6 ms·
Well, if they can use complex numbers, I think quaternions[0] are fair game for a 3D elephant. [0]https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia
by leblancfg 9y ago
Well, if they can use complex numbers, I think quaternions[0] are fair game for a 3D elephant.
[0]https://en.wikipedia.org/wiki/Quaternion https://en.wikipedia.org/wiki/Quaternion
- logfromblammo 9y agoThat seems like cheating. If you can use quaternions to squeeze out more degrees of freedom, you could also use octonions. You could use any number of additional dimensions that square to -1.
- Myrmornis 9y agoI thought those things weren't so easy to come by -- that was why Hamilton was excited enough to carve it into a bridge wasn't it?
- logfromblammo 9y agoI think the difficulty is actually in arranging them such that they combine to make an interesting algebra.
- EtDybNuvCu 9y agoWe lose features too, as we climb in complexity. Lucky 10000: https://en.wikipedia.org/wiki/Cayley–Dickson_construction https://en.wikipedia.org/wiki/Cayley–Dickson_construction
- tensor_rank_0 9y agobut if you want a normed ring division algebra you must stop at 8 dimensions.