phi) =
\left[
\begin{array}{cc}
M_1 & \kappa \phi\\
\kappa \phi & M_2
\end{array}
\right]
\end{eqnarray}
in the interaction basis.
The dynamics of $\phi$ is governed by the equation of motion $\ddot{\phi} + 3H\dot{\phi} + V'(\phi) = 0$, where $V(\phi)$ is the potential that we take $V(\phi) \simeq (1/2)m_\phi^2\phi^2$.
For $m_\phi\ll 3H$, $\phi$ is almost constant, namely, $\phi \simeq \sqrt{2\rho_\phi}/m_\phi$ with $\rho_\phi$ the energy density of $\phi$, and when $H$ drops below $m_\phi$, $\phi$ starts to oscillate.
As we will see below, $m_\phi\ll 3H$ is always satisfied when the $N_1$ production rate is maximal, and thus we take $\phi$ as a constant in this regime.
The mixing angle between $\nu_{R1}$ and $\nu_{R2}$ is given by $\sin\theta_N \simeq \kappa \phi / M_2$ in the case that $M_1 \ll M_2$, and thus in the constant $\phi$ regime we obtain $\sin^22\theta_N \simeq 4\kappa^2 \rho_\phi/(m_\phi^2M_2^2)$, where the relevant $\theta_N$ is determined by $\rho_\phi(T_{\rm max})$ with $T_{\max}$ being the temperature at which the production rate becomes maximal, namely, $T_{\rm max} \sim T_c$ for $M_2\lesssim T_c$ and otherwise $T_{\rm max}\sim M_2$.
As mentioned above, $\phi$ is constant until it starts to oscillate, so we can take $\rho_\phi(T_{\rm max}) \simeq \rho_\phi(T_{\rm osc})$ with $T_{\rm osc}$ given by $m_\phi = 3H(T_{\rm osc})$.
Then, we obtain
\begin{eqnarray}
\sin^22\theta_N &\simeq&
0.3\times
\left[
\frac{r_g}{30}
\right]^{1/4}
\left[
\frac{\kappa}{10^{-9}}
\right]^2
\left[
\frac{m_\phi}{10^{-4}~{\rm eV}}
\right]^{-1/2}\nonumber\\
&&
\times
\left[
\frac{M_2}{100~{\rm GeV}}
\right]^{-2}
\left[
\frac{r}{10^{-4}}
\right],\label{eq:phi-mixing}
\end{eqnarray}
with $r_g= g_*(T_{\rm osc})/g_*(T_0)$, and $r=\rho_\phi^0/\rho_{\rm DM}$ with $\rho_\phi^0$ and $\rho_{\rm DM}$ being the energy density of $\phi$ and dark matter at the present.
Here we have used $g_*(T_0)\simeq3.36$.
We also require that $\phi$ never thermalizes by taking a sufficiently small $\kappa$ not to affect the big bang nucleosynthesis, which results in $\kappa^2 \lesssim M_2/M_{\rm Pl}$.
In addition, $m_\phi$ should be smaller than $H(T_{\rm max})$ in order for $\phi$ at $T_{\rm max}$ to be constant, where $H(T_{\rm max})\simeq 10^{-5}$ eV for $M_2 < T_c$ and $H(T_{\rm max})\simeq 10^{-5}\times (M_2/T_c)^2$ for $M_2 > T_c$.
It is worth mentioning that the dynamics of $\phi$ may be tied to inflationary models.
In particular, the condition of $\rho_\phi^0\ll\rho_{\rm DM}$ implies that the initial amplitude of $\phi$ is bounded
\begin{eqnarray}
\phi\lesssim 4\times10^{11}~{\rm GeV}\left(\frac{r_g}{30}\right)^{1/2}\left(\frac{r}{10^{-4}}\right)^{1/2}\left(\frac{10^{-4}~{\rm eV}}{m_\phi}\right)^{1/4}.
\end{eqnarray}
On the other hand, $\phi$ could be largely displaced from the origin during inflation and its oscillation at a later time possibly dominates the dark matter energy density, in an analogous manner to the Polonyi/moduli problem \cite{Coughlan:1983ci,Ellis:1986zt,Goncharov:1984qm}.
To suppress $\phi$ in our case, we may utilize a relatively strong coupling between $\phi$ and inflaton, which renders the adiabatic suppression of the amplitude of the coherent oscillations \cite{Linde:1996cx}.
Its actual dynamics, however, depends on the inflationary models and how $\phi$ couples to the inflaton, which we leave unspecified for the future work.
Finally let us comment on the $\theta_N$ at the present, which is relevant for the decay of $N_1$.
Below $T_{\rm osc}$, since $\rho_\phi$ drops as a matter energy density, we obtain
\begin{eqnarray}
\frac{\sin^22\theta_N(T_0)}{\sin^22\theta_N(T_{\rm osc})} \simeq 1.2\times 10^{-46}
\left[
\frac{r_g}{30}
\right]^{-1/4}
\left[
\frac{m_\phi}{10^{-4}~{\rm eV}}
\right]^{-3/2},
\end{eqnarray}
and therefore a sufficiently small mixing to avoid the X-ray constraint can be achieved.
\section{Discussion/Conclusion}
Before concluding our discussions, let us briefly point out another
potentially interesting production mechanism: the production of $N_1$
from a heavier RHN decay. We can consider the decay of $N_2$ (and/or
$N_3$) which is thermally decoupled while it is relativistic
(otherwise $N_2$ number density would be too small due to the
Boltzmann suppression). $N_1$ abundance then can be estimated as
\begin{eqnarray}
\Omega_{N_1}h^2
&\simeq& 10^{-10}
\left[
\frac{\Theta^2_{11}}{10^{-12}}
\right]
\left[
\frac{M_1}{10~{\rm keV}}
\right]
\left[
\frac{g_*(T_0)}{g_*(T_{\rm FO})}
\right]
\end{eqnarray}
where we used the branching fraction of $N_2$ decay for the process
$N_2\to N_1+$(mesons, leptons), ${\rm Br}(N_2\to N_1)\simeq \Gamma(N_2
\to N_1)/\Gamma(N_2 \to SM) \simeq M_2 \Theta^2_{11}\Theta^2_{22}/
M_2 \Theta^2_{22} \simeq \Theta^2_{11}$, and the ratio of $g_*$
accounts for the change in the effective degrees of freedom from the
$N_2$ freeze-out epoch to the present time. This production
contribution is hence subdominant compared with RHN oscillation
production in the parameter region of our interest.
Let us next mention the small-scale structure constraints applicable to our scenario. We here discuss the Lyman-$\alpha$ forest constraints which can give the lower limit on the DM mass from the DM free streaming scale $\lambda_{FS}\sim 1 ~\mbox{Mpc} ( {\rm keV}/{M_1}) ({\langle p/T \rangle}/{3.15})$ \cite{kev01}.
