Chance

2010-02-10 09:59

Applied probability and statistics

Speaking of probability and statistics, there is the story of a statistician who told a friend that he never took airplanes: "I have computed the probability that there will be a bomb on the plane,” he explained, "and although this probability is low, it is still too high for my comfort." Two weeks later, the friend met the statistician on a plane. "How come you changed your theory?" he asked. "Oh, I didn't change my theory; it's just that I subsequently computed the probability that there would simultaneously be two bombs on a plane. This probability is low enough for my comfort. So now I simply carry my own bomb."

- Excerpt from Raymond Smullyan, To Mock a Mockingbird and Other Logic Puzzles (1st edition), Knopf, June 1985

Postad av Martin Kaarup

Kommentarer (0)   Kategorier:  Predictability    Chance

2009-11-24 09:45

The butterfly effect anno 1914

Excerpt from Henri Poincaré's Science and Method (1914), where he tries to address the question "How can chance emerge in a deterministic world?"

"A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say the effect is due to chance.

If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment.

But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately.

If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we would say that the phenomenon had been predicted.

But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena.

A small error in the former will produce an enormous error in the latter. Prediction becomes impossible and we have the fortuitous phenomenon."

Postad av Martin Kaarup

Kommentarer (0)   Kategorier:  Chaos Theory    The Butterfly Effect    Predictability    Chance    Newtonian Mechanics