Re: [math-fun] Antikythera device -- could it have been intended for navigation?
I finally talked myself into sending an email to the people behind the http://www.antikythera-mechanism.gr/ web site (who also have authored numerous articles about the device). Here's the email I sent them. I was stimulated by recent speculation the antikythera device was perhaps designed by Archimedes, seems to have predicted calandar, moon, sun, planets, and knew (via a "pin and slot drive" mechanism) an approximate version of Kepler's ellipse fact of non-uniform speed and non-circular motion. Then I found your web site http://www.antikythera-mechanism.gr/ and some popular press articles. What I want to begin exploring in this email is the speculation -- which I hardly saw anyplace -- that the device could have been intended by its designer for navigational use. On the website the only mention of this idea is the following disparaging quote by Martin Allen: "Another common suggestion is that it could have been an aid to navigation, especially as the ancient inhabitants of Rhodes were notorious for their navigational skills. However this seems unlikely as it would be an impractical device to use at sea, and seems excessive for the purposes of navigation. It would have been a more useful tool to astronomers, for assisting in making land based astronomical measurements. Indeed, with knowledge of eclipse timings it would assist in making measurements on a world scale, for example longitude. The first Mechanisms could have been built purely on the basis of seeing if it could be done. Indeed researchers are still making models of the mechanism today, to see if the theory can be put into practice. Unfortunately this does not apply in the case of the Antikythera Mechanism, as it is not thought to be the first of its kind." OK. First of all, nothing at all like this mechanism has ever been found. It is the unique exemplar. So I don't see how you know it is not the first of its kind. The only thing we know for sure is, it did not catch on and "stay invented." It instead was "lost" and its discovery millennia later in the shipwreck "stunned the world" hence I conclude it was really very very lost, not a soul had the faintest clue any such device ever existed. You cannot get more lost than that. So if it was not the first, it had to have been one of the nearly-first, for the simple reason that if this device had caught on big time with 1000 copies produced, then it would have been too well known to have become lost. So in fact it WAS the first, or nearly so -- Allen's claim just was wrong. Second, it was in roughly the right place and time that it may have been designed by Archimedes. (300 ton Roman ship guessed to have sunk 85 to 60 BC. Archimedes lived about 287 to 212 BC in Syracuse, from which it is believed the ship came.) So one might speculate that Archimedes or someone associated with him designed it and for a reason, and that reason was as an experimental navigation device for sea travel. The fact the planets would have been "excessive" is irrelevant -- this was an experimental device. The claim this would have "impractical for shipboard use" is based on nothing whatever that I can see. What the heck is impractical? See below for realistic practicality remarks. The experiment (we could continue speculating) was a failure and/or terminated by Archimedes' assassination and/or the theft of the device by the Romans and/or their ship's sinking, and hence the whole idea was lost, not to be rediscovered for 1700 years. The Greeks knew the Earth was round, and they knew how big the Earth was. Eratosthenes of Cyrene (lifespan about 276 to 194 BC, and a known friend of Archimedes) famously measured the Earth's circumference accurate to about 2% using trigonometry. This knowledge was later largely lost, for example Columbus famously had the idea, which was famously controversial, that the Earth was round, but he had a completely wrong idea of its size. Now much later, the British famously had trouble with sea navigation and in 1714 offered a huge monetary prize to anybody who could solve the longitude problem. This was solved by the invention of the first accurate chronometers by John Harrison during 1730-1767, and by 1825 their use was widespread. This was technically difficult and I would think beyond what the Greeks could have hoped to do pre-industrial era. At that time (1700) mainstream thought was that it would in fact be infeasibly difficult to design an accurate-enough chronometer, and therefore the top candidate method (which never was able to compete with the chronometer based method) was based on astronomy. The motions of the moon and planets in fact ARE a chronometer of more-than-sufficient accuracy, provided you can (a) predict and (b) measure them, and then (c) make the necessary computations to use the predictions and measurements to deduce your location. All of these things are not trivial, especially if the measurements have to be conducted accurately from a ship at sea, but they are possible. In fact, the chronometer-based method requires sextant measurements to be conducted from ship, and it was very successful for 100 years, and was even used by Ernest Shackleton from a 20 foot rowboat in stormy seas during a desperate 800 mile journey from Antarctica to S.Georgia in 1916. If it could be done from such a rowboat in those seas, it simply is flat out wrong to say it was impractical from much larger Ancient Greek and Roman ships (remember, the wreck it was found on was 300 tons) in the comparatively friendly waters of the Mediterranean. And while I am at it, let me say that a chronometer is a hell of a lot more delicate than the antikythera device, but nevertheless was practical for use, even from a 20 foot rowboat in 800 mile journey in worst seas in world. So once again, I flat out dispute any entirely cavalier and entirely unsupported assertion the antikythera device could not have been intended for ship navigation because it would have been "impractical for ship at sea." And since I am postulating device experimental, it was not even necessary, for me