Is “lockdown bod” a thing yet?

For obvious reasons, I’m not getting out much. But even sequestered away it is hard to escape how mad everyone in Britain has gone for the online pub quiz. Myself, I went with online chess for a few weeks as my ritualistic bit of fun, but that fell away at some point and now in its place has arisen the New Yorker’s online crossword. Thanks to partner mode it has even become vaguely social. And I couldn’t finish one of them on my own.

It has become de rigueur in academia to talk about imposter syndrome and the ways you can diminish yourself mentally by constantly comparing yourself to your peers. If you are afflicted by this I recommend avoiding the bios of the crossword compilers. They are a precocious and accomplished bunch — the youngest being the worst offenders. They’ve had careers in silicon valley, published books, involved in research and advocacy, write film criticism. Some of the clues are too clever for their own good, if you ask me.


I’m waiting for “lockdown bod” to enter in general usage. It should refer to either the weight gain following from the enforced sedentary lifestyle and comfort eating, or the effect of the hundreds of press-ups and crunches churned out to access those sweet endorphins. So far it hasn’t even registered on the urban dictionary. They do have a pretty amusing definition for “lockdown” though.


I’ve been reading my way through Claire Tomalin’s biography of Samuel Peyps. Pepys’ celebrated diary covers a particularly interesting decade of English history (1660-1669). It was the start of restoration England. Briefly, this means that after a civil war England had replaced the Monarchy with a man called Oliver Cromwell, who subsequently and inevitably died, leaving a power vacuum that they resolved by simply restoring the monarchy, bringing Charles II back to England as King. Bear in mind that his father, Charles I, had been fought against and ultimately executed by many of the same people who were now bringing him back.

This was also the decade of the Great Fire of London and the Great Plague of London. The latter being the final in a long series of outbreaks that seemed to resurface every decade or so. We are beginning to get a little first hand appreciation of how plague affected the lives of those who lived through it. Take the following from a recent New Yorker article on Shakespeare and the plague:

As a shareholder and sometime actor in his playing company, as well as its principal playwright, Shakespeare had to grapple throughout his career with these repeated, economically devastating closings. There were particularly severe outbreaks of plague in 1582, 1592-93, 1603-04, 1606, and 1608-09. The theatre historian J. Leeds Barroll III, who carefully sifted through the surviving records, concluded that in the years between 1606 and 1610—the period in which Shakespeare wrote and produced some of his greatest plays, from “Macbeth” and “Antony and Cleopatra” to “The Winter’s Tale” and “The Tempest”—the London playhouses were not likely to have been open for more than a total of nine months.

What Shakespeare actually wrote about the plague – Stephen Greenblatt

Pepys was heavily involved in the government of the day — he was a naval administrator during the period he wrote the diary and later would become an MP. It is not hard to compare Pepys’ time of political upheaval and plague with our own time of Brexit and pandemic. If the Diary were to exist today it would be a little like Dominic Cummings keeping a private blog to record the arguments with his wife alongside the details of his work as Boris Johnson’s personal advisor. The real innovation of the diary was Pepys’ decision to record not just his professional activities and first hand accounts of events in London, but also his unsparing depiction of his own personal life.

In one particular respect Peyps comes out of his own account very badly, as alludes to his casual harassment and describes the outright exploitation of women in detail. His misdeeds line up pretty precisely with many of the reports that have come out during the #metoo era. He would take advantage both of the female servants employed in his home, other houses he was a guest at, and the young daughters in families he developed a half friendly, half patronage relationship with. A reader of Pepys’ diaries is left to deduce how the women might have really felt about Pepys’s behavior; present day accounts of exactly the same kinds of abuse provide a convincing answer.


Nothing happening today really feels at all novel when held up against the full perspective of history. We may look at the current culture wars, or the 5G and QAnon conspiracy theories, and wonder to ourselves what the world is coming to. Pepys was caught up in the Popish plot — a public hysteria based on the idea there was a Catholic conspiracy to overthrow Protestantism in England. Although he wasn’t Catholic, he had political connections to the King’s Catholic brother, and this led to a brief stint in the Tower of London.

The manner in which the sordid (or “convoluted” if you prefer a less pejorative term) details of the King’s personal life became a matter of public scrutiny feels very reminiscent of certain heads of state today.

