by Mark Adams
“The other thing we need to consider is that in the Timaeus itself Plato is trying to not only provide bits and pieces of this story, however accurate or faithful, but his own ideas about how the universe works and how knowledge works,” Masse said. Plato wrote often of the cyclical repetition of time, what the classical scholar Desmond Lee called “the notion of periodic destructions by natural cataclysm, followed by a slow redevelopment of civilization.” In the Timaeus, Plato may have been taking the pieces of an incomplete story that had originated in Egypt and using them to explain the order of the universe.
Plato felt so strongly about the oral transmission of stories concerning the periodic deviations of the heavenly bodies that he explicitly addressed them in his final work, the Laws, in which three men on a pilgrimage to the birthplace of Zeus on Crete discuss how to create a hypothetical city:
ATHENIAN: Do you consider that there is any truth in the ancient tales?
CLINIAS: What tales?
ATHENIAN: That the world of men has often been destroyed by floods, plagues, and many other things, in such a way that only a small portion of the human race has survived.
CLINIAS: Everyone would regard such accounts as perfectly credible.
Catastrophist hypotheses may be slightly more acceptable than they were twenty years ago, but they’re still a long way from “perfectly credible.” Masse argues that by ignoring the Saïs priest’s warning about periodic destructions, we may be missing the essential scientific point of Plato’s Atlantis story: “that current models substantially underestimate the risk and effects of catastrophic cosmic impact.”
Plato may have thought he was clear about the devastating consequences of cosmic eruptions, but that doesn’t mean anyone listened. Impact craters don’t get much attention, because they’re rare: Fewer than two hundred confirmed examples have been located on the face of the planet. Some have been worn away over time by erosion, glaciers, floods, earthquakes, and other geophysical processes. Many more have presumably vanished beneath the 70 percent of the Earth’s surface that is covered by water and ice. “People still don’t have a clue about oceanic impact,” Masse told me. “Did you know there has not been an ocean impact crater identified and confirmed for the last 25 million years?”
A few hundred scattered craters over the earth’s 4.5 billion years doesn’t sound so scary—until you point a telescope at the night sky. As Masse notes in a recent paper, astrophysicists have logged more than forty-two thousand impact craters with diameters of three miles or more on Mars, which has a surface area less than a third of the Earth’s. The moon, which has less than a twelfth of the Earth’s surface area, “exhibits more than thirty thousand craters greater than one kilometer in diameter,” or 0.6 miles across. The moon’s lack of an atmosphere and weaker gravitational effects amplify the size of its impact craters, which persist indefinitely due to the absence of erosion. Still, those thirty thousand impacts, if occurring on Earth, would have ranged from at least 240 Hiroshima explosions to, in a handful of cases, greater than the cometary collision that killed the dinosaurs.
Some extraterrestrial objects wreak havoc without ever reaching the ground. Plato’s rendition of the Phaethon myth, which along with the more detailed version in Ovid’s Metamorphoses Masse called “a perfect description of an impact event,” is one possible example. (Explosions in the sky, like the 2013 airburst in Russia, are classified as impact events.) On June 30, 1908, a meteor exploded a few miles above the ground in a sparsely populated area near the Podkamennaya Tunguska River in Siberia. Indigenous Evenki reindeer hunters reported being knocked down by a sudden wind and witnessing a second sun in the sky—the fireball caused by the exploding meteor. Eight hundred square miles of trees were flattened. In Perilous Planet Earth, Trevor Palmer notes that “had the Tunguska object arrived just four hours later, destroying St. Petersburg”—then the center of soon-to-be-revolutionized Russian politics—“the history of the twentieth century could have been very different from what it was.” A recent model of a Tunguska-size air burst over modern Manhattan estimates 3.9 million deaths. Masse says the frequency of such events has recently been recalculated at every two hundred years.
