Roman Rocks in Mathematics and Medicine

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(Note: This article was first published in the WUhistory blog. Do check out their site as they have really awesome historical articles!)

If you go around asking random strangers in a clandestine political gathering what have the Romans ever done for us? they’ll probably answer with the aqueducts, irrigation, sanitation, roads, etc.. They’re quite right for saying so. Anyone willing to deny the Romans these achievements is simply being blasphemous, and in Roman times that deserves a quick good stoning. But we don’t have to do that anymore. The stones you pick up for throwing might even be remnants of the Rome that was once the beacon of majesty and center of culture in the west. In fact, these stones are lying everywhere, scattered all over the place. You might be surprised if I tell you that you can even find these in two unlikely areas: advanced mathematics and urinary diseases.

Advanced mathematics? So their mean streak extends far beyond the battlefield and into classrooms? Yes and no. Let me explain by first talking about the Roman Numerical System (RNS). 

The RNS has been the subject of multiple maths-based jokes and memes. I, for one, was one of those who joined in on the fun and launched ridicule at it with much gusto. However,  a lot of the fun depended on not knowing the reality of it – ignorance is bliss, so they say. And it was that very same ignorance that was at play. Then it occurred to me: if we, people of posterity, cared even just a little bit for knowledge and truth, then we would have to do away with ignorance even at the expense of fun.

We need to clarify some things.

People are wont to parrot the misguided claim that the RNS is difficult to work with, especially when doing operations with large numbers. There is some truth to this. Just try to look at the equation XXX x X(XXX) without getting even a little bit befuddled. However, this is a misguided criticism based on a wrong understanding of its utility. İt is like criticising a butter knife for not being able to cut through meat easily. Sure, some talented Romans used the RNS to perform basic (quick) maths but it was mostly used to write and record the results of small and more complicated operations, without actually being used in most calculations.

When doing actual operations with large numbers Romans used abaci (plural of abacus). This device had already been in use in Roman society since the 4th-3rd century BCE. In later years, the Romans were able to develop a more portable version which we now call a hand abacus. For them to perform operations with the abacus, counters were needed, and for that the Romans used pebbles which in Latin is called calculi. İt is from this Latin word where the modern calculate comes from; and, if you’re being observant enough, calculus (singular of calculi).

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A Roman hand abacus from the Museo Nazionale Ramano

You see, the first syllable that gives calculus its familiar sound comes from another Latin word, calx, which means limestone or chalk. Notice the following: The element that makes calculi hard is, you guessed it, calcium (forming the compound calcium carbonate). The process by which calcium concentration in the body increases is called calcification. Abnormal calcification in the body leads to calculi formation inside the body’s organs. When left unchecked, then urine big trouble.

It is this type of calculus that the ancients dreaded. Those who suffered from this kind of ailment “have very limpid urine, because the thickest and foulest part remains and is concreted” said Hippocrates, the father of medicine. Celcus registers a flourish of graphic pain in his account of it: “at times blood, or something blood-stained or purulent, is excreted with the urine; this some pass more readily standing, some whilst lying on the back and especially those with large calculi, some even pass urine bending forwards whilst they relieve the pain by drawing out the penis.” Rolling stones collect no moss, but stones rolling down the urethra hurt like Cannae. This calculus didn’t just inspire fear. It took away lives. One of those whose life was ended abruptly by this nightmare was Epicurus. He “died of renal calculus after an illness which lasted a fortnight”, according to Diogenes Laertius (renal calculi are also known as kidney stones). For those who don’t know who Epicurus is, he’s one of the major Greek philosophers, up there in stature and breadth with the likes of Plato and Aristotle. He founded his own school, famous for its lush garden, and advocated for materialism and moderation. The body of thought attributed to him, Epicuranism, is concerned with asking important and deep questions such as “what is the greatest pleasure?”, “did he rue not going to the loo?”, “what is the universe made of?” and things like that.

