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13165
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Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
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Full Idea:
Geometry does not ask 'why?' ..When from the exterior angle equalling two opposite interior angles it is shown that the interior angles make two right angles, this is not a causal demonstration. With no exterior angle they still equal two right angles.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452], p.161-2), quoted by Paolo Mancosu - Explanation in Mathematics §5
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A reaction:
A very nice example. It is hard to imagine how one might demonstrate the cause of the angles making two right angles. If you walk, turn left x°, then turn left y°, then turn left z°, and x+y+z=180°, you end up going in the original direction.
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9569
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The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
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Full Idea:
It is unsurprising that geometry was discovered in the necessity of Nile land measurement, since everything in the world of generation goes from imperfection to perfection. They would naturally pass from sense-perception to calculation, and so to reason.
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From:
Proclus (Commentary on Euclid's 'Elements' [c.452]), quoted by Charles Chihara - A Structural Account of Mathematics 9.12 n55
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A reaction:
The last sentence is the core of my view on abstraction, that it proceeds by moving through levels of abstraction, approaching more and more general truths.
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19673
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Galileo mathematised movement, and revealed its invariable component - acceleration [Galileo, by Meillassoux]
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Full Idea:
Galileo conceives of movement in mathematical terms. ...In doing so, he uncovered, beyond the variations of position and speed, the mathematical invariant of movement - that is to say, acceleration.
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From:
report of Galileo Galilei (Two Chief World Systems [1632]) by Quentin Meillassoux - After Finitude; the necessity of contingency 5
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A reaction:
That is a very nice advert for the mathematical physics which replaced the Aristotelian substantial forms. ...And yet, is acceleration some deep fact about nature, or a concept which is only needed if you insist on being mathematical?
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