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A small selection of the frequently asked questions about information theory are now listed and answered briefly.
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.
Q11: Can the randomness of a result be proven?
A11: In a work of Gregory J. Chaitin (Argentina) [C2] he showed that there is no algorithm for determining whether a sequence of symbols is random or not. One must be informed of the fact if a random process has been involved (e.g., that a sequence was produced by a random number generator).
Q12: Is the criteria for information mostly subjective?
A12: Subjective aspects play a significant role when the sender decides which type of code he wants to use. He decides whether to write a letter or make a phone call. Even the way the message is transmitted is colored by his personality and by the circumstances. The transmission may be joyful, stupid, agitated, boring, or may have a special emphasis.
Q13: Does the synergy of the German physicist Hermann Haken not mean that order can arise from disorder and that evolution could thus be possible?
A13: Haken always quotes the same examples for the origin of ordered structures. I once asked him after a lecture whether he could store these ordered structures; his answer was negative. A code is required for storing an achieved state. No codes are found in physical systems and every structure collapses when the causing gradient is suspended (e.g., a specific temperature difference).
Q14: What is your opinion of the Miller experiments which appear in school texts as “proof” of chemical evolution?
A14: No protein has ever been synthesized in such an experiment; they refer to proteinoids and not proteins as such. Even if they succeed in obtaining a true protein with a long amino acid chain and the correct optical rotation, it would still not be the start of evolution. There must be a coding system to store information about this protein so that it can be replicated at a later stage. A coding system can never originate in matter as precluded by Theorem 11. The Miller experiments, thus, do not contribute to an explanation of the origin of life.
Q15: SOS signals are periodic; does this not contradict your necessary condition NC2 (paragraph 4.2)?
A15: OTTO is also periodic, but it still is information. It is possible that brief sequences of symbols can contain periodic repetitions, but nobody would regard the decimal number 12.12 as a periodic fraction just because of the repetition of the digits.
Q16: Can new information originate through mutations?
A16: This idea is central in representations of evolution, but mutations can only cause changes in existing information. There can be no increase in information, and in general the results are injurious. New blueprints for new functions or new organs cannot arise; mutations cannot be the source of new (creative) information.
Q17: When the structure of a crystal is studied by means of a microscope, much information may be gained. Where and who is the sender in this case?
A17: No coding system is involved in this example, and reality is observed directly. This case lies outside the domain of definition of information as discussed in chapter 5. The substitutionary function is absent, so that the theorems cannot be applied.
A18: Of course, one could select other definitions, as often happens. My purpose was to demarcate a region where assertions of the nature of natural laws can be made. It is only in this way possible to formulate definitive assertions for unknown cases by means of known empirical theorems. The domain of definition is, thus, not as arbitrary as it might appear, but it has been dictated in the last instance by empirical realities.
Q19: Biological systems are more complicated than technical systems. So, shouldn’t an individual definition be introduced for biological information?
A19: Biological systems are indeed more complicated than all our technical inventions. However, we do not require a special principle for the conservation of energy, for example, for biological systems. The reason for this is that the principle of conservation of energy which applies in all physical systems is not only applicable in the limited area of inanimate matter but is universally valid and is thus also valid for all living systems. This is noted in the principles N2 and N3 (see chapter 2.3). If the stated theorems about information are laws of nature, then they are valid for animate as well as inanimate systems. A different definition and different principles are, therefore, not necessary for biological systems.
Q20: Are laws of nature always quantifiable? Don’t the statements only achieve this status when the observations have been successfully expressed in mathematical equations?
A20: In 1604, Galileo Galilei (1564–1642) discovered the law of falling bodies. He expressed the regularities he discovered in the form of verbal sentences in Italian (in La Nuova Scienza), which can be translated into other languages. Later, these sentences were translated with the help of a meta-language, that is the mathematical language. The mathematical language has the advantage that it allows an unambiguous and especially short presentation. Equations are an expression of quantitative details; however, they only represent a part of the mathematical equipment. The phraseology of mathematical logic uses a formula apparatus but does not deal with quantitative dimensions. They represent a different and indispensable form of expression. With relation to question 20, we have to consider two aspects:
1. Not all observations in nature which can be formulated in mathematical terms are necessarily laws of nature. These must fulfill two important criteria: laws of nature must be universally valid and absolute. They must not be dependent on anything, especially not on place or time. It is, therefore, irrelevant who is observing nature, when and where and in what stage nature is. The circumstances are affected by the laws and not vice versa.
