## Information and evolutionary paradigm selection of information

Note that some statements about the connection between evolution and information today seem truisms. In the course of evolution the amount of information increases. The information grows by means of either being "selected" from the noise, which masks it, or the creation of new information as a result of the memory of some random choice. For instance, the information increases in the process of crystallisation of liquid, but it is not new information. It is known as a priori information, i.e. which was earlier hidden by "entropy noise". In the course of evolution the appearance of new information is a result of some "memory" and genetic recombinations. New information is created when every individual appears in this world. New information is created also when new species and superior taxa appear. From the linguistic point of view, this means that in the course of evolution the length of the alphabet increases.

The genetic information is transmitted from one generation to another just after its transformation within an ecosystem, which consists of populations. In turn, populations are the elementary units of microevolution (Svirezhev, 1989). Still Timofeev-Resovsky has emphasised that for evolution the quality (not the quantity) or the cost of information is important (Timofeev-Resovsky, 1958, 1961b).

If we look in any detailed physical handbook we see that, for instance, entropy of 1 mol of CO2 (this gas is very popular in ecology) at 25°C and 1 atm is equal to 214 J/K. Let us remember that the number of molecules in 1 mol is equal to nmol = R/k, where R is the gas constant, R < 8.314 J/K mol, so that nmol < 6.07 X 1023 molecules. Therefore, the entropy of a single molecule of CO2 will be equal to 213.5/6.07 X 1023 = 3.52 X 10~22 J/K. From Eq. (1.1) we get ln W = 3.5 X 10~22/L37 X 10~23 < 25.7 and W = e25 7 < 1.4 X 1011. The latter means that every CO2 molecule may be situated at one of the 1.4 X 1011 different states.

Now we would like to tell the following story, which is absolutely heretical from a physical point of view. Since the CO2 molecules differ from each other by the values of some parameter (in thermodynamics either the energy or temperature can be considered as the parameter), we can assume that there is a pool filled by nm = 1.4 X 1011 different molecules of CO2. We are two Panglossists (see Chapter 12), i.e. we believe that we are living in the best world; therefore, the CO2 molecule in our world is the best of the possible number of 1.4 X 1011 molecules. Thus, our CO2 is a result of sequential choice and we next test the chosen molecule in order to find the single "best" one among them. We again ask Ecodemon to help us. The probability that already the first attempt of Ecodemon would be successful is equal to p = 1 /nm = 1/1.4 X 1011 < 0.7 X 10"11. But Ecodemon can solve the problem by exhaustion with nm steps (maximum). If every step is about 10~2 s (mean time of carbon oxygenation), then in the most pessimistic scenario all the processes will be finished in the course of 45 years. This is only an instant in the geological time scale. It is obvious that similar arguments take place for the whole chemosphere of our Universe, which has already existed for 12 X 109 years. Therefore, we can say that all chemical elements and their (non-organic) compositions already existed at the initial stage of the evolution of the Universe.

Note that in these considerations we use a teleological paradigm (we assume that some "best" objects exist) and an evolutionary approach (i.e. we can find these "best" objects if we use some sequential evolutionary procedure and some selective principle). This method is very popular in the biological sciences where the selective principle is natural selection, but it is also used implicitly in theoretical physics. However, if in biology the entire course of evolution is interesting then in physics we are interested only in the initial and final states of the studied system; the ways that lead from the initial to the final state are not essential. This kind of method is called thermodynamic. From the evolutionary point of view, such a thermodynamic approach has a right to exist only if the system manages to test all intermediate states before attaining in the course of "reasonable" time some final state that may be considered as equilibrium. In other words, it is assumed that the velocity of the system's movement across intermediate states is sufficiently high. We saw that clearly with chemical systems. For biological systems the answer to the question "Is it possible for biological objects to attain some 'best' state in the process of biological evolution in a 'reasonable' time?" is not evident.

