3. Dialectical Materialism

What is dialectics?

“Everything flows and nothing stays.”
(Heraclitus)

Dialectics is a method of thinking and interpreting the world of both nature and society. It is a way of looking at the universe, which sets out from the axiom that everything is in a constant state of change and flux. But not only that. Dialectics explains that change and motion involve contradiction and can only take place through contradictions. So instead of a smooth, uninterrupted line of progress, we have a line that is interrupted by sudden and explosive periods in which slow, accumulated changes (quantitative change) undergo a rapid acceleration, in which quantity is transformed into quality. Dialectics is the logic of contradiction.

The laws of dialectics were already worked out in detail by Hegel, in whose writings, however, they appear in a mystified, idealist form. It was Marx and Engels who first gave dialectics a scientific, that is to say, materialist basis. As Trotsky explained:

“Hegel wrote before Darwin and before Marx. Thanks to the powerful impulse given to thought by the French Revolution, Hegel anticipated the general movement of science. But because it was only an anticipation, although by a genius, it received from Hegel an idealistic character. Hegel operated with ideological shadows as the ultimate reality. Marx demonstrated that the movement of these ideological shadows reflected nothing but the movement of material bodies.” ¹⁸

In the writings of Hegel there are many striking examples of the law of dialectics drawn from history and nature. But Hegel's idealism necessarily gave his dialectics a highly abstract, and arbitrary character. In order to make dialectics serve the “Absolute Idea”, Hegel was forced to impose a schema upon nature and society, in flat contradiction to the dialectical method itself, which demands that we derive the laws of a given phenomenon from a scrupulously objective study of the subject matter as Marx did in his Capital. Thus, far from being a mere regurgitation of Hegel's idealist dialectic arbitrarily foisted on history and society as his critics often assert, Marx's method was precisely the opposite. As Marx himself explains:

“My dialectic method is not only different from the Hegelian, but is its direct opposite. To Hegel, the life-process of the human brain, i.e., the process of thinking, which, under the name of 'the Idea', he even transforms into an independent subject, is the demiurgos of the real world, and the real world is only the external, phenomenal form of 'the Idea'. With me, on the contrary, the ideal is nothing else than the material world reflected by the human mind, and translated into forms of thought.” ¹⁹

When we first contemplate the world around us, we see an immense and amazingly complex series of phenomena, an intricate web of seemingly endless change, cause and effect, action and reaction. The motive force of scientific investigation is the desire to obtain a rational insight into this bewildering labyrinth, to understand it in order to conquer it. We look for laws that can separate the general from the particular, the accidental from the necessary, and enable us to understand the forces that give rise to the phenomena which confront us.

In the words of the English physicist and philosopher David Bohm:

“In nature nothing remains constant. Everything is in a perpetual state of transformation, motion, and change. However, we discover that nothing simply surges up out of nothing without having antecedents that existed before. Likewise, nothing ever disappears without a trace, in the sense that it gives rise to absolutely nothing existing at later times. This general characteristic of the world can be expressed in terms of a principle which summarises an enormous domain of different kinds of experience and which has never yet been contradicted in any observation or experiment, scientific or otherwise; namely, everything comes from other things and gives rise to other things.” ²⁰

The fundamental proposition of dialectics is that everything is in a constant process of change, motion and development. Even when it appears to us that nothing is happening, in reality, matter is always changing. Molecules, atoms and subatomic particles are constantly changing place, always on the move. Dialectics is thus an essentially dynamic interpretation of the phenomena and processes that occur at all levels of both organic and inorganic matter.

The American physicist Richard P. Feynman (1918-1988) notes:

“To our eyes, our crude eyes, nothing is changing, but if we could see it a billion times magnified, we would see that from its own point of view it is always changing: molecules are leaving the surface, molecules are coming back.” ²¹

So fundamental is this idea to dialectics that Marx and Engels considered motion to be the most basic characteristic of matter. As in so many cases, this dialectical notion was already anticipated by Aristotle, who wrote: “Therefore… the primary and proper meaning of 'nature' is the essence of things which have in themselves…the principle of motion.” ²² This is not the mechanical conception of motion as something imparted to an inert mass by an external “force”, but an entirely different notion of matter as self-moving. For them, matter and motion (energy) were one and the same thing, two ways of expressing the same idea. This idea was brilliantly confirmed by Albert Einstein's theory of the equivalence of mass and energy. This is how Engels expresses it:

“Motion in the most general sense, conceived as the mode of existence, the inherent attribute, of matter, comprehends all changes and processes occurring in the universe, from mere change of place right up to thinking. The investigation of the nature of motion had as a matter of course to start from the lowest, simplest forms of this motion and to learn to grasp these before it could achieve anything in the way of explanation of the higher and more complicated forms.” ²³

"Everything flows"

Everything is in a constant state of motion, from neutrinos to super-clusters. The earth itself is constantly moving, rotating around the sun once a year, and rotating on its own axis once a day. The sun, in turn, revolves on its axis once in 26 days and, together with all the other stars in our galaxy, travels once around the galaxy in 230 million years. It is probable that still larger structures (clusters of galaxies) also have some kind of overall rotational motion. This seems to be a characteristic of matter right down to the atomic level, where the atoms that make up molecules rotate about each other at varying rates. Inside the atom, electrons rotate around the nucleus at enormous speeds.

The electron possesses a quality known as intrinsic spin. It is as if it rotates around its own axis at a fixed rate and cannot be stopped or changed except by destroying the electron as such. If the spin of the electron is increased, it so drastically alters its properties that it results in a qualitative change, producing a completely different particle. The quantity known as angular momentum—the combined measure of the mass, size and speed of the rotating system—is used to measure the spin of elementary particles. The principle of spin quantization is fundamental at the subatomic level but also exists in the macroscopic world. However, its effect is so infinitesimal that it can be taken for granted. The world of subatomic particles is in a state of constant movement and ferment, in which nothing is ever the same as itself. Particles are constantly changing into their opposites, so that it is impossible even to assert their identity at any given moment of time. Neutrons change into protons, and protons into neutrons in a ceaseless exchange of identity.

Engels defines dialectics as “the science of the general laws of motion and development of nature, human society and thought.” In Anti-Dühring and The Dialectics of Nature, Engels gives an account of the laws of dialectics, beginning with the three most fundamental ones:

1) The law of the transformation of quantity into quality and vice versa;
2) The law of the interpenetration of opposites, and
3) The law of the negation of the negation.

At first sight, such a claim may seem excessively ambitious. Is it really possible to work out laws that have such a general application? Can there be an underlying pattern that repeats itself in the workings, not only of society and thought, but of nature itself? Despite all such objections, it is becoming increasingly clear that such patterns do indeed exist and constantly re-appear at all kinds of levels, in all kinds of ways. And there are an increasing number of examples, drawn from fields as diverse as subatomic particles to population studies, which lend increasing weight to the theory of dialectical materialism.

The essential point of dialectical thought is not that it is based on the idea of change and motion but that it views motion and change as phenomena based upon contradiction. Whereas traditional formal logic seeks to banish contradiction, dialectical thought embraces it. Contradiction is an essential feature of all being. It lies at the heart of matter itself. It is the source of all motion, change, life and development. The dialectical law that expresses this idea is the law of the unity and interpenetration of opposites. The third law of dialectics, the negation of the negation, expresses the notion of development. Instead of a closed circle, where processes continually repeat themselves, this law points out that movement through successive contradictions actually leads to development, from simple to complex, from lower to higher. Processes do not repeat themselves exactly in the same way, despite appearances to the contrary. These, in a very schematic outline, are the three most fundamental dialectical laws. Arising from them there are a whole series of additional propositions, involving the relation between whole and part, form and content, finite and infinite, attraction and repulsion and so on. These we shall attempt to deal with. Let us begin with quantity and quality.

Quantity and quality

The law of the transformation of quantity into quality has an extremely wide range of applications, from the smallest particles of matter at the subatomic level to the largest phenomena known to man. It can be seen in all kinds of manifestations, and at many levels. Yet this very important law has yet to receive the recognition it deserves. This dialectical law forces itself to our attention at every turn. The transformation of quantity into quality was already known to the Megaran Greeks, who used it to demonstrate certain paradoxes, sometimes in the form of jokes. For example, the “bald head” and the “heap of grain”—does one hair less mean a bald head, or one grain of corn a heap? The answer is no. Nor one more? The answer is still no. The question is then repeated until there is a heap of corn and a bald head. We are faced with the contradiction that the individual small changes, which are powerless to effect a qualitative change, at a certain point do exactly that: quantity changes into quality.

The idea that, under certain conditions, even small things can cause big changes finds its expression in all kinds of sayings and proverbs. For instance: “The straw that broke the camel's back”, “many hands make light work”, “constant dripping wears away the stone”, and so on. In many ways, the law of the transformation of quantity into quality has penetrated the popular consciousness, as Trotsky wittily pointed out:

“Every individual is a dialectician to some extent or other, in most cases, unconsciously. A housewife knows that a certain amount of salt flavours soup agreeably, but that added salt makes the soup unpalatable. Consequently, an illiterate peasant woman guides herself in cooking soup by the Hegelian law of the transformation of quantity into quality. Similar examples from daily life could be cited without end. Even animals arrive at their practical conclusions not only on the basis of the Aristotelian syllogism but also on the basis of the Hegelian dialectic. Thus a fox is aware that quadrupeds and birds are nutritious and tasty. On sighting a hare, a rabbit, or a hen, a fox concludes: this particular creature belongs to the tasty and nutritive type, and—chases after the prey. We have here a complete syllogism, although the fox, we may suppose, never read Aristotle. When the same fox, however, encounters the first animal that exceeds it in size, for example, a wolf, it quickly concludes that quantity passes into quality, and turns to flee. Clearly, the legs of a fox are equipped with Hegelian tendencies, even if not fully conscious ones.

“All this demonstrates, in passing, that our methods of thought, both formal logic and the dialectic, are not arbitrary constructions of our reason but rather expressions of the actual inter-relationships in nature itself. In this sense, the universe throughout is permeated with 'unconscious' dialectics. But nature did not stop there. No little development occurred before nature's inner relationships were converted into the language of the consciousness of foxes and men, and man was then enabled to generalise these forms of consciousness and transform them into logical (dialectical) categories, thus creating the possibility for probing more deeply into the world about us.” ²⁴

Despite the apparently trivial character of these examples, they do reveal a profound truth about the way the world works. Take the example of the heap of corn. Some of the most recent investigations related to chaos theory have centred on the critical point where a series of small variations produces a massive change of state. (In the modern terminology, this is called “the edge of chaos”.) The work of the Danish-born physicist Per Bak (1947-2003) and others on “self-organised criticality” used precisely the example of a sand-heap to illustrate profound processes which occur at many levels of nature and which correspond precisely to the law of the transformation of quantity into quality.

