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St. Thomas on the "butterfly effect"!

Started by Geremia, April 02, 2018, 04:30:42 PM

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The "butterfly effect" appears to be a modern variant of the ancient philosophical axiom "Parvus error in principiis, magnus in conclusionibus" or "Parvus error in principio, magnus est in fine":
QuoteA small error in the beginning (or in principles) leads to a big error in the end (or in conclusions).
See St. Thomas Aquinas De Ente et Essentia, proemium, which references Aristotle De Cœlo bk. 1, specifically 271b:
Quote...the least initial deviation from the truth is multiplied later a thousandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end.
Upon which St. Thomas commentates (In De caelo lib. 1 l. 9 n. 4 [97.]): who makes a slight departure from the truth in his principles gets 10,000 [i.e,. many] times farther from the truth as he goes on. This is so because all things that follow depend on their principles. This is especially clear in an error at the crossroads: for one who at the beginning is only a slight distance from the right road gets very far away from it later on.* And he gives, as an example of what he is talking about, the case of those who posited a smallest magnitude, as Democritus posited indivisible bodies. By thus introducing a least quantity, he overthrew the most important propositions of mathematics — for example, that any given line can be cut into two halves. The reason for this effect is that a principle, though small in stature, is nevertheless great in power, just as from a small seed a mammoth tree is produced. Hence it is that what is small in the beginning becomes multiplied in the end, because it reaches unto all that to which the power of the principle extends, whether this be true or false.
*St. Thomas's example here is exactly that of Chaos: A Mathematical Adventure, ch. 2 "Vector Fields", 9:10ff.; see also ibid. ch. 7 "Strange Attractors & the Butterfly Effect".