Are Bivectors Always Plane Segments?

In this short, I show the distinction between blades and more general k-vectors, and why we have to think about this distinction. I've generally avoided talking about these kinds of issues before because they only start to appear at four dimensions, but it's an important distinction to keep in mind as you get more advanced in geometric algebra.

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[degrees]

Yeah it’s important. Seeing that there are more bivectors than blade bivectors opens a path to classify rotations in nD.

[olbluelips]

I’m becoming rapidly obsessed with geometric algebra. It seems to just magically do everything I want it to do! I’m going to try to implement some concepts from geometric algebra into my engine. The concept of bivectors was exactly the missing piece I needed!

[tylerfusco]

This is the first channel where I actually watch shorts on! I genuinely enjoy these, and they’re WAY higher quality than any other shorts ive seen

[hapehiftr]

a 4d double bivector looks like 2 orthogonal planes but there is a way to choose seperate planes that are still gives the same bivector.
2 equal magnitude orthogonal bivectors corresponds in some sense to the hopf fibration.
Choosing 2 arbitrary orthogonal circles in the fibrarion gives the same bivector.

[KingdomHearts]

And a blade's square isn't even necessarily positive, right? In particular for orthogonal vectors (at least for 2-dimensional blades): for example, u = e1+e2, v = e1-e2 => (u \wedge v)² = -4 = -u²v²

[shoam]

What are they if they aren't blades?

[raydencreed]

What is it if not an oriented plane segment?

[beinganangeltreon]

your video made me think of things new to me, thanks!
notes arising from your video:

at a video about the universe being curvy or folded and some enrgy (gravity) travelling volumewide through the curves or folds. I made a comment: I just made notes about something similar. Things that two intersecting vectors can make at math besides a plane are called blades, if blades actually exist, or can be made, at actual 3D space (4D spacetime) then they could extend in differently dimensional ways, and energy forms, like RF, EM, or noting your video, gravity could traverse them perhaps with less absorption or attenuation from having less stuff around, then, if the universe had any folding we could detect it from making astrophysics blade antennas, the note kind of says a path to detect and make blades.
note:

So then, if blades can be detected or made, and if you can find or create a potential energy difference between them you could push or suck things between parts of the blades to other areas at the blades, like from earth to outer space places, or places between locations on Earth.

[DrDeuteron]

GA is wonderful, but it simply will not catch on in physics. We need our axial vectors and pseudo vectors.