Stephen P. King (email@example.com)
Fri, 17 Sep 1999 12:34:37 -0400
Dear Hitoshi, Bill, and Friends,
Here I go again! ;-) We are getting back to the problem that Vaughan
Pratt addresses in his paper ratmech.ps
(http://boole.stanford.edu/chuguide.html#ratmech) The relation between
noumenon and phenomenon is reflected in the mind-body problem to which a
solution is addressed. I am unhappy that the paper is very difficult to
comprehend as it is written in the language of theoretical computer
science, but I am working hard to translate it over for our use. (BTW, I
understand Lance's objections, but we do need some falsifiability in our
models of the world!)
Hitoshi Kitada wrote:
> Dear Bill,
> Bill <WDEshleman@aol.com> wrote:
> Subject: [time 775] Re: [time 771] Re: Noumenon and Phenomenon
> > Hitoshi,
> > [WDE]
> > > > Kant believes that the category of cause and effect applies only to
> > > > phenomena; cause and effect does not apply to the noumena.
> This statement seems to have a common part with Leibniz' thought as referred
> to at the end of this response.
Yes, I see this also and my comment is there also!
> > > >
> > > > The question is then, how do we approach discovery and analysis
> > > > of prospective mathematical candidates to represent the noumena?
> > > >
> > > > The key, I suggest, is in the mathematical meaning of a
> > > > "suspension of cause and effect" for the noumena. This
> > > > "suspension of cause and effect" implies at least two intuitive
> > > > features that the noumena might possess:
> > > >
> > > > 1) The noumena is an orthogonalization of cause and
> > > > effect, or simply an orthogonalization of appropriate
> > > > phenomena.
> > > > 2) Communication between the appropriate phenomena,
> > > > via the noumena, would be instantaneous.
> > > >
> > > I wonder how the ""suspension of cause and effect" for the noumena"
> > > implies the "orthogonalization of cause and effect" and how this
> > > "orthogonalization"
> > > yields the "instantaneousness" of "communication between the
> > > appropriate
> > > phenomena via the noumena." Could you explain more? I seem not to
> > > understand the word "noumena" in your context enough.
> > To me the noumenon is a pure mathematical object with invisible structure,
> > visible only through its properties; i.e., its appropriate phenomena.
> > Since I
> > supply intuitions only, maybe you can tell me what made you decide in the
> > first place, to orthogonalize QM and GR.
> This is not my decision but mathematical intuition led me to it. The first
> thing I noticed on April 22, 1992 just after I had finsihed my investigation
> of N-body QM problem was that the Enss result can be interpreted to define
> local time for each local system. Shortly after that I noticed that the local
> time can be identified with the proper time of GR as the proper time of the
> center of mass of an LS. Then the independence became clear and it was quite
> natural to look the space of the possible states of the universe as the
> formula (1) in axiom 1 in time_I.tex. This formula (1) gives the
> orthogonality (or orthogonalization) of QM and GR. I note that the
> independence is sufficient for the consistent unification of QM and GR.
> Orthogonality is just a convenient way to actualize the independence,
> although I have not tried to find other ways to actualize this independence.
It has seemed intuitive to me that the identification of local time to
the internal behavior of each local system implies that each local
system would have its own phenomena, just as it has its own noumena. It
seems obvious that if a) we consider "noumena" to be "mind" and b) and
assume that somehow "phenomena" is "body" then we are dealing with the
good old mind-body interaction problem!
This problem would be simple if we only had to deal with a single mind
and a single body, this seems to be that Matti assumes mathematically;
but we have a "many body" interacting with "many minds" and vise versa
> > If Kant didn't inspire you, who or
> > what did?
> Nobody or nothing did it. Just my mathematyical intuition. But I think this
> kind of inspiration must have emerged in many minds already.
> > Was it an a priori concept in your mind that managed to surface?
> I do not think it was a priori _only_ in my mind, but I think it is a priori
> in anyone's mind that manages to surface. Anyone has its own inside: The
> outside exists if and only if the inside exists. Then the discrepancy between
> the two leads one to think them independent, otherwise he/she cannot be
Yes, this illustrated the problem inherent in assuming some type of
monism, it renders the "mind" or "body", noumena or phenomena, a mere
epiphenomena or artifact, and thus avoids having to explain how they
> > By instantaneous I mean, in your case, that a GR deflection is immediately
> > followed by an appropriate QM deflection propagated faster than light
> > (or infinite) speed, and vice versa for a QM deflection.
