The wrangler’s insecurity.

[This is my third post on Newton. Previous posts: one and two.]

If you were to take a look around you during a math department seminar or colloquium, you would witness the audience’s attention begin to drift as the talk sunk further into detail and became increasingly difficult to follow. Losing interest in a talk is more or less expected, and the professional mathematicians in the audience come prepared. Maybe they bring a paper to read, or possibly exam scripts to grade. Sometimes they will turn to a fresh page of their notebook and begin doing some actual mathematics of their own.

As a graduate student at McGill, I remember watching a postdoc fill up a page with long exact sequences and all kinds of diagrams, the notation veering into doodles as he got stuck at what must have been a familiar dead-end. It was a rare, voyeuristic glimpse into someone else’s solitary mathematical practice. I later asked this postdoc — whose notebook I presumed was full of such pages — if he ever went back and reread what he had written. No, he admitted, with a guilty smile.

Which was a relief. Not only because my own notebooks were full of repetitious dead-ends, but also because I too almost never went back to review anything I’d written.

Much has been made of Imposter Syndrome among academics — doubting whether we have truly earned whatever position we have reached given how paltry our contributions can sometimes feel. There is a related sense of insecurity to be found in wondering if you are doing mathematics correctly. To be clear, I don’t mean whether a proof we have written up is sound, but whether or not our process of formulating and devising them is the the “proper” way. As if there might be a correct way (or even a professional way) of doing mathematics.

These are not new concerns to have.

Isaac Newton was incredibly secretive in his work and did not have anything approaching students as we might describe them. But after his death, the calculus he developed would form the foundation of modern mathematical and scientific education at Cambridge.

Those who scribbled hastily on those exam papers were students, above all, of Newton’s mathematical physics. Though Newton had not cultivated a following during his own tenure at Cambridge, by the end of the eighteenth century the principals laid down in the Principia — and in particular the mathematical contents of that book — formed the basis for an intensely competitive system of testing at the university by which students were ranked in descending order based on their results on terminal examinations. known as the “Mathematical Tripos.” (The origin of the term Tripos is uncertain, but it may refer to the three legged stool on which students originally sat to take the oral examinations.)

The Newton Papers – Sarah Dry, pg 85

The material, and especially the notation, would be modernized as European influences arrived, but Newton did not lose his centrality. The manner in which he actually arrived at his great insights became a matter of interest. There is a great distinction between how discoveries are made, and how they finally appear on the page. Everyone knew how they personally went about doing mathematics, and even how their tutors told them to do mathematics, but was that the same as how Newton went about making his original discoveries? For all they knew, it might have all been provided to him by divine revelation.

On the Quadrature of Curves. See the Cambridge website to view more scans of Newton’s papers.

In 1872 a means of settling the question presented itself. Newton’s papers — or at least a large portion of them, covering far more than mathematical physics — had resided for nearly 150 years in the library of one of England’s aristocratic houses: Hurstbourne park. But now the Earl of Portsmouth was donating the scientific portion of papers back to the University of Cambridge.

Newton had been famously coy about his own methods, suggesting that he had kept his true means of discovering the Principia private and had only cast them publicly in the language of geometry. The question was therefore whether he adhered to the rigorous, manly, and above all morally upright techniques of thinking that Cambridge undergraduates were coached to acquire. To answer this Stokes and Adams were forced to consider whether Newton himself should — or could– be held accountable to the techniques that were mastered in his name. The Newton papers had the potential to probe more deeply the shadowy divide between patient work and divine inspiration, offering the promise of settling not simply what Newton had done but how he had done it. […] the question had a special urgency at Cambridge where the moral value of study was paramount. In that respect the Newton papers mattered for every undergraduate preparing for the Tripos and for what the Tripos itself stood for. Would the man who served as a model for what should be learned also reveal himself through his private papers, as a model for how to learn?

The Newton Papers – Sarah Dry, pg 88

Sarah Dry, author of The Newton Papers, a chronicle of the journey Newton’s writings took after his death, presents an interesting comparison of the two mathematicians, John Couch Adams and George Gabriel Stokes, who were tasked with making sense of his old notebook papers.

John Couch Adams (1819-1882),

On the one hand was John Couch Adams, whose ability to compute mathematically in his head was the stuff of Cambridge legend. This savant-like ability came with a tenacious reluctance to write anything down. This reluctance cost English astronomers the first opportunity to observe Neptune. Having deduced, from Uranus’ orbital irregularities, where a mystery planet should be found in the night sky, he failed to explain himself clearly to the astronomical bigwigs, who had little patience for the recent graduate. Roughly a year later, in 1846, the Frenchman Urbain Le Verrier managed to solve the problem and pointed his country’s own telescopes in the right direction. Adams was left with nothing but his incomplete written accounts and undated papers declaring his discovery, making establishing precedence impossible. Not that he seemed much bothered by losing out on the glory. He was personally very satisfied simply to have managed the computation.

