On 8/8/2016 6:18 AM, Stathis Papaioannou wrote:
On Monday, 8 August 2016, Brent Meeker <[email protected] <mailto:[email protected]>> wrote:On 8/7/2016 11:20 AM, Bruno Marchal wrote: Not necessarily. A digital computer also requires that time be digitized so that its registers run synchronously. Otherwise "the state" is ill defined. The finite speed of light means that spacially separated regions cannot be synchronous. Even if neurons were only ON or OFF, which they aren't, they have frequency modulation, they are not synchronous. Synchronous digital machine can emulate asynchronous digital machine, and that is all what is needed for the reasoning. If the time variable is continuous, i.e. can't be digitized, I don't think you are correct.If time is continuous, you would need infinite precision to exactly define the timing of a neuron's excitation, so you are right, that would not be digitisable. Practically, however, brains would have to have a non-zero engineering tolerance, or they would be too unstable. The gravitational attraction of a passing ant would slightly change the timing of neural activity, leading to a change in mental state and behaviour.
I agree that brains must be essentially classical computers, but no necessarily digital. The question arose as to what was contained in an Observer Moment and whether, in an infinite universe there would necessarily be infinitely many exact instances of the same OM. But having a continuous variable doesn't imply instability. First, the passing ant is also instantiated infinitely many times. Second, if a small cause has only a proportionately small effect then there is no "instability", more likely the dynamics diverge as in deterministic chaos. But in any case it would allow an aleph-1 order infinity of OMs which would differ by infinitesimal amounts.
But I also question the coherence of this idea. As discussed (at great length) by Bruno and JKC, two or more identical brains must instantiate the same experience, i.e. the same OM. So if there are only a finite number of possible brain-states and universes are made of OMs, then there can only be a finite number of finite universes.
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