Snow time

Before 720 million years ago, we find thick limestone deposits left by decaying algae. These were sequestering carbon, taking carbon dioxide out of the atmosphere, and cooling the Earth. At some point a positive feedback cycle kicked in, as polar seas froze and reflected more sunlight, cooling the planet further. The result was a succession of extreme Ice Ages. The Ice Age of the last two million years, which merely covered high latitudes with glaciers, off and on, were nothing compared to the Snowball Earth of the Cryogenian: at a minimum, polar seas were frozen, and tropical seas were slushy with icebergs. It’s possible that things were even more extreme: the entire sea may have been covered by a thick layer of ice, with a few photosynthetic algae surviving in the ice, and other organisms hanging on around deep sea hot water vents. A limited amount of oxygenated meltwater seeping into the ocean from under the glaciers may have kept early oxygen-breathers alive. For a hundred million years, climate oscillated abruptly between two steady states, frozen and warm.

It’s only in the last two decades we’ve begun to figure out this amazing story. If there’s a lesson here, it’s that Earth over the long run is far from a stable system. We will see again and again that the history of life, like human history, has been punctuated by catastrophes.

Above, a rock dropped from an iceberg or glacier into the middle of a tropical ocean

Power laws, earthquakes, and war

On Boxing Day (December 26) 2004, a tsunami resulting from a 9.0+ magnitude earthquake killed about 250,000 people around the Indian Ocean. This was one of the deadliest natural disasters in recorded history. The Indian Ocean tsunami illustrated a major theme on this blog: the importance of catastrophes in human history, and in the history of life and the universe.

Earthquakes are one example of a phenomenon following a power law statistical distribution. The frequency of earthquakes drops off as an exponential function of their magnitude, so that on a logarithmic scale, the magnitude-frequency relationship looks linear. This is known as the Gutenberg-Ritter relation. (The deviation from linearity in the upper left part of the chart below may reflect measurement error, with a lot of tiny earthquakes not being detected.)

Power law distributions are found in many other contexts, for example, in the frequency of wars versus their magnitude (as measured by the number of war deaths). A power law distribution is very different from the more familiar bell-curve Gaussian normal distribution: extreme “black swan” events that are astronomically unlikely under a normal distribution may happen at appreciable frequency under a power law distribution. Depending on the exponent, a power law distribution may not have a well-defined variance, or even a well-defined mean.

For a technical discussion of why small scale processes sometimes aggregate to generate normally distributed outcomes, and other times aggregate to produce power law distributions, here’s an article on The common patterns of nature. A take home lesson – not always covered in introductory treatments of statistics and probability theory – is that catastrophes and extreme outcomes can be an expectable part of the natural order.

The limits to growth

Different decades have been obsessed with different doomsdays. From the 1940s to the early 1960s, people worried especially about nuclear war. From the late 1960s on, fears of overpopulation and ecological doom came to the fore. John Brunner’s Stand on Zanzibar (1968) is still one of the best science fictional imaginings of a planet cracking apart under the stress of overpopulation, a richly detailed piece of world-building. Like all visions of the future, it reflects the time it was conceived in, carrying a sense that the cultural revolutions of the 60s were spinning out of control.

For non-fiction there was The Limits to Growth (1972). Here is Scenario 1 from the book, generated by a computer model of the interaction of population, resources, industry, food, and pollution. Fiddling with the model suggested that it would be very hard to avoid a massive collapse in one form or other. If the exhaustion of resources didn’t get you, pollution would do the job.

The idea that overshoot-and-collapse is a fundamental recurring pattern in human history continues to be influential. Jared Diamond’s Collapse is a recent expression. Yet one of Diamond’s case studies, Easter island, now seems fairly shaky. And the most famous decline-and-fall of all – that of the Roman empire – also doesn’t look much like a Malthusian crunch. Here’s my recent take on this: a story of “barbarigenesis,” wealth/power mismatch, rent-seeking, and collapse.

None of this is meant to suggest that we shouldn’t worry about our ecological future. Rather that we should be thankful that we’re now getting to be rich enough that we can worry less about immediate subsistence threats and more about distant dangers.

Gradualism

1824 – 1836

Charles Lyell’s great work, Principles of Geology, came out between 1831 and 1833. Lyell advocated an uncompromising uniformitarianism: the same geological forces at work today, causing small changes over the course of lifetimes, were at work in the past, causing massive changes over the course of geological ages. We’ve seen over the course of this blog that uniformitarianism is not a completely reliable guide either to geology or to human history, which have been punctuated often enough by catastrophes – asteroid strikes, continent-scale floods, volcanic eruptions, and devastating wars and plagues. But the theory is nonetheless at least part of the story of history, and Lyell’s work was deservedly influential.