2. In order to be a law of nature, the facts under observation need not be formulated mathematically, although this does not exclude the possibility that a formal expression may one day be found (see examples a, b). It must also be noted that a number of correctly observed laws of nature could later be included in a more general principle. A law of nature need not necessarily be represented by quantitative values. The description of an observation in qualitative and verbal terms suffices, if the observation is generally valid, i.e., can be reproduced as often as you like. It is only important to remember that laws of nature know no exceptions. These aspects should be made clearer in the following examples:
These examples confirm that laws of nature do not necessarily have to be quantifiable. If preferred reactions, rotary directions, or other general principles are being described, then mathematical formulas are not always effective. In some cases, the observations of the laws of nature can be deduced from more general laws. Thus, for example, the law of induction is already contained in the Maxwell equations. All the aspects of the laws of nature discussed here are equally valid in relation to theorems about information. According to their nature, the generally valid facts about information can be observed, but they are not quantifiable. Thus, the statements are described verbally. This type of description is no criterion as to whether a fact is a law of nature or not.
Q21: Can the laws of nature change in time?
A21: The laws of nature are valid everywhere in the universe and at all times without exception. There can be absolutely no exceptions. It would be tragic if the laws of nature did change as time went on. Every technical construction and measuring apparatus is a practical application of the laws of nature. If the laws of nature changed, bridges and tower blocks, calculated correctly taking the laws of nature into account, could collapse. As all physiological processes are also dependent on the laws of nature, then a change in these laws would have catastrophic consequences.
Q22: Is the sender already included in your definition of information? If a sender is already included in the definition, then the conclusion that there must be a sender is self-evident.
A22: Of course, the sender is included in neither the definition nor the prerequisite. That would be a circular argument. The laws of nature are deduced completely from experience. Thus, the existence of a sender when there is a code, has been observed a million times over. In the work in hand, the difference between theorems and definitions is clearly made. Theorems should be viewed as laws of nature. They are observed. In Theorems 1, 9, and 11, we talked about a sender. I would like to stress that this is neither a definition nor a prerequisite. The statements are much more the result of countless observations.
Q23: Can a law of nature be toppled? Or, to phrase it differently, are the laws of nature confirmatory?
A23: If we are talking about true laws of nature (true in the sense that they are not merely what we assume to be laws of nature), then they are universally valid and unchangeable and they can never be toppled. Their main feature is that they are fixed. In their practical implementation, the laws of nature cannot be proven in a mathematical sense, but they are founded and refuting in character. With their help, we are able to make accurate predictions about the possible and the impossible. For this reason, no invention which offends a law of nature is accepted by a patent office (e.g., perpetua mobilia offend the principle of the conservation of energy). Assumed law of nature: A law which is often assumed to be a law of nature but which in reality is no such thing, may be held as such for a period of time. However, it can be toppled by an example showing the opposite (falsification). True law of nature: These are true laws of nature which can never be toppled because examples of the opposite cannot exist. The validity of a law of nature cannot be proven mathematically; however it is proven in continual observations.
Q24: How many laws of nature are there?
A24: The total number of laws of nature cannot be stated exactly for two reasons: We can never be sure whether we have recognized all phenomena reliant on the laws of nature. Sometimes a number of laws can be summed up in the framework of one superordinate standpoint. There is then no point in listing each individual law. The quest for the world formula which is often mentioned assumes that there is one formula which can express all our laws of nature. However, this seems to be a utopian goal.
Q25: Have you lectured on your concept of information as a law of nature in front of specialists?
A25: I have lectured on this topic in countless national and international universities. In June 1996, I also presented my concept at an international congress which was especially concerned with the discussion on information [G18]. There was always a lively discussion, and the specialists tried to find an example of the opposite (one example would be enough to topple an assumed law of nature). A true law of nature cannot be toppled.
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