h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Quaternions are numbers such as 13+7i+9j-6k, i,j,and k being the three imaginary variables. They obey the following multiplication rules:

i^2=j^2=k^2=ijk=-1
ij=k, ki=j, jk=i
ji=-k, ik=-j, kj=-1

Multiplication here is not commutative. It actually works a lot like cross products, except you get the real term involved. These have actually had applications, however, I cannot name one of them.

On another note, all these years, what we thought was i is actually -i !!!!!! (all exclamation points, not factorials) We need to have a group that will update all references in textbooks to account for this new discovery. I heard about this news today from a researcher I know, Jay Ustkih Ding, at Yale University. He will release it in a paper next week. He predicts that the stock market will fall 10% on this drastic news. It may also put much of the math from the past 100 years on shaky footing. The crucial part of his proof was showing that ######CENSORED BY THE POWERS THAT BE ###### by ######WE WON'T LET YOU FIND OUT, HAHAHA ######. This obvious proof is surprisingly difficult to find.

1+8/8+0+5*8

uh *huh*....
and why, for heaven's sake, does the i we 'once knew' = -i?
actually i can be i and -i...
like all good square roots both values satisfy x^2=y
sqrt(2)^2 = (-sqrt(2))^2 = 2
then
i^2= (-i)^2 = -1