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Posts Tagged ‘Chaos

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality”*…

An illustration featuring a person gardening surrounded by large, stylized infinity symbols and vibrant clouds, symbolizing concepts of infinity in mathematics.

As Gregory Barber explains, two new notions of infinity challenge a long-standing plan to define the mathematical universe…

It was minus 20 degrees Celsius, and while some went cross-country skiing, Juan Aguilera, a set theorist at the Vienna University of Technology, preferred to linger in the cafeteria, tearing pieces of pulla pastry and debating the nature of two new notions of infinity. The consequences, Aguilera believed, were grand. “We just don’t know what they are yet,” he said.

Infinity, counterintuitively, comes in many shapes and sizes. This has been known since the 1870s, when the German mathematician Georg Cantor proved that the set of real numbers (all the numbers on the number line) is larger than the set of whole numbers, even though both sets are infinite. (The short version: No matter how you try to match real numbers to whole numbers, you’ll always end up with more real numbers.) The two sets, Cantor argued, represented entirely different flavors of infinity and therefore had profoundly different properties.

From there, Cantor constructed larger infinities, too. He took the set of real numbers, built a new set out of all of its subsets, then proved that this new set was bigger than the original set of real numbers. And when he took all the subsets of this new set, he got an even bigger set. In this way, he built infinitely many sets, each larger than the last. He referred to the different sizes of these infinite sets as cardinal numbers (not to be confused with the ordinary cardinals 1, 2, 3…).

Set theorists have continued to define cardinals that are far more exotic and difficult to describe than Cantor’s. In doing so, they’ve discovered something surprising: These “large cardinals” fall into a surprisingly neat hierarchy. They can be clearly defined in terms of size and complexity. Together, they form a massive tower of infinities that set theorists then use to probe the boundaries of what’s mathematically possible.

But the two new cardinals that Aguilera was pondering in the Arctic cold behaved oddly. He had recently constructed them, along with Joan Bagaria of the University of Barcelona and Philipp Lücke of the University of Hamburg, only to find that they didn’t quite fit into the usual hierarchy. Instead, they “exploded,” Aguilera said, creating a new class of infinities that their colleagues hadn’t bargained on — and implying that far more chaos abounds in mathematics than expected.

It’s a provocative claim. The prospect is, to some, exciting. “I love this paper,” said Toby Meadows, a logician and philosopher at the University of California, Irvine. “It seems like real progress — a really interesting insight that we didn’t have before.”

But it’s also difficult to really know whether the claim is true. That’s the nature of studying infinity. If mathematics is a tapestry sewn together by traditional assumptions that everyone agrees on, the higher reaches of the infinite are its tattered fringes. Set theorists working in these extreme areas operate in a space where the traditional axioms used to write mathematical proofs do not always apply, and where new axioms must be written — and often break down.

Up here, most questions are fundamentally unprovable, and uncertainty reigns. And so to some, the new cardinals don’t change anything. “I don’t buy it at all,” said Hugh Woodin, a set theorist at Harvard University who is currently leading the quest to fully define the mathematical universe. Woodin was Bagaria’s doctoral adviser 35 years ago and Aguilera’s in the 2010s. But his students are cutting their own path through infinity’s thickets. “Your children grow up and defy you,” Woodin said…

More on the fascinating state of play at: “Is Mathematics Mostly Chaos or Mostly Order?” from @GregoryJBarber in @quantamagazine.bsky.social‬.

* Albert Einstein

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As we get down with Gödel, we might send insightful birthday greetings to John Allen Paulos; he was born on this date in 1945. A mathematician, he is best known as an advocate for– and a skilled teacher of– mathematical literacy. His book Innumeracy: Mathematical Illiteracy and its Consequences (1988) was a bestseller, and A Mathematician Reads the Newspaper (1995) extended the critique. Paulos was a regular columinst for both The Guardian and ABC News. And in 2001 he created and taught a course on quantitative literacy for journalists at the Columbia University School of Journalism– an exercise that stimulated further programs at Columbia and elsewhere in precision and data-driven journalism.