One of the examples of this is that of a pile of sand—a precise analogy with the heap of grain of the Megarans. We drop grains of sand one by one on a flat surface. The experiment has been conducted many times, both with real sand heaped on tables, and in computer simulations. For a time they will just pile up on top of each other until they make a little pyramid. Once this point is reached, any additional grains will either find a resting place on the pile, or will unbalance one side of it just enough to cause some of the other grains to fall in an avalanche. Depending on how the other grains are poised, the avalanche could be very small, or devastating, dragging a large number of grains with it. When the pile reaches this critical point, even a single grain would be capable of dramatically affecting all around it. This seemingly trivial example provides an excellent “edge-of-chaos model”, with a wide range of applications, from earthquakes to evolution; from stock exchange crises to wars.

The pile of sand grows bigger, with excess sand slipping from the sides. When all the excess sand has fallen off, the resulting sand-pile is said to be “self-organised.” In other words, no one has consciously shaped it in this way. It “organises itself”, according to its own inherent laws, until it reaches a state of criticality, in which the sand grains on its surface are barely stable. In this critical condition, even the addition of a single grain of sand can cause unpredictable results. It may just cause a further tiny shift, or it may trigger a chain reaction resulting in a catastrophic landslide and the destruction of the pile.

According to Per Bak, the phenomenon can be given a mathematical expression, according to which the average frequency of a given size of avalanche is inversely proportional to some power of its size. He also points out that this “power-law” behaviour is extremely common in nature, as in the critical mass of plutonium, at which the chain reaction is on the point of running away into a nuclear explosion. At the sub-critical level, the chain reaction within the plutonium mass will die out, whereas a supercritical mass will explode. A similar phenomenon can be seen in earthquakes, where the rocks on two sides of a fault in the earth's crust reach a point where they are ready to slip past each other. The fault experiences a series of little slips and bigger slips, which maintain the tension at the critical point for some time until it finally collapses into an earthquake.

Although the proponents of chaos theory seem unaware of it, these examples are all cases of the law of the transformation of quantity into quality. Hegel invented the nodal line of measure relations, in which small quantitative changes at a certain point give rise to a qualitative leap. The example is often given of water, which boils at 100°C at normal atmospheric pressure. As the temperature nears boiling point, the increase in heat does not immediately cause the water molecules to fly apart. Until it reaches boiling point, the water keeps its volume. It remains water, because of the attraction of the molecules for each other. However, the steady change in temperature has the effect of increasing the motion of the molecules. The volume between the atoms is gradually increased, to the point where the force of attraction is insufficient to hold the molecules together. At precisely 100°C, any increase in heat energy will cause the molecules to fly apart, producing steam.

The same process can be seen in reverse. When water is cooled from 100°C to 0°C, it does not gradually congeal, passing from a paste, through a jelly, to a solid state. The motion of the atoms is gradually slowed as heat energy is removed until, at 0°C, a critical point is reached, at which the molecules will lock into a certain pattern, which is ice. The qualitative difference between a solid and a liquid can be readily understood by anyone. Water can be used for certain purposes, like washing and quenching one's thirst, which ice cannot. Technically speaking, the difference is that, in a solid, the atoms are arranged in a crystalline array. They do not have a random position at long distances, so that the position of the atoms on one side of the crystal is determined by the atoms on the other side. That is why we can move our hand freely through water, whereas ice is rigid and offers resistance. Here we are describing a qualitative change, a change of state, which arises from an accumulation of quantitative changes. A water molecule is a relatively simple affair, one oxygen atom attached to two hydrogen atoms governed by well-understood equations of atomic physics. However, when a very large number of these molecules are combined, they acquire a property which none of them possesses in isolation—liquidity. Such a property is not implied in the equations. In the language of complexity, liquidity is an “emergent” phenomenon.

As Mitchell Waldrop says:

“Cool those liquid water molecules down a bit, for example, and at 32°F they will suddenly quit tumbling over one another at random. Instead they will undergo a 'phase transition', locking themselves into the orderly crystalline array known as ice. Or if you were to go the other direction and heat the liquid, those same tumbling water molecules will suddenly fly apart and undergo a phase transition into water vapour. Neither phase transition would have any meaning for one molecule alone.” ²⁵

The phrase “phase transition” is neither more nor less than a qualitative leap. Similar processes can be seen in phenomena as varied as the weather, DNA molecules, and the mind itself. This quality of liquidity is well known on the basis of our daily experience. In physics, too, the behaviour of liquids is well understood and perfectly predictable—up to a point. The laws of motion of fluids (gases and liquids) clearly distinguish between smooth laminar flow, which is well defined and predictable, and turbulent flow, which can be expressed, at best, approximately. The movement of water around a pier in a river can be accurately predicted from the normal equations for fluids, provided it is moving slowly. Even if we increase the speed of the flow, causing eddies and vortices, we can still predict their behaviour. But if the speed is increased beyond a certain point, it becomes impossible to predict where the eddies will form, or, indeed, to say anything about the behaviour of the water at all. It has become chaotic.

Mendeleyev's periodic table

The existence of qualitative changes in matter was known long before human beings began to think about science, but it was not really understood until the advent of atomic theory. Earlier, physics took the changes of state from solid to liquid to gas as something that occurred, without knowing exactly why. Only now are these phenomena being properly understood.

The science of chemistry made great strides forward in the 19th century. A large number of elements were discovered. But, rather like the confused situation that exists in particle physics today, chaos reigned. Order was established by the great Russian scientist Dimitri Ivanovich Mendeleyev (1834-1907) who, in 1869, in collaboration with the German chemist Julius Lothar Meyer (1830-95), worked out the periodic table of the elements, so called because it showed the periodic recurrence of similar chemical properties.

The existence of atomic weight was discovered in 1862 by Stanislao Cannizzaro (1826-1910). But Mendeleyev's genius consisted in the fact that he did not approach the elements from a purely quantitative standpoint, that is, he did not see the relation between the different atoms just in terms of weight. Had he done so, he would never have made the breakthrough he did. From the purely quantitative standpoint, for instance, the element tellurium (atomic weight = 127.61) ought to have come after iodine (atomic weight = 126.91) in the periodic table, yet Mendeleyev placed it before iodine, under selenium, to which it is more similar, and placed iodine under the related element, bromine. Mendeleyev's method was vindicated in the 20th century, when the investigation of X-rays proved that his arrangement was the correct one. The new atomic number for tellurium was put at 52, while that of iodine is 53.

The whole of Mendeleyev's periodic table is based on the law of quantity and quality, deducing qualitative differences in the elements from quantitative differences in atomic weights. This was recognised by Engels at the time:

“Finally, the Hegelian law is valid not only for compound substances but also for the chemical elements themselves. We now know that 'the chemical properties of the elements are a periodic function of their atomic weights,' … and that, therefore, their quality is determined by the quantity of their atomic weight. And the test of this has been brilliantly carried out. Mendeleyev proved that various gaps occur in the series of related elements arranged according to atomic weights indicating that here new elements remain to be discovered. He described in advance the general chemical properties of one of these unknown elements, which he termed eka-aluminium, because it follows after aluminium in the series beginning with the latter, and he predicted its approximate specific and atomic weight as well as its atomic volume. A few years later, Lecoq de Boisbaudran actually discovered this element, and Mendeleyev's predictions fitted with only very slight discrepancies. Eka-aluminium was realised in gallium… By means of the—unconscious—application of Hegel's law of the transformation of quantity into quality, Mendeleyev achieved a scientific feat which it is not too bold to put on a par with that of Leverrier in calculating the orbit of the until then unknown planet Neptune.” ²⁶

Chemistry involves changes of both a quantitative and qualitative character, both changes of degree and of state. This can clearly be seen in the change of state from gas to liquid or solid, which is usually related to variations of temperature and pressure. In Anti-Dühring, Engels gives a series of examples of how, in chemistry, the simple quantitative addition of elements creates qualitatively different bodies. Since Engels' time the naming system used in chemistry has been changed. However, the change of quantity into quality is accurately expressed in the following example:

and so on to C₃₀H₆₀O₂, melissic acid, which melts only at 80° and has no boiling point at all, because it does not evaporate without disintegrating.”²⁷

The study of gases and vapours constitutes a special branch of chemistry. The great British pioneer of chemistry, Michael Faraday (1791-1867), thought that it was impossible to liquefy six gases, which he called permanent gases—hydrogen, oxygen, nitrogen, carbon monoxide, nitric oxide and methane. But in 1877, the Swiss chemist Raoul Pierre Pictet (1846-1929) managed to liquefy oxygen at a temperature of –140°C under a pressure of 500 atmospheres. Later, nitrogen, oxygen and carbon monoxide were all liquefied at still lower temperatures. In 1900, hydrogen was liquefied at –240° and, at a lower temperature, it even solidified. Finally, the most difficult challenge of all, the liquefaction of helium, was achieved at –255°. These discoveries had important practical applications. Liquid hydrogen and oxygen are now used in large amounts in rockets. The transformation of quantity into quality is shown by the fact that changes of temperature bring about important changes of properties. This is the key to the phenomenon of superconductivity. Through super-cooling, certain substances, beginning with mercury, were shown to offer no resistance to electric currents.

The study of extremely low temperatures was developed in the mid-19th century by the mathematician and physicist William Thomson (later Lord Kelvin) (1824-1907), who established the concept of absolute zero (the lowest possible temperature), which he calculated to be –273°C. At this temperature, he thought, the energy of molecules would sink to zero. This temperature is sometimes referred to as zero Kelvin, and used as the basis for a scale to measure very low temperatures. However, even at absolute zero, motion is not done away with altogether. There is still some energy, which cannot be removed. For practical purposes, energy is said to be zero, but that is not actually the case. Matter and motion, as Engels pointed out, are absolutely inseparable—even at “absolute zero”.

