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> all number sequences can be found within the digits of pi quite easily I dispute that, although I guess the general brute-force solution is 'easy' given infi

> all number sequences can be found within the digits of pi quite easily I dispute that, although I guess the general brute-force solution is 'easy' given infinite time.

geofft 10y ago
Yeah, this isn't known to be true. pi has not been proven to be a disjunctive number (a real number whose expansion contains all possible finite strings), let alone a normal number (where all finite strings occur with the probability you'd expect if the digits were random). Both of these, however, are generally conjectured to be true, but it's just a conjecture. https://oeis.org/wiki/Disjunctive_numbers#Is_pi_a_disjunctive_number.3F https://oeis.org/wiki/Disjunctive_numbers#Is_pi_a_disjunctiv... https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
lutusp 10y ago
>> all number sequences can be found within the digits of pi quite easily > I dispute that, although I guess the general brute-force solution is 'easy' given infinite time. Look at it this way -- if it were not true, then the digits of Pi would not be normally distributed (see https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number), and that would be a rather extraordinary mathematical finding. If Pi's digits are normally distributed, then one can reliably predict the time required for finding any particular digit sequence using probability theory. And given the presumption of normalcy, that probability is the same for any digit sequence of a given length. The probability for finding a given test digit sequence in the first 100 million digits of Pi is given here: https://www.angio.net/pi/whynotpi.html https://www.angio.net/pi/whynotpi.html But it has to be emphasized that, given a finite test sequence and an infinite sequence of Pi's digits as a search space, the probability is 1.0.
- oneeyedpigeon 10y ago
  You're both giving me too much credit. I was merely making the less sophisticated point that it's not 'easy' to find an arbitrary-length sequence in pi because that might take longer than the lifespan of the universe when the needle gets long enough. Your response was much more interesting, though, thanks :)
rnhmjoj 10y ago
Seen this already? https://github.com/philipl/pifs https://github.com/philipl/pifs

> all number sequences can be found within the digits of pi quite easily I dispute that, although I guess the general brute-force solution is 'easy' given infinite time.

geofft 10y ago

Yeah, this isn't known to be true. pi has not been proven to be a disjunctive number (a real number whose expansion contains all possible finite strings), let alone a normal number (where all finite strings occur with the probability you'd expect if the digits were random). Both of these, however, are generally conjectured to be true, but it's just a conjecture. https://oeis.org/wiki/Disjunctive_numbers#Is_pi_a_disjunctive_number.3F https://oeis.org/wiki/Disjunctive_numbers#Is_pi_a_disjunctiv... https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number

lutusp 10y ago

>> all number sequences can be found within the digits of pi quite easily > I dispute that, although I guess the general brute-force solution is 'easy' given infinite time. Look at it this way -- if it were not true, then the digits of Pi would not be normally distributed (see https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number), and that would be a rather extraordinary mathematical finding. If Pi's digits are normally distributed, then one can reliably predict the time required for finding any particular digit sequence using probability theory. And given the presumption of normalcy, that probability is the same for any digit sequence of a given length. The probability for finding a given test digit sequence in the first 100 million digits of Pi is given here: https://www.angio.net/pi/whynotpi.html https://www.angio.net/pi/whynotpi.html But it has to be emphasized that, given a finite test sequence and an infinite sequence of Pi's digits as a search space, the probability is 1.0.

oneeyedpigeon 10y ago
You're both giving me too much credit. I was merely making the less sophisticated point that it's not 'easy' to find an arbitrary-length sequence in pi because that might take longer than the lifespan of the universe when the needle gets long enough. Your response was much more interesting, though, thanks :)

rnhmjoj 10y ago

Seen this already? https://github.com/philipl/pifs https://github.com/philipl/pifs