by Werner Gitt
Figure 23: The four possible combinations of sender and recipient.
There also are cases where both the sender and the recipient are parts of a complete transmission system (Figure 24).
Figure 24: A complete transmission system in which sender and recipient are integrated. The entire system is based on conceptual ideas and always requires a mental source.
Example: In the system used for the transmission of exact (atomic) time in Germany, the atomic clock located at the Physikalisch-Technischen Bundesanstalt (Federal Institute of Physics and Technology) in Braunschweig, transmits the exact time over the transmitter designated as DCF77 in Mainflingen (near Frankfurt/Main). A specially designed code is employed (compare Theorems 6 to 11) and these signals can then be decoded by commercially available receiving equipment to provide time and date. Both the transmitter and the receiver are "systems created by intelligence" (the lower link in Figure 23). All the parts of this system have been produced by intelligent minds, as shown in Figure 24.
Chapter 9
The Quality and Usefulness of Information
Shannon’s information theory can be regarded as an extension of probability theory. He takes the bit as the unit of measurement of information, and a book with 200 pages then contains twice as much information as one with 100 pages if the pages contain the same number of letters. Meaning is completely ignored. Wolfgang Feitscher gave a striking description of this situation: "When considering semantic information, we are like a chemist who can weigh substances, but cannot analyze them." In this sense, Shannon solved the problem of weighing information, but the analysis question is still untouched. To rise above Shannon’s theory, it is necessary to define measures for semantic information which must be generally valid. We will now discuss some aspects which may pave the way for solving this difficult problem.
A semantic measure would not be a measure of quantity but of quality. It could happen that a book of several volumes may have a lower semantic evaluation than a thin brochure. A qualitative evaluation of information involves some parameters which depend very strongly on a subjective appraisal, and this has an appreciable aggravating effect on the problem. Figure 25 (page 117) depicts a graph of the semantic value of information with respect to its usefulness. There are five value levels.
1. Extremely important information: This is the highest level because of its high apobetics content (e.g., essential and vital information).
2. Important information: Information which is required for achieving some purpose (e.g., knowledge of planned routes, telephone numbers, address lists, and subject knowledge).
3. Valuable information: This includes information which is of general value in the sense of being informative, constructive, edifying, or amusing (e.g., daily news, weather reports, general increase of knowledge, and novelties).
4. Trivial information: Insignificant or meaningless information (e.g., already known or useless information, clichés, banalities, or small talk).
5. Harmful information: Information with negative consequences, leading to false results, misconceptions, and other negative effects (e.g., deliberate or erroneous misinformation, slander, cursing, agitation, false propaganda, charlatanry, malicious gossip, expletives, sectarian doctrines, unbiblical theology, pornographic, ideological, and astrological publications, and pulp magazines).
Valuable information (1 to 3) is accorded a positive sign, and worthless information (4 and 5) a negative sign, so that now we can regard information as a signable quantity. In the x direction (Figure 25) we distinguish between usable (positive) and useless (negative) information. We thus have four quadrants for evaluating information, characterized as follows.
Figure 25: Graph representing the evaluation levels of the usability of semantic information. There is no indication of scale, so we are mainly dealing with a qualitative evaluation of semantic information. Valuable information is accorded a positive, and worthless information a negative, sign. Usable and useless information are also distinguished by their sign.
First quadrant: This is the most important domain, since it is comprised of all information that is both useful and valuable. "Useful" means that the information is available and accessible and can in principle be implemented. On the one hand, usefulness is an objective property, but the concept of value concerns a person, an event, a plan, or a purpose, and it is always subjective.
Second quadrant: The information in this quadrant is also valuable, as in the case of the first quadrant, but it cannot be used. There are various possible reasons for this:
– It is not yet available (e.g., cure for cancer; a book on an important theme which has not yet been written).
– It cannot be located in the gigantic flood of information.
– The author has it available, but it has not yet been transmitted (published).
– It is not of topical interest any more.
Third and fourth quadrants:This is the domain of worthless information. At the trivial level, this is comprised of meaningless or unordered information: insignificant, inane, or nonsensical information. In the amplified harmful form, information can be false (inadvertently), deliberately falsified, or evil, and can have negative effects. The fourth quadrant indicates that such information exists, while the third quadrant depicts information that is not yet available or accessible (e.g., trash literature which is unpublished). According to certain statistics an American youth at the end of his school career attended 11,000 school periods, watched TV for 22,000 hours, during which he heard 350,000 promotional slogans, and saw 20,000 murders. That has to have injurious effects. It is, in human terms, necessary to avoid the fourth quadrant, and, in technical terms, security measures must be taken to prevent damage (e.g., error-detecting codes in data processing systems, and control procedures for preventing instability in manufacturing processes).
