On 08 Aug 2016, at 19:52, Brent Meeker wrote:
On 8/8/2016 6:18 AM, Stathis Papaioannou wrote:
On Monday, 8 August 2016, Brent Meeker <meeke...@verizon.net> 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.
"OM" is ambiguous. I guess you mean the same 1-OM. I say this, because
many people can easily confuse a "OM" with a computational state, when
in the computationalist frame. But the whole goal here is to show that
a "1-OM" is associated, from the 1-OMs' view, to an infinity of 3p-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.
There can only be a finite number of finite universes, if there are
universes. But with the FPI, universe are emerging pattern coming from
a statistics on all infinite works of all finite universal machine/
number, so the physical reality is somehow constrained to have an
infinite and continuous, and non computable, components. If only the
random oracle generated by the iterated self-duplication, from the
first person views.
Theoretical computer science makes sense of all this, thanks to the
incompleteness phenomenon, and the intensional nuances it brings for
knowledge and observation, as opposed to relative belief/or proof.
Bruno
Brent
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