Looks like the current votes in this thread don’t really appreciate just how fast total permutations of large sets grow. It’s one of the few things that can dwarf that number for the total number of atoms in the observable universe.
i mean i didn’t do a very good job explaining what i meant by that either. could be i just assumed this is something everyone knows (i work in tech, so this is something i am too familiar with. it is very normal someone who doesn’t might not know this).
Yeah, some responses think you don’t understand scientific notation. At least it’s kinda funny, they misunderstood what you were saying so much they thought you misunderstood what the comic was saying when you were actually pointing out that the comic appears to be underestimating the size of the problem space it’s pretending to pretend to enumerate (aka it can be very difficult to write for a character that is intended to be smarter than the author, even when the author is really smart like this one is).
In other words, every entry in the lookup can be mapped to a 0.8 KiB string. That means for any sequence longer than 0.8 KiB, there MUST be a permutation you can make which has no answer (pigeonhole principle). Because so many entries answers long structured sentences, short random ones must mostly be filtered out.
This text itself is past halfway to that limit. If I doubled the length then lookup-only is no longer possible and a logic parser is an absolute must. Applying compression to the query only increases what can be answered by a fixed factor.
I think you’re off by 2 bits (round up and don’t forget to always add 1 at the end), but regardless I think the comparison doesn’t work.
True that it would be comparable in size to a 0.8 KiB string but not necessarily in complexity. If his lookup table didn’t do it by character but by word or sound it could have a ton more information stored there.
Your comment stored as a string isn’t nearly maximally information dense, like you’ve made god’s info
But we’re talking permutations of sound combinations that can be of arbitrary length. Going by that alternating consonant/vowel pattern above (which simplifies it because you can have consecutive consonant or vowel sounds in words and phrases), the numbers of pairs would be 120,000. That’s less more than 100,000, so for each pair in a phrase, you add at least 5 0s to the total possibilities. 2000 / 5 is 400. Unless I screwed something up, that means the maximum length of a query is 400 consonant/vowel pairs before you have to introduce gaps (which goes against the random noises that got responses). Halve that because it can start with either a consonant or vowel sound.
A rough estimate of the number of sounds in the above paragraph is something like 225, and I simplified my count by ignoring consecutive consonant sounds (which it is full of).
Like yeah, 10 to the 2000 is a huge number but when you’re dealing with permutations, you use up numbers very fast. A more popular counter example is the stat about the total number of permutations for a deck of cards, where they say if you shuffle it well, you probably have a unique sequence of cards that has never been seen before. Iirc, that number is within a the ballpark of the order of magnitude of that total atoms in observable universe estimation. And that’s just with 52 possibilities and no repetition (calculated by factorial, whereas sound combination possibilities grows even faster and isn’t limited to 52 options).
Edit: corrected that bit where I rounded the 120,000 to 100,000 to simplify the math by looking for a minimal value rather than the actual value.
10^2000 isn’t even that big though? That’s maybe 1500 English words or so.
Looks like the current votes in this thread don’t really appreciate just how fast total permutations of large sets grow. It’s one of the few things that can dwarf that number for the total number of atoms in the observable universe.
i mean i didn’t do a very good job explaining what i meant by that either. could be i just assumed this is something everyone knows (i work in tech, so this is something i am too familiar with. it is very normal someone who doesn’t might not know this).
Yeah, some responses think you don’t understand scientific notation. At least it’s kinda funny, they misunderstood what you were saying so much they thought you misunderstood what the comic was saying when you were actually pointing out that the comic appears to be underestimating the size of the problem space it’s pretending to pretend to enumerate (aka it can be very difficult to write for a character that is intended to be smarter than the author, even when the author is really smart like this one is).
I wonder if you got this from HPMoR, because I think I’ve seen it there
3000 years agoIt was an observation I’ve made from reading/seeing other examples. Not surprising that others have noticed it.
Is that a parody fan fic that points out Rowling doing that with any character with more intellect than a rock or dehydrated slug?
Yeah, but its author also now demonstrated specific views
There are between 10^78 to 10^82 atoms in the observable universe.
10^2000 is a rather large number.
Scientific notation is neat
https://en.wikipedia.org/wiki/Scientific_notation
Sure but combinatorially that’s very small… 1400 a-z characters will have numbers of combinations exceed that number.
No. Go read the wiki and then try working out how large 10^2000 is.
Then do some quick maths on the combinations of phonetics (read the comic again to work out why phonetics and not combinations of a-z characters).
Then have your mind blown by how many orders of magnitude you’re away from being correct.
Or be incurious and fail to take this opportunity to comprehend the universe a tiny bit better.
Log2(10^2000) = 6643 bits
In other words, every entry in the lookup can be mapped to a 0.8 KiB string. That means for any sequence longer than 0.8 KiB, there MUST be a permutation you can make which has no answer (pigeonhole principle). Because so many entries answers long structured sentences, short random ones must mostly be filtered out.
This text itself is past halfway to that limit. If I doubled the length then lookup-only is no longer possible and a logic parser is an absolute must. Applying compression to the query only increases what can be answered by a fixed factor.
I think you’re off by 2 bits (round up and don’t forget to always add 1 at the end), but regardless I think the comparison doesn’t work.
True that it would be comparable in size to a 0.8 KiB string but not necessarily in complexity. If his lookup table didn’t do it by character but by word or sound it could have a ton more information stored there.
Your comment stored as a string isn’t nearly maximally information dense, like you’ve made god’s info
Even if you compress it by 99.9% losslessly, it will only make it ≈ 0.8MB, which is big but not that big
going by phonemes, assuming we must alternate vowel and consonant phonemes, 10^2000 combinations covers a maximum length of about 1500 phonemes.
Humans have the ability to produce about 600 different consonant sounds and 200 vowel sounds so it seems safe to say all bases are covered.
But we’re talking permutations of sound combinations that can be of arbitrary length. Going by that alternating consonant/vowel pattern above (which simplifies it because you can have consecutive consonant or vowel sounds in words and phrases), the numbers of pairs would be 120,000. That’s
lessmore than 100,000, so for each pair in a phrase, you add at least 5 0s to the total possibilities. 2000 / 5 is 400. Unless I screwed something up, that means the maximum length of a query is 400 consonant/vowel pairs before you have to introduce gaps (which goes against the random noises that got responses). Halve that because it can start with either a consonant or vowel sound.A rough estimate of the number of sounds in the above paragraph is something like 225, and I simplified my count by ignoring consecutive consonant sounds (which it is full of).
Like yeah, 10 to the 2000 is a huge number but when you’re dealing with permutations, you use up numbers very fast. A more popular counter example is the stat about the total number of permutations for a deck of cards, where they say if you shuffle it well, you probably have a unique sequence of cards that has never been seen before. Iirc, that number is within a the ballpark of the order of magnitude of that total atoms in observable universe estimation. And that’s just with 52 possibilities and no repetition (calculated by factorial, whereas sound combination possibilities grows even faster and isn’t limited to 52 options).
Edit: corrected that bit where I rounded the 120,000 to 100,000 to simplify the math by looking for a minimal value rather than the actual value.
More sounds doesn’t make it better lol. With that many, you get a max length of around 700-800 sounds
It all comes down to how long of a string of words/characters you allow.
It’s pretty big number. Many zeroes. Much more than 20,000