Sweet. Now that I’m public about being manic depressive, I get to write about fun analogies with various aspects of mathematics and computing. Today’s analogy: depression and mania are like least and greatest fixpoints in lattices.
To the depressive mind, the world is as bad as it could possibly be given some of the available evidence. (I say “some” because a depressed person tends to ignore a good deal of positive evidence). Negative facts are probably true unless obviously false. Random ideas are almost certainly worthless, since few random ideas are backed by hard evidence.
Mania is the opposite: every hunch not obviously wrong is probably correct, every idea potentially brilliant. Logic is no barrier to this excessive optimism; when manic I was constantly reassuring myself that I didn’t “know” various crazy ideas for certain, that I was only “exploring” the possibilities.
In other words, “manic depression” is just “guess and check”, but with the guessing and the checking partitioned too far apart in time. Sane thought requires both forces working in concert; enough fluidity to keep new thoughts and associations flowing, and enough doubt and reiteration to prune away the garbage.
To make the analogy specific: the lattice is a space of sets ideas we believe in, and we’re taking the fixpoint of the “basic thought” operator which takes a applies basic reasoning to support or refute existing ideas and propose new ones. If the lattice is the set of positive statements, mania will pick out the greatest fixpoint, the everything we could possibly believe in that isn’t obviously ridiculous, and depression will choose the opposite. The situation is flipped if we consider the dual lattice of negative statements.
This analogy is why the underlying fundamentals of manic depression can be simple, and hopefully simply curable, even while its symptoms and consequences are not. We take a simple heuristic tweak, run it through all the vast complexity of the human brain, and repeat until something snaps.
Incidentally, once we figure out how to correct the tweak, deciding what to do with this ability (or how to control it) will become important. There’s a TED talk by Joshua Walters on being manic depressive where he notes, “There’s no amount of drugs you can take that will get you as high as if you think you’re Jesus Christ.“ Very true (I know the feeling if not the particular scenario), and perhaps a bit dangerous if we’re eventually able to turn mania and depression on and off at will.