Is biology Turing complete?

Sometimes suspicions plague me. I might pace, sweat, and foam obsessed with an enduring and rouge thought. Lately, I've been troubled by suspicions of biological computation.

Allow me to elaborate. In the 1930s a one Alan Turing set about to define exactly what it was to calculate. He laid out mathematical principals describing his results and thereby formalized computation. The rules he described were simple and powerful. He proved that a pencil, long spool of paper, and a short table of commands could be used to perform any computation. Most computers ever constructed have followed Turing's mathematics. Supercomputers, desktops, and calculators can all be drawn out as a limited series of pencil strokes on a long spool of paper.

Now, consider cellular biology. Cells have long spools of DNA, proteins to read and write DNA, and a set of rules that protein's follow. Every animal, plant, and parasite is derived from those cellular processes. Yet, there is little talk of biology as a computer. Well, if you ask me biology is computing. Moreover, it is computing more and more cheaply than all the supercomputers, desktops, and calculators of the world.

So I'm hell bent now to prove it, to shake the thought, or put it away. If anybody has any evidence pass it along, or wish me luck.



E said...

Remind me to show you a disturbing picture (that relates to this post) when I see you Saturday.

Christopher said...

I hazard the opinion: no. Biology is not Turing complete. Because: you can't write down the "table of operations", to use your analogy.

You might be tempted to say that you can, because biology is made, like you said, of a generally limited number of chemical elemenents, combined principally into limited types of structures (protein, DNA, lipid...) which behave according to rules.

I believe, however, that the devil is in the details. (caveat: I have a very limited knowledge of biochemistry) Consider hemoglobin, which has an iron atom surrounded by a protein structure. That protein structure is highly conjugated (electron density is widely distributed) in a very specific way so that depending on whether or not an oxygen molecule is associated with the iron atom, the protein structure warps and changes its affinity for that oxygen molecule in exactly such a way that oxygen can be readily absorbed in the lungs and readily released in the tissues by the same structure. That balancing act depends very precisely on the quantum mechanics of the conjugated electron wave functions.

I bring all this up to make the point that important, large scale biological functions, e.g. the distribution of oxygen throughout an organism, depend directly and delicately on quantum mechanics. And the exact solutions to any quantum mechanical system involving more than one electon *cannot be solved* by modern science. Thus you cannot write down all the rules, and it is not clear that any finite set of operations can calculate a given biological process.

That's my take, at least.