/sci/ - Science & Math » Thread #13816906

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Quaternions for dummies / Maxwell's/Faraday's equations in 1 line

Anonymous Thu 04 Nov 00:11:58 2021 No.13816906 View Reply Original Report

Quoted By: >>13816920 >>13816933 >>13820008

Fuck !
Why didn't I have this guy to teach me spinors and Minkowski's fields...

https://mattferraro.dev/posts/geometric-algebra

Anonymous

Anonymous Thu 04 Nov 2021 00:19:54 No.13816920 Report

Quoted By: >>13816930

>>13816906
be honest, is that your site?

Anonymous

Anonymous Thu 04 Nov 2021 00:22:52 No.13816930 Report

Quoted By:

>>13816920
Nope, got into it through lobster.rs

Anonymous

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Anonymous Thu 04 Nov 2021 00:23:45 No.13816933 Report

Quoted By: >>13818737 >>13818820 >>13820230

>>13816906
Geometric algebra is undoubtedly the future of mathematics. I think the only thing that held it back for so long was the lack of tools to visualize the geometry part for students

https://www.youtube.com/watch?v=60z_hpEAtD8&ab_channel=sudgylacmoe

Anonymous

Anonymous Thu 04 Nov 2021 02:27:54 No.13817149 Report

Quoted By:

bump

Anonymous

Anonymous Thu 04 Nov 2021 15:56:25 No.13818737 Report

Quoted By: >>13818783

>>13816933
Its not. It looks nice when everything is wrapped up as some geometric products of multivectors. But when you go to actually do the computations you realize it takes 2x real numbers to actually describe anything and it like 4x the amount of adds and multiplies to do any calculations and so you go back to points and vectors and matrices because you don't want to do 4x the work. This is the real reason geometric algebra has failed, because it isn't efficient at all except at writing down very compact expressions.

Anonymous

Anonymous Thu 04 Nov 2021 16:05:25 No.13818765 Report

Quoted By: >>13818822 >>13818840

Second line is incorrect.

Anonymous

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Anonymous Thu 04 Nov 2021 16:10:17 No.13818783 Report

Quoted By: >>13818813 >>13818837

>>13818737
> But when you go to actually do the computations you realize it takes 2x real numbers to actually describe anything and it like 4x the amount of adds and multiplies to do any calculations and so you go back to points and vectors and matrices because you don't want to do 4x the work.

Yes, because this entire time various fields in pic related have been making simplying and restrictive assumptions about the space and the algebra. This has lead to the appearance of a disjointed and fragmented landscape not built from any unifying principles. Techniques such as the cross product are only available in 3d, rotation matrices on quaternions, arcane names like weyl spinnors.

When all of these ideas can be built from one mathematical set of rules. You learn those rules first, and use the speed ups later. Starting with the speeds ups doesn't lead to any intuition

Anonymous

Anonymous Thu 04 Nov 2021 16:20:18 No.13818813 Report

Quoted By: >>13818820 >>13818825

>>13818783
And yet, no notable physics is done with it despite the fags praising it having decades to do it. If it's so elegant and powerful, why haven't any of these morons been able to reformulate QED using it?

Anonymous

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Anonymous Thu 04 Nov 2021 16:24:46 No.13818820 Report

Quoted By: >>13818854

>>13818813
>And yet, no notable physics is done with it despite the fags praising it having decades to do it.
As I said previous in >>13816933
> think the only thing that held it back for so long was the lack of tools to visualize the geometry

being introduced to this stuff without geometric animations available now on youtube is like reading https://archive.org/details/electricityndmag02maxwrich/page/n265/mode/2up?q=quaternion from scatch. There is a reason heaviside with his telegraph equation became the go too.

Also, as author of video says, once the few physicists who can sift the math stitch together the mosiac, they ask themselves why bother redoing it all again. This is why I say its of the future, only now do we have the tools to teach it right

Anonymous

Anonymous Thu 04 Nov 2021 16:25:06 No.13818822 Report

Quoted By: >>13818854

>>13818765
No its not.

Anonymous

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Anonymous Thu 04 Nov 2021 16:25:49 No.13818825 Report

Quoted By: >>13818854

>>13818813
Also Kohl Fuey has been using the clifford alegbra in particle physics

https://www.youtube.com/watch?v=_E2iiuunK-E&ab_channel=QuantaMagazine

Anonymous

Anonymous Thu 04 Nov 2021 16:29:17 No.13818837 Report

Quoted By: >>13818865

>>13818783
Bro it's not really that mind blowing. Its just treating subspaces as a mathematical object in their own right instead of just using vectors and dealing with subspaces using projections and spans. So you don't really gain much, even in terms of understanding, and now every calculation you do will on average have an extra +0*0+0*0 or something stupid and worthless that just eats up clock cycles for nothing. This is why everyone who does geometry has rejected this shit because it is just not practical when you try to use it in the real world.

Anonymous

Anonymous Thu 04 Nov 2021 16:29:38 No.13818840 Report

Quoted By:

>>13818765
Third line is.

Anonymous

Anonymous Thu 04 Nov 2021 16:33:37 No.13818854 Report

Quoted By: >>13818873

>>13818822
Sure it is. Where is it coming from? It's using a rule defined later in the cheat sheet. Therefore it's nonsense.
>>13818825
>Clifford algebras
You shouldn't cite things you don't understand. Where, precisely, in QED do you think Clifford algebras are used? To what extent in computing loop integrals do you think they're used? If you can't answer such a fundamental question, then why bring it up at all? Sounds like you're just regurgitating shit you heard random people say without knowing its validity.
>>13818820
>You need a visualization to do physics
Not really, no. Feynman diagrams only really work for intuition up to NLO calculations and when resumming large logs are only explicitly given up to NLO accuracy at most. Everything else is automated with respect to the rules defined in QED, e.g. event3 MC Parton generator computing decay processes from e+e- up to NNLO.

