Like some others responding here, I am hesitant to assign time to a spatial parameter, but the idea of visualising 4d space is interesting all the same, thanks for posting.

Another story I read very recently on this subject has had me thinking since.

In it, the author outlined a very simple method of visualising 4d axes, as opposed to 3d.

We think firstly of the standard xyz axes, with their origin at the centre of a cube.

Instinctively, we imagine each axis extending out of the centre of a face, perpendicular to the surface. Because there are three pairs of adjacent faces, we get 3 axes; each intersecting the centre of two faces.

But, if we think of them instead extending out of each corner, we get four axes, as there are four pairs of adjacent corners.

That gives us a perfectly symmetrical, fully orthogonal 4d cartesian system.

It took me a couple of days to think how to check validity of that, and unfortunately I lost the link to the story before I could get back to subsequently applaud.

To check validity, imagine removing any single axis, without adjusting any angles.

The standard 3d axis set appears as if by magic.

I thought that simple route towards 4d visualisation was pretty damned cool, as it seems so easy, and yet I’d never heard of it before, despite regularly having to use multi-dimensional mathematics.


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