[Fis] definitions of information by Theil (1972) derived from Shannon (1948); Circularity and self

Karl Javorszky karl.javorszky at gmail.com
Tue Jan 31 17:02:20 CET 2023


Dear Colleagues,

Very interesting points, and they all relate.

Pedro:

The Catars (Albigenser) shall yet be recognized as martyrs for the right
cause. Their concept of duality is a dark mystery in contemporary terms
because the intellectual content had not been worked on, discussed,
restated, analyzed. I’d love to hear of an updated concise treatise about
the Catar idea of a basic split in the middle of the world. Their voice has
been terminated, but the idea keeps returning (*et expellas furcam natura
recurrit*).

Lou:

The idea of entries into a lexicon in which entries are by their nature
indexed and cross-referenced is what you point out as missing. This person
has repeatedly brought up the fact that, after some hocus-pocus with
natural numbers, one is in possession of a catalog of possible
coincidences. One can rank the possible coincidences according to their
predictability, from impossible over {slight, low, median, high} probably
to certainty. This is a numeric *Canto General*, enumerating all little
pieces that can assemble into a whole. The basic edition is some 23.000 x
136 x 72 x 71 cells of a table, in which are the Lego pieces, of which now
we can assemble anything that can be assembled from the pieces in the
table. (We have counted 46.260 cycles in our basic tables.) The
combinatorics among the elements (content of cells) of this data set is
what we talk about. This is as complete a library as there ever can be one.
Its contents are {phonemes, letters, words, sentences, phrases, paragraphs,
pages, chapters, essays, books, ideologies, logical systems}. The nature of
the units one uses depends on the focus. The cell contents are probably of
interest to quantum counting people. We discuss that level, which is in an
extra database, the Catalog of Possible Contemporaries. (The extra database
is for convenience only; its contents are aggregated cells from the basic
data set.) Later generations will presumably build up a further table Forms
and Shapes of Contemporary Coincidences, and then the real learning will
begin. (Like the Dictionary of Basic Fuseki, only far more generalized
and *a+b=c
*based.)

It would be a heroic guess, which level of agglomeration of basic facts
would correspond to our ideas of ‘apple’, ‘warm’, ‘eat’. Bundles of cycles
form an archetype which can be remembered. There is a connection to
the *semantic
markers,* which build up an idea, here. This level of agglomeration of
basic facts has undergone several transmutations and metamorphoses. Yet,
the rules of the translations from one system of values into a different
system of values (an experience can be differentiated, it is often referred
to by the same name, an apple is something that has the properties
remembered) are subservient to a more basic set of rules. The concept
building rules are an implication (among many others) of the facts that are
the archaic rules. (They say: 'you can’t make bacon from a dog’.) The
general rules are still valid in the meta-databases which have their own
varied rules. (One cannot think illogical.) The descendants of certainties
are varied in form and content, but they all depend on the basic certainty,
of which they are an implication/deduction. There is an identifying tag on
each descendant, which allows a blockchain-like reverse accounting until
one arrives at *a=a, a+b=c, pos(k, reorder), contemporary with(), etc. *markers
which identify the path of the sequence of steps this specific
constellation can have been generated. The indexes are given by Nature, as
each member of each cycle in any reorder is exactly known. The aggregation
of elementary facts into meaningful signs of whatever is a technique
already well known by the applied sciences. The vocabulary of the 21st
century version of a homunculus is (in theory, potentially) rather detailed
and it contains (is based on) the relation of every possible fact to any
other possible fact. The nearness of spiders and butterflies can find a
numerical expression that relates it to the nearness of wolves and bears.

An example: We play with cards, building towers on strategic places. The
Sumerian method counts the height of the stack of cards in each position
when evaluating the chances of the next move. The method we propose here is
to look at the face side of the cards too. This knowledge will bring no
advantages in the present game. It is even unthinkable to discuss the
individualities of the tiles that make up a tower under the rules of the
game we presently play. There is simply no such thing, in the rules
presently observed. Discovering inner relationships among tiles of
different towers brings a new dynamic to the game. The face side of the
cards shows that it is optimal to play with around *66 *units of *136 *total,
that the tiles/cards are individuals, that they are ordered, and that they
are ordered in several ways, some of these orders being partly
contradictory. What they demonstrate is, that *there is a web of
relations *among
units. One can use the natural web of order relations to index and identify
whichever discernible agglomerations one wants to give a name to.

Terrence:

Like in a good Zen koan, your answer is in your question. You say: “ …
relations … add a level of incompletability…”, “we have crossed out of the
realm of computation in any standard sense”. The solution, therefore is,
that “…complete conception of information … confront this challenge, or
else bracket such considerations as unanalyzed givens”. Brilliant
observation.

It is in this same sense that introducing a new level of awareness and
attention to details frankly outsteps the boundaries of counting as known
before and becomes a ‘finite automat’, based on combinatorics among natural
numbers during periodic changes. This is the set of tables mentioned above.
This numeric heap is indeed an unanalyzed given. There is no contradiction.
The answer to all questions is not *42*, as some of us had wished, but the
interplay among *~ 66 - ~ 70 *logical units. This is the factually correct
answer, generates several matrices and gives a reference grid to anything
and all. There is no soul visible in this numeric heap. The facts of the
matter remain the facts of the matter and nothing else. Gone is all the
transcendence. That the know-all is itself dumb is no contradiction.

That there appears to remain an unsolvable remainder is detailed in Zen
Flesh Zen Bones by Paul Reps.

