Random

 

Turn, Turn, Turn

To everything turn, turn, turn
There is a season turn, turn, turn
And a time to every purpose under Heaven

Heaven may know the purpose, but on Earth sometimes stuff just happens.

Absence of evidence is not evidence of absence. And the fact that some behavior is cyclical and not random, does not negate the fact that other behavior is random and not cyclical.

Random behavior may look cyclical when viewed at a small scale, but that does not mean that it is cyclical at every scale. Randomly flipping a coin follows a random normal logistic distribution. That distribution has a behavior that can be defined mathematically with a precise mean and variance. I have suggested than the universe is hyperbolic and the variance is due to this effect. The range, s, is such that its Cumulative Distribution Function at the median should be equal to 50%, i.e. 50% heads/50% tails.  This requires that the range of this function, s, be 0.5. The random normal distribution function can thus be defined as  ½ *sech²(x-µ), where μ is the mean. This looks like ½*cos²(x-μ) for one cycle, but the logistic distribution with a hyperbolic secant has a period of 2πi, where i is the imaginary number, which means in the real domain it does not repeat, while the non-hyperbolic Euclidean cosine has a period of 2π which means in the real domain it does repeat.

Both equations above have a mean, µ, of 0.  They appear very similar between -.75 and .75.  However the traditional Euclidean cosine squared function cyclically repeats, while the random, hyperbolic secant squared function does not repeat. 

Things that are cyclical, like the seasons, can follow a deterministic function.  Things that are random, like the weather, do NOT have to follow a deterministic function.  Some things can be solved.  Some things cannot be solved.  Going all Serenity Prayer on this, Wisdom is knowing the difference.