Sir George Gabriel Stokes, 1st Baronet (1819-1903)

George Gabriel Stokes (of Navier-Stokes and Stokes’ Theorem) on the other hand, wrote compulsively, both mathematically and in personal correspondence (often to ease his own insecurities). Later in life he became editor of the Philosophical Transactions of the Royal Society, then the foremost journal in science, and this involved dealing with a huge amount of correspondence. Unfortunately he was a hoarder of papers of all and every kind, filling the rooms at his disposal with tables on which to pile up his papers. This was all compounded by his inclination towards procrastination

They might have made a formidable team, had their temperaments combined to negate the other’s weaknesses. Instead the project to deliver a verdict on the value of Newton’s papers and reveal his way of thinking was subject to great delay. Of the two however, it seems that Adams was the one who was most readily able to probe the documents deeply. Sarah Dry quotes Glaisher (Adam’s obituarist) as saying:

[…it was a] difficult and laborious task, extending over years, but once which intensely interested him, and upon which he spared no pains. In several instances he succeeded in tracing the methods that Newton must have used in order to obtain the numerical results which occurred in the papers. The solution of the enigmas presented by these numbers written on stray papers, without any clue to the source from which they were derived, was the kind of work in which all Adam’s skill, patience, and industry found full scope, and his enthusiasm for Newton was so great that he had no thought of time when so employed. His mind bore naturally a great resemblance to Newton’s in many marked respects, and he was so penetrated with Newton’s style of thought that he was peculiarly fitted to be his interpreter. Only a few intimate friends were aware of the immense amount of time he devoted to these manuscripts of the pleasure he derived from them.

John Glaisher — Memoir of the life of John Couch Adams

What Adams was doing, in his own manner, was nerding out. As with the discovery of Neptune, it seems that his motivations were overwhelmingly personal, and less in service to the scientific community. Imagine a referee today reading the paper under review very carefully, but forgetting to take notes and neglecting to get back to the editor. Nevertheless, conclusions were eventually drawn out of their little committee and a report of their findings was presented.

Here was confirmation that Newton had indeed worked by process of refinement that inevitably included false starts and error. In this sense, Newton revealed himself to be less an otherworldly genius and more a figure with whom the Cambridge wranglers could identify, a tireless worker in the mathematical trenches, where progress was made by increments rather than leaps. Adams knew the feeling well. In 1853 he had published an important paper pointing out errors made by Laplace in determining lunar motion and promising to provide the correct calculations soon; it had taken him six long years to get the final numbers. Here, in the papers, was evidence that Newton had worked just as hard to come up with his results.

The Newton Papers – Sarah Dry, pg 105

By the time I had finished my PhD I had produced a sizable pile of used dollar-store notebooks. Browsing through them I could recognize the contours of what I’d spent the past four years trying (and occasionally succeeding) to do. I might even have reconstructed from the pictures and computations I had written out what I might have actually been thinking at the time. And aside from myself, there are a few people in the world who could possibly make sense of their contents. It all went in the recycling. If somehow one of my notebooks did manage to survive, and made its way into the hands of future scholars, I would be alarmed to consider them giving the content more than cursory attention.

The hundreds (?) of pdfs that I have produced, now sitting out there in the cloud stand a far better chance at outliving me. And not just my published work and arxiv pre-prints (which number in the tens). But everything I ever committed to a latex document in my own personal space up there in the cyber heavens. Among all the discarded drafts that might find evidence of something interesting. Not only what I managed to do, but also what I failed to do. What I thought I had succeeded in doing, but had in fact betrayed my own good sense. When I have found mistakes, I am occasionally mindful enough to leave a short note in all-caps to make it clear where the point of failure lies. There is a great deal we can learn from knowing what other mathematicians have tried and failed to do.

Unlike physical notebooks, our cloud storage is password protected. Digital inheritance is already “a thing”, but it seems unclear to me how it will work out in practice. Kafka left his manuscripts in the possession of Max Brod with the instructions that they be destroyed in the event of his death. Brod told Kafka himself that he certainly wouldn’t, and indeed when Kafka died at the age of 40 as a consequence of tuberculosis, Brod set about getting Kafka’s work published. I haven’t taken a survey, but I would imagine that most young writers have made no attempt to ensure their passwords and unpublished estates are in suitable hands. In principal it is possible to submit a request to Google for access to the accounts of the deceased, but I can’t imagine there are any guarantees. I certainly have no idea what the terms and conditions that I have accepted have to say about such eventualities.

Newton died a man of wealth and importance. With neither wife nor children he had no direct descendants, but he did have a slew of half-nephews, half-nieces, and children of his half-sisters. The assets of obvious value were split between them. Those assets of less obvious value — the leftover pile of notebooks and “reams of loose and foul papers” fell into the possession of Catherine Conduitt. She was one of Newton’s half-nieces, and wife to John Conduitt, who had actively assisted Newton in his duties as master of the Royal Mint. This was the consequence of some rather wild tying-up of loose ends:

Newton had died while holding the post of master of the Mint, which in those days required that its holder assume personal responsibility for the probity of each new coinage of money. That meant that at Newton’s death he had nominal debts amounting to the entire sum of Great Britain’s national coinage. John Conduitt agreed to take on this debt until the coinage had been certified, accepting liability for any imperfections in the coins. In exchange for assuming this risk, he asked for, and was granted Newton’s manuscripts.

The Newton Papers – Sarah Dry, pg 15

The Conduitts took ownership of these papers with the view of producing a biography, and begin the work of securing Newton’s posthumous reputation. They became the first in a long line of people who had access to the papers, but lacked the tools really required to properly make sense of them. Their daughter, Kitty Conduitt married John Wallop who would become the Earl of Portsmouth, and papers would enter the library of Hurstbourne Park, seat of the Portsmouth family. (That is to say they fell into the possession of the aristocracy.) And it was there that they would remain, save occasional minor forays, and the recovery of the substantial portion of scientific papers by Stokes and Adams. What finally shifted the remaining papers out into the open was the fall of the English Aristocracy. In 1936, under the financial pressure of death duties and a recent divorce, Gerald Wallop, the ninth Earl of Portsmouth had the papers put up for auction at Sothebys.

