David Hestenes - Tutorial on Geometric Calculus
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- Опубликовано: 25 авг 2024
- Part of the "5th conference on Applied Geometric Algebras in Computer Science and Engineering".
For the full set of videos, see:
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David Hestenes' website:
geocalc.clas.as...
Books:
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WIKIPEDIA:
en.wikipedia.o...
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This talk will be remembered in the history of math and physics
Why?
Wow!!! What an absolute treasure Dr. Hestenes is!!! Thanks for the inspirational tutorial.
This is... wonderful. I'm just discovering all this stuff; I'm at a very low level in it at the moment. But I'm already condemning even my very earliest math training for not properly tying thing to the most useful "basiic level" right from the start.
I did applied geometric algebra for a postdoc, it's an utterly fascinating topic with some *very* deep ideas. It's an utterly beautiful topic.
I love GA and I believe in everything he's talking about, but sociologically, this talk has a lot of red flags that I can see as barriers to acceptance. Hestenes is positively brilliant, but also seemingly bitter about the reluctance with which his ideas have been adopted. He also elevates GA to supercede many other fields as their superior, and the fact that they have not abandoned their antiquated ways can only be due to ignorance, stupidity, and dogma. This is the same script as every quack "theorist" with a radical new paradigm that just can't break into the scientific journals.
I'm saying this out of love, for GA, its potential, and appreciation of Dr. Hestenes' tireless efforts. My humble suggestion is that in the future, in order to optimize the adoption rate, he sticks to the successes of the math and leans away from narrating his struggle. GA is catching on, so let's put our best foot forward and face victory with grace.
Thank you for your well thought comment. I've had this feeling since I learned of the existence of geometric algebra, but hadn't been able to put it into words.
데이비드 헤스테네스의 저서를 번역하는 것이 지난 9년 간의 목표 중 하나였다.
Each time I watch this I feel like I get it a little more
Es un regalo, is a Gift, para un mexicano ésta conferencia Gracias por éste trabajo.
Brilliant! We need more of this unification, can't believe I was taught and made to struggle through so many disparate topics when they're really all the same... 😅 Makes much more sense now....thanks Pr.
Thank you for uploading this. I'm developing a series of materials in support of Professor Hestenes' wish to build an integrated, high-school-level curriculum on math & physics around GA. I've made videos based upon some of those materials. I'll be grateful for any comments.
Because RUclips tends to treat comments that contain links as "spam", I won't give links to my videos. However, some of them are among my latest 5 videos.
i would like to view any/all of the videos
@@toshieyork9942 I have a playlist of the videos on my channel, now: "Geometric Algebra of Clifford, Grassman, and Hestenes". You're also invited to join the GA groups on LinkedIn:
"Geomtric Algebra", and "Pre-University Geometric Algebra".
@@JimSmithInChiapas MANY THANKS!!!
Very very interesting! Just starting in this topic, but it is mind blowing. Thanks for all your work!
Thanks for sharing this.
Thanks legend.
Me learning about grad, div & curl in vector fields: *Is this differentiation?*
This guy: *Yes.*
When viewed through multivector fields on curved manifolds, mathematics and physics make everything so tied together. The only things lacking from this conversation were some algebraic topology and combinatorics representations. Otherwise, GA and its calculus are far-encompassing and my favorite study area.
His office isn't far from me, and every time I resolve to see him I end up sidetracked. After seeing this I definitely plan on stopping by!
Where is the SVD ?
This is the question.
Since 1995, I try to find it in Geometric Algebra. For sure, it is embedded somewhere in GA but SVD and PCA are still to be expressed.
Try looking for this : "On SVD and Polar Decomposition in Real and Complexified Clifford Algebras - Dmitry Shirokov"
Does this answer your question?
46:10 has the coordinate version of generalized stokes and then translates it into the vector derivative formulation. It's a good motivation!
Is the claim that this version of the generalized Stokes Theorem is more coordinate-free than the usual one with differential forms? That one doesn't use coordinates either, so I'm mystified about the claimed improvement.
@@davidmetzler well, he calls it coordinate independent because he does it without charts, but at the cost of needing to embed the manifold in some abient space. A question of taste, I guess. Btw, David, love your videos!
I have been wondering whether geometric calculus applies to multivariable calculus, and calculus in general. I looked into 'Clifford algebra to geometric calculus' which mentioned that this was applicable to multivariable calculus at the beginning, but I wasn't able to find anything about that in the contents. I would appreciate any answer as money is an issue and I can see that learning geometric algebra, differential geometry, and then geometric calculus will take a fair bit of time.
The ideas of graded algebras within topology seem very similar in concept to these at least functorially similar
What does he mean by SVD? And what does conformal mean?
SVD = Singular value decomposition
conformal = preserving angles
What is the name of the person mentioned at 1:09:08? I can't quite make it out.
Garret Sobczyk
Thank you!
L'idea è suggestiva e affascinante ma qualcosa non torna. Supponiamo di avere due vettori a e b ortogonali e di modulo 1 , allora
a scalar b=0
a esterno b=ab
allora
a scalar (ab)=0 mentre
a esterno (ab)=b diverso da zero.
Dov'è l'errore=Where is wrong?
b = a∧b implies b=0 (or a = 0).
Geometrically speaking, if c = a∧b, and a and b are not zero, c points out of the plane spanned by a and b.
Geranie Balkonov The rules of geometric product areassociativiti (ab)c=a(bc)distributivity and that product aa is e real numer.In usual interpretation there is something that non turn back.I think that Hestenes ideas ara good but need to think deeply on some thing.In Grassmann algebra there are three product, 'esterno', tensorial and is possible to define a 'simmetrization' product.
Sorry, the wrong is mine. I confused in a passage scalar product with geometric product. This theory is very,very,very great. Thank to a great man, David Hestenes. There are very simple model with Matrix also in 2D and 3D.
watch this at 2x speed, thank me later
Then it sounds like Scatman at normal speed :-)
My question would have probably been: “Can geometric calculus help us build the coveted Jurassic Park?”
Spacetime algebra.
@aDBo'Ch 1 Yes sir.
Bullshit. Coordinate free Maxwell equations were already produced in the 1930’s by Andre Mercier, using Clifford algebra.
Isn't Clifford Algebra the same as Geometric Algebra?
@@rotgertesla Yes. Indeed. But that wasn’t the point.
Thanks so much for your contributions. I have such high regard for the work you have done, but Gauss's Gordian Knot does and will be forever the most significant conjecture, here it is:
I am coming ever more to the conviction that the necessity of our geometry cannot be proved, at least not by human comprehension nor for human comprehension. Perhaps in another life, we will come to other views on the nature of space that are currently unobtainable for us.
It will never be possible to unify physics with mathematics until it is realized space is something that no one will ever observe. No one has ever observed a point, and for all those that claim they can demonstrate a point to me, I say to them "no that is a picture of a point"
I have an unscientific explanation if u are interested.
Whence you play a tone on a guitar, it resonate in harmonics right. First, third, fifth . . and where does the other frequencies go to? (for ex. 1.5f) I know they annihilate each other but in theory their information (their entrophy) should still exist. I believe this annihilated frequencies are the building blocks of space-time.
It is a fantasy but a deep one. 😅
where can I find more info on the conjecture please. preliminary searches for gauss's gordian knot weren't successful
@@ThePishty1 Gauss's leters to his friends. I have some other references I will send when I find them.
@@RichardAlsenz thank u sir, is there a book with his letters to his friends ?