Re: What evidence is there that a neuron is digital computer ?
- From: Don Stockbauer <donstockbauer@xxxxxxxxxxx>
- Date: Mon, 20 Jul 2009 05:35:22 -0700 (PDT)
On Jul 20, 4:24 am, Josip Almasi <j...@xxxxxxxxxxx> wrote:
Miguel Negrao wrote:
Yes, indeed I didn't formulate my question very well. It's clear that
our brain can compute like a turing machine, because we can make all the
steps needed to operate a turing machine in our mind (albeit very
slowly) therefore we can in practice run any program in our mind.
Neural nets can emulate turing machine.
You might want to check some of these:
Turing Computability With Neural Netshttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.8383
Computational capabilities of recurrent NARX neural networkshttp://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.9781
Turing Machines are Recurrent Neural Networkshttp://lipas.uwasa.fi/stes/step96/step96/hyotyniemi1/
... or just take the keywords and google yourself, it's easy to find.
Note, however, that above proofs don't imply equivalence, and also, they
are based on mathematical model of a neuron, a simplification:http://en.wikipedia.org/wiki/Artificial_neuron
... and all of that may have nothing to do with what really happens.
IMHO our brains do something just like that, perform all the steps
needed as you said, but not so slowly as you may think, since we don't
really need to think/speak each step.
And once we train our FRNN/NARX nets, we just dump their states, and
voila! There's our program;)
My
question is weather there are operations in the brain which are not
computable.
I don't think this question can be answered just yet.
Now, as far as I understand the concept of computable regards discrete
systems. So to ask something like wether a pendulum is computable
doesn't seem to make any sense because the system is not even discrete,
and it's discretization is not the same as the original system. If this
is correct, then since most systems are obvisouly continuous (like the
weather, of balls of snooker) then first to prove the the neuron is a
digital computer it would first have to be established that it operates
as a discrete system.
Note that a turing-computable function needs not operate with discrete
values, it only has to have discrete states.http://en.wikipedia.org/wiki/Computable_function
From some of the answers I read it seems clear that the neuron
operates in the analog domain, that is, it operates with continuous
levels of voltage. But since there are discrete firings, it seems it has
some elements of discreteness also. If the elements that operate at a
continuous level are indeed irreducable (cannot be accounted for by some
other discreete version of the system) then what a neuron does would not
even be a "computation" in any correct sense of the word, right ?
Wrong. Analog computers also compute. Search i.e. 'operational amplifier
neuron'.
Also search "abacus".
.
- References:
- What evidence is there that a neuron is digital computer ?
- From: Miguel Negrao
- Re: What evidence is there that a neuron is digital computer ?
- From: Doc O'Leary
- Re: What evidence is there that a neuron is digital computer ?
- From: Miguel Negrao
- Re: What evidence is there that a neuron is digital computer ?
- From: Josip Almasi
- What evidence is there that a neuron is digital computer ?
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