Check out this very interesting video.

It's a fascinating new way of visualising the higher dimensions, from the zeroth dimension (a point) to the tenth (beyond the total of all possible timelines in all possible universes).

It helps if you're familiar with Flatland by Edwit Abott Abott.

noooo not this video again

why won't it just die it's so stupid

mort hog posting this surprises me none

I hated this because whenever I think of dimension I think of spatial dimension.

Stupid maths degree.

The 'standard' models of higher dimensional theories require additional spatial dimensions but I think the idea of treating dimension n as all of dimension n-1 collapsed into a single point still works the same. I don't think it matters whether it is a spatial or temporal dimension, this visualisation works the same.

There's an important difference between spatial and temporal dimensions. The faster I move through a spatial dimension the slower I move through a temporal dimension, but the faster I move through any given spatial dimension does not affect how fast I can move through any other spatial dimension.

Having said that, though, I'm not sure how to determine how the higher dimensions expressed in the video were spatial or (additional) temporal dimensions. The 4th dimension was clearly a temporal dimension, and then the 5th was the assembley of possible timelines. I think this might still be a spatial dimension..

Ugh...

The first experience I had with "higher-dimensions" was with optimization. In my Thermal Fluid System Design course we had a computer cooling problem where we were expected to make some effort to optimize a heat sink.

Given that the design involved a number of parameters (fin length, height, width, spacing, material, number of fins) you couldn't just plot a cost function against some parameter and pick the max or min. Three varied parameters is the best you can do graphically, maybe 4 if you show the 3-space graph changing with time.

I wound up just parametrically designing it for lack of time to really think about it (varying a parameter while holding everything else constant). But going back to it later, the more correct ways like gradient descent fascinated me in how they work with n-dimension problems in the same way you can visualize it working in 3-dimension problems.