by Jeroen Bouterse
It’s my favorite topic of the year, I tell the kids, before scanning my conscience for signs that I have just lied to them. No, this feels about right, and in any case, they didn’t need my reassurance: after a dry unit about ratios, at my mention of the word “probability” I can practically hear the sound of neurons firing. Whether they know of any contexts in which chance turns up? Boy, do they. My twelve-year old students inform me about dice, cards, spinners, lotteries, casinos, about your chances of survival in Squid Game, about unearthing rare minerals in Minecraft, and about whether the stuff you want to buy is actually in stock because sometimes they run out and there’s no telling in advance when. Also the weather.
I love introducing them to the math of probability precisely because it is a topic that they have already thought about so much, but that I know many of them have incoherent intuitions about. Not that I don’t, of course, but I am a little bit ahead of them and I know from experience what I am working with. Somebody will opine that the chance that it’s going to rain next month is “fifty-fifty” because it either will or it won’t. Somebody will say that there is a 1/7 chance that someone’s favorite day of the week is Thursday. Somebody will reason that since the highest sum you can roll with two D6-dice is a 12, the chance you roll a 10 is 1 in 12, which…
Oh wait, is it? Anyway, you get the point: the process feels properly Socratic, taking slightly muddled concepts that students already feel strongly about, and providing the right nudges to make them reconsider some of those concepts and make others click together. It is a significant source of satisfaction every year to see just how fast ‘the group’ moves from guessing that a sequence of three coin flips has six possible outcomes (unless it can land on its side, which they also unerringly point out), to calculating the number of four-digit pin codes where all the digits have to be different.
It’s also becoming a little predictable, now that I teach this level for the third time. Though I was surprised to learn that this cohort of young teenagers had already binged Squid Game, I don’t generally expect them to say anything unexpected about mathematics. Until, last week, we were classifying certain things according to likelihood. I always include an apodictic claim like “1 + 1 = 2” in the mix, and students usually say that its probability is, indeed, 1. This time, I wondered out loud why we are so sure of this. Read more »

Cauleen Smith. Space Station Chinoiserie #1: Take hold of the Clouds, 2018.
Last night I (Danielle Spencer) went to the New York Film Festival screening of Memoria (dir. Apichatpong Weerasethakul) in Alice Tully hall at Lincoln Center. I last joined a large gathering 19 months ago, in March of 2020.
In the world of Star Trek, no one ever goes hungry or lacks access to healthcare. No one wants for housing, education, social inclusion or any other basic need. In fact, no citizen of the United Federation of Planets is ever seen to pay for everyday goods or services, only for gambling or special entertainments. The Federation suffers no scarcity of any kind. All waste is presumably fed into the replicators and turned into fresh food or new clothes or whatever is needed. Yet despite ample social safety nets, there’s no end to internecine politicking, human foibles and failures, corruption and vanity, charisma and venality. The world of Star Trek appeals so widely, I think, because it presents us with something colorfully short of a utopia, a flawed human attempt toward a just, caring, and individually enabling social order. It imagines a society based on a shared set of human values—fairness, cooperation, political and economic egalitarianism—where basic human needs are equitably answered so that no one has to compete for basic subsistence and wellbeing. As the venerable 

What is the present? When did it begin? Stoics simply consult the calendar for an answer, where they find each new span of 24 hours reassuringly dubbed Today. Archaeologists speak of “Years Before Present” when referring to the time prior to January 1, 1950, the arbitrarily chosen inauguration of the era of radiocarbon dating following the explosion of the first atomic bombs. And the Judeo-Christian West makes of the present age a spatio-temporal chronotope, a narrative rooted in the time and place of birth of a particular figure, whose “presence” as guarantor is inextricable from the dating system, whether the appellations used are the frankly messianic Before Christ and Anno Domini, or the compromise variations on an ecumenical “Common Era”.



I recently spent a few weeks in the UK, which is suffering from a labor shortage post lockdown like the US. Though, unlike the US, some of the UK’s problems are self-inflicted Brexit wounds. The shortages are rippling through every sector, and as in the US, that includes hospitality. Coming out of lockdown, no doubt initiated by hygiene concerns, some restaurants I visited in New York used QR codes instead of handing out menus.
Shortly after my arrival at Cambridge I struck up a warm friendship with a very bright young faculty member, Jim Mirrlees (who was to get the Nobel Prize later), recently returned from a stint of research in India. (Although he was a high-powered theoretical economist, he had what seemed to me an almost religious/moral fervor for doing something to help poor countries). Even more than Frank Hahn, he got involved in the theoretical analysis in my dissertation, and helped me in making some of the proofs of my propositions simpler and less inelegant.
Considered the epitome of genius, Albert Einstein appears like a wellspring of intellect gushing forth fully formed from the ground, without precedents or process. There was little in his lineage to suggest genius; his parents Hermann and Pauline, while having a pronounced aptitude for mathematics and music, gave no inkling of the off-scale progeny they would bring forth. His career itself is now the stuff of legend. In 1905, while working on physics almost as a side-project while sustaining a day job as technical patent clerk, third class, at the patent office in Bern, he published five papers that revolutionized physics and can only be compared to Isaac Newton’s burst of high creativity as he sought refuge from the plague. Among these were papers heralding his famous equation, E=mc^2, along with ones describing special relativity, Brownian motion and the basis of the photoelectric effect that cemented the particle nature of light. In one of history’s ironic episodes, it was the photoelectric effect paper rather than the one on special relativity that Einstein himself called revolutionary and that won him the 1922 Nobel Prize in physics.
For my whole life, the world has been ending. For various alleged reasons. . . but always there’s been an overhang of dread and fear, the end times already here, human cussedness and sinfulness and greed at work in every moment, everywhere, eating away at what’s left of goodness and preparing the Day of Wrath, the horror, the tribulation, the Last Conflict, the End.