What got you into Geometric Algebra?
I have always been always interested in geometrical problems and one of the things I wanted to study was the contact of objects. You can have a complicated robot that has to avoid touching a complicated environment. There is a mathematics called mathematical morphology that describes that, but I wanted to make it more of a signal processing theory, so that you can put geometric signals in it, compute with them and process these signals, even if they are a bit noisy. I had developed a tool for this called the slope transform. In order to create this, I needed a lot of math books. Every problem I encountered, required a different book in a different field of math, which I didn’t like, because it was just one problem. I went to a conference and there was a guy talking about GA, something I had never heard of back then. All these problems that I had been sweating over the past three years, with all those math books, were in this talk of only half an hour. I knew then that GA was what I needed, but GA itself could’ve been developed better, it needed improvement. From that point onward, I actively helped in the development and improvement of it.
How does Geometric Algebra fit into Intelligent Autonomous Systems?
Back when I used to do it, the robot could understand enough about the environment from its vision sensors, so that when it had to grab something or avoid something, it could do that. But nowadays you want a little bit more than that. What we are looking into right now, is building a neural network that learns about geometry, with GA built in it. The initial results are that these neural networks converge a lot faster, need a lot less data and a lot less computing power. When you want to learn about geometry, you can set up the “brains” using geometric algebra and tailor for geometry.
Your talk was about kinematics. Does GA simplify a lot of things in that field?
Yes, I hope my talk demonstrated that the old way of doing kinematics is a bit messy. People have been doing everything using vectors, because that is all they had, but that does not mean it is the best option. There are things that can be expressed more naturally and simply with less parameters, fewer equations, better numerical behaviour… when using the right algebra. the algebra that describes what you need and nothing more (ex. GA). In the old way made it work by setting all sorts of limitations on your system, but with GA, the system automatically takes care of those limitations. That means you can put it into the compiler rather than into the software, which has all sorts of advantages.
Have you experienced any limitations with GA?
There are things that still need to be developed, but so far there haven’t been any. It is sort of a competitor to linear algebra. Linear algebra has had 100 years of research in different ways to process data that is uncertain, optimal estimation, tracking of objects… Since linear algebra is a part of GA, we could just copy the research that has already been done, but we believe that with the new data structures geometric algebra provides, we can do better than simply copying.
How long do you think it will take for GA to become mainstream?
I’ve seen it take off tremendously after Steven De Keninck got involved by making a website, organizing a discord and so on… Young people seem to be getting the point. Also, if you look at Todd Ell, he is trying to teach GA to 16,000 engineers from his Collins Aerospace company, because this is the way their software is going to work from now on. And once someone big like him shows us the practical advantages, others will follow. I do not think we will have to wait another 25 years. One of the main problems right now is that it is hard for people to learn new stuff once they leave university, The algebra is not the problem, it is we that have not yet found the right way of transferring it to people who are not actively studying. But it will get there, GA deserves to be known better.