The Symbolic Middle Ages

According to Dorothy Kim, assistant professor of English at Vassar:

Today, medievalists have to understand that the public and our students will see us as potential white supremacists or white supremacist sympathizers because we are medievalists. The medieval western European Christian past is being weaponized by white supremacist/white nationalist/KKK/nazi extremist groups who also frequently happen to be college students… What are you doing, medievalists, in your classrooms? Because you are the authorities teaching medieval subjects in the classroom, you are, in fact, ideological arms dealers. So, are you going to be apathetic weapons dealers not caring how your material and tools will be used? Do you care who your buyers are in the classroom? Choose a side.

You really have no excuse to address whether your medieval studies is a white supremacist medieval studies or not. You also do not have a choice in whether you are part of this debate because the debate is already prevalent and public. Our students are watching and will make judgements and calls on what side you are really on. I suggest overt signaling of how you are not a white supremacist and how your medieval studies is one that does not uphold white supremacy. Neutrality is not optional.

OK, I’ll choose a side, and that side is a firm stand against this sort of twaddle. I really hate moral bullying – “If it’s important to me, then it needs to be important to you! You’re not allowed not to care – if you deny the problem, you’re part of the problem!”

But maybe the only “problem” is your own warped perception of reality?

Apparently the “alt-right,” whatever that is, takes inspiration from the Middle Ages (and from the Classics too). They like the idea of Crusaders cracking Muslim skulls, and they also like to contemplate a Europe before the advent of mass non-European and non-Christian immigration. But how many people are we actually talking about here? And how big of a problem is this, really? People can idealize any era of history that they want, for whatever reason they want. We always feel sad when other people don’t share our enthusiasm for our subject – well, here are people who love the Middle Ages! How about harnessing that enthusiasm and nudging it towards the academic consensus – on the off chance that one of these types should actually appear in our classrooms? It’s really no different from how one treats students who idealize ancient Egypt, Native Americans, the Caliphate, matriarchal prehistory, or pseudo-history of the Da Vinci Code variety. You accept the students where they are, and gently explain that their vision of the past might not be accurate – and you make sure to explain that whatever happened in the past, doesn’t necessarily make for good policy today.

I really don’t believe that “the public and our students will see us as potential white supremacists or white supremacist sympathizers because we are medievalists.” On the contrary, the vast majority of the public, insofar as they are aware of us at all, are like the audience for Joseph Epstein when he “open[ed] the blinds to reveal the baboons at play, as if to say, ‘Betcha didn’t think their behinds were quite so purple as that.'” Most people roll their eyes at the sheer craziness of a lot of academic dispute, and shed no tears when politicians cut our funding.

In fact, let me turn Prof. Kim’s invitation on its head: what have you done, medievalist, to combat the craziness? What have you done to prove to Middle America that your discipline and profession deserve to be taken seriously?

Jews in Antiquity

I find it interesting that in all of the Histories of Herodotus, there is no overt mention of Jews or Judaism. Herodotus describes the Persian conquest of Babylon (539 BC), an event of great significance in Jewish history, but there is no notice that the Jews were ever in captivity there, or that Cyrus allowed them to return to Jerusalem. In all of Herodotus’s anthropological investigation of the various peoples of the world in the fifth century BC, there is no notice of the Jews at all (unless they are the “Palestinian Syrians” who supplied some ships for Xerxes’s invasion of Greece in 7:89). Come to think of it, there is no mention of the Jews in Arrian’s Anabasis of Alexander (second century AD), even though Alexander (d. 323 BC) had besieged the Phoenician city of Tyre, and then headed down to Egypt to found Alexandria (and to receive word that he was divine at the oasis of Siwa).

This is strange considering how influential the Jews were later to become. Judaea was the trouble spot for the Romans. I suppose that the Jews had largely settled around Jerusalem (elevation: 750 m), while the road to Egypt passed along the coast – i.e. it was easy for people ignore the Jews in the 5th and 4th centuries BC.

