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id="toc-Types_of_model-sublist" class="vector-toc-list"> <li id="toc-Model_in_specific_contexts" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Model_in_specific_contexts"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span><i>Model</i> in specific contexts</span> </div> </a> <ul id="toc-Model_in_specific_contexts-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Physical_model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Physical_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Physical model</span> </div> </a> <ul id="toc-Physical_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Conceptual_model" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Conceptual_model"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Conceptual model</span> </div> </a> <ul id="toc-Conceptual_model-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Uses_of_models" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uses_of_models"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Uses of models</span> </div> </a> <ul id="toc-Uses_of_models-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Properties_of_models,_according_to_general_model_theory" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Properties_of_models,_according_to_general_model_theory"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Properties of models, according to general model theory</span> </div> </a> <ul id="toc-Properties_of_models,_according_to_general_model_theory-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled 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Available in 19 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-19" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">19 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%85%D9%88%D8%B0%D8%AC" title="نموذج – Arabic" lang="ar" hreflang="ar" data-title="نموذج" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Модель – Chuvash" lang="cv" hreflang="cv" data-title="Модель" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Modell" title="Modell – German" lang="de" hreflang="de" data-title="Modell" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Mudel" title="Mudel – Estonian" lang="et" hreflang="et" data-title="Mudel" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Mod%C3%A8le" title="Modèle – French" lang="fr" hreflang="fr" data-title="Modèle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Samhail_(l%C3%A9iri%C3%BA)" title="Samhail (léiriú) – Irish" lang="ga" hreflang="ga" data-title="Samhail (léiriú)" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Unongo" title="Unongo – Zulu" lang="zu" hreflang="zu" data-title="Unongo" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%9D%E1%83%93%E1%83%94%E1%83%9A%E1%83%98" title="მოდელი – Georgian" lang="ka" hreflang="ka" data-title="მოდელი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%AE%D0%BB%D0%B3%D1%96" title="Үлгі – Kazakh" lang="kk" hreflang="kk" data-title="Үлгі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Kielelezo" title="Kielelezo – Swahili" lang="sw" hreflang="sw" data-title="Kielelezo" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Модель – Kyrgyz" lang="ky" hreflang="ky" data-title="Модель" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Modell_(fogalom)" title="Modell (fogalom) – Hungarian" lang="hu" hreflang="hu" data-title="Modell (fogalom)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Model" title="Model – Malay" lang="ms" hreflang="ms" data-title="Model" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Modell" title="Modell – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Modell" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Model_tushunchasi" title="Model tushunchasi – Uzbek" lang="uz" hreflang="uz" data-title="Model tushunchasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Модель – Russian" lang="ru" hreflang="ru" data-title="Модель" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%DB%86%D8%AF%DB%8E%D9%84" title="مۆدێل – Central Kurdish" lang="ckb" hreflang="ckb" data-title="مۆدێل" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BC%D1%81%D0%B8%D0%BB%D0%B0" title="Амсила – Tajik" lang="tg" hreflang="tg" data-title="Амсила" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C" title="Модель – Ukrainian" lang="uk" hreflang="uk" data-title="Модель" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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entity</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For fashion model, see <a href="/wiki/Model_(person)" title="Model (person)">Model (person)</a>. For other uses, see <a href="/wiki/Model_(disambiguation)" class="mw-disambig" title="Model (disambiguation)">Model (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951" /><div