## Dimensions[edit source]

I'm somewhat confused. Things the book says about dimensions:

- Core:
- "solid metallic core fourteen hundred kilometres in diameter." [1400 km ⌀]
- "The Core’s only fourteen hundred klicks in diameter" [1400 km ⌀]

- Level numbers:
- "Arithmetic Shellworlds invariably held fifteen interior surfaces" [+ the exterior Surface?]
- "Sursamen Levels: Inhabitants" lists exterior surface as level 0, and core as "level" 16
- But level 16 would be inside the solid core, so not really a level?
- And level 0 is the exterior surface, open to space, so it doesn't have a ceiling and its atmosphere doesn't count towards diameter?

- Total:
- "and were forty-five thousand kilometres in external diameter." [45,000 km ⌀]

- Level height:
- "In an Arithmetic Shellworld, the levels were regularly spaced at fourteen-hundred-kilometre intervals." [1400 km]
- "halfway down the first section of the Tower, seven hundred kilometres from the Surface." [700 km]
- "We’re fourteen hundred kilometres above the Deldeyn province" [1400 km]
- "ambient-drop ... through nearly a thousand klicks of near-vacuum" [1000 km]
- "and then hit the atmosphere" [which therefore must be 400 km high]
- roughly similar to Earth's atmosphere, though they have lower gravity

- “above a dark shaft fourteen hundred kilometres deep” [1400 km of floor height?]

- Open tower:
- "It is the end of a Tower which leads all the way down to the Machine Core"
- “you are looking across twenty-one thousand kilometres of vacuum to the lair of the Xinthian itself” [21,000 km]

So if core has a radius of 700 km, then each level is 1400 km, and there are 15 of these levels and then the surface, the total diameter would be (700+(1400*15))*2 = 43400. So does this neglect the floor thickness? If there are 15 floors between levels (including the exterior Surface) then these would be (45000-43400)/15 = 106.667 km thick. Maybe he included a floor around the solid core also? Then it works out to exactly 100 km floor thickness, but that's an additional thickness around the core, which seems odd. I couldn't find a mention of the floor thickness.

So the open tower would extend from the exterior surface to the surface of the machine core (which then had a door into it that had to be blasted open?) So that would cross 14 levels, so 21000/14 = 1500 km per level, which would imply 100 km for each floor thickness? So 14*1400 + 14*100 = 21000 Including exterior surface thickness but excluding machine core ceiling thickness. That seems to make sense? Omegatron (talk) 00:31, September 10, 2020 (UTC)

## Tower spacing[edit source]

- "No more than six out of a million Towers on any Shellworld"
- "a concentric succession of spherical shells, supported by over a million massive, gently tapering towers"
- "A million Towers held the world up."
- In the Machine Core: "There’s no Towers."

This sounds like 1 million towers for the entire world, not per level. And 14 levels not including Machine Core. So 1e6 / 14 = 71428 per level, which looks something like this:

If the Sarl 8th Level is about 12,205 km radius (not sure about this, see above), then the surface area of their level is 1.48e9 km², or about 20,700 km² per tower. If the towers are in a square/diamond pattern on a small scale, as in the image, then they are roughly 150 km apart.

"must have flown over six hundred thousand strides – six hundred kilometres. They had passed twelve Towers to their right, and flown left by one tower every five."

600 km / 12 = 50 km apart. Hmm.... Omegatron (talk) 04:57, September 10, 2020 (UTC)