Laws of Formalisms

Laws of Formalisms

 

Exhaustion: if a formalism is old, then we probably know everything worth knowing about it.

Sterility: If a formalism needs lots of work to justify simple results, then it’s probably the wrong one.

          Similarity: If two wildly different formalisms are doing oddly similar things, then there’s probably one uniting them.

          Contagion: If two formalisms derive from a single one, then they probably do the same things.

          Illusion: If a formalism’s ideal/abstract entities outweigh its concrete/calculational one, then it can probably say nothing new.

          Connection: A formalism’s value equals the extent to which it can freely interact with other formalisms.

Fluidity: In a good formalism, what you can do you can also undo.

          Diversity: Many theories derive the same theorems. There is no single best explanation.

          Novelty: Only essentially new ideas count. Stale thought sickens.

          Obscurity: The destructiveness of a formalism equals the number of thoughts it prevents us from thinking.

          Humanity: Proving that you can do it, given infinite time and unlimited knowledge, is not the same as proving that you can do it, given little time and paltry knowledge.

Inquiry: Questions teach us more than answers. The aim of math is to produce better questions.