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Comment by azeemba | Hacker News Reader

The animation looks awesome! Looks like the author used matplotlib (as they mention in a comment on the website): https://github.com/vankessel/sandbox/blob/master/graph/inter...

In the past, I have used manim to make mathematical animations: https://www.manim.community/ Manim is more flexible but that comes with some overhead of complexity and learning. Example of some animations using manim:

- List of videos using manim: https://www.manim.community/awesome/

- A blog post I made: https://azeemba.com/posts/degenerate-matter.html

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I couldn't disagree more to be honest, about this post. Animations are good when they provide object permanence, and let you track what's changing and how.

This post linearly interpolates complex functions blindly, which doesn't tell you anything useful, unless the thing being interpolated is an affine or projective transform where that makes sense.

e.g. For complex powers, the most natural animation is to animate the exponent, which will show a continuous folding or unfolding. Here the squaring just looks like the extra 360° appears out of nowhere.

For mobius-like transforms, interpolating the inverse might be better.

One particularly good example is e.g. visualizing equally spaced points on a circle, and their various combinations as roots and poles of complex functions.

The goal of math animation should be to highlight and travel the natural geodesics of the concept space, with natural starts and stops too.

The rest is cargo culting.

Not sure what you mean by this.

> The goal of math animation should be to highlight and travel the natural geodesics of the concept space, with natural starts and stops too.

> The rest is cargo culting.

A geodesic as I understand it is the curve representing the shortest path between two points in some manifold.

So take one thing that I have found math animations useful for: showing the path of travel of some parametric system. Is that a geodesic? Not necessarily in the cartesian space of the system. I don't know what it would mean for it to be a natural geodesic of the concept space.

For me the goal of math animation is the same as the goal of any math visualisation: to improve understanding and intuition. When I animate something (Which I only ever do for myself) that is why I do it. Am I cargo culting in your estimation?

Let's take another example: Say I do an animation of some sort of force problem in mechanics. I can show the paths of some particles in the simulation and the magnitude and direction of the various vectors vs time. Is that cargo culting? It's definitely not any kind of geodesic. Does it help my understanding? Quite possibly.

In that sense in the blog post you are addressing, in my opinion the position vs momentum distribution animation is really great because it really helps my intuition of how those probability distributions are related and how one would change as the other changes.

I animated the power in this video after 18sec : https://www.shadertoy.com/view/Ms2Bz3

Please note that complex powers involve the complex logarithm, which is multivalued, it should be a surface in 3D to really see the whole function. The animation I made is only taking one value of the power

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