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I recently started to have interest in the characteristics of life. Especially, I wonder if there are some kind of mathematical description of the true meaning of life and how it is emerged. Why does self-reproducing structures appears, trying to retain itself in the world governed by physical and chemical laws? The laws seems mathematical to me. So I thought there might be some formulation of the characteristics of life in a way

I know that the question may be ill-defined, naive or off-topic in mathematics. However, I'm really curious if there were any attempts to describe or define clearly any properties in living objects using pure mathematics. Are there any?

Edit: I found some discussion made in Timothy Gowers's Weblog. The book What is Life? by Erwin Schrödinger, although I don't know much, also seems to describe this matter.

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This is probably not what you are looking for, but it came to mind: do you know that "game of life" – Simon Markett Jun 12 '12 at 15:34
Should I delete this question or change this to a community wiki? I'm new to this site so any corrections are welcome. – Jineon Baek Jun 12 '12 at 15:34
Actually having had a look at my own link this might be pretty close to the best you can hope for... – Simon Markett Jun 12 '12 at 15:35
@SimonMarkett Yes, I heard of it before. I think the game of life partially answers the question. It has simple rules and various patterns emerging from the rules, some even reproducing another patterns! – Jineon Baek Jun 12 '12 at 15:39
@JineonBaek: You should probably read the book Gödel, Escher, Bach by Douglas Hofstadter. It attempts to explain consciousness by (among other things) examining self-referentiality in formal systems. – Dejan Govc Jun 12 '12 at 15:52

This is an immense question and partial answers can come from both books What is Life? (the other by Lynn Margulis et al), as well as many others. Considerations of the second law of thermo are easy if you just say the Earth is not a closed system, so we take in low entropy from the sun and radiate high entropy to space. They are harder if you try to justify the formation of structures.

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Thanks for the recommendation! I will check that book too. – Jineon Baek Jun 13 '12 at 6:05

Not a direct reference, but I suggest you visiting John Baez's Azimuth blog and Azimuth wiki. Time to time there are posts directly connected to biology. For example, study the tag biology, but don't miss other posts too, they may be relevant (like biodiversity).

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I would highly recommend you the book - 'Shadows of the mind' - by Roger Penrose. He explores the character of human mind and consciouness by using arguements from logic, computation and quantum mechanics.

Penrose hypothesizes that:- 1. Human consciousness is non-algorithmic, and thus is not capable of being modeled by a conventional Turing machine-type of digital computer.

  1. Quantum mechanics plays an essential role in the understanding of human consciousness, specifically, he believes that microtubules within neurons support quantum superpositions.

  2. The objective collapse of the quantum wavefunction of the microtubules is critical for consciousness.The collapse in question is physical behaviour that is non algorithmic and transcends the limits of computability.

  3. The human mind has abilities that no Turing machine could possess because of this mechanism of non-computable physics.

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