I was reading a popular science book about the history of Chaos theory and was curious about the part when Edward Lorenz discovered the so-called butterfly effect.

Long story short, he omitted to key in an extra decimal place into his computer simulation of weather, thinking that it wouldn't make much a difference, but instead got a completely different result in a relatively short period of time. This led him to his theory about chaotic system.

Sure, it might be counter-intuitive to think that a small error can magnify that fast, but even with hindsight this shouldn't be THAT surprising at all. I mean, for example, Hadamard had coined the term well-posedness and sensitivity to initial condition decades before that. Edward Lorenz, being a fine mathematician as he was, should be familiar with these things shouldn't he?

I'm not an expert in this so there could be many points that I overlooked. I hope that the question is not too broad.

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    Before Lorenz, I think people assumed that such ill-posed problems were very rare -- pathological examples, if you like. Lorenz showed that they were very common. – TonyK Jun 18 '17 at 13:27
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    It's not surprising at all. Robert Frost wrote The Road Not Taken in 1920, a poem which contemplates the enormous magnitude of the consequences of a very marginal decision, although the name the butterfly effect only came later. – Robert Frost Jun 18 '17 at 13:32
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    Could it be that around 1960 was the time that computers became widespread enough and fast enough that numerical experiments of any kind became possible (and not hidden away for national security reasons)? I.e., before it was too expensive or had a too long wait time to run the same computation multiple times "on a lark" so that the first and only result was almost always The Result? – LutzL Jun 18 '17 at 14:55
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    @JohnB And even Van der Pol himself observed strange kind of oscillations when he was working with electronic devices, before Cartwright and Littlewood. I think that was either in P. Holmes reviews on history of dynamical systems or in Aubrey's Writing the History of Dynamical Systems and Chaos: Longue Durée and Revolution, Disciplines and Cultures : someone described electrical scheme with a headphones that allowed perception of oscillations as a sound. P.S. Found similar quote here – Evgeny Jun 18 '17 at 22:52

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