>From: hal.domain.name.hidden ("Hal Finney")
>To: everything-list.domain.name.hidden
>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.
>
>Hal Finney
>
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Received on Thu Jan 27 2005 - 21:04:51 PST