by Bruce E. R. Thompson.
Historians sometimes make mistakes. (Don’t we all?)
A notable mistake occurs in a document from the 3rd Century C. E. in the writings of a philosopher/mathematician named Iamblichus. Iamblichus himself is of no great importance, so this essay is not about him. However, he was a member of the Pythagorean brotherhood, and in that capacity he was the first biographer to write an account of the life of Pythagoras.
The Pythagorean brotherhood was a secretive society, founded by the well-known Greek mathematician who first proved what every school child learns: that the square of the hypotenuse is equal to…but this essay is not about that either. By the time of Iamblichus, the secret society had existed for some eight centuries without many of its secrets leaking out. It was in part a mystical religious society. Pythagoras was revered as a near demigod. Early testimony suggests that he believed in reincarnation – and taught the doctrine to his followers. The members of his society were required to be strict vegetarians. It also functioned in part as a kind of craft guild. The members of the brotherhood made themselves useful to Greco-Roman traders, businessmen, and kings because they were exceptionally skilled at bookkeeping. They could perform mathematical calculations involving sums well beyond the reach of the simple abacus used by street merchants.
Because the brotherhood guarded its secrets so carefully, almost the only source we have concerning the life of Pythagoras comes from the biography written by Iamblichus. So it dismays some historians that Iamblichus has been caught in a provable error. Perhaps that means that nothing in the biography can be trusted! Perhaps we know nothing at all about the life of one of the most influential figures in Greek philosophy!
Charles S. Peirce, however, drew a different conclusion. Like me, Peirce was fond of wild speculation. (If you’ve seen my essay on the location of Atlantis, or the one on the Shakespeare authorship question, you know what I mean.) Peirce thought that an error in a biography written by someone who revered his subject as nearly a demigod was something surprising that needed to be explained. And explanations always begin with wild, creative speculation – followed, of course, by some deductive extrapolation of the consequences that would follow if our speculation should happen to be true, which, in turn, must be followed by a look at the real world to discover whether or not these consequences are borne out.
Iamblichus tells us that Pythagoras spent many years in Egypt, and we have no reason to doubt that this is true. He then also claims that, while Pythagoras was in Egypt, he was taken prisoner by Cambyses II, second ruler of the Achaemenid Empire, and that he later escaped. Cambyses invaded Egypt around the year 525 B.C.E. The problem with this story is that other sources make clear that Pythagoras was not in Egypt at that time. He had already moved to Magna Graecia (what we call the Italian boot), where he founded his brotherhood and spent the rest of his life.
Perhaps Iamblichus was just making stuff up. Perhaps Pythagoras was never abducted at all, and the rest of the “biography” is equally just a fabrication. But that hypothesis forces us to imagine that a secret society that could keep secrets for eight hundred years was so inept that they could fall prey to fictions regarding their near-sacred founder. It seems unlikely that Iamblichus could have omitted that episode in the life of their founder if it were true, or invented it if it were false. But perhaps Iamblichus made a minor – perhaps even understandable – error. Perhaps Pythagoras was abducted, but by someone else – someone who could be easily confused with Cambyses.
The first ruler of the Achaemenid Empire, Cambyses’ father, Cyrus the Great, also made an incursion to the south, capturing Lydia in the southwest corner of Asia Minor. His invasion did not reach all the way to Egypt, but it does nicely coincide with a time when Pythagoras had left Egypt to return to his native Samos, an island just off the coast of Lydia. It is easy to make up half a dozen reasons why Pythagoras might have been in Lydia rather than on the island of Samos when the invaders arrived. Visiting old friends? Looking after his father’s trading interests on the mainland? Changing ships?
So, we now have a plausible hypothesis: it was Cyrus, not Cambyses, who abducted Pythagoras. If this hypothesis is true, what would have happened next?
After securing Lydia, Cyrus returned to his capital city, Ecbatana, high in the Zagros Mountains. He would, of course, have taken Pythagoras with him as a slave, and Pythagoras would, of course, have tried to escape. But where could he escape to? To the west there was the entirety of the Achaemenid empire where Cyrus ruled. He could easily be recaptured. The obvious alternative was to escape to the east, over the Khyber Pass into India where Cyrus could not follow. A trading ship could then take him home.
And here is where our method of reasoning has its greatest payoff: when we see that our hypothesis not only explains the facts that originally prompted us to propose it, but also facts that we had not initially seen as part of the problem. We have evidence that Pythagoras believed in reincarnation. But how could he have acquired a belief so foreign to the Greek world? The belief, and its attendant dietary practices, is generally associated with the religions of India! But if Pythagoras visited India, the mystery vanishes. The Pythagorean brotherhood used a method of calculation that extended beyond the reach of calculations performed on an abacus. Where did such a method of calculation exist? In India, where the numerals used in base-ten arithmetic had already been developed. We call these numerals “Arabic” because they were introduced into the West by Arabic traders – but the Arabic traders had learned them from India! Why didn’t the Pythagorean brotherhood share their knowledge of numbers with other Greek mathematicians. Because they made their living as accountants. It was a trade secret!
But this essay isn’t really about the Pythagorean brotherhood and its trade secrets. It is about a poem by Walt Whitman, titled “All is Truth,” from Leaves of Grass, which ends,
“Meditating among liars and retreating sternly into myself,
I see that there are really no liars or lies after all,
And that nothing fails its perfect return,
and that what are called lies are perfect returns,
And that each thing exactly represents itself and what has preceded it,
And that truth includes all, and is compact just as much as space is compact,
And that there is no flaw or vacuum in the amount of the truth –
but that all is truth without exception;
And henceforth I will go celebrate any thing I see or am,
And sing and laugh and deny nothing.”
Charles Peirce and Walt Whitman were contemporaries. Both lived through the Civil War and its aftermath. Both were New Englanders. I have no reason to believe that they knew each other, or influenced each other in any way. But I sometimes catch them thinking along the same lines.
Peirce’s point in his musings about the life of Pythagoras was to show that even errors – when revealed as such – can lead us to truths more profound and interesting than if we had known the simple truth in the first place. Even falsehoods must be taken seriously as road signs pointing us toward the truth. This is what Walt Whitman means by their “perfect return.”