**From:** Tim Freeman (*tim@fungible.com*)

**Date:** Mon Jul 14 2008 - 12:41:13 MDT

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From: "Thomas McCabe" <pphysics141@gmail.com>

*>...Currently, we're looking for information on what causes Moore's
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*>Law-style exponentials in computer hardware, so we can predict what
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*>will happen given conditions different from those of the past forty
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*>years....Any links to other theories, or literature on the subject,
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*>would be greatly appreciated.
*

I always assumed that a random innovation takes a random amount of

time and causes an improvement by a random small percentage, and

there's a probability distribution on those percentages and times. If:

* many small innovations happen, and

* there aren't any physical limits that skew your probabilities,

then the law of large numbers takes over, so you have predictable

exponential progress that depends only on the probability

distributions.

I don't have a link for that. It always seemed obvious.

The above hypothesis does predict that spending more money so you get

more small innovations would give you a larger growth rate for the

exponential growth. I haven't looked at the numbers. If the research

spending has been fairly constant, and we got a constant exponential

growth rate, then that's consistent with my theory. If the research

spending is growing exponentially, and we get a constant exponential

growth rate instead of something super-exponential, then that's

inconsistent with my theory.

*>1)., Moore's Law was a self-fulfilling prophecy because it was used
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*>to set industry goals,
*

That's a conspiracy theory. Each competitor would benefit by beating the

prediction, and none of them do, for no particular reason. Doesn't work.

*>2)., most technological growth is exponential, because the rate at
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*>which technology improves is proportional to the amount of technology
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*>already in existence.
*

That seems to me to predict super-exponential growth, since I'd expect

a random research result to give you a random percentage improvement,

and improved technology should help you get research results faster

from one year to the next.

Maybe the research is inherently sequential? If it is only possible

to discover small improvement nubmer n+1 after completely understanding

small improvement number n, and there are humans in the loop with a

limited learning rate, then you could expect Moore's law to hold no

matter how much money you throw at the problem.

-- Tim Freeman http://www.fungible.com tim@fungible.com

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