Hi Bartosz,

No, I am afraid I can not point you to the paper. It was once posted on a web site of mine, but that site is no more. On the other hand, given the response this topic generates here I think I might dig up that paper, polish it a bit, and submit it for publication.

I'm not going to try and go into detail here. If I did, Craig and Steve wouldn't just kill this thread, they'd delete my registration and ban me from the forum. It gets pretty esoteric. I will tell you that my definition uses fractal dimension theory and defines the randomness of a finite set as the ratio of the information dimension (D_i) of the set to the capacity dimension (D_c) of the space it occupies. This makes the randomness calculable, and applicable in any real number of dimensions (not just in integer numbers of dimensions). Also, my definition has the added (not to mention surprising and unintended) property of being a generalization of the Chi-squared rule (which is to say that in an appropriately restricted space it reduces to the Chi-square rule). But most importantly, it completely removes the intuitive notion of randomness of outcome from the nature of the process which generated the results. In effect, one is left to argue about whether a process is random or chaotic, but the randomness of the outcome is definitively quantifiable and calculable.