Nick, Peter and Fraser return to the Library of Babel and discuss how to go about building one.

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Hello and welcome to the Cognitive Engineering Podcast produced by Tell Me Studios for Aleph Insights. In this series of podcasts we take a look at interesting topics and discuss what we think they tell us about analysis and decision making. I'm Fraser McGruer and I'm here with Nick Hare and Peter Coghill of Aleph Insights and this week we're discussing the Library of Babel. Does it exist and if so how big is it? Perhaps you can start us off by just give us

What would you do? Okay so sorry just one thing I want to double check there. So are we saying or are you saying that this book if each page or each book I forget which was an atom in the universe are we from what we know about the universe we're saying actually it's bigger than any universe that

we think could exist? Yeah I mean the number of atoms in the universe is roughly right I don't possibly one with you know let's say roughly one with about 100 zeros. Now when you're talking about the numbers of zeros roughly has to be caveated a lot here right. If I say you know roughly one with 100 zeros if it's one with 98 zeros right kind of sounds similar that's 100 times smaller than one with 100 zeros. So when you're talking about numbers of zeros the differences are vast so but you know so we've got to caveat that it's not like oh it's kind of somewhere around there we're talking about things you know every zero you add is multiplying something by 10 this is why you know one with two million zeros is just it's a number just beyond the comprehension

of. Okay so therefore this sort of begs the question is why would one imagine that you could actually build the library of Babel? Over to you our engineer Peter. So it's I think it's probably

clear that we couldn't repurpose all the matter in the universe to form this library they're just well there wouldn't be enough of it to start with and if we did manage to tap into other universes and steal all their matter we'd still struggle right so even with hugely vast technology it would be it would a seem a bit pointless and b probably be impossible but that's not to say that we couldn't generate some sort of algorithm that that calculates on the fly parts of the library for you so you could have as you could simulate the the library in some way so if you would specify a room a bookshelf a book then it would tell you what was in that book it would be it could generate that book on the fly for you and there are bound to be mathematical algorithms that can be employed but a simple one to imagine would just be a random number generator that just randomly generates that that book for you and then checks whether or not it's already generated that book if it has just generate a new one and present that and then remember where that book was and that would be a brute force simplistic way of doing it because you're the the library of Babel doesn't specify as described by Borges any particular order of books so it doesn't matter if they're presented randomly to you now he does though allude to potential for another degree of magnitude which the order of order of books does matter and the main protagonist of it sort of explores this idea in which case um i correct me if i'm wrongly but i think then it does become an infinite library because your patterns become infinitely complex and you have to then sort of practically spiral out in more and more complex patterns and you end up taking up an infinite

amount of space no i mean i i don't think i'm not sure i mean if there's let's we've got our one let's say we had our one with two million noughts uh let's call that a Babel or i've got a Babel of books and um and each one of those can be in each of a Babel positions right so we could we could have there's one ordering in which uh the books are start from all blanks the and then the next one is all blanks with an a at the end the next one is all blanks with a b at the end and and you could order them like that in a way that we might think of as fairly sensible um and then then you could uh you know be easy you'd know where where to go roughly which direction to go in to find something there's but but the point is that there is still a finite number of potential orderings for any given potential arrangement um and here we go yeah i mean you might you therefore have if you think about you're zooming out again another level and you might think of each particular book right as being like a letter in another bigger library right so but there is still only a finite number of potential orderings of those books now it's bigger by vastly bigger than the number of books it's vastly bigger than a Babel um this number so so it's but but the point is that there is still a finite number of potential orderings if you wanted to have a uh a library of libraries of Babel where every on every bookshelf there was a separate library of Babel and within each of those libraries there was a different ordering of books um you're presented with the same problem but just at a bigger scale uh but but but anyway the question is why why we would want to know that yeah and and but also just go back to this question of like how Peter's see I know this is one reason we were discussing is I took issue with Peter's characterization of one way you could do it I think it's a typical engineer's way of doing it right which is kind of this will his approach will definitely work but there is and we should say at this point there is a website it's a very clever website which actually does this and we were debating whether or not it was going to what it would do is randomly generate and then cache uh the uh the the books on the fly and I said well no you could you could do it with a deterministic algorithm so you could say for any given bit of text you could say whereabouts you know you could you could you could say well you know he is he is a book with that text in right if I if you complete and if you would completely specify uh a a book that completely give me the you know the the uh 410 pages of text um then you could you could get an algorithm which would turn that into a number uh and a location within the library do you sort of mean so okay so so the but the point but the point is that what I'm saying is the that is a very small program right it's a bit like I mean so because every combination is in the library of babel and in that sense like it doesn't actually contain any information the library of babel contains no information so the question is when those librarians are going around looking for combinations of letters um why they would never be surprised in that sense like you know that in there somewhere is any given set of text right so you know what are you learning when you find a book with some things in it I don't know the

