Once upon a timeI blogged about Odlyzko's contention that n log(n), rather than Metcalfe's n*n, is a much more realistic evaluation of growth in a network. For some reason this popped up in my head again with relation to specialization.
Given a particularly productive endeavor, how many people can be sustained by involving themselves in providing services for the people working on the initial product? Somebody, after all has to do some food production, or make cloth; the chef and the dry cleaner show up later on.
Innovations and new technology undoubtedly blunt the signal, and then there is the valuation of whatever it is being produced; tricky stuff to figure out.
But 1 log(1) gets you nowhere, 100 log(100) would suggest the first 100 could provide the impetus for another 100, and 1000000 log(1000000) suggests a million productive people can form the basis for jobs for an additional 5 million.
Sounds possible. Government would have to stay out of the way, of course. It's very necessary whatever is productive to actually be productive, and not just politically convenient, or else you get a whole bunch of government jobs and a shortage of chickens.
How would one go about verifying such an idea?
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