Thoughts on Book 9 of the Histories of Herodotus

Sharp-eyed readers will note that I never got around to writing something about the final book of the Histories, which we read in an HON 301 course this past spring (the other posts: 1, 2, 3, 4, 5, 6, 7, 8). The end of the semester is always busy, you must understand. You’ll find some scribblings below, but I’d also like to say that I just finished off my summary of the work, which is now on its own page – see the link above. The Histories is very long, very detailed, and not always straightforward in its narrative, so last summer, in preparation for my CIC seminar at the Center for Hellenic Studies, I started summarizing each chapter as I read it, which forced me to pay attention to the contents, and which produced a document I could review if I needed to. Events got ahead of me, however, and so I couldn’t get it done until now. In Herodotean fashion, I dedicate the fruit of my labors to the service of humanity.

As for Book Nine, the main event, of course, is the battle of Plataea (479 BC), the last major episode in the Persian Wars. Following the Persian defeat at the naval battle of Salamis the previous year (detailed in Book Eight), the Persian King Xerxes hightails it back to Asia, leaving his general Mardonius in charge of the war. After wintering in Thessaly, Mardonius moves south into Attica to try to bribe the Athenians into becoming allies, but the Athenians have once again retreated to the island of Salamis for safety. In the meantime, the Spartans are building a wall across the Isthmus of Corinth to guard the Peloponnese; the Athenians are worried that the Spartans will abandon them, and suggest to the Spartans that they just might take up the Persian offer. Fortunately, the Greek alliance holds, and the Spartans, the Athenians, and other non-Medized Greeks march out to face the Persians and their allies in Boeotia, and the Battle of Plataea ensues. It is not pretty, but the Greeks are ultimately victorious, and that is the end of the Persian attempt to conquer Greece. In an edifying parallel development (which Herodotus claims happens on the same day as Plataea), the Greeks fight another battle across the Aegean Sea at Mycale, defeating the Persians there and freeing Ionia once again. 

Herodotus does not shy away from depicting how fractious the Greek alliance is. Athens and Sparta and perennially suspicious of each other, and the squabbling between the Athenians and Tegeans (at 26-27) about which of them would get the place of honor on the wing at Plataea is a marvel to behold. Herodotus gives overall credit to the Spartans for the victory, but he also illustrates that this battle is no Thermopylae – the Spartans voluntarily give up fighting directly against the Persians (the Athenians, they acknowledge, have more experience in this activity), and when they find that the cavalry attacks are too much for them, they are only too willing to retreat to “the Island,” a defensible hill between two streams (although one Spartan captain, Amompharetus, refuses to go, and a mighty quarrel ensues between him and the Spartan general Pausanias about this). Emboldened by this apparent Spartan cowardice, Xerxes orders an attack, and at this point the Spartans rise to the occasion: “In spirit and strength, the Persians were the equals of the Greeks, but they had no armor, and they were unskilled besides and no match for their enemies in cunning. They made their charges singly or in tens… and so they were destroyed” (62).

But I think that the Greek fractiousness serves a literary purpose. Herodotus is not necessarily trying to show how a plucky underdog or a lovable band of misfits can ultimately be victorious over a superior foe, although I’m sure there is some of that. Rather, he is contrasting the Greek penchant for debate with the Persian custom of obedience. When the Athenians and Tegeans argue about placement on the wing, they each present numerous reasons why they themselves should get it. The Athenians are more convincing, and the rest of the Greeks shout their approval of the Athenian position. This is how the Greeks conduct themselves – they debate their issues in public. Compare this to the Persian “debate” prior to their attack at Plataea – in a war council, Artabazus suggests that the Persians retreat to Thebes, and from there attempt to bribe the various Greeks into Medizing. Mardonius, however, fearful that the longer they wait, the stronger their opponents will get, is in favor of attacking right away, contrary to the results of the sacrifices by the prophet Hegistratus. “Against this argument of his, no one took a stand, and so his plan won out. For he and not Artabazus had the supreme power of command from Xerxes.” When Mardonius asks his commanders if any of them knows of any oracles about Persian defeat in Greece, the commanders “kept silent, some because they did not know the prophecies, some because, though they knew them, they did not think that opening their mouths was a safe thing to do” (42). Thus does their leader pull rank, and they are all obliged to follow him to destruction.