role="note" class="hatnote navigation-not-searchable">"Modelling" redirects here. For the MDPI journal, see <a href="/wiki/Modelling_(journal)" class="mw-redirect" title="Modelling (journal)"><i>Modelling</i> (journal)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG/220px-Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG/330px-Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG/440px-Beta-D-Gulopyranose_Molek%C3%BClbaukasten_9288.JPG 2x" data-file-width="3168" data-file-height="3162" /></a><figcaption>Model of a molecule, with coloured balls representing different atoms</figcaption></figure> <p>A <b>model</b> is an informative representation of an object, person, or system. The term originally denoted the <a href="/wiki/Plan_(drawing)" title="Plan (drawing)">plans</a> of a building in late 16th-century English, and derived via <a href="/wiki/French_language" title="French language">French</a> and <a href="/wiki/Italian_language" title="Italian language">Italian</a> ultimately from <a href="/wiki/Latin" title="Latin">Latin</a> <i lang="la"><a href="https://en.wiktionary.org/wiki/modulus#Latin" class="extiw" title="wikt:modulus">modulus</a></i>, <span class="gloss-quot">'</span><span class="gloss-text">a measure</span><span class="gloss-quot">'</span>.<sup id="cite_ref-OED_model_1-0" class="reference"><a href="#cite_note-OED_model-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Models can be divided into physical models (e.g. a <a href="/wiki/Ship_model" title="Ship model">ship model</a> or a fashion model) and abstract models (e.g. a <a href="/wiki/Numerical_weather_prediction" title="Numerical weather prediction">set of mathematical equations</a> describing the workings of the atmosphere for the purpose of weather forecasting). Abstract or <a href="/wiki/Conceptual_model" title="Conceptual model">conceptual models</a> are central to <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>.<sup id="cite_ref-MWCD_2-0" class="reference"><a href="#cite_note-MWCD-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Geosciences_3-0" class="reference"><a href="#cite_note-Geosciences-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Scholarly_research" class="mw-redirect" title="Scholarly research">scholarly research</a> and <a href="/wiki/Applied_science" title="Applied science">applied science</a>, a model should not be confused with a <a href="/wiki/Theory" title="Theory">theory</a>: while a model seeks only to represent reality with the purpose of better understanding or predicting the world, a theory is more ambitious in that it claims to be an explanation of reality.<sup id="cite_ref-Wunsch1994_4-0" class="reference"><a href="#cite_note-Wunsch1994-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Types_of_model">Types of model</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=1" title="Edit section: Types of model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Model_in_specific_contexts"><i>Model</i> in specific contexts</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=2" title="Edit section: Model in specific contexts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a noun, <i>model</i> has specific meanings in certain fields, derived from its original meaning of "structural <a href="/wiki/Design" title="Design">design</a> or <a href="/wiki/Layout_(disambiguation)" class="mw-redirect mw-disambig" title="Layout (disambiguation)">layout</a>": </p> <ul><li><a href="/wiki/Model_(art)" title="Model (art)">Model (art)</a>, a person posing for an artist, e.g. a 15th-century criminal representing the biblical Judas in Leonardo da Vinci's painting <a href="/wiki/The_Last_Supper_(Leonardo)" title="The Last Supper (Leonardo)"><i>The Last Supper</i></a></li> <li><a href="/wiki/Model_(person)" title="Model (person)">Model (person)</a>, a person who serves as a template for others to copy, as in a <a href="/wiki/Role_model" title="Role model">role model</a>, often in the context of advertising commercial products; e.g. the first <i>fashion model</i>, Marie Vernet Worth in 1853, wife of designer <a href="/wiki/Charles_Frederick_Worth" title="Charles Frederick Worth">Charles Frederick Worth</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li><a href="/wiki/Model_(product)" class="mw-redirect" title="Model (product)">Model (product)</a>, a particular design of a product as displayed in a catalogue or show room (e.g. <a href="/wiki/Ford_Model_T" title="Ford Model T">Ford Model T</a>, an early <a href="/wiki/Car_model" title="Car model">car model</a>)</li> <li><a href="/wiki/Model_organism" title="Model organism">Model (organism)</a> a non-human species that is studied to understand biological phenomena in other organisms, e.g. a guinea pig starved of vitamin C to study scurvy, an