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Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological" /> <meta property="article:author" content="https://ens.academia.edu/Ma%C3%ABlMont%C3%A9vil" /> <meta name="description" content="Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological" /> <title>(PDF) Which first principles for mathematical modelling in biology | Maël Montévil - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/40232744/Which_first_principles_for_mathematical_modelling_in_biology" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '92477ec68c09d28ae4730a4143c926f074776319'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1732782794000); window.Aedu.timeDifference = new Date().getTime() - 1732782794000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are expressed in terms of symmetries and the associated conservations, on the one side, and optimization on the other side. In biology, we argue instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and the historicity of biological phenomena. By contrast, the relative regularity of some aspects of biological organisms, which we call constraints, should be regarded as the consequence of a mutual stabilization of the parts of organisms. We exemplify several aspects of this framework with the modeling of allometric relationships. Our change of perspective leads to reconsider the meaning of measurements and the structure of the space of description.","author":[{"@context":"https://schema.org","@type":"Person","name":"Maël Montévil"}],"contributor":[],"dateCreated":"2019-09-02","dateModified":null,"datePublished":"2019-01-01","headline":"Which first principles for mathematical modelling in biology","inLanguage":"en","keywords":["Biophysics","Philosophy of Physics","Philosophy of Biology","Organizational Change","Mathematical Biology","Autopoiesis","Functionalism","Mathematical Modelling","Morphogenesis","Theoretical biology","Allometry"],"locationCreated":null,"publication":"Rendiconti di Matematica e delle sue 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window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":40232744,"created_at":"2019-09-02T06:04:42.283-07:00","from_world_paper_id":null,"updated_at":"2021-01-17T19:44:44.364-08:00","_data":{"abstract":"Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are expressed in terms of symmetries and the associated conservations, on the one side, and optimization on the other side. In biology, we argue instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and the historicity of biological phenomena. By contrast, the relative regularity of some aspects of biological organisms, which we call constraints, should be regarded as the consequence of a mutual stabilization of the parts of organisms. We exemplify several aspects of this framework with the modeling of allometric relationships. Our change of perspective leads to reconsider the meaning of measurements and the structure of the space of description.","publication_date":"2019,,","publication_name":"Rendiconti di Matematica e delle sue Applicazioni"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Which first principles for mathematical modelling in biology","broadcastable":true,"draft":false,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [28744524]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":60463460,"attachmentType":"pdf"}"><img alt="First page of “Which first principles for mathematical modelling in biology”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/60463460/mini_magick20190902-26868-1nlldi6.png?1567430508" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/assets/single_work_splash/adobe.icon-574afd46eb6b03a77a153a647fb47e30546f9215c0ee6a25df597a779717f9ef.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Which first principles for mathematical modelling in biology</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="28744524" href="https://ens.academia.edu/Ma%C3%ABlMont%C3%A9vil"><img alt="Profile image of Maël Montévil" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/28744524/11941342/13306232/s65_ma_l.mont_vil.jpg" />Maël Montévil</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2019, Rendiconti di Matematica e delle sue Applicazioni</p></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">Like theoretical physics, theoretical biology is not just mathematical modeling. Instead, theoretical biology should strive to find suitable first principles to ground the understanding of biological phenomena and ultimately frame biological experiments and mathematical models. First principles in physics are expressed in terms of symmetries and the associated conservations, on the one side, and optimization on the other side. In biology, we argue instead that a strong notion of variation is fundamental. This notion encompasses new possibilities and the historicity of biological phenomena. By contrast, the relative regularity of some aspects of biological organisms, which we call constraints, should be regarded as the consequence of a mutual stabilization of the parts of organisms. We exemplify several aspects of this framework with the modeling of allometric relationships. Our change of perspective leads to reconsider the meaning of measurements and the structure of the space of description.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":60463460,"attachmentType":"pdf","workUrl":"https://www.academia.edu/40232744/Which_first_principles_for_mathematical_modelling_in_biology"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":60463460,"attachmentType":"pdf","workUrl":"https://www.academia.edu/40232744/Which_first_principles_for_mathematical_modelling_in_biology"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="60463460" data-landing_url="https://www.academia.edu/40232744/Which_first_principles_for_mathematical_modelling_in_biology" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="67576868" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/67576868/Variations_on_the_theme_of_invariants_conceptual_and_mathematical_dualities_in_physics_vs_biology">Variations on the theme of invariants: conceptual and mathematical dualities in physics vs biology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2771586" href="https://ens.academia.edu/GiuseppeLongo">Giuseppe Longo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Human Evolution, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">In a work of Bailly and Longo (2010), a comparison between the invariants in physics and some particular invariants in biology is presented through conceptual dualities that we highlight and further specify here in their main theoretical differences. Many controversies in relating physics and biology, for instance the question of a physicalist approach in biology, derive from strong and well-established epistemological and cultural guardrails. Our purpose is to identify at least some of the patterns or principles that may guide theory building in biology by physico-mathematical methodologies which simultaneously takes into account its autonomy. In other terms, we discuss biological extensions of physical theories that are based just on &quot;conceptual practices&quot; from physics and not necessarily on its laws and objects. To this purpose we stress the divergence between mathematical invariants and variables in physics with respect to biological variability (and evolvability), whi...