Of course, public debate is not always the best way to determine policy, especially in times of war. But the overall message, I think, is the same one that the US tried promulgating during World War II and the Cold War: totalitarian societies always look terrifying from the outside, projecting as they do this image of unity and efficiency. But it’s all an illusion, and based on fear of being sent to a concentration camp or Gulag. The US was a “nation of joiners,” in the words of Arthur Schlesinger, Sr. – that is, American “civil society” was made up of a lot of voluntary groups that people joined because they wanted to, or because there was some tangible benefit to them (e.g. professional organizations, churches, service clubs, choirs, bowling leagues, etc.). It might look like a mess from the outside, that all of society is not moving forward in lock step to some goal, but it gives people a stake in their own country, and when moved to, they will all get together and defeat their enemies. And it is certainly edifying that many of the Medized Greeks abandon their loyalty to Persia the minute they think it is safe to do so.

The utility of public debate is not the only piece of pro-Hellenic propaganda in Book Nine. In numerous places, the Persians (and their allies like the Thebans) believe that all they need to do is to use their wealth to bribe the Greeks into taking their side (e.g. in 4, 41, 87, or 120). They don’t seem to realize that, to most Greeks, there are more important things than money. This lesson is underlined when, after the battle of Plataea, Pausanias orders Mardonius’s servants to prepare a meal in the Persian manner, and his own servants to prepare a meal in the Spartan manner. The contrast cannot be more stark – the Persian meal is a model of decadent luxury, while the Spartan meal is very simple indeed – prompting Pausanias to declare that the Persian king is foolish: given that he is used to such extravagance, what good can he possibly derive from conquering the poor Greeks? (The final chapter of the book [122] further emphasizes that “from soft countries come soft men. It is not possible that from the same land stems a growth of wondrous fruit and men who are good soldiers.”) Finally, there is the elaborate story (at 108-113) about how Xerxes falls in love with the (unnamed) wife of his brother Masistes, and so he contrives to marry his own son with Masistes’s daughter Artaynte, hoping that this tie will bring him closer to his sister-in-law. Instead, he falls for Artaynte, and conducts an affair with her, his own niece. This affair is discovered by Xerxes’s wife Amestris, who places the blame for it on Masistes’s wife; Amestris thus has Masistes’s wife mutilated. As a result of this outrage, Masistes leaves for Bactria in order to raise a revolt there, but Xerxes’s troops overtake him and kill him before he gets there. Now, Herodotus certainly deals with Greek misbehavior and malfeasance throughout The Histories, but to close out his work with such a story of incest and intrigue at the Persian court is surely a deliberate attempt to impress upon the reader who the bad guys are.

One final observation. In Book Nine, there are numerous instances of “prophets,” like Hegistratus, making sacrifices – but these sacrifices are not just to propitiate some god, but to determine his or her will. I suppose this is a form of haruscipy – the examination of the entrails of an animal to see what the future holds – perhaps a replacement for augury, the practice of discerning the will of the gods by the flight patterns of birds (as Calchas does in Book One of the Iliad). So if you don’t have time to consult the Oracle at Delphi (or that of some other well-known shrine like Dodona), you can have a personal seer providing answers to immediate questions. I must say that the Greek faith in such customs is something that has always puzzled me about them, or at least serves as the strongest counter-example to the notion that they are “rational.” Of course, the Oracle isn’t stupid, and often gives ambiguous answers so that whatever happens, it’s always right. But why no one ever saw through this (at least, Herodotus gives no evidence of any skepticism either on his own part or the part of any of his subjects) is a mystery to me. I suppose we have to wait until the fourth century and the further development of Greek philosophy under Plato, Aristotle, and others, before we encounter doubt about Fate.

