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I was 20 minutes into this before I realized the interactive bits were automatically turning themselves off and on based on which one was visible in the viewport. That seems obvious, but the fact that it worked so intuitively and without bugs on my system says a great deal. This is what master UX design looks like.
How can one learn to create these visualizations?
I don't want to dissuade you, but you probably should not try to do it the same way he does: completely from scratch using pure JS + WebGL and without any frameworks. He's able to pull it off because he clearly has an incredible depth of knowledge of how it works, but mere mortals like you and me will likely get stuck in the bog of minutiae. I recommend starting off by playing around with Three.js, which will get you…
When I increased the slider that allows you to change the flow of time for the gas in the cube, it really looked like visualizations I've seen of increasing the temperature of a gas. Is there a deeper relationship here? Could an observer tell the difference between a cube $A$ of gas in which the flow rate of time were doubled and a cube $B$ of gas with normal time passage, but a correspondingly increased temperature? If so, what would give it away?
I was 20 minutes into this before I realized the interactive bits were automatically turning themselves off and on based on which one was visible in the viewport. That seems obvious, but the fact that it worked so intuitively and without bugs on my system says a great deal. This is what master UX design looks like.
One suggest to Bartosz: breaking one long essay into many smaller pages or hiding content until the viewer has indicated understanding of previous steps will be even more useful (see: https://tigyog.app/d/H7XOvXvC_x/r/goedel-s-first-incompleten...).
Explorable models are a great way to increase engagement and understanding. Beyond that, I would supplement this with highly frequent comprehension questions to check for learning. I bet you'd find a way to make it fun and approachable.
Earlier quoted context omitted.
> Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. Isn't that true though? You can only approximate it, right?
In practice, yes you can only approximate it, because in theory it requires an infinite series of sinusoidal waves. But since maths is all about the theory, Laplace's objections were silly. (though I admit I don't know what the state of acceptance of infinite series was at that time) Also, it's fine to cut off the infinite series of sinusoidal waves because all physical systems cut off around a given frequency, for e…
Interesting side note - using the "basic" frequency/amplitude slider section, you can tell if you have any hearing loss in a certain ear at a certain frequency, as well as high frequencies in general.
As an ex-musician, I have some hearing loss caused by playing and being around extremely loud music. Between 6KHz and 7KHz, I felt the sound shift towards my right hear, indicating some hearing loss at that frequency in my left ear. Between 10KHz and 11.5KHz, I felt a strong shift toward my left ear, indicating hearing loss at those frequencies in my right ear. Above about 12.3KHz, I lost the sound entirely.
One very gentle bit of feedback (haha) to the author would be to provide anchors to each section so they could be more easily linked.