Order out of chaos

Paul McGarr (1990)


From Newton to Laplace's Demon
Determinism, reversibility, reducibility and non-linearity
The dynamics of scientific development
Order out of chaos
Dialectics or mysticism




Chaos is the most fashionable word in science today. From mathematics to physics, chemistry and biology few branches of science have been left untouched by the rise of 'chaos theory'. It is at the centre of series of developments which, taken together, mean our understanding of nature is at its most exciting stage since the scientific revolutions of the first quarter of this century. Those revolutions, associated above all with the name of Albert Einstein, gave birth to relativity theory and quantum mechanics-both of which radically transformed and deepened our understanding of nature. Some see the situation today as just as revolutionary in its likely impact. 'Twentieth century physics will be known for relativity, quantum physics and chaos. Like the earlier two this revolution requires us to discard come cherished assumptions about the world.' [1] Why should any of this be of interest to revolutionary socialists?

Firstly, socialism rests on the premise that it is possible for human beings to rationally and collectively plan and produce to satisfy our needs. Our ability to do that depends crucially on our ability to control and exploit the world we are part of. The greater our scientific understanding of nature the greater the potential to do that. Socialism is about winning a world of freedom, but not one which floats above the nature we live in and grew out of. 'Freedom does not consist in the dream of independence from natural laws,' Engels argued, 'but in the knowledge of these laws and the possibility this gives of systematically making them work towards definite ends.' [2] A glance at some of the key problems facing humanity today should underline the point. From the greenhouse effect to AIDS, science is crucial both to understanding the problems and to solving them.

Secondly, Marxism is an attempt to scientifically understand the world with a view to changing it. It is therefore the enemy of all superstition, irrationality and mysticism and the ally and supporter of the development of a rational understanding of all aspects of the world, social and material.

Human beings and the society they create developed out of and exist as part of the natural world. Natural science alone cannot explain the workings of human society. But any attempt to understand human society not firmly grounded on a scientific understanding of nature is doomed to failure. The Marxist tradition has always understood and emphasised this. Marx himself put it simply. Science, he said, 'underlies all knowledge.' [3] Engels stressed that 'science is essential to a conception of nature which is dialectical and at the same time materialist.' [4]

Marxists, however, cannot uncritically accept all the ideas developed by scientists. At every stage in the development of modern science those directly engaged in it have combined advances in a real understanding of nature with a host of other ideas, speculations and interpretations. This is particularly true of new developments in science whose interpretation is usually a matter of sharp debate. This debate is often concerned with testing and checking whether a new theory really does fit the material facts. But the debate also in part reflects ideas in society at large. Science does not take place in isolation from the rest of society. The ideas, philosophies and prejudices in society cannot but permeate the thinking of scientists.

Equally, philosophers and politicians, ideologues and intellectuals have always drawn on scientific ideas to bolster and justify their views. Scientific developments have at times been used to bolster a host of irrational, idealist and reactionary notions. Darwin's theory of evolution, itself a revolutionary step forward in science, has been, and still is, abused by all sorts of reactionaries. Chaos theory has suffered similar abuse. When a spectrum spanning reactionary Tory and ex-Times editor William Rees-Mogg, former Labour deputy leader Denis Healey and the Communist Party magazine Marxism Today unite in citing advances in modern science as proof that a rationally planned society is impossible, it is time revolutionary socialists took note. [5]

Marxists must encourage and welcome every advance in a scientific understanding of the world, whilst fighting against the ideological crap such advances can be wrapped in or which the science is abused to justify.

None of this is to suggest Marxism is a substitute for natural science. The workings of nature have to be discovered by scientific investigation and it is perfectly possible for a political reactionary to be a brilliant scientist. [6]

Chaos theory has been most popularised through the example of the so called butterfly effect. This is usually presented as follows. New developments in science show the weather may be so sensitive to tiny variations that the faint beat of a butterfly's wings can be the cause of a hurricane thousands of miles away. [7]

This incredible sensitivity, in which tiny variations in causes produce enormous and unpredictable differences in effects – whence the label chaos – is said to rule out accurate long term weather forecasts. Big deal, you might say, the weather is after all a very, very complicated thing. Yes, but the same 'chaotic' behaviour, it turns out, can be true of very simple systems previously thought to be well behaved and understood. The simple pendulum, for centuries the very symbol of regular predictable behaviour, can under certain conditions behave 'chaotically'. [8] Another example is the motion of just three bodies obeying the law of gravity discovered by Newton over 300 years ago. Such a system would seem to be absolutely straightforward, but it's not, and it too can behave chaotically. [9]

Some draw simple and direct conclusions from such examples. 'The "inexorable laws of physics", on which – for instance – Marx tried to model his laws of history, were never really there. If Newton could not predict the behaviour of three balls, could Marx predict that of three people?' is the view of one leading mathematician involved in developing chaos theory. [10]

Chaos theory has been latched onto both by apologists for the existing system and by some on the left disoriented by the collapse of Stalinism. For defenders of the status quo the chaos, in the ordinary sense of the word, of the capitalist world economy can be an embarrassment. An apparently scientific justification for it which 'proves' nothing else is possible is comforting and convenient. On the other hand, some who for years have looked to the state capitalist Stalinist regimes as socialist, and are now bewildered by the dazzling speed with which those regimes have collapsed, have turned to chaos theory to cover and justify their scramble into the arms of the anarchy and chaos of the market. [11]

I don't wish to discuss the politics of those abusing chaos theory. They have been more than adequately dealt with by others elsewhere. [12] What I want to do is focus on the science itself and what it really does tell us about the world we live in. [13] To make the argument as accessible as possible much of the detail of the science has been necessarily omitted or simplified. Those interested in pursuing it in more detail will find references in the footnotes. [14] There is bias towards physics, as opposed to other sciences, in the article. This is partly because I think that is where the main developments and arguments are concentrated and best understood. But partly it also reflects my own particular ignorance.

So what is chaos theory all about? To understand it a historical perspective is necessary.


