From hpstapp@lbl.gov Thu Jun 21 16:37:50 2007
Subject: Re: Process 1
On Wed, 20 Jun 2007, Imants Baruss wrote:
> Hi Henry:
>
>
>
> I just finished reading your book "The Mindful Universe" and found it
> quite
> interesting. I do have some questions: Does process 1 occur while the
> brain
> (and the rest of the universe) is in a state of superposition or when
> there
> is an actual single brain present (although that would make it coincide at
> least for a time with process 2)?
Process 1 is instantaneous in von Neumann's nonrelativistic formulation.
It is, for vN, the physical/mathematical act of reducing the state at time
t to a new state (density matrix). The process zero that determines what the
instantaneous collapse at time t will be (and the time t when it will occur)
is not given by the Schroedinger equation, which governs the evolution
between collapses. Process zero is best understood to be occurring in a mental
realm. In the relativistic (Tom &Schw) formulation process zero has access
to the state on the spacelike surface Sigma i-1, and the collapse occurs
at a "later" spacelike surface sigma i that is pushed forward from sigma i-1
over some small region R. One could believe that a combined physical-mental
process is occurring over this spacetime region, but the net affect of that
combined process will be a projection that acts at the "instant" sigma i
upon the state generated by the Schroedinger equation from the state on the
surface sigma i-1.
> Is process 0 part of process 2?
Process 0 could be understood to be occurring purely in some mental realm,
because the physical state continues to evolve via process 2 (the Schroedinger
equation) over the (small) region R between sigma i-1 and sigma i. Alternatively,
there could be an interaction between the mental and physical realms in this
region, with the final state ultimately collapsed in a way that injects the
conceptual output into the final physical state. But the mathematics says
that the physical state evolves via proess 2 (The Schroedinger Equation)
between the instantaneous events. This accords with the idea that process 0
is occurring outside the realm represented by the physical/mathematical
space-time-imbedded (i.e., physical) process represented by the laws
described in physics text books.
> What is
> the range over which the frequency of process 1 occurs? I am aware that
> Gaussian wave packets spread with time between collapses. Is there a limit
> to the amount that they can spread before the intervention of process 1 in
> everyday life?
What I am imagining is that the brain tends, as a result of genes plus
training, to produce at various times paricular quasi-stable classically
describable coherent QM states of the electromagnetic field in portions
of the brain. If the state is quasi-stable then a big part of the density
matrix could evolve slowly, even though the pertinent quantum phase factor
exp -iEt could be rapidly varying.
If in the quantum zeno argument (See p. 254 of my MM&QM, 2nd Ed)
one chooses P so that it projects onto a quasi-stable coherent state of the
elecrtomagnetic field then if this projection at t=0
is followed by a projection at time t onto the same state then the
result is
P expiHt P exp-iHt P.
But H sandwiched between coherent states gives the *classical*
frequency, rather than the quantum frequency. So if the projections P
are onto a quasi-stable (stationary) classical state, and the probing rate
is rapid on the scale frequency of this quasi-stable classical state, then
the terms first order in time will cancel:
P (1-iHt)P(1+iht)P = 1 + P(-iHt)P + P(+iHt)P + tt PHPHP
So if a time interval is chopped up (by the probing actions P) into small
intervals on the scale of the frequency of the *classical* coherent stete,
then the probability that the state will stay in the state represented by this
projection operator tends to unity as the rapidity of the choppings hend to
zero---on the scale of the CLASSICAL Frequency.
I wish I had made this point in my book. It makes the needed rapidities
more reasonable and accessible, and gives a mathematical basis for the
condition that the inputted concepts should be classically describable, and
represented in terms of projections onto coherent states of the EM field,
as suggested in my paper "Light as Foundation for Being" in the book
"Quantum Implications: Essays in Honor of David Bohm" Eds. Hiley & Peats,
Routledge & Kegan Paul Kegan, 1987.
Henry
From hpstapp@lbl.gov Sun Jun 24 19:46:31 2007
Subject: Re: Questions
On Fri, 22 Jun 2007, Imants Baruss wrote:
> Hi Henry:
>
> Thank you for your quick and detailed response.
>
> When you say:
>
> "Process 0 could be occurring purely in some mental realm, . . . [such
> that]
> there could interaction between the mental and physical realms in this
> region, with the final state collapsed in a way that injects the
> conceptual
> input into the physical state."
>
> you are, in effect, proposing a second mechanism of interaction between a
> mental and physical realm. What is that mechanism?
