The Ancient Greek Steam Engine

I can already hear you groaning. Here we go again, you're probably thinking. Another revisionist theory that Justin likes, big surprise. You may be surprised to learn, then, that this is no theory: sometime between 10 and 70 CE, Hero of Alexandria created what is believed to be the world's first steam engine. No joke, no hair-brained theory, just cold, hard, unforgiving historical facts. Still don't believe me? Just take a look at this illustration from his book:

Not sure what you're looking at? Well, it worked like this: you poured water into that bowl on the bottom, then build a flame underneath it and waited for awhile. Eventually, that water transforms into steam, which shoots up through the two pipes and into the circular object in the center, which was more like a pinwheel than a globe. The steam would travel out of the two spouts out of the pinwheel, causing it to spin. Presto, ancient Mediterranean steam engine!

In addition to this, Hero is also credited with the invention of the force pump, the syringe, a wind-powered organ, and the vending machine. So, the next time you buy yourself a soda or sodium-coated snack, think of Hero and wonder to yourself what else he may have jotted down on some note paper which was lost along with most of his work when the Serapeum was destroyed in 391 CE by a Christian mob.

Why do All Roads Lead to Rome?

The simple answer is that the Romans built them. There. Satisfied? I didn't think so. We see in the Romans a penchant to absorb and syncretize the things that they admired from other cultures, and in one respect, roads were no different. Government building of roads has been with humanity since at least the Ancient Persian Empire, and it is likely that the Etruscans brought a road-building ethic with them from Asia Minor, and that the Romans appropriated this idea. And if there was one thing that the politicians could all agree on, it was roads.

The Romans didn't just level dirt paths; they had a method of paving these roads which made them durable and easy to drive on. Merchants from all over mainland Europe used carts to transport goods, and sturdy, flat roads ensured that their more expensive breakable items would remain intact on the way to market. Travelers and pilgrims eager to visit the famous Temple of Saturn in the heart of Rome could now make the trip without fear of getting lost, since Augustus made the Temple the starting point for the marker stones. If the numbers on the stones got smaller, you were heading for Rome, hence the famous saying.

The politics of roads was always contentious, with many Patrician Senators using their vast treasuries to pave large, wide roads and name them after themselves. Like the Gladiatorial games, this was a good way to endear themselves to an underrepresented populace of mostly Plebeians. However, anyone who built a road in the early Republic was required to pay for its upkeep, which could be a problem if a wealthy Senator got involved in shady financial dealings that went south.

Eventually, the Roman Empire was connected by a large system of roads, which were eventually all made public property. Armies could march over the roads very easily compared to marching through dangerous forests and hunting paths. While this also helped the enemy armies of 'barbarians' to invade, the Romans made a habit of building a system of outposts and forts near choke points, and had a swift communication system to help ward off the smelly hordes. The roads lasted for centuries, some of them being preserved up to this present day.

Archimedes

Unfortunately, Archimedes is one of those semi-mythical guys who wasn't written about heavily until hundreds of years after his death. What we do know about him is a combination of contemporary and later sources, all of which agree on at least one thing: he was crazy smart.

He approximated pi to an unprecedented degree, which by itself is one heck of an accomplishment. He built world-changing inventions, created new mathematical formulas which incorporated infinity and zero (two concepts which scared the daylights out of Aristotle), applied buoyancy, and created complicated pulley systems which allowed for the earliest cranes to be built. I have focused mostly on how his inventions applied to warfare and farming, but those were the two chief interests of the ancient Mediterranean, when you get right down to it.

Though he died an untimely death at the hands of a foolish Roman Legionnaire, his concepts and inventions continued to change history long after his death. That is, the inventions that they could duplicate continued to change the world. There were several items the plunderers found in his workshop which could not be re-created and were taken as trophies by Marcellus and his Captains. One of them was a sphere with gears and levers which could calculate the exact position of the known planets.

Pax vobiscum

It's All Greek To Me!

How do you know what you know? Seriously, think of something you are sure is true right now. How did you come to know that truth? Do you believe that humans are basically good or evil? Do we have souls, or are we purely material, and what is the meaning of life? Is there a God, and is she in a good mood? With the economy the way it is, it's unlikely that most of us have had a lot of time to ponder the deeper meanings in life. Socrates would be greatly disappointed in us for this. And so would Archimedes.

