Posts Tagged ‘Blaise Pascal’
“Stercus accidit”*…
As we try to understand the rifts afflicting our nation and world, many turn to Marx and his framework of class. But in a provocative essay, Catherine Nichols suggests that it was David Hume (in an 1752 essay that identified the unfettering of wealth from land) who identified the origin of our political divisions…
Describing the political map in terms of Left and Right is an accepted convention all over the world, almost to the point of cliché. Yet it is surprisingly complicated to explain whose interests lie on each side of this spectrum. For example, if the Left supports the interests of workers over the interests of employers, why are Left-leaning regions of the United States and elsewhere in the world among the richest? When Japan and South Korea sought to become economic powerhouses in the later 20th century, they adopted Leftist policies such as strong public education, universal healthcare and increased gender equality – if countries seeking to compete in capitalist arenas adopt broadly Leftist policies, then how do we explain why Leftists are always talking about overthrowing capitalism? And if the Left is somehow both the party of workers’ rights and the party of material wealth, then whose interests are supported by the Right? Given such contradictions, how did these terms become so central to modern politics?
The terms ‘left’ and ‘right’ come from the seating arrangements in the National Assembly during the French Revolution, where the combatants used the medieval estate groupings to define their battle lines. According to their writings, land-owning aristocrats (the Second Estate) were the party of the Right, while the interests of nearly everyone else (the Third Estate) belonged to the Left. This Third Estate included peasants working for the landowners but also every other kind of business owner and worker. Decades later, Karl Marx offered a different analysis of capitalism: he put owners of both land and businesses together on one side (the bourgeoisie), while grouping workers from fields and factories on the other side (the proletariat) in a single, world-wide class struggle. The trouble with both these ways of parsing Left and Right is that voting patterns never seem to line up with class. Both historic analyses leave us with questions about the contemporary world – and not just the paradox of why so many Left-leaning places are so rich. Why, for example, do working-class conservatives appear to vote against their material interests, year in and year out, across generations?
The 18th-century philosopher and political theorist David Hume had answers to these questions, though he was writing decades before the French Revolution. While his essay ‘Of Public Credit’ (1752) was a warning about the dangers of Britain’s increasing reliance on debt financing, his apocalyptic vision of the future turned out to describe some features of our current political map surprisingly well. Hume was writing because he believed that debt financing had the power to upend Europe’s traditional power structure and culture by creating a new source of money divorced from tradition or responsibility: stocks and bonds. Unlike land, anyone with some cash could buy war bonds and get an immediate passive income in the form of interest. This was the thin end of the wedge caused by the debt financing that Hume believed was destroying every part of society. The governments of antiquity, Hume argued, saved money to use in battle and then waged wars in self-defence, or else to expand their territory. But the British had invented a new form of warfare that Hume saw no precedent for, even in the merchant states of Nicollò Machiavelli’s Italy: war for trade, funded with money borrowed from private stockholders…
[Nichols unpacks Hume’s observations (centrally, that three groups with stakes in the status quo, heretability, and the sanctity of “family and family hierarchy”tradition”– landowners, aging parents, and want to preserve old power structures, including the family– and traces their relevance, from Hume’s time to ours…]
… There are many reasons for people aligning Right or Left, which is why analyses of class and material interests fall short of describing the realities of people’s politics. Hume foresaw that these specific groups would resent the economic sea-change of the 18th century – and he was correct. Many people would rather have land and power than money and liberty.
Still, the power of the Right hasn’t doomed the Left – no more than the Spanish Inquisition doomed the rise of the Left in 18th-century England and France. As long as governments want to keep the value of their currencies from falling, someone in their ranks will be using the methods of the Left and inventiveness that brought us everything from our banking system to gay marriage. We don’t need to resurrect communism or focus narrowly on class, following Marx. The experiments are far from over, and we should remember that the Left is generally where money comes from in modern times. We give away too much power when we forget it…
Rethinking Right and Left: “Landholder vs stockholder,” from @catherinenichols.bsky.social in @aeon.co.
As for how it’s going at the moment (and further to Hume and the quote in this post’s title), see: “MAGA’s Betrayal of Small Business,” from @pkrugman.bsky.social.
* “shit happens”– often attributed to David Hume, reflecting his skeptical view that human understanding, particularly of cause-and-effect, is limited to habitual belief from experience, implying that unforeseen, messy outcomes (“shit”) inevitably occur in life despite our reasoning.
