[math-fun] Antikythera device & lunar navigation
Been reading a bit about the history of navigation. The British were successful in locating many places, such as Jamaica, via astronomical methods before the chronometer was developed. The method they used was that some astronomical event -- Jupiter's moons and the transits of Mercury were the most used and popular -- would be clocked both in Jamaica and at Greenwich. Then they'd send each other the info. As a result, they could synchronize high accuracy pendulum clocks in both places. Thus they could deduce the longitude of Jamaica. This however required a decent observatory and high accuracy pendulum clocks, neither of which could be used on a ship. But this could be done, and was done, and was the basis of their early charts. Later, a competition arose between the clock makers, especially the genius John Harrison who developed a number of great inventions laying the basis for precise instrumentation of all kinds, versus the astronomers, in solving the ship navigation problem. The clock-based method ultimately won. However, laying his thumb very heavily on the scale trying to bias the judges was Astronomer Royal Nevil Maskelyne, who if this were a Hollywood movie, would be the bad guy. The astronomers published lunar tables for navigation purposes. Kepler published tables in 1627. Street in 1661. Note Newton's "Principia" came out in 1787 so all those were before his Laws were known. In 1753/5 solar and lunar tables were published by Tobias Mayer. The British Admiralty found the the typical error in the moon's location got from these tables was 1 arcminute, i.e. 1/216000 of a full circle. They then published Nautical Almanacs with updated tables and full instructions on how to use them to navigate. E.g. in the 1767 almanac there are tables of the moon-to-sun angle and angles to seven fixed stars, for times every 3 hours, and instructions are given to convert measurements of these things to "time at Greenwich" -- including making corrections for "parallax" and "refraction." These tables kept improving as the years went by due to further astronomical observations and corrections based on them -- as well as errors detected+corrected of which there were perhaps 100. (There also were tables concerning Jupiter's moons published 1821). The French and Spanish then published their own such almanacs and tables, then the Portuguese and Danes. However as I said chronometers won versus astronomy for ship navigation, and indeed it ultimately became popular for important ships to carry many, not just one, chronometer. The observatory at Greenwich held an annual contest to determine the best available chronometers during 1822-1835. When the trans-ocean telegraph cable came it became possible to sync clocks without need for chronometers or astronomy, but the old determinations were found to be quite correct. Prof. Edmunds sent me a paper claiming the antikythera device would have error in moon location of 20 degrees hence useless for navigation. However, his error assessment was totally irrelevant since it was for a 19-year-duration prediction. The history I have recounted makes it clear that at least in principle an antikythera-like device could have attained accuracy of 1 arcminute, although I doubt that was ever actually achieved, and even if my whole "it was intended for navigation" hypothesis is correct then still clearly the antikythera must have either been a failure or never reached widespread success as a navigation tool, and must have been only an experimental device. For it to be an actually wide-used and useful navigation device would have required a network of observatories, chart production, a small science well known to many, and very many copies of the device produced... which I think could not have been forgotten to this great an extent if it happened. So it didn't.
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Warren Smith