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“The distinction between simplicity and complexity raises considerable philosophical difficulties when applied to statements. But there seems to exist a fairly easy and adequate way to measure the degree of complexity of different kinds of abstract patterns. The minimum number of elements of which an instance of the pattern must consist in order to exhibit all the characteristic attributes of the class of patterns in question appears to provide an unambiguous criterion” (Hayek 1988-2022, vol. 15, p. 260).

The complexity of a given meaning is determined by the size of the minimal action necessary to reproduce that meaning. As a product of culture, man himself is also a meaning. In order to be able to transmit more and more cultural experiences, he must become more complex. With each generation, the minimal action required to reproduce man as a cultural being grows, and with it the complexity of learning.

The complexity of a minimal action converges to the entropy of its source, that is, the minimal subject. As we saw above, the complexity of a culture-society is determined by the number of alternative meanings (counterfacts) it can generate. At the same time, the complexity of a culture-society is defined by the size of the minimal action necessary for its reproduction. Thus, the entropy of the culture-society considered as a source of messages (counterfacts) is approximately equal to the average complexity of all possible messages from this source:

“Shannon’s entropy does not make sense for a particular string of bits. Entropy is a property of an information source. There are many possible messages, each with its own probability. Entropy measures the size of that universe of possibilities. In contrast, the algorithmic entropy makes sense for any particular string of bits. The strings themselves can have a higher or lower information content, according to whether they require longer or shorter descriptions. The two entropies are related to each other. For a source that produces binary sequences, the Shannon entropy is approximately the average of the algorithmic entropy, taking an average over all the possible sequences that the source might produce: H ? ave(K). Shannon entropy is a way to estimate the algorithmic entropy, on average” (Schumacher 2015, p. 231).

In other words, the complexity of meaning, when measured in cultural bits, converges on average to the entropy of the subject, be it culture-society as a whole or an individual taken as a source of (counter)facts. As Protagoras said, “man is the measure of all things: of the things which are, that they are, and of the things which are not, that they are not” (Plato 1997, p. 169). The minimal subject is a measure of the complexity of man, that is, of the unpredictability, uncertainty, randomness and surprise of his actions performed and not performed. The minimal subject is both the source and the product of the minimal action, and together they constitute the minimal meaning.

The historical increase in the complexity of a culture-society is reflected in the increase in both the number of (counter)facts it produces and the average size of the minimal action required to reproduce an individual meaning. The transition from cultural selection based on the alternation of human generations to traditional choice based on the alternation of generations of meanings raised both the entropy of the source of (counter)facts and the complexity of the (counter)facts themselves.

When we apply the achievements of information theory to culture, we must note the difference between the terms “information” and “meaning.” Information is determinateness in general or certainty, its measure is the reduction of uncertainty. The unit of information is a bit, “1” or “0.” In contrast to information, meaning is directed certainty, an act of change in a certain direction. Examples of directed certainty are the evolution of living beings and the evolution of meanings. Humans process information (certainty) into meaning (mediated, that is, directed certainty) by matching information with needs. The unit of meaning is the cultural bit—not just “1” or “0,” but also “+” or “–.” Meaning is information in human action that reproduces the patterns of the world.

“The orderly structures and patterns of which we are most immediately aware are those within our own minds, bodies, and behavior, but virtually all human beings have a strong conviction that corresponding to these patterns of mind and body are similar patterns in what might be called the ‘real world’” (Boulding 1985, p. 9).

At the same time, meaning is not limited to a mental act that operates with abstraction. Thinking in itself is not an interaction with meanings as with some “supramundane” entities. Meaning is a material action and the result of an action. When we compare meanings with each other, we can distinguish between their general and particular properties. A clock is a device for measuring time. But this general property of being a clock does not exist in itself. It exists in the context of human activities related to clocks. The abstraction of a clock only makes sense in action, for example when you read and think about what is written in this book.

In his book The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design (1986), Richard Dawkins cited 18th-century theologian William Paley’s argument that if we find an object as precise and complex as a clock on a heath, we can assume that it did not come into being spontaneously, but was designed. Paley applied this argument to nature to prove the existence of God. Dawkins believed that Darwin’s theory of natural selection provided an answer to Paley’s argument:

“Natural selection, the blind, unconscious, automatic process which Darwin discovered, and which we now know is the explanation for the existence and apparently purposeful form of all life, has no purpose in mind. It has no mind and no mind’s eye. It does not plan for the future. It has no vision, no foresight, no sight at all. If it can be said to play the role of watchmaker in nature, it is the blind watchmaker” (Dawkins 1996, p. 5).

Dawkins argued that natural selection could have created the animal world even without the will of God, and Donald Campbell argued that cultural selection could have created knowledge and civilization even without the will of man. In his works of the 1950s and 60s, Campbell put forward the theory of “blind variation and selective retention,” according to which man creates cultural variations randomly, without foreseeing the future course of events, and these variations are then subjected to selection in which only those variations that have proven useful are stored and passed on through learning. Learning is “the retention of adaptive response patterns for subsequent utilization, thus abbreviating the trial and error process” (Campbell 1959, p. 158). Taking Dawkins and Campbell’s argument further, we can conclude that man is not a subject of culture at all, that culture does not need human design, that meanings develop on their own: they arise randomly and are passed on through involuntary learning. However, some people feel uneasy with this assumption:

“…Historical analyses of scientific and technological change suggest that cultural change is not quite so directed, and foresight not quite as accurate, as commonly assumed. Historical figures often claim retrospectively to have guided cultural change in particular directions, yet such claims may have the benefit of hindsight and be self-servingly exaggerated. However, there is a general lack of systematic evidence regarding this issue, at least compared to the careful experiments conducted by Luria and Delbruck in biology. We should therefore be prepared to accept that cultural evolution may, at least in some instances, be directed rather than blind and that there is a valid difference here between cultural and biological evolution” (Mesoudi 2011, p. 46). [Luria and Delbruck’s experiments in the 1940s showed that mutations in bacteria are not the result of selection pressure, but occur by chance.—A.K.]

So, is any new meaning a matter of chance? Henry Quastler once posed this question as follows: “How does one know that at least some new information has emerged or that the new work is more than a rearrangement, according to existing laws, of previously existing patterns?” (Quastler 1964, p. 17).

We showed above that a meaning s can be reduced to a minimal action s*. A minimal action is the shortest description of a meaning that allows its reproduction. Obviously, a new meaning emerges if it cannot be reduced to another meaning. It is known from information theory that the closer the length of string s is to the length of the minimal action s*, the more random the meaning is: “Among all the descriptions of s, there is a shortest one called s*, and the length of s* is the algorithmic entropy K(s). This led to a neat definition of randomness: A string s is random if it has no description much shorter than itself. Its entropy is about equal to its own length: K(s) = L(s*) ? L(s)” (Schumacher 2015, p. 240).