Karl:

Let me contribute from my own field also something to beliefs, religion,
hope, etc. After 40 years in the profession, one believes to have
recognized the economy of the good word. We know from animals, that in a
stress situation, the animal disgorges any food not yet digested (next to
lessening its mass [for a possible flight] in other ways, too). One has the
suspicion that a percentage of the population has discovered that to be
near to such persons who experience acute stress, has the advantage of
being able to take away parts of the still valuable matter the subject has
disgorged. Maintaining the feeling of stress in a dependent group maintains
the feeling in the subjects that they should get rid of something, in order
to be lighter, in many senses. He who helps you in crises, he contributes
to your feeling of being lighter after the encounter. The industry of
providing comfort has a provider side also, with its own interests and
rules. It is reasonable to agree among the providers of comfort that the
comfort one provides is one and indivisible, perfect and free of
contradictions, all parts fitting as they should. The concept is easy to
agree on, is uniform and can be well communicated. No wonder then, that the
Catars were judged heretic. The complexity of a world view in which the
world is although one whole, contains parts, and that the parts do not fit
always smugly, would have overextended the didactic capacities of
seminaries. Keep the teaching simple, the audience is simple. The creation
is perfect and there are no inner contradictions and discongruencies within
it. Such teaching fully keeps within the Sumerian tradition. The comfort
providing establishment had a debatable point in killing the Catars,
discouraging by this precedent any research into diversity and deviation as
academic subjects as such. We have a neurological preference for perceiving
similarities over the perceptions of diversities. A true comfort helps the
customer to feel good. We are hereditary dependent on the substance that
gets generated as we process analogies, similarities, identities.  Junkies
everywhere.



Thanks for the nice session.

Karl



Am Di., 31. Jan. 2023 um 15:41 Uhr schrieb Louis Kauffman <loukau en gmail.com
>:

