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A 4D HyperEarth: 1000x More Space for Real Estate
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[QUOTE="Hornbein, post: 6887594, member: 489043"] While it does appear that way I didn't actually pick a unit. The assumption is that the diameter and mass of atoms remains the same. (There's no reason to think atoms or even elementary particles could exist at all in 4D, but if we exclude them then there is little fun to be had.) So different atoms work out differently. The Earth is mostly iron so it shrinks significantly less than does a human being. In short, this is a property of the materials, not of the space. Using this scheme a 4D sumo wrestler with the same mass of atoms as ours would be 3 millimeters tall, about the length of a small 3D ant, but still weighing 150kg. I say he is more "compact" than are we. To be quantitative an atom has a compactness of one. As the number of atoms in an aggregate grows its compactness also grows. This however happens remarkably slowly, with the twelfth root (!) of the number of atoms. Consider a 3D volume that holds a trillion atoms. In 4D such a volume has a tenth the diameter. I say it has a compactness of ten. Getting back to 4D Earth, it is only ten times as compact as Mr. Sumo. (It would be about 80 times if the Earth were made of water instead of iron.) So a 4D Akebono would see ten times more curvature of the horizon than do we. Not much. So if Akebono hops on an airplane does he get across the Pacific ten times faster? Or is it that California is only 250 meters from Nihon so it's almost no time at all? Hmm, gotta work on that one. 4D human-scale things have a lot more surface area than ours, so there is much more friction and drag. Cross-Pacific travel could take either more time or less time. [/QUOTE]
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A 4D HyperEarth: 1000x More Space for Real Estate
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