Original URL: http://www.theregister.co.uk/2013/04/17/archimedes_2300th_birthday/

Move over, Mythbusters: Was Archimedes an ancient STEVE JOBS?

Happy 2,300th, old man... Beware of turtleneck-wearing Greeks?

By Simon Sharwood

Posted in Science, 17th April 2013 09:04 GMT

Happy birthday Archimedes! The Syracusan mathematician, engineer and philosopher came into the world in 287BC. We don't know the exact date of his birth 2,300 years ago, but an appreciation of the twenty-third centenary of his birth seems apt.

An engraving from 1824 edition of Mechanics Magazine. Source:Wikimedia (public domain)

Archimedes is most famous for four things. His utterance “Give me a [firm] place to stand and I will move the earth" (ΠΑ ΒΩ ΚΑΙ ΧΑΡΙΣΤΙΩΝΙ ΤΑΝ ΓΑΝ ΚΙΝΗΣΩ ΠΑΣΑΝ*) means he’s credited as a pioneer of the study of leverage and mechanical advantage. That expertise is the reason for his second claim to fame, namely some rather nifty weapons deployed in the siege of Syracuse - most famously a crane-type "Claw" and, according to legend, "The Death Ray", an array of mirrors (possibly polished shields) used to focus sunlight on approaching ships, apparently resulting in said ships bursting into flame. He also devised the first law of hydrostatics** during his “Eureka” moment in the bath. His screw for lifting water is also noteworthy.

We'll get to all of that soon.

But first, a little background. Although Archimedes' home town is on the island of Sicily, which we now think of as Italian, in his day Syracuse was Greek and had thought of itself as Greek even before Alexander the Great spread Greek culture across the eastern Mediterranean and beyond. Archimedes’ father was an astronomer and he grew up at a time Aristotle had been dead just 50 or so years. Perhaps the young Archimedes or his father knew some folks who had met the great man?

By Zeus! Where can I find a decent boffin?

Such meetings are purest speculation, but we are pretty sure Archimedes could access the great philosophical and scientific works of the time. Other philosophers were accessible too. Many were, by Archimedes' twenties, concentrated in Alexandria, a city which by around 260BC was one of the more stable parts of Alexander's fractured former empire. Ancient sources suggest Archimedes spent time there so he could hobnob with fellow boffins.

Sadly none of those sources were his contemporaries, a common problem for historians who often have to sort the hearsay from the good bits of ancient texts. But it is known that Alexandria was a centre for scholarship and it's in no way drawing a long bow to suggest that a talented mathematician from Syracuse could have made his way across the Mediterranean to study there.

The parts of Archimedes’ life we’re on the most solid ground with are his work on hydrostatics, mathematics and geometry, because he wrote books about them that survive to this day. You can see them, in a rather lovely 1897 edition, at Archive.org.

One of his works, On Spirals, is considered to use techniques that are not too far short of those used in calculus, which was of course invented more than 1,500 years after Archimedes death, by Isaac Newton and Gottfried Leibniz. On Floating Bodies is Archimedes' two-part masterwork on hydrostatics, the study of fluids. On the Equilibrium of Planes outlines theories that plainly came in handy in 212BC, when Archimedes constructed machines of war capable of lifting rather heavy objects or projecting same over large distances.

Archimedes got the gig building weapons after impressing Syracuse’s King Hieron, who may have been a relative, after “on one occasion by means of a triple pulley launched with his left hand alone a merchant ship”. The source for that quote is ancient historian Diodorus Siculus, a writer of poor repute who churned out works between 60BC and 30BC. As other ancient sources include a similar tale, we’ll happily use it here.

Punic? This war is MASSIVE

Once Syracuse became embroiled in Rome's second Punic War against Carthage (the one featuring Hannibal and the elephant trip over the Alps), Hieron pressed Archimedes into service against the Roman commander Marcellus.

According to Roman biographer Plutarch's Life of Marcellus, Archimedes "...first hauled up out of the water some of the enemy's barges by means of a mechanical device, and after raising them to the walls of Syracuse, sent them hurtling down, men and all, into the sea."

That device, probably a crane of some sort, saw the Romans withdraw a little, at which point “the old man made it possible for the Syracusans, one and all, to lift up stones the size of a wagon, and by hurling them one at a time to sink the barges.” Which sounds rather like a catapult of some sort, with a loading mechanism that used pulleys. It’s worth noting that catapults had been used a couple of hundred years before the siege of Syracuse, a detail that becomes important later on.