John Maynard Keynes, 1st Baron Keynes (1883-1946)

If there is a hero in Dry’s account of the Newton Papers, it must be John Maynard Keynes. His heroic virtue being exceptional taste and judgement. Having begun collecting books as a child (possibly his first foray into speculation) he developed a rather prescient sense for what should be considered valuable. Unlike the majority of collectors he shared the marketplace with, Keynes was actually interested in reading the books themselves. He was less interested in the superficial qualities: illuminations, illustrations, binding, or an illustrious list of prior owners left him unmoved.

Keynes’s new style of collection was self-consciously intellectual, as opposed to aesthetic or literary. It asserted that a particular history of ideas or chain of thought linked certain men through the ages. And it projected the implicit assumption that its creator was an inheritor of both the material and the intellectual masterpieces of a previous age. Keynes was a thoroughgoing Bloomsburyite in his respect. The paintings on the wall, the rugs on the floor, the furnishing in the room, and the books on the shelves were never just things: they were the physical embodiment of ideas and values whose display was a source of both aesthetic pleasure and moral reinforcement. A book in the hand, like the good life in Bloomsbury of the Sussex countryside, linked the life of the mind with that of the physical world.

The Newton Papers – Sarah Dry, pg 147

You might already get the sense that Dry sees Keynes as simply bringing a new set of beliefs to the table, complete with their own set of limitations. Indeed, Keynes considerable contribution to our modern impression and understanding of Newton as half magician and half scientist, was really a very hot take based on an initial reading. He was the one who announced that the papers reveal Newton devoted great time and energy to the disreputable pursuits of alchemy and heretical theology. Yet the fact that so many of Newton’s papers have remained together and in the possession of the University of Cambridge can be attributed to his prescience sense of the papers’ importance.

Abraham Shalom Yahuda (on the right) (1877–1951)

Kaynes was only one of two major buyers at Sotheby’s. Abraham Yahuda, a scholar of ancient languages, bought most of Newton’s theological writings. Yahuda had found himself alienated from his own field of scholarship, due to recent developments in Higher Criticism applied to biblical scholarship. The Documentary Hypothesis was a shocking new line of textual analysis that argued the origins of the Torah were of combination and synthesis with earlier texts. As a consequence, these texts cease to resemble one coherent whole revealed to man, and begin to look more like artifacts of history and culture.

For Yahuda this was a vision of criticism taken to extremes, the text reduced to nothing but error, the possibility of meaning dissolving amid a multiplicity of authors, leaving only commentary, a Talmud with no Torah left in it. He thought in particular that too many sources were being attributed to the Pentateuch and that too many “experts” were exerting themselves “in the art of text alterations and source-hunting.” Thus “the original text was distorted and disfigured and in its place was offered a quite new text of pure invention.” In Newton, who himself sought to return a blemished Christianity to its purer origins, Yahuda found a kindred soul. Interpreting ancient texts didn’t require robbing them of fixed meaning. Both Newton and Yahuda sought instead to find a singular truth amid the variations.

The Newton papers – Sarah Dry, pg170

As a consequence of Yahuda’s desire to find an ally in Newton, those theological papers now reside in The National Library of Israel.

The final portion of Dry’s book concerns the subsequent attempts at synthesis of the material. The fact of the matter is that the task was simply impossible. There is too much material, covering too many subjects for any grand unifying conclusions to be drawn. It was hard to even put together a definitive edition of the Principia that covered all the different editions as well as Newton’s own marginalia. When finally published it was controversial due to the inevitable editorial decisions to include or not include certain material.

It is worth making one final point clear. I have never read Newtons’ Principia. I don’t believe you could find a research mathematician alive who has — unless their research happens to be the history of mathematics. It is a book whose significance is measured in its influence. Many decisions in its composition — in particular the modelling Newton’s Laws on the axioms in Euclid’s Elements — were very important. But you should not read it. When we discuss “great” books, there is usually the tacit understanding that we are missing out if we have not actually read the book. I am quite certain that we have not missed out.

August 28, 2021

On English Magic

Jonathan Strange and Mr Norrell, Susanna Clarke’s alternate history fairy-tale, opens with one of its characters asking a question that carries through the rest of the novel’s thousand pages.

“Mr Segundus wished to know,” he said, “why modern magicians were unable to work the magic they wrote about. In short, he wished to know why there was no more magic done in England.”

This is an England that had once been a very magical place, yet is no longer so. Over the decade “history” the novel covers (1806-1817) we see two new magicians arrive to provide their spells in service to their county in the Napoleonic Wars. The magic of previous generations had been lost, or forgotten, or become dysfunctional in some way. This was apparently despite the many books about/of magic that had been written by the very real magicians of the past, making their secrets and practices clear. Indeed, as the novel opens, England has many leaned societies of magicians, but these members are exclusively of a “theoretical” type — quite unable to cast a single simple spell.

The title characters are our heroes, of a sort. Mr Norrell, an uncharitable and unsociable Yorkshire gentleman who had devoted his youth to carefully studying the remaining books of magic, while also hoarding them away from others. Jonathan Strange, the more sympathetic of the two, is of a more obsessive and intuitive character, sociable and likable, ready to befriend Norrell, and complement his own innate ability by becoming Norrell’s apprentice.