From Newton to Laplace's Demon

The starting point has to be the scientific revolution of the 16th and 17th centuries associated with Copernicus, Brahe, Kepler and Galileo, which culminated in the work of the English scientist Isaac Newton. Newton's laws of motion and gravity and the world view they gave rise to have shaped science ever since. [15]

Newton's ideas didn't leap out of thin air, or out of his head as a result of the proverbial apple falling on it. Newton was a scientific genius, but he was also a product of the society he lived in. The problems he thought about and worked on were those thrown up by a society in which the bourgeoisie was expanding its wealth and power and in the process transforming the way human beings interacted with nature. [16]

The bourgeoisie's drive to expand trade and production meant it had a vital interest in understanding, controlling and exploiting the natural world. This lay behind the great scientific breakthroughs which led up to and then followed Newton's work.

What was the essence of Newton's achievement? There were three key points. Firstly, he formulated universal laws of motion, laws which applied to all bodies. They implied that knowing the condition of and forces between any set of bodies at one time we could predict their future behaviour for all time. A simple set of laws [17] was sufficient to explain and predict the behaviour of an enormous range of seemingly different phenomena. Newton's laws have proved themselves in practice over the last 300 years and are still vital to science today.

Secondly, Newton developed his law of gravity. [18] Again the law is universal. Every body in the universe obeys it. Together with his laws of motion, the law of gravity meant that the motion of the planets, and potentially the whole universe, could be understood and predicted. [19]

Thirdly, Newton helped develop the integral and differential mathematical calculus. [20] This gave scientists the possibility of handling continuous change precisely for the first time – velocity or acceleration for instance. This again was a huge step forward and the calculus remains vital in almost every science today.

Newton's work and its later development led to a series of breathtaking advances in human understanding of nature without parallel in previous history. The motion of falling bodies, of projectiles, of the moon, and thus the tides, could now be predicted, as could the motion of every other body in the solar system and later beyond. New planets (Uranus, Neptune and Pluto) were discovered when astronomers pointed their telescopes where Newton's law predicted a planet should be to account for the motion of the then known planets. Nothing, it seemed, was beyond human capacity to understand and predict. His work represented the culmination of a series of decisive advances in human understanding of nature. And though Newton's laws have now been superseded by others requiring a fundamental change in our understanding of nature, they are nevertheless valid in a wide variety of situations and remain a massive stride forward.

The impressive achievements of Newtonian science had a profound impact on every aspect of society. Other sciences looked to Newton's mechanics as a model for what they should try to achieve, in particular the idea of simple universal laws as explaining a wide range of seemingly disparate phenomena. Philosophy, music, art and politics also looked to Newtonian science. The work of influential thinkers such as Locke and Kant drew heavily on it. The 18th century Enlightenment, which played a crucial role in the further development of science and in the process which culminated in the French Revolution, was in large part inspired by the idea, gloriously proved by Newtonian science, that the world was intelligible to human reason.

In the century or so after Newton's death his theories were advanced and refined by figures like Fermat, Maupertius, Euler, Lagrange and Hamilton. This process culminated in the work of the French scientist Pierre Laplace in the early years of the 19th century. Building on the work done in the previous century, he resolved a number of key mathematical problems in Newton's theories and effectively pushed God out of the picture. 'I have no need of that hypothesis,' is said to have been Laplace's reply to Napoleon, who had asked him God's place in his theory. [21]

Laplace took Newtonian science to its extreme and logical conclusion. Newton's laws were thought to be universal and are deterministic and time reversible. What does this mean? Universal mearis they are supposed to apply to all particles of matter in the universe. If so, the laws say the motion of every particle is entirely determined by the initial conditions and the forces arising from other particles. The implication is that everything that happens in the universe, down to the smallest movement of the smallest particle, must be fixed in, complete detail.

This is as true of the past as of the future, because the laws are time reversible. This doesn't mean that time runs backwards but that, given the conditions at any instant and the forces acting, the laws do not just determine what will happen to a particle but tell you what has happened to it in the past. So given the mass, position, velocity and so on of a bullet, Newton's laws tell not only where it will land but where it started from too. There is nothing in the laws to distinguish between changes running forwards from backwards in time. A movie of a strictly Newtonian world run backwards would not violate any of the laws. The point may seem unimportant, but is vital in understanding later developments and some of the key arguments today.

Given the number of particles in the universe it is impossible for us to ever be able to perform the relevant calculations, but that doesn't alter the inescapable conclusion that if Newtonian mechanics is universal and sufficient to explain the workings of nature then everything – past, present and future – is determined in its smallest detail. Laplace spelt out his conclusion in a famous statement by imagining a hypothetical 'intelligence' or 'demon':

Consider an intelligence which, at any instant, could have a knowledge of all forces controlling nature together with the momentary conditions of all the entities of which nature consists. If this intelligence were powerful enough to submit all this data to analysis it would be able to embrace in a single formula the movements of the largest bodies in the universe and those of the lightest atoms; for it nothing would be uncertain; the future and the past would be equally present to its eyes. [22]


Determinism, reversibility, reducibility and non-linearity

Laplace represents the extreme and one sided development of a massive step forward in a scientific understanding of nature. The Laplacean world view is one of a regular, endless 'clockwork' universe. At the heart of the picture are four concepts central to understanding later developments.

The first is determinism, in the sense already explained. Scientific developments in the two centuries since Laplace have partly undermined this. The rise of the science of heat – thermodynamics – in the course of the 19th century was the first blow. In explaining the processes which underlay heat flow scientists discovered laws which were probabilistic, based on chance and randomness. These sat uneasily alongside what were supposed to be underlying universal and deterministic Newtonian laws. Scientists like Maxwell, Gibbs and Boltzman made enormous efforts to reconcile the two types of laws, deterministic and probabilistic. They had some success for certain classes of phenomena, but enormous problems still remained. [23] Ludwig Boltzman, who made the greatest efforts to reconcile the deterministic laws of dynamics with the probabilistic laws of thermodynamics, is believed to have been driven to commit suicide in 1906 because of the unresolved problems.