Nowadays, incredibly low temperatures are routinely achieved, and play an important role in the production of superconductors. Mercury becomes superconductive at exactly 4.12° Kelvin (K); lead at 7.22°K; tin at 3.73°K; aluminium at 1.20°K; uranium at 0.8°K, titanium at 0.53°K. Some 1,400 elements and alloys display this quality. Liquid hydrogen boils at 20.4°K. Helium is the only known substance which cannot be frozen even at absolute zero. It is the only substance that possesses the phenomenon known as superfluidity. Here too changes of temperature produce qualitative leaps. At 2.2°K, the behaviour of helium undergoes so fundamental a change that it is known as helium-2 to distinguish it from liquid helium above this temperature (helium-1). Using new techniques, temperatures as low as 0.000001°K have been reached, though it is thought that absolute zero is unattainable.

So far, we have concentrated on chemical changes in the laboratory and in industry. But it should not be forgotten that these changes take place on a much vaster scale in nature. The chemical composition of coal and diamonds, barring impurities, is the same—carbon. The difference is the result of colossal pressure, which, at a certain point transforms the contents of the coal-sack into a duchess' necklace. To convert common graphite into diamonds would require the pressure of at least 10,000 atmospheres over a very long period of time. This process occurs naturally beneath the earth's surface. In 1955, the big monopoly GEC succeeded in changing graphite into diamonds with a temperature of 2,500°C, and a pressure of 100,000 atmospheres. The same result was obtained in 1962, with a temperature of 5,000°C, and a pressure of 200,000 atmospheres, which turned graphite into diamond directly, without the aid of a catalyst. These are synthetic diamonds, which are not used to adorn the necks of duchesses, but for far more productive purposes—as cutting tools in industry.

Phase transitions

A most important field of investigation concerns what are known as phase transitions—the critical point where matter changes from solid to liquid or from liquid to vapour; or the change from nonmagnet to magnet; or from conductor to superconductor. All these processes are different, yet it has now been established beyond doubt that they are similar, so much so that the mathematics applied to one of these experiments can be applied to many others. This is a very clear example of a qualitative leap, as the following passage from James Gleick (1954-) shows:

“Like so much of chaos itself, phase transitions involve a kind of macroscopic behaviour that seems hard to predict by looking at the microscopic details. When a solid is heated, its molecules vibrate with the added energy. They push outward against their bonds and force the substance to expand. The more heat, the more expansion. Yet at a certain temperature and pressure, the change becomes sudden and discontinuous. A rope has been stretching; now it breaks. Crystalline form dissolves, and the molecules slide away from one another. They obey fluid laws that could not have been inferred from any aspect of the solid. The average atomic energy has barely changed, but the material—now a liquid, or a magnet, or a superconductor—has entered a new realm.” ²⁸

Newton's dynamics were quite sufficient to explain large-scale phenomena but broke down for systems of atomic dimensions. Indeed, classical mechanics are still valid for most operations that do not involve very high speeds or the processes that take place at the subatomic level. Quantum mechanics will be dealt with in detail in another section. It represented a qualitative leap in science. Its relation to classical mechanics is similar to that between higher and lower mathematics and that between dialectics and formal logic. It can explain facts which classical mechanics could not, such as radioactive transformation, the transformation of matter into energy. It gave rise to new branches of science—theoretical chemistry, capable of solving previously insoluble problems. The theory of metallic magnetism underwent a fundamental change, making possible brilliant discoveries in the flow of electricity through metals. A whole series of theoretical difficulties were eliminated, once the new standpoint was accepted. But for a long time it met with a stubborn resistance, precisely because its results clashed head-on with the traditional mode of thinking and the laws of formal logic.

Modern physics furnishes a wealth of examples of the laws of dialectics, starting with quantity and quality. Take, for instance, the relation between the different kinds of electromagnetic wave and their frequencies, that is, the speed with which they pulsate. The work of Scottish physicist James Clerk Maxwell (1831-79), which Engels was very interested in, showed that electromagnetic waves and light waves were of the same kind. Quantum mechanics later showed that the situation is much more complex and contradictory, but at lower frequencies, the wave theory holds good.

The properties of different waves are determined by the number of oscillations per second. The difference is in the frequency of the waves, the speed with which they pulsate, the number of vibrations per second. That is to say, quantitative changes give rise to different kinds of wave signals. Translated into colours, red light indicates light waves of low frequency. An increased rate of vibration turns the colour to orange-yellow, then to violet, then to the invisible ultraviolet and X-rays and finally to gamma rays. If we reverse the process, at the lower end, we go from infrared and heat rays to radio waves. Thus, the same phenomenon manifests itself differently, in accordance with a higher or lower frequency. Quantity changes into quality.

Source: R. P. Feynman, Lectures on Physics, chapter 2, p. 7, Table 2-1.

Order out of chaos

The law of quantity and quality also serves to shed light on one of the most controversial aspects of modern physics, the so-called uncertainty principle, which we will examine in greater detail in another section. Whereas it is impossible to know the exact position and velocity of an individual subatomic particle, it is possible to predict with great accuracy the behaviour of large numbers of particles. A further example: radioactive atoms decay in a way that makes a detailed prediction impossible. Yet large numbers of atoms decay at a rate so statistically reliable that they are used by scientists as natural “clocks” with which they calculate the age of the earth, the sun and the stars. The very fact that the laws governing the behaviour of subatomic particles are different to those which function at the “normal” level is itself an example of the transformation of quantity into quality. The precise point at which the laws of the small-scale phenomena cease to apply was defined by the quantum of action laid down by Max Planck (1858-1947) in 1900.

At a certain point, the concatenation of circumstances causes a qualitative leap whereby inorganic matter gives rise to organic matter. The difference between inorganic and organic matter is only relative. Modern science is well on the way to discovering exactly how the latter arises from the former. Life itself consists of atoms organised in a certain way. We are all a collection of atoms but not “merely” a collection of atoms. In the astonishingly complex arrangement of our genes, we have an infinite number of possibilities. The task of allowing each individual to develop these possibilities to the fullest extent is the real task of socialism.

Molecular biologists now know the complete DNA sequence of an organism, but cannot deduce from this how the organism assembles itself during its development, any more than knowledge of the structure of H2O provides an understanding of the quality of liquidity. An analysis of the chemicals and cells of the body does not add up to a formula for life. The same is true of the mind itself. Neuroscientists have a great deal of data about what the brain does. The human brain consists of ten billion neurons, each of which has an average of a thousand links with other neurons. The fastest computer is capable of performing around a billion operations a second. The brain of a fly sitting on a wall carries out 100 billion operations in the same time. This comparison gives an idea of the vast difference between the human brain and even the most advanced computer.

The enormous complexity of the human brain is one of the reasons why idealists have attempted to surround the phenomenon of mind with a mystical aura. Knowledge of the details of individual neurons, axons and synapses, is not sufficient to explain the phenomenon of thought and emotion. However, there is nothing mystical about it. In the language of complexity theory, both mind and life are emergent phenomena. In the language of dialectics, the leap from quantity to quality means that the whole possesses qualities that cannot be deduced from the sum of the parts or reduced to it. None of the neurons is conscious. Yet the sum total of neurons and their connections are. Neural networks are non-linear dynamical systems. It is the complex activity and interactions between the neurons that produce the phenomenon we call consciousness.

The same kind of thing can be seen in large numbers of multi-component systems in the most varied spheres. Studies of ant colonies at Bath University have shown how behaviour not witnessed in individual ants appears in a colony. A single ant, left to itself, will wander around at random, foraging and resting at irregular intervals. However, when the observation shifts to a whole colony of ants it immediately becomes evident that they become active at perfectly regular intervals. It is thought that this maximises the effectiveness of their labours: if they all work together, one ant is unlikely to repeat a task just performed by another. The degree of coordination at the level of an ant colony is such that some people have thought of it as a single animal, rather than a colony. This too is a mystical presentation of a phenomenon which exists on many levels in nature and in animal and human society, and which can only be understood in terms of the dialectical relation between whole and part.

We can see the law of the transformation of quantity into quality at work when we consider the evolution of the species. In biological terms a specific “breed” or “race” of animal is defined by its capacity to inter-breed. But as evolutionary modifications take one group further away from another a point is reached where they can no longer inter-breed. At this point a new species has been formed. Palaeontologists Stephen Jay Gould (1941-2002) and Niles Eldredge (1944-) have demonstrated that these processes are some times slow and protracted and at other times extremely rapid. Either way, they show how a gradual accumulation of small changes at a certain point provokes a qualitative change. Punctuated equilibria is the term used by these biologists to describe long periods of stability, interrupted by sudden bursts of change. When this idea was proposed by Gould and Eldredge of the American Museum to Natural History in 1972, it provoked an acrimonious debate among biologists, for whom, until then, Darwinian evolution was synonymous with gradualism.

For a long time, it was thought that evolution precluded such drastic changes. It was pictured as a slow, gradual change. However, the fossil record, although incomplete, presents a very different picture, with long periods of gradual evolution punctuated by violent upheavals, accompanied by the mass extinction of some species and the rapid rise of others. Whether or not the dinosaurs became extinct as a consequence of a meteorite colliding with the earth, it seems highly improbable that most of the great extinctions were caused in this way. While external phenomena, including meteorite or comet impacts, can play a role as “accidents” in the evolutionary process, it is necessary to seek an explanation of evolution as a result of its internal laws. The theory of “punctuated equilibria”, which is now supported by most palaeontologists, represents a decisive break with the old gradualist interpretation of Darwinism, and presents a truly dialectical picture of evolution, in which long periods of stasis are interrupted by sudden leaps and catastrophic changes of all kinds.

There is an endless number of examples of this law covering a very wide field. Is it possible now to continue to doubt the validity of this extremely important law? Is it really justified to continue to ignore it or to write it off as a subjective invention, which has been arbitrarily applied to diverse phenomena that bear no relation to one another? We see how in physics the study of phase transitions has led to the conclusion that apparently unrelated changes—of the boiling of liquids and the magnetising of metals—all follow the same rules. It is only a matter of time before similar connections will be established which will reveal beyond a shadow of doubt that the law of the transformation of quantity into quality is indeed one of the most fundamental laws of nature.

Whole and part

According to formal logic, the whole is equal to the sum of its parts. On closer examination, however, this is seen not to be true. In the case of living organisms it is manifestly not the case. A rabbit cut up in a laboratory, and reduced to its constituent parts is no longer a rabbit. This fact has been grasped by the advocates of chaos theory and complexity. Whereas classical physics, with its linear systems, accepted that the whole was precisely the sum of its parts, the non-linear logic of complexity maintains the opposite proposition, in complete agreement with dialectics:

“The whole is almost always equal to a great deal more than a sum of its parts,” says Waldrop. “And the mathematical expression of that property—to the extent that such systems can be described by mathematics at all—is a non-linear equation: one whose graph is curvy.” ²⁹

We have already quoted the examples of the qualitative changes in chemistry used by Engels in Anti-Dühring. While these examples remain valid, they by no means tell the whole story. Engels was limited, of course, by the scientific knowledge of his time. Today it is possible to go much further. The classical atomic theory of chemistry sets out from the idea that any combination of atoms into a greater unity can only be an aggregate of these atoms, that is, a purely quantitative relation. The union of atoms into molecules was seen as a simple juxtaposition. Chemical formulae such as H2O, H2SO4, etc. presuppose that each of the atoms remains basically unchanged even when it enters a new combination to form a molecule.

