1) The idea of constructing things out of axioms. This is probably old hat to everyone here, but I was clumsily groping towards how to describe a bunch of philosophical intuitions I had, and then I was learning math proofs and understood that any "universe" can be described in terms of a set of statements, and suddenly I understood what finally lay at the end of every chain of why?s and had the words to talk about a bunch of philosophical ideas...not to mention finally understanding what math is, why it's not mysterious if physics is counterintuitive, and so on. (Previously I had thought of "axioms" as"assumptions", rather than building blocks.). Afterwards, I felt a little cheated, because it is a concept much simpler than algebra and it ought to have been taught in grade school.
2) Something more specialized: I managed to get a B.S. in neuroscience without knowing about the thalamus. I mean, knew the word and I knew approximately where it was and what it did, but I did not know that it was the hub for everything. (By which I mean, nearly every connection is either cortico-cortico or cortico-thalamic). After graduation, I was involved in a project where I had to map out the circuitry of the hippocampus, and suddenly... Oh! This is clearly one of the single most important organizational principles of the brain and I had no idea. After that, a whole bunch of other previously arbitrary facts gradually began to made sense...Why did no one simply show us a picture of a connectome before and point out that big spot right in the middle where it all converges?
3) We learned all this minutia of history, but no one really talked about the hunter-gatherer <--> agriculture transition and its causes. Suddenly, historical trends in religion, the demographic transition, nutrition, exercise, cultural differences, and a bunch of other things start clicking together.
I think what all these 3 things have in common, is that they really aught to have been among the very first lessons on their respective subjects...but somehow they were not.
a concept much simpler than algebra and it ought to have been taught in grade school.
Well, algebra is also not taught in grade school. Considering Piaget's theory of cognitive development, with abstract thought only getting in place in the teens, I wonder if maybe it's not possible to teach it until middle/high school, even if its simple once the cognitive machinery is activated...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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