In 1837 Charles Darwin, a careful reader of Lyell, published a short article entitled On the Formation of Mould. This would eventually led to his last book, The Formation of Vegetable Mould through the Action of Worms. Darwin’s work on soil formation was Lyellianism in miniature. He demonstrated, through a combination of careful reasoning and experiment, that the surface layer of pasture soil is formed by earthworms. “Although the conclusion may appear at first startling, it will be difficult to deny the probability that every particle of earth forming the bed from which the turf in old pasturelands springs, has passed through the intestines of worms.” Reading Darwin on worms you get the feeling he identifies with his humble subjects, gradually remaking the world through their patient industry.

The doctrine of progress through gradual change was appealing for more than just scientific reasons. In the 1830s, English liberals (of whom Darwin was one) were attempting to reform their society gradually, without the violence of the French Revolution, and without turning over politics to a Great Man in the style of Napoleon. (Darwin was also a gradualist with regard to his own work: he came up with the theory of natural selection in 1838, but England at the time wasn’t ready for anything so radical, and he didn’t publish On The Origin of Species for another twenty years.)

George Eliot (Mary Ann Evans), a friend of Darwin’s, set her greatest novel, Middlemarch, around the time of the Reform Act of 1832, which moved England one big step closer to a genuinely representative government. The novel’s heroine, Dorothea Brooke, might in another age have been a famous saint, another Theresa of Avila. In the England of her time she has another fate. Here is the famous conclusion of the novel, a paean to gradualism and the cumulative force of small deeds:

Her full nature … spent itself in channels which had no great name on the earth. But the effect of her being on those around her was incalculably diffusive: for the growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs.

Empires and barbarians

The fall of Rome involved the disintegration of the Roman state; the collapse of long-distance trade; the disappearance of mass-produced pottery, coinage, and monumental architecture over large areas; declining literacy among commoners and elites; great insecurity of life and property, and demographic collapse. The process was drawn out and played out differently in different regions. In the Eastern Mediterranean and Middle East, central government supported by taxation continued; in the West it largely disappeared. The nadir in the West was perhaps the tenth century. We might set the turning point at the battle of Lechfeld (955): a last set of invaders off the steppes, the Magyars, was defeated by the Emperor Otto, and then adopted Christianity, gave up nomadic marauding, and settled down as feudal lords in Hungary.

The fall of Rome illustrates a general lesson. The overall trend of history is for more complex societies to replace less complex. (Important note: “more complex” is not the same as “nicer.”) But the process is an uneven one, in part because military effectiveness is only loosely coupled with social complexity. Tribal peoples with states next door often react by developing states of their own, partly to defend against their civilized neighbors, partly to prey on them. The resulting societies – no longer tribal, not really civilized, but barbarian – have sometimes been more than a match militarily for their more complex neighbors. In Europe, the result over nearly a millennium was a great leveling process. Rome declined under barbarian assault, while state organization, class stratification, and Christianity spread eventually as far as the Slavic East and the Scandinavian North. (See Peter Heather’s Empires and Barbarians.)

By the end of the first millennium, Western Christendom had some consciousness of itself as distinct from the Islamic world; this would later help motivate the Crusades, but it would never be enough to spur unification. Much later, in the twentieth century, Europe would be divided by a different set of meta-ethnic frontiers, centered on the clash of ideologies, rather than civilization versus barbarism. But that’s a story for later

Bring out your dead

579 – 658

We’re now taking history less than one century per day.

Something major happened to Earth’s atmosphere in 535. We have reports from around the world of the sun being darkened or blotted out for more than a year, and evidence from tree rings and ice cores of an extreme cold spell. The culprit might have been dust thrown into the atmosphere by volcano or a comet. This on its own must have been bad news for the world’s population. But even more consequential was what happened starting seven years later. In 542, bubonic plague made an appearance in the Egyptian port of Pelusium, and rapidly spread around the Mediterranean, eventually reaching much of western Europe and Persia. (China seems to have gotten off more lightly.) It’s possible the epidemic had its origin among rodents in the east African Great Lakes region: disturbances to these populations after 535 may have contributed to the spread of plague, either up the Nile valley, or to trading towns on the Indian Ocean. Recent genetic evidence has confirmed that plague bacteria from this period are almost identical to those from the later, better known Black Death in the late Middle Ages. The plague struck repeatedly around west Eurasia for the next 200 years, before disappearing. The death toll must have been many tens of millions.755

Major movements of peoples would follow the plague in the sixth and seventh centuries. The Byzantine reconquest of most of the western Roman Empire, under Justinian, came undone as a new wave of Germanic barbarians, the Lombards, occupied Italy. The Anglo-Saxons expanded from the east of England to occupy most of present-day England. Slavs moved south to occupy most of the Balkans. And, most consequentially, Arabs under the banner of Islam occupied most of the Middle East and North Africa.

