Viewing profile — hamish_todd

You are correct and this is another failing of the article. Hestenes has very little relevance to the field today - the Atiyah/Penrose school, via Jon Selig, is much more influenti…

You're certainly correct that it would be the done thing in physics (and I have written a draft for my blog). But note that Geometric Algebra is significantly a tool for graphics/g…

Very sorry to hear about the brain fog, that's rough. Best of luck getting through it. > in some cases What cases do you have in mind? > why are these your operators in the first p…

Ah! If you do it would probably would need to be a followup rather than addendum

If you want to learn physics from a geometric viewpoint, GA is brilliant. Here's a playlist of my stuff, which is aimed at computer graphics folks: https://youtube.com/playlist?lis…

In physics and especially computer graphics, yes. These are two fields that are culturally very different from algebraic geometry, in that mathematical techniques that appear at al…

The geometric product is transform composition. It plays the same role as matrix multiplication: if a group is represented by a set of matrices or multivectors then the GP will be …

He's distressingly wrong about this, the geometric product is transform composition (Apologies to folks who have seen me repeat this a million times; but it's very important folks …

Can do either! If your multivectors represent linear transformations then their products will also be linear transformations. If they're affine transformations then their products …

The geometric product is transform composition. TRANSFORM COMPOSITION! (sorry, it's not your fault or even his that you didn't know this - GA textbooks should have it as the first …

I'm a GA researcher. I did this livestream of my reaction to the article https://m.twitch.tv/videos/2282548167 TLDR it is quite a bad article. One of the closest thing he has to a …

Since Geometric Algebra == Clifford Algebra, Michael Atiyah, Roger Penrose, and Paul Dirac disagree with you.

You're making the word "some" do a lot of work in this comment. It's true that eg I would represent the inertia tensor with a matrix. But I would calculate it with GA... and I stru…

The geometric product does transform composition. It has all the properties you want for multiplication in an algebra, or indeed a monoid or group. So it is like matrix multiplicat…

There are ten thousand examples I want to give of why you're wrong. We have to start somewhere so here's a favourite, the "universal projection formula": (A.B)/B Projects any A ont…

A quaternion is some amount of identity averaged with some amount of line reflection. You can visualize the line reflection as a pair of planar reflections at 90 degrees to each ot…

The second paragraph of the conclusion: "Nor should we be trying to make everything look more like complex numbers and quaternions. Those are already weird and confusing; we should…

I did two streams where I went through this article and explained the many places it is wrong. The second part of the article has more maths in it, so most of the content is there,…

Hey folks, here are two lectures by me on GA, at the Game Developer Conference: https://www.youtube.com/watch?v=en2QcehKJd8 https://www.youtube.com/watch?v=dSe7eg8Dj98 They include…

From that page: "When Euler Angles interpolation is used, Unity internally bakes the curves into the Quaternion representation used internally. This is similar to what happens when…

Where in the docs does it say that? Euler angle lerps, in the general case (eg none of the starts or ends are 0), look like complete shit. You need the log quat representation. Exp…

Unity uses quats in its object transforms?

It's an extremely common misconception that because GPUs have matrix matrix and matrix vector products in the standard, that means GPU companies must be accelerating them. In fact,…