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Can someone visually explain the world from the 'Tower of Babylon' story?

Where does the sun go at night if the world is a cylinder? Is the sun outside/inside of the cylinder or on the same level as the “Earth”?

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The world described in Chiang's Tower of Babylon isn't a tube or a cylinder, it's a series of concentric spheres.

The smallest sphere is the Earth itself, with all of its people and mountains and plains and seas. Above that is the air (clouds, etc) and above that is the Moon, the Sun and then the stars. At the very highest point, farthest from the ground is the "Vault of Heaven", a granite sphere that encompasses everything that we've already mentioned.

The Moon

With the passage of the weeks, the sun and moon peaked lower and lower in their daily journeys. The moon flooded the south side of the tower with its silver radiance, glowing like the eye of Yahweh peering at them. Before long, they were at precisely the same level as the moon when it passed; they had reached the height of the first of the celestial bodies. They squinted at the moon's pitted face, marveled at its stately motion that scorned any support.

The Sun

When they were at the level of the sun, they traveled entirely at night. During the day, they tried to sleep, naked and sweating in the hot breeze. The miners worried that if they did manage to sleep, they would be baked to death before they awoke. But the pullers had made the journey many times, and never lost a man, and eventually they passed above the sun's level, where things were as they had been below.

Now the light of day shone upward, which seemed unnatural to the utmost. The balconies had planks removed from them so that the sunlight could shine through, with soil on the walkways that remained; the plants grew sideways and downward, bending over to catch the sun's rays.

The stars

Then they drew near the level of the stars, small fiery spheres spread on all sides. Hillalum had expected them to be spread more thickly, but even with the tiny stars invisible from the ground, they seemed to be thinly scattered. They were not all set at the same height, but instead occupied the next few leagues above. It was difficult to tell how far they were, since there was no indication of their size, but occasionally one would make a close approach, evidencing its astonishing speed. Hillalum realized that all the objects in the sky hurtled by with similar speed, in order to travel the world from edge to edge in a day's time.

The Vault of Heaven

They were close enough now to perceive the vault of heaven, to see it as a solid carapace enclosing all the sky. All of the miners spoke in hushed tones, staring up like idiots, while the tower dwellers laughed at them.


Chiang's book is pretty consistent with earlier (Babylonian, Messopotamian, Hebrew, etc) interpretations of cosmology with the Earth at the centre of the firmament with various celestial bodies traveling around it in circles, and with the heavens existing above that all.

enter image description here enter image description here


The twist ending revealed at the end of the book is that the structure of the cosmos is actually a

paradoxical spherical tesseract, with the Vault of Heaven (and everything inside it, including the Earth itself) existing deep within the Earth, recursively.

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    Thanks for your answer. I am puzzled because at the end it digs up into the vault and ends up he surfaces on earth more or less where he started to climb the tower. Now it could be a toroidal world except that “...men had sailed to the edges of the world, and seen the ocean falling away into the mist to join the black waters of the abyss far below”. The world has a edge from which one can fall and the top is connected to the bottom. The story says it is a cylinder. But where does the sun goes once it crossed its dedicated space in the sky? Does it vanishes and come back every morning? – Eva Feb 20 '19 at 19:15
  • @Eva - Hence why it's paradoxical. He finds himself in a surprising place. Having dug directly up, he finds himself back at the bottom. – Valorum Feb 20 '19 at 19:17
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    Ted Chiang: “and then it came to him: a seal cylinder. When rolled upon a tablet of soft clay, the carved cylinder left an imprint that formed a picture. Two figures might appear at opposite ends of the tablet, though they stood side by side on the surface of the cylinder” – Eva Feb 20 '19 at 19:20
  • @Eva - Yes, with his limited understanding of non-euclidian topography he's trying to puzzle out how you could move from a to z without passing through the intervening letters. Obviously we know better. – Valorum Feb 20 '19 at 19:24
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    I was hoping Mr. Chiang had a better solution for the “where the sun goes at night” issue. Nonetheless, great short story! Thanks for your time! – Eva Feb 20 '19 at 19:36
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The answer can best be described using an analogy the author himself used near the end of the story:

