[Fis] FIS discussions. What is information - Shannons numbers or nature's numbers?

[Karl Javorszky]

The following is Part 1 of a two-parts piece

Dear Jerry,



Thank you for the insightful questions. I shall work them through:



*What are the objectives of the inquiry into the scientific nature of
information? It seems that the very name, FIS, suggests that Shannon
information is insufficient for scientific information.  One might
ask “Why”?  Is it because of the nature of matter?  Do the constraints on
the nature of matter the boundary of the concept of information?  *



The problem with the classical concept – now known as the Shannon concept -
of information is not relating to that what Shannon does impeccably well.
We discuss here an extension to the Shannon system, by 1. Showing it to be
a special case, and 2. Placing it in a more general framework. The urge to
do this comes not from Shannon doing anything wrong, but from our wish to
understand why Nature uses 3 places, on each place 1 token of 4, to
transmit information. In the Shannon world, words in a sentence have no
inner relations to each other. We see however, that the system only
functions (the organism only lives) if the words are in a specific
succession. Nature employs an inner web of rules that governs the
permissibility of some logical statements (specific triplets) on some
places. We are looking for the inner thread that strings the possible
logical statements one after the other, according to a rule. This rule we
want to make easily understandable. Shannon does not talk about this
subject, because in his view, each place can be filled up by {0,1},
independently of the content of preceding or subsequent carrier units
transmitting the message.



*One aspect of Shannon information is that it requires that the
transmissible form of information be represented in terms of bits and
bytes.  Indeed, bits and bytes are the only permissible forms of
representation of Shannon information.  The units of Shannon information
are numeric of indefinite magnitude, are they not? As numeric units,
Shannon units are unbounded in scale and are unlimited in scope.  This fact
that Shannon information can represent unbounded scales (magnitudes) is one
key element of the wildly successful theory*.



Shannon sees the alternatives to be lined up, one statement of {0,1}
following the next until all *n* units are either 0 or 1. We however look
at the whole collection of *n* elements, not concentrating on their
*sequence* but on their *structure*. The term structure describes the
sentences of the form: *among all n, <i> are in the most numerous subset
and <j> are in the second most numerous subset and <k> are in both of these
and among the <k>, <q> are such that they also belong to the <f>-th most
numerous subset too. *Etc. etc. It is debatable, how many of these
overlap-describing sentences can coexist, but this is what we look into.



(Example: we conduct a marketing sweep over a population and will find out,
how many married women in the age bracket 30-35 are concurrently running a
car and donate to a poverty cause.) After generalising the marketing
manoeuvres, one will arrive at a web of boundaries delineating elements
against other elements while including them also in subsets with other
elements. For lack of a better word, one may propose the overlapping
inclusion/exclusion boundaries generated by belonging-to in their entirety
as the *structure* of the collection. As we regard the structure of the
collection, it is – at first – irrelevant, where the elements are, and who
their neighbours in a linear line-up would be.



*Another aspect of information is the scope of the meanings of information.
What are the limits on the scope of Shannon information?  How are the scope
of the bits and bytes represented in the the theory? Is the scope of a
Shannon message constrained numerically in any way?  If so, how is the
scope of information represented in a Shannon message?*

*The Shannon hypothesis of Information is that all communication can be
encoded into transmissible forms of numbers that contain the message.*



All carriers and methods of carrying messages are basically a match of a
state of the set to a number on *N*. How many different messages can be
transmitted is determined by a setup of {carriers, symbols, rules [of
writing/reading the symbols on the carriers]}. To transmit Q different
messages, one may need *k *carrier objects if one uses *s* different
symbols and uses the rules of reading the carriers {sequentially,
commutatively}. The Shannon method is the simplest, therefore the most
practical, by using 2 symbols (black/white, full/empty, 0/1, etc.) and
reading them in a sequence. Shannon uses what is in the art world *méthode
brutaliste*. It is great, applicable and faultless, does what it should,
but it is neither optimal, nor sophisticated. You cannot beat Shannon for
straightforwardness, identification precision, practicability for very
simple machines. What you can compete on is efficacy and intelligence based
on comparisons and similarities.



Let me digress into the world of spy-craft and invent a devilishly cunning
opponent. He used to send his messages to his agents here, very well-built
agents, by the way, by sending them necklaces of *n *pearls. Our able
colleagues in the field have always found an opportunity to secure the
necklace and we discovered that on each of the pearls a small number was
etched. The numbers went 1 thru *n*. It looked as if the jeweller had
selected *n* pearls and enumerated them, which would be reasonable. What we
figured out, however, was that the pearls were not in that sequence on the
ficelle as the indication had suggested: their sequence was always
different. So, we went to hunt for, and found a deciphering book which
unveiled: 365412: declare war 243156: offer more bribes and many more of
the sinister machinations of our eternal foe. We immediately made sure that
during some routine controls, the string of the necklace got unhappily
torn, and the pearls were restored on a new ficelle, with profound excuses
from us.