It is not meaningful to ask if one "deflection" is prior to the other,
the key, as Hitoshi explains below, is that the two are "synchronized"
or "in harmony" with each other.
> This would be rephrased as a consistency requirement for the inside and the
> outside. If any delay existed, consistency would be lost. In this sense, this
> FTL requirement seems to be the same as Libniz' "pre-established harmony"
> that would explain the windowless monads behave in harmony with the outside.
This FTL requirement seems to only apply to the behavior within the LS.
The analogy with the Leibnitzian monad is almost exact, but I think that
Pratt's criticism stands. As he mentions in the abstract of ratmech:
"This paper addresses the chief stumbling block for Descartes'
17th-century philosophy of mind-body dualism, how can the fundamentally
dissimilar mental and physical planes causally interact with each other?
We apply Cartesian logic to reject not only divine intervention,
preordained synchronization, and the eventual mass retreat to monism,
but also an assumption Descartes himself somehow neglected to reject,
that causal interaction within these planes is an easier problem than
If we are content to just accept the "pre-established harmony" or
"preordained synchronization" between internal FTL behavior of Local
systems and external "timelike" behavior, we are merely offering a hand
wave to model how it is that the "preordained synchronization" is
possible in the first place, since it, to me, is equivalent to saying
that the Langrangians of motion of many body systems exist a priori, and
this implies that the equivalent logical NP-Complete problems are
"computed by Nature" for free! We should know: "There is no computation
We need to understand what is "computation", so the burden is on me to
> Perhaps, we might
> > say that cause and effect for phenomena, is replaced with vice versa for
> > the noumena.
Almost, Pratt has it explained:
"A physical event a in the body A impresses its occurrence on a mental
state x of the mind X , written a=|x. Dually, in state x the mind infers
the prior occurrence of event a, written x |= a. States may be
understood as corresponding more or less to the possible worlds of a
Kripke structure, and events to propositions that may or may not hold in
different worlds of that structure.
With regard to orientation, impression is causal and its direction is
that of time. Inference is logical, and logic swims upstream against
time. Prolog's backwardchaining strategy dualizes this by viewing logic
as primary and time as swimming upstream against logic, but this amounts
to the same thing. The basic idea is that time and logic flow in
Can a body meet a body? Only indirectly. All direct interaction in our
account of Cartesian dualism is between mind and body. Any hypothesized
interaction of two events is an inference from respective interactions
between each of those events and all possible states of the mind.
Dually, any claimed interaction of two states is inferred from their
respective interactions with all possible
events of the body."
This begins to make sense when we consider that phenomena are "events
of the body" and noumena are "states of mind"! We understand noumena is
be given in terms of information (or equivalently wave functions and
operators!) and their n-ary relation structures (such as CABAs and
Hilbert projection spaces) and phenomena is given in terms of "classical
particles" with their cause and effect relations.
The interaction of the two is implicit in the idea of "clocking" that
Lance and I have been discussing. I have been working on an alternative
way of thinking of the Chu transform, and have only a very rough sketch
cut and pasted from:
> BTW, did my definition of a clock make any sense to you:
> "...The way that an analog clock is defined by the "face", the
> "hands" and an observer's comparison of the two..."
> I understand your definition. I am not sure it is complete. Part of the
> problem is with what may be an overly naive notion of "an observer." My
> point is that the observer is itself a clock, so there is no way to define
> the clock independent of the act of coordination.
I do not believe if it is necessary to define a clock "independent of
the act of coordination", since the action of a clock is to coordinate.
I think it would help us to consider two observers observing each other
in terms of two clocks, A and B, becoming synchronized with each other.
Perfect bisimulation equivalence implies that the the simulation of A's
behavior by B's behavior is identical to B's simulation of A's behavior
by A's behavior.... This is what happens when we have perfect
synchronization between two systems! ;-)
The "simulation" is noumena and the "behavior" is phenomena. The
identification becomes obvious in the binary since we can switch the two
around and recover the same situation, just going in the other
direction. This in analogous to the situation CPT symmetry there if we
were to reverse all dynamics in the world, we could not tell the
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