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Do We Need the Digits of $\pi$?
Working out digits of Pi.
What are the limitations?
- Faster computers
- More accurate measuring devices
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The answer to this question (with whatever method) must be "not very exact." – user123454321 Jan 01 '13 at 02:01
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Perhaps better yet: see this post – amWhy Jan 01 '13 at 02:07
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Perhaps you'll want to start with approximations of $\pi$. – amWhy Jan 01 '13 at 02:16
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1The amount of information you can fit in the observable universe (I've heard the figure $10^{120}$ bits but I have no idea how reliable it is). – Qiaochu Yuan Jan 01 '13 at 02:18
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1See the $2^{305}$ entry in the table by Seth Lloyd on the Wiki for Orders of Magnitude. Regards – Amzoti Jan 01 '13 at 02:24
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@Amzoti That would be the ultimate limit, for sure – rraallvv Jan 01 '13 at 02:31
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@amWhy Those questions are more related to how it is calculated – rraallvv Jan 01 '13 at 02:32
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@amWhy I've edited accordingly – rraallvv Jan 01 '13 at 02:44
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At this point, the limitations in the calculation of $\pi$ are computational. We don't compute $\pi$ by measuring anything--the number of digits we know is already much more than you could obtain by any measurement in the visible universe, even if you could measure with accuracy down to the level where quantum effects start coming into play.
There are a number of methods of calculating $\pi$ (see e.g. Wikipedia), which are limited by processing speed and time. The current world record, apparently, is about 10 trillion digits.
Jonathan Christensen
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If stored in binary form via single particles, the entire data that can be stored in the observable universe is roughly $10^{92}$ bits, therefore this would create a upper bound. However, there can be alternative, semi-analogous storing methods which would allow for way higher storage capabilities, maybe even infinite precision (iff there is a physical property that is not quantisized and exactly measurable, which, from the current standpoint of physics, is highly unprobable)
CBenni
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Well then, we should also be able to consider the ever expanding multi-verse too as that provides a huge store and possibilities. – Amzoti Jan 01 '13 at 02:51
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well of course we can; However, we cannot observe it. We can only observe the universe we are actually in. Some theories of physics describe infinite-dimensional continuums from which our universe with our timeline is just a 4-dimensional submanifold. In the infinite dimensional universe, we can without doubt store any arbitrary amout of data, alone by the fact that there will be a universe in which electrical charge is not quantizised. – CBenni Jan 01 '13 at 02:57
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1@Amzoti therefore, I assume that the question was asked about our universe at one given point in time. – CBenni Jan 01 '13 at 02:57
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