# [time 415] Re: On the Problem of Information Flow between LSs

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Tue, 22 Jun 1999 07:30:39 +0300 (EET DST)

Dear Stephen,

my response is postponed. I spent a weekend in summer cottage.
Sauna, swimming and other pleasures of life.

[SPK]
Dear Matti,

Matti Pitkanen wrote:
>
> Dear Matti,
snip
> [Stephen]
> About dissipation and consciousness: I believe that the two processes
> are the reverse of each other! This notion is inspired by Roger
> Penrose's argument in The Emperor's New Mind were he shows that the
> annihilation of information by black holes is balanced by the creation
> of "flow lines" in a phase space container representing the entire
> universe.
>
> [MP]
> Yes. Dissipation and consciousness are reverse in the sense that
> gain of conscious information means loss of unconscious information
> defined as information of quantum history. Hence dissipation is direct
> measure for consciousness. The question is only about length scales:
> in which length scales dissipation occurs. Only in atomic or perhaps
> also in longer length scales.

[SPK] There is an equation in information theory where dissipation is
measurered in terms of free energy and information entropy that I need
to look up...

[Matti]
OK

Here is an excerpt from a letter from Robert Fung:

Wed, 03 Feb 1999 10:15:40 -0500
[SPK]
> http://www.math.washington.edu/~hillman/postings.html
>
> "The Causal Symmetry of Shannon's Entropy. My claim that Shannon's
> entropy exhibits a causal symmetry'' proved to be a bone of
> contention. This file strings together several postings of mine
> defending that claim, beginning with the post which contained my
> original statement of the symmetry."
[RF]
This is easy to show. John H. Karl does a good job of it in
"An Introduction to Digital Signal Processing" in the pages on
maximum entropy. Essentially the Shannon entropy is the average
information per unit of time.

[Matti]
Information density in time direction.

[RF]
It really refers *only* to non-deterministic data:

h=-K \sum_i^n P_i ln P_i

Shannon derived the following based Norbert Wiener's work in solving
the problem of predicting time-series in the frequency domain
(Weiner-Khintchine theorem)

h ~ \int_{-\pi}^{\pi} ln Phi(w) dw

over the Nyquist interval (from -PI to PI), where Phi(w) is the
power spectrum so that h is proportional to this integral. He did this
because a
"stationary time series" has no Fourier transform but it does have a
power
spectrum ! Stationary time series are ones which have invariant
statistical
properties that hold up across ensembles (the collection of all
possible
realizations).

But, this integral will diverge to negative infinity if the power
spectrum is zero over any finite bandwidth.

So the necessary condition is that all non-deterministic information
in a time-series must obey h > -\infty. This is the Paley-Wiener
condition.

Looking now to the convolution theorem, the power spectrum is
expressible via the convolution symmetries in terms of the Fourier
transform of
the the autocorrelation:

FFT(f* x f) = F* F = |F|^2

where FFT(x) is the Fourier transform of x. and f* x f is the
autocorrelation
of f in the time-domain, and F is the Fourier transform of f.

This, as you noted earlier, has the time reversal built into it in
terms of the complex conjugates f*.

The cross-correlation:

f* x g

is similar to "convolution" but the difference is that the ordering
of the time-series is not reversed as in convolution. Convolution is
therefore commutative, but cross-correlation is not. They are
time-reversed
versions of each other !

This should give you a good idea of the link between time-reversal
and Shannon entropy.

This is very important to understand carefully because it applies
to so much of what we are discussing.

[MP] Let me try to translate this to TGD framework. What is possibly
nontrivial is related to multiverse nature of quantum history.

The information in question is nonlocal and about spacetime.
In quantum TGD frameowork one can certainly construct information
measures giving information about spacetime surface (involving, say,
autocorrelations of classical fields). In quantum
context one would consider quantum expectation values
for this kind of information measures.

Time reversal is with respect to the geometric time associated with
the spacetime surface. At quantum TGD level this reversal is only
indirectly related to the fundamental psychological irreversibelity
is with respect to subjective time ticking quantum jump by quantum jump:
this time only approximately corresponds to the increasing value
of geometric time.

Irreversible time development at spacetime
level emerges when one replaces sequence of quantum jumps between quantum
histories with single dissipative quantum history: in particular, when
one replaces irreversible time developments of classical fields
on spacetime level by single dissipative time development of classical
field in fixed average spacetime. This is effective description
replacing family of spacetime surfaces with their dissipative
'almost envelope'. Fundamental description assings
dissipation to the sequence of quantum histories.

[SPK]
> > > Remember that we define the information content in a given data base
on its
> > > entropy and/or the amount of time/energy needed to computer an
ordering of
> > > that data; in the first case we are defining the data base's Shannon
entropy
> > > measured/observed and of the latter we are defining the
thermodynamic
> > > entropy generated.
[RF]
> > Right, we define the information content of the
> >database not in terms of the amount of non-deterministic information
> >it contains (Shannon entropy) but in terms of the total of non->deterministic
> > and deterministic information (Shannon entropy + negentropy).
> > Useless information is still information just the same, and it takes
> > effort and energy to store it as useless information. We may know
> > that the information is redundant and useless but it contribution
> > to the decrease of thermodynamic entropy is important because it
> > organizes energy despite it's uselessness.
> >
> > So I think here we've nailed down the difference in these
entropies
> > very clearly.
[SPK]
> I am still confused with the words. :( I need a better feel of
what
> "negentropy" is.
[RF]
"Redundant information" or "negentropy" is not entropy.
It is lots of deterministic information.