Reviewers have noted the imbalance between the two protagonists, with Strange being the more compelling of the two, yet only actually arriving in the narrative proper a third of the way in. I personally found a great deal interesting in Norrell, however, when I recognized parallels between him and the Isaac Newton I had recently been reading about. Indeed, as I previously described, many of Newton’s pursuits could be described as attempts to recover magical techniques or knowledge from the past that had become lost or forgotten. Norrell’s inclination towards either preserving his recovered knowledge and even monopolize magic are reflected in many of Newton’s own inclinations. The ultimate difference being that science is not magic, and Newton himself was indebted to many of his contemporaries, (most controversially to John Flamsteed for astronomical data). But if you were trying to imagine the mentality of a man like Isaac Newton, I think you could do much worse than consider the character of Norrell.

It can be considered a kind of rule in story telling that you make a promise at the start of a story and you must deliver on it by the end. The question of why there is no magic done in the England certainly makes a clear promise that some kind of light will be shed on the matter. While neither the reader, nor the characters, get direct or complete answers to that question, we do however learn a great deal that is interesting on the subject. Plenty can be deduced a careful reader — enough to leave the book satisfied.

—

Jonathan Strange and Mr Norrell was a publishing sensation. Bloomsbury invested heavily in marketing it, imagining that it would allow them to expand beyond their foundation of Harry Potter sales. I think it is fair to say that almost twenty years on, it is regarded as a classic. In as far as such a thing could be said at this point. I certainly found the length no obstacle, and by the final third I was enraptured by the characters’ unfolding trajectories and their ultimate ends.

It is easy to say that a novel is just words on the page, but the word “just” is doing a great deal of heavy lifting. I find myself increasingly paying attention to what goes on in an individual paragraph the way that film buffs concern themselves with actors, cinematography, and special effects. Take the following paragraph, which demonstrates quite well the Austen-esque prose styling along with Clarke’s ability to capture the regional richness of England which I either never really encountered or appreciated before in English fiction.

At no. 9 Harley-street Lady Pole’s country servants were continually ill at ease, afraid of going wrong and never sure of what was right. Even their speech was found fault with and mocked. Their Northamptonshire accent was not always intelligible to the London servants (who, it must be said, made no very great efforts to understand them) and they used words like goosegogs, sparrow-grass, betty-cat and battle-twigs, when they should have said gooseberries, asparagus, she-cat and ear wigs

pg 173

The list of alternates given in that paragraph pass by quickly in the way that good set dressing, special effects, and cinematography do, but this is harder to pull of than you might imagine. The following paragraph similarly stood out to me, again for it’s command of its setting, but also for the kind of fantastical whimsy that the likes of Lord of the Rings, Harry Potter, and Neil Gaiman manage to tap into. If it could be meaningfully produced industrially you’d find it sold in the Harry Potter stores scattered all across England.

Whereupon Mr Strange told them how, to his certain knowledge, there had been four copies of The Language of Birds in England not more than five years ago: one in a Gloucester bookseller’s; one in the private library of gentleman-magician in Kendal; one the private property of a blacksmith near Penzance who had taken it in part payment for mending an iron-gate; and one stopping a gap in a window of the boy’s school in the close of Durham Cathedral.

pg 281

For those of you reading this who are put off by a thousand page door stop, there is also the BBC miniseries adaptation that I hear was pretty good. And if you would prefer a shorter novel, her second, Piranesi was released last year, is much shorter, and also very good. The New Yorker wrote a good profile of Clarke discussing it.

May 8, 2021

Hence, alchemy.

[This post is something of a sequel to my previous post.]

William Chaloner was born sometime around 1650, making him maybe a decade older than Isaac Newton. He did not receive the schooling Newton did, and he certainly didn’t have a chance at Cambridge. He had the misfortune to be apprenticed into a trade with little future: making nails. A machine — the slitting mill — had arrived that readily produced rods of steel that could easily be cut up and hammed into nails, rendering a previously skilled trade an unskilled one. With protective guilds unwilling to admit him into a more lucrative trade, and arriving in London with no obvious means to support himself, he turned to criminal enterprises.

That is, Chaloner’s first attempt to rise above mere subsistence turned him into a purveyor of sex toys. London in the 1690s was as famous, or perhaps notorious, for its spirit of sexual innovation as Berlin would be in the 1920s. Prostitution was ubiquitous, as much a part of the life of the wealthy as it was that of the poor, who supplied most of the trade’s worker’s. The best brothels vied to outdo each other in their range of offerings — so much so that Dr. John Arbuthnot, a man about town in the early eighteenth century apparently spoke for many when he told a madam at one of the better houses, “A little of your plain fucking for me if you please!”

Newton and the Counterfeiter by Thomas Levenson, pg 57

Chaloner soon moved on to various forms of con-artistry: quack medical advice, divination, and “thief-taking”. The latter involved informing on criminals or political subversives in order to collect financial reward. The Metropolitan police would not be formed until the 19th century, so such people were often the only avenue available for bringing criminals to justice. But the thief-takers often played both sides, exploiting whatever opportunities they could get, and often goaded people into committing crimes so that they could be “caught”. Chaloner made it his business to play both sides.

However much Chaloner made from such rackets — and it would not have been inconsiderable — he wanted more. And the biggest racket in all of England was going on in plain sight, with evidence everywhere to be seen. The racket in question was counterfeiting the King’s coin.

It was not an especially sophisticated game. The low production quality of hammered coins meant that an enterprising fellow could clip the edge of a coin and the coin would still be a coin, but you also had a fingernail of precious gold or silver. And in England it was silver that was of interest. The state of the commodity markets in Europe meant that you could take your pile of silver clippings to continental Europe, buy their cheaper gold, then return to England and convert it all back to silver at a profit and start clipping all over again. Classic arbitrage.