“and then it came to him: a seal cylinder. When rolled upon a tablet of soft clay, the carved cylinder left an imprint that formed a picture. Two figures might appear at opposite ends of the tablet, though they stood side by side on the surface of the cylinder”

Imagine a 2 dimensional universe which has length and height. Lets draw this on a piece of paper. Along the bottom edge of the paper we would draw an island surrounded by water. In the height direction, from the middle of the island to the top of the page, we would draw a line that would be the tower. Then make a cylinder of the page by joining the top of the page to the bottom edge of the page.

If you did this, you would see the top of the tower now touches the underneath side of the island. You can then imagine that if you joined the two ends of the cylinder together, you would have a toroidal universe (ie donut shaped).

So the story describes this by imagining our two dimensional paper now being 3 dimensional space!

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    I felt that this passage was more to do with the protagonist's lack of understanding of non-Euclidian geometry than as an actual, factual description of the universe – Valorum May 8 '19 at 17:05
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    That's ok, except its not an "actual, factual description of the universe". It is just an analogy in 2 dimensions. – Ben Law May 10 '19 at 0:00
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Since I cannot comment, I'd like to point out that the accepted answer is incorrect. Reason: the object given in the answer is topologically just a 4-ball (D^4), it is simply mathematically impossible to have the outcome that happens at the end of the story because in such a world continuing in any direction would lead to a boundary whereas

in the story there is no boundary and going through the vault brings them back to the surface.

Ted Chiang's work is characterized by a fidelity to the mathematical and scientific consequences of his imagined world, there is no reason to suppose he would make such an egregious error.

Ben Law has it right. The sealed cylinder analogy makes it clear that the world is mostly likely a

Three-torus. Moreover, this space can be equipped with a flat metric, so its geometry is Euclidean. The cylinder analogy is a faithful rendering of a standard mathematical construction taught in college of the two dimensional version of the 3-torus.

There are a few other possibilities, which are ruled out by the cylinder analogy. Much like the cylinder analogy is a standard picture of a two dimensional version of the world, the other possibilities have their own standard pictures.

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    Hi, welcome to SF&F. This could be a valid answer in its own right, since it's a step beyond what the existing answer says, except that you really need to provide some evidence that this is the case. Can you cite anything from the work or notes from the author that supports this? Please read How to Answer. – DavidW Jul 16 '19 at 18:29
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    @DavidW The sealed cylinder analogy is simply the first half of the standard construction of a flat 2-torus taught to math undergrads. It's the only mathematically relevant description of the global structure of the universe in the story. – user118721 Jul 16 '19 at 20:06
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    @DavidW Hi. I hope all this back and forth is not against the rules. The amount of evidence provided by Chiang is commensurate to that of a hypothetical story where its author shows a person who has just circumnavigated his planet as inferring it to be a two-dimensional sphere. – user118721 Jul 16 '19 at 20:38
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    @Valorum The paragraphs of description you have provided in your answer about the moon, stars etc. are perfectly consistent with a variety of topologies. The only determining factor then is the cylinder analogy. I'm afraid your 'paradoxical spherical tesseract' is simply a gif of a rotating cube in four dimension projected in to three dimensional euclidean space. – user118721 Jul 16 '19 at 20:49
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    @Valorum Perhaps, one could make the case that it is S^4, much like Dante's idea of the universe, but the story explicitly forbids the world given in your answer since the vault of the heaven leads to the surface, which wouldn't happen if it was a 'tesseract'. Also I should point out there is no such thing as non-euclidean topography. – user118721 Jul 17 '19 at 0:36
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Textual evidence

If we look at the text, we can note a few things:

  1. the earth is flat
  2. the sun rises and sets from east to west
  3. the sun, moon, and stars move in arcs through the sky
  4. there lies above the earth a solid firmament (the "vault"), and above it waters

From this information it seems pretty clear that the implication is the earth is the ancient Biblical "flat earth" disc, with the celestial bodies moving in arcs over the disc from east to west, and continuing their arcs under the disc of the earth (like a sphere with the earth bisecting it), with the firmament and waters of heaven above:

enter image description here

but with one twist:

  1. the top of the sphere is connected to the bottom

Shape of world

Hence the universe is shaped something like a torus, where as you ascend upwards from earth one eventually reaches the underside of the earth, and may even tunnel through it to reach the surface again:

enter image description here

With the implication that earth is both the heavens above and the hell below.

