Narrative Geometry and Literary Embellishment

Archimedes’s emblematic death makes sense psychologically and embodies a rich historical picture in a single scene.

Transcript

Archimedes died mouthing back at an enemy soldier: “Don’t disturb my circles.”

Or that’s how the story goes. Is this fact or fiction? We have third-hand accounts at best so there is plenty of room for doubt. But I’m putting my money on fact nonetheless. I think this standard story makes sense. I think it works psychologically with what little we know about Archimedes as a person, and I think it fits contextually with what we know about Archimedes’s era and circumstances. So let’s investigate this, and let’s use the death of Archimedes to reflect on these broader themes.

Archimedes was killed when the Romans invaded his city, Syracuse. There is little doubt about that. The precise details are less clear. There are various versions of the story from several ancient authors. These passages are all conveniently collected at the Archimedes website by Chris Rorres, which I highly recommend.

Let’s quote the standard version from Plutarch: “Archimedes was working out some problem by a diagram, and having fixed his mind and his eyes alike upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow him. Archimedes declined to do so before he had worked out his problem to a demonstration. The soldier, enraged, drew his sword and ran him through.”

It is quite popular to cast doubt on the story of Archimedes’s death. One example is the recent biography “Archimedes: Fulcrum of Science” by Nicholas Nicastro (pages 43-44). This biography argues that the standard story “doesn’t pass the smell test” to use Nicastro’s words. Because “any properly self-interested soldier would know the reward for capturing Archimedes.” Indeed, Archimedes was famous and the Roman commander wanted him captured alive, it is said.

So the idea that “the soldier recognizes Archimedes but simply liquidates a valuable prisoner – indeed one who amounted to a strategic asset for Rome – simply because he was lackadaisical in responding to orders doesn’t pass the smell test,” according to Nicastro’s biography.

I’m not so sure about that. We know about police brutality. We know for example that George Floyd was killed by police while being apprehended, after being suspected of using a counterfeit twenty-dollar bill. And that was on an ordinary Monday in a peaceful, prosperous country.

The soldier who killed Archimedes was not having a normal Monday dealing with petty delinquents. This soldier was in enemy territory in an active war zone. You would think that this soldier would have been on high alert against ambushes and sudden movements, quite rightly.

And let’s consider what the soldier’s opinion of Archimedes would have been. Archimedes was well known and famously led the military engineering efforts that fended off the Romans for years. What would the soldier think of the figurehead of the enemy? Would he find that such a great geometer must be spared for the greater good? Or would he think that Archimedes was a terrorist responsible for the deaths of his friends?

This soldier may very well have seen first hand the death and suffering inflicted by Archimedes’s famous warfare machines. Maybe for example a friend of his drowned when Archimedes sunk a Roman ship during one of the previous invasion attempts. Or maybe his brother had his legs crushed by one of Archimedes’s catapults, and returned home as a cripple, which made such an impression on the younger brother that an unstoppable hatred festered in him and he swore to dedicate his life to revenge against this evil Greek insurgent.

Indeed, maybe on this very day, the day that he came to stand before Archimedes, this soldier has already had to watch helplessly as a close friend and brother in arms died a gruesome death. Such things can happen in war.

So I don’t think we can say: the soldier wouldn’t have killed Archimedes because he had orders not to and, rationally speaking, it would have been in his best interest to obey. This soldier may very well have been under immense and acute psychological pressure and trauma at this moment, when he happened to come face to face with the very symbol of everything he had been taught to hate. That’s what I think about this so-called “smell test.”

But that’s the soldier’s psychology. Now let’s consider it from Archimedes’s point of view. Would Archimedes be calm and collected and compliant when the soldier comes to arrest him? No, he would not.

The invasion is even more traumatic for Archimedes. Archimedes was born in Syracuse and spent his life there. There is every reason to think that these roots meant a lot to Archimedes. Archimedes was famous already in his lifetime. No doubt he had generous offers to go elsewhere, just like superstar academics today. But Archimedes stayed.

