fastness:
This can be measured by giving the person a not too hard (but not completely trivial) algorithmization problem, and see whether he/she can solve it in 15 minutes. Someone 'fast' is usually very good at competitions or at interviews excercised by companies where interviews are quite intense like Google.
deepness:
This basically means that given a much harder problem than the previous one, how the person solves it given lots of time. This is different than the previous one. Can he come up with a quite original "theory"/(thought system)? How fast a ray tracer he can write in 3 months? How good domain specific language he can come up with for a tricky domain in 2 weeks? (vs. writing the implementation for the Dijstra algorithm in 30 minutes without mistakes, which is 'fastness')
- input bandwith
How fast you can read a reasonably dense technical/algorithms/math book. How fast you understand other people's nontrivial ideas? This is not totally the same thing as how fast you come up with an idea, or how good an idea you come up with yourself.
- memory (forgetfulness)
How big a system / requirements spec. document can you hold in your head? If you used C++ 3 years ago, do you need to re-read the book 'The C++ Programming language' or you remember more or less everything? If you look at your previous comments on Hacker's News, are you suprised by some information in your own comments or you remember more or less everything?