Prof. E. Colman[1]

Dynamic and Statistical Regularity in Physics and Biology

Written: 1931;
Source: Science at the Crossroads: Papers Presented to the International Congress of the History of Science and technology Held in London from June 29th to July 3rd, 1931 by the delegates of the U.S.S.R, Frank Cass and Co., 1931;
Online Version: For May, 2002.

The problem of the character of regularity plays a decisive part in the history of philosophy, of the natural and social sciences. And even though dynamic and statistic regularity exhaust all varieties of laws in the material world and in the consciousness that pictures it (since these are dialectical laws) as little as causality exhausts all types of relations, though the entire problem is closely connected with other questions of main philosophical categories, such as necessity and freedom, causality and chance, continuity and discontinuity, etc. in their application to physics and biology, nevertheless the problem itself does form a certain whole and is sufficiently in the centre of daily interests to serve as the theme for a separate discussion.

Without an understanding of regularity from the standpoint of dialectical materialism, physics and biology cannot steer a way through the Scylla of mechanistic fatalism and the Charybdis of indeterminism. But special importance attaches to the question, because as the crisis in capitalism develops, bourgeois world science grows more reactionary, making irresistibly towards unconcealed fideism.

If, twenty years ago, bourgeois philosophers, despite spontaneous materialism of the majority of physicists, saw in radio-active disintegration of matter a proof of the disappearance of matter, and if, further, the theory of relativity has been taken as affirmative evidence of philosophical relativism, subjectivism, the bourgeois physicists of to-day, resting their arguments upon the quanta theory, declare that causality has been overthrown and solemnly place upon the throne thus vacated the causa finalis of Aristotles. From the multitude of recent instances we shall select a few: in his article Die Kausalitat in der gegenwartigen Physik, pubhshed in the February number of Die Naturwissen schaften, M. Schlick regrets his earlier errors. He admits that he made all too great concessions to materialism and adopts the viewpoint that past and future cannot be differentiated, that natural phenomena are undetermined and indeterminable, denying causality and determinism.

In his address, published in the January number of Nature under the title Present Status of Theory and Experiment as to Atomic Disintigration and Atomic Synthesis, R. A. Millikan drew a comparison between three stages of theological thought on the relation between God and the World: first, the conception resting upon the second principle of thermo-dynamics, of a God that was necessary to wind up the slowing down world mechanism; second, the theory based upon the Darwinian theory of evolution, of the identity of God with the world, which it is claimed, represents the philosophical attitude of most great scientists from Leonardo da Vinci to Newton and Einstein, and fnally, the return to the medieval theistic theology of an unbroken act of creation, with which Millikan expresses a certain sympathy in the following words: "This has been speculatively suggested many times before, in order to allow the creator to be continually on his job. Here is, perhaps, a little bit of experimental fingerpointing in that direction," and which, it is alleged, finds support in the discovery of cosmic rays.

A. S. Eddington, in The End of the World from the Stand Point of mathematical Physics (in the March issue of Nature, takes up the position that the world is spatially finite, has a beginning in time and is developing towards a greater and greater lack of organisation. To us Marxist-Leninists it is obvious that this physical theory merely reflects the general tendency in bourgeois ideology, which interprets the approaching and inevitable end of the capitalist system as the approach of anarchy.

Nevertheless, viewed even from the theological, reactionary aspect, such a theory can offer little to the investigator. From the data adduced by Eddington himself:--An original world radius of 1,200 million light-years, a world radius to-day ten times as great, and the fact that the world radius doubles every 1,500 million years, it can be calculated, without much difficulty, that God created the world about 5 milliard years ago. This, it is true, indicates some error in the Bible, but it also contradicts the period of billions of years, accepted by Eddington himself elsewhere, that is necessary for the origin of stars and chemical elements.

In times of crisis the ideological pressure of the ruling class upon scientific creation is exerted more powerfully than at any other time.

In the social sciences the determination of the character of laws, their cognitive power--the scope of their content and their ability to serve scientific predictions--and their limits, is as important as it is in the natural sciences. In the Soviet Union, where the foundations of Socialist economy are nearing completion, where, consequently, the basis for free play of market forces is continually growing narrower, being thrust aside and replaced by socialist planning, questions relating to the validity of statistical methods, to the reliability of predictions, to methods of planning as a whole, are extremely acute and cannot be answered in the absence of a sure methodological basis. The problem of planning, of subjecting elemental forces to planned direction, is the vital point both of the theory and the practice of economy and policy.

