From: steven0461 (steven0461@gmail.com)
Date: Tue Jul 15 2008 - 13:42:46 MDT
http://en.wikipedia.org/wiki/Benford's_law<http://en.wikipedia.org/wiki/Benford%27s_law>mentions:
"the observation that real-world measurements are generally distributed
logarithmically, thus the logarithm of a set of real-world measurements is
generally distributed uniformly"
The intuition I get from this is that if you have some big random set of
algorithms or recipes (here representing the different possible ways to
shape matter so as to get computing power out of it), then, as an observed
mathematical regularity, the output numbers from those algorithms (here
representing quantitative measures of computing power) will be distributed
logarithmically; and so a linear increase in "algorithm quality" will
correspond to an exponential increase in computing power. Moving from the
56th to the 57th percentile of good algorithms will increase the output by
the same *percentage* as moving from the 57th to the 58th percentile. (Here
the distribution would be cut off at some physical limit.) You could
probably construct an argument why a fixed amount of research effort
corresponds roughly to moving a fixed amount of "algorithm quality" measured
in percentiles.
So I would agree that "most technological growth is exponential" in
quantitative performance, but not because "the rate at which technology
improves is proportional to the amount of technology already in existence",
but because the logarithm of quantitative performance is just a more natural
scale for measuring technological progress. There's not much of a Moore's
law for log(computing power).
This is unrigorous and probably confused in a few places and it doesn't
explain why the doubling time is what it is, or why the doubling time has
been so constant (if it has been). Still, I think it's where a deep
explanation would have to start.
steven
http://www.acceleratingfuture.com/steven
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