Stephen Speicher

Archimedes and the siege of Syracuse

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Quite by accident I came across a paper that mentioned some of the incredible exploits of Archimedes in the siege of Syracuse by Marcellus around 214 to 212 B.C. I was previously aware of some of Archimedes remarkable achievements, but I was not aware of the story about him orchestrating a burning of the Roman ships by placing mirrors so as to focus the sunlight on the ships. Evidently this has usually been considered to be a myth, but some historians think it may be true. Before I spend any time researching this, does anyone know much about the burning mirrors story?

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Quite by accident I came across a paper that mentioned some of the incredible exploits of Archimedes in the siege of Syracuse by Marcellus around 214 to 212 B.C. I was previously aware of some of Archimedes remarkable achievements, but I was not aware of the story about him orchestrating a burning of the Roman ships by placing mirrors so as to focus the sunlight on the ships. Evidently this has usually been considered to be a myth, but some historians think it may be true. Before I spend any time researching this, does anyone know much about the burning mirrors story?

This isn't about Archimedes, but here's a similar story from ancient history:

In an important battle in Asia Minor, Alexander the Great surrounded a great city with his legions. Certain that surprise would enable him to take the city, he wanted to execute a dawn attack. However, he faced an enormous problem: how to coordinate things so that the entire army, now spread for miles and miles around the perimeter, would attack simultaneously. The city was extremely well defended, its army known for its bravery and cunning, so timing was critical - one late battalion could spell defeat.

Alexander met with his generals through the night, making plans and trying to solve the coordination problem. Shorty before the sun rose, a minor officer came to Alexander's tent with a possible solution. He had found, after accidentally spilling a local fruit drink on his clothes, that the stained fabric changed colors when struck by sunlight. He suggested dipping strips of cloth torn from old togas in the fruit drink and distributing them to all the commanders on the perimiter, with instructions to attack immediately when the color of the cloth changed.

Alexander did exactly that. The sun came up, the colors changed, and the simultaneous attack from all sides was perfectly executed. The city fell in less than two hours.

Thus was born one of the great military advances of the ancient world: Alexander's Rag Time Band.

(Sorry - really I am. I'd have put it under the joke thread, but it just fit so well here.)

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Stephen, yes it is claimed from the ancient sources that Archimedes used a large assembly of bronze shields as a kind of focus for the sun's light, burning the Roman ships. The literary sources, describing the siege of Syracuse (the city he was defending), go into great detail about all kinds of ingenious machines by which Archimedes was single-handedly able to fight off the whole Roman army for three years. However, not all of them mention the burning of the ships via focus; combined with the traditional cynicism and skepticism with which today's historians approach antiquity, many believe that it indeed is little more than a fairy tale. However, that is a problem with those armchair historians, not with Archimedes. If we didn't have dozens of cities all across the world called Alexandria, how many modern historians would believe the ancient accounts of Alexander the Great? In any case, I remember reading about Archimedes' feat and some people actually being successful in replicating it.

In fact, I just found this interesting website via Google, which conclusively proves that Archimedes could have done it. Usually the web is suspect on questions like these, but the site looks quite scholarly:

http://www.mlahanas.de/Greeks/Mirrors.htm

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Apparently, Archimedes was filmed in the act! Of course, it is a silent movie. You can see it here:

http://www.cs.drexel.edu/~crorres/Archimed...ia/Cabiria.html

Fascinating find. Thanks, Lee.

While I was away today, and after I first wrote my post beginning this thread, I started reading a couple of papers from the 1700s about re-discovery of the Archimedes' burning mirrors idea. It is an interesting problem, both from an historical context and in the context of physics. The more that I read about this the more fascinating it becomes.

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Thus was born one of the great military advances of the ancient world: Alexander's Rag Time Band.

(Sorry - really I am. I'd have put it under the joke thread, but it just fit so well here.)

As a moderator I should spank you, but right now I am laughing too much. :)

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In fact, I just found this interesting website via Google, which conclusively proves that Archimedes could have done it. Usually the web is suspect on questions like these, but the site looks quite scholarly:

http://www.mlahanas.de/Greeks/Mirrors.htm

I see that that site mentions both Kircher and Buffon, about whom the former is dicussed and the latter is the author of two older papers from the 1700s I just started reading. I love it when history and physics comes together!

p.s. Do you have reference to the earliest mentions of Archimedes' burning mirror exploits?