Franklin’s Family

One of the interesting things we learned this summer in Philadelphia is that Benjamin Franklin lived in a common-law relationship with his wife Deborah Read, from 1730 until her death in 1774. Was this on account of Franklin’s principled unorthodoxy, the same spirit that impelled him to reject organized religion and to appear at the court of the French king wearing a rustic fur hat? Not really – it was simply that Read could not prove that her first husband was actually dead, and could thus not remarry without committing bigamy. Franklin and Read spent much time apart, however – allegedly she hated sea travel, and so did not accompany Franklin on his many trips to Europe. Another theory “suggests that a debate over the failed treatment of their son’s smallpox was the culprit.” See an extensive article in this month’s Smithsonian Magazine for more details.

Franklin already had an illegitimate child by another relationship before he set up house with Read; this was William Franklin (d. 1813). William grew up to be the last colonial governor of New Jersey and interestingly, remained a steadfast loyalist during the Revolutionary War. He ended his days in London unreconciled to his father.

Lakepoint Station

A school fundraiser this evening took us to Lakepoint Station, a Family Entertainment Center (“FEC”) at Lakepoint Sporting Community in Emerson, Georgia, a “premier sports vacation destination… home to several world-class venues” and “a must-visit location for travel sports since 2013.” I admit that this is not exactly my cup of tea (entirely too much attention is paid to SPORTS in this country), although I’m happy that it’s bringing money into the area. Lakepoint Station itself features video games, miniature golf, a hall of mirrors, a laser tag room, and a rock climbing wall; I think the idea behind it is that mom can take the younger siblings here while dad watches his eldest play in his Little League tournament. I will say that this historian appreciated the theme of Lakepoint Station, which was Bartow County’s history of mining and railroads. A structure out back takes the form of a large rock, which houses various attractions hosted by “Miner Joe,” and outside children can pan for gems in a long sluice. The miniature golf course has various railroad accoutrements, a decorative caboose sits on site, and the venue is right next to the functioning Western and Atlantic Railroad. Best of all, enlarged historic photos adorn the walls of the interior, so your kids may actually learn something!

Cities

post at a blog called A Fine Theorem contains an interesting nugget:

The Romans famously conquered Gaul – today’s France – under Caesar, and Britain in stages up through Hadrian. Roman cities popped up across these regions, until the 5th century invasions wiped out Roman control. In Britain, for all practical purposes the entire economic network faded away: cities hollowed out, trade came to a stop, and imports from outside Britain and Roman coin are near nonexistent in the archaeological record for the next century and a half. In France, the network was not so cleanly broken, with Christian bishoprics rising in many of the old Roman towns.

Here is the amazing fact: today, 16 of France’s 20 largest cities are located on or near a Roman town, while only 2 of Britain’s 20 largest are. This difference existed even back in the Middle Ages. So who cares? Well, Britain’s cities in the Middle Ages are two and a half times more likely to have coastal access than France’s cities, so that in 1700, when sea trade was hugely important, 56% of urban French lived in towns with sea access while 87% of urban Brits did. This is even though, in both countries, cities with sea access grew faster and huge sums of money were put into building artificial canals. Even at a very local level, the France/Britain distinction holds: when Roman cities were within 25km of the ocean or a navigable river, they tended not to move in France, while in Britain they tended to reappear nearer to the water. The fundamental factor for the shift in both places was that developments in shipbuilding in the early middle ages made the sea much more suitable for trade and military transport than the famous Roman Roads which previously played that role.

