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My attempt at a UK-style diary column…

New Hampshire’s state motto — Live Free or Die — struck me from the moment I first read it off a rear license plate as amusingly over-determined. Sure, the sentiment calls back to New England’s revolutionary tradition, but is now laden with so much other import that you have to laugh when you read it. Like with many other of the state mottoes I feel the need to ask “OK, but what are we really concerned about here?

In the case of New Hampshire the answer to that question seems to be “covered bridges”. Which are quite literally what the name suggests. That is to say bridges built with their own roofs, preventing snow and ice accumulating on the road surface beneath. I am to understand that such bridges last longer, are safer to use, and attract an unusual degree of local pride. Based on the selection postcards available on the rack I perused, they are far prouder of their covered bridges than most of the White Mountain peaks. Driving past a particularly congested covered bridge we could see visitors slowing down to gawk and take photographs of themselves.

It’s all much less “Live Free or Die”, and much more “We Like Our Safer Bridges.”

They liked their covered bridge so much they framed it.

The day after new year I went out for a jog around the small-town-liberal-arts-college-campus. With their leaves wet and glistening in sodden piles on the ground around them, the trees had the air of men who had thrown off their soiled garments and stood there completely exposed to the elements. They continued to hold up their branches — as dignified as they had been in their summer pomp.

One tree had been decorated in the fashion of a Christmas tree. I suppose we were still close enough to Christmas that this remained acceptable. Except that instead of the usual hung ornaments, baubles, tinsel and lights, the branches were laden with surgical masks, N95s, mini whiskey bottles, larger gin bottles, and the lids off tin cans, hanging by the ring pull. I imagine a student art project, or perhaps a particular kind of creative writing teacher trying to demonstrate the value of ritual and tradition, and the value of subverting it.

I jog by two kids throwing a blue American football back and forth while an adult supervised. They were wearing facemasks outdoors. I later pass a woman walking her dog and I began to sense a growing trepidation. Omicron was looming on the horizon.


I bought an LCD computer monitor for $25 on Craigslist and I’m feeling the thrill like it is 2002. The online listing site still lives, looking every bit like it is still 2002.

We drove across town to pick up the monitor, and I paid the man in cash. “I’m sorry, I just don’t like letting people into my house,” the seller told me as he led the way into his garage where he would demonstrate the monitor actually working before I took off with it. I told him that was entirely understandable, especially these days, but I realized his concern was not Covid related. After all, I was the only one of the two of us wearing a mask.

He was an older man, lean and wearing faded jeans and sneakers. His garage was tidy and well organized. The mind runs to dark and sensational places when a man explains that he doesn’t like letting strangers into his house. But these are usually the least interesting explanation for a man’s abiding attachment to his own privacy.

I just finished reading Lauren Hough’s collection of autobiographical essays Leaving isn’t the Hardest Thing. One of her more famous essays that appeared a few years back recounted her years working as a “cable guy” in a DC suburb. She often had to explain to customers that if they wanted their internet back, they were going to have to let her go down into their basements. “Unless you have kids in cages, I don’t care,” she would assure them. As she discovered, people have all kinds of reasons to be cautious about letting strangers into their home, many of them not actually sinister.

High Resolution

I feel a real thrill at the prospect of making a New Year’s resolution. While usually inclined toward maintaining my set routine, I remain vulnerable to the countervailing compulsion to rearrange my life, as some are drawn to rearranging the furniture every couple of months. Even the common varieties of vague and Protestant resolution stir something in me. Cook more, eat vegetarian, cut the processed sugar, cut the booze, hit the gym, walk a mile a day; I’m not a fan of the misery and the defeat and, worst of all, the society that makes people suffer for their bodies, yet the idea of experimenting with the way I live persists. Also, I am always eager to hear from someone who has made a resolution because, to my mind, they are setting off on a kind of adventure.

I have a history of resolutions — New Year’s and otherwise. As a graduate student in Montreal I spent a year exclusively reading books written by women. Another year I read the news exclusively in French. Lent 2017, now living in Israel, I ignored the news entirely. In 2020 I started listening to a slow French news podcast every day, and I succeeded until the national lock-down was declared. That resolution was less failed, more redundant. While half the world was planning on Duolingo-ing their way through their confinement, I realized that my resolution had become superfluous. Like it or not, the entire world’s collective furniture was being rearranged. I no longer had to worry about breaking up my own routines or trying out a new way to live. Not when going to the supermarket became a surreal and uncertain experience. Not when the pandemic began to change the way we dreamed.