Too large a free streaming scale can be excluded due to the suppression of small-scale structure formation.
The average momentum of $N_1$ produced by the nonresonant oscillation of thermalized $N_2$ can be estimated as $\langle p_1\rangle \sim 2.8T$, analogous to the conventional (nonresonant) active-sterile oscillation scenario. Taking account of momentum redshifting by a factor $(g_*(T_{N_2\rightarrow N_1})/g_*(T\ll {\rm MeV}))^{-1/3}$ due to the change in the effective
degrees of freedom, Lyman-$\alpha$ data leads to the RHN DM mass bound $M_1 \gtrsim 10 $ keV for our scenario \cite{ir2017} (when $N_2\rightarrow N_1$ occurs most efficiently before the QCD phase transition which is the case for the parameter range discussed so far). Such a DM mass range can be realized in our scenario as explicitly demonstrated through the concrete examples in the last section while being compatible with both the right relic abundance and seesaw mechanism.
Among the possible extensions of our DM scenarios, we plan to study the leptogenesis as well as the neutrino observables such as the neutrinoless double beta decay in our future work. For instance, even though we have focused on the DM production in this article, the neutrino Yukawa couplings in our model can be further constrained by seeking the production of desirable baryon asymmetry in the Universe. The realization of leptogenesis when $N_2$ and $N_3$ are heavy enough and/or are degenerate in their masses with sufficient $CP$ violations \cite{Fukugita:1986hr,Asaka:2005pn,Pilaftsis:2003gt} will be explored in our forthcoming paper. The $CP$ phases in the neutrino Yukawa couplings are of great importance not only for the leptogenesis but also for the DM production in our scenario, and the presented production mechanism for the RHN DM could uncover a new connection between DM and leptogenesis to bring considerable opportunities for subsequent studies.
\begin{acknowledgments}
This work was supported by IBS under the project code IBS-R018-D1.
We thank A. Kamada, A. Merle and T. Asaka for useful discussions and, in particular, the anonymous referee for the constructive suggestions.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,208 |
{"url":"http:\/\/math.stackexchange.com\/questions\/130950\/free-groups-unique-up-to-unique-isomorphism","text":"# Free groups: unique up to unique isomorphism\n\nA free group $F_S$ over a set $S$ is unique up to unique isomorphism. After reading this answer here I think this means that if $F^\\prime_S$ is another free group over $S$ then there exists exactly one isomorphism $\\varphi : F_S \\to F_S^\\prime$ such that $\\varphi \\circ i = i^\\prime$ where $i: S \\to F_S$ and $i^\\prime : S \\to F^\\prime_S$ are the inclusions.\n\nWhy is uniqueness of the isomorphism interesting at all? Wouldn't it be good enough to know that all free groups over $S$ are isomorphic to define free groups?\n\n-\nWouldn't it be enough for what? \u2013\u00a0 Mariano Su\u00e1rez-Alvarez Apr 12 '12 at 17:20\n@MarianoSu\u00e1rez-Alvarez Enough to define what a free group is. \u2013\u00a0 Rudy the Reindeer Apr 12 '12 at 17:20\nBut the definition of free groups is completely independent of the fact that they are unique up to unique isomorphism: the latter is a property that one proves after we define what a free group i and even after we prove that they actually exist. \u2013\u00a0 Mariano Su\u00e1rez-Alvarez Apr 12 '12 at 17:23\nI think he is asking why \"unique up to unique isomorphism\" is a property worth talking about. I'm not really sure myself(though I've been told it is an important property). Mr. Kent, can you verify if this is what you're asking? \u2013\u00a0 John Stalfos Apr 12 '12 at 18:12\n@JohnStalfos Thank you, I'm asking both: what is means and why it's worth talking about. \u2013\u00a0 Rudy the Reindeer Apr 12 '12 at 19:02\n\nOne reason you are interested in \"unique up to unique isomorphism\" is that it makes things more \"canonical.\"\n\nConsider for example the following true fact: every $n$-dimensional vector space over $\\mathbb{R}$ is isomorphic to $\\mathbb{R}^n$.\n\nHowever, except for $n=0$, the isomorphism is neither unique nor \"canonical\": if I go home and do computations based on my favorite isomorphism and I tell you the answer, and you go home and you do your computations based on your favorite isomorphism, and then we come back tomorrow and describe our results, in order to translate one result into \"the language of the other\" we need to find out what my favorite isomorphism is, what your favorite isomorphism is, and perform the entire translations in order to compare \"my\" translation into $\\mathbb{R}^n$ with yours and find out if we are both correct.\n\nHowever, when there is a canonical choice of isomorphism, then we can simply both go home and translate (via this unique isomorphism), and then present the results the next day. They must match, because there is essentially only one way to translate.\n\n(Canonicity is very useful; for instance, that is one reason why, still talking about linear algebra, the isomorphism in finite dimension between a vector space and its double dual is so much more important than the isomorphism between a vector space and its dual. The former is canonical, while the latter is not.)\n\nFrom a point of view of category theory, uniqueness up to unique isomorphism allows for easy functorial properties to be derived, whereas merely isomorphic means a lot more book-keeping is needed, and it may be impossible to state a \"coordinate-free\" functorial property (where I'm thinking of 'coordinate-free' somewhat fuzzily to refer to not having to invoke specific, arbitrarily chosen isomorphisms to state or prove them).\n\n-\nHi @Arturo. I was wondering if you would tell me whether my understanding is correct: If e.g. we're in the category of sets and $A$ is an initial object in Set then it's unique up to isomorphism which means that if $B$ is another initial object then $A$ and $B$ are isomorphic? That is, any two initial objects in a category are isomorphic. Thank you a lot! \u2013\u00a0 Rudy the Reindeer Apr 17 '12 at 7:42\nI think the answer is yes. \u2013\u00a0 Rudy the Reindeer Apr 17 '12 at 14:04\n@ClarkKent: Sorry, I didn't see the question. Yes, in any category, two initial objects are isomorphic via a unique isomorphism: if $I$ and $I'$ are both initial, then there is a unique map $f\\colon I\\to I'$ (because $I$ is initial), a unique map $g\\colon I'\\to I$ (because $I'$ is initial), and so $f\\circ g\\colon I'\\to I'$ must be the unique map $I'\\to I'$ (which is $\\mathrm{id}_{I'}$, and $g\\circ f\\colon I\\to I$ must be the unique map $I\\to I$ (which is $\\mathrm{id}_I$), so $f$ and $g$ are isomorphisms, and they are the unique isomorphisms. In $\\mathbf{Sets}$, $\\varnothing$ is the initial obj \u2013\u00a0 Arturo Magidin Apr 17 '12 at 15:29\nThank you very much!! \u2013\u00a0 Rudy the Reindeer Apr 17 '12 at 15:35\n\nUniqueness up to unique isomorphism implies that there is no automorphism $f:F_S\\to F_S$ which is the identity on the image of $i:S\\to F_S$.\n\n-\nThank you. I'm trying to understand: reading Wikipedia makes it sound as if essentially unique is a synonym of unique up to unique isomorphism, is this right? \u2013\u00a0 Rudy the Reindeer Apr 12 '12 at 19:06\nThen maybe \"unique up to unique isomorphism\" means that for two free groups $(i, F_S), (i^\\prime, F_S^\\prime)$ there is an isomorphism $\\varphi: F_S \\to F_S^\\prime$ such that $\\varphi \\circ i = i^\\prime$? \u2013\u00a0 Rudy the Reindeer Apr 12 '12 at 19:07\n@ClarkKent: There is a unique isomorphism with that property; and that follows from the universal property of the free group. \u2013\u00a0 Arturo Magidin Apr 12 '12 at 23:30\n@ArturoMagidin Thank you! \u2013\u00a0 Rudy the Reindeer Apr 13 '12 at 9:07","date":"2015-05-30 14:50:42","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\": 0.8989365696907043, \"perplexity\": 280.64378357383856}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-22\/segments\/1432207932182.13\/warc\/CC-MAIN-20150521113212-00183-ip-10-180-206-219.ec2.internal.warc.gz\"}"} | null | null |
Ouko is a Kenyan surname. Notable people with this surname include:
Peter Ouko, Kenyan activist
Robert Ouko (1948–2019), Kenyan athlete
Robert Ouko (1931–1990), Kenyan politician
William Ouko, Kenyan lawyer and jurist
Surnames of Kenyan origin | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,704 |
\section{Introduction}
Bayesian optimization (BO) is an approach for
the global optimization of black-box functions
that are expensive to evaluate~\cite{pelikan1999boa,brochu2010tutorial,shahriari2016taking}.
