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.