And he wrote his treatises in the local dialect of Greek, rather than adapting to the more prestigious version of Greek spoken in Athens and Alexandria. Perhaps again a sign of local pride.

Archimedes also mentions his father, who was apparently an astronomer. So that’s another sign that Archimedes attached some importance to his heritage.

And of course Archimedes was heavily involved in the defense of the city as a military engineer for many years. Obviously another sign of considerable patriotism.

And now, all of that is being destroyed. Archimedes’s birthplace, his home for his entire life, burnt and ransacked by a heartless military force.

If Archimedes looks out his window all he sees is everyone he ever loved being slaughtered, and generations of cultural heritage being sadistically trampled to dust by soldiers’ boots.

This would be heartbreak and trauma enough. But it’s worse. It’s worse for Archimedes because he was in charge of the defense. It’s his fault. All this blood is on his hands. Or so it would seem to him.

Archimedes was given every resource to orchestrate the Syracusan defense. All those notorious warfare machines that held the Romans at bay for so long: that’s not something you throw together in your basement. Archimedes must have been entrusted with massive resources and he must have had considerable manpower under his command.

His friends and brothers had put their faith in him in their hour of need, and he failed. Archimedes has let them all down. He has let his father down, and his forefathers.

Not only is Archimedes watching his city burn. He is also overcome by the crushing guilt that this is all because of his personal failure.

How do you think this guy is going to react when an enemy soldier comes to take him away? He’s not in a mood to be read his Miranda rights, is he?

It was time for Archimedes to go. Shot down on the pavement. It was the only honorable option left.

Most of the historical accounts frame the death of Archimedes in terms of the trope of the absent-minded professor, lost in a diagram, oblivious to the world around him. I imagine that this is a sanitized account. Most of the historical accounts were written under Roman rule.

Maybe the real events were quite a bit uglier and a lot less flattering for Roman historians to repeat. Maybe Archimedes was not so cartoonishly lost in geometrical thought at that moment as story-tellers pretend. Maybe he knew full well what was going on, like any normal person would. Especially since he was obviously very well aware of the prospect of Roman military invasion, and he would understand very well what it meant when Roman soldiers had reached his house.

Archimedes was an experienced military engineer who had lived under the immediate threat of military attack for years. Is it too much to imagine that such a person would carry a weapon, perhaps a small dagger?

Well, now is the time to use it. If not now, when?

Of course by the time it comes to that you have already lost. You don’t have a dagger because you think you will be able to fight your way out. You carry the dagger because when the time comes to use it your choices are: die on your knees or take one ------ down with you.

That’s how I would write Archimedes: The Gritty Reboot.

If that’s what happened then Roman historians would hardly want to admit it. It doesn’t do their self-image any favors that the great Archimedes would rather die than be taken alive by Romans. So the literary cliché of a philosopher so absorbed in thought that he does not notice his surroundings is a welcome euphemism readily at hand.

I quoted earlier the standard story from Plutarch, which leans into this cliché very heavily. Actually Plutarch also goes on to give two other versions of the death of Archimedes. “Others write”, he says. And then he says for instance that Archimedes was killed because a soldier mistook his astronomical instruments for gold trinkets and killed him to plunder his valuables. I don’t think so, but even this version clearly has some elements of truth. Namely, there was indeed plundering by the soldiers and some flashy-looking astronomical instruments made by Archimedes were indeed stolen by the Romans and publicly displayed in Rome. So this would have given some credence to the story.

Maybe Plutarch is relieved that there is some ambiguity regarding the death of Archimedes. Maybe he knew full well that these alternative stories are not true. Indeed, he first tells the standard story as if it was unequivocal fact, and then he adds the qualifier “others write” when telling the other versions. As if he knew they were false.

