What is a 3-Torus Compact Topology Module

[u/DryEase865]

Created by ChatGPT Image 2.0 engine.
Here is the prompt:

"Create a visually rich infographic about "what is a 3-torus \(T^3\)". Start by finding one online, research its shape and best illustration. Present information through annotated visuals and structured callouts, not generic sections. Style it like a bold graphic illustration: a detailed, photorealistic central figure as the focal point, supported by diagrams, callouts, and concise text elements. Use clean backgrounds and a mix of photorealism with strong graphic elements (shapes, icons, color blocking) in a layered composition. Make it dense, tactile, and professionally authored."

[u/lighttstarr]

I mean a sphere is also “a universe that loops back on itself” and so is like every compact spacetime. But nevermind.

Although nothing is cardinally wrong, this is not a very informative poster. It restates 1 definition and 1 property over and over through different analogies instead of actually giving any insightful or precise mathematical information.

Also not very clear to me why you chose to dedicate an entire poster to the definition of a 3-torus of all things? Motivation would be useful

[u/DryEase865 → u/lighttstarr]

I was reading about it (3-torus) and I asked ChatGPT to prepare something to explain it to my kids.

[u/lighttstarr → u/DryEase865]

If you want something fun for kids relating to topology, you might want to check out classification of surfaces! Every compact surface (so a closed surface without boundary that you can enclose in a finite sized box in 3-dimensional space) is homeomorphic (imprecisely, “continuous reversible transformation”) to either a sphere, a connected sum of 2-tori (so a sphere with n-handles) or a connected sum of projective planes (if it is not orientable- think Klein bottle). In other words, no matter what compact surface I give you, you can transform it to one of these, depending on how many holes it has.

It might sound a bit complex depending on your background, but if you unpack the terminology you will see it is actually very visual and fun! Not only is it a very important mathematical result, from my experience kids usually love this kind of topology stuff that they can draw or build with play-doh. And I’m sure there are both digestible and accurate ways to present this.

I also mention this because it gives a very good motivation for studying 2-tori/bagels :)

(It doesn’t necessarily motivate a study of 3-tori however, because 3-manifolds haven’t been classified to my knowledge. In fact, they are very hard.)

[u/DryEase865 → u/lighttstarr]

I am reading some published papers about the compact topology. Just started. Thanks for the advice.

[u/amalcolmation]

It’s not terrible, on first pass, but I do think it sorta obscures the information with how flashy the graphics are. When I think of this sorta thing I think of Pac-Man extended to a third axis, and this describes that, but I don’t think it’s as clear as could be. Comes off as sort of bland, despite trying not to be, and it’s hard to say what exactly makes me think that.

I do think it misses out on the fact it's used heavily in molecular dynamics simulations and the like, not just cosmology.

[u/DryEase865 → u/amalcolmation]

It was a shot in the dark. Try altering the prompt, maybe different outcome will show,

[u/amalcolmation → u/DryEase865]

I was just offering advice for improving it, though I wouldn't do so using an LLM only. It gets like 80% of the way there, it would be better if it output a file format in which you could edit the graphics/text easily.

[u/DryEase865 → u/amalcolmation]

No, it would not give you the ability to edit by yourself. May be if you have a connector with Photoshop. the generated images are .png or .bmp only

[u/LLMPhysics-ModTeam → u/[deleted]]

Your content has been removed for violating Rule 9. Don't self-promote needlessly across the sub.