experiment that would be immoral to conduct on a person</li> <li><a href="/wiki/Model_(mimicry)" class="mw-redirect" title="Model (mimicry)">Model (mimicry)</a>, a species that is mimicked by another species</li> <li><a href="/wiki/Model_(logic)" class="mw-redirect" title="Model (logic)">Model (logic)</a>, a structure (a set of items, such as natural numbers 1, 2, 3,..., along with mathematical operations such as addition and multiplication, and relations, such as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle <}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo><</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle <}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33737c89a17785dacc8638b4d66db3d5c8670de1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle <}" /></span>) that satisfies a given system of <a href="/wiki/Axiom" title="Axiom">axioms</a> (basic truisms), i.e. that satisfies the statements of a given <a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">theory</a><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Model_(CGI)" class="mw-redirect" title="Model (CGI)">Model (CGI)</a>, a mathematical representation of any surface of an object in three dimensions via specialized software</li> <li><a href="/wiki/Model_(MVC)" class="mw-redirect" title="Model (MVC)">Model (MVC)</a>, the information-representing internal component of a software, as distinct from its user interface</li></ul> <div class="mw-heading mw-heading3"><h3 id="Physical_model">Physical model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=3" title="Edit section: Physical model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Model.village.arp.750pix.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Model.village.arp.750pix.jpg/220px-Model.village.arp.750pix.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Model.village.arp.750pix.jpg/330px-Model.village.arp.750pix.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Model.village.arp.750pix.jpg/440px-Model.village.arp.750pix.jpg 2x" data-file-width="750" data-file-height="563" /></a><figcaption>Part of the one-ninth <a href="/wiki/Scale_model" title="Scale model">scale model</a> of <a href="/wiki/Bourton-on-the-Water" title="Bourton-on-the-Water">Bourton-on-the-Water</a> at Bourton-on-the-Water, <a href="/wiki/Gloucestershire" title="Gloucestershire">Gloucestershire</a>, England</figcaption></figure> <p>A physical model (most commonly referred to simply as a model but in this context distinguished from a <a href="/wiki/Conceptual_model" title="Conceptual model">conceptual model</a>) is a smaller or larger physical representation of an <a href="/wiki/Physical_object" title="Physical object">object</a>, person or <a href="/wiki/System" title="System">system</a>. The object being modelled may be small (e.g., an <a href="/wiki/Atom" title="Atom">atom</a>) or large (e.g., the <a href="/wiki/Solar_System" title="Solar System">Solar System</a>) or life-size (e.g., a <a href="/wiki/Model_(person)" title="Model (person)">fashion model</a> displaying clothes for similarly-built potential customers). </p><p>The <a href="/wiki/Geometry" title="Geometry">geometry</a> of the model and the object it represents are often <a href="/wiki/Similarity_(geometry)" title="Similarity (geometry)">similar</a> in the sense that one is a <a href="/wiki/Scale_(ratio)" title="Scale (ratio)">rescaling</a> of the other. However, in many cases the similarity is only approximate or even intentionally distorted. Sometimes the <a href="/wiki/Distortion" title="Distortion">distortion</a> is systematic, e.g., a fixed scale horizontally and a larger fixed scale vertically when modelling <a href="/wiki/Topography" title="Topography">topography</a> to enhance a region's mountains. </p><p>An architectural model permits visualization of internal relationships within the structure or external relationships of the structure to the environment. Another use is as a <a href="/wiki/Toy" title="Toy">toy</a>. </p><p>Instrumented physical models are an effective way of investigating fluid flows for <a href="/wiki/Engineering" title="Engineering">engineering</a> design. Physical models are often coupled with <a href="/wiki/Computational_fluid_dynamics" title="Computational fluid dynamics">computational fluid dynamics</a> models to optimize the design of equipment and processes. This includes external flow such as around buildings, vehicles, people, or <a href="/wiki/Hydraulic_engineering" title="Hydraulic engineering">hydraulic structures</a>. <a href="/wiki/Wind_tunnel" title="Wind tunnel">Wind tunnel</a> and <a href="/wiki/Water_tunnel_(hydrodynamic)" title="Water tunnel (hydrodynamic)">water tunnel</a> testing is often used for these design efforts. Instrumented physical models can also examine internal flows, for