Historicity at the Heart of Biology: a Challenge for Mathematical Thinking
Systems Biology
How do mathematical models convey meaning? What is required to build a model? An introduction for biologists and philosophers.
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Mathematical modeling is a very powerful tool for understanding natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter, we highlight the key ingredients and steps of modeling and focus on their biological interpretation. In particular, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.
Keywords: Equations, Mathematical modeling, Parameters, Proliferation, Theory
Montévil, Maël. 2018. “A Primer on Mathematical Modeling in the Study of Organisms and Their Parts.” In Systems Biology, edited by Mariano Bizzarri, 41–55. Methods in Molecular Biology. New York, NY: Springer. https://doi.org/10.1007/978-1-4939-7456-6_4
Biological evolution involves the appearance of new traits, new phenotypes and new processes but the mathematical understanding of such novelties is still lacking. In this paper, I argue that the notion of a new possibility should be and can be a fundamental notion in biology. This idea has been used…
We are a group of mathematicians who denounce a mathematization of the world oriented towards purely quantitative analyses and reductionism, rather than invention and construction of understanding. The prevailing use of mathematics as a search for “optimal paths” in economy, biology and general human…
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Nicholas Georgescu Rœgen and René Passet, as well as MIT, have emphasized that entropy and negentropy should be central to economic analysis. We will see that this requires us to consider anti-entropy as a dynamic factor, and to specify its role in a contributive economy, according to biology.
By analogy with theoretical physics, theoretical biology is not limited to 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…
Constructivist Foundations
I discuss convergences between the approach of N. Palfreyman and J. Miller-Young and my work aiming for a theory of organisms, in particular on randomness.
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Open peer commentary on the article “What Is a Cognizing Subject? Construction, Autonomy and Original Causation” by Niall Palfreyman & Janice Miller-Young. http://constructivist.info/13/3/362.palfreyman Upshot: I discuss convergences between the approach of the authors and my work aiming for a theory of organisms. I also discuss some pitfalls and challenges pertaining to biological randomness, which, I argue, require original developments.
Montévil, Maël. 2018. “A Few Pending Challenges from the Perspective of a Theory of Organisms.” Constructivist Foundations 13 (3): 377–79. http://constructivist.info/13/3/377.montevil