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Variations on the theme of invariants: conceptual and mathematical dualities in physics vs biology","attachmentId":78342581,"attachmentType":"pdf","work_url":"https://www.academia.edu/67576868/Variations_on_the_theme_of_invariants_conceptual_and_mathematical_dualities_in_physics_vs_biology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/67576868/Variations_on_the_theme_of_invariants_conceptual_and_mathematical_dualities_in_physics_vs_biology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="27942089" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27942089/Theoretical_principles_for_biology_Variation">Theoretical principles for biology: Variation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="235670" href="https://cnrs.academia.edu/MatteoMossio">Matteo Mossio</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9444291" href="https://cnrs.academia.edu/ArnaudPocheville">Arnaud Pocheville</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2771586" href="https://ens.academia.edu/GiuseppeLongo">Giuseppe Longo</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="28744524" href="https://ens.academia.edu/Ma%C3%ABlMont%C3%A9vil">Maël Montévil</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2016</p><p class="ds-related-work--abstract ds2-5-body-sm">Darwin introduced the concept that random variation generates new living forms. In this paper, we elaborate on Darwin's notion of random variation to propose that biological variation should be given the status of a fundamental theoretical principle in biology. We state that biological objects such as organisms are specific objects. Specific objects are special in that they are qualitatively different from each other. They can undergo unpredictable qualitative changes, some of which are not defined before they happen. We express the principle of variation in terms of symmetry changes, where symmetries underlie the theoretical determination of the object. We contrast the biological situation with the physical situation, where objects are generic (that is, different objects can be assumed to be identical) and evolve in well-defined state spaces. We derive several implications of the principle of variation, in particular, biological objects show randomness, historicity and contextuality. 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But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart’s new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) the microscope; (ii) classification; (iii) evolution; (iv) genetics, and (v) the structure of DNA. The sixth, Stewart says, is well on its way. It is mathematics. I’m ashamed to admit it, but I did not pass my high school biology exam (in the UK it was called the “Ordinary Level” exam, or “O” Level). 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ds2-5-body-link" href="https://www.academia.edu/50011085/From_Gregor_Mendel_to_Eric_Davidson_Mathematical_Models_and_Basic_Principles_in_Biology">From Gregor Mendel to Eric Davidson: Mathematical Models and Basic Principles in Biology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7656179" href="https://bgu.academia.edu/UteDeichmann">Ute Deichmann</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Computational Biology</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"From Gregor Mendel to Eric Davidson: Mathematical Models and Basic Principles in Biology","attachmentId":68155877,"attachmentType":"pdf","work_url":"https://www.academia.edu/50011085/From_Gregor_Mendel_to_Eric_Davidson_Mathematical_Models_and_Basic_Principles_in_Biology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50011085/From_Gregor_Mendel_to_Eric_Davidson_Mathematical_Models_and_Basic_Principles_in_Biology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="46953425" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/46953425/Mathematical_Models_Explanation_Laws_and_Evolutionary_Biology">Mathematical Models, Explanation, Laws, and Evolutionary Biology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="707657" href="https://mugla.academia.edu/MehmetElgin">Mehmet Elgin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">History and Philosophy of the Life Sciences, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Mathematical Models, Explanation, Laws, and Evolutionary Biology","attachmentId":66305092,"attachmentType":"pdf","work_url":"https://www.academia.edu/46953425/Mathematical_Models_Explanation_Laws_and_Evolutionary_Biology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/46953425/Mathematical_Models_Explanation_Laws_and_Evolutionary_Biology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="34783705" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/34783705/Marriages_of_mathematics_and_physics_A_challenge_for_biology">Marriages of mathematics and physics: A challenge for biology</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="27548681" href="https://sfsu.academia.edu/ArezooIslami">Arezoo Islami</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2771586" href="https://ens.academia.edu/GiuseppeLongo">Giuseppe Longo</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Keywords: Geometric vs algebraic constructions Ontological and historical differences Synthesis and applications Eastern and western traditions Measurement Space Biological evolution and mathematics a b s t r a c t The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of " geometric judgments " from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and reexamine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) " space " should be revisited for the purposes of life sciences.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Marriages of mathematics and physics: A challenge for biology","attachmentId":54642666,"attachmentType":"pdf","work_url":"https://www.academia.edu/34783705/Marriages_of_mathematics_and_physics_A_challenge_for_biology","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/34783705/Marriages_of_mathematics_and_physics_A_challenge_for_biology"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":60463460,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":60463460,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_60463460" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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