The Romans were people who knew what to do with stones. Octavian best captured this Roman spirit when he transformed the ruins of Rome into a gallery of marble. So it isn’t surprising that a medical treatment for this stony sickness was already in practice at that time, though the procedure may sound totally agonizing to our modern ears. Aretaeus, a Cappadocian physician who practiced in Rome, described the method as such: “if it be the impaction of calculi which stops the urine, we must push away the calculus and draw off the urine, with the instrument, the catheter, unless there be inflammations.” Try to look down and imagine the operation being done in front of your eyes. You’re welcome. Because of advances in medical anesthesia, to be free from stones can also be pain free, but not so financially. Some anesthetics may even have euphoric effects that will make you piss yourself laughing until a nurse tells you to knock it off.

But what is the marble, I mean moral of this discussion?

Omnem movere lapidem, leave no stone unturned, says old wisdom. Scrutinize everything, hints of riches may be found underneath an unassuming pebble. This we learn early in school early on. But this emphasis on rock-turning distracts us from the stone forming processes inside schoolchildren, an invisible horror that most teachers fail to recognize. An American survey reports that “88% of teachers. . . encourage students to hold their urine” and “only 24% of surveyed teachers promoted healthy voiding behavior.” While we put premium on teaching kids to “hold their own”, this isn’t exactly the type of stoicism that should be encouraged among these wee humans. Potty prohibition has long-term effects that we are only beginning to understand. Overactive bladder (OAB) symptoms in adult women may well be influenced by childhood toilet training, as found by this 2007 study saying that, “Childhood symptoms of daytime urinary frequency, nocturia, urinary incontinence, nocturnal enuresis as well as urinary tract infections are strongly associated with OAB symptoms in middle-aged and older women.” Who knows, maybe there are other adverse health effects brought by this malpractice that we just don’t know at the moment and are unable to because the scientists that should be doing this kind of research are still soiling themselves from childhood trauma.

Herein lies the dilemma.

The calculus that we shouldn’t tarnish gets exactly that: tarnished. While the calculus that should alarm us gets hardly noticed at all. What does this say? Doesn’t this indicate a failure to communicate? Exactly. Just think of the RNS issue. More than that though is a problem in the organization of education that prioritizes difficulty and rigidity over everything else. Examinations are highly concerned with finding faults and judging the failures of students, instead of being opportunities for consultation and enrichment. Schools become foundries where brains are turned into exam-passing machines. Not only is this difficult to do, but it makes subjects of difficult nature even more difficult. Mathematics is almost always the first casualty. Enjoyment is taken out of the equation. The result of this calculation is rather dreary, proving that this foreboding of failure is the failure. A 2015 Oxford University study points to the US and the UK as two of the world’s “worst culprits for educating students just to pass an exam”, which is embarrassing, given that these two countries are intellectual powerhouses in various academic fields. The same study also found out that “while UK 15-year-olds are close to average for maths, literacy and problem-solving, performance drops significantly among 16- to 24-year-olds.” This dip in ability should ring the alarm for immediate radical change, for if this continues, more and more students will proceed with their education without being equipped with necessary critical-thinking skills necessary to survive.

And if we’re talking about survival, we need to talk about health.

A radical change in how we conduct education and how we assess learning should start with our mode of instruction to children. The sheer number of teachers instructing their students to shut up and forever hold their pees is highly indicative of how education tries to suppress the biological functions of children’s bodies to turn them more martial and mechanical. There are better ways to deliver education to students than this, right? A way where natural expression isn’t prohibited, but acknowledged and supported.

I think there is a Roman lesson from the RNS that is helpful in this conundrum. The RNS presented problems when doing complicated computations, but that didn’t stop the Romans from achieving feats that demanded mathematical rigour and excellence. How did they do it, then? They realized that the solution to their problems lay not on what is strictly considered mathematical, but it simply lay on the ground: pebbles. Exams only present some of the correct ways of dealing with problems, but not all. And education should allow and encourage students to find all the possible ways to solve a problem, not just what is prescribed by authority and tradition.

The solution to item #5 might not be arrived at with the methods learned in the classroom. Maybe it can be solved with the stone found in your nearest toilet. So go excuse yourself and take a leak. 

Just be sure to take a good aim. In that way you’ll be hitting two birds with one stone.

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