to be right, that it be practical anyhow. Now, the fact that Archimedes personally knew Eratosthenes who knew the Earth was round and measured it, using astronomical+trig methods, accurate to 2%, and the fact Archimedes who was the son of an astronomer and known to have constructed a brass "planisphere," also surely was aware of the "epicycles" celestial motion prediction methods known to Aristotle (384 - 322 BC) which are highly "gearlike" in nature, all lead to the suspicion Archimedes could well have thought of the idea of trying to do navigation via astronomy. To solve the prediction and perhaps some part of the computation problem, a gear-device, the antikythera, would hit the spot. The observation problem would be solved by use of a sextant or primitive analogue thereof. If there was such a device, it was lost, but there must have been devices of this nature for at least 50 years prior to Archimedes since otherwise it would have been simply impossible for the Greeks to have measured with enough accuracy to see the need for their theories of "epicycles." Also I point out Archimedes according to legend designed+built devices involving giant solar mirrors, suggesting sextant-like devices would not have been ridiculously far from his ken. I might also point out that there is a hell of a lot of economic incentive to navigate, and not much incentive to do astronomy. So, let us summarize, in view of that Martin Allen quote above about why this was not a navigation device: ALLEN CLAIM1. it would be an impractical device to use at sea, and seems excessive for the purposes of navigation. ANSWER1: these both refuted. ALLEN CLAIM2: It would have been a more useful tool to astronomers, for assisting in making land based astronomical measurements. Indeed, with knowledge of eclipse timings it would assist in making measurements on a world scale, for example longitude. ANSWER2: Who cares about astronomers? Which is more likely to be a hugely greater economic driving motivation -- astronomers or seamen? Wasn't Archimedes interested in practical engineering (pulley, lever, allegedly war weapons including sea-related ones) And anyhow I do not see that the two are incompatible, and am fully happy with the comment re longitude. However, the "eclipse timings" remark seems like largely bullshit to me, in the sense that those are not useful for much of anything since eclipses very rare and do not occur when & where you want, they occur when & where they want. ALLEN CLAIM 3. The first Mechanisms could have been built purely on the basis of seeing if it could be done. ANSWER3: well, again, this comment is fine with me, albeit it you in trying to use this argument are conflicting with your own statement about how this device was "thought not to be the first." So anyhow, in summary, the lame arguments by Martin Allen in that quote, all either support my hypothesis, or are refuted, and some to some extent are self-contradictory. They have no force against my hypothesis. Now what would it take to make a device good enough for navigation? Earth circumference is 25000 miles. To be accurate to 25 miles, which is good enough to be useful, then, you want accuracy of order <=1 part in 1000. So we'd want to measure some subset of the 6 angles between, e.g. sun, moon, fixed stars, and earth-horizon accurate to 1 part in 1000, i.e. 1/3 of a degree. Was this something Greeks could hope to do? I say "yes." Indeed, their knowledge of the calendar already was of that order of accuracy. Next, you want prediction accuracy for those angles from your antikythera device, to be accurate to <=1 part in 1000 or better. Was that something the Greeks could hope to accomplish? Again I think yes -- maybe not immediately, but after enough astronomical observation, record-keeping, and device development, then yes. And keep in mind the device could be re-set back to the truth whenever the ship came to a place like Greenwich where there were better astro-measuring devices and a known location on Earth. I.e. it did not require high accuracy for years, only for the duration of sea voyage <2 months at most, so error-growth thus was limited. To deduce latitude: measure angle(sun, horizon) at noon ("noon" means when min-angle maximized) and know the calendar day. That is all you need. Also measuring angle to North Star will do. To deduce longitude, you need the time and angles, and the time is in fact related to the angles by a mathematically known relationship hence need not be measured with any kind of mechanical clock. So... this all is hardly a proof, but I think is enough to make it an interesting and somewhat plausible speculation, that Archimedes or somebody of his ilk, built device to explore possible use for navigation. Arguments against this hypothesis have been confused, to say the least. This does not mean I'm right and they are wrong, but it does mean those counterarguments cannot be taken seriously at this time. If there were a pointer somehow related to "your longitude" on the device, that would clinch the case, but that might be too much to ask even if the whole hypothesis is true. Some of the broken-off pieces claimed by some to be for the planets -- were they really? How much evidence is there those really did planets? Maybe they had other functions related to longitude. (I have no idea, I'm just wondering. If you do not know the gear ratios corresponded to planet-period ratios, then we are free to speculate other speculations.) PS. 1. As far as I can tell, there is no convincing evidence the other stuff was planets, except perhaps for Mars (which incidentally would have been the planet most useful for navigation). 2. Wikipedia has this: "The device is rather small, indicating that the designer was aiming for compactness and, as a result, the size of the front and back dials is unsuitable for public display. A simple comparison with the size of the Tower of the Winds in Athens would suggest that the Antikythera mechanism manufacturer designed the device for mobility rather than public display in a fixed location."
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Warren Smith