Occasional reflections on Life, the World, and Mathematics

Archive for the ‘Academic’ Category

Worst mathematics metaphor ever?

I’ve come to accept “growing exponentially” — though I once had to bite my tongue at a cancer researcher claiming that “exponential growth” of cancer rates began at age 50, because earlier the rates were just generally low — and didn’t say anything when someone recently referred to having “lots of circles to square”. But here’s a really new bad mathematics metaphor: the Guardian editorialises that after Brexit

Europe will be less than the sum of its remaining parts.

“More than the sum of its parts” or “less than” is something you say when you’re adding things together, and pointing out either that you don’t actually get as much extra as you’d think or, on the contrary, that you get more. That you get less when you take something away really doesn’t need much explanation and, in any case, it’s not about the sum of the parts. Whether the remains of Europe are more or less than the sum of the other parts seems kind of irrelevant to whatever argument is being suggested.

“Getting a bit of extra assistance is never cheating”

If I were a philosophy student with a looming deadline for an essay on casuistry, I know I’d turn to BuyEssay for expert help. The Guardian has reported on government moves to crack down on essay mills, that sell individually crafted essays for students who need “extra help” –anything from a 2-page essay to a PhD dissertation (for just £6750!) The article reprints some of the advertising text that these websites offer to soothe tender consciences.

“Is Buying Essays Online Cheating?” it asks, in bold type. You’d think this would be an easy question, hardly something you could spin a 300-word essay out of. But they start with a counterintuitive answer: “We can assure you it is NOT cheating”. The core of the argument is this:

What is essential when you are in college or university is to focus on scoring high grades and to get ready for your career ahead. In the long run, your success will be all that matters. Trivial things like ordering an essay will seem too distant to even be considered cheating.

Given that high grades are so essential, it seems almost perverse that universities make it so difficult to obtain them. Why do they put all these essays and other hurdles in the way — “unreasonable demands from unrelenting tutors in expecting extensive research in a short time”, as the essay puts it? It’s shitty customer service, that’s what it is.

The only critique I might make is that the essay is a bit generic. I’d worry that when I submitted it for the assignment “Is Buying Essays Online Cheating”, that the marker might notice that someone else bought almost the same essay for the assignment “Is Murder Wrong?” In the long run, your success will be all that matters. Wasn’t this the plot of Woody Allen’s Crimes and Misdemeanors?

Who tricked whom into eating potatoes?

Reading Richard Evans’s The Pursuit of Power: Europe 1815–1914, I discovered this anecdote about Ioannis Kapodistrias, appointed by Russia as governor of Greece in the late 1820s:

He introduced the potato into Greece, in an effort to improve people’s diet. At first, this met with deep skepticism among the peasantry, who refused to take up his offer of free distribution of seed potatoes to anyone who would plant them. Trying a new tactic, Kapodistrias had the potatoes piled up on the waterfront at Nafplio and surrounded by armed guards. This convinced local people and visitors from the countryside that these new vegetables were precious objects, and thus worth stealing. Before long, as the guards turned a blind eye, virtually all the potatoes had been taken — and their future in Greece was assured.

This reminded me of something I read many years ago, in Fernand Braudel’s The Identity of France:

In France, despite its early success, it was not until the mid-eighteenth century that the potato was regarded as truly ‘worthy’ to be eaten, with partisans prepared to defend it on both dietary and culinary grounds… In the géneralité of Limoges, potatoes were originally banned because they were thought to cause leprosy…

