Explaining 4D rotation

I am working on a technical paper that describes a technique I once came up with for rotating objects in four dimensions. And I want my explanation to be really clear.

I don’t just mean clear to mathematicians. I mean clear to anybody who might be interested in the question of how you might rotate things in four dimensions.

So I need to find a way to describe what I did that doesn’t just rely on lots of mathematical formulas. The description needs to make visual sense. But how do you create an explanation that is visually clear if the “visual” in this sense is four dimensional?

I’m probably going to need to figure out some really good analogies to lower dimensions — to something that can happen in just two or three dimensions. And I think that approach should work.

But isn’t it funny that this should be so difficult? Sometimes it’s harder to come up with a clear explanation of something you did than it was to do it in the first place.

8 thoughts on “Explaining 4D rotation”

  1. Can’t you use time as the fourth dimension? Or do you want to show a five dimensional rotation?

  2. Sorry, I wasn’t clear. I wasn’t referring to the general idea of 4D rotation but rather to a specific technique and interface I developed for 4D rotation.

  3. Thanks! Yes, Ben’s videos are very beautiful, and they do a great job of explaining rotation of three dimensional objects using quaternions.

    I’m focusing on a related but different explanation: An interactive technique I developed to intuitively rotate four dimensional objects.

    One way to describe the difference is that Ben’s techniques map well to the space of 3×3 rotation matrices. What I will be describing maps to the space of 4×4 rotation matrices.

  4. Yes, that certainly works — I’ve used that before — but I don’t think it is as intuitive as I would like.

    When I hold an object in my hand and rotate it to look at it from different points of view, I am not mentally dividing the rotation into pre-defined labeled axes. I just rotate from “here” to “there”. To me that is an intuitive 3D rotation.

    The technique that I developed for 4D rotation has some of that same intuitive quality. I’m just working on a way to describe how it works under the hood so the mechanism is understandable to non-mathematicians.

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