Plagues and peoples

210 – 309

Every day on Logarithmic History we cover an interval 5.46% shorter than the preceding day. From covering the first 754 million years after the Big Bang on January 1, we’re down to one century worth of history today.

And it’s a bad century for both Rome and China. Rome goes through an economic crisis, with a huge currency devaluation. Political life goes to hell too. From 235-284 there are 20 Emperors; 18 of them die violently. The Roman Empire experiences multiple, destructive invasions by barbarians. Previously under the Pax Romana, most of the cities of the Empire, including Rome, had been unwalled; now there is a spate of wall-building. The empire recovers toward the end of the century, but in a more heavily militarized and authoritarian form. And in China the Han dynasty disappears entirely after 220, to be replaced by three kingdoms of barbarian origin.

This coincidence of catastrophes may be more than just bad luck. Put it this way: If we look at the Big Picture, going way back on our calendar, and turning for a moment from human history to the evolution of life, we can summarize biological evolution since the Cambrian as:

• A process of escalation, in which arms races among organisms are major drives of progressive evolution …

but …

• Now and then, a physical catastrophe punctuates the history of life, causing mass extinctions, from which living things slowly recover.

Returning to human history, we can summarize social evolution since the adoption of agriculture as:

• A process of escalation, in which conflicts between rival groups (matrilineal and patrilineal kin groups, empires, and – we will see – major religions) are drivers of increasing social complexity …

but…

• Now and then, a biological catastrophe – in the form of an epidemic of some new disease – punctuates human history, causing major population losses, and often political and social collapse as well (i.e. the “germs” in Guns, Germs and Steel).

One such catastrophe contributed to the collapse of New World societies in the face of Old World diseases after 1492. But the Old World too must have had its own earlier catastrophes as the great killer diseases – the diseases of civilization that need a minimum population to keep going – established themselves.

Epidemic disease may have made a major contribution to the fall of Rome and of Han China. Rome suffered two massive epidemics, one from 165-180, another from 251-266. It’s plausible (and some day geneticsts will tell us whether it’s true or not) that these epidemics represent the arrival of smallpox and measles in the West. There is also evidence from the current distribution of tuberculosis strains that the expansion of the Roman Empire, and trade across borders, helped to spread this disease. And we’ll run into bubonic plague in a few days time (Saturday, October 13). There may be a similar story to tell about China, also stricken by epidemics at this time. The opening of the Silk Road and of trade across the Indian Ocean allowed precious goods and new ideas to travel between civilizations. It also opened the way for lethal microorganisms.

In addition to “Guns, Germs and Steel,” a classic book here is William McNeill’s Plagues and Peoples. For the Roman empire, more up-to-date, and with a wealth of information, is The Fate of Rome: Climate, Disease, and the End of an Empire.

Snow time

744 – 705 million years ago

The United States has been hit by a major winter storm. I’ve been out shoveling snow from the driveway several times today. In-person classes at my university were cancelled, and I’ll probably take the light rail into school tomorrow rather than braving the streets with my car.

But things have been worse. Before 720 million years ago, we find thick limestone deposits left by decaying algae. These were sequestering carbon, taking carbon dioxide out of the atmosphere, and cooling the Earth. At some point a positive feedback cycle kicked in, as polar seas froze and reflected more sunlight, cooling the planet further. The result was a succession of extreme Ice Ages. The Ice Age of the last two million years, which merely covered high latitudes with glaciers, off and on, were nothing compared to the Snowball Earth of the Cryogenian: at a minimum, polar seas were frozen, and tropical seas were slushy with icebergs. It’s possible that things were even more extreme: the entire sea may have been covered by a thick layer of ice, with a few photosynthetic algae surviving in the ice, and other organisms hanging on around deep sea hot water vents. A limited amount of oxygenated meltwater seeping into the ocean from under the glaciers may have kept early oxygen-breathers alive. For a hundred million years, climate oscillated abruptly between two steady states, frozen and warm.

It’s only in the last two decades we’ve begun to figure out this amazing story. If there’s a lesson here, it’s that Earth over the long run is far from a stable system. We will see again and again that the history of life, like human history, has been punctuated by catastrophes.