How is the problem of dynamic and statistical regularity raised and solved by contemporary philosophical tendencies in the natural sciences? The two extremes are represented by mechanism, which in truth only recognises the rule of dynamic laws, interpreting them in a narrowly mechanical fashion as the spatial translation of particles without quality, and by indeterminism, which disguises its denial of necessity and conditionality by recognising only statistical laws, alleged to be the expression of free, undetermined chance.

The mechanistic conception of regularity that is characteristic of the metaphysical period of the natural sciences in the 19th century, was formulated most clearly by H. Helmholtz in the following words, taken from his Innsbruck address in 1869 Ueber das Ziel und die Fovtschritte der Naturzeissenschaft : "If, however, movement is the primary change underlying all other changes in the world, all elemental forces are forces of movement and the aim of the natural sciences is to find the movements underlying all other changes and to find their motive ponler, that is, to resolve them into mechanics."

For our purpose to-day, we are less interested in the unscientific identification of movements with mechanical space displacement than in another no less significant methodological error committed by Helmholtz: he does not understand the difference between the general and the particular. Engels, who understood quite as well as Helmholtz that every movement is connected in one way or another with mechanical movement but who, unlike Helmholtz, was a dialectician, did not propose to investigate the general, the average and the indifferent but, on the contrary, the particular feature in which one kind of movement differs from another. We would add that the inability to recognise the particular is closely connected with the mechanisticdismemberment of matter into identical atoms without quality and that the assertion that dynamic laws are alone objective necessarily implies that statistical regularity is recognised asbeing valid only subjectively (in nature it is alleged not to exist, it merely reflects our ignorance).

In biology the same methodological error underlies the mechanistic conception as in physics: a false understanding of the relations between the general, particular and individual that, in its turn, can be explained by the theory of knowledge which, subjective in its nature, denies the objectivity of quality to the individuals treated by biology, reducing them to physical-chemical processes and finally to mechanical movement. This subjectivism may possess a rationalist character, when the particular is deduced from the general, given a priori, or it may be of an empirical character, when the general itself is regarded as a subjective category and is built up of individual parts. Thus the connection between the general and the particular is reduced to one of quantity only. The univocacy of natural phenomena is a necessary premiss to this, for only on this condition can dynamic regularity be applied, and mathematical apparatus be brought into play, without further ado, upon all the complicated processes and forms of the organic world.

The attempts that have been made to mathematicise biology are extremely characteristic, for their inadequacy, their inability to comprehend the multiplicity and diversity of the subject, is at times clearly apparent, particularly in concrete matters. We would take as an example the work of Ronald Ross: The Prevention of Malaria, in which a complete system of equations has been elaborated to portray the dynamics of malaria epidemics although the author is finally compelled to admit that it contributes but little to the elucidation of the actual conditions. Muhlens, the German investigator of malaria, is quite right in remarking that the extent and the severity of malaria epidemics are not dependent simply upon the number of flies and parasite-carriers, but also upon numerous other factors, including not only general, hereditary, climatic and seasonal conditions, but also the individual disposition of flies and human beings etc. Ross' purely quantitative calculations cannot, however, reflect qualities.

Still more significant is the attempt to portray biological laws of the relations between organic species living together, of conditions of hereditary transmission, in differential equations, an attempt made by Volterra in which he formulates three main mathematical laws of the fluctuations of species living together: (I) The law of the periodic cycle; (2) the law of the conservation of the average; (3) the law of the perturbation of the average. Volterra himself realises that mathematical treatment implies a detachment from reality, that it is unable to present even an approximate picture, that it is a crude schematisation, isolating processes from their actual context. For example, two factors only are taken into account, the power of reproduction and the rapacity of species living together. None of these equations do much towards assisting the investigation of reality. If we compare Volterra's mathematical theory of the struggle for existence with the biological treatment accorded this problem by Darwin in his Origin of Species, the superiority of the latter admits of no doubt.