A portrait of John Allen Paulos, a mathematician known for advocating mathematical literacy, smiling while wearing a dark blazer over a white shirt.

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Happy 4th of July to readers in the U.S… but are we commemorating the right day?

Written by (Roughly) Daily

July 4, 2025 at 1:00 am

“Power always reveals”*…

An illustration depicting a giant figure, representing Leviathan, made up of numerous smaller human forms falling away, holding a sword and staff, with a distant medieval town in the background.

Apposite to yesterday’s post, a provocative piece by Ben Ansell, who is reacting to a [terrific] piece by Henry Farrell in which Farrell, as he contemplates Trump’s moves, unpacks the “coordination” problems facing– and, Farrell suggests, often limiting– autocratic rulers…

… But you will notice an assumption I and Henry have been making – that Trump is like any other authoritarian leader. I suspect that in lots of ways Trump does wish to behave like one – certainly the treatment of Kilmar Abrego Garcia and his current refusal to follow court judgments meets that mark.

But Trump is attempting this in an otherwise democratic system and I think there is a risk that we overstate the degree to which that system has already deteriorated by assuming that the language and logic that we use to describe authoritarianism fits his case. Part of the risk is we give up on democracy while it’s still here. But the other danger is that we think Trump behaves like a rational authoritarian leader, a la Svolik, when it’s all just bluntly a lot dumber than that…

… In an earlier post I referred to Donald Trump as a ‘chaotic authoritarian’. I don’t think it’s implausible that a democracy could have such a figure as a leader, though I do think it’s unlikely that it would remain democratic indefinitely under such leadership.

But in the absence of already having subverted elections, stymied courts, shut down the media, banned opponents and the other types of effective institutional backsliding that are the tell-tale signs of a democracy dying, I think we might do better to think about how such a figure operates in, what for now, is a democracy.

The temptation when talking about dictators is to reach for Thomas Hobbes. We depict them as the Leviathan – imposing order on the body politic to prevent chaos but also any rivals. Hobbes’ vision was after all a painstaking justification for monarchical absolutism.

If you are not familiar with Leviathan, well do read it, it’s a banger. But the very basic gist is a theory of government built from the ground up. Hobbes even starts with a slightly rococo account of how we process sensations. But his core mechanism is to imagine a world without government – his famous state of nature – in which every individual was essentially on their own. A self-help system if you will, but not the kind in the woo-woo psychology section of the bookstore – the kind where if you don’t look after number one, you’ll get an axe in the back of the head.

The Hobbesian state of nature is anarchy and life in it is – say it with me – ‘solitary, poor, nasty, brutish and short’. And so anyone living in this state would seek to escape this ceaseless terror and have some entity that could guarantee security. Hobbes is a social contract theorist, and the contract upon which we could all be presumed to agree is a third party that can ruthlessly crush insecurity. An absolute sovereign power that would protect its subjects…

… The Hobbesian vision of the state is draconian of course and in… err… pretty sharp contrast with the social contract theories of John Locke or Jean Jacques Rousseau. But one way it has come down to us is in how we think about authoritanism. As about order and control, crushing dissent mercilessly, but also preventing anarchy, rebellion, and so forth. It is governing with an iron fist. Rational authoritarianism if you will.