As a consequence, the silver coins of England were beginning to look somewhat diminished. Many of them weren’t even silver at all. Many were outright counterfeits made of baser metals. This caused all kinds of problems, not least of which was the ability of King William III to pay his own troops to fight his war in France. Foreign bankers were unwilling to accept English currency at a good price, and silver was vanishing from England for mainland Europe.

The solution was the Great Recoinage of 1696. The old coins were to be replaced with new machine-struck coins that bore milled edges to prevent clipping and render counterfeiting extremely difficult. This British state at this point in history was rife with corruption, sinecures, and cronyism, so initially at least this whole project was chaotic and in real danger of disaster. It was during this financial turmoil that Chaloner seized the opportunity and set up sophisticated counterfeiting operations that managed to produce high quality fakes of the new coins.

Reading Newton and the Counterfeiter by Thomas Levenson, it is unclear if counterfeiting really was so great a scam. Certainly there was no effective law enforcement in England at this time. And while Chaloner was committing a capital offense, juries were unwilling to sentence men to death on the contradictory hearsay that actually arrived in court. That said, the kind of operation Chaloner ran required the cooperation of a great many people. Not only the skilled craftsmen required to make the dies used to cast the fake coins, and the crew to actually run the production line, but also the actual buyers for the knock-off coins. All these people could potentially betray you. Even if you did not face the executioner, you might have to endure a brief stay in London’s hellish Newgate jail.

The jail used in 1696 was almost brand new, constructed on top of the ruins left by the Great Fire of 1666. The facade of the rebuilt prison was given a hint of the elegance with which its architect, Sir Christoper Wren, hoped to endow the whole city. But such graces did nothing to alter the essential character of a place that was, as Daniel Defoe’s Moll Flanders put it, not “the emblem of hell itself” but a kind of entrance to it” too. Defoe wrote from personal experience: he had been imprisoned there briefly, for debt. Other celebrated inmates confirmed Defoe’s judgement. Casanova, imprisoned at Newgate under accusation of child rape, called it “this abode of misery and despair,” and infernal place “such as Dante might have conceived.”

pg 151

Chaloner would be pursued, with unusual diligence, for his crimes by the recently appointed Warden of the Mint who he had been provoking with the particular flagrancy of his crimes and deceits. In what was an act of considerable bravado Chaloner, who had already been caught for counterfeiting activities, conducted a political campaign to gain access to the Royal Mint, ostensibly to offer his “expertise”, but in reality to take whatever advantage he could. This political campaign involved impugning the newly arrived Warden. As perhaps the title of Levenson’s book has given away, this Warden was Isaac Newton, the celebrated natural philosopher.

Given the absence of anything remotely like a rigorous understanding of economics, soliciting Newton’s views on the currency crisis in England was a pretty reasonable thing to do. That said, everyone seemed to have a view on potential solutions. Newton’s own views would be borne out — not just his understanding that re-coinage was necessary, but also the inevitable failure of having a currency simultaneously based on both gold and silver, and his prescient views on the potential of fiat currency. But his duties as Warden of the Mint were simply to oversee the re-coining, and prosecute clippers and counterfeiters.

The first of these tasks Newton was eminently suited, given his facility with quantitative reasoning. He also had the virtue of considering his position as more than a mere sinecure. Having tired of life in Cambridge, he had been seeking some eminent position in London with which to apply his talents. He made the entire process the object of his attention, from the amount of coal consumed each day, to the rate at which the crews could, and reasonably should, hammer our the coins. Under his oversight the re-coining was completed ahead of schedule. (And to the standards of the day, far more safely than it would have otherwise been done).

The second of his tasks — prosecuting counterfeiters — he abhorred. Nevertheless Newton proved himself to be utterly ruthless. The full details of the lengths he went to have been lost — in that the paperwork was deliberately destroyed in part of what was likely a cover-up.

Conduitt chose not to explain why Newton wanted to destroy the papers, but one inference is that Newton enjoyed the role of inquisitor too much. In this view, Newton proved willing, perhaps eager, to terrorize his captives in pursuit of the necessary confessions and betrayals with a viciousness that even that strong-stomached time would tolerate. Formally, torture had not been used in England as an investigative tool for about half a century before Newton came to the Mint. Elizabeth I had face repeated rebellion, often animated by Catholic ambitions on her Protestant throne — and she was England’s most prolific torturing monarch …

But while official torture fell out of favor, interrogators still knew how to put the boot in as needed. Isaac Newton had plenty of ways to extract the information he wanted from reluctant prisoners and he made use of them. Most of them were within the customary bounds of police detection: trading in fear, not pain. He offered brief reprieves for information: he coerced husbands with threats and promised rewards to wives and lovers. But there is one — and only one– reference to his use of more brutal methods in the records he did not burn. In March 1698, Newton received a letter from Newgate written by Thomas Carter, one of Chaloner’s closes associates. The letter was one of a flurry of messages Carter had sent to confirm that he was eager to testify against his former co-conspirator, but this one had a postscript. “I shall have Irons put on me tomorrow,” he wrote, “if yo[ur] Worship not order to the contrary.” In other words: Don’t hurt me! Please. I’ll talk. I’m ready.

Newton and the Counterfeiter by Thomas Levenson pg 165

Ultimately, Newton was victorious. He was patient and methodical and able to rally his superior resources to hound his man, subjecting Chaloner to an extended stay in Newgate while he gathered witnesses and finally wrong-foot him in the trial. The trial itself being a brief and prejudiced affair, as characterized English justice at that time.