> Dear Joseph,
> Please note that computing at the present time is based on eliminating
> circularity at the base hardware level so that simple operations can happen
> reliably such as NOR gates.
> The rest of computing, both hardware and software is related to recursion
> and hence to controlled circularity. A recursive process involves the
> repeated application of a transformation, coupled with a
> count of that repetition so that stopping avoids an infinite loop. At the
> level of design we may create the recursion as a circular definition X =
> F(X) but this is reworked into x_{n+1) = F(x_{n}}, and the count on n is
> crucial for
> the execution of the process. Other forms of circularity are avoided by
> rule. For example, one cannot put the file representing the desktop of your
> computer into another file. This is equivalent to avoiding self-referential
> paradox. Furthermore, in the structure of circuitry one concatenates basic
> elements such as NOR gates into graph structures with cycles
> (circularities) again in controlled ways (flip flop circuits for counting
> e.g.).
> In biological systems there are many such cycles that are important for
> organic processes at all levels. If one understands by circularity, the
> presence of cycles in the graphical structure of things and processes, then
> one sees that circularity is a concept that is ubiquitous in information
> science.
>
> We have an apparent contradiction that is not a contradiction!
> The attitude that there should not be a place for circularity seems to be
> the same as saying
> that it always needs to be noted and sometimes it needs to be controlled.
>
> Note again Terry Deacon’s paragraph. He is not saying that there is no
> place for circularity, but rather that we have to enlarge our view of even
> circularity beyond the formal Goedelian self-reference.
>
> "I can't resist commenting. The problem, of course, is that formal
> relations and models must be instantiated in some medium. But referential
> circularities that include reference to these media involve more than
> formal Gödelian circularities. They entangle epistemological and
> ontological relations in ways that add a level of incompletability that
> cannot be avoided when considering living and mental processes of
> interpretation. Thus, when we refer to "self" in descriptions of the "I" of
> human interpretive agency, or even when just describing bacteria as
> "self"-reproducing, we have crossed out of the realm of computation in any
> standard sense. Ultimately, I would argue, that any complete conception of
> information that includes the interpretation of referential and pragmatic
> attributes must confront this challenge, or else bracket such
> considerations as unanalyzed givens.”
>
> The matter of “crossing out of the realm of computation” is illustrated by
> the Penrose Thought Experiment.
>
> Penrose Thought Experiment.
> Suppose that “I” am a specific consistent Turing machine.
> Then I can be encapsulated as a formal system S, and everything that I can
> prove can be proved by S and vice versa.
> So now I examine the system S and prove Goedel’s incompleteness theorem
> for S. I produce a sentence G that cannot be proved by S, but such that I
> can prove G.
> Since I and S have identical proving abilities, this is a contradiction.
> Therefore I am not one specific Turing machine.
>
> This thought experiment led to a book by Roger Penrose (The Emperor’s New
> Mind), much debate and a second book (“Shadows of the Mind”) and so I
> certainly do not put this
> forward as doctrine, but nevertheless, when we refer to "self" in
> descriptions of the "I" of human interpretive agency we have crossed out of
> the realm of computation in any standard sense.
>
> Very best,
> Lou
>
> On Jan 31, 2023, at 1:36 AM, joe.brenner en bluewin.ch wrote:
>
> Dear Terry, Dear All,
>
> I agree with Terry. Circularity is an idealized concept that has no place
> in information science.
>
> Machines instantiate circularity to all intents and purposes, give or take
> a few atoms of wear and some vibrations. Real complex processes do not.
>
> As for self, as in "self"-organization, this is another idealized concept
> that fails to take into account hetero components in a process, actual or
> potential.
>
> Why people tend to cling to binary concepts, including in the grounding of
> phenomena, is a question for psychology more than anything else.
>
> Best,
> Joseph
>
> ----Original Message----
> From : deacon en berkeley.edu
> Date : 30/01/2023 - 21:58 (E)
> To : loukau en gmail.com
> Cc : fis en listas.unizar.es, stanowskimariusz en wp.pl, nikitashk en gmail.com,
> igamberdiev en mun.ca
> Subject : Re: [Fis] definitions of information by Theil (1972) derived
> from Shnnon (1948); back to the basics?
>
> I can't resist commenting. The problem, of course, is that formal
> relations and models must be instantiated in some medium. But referential
> circularities that include reference to these media involve more than
> formal Gödelian circularities. They entangle epistemological and
> ontological relations in ways that add a level of incompletability that
> cannot be avoided when considering living and mental processes of
> interpretation. Thus, when we refer to "self" in descriptions of the "I" of
> human interpretive agency, or even when just describing bacteria as
> "self"-reproducing, we have crossed out of the realm of computation in any
> standard sense. Ultimately, I would argue, that any complete conception of
> information that includes the interpretation of referential and pragmatic
> attributes must confront this challenge, or else bracket such
> considerations as unanalyzed givens.
>
> — Terry
>
> On Mon, Jan 30, 2023 at 12:58 AM Louis Kauffman < loukau en gmail.com>
> wrote:
>
>> Most certainly!
>> All structures with any form have circularities. The simplest is one
>> distinction and the back and forth between the whole and the division into
>> apparent parts.
>>
>> On Jan 30, 2023, at 1:35 AM, Karl Javorszky < karl.javorszky en gmail.com>
>> wrote:
>>
>> Definitions are circular. Like crossing  points in a web of a roads.
>>
>> How nice it would be, if anyone would create (actually, find or discover)
>> a web which connects units of the system to each other!?