This reflected precisely the mode of thinking of formal logic, which states that the whole is only the sum of the parts. Thus, since the molecular weight equals the sum of the weights of the respective atoms, it was assumed that the atoms themselves had remained unchanged, having entered into a purely quantitative relationship. However, many of the properties of the compounds could not be determined in this way. Indeed, most chemical properties of compounds differ considerably from those of the elements of which they are made up. The so-called principle of juxtaposition does not explain these changes. It is one-sided, inadequate and, in a word, wrong.

Modern atomic theory has shown the incorrectness of this idea. While accepting that complex structures must be explained in terms of aggregates of more elementary factors, it has shown that the relations between these elements are not merely indifferent and quantitative, but dynamic and dialectical. The elementary particles which make up the atoms interact constantly, passing into each other. They are not fixed constants but are at every moment both themselves and something else at the same time. It is precisely this dynamic relationship that gives the resulting molecules their particular nature, properties and specific identity.

In this new combination the atoms are and are not themselves. They combine in a dynamic way to produce an entirely different entity, a different relationship, which, in turn, determines the behaviour of its component parts. Thus, we are not dealing merely with a lifeless “juxtaposition”, a mechanical aggregate, but with a process. In order to understand the nature of an entity it is therefore entirely insufficient to reduce it to its individual atomic components. It is necessary to understand its dynamic interrelations, that is, to arrive at a dialectical, not a formal, analysis.

David Bohm was one of the few to provide a worked out theoretical alternative to the subjectivist “Copenhagen interpretation” of quantum mechanics. Bohm's analysis, which is clearly influenced by the dialectical method, advocates a radical rethinking of quantum mechanics and a new way of looking at the relationship between whole and parts. Bohm points out that the usual interpretation of quantum theory does not give an adequate idea of just how far reaching was the revolution affected by modern physics:

“Indeed, when this interpretation is extended to field theories, not only the inter-relationships of the parts, but also their very existence is seen to flow out of the law of the whole. There is therefore nothing left of the classical scheme, in which the whole is derived from pre-existent parts related in predetermined ways. Rather, what we have is reminiscent of the relationship of whole and parts in an organism, in which each organ grows and sustains itself in a way that depends crucially on the whole.” ³⁰

A molecule of sugar can be broken down into its constituent parts of single atoms but then it is no longer sugar. A molecule cannot be reduced to its component parts without losing its identity. This is precisely the problem when we try to treat complex phenomena from a purely quantitative point of view. The resulting over-simplification leads to a distorted and one-sided picture of the natural world since the qualitative aspect is entirely left out of account. It is precisely through quality that we are able to distinguish one thing from another. Quality lies at the basis of all our knowledge of the world because it expresses the fundamental reality of all things, showing the critical boundaries that exist at all levels of material reality. The exact point at which small changes of degree give rise to a change of state is one of the most fundamental problems of science. It is a question that occupies a central place in dialectical materialism.

Complex organisms

Life itself arises from a qualitative leap from inorganic to organic matter. The explanation of the processes by which this occurred constitutes one of the most important and exciting problems of present-day science. The advances of chemistry, analysing in great detail the structures of complex molecules, predicting their behaviour with great accuracy and identifying the role of particular molecules in living systems, paved the way for the emergence of new sciences, biochemistry and biophysics, dealing respectively with the chemical reactions that take place in living organisms and the physical phenomena involved in living processes. These, in turn, have been merged together in molecular biology, which has registered the most amazing advances in recent years.

In this way, the old fixed divisions separating organic and inorganic matter have been entirely abolished. The early chemists drew a rigid distinction between the two. Gradually, it was understood that the same chemical laws applied to organic as to inorganic molecules. All substances containing carbon (with the possible exception of a few simple compounds like carbon dioxide) are characterised as organic. The rest are inorganic. Only carbon atoms are capable of forming very long chains, thus giving rise to the possibility of an infinite variety of complex molecules.

In the 19^th century chemists analysed the properties of “albuminous” substances (from the Latin word for egg-white). From this, it was discovered that life was dependent upon proteins, large molecules made up of amino acids. At the beginning of the 20th century, when Planck was making his breakthrough in physics, Emil Fischer was attempting to join up amino acids in chains in such a manner that the carboxyl group of one amino acid was always linked to the amino group of the next. By 1907, he had succeeded in synthesising a chain of eighteen amino acids. Fischer called these chains peptides, from the Greek word “to digest”, because he thought that proteins would break down into such chains in the process of digestion. This theory was finally proven by Max Bergmann in 1932.

These chains were still too simple to produce the complex polypeptide chains needed to create proteins. Moreover, the task of deciphering the structure of a protein molecule itself was incredibly difficult. The properties of each protein depend on its exact relation to each amino acid on the molecular chain. Here too, quantity determines quality. This posed a seemingly insurmountable problem for biochemists, since the number of possible arrangements in which nineteen amino acids can appear on a chain comes to nearly 120 million billion. A protein the size of serum albumen, made up of more than 500 amino acids, therefore has a number of possible arrangements of about 10⁶⁰⁰, that is, 1 followed by 600 zeros. The complete structure of a key protein molecule—insulin—was established for the first time by the British Nobel Prize winner biochemist Frederick Sanger in 1953. Using the same method, other scientists succeeded in deciphering the structure of a whole series of other protein molecules. Later, they succeeded in synthesising protein in the laboratory. It is now possible to synthesise many proteins, including one as complex as the human growth hormone which involves a chain of 188 amino acids.

Life is a complex system of interactions involving an immense number of chemical reactions which proceed continuously and rapidly. Every reaction in the heart, blood, nervous system, bones and brain interacts with every other part of the body. The workings of the simplest living body are far more complicated than the most advanced computer, permitting rapid movement, swift reactions to the slightest change in the environment, constant adjustments to changing conditions, internal and external. Here, most emphatically, the whole is more than the sum of the parts. Every part of the body, every muscular and nervous reaction, depends upon all the rest. Here we have a dynamic and complex, in other words dialectical, interrelationship, which alone is capable of creating and sustaining the phenomenon we know as life.

The process of metabolism means that, at any given moment, the living organism is constantly changing, taking in oxygen, water, and food (carbohydrates, fats, proteins, minerals and other raw materials), negating these by transforming them into the materials needed to sustain and develop life and excreting waste products. The dialectical relationship between whole and part manifests itself in the different levels of complexity in nature, reflected in the different branches of science:

a) Atomic interactions and the laws of chemistry determine the laws of biochemistry, but life itself is qualitatively different.

b) The laws of biochemistry “explain” all the processes of human interaction with the environment. And yet human activity and thought are qualitatively different to the biological processes that constitute them.

c) Each individual person, in turn, is a product of his or her physical and environmental development. Yet the complex interactions of the sum total of individuals who make up a society are also qualitatively different. In each of these cases the whole is greater than the sum of the parts and obeys different laws.

In the last analysis, all human existence and activity is based on the laws of motion of atoms. We are part of a material universe, which is a continuous whole, functioning according to its inherent laws. And yet, when we pass from a) to c), we make a series of qualitative leaps, and must operate with different laws at different “levels”; c) is based upon b) and b) is based upon a), but nobody in their right mind would seek to explain the complex movements in human society in terms of atomic forces. For the same reason, it is absolutely futile to reduce the problem of crime to the laws of genetics.

An army is not merely the sum total of individual soldiers. The very act of combining in a massive force, organised on military lines transforms the individual soldier both physically and morally. As long as the cohesiveness of the army is maintained, it represents a formidable force. This is not only a question of numbers. Napoleon was well aware of the importance of morale in war. As part of a disciplined numerous fighting force, the individual soldier is capable of achieving feats of bravery and self-sacrifice in situations of extreme danger, of which, under normal conditions, as an isolated individual, he would never imagine himself capable. Yet he remains the same person as before. The moment the cohesiveness of the army breaks down under the impact of defeat, the whole dissolves into its individual “atoms”, and the army becomes a demoralised rabble.

Engels was very interested in military tactics, for which Marx's daughters nicknamed him “the General”. He closely followed the progress of the American Civil War and the Crimean War, about which he wrote many articles. In Anti-Dühring, he shows how the law of quantity and quality relates to military tactics, for example, in the relative fighting capacity of the highly disciplined soldiers of Napoleon and the Egyptian (Mameluke) cavalry:

“In conclusion, we shall call one more witness for the transformation of quantity into quality, namely Napoleon. He describes the combat between the French cavalry, who were bad riders but disciplined, and the Mamelukes, who were undoubtedly the best horsemen of their time for single combat but who lacked discipline, as follows:

“'Two Mamelukes were undoubtedly more than a match for three Frenchmen; 100 Mamelukes were equal to 100 Frenchmen; 300 Frenchmen could generally beat 300 Mamelukes, and 1,000 Frenchmen invariably defeated 1,500 Mamelukes.' Just as with Marx a definite, though varying, minimum sum of exchange-value was necessary to make possible its transformation into capital, so with Napoleon a detachment of cavalry had to be of a definite minimum number in order to permit the force of discipline, embodied in close order and planned utilisation, to manifest itself and even rise superior to greater numbers of irregular cavalry, who were better mounted, more dextrous horsemen and fighters, and at least as brave as the former.” ³¹

The molecular process of revolution

The process of chemical reaction involves crossing a decisive barrier known as a transition state. At this point, before the reactants become products, they are neither one thing nor the other. Some of the old bonds are breaking and other new ones are being formed. The energy needed to pass this critical point is known as Gibbs energy. Before a molecule can react, it requires a quantity of energy, which, at a certain point, brings it to the transition state. At normal temperatures only a minute fraction of the reactant molecules possess sufficient energy. At a greater temperature, a higher proportion of the molecules will have this energy. That is why heating is one way to speed up a chemical reaction. The process can be assisted by the use of catalysts, which are widely used in industry. Without catalysts, many processes, though they would still take place, would be so slow that they would be uneconomic. The catalyst cannot change the composition of the substances involved nor can it alter the Gibbs energy of the reactants, but it can provide an easier pathway between them.

