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rwallace comments on The Curve of Capability - Less Wrong
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That is what I'm claiming, so if you can demonstrate one, you'll have falsified my theory.
I don't think so, I think that's a different thing. In fact...
... I would've liked to use the law of increasing returns as a positive example, but I couldn't find a citation. The version I remember reading about (in a paper book, back in the 90s) said that every doubling of the number of widgets you make, lets you improve the process/cut costs/whatever, by a certain amount; and that this was remarkably consistent across industries -- so once again we have the same pattern, double the optimization effort and you get a certain degree of improvement.
I think I read that, too, and the claimed improvement was 20% with each doubling.
That would look linear on a log-log graph. A power-law response.
I understood rwallace to be hawking a "curve of capability" which looks linear on a semi-log graph. A logarithmic response.
Of course, one of the problems with rwallace's hypothesis is that it becomes vague when you try to quantify it. "Capability increases by the same amount with each doubling of resources" can be interpreted in two ways. "Same amount" meaning "same percentage", or meaning literally "same amount".
Right, to clarify, I'm saying the curve of capability is a straight line on a log-log graph, perhaps the clearest example being the one I gave of chip design, which gives repeated doublings of output for doublings of input. I'm arguing against the "AI foom" notion of faster growth than that, e.g. each doubling taking half the time of the previous one.
So this could be falsified by continous capability curves that curve upwards on a log-log graphs, and you arguments in various other threads that the discussed situations result in continous capability curves are not strong enough to support your theory.
Some models of communication equipment suggest high return rates for new devices since the number of possible options increases at the square of the number of people with the communication system. I don't know if anyone has looked at this in any real detail although I would naively guess that someone must have.