In programming, as in everything else, to be in error is to be reborn.
In computing, invariants are ephemeral.
When we write programs that “learn,” it turns out that we do and they don’t.
Often it is the means that justify the ends: Goals advance technique and technique survives even when goal structures crumble.
Make no mistake about it: Computers process numbers – not symbols. We measure our understanding (and control) by the extent to which we can arithmetize an activity.