Wednesday, May 30, 2007

Gambling And Synchronized Oscillators

The classic example of synchronized oscillators is that of two grandfather clocks side by side with their pendulums swinging in the same direction at the same time. The theory is that, over time, tiny vibrations in the support, the wall and even the air act as feedback mechanisms between the two clocks. Although they start with their pendulums swinging individually, out-of-phase, over time—sometimes very long periods—the pendulums will gradually work themselves into phase, that is, into sync with each other. The synchronized state will be a stable state which then will last until the system of the two clocks is disturbed.

This phenomenon was first observed hundreds of years ago by Christiaan Huygens.

In the modern world physicists and mathematicians have deeply explored the concept of synchronization among oscillators, and have observed the effect throughout many diverse systems, from electrical circuits to fireflies. (An interesting pop account is in, “Sync: The Emerging Science Of Spontaneous Orderby Steven H. Strogatz)

I’ve often wondered if synchronized oscillators could help with gambling.

For instance, a roulette wheel can be thought of as an oscillator, a system that fluctuates between disorder and order. The wheel spinning with the ball bouncing along the rim is an unstable, disordered state. When the ball drops into a slot, the system state becomes stable, ordered. I wonder if a software model could be constructed which oscillates randomly, say, some manner of random number generator. But that software oscillator would provide for input feedback in the form of a sequence of winning numbers from a given roulette wheel. Could the model be constructed so that the numbers from the roulette wheel would modify the random oscillations of the software system in such a way that the two systems would become synchronized? It wouldn’t be necessary for the systems to be completely synchronized—from a gambling point of view a loosely-coupled system which only occasionally moves in lock-step would be fine. (You only need to beat the odds, not the system.)

Similarly, a daily lottery drawing can be thought of as an oscillator, a system that fluctuates between the ordered state of a selected winning draw and the disordered state of the universe of all possible draw combinations. Could a software model be constructed which mimics that oscillation and which inputs a sequence of previous winning numbers as feedback in an attempt to synchronize the software oscillator with the lottery oscillator? Again, a loose-coupling is fine—you only have to win once.

Thoughtful gamblers attempt to maintain awareness of a great many interesting mathematical domains in their quest for thoughtful play. Complexity theory, chaos theory, catastrophe theory, Parrondo’s Paradox and many others.

I suspect over the coming years our understanding of “randomness” will change greatly. At the moment, I think the study of oscillators and their interaction is the most promising avenue to explore.

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