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As pi is infinite, it also stores any imaginable information. Someone actually went ahead and implemented a file system based on this idea: https://github.com/
by _jomo 8y ago
As pi is infinite, it also stores any imaginable information. Someone actually went ahead and implemented a file system based on this idea:
https://github.com/philipl/pifs https://github.com/philipl/pifs
- misja111 8y agoThis is brilliant, thank you! edit: am I the only one who thinks that this whole pifs filesystem was meant as a joke?
- petters 8y agoEveryone knows it is a joke.
- amelius 8y ago> As pi is infinite, it also stores any imaginable information. Whether that is true is related to the normalness [1] of the number pi, but this property has not been proven. See also: [2]. [1] https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number [2] http://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/ http://www.askamathematician.com/2009/11/since-pi-is-infinit...
- andrepd 8y agoI think normalness is a stronger property than "possesses all sequences of the alphabet of its digits", since it means that + "all subsequences are equally likely"
- mkirklions 8y agoThat was a fun read. Ive always thought about this when people say 'THE UNIVERSE IS INFINITE SO WE ARE EATING DINNER AT HELMS DEEP SOMEWHERE'. Naw man, physics still apply, you dont get gandalf just because you went a few million light years toward Andromedia
- gowld 8y agoThe difference is that Pi is apparently normal, up to all extensive existing evidence. The Universe is not normal. Anyway, Physics doesn't preclude Helms Deep.
- humblebee 8y agoThere is a great Numberphile video loosely related to this (no magic though) "Googol and Googolplex - Numberphile" - https://www.youtube.com/watch?v=8GEebx72-qs https://www.youtube.com/watch?v=8GEebx72-qs
- sethgecko 8y agoHow do you even calculate pi with such accuracy?
- snarfy 8y agohttps://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...
- jgtrosh 8y agoHe claims 100% compression, but that clearly disregards the digit ID which is potentially quite large to store. Any idea as to how to compute stats for actual compression (size(content)/size(index))?
- TazeTSchnitzel 8y agoSize of the index would just be log2(index), right?
- Jabbles 8y agoYes but index would be ~2^(length of content)
- jasode 8y agoYour calculation works backward from already knowing the index. I assume jgtrosh's question is more of a probability and estimation question. E.g. the string "Hello world" takes up 11 bytes and what's the size of the index into pi? To generalize a little more, to store any 11-byte sequence, what is the estimated size to store its index? To find the exact 256^11 byte sequence in pi, there will be many cases where the sizeof(index) is greater than the data itself.
- tzahola 8y agoAssuming that pi is a normal number [1], its digits are uniformly distributed. Therefore the density of a given binary sequence of length N in pi’s binary expansion is 2^-N. So on average, the offset for a given binary sequence will be on the order of 2^N (I’ve used some hand-waving here). You need N bits for that, you you’ve gained basically nothing. [1] https://en.m.wikipedia.org/wiki/Normal_number https://en.m.wikipedia.org/wiki/Normal_number
- jimktrains2 8y agoA friend and I tried to do this in highschool and realized it wasn't so useful except for a cool factor.
- 8y ago
- tzahola 8y agoUndortunately with this solution you’re still storing the same amount of information as you’d normally do. It’s just encoded as offsets into pi’s decimal expansion. You can’t cheat entropy.
- hsnewman 8y agoCan pi be recursive then? Can it contain itself? I think not.
- vollmond 8y agoTo be fair, no other filesystem could contain pi either, right?
- avian 8y agoNo. If pi would contain itself it would be a rational number. We have a proof that pi is irrational, hence it cannot contain itself.
- gowld 8y agoSpecifically, if pi contains itself, that means "pi - pi/b^k" is a terminating fraction N in base b", where b is your choice of base (like base 10), and k is some positive integer. So pi = N/(1-b^k) which is rational. (And if you set k=0, you get that pi "contains itself" in the sense that pi from the 1st digit onward is of course pi)
- klmr 8y ago> Can it contain itself? Well it does, trivially. You’re probably thinking of set theory but the file system is about storing information in a sequence and an offset. Seen that way, π can be stored with offset 0.
- deleted 8y ago[deleted]
- gnulinux 8y agoIf it's normal then it contains all finite strings uniformly in its base-b expansions. Pi is not a finite string so it wouldn't have to contain itself uniformly. More specifically if it contains itself then it's a rational number, but we know that pi is not a rational number. Note that we don't know whether pi is a normal real number.
- John_KZ 8y agoThat's not necessarily true and probably is false. What we know about Pi is that it includes an infinite number of elements, but this says nothing about the structure of those elements. An infinitely long random sequence will probably hold every pattern possible (I'm not a mathematician so correct me if I'm wrong) but any structured or repeating sequence doesn't.
- chimeracoder 8y ago> An infinitely long random sequence will probably hold every pattern possible (I'm not a mathematician so correct me if I'm wrong) but any structured or repeating sequence doesn't. This is not true. Pi is probably irrational, which means we know it doesn't repeat itself. However, it is not proven to be normal, so it's a conjecture (but not fact) that it contains every finite sequence of digits at some point.
- gowld 8y agoThat's the worst possible typo for this conversation. Pi is provably irrational, and probably normal!
- chimeracoder 8y ago> That's the worst possible typo for this conversation. Damn autocorrect! And it's too late to edit it, too. Yes, that should say "provably irrational".