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Books > Science & Mathematics > Mathematics > Applied mathematics
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Mathematics And The Natural Sciences: The Physical Singularity Of Life (Hardcover)
Loot Price: R3,174
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Mathematics And The Natural Sciences: The Physical Singularity Of Life (Hardcover)
Series: Advances in Computer Science and Engineering: Texts, 7
Expected to ship within 10 - 15 working days
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This book identifies the organizing concepts of physical and
biological phenomena by an analysis of the foundations of
mathematics and physics. Our aim is to propose a dialog between
different conceptual universes and thus to provide a unification of
phenomena. The role of "order" and symmetries in the foundations of
mathematics is linked to the main invariants and principles, among
them the geodesic principle (a consequence of symmetries), which
govern and confer unity to various physical theories. Moreover, an
attempt is made to understand causal structures, a central element
of physical intelligibility, in terms of both symmetries and
symmetry breakings. A distinction between the principles of
(conceptual) construction and of proofs, both in physics and in
mathematics, guides most of the work.The importance of mathematical
tools is also highlighted to clarify differences in the models for
physics and biology that are proposed by continuous and discrete
mathematics, such as computational simulations.Since biology is
particularly complex and not as well understood at a theoretical
level, we propose a "unification by concepts" which in any case
should precede mathematization. This constitutes an outline for
unification also based on highlighting conceptual differences,
complex points of passage and technical irreducibilities of one
field to another. Indeed, we suppose here a very common monist
point of view, namely the view that living objects are "big bags of
molecules". The main question though is to understand which
"theory" can help better understand these bags of molecules. They
are, indeed, rather "singular", from the physical point of view.
Technically, we express this singularity through the concept of
"extended criticality", which provides a logical extension of the
critical transitions that are known in physics. The presentation is
mostly kept at an informal and conceptual level.
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