>>
>> Such an inner web of relations can easily be found and has been found and
>> has been published. Here's once again.
>>
>> Use a,b , a,b <= 16, a<=b as pairs. Each pair is the basic element . The
>> cohort in which a,b have 16 different varieties is 136 strong.
>>
>> Now order this collection. Then reorder. Pay attention to details.
>>
>> You find cycles.
>>
>> The cycles connect elements to each other in ways that will surprise you
>> and cause torpor. In a catatonic regression, some people cease thinking.
>> This will not be the danger in this case. You all are fit for the challenge
>> of discovering relations.
>>
>> The web of references you talk about is in existence. Appurtenances of
>> elements to cycles give numeric data, with which other elements any given
>> element is related by means of belonging to cycles of a different order
>> aspect.
>>
>> Ask and find your wishes already fulfilled. Just look what happens if you
>> listen to people talking to you. Try conceptualising cycles.
>>
>> Good luck!
>>
>> Karl
>>
>>
>> On Mon, 30 Jan 2023, 09:08 Louis Kauffman, < loukau en gmail.com> wrote:
>>
>>> Dear Nikita,
>>> First of all, lets be clear about definitions in the usual sense of the
>>> word. We define a term by relating it to other terms and to experiences.
>>>
>>> In a dictionary terms are defined in relation to other terms.
>>> This often leads to circularity.
>>> For example, If I look up “difference” in the dictionary I find that it
>>> means “not the same”.
>>> If I look up “same” in the dictionary I find that it means “not
>>> different”.
>>> The dictionary shows relationships of words and relies on our experience
>>> for many of the meanings.
>>>
>>> In mathematics we do not refer to experience in our definitions, but
>>> rather to axioms that delimit the relationships. Thus if P and Q are
>>> distinct points in Euclidean Geometry, then there is a line L uniquely
>>> determined by P and Q so that P and Q are on that line L. This property
>>> is an Axiom of the Geometry. We do not specify what P and Q “are” or what a
>>> line “is”, but we have in mind certain models that do
>>> satisfy these axioms. This is an efficient way to proceed for the ways
>>> of mathematical thinking. We even have certain kinds of definitions that
>>> partake of circularity. For example, I can say consider a group G generated
>>> by
>>> elements a,b so that a = bab^{-1}. The equation I just wrote “defines” a
>>> in terms of itself. There is nothing wrong with this and we regard it as a
>>> constraint on the way a “behaves”.
>>>
>>> In mathematics we allow circularities as constraints and want
>>> definitions to be free of circularities. This amounts to a terminology for
>>> definitions that distinguishes them from constraints.
>>>
>>> I say that you cannot have a mathematical definition of distinction
>>> because the best we could ever do about distinction is to indicate a
>>> relationship or a constraint such as “we take the form of distinction for
>>> the form.”.
>>>
>>> Eucid himself did not adhere to the present-day version of definitions
>>> in mathematics (after all he wrote in 500BC!). Euclid says that “A point is
>>> that which has no part.” and he says that “A straight line lies evenly upon
>>> itself.” Each of these statements has great insight, but requires much
>>> extra discussion and an understanding of the models for Geometry that are
>>> intended.
>>>
>>> Just so the von Foerster sentence tells us that whatever an “I”,  it is
>>> constrained to be a relation between itself and observing itself.
>>> We appreciate this because we recognize it as a property of the “I” with
>>> which we are familiar.
>>>
>>> NOW, you say that you will take I as "a computing device that works
>>> according to a DNA program”. I see what you mean. I could regard myself as
>>> a computing device that works according to a DNA program.
>>> I could regard myself (as Paul Erdos used to say) as a “device for
>>> turning coffee into theorems”. I have to tell you that I like to think of
>>> myself as a biocomputer on some days of the week, but not all. And on those
>>> other days I would dispute that I am any kind of computer device or formal
>>> system. I would debate that I have properties that go beyond the
>>> constraints of such formal devices. I would argue this on the basis of
>>> Godelian incompleteness,or on the basis of simple abilities to step back
>>> and survey situations that are presented to my “device”. If I am a device
>>> it is a special device that is equipped to create meta-levels and then join
>>> with these
>>> meta-levels in a continuing process of comprehension.
>>>
>>> In any case, I say that when you make statements such as “defining I” as
>>> "a computing device that works according to a DNA program” you are actually
>>> suggesting certain types of models for I and you then
>>> implicitly ask us to debate whether the constraints of your models might
>>> remove them from being the only answer to the question of making such a
>>> definition. In the case of “I” , I suggest that a computational device
>>> model is interesting and fruitful but not the whole story.
>>>
>>> It is important to distinguish definitions from models.
>>>
>>> Very best,
>>> Lou
>>>
>>> On Jan 29, 2023, at 11:59 AM, Nikita Shklovskiy < nikitashk en gmail.com>
>>> wrote:
>>>
>>> Dear Lou,
>>> Great! let's use fruitful starting points. Determining the difference in
>>> the treatment of Heinz von Foerster
>>> “I am the observed relation between myself and the observing myself”
>>> everything suits me, only I need to introduce the definition of “I”. For
>>> the Biosphere, this was done by Efim Lieberman in 1972: ""I" is a computing
>>> device that works according to the DNA program." In other words, a
>>> biological cell or several cells. In the Noosphere, I propose the
>>> definition of "I" as a "human phenomenon" i.e. "an animal of the species
>>> Homo Sapience, successfully trained in human language, i.e., a computing
>>> device capable of interfering with a program in human language." I'm not
>>> afraid of circular definitions and I understand that definitions can be
>>> complex. But it seems to me that using words in science without agreeing on
