Originally published July 12, 2016

Lists are really, really appealing for some reason, perhaps because they are so simple and orderly and thus memorable.

Peter McIntyre wrote an article (listicle, is the pejorative) called 52 Concepts to Add to Your Cognitive Toolkit. Despite being written in pandersome newspeak it's really good; I endorse it. Most of those concepts are essential to thinking and if you don't know any you should familiarize yourself post-haste. I cannot emphasize this enough. Fluency in these concepts is by my account an adulthood developmental stage. No such listicle could ever be complete, and to my reckoning the most important omissions are:
Wow, a list. So shiny, so nice. Very compelling.

Some of these concepts are monster-topics that take weeks to understand. Others take less than an hour. Caveat emptor.

I am fascinated by the concept of a "cognitive toolkit" or "conceptual ontology" or "insight collection" or "conceptual vocabulary" or whatever you want to call it. It should probably be on a list of essential concepts! The fascinating thing is that it seems to comprise a list of concepts. Like the way you think is partially embedded by something as simple as a communicable list of ideas.

The 'vocabulary' metaphor for the conceptual ontology helped me realize something important. Earlier I had the minor insight that the set of words you can use is much smaller than the set of words you can recognize. The same is true for concepts. To understand other people's thinking, you only need to be able to recognize the chunked concepts involved, but to think, you have to be able to use these concepts, which requires practice. Pen-and-paper exercises and spaced repetition thereof might help. I nearly put spaced repetition in my above list, but worried it would start to become a list of all the concepts I know and utilize. Like, did you know spaced repetition helps all kinds of knowledge, not just declarative? God damn, son.

Richard Feynman attributed much of his research success to using a 'different box of tools'. It makes sense. Exploring in a different way than everyone who has come before is probably a prerequisite for finding new things. It seems to me that humans, even the brightest, mostly think the same thoughts, over and over, in the same ways, and have only a few tools and heuristics for thinking. Quoth Gian-Carlo Rota:
Every mathematician has only a few tricks.

A long time ago, an older and well known number theorist made some disparaging remarks on Paul Erdos's work. You admire Erdos's contributions to mathematics as much as I do, and I felt annoyed when the older mathematician stated, in flat and definitive terms, that all of Erdos's work could be ``reduced'' to a few tricks which Erdos repeatedly relied upon in his proofs. Actually, what the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks that they use over and over. Take Hilbert. The second volume of Hilbert's collected papers contains all of Hilbert's papers in invariant theory. I have made a point of reading some of these papers with care. It was very sad to note how some of Hilbert's beautiful results have been completely forgotten.

But it was surprising to realize, on reading the proofs of Hilbert's striking and deep theorems in invariant theory, that Hilbert's proofs relied on a few tricks that he used over and over. Even Hilbert had only a few tricks!
The way I see it, the way humans have different incommunicable cognitive habits is in large part responsible for differences in quality of their intellectual work, and an important proximate cause of people's uniqueness. I often see deep links between my thinking and other people's thinking, always so deep that I can't articulate them. It makes me wonder whether I have some ultra-deep grognor-only intuitions that languish, unused, because I never see them in anyone else and thus they never get reinforced.

Anyway these deep thought-structures are definitely not simply lists of cognitive habits or heuristics. If you could condense Erdos's briliance into such a thing, you would be as brilliant as him. Even so, lists seem, surprisingly, to compose a large part of people's cognitive faculties.

1 comment:

  1. Months after writing this post, I learned that Daniel Dennett wrote a book full of cognitive tools, using his idiosyncratic term "intuition pumps". Intuition pump is a concept that definitely belong on this list, so I added it. Now I have to get my hands on that book some day.