The King’s policy of alliance with Catholic France was generally disliked. So was the fact that he had not only a Catholic wife but Catholic mistresses; some of Nell Gwyn‘s popularity came from her supposed merry declaration, ‘I am the Protestant whore.’

Samuel Pepys – The Unequalled Self, by Claire Tomalin

Nell Gwyn had been a celebrity in her own right, aside from being one of the King’s many mistresses. The quote is provocative enough in its re-appropriation of the accusation that it feels quite modern – good enough for a T-shirt or twitter bio.


I’ve been doing remote classes and consultation sessions, so I’ve spent a lot of time with my old Wacom tablet. While it seems that many of my peers have opted for the iPad and tablet option, I think I much prefer having a desktop computer with a large LCD monitor set at the right height. It has been a long time since I drew any comics, but I decided to entertain the kids with the above doodle before class started.

You pronounce sfumato like tomato.

In the late 15th Century the Italian mathematician and Franciscan friar, Luca Pacioli, published a book on geometry, perspective, and achitecture entitled Divina Proportione — the title a reference to the divine ratio. Having the misfortune of writing over five hundred years ago, he did not have access to LaTex or any kind of similar mathematical markup language, and indeed the typesetting had to be done the old fashioned way. He did however enjoy the services of Leonardo da Vinci for producing the illustrations. Which is a considerable consolation. (You can browse an original copy online.)

These illustrations were the only work published in Leonardo’s lifetime — his celebrated notebooks coming to light posthumously. The illustrations cover variations of the Platonic solids, and in what would have been at the time an innovative approach to mathematical visualization, Leonardo not only drew them as solids, but also as hollowed out skeletons. This aptitude for conveying the three dimensional on the page can also be seen in his famous and influential anatomy sketches from his notebooks.

Being, quite literally, a Renaissance man, mathematics figured among Leonardo’s many interests, often overlapping with his engineering, scientific, and artistic pursuits. Although it has been claimed that Leonardo employed the golden ratio in his art, this seems unlikely. Leonardo documented his process and thinking in his notebooks, often expounding in great length, composing books that would go unpublished, yet there is no mention of him claiming to employ the ratio in his composition.

We do however have extensive evidence for Leonardo’s obsessive hunt to square the circle:

He filled his notebooks with shaded drawings in which he overlapped two half-circles and then created triangles and rectangles that had the same area as the resulting crescents. Year after year, he relentlessly pursued ways to create circular shapes with areas equivalent to triangles and rectangles, as if addicted to the game. Though he never gave the precise dates of any milestones he reached when making a painting, he treated these geometric studies as if each little success was a moment in history worthy of a notarial record. One night he wrote momentously, “Having for a long time searched to square the angle to two equal curves…now in the year 1509 on the eve of the Calends of May [April 30] I have found the solution at the 22nd hour on Sunday.

Leonardo da Vinci, The Biography — Walter Isaacson.

I think all of us mathematicians should take a great deal of comfort in how universal an experience it is to arrive at such false dawns. Kenneth Clarke has commented that the pages Leonardo devotes to these mathematical efforts are essentially of no value — neither to the mathematician nor the art historian. It is worth bearing in mind that most mathematical notebooks are mostly full of ideas that are wrong, incorrectly formulated, or badly expressed.


As the above discussion may suggest, I am currently in the middle of reading my way through Walter Isaacson’s biography of Leonardo da Vinci. Leonardo is a towering and influential cultural figure that it is easy to look over how little you really know about him. Not only the man, but also his actual work. Certainly, you recognize a handful of his paintings on sight, and you may also be aware that he designed unworkable helicopters and impractical war machines in his notebooks, but unless you have taken an art history course (I have not) you wouldn’t know why his artwork was really so remarkable, or indeed appreciate the broad scope of what can be found in his notebooks.

You might believe a well cultured individual would have an appreciation for the works of the Renaissance master. That this hypothetical being could walk into the Louvre, have a gander at the Mona Lisa, and they would experience a whole bunch of appreciation. But I don’t think this hypothetical “well cultured” individual exists. Indeed I would argue that a well cultured individual walking around an art gallery is essentially going in to be overwhelmed. If you spend any time looking at the Renaissance art you actually find yourself deep inside the uncanny valley. This might seem obvious, but we’re used to photographs so our sense of what is real is fundamentally adjusted.