This prompted an interesting comparison from Steve Sailer:

Maybe this is analogous to the recent shift from landline telephone networks to wireless telephone networks. Landline networks, like Roman roads, required a lot of social organizational capital to build and maintain, as Americans had in the AT&T era, but many other countries did not. Lots of cultures, such as the 20th Century Italians, had a hard time maintaining a landline system.

In contrast, cell phone networks don’t require a society to be good at cooperating, so even anarchic Somalia can have decent cell phone service. You just have to have a few people who knew what they are doing.

Similarly, medieval shipping networks required concentrations of technically advanced shipwrights here and there, but didn’t require a giant Roman-like state to keep the roads repaired. The ocean repairs itself.

It is striking how land-oriented Roman culture was despite emerging on the Italian peninsula where no place is very far from the sea, the land is mountainous, and the sea is relatively calm and warm. In contrast, England has fairly mild terrain and the Atlantic ocean is more tumultuous than the Mediterranean sea.

Maybe the explanation is that British rivers were better for transport than Italian rivers south of the Po due to more rain and less severe slopes, so it was easier to get started with inland shipping and then continue out into the ocean as your technique improved. But Italian rivers tended to be short and steep and go dry now and then, so they weren’t as good launching pads for eventual saltwater navigation.

Maybe, but Venice and Genoa did dominate maritime trade on the Mediterranean in the high and late Middle Ages…

For my part I am interested in how little influence the Roman Empire ultimately had on Britannia, certainly when compared to Gaul. I assume this is one reason why French is a Romance language while English is a Germanic one.

Lady Di

This day marks the twentieth anniversary of the death of Diana, Princess of Wales, at the age of 36 in a car crash in the Pont de l’Alma tunnel in Paris. Her lover Dodi Fayed and driver Henri Paul also perished in the wreck. Paul had three times the legal limit of alcohol in his blood, and had been driving over 100 km/h, in an attempt to evade a number of photographers chasing them on motorcycles. 

Monogram of Diana. Wikipedia.

Lady Di’s relative youth and the violence of her death were shocking, of course, but what was most remarkable was the great outpouring of sympathy for the deceased. She had admitted to cheating on Prince Charles prior to their divorce and since that time had led a sort of Eurotrash lifestyle, but to a lot of people these things then became badges of “authenticity,” especially when compared to the rest of the allegedly stuffy, uptight royal family – her flaws became her virtues. Press coverage was nonstop, a great carpet of flowers and teddy bears appeared in front of Buckingham Palace, and even Prime Minister Jean Chrétien ordered flags to fly at half-mast in Canada. The Queen remained at Balmoral, her Scottish summer residence, in the week following the crash; by Thursday the headlines were reading “Show us you care!” – the idea being that King George VI had refused to leave London during the Blitz, so Her Majesty should come down to be with her people in their hour of need. I recall someone later writing that this drift “deserved a special Pulitzer for ass-saving improvisation,” as it usefully deflected peoples’ animosity away from the “paparazzi,” whom they blamed for Diana’s death.

Coat of arms of Diana during her marriage to Prince Charles – i.e. the Spencer arms, impaled with the arms of the Prince of Wales. Wikipedia.

There are theories that World War I started because all the Events of 1914 took place starting on June 28 – i.e. during the summer – and that people would have been a lot less hotheaded if the Archduke had been assassinated in January.* Summertime is the “silly season,” and my personal theory is that the higher temperatures and extended daylight hours made the reaction to Diana’s death a lot more intense than it otherwise would have been.

Coat of arms of Diana following her divorce – i.e. the Spencer arms, on a lozenge. Wikipedia.

