Your output is only as good as your input.
When you have eliminated all which is impossible,
then whatever remains, however improbable,
must be the truth.
Sherlock Holmes, The Blanched Soldier
The Hebrew Tractate (circa 3rd century AD) Pirkei Avot (“Chapters of the Fathers”) begins with chronological information:
Moses received the Torah from Sinai and gave it over to Joshua. Joshua gave it over to the Elders, the Elders to the Prophets, and the Prophets gave it over to the Men of the Great Assembly. … Shimon the Righteous was among the last surviving members of the Great assembly. … Antignos of Socho received the tradition from Shimon the Righteous. … Yossei the son of Yoezer of Tzreidah, and Yossei the son of Yochanan of Jerusalem, received the tradition from them. … Joshua the son of Perachia and Nitai the Arbelite received from them. … Judah the son of Tabbai and Shimon the son of Shotach received from them. … Shmaayah and Avtalyon received from them. … Hillel and Shammai received from them.
While the uninterrupted chain of teacher-student interaction assures that the Jewish tradition has been faithfully passed over the generations of scholars, the book provides no exact dates and does not help historians to place the pertinent events on a reliable time-line. Other sources may have been more explicit in this respect. For example, Ptolemy (1-2 century AD) in his Almagest described an occultation (an event similar to a solar eclipse, with the role of the Moon played by a planet and that of the Sun by a star) [p. 108]:
We again took one of the precisely recorded ancient observations, for which it is said that in the year 45 of Dionysius, on Parthenon 10, the planet Jupiter covered the southern Aselli at dawn. Now the moment is at dawn, in the 83rd year from the death of Alexander, Epiphi 17/18 in the Egyptian calendar.
Obviously, to determine the date of this celestial event one still needs the date of Alexander’s death, or a translation of the Egyptian calendar (to the extent that it is well defined) into the modern terms. In the absence of the definite chronological data of past events, the task of dating is not only hard, it will for ever be open to revision and controversy.
The latest champion of chronological revision — and a fundamental revision at that — is well-known Russian mathematician Anatoly Fomenko. Fomenko and his team would reset the popular timetable by about a thousand years. For example, according to their research, the Book of Revelation (attributed to St. John) should be dated near the prophecies of Isaiah, Jeremiah, Ezekiel, and Daniel [p. 151] and Ptolemy wrote his Almagest not earlier than 1350 AD [p. 112].
Now, Fomenko is a full member of the Russian Academy of Sciences, professor, head of the Differential Geometry and Applications Department of the Faculty of Mathematics and Mechanics in Moscow State University. He authored 180 scientific publications, 26 monographs and textbooks on mathematics. As a student at the Moscow State University, I remember being hugely impressed by his fantastic illustrations of topological concepts (some of which are available in his Mathematical Impressions.) These appeared years before the beauty of Benoit Mandelbrot’s fractals has captured the minds and souls the world over. Not that Fomenko was the first to question the accuracy and reliability of various chronological sources. None other than the great Isaac Newton claimed that the chronology of the ancient Greece was too long by about three centuries [p. 7]. Newton’s The Chronology of Ancient Kingdoms Amended was published posthumously in 1728 [p. 54].
Diacu learned of Fomenko’s research in 1994 and, after a period of gestation, felt his curiosity piqued again in 2000. Early on, Diacu shared his ideas with Don Saari. The latter’s reaction was [p. 13] “This sounds like a detective story. Share it with people, write a book about it.” This set the author on a long investigation that eventually led to the present volume, the first edition of which came out in 2005. If you, like me, are not an expert on chronology, the book comes as a revelation.
First of all the book is not solely — and, perhaps, not even primarily — about Fomenko’s research. Diacu gives a rather comprehensive outline of the history and the methods of chronology. It is my impression that not a single work on chronology has met with universal approval. Diacu’s book is about that too. The author took an active role in debunking a notorious theory of Immanuel Velikovsky who offered an explanation of the biblical episode involving Joshua arresting the motion of the Sun. Unlike many others (including Martin Gardner, see, e.g., his Fads and Fallacies) who dismissed Velikovsky’s theories out of hand as preposterous, Florin Diacu went to a considerable length to pinpoint a flaw in Velikovsky’s argument.
The first chapter, where we learn of Velikovsky and his saga, reflects the spirit of the book as a whole. Diacu’s attitude is consistent and truly scientific throughout. He weighs the arguments of proponents and opponents of a theory or a method against each other and does not take sides until he is able to lay a convincing foundation either way.
