Hi Steve,

But that's my point precisely, that you most certainly can know. 100 heads up pennies are not random, regardless of how they were produced. This is the crucial idea behind my definition. That a data set can be random or not, independently of the process that produced it.

You suggest that any result is random, if and only if it is produced by a random process (e.g. coin tossing). Therefore, if the process by which a result is produced is deterministic, the result can not be random.

But coin tossing is a purely deterministic process, governed by causality and the laws of physics. If we could know the initial conditions with sufficient precision, we could accurately predict the outcome of each and every toss. But since we can not predict the outcome, or control it, we call the process random when in fact it is not.

In the same way we call radioactive decay events random when they in point of fact are not. We use the word random when what we really mean is "unpredictable."

By my thesis, "randomness" is a well defined, quantifiable and analytical property of the finite data set, and the data set alone. It is completely independent of the process that produces the data set.

Analyzing various RNG algorithms I have shown not only how well they worked, but when they failed. The famous example is RANDU. I analyzed the output of RANDU and showed that it was fine up to a certain number of data points, and I showed at which point the output became non-random (a point that varies based on the number of dimensions in the space your generating data for.

Moreover, it can be shown that my analysis method, under appropriately judicious constraints, reduces to the famous Chi Squared calculation. However, unlike the Chi Squared calculation my method quantifies the randomness of the data set order. In other words, the sequence 1, 2, 3, 4, ..., n, will be shown quite non-random, whereas the exact same set of digits in a different order could be quite random. And the best part is that my method can quantify the degree of randomness for a whole host of different sequential possibilities, specifying which is the most random, which is the least, and all points in between.

Joe