(no subject)

[proximoception]

Is the mistake in the first paragraph of "The Library of Babel" deliberate?

The universe (which others call the Library) is composed of an indefinite, perhaps an infinite, number of hexagonal galleries, with enormous ventilation shafts in the middle, encircled by very low railings. From any hexagon the upper or lower stories are visible, interminably. The distribution of the galleries is invariable. Twenty shelves - five long shelves per side - cover all sides except two; their height, which is that of each floor, scarcely exceeds that of an average librarian. One of the free sides gives upon a narrow entrance way, which leads to another gallery, identical to the first and to all the others. To the left and to the right of the entrance way are two miniature rooms. One allows standing room for sleeping; the other, the satisfaction of fecal necessities. Through this section passes the spiral staircase, which plunges down into the abyss and rises up to the heights. In the entrance way hangs a mirror, which faithfully duplicates appearances. People are in the habit of inferring from this mirror that the Library is not infinite (if it really were, why this illusory duplication?); I prefer to dream that the polished surfaces feign and promise infinity...

Or is it there to make you stay up all night with someone trying to work out what all this would look like, only to find that there is exactly enough room for two identical labyrinths to weave through one another infinitely with no foot access between them (and where in the Library could one get a rope to climb down the air shaft?). There wouldn't even need to be another labyrinth: directly above and below every single chamber could be rooms filled with intelligible books, or the fabled smaller magic books, or identical copies of the concordance to the volumes of the library, or of the one true book that saves you, or even with the cylinder-spined book of God. The only way you might ever know these rooms existed - depending on the thickness of the floors and the width of the air shafts - would be upon suicide, in your infinite fall through the shaft, as you saw over and over again, while disintegrating, everything withheld from you your entire life. Could even Borges have imagined such cruelty in the demiurge?

Comments

[grashupfer.livejournal.com]

What's the mistake?

[proximoception.livejournal.com]

"One of the free sides gives upon a narrow entrance way, which leads to another gallery..."

There have to be two narrow entrance ways. It can't be just dyads [o-o] of hexagons because the story mentions going sideways several miles a couple times. Looks like the only way the hexagons can be connected, logistically, is if they go on infinitely [-o-o-o-o-o-o-o-o-o-] in parallel lines, and the stairways connect them to other infinite strings of parallel rooms 60 degrees off from the strings above them - then below them the angle of the first layer is resumed. We found about three plans where this seems possible, though there may be others - they differ mainly in hallway lengths.

Chambers in the complex can't be one floor down from chambers exactly above them - that space has to either be empty (or full of rock), contain unconnected chambers, or contain the chambers of that second labyrinth you can't get to from the first one.

[andalus.livejournal.com]

i think the language points to two hallways in each, he only mentions one hallway because it's implied that when one goes down the hallway and finds "another, identical" hex, that hex will have another hallway, plus the one he just came from. which also means only one bathroom per hex.

[proximoception.livejournal.com]

So it's as though we're being led from room to room on a tour? Doesn't really come across that way in the story, to me. And if you were you might not notice the bathroom and sleeproom right behind you as you come into the new chamber, just the ones in front.

[localcharacter.livejournal.com]

Ah, the topological question—that would be Chapter 4 of William Goldbloom Bloch's The Unimaginable Mathematics of Borges' Library of Babel. Though I don't think he comes up with anything quite as striking as the image of death as an infinite fall through inaccessible worlds.

[andalus.livejournal.com]

what does he come up with???

[localcharacter.livejournal.com]

Well, he's a mathematician, not a poet—though the book certainly has some beautiful images. The whole book is an attempt to unfold the mathematical ideas implied by the story, so I can't really summarize it: in one sense, Borges' story is a summary in anticipo of this book.

[proximoception.livejournal.com]

I checked the book out. He:

1. Like we did, considers the possibility that it's dyads all up and down - without noting that it's disproven by the text talking about going miles and miles off to the right.

2a. Like us, notes that there could be islands.

3. Like us, how there could be infinitely loopity snake lines (this impresses him, because what if someone screamed on the other side of the wall a lifetime might not suffice to get you to where they are and help them - this does not sound like a major concern of the librarian, however, and baselessly assumes also that the walls are thin). He fails to note that whatever labyrinth is formed this way must exist the same way on every floor. As you pointed out last night, the implications of a crazity winding labyrinth would have interested the speaker enough for him to speak of them.

4. He has a whole section discussing the implications of interpreting the weird line as meaning there is a stairway in one opening but not one in another - it just goes on and hits another room. I don't understand his warrant for this, given how it's translated above.

