> This is also a jab at mathematicians who are in addition to using variable names which are short and nondescript (e.g. "x"), are also "typeface sensitive" (in addition to case sensitive). In other words, one can typically find a statement involving three different "X" variables, referring to three different objects, and they are distinguished by their font and case.
The pain, across math, engineering, and physics, is all of the formulae with overloaded notation, sometimes from the Greek, sometimes the Roman alphabet.
Formulas are great as a summary and reminder for the seasoned practitioner, but can be a huge barrier to entry for the student.
Perhaps GitHub repos with well-written code and test cases for the neophyte can, as they say these days, "flatten the curve".
I remember always being annoyed at spherical coordinates when I was taking both math and physics classes in university. They use the same symbols but two of them are swapped.
Well, to be fair, sometimes the X is a Greek upper case Chi. Mathematics ran out of Greek and Roman a while back and Hebrew has appeared - א (as in "Aleph Null")
I did a category theory class a few months back. Huge barrier at times - so many moving pieces. "Err, which properties do 𝒞 and mumble(𝒟) have here, in this paragraph???"
I wanted to create an interactive version of some topics. Just mouseover elaboration and graphics, to reduce the amount of state one has to keep track of mentally, and its associated cognitive load. But the state of in-browser rendering of category diagrams wasn't quite there yet.
Best part of the class was the "after-math" (that's a 3-interpretation pun). An iterative improvement on past versions of the class, formalizing an observed custom - after the 1 hr math lecture, the room was reserved for a second hour, so people could hang out, with the instructors, in front of blackboards. In part, clarifying and explaining things in different ways.
One instructor observed something very vaguely like "I'd never approach things the way I do in lecture, if I was tutoring someone one-on-one."
One can imagine technical fixes. Mouse-over equations. FAQs. Presenting the material from multiple perspectives.
Many of them could implemented on clay tablets. And that newfangled wood pulp. My best understanding is, that as a society, incentives are poorly aligned with creating non-wretched education content in the sciences, and I assume in math.
So my hope for XR in education, is not just the power of tools like eye tracking, but that incentives are disrupted enough to get us unstuck.
Consider eye tracking. When I show people this video[1](IBM's STM stopmotion) in person, it was very common for them to ask me "what are the ripples?". Apparently it was enough of a thing for IBM to do supplementary content on it. But if I'm not there, what UI would youtube need to have a similar dynamic?
Someone did an art project. You sit by yourself and watch a drama. An interesting drama. But why is it interesting? The video is a graph, like one of those old "choose your own adventure" games. And there's an eye tracker. So if your gaze shows you're interested in character A...
Why not ripples? Imagine the richly interwoven tapestry of science and engineering as that graph, adaptively explored, driven by interest, misconceptions, and learning objectives.
And imagine being able to watch someone's gaze patterns as they try to understand a paragraph of math. Backed by a database of everyone's patterns. And being able to respond. Not as well as an excellent human tutor in some ways, but in some ways even better.
Or we could just copy the usual wretched content into 3D and call it a day.
"Consider eye tracking... imagine being able to watch someone's gaze patterns as they try to understand"
Let's not? Ever? It reminds me of dystopias where a government tries to sense how really interested people are in the latest propaganda and punishes those who are too bored. Or just a small school ran as a totalitarian regime where you're not even allowed to be bored.
The pain, across math, engineering, and physics, is all of the formulae with overloaded notation, sometimes from the Greek, sometimes the Roman alphabet.
Formulas are great as a summary and reminder for the seasoned practitioner, but can be a huge barrier to entry for the student.
Perhaps GitHub repos with well-written code and test cases for the neophyte can, as they say these days, "flatten the curve".