Douglas_Knight comments on Mechanics without wrenches - Less Wrong
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Have there been studies of how worker productivity is distributed? We should at least be able to get economy-wide income data, which gives us nearly the same info if we assume peoples' pay tracks the value they add.
In math, it does feel as though one's mathematical power is something like exponential in the amount of time one has spent on solid math study, at least until one hits the frontiers of one's subfield. Algebra I takes a year to learn, but a few years later, the content of algebra I seems similar to the content of a section (not even a chapter) within a semester's course. I suspect similar increases in my ability to learn other competencies as I "learn how to learn" those fields, but it is harder to quantify. Do any of you programmers, or others, care to estimate how your productivity has changed with focused efforts to learn, or to learn how to learn?
That's probably because the real content, eg, the idea of a variable, is invisible to you now. To someone who already knows it, it can't be drawn out any longer than a section. There is a phrase "mathematical sophistication" for such content that's hard to pin down. Also, people may teach it inefficiently, as they don't remember what the gap is.