Antikythera Mechanism

WHEN a Greek sponge diver called Elias Stadiatos discovered the wreck of a cargo ship (it is now accepted that the wreck occurred during the first century B.C.) off the tiny island of Antikythera in 1900, it was the statues lying on the seabed that made the greatest impression on him. He returned to the surface, removed his helmet, and gabbled that he had found a heap of dead, naked women. The ship’s cargo of luxury goods also included jewellery, pottery, fine furniture, wine and bronzes dating back to the first century BC. But the most important finds proved to be a few green, corroded lumps—the last remnants of an elaborate mechanical device (known today as the Antikythera Mechanism).

Greek ?rchaeological National Museum: Antikythera Mechanism

The Antikythera mechanism, as it is now known, was originally housed in a wooden box about the size of a shoebox, with dials on the outside and a complex assembly of bronze gear wheels within. X-ray photographs of the fragments, in which around 30 separate gears can be distinguished, led the late Derek Price, a science historian at Yale University, to conclude that the device was an astronomical computer capable of predicting the positions of the sun and moon in the zodiac on any given date. A new analysis, though, suggests that the device was cleverer than Price thought, and reinforces the evidence for his theory of an ancient Greek tradition of complex mechanical technology.

Michael Wright, the curator of mechanical engineering at the Science Museum in London, has based his new analysis on detailed X-rays of the mechanism using a technique called linear tomography. This involves moving an X-ray source, the film and the object being investigated relative to one another, so that only features in a particular plane come into focus. Analysis of the resulting images, carried out in conjunction with Allan Bromley, a computer scientist at Sydney University, found the exact position of each gear, and suggested that Price was wrong in several respects.

In some cases, says Mr Wright, Price seems to have “massaged” the number of teeth on particular gears (most of which are, admittedly, incomplete) in order to arrive at significant astronomical ratios. Price’s account also, he says, displays internal contradictions, selective use of evidence and unwarranted speculation. In particular, it postulates an elaborate reversal mechanism to get some gears to turn in the right direction.

Since so little of the mechanism survives, some guesswork is unavoidable. But Mr Wright noticed a fixed boss at the centre of the mechanism’s main wheel. To his instrument-maker’s eye, this was suggestive of a fixed central gear around which other moving gears could rotate. This does away with the need for Price’s reversal mechanism and leads to the idea that the device was specifically designed to model a particular form of “epicyclic” motion.

The Greeks believed in an earth-centric universe and accounted for celestial bodies’ motions using elaborate models based on epicycles, in which each body describes a circle (the epicycle) around a point that itself moves in a circle around the earth. Mr Wright found evidence that the Antikythera mechanism would have been able to reproduce the motions of the sun and moon accurately, using an epicyclic model devised by Hipparchus, and of the planets Mercury and Venus, using an epicyclic model derived by Apollonius of Perga. (These models, which predate the mechanism, were subsequently incorporated into the work of Claudius Ptolemy in the second century AD.)

A device that just modelled the motions of the sun, moon, Mercury and Venus does not make much sense. But if an upper layer of mechanism had been built, and lost, these extra gears could have modelled the motions of the three other planets known at the time—Mars, Jupiter and Saturn. In other words, the device may have been able to predict the positions of the known celestial bodies for any given date with a respectable degree of accuracy, using bronze pointers on a circular dial with the constellations of the zodiac running round its edge.

Mr Wright devised a putative model in which the mechanisms for each celestial body stack up like layers in a sandwich, and started building it in his workshop. The completed reconstruction, details of which appeared in an article in the Horological Journal in May, went on display this week at Technopolis, a museum in Athens. By winding a knob on the side, celestial bodies can be made to advance and retreat so that their positions on any chosen date can be determined. Mr Wright says his device could have been built using ancient tools because the ancient Greeks had saws whose teeth were cut using v-shaped files—a task that is similar to the cutting of teeth on a gear wheel. He has even made several examples by hand.

How closely this reconstruction matches up to the original will never be known. The purpose of two dials on the back of the device is still unclear, although one may indicate the year. Nor is the device’s purpose obvious: it may have been an astrological computer, used to speed up the casting of horoscopes, though it might just as easily have been a luxury plaything. But Mr Wright is convinced that his epicyclic interpretation is correct, and that the original device modelled the entire known solar system.

The Greeks had a word for it

That tallies with ancient sources that refer to such devices. Cicero, writing in the first century BC, mentions an instrument “recently constructed by our friend Poseidonius, which at each revolution reproduces the same motions of the sun, the moon and the five planets.” Archimedes is also said to have made a small planetarium, and two such devices were said to have been rescued from Syracuse when it fell in 212BC. This reconstruction suggests such references can now be taken literally.

It also provides strong support for Price’s theory. He believed that the mechanism was strongly suggestive of an ancient Greek tradition of complex mechanical technology which, transmitted via the Arab world, formed the basis of European clockmaking techniques. This fits with another, smaller device that was acquired in 1983 by the Science Museum, which models the motions of the sun and moon. Dating from the sixth century AD, it provides a previously missing link between the Antikythera mechanism and later Islamic calendar computers, such as the 13th century example at the Museum of the History of Science in Oxford. That device, in turn, uses techniques described in a manuscript written by al-Biruni, an Arab astronomer, around 1000AD.

