My last post worked (I got it in my email). I'll repost one later and then
post on the measure thread - though it's still a very busy time for me so maybe
not today.
--- On Mon, 2/22/10, Jesse Mazer <laserma...@hotmail.com> wrote:
> OK, so you're suggesting there may not be a one-to-one relationship between
> distinct observer-moments in the sense of distinct qualia, and distinct
> computations defined in terms of counterfactuals? Distinct computations might
> be associated with identical qualia, in other words?
Sure. Otherwise, there'd be little point in trying to simulate someone, if any
detail could change everything.
> What about the reverse--might a single computation be associated with
> multiple distinct observer-moments with different qualia?
Certainly. For example, a sufficiently detailed simulation of the Earth would
be associated with an entire population of observers.
> You say "Suppose that a(t),b(t),and c(t) are all true", but that's not enough
> information--the notion of causal structure I was describing involved not
> just the truth or falsity of propositions, but also the logical relationships
> between these propositions given the axioms of the system.
OK, I see what you're saying, Jesse. I don't think it's a good solution though.
First, you are implicitly including a lot of counterfactual information
already, which is the reason it works at all. "B implies A" is logically
equivalent to "Not A implies Not B". I'll use ~ for "Not", "-->" for
"implies", and the axiom context is assumed. A,B are Boolean variables / bits.
So if you say
A --> B
B --> A
that's the same as saying
A --> B
~A --> ~B
which is the same as saying B = A. Your way is just a clumsy way to provide
some of the counterfactual information, which is often most consisely expressed
as equations. So if you think you have escaped counterfactuals, I disagree.
The next problem is that for a larger number of bits, you won't express the
full dynamics of the system. For example with 10 bits, there are more possible
combinations than your system will have statements. I guess you see that as a
feature rather than a bug - after all, it's what allows you to ignore "inert
machinery". I don't like it but perhaps that's a matter a taste.
Now, that may work OK for bits, but it really seems to lose a lot for more
general systems. For example, suppose A,B,C are trits, or perhaps qubits, or
real numbers such as positions. Your logical implications remain limited to
Boolean statements. Do you really want to disregard so much of the system's
dynamics? I see no reason to do so when using counterfactuals in the usual way
works just fine. I consider any initial value problem to be a computation,
including those that use differential equations.
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