“Don’t raise your voice, improve your argument.”
[Address at the Nelson Mandela Foundation in Houghton, Johannesburg, South Africa, 23 November 2004]”
Most of us dislike conflict and will do anything to avoid the unnecessary unpleasantness of raised voices and difficult conversations. There are those among us, however, who would welcome the opportunity to engage in an animated discussion. The late Christopher Hitchens wrote in Letters to a Young Contrarian, “Time spent arguing is, oddly enough, almost never wasted.” The Ancients would be in complete agreement.
Xeonophanes was a contemporary and outspoken critic of Pythagoras. Heraclitus was quick to scorn Homer; even Pythagoras and Xenophanes did not escape his ridicule. Leontion’s audacious criticism of the celebrated and unassailable philosopher, Theophrastus, was still talked about centuries after her passing. Plato recorded the iconic debate on love in the famed Symposium. The fundamental standard within all of these historical scuffles was the subject matter. The debate was about ideas, not about personal vendettas or trivial disagreements.
Great thinkers engage in debate, not conflict. As Joseph Joubert, French moralist and essayist, once said, “It is better to debate a question without settling it than to settle a question without debating it.” Our world is in need of thinkers who look for solutions when they put forward their ideas in a way that welcomes an open dialogue. Argue the merits of the position, rather than stooping to pettiness and vain posturing. Recall Aristotle’s words, “It is the mark of an educated mind to be able to entertain a thought without accepting it.”
“In all debates, let truth be thy aim, not victory, or an unjust interest.”
Pythagorean Theorem — or Pythagoras’ theorem: in any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Pythagoras of Samos, the creator of one of the most famous equations of all time, has a rather obscure history. He wrote very little about himself, delegating the task of documenting his life and views to his followers. What we do know is that in his world of the mid-sixth century BCE, he was considered to be a thinker and a mystic.
In today’s world, Pythagoras’ school would be considered more like a religious cult than a philosophical establishment. His teachings included many eccentric doctrines including, the veneration for, and abstinence from, the eating of beans. He advocated reincarnation and the transmigration of souls. Most see him as the founder of the modern belief in numerology, later popularised by Nostradamus.
Pythagoras argued that the ultimate nature of reality is number, which he developed out of his theory of music. He claimed that music had a special power over the soul. The proof was found in the intervals between musical tones, which could be expressed as ratios between the first four integers, number 1 – 4. His discovery of irrational numbers did play havoc with his beliefs on the origin of the universe; however, they have proven to be a major and lasting development in mathematical thinking.
After his death, his followers split into two camps; one embraced his religious and mystical teachings, while the other pursued his scientific and mathematical philosophy. Ideas and beliefs, whether or not they prove to be valid, must be considered, lest we overlook the very insight that will bring us to the next stage of development.
“It is the mark of an educated mind to be able to entertain a thought without accepting it.”