Everybody has heard of Pythagoreans already in early school years. These ancient Greek hippies discovered delightful geometric rules, such as the one concerning the right-angled triangle: how Ms. Hypotenuse squares with two clashed brothers from the Sides family. Their discovery led them to a wonderful idea which has proved so impressive that many people stick to it even today. If rules of geometry really represent universal laws, and if these laws are as simple as the theorem of Pythagoras’ and as mutually consistent as geometrically obtained rules obviously are, then this implies something utterly astonishing: that our world is, in principle, as harmonious as an opera or symphony. For Pythagoreans, musical harmony was, much the same as geometry, an undeniable proof, both aesthetic and logical, that gods exist. They can also be understood, at least indirectly, through the most effective and logical way in which they organised their lowest basement, where we now so, oh so happily live – at least when we obtain all the needed knowledge of the rules of harmony.
Even though Pythagoreans presented themselves as saints of the universal harmony of skies and minds, they had been actually pretty upsetting guys. Their teaching had been annoying for many citizens who lived their lives unblessed with higher truths. Like their vicious buddy Socrates a century later, Pythagoreans really pissed fellow citizens off a lot, so they needed to run from city to city quite regularly.
During one of such escapades, taking them across the Aegean see from mainland Greece to Sicily, a tragedy happened. It actually started with a wholly glorifying event, with the Eureka moment, when their comrade Hippasus of the Metapontum came to an important discovery. He found out, in geometry of course, that the universe is after all not harmonious at all. Simply, he showed that harmonic proportions are only part of the law of the universe. For instance, you can split an apple in 2, 3, of whatever equal parts, but you can not split it in 2 or π parts, simply because these two can not be defined in relational terms, so they are irrational numbers, behaving quite inharmoniously when observed in a conventional way.
Now you can surely accurately predict what happened next to Hippasus. Betrayal is a mortal sin and shall not be ever tolerated. He who brings disharmony to the community of decent and good thinking people by his irrational claims must be severely punished. So Hippasus was thrown across the board by the priests of harmony themselves to feed the fish.
Pretty much everything has changed by the present day, but not this. Fish are still well fed with irrationals. The heresy progressed to previously unimaginable dimensions. In modern times, practically everybody is irrational. Think about irrational ecologists who give bears in forest or rare coast birds equal weight in their public demands to poverty reduction or human rights. Or the irrational corporations’ executives who want to abolish all national borders and cultural localisms to win the market and new consumers. What is rational for one group is for all other groups irrational. So in fact to most people most things most of the times appear as irrational. Somewhat annoying!
Irrationality is, after all, not a threat at all. Just the opposite is the case – as Christopher Hitchens explained in his book Memoir: rationalisation of the irrational is the real threat. Imagine that you are involved in a ferocious quarrel about important public issue. The other guy is against your views though he actually wants to achieve the same abstract public good – only that he sees it differently and chooses dissimilar approach to it. So in public conflicts, “irrational” opponents need to understand one basic thing: they stand on different banks of the social river, which they do not want to cross, but the river itself still flows in the same direction for both. There is a rational and irrational part in every public discussion, and both need to be recognised and democratically respected all the way from initial disagreements to the final recognition of equally legitimate, but directly incompatible claims, logics and styles.
It took ancient Greeks only a century or so to discover this on their own and to formulate another rule, so beautiful that it has charmed us to the present day. It is a well confirmed rule in art (Leonardo da Vinci’s illustrations of polyhedra in De divina proportione ), architecture (Athenian Parthenon), and even psychology that the highest harmony is best described as “golden ratio” or or Fibonacci numbers. This is precisely the ratio between rational and irrational portions of the whole. Large part of organic patterns is actually structured in golden proportion. Now, when the irrational is not a threat any more but a precondition for harmony, the task remains to discover how to convey the golden rule from art, philosophy and nature to reasoning about complex social matters.