> which now contains anything we ever have written or ever will write
It's actually possible to demonstrate that this can't be true. You can calculate an upper bound on the number of different states enumerable in this universe. Basically you assume that each elementary particle is a computer operating at a clock rate of the Planck frequency and multiply by the time between the big bang and the heat death of the universe. The number turns out to be surprisingly small, about 2^500 or so. Longer than this (i.e. any longer than a tweet), and this universe is no longer capable of enumerating all the possibilities.
This would only be true if the library stored all of its books on disk. It doesn't need to because of the algorithm it uses to generate the books, which is described here: https://libraryofbabel.info/theory4.html (davegauer linked to this description as well)
You shouldn't think that this means the books do not exist. The concepts of presence and absence which underlie our understanding of existence were long ago inflected by the existence of virtual archives. Any digital archive, like JSTOR for example, exists as a mass of zeroes and ones, and only enters a form intelligible to the human eye once an article is loaded from its reserve. But I doubt anyone would say that these articles don't exist before they are loaded, come into being from nothing when someone opens them, and cease to exist again when they are closed.
Already when Borges envisioned it, the library was more capacious than the universe.
> This would only be true if the library stored all of its books on disk.
Disk? Who said anything about disk? The calculation assumes that a single sub-atomic particle can store an entire work. Not only that, but that a sub-atomic particle can generate a different work every Planck time, and store them all.
That's really the point: our imaginations are much bigger than the universe we live in.
> the algorithm it uses to generate the books, which is described here:
Sorry, I don't see the description? All I see is:
"I found a successful formula combining modular arithmetic and bit-shifting operations, and the result is the library you see today."
It doesn't actually say what the formula is.
> Any digital archive, like JSTOR for example, exists as a mass of zeroes and ones, and only enters a form intelligible to the human eye once an article is loaded from its reserve.
How is my model any different?
> the library was more capacious than the universe.
Borges was writing fiction so he was free to ignore the laws of physics. But libraryofbabel.info actually exists, so it is not.
1) You are assuming that the works need to be stored at all. They do not. As long as the same block of text can be located based on the same input, it is just as available as it would be if it were stored on disk or on any other type of storage device you imagine.
2) The PRNG is irrelevant to this point. The article I linked to offers a detailed description of how to generate text without storing it on disk.
3)Your model is identical to JSTOR's, as is libraryofbabel.info's. That's my point - all of these are ways of creating a digital archive (or in your case some sort of quantum archive). The point is that libraryofbabel.info is able to archive more text than your model - more pages of text than there are atoms in the universe.
4)The concepts you should think about more thoroughly are: fiction/reality, existence/nonexistence, actuality/possibility/virtuality. The texts the website contains have a potential existence - each of them can be summoned up at any time. But they do not have the sort of actual existence which would require one or more atoms to be available for the storage of each text. The script capable of generating them all takes up less than a MB.
> As long as the same block of text can be located based on the same input, it is just as available as it would be if it were stored on disk or on any other type of storage device you imagine.
No, that's not true. There is a salient difference between JSTOR and LofB, namely, that JSTOR keys are all much shorter than the works they summon. JSTOR works thus have more information content than their keys. This is a consequence of the fact that JSTOR only contains a tiny subset of all possible works.
To get a work out of LofB I have to actually generate all of the information content of that work in order to produce the key. LofB keys are, on average, the same length as the works. So I have to do more work to get something out of LofB than I do to get something out of JSTOR. In fact, I have to do all of the work. So it is not true that LofB works are "just as available" as JSTOR works.
LofB is like the parent who responds to a child's request for a bedtime story by asking the child to describe in every detail the story they want to hear and then parroting that back to them. Any story the child asks the parent to tell, it will tell. But neither the child's mind nor the parent's mind contains all possible stories.
LofB doesn't contain all possible works any more than a floating point register contains all possible floating point numbers. LofB only contains (to the extent that it can be said to contain anything) those works which are actually summoned, just as a floating point register only contains those floating point numbers which are actually stored in it, just as a human mind contains only those stories it actually thinks about. "Contains" is not a synonym for "can potentially generate given the right input."
First off, we should acknowledge that your argument has shifted significantly - from an ontological to a practical concern. The ontological question, whether the archive exists or not, is independent from the practical question of whether or not it is useful. Initially you said that no archive could contain more than ~10^80 objects because the number of atoms in the universe placed an upper limit on its contents. Now you say that this website does not contain its books because of the amount of work necessary to retrieve them. Would you consider this to be different if the quantity of texts was less than 10^80? If not, we should recognize that you have shifted from your earlier argument, which was untenable.
As for your present argument, i would first point out that you should not treat quantitative differences as essential differences. Any archival system requires some sort of key system for retrieval. Print libraries have the Dewey decimal system, the internet has URLs, and libraryofbabel.info has its book locations, strings of letters and numbers which you are correct to point out are just as information-rich as the texts themselves. But you claim that because of the size of keys, the texts in this digital archive do not exist - this is fallacious. How large must a key-value system get before it ceases to exist? If a poem's title is longer than its text does it cease to exist? Greek philosophers parodied the confusion of quantitative and qualitative thought by asking how many grains of sand we needed to add together before we had a heap. Once again, you have confused a practical and an ontological argument - the length of keys (and quantity of text) may affect the usefulness of libraryofbabel.info, but they cannot affect its existence.
