Sorry for the late reply. So my answer to the metaphysical question is "No, it does not exist". This was an epiphany for me during my time as a patent examiner. I was talking to an older examiner and expressed the frustration that people were just claiming ideas that essentially already existed. I didn't express this quite in the way that I did just now, but this idea was an embedded though somewhat camouflaged implicit assumption in my frustration. When the older examiner told me that the ideas didn't exist until the inventor invented them, I argued with him vociferously for a while, but he eventually won the argument, and I had that epiphany. I went on to convince myself mathematically that some combinations simply do not exist anywhere in the universe before someone makes them. That is the basis for intellectual property law (done properly). This string of words, right here, has never been put together before, although I am drawing from a list of previously used words, and using a fairly well defined algorithm (English syntax) to put them together. So, if I were to copyright these words, I am not stealing pre-existing property from mankind. No, this string of words never before existed. If I pick out a number at random with one hundred digits, I will guarantee you will not find that string of digits was actually written out before.
It is the difference between writing an algorithm and actually executing the algorithm. You can write down the algorithm, "Print all numbers 1 - google" but you can't actually execute it. Not within the limits of our universe. If I pull out that random 100 digit number, out of sequence, I will guarantee no one else ever before has pulled out that same number, out of sequence, and written it down. Here is one:
Well, just type your own damn string of numbers. I tried to post one on Slashdot, but I got the error message, "Filter error: That's an awful long string of letters there." And it won't let me post. Whatever happened to freedom of expression? Why is Slashdot censoring my strings of one hundred digit numbers? Why does Slashdot discriminate between the algorithm "write a one hundred digit string of numbers" and an actual string of one hundred digits?
Anyway, go find whatever random 100 digit number you generated anywhere, other than where you wrote it. It will make going back in time and winning yesterdays Powerball look pretty easy. And just because you can search it on the Library of Babel, and come up with locations, doesn't mean they exist. Those locations have literally never existed before you searched for them, in much the same way that writing an algorithm for "writing out all the numbers 1 to the number above" and executing that algorithm is not the same. Is there a difference between the algorithm "Store all the numbers 1-google without compression" and the algorithm "Store all the numbers 1-google with compression"? There is. If there is not, you can prove basically anything about "compression". That is a basic logical tenet. If you can prove a statement and it's opposite, you can prove anything within the logic you are using. One difference between those two algorithms is this: the first algorithm cannot be executed, and the second one can. It is essentially the same difference between the algorithm "Describe all inventions that will be the subject of a US patent application filed in year 2017" and the algorithm "Provide a printout in under a year describing all inventions that will be the subject of a US patent application filed in the year 2017". I know an algorithm for the former, and have written it down, but I will never execute it. In 2018, it will be relatively easy to provide an algorithm for the latter (possibly excepting patents on gene sequences). If you have an algorithm *now* for the latter, you can be much richer than the Powerball winners. The best and most efficient algorithm for the latter is called "Earth" and that algorithm exists now, and will execute the former and latter algorithms in 2017. Nowhere else in the Universe does the latter algorithm exist, and it would not be complete without me, without you, without Slashdot, and without these words. Now there is some metaphysics for you to ponder.
In my way of thinking, all of the ascii data that makes up any statement is always physically stored somewhere, and never appears by magic, or some non-physical process. The exceptions are randomly generated data and algorithmically generated data. Now, I would assert that "Print out all the numbers from 1-10" is a very simple algorithm written in plain English. Storing that requires an amount of computer space which is different from "1 2 3 4 5 6 7 8 9 0". Notice that if the first algorithm is stored on the computer, the ascii value for "7" is a bit sequence that is not stored. In the second data set, the ascii value for 7 is stored. That is the basic difference.
It is really even easier than that to understand. I can say that I know how to count from one to google. I do. I know exactly how to count from one to google. But I just can't physically do it, and neither can any computer. It takes too long. The algorithm is simple, and has a well defined beginning and end. If you ask me to do it, I will fail. If you ask a computer to do it, it will not halt until it is shut down. Even if the computer is merely counting in one of it's internal registers, and not doing any I/O, it would not make it before the universe imploded. It would need approximately a 333 bit internal register (I use 10 exp 3 = approx 2 exp 10 as a conversion), which is almost trivial to make with today's technology. But even if you ran it at tens or hundreds of gigahertz, you would not make a substantial dent in your counting sequence in one year. Ok, to make it simple, say we (or the computer) counts at a terrahertz, or from one to 10 exp 12 in one second. How high can we count in a year? A year is 31,536,000 seconds. Let's just round it up to 100,000,000 seconds, or 10 exp 8. So we've counted up to 10 exp 20 in one year, using our approx. 3 terrahertz computer. Oh, I know! Let's count for a hundred billion years. Great, now we have surpassed the life of the universe, and we've only made it to 10 exp 31. Oh, I know, let's use more than one computer register, and count in parallel! Even if we turned the entire mass of the solar system into computer registers that could help with the counting, we would not get close to our goal of counting to google. Only when we used every fundamental particle in the universe to represent one bit in our computer, and counted for a time on the order of the lifetime of the universe, are we beginning to be in the rough order of magnitude of counting one to google. But then, that is just counting, not storing all the data. Oh, I can store all the data for you! I will just use a compression algorithm. Here is all the data, compressed into one simple algorithm: "All the numbers from one to google". I've stored it! If you want me to retrieve a number, * just tell me what the number is *, and I will retrieve it! I have them all, right here, up in my noggin. If the number is part of the "stored" numbers one to google, I will let you know. Now there is a metaphysical argument for you.
The true metaphysical argument here is about how fantastically unique we all are if you can begin to understand these numbers. I have more than 300 unique bits in the leftmost millimeter of the tip of my left big toenail. No one will ever be anything remotely like me as I am right now at this moment, sitting here in my room, even if the universe repeats itself a hundred gajillion times. What I am experiencing right now is a miracle of large numbers, which cannot be stored, lost forever if I don't experience it myself, right now, this moment.
Seriously, nothing is really stored in the Library of Babel, as far as I can tell. Instead, it is a program which generates a book or image based on a reference. There is a huge difference. In other words, I can make a reference to every book that is 410 pages long very easily. In fact, I just did make that reference, in the last sentence. Any example of a 410 page book seems to be within the bounds of my reference, and, once I see the book, I could imagine it to be located here... wherever "here" is imagined to be (but within a space larger than the universe). So it would be quite a different matter to actually embody all of those books. It is literally the difference between saying "All the numbers 1-10" and "1 2 3 4 5 6 7 8 9 10". Those two sentences may mean the same thing, but they are not literally the same thing. If I said "All the numbers 1-google" I only made a reference! I did not actually say all those numbers. It would be physically impossible for me to put a sentence next to it that listed all the numbers one to google. What the Library of Babel has managed to do is to make a sophisticated algorithm to reference many books. It is a programmed reference.
I am glad you provided me with that link. People like you make posting worthwhile. I hadn't heard of the Library of Babel before. I think I should provide a link to the USPTO. I'd like to see them chew on that for a while.
Time-sharing is the junk-mail part of the computer business. -- H.R.J. Grosch (attributed)