On at least one point, catastrophist Donnelly trumps evolutionist Darwin: When catastrophe inevitably strikes, evolutionary laws favoring the survival of the fittest are temporarily suspended. “It’s more like survival of the luckiest,” Masse said, echoing Plato’s claim that only illiterate mountain dwellers survived the great floods. While post-Sandy New York was slowly adjusting to elevated flood dangers from rising sea levels, Dallas Abbott was examining sediment deposits that indicated a sixty-foot-high tsunami, caused by an asteroid impact, might have slammed into Manhattan as recently as 300 BC.13
I assumed Masse would blame Velikovsky for scientists’ reluctance to share Plato’s concerns about catastrophes, but he said that actually, with some Venus-size caveats, he respected Velikovsky’s work. While it’s true that Worlds in Collision was a little kooky, Velikovsky—like Schliemann at Troy—had accomplished two difficult tasks: breaching the wall between natural sciences and myth and capturing the public’s attention. It was a skill Plato also possessed—as demonstrated by his use of the Atlantis tale in the Timaeus—the ability to take important, complicated ideas and “really pull them together to tell a fascinating story,” Masse said.
I told Masse that it was almost time for me to sort through all the conflicting information I’d gathered and reach some conclusions about Atlantis.
“In a sense, you’re like Plato,” Masse said. “There are nuances in the stuff all of us are telling you, which you have to draw upon to make an informed, knowledgeable story. Are you in denial that you are following in his footsteps?”
The very idea struck me as so ridiculous that I laughed out loud. Aristotle was the sort of person who followed in Plato’s footsteps. I couldn’t even get through the Timaeus without a personal tutor. After thinking about it for a while, though, I realized that I had formulated answers to—or at least plausible explanations for—almost every problem in Plato’s Atlantis story: the mountains, the shoals, the circles, the Pillars of Heracles, even the cataclysm. I may have been suffering from the sort of Atlantean overconfidence that invited the wrath of Zeus, but I even thought I might provide something the Atlantis story has always lacked: an ending.
All I had to do first was decipher the meaning of Plato’s numbers.
CHAPTER TWENTY-EIGHT
The Plato Code
In the Green Mountains of Vermont
In 1666, the Atlantis tale briefly crossed paths with another unsolved mystery of antiquity in the person of a Jesuit scholar working in Rome. Athanasius Kircher had just published his monumental work of speculative science, Mundus Subterraneus, which included his upside-down map of Atlantis that is the most famous ever drawn. (It’s the one Rand Flem-Ath had tried to convince me was a dead ringer for Antarctica.) A dying friend sent a gift Kircher had long coveted—an illustrated manuscript, filled with colored drawings of plants, astronomical charts, and naked women. What made the book unique was its minuscule handwritten text, comprised of alphabetic characters never seen elsewhere and thus completely indecipherable. Kircher was not a man who lacked confidence. He claimed, erroneously, to have decoded hieroglyphics almost two hundred years before the discovery of the Rosetta stone. But even he didn’t dare to pretend to have broken this mysterious manuscript’s baffling code. After Kircher’s death, the manuscript vanished until 1912, when it was purchased by the Polish antiquities dealer Wilfrid Voynich. By 1969 what’s now known as the Voynich Manuscript made its way to Yale University. There it fell into the hands of a philosophy professor named Robert Brumbaugh.
Brumbaugh, who died in 1992, was not a typical philosophy professor. He had worked as a code breaker in the US Army Signal Corps during World War II. He specialized in translating difficult material, such as Plato’s ideas, into simple English
that college freshmen could understand. And he was willing to tackle offbeat subjects that made less curious academics uncomfortable. Brumbaugh once floated a hypothesis that the Pythagorean aversion to eating legumes had a hereditary cause, an enzyme debility that sometimes resulted in a deadly reaction to the consumption of fava beans. Brumbaugh’s son told me that his father became a little obsessed with deciphering the Voynich, to the degree that his mother, also a former code breaker, “eventually had to sit him down and say, enough.” Brumbaugh finally concluded that the text might have been a “treatise on the Elixir of Life” and possibly part of a Renaissance con game. He may have been right on both counts—despite his own efforts and subsequent quantum leaps in cryptological computing power, the manuscript still hasn’t been decoded.