>>> their meaning is counterproductive.
>>> I will be happy to discuss your
>>>   point of view on this!
>>> Yours
>>> Nikita
>>>
>>> Вс, 29 янв. 2023 г. в 18:59, Louis Kauffman < loukau en gmail.com>:
>>>
>>>> Dear Nikita,
>>>> Distinction is a very fertile starting place as an idea or concept.
>>>> We formalize aspects of this idea but not the idea itself.
>>>> This is because any formal definition is a kind of distinction.
>>>> e.g the definition of prime number explicates the distinction between
>>>> primes and composites.
>>>> Thus to define distinction in a formally would involve using that
>>>> concept in its very definition.
>>>> Circular definitions such as G. Spencer-Brown’s “We take the form of
>>>> distinction for the form.” or Heinz von Foerster’s
>>>> “I am the observed relation between myself and observing myself.”
>>>> are very useful for discussion, and for finding new formalisms.
>>>> I say that there cannot be a definition of distinction that is not
>>>> circular.
>>>> You may have a different point of view on this matter!
>>>> Best,
>>>> Lou Kauffman
>>>>
>>>> On Jan 29, 2023, at 4:50 AM, Nikita Shklovskiy < nikitashk en gmail.com>
>>>> wrote:
>>>>
>>>> *Information “is any (distinguishable) regularity of zeros and ones”*
>>>> great!
>>>> the only problem of Your Binary Universe is to give definition for
>>>> DISTINGUISHABILITY.
>>>> And to tell us who is the oner of this equipment:)
>>>>
>>>> Вс, 29 янв. 2023 г. в 13:27, Mariusz Stanowski < stanowskimariusz en wp.pl>:
>>>>
>>>>
>>>>> Dear All,
>>>>>
>>>>> A lot of the confusion about definitions of fundamental terms such as
>>>>> information is due to the transfer of terms found at a higher (human) level
>>>>> of complexity to a lower (more fundamental) level. Hence the variety of
>>>>> definitions of these concepts, which sometimes contradict each other. At
>>>>> the lower level, these terms become equivalent because there is less
>>>>> differentiation needed, e.g. in the micro world there is no longer a sender
>>>>> and a receiver, we are dealing only with interactions. Also *information,
>>>>> form, feature, structure, object, anything that can be distinguished *-
>>>>> are all equivalent at the basic level.
>>>>>
>>>>> This also applies to physical theories that try to get to the roots of
>>>>> the universe by creating complicated theories such as big bang, string
>>>>> theory or multiverse. What the theorists fail to notice is that
>>>>> complication does not bring us closer but further away from reaching the
>>>>> foundations. To reach this level, it is essential to use the minimum
>>>>> necessary concepts with which one can describe the universe. Such a
>>>>> simplest model is the binary model, on which basically everything can be
>>>>> explained/understood. An example of such a binary model is Binary Model of
>>>>> Universe, which is simply a *binary structure* (only zeros and ones).
>>>>> On this model it is also easy to understand what information is: *it
>>>>> is any (distinguishable) regularity of zeros and ones.*
>>>>>
>>>>> Best regards
>>>>>
>>>>> Mariusz
>>>>>
>>>>>
>>>>>
>>>>> W dniu 26.01.2023 o 06:28, Francesco Rizzo pisze:
>>>>>
>>>>> Dear Mariuzs, Nikita and all. When I intervene in the discussion, I
>>>>> never claim to possess the truth, but I tend to contribute to forming the
>>>>> process of possible truth by taking into account everyone's contribution. I
>>>>> have repeatedly supported the need to have: - a general conception of
>>>>> knowledge based on the triad: meaning, information, communication;- a
>>>>> particular measurement-evaluation applied in the various natural and human
>>>>> knowledge. as a quantum-semiological economist, economy like physics are
>>>>> sciences based on the value of form or the form of value (even Ettore
>>>>> Maiorana, the late physicist, thought so). So these two sciences are a
>>>>> matter of form, not of (material) substance. If this is the case,
>>>>> information presupposes meaning and is the prerequisite for communication.
>>>>> . What interaction can there be between a stone and a tree, a car and a
>>>>> poem, a  star and an ant, etc.? In fact, between two machines there can
>>>>> only be a transmission of signals with a common code, while the
>>>>> communication process between human beings it is a transmission of meaning
>>>>> based on the interaction of signs (such as, for example, the economic
>>>>> market) involving a lexical code of the issuing source different from the
>>>>> lexical code of the recipient recipient. I have already said more than I
>>>>> thought I would write, because I'm busy writing an important book, at least
>>>>> for me. However, let us never forget that knowledge is a process based on
>>>>> love or on acceptance of the other (thought), while not sharing it. A
>>>>> hug-Francesco.
>>>>>
>>>>> Cari Mariuzs, Nikita e tutti.
>>>>> quando intervengo nella discussione non pretendo mai di possedere la
>>>>> verità, ma protendo a contribuire
>>>>> a formare il processo della verità possibile tenendo conto del
>>>>> contributo di tutti. Più volte ho sostenuto
>>>>>  la necessità di avere:
>>>>>  - una  concezione generale della conoscenza basata sulla triade:
>>>>> significazione, informazione, comunicazione;
>>>>> - una misurazione-valutazione particolare applicate nelle diverse
>>>>> conoscenze naturali e umane.
>>>>> In questo senso, non posso non ricordare che, nella qualità di
>>>>> economista quantista-semio-logico, l'economia
>>>>> come la fisica sono delle scienze fondate sul valore della forma o la
>>>>> forma del valore (anche Ettore Maiorana, il fisico
>>>>> scomparso, la pensava così). Quindi queste due scienze sono una
>>>>> questione di forma, non di sostanza (materiale).
>>>>> Se le cose stanno così l'informazione presuppone il significato ed è
>>>>> il presupposto della comunicazione.
>>>>> Si può parlare di interazione nella comunicazione e di differenza o
>>>>> contrasto nell'informazione. Che interazione
>>>>> vi può essere tra una pietra e un albero, una macchina e una
>>>>> poesia, una  stella e una formica, etc.?
>>>>> Difatti, tra due macchine vi può essere solo una trasmissione di
>>>>> segnali con un codice comune, mentre
>>>>> il processo comunicativo tra esseri umani è una trasmissione di senso