The Socratic Method is the practical application of Socrates' belief in self-examination. It began circa 430 BCE, so the story goes, with a bunch of young Athenians who were trying to find the answers to life's biggest questions. They sought out Socrates, a bricklayer and veteran, who had a most curious way of discussing matters of truth. Rather than making quotable statements or using flowery words to push his point across, he asked questions. For example, if one of them stated that “Love always gives and never seeks to receive,” Socrates might answer, “If love never receives, what will it have left to give?” His entire point in life was to make people say, “Hmmmmm . . . .”

While he was mostly concerned with ethical and spiritual matters, he did use his questioning method as a way of trying to understand the world around him. Archimedes was born hundreds of years after Socrates' death, but it seems obvious from his discoveries that he used the same principles of critical thinking. One of the most famous stories (though it's believed to be Apocryphal) is that of the riddle that King Heiro II posed. A local goldsmith had forged a golden crown, and the King was suspicious that it was a fake. He asked Archimedes to find a way to prove it, so the mathematician went to work. He thought deeply about the subject, but couldn't come to a good conclusion, so he took a bath to relax before going at the problem again. While in the bath, he observed the water rising and falling, and realized that he could use the principle of buoyancy (which he basically created) to determine whether the crown was real or a cheap knock-off.

Greek thinking started with how to think, and it was only when the ancients strayed from the art of questioning that they plunged the known world into an intellectual dark age, with only a few bright lights like Archimedes to lead the way. Aristotle, a student of Plato (who was a student of Socrates) went about using inquisition to determine the natural world. After Alexander the Great, his student, took that knowledge with him to every place he conquered, it became concrete fact for the next thousand years. History loves irony, and so it stands that the scholastic line of Socrates ends with someone claiming absolute truth over the natural world.

Pax vobixcum

Things That Archimedes Made

Following in the footsteps of other great eccentric Greek mathematicians, Archimedes seems to have gone about his life by trying to learn something new every day. To make an exhaustive list of everything he discovered, invented, or improved would take far more space than what should be contained in these virtual pages, so today we'll take a look at just a few of his mind-boggling creations.

The pulley itself is so ancient that its creator's name has been lost in the mist of time. Archimedes experimented heavily with pulleys and created the world's first block and tackle system (basically a mechanism in which two or more pulleys are utilized). He discovered that each pulley he added made the load seem lighter, since the force was being transferred equally among all the pulleys in the array. This allowed merchants to construct great cranes capable of lifting heavier cargo, which meant more money on arrival.

But his genius did not end at maritime physics. While trying to find an easier way to irrigate highland farms, he invented Archimedes' screw, a device capable of carrying water upward. Now, ground water could be raised to the surface and reused on the crops. It could even be carried up mountains, if the pipes and screws were long enough. This revolutionary invention was so useful that the Romans later built it into all their farmland and even used it to carry drinking water into high fortified camps. Here's a great image of how this works:

During the First Punic War, he invented a primitive odometer. It was an array of gears and levers which would drop a ball into a small box for each mile it traveled. To have done this during a time when people believed that disease was caused by the moon is not only surprising; it's mind-bogglingly astonishing. In addition to this, he created several astronomical implements, some of which were carried away as loot by the Roman commander who sacked Syracuse.

In between revolutionary and brilliant inventions, he did Calculus. But wait! Didn't Sir Isaac Newton invent Calculus? No more than Henry Ford invented the automobile. Newton greatly expanded the science, which laid dormant for more than a thousand years, but it was Archimedes himself who made the first foray into the measurement of the infinite. Unfortunately, there was no one around capable of understanding Archimedes' work, let alone carry it on. Though he served as a bright light for a time, the world went dark again at his passing, and the Greeks and Romans went back to their day-to-day business, being afraid of things they didn't understand. His work lives on, and he remains one of the most important mathematicians and inventors in all of history.

The Siege of Syracuse

Located in south-eastern Sicily, Syracuse was an old Corinthian-Greek Colony with old-time values. Ruled over by kings and tyrants since its founding in 733 BCE, Syracuse enjoyed the many benefits of its central Mediterranean locale and became very wealthy through trade with Egypt, Rome, Carthage, Asia Minor, Palestine, and Spain. After the Pyrrhic war in 275 BCE, however, it was the sole remaining Greek settlement west of the Peninsula itself, and in a very tenuous position sandwiched between Rome and Carthage.

