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 AM 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 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.

  1. Engels, F. Dialectics of Nature, pp. 345-6.

  2. Hegel, G. Science of Logic, Vol. 1, p. 258.

  3. Hoffmann, B. The Strange Story of the Quantum, p. 159.