Kevin wrote:
Kevin's random babbling follows:
Is there a working definition of what "complexity" exactly is? It seems to be quite subjective to me. But setting that aside for the moment...
I think the situation is similar to that with the concept of "intelligence" in the sense that it means different things to different people. Indeed there are many formal definitions of various kinds of complexity, each measuring different things.
For example, is a book on number theory complex? Well in the everyday sense of the word most people would say that it is. In the Kolmogorov sense it's actually quite simple as the theorems all follow from a small set of axioms and hence it is quite compressible. In the logical depth sense (that is, how many computation cycles would be required to reproduce the work) the complexity is quite high. Another example might be breaking prime number based encryption systems -- there is little information complexity but a lot of computation time complexity.
Anyway, something can be very complex in one sense while being very simple in another. This just seems to show that our intuitive vague notion of complexity seems to cover a number of very loosely related things. Which is a problem when people write about complexity without being precise about what kind of complexity they are taking about. Basically they could be talking about just about anything, which is one of the reasons that I gave up reading non-mathematical papers on complexity and systems.
Strictly speaking, the noumenal and the phenomenal cannot be separated or thought of distinctly IMO. From this viewpoint, complexity is merely apparent and not fundamentally "real complexity"...
I'd agree to an extent. Though if all viewpoints have some common deep down underlying basis of reference such as Turing computation then perhaps this is THE ultimate viewpoint with which to view the problem? This is essentially the approach Kolmogorov compelexity takes. As we move away from UTMs towards complex AGI systems the apparent complexity of things will of course start to change in the sense that you suggest. However many of the more fundamental kinds of complexity (like Kolmogorov and logical depth above) will still hold firm for very complex things. In other words: just because your AGI is really smart doesn't mean that it can now do a large NP hard problem in a small amount of time --- the problem is likely to remain very "complex" in some sense (excluding weird stuff like finding new laws of physics and computation etc... of course).
Cheers Shane
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