The process in question is process 0. The best general model I know of, so
far, is Whitehead's actual occasion, which gathers information from the
already fixed and settled past, both experiential/conceptual and
physical, and produces a new psychophysical entity, which at the
psychological level is the output concept, and at the physical level
is the process 1 action S-->S'=PSP + P'SP', with P'=(1-P), where
P the projection onto the (classically describable) subspace that
corresponds functionally to the physical structure (template for action)
which if held in place for a sufficient interval will tend to produce the
physical state that will tend to produce a conceptual feed back that matches
the output concept. The existence of this kind of feed-back depends, of
course, on the existence of an appropriately functioning physical substrate.
A long trial-and-error evolutionary period is presumeably require to bring
such a physical substrate into existence.
>
> You say that: "if a time interval is chopped up (by the probing actions P)
> into small intervals on the scale of the frequency of the *classical*
> coherent stete, then the probability that the state will stay in the state
> represented by this projection operator tends to unity as the rapidity of
> the choppings hend to zero---on the scale of the CLASSICAL Frequency."
>
> Is the lower limit actually zero?
No!
> Can continuous observation occur?
No! Whitehead claimed to rule out this possibility by a consideraion
of Zeno's paradox: it would forbid change. It is interesting that,
accoding to QM, continuous observation would forbid change of the state
associated with P eigenvalue +1 to P eigenvalue -1.
> And, if
> so, do you not run into problems with the projection postulate? If not,
> what
> would the lower limit be?
>
The process 0 must, among other things, decide when the next
projection event will occur.
> On page 252 of MM&QM you say that experiences are associated with
> occurrences of process 1. So, as experiences go on for me, there are
> continuous reductions by projection operators and collapses.
According to this theory the "stream of consciousness" is like
a stream of bullets from a machine gun", or like the successive
frames of a movie screen. As James says, perception comes in discrete
drops or buds. Whitehead says potentiality is continuous but actuality
is incurably discrete. Von Neumann's process 2 evolution of the state
of the universe (which represents potentiality) is continuous but the
reduction events (which are the physical counterparts of the actual
conceptual events) are discrete. C. Koch in his new book emphasizes the
evidence that perception is, in fact, as James said, discrete: the "wagon
wheel", familiar in movies, occurs in broad daylight!!
> On page 35 (of
> the published version) of The Mindful Universe you talk about calling up
> "associations via stored memories" etc. as brain states necessary to set
> up
> a process 1 action. But all of the calling up etc. must already be made up
> of sequences of process 1 actions because experience is going on during
> that
> time. Is that not so?
There are many rationally coherent possibilities available to the theory
builder at this stage of theory building.
At the very least the construction of the actual occasion will have
available to it the information residing in the portion of the state of the
universe on the spacelike surface sigma i-1 that gives
the earlier-time boundary of the space-time region R associated with
the occasion. This information contains the brain-stored information
from the prior history of the brain. It is an open question whether this
information is enough to explain ALL mental events. One question here is
whether or not the "evidence for telepathy" is to be accepted as in need of
explaining in terms of a real non-physical type of communication of
information. If telepathic communication within the realm of concepts is
really needed, then the input to the actual occasion could include direct
information about concepts actualized in the past, either at events
in the backward lightcone of R, or, even more radically, at any event in the
past of the above mentioned surface sigma i-1. More conservatively, one might
try to allow, in the construction of the actual occasion, only the
information contained in the physical state along the earlier-time
boundary of R. The process 0 could then involve reconstructing
concepts from the information present in that physical state of the
brain, and involve using these concepts to form the output concept, which
will then be injected into the brain via process 1. Perhaps this whole
process could be represented by an evolution of the brain state that
images in the brain, in purely physical terms, the process 0 described above.
This conceivably possible physical representation of process 0 in region R
in spacetime leads, however, to a collapse, and hence is different from
process 2. If the empirical data, critically evaluated, entails telepathic
communication, or survival of personality after bodily death,
[Before rejecting this latter possibility a careful scientist should
acquaint himself with the evidence. A sifting of the evidence that needs
to be taken into account before a scientifically credible claim
can be made can be found in the book "irreducible Mind" by Kelly and Kelly.]
then the possibility that process 0 may not be fully representable in the
physical domain becomes a more reasonable possibility. Since ideas do
actually exist, and presumeably have a reason to exist, it is not totally
unreasonable to consider the possibility that they may play a dynamical
role that is not fully representable in existing contemporary physical theory,
which involves, irreducibly, participating observers, and make them function
in ways that are not explained in terms of the known physical laws.
> And just as a practical matter, what would you say is
> the minimum frequency, in Hertz, at which such process 1 actions take
> place
> during ordinary waking consciousness --- effortless consciousness, I
> presume, since effort would increase the frequency.