The rise of quantum mechanics – dealing with the behaviour of matter at very small, atomic, scales – in the first quarter of this century struck an even deeper blow at determinism. [24] It did this in two ways, firstly through what is called the Heisenberg Uncertainty Principle. Basically this says that you cannot simultaneously know both the exact position and velocity of a particle. The more accurately you know one, the greater the uncertainty in the other. It is a well established scientific law which has been confirmed over and over again. When you remember, for instance, that Newton's laws depend on knowing the initial position and velocity in order that the future behaviour of a particle can be determined, the consequences of Heisenberg's principle for determinism are clear.

Secondly, quantum mechanics is an inherently probabilistic theory. Its basic law, Schrödinger's equation, is just as deterministic as any of Newton's. But the quantities it describes and determines are the probabilities of a measurement on a particular system having a particular outcome. Quantum mechanics is a theory which applies at very small scales, though this does not mean it doesn't have effects at larger scales. The word processor on which I am writing this depends on the application of quantum mechanics for its operation. The theory, however, works in such a way that above a certain scale the 'classical' Newtonian laws remain generally valid.

The result is, nevertheless, a tension between the probabilistic underlying laws of quantum mechanics and the deterministic laws of the macroscopic world.

A point worth stressing is that the probabilistic nature of the laws in quantum mechanics is fundamental and quite unlike the probabilistic outcome of, say, tossing a coin. In coin tossing the problem is our ignorance of the starting conditions of the coin's motion, how hard and in what direction we set it spinning. If we measured these factors, we could predict with certainty the outcome of a coin toss. In quantum mechanics the probabilistic nature of the laws is fundamental and not in our ignorance of the starting conditions of a particular process. [25]

The second concept central to the problems of the Laplacean world view is time reversibility. As described earlier the laws of classical dynamics are strictly time reversible. The problem is that most processes in nature are not reversible in this sense, but rather are irreversible. Try unstirring the milk from your coffee or unbreaking an egg to see what I mean.

The 19th century saw the development of exact branches of science whose laws were very definitely irreversible. Thermodynamics, already mentioned in connection with determinism, is a clear example. Heat flows from hot to cold, never – on its own – the other way round. [26] The famous Second Law of Thermodynamics makes precise the notion that certain processes in nature only go one way. [27]

Another example of irreversible processes in natural science is Darwin's theory of evolution, which is about change which has proceeded in a definite direction. In this case there is a further problem as, until recently, the irreversible processes in thermodynamics were thought to be ones which, put crudely, led to greater uniformity and disorder, whereas the change in evolution has been towards more complexity and more order. [28]

The third key concept, which is connected to the problems hinted at with both determinism and reversibility, is reducibility. The Laplacean world view is one in which all phenomena and laws of nature ought to be able to be reduced to the operation of the underlying laws – remember Laplace's demon. This was for a long time the view of most scientists.

But there is an immediate problem, given the existence of irreversible and probabilistic processes and laws in nature. How can probabilistic laws be compatible with, let alone reduced to, deterministic laws, or how can irreversible and reversible laws be reconciled?

The final area to look at is the question of non-linearity. Newton's laws, and their further development by people like Laplace, were highly successful mainly because they were applied to a range of relatively simple problems. Compared with what had gone before, the range of phenomena they dealt with was vast. Nevertheless, in truth, the majority of real phenomena could, at best, be dealt with by approximations. Equations describing particular phenomena could often be written down, but solving them was an altogether different matter.

At the heart of the problem are the mathematical notions of linearity and non-linearity. The technical details are not important here. The crucial aspect is that in a linear set of equations any solution added to another produces a third solution. This allows us to understand very complex behaviour as the straightforward addition of more basic simple behaviours. For instance, very complex wave motions, such as those of some musical sound waves or vibrations in an aeroplane, can be explained as the straightforward sum of a set of very simple wave motions. A linear system is one in which the whole is equal to the sum of the parts. The vast bulk of the physics of the last 300 years has dealt with such linear systems. Even quantum mechanics, which radically altered many fundamental aspects of Newtonian science, is a linear theory (but general relativity is not).

Non-linear equations, however, are much more difficult to deal with. They do not have the simple additive property of linear systems. They are very difficult to handle mathematically for that reason, and for the same reason scientists have spent an awful lot of time trying to avoid problems in which they occur. Non-linear systems give rise to highly complex behaviour which cannot be understood as the straightforward combined effect of simpler behaviours. Non-linear systems are ones in which the whole is different from the sum of the parts.

The problem is that many, if not most, natural phenomena appear to be non-linear. It has only become possible to investigate such non-linear phenomena in any really systematic way fairly recently, in particular with the rise of fast modern computers. This again is a key element in the development of chaos theory.


The dynamics of scientific development

As should be clear from the examples cited above, there have been a whole series of major scientific developments since the Newtonian scientific revolution.

As new phenomena have been subject to scientific investigation new laws have been discovered. These have often been in seeming contradiction with already established laws. Sometimes the problems have been resolved by new developments which unify and reconcile seemingly contradictory laws by going beyond them to a new, deeper understanding of nature.

The nature of light, for instance, was argued about for centuries. Newton said it could be explained as a series of particles. Then experiments by Thomas Young in 1802 showed light also behaved like a wave. The problem was only resolved with the development of quantum mechanics this century.

Again, a bewildering variety of seemingly different laws and phenomena in mechanics, heat, electricity and chemistry were unified in the mid-19th century with the development of the idea of energy and the law of the conservation of energy. Or again, the laws of electromagnetism developed by Maxwell in the latter half of the last century were incompatible with Newtonian dynamics. It was the successful resolution of this contradiction which gave birth to Einstein's relativity theory at the beginning of this century.

