Mathematics is a powerful tool to express the computable part of the reality of the physical world. For living systems, mathematical relations emerge internally as an abstracting capacity in the course of development and adaptation to the external world. All living systems possess internal coding structures which represent their embedded description. They are anticipatory in the sense that the embedded description generates deterministic model of their behavior. If the model does not provide a correct result, they can evolve through the acquisition of new statements inside the embedded description that overcome limitations of the existing model. The newly generated statements acquire meaning in and from the changing environment. The growth of complexity, being a consequence of the internal active adaptation to externality performed by the systems, increases the amount of external work and generates the observed patterns of spatiotemporal structures of evolving systems. In living systems, the symbolic memory constraints are dynamic processes in themselves, co-evolving with the other components of biological systems. Separation of the symbolic memory and the dynamic laws (defined as the epistemic cut), required for self-replication of biological systems, forms the basis for their onto-epistemic relation to reality. In this regard, living systems possess their own internal abstracting capacity and invent mathematics. The digital structure of the genetic code is a manifestation of this mathematics.
Keywords: Biological code; Biological evolution; Complexification; Computation; Epistemic cut; Hypercycle; Internal measurement; Relational biology; Univalent foundations.
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