**From:** steven0461 (*steven0461@gmail.com*)

**Date:** Tue Jul 15 2008 - 13:42:46 MDT

**Next message:**Lee Corbin: "Re: [sl4] prove your source code"**Previous message:**Joshua Fox: "Moore's Law was: Re: [sl4] Call for information: Moore's Law"**In reply to:**Tim Freeman: "Re: [sl4] Call for information: Moore's Law"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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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