But beyond the torture and lack of due process, there was a central hypocrisy to Newton’s activities. Newton and his famous chums were themselves guilty of crimes quite reminiscent to the ones he was prosecuting. The main difference, I think, was that Newton was practicing the upper class equivalents, which were not concerned with actually making a pile of money, but of a more recreational nature. Here is a passage on his relationship with John Locke:

In part, he relished the opportunity to tutor so well regarded a man. He gave Locke a private, annotated edition of the Principia and composed for him a simplified version of the proof that gravity makes the planets travel elliptical orbits. But Newton’s intimacy with Locke seems to have extended well beyond such benevolent displays of mastery. From the beginning, Newton allowed himself to write openly about secret matters. Both men had subterranean interests — in alchemy, for one, the ancient study of processes of change in nature; and in questions of biblical interpretation and belief, which brought them to the edge of what the established English church would damn as heresy.

Newton and the Counterfeiter by Thomas Levenson pg 43

And more seriously, and quite parallel to the crime of counterfeiting Newton was a very active alchemist. Literally attempting to turn base metals into gold. A process if successfully performed at scale would have created unprecedented economic chaos. But like I say, that wasn’t his ultimate goal. Really he was looking to alchemy to settle the theological implications of his scientific endeavors. He saw performing alchemy as a means of proving the intervention of “God” (or rather Newton’s own notion of God) in the natural world:

He knew that all the theorizing, all the theological argument, all the indirect evidence from the perfect design of the solar system could not match the value of one actual, material demonstration of the divine spirit transforming one metal into another in the here and now. If Newton could discover the method God used to produce gold from base mixtures, then he would know — and not just believe — the the King of Kings would indeed reign triumphant, forever and ever.

Newton and the Countereiter by Thomas Levenson pg 85

It should be understood that once you set aside all the secrecy and strange codes that Newton cloaked his alchemist pursuits in, the experiments he performed were serious and rigorous. Even if he failed to make any progress or establish any new body of knowledge. In this enterprise at least he resembles quite closely many of his peers — making quite serious, but ultimately unsuccessful attempts at making a breakthrough.

–

William Chaloner was hanged from the neck until he was dead, on 22 March 1699. It was not the worse fate he could have met under English law. Newton was not in attendance. He would live on until 1727 when he died in his eighties and buried in Westminster Abbey.

–

Levenson has a recently released book that seems to pick up where this one left off, tracking the rise of modern finance and the influence the Scientific Revolution had on it. I’ve also stumbled on this podcast where Cambridge historian of science, Patricia Fara, discusses her own upcoming book which seems to have considerable overlap with Levenson’s. The first question she is asked is how Isaac Newton managed to die a wealthy man, which was actually a pretty good place to start. (Newton had invested in the East India Trading company, which means, among other things, slavery.)

March 21, 2021

There has been a murder in Gathertown

If you orient yourself temporally you may remember that back in August there was a online fracas involving mathematics. A teenage girl, doing her makeup before work, decided to take the opportunity to lay down for her TikTok followers her skepticism about the idea of math generally:

Who came up with this concept? “Pythagoras!” But how? How did he come up with this? He was living in the … well I don’t know when he was living, but it was not now, where you can have technology and stuff, you know?

Grace Cunningham, TikTok user.

As was keenly observed by the many keen observers out there, the initial response was a pile-on that combined general misogyny with gen-Z hatred; it was the latest installment in the long running complaint about kids these days. This reactionary abuse was soon countered by a more positive wave of responses that acknowledged that her questions were not only legitimate, but exactly the kind of questions our curriculum does little to answer.

I don’t think many mathematicians are particularly satisfied about the way our subject is generally taught. At the university level I find it hard to love force marching students through rote material, stripping centuries worth of mathematics of all its scientific and historical context along the way. So obviously I am happy to see any student kicking back at what we inflict on them. But for those who have made mathematical communication their vocation it was a solid gold opportunity to evangelize. Euginia Cheng wrote a pdf answering Grace Cunningham’s formalized list of questions, and Francis Su wrote a twitter thread.

Grace Cunningham was calling the bluff on the pretenses of her education. In particular, the pretense that you should obviously be learning whatever we are telling you. “Why are we even doing this?” is a legitimate question in a mathematics course, and “why on earth did anyone prove these theorems in the first place” is an even better one. “How did people know that they were right,” presents the awkward truth that people most often are certainly incorrect about many things. What makes these questions awkward is that the people teaching you mathematics will frequently know little to nothing about the history and context within which the theory was developed. Mathematicians are terrible, as a rule, at scholarship, and the history of ideas within mathematics is an essentially distinct field. Most of the context that I have for the mathematics I do is essentially gossip, urban myth, and pablum. Fortunately, while we might be terrible historians we remain excellent gossips, so at least we have plenty of stories to tell.

(I should also concede that it is impossible to generalize in any way about most of my peers. Many of them are tremendously knowledgeable about all kinds of things and wonderful educators. I am, at least to some extent, either projecting or talking about our very worst failings.)

I was dissatisfied by the responses I found to Cunningham’s questions. Not least of all because I don’t think they really answer the questions. No actual historical context was given. The answers more resemble the kind of general motivation and propaganda we give students to encourage them to listen in class and do their homework. I think a good answer would address the fact that the people who developed much of classroom mathematics had some pretty wild ideas about what they were doing. Their motivations would be pretty alien to us, and is a far cry from their homework, exams, or getting a well paid job.

