SuicideJunkie wrote:Are the innermost cylinders of hell shorter than the outer ones?.
's a picture.
The story is ambiguous about their relative heights.
Each circle is vertically offset from the others, making each circle effectively a (2D) ring shape, a circle with a smaller circle (the next circle) cut out.
But if you assign a volume to each "circle" you'd include that empty, floor-less space, making each circle a cylinder.
The barriers weren't walls, so much as cliffs with a combined height equal to most of the Earth's radius (possibly radius/sqrt(2)).
Randal was obviously fitting things into his box metaphor, but IMHO the best interpretation f his image is that each of those boxes is a cylinder, like in Inferno
. Also (to nitpick), the picture should be labeled Inferno
, as The Divine Comedy
had two other parts, each requiring different heist diagrams.
The most interesting discrepancy is that Dante doesn't depict anybody trying to get out, and (in fact) makes a point that they are there of their own free will (in a sense).
Dante also displayed clear knowledge of geometry and geography in this work so we're clearly supposed to take the measurements he does provide as fully applicable to math.
The thing about recursion problems is that they tend to contain other recursion problems.