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Taking no chances.

The trend of physics over the last 80 years has been to introduce randomness and uncertainty into more and more processes that classical physics considered well determined. Now comes an instance of the reverse. Vladimir Vulovic and Richard E. Prange of the University of Maryland in College Park propose that a process commonly thought to be random is in fact well determined by its initial conditions. Their example is the flipping of a coin.

Coin flipping has been considered the epitome of a random and chancy process, used as an example by students of games of chance since Blaise Pascal. Expressing surprise that it has taken three centuries to figure the contrary, Vulkovic and Prange argue that coin flipping obeys Mewton's laws, and that each flip depends on the impulse given the coin by the thumb and the height above the floor from which the coin starts. Any randomness, they say, is not in the flipping itself, but in imprecise knowledge of the starting conditions. If you could know the impulse given by the thumb in a particular case, or had a well-calibrated mechanical flipper, you could predict how the coin would fall (ignoring effects of the air and assuming a perfectly flat floor). The same considerations should apply to the fall of dice or the spin of a roulette wheel, they propose.

The mathematical source of this odd result comes from an extension of the work of Pascal and Pierre de Fermat, which is that many equations may have completely determined solutions (as in this case) and yet give "unpredictable" and truly random results. This happens, according to Vulovic and Prange, "because predictions of the future depend with excruciating sensitivity on the starting data. . . . However, even if precise predictions are not in practice possible, the equations can predict probabilities of various outcomes."
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Title Annotation:predicting supposedly random behavior such as coin flipping
Author:Thomsen, Dietrick E.
Publication:Science News
Date:Apr 6, 1985
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