Also, if you don't understand any of the jargon I just laid out, then you're way in over your head and have no idea what you're talking about.

Anonymous

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Anonymous Thu 04 Nov 2021 16:37:44 No.13818865 Report

Quoted By:

>>13818837
To one who has already learned and connected all these dijointed fields, its not that impressive. But to one still piecing it all together, they will learn it all much faster using the underlying principles in geometric algebra.

If not mind blown by the complex number intepretation, the torque intepretation, or the dirac spinnor intepretation. Than I'll leave you with this.

The Gibbs/Heaviside equation is missing a degree of freedom found in maxwells original quaternions.

https://www.scirp.org/pdf/jmp_2020092111325330.pdf

There is a whole avenue of electrodynamics that we haven't considered in over 100 years because the gibbs-heavside equations don't reveal it.

Using geometric algebra is one method of getting it back

As in above pic related

Charge density, in geometric algebra, is current not moving through space, but through time

IF that doesn't blow your mind, i'm not sure anything would

Anonymous

Anonymous Thu 04 Nov 2021 16:39:52 No.13818873 Report

Quoted By: >>13818901

>>13818854
>>Clifford algebras
is a set geometric algebra

just listen to her youtube series
https://www.youtube.com/watch?v=3BZyds_KFWM&list=PLNxhIPHaOTRZMO1VjJcs7_3dgyJ2qU1yZ&ab_channel=CohlFurey

>Not really, no
Dude, like 5% of the population can do an integral, you think feynman diagrams help them?

Anonymous

Anonymous Thu 04 Nov 2021 16:49:03 No.13818901 Report

Quoted By: >>13818943

>>13818873
>No original ideas
Gotcha, so you're just like a retarded cultist preaching for people to adopt a system you don't comprehend. You say it's useful for QED yet you don't even know the fundamentals of QED and just cite a random YouTube video. Not clicking it. Not watching it. If you have something constructive to add, I'll read it. But you don't seem to have any genuine ideas of your own.
>You think Feynman diagrams help them?
Are you fucking stupid? You're the one who said physicists need visualizations to compute integrals. I explained to you that it's simply untrue. Hell, Feynman's integral techniques were purely mathematical with no visual interpretations, and they revolutionized QED with his use of functional analysis (cf. Path integral s). Good luck visualizing that. And now your argument is that most people can't compute an integral, so how would visualizations help them anyway? You're basically refuting your own asinine argument: if Feynman diagrams (i.e. visual aids) won't help them, then by your own argumentation the visualization of geometric algebra won't help QED calculation. Congratulations, you just refuted your own argument. Fucking dumbass.

Anonymous

Anonymous Thu 04 Nov 2021 17:07:10 No.13818943 Report

Quoted By:

>>13818901
lol @ seething physishit scared of losing the shibboleths that make him part of the special group

Anonymous

Anonymous Thu 04 Nov 2021 22:34:36 No.13820008 Report

Quoted By:

>>13816906
I clicked and im sad i cant enlarge the pic of the kitties

Anonymous

Anonymous Thu 04 Nov 2021 22:49:05 No.13820050 Report

Quoted By: >>13820059 >>13820160

Speaking of advanced math, can someone tell me which group is created/generated by the set of all unitary generators in a given Hilbert space?
Im trying to describe all kets as basically being one specific state on which some unitary operator effects a transformation. While its easy to define unitary operators, i dont know how to define all the operators, if that makes sense.

Anonymous

Anonymous Thu 04 Nov 2021 22:53:39 No.13820059 Report

Quoted By:

>>13820050
>group is created/generated by the set of all unitary generators in a given Hilbert space?
I mean unitary operators.

Anonymous

Anonymous Thu 04 Nov 2021 23:38:28 No.13820160 Report

Quoted By: >>13821374

>>13820050
The Unitary operators are the automorphisms of a Hilbert space. Nothing to it.

Anonymous

Anonymous Fri 05 Nov 2021 00:05:10 No.13820230 Report

Quoted By: >>13820262

>>13816933
Its not the future of mathematics -its random bits mashed together by Hestenes for no unified reason whatsoever. Ignore it and just read regular books.

Anonymous

Anonymous Fri 05 Nov 2021 00:19:03 No.13820262 Report

Quoted By:

>>13820230
Its underlying principles build out a natural intuition of

complex numbers
a multi-dimensional notion of cross product
Vector rotations
pauli spin matrices

all from the notion of the geometric product

But above all, it re opens the window of electrodynamics without the simplfying assumptions that gibbs-heaviside did for their telegraph equation. Which is great for transverse waves, but forgets the insights of impulse electricity found in Maxwell's heretical form of quaternion, and later conventions of the biquaternion and handed quaternion alegbras that expose it mathematically

Those who've learned maths do not have a use for it, but as someone who cares about pedagogy, I know that I would've easily saved a years worth of math training if they started me on this

Anonymous

Anonymous Fri 05 Nov 2021 09:12:27 No.13821374 Report

Quoted By:

>>13820160
Right but on a given space they must resemble the structure of some known groups, right? Im intentionally using sloppy language because im not teaching anyone anything, im asking a question.
For instance in elementary QM the shift operator is "similar" to the real number line with addition, which is a Lie group. There are of course other operators, infinite in fact. Is there a way to write down a finite set of operators that generate all possible generators in a given hilbert space?

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