Climbing past the complex numbers.

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[Mosux]

I once came across a physics paper that employed the Trigintaduonions (T). Thirty-two dimensional numbers!

[AmryL]

I'd love to one day learn enough to understand a word of what this video is teaching.

[RealClassixX]

"Coming up" with quaternions for myself during a boring university lecture is still one of my proudest moments.

[zlodevil]

I would love to see a video on the splithypercomplex numbers!

[Zebinify]

And there's a nice trivia for the "motivation" of this construction. If we would like to preserve the norm multiplication rule, |X Y| = |X||Y|, we have to stick to the 2^n dimensions.

[allinclusive]

Since quaternions have very interesting properties when it comes to describing rotations in 3D space, I'd love to see a video about practical (or not so practical) applications of these higher dimensional algebras. Also, what about algebras, that don't obey this 2^n dimension rule? Great video! 🎉

[Generalth]

Why was Hamilton considered such a jokester?

Because he always said i j k.

[briangronberg]

This is fantastic. I’ve been looking forward to this video for a while so thank you, Professor!

[almazu]

it would be nice to see a video about the split octonians

[littlekeegs]

Seeing how we start losing common features like having no zero divisors or communitivity as we apply this construction, I'd be curious if we lose anything else after the sedenions, or if they have the same basic properties after that.

[dcterr]

Amazing construction! I already know about the first five of these algebras, but I've never seen this way to get from each one to the next, and I never even knew there were infinitely many of them! Great, educational video!

[SpartaSpartan]

The most famous onsight in history was Hamilton's onsight of the quaternions

[rohitg]

Would love to see some examples of zero divisors in the sedonians

[youtubepooppismo]

I love the cayley dickson construction!

[LuigiElettrico]

I love complex numbers. Subscribed! Any video on this topic is appreciated.

[jakobthomsen]

Really cool! And yes, interested in the split (and the dual) variants!

[herothecrow]

This is the epitome of

“Elementary students when their math has letters”
“Higher math students when their math has numbers”

[meerak]

The Title or Description should mention that this is covering the Cayley Dickenson Construction as this is one of the better and more complete lectures on the topic.

[eveeeon]

I find the rules for going from one algebra to the next fascinating. The video states that it was produced by looking at R->C->H, but is this the only set of rules that can do this? And is it minimal or maximal? Can you remove or add additional rules? I'm guessing you can't just remove them, but what about removing and adding a different rule, or reframing the whole picture.

[edhodapp]

This did it for me. I just joined your Patreon. Sigh, I work full time writing code for folks, so not always possessing enough free time, but I like to try. :)