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data-author-id="309859080" href="https://independent.academia.edu/BellomoN">N. 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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). Reading Chapter 2 of the book (“Creatures Small and Smaller”) brought back a lot of horrible memories about, well, mem...</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":"Putting the in Biology : A Review of The Mathematics of Life Reviewed by","attachmentId":89788425,"attachmentType":"pdf","work_url":"https://www.academia.edu/84930342/Putting_the_in_Biology_A_Review_of_The_Mathematics_of_Life_Reviewed_by","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/84930342/Putting_the_in_Biology_A_Review_of_The_Mathematics_of_Life_Reviewed_by"><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="3" data-entity-id="107842473" 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/107842473/The_historical_nature_of_biological_complexity_and_the_ineffectiveness_of_the_mathematical_approach_to_it">The historical nature of biological complexity and the ineffectiveness of the mathematical approach to it</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="922189" href="https://uniroma2.academia.edu/SaverioForestiero">Saverio Forestiero</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Theory in Biosciences</p><p class="ds-related-work--abstract ds2-5-body-sm">Contemporary scientific knowledge is built on both methodological and epistemological reductionism. The discovery of the limitations of the reductionist paradigm in the mathematical treatment of certain physical phenomena originated the notion of complexity, both as a pattern and process. After clarifying some very general terms and ideas on biological evolution and biological complexity, the article will tackle to seek to summarize the debate on biological complexity and discuss the difference between complexities of living and inert matter. 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I also underline that the creation of the journal The Bulletin of Mathematical Biophysics was instrumental in legitimating the efforts of Rashevsky and his students, and I finally argue that his pioneering efforts, while still largely unacknowledged, were vital for the development of important scientific contributions, most notably the McCulloch-Pitts model of neural networks.</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":"The dawn of mathematical biology A aurora da biologia matemática","attachmentId":85229913,"attachmentType":"pdf","work_url":"https://www.academia.edu/78047062/The_dawn_of_mathematical_biology_A_aurora_da_biologia_matem%C3%A1tica","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/78047062/The_dawn_of_mathematical_biology_A_aurora_da_biologia_matem%C3%A1tica"><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="5" data-entity-id="18595744" 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/18595744/A_mathematical_view_of_biological_complexity">A mathematical view of biological complexity</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="38635640" href="https://independent.academia.edu/Jos%C3%A9RobertoCastilhoPiqueira">José Roberto Castilho Piqueira</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Nonlinear Science and Numerical Simulation, 2009</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":"A mathematical view of biological complexity","attachmentId":40148189,"attachmentType":"pdf","work_url":"https://www.academia.edu/18595744/A_mathematical_view_of_biological_complexity","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/18595744/A_mathematical_view_of_biological_complexity"><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="6" data-entity-id="78047064" 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/78047064/The_dawn_of_mathematical_biology">The dawn of mathematical 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="28508546" href="https://independent.academia.edu/DanielSanderHoffmann">Daniel Sander Hoffmann</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv: History and Philosophy of Physics, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper I describe the early development of the so-called mathematical biophysics, as conceived by Nicolas Rashevsky back in the 1920&#39;s, as well as his latter idealization of a &quot;relational biology&quot;. I also underline that the creation of the journal &quot;The Bulletin of Mathematical Biophysics&quot; was instrumental in legitimating the efforts of Rashevsky and his students, and I finally argue that his pioneering efforts, while still largely unacknowledged, were vital for the development of important scientific contributions, most notably the McCulloch-Pitts model of neural networks.</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":"The dawn of mathematical biology","attachmentId":85229916,"attachmentType":"pdf","work_url":"https://www.academia.edu/78047064/The_dawn_of_mathematical_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/78047064/The_dawn_of_mathematical_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="7" data-entity-id="21181908" 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/21181908/Mathematical_Biology_and_the_Existence_of_Biological_Laws">Mathematical Biology and the Existence of Biological Laws</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="4459747" href="https://uniromatre.academia.edu/MDorato">Mauro Dorato</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Probabilities, Laws, and Structures, 2012</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 Biology and the Existence of Biological Laws","attachmentId":41751204,"attachmentType":"pdf","work_url":"https://www.academia.edu/21181908/Mathematical_Biology_and_the_Existence_of_Biological_Laws","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/21181908/Mathematical_Biology_and_the_Existence_of_Biological_Laws"><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="93413840" 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/93413840/From_Cells_to_Organisms_Current_Topics_in_Mathematical_and_Theoretical_Biology">From Cells to Organisms: Current Topics in Mathematical and Theoretical 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="110569012" href="https://independent.academia.edu/DeutschAndreas">Andreas Deutsch</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Acta Biotheoretica, 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":"From Cells to Organisms: Current Topics in Mathematical and Theoretical Biology","attachmentId":96158179,"attachmentType":"pdf","work_url":"https://www.academia.edu/93413840/From_Cells_to_Organisms_Current_Topics_in_Mathematical_and_Theoretical_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/93413840/From_Cells_to_Organisms_Current_Topics_in_Mathematical_and_Theoretical_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="1454554" 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/1454554/Stepping_Beyond_the_Newtonian_Paradigm_in_Biology_Towards_an_Integrable_Computational_Model_of_Life_Accelerating_Discovery_in_the_Biological_Foundations_of_Science_INBIOSA_White_Paper">Stepping Beyond the Newtonian Paradigm in Biology. Towards an Integrable Computational Model of Life: Accelerating Discovery in the Biological Foundations of Science. INBIOSA White Paper</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="34504635" href="https://independent.academia.edu/MarchalBruno">Bruno Marchal</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33396608" href="https://independent.academia.edu/Andr%C3%A9eEhresmann">Andrée Ehresmann</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="266561" href="https://stir.academia.edu/LeslieSmith">Leslie S Smith</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34443303" href="https://uni-tzuebingen.academia.edu/OttoR%C3%B6ssler">Otto Rössler</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="3551295" href="https://swinburne.academia.edu/ArranGare">Arran Gare</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="214174" href="https://independent.academia.edu/PlamenLSimeonov">Plamen L Simeonov</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="23287253" href="https://michiganstate.academia.edu/RobertRootBernstein">Robert Root-Bernstein</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on cross-disciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. Keywords: integral biomathics, theoretical biology, biological mathematics, theoretical physics, endophysics, semiotics, observer-participation, developmental biology, neuroscience, natural computing, biocomputing, category theory, logic, positivism, scientific revolution, determinism, non-deterministic chaos, first-person perspective, complementarity, emergence, complexity, holism, reductionism, information, information integration, communication, change, development, hierarchies, scale and hyperscale, self-organization, autopoiesis, internalism, mechanicism, vagueness, class identity, individual identity, biological time, mind-body problem, non-locality, virtualization, distribution, genetic transcoding, neural systems, memory, cognition, consciousness, quantum effects in biology, life.</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":"Stepping Beyond the Newtonian Paradigm in Biology. 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