Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Can we ever know the sum of the first $10^{10^{100}}$ digits of $\pi$?

Can we calgulate the $n$th digit of $\pi$ when the Kolmogorov-complexity of $n$ is larger than the complexity of the calculating system?

Example: We cannot calculate digit number 314159265358 of $\pi$ on a typical pocket calculator.

EDIT: As Goldstern remarks, we cannot write down all the digits simultaneously. But can we know every desired shorter string of digits, for instance the first billion following the digit number $10^{{10}^{90}}$ and then note their sum, and so on?

share|improve this question
1  
I don't see a mathematical question here, but perhaps I'm just blind. –  Alex Becker Feb 2 '13 at 12:47
1  
The second question is along the lines of scottaaronson.com/blog/?p=46 -- we take a number which is so large as to be uncomputable with and ask whether we can compute some very trivial aspect of it. (See also math.stackexchange.com/questions/271834/… ). No one seems to have made much progress on either of those questions. –  David Speyer Feb 2 '13 at 12:53
4  
The sum of the first $10^{10^{100}}$ digits of $\pi$ has most likely more than $10^{80}$ digits, so where would you write it down? –  Goldstern Feb 2 '13 at 13:50
1  
That is just implied by my question: If matheamtics is primarily communication between inhabitants of the universe, does this sum belong to mathematics? Or is the "universe of discourse" larger? –  Rhett Butler Feb 2 '13 at 15:05
8  
Given your name, perhaps you will understand when I answer your questions, "Frankly, my dear, I don't give a damn." –  Gerry Myerson Feb 2 '13 at 23:09
show 1 more comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.