Hi Kai,

Before we persue this part of the conversation any further, I want to ask how much do you know about uncertainty, and the Heisenberg Uncertainty Principle in particular? For example, do you understand that position and momentum (x-p_X) make up just one of many uncertainty relationships in quantum mechanics (albeit by far the best known)? Do you understand the physics that gives rise to these mathematical artifacts?

It was just a couple of weeks ago that I saw a story on the Drudge Report where some astrophysicists were warning that, on pain of the Schroedinger's Cat experiment, mankind was actively shortening the life of the universe by using telescopes. I didn't read enough of the story to determine if they were serious. Instead I chose to keep the hope that they were just using assinine hyperbole to make a tangential point.

In any case, and regardless of these tangential points, you're really only obfuscating my original point. You ask if I will admit that some things are unpredictable. Of course I will. And they would remain unpredictable whether I admitted it or not. I am also saying that just because something is unpredictable, that does not mean it's (even partially) random.

Chaotic systems are not random. They are wholly deterministic. And if you take two identical instances of a chaotic system, give them exactly identical initial conditions and subject them to identical forces they will produce exactly identical results every time.

The problem is that we can not know those initial conditions with sufficient precision to accurately predict the outcome. Neither can we manipulate those initial conditions with sufficient precision to control the outcome. And this has nothing to do with quantum physics or any uncertainty relationships. Certainly not in the case of macroscopic systems like weather and tossing coins. It simply has to do with the sensitivity of the system to those influences.

Now, with all of that said, my original statement remains unchanged. I have simply noted that to date we have used the idea of randomness to deal with unpredictability, but we have done so with much waving of hands, much intuition, and little mathematical formalism, giving rise to such amorphous abstractions as the ill-defined "pseudo"-randomness.

By my thesis, randomness is a well-defined and analytically quantifiable property of the data set alone, independent of the process by which the data set was generated.

Consequently, it is a corrolary of my formalism that a fully random system (if indeed there is such a thing) is quite capable of producing non-random results (e.g. it is equally likely that tossing 100 uniquely identifiable pennies will produce a 100 heads outcome as any other possible outcome). Also, a fully deterministic system is equally capable of producing quite random results. Hence, the age old question is answered, rendering pointless the intuitively-defined distinction of "pseudo"-random.

Understand that I have done this. I have written the code and tested the outputs of several RNGs, including the infamous RANDU. My analyses showed that many of these RNG algorithms produced quite random data sets, at least up to the point they were tested. In some cases, e.g. RANDU, I showed not only how random the output was to a certain point, but then how non-random it became after that point.

It is an interesting feature (for lack of a better word) of my test that under appropriately judicious constraints it reduces to the famous Chi-square calculation mentioned elsewhere. However, unlike the Chi-square calculation, my algorithm is sequence dependent. In other words, if you use the numeric sequence 0, 1, 2, 3, 4, ..., n, as input it will be shown to be quite non-random. However, the exact same set of integers in different sequences will yield varying degrees of randomness. In other words, it is no longer a case of asking "Is this data random or not?" Instead we can now ask "How random is this data?"

Joe.