Considering the amount of online cross-pollination between Voynich fanatics (among whom Brumbaugh is a celebrity) and the fundamentalist Atlantology crowd, I was surprised that no one seemed to have noticed Brumbaugh’s attempt to decode another problematic manuscript: Plato’s Critias. In a little-known 1954 book titled Plato’s Mathematical Imagination, Brumbaugh noted that for more than two thousand years scholars have been confused by Plato’s seemingly baffling use of numbers. Atlantologists, of course, had seized on precise details such as the nine thousand years, the three concentric circles, and the measurements of Atlantis’s capital and its enormous oblong plain, contorting the mathematics when necessary to fit a particular hypothesis.
Rather than pausing to wonder what the genius who proclaimed LET NO ONE IGNORANT OF GEOMETRY ENTER HERE over the entrance to his school might have been up to with all those numbers and forms, scholars have almost universally dismissed passages that contain mathematics as “nonsense or riddles,” Brumbaugh noted. Yes, the numerical sections of Plato’s works are doubly impenetrable, the most obscure writings of an exceedingly elusive writer. But Brumbaugh saw this as no excuse on the part of scholars to pretend they don’t exist. “In literature, it may be allowable to introduce meaningless passages to create an effect of difficulty,” he wrote. “In philosophy, it is not.”
According to Elizabeth Barber’s Silence Principle, storytellers don’t bother to give their audiences information they can assume is already known. Anything not stated explicitly in a narrative is likely to be forgotten over time. If two thousand years from now humans are cannibals who have obliterated the earth’s forests and live in houses made of gingerbread, the story of Hansel and Gretel will require footnotes. Brumbaugh believed that Plato intended the numbers in the Critias not to be taken literally but to conjure up images that, for his audience at the Academy, would add an additional layer of meaning to the text. Illustrated manuscripts did not yet exist in the fourth century BC, so Plato (in Brumbaugh’s opinion) included Pythagorean-influenced math that “was intended to be metaphorical.”
In one example Brumbaugh cites, near the start of Book VIII of the Republic, Socrates mentions “the 4 and 3 joined to the pempad,” which scholars generally agree refers to the most famous of Pythagorean diagrams, the 3-4-5 right triangle. Beyond that, those same scholars have mostly scratched their heads about what the heck Plato was trying to say. Brumbaugh points out that book VIII is where Plato considers the five types of leader (in descending order of desirability: aristocrat, timocrat, oligarch, democrat, tyrant). These character types are the products of the three parts of the soul discussed in books II–IV (intelligence, spirit, and appetite), combined with the four ascending levels of understanding described in books V–VII (conjecture, opinion, understanding, reason; we will come back to this in a moment). A passage that the eminent Plato scholar James Adam described as “notoriously the most difficult in his writings” suddenly becomes clearer when drawn out as it might have been on a wax tablet at the Academy:
Two of Plato’s works containing the most—and strangest—numbers were, of course, the Timaeus and Critias. The only Atlantis-related figures Plato cites in the Timaeus are the dates—eight thousand years since the founding of Egypt, and nine thousand since the destruction of Atlantis and Athens. Critias pauses the story and Timaeus jumps in with his very Pythagorean discussion of numbers and harmonics, the World-Soul, and so on. Brumbaugh notes that in the data-rich Critias, only a single number, the twenty-thousand-strong fighting force, is used to describe Athens. Atlantis, on the other hand, is described in the rich numerical detail that has led people to search for the lost city. Brumbaugh homes in on Plato’s statement that the kings of Atlantis “met alternately every fifth and every sixth year paying equal honor to the odd and to the even.”
In a casual reading, this is the sort of ho-hum detail even an ardent Atlantologist glosses over. For Brumbaugh it was a stop-the-presses moment. Isn’t Plato’s indifferent attitude about the ratio of fives and sixes a little strange, he asks, coming on the heels of the Steinway-precise tunings of the World-Soul in the Timaeus? One of the key tenets of Pythagoreanism was that odd numbers were male and evens were female. In Plato’s final dialogue, the Laws, the gods of Olympus receive the “superior” honors in odd numbers while those of the underworld are honored by the “secondary” evens. Brumbaugh cites numerous examples of fives and sixes in the text of the Critias, both explicit and implied. If one draws a diagram of the three-ringed city and counts the total widths of sea and land, they add up to a ratio of 6:5. The central island is five stades across; the statue of Poseidon has six horses. Poseidon sires five sets of twin sons; six of them must vote in favor if an Atlantean king is to be put to death. Nowhere else in his body of work does Plato use such alternating numbers.