Whatever Trump is trying to achieve, it’s not hitting this mark. Instead of authoritarianism containing chaos, it is chaos personified. Instead of quelling the anarchic state of nature, it is spreading anarchy and confusion. Hobbes’ frontispiece Leviathan is a steady ruler, holding sword and staff, made up out of their ordered subjects [In contrast to the disintegrating beast in the illustation above]…

… Hence, it’s not clear to me that the standard tools we use to think about authoritarianism accordingly make that much sense with Trump. Is he really thinking about how to coordinate among the elites to keep his support base? Because he’s not doing a brilliant job here having already lost the support of the Wall Street journal editorial board, a litany of very conservative judges, and increasingly corporate elites…

… what I find most interesting about Trump’s anti-Leviathan is that his rule is creating anarchy everywhere else too. And that means not only are his promises not credible but nor are his threats…

[Ansell reviews Trumps’ attack on universities, his approach to tariffs, and trade policy, his “crackdown” on immigration, and his foreign policy (or lack thereof)…]

… We will spend a lot of time over the next few years trying to figure out if Trump’s America remains a democracy. Already the main indices we use are starting to downgrade the USA. I struggle as to whether that coding is premature or not – we will of course know much more by the midterms about the stability and freedom of elections, though by then it could be too late.

It is very clear that Trump wishes to act as an authoritarian. But it is not yet obvious to me that analysing him using the logic of dictatorship makes sense. Because he lacks the control, the ruthlessness, and the rationality of normal authoritarian leaders. As Henry says in his post, ‘absolute power can be a terrible weakness.’ True. However, for many – perhaps most – dictators, absolute power is a terrible (in the original sense of that word) strength. Think to the horrors of the twentieth century.

That, however, is not Donald Trump. He may be the master of chaos. But he is not the Leviathan…

What if we abandoned the social contract for the state of nature? “Donald Trump’s Anti-Leviathan,” from @benansell.bsky.social (with @himself.bsky.social).

* “Power doesn’t always corrupt. Power always reveals. When you have enough power to do what you always wanted to do, then you see what the guy always wanted to do.” – Robert Caro (riffing on Lord Acton: “Power tends to corrupt and absolute power corrupts absolutely”) Or as David Brin put it: “it is said that power corrupts, but actually it’s more true that power attracts the corruptible.”

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As we rein in reigns, we might recall that it was on this date in 1945 that Hermann Göring, head of the Luftwaffe and Adolf Hitler’s designated successor as leader of Nazi Germany, wired the Führer asking permission to assume leadership of the crumbling regime. The telegram caused an infuriated Hitler to strip Göring of power and to appoint new successors, Joseph Goebbels and Karl Dönitz, as chancellor and head of state, respectively.

A historical telegram from Hermann Göring to Adolf Hitler, dated April 23, 1945, discussing military decisions and indicating urgency regarding leadership amidst the crumbling Nazi regime.

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Written by (Roughly) Daily

April 23, 2025 at 1:00 am

“The older one gets the more convinced one becomes that his Majesty King Chance does three-quarters of the business of this miserable universe”*…

Bockscar en route to Nagasaki, 9 August 1945. US Air Force photo

In an essay adapted from his book Fluke: Chance, Chaos, and Why Everything We Do Matters, Brian Klass argues that social scientists are clinging to simple models of reality – with disastrous results. Instead, he suggests, they must embrace chaos theory…

The social world doesn’t work how we pretend it does. Too often, we are led to believe it is a structured, ordered system defined by clear rules and patterns. The economy, apparently, runs on supply-and-demand curves. Politics is a science. Even human beliefs can be charted, plotted, graphed. And using the right regression we can tame even the most baffling elements of the human condition. Within this dominant, hubristic paradigm of social science, our world is treated as one that can be understood, controlled and bent to our whims. It can’t.

Our history has been an endless but futile struggle to impose order, certainty and rationality onto a Universe defined by disorder, chance and chaos. And, in the 21st century, this tendency seems to be only increasing as calamities in the social world become more unpredictable. From 9/11 to the financial crisis, the Arab Spring to the rise of populism, and from a global pandemic to devastating wars, our modern world feels more prone to disastrous ‘shocks’ than ever before. Though we’ve got mountains of data and sophisticated models, we haven’t gotten much better at figuring out what looms around the corner. Social science has utterly failed to anticipate these bolts from the blue. In fact, most rigorous attempts to understand the social world simply ignore its chaotic quality – writing it off as ‘noise’ – so we can cram our complex reality into neater, tidier models. But when you peer closer at the underlying nature of causality, it becomes impossible to ignore the role of flukes and chance events. Shouldn’t our social models take chaos more seriously?

