Irrational numbers and Planck's constant

[DiracPool]

[Mentor's note: this was originally posted in the Quantum Physics forum, so that is what "this section" means below.]

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I wasn't sure whether to post this question in this section or the general math section, so I just decided to do it here..

The question is, does it make sense to give any credulity to numbers that run on for more than 34 decimal places? I've thought about this for a while but that "Mile of Pi" video from numberphile that was just posted recently I think catalyzed this post:

https://www.physicsforums.com/threads/one-mile-of-pi.804514/#post-5050728

If we can't really talk about space less to the plank length (10^-35) and time less to the plank time (10^-43), then what does it really mean to compute Pi to one million decimal places?

So, in summary, does computing any irrational number to more than to the vicinity of the Planck constant have any physical meaning at all? What's the purpose?

 

[bhobba]

So, in summary, does computing any irrational number to more than to the vicinity of the Planck constant have any physical meaning at all? What's the purpose?

Depends on the application - pi turns up in all sorts of strange places having nothing to do with a circle eg Buffons needle:
http://en.wikipedia.org/wiki/Buffon's_needle

Thanks
Bill

 

[Doug Huffman]

Pi is a fine source of pseudo-random numbers.

 

[jtbell]

It seems to me that there's lots of abstract mathematics that doesn't have a physical significance that we know of. That's never prevented mathematicians from being interested in such things.

 

[matt312]

That is a interesting question. From my point of view when your solving a physics problem I think it is only to what is reasonable to solve the problem. I was doing a problem in physics which required a answer from a geometry problem and some trigonometry for a electromagnetic wave. I guess it depends on the problem.