Book Review Decoding the Heavens: A 2,000-Year-Old Computer— and the Century-Long Search to Discover Its Secrets Reviewed by Christián Carman
Decoding the Heavens: A 2,000-Year-Old their catch. One of the Computer—and the Century-Long Search to divers, after diving Discover Its Secrets down 42 meters, re- Jo Marchant turned clearly upset, Da Capo Press, February 2009 saying he had seen ISBN-13: 978-03068-174-27 human bodies at the bottom of the sea. In 1980, Nobel Prize winner Richard Feynman Captain Kontos im- visited the National Archaeological Museum of mediately descended Athens. While he saw incredibly beautiful statues and returned min- that expressed the best of Greek art, he became utes later holding fascinated with just one object: item 15,087. In a human arm—of a a letter to his family, he said that he didn’t see bronze statue. It was anything really unusual in the museum except the first archeological for one thing: “Among all those art objects there shipwreck and, so far, was one thing so entirely different and strange the most important. that it is nearly impossible. It was recovered from The treasures found fill several rooms today at the sea in 1900 and is some kind of machine with the National Archaeological Museum of Athens: gear trains, very much like the inside of a modern beautiful bronze statues, jewelry, weapons, and wind-up alarm clock. The teeth are very regular and furniture. But there were also fragments that, many wheels are fitted closely together. There are when they split open, contained what appeared to graduated circles and Greek inscriptions. I wonder be some kind of navigation device, the device that if it is some kind of fake.” caught Feynman’s attention and that is now known Where did this object come from? At the begin- as the Antikythera Mechanism. Decoding the Heav- ning of the twentieth century, a group of Greek ens by Jo Marchant tells the story of this device. sponge divers, led by Dimitrios Kontos, concluded A study of the ceramics and other daily-use their fishing season in North Africa and returned items found in the shipwreck—including some home. On their way back, while they crossed the coins recovered in a second expedition led by channel between Kythera Island and Crete, a severe Jacques Cousteau in the 1970s—concluded that storm forced them to stop on a small island named the objects date from around 80–50 BC. A sample Antikythera. After the storm they began to dive of the wood of the ship dated by the carbon-14 off the coast of Antikythera, hoping to supplement method showed that the ship had been built at least 100 years before the shipwreck. The frag- Christián Carman is a faculty member in the Instituto de ments of the Mechanism show clear signs of having Estudios sobre la Ciencia y la Tecnología at the Universi- suffered the inhospitality of the sea for two millen- dad Nacional de Quilmes, Argentina. His email address nia. However, it is still possible to see clearly many is [email protected]. of the gears in the Mechanism, some fragmented DOI: http://dx.doi.org/10.1090/noti1012 scales, a few pointers, and several words in Greek.
June/July 2013 Notices of the AMS 741 The style of the script of these inscriptions helps a stellar calendar that indicated which stars rise to date the construction of the Mechanism between or set at the sunset or sunrise. So, when the sun 150–100 BC, although an error of a century before pointer pointed to a certain letter, one could read or after those dates cannot be ruled out. on the front of the Mechanism what star would After a century of research, we have a fairly rise or set that day. Usually, these parapegmata complete idea of the structure and operation of also include some atmospheric phenomena, such the Mechanism: it was a sort of computer that, as winds, storms, etc., but as far as we know, there when one moved a handle, predicted astronomical is no mention of atmospheric phenomena in the and other events through a series of pointers on Antikythera Mechanism. different scales. The entire Mechanism was made Price thought that, with his research, the An- of bronze and was protected by a wooden case the tikythera Mechanism would be accorded a dis- size of a large dictionary. The fact that the Greeks tinguished place in the history of astronomy could have built such a complex geared mechanism and technology, but this was not the case. Otto is certainly revolutionizing our knowledge of the Neugebauer, the greatest authority on the subject history of technology. Not only is the Mechanism and Price’s mentor, published the monumental fascinating in itself but the research into its use History of Ancient Mathematical Astronomy in and the history of its discovery