answer but but okay sorry let's just get it back to the question at the beginning right which was um does it exist and if so how big is it I can answer that for you right um does it exist no it doesn't that's the end of the question that's the answer so but but but if we do want to complicate it I will only be prepared to complicate it to this extent right which is does it exist maybe um and if so how big it is is it I don't know but probably very big okay in fact no definitely very big and I don't know that's as far as I get guys why what are you doing sitting wait sorry what are you two doing sitting around discussing for god's sake about oh does it really exist so I take issue with I mean where do you guys get this stuff okay okay look there's there's a there's

a concept uh called Kolmogorov complexity right which is a way of trying to describe the complexity of an algorithm so there's one way of looking at it but let me get say I give you a string of 100 ones and I say look don't give me an algorithm which generates that well it's easy isn't it just print one you know a hundred times you can you could likewise if I give you a string of zeros same same deal right now if if uh if I give you some completely random set of ones and zeros there may be no way of expressing that in anything smaller than the string of ones and zeros I've just given you it might be that that's the best way the the shortest way of describing and this is it's not just this now this sounds ridiculous and abstract right but actually that's fundamental to compression which is fundamental to the functioning of the internet right the fact that you the fact that there are ways of compressing strings of data into smaller into programs that are themselves smaller or bits of data that are smaller than those original strings of data is absolutely vital that the thing is that I'm what I'm saying I think what we're saying is you can compress the library of babel into something absolutely miniscule you could get the library of babel into a text file right um despite the fact that it's it requires one one to the ten to the power of two million universes to actually build before we wrap up wrap up is there anything

you want to add okay everyone's looking blank okay so look whenever I edit our podcasts I obviously a part of that process is I always listen back to them I go oh that's interesting or I should have said this or I have no idea what we've just been talking about for the last 10 or 15 minutes I have no idea and what intrigues me is is one whether people listening know what you're talking about I don't know if they're if they're like me I don't know but also what intrigues me is two when I'm listening back to it well I suddenly you know there'll be a moment of epiphany and I'll go ah okay that's what they were talking about so look I mean make this accessible for me

you know what an mp3 is right you've heard of that I know it's a kind of music file correct an mp3 is very small typically of a pop song it might be four megabytes or something right four four billion bits of data right that's that's really quite small I mean it relies on the fact that you can take a piece of essentially sound and and make the amount of data small by relying on tricks such as saying okay well here we've got this isn't actually how it works but roughly okay we've got 10 seconds of silence here so instead of actually recording having a huge string of zeros we're just going to say repeat zero you know 10,000 times or whatever that's that's so that's how we compress data right compression algorithms essentially do that they find patterns in the data and and therefore shrink the size of the amount of information you need now the point about the the point about the library of Babel is that it's given given its size surprisingly totally compressible in the same way that if I asked you to list if I if I said well I I want I've got a specific number in mind you know 1,900,250 you know there's that specific number can't be compressed into anything other than itself but if I said every if I said I want every number from naught to 20 million that's that could be compressed into something very small because it's just a recipe for producing numbers and the recipe for producing the library of Babel is tiny compared to the library of Babel itself okay let's stop there I'm just slightly concerned

that you sit around talking about this sort of stuff but you know I guess that's what you're sort of paid to do that's that's your job right that's that's what you guys do no we're definitely not paid to talk about this kind of thing we do that for fun okay let's stop there chaps thank you very much I'm mystified to be honest as to I'm in the same position as I was 15 minutes ago so thank you very much thank you as always for listening to the Cognitive Engineering podcast with Nick Hare and Peter Coghill and until next time goodbye