In my college in Antarctica we were taught

  x ^ y = y x^T - x y 
  
  exp(ε x ^ y) v ~ v + ε x ^ y * v
  = ε y (x,v) - v + ε x (y,v)

because we use the left-hand rule down under.

But 3D is the D that matters for 3D games. video games are concrete mathematics, not abstract mathematics.

I miswrote. Rotation calculations are represented (in quaternions and in geometric algebra calculations) as a 3D subspace of R^4, with the "extra" dimension accounted for by constraining quaternions to the unit hypersphere.

Rotations do involve magnitudes when interpreted as an axis (2 dimensional manifold embedded in R^3) and a magnitide (0 to 2pi)

https://en.wikipedia.org/wiki/Axis%E2%80%93angle_representat...

SO(3) is a coordinate-free abstraction that isn't relevant to the topic of GA vs Quaternions for calculating concrete values in computer graphics

> getting discouraged and quitting

is bad for both player and business

You're (exactly like unoti) assuming there is a business. If it's just a game, and no business, it's not "bad for business".

> reliably throws out improbable events.

which is another way of wording "reliably generates and serves improbable events"

Don't quite understand the point of your comment, maybe I am missing some context, but yes. Are you objecting to my "throws out"? I suppose it is suboptimal because it could be misinterpreted as meaning "eliminates" rather than the intended "generates".

> There is just as much money to be made in tearing down a civilization as in building one up.

Do you think Steve Jobs, Mark Zuckerberg, and Larry Page, Jeff Bezos, and Bill Gates agree with this statement?

Why wouldn't they?

I have allergies and my nose runs a lot. Somehow I manage to not throw my tissues on the ground.

Is it so hard to carry an ash box with a cigarette box?

ToS aren't signed. They are terms of service, not license agreements.

ToS merely need to be disclosed, and the site cna decline service if you violate the terms. A license agreement may subject you to penalties for violating the agreement.

Thanks for the clarification.

Like hiQ, you can file a lawsuit and try to win. You might want to wait to see if hiQ wins their case.

Per hiQ's arugment, but not per any existing ocourt decision.