BO has been successfully used for a wide variety of applications,
such as
computer vision~\cite{denil2012learning},
recommendations~\cite{gonzalez2017preferential,galuzzi2019bayesian},
chemical design~\cite{griffiths2017constrained},
material science~\cite{seko2015prediction,ueno2016combo},
probabilistic programs~\cite{rainforth2016bayesian},
and the automatic selection of machine learning algorithms~\cite{snoek2012practical,bergstra2013hyperopt,thornton2013auto,kotthoff2017auto,klein2017fast}.
Gaussian processes (GPs)~\cite{rasmussen2006gaussian}
are commonly used as surrogates to model a distribution over target functions.
The next data point to be evaluated is selected by an acquisition function
calculated using GPs in such for finding optimal points with fewer
target function evaluations.
With GPs, it is important to use appropriate kernel functions.
Neural networks have been used
as components of kernel functions~\cite{wilson2011gaussian,huang2015scalable,calandra2016manifold,wilson2016deep,wilson2016stochastic},
which enable us to learn flexible kernel functions for
high-dimensional data with complex structure
by the high representation power of deep learning.
For example, neural network-based kernels are obtained by
transforming the input of RBF kernels by neural networks.
However, many training data are required
for training neural networks.
Therefore, the use of neural networks in BO is limited,
since obtaining a large amount of training data is expensive.
To learn expressive kernels
with a small amount of training data in a test task,
transfer learning and meta-learning methods have been
proposed~\cite{yu2005learning,bonilla2008multi,wei2017source,iwata2019efficient,harrison2018meta,tossou2019adaptive,iwata2020few,patacchiola2020bayesian}.
With such methods,
the knowledge learned from training tasks
is transferred to test tasks,
where the training tasks are related to but different from test tasks.
These existing methods train neural network-based GPs
by maximizing the marginal likelihood.
Therefore, although they improve the performance of estimating
target functions, they do not necessarily improve the BO performance
since it is not directly optimized,
and the acquisition function to be used is not considered for training.
In this paper, we propose a meta-learning method
for training neural network-based kernels
by directly maximizing the BO performance
with the consideration of the acquisition function to be used.
We model a policy, which takes the current evaluated data points as input
and outputs the next data point to be evaluated,
a neural network,
where neural network-based kernels, GPs, and mutual information-based
acquisition functions (MI)~\cite{contal2014gaussian} are used as its layers.
By incorporating the MI into the policy network,
the neural networks in the kernel function are trained
such that the BO performance is improved when MI is used.
We call our model the deep kernel acquisition function.
Since the predictive mean and variance given the evaluated data points
are calculated in a closed form by GP, and
the MI is also calculated in a closed form,
we can backpropagate the gap through the GP and MI
to update the neural network parameters.
We can use other acquisition functions,
such as expected improvement~\cite{mockus1978application,jones2001taxonomy}
and upper confidence bound~\cite{auer2002using,srinivas2010gaussian},
instead of MI if they are differentiable.
We formulate BO as a Markov decision process,
where the current evaluated data points are a state,
the next data point to be evaluated is an action,
and the BO performance is a reward.
For evaluating the BO performance,
we use the gap~\cite{wang2016bayesian,berkenkamp2019no}
which is the difference between the true optimum value
and the best value found.
The proposed method trains the policy network
by minimizing the expected gap using
the policy gradient method~\cite{sutton1999policy}
with a reinforcement learning framework.
The expected gap is calculated by
running BO procedures on randomly sampled training tasks
for each training epoch using
an episodic training framework~\cite{ravi2016optimization,santoro2016meta,snell2017prototypical,finn2017model,li2019episodic}.
Since the policy network is shared across different tasks,
we can gain useful knowledge for BO from a wide variety of training tasks,
and use it for unseen test tasks that
are different from training tasks.
Figure~\ref{fig:method} illustrates the training framework of the proposed method.
\begin{figure}[t!]
\centering
\includegraphics[width=35em]{images/framework_horizontal.png}
\caption{Framework of our proposed method. We are given multiple tasks for training, where feature vectors and their response values are known. Training tasks are used for training our model (deep kernel acquisition function), which consists of neural network-based kernels, Gaussian processes, and mutual information-based acquisition functions. Our model takes a set of evaluated data points as input, and outputs acquisition values. Using the acquisition values, a data point is selected to be evaluated next. For each training epoch, first, a task is randomly selected from the training tasks. Second, we run Bayesian optimization using our model on the selected task and evaluate the gap. Third, the parameters of the neural network-based kernels are updated by minimizing the gap using reinforcement learning, where a loss is backpropagated through the acquisition function and the Gaussian process.}
\label{fig:method}
\end{figure}
\begin{comment}
Our major contributions are as follows:
\begin{enumerate}
\item We propose a meta-learning method that can learn neural network-based kernels by directly maximizing the BO performance.
\item We model the policy to select the next data point to be evaluated by a neural network
that contains neural network-based kernels, GPs, and an acquisition function
as its components.
\item We experimentally confirm that the proposed method outperforms
the existing methods
in BO tasks using three text document datasets.