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Well it's a bit hard to find sources on such a narrow subject, but it seems that the two earliest writers to explicitly mention "burning mirrors" rather than simply some vague references to fire, were Cassius Dio and Claudius Galen (the doctor). Both lived in the 2nd century AD.

However, we have recently (1976) discovered an actual treatise entitled "On Burning Mirrors", written by one Diocles written in the 2nd century BC; thus it's clear that by that time, less than 100 years after Archimedes, the principles were already known.

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However, we have recently (1976) discovered an actual treatise entitled "On Burning Mirrors", written by one Diocles written in the 2nd century BC; thus it's clear that by that time, less than 100 years after Archimedes, the principles were already known.

My somewhat outdated, second edition of The Oxford Classical Dictionary, "Diocles (4)," suggests that Diocles (for whom no place name is given, unlike the others of that name) lived around 200 BC, thus making him possibly a contemporary of the aging Archimedes. However, this short article is vague.

The manuscript of Diocles, peri pureiOv, "On Burning Mirrors," survives in two partial forms: (1) a "defective" manuscript in Arabic, apparently discovered in our own time; and (2) long excerpts in the work of Eutocius, apparently titled Commentary on Archimedes (but the OCD, 2nd, is unclear about that because it is dense with abbreviations in Latin of Greek titles!).

The brief bibliography to the short OCD, 2nd, article suggests Heath, History of Greek Mathematics, vols I (pp. 264ff) and II (pp. 47ff) for the math that Eutocius (and therefore Diocles) addressed.

In the OCD I can find no date for Eutocius, suggesting he was medieval. George Sarton, History of Science: Hellenistic Science ..., p. 81, describes a Eutochius of Ascalon in the Archimedean tradition, living in the first half of the 6th Century AD.

Short OCD articles are often cryptic, so I might be misinterpreting this one. Regardless, you might try the newer, third edition as a starting point if you don't find anything else as a lead. Of course, Sarton's introduction to history of science in the Greek period is usually thoroughly documented with the ancient and medieval works, at least up to those known in Sarton's own time. Besides, Sarton is always a pleasure to read.

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My somewhat outdated, second edition of The Oxford Classical Dictionary, "Diocles (4)," suggests that Diocles (for whom no place name is given, unlike the others of that name) lived around 200 BC, thus making him possibly a contemporary of the aging Archimedes. However, this short article is vague.

The manuscript of Diocles, peri pureiOv, "On Burning Mirrors," survives in two partial forms: (1) a "defective" manuscript in Arabic, apparently discovered in our own time; and (2) long excerpts in the work of Eutocius, apparently titled Commentary on Archimedes (but the OCD, 2nd, is unclear about that because it is dense with abbreviations in Latin of Greek titles!).

The brief bibliography to the short OCD, 2nd, article suggests Heath, History of Greek Mathematics, vols I (pp. 264ff) and II (pp. 47ff) for the math that Eutocius (and therefore Diocles) addressed.

In the OCD I can find no date for Eutocius, suggesting he was medieval. George Sarton, History of Science: Hellenistic Science ..., p. 81, describes a Eutochius of Ascalon in the Archimedean tradition, living in the first half of the 6th Century AD.

Short OCD articles are often cryptic, so I might be misinterpreting this one. Regardless, you might try the newer, third edition as a starting point if you don't find anything else as a lead. Of course, Sarton's introduction to history of science in the Greek period is usually thoroughly documented with the ancient and medieval works, at least up to those known in Sarton's own time. Besides, Sarton is always a pleasure to read.

When I checked my copy of the third edition of the OCD, the bibliography for Diocle(4) was Diocles on Burning Mirrors by G.J. Toomer. I think that this is it.

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However, we have recently (1976) discovered an actual treatise entitled "On Burning Mirrors", written by one Diocles written in the 2nd century BC; thus it's clear that by that time, less than 100 years after Archimedes, the principles were already known.

Now I'm angry at you! This Diocles connection is so fascinating that I am spending more time with this than I intended. :) (Thanks!)