Since the real version is so embarrassing for the Romans, muddying the waters with some misleading alternatives is a convenient way to trick the reader into thinking that no one really knows for sure what happened. Throw a little fake news in there to dilute the facts.

It is very much possible that the circumstances of Archimedes’s death were very well known and documented at the time and for generations afterwards. It is reported that a personal friend of Archimedes wrote a biography. Which is now lost but which could have been a very excellent and reliable source available for some time.

Another credible source is the Greek historian Polybius. He writes about Archimedes’s military machines but he doesn’t mention the death of Archimedes in surviving texts. Some parts of his works have been lost, perhaps very conveniently for the Romans. Polybius was writing not too long after the fact. He could have spoken to eyewitnesses who were actually there on the ground during the siege of Syracuse.

So, we should not say: It’s all just a bunch of legends made up hundreds of years later. There were better sources. There were serious historians who tried to keep a record of these things. We should not be so pessimistic.

The existence of these better sources may have acted as a deterrent on historians like Plutarch and Livy, whose works are all we have now. They mention the death of Archimedes in passing. Their main concern is not to preserve a maximally accurate record of exactly what happened to Archimedes. They retell the story because it suits their purposes. Because it is vivid and gripping story as well as an occasion to make a moral point. And they are probably not opposed to tweaking the story to those ends.

Nevertheless they would not want to be caught saying something that is provably false. The possibility that some readers may have access to quite reliable historical accounts in other sources could very well be a check on the freedom that these other writers could afford to allow themselves.

And presumably they had some professional integrity as well. Sometimes I wonder about the modern historians who are so quick to dismiss ancient writers as if they just wrote fiction and legends and made up whatever they thought sounded cool. I wonder what it says about our modern colleagues that they find this kind of behavior from a history writer to be plausible and in character.

Of course third-hand and forth-hand accounts are distorted. Of course we should be mindful of what layers of biases and hidden agendas that these accounts have been subjected to. But that’s very different from making stuff up out of thin air.

The scholarly norms back then were different as well. Historians were expected to be storytellers with flair. Not be academic bores like today. So history writers back then would allow themselves more literary leeway that allowed them to add some stylistic embellishments. But the game was to do that will remaining faithful to the basic facts.

For example, according to one modern analysis (Archimedes and the Roman Imagination, 92), one version of the story of the death of Archimedes elegantly frames it in terms of concentric circles. First the walls of the city are breached, then the soldier breaks into Archimedes’s house, and finally, as a last layer of concentric fortifications, Archimedes wraps his arms around his precious diagram. So the theme of geometricity is echoed in the narrative structure itself. Exquisite. Things like that are fun to play with as a writer. And that’s the kind of embellishment that you can add without doing any harm to the essence of the historical facts.

Here’s another in my opinion misguided objection to the historical reliability of the story. I quote from the MAA Press book “Archimedes: What Did He Do Besides Cry Eureka?” Regarding Archimedes’s last words, this book writes:

“Who would have reported them? Would a soldier who had killed Archimedes, against orders from his commanding general, offer this incriminating evidence?” (3)

Well, yes. Yes, he would. The Roman army routinely tortured enemies for information. The solider would surely know that very well, perhaps first hand. This is the same Roman army who have given us the word “decimate”: that is to say, in case of disobedience, kill one in every ten of your own soldiers just to make a point and maintain discipline.

Obviously the soldier is at the mercy of the army. They know where he lives. They know where his family lives. Of course they can easily apply any amount of pressure. Of course the soldier will talk. How could he not?

Besides, the soldier would not have been alone, would he? I would think that, when clearing enemy territory in an active battlefield, soldiers would presumably prefer to stick together in groups rather than wander off on their own. So why wouldn’t the other soldiers report what happened? Of course they would.

That doesn’t mean that the reported last words of Archimedes are historically accurate, of course. I don’t think they are. And indeed the sources do not agree about it verbatim anyway. But the problem is not that it would not have been knowable or that actual facts were not available to historical writers. Things like last words were precisely the kind of thing that an ancient history writer will embellish a little bit for style and flair and drama and narrative when writing their own as it were reboot of this established story. But they were not fiction writers and their literary freedom was checked by professional integrity.

