On 09 Aug 2016, at 02:57, Stathis Papaioannou wrote:
On 9 August 2016 at 03:52, Brent Meeker <meeke...@verizon.net> 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.
Even in a continuum, there would be brain states and mental states
that are effectively identical to an arbitrary level of precision.
We maintain a sense of continuity of identity despite sometimes even
gross changes to our brain. At some threshold there will be a
perceptible change, but the threshold is not infinitesimal.
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.
A human brain can probably only have a finite number of thoughts,
being of finite size, but a turing machine is not so limited.
Turing machines, combinators, programs, numbers, ... are finite
entities. The universal Turing machine is a number/finite-code. During
any computation, the Turing machine look only at a finite portion of
its tape, but it can be as great as needed. Similarly, the humans can
see only finite number of things at a time, and when they have a
memory brain overflow, they will use wall, or paper, or magnetic tape.
It is the essence of a machine to be a finite entity---I would say,
and it is the essence of a digital machine to be a finite entity
admitting a finite description (that we can put into a number, and
store on a disk).
Bruno
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Stathis Papaioannou
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