Finally we would refer to Faure Fremiet's work: La cinetique du developpment. He attempted to treat the laws of the growth of organic being on the basis of the differential equation and gives a brief formulation of his attitude in the following words: "L'ontogonese peut etre definie par les variations, en fonctions du temps, de deux characteristiques, qui sont: (I) La masse du substance constituant un systeme organise; (2) le degre de heterogenite et la complexite physicochimique de ce sysetme."

The main defect in all these attempts is that they leave out of account the specific peculiarities of the given process, the given concrete, complex phenomenon (malaria, ecology, heredity), that the particular which characterises these laws and these alone, is ignored. The infinitely involved universal connection which characterises the objective reality in the given concrete form is simplified, coarsened and obliterated, is reduced to a narrow causality partially grasped, representing only a small part of the world in all its intricacy.

The diametrically opposed standpoint adopted in the critical situation prevailing in the natural sciences to-day, is expressed most clearly in that version of the so-called principle of indeterminacy given by its author Heisenberg, and his numerous adherents. This principle of indeterminacy is translated from the mathematical into human language in the following way: in principle it is impossible to determine with equal accuracy both the position and the speed of an electron. The more exact our measurement of one of these magnitudes, the less exact is the other; this is not a result of imperfections in our instruments; indeed, the contrary is true--that the process of measurement itself exercises an influence upon the position and the speed of the electron, and the more exact the measurement is, the greater the influence. Thence it follows fhat if we know the original state of the electron (position and speed), we cannot determine its state within any given time, from which Heisenberg draws the following conclusion (see Zeitschrift fur Physik No. 43, 1927):

"Since all experiments are subject to the laws of quanta mechanics, the invalidity of the law of causality is definitely established by quanta-mechanics." It is clear, in this instance, that the methodological root of the error lies in the undialectical conception of the relation between the general and the particular. Heisenberg, and quanta mechanics as a whole, correctly emphasise the existence of mutual inter-action in any actual process, but cannot by themselves tackle the problem it raises. Marx, who dealt with the question of the mutual inter-action of the laws of capitalist production wrote in Capital (vol. III. Chap. X.):

"It is evident that the essential fundamental laws of production cannot be explained by the inter-action of supply and demand (quite aside from a deeper analysis of these two motive forces of social production which would be out of place here). For these laws cannot be observed in their pure state, until the effects of supply and demand are suspended, are balanced. As a matter of fact supply and demand never balance, or if they do, it is by mere accident, it is scientifically rated at zero, it is considered as not happening. But political economy assumes that supply and demand balance one another. Why? For no other reason, primarily, than to be able to study phenomena in their fundamental relations, in that elementary form which corresponds to their conception, that is to say, to study them unhampered by the disturbing interference of demand and supply." In eliminating the variations of demand and supply, Marx engages in a process of abstraction, but this abstraction retains the essential features of capitalism, the laws which characterise it and it alone, while an "abstraction" of the law of surplus value which retained supply and demand would divest the given form of production of its specificum, would resolve the particular in the general and lead to that "inadequacy and sterility of the pure concept of inter-action" of which Lenin speaks in commenting upon Hegel and demanding intermediation (connection) in the application of the principles of causation."

The so-called mathematical pendulum is an abstraction, distinguished from a real physical pendulum in that an abstraction is made of the mass of threads and the entire mass of the swinging body is considered as concentrated upon one point. Then it is not difficult to represent the law of oscillation of such a pendulum in empty space by a typical dynamic law. Given the length of the pendulum as l, the gravitation acceleration as g and the initial amplitude as a the corresponding amplitude a can be calculated for any time t with the required accuracy. Quanta mechanics maintains, as against this, that the smaller the content in which the mass of the swinging body is concentrated, the nearer ne approach to molecular, atomic, electronic dimensions, the clearer becomes the statistical character of the laws, the law of Brown's movement, that is, of the heat movement of the molecules of any given body, which runs: the average of the squares of the defections x of each particle from its initial position is directly proportional to the product of the average of its kinetic energy E x the time t for which this average is ascertained. Consequently, conclude Heisenberg, Schlick and others, we are not in the least entitled to make the abstractions that lead to this dynamic law. Here it is quite clear that they fail to understand the general and the particular. The statistical laws of Brown's movement, to which, in the given case, quanta mechanics refers, are equally valid for the movement of any body and are therefore able to tell us as little of the movement of a pendulum as the law of supply and demand tells us of the actual essential laws of the capitalist mode of production.

