Re: [math-fun] Antikythera device in volume production ?
Thanks, Robert, for posting this terrific paper! Mike G. Edmunds, Cardiff University, Tony Freeth, Antikythera Mechanism Research Project. "Using Computation to Decode the First Known Computer". IEEE Computer July 2011. Some comments in this paper caught my eye: "We believe the gears were laid out and cut by hand, with the teeth appearing to be *** simple equilateral triangles, *** slightly rounded at the tips." "The Antikythera mechanism is *** engineered at a tiny scale *** Â-the offset between the axis of the gear with the pin and that of the one with the slot is just over 1 millimeter." "For example, *** the random error in tooth-center placement varies between gears from about 0.1 to 1 degree. *** A few showed a more systematic variation characterized by a sinusoidal variation around the whole gear." "The moon position indicator, however, involves Âgearing up, amplifying angular errors so that *** the indicated position could differ by 20 degrees from the designerÂs intention. *** Such a large error is easily noticed when comparing predictions with the moonÂs actual position in the sky; *** it [the error] exceeds the amplitude of the Âfirst anomaly variation that the mechanism was so cleverly designed to incorporate. *** A possible interpretation is that truly accurate prediction was not the deviceÂs primary purposeÂapproximate prediction of astronomical phenomena by mechanical means was achievement enough." My conclusions: 1. The Antikythera device was clearly a scaled-down version of previous devices, some of which were probably made over 100 years prior. 2. The Antikythera device was in _volume production_, since the triangular gears and "play"/"error" in the mechanism would have exceeded the designer's original specifications. Why bother designing & building a clever anomaly mechanism if it didn't work at the end of the day? Clearly, the high precision of this particular function was not essential for the bulk of the customers of the device. The triangular gears are likely the result of faster production, and smaller size, since triangular gears are not ideal in terms of strength, wear or "play". 3. The manufacturer of the device was disconnected enough from the designer, that the designer was not in a position to veto the production of a sloppy mechanism. Those of us in the software business are well aware of the "maintenance programmer" who -- with insufficiently complete understanding of the workings of the original program -- unwittingly makes modifications which destroy some of the features of the original design. At 01:49 PM 12/6/2012, Robert Munafo wrote:
The known gearing, along with the number of teeth in most of the known gears, is described in detail here:
http://cs.iupui.edu/~tuceryan/pdf-repository/Edmunds2011.pdf
On 12/8/2012 10:27 PM, Henry Baker wrote:
Thanks, Robert, for posting this terrific paper! ...
A substantial reference I highly recommend to anyone interested in the Antikythera device and the science, mathematics, and technology of the period is: Lucio Russo, The Forgotten Revolution, Springer, 2004 Russo collects a wealth of evidence suggesting that pockets of Greek science in the period 300BC-100BC were much more advanced than usually thought, then most of their discoveries were later lost or misunderstood. Many of his conclusions are controversial, e.g., their understanding and applying the inverse square law of gravitation. But if you accept even half his arguments, you'll seriously rethink your view of the history of science. He also makes a good case that the definitions of point and line in Euclid's Elements were added later and Euclid had a more modern and axiomatic view than modern readers realize. Even if you don't accept all his conclusions, you'll want to read all the ancient source material he has collected. There's a short summary here: http://en.wikipedia.org/wiki/Lucio_Russo George http://georgehart.com/
="Henry Baker" <hbaker1@pipeline.com>
1. The Antikythera device was clearly a scaled-down version of previous devices, some of which were probably made over 100 years prior.
2. The Antikythera device was in _volume production_, ... Why bother designing & building a clever anomaly mechanism if it didn't work at the end of the day?
Another *possibility* is that this particular instance of the (presumably) mass produced, scaled-down Antikythera device that was found was a kind of model, not necessarily fully functional nor intended to work perfectly, but instead was a sort of sample prototype or template which was accompanied by (perhaps implicitly understood?) instructions like: "Make one of these. Only bigger. And don't forget to calibrate it." So much time, so little known.
The paper note (since lost) attached to the device read: "I'm returning this device for a full refund. It is so inaccurate, it'll be a miracle if we make it back to Syracuse without hitting the shoals near Antikythera." At 10:20 PM 12/10/2012, Marc LeBrun wrote:
="Henry Baker" <hbaker1@pipeline.com>
1. The Antikythera device was clearly a scaled-down version of previous devices, some of which were probably made over 100 years prior.
2. The Antikythera device was in _volume production_, ... Why bother designing & building a clever anomaly mechanism if it didn't work at the end of the day?
Another *possibility* is that this particular instance of the (presumably) mass produced, scaled-down Antikythera device that was found was a kind of model, not necessarily fully functional nor intended to work perfectly, but instead was a sort of sample prototype or template which was accompanied by (perhaps implicitly understood?) instructions like:
"Make one of these. Only bigger. And don't forget to calibrate it."
So much time, so little known.
participants (3)
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George Hart -
Henry Baker -
Marc LeBrun