All were happy in the Department, until we found out that the lady no more
received pearls but flacons of exquisite perfume that contained
miraculously also always *n* distinguishable chemical compounds. (If they
had used wine, they would have mixed distinguishable chateaux.) It was now
the proportion of the ingredients among each other that they cunningly used
as a method of identifying an element of *N*. We could gain only a fragment
of the deciphering book, where the rules said: if the moisturising
ingredient is more than the orange fragrance ingredient and the glycerine
content does not exceed the fatty acids of free radicals, then: talk about
a treaty with his neighbour, if the relation of the two most common
ingredients exceeds the relation of the fourth to the fifth most common
ingredients, then: offer to cooperate in mining, and so forth, always a
changing composition of the fluid matched to a number on *N*. Then they
added insult to injury and went back to pearls but added dispersed
differing symbols to the pearls, and had the cheek to present us the pearls
in a pouch and saying this saves us the trouble *de rompre la ficelle*.
Obviously, it is more trouble to handle actual materials with microscopes
and measurement equipment than to handle pearls of a necklace onto each of
which one etches as many symbols as one wishes. This was an unusual and
fascinating challenge for us, but we were at loss, because we have
internalised at the age of 7 the implicit instructions of Teacher alongside
with her explicit instructions about what to do if we see an *a* and a *b*
together. Implicitly, there was a sneer at those who did other things with
*a* and *b* than add them up to *c* like everybody who has understood what
is important and what is to be focused. Teacher discouraged implicitly,
between the lines, doing anything else with charming *a* and handsome *b *but
adding them up into *c*. We had just too much engrained the habits of
dwellers in our caves, watching the passing shadows which Fate ordered to
pass before the entrance of the cave. We would never have played ourselves
alone, on our own volition, on the instruction of no one from above or
outside, being in a cave, with reflectors, human-sized puppets of pairs and
cameras and their positions, generating our own shadows and discussing what
we see. That would have been wandering off the right path of how one has
been instructed to think. We were desperate.

Then we called in the reptiles from Bletchley Park. At that time, they
still had some basic science people there working on the theory of messages
transmission, specifically the cryptology aspect of it, so they could offer
us some useful hints that helped us along. (In Vienna, it so everyday to
talk in double meanings, and to talk in dialect is to belong to the
speakers of that dialect, and cryptography is just the question of how
private a dialect can get, until only two people understand it, and all
these aspects have caused Wittgenstein to occupy himself with the clear
message, not the purposefully hidden one.) They pointed out that indeed
there is an advantage in presenting the pearls of a necklace in a pouch as
opposed to lined up, *if the sender uses between 32 and 97 pearls. *They
even pointed out that using roughly 11 elements sequenced, 6 times
concurrently, while reading the assembly of 66 elements as a whole, as a
complete collection, would allow information compression and de-packaging.
Nature appears to use this method of translating 3x4x6 roughly into 64
which again points to one in 20, which is sequenced again. They said, there
is a sleeper cell, sleeping quite professionally, somewhere in Zaragoza *(où
a été trouvé le fameux manuscrit)*, but actually everywhere on the planet.
One hears that the principal statement of this radical group - they profess
allegiance to their faith that there are two independent or
more-or-less-independent logical systems at work – is actually totally
public in the Online Encyclopaedia of Integer Sequences.


Follows Part Two


Am So., 20. Okt. 2019 um 08:47 Uhr schrieb Bruno Marchal <marchal en ulb.ac.be
>:

