Stop us if you’ve heard this one: a genius from centuries gone by, forced to hide his heretical beliefs from his peers, instead buried his ideas in a complex code, hidden in plain sight until some future scholar could decipher the truth.
Is it The Da Vinci Code? No. Isaac Newton’s weirdly extensive research on how to create the Philosopher’s Stone? Also no. According to a theory put forward in 2010 by University of Manchester science historian Jay Kennedy, the tortured genius in this case is none other than the ancient wrestler-turned-philosopher, Plato himself.
“Plato’s books played a major role in founding Western culture,” Kennedy explained when his ideas were first published in the journal Apeiron.
“But they are mysterious and end in riddles,” he continued. “In antiquity, many of his followers said the books contained hidden layers of meaning and secret codes, but this was rejected by modern scholars.”
But after half a decade studying Plato’s writing, Kennedy had made what headlines said was a revolutionary discovery.
“It is a long and exciting story, but basically I cracked the code,” he said. “I have shown rigorously that the books do contain codes and symbols and that unraveling them reveals the hidden philosophy of Plato.”
So what’s the claim?
In short: Plato organized his works so as to convey secret messages about heretical music theory.
For example, in his best-known work, the Republic, Kennedy found that Plato placed clusters of words related to music after each twelfth of the text – a division which he claimed was related to “the twelve notes of a Greek musical scale.”
Splitting the texts equally like this, he argued, you discover “significant concepts and narrative turns” located at each juncture, with positive concepts found at “harmonious” places – that is, the “notes” that sound good together with the 12th – and negative concepts found at dissonant ones.
“The regularity of that pattern was supposed to be noticed by Plato’s readers,” Kennedy told NPR at the time.
But why the secrecy? The extra claim underlying this theory is that Plato was a closet Pythagorean – a follower of the cult founded by Pythagoras, which held that mathematics and numerology (and, importantly, a severe hatred of beans) were the key to understanding the cosmos.
“Simply put, they were threatening to overthrow the gods on Olympus and put numbers and mathematics in its place,” Kennedy explained. “Prior to Socrates being executed, a number of other philosophers were banished or fled because of threats to themselves. It was dangerous in those days to be a philosopher.”
Doesn’t that all sound a bit farfetched?
Actually, it does – but probably not for the reasons you’re thinking.
To the untrained eye, the most bizarre bit of the proposition “Plato set out a hidden musical code in his philosophical writings based around the mystic properties of certain numbers” is probably … well, pick any part, really. But to the scholars who saw Kennedy’s paper back in 2011, the problems with the argument had little to do with the idea that Plato might have been some kind of weird numerology obsessive.
“There can be little doubt that numbers do matter in Plato’s philosophy,” agreed music theorists John Z McKay and Alexander Rehding in a 2011 response paper, published in the very next volume of the same journal that published Kennedy’s thesis.
“Certainly from a music-theoretical viewpoint, Plato’s allegiance to a Pythagorean worldview has hardly been under any doubt.”
Neither is the idea of Plato devoting philosophical space to his mathematical musings particularly controversial. The ancient writer had form, after all: “Plato himself gives one important example of a musically significant number in the much-discussed ‘Myth of Er’ of the Republic,” point out McKay and Rehding. “Here, Plato famously writes about a group of eight sirens standing on the rim of the circles of the Spindle of Necessity, each singing a note of constant pitch, ‘and the eight notes together make up a single scale.’”
So if the pattern is there, and Plato is confirmed the kind of strange dude who would do that kind of thing, what’s the problem with Kennedy’s arguments?
If McKay and Rehding are to be believed, the truth is that Kennedy didn’t go weird enough. It’s fine to say that Plato might have set out his works along a musical or numerological framework, they say – it’s just that it wouldn’t have been the one Kennedy proposed.
“The main problem with Kennedy’s musical argument is that his stichometric calculations make it necessary for him to give heightened relevance to the factor 12,” they write. “As we have seen, [this] is an expedient number for his purposes[,] but [it] does not play a particularly prominent role in Pythagorean music-theoretical traditions.”
Rather, in the Pythagorean tradition, the most important number was 10 – as the fourth triangle number, or tetractys, they found it particularly significant. In fact, the pair point out, rather than 12, “Orthodox Pythagorean traditions demand that musical ratios can only be formed from numbers taken from the tetractys (and their multiples).”
This isn’t just abstract theorizing by McKay and Rehding. Plato was actually pretty explicit in describing his musical philosophies: the Timaeus, a dialogue written by the thinker in around 360 BCE, contains a description of a musical scale based on the tetractys and built out of a complex system of ever-reducing ratios.
And that scale, it should be made clear, is nothing like the 12-note chromatics we’re used to hearing today. It spans four octaves, for starters; the intervals between successive notes are unequal, and it contains 22 notes in total – a number you may recognize as being not a multiple of 12, or indeed 10, at all.
