[Fis] definitions of information by Theil (1972) derived from Shnnon (1948); back to the basics?

Mon Jan 30 09:08:04 CET 2023

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 at 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 at gmail.com <mailto:loukau at 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 at gmail.com <mailto:nikitashk at 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 at wp.pl <mailto:stanowskimariusz at 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 at gmail.com <mailto:nikitashk at 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!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7MnbnxAKTAGn$  <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 at hotmail.com <mailto:lidinkl at 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 at aol.com <mailto:howlbloom at aol.com>>
>>> Sent: 24 January 2023 08:21
>>> To: lidinkl at hotmail.com <mailto:lidinkl at hotmail.com> <lidinkl at hotmail.com <mailto:lidinkl at hotmail.com>>; fis at listas.unizar.es <mailto:fis at listas.unizar.es> <fis at listas.unizar.es <mailto:fis at listas.unizar.es>>; loet at leydesdorff.net <mailto:loet at leydesdorff.net> <loet at leydesdorff.net <mailto:loet at 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 at hotmail.com <mailto:lidinkl at hotmail.com>>
>>> To: fis at listas.unizar.es <mailto:fis at listas.unizar.es> <fis at listas.unizar.es <mailto:fis at listas.unizar.es>>; Loet Leydesdorff <loet at leydesdorff.net <mailto:loet at 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!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7MnbnzGw45xZ$  <https://urldefense.com/v3/__https://doi.org/10.1007/s11245-016-9370-7__;!!D9dNQwwGXtA!SXg13tbkdIexlHicpgmmFoFwIcpgeHl3c2rgtD9HsQHuKRQodSQhjWMYAL-3r-YyBOXRc3vMzQUkPXSVFHs$>
>>> From: Fis <fis-bounces at listas.unizar.es <mailto:fis-bounces at listas.unizar.es>> on behalf of Loet Leydesdorff <loet at leydesdorff.net <mailto:loet at leydesdorff.net>>
>>> Sent: 23 January 2023 23:29
>>> To: fis at listas.unizar.es <mailto:fis at listas.unizar.es> <fis at listas.unizar.es <mailto:fis at 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 would 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 at leydesdorff.net  <mailto:loet at leydesdorff.net>; https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7MnbnxIqJY8F$  <https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLGpM1vg4$>
>>> https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7Mnbn-fzm2en$  <https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLaBGhTzQ$>
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>> INFORMACIÓN SOBRE PROTECCIÓN DE DATOS DE CARÁCTER PERSONAL
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>> -- 
>> Никита Ефимович Шкловский-Корди
>> Гематологический центр.
>> https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7Mnbn1L_blvi$  <https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!QLdEAAkck5P0ZkLQDyQDcdKf2gUGrgh2RH5IB6kZGvMx3v5eR_KkaqOPkhrRAdcybXbLYH27fsNcSIXPnTse$>  -  сайт  Андрея Ивановича Воробьева
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> 
>> INFORMACI�N SOBRE PROTECCI�N DE DATOS DE CAR�CTER PERSONAL
>> 
>> Ud. recibe este correo por pertenecer a una lista de correo gestionada por la Universidad de Zaragoza.
>> Puede encontrar toda la informaci�n sobre como tratamos sus datos en el siguiente enlace: https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas <https://sicuz.unizar.es/informacion-sobre-proteccion-de-datos-de-caracter-personal-en-listas>
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>> ----------
> 
> -- 
> Никита Ефимович Шкловский-Корди
> Гематологический центр.
> https://urldefense.com/v3/__http://WWW.AI-VOROBIEV.RU__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7Mnbn1L_blvi$  <https://urldefense.com/v3/__http://www.ai-vorobiev.ru/__;!!D9dNQwwGXtA!RcW2BAuVHXHw_TEldQMQpjWPzzeV2O0M_4ukkLvSZx9DCB2GviaykLNisPEYPtpkl8AG7Mnbn0Yv9vFg$ >  -  сайт  Андрея Ивановича Воробьева

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