Syracuse survived for quite a while after Pyrrhus' final defeat because its leaders made smart alliances and used skilled diplomacy to ensure the protection of either Rome or Carthage. When the first Punic War broke out, Syracuse was at the center of the action and made an alliance with Carthage from fear of Rome. Luckily, Rome and Carthage fought each other so bitterly that by the time Rome got around to dealing with the unlucky Sicilian Greeks, they had already lost so many in battle that they were willing to settle for an apology and a cut of their trade. However, when the second Punic War broke out, Syracuse made the mistake of allying with Carthage again, and the Romans were determined to make them pay. However, Roman vengeance would come at a high cost to the Republic because of one resident of Syracuse whose mind possessed knowledge that could bring both great prosperity and very great destruction. This man's name was Archimedes.

I like to think of Archimedes as a sort of ancient world Da Vinci, except without the moral qualms about creating weapons. Where Da Vinci was purposefully putting gears in the wrong place so that his designs would ultimately fail, Archimedes was not only sketching these out, but utilizing them to a terrible degree of success. For this week's Famous Friday, we'll delve into Archimedes' discoveries in greater detail, but since it's Military Monday, let's focus on his original and horrific siege weapons.

The most famous of his weapons was The Claw, which utilized pulleys and complicated weight balancing to capsize Roman Triremes. Seriously, this crane-like weapon would hook onto the bow or stern of the boat, lift it out of the water, and send it crashing against the nearby rocks. Each boat carried about two hundred soldiers, so you can imagine the carnage that ensued when this happened over and over:

Another of his creations was an improved catapult. Again, using pulleys and counterweights, he was able to create an engine capable of throwing a 500 pound rock with much better accuracy than the inferior Roman scorpions and ballistae. He also contributed to the building of other weapons which could fire missiles and keep the Romans at bay.

The most controversial of his creations was his 'death ray.' Several authorities have tested it using various techniques, and some have been successful, while most have ended in a wash. Supposedly, Archimedes built a large array of bronze mirrors which could be turned, focusing their reflected light into a concentrated beam onto an approaching ship. The Roman ships, which were sealed with tar, caught on fire and sunk. While this does seem a bit far-fetched, I wouldn't put it past old Archie to give it a try. After all, it was Hiero II, the king of Syracuse and relative of Archimedes, who frequently challenged the genius and gave him the funding he needed to build better weapons since the first Punic War, so why wouldn't this mathematician try literally everything he could think of? Were there easier ways to light ships on fire? Yeah, lots. But if I were an invading Roman, I might think twice about mixing it up with an enemy who can light my ships on fire without shooting anything.

Syracuse eventually fell to sheer Roman determination, and Archimedes was killed, possibly while drawing circles in the sand. If not for him, the last Greek colony on Italian soil would surely have fallen in the first year, and Carthage wouldn't have stood a chance of surviving the Second Punic War. By the time the Roman army came to the gates of Carthage, they had suffered so many casualties from Syracuse and from fighting Hannibal for ten years that they allowed Carthage to live, albeit under severe economic sanctions. And when Carthage was finally leveled in the Third Punic War, there were no more brilliant mathematicians around to set Romans on fire from a distance.

Pax vobiscum

Technology Tuesday: Triremes

A few years ago I worked as a substitute teacher, and wanting to make Geometry interesting to high school students, I told them all about Thales, the Greek Mathematician who calculated the exact height of the Egyptian pyramids by measuring their shadows circa 500 BCE, and of Eratosthenes, who calculated almost perfectly the circumference of the Earth sometime around 220 BCE. They were astounded to learn that Geometry was, in fact, one of the oldest forms of Mathematics on the planet. However, the one theory they wouldn't believe was that of a Phoenician voyage to the Americas – which supposedly took place in the 400's BCE. One student remarked, “How did they get across the Atlantic? In rafts?”