Just to make this explicit: How many of us who have ever taught or taken calculus a calculus course have even done any astronomy? Just from doing a little reading, an obvious observation seems to be that when people sat down to first learn calculus from Newton’s Principia, the big incentive for them was the promise of a serious set of answers about the Sun, the Earth, the Moon, the stars, and even comets. A modern mathematician explaining their motivation for calculus today is a little like a 21st century Western evangelical Christian explaining what the “Old Testament” is all about to an orthodox rabbi.

My modest reading has focused on the life of Isaac Newton. I read Jame’s Gleick’s biography of Newton (highly recommended) and I have a few more on the shelf. I already had some understanding that aside from developing calculus Newton was a heretic, alchemist, and later in life warden of the royal mint. I knew he lived through times of plague, apocalypse, dictatorship, conspiracies, and his work was a major part of the scientific revolution. Particularly pertinent to Cunningham’s question is the fact that for centuries after Newton’s death there was a suppression of the full range of Newton’s intellectual activities. It was only when John Maynard Keynes acquired a substantial portion of Newton’s surviving papers at auction that the truth came out. For a long time Newton’s preoccupations would be considered intellectually inconvenient for all those trying to boost his posthumous reputation, and that of British science with it.

The idea of knowledge as cumulative — as a ladder, or a tower of stones, rising higher and higher — existed only as one possibility among many. For several hundred years, scholars of scholarship had considered that they might be like dwarfs seeing further on the shoulders of giants, but they tended to believe more in rediscovery than progress. Even now, when for the first time Western mathematics surpassed what had been known in Greece, many philosophers presumed they were merely uncovering ancient secrets, found in sunnier times and the lost or hidden.

Isaac Newton – James Gleick (pg 34-35)

Here is a not entirely fanciful reading of Newton’s life: starting his university career dissatisfied with the existing knowledge, and curious about the latest developments in astronomy, Newton develops his theory of calculus. But he is not yet really a scientist. He is still very much a wizard. A young man who has uncovered some profound secrets and is keen to discover more. He invests huge amounts of time and energy in alchemy and theology. The alchemy involved tracking down obscure texts that he hoped would contain the secret knowledge of transforming base metals into precious metals, and his notebooks from this period often amount to his copying out these texts. It also involved working with mercury, a poisonous metal known to drive the alchemists who used it to madness.

His theological interests were no less hazardous since they would have been viewed as clearly heretical to both the Protestant and Catholic religious authorities at the time. By studying the earliest Greek manuscripts he discovered that the concept of the Trinity — that the Godhead is three and one; Father, Son, and Holy Spirit — emerged late in the early church, and certainly couldn’t be considered part of the original Christian tradition. Newton concluded Jesus was not at the same level as God and had never claimed to be. At a time in England when having Catholic sympathies could land you in trouble, this was a dangerous view to have.

I would argue that Newton transformed from a wizard into a scientist the moment the German mathematician Leibniz independently derived his own theory of calculus. No longer had Newton uncovered a forgotten knowledge, but he had derived a theory that someone else could also derive. He was now entered into a race to establish the precedence for his own results — and this meant writing up.

For decades his tools of calculus had languished in notebooks and in his mind. Now he had to write them down, and he chose to present them in the style of Euclid’s Elements, with axioms, definitions, lemmas, theorems. And most intriguingly, in order to prove the correctness of his theory, he drew upon experimental data: astronomical observations from the newly establish Greenwich observatory and tidal charts. He was able to explain and predict natural phenomena that perplexed his contemporaries such as the sudden appearance of comets, and their unusual paths across the night sky. We can recognize this now as a prototype of the modern scientific method, but back then it was controversial, becoming part Newton’s dispute with Leibniz.

Newton wrote many private drafts about Leibniz, often the same ruthless polemic again and again, varying only by a few words. The priority dispute spilled over into the philosophical disputes, the Europeans sharpening their accusations that his theories resorted to miracles and occult qualities. What reasoning, what causes, should be permitted? In defending his claim to first invention of the calculus, Newton stated his rules for belief, proposing a framework by which his science — any science — out to be judged. Leibniz observed different rules. In arguing against the miraculous, the German argued theologically. By pure reason, for example, he argued from the perfection of God and the excellence of his workmanship to the impossibility of the vacuum and of atoms. He accused Newton — and this stung — of implying an imperfect God.

Newton had tied knowledge to experiments. Where experiments could not reach, he had left mysteries explicitly unsolved. This was only proper, yet the German threw it back in his face: ‘as if it were a Crime to content himself with Certainties and let Uncertainties alone.’

Isaac Newton – James Gleick (pg 176-177)

Data is now the recognized currency of modern science, and theology is, well, theology. The mathematical analysis that makes calculus rigorous didn’t come until much later. Newton had started using infinite series in his calculus, but it was understood that you had to be careful because sometimes you could get some bad results.

When Cunningham asks her TikTok followers how early mathematicians knew they were right, in Newton’s case at least, it seems that there are three answers. Newton first convinced himself with arguments we would not consider mathematically rigorous along with his his own empirical observations. Decades later he convinced his peers by publishing a full written account of his theory (in Latin) that provided supporting data. Then a century or so later the full theory of mathematical analysis was developed.

