On Wed, Aug 24, 2011 at 03:12:31PM -0700, David Nyman wrote:
> This paper presents some intriguing ideas on consciousness, computation and 
> the MWI, including an argument against the possibility of consciousness 
> supervening on any single deterministic computer program (Bruno might find 
> this interesting).  Any comments on its cogency?
> http://arxiv.org/abs/gr-qc/0208038
> David

I've done a partial read of this paper, and already in section 5 I see
a problem.

In section 5, Eastmond attempts to derive a paradox from the
assumption of an infinite number of observer moments in a lifetime (as
might be the case with quantum immortality, for example).

He starts with a mapping between the lifetime of OMs and the rational
numbers between 0 & 1. Then he argues that in observing one's current
observer moment, determining which half of the unit interval the OM is
mapped to gives 1 bit of information. Further subdividing the interval
gives, of course, more bits of information. He then concludes that an
infinite number of bits of information is needed to specify the OM.

The paradox is derived by using Cantor's argument to show that there
are an uncountable number of infinite length bitstrings, many more
than the OMs.

The problem with this argument is that all rational numbers, when
expressed in base2, ultimately end in a repeating tail. In decimal
notation, we write dots above the digits that repeat. Once the
recurring tail has been reached, no further bits of information is
required to specify the rational number. Another way of looking at it
is that all rational numbers can be specified as two integers - a
finite amount of information.

I notice this paper is an 02 arXiv paper, so rather old. It hasn't
been through peer review AFAICT. There was a bit of a critique of it
on Math Forum, but that degenerated pretty fast.


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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