Many natural events and processes are cyclical. Examples surround us. As one example, aerial photographs reveal that all rivers in the world meander, and those meanderings are cyclical. Rivers meander because they seek the path of least resistance, not because of differences in the structure of the soil. Just like water can only flow downstream in the river, time cannot reverse in trading. In addition, prices can only be higher or lower, just like the river can only bend to the right or left. These constraints form a special kind of random walk that mathematicians call "drunkard's walk", In its simplest form the "drunk" steps only into a square to the right or into a square to the left as he steps forward. He must make a new decision with each step. To make the decision random, he flips a coin to determine the direction he will take. Repeated many times, the overlay of paths that he follows will look like a smoke plume. The problem can be solved through a rather famous partial differential equation called The Diffusion Equation. The density of the smoke particles in the plume is analogous to the probability of the drunkard's location. A multiple exposure photograph of the drunkard's walk repeated over and over would show the randomness. This photograph would show the composite paths to have a uniform density, widening from the initial position. The uniform density would make the sum of his paths look like a smoke plume. The smoke plume is analogous to a trend in the market.

Random walk does not necessarily mean chaos. A minor variation of the drunkard's walk problem is to allow the random coin flip decision to control the change of direction rather than the direction itself. That is, the random variable becomes momentum instead of direction. The partial differential equation describing this condition is called The Telegrapher's Equation. Among other things, the equation obviously describes electric waves along telegraph wires. You can picture the result as the drunk reeling back and forth. He overcorrects around a general direction trying to reach an objective. This formulation of the problem, expressed in terms of physics, accurately portrays the river and explains why the river meanders. In a multiple exposure photograph the paths are still randomly distributed. Nevertheless, the cycles are apparent in the shorter case of a single path. This is why rapid identification of a cycle using a short data base is important - the cycle is identified before it disappears. Long term measurements are not satisfactory because the cycle characteristics are not stationary over the longer period.

If enough traders ask themselves "Will the market go up today?", the random variable is direction. Thus, conditions are established for the solution of The Diffusion Equation. On the other hand if enough traders ask themselves 'Will the trend continue?', the random variable is now momentum. You could then expect the conditions to be established for the solution of The Telegrapher's Equation. That is, the market is ripe for short term cycle activity.

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