Пікірлер

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  @wenzhang3654 күн бұрын

  This is amazing!

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  @YT2go4me6 күн бұрын

  Great video. Thanks for sharing

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  @naakatubeАй бұрын

  Great video ❤❤❤

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  @yieldsfalsehood8863Ай бұрын

  2:13 the leftmost pair of P's are at an awry angle.

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  @its47752 ай бұрын

  Very interesting stuff

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  @adrianjohn81112 ай бұрын

  nice explanation

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  @ricardodelzealandia62902 ай бұрын

  Irrespective of curriculum, where on the internet is there a course that teaches geometric algebra from beginning to end? I can't find anything and I can't find any schools teaching it locally (Sydney, Oz). I need a standard uni-like program with exams and course work.

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  @mingmiao3643 ай бұрын

  [Solved] I'm lost at 9:32, is "u wedge v" a real number (as it can be added to u dot v, the number given by the dot product)? In that case isn't the uv (the left hand side) just a number as well? OR should the + sign understood purely as a simple rather than the usual addition between real numbers? [Edit] I figured it out (after watching Alan Macdonald's playlist, cited in the latter part of this video): the plus sign in the definition of geometric product uv = u dot v + u wedge v is understood purely symbolically, instead of the the usual addition in R. That is, uv is an ordered pair (u dot v, u wedge v), not a real number. The plus sign is merely a suggestive notation to facilitate computation in a more natural manner. Just like with complex numbers a+bi, we can still do complex arithmetic without the symbols + and i but they make things easier to memorize. Thanks for the presentation. It is really eye opening!

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  @josemanuelbarrenadevalenci6533 ай бұрын

  A lot of errors In "Drawing with ideal points" you use R (3,0,1) but define the point as a trivector. Which occurs in R*(3,0,1)

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  @solarium_4 ай бұрын

  ive been trying to remember this version for forever, thank you so much! one of my favorite string tricks!

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  @srinivasachakravarthy60724 ай бұрын

  Thank you for that lovely introduction.

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  @user-dz7xk4dr4v5 ай бұрын

  Hi! May you send me the email of one of the authors? I'm using your research for a paper and could use some more information :)

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  @omargaber31226 ай бұрын

  It's amazing and genius , thank you very much❤

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  @yorailevi67476 ай бұрын

  I wish Logan would continue the geometric algebra series lectures!

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  @yorailevi67476 ай бұрын

  Good lecture, a question; with everything matrix it's easy to make a computer do numerical calculations, how can geometric algebra can be used to do the same calculations?

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  @mervynlarrier94246 ай бұрын

  Software libraries are one way. You can also do the math by hand and then program code the final result depending on what you're doing.

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  @ivanmaxwell40066 ай бұрын

  Thanks for the lesson mr.dema!

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  @hyperduality28386 ай бұрын

  Convergence (syntropy) is dual to divergence (entropy) -- the 4th law of thermodynamics! "Always two there are" -- Yoda.

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  @hyperduality28386 ай бұрын

  Perpendicularity in hyperbolic geometry is measured in terms of duality! "Always two there are" -- Yoda.

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  @AsperaAdAstra7 ай бұрын

  I think Im going to start a youtube channel in english to start geometry from scratch.

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  @150metri13 күн бұрын

  Have you done that? what is your channel?

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  @PaulMurrayCanberra7 ай бұрын

  18:25 so, i is a bivector (confusing, because I is the unit n-vector). what does it mean to raise a scalar to the power of a blade? You know what - I'll ask chatgpt.

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  @PaulMurrayCanberra7 ай бұрын

  2:57 - "And importantly, the subspaces must be (mumble)". Damn. I bet this is going to be a problem in a minute.

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  @ewthmatth7 ай бұрын

  WRONG VIDEO... HELLO?? 📣

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  @alphalunamare7 ай бұрын

  This has totally failed to explain for why.

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  @Tatiana-zs3dc8 ай бұрын

  Great job 👏

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  @blind3778 ай бұрын

  very good video

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  @blind3778 ай бұрын

  ABSOLUTELY AGREE, as a recent compsci grad who took many courses in LA, i agree, and would have muched preferred this, i thought my classes were stale, and I think geometric algebra is a really good framework and context for solving some of the most pressing problems across multiple fields in science.

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  @iamastudent-arun12128 ай бұрын

  How the hell can i see

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  @scollyer.tuition9 ай бұрын

  Isn't the definition of compactness given here missing the word "open"?

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  @Firnael9 ай бұрын

  Really inspiring work ! I think there is a typo at 30:29, f(y_n) should be "1/y^2 - x", instead of "1/y^2 + x" (even though it does not affect the derivative, it should mess with your signs, but you fixed it at 30:36) Very cool anyway !

