Post AxSVcdYEsCYTEV5ZLM by futurebird@sauropods.win
 (DIR) More posts by futurebird@sauropods.win
 (DIR) Post #AxSVMz0LLJ5J8TlnqC by gregeganSF@mathstodon.xyz
       2025-08-23T10:32:09Z
       
       1 likes, 1 repeats
       
       You wake up in a universe with a different number of spatial dimensions.Your senses are confused, and you’re too embarrassed to ask someone on the street “Hey, how many dimensions does space have?”But then you chance upon someone who likes mathematical puzzles, and ask them, “If I picked two points at random inside a hypercubic crate, what would the probability be that the line joining them intersected two opposite sides of the crate?”They scribble on some paper for a while, then reply “One ninth.”How many dimensions does space have here?
       
 (DIR) Post #AxSVcdYEsCYTEV5ZLM by futurebird@sauropods.win
       2025-08-23T10:42:55Z
       
       1 likes, 0 repeats
       
       @gregeganSF "Your senses are confused, and you’re too embarrassed to ask someone on the street “Hey, how many dimensions does space have?”"So relatable. I hate when this happens. As for the question is this about what it means to be convex in higher dimensions? I have a hard time separating an intersection in a model or shadow of a higher dimensional object from a real intersection. And I thought higher dimensional hypercubes were all convex...
       
 (DIR) Post #AxSXNtIsDzFxeTzwrQ by gregeganSF@mathstodon.xyz
       2025-08-23T11:02:36Z
       
       0 likes, 0 repeats
       
       @futurebird The hypercubes are all definitely convex. But the line that contains the two points (extended indefinitely beyond them, not the line segment that lies only between them) might intersect two sides of the hypercube that are not an opposite pair, just as the line through two points inside a square might intersect either two opposite edges, or two adjacent edges.