The Great Cycle Rule

History contains a lot of data, but when it comes to the largest scale patterns, our data is very limited. Even so, I think we’d be crazy not to notice whatever patterns we can find at those largest scales, and ponder them. Yes we can’t be very sure of them, but we surely should not ignore them.

I’ve said that history can be summarized as a sequence of roughly exponential growth modes. The three most recent modes were the growth of human foragers, then of farmers, then of industry. Roughly, foragers doubled every quarter million years, farmers every thousand years, and industry every fifteen years. (Before humans, animal brains doubled roughly every 35 million years.)

I’ve previously noted that this sequence shows some striking patterns. Each transition between modes took much less than a previous doubling time. Modes have gone through a similar number of doublings before the next mode appeared, and the factors by which growth rates increased have also been similar.  In addition, the group size that typified each mode was roughly the square of that of the previous mode, from thirty for foragers to a thousand for farmers to a million for industry.

In this post I report a new pattern, about cycles. Some cycles, such as days, months, and years, are common to most animals days, months, years. Other cycles, such as heartbeats lasting about a second and lifetimes taking threescore and ten, are common to humans. But there are other cycles that are distinctive of each growth mode, and are most often mentioned when discussing the history of that mode.

For example, the 100K year cycle of ice ages seems the most discussed cycle regarding forager history. And the two to three century cycle of empires, such as documented by Turchin, seems most discussed regarding the history of farmers. And during our industry era, it seems we most discuss the roughly five year business cycle.

The new pattern I recently noticed is that each of these cycles lasts roughly a quarter to a third of its mode’s doubling time. So a mode typically grows 20-30% during one period of its main cycle. I have no idea why, but it still seems a pattern worth noting, and pondering.

If a new mode were to follow these patterns, it would appear in the next century, after a transition of ten years or less, and have a doubling time of about a month, a main cycle of about a week, and a typical group size of a trillion. Yes, these are only very rough guesses. But they still seem worth pondering.

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  • Robert Koslover

    Hmm. If we consider just your own lifetime, we can observe that you have steadily promoted the bold extrapolation of trends that are typically best-plotted on logarithmic scales, throughout at least one (now approaching two) age-doubling periods. Using this same process, at least to the extent I understand it, I hereby predict that you will continue to employ this methodology to many interesting problems yet to be identified, and that you will persist in this activity until you are at least a centenarian (and perhaps well beyond that, if you remain alive and lucid) since that condition would require less than one more doubling of your present age. 🙂

  • Marvin McPortain

    There’s one other common thread: every progression drastically increased our energy consumption per capita. I’ll invite you to calculate the total energy consumption of this trillion of people during the next century. Compare that with the amount of all fossil fuels (including Uranium). Then you’ll see how quickly we’d need to transition to renewable energy to make this next step happen.

    • Anders Sandberg

      Basically, there is no clear rule here. I did some estimates of the energy requirements of different kinds of technological singularities and computational modes, including scaling like Chaisson’s power density models. With the right architecture trillions of ems can run on renewable energy – but there are a lot of arbitrary moving parts. Typically, of course, bigger civilisations use more energy.

  • arch1

    For this 1:3 ratio of cycles to doubling times to be more than a coincidence, wouldn’t there have to be some consistent causal pattern across the growth modes (e.g. cycle period controls doubling time, or doubling time controls cycle period, or something else controls both)?

    If so, then unless it was forager doubling time that controlled ice age recurrence time (which seems unlikely), whatever factors F controlled ice age recurrence time directly or indirectly controlled forager doubling time, while themselves being part of an *overall* pattern (again, presumably causal) that *also* caused forager doubling time to fit neatly within the reduced-doubling-time pattern you’re highlighting.

    All of which seems like a very tall order for these mystery factors F.

    • This is the essential problem with “weak clues.” It amounts to cherry picking coincidences.

      • To cherry pick, I’d need to pick. But I’m telling you about all the big correlations I can see.

  • Anders Sandberg

    A dynamical systems approach: The growth of a system can be represented a X'(t)=MX(t), where M is some matrix denoting how the different components of X(t) interact. If it has eigenvalues lambda_i the solutions are of the form X(t)=sum_i c_i exp(lambda_i t). Obviously there is some big positive real part of some eigenvalue (let’s say lambda_1) driving the overall exponential growth. If we look at the rest, X(t)/c_1 exp(lambda_1 t) = 1 + sum_{i>1} (c_i/c_1) exp( (lambda_i – lambda_1) t), we can get oscillations if some of those lambda_i have imaginary components. The frequency depends on the size of the components: there is no particular reason except the structure of M for it to be a 1:3 ratio, and maybe a different economy/species would have a different ratio.

    So when we move to a new growth mode M changes so the main eigenvalue lambda_1 becomes larger. If all eigenvalues are multiplied by the same factor then the frequency also scales up proportionally. That would fit Robin’s suggestion.

    Of course, the next mystery is why growth modes merely multiply eigenvalues (for example by replacing M with kM where k>1). It is unsurprising that we get exponential growth in a model like this, but it is not obvious why growth modes should have related matrices. At least not to me.

    • Yup, it isn’t at all obvious, but it is intriguing.

  • Jens Nordmark

    It would be cool if one could find corresponding cycles for the pre-human modes.

  • Theresa Klein

    If a new mode were to follow these patterns, it would appear in the next
    century, after a transition of ten years or less, and have a doubling
    time of about a month, a main cycle of about a week, and a typical group
    size of a trillion.

    The Twitter News Cycle in a nutshell.

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