Rajchman had two students, one of whom (Antoni Zygmund, who also studied under Mazurkiewicz, and founded the Chicago school of analysis) had 40 students, five of whom had over 100 students of their own. 18 of those 40 had at least one student of their own. Consequently Rajchman had 1658 descendants in only a century, a mentorship growth rate of 7.7% per year despite Rajchman himself having his career cut short by being murdered by the Nazis in 01940 and apparently ceasing to mentor anyone officially for the previous 15 years of his career.
Yes but the exponential scaling doesn't really work to anyone's benefit. It just means that N people can each mentor an average of N people and so on and so forth. An active community means that the people who are working on the problems can all share results and bring people up to speed. I'm not convinced THIS scales well.
I can buy more people in physics working on more problems. There are a wealth of interesting problems in physics and more people all going in different directions would be great. But ten times as many people working on the LHC? A hundred times as many people working on string theory? I don't buy it.
To me, the ideal model of fully open, accessible research is the speedrunning community. I don't see speedrunning as all that different from experimental work. You probe, you hypothesize, you have breakthroughs, you compete in what's generally a pretty healthy way, and you communicate and document. Look at how this scales, how many people get in and get obsessed, etc. To really master quantum hall, you need to have have a devotion to the field that's comparable to "completing Super Mario 64 with half an A press."
Yeah, although maybe mentorship can scale reasonably well (or at any rate much faster than we are scaling it at present), I agree with you about collaboration: ten times as many people working on the LHC (or HEP in general) probably wouldn't be very effective. Now that we have Sci-Hub, the General Index, Wikipedia, Stack Exchange, and Google Scholar, we can probably collaborate a little more effectively than before, but not enough to cram orders of magnitude of people into a given subfield.
There might be a path forward in the work on making computational work easily reproducible, by people like Konrad Hinsen, Yihui Xie, Jeremiah Orians, Eelco Dolstra, Ludovic Courtès, Shriram Krishnamurthi, Ricardo Wurmus, and Sam Tobin-Hochstadt, but clearly it hasn't been a panacea so far. Speedrunning results are in many cases reproducible by virtue of nailed-down console hardware and bit-identical game images, but that's harder to achieve even for FEM simulations of turbulent MHD systems, much less actual experimental MHD systems like a Farnsworth fusor.
How do people initially get up to speed on speedrunning? Are there tutorials, the equivalent of a textbook with problem sets, some other onramp? Can we gamify learning quantum mechanics? (I've tried QiskitBlocks but so far haven't been impressed.)
Rajchman had two students, one of whom (Antoni Zygmund, who also studied under Mazurkiewicz, and founded the Chicago school of analysis) had 40 students, five of whom had over 100 students of their own. 18 of those 40 had at least one student of their own. Consequently Rajchman had 1658 descendants in only a century, a mentorship growth rate of 7.7% per year despite Rajchman himself having his career cut short by being murdered by the Nazis in 01940 and apparently ceasing to mentor anyone officially for the previous 15 years of his career.