The 'Death Ray'

The so-called "Death Ray", illustrated on the front page of a Latin edition of Alhazen's Thesaurus opticus (click to enlarge). Picture source: Wikimedia Commons

Archimedes is also said to have devised a giant crossbow of some sort, to further harry the Roman fleet.

And then there’s the “death ray”, an item so intriguing Mythbusters devoted two episodes to it.

Diodorus Siculus described it as follows:

The old man then devised an hexagonal mirror, and at an appropriate distance from it set small quadrangular mirrors of the same type, which could be adjusted by metal plates and small hinges. This contrivance he set to catch the full rays of the sun at noon, both summer and winter, and eventually, by the reflection of the sun's rays in this, a fearsome fiery heat was kindled in the barges, and from the distance of an arrow's flight he reduced them to ashes.

Remember how we said Diodorus Siculus isn't super-reliable? Plutarch's better regarded, but didn't mention the death ray. He's not the only source not to do so.

Was it real? Ancient writers did love to embellish details, or pick the best bits of a story. If you doubt that assertion, consider the many variations between the four gospels. We suggest such an exercise not to call their content or origins into question, but instead to offer a second example of ancient biography of a single person written by different authors and featuring different versions of events.

Accounts of Archimedes’ death are quite uniform and show us he was a rather unusual chap. Rome eventually defeated Syracuse and as legionaries roamed the streets came upon an old man who seemed rather distracted. Troops challenged him, but Archimedes asked for more time to complete the mental arithmetic that so consumed him, unaware of the imminent danger posed by Rome’s conquering army. A Roman quickly lost patience and Archimedes ended his days on the end of a gladius, the steel sword used by Rome’s infantry.

The turning of the screw

Bainbridge hydro-electric project - the Archimedes screw

The Bainbridge hydro-electric project - modern-day implementation of the Archimedes screw.
&copy; Copyright Anthony Harrison, licensed for reuse under this Creative Commons Licence.

Archimedes’ screw is also worth a mention. Essentially a helix around a shaft, if the device’s bottom is placed in water and its central shaft turned, water will rise to the top.

In the ancient world, when muscle and sinew – either of man or beast – was the only source of energy***, a device like the screw would have been invaluable.

But did Archimedes invent the screw? It’s impossible to say, although as he wrote on spirals, hydrostatics and how to calculate the biggest sphere one can fit inside a cylinder, he clearly understood its principles very well.

Assuming he went to Egypt, your correspondent's personal hypothesis is that Archimedes would have had ample opportunity to see the water-drawing technologies that civilisation developed during its thousands of years living with the Nile’s seasonal fluctuations. We know the Egyptians were engineering-savvy enough to build the pyramids. Might they also have concocted a screw?

One water-drawing gadget we know the Egyptians devised is the shaduf, a device that sees a lever/stick popped on an axle supported by two vertical struts. The lever has a weight on one end and a bucket on the other, an arrangement brought into modern times as a drinking bird trinket.

Shaduf users pull the bucket-bearing side of the lever down, an easy task thanks to the wonders of mechanical advantage. Once the bucket reaches water – shadufs are placed next to a water source – the user lets the bucket fill, then lets go, at which point the weight on the lever's opposite end pulls it skywards without any effort.

Water is thus drawn with rather less effort than would otherwise be the case, making the shaduf a tremendously useful machine - so useful we know Egyptians used them from at least 2000 BC.

My theory is that seeing shadufs at work set Archimedes' mind whirring. His ability to codify the maths and physics of such machines led, eventually, to his various weapons. Other inspiration came from seeing, or hearing of, ancient siege engines.

Armed with little more than an unfinished classics degree and a suspicious mind, your correspondent therefore wonders if Archimedes may not have been quite the innovator he's painted. Might he instead have been something of an ancient Steve Jobs, inasmuch as both went to a technological hot spot (Xerox PARC/Egypt), beheld wonders (the WIMPS GUI/shadufs) and then brought them to the outside world in a form more elegant and functional than had yet been seen? ®

* Originally written in Doric Greek (for those of you experiencing Google Translate fails.)

** "Any object, wholly or partially immersed [submerged OR partially submerged] in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object." In On Floating Bodies, he added the clarification that for the object which had been dropped in the fluid, the volume of displaced fluid was equal to the volume of the object.

*** Your correspondent is aware of ancient water wheels at sites like Barbegal, but they’re a story for another day.