The Progress Equation

In 1960: The Year the Singularity was Cancelled, Scott Alexander discusses what I'll call the progress equation. The equation states that technological progress increases the carrying capacity of the environment (the size of the largest population which can sustain itself with the resources available), but also, that technological progress is itself proportional to population (more people, more brains, more progress). This turns out to imply hyperbolic growth, with a singularity of infinite population around 2026.

As indicated in the title of Scott's post, the progress equation stopped being a good model of population growth around 1960. My personal interpretation is that this is merely the time when technological growth outpaced population growth: the carrying capacity started rising faster than the exponential growth of the population. You see, the progress equation assumes that the population is always around carrying capacity (we could call this "the Malthusian assumption"). This is usually a pretty fair assumption; populations will boom and crash, but hover around the carrying capacity.

However, once the population is large enough that technological growth outpaces population growth, we should expect to enter into the exponential regime: population and technology grow at a merely exponential pace, so we don't see a hard singularity like we get if we extrapolate hyperbolic growth. More thoughts on this here.

Bronze Age Collapse

I recently watched this video series on the Bronze Age Collapse. It's very speculative, because we know very little about what really happened; in most places, writing and permanent settlement disappear shortly after, making records of the event scarce. One theory is that a powerful armada, "the sea people", simply wiped out every mediterranean civilization at once for some reason. But the theory which the video series focuses on is the "system collapse" theory:

  • Over time, civilization builds up infrastructure.
  • Infrastructure increases the carrying capacity, and also smooths out small boom and bust cycles.
  • However, infrastructure also tends to centralize things, meaning that people become dependent on infrastructure.
  • Resources tend to have fixed maintenance costs. As a society gains more infrastructure, maintenance costs increase.
  • When a severe bust cycle hits, a society's resources may fall below the maintenance costs of its centralized infrastructure. The infrastructure then fails. Because society has become dependent on this infrastructure, this exacerbates the problem. This can create a domino effect between different types of infrastructure, so everything collapses at once.
  • Because Bronze Age civilization was highly dependent on trade, the domino effect also continued across the whole set of bronze-age civilizations across the Mediterranean.

This suggests a modification of the progress equation. Rather than "technological progress" being a number which just counts up as people invent things, we can think of it as requiring some population size to support. When the population dips below that number, technological progress is lost. This further worsens the situation for the remaining population, causing a dramatic crash.

Seeing Like a State

Why does technological progress usually lead to centralization and increasing dependence? By design. Combining insights from Seeing like a State and The Dictator's Handbook, we can see how increasing centralization and dependence is to the advantage of a state. It allows the state to extract resources more efficiently, even if it's not to the overall benefit of the people. (It becomes amazing that we make progress at all, when you think of it this way: it's often to the state's advantage to keep the population ignorant and poor.)

Urban Sprawl

The youtube channel Not Just Bikes provides detailed pro-walkability anti-urban-sprawl rants, by a knowledgeable urban planning enthusiast. In the series Strong Towns (which summarizes points from a book of the same name), it describes how urban sprawl operates in North America. The point that's relevant for us is the infrastructure Ponzi scheme: how cities usually can't presently afford to maintain the infrastructure they build, instead relying on future growth to pay for it. This leads to a cycle:

  • Build fancy new stuff to facilitate growth and bring in tax dollars, without worrying about how to pay for maintenance costs later.
  • Grow. Rake in tax dollars. Use them to keep up the old infrastructure.
  • Panic when the new infrastructure starts to decay, and there's not enough money to pay for its upkeep.
  • Return to the first step, building an even larger set of new developments, to bring in growth and therefore tax dollars which will repair older infrastructure.

This works pretty well until it doesn't. Then you get bankrupt cities like Detroit, with crumbling districts slowly returning to nature.

I think you can see where I'm going with this. I don't think I can Bronze Age civilizations had urban sprawl, but I think ancient empires may have fallen into the same growth-dependent "ponzi scheme" as modern cities. This exacerbates the instabilities created by centralized infrastructure. With growth-dependent economics, a crisis can be caused when growth merely slows down too much to keep the Ponzi scheme going.

Will we see collapse?

Is the modern population highly dependent on highly centralized technology? Yes. Do we have growth-dependent economics? Yes. Has that growth been slowing down? Arguably, yes. Are modern civilizations highly interdependent, relying on trade for basic needs? Yes. We've just seen the consequences of a global trade disruption. The prices of everything have recently increased by about 15%. That's a mark-up which many cannot afford. Many items are in severely short supply. (I recently walked into a local bike shop to buy a bike. They didn't have any, except for a few multi-thousand dollar models which I guess they keep around in case a wealthy customer comes in. The shopkeeper told me to check back next week to see if they'd gotten anything in.)

