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

[Karl Javorszky]

This is Part Two of the Letter to Jerry ("Shannon and the Tautomat")



*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)? Is this a conundrum? Or, it merely a matter of "getting the
physics right”?*



In the last few generations I had the enjoyment to watch, there was a
movement to the

 subjectification of reality. There is less talk nowadays about the
Principle to which one has to subject himself. If the Great Idea, which is
independent of today’s small despairs and hopes, goes through dead bodies
to show us its supreme merits, it is received with more suspicion than in
my parents’ and grandparents’ times. Similarly, it used to be that Physics
rules supreme. After the discoveries of the last centuries, it was natural
that the measuring scientists believed they had figured out the answers. in
actual fact, it seems, Physics is subject to Mathematics is subject to
Logic is subject to Philosophy is subject to Physiology is subject to
Regulation Theory (formerly known as Theology). No, unfortunately, it is
now the theory of Physics that has to re-adjust to the facts coming from
life sciences, just like these had to give up long-held dogmata after being
repeatedly shown facts of evidence. The table has turned now. The fact is
that you cannot procreate unless some circumstances are ideal. The
requirements of maintaining an ideal surrounding leads to requirements
relating to ordered changes in the environment (that the changes that come
– e.g. by tide and daylight rhythms – will happen in an ordered way, where
all the rules that come from *a=a *are observed) and that the elements are
complying with the changes in the surrounding environment. Therefore the
surrounding environment has to be made up such that it obeys laws that
govern well ordered assemblies that undergo changes. Sorting pictures the
ranking of elements of a set according to a property (e.g. being well
prepared for cold/drought/predators, etc.)

Sorting things around and reordering them again, and watching the patterns
they make as they follow the rules of combinatorics, one discovers that
whatever small thing it is that consists of two parts, in an idealised
assembly, under external influences the elements will group up,
spontaneously, because it is in their nature to react so. Please watch the
exciting life of elements of a set while being reordered. One can educate
himself massively on the subject of ‘order’ by playing with his tautomat.
Like playing with a general version of the Rubik cube.

Had our culture allowed concepts of individuality of elements as the basis
of Logic and therefore of Arithmetic and all her descendants, we would live
in a different society. It could not have happened before our times anyway,
because one needs computers to delineate and concretise the concepts that
we discuss. We have now the technical means to sing about the heroics of
the little individual Dinge an sich; what we need now is the inner
permission to be curious. Some songs will sound familiar to professionals:
there are charms, up and down jumpers, spinners, bosoms, muons and some
more. The individual Dinge are quite flexible: in dependence of external
influences, they will match up with distinctly separate gangs of other
individual Dinge, therefore taking part in several great adventures. The
problem is that you do not need to excavate a huge circular tunnel with the
circumference of a great number of kilometres, so a small city’s worth of
well-paid professionals will not earn their bread, once people say, well
one can figure that out much cheaper! Bring me *n* urns and *n* balls,
*d *colors,
some robots and a few scribes and you will see what particles build up a
unit (the term *particle *in itself is an authoritarian one, imposing
identity on the object named by suggesting it is a part, a small one, of a
greater Ding. It is otherwise: the greater is built up of the parts, not
the smaller gets created by misadventures of the Whole. Let us stay with
Kant, it is the Ding an sich, but now, ready for a spin out in the world,
painted in two colors. These coloured things team up for some moments for
some tasks, and some of them stay together for very long, but the world is
not a collection of fragments of a broken Ultimate Whole.)



*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?”;** “The union of units unite the unity."*



The chemical elements are logical archetypes. That they exist and that they
have such characteristics, which allow them to be grouped in several ways
into types, is beyond any question. They are part of the setup.

Let us discuss a large warehouse with many items that are subject to
seasonal fluctuations of demand. The inner logistics of the warehouse has
to keep up with optimising the retrieval costs by re-arranging the contents
such that the most often sold product shall be the closest to the packaging
area. Now we state two hypothesises: 1) if the warehouse is not optimised,
pileups, traffic jams, are to be expected among delivery boys fetching the
merchandise, 2) the actions of optimising the warehouse contribute to the
inner traffic of the warehouse, and by that means cause pileups, traffic
jams, are to be expected among delivery boys fetching the merchandise. The
quantity and the quality (type, constituents) of the pileups will differ,
but pileups will come into existence. Some points in space are more sought
after than other points (entrance and exit of the warehouse). The pileups
are distinguishable. These are what is called chemical elements. We are
playing presently with interference patterns coming from the two differing
sub-segments of the common space, but arranging playing-card type pictures
of triangles intersecting each other is a very time-consuming hobby. Anyone
interested in naturally generated hiccups and pileups in theoretical space?



Now the time has come to go beyond answering your questions and offering a
concept which can clarify the relation between the special case (Shannon)
and the general system. This relates to the sadly neglected topic of the
cuts.

As we have learnt that 5 is 1+1+1+1+1, we have seen this demonstrated on
the number line, with cuts creating the unit distances. Then we have learnt
that 2+3=5. We have seen two and then three units placed alongside each
other and we have counted that these are indeed five. What we neglected to
ask, is the following: what happened to that noble and valiant Cut of the
Second Class that formerly separated the Two from the Three? Had it been
demoted to a simple, unimportant, common Cut First Class? Does this little
inexactitude not come back and hunt us as a mysterious vanity of Nature?

Shannon keeps the deep silence of one who has ridden roughshod across the
Society of Cuts. Not so us.

We account for the cuts very exactly, because it is them who determine the
structure of the set. If you have a Cut of Class {(2,(7,4,3),/insert funny
notation here/, etc. } (that is a cut that separates two from among seven
of which 4 are in 1 more group and 3 in 2 more groups) being different from
a Cut of Class {8,(11,7,0,5)}, then you can keep count of the cuts and
keeping count of the states of the set is more or less superfluous. If you
have a usual distribution of the types of cuts, then the actual measurement
(experience) can be compared to that, on the level of the messages about
cuts, which more or less exactly describes the state of the set. The
additional advantage of bookkeeping the cuts is that they translate into
First Class cuts, if the need arises to become linearised. If we play with
136 puppets (as is the most reasonable way to do), Shannon has 136 cuts
that are all alike. The tautomat generates a varied diversity of cuts that
are a description of the set’s state. If we match each state of the
tautomat to one of the states of Shannon, we see that in the intervals 1-32
and 97-135ff Shannon has more alternatives to carry messages expressed by
the state of the set that numbers *n* elements. Within the range of 33-96
however, with a peak at 67, up to 3.4 times more alternatives are there for
the state to have states in its form (reading) as a complete assembly than
as a sequenced collection of elements.

Information is a description of the remaining alternatives. The remaining
alternatives do not exist in this moment /they remain/. This is the reason
the birth of the concept is so much of endless pain and futile efforts. In
logic it is strictly forbidden to talk about things that do not exist.
Maybe one can help with the idea that we talk about the cuts, because the
cuts do exist. Their biodiversity has not been addressed yet. The cuts
appear to be the origami mechanism that unfolds from a linear order into an
elaborate composition.



The last point is a reassuring thought: we already do have a very detailed
table of all possible collections of cuts – of group boundaries – which
come from the elements’ belonging-to to cycles. It looks promising to
investigate, how the collection of cuts does not change if the set is
linearised. It appears that the cuts are the actual carriers of
information, as they detail, which alternatives remain, and this
independently of linear or spatial neighbourhood.

Thank you for addressing by your questions some interesting topics.
Karl

Am Mo., 21. Okt. 2019 um 15:51 Uhr schrieb Karl Javorszky <
karl.javorszky en gmail.com>:

>
> 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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