marctenbosch

I think it is a good idea because both components contain useful complementary information (the cosine/sine of the angle and the plane they form), and the algebra corresponds to geometric operations.

Having an algebra that corresponds to geometric operations is good because you get a high-level framework for how to manipulate quantities instead of having to do things case by case.

Ok I understand your question better, might update the article. Like the other commenter said, you can keep applying the geometric product more than once. To find what happens you can just work with the basis vectors.

So, you basically have three case: x (xx) = x (1) = x -> a vector

x (xy) = x (x.y + x^y) = x (x.y) + xxy = x (x.y) + y -> a vector

x (yz) = x (y.z + x^y) = x (y.z) + xyz -> a vector + a trivector. This only happens if the three vectors are independent, which can never be the case for -ava

I think matrices are easier for people to visualize because they can think about them as a vector frame and coordinate transformations.

Quaternions are seen as this abstract 4D space somehow containing 3D space transformations, and people have a much harder time visualizing 4D space. I do not think spending a lot of time trying to visualize this 4D space, like this video does, is the right way to go. Rotors make that method obsolete.

Skew symmetric matrices are isomorphic to bivectors :)

99% of the time this is true.

The outer product is the antisymmetric part of the tensor product.

The same way quaternions do.

Yeah, I spent a long time trying to find a very clean path to the geometric product and failed so far, but I feel I am getting closer, ahah.

The [Aside] section of "The Reflection Formula (Geometric Product Version) "http://marctenbosch.com/quaternions/#h_13 has the answer you seek ;)

Yes, anything you can do on quaternions you can do on rotors. (Updated the article)

I have not seen a clean version of the code online but it is almost the same as for a quaternion.

The VR version has haptics. It's kinda interesting. I think there is a little bit of intuition to be gained.

Ah, miegakure is not out yet, sorry!

Something like that, yes.

A new build is being reviewed by Apple!

Are you on an iPhone 6+ or 7+? If so, a new build is being reviewed by Apple.

I am aware of the issue and fixing right now!

Thanks! Each puzzle is about doing some crazy thing that only a 4D being could do, such as binding two rings without breaking them, or stealing something from a building that is closed from all sides but not in the fourth dimension. We'll show more of that soon.

The avatar is 3D with some 4D thickness.

Jim Rossignol from Rock Paper Shotgun played a recent build:

http://www.rockpapershotgun.com/2014/03/18/miegakure-preview...

He said: "Flipping through dimensions is remarkably intuitive- [...] I shifted dimensions, messing about with this strange toy until I quickly understood most of the problems that I faced."

The game is actually completely continuous. The crazy deforming shape at the beginning of the trailer is a 3D slice of an object called a 120-Cell, which is a true 4D shape.

It's actually highly unlikely the game will not come out.

Well, experimental games take a long time to make! It's to be expected.