Listening to Lord Bragg and his guests discussing random and pseudorandom numbers taught me a thing or two, and raised a couple of “issues”. One, trivial, can be dismissed at once: why was there no discussion of the amazing prescience of the shuffle function on so many people’s iPods? Because it interests no-one except the iPod listener. Trickier was the way the various guests seemed to skirt around the predestination issue. In answer to the general question of whether, if you knew all the existing preconditions of a coin-toss, you could predict the outcome, the answer seemed to be a less than convincing “Well, you can never really know all the preconditions.”
OK, but ...
Lodged deep in my memory was a snippet from an elementary stats lecture in which the statistician with the stiffest neck ever said something about coin tossing, or dice throwing, harnessing the unpredictability of average human motor control to generate randomness. Off I went looking, and found this: Dynamical bias in the coin toss, and the first author is the magicians’ mathematician, Persi Diaconis, so I had to pay attention. That paper actually goes beyond my memory, to prove that even a manual coin toss has a bias to come up as it started. However, the paper does begin from the standpoint of a coin-tossing machine, in which case, of course, the preconditions are (or can be made to be) constant. The conclusion:
With careful adjustment, the coin started heads up always lands heads up – one hundred percent of the time. We conclude that coin-tossing is ‘physics’ not ‘random’.
That ought to have been enough to be getting on with, but I kept digging. Here's the abstract of the paper:
We analyze the natural process of ﬂipping a coin which is caught in the hand. We prove that vigorously-ﬂipped coins are biased to come up the same way they started. The amount of bias depends on a single parameter, the angle between the normal to the coin and the angular momentum vector. Measurements of this parameter based on high-speed photography are reported. For natural ﬂips, the chance of coming up as started is about .51
Not exactly an edge I’d bet the farm on, especially not with Diaconis (presumably) inserting stuff like this:
In Section Three we prove that the angle ψ between M [with an arrow above it] and the normal to the coin stays constant. If this angle is less than 45°, the coin never turns over. It wobbles around and always comes up the way it started. Magicians and gamblers can carry out such controlled ﬂips which appear visually indistinguishable from normal ﬂips.
It was, however, enough of an edge to get some elements of the press interested. And the kicker in that story -- *Note: In football's inaugural kickoff coin toss, the coin is not caught but allowed to bounce on the ground. That introduces an extra complication, one mathematicians have yet to sort out. -- leads effortlessly to Coin Toss Makes Team See Life Is Random
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