And there it is. The all-too-common misunderstanding about history that constantly pervades Western culture. We think of the ancients as being nothing but primitive, superstitious fear-mongers who jumped at their own shadows and had no technological achievements of interest. This is one of the reasons I am writing this blog; to show that mankind has been ingeniously solving problems since long before the industrial revolution, and to remind us that some of the problems we face today may have a solution in the past. After all, those who forget the past are doomed to . . . um . . . something something.

Well, anyway, let's press on. The ancient people didn't get across the Mediterranean in rafts or skiffs, or any other short-range vessel. They used one of the oldest ships around: the Trireme. The Trireme is so old that no one is really sure who invented it, or even which people group started using them first. Yet they could travel fifty to sixty miles a day if the crew worked at a moderate pace. If they worked harder, they could travel more than a hundred and fifty miles (theoretically). What was the secret of their power?

Well, the Trireme gets the tri- from the number three, as in three rows of hardworking oarsmen. The ship's interior was designed with the two sides slanting inward toward a fairly pointed bottom. Holes were cut in the side for oars, and the ship was big enough to accommodate 170 rowers who were guided by a few midshipmen who gave the rhythm. Add 20 or so Marines on the deck to prevent boarding, and you've got yourself an authentic fully-manned Trireme, a fearsome weapon when wielded by those who used them the best: the Athenians.

Athens is a coastal city, just like most powerful Greek cities. However, Athens had a rich countryside in which they cultivated olives, wheat, and other foodstuffs, and its mountains were full of precious metals, of which the rich speculators in Athens took full advantage. Yes, this future capital of Greece had a lot going for it, and constant naval trade meant that this city was always ready to drive off invaders by sea.

The Romans would later spend several months out of every year training their soldiers, but Athens had no need to train its navy because they were constantly keeping in shape by serving the merchants and ensuring commerce to places like Palestine, Egypt, Carthage, and even Rome itself. Because of this, anyone hoping to attack Athens would have to do so by land, which is what inevitably led to its downfall.

The Athenian Trireme was built hull-first from soft, light woods, with the ribs and girders being added after the woodwork was finished. It was light enough that the crew could carry it to shore without much difficulty, but this also meant that it could fall prey to heavier ships. However, heavier ships were typically slower, and the main tactic used by Trireme crews in this time was to ram the other ships diagonally from the side to tear a huge breach in their hull. This was easy to do in a light, nimble Trireme, and heavier ships made from stronger woods often fell prey to these jackrabbits of the sea.

So could these ships, which were very expensive, time-consuming to produce (6000 man hours per ship!), and exhausting to operate have really traveled from the Western Mediterranean all the way to Brazil? Personally, I think it's possible, but I don't think it was accomplished. If they did, there's little evidence to suggest that any pan-Atlantic commerce was taking place, as some who promote this theory claim, and I can't imagine that such commerce would even cover the expedition cost, much less turn a profit. However, there is a Carthaginian coin that dates to 350 BCE which has what looks like a tiny world map near its edge that seems to depict some land beyond Spain. Perhaps they had at least discovered that there was land beyond the seemingly endless ocean, but short of a sudden windfall of evidence, this theory remains on the fringe.

While the odds are stacked against them, I think that this subject should be discussed in the classroom. What keeps most subjects alive and interesting are the questions which arise from them, and I think that the world of history education needs to stop being afraid of these kinds of questions, especially when the events that are in question happened so long ago. Again, after weighing the evidence myself, I find that it's only wishful thinking that makes me want to believe it, therefore I cast it out since it cannot be supported. But the act of weighing that evidence was fun, and I think that if school were more fun, more kids would give it an honest chance.

Pax vobiscum

Culture Wednesday: More Than a Theorem

Anyone who's learned even the most rudimentary geometry has heard his name. Yes, in his own way, Pythagoras achieved the Greek ideal of fame that causes him to live forever, even if he is relegated to the pages of High School textbooks. But there is more to this mathematician than a simple ratio. Among other things, he believed himself to be the reincarnation of a Trojan hero, and refused to eat beans. His mathematekoi brotherhood was thought to be the most well-learned in the ancient world, but they did not hesitate to murder one man who would expose their most embarrassing secret: irrational numbers.