the design of ductwork systems, pollution control equipment, food processing machines, and mixing vessels. Transparent flow models are used in this case to observe the detailed flow phenomenon. These models are scaled in terms of both geometry and important forces, for example, using <a href="/wiki/Froude_number" title="Froude number">Froude number</a> or <a href="/wiki/Reynolds_number" title="Reynolds number">Reynolds number</a> scaling (see <a href="/wiki/Similitude" title="Similitude">Similitude</a>). In the pre-computer era, the UK economy was modelled with the hydraulic model <a href="/wiki/MONIAC" class="mw-redirect" title="MONIAC">MONIAC</a>, to predict for example the effect of tax rises on employment. </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:MONIAC_computer.jpg" class="mw-file-description" title="Water-powered model of the UK economy – MONIAC in the Science Museum, London"><img alt="Water-powered model of the UK economy – MONIAC in the Science Museum, London" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/MONIAC_computer.jpg/82px-MONIAC_computer.jpg" decoding="async" width="82" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/MONIAC_computer.jpg/123px-MONIAC_computer.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/MONIAC_computer.jpg/164px-MONIAC_computer.jpg 2x" data-file-width="1515" data-file-height="2218" /></a></span></div> <div class="gallerytext">Water-powered model of the UK economy – <a href="/wiki/Phillips_Machine" title="Phillips Machine">MONIAC</a> in the Science Museum, London</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Hannah_Harper_2.jpg" class="mw-file-description" title="Female model demonstrating brassiere for similarly-built potential buyers"><img alt="Female model demonstrating brassiere for similarly-built potential buyers" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Hannah_Harper_2.jpg/120px-Hannah_Harper_2.jpg" decoding="async" width="80" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Hannah_Harper_2.jpg/250px-Hannah_Harper_2.jpg 2x" data-file-width="400" data-file-height="600" /></a></span></div> <div class="gallerytext">Female model demonstrating <a href="/wiki/Brassiere" class="mw-redirect" title="Brassiere">brassiere</a> for similarly-built potential buyers</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Models_of_battle_at_australian_war_memorial_museum.jpg" class="mw-file-description" title="Model of a war scene — Australian War Memorial, Canberra"><img alt="Model of a war scene — Australian War Memorial, Canberra" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Models_of_battle_at_australian_war_memorial_museum.jpg/120px-Models_of_battle_at_australian_war_memorial_museum.jpg" decoding="async" width="120" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Models_of_battle_at_australian_war_memorial_museum.jpg/250px-Models_of_battle_at_australian_war_memorial_museum.jpg 1.5x" data-file-width="1600" data-file-height="1067" /></a></span></div> <div class="gallerytext">Model of a war scene — <a href="/wiki/Australian_War_Memorial" title="Australian War Memorial">Australian War Memorial</a>, Canberra</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:USDA-ARS_Guinea_Pig.jpg" class="mw-file-description" title="Guinea pig used as animal model for studying human leptospirosis"><img alt="Guinea pig used as animal model for studying human leptospirosis" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/USDA-ARS_Guinea_Pig.jpg/80px-USDA-ARS_Guinea_Pig.jpg" decoding="async" width="80" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/USDA-ARS_Guinea_Pig.jpg/120px-USDA-ARS_Guinea_Pig.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/USDA-ARS_Guinea_Pig.jpg/160px-USDA-ARS_Guinea_Pig.jpg 2x" data-file-width="1804" data-file-height="2700" /></a></span></div> <div class="gallerytext"><a href="/wiki/Guinea_pig" title="Guinea pig">Guinea pig</a> used as animal model for studying human <a href="/wiki/Leptospirosis" title="Leptospirosis">leptospirosis</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:MD-11_12ft_Wind_Tunnel_Test.jpg" class="mw-file-description" title="NASA wind tunnel with the scale model of an aeroplane"><img alt="https://www.nasa.gov/sites/default/files/styles/side_image/public/thumbnails/image/edu_wind_tunnels_1.jpg?itok=pZg9nFzN" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/MD-11_12ft_Wind_Tunnel_Test.jpg/120px-MD-11_12ft_Wind_Tunnel_Test.jpg" decoding="async" width="120" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/MD-11_12ft_Wind_Tunnel_Test.jpg/180px-MD-11_12ft_Wind_Tunnel_Test.