The methods of chronology are many; some employ mathematics. For example, Ptolemy’s description of an occultation can be used the other way round, to determine the date of Alexander’s death according to the modern calendar. What it takes is to calculate the relative positions of celestial bodies and determine when their configuration fits Ptolemy’s description. Fomenko has developed a great number of ingenious methods that use mathematical and computational tools. If there is a flaw in any of his conclusions, it lies with his interpretation of data.
To identify the zodiacal stars in Ptolemy’s table, Fomenko used the least squares method, comparing the calculated routes of fast moving stars and the entries recorded in the table. The results were highly dependent on the assumed grouping of the stars [p. 107].
To verify whether it would be possible to identify royal dynasties described in various sources, Fomenko attached to a each dynasty the sequence of durations of consecutive reigns and measured the distance in the space of such sequences. He found thirteen pairs of dynastic sequences that seemed to overlap. Among the least alarming were, say, First (AD 527–820) and Second (829–1204) Byzantine Empires. But he also found similarities between Biblical Kingdom of Judah (capital in Jerusalem, 10th–7th centuries BC) and Eastern Roman Empire (capital in Constantinople, 306–700 AD). In a similar vein, Fomenko compared the sequences of years in office of Popes extracted from various documents. There, too, he found significant overlaps, but he often overlooked the Popes who served very short terms [ch. 7]. As Diacu observed, it is difficult to accept kings’ or Popes’ identification without investigating biographical details. And the biographies of homologous (in Fomenko’s view) figures often appeared starkly different. For example, Fomenko identified Pope Meltiades with Boniface II. However, Meltiades was known to be of African origin and was buried in the Catacomb of Callistus, while Boniface II was the first pontif of German origin; his tomb is in St. Paul’s Basilica, Rome.
Fomenko has applied mathematics to study ancient horoscopes discovered in Egyptian tombs. Diacu presents the story that underscores the difficulties involved. The reader is similarly treated to Fomenko’s study of maps.
One field where Fomenko’s work was roundly trounced [pp. 158–165] is etymology. At the beginning of his chronological exploits, Fomenko realized the deficiency of his training in statistics. He taught himself the subject and applied statistics to dating various historical chronicles. By the time he ventured into comparative linguistics, he did not mind lacking any expertise and has made multiple gross blunders. In chapter 8 of his book, Diacu gives sufficient information on linguistic methods for the readers to be able to make the inescapable conclusion on their own.
The penultimate chapter describes several methods of scientific dating of which Fomenko is highly critical. Radiocarbon dating compares the relative quantities of carbon-12 and carbon-14 (one is stable, the other subject to decay.) Dendrochronology looks into the shape and size of tree cross-section rings and identifies the anomalies with historic weather records and volcanic activity. Thermoluminescence investigates the extra light emitted when a crystalline material reaches a temperature of about 500°C. If the atoms of a radioactive element are trapped inside a crystal structure, the released radiation leaves traces inside the structure. An electron microscope allows to detect such marks and make conclusions of the sample age. There is also archeomagnetic dating, which compares magnetic information stored in a sample with the changes in Earth’s magnetic field. None of these is 100% accurate, but each provides workable information if applied judiciously. The shortcomings of the methods are well known; Fomenko in his critique overlooks the fact that all the methods undergo continuous improvement.
The science of chronology is hard. Few historical sources reached us in their original form. When they do, it is not always possible to establish their exact age. The copies, on the other hand, are suspect of accidental and deliberate mistakes and of misrepresentation. Thus, it is not uncommon to question reliability of historical sources. Even the Bible has its detractors who think it is pure mythology. Diacu describes the work of Fomenko in this spirit: Fomenko has raised legitimate questions and devised ingenious methods to obtain the answers. Some of his assertions are patently false, some warrant continued attention.
In the Afterword written especially for the second edition of the book, the author indicates that in the intervening years he was able to discover two additional sources: one that supports one of Fomenko’s conclusions, the other that refutes another of his claims. There remain many as yet unsettled points that require further investigation. The book expertly leads the reader to understand of what the controversy is about. It becomes clear that uncertainties and disagreements permeate the science of chronology. Fomenko poured some gas into the fire, but there were many others who kept the fire burning and others who wanted it contained. As I intimated earlier, this wonderful book is more about chronology in general than about one man’s work. I would say that had not Fomenko existed, he should have been invented to give Florin Diacu motivation for writing.
Alex Bogomolny is a former associate professor of mathematics at University of Iowa. He lives in New Jersey, maintains a popular site Interactive Mathematics Miscellany and Puzzles, with a server somewhere in Michigan, and blogs at CTK Insights.