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I'm guessing the answer to this question is no, but... for an irrational number like pi, can we guarantee that a certain digit sequence will occur somewhere in
by FredPret 2y ago
I'm guessing the answer to this question is no, but... for an irrational number like pi, can we guarantee that a certain digit sequence will occur somewhere in its infinite reaches?
That would be a wildly impractical but very fun way to encode information - if everybody had a couple of petabytes of pi on their harddrive one day, you could just send the starting and ending digit to communicate an arbitrary amount of information this way.
Of course you'd first have to search through the whole universe of digits to find a sequence that's just right.
- Arnavion 2y agoSuch numbers are called "normal numbers". Pi likely is one based on all the digits we've computed for it, but we don't have any way to prove a given number like pi is normal or not. Relevant Numberphile video: https://www.youtube.com/watch?v=5TkIe60y2GI https://www.youtube.com/watch?v=5TkIe60y2GI
- FredPret 2y agoVery interesting, thank you. He starts talking about this at 8:20
- thfuran 2y ago1.01001000100001... is infinite and non-repeating, but doesn't contain all substrings. A number that does is called a "normal" number, and it's not known whether pi is. It seems to be pretty normal though.
- kurisufag 2y agothis in practice: https://github.com/ajeetdsouza/pifs https://github.com/ajeetdsouza/pifs