The contradictions, however, have not always been successfully resolved, and even where they have been, new ones have soon arisen. For instance, the twin pillars of modern physics-on the one hand general relativity, which deals with the large scale structure of gravity, space, time and matter, and on the other quantum mechanics, which deals with the small scale structure of matter and successfully explains all other basic forces in nature but gravity – are incompatible. An enormous amount of work has gone into trying to resolve this contradiction with, so far, only limited success. [29]

Behind this dynamic of scientific development lie two fundamental and related processes. Firstly, in capitalist society the drive to increase and extend human understanding of nature is constant, albeit in the distorted form of the drive to maintain and increase profit at the expense of competitors. Marx and Engels, writing in the Communist Manifesto, put it sharply: 'The bourgeoisie cannot exist without constaptly revolutionising the instruments of production.' [30] Looking at what this had already achieved by the middle of the 19th century they continued:

The bourgeoisie, during its rule of scarce one hundred years, has created more massive and more colossal productive forces than have all preceding generations together. Subjection of Nature's forces to man, machinery, application of chemistry to industry and agriculture, steam navigation, railways, electric telegraphs, clearing of whole continents for cultivation, canalisation of rivers ... [31]

The ruling class's drive to accumulate underlies, indeed necessitates, a drive to expand and improve a scientific understanding of nature. That the driving force is the pursuit of profit decisively shapes the areas of research and the problems posed, but does not affect the truth of the natural science developed. To serve the purpose to which the ruling class wants to put it the science has to work. [32] The result has been an enormous increase in human understanding of nature as capitalism has spread across and transformed the world.

None of this is to say scientists consciously sit down and work to maximise the profit of the bosses – though in some cases this is undoubtedly true. Rather the problems thrown up and on which they work are shaped and determined by the society they live in and it is one in which the fundamental drive is accumulation in the pursuit of profit.

A graphic example is the development of the science of thermodynamics already mentioned. It was developed in direct response to the need to understand and improve the steam engine, which was playing a key role in the industrial revolution of the late 18th and early 19th centuries. Sadi Carrot, the founder of the science of thermodynamics freely acknowledged that the science came as a response to the needs of this practice. [33] 'The rapid spread of the British steam engine brought about a new interest in the mechanical effect of heat.' Thermodynamics was 'born out of this interest', is the view of one eminent modern thermodynamicist. [34]

Equally, though, science has a logic of its own, which if it cannot be fully understood without placing it in the context of the development of capitalism cannot be simply reduced to that. The internal problems and contradictions of particular branches of science, and between them, also play a key role in scientific developments. None of this is to deny that at times accidental and inspirational breakthroughs and discoveries have played a vital role in developing science. But to understand the general course of development the processes I have described are central.

A third feature of the historical development of science, and one which is important in understanding chaos theory, is the tendency for science under capitalism to be broken up into narrow, specialised compartments. To a degree this is inevitable, given the enormous expansion in the range of phenomena subject to scientific investigation in the last few centuries. It also has its uses in allowing rapid progress to be made in particular areas.

This tendency to compartmentalise science has increased markedly in the post Second World War period. Science has increasingly become 'industrialised', with most scientists working on highly specialised, narrow problems within some large institution over whose priorities they have little or no control – whether university, government department or multinational firm.

However, a price is paid for this, in that it is all too easy for scientists to completely lose sight of any overall understanding. The connections and relations between different branches of science and the total picture can be missed through the narrow spectacles of specialisation. [35]

One of the interesting aspects of the development of chaos theory is that in large part it has developed through people breaking free from this kind of compartmentalisation, through scientists – whether consciously or otherwise – seeking the connections between different branches of science and trying to understand the overall picture rather than just one part of it.



Chaos theory [36] really dates from the 1960s. Some elements of it had been discussed before. The French mathematician Henri Poincaré made some pioneering studies at the turn of the century, but until the 1960s little systematic work was done.

A key step was taken by Edward Lorenz, who was working on simple models of the earth's weather at the Massachusetts Institute of Technology in the early 1960s. He used a computer and a simple set of strictly deterministic equations to try and begin to understand something about the weather. The advent of this kind of use of fast computers in the years since the Second World War was, and remains, central to the whole development of chaos theory.

What he found has been popularised as the butterfly effect. Instead of two very close starting points giving rise to roughly the same kind of future development, as Lorenz and just about every other scientist at the time would have expected, they could lead to enormously different and unpredictable behaviours in the future. No matter how close he made the two starting points the same happened. The tiniest difference in initial conditions could lead to enormous and unpredictable differences in outcome.

Lorenz's work has since been developed and generalised and found to be a fairly typical property of many non-linear systems. The result is an understanding of two things. Firstly, in many cases seemingly simple deterministic laws give rise to fantastically complicated behaviour which is incredibly sensitive to initial conditions – a generalised butterfly effect.

This is not a result of our ignorance of the initial conditions or failure to measure them accurately. Some systems are so sensitive to the initial conditions that, no matter how close two starting points may be, their future behaviour will still diverge wildly at some point. This notion can be made mathematically rigorous.

Secondly, it turns out the behaviour of such chaotic systems can't be predicted other than in the very short term – again this can be made rigorous mathematically. What does it mean? You can, given certain conditions, predict, for example, the motion of a satellite years in advance within minutes by solving some simple deterministic equations derived from Newton's laws. The satellite will more or less repeat the same motion or orbit over and over again. Once you've worked out the behaviour for one orbit you can predict how it will behave from then on. It will simply repeat the same or very similar motion. At worst you may have to take account of some long term effects which slowly but predictably and fairly smoothly modify the orbit.

However, in chaotic systems this kind of prediction is not possible. The underlying equations are still strictly deterministic, and can often be derived from Newton's laws. But the only way to see what the future behaviour will be is to wait and see – whether it be in the real world or on a computer model. The problem is, the motion never exactly repeats itself at any point. To find out what happens you have to, figuratively speaking, go along for the ride. Unlike in non-chaotic systems, the behaviour in the past is not much use in telling what will happen in future.

Two further points are worth making here. The first concerns the butterfly effect. The point isn't that the metaphorical flapping of a butterfly's wings is the cause of the hurricane. Rather it is that under certain conditions a small quantitative change in the totality of causes can give rise to qualitatively different future behaviours. Many writers and scientists have tied themselves in all sorts of philosophical knots trying to come to terms with this. It is, however, hardly a new or revolutionary notion, even if its exact mathematical formulation in dynamical systems is. A number of Ancient Greek philosophers, not to mention Hegel, or for that matter Marx or Engels, would not have been the slightest bit troubled or surprised that nature exhibited this kind of behaviour. Such behaviour has also long been well known in many branches of physics. Examples include critical point phenomena and phase transitions (such as water freezing) in which, at a certain point, quantitative change is transformed into qualitative change.

Secondly, chaos theory does not simply say certain kinds of phenomena are incredibly sensitive to initial conditions and have an inherent unpredictability. It is the one sided presentation of the theory in this form which opens the door to those who seek to use it to justify a retreat away from the possibility of understanding and controlling nature – and so, the argument goes, society.

The point, however, is that most of the systems which exhibit chaotic behaviour were either not investigated by scientists previously or, if they were, were not well understood. Chaos theory has now begun to show that such phenomena cannot be understood in the way more regular, non-chaotic behaviour can be. But it does not mean we can say nothing about such chaotic behaviour at all.

For a start many systems exhibit both regular, predictable and chaotic, unpredictable behaviour. There have been enormous developments in understanding how the regular ordered behaviour can break down in certain conditions and give rise to the chaotic behaviour. This is in itself a huge step forward in our understanding of nature. To begin to understand even the process by which turbulence in fluids starts would be something which has defeated the best efforts of scientists to date.

But that's not all. While detailed predictions of what will happen to, say, a single particle in a chaotic 'orbit' are not possible, chaotic behaviour is not quite as 'chaotic' as the name implies. The chaotic motion is often bounded – it can't go beyond certain limits. In the case of the weather chaos theory suggests that while it probably will never be possible to predict whether it will rain or be sunny in London on a particular day in six months time – as opposed to, say, three days time – it may very well become possible to say the weather cannot go beyond certain limits. [37]

In other words, the qualitative general behaviour of systems about which little could previously be said can, or potentially can, be understood. Some readers may have seen the often dazzlingly beautiful computer generated pictures which litter books on chaos. Many of these are 'fractals' or 'strange attractors'. They illustrate the complex and beautiful order which can underly 'chaotic' behaviour. [38]

Chaos theory has developed at breakneck speed over the last couple of decades into one of the 'hottest' areas of modern science. And it has done so in large part by breaking down many of the barriers between different branches of science. Today it links together scientists and results from the most 'pure' reaches of mathematics – such as number theory and topology – through most branches of physics, chemistry, biology and medicine. The scientists working in chaos theory have come together from an enormous variety of different backgrounds and disciplines. Their attempts to deal with the particular specialised problems they were working on pushed them into breaking out of these specialised compartments.

Even though still in it's infancy, chaos theory has already pointed to the possibility of real advances in human understanding and control of nature and promises much more. It promises to throw some light on the phenomena of fluid turbulence – until now little understood but with potentially serious consequences for ships, aeroplanes, oil rigs and a host of other devices. In medicine, fibrillation of the heart – when it suddenly goes from regular beats to uncontrollable oscillations with often fatal consequences – promises to be better understood and potentially controlled through the development of chaos theory. The seemingly bizarre 'reactors' found in chaotic behaviour have already been used to transmit moving pictures across basic telephone lines. There are many other examples.

In short, chaos theory is a step forward in, not a retreat from, our understanding of nature. Of course, as we begin to grapple with and understand areas of nature previously not .understood, the old notions no longer fit in the way they did. That, however, should come as no surprise to anyone with even a cursory knowledge of the history of science. In particular chaos theory suggests that the age old division in science between on the one hand deterministic and on the other unpredictable, random behaviour will no longer do. The two notions, seemingly mutually exclusive and opposed, now have to be seen as two sides of the same reality. The deeper understanding of nature being developed by modern science shows that phenomena can be both deterministic and at the same time unpredictable and random.

This kind of development, in which concepts and phenomena which seemed to stand in opposition to each other are shown, as science advances, to be connected aspects of a underlying unified reality is nothing new. For centuries it was thought there were waves in nature and there were also particles – the two being quite distinct. With quantum mechanics came the understanding that the two are just different aspects of a unified reality – every material object is both particle and wave. Motion or energy was seen for a long time as something that otherwise passive mass or matter had imparted to it. Einstein's special relativity, and his famous equation E=MC2, showed that matter in a very fundamental sense was motion or energy and vice versa. It also showed that space and time were dynamically related.

Until this century matter and space and time were seen as separate. Matter moved across a passive backdrop of space and time. With the development of general relativity we now understand that space, time and matter are dynamically related. Matter, in a fundamental sense, shapes and determines space and time, which in turn affect the behaviour of matter. Even the very notion of 'empty space', the vacuum, will no longer do. Quantum mechanics predicts, and this has been confirmed, that particles can spontaneously come into existence out of the vacuum which is itself bubbling with energy.

These ideas, even though they seem to undermine previously well established notions, are not ones which should cause any worry to Marxists. Lenin, writing at the start of this century about the enormous upheaval in science then just beginning, put it well, and in a way which remains true today:

The limit within which we have hitherto known matter is vanishing and our knowledge is penetrating deeper; properties of matter are likewise disappearing which formerly seemed absolute, immutable and primary and which are now revealed to be relative and characteristic only of certain states of matter. For 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. [39]


Order out of chaos

One of the most exciting things in the development of chaos theory is that underlying a whole range of seemingly different chaotic behaviours there appear to be some surprisingly simple universal laws. Much of the work on this is still in its infancy, but it promises to be a big step forward. The most spectacular example to date flows from the work of the US scientist Mitchell Feigenbaum in the mid-1970s. Essentially this showed that, in a wide class of systems which undergo transitions, at certain points, from regular predictable behaviour, to unpredictable chaotic behaviour the process of transition has a universal character. The same 'path to chaos', the same numbers, the same laws, crop up over and over again in wildly different situations.

The final area I wish to look at concerns the questions of reversibility and reducibility mentioned earlier. The work of many scientists, above all the Belgian Nobel prize winner Ilya Prigogine and his collaborators, has begun to point towards how the difficulties with these notions described earlier can begin to be resolved.

The details are beyond the scope of this article, [40] but the key points are worth describing. It seems that not only do certain systems in nature undergo a transition from regular ordered behaviour to chaotic unpredictable behaviour, but under certain conditions out of that chaos can spontaneously arise new higher forms of ordered behaviour.

By way of illustration, a simple example of the spontaneous emergence of new forms of order, not in this case out of chaos, occurs with the onset of convection when heating a fluid such as water. At first heat rises through the fluid by conduction. At a certain critical point however, and under certain conditions, millions of molecules suddenly switch into large scale – by molecular standards – coherent motion in hexagonal convection cells know as Bénard cells.

It seems that in sufficiently complex systems, usually those in which there is dynamic interaction between a system and its environment (unlike the beloved 'isolated' systems of much of classical science), the spontaneous emergence of new order out of often previously chaotic behaviour may be typical.

It also seems the laws governing the new emergent order in this situation are often not reducible to those governing the dynamics of the previous regime. One can, for instance, get irreversible laws and behaviour emerging from systems governed by underlying reversible laws.

Again, much of this work is relatively new, but it points the way to the possibility of a deeper scientific understanding of nature: an understanding in which we can begin to grasp how different levels and aspects of nature can have behaviour and laws which, while they emerge out of more basic underlying laws, are not reducible to them. So for instance, we can begin to understand precisely how the laws of molecular biology arise out of physics but are not simply reducible to them. It promises to be an understanding of the material world in which matter itself is capable in its dynamic interactions of producing both chaos and order. And, above all, it promises to be a conception of nature in which we can begin to explain, in much more detail than previously, how life, ourselves and consciousness are the creation of the natural material world itself – but a creation which is not simply reducible to the laws which govern lower forms of the self organisation of matter. [41]


Dialectics or mysticism

In the development of the scientific theories I have attempted to describe here there are two tendencies apparent among many of the scientists involved. As they begin to break out of narrow specialised compartments and see the connections between different aspects of our understanding of nature, many scientists begin to think dialectically.

By that I mean not a rejection of formal logic, but rather a recognition that because every aspect of the world, including nature, is undergoing continual change and development the fixed static categories of formal logic are not sufficient. Dialectics is a critique of the limits of those static categories to fully grasp a dynamic, developing world.

The science itself tends to push scientists in this direction, whatever their ideological predisposition. This should be clear from the discussion above. When scientists begin to find that in nature quantitative change can at certain points be transformed into qualitative change, when they find that seemingly distinct and opposed phenomena and notions are really different aspects of a deeper truth, when they find that order can dissolve in chaos but out of chaos can also emerge new higher forms of order, the tendency towards dialectical thinking is hardly surprising and few genuine Marxists will be shocked.

Above all, the understanding being developed by science today is one in which nature is historical, has developed and changed. In one sense this is self evidently true. The sun, earth, life and human beings have developed in and out of nature through time. But it is also true at a more fundamental level. The clearest example is the fundamental forces of nature themselves – electromagnetic, weak nuclear and strong nuclear (gravity has yet to be integrated into the understanding). They were one, single force in the early stages of the development of the universe. As nature developed unity was broken and the distinct forces we see today came into existence. [42]

Some may object that the dialectical structure of nature outlined in the preceding paragraphs is purely in our understanding of nature, in our theories, ideas and models, not in nature itself. It certainly is true that it is in our ideas. And it is equally true that our understanding of nature, like human thought in general, is not a simple reflection of the material world, not identical with it.

Two points, however, must be made. Firstly, for example, few scientists when pushed would deny that at certain points quantitative change gives rise to qualitative transformations in nature itself, not just in our understanding of nature. Again, the same applies to the fact that seemingly distinct and opposed phenomena, aspects of nature, turn out to be united. Real material objects, for instance, are both particles and waves – and not just in our minds. Again, nature at a certain level of complexity does give rise to new forms of order emerging out of underlying simpler structures, but with forms of behaviour and laws not reducible to them.

More generally, while human thought and nature are not identical, nor are they totally separate. There is a unity between them. 'Thinking and being are thus no doubt distinct, but at the same time they are in unity with each other', wrote Marx. [43] It is a unity firstly guaranteed by human beings being part of, emerging out of nature. 'Human reason is nature's youngest child', as Trotsky put it. [44] And, secondly, it is guaranteed by the practice of human beings interacting with and attempting to master and transform nature. 'The dialectic of consciousness (cognition) is not thereby a reflection of the dialectic of nature, but is a result of the lively interaction between consciousness and nature and – in addition – a method of cognition issuing from this interaction', argued Trotsky. [45]

The same interaction, the same practice, is the only guarantee that our ideas can give us objective knowledge of the material world. Marx, in a famous statement, put it simply:

The question whether objective truth is an attribute of human thought, is not a theoretical but a practical question. Man must prove the truth, ie the reality and power, the 'this-sidedness' of his thinking in practice. The dispute over the reality or non-reality of thinking that is isolated from practice is a purely scholastic question. [46]

Engels agreed, 'The result of our action proves the conformity of our perceptions with the objective nature of the things perceived.' [47]

That our knowledge is always relative and historically conditional, and shown to be so as our practice develops further, does not mean it ceases to be objective knowledge. Newton's laws, for instance, have been surpassed as our understanding of nature has deepened. But they remain valid, objectively true by the only possible criterion, practice, within certain limits. The notion that we can have eternal, unconditional, objective knowledge is pure metaphysics. To assert the conditional nature of objective knowledge is not to lapse into pure relativism. Lenin stressed:

The materialist dialectics of Marx and Engels certainly does contain relativism, but is not reducible to relativism, that is, it recognises the relativity of all our knowledge, not in the sense of denying objective truth but in the sense that the limits of approximation of our knowledge to this truth are historically conditional. [48]

Interestingly, some scientists today find themselves drawn to note how much of what they are saying about the natural world fits with the conception outlined by Engels, above all in his The Dialectics of Nature. Ilya Prigogine looking back at the view of nature he has outlined writes, 'To a certain extent, there is an analogy' between the problems he is looking at, the scientific solutions he begins to suggest and 'dialectical materialism.' [49]

He goes on:

Nature might be called historical, that is capable of development and innovation. 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. For them, understanding nature meant understanding it as being capable of producing man and his societies. [50]

And it is indeed true that the more one reads of developments in modern science the more Engels' consistent materialist, and therefore dialectical, approach to an understanding of nature – though of course not the details of the science he was dealing with over 100 years ago – seem to be confirmed.

Some scientists will no doubt argue they are simply discovering how nature works and this has nothing to do with philosophy or dialectics. So be it. The science will stand or fall on its truth, its success in practice, whatever the philosophical thoughts in the heads of the scientists or anyone else. However, it is also clear that many modern scientists-at least those who think about the meaning of the work they produce for a general understanding of nature – fall into all sorts of mystical rubbish when they reject an attempt to have a consistent materialist, dialectical approach.

So Prigogine can at the end of a generally marvellous book write gems like 'time is a construction and therefore carries an ethical responsibility', or lapse into despair with 'permanent rules seem gone forever. We are living in a dangerous and uncertain world' and conclude with references to the 'God of Genesis'. [51]

Other scientists like Paul Davies can also combine marvellous insight, for instance in his book The Cosmic Blueprint, with a host of mystical ideas talking of science as a 'surer path to God than religion' [52] and saying, 'Science, it is usually believed, helps us build a picture of objective reality-the world "out there". With the advent of the quantum theory that very reality appears to have crumbled.' [53] And physicist Stephen Hawking concludes A Brief History of Time by talking of the goal of science, 'the ultimate triumph of human reason', as to 'know the mind of God.' [54]

The choice, increasingly, for scientists trying to think about what their work tells us about nature is not between 'pure science' on the one hand and 'dialectics' on the other. It is rather that the problems thrown up by science require theoretical and philosophical thought of some kind to begin to grapple with them. That has always been true, but more so than ever today. One can either attempt to be a consistent materialist, and that means thinking about and understanding nature dialectically, or something else will fill the vacuum.



Chaos theory, far from being a retreat from knowledge, is an exciting step forward in human understanding and therefore potential control of nature.

Socialists have a role to play, not in the working out of the science – that has to be done by scientists – but in rescuing it from the abuse it has suffered and continues to suffer from people like those cited earlier in this article.

As with much other science, the likelihood is that the uses to which it will be put will be distorted by capitalism. Its full development, and that of science in general, will be immeasurably easier in a society in which human beings rationally and collectively set out to deepen our understanding of nature in order to satisfy human need, not profit.

In such a socialist society many of the artificial divisions and much of the ideological litter which distort and limit a real scientific understanding of the world can begin to be swept away. Then the massive strides taken by science under capitalism will be even greater. And then we can also begin to fully achieve that freedom which Engels spoke of, not of 'independence from natural laws' but 'in the knowledge of these laws and the possibility this gives of systematically making them work towards definite ends', [55] the definite ends being the full development of human potential, collective and individual. That, though, requires not simply scientific advance, but a revolution in society.



My thanks to Ian Percival, Tania Monteiro, Andy Wilson, Duncan Blackie and to the editorial board of Socialist Worker for their patience and good humour.


1. W Brown in the Independent 25/7/1990.

2. F Engels quoted in Materialism and Empirio-Criticism by V I Lenin, Foreign Languages Press (Peking, 1972), p219.

3. Quoted in preface to Dialectics of Nature by F Engels, Progress Publishers (Moscow, 1982), p6.

4. In his preface to Anti-Dühring, quoted in F Engels, Dialectics ..., op cit, p6.

5. See article by D Bodarris, the Independent 20/2/90; for Mogg, interview in the Independent 14/10/89; for Healey, 'That Certain Feeling' Marxism Today, July 1990.

6. The German scientist Max Planck, who ended up collaborating with the Nazis but who was nevertheless a key figure in the development of quantum theory, is a case in point.

7. Or as Lawrence Wong more poetically put it at a meeting at the SWP's 1990 Skegness Easter Rally, 'A butterfly flaps its wings in Beijing and you get a storm in Eastern Europe.'

8. If the pendulum is periodically 'kicked'. A simple toy in which a metallic pendulum is suspended over three magnets illustrates chaotic behaviour.

9. This chaotic behaviour was first discovered by the French mathematician Henri Poincaré, for the case of what is called Hill's reduced model – basically a dust speck orbiting two large planets – almost a century ago, but the dust along with the chaos was effectively swept under the carpet until recent decades.

10. I Stewart, Does God Play Dice? The Mathematics of Chaos (Basil Blackwell, 1989), p40. Stewart is a leading mathematician and expert in chaos theory. Despite the quoted extract, and others in similar vein, this book is the best introduction to the subject of chaos theory for anyone with at least some mathematical training – at around the English O level standard.

More accessible is James Gleick's Chaos: Making a New Science (Sphere, 1988). This requires little or no formal mathematics and brilliantly gives a flavour of the excitement in science caused by the development of chaos theory. Gleick tends to overstate the degree to which chaos theory was developed by maverick individuals in the scientific community who, using unorthodox approaches – and with parallel unorthodox lifestyles – broke from the constraints imposed by the division of science into narrow specialised compartments. By way of corrective it is worth noting that many of the key figures in the development of chaos theory worked for, and depended for their resources on, huge institutions. Eduard Lorenz at the Massachusetts Institute of Technology and Benoit Mandelbrot of the giant computer multinational IBM are two examples.

