On 08 Jul 2011, at 23:33, meekerdb wrote:
On 7/8/2011 2:04 PM, Bruno Marchal wrote:
The usual analogy is that your mind is your software, and your
brain is the main operating system. It is obviously Turing
universal (once you know the definition and think a little bit),
and the comp assumption is that it is not more than Turing universal.
It's not obvious to me. My "tape" seems quite finite.
All universal machine are finite. This is explicit in Turing's
discovery paper of the universal machine. The universal machine
discovered by Turing is the finite number that we can put on a tape
making the Turing machine behave like a universal one.
A universal machine or number is a u such phi_u(x,y) = phi_x(y).
Look at wolfram competition: finding the least finite table for a
universal cellular automata.
The infinite tape used in Turing machine is ... a error in pedagogy.
Universal machine, like cells, brains, and computers are finite being.
By their nature, they will look for bigger memory, but their
universality is a feature of their code/programs/description.
Secondly: you don't know if your tape is finite, and with comp you
know it is not. But this is irrelevant for being universal.
Bruno
http://iridia.ulb.ac.be/~marchal/
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