Nobody knows how long the documents were lying in a dumpy basement of the papal summer residence in Castel Gandolfo. In a crowded room, sharing space with John Paul II wetsuits, Benedict XVI hockey sticks, and Francis I baseball bats, boxes of ancient parchments were patiently waiting for their time to be seen again. Evidence suggests that the first occupant of the residence - Pope Urban VIII - passionate enemy of science and the last Pope to expand Christendom by military means, brought them there to study.
When our team found them many papers were partially destroyed, and a year later only a small fraction has been translated. But a few that we studied in depth illuminate a path that connects events separated by two millennia.
Below is is one of the first documents that we came across. It is a medical case history unearthed from what appears to be a 20,000-bed Mathematics Trauma Center (MTC) that the Roman Imperial Army was operating at the time of Caligula.
Math fiasco in Bayern
Name: Gluteus Maximus
Rank: Centurion
Legion: Legio XXII Primigenia
Coverage: Kaligula Care (pending final Senate legislation)
Case worker: Galla Placidia
Interview transcript:
Gluteus Maximus: Ave Caesar!
Galla Placidia: (confused) Fine, thank you. How big is your legion?
Gluteus Maximus: We had MMMMMCMXCI legionaries including auxiliaries.
Galla Placidia: Tell me about your last campaign.
Gluteus Maximus: We were operating in lower Bavaria. The place was swarming with hostiles. The Emperor's circular stipulated that every member of the legion must capture or kill at least IV Vandals and Goths per day.
Galla Placidia: So how many did you have to get daily?
Gluteus Maximus: (with some anxiety and clearly reciting from memory) MMMMMMMMMMMMMMMMMMMMMMMCMLXIV.
Galla Placidia: Does your legion have a math support unit?
Gluteus Maximus: Yes, we had about LIX warfighters with additional large number training. Unfortunately we have lost them early on in the campaign. They were not meeting the quota of captured Vandals and I had to put them on the rack - routine punishment for cowardice. I wanted my officer to put the rack on a low setting and (with growing agitation) I tried explain how to do it. It is a simple trick with numbers but I used X for the unknown quantity that I was looking for. He took X for the rack setting, maximal as it happens, and the entire math unit was put out of commission and had to be sent back to Rome to recuperate.
Galla Placidia: Did you start training another math unit?
Gluteus Maximus: Of course. I had LXXXVIII volunteers, but they seemed to be cursed. Soon after we started abacus workouts many lost digits to some freak accidents, others developed an unusual taste for fighting and were too tired to learn anything, and the rest did not have what it takes to deal with numbers.
Galla Placidia: How did you manage without a math unit?
Gluteus Maximus: It was horrible. Goths and Vandals were down in the valley. They arranged their forces in a large rectangle. We had two warfighters, one was putting a pebble in the jar for each row and the other for each column of the enemy infantry. The first jar had MMMMMMMMMDCCCXCIX pebbles and the other MMMMMMDCCXCVIII. But without the math unit we were unable to to proceed. The War Manual stipulates that we should not engage the enemy when there are more then two of them for every one of us, and (with desperation in his voice) we could not make this determination (he starts sobbing quietly).
So their forces were growing day by day, and we were digging in and requesting a new math unit from Rome.
Galla Placidia: What happened next?
Gluteus Maximus: (defiantly) In the end, a courier came from Rome and I was put on the rack!
Interview analysis and diagnosis: Gluteus Maximus suffers from an advanced form of math phobia and fear of numbers masquerading as letters. The simple act of counting gives him the sweats, and advanced operations such as combining two numbers as length or area result in a partial shutdown of major organs. Diarrhea, fingernail sensitivity, chest pains, shallow breathing, and aggression frequently occur in a context of even small numerical challenges. When faced with inverse mathematical operations such as getting length out of area and another length, massive panic attacks ensue.
Recommendation: Keep in the Mathematics Trauma Center for as long he has the insurance coverage. Release afterward. The affliction is not treatable at the moment.
Collapse explained
For the last 250 years the Gibbon book, The Rise and Fall of the Roman Empire has been a definite source on the history of the Roman Empire. Beautiful and engaging writing, if a tad old fashioned, and a mountain of historical data. Yet these newly found documents reveal the fatal weakness of the Roman Empire that gets barely mentioned in Gibbon's treatise - the Roman numerals! We may quarrel over whether the economy can be based on central planning, the invisible hand of the market or something else entirely, but there is no doubt whatsoever that it cannot be based on the Roman numbering system. With Roman numerals addition is hard, multiplication awful (even today people do not know how to do it correctly ), division nearly impossible, and did I mention that there is no zero? The discovery of the logarithm, a gateway drug to higher mathematics, is out of the question. Everyday Roman life created multiple venues for mathematical exploits. Think of the military practice of decimation as a gentle entry into modular arithmetic, or reality shows of Christians and lions as a path towards the study of two-player games. But in every case, the flawed numbering system stands in the way, not only hindering the development of mathematics, but also compromising banking, record-keeping, and business. With this kind of system you could not send a kid to buy a loaf of bread or a ticket for a gladiator show because they would need two decades to learn how to figure out the proper change!
Roman Empire is a case of "one aqueduct too many". Excessive investment in public utilities, military and entertainment that left science in the dust. It is hard to speculate, but with minor capital outlay Romans could have had decimal system, and with it made inroads into analysis and calculus, Fourier analysis, number theory and the rest of mathematical gems. Sustained scientific effort would put us on a path of having steam engine around V century, and electricity and nuclear energy by the end of IX century. As always, nay-sayers point out that Vandals armed with the nuclear-tipped spears would have been a much tougher enemy, and having a Second World War thousand years earlier is also a dubious benefit.
Our team avoided these idle speculations and pushed forward!
Why so slow?
Discovery of the true reasons for the fall of Rome, a tour de force of modern historical research and a shining example of investigative spirit for the next generations to follow, forced our team to instantly refocus on a new task. Without science paving the way for welfare and progress, and mathematics that keeps science honest, the Empire was doomed and this fact is profoundly obvious in the hindsight. So what stymied our less successful predecessors from making this discovery decades ago?
We may never know, but one possible explanation is that the fall and decline was so unbelievably slow. Rome lasted for over a millennium; first five hundred years as a republic, and then another five centuries as a crumbling Empire.
With this in mind we started searching for factors that could counterbalance the lack of strong science and education, and provide exoskeleton that keeps the society going even when the rational thought is in retreat. This work is still in progress and several competing theories emerged. One of them is a "Theory of good life." Aqueducts, good roads, daily reality shows at the local colosseum, and heated towel racks and bathroom floors should not be altogether written off. These are important and pleasant things; despite the fact that they represent spiraling consumption, and, if government is involved, a source of endless deficits. Others argue that a millennium back then is roughly equivalent to twenty years today, short enough to burn through a scientific surplus if you've got it. Supporting data comes from analyzing military salaries. In Roman times military pay while generous would stay fixed for two and half centuries at a time without much grumbling from the rank and file. Today numerous examples indicate that government morale drops considerably after barely a half a decade of a pay freeze. That is a 50:1 ratio that leads to our time scale adjustment. But the leading theory is that of an Endless War. It has to do with campaigns in far away places and against insignificant enemies. It requires that through conquest, resource-grabbing, or simple arrogance, one continuously produces armies of low-grade adversaries. These enemies can do only an occasional harm, but they represent enough of a threat to suspend the common sense of general population for a long time.
Whichever theory is true remains to be seen, but suddenly the problems of our toga wearing predecessors seem no different that what our republic is grappling with today.
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