I imagine the the frequency for effortless thought might be the
order of 100 hertz, increasable by a factor of 10 by effort.
But I know of no principle that limits the frequency of the injecting
of conceptual elements into the physical process.
>
> I look forward to your responses.
>
> Have a good weekend!
>
> Imants
>
>
From hpstapp@lbl.gov Tue Jun 26 10:56:21 2007
To: Imants Baruss
On Mon, 25 Jun 2007, Imants Baruss wrote:
> Hi Henry:
>
> Thanks for getting back to me again.
>
> You said:
>
> "The process in question is process 0. The best general model I know of,
> so
> far, is Whitehead's actual occasion, which gathers information from the
> already fixed and settled past, both experiential/conceptual and
> physical, and produces a new psychophysical entity, which at the
> psychological level is the output concept, and at the physical level
> is the process 1 action S-->S'=PSP + P'SP' ,with P'=(1-P), where
> P the projection onto the (classically describable) subspace that . . ."
>
> Does the actual occasion have duration in time? From what you have said,
> this appears to be the case.
My favored theory is the one proposed in my article "Process Time
and Einstein Time" in the book "Physics and the Ultimate Significance of
Time" ed David R. Griffin SUNY 1985. Think of spacetime as spread out
horizontally. Just after the event on the spacelike surface sigma-1 has
occurred, one can extend the quantum state S of the universe away from
sigma-1 via the Schroedinger equation so as to cover all of space and time.
After the collapse on sigma-2 one can extend the state away from
sigma-2 so that it is now defined in a new way over all of spacetime.
Let these two definitions of the state S can be defined in two different
copies of spacetime, one lying one unit above the other in a fifth dimention,
called Process Time. In this way we build the idea of a evolution in
Process Time, punctuated by the creation of definite output ideas at the
unit intervals in Process time. Each such conceptual output is registered
in the physical universe by a collapse, or reduction, which occurs on
the associated spacelike surface sigma-i.
In this conceptualization, Process occurs in Process Time, not in spacetime.
There is conceptual development between process time i-1 and process time i.
An output conceppt is formed at the discrete moment of Process Time "i", and
is imposed on the quantum state along the associated surface sigma-i.
> If that is true, then we are unaware of the actual occasion, because our
> experience is associated with process 1 which occurs at the culmination of
> process 0.
Yes! It does indeed seem---in our experience---that the actual process is
not experienced: only the punctuated discrete actual outputs are experienced
in any clear way.
>
> You make it sound as though the actual occasion could take awhile. In that
> case, can it enfold any occurrences of process 1?
The overall process is a sequence of subprocesses, each one producing a new
output concept that is injected into the physical state by a Process 1 action.
> And in that case, would
> this be similar to Dan Dennett's horserace theory of consciousness whereby
> multiple threads are co-opting cognitive resources and the one that can
> co-opt the most is the winner and becomes that which we experience
> explicitly in awareness? In other words, these process 0 threads could be
> going on uninterrupted through process 1 events, or do you think that
> process 0 events necessarily take place between process 1 events?
A struggle for "physical" resources may indeed be part of what is going on,
via Process 2. But that mechanical struggle does not produce the
super-mechanical choice---which violates the Schroedinger law of
evolution--- of the kind needed to fix the Process 1 input that
is needed to make quantum theory work! What is going on at the conceptual
level, in the construction of the new input concept, may indeed "resemble"
Dennetts's struggle for physical resources. But it need not be, and cannot
be, mere locally implemented Schroedinginger evolution. The Process 0
struggle can be a struggle between concepts/values. When you/Dennett
speak of struggle for "cognitive" resources there is a blurring of the crucial
distinction between physical resources, defined in the mathematical
language of physics, and experiences per se, or idea-like qualities,
which are described in a different kind of language. Both kinds of
"enities" are parts of science. Our task is to create a theory that
explains in a useful way the relationship between the parts of science
described in these two ways. That is what Bohr saw as needed, and tried
hard to do.
>
> You say on page 243 of MM&QM that "S-->S'=PSP + P'SP' ,with P'=(1-P)" is
> "one of the key equations of quantum theory." But I'm wondering, why not
> just S = PS + (1-P)S where PS can represent "yes" and "(1-P)S" can be
> "no".
> What's wrong with that?
S is a density matrix, and a change of state vector |Psi> --> P |Psi>
changes state S=|Psi>S'=PSP + P'SP' [P'= (1-P)]
is a real change: it destroys the "interference" terms in the
density matrix.
> That way you have a reorganization of the wave
> function, but no reduction because there are no cross-terms (the ones you
> give on page 244 of MM&QM) requiring elimination.