Nor was there necessarily any language barrier preventing Archimedes and the soldier from understanding one another, if we assume that the soldier was Latin-speaking. Before it came to war these regions had been close partners in diplomacy and trade. People may have known quite a bit of each other’s languages. Archimedes, who was highly educated and part of the king’s entourage, may very well have been able to express himself in Latin. (Ivo Schneider, Archimedes, 2nd ed., xvi)

In any case, the orders were supposedly to capture Archimedes alive. That’s what the Romans wanted. But what did Archimedes want? Did Archimedes want to be paraded around Rome like a trophy of war? So that tipsy dinner party guests could make fun of the freak with the big brain? Or did Archimedes want to sell his engineering skills and warfare know-how to his mortal enemies while the bodies of his childhood friends and neighbors were still warm?

I don’t think so. I think Archimedes would rather spit this soldier in the face and die a martyr’s death.

Not unlike Socrates two hundred years earlier. As Archimedes would have been well aware, Socrates basically chose death. Socrates was sentenced for corrupting the minds of young people with dangerous ideas.

But Socrates’s death sentence could easily have been avoided, it seems. First the trial itself, a democratic jury trial, had the possibility of bargaining built in. Socrates could have proposed a realistic alternative to the death penalty as a compromise, which could very well have worked. But he refused to do so out as a matter of principle.

Then even after being sentenced Socrates still had the chance to escape. He had powerful friends, rich friends. Some of them could have pulled some strings and made some bribes and probably Socrates could have been able to escape. Then he would have had to leave Athens and start over a couple of islands down, but alive.

Socrates wanted to make a point instead, and it worked. Maybe if he had let the Athenians boss him around then that would only have emboldened this mob to go after the next guy in the same way. Instead, Socrates died, to the shame of Athens. Right after this Plato and Aristotle thrived in Athens for many decades. Perhaps not a little thanks to Socrates’s sacrifice and moral victory in death.

In a better world, Archimedes’s death could have had much the same effect. After Socrates’s death, the Athenians had enough moral backbone to realize that they had screwed up and they got their act together. No such luck for Archimedes. The Romans were unfortunately beyond redemption. Even Archimedes’s martyr death was not enough to stem the greed and cruelty of these militaristic imperialists, unfortunately.

We know that now, after the fact. But Archimedes could not have known that. Archimedes could very reasonably have felt that dying like a man of principle and honor was the only remaining gift he could give to his countrymen.

Let’s look at the Romans now. There’s the invading general, Marcellus. The sources would have us believe that he was ever so noble, and he was ever so concerned that Archimedes not be harmed, and after this unfortunate death Marcellus paid his respects to Archimedes’s surviving relatives etc., etc., blah, blah, blah. You can decide for yourself how much of this transparent propaganda you want to believe. To me it sounds more like a slimy politician’s talking points at a staged photo op.

Of course even propaganda carries some information. In this case we see what the Romans actually cared about. They were very preoccupied with honor. They go to great lengths to explain how Marcellus’s actions were so honorable and noble. Remember, this was still good Rome. Republican Rome, democratic Rome. They still have some integrity in their own way. Before long it was to get a lot worse, and wannabe-emperors didn’t even need to pretend to be honorable anymore.

Anyway, the Romans cared about honor but not about science. Archimedes died working out some theorem. What theorem? Nobody could care less among the Roman writers.

Marcellus stole some of Archimedes’s instruments. Planetaria and spheres. Model representations of the universe. Archimedes’s planetarium perhaps used intricate combinations of cogwheels to represent the motions of the planets mechanically. These instruments don’t exist anymore, of course. No scientific interments from that era have survived the centuries. But the written sources speak in some detail about how Marcellus brought back these Archimedean devices.

