On 9/19/2011 3:20 AM, Russell Standish wrote:
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?



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.

Exactly why are there not a continuum of OMs? It seems to me if we parametrize the cardinality of distinct OMs to *all possible* partitionings of the tangent spaces of physical systems (spaces wherein the Lagrangians and Hamiltonians exist) then we obtain at least the cardinality of the continuum. It is only if we assume some arbitrary coarse graining that we have a countable set of 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 must dispute this claim because that reasoning in terms of 'two integer' encoding of rationals ignores the vast and even infinite apparatus required to decode the value of an arbitrary pair of 'specified by two integers' values. The same applies to the notion of digital information. Sure, we can think that the observed universe can be represented by some finite collection of finite bit strings, but this is just the result of imposing an arbitrary upper and lower bound on the resolution of the recording/describing machinery. There is no ab initio reason why that particular upper/lower bound on resolution exists in the first place.

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.


Ideas are sometimes like vine or a single malt whiskey that must age before its bouquet is at its prime.



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