Genomathematics or the Science of Erased Trajectories

Abstract

The approach presented here is part of a new epistemology: that of speculative but calculable sciences. Unlike classical science, which only describes and measures what exists, and unlike literary or philosophical speculation, which imagines without constraints of verification, these sciences aim to explore biological and evolutionary trajectories that are possible yet erased—hypothetical yet plausible—while relying on rigorous and reproducible methods.

Several earlier approaches paved the way without fully taking this step: information theory applied to the genome (Shannon, Kolmogorov), fractal and chaotic biology (Mandelbrot, Goodwin), or the speculations of exobiology (Crick, Sagan) on the universal laws of life. All highlighted the importance of mathematical patterns, but none proposed a systematic method for generating and testing alternative versions of life in a reproducible way.

This is precisely what the present approach allows: by applying systematic transformations of the genome (A↔G, C↔T inversions), identifying multi-scale numerical invariants, or reconstructing phenotypes that never came to be through 3D modeling and bioinformatics, it becomes possible to formalize the study of virtual life. The results—whether expressed as arithmetic constants, mirror genomes recognized as plausible by databases, or faces derived from alternative evolutionary paths—do not stem from free imagination but from transparent and verifiable calculations.

In this sense, speculative but calculable sciences constitute a distinct domain: they do not merely document life as it is or was, but also map its erased potentialities—revealing invisible constraints, unrealized possibilities, and universal invariants underlying the logic of the living.

Their scope extends far beyond intellectual curiosity. These sciences open concrete perspectives in personalized medicine (through the modeling of virtual genetic twins), in augmented paleogenetics (exploring the erased trajectories of human evolution), in neuroscience (simulating alternative brain architectures), and in exobiology (offering universal criteria for life detection). They also hold direct relevance for synthetic biology: mirror genomes and numerical invariants provide a theoretical laboratory to test novel genetic architectures prior to experimental construction. Thus, speculative genomathematics provides a framework for anticipating the viability of artificial organisms, exploring evolutionary paths never selected by nature, and expanding the repertoire of life forms created by humans.

At a time when biology is increasingly turning to artificial intelligence, modeling, and the fabrication of new organisms, it is essential to recognize this field as an autonomous discipline—not as a fringe of science, but as its natural extension into possible worlds.