But Kennedy’s problems don’t stop there. Even if the even dozen had been as important to Plato and Pythagoras as it seems to be to Kennedy, his ideas would still be facing criticism – and this time, it would come from a group of people even more notoriously nitpicky than music theorists: mathematicians.
The Ancient Greeks could not create our modern scale
Many of the concepts of the building blocks of music – eight notes per octave, 12 notes in a chromatic scale, each semitone evenly spaced in frequency – are so baked into our psyche today that it’s probably difficult to imagine setting up a music theory based on any other system. The truth is, however, that these are all pretty recent conventions: the system more properly called 12 equal temperament didn’t really become standard in the West until the 19th century.
There’s a good reason for that – although it’s not the one that many historical musicians gave at the time, which was something along the lines of “uneven intervals between each note just sounds better!” Thanks to the logarithmic relationship between notes and their frequencies, it actually requires quite a lot of mathematical precision to space semitones equally: it relies on being able to calculate the twelfth root of 2, an irrational number that would have been difficult to obtain throughout much of history and downright impossible for ancient writers like Plato.
“When Kennedy refers to a ‘musical scale with twelve regularly spaced notes’… that corresponds to the twelve-part structure he observes in the Platonic dialogues, it remains unclear what exactly Kennedy is referring to,” write McKay and Rehding. “It seems that the modern chromatic scale with its evenly spaced semitones would be the closest scale equivalent but this option was… not available to Plato and his age.”
That’s because, to the Ancient Greeks – and in fact, very specifically and famously to Pythagoreans like Plato – irrational numbers weren’t just confusing, they were downright blasphemous. That’s precisely why any musical scales created by these classical thinkers rely on such hyper-specific ratios, like the leimma – a frequency ratio of 243:256, which, McKay and Rehding note, “appears complex, [but] is easily constructed on the monochord and, more importantly to the Pythagoreans… is composed of rational numbers.”
But it’s not impossible, right?
So, big deal, you might think – there’s a discrepancy between Plato’s theories and praxis. The dude lived 2,500 years ago, after all; maybe it was just too difficult to get those ratios precise, and so he settled for equally spaced notes when he set out his musical code.
Well, sure – and in a way, Kennedy proposed this himself, suggesting that Plato may have subscribed to what’s known as a Harmonicist branch of music philosophy. If true, that would help his argument: the Harmonicists were basically the pragmatists of the ancient music scene, happy to split an octave into, say, five parts by simply listening to how the notes sounded in relation to each other.
But this is basically impossible, argue McKay and Rehding – at least, if you want to maintain that Plato was a Pythagorean. “It is important to bear in mind the enormous philosophical gap between Harmonicists and Pythagoreans,” they point out. “Kennedy’s suggestion that Plato’s secret twelve-tone scale may have been based on Harmonicist thinking… is complicated by the fact that the two camps saw that the differences in methodology between them posed insurmountable and irreconcilable obstacles.”
“Especially considering the discussions of music in the Republic, it seems safe to say that Plato did not associate his work with the Harmonicists,” they write.
So why did Plato incorporate these patterns into his work at all, you may ask? Well, it’s not totally clear – but as we’ve established, the guy did like his numerological patterns. Maybe he was just having fun; maybe it came down to some practical reason, like the length of a scroll, or for ease of reading.
Maybe he wasn’t doing it on purpose at all.
No, seriously. In a 2012 breakdown of Kennedy’s methodology, UCL professor of History and Philosophy of Science Andrew Gregory pointed out that the original paper may have relied on some, let’s say, overly generous statistical analysis.
“Kennedy asserts that: ‘Passages describing the divine wisdom and justice of the ideal philosopher often recur near the center of the dialogue,’” he noted. “A key question for this assertion, and for the more general notion that the dialogues are divided into twelfths, is how near is near enough to count?”
Taking Plato’s Cratylus as an example text, Gregory basically reverse-engineered the claim: rather than counting how many passages were “near” the center of the dialogue, he aimed to find out what percentage of the dialogue counted as “near the center” based on where these passages were found.
The results, if you’re hoping for a world in which Plato was some kind of mad magical mathematician inexplicably hiding musical numerological patterns in his works for future scholars to stumble upon thousands of years later, were discouraging.
“With a spread of 4.6 percent per point, this means that 50.6 percent of any work is in the catchment area of the significant points,” Gregory found. “More alarmingly, Kennedy also claims a quarter tone thesis… that would mean that all of the work is in the catchment area.”
Like pretty much all Ancient Greeks, there’s no question that Plato was a Weird Dude: after all, we’re talking about the guy who thought plucked chickens were the same things as humans and then basically invented The Matrix. But when it comes to the idea that he would split his philosophies into 12 to honor a musical system he likely had never even heard of – well, let’s just say that even Plato had his limits.
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