All the techniques that Leonardo developed are available to artists today — perspective, understanding light and shadow, the sfumato painting techniques. And then there are all the modern tools and art supplies. Then there is what is being depicted itself: scenes from biblical narratives dressed up in a Renaissance setting. So the scenes are weird, the setting is weird, the people look weird. I want to reiterate that point. Looking at people in renaissance paintings is often like looking at computer generated special effects from ten or twenty years ago. The comparison is very apt. The preoccupations of a CGI artist are actually very similar to what you’ll find Leonardo wrestling with in his notebooks.

It is not that there isn’t much to appreciate in these works of art — I’ve certainly enjoyed reading Isaacson’s biography. But I think the person who wanders around an art gallery with a proper sense of appreciation is really just a certain kind of nerd. Like the rest of us.

Snuff

It was during second dessert — a euphemistic term for booze, chocolates, and conversation away from the dining hall — when the snuff box arrived. I had been listening to a philosopher convince me that certain metaphysical questions were interesting. While I declined a sniff of the stuff, he took a pinch between his finger and thumb, raised it to his nostril and inhaled. To my admiration he did this as if this were a perfectly normal and natural thing to do. Which it really wasn’t, at least as far as I was concerned. You can be attending an alumni dinner in the middle of Hillary term, passing around the dessert wines, and the whole business will still feel like fancy dress and pretend. Maybe the point at which you accept the snuff is the same point at which everything else seems completely natural as well.

Anyone following the ongoing controversy around the relative health benefits and dangers of vaping over cigarette smoking, should know that there have always been other means of ingesting tobacco and obtaining the nicotine hit. Just so that everyone is on the same page let me give the briefest of background. Snuff, which goes back as far as tobacco itself, is the product of pulverizing tobacco leaves down to a powder fine enough to inhale. It has had varying degrees of popularity, but never held the iconic status that the cigarette enjoyed through the 20th century. You can still buy it, and some use it.

The obscurity has led to many faux pas. I’ve been informed that guests, at past Oxford dinners, unfamiliar with the usual customs have laid out lines of the brown powder so as to hoover it up their snout like coke. Of course you can’t jump to too many conclusions; lines of coke have been rendered iconic by TV and cinema, and even individuals as sheltered as myself are aware of it.

The Wikipedia does reveal that a certain crevice in the hand, under a tendon leading to your thumb, is often referred to as the “anatomical snuffbox“. The French even have a word for it: the tabatière. So if you feel inclined to partake when the snuff box arrives, you can deposit a little pile there and show off a little vocabulary.

You can also go ahead and buy your own snuff box to impress/intimidate your house guests. Etsy offers an impressive range. They can get pretty pricey though. A snuff box bequeathed to Magdalen was considered valuable enough to be stolen a couple of decades ago. The controversy around the culprit apparently lingers on.

You can also find quite striking snuff boxes featuring hand painted Victorian erotic vignettes. For what it’s worth.

Oxford, Hearties, and Clever-Sillys.

I’m now halfway through Michaelmas term (that’s Fall semester to Americans, and Autumn term to almost everyone else in the UK) so I’ve been able to settle into a routine here at Oxford. I’ve been having a whale of a time cycling backwards and forwards across town, while my experience with the university has been wonderful, but also quite obscene.

Most of my academic life these days is spent in the Andrew Wiles building — an ultra modern mathematics facility that is just over five years old now. There is a chapel right outside the main entrance however, so you won’t be forgetting where you are in a hurry. Then for lunch I head over to Magdalen College to eat at high table with the other fellows.

The college is more in line with what you might expect from watching Inspector Morse or Harry Potter. Describing it as a 19th Century Gentleman’s private club only goes so far, because you have to explain that it also has it’s own chapel, and extensive grounds which includes a deer park. All that aside, the most refreshing thing about the college system is that I’m sitting down to eat with other academics in the college, who come from all across the sciences and humanities. The last time I was regularly encountering anyone outside the mathematics department socially was during my undergraduate degree, and I’ve badly missed it.

Between the mathematics building and the college you are caught between two extremes of academic opulence.

