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.

  1. Waldrop, M. op. cit., p. 65.

  2. Bohm, D. Causality and Chance in Modern Physics, p. x.