From: Matt Mahoney (matmahoney@yahoo.com)
Date: Tue Mar 18 2008 - 18:11:18 MDT
--- Stathis Papaioannou <stathisp@gmail.com> wrote:
> On 18/03/2008, Lee Corbin <lcorbin@rawbw.com> wrote:
>
> > > Now, suppose the first operator transfers the final state of his
> > > machine *as well as* every other possible state, again not telling
> > > which is which, and the second operator just happens to choose the
> > > right state to input. Is there interruption of consciousness?
> >
> > No interruption. The last state on the Australian machine is
> > identical to the first state on the Vienna machine.
>
> Sorry for labouring the point (I'd be surprised if anyone other than
> you and I have followed the thread this far) but I intended that there
> be no overlap. The Australian operator reads the last state S(n) of
> his machine, and transfers this information to the Vienna operator who
> works out (from knowledge of the machine's operation) that he must
> start up his machine in state S(n+1). In this way the combined
> machines + operators can reliably carry out the same computations as a
> single machine. But if the Australian operator simply provides a list
> of all possible states, knowing but not telling which one is S(n),
> that seems to me exactly the same as providing no information at all;
> i.e. the same as if the Vienna operator knew nothing about the
> antipodean device and simply tried random states, one of them just
> happening to be S(n+1). How does this affect whether consciousness is
> interrupted?
I admit I haven't followed the whole thread. But if you insist that
consciousness exists, then you need a plausible mathematical model of it to
draw any conclusions. Suppose you model a sequence of mental states S(1),
S(2), ..., S(n) as strings or natural numbers N such that the information gain
between successive states, K(S(i+1)|S(i)) is small, but still larger than the
information loss, K(S(i)|S(i+1)). An example would be a series of bit strings
where S(i+1) is formed by appending a random bit to S(i). In this case,
K(S(i+1)|S(i)) = 1 > K(S(i)|S(i+1)) = 0. The inequality defines the direction
of perceptual time. Furthermore, K(S(j)|S(i)) quantifies the perceptual
experience that occurs from time i to time j. The model is plausible because
intelligent systems typically gain and lose information this way by evolving
slowly over time.
If you accept this model, then it is possible to implement the scenario you
described by ordering the states S(1) through S(n) using conditional
algorithmic complexity to deduce the most recent state. Also, there is no
perceived interruption of consciousness because what is perceived during the
transition is described by a small program P that inputs S(n) and outputs
S(n+1) in a perceived time of |P|, no different than any other step.
The model has some other interesting implications. For example, it implies
the possibility of conscious experience in more than one dimension of time, or
in a type of time where there is no clear distinction between past and future.
In our directed one-dimensional model, it implies the existence of birth but
not death: it is not possible to not have experience because for every state
S(n) there is an infinite sequence S(n+1), S(n+2) such that each
K(S(n+i+1)|S(n+i)) is small. (However, the sequence going back in time is
finite.)
Although you can perceive the death of others, you cannot perceive your own
death. The model implies a multiverse because for each state S(i) in N there
are many states S(j) such that K(S(j)|S(i)) is small. For every universe
where you die at time t there is another where you don't, and you continue to
experience in that other universe.
Finally, the model implies that you have conscious experience because N
exists.
-- Matt Mahoney, matmahoney@yahoo.com
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