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

[spike]

From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of John Clark



 

​>…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?​   John K Clark

 

 

 

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:

 

 



 

 

We could even estimate the number of terms we need to get to your 10^100^100^100th digit, but we don’t need to for we can already see how the Taylor series is at least 17 different kinds of cool, with wicked being one of them. 

 

Wouldn’t it have been cool to have been the guy who discovered that expansion?  Imagine it: Hey cool, check this guys!  This thing just goes on and on, each fraction getting smaller!  It goes on… forever!  We can’t even possibly write pi as a fraction! 

 

Oh for a thousand lifetimes to be able to dig deeper and wider.

 

spike

 

 

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