There are certain analogies between this phenomenon and the role of the individual in history. It is a common misconception that Marxism has no place for the role of individuals in shaping their own destiny. According to this caricature, the materialist conception of history reduces everything to “the productive forces”. Human beings are seen as mere blind agents of economic forces or marionettes dancing on the strings of historical inevitability. This mechanistic view of the historic process (economic determinism) has nothing in common with the dialectical philosophy of Marxism.

Historical materialism sets out from the elementary proposition that men and women make their own history. But, contrary to the idealist notion of human beings as absolutely free agents, Marxism explains that they are limited by the actual material conditions of the society into which they are born. These conditions are shaped in a fundamental way by the level of development of the productive forces, which is the ultimate ground upon which all human culture, politics and religion rest. However, these things are not directly shaped by economic development but can and do take on a life of their own. The extremely complex relation between all these factors has a dialectical character, not a mechanical one. Individuals do not choose the conditions into which they are born. They are “given”. Nor is it possible, as idealists imagine, for individuals to impose their will upon society, simply because of the greatness of their intellect or the strength of their character. The theory that history is made by “great individuals” is a fairy story fit to amuse five-year olds. It has approximately the same scientific value as the “conspiracy theory” of history, which attributes revolutions to the malign influence of “agitators”.

Every worker knows that strikes are not caused by agitators but by bad wages and conditions. Contrary to the impression sometimes given by certain sensationalist newspapers, strikes are not common occurrences. For many years, a factory or workplace can remain apparently peaceful. The workforce may not react, even when their wages and conditions are attacked. This is especially true in conditions of mass unemployment or when there is no lead from the tops of the trade unions. This apparent indifference of the majority often leads the minority of activists to despair. They draw the mistaken conclusion that the rest of the workers are “backward”, and will never do anything. But, in fact, beneath the surface of apparent tranquillity, changes are taking place. A thousand small incidents, pinpricks, injustices, injuries, gradually leave their mark on the consciousness of the workers. This process was aptly described by Trotsky as “the molecular process of revolution”. It is the equivalent of the Gibbs energy in a chemical reaction.

In real life, as in chemistry, molecular processes take their time. No chemist would ever complain because the anticipated reaction was taking a long time, especially if the conditions for a speedy reaction (high temperature, etc.) were absent. But eventually, the chemical transition state is reached. At this point, the presence of a catalyst is of great assistance in bringing the process to a successful conclusion, in the speediest and most economical manner. In the same way, at a given point, the accumulated mood of discontent in the workplace boils over. The whole situation is transformed in the space of 24 hours. If the activists are not prepared, if they have allowed themselves to be deceived by the surface calm of the previous period, they will be taken completely off guard.

In dialectics, sooner or later, things change into their opposite. In the words of the Bible, “the first shall be last and the last shall be first.” We have seen this many times, not least in the history of great revolutions. Formerly backward and inert layers can catch up with a bang. Consciousness develops in sudden leaps. This can be seen in any strike. And in any strike we can see the elements of a revolution in an undeveloped, embryonic form. In such situations, the presence of a conscious and audacious minority can play a role quite similar to that of a catalyst in a chemical reaction. In certain instances, even a single individual can play an absolutely decisive role.

In November 1917 the fate of the Russian Revolution was ultimately determined by two men—Lenin and Trotsky. Without them, there is no doubt that the revolution would have been defeated. The other leaders, Kamenev, Zinoviev and Stalin, came under the pressure of other classes and capitulated. The question here is not one of abstract “historical forces” but the concrete one of the degree of preparation, foresight, personal courage and ability of leaders. After all, we are talking about a struggle of living forces not a simple mathematical equation.

Does this mean then that the idealist interpretation of history is correct? Is it all decided by great individuals? Let the facts speak for themselves. For a quarter of a century before 1917, Lenin and Trotsky had spent most of their lives more or less isolated from the masses, often working with very small groups of people. Why were they unable to have the same decisive effect, for example, in 1916? Or in 1890? Because the objective conditions were absent. In the same way, a union activist who continually called for a strike when there was no mood for action would soon end up a laughing stock. Similarly, when the revolution was isolated in conditions of unspeakable backwardness and the class balance of forces changed, neither Lenin nor Trotsky could prevent the rise of the bureaucratic counterrevolution headed by a man in every way their inferior, Stalin. Here, in a nutshell, we have the dialectical relation between the subjective and objective factor in human history.

The unity and interpenetration of opposites

Everywhere we look in nature, we see the dynamic co-existence of opposing tendencies. This creative tension is what gives life and motion. That was already understood by Heraclitus 2,500 years ago. It is even present in embryo in certain Oriental religions, as in the idea of the ying and yang in China, and in Buddhism. Dialectics appears here in a mystified form, which nonetheless reflects an intuition of the workings of nature. The Hindu religion contains the germ of a dialectical idea, when it poses the three phases of creation (Brahma), maintenance or order (Vishnu) and destruction or disorder (Shiva). In his interesting book on the mathematics of chaos, Ian Stewart points out that the difference between the gods Shiva, “the Untamed”, and Vishnu is not the antagonism between good and evil, but that the two principles of harmony and discord together underlie the whole of existence:

“In the same way mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical beauty.” ³²

In Heraclitus, all this was in the nature of an inspired guess. Now this hypothesis has been confirmed by a huge amount of examples. The unity of opposites lies at the heart of the atom, and the entire universe is made up of molecules, atoms, and subatomic particles. The matter was very well put by R.P. Feynman: “All things, even ourselves, are made of fine-grained, enormously strongly interacting plus and minus parts, all neatly balanced out.” ³³

The question is: how does it happen that a plus and a minus are “neatly balanced out?” This is a contradictory idea! In elementary mathematics, a plus and a minus do not “balance out”. They negate each other. Modern physics has uncovered the tremendous forces which lie at the heart of the atom. Why do the contradictory forces of electrons and protons not cancel each other out? Why do atoms not merely fly apart? The current explanation refers to the “strong force” which holds the atom together. But the fact remains that the unity of opposites lies at the basis of all reality.

Within the nucleus of an atom, there are two opposing forces, attraction and repulsion. On the one hand, there are electrical repulsions which, if unrestrained, would violently tear the nucleus apart. On the other hand, there are powerful forces of attraction which bind the nuclear particles to each other. This force of attraction, however, has its limits, beyond which it is unable to hold things together. The forces of attraction, unlike repulsion, have a very short reach. In a small nucleus they can keep the forces of disruption in check. But in a large nucleus, the forces of repulsion cannot be easily dominated.

Beyond a certain critical point, the bond is broken and a qualitative leap occurs. Like an enlarged drop of water, it is on the verge of breaking apart. When an extra neutron is added to the nucleus, the disruptive tendency increases rapidly. The nucleus breaks up, forming two smaller nuclei, which fly apart violently, releasing a vast amount of energy. This is what occurs in nuclear fission. However, analogous processes may be seen at many different levels of nature. Water falling on a polished surface will break up into a complex pattern of droplets. This is because two opposing forces are at work: gravity, which tries to spread out the water in a flat film spread over the whole surface, and surface tension, the attraction of one water molecule to another, which tries to pull the liquid together, forming compact globules.

Nature seems to work in pairs. We have the “strong” and the “weak” forces at the subatomic level; attraction and repulsion; north and south in magnetism; positive and negative in electricity; matter and anti-matter; male and female in biology; odd and even in mathematics; even the concept of “left and right handedness” in relation to the spin of subatomic particles. There is a certain symmetry, in which contradictory tendencies, to quote Feynman, “balance themselves out”, or, to use the more poetical expression of Heraclitus, “agree with each other by differing like the opposing tensions of the strings and bow of a musical instrument”. There are two kinds of matter, which can be called positive and negative. Like kinds repel and unlike attract.

Positive and negative

Positive is meaningless without negative. They are necessarily inseparable. Hegel long ago explained that “pure being” (devoid of all contradiction) is the same as pure nothing, that is, an empty abstraction. In the same way, if everything were white, it would be the same for us as if everything were black. Everything in the real world contains positive and negative, being and not being, because everything is in a state of constant movement and change. Incidentally, mathematics shows that zero itself is not equal to nothing, or as Engels put it:

“Zero, because it is the negation of any definite quantity, is not therefore devoid of content. On the contrary, zero has a very definite content. As the borderline between all positive and negative magnitudes, as the sole really neutral number, which can be neither positive nor negative, it is not only a very definite number, but also in itself more important than all other numbers bounded by it. In fact, zero is richer in content than any other number. Put on the right of any other number, it gives to the latter, in our system of numbers, the tenfold value. Instead of zero one could use here any other sign, but only on the condition that this sign taken by itself signifies zero = 0. Hence it is part of the nature of zero itself that it finds this application and that it alone can be applied in this way. Zero annihilates every other number with which it is multiplied; united with any other number as divisor or dividend, in the former case it makes this infinitely large, in the latter infinitely small; it is the only number that stands in a relation of infinity to every other number. 0/0 can express every number between –∞ and +∞, and in each case represents a real magnitude.”³⁴

The negative magnitudes of algebra only have meaning in relation to the positive magnitudes, without which they have no reality whatsoever. In the differential calculus, the dialectical relation between being and not being is particularly clear. This was extensively dealt with by Hegel in his Science of Logic. He was greatly amused by the perplexity of the traditional mathematicians, who were shocked by the use of a method which makes use of the infinitesimally small, and “cannot do without the suggestion that a certain quantity is not equal to nil but is so inconsiderable that it may be neglected,”³⁵ and yet always obtains an exact result.

Moreover, everything is in a permanent relation with other things. Even over vast distances, we are affected by light, radiation, gravity. Undetected by our senses, there is a process of interaction, which causes a continual series of changes. Ultraviolet light is able to “evaporate” electrons from metal surfaces in much the same way as the sun's rays evaporate water from the ocean. Mathematician and physicist Banesh Hoffmann states:

“It is still a strange and awe-inspiring thought, that you and I are thus rhythmically exchanging particles with one another, and with the earth and the beasts of the earth, and the sun and the moon and the stars, to the uttermost galaxy.” ³⁶

The Dirac equation for the energy of an individual electron involves two answers—one positive and one negative. It is similar to the square root of a number, which can either be positive or negative. Here, however, the negative answer implies a contradictory idea—negative energy. This appears to be an absurd concept from the standpoint of formal logic. Since energy and mass are equivalent, negative energy, in turn, means negative mass. Paul A.M. Dirac (1902-84) himself was disturbed by the implications of his own theory. He was compelled to predict the existence of particles which would be identical to the electron, but with a positive electric charge, a previously unheard of matter.