\end{enumerate}
The remainder of this paper is organized as follows.
In Section~\ref{sec:related},
we briefly review related work.
In Section~\ref{sec:proposed},
we define our task and propose our meta-learning method of neural network-based kernels for BO.
In Section~\ref{sec:experiments},
we experimentally demonstrate the effectiveness of the proposed method,
and present concluding remarks and discuss future work
in Section~\ref{sec:conclusion}.
\end{comment}
\section{Related work}
\label{sec:related}
BO has been formulated as reinforcement learning problems~\cite{volpp2019meta,vishnu2019meta}.
MetaBO~\cite{volpp2019meta} models an acquisition function
by a neural network that takes the outputs of Gaussian processes,
which are the mean and variance of the response value at a query point,
as input. The kernel parameters of GPs are estimated
by maximizing the marginal likelihood to fit the training data,
and then the neural network parameters are estimated by reinforcement learning.
On the other hand, the kernel parameters in the proposed method
are estimated to improve the BO performance,
which enables us to estimate the mean and variance
of the response value that are appropriate for BO.
Vishunu et al.~\cite{vishnu2019meta} uses recurrent neural networks
to model a policy that takes the sequence of evaluated data points as input.
In their model, they do not use GPs,
although GPs have been successfully used for a wide variety of BO problems.
Other works
\cite{volpp2019meta,vishnu2019meta}
completely depend on neural networks
for modeling acquisition functions,
which require much training data.
In contrast to all of the existing methods,
we can exploit the knowledge on acquisition functions
in the BO literature with the proposed method using
a mutual information-based acquisition function
as a layer in the neural network.
It would help to improve the performance
especially with a small number of training data
since we do not need to train the neural network from scratch.
Although many meta-learning methods have been proposed~\cite{schmidhuber:1987:srl,bengio1991learning,finn2017model,vinyals2016matching,snell2017prototypical,garnelo2018conditional}
including GP-based methods~\cite{harrison2018meta,tossou2019adaptive,fortuin2019deep,iwata2020few},
they are designed for supervised learning,
but not for BO.
\section{Proposed method}
\label{sec:proposed}
\subsection{Problem formulation}
Suppose that we are given $S$ datasets on
BO tasks
$\{\{(\vec{x}_{sn},y_{sn})\}_{n=1}^{N_{s}}\}_{s=1}^{S}$ in the training phase,
where
$\vec{x}_{sn}\in\mathcal{X}$
is the $n$th feature vector in the $s$th task,
$y_{sn}=f_{s}(\vec{x}_{sn})$ is its scalar response value
by task-specific black-box function $f_{s}(\cdot)$,
and $N_{s}$ is the number of examples in the $s$th dataset.
We assume that feature spaces $\mathcal{X}$ are identical across tasks.
The number of data points can be different across tasks.
In the test phase,
we are given a set of feature vectors for a test task
$\mathcal{D}_{*}=\{\vec{x}_{*n}\}_{n=1}^{N_{*}}$,
where
$\vec{x}_{*n}\in\mathcal{X}$ is the $n$th feature vector in the test task.
Although the test task is related to some of the training tasks,
it is different.
Our goal is to find point $\vec{x}\in\mathcal{D}_{*}$
that has higher response value $f_{*}(\vec{x})$ with fewer queries,
where $f_{*}(\cdot)$ is the target function of the test task we want to maximize.
For simplicity, we assume that a set of feature vectors
for each task is given. When no set is given,
the proposed method is applicable
by generating a set of feature vectors.
\subsection{Gap minimization}
For each timestep in the $s$th task,
BO selects
a data point in $\mathcal{D}_{s}=\{\vec{x}_{sn}\}_{n=1}^{N_{s}}$
to evaluate next using policy function $a(\cdot)$:
\begin{align}
n_{s,t+1}=\mathop{\rm arg~max}\limits_{n\notin\mathcal{N}_{st}}a(\vec{x}_{sn};\mathcal{N}_{st},\bm{\Psi}),
\label{eq:n}
\end{align}
where $n_{st}\in\{1,\cdots,N_{s}\}$
is the data point index of the query at the $t$th timestep in the $s$th task,
$\mathcal{N}_{st}\subseteq\{1,\cdots,N_{s}\}$
is the set of evaluated data point indices until the $t$th timestep,
$n\notin\mathcal{N}_{st}$ represents a data point index
that is not included in evaluated data points $\mathcal{N}_{st}$,
and $\bm{\Psi}$ is the parameters of the policy function.
When $\mathcal{N}_{st}$ is the evaluated data points, we assume that
their feature vectors and response values
$\{(\vec{x}_{sn},y_{sn})\}_{n\in\mathcal{N}_{st}}$ are observed,
and omit the dependency of $\{(\vec{x}_{sn},y_{sn})\}_{n\in\mathcal{N}_{st}}$ in the equations.
For the evaluation measurement of BO, the following expected cumulative gap is used,
\begin{align}
R = \mathbb{E}_{s}\left[\sum_{t=1}^{T}p(\mathcal{N}_{st})r_{s}(\mathcal{N}_{st})
\right],
\label{eq:R}
\end{align}
where $\mathbb{E}_{s}[\cdot]$ denotes the expectation over tasks,
$T$ is the number of data points to be evaluated,
$p(\mathcal{N}_{st})$ is the probability that the evaluated data points are $\mathcal{N}_{st}$ at the $t$th timestep,
and
\begin{align}
r_{s}(\mathcal{N}_{st})=\max_{n\in\{1,\cdots,N_{s}\}}y_{sn}-\max_{n\in\mathcal{N}_{st}}y_{sn},
\label{eq:r}
\end{align}
is the difference between true maximum value
$\max_{n\in\{1,\cdots,N_{s}\}}y_{sn}$
and the maximum value in the evaluated data points until the $t$th timesteps
$\max_{n\in\mathcal{N}_{st}}y_{sn}$
in the $s$th task.
Since we are given the set of feature vectors and their response values
$\{(\vec{x}_{sn},y_{sn})\}_{n=1}^{N_{s}}$ for the training tasks,
we can calculate gap $r_{s}(\mathcal{N}_{st})$ in Eq.~(\ref{eq:r}) for the training tasks.
The probability of the evaluated data points is factorized using
a policy function:
\begin{align}
p(\mathcal{N}_{st})=\prod_{\tau=1}^{t}p(n_{s\tau}|a(\cdot;\mathcal{N}_{s,\tau-1},\bm{\Psi})),
\end{align}
where
\begin{align}
p(n_{st}|a(\cdot;\mathcal{N}_{s,t-1},\bm{\Psi}))
=\left\{
\begin{array}{ll}
1 & \text{if $n_{st}=\mathop{\rm arg~max}\limits_{n\notin\mathcal{N}_{st}}a(\vec{x}_{sn};\mathcal{N}_{s,t-1},\bm{\Psi})$},\\
0 & \text{otherwise},
\end{array}
\right.
