On Sat, 21 Aug 1999 GSLevy.domain.name.hidden wrote:
> In a message dated 99-08-19 18:46:00 EDT, Jacques Mallah writes:
> << Since the number of implementations is infinite and they are
> parameterized by continuous parameters, only infinite groups of them have
> any significance. This is analagous to coloring a surface. It does not
> matter if one point on a surface is colored, what matters is the *area*
> that is colored. Measure is analagous to such an area. It is
> quantifiable because just as two people have twice as much consciousness
> as one person, doubling the number of implementations would double the
> measure. >>
>
> Jacques, I have a lot of trouble understanding what your conception of
> measure is. Can it be expressed in some kind of units such as bits for
> example? If it it can be expressed in bits, how can making two copies of an
> identical document increase the amount of information (i.e., measure) ?
It is not related to quantities of information such as bits.
A document is not the sort of thing that can have measure; an
observation is, and with computationalism, a computation is. I suppose
that to a structuralist such as Wei Dai, the information written on a
document can give rise to consciousness and thus have measure.
> Or is measure just the number of copies of the document without regard to the
> information? Then, what possible significance (your word) would there be in
> differentiating between the original and the copy?
Again, documents don't have measure in the first place. Measure
is the amount of consciousness, which I take to be proportional to the
number of implementations of a computation. Effective probabilities are
proportional to the measure, but the measure is a more fundamental
concept.
> If measure is conserved, does making a copy spreads the measure between the
> original and the copy, and thus the original ends up with less measure?
(If by copy it is understood that one makes a working copy of a
computer and runs the program, then) yes.
> If measure is not conserved, does making a copy generates more measure?
(as above) yes, at least that's what happens in my view.
> You use the word "significance." Why? Is it the same as saying that measure
> has "value?" Is an original more "valuable" or have more measure than the
> copy? Furthermore, why would deleting either the original or the copy be a
> loss in measure?
Value is subjective. To a 'good' person, measure does have
value. 'Significance' in my above quote refers to the fact that a single
point, relative to an infinite number, has measure zero. You can say that
the switch from finite to infinite numbers forces us to use a renormalized
way of quantifying measure. I.e. if we define the measure of Bob at t0
to be 1, and in our model that person has N copies, then as N approaches
infinity the measure of a single copy approaches 0. But a person with 2N
copies would have measure 2, and this ratio of 1:2 is preserved in the
limit.
> Could you please assign some units to quantify measure so that we can assess
> its conservation (and other) properties. I believe that this is the first
> step that must be taken to have a meaningful discussion.
It is dimensionless. You can change units by multiplying it by
any constant number, and that number can be infinite as in the above
example with Bob.
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Thu Aug 26 1999 - 11:41:36 PDT