Mathematics and the natural sciences : the physical singularity of life
著者
書誌事項
Mathematics and the natural sciences : the physical singularity of life
（Advances in computer science and engineering / editor-in-chief, Erol Gelenbe, . texts v. 7）
Imperial College Press , World Scientific Pubulishing (distributor), c2011
- タイトル別名
-
Mathématiques et sciences de la nature : La singularité physique du vivant
大学図書館所蔵 件 / 全1件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 299-312) and index
English translation of the revised version of: F. Bally and G. Longo, "Mathématiques et sciences de la nature. La singularité physique du vivant", Hermann Paris (2006).
内容説明・目次
内容説明
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.
目次
- Introduction
- Incompleteness and Indetermination
- Space and Time in Biology
- Invariances and Symetries
- Causality and Symetries
- Extended Criticality
- Randomness and Determination
- Towards a Conclusion .
「Nielsen BookData」 より