Maxwell's Demon, Physical Information, and Hypercomputation

The second law of thermodynamics is one of the cornerstones of physics. Indeed, even among the most well-tested fundamental scientific principles, it enjoys a somewhat special status, prompting Arthur Eddington to write in his 1929 book The Nature of the Physical World rather famously:

The Law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations—then so much the worse for Maxwell's equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

But what, exactly, is the second law? And what about it justifies Eddington's belief that it holds 'the supreme position among the laws of nature'?
In order to answer these questions, we need to re-examine the concept of entropy. Unfortunately, one often encounters, at least in the popular literature, quite muddled accounts of this elementary (and actually, quite simple) notion. Sometimes, one sees entropy equated with disorder; other times, a more technical route is taken, and entropy is described as a measure of some thermodynamic system's ability to do useful work. It is wholly unclear, at least at first, how one is supposed to relate to the other.
I have tackled this issue in some detail in a previous post; nevertheless, it is an important enough concept to briefly go over again.

The Universal Universe, Part IV: Computational Complexity

Let me start this post on a personal note and apologize for the unannounced break -- I was on vacation in Norway, and, due to poor planning on my part, had an exam right afterwards, which kept me from attending to the blog as I planned.
It all turned out for the best in the end, though, since during my stay in Norway, I stumbled across this great essay by Scott Aaronson (discussed on his blog here), which alerted me to something I haven't paid a lot of attention to, but should have -- the field of computational complexity, and especially its implications for philosophy. Having now had some time to digest the contents, I think there's some important issues for me to think, and write, about.
Of course, I was aware of the field of computational complexity and its basic notions prior to reading that essay, but thought of it as in some way concerning 'merely' problems of practicality -- making the classic philosopher's error (not that I'm a philosopher, but this apparently doesn't keep me from committing their errors) of being content with showing something 'in principle' possible, ignoring the issues involved in making it possible 'in practice' as mere technicality.
Aaronson, now, has taken up the challenge of breaking this unfortunate habit, and does so with great clarity, showing that often enough, thinking about merely what is possible in principle, or, in more appropriate terms, what is computable, without thinking about the difficulty involved in actually undertaking that computation, misses most of the good stuff. One particularly interesting argument is his resolution of the so-called 'waterfall problem', which essentially poses that any physical process can be interpreted as implementing any computation, making thus the proposal that sentience can come about merely through computation somewhat suspect -- apparently forcing us to conclude that if there is a computation that gives rise to sentience, every (or nearly every) physical system can be viewed as implementing that computation, and hence, giving rise to sentience.

Consciousness Explained Anyway

Today, we are going on a slight diversion from the course of this blog so far, in order for me to write down some thoughts on the nature of human consciousness that have been rattling around in my head.
In a way, this is very apropos to the overarching theme of computationalism (which I personally take to be the stance that all of reality can be explained in computable terms, a subset of physicalism) that has pervaded the posts so far (and will continue to do so), because the idea that consciousness can't be reduced to 'mere computation' is often central to supposed rebuttals.
In another way, though, consciousness is far too high-level a property to properly concern ourselves with right now; nevertheless, I wanted to write these things down, in part just to clear my head.
My thoughts on consciousness basically echo those of the American philosopher Daniel Dennett, as laid out in his seminal work Consciousness Explained. However, while what Dennett laid out should perhaps most appropriately be called a theory of mental content (called the Multiple Drafts Model), I will in this (comparatively...) short posting merely attempt to answer one question, which, however, seems to me the defining one: How does subjective experience arise from non-subjective fundamental processes (neuron firings, etc.)? How can the impression of having a point of view -- of being something, someone with a point of view -- come about?