John Clark-12 wrote:
> 
> On Mon, Sep 3, 2012 at 9:11 AM, benjayk
> <benjamin.jaku...@googlemail.com>wrote:
> 
>> Showing scientifically that nature is infinite isn't really possible.
>>
> 
> Maybe not. In Turing's proof he assumed that machines could not operate
> with infinite numbers, so if there is a theory of everything (and there
> might not be) and if you know it and if you can use nothing but that to
> show independently of Turing that no machine can solve the Halting Problem
> then that would prove that irrational numbers with a infinite number of
> digits play no part in the operation of the universe; on the other hand if
> this new physical theory shows you how to make such a machine then we'd
> know that nature understands and uses infinity. I admit that I used the
> word " if " a lot in all that.
> 
Even the usual computer can use infinite numbers, like omega. Really going
from 1 to omega is no more special or difficult than going from 1 to 2. We
just don't do it that often because it (apparently) isn't of much use.
Transfinite numbers mostly don't express much more than finite numbers, or
at least we haven't really found the use for them.

Irrational numbers don't really have digits. We just approximately display
them using digits. Computers can also reason with irrational numbers (for
example computer algebra systems can find irrational solutions of equations
and express them precisely using terms like sqrt(n) ).

With regards to nature, it seems that it in some ways it does use irrational
numbers. Look at the earth and tell me that it has nothing to do with pi. It
is true though that it doesn't use precise irrational numbers, but there
doesn't seem to exist anything totally precise in nature at all - precision
is just an abstraction.

So according to your standard, clearly nature is infinite, because we can
calculate using transfinite numbers.
But of course this is a quite absurd conclusion, mainly because what we
really mean by infinite has nothing to do with mathematically describable
infinities like big ordinal or cardinal numbers. With regards to our
intuitive notion of infiniteness, these are pretty finite, just like all
other numbers.
What we usually mean by infinite means more something like "(absolutely)
boundless" or "incompletable" or "inexhaustable" or "unbound" or "absolute".
All of these have little do with what we can measure or describe and thus it
falls outside the realm of science or math. We can only observe that we
can't find a boundary to space, or an end of time, or an end to math, but it
is hard to say how this could be made precise or how to falsify it (I'd say
it is impossible).

My take on it is simply that the infinite is too absolute to be scrutinized.
You can't falsify something which can't be conceived to be otherwise. It's
literally impossible to imagine something like an absolute boundary
(absolute finiteness). It is a nonsense concept. Nature simply is inherently
infinite and the finite is simply an expression of the infinite, and is
itself also the infinite (like the number 1 also has infinity "in it"
1=1*1*1*1*1*1*1*.... ).

benjayk
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