>>>>> basato sull''interazione di segni
>>>>> (come, ad esempio,  il mercato economico) implicante un codice-lessico
>>>>> della fonte emittente diverso dal codice-lessico
>>>>>  del destinatario ricevente.
>>>>> Già ho detto più di quanto pensavo di scrivere, perchè sono impegnato
>>>>> nella conclusione della scrittura di un libro
>>>>> importante, almeno per me. Comunque non dimentichiamo mai che la
>>>>> conoscenza è un processo fondato sull'amore o
>>>>> sull'accettazione dell'altro (pensiero), pur non condividendolo.
>>>>> Un abbraccio-
>>>>> Francesco.
>>>>>
>>>>> Il giorno mer 25 gen 2023 alle ore 21:18 Nikita Shklovskiy <
>>>>> nikitashk en gmail.com> ha scritto:
>>>>>
>>>>>>
>>>>>> Dear colleagues!
>>>>>> It seems to me that the general concept of information can be
>>>>>> obtained in the form of an axiom. This can be done by adding two more
>>>>>> concepts to the definition: “language system” and “meaning”. In the case of
>>>>>> the definition “information is everything that the sender emits that the
>>>>>> recipient can interpret”, four additional definitions will have to be
>>>>>> introduced for the concepts “sender”, “receiver”, “radiates”, “interprets”.
>>>>>>
>>>>>> Efim Lieberman in 1972 realized the need to take into account the
>>>>>> actions spent on calculations in all biological cells
>>>>>> https://urldefense.com/v3/__https://doi.org/10.1016/j.biosystems.2022.104653__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDR7bRA04$ 
>>>>>> <https://urldefense.com/v3/__https://doi.org/10.1016/j.biosystems.2022.104653__;!!D9dNQwwGXtA!RnOEih8sgWzPRFRCWueR81K14O1xTQkUPMFOGyIS_e3Qqoj80tIU3rGT-kvAHkPBy0yw5FbjkjoGfol-47zh$>
>>>>>>
>>>>>> In this paradigm, it is clear that information does not exist without
>>>>>> material carriers - code elements.
>>>>>>
>>>>>> For all the cells of the world, we have one language system, which is
>>>>>> called "Genetic Language". This is a special case of the well-defined
>>>>>> information written on the DNA that created the entire Biosphere.
>>>>>> Another special case is the language system of human language - this
>>>>>> information formed the Noosphere.
>>>>>>
>>>>>> The general axiomatic definition turns out to be triple and looped:
>>>>>> “information is something from which a language system can derive meaning;
>>>>>> meaning is what the language system extracts from information, and the
>>>>>> language system is what extracts meaning from information.” As in the
>>>>>> Christian Trinity, these three concepts are “consubstantial and
>>>>>> indivisible.”
>>>>>>
>>>>>>
>>>>>> вт, 24 янв. 2023 г. в 10:34, konstantin lidin < lidinkl en hotmail.com>:
>>>>>>
>>>>>>
>>>>>>> Thank you, Howard.
>>>>>>> Your definition of information practically coincides with Shannon's
>>>>>>> definition, only elementary (sub-elementary) particles act as inductors and
>>>>>>> recipients.
>>>>>>> In the next step, however, this approach leads us to the notion of
>>>>>>> information quality. A message can contain both a signal (relevant
>>>>>>> information) and noise. But the notion of relevance of information is
>>>>>>> subjective. Relevance is compliance with the goals that the
>>>>>>> inductor-recipient pair sets when exchanging information.
>>>>>>> Do you think quarks and protons have goals and free will?
>>>>>>> This is a very important question, because in most areas, except for
>>>>>>> the Shannon theory of communication, the quality of information is ignored.
>>>>>>> The subjectivity of this parameter looks too shocking to include it in a
>>>>>>> decent academic model (about the same way the Heisenberg uncertainty
>>>>>>> principle is still perceived)
>>>>>>> ------------------------------
>>>>>>> *From:* Howard Bloom <howlbloom en aol.com>
>>>>>>> *Sent:* 24 January 2023 08:21
>>>>>>> *To:*lidinkl en hotmail.com <lidinkl en hotmail.com>; fis en listas.unizar.es
>>>>>>> <fis en listas.unizar.es>; loet en leydesdorff.net <loet en leydesdorff.net>
>>>>>>> *Subject:* Re: [Fis] definitions of information by Theil (1972)
>>>>>>> derived from Shnnon (1948); back to the basics?
>>>>>>>
>>>>>>> the definition of information in my book The God Problem: How a
>>>>>>> Godless Cosmos Creates:
>>>>>>>
>>>>>>> information is anything a sender emits that a receiver can
>>>>>>> interpret.
>>>>>>>
>>>>>>>
>>>>>>> the first information appears when the first quarks emerge in the
>>>>>>> first 10-34 of a second of the big bang.  quarks read each other's social
>>>>>>> signals of attraction or repulsion and acted on them to gang up in groups
>>>>>>> of two or three, thus forming protons and neutrons, which also gave off
>>>>>>> social signals and agglomerated in proton-neutron teams.
>>>>>>>
>>>>>>> with warmth and oomph--howard
>>>>>>>
>>>>>>>
>>>>>>> -----Original Message-----
>>>>>>> From: konstantin lidin <lidinkl en hotmail.com>
>>>>>>> To: fis en listas.unizar.es <fis en listas.unizar.es>; Loet Leydesdorff <
>>>>>>> loet en leydesdorff.net>
>>>>>>> Sent: Mon, Jan 23, 2023 1:31 pm
>>>>>>> Subject: Re: [Fis] definitions of information by Theil (1972)
>>>>>>> derived from Shnnon (1948); back to the basics?
>>>>>>>
>>>>>>> Unfortunately, Shannon's definition can only be used in a very
>>>>>>> narrow class of cases. When we consider any process other than the
>>>>>>> transmission of a message from the inductor to the recipient, this
>>>>>>> definition does not work.
>>>>>>> The most authoritative researchers of the philosophy of information
>>>>>>> admit that there is still no general definition. The concepts of
>>>>>>> information in different spheres differ significantly and cannot be
>>>>>>> combined into something commonly used
>>>>>>> Baumgaertner, B., Floridi, L. Introduction: The Philosophy of
>>>>>>> Information. * Topoi* *35*, 157–159 (2016).
>>>>>>> https://urldefense.com/v3/__https://doi.org/10.1007/s11245-016-9370-7__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDeq7Ehek$ 
>>>>>>> <https://urldefense.com/v3/__https://doi.org/10.1007/s11245-016-9370-7__;!!D9dNQwwGXtA!SXg13tbkdIexlHicpgmmFoFwIcpgeHl3c2rgtD9HsQHuKRQodSQhjWMYAL-3r-YyBOXRc3vMzQUkPXSVFHs$>
>>>>>>> ------------------------------
>>>>>>> *From:* Fis <fis-bounces en listas.unizar.es> on behalf of Loet
>>>>>>> Leydesdorff <loet en leydesdorff.net>