Fortunately, it burned itself out. It reminded me of a medieval political assassination (e.g. that of Thomas of Lancaster or Simon de Montfort); often, such deaths were followed by a burst of miracles at the tomb of the deceased, but these tended to taper off as grief for him waned, and without the active involvement of interested parties, the initial sympathy generally did not evolve into a sustained saint’s cult. I seem to remember that a memorial march on the first anniversary of Diana’s death attracted much fewer people than anticipated, and two years ago the Express newspaper found her gravesite at Althorp, Northants., to be in an unkept state. Furthermore, I am really glad that the Queen has not abandoned her old-school reserve and devotion to duty, that she has not started oversharing her personal feelings with celebrity journalists or publicly working out at the gym, because that’s what people expect these days – and that she retains the respect and affection of her subjects for it. Christopher Hitchens was perhaps too harsh when he called Diana a “silly, trivial woman” and a “simpering Bambi narcissist,” but the revelation that she had borderline personality disorder in retrospect makes complete sense and suggests that she was not really someone worthy of admiration.

Royal Standard for members of the Royal Family without assigned arms (i.e. the royal arms, within a bordure ermine). This covered Diana’s coffin during her funeral, “the most hyped non-event in history” (Hitchens, again). Wikipedia.

* Modris Eksteins, Rites of Spring (1989):

The days of that summer were long and full of sunshine; the nights were mild and moonlit. That it was a beautiful and unforgettable season is part of the lore of that summer of 1914, part of its poignancy and mystique…. The fine days and nights of that July and August encouraged Europeans to venture out of their homes and to display their emotions and prejudices in public, in the streets and squares of their cities and towns. The massive exhibitions of public sentiment played a crucial role in determining the fate of Europe that summer. Had it been a wet and cold summer, like that of the previous year or the next one, would a fairground atmosphere conductive to soap-box oratory and mass hysteria have developed? Would leaders then have been prepared to declare war so readily? There is evidence that the jingoistic crowd scenes in Berlin, St. Petersburg, Vienna, Paris, and London, in the last days of July and in the early days of August, pushed the political and military leadership of Europe toward confrontation.

Jeannie Rousseau de Clarens

From the New York Times:

Jeannie de Clarens, an amateur spy who passed a wealth of information to the British about the development of the V-1 and V-2 rockets during World War II and survived stays in three concentration camps for her activities, died on Aug. 23 in Montaigu, southeast of Nantes, France. She was 98.

The death was confirmed by her son, Pascal.

In 1943 Jeannie Rousseau, as she was then known, was an interpreter in Paris for an association of French businessmen, representing their interests and helping them negotiate contracts with the German occupiers. She was young and attractive. She spoke flawless German. She was a favorite with the German officers, who were completely unaware that the woman they knew as Madeleine Chauffour had been reporting to a French intelligence network, the Druids, organized by the Resistance.

Getting wind of a secret weapons project, she made it her mission to be on hand when the topic was discussed by the Germans, coaxing information through charm and guile.

“I teased them, taunted them, looked at them wide-eyed, insisted that they must be mad when they spoke of the astounding new weapon that flew over vast distances, much faster than any airplane,” she told The Washington Post in 1998. “I kept saying, ‘What you are telling me cannot be true!’ I must have said that 100 times.”

One officer, eager to convince her, let her look at drawings of the rockets.

Most of what she heard was incomprehensible. But, blessed with a near-photographic memory, she repeated it in detail to her recruiter, Georges Lamarque, at a safe house on the Left Bank.

In London, intelligence analysts, led by Reginald V. Jones, marveled at the quality of the information they were receiving from Paris, notably a startling document called the Wachtel Report. Delivered in September 1943, it identified the German officer in charge of the rocket program, Col. Max Wachtel; gave precise details about operations at the testing plant in Peenemünde, on the Baltic coast in Pomerania; and showed planned launch locations along the coast from Brittany to the Netherlands.

Relying on this information, the British organized several bombing raids against the plant, which delayed development of the V-2 and spared untold thousands of lives in London.

In “1940-1944: The Secret History of the Atlantic Wall” (2003), the historian Rémy Desquesnes called the Wachtel Report a “masterpiece in the history of intelligence gathering.” When Mr. Jones asked who had sent the report, he was told that the source was known only by the code name Amniarix, and that “she was one of the most remarkable young women of her generation.”

