“The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.” ― George Bernard Shaw in Maxims for Revolutionists (1903)
The Pythagoreans were a sect (circa 6th century BC) who believed that all things are number. They also believed that all magnitudes (or numbers) were commensurable, e.g., for any two lengths, you could find a common unit such that both given lengths would be a whole number of units. In modern parlance, for the Pythagoreans all numbers were rational.
Myth has it that one of them, Hippasus of Metapontum, discovered that √2 is irrational or incommensurable, i.e., you cannot find a unit length such that the side of a square and the diagonal of the same square were both a whole number of units. ![](data:image/png;base64,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)
In one version of the myth, distraught by the existence of an irrational number, the other Pythagoreans threw Hippasus into the sea, hoping to drown him and his unpalatable discovery.
Another variant has the drowning as a punishment from the gods and that the irrational number was the golden ratio, relating the side length and diagonal of a regular pentagon. A third variant mentions a celebration sacrificing hundreds of oxen. No matter which variant is true, it shattered the foundations of the Pythagorean world, and someone died. Moreover, given that we use the word irrational to denote things that go contrary to our reasoning, irrational numbers could claim to be the first mathematical pun and serve as a reminder of the difficulty in conquering our prejudices.
The main reason though for recounting this story is that, as in Shaw’s quote, significant progress in mathematics may often be inseparable from such unreasonable or uncomfortable developments. In an earlier blog we outlined a five-fold path to mathematical wisdom. We considered √2 as an example, looking at it from four (of five) perspectives – formal, algorithmic, graphical and practical – leaving a unifying and historical perspective for now: that of √2 being irrational.
Unfortunately, irrational numbers are often treated as something esoteric and/or as a formal construct to complete the number system – and the traditional proof of the irrationality of √2 is also presented in an unduly abstract and algebraic manner. It is likely that the Pythagoreans had more accessible and illuminating proofs of the irrationality of √2. We outline two proofs that are candidates for the Pythagorean approach (further details can be found on Wikipedia).
Both proofs relate to geometric/practical aspects of √2. One proof considers √2 as the length of the diagonal of a unit square. √2 being rational would imply that you could find two whole numbers, a and b, with b being the side length of a square and a the length of the diagonal (√2=a/b). If it helps, consider a=577 and b=408.
In the other proof, if b gives the side length of a square, then a gives the side length of a square that has double the area.
![](data:image/png;base64,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)
Both proofs hinge on getting successive smaller variants of the constructs, giving pairs of smaller whole numbers that also define √2. The diagrams below show how the first descent is constructed.
![](data:image/png;base64,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)
Both diagrams tell us that if a/b=√2 then (2b-a)/(a-b)=√2 too. And one can iterate indefinitely! But, starting from a finite pair, one cannot have an infinite descent via whole numbers, hence the irrationality.
What is beautiful (and useful!) about these proofs is that one can reverse direction – iterating outwards to larger squares, one gets an iterative scheme for calculating √2. If a/b=√2 then (2b+a)/(a+b)=√2 too! Starting with as poor a pair as (1,1), i.e. √2 ≈ 1, we get
![](data:image/png;base64,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)
The above ‘Pythagorean’ approach has been used by artisans (and mathematicians) for millennia – using repeated subtraction of given quantities to find the greatest common measure, the same technique underlying the Euclidean algorithm for finding the greatest common divisor.
The technique is even more readily applied in the construction of a pentagon-pentagram pair, an icon used by the Pythagoreans, hence the possibility that the golden ratio could have been the first number to be proved irrational. 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)
But there is even more mathematics to be mined here - by studying how the Pythagoreans recovered from the unexpected collapse of their foundations, embracing irrationality and accounting for it. Other cultures, Babylonian and Indian, had separately – and earlier – grappled with √2 and may have recognised its irrationality. Irrationals also provide a further perspective on the paradoxes of Zeno, which force one to engage with the inadequacies of discrete and continuous models for the world we inhabit. Intrigued? Then tune in next time for paradise lost, paradox regained.