The desire to find a different way to live is tightly coupled with a prurient interest in the way other people live. Praise be then to those brave voyagers reporting back to us with their experiences and collected wisdom via You-tube. They have tried doing 100 press-ups a day, 100 crunches a day, and 100 squats a day. They have tried reading 100 pages a day, writing 1000 words a day, and writing a novel in a month. You can find them quitting smoking, vaping, drinking, coffee, sugar, gluten, video games, world of warcraft specifically, social media, and the internet. You can find them trying meat for the first time, playing magic the gathering for the first time, watching a BTS music video for the first time, a kitten seeing snow for the first time, Amish girls seeing an airport for the first time, and Koreans trying bourbon for the first time. People have will tell you how they found eating like Taylor Swift, Donald Trump, Christiano Ronaldo, Adele, Michael Phelps, and The Rock. There are people who try, and debate the merits of, military rations from across the world.

To my mind, we (and especially these Youtubers) are all the descendants of Henry David Thoreau, the New England writer, proto-naturalist, proto-activist, and abolitionist. From July 1845 to September 1847 Thoreau lived apart from his town and community, working with his hands, in a cottage on the edge of Walden pond. His written account of the experiment was published almost seven years later so we can, as the expression goes, read all about it — from growing beans to visiting town every once in a while. But he also explains his motivations — principally, a deep cynicism about the lives of the men around him. He saw them “digging their graves before they are born” and living under the tyranny of their own opinions of themselves.


But men labor under a mistake. The better part of the man is soon plowed into the soil for compost.

Walden – Thoreau

It is not easy to transpose a thinker of the past into current circumstances. If Thoreau was alive today I can’t be sure if we’d find him vlogging about polyamory, a mid level marketing scheme, or radical politics. Quite possibly all of the above. I doubt that he would be the kind of person to play the incredibly sincere looking video game adaptation of his book.

In lieu of Thoreau, we have the likes of the Try Guys, who arrived on the video landscape with a four minute report on wearing women’s underwear for the first time.

You cannot watch such a video of those young men and not acknowledge that they are bucking against the tyranny of their own opinions of themselves. And having glanced through all these videos of people trying, quitting, warning and advising I suspect there is also the underlying cynicism about the way we live our lives that reflects something of Thoreau as well.

So what is my own new years resolution? As a teenager I read a book whose title and precise nature has faded from memory, but what I do remember is that the author, by way of illustrating some other point, briefly described spending a year reading the complete works of Shakespeare. At first, he recounted, it was difficult going, trying to soldier on through all that pentameter. But with perseverance the language opened up and he developed an authentic appreciation of the plays. It was far neater experience than I would today grant credence to, but it struck me at the time as a deeply worthy thing to do. I know for a fact, however, that I would not be able to read that much Shakespeare in a year. Aside from anything else, I am generally committed to reading wherever my fancy takes me. Instead, and by way of trying to get some Shakespeare into my system, I will commit myself to devoting each year to a different play. And I will begin, in 2022, with Macbeth.

A Kind of Visitation or Possession

The biographer of Isaac Newton is in an unenviable position. Usually the writer thrives on the access they can get to their subject — their writings, correspondence, contemporaneous accounts. But in Newton’s case, the biographer is cursed with too much material. Newton’s unpublished writings form an extensive body of work spanning an impressive and embarrassing array of interests; from science and mathematics, to alchemy and heretical theology, Newton was a compulsive note taker. Susan Dry’s The Newton Papers gives a careful account of how these papers managed to escape their fate languishing forgotten in one of England’s aristocratic estates, and into the hands of scholars who could read and make sense of them. Or so they hoped. The writings were so extensive, that they were impossible for any individual to meaningfully absorb. The hope that a definitive or comprehensive view of Newton might be revealed revealed itself to be futile. Dry even concludes that the endeavor is fundamentally misguided.

The first two Newton books I wrote about here took two distinct strategies to avoid the trap presented. James Gleick’s Isaac Newton took the light touch, providing a readable biography that was blessed with being selective in what it presented to a reader. Thomas Levenson’s Newton and the Counterfeiter focused on a lesser known chapter of Newton’s life — his role as Warden of the Royal Mint. Levenson’s book was blessed with seeing Newton out in London, interacting with the world, and thus managed the feat of stepping far enough back from the man that we could begin to see him more fully in his time and place. What emerged was a far more interesting portrait than one man being the turning point of history.

Levenson’s most recent book, Money for Nothing, takes this a step further, to the point that we no longer have a “Newton book”. The real subject is the South Sea Bubble, the arrival of modern finance, and the connection to the “Scientific Revolution”. Newton’s significance, beyond having himself bought shares in the South Sea Company, is that he had developed the keenest understanding yet of the relationship between equations and the world that they could represent.

