Bruno raises a lot of good points, but I will just focus on a couple
of them.
The first notion that I am using in this analysis is the assumption that a
first-person stream of consciousness exists as a Platonic object. My aim
is then to estimate the measure of such objects. I don't know whether
people find this plausible or not, so I won't try to defend it yet.
The second part, which I know is more controversial, is that it is
possible to represent this object as a bit string, or as some similar,
concrete representation. I think there are a couple of challenges
here. The first is how to turn something as amorphous and intangible
as consciousness into a concrete representation. But I assume that
subsequent development of cognitive sciences will eventually give us a
good handle on this problem and allow us to diagram, graph and represent
streams of consciousness in a meaningful way. As one direction to pursue,
we know that brain activity creates consciousness, hence a sufficiently
compressed representation of brain activity should be a reasonable
starting point as a representation of first-person experience.
Another issue that many people have objected to is the role of time.
Consciousness, it is said, is a process, not a static structure such as
might be represented by a bit string. IMO this can be dealt with by
interpreting the bit string as a multidimensional object, and treating
one of the dimensions as time. See, for example, one of Wolfram's 1-D
cellular automaton outputs:
http://en.wikipedia.org/wiki/Image:CA_rule30s.png
We see something that can alternatively be interpreted as a pure bit
string; as a two-dimensional array of bits; or as a one-dimensional
bit string evolving in time. In the same way we can capture temporal
evolution of consciousness by interpreting the bit string as having a
time dimension.
An important point is that although there may be many alternative ways
and notations to represent consciousness, they should all be isomorphic,
and only a relatively short program should be necessary to map from one
to another. Hence, the measure computed for all of these representations
will be about the same, and therefore it is meaningful to speak of this
as the measure of the experience as a platonic entity.
Bruno also questioned my use of a physical universe in my analysis.
I am not assuming that physical universes exist as the basis of reality.
I only expressed the analysis in that form because we were given a
particular situation to analyze, and that situation was expressed as
events in a single universe.
The Universal Dovetailer does not play a principle role in my analysis,
because it does not play such a role in Kolmogorov complexity. At most,
the Universal Dovetailer can be used as a heuristic device to explain
what it might mean to "run all computatations" in order to explain
K complexity.
I think one difference between K complexity and Bruno's reasoning with the
Universal Dovetailer is that the former focuses on sizes of programs while
Bruno seems to work more in terms of run time. In the K complexity view,
the measure of an information object is (roughly) 1/2^L, where L is the
size of the shortest program which outputs that object. Equivalently,
the measure of an information object is the fraction of all programs
which output that object, where programs are sampled uniformly from
all bit strings (or from whatever the input alphabet is for the UTM).
This does not have anything to do with run time. Some bit patterns
may have short programs that take a very long run time to output them.
Such bit patterns are considered to have low complexity and high measure,
despite the long run time needed.
I think Bruno has sometimes said that the Universal Dovetailer makes some
things have higher measure than others because they get more run time.
I'm not sure how this would work, but it is a difference from the
Kolmogorov complexity (aka Universal Distribution) view that I am using.
Okay, those are some of the foundational questions and assumptions that
I think are raised by Bruno's analysis. The rest of it goes through as
I have described many times.
Hal
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Received on Thu Jun 22 2006 - 14:30:05 PDT