In biology, as in physics, indeterminism is characterised by a failure to understand the relation between the general and the particular. The particular, the individual, the qualitative specificum, its uniqueness and irrepeatability is emphasised and the general is transformed into an illusion or at best portrayed as subjective. Such a methodological attitude leads to the denial of general laws, or else tiese laws are degraded to something subjective, relative, the product of logic. Organic processes are regarded as spontaneously originating in themselves and one of the arguments adduced in proof thereof is the periodicity of the appearance of life. Indeterminism in its most varied forms replaces causation, and we reach Verworn's conditionalism, not far removed from Machism, which replaces the explanation, the discovery of the nature of a process by a description of its conditions, its causal connections, by functional relations.

Vitalism comes into the same category, for it too denies causation in favour of teleology, or at least places limits upon it. Thus, for example, Driesch writes in the Biologisches Zentralbratt, 1927: " In the inorganic sphere we can make predictions if the instantaneous constellation, instantaneous velocity and fundamental law are fully known; we cannot do this in biology." Indeterminism in present day physics has exerted a powerful influence upon biology; this is shown very clearly in Bertalanffy's articles which put forward finality and teleology as against causality and the law of the conservation of energy. It is significant that both indeterminism, which denies prediction, and fatalism which in principle does not exclude it, though in fact depriving it of any significance since, by that theory, the course of events is absolutely determined beforehand and cannot be changed, are closely allied from the point of view of the theory of knowledge. Thus, for example, Eimer's orthogenesis and Berg's nomogenesis, permit predictions of further developments, which does not, however, deprive either of its vitalist character. On the other hand emergent evolution, the Gestalt theory etc. which have a vitalist character, maintain that evolution is quite unpredictable, indecomposable and cannot be traced back to its origin. Thus absolute necessity falls into line with absolute chance.

In biology, the greatest interest, from the methodological point of view, attaches to that variety of indeterminism, expressed in the form of statistiscal regularity, which dates back to the time of Quetelet, who laid the foundations for statistics of variation. In the works of Quetelet, as of Dalton, and particularly of the biometrical school of Pearson which has given mathematical form to these laws, statistical regularity means nothing but the admission that dynamic laws and, in particular, their chief factor, conditionality, do not suffice, that is, the factor of chance is recognised. It should be pointed out, however, that statistical laws, which were worked out in reaction against the mechanistic character of dynamic regularity, against the denial of quality, do themselves to a certain extent repeat the same mechanistic error: soon everything became a matter of quantity, of the average, of the purely formal enumeration of external circumstances, while the inner connections and the structure of processes were ignored and often distorted, as, for example, in Galton's famous laws.

The solution of the problem lies in the synthesis of both forms of regularity, each of which is merely a factor of the other: in reality the two exist in an internally contradictory unity, inherent in each process, each movement of matter; it is precisely their inter-penetration and struggle that embody the immanent development of matter; the mathematical expression of these laws is not adequate to reality; hence it follows that the knowledge which is based only on dynamic, or alternatively only on statistical regularity, is certain to be incomplete, one-sided, approximate and if it claims to comprehend the whole of reality, it will also be unscientific. That is why Marx, who discovered the essential laws of capitalist production, and in doing so abstracted supply and demand, declared that these laws " only operate in an extremely intricate and approximate fashion, as the average, impossible to determine accurately, of eternal fluctuations, as the prevailing tendency." (Capital. Vol. III. Chapter 9). The natural sciences to-day, convulsed by the problem of reconciling the corpuscular and the wave theory of light and matter, of reconciling continuity and discontinuity, can find a way out of this blind alley only with the aid of materialist dialectics, with its conception of every law as a unity of the inter-penetration and struggle of contradictions.

The protracted and painful labour through which the natural sciences to-day are giving birth to dialectical materialism strengthens our conviction that without the midwife of history, the revolution, the matter will not proceed, that it is only the new generation of proletarian investigators of nature, liberated from the ideological slavery of capitalism, that will finally destroy the old traditions of metaphysical methodology that now hamper science; for the essential reason that prevents the bourgeois investigator of nature, the spontaneous materialist, from recognising dialectics and which, even in the period of capitalist decline, urges him towards idealism, is his close association with the ruling class and their ideology.