After arriving I wanted to read something that would give me a good feel for the history of the place, but at the same time I wasn’t very excited about any of the worthy door-stoppers that I was being pointed towards. I really wanted something salacious. As luck would have it I found just the thing.

Look Back in Laughter: Oxford’s Postwar Golden Age by R.W. Johnson is the 2015 memoir of former Oxford don, Rhodes scholar, and Magdalen College Bursar (at a particularly precarious time in the college’s history). I should say that I mentioned this book with some of my more senior college colleagues, and they assured me that the book was either completely sensationalized or a complete pack of lies.

There are actually several strands going through the memoir. I certainly began to get the immediate feel for the world of dons, the Senior Commonroom, hearties (what Americans would call jocks), and clever-sillys (a certain kind of academic). Johnson arrives at Magdalen as a Rhodes scholar, narrowly escaping trouble in South Africa where he had been involved in anti-apartheid activism, and soon found himself a fellow at the tender age of 25. The decades he spent there covered many seismic shifts: the admission of women into the college, the opening up of Oxford to the wider academic world, and the increasing influence of the PPE course on public policy, politics, and journalism. This last strand is particularly striking; the last insert photos is a group shot of the Lib-Dem/Conservative coalition government, signed by three of Johnson’s former students. Two other ministers were also Magdalen alumni. Johnson also describes how the Economist became increasingly dependent on him to pass on gifted undergraduates for exciting jobs at the magazine (which inevitably led to swift success and promotion). Previous generations of Oxford graduates would have had to slog for years at local newspapers under the barely concealed contempt of their editors.

The idea that many of us may have of Oxbridge as being some engine of meritocracy, excellence, and academic success only arrived in the 20th Century when the “Red dean”, Harry Weldon, decided that they should start admitting students on merit, rather than the pedigree of their boarding school. This was somewhat controversial at the time with many dons (C.S. Lewis is cited) as being unashamed snobs. Indeed, world class academics only began to be hired around this time as well. Johnson goes so far as to describe most of Magdalen’s history as “disgraceful”.

Like just about everyone else, I think, I knew that Magdalen was intellectually extremely distinguished and we all assumed that that his had always been so.

This was in fact quite wrong. Only much later did I learn that for a great deal of its history Magdalen’s dons had been undistinguished and slothful. The college had not long been founded when, in 1520, many of the fellows had to be summoned to answer charges of gambling, hunting, frequenting taverns, misbehaving in Chapel, and the like. But again in 1584 it was reported that all these vices were common, that both President and Bursars were corrupt and that all discipline had broken down, forcing the Visitor, the Bishop of Winchester, to intervene to insist that the founder’s statutes be upheld.

Look Back in Laughter; Chapter 4

The most stunning details come from the chapter covering the three years Johnson spent as Bursar, in which he uncovered extensive financial impropriety, and what I believe can only be accurately described as outright corruption. In short, the college’s once extensive resources were being plundered while the buildings and grounds were being neglected to a dangerous and illegal extent (portions of the college being listed buildings and protected under law). The following passage concerns what happened when he started reviewing the properties that the college was leasing (often at below market rates, and left unreviewed for decades).

Another was someone whom everyone seemed afraid of. I called in Strutt, the Head Porter, and asked him what he know of this case. The man was a major international criminal, he said, specializing in child pornography. Even in Amsterdam he had come across his traces. The police were frightened of him for he was extremely careful and sophisticated in his dealings so nothing could ever be finally be pinned on him and any who approached him would be hounded by the best lawyers money could buy. In addition he had bought several city councilors who could be relied on to make a lot of trouble if their patron was seriously bothered.

From Strutt I got the name of a private detective and asked him to investigate. Rather breathtakingly, he reported soon thereafter that he had broken into the man’s flat, opened his mail and tapped his phone. he had also followed the man round Oxford and said he never took the same road home twice a week. it was the same with all his other dealings — his letters and phone calls were all in code. There were, he said, the marks of a top-class professional criminal with very large assets at risk. Next he traced the man to a large meeting held at a manor house outside Oxford attended by two-dozen men arriving in chauffeured limousines. The detective noted all the number plates but was himself seen while doing so. The meeting immediately broke up. Using his contacts in the police, the detective was able to ascertain that everyone at the meeting hat left the country within 12 hours — a sign that our man was part of a sophisticated international syndicate. At which point I realized that the whole thing was simply beyond me. I was looking at an investigation on which a proper police force might deploy many men for over a year. But the police wouldn’t touch the case and I couldn’t do much with a solitary private detective. I had to let it go.