Above, a rock dropped from an iceberg or glacier into the middle of a tropical ocean

Power laws, earthquakes, and war

On Boxing Day (December 26) 2004, a tsunami resulting from a 9.0+ magnitude earthquake killed about 250,000 people around the Indian Ocean. This was one of the deadliest natural disasters in recorded history. The Indian Ocean tsunami illustrated a major theme on this blog: the importance of catastrophes in human history, and in the history of life and the universe.

Earthquakes are one example of a phenomenon following a power law statistical distribution. The frequency of earthquakes drops off as an exponential function of their magnitude, so that on a logarithmic scale, the magnitude-frequency relationship looks linear. This is known as the Gutenberg-Ritter relation. (The deviation from linearity in the upper left part of the chart below may reflect measurement error, with a lot of tiny earthquakes not being detected.)

Power law distributions are found in many other contexts, for example, in the frequency of wars versus their magnitude (as measured by the number of war deaths). A power law distribution is very different from the more familiar bell-curve Gaussian normal distribution: extreme “black swan” events that are astronomically unlikely under a normal distribution may happen at appreciable frequency under a power law distribution. Depending on the exponent, a power law distribution may not have a well-defined variance, or even a well-defined mean.

For a technical discussion of why small scale processes sometimes aggregate to generate normally distributed outcomes, and other times aggregate to produce power law distributions, here’s an article on The common patterns of nature. A take home lesson – not always covered in introductory treatments of statistics and probability theory – is that catastrophes and extreme outcomes can be an expectable part of the natural order.

Steven Pinker and Nichlas Nassim Taleb have squabbled about the implications of all this for the probability of a peaceful future. Here’s a level-headed review. Several recent books carry this argument further. In Only the Dead: The Persistence of War in the Modern Age, Bear Braumoeller makes the case there is no good reason to think that war is in decline. Rather “international orders” – whether the nineteenth century Concert of Europe, or the post World War II liberal order – have often made for peace among participants and conflicts with non-participants. On the other side, in The Stupidity of War: American Foreign Policy and the Case for Complacency, John Mueller makes the case that the likelihood of war was and is greatly exaggerated, both during and after the Cold War, and argues for the virtues of complacency and appeasement. Of course this year’s Russian invasion of Ukraine forces us to revise our estimate of the probability of major war upward, but it doesn’t prove Pinker wrong: a snow storm in April doesn’t prove that March isn’t a wintrier month.

And here are a couple of blog posts from me about why the bloody early twentieth century was maybe more than just a run of bad luck.

Gradualism

1823 – 1835

Charles Lyell’s great work, Principles of Geology, came out between 1831 and 1833. Lyell advocated an uncompromising uniformitarianism: the same geological forces at work today, causing small changes over the course of lifetimes, were at work in the past, causing massive changes over the course of geological ages. We’ve seen over the course of this blog that uniformitarianism is not a completely reliable guide either to geology or to human history, which have been punctuated often enough by catastrophes – asteroid strikes, continent-scale floods, volcanic eruptions, and devastating wars and plagues. But the theory is nonetheless at least part of the story of history, and Lyell’s work was deservedly influential.

In 1837 Charles Darwin, a careful reader of Lyell, published a short article entitled On the Formation of Mould. This would eventually led to his last book, The Formation of Vegetable Mould through the Action of Worms. Darwin’s work on soil formation was Lyellianism in miniature. He demonstrated, through a combination of careful reasoning and experiment, that the surface layer of pasture soil is formed by earthworms. “Although the conclusion may appear at first startling, it will be difficult to deny the probability that every particle of earth forming the bed from which the turf in old pasturelands springs, has passed through the intestines of worms.” Reading Darwin on worms you get the feeling he identifies with his humble subjects, gradually remaking the world through their patient industry.

The doctrine of progress through gradual change was appealing for more than just scientific reasons. In the 1830s, English liberals (of whom Darwin was one) were attempting to reform their society gradually, without the violence of the French Revolution, and without turning over politics to a Great Man in the style of Napoleon. (Darwin was also a gradualist with regard to his own work: he came up with the theory of natural selection in 1838, but England at the time wasn’t ready for anything so radical, and he didn’t publish On The Origin of Species for another twenty years.)

George Eliot (Mary Ann Evans), a friend of Darwin’s, set her greatest novel, Middlemarch, around the time of the Reform Act of 1832, which moved England one big step closer to a genuinely representative government. The novel’s heroine, Dorothea Brooke, might in another age have been a famous saint, another Theresa of Avila. In the England of her time she has another fate. Here is the famous conclusion of the novel, a paean to gradualism and the cumulative force of small deeds:

Her full nature … spent itself in channels which had no great name on the earth. But the effect of her being on those around her was incalculably diffusive: for the growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs.