Paul McGarr


Engels and natural science

(Part 2)


Science after Engels

In the century since Engels’ death almost every area of science has been radically transformed by new breakthroughs in our understanding of nature.

Geology, for instance, has been revolutionised by the theory of plate tectonics, or “continental drift”. Instead of seeing the land masses on the Earth’s surface as permanent features we have a scientific understanding of the way they have developed, changed and moved during the Earth’s history. Nor is this a finished process: the continents continue to move today. New land is continually being created and existing continental material destroyed. The new understanding means we can begin to explain the development and change of natural phenomena from mountain ranges to oceans and earthquakes in a way that was impossible before. The understanding of plate tectonics also casts new light on biological evolution.

For a long time many geologists resisted the theory of plate tectonics, despite the growing evidence in its favour. It has only been fully accepted in the last 30 years or so. These scientists would perhaps have been less resistant to the new understanding if they had been accustomed to think in the spirit of Engels’ argument that all of nature changes, that what appears to be static and fixed usually turns out to be otherwise. Of course Engels knew nothing of plate tectonics, but his general attitude did lead him to warn against the idea that “the five continents of the present day had always existed”. [67]

Biology has undergone an even more revolutionary transformation since Engels’ death. First Mendelian genetics, then in more recent decades molecular biology – and a host of other advances – have transformed our understanding of living organisms. But, as so often with powerful new breakthroughs, the very success has bred a distorted one sided view among many biologists. In biology this is often linked to political and ideological questions – as arguments about human biology easily lead to arguments about human nature and society.

The fashionable approach, at least among molecular biologists, is best termed a “reductionist determinism”. In this view everything about, say, human biology and behaviour is a mechanically and directly determined consequence of our genes – strings of DNA molecules inside every cell in our bodies. At its most extreme this leads to claims that there are genes for aggression, homosexuality, criminality, homelessness and the like. It leads to sociobiology, in which human behaviour and social development are viewed as a direct consequence of our genes – so war, sexism, racism and so on are seen as a product of our biological evolution. And it leads to a view of human beings as robot like receptacles manipulated by “the selfish gene”. Without going this far many biologists argue as though genes are all that really matter, all we need to know to understand our biology and even our behaviour.

Most of this is a mixture of poor science, ideology, and fanciful “just so” stories about evolution. Some of those pushing such arguments are motivated by reactionary politics. Others are influenced, often unconsciously, by the money available for research in these areas – molecular biology and genetics are big business today. Some are simply carried away with the real success of molecular biology and genetics in advancing our understanding into generalising from this to a mistaken overall view, in much the same way as Engels argued happened to many scientists after the 16th and 17th century scientific revolution.

Fortunately, there are a growing number of eminent biologists who forcefully challenge this approach. Two of the most well known who have written popular works expounding their view are Richard Lewontin in the US and Steven Rose in Britain. They argue that a proper understanding of biology, and of the huge advances of recent decades, demands a totally different approach, what they themselves call a “dialectical biology”. Moreover, these scientists frankly acknowledge that their general approach is inspired by Engels, as can be seen from the work contained in such books as Not in Our Genes, The Making of Memory, The Doctrine of DNA and The Dialectical Biologist [68] – none of which demand a formal or technical training in biology.

There are two reasons for dealing in greater detail with the advances in physics since Engels’ death. Firstly, the revolution in physics of the last 100 years has been the most spectacular in any science. It has radically transformed the most basic notions which underpinned all previous science. Secondly, while in biology there are at least some eminent working scientists, even if they are a minority, who argue for a dialectical approach, this is not the case in physics.

The difference can be illustrated from a glance at the 1993 shortlist for the prestigious annual Rhone-Poulenc science book prize. The eventual winner was The Making of Memory by Steven Rose. This is a beautifully written account of how science works by someone who has made major contributions to it. It is also a sharp critique of reductionist and determinist biology and an unashamed defence of what the author has called “a dialectical biology”.

Steven Rose’s book was in fact a surprise winner of the award. The pre-award favourite was instead The Mind of God, a book on modern physics by the eminent theoretical physicist Paul Davies. In it he claims the lesson of physics today is that, “We have to embrace a different concept of understanding from that of rational explanation. Possibly the mystical path is a way to such an understanding”. [69]

Davies’s previous work was also a popular best seller on modern physics written with John Gribbin, a respected scientist, an astrophysicist by training and physics consultant for the reputable New Scientist magazine. The title of their book indicates their key argument. It is called The Matter Myth. Their central thesis is that “materialism is dead ... During this century physics has blown apart the central tenets of materialist doctrine in a sequence of stunning developments”. [70] They go on to indicate what these developments are: “first came the theory of relativity ... then came the quantum theory ... another development goes further, the theory of chaos”. [71]

If these authors, and they are fairly typical of much that passes for serious thinking about modern physics, are right it is a serious matter. It is therefore worth looking at the argument in some detail. In fact, far from undermining materialism the very advances cited by these and similar authors are in fact huge advances in a materialist understanding of nature. Moreover, they are also a marvellous confirmation of the general arguments put forward by Engels, weighty evidence for the necessity of a dialectical approach to understanding the natural world. The first two of the scientific advances cited, relativity and quantum theory, were part of the revolution which transformed science in the first few decades of this century, most famously associated with the work of Albert Einstein.

This revolution arose from a profound crisis in science. By the time of Engels’ death there were a series of glaring contradictions between different branches of physics. Theories which successfully explained different physical phenomena contradicted each other in fundamental ways. It was out of the attempt to resolve these contradictions that the new scientific revolution was born. A new, deeper understanding was built which went beyond the previous contradictory elements, and at the same time showed why these had worked within certain limits. This process is a fairly typical one in the history of science. In the historical development of scientific ideas Engels’ arguments about how change takes place are well grounded.

Relativity theory was developed by Einstein between 1905 and 1915. The first step, known as “special relativity”, was born of a contradiction between theories of motion, dynamics, on the one hand, and theories of electromagnetism – phenomena such as radio and light waves as well as electric and magnetic forces – on the other. In dynamics, Newton’s laws of motion had stood the test of over two centuries. Then in the 1860s James Clerk Maxwell had put the understanding of electromagnetism on a similar footing by describing all electromagnetic phenomena in terms of a series of simple and beautiful laws. Maxwell’s equations were a huge breakthrough, they enabled the prediction of radio waves and led to a host of other developments, and they remain today a key element of modern science.

The problem, though, was that there was a contradiction between Newton’s laws and Maxwell”s. The crux of the matter is that Newton’s laws appeared to remain the same for any two observers moving at constant velocity relative to each other while Maxwell’s didn’t. This led to all sorts of contradictions. For example, it meant two different physical explanations of the electrical dynamo and motor – one converting electricity to motion, the other the reverse – processes which appeared in fact to be connected. Einstein solved the problems by going beyond both existing theories.

The cornerstones of relativity are two principles about nature first put forward by Einstein in 1905. The first – in view of the contradiction between Newton and Maxwell – was to insist that the laws of physics must be the same for any observer no matter what their velocity. The second principle is that the velocity of light is constant, the maximum velocity possible in nature, and that its velocity is independent of the motion of the source of that light.

It is the last part of this that seems outrageous. Imagine measuring the speed of a ball thrown to you and finding it to be the same whether the ball is thrown by a motionless friend standing nearby or from another friend speeding by in a supersonic aircraft. Since the speed of such balls would not be the same why should it be for light? But when looking at nature we should always bear in mind Engels’ warning about the dangers of “sound common sense”. For in fact it does turn out that if you measure the speed of light it is always the same, no matter how fast you yourself or the source of the light may be moving. This is now a well established fact of nature.

A series of consequences follow from Einstein’s arguments which seem to challenge commonsense notions of time and space. These new notions have since been tested and confirmed in countless experiments. The old notions are themselves abstractions, generalisations, from how the world behaves when things are moving at low speeds relative to ourselves. Einstein showed that those notions break down and do not fit the way real material objects behave at speeds which begin to approach the speed of light. This is why Maxwell’s electromagnetic theory, which deals with light waves, did not sit happily with Newton’s laws. A crucial element in the new understanding is that what appear to be simultaneous events to one observer may not appear to be so for another observer moving relative to the first. Another consequence is that moving clocks run slow. An accurate clock flown round the world on a jet will show a different time on return to an exactly similar clock left at home. For most phenomena we have direct experience of, the effect is tiny, but it becomes large and important as speeds approach that of light.

Einstein’s theory was a key step in the defeat of the notion implicit in Newtonian physics of an absolute space and time, and absolute motion. It was a vindication of the idea that all motion was relative. Also, until Einstein, physics had seen matter, mass, as something dead and inert which had to have energy imparted to it. To be sure, energy could be transformed from one form to another but mass itself was something quite distinct. Now Einstein’s relativity, with its famous equation E=mc2, showed that mass could be transformed into energy and vice versa.

Einstein later extended his theory to provide a new explanation of gravity, which had not been incorporated into his earlier theory of “special relativity”. “General relativity” starts from a simple fact. In Newton’s theory mass appears, but there are two different masses – what are known as the gravitational and inertial masses. One is the mass which is the source of the force of gravity, the other is the measure of a body’s resistance to change of motion. In fact the two, though in Newtonian physics quite distinct aspects of matter, are always found to be the same. Weightlessness in a falling lift is one example. Einstein’s theory is an attempt to explain facts like this. It attempts to incorporate gravity into the new relativistic dynamics.

General relativity is not, as often presented, simply an exotic tool for speculation about the universe – though it can help in that too. Something as straightforward as the orbit of the planet Mercury around the sun was never fully explained by Newton’s laws – despite the best efforts of generations of brilliant physicists, astronomers and mathematicians. General relativity now makes it possible to explain it. Again the theory was spectacularly confirmed in 1919 when its novel prediction that light from stars should bend when it passed close to the sun was shown to be correct.

There certainly are difficult mathematics in general relativity’s description of matter and space. For instance, it insists that the geometry of space containing matter is not Euclidean – the kind we are taught at school – but rather what is called “curved”. A way to try and picture the difference is to compare the kind of geometry possible on the surface of a balloon to that on a flat surface. On the flat surface the three angles of a triangle always add up to 180 degrees. On a balloon this is not true. On a flat surface a line never joins itself no matter how far extended, on a balloon this is again not true. In general relativity, however, the “curved” geometry is in the three dimensions of space (or, strictly speaking, the four dimensions of space – time) not just on a two dimensional surface, whether flat or balloon like. Despite the difficulties however, the final form of the theory is the most beautiful and elegant in modern physics. And the key notion in the theory is not so difficult. It is simply that the old notion of matter which exists in a passive, unaffected background of space will not do. Rather matter and the space it exists in are connected and influence each other in fundamental ways. The geometry of space and the distribution of matter mutually determine each other.

Neither special nor general relativity are in any way a challenge to materialism. By the turn of the century existing scientific theories simply could not explain a growing number of observed facts of nature and, moreover, the theories that explained different facets of nature contradicted each other. The new theories resolved those contradictions, explained the unexplained, and showed both why the old theories had worked within limits and why they broke down beyond those limits.

Engels certainly had no inkling of relativity theory, or that the 200 year old Newtonian laws of motion and gravity were to be overturned within years of his death. But the development of relativity and its core notions illustrate many of Engels’ key arguments. He had insisted that all motion was relative. “Motion of a single body does not exist, it can be spoken of only in a relative sense”. [72] More importantly, the whole thrust of relativity theory is a precise illustration of Engels’ argument that abstractions which fit aspects of nature within certain limits then break down when pushed beyond those limits, and thus require a new understanding. Again the new understanding that matter was not something separate from motion and energy but that each was capable of being transformed into one another in a definite law governed manner is exactly the kind of process Engels pointed to as a unity of opposites, a characteristic revelation of a deeper understanding of nature. Someone who had argued that the science of his day pointed to the fact that motion and transformation were “the mode of existence, the inherent attribute, of matter” would have been less surprised than many by relativity theory.

Finally, the key notion in general relativity, that space and matter were not mutually opposed aspects of nature, with matter existing against a passive backcloth of space, but that the two were intimately connected and mutually determining, is, again, about as sharp an example as you could find of the interpenetration of opposites, the kind of “dialectical” understanding Engels argued for and which he insisted scientific advances increasingly demanded.

The second revolution in the early part of the century came with quantum theory. This too came out of glaring contradictions between existing theories and observed facts – especially in the behaviour of small objects like atoms.

Atoms, for instance, simply should not exist on the basis of the old understanding. If Newton and Maxwell were right – even when reconciled by relativity – then every atom should collapse in a burst of radiation in a very short time. This, fairly obviously, is not true. It was out of such problems – and a host of others ranging from the behaviour of metals when ultraviolet light was shone on them to how bodies absorbed and emitted radiation – that quantum mechanics developed.

At first this was done on a fairly ad hoc basis – simply adding in bits to old theories even if these bits flatly contradicted other parts of the theory. But in the 1920s and 1930s a radically new theory was developed. Three aspects of this “quantum mechanics” are important. Firstly it argues all objects can behave as both waves, like radio waves, and bulletlike particles. So light, usually thought of as a radio-like wave, can behave as a particle, while an electron, a particle, can also behave like a wave. What had previously, and still now to common sense, seemed two mutually exclusive and opposed notions were revealed to be intimately connected, to be two sides of the same coin.

Secondly, quantum mechanics also says there is an intrinsic uncertainty in nature. For instance, an electron can have a well defined and precise position or velocity, but not both at the same time. Thirdly, the theory says some phenomena in nature are inherently probabilistic, governed by chance. So it is impossible to predict in advance, say, which of the various possible energies an electron around an atom will be in or exactly when a radioactive particle will emit radiation.

It suggests this randomness is not the same as that, for example, of rolling a die or tossing a coin, but fundamental. In coin tossing the randomness is a result of our ignorance. If we measured the initial motion of the coin as it left our hands then we could predict which way it would land. The randomness in quantum mechanics is not of this kind, not simply a result of our ignorance. Rather it suggests that, for example, it is not possible even in principle to predict exactly which energy is possessed by an electron around an atom. Instead it suggests that all we can do is predict the probability of it having each of the range of possible energies.

One point should be emphasised. Quantum theory does not throw determinism out of the window and leave us with a picture of a world completely governed by chance, random events. It is rather a picture of a world of subtle interplay between chance and necessity. Quantum theory deals with predicting the probability of events, such as an electron around an atom having a particular energy, and how those probabilities evolve in time in a strictly deterministic fashion. Quantum theory deals mostly with very small atomic scales and, as it has to, agrees with older theories on how large, macroscopic, objects behave. Moreover it seeks to explain how uncertainty at the small scale results in the quite predictable and deterministic behaviour characteristic of the larger, macroscopic, scale of which we have direct experience.

Many features of quantum theory seem bizarre and run counter to many common sense assumptions. Yet it makes sense of real facts about nature which on the old understanding could not be explained. It has been spectacularly confirmed in countless experiments. Your TV or pocket calculator wouldn’t work if its predictions weren’t accurate. It is a step forward in a materialist understanding of the world, not a retreat.

Nevertheless there are severe problems in interpreting quantum theory, despite its predictive success. Quantum theory describes matter in terms of something known as a “wave function” – which sums up the fact that all matter has both wave-like and particle-like attributes. There is deep and unresolved controversy among scientists about what this “wave function” means. Most scientists think of it as a kind of description of all the possible states open to the matter under consideration at any time and a measure of the relative probability of that matter, say an electron around an atom, being in any of those states. When the matter under consideration interacts with something else, most obviously when it is measured, it is found to be in one definite state. This is called the “collapse of the wave function”. There is again huge and unresolved controversy among scientists about this process. No one knows the answers.

Many physicists simply get on with using the theory, which has been among the most successful in the history of science. They push the problems to one side. The long time “orthodox” interpretation of quantum mechanics, usually called the Copenhagen interpretation, is little more than a gentlemen’s agreement not to ask awkward questions.

A lot of good things have been written on the problems thrown up by both quantum mechanics and its relation to our understanding of other aspects of nature. As yet, though, they remain unresolved questions. Those who think science is a closed world free of contradiction and with definite answers to all questions are very mistaken. [73]

It is also true that quite a lot of nonsense has been written by quite reputable and otherwise quite sane scientists. Some, for instance, argue that a conscious observer is necessary for the collapse of the wave function. Seeing as the world – and the collapsing wave functions – certainly existed long before human beings, this is simply another way of describing god. Another notion that is quite fashionable is what is sometimes called the “many worlds” interpretation of quantum mechanics. This argues that every “measurement” results in the universe splitting into parallel worlds all of which really exist. [74] It avoids the real problems associated with the “collapse of a wave function” by saying it doesn’t really happen, but instead all the possibilities summed up in the wave function really turn out to be true, each in one of a myriad of parallel universes. This may be the stuff of interesting science fiction, but as serious science it leaves a lot to be desired.

Amid all the unresolved problems we should remember that the contradictions and problems with the newer theories are not essentially worse than those with older theories – it is just that we are used to ignoring the earlier problems. For instance, in Newton’s theory of gravity, force is supposed to act instantaneously at any distance. A little thought will reveal that this really is a bizarre notion, which didn’t stop people using the theory for hundreds of years and continuing to use it within certain limits today. The great 19th century scientist Michael Faraday was one of the few who, long before Einstein, pointed out the difficulty of the “spooky action at a distance” at the heart of Newton’s theory.

Whatever the correct interpretation of quantum mechanics turns out to be, there is no doubting that it is not a challenge to materialism, but a step forward in a materalist understanding. Once again the problems it gives rise to should be set against the fact that the old theories simply could not explain elementary facts about nature while quantum mechanics does, and in addition has led to enormous advances across a whole range of science and technology.

However, given the deep and unresolved problems within it, quantum theory is unlikely to be the last word on how matter behaves at a subatomic level. At some point a new understanding will be developed which will resolve some of the problems. No doubt, it will in turn throw up fresh contradictions and problems. John Bell, a leading figure in quantum theory, said:

The new way of seeing things will involve an imaginative leap that will astonish us. In any case, it seems that the quantum mechanical description will be superseded. In this it is like all theories.

And he concluded in a phrase that echoes Engels’ whole approach to science: “To an unusual extent its [quantum mechanics’] fate is apparent in its internal structure. It carries in itself the seeds of its own destruction”. [75]

Engels would have been as shocked and suprised as anyone at the picture of the subatomic world thrown up by the development of quantum mechanics. But many of quantum theory’s key notions illustrate Engels’ arguments about nature. It shows how chance and necessity are not mutually exclusive opposed notions, how in fact chance at one level of nature can give rise to deterministic behaviour at another level. It shows that old notions, of wave-like behaviour and particle-like behaviour, which fit most aspects of nature of which we have direct experience, break down when pushed past certain limits and instead require a new understanding to be developed.

The leading British scientist John Haldane (typically, though, a biologist!) writing in 1940, after discussing Engels and the various points on which he was wrong, commented, “When all such criticisms have been made, it is astonishing how Engels anticipated the progress of science in the 60 years which have elapsed since he wrote ... Had Engels’ methods of thinking been more familiar, the transformation of our ideas on physics which have occurred during the last 30 years would have been smoother”. [76] Quantum theory and relativity, though now well established and accepted, were controversial for many years after they were born. Looking back at the controversy after reading Engels, Haldane concluded, “Had these books been known to my contemporaries, it was clear that we should have found it easier to accept relativity and quantum theory”. [77]

In the decades since the development of quantum theory our understanding of the basic structure of matter has been further revolutionised. Whereas 60 years ago it was thought all matter was made up of protons, neutrons and electrons which were acted upon by eletromagnetic and other forces, now a much richer picture has been uncovered. Protons and neutrons have been shown to be complex systems made up of more “elementary” objects called quarks. New forces have been discovered and explained, such as the “colour” force (which, in fact, has nothing do with colour) thought to be responsible for the interaction between quarks. Every few years some scientists think they have found the “ultimate building blocks” of matter or a “theory of everything”. But it has always turned out that, once probed beyond certain limits, the ultimate turns out to nothing of the kind, and that matter and its behaviour are an inexhaustible fount of surprises.

Even the notion of the vacuum, empty space, has now been shown to be mistaken on closer investigation. Rather the vacuum seems to be a bubbling sea in which particles, packets of matter and energy, continually froth in and out of existence. This is not just speculation. This process plays a key role, for example, in the spontaneous emission of light by some atoms. The general picture emerging from modern physics is that change, continual process, interaction and transformation are a fundamental property of matter, and of the space which can no longer be seen as separate from it.

The most striking thing about the picture of matter in physics today is how well it sits with Engels’ arguments about all of nature having a history, how seemingly separate facets of nature are connected, and how the essence of matter is precisely its continual transformation and change.

For instance, it is now thought that all the known forces and particles of nature are connected (all forces are now thought to be carried by particles of matter, or energy – the two are equivalent). The emerging view is that all the fundamental forces of nature are in fact different aspects of a single unified force. Moreover, in this new understanding nature has a history in a sense far more fundamental than even Engels thought possible, though very much in the spirit of his arguments.

It seems that at the very high energies typical early in the history of the universe all the forces were unified. As the universe has expanded and cooled, and so the typical energies of processes have fallen, this symmetry, this unity, has repeatedly been broken until today, at the energies we can now usually have access to, the various forces and their associated particles appear as separate and distinct.

Moreover, all the known “particles” and “forces” of matter are simply different and transient manifestations of the same underlying essence (which most scientists would today call energy). They are all capable of being transformed into another. So, for instance, a proton and an anti-proton (two particles which are identical except the “anti” particle has the opposite electrical charge) mutually annihilate each other if they meet. The released energy, or more accurately transformed matter, can then go through further transformations and so give rise to a host of other different “particles” of matter.

Again the generally accepted explanation for the development of the universe – known as the “standard cosmological model” or more popularly the “big bang” – is one in which matter has undergone repeated qualitative transformations when quantitative change has reached critical points. That development has proceeded through a dynamic internal to matter. Differentiated facets of the totality of matter, which has an underlying unity, have been progressively transformed as they mutually interact. We have an evolution from quarks, to protons and neutrons, to neutral atoms, to gas clouds, stars and galaxies, the formation of heavier elements like carbon, the formation of planets and through a series of further transformations to the emergence of organic life and conscious human beings. [78]

At each stage qualitatively novel behaviour of matter emerges. So quarks having existed freely were, when the temperature of the universe fell below a critical point, permanently confined inside particles like protons and a qualitatively new kind of physics emerges (at the energies existing in the universe today free quarks cannot exist). Later, below another critical point, protons and neutrons could capture electrons and the whole possibility of the rich new arena of atomic and molecular processes emerges for the first time. It needed the first such molecules to be further transformed in the very special conditions of stellar interiors, and then those stars themselves to explode in cataclysmic events called supernovae, before the elements crucial to the formation of planets like Earth were even possible. And a further long series of transformations of matter have, billions of years later, resulted in the qualitatively new phenomena of human beings, consciousness and society.

Even a cursory acquaintance with what 20th century physics has uncovered about nature and its various aspects and historical development shows that Engels’ general approach is more relevant than ever.

The final development cited as challenging materialism is chaos theory. This has only fully developed in the last 30 years. Many of the problems and issues it deals with were raised by scientists long ago, above all Henri Poincaré at the turn of the century. But the investigation of the problems only became possible with the development of the modern fast computer.

Chaos theory basically says that some physical systems, though governed by laws which predict exactly what something will do, can nevertheless behave unpredictably. The weather is the example most often cited, usually in the picturesque example of the “butterfly effect” – in which it is said the flapping of a butterfly’s wings on one side of the world can ultimately result in changes which accumulate in such a way as to lead to a hurricane on the opposite side of the globe. [79] In fact very simple physical systems also behave in this “chaotic” way. Three bodies orbiting each other under the influence of gravity, or a simple pendulum swinging over a magnet are two examples. Such physical systems are unpredictable in that their evolution is so sensitive to tiny changes in the initial conditions from which that evolution starts that the only way to see what happens is to wait and see.

This theory has been seized on to argue that any attempt to explain the world, to consciously act to change it in a certain way, is doomed to failure. All we are left with is unpredictability and chaos. Attempts at social or economic planning won’t work, the chaos of the market is all that’s possible, runs the argument. This is to miss the whole point of the theory. It deals mainly with phenomena which previously were not understood at all. Now where ignorance reigned something can be explained, even if some old notions have to be rethought to do so. In fact chaos theory shows there is a pattern, a structure – albeit often a very complicated one – underlying many phenomena previously not understood at all. The dynamics of heart attacks, or fluid turbulence, to take just two examples, have never been really understood. Now chaos theory has provided the first steps of an explanation. [80]

Chaos is a property of what mathematicians call non-linear systems. Until the last few decades almost all physics for the last 300 years dealt with what mathematicians call linear systems. Linear systems are much easier to deal with mathematically. The basic difference is that in a linear system the whole is equal to the sum of the parts, while in a non-linear system the whole is not simply the sum of the parts – an idea that has been fundamental to a dialectical understanding at least since Hegel.

Great strides forward can be and have been made by studying those parts of nature which can be approximately taken as linear. But all real physical situations are non-linear. Sometimes the non-linear effects can be ignored, but very often they cannot. Because non-linear mathematics is far more difficult to deal with than linear, most science shied away from non-linear problems until the advent of fast computers and chaos theory.

Two key aspects of chaos theory are interesting. Firstly, it shows that at various points small quantitative changes produce large qualitative changes in behaviour. Chaos theory is saying, and explaining why, this – as Engels argued – is a fairly universal feature of the natural world.

Secondly chaos theory shows that in the natural world determinism and unpredictability, seemingly two opposed and mutually exclusive notions, are in fact intimately linked. A process can in a very real and important sense be both at the same time. [81] In quantum theory unpredictability at one level can give rise to deterministic behaviour at another level of nature. Chaos theory shows the opposite is also true. A system can be governed by strictly deterministic laws yet give rise to unpredictable behaviour.

Again this is not a result of ignorance. When specifying the initial conditions of any system there is always a margin of error, summed up in the notion of something being “correct to within one part in, say, 100 million”. In a “chaotic” system, no matter how small this margin of error is, it can be shown that a difference still smaller than this will lead to wildly and unpredictably different outcomes in the future evolution of the system. If you say, well, let’s make the specification of initial conditions more precise to overcome this divergence the same phenomenon can then be shown for a still smaller difference in initial conditions and so on (this whole notion can be made mathematically precise).

Chaos theory is one of the components which have provided the basis for more recent new developments which are some of the most exciting in science for many years. These have been dubbed “the science of complexity”.

These developments also draw on new developments in thermodynamics, the science of processes involving heat. Thermodynamics has long sat uneasily alongside other areas of physics. It originated in the work of scientists like Sadi Carnot in the early years of the 19th century and grew directly out of attempts to understand what were the scientific principles underlying the steam engines that were playing a key role in the industrial revolution. Thermodynamics soon began to pose problems as it seemed quite different to the understanding developed in most of the rest of physics. For instance, whereas, say, Newtonian science was deterministic, the laws of thermodynamics were probabilistic.

Secondly, Newtonian science was strictly time reversible. This means that there is nothing in, say, Newton’s laws of motion to distinguish changes running forwards or backwards in time. Put crudely a movie of a strictly Newtonian world would not look wrong if it were run backwards. The obvious problem is of course that most real processes in the world are not reversible – try unbreaking an egg or unstirring the milk from your coffee. Thermodynamics deals with such irreversible changes, heat flows from hot to cold, never the other way around. Time, and development in a definite direction in time, plays a key role in thermodynamics, in a way that is not true of most of the rest of the laws of physics.

In short, thermodynamics was not easily reconciled with the laws thought to govern the particles or molecules of which something was composed. This was not helped much even with the scientific revolution of relativity and quantum mechanics – both are still time reversible in the sense described above. In addition most thermodynamic theory was developed around understanding processes involving heat which were near a stable equilibrium – mainly because this was mathematically easier. [82]

In recent years however scientists like the Belgian Nobel Prize winner Ilya Prigogine have started to study thermodynamics when processes are far from equilibrium – which is much more typical of the real world. Other scientists have built on this kind of work and elements of chaos theory to try and look at the connections between different aspects of nature, and in particular to seek to understand the dynamics, the processes of change, which underlie complex physical systems in general, to try and understand the common patterns. It is an attempt, though most of the scientists involved would not use such language, to develop a “dialectics of nature”.

One of the key notions these scientists have developed is that of emergent properties in complex systems. They point to, and seek to explain, how matter itself at certain levels of complexity develops new behaviour which grows out of the underlying laws, but cannot be simply reduced to these underlying laws. It requires an understanding on that new level.

A picture of nature is beginning to emerge in which at certain points physical systems not only can undergo a transition from regular ordered behaviour to chaotic unpredictable behaviour, but of how matter, once it reaches a certain level of complexity of organisation, can spontaneously generate new higher forms of ordered behaviour. It is a picture of potential development in nature whose essence is exactly that which Engels was grappling with in his discussion of the “negation of the negation”. Some physical systems can be pushed from a stable ordered state into a chaotic state by some pressure, change or impulse (it is “negated”). But under certain conditions some of these systems can then develop in such a way as to give rise to new higher forms of ordered behaviour, often with novel properties (the “negation is negated”).

This kind of pattern seems to be typical of many complex systems in nature and scientists are now beginning to seek to understand it. There is some evidence, though it is not established, that complex organisations of matter with genuinely novel and “creative” properties are those “on the edge of chaos”, systems balanced in a dynamic tension between the tendency towards a dead, stable, repetitive order on the one hand and an unpredictable, disordered, chaotic state on the other. [83]

Where these developments will lead no one yet knows, though one can be certain there will be as much abuse of them as there has been of almost every new scientific development from Darwin to chaos theory. Phil Anderson, who won a Nobel Prize for his work on what is called condensed matter physics, is one of those involved in developing some of this work. He points to the potential of the new science which is beginning to show how “at each level of complexity entirely new properties appear. And at each stage entirely new laws, concepts and generalisations are necessary. Psychology is not applied biology, nor is biology, chemistry”. [84]

Anderson gives a simple but illustrative example of the point from everyday experience – water. A water molecule is not very complicated: one big oxygen atom with two smaller hydrogen atoms stuck to it. Its behaviour is governed by well understood laws and precise equations of atomic physics. But if a few billion of these molecules are put together they collectively acquire a new property that none of them possesses alone, liquidity. Nothing in the underlying laws governing the behaviour of the individual atoms tells you about this new property. The liquidity is “emergent”. In turn, argues Anderson, this “emergent property” produces “emergent behaviour”. The liquidity can, through cooling, suddenly be transformed into the solid, crystalline structure of ice. Again this behaviour simply has no meaning for an individual water molecule alone.

Further simple examples, by way of illustration, occur with the onset of convection when heating a fluid such as water. At first the heat rises through the fluid by conduction. At a certain critical point, however, and under certain conditions, an abrupt qualitative change in behaviour occurs. Suddenly millions of molecules switch into large scale – by molecular standards – coherent motion in hexagonal convection cells, known as Bénard cells. Again certain chemical reactions exhibit this kind of spontaneous emergence of structure or order. In these “chemical clocks” millions of molecules undergo rhythmic and structured transformations on a vast scale – again relative to the molecular scale at which the underlying reactions take place. These are examples of what is possible in relatively simple physical systems. The possibilities in more complex systems are correspondingly richer.

The kind of understanding Anderson and similar scientists are beginning to develop is exactly what Engels meant by a dialectical understanding of the change of quantity into quality. It is an understanding which shows how matter itself, through interactions among different facets of the same totality (all have evolved historically from the seemingly undifferentiated and homogenous early universe), is qualitatively transformed and develops through history.

It remains true that modern science continues to throw up as many questions as it answers, but just because new questions are posed should not lead us to ignore the many and important answers found over the last century. No doubt some of the various hypotheses put forward today to explain aspects of nature will, as Engels put it “be weeded out by experience”. Some severe weeding will surely be necessary since, as always in the history of science, theories which explain various parts of nature are riddled with problems and are often mutually incompatible. Quantum mechanics and general relativity, for instance, seem to be incompatible at a fundamental level. Again non-linear processes are increasingly seen as vital in an understanding of nature, but while general relativity and chaos theory are radically non-linear, quantum theory is not. All three are time reversible, in the sense explained earlier, yet the new thermodynamics, not to mention the real world, points to the fundamental importance of irreversible processes in nature. [85]

Which aspects of existing and any new theories are correct, which only of limited value, and which figments of the imagination will become clear when we find a way to tease the answers out of the only ultimate arbiter – matter, in all its many aspects and changes. Lenin, the leader of the 1917 Russian Revolution, in commenting on the scientific revolution of his day put the argument well:

Our knowledge is penetrating deeper, properties of matter are disappearing which formerly seemed absolute, and which are now revealed to be relative and characteristic only of certain states of matter. The sole property of matter with whose recognition philosophical materialism is bound up is the property of being an objective reality, of existing outside our mind. [86]

I have already pointed to the way some leading biologists consciously draw on the tradition founded by Engels. Today some physicists and scientists in other fields are also beginning to recognise the connection between the way they are pushed to think and the approach advocated by Engels. Ilya Prigogine, who has played a key role in the new thermodynamics, for instance says, “To a certain extent there is an analogy” between the problems he is grappling with and “dialectical materialism”.

And he says the key understanding emerging from modern scientific developments is that “nature might be called historical, that is, capable of development and innovation.” And he goes on to comment:

The idea of a history of nature as an integral part of materialism was asserted by Marx and in greater detail by Engels. Contemporary developments in physics have thus raised within the natural sciences a question that has long been asked by materialists. [87]

Richard Levins and Richard Lewontin dedicated their 1985 book The Dialectical Biologist, “To Frederick Engels, who got it wrong a lot of the time but who got it right where it counted”. [88]

Many scientists will say they have no need of philosophy to make sense of nature, that they are simply discovering how nature works. So be it. The science will ultimately stand or fall on its truth, its success in practice, whatever the thoughts in the heads of the scientists or anyone else.

But it is worth noting the dangers many modern physicists, or at least those who think about the meaning of the science they produce, fall into when they reject an attempt to have a consistent materialist, dialectical approach. I quoted earlier physicist Paul Davies’s book The Mind of God and its talk of possibly needing to embrace “the mystical path”. He is certainly not alone in such thoughts. Physicist Stephen Hawking concludes his otherwise excellent best seller, A Brief History of Time, by talking of “the ultimate triumph of human reason” as “to know the Mind of God”. [89] Even Ilya Prigogine ends a generally marvellous book with stuff like “time is a construction and therefore carries an ethical responsibility” and references to the “God of Genesis”. [90] It is worth recalling Engels’ warning against the illusion that science can do without philosophy and the dangers into which “sober headed empiricists” can fall. [91]




It should be clear that Engels’ general approach to and arguments about science were correct and stand up well against the scientific developments in the 100 years since his death. In fact those developments are a powerful argument for the necessity of a dialectical understanding of nature.

What are the key elements in such an understanding? The first is that nature is historical at every level. No aspect of nature simply exists: it has a history, it comes into being, changes and develops, is transformed, and, finally, ceases to exist. Aspects of nature may appear to be fixed, stable, in a state of equilibrium for a shorter or longer time, but none is permanently so. This is the inescapable conclusion of modern science. Instead of expecting constancy or equilibrium as the normal condition a dialectical approach means expecting change but accepting apparent constancy within certain limits.

The second key element on which Engels was right is the need to see the interconnections of different aspects of nature. Of course it is necessary to break nature up, isolate this or that aspect, in order to understand and explain. But this is only part of the story, and unless complemented by seeing whatever parts have been isolated for study in their interconnections and relationships leads to a one sided, limited understanding. Parts only have full meaning in relation to the whole. This is not any kind of argument for a mystical “holism”. The real relationships between different aspects of nature must be established and worked out scientifically. It is simply an insistence that such investigation is necessary for a full understanding to be established.

As in most questions there is a connection between the way nature is viewed and the dominant ideology in society. The fact that a way of thinking about nature in which equilibrium is the norm and in which the focus is on isolated parts, “atoms”, is typical is no accident in modern capitalist society. Though originally revolutionary, the capitalist class now has to believe – and tell us to believe – that its way of organising society is best. It has to suggest, whatever the daily accumulating evidence to the contrary, that stability and equilibrium are the normal conditions. It has to suggest that there is no reason why the current way of running society need change radically. Its vision of society is precisely one of atomised individual units. The family, the individual, are paramount. “There is no such thing as society,” as Margaret Thatcher argued. When this is the dominant ideology in society it is no suprise that it often influences the way scientists think about nature.

What of the general patterns, “laws”, which Engels argued characterise processes of change and development in nature? I would argue that there is no question that Engels’ arguments about quantitative change giving rise at certain points to qualitative transformations are generally correct. In every field of science, every aspect of nature, one cannot but be struck by precisely this process. Any attempt to understand the natural world which does not expect this to be a typical feature of change and development cannot be reconciled with the developments of modern science. Of course to expect such patterns of change does not tell you anything at all about the specific nature of real processes. The natural world has to be investigated and its behaviour established and explained scientifically.

A consequence of this view, however, is the understanding, more and more supported by modern science, that a radically anti-reductionist view of nature is necessary. As quantitative change gives rise to qualitative transformation, new organisations of matter arise. These have genuinely novel ways of behaving which, while compatible with the laws governing the underlying components, are not simply reducible to them. Biology is not simply applied physics and chemistry. Nor are human behaviour and consciousness simply applied molecular biology. Still less are politics, economics and history applied biology. An understanding is necessary which sees the connections between all these different levels of the organisation of matter, for they are all the result of nothing more than the greater or lesser complexity of organisation of matter – there are no mystical or vital principles at work. But an understanding of nature is also necessary which sees that each level has its own laws, ways of behaving, which cannot be read off from the laws governing a different level.

Throughout nature it seems that things which appear to have any persistence, any stability, for a greater or shorter time, are the result of a temporary dynamic balance between opposing or contradictory tendencies. This is as true of simple physical objects like atoms as of living organisms. When that balance is broken – as it always is at some point – change can result which leads to a new development, a transformation to a new situation which is not simply a disintegration or a circular recreation of what was there before. But this is a potential, a possibility, rather than a general feature. Furthermore the way changes take place, and the kinds of possibilities, tendencies or patterns that can occur are different at different levels of the organisation of matter.

This is especially true of the kinds of processes which Engels talks of as examples of “negation of the negation”. It seems to have little validity when talking of change in simple physical objects. It becomes important when talking of more complex persistent systems which have the capacity when absorbing impulses to preserve, and possibly transform, themselves. So it fits much better when looking at biological organisms, whose condition of existence is precisely the continual absorption and transformation of external matter. It is even more apparent in the subclass of living bodies who have reached the further stage of development of consciousness and then self consciousness. These are constantly under the influence of external causation (they are being negated) but by becoming aware of this have the possibility of incorporating it under their own control (above all at the collective, social level) and in the process transforming themselves, and their relations with the external world. Living organisms open up kinds of development, processes of change, which are not there in the same form in the non-living world. Even more so is it the case that with the emergence of human consciousness and society new patterns of development and change become possible.

In addition, though, the concept is also important when looking at the evolution of the totality of matter itself. All these various levels of the organisation of matter are different facets of the same material totality, which though differentiated has an underlying unity. This totality has developed to give rise to the different patterns of change exhibited at different levels of the organisation, and stages of the history, of the natural world. The levels and the patterns of change open at each are different, but they are connected aspects of the underlying unity.

A genuine dialectical view of nature would require the investigation of all these issues, a study of processes of change and development at every level of nature, their similarities and their differences. To construct such an understanding, based firmly on the real results of a developing scientific understanding of nature, would be the best tribute to Engels’ pioneering work which still remains by far the best starting point for the philosophy of science. Engels’ arguments on science have for too long been ignored, dismissed or distorted – by socialists sometimes as much as by others. One hundred years after his death it is time that changed. But in learning from Engels and seeking to build on his insights we should do so in the spirit in which he himself worked: “How young the whole of human history is, and how ridiculous it would be to attempt to ascribe any absolute validity to our present views”. [92]




67. Engels, The Dialectics of Nature, MECW, op. cit., p.321.

68. S. Rose, R. Lewontin and L. Kamin, Not In Our Genes (Penguin, 1984); S. Rose, The Making of Memory (London, 1992); R. Lewontin, The Doctrine of DNA (London, 1993); R. Levins and R. Lewontin, The Dialectical Biologist (Harvard University Press, 1985). Why biologists are more inclined to a dialectical approach than most other scientists is an interesting question. I suspect it is a result of a combination of factors. One is that the scientific material itself more clearly pushes biologists towards a dialectical understanding. Secondly, political and philosophical argument is forced upon biologists in a far sharper way than in many sciences, given, for example, arguments about human nature etc. Thirdly, the fact that a number of the individual biologists concerned have at various points been connected to Marxist political traditions, and more so than in, say, physics, must play a part.

69. P. Davies, The Mind of God (London, 1992), pp.231-232. To be fair to Davies he is one of the few writers on modern physics who asks the right questions. Most of his attack on materialism is in fact a well justified refutation of mechanical materialism. The thrust of much of this is little different from Engels’ own arguments. I do not know if Davies has ever read Engels. Unfortunately, whether through ignorance of this tradition or otherwise, Davies’s correct rejection of mechanical materialism leads him to mistakenly reject genuine materialism.

70. P. Davies and J. Gribbin, The Matter Myth (London, 1991), p.7.

71. Ibid., p.8.

72. Engels, The Dialectics of Nature, MECW, op. cit., p.527.

73. Good discussions of the problems and interesting suggestions of possible solutions, written in a fairly non-technical fashion, can be found, for example, in P. Coveney and R. Highfield, The Arrow of Time (London, 1991), and M. Gell-Mann, The Quark and the Jaguar (Little Brown, 1994). Some of the problems are beginning to be resolved in the most convincing way by a new generation of fascinating experiments, many centred in France under scientists like Serge Haroche. They are beginning to demonstrate how the transition from the strangeness of the quantum mechanical behaviour of atomic objects to the more familiar behaviour of larger scale objects takes place. (Lecture by Serge Haroche, Royal Society, London, October 1994.)

74. This was the theme of a major article in the March 1994 edition of the reputable Scientific American magazine, for instance.

75. Quoted in The Arrow of Time, op. cit..

76. H. Sheehan, op. cit., p.31.

77. Ibid., p.319.

78. The whole of the October 1994 issue of the excellent Scientific American magazine is devoted to an overview of this whole process through its various stages. On reading through this after reading Engels one cannot help feeling that it should have been dedicated to his memory. In passing it is worth saying that the “big bang” model has its own limitations. It is only valid up to a point. The laws of physics in their present form break down at the very high energies and densities as we try and track evolution back towards the “bang”. No one can yet trace that development back beyond a certain point as a result. On the same theme even the fundamental principle of the conservation of energy is only strictly valid within certain limits. It is now established that it can be violated provided the time scale involved in the violation is small enough – as a consequence of the uncertainty principle of quantum mechanics.

79. It is misleading, as is often suggested, to say the butterfly alone “causes” the hurricane. The real point is that a tiny change in the totality of causes can result in radically different outcomes.

80. One interesting aspect of chaos theory is that the old notions about dimensions have had to be radically changed. Usually one thinks of something having one (a line), two (a surface) or three (a solid) dimensions. In chaos theory this understanding is shown to be limited and insufficient to grasp reality. Objects can have fractional dimensions (eg 1.57). The beautiful pictures often seen in books on chaos are of such “fractals”.

81. For a fuller discussion of chaos theory see my “Order out of Chaos”, International Socialism 48, 1990. Also see, for instance, I. Stewart, Does God Play Dice? (Basil Blackwell, 1989); J. Gleick, Chaos: Making a New Science (Sphere, 1988).

82. Thermodynamics and classical dynamics can be reconciled (via statistical mechanics) for systems at, or near, equilibrium. But this reconciliation breaks down for systems far from thermodynamic equilibrium. Engels’ discussion of mathematics, of which he had a good knowledge and keen interest, is another important aspect of his work. His attitude is refreshing compared to much modern philosophical discussion on mathematics. All too often such discussion sees mathematical concepts as either simply the free creation of the human mind, completely divorced from the real world, or as existing independently of the material world or human thought in some “timeless, etherial sense”. This is the view of the leading mathematician Roger Penrose (see R. Penrose, The Emperor’s New Mind, London, 1990). In this view, known as Platonism, as the notion has much in common with arguments advanced by the ancient Greek philosopher, these eternal concepts exist “out there” as much as “Mount Everest” (Penrose, p.xv) and are “discovered” when mathematicians succeed in breaking through to this “Platonic” world by an act of insight or when they “have stumbled across the "works of God"“ (Penrose, p.126).

In contrast to such approaches, Engels insists that mathematical concepts are rooted in the material world. “The concepts of number and figure have not been derived from any source other than the world of reality” (Anti-Dühring, op. cit., p.36). For instance, “Counting requires not only objects that can be counted, but also the ability to exclude all properties of the objects considered except their number – and this ability is the product of a long historical development based on experience. Like the idea of number, so the idea of figure is borrowed exclusively from the external world and does not arise in the mind out of pure thought. There must have been things which had shape and whose shapes were compared before anyone could arrive at the idea of figure.

“Pure mathematics deals with the space forms and quantity relations of the real world – that is with material which is very real indeed. The fact that this material appears in an extremely abstract form can only superficially conceal its origin from the external world” (Anti-Dühring, op. cit., pp.36-37). Though Engels insists mathematics is in this way rooted in the real world, it is not simply a reflection of it but rather an abstraction from it: “In order to make it possible to investigate these forms and relations in their pure state, it is necessary to separate them entirely from their content, to put the content aside as irrelevant, thus we get points without dimensions, lines without breadth and thickness, a and b, x and y, constants and variables; and only at the very end do we reach the free creations and imaginations of the mind itself, that is to say imaginary magnitudes.” Engels was certainly not arguing that mathematical concepts did not soar far away from their material origins as they were developed. He attacked, for instance, those who were unhappy with the idea of what mathematicians call imaginary numbers – like i, the square root of –1.

Engels went on to comment on the problem of why it is that “pure” mathematics can be “applied” to the real world – a problem which has long exercised philosophers of mathematics. “Like all other sciences, mathematics arose out of the needs of men ... but, as in every department of thought, at a certain stage of development the laws, which were abstracted from the real world, become divorced from the real world, and are set up against it as something independent, as laws coming from the outside, to which the world has to conform.

“In this way ... pure mathematics was subsequently applied to the world, although it is borrowed from this same world and represents only one part of its forms of interconnection – and it is only just because of this that it can be applied at all” (Anti-Dühring, op. cit., p.37). Engels’ comments are certainly a long way short of a fully worked out philosophy of mathematics but they contain much that provides a useful starting point in any serious attempt to construct such an understanding.

83. See for a discussion of all these points, for example: The Arrow of Time, op. cit., M. Mitchell Waldrop, Complexity (Viking, 1993), and I. Prigogine and I. Stengers, Order Out of Chaos (Flamingo, 1985).

84. Quoted in M. Mitchell Waldrop, op. cit., p.82. Anderson won his Nobel Prize in 1977 for his detailed explanation of a marvellously dialectical process in nature. Metals are either conductors or insulators of electricity. But it was then found that certain metals could undergo a transition from being a conductor into an insulator. Anderson explained how this startling transformation happened.

85. In fundamental particle physics many of the theories put forward today to overcome some of the difficulties with existing explanations combine two elements. On the one hand they often seem to contain genuine insights which will one day have to be incorporated into any new understanding. But on the other they are often riddled with fanciful notions and wild flights of speculation which are far removed from any meaningful contact with any aspect of the world open to us at present – and very often even the advocates of these theories are not sure what they are really talking about.

A good example is the latest attempt to reconcile quantum theory with gravity-string theory. This seems to have genuine insight. All previous attempts have been plagued by infinite quantities which occur in the mathematical descriptions and which make a nonsense of them. The easiest way to picture why these arise is to recall that in, for example, gravity the force changes in inverse proportion to the square of the distance – 1/rē In established explanations particles like, for instance, electrons are pictured as being point-like, having no extension. Think what happens to an expression like 1/rē when r becomes zero. In a more complicated but analogous manner many of the fundamental problems in modern science are rooted in the very notion of point-like particles which dominates physics. String theory gets rid of these infinities and for the first time seems to point to a genuine reconciliation of quantum theory and gravity. The key element is that it sees particles not as point-like objects but rather as two dimensional “strings”, with energies and masses of different particles being analogous to various “harmonics” on a guitar string. The problem, however, is that the whole theory only makes sense in a “space” of ten dimensions which somehow is structured in such a way that we only see the three dimensions of everyday experience. The theory seems to be saying the essence of reality is a ten dimensional space, but the appearance is three dimensions of everyday experience. There are severe problems with this notion. One, for instance, is that some key mathematical structures vital to explaining the world are only valid in a space of three dimensions. In consequence no one, including its inventors, is sure what string theory means, or how real the extra dimensions are supposed to be. And as yet no one has found a way to extract from it testable consequences. Is it the starting point of a new understanding or a flight of speculation that will turn out to have no connection with the way the world really is? (For a discussion of string theory see F. David Pleat, Superstrings, Cardinal, 1988).

86. V.I. Lenin, Materialism and Empirio-Criticism (Peking, 1972), p.311.

87. I. Prigogine and I. Stengers, Order out of Chaos (London, 1988), p.252.

88. R. Levins and R. Lewontin, The Dialectical Biologist (Harvard University Press, 1985).

89. S. Hawking, A Brief History of Time (Bantam, 1989), p.175.

90. I Prigogine and I Stengers, op. cit., p.313.

91. For a more detailed discussion of the ideas of modern science covered in this section the following references are a good starting point. One of the best is undoubtedly P. Coveney and R. Highfield, The Arrow of Time, which covers almost all the ground discussed here. Also useful are M. Mitchell Waldrop, Complexity, I. Prigogine and I. Stengers, Order out of Chaos, and M. Gell-Mann, The Quark and the Jaguar. Those interested can find further references in these works. All require effort but none require a formal mathematical or scientific training to understand. Anyone wanting to go into the arguments in a more detailed fashion could try the fairly comprehensive collection of essays, P. Davies (ed.), The New Physics (Cambridge University Press, 1989) – many, but not all, of these require a fairly good knowledge of mathematics.

92. Engels, Anti-Dühring, MECW, op. cit., p.106.


Last updated on 17.4.2004