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> Linear algebra is exactly where "dimension" gets its abstract but very limited definition as a property of spaces, best summarized as an axis or direction, ra
by tgflynn 7y ago
> Linear algebra is exactly where "dimension" gets its abstract but very limited definition as a property of spaces, best summarized as an axis or direction, rather than a kind of space itself
Yes, but adding an extra dimension to a given space (more correctly stated as asserting that a space of dimension d is embedded in a space of dimension d + 1) vastly expands the "number" of points that are available, so adding a dimension doesn't just give you access to an additional d-space but to a whole continuum of other d-spaces. I think this is what people are referring to when they use the word "dimension" in this kind of context.
- andrewflnr 7y agoMost people have no such precise idea when they talk about "dimensions". Those who do would, when pressed, admit that even if you could be said to travel through or along some other dimension to reach another world, or even an infinity of other worlds, said dimension is not the same as those worlds, just a term for a relationship between them. Moreover, I don't care about what people think they're saying with their crap terminology. I demand actual accuracy, or at minimum precisely delimited uncertainty, from people taking millions of dollars in government funding to write about aliens. This is not too much to ask. (You do remember the context, right? Evaluating the credibility of a purportedly factual report written under a government contract, not a bar debate about cosmology)