On Nov 6, 2006, at 1:57 PM, Daniel C. wrote:
On 11/6/06, Levi Pearson <[EMAIL PROTECTED]> wrote:
Well, that's too bad. Sounds like it could have been an interesting
article, though I think its relevance to the mozy.com contest is
pretty tenuous, and I'd still like to see how Turing machines fit
into it. Given your description of it and what I know of computer
science, I can't imagine what sort of point it was trying to make
with them.
It was an interesting article, but the only thing I took away from it
is the idea that no real machine can decide all strings in the
language of matching parentheses because you can always exceed the
memory of the machine by one.
That's not really a very interesting point in itself, though, since
it's equivalent to the intuitively true statement that you could
count as fast as you could for your entire life and still not count
all the counting numbers. It shouldn't require a very deep or
interesting article to make that point clear, though I suppose it's a
good thing to point out to people who have not thought much about the
limits of physical computers. It's just the tip of the limitation
iceberg, though.
Clearly our real, physical machines have memory limitations, and if a
linear growth in space requirements is our only obstacle to solving a
particular problem, we're in pretty good shape since memory
capacities have been growing exponentially for a while. It's when
memory requirements grow exponentially as well that we have
problems. And still, none of this has anything to do with Turing
machines. :)
--Levi
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