Saturday, 11 July 2015

Pythagorus never ate beans

Mere words escape me when in the presence of a great man

Pythagoras was a very interesting individual. Most folk only know him through the famous theorem which bears his name. And what an elegant theorem it is, although there is a debate about whether he uncovered/discovered it himself. Anyway, no blog would be complete without citing the theorem at least once: 'Pythagoras theorem states that in any right angled triangle, the sum of the square of the hypotenuse is equal to the sum of the squares of the other two sides. Thus, if we are given the dimensions of any of the two sides of a right angled triangle we can calculate the length of the third side by applying this theorem.

What we know of this great man is through the work of others as he has left us no extant writings. He was born in Samos, Ionia, in 569BC. His father was a wealthy merchant and therefore Pythagoras received a liberal and extensive Greek education. He was a true seeker of knowledge, and in his younger years, travelled widely to be taught by the greatest minds of his time. At some time, he acquired a love for mathematics and mysticism. He should be commended for the first accomplishment and condemned for the second.

In about 518BC, he settled in southern Italy. At Croton he founded a scientific and religious school. His teachings were a curious mix of sound mathematics, science and weird, spiritual mumbo-jumbo (not Mugumbo- that would be just silly). He believed 'everything was number' and taught that at the most fundamental level, reality is mathematical in nature. He attracted acolytes who had to obey strict rules. They were not allowed possessions, practiced vegetarianism and eschewed beans. They were probably the only non-flatulent mathematicians in the entire history of the world.

The school practiced profound secrecy, on the pain of death, and therefore nothing is known of Pythagoras's actual work. However, there is no doubt that Pythagoras and his pupils made significant developments in mathematics. They were very much interested in abstract mathematical principles and not concerned about practical applications that might ensue. The 'Pythagoreans' were the first to note (pun intended), that vibrating Lyre strings produced harmonious tones when the ratios of the lengths of the strings are whole numbers. Of interest, the advances in mathematics were made in spite of not having a sophisticated notation for number. Modern numbers are wonderfully kind for those who dare to manipulate them. But how would a mathematician fare, for instance, if he had only access to the Roman numeral system. Try doing basic mathematics with IV and XII and you will quickly learn what an impediment this would be. The ancient Greek system was no better. Therefore, the Greek contribution to mathematics tended to be in the discipline of geometry. Geometric problems can easily be expressed in algebraic form, but the ancient Greeks would have none of it.

The discovery of irrational numbers is attributed to the Pythagoreans. According to history, (?legend) the Pythagorean philosopher, Hippasus of Metapontum, in the 5th century BC, discovered these 'naughty numbers'. Mathematics would never be the same and the Pythagoreans were deeply shocked and perturbed. It is recorded that for his contribution to knowledge, Happasus (for it is he) was drowned by his peers for impiety. So what do I mean by an irrational number and why did the ancients get so excited and upset? Consider the square root of 4. We come up with a nice sensible number of 2. Wonderful in its poetic symmetry (steady Flaxen). But what about the square root of 2? Here we enter the dark world of mathematics. A slight digression is required to inform those not versed in mathematical principles. A rational number is a number that can be written as a ratio. Thus the number on the top (numerator) and the number on the bottom (denominator) are whole numbers. Therefore 8/4 and 10/2 would constitute rational numbers. An irrational number has endless non-repeating numbers to the right of the decimal point.  Pi (22/7) and the square root of  2 are impressive exponents. Just as an aside and to fuck your mind up, there are an infinite number of irrational numbers between 0 and 1. Makes you think, dun it? Digression endeth.                          

Regardless, I can't see why a man should lose his life as a consequence. Surely a slight castigation and a light scourging would suffice. Seems the ancients were just as barbaric as us 'moderns'. Perhaps we should take some comfort in this.

So what can we say in conclusion of this most singular and fascinating, individual. Apart from not liking beans, he seems a man possessed of an astonishing versatile intellect and what little we know, he also appeared to have his modicum of human and intellectual frailties. The introduction of mysticism into science has no place unless you are a quantum theoretical physicist. In which case it is essential. How otherwise are they able to contemplate multiple dimensions and the mysteries of space and time.  

Mayhap posterity should be kind to Pythagoras. He lived in turbulent political times and intellectual discovery was in its infancy. Often great men are drawn to simple unifying concepts. Einstein spent most of his life trying to unify all the forces of nature but ultimately failed. Pythagoras set out to solve the world's conundrums based solely on number. We can scoff at his naivety. But it is due to advances in thought by the likes of Pythagoras that we are privileged to think this way. Modern man is indeed blessed if only we can bother to recognise it.    

No comments:

Post a Comment