On 13/10/2015 11:43 pm, Quentin Anciaux wrote:
2015-10-13 14:26 GMT+02:00 Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>>:
On 13/10/2015 11:00 pm, Quentin Anciaux wrote:
2015-10-13 13:44 GMT+02:00 Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>>:
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?
If you don't reject it, your explanation of computation is circular if
you don't have a *definition* of what is a physical computation
without using the mathematical definition.
I find it difficult to parse this 'sentence'. I am not obsessed with
definitions. A calculation consists of taking an input and calculating
an output according to some predefined rules. One can give a precise
mathematical formulation of this process if one wishes, but such a
formulation is not necessary for one to actually *do* the calculation.
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 --
You do have to, for not to be circular.
Nothing circular here -- I not not obsessed with definitions. I just get
on and do it.
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?
Who said it was ? If it is not, then reality can be explained in terms
of computations alone, and matter could be a product of
computations... You dislike that idea, that somehow must mean matter
is primary in your view... so IMO, you're saying matter is primary,
don't you ?
I am not denying that, in all likelihood, matter is primary. I do not
have any problems with that idea. In fact, it is a very productive
position to take, and has led to all manner of useful results: none of
which have been produced by computationalism. Matter is primary, and
mathematics is simply a game played according to a set of rules
developed from our experience of the physical world. The utility of
mathematics is completely explained by the fact that it is based on
physical experience. The utility of physics is explained in the same way.
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.
Yes so to prove them equivalent, you have to prove the mapping between
input and output for all input... how do you achieve that without
mathematical induction ?
I can use mathematical induction if that is found to be useful. I don't
have to believe that mathematics is fundamental, or physics is
derivative, in order to do that.
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