5. He doesn't go into what it would take to make each level an infinite, regular plane (the way we decided the story strongly implies it is), rather than an infinite line, whether straight or squiggly, or a dyad - how each would have to consist of parallel infinite lines and be 60 degrees off from the ones above and below.

6. He doesn't pick up on the secret labyrinth and secret rooms this renders possible.

7. He for little reason and to no consequence decides to give his hexagons certain measurements from a couple libraries Borges was familiar with.

Still, he does dig up some info about Borges originally wanting the rooms to be circles but not liking the wasted space in the interstices, hence the adaptation of hexagons. But with the super-short hallways this necessitates, you can't have regularity, you can only have a long squiggle (making it very difficult to say what might be different 'off to the right'), or various long squiggles and islands eternally cut off from each other (since all levels have to be duplicates if you're not going with our alternating angles method). There's something unappetizing about perfect regularity up and down and very random squiggliness existing identically on every single level, though it can't be discounted as an option. "To the right" might therefore just mean an arbitrary direction that the squiggle goes - downsquiggle as compared to upsquiggle. This might also explain the "14-92" number system: level 14, hex 92, counting from some arbitrary starting hex and level. You'd need level number, strand number AND hex number for the one we were discussing.

[andalus.livejournal.com]

i took the cycle number to be a measure of time myself, being something that the libraries are able to measure with some precision, unlike location, which is always vague and offhand

[andalus.livejournal.com]

but wait, no. (barring the fact that the preposition is more ambiguous in Spanish.) One which my father saw in a hexagon on circuit fifteen ninety-four... "A hexagon on" means (in english) that the hex itself is not demarcated. so there is a third number. "circuit" implies closed circuits, which is impossible in a horizontally regular libraryverse. and the last paragraph implies the idea of a circular universe isn't commonplace, so the straight lines of our regular libraryverse wouldn't be considered circuits. in english.

always the possibility that it was once known that the straight lines were circuits and the naming stuck though the meaning was lost.

[proximoception.livejournal.com]

Circuit does imply regularity. They could exist as artificial bounds, though - there's a lot of talk of zones and what not. They could even mean a four staircase square including all hexagons nearby. And if there are closed circuits, horizontally:

a. They must be very wide, since you can go many miles off to 'the right' (at which point it's implied you are in a foreign land, since the language is different).

b. As we established, everything under or over the circuit (since the circuit-ness of infinite lines is the librarian's personal heresy, not a general asumption) has to follow the same pattern. So if you're on 14-94, there's only one coordinate needed to establish your floor. The fourteen might mean it's the fourteenth grouping of however many numbers, but that seems a bit silly when base ten pretty much does that already. E.g. the fourteenth block of a hundred floors = 1394.

How is time regular in the library? How could it even be measured? I'd say the closest thing to measurement they could have would be the time it takes to get from one side of a hex to another, or from one staircase to another if the halls are regular lengths.

[proximoception.livejournal.com]

Does Spanish have a preposition that could mean either 'on' or 'at,' like French?

[andalus.livejournal.com]

"en" means at or on. but im looking at the spanish now while on the phone with j, and the preposition is "del,"

Uno, que mi padre vio en un hexágono del circuito quince noventa y cuatro

one which my father saw in a hexagon of circuit (continuous) 15 94

another ambiguity:

Por ahí pasa la escalera espiral, que se abisma y se eleva hacia lo remoto.

Por ahi is like "over there" or "along that way," making it very hard to place the staircase, though it's in the direction of the bathroom/vestibule.

[proximoception.livejournal.com]

Continuity 15-94? Because that could be a line.

[erotetica.livejournal.com]

Dude, if there's railings can't you just do what Solid Snake does?

[proximoception.livejournal.com]

I don't know what Solid Snake does, but if you're talking about swinging down somehow, that depends on the distance between floors. Suppose there's ten feet of concrete in between the railing and the top of the opening of the floor below - no way you could swing down. Depending on the width, there might also not be a viable angle for jumping across.

[andalus.livejournal.com]

if whatsisface is right about Borges being concerned with the spatial economy of his libraverse we should assume minimal space wasted anywhere. (remember as he says, if each book were the size of a proton the universe would still not be large enough to contain the library.) the hexes are chosen because they fit snugly (unlike pentagons) over a plane, so the library rooms must tesselate.

two Ls

[andalus.livejournal.com]

interesting. there are two semi-regular tessellations involving hexagons.

