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The Nodal Line of Measurements

Prepared by the Leningrad Institute of Philosophy under the Direction of 
M. Shirokov 1941 

Pure quantity exists only in abstraction. In objective actuality every quantitative definiteness appertains to a certain quality. Three, four, five, etc. as generalities do not exist, but there are three or four trees, stones, tons of iron, metres of cloth, etc.

Conversely quality also does not exist independently of quantity. Every quality belongs to a thing that has this or that magnitude, every qualitative definiteness has at every given moment a definite intensity and degree of its development, has this or that quantitative characteristic. A piece of iron that has no definite magnitude, weight and temperature does not exist. Nor does a tree exist without a definite diameter to its trunk, number of branches and leaves, etc. Every light-ray has this or that wavelength, every electric current this or that voltage. The determined means of production in every country is characterized by this or that degree of development.

The establishment of such quantitative definitions, specific for each particular thing at each given moment of its development, has great practical and theoretical importance. However, the connection of quality and quantity in the examples just given has a more or less external character, each given magnitude is independent of the general characteristic of the quality. The fact that this piece of iron weighs three tons, and that four, is quite fortuitous for iron as a definite chemical element. The fact that in this country there are three trusts, in that ten, says in itself very little about the quality of capitalism as a special system of production.

In this way in every particular case the quantitative definiteness of a thing emerges as its external definiteness, “indifferent” to its quality. But as soon as we begin to scrutinize a thing in the whole course of its development we discover the profound internal connection of its quantitative and qualitative definitenesses.

Quality is developed on the basis of the internal contradictions of a thing. Development proceeds as determined by the form of movement characteristic of that quality and continues until the limiting stage within that type is reached. The contradiction of nascent capitalism pushes it inevitably to the development of machine technique, to the seizing of markets, to the annihilation of small-scale property, to domination in all fields of production. Socialism that has come into existence and has conquered but has still not yet fully developed proceeds inevitably to the full development of the possibilities of planned economy and goes on to the creation of productive forces adequate to socialism as a type of society.

In this case it is clear that quantitative development is by no means indifferent to the quality of the developing process, its connection with that quality is not external and fortuitous. Each particular quality has a corresponding quantitative measure so that the quantitative changes within a developing whole are determined by that quality. There are fixed limits in quantitative changes within which alone the quality can remain indifferent to the quantity. The point at which magnitude ceases to be indifferent is dependent upon the internal connection of quantitative and qualitative changes. Therefore change does not depend merely on quantitative development but on the special relation of quality to quantity in each particular case.

Conversely, we know that every quality is finite, that every qualitative definiteness has an internal final limit that belongs to it and that the fullest development of quality is at the same time the revelation of its limit. Imperialism, the highest stage of capitalist development, is at the same time the last stage of its development.

But capitalism became capitalist imperialism only at a definite, very high stage of its development, when certain of its fundamental properties had begun to change into their opposites, when the features of a period of transition from capitalism to a higher socio-economic system had begun to take shape and reveal themselves all along the line.”*

* Lenin, Imperialism, chap. vii.

The concentration of powerful productive forces in the hands of a few capitalists is the highest stage of private property in the means of production. And at the same time the concentration reveals the final limit of private property, it makes possible and necessary the transition to socialism.

For a full knowledge of the quality of a thing it is necessary to determine its final limit, that highest stage of its development at which it goes over into another quality – into its opposite. To know the quality of a metal we need to determine the temperature at which it melts. To know the quality of a building material we must find out its resistance to strain, its conditions of fracture, its heat conductivity. Thus for the knowledge of a quality we must disclose the highest stage of its development, the point of demarcation for its changes, the quantitative final limit of its existence as the given quality.

That is to say, both quantity and quality are disclosed more fully in their unity. The disclosure of this unity is measurement in the widest sense.

The transition of quantity into quality and the reverse is nothing else than the revelation of the internal contradictions of measurement. And that nodal point of change, at which the transition of quantity into quality takes place, expresses very fully the measurement of the given thing.

Quantitative and qualitative changes, taken as themselves, seem to be something indeterminate, fortuitous, and external. In measurement we disclose their necessary connection, we reveal their importance in the unity of the process. Thus measurement is nothing else than the law of the connection of quantitative and qualitative changes – a law that belongs to everything.

It is a great service to know the empirical numbers of nature, for example, the mutual distances of planets, but an immeasurably greater service is to make such empirically determined quantities vanish, by raising them to the general form of quantitative definitions, so that they become moments of law or measurement” (Lenin).

It was in this manner that Hegel determined the significance of the transition from external quantitative definiteness to measurement; he regarded measurement as the law-governed unity of a thing in its development, and development as that which gives the necessary basis to quantitative definiteness itself.

