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Worldbuilding

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  • $\begingroup$ "a head with the same surface area as a human's would have a microscopic brain" Uhm, that's not how hyperbolic space works. At small scales (like, say, the scale of a human), its approximately euclidean. $\endgroup$ Commented Feb 16, 2018 at 4:57
  • $\begingroup$ Don't circles grow expinentially in that space? I expect their brain volumes to be a fraction of ours. $\endgroup$ Commented Feb 16, 2018 at 5:07
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    $\begingroup$ They grow exponentially, not shrink exponentially. At small scales, volumes are cubic. See math.stackexchange.com/q/1445278/49592 $\endgroup$ Commented Feb 16, 2018 at 5:10
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    $\begingroup$ @PyRulez That does not make sense. If they grow exponentially, then they must shrink exponentially. If going from a combination of radius R1 and surface area S1 out to a larger radius R2 produces the exponentially larger surface area S2, then going back down to R1 should result in the original S1. Either they grow exponentially or they do not. Is your last comment suggesting that they grow exponentially, but not at small scales? IE: from R1=1cm to R2=2cm surface does not grow exponentially, but from R1=1km to R2=2km surface does grow exponentially? $\endgroup$ Commented Feb 16, 2018 at 17:09
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    $\begingroup$ Just trying to interpret the relationship between surface area or volume and brain ability, and how the two might differ in hyperbolic space, then thinking about how special relativity actually implies that actual space is non-euclidean, seems to raise some interesting questions. $\endgroup$ Commented Feb 16, 2018 at 19:41