For an Academy audience conversant in Pythagorean concepts, the idea that odds and evens could be used interchangeably would have been as unthinkable as Le Cordon Bleu students casually substituting vinegar for butter. Brumbaugh concludes that these clashing odds and evens demonstrate that “Plato meant his Atlantis to be a blueprint of a bad society, eventually corrupted by prosperity, disorganization, and a lack of education.”
Like a chess grandmaster checkmating a line of novices in succession at a charity tournament, Plato may have been playing several sophisticated numbers games simultaneously with his disciples that are only now coming to light. Stavros Papamarinopoulos had e-mailed me two recently uncovered examples of hidden mathematics in Plato’s dialogues. The first was a paper by math scholars Antonis Vardulakis and Clive Pugh, which examined the importance of the number 5040 in the Laws, which Plato wrote was the optimum number of families in his ideal city of Magnesia. The number 5040 is the product of 1 x 2 x 3 x 4 x 5 x 6 x 7 and appears in Laws exactly seven times. Buried even more deeply in the dialogue, Vardulakis and Pugh believe, were hidden theorems about consecutive prime numbers and divisibility of composite (i.e., nonprime) numbers—the sorts of sophisticated mathematical concepts that wouldn’t have required an explanation for an audience at the Academy.
The other example Papamarinopoulos had mentioned was one I’d heard about on the radio but hadn’t given much thought because I wasn’t sure if it applied to Atlantis. In 2010, Jay Kennedy, an instructor at the University of Manchester in England, announced that he had discovered a hidden mathematical and musical code in several works by Plato. Kennedy employed a tool known as stichometry, or line counting, to reach his conclusions. He had used a computer program to estimate the number of lines in Plato’s original manuscripts and found that within a very small margin of error, they all had line counts that tallied up to multiples of 1,200. (The Republic, for example, had 12,000.) Kennedy argued that Plato had structured his dialogues in twelve parts, based on the twelve-note Pythagorean harmonic scale.14 To mark the transition between each of these twelve sections—in other words, at the 1/12 mark, the 2/12 mark, and so on up to the 11/12 mark—Plato inserted a symbolic passage.
What was fascinating about Kennedy’s discovery was that Plato seems to have used this twelve-part architecture not simply as an organizing principle, like a harmonic outline, but as a rhetorical device. In
several dialogues, at precisely the midpoint (6/12, or a 6:12 ratio), Plato inserted “passages describing the divine wisdom and justice of the philosopher,” Kennedy writes. In the Republic, this is where Socrates discusses the philosopher-king. In the Timaeus, the title character pauses his windy discourse on the four basic elements and their atomic triangles to remind everyone that the Divine Craftsman has arranged these particles in perfect harmony.
The code Kennedy found coincides with the primary ratios of Pythagorean harmony. “According to Greek theory,” he wrote in an article for the philosophy and science journal Apeiron, “the third (1:4), fourth (1:3), sixth (1:2), eighth (2:3) and ninth (3:4) notes on the twelve-note scale will best harmonize with the twelfth. Passages near these relatively harmonious notes are dominated by positively valued concepts, while passages near dissonant notes (the fifth, seventh, tenth and eleventh) are dominated by negative ones.” In the Timaeus, Kennedy notes, Plato describes the harmonious creations of the Divine Craftsman at the harmonious eighth and ninth passages. At the disharmonious tenth and eleventh passages, he discusses the physical decay of the body and diseases of the soul.
Obviously, I was getting warmer. More than once I caught myself daydreaming that I was on the verge of a Da Vinci Code–type breakthrough, that like Professor Robert Langdon unscrambling the numbers of Fibonacci’s sequence to find the real murderer I could follow Plato’s mathematical clues all the way to a solution to the Atlantis riddle. Occasionally, while driving, I silently rehearsed the introduction Steve Kroft would give me on 60 Minutes: “For more than two thousand years, the mystery of Atlantis has befuddled history’s greatest minds. Now, one intrepid reporter has achieved what was once considered impossible . . .”