\label{eq:pn}
\end{align}
using Eq.~(\ref{eq:n}).
The data point with the highest policy function value is included in the evaluated data points.
We use the initially given evaluated data points for $\mathcal{N}_{s0}$.
This BO formulation can be regarded as a Markov decision process,
where evaluated data points $\mathcal{N}_{st}$ is the state,
data index to be evaluated the next $n_{s,t+1}$ is the action,
and gap $r_{s}(\mathcal{N}_{st})$ is the negative reward.
Therefore, we can train parameters $\bm{\Psi}$ of the policy function by
a reinforcement learning algorithm
described in Section~\ref{sec:train}.
\subsection{Policy function}
\label{sec:model}
\begin{figure*}[t!]
\centering
\includegraphics[width=33em]{images/model_long.png}
\caption{Our policy model takes query feature vector $\vec{x}$ and set of evaluated data points $\{(\vec{x}_{n_{\tau}},y_{n_{\tau}})\}_{\tau=1}^{t}$ as input and outputs acquisition function value $a$ of the query. First, query and observed feature vectors are nonlinearly transformed by neural network $g$. Second, mean $\mu$ and variance $\sigma^{2}$ of the response value at the query are estimated by GP using the transformed feature vectors, observed response values $\{y_{n_{\tau}}\}_{\tau=1}^{t}$, and kernel parameters $\alpha$, $\beta$, and $\eta$ in Eqs.~(\ref{eq:mu},\ref{eq:sigma}). Finally, acquisition function value $a$ of the query is calculated by mean $\mu$, variance $\sigma^{2}$, and $\xi$ based on GP-MI in Eq.~(\ref{eq:a}). We omit dependency between $\xi$ and past variance $\sigma^{2}$. White and gray circles represent observed and hidden variables. Rectangles represent functions.}
\label{fig:model}
\end{figure*}
We model the policy function in Eq.~(\ref{eq:n})
by incorporating deep kernel learning (DKL)~\cite{wilson2016deep},
Gaussian process (GP), and
a mutual information-based acquisition function (MI)~\cite{contal2014gaussian}
as shown in Figure~\ref{fig:model}.
By using DKL,
we can flexibly learn representations from the given data,
which is especially important for such high-dimensional data
as text documents.
We share neural networks in deep kernels across different tasks,
enabling us to learn shared knowledge across tasks,
and use it for unseen test tasks.
MI has been successfully used for BO tasks.
By using MI as a component in our model,
we can exploit its useful knowledge designed for BO.
Instead of MI,
we can incorporate other types of acquisition functions designed for BO
if they are differentiable in the proposed method.
With MI, the acquisition function is given by
\begin{align}
a(\vec{x};\mathcal{N}_{st},\bm{\Psi})=\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})
+\sqrt{\nu}\left(\sqrt{\sigma^{2}(\vec{x};\mathcal{N}_{st},\bm{\Psi})+\xi_{st}}-\sqrt{\xi_{st}}\right),
\label{eq:a}
\end{align}
where
$\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})$ and
$\sigma^{2}(\vec{x};\mathcal{N}_{st},\bm{\Psi})$ are
the mean and variance at $\vec{x}$ given $\mathcal{N}_{st}$,
\begin{align}
\xi_{s,t+1}=\xi_{st}+\sigma^{2}(\vec{x};\mathcal{N}_{st},\bm{\Psi}),
\end{align}
and $\nu>0$ is a hyperparameter.
With a GP with a zero mean and kernel function $k(\cdot,\cdot;\bm{\Psi})$,
the mean and variance are given by
\begin{align}
\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})=\vec{k}_{st}^{\top}(\vec{K}_{st}+\beta\vec{I})^{-1}\vec{y}_{st},
\label{eq:mu}
\end{align}
\begin{align}
\sigma^{2}(\vec{x};\mathcal{N}_{st},\bm{\Psi})=k(\vec{x},\vec{x};\bm{\Psi})-\vec{k}_{st}^{\top}\vec{K}_{st}^{-1}\vec{k}_{st},
\label{eq:sigma}
\end{align}
where $\vec{k}_{st}=[k(\vec{x},\vec{x}';\bm{\Psi})]_{\vec{x}'\in\mathcal{N}_{st}}\in\mathbb{R}^{|\mathcal{N}_{st}|}$
is a kernel vector between $\vec{x}$ and the evaluated data points at timestep $t$,
$\vec{K}_{st}=[k(\vec{x},\vec{x}';\bm{\Psi})]_{\vec{x},\vec{x}'\in\mathcal{N}_{st}}$
is the kernel matrix of the evaluated data points with size $(|\mathcal{N}_{st}| \times |\mathcal{N}_{st}|)$,
and $\beta>0$ is the observation noise parameter.
We use the RBF kernel with neural network transformation for DKL,
\begin{align}
k(\vec{x},\vec{x}';\bm{\Psi})&=\alpha\exp\left(-\frac{1}{2\eta}\parallel g(\vec{x};\bm{\Theta})-g(\vec{x}';\bm{\Theta})\parallel^{2}\right)
+\beta\delta(\vec{x},\vec{x}'),
\label{eq:k}
\end{align}
where $g(\cdot;\bm{\Theta})$ is a neural network with parameter $\bm{\Theta}$,
$\alpha$ and $\eta$ are kernel parameters,
and $\delta$ is the Kronecker delta function,
i.e., $\delta(\vec{x},\vec{x}')=1$ if $\vec{x}=\vec{x}'$ and $\delta=0$ otherwise.
The parameters in the policy function
consist of the parameters of the neural networks and the kernel parameters,
$\bm{\Psi}=\{\bm{\Theta},\alpha,\beta,\eta\}$.
The policy function in Eq.~(\ref{eq:a})
acts as a neural network that
takes query point $\vec{x}$ and set of evaluated data points $\mathcal{N}_{st}$ as input,
and outputs a scalar value,
where neural network $g$ and GP are used as its components.
Since the number of evaluated data points $\mathcal{N}_{st}$ is different across
different timesteps,
standard neural networks cannot be used as a
policy function when they assume that the input layer's size is fixed.
On the other hand, our model can handle different numbers of evaluated data points
using the GP framework, where the mean and variance given evaluated data points
are calculated in a closed form.
\subsection{Training procedure}
\label{sec:train}
We train parameters $\bm{\Psi}$
by minimizing the following expected cumulative gap with discount factor $\gamma\in(0,1]$,
\begin{align}
L(\bm{\Psi}) = \mathbb{E}_{s}\left[\mathbb{E}_{a}\left[\sum_{t=1}^{T}\gamma^{t-1}r_{s}(\mathcal{N}_{st})\right]\right],
\label{eq:L}
\end{align}
where evaluated data points $\mathcal{N}_{st}$ are selected
according to policy $a$ with parameter $\bm{\Psi}$.
