A Pythagorean Problem

There is no mathematical theorem used more in my daily life than the Pythagorean Theorem.  Even my non-mathematical friends make second-hand use of the theorem by calling me with a query about how much material they need for a project involving a triangle (or a shape that approximates a triangle).

Since I hold this theorem in high regard, you might suspect I have an equally high opinion of Pythagoras (c.580-500 BCE).  In particular, you might think I admire the mathematical ‘school’ he founded with his wife.  This school, a type of commune, admitted women. Pythagoras appears to have valued intelligent women in an era that most definitely did not!

But sadly, when you put a man on a pedestal, you will find he has feet of clay.

The Pythagorean School firmly believed that all numbers could be expressed as the ratio of integers – the classical definition of a rational number.  This idea went beyond a belief for them.  It was a dogma.

Despite this strongly held tenet, one of their number – Hipassus – made the shocking discovery of √2, the most irrational number of all!  (See, this is exactly the kind of outrageous thinking that happens when you foolishly spend all day contemplating geometry.)

Legend tells that the otherwise rational members of the Pythagorean school were so incensed by the heresy of Hipassus that they tied weights to his legs and threw him into the sea.

How shocking for a group of learned philosophers!  Even in nascent academia, dissension had a heavy price.

The record is unclear as to whether Pythagoras endorsed this punishment.  Even if he did not, I question a leadership style that brooks no opposition.

Perhaps we should make allowance for these early thinkers.  Greek philosophy may be the basis of western thought, but that philosophy was embryonic.   Many centuries were to pass before the Enlightenment shone a bright light on the Rights of Man, and further centuries were to pass before the Rights of Woman were duly considered.  Millennia separated the Pythagorean violence from Justin Trudeau’s exhortation “to let yourself be vulnerable to another point of view”.  Open-mindedness was a foreign concept to our ancient friends

Nevertheless, it is disappointing that intelligent people believed an appropriate response to divergent thinking was ostracism or death.  It would be nice to think that we have evolved beyond such foolishness, but you know we have not.

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