Negentropy is related to the deterministic "fields" that bind
together the non-deterministic aspects of local systems (If
Hitoshi
will let me get away with such a statement ! )

****

[MP]
> From TGD view point the loss of information in blackholes if it really
> occurs (also transformation to information in the interior could be
> in question) would mean that blackholes would be extremely conscious
> objects. Perhaps the most intelligent hermites of the universe
> eating information around us with horrible greediness! Perhaps the
> ultimate fate of thinker is to become hermite, black monolite creating
> deep horror. Forgetting all about infinite primes and hierarchies of
> consciousness and Gods(;-).

Have you ever read the work of H. P. Lovecraft? :)

[MP]I know Lovecraft but I am not sure whether I have read anything from
him. I have become very lazy reader: most books I read, create the
expression that I have read all this thousands of times (;-).

[MP]
> In my homepage I have told about my long lasting altered state of
> consciousness about 15 years ago or so. One of the great ideas was that
> all intelligent systems are fighting and killing for
> 'flogiston'. 'Flogiston' is of course information! Conscious systems
eat
> information and transform it to conscious information. I later checked
> the meaning of flogiston and learned that it was mysterious
> thermodynamical substance postulated in early days of thermodynamics. It
> seems that 'flogiston' concept makes sense after all! Perhaps
> the thermodynamics as we know it will be replaced with theory
> of conscious information and information could be called flogiston
> quite well.

[SPK] Like phlogiston, information is not a "substance" in the classical
sense, but like "average kinetic energy" which replaced it, it is a
measureble quantity. We are moving away from the old mechanical model of
Realty...

[Matti] People have been talking about information society for
years and only now information is beginning to find its way to my own
mental landscape...

> [Stephen]
> When I found Vaughan Pratt's paper (ratmech.ps) discussing a
> duality between time and logic I was convinced that the idea was
correct,
> but I have been unable to communicate this idea to others. Even Pratt
> himself does not understand me. :( He has not worked out the way to
> formulate entropy within his notion.
> Your idea of the pinary cutoff is wonderful! It goes along way
> in explaining why any observer has a "field of perception" that appears
>to
> be "complete" to them. I have long argued that each observer has their
> own finite universe but have not been understood. :( Matti, my friend,
> you are explaining what I can not. I thank you.
>
> [MP]
> You are quite right.
> For me understanding of pinary cutoff was pleasant surprise since it is
> forced by real to p-adic quantum TGD correspondence and I regarded
> the concept as unsatisfactory. It is counterpart of length scale cutoff
> of QFT:s and there are unpleasant associations about infinities.
> It seems that quantum TGD proper and TGD inspired theory of cs are
> now converging to single theory.

[SPK] They should converge! :) An essential notion of any "quantum"
theory must have an explanation of what an observer is. :) I am very
interested in the nature of "length scale"!
Say we have a huge number of observers, each with their own
standard of length and duration: a clock of their own. Assuming that it
takes a non-zero duration for each observer to compare their standard to
all of the objects on their environment and that the comparasons
(measurements) can not be done simultaneously without some cooperation by
the observers with each other. But there is a difficulty!
It is usually thought that the standard of one observer can be
transformed via a number of finite steps into one identical to that of
another, thus we can think of this procedure as an "algorithm". We then
rephrase the above story in terms of Peter's new computer theory...

[MP] The idea of observer makes sense as a high level abstraction
(like clock and computer or dissipative dynamcis) but I am sceptic about
observer as *fundamental* concept. I am happy with observation/moment of
consciousness as a fundamental concept. But this is not a news
anymore(;-).

This comparison of standards: is it really needed? Or does our brain
perform something like this?

> [Stephen]
> I highly recommend Michael C. Mackey's book Time Arrows. If you can't
> get it from the library let me know any I will send you copies of the
> relevant parts. His "God Theorem" is very important for your ideas
> relating dissipation to consciousness. It proves that an invertible
> system U can have subsystems U_i that are not invertible and are thus
> dissipative and irreversible. The way that mapping between the Real
> valued states and p-adic valued states occurs is indicative. I do not
> know how to represent this mathematically....
>
> [MP]
> It would be interesting to learn about Mackey's thoughts: my basic
> philosophy is of course somewhat different: entire U is invertible in
> my approach. In your and Hitoshi's approach situation is different. In
> any case, dissipation is for me a direct experimental proof for quantum
>jumps between quantum histories concept.

[SPK] We agree with Mackey on this: U as a whole is invertible! It is
the finite subsets of U, the Local Systems that are not invertible! I see
your quantum jumps as instances of interactions among the LSs. The key
is to work out a model of how these "jumps" behave to generate the
illusions that we communicate about: our "common reality".

