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Moving from cold, hard to fuzzy, nonlinear logic.


Pythagoras was born around 570 BC. He spent his youth traveling to Egypt, Syria and Babylon, where he immersed himself in the mystical teachings of the East. At the age of about 40, he established his own quasi-religious cult in Crotona, southern Italy. His teachings attracted hundreds of followers, some of whom suffered severe privations – including a five-year vow of silence – to become a part of his inner circle, known as the mathematikoi.

The cult’s philosophy was based on reason and number. To the Pythagoreans, number was all. Each number had a special, almost magical meaning. The monad, unity, represented the original unity from which the universe was created, and was associated with divine intelligence. The dyad, two, represented the division of this unity into duality. (The even numbers, which contained the number two, were therefore seen as representing weakness and mutability.) Three represented all things with a beginning, middle and end. Four represented completion – like the four seasons.

The most perfect number was the decad, ten. The sum of one, two, three and four, it represented the totality of forces that make up the universe. In reference to the decad, the Pythagoreans compiled a list of ten opposing principles, which divided phenomena into two classes:

good  • evil
limited  • unlimited
odd  • even
one  • plurality
right  • left
male  • female
at rest  • in motion
straight  • crooked
light  • darkness
square  • oblong

By aligning themselves with the qualities in the first column, the Pythagoreans believed they could achieve purity and become closer to the gods.

The reasons why they chose these ten pairs has puzzled scholars from Aristotle on, but some can be guessed at. In Pythagoras’s philosophy, for example, the universe consisted of two components: the Limited, which signified order, and the Unlimited, which represented chaos and plurality. The former was associated with the monad and odd numbers, the latter with the dyad and even numbers. Pythagoras’s biographer, Iamblichus, wrote: “The right hand he called the principle of the odd number, and is divine, but the left hand is the symbol of the even number and of that which is dissolved.” The right hand is controlled by the left side of the brain, which we now associate with linear, logical reasoning of the sort championed by the Pythagoreans. This preference for the right hand has passed on through language – the word “sinister” comes from the Latinsinestra, meaning left.

So what does all this ancient, mystical stuff have to do with the hard, cold logic of neoclassical economics – which views humanity as a mere aggregate of rational, self-interested actors? The model for economists has long been Newtonian, mechanistic physics, which, in turn, is explicitly based on Pythagorean thought. So this list of pairs is like two complementary strands of the dna of economics. Consider that neoclassical economics:

*is based on the idea of scarcity and emphasizes limited resources like oil at the expense of unlimited resources like wind;

*rejects uncertainty and duality (symbolized to the Pythagoreans by evenness);

*is based on the primacy of the individual (one) over society (plurality);

*values right-handed logic, ignoring emotion and left-handed thought;

*is based on a male paradigm that undervalues things like childcare;

*sees the economy as a static system, maintained at rest by the invisible hand of capitalism;

*uses a simplistic, linear (straight) approach to model complex, nonlinear (crooked) phenomena;

*attempts to shine the light of reason and observation over the economy, rejecting the indeterminacy (darkness) of human systems;

*reduces complex and often strongly biased social and political systems to the simple symmetry (squareness) of mathematics.

Neoclassical economists are Pythagoreans. They still think that number is all. And they are still trying to find good and attain Utopia by aligning themselves with the first column of this ancient list.

Since the 1960s, a number of new sciences have emerged that directly challenge the Pythagorean paradigm. Fuzzy logic, fractals, network theory and nonlinear dynamics deal with systems that are indeterminate, crooked, plural and in motion. Feminists and ecologists have also pointed out the defects in the neoclassical system. As economists incorporate these voices and developments, we will come nearer to an economics that is not just post-autistic, but post-Pythagorean.

David Orrell is a mathematician and author whose work has appeared inNew Scientist, the Financial Times, BBC Radio and CBC TV. He is the author of Apollo’s Arrow: The Science of Prediction and the Future of Everything and The Other Side of the Coin: The Emerging Vision of Economics and Our Place in the World.

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