Re: two Ls

[andalus.livejournal.com]

the right is out because no two hex sides match up. but the left is interesting with a major drawback: the squares dont match up at any other angle. which means that either 1) you have lines infinitely cut off from parallels or 2) you offset the open ends of each hex. instead of parallel opening you could have either an acute or an obtuse angled openings, leading to either an infinite zigzag or infinite, cut-off hexagons made of six connected hexagon. with the hexa-hexagons one could imagine having upper and lower hexa-hexagons to be offset, leading to slight maneuverability between different hexa-s on the same plane, however, not without leaving many empty hexes. also many stairwells would be multi-level. IN SHORT ignore this because it's too complex to be feasible.

[andalus.livejournal.com]

imagine the dodecahedron to be the spiral staircase, which goes to the next hexagon clockwise or counterclockwise per level. actually, the second next hex, since a given hex only has hallways to connect to two docecas each, meaning half the hexes adjacent to a given dodeca would not connect to it. here the difficulty is getting to a hex immediately above you, i dont know if it's impossible but it seems terribly difficult.

im going to abandon semi-regulars, what if we assume that it's a regular hexagon tessellation and the hallways take up no more length than the thickness of the walls. in this case the hallways must be offset. and if they are regularly offset then we're left with closed loops. BUT. they could be distributed in some regular way. and since any given edge is a hallway one time out of three, you could have stairways going up three flights at once and have it be regular vertically as well. OR you could have stairways going up a random number of flights each, making it possible to be entirely random horizontally and vertically, which was what was suggested in whatsisface's conception.

[proximoception.livejournal.com]

Regular tessellation works fine. Just think of the actual rooms as slightly smaller hexagons within the larger hexagon formed by them, their walls and exactly half of each hallway, including half of the top of each stairway, to which they're connected.

They can be dyads, they can be lines. If hex-rooms only exist on every other floor, they can be regular planes - with room left for an entire, identical second labyrinth.

If space is at the same time infinite, worth conserving, and to be filled with only one labyrinth then the book guy's solution is the only one: infinite snaking. Which can create an infinite plane too, near as I can tell, while also leaving room for the cyclicality that the straight lines do.

I guess you're saying the floorplans of the levels wouldn't have to be identical if stairways could skip one or more floors as needed? The stairways would have to pierce through the middle of one border between hexagons no matter where they are, so as to go through either a hallway or middle of a wall on each level, therefore the hex grid itself would have to be regular. Otherwise I'm failing to see why you couldn't do it, yeah.

I think one problem with all of this is that spatial irregularities are never spoken of. Maybe if you live in a labyrinth all your life they don't seem very important, maybe not even very difficult to deal with.

Makes the story seem even more darkly about atoms.

[andalus.livejournal.com]

hah. the dipole would be a classic O2 molecule, two atoms with 6 valence electrons forming a double bond with each other. the lattices are more like carbon lattices, but those require other elements. maybe the one librarian to two hexagon ratio is a clue. maybe they're decaying.

[andalus.livejournal.com]

one librarian to three hex, sorry.

well it could be graphite:



but those have three bonds per atom.

[proximoception.livejournal.com]

It was one to three, but used to be one to one I thought?

People do seem to be increasingly dying of lung disease as time goes on - but I took that to be from the particles of suicides (only other cause of death mentioned) disintegrated by air erosion when falling through the shafts. The books and environment somehow seem like they must be undecaying.

But the traveling inquisitors do speak of broken stairs. A world the demiurge simply abandons is gnostic enough (see Frost's "The Wood Pile").

[proximoception.livejournal.com]

Only problem with random numbers of flights is that it closes off the possibility of that border area being used for another flight - unless it's irregular where the narrow hallway is - to the left, right or middle of the border region. And if it is, where the stairway comes up might be irregular too, allowing several invisible stairways to be tunneling up through the wall in any given border area.

But I dislike all this irregularity. The point of the hexes and everything they contain, including stairs, is to be not just space-saving but labor-saving: the same. Even extra-long stairs violate this.

What's circuit in Spanish?

[andalus.livejournal.com]

i thought this the other night, what if it's not a spiral staircase the way we normally think of it, a free-standing spiral staircase, but, instead, merely a spirally-winding one. if a staircase passed along the outer circumference of the hex, inside the wall, and opening at the hallway, it could still be called a spiral -- a closed spiral but still a spiral. so if flights were every 60 degrees you could have rows of infinite parallels without any dead spots or unreachable labyrinths.




but, right as i was writing this, it occurred to me: with this configuration it is possible to have INFINITE, REGULAR HORIZONTAL PLANES MADE UP ONLY OF DYADS. Take a look!

