Don wrote:
The key word is not "infinite", it's the word "if"
The statement was "IF we had an infinite computer ...."
Of course. "If".
It doesn't matter one bit whether such a device is possible - it's a
perfectly valid "thought device" for thought experiments. It's easy
to imagine what we would do with such a computer and how it could be
used without stretching our brains too far.
Sorry, Don, I can't agree that it doesn't matter.
I assert that it matters a little, at least.
We can also imagine the moon being made of green cheese without this
actually being the case. I don't see any problem with considering the
behavior of a machine with certain characteristics just because we can't
produce one.
Of course we can imagine the moon being made of green cheese.
The problem I have with that -- and the reason I assert that it
_does_ matter -- is that if one begins by assuming an utterly
false premise, one can prove _anything_. And you don't need _any_
computer for that! Don't need to stretch the brain much at all.
Surely logic matters a little, doesn't it?
The only reason I responded in the first place, is that I have heard
_many_ people make the naive assertion, "There are a finite number of
go games, so 'if' we had enough time, we could just brute-force search
the game tree." My problem with that, is that it is no more true than
to state that the moon is made of green cheese.
It seemed to me that I was hearing that same naive assertion, again.
And then when it is followed by, "That's true, isn't it? What am I
missing?" I feel compelled to answer. (They always seem to ask that!)
"If" is definitely the operative word, as you say.
People are free, of course to imagine all sorts of falsehoods, and,
should one want to label them "thought experiments" that's fine with me.
People can and do believe all sorts of things that simply are not true;
it seems that humans are capable of believing _anything_!
Perhaps I overreacted to hearing the same tired nonsense yet again,
but "It ain't necessarily so." (And he did ask what he was missing.)
Actually, it has been proved, I think, not only that there is a
finite amount of matter (storage space) but also that the age of
the universe is finite. I'm not up to reproducing the proof in
this forum; it's just what I "believe". Perhaps I am wrong.
To be quite honest, I have only a vague understanding of what is
called "computational complexity" -- but it's clear enough that,
_even_given_an_infinite_amount_of_storage_ it would take longer
than the age of the universe to exhaustively search the game tree,
and it is equally clear that, _even_given_infinite_time_ it would
take more bits than there are particles in the universe.
Thus, "IF" there is _not_only_ a finite amount of matter, _and_
"IF" the age of the universe is _also_ finite, then unicorns do
not exist (in my opinion).
Your mileage may _not_ vary; that's just the truth. (Again, my
opinion. Readers are free to believe any foolish thing they wish.)
I assert further that some peoples' opinions have more value than
others'. (My opinion.)
I'm not trying to get all bent-out-of-shape about this; just sharing
my _opinions_ with the readers. (I'm hopeful that they will see the
light.)
"If" my presentation seems a bit didactic, it's only because I'm right.
--
Rich
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