Though he seems harmless in his textbook depictions, Pythagoras was considered by many in the ancient world to be a dangerous cult leader, and a malcontent. He lived during that necessary twilight between oral tradition and written history, and thus his life and work is shrouded in an unfortunate cloud of mystery and myth. It is said that he traveled all throughout the world to gain knowledge of mathematics, science, medicine, astronomy, astrology, and mysticism from whomever would teach him. I think it likely that he traveled to Egypt, home of the famous ancient mathematician Thales, who accurately calculated the height of a pyramid by measuring its shadow. The Greek philosophy of math and science was that it was attainable, that they could actually observe and learn from what they saw to predict or manipulate future behavior. However, it was also steeped in Pagan mysticism, something which taints their learning somewhat and caused many, especially Pythagoras, to go off the rails.

Eccentric though he was, even by ancient weirdo standards, he built a school around this central tenet: All is number. He believed that numbers could be used not only to define all things, but could even give them greater meaning. His disciples took this motto to heart, and immediately began measuring angles and lengths to find the hidden constant ratios between them. In fact, most of the really boring parts of Geometry today (constructions, proofs) were what the Pythagoreans discovered when they were just playing around. They would challenge each other with number riddles like, “can you form a right triangle if given two points?”

One story claims that Pythagoras discovered the mathematical value of music. He was passing by a smithy one day, and the ringing of the anvils was sticking in his head. He noticed the relationship between their individual pitches, and examined three of them to discover that the middle one was one-third bigger than the smallest, and that the largest was one third bigger than the middle. Through experiments that the school performed on strings, bells, and other instruments, they created the octave as a means of dividing the musical notes, something we still do in Western music today.

As clever as these stories make him out to be, my belief is that Pythagoras was just the charismatic leader of some very bright young Greeks. I believe his school as a group made much of the discoveries that he is given credit for, just like professors will occasionally take credit for their students' findings today. In either case, he should at least be honored for cultivating an environment in which learning and discovery could take place.

However, this was long before the days of public education, and knowledge of every sort was a tightly guarded secret, particularly mathematics. As we will see in coming weeks, mathematics can kill people, and it often does so in great quantities with a minimal effort. For the Pythagoreans, the biggest secrets that they kept were the ones that they hated and couldn't explain.

Pythagoras and his followers were so convinced that everything could be expressed as a ratio of whole numbers that when they discovered ratios that didn't work out to nice, neat, clean whole numbers they were thrown into a crisis of faith. You see, this wasn't “just math” to them; this was their religion. Everything they held to be true, yes, the very order of the universe was at stake, and if it was just all random, irrational events, then knowledge itself was a fools game, a mirage in the desert of unpredictability.

Try this to see what I mean: draw yourself a square. Go ahead, draw one. Now, assign each side the number 1. Doesn't matter how big you've made it, just pretend you've created your own unit of measurement, name it after yourself if you like. Now that you have your square, draw a diagonal line from one corner to the other. Great. Now, using the Pythagorean Theorem, a^2 + b^2 = c^2, calculate the length of that diagonal. You should get 1^2 + 1^2 = c^2, and c^2 is equal to 2. So how long is that diagonal? The number √2, if you bother to plug it in, should make your calculator go crazy with an endless stream of numbers. However, it's a decimal answer, and therefore not a whole number. The Pythagoreans probably convinced themselves that there must be some sort of mistake in all of this, but their equations would continue to come out irrational, that is, being unable to express in a ratio of whole numbers. And since the square was one of their 'sacred shapes,' there's no doubt that they wanted to keep this a secret until they could find a way to make it work.

Well, enter Hippasus, a Pythagorean disciple who couldn't keep this cat inside its loosely constructed bag. He blew the whistle to the general public and alerted everyone in the Mediterranean that Pythagoras and his school were just a bunch of frauds. Little is truly known about this character as well, though some believe he created a rival school of mathematics. In either case, it is believed that he was murdered by Pythagorean zealots while trying to leave town. Yes, that's right, he was murdered for mathematics.

Pythagoras himself was killed during a political uprising in Croton in which he found himself on the wrong side. Supposedly, he ran from his assassins and was gaining ground until he came to a field of beans. He stopped and declared that he would not cross a field of beans, at which point I like to imagine his attackers stopping for a second to tilt their heads in unison before promptly dispatching this mathematical primadonna.

Pax vobiscum