Geometric Algebra

“A lot of people have a lot of geometric insight But maybe not the mathematical sophistication. And I think this will certainly sort of give them a big advantage because it seems to me to be the way the world works. This, if it's a unifying language, it's what …”

“It's anti-commutative. It's not a commutative algebra. So immediately you throw away everything you've learned as a kid and through school and through university. So it makes perfect sense once you're into it, but there's a little, you know, there's a little h…”

“Electromagnetism is also, I should have mentioned this, is a field whereby you really get huge simplification.”

“I don't think it's not computational anymore, because we're building up more and more tools.”

“If people have worked with computer vision, they will know that often things don't work. So instead of a rotation matrix R, they try R transpose. And instead of a translation vector T, they try R transpose T. And they mess around until it works because it's ki…”

“Geometric algebra won't really give you anything that you can't do conventionally. What it might enable you to do is to see how, how to do that thing.”

“Underlying, you've got an algebra of A much bigger algebra than three-dimensional space where I've got three vectors. So actually, computationally, there's more going on. There's more going on. Yeah, but at a higher level, you know, I can get code to do all th…”

“So I've said that I have these geometric objects, my rotations are objects, so I can write down coordinate free expressions. But not only can I write them down, I can differentiate with respect to them, easily. So, because I have this algebra of objects. I can…”

“So if you know this language, you can not only do rigid body dynamics in engineering, classical mechanics. You can do linear algebra without matrices and without tensors. And you can do complex things in quantum space-time physics with the same mathematical sy…”

“We have a community, not a massive community, but there are lots of people who are very interested in, in you know, potentially getting instructions for chip sets, et cetera. FPGA is, it is. So, and of course we have quite a lot of Programs that people have be…”