[ExI] Simulating the brain (was Question for the psych squad?)
John Clark
johnkclark at gmail.com
Wed Jul 12 01:49:04 UTC 2017
On Tue, Jul 11, 2017 at 1:58 PM, spike <spike66 at att.net> wrote:
> >
>> >
>> …I know this is a bit heretical but perhaps irrational numbers really do
>> have a last digit. If the computational resources of the entire universe
>> is insufficient to calculate the 10^100^100^100 digit of PI, and given that
>> there are only about 10^81 atoms in the observable universe that seems
>> like a reasonable assumption, could the 10^100^100^100 digit of PI
>> even be said to exist?
>
>
>
> >
> Sure can John. We don’t even need to resort to the definition of a
> rational number to show that pi is irrational, with a definition: if there
> is a last digit then you can write it as a fraction, which makes it
> rational.
>
> The Taylor series expansion of pi doesn’t know or care how many atoms
> there are:
>
>
>
>
The key issue are
those 3 little dots,
the "..."; if the physical universe says the series can't continue forever
is it really correct to say it nevertheless does?
I know
the above is
the definition but
definitions are easy, they
don't
imply that the thing defined actually exists; I could define "glixclog" as
the prime
number
that is greater than 11 but less than 13.
You could argue I'm not playing fair because a prime number between 11 and
13 is a logical absurdity,
and that's true
but if the universe can't calculate
the
10^100^100^100 digit of PI
and the 10^100^100^100 digit of PI
can't effect the universe then is a claim of it's existence any less absurd?
We usually say a metal circle
made by a blacksmith
is a
n
approximation of a Euclidean circle, but maybe we've got
it
backwards, maybe a
Euclidean circle is a approximation of a
real
physical circle made of matter. I guess it
all
comes down to one
question: which
is more fundamental, physics or mathematics?
I don't know the answer to any of these questions
I'm just asking.
John K Clark
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