Between the two extremes of bourgeois philosophy concerning the characterof natural laws, between mechanism and indeterminism, there lies a vast field of dualistic and eclectic intermediate tendencies. The most typical is represented by the Machists, among them Mises, who proceed from the principle that while dynamic laws govern the individual elements forming a manifold, statistical laws govern the manifold as a whole. This they regard as the objective treatment of statistical laws, frequently expressing their outlook in the following way: statistical law is the law of the macrocosm, dynamical law the law of the microcosm. But there is no whole which cannot itself be a part, not any part that cannot be represented as a whole manifold; our earth is a macrocosm in comparison with the molecules of which it is composed, but a microcosm, in comparison with the stellar system of the Milky Way. Thus the objective in the definition of the character of regularity is lost, and everything depends upon how we regard the given object. On the other hand, this definition is metaphysical, for dynamic and statistical laws are represented as existing apart from each other. Hence it follows that the eclectics' struggle against the-mechanistic conception of statistical regularity as a provisional substitute for our ignorance (since finally the law of the whole is recognised to be merely the sum of individual laws), is conducted from a formalist standpoint. While conceding to the mechanists that the relation between statistical and dynamical regularity is the same as the relation between the law of the whole and the law of the parts, they exclaim against the attempts of the mechanists to reduce the laws of the whole to the laws of the parts. Eclectics draw a distinction between additive and non-additive properties, and maintain that it is the non-additive properties, which are not peculiar to each separate element of the manifold, but attach to it as such, that are portrayed by statistical laws; for this reason the statistical laws of the whole cannot be ascertained by the quantitive summing up of the laws of single events. This argument, however, does not achieve its purpose. Mechanists may dissociate themselves completely from an identification of the laws of the whole with the simple sum of the laws of the individual parts--they are still at their former position, in which they maintain that quality, can be reduced to quantity.

Actually, what meaning is there in the assertion that, for example, the statistical laws of the state of gas as a whole, cannot be reduced to the multiplicity of the dynamic laws of its molecules. This is a case of a non-additive manifold: all molecules are in process of inter-action, such properties of the whole as temperature, pressure and volume cannot be developed as the simple sum of the properties of separate molecules. But does that mean that it is altogether impossible to develop the laws of the whole on the basis of the dynamical laws of movement of the individual parts? The question itself engenders agnosticism. In fact, the process of inter-action exists; connections between the particles are formed; why then should our knowledge fail to follow the process of origin? Perhaps because we cannot tackle the matter mathematically? That is the answer given by the mechanists: if we could solve the differential equations of the movement of the individual parts, we should thereby comprehend the movement of the whole and consequently, in principle, the laws of the whole can be reduced to the laws of the parts. Not at all! We can adduce examples in which, in the case of the simplest mechanical movement, we are able to resolve the system of the differential equations of a non-additive manifold. But what does that give us? The knowledge of the behaviour of each individual particle, but that still does not tell us anything of the behaviour of the mechanical manifold as a whole. Further, if we could indicate a way of ascertaining, from a knowledge of the laws of all the parts, the laws of the whole, we should still not be able to speak of reduction, for, first of all, this would certainly introduce a new quality, and secondly it would be inconvertible: from the laws of the parts we would have ascertained full quantitative knowledge of the laws of the whole, but the contrary does not hold. Such a way is indicated by passing to the limit. The distribution of the characteristic magnitudes (position, speed, etc.), approaches, with exceeding over all limits, that distribution which can be ascertained as a statistical regularity by the calculation of probability. It is also to be expected, therefore, that dynamic laws are the laws of the particular, the laws of the quality which gives its general character to statistical regularity.