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  @danielharringtonportfolio18729 ай бұрын

  Thank you! I've never had my work called inspiring before I am flattered. I double checked the math and it seems you are right, I think it is a remnant from some factoring I decided I didn't need to do but good catch!

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  @pacchutubu9 ай бұрын

  Is this part of any playlist?

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  @eustacenjeru722510 ай бұрын

  Great mathematics

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  @raytonlin110 ай бұрын

  Very cool!

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  @rv70610 ай бұрын

  "Geometric algebra" is just a goofy way of saying "some relatively elementary geometric aspects of Clifford algebras". It hardly deserves the name of "theory". It's stuff like the determinant trick to compute curl in vector calculus.

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  @KipIngram10 ай бұрын

  I *could not* agree with you more. I think geometric algebra brings a unity and clarity to things that we just don't get from the standard way all this stuff is taught. I think teaching us cross products instead of bivectors is... well, it's offensive. It's like saying "All you ever need to know is the stuff you can do with this hack." The cross product *only works* in 3D. Even when we use it in 2D we're really "cheating" - those 2D cross products fall outside of our "space at hand." We're expected to just hum and overlook this fact.

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  @rahmasalama337510 ай бұрын

  Thank you very much for the detailed explanation

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  @thomasolson744711 ай бұрын

  I feel like I just keep going further down the rabbit hole with this stuff. I'm glad I didn't go to school for this. I might go insane trying to understand it. cos(arctan(i*v/c))=cosh(arctanh(v/c))=γ=1/sqrt(1-(v/c)^2)=c/sqrt(c^2-v^2) sin(arctan(i*v/c))=i*sinh(arctanh(v/c))=i*(v/c)*γ=i(v/c)/sqrt(1-(v/c)^2)=i*(v/c)*c/sqrt(c^2-v^2)=i*v/sqrt(c^2-v^2) This works for vector addition, but you have to include the 'i' or you do regular vector addition. (i*tanh(θ)+i*tanh(φ))/(1-i^2*tanh(θ)*tanh(φ))=i*tanh(θ+φ) It seems to me like sinh and cosh were invented because of 'i' getting passed into pythagorean theorem. I could also put 'i' in the denominator of 'v,' which would change very litte, just the sign and imply a real time in 'c' and an imaginary time in 'v.' The real axis would be the frame of reference frozen in time. The imaginary axis would be the time sticking out perpendicularly. There is a parabola associated with it. I think '-c/(2a)' in a*x^2+b*^x+c (not speed of light) represents the mass. It becomes sqrt([M]/[T]). I feel like it has meaning in the context of the reference frame I just mentioned, but I'm drawing up a blank.

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  @paolorepeto436811 ай бұрын

  Let suppose s is the supremum of near standards s. There are two alternatives: 1) s is near standard and 2) s is not near standard. If 1, s+1 is near standard so s cannot be the supremum. If 2 s-1 should be near standard but it is not possible. Booth case s lead to a false consequence, so there is not a supremum of the set of near standard.

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  @paolorepeto436811 ай бұрын

  The set of infinitesimal ha not a supremum

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  @ebog484111 ай бұрын

  THIS IS THE WRONG VIDEO HOW COULD YOU DO THIS TO US

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  @shinn-tyanwu415511 ай бұрын

  Great teaching 😊

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  @danielbellissimo410711 ай бұрын

  Great work.

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  @anisomorphism11 ай бұрын

  Strongly, strongly, strongly disagree. Geometric algebra is essentially "mathematics marketing" by Hestene - who actively discourages reading more broadly about mathematics and attempts to rename and recreate existing mathematics into his own niche. Already this is the sign of a degenerate mathematical program. Worse, is that the already established ideas of lie groups and representation theory better explain the relationship of inner products and Clifford algebras to the rotation groups. Geometric algebra obscures the basic tensor algebra by presenting it first as if it is symbolic manipulation magic and second as if it replaces ordinary linear algebra somehow. (It doesn't, to make use of Clifford Algebras we need to understand their matrix representations which is already standard material in the subject) Geometric algebra is not real mathematics, if you want a geometry-focused curriculum then just pick a linear algebra book that focuses on applications to geometry such as the one by Kostrikin and Manin. And if you want to learn about Clifford algebras, there are accessible resources such as the book by Garling, any book on representation theory of lie groups, or see how they are used in quantum mechanics. Do not be misled by math marketing, this stuff is over 100 years old and is better understood elsewhere.

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  @timpani1129 ай бұрын

  Just to be clear, who is "Hestene"? Are you maybe referring to David Hestenes?