The origins of much modern technology, from railway engines to robots, can be traced back to the elaborate mechanical toys, or automata, that flourished in the 18th century. Those toys, in turn, grew out of the craft of clockmaking. And that craft, like so many other aspects of the modern world, seems to have roots that can be traced right back to ancient Greece.

Antikythera Mechanism Part 1: by Nature Video

Antikythera Mechanism Part 2: by Nature Video

Virtual Reconstruction of the Antikythera Mechanism (by M. Wright & M. Vicentini)

The Antikythera Mechanism – 3D

Reconstructing The Antikythera Mechanism

A video series documenting the reconstruction of The Antikythera Mechanism in its most authentic form to date, with the intention of establishing the precise machining tools, techniques and technology used to create it.

PS1: The Sun-Moon Assembly

It is interesting to speculate how the first century B.C. designers of the Antikythera Mechanism were able to discover the excellent rational approximation 254/19 = 13.36842105 to the astronomical ratio 13.368267.. . The error is 0.00015, which corresponds to one part in 86,000.

The most economical explanation is that in keeping records, early astronomers were struck by the almost exact duplication of the pattern of equinoxes and solstices (sun) and phases of the moon in a 19-year cycle. Nineteen years almost exactly matches 235 lunar-phase cycles (“synodic months”), which correspond to 235+19=254 revolutions of the moon with respect to the stars. It picks up an extra one each year from its trip with us around the sun.

But part of the answer comes from the astronomical ratio itself, which turns out to be one of those numbers that can be very well approximated by rationals.

The sun marker and the moon marker were driven by the twocentral gears (the moon axis threaded through the sun’s),exactly like the hour and minute hands on a modern clock.The train of gears linking the sun’s motion to that of themoon can be described by the meshing pattern and thenumbers of teeth.

The sun gear has 64 teeth. It meshes with the smaller of a 38,48 gear pair.
The 48 meshes with the smaller of a 24,127 gear pair.
The 127 meshes with the 32 teeth of the moon gear.
The ratio of angular speeds can then be calculated as
64   48   127 254
— X — X — = —   = 13.36842..
38   24   32     19

which is an excellent approximation of the astronomical ratio 13.368267.. .

Greek ?rchaeological National Museum: Antikythera Mechanism

More about The Antikythera Mechanism

http://www.brocktonmass.com/weights/history.html

….at the last website is the complete schematic breakdown of the device , shown in five gear colors , blue , yellow-sun gear , green , orange , purple and dark green. Thirty gear numbers are shown , each having one of the above colors. The key number constant used in all thirty gears is the modern metric to english conversion constant …( 39.3700787 inches = 1 meter )… rewritten to this form :

39.3700787 / ( 10 ^ 3 ) = m = 1/25.4

….all thirty gears are linked and can be turned all at once by the rotation of any one gear in the system . I chose the blue(50) gear as a starting point and turned this gear exactly one-revolution or 360 degrees. The gematric formula for this angle is the sacred number 72 , times one half the metric standard 254 ( 254/2 = 127 ):

72 * 127 * m = 360 degrees

….this angle is transferred to the second blue(50) gear because of its being self similar to the first blue(50) gear. This angle is also transferred to the blue(32) gear because of a shared axle. The next step is the blue(32) gear’s link to gear , blue(127) .

This link is the famous sacred Alautun time cycle number …2304…from Aztec and Mayan culture. Here is a link with the explanation of the number:

http://www.mayadiscovery.com/ing/history/tiempo/tiempo2ing.swf

….this is very important to the explanation of the Antikythera device because both the 1152 and 2304 units are Mayan calendar constants measured in DAYS !! the same as the Antikythera mechanism !!

20 calabtun = 1 kinchiltin = a cycle of 11520000000 days
20 kinchiltin = 1 alautun = a cycle of 23040000000 days

…so I would say that 1152 ( kinchiltin ) is a thing of Mayan origin as is the 2304 (alautun ) number.

blue(127) = 2304 * m = 32 / 127 * 360 = 90.70866132 degrees
blue(24) = 2304 * m = 32 / 127 * 360 = 90.70866132 degrees

…that is when you turn the starter blue(50) gear 360 degrees, the blue(127) gear will turn 90.70866132 degrees. The blue(24) gear shares an axle with the blue(127) gear and thus shares the rotation of the blue(127) gear. Blue(24) gear then transfers this rotation to the blue(48) gear . This angle of rotation is the gematric number known as the Egyptian foot number ..1152…:

http://www.celticnz.co.nz/Clandonwebsitefiles/Clandon2a.htm

blue(38) = 1152 * m = 32/127*24/48*360 = 45.35433066 degrees
blue(48) = 1152 * m = 32/127*24/48*360 = 45.35433066 degrees

…blue(38) shares an axle with blue(48) and thus transfers this angle of rotation to the so-called Sun gear… yellow(64)..The number 19 appears here not as years of the Metonic cycle but as DAYS!! on the edge of gear wheels:

Sun gear = 36 * 19 * m = 32/127*24/48*38/64*360 = 26.92913383 degrees

….all of the green gears share the same angle of rotation as the Sun gear. The orange gears appear when the second gear with 38 cogs appears as orange(38). It has the same angle of rotation as the blue(38) gear:

orange(38) = 1152 * m = 32/127*24/48*360 = 45.3543306 degrees
orange(53) = 1152 * m = 32/127*24/48*360 = 45.3543306 degrees

…orange(53) shares an axle with orange(38) and thus transfers this angle of rotation to orange(96)

orange(96) = 25 + m = 53*12 * m = 32/127*24/48*53/96*360 = 25.0393700787 degrees

…orange(15) and orange(27) gears share axles with orange(96) and thus transfers angular rotation to the large gear purple(223):

purple(223) = 53*12*27*m/223 = 36*m+360/223 = 32/127*24/48*53/96*27/223*360 degrees

..purple(53) edges with purple(223) thus picking up an angular rotation of:

purple(53) = 54 * 6 * m = 32/127*24/48*27/96*360 = 12.7559055 degrees
purple(30) = 54 * 6 * m = 32/127*24/48*27/96*360 = 12.7559055 degrees

…purple(30) shares an axle with purple(53) and thus the same rotation. Purple(30) edges with purple(54) resulting in an angle turn of 7.086614166 degrees for purple(54):

purple(54) = 180 * m = 7.086614166 degrees

…three other gears share this angle of rotation and thus the same axle, purple(20) , dk green(53) , dk green(15). dk green(15) transfers the angle to gear dk green(60) and gear dk green(12) which shares an axle with dk green(60):

dk green(60) = 180 / 4 * m = 32/127*24/48*15/96*15/60*360 = 1.771653542 degrees
dk green(12) = 180 / 4 * m = 32/127*24/48*15/96*15/60*360 = 1.771653542 degrees

…dk green(12) transfers the angle of rotation to the last gear in the chain, dk green(60)

dk green(60) = 9 * m = 32/127*24/48*15/96*15/60*12/60*360 = .354330708 degrees

…showing the angles of rotation in spreadsheet form: cl = clockwise, c
cl counterclockwise

GEAR GEMATRIA GEAR RATIO ROTATION ANGLE

blue(50) 72 * 127 * m 1 360 ccl
blue(50) 72 * 127 * m 1 360 cl
blue(32) 72 * 127 * m 1 360 cl
blue(127) 2304 * m 32/127*360 90.70866132 ccl
blue(24) 2304 * m 32/127*360 90.70855132 ccl
blue(48) 1152 * m 32/127*24/48*360 45.35433066 cl
blue(38) 1152 * m 32/127*24/48*360 45.35433066 cl

sun gear(64) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl

green(32) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl
green(32) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl

orange(38) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(53) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(96) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(15) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(27) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl

purple(223) 53*12*27*m/223 32/127*24/48*53/96*27/223*360 3.031672609 ccl
purple(53) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(30) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(54) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(20) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(60) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(15) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(60) 15 * m 32/127*24/48*27/96*30/54*20/60*15/60*360 .59055118 ccl

dk green(53) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
dk green(15) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
dk green(60) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(12) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(60) 9 * m 32/127*24/48*15/96*15/60*12/60*36 .354330708 ccl

…how does this data relate to the earth-moon interaction? One can observe that the last gear in the chain of 360 degree rotation , blue(32)…if one makes this gear analogous to the moon lunar cycle…29.530588 days in one orbit around earth , then blue (32) and the lunar cycle share an axle that rotates 360 degrees. Transferring this 360 degree rotation of the lunar cycle to the earth cycle around the sun…365.246743 days in one tropical year , on this earth cycle axle , place the 5 sets of 47 (235) markings of the exterior dials of the device on the earth axis of rotation and multiply by the metric m :

29.530588 / 365.2467463 * 5 * 47 *m * 36 = 26.92913386 degrees = 19 * 36 * m = sun gear(64)
29.530588 / 365.2467463 * 235 / 254 = 26.92913386 degrees = 19 * 36 * m = sun gear(64)

…this is exactly the angle turned by the sun gear when the blue(50) gear is rotated once!! Checking the number constants I wanted to see if the number 37 is any where in the angles of rotation or in the gear numbers. Strangely it sits at the heart of the Earth/Moon link. When the lunar cycle 29.530588 days is rotated once (360 degrees) on the Earth cycle .365.246743 days… an angle of rotation is generated on the Earth cycle rim:

29.530588 / 365.246743 * 360 = degrees of rotation of Earth orbit disc = 29.10638332

….37 derives this angle through the 47 markings on the outside dials of the device:

(( 37 ^ 2 ) – 1 ) / 47 = 29.10638332 degrees

…which means the 37 form can generate the sun gear angle for all of the green gears:

(( 37 ^ 2 ) – 1 ) / 47 * 235 / 254 = 26.92913386 degrees = 36 * 19 * m

Antikythera Mechanism – Reconstruction

Antikythera Mechanism