make a compel- 1975, a couple of years after Price’s work on the ling story. Marchant’s book is simply captivating Antikythera. HAMA, as it is often called, comprises as it highlights the mysteries of the research in 1,456 pages over three volumes and mentions a way more reminiscent of crime novels than of the Antikythera only in one footnote—and a very scientific books. critical one indeed. Someone said metaphorically Important research on the Antikythera Mecha- that this constituted the second shipwreck of the nism was done in the first half of the twentieth cen- Antikythera Mechanism. tury, but a detailed understanding of its structure But the story continues. The next protagonist and function had to wait until the 1950s. Derek de is Michael Wright, who was curator of mechanical Solla Price, a scholar from Yale University, with the engineering at the London Science Museum. Having help of Charalambos Karakalos, was the first to read Price’s work, Wright found several errors and obtain radiographs of the fragments to see in detail has worked hard since the 1990s to correct them how many gears the mechanism had, how many and to discover new features of the Antikythera. teeth each gear had, and how they were connected. Wright designed and built with his own hands a In this way he discovered, for example, that one tomography scanner and for several summers pointer would show the position of the sun in the traveled to Athens to study the fragments with an zodiac and another the position of the moon and Australian colleague, Alan Bromley. that the moon pointer revolved 254 turns for every We can mention three important contributions 19 turns of the sun pointer (the ancient Greeks of Wright. First of all, he proposed that the Mecha- knew that in 19 years there are almost exactly 254 nism should be understood as a planetarium, i.e., lunar sidereal months). that it shows not only the positions of the sun and In one of the extant fragments of the Antiky- the moon but also of the five planets known at the thera, there are remnants of two concentric rings. time the Antikythera was built: Mercury, Venus, On the inner ring one can read the word XELAI, Mars, Jupiter, and Saturn. There was one pointer which means Libra in Greek. The marks inscribed for each planet, all concentric like the hands of a on this ring allow us to conjecture that there were clock and each turning at its own speed, with those 360 marks divided into twelve sections, each one of the moon and sun and sharing the same zodiac corresponding to a zodiac sign. We can then guess scale. New discoveries published last year con- that this was a part of a zodiac dial on which point- firm Wright’s intuition. In addition, the planetary ers showed the positions of the sun and moon. On pointers exhibit retrograde motion that reflects the outer ring we can read the names of months in the known retrograde motion of the planets. Nev- the Egyptian calendar. We can also infer that that ertheless, the exact way in which the Antikythera ring had 365 divisions, corresponding to the 365 models planetary motion is conjectural: the gears days of the year. We know that Greek astronomers are missing, so the proposals for how the Mecha- used the Egyptian calendar because of its simplic- nism worked cannot be directly tested. ity, since it always had 365 days without leap years. The second of Wright’s proposals is related to Because it takes the sun one year to traverse the a strange cap found in the back of one fragment zodiac, one arrow could show both the position of the Antikythera. The cap has a hole in one of of the sun in the zodiac and the day of the year. its borders and a gear close to its center. Wright In the inner ring one can see some small let- realized the purpose of this strange device. The ters close to the marks. They are in alphabetical cap was attached to the moon pointer so that order: alpha, beta, gamma, etc. Price deciphered the cap went once around the dial each sidereal the meaning of these letters. According to his month. The gear on the cap turns a little sphere, analysis, they belong to a parapegma, which was which rotates at the rate of the synodic month. The
