Mathematics and the Natural Sciences: The Physical Singularity of Life (Advances in Computer Science and Engineering: Texts)

Francis Bailly, Giuseppe Longo

This publication identifies the organizing techniques of actual and organic phenomena via an research of the rules of arithmetic and physics. Our target is to suggest a conversation among assorted conceptual universes and hence to supply a unification of phenomena. The position of 'order" and symmetries within the foundations of arithmetic is associated with the most invariants and rules, between them the geodesic precept (a outcome of symmetries), which govern and confer cohesion to varied actual theories. additionally, an try out is made to appreciate causal buildings, a relevant component to actual intelligibility, by way of either symmetries and symmetry breakings. A contrast among the foundations of (conceptual) building and of proofs, either in physics and in arithmetic, publications lots of the paintings.
the significance of mathematical instruments is additionally highlighted to explain adjustments within the types for physics and biology which are proposed through non-stop and discrete arithmetic, similar to computational simulations.
for the reason that biology is very advanced and never in addition understood at a theoretical point, we advise a "unification by way of concepts" which at least should still precede mathematization. This constitutes an summary for unification additionally in line with highlighting conceptual alterations, complicated issues of passage and technical irreducibilities of 1 box to a different. certainly, we think right here a truly universal monist perspective, specifically the view that residing gadgets are "big luggage of molecules". the most query although is to appreciate which "theory" can assist higher comprehend those luggage of molecules. they're, certainly, fairly "singular", from the actual viewpoint. Technically, we exhibit this singularity in the course of the inspiration of "extended criticality", which gives a logical extension of the severe transitions which are recognized in physics. The presentation is generally saved at an off-the-cuff and conceptual point.

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