>>>>>>> *Sent:* 23 January 2023 23:29
>>>>>>> *To:*fis en listas.unizar.es <fis en listas.unizar.es>
>>>>>>> *Subject:* [Fis] definitions of information by Theil (1972) derived
>>>>>>> from Shnnon (1948); back to the basics?
>>>>>>>
>>>>>>> Theil (1972) pp. 1 and 2:
>>>>>>> *1.1. * *Information*
>>>>>>> Consider an event *E *with probability *p; * the nature of the
>>>>>>> event is irrele­vant. At some point in time we receive a reliable message
>>>>>>> stating that *E *in fact occurred. The question is: How should one
>>>>>>> measure the amount of information conveyed by this message?
>>>>>>> *Information*
>>>>>>> Since the question is vague, we shall try to answer it in an
>>>>>>> intuitive manner. Suppose that *p *is close to 1 (e.g., *p = *.95).
>>>>>>> Then, one may argue, the message conveys very little information, because
>>>>>>> it was virtually certain that *E w*ould take place. But suppose
>>>>>>> that *p = .01, *so that it is almost certain *E *will not occur. If *E
>>>>>>> *nevertheless does occur, the message stating this will be
>>>>>>> unexpected and hence contains a great deal of information.
>>>>>>>
>>>>>>> These intuitive ideas suggest that, if we want to measure the
>>>>>>> information derived from a message in terms of the probability *p * that
>>>>>>> prevailed before or to the arrival of the message, we should select a *decreasing
>>>>>>> * function. The function proposed by SHANNON (1948) is  when the
>>>>>>> probability prior to the message is zero) to 0 (zero information when the
>>>>>>> probability is one).
>>>>>>>
>>>>>>> The unit of information is determined by the base of the logarithm.
>>>>>>> Frequently 2 is used as a base, which implies that any message concerning a
>>>>>>> 50-50 event has unit information: h() = log 2 2 = 1, and
>>>>>>> information is then said to be measured in binary digits or, for short, *bits.
>>>>>>> * When natural logarithms are used, the information unit is a
>>>>>>> *nit. *
>>>>>>>
>>>>>>> *best, loet*
>>>>>>>
>>>>>>> *_______________*
>>>>>>> *Loet Leydesdorff*
>>>>>>>
>>>>>>> *"The Evolutionary Dynamics of Discusive Knowledge"
>>>>>>> <https://urldefense.com/v3/__https://link.springer.com/book/10.1007/978-3-030-59951-5__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLLuhNS00$>(Open
>>>>>>> Access)*
>>>>>>> Professor emeritus, University of Amsterdam
>>>>>>> Amsterdam School of Communication Research (ASCoR)
>>>>>>> loet en leydesdorff.net ; https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKD_sM0Hek$ 
>>>>>>> <https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLGpM1vg4$>
>>>>>>> https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDc1rBTpo$ 
>>>>>>> <https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLaBGhTzQ$>
>>>>>>> ORCID: https://urldefense.com/v3/__http://orcid.org/0000-0002-7835-3098__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDClgI3go$ 
>>>>>>> <https://urldefense.com/v3/__http://orcid.org/0000-0002-7835-3098__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLH5t9V6o$>;
>>>>>>>
>>>>>>>
>>>>>>> _______________________________________________
>>>>>>> Fis mailing list
>>>>>>> Fis en listas.unizar.es
>>>>>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>>>>>> ----------
>>>>>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>>>>>
>>>>>>> Ud. recibe este correo por pertenecer a una lista de correo
>>>>>>> gestionada por la Universidad de Zaragoza.
>>>>>>> Puede encontrar toda la información sobre como tratamos sus datos en
>>>>>>> el siguiente enlace:
>>>>>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>>>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse
>>>>>>> de baja desde la propia aplicación en el momento en que lo desee.
>>>>>>> http://listas.unizar.es
>>>>>>> ----------
>>>>>>>
>>>>>>>
>>>>>>> __________________________
>>>>>>> Howard Bloom
>>>>>>> Howardbloom.net
>>>>>>> <https://urldefense.com/v3/__http://howardbloom.net/__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7MnbnxrQh-_h$>
>>>>>>> https://urldefense.com/v3/__http://www.howardbloom.institute__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDfJDNAFU$ 
>>>>>>> <https://urldefense.com/v3/__http://www.howardbloom.institute__;!!D9dNQwwGXtA!Tpag3KoyVBTYFmRC_S68cEwcSi0ATPLOm2w3nZyWcoVHrX7gRvMJvrxjco3GXYAurl7cvBFKQpIiH-Gj5ho$>
>>>>>>> trailer for BRIC-TV's 66-minute film, The Grand Unified Theory of
>>>>>>> Howard Bloom,  https://urldefense.com/v3/__https://youtu.be/rGkOkChazUQ__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKD-VV2Um0$ 
>>>>>>> <https://urldefense.com/v3/__https://youtu.be/rGkOkChazUQ__;!!D9dNQwwGXtA!Tpag3KoyVBTYFmRC_S68cEwcSi0ATPLOm2w3nZyWcoVHrX7gRvMJvrxjco3GXYAurl7cvBFKQpIi5mKNcrg$>
>>>>>>> Best Picture, Science Design Film Festival. Best Documentary
>>>>>>> Feature, Not Film Festival, Italy. Now available  on Apple TV, Amazon,
>>>>>>> Google Play, Microsoft, Vimeo, Vudu, and Fandango.
>>>>>>>
>>>>>>> Author of: The Lucifer Principle: A Scientific Expedition Into the
>>>>>>> Forces of History ("mesmerizing"-The Washington Post),
>>>>>>> Global Brain: The Evolution of Mass Mind From The Big Bang to the
>>>>>>> 21st Century ("reassuring and sobering"-The New Yorker),
>>>>>>> The Genius of the Beast: A Radical Re-Vision of Capitalism ("A
>>>>>>> tremendously enjoyable book." James Fallows, National Correspondent, The
>>>>>>> Atlantic),
>>>>>>> The God Problem: How A Godless Cosmos Creates ("Bloom's argument
>>>>>>> will rock your world." Barbara Ehrenreich),
>>>>>>> How I Accidentally Started the Sixties (“Wow! Whew! Wild!
>>>>>>> Wonderful!” Timothy Leary),
>>>>>>> The Mohammed Code (“A terrifying book…the best book I’ve read on
>>>>>>> Islam.” David Swindle, PJ Media), and
>>>>>>> Einstein, Michael Jackson & Me: a Search  for Soul in the Power Pits
>>>>>>> of Rock & Roll ("Amazing. The writing is revelatory." Freddy DeMann,
>>>>>>> manager of Michael Jackson and Madonna), Best Book of 2020, New York Weekly
>>>>>>> Times.
>>>>>>> A Quartz Magazine Pro
>>>>>>> Former Visiting Scholar, Graduate Psychology Department, New York
>>>>>>> University, Former Core Faculty Member, The Graduate Institute; Current
>>>>>>> Kepler Space University Senior Scholar.
>>>>>>> Founder: International Paleopsychology Project. Founder, Space
