Re: poly: Computers induce fast growth?

Robin Hanson, <hanson@econ.berkeley.edu>, writes:
> I've just revised my short paper on long term growth as a
> sum of exponentials (http://hanson.berkeley.edu/longgrow.html).
> And damn if I'm not starting to come around to the simplistic
> view that the economy will start to follow Moore's law of
> doubling every one to two years once computer hardware
> dominates brain hardware.

>From your paper:

: Doubling Date Began DT WP
: Time To Dominate factor factor
: ---------- ------------ ------ ------
: 1,090K yrs <1000K B.C. ? >1.9
: 140K yrs 710K B.C. 7.8 34
: 864 yrs 4700 B.C. 161 172
: 69 yrs 1735 12.5 7.5
: 15.5 y 1928 4.5 >12.5
:
: For each term, I've listed its doubling time and date when it began
: to be the largest term in the sum. I also list the factor by which the
: doubling time increased from the previous term, and the total WP growth
: factor during the time when that term dominated.
:
: The big questions to ask are: how soon might the world economy jump again
: to a faster growth mode, and how much faster might that mode be? One
: approach is to assume that DT and WP factors are independently drawn
: from the same distribution. If the current mode were to last through a
: WP factor the same as one of the last three modes, it would last until
: either 1988, 2024, or 2060. And if the next DT factor were the same as
: one of the last four DT factors, the next doubling time would be either
: would be .1, 1.2, 2.0, or 3.5 years. This suggests dramatic change within
: the foreseeable future!

I would find this extrapolation more convincing if there were some
stability in the DT and WP columns. Instead they vary amongst themselves
by more than an order of magnitude. And with only four or five samples,
the next line could easily be yet another order of magnitude larger or
smaller.

It's also not clear that WP is the right "clock" for timing transitions.
Again, the lack of consistency is disturbing. I suppose one thing you
could do is to depict "number of doublings", which would just be the
log base two of WP, giving >0.9, 5.1, 7.4, 2.9, >3.6. This somewhat
artificially shrinks the differences and makes the numbers look a little
more consistent. But it seems plausible to say that each era lasts from
3 to 8 doublings, with a little fudging, therefore we wouldn't expect
to see much more than 8 until the next era, which gives your 2060 date.
OTOH we could hardly rule out 10 or 15 doublings, either, carrying us
well into the 22nd century.

As for the doubling times, if we extrapolate the last three entries in
the DT column it wouldn't be that surprising to see a further factor
of 3 decrease in the DT factor, making the new DT factor be 1.5 and the
new doubling time be 10 years. This would not be dramatic.

Overall it seems that the paucity of data makes it difficult to rule
out any a priori plausible scenario for economic growth rates over the
next couple of centuries. We could switch to a doubling time of .1
year tomorrow (1000 fold growth per year) or we could see only moderate
changes over the next 300 years, all basically consistent with the data.

Hal
Received on Fri Sep 11 00:43:39 1998