Read the whole thing.

Babylonian Trig

Evelyn Lamb in Scientific American:

Don’t Fall for Babylonian Trigonometry Hype

Separating fact from speculation in math history

You may have seen headlines about an ancient Mesopotamian tablet. “Mathematical secrets of ancient tablet unlocked after nearly a century of study,” said the Guardian. “This mysterious ancient tablet could teach us a thing or two about math,” said Popular Science, adding, “Some researchers say the Babylonians invented trigonometry—and did it better.” National Geographic was a bit more circumspect: “A new study claims the tablet could be one of the oldest contributions to the study of trigonometry, but some remain skeptical.” Daniel Mansfield and Norman Wildberger certainly did a good job selling their new paper in the generally more staid journal Historia Mathematica. I’d like to help separate fact from speculation and outright nonsense when it comes to this new paper.

What is Plimpton 322?

Plimpton 322, the tablet in question, is certainly an alluring artifact. It’s a broken piece of clay roughly the size of a postcard. It was filled with four columns of cuneiform numbers around 1800 BCE, probably in the ancient city of Larsa (now in Iraq) and was removed in the 1920s. George Plimpton bought it in 1922 and bequeathed it to Columbia University, which has owned it since 1936. Since then, many scholars have studied Plimpton 322, so any picture you might have of Mansfield and Wildberger on their hands and knees in a hot, dusty archaeological site, or even rummaging through musty, neglected archives and unearthing this treasure is inaccurate. We’ve known about the artifact and what was on it for decades. The researchers claim to have a new interpretation of how the artifact was used, but I am skeptical.

Scholars have known since the 1940s that Plimpton 322 contains numbers involved in Pythagorean triples, that is, integer solutions to the equation a2+b2=c2. For example, 3-4-5 is a Pythagorean triple because 32+42=9+16=25=52. August 15 of this year was celebrated by some as “Pythagorean Triple Day” because 8-15-17 is another, slightly sexier, such triple.

The far right column consists of the numbers 1 through 15, so it’s just an enumeration. The two middle columns of Plimpton 322 contain one side and the hypotenuse of a Pythagorean triangle, or a and c in the equation a2+b2=c2. (Note that a and b are interchangeable.) But these are a little brawnier than the Pythagorean triples you learn in school. The first entries are 119 and 169, corresponding to the Pythagorean triple 1192+1202=1692. The far left column is a ratio of squares of the sides of the triangles. Exactly which sides depends slightly on what is contained in the missing shard from the left side of the artifact, but it doesn’t make a huge difference. It’s either the square of the hypotenuse divided by the square of the remaining leg or the square of one leg divided by the square of the other leg. In modern mathematical jargon, these are squares of either the tangent or the secant of an angle in the triangle.

We can interpret one of the columns as containing trigonometric functions, so in some sense, it is a trig table. But despite what the headlines would have you believe, people have known that for decades. The mystery is what purpose the tablet served in its time. Why was it created? Why were those particular triangles included in the table? How were the columns computed? In a 1980 paper titled “Sherlock Holmes in Babylon,” R. Creighton Buck implied that through mathematics and cunning observation, one could sleuth out the meaning of the tablet and offered an explanation he thought fit the data. But Eleanor Robson, in “Neither Sherlock Holmes nor Babylon,” writes, “Ancient mathematical texts and artefacts, if we are to understand them fully, must be viewed in the light of their mathematico-historical context, and not treated as artificial, self-contained creations in the style of detective stories.” It’s arrogant and will probably lead to incorrect conclusions to look at ancient artifacts primarily through the lens of our modern understanding of mathematics.

What did it do?