>>>>>>> Development Steering Committee.  Member Of Board Of Governors, National
>>>>>>> Space Society. Founding Board Member: Epic of Evolution Society. Founding
>>>>>>> Board Member, The Darwin Project.
>>>>>>> _______________________________________________
>>>>>>> Fis mailing list
>>>>>>> Fis en listas.unizar.es
>>>>>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>>>>>> ----------
>>>>>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>>>>>
>>>>>>> Ud. recibe este correo por pertenecer a una lista de correo
>>>>>>> gestionada por la Universidad de Zaragoza.
>>>>>>> Puede encontrar toda la información sobre como tratamos sus datos en
>>>>>>> el siguiente enlace:
>>>>>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>>>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse
>>>>>>> de baja desde la propia aplicación en el momento en que lo desee.
>>>>>>> http://listas.unizar.es
>>>>>>> ----------
>>>>>>>
>>>>>> _______________________________________________
>>>>>> Fis mailing list
>>>>>> Fis en listas.unizar.es
>>>>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>>>>> ----------
>>>>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>>>>
>>>>>> Ud. recibe este correo por pertenecer a una lista de correo
>>>>>> gestionada por la Universidad de Zaragoza.
>>>>>> Puede encontrar toda la información sobre como tratamos sus datos en
>>>>>> el siguiente enlace:
>>>>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse
>>>>>> de baja desde la propia aplicación en el momento en que lo desee.
>>>>>> http://listas.unizar.es
>>>>>> ----------
>>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Fis mailing listFis en listas.unizar.eshttp://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>>>> ----------
>>>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>>>
>>>>> Ud. recibe este correo por pertenecer a una lista de correo gestionada por la Universidad de Zaragoza.
>>>>> Puede encontrar toda la información sobre como tratamos sus datos en el siguiente enlace: https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de baja desde la propia aplicación en el momento en que lo desee.http://listas.unizar.es
>>>>> ----------
>>>>>
>>>>> _______________________________________________
>>>>> Fis mailing list
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>>>>> ----------
>>>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>>>
>>>>> Ud. recibe este correo por pertenecer a una lista de correo gestionada
>>>>> por la Universidad de Zaragoza.
>>>>> Puede encontrar toda la información sobre como tratamos sus datos en
>>>>> el siguiente enlace:
>>>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse
>>>>> de baja desde la propia aplicación en el momento en que lo desee.
>>>>> http://listas.unizar.es
>>>>> ----------
>>>>>
>>>> --
>>>> Никита Ефимович Шкловский-Корди
>>>> Гематологический центр.
>>>> https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDKRDdDwQ$ 
>>>> <https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!QLdEAAkck5P0ZkLQDyQDcdKf2gUGrgh2RH5IB6kZGvMx3v5eR_KkaqOPkhrRAdcybXbLYH27fsNcSIXPnTse$>
>>>> -  сайт  Андрея Ивановича Воробьева
>>>> _______________________________________________
>>>> Fis mailing list
>>>> Fis en listas.unizar.es
>>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>>> ----------
>>>>
>>>> INFORMACI�N SOBRE PROTECCI�N DE DATOS DE CAR�CTER PERSONAL
>>>>
>>>> Ud. recibe este correo por pertenecer a una lista de correo gestionada
>>>> por la Universidad de Zaragoza.
>>>> Puede encontrar toda la informaci�n sobre como tratamos sus datos en el
>>>> siguiente enlace:
>>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>>> Recuerde que si est� suscrito a una lista voluntaria Ud. puede darse de
>>>> baja desde la propia aplicaci�n en el momento en que lo desee.
>>>> http://listas.unizar.es
>>>> ----------
>>>>
>>>>
>>>> --
>>> Никита Ефимович Шкловский-Корди
>>> Гематологический центр.
>>> https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!UZQ6jNO_q7teEZNXet1afMPfETsTlcXMWrXexAcKEBa_oEIo0SMXr5D0BktqZbMfjo4je04tFw4EaRdt3ZKDKRDdDwQ$ 
>>> <https://urldefense.com/v3/__http://www.ai-vorobiev.ru/__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7Mnbn0Yv9vFg$>
>>> -  сайт  Андрея Ивановича Воробьева
>>>
>>>
>>> _______________________________________________
>>> Fis mailing list
>>> Fis en listas.unizar.es
>>> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
>>> ----------
>>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>>
>>> Ud. recibe este correo por pertenecer a una lista de correo gestionada
>>> por la Universidad de Zaragoza.
>>> Puede encontrar toda la información sobre como tratamos sus datos en el
>>> siguiente enlace:
>>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de
>>> baja desde la propia aplicación en el momento en que lo desee.
>>> http://listas.unizar.es
>>> ----------
>>>
>>
>> _______________________________________________
>> Fis mailing list
>> Fis en listas.unizar.es
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>> ----------
>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>>
>> Ud. recibe este correo por pertenecer a una lista de correo gestionada
>> por la Universidad de Zaragoza.
>> Puede encontrar toda la información sobre como tratamos sus datos en el
>> siguiente enlace:
>> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
>> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de
>> baja desde la propia aplicación en el momento en que lo desee.
>> http://listas.unizar.es
>> ----------
>>
>
>
> --
>
> *Professor Terrence W. DeaconUniversity of California, Berkeley*
>
>
>
>
> _______________________________________________
> Fis mailing list
> Fis en listas.unizar.es
> http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
> ----------
> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
>
> Ud. recibe este correo por pertenecer a una lista de correo gestionada por
> la Universidad de Zaragoza.
> Puede encontrar toda la información sobre como tratamos sus datos en el
> siguiente enlace:
> https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas
> Recuerde que si está suscrito a una lista voluntaria Ud. puede darse de
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> ----------
>
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