David Blenkinsop, <blenl@sk.sympatico.ca>, writes:
> Hmmm, having never read up on the Kolmogorov complexity measure, I wonder, is
> this roughly comparable to *entropy*, as in maybe complexity is a more
> interestly structured kind of "messiness" or something like that? That would
> make a certain amount of sense to me, if consciousness gets an objective
> definition at least in part from fullfilling a math "touchstone" of minimal
> complexity, the Kolmogorov measure being comparable to entropy as a measure of
> randomness.
Yes, I believe Kolmogorov complexity is similar to entropy. K. complexity is defined on abstract strings of characters, while entropy is a property of physical systems, and the mathematical formulation is different, but they seem to measure much the same thing.
> The problem with this is, if you look at entropy as such, the true definition
> of it is apparently quite dependent on the knowledge of any given observer
> (notwithstanding that thermodynamics texts often depict entropy as a strictly
> objective measure of some quantity "contained" in a system). In contrast to
> the common, objective, idea of entropy, Chapter 4 of Drexler's _Nanosystems_
> text talks about a system's entropy being dependent on the knowledge that an
> outside observer happens to have. Basically, highly "orderly" systems, like
> crystals, are "orderly" just because it's so much easier for a scientist to
> measure and write down an accurate expression of where all the crystal's atoms
> are supposed to be, this is in contrast to a high entropy system like a gas,
> where measurements leave a lot of uncertainty about exactly where the atoms
> are. In other words, the entropy is not really a local, objective, property at
> all, instead it depends on what the observer knows or is able to find out! As
> a fairly strong impression, doesn't it seem that the Kolmogorov complexity is
> going to be a lot like this, that we're not going to get anything objective
> out of it, for defining a state of objective material consciousness?
How, then, would you explain the third law of thermodynamics, which says that closed physical systems always increase (or at least never decrease) their entropy? This is an objective description of the behavior of physical systems, and does not depend on the state of knowledge of any observer. Liquids evaporate to form gasses, no matter what anyone thinks of the matter.
Where the subjective component comes in, I think, is in terms of our interpretation of what the system is doing. We define what are liquids and what are gasses, and in making that definition we classify more systems as gasses than as liquids (there are more ways molecules can be arranged which fall into the category of "gas" than of "liquid"). So our interpretation of what happens depends on our definitions, and that is where there is a subjective component. But the behavior of the system is independent of our thoughts.
In the case of Kolmogorov complexity, the mathematics does not include a subjective element in quite the same way, but it does leak in. K. complexity is described in terms of some idealized computer which looks at the situation, but there are an infinite number of such computers, and each will come up with a different value for the complexity. You can show that, in some sense, they won't disagree too drastically over the broad range of all possible strings, but there is still room for considerable disagreement.
> Maybe the best approach here is just to admit that there isn't any truly
> objective separation between conscious matter and unconscious, at least
> nothing of an objectively *scientific* nature.
In terms of the dilemma I raised, the question is whether there is an objective fact of the matter whether a given system is conscious or not. Can you imagine that it is truly possible that some other person is not conscious? Not just that they might not be conscious, but that it is as legitimate to say that they aren't conscious as that they are, and likewise that it is as legitimate to say that your kitchen sink is conscious as that it is not.
Unless you can accept this level of subjectivity of consciousness, you can't evade the dilemma. There are points of view from which the brain and the sink run the same program. If all such interpretations are equally valid (rejecting my argument that some such interpretations are objectively more valid than others), then we may equally validly decide that the two systems are conscious or not.
Hal