Dynamical real numbers and living systems

TL;DR

This paper introduces a novel extended calculus based on second derivative discontinuous solutions, representing real numbers as living, evolving structures, with implications for understanding living systems and dynamics.

Contribution

It presents a new extended calculus framework and a dynamical representation of real numbers as living, evolving entities, linking mathematics with biological system modeling.

Findings

Real numbers can be visualized as living, cell-like structures.

Extended calculus captures nonstandard dynamics relevant to living systems.

An intelligent version of Newton's first law is proposed.

Abstract

Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical representation of the ordinary real number system. Every real number can be visualized as a living cell -like structure, endowed with a definite evolutionary arrow. We discuss the relevance of this extended calculus in the study of living systems. We also present an intelligent version of the Newton's first law of motion.