You consider three heterogeneous things in your examples - a floating point register and the set of possible floating point numbers, libraryofbabel.info and the texts it contains, the human mind and what it "actually thinks about". Let us begin with the last - you claim that the human mind only contains what it "actually thinks about." If this is so, what is a memory? Your failure to grapple with the difficult category of possibility leads to the ontological confusion in your argument.
If we limit our consideration to practicality, I would agree that the libraryofbabel.info is not useful in the same way as a digital archive like JSTOR. In other libraries, one can find texts by subject matter, author, period, etc. and learn something new from their contents. libraryofbabel.info exists to show us the same language we have encountered already in a new context. This allows us to reflect on the essence of language, which is not restricted to the intentions of a conscious and rational speaking subject (as you imagine when you speak of what we "actually think about"), but is always open on irrational excess.
I'm actually making an ontological argument, though I concede that I was not entirely clear.
Imagine I give you a box which I claim contains all the positive integers. You object because there are an infinite number of positive integers and no physical object can possibly contain an infinite number of things. So to prove my claim I invite you to query the box and ask it "Do you contain X" for any X you care to name.
So you ask: "Do you contain 1?" and the box answers "yes". "Do you contain 842198843?" Yes. "Do you contain Graham's number?" Yes. The busy-beaver number for a million-state Turing machine? Yes.
But then you ask it, "Do you contain negative one?" and the box answers "Yes." And now you protest: I claimed that the box contained only positive integers. No, I reply, I claimed that it contained all of the positive integers, not only the positive integers. In fact it contains all the negative integers too. But this in no way diminishes the power of my initial claim, because surely if it is noteworthy that I built a box that contains all of the positive integers then it must be twice as noteworthy that I built a box that contains all of the positive integers and all of the negative integers too!
So then you ask it, "Do you contain one half?" Yes. Again you protest because one half is neither a positive nor a negative integer, and again I respond with the same argument. "Do you contain pi?" Yes. Same argument. "Do you contain the Godel number of the proof that Peano arithmetic is consistent?" Yes. Ditto.
So you ask, "Do you contain a unicorn?" Yes. Aha! Now you've got me, because whatever else the box may contain, it obviously does not contain a unicorn. No, I reply, of course it does not contain an actual physical unicorn. It contains the phrase "a unicorn". In fact, it contains all possible phrases. It is not merely a box that answers "yes" to any question that is put to it. It is a box that in fact contains all numbers and phrases (is this starting to sound familiar?) and so "yes" is actually the correct answer to any question of the form, "Do you contain X" for any possible utterance X.
The LofB is just my box with a slightly different UI. It is a UI that does a better job than mine of obfuscating the fact that what it underneath the UI is completely uninteresting, and the question of whether or not my claim that the box "really contains" all the things that I claim it contains is just wordplay. The interesting question is not "to what questions will the box answer 'yes'" (or "What works does the LofB contain?") because the answer is "all of them." The interesting question is "What queries can be made of the box/LofB?" Because the queries have to exist in this universe and so they are subject to the constraints of the laws of physics. And in particular, their number is finite. Not only finite, but fairly small: less than 2^500 or so. It's a number that's so small you can actually write it out by hand in a matter of minutes!
It is that tiny subset of the vast space of possible queries that is the interesting thing. Of all the possible questions we could potentially choose to ask, we will only ever be able to ask a tiny, tiny subset of them. So we should choose wisely. And, I submit, quibbling further over the LofB would not be a wise choice.
Roughly: the state-space of the universe isn't large enough to contain a distinct physical realisation of every book in Borges' library, though it is about large enough to contain every possible tweet (I think.)
There are about 10^80 elementary particles in the known universe.
No physical process can happen faster than the Planck frequency (the frequency of light at which a single photon would have enough energy to form a black hole), about 10^43 Hz.
The universe is about 10^16 seconds old.
Multiply all those numbers together and you get 10^140 = 2^465.
Even if you allow 10^100 seconds (a conservative estimate of the time until the heat death of the universe) you still only get about 2^700 possible enumerable states.
Of course, if you want all the enumerates states to exist simultaneously then you can only encode one state per particle, and the number drops to 10^80 = 2^265, about 53 5-bit characters, not even a third of a tweet.
It's actually possible to demonstrate that this can't be true. You can calculate an upper bound on the number of different states enumerable in this universe. Basically you assume that each elementary particle is a computer operating at a clock rate of the Planck frequency and multiply by the time between the big bang and the heat death of the universe. The number turns out to be surprisingly small, about 2^500 or so. Longer than this (i.e. any longer than a tweet), and this universe is no longer capable of enumerating all the possibilities.