Galileo BAD, Archimedes GOOD
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Quoted By: >>13437107 >>13437124 >>13437411 >>13437511 >>13437519 >>13439180
>Galileo is the most overrated figure in the history of science. [...] Here’s a simple snapshot of Galileo at work.
>The cycloid. [...] The cycloid is the path traced by a point on a rolling circle. [...] What’s the area of the cycloid? That was a natural question in Galileo’s time. Finding areas of shapes like that is what geometers had been doing for thousands of years. Archimedes for instance found the area of any section of a parabola, and the area of a spiral, and so on. The cycloid was a natural next step. It fit right into this tradition.
>Of course nobody cared about the area of the cycloid as such. That’s not the point. [...] Archimedes, when he found his areas, gave clever geometrical arguments; gorgeous proofs. The point is not that he gave you a “formula” to compute various areas. How often have you needed to know the area of a spiral anyway? Never, of course. The point is not the result. The point is that Archimedes took human thought to a new level. His proofs are beautiful; they are logically flawless. They give you a sense that you are at the pinnacle of what the human mind can achieve. Everybody wanted to see more that kind of thing.
>So solving problems like the area of the cycloid then, in this sense, in the Archimedean sense, was the way to prove yourself a worthy geometer. So Galileo tried. And failed. All those brilliant feats of ingenuity that Archimedes and his friends had blessed us with; it just wasn’t happening for Galileo. He just wasn’t any good at it.
>In fact he said so himself. Here is a quote from Galileo on Archimedes: “Those who read his works realise only too clearly how inferior are all other minds compared with Archimedes’, and what small hope is left of ever discovering things similar to those he discovered.”
>That’s Galileo. And he’s quite right. Except maybe it’s not that *all* other minds are inferior to Archimedes. Although certainly Galileo’s is.
http://intellectualmathematics.com/blog/galileo-bad-archimedes-good/
>The cycloid. [...] The cycloid is the path traced by a point on a rolling circle. [...] What’s the area of the cycloid? That was a natural question in Galileo’s time. Finding areas of shapes like that is what geometers had been doing for thousands of years. Archimedes for instance found the area of any section of a parabola, and the area of a spiral, and so on. The cycloid was a natural next step. It fit right into this tradition.
>Of course nobody cared about the area of the cycloid as such. That’s not the point. [...] Archimedes, when he found his areas, gave clever geometrical arguments; gorgeous proofs. The point is not that he gave you a “formula” to compute various areas. How often have you needed to know the area of a spiral anyway? Never, of course. The point is not the result. The point is that Archimedes took human thought to a new level. His proofs are beautiful; they are logically flawless. They give you a sense that you are at the pinnacle of what the human mind can achieve. Everybody wanted to see more that kind of thing.
>So solving problems like the area of the cycloid then, in this sense, in the Archimedean sense, was the way to prove yourself a worthy geometer. So Galileo tried. And failed. All those brilliant feats of ingenuity that Archimedes and his friends had blessed us with; it just wasn’t happening for Galileo. He just wasn’t any good at it.
>In fact he said so himself. Here is a quote from Galileo on Archimedes: “Those who read his works realise only too clearly how inferior are all other minds compared with Archimedes’, and what small hope is left of ever discovering things similar to those he discovered.”
>That’s Galileo. And he’s quite right. Except maybe it’s not that *all* other minds are inferior to Archimedes. Although certainly Galileo’s is.
http://intellectualmathematics.com/blog/galileo-bad-archimedes-good/
