/sci/ - Science & Math

>omg, my brain, it feels so big!!!
>its full of so much schizo kike jargon and fancy basedence polysyllables
>oh no
>i can't hold it in any longer
>i'm…
>i'm gonna…
>i'm gonna QUANTUUUUUUUUMMMMMM!!!!!!

>>16087028
Real numbers do not belong in physics. Real numbers were a mistake, a silly abstract toy never meant to appear in applications. They have no physical meaning and they should be abolished wherever rational numbers suffice - i.e. everywhere.

>>16087028
OP, if you are fine with quaternions, how can you honestly sit here and tell us that imaginary numbers are bullshit?

>>16087090
Quaternions are just a Clifford algebra. Nobody treats them as numbers. You don't suddenly do math with quaternionic numbers by making them pop up in your equations. At best we study them as a Lie group and its representations.

>>16087058
Rational numbers do not belong in physics. Rational numbers were a mistake, a silly abstract toy never meant to appear in applications. They have no physical meaning and they should be abolished wherever integers suffice - i.e. everywhere.

>>16087280
the factnuke that destroyed physics.

>>16087035
>QUANTUUUUUUUUMMMMMM
*Quantooom

>>16087122
>Clifford algebras don't show up in equations
I'm not really sure what you're even saying here, honestly.

>>16087028
>Complex numbers were a mistake
I unironically agree. Most of the time imaginary numbers are just abstract representations of something else, eg bivectors in 2D, and by abstracting that away you lose geometric intuition.

>>16087028
>Retarded undergrad doesn't understand what isomorphic means
A tale as old as time. Keep on studying, midwit

>>16087028
I like em for electrical stuff, radio stuff

Split-complex numbers are unironically cooler and more useful than complex numbers. They are so heckin underrated.

>>16088529
redpill me on clifford algebra
is it worth reading doran as an undergrad?

>>16087122
Complex numbers are just a Clifford algebra as well.

>>16090802
Well, trivially they are. And that's the only legitimate view on complex """numbers""". They are not numbers. You do not multiply by them. You do not regard them as a physical space like euclidean or minkowski space. They are just a Clifford algebra acting via representations.

>>16087058
Ive literally said this before.

>>16087122
>>16090802
>>16090810
Clifford algebras are just Grassmann algebras with uglier notations.

>>16090814
Wait, no...I mean the polar opposite.

Integers past 1 dont exist in reality, adjust all of math to fit the new narrarive.

>>16090819
Clifford algebras _generalize_ exterior algebras.

>>16090825
How so? It's actually less general.

>>16090827
Dude, [math]\Lambda(V)[/math] is canonically isomorphic to [math]{\rm Cl}(V,Q)[/math] for [math]Q[/math] identically zero.

>>16090827
Exterior algebra /\(V) is the Clifford algebra Cl(V,Q) with the quadratic form Q=0.

>>16090840
So it explicitly only applies in that space depending on the choice of Q: it is less general.

Grassmann algebras also apply in this space simultaneously with any choice of Q.

>>16090843
Is Barkon banned?
Right fuck this, we want Barkon back
Who else is gonna save sci?
We need him bros.

BRING BARKON BACK

>>16090830
>>16090840
>>16090843
>he deleted his post
Oh, absolutely, because when I think of a wild Friday night, I definitely imagine discussing the isomorphism between the exterior algebra and the Clifford algebra with a zero quadratic form. It’s the kind of topic that just screams ‘party’, doesn’t it?
But seriously, let’s break it down for all the non-mathematicians who might be eavesdropping on this totally riveting conversation. In the thrilling world of algebra, saying that Λ(V)
is canonically isomorphic to Cl(V,Q)
for Q
identically zero is like saying, “Hey, these two seemingly different things are actually the same when you strip away all the fun parts.” It’s like realizing your two favorite celebrities are the same person because you’ve only ever seen them wearing different hats. Mind-blowing, right?
So, next time you’re at a party and want to clear the room, just drop this little algebraic truth bomb and watch the magic happen. Or, you know, actually talk about something people care about. Your call!

