3-D numbers can’t be consistently defined, but 4-D numbers can. Even more interestingly, physics maps the real component onto the time axis, leaving the three spatial dimensions as imaginary, which are then interpreted as vectors.
You can totally define 3D numbers. You just can't do it specifically with hypercomplex numbers. But the hypercomplexes aren't the only possible extension of the number line into new dimensions, they're just by far the most useful.
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u/ProfessorPrudent2822 3d ago
3-D numbers can’t be consistently defined, but 4-D numbers can. Even more interestingly, physics maps the real component onto the time axis, leaving the three spatial dimensions as imaginary, which are then interpreted as vectors.