[ExI] Simulating the brain (was Question for the psych squad?)

[John Clark]

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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