
A trick to visualizing higher dimensions [video] - sillysaurus3
https://www.youtube.com/watch?v=zwAD6dRSVyI
======
jpeanuts
A Mathematician and an Engineer attend a lecture by a Physicist. The topic
concerns Kulza-Klein theories involving physical processes that occur in
spaces with dimensions of 9, 12 and even higher. The Mathematician is sitting,
clearly enjoying the lecture, while the Engineer is frowning and looking
generally confused and puzzled. By the end the Engineer has a terrible
headache. At the end, the Mathematician comments about the wonderful lecture.
The Engineer says "How do you understand this stuff?" Mathematician: "I just
visualize the process" Engineer: "How can you POSSIBLY visualize something
that occurs in 9-dimensional space?" Mathematician: "Easy, first visualize it
in N-dimensional space, then let N go to 9"

[1]
[http://www.math.psu.edu/tseng/mathjoke1.html](http://www.math.psu.edu/tseng/mathjoke1.html)

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rocqua
I really like 1blue3brown, but this one didn't quite resonate with me. To me,
it felt like a long winded way to make it intuitive that the point (1, 1 ...
1) has distance sqrt(n) from the origin, where n is the number of dimensions.
I think there'd be move value in explaining things like 'most volume is near
the edge' and 'most points are far apart'. Granted, that is less about
building intuition, and more about specifically dispelling heuristics from 2
and 3 dimensions.

I'd still wholeheartedly recommend his other videos though. Especially [1]
where he gives a very nice topological result regarding inscribed rectangles
in closed loops. In the same vein is [2] proving the borsuk-ulam theorem.

[1]
[https://www.youtube.com/watch?v=AmgkSdhK4K8](https://www.youtube.com/watch?v=AmgkSdhK4K8)

[2]
[https://www.youtube.com/watch?v=FhSFkLhDANA](https://www.youtube.com/watch?v=FhSFkLhDANA)

~~~
fizixer
I think a major qualifier to all the 3+ D vis. schemes is that, no matter how
elaborate or clever the trick is, you can never experience such a space the
way you experience 2D or 3D space. (all the tricks are only approximate
visualizations).

~~~
JoshTriplett
The levels in Braid that have time moving forward and backwards as you move
left and right are the closest thing I've seen to "experiencing" space-time
where time is a dimension. As you think hard enough about the puzzles, you can
imagine moving in time the way you move in space, treating it as just another
dimension.

~~~
fizixer
I knew someone would invoke time. I'm aware of 4D space-time as a possible
visualization scheme for 4 dimensions.

By '2D or 3D space', I specifically meant being able to experience 3+
dimensions the way we experience 2 or 3 spatial dimensions.

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npgatech
I totally applaud 1blue3brown's videos but for some reason, his approach
leaves me more confused than ever. Long winded unnecessary visualizations,
especially when animated, annoys me for a reason that I cannot explain.

Don't get me wrong, visualizations are powerful but I think I prefer static
visualizations. Animations overload the visual system with "visual bloat", if
you will.

Also, this video did not help me visualize higher dimensions. I prefer a
simpler approach - just project down to 3 dimensions (or 4 if you add time at
the risk of animating).

~~~
sillysaurus3
How would you project a 10D sphere into 3 dimensions? Worse, the projection
tricks you into believing you've gleaned some insight.

The animation was critical for understanding the relationship between the
values as they change.

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zengargoyle
I have found with 1blue3brown that I sometimes have to wait a while and ponder
things and go back and watch the video again some time later. So this
particular video was working for me up to a point and then I maybe just missed
some important point that hopefully I'll catch on a re-watch next week or so.

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emerged
Beautifully animated as always, but it didn't help me visualize higher
dimensions at all.

