In The Library of Babel, author Jorge Luis Borges imagined a library that contained every possible combination of text (including lower-case letters, period, comma and space) arranged into pages of text, which are bound into books, which are arranged on shelves, which are housed in hexagonal rooms interconnected into a grand Library. Specifically:
The universe (which others call the Library) is composed of an indefinite, perhaps infinite number of hexagonal galleries. In the center of each gallery is a ventilation shaft, bounded by a low railing. From any hexagon one can see the floors above and below-one after another, endlessly. The arrangement of the galleries is always the same: Twenty bookshelves, five to each side, line four of the hexagon's six sides; the height of the bookshelves, floor to ceiling, is hardly greater than the height of a normal librarian. One of the hexagon's free sides opens onto a narrow sort of vestibule, which in turn opens onto another gallery, identical to the first-identical in fact to all. To the left and right of the vestibule are two tiny compartments. One is for sleeping, upright; the other, for satisfying one's physical necessities. Through this space, too, there passes a spiral staircase, which winds upward and downward into the remotest distance. In the vestibule there is a mirror, which faithfully duplicates appearances. Men often infer from this mirror that the Library is not infinite-if it were, what need would there be for that illusory replication? I prefer to dream that burnished surfaces are a figuration and promise of the infinite. . . . Light is provided by certain spherical fruits that bear the name "bulbs." There are two of these bulbs in each hexagon, set crosswise. The light they give is insufficient, and unceasing.
From that, people have conjured up actual structures of what this would look like, including the possibility of having more than one exit from each hexagon.
Visualizing the number of Bitcoin addresses sometimes people use the analogy of drawers or dropboxes to show them. The sheer number of Bitcoin addresses (2160, which is 1048; one quindecillion addresses) gives them their security, but how to visualize that sheer enormity?
This video by CRI does the math for equating them to pirate chests filled with gold buried around the earth.
Assuming 2 square feet needed per chest, if you layered the entire surface of the earth with them, that's only 2.3 x1015 chests; many orders of magnitude smaller than the number of Bitcoin addresses there are. You'd need 600 nonillion (600 thousand billion billion billion) earth-sized planets all covered with treasure chests to equal the number of Bitcoin addresses.
But let's take the Library of Babel idea and stick these things into rooms, where we can be a bit more space efficient. Instead of treasure chests, let's think bank safe-deposit boxes. The smallest bank-deposit boxes are 5 inches wide, 2 inches tall, and 12 inches deep. Plenty of room for stashing your life savings, if represented in something value-dense like gold or gems.
So, how many bank vaults of these boxes do we need to represent all the Bitcoin addresses? Well, let's make columns 50 boxes tall, which is 8 feet, 4 inches tall. That means 50 boxes get stacked in a 5x12" footprint of space, and so to get 1,000 of them, you'd need 20 columns, which is also 8 feet, 4 inches.
Now, let's arrange those spans of 1,000 in clusters of 10,000. We can arrange them in a "U"-shaped gallery, with accessible 4-foot-wide walkways, like so (top view):
That gallery takes up a footprint of just about 22 feet long, and 12 feet wide. Every single 4 digit PIN could be found within a gallery of this size. The opening on the end makes it easy to string them together into side-by side galleries, which you can then walk through in a zig-zag pattern:
Pacing from the start of one gallery to the beginning of the next is about 54 feet. Stringing 20 such together into a wing that you can walk by going down and back results in a space taking up 120 feet long by 48 feet wide, and holding 200,000 boxes:
That means every five wings is 1,000,000 boxes, taking up a footprint 120 x 240 feet:
Walking this whole series of wings is a little over a mile of hallways to zig-zag through. So, how far have we come? These five wings hold 1,000,000 boxes, but that's only 106, and we need to get up to 1048. We're going to need many orders of magnitude higher than this, so let's kick it up a notch!
We know we're going to need a mode of travel faster than human walking speed as we expand further, so let's assume the openings these wings we're lining up side-by-side open up onto a Hyperloop track or some other super-fast human-transportation vehicle that headed off in a straight line. We can put a series of wings on each side of the track, so every 240 feet of track, we can fit in 2,000,000 boxes. And let's make this multiple floors; stacking those wings one on top of each other five high, so it's 10,000,000 boxes accessible from each 240 feet of track.
That means within 2,400 feet of track you could fit enough boxes that every possible birthdate (an 8-digit number) would be able to be represented.
With 168,000 feet of track (almost 32 miles), you could fit enough boxes for all 7 billion humans on earth to have their own box.
So how long do we need to make that track to fit in all the Bitcoin addresses?
That is an amazingly large number! It makes the Hyperloop's envisioned 600 mph speed look paltry. Even if we upgraded the transportation system used within the structure to be teleportation (breaking you down into energy such that you are then transmitted at the speed of light to the destination to be reassembled), traveling at the speed of light would take over an octillion (1027) years for the signal to reach the far end and reassemble you. The entire observable universe is about 585 billion light years (5.843x1011) in circumference, so if you bent that track very slightly to bend around on itself and form a spring/helix shape, you would go around the entire observable universe 1.9 quadrillion (1015) times!!
So, yes, there are quite enough Bitcoin addresses to go around, and the odds of two people picking the same two are quite astronomically small. ✨