Also useful is the series of articles in the weekly British science magazine New Scientist, 'Chaos Reigns'. The first article, Chaos: a Science for the Real World by Ian Percival, is in the issue of 21 October 1989. Others follow in five subsequent issues.

11. Chaos theory has been put to more interesting use in some fields. For instance, the Hungarian born composer Gyorgy Ligeti, who last year had a season devoted to his work at London's South Bank Centre, cited – in a talk there on 19 October 1989 – chaos theory as inspiring and underpinning the structure of much of his recent music.

12. See, for instance: C Harman 'The Myth of Market Socialism', International Socialism 2:42; A Callinicos 'The Politics of Marxism Today', International Socialism 2:29; A Callinicos Against Postmodernism (Polity, 1989).

13. Some who claim to be on the left have reacted to the kind of misuse of chaos theory cited above by rejecting much of modern science and renouncing chaos theory in particular. This is a foolish and misguided response. See, for example, 'Chaos Theory: the Science of Despair' by John Gibson and Manjit Singh in Living Marxism (published by the Revolutionary Communist Party), December 1989. This masquerades as an attempt to rescue science from those, referred to in the text, who misuse chaos theory. With friends like this one doesn't need enemies. The authors seem to think there has been nothing worthwhile achieved in science since the days of the 18th century Enlightenment. though, interestingly, the same publication manages to defend nuclear power and dismiss AIDS and the BSE mad cow disease as ideological scares by the ruling class. 'If you can't eat a hamburger what's the point in trying to change the world?' Gibson and Singh end up with old fashioned dualism, a rigid mechanical determinism for the natural world, while completely separating human beings and human consciousness from any connection with the material world. Worst of all, they single out for particular attack the two writers – Ilya Prigogine and Paul Davies – who, whatever their many faults, have many of the most interesting things to say about modern science, as I'll argue later.

14. By far the best book for anyone wanting an overview of modern physics and the science underlying the issues dealt with in this article is The New Physics, edited by Paul Davies (Cambridge University Press, 1989). This is a collection of essays, some (but not all) quite technical, written by leading scientists about the problems and developments in the most problematic and exciting areas of physics today.

15. I don't have space to go into the scientific revolution here. It was intimately bound up with the breakdown of the old feudal order and the struggles which culminated in the victory of bourgeois revolutions in Europe. For a brief account see articles by myself in Socialist Worker Review, September 1988, and by Andy Wilson in Socialist Worker Review, October 1988.

16. Again I don't have space to go into this. But it is unnecessary anyway, as it is brilliantly done in Boris Hessen's 'The Social and Economic Roots of Newton's Principia' in Science at the Cross Roads: Papers presented to the International Congress of the History of Science and Technology, held in London from June 29th to July 3rd 1931, by the delegates of the USSR, Frank Cass (London, 1971). Hessen's article is a masterpiece which caused an enormous stir among both scientists and historians when it first appeared. His paper and the others in this volume, including an interesting one by Bukharin, are vital reading for any socialist with a serious interest in science. All of the papers, including Hessen's (though to a lesser extent than any of the others), are marked by the period they are written in, the era of the Stalinist counter-revolution in the USSR. Apart from assorted nonsense about the reality of the USSR under Stalin, the mechanical deterministic distortion of Marxism which Stalinism developed permeates many of the articles. Nevertheless many of the authors still retain enough elements of genuine Marxism for it to shine through at times. This is especially true of Hessen's article. Hessen disappeared in the Stalinist purges of the mid-1930s.

17. That in the absence of forces every body stays at rest or continues in uniform motion (ie constant speed in a straight line); that the acceleration of any body is proportional to the net force acting on it and inversely proportional to its mass; that to every action there is an equal and opposite reaction.

18. That any two bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance separating them.

19. The universality of Newton's laws was a death blow to the old world view derived from the ancient Greek philosopher Aristotle, which strictly separated laws governing phenomena on earth and those elsewhere in the universe. With Newton for the first time laws derived from generalising our experience here on earth could be used to explain phenomena in the rest of the universe.

20. This was developed independently, it seems, by Newton and Leibnitz, and fierce controversy between supporters of the two raged for along time. Newton, for philosophical reasons, did not use the calculus in his presentation of his work in his Principia. The calculus rested for a long time on fairly shaky mathematical ground, but it worked. It was only made rigorous much later with the work of 19th century mathematicians like Augustin-Louis Cauchy. See, for instance, Mathematics in Western Culture by Morris Kline (Penguin, 1987).

21. Quoted in Order out of Chaos by I Prigogine and I Stengers (London, 1988), p52.

22. Quoted in Paul Davies The Cosmic Blueprint, (London 1988) p10.

23. The success came in systems which could be considered 'isolated'. The problem is that most real systems are far from isolated and undergo constant interaction with their environment. For a detailed discussion of the whole issue see I Prigogine and I Stengers, op cit.

24. I shall make no attempt to explain quantum mechanics here. For those interested there are innumerable books at a variety of technical levels. Some are very good – a lot are dreadful. Chapter 7 of I Prigogine and I Stengers, op cit, is useful in relating quantum mechanics to the other issues discussed in this article. E Squires The Mystery of the Quantum World (Hilger, 1986), is useful and not too technical while 'Conceptual Foundations of Quantum Mechanics' by Abner Shimony in The New Physics, ed Paul Davies (Cambridge University Press, pp373ff), is useful for those familiar with the mathematical formalism of quantum mechanics.

25. Some scientists argue this is not the case. They say quantum mechanics is 'incomplete', the probabilities are an illusion and there are 'hidden variables' following deterministic laws behind them. However, recent experiments show any such 'hidden variable' theory has fundamental problems. In particular it would seem to require faster than light communication, violating the well established theory of special relativity. See 'Conceptual Foundations of Quantum Mechanics' by A Shimony in The New Physics, op cit.

26. You can make this happen only by doing work, and so using energy, supplied from outside the immediate system under consideration – as in a fridge which consumes electricity. A point worth making