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What is "influence"? What can we know of it?

 At Quora, someone recently asked me who was the greater influence upon Plato: Socrates or Parmenides? It is a fascinating question, to which I could only answer with some further related questions, a dash of context, and a joke.  I enjoyed it all so much, though, that I will reproduce it here.  To begin with, there is no good metric of “influence.” You can’t measure influence like inches or Celsius degrees and say X is exercising more of this unidimensional stuff than Y is. Who influenced John Dewey more: Charles Darwin [pictured] or William James? Except that in the Dewey case we have much more information. We know what Darwin’s views on a wide range of subjects were, and what James’ were, and we can work to understand how Dewey’s thought was formed by each. We don’t depend on Dewey to tell us what James said or thought! In the Plato analog, though, we do largely depend on Plato to tell us what Socrates said or thought. There are other sources who help at the edges — Ar...

Did Aristotle Get the Point of this Story?

Aristotle, in his book on POLITICS, tells the following story about Thales, the Ionian philosopher portrayed above and best known for the theory that water is the essence of all matter. "Thales, so the story goes, because of his poverty was taunted with the uselessness of philosophy; but from his knowledge of astronomy he had observed while it was still winter that there was going to be a large crop of olives, so he raised a small sum of money and paid round deposits for the whole of the olive-presses in Miletus and Chios, which he hired at a low rent as nobody was running him up; and when the season arrived, there was a sudden demand for a number of presses at the same time, and by letting them out on what terms he liked he realised a large sum of money, so proving that it is easy for philosophers to be rich if they choose, but this is not what they care about." Fascinating story. Someone who apparently had the reputation of being what we would call today an 'ab...

Still Thinking About Numbers

As I mentioned in a blog entry last week, the value of pi slips away from you if you try to state it as a simple fraction, even in a good try such as 22/7.  If we represent numbers in decimal rather than fractional form we can express the strangeness of pi, its irrationality, in a different way. We can turn any simple fraction into one of three sorts of number: a simple integer, an integer followed by a string of decimals that comes to a definite end, or an integer followed by the string of decimals that doesn’t come to an end but that settles down into satisfyingly dull repetition.        Here are some simple fractions: 9/3, 11/4, and the aforementioned 22/7. The first, 9/3, resolves itself into the integer 3. 11/4 is 2 ¾, or in decimal form 2.75. That is where it terminates. 22/7 is 3 1/7 or in decimal form 3.142857142857.... It is a repeating decimal. That is: the sequence "142857" will continue repeating for as long as you have the patience to ...