Derek asked whether I was agreeing with Roger Penrose by suggesting that we are missing some fundamental key to the understanding of consciousness and reality generally. I'm not arguing that the brain can only be simulated by a quantum computer. I'm only suggesting that the 'deep' problems always seem to be just over the horizon. There seems to be something essentially hard about distinguishing thoughts from the titanic amount of computations in the brain. Which ones are contributing towards consciousness, and what is the shape of the algorithms that they form? Do we approach a godellian paradox when we use consciousness to analyze consciousness?
The universe is the densest possible representation of the universe, and therefore you need processing power and storage on the same level of complexity to fully understand it. However the reductionist approach states that you can understand the processes of a complex system, without possessing 100% information about the system. Surely the same is true of the brain, we will have to make simplifications to represent the brain in a brain but not necessarily gross ones. So what I'm suggesting is that we need newer powers of analysis to make such understanding possible to humans, either that or we must use something superhuman (such as a very large computer) to analyze the processes involved. To do that the computer would have to be very smart indeed, and thus we find ourselves at another paradox.
The Church-Turing thesis proves that any Turing machine can simulate any other given enough storage capacity, the question is how much storage capacity is required to truly characterize the processes in the brain? Is it something on another level of complexity or is it simple? Some have argued that consciousness is the sensation of having a nervous system – there is no mystery to consciousness – all things have it to greater or lesser degrees, depending on the sophistication of the ways that they interact with the universe.
These are the hard questions of the day, and is it possible that they are not solvable?