http://www.yorku.ca/dept/psych/classics/Lovelace/menabrea.htm
http://www.yorku.ca/dept/psych/classics/Lovelace/lovelace.htm
On Tue, 15 Feb 2000, Egerland, Matthias wrote:
> > MENABREA:
> > from the moment that
> > the nature of the calculation to be executed or of the problem to be
> > resolved have been indicated to it, the machine is, by its own intrinsic
> > power, of itself to go through all the intermediate operations which lead to
> > the proposed result, it must exclude all methods of trial and guess-work,
> > and can only admit the direct processes of calculation.
>
> Egerland:
> This is the main point about the Analytical Engine. Menabrea says that
> the machine needs to be independent from humans to fulfil its main
> purpose - being a useful tool by improving correctness and time
> efficiency when humans have to deal with complicated mathematics.
>
> At the same time the author is completely aware of the fact, that this
> machine can not make use of intuition. For solving mathematical
> equations it has to take a completely different approach than an
> 'intelligent' being.
This is similar to the mathematician Roger Penrose's recent objections
to AI. He thinks computation cannot capture mathematicians' intuitions.
The Emperor's New Mind
Roger Penrose, Oxford University Press, 1990
http://www.friesian.com/penrose.htm
http://ase.tufts.edu/cogstud/papers/penrose.htm
But what it the evidence, really, that the unconscious processes
underlying intuition are not also computational?
See:
Why Godel's Theorem Cannot Refute Computationalism
Geoffery LaForte, Patrick J. Hayes Kenneth M. Ford
http://www.coginst.uwf.edu/~glaforte/papers/whyGodel.ps
Mathematics and the Mind
Edward Nelson Department of Mathematics
Princeton University
http://www.math.princeton.edu.~nelson/papers/tokyo.ps.gz
Have a look at the above, in connection with next weeks Skywriting
assignment, which is:
J.R. Lucas (1961) Minds, Machines and Goedel. Philosophy 36 112-127.
http://cogprints.soton.ac.uk/abs/phil/199807022
We will only be quote/commenting Lucas, which is in HTML, but you are
welcome to bring in the other two papers (which are alas in PS, unless
you can figure out a way to convert it to quotable ascii).
> Egerland:
> So the main goal was finding a possibility to make the machine
> calculate without 'thinking'. Hence, the machine could only be as
> powerful as its inventor, who had to find this very fundamental way of
> solving mathematical equations.
Two things here: Is the assumption that thinking is not itself
computational necessarily (or even probably) true? Turing clearly
thinks otherwise.
Second, the "no more powerful than its inventor" argument is Lady
Lovelace's, isn't it. But can't my weak mind find an algorithm that
happens to be more powerful than itself (just as I can build a machine
that's stronger than me?
> Egerland:
> Here Menabrea says explicitly that the only intelligence in conjunction
> with this machine has to be in the head of the designer of the cards,
> who can be considered as the 'programmer'. Neither the workman nor the
> machine itself need to have a (high level) of intelligence.
Is this really a limitation of computers, or a limitation in the
imagination of the early designers of computers? For two possibilities
are surely open: (1) that a human mind can write a programme that can do
things that particular mind alone cannot do and (2) that the human mind
is itself just the implementation of a computer programme (and even a
programme that it is capable of discovering and formulating explicitly).
I am not saying any of this is so, but I am suggesting that no reason
has yet been given why it could not be so.
Thoughts?
Stevan
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