[Matti]
Really sorry to say this: we do not!!(;-) It was only a typo! My
intention was to write non-invertible but 'in-' somehow led me to think
that 'non-' is not needed. It would be wonderful to agree with someone at
least once in life!

But I could perhaps agree (with certain preservations of course!(;-)) that
quantum jumps can be seen as interactions between LS and its complement.

[MP]
> There is also interesting connection with self organization. Self
> organization can be understood as iteration. Iteration creates fractal
> like fixed points: for instance dissipation without energy feed leads
> rapidly to the state in which nothing moves.

[SPK] Look at the discussion of fixed points in Peter's work! Is this

[Matti] Interesting question. 'Dissipation without energy feed' was
meant for situation in which there is no external energy feed
to the subsystem so that system dissipates its energy and 'comes
at rest'. "Adiabatic" in thermodynamics means "no entropy generation".
What would this mean in quantum context?
If subsystem, which is sufficiently entangled with the surrounding world
develops without participating in quantum jumps, it would not have
moments of consciousness and no dissipation: same for its subsystems.
Entanglement would shield subsystem from the occurrence of dissipation.
Could this be a synonym for adiabaticity? Time development would roughly
mean iteration by U.
Could the system end up to a fixed point of time development operator
U==U_a, a --> infty and would not generate entanglement entropy anymore.
Just a thought....

What is the http address to Peter's work?

[MP]
> The informational time development operator U==U_a, a--> infty indeed
acts
> as iteration in good approximation on subsystems which do not suffer
> quantum jump. N quantum jumps corresponds to U^N in good approximation.
> This would mean that dissipation of energy leading to fixed point, limit
> cycle etc.. would indeed be iteration basically. I am beginning to look
> for more details related to this.

We should go over Mackey's work in relation to this, his research
into
thermodynamic entropy's subtleties is very interesting, to say the
least. :)

> [Stephen]
> The irreversibility of quantum jumps as an action of collapsing
> the many possibilities down to one actuality is in a fundamental way the
> reverse of a dissipation (like the thermodynamic evolution of a system's
> phase space) that maps one flow to many. Perhaps "flow" is the wrong
> word... The key is that we have dual semigroups of dynamics, one
> semigroup representing the evolution of consciousness and the other the
> evolution of dissipation. Both involve a "time" but they "flow in
> opposite directions".
>
> [MP] I think the best manner to say this is to say that information
> of quantum state is transformed to conscious information and destroyed
> as unconscious information. But there is paradox involved: entropy
> is potential information and it seems to be a matter of taste whether
> to speak of entropy or potential information. This is like creativity.
> Discoveries are not possible without diverging period when one generates
> counter arguments and is totally lost in fog!(;-)

[SPK] Umm, I am reminded of how the key irreversibility (and heat
generation!) in a computer is the act of errasing the memory... There is
work being attepted to minimize, if not eliminate, this heat by never
errasing the memory. The idea is called "reversible computing". I had a
brief correspondence with a nice fellow at MIT that was working on this.
I told him that he was chasing a chimera! :)

[MP]
In quantum jump informational time evolution U could be regarded as
quantum computation lasting for infinitely long lightcone proper time
(but only a single moment of subjective time).

Ideal quantum computation would mean single U followed
by quantum jump for the entire computer.
The problem is that quantum computer contains several subs-system
complement
pairs besides the desired one and some undesired pair can win
entanglement entropy generation race and make quantum jump.

One must be very careful with 'reversible'. Time development
operator U_a for entire universe is reversible just like Schroedinger
time evolution. In general it however changes the information content
(say increases information about the position of Universe=3-surface in
configuration space).

Question: What could be the role of informational time development in the
understanding of memories? Information currents are involved with
memories.

> [Stephen]
> The unity of the two is realized at the Grundlagen level of the
> Totality, which is one. It has no dynamics in itself as seen by the fact
> that it has no time associated. Mackey's proof that invertible systems
> have no time (he does not say this exactly but it is implied) while
> non-invertible systems will have time.
>
> [MP]
> This is realized very precisely in TGD. Without the classical
> nondeterminism of Kaehler action classical dynamics would be invertible.
> There would be no time. There would be no consciousness since in von
> Neumann inspired scenario since only quantum entanglement between
> cognitive and material spacetime sheets can be reduced by quantum jumps
> in this scenario.

[SPK] I wish I understood Kaehler action better. :( I don't know what
this term means! I also do not comprehend what "cognitive and material
spacetime sheets" are. The ideas that I have that seem to correlate to
them are the dual aspects of a Chu space: SET and anti-SET, Mind and
Body, Information and Matter. The pictures in my mind of these looks
very similar, but the devil is in the details!

[MP]
Perhaps you are trying to see Kaehler action from
too computational point of view. Chu spaces seem to be rather
non-geometric
concepts: closely related to formal logic, symbolic systems
and these kind of things: unfamiliar to me. Kaehler action, cognitive
spacetime sheets, etc. are rather concrete geometric concepts. There
are 2-dimensional illustrations on my homepage: they might help.

Best,
Matti Pitkanen

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