742 Notices of the AMS Volume 60, Number 6 sphere, representing the moon, was probably half to the geometrical Greek model just mentioned. white (or silver) and half black, and as it rotated it This nonuniform motion was performed by what showed the lunar phases. is perhaps the most striking and surprising feature The third of Wright’s contributions is related to of the Antikythera Mechanism: the pin-and-slot the calendar. As already mentioned, the Egyptian device for producing the irregularities in the lunar calendar has 365 days without leap years. This motion. This clever device, mentioned nowhere in means that, every four years, the calendar ring the ancient astronomical literature, produces a would be misaligned by one day with respect to back-and-forth oscillation that is superimposed on the zodiac ring. Now, Price discovered that below a steady progress in longitude. The key part of the the calendar ring there are little holes, one per day, device is the pin of one gear that, when introduced but he didn’t know why they were there. Wright in a slot in another gear slightly off-center with realized that these little holes serve to move the respect to the first, moves the second gear at the calendar ring by one day. He showed that the cal- average rate of the first one. However, because of endar ring was not attached to the Mechanism, but the eccentricity, the second gear has a nonconstant it was movable and it could have had pins that, if motion. This nonuniform motion is transmitted located in these holes, would keep the ring fixed. through a gear chain to the moon pointer. At the beginning of the new millennium, the Freeth’s team also managed to understand British filmmaker Tony Freeth and the astrono- almost everything on the back of the Mechanism. mer Mike Edmunds (Cardiff University) created Their work suggests that on the back of the Mecha- the Antikythera Mechanism Research Group, an nism there were two large dials, one next to and international multidisciplinary team whose aim above the other, together with some subsidiary is to decipher the mysteries of the Antikythera. rings inside them. The upper ring was a complex The team got permission to work directly with the luni-solar calendar, while the lower ring was an fragments and to apply two new technologies to eclipse predictor. their examination. The lower ring was divided into 223 cells (each Freeth convinced X-Tek, a company specialized corresponding to a synodic month) distributed in building very powerful tomography scanners, to over four turns of a spiral. Most cells are empty, build a new scanner designed to look at the Anti- but in the months in which an eclipse would take kythera fragments. The scanner was able to take place, the cell indicated that an eclipse would ten images per millimeter. After uploading all the happen, the time at which it would happen, and information into their software, the team was able whether it would be a solar or a lunar eclipse. to reconstruct the fragments in three dimensions, Eclipses repeat every 223 months in a pattern greatly assisting new research. known as the Saros cycle. If a solar eclipse took Second, the team used a technique known as place today, then 223 months from now a very PTM (Polynomial Texture Mapping) developed by similar solar eclipse would take place. Therefore, Tom Malzbender, an employee of Hewlett Packard, that pointer could be used for predicting eclipses which involves taking pictures of an object with a indefinitely. But the prediction of the succeeding fixed camera but with flashes at many different cycles is not perfect. From one cycle to another, angles in such a way that, when you examine the the occurrence of eclipses shifts 8 hours. The shift pictures using special software, you can play with is compensated for by a subsidiary mechanism light and see even the slightest surface irregularity. inside the Saros ring: this subsidiary ring turns This helps in the reading of the Greek characters very slowly (one turn every 54 years, that is, every and scale marks. Malzbender developed this tech- three Saros cycles), indicating whether one needs nique so as to show shadows in a more realistic to add 8 hours, 16 hours, or nothing to the value way in animated films. Later he realized that the of the time inscribed in the cell. technique would be very helpful for reading an- The luni-solar calendar on the upper back ring cient inscriptions. is based on the Metonic cycle. According to this Using these two technologies, Freeth’s team has cycle, 235 synodic months are almost exactly 19 succeeded in reconstructing much of the Mecha- years. Therefore, this calendar repeats every 19 nism and has made important new discoveries. years. It is interesting to note that, because every One is related to the way the Mechanism showed Greek city had its own calendar, the month names the sidereal motion of the moon. Although the of the extant part of the dial allow Freeth’s team moon never exhibits retrograde motion, the ir- to conjecture that the Mechanism was made to be regularities in its motion are notorious. Of course, used in Corinth or any of its colonies; one of them Greek astronomers had a geometrical model re- was Syracuse. flecting this motion using an epicycle and a defer- Now, we know that Archimedes lived in Syra- ent. Now Freeth and his team discovered that the cuse, making him an extraordinary candidate for same nonuniformity is present in the Antikythera’s the originator of the Mechanism. It seems that the pointer for the moon, so that the pointer has the Antikythera Mechanism was built at least a decade same motion that the moon would have according after the death of Archimedes, so he probably is