Knowledge of measurement plays an important role in science and practice. Every kind of physical energy, every chemical element has measure, which is reflected in a whole order of unalterable magnitudes – constants as they are called. Specific gravity, melting point, boiling point, atomic weight, valency, etc. – are such specific magnitudes as express the measurement of a chemical element. The constant of world gravitation, the magnitude of the quantum of energy, the mechanical equivalent of different aspects of energy, Avogadro’s constant – these are examples of magnitudes that reflect the measurement of physical processes. We measure the quality of a bridge by that load which the bridge can carry. Each machine has in given conditions the rate of output specific for it. A zoologist, in studying this or that animal, tries to establish its limit of growth, its age, its temperature, its blood constituents, etc. The differences in the qualification of workers of one and the same speciality finds its reflection, under equal conditions, in the different productivity of their labour.

In many cases serious political conflict centres round this question of measurement, as for instance when it is applied to the question of socialist advance or retreat, of finding the nodal point of a decisive turn. As an example we will consider the transition from the period of merely restricting the kulak to the period of the liquidation of kulaks as a class. Stalin in his speech at the Agrarian Conference gave convincing arguments for believing this transition to be opportune. He contrasted the quantity of wheat produced in kulak farms and in the socialist sector for the years 1927 and 1929, regarding these quantitative relationships as the index of the qualitative difference in the relation of two classes at the cited periods. In 1927 the relation of forces was such that a decisive advance on kulakism was impossible. The Zinoviev-Trotskyist party, which was at this time declaiming against the kulak, did not understand our unpreparedness for advance. Essentially the measures proposed by the opposition would have led to the policy of “scratching at kulakism,” and not to its liquidation. “To advance on kulakism meant so to prepare ourselves that when we do smite it it can no more rise to its feet.”* This preparation was expressed in the Party line on collective farm and soviet-farm construction. And at last that moment came when the quantity of socialist wheat exceeded the quantity of kulak wheat; that was the nodal point of the related measurements, that was the moment when it was possible to introduce a qualitative change of tactics. In order to introduce this at the right time it was necessary to determine rightly the measurement of the relations of class forces. The Central Committee of our Party rightly determined this measurement and in 1929 initiated successfully the transition to the liquidation of kulaks as a class on the basis of all-round collectivization.

* Stalin, Question of Leninism.

In speaking of measurement in all the examples we have given we were at the same time speaking of the transition of one quality into another. Nor was it by chance. Measurement, expressing the contradictions between quantity and quality, is the law of the transition of quantitative changes into qualitative changes and of the reverse process, and is therefore the law of transition from one process to a qualitatively different process.

Measurement marks the final limit of a given quality. It is only possible to discover that limit by investigating the changes of a thing in a thoroughly practical and experimental way. To determine the measurement of the policy of restricting the kulak means to indicate that moment in which it passes over into the policy of liquidating the kulak. Measurement is found only in the process of change, in the process of turning one measurement into another.

Every measurement “exists only in that connection, which leads to the general” and expresses that connection by being the law of transition from one process to another. Every measurement is of internal necessity linked up with a number of others. In this internal connection they form a single line of development, a number of nodal points of qualitative changes – they form a nodal line of measurements.

An order of determined and logical changes in the length of a violin string gives a single order of musical tones and overtones. The solid, liquid and gaseous states of a substance are a single chain of quantitative and qualitative changes, a single nodal line of measurements of the aggregate states of the substance.

Knowledge finds in nature many different and, from their appearance, mutually unconnected, things and phenomena. The discovery of the nodal line of measurements leads to the disclosure of their internal connection, of the unity in the diversity, to the reflection in a concrete whole of the uniqueness of this or that field of nature. Engels, touching on the importance of the law of conversion of energy, wrote: “In science we have succeeded in ridding ourselves from the fortuitousness of the occurrence of this or that quantity of physical forces, because their mutual connection and their transition into each other have been revealed.”*

* Engels, Dialectic of Nature.

Measurement is the law of the connection of quality and quantity. The nodal line of measurements is a yet wider and more general law of a whole number of quantitative and qualitative changes. Where in appearance there is a simple, joint existence of separate things, a more profound knowledge will disclose their law-governed connection as links of a nodal line of the measurements of nature, a line complete in itself yet with infinite ramifications.

The nodal line of measurements expresses the internal connection of the development of material forms. However, it may happen the discovery of the nodal line of measurements will precede the discovery of the actual course of development. Even before the transmutation of chemical elements was verified in experiment chemists were occupied with the question of their classification. The great scientist, Mendeleyev, revealed what is called the periodic law of elements. He based this classification upon their atomic weights, a specific quantity belonging to each element, and by arranging the elements in the order of increasing atomic weights showed that the qualities of elements form a law-governed system – or, speaking in the language of dialectic, a nodal line of measurements.

