Beware of bugs in the above code; I have only proved it correct, not tried it.

Programmers waste enormous amounts of time thinking about, or worrying about, the speed of noncritical parts of their programs, and these attempts at efficiency actually have a strong negative impact when debugging and maintenance are considered. We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%.

I remember that mathematicians were telling me in the 1960s that they would recognize computer science as a mature discipline when it had 1,000 deep algorithms. I think we've probably reached 500.

There's ways to amuse yourself while doing things and thats how I look at efficency.

I think people who write programs do have at least a glimmer of extra insight into the nature of God... because creating a program often means that you have to create a small universe

AI has by now succeeded in doing essentially everything that requires 'thinking' but has failed to do most of what people and animals do 'without thinking'-that, somehow, is much harder.

It would be nice if we could design a virtual reality in Hyperbolic Space, and meet each other there.