The problem is that social scientists don’t seem to know how to incorporate the nonlinearity of chaos. For how can disciplines such as psychology, sociology, economics and political science anticipate the world-changing effects of something as small as one consequential day of sightseeing or as ephemeral as passing clouds?

On 30 October 1926, Henry and Mabel Stimsonstepped off a steam train in Kyoto, Japan and set in motion an unbroken chain of events that, two decades later, led to the deaths of 140,000 people in a city more than 300 km away.

The American couple began their short holiday in Japan’s former imperial capital by walking from the railway yard to their room at the nearby Miyako Hotel. It was autumn. The maples had turned crimson, and the ginkgo trees had burst into a golden shade of yellow. Henry chronicled a ‘beautiful day devoted to sightseeing’ in his diary.

Nineteen years later, he had become the Unites States Secretary of War, the chief civilian overseeing military operations in the Second World War, and would soon join a clandestine committee of soldiers and scientists tasked with deciding how to use the first atomic bomb. One Japanese city ticked several boxes: the former imperial capital. The Target Committee agreed that Kyoto must be destroyed. They drew up a tactical bombing map and decided to aim for the city’s railway yard, just around the corner from the Miyako Hotel where the Stimsons had stayed in 1926.

Stimson pleaded with the president Harry Truman not to bomb Kyoto. He sent cables in protest. The generals began referring to Kyoto as Stimson’s ‘pet city’. Eventually, Truman acquiesced, removing Kyoto from the list of targets. On 6 August 1945, Hiroshima was bombed instead.

The next atomic bomb was intended for Kokura, a city at the tip of Japan’s southern island of Kyushu. On the morning of 9 August, three days after Hiroshima was destroyed, six US B-29 bombers were launched, including the strike plane Bockscar. Around 10:45am, Bockscarprepared to release its payload. But, according to the flight log, the target ‘was obscured by heavy ground haze and smoke’. The crew decided not to risk accidentally dropping the atomic bomb in the wrong place.

Bockscar then headed for the secondary target, Nagasaki. But it, too, was obscured. Running low on fuel, the plane prepared to return to base, but a momentary break in the clouds gave the bombardier a clear view of the city. Unbeknown to anyone below, Nagasaki was bombed due to passing clouds over Kokura. To this day, the Japanese refer to ‘Kokura’s luck’ when one unknowingly escapes disaster.

Roughly 200,000 people died in the attacks on Hiroshima and Nagasaki – and not Kyoto and Kokura – largely due to one couple’s vacation two decades earlier and some passing clouds. But if such random events could lead to so many deaths and change the direction of a globally destructive war, how are we to understand or predict the fates of human society? Where, in the models of social change, are we supposed to chart the variables for travel itineraries and clouds?

In the 1970s, the British mathematician George Box quipped that ‘all models are wrong, but some are useful’. But today, many of the models we use to describe our social world are neither right nor useful. There is a better way. And it doesn’t entail a futile search for regular patterns in the maddening complexity of life. Instead, it involves learning to navigate the chaos of our social worlds…

[Klass reviews the history of our attempts to conquer uncertainty, concluding with Edward Norton “Butterfly Effect” Lorenz and what he discovered when he tried to predict the weather…]

… Any error, even a trillionth of a percentage point off on any part of the system, would eventually make any predictions about the future futile. Lorenz had discovered chaos theory.

The core principle of the theory is this: chaotic systems are highly sensitive to initial conditions. That means these systems are fully deterministic but also utterly unpredictable. As Poincaré had anticipated in 1908, small changes in conditions can produce enormous errors. By demonstrating this sensitivity, Lorenz proved Poincaré right.

