Antikythera MechanismINFO 50110/13/2015Kelly McClinton

Outline

- Introduction- Context- Materials / Data Set- Methods Used / Expected Results- Models- Conclusion

• What is it? • Who Built It?• When did the ship sink?

Ancient Context

• Modern Context:

• Where?• When?• Who?

Antikythera YouthExtracting an AmphoraWrestler Statue

• Previous Scholarship• Exhaustive!• 1900/1901: Shipwreck Discovered• 1902: Mechanism Noted• 1959: Mechanism Illustrated• 1974:

• Price/Karakalos• Mechanism Transcribed / Read

• 2005: Antikythera Mechanism Research Project(AMRP)• 2006:

• 1st Article published. Glyphs = eclipse predictions?• 2008: 2nd article published• 2014: 3rd article published: “Eclipse Predisction on the ancient Greek astronomical

calculating machine known as the Antikythera Mechanism”

What’s an eclipse?

Focus of the Study

• Examine the mathematical concepts of the system

• Create a mathematical model of the system

• Compare the resulting data

• Criteria for the model

Materials / Data SetOur Set: 82 fragments, conserved in the National Archaeological Museum in Athens.

https://www.youtube.com/watch?v=bAqqA3fMwI8

Methods Used / Expected Results:

• Polynomial Texture Mapping (now sometimes called Reflectance Transformation Imaging (RTI)• https://vimeo.com/28335954 • Technique for looking at fine surface details • How does it work? Combines many digital images, lit from different directions• Apply various filters

• Specular enhancement• Diffuse gain

Methods Used / Expected Results:

• Microfocus X-Ray Computer Tomography (X-Ray CT)• https://www.youtube.com/watch?v=oEpf2Lskpsg • High-Res, 3D X-Ray images• Technique for revealing internal structure• How? Works just like an X-Ray • Projects images of the sample from many angles onto an Xray detector.• These are then combined mathematically into a 3D X-ray volume

Questions Asked• What are the organizing principles of the glyph distribution?

• What are the organizing principles of the Index Letter Groups?

• Why are the index letters in a non-alphabetical order?

• What is the overall structure of the eclipse inscriptions?

• How were the eclipse times determined?

New Models Proposed• Eclipse Year Model

• Zig Zag Model

Results• Glyph Distribution (around the Saros dial)

• Index Letter Groups (refer to to glyphs that include a predicted solar or lunar eclipse)

• Predicted Eclipse Times (each glyph includes a predicted time in hours)

Eclipse Year Model• References the Saros Cycle

• Chance resonance between three orbital periods of the Moon, which is fundamental to the design of the Antikythera Mechanism

• Divides the Saros dial on the Antikythera Mechanism into 19 mean eclipse years on a spreadsheet

• Defined entirely using integers

Eclipse Year Model

• Results in 223 units for each eclipse year

• ½ were needed for the distance between the node points

• These are called Eclipse Year units or EYu for short

• 1 EYU = .78 days / EY = 446 EYu

• Distance between eclipse node points = 223 EYU

1 EYu = psyn/38 = (19/235)/38 = 1/470 years

= 365.25/470 days = 0.777 days

Eclipse Year Model

• Guess and Check / Massaging the Model

• Results: • Exactly generates the (known) Index Letter Groups• One exception: is in the right L. 18 group but in the wrong

place within the group. • It is relatively easy to establish that this is not caused by

the node points being in the wrong place: it can be proved that changing the positions of the node points cannot fix the problem.

1 EYu = psyn/38 = (19/235)/38 = 1/470 years

= 365.25/470 days = 0.777 days

• An arithmetic model that closely conforms with the glyph times

• Uses linear zigzag functions for both lunar and solar anomaly

• Based on type of model developed by the Babylonians

• https://www.geogebra.org/m/29447 • Assumption: the times of eclipses

on the Saros Dial are the times of maximum eclipse

• Built in an Excel spreadsheet, since this readily emulates the columns of Babylonian System B.

• Test: Matches the glyphs.

Zig Zag Model

Results: ZZM does not exactly match the glyph times. It may have been that there were other types of rounding errors. These were not in general well understood in antiquity.

Zig Zag Model• Fixed period parameters:

• synodic month, psyn = 29.531 days• anomalistic month, panom = 27.554 days• solar year, py = 365.25 days

• Variable input parameters:• Minimum lunar month length = 29.27 days • Mean lunar month length = 29.53 days • Maximum lunar month length = 29.82 days• Minima and maxima parameters: ml , Ml , ms, Ms,

• Free parameter• Lunar anomaly = Number of days Lapo→FM1

• Solar anomaly = Number of days Sapo→FM1

• Time of FM1

• Time of NM1

• bn = Mod(b1 + (n-1)*psyn, py) / py

• sn = (bn<=0.5)*((0.5< bn)*ms + bn*Ms)/0.5 + (0.5< bn)*((bn -0.5)*ms +(1- bn)*Ms)/0.5

Current Excavation

Discussion Questions

• Is the mechanism a computer? Why/why not?

• The fragments are a “set.” Freeth organized them in terms of 1) what the Greeks would have known about and 2) what would fit the mathematical model. Can you think of other ways to organize this same set?

• Did reading this paper and learning about the mechanism change your views on ancient Greece / ancient science at all? Why/why not?

Additional Resources

• 2015 Expedition Update: https://cdanews.com/2015/10/antikythera-shipwreck-reveals-riches-of-ancient-greek-aristocrats-video/ • RTI Viewer:

http://culturalheritageimaging.org/What_We_Offer/Downloads/View/index.html• Sample Files: http://www.asia.si.edu/research/squeezeproject/how_to.asp • Explore the full article online:

http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0103275• Great Research Site: http://www.antikythera-mechanism.gr/