It also just so happens that the US government has been creating money like mad. It's easy to tell a story where the inflation of prices will only get worse, the dollar collapses, and things spiral further out of control from there.

But I think every age has similarly compelling doomsday stories. They've got a fairly bad track record overall. The same pessimistic story could have been told around 2008, and at many other times. If we're going to collapse now, why didn't we then? Centralization and trade-dependence are not new. We have a few advantages which Bronze Age civilization did not.

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14 comments, sorted by Click to highlight new comments since: Today at 2:55 AM

Dear Abram,

The system collapse theory of Bronze Age Collapse is nuanced, complex, sophisticated and most likely wrong.

As a general rule, historians love explanations that emphasize 'complexity' and 'nuance'. Be very wary of these explanations. They sound great as a verbal explanation but they are highly flexible hypotheses that are difficult to falsify and can easily explain any amount of data. The perfect fit for verbal bullshitters - which probably accurately describes the vast majority of non-quantitative social theorists -like historians.

A little experience with dynamical systems will show how problematic these models are. Be wary anytime somebody is talking about 'multicausal' explanations. There are typically two regimes: something is made out of many many independent factors, giving Gaussian distributions or there is one or two dominant eigenfactors that explain the vast majority of the variance. I could say more about this. 

The most likely explanation for Bronze Age collapse is changes in warfare: elite corps of chariot archers losing out to javelin -throwing massed infantry consisting of a melange of experienced mercenaries. Earlier infantry-based tactics were ineffective against the sophisticated hit-and-run tactics of corps of chariot archers but eventually new tactics were devised - like using javileneers to hit the horses and wheels of chariots. 

 Writing and much of the archeological finds of this period rely on a demand for luxury- trade and elite scribes. Once the chariot-archer elites disappeared so did their luxury trade and elite scribes; hence a 'collapse'. 

Much more can be found in Drews' excellent book "The End of the Bronze Age: Changes in Warfare and the Catastrophe ca. 1200 B.C."

Thanks, very interesting!

I still think that a good modification to the progress equation would be to lose progress if population dips below some number, and, that this predicts that severe population crashes will be amplified even further as progress is lost.

Or, in less formal terms: I still think knowledge can be lost quickly in times of chaos, particularly when population takes a nose-dive.

So I believe in the gears of the theory I was referring to, even if it's not the "primary cause"?

Dear Abram,

I have a little bit of a knee-jerk reaction to 'complex, nuanced, multicausal' explanations by historians in general and the Late Bronze Age collapse specifically. On a reread my reaction was perhaps a little overzealous.

The system collapse theory, due to Joseph Tainter(?), is not crazy. It does suffer from being overly flexible, hard to test etc. 

 I agree that "I still think knowledge can be lost quickly in times of chaos, particularly when population takes a nose-dive."

The following is also plausible

" a good modification to the progress equation would be to lose progress if population dips below some number"

Something like this is often argued to have happened with Tasman island, with Tasmanians losing basic technology like fishing, firemaking, and generally being less technologically sophisticated than their ancestors 8000 years before. However, last time I actually checked the details; Tasmanians losing firemaking at least seemed to be a myth.

Two undeniable historical cases of losses of technological ability are the late Western Roman Empire and the end of the Hellenistic Age. This is probably not tied to large changes in population size. Knowledge being lost quickly in times of chaos is not implausible, e.g. the siege of Syracuse or the Crisis of the Third Century. Many theories about these historical epochs are possible and contested. 

EDIT: another case of a large loss of knowledge is the Sacking of Baghdad (1258) by the Mongols. It does fit in "I still think knowledge can be lost quickly in times of chaos, particularly when population takes a nose-dive." On the other hand, is no need for an overtly complex theory. Horse-archer based steppe peoples burning down settled-down societies is a repeating theme in history. 

EDIT2: I looked into Joseph Tainter's theory of system collapse. He looks at three cases: Chaco collapse, Maya collapse, fall of Rome. From my reading of the literature there is fairly good evidence for a drought explanation for the Maya collapse - actually there are multiple Mayan collapses, drought based stories are apparently plausible for all three of them, but I am not an expert. My impression was that most experts in the Chaco favor enviromental causes as well - I don't know enough to have a strong opinion. 

The fall of Rome is of course hotly contested, so I won't go into it. Suffice to say there are many possibilities here. A strong contender is probably Peter Turchin's Assabiyah theory. 

Your argument has a Holocene, sedentary, urban flavor, but I think it applies just as well to Pleistocene, nomadic cultures; I think of it as an argument about population size and 'cognitive capital' as such, not only about infrastructure or even technology. Although my confidence is tempered by mutually compatible explanations and taphonomic bias, my current models of behavioral modernity and Neanderthal extinction essentially rely on a demographic argument like the one made here. I don't think this comment would be as compelling without a reminder that almost everyone explains these phenomena via interspecies differences in individual cognitive adaptation, as opposed to demography.

