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Yes.
And if you're thinking of a compression algorithm, nope, pigeonhole principle.
Yes
Can you prove this? Or link a proof?
I don't know of one but the proof is simple. Let me try (badly) to make one up:
If it doesn't go into a loop of some kind, then it necessarily must include all finite strings (that's a theoretical compsci term).
Basically, take a string of any finite length, and then view pi in inrements of this length. Calculate it out to double the amount of substrings of length of your target string's interval you have [or intervals]. Check if your string one of those intervals. If not, do it again until it is, doubling how long you calculate each time.
Because pi is non-repeating, each doubling in intervals must necessarily include at least one new interval from all other previous ones. And because your target string length is finite, you have a finite upper limit to how many of these doublings you have to search. I think it's n in the length of your target string.
Someone please check my work I'm bad at these things, but that's the general idea. It's also wildly inefficient This doesn't work with Infinite strings because of diagnonalization.
No this does not work. Counter example can be found in the comments here of a non-repeating number that definitely does not contain all finite strings.
Edit: I think the confusion is about the word non-repeating. Non repeating does not mean a subsequence cannot repeat but that you cannot write the number as a rational or with a finite decimal representation. I.e. it's not 3.ba repeating. Where a is a finite sequence that repeats infinitely and b is a finite sequence.
Edit edit: another assumption you make is that pi does not go into a loop of some kind. You would need to prove that.
Are you talking about a different base/character set? I think every single person understands that.
See my other comment
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My birthday in American MMDDYYYY format shows up in the first few ten-million digits, but in standard DDMMYYYY format, it's not in any of the digits that site is able to check.
Self-doxxing! Makes me wonder how many of the dates would fit.
Around 60% of 8-digit strings appear in the digits their algorithm knows about, according to the website. So I figured it's not THAT identifying.
standard DDMMYYYY
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Yeah. This is a plot point used in a few stories, eg Carl Sagan's "Contact"
Replace numbers with letters, and you have Jorge Luis Borges' The Library of Babel.
https://libraryofbabel.info/ kinda blows my mind.
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Yes, this is implied. It's also why many people use digits of pi as passwords and make the password hint "easy as pi".
Not sure if this is sarcasm, but I sure hope so...
It's a Criminal Minds reference, though people do use this method, including me.
I use encryption and... modern... 2024 standards.
Pi, tho. I mean, you do you.
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this post was submitted on 26 Dec 2024
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