If you can participate, we will port any 3D objects or animations to VR via the Unity. The meeting will be held on January 11, 2022 at 7pm PST.

We would appreciate a response by Monday, November 22 to mike@stereosphere.com .Any questions?

Thanks for a wonderfully informative blog post!

Michael Fleming

]]>Hi Slehar

I think I dont know you or why you suddently write to me. Ok i am interested in geometric algebra, and your presentation of the subject looks pretty and interresting.

So what do you want from me ?

Mvh John

> Den 29. okt. 2021 kl. 19.35 skrev slehar : > > >

]]>Or like a 3-D (or more!) vector with freedom of motion on the surface of the (N-) sphere

]]>Re: * “Doesn’t a vector times a trivector (in 3D) produce a bivector, not a scalar? For example, doesn’t e1*(e1*e2*e3) = e2*e3?” * – Yes it does and the trivector i := (e1*e2*e3) is pseudo-scalar which behaves like imaginary unit. It is commutative with every other vector (it can be easily proven) and i^2 = -1. And of course i*e1=e1*i = e2*e3 is a bivector indeed. The 3-rg grade Clifford Algebra Cl3,0(R) can be “self-complexified” using trivector i as the imaginary number unit. Clifford algebra described by the 8-Dimensional base vector set {1, e1, e2, e3, e1e2, e2e3, e3e1, i} x R is isomorphic with the 4-Dimensional complex Clifford algebra Cl(2)xC (which incidentally, is isomorphic with Dirac’s spinor space), which can be written symbolically as {1, e1, e2, e3} x C (R=Real, C=Complex number field, notice that e3=-i*e1*e2). Clifford Algebra Cl3,0(R) describes the entire physics as we know it.

I think you might be right. I’m really a newbie with Clifford Algebra. But yes, it collapses dimensions one by one with each vector.

]]>Thanks for this very helpful guide. Yet I’ve been completely stuck on the above sentence. Doesn’t a vector times a trivector (in 3D) produce a bivector, not a scalar? For example, doesn’t e1*(e1*e2*e3) = e2*e3?

cf. page 23 of https://www.ime.unicamp.br/~agacse2018/GA_Lecture1.pdf (“The PseudoScalar in 3d”)…?

I’ve been stuck on this sentence. Doesn’t a vector times a trivector (in 3D) produce a bivector, not a scalar? For example, doesn’t e1*(e1*e2*e3) = e2*e3? cf. page 23 of https://www.ime.unicamp.br/~agacse2018/GA_Lecture1.pdf (“The PseudoScalar in 3d”)…?

(perhaps older comments address this but the page isn’t displaying them to me)

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