> Hi Jerry, Hi colleagues,
>
>
> On 19 Oct 2019, at 07:18, Jerry LR Chandler <jerry_lr_chandler en me.com>
> wrote:
>
>
>
>
> This re-posted because the first sending was not distributed.
>
> Begin forwarded message:
>
> *From: *Jerry LR Chandler <jerry_lr_chandler en icloud.com>
> *Subject: **Re: [Fis] FIS discussions*
> *Date: *October 13, 2019 at 10:56:19 PM CDT
> *To: *annette.grathoff en is4si.org
> *Cc: *fis <fis en listas.unizar.es>
>
> Dear Annette, List
>
> On Oct 13, 2019, at 4:04 PM, annette.grathoff en is4si.org wrote:
>
> The next huge difficulty (connected to the unclear status of matter) is to
> model the influence of *what makes a difference* on relationships which
> enable matter. Threshold levels are nice, but how can the quality of
> relationships be in-formed through the special quality (pattern) carried
> and transmitted by *a difference which makes a difference*? Philosophy
> helps us in understanding how meaningful communication can develop in
> contextual environments and Sociology hints to connections between
> meaningfulness and stability respectively cooperation and trust. But this
> both is observed in very highly developed systems and provides little help
> for understanding more basic dynamics. Regarding those, I bet on wave
> mechanics to promote our basic knowledge here (but you know that I got very
> involved in this in my project, so bias is not excluded).
>
>
> What are the objectives of the inquiry into the scientific nature of
> information? It seems that the very name, FIS, suggests that Shannon
> information is insufficient for scientific information.  One might
> ask “Why”?  Is it because of the nature of matter?  Do the constraints on
> the nature of matter the boundary of the concept of information?
>
> One aspect of Shannon information is that it requires that the
> transmissible form of information be represented in terms of bits and
> bytes.  Indeed, bits and bytes are the only permissible forms of
> representation of Shannon information.  The units of Shannon information
> are numeric of indefinite magnitude, are they not? As numeric units,
> Shannon units are unbounded in scale and are unlimited in scope.  This fact
> that Shannon information can represent unbounded scales (magnitudes) is one
> key element of the wildly successful theory.
>
> Another aspect of information is the scope of the meanings of information.
> What are the limits on the scope of Shannon information?  How are the scope
> of the bits and bytes represented in the the theory? Is the scope of a
> Shannon message constrained numerically in any way?  If so, how is the
> scope of information represented in a Shannon message?
>
> The Shannon hypothesis of Information is that all communication can be
>  encoded into transmissible forms of numbers that contain the message.
>
>
>
> How would you relate Shannon hypothesis with the hypothesis of Digital
> Mechanism in the cognitive science (aka philosophy of mind, aka theology of
> numbers)?
>
> I would say that Shannon hypothesis, as you define it, implies the
> Mechanist hypothesis. In that case the whole of physics becomes a branch of
> arithmetic (including meta-arithmetic).
>
> The difference which makes all difference, in that case, is the difference
> between 0 and 1, or it is the difference between the combinators S and K,
> or any difference making a structure into a universal machinery in Turing’s
> sense.
>
>
>
>
> Does the same hypothesis,  the same critical concept, apply to the
> neighboring concept of real scientific information, that is, the natural
> forms of scientific information as used by working scientists
> (physicists, engineers, chemists, biologists, physicians, ecologists, and
> other specialists)?
>
>
> No. As all computations are executed in the arithmetical reality, physics
> becomes a perspectival statistics on all computations, and this entails
> that matter is NOT Turing emulable. Digital Mechanism makes Digital
> physicalism impossible. Arithmetic determines a differentiating flux of
> consciousness, but the statistics cannot make matter entirely Turing
> emulable. If “I” can survive with a digital virtual body, then my body
> cannot be Turing emulable, as it is determined by a statistics on a non
> computable domain. No machine can determine which machines support her, and
> its body is determined by all computations going through its current
> relative state. You can derive the quantum logics from this.
>
>
>
>
>
>  Is this a conundrum?
> Or, it merely a matter of "getting the physics right”?
>
>
> Physics has to be justified from a theory of information, in its large
> sense of “theory of consciousness”.
>
>
>
>
> By the way, I would argue that the clarity of the status of matter, i.e.,
> the chemical table of elements and their compositions, augmented by a huge
> range of physical measurements that span variables from all physical units
> of measure, is vastly clearer than any theory of physics.
>
>  Does not the theory of wave mechanics emanate from the physics of atoms
> and composites?   Or, shall we simply agree that the relationships from
> between physical theories form a “which came first, the chicken or the egg?”
>
>
>
> Assuming Mechanism, everything (quanta and qualia) arise from elementary
> arithmetic, or from elementary combinator theory (or from any other
> universal machinery). It happens that the two SK equations of the
> combinator theory are enough:
>
> Kxy = x
> Sxyz = xz(yz)
>
> + some identity axioms, but no need of logics (!). Well, we add often the
> difference axiom S ≠ K, to avoid the trivial combinatory algebra with one
> unique identity combinator, as III = I, and IIII = (II)II trivially.
>
> Then we can prove (using logic) that without assuming at least one
> universal machinery (like the numbers, or the combinators) we cannot get
> anyone of them. With assuming any of them, we get them all, and their many
> interaction, conflicts, quantum physical realities, etc.
>
> We are back at Pythagorus, when we assume Mechanism, or Shannon
> hypothesis, I would say. But with Church’s thesis and computer science,
> that is also much more than Pythagorus. It is basically the whole
> neoplatonist theology up to Damascius.
>
> Best,
>
> Bruno
>
>
>
>
>
>
>
>
> Cheers
>
> Jerry
>
> “The union of units unite the unity."
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> _______________________________________________
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