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Claws and Combinatorics in the Ancient World
February 20, 2007 8:07 PM   Subscribe

We've talked about the Archimedes death ray, but it is not the only mysterious ancient war machine the Greek scientist constructed. A contemporary Greek historian describes a wide number of clever devices developed by Archimedes during the siege of Syracuse by Roman forces - most notably a mysterious "Claw" that destroyed invading ships. You can see animations and scale models that attempt to reconstruct the Claw. Other, less-warlike, Archimedes secrets are being revealed as the Archimedes Palimpset, an overwritten text of some of the scientist's mathematical writings, has been gradually recovered using new techniques. Among the suprises is the Stomachion, a mathematical puzzle (tangrams, anyone?) and early discussion of combanitorics.
posted by blahblahblah (18 comments total) 5 users marked this as a favorite

Don't forget infinitesimal calculus. Archimedes was all over Newton*'s game.

and Leibniz. and Bhaskara Achārya. Did I mention that the king's crown ain't got nothin on Archimedes?
posted by tylermoody at 8:24 PM on February 20, 2007

I am very good at math, compared to the average person. I was taking multi-variable calculus when I was 17, and kept going up through differential equations and discrete in college.

But thinking about it now, I never really grokked calculus - I could just apply the rules well.

He figured it out - and a bunch of other stuff as well - entirely on his own. Goddamn. I'm jealous of that kind of mind.
posted by flaterik at 8:48 PM on February 20, 2007


Er, combinatorics, I'm afraid.
posted by gurple at 9:47 PM on February 20, 2007

scared of math?
posted by owhydididoit at 9:52 PM on February 20, 2007

Stop for it.
posted by lemuria at 10:28 PM on February 20, 2007 [1 favorite]

"Give me a place to stand and I shall move the Earth." Seriously.
posted by cenoxo at 11:10 PM on February 20, 2007 [1 favorite]

Gurple. Er, combinatorics, I'm afraid.

I am afraid my apparent misspelling was correct. Archimedies was far too advanced for combinatorics, a mere branch of mathematics. No, instead he was indeed interested in combanitorics, study of the third-person plural of the spanish verb combar in the present indicative. Which is especially interesting because the Spanish language would not be developed for another 1,000 years!!!

Pretty amazing...
posted by blahblahblah at 11:19 PM on February 20, 2007 [1 favorite]

Archimedes is the shiznit (imagine what he'd have done with a real number system, not mention other tools and a modern support structure), but I'm pretty underwhelmed by the tangrams reference. Cutting a square into triangles isn't very hard. Cutting it into triangles that can be put back together is only slightly harder.

I'm also not sure how fair it is to say that Archimedes "almost discovered calculus" (as some do). His method found areas and perimeters but relied on numerically figuring out each step as I understand it. It was totally lacking in the concept of the limit, which is the entire beauty of calculus--you don't have to do an infinite number of steps to get the exact answer. It was also totally lacking the idea of general application to functions, but that may be more because Greek mathematics itself lacked this concept.
posted by DU at 5:49 AM on February 21, 2007

the Spanish language would not be developed for another 1,000 years!!!

posted by Floydd at 6:10 AM on February 21, 2007

I'm a Big fan of ol' Archimedes, yet reading this great FPP, i could not help but think:

"not the Craw! the CRAWWWWW!"

we now return to regular programming....
posted by storybored at 7:31 AM on February 21, 2007

Let's not forget archimedes's screw or the-thing-that-pumps-water-without-science-having-invented-pumps-yet.

Archimedes is the Lockheed Skunk Works of the ancient world. We're still trying to figure out if he built what history says he built, and how. But when you look at his contraptions, you realize he is simply combining the mechanical advantage of a few simple machines.

What is the claw, but a lever and a pulley, with gravity doing most of the work?
posted by Pastabagel at 7:47 AM on February 21, 2007

Mythbusters did a very good episode on the Archimedes Death Ray where they invited viewers to create one and test it against theirs. Saw it last sunday, not sure if it was a repeat or not.
posted by Vindaloo at 9:01 AM on February 21, 2007

It was a repeat. The link to the discussion of that episode, including some comments from one of the hosts, is the very first link in this thread. It first aired September 29th, 2004 in the States, and spawned a fan competition (that very few participated in, in spite of tons of know-it-alls complaining MB did things wrong), to try to do better than the Mythbusters. That attempt included MIT's efforts, which also were proved false with period materials (Much to the professor's frustration).

Episodes & synopsis:

MIT's Death Ray work:

MIT's work with Mythbusters:

The claw is cool, but falls into the same category as the Death Ray....too impractical because of it's limitations to have been of actual use. I often think of Archimedes as an architect.....drawing out many many ideas, but only bringing the practical ones to life. The practical ones hold my interest well enough!
posted by mattfn at 9:56 AM on February 21, 2007

This is great... I ran across the Archimedes Palimpset site awhile back and thought it was amazing... Now your post has given me a wealth of additional information to soak up, thanks!
posted by amyms at 12:57 PM on February 21, 2007

Two quotes from about Archimedes, from his contemporaries:
"From this day forth Archimedes is to be believed in everything that he may say".
- King Hiero of Syracuse

"Spare the mathematician!"
- Roman General Marcellus

Also, according to This show, he also designed a pretty amazing seavessel, as well - for which he might have designed the above mentioned screw.
posted by absalom at 2:52 PM on February 21, 2007

Great stuff, blahblahblah.

There is also a British doco (series) in which a bunch of practically-minded archaeologists tried to recreate ancient technologies, including an episode in which they did Archimedes' claw. Life-size.

No more info than that at the moment, I'm afraid. No YouTube here, but maybe I can find it on the BBC site...(only guessing it was a BBC doco)...?
posted by UbuRoivas at 5:04 PM on February 21, 2007

* unleashes google-claw:

Secrets of the Ancients

The Claw

The mathematician Archimedes invented a terrifying machine known as The Claw, which was used successfully against the Romans when they attempted to conquer Syracuse. Despite the slight inconvenience that there is no record of the machine's appearance or its mechanism, engineer Jo da Silva attempts to recreate it for Secrets.

posted by UbuRoivas at 5:19 PM on February 21, 2007

mattfn: The claw is cool, but falls into the same category as the Death Ray....too impractical because of it's limitations to have been of actual use.

Except that the Roman tactic was to use large scaling towers with ladders attached to their ships (called Sambucae) to attempt to overwhelm the seaward walls of Syracuse. Accounts of the time say that from longer ranges, the Greeks used siege weapons on the walls to bombard the ships, but they were useless at close range. Thus, Claws that swung over these ships and destroyed them were not just possible, but needed.
posted by blahblahblah at 8:10 PM on February 21, 2007

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