From: [EMAIL PROTECTED] ("Hal Finney") To: firstname.lastname@example.org Subject: Re: Belief Statements Date: Thu, 27 Jan 2005 12:16:24 -0800 (PST)
It is true that there are some physical systems for which we can predict the future state without calculating all intermediate states. Periodic systems will fall into this category if we can figure out analytically what the period is. But there are other systems where this is thought to be impossible; for example, chaotic systems.
Chaotic systems are ones whose future behavior is sensitively dependent on the current state. Making even an infinitisimal change to the current state will cause massive changes in the future. I don't think it would be possible with any computational model to predict the state of a chaotic system far in the future without computing intermediate states.
My guess is that consciousness as we know it is inherently chaotic. It seems like small changes to our beliefs and knowledge can lead to large changes in behavior. So often we experience being torn between alternate courses of action, where the tiniest change could tip us from one choice to the other.
Neural behavior is inherently chaotic as well. Neurons are believed to sum the recent activity levels on their synapses and when this exceeds a threshold, the neuron suddenly and catastrophically fires a nerve impulse. It then goes through a refractory period (about 1 millisecond) in which it is unable to fire again until it has "rested" and regathered its strength, at which point it goes back to summing its inputs. If we plotted the net input strength to the neuron, it would be an irregular line with lots of little jags and bumps, and whenever it manages to exceed a certain level, there is a sudden firing. Probably we would often see the stimulation level approach that threshold line and fall back, not quite meeting the threshold, until we just reach it and another nerve impulse is fired. This kind of sensitive dependence on initial conditions is a recipe for mathematical chaos.
Of course, this is not a rigorous proof, and it is conceivable that consciousness is not in fact chaotic even though it subjectively seems so, and even though its subtrate (the brain's neural net) is. Nevertheless it would be almost unbelievably bizarre to imagine that you could calculate the mental state of an 80 year old man, with all the memories of a lifetime, without actually calculating the experiences that led to those memories.
In Egan's story, the computer is supposed to calculate his conscious experience of the 10th second first, then the 9th second, and so on. Suppose in the first (subjective) second he stutters on saying the number "one", out of nervousness. Then the memory of that stutter will be present as he recites all the other numbers. Perhaps he will enunciate them more carefully in order to compensate. So when the system calculates that 10th second, it has to know what happened during the first second. Those events will be latent in his memories during the 10th second, and may influence his behavior. His conscious reactions to earlier events are in his memory at later times. So I don't see how it could possibly work to calculate the 10th second first.
Two other minor points: in Egan's story, this experiment was not being done on "dust". It was done on an ordinary computer. It was the result of this experiment, which is of course that there was no subjective awareness of the time scrambling, which was supposed to lend credence to the dust hypothesis.
Second, quantum computers cannot efficiently solve NP complete problems, or at least they are not known to be able to. It's possible that ordinary computers can solve NP complete problems; no one has ever proven that they can't (this is the famous P = NP problem of computer science). And if it turns out that ordinary computers can handle them efficiently, then of course quantum computers will be able to as well, since they are a superset of ordinary computers. But if it turns out that P != NP and ordinary computers can't solve NP problems efficiently, there is no evidence that the situation will be different for quantum computers.
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