Pyrian on 5/7/2022 at 15:48
We have whole branches of mathematics built around numbers that clearly don't exist, lol.
Qooper on 5/7/2022 at 15:59
Exactly my point. What does it mean for a concept to not exist? Concepts are great for a range of cool stuff, but they're not so good at not existing. Like, a cake can easily cease to exist. It's a trivial task for a cake to accomplish. But for a concept it's a whole different concept. In the end it's a very bureaucratic process involving dirty politics and possibly some four-dimensional Gerrymandering.
Komag on 5/7/2022 at 20:50
I haven't quite followed the thread, but it sorta reminds me of procedural generation, where you can put in coordinates and what is there is "determined", without having to build the entire world forever. It sort of always exists in theory, and can be visited if desired.
Is that in any way related, or am I way off on that comparison?
lowenz on 5/7/2022 at 21:31
You're perfectly on spot!
Pyrian on 6/7/2022 at 00:59
Yeah, it's basically No Man's Library, lol.
demagogue on 6/7/2022 at 10:03
I think at the end of the day the test is, if you re-ran it forever (a vastly long time), would it eventually reproduce every possible text meeting the criteria? And I think the answer to that would be yes, if it's really random; just by the pigeon hole principle alone.
And while it's been a while, I seem to recall from my logic courses way back when, that if you have two functions that produce the same outputs for the same inputs, one being the idealized one Borges cooked up in his head and the other being whatever procedural algorithm is running this show, then they're logically equivalent. So in that respect, I think this is "real", real enough to formally count as equivalent.
Qooper on 6/7/2022 at 11:52
I don't know about this particular software, but mathematically speaking, if you had a unique ordering for an infinite set of all possible texts, you wouldn't need the texts, only the ordering. You could generate any element in the set just by looking at the ordering. Same as integers. The ordering _IS_ a kind of generation rule.
Haplo on 14/7/2022 at 01:45
This is what my FM "The Library of Babel" was about, inspired by "The Library of Babel" by Borges. I even created an "infinite" library with around 3 billion permutations in it.
(
https://www.ttlg.com/forums/showthread.php?t=137729)
Cipheron on 17/7/2022 at 07:53
Quote Posted by Qooper
I don't know about this particular software, but mathematically speaking, if you had a unique ordering for an infinite set of all possible texts, you wouldn't need the texts, only the ordering. You could generate any element in the set just by looking at the ordering. Same as integers. The ordering _IS_ a kind of generation rule.
Yeah, nothing is being stored in the end, only numbers crunched as needed.
An interesting conclusion of that is that if you give them any phrase such as "and so it came to pass" and ask how many "books" have that exact phrase then to generated them you merely need to fix those letters in place and randomly generated everything else in the 'book' and say "there's your book, you're welcome". There's no need to "search" any books for the phrase.
SD on 17/7/2022 at 16:11
Quote Posted by Cipheron
Yeah, nothing is being stored in the end, only numbers crunched as needed.
It stands to reason when you consider there are (as per the OP) 10⁴⁶⁷⁷ unique books, and only about 10⁸⁰ atoms in the entire universe.
It's an entirely interesting concept, but I don't see it ever having any practical application, simply because the quantity of nonsense you'd have to wade through simply to get to anything coherent would be more than you could manage in a lifetime.
