On 08 Feb 2011, at 09:03, Andrew Soltau wrote:

On 06/02/11 22:06, Russell Standish wrote:
Neurobiologists Find that Weak Electrical Fields in the Brain Help
Neurons Fire Together


Reminds me of what Colin says he is doing...


Fascinating. At every turn we seem to find additional complexity and holistic phenomena in the processes of life giving rise to biological computation. It reminds me of Bonnie Bassler's quorum function which enables bacteria in the body to act in concert as a single organism.


Ah ah ! I <3 Bonnie. I <3 bacteria. It is always a pleasure to listen to her.

Bacteria are 100% Turing universal.

Give me one thousand molecular biologists, and I will build the most powerful parallel computers. The difficulty: mixing a big number of phages and bacteria. Ethical difficulties too.

Are bacteria Löbian? I doubt this, but who knows, really. I mean, in great numbers.

I think that the eucaryote cells is a bacteria (+ virus, for the nucleus) construction, like the choroplast is a descendent of the cyanobacteria.

We are bacteria colonies, bacteria swarm.

All my interest in mechanism stemmed from my interest for bacteria and cells, notably at the molecular level. I discovered the computer science "IF ... THEN" in the Lactose Operon (Jacob and Monod, and then in Gödel's paper).

I consider Kleene second recursion theorem (AxEeAz phi_e(z) = phi_x(e, z)) as being the most fundamental theorem in "abstract biology". I apply it in the long version of the thesis to program finite and infinite 'planaria' (my favorite worm). The program, when cutted in part, is such that each part generate the whole program, like the bio Planarias who are the champion of animal regeneration. I used an operator form of the theorem due to John Case.

I think recursion theory contains an abstract biology, an abstract psychology and an abstract theology, including the theory of matter.


And recursion theory is easily embedded in the theory of diophantine polynomial. You don't even need more than a polynomial of degree 4, by the work of Matiyazevitch and Jones.

This is hardly believable. You can verify the truth on any sigma_1 true sentence by less than 100 additions and multiplication. Of course to emulate the collision between the Milky Way and Andromeda with a low degree universal diophantine polynomial, you will have to encode a lot of information in individual numbers. But no matter the complexity of the task, you can verify it in less than 100 hundred operation (addition and multiplication).
You might as well code for the quantum vacuum.

The simple counting algorithm 0, 1, 2, 3, ... is not turing universal, but that was close! Just one 100 operations for testing arbitrary lengthy computations.

Diophantine polynomials are Turing universal. That would have pleased Hypatia who was teaching Plotinus and Diophantus in Alexandria, some time ago. I am pretty sure.

Of degree four!
The question of the existence of a universal diophantine polynomial of degree three remains open. We know that there are no universal diophantine polynomial of degree two. (diophantine means that the variables variate on the integers). On the reals, you don't get the Turing universality with the polynomials,. You need the sine or the cosine, to reintroduce the natural numbers, or the complex numbers.



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