A Discussion With Pythagoras - Part 2
Pythagoras extended the reach of numbers to music. He came to the conclusion that harmonious tones were produced by vibrating strings when the length of strings were ratios of whole numbers. It may have come as a surprise to him when he discovered that other stringed instruments had this same property.
There are several theories attributed to Pythagoras although we cannot directly prove it:
1. The sum of the angles of a triangle equals one hundred and eighty degrees;
2. Constructing figures using geometrical algebra. For example, they solved a(a-x)=x(squared) using geometry, not algebra as we do today.
3. Theorems concerning the five regular solids (circle, parallelogram, square, rectangle and trapezoid).
4. Irrationals were discovered, for example, the square of a number (the square of 2 yields 1.414 which is an irrational number while the square of 4 is 2, a rational number).
5. He may have been the first to recognize the fact that Venus wasn't only an evening star but a morning star as well. He also believed that the earth was at the center of the universe and that the moon inclined towards the equator.
His studies in astronomy must have led him to think about what happens after death. He believed in transmigration, or the belief that the body passes into another body at the time of death. A story is told where he asked a master not to beat a howling dog since he recognized a dear friend who had passed away.
In most references to the Pythagorean Society, the authors make no mention of the Pythagoreans. Instead they use anonymous references to 'ingenious persons'. I would have thought this was perhaps because the Society may have been held in contempt but this is not the case. It was a mark of respect not to make direct reference to Pythagoras.
Two years before his death, he was living in Croton (or Crotone) in Italy. Croton attacked a neighbor, Sybaris. Pythagoras may have chosen the wrong side (that of Sybaris) which led to an attack on Croton by Cylon, a noble from the city itself. All the Pythagoreans were killed except for two who barely escaped.
Cylon may have taken vengeance on the Pythagorean Society since he had been refused admission due to his high-handed tyrannical manner. These were character defects which neither Pythagoras nor his followers would tolerate.
Some believe that Pythagoras committed suicide after the attack but others say he
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