Objective function $L(\bm{\Psi})$ is minimized by the policy gradient method~\cite{sutton1999policy} using the following gradient,
\begin{align}
\frac{\partial L(\bm{\Psi})}{\partial\bm{\Psi}}=\mathbb{E}_{s}\left[\mathbb{E}_{a}\left[\sum_{t=1}^{T}G_{t}\frac{\partial\log p(n_{st}|a(\cdot;\mathcal{N}_{s,t-1},\bm{\Psi}))}{\partial\bm{\Psi}}
\right]\right],
\end{align}
where $G_{t}=\sum_{\tau=t}^{T}\gamma^{\tau-t}r_{s\tau}$
is the sum of the future gaps with discount factor $\gamma$ at the $t$th timestep.
The training procedure
is shown in Algorithm~\ref{alg}.
For each training epoch, we first randomly sample a task in Line 3
and randomly generate initial evaluated data points
$\mathcal{N}_{s0}\subset\{1,\cdots,N_{s}\}$ in Line 4.
Next we generate
BO episode $n_{s1}, \mathcal{N}_{s1}, R_{s1}, \cdots, n_{sT}, \mathcal{N}_{sT}, R_{sT}$ using policy $a(\cdot;\mathcal{N}_{s,t-1},\bm{\Psi})$ and transition $\tilde{p}(n_{st}|a(\cdot;\mathcal{N}_{s,t-1},\bm{\Psi}))$
in Lines 5--10,
where we use the following stochastic transition function
\begin{align}
\tilde{p}(n_{st}=n|a(\cdot;\mathcal{N}_{s,t-1},\bm{\Psi}))
=\left\{
\begin{array}{ll}
\frac{\exp(a(\vec{x}_{sn};\mathcal{N}_{s,t-1},\bm{\Psi}))}
{\sum_{n'\notin\mathcal{N}_{s,t-1}}\exp(a(\vec{x}_{sn'};\mathcal{N}_{s,t-1},\bm{\Psi}))}
& \text{if $n_{s\tau}\notin\mathcal{N}_{s,t-1}$}\\
0 & \text{otherwise},
\end{array}
\right.
\label{eq:pntilde}
\end{align}
instead of the deterministic transition in Eq.~(\ref{eq:pn}).
Next we calculate the sum of future gaps $G_{t}$ in Lines 11--13.
Then, we calculate loss
\begin{align}
\tilde{L}=\sum_{t=1}^{T}G_{t}\log\tilde{p}(n_{st}|a(\cdot|\mathcal{N}_{s,t-1},\bm{\Psi})),
\label{eq:Ltilde}
\end{align}
and update parameters $\bm{\Psi}$ by minimizing the loss using a stochastic gradient method in Lines 14--15.
Since loss $L$ is differentiable, we can backpropagate it
through the MI to update the neural network parameters
and the kernel parameters.
We use the average of the discounted sum of the future rewards
as a baseline to reduce the
variance~\cite{weaver2001optimal,greensmith2004variance}.
\begin{algorithm}[t!]
\caption{Training procedure of our model.}
\label{alg}
\begin{algorithmic}[1]
\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}
\REQUIRE{Datasets $\{\{(\vec{x}_{sn},y_{sn})\}_{n=1}^{N_{s}}\}_{s=1}^{S}$,
number of queries $T$, discount factor $\gamma$}
\ENSURE{Trained model parameters $\bm{\Psi}$}
\STATE Initialize model parameters $\bm{\Psi}$.
\WHILE{End condition is satisfied}
\STATE Randomly sample a task, $s\sim\mathrm{Uniform}(1,\cdots,S)$.
\STATE Randomly sample initial evaluated data points $\mathcal{N}_{s0}$.
\FOR{$t \in \{1,\cdots,T\}$}
\STATE Calculate acqusition function $a(\vec{x};\mathcal{N}_{s,t-1},\bm{\Psi})$ by Eq.~(\ref{eq:a}) for $\vec{x}\in\{\vec{x}_{sn}\}_{n\notin\mathcal{N}_{s,t-1}}$.
\STATE Sample query data index $n_{st}$ according to Eq.~(\ref{eq:pntilde}).
\STATE Update evaluated data points $\mathcal{N}_{st}\gets\mathcal{N}_{s,t-1}\cup n_{sn}$.
\STATE Calculate negative reward $r_{s}(\mathcal{N}_{st})$.
\ENDFOR
\FOR{$t \in \{1,\cdots,T\}$}
\STATE Calculate discounted sum of future negative rewards
$G_{t}=\sum_{\tau=t}^{T}\gamma^{\tau-t}r_{s}(\mathcal{N}_{s\tau})$.
\ENDFOR
\STATE Calculate loss $\tilde{L}$ in Eq.~(\ref{eq:Ltilde}) and its gradient.
\STATE Update model parameters $\bm{\Psi}$ using loss $L$ and its gradient using a stochastic gradient method.
\ENDWHILE
\end{algorithmic}
\end{algorithm}
\section{Experiments}
\label{sec:experiments}
\subsection{Data}
We experimentally evaluated the effectiveness of our proposed method
using text document datasets
with a BO task to find a document that resembles
an unknown target document with fewer evaluations.
This BO task simulated a recommendation system, where
a user seeks a document that matches her preferences
by evaluating a limited number of documents.
The user's evaluation for each document is the target function,
where evaluation is expensive since the documents must be read.
We represented a document as bag-of-words $\vec{x}_{sn}=(x_{sn1},\cdots,x_{snJ})$, or a word frequency vector,
where $x_{snj}$ is the number of occurrences of the $j$th vocabulary term in the $n$th document for the $s$th user,
and $J$ is the vocabulary size.
Each user was a task, where preferences were different across users,
but the target functions of different users were related since the vocabulary terms were shared across users,
and some users have similar preferences.
We used the following three text document datasets: Reuter, NeurIPS,
and WebKB.
The Reuter data were constructed from documents that appeared on the Reuters newswire categorized into eight classes~\footnote{The original Reuter data were obtained from ~\url{http://www.daviddlewis.com/resources/testcollections/reuters21578/}.}~\cite{apte1994automated}.
The NeurIPS data were constructed from conference papers
in Neural Information Processing Systems 1--12
categorized into 13 research topics~\footnote{The original NeurIPS data were obtained from~\url{https://cs.nyu.edu/~roweis/data.html}.}.
The WebKB data were constructed from web pages categorized into four universities~\footnote{The original WebKB data were obtained from~\url{http://www.cs.cmu.edu/afs/cs.cmu.edu/project/theo-20/www/data/}.}~\cite{cravenlearning}.
We omit vocabulary terms that occurred in less than 50 documents
as well as documents that contained fewer than 50 words.
The number of documents was 1,909 and the number of vocabulary terms was 799
in the 20News data,
592 and 1,655 in the NeurIPS data, and 3,264 and 1,365 in the WebKB data.