On August 2nd, 1932, Robert A. Millikan (1868-1953) and Carl David Anderson (1905-91) of the California Institute of Technology discovered a particle the mass of which was clearly that of an electron, but moving in the opposite direction. This was not an electron, proton or neutron. Anderson described it as a “positive electron” or positron. This was a new kind of matter—antimatter—predicted by Dirac's equations. Subsequently, it was discovered that electrons and positrons, when they meet, annihilate each other, producing two photons (two flashes of light). In the same way, a photon passing through matter could split to form a virtual electron and a positron.

The phenomenon of oppositeness exists in physics, where, for example, every particle has its anti-particle (electron and positron, proton and anti-proton, etc.). These are not merely different, but opposites in the most literal sense of the word, being identical in every respect, except one: they have opposite electrical charges—positive and negative. Incidentally, it is a matter of indifference which one is characterised as negative and which positive. The important thing is the relationship between them.

Every particle possesses the quality known as spin, expressed as a plus or a minus, depending on its direction. Strange as it may seem, the opposite phenomena of left and right-handedness, which is known to play a fundamental role in biology, also has its equivalent at the subatomic level. Particles and waves stand in contradiction to each other. The Danish physicist Niels H.D. Bohr (1885-1962) referred to them, rather confusingly, as “complementary concepts”, by which he meant precisely that they exclude one another.

The most recent investigations of particle physics are casting light on the deepest level of matter so far discovered— quarks. These particles also have opposing “qualities” which are not comparable to ordinary forms, so physicists are obliged to make up new, artificial qualities to describe them. Thus we have up quarks, down quarks, charm quarks, strange quarks, and so on. Although the qualities of quarks have still to be thoroughly explored, one thing is clear: that the property of oppositeness exists at the most fundamental levels of matter yet known to science.

This universal phenomenon of the unity of opposites is, in reality, the motor-force of all motion and development in nature. It is the reason why it is not necessary to introduce the concept of external impulse to explain movement and change—the fundamental weakness of all mechanistic theories. Movement, which itself involves a contradiction, is only possible as a result of the conflicting tendencies and inner tensions which lie at the heart of all forms of matter.

The opposing tendencies can exist in a state of uneasy equilibrium for long periods of time, until some change, even a small quantitative change, destroys the equilibrium and gives rise to a critical state which can produce a qualitative transformation. In 1936, Bohr compared the structure of the nucleus to a drop of liquid, for example, a raindrop hanging from a leaf. Here the force of gravity struggles with that of surface tension striving to keep the water molecules together. The addition of just a few more molecules to the liquid renders it unstable. The enlarged droplet begins to shudder, the surface tension is no longer able to hold the mass to the leaf and the whole thing falls.

Nuclear fission

This apparently simple example, of which many equivalents can be observed a hundred times in daily experience, is a fairly close analogy to the processes at work in nuclear fission. The nucleus itself is not at rest, but in a constant state of change. In one quadrillionth of a second, there have already been billions of random collisions of particles. Particles are constantly entering and leaving the nucleus. Nevertheless, the nucleus is held together by what is often described as the strong force. It remains in a state of unstable equilibrium, “on the edge of chaos”, as chaos theory would put it.

As in a drop of liquid which quivers as the molecules move around inside it, the particles are constantly moving, transforming themselves, exchanging energy. Like an enlarged raindrop, the bond between the particles in a large nucleus is less stable, and more likely to break up. The steady release of alpha particles from the surface of the nucleus makes it smaller and steadier. As a result, it may become stable. But it was discovered that by bombarding a large nucleus with neutrons they can be made to break up, releasing part of the colossal amounts of energy locked up in the atom. This is the process of nuclear fission. This process can occur even without the introduction of particles from without. The process of spontaneous fission (radio active decay) is going on all the time in nature. In one second, a pound of uranium experiences four spontaneous fissions, and alpha particles are emitted from around eight million nuclei. The heavier the nucleus, the more likely the process of fission becomes.

The unity of opposites lies at the root of life itself. When spermatozoa were first discovered, they were believed to be “homunculae”, perfectly formed miniature human beings, which—like Topsy in Uncle Tom's Cabin—”just grow'd”. In reality, the process is far more complex and dialectical. Sexual reproduction depends on the combination of a single sperm and egg, in a process in which both are destroyed and preserved at the same time, passing on all the genetic information necessary for the creation of an embryo. After undergoing a whole series of transformations, bearing a striking resemblance to the evolution of all life from the division of a single cell, eventually results in an entirely new individual. Moreover, the result of this union contains the genes of both parents, but in such a way as to be different from either. So what we have is not simple reproduction, but a real development. The increased diversity made possible by this is one of the great evolutionary advantages of sexual reproduction.

Contradictions are found at all levels of nature, and woe betide the logic that denies it. Not only can an electron be in two or more places at the same time, but it can move simultaneously in different directions. We are sadly left with no alternative but to agree with Hegel: they are and are not. Things change into their opposite. Negatively charged electrons become transformed into positively charged positrons. An electron that unites with a proton is not destroyed, as one might expect, but produces a new particle, a neutron, with a neutral charge.

The laws of formal logic have received a humiliating drubbing in the field of modern physics, where they have shown themselves to be hopelessly inadequate to deal with the contradictory processes that occur at the subatomic level. Particles which disintegrate so rapidly that it is difficult to say whether they exist or not, pose insurmountable problems for a system which attempts to ban all contradiction from nature and thought. This immediately leads to new contradictions of an insoluble character. Thought finds itself in opposition to the facts established and repeatedly confirmed by experiment and observation. The unity of the proton and the electron is a neutron. But if a positron should unite with a neutron, the result would be the shedding of an electron and the neutron would change into a proton. By means of this ceaseless process, the universe makes and re-makes itself over and over again. No need then for any external force, no “first impulse”, as in classical physics. No need for anything whatsoever, except the infinite, restless movement of matter in accordance with its own objective laws.

Polar opposites?

Polarity is an all-pervasive feature in nature. It does not only exist as the North and South Poles of the earth. Polarity is to be found in the sun and moon and other planets. It also exists at the subatomic level, where nuclei behave precisely as if they possess not one but two pairs of magnetic poles. Engels desribed it thus:

“Dialectics, has proved from the result of our experience of nature so far that all polar opposites in general are determined by the mutual action of the two opposite poles on each other, that the separation and opposition of these poles exist only within their mutual connection and union, and, conversely, that their union exists only in their separation and their mutual connection only in their opposition. This once established, there can be no question of a final cancelling out of repulsion and attraction, or of a final partition between the one form of motion in one half of matter and the other form in the other half, consequently there can be no question of mutual penetration or of absolute separation of the two poles. It would be equivalent to demanding in the first case that the north and south poles of a magnet should mutually cancel themselves out or, in the second case, that dividing a magnet in the middle between the two poles should produce on one side a north half without a south pole, and on the other side a south half without a north pole.” ³⁷

There are some things which people consider to be absolute and immutable opposites. For instance, when we wish to convey the notion of extreme incompatibility, we use the term “polar opposites”—north and south are taken to be absolutely fixed and opposed phenomena. For over a thousand years, sailors have placed their faith in the compass, which guided them through unknown oceans, always pointing to this mysterious thing called the North Pole. Yet closer analysis shows that the North Pole is neither fixed nor stable. The earth is surrounded by a strong magnetic field (a geocentric axis dipole), as if a gigantic magnet were present at the centre of the earth, aligned parallel to the earth's axis. This is related to the metallic composition of the earth's core, which is mainly made up of iron. In the 4.6 billion years since the solar system was formed, the rocks on earth have formed and reformed many times. And not only the rocks but everything else. Detailed measurements and investigation has now proved beyond doubt that the location of the magnetic poles is continually shifting. At the present time, they are moving very slowly—0.3 degrees every million years. This phenomenon is a reflection of complex changes taking place in the earth, the atmosphere and the sun's magnetic field.

So small is the shift that for centuries it remained undetected. However, even this apparently imperceptible process of change gives rise to a sudden and spectacular leap, in which north becomes south and south becomes north. The changes in the location of the poles are accompanied by fluctuations in the strength of the magnetic field itself. This gradual process, characterised by a weakening of the magnetic field, culminates in a sudden leap. They change place, literally turning into their opposite. After this, the field starts to recover and gather strength again.

This revolutionary change has occurred many times during the history of the earth. It has been estimated that more than 200 such polar reverses have taken place in the last 65 million years; at least four have occurred in the last four million years. About 700,000 years ago, the north magnetic pole was located somewhere in Antarctica, the present south geographical pole. At this moment, we are in a process of weakening of the earth's magnetic field, which will inevitably culminate in a new reversal. The study of the earth's magnetic history is the special field of an entirely new branch of science— palaeomagnetism—which is attempting to construct maps of all the reversals of the poles throughout the history of our planet. The discoveries of palaeomagnetism, in turn, have provided conclusive evidence for the correctness of the theory of continental drift. When rocks (especially volcanic rocks) create iron-rich minerals, these respond to the earth's magnetic field, as it exists at that moment, in the same way that pieces of iron react to a magnet, their atoms orienting in line with the field axis. In effect, they behave like a compass. By comparing the orientations of minerals in rocks of the same age in different continents, it is possible to trace the movements of the continents, including those which no longer exist, or only exist as tiny remnants.

In the reversal of the poles we see a most graphic example of the dialectical law of the unity and interpenetration of opposites. North and south—polar opposites in the most literal sense of these words—are not only inseparably united but determine each other by means of a complex and dynamic process, which culminates in a sudden leap in which supposedly fixed and immutable phenomena change into their opposites. And this dialectical process is not the arbitrary and fanciful invention of Hegel or Engels, but is conclusively demonstrated by the most recent discoveries of palaeomagnetism. Truly it has been said, “when men are silent, the stones cry out!”

Attraction and repulsion is an extension of the law of the unity and interpenetration of opposites. It is a law that permeates the whole of nature, from the smallest phenomena to the largest. At the base of the atom are immense forces of attraction and repulsion. The hydrogen atom, for example, is made up of a proton and an electron held together by electrical attraction. The charge carried by a particle may be positive or negative. Similar charges repel each other, whereas opposite kinds attract. Thus, within the nucleus, protons repel each other, but the nucleus is held together by tremendous nuclear force. In very heavy nuclei, however, the force of electrical repulsion can reach a point where the nuclear force is overcome and the nucleus flies apart.

