Subject:
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Re: 22/7 & infinities (was: Re: The nature of the JC god, good or evil?)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Mon, 23 Aug 1999 02:10:33 GMT
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Viewed:
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1417 times
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In lugnet.off-topic.debate, Todd Lehman writes:
<Massive snip>
> Note that there are some irrational numbers which can't be expressed
> algorithmically in terms of rational numbers. I forget if this subset is a
> larger or a small infinity than the ones which can be, but it's a really
> fascinating subset of irrationals which gets into random number territory.
You mean the transcendental numbers, presumably? I seem to recall
reading that practically every number along the real number line
is transcendental, with just odd blips where you encounter an isolated
rational or irrational number. But I may be mistaken on that - and that
alone doesn't prove the transcendentals constitute a bigger infinity
than the irrationals.
I'd agree that Larry is technically correct about numbers and infinities - but
I'm dubious about his claim that all that theory shows
that we understand infinities. In my experience
the more I studied number theory and logic theory the less convinced I
became that I actually understood what was going on - even when could
work through the proofs line by line and know why each individual step worked
there always seemed to be something deeper that was escaping me.
Moving more to science, I agree with Larry to the extent that being able
to predict things is very important. HOWEVER, being able to predict something
doesn't show that we really understand it. Quantum mechanics is hugely
successful in its predictive ability, but we still don't understand what's
really
physically going on behind those equations. And as far as I know no one
has yet managed to solve the measurement problem (
very roughly speaking, the fact that according
to the laws of quantum mechanics, you should basically never ever be
able to measure ANYTHING!). Physicists generally 'solve' this problem
by ignoring it, which works quite well for predicting things, but it certainly
gives good intellectual/academic reasons for suspecting that there are
areas that will always be outside the realm of science as we know it.
Godel's theorem [A] for me tends to reinforce the point.
> [1] Except God or mathematics.[2][3]
>
> [2] Is God part of the Universe, or is he outside of it, or is God the
> Universe itself?
>
> [3] Is mathematics part of the Universe?
Again, IMO these questions give away our lack of understanding. And the last
one doesn't even concern God!
Things aren't clear cut either way on the religious/secular debate. Shame
in most of these debates, so many people on BOTH sides make statements
without thinking through the consequences of what they are saying, and/or
argue by putting up straw men[B] (This debate has been more sensible than
some I've seen, but even so, from what I've read I'd say Larry and John N
are both guilty on both counts) (Sorry guys! <grin>)
[A] very roughly speaking, there are things that are definitely true but at
the same
time impossible to prove logically.
[B] making out the position of the other side to be not quite what it actually
is,
then arguing against the new made-up position, rather than against what the
other side are actually saying.
Simon
http://www.SimonRobinson.com
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