We calculated the similarity
by the negative Euclidean distance
between the representations obtained by neural networks.
For the neural network,
we used a four-layered feed-forward neural network with 32 hidden units
and a rectified linear unit, $\mathrm{ReLU}(x)=\max(0,x)$, for the activation.
The neural network was trained by minimizing the cross-entropy loss using category labels
as in the text classification.
We used the last hidden layer as the representations of documents.
By transforming the word frequency vectors to the representations by the neural network,
the similarity reflected the topics of documents that were related to the category labels.
For each BO task,
we randomly selected a target document and 500 candidate documents,
and calculated their similarity,
where the target document was considered the user's most preferred document.
We generated $\{20,40,\cdots,100\}$ training, 20 validation, and 50 test tasks
for each dataset.
For each validation and test task,
an initial evaluated data point was randomly selected.
We ran ten experiments for each dataset,
and evaluated the performance based on the average of the cumulative gaps,
$\hat{R} = \frac{1}{ST}\sum_{s=1}^{S}\sum_{t=1}^{T}r_{s}(\mathcal{N}_{st})$,
in the test BO tasks.
\subsection{Proposed method setting}
We used a four-layered feed-forward neural network
with 32 hidden units and ReLU activation
for neural network $g$ in the kernel functions.
The discount factor was $\gamma=0.99$.
The number of queries was 10 for each task,
and the number of initial evaluated data points was $|\mathcal{N}_{s0}|=1$.
We used three types of acquisition functions: MI,
expected improvement (EI)~\cite{mockus1978application,jones2001taxonomy},
and upper confidence bound (UCB)~\cite{auer2002using,srinivas2010gaussian}.
With EI,
the acquisition function is given by
\begin{align}
a(\vec{x};\mathcal{N}_{st},\bm{\Psi})&=
\left(\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})-\max_{n\in\mathcal{N}_{st}}y_{sn}\right)\Phi(\vec{x}')
\nonumber\\
&+\sigma(\vec{x};\mathcal{N}_{st},\bm{\Psi})\phi(\vec{x}'),
\label{eq:a_ei}
\end{align}
where $\phi$ and $\Phi$ are the probability and cumulative density functions of the standard normal distribution,
and
\begin{align}
\vec{x}'=\frac{\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})-\max_{n\in\mathcal{N}_{st}}y_{sn}}{\sigma(\vec{x};\mathcal{N}_{st},\bm{\Psi})}.
\end{align}
With UCB,
the acquisition function is given by
\begin{align}
a(\vec{x};\mathcal{N}_{st},\bm{\Psi})=\mu(\vec{x};\mathcal{N}_{st},\bm{\Psi})
+\sqrt{\nu}\sigma(\vec{x};\mathcal{N}_{st},\bm{\Psi}),
\label{eq:a_ucb}
\end{align}
where $\nu>0$ is the hyperparameter.
For the hyperparameter of MI and UCB, we used $\nu=\frac{\log 2}{10^{-6}}$ like in a previous work~\cite{contal2014gaussian}.
We optimized the model parameters using Adam~\cite{kingma2014adam} with learning rate $10^{-3}$
and batch size 16.
The validation data were used for early stopping, and the maximum number of epochs was 1,000.
We pretrained the model parameters by maximizing the marginal likelihood.
We implemented the proposed method with PyTorch~\cite{paszke2017automatic}.
\subsection{Comparing methods}
We compared the proposed method with
the following five methods: DKL, GP, RL, MetaBO, and Random.
DKL is deep kernel learning~\cite{wilson2016deep},
where GPs with neural network-based kernels
were trained by maximizing the marginal likelihood,
\begin{align}
\sum_{s=1}^{S}\sum_{n=1}^{N_{s}}\log\rm{Normal}(\vec{y}_{s}|\vec{0},\vec{K}_{s}),
\label{eq:marginal}
\end{align}
where $\vec{y}_{s}=(y_{s1},\cdots,y_{sN_{s}})$ is the vector of response values in the $s$th task,
$\vec{K}_{s}\in\mathbb{R}^{N_{s}\times N_{s}}$ is the kernel matrix between feature vectors in the $s$th task,
and $\rm{Normal}(\cdot|\bm{\mu},\bm{\Sigma})$ is the multivariate normal distribution
with mean $\bm{\mu}$ and covariance $\bm{\Sigma}$.
We used the same neural network architecture with the proposed method.
GP is a Gaussian process with an RBF kernel,
where kernel parameters $\alpha$, $\beta$, and $\eta$
were trained by maximizing the marginal likelihood in Eq.(\ref{eq:marginal}).
In DKL and GP, we used three types of acquisition functions: MI, EI, and UCB.
RL is a reinforcement learning-based method with a policy modeled by neural networks
as in a previous work~\cite{vishnu2019meta}.
For the neural networks, we used deep sets~\cite{zaheer2017deep}
for taking a set of evaluated data points as input,
\begin{align}
\vec{z}_{st}=g_{\mathrm{RL}}\left(\frac{1}{|\mathcal{N}_{st}|}\sum_{n'\in\mathcal{N}_{st}}f_{\mathrm{RL}}(\vec{x}_{sn'})\right),
\end{align}
where $\vec{z}_{st}$ is a vector representation of the evaluated data points at the $t$th timestep,
and
$f_{\mathrm{RL}}$ and $g_{\mathrm{RL}}$ are three-layered feed-forward neural networks with 32 hidden units.
The policy was modeled by concatenating the representation and
a query data point,
\begin{align}
p_{\mathrm{RL}}(n_{st}=n|\mathcal{N}_{s,t-1})
\propto
\left\{
\begin{array}{ll}
\exp(h_{\mathrm{RL}}([\vec{x}_{sn},\vec{z}_{s,t-1}]))
& \text{if $n_{s\tau}\notin\mathcal{N}_{s,t-1}$}\\
0 & \text{otherwise},
\end{array}
\right.
\label{eq:pnrl}
\end{align}
where $[\cdot,\cdot]$ represents the concatenation,
and $h_{\mathrm{RL}}$ is a four-layered feed-forward neural network with 32 hidden units.
MetaBO is a meta-learning method for BO based on reinforcement learning~\cite{volpp2019meta},
where the acquisition functions were modeled by a neural network that took
the GP's outputs and query data point,
\begin{align}
p_{\mathrm{M}}(n_{st}=n|\mathcal{N}_{s,t-1})
\propto
\left\{
\begin{array}{ll}
\exp(h_{\mathrm{M}}([\mu(\vec{x}_{sn}),\sigma^{2}(\vec{x}_{sn}),\vec{x}_{sn}]))
& \text{if $n_{s\tau}\notin\mathcal{N}_{s,t-1}$}\\
0 & \text{otherwise},
\end{array}
\right.
