Hyperbolic growth

(Reposted from Facebook,  I would prefer put it here than have it lost to the sands of time.)

My view of the future is strongly influenced by the history of economic output. I think it’s instructive to look at the sequence of doubling times—how long did it take economic output to double, and then how long did it take it to double again, and so on? Here are the lengths of the first 8 doublings since 0 AD (followed by the year that the doubling ends):

1000 (ending in 1000)
600 (ending in 1570)
200 (ending in 1765)
100 (ending in 1860)
40 (ending in 1900)
40 (ending in 1940)
20 (ending in 1960)
15 (ending in 1975)
20 (ending in 1995)
>20 (to present)

(Source: Brad DeLong stitched together some estimates in 2006 which I believe are roughly right. These are the “ex-Nordhaus” here. The last two doublings are what Tyler calls the “great stagnation“, also accompanied by flat median wages.)

Here’s the same data as a graph, for visual thinkers:


And with a log transform:


Growth has accelerated tremendously over human history, but the change was gradual. If we measure time by economic doublings rather than calendar years, then about half of history was part of the rapid acceleration surrounding the industrial and agricultural “revolutions.” So it seems more appropriate to think in terms of periods of rapid acceleration and slow acceleration, with both conditions being relatively common.

We have been in a period of slowing growth for the last forty years. That’s a long time, but looking over the broad sweep of history I still think the smart money is on acceleration eventually continuing, and seeing something like this (though I have little idea whether it will start in 2025 or 2045 or 2075):

20 (ending in 2025)
10 (ending in 2035)
5 (ending in 2040)
2 (ending in 2042)
1 (ending in 2043)
0.5 (ending in June 2043)…

This is consistent with my view of particular technologies that are currently progressing rapidly (especially computing hardware, AI, robotics, and energy).

If you are alive in 10,000 BC and you are trying to predict when humans will achieve some ambitious technological milestone, it basically doesn’t matter what you are trying to predict—when we’ll go to space, or cure any particular disease, or automate fishing, or double our life expectancies, or whatever else. You can get to within a few percent by just estimating when the industrial revolution will occur. And you can estimate the timing of the industrial revolution pretty well, by noticing that the world economy is doubling every 4000 years and just predicting “a few doublings from now.”

Similarly, if you are alive today and want to forecast the time at which any particular ambitious technological development will occur, I think you should just be trying to predict when the world economy will be doubling every few years—which I think will be happening within “a few doublings,” something like 20-80 years.

This kind of curve extrapolation is speculative. That said, I think that it’s less speculative than simply extrapolating the last 40 years of slowing growth into the indefinite future—the fact that we’ve lived through one trend doesn’t make extrapolating it any more responsible, it just makes it feel more like common sense.

2 thoughts on “Hyperbolic growth

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