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/MD-11_12ft_Wind_Tunnel_Test.jpg/240px-MD-11_12ft_Wind_Tunnel_Test.jpg 2x" data-file-width="2619" data-file-height="2235" /></a></span></div> <div class="gallerytext"><a href="/wiki/NASA" title="NASA">NASA</a> wind tunnel with the scale model of an aeroplane</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Conceptual_model">Conceptual model</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=4" title="Edit section: Conceptual model"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:AtmosphericModelSchematic.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/AtmosphericModelSchematic.png/300px-AtmosphericModelSchematic.png" decoding="async" width="300" height="284" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/AtmosphericModelSchematic.png/450px-AtmosphericModelSchematic.png 1.5x, //upload.wikimedia.org/wikipedia/commons/7/73/AtmosphericModelSchematic.png 2x" data-file-width="540" data-file-height="512" /></a><figcaption>Weather models use <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a> based on the laws of <a href="/wiki/Physics" title="Physics">physics</a>, and a coordinate system which divides the planet into a 3D grid.</figcaption></figure> <p>A <a href="/wiki/Conceptual_model" title="Conceptual model">conceptual model</a> is a theoretical representation of a system, e.g. a <a href="/wiki/Numerical_weather_prediction" title="Numerical weather prediction">set of mathematical equations</a> attempting to describe the workings of the atmosphere for the purpose of weather forecasting.<sup id="cite_ref-MetOffice_8-0" class="reference"><a href="#cite_note-MetOffice-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It consists of <a href="/wiki/Concept" title="Concept">concepts</a> used to help understand or <a href="/wiki/Simulation" title="Simulation">simulate</a> a subject the model represents. </p><p>Abstract or <a href="/wiki/Conceptual_model" title="Conceptual model">conceptual models</a> are central to <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>,<sup id="cite_ref-MWCD_2-1" class="reference"><a href="#cite_note-MWCD-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Geosciences_3-1" class="reference"><a href="#cite_note-Geosciences-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> as almost every <a href="/wiki/Scientific_theory" title="Scientific theory">scientific theory</a> effectively embeds some kind of model of the <a href="/wiki/Universe" title="Universe">physical</a> or <a href="/wiki/Human_condition" title="Human condition">human sphere</a>. In some sense, a physical model "is always the reification of some conceptual model; the conceptual model is conceived ahead as the blueprint of the physical one", which is then constructed as conceived.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Thus, the term refers to models that are formed after a conceptualization or generalization process.<sup id="cite_ref-MWCD_2-2" class="reference"><a href="#cite_note-MWCD-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Geosciences_3-2" class="reference"><a href="#cite_note-Geosciences-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=5" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Conceptual_model_(computer_science)" class="mw-redirect" title="Conceptual model (computer science)">Conceptual model (computer science)</a>, an agreed representation of entities and their relationships, to assist in developing software</li> <li><a href="/wiki/Economic_model" title="Economic model">Economic model</a>, a theoretical construct representing economic processes</li> <li><a href="/wiki/Language_model" title="Language model">Language model</a> a probabilistic model of a natural language, used for speech recognition, language generation, and information retrieval <ul><li><a href="/wiki/Large_language_model" title="Large language model">Large language models</a> are artificial neural networks used for generative artificial intelligence (AI), e.g. ChatGPT</li></ul></li> <li><a href="/wiki/Mathematical_model" title="Mathematical model">Mathematical model</a>, a description of a system using mathematical concepts and language <ul><li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a>, a mathematical model that usually specifies the relationship between one or more random variables and other non-random variables</li> <li><a href="/wiki/Model_(CGI)" class="mw-redirect" title="Model (CGI)">Model (CGI)</a>, a mathematical representation of any surface of an object in three dimensions via specialized software</li></ul></li> <li><a href="/wiki/Medical_model" title="Medical model">Medical model</a>, a proposed "set of procedures in which all doctors are trained"</li> <li><a href="/wiki/Mental_model" title="Mental model">Mental model</a>, in psychology, an internal representation of external reality</li> <li><a href="/wiki/Model_(logic)" class="mw-redirect" title="Model (logic)">Model (logic)</a>, a set along with a collection of finitary