Anomalies

Abstractions, it has been said, tend to leak.  But where is the abstraction, young padawan?  Examine the real machine all you like, you will not find it there.  An abstraction is not a thing, it is an idea -- and the 'leak' is a divergence between the ideal and actual performance of a system.

It's become something of a hobby of mine to hunt for anomalies -- cases where the idea of the system clearly fails to account for the actual behavior.  The anomalies clarify the limits of the abstraction by establishing the domains over which they fail to generalize; as such they're the natural starting place in the hunt for useful invariants.  That is to say, the search for truth -- in a word, philosophy. 

And everything, my friends, is grist for philosophy.  Ayn Rand did not get many things right, but one thing that she got very right is that philosophy, far from being useless, is an inescapable activity for the reason alluded to earlier: because we live in a world of functional abstractions, which are the original labor-saving devices, and these abstractions leak.

Of course philosophy, like anything else, can be done well or badly, and one does not need to look far for hilariously awful examples.  What's wrong with our thoughts is what's wrong with the abstractions from which they're built: when they are ill-formed, the result is garbage. 

What separates an outstanding philosopher from the rest of us is a relentless will to push abstractions a little further than they were designed to go, right up to -- and sometimes well past -- their breaking points.  If you can spot where the thinking goes wrong, you're hot on the trail of an anomaly and at the beginning of wisdom.