From: Stathis Papaioannou (stathisp@gmail.com)
Date: Tue Mar 18 2008 - 20:54:55 MDT
On 19/03/2008, Matt Mahoney <matmahoney@yahoo.com> wrote:
> 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.
Typically, yes. I guess it's possible to have no net information gain,
or even net information loss over time, and still experience a
continuous stream of consciousness. But even in dementia, no mental
state will contain information that is contained in a subjectively
future state, even if the total information in a future state is
actually less.
> 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.
Does S(n+1) have to be generated by P from S(n) or is the raw fact
that S(n) and S(n+1) simply occur sufficient to generate subjective
continuity? Lee would argue that the causal link is important, I would
say that the moments of consciousness order themselves due to a rule
such as you describe.
> 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.
Right: the direction, or even existence, of time in the real world (if
such there is) is irrelevant. S(n+1) could objectively precede S(n)
and it would make no subjective difference.
> 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.)
What if each S has to be implemented on real hardware in a finite
single world cosmology? I don't see how you could fit in more states
by making the difference between them smaller and smaller, since at
some point there will be no subjective difference between one state
and the next.
-- Stathis Papaioannou
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