>
> When you write "PSP", on what is it that the right-most P operates, given
> that P is the projection operator?
>
The basic probability formula is
=Tr SF/Tr S.
After the psychophysical event the new probabilities are
' = Tr S'F/TrS'
with S'=PSP+P'SP'! This is the correct quantum law! Your rule
S' = PS+P'S would give =': there would be no change in
probabilities associated with the new conceptually expressed
knowledge.
> I assume that S is just the state vector and you describe it as "the state
> S(t) of the brain" on page 1319 of Schwartz et al and "the quantum state S
> of the system being acted upon" on page 243 of MM&QM.
I follow the lead of the mathematical physicists who distinguish "state"
from "state vector", and use the former word to describe the density
matrix, which contains all of the empirically accessible information.
> But then on page 243
> you also describe S as an "action" somewhat reminiscent of objects as
> morphisms in category theory. Are there any mathematical consequences of
> such a reconceptualization?
>
> In general, of course, S will have continuous components. What does the
> process 1 reduction look like when S is continuous?
>
S is changed abruptly by process 1 over a macroscopic region.
> You said:
>
> ". . . the earlier-time boundary of the space-time region R associated
> with
> the occasion. This information contains the brain-stored information
> from the prior history of the brain."
>
> Given the problems of localizing memory in the brain going back to Karl
> Lashley, do you think that memory resides within the physical structure of
> the brain in some sort of classically describable manner? Or do you think
> that memories could be encoded e.g. as spinor fields as suggested by
> Takahashi, Jibu, and Yasue, so that memory itself is already a superposed
> state? Or is memory "purely mental" in some sense?
>
Due to these difficulties, I "allow" a lot of memory to be stored
(holistically/holographically) in the brain, but do not rule out
direct "telegraphic" access to concepts created by prior occasions.
Whitehead seems to allow "telegraphic" access to the outputs of
prior (fixed and settled) occasions, but allows also inputs to actual
occasions that come via physically described (i.e., brain) processes.
At this point in theory development I also allow both kinds of inputs
into the actual occasions.
> You said:
>
> "I imagine the the frequency for effortless thought might be the
> order of 100 hertz, increasable by a factor of 10 by effort."
>
> So you don't agree with Chris Nunn on page 126 of TMU that 100 Hz would be
> the maximum frequency?
>
I do not agree with Chris Nunn on this point!
We are dealing here with effects of the conceptual actual occasion,
which take place in process time, upon the physical brain. I see no reason
why the conceptual process in process time could not produce outputs that
are applied more quickly in physical time, e.g., on the millisec level.
> Also on page 126 and in your previous e-mail of June 21, 2007, you make a
> distinction between a "classical" frequency and "quantum" frequency. Are
> you
> using the term "classical" to refer to the rate at which processes 1&3
> occur
> and "quantum" frequency as the frequency associated with the energy of a
> system?
>
In the quantum coherent state associated with, for example, a SHO
(simple harmonic oscillator) there is the classical frequency of the
classical "pendulum", and also the quantum frequency give by the Planck
formula relating frequency to energy. The latter increases as the ampitude
of the swing increases, while the classically observed frequency remains
fixed. The quantum frequency is essentually n times he classical frequency,
where n is the average number of "quanta" in the classical coherent state.
If the coherent state in question (say of the EM field) stays essentually in
place, due to the fixed circuitry of the brain, and P projects onto such a
state, then QZE should kick in when
the frequency get large compared to the classical, rather than quantum.
freaquency!
Your questions are all very good question, and they make me painfully
aware of many important things that I should have spelled out in more detail
in my two books.
HPS
> Cheers!
>
> Imants
>
>
From hpstapp@lbl.gov Fri Jun 29 10:20:58 2007
On Thu, 28 Jun 2007, Imants Baruss wrote:
> You said:
>
> "In this conceptualization, Process occurs in Process Time, not in
> spacetime. There is conceptual development between process time i-1 and
> process time i. An output concept is formed at the discrete moment of
> Process Time "i", and is imposed on the quantum state along the associated
> surfaces sigma-i."
>
> I don't know if you are aware of them, but there have been efforts in the
> past to accommodate consciousness into spacetime by adding dimensions
> although the only one I can put my hands on at the moment is:
>
> McLaughlin, S. C. (1986). Dimensionality and states of consciousness. In
> B.
> B. Wolman and M. Ullman (Eds.), Handbook of states of consciousness. New
> York: Van Nostrand Reinhold.
>
> The general idea is that spacetime is modified by conscious volitional
> acts
> in a fifth dimension. That is similar to your conception (although without
> the qm).