On behavioral modernity, I am a gradualist; I do not think there was a sudden pulse of innovation. Signs of modernity, like a wider resource base, public symbol use, and certain technologies appear and then disappear, before becoming a permanent fixture later in the record. The most striking example of this would be ancient Australia, where humans did not reliably demonstrate all features of behavioral modernity for the first 25,000 years of residence even though these features were present in contemporaneous cultures in different geographic locations; Australia also happens to be one of the last places to which humans migrated. The idea here is that reduced population size, and thus density, affects the fidelity and bandwidth of social learning in lots of ways (e.g. decreased redundancy and specialization), resulting in a less sophisticated behavioral repertoire, as well as reduced selection for public symbol use (since there are no frequently encountered outgroups to which to signal).

On Neanderthal extinction, I think this is a collapse in the sense of your post, by a failure to reliably transmit cognitive capital. The life history of hominins is similar to a case of growth-dependent economics, where large energy and time investments are made under the expectation of future economic productivity. While I think environmental effects started the decay, temperate specialists as the Neanderthals were, I think they went extinct ultimately because these effects started a process that gradually invalidated the preconditions for reliable cultural transmission in that species.


I think they went extinct ultimately because these effects started a process that gradually invalidated the preconditions for reliable cultural transmission in that species

Yeah. I hope Youtube knows what it's doing.

In the videogame "Starcraft", it's economics (macro) that wins wars. A player can win every single battle (micro) and still lose the game, if the other player's economy is improving their relative position faster than they are losing militarily. A common tactic is to make small attacks on the other player's economy production units, attempting to do a lot of economic damage without fighting any military units. The true scope of the damage might not be obvious, since the "fog of war" conceals most of what the other player is doing. I remember one game where I thought I was doing quite well, despite several early attacks damaging my economy, and then suddenly a giant army just marched through my base destroying everything. Not good. It seems that for a city to be prosperous it needs to have an economy capable of producing a powerful military force, then actually use that economy to produce a powerful military force. It's probably not a healthy way to live, but sometimes when I look out at a city I think back to my Starcraft days. When I feel good about the city, I imagine unit production buildings and dug-in artillery as far as the eye can see. When I feel bad about the city, I imagine Zerglings and fire. This is probably not a healthy way to live, but it does focus the mind.

Thinking back, I had some friends who told me that I should focus more on doing what I enjoyed, and focus less on doing the right thing. In retrospect, those were bad friends who wanted to justify their own lack of vision.

"The Last Psychiatrist" (blog) explains that it's easier to reform society than to reform oneself, and people often look to fix the society around them instead of looking to fix themselves. The apocalypse to avoid is not of society collapsing, but of the individual collapsing: of failing to obtain a house and have children, or whatever most represents individual collapse.

The point that’s relevant for us is the infrastructure Ponzi scheme: how cities usually can’t presently afford to maintain the infrastructure they build, instead relying on future growth to pay for it.

Ive seeen is pushback against that. Apparently the claim as not that suburbs aren't supporting, but things look different when you include business districts.

Interesting, any references?

It becomes amazing that we make progress at all, when you think of it this way: it's often to the state's advantage to keep the population ignorant and poor.

States are also in competition with each other. A state with more military innovations can invade you. A state with more advanced culture can assimilate you. Your population can defect and move to a state that offers them a better deal.

Right. My point is just that the state will heavily favor centralized technology to address these challenges, because it prefers to maintain control. Seeing like a State illustrates how this can result in much worse productivity overall (in contrast to pre-existing noncentralized systems), while still being much better for the state (due to increased tax revenue, and diminished risk of rebellion).

It occurs to me that from a system robustness perspective, luxury is actually great, because it implies surplus capacity (assuming society can and will divert luxury-production to essentials-production in a crisis).

From the perspective of the state, you want to tax that excess, and store as much of it as you can for lean times (at which point you do hand it back out to the people, to preserve the population). This was a major function of bronze age states. So yeah, it increases robustness, but the state still isn't really incentivized to let people keep wealth (except for the key players, which the state has to make happy to avoid coups).

In Dictators Handbook, Bruce Bueno de Mesquita presents evidence that centralized authoritarian governments (like most bronze age governments) tend to avoid enriching their citizens if they can accumulate resources without doing so. In the other hand, if the people themselves are the only available source of wealth (ie if natural resources are scarce and a state's economy must therefore rely on skilled labor and trade), the state will tend to become less authoritarian, I think.