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3   Price Question: What is "Information"?
 
A possible answer (e.g. mine) to this question can be found in chapter 5.2.

 
3.1   Babylonian Confusion of Terms

The flood of information about information is already considerable. There is

quantitative, semantic, pragmatic, binary, genetic, neuronal, cybernetic, machine, biological, animal, social, psychological, structural, coded, hormonal, human and organismic information

etc. and so on.

It is hardly possible to know all the polemics already published on the subject of information, let alone discuss them.

Here, it seems to me that a sampling in the manner of mathematical statistics would be more appropriate in order to obtain at least a rough overview of the "population of the state of knowledge" by means of randomly selected writings.

However, this can only be the beginning, because even today the following sentence is undoubtedly still fully valid [78]:
„Die Frage nach dem Wesen der Information gehört bekanntlich zu den kompliziertesten und meistumstrittenen Problemen der modernen Wissenschaft.“
(The question of the nature of information is known to be one of the most complicated and controversial problems of modern science.)

But first some definitions and opinions on the subject of information as an introduction to the philosophical problem. For example:

Information is information, neither matter nor energy.“ [79] p.165

 
---- etc. ----
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3.3   Information Terms

The variety of already existing definitions of information, as indicated in section 3.1, could well lead to the impression that there is little point in trying to discover any order behind this jumble of contrary opinions.

And yet, in my opinion, the many terms can at least be divided into two groups: Subject-specific valid and generally valid information terms.

In the following, three subject-specific information terms are first explained in a brief overview:

a)   Biological Informations        

b)   Psychological Informations

c)   Social Informations

Subsequently, some generally valid aspects and terms are discussed:

d)   Information, Substance and Energy

e)   The Non-conservation Law of Information

f)    Quantitative Information           

g)   Semantic Information

h)   Pragmatic Information            
 
i)    Information and Choice

j)    Information and Order

 ---- etc. ----
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3.3 a   Biological Informations

Already at the gateway to the field of biology, we have to choose between four major information systems  [105] p.1:

1.) Genetics of the cell

2.) Nervous system and brain

3.) Hormonal system

4.) Immunobiological system

For example, we choose system 1 and thus restrict ourselves in the following only to genetic information.

Every living thing on earth basically consists of at least one cell or of several cells. This applies without exception to every plant, animal (including us), bacterium and fungus.

Each of these cells contains protein molecules as well as a tiny amount of a certain substance called nucleic acid, which means "cell nucleus acid". However, nucleic acid is also found in all cells of nucleus-less bacteria and blue-green algae and is anything but a liquid, as the name "acid" would suggest. Nucleic acid consists of rather robust molecular filaments with a strict, almost crystalline order.

Schrödinger once coined the term "aperiodic crystals" for all living beings [106]. This is particularly true for nucleic acid. It consists of chain-like structured macromolecules in which only 4 types of molecules are strung together non-periodically (i.e. in an apparently random arrangement) like pearls on a string. In higher organisms, individual macromolecules of nucleic acid contain millions of such beads.

---- etc. ----
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3.3 b   Psychological Informations

Every animal creature is forced, under penalty of its physical destruction, to inform itself sufficiently about its environment and its own condition at every moment of its life and to initiate appropriate measures immediately in case of danger.

This behavioural control, which is shaped by external information, appears most clearly in the higher, mobile living beings almost as a condition of existence. It is an incessant interweaving of internal and external information processing.

For orientation in space alone, animal organisms (including WE) mostly unconsciously use two typical types of information [125] p.81:

Firstly, determining the position of the organism in space by checking the position of the body in relation to the centre of the earth, and secondly, determining the direction and distance of objects or other living bodies.

There is a constant change between passive information intake and active behaviour control.

This stream of information also accompanies us without interruption from the cradle to the grave.

---- etc. ----
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3.3 f   Quantitative Information
          (also called syntactic or selective information)

A quantitative measure of information was first proposed by Ralph Hartley in 1928 [133]. This "quantity-based" measure has nothing to do with meaning content. Rather, it is based on the idea that every piece of information is fundamentally associated with a choice of variants.

For any symbol to actually be a carrier of information, it must represent at least one selection from two variants. In Morse code, for example, there are not only strokes, but also dots and pauses. Only with strokes of the same length as the only character variant or only with dots or even only with infinitely long pauses, no information can be transmitted.

According to Hartley, only the number  s  of possible character variants of a symbol determines the "information content" or the "amount of information" of the symbol in question:

H   =   log s                          (1)

Die Informationsmenge  H  ist demzufolge mit dem Logarithmus der möglichen Variantenanzahl  s  identisch. H ist zunächst nur eine dimensionslose Zahl.

Here, s  must always be greater than or equal to 2. If only 1 variant is available for a symbol, the information quantity is zero because of  log 1 = 0. There is no choice here.

This corresponds completely to everyday experience: What I already know, I can no longer experience as news!

Sometimes the amount of information is also referred to as the "surprise amount" [134] p.230.

The more surprising an incoming message is, the greater the amount of information it contains. Zero information is therefore equal to zero surprise.

 ---- etc. ----

In order to calculate the amount of information H of the "whole" symbol, the individual amounts of information  Hi  must not simply be added together. They must be statistically averaged.

For non-equally probable character variants of a message symbol, the information quantity of such a symbol is therefore according to Shannon [136] p.393

H* = - K · Σ ( pi · log pi )                          (6)

witht     H*: statistically averaged amount of information
               (was also called "information entropy" by Shannon)

K:  actor for normalising the logarithmic base

Σ:   um, here from i = 1 to s ,    with  s: Number of possible character variants  i

pi:   probability for the occurrence of the special character variant i

In deviation from Shannon's original work, I have not denoted the number of character variants with  n  here, but with  s , following Hartley's formula (1). And instead of   H   I have written  H*.

In contrast to Hartley's information set  H, Shannon's information set  H*  represents a statistical mean (an expected value). This is illustrated by the following derivation.

---- etc. ----
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3.3 h   Pragmatic Information

Semiotic pragmatics examines the effect of information on the receiver. Pragmatic information is value-related information.

However, the value or usefulness of a message can only be assessed in the context of the common target system of sender and receiver [154] p.43. Thus, pragmatic information is decisively characterised by subjective aspects.

Pragmatic information is thus not an objective quantity that can be regarded as a physical property of a system independent of the assessment by the sender or the receiver.

Wolkenstein demonstrated the extent to which the value of information depends on the state of the receiver using the example of a university textbook for mathematics [117] p.188:

The information it contains can be almost as worthless to a professor of mathematics as it is to a pre-school child. It is quite different for a student of mathematics.

A certain book (with its unchanged syntactic and semantic information content) can therefore not only have a different value for several people, but also take on increasing and decreasing value over time for one and the same person.

In contrast to semantic information, pragmatic information in many cases has an instructional character and then also usually triggers certain actions in the recipient.

---- etc. ----
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