operations, and relations that are defined on it, satisfying a given collection of axioms</li> <li><a href="/wiki/Model_(MVC)" class="mw-redirect" title="Model (MVC)">Model (MVC)</a>, information-representing component of a software, distinct from the user interface (the "view"), both linked by the "controller" component, in the context of the model–view–controller software design</li> <li><a href="/wiki/Model_act" title="Model act">Model act</a>, a law drafted centrally to be disseminated and proposed for enactment in multiple independent legislatures</li> <li><a href="/wiki/Standard_model_(disambiguation)" class="mw-disambig" title="Standard model (disambiguation)">Standard model (disambiguation)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Uses_of_models">Uses of models</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=6" title="Edit section: Uses of models"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to Bruce Edmonds, there are at least 5 general uses for models<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>: </p> <ul><li><b>Prediction</b>: The ability to reliably anticipate unknown data. This includes data within the domain of the training data (<a href="/wiki/Interpolation" title="Interpolation">interpolation</a>), and outside the domain (<a href="/wiki/Extrapolation" title="Extrapolation">extrapolation</a>).</li> <li><b>Explanation</b>: The ability to establish plausible chains of causality, by proposing mechanisms that can explain patterns seen in data.</li> <li><b>Theoretical exposition</b>: The ability to discover or propose new hypotheses, or refute existing hypotheses about the behaviour of the system being modelled.</li> <li><b>Description</b>: Using the output of a model to (partially) represent important aspects of the system being modelled.</li> <li><b>Illustration</b>: Using the output of the model as a tool communicate an idea or explanation.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Properties_of_models,_according_to_general_model_theory"><span id="Properties_of_models.2C_according_to_general_model_theory"></span>Properties of models, according to general model theory</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=7" title="Edit section: Properties of models, according to general model theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Herbert_Stachowiak" title="Herbert Stachowiak">Herbert Stachowiak</a>, a model is characterized by at least three properties:<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <dl><dt>1. Mapping</dt> <dd>A model always is a model <i>of something</i>—it is an image or representation of some natural or artificial, existing or imagined original,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> where this original itself could be a model.</dd> <dt>2. Reduction</dt> <dd>In general, a model will not include all attributes that describe the original but only those that appear relevant to the model's creator or user.</dd> <dt>3. Pragmatism</dt> <dd>A model does not relate unambiguously to its original. It is intended to work as a replacement for the original</dd> <dd>a) for certain subjects <i>(for whom?)</i></dd> <dd>b) within a certain time range <i>(when?)</i></dd> <dd>c) restricted to certain conceptual or physical actions <i>(what for?)</i>.</dd></dl> <p>For example, a street map is a model of the actual streets in a city (mapping), showing the course of the streets while leaving out, say, traffic signs and road markings (reduction), made for pedestrians and vehicle drivers for the purpose of finding one's way in the city (pragmatism). </p><p>Additional properties have been proposed, like <i>extension</i> and <i>distortion</i><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> as well as <i>validity</i>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> The American philosopher Michael Weisberg differentiates between concrete and mathematical models and proposes computer simulations (computational models) as their own class of models.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=8" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Conceptual_framework" title="Conceptual framework">Conceptual framework</a></li> <li><a href="/wiki/Metamodeling" title="Metamodeling">Metamodeling</a></li> <li><a href="/wiki/Model_aircraft" title="Model aircraft">Model aircraft</a></li> <li><a href="/wiki/Model_car" title="Model car">Model car</a></li> <li><a href="/wiki/Model_house" class="mw-redirect" title="Model house">Model house</a></li> <li><a href="/wiki/Model_railway" class="mw-redirect" title="Model railway">Model railway</a></li> <li><a href="/wiki/Model_rocket" title="Model rocket">Model rocket</a></li> <li><a href="/wiki/Rail_transport_modelling" title="Rail transport modelling">Rail transport modelling</a></li> <li><a