Chaos theory, to this day, explains why our weather forecasts remain useless beyond a week or two. To predict meteorological changes accurately, we, like Laplace’s demon, would have to be perfect in our understanding of weather systems, and – no matter how advanced our supercomputers may seem – we never will be. Confidence in a predictable future, therefore, is the province of charlatans and fools; or, as the US theologian Pema Chödrön put it: ‘If you’re invested in security and certainty, you are on the wrong planet.’

The second wrinkle in our conception of an ordered, certain world came from the discoveries of quantum mechanics that began in the early 20th century. Seemingly irreducible randomness was discovered in bewildering quantum equations, shifting the dominant scientific conception of our world from determinism to indeterminism (though some interpretations of quantum physics arguably remain compatible with a deterministic universe, such as the ‘many-worlds’ interpretation, Bohmian mechanics, also known as the ‘pilot-wave’ model, and the less prominent theory of superdeterminism). Scientific breakthroughs in quantum physics showed that the unruly nature of the Universe could not be fully explained by either gods or Newtonian physics. The world may be defined, at least in part, by equations that yield inexplicable randomness. And it is not just a partly random world, either. It is startlingly arbitrary…

… How can we make sense of social change when consequential shifts often arise from chaos? This is the untameable bane of social science, a field that tries to detect patterns and assert control over the most unruly, chaotic system that exists in the known Universe: 8 billion interacting human brains embedded in a constantly changing world. While we search for order and patterns, we spend less time focused on an obvious but consequential truth. Flukes matter.

Though some scholars in the 19th century, such as the English philosopher John Stuart Mill and his intellectual descendants, believed there were laws governing human behaviour, social science was swiftly disabused of the notion that a straightforward social physics was possible. Instead, most social scientists have aimed toward what the US sociologist Robert K Merton called ‘middle-range theory’, in which researchers hope to identify regularities and patterns in certain smaller realms that can perhaps later be stitched together to derive the broader theoretical underpinnings of human society. Though some social scientists are sceptical that such broader theoretical underpinnings exist, the most common approach to social science is to use empirical data from the past to tease out ordered patterns that point to stable relationships between causes and effects. Which variables best correlate with the onset of civil wars? Which economic indicators offer the most accurate early warning signs of recessions? What causes democracy?

In the mid-20th century, researchers no longer sought the social equivalent of a physical law (like gravity), but they still looked for ways of deriving clear-cut patterns within the social world. What limited this ability was technology. Just as Lorenz was constrained by the available technology when forecasting weather in the Pacific theatre of the Second World War, so too were social scientists constrained by a lack of computing power. This changed in the 1980s and ’90s, when cheap and sophisticated computers became new tools for understanding social worlds. Suddenly, social scientists – sociologists, economists, psychologists or political scientists – could take a large number of variables and plug them into statistical software packages such as SPSS and Stata, or programming languages such as R. Complex equations would then process these data points, finding the ‘line of best fit’ using a ‘linear regression’, to help explain how groups of humans change over time. A quantitative revolution was born.

By the 2000s, area studies specialists who had previously done their research by trekking across the globe and embedding themselves in specific cultures were largely supplanted by office-bound data junkies who could manipulate numbers and offer evidence of hidden relationships that were obscured prior to the rise of sophisticated numerical analysis. In the process, social science became dominated by one computational tool above all others: linear regressions. To help explain social change, this tool uses past data to try to understand the relationships between variables. A regression produces a simplified equation that tries to fit the cluster of real-world datapoints, while ‘controlling’ for potential confounders, in the hopes of identifying which variables drive change. Using this tool, researchers can feed a model with a seemingly endless string of data as they attempt to answer difficult questions. Does oil hinder democracy? How much does poverty affect political violence? What are the social determinants of crime? With the right data and a linear regression, researchers can plausibly identify patterns with defensible, data-driven equations. This is how much of our knowledge about social systems is currently produced. There is just one glaring problem: our social world isn’t linear. It’s chaotic…

