[munk-a]

Linear transformations can be more easily visualized as scaling coordinate systems - this is actually a pretty easy way to grok what's actually going on with the math. Big bang theory is pointlessly obscure (and uses four dimensions in its zero-zero-zero-zero because apparently four dimensions is enough to be "ooh mysterious" without making anyone feel like a dolt - just use two dimensions guys - everyone has worked with graph paper) but here's an interesting video[1] that sort of touches on the fact that linear transformations (by definition) keep the origin consistent.

1. Just as an aside - 3Blue 1Brown is an amazing resource https://www.youtube.com/watch?v=kYB8IZa5AuE

[tromp]

It's 4 dimensions for 3D space plus time, as he makes explicit with "at the moment I first sat on it".

[munk-a]

That assumes that the world is naturally described in four dimensions (the three primary spacial ones and time) - but that's just a habit of humans. It's perfectly valid to describe space-time in one dimension or, if you're a bosonic string theorist, 26. The habit of identifying three dimensions (and leaving out obvious things like spin) is just one that's indoctrinated into us by our common mode of education. 3+1D is certainly very sensible - but it isn't the only right answer by a long shot. And, again, 2D is much more socially common - going to 4D really just feels like being pointlessly obscure.

[billconan]

thank you for your explanation.

He said function "on" the coordinate system. I read it as "function in the coordinate system".