Look Back in Laughter, RW Johnson, Chapter 12

I don’t think I will think about the difference between an academic and an administrative role in the University quite the same way again.

The Radcliffe Camera
The Natural History Museum.

Cycling around Munster, (long) after the siege.

Back in May I was visiting Giles in Munster. Aside from meditating on what exactly a symmetry restricted group should be, and going to see Detective Pikachu, we did a fair amount of cycling back and forth across the city. Munster enjoys a reputation (perhaps self-proclaimed) of being the cycling capital of Germany, and with all the cycle paths and low levels of automobile use it is not hard to fall in love with the place and wonder why we aren’t all living is such a fashion.

If you are observant enough while wandering around the city, you will notice three metal cages hanging from the steeple of St Lambert’s church. Those cages once held the mutilated remains of religious radicals who had been so jazzed up by the Reformation that they had declared Munster the New Jerusalem and announced the imminent apocalypse, Jesus’s return, and all the rest of it. So deplorable was their rule of the city (and embarrassing) that both Catholics and Lutherans united to lay siege to the Munster to bring an end to New Jerusalem.

This photo of Muenster Cathedral (St. Paulus Dom) St Lambert’s Church is courtesy of TripAdvisor

Giles was good enough to lend me his copy of New Jerusalem: The short life and terrible death of Christendom’s most defiant sect, by Paul Ham. (A good alternative source is this episode of In Our Time on the Siege of Munster, although the reintroduction polygamy is not even given a mention). It makes for quite remarkable reading. To a contemporary reader the most obvious parallel is to ISIS. I would go so far as to say that everything you could find in the rise and fall of ISIS you can also find in the history of New Jerusalem. Down to the beheadings.

The founding of New Jerusalem was the culmination of the work of many personalities. They were all united in the Anabaptist cause: abandoning infant baptism as a perversion of the “true” gospel by the church in Rome. While the followers of Luther took a more pragmatic, and even conservative, approach to religious reform, these “re-baptisers” were revolutionaries outside any kind of religious establishment who were provocative to the point of inciting violence. (Baptism is no small point; you will still find many protestant churches today which require adult baptism for membership.)

Melchior Hoffman, an Anabaptist preacher, prefigured the events in Munster when he declared Strasbourg to be the New Jerusalem, and the site of the apocalypse the following year, 1533. The authorities back then took such rantings seriously enough that they threw him in a dungeon, where he could safely be forgotten. Then came John Matthais, a self proclaimed prophet, who received the divine revelation (or simply decided, depending on your point of view) that Hoffman had got the time and place wrong, and that Munster was in fact the right location. Initially it seemed that this prophesy was realized, as in February 1534 the city was taken into Anabaptist control. This turn of events was seen as an embarrassment, nuisance, and danger to the various authorities involved. Ultimately it fell to Bishop Waldeck — more a nobleman or prince than an actual religious leader — to marshal an army and lay siege to the city. Due to the commitment and tenacity of those under siege, Munster’s excellent fortifications, and the drunkenness of the mercenaries that Waldeck employed, the whole sorry business lasted a year and a half.

John Matthais would go on to have himself cut to pieces by the armies of Bishop Waldec in possibly the most ill advised cavalry charge in history. It is Matthais’ second in command, John of Leiden, who takes over control of New Jerusalem and ruled it through most of the rebellion. Leiden’s rule quickly becomes a tyranny marked with the reintroduction of polygamy and summary executions by decapitation. The whole episode was marked with a strange combination of farce and grim horror.

While ISIS is the most obvious modern parallel, with its explicitly apocalyptic mission, reading the accounts of meetings between radical preachers and Luther calls to mind the general dangers of political radicalism.