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As we sort the Whigs from the Tories, we might recall that it was on this date 1656 that Blaise Pascal (writing under the pseudonym Louis de Montalte) published the first of his Provential Letters (Lettres provinciales), a series of eighteen polemical letters using humor to attack Jesuits for their use of casuistry and their moral laxity. Though the Letters were a popular success, they had little immediate effect on politics or the clergy. But they influenced later French writers like Voltaire and Jean-Jacques Rousseau and ultimately persuaded Pope Alexander to condemn “laxity” in the church and order a revision of casuistic texts.
“Chance, too, which seems to rush along with slack reins, is bridled and governed by law”*…
And the history of our understanding of those laws is, as Tom Chivers explains (in an excerpt from his book, Everything is Predictable), both fascinating and illuminating…
Traditionally, the story of the study of probability begins in French gambling houses in the mid-seventeenth century. But we can start it earlier than that.
The Italian polymath Gerolamo Cardano had attempted to quantify the maths of dice gambling in the sixteenth century. What, for instance, would the odds be of rolling a six on four rolls of a die, or a double six on twenty-four rolls of a pair of dice?
His working went like this. The probability of rolling a six is one in six, or 1/6, or about 17 percent. Normally, in probability, we don’t give a figure as a percentage, but as a number between zero and one, which we call p. So the probability of rolling a six is p = 0.17. (Actually, 0.1666666… but I’m rounding it off.)
Cardano, reasonably enough, assumed that if you roll the die four times, your probability is four times as high: 4/6, or about 0.67. But if you stop and think about it for a moment, that can’t be right, because it would imply that if you rolled the die six times, your chance of getting a six would be one-sixth times six, or one: that is, certainty. But obviously it’s possible to roll six times and have none of the dice come up six.
What threw Cardano is that the average number of sixes you’ll see on four dice is 0.67. But sometimes you’ll see three, sometimes you’ll see none. The odds of seeing a six (or, separately, at least one six) are different.
In the case of the one die rolled four times, you’d get it badly wrong—the real answer is about 0.52, not 0.67—but you’d still be right to bet, at even odds, on a six coming up. If you used Cardano’s reasoning for the second question, though, about how often you’d see a double six on twenty-four rolls, it would lead you seriously astray in a gambling house. His math would suggest that, since a double six comes up one time in thirty-six (p ≈ 0.03), then rolling the dice twenty-four times would give you twenty-four times that probability, twenty-four in thirty-six or two-thirds (p ≈ 0.67, again).
This time, though, his reasonable but misguided thinking would put you on the wrong side of the bet. The probability of seeing a double six in twenty-four rolls is 0.49, slightly less than half. You’d lose money betting on it. What’s gone wrong?
A century or so later, in 1654, Antoine Gombaud, a gambler and amateur philosopher who called himself the Chevalier de Méré, was interested in the same questions, for obvious professional reasons. He had noticed exactly what we’ve just said: that betting that you’ll see at least one six in four rolls of a die will make you money, whereas betting that you’ll see at least one double six in twenty-four rolls of two dice will not. Gombaud, through simple empirical observation, had got to a much more realistic position than Cardano. But he was confused. Why were the two outcomes different? After all, six is to four as thirty-six is to twenty-four. He recruited a friend, the mathematician Pierre de Carcavi, but together they were unable to work it out. So they asked a mutual friend, the great mathematician Blaise Pascal.
The solution to this problem isn’t actually that complicated. Cardano had got it exactly backward: the idea is not to look at the chances that something would happen by the number of goes you take, but to look at the chances it wouldn’t happen…
…
… Pascal came up with a cheat. He wasn’t the first to use what we now call Pascal’s triangle—it was known in ancient China, where it is named after the mathematician Yang Hui, and in second-century India. But Pascal was the first to use it in problems of probability.
It starts with 1 at the top, and fills out each layer below with a simple rule: on every row, add the number above and to the left to the number above and to the right. If there is no number in one of those places, treat it as zero…
… Now, if you want to know what the possibility is of seeing exactly Y outcomes, say heads, on those seven flips:
It’s possible that you’ll see no heads at all. But it requires every single coin coming up tails. Of all the possible combinations of heads and tails that could come up, only one—tails on every single coin—gives you seven heads and zero tails.
There are seven combinations that give you one head and six tails. Of the seven coins, one needs to come up heads, but it doesn’t matter which one. There are twenty-one ways of getting two heads. (I won’t enumerate them all here; I’m afraid you’re going to have to trust me, or check.) And thirty-five of getting three.