Of course the Romans didn’t know what to do with these scientific instruments, since they didn’t have any scientific tradition. No academy or museum or library that could do anything with these Archimedean masterpieces.

So Marcellus just kept one of them at home, in his living room, like a hunting trophy stuffed animal head.

Another one of these models was put in the Temple of Virtues in Rome. They just stuck this valuable scientific device in a Sunday church so the plebs could gawk at it. Because no one in Rome had the competence to do anything better with it. That is what happened with important scientific artifacts in this barbaric culture.

Then there is Cicero, another one of these pseudo-intellectuals. Cicero was a career politician and his first appointment was in provincial Sicily, Archimedes’s home. That was 137 years after Archimedes was killed and this formerly Greek-speaking territory was absorbed by the Romans.

Cicero bragged that “I managed to track down [Archimedes’s] grave. The Syracusians knew nothing about it,” in Cicero’s words. Yes, they were all savages, you see, and Cicero, the white savior, is here to singlehandedly rescue mankind’s cultural heritage. According to himself.

Cicero claims that the tomb was “completely surrounded and hidden by bushes of brambles and thorns” and when he discovered it “I immediately said to the Syracusans, some of whose leading citizens were with me at the time, that I believed this was the very object I had been looking for. Men were sent in with sickles to clear the site, and when a path to the monument had been opened we walked right up to it.”

Right, so as you can see Cicero could hardly contain himself when he found the grave. He was so excited that he immediately went and sat down in a shaded area and had some chilled wine with his very important friends. Clearing a path to the grave was a top priority, so they only kept, like, two or three slaves at most to fan them with palm leaves while they waited for the other slaves to cut the path. My God.

You know Archimedes’s saying: Give me place to stand and I shall move the earth. If it was Cicero it would go: Give me a place to sit and I shall order some slaves to move the earth. Oh, and did I mention that my friends happen to be very important dignitaries by the way?

But Cicero is not done yet. Apparently he thought his bragging up to this point was too subtle for you dimwits, because now he’s going to spell it out for you:

“So one of the most famous cities in the Greek world, and in former days a great centre of learning, would have remained in total ignorance of the tomb of the most brilliant citizen it had ever produced, had [I] not come and pointed it out!”

That’s the great Cicero for you, supposedly a master of rhetoric and style. He apparently found that the very obvious moral of the story would have been too obscure without him simply stating directly that he was saving people from “total ignorance.” Apparently that’s what passes for a great orator in this lousy age. Not only telling a story blatantly designed for self-aggrandizement, but then, as if that was not enough, he just turns and looks directly into the camera and just flat out brags explicitly. What an absolute windbag.

I am in good company with these condemnations. Let me quote the great Heiberg (Mathematics and Physical Science in Classical Antiquity). Johan Ludvig Heiberg, the great classical scholar who published the definitive editions of the works of Archimedes and Euclid and so on, more than a hundred years ago. A legend in the field.

Like me, Heiberg laments the harm done to science by what he calls “the cold breath of Rome” (73). And he has some choice words for Cicero in particular. Here’s what he writes:

“The Romans, with their narrow, rustic horizon, had always in their heart of hearts that mixture of suspicion and contempt for pure science which is still the mark of the half-educated --- and sometimes bragged of it. Cicero, the arch-dilettante, boasts that his countrymen, God be thanked, are not as these Greeks are, but restrict the study of mathematics to what is useful and practically applicable.” (80)

By contrast, Heiberg is full of enthusiasm for “the Ionian school in the full blaze of its glory,” as he writes, when scholars “breathe a spirit of exact, critical, keen observation” and “attack charlatans and speculative theorists with a vigorous and often fiercely sarcastic polemic.” (24)

“One longs to recover something of that robust Ionian criticism” (37), says Heiberg. Yes! Let’s bring it back indeed. Sarcastic polemic and all. Then Archimedes will not have died in vain.