# [time 412] Re: [time 399] On the Problem of Information Flow between LSs

Stephen P. King (stephenk1@home.com)
Sat, 19 Jun 1999 01:26:09 -0400

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.

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...

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.

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-correaltion:

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.

[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]
> 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.

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...

> [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.

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...

> [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.

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".

[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.

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

[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 realtion 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!(;-)

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! :)

> [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.

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!

Later,

Stephen

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