I'm interested in the topic life, as every one should and when it crosses my mind I started reading about its different explanations like in biology they say life is combination of metabolism and reproduction , in chemistry it's chemical reaction but can it be defined mathematically ?

  • It's generally not useful to define "Life" mathematically - usually one models some aspect of life mathematically. Even then, it will depend on context - when the question is about making predictions (eg about a population), that's usually modeled using differential equations, whereas other things are modeled by force diagrams. In any case, this doesn't seem like a philosophy question. – James Kingsbery Aug 8 '16 at 19:29

Nothing that is not sheerly mental or ideal can be defined mathematically.

It may be modeled mathematically, but in that case, it constitutes a theory or simulation in a science other than mathematics.

If your only standard for 'life' is self-organization, then there are examples of self-organizing, self-reproducing algorithms starting from https://en.wikipedia.org/wiki/Von_Neumann_universal_constructor.

But such abstract machines have no physical manifestations by nature. And when they are given them, those manifestations are models attempting to approximate a single aspect of biological maintenance and evolution, either to study those principles, or to use them in engineering. Which makes them biology or robotics, and not mathematics.

  • Recently a self-replicating pattern was also produced in Conway Life – Tim kinsella Aug 4 '16 at 18:33
  • I wonder whether your distinction between a model and the phenomenon modeled becomes hair-splitting when it comes to things like life, intelligence, consciousness. In the same way that simulated intelligence is really just intelligence, if simulated organisms can evolve inside of some cellular automaton, then maybe they deserve to be called organisms. – Tim kinsella Aug 4 '16 at 18:38
  • @Timkinsella No, it doesn't. Intelligence is not a physical phenomenon. It is an epiphenomenon that can be captured entirely in information. Life just isn't similar. – user9166 Aug 4 '16 at 20:20

I don't know if this is what a philosophy site means by the meaning of life. But anyway chemists do not say life is just any chemical reaction. Acid dissolving limestone is not life. They say it is any chemical reaction that takes in energy from the environment (metabolism) and reproduces itself (or, to be more precise, takes in lower entropy energy, and disperses energy at higher entropy, so it is out of thermal equilibrium with the environment). So it is the biological definition that you give.

Notice that on this definition it is problematic whether viruses count as life. And this is intentional. People do not agree whether they are a form of life themselves. Viruses have no metabolism, and they trigger host cells to reproduce them.

The software product Avida more or less defines life as a system that that more or less accurately reproduces itself. See https://en.wikipedia.org/wiki/Avida . And I believe you can configure it so that your "organisms" need a certain rate of inputs to survive -- which is a kind of mathematical metabolism.

Avida is adapted from Conway's Game of Life https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life as a way to make it useful for actual evolutionary modelling.

But there is no one universally accepted mathematical definition of life.


Life has many aspects and a long long history. The long history is the hardest thing to capture mathematically. Sometime math just tries to learn from or imitate life, as in neural networks, evolutionary algorithms, and bionics in general. Some mathematical disciplines like game theory, Turing completeness, and machine learning are somewhat related to life. Necessary mathematical conditions of life include being self-reproducing and being self-reflecting.

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