Ultimately, this mathematical insight is at the heart of modern physics, the science that Newton, more than any other single thinker, would create. It it’s simplest form, the idea is this: the full picture, the complete geometrical representation of all the available solutions to a system of equations, can be understood as all the possible outcomes for a given phenomena described by that mathematics. Each specific calculation, fed with observations of the current state of the whatever you’re interested in, the flight of a cannonball, the motion of a planet, how a curveball swerves, how rapidly an outbreak of the plague might spread, makes a prediction for what will happen next. In his twenties, working on his own, with almost no systematic experience of the study of the real world, Newton did not yet grasp the full power of the ideas implied by the way he had begun to think about the math.
That would come in time. But what made his annus mirabilis so miraculous, was the speed and depth with which Newton forged the foundations of his ultimately revolutionary way of comprehending the world.

Money For Nothing, Thomas Levenson

Levenson explains that this was not the Ponzi scheme of capitalism that many claim it is. The value the South Sea shares was a measure of trust that the Treasury could reliably pay out in future. Even in these early days of state finance, there was an understanding that a state that was constantly borrowing could also be worthy and trusted creditor. The theory was that the size of the national debt as it stood was only important when considered against the future productivity of the nation. In principal, and indeed in practice, a nation that invested in itself would grow and develop economically, allowing itself to making good on future repayments.

The second advantage that the British government possessed was the inexorable passage of time. The funds it borrowed at any moment became bets on the nation’s economic life year over year. The wager was that the ongoing work of every new enterprise, each voyage, everything that Britons did to get and spend in the future, would create enough wealth to support the debts being incurred. The chancellor of the Exchequer didn’t have to treat every expense as a pay-as-you-go imperative. Whole nations, as London’s monetary thinkers has discovered, need not perform the virtues embodied in the very good advice to pay off a credit card balance in full every month. Rather, the task was to balance the needs of the moment with an analytical picture that could be drawn of Britain as a whole, all its getting and spending and accumulation, integrated over years to come.

Money For Nothing

Making this case can be divisive. Indeed many, such as Daniel Defoe, seem to have been divided within themselves about this development; on one hand despising the traders and stockjobbers who ran the secondary markets, while supporting the state borrowing that they enabled on the other. Many readers, if they were to correctly read the argument I believe the book is making, would probably object to it. The argument is that national debt and secondary markets for financial products are important, necessary, and work (except when they don’t). Making this argument can be as tricky as convincing someone of the merits of modern art or free verse. In the case of government borrowing and stock markets, the most obvious problem you have in this case is what ultimately befell the South Sea Company.

After almost a decade of providing reliable and unremarkable returns via direct Treasury payments, there was in 1720 an attempt to convert a huge amount of illiquid government debt into the liquid and more manageable form of South Sea Shares. At this point, the win-win-win equation that held between company, shareholder, and government was badly abused. Just about every kind of financial crime was practiced (insider trading, artificially pumping up prices, and outright bribery), and over course of the year the price of the shares increased ten-fold, from 100 GBP to 1000 GBP.

Among the reasons Levenson presents for the South Sea Stock crashing at the moment it did, was a collective realization that the stock could not offer a rate of return any better than the most ordinary of private loans.
In truth the company couldn’t even offer that. In a desperate attempt to prop up the share price, a completely unsustainable dividend of 50 GBP was offered to shareholders. While that would be a magnificent return on the “par” price of 100 GBP, on the recent sale price of 1000 GBP this was a very ordinary 5% return.

William Hogarth – The South Sea Scheme

I cannot help but draw analogies with the current excitement around cryptocurrencies. In place of Hogarth’s satirical paintings, Defoe’s commentary, and Pope’s poetry, which accompany Levenson’s account, we have Twitter memes about buying the dip and right-clicking NTF art. We can also imagine that once cryptocurrencies begin to look a lot more “boring”, there might be a major correction. From this perspective the volatility of cryptocurrencies is less a liability and more of a feature.

If we are to embrace the analogy, there is a dis-quietening reality that the South Sea Bubble offers. Although the share price crashed, the political careers ended, and assets seized from many of the incriminated, the financial tools and derivatives that made it all possible would go on to form the backbone of modern finance (with some occasional regulation, if you can believe it). Similarly, even if bitcoin and etherium suffer some almighty crash, it doesn’t mean that it won’t find a place in the long term landscape of finance.

