Re: Singulatarian in Spite of Myself?

Date: Thu Mar 23 2000 - 09:32:28 MST

[This is a repost]

Robin writes:
> Long-Term Growth As A Sequence of Exponential Modes

Very interesting paper! A few comments and nitpicks:

> Economic historians have put a lot of work into estimating world product
> over the last century, while demographers and historians have worked to
> estimate world population over the last ten thousand years.

I had trouble parsing this sentence. In the first part, it wasn't clear
whether "over the last century" referred to when the work was done,
or the period for which the estimates were prepared. It was only upon
more thought that I decided that it was unlikely that anyone would claim
that demographers and historians had been active for ten thousand years,
so the "over the" clauses both referred to the period being studied.

I was surprised by the implication that not much work has been done on
estimating world product for the period prior to the twentieth century.

> I list the number of doubles in the doubling time between terms
> [...]
> Doubling Date Began Doubles Doubles
> Time (DT) To Dominate of DT of WP
> ---------- ------------ ------ -------
> 515K yrs <1000K B.C. ? >0.5
> 13K yrs 615K B.C. 1.9 4.7
> 860 yrs 4760 B.C. 7.3 7.4
> 58 yrs 1732 3.9 3.2
> 15 yrs 1903 1.9 >6.3

This "Doubles of DT" also took me a few minutes to figure out. It is
the log base 2 of the ratio of the doubling time in the row and the
one above it. So it is how many times the previous DT would have to be
doubled to get to the current DT. I'm not sure what would be a better
way to explain it, but the wording is confusing, doubles of doubles.

> To examine the sensitivity of this model, we can compare results using
> an another of De Long's time series, this one without his "somewhat
> arbitrary" factor of four to account for the extra improvements in
> product quality since 1800.

Not being familiar with De Long's work, I was alarmed to learn that he
had included a factor like this in his estimates. Product quality is
awfully subjective. It makes me wonder how meaningful it is to even try
to estimate total world product over a period of centuries and millennia.

Using the CES model, which considers interactions between the "new" and
"old" economies, the fit is:

> Doubling Date Began Doubles Doubles Transition
> Time (DT) To Dominate of DT of WP Power
> ---------- ------------ ------ ------- ----------
> 1367K yrs <1000K B.C. ? >0 ?
> 130K yrs 691K B.C. 3.4 5.3 1 (fixed)
> 908 yrs 4904 B.C. 7.2 7.6 2.4
> 6.3 yrs 2019 7.2 >9.2 0.094

I was puzzled by 2019 as the date the most recent technology "began"
to dominate, and at first I thought it must be a typo. Later on it is
explained that technically, by this model, the "old" economy, based on
agriculture, is still larger than the "new" economy, based on industry.
Not until 2019 will the new economy grow larger than the old economy.

Is this consistent with economic data? Is the total GWP today from
agriculture still greater than that from industry? We are always being
told that farmers make up only a tiny percentage of the US population now.
Granted, in much of the world farming is a dominant activity, but I would
have thought that the total industrial output of the Western countries
would be larger than worldwide agriculture.

It also seems questionable whether the industrial revolution can sustain
a doubling rate of 6.3 years. The figures from the other model of 58
or 15 years seem more reasonable. Wouldn't we expect something like
the DJIA to model the growth rate of industry over much of this century?
I think it had a doubling time of more like 15-20 years, until this past
decade anyway.

Also, how do you figure 9.2 doubles of WP for the industrial term?
You say that this is the number of doubles "during a term's period",
but when did the period for the industrial term start? I thought you
would start from 2019.

> Figure 2 and Figure 3 show how a new transition might look, if it had the
> fantastic doubling time of two weeks, had the same stong complementarity
> with our current economy that industry had with farming, and if it first
> started to have a noticable effect on growth rates in 2041 (increasing
> the growth rate that year by 30% over its previous rate, but only 2%
> in the previous year). Transitions starting at any other time would look
> very similar. By 2046, i.e., within five years of becoming noticeable,
> the economy would grow by larger factor than it had from one million
> B.C. to 2040.

These are amazing graphs, but there are some confusing aspects. I can't
seem to figure out why, qualitatively, the "next" transition looks
so different in figure 2 from the previous ones. For all the other
transitions we see leveling, then a bump, then more leveling. For the
next transition we just see it take off straight up. Why is it that the
earlier transitions looked like they leveled off but this one doesn't?

For figure 3, it appears to show that this two-week doubling transition
will lead to an annual growth rate of about 8. But in fact it should
be something like sixty million? Is this chart showing the log of the
annual growth rate, or the actual growth rate itself?

> The data I've used are questionable, the model vastly oversimplified, and
> the predictions perhaps too fantastic to believe. But if anything like
> these predictions are plausible, it seems a subject well worth further
> investigation. This small note will hopefully be but the earliest of
> first efforts on this important topic.

Yes, this is truly amazing to consider. A good example of how stepping
back and taking the long view gives you a new perspective. The transition
we are going through today is just one of many, historically, and there
is no reason to expect them to stop. We tend to fall into the trap of
assuming that tomorrow will be like today, when the better assumption
is that the changes we will see tomorrow can be understood by looking
at the changes which have occured in the past.


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