Nature's Fundamental Symmetry Breaking

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.