To be clear, I do not welcome a bitcoin future. Plenty of people, in particular those who understand what a blockchain actually is, are writing in strong terms about how little this offers. But at the heart of why I don’t like cryptocurrency is my suspicion of the world it would produce. As of the moment the main contributions of cryptocurrency to society are enabling cyber criminals looking to profit from ransomware, and diverting huge amounts of computational hardware, time, and energy towards “mining” these tokens. It is a libertarian future where governments can’t meddle with money on our behalf.

The South Sea Bubble, a Scene in ‘Change Alley in 1720 1847, exhibited 1847 Edward Matthew Ward 1816-1879 Presented by Robert Vernon 1847 http://www.tate.org.uk/art/work/N00432

Where is Newton left in all of this? As best we can tell, he wisely sold his initial investment in the South Sea Company, at a profit, mid way through the bubble. He then unwisely reinvested later, as the price continued its precipitous rise, and lost out when the bubble crashed. So Newton, for all his unprecedented insight, was just as vulnerable to making a fool of himself as the rest.

Instead Levenson presents us with with Archibald Hutcheson MP, who despite his lack of scientific training best embodied the scientific analysis of the market when he sat down an began computations to derive how much the shares would have to return to justify their price.

This was recognizably a scientific revolutionary’s way of thinking. In the Principia Newton had constructed mathematical models that could explore the behavior over time of the moons of Jupiter or could predict the motion of a comet with a track that remained mostly unknown. He published his results both as an exercise in scientific reasoning and with persuasive intent: he sought to persuade his readers that what he had discovered “cannot fail to be true.” In his earlier writings, Hutcheson attempted much the same double act. His work focused on the dynamics of budgets instead of celestial bodies, but it spoke in the same unassailable language of numbers in flux — and thus asserted a claim to like power: just as Newton had declared his system of the world, Hutcheson’s arguments could not fail to be on the money.

Money For Nothing

Although this paragraph is immediately followed by a caveat.

There was, of course, a key difference between Hutcheson’s calculations and the utterly authoritative demonstrations in the Principia. When Newton bragged about his work’s unassailable accuracy, he could let nature be the judge, pointing to the agreement between his mathematical account of a comet’s flight and the track it actually traversed. Hutcheson could not command such certainty. Instead, he used the cultural power Newton and his friends had given to mathematical reasoning to strengthen his political argument. Whatever truth his algebra might contain was continent on the uncertain behavior of the human actors involved in any financial choice.

Money For Nothing

I have often been perplexed to read of kings, rulers, and governments being compelled to certain courses of action by economic necessity. It is hard to buy into a motivation you have little intuition for, and that belongs to a game for you don’t know the rules. Currency crises and borrowing crises and monetary crises and even national productivity crises are often referenced with little explanation. This is all to admit a glaring hold in my own education, but I certainly can’t imagine that I’m the only one.

It is a testament to the success of Levenson’s book that I found it as enlightening as I did. Having read no previous account of the South Sea Bubble, I was effectively going in cold. Levenson takes the reader through all the mechanics of the swaps and trades, providing the important back of the envelope calculations that make sense of what happened. There is no unnecessary hand-holding, and I did reread certain passages, but it was all there.
On top of this, Levenson populates his account with an impressive dramatis personae, providing a vivid portrait of British society reacting to these events. The final chapters outlined the future success of British state borrowing, and I possessed a good sense of what that actually meant. I will be able to make far sense of at least some of the history I was reading than I did before.


There are some conspicuous omissions in Levenson’s narrative. While the South Sea Company’s involvement in the slave trade is covered (practiced, but not profitably) there is no consideration of how the rise of credit based finance might have driven the growth of the trade itself. There is far more discussion of how financing Britain’s wars made a secondary market for government issued debt necessary, and it is argued that the success of the treasury policy that Robert Walpole, Britain’s first Prime Minister, developed in the aftermath of the bubble both incentivized avoiding war while also enabling Britain to “punch above it’s weight” when it did go to war. I found the passages that did address this particularly interesting, and would have read more. But there was no reflection on the implications of a system that enabled Empire, and while Levenson mentions the industrial revolution in Britain as a triumph for capital, I was left wondering about the huge social cost to the working classes of Britain.

To be fair, this would be the subject of a different book. (David Graeber’s Debt springs to mind). There is a very specific moral that Levenson wants to lead the reader to: That the crash of 2008 was fundamentally no different from the crash of 1720. Financial markets are ingenious human inventions, but they need careful supervision and regulation.

A fine message — and I agree. But given what was being invested in back in 18th Century England, you might imagine that some people would have been quite happy to have seen the system crash, investors ruined, and a political system collapse. There are very different kinds of consequences out there that investors or a nation should consider than a crash. Dangers we should also be vigilant for and legislate against.

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.)