June/July 2013 Notices of the AMS 743 not the maker of this particular device, but he Pan-Hellenic games would take place that year. It could have started the tradition. As is patent from was like a tablet PC of ancient times! the complexity of the Antikythera, this is probably The research is still in progress, and every year not the first such mechanism ever made. new discoveries arise. The Antikythera Mechanism The luni-solar calendar has two subsidiary dials inside: one revolved once every 76 years (i.e., four probably still has some mysteries to reveal, and Metonic cycles) and indicated when one day had to the best way to be prepared to understand it is to be skipped in the Metonic calendar (once every four read Jo Marchant’s book. cycles) in order to correct it. The second—one of Marchant invested several years in research, the most amazing—revolved one revolution every and the dedication and seriousness with which 4 years and was divided into four cells: in them we can read the names of the Pan-Hellenic games, she directed that research is reflected in the book. so that the arrow indicates what games would She does not avoid technical issues when they are be played that year: the Olympics, the Nemean necessary and usually presents them clearly. It is games, etc. a self-contained book: you have in it all the astro- So in one device you can learn the position of nomical and historical knowledge that you need to the sun and moon (and probably also the planets) in the zodiac, and the day of the year; you have an understand the story of the Antikythera. Marchant eclipse predictor that tells you the time and kind documents her sources well and also provides a of eclipse, and you also know whether you have to Further Reading section. Inevitably, the book con- add 8 or 16 hours to the time indicated; you have a tains some imprecisions. Nevertheless, it is, all in luni-solar calendar that tells you which years have all, an excellent book that tells a fascinating story 12 and which have 13 months, which months have in a fascinating way. Decoding the Heavens is, I 29 and which have 30 days, which day would be omitted in case you have a 29-day month, when think, required initial reading for anyone seeking you have to omit one day every 76 years for cor- an introduction to the story of the research into recting the calendar; and, finally, you know which the mysteries of the Antikythera Mechanism.
Book Review Seduced by Logic Reviewed by Judith V. Grabiner
Seduced by Logic: Émilie du Châtelet, Mary instance, in the case of Hypatia of Alexandria Somerville and the Newtonian Revolution (c. 370–415 CE), her father was the mathemati- Robyn Arianrhod cian Theon of Alexandria. Maria Gaetana Agnesi Oxford University Press, 2012 (1718–1799), who had an on-the-make father who US$34.95, hardcover, 338 pages showed her off as a prodigy, also benefited from ISBN-13: 978-0-19-993161-3 liberal religious trends in eighteenth-century Italy. Sophie Germain (1776–1831) grew up in a Paris In a world where over 30 percent of American home that was a meeting place for intellectu- Ph.D.’s in mathematics are earned by women, als, and as mathematics in Revolutionary France we forget how rare female mathematicians have became more widely accessible through lectures been in the past. Counting the women with well- and notes from the École Polytechnique, adopted documented contributions to mathematics before a male pseudonym to correspond with Lagrange the nineteenth century can be done on the fingers and Gauss. The first actual European Ph.D., Sofya of one hand. Each of these women “made it” only Kovalevskaya (1850–1891), came from an influen- because of highly unusual circumstances. For tial Russian family but had to contract a fictitious marriage in order to leave her home country to Judith V. Grabiner is the Flora Sanborn Pitzer Professor study mathematics in Germany. As Londa Schiebin- of Mathematics at Pitzer College, Claremont, California. ger has documented in her magisterial The Mind Her email address is [email protected]. Has No Sex (Harvard, 1989), various theories about DOI: http://dx.doi.org/10.1090/noti1013 the nonintellectual nature of women reinforced
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