Many notions are purely relative in character. For example, if one is asked to say whether a road is on the right or left side of a house, it is impossible to answer. It depends on which direction one is moving relative to the house. On the other hand, it is possible to speak of the right bank of a river, because the current determines the direction of the river. Similarly, we can say that cars keep to the left (at least in Britain!) because the movement of a car singles out one of the two possible directions along the road. In all these examples, however, the notions “left” and “right” are shown to be relative, since they only acquire meaning after the direction by which they are defined as indicated.

In the same way, if we ask, “Is it night or day?” the answer will depend on where we are. In London it is day, but in Australia it is night. Day and night are relative notions, determined by our position on the globe. An object will appear bigger or smaller depending upon its distance from a given point of observation. “Up” and “down” are also relative notions, which changed when it was discovered that the world is round, not flat. Even to this day, it is hard for “common sense” to accept that people in Australia can walk “upside down”. Yet there is no contradiction if we understand that the notion of the vertical is not absolute but relative. For all practical purposes, we can take the earth’s surface to be “flat” and therefore all verticals to be parallel, when dealing for instance, with two houses in one town. But when dealing with far larger distances, involving the whole earth’s surface, we find that the attempt to make use of an absolute vertical leads to absurdities and contradictions.

By extension, the position of a planetary body is necessarily relative to the position of others. It is impossible to fix the position of an object without reference to other objects. The notion of “displacement” of a body in space means no more than that it changed its position relative to other bodies. A number of important laws of nature have a relativistic character, for example the principle of the relativity of motion and the law of inertia. The latter states that an object on which no external force acts can be not only in a state of rest but also in a state of uniform straight-line motion. This fundamental law of physics was discovered by Galileo.

In practice, we know that objects upon which no external force is applied tend to come to rest, at least in everyday life. In the real world, the conditions for the law of inertia to apply, namely the total absence of external forces acting on the body, cannot exist. Forces such as friction act on the body to bring it to a halt. However, by constantly improving the condition of the experiment, it is possible to get closer and closer to the ideal conditions envisaged by the law of inertia, and thus show that it is valid even for the motions observed in everyday life. The relative (quantitative) aspect of time was perfectly expressed in Einstein’s theories, which conveyed it far more profoundly than the classical theories of Newton.

Gravity is not a “force”, but a relation between real objects. To a man falling off a high building, it seems that the ground is “rushing towards him”. From the standpoint of relativity, that observation is not wrong. Only if we adopt the mechanistic and one-sided concept of “force” do we view this process as the earth’s gravity pulling the man downwards, instead of seeing that it is precisely the interaction of two bodies upon each other. For “normal” conditions, Newton’s theory of gravity agrees with Einstein’s. But in extreme conditions, they completely disagree. In effect, Newton’s theory is contradicted by the general theory of relativity in the same way as formal logic is contradicted by dialectics. And, to date, the evidence shows that both relativity and dialectics are correct.

As Hegel explained, every measurement is really the statement of a ratio. However, since every measurement is really a comparison, there must be one standard, which cannot be compared with anything but itself. In general, we can only understand things by comparing them to other things. This expresses the dialectical concept of universal interconnections. To analyse things in their movement, development and relationships is precisely the essence of the dialectical method. It is the exact antithesis of the mechanical mode of thought (the “metaphysical” method in the sense of the word used by Marx and Engels) which views things as static and absolute. This was precisely the defect of the old classical Newtonian view of the universe, which, for all its achievements, never escaped from the one-sidedness that characterised the mechanistic world outlook.

The properties of a thing are not the result of relations to other things, but can only manifest themselves in relations to other things. Hegel refers to these relations in general as “reflex-categories”. The concept of relativity is an important one, and was already fully developed by Hegel in the first volume of his masterpiece Science of Logic. Trotsky demonstrated how we see this, for example, in social institutions such as kingship.

Naïve minds, think that the office of kingship lodges in the king himself, in his ermine cloak and his crown, in his flesh and bones. As a matter of fact, the office of kingship is an interrelation between people. The king is king only because the interests and prejudices of millions of people are refracted through his person. When the flood of development sweeps away these interrelations, then the king appears to be only a washed-out man with a flabby lower lip. He who was once called Alfonso XIII could discourse upon this from fresh impressions.

The leader by will of the people differs from the leader by will of God in that the former is compelled to clear the road for himself or, at any rate, to assist the conjuncture of events in discovering him. Nevertheless, the leader is always a relation between people, the individual supply to meet the collective demand. The controversy over Hitler’s personality becomes the sharper the more the secret of his success is sought in himself. In the meantime, another political figure would be difficult to find that is in the same measure the focus of anonymous historic forces. Not every exasperated petty bourgeois could have become Hitler, but a particle of Hitler is lodged in every exasperated petty bourgeois.[37]

In Capital, Marx showed how concrete human labour becomes the medium for expressing abstract human labour. It is the form under which its opposite, abstract human labour, manifests itself. Value is not a material thing which can be derived from the physical properties of a commodity. In fact, it is an abstraction of the mind. But it is not on that account an arbitrary invention. In fact, it is an expression of an objective process, and is determined by the amount of socially necessary labour power expended in production. In the same way, time is an abstraction which, although it cannot be seen, heard or touched, and can only be expressed in relative terms as measurement, nevertheless denotes an objective physical process.

Space and time are abstractions, which enable us to measure and understand the material world. All measurement is related to space and time. Gravity, chemical properties, sound, light, are all analysed from these two points of view. Thus, the speed of light is 186,000 miles per second, while sound is determined by the number of vibrations per second. The sound of a stringed instrument, for instance, is determined by the time in which a certain number of vibrations occur and the spatial elements (length and thickness) of the vibrating body. That harmony which appeals to the aesthetic feelings of the mind is also another manifestation of ratio, measurement and therefore time.

Time cannot be expressed except in a relative way. In the same way, the magnitude value of a commodity can only be expressed relative to other commodities. Yet value is intrinsic to commodities, and time is an objective feature of matter in general. The idea that time itself is merely subjective, that is to say an illusion of the human mind, is reminiscent of the prejudice that money is merely a symbol, with no objective significance. The attempt to “demonetise” gold, which flowed from this false premise, led to inflation every time it was attempted. In the Roman Empire, the value of money was fixed by imperial decree, and it was forbidden to treat money as a commodity. The result was a continuous debasement of the currency. A similar phenomenon has taken place in modern capitalism, particularly since the Second World War. In economics, as in cosmology, the confusion of measurement with the nature of the thing itself leads to disaster in practice.

  1. Trotsky, L. The Struggle Against Fascism in Germany, p. 399.