These questions have complicated answers for Newton, but they are really no less complicated for us today, even if they are quite different answers. We live in the age of the arxiv, computer assisted proofs, machine learning, and bodies of work that amount to many hundreds of pages. I’m not going to lie; I love the drama of it all. Some would like to present mathematical proof and progress as being an enterprise free from being sullied with the humanity of its practitioners. For my part I am of the belief that the reasons people commit themselves to mathematics are more complicated than just the aesthetic appreciation of equations.

January 31, 2021

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.

May 23, 2020

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.

March 30, 2020

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.

January 18, 2020

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.

November 23, 2019

Hoodoo what you won’t do.

The past month has been packed. In fact, my life has literally been packed up into boxes, as the first thing I did this month was leave Israel and move back to England, where I am starting a postdoc at Oxford. It has been seven years since I last lived in England, but I haven’t had much time to really take it all in because no sooner had I arrived, set up all my new passwords and bought a bike, I was flying off again to Montreal, Utah, and Chicago to give talks and finish a paper. Most of my life is still packed up in those boxes, but hopefully not for too much longer.

I was in Utah two weekends, so we managed to spend one of those weekends down in the south of the state, visiting the national parks and hiking around Bryce Canyon — a “natural amphitheater” carved into the valley by millions of years worth of rain and wind. These natural forces have sculpted a landscape of striking red rock formations featuring stone spires known as Hoodoos. The Paiute native Americans who lived and roamed these valleys, before the arrival of Europeans, were as taken by the Hoodoos as the camera-toting tourists pulling up in their cars today. The Paiute had a mythology that these formations were the magically petrified remains of “Legend People”, victims of a trickster Coyote god. Who exactly such Legend People might have been remains unclear, but European settlers managed to identify one rock formation as having an uncanny resemblance to Queen Victoria:

The almost central rock formation has an uncanny resemblance to the iconic full profile of the illustrious British monarch.

The Canyon today takes its name from the Mormon homesteaders who settled in the area in 1874. Ebenezer Bryce was a Scottish ship’s carpenter born in 1830, who converted into the Church of Jesus Christ of Latter Day Saints, and, after being disowned by his father, moved out across the Atlantic to Utah. At the age of 17. After marrying a Mary Park in Salt Lake City he did what many of the Church’s faithful were encouraged to do: homestead. And homestead they did — not only in multiple locations in Utah, but also then in Arizona as well. All while having a fantastic number of children.

Before we made the trip I found I had to supplement my limited supply of clothing (most of my clothes being boxed away at some unknown location) if I was going to survive the weekend. So off we went to the Deseret Industries (an LDS equivalent of the Salvation Army thrift store), where aside from picking up some suitable synthetic fabrics, I found a book that took me back to high-school.

Back in 2017 my AS English Literature teacher, Alan Currie, passed away. He had covered Hamlet and Keats — if only I had such lessons to guide me through all of the English canon. But perhaps more interesting and formative for me than the examined syllabus, was the month or so we had after the AS exams had been completed. In principal, we were supposed to use that time to start preparing for the second year — which I had dropped out of (unfortunately and completely unnecessarily). In practice it seemed like the teachers took the opportunity to expose us to the breadth and variety of all English literature offered. Although these classes were redundant in terms of my final grade, I was engrossed enough to go to every one of them.

I remember one class Mr Currie came in with large A3 photocopies from the Times Literary supplement. It contained the shortlist for the TLS/Foyles (2007) poetry competition. Held every year, and now called the Mick Imlah prize, this is was an open competition and all the poems were featured anonymously; readers were provided with a coupon they could cut out and submit a vote on the winner. We spent the class poring over the poems like they were the football pools, trying to work out which was the best, and which ones could possibly be the work of a celebrated poet. Not that I think any of us aside from Mr Currie could have named a contemporary poet outside of those featured in the GCSE anthology. I remember being excited by the sense that literature was a thing going on right now, and not only was I invited to judge, but it was clear that I could also have been submitting poems (were I so inclined).

Now thanks to the Oxford libraries online archive access I’ve been able to go back and find out who actually won (The Mauve Tam-o’-Shanter by Paul Groves).

It was around this time that I set myself the challenge of reading the 1001 Book to Read Before You Die. I can’t remember exactly when I gave up on this. I think it was the moment I decided it was OK to read at a book that was not on the list. At that point the challenge took a far less definite form.

Possibly picking up on my sudden inclination to read as much of the canon as quickly as possible, Mr Currie began suggesting books to me. Usually these books were taken from the dog-eared copies of former set texts that had been retired to a supply cupboard. I remember Mr Currie showing me one classic of American literature, told from multiple viewpoints. It stuck in my mind because Mr Currie was amused to show me one unusual chapter in the middle of the text:

Mr Currie was amused.

I was unable to recall which book this had been. Until I found myself lying in a tent within Dixie national forest, flipping through the copy of As I Lay Dying by William Faulkner I’d bought the day before from Deseret Industries, and discovered that this was in fact the book Mr Currie had suggested to me. Two chapters into the book I discovered that I remembered reading it — or at least those initial chapters. I hadn’t read any further than those first chapters, but had set it aside for some unknown reason — possibly I simply hadn’t known what to make of it.

It is strange to try and imagine what you might have made of a book when you were a decade younger. It would be nice to imagine my capacity as a reader has improved — although there is a thriving industry of commentators reporting that our attention spans have been dramatically reduced. I found myself having to reread the first sixty pages to get my head around what was going on. I’m not sure I would have been up for that in high school. Mr Currie would certainly have approved of my perseverence. I imagine he would have laughed and admitted he had done likewise. And trouble understanding half of the characters were saying.

October 1, 2019

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.)

August 10, 2019