Sophistry has a smell. Sometimes an argument smells of it, but it may
be a lot harder to pin down where the specious logic is – especially
when it’s all dressed up in a mathematical formalism that may be
inaccessible to the non-mathematician/logician. However the problem
with the arguments relating to consciousness in this paper is not so
hard to pin down, and indeed Stephen King is on the right track with
his objection.

Eastmond argues that an infinite conscious lifetime is impossible
because, in ‘finding oneself’ at a particular point in that lifetime,
one would have to gain an infinite amount of knowledge, which is
absurd.  He concludes that such an infinite lifetime is in principle
impossible. The flaw lies in the way the author glosses over the
notion of “gaining information”. In examining the problem, he treats
this “gaining of information” as if it occurred magically the moment
one finds oneself at a certain point in a lifetime, but in fact such
information has to be acquired by a concrete computation. For example,
if I am to gain information about my current lifetime position, I need
to examine a calendar and compare this to stored or acquired knowledge
about my date of birth. In the case of an infinite lifetime, the size
of the computation required is arbitrarily large (but finite) in the
case of an infinite lifetime with a lower bound (a life time with a
starting point), or simply uncomputable in the case of an infinite
lifetime with no lower bound.  This is the same as saying that one
cannot calculate the age of a person who has always existed. The fact
that such a person’s age is uncomputable does not however mean that
such a person cannot exist.

The favoured theory in modern cosmology suggests that the universe is
spatially infinite. How then do we calculate the position of our
planet in this universe? If astronomers had infinite access to the map
of the universe, they could still never calculate our position,
because the calculation would be infinite. Given that time is known to
be interconvertible with space, it follows that the same logic would
apply to locating an event on an infinite timeline. The situations are
mathematically indistinguishable, yet this does not prove away the
spatially infinite universe theory.

In an infinite lifetime with no lower bound, we can never know our
age, and the amount of information ‘gained’ when we find ourselves at
a point of time in such a lifetime is a function of how much
information we can process (concrete processing limitations) and the
amount of information available to us about our position. Whichever is
smaller forms the limit.

There is also a flaw in the reasoning in relation to the proposed
conscious computer which resets itself in order to generate repeated
(and therefore infinite) conscious moments. We must remember that the
information gain is made by the conscious entity and must form part of
its conscious computation. Otherwise where is the supposed gain
occurring? All we would have is an objective description of a
perfectly mathematically conceivable situation – an infinite set of
values for the set of conscious moments, or an infinitely long string
to define a moment within that set.  So the computer must gain the
information. But it cannot do so if it continually resets. The
invocation of thermodynamics does not help if the computer cannot
access information about entropy. It can escape this problem with an
endless incrementing loop, but then it needs an infinite memory to
store this growing string. Its computational limitations inevitably
force its incrementing register to 'clock over' (like Y2K) at some
point, causing it to repeat itself.

So  unless we grant the possibility of an infinite mind/computer, an
infinite lifetime necessarily entails the repeat  of conscious
experience (just as cosmologists grant that the spatially infinite
universe with locally finite information must entail a Nietzschean
infinite recurrence). Such a lifetime is perfectly imaginable. Indeed,
theoretically an infinite lifetime with no repetition is possible with
infinite computational resources.
With these flaws the remaining argument regarding the impossibility of
a deterministic and conscious computer need not even be addressed,
since they are built on unsound foundations.


On Aug 25, 8:12 am, David Nyman <david.ny...@gmail.com> 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

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