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Suppose a narrow field where only two human beings can understand. How could the society judge the progress of the field or the merit of a new project? I don't

Suppose a narrow field where only two human beings can understand. How could the society judge the progress of the field or the merit of a new project? I don't think it is possible to avoid collusion or groupthink in such a field and it would be difficult to differentiate the two. So does it mean we should curb some superhuman thinking and let them explain better to other human being? I'd think so. It is all about balance or trade-off, but at some point, a field would become too esoteric for a society and it might need to slow down the short-term progress to ensure consistent long-term progress. It seems the math field as a whole (or more specifically the number theorists?) needs more of good communicators who can link the cutting edge and more general public. The math academia could give incentives to such activities in addition to pushing the boundaries.

sandworm101 7y ago
That assumes there is some link to the general public, to the real world. Lots of math has absolutely no practical use, yet. Why bother explaining the cutting edge when even those who understand it cannot fathom how it would ever be used?
knzhou 7y ago
Scientists and mathematicians already spend an extreme amount of energy trying to think of the shortest, cleanest possible route for people to learn their fields. The resulting documents take years to create, and are called textbooks. (At least, the good textbooks are like this.) Often people will work for thousands of hours on their books, essentially for free. Students go from outsiders to participants by reading them, all the time. The problem is that things genuinely are hard, and there's only so much compression you can do before you're reduced to meaningless handwaving. Textbooks are already compressed by a factor of 100 relative to the original research literature, sometimes even oversimplified. Demanding something a factor of 100 better than a textbook is going to get you something like one of those useless "learn C++ in 24 hours" paperbacks.

sandworm101 7y ago

That assumes there is some link to the general public, to the real world. Lots of math has absolutely no practical use, yet. Why bother explaining the cutting edge when even those who understand it cannot fathom how it would ever be used?

knzhou 7y ago

Scientists and mathematicians already spend an extreme amount of energy trying to think of the shortest, cleanest possible route for people to learn their fields. The resulting documents take years to create, and are called textbooks. (At least, the good textbooks are like this.) Often people will work for thousands of hours on their books, essentially for free. Students go from outsiders to participants by reading them, all the time. The problem is that things genuinely are hard, and there's only so much compression you can do before you're reduced to meaningless handwaving. Textbooks are already compressed by a factor of 100 relative to the original research literature, sometimes even oversimplified. Demanding something a factor of 100 better than a textbook is going to get you something like one of those useless "learn C++ in 24 hours" paperbacks.