>
In QM this fifth dimension represents merely a time (Process Time)
in which unfolds some conceptual process that interacts, on occasion, with
those aspects of nature that are represented in the (quantum) physicist's
physical/mathematical (Hilbert space) description of physical systems.
This latter (physical) description is mathematically tied to space-time:
it is built upon operators that are tied to spacetime. The fifth
dimesion is a conceptual time dimension in which to place the process O that
selects the physical time and the physical form of the process 1 actions
that are needed to make the connection between the quantum mathematics and
human experience. In quantum theory, as currentlty formulated, taught, and
applied, the process 1 action is treated as something that comes in from
outside the realm of processes explicitly controlled by the known physical
process 2. Without this process 1 psycho-physical action one is led to a
many-worlds scenario, which has not yet been satisfactorily tied to
experience---and surely, in my opinion---never will. One needs an extra
(not process 2) process to make QM work, Process Time is merely a conceptual
time that allows us to conceive of the unfolding of this process, without
prejudice as to it ultimate meeaning.
> You said:
>
> "S is a density matrix, and a change of state |Psi> --> P |Psi>
> changes S=|Psi>
> Ok. You introduced an intuitive notion of a density matrix on page 70 of
> TMU
> and you had already said that you were talking about density matrices in
> the
> first e-mail, but it is only now that I see that the S's are density
> matrices.
I apologize for not making this notation clear from the outset.
>
> In your density matrix, the diagonal entries are essentially probabilities
> for particular possible events and off-diagonal entries are interference
> effects between those events? I take it that the brain or parts of the
> brain
> are to be considered mixtures of ensembles described by density matrices?
> Or
> are you talking about pure states of ensembles? Would you say that the
> brain
> is a statistical ensemble described by a density matrix?
In QM, the state of any system is, for scientific/empirical purposes,
represented by a density matrix S. The state of the brain, as part of a
larger system that includes its physical environment, is represented
as a continuous statistical ensemble (in the classical sense of a weighted
collection of dynamically-independent components, each of which is a pure
quantum state of finite (but small) size. To tie this S to a prediction
about experiences one must tie the possible experience of interest
to an associated projection operator P, in such a way the
reduction of S to the part of itself that is compatible with that experience
is PSP. The probability the a probing action designed to elicit the
experience associated with P, if this probing action is applied to the
system in state S, is Prob (P|S)=Tr PSP/Tr S= Tr PS/Tr S= Tr SP/Trs.
>
> I realize that the expected values of measurables are just the traces of
> the
> product of the measurables with the density matrix, but I'm not sure how
> such measurables or the traces are related to our ongoing experience
> which,
> you have said, is made up of process 1 reductions. The clarification for
> my
> confusion is no doubt already in what you have said previously, but I'm
> just
> trying to muddle my way toward the light!
>
The Process 1 represents just the "posing" of the question:
S-->PSP + P'SP'. It reduces S to the sum of the two term corresponding
to two answers (Yes or No) to the question "Will my experience be the
one associated with projection operator P ?" Note that
Tr PSP + Tr P'SP' = Tr PS + Tr P'S = Tr (P+P')S = Tr (P+(1-P))S=Tr S
Hence
Prob(P|S) + Prob(P'|S) = 1.
The probability of "Yes" plus the probability of "No' is 1!
> You said:
>
> "Due to these difficulties, I "allow" a lot of memory to be stored
> (holistically/holographically) in the brain, but do not rule out
> direct "telegraphic" access to concepts created by prior occasions.
> Whitehead seems to allow "telegraphic" access to the outputs of
> prior (fixed and settled) occasions, but allows also inputs to actual
> occasions that come via physically described (i.e., brain) processes.
> At this point in theory development I also allow both kinds of inputs
> into the actual occasions."
>
> To the extent that "access" refers, in part, to Process 0 recruitment of
> information from physical memory, this implies a mechanism of interaction
> between physical and mental domains in addition to Process 1.
>
Yes! Process 1 is the EFFECT of Process 0 upon the quantum state, and
is therefore a crucial part of the practical procedure for computing
probabilities. How the Process 1 comes to be what it turns out to be
is not specified by the machinery of QM: Process 1 is, in practice,
determined by "a free choice on the part of the experimenter." Of course,
that "free choice" is certainly strongly influenced by what was going
on in his brain a short time before, and might conceivably be influence
directly by some far earlier experiences of the same person, and perhaps
even directly by experiences of fasr-away-others (telepathy). I do not,
at this early stage of theory building, close off any of these possibilities
for how Process 0 gathers information from the physical world.
HPS