href="/wiki/Scale_model" title="Scale model">Scale model</a></li> <li><a href="/wiki/Scientific_model" class="mw-redirect" title="Scientific model">Scientific model</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=9" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-OED_model-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-OED_model_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output 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Retrieved <span class="nowrap">2025-03-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Different+Modelling+Purposes&rft.btitle=Simulating+Social+Complexity%3A+A+Handbook&rft.place=Cham&rft.pages=%3Cspan+class%3D%22nowrap%22%3E39-%3C%2Fspan%3E58&rft.pub=Springer+International+Publishing&rft.date=2017&rft.isbn=978-3-319-66948-9&rft.aulast=Edmonds&rft.aufirst=Bruce&rft_id=https%3A%2F%2Fdoi.org%2F10.1007%2F978-3-319-66948-9_4&rfr_id=info%3Asid%2Fen.wikipedia.org%3AModel" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Herbert Stachowiak: <i>Allgemeine Modelltheorie</i>, 1973, S. 131–133.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.automation.com/en-us/articles/february-2024/trick-easy-acronym-conceptualize-digital-twin?listname=Automation%20&%20Control%20News%20&%20Articles#authorInfo">"TRICK: An Easy Acronym to Conceptualize Digital Twin"</a>. <i>automation.com</i><span class="reference-accessdate">. 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In: <i>Journal of Universal Computer Science</i>, vol. 16, 2010, no. 20, S. 3120</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Dietrich Dörner: <i>Thought and Design – Research Strategies, Single-case Approach and Methods of Validation</i>. In: E. Frankenberger et al. (eds.): <i>Designers. The Key to Successful Product Development</i>. Springer-Verlag, Berlin et al. 1998, S. 3–11.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">M. Weisberg: <i>Simulation and Similarity - using models to understand the world.</i> Oxford University Press, New York 2013</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Model&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a 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class="vector-sticky-header-end" aria-hidden="true"> <div class="vector-sticky-header-icons"> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-talk-sticky-header" tabindex="-1" data-event-name="talk-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbles mw-ui-icon-wikimedia-speechBubbles"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-subject-sticky-header" tabindex="-1" data-event-name="subject-sticky-header"><span class="vector-icon mw-ui-icon-article mw-ui-icon-wikimedia-article"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-history-sticky-header" tabindex="-1" data-event-name="history-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-history mw-ui-icon-wikimedia-wikimedia-history"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only mw-watchlink" id="ca-watchstar-sticky-header" tabindex="-1" data-event-name="watch-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-star mw-ui-icon-wikimedia-wikimedia-star"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-edit-sticky-header" tabindex="-1" data-event-name="wikitext-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-wikiText mw-ui-icon-wikimedia-wikimedia-wikiText"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-ve-edit-sticky-header" tabindex="-1" data-event-name="ve-edit-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-edit mw-ui-icon-wikimedia-wikimedia-edit"></span> <span></span> </a> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only" id="ca-viewsource-sticky-header" tabindex="-1" data-event-name="ve-edit-protected-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-editLock mw-ui-icon-wikimedia-wikimedia-editLock"></span> <span></span> </a> </div> <div class="vector-sticky-header-buttons"> <button class="cdx-button cdx-button--weight-quiet mw-interlanguage-selector" id="p-lang-btn-sticky-header" tabindex="-1" data-event-name="ui.dropdown-p-lang-btn-sticky-header"><span class="vector-icon mw-ui-icon-wikimedia-language mw-ui-icon-wikimedia-wikimedia-language"></span> <span>19 languages</span> </button> <a href="#" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive" id="ca-addsection-sticky-header" tabindex="-1" data-event-name="addsection-sticky-header"><span class="vector-icon mw-ui-icon-speechBubbleAdd-progressive mw-ui-icon-wikimedia-speechBubbleAdd-progressive"></span> <span>Add topic</span> </a> </div> <div class="vector-sticky-header-icon-end"> <div class="vector-user-links"> </div> </div> </div> </div> </div> <div class="mw-portlet mw-portlet-dock-bottom emptyPortlet" id="p-dock-bottom"> <ul> </ul> </div> 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