No truly unique pages.
September 27, 2015 at 4:31 pm #1651
I have a question that arose after doing some searching. Why is it that if you search for a specific string of 3200 characters, the search results still say “20 of ~10^29 possible exact matches”?
Try it yourself. Go to the search and enter 3200 Z’s. The result for with random characters will only return one result:
“Title: zsjabmnfnlhxntbl Page: 138
The result for with random English words is the same:
“Title: zsjabmnfnlhxntbl Page: 138
As is the FIRST result for exact match. But under the exact match section, it also says “more exact matches“. And here, you find that there are displayed 20 of ~1029 possible exact matches. How can these pages all exist as exact matches, but they don’t show up under the other search options? Why do they exist in the first place? Wouldn’t it be much more special if each string of 3200 characters were truly unique. You could write a 3200 character message to someone and know that it is only on that exact page that the message exists.September 27, 2015 at 5:01 pm #1654
Okay, but: the figure of 10^29 is incorrect.
http://www.wolframalpha.com/input/?i=sum+of+36^n+for+n+from+1+to+3260 – the number of possible hexagons (any combination of 0-9 and a-z, any length from 1 to 3260) – returns 3.617320234859102056238887935515875894510… × 10^5073
http://www.wolframalpha.com/input/?i=%283.617320234859102056238887935515875894510%C3%9710^5073+*+4+*+5+*+32+*+410%29+%2F+29^3200 – that, times the number of walls per hexagon, times the number of shelves per wall, times the number of books per shelf, times the number of pages per book, divided by the number of possible pages (which is the statistically probable number of a certain page in the Library) – returns 2.0126002014193314097397138925541776679717654230295356369… × 10^399
That is nowhere near 10^29.September 27, 2015 at 6:16 pm #1656
Right you are, but I hadn’t thought that this number was meant to indicate the number of actual pages. It is indicating the number of pages with 3200 Z’s all in a row. It’s the same with any specific string of 3200 characters. That is to say, any 3200 character message you write will exist 10^29 times, rather than just once, which is what I would expect.September 27, 2015 at 6:25 pm #1657
Oh, sorry, I misread your post.
But anyway, the library doesn’t use numbers: it only used 26 letters, comma, full stop and space, so 29 characters. I changed your formulas to reflect this, and instead of 10^399, it comes up with 10^93, unless I made some mistake. But still, why would it have that number? What does it mean? Is that the reason that unique strings of 3200 characters appear more than once? Shouldn’t they appear only once?September 27, 2015 at 8:26 pm #1663
The number of possible search results is based on the algorithm the search function uses. Each page of 3200 characters appears multiple times before the random number generator begins to repeat. I’ve explained it in more detail in another forum post – I’ll look for the link.September 27, 2015 at 8:35 pm #1667September 27, 2015 at 8:41 pm #1668
Ok, thanks, that clears it up!December 12, 2017 at 8:00 pm #23615
i still don’t understand why a page appears in more than one bookDecember 31, 2017 at 7:43 am #23854
The algorithm is designed so as to remain random up until the point that it loops, which should provide exactly one of every possible book within that spectrum. The issue is that, by providing books, you inevitably will get duplicate pages, where the same page might appear in two identical books with one letter off, or two books that are completely different excluding that single page.December 31, 2017 at 9:19 am #23856
@Haplo and @Ray
Pretty much what Ray said. To illustrate it, imagine we have books that are 5 pages long and each page has 3 letters in it. We might have a few books that look like this:
Book 1: [aaa, cat, aaa, aaa, aaa]
Book 2: [aaa, aaa, aaa, aaa, cat]
Book 3: [bbb, cat, bbb, bbb, bbb]
Book 4: [aaa, cat, aaa, aaa, aab]
In Book 1, we see Page 2 has “cat”. Book 2 is the same, except the cat page is on Page 5. Book 3 is completely different from Book 1, except the cat page is still Page 2 (just like Book 1). Lastly, Book 4 is identical to Book 1, except on Page 5 it’s “aab” and not “aaa”. Even though there are TINY differences, these are all considered “unique” books programmatically. Contextually, they appear the same to humans, but you have to realize that the Library contains all combinations of all pages in all positions in all books. This includes every tiny difference such as Book 1 and 4 above, where only 1 letter is different. Or something even crazier like:
Book 5: [one, two, dog, cat, red]
Book 6: [don, etw, odo, gca, tre]
What happened here, was that I took the letter “d” from “red” in Page 5 of Book 5, placed it at the beginning of Book 6, and shoved the rest of the letters to the right. It’s basically a 1-character shift for the entire book.