Engels points out the universal role of attraction and repulsion:

“All motion consists in the interplay of attraction and repulsion. Motion, however, is only possible when each individual attraction is compensated by a corresponding repulsion somewhere else. Otherwise in time one side would get the preponderance over the other and then motion would finally cease. Hence all attractions and all repulsions in the universe must mutually balance one another. Thus the law of the indestructibility and uncreatability of motion is expressed in the form that each movement of attraction in the universe must have as its complement an equivalent movement of repulsion and vice versa; or, as ancient philosophy—long before the natural-scientific formulation of the law of conservation of force or energy—expressed it: the sum of all attractions in the universe is equal to the sum of all repulsions.”

In Engels' day, the prevailing idea of motion was derived from classical mechanics, where motion is imparted from an external force that overcomes the force of inertia. Engels was quite scathing about the very expression “force”, which he considered one-sided and insufficient to describe the real processes of nature. Engels wrote:

“All natural processes are two-sided, they are based on the relation of at least two operative parts, action and reaction. The notion of force, however, owing to its origin from the action of the human organism on the external world, and further from terrestrial mechanics, implies that only one part is active, operative, the other part being passive, receptive.” ³⁸

Engels was far in advance of his time in being highly critical of this notion, which had already been attacked by Hegel. In his History of Philosophy, Hegel remarks that “It is better (to say) that a magnet has a soul (as Thales expresses it) than that it has an attractive force; force is a kind of property that, separate from matter, is put forward as a kind of predicate—while soul, on the other hand, is this movement itself, identical with the nature of matter.” This remark of Hegel, approvingly quoted by Engels, contains a profound idea—that motion and energy are inherent to matter. Matter is self-moving and self-organising.

Even the word “energy” was not, in Engels' opinion, entirely adequate, although greatly to be preferred to “force”. His objection was that “It still makes it appear as if 'energy' was something external to matter, something implanted in it. But in all circumstances it is to be preferred to the expression 'force'.” ³⁹ The real relation has been demonstrated by Einstein's theory of the equivalence of mass and energy, which shows that matter and energy are one and the same thing. This was precisely the standpoint of dialectical materialism, as expressed by Engels, and even anticipated by Hegel, as the above quotation shows.

Negation of the negation

Every science has its own vocabulary, the terms of which frequently do not coincide with everyday usage. This can lead to difficulties and misunderstandings. The word “negation” is commonly understood to signify simple destruction, or annihilation. It is important to understand that in dialectics negation has an entirely different content. It means to negate and to preserve at the same time. One can negate a seed by crushing it underfoot. The seed is “negated” but not in the dialectical sense! If, however, the same seed is left to itself, under favourable conditions, it will germinate. It has thus negated itself as a seed and develops into a plant, which at a later stage will die producing new seeds.

Apparently, this represents a return to the starting point. However, as professional gardeners know, identical seeds vary from generation to generation, giving rise to new species. Gardeners also know that certain strains can be artificially induced by selective breeding. It was precisely this artificial selection which gave Charles Darwin a vital clue to the process of natural selection which takes place spontaneously throughout nature, and is the key to understanding the development of all plants and animals. What we have is not only change but actual development, generally proceeding from simpler to more complex forms, including the complex molecules of life itself, which, at a certain stage, arises from inorganic matter.

Consider the following example of negation from quantum mechanics. What occurs when an electron unites with a photon? The electron experiences a “quantum leap” and the photon disappears. The result is not some kind of mechanical unity or compound. It is the same electron as before but in a new state of energy. The same is true when the electron unites with a proton. The electron vanishes and there is a leap in the proton's state of energy and charge. The proton is the same as before but in a new state of energy and charge. It is now electrically neutral and becomes a neutron. Dialectically speaking, the electron has been negated and preserved at the same time. It has disappeared, but is not annihilated. It enters into the new particle and expresses itself as a change of energy and charge.

The ancient Greeks were well acquainted with the dialectic of discussion. In a properly conducted debate, an idea is put forward (the Thesis) and is then countered by the opposing view (the Antithesis) which negates it. Finally, through a thorough process of discussion, which explores the issue concerned from all points of view and discloses all the hidden contradictions, we arrive at a conclusion (the Synthesis). We may or may not arrive at agreement but by the very process of discussion, we have deepened our knowledge and understanding and raised the whole discussion onto a different plane.

It is quite evident that almost none of the critics of Marxism have taken the trouble to read Marx and Engels. It is frequently supposed, for example, that dialectics consists of “Thesis-Antithesis-Synthesis”, which Marx is alleged to have copied from Hegel (who, in turn, was supposed to have copied it from the Holy Trinity) and applied to society. This childish caricature is still repeated by supposedly intelligent people today. As a matter of fact, not only is Marx's dialectical materialism the opposite of Hegel's idealist dialectic, but the dialectic of Hegel is itself very different from that of classical Greek philosophy.

George Plekhanov rightly ridiculed the attempt to reduce the imposing edifice of Hegelian dialectic to the “wooden Triad” of Thesis-Antithesis-Synthesis. The advanced dialectics of Hegel bears approximately the same relation to that of the Greeks as modern chemistry to the primitive investigations of the alchemists. It is quite correct that the latter prepared the ground for the former, but to assert that they are “basically the same” is simply ludicrous. Hegel returned to Heraclitus, but on a qualitatively higher level, enriched by 2,500 years of philosophical and scientific advances. The development of dialectics is itself a dialectical process.

Nowadays the word “alchemy” is used as a synonym for quackery. It conjures up all kinds of images of spells and black magic. Such elements were not absent from the history of alchemy, but its activities were by no means limited to this. In the history of science, alchemy played a most important role. Alchemy is an Arabic word, used for any science of materials. Charlatans there were, but not a few good scientists too! And chemistry is the Western word for the same thing. Many chemical words are, in fact, Arab in origin—acid, alkali, alcohol, and so on.

The alchemists set out from the proposition that it was possible to transmute one element into another. They tried for centuries to discover the “philosopher's stone”, which they believed would enable them to turn base metal (lead) into gold. Had they succeeded, it would not have done them a lot of good, since the value of gold would have quickly sunk to that of lead! But that is another story. Given the actual level of technique at that time, the alchemists were attempting the impossible. In the end, they were forced to come to the conclusion that the transmutation of the elements was impossible. However, the endeavours of the alchemists were not in vain. In their pursuit of an unscientific hypothesis, the philosopher's stone, they actually did valuable pioneering work, developing the art of experiment, inventing equipment still used in laboratories today and describing and analysing a wide range of chemical reactions. In this way, alchemy prepared the ground for the development of chemistry.

Modern chemistry was able to progress only by repudiating the alchemists' basic hypothesis—the transmutation of the elements. From the late 18th century onwards, chemistry developed on a scientific basis. By setting aside the grandiose aims of the past, it made giant steps forward. Then, in 1919, the New Zealand nuclear physicist Ernest Rutherford (1871-1937) carried out an experiment involving the bombardment of nitrogen nuclei with alpha particles. This led to the breaching of the atomic nucleus for the first time. In so doing, he succeeded in transmuting one element (nitrogen) into another element (oxygen). The age-old quest of the alchemists had been resolved but not at all in a way they could have foreseen!

Now look at this process a bit more closely. We start with the thesis: a) the transmutation of the elements; this is then negated by its antithesis b) impossibility of transmuting the elements; this, in turn, is overturned by a second negation c) the transmutation of the elements. Here we must note three things. Firstly, each negation marks a definite advance, indeed, a qualitative leap forward. Secondly, each successive advance both negates the earlier stage, reacts against it, whilst preserving all that is useful and necessary in it. Lastly, the final stage—the negation of the negation—does not at all signify a return to the original idea (in this case, alchemy), but the reappearance of earlier forms on a qualitatively higher level. Incidentally, it is now possible to convert lead into gold, but would be too expensive to be worth the trouble!

Dialectics envisages the fundamental processes at work in the universe, in society and in the history of ideas, not as a closed circle, where the same processes merely repeat themselves in an endless mechanical cycle, but as a kind of open-ended spiral of development in which nothing is ever repeated exactly in the same way. This process can be clearly seen in the history of philosophy and science. The entire history of thought consists of an endless process of development through contradiction.

A theory is put forward which explains certain phenomena. This gradually gains acceptance, both through the accumulation of evidence which bears it out, and because of the absence of a satisfactory alternative. At a certain point, discrepancies appear, which are initially shrugged off as unimportant exceptions. Then a new theory emerges which contradicts the old one and seems to explain the observed facts better. Eventually, after a struggle, the new theory overthrows the existing orthodoxy. But new questions arise from this, which in turn have to be resolved. Frequently, it appears that we return again to ideas which were earlier thought to be discredited. But this does not mean a return to the starting point. What we have is a dialectical process, involving a deeper and deeper understanding of the workings of nature, society, and ourselves. This is the dialectic of the history of philosophy and science.

Joseph Dietzgen (1828-1888), a companion of Marx and Engels, once said that an old man who looks back on his life may see it as an endless series of mistakes which, if he could only have his time back again, he would doubtless choose to eliminate. But then he is left with the dialectical contradiction that it was only by means of these mistakes that he arrived at the wisdom to be able to judge them to be such. As Hegel profoundly observed, the selfsame maxims on the lips of a youth do not carry the same weight as when spoken by a man whose life's experience has filled them with meaning and content. They are the same and yet not the same. What was initially an abstract thought, with little or no real content, now becomes the product of mature reflection.

It was Hegel's genius to understand that the history of different philosophical schools was itself a dialectical process. He compares it to the life of a plant, going through different stages, that negate each other, but which, in their totality, represent the life of the plant itself:

“The more the ordinary mind takes the opposition between true and false to be fixed, the more is it accustomed to expect either agreement or contradiction with a given philosophical system, and only to see reason for the one or the other in any explanatory statement concerning such a system. It does not conceive the diversity of philosophical systems as the progressive evolution of truth; rather, it sees only contradiction in that variety. The bud disappears when the blossom breaks through, and we might say that the former is refuted by the latter; in the same way, when the fruit comes, the blossom may be explained to be a false form of the plant's existence, for the fruit appears as its true nature in place of the blossom. These stages are not merely differentiated; they supplant one another as being incompatible with one another. But the ceaseless activity of their own inherent nature makes them at the same time moments of an organic unity, where they not merely do not contradict one another, but where one is as necessary as the other; and this equal necessity of all moments constitutes alone and thereby the life of the whole.” ⁴⁰

The dialectics of Capital

In the three volumes of Capital, Marx provides a brilliant example of how the dialectical method can be used to analyse the most fundamental processes in society. By so doing he revolutionised the science of political economy, a fact that is not denied even by those economists whose views sharply conflict with those of Marx. So fundamental is the dialectical method to Marx's work, that Lenin went so far as to say that it was not possible to understand Capital, and especially its first chapter, without having read the whole of Hegel's Logic! This was undoubtedly an exaggeration. But what Lenin was driving at was the fact that Marx's Capital is itself a monumental object lesson on how dialectics ought to be applied.