You see the pattern? 1 7 21 35—it’s row seven of the triangle…
Pascal’s triangle is only one way of working out the probability of seeing some number of outcomes, although it’s a very neat way. In situations where there are two possible outcomes, like flipping a coin, it’s called a “binomial distribution.”
But the point is that when you’re trying to work out how likely something is, what we need to talk about is the number of outcomes— the number of outcomes that result in whatever it is you’re talking about, and the total number of possible outcomes. This was, I think it’s fair to say, the first real formalization of the idea of “probability.”..
On the historical origins of the science of probability and statistics: “Rolling the Dice: What Gambling Can Teach Us About Probability,” from @TomChivers in @lithub.
See also: Against the Gods, by Peter Bernstein.
And for a look at how related concepts shape thinking among quantum physicists, see “The S-Matrix Is the Oracle Physicists Turn to in Times of Crisis.”
* Boethius, The Consolation of Philosophy
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As we roll the bones, we might send carefully-calculated birthday greetings to a central player in this saga, Abraham de Moivre; he was born on this date in 1667. A mathematician, he’s known for de Moivre’s formula, which links complex numbers and trigonometry, and (more relevantly to the piece above) for his work on the normal distribution and probability theory. de Moivre was the first to postulate the central limit theorem (TLDR: the probability distribution of averages of outcomes of independent observations will closely approximate a normal distribution)– a cornerstone of probability theory. And in his time, his book on probability, The Doctrine of Chances, was prized by gamblers.
“I used to measure the skies, now I measure the shadows of Earth”*…
From ancient Egyptian cubits to fitness tracker apps, humankind has long been seeking ever more ways to measure the world – and ourselves…
The discipline of measurement developed for millennia… Around 6,000 years ago, the first standardised units were deployed in river valley civilisations such as ancient Egypt, where the cubit was defined by the length of the human arm, from elbow to the tip of the middle finger, and used to measure out the dimensions of the pyramids. In the Middle Ages, the task of regulating measurement to facilitate trade was both privilege and burden for rulers: a means of exercising power over their subjects, but a trigger for unrest if neglected. As the centuries passed, units multiplied, and in 18th-century France there were said to be some 250,000 variant units in use, leading to the revolutionary demand: “One king, one law, one weight and one measure.”
It was this abundance of measures that led to the creation of the metric system by French savants. A unit like the metre – defined originally as one ten-millionth of the distance from the equator to the north pole – was intended not only to simplify metrology, but also to embody political ideals. Its value and authority were derived not from royal bodies, but scientific calculation, and were thus, supposedly, equal and accessible to all. Then as today, units of measurement are designed to create uniformity across time, space and culture; to enable control at a distance and ensure trust between strangers. What has changed since the time of the pyramids is that now they often span the whole globe.
Despite their abundance, international standards like those mandated by NIST and the International Organization for Standardization (ISO) are mostly invisible in our lives. Where measurement does intrude is via bureaucracies of various stripes, particularly in education and the workplace. It’s in school that we are first exposed to the harsh lessons of quantification – where we are sorted by grade and rank and number, and told that these are the measures by which our future success will be gauged…
A fascinating survey of the history of measurement, and a consideration of its consequences: “Made to measure: why we can’t stop quantifying our lives,” from James Vincent (@jjvincent) in @guardian, an excerpt from his new book Beyond Measure: The Hidden History of Measurement.
And for a look at what it takes to perfect one of the most fundamental of those measures, see Jeremy Bernstein‘s “The Kilogram.”
* “I used to measure the skies, now I measure the shadows of Earth. Although my mind was sky-bound, the shadow of my body lies here.” – Epitaph Johannes Kepler composed for himself a few months before he died
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As we get out the gauge, we might send thoughtfully-wagered birthday greetings Blaise Pascal; he was born on this date in 1623. A French mathematician, physicist, theologian, and inventor (e.g.,the first digital calculator, the barometer, the hydraulic press, and the syringe), his commitment to empiricism (“experiments are the true teachers which one must follow in physics”) pitted him against his contemporary René “cogito, ergo sum” Descartes– and was foundational in the acceleration of the scientific/rationalist commitment to measurement…
“All of our reasoning ends in surrender to feeling”*…
click here (and again) for the full infographic
From the indispensable David McCandless, at Information is Beautiful.
* Blaise Pascal
***
As we shore up our syllogisms, we might recall that it was on this date in 1881, two days before his death, that British Prime Minister Benjamin Disraeli demurred from a visit by Queen Victoria, muttering “no, she will only ask me to take a message to Albert.”
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