More geeky math stuff:

Quaternions: upping the dimensions of complex numbers

The basic idea behind quaterions is: we see some amazing things happen when we expand the dimensionality of numbers from 1 (the real numbers) to 2 (the complex numbers). What if we add more dimensions?

It doesn't work for three dimensions But you can create a system of numbers in four dimensions. As with complex numbers, you need a distinct unit for each dimension. In complex, those were 1 and i. For quaternions, you need for units: we'll call them "1", "i", "j", and "k". In quaternion math, the units have the following properties:

1. i² = j² = k² = ijk = -1
2. ij = k, jk = i, and ki=j
3. ji = -k, kj = -i, and ik=-j

No, that last one is not an error. Quaternion multiplication is not commutative: ab &neq; ba. It is associative over multiplication, meaning (ab)c = a(bc). And fortunately, it's both commutative and associative over addition.

Huh.

I'm afraid the first thought that went through my head was "Cash? Are urologists stiffed that often?"

I would think "stiff" and "urology" are about as far apart as a far thing on far day.

Why does my office have the damn a/c turned up to "Ice Station Zero" level today?!? Brrrrrrrr...

Does anyone else think that Captain Pike looks like Hec? [link]

I look like you left your G.I. Joe face down on the barbecue?

I look like you left your G.I. Joe face down on the barbecue?

Only if you happened to be exposed to Space Radiation....

Only if you happened to be exposed to Space Radiation....

Ah. A space barbecue.

In quaternion math, the units have the following properties

That's really really cool.

I am to math as Hec is to cats.

Why does my office have the damn a/c turned up to "Ice Station Zero" level today?!?

Better "Ice Station Zebra" than BF Egypt like I've got.

Ah. A space barbecue.

This is only going to lead to a knock-down, dragged-out fight over who has the best space barbecue sauce.