Free Pythagorus by Kitty Ferguson

pyramid) – a four-sided solid – out of four equilateral triangles, and they probably knew this by the time Philolaus wrote the first Pythagorean book in the second half of the fifth century. [5] The word tetractus , however, was in use during Pythagoras’ lifetime. It hints that there was more ‘fourness’ to the idea than the fact that 4 was the largest number in the ratios. The tetrahedron or pyramid is a solid in which each face is a tetractus, but which also uses the number 4 in other manners – 4 faces, 4 points.

    When Aristotle, in the fourth century B.C., was researching the Pythagoreans, he found a list of connections they made between numbers and abstract concepts. He apparently could not discover what they connected with the numbers 6 and 8.
Mind
Opinion
The number of the whole
Justice
Marriage
?
Right time, due season, or opportunity
?
Justice
Perfect
    It is not difficult to understand how Mind might be 1 and Opinion 2. Justice appears twice because of an association with squareness. The Greeks did not think of 1 as a number. ‘Number’ meant plurality, more than 1. So, for them, the smallest number that is the square of any whole number was 4. [6] The first number that is the square of an odd number is 9, and that, too, they associated with justice. The idea that ‘square’ means an evened score – with all need for retaliation at an end – still shows up in the colloquial phrase ‘That makes us square’. Marriage (5) was the sum of the first odd and even numbers (2 and 3). The link between 7 and ‘right time’ or ‘due season’ reflected wider Greek thought. Life happened in multiples of 7. A child could be born after 7 months in the womb, cut teeth 7 months later, reach puberty at 14, and (if a boy) grow a beard at 21.
    The Pythagoreans followed one line of thought that seems particularly odd today, accustomed as most of us are to thinking of squares and cubes of numbers but not of other geometric shapes possibly connected with them in a similar manner. The ‘square’ of 4 was 16, but the ‘triangle’ of 4 was 10, the perfect number. Both ideas were equally picturable with pebbles.
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    Stacking the pebbles so as to discover that the ‘cube’ of 4 was 64, you might just as easily pile them up another way so that the ‘pyramid’ of 4 was 20. Montessori teaching exploits the delight of playing games like this with little objects like pebbles – in the case of Montessori, beads.
    Having come to the conclusion not only that numbers, but the specific numbers 1, 2, 3, and 4 and the ratios between them were the primordial organising principle of the universe, Pythagorean thinking moved in other directions, some of which seem strange and primitive, but it is not surprising that they overestimated the simplicity of the rationality they had glimpsed and were too expectant of immediate applications and results. They were not unlike the earliest followers of Jesus, coming away from what was for them a transforming experience and trying to apply it to the everyday world, thinking all would be resolved soon. The Pythagoreans had discovered a new road to ‘truth’. Great thinkers thought about truth and proposed answers. Only a shaman – and many regarded Pythagoras as what we today would call a shaman – was sure he had the answer. In fact, Pythagoras and his followers did, but they travelled their new road weighted down with ancient baggage. Still in the age of oracles, divination, and mystic utterances, with its preconceptions about the universe and nature, their naive conception of the world carried over into a naive conception of the power of numbers.
    The halcyon days in Croton lasted thirty years. Iamblichus’ biography included long lists of names, which he probably got from Aristoxenus, of Pythagoras’ first followers, who sat at his feet, heard his