Chapter 10
Some Quantitative Evaluations of Semantics
We can now begin to evaluate semantic information quantitatively, after having considered the essentials at the semantics level in the preceding chapters. Let us take the semantic value S to represent a quantitative evaluation of the quality of the information. Then six quantities can be used, namely semantic quality q, relevance r, timeliness a, accessibility z, existence e, and comprehensibility v. It is obvious from these concepts that we are considering the information from the point of view of the recipient and his subjective appraisal. These quantities are normalized on a scale from 0 to 1, and they are all positive, except for q which can also take on negative values, as should be clear from the previous chapter. These six variables are now discussed briefly.
1. Semantic quality q (a subjective concept, mainly concerns the recipient): This is used as a measure of the importance of the meaning of some information. Different qualities can be considered according to the goal and the kind of information. Some significant aspects of creative information in particular are depicted in Figure 22 (page 109). For a computer program, for example, the following criteria are relevant and crucial on the semantic level and in part at the pragmatic level:
– Efficacy of the applied algorithm (e.g., simple method of solution, speed of convergence, and absence of instability).
– Minimal computing time (this can be a decisive cost factor when time has to be paid for).
– Portability, meaning that the program can also run on other computer systems.
– Reliability, meaning that the program has been tested comprehensively and is fully debugged so that the desired results will be obtained with a high degree of certainty.
– The programming language used.
The weight of each aspect depends on both objective and subjective evaluations. For inane or nonsensical information q is taken as zero, while for the best possible information q = 1.
2. Relevance r (subjective concept, mainly concerns the recipient): This aspect reflects individual interests in particular and it includes its relevance for achieving some purpose (e.g., an econom
ical, a technical, or a strategic goal, collector’s value, or life purpose). If r = 1 for person A, the same information can be totally irrelevant for B (r = 0). The weather forecasts for Australia are normally of no importance for somebody in Europe (r = 0), but their relevance can increase dramatically when that person is planning to go there. For a farmer, the agricultural news has a relevance completely different from the latest research results in physics. It is obvious that relevance depends entirely on the recipient. A gale and storm tide warning over the radio is highly relevant for inhabitants of a coastal island, while continental residents who live inland are not concerned. The main problem of relevance is to estimate it correctly. If relevance has been appraised erroneously, it might have catastrophic effects. There are innumerable cases in human history where wrong decisions were made on the grounds of a faulty appraisal of the relevance of information. The cost was astronomical in terms of lives and property.
3. Timeliness t (subjective concept, mainly concerns the recipient): It is in many cases necessary that relevant information should be available at the required moment. Newsworthiness is time-dependent, so that t = 0 for yesterday’s news, and t = 1 for highly relevant information received at the right moment. When a person is standing in the rain and somebody tells him that it is raining, the newsworthiness of this information is zero (t = 0), although it is topical and relevant.
4. Accessibility a (subjective concept, mainly concerns the recipient): The most important information is worthless if it cannot be accessed; then a = 0 (no access). On the other hand, a = 1 when the recipient has full access to the information transmitted by the sender. With the increasing flood of information the "know-where" is becoming steadily more important, and aids like catch-word registers, lexicons, card systems, and data banks are available. Associative storage would be a great help, but only the brain can provide this ideal access principle. In many countries there are computer centers with online facilities which provide direct access to information (Internet). These data banks contain information on such diverse topics as technology, physics, materials, books, and the social sciences, etc.
Even if information is accessible, a rating may still be zero when:
– the information cannot be seen by the recipient (e.g., I am dying of thirst in the desert close to a spring but I do not know that it is there.)
– the information is coded in a language that the recipient does not understand (e.g., an English tourist in China who cannot read Chinese)
– the information is coached in technical terms which can only be understood by adepts (e.g., legal texts that laymen cannot follow, or a mathematical book which is "Greek" to the uninitiated)
– the sender deliberately excludes some potential recipients (e.g., secret encrypted information, data protection in EDP systems, and sealing a letter)
5. Existence e (objective concept, mainly concerns the sender): Whereas accessibility involves the possibility that an individual can lay his hand on information which is in principle available, existence concerns the basic question of whether the information exists at all. Accessibility involves the recipient only, but existence depends solely on the sender. The value of e lies between 0 and 1, and it indicates how much of the available or desired information about the present case can be obtained (e.g., what fraction has already been researched). The existence e is zero for questions which are completely open, and if something is fully known, e = 1. The previously open question of whether there is life on the moon (e = 0) has now been answered completely (e = 1). For information to cure cancer of the liver, e = 0; in the case of stomach cancer it lies somewhere between 0 and 1, depending on the stage of development. It is quite difficult to make an estimate of the value of e, since the totality of relevant information is in general not known at a given moment. The great physicist Isaac Newton (1642–1727) estimated his contribution to scientific research as a very small e value in spite of his many valuable findings. He said [M3], "I do not know what the world thinks of me; but to myself I appear as a little boy playing on the beach and who finds joy in discovering a smoother pebble or a prettier seashell than the ordinary, while the great ocean of truth lay undiscovered before me."