[andalus.livejournal.com]

fuck, it's just barely not working.

[proximoception.livejournal.com]

My plot to drive you mad and steal your cookies seems to be working.

[proximoception.livejournal.com]

I don't understand what you're talking about when you say "if flights were every sixty degrees." If flights came out into entrance halls 60 degrees off from where they left from, you mean?

"The stairway sinks abysmally and soars upward to great distances." This surely implies you can see it do so; at the very least it's a continuous stairway, the way one coming in on one side of the entrance and going out on the other would not be (and I'd have a hard time not seeing that as two staircases, rather than one interrupted one).

But even if it did exist I'm confused how that could lead to dyad planes. Only the one stairway could exist, in any connected tower of dyads - doesn't matter how much the staircase spins or how far off to the side it goes. The tower can lean or spiral around insanely, but it's still never an infinite plane on one level - hell, you could never even go back up. Two hexes at any given altitude in any self-continuous labyrinth. Only one staircase going up and down.

[andalus.livejournal.com]

he only says the staircase rises to the heavens and lowers to the depths, not that one would actually see it. each hex has its own staircase, see. so the dyad has two staircases, so you could go up a flight in one hex, cross the hallway into another hex which is offset from the previous by 60 degrees, then go down a flight in that hex and you would be in a hexagon unconnected to the two you started on but on the same level. the pattern this creates is, some some minor problems, infinite.

[proximoception.livejournal.com]

Departs way too much from what's implied, esp. if you're talking about a total of four staircases opening out into each hallway.

[grashupfer.livejournal.com]

The minimal space waste would immediately make me think of honeycombs, which would then link this story up with Thomas Browne, one of the sources for so many of JLB's ideas.

[proximoception.livejournal.com]

The sexangular Cels in the Honeycombs of Bees, are disposeth after this order, much there is not of wonder in the confused Houses of Pismires, though much in their busie life and actions, more in the edificial Palaces of Bees and Monarchical spirits; who make their combs six-corner'd, declining a circle, whereof many stand not close together, and compleatly fill the area of the place; But rather affecting a six-sided figure, whereby every cell affords a common side unto six more, and also a fit receptacle for the Bee it self, which gathering into a Cylindrical Figure, aptly enters its sexangular house, more nearly approaching a circular Figure, then either doth the Square or Triangle. And the Combes themselves so regularly contrived, that their mutual intersections make three Lozenges at the bottome of every Cell; which severally regarded make three Rows of neat Rhomboidall Figures, connected at the angles, and so continue three several chains throughout the whole comb.

Hmm.

[grashupfer.livejournal.com]

All that I say here will be rambling and disordered. Too many things to keep straight. If the set-up is like a honeycomb (which is a pretty picture in my mind) the sphere becomes a problem, because any sort of center to this library would need more than two entranceways, I think, which violates one of the statements. My struggles with visualizing all of this probably hint at the low number of my IQ. But this might be the point. Especially if the Library of Babel is a metaphor for mind or language or their function. Poe used an epigraph from Browne's Urn Burial for "The Murders in the Rue Morgue." It's the line about the "song the sirens sang," something unknowable but "not beyond all conjecture." The narrator of the story then says almost immediately following: "the mental features discoursed of as the analytical are, in themselves, but little susceptible of analysis." Borges uses that same song the sirens sang in his list of things one might find in the total library in the essay of that name. He also re-wrote Poe's three detective stories in three of his own: Death and the Compass, The Garden of Forking Paths, and Ibn Hakkan Dead in His Labyrinth using some of Browne's (and others') gemoetrical ideas in each for his own more secular purposes. The layout of the library is puzzling but not beyond all conjecture. Fun.

[proximoception.livejournal.com]

Could be that multi-entrance rooms exist but simply haven't been discovered yet - if one had been, it would have been noted in the story, and probably incorporated into all the theologizing.

Sorry, we were using visual references when we hashed it out. Should probably reproduce some here - this must all seem nonsensical.

What the sirens sing and why, for some reason, we all forget it is a major plot point in Aegypt.

Purloined Letter -> Death & Compass? I'll need to look into that, Garden of Forking Paths I honor high as can be.

[grashupfer.livejournal.com]

Yup. John Irwin wrote some great chapters about a three/four oscillation between Pruloined Letter & Death & the Compass.