From: Matt Mahoney (firstname.lastname@example.org)
Date: Wed Mar 19 2008 - 14:10:52 MDT
--- Stathis Papaioannou <email@example.com> wrote:
> On 19/03/2008, Matt Mahoney <firstname.lastname@example.org> 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
> > draw any conclusions. Suppose you model a sequence of mental states
> > S(2), ..., S(n) as strings or natural numbers N such that the information
> > between successive states, K(S(i+1)|S(i)) is small, but still larger than
> > information loss, K(S(i)|S(i+1)). An example would be a series of bit
> > 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
> > 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
> > intelligent systems typically gain and lose information this way by
> > 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
> > described by ordering the states S(1) through S(n) using conditional
> > algorithmic complexity to deduce the most recent state. Also, there is
> > perceived interruption of consciousness because what is perceived during
> > 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.
In the model, continuity depends only on the algorithmic similarity of S(n)
and S(n+1). In practice, this would require some communication between the
> > The model has some other interesting implications. For example, it
> > 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
> 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
> > not death: it is not possible to not have experience because for every
> > 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
> > 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.
The model assumes that the set of states is isomorphic to N. Any real
implementation with finite memory must have finite subjective experience. All
implementations must have finite memory because the universe has a Bekenstein
bound of about 10^122 bits.
I realize there is a fundamental conflict because the model says that
consciousness is immortal but any implementation is mortal.
-- Matt Mahoney, email@example.com
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