I just glanced through several papers on Diocles from The Philosophical review, one by a favorite author of mine, D'Arcy Wentworth Thompson (On Growth and Form, a great book). Another by Werner Jaeger, from Harvard, each paper from some 60 odd years ago. Apparently Diocles of Carystus was not very well-known at all. It wasn't until the time of these two papers that it was learned that Diocles followed Aristotle and studied his biology as a student of Aristotle, not that he lived before Aristotle as was previously thought. Interestingly (to me), Diocles followed a lot of Aristotle's teology. I will study these papers on Diocles in some depth, since he seems to be an interesting person previously unknown to me.

I also glanced through a paper in Isis on a review of the book you refer to, published in 1976. The title is Diocles on Burning Mirrors: The Arabic Translation of the Lost Original, G.J. Toomer, Springer-Verlag, 1976. Based on a quick look at the review paper there is a lot of interesting historical math and physics involved with what Diocles has done.

A whole new additional perspective on Archimedes and the Ancient's grasp of mathematics and physics just opened for me. Thanks for that. Now, if I will ever find the time to pursue this in depth....

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The Mythbusters on the Discovery Channel tried and failed even when they used mirrors.

Perhaps. But, though I do not know these "Mythbusters," I do not consider the Discovery channel a reliable scientific source.

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When I checked my copy of the third edition of the OCD, the bibliography for Diocle(4) was Diocles on Burning Mirrors by G.J. Toomer. I think that this is it.

Yes, I was just looking through a review paper of this by A. Mark Smith in Isis, Vol. 69, No. 2, pp. 290-292, June 1978. If you have any interest in the history of mathematics and physics, this seems to be a fascinating chapter to explore.

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My somewhat outdated, second edition of The Oxford Classical Dictionary, "Diocles (4)," suggests that Diocles (for whom no place name is given, unlike the others of that name) ...

It is Diocles of Carystus. In the Thompson paper I mentioned previously, he lists an astounding number of others named Diocles, and he indicates that "Diocles was one of the commonest names."

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A whole new additional perspective on Archimedes and the Ancient's grasp of mathematics and physics just opened for me.
Stephen, you do know that the Greeks invented the steam engine in the 2nd century BC, right? :)

Also, in regards to Diocles, from what I understand he was an obscure person from antiquity (hence why it was the 60s papers that make him famous), until we discovered in 1979 the Arabic manuscript of his book on optics, and were able to place him in a proper context of history of math and science.

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I don't have sufficient background in physics to answer the question definitively. But back in the 70s I did design and build several small amateur telescopes; and from the smattering of optics I picked up then, it seems unlikely that Archimedes could burn ships at a distance.

The Greeks certainly had (small diameter) burning lenses. But remember, their mirrors were of bronze. Herbert Hoffmann's "Collecting Greek Antiquities," (New York, 1971) pp. 53-56 discusses and illustrates ancient bronze mirrors.

How efficient are even highly polished bronze mirrors? Not very, compared to modern silvered glass mirrors (otherwise we would still be using them!)

The difficulty in efficiently gathering and focusing enough sunlight to cause a fire at a distance seems insurmountabe, even for a genius like Archimedes.

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I don't have sufficient background in physics to answer the question definitively.  But back in the 70s I did design and build several small amateur telescopes; and from the smattering of optics I picked up then, it seems unlikely that Archimedes could burn ships at a distance.

The Greeks certainly had (small diameter) burning lenses.  But remember, their mirrors were of bronze.  Herbert Hoffmann's "Collecting Greek Antiquities," (New York, 1971) pp. 53-56 discusses and illustrates ancient bronze mirrors.

How efficient are even highly polished bronze mirrors?  Not very, compared to modern silvered glass mirrors (otherwise we would still be using them!)

The reflectivity coefficients are not as greatly different as you might think. Specular reflection depends highly on the smoothness of the surface, removing irregularities on the order of the wavelength of the incident light. Also, keep in mind that here we are interested in the irradiance, the energy delivered to an area in a given time.

The difficulty in efficiently gathering and focusing enough sunlight to cause a fire at a distance seems insurmountabe, even for a genius like Archimedes.

