![]() It is not known for certain why the Greeks abandoned the highly developed algebra of the Babylonians for geometry but it is assumed that the discovery of irrational numbers played a significant role in this decision. ![]() His concept of mathematics is not the arithmetic of the natural numbers but geometry he famously had the saying, “let nobody ignorant of geometry enter here” erected over the entrance to his school. Plato, who certainly had a lot of sympathy for the Pythagoreans, goes a lot further. Now what is important here is that the arithmetic of the natural numbers is a long way from being mathematics, even in the 6 th century BCE, both Egyptian and Babylonian mathematics went way beyond this so to claim, as Kennedy does, that the Pythagoreans are fulfilling Galileo’s quote is to say the least stretching things somewhat. I’m not going to expand on Pythagorean harmony theory except to say that it permeates the history of Western science and philosophy all the way up to Newton, with many scholars such as Newton himself, Tycho and Kepler being big fans. ![]() If something as simple as the diagonal of a square cannot be expressed as the ratio of two natural numbers then the whole foundations of the Pythagorean philosophy are undermined. Naturally the discovery of irrational numbers completely blew this idea out of the water. In fact the word harmony has its roots in arithmetic and it is through the Pythagorean philosophy that it became a fundamental concept in music theory. The Pythagoreans, who were a religious cult living in a commune in Southern Italy, believed that the natural numbers are the building blocks (the atoms) that constitute the universe, they also believed that everything could be expressed in terms of ratios between natural numbers some of these ratios being harmonious and others discordant. Kennedy starts with the Pythagoreans and so shall I. This is however very much a simplification of a very tricky subject so I would request the professional philosophers and historians of science such as Jim Harrison, John Lynch and the Albino Aussie Anthropoid TM to go gently on their criticism, though if they or anybody else has anything informative and or constructive to add then I would be more than happy should they choose to do so. Mike’s comment as well as several of those from Kennedy display an ignorance of what exactly Galileo’s quote is supposed to express and so I have decided to write a short exposition on mathematics and its use in the sciences and how that use was categorised from a philosophical standpoint. I wonder what Kennedy thought the Ptolemaic model of the universe was based in if not the idea the universe ran by predictable laws expressible in the language of mathematics. ![]() In a comment to my second post on the subject Mike from Ottawa, as well as pointing out a substantial typo in my text, wrote the following: The title of this post is probably the most well known genuine quote from the Tuscan polymath Galileo Galilei he never actually said, “but it moves”! This quote turned up recently in my posts on the paper from Jay Kennedy concerning his discovery of possibly Pythagorean harmonies in the text structure of the writings of Plato.
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