sharks and fish

Environments for Life

Life on Earth is not singular. In a fantastic variety of environments, from deep ocean thermal vents to Antarctic dry valleys, life thrives. The fossil record reveals cohorts of species evolved and reinvented many times for each environment. Life is so successful that it has transformed the atmosphere and crust of our planet.

If life is robust, then life should emerge in systems simpler than the quantum-mechanical totality of the young planet Earth in its young solar system. The mathematical challenge is to identify the essential system properties and understand the origins of life in terms of those properties.

The ancient Earth was not uniform; there were a multitude of different chemical environments. That some hypothetical "typical" early environment did not support RNA replication does nothing to rule out that some early environment would support it.

Mathematical Context

John Von Neumann created a cellular automaton into which a self-replicating universal (Turing) machine can be embedded. The universality (computational) attribute is used to distinguish self-replicating machines from crystals.

Von Neumann proved that a universal self-replicating machine could be embedded in a particular deterministic cellular automata. This is an important result, especially notable for its use of a tape for holding the genetic information before the discovery of the structure of DNA. But it doesn't reveal how such a machine would emerge by evolution, or even if that cellular automata was capable of evolving a self-replicating machine.

The Game Theory of Life seeks to prove that universal self-replicating machines will evolve from systems (cellular automata or others) obeying the rules of the nucleotide-game.

Game Theory

That game theory has been applied to animal populations is not news. The present effort applies game theory on several levels: genetic molecules as players, organisms as players, and species as players.

How can molecules be players? In a gas or liquid, molecules collide billions of times per second. As they rotate and gyrate, if molecules have orientations which mesh, then they will be tried. So reactions can be characterized as transformations between molecule types with reaction rates or probabilities.

How do genetic molecules choose strategies? These games are played with huge numbers of players of each species. Mutations in those players' genomes try variations of strategy simultaneously. With time, variations more and more different from the original are tried. If the species doesn't go extinct in the meantime, improved molecules and genomes will win out.

Mutation is thus a crucial component of these games.


This treatise seeks to elucidate the abstract processes by which life develops. Particulars of elements and molecules are not considered; only the functional properties vis-a-vis other molecules which makes them important. The conditions proposed here are a work in progress, attempting to find a set sufficient to produce a Proof of Life.

Notions such as energy and conservation laws are not employed in the nucleotide-game. Von Neumann's Universal Constructor, which motivates the nucleotide-game, is a cellular automaton; and as such does not necessarily obey familiar conservation laws.


At a larger scale, the type of microbial communities discussed in On The Origin of Collectives -- Bacterial Evolution cooperate and coordinate their replication (without being enclosed by a communal membrane). Eukaryote cells are microbial communities with an enclosing communal membrane.

Plants and Animals

The rhythm of the lives of many eukaryote species is synchronized with seasons, the environmental effects of Earth's axial tilt of 23o. In locales where climates vary severly with the seasons, generations become discrete in nature. This leads to amazing behavior like Prime Number Selection of Cycles in a Predator-Prey Model ([11]).

Life's strong presence in subterranean and deep ocean climes is strong evidence that seasons are not a necessary ingredient for microbial evolution.


Some of the terms used here are borrowed from biology and chemistry. But they should be understood to apply to any nucleotide-game system.
a nucleotide polymer which translates a nucleotide sequence to a non-genetic polymer.
form a new nucleotide polymer whose complement is identical to the original nucleotide polymer
a genetic molecule that itself catalyzes a chemical reaction.
the minimum complete set of genetic material an individual of a species has.

The first chapter is Viroids -- the Nucleotide Game.

Copyright © 2003, 2004, 2005, 2007 Aubrey Jaffer

I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.  My actions and comments do not reflect in any way on MIT.
The Game Theory of Life
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