Hitoshi Kitada (hitoshi@kitada.com)
Tue, 6 Apr 1999 15:16:03 +0900
Dear Ben,
Thank you for your articulate questions and the expression of the
understanding of the proof. You are the first who expressed explicitly the
understanding of proof of theorem 2 (except for the referee), since the paper
was published. I have been suspicious that nobody could understand the proof.
Thanks!
----- Original Message -----
From: Ben Goertzel <ben@goertzel.org>
To: <time@kitada.com>
Sent: Tuesday, April 06, 1999 7:47 AM
Subject: [time 183] Re: [time 180] Re: [time 178] Questions
>
> Hi,
>
> OK thanks so much for the clarification, I understand much better now...
>
> >Axiom 1 (and the definition 2 of local systems) asserts that the Hilbert
spaces
> >H_{n \ell} and H_{n' \ell'} associated to L1 and L2 are different.
>
> Yes, this is the crux of it all. What justifies this assumption? Is this
> a standard
> assumption of physical theory ... I suspect not....
I think it is not standard, but I will clarify the meaning below, which
justifies the assumption.
>
> Doesn't it violate common sense in some way -- i.e. if particles in distant
> locations
> have interacted before, they may be correlated in their patterns of
> movement even
> when you subtract off the center of mass.
You are right:
The particles are correlated in their patterns of "movement." But it is so,
_as far as_ they are considered to "move" according to the "time" of the
system to which the particles belong. In other words, the reference frame of
the "movement" is the space-time of the system. The "before" in the above
quotation of your opinion should thus be understood the "before" measured in
the frame of this "time" of the system. Namely space-time is proper to each
local system. This is the first point.
Second, here is another implicit assumption. The particles' "correlation"
cannot be known unless the correlation is observed or measured. If no one
observes the system, the correlation cannot be known, or is forgotten. The
forgotten correlation cannot be traced further. One needs to start to measure
other
systems similar to that one, in order to reproduce the observation. In this
sense, the word "observation" has an implicit assumption behind it that the
_different_ observations could be identified if one's memory tells one that
the situation looks the same as before ("before" in the time coordinate of the
one's, and "one" can be a set of observers, e.g., a set of modern physicists,
that has a time coordinate which might have begun in the 16th century or so
(with Galileo Galilei and/or others?)).
I distinguish this difference of observations. Thus local systems have
different Hilbert spaces as in axiom 1, even when they have common particles.
In other words, the local system is the notion that describes the object of
observation, that is different from time to time (time is again the time of
the observer) and from observer to observer.
>From this viewpoint that distinguishes the difference of observations,
subjectivity is important. The observer chooses the object of observation. And
according to its memory (or records), it classifies the observations with
positing some criteria. Local system gives the raw data that have not been
given any classification. The pair of the observer and the local system
observed by the observer is the fundamental element of this formulation. In
this sense, the observation cannot be separated from the observer. At this
point, your observation in your article "Chance and Consciousness" is
important:
> So consciousness is distributed rather than unified. But what does
> neuropsychology tell us about the <b>role</b> of consciousness? It tells
us,
> to put it in a formula, that consciousness serves <b>to group disparate
> features into coherent wholes</b>. This conclusion has been reached by many
> different researchers working under many different theoretical
presuppositions.
> There is no longer any reasonable doubt that, as Umilta (1988) has put it,
"the
> formation of a given percept is dependent on a specific distribution of
focal
> attention."<p>
Here you mention that what consciousness is doing is "to group disparate
features into coherent wholes." Observation is the same: it is a grouping
_disparate_ features into one whole. This is the pair of a local system and
the observer: the local system is the whole that the conscious observer groups
into one. It is arbitrary except for the observer's choice.
Further, Consciousness of the observer gives the QM nature of the observed
local system a classical nature as you describe:
> In more modern language, what quantum physics tells us is that an event
does
> not become <b>definite</b> until someone observes it. An unobserved quantum
> system remains in an uncertain state, a superposition of many different
> possibilities. Observation causes "collapse" into a definite condition,
which
> is chosen <b>at random</b> from among the possibilities provided. This
> peculiar but well-
>
> established
> empirical fact makes it natural to associate <b>consciousness</b> with
> <b>quantum measurement</b> (Wigner, 1962; London and Bauer, 1983; Goswami,
> 1990).<p>
and
> Consider the classic double-
>
> slit
> experiment. A particle passes through one of two slits in a barrier and
leaves
> a mark on a plate on the other side of the barrier, indicating which slit it
> passed through. If one observes each particle as it passes through the
> barrier, the marks on the plate will be consistent with one's observations:
> "Fifteen hundred through the top slit, six hundred and ninety through the
> bottom slit," or whatever. But if one does <b>not</b> observe the particles
> passing through the barrier, then something very strange happens. There are
> marks on the plate <b>where there shouldn't be any</b> -
>
> -
>
> marks that could not have been made by particles passing through
<b>either</b>
> slit. Instead of passing through the slit like a good particle should, the
> particle acts as if it were a <b>wave</b> in some mysterious medium,
squeezing
> through the slit and then rapidly diffusing. The key point is whether the
> particle was <b>looked at</b> or not.<p>
This corresponds to my assumption that the observed values must be classical
(axiom 4, 5).
Subjectivity thus plays two roles: 1) grouping the objects that the observer
observes, and 2) converting the QM values to Classical values.
As we have seen, 1) corresponds to the notion of local system that is
arbitrary except for the observer's choice, and 2) corresponds to axioms 4 and
5 and the related assumptions.
We thus see the parallel between your theory and mine. In my opinion, it looks
more than parallel, even they seem to be stating the same thing in different
contexts.
I should be happy if you would let us know your opinions and/or impressions on
these points.
I tried to add some of my vague impressions about Big Bang theory, but
rethought that they are too vague yet to post here.
Best wishes,
Hitoshi
>
> what am I misunderstanding this time? ;)
>
> ben
>
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