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But why? Serious question. I'm sure something interesting/useful might come out of it, and even if it doesn't just go for it, but is there any mathematical trut
by 725686 2y ago
But why?
Serious question.
I'm sure something interesting/useful might come out of it, and even if it doesn't just go for it, but is there any mathematical truth that can be gleaned by calculating pi to more and more digits?
- xyst 2y agoLike cryptography algos use prime numbers. Probably something out there that uses pi digits.
- sweezyjeezy 2y agoNot particularly, only thing I can think of is if we analysed it and saw there was some bias in the digits, but no one expects that (pi should be a 'normal number' [1]). I think they did it as a flex of their hardware. [1] https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
- robxorb 2y agoIsn't there a non-zero chance that given an infinite number of digits, the probability of finding repeats of pi, each a bit longer, increases until a perfect, endless repeat of pi will eventually be found thus nullifying pi's own infinity?
- Antipode 2y agoThe chance of that loop repeating forever is 0.
- robxorb 2y agoInfinity has entered the chat.
- kevinventullo 2y agoIn this case, the infinite sum 0+0+0+0+… is still zero.
- djkorchi 2y agoNo, because it would create a contradiction. If a "perfect, endless repeat of pi" were eventually found (say, starting at the nth digit), then you can construct a rational number (a fraction with an integer numerator and denominator) that precisely matches it. However, pi is provably irrational, meaning no such pair of integers exists. That produces a contradiction, so the initial assumption that a "perfect, endless repeat of pi" exists cannot be true.
- robxorb 2y agoYes and that contradiction is already present in my premise which is the point. Pi, if an infinite stream of digits and with the prime characteristic it is normal/random, will, at some point include itself, by chance. Unless, not random... This applies to every normal, "irrational" number, the name with which I massively agree, because the only way they can be not purely random suggests they are compressible further and so they have to be purely random, and thus... can't be. It is a completely irrational concept, thinking rationally.
- linearrust 2y ago> Pi, if an infinite stream of digits and with the prime characteristic it is normal/random, will, at some point include itself, by chance. What you are essentially saying is that pi = 3.14....pi........... If that was the case, wouldn't it mean that the digits of pi are not countably infinite but instead is a continuum. So you wouldn't be able to put the digits of pi in one to one correspondence with natural numbers. But obviously we can so shouldn't our default be to assume our premise was wrong? > It is a completely irrational concept, thinking rationally. It is definitely interesting to think about.
- traes 2y agoThe belief that a normal number must eventually contain itself arises from extremely flawed thinking about probability. Like djkorchi mentioned above, if we knew pi = 3.14....pi..., that would mean pi = 3.14... + 10^n pi for some n, meaning (1 - 10^n) pi = 3.14... and pi = (3.14...) / (1 - 10^n), aka a rational number.
- golergka 2y agoAs a general principle, when you do something very complex just for fun, you usually learn a lot of useful stuff along the way.
- hn_throwaway_99 2y agoThe work was done by a team at "Storage Review", and the article talks a lot about how the were exercising the capabilities of their processor, memory, and storage architecture.
- panarky 2y agoIsn't everyone as curious as I am about what the pi-quadrillionth digit of pi will turn out to be? The suspense is killing me.
- aaron695 2y ago[dead]