http://popups.lib.uliege.be/1373-5411/index.php?id=3217 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3205 Mathematics and physics are shown to have a symbiotic relationship as emergent aspects of a universal rewrite system. In addition to explaining the 'unreasonable effectiveness' of mathematics in physics and the 'unreasonable effectiveness' of physics in mathematics, this emergent nature of both subjects makes sense of the distinction between syntactic and semantic approaches to logical reasoning. The system is also shown to generate constraints on the kinds of mathematics and physics that are possible, explaining, in particular, why symmetry is so significant in the subjects' foundations, and specifying which symmetries are most significant, as well as indicating their points of origin. Quantum mechanics emerges from this structure in a very specific form which enables us to understand the origin of symmetry breaking in physics and many other aspects of fundamental physical theory. Gravity also has special characteristics which explain its uniqueness among the four physical forces. Wed, 11 Sep 2024 17:03:03 +0200 Tue, 08 Oct 2024 13:25:37 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3205 http://popups.lib.uliege.be/1373-5411/index.php?id=3221 Assuming that Nature is described by a universal rewrite system and operates according to a process that we can refer to as Nature's code, we define certain numbers as being crucial indicators of how the code operates, whether in biology, chemistry or physics. We also show how these numbers originate in the most extraordinarily simple way from two numbers which correspond to the two distinct processes - conserve and create - within the system which can in tum be related to the properties of duality and anticommutativity. The numbers emerge in a number of distinct series which have distinct algebraic and geometrical representations. The geometrical structures translate easily from 3- to higher-dimensional representations, especially those of dimension 4 and 8, and also connect significantly with rotational symmetries and with Lie groups, up to E8. The fundamental particles of physics are a classic case of the operation of the number series, in which all the significant numbers are represented, and no others. The structure leads to a complete classification of fermions and bosons within an overall E8 representation. An almost parallel system emerges in the genetic code, leading to the processes of transcription and translation. Thu, 12 Sep 2024 09:34:05 +0200 Thu, 12 Sep 2024 09:34:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3221 http://popups.lib.uliege.be/1373-5411/index.php?id=3216 The question we are concerned with is: how can the highly ordered replicating state which we call 'life' form within a universe where the tendency of natural processes is towards a state of increasing disorder? The existence of a machine order code or driving process for life to emerge seems to be suggested by the generation of a universal rewrite system, with its own mathematical structure, from the single assumption of a zero totality universe; and it would appear that the successive stages which this system automatically generates correspond with the algebraic and geometrical structures which are fundamental in physics and biology in particular. The system has a number of significant aspects - cardinality, rather than ordinality, 'bifurcation' at each stage, and a key stage at which symmetry breaking first occurs. The progressive stages are worked out here in both algebraic and geometrical terms and illustrated through detailed applications to genetics and particle physics. Thu, 12 Sep 2024 09:33:40 +0200 Thu, 12 Sep 2024 09:33:50 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3216