There are a few theories about how Plimpton 322 was created and used by the person or people who made it. Mansfield and Wildberger are not the first to believe it’s some sort of trig table. On the other hand, some believe it links the Pythagorean theorem (known by these ancient Mesopotamians and many other civilizations long before Pythagoras) with the method of completing the square to solve a quadratic equation, a common problem in mathematical texts from that time and place. Some believe the triples were generated using different numbers not included in the table in a “number theoretic” way. Some believe the numbers came from so-called reciprocal pairs that were used for multiplication. Some think the tablet was a pedagogical tool, perhaps a source of exercises for students. Some believe it was used in something more like original mathematical research. Academic but readable information about these interpretations can be found in articles by Buck in 1980, Robson in 2001 and 2002, and John P. Britton, Christine Proust, and Steve Shnider from 2011.

If it is a trigonometry table, is it better than modern trigonometry tables?

Mansfield and Wildberger’s contribution to scholarship on Plimpton 322 seems to be speculation that the artifact could be used to do trigonometry in a more exact way than we do now. In a publicity video by UNSW that must have accompanied the press releases sent to many math and science journalists (but not to me—what gives, UNSW?), Mansfield makes the claims that this table is “superior in some ways to modern trigonometry” and the “only completely accurate trigonometry table.”

It’s hard to know where to start with this part of their claims. For one, the tablet contains some well-known errors, so claims that it is the most accurate or exact trig table ever are just not true. But even a corrected version of Plimpton 322 would not be a revolutionary replacement for modern trig tables….

Is base 60 better than base 10?

Perhaps the utility of different types of trig tables is a matter of opinion, but the UNSW video also has some outright falsehoods about accuracy in base 60 versus the base 10 system we now use. Around the 1:10 mark, Mansfield says, “We count in base 10, which only has two exact fractions: 1/2, which is 0.5, and 1/5.” My first objection is that any fraction is exact. The number 1/3 is precisely 1/3. Mansfield makes it clear that what he means by 1/3 not being an exact fraction is that it has an infinite (0.333…) rather than a terminating decimal. But what about 1/4? That’s 0.25, which terminates, and yet Mansfield doesn’t consider it an exact fraction. And what about 1/10 or 2/5? Those can be written 0.1 and 0.4, which seem pretty exact.

Indefensibly, when he lauds the many “exact fractions” available in base 60, he doesn’t apply the same standards. In base 60, 1/8 would be written 7/60+30/3600 which is the same idea as writing 0.25, or 2/10+5/100, for 1/4 in base 10. Why is 1/8 exact in base 60 but 1/4 not exact in base 10? It’s hard to believe this is an honest mistake coming from a mathematician and instead makes me even more suspicious that his work is motivated by an agenda.

Plimpton 322 is a remarkable artifact, and we have much to learn from it. When I taught math history, I loved opening the semester by having my students read a few papers about it to show how much scholarship has gone into understanding such a small document and how accomplished scholars can disagree about what it means. It demonstrates differences in the way different cultures have done mathematics and outstanding computational facility. It has raised questions about how ancient Mesopotamians approached calculation and geometry. But using it to sell a questionable pet theory won’t get us any closer to the answers.

Victorian Childbirth

My grad school colleague Anne Huebel has penned an entry on Remedia: the history of medicine in dialogue with its present.

Managing Victorian Reproduction: Medical Authority over Childbirth in British Advice Literature

“Obey implicitly the advice and directions of your medical attendant.” Such was the advice of Dr. Thomas Bull for women in labor. Dr. Pye Henry Chavasse, Bull’s contemporary and rival in the advice literature industry, agreed. Doctors Bull and Chavasse wrote popular books on pregnancy, childbirth, and infant care in mid-nineteenth-century Britain. Like William Smellie a century earlier, they emphasized a doctor’s right to manage a woman’s health and to expect obedience in return for their medical care. Both authors described how women should regulate their lives and bodies prior to and during pregnancy, labor, and lying-in, all of which occurred in the patient’s home. On the surface, the books encouraged women to take control of their health; however, they in fact advanced the medical management of women’s bodies.

Much more at the link.