Instead, Rothman set off on the well-worn pilgrimage to Wittenberg, as reform-minded novitiates tended to. There, Luther and Melanchthon deigned to meet this impassioned young man, as they had met Hoffman and so many other zealous young preachers. They noted his intelligence and eloquence, yet something about Rothmann troubled them. His passions were unguarded, and untutored. His self-righteousness lacked the grace of humility. They concluded that he was probably mentally unfit for the job. As Melanchthon observed, Rothmann might turn out to be exceptionally good or exceptionally bad.

New Jerusalem, Chapter 7 — Paul Ham

I find the reformation, or at least what little I understand about it, deeply fascinating. It is on the list of subjects that, once you understand a little of what it meant and continues to mean, you are staggered by the degree with which you misunderstood so much of what is going on in the world today.

(For whatever it is worth, Detective Pikachu was fun but completely disposable.)

Gromov, cheese, pretending to quit mathematics, and French.

In December last year, the Notices of the AMS ran a collection of reminiscences in memory of Marcel Burger (1927-2016), the late French differential geometer. He was also a former director of the Institut des Haute Etudes Scientific and, according to the Wikipedia, played a major role in getting Gromov positions in Paris and at the IHES in the 80s. Gromov contributed to the article, listing Berger’s mathematical achievements, before sharing a more personal anecdote:

Within my own field Gromov has had a profound influence. His essay Hyperbolic Groups led to the term “combinatorial group theory” being more or less abandoned and replaced with “geometric group theory”. As a graduate student I found the monograph frequently cited as the origin for an astounding range of ideas. At some point I had trouble finding a copy of the paper online and for a brief moment wondered if the paper itself were just an urban myth or elaborate hoax.

Gromov’s foray into group theory is just one episode in a long career. His first major breakthrough was in partial differential equations; the “h-principal” which, according to Larry Guth, was analogous to observing that you don’t need to give an explicit description of how to put a wool sweater into a box in order to know that you can actually put it into the box. It is actually a little hard, at least for myself, to get a full grasp on Gromov’s other contributions as they span unfamiliar fields of mathematics, but I recommend this nice What is… article, written by the late Marcel Berger, describing Gromov’s contribution to the understanding of isosystolic inequalities.

There is the perception about great mathematicians that, while they are no doubt very clever, somehow they have lost a little of the common sense that the rest of us possess. I’m naturally inclined to discount such thinking; I am far happier believing that we are all fool enough to take absence of common sense, on certain occasions. However, it is hard to dismiss the  idea entirely given the following admission by Gromov, in his personal autobiographical recollections he wrote on receipt of the Abel prize in 2009:

The passage speaks for itself, but I wish to emphasize that Gromov’s discovery of the correct pronunciation of French verb endings came after ten years of living in Paris. You don’t have to have extensive experience learning foreign languages to appreciate how remarkable an oversight this is. It certainly puts his remarks in other interviews about dedicating one’s life to mathematical pursuits in a rather strong light.

If you read the entire autobiographical essay you will find it rather short on biography. The best biographical details I have found came from this La Monde article written on his being awarded the Abel prize. Even then the details seems to be coming second hand. The most interesting parts concern his leaving the Soviet Union:

I wanted to leave the Soviet Union from the age of 14. […] I could not stand the country. The political pressure there was very unpleasant, and it did not come only from the top. […] The professors had to teach in such a way as to show respect for the regime. We felt the pressure of always having to express our submission to the system. One could not do that without deforming one’s personality and each mathematician that I knew ended up, at a certain age, developing a neurosis accompanied  by severe disorders. In my opinion, they had become sick. I did not want to reach that point.

Gromov, according to Georges Ripka, via La Monde (apologies for my translation)

As the article goes on to explain, Gromov decided his best chance to escape was to hide his mathematical talent. He quit math, quit his university, and burned all his academic bridges. He stopped producing mathematics. Or at least writing it. He joined some meteorological institute and did research on paper pulp. Eventually, he was granted permission to emigrate to Israel, but on landing in Rome in 1974 he set off for the States instead, where Jim Simons secured him a position at Stony Brook.

(As a side note, this is Jim Simons of Renaissance Technology and Simons foundations fame. Simons, aside from his mathematical contributions, is probably one of the most important mathematicians alive in terms of funding, supporting, and propagandizing for mathematics. He is considered influential enough for the New Yorker to profile. Alongside Gromov, he is one of the names that every mathematicians should know.)