On 13/10/2015 11:00 pm, Quentin Anciaux wrote:
2015-10-13 13:44 GMT+02:00 Bruce Kellett <[email protected]
<mailto:[email protected]>>:
A computer made of silicon can emulate a Turing machine. A brain
made of wetware can be emulated by a silicon computer, or a Turing
machine. The fact that a Turing machine can be define
mathematically is entirely secondary.
The fact that a computer made of matter can emulate a Turing machine
is because we have a definition of a turing machine which is a
mathematical concept... but if you reject the mathematical definition,
I wonder how you can say that a "computer" emulate a turing machine...
You should first define computation in terms of matter, and shows that
the "mathematical" game is coincidentally like it.
Who said I reject the mathematical definition of a Turing machine? A
computer emulates a Turing machine in the sense that the silicon based
computer can do everything that an ideal Turing machine can do -- in
fact, the modern computer on your desk is a perfect universal Turing
machine. I don't have to *define* computation in terms of matter -- I
simply have to compute the output from the given input.
Also I wonder how you could justify with such theory the equivalence
between two computations... if not by using abstract computation
theory to justify it...
Two computations are equivalent if they give the same answers.
How do you justify it ? I can easily write an emulator of another
machine and justify the correct functionning by logic alone, no
matter involve... so if logic is just a game, and matter is the end
point, algorithm *can't* be used as justification of the correct working.
Who said matter was the end point?
You... why do you insist on matter, if it is not primary and can be
made of something else ?
Who said matter was not primary?
I can justify the equivalence of two computations by pointing to
the fact that they give the same numerical output.
Then you say it only if you have achieved all possible outputs ?
because you can't use mathematical induction to justify they will on
the same domain.
A computation has one input and one output -- it is a mapping between
the input and the output. Different inputs may give different outputs,
but then they are different calculations.
Computations might be definable in terms of algorithms, but more
than one algorithm can give the same computation -- give the same
result for the given input.
Yes, an infinity of them... but that's a mathematical result... no
matter is used in the reasoning .
That mathematical result can be instantiated by actually doing the same
calculation -- same output for the given input -- in a number of
different ways. I can do this without recourse to any mathematics at
all. The material world can be considered as a model instantiating the
mathematical result. This does not diminish either the physical or the
mathematical -- they ride on this together.
Bruce
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