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# Understanding history's greatest philosophers, Pythagoras

## Pythagoras

## Pythagoras's life

Pythagoras is believed to have lived in 570-495 BCE, it is believed that he was born on an island called Island of Samos, off the coast of Turkey. We do not know much of the Greek philosopher as he left no writings to himself but it is believed that he traveled widely as a young man and went to the school of Milesian and also went to Egypt (the height of learning at the time). At the age of 40 he set up a community in Croton, southern Italy. The community consisted of around 300 people all academically studying under Pythagoras. At 60 he married a young girl called Theano of Crotona and left Croton and fled to Metapontum where he died soon after. The community of Croton was lost and disappeared in the 4^{th} century BCE.

## Childhood of philosophy

Pythagoras studied at the Milesain School and started to seek rational answers, the island of Miletus (where he was born) had already given birth to some philosophers. Pythagoras is marked out as the creator of western philosophy. He learned about the rudiments of geometry, during his travels through Egypt. With this childhood background is it really surprising that he is now one of the most remembered philosophers in history!

## Pythagoras's theorem diagram

## Pythagoras's Theorem

Pythagoras is generally famous for triangles as his famous theorem is A^{2}+B^{2}=C^{2}. What this means is that if you square the lengths of a triangle on side A and B then add them you'll get side C squared so once you find the answer to the first sum you need to find the square root of your answer. Pythagoras's theorem also suggested that all shapes and ratios are governed by principles that can be discovered. Once he had completed this theorem he believed that his theorem could in time explain the structure of the cosmos!

## Pythagoras's theorem

### Did you understand Pythagoras's theorem?

## Number Ruler

## Number is the ruler of forms and ideas

This is one of Pythagoras's side theorems he came to it using the logic that everything in the universe conforms of mathematical rules and ratios, so if you understand number and mathematical relationships, you come to understand the structure of the universe. Also mathematics is a key model for philosophical thought. Therefore number is the ruler of forms and ideas.

## The Pythagorean academy

Pythagoras was a very religious and superstitious man. He believed in reincarnation and the transmigration of souls, he formed a religious cult which later became a community called Croton. His followers had to follow strict behavioural and dietary rules, while studying his religious/philosophical theories. His followers were known as the Pythagoreans, saw Pythagoras as a wise mystical man, this went to such an extent that they thought that his discoveries were "revelations", these may in fact be theories that others in the cult came up with. His students recorded all his work and life story, including his wife and daughters. The two sides of Pythagoras's beliefs seem to be irreconcilable, However Pythagoras him self didn't see them as contradictory. For him, the grand goal of life is freedom from the cycle of reincarnation, which you could only achieve if you follow his Pythagorean academy rules and think scientifically. In geometry and mathematics he found truths that he regarded as self-evident, of course as Pythagoras quotes "There is geometry in the humming of the strings, there is music in the spacing of the spheres". Due to his discoveries Pythagoras believed that his observations were more valuable than most thought at the time, which of course is right. For proof of this we look towards the Egyptian discovery that was, if a triangle's sides have the ratio 3:4:5 then it must have a right angle (90ยบ) and this was useful to know for things such as architecture. But of course Pythagoras uncovered the undying principle behind all right-angled triangles. His theorem, which has since been proofed. This discovery had such potential of greatness and Pythagoras knew it. He concluded that the entire cosmos was governed by mathematical rule. He then claimed that number (numerical ratios and mathematical axioms) can be used and calculated to show the vet structure of the universe. Pythagoras never dismissed the Milesain theory (that everything in the universe is made up of one single material and the material changes to create other things, this material is usually water). This was such a profound way of imagining the cosmos that surely they should be forgiven for their extreme faith. Forming a relationship between geometry and numbers Pythagoreans discovered square and cube numbers and saw this as "good", only for the even numbers, and "evil" for the odd, the number four in particular specifying "justice". The number ten, in the forms of tectractys (a triangular shape completely made of dots) had particular significance in a Pythagorean ritual. The cult saw the number one as a single unit, a unity, from which all other things could be derived. They saw the number two as thinking, a line. Three was surface, four was solid (you can already see the obvious forming of modern concept of dimensions). The Pythagorean explanation of the creation of the universe and cosmos followed a mathematical pattern: on the unlimited (the infinite that existed before creation), God imposed a limit, so what existed had an actual fixed size! So according to this theory God controls the size of anything that exists or forms.

No wonder the cult disappeared after 100 years.

## Greek Architecture

## Classical Architecture

The classical architecture of ancient Greece follows Pythagorean mathematical ratios. Harmonious shapes and ratios are used throughout the entire structure of the architecture.

## Numerical Harmony of Pythagoreanism

Pythagoras is most famous for triangles but his most important discovery was the relationship between numbers: the ratios and prepositions. This discovery is reinforced by his investigations into music, and in particular into the relationships between notes that sounded pleasant together. There is a story that Pythagoras first stumbled onto this idea due to listening at a blacksmiths work. He realised that the sound of the hammer hitting an anvil half the size of another anvil is one Western octave (eight notes) apart. While this story could very possibly be, the most likely scenario is that he was experimenting with a stringed instrument and discovered it that way. What he had discovered was that the intervals between these were harmonious due to the relationship between the strings was so precise and simple mathematical ratios. This series, known as the harmonic series, confirmed to Pythagoras the sheer elegance of mathematics, he had found, also, in abstract of geometry the natural world.

## Reason is immoral, all else is mortal

Pythagoras now believed that he had proved the structure of the universe through mathematical terms but also forming an exact science, as well as number governs harmonious proportions. He then attempting to apply his theories to the whole cosmos, proving harmonic relationship between stars and planets, elements were also included. His ideas were taken up by astronomers from the medieval and renaissance time periods. These astronomers developed a whole new spectacle to Pythagoras's music to the spheres quote, later his theory that elements were arranged harmoniously was looked at again 2,000 years after Pythagoras's death, in 1865. The person who enlightened his ancient theory was named English chemist called John Newlands, Newlands discovered that when elements were arranged in their atomic weight that similar priorities occurred every eight elements along, just like the notes of music. This discovery is now known as the Law of Octaves, this was the stat of what is now known as the Periodic Table. Pythagoras also established the principle of deductive reasoning, which is simple sums such as "2+2=4" to built towards a final conclusion or fact. This theory was refined by Euclid, a medieval mathematician. Pythagoras developed philosophy by his abstract thinking and superior to the evidence of the senses. Plato also took this up later after Pythagoras, and resurfaced in renaissance philosophy, especially in the 17^{th} century. The Pythagorean attempt to combine reasoning and religion was the first attempt at anything like this. Almost everything we know about Pythagoras is from other people or philosophers, even bare facts from his life! Yet he has achieved a godly status for his theories. Weather he was the originator of these ideas or not, he certainly spread them. Pythagoras was a key developer to philosophical thought.

## The Philosophy Book

## Hub Help

This book has been a great help for this hub and also tells you of more philosophers from 700 BCE-2011 CE