“If Marx did not leave behind him a 'Logic' (with a capital letter), he did leave the logic of Capital, and this ought to be utilised to the full in this question. In Capital, Marx applied to a single science logic, dialectics and the theory of knowledge of materialism [three words are not needed: it is one and the same thing] which has taken everything valuable in Hegel and developed it further.” ⁴¹

What method did Marx use in Capital? He did not impose the laws of dialectics upon economics but derived them from a long and painstaking study of all aspects of the economic process. He did not put forward an arbitrary schema and then proceed to make the facts fit into it but set out to uncover the laws of motion of capitalist production through a careful examination of the phenomenon itself. In his Preface to the Critique of Political Economy, Marx explains his method:

“I am omitting a general introduction which I had jotted down because on closer reflection any anticipation of results still to be proved appears to me to be objectionable, and the reader who on the whole desires to follow me must be resolved to ascend from the particular to the general.” ⁴²

Capital represented a breakthrough, not only in the field of economics, but for social science in general. It has a direct relevance to the kind of discussions which are taking place among scientists at the present time. When Marx was alive, this discussion had already begun. At that time, scientists were obsessed with the idea of taking things apart and examining them in detail. This method is now referred to as “reductionism”, although Marx and Engels, who were highly critical of it, called it the “metaphysical method”. The mechanicists dominated physics for 150 years. Only now is the reaction against reductionism gathering steam. A new generation of scientists is setting itself the task of overcoming this heritage, and moving on to the formulation of new principles, in place of the old approximations.

It was thanks to Marx that the reductionist tendency in economics was routed in the middle of the 19th century. After Capital, such an approach was unthinkable. The “Robinson Crusoe” method of explaining political economy (“imagine two people on a desert island…”) occasionally resurfaces in bad school textbooks and vulgar attempts at popularisation, but cannot be taken seriously. Economic crises and revolutions do not take place between two individuals on a desert island! Marx analyses the capitalist economy, not as the sum total of individual acts of exchange, but as a complex system, dominated by laws of its own which are as powerful as the laws of nature. In the same way, physicists are now discussing the idea of complexity, in the sense of a system in which the whole is not just a collection of elementary parts. Of course, it is useful to know where possible the laws that govern each individual part, but the complex system will be governed by new laws which are not merely extensions of the previous ones. This is precisely the method of Marx's Capital—the method of dialectical materialism.

Marx begins his work with an analysis of the basic cell of capitalist economy—the commodity. From this he explains how all the contradictions of capitalist society arise. Reductionism treats things like whole and part, particular and universal as mutually incompatible and exclusive, whereas they are completely inseparable, and interpenetrate and determine each other. In the first volume of Capital, Marx explains the twofold nature of commodities, as use-values and exchange-values. Most people see commodities exclusively as use-values, concrete, useful objects for the satisfaction of human wants. Use-values have always been produced in every type of human society.

However, capitalist society does strange things to use-values. It converts them into exchange-values—goods that are produced not directly for consumption, but for sale. Every commodity thus has two faces—the homely, familiar face of a use-value, and the mysterious, hidden face of an exchange-value. The former is directly linked to the physical properties of a particular commodity (we wear a shirt, drink coffee, drive a car, etc.). But exchange value cannot be seen, worn or eaten. It has no material being whatsoever. Yet it is the essential nature of a commodity under capitalism. The ultimate expression of exchange-value is money, the universal equivalent, through which all commodities express their value. These little pieces of green paper have no relation whatever to shirts, coffee or cars as such. They cannot be eaten, worn or driven. Yet such is the power they contain, and so universally is this recognised, that people will kill for them.

The dual nature of the commodity expresses the central contradiction of capitalist society—the conflict between wage-labour and capital. The worker thinks he sells his labour to the employer, but in fact what he sells is his labour power, which the capitalist uses as he sees fit. The surplus value thus extracted is the unpaid labour of the working class, the source of the accumulation of capital. It is this unpaid labour which maintains all the non-working members of society, through rent, interest, profits and taxation. The class struggle is really the struggle for the division of this surplus value.

Marx did not invent the idea of surplus value, which was known to previous economists like Adam Smith and Ricardo. But, by disclosing the central contradiction involved in it, he completely revolutionised political economy. This discovery can be compared to a similar process in the history of chemistry. Until the late 18th century, it was assumed that the essence of all combustion consisted in the separation from burning substances of a hypothetical thing called phlogiston. This theory served to explain most of the known chemical phenomena at the time. Then in 1774, the English scientist Joseph Priestley (1733-1804) discovered something which he called “dephlogisticated air”, which was later found to disappear whenever a substance was burned in it.

Priestley had, in fact, discovered oxygen. But he and other scientists were unable to grasp the revolutionary implications of this discovery. For a long time afterwards they continued to think in the old way. Later, the French chemist Antoine Lavoisier (1743-1794) discovered that the new kind of air was really a chemical element, which did not disappear in the process of burning, but combined with the burnt substance. Although others had discovered oxygen, they did not know what they had discovered. This was the great discovery of Lavoisier. Marx played a similar role in political economy.

Marx's predecessors had discovered the existence of surplus value, but its real character remained shrouded in obscurity. By subjecting all previous theories, beginning with Ricardo, to a searching analysis, Marx discovered the real, contradictory nature of value. He examined all the relations of capitalist society, starting with the simplest form of commodity production and exchange, and following the process through all its manifold transformations, pursuing a strictly dialectical method.

Marx showed the relation between commodities and money, and was the first one to provide an exhaustive analysis of money. He showed how money is transformed into capital, demonstrating how this change is brought about through the buying and selling of labour power. This fundamental distinction between labour and labour power was the key that unlocked the mysteries of surplus value, a problem that Ricardo had been unable to solve. By establishing the difference between constant and variable capital, Marx was able to trace the entire process of the formation of capital in detail, and thus explain it, which none of his predecessors were able to do.

Marx's method throughout is rigorously dialectical, and follows quite closely the main lines traced by Hegel's Logic. This is explicitly stated in the Afterword to the Second German edition, where Marx pays a handsome tribute to Hegel:

“Whilst the writer pictures what he takes to be actually my method, in this striking and [as far as concerns my own application of it] generous way, what else is he picturing but the dialectic method?

“Of course the method of presentation must differ in form from that of inquiry. The latter has to appropriate the material in detail, to analyse its different forms of development, to trace out their inner connection. Only after this work is done, can the actual movement be adequately described. If this is done successfully, if the life of the subject matter is ideally reflected as in a mirror, then it may appear as if we had before us a mere a priori construction…

“The mystifying side of Hegelian dialectic I criticised nearly thirty years ago, at a time when it was still the fashion. But just as I was working at the first volume of Das Kapital, it was the good pleasure of the peevish, arrogant, mediocre'Epigonoi' who now talk large in cultured Germany, to treat Hegel in the same way as the brave Moses Mendelssohn in Lessing's time treated Spinoza, i.e., a 'dead dog'. I therefore openly avowed myself the pupil of that mighty thinker, and even here and there, in the chapter on the theory of value, coquetted with the modes of expression peculiar to him. The mystification which dialectic suffers in Hegel's hands, by no means prevents him from being the first to present its general form of working in a comprehensive and conscious manner. With him it is standing on its head. It must be turned right side up again, if you would discover the rational kernel within the mystical shell.

“In its mystified form, dialectic became the fashion in Germany, because it seemed to transfigure and to glorify the existing state of things. In its rational form it is a scandal and abomination to bourgeoisdom and its doctrinaire professors, because it includes in its comprehension and affirmative recognition of the existing state of things, at the same time also, the recognition of the negation of that state, of its inevitable breaking up; because it regards every historically developed social form as in fluid movement, and therefore takes into account its transient nature not less than its momentary existence; because it lets nothing impose upon it, and is in its essence critical and revolutionary.” ⁴³

^{18. Trotsky, L. In Defence of Marxism, p. 66.↩}

^{19. Marx, K. Capital, Vol. 1, p. 19.↩}

^{20.David Bohm, Causality and Chance in Modern Physics, p. 1.↩}

^{21. R.P. Feynman, Lectures on Physics, chapter 1, p. 8.↩}

^{22. Aristotle, Metaphysics, p. 9.↩}

^{23. Engels, F. Dialectics of Nature, p. 92.↩}

^{24. Trotsky, L. In Defence of Marxism, pp. 106-7.↩}

^{25. Waldrop, M. Complexity, The Emerging Science at the Edge of Order and Chaos, p. 82.↩}

^{26. Engels, F. Dialectics of Nature, pp. 90-1.↩}

^{27. Engels, F. Anti-Dühring, p. 162.↩}

^{28. Gleick, J. Chaos, Making a New Science, p. 127.↩}

^{29. Waldrop, M. op. cit., p. 65.↩}

^{30. Bohm, D. Causality and Chance in Modern Physics, p. x.↩}

^{31. Engels, F. Anti-Dühring, p. 163.↩}

^{32. Stewart, I. Does God Play Dice? p. 22.↩}

^{33. Feynman, R. op. cit., chapter 2, p. 5.↩}

^{34. Engels, F. Dialectics of Nature, pp. 345-6.↩}

^{35. Hegel, G. Science of Logic, Vol. 1, p. 258.↩}

^{36. Hoffmann, B. The Strange Story of the Quantum, p. 159.↩}

^{37. Engels, F. Dialectics of Nature, p. 96.↩}

^{38. Ibid pp. 95-6 and p. 110.↩}

^{39. Ibid p.108 and p.107.↩}

^{40. Hegel, G. The Phenomenology of Mind, p. 68.↩}

^{41. Lenin, V. Collected Works, Vol. 38, p. 319; henceforth referred to as LCW.↩}

^{42. Marx, K and Engels, F. Selected Works, Vol. 1, p. 502; (henceforth MESW)↩}

^{43. Marx, K. Capital, Vol. 1, pp. 19-20.↩}