"In Capital, Marx first analyses the simplest, most commonplace, fundamental relation of bourgeois economy, encountered a million times--the exchange of commodities. In this simple phenomenon (In this "cell" of bourgeois society) the analysis covers all contradictions (or the germs of all contradictions) in present-day society. Further on we are given the development (and growth and movement) of these contradictions and this society, of their individual parts, from beginning to end." In this way, according to Lenin, the dialectical method does not rest solely upon dynamic regularity (as the mechanists would have it), nor solely upon statistical regularity (as suggested by those who would solve the problem in a formalist-idealist fashion). The dialectical materialist will conduct his investigations, not with the object of replacing statistical by dynamical laws, but in order to comprehend the object in the internally-contradictory unity of its content and its form, of the particular and the general, of the accidental and the necessary, of the discrete and the continuous. Our course lies not in "maintaining the old conception of necessity" and "forcing upon nature, in the form of a law, a logical construction contradicting both itself and reality," nor in "declaring the chaotic realm of accident to be the sole law of living nature," (Engels, Naturdialektik) nor in making an eclectic choice, but "in showing that the Darwinian theory represents in fact the correctness of the Hegelian conception of the essential connection between necessity and chance," in showing that "the division of the single and the understanding of its opposing parts is the essence of dialectics," " in examining the correctness of this aspect of the content of dialectics by a study of the history of science, in which we conceive of the "identity of contradictions" not only as "a sum of examples" but as "the cognitive law (and the law of the objective world)."

Both in theory and practice the question of the limits of application of laws is of particular importance. Lenin's contention that "the conception of law is merely a stage in the human understanding of the unity and connection, the mutual dependence and uniformity of the world process," his statements that, particularly in present day physics, " a struggle must be conducted against making the idea of law absolute and primitive, against giving it the charadter of a fetish," that, in phenomena, the law selects the calm and consequently, every law is partial, incomplete, approximate, all this refers both to dynamic and to statistical laws, for every example of the general is from another aspect an example of the individual. Everything depends upon the understanding how to determine in the given case and in the given circumstances, the limits of the general, upon avoiding a complete break with what forms the essence of the phenomenon, and falling into empty abstraction. Such moderation can be acquired only by studying concrete conditions and their transformations, only by practice, of which Lenin said:--"Practice stands higher than (theoretical) knowledge, for it possesses the distinction not only of general validity, but also of direct reality." In statistics, which is concerned with the laws of the general, the question of limits is often forgotten. In the writings of his youth : Who are the friends of the People; The development of Capitalism in Russia; A new, Economic Movement in Peasant Life; Lenin pointed out to bourgeois statisticians, frequently and in detail, how little scientific value attaches to the general average, the fictitious average, how statistics becomes a game with figures when, for example, the farms of poor peasants are added to the farms possessed by peasants who employ wage labour and to the farms of the large landowners and the total is divided by the total number of farms, etc., etc. Stalin, in a speech delivered in April, 1929, developed this idea by applying it to conditions in the Soviet Union at that time, conditions which have already been completely changed. Dealing with the extent of the area sown, he said:--" The method of averages if not corrected by the data of the different districts, is not a scientific method. In the Development of Capitalism Lenin criticises the bourgeois economists who apply the method of averages without referring to the facts of the different districts under cultivation. If we consider the movement of the area sown, that is, if we consider the matter scientifically, we see that in some districts this area is steadily increasing, in others, often because of meteorological conditions, falling, although nothing points to a steady decrease in the area sown anywhere." Statistical laws lose their scientific value, if the essential aspect of the phenomenon is forgotten, if the particular is metaphysically denied instead of being dialectically handled.

The most important factor in the unity of dynamic and statistical regularity is the direction of the movement of the law which, whether manifested as a dynamic or a statistical law, is in process of self-movement. In which direction do the internally contradictory tendencies develop? To follow the direction of the development of a law we have to consider not the process as a whole, for there the direction is expressed always as a negation of negation, but, as Engels pointed out in Anti-Duhring, we must study concretely this negation of negation.

Only by investigation in the different spheres of science conducted by dialectical materialists from this standpoint, shall we be able to work out the problem of the conditions in which the opposing factors of a law melt into each other without running the danger "of playing a futile game with empty analogies, of falling into abstruse Hegelianism," against which Lenin uttered a warning. Each of the brilliant concrete examples of the negation of negation adduced by Marx, Engels and Lenin will form the backbone for researches into all the new material offered by the most recent developments in society and its ideology, including both physics and biology.


[1] The biological material was supplied by Professor A. M. Krinitzky. Vice-Director of the State Institute of Micro-Biology (Moscow).