The corner was not really turned until the severe famine of 1769-70. The following year, the Academy of Besançon set an essay competition on the subject: “Suggest food plants which might be used in times of famine to supplement those usually eaten.’ All the essays mentioned the potato — notably the winning entry, which came from Parmentier. He then embarked upon a massive propaganda campaign, deploring ‘the mocking humour of our scornful citizens’. He published widely, gave advice on the growing and storing of the potato, organized gourmet dinners in his own home at which nothing but dishes made from potatoes were served…, brought to Paris all the varieties then cultivated in France and had even more shipped from America to give a better selection. He finally obtained from Louis XVI, in 1786, permission to set up an experimental plantation on about 20 hectares just outside Paris in Neuilly, on the untended and infertile soil of the plain of Sablons. It was a complete success. In his efforts to attract consumers, Parmentier concluded that the best method would be to entice people to steal his potatoes. So he ostentatiously had his plantation guarded by the maréchaussée, the local police — but only by day. Similarly, he advised landowners not to force potatoes on their peasants, but to plant one fine field full themselves and ‘expressly forbid anyone to enter’ — a more subtle approach than that of Frederick II of Prussia who sent in the troops to make the peasants plant potatoes.

Is it possible that Kapodistrias knew of Parmentier’s example? I guess so. Was this actually a well-known method for tricking the childish peasants into trying something new? Maybe. Or are these anecdotes, rather, merely recrudescences of a universal myth about how to trick the childish peasants? I’m not interested enough to track down the references…

16th century Sokal hoax

Many of our readers will recall the celebrated hoax perpetrated by mathematical physicist Alan Sokal in 1996 against the humanities journal Social Text. Sokal submitted an article “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity” for an issue on “Science Wars”. The article strung together buzzwords helter-skelter to conclude with a flattering claim of the importance of social theory for natural science. The fact that it was published is cited even today by supercilious physicists and insecure journalists as conclusive proof that academic jargon in the humanities and social sciences is all fake.

Anyway, I was just reading Montaigne’s essay “Du pedantisme” (On pedantry), and found the following anecdote:

J’ay veu chez moy un mien amy, par maniere de passetemps, ayant affaire à un de ceux-cy, contrefaire un jargon de Galimatias, propos sans suitte, tissu de pieces rapportées, sauf qu’il estoit souvent entrelardé de mots propres à leur dispute, amuser ainsi tout un jour ce sot à debattre, pensant tousjours respondre aux objections qu’on luy faisoit. Et si estoit homme de lettres et de reputation, et qui avoit une belle robbe.

I observed at my home a friend of mine making sport of one of these [pedants] by making up a nonsense jargon, propositions with no succession, a patchwork of pieces that had nothing in common except for some buzzwords  that he stuck in that related to their topic, and he amused himself a whole day with this crazy debate, always managing to think of new answers to the man’s objections. And this was a greatly reputed man of letters.

The view from one-in-a-billion

Nautilus just published my new article, a nontechnical introduction to large deviations: The theory of how unlikely rare events are, and which way a rare event chooses to occur, given that it occurs.

The secret to a long life

It’s well known that marriage is an important factor in longevity. But maybe we’ve been interpreting that wrong, or, at least, not optimising.

From the Gerontology Research Group article on the current oldest living person, Italian Emma Morano:

In 1926, Mrs. Morano was married to Giovanni Martinuzzi, a marriage she would rather not talk about… Having separated – but not divorced – from her husband in 1938, Mrs. Morano has lived alone ever since, and accredits this as one of the key secrets to her longevity.

From portent to program: Factless fascism

I’m old enough to remember when “relativism” was the second-favourite scare word hurled by the Right (after “socialism”, of course). The truth of the matter was that leftist intellectuals had put a lot of effort into analysing the way worldviews are created by and support particular power relations. This seems like good work, in principle, and obviously useful in interrogating the making of history, economics, and social ideologies, and has made important contributions to the philosophy of science. There have been excesses — edging into denial of scientific truth or progress.

The arch-cultural reactionary Dinesh D’Souza in his heyday (before he became completely ridiculousused the then-modish term deconstruction as a catch-all for this iconoclastic posture toward literary and (it is implied, more than actually shown) moral authorities of the past to exemplify the inconsistent application of moral relativism as a political weapon:

Marx, for instance, never seems to be deconstructed, nor does Foucault, or Lacan , or Derrida, or Barthes. Malcolm X and Martin Luther King, Jr, seem to enjoy immunity. There may be an entire gender exception for women.

