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Exponential Assembly - An Exponentialist Assessment

(post to sci.nanotech 9th February 2006)

Hi,

Like Drexler, Zyvex are exponents of the exponential nature of manufacturing via MNT, and have written about exponential assembly:

http://www.zyvex.com/Research /exponential.html

A rough guide to understand what exponential assembly would mean, in terms of assembler population doubling times, are the two competing memes of the Rule of 70 and the Rule of 72  Basically, divide your growth rate (per fixed time period) into 70 (or 72) and you get the population "doubling time". (expressed in multiples of the same fixed time period).

Search Google for these two slightly different versions of these popular rules of thumb and you get the following:

Rule of 72 - 25,000,000 hits

Rule of 70 - 41,700,000 hits

The former is mainly used in the world of finance, and the latter in population dynamics, population ecology, demography and so on (and hence exponential assembly). Essentially, both rules of thumb allow you to quickly derive a doubling time (for an amount of money, or a population)

I've written an article that compares the Rule of 70 and the Rule of 72:

http://members.optusnet.com.au /exponentialist/RuleOf70andRul eOf72.htm

I hope you find it useful and interesting. If you did, you might also enjoy the following:

http://members.optusnet.com.au /exponentialist/The_Scales_Of _70.htm

"The Scales of 70" extends the Rule of 70/Rule of 72 to positive and negative rates of variable rate compound interest, and hence is much less naive than the Rule of 70 / Rule of 72. Essentially, though, it is just a more flexible rule of thumb.

"The Scales of e" extends the Scales of 70 even further, to a realistic and accurate model of variable rate compound interest (allowing for both positive and negative rates of growth):

http://members.optusnet.com.au /exponentialist/The_Scales_Of _e.htm

I believe that Exponential Assembly, when it arrives, will follow a "growth" pattern bound by "The Scales of e." Hence, despite Zyvex's or anyone else's best efforts, assembler population doubling times will not be fixed or constant.

The Scales of e demonstrates that variable positive rates of compound interest will result in variable population doubling times. Occasionally, due to lack of availability of raw materials, growth rates may be temporarily reduced to zero and the Scales of e will be perfectly balanced between positive and negative rates of population growth.

Less rarely, but still possible, might be periods of negative assembler population growth rates (e.g.. an industrial accident, a "spoiled" batch, a fire etc). Hence, the Scales of e might will swing the other way, to accommodate a few "population halvings", before once again swinging back to irregular population doublings.

Regards,

David

Bibliography

Freitas, Robert, A., Merkle, Ralph, C., Kinematic Self-Replicating Machines. Landes Bioscience. 2004. pp.138-140.