Mendeleyev was led to his discovery by realizing the connection of particular elements with the quantity that is specific for them. He himself believed the conversion of elements into each other to be impossible and denied them any common origin. But when the general law was found it had great influence on the study of the properties of particular elements. Furthermore, on the basis of the periodic law Mendeleyev was able to foretell the properties of elements still undiscovered, whose places were then empty in the table of the periodic law. The investigations that followed brilliantly justified Mendeleyev’s predictions. “Mendeleyev, by unconsciously applying the Hegelian law of transition of quantity into quality, accomplished a scientific exploit worthy to be set alongside with the discovery of Leverrier, who calculated the orbit of the unknown planet Neptune.”* After Mendeleyev the periodic law underwent a number of essential changes and amplifications but its basic idea receives ever greater confirmation. The periodic law plays an important role in the study of that internal form of movement which lies at the basis of qualitatively different elements.

* Engels, Dialectic of Nature.

One of the greatest of the services of Marx in creating the theory of historic materialism was the discovery of the logical connection of a number of social formations. “In general features, the Asiatic, the antique, the feudal and modern bourgeois means of production can be established as progressive epochs of the economic history of society.”* Social history as a whole, consisting as it does of the successive replacements of one social system by another each of which is characterized by the determined level of productive forces and of the productivity of social work, forms a single nodal line of measurements.

* Marx, Foreword to Critique of Political Economy.

In politics the nodal line of measurements plays also an important role. As Lenin pointed out, the basic trait of opportunism is “the changing of principles, lack of principle... jumping over gaps.” In contrast to opportunist lack of principle the Leninist policy is the conducting of a single line through all stages of revolutionary conflict. Lenin, in reckoning up the qualitative differences between stages, always indicated the internal connection of the particular stages with each other. Stalin on this basis has worked out the practical strategy and tactics of Bolshevism. Bolshevik strategy is built on the evaluation of the peculiarities of each stage, determines the measurement of the decisive turn from stage to stage, and realizes through a number of stages the one final aim of the proletariat. Trotsky opposes to the Leninist doctrine on the stages of revolution his own conception of the strategy of class struggle. In The Lessons of October he defined strategy very generally and abstractly, as “the art of conquering, i.e. of winning power.” For Trotsky strategy is a plan “in general” that does not allow variation, nor takes account of the uniqueness of the stages in all the relations of class forces under all sorts of conditions. The dialectical unity of the nodal line of measurements in the Leninist doctrine of strategy is replaced by Trotsky by the abstract metaphysic of the single blow. It is quite clear that this conception of strategy is for Trotsky the foundation on which he justifies the armed Bolshevik rising of 1917. But this revolutionary strategy, which became necessary at the transition from bourgeois-democratic revolution to socialist revolution, was for Lenin the realization of a single line that had been thought out and expounded long before, the logical growing of one stage of revolution into another. Trotsky, however, declares this change of strategy to be a change of principles and is subsequently compelled to set in opposition to the Bolshevist dialectic the metaphysic of his own “permanent revolution.”

Profoundly dialectical also is the Leninist plan of New Economic Policy. In his speech at the Eleventh Congress of the Party Lenin showed in the stages they had passed through and those that still awaited them that single line of development which included and justified N.E.P. The transition to a developed socialist offensive which the Party subsequently carried forward under Stalin’s leadership was nothing else than the realization of one of the nodes of the Leninist line.

And so, the nodal line of measurements opens the road to the knowledge of the whole connection of development in all fields of nature and society. But no nodal line exists independent of the others. In essence everything in the world is the nodal line of its own internal differences and at the same time one of the measurements in some wider nodal line. The stages of capitalism form the nodal line of capitalist development, but capitalism in its turn is one of the measures in the general chain of the history of society, just as society is only one link in the eternal development of the universe of matter.
All nature, to the knowledge of which we can attain, forms some system, some accumulated connection of bodies, and under the word ‘body’ we understand all material realities, beginning with the stars and ending with the atom and even with a particle of ether, in so far as we admit the reality of the latter.”Engels, Dialectic of Nature.
Every partial measurement can be understood only as an expression of the general line of development. If the metaphysical fallacy lay in taking particular things in isolation, the dialectical conception of nature requires the finding of the place of a given process in the general connection of development. Through this connection of emergence and annihilation we can ever more completely and more deeply disclose all the uniqueness of a given thing.
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