I’ve never been sufficiently au fait with the humanities and social sciences — “critical theory” — to judge whether these extreme denials of objective truth were ever as central to leftist discourse as some critics would suggest. I think this has been overall very productive intellectually and scientifically. But as a political tactic it was, it seems clear now, tragically short-sighted. The Left made a serious strategic error in trying to shortcut its way out from under the dead hand of the past  by promoting relativism and attacking the authority of science and rational discourse. The right wing were taking notes, and while the older generation — figures like William F. Buckley, John Silber and Allan Bloom — started by ridiculing the anti-rationalist turn, the younger generation saw it as a program to be emulated and developed. Fascists have always had an uncomfortable relationship with objective reality, that seems to be offering only stubborn opposition to the imposition of the authoritarian will.

Nietzsche — the doyen of this kind of analysis, but conflicted in this as in everything else — framed what should have been the core left-wing critique of relativism in Die Fröhliche Wissenschaft [The Gay Science]:

Ein Jude umgekehrt ist, gemäss dem Geschäftskreis und der Vergangenheit seines Volks, gerade daran — dass man ihm glaubt — am wenigsten gewöhnt: man sehe sich darauf die jüdischen Gelehrten an, — sie Alle halten grosse Stücke auf die Logik, das heisst auf das Erzwingen der Zustimmung durch Gründe; sie wissen, dass sie mit ihr siegen müssen, selbst wo Rassen- und Classen-Widerwille gegen sie vorhanden ist, wo man ihnen ungern glaubt. Nichts nämlich ist demokratischer als die Logik: sie kennt kein Ansehn der Person und nimmt auch die krummen Nasen für gerade. (Nebenbei bemerkt: Europa ist gerade in Hinsicht auf Logisirung, auf reinlichere Kopf-Gewohnheiten den Juden nicht wenig Dank schuldig; voran die Deutschen, als eine beklagenswerth deraisonnable Rasse, der man auch heute immer noch zuerst „den Kopf zu waschen“ hat. Ueberall, wo Juden zu Einfluss gekommen sind, haben sie ferner zu scheiden, schärfer zu folgern, heller und sauberer zu schreiben gelehrt: ihre Aufgabe war es immer, ein Volk „zur Raison“ zu bringen.)

On account of his people’s business relations and past, the Jew is not used to being believed. You see this in the way Jewish scholars are obsessed with logic, that is, compelling assent through reasons. They know that they can succeed in this way, even when the prejudice of race and class tell against them, even when one would rather not believe them. Nothing is as democratic as logic: It recognises no personal distinctions, and takes even the crooked nose for straight.(Europe must be grateful to the Jews particularly with respect to logicalising — for clearer habits of thought. Above all the Germans, a pitifully irrational race. Everywhere where the Jews have gained influence, they have taught people to reason more precisely and write more clearly. It has always been their task to bring a people “to its senses”.)

And so we find ourselves in the 21st century with a senior adviser to a Republican president criticising, in 2002, the naivety of what he called the “reality-based community”, stating

That’s not the way the world really works anymore. We’re an empire now, and when we act, we create our own reality. And while you’re studying that reality — judiciously, as you will — we’ll act again, creating other new realities, which you can study too, and that’s how things will sort out.

And sure enough, as soon as a new Republican is elected, we have his surrogates even more openly attacking the very notion of objective reality:

 And so one thing that has been interesting this entire campaign season to watch, is that people that say facts are facts—they’re not really facts. Everybody has a way—it’s kind of like looking at ratings, or looking at a glass of half-full water. Everybody has a way of interpreting them to be the truth, or not truth. There’s no such thing, unfortunately, anymore as facts.

And so Mr. Trump’s tweet, amongst a certain crowd—a large part of the population—are truth. When he says that millions of people illegally voted, he has some—amongst him and his supporters, and people believe they have facts to back that up. Those that do not like Mr. Trump, they say that those are lies and that there are no facts to back it up.

You may think you’re talking about facts and evidence, but for those on the inside these are just ways of saying whether you “like Mr. Trump”. They tried out their message first on evolution as a matter of “belief”, honed the message on climate science — a harder nut to crack — and finally brought us to where groundless claims that millions of people voted illegally are also matters of belief.

