Pattern comments on Reason and Intuition in science

Pattern 20 Dec 2019 19:31 UTC
4 points
Styling: try breaking things up into more paragraphs.

[1] But no one ever made a discovery through syllogisms
So by “reason” you mean “logic”.

[2] all mathematicsat bottom is about geometric relations even when it doesn’t seem so.
Counterexample: Logic.
Probability—if you squint, sure.

[3] the Euclidian proof of the Pythagorean theorem, based on syllogism,
A link to the proof in question would be nice. Here? Sure, that’s ugly. But if that’s how it was discovered, then that disproves [1]. Though coming up with your own proof might work better than trying to understand that one, sure.
the imagistic proof of the three squares
Is this still the Pythagorean theorem (here?), or a different result?

[4] Thus all mathematics and all science in general—mathematics is only the prototype and most precise of the sciences—is about the definitions, not about the proof, not about the process or —absurd!—the “algorithm.”
From Hammers and Nails:
A Hammer is someone who picks one strategy and uses it to solve as many problems as possible.
A Nail is someone who picks one problem and tries all the strategies until it gets solved.
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I am reminded of a classic speech of the mathematician Gian-Carlo Rota. His fifth point is to be a Hammer
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The greatest mathematicians of all time created vast swathes of their work by applying a single precious technique to every problem they could find.
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It’s amusing to note that in the same speech, Rota expounded the benefits of being a Nail just two points later
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To be a Nail is to study a single problem from every angle.
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to be a Hammer is to study a single technique from every angle.