Where the author talks about imaginary numbers being completely "made up" and suggests you shouldn't bother with trying to understand them, I think that's selling them short.<p>Imagine, if you will, trying to explain to the ancient Greeks the idea of a number that can't be written as a division of integers (the irrational numbers). That would have seemed completely "made up" to them, but we don't really see them that way, they just "are". That concept is has since become normalized, in terms of everyday concepts (like the area of a unit circle). Similar situations arise with fractions or negative numbers to some indigenous tribes, etc.<p>I guess what I'm saying is that complex numbers only as fictitious or imaginary as any other set of numbers that we otherwise feel like we have a good handle on.
Not bad, but I find this to be a state of the art explanation of quaternions: <a href="http://acko.net/blog/animate-your-way-to-glory-pt2/#quaternions" rel="nofollow">http://acko.net/blog/animate-your-way-to-glory-pt2/#quaterni...</a>
Another good reference:<p><a href="http://www.songho.ca/math/quaternion/quaternion.html" rel="nofollow">http://www.songho.ca/math/quaternion/quaternion.html</a>
This recently posted YouTube video by UNSW Professor Norman J. Wildberger discusses the discovery of the quaternions by Hamilton and the subsequent discovery of the octonians. It's 59 minutes, 30 seconds long, and it was published on March 5, 2014:<p>MathHistory18: Hypercomplex numbers <a href="https://www.youtube.com/watch?v=uw6bpPldp2A" rel="nofollow">https://www.youtube.com/watch?v=uw6bpPldp2A</a> [video]