Speaking of Allan Bloom, the University of Chicago philosopher who had a hit book in the mid-1980s The Closing of the American Mind, which was mainly about how the kids today with their crazy rock-and-roll music were having more sex than he had at their age, which was driving him crazy. But I remember one really striking idea that he was pushing was that, just as the Romans conquered the Greeks militarily, but then as a consequence of absorbing the Greek world ended up being dominated by Greek culture and philosophy, so the Anglo-American world conquered Germany militarily, but are now dominated by the German Weltanschauung, and Nietzsche in particular.

Likely probabilities

The BBC comments on Trump’s latest outrage:

The day after a video tape emerged in which he suggested he could have any woman he wants because he’s a star and so could just “grab them by the pussy”, Mr Trump is in a whole ocean of hot political water.

Enough, quite possibly, to sink any chance he had of winning the White House.

What does it mean to have “quite possibly” no chance? How does it differ from having quite likely a small chance? Or definitely a modest chance?

I suppose this could be describing a combination of an unknown state of facts that determine the probabilities for a random outcome. Imagine a bag of red and blue marbles, from which the election will be determined by picking a random one. (Red for Trump.) She is saying, “Quite possibly there are no red marbles left in the bag.” I’m don’t think that’s a good description of the situation, though. To the extent that Trump has a better chance of winning than you might think by looking at the polls or the near universal opprobrium he is exposed to, it doesn’t seem to me it’s on the basis of facts that are already determined but unknown.

Statistics and causal truth: Police edition

As usual, Andrew Sullivan — who has now returned temporarily to blogging, attracted like a moth to the Trump conflagration — manages to take a common, superficially convincing argument, and express it with moral fervour and personal conviction that makes the tenuous logic really conspicuous. In this case, it’s the argument based on the much-discussed study by Roland G. Fryer, Jr. of the rate of various violent outcomes of police stops, finding that black people are more likely than white to be physically abused by police, but not more likely to be shot.

(Here’s an excellent NY Times report, and  the original study.)

…the Black Lives Matter activists, whose core and central argument is that black men are disproportionately killed by cops. The best data shows this is false…  I find [the study] conclusive. Feelings do not, er, trump data in a deliberative democracy. A reader writes:

I understand that there has been the recent study suggesting that given an interaction with a police officer occurs, then the police officer is no more likely to use a gun with a black person than with a white person. However, given that many black men have a much higher rate of interaction with police (such as, anecdotally, Philando Castile, with 52 traffic stops), then is it not fair to say that black men are disproportionately killed by cops?
The point is that there is no evidence of individual racism in these police encounters, despite the impression from many chilling phone videos. The structural bias still exists as a whole, as I said, but the narrative about cops being more likely to kill a black member of the public when encountering him is false.

I have no criticism to make of the study — I have not analysed it in any depth, but it seems credibly and even impressively done — even if I find the premise absurd, that a single study of such a complex phenomenon could be “conclusive”. But they do not “trump” the data that black people make up 13% of the US population, but 31% of those killed during an arrest, and 42% of those killed during an arrest when unarmed. The point is, what these facts (and many others, including the others) mean jointly depends on what we think is the reason for black people being so much more likely to be arrested.


More damned statistics

The news website Vox published this chart last year, by Dara Lind, based on FBI data on people killed by police during arrest. The most chilling thing about it is that refined statistical analysis on people killed by police is possible, with all kinds of elaborate subgroup analyses. That’s because there were 426 cases in that year. In general I’m all in favour of more data, which makes it possible to study problems in a more refined way, but I’m happy that the statistics gathered by the Independent Police Complaints Commission don’t have much to work with: In the same year there were 15 deaths in or following police custody in England and Wales.

UPDATE:  I thought the US number seemed surprisingly small — only about 5 times the UK number on a per capita basis, despite the fact that British police don’t routinely carry firearms. In fact, The Guardian’s documentation of all police killings in the US lists 1146 people killed by police in 2015. I presume this has to do with the fact that the FBI statistic only counts people killed during arrest.

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