Where does the sun go?

This leads to the question of why the sun isn't seen in its 'second' night-time trajectory as the protagonist scales the top layers of the tower.

One possibile explanation is that the sides/edges of the earth extend downwards further than the bottom (like an upside down bowl), and that the sun's orbit is on a tilt, so that the top half is visible from the earth's surface, but ascending to its underside the sun is obscured in its second half by the sides of the earth itself.


References:

  1. How men had sailed to the edges of the world and seen the ocean falling away into the mist to join the black waters of the Abyss far below...

    Gradually, the sky grew dimmer as the sun sank beneath the edge of the world, far away.

  2. Consider, when the sun sinks behind the peaks of the mountains to the west, it grows dark down on the plain of Shinar.

  3. With the passage of the weeks, the sun and moon peaked lower and lower in their daily journeys... Before long, they were at precisely the same level as the moon when it passed; they had reached the height of the first of the celestial bodies...

    Then they approached the sun. It was the summer season, when the sun appears nearly overhead from Babylon, making it pass close by the tower at this height...

    When they were at the level of the sun, they travelled entirely at night... eventually they passed above the sun's level, where things were as they had been below.

    Now the light of day shone upward, which seemed unnatural to the utmost. The balconies had planks removed from them so that the sunlight could shine through, with soil on the walkways that remained; the plants grew sideways and downward, bending down to catch the sun's rays.

    Then they drew near the level of the stars, small fiery spheres spread on all sides... They were not all set at the same height but instead occupied the next few leagues above. It was difficult to tell how far they were, since there was no indication of their size, but occasionally one would make a close approach, evidencing its astonishing speed. Hillalum realized that all the objects in the sky hurtled by with similar speed, in order to travel the world from edge to edge in a day's time.

  4. What had before seemed a pale sky now appeared to be a white ceiling stretched far above their heads. They were close enough now to perceive the vault of heaven, to see it as a solid carapace enclosing all the sky.

  5. He had returned to the earth. He had climbed above the reservoirs of heaven and arrived back at the earth. Had Yahweh brought him to this place to keep him from reaching further above? Yet Hillalum still hadn't seen any signs, any indication that Yahweh noticed him. He had not experienced any miracle that Yahweh had performed to place him here. As far as he could see, he had merely swum up from the vault and entered the cavern below.

    Somehow the vault of heaven lay beneath the earth. It was as if they lay against each other, though they were separated by many leagues. How could that be? How could such distant places touch? Hillalum's head hurt trying to think about it.

    And then it came to him: a seal cylinder. When rolled upon a tablet of soft clay, the carved cylinder left an imprint that formed a picture. Two figures might appear at opposite ends of the tablet, though they stood side by side on the surface of the cylinder. All the world was as such a cylinder. Men imagined heaven and Earth as being at the ends of a tablet, with sky and stars stretched between; yet the world was wrapped around in some fantastic way so that heaven and Earth touched.

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  • Am I correct in thinking your diagram is meant to be a lower dimensional flatland style analogue, where the 2D surface of the torus is meant to be analogous to the idea that 3D space in the story is curved into a hypertorus? In both cases that would mean we were just talking about a Euclidean space with an unusual topology, as discussed in this article. But if that's the idea, why do you depict the orbits of the sun and moon as being off the 2D surface of the torus? – Hypnosifl Feb 23 at 4:47
  • @Hypnosifl yeah the bounds of the 'sky' portion of the torus should extend wider to include the orbits of the sun and moon, will update the image to be clearer. – brazofuerte Feb 23 at 14:08

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