Polymath and the origin of life has finished its second month. Remember, Tim Gowers plans to set up a polymath project to explain abiogenesis. The project should use cellular automata or similar devices to explain the emergence of life. Right at the beginning of his proposal he has posed a couple of questions on what properties these machines or models should have and what exactly should constitute the scope of the project. I quote:
Question 1: Should one design some kind of rudimentary virtual chemistry that would make complicated “molecules” possible in principle?
The alternative is to have some very simple physical rule and hope that the chemistry emerges from it (which would be more like the Game of Life approach).
If the emergence of life does not depend on the details of the underlying chemistry we could choose a ‘simple’ model and proceed. However, that seems to be circular. We do not know enough examples of ‘life’ to know what exactly constitutes a viable approximation to chemistry. We might get lost in arbitrariness.
The other approach uses the one known example of ‘life’and its ‘fundamental’ laws. Approximations to it might still result in the emergence of some sort of chemistry and then ‘life’.
If I had to choose, I would take the second approach. Even if we do not succeed in generating life, finding suitable approximations to Schrödinger’s equation which result in toy chemistries seems to be already a respectable finding.
Question 2: How large and how complicated should we expect “organisms” to be?
If everything turns out to be working we might be able to describe “organisms” in a different frame and size thus may not play an important role.
Added later: I haven’t quite made clear that one aim of such a project would be to come up with theoretical arguments. That is, it would be very nice if one could do more than have a discussion, based on intelligent guesswork, about how to design a simulation, followed (if we were lucky and found collaborators who were good at programming) by attempts to implement the designs, followed by refinements of the designs, etc. Even that could be pretty good, but some kind of theoretical (but probably not rigorous) argument that gave one good reason to expect certain models to work well would be better still. Getting the right balance between theory and experiment could be challenging. The reason I am in favour of theory is that I feel that that is where mathematicians have more chance of making a genuinely new contribution to knowledge.
When I was a teen some twenty-five or thirty years ago I was very impressed by the genetic model in Gödel, Esch, Bach of Douglas Hofstadter. I took my Apple IIe computer and coded a version. (The specification left some elbow room for interpretations to say the least). The microprocessor was a Motorola 6502, 8-bit running at 1 MHz. A month later it became clear: I cannot generate anything even remotely similar to ‘life’. I guess, nobody could that. Today I am writing this blog entry on a dual core laptop Intel P8400 running at 2,26 GHz and I am not trying to code that genetic model again. Why?
It is not only the computing power what distinguishes me from my earlier version. I also do no longer believe that ’emergence’ should be treated as a phenomenon which can be reached in a finite number of steps. I rather think that some sort of ‘limit’ should be involved, like in the definitions of the first infinite ordinal number, velocity or temperature. If that is the case, then the use of computers is limited until the ‘correct’ approximations are known and the question on the ‘size’ of organisms also is answered: they might be huge.
I have distilled a couple of items, which I think have to be addressed in one way or the other to make the project a ‘success’ (whatever that means).
- Find a suitable definition or concept of life. This definition has to be fairly robust and still open for interpretation. Something like: life is emergent and evolves. A crystal emerges, but does not evolve and car designs evolve, but do not emerge. If we find something that emerges and evolves we are done.
- Currently we do not know what emergence and evolution are. Therefore we collect examples of emergent behavior in all branches of science (this is true polymath and emergence seems to be in all concepts proposed so far). Describe these examples in a way accessible to all participants.
- Use taxonomy or whatever other scientific method to extract the ‘abstract’ information from these examples.
- Single out or even develop a mathematical theory related to emergence like calculus to mechanics.
- Explain evolution and its circularity within this framework.
- Make it happen! This is the more practical part of modelling an emergent and evolving phenomenon.
These items do not have a natural order. Currently most work was done on developing foundations for the practical part (the last item). Gowers gave a list of 7-8 desirable properties and discussed momentum- and energy conservation.
Let me just note that energy conservation seems problematic. While fundamental physical laws exhibit time translation symmetry, it is not obvious whether and how the same holds for e.g. evolutionary adaption. What does that mean? The following could happen: If we switch from the description of the system on a fundamental level (with energy conservation) to the description of the system on the ‘life’ level by say some ‘limit’ procedure we might get emergent laws depending on time. Such an effect might be necessary or even desirable to explain concepts like adaption, learning and free will. Energy conservation (aka time shift symmetry) might play the same negligible role for ‘life’ as quantum tunneling for cannon balls.
In the project, the emphasis so far seemed to be on understanding how one has to code the problem. However, also definitions were given, toy chemistries were proposed, examples of emergent behavior were given and so on. My items do not seem to be too far off and if that is true there seems to be much work to be done in 2010.