This is a very old problem but it has again become modern since we have known that genetic information is represented in the form of polynucleotide sequences, so that a single nucleotide base can be considered as one letter of a genetic text (genome). For instance, the human genome contains about 1010 nucleotide bases (indeed, the characteristic size of a nucleotide base pair is equal to 6 X 10~10 m; since the human genome is represented in the form of 2 m of "double-stranded" DNA, the total number of nucleotide base pairs will be 1/3 X 10210 < 0.35 X 1010). Since the alphabet of nucleotides contains only four letters, the number of different genetic texts (genomes) will be equal to (4)0 35x10 < (10)2X1° . This number is monstrously immense; for instance, the number of all elementary particles in our Universe is 10100 and has been in existence for only 4 X 1017 s! Here we first meet the so-called "combinatorial" numbers, which are not comparable with "physical" ones (the number of particles is a typical "physical" number). However, combinatorial operations with physical numbers can generate combinatorial numbers.

Thus, it is an absolutely non-realistic idea to attain a single "best" combination in the course of "reasonable" time, if we have such a number of possible combinations. In other words, the sorting of combinations by natural selection is out of the question (Blumenfeld, 1977a). Therefore, evolutionary trajectories are random (non-deterministic) and they cannot be repeated. Therefore, Darwinism, which is based on the paradigm of natural selection, is not true. All of us are only a result of the "game of chance" on this planet Earth.

Again I saw that under the sun the race is not to the swift, nor the battle to the strong, nor bread to the wise, nor riches to the intelligent, nor favour to the men of skill; but time and chance happen to them all.

The Bible. Ecclesiastes, 9.

But the situation is not absolutely so pessimistic and there are some ways out of the contradiction. The first way is "thermodynamic", when the problem is assumed to be irrelevant since only the initial and final states are interesting for us; we assume only that the transition from the initial to the final state is possible without any detailed description in which way it is realised. There are also other possibilities.

If we look at the picture of evolution (as a whole), we see that evolution possesses a very long "memory": the genome of dinosaur cannot change in such a way that in the next evolutionary step a mammoth would occur. Timofeev-Resovsky said about this: "There cannot appear the mutation of the colour of the tail tip in the human genome". One of the main evolutionary problems, the appearance of new species, is always meeting the question of how the appearance can be explained, since it represents a jump in the continuous evolutionary movement under mutation pressure. This contradiction resolves the so-called hypothesis of "Meccano" (Timofeev-Resovsky, 1961b;Eigen, 1981;Ivanitzkyetal., 1985). (We all know this children's construction set consisting of miniature metal or plastic parts from which mechanical models can be made.) We show the principal mechanism of the hypothesis by the following example (Shnol, 1989).

Let at the beginning five-letter short words be formed spontaneously from a four-letter alphabet: the possible number of these is 45 = 1024. They can be sorted out by some criterion in the course of a relatively short time t1 < t X 1024, where t is the time of one test. From these words the 20 most "perfect" words are selected. Then we begin to compose phrases from them. By assuming (for simplicity) that each of these phrases contains five words, their number is (20)5 = 3 X 106. From these phrases we select again the five best ones, and compose stanzas. From these stanzas we compose a poem, etc. "I process thousands of tons of verbal ore in order to find one unique word" (Mayakowsky, the Russian poet). Step by step the perfection of the text is reached. Even if something is insufficiently perfect at higher hierarchical levels then we shall change only individual blocks, but do not split all the text into single letters. Any time will be insufficient for a senseless work. Thus, we assume that evolution in general, and the evolution of genetic information in particular, is proceeding in accordance with the principle of "Meccano".

Let us try to formalise our preceding reasoning. At the first stage of aggregation we construct r1 -letter words in an R0-letter alphabet. The number of possible words is equal to (R0)r1, and then the time of total sorting will be equal to t1 = t1 (R0)r1 where t1 is the test time at this stage. Then we select from these words R1 the best words, which will be "letters" at the next stage when we shall construct r2-word phrases. The possible number of these is equal to (R1)r2, and the time of total sorting will be equal to t2 = T2(R1)r2, etc. until at the final fth stage we get a text of given length n. It is obvious that n < r1 X r2 X ••• X rf. The total time of such type of evolution is equal to

One can see that the time of sorting by the "Meccano" principle tc is essentially less than the time of total sorting, which is equal to t0 = tR0 . This becomes especially visual, if we simplify Eq. (8.1) by setting t{ = t, Ri = R and rt = r. Then we get (Ivanitzky et al., f tc=n Ti<^i-i)ri