\label{eq:pnmb}
\end{align}
where $h_{\mathrm{M}}$ is a four-layered feed-forward neural network with 32 hidden units,
and $\mu(\vec{x}_{sn})$ and $\sigma^{2}(\vec{x}_{sn})$ are the mean and variance
estimated by the GP with RBF kernels.
The kernel parameters were trained by maximizing the marginal likelihood.
With RL and MetaBO, we trained neural networks
by the policy gradient method, as in our proposed method.
\subsection{Results}
\begin{figure*}[t!]
\centering
{\tabcolsep=0em
\begin{tabular}{ccc}
& Reuter &\\
\includegraphics[height=9.8em]{images//anaresult_d0r0a0.png}&
\includegraphics[height=9.8em]{images//anaresult_d0r0a1.png}&
\includegraphics[height=9.8em]{images//anaresult_d0r0a2.png}\\
& NeurIPS &\\
\includegraphics[height=9.8em]{images//anaresult_d1r0a0.png}&
\includegraphics[height=9.8em]{images//anaresult_d1r0a1.png}&
\includegraphics[height=9.8em]{images//anaresult_d1r0a2.png}\\
&WebKB&\\
\includegraphics[height=9.8em]{images//anaresult_d2r0a0.png}&
\includegraphics[height=9.8em]{images//anaresult_d2r0a1.png}&
\includegraphics[height=9.8em]{images//anaresult_d2r0a2.png}\\
(a) MI & (b) EI & (c) UCB \\
\end{tabular}}
\caption{Average test cumulative gap with different numbers of training tasks on Reuter, NeurIPS, and WebKB data.
Bars show standard error.
We used three kinds of acquisition functions (a) MI, (b) EI, and (c) UCB with the proposed method, DKL,
and GP.
RL, MetaBO, and Random are the identical among (a), (b), and (c).}
\label{fig:result_ndataset}
\end{figure*}
Figure~\ref{fig:result_ndataset} shows the average test cumulative gap
with different numbers of training tasks.
The proposed method achieved the lowest gap in all cases.
As the number of training tasks increased,
the gap decreased with the proposed method, RL, and MetaBO,
indicating that the reinforcement learning-based methods
learned how to select queries in BO using a wide variety of training tasks.
With DKL, the decrease based on the number of training tasks
was smaller than the reinforcement learning-based methods
because it was trained by fitting to the training data by maximizing the marginal likelihood.
Thus it did not directly improve the BO performance.
RL's gap was high, especially when the number of training tasks was small.
Since RL needs to train the policy from scratch using training tasks,
it requires many training tasks.
On the other hand, since MetaBO used GP's result for modeling the policy,
it outperformed RL.
Furthermore, for modeling the policy, the proposed method uses
acquisition functions, i.e., MI, EI, or UCB, which were
developed for BO by experts.
Therefore, the proposed method outperformed MetaBO and RL.
GP's gap was high,
indicating that learning kernels with neural networks
is important for modeling high-dimensional data.
\begin{figure*}[t!]
\centering
\begin{tabular}{ccc}
\includegraphics[height=9.3em]{images//anaresult_d0r0a0n20d6.png}&
\includegraphics[height=9.3em]{images//anaresult_d1r0a0n20d6.png}&
\includegraphics[height=9.3em]{images//anaresult_d2r0a0n20d6.png}\\
(a) Reuter & (b) NeurIPS & (c) WebKB \\
\end{tabular}
\caption{Average test gap with different numbers of evaluated data points on Reuter, NeurIPS, and WebKB data.
We used MI acquisition functions, and 20 training tasks.
Bars show standard error.}
\label{fig:result_observation}
\end{figure*}
Figure~\ref{fig:result_observation}
shows the average test gap with different amounts of evaluated data points using MI acquisition functions.
The gaps of the proposed method and DKL were almost the same when the number of the evaluated data points was large.
However, the gap of the proposed method was better than DKL when the number of the evaluated data points was small.
This result demonstrates the effectiveness of training neural networks by minimizing the expected cumulative gap
for finding higher response values with fewer evaluations.
Although MetaBO's gap was low when the number of evaluated data points was relatively small,
the gap's decrease based o the number of evaluated data points was slower than the proposed method.
\begin{table}[t!]
\centering
\caption{Training time in seconds.}
\label{tab:time}
\begin{tabular}{lrrrrr}
\hline
& Reuter & NeurIPS & WebKB \\
\hline
Ours & 931.886 & 1080.168 & 993.435 \\
DKL & 131.102 & 224.183 & 201.535 \\
GP & 150.889 & 251.762 & 215.716 \\
RL & 451.380 & 637.127 & 583.239 \\
MetaBO & 934.847 & 1079.129 & 1064.673 \\
\hline
\end{tabular}
\end{table}
Table~\ref{tab:time}
shows the computational time in seconds for training with computers with GeForce GTX 1080 Ti GPUs.
The training times with DKL and GP, which were trained with the supervised learning framework,
were shorter than the other methods, which were trained with a reinforcement learning framework.
It is because reinforcement learning-based methods run BO for each training epoch.
The proposed method and MetaBO required more training time than RL
since they calculated GPs in their methods.
\section{Conclusion}
\label{sec:conclusion}
We proposed a meta-learning method
for learning neural network-based kernels for BO
to minimize the expected cumulative gap between the true optimum value
and the best found value.
The proposed method learns knowledge in various training tasks,
and can use it for unseen test tasks by sharing neural networks.
Since the proposed method incorporates acquisition functions,
such as mutual information and expected improvement,
for modeling a policy that selects the next data point to be evaluated,
we can employ the knowledge in the existing acquisition functions,
which enables us to learn policies with fewer training tasks.
Although our results are encouraging,
we must extend our approach in several future directions.
First,
we will apply it to other types of high-dimensional structured data,
such as images and time-series,
using convolutional and recurrent neural networks in kernel functions.
Second, we plan to improve our proposed method using
reinforcement learning techniques, which includes actor-critic methods~\cite{grondman2012survey}.
\bibliographystyle{abbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,418 |
ListsAddToListSelectionContainerView = Backbone.View.extend({
events: {
'change': 'checkForNewList'
},
initialize: function (options) {
this.establishment = options.establishment
this.collection.per_page = 1000;
this.collection.user_id = CurrentUser.get('id');
this.establishment_id = this.establishment.get('id');
var params = this.collection.predicate();
this.listenTo(this.collection, 'reset', this.render);
this.collection.fetch({
reset: true,
data: params
});
},
render: function () {
this.collection.each(function (list) {
this.renderListOption(list)
}, this);
this.$el.append("<option class='list_option' value='new'>Create new list</option>");
},
renderListOption: function (list) {
this.$el.append(render('lists/add_to_list_selection_option', list));
},
checkForNewList: function (e) {
if (e.target.value === 'new') {
ModalView.show(new ListsCreateNewListModalView({
el: '#inner_modal_content',
model: this.establishment
}));
}
}
});
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,078 |
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