>>16090853
I think that you are actually a closet physicist confused by the wikipedia article. The exterior algebra operators apply to any vector space, the Clifford algebras are limited to the choice of quadratic form in Cl(V,Q). It is more useful to work with Clifford algebras that preserve the structure of Q, but by definition this limits the application of the operators to Cl(V,Q).

The exterior algebra is more general.

>>16090853
Sorry, your incel seething about parties makes your post too incoherent to be comprehensible. Please try to make your point again clearly and without making up false dichotomies in your fantasy about social life and mathematical knowledge being allegedly incompatible (spoiler: they're not).

>>16090861
In what sense is exterior algebra "more general"?

>>16090853
Please kill yourself, you are a pure noise machine. Instead of actually making an interesting post for math undergrads to read, you first made a meta self-depreciating Reddit tier observation, then talked to some imagined crowd of complete mathlets with a useless fluff analog.

>>16087028
How about I share a little something with you that'll make you tard out and have to go into the retard squishier...

i

>>16091860
Imagine managing to sound stupid after communicating just 1 paragraph of information to me on the internet. Grim.

>>16092158
Do you dispute
>Oh, absolutely, because when I think of a wild Friday night, I definitely imagine discussing the isomorphism between the exterior algebra and the Clifford algebra with a zero quadratic form. It’s the kind of topic that just screams ‘party’, doesn’t it?
is cringe fluff? Honestly who the shit talks like that? Who is so smarmy and self-concious about talking autistically for a hot minute among other autists on a website tailor-made for aspie weebs? Do you think you are some character in a 90s sitcom, you narrating to an audience or something?
And what garbage analogy is that?
>“Hey, these two seemingly different things are actually the same when you strip away all the fun parts.” It’s like realizing your two favorite celebrities are the same person because you’ve only ever seen them wearing different hats. Mind-blowing, right?
So, next time you’re at a party and want to clear the room, just drop this little algebraic truth bomb and watch the magic happen. Or, you know, actually talk about something people care about. Your call!
This means absolutely nothing. There are loads of correspondencies, equivalences, and (homo/iso)morphisms in math. Any math undergrad knows about these -- you know, the likely target audience of threads like these. So why talk like an absolute r/explainlikeimfive tard, like we are absolute turbonormies and can handle only absolutely peak-abstract to the degree of meaninglessness, so we so you have to break it down to maximally obscuratist metaphors of what hats certain celebrities are wearing?

>>16092158
Do you dispute
>Oh, absolutely, because when I think of a wild Friday night, I definitely imagine discussing the isomorphism between the exterior algebra and the Clifford algebra with a zero quadratic form. It’s the kind of topic that just screams ‘party’, doesn’t it?
is cringe fluff? Honestly who the shit talks like that? Who is so smarmy and self-concious about talking autistically for a hot minute among other autists on a website tailor-made for aspie weebs? Do you think you are some character in a 90s sitcom, you narrating to an audience or something?
And what garbage analogy is that:
>“Hey, these two seemingly different things are actually the same when you strip away all the fun parts.” It’s like realizing your two favorite celebrities are the same person because you’ve only ever seen them wearing different hats. Mind-blowing, right?
>So, next time you’re at a party and want to clear the room, just drop this little algebraic truth bomb and watch the magic happen. Or, you know, actually talk about something people care about. Your call!
This means absolutely nothing. There are loads of correspondencies, equivalences, and (homo/iso)morphisms in math. Any math undergrad knows about these -- you know, the likely target audience of threads like these. So why talk like an absolute r/explainlikeimfive tard, like we are absolute turbonormies and can handle only absolutely peak-abstract explanations to the degree of meaninglessness, so you have to break it down to maximally obscuratist metaphors of what hats certain celebrities are wearing?

>>16092161
Is this place full of retarded redditors, who were raised by single mothers?

>>16092170
Kek, a trivial math fact triggered you so much you had to cry, but since you have no friends, no wife, and no life, you had to cry to chatgpt? Lol, lmao even.

>>16092236
Reddit is that way, midwit.

>>16092436
You sure seem to know the shortest way from here to reddit.

>>16092236
that's not chatgpt

>>16092454
>I'm not a lonely loser, I have many friends to talk to. Their names are gpt, copilot, claude, llama, gemini, ...