Wednesday, February 04, 2009

Dynamics of Coin Tossing is Predictable

Y'know, sometime when I'm bored, I browse various journals that I seldom read just to find something I could occupy my time, or even something to read in bed that can put me to sleep! :) It is during such browsing time that I often find many articles that often is more interesting than what I anticipated.

This could possibly one such article, and I find that I'm spending way more time than I should reading it. The article discusses in great detail the dynamics of coin tossing[1], and that, as we expected, it isn't random once we know the initial condition even when we include various other complexities such as air resistance, and the various strange trajectory and spinning motion.

Abstract: The dynamics of the tossed coin can be described by deterministic equations of motion, but on the other hand it is commonly taken for granted that the toss of a coin is random. A realistic mechanical model of coin tossing is constructed to examine whether the initial states leading to heads or tails are distributed uniformly in phase space. We give arguments supporting the statement that the outcome of the coin tossing is fully determined by the initial conditions, i.e. no dynamical uncertainties due to the exponential divergence of initial conditions or fractal basin boundaries occur. We point out that although heads and tails boundaries in the initial condition space are smooth, the distance of a typical initial condition from a basin boundary is so small that practically any uncertainty in initial conditions can lead to the uncertainty of the results of tossing.

Sometime it is nice to see what we know should happen, and someone else did all the dirty and tedious work to show this. :)


[1] J. Strzałko et al., Phys. Rep. v.469, p.59 (2008).

1 comment:

Chris said...

Ah, gambling physics.

I want a paper on predicting a dice roll. Complete with experimental results from a robotic throwing arm which can guarantee precise initial conditions at the casino!