Calculations indicate otherwise, but, even more importantly, reality is the final arbiter. Dr. Ioannis Sakkas, encouraged by historian Prof. Evanghelos Stamatis, built 200 bronze-coated mirrors and in 1973 they assembled the mirrors along with some 60 men on the pier of the Skamanga naval base near Athens, Greece. When commanded, the mirrors were focused on a wooden boat located 160 feet from the pier; the boat was smoking within seconds, engulfed in flames soon afterwards. Dr. Sakkas noted that Archimedes would have had better working conditions, since Sakkas had a weak winter Sun and his plywood boat burned more slowly than the cedarwood of the ancient ships. Since the time of this reported experiment, Dr. Sakkas repeated the same positive results five times.

This event is mentioned briefly in the scientific literature, and reported widely in, for instance, the November 11, 1973 edition of the New York Times, and in the November 26, 1973 issue of Time magazine.

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I found some interesting sites about Diocles by Googling him.

Brief Overview of Diocles and his Work

Mathematics of what Diocles Did

History of the Burning Mirrors

What I found interesting was that apparently Leonard da Vinci also worked on a problem similar to this. On the last website, there's a link to an image of a page of da Vinci's notebook where he apparently studied burning mirrors. Also, looking at what Diocles did mathematically, it's interesting to see that he established several important theorems about parabolas, something my Precalculus class is covering right now. It's fun to know the history of this stuff.

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Also, looking at what Diocles did mathematically, it's interesting to see that he established several important theorems about parabolas, something my Precalculus class is covering right now. It's fun to know the history of this stuff.

Since I became motivated by this subject a day or two ago, I have been going through a whole bunch of papers, each on a different level. If you enjoy the history and the math, there is one paper that you might find fascinating, and the math is presented at a level in line with your class. If you are interested, let me know and I can send you a pdf of this paper. (It's a little less than 4mb.)

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I hope Archimedes did succeed ... though I have a lingering doubt that the reports of successful replications may turn out to be urban legends.

Speaking of scientific achievements in ancient Greece and Rome ... has everyone read Isaac Asimov's intriguing short story, "The Red Queen's Race" ... "you have to run as fast as you can, just to stand still"?

(Hope our gentle moderators don't chide me for diverting just about every thread I reply to, toward literature!) :)

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(Hope our gentle moderators don't chide me for diverting just about every thread I reply to, toward literature!)  :)

As long as you do not mind all that talk about last night's Dodger game in your literature thread. :)

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I don't find it at all surprising that polished metal mirrors in large numbers could, with human aiming, create high temperatures at the aimed spot. It's simple physics. Also, the ability of individual men to visually track the target spot in unison would be straightforward. Probably easier than playing a modern video game. The trick is probably that there'd have to be a single commander specifying the target spot. ("Aim just above the waterline straight down from the fifth oar and keep it there!")

The thought also occurs to me that this might have also made some kind of "terror weapon" to demoralize enemy troops trying to attack a fortified walled city in the daytime (subject to the sun being in the right position to make it possible.) A couple of hundred guys manning the walls, aiming their polished metal rectangles at the same spot in a crowd of enemy troops would probably cause panic as they began to get burned. The target wouldn't have to just be ships at sea. In fact, it would be a very logical way to systematically pick off officers, subject to the effective range of the mirrors as the reflected light spread out over distance.

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The trick is probably that there'd have to be a single commander specifying the target spot. ("Aim just above the waterline straight down from the fifth oar and keep it there!")

One of the reports of the Sakkas experiment indicated that it took a little while to coordinate the aiming of all the mirrors, but once done, voila!

The thought also occurs to me that this might have also made some kind of "terror weapon" to demoralize enemy troops trying to attack a fortified walled city in the daytime (subject to the sun being in the right position to make it possible.)

One of the papers I have been reading mentioned an historical example of just that (but I cannot put my finger on the reference right now).

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The main problem with this weapon, and why it wasn't used much in antiquity, is that it required what in ancient times was tantamount to a mathematical genius to get all the foci properly, and the angles with which the polished surfaces were inclined. That's the only way I can explain why such an absolutely terrifying weapon was not used constantly.

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