6. Comprehensibility c (subjective concept, concerns both the sender and the recipient): This factor describes the intelligibility of information; when the information cannot be understood at all, c = 0, and c = 1 when it is completely understood. Both sides may be at fault if all of the transmitted information does not reach the recipient. The sender might not have expressed himself clearly enough, so that the recipient grasps the intended semantics only partially in spite of being highly intelligent, or the recipient may not be intelligent enough to understand everything correctly. The mental alertness of the recipient is also important for another reason: Verbally formulated information (the explicit part) often contains implicit information which has to be read "between the lines." The recipient only receives this latter part by contemplation and having the required background knowledge.
Note: Many of the above-mentioned factors cannot be distinguished sharply and might overlap. The question of interlinking between the six parameters is not discussed further at this stage; it might be investigated in the future.
Chapter 11
Questions Often Asked about the Information Concept
My talks at universities and technical institutes are usually followed by lively discussions. A small selection of the frequently asked questions are now listed and answered briefly.
Q1: Have you now proved the existence of God?
A1: Conclusions must always be based on scientific results and these may give rise to further ideas. It is, however, scientifically impossible to prove the existence of God, but many aspects of this world cannot be understood at all if God is excluded.
Q2: Do your assertions refute evolution?
A2: The information theorems are natural laws and many fallacies have been revealed by means of natural laws. The basic flaw of all evolutionary views is the origin of the information in living beings. It has never been shown that a coding system and semantic information could originate by itself in a material medium, and the information theorems predict that this will never be possible. A purely material origin of life is thus precluded.
Q3: Does the definition of information not depend on the individual? In contrast to matter and energy, information does not exist as such of itself.
A3: Yes, of course. Consider three persons, Albert, Ben, and Charles who want to inform Dan which one of them was in the room. They decided that colors would be used to distinguish between them: Albert = yellow, Ben = blue, and Charles = red. When Dan arrives later, he finds a blue note, and concludes that Ben is there. Any other person would not regard this piece of paper as information. This code agreement exists only between Albert, Ben, Charles, and Dan (see Theorems 6, 7, and 9). It is obvious that information can only be created by a cognitive mental process.
Q4: Please give a brief definition of information.
A4: That is not possible, because information is by nature a very complex entity. The five-level model indicates that a simple formulation for information will probably never be found.
Q5: Is it information when I am both sender and recipient at the same time? For example, when I shout in a valley and hear the echo.
A5: This is not a planned case of information transfer, but there are situations like writing a note to oneself or entries in a diary.
Q6: Is a photograph information according to your definition?
A6: No! Although the substitutionary function (chapter 5) is present, there is no agreed-upon code.
Q7: Does information originate when lottery numbers are drawn? If so, then that could be regarded as information arising from chance.
A7: The information resides in the rules of the game; they are composed of a fixed strategy which includes apobetics, namely to win. The actual drawing of numbers is a random process involving direct observation of reality, and, according to
the theorems in chapter 5,we are thus outside the domain of the definition of information, but we do have information when the results of the draw are communicated orally or in writing.
Q8: Is there a conservation law for information similar to the conservation of energy?
A8: No! Information written with chalk on a blackboard, may be erased. A manuscript for a book with many new ideas written painstakingly over several years, will be irrevocably lost when someone throws it in the fire. When a computer disk containing a voluminous text is formatted, all the information is also lost. On the other hand, new information can be created continuously by means of mental processes (Theorem 30).
Q9: Does information have anything to do with entropy as stated in the second law of thermodynamics?
A9: No! The second law of thermodynamics is only valid for the world of matter (the lower level in Figure 14), but information is a mental entity (Theorem 15). There is, however, a concept on the statistical level of Shannon’s information, which is called entropy (see appendix A1.1). This is something completely different from what is known as entropy in physics. It is unfortunate that two such different phenomena have the same name.
Q10: Natural languages are changing dynamically all the time. Doesn’t this contradict your theorem that coding conventions should be conserved?
A10: New words arise continuously, like skateboards, rollerblades, wind surfing, paragliding, etc., but all of them meet a very specific need and perform a real function. There is consensus about their meaning, and nobody would confuse a rollerblade with a switchblade or paragliding with paramedical. If random strings of letters are written on a blackboard, nobody would be able to do anything with them. In this case there will be no agreed-upon convention.