… The deeply flawed assumptions of social modelling do not persist because economists and political scientists are idiots, but rather because the dominant tool for answering social questions has not been meaningfully updated for decades. It is true that some significant improvements have been made since the 1990s. We now have more careful data analysis, better accounting for systematic bias, and more sophisticated methods for inferring causality, as well as new approaches, such as experiments that use randomised control trials. However, these approaches can’t solve many of the lingering problems of tackling complexity and chaos. For example, how would you ethically run an experiment to determine which factors definitively provoke civil wars? And how do you know that an experiment in one place and time would produce a similar result a year later in a different part of the world?

These drawbacks have meant that, despite tremendous innovations in technology, linear regressions remain the outdated king of social research. As the US economist J Doyne Farmer puts it in his book Making Sense of Chaos (2024): ‘The core assumptions of mainstream economics don’t match reality, and the methods based on them don’t scale well from small problems to big problems.’ For Farmer, these methods are primarily limited by technology. They have been, he writes, ‘unable to take full advantage of the huge advances in data and technology.’

The drawbacks also mean that social research often has poor predictive power. And, as a result, social science doesn’t even really try to make predictions. In 2022, Mark Verhagen, a research fellow at the University of Oxford, examined a decade of articles in the top academic journals in a variety of disciplines. Only 12 articles out of 2,414 tried to make predictions in the American Economic Review. For the top political science journal, American Political Science Review, the figure was 4 out of 743. And in the American Journal of Sociology, not a single article made a concrete prediction. This has yielded the bizarre dynamic that many social science models can never be definitively falsified, so some deeply flawed theories linger on indefinitely as zombie ideas that refuse to die.

A core purpose of social science research is to prevent avoidable problems and improve human prosperity. Surely that requires more researchers to make predictions about the world at some point – even if chaos theory shows that those claims are likely to be inaccurate.

We produce too many models that are often wrong and rarely useful. But there is a better way. And it will come from synthesising lessons from fields that social scientists have mostly ignored.

Chaos theory emerged in the 1960s and, in the following decades, mathematical physicists such as David Ruelle and Philip Anderson recognised the significance of Lorenz’s insights for our understanding of real-world dynamical systems. As these ideas spread, misfit thinkers from an array of disciplines began to coalesce around a new way of thinking that was at odds with the mainstream conventions in their own fields. They called it ‘complexity’ or ‘complex systems’ research. For these early thinkers, Mecca was the Santa Fe Institute in New Mexico, not far from the sagebrush-dotted hills where the atomic bomb was born. But unlike Mecca, the Santa Fe Institute did not become the hub of a global movement.

Public interest in chaos and complexity surged in the 1980s and ’90s with the publication of James Gleick’s popular science book Chaos (1987), and a prominent reference from Jeff Goldblum’s character in the film Jurassic Park (1993). ‘The shorthand is the butterfly effect,’ he says, when asked to explain chaos theory. ‘A butterfly can flap its wings in Peking and in Central Park you get rain instead of sunshine.’ But aside from a few fringe thinkers who broke free of disciplinary silos, social science responded to the complexity craze mostly with a shrug. This was a profound error, which has contributed to our flawed understanding of some of the most basic questions about society. Taking chaos and complexity seriously requires a fresh approach.

One alternative to linear regressions is agent-based modelling, a kind of virtual experiment in which computers simulate the behaviour of individual people within a society. This tool allows researchers to see how individual actions, with their own motivations, come together to create larger social patterns. Agent-based modelling has been effective at solving problems that involve relatively straightforward decision-making, such as flows of car traffic or the spread of disease during a pandemic. As these models improve, with advances in computational power, they will inevitably continue to yield actionable insights for more complex social domains. Crucially, agent-based models can capture nonlinear dynamics and emergent phenomena, and reveal unexpected bottlenecks or tipping points that would otherwise go unnoticed. They might allow us to better imagine possible worlds, not just measure patterns from the past. They offer a powerful but underused tool in future-oriented social research involving complex systems.

