Dear George,
    Could it be that Consciousness is more related and identifiable with the "processing" of Information than with Information itself? Consider the example often raised (I do not know the original source) of a Book that contained a "complete description" of Einstein's Brain. It was claimed that this book was in fact equivalent to Einstein himself even to the degree that one could "have a conversation with Einstein" by referencing the book. (Never mind the fact that QM's non-cummutativity of canonical conjugate observables make it impossible for *any* classical object to be completely specified in a way that is independent of observational frame, but I digress...)
    It seems to me that hidden in this idea is the assumption that it is possible to enumerate all possible responses that a given object can have with *any other* object and that this enumeration can be faithfully represented in a finite string of symbols. A simple Diagonalization argument proves that this is simply impossible, so why does the idea persist?
    Computer scientist of the stature of Peter Wegner have pointed this out and it seems to have fallen on deaf ears:
    His proposed solution is to start of by considering the use of non-well founded set theory and the logic that follows. I find this proposal to be very interesting because it implicitly involves a means to represent self-referential statements in a way that is non-paradoxical...
    Could it be that the "hard Problem" of consciousness follows inevitably from our hard-headed insistence that the Universe is Classical ("object have definite properties in themselves") in spite of the massive pile of unassailable evidence otherwise? If we treat Consciousness as "what a quantum computer (brain!) does", i.e. process qubits, instead of a classical object, maybe, just maybe we might find the "problem" not to be so intractably "hard" after all! ;-)
----- Original Message -----
Sent: Thursday, July 06, 2006 6:19 PM
Subject: Symmetry, Invarance and Conservation (Was Number and function for non-mathematician)

In the July 1-7 2006 edition of New Scientist there is a review of the book "The Comprehensible Cosmos" by Victor Stenger. You can see here a power point presentation on symmetry by Stenger.

Stenger discusses the idea of symmetry, in particular the work of Emmy Noether who proved that the conservation of energy is a direct consequence of time translation symmetry: the same result is obtained if an experiment is performed now or at a different time.

Other natural laws can be traced to other symmetries: i.e., conservation of momentum to space translation symmetry etc...

I think it may be valuable to express some of our ideas as symmetries/invariances/conservation/equivalence. For example the invariance/conservation of information with regard to the recording substrate is obvious. Information does not change if you transfer it from your hard drive to your floppy (ie., hardware translation symmetry.) This fact, however, may be of far reaching consequence. If one assumes that consciousness is a type of information then consciousness become independent of its physical basis: "The message is independent of the medium!" Or even better: "The message needs no medium!" Marshall McLuhan got it all wrong! :-)

George Levy

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