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  @tiagorodrigues37308 ай бұрын

  All algebra is symbolic manipulation magic, though. We don't care about the objects, we only care about their properties. The point of Hestenes's program is to simplify mathematics _teaching._ You've already learned all the notations, matrix representations, tensor calculus, Lie groups, spinors, Pauli matrices, then of course you're going to think this is just a notational trick which “obscures” the “fundamental” linear Algebra representation. While it is true that we'll generally need to figure out a system of coordinates in order to compute the vectors on a computer, we can manipulate them symbolically without caring about which system of coordinates we are using, and that is why the join, meet, project and reject operators are so much easier to remember.

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  @okoyoso2 ай бұрын

  Fun to see the vector algebra war is still alive in 2024.

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  @morgengabe111 ай бұрын

  I think they should can the linear algebra course and do: algebra 1 - intro to linear/nonlinear algebra; work on set theory and associative/commutative sequences algebra 2 - combinatorial methods/proof writing; toplogical/transformation/hausdorff groups algebra 3 - structural analysis; the heirarchy of algebraic structures

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  @abbasi240411 ай бұрын

  Amazing video. Can you please guide me that if we want to construct half plane model for triangle group (2,3 5) then how we can construct?

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  @tissuepaper9962 Жыл бұрын

  okay, I gotta say, somebody needs to fix the terminology being used in higher math. "blade" is a stupid name like "magma", "ring", etc. that isn't descriptive (meaning you have to simply memorize the definition instead of having the name as a mnemonic), and the fact that "k-vector" and "multivector" refer to different types of objects is awful. same goes for the distinction between a "k-blade" and "n-blade". It was hard enough to learn to use complex numbers without a pile of stupid, obfuscated names to memorize. it's a hard sell for a teacher whose students really only need to be able to solve these things by hand in 2D.

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  @angeldude10111 ай бұрын

  How about: plane, line, point. Compositions of these include rot(at)ors, translators, motors. Probably the weirdest term in this set would be "flector," which is just a composition of a rotation and a reflection. There's also the "pseudoscalar" which still has a pretty bad name. Plane = 1-blade Line = 2-blade Point = 3-blade Line + Scalar = Rotor Rotor + Pseudoscalar = Motor Plane + Point = Flector Plane * Plane = Rotor Plane * Rotor = Flector Plane * Flector = Motor Plane * Motor = Flector Line * Line = Motor Line * Motor = Motor Point * Point = Translator Rotor * Translator = Motor Plane * Line = Flector Plane * Point = Motor Line * Point = Flector Alternatively "Mirror" and "Axis" for 1-blades and 2-blades.

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  @tissuepaper996211 ай бұрын

  @@angeldude101 I'm not the one you need to convince, lol. I haven't understood enough about this stuff to tell you whether using that familiar terminology is actually more intuitive or conducive to understanding. To be honest with you, I like wordy names better and find the more common short names annoying. Instead of e.g. "magma", I don't get what would be so bad about just saying "a set closed over a single binary operation". I could tolerate the name "binar" which is rarely used for the same algebraic structure, because it serves as a mnemonic for the definition, but I still think there's a problem when it's easier to remember the name, given the definition, than it is to remember the definition, given the name.

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  @anisomorphism11 ай бұрын

  Good news, it isn't used in higher mathematics. Nobody actually studies geometric algebra, they study representation theory of lie groups and lie algebras. They are not called blades, rather they are just referred to as n-vectors or n-forms.

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  @davidhand9721 Жыл бұрын

  Making your Rpqr into Rpqr* seems like a word game. Isn't the geometric interpretation of v in Rpqr* the same as vI in Rpqr?

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  @dreastonbikrain1896 Жыл бұрын

  36:24 you said it right the first time, i.e.: R_{n,0,1} is projective geometric algebra (with the caviat that the dual space is which we care about hence: R_{n,0,1}*. Spacetime algebra (the non projective one) has signature R_{1,3,0}. If I recall correctly the new shiny projective spacetime algebra has signature R_{3,1,1}. All of this assuming that the signature means {+,-,0}.

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  @dreastonbikrain1896 Жыл бұрын

  14:08 Uuuh shiny new notation idea which I somehow did not think about for dealing with graded parts of multivectors, ... I will steal that sir - thank you!

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  @cory.doras69 Жыл бұрын

  This is so absolutely amazingly well done! Where can I find more of Kevin's work? I've been knitting and crocheting for over a decade and this really resonates with me!

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  @fazioleonardo2821 Жыл бұрын

  Thanks a lot four your clear explanations. First time I feel I understand compactness !