Additionally, social scientists could incorporate chaotic dynamics by acknowledging the limits of seeking regularities and patterns. Instead, they might try to anticipate and identify systems on the brink, near a consequential tipping point – systems that could be set off by a disgruntled vegetable vendor or triggered by a murdered archduke. The study of ‘self-organised criticality’ in physics and complexity science could help social scientists make sense of this kind of fragility. Proposed by the physicists Per Bak, Chao Tang and Kurt Wiesenfeld, the concept offers a useful analogy for social systems that may disastrously collapse. When a system organises itself toward a critical state, a single fluke could cause the system to change abruptly. By analogy, modern trade networks race toward an optimised but fragile state: a single gust of wind can twist one boat sideways and cause billions of dollars in economic damage, as happened in 2021 when a ship blocked the Suez Canal.

The theory of self-organised criticality was based on the sandpile model, which could be used to evaluate how and why cascades or avalanches occur within systems. If you add grains of sand, one at a time, to a sandpile, eventually, a single grain of sand can cause an avalanche. But that collapse becomes more likely as the sandpile soars to its limit. A social sandpile model could provide a useful intellectual framework for analysing the resilience of complex social systems. Someone lighting themselves on fire, God forbid, in Norway is unlikely to spark a civil war or regime collapse. That is because the Norwegian sandpile is lower, less stretched to its limit, and therefore less prone to unexpected cascades and tipping points than the towering sandpile that led to the Arab Spring.

There are other lessons for social research to be learned from nonlinear evaluations of ecological breakdown. In biology, for instance, the theory of ‘critical slowing down’ predicts that systems near a tipping point – like a struggling coral reef that is being overrun with algae – will take longer to recover from small disturbances. This response seems to act as an early warning system for ecosystems on the brink of collapse.

Social scientists should be drawing on these innovations from complex systems and related fields of research rather than ignoring them. Better efforts to study resilience and fragility in nonlinear systems would drastically improve our ability to avert avoidable catastrophes. And yet, so much social research still chases the outdated dream of distilling the chaotic complexity of our world into a straightforward equation, a simple, ordered representation of a fundamentally disordered world.

When we try to explain our social world, we foolishly ignore the flukes. We imagine that the levers of social change and the gears of history are constrained, not chaotic. We cling to a stripped-down, storybook version of reality, hoping to discover stable patterns. When given the choice between complex uncertainty and comforting – but wrong – certainty, we too often choose comfort.

In truth, we live in an unruly world often governed by chaos. And in that world, the trajectory of our lives, our societies and our histories can forever be diverted by something as small as stepping off a steam train for a beautiful day of sightseeing, or as ephemeral as passing clouds…

Eminently worth reading in full: “The forces of chance,” from @brianklaas in @aeonmag.

* Niccolò Machiavelli, The Prince

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As we contemplate contingency, we might recall that it was on this date in 1906, at the first International Radiotelegraph Convention in Berlin, that the Morse Code signal “SOS”– “. . . _ _ _ . . .”– became the global standard radio distress signal.  While it was officially replaced in 1999 by the Global Maritime Distress Safety System, SOS is still recognized as a visual distress signal.

SOS has traditionally be “translated” (expanded) to mean “save our ship,” “save our souls,” “send out succor,” or other such pleas.  But while these may be helpful mnemonics, SOS is not an abbreviation or acronym.  Rather, according to the Oxford English Dictionary, the letters were chosen simply because they are easily transmitted in Morse code.

220px-Thesos

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Written by (Roughly) Daily

November 3, 2024 at 1:00 am

“Two dangers constantly threaten the world: order and disorder”*…

After two days of posts on the state of our civil society, a palette-cleanser: Jordana Cepelewicz with a possibly-consoling reminder…

When he died in 1930 at just 26 years old, Frank Ramsey [see here] had already made transformative contributions to philosophy, economics and mathematics. John Maynard Keynes sought his insights; Ludwig Wittgenstein admired him and considered him a close friend. In his lifetime, Ramsey published only eight pages on pure math: the beginning of a paper about a problem in logic. But in that work, he proved a theorem that ultimately led to a whole new branch of mathematics — what would later be called Ramsey theory.

His theorem stated that if a system is large enough, then no matter how disordered it might be, it’s always bound to exhibit some sort of regular structure. Order inevitably emerges from chaos; patterns are unavoidable. Ramsey theory is the study of when this happens — in sets of numbers, in collections of vertices and edges called graphs, and in other systems. The mathematicians Ronald Graham and Joel Spencer likened it to how you can always pick out patterns among the stars in the night sky…

… In fact, Ramsey theory isn’t just about inevitable patterns found in graphs. Hidden structure emerges in lists of numbers, strings of beads and even card games. In 2019, for example, mathematicians studied collections of sets that can always be arranged to resemble the petals of a sunflower. That same year, Quanta reported on research into sets of numbers that are guaranteed to contain numerical patterns called polynomial progressions. And last year, mathematicians proved a similar result, about sets of integers that must always include three evenly spaced numbers, called arithmetic progressions.

In its hunt for patterns, Ramsey theory gets to the core of what mathematics is all about: finding beauty and order in the most unexpected places…

Finding order in chaos: “Why Complete Disorder Is Mathematically Impossible,” from @jordanacep in @QuantaMagazine.

* Paul Valery

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As we ponder patterns, we might send paradigm-shaping birthday greetings to a woman who found order and pattern of a different– and world-changing– sort: Rosalind Franklin; she was born on this date in 1920. A biophysicist and X-ray crystallographer, Franklin captured the X-ray diffraction images of DNA that were, in the words of Francis Crick, “the data we actually used” when he and James Watson developed their “double helix” hypothesis for the structure of DNA. Indeed, it was Franklin who argued to Crick and Watson that the backbones of the molecule had to be on the outside (something that neither they nor their competitor in the race to understand DNA, Linus Pauling, had understood).  Franklin never received the recognition she deserved for her independent work– her paper was published in Nature after Crick and Watson’s, which barely mentioned her– and she died of cancer four years before Crick, Watson, and their lab director Maurice Wilkins won the Nobel Prize for the discovery.

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“The function of economic forecasting is to make astrology look respectable.”*…

For as long as there have been markets, there have been those who forecast them. Bob Seawright explains why, for all of that “practice,” forecasting is never– and never can be– a precise nor “perfect” pursuit…

… On our best days, wearing the right sort of spectacles, squinting and tilting our heads just so, we can be observant, efficient, loyal, assertive truth-tellers. However, on most days, all too much of the time, we’re delusional, lazy, partisan, arrogant confabulators. It’s an unfortunate reality, but reality nonetheless.

But that’s hardly the whole story.

We are our own worst enemy, but there are other enemies, too. Despite our best efforts to make it predicable and manageable, and even if we were great forecasters, the world is too immensely complex, chaotic, and chance-ridden for us to do it well…

Eminently worth reading in full for Seawright’s accounts of human nature, complexity, chaos, and chance– and of the ways in which they make confident predictions of the future a “Fool’s Errand.”

As Niels Bohr once said (paraphrasing a Danish proverb), “it is difficult to make predictions, especially about the future.”

(Image above: source)

* John Kenneth Galbraith

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As we seek clarity, not certainty, we might recall that it was on this date in 1983 that Thomas Dolby’s “She Blinded Me with Science” reached #5 on the Billboard Hot 100 chart.

Written by (Roughly) Daily

May 14, 2024 at 1:00 am