Kolmogorov

Kolmogorov being the name of a very famous Russian mathematician, a mathematician who may have corresponded with one of the mathematicians who taught me. Included here for his definition of complexity.

In the world of consciousness, some people talk of being conscious of something, while other people talk of being conscious.

My thought this morning was that I favour the former contingent; that one cannot be conscious without being conscious of something. A thought given a bit of flesh and blood by associating back to Kolmogorov Complexity. One of the ideas there being that something is not random if it can be described in less space than it occupies itself. Or put another way, a long but finite series of numbers is not random if it can be completely described by some shorter series of numbers. With the complication that a description requires a language, a language which also needs to be described. From where one jumps to the machinations of Gödel, for whom the proofs of complicated propositions could be mapped onto large integers.

If we then think of the conscious field as being the more or less immediate product of something like the LWS-N of reference 2, for that field to be conscious it is necessary (but by no means sufficient) that the information in it be not random in the Kolmogorov sense sketched above.

Or put another way, there has to be some regularity. There have, for example, to be some lines or spots. And if the world outside is not furnishing any such, we have to make do with the noises coming from within, thinking here of when all is quiet outside, one can usually hear or otherwise be conscious of quite a lot of stuff going on inside. We cannot be conscious of the void outside unless there is something more than a void inside to provide a contrast.

There is a balance here in that an empty field is uninteresting. And a field so full as to be random is also uninteresting, amounts to much the same thing as an empty field. The interest lies in what lies between. With some people responding best to very busy fields, some to less busy fields. Perhaps, at some point in the not too distant future, we will be able, experimentally, to establish upper and lower bounds for how much information can be conscious.

PS: slightly depressed to find that I bought the book at reference 1 more than two years ago and have barely done more than peek at it. But at least I still knew where it was.

Reference 1: An Introduction to Kolmogorov Complexity and Its Applications – Ming Li and Paul M.B. Vitányi - 5 Mar 2009.

Reference 2: http://psmv3.blogspot.co.uk/2018/01/an-introduction-to-lws-n.html.