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Grant Sanderson
@
3blue1brown
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Animated videos about math: 3blue1brown.com
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1,725
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228
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49,939
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Grant Sanderson
@3blue1brown
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22m |
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In New York next Tuesday? I'll be giving a talk at @MoMath1. I'd love to see you there!
3blue1brown.momath.org
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Grant Sanderson
@3blue1brown
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42m |
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I think it’s a lovely representation, and as Marc says in the article, the math is essentially the same. In general, it’s healthy to have multiple perspectives on a given topic.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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I can't help but feel like there's an inside joke I'm missing here...
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Grant Sanderson
@3blue1brown
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Nov 3 |
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I feel like it shows up under a number of different names and contexts. Often, instead of talking in terms of vectors and bivectors, the same ideas are expressed in terms of "multilinear forms", which are the dual constructs.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Preach!
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Agreed! Even though relating 3d rotations to individual points on a hypersphere is weird, and perhaps unnecessary for 3d programmers, this double cover relates to a lot of other corners of math/physics (e.g. the angle doubling in quantum spin matrices)
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Also, it's easy to underestimate how hard something is to understand once you get it. Once you wrap your head around bivectors et. al., it all feels so reasonable, but getting it is actually highly non-trivial (I'd claim). Certainly harder to grok than complex numbers.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Yeah, it's nice and all, but I think it's going a bit too far to say it "subsumes" the notions of complex numbers, quaternions, etc. since two mathematical constructs can be isomorphic while still representing different mindsets and viewpoints.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Geometric algebra is the mathematical equivalent of opening bananas from the non-traditional side. The people who are into it are *really* into it, and love telling the rest of the world how they're doing things completely wrong, and have yet to see the light of truth.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Man, that's a great description of geometric algebra. Well worth anyone's time!
That said, quaternions _are_ still worth learning about. 1) Because it never hurts to see something from multiple perspectives, 2) They relate to more than just 3d rotation.
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Grant Sanderson
@3blue1brown
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Nov 3 |
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Yup! That's a bug. What computer/browser are you using.
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Grant Sanderson
@3blue1brown
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Nov 2 |
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What an amazing shot from @trevormahlmann! twitter.com/arstechnica/st…
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Grant Sanderson
@3blue1brown
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Nov 2 |
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Dang this is cool! twitter.com/smartereveryda…
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Grant Sanderson
@3blue1brown
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Nov 1 |
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What program did you use?
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Grant Sanderson
@3blue1brown
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Oct 31 |
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I'm so happy about this! twitter.com/mscccc/status/…
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Grant Sanderson
@3blue1brown
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Oct 31 |
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Poem by Lewis F. Richardson (about turbulence)
Big whirls have little whirls
which feed on their velocity,
and little whirls have lesser whirls
and so on to viscosity.
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Grant Sanderson
@3blue1brown
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Oct 30 |
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Ha, that shows you for trusting me with a physical demo! Always bring backup materials when you when ask a math enthusiast to interact with the real world.
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Grant Sanderson
@3blue1brown
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Oct 30 |
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Sounds like your right brain learned how to tweet.
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Grant Sanderson
@3blue1brown
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Oct 29 |
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Thanks so much!
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Grant Sanderson
@3blue1brown
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Oct 29 |
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Are you familiar with Andrew Bird?
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