hal-03319553
https://ens.hal.science/hal-03319553
https://ens.hal.science/hal-03319553/document
https://ens.hal.science/hal-03319553/file/2021_08_12_SpaceTimeIslamiLongo.pdf
doi:10.1016/j.pbiomolbio.2017.09.006
[SHS] Sciences de l'Homme et de la Société
[ENS-PARIS] Ecole Normale Supérieure de Paris
[CNRS] CNRS - Centre national de la recherche scientifique
[CDF] Collège de France
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[AO-PHILOSOPHIE] Archives ouvertes de la Philosophie
[REPUBLIQUE-DES-SAVOIRS] République des Savoirs : Lettres, Sciences, Philosophie - USR 3608
[PSL] Université Paris sciences et lettres
[ENS-PSL] École normale supérieure - PSL
[CDF-PSL] Collège de France - PSL
Marriages of Mathematics and Physics: a challenge for Biology
Islami, Arezoo
Longo, Giuseppe
[MATH] Mathematics [math]
[SHS.PHIL] Humanities and Social Sciences/Philosophy
[SCCO] Cognitive science
[PHYS] Physics [physics]
[SDV] Life Sciences [q-bio]
ART
Cognition
Foundations of Mathematical Knowledge
Mathematical Knowledge
Cognition and Foundations of Mathematical Knowledge
Geometric vs algebraic constructions
Ontological and historical differences
Synthesis and applications
Eastern and western traditions
Measurement
Space
Biological evolution and mathematics
The human attempts to access, measure and organize physical phenomena have led toa manifold construction of mathematical and physical spaces. We will survey the evolution of geome-tries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra inthis transition and its Western symbolic development is emphasized. In this relation, we will also dis-cuss changes in the ontological attitudes toward mathematics and its applications. Historically, the en-counter of geometric and algebraic perspectives enriched the mathematical practices and their founda-tions. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematicalanalysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations ofMathematics. After the success and the limits of the logico-formal analysis, it is necessary to broadenour foundational tools and re-examine the interactions with natural sciences. In particular, the way thegeometric 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 thecurrent notions of mathematical (phase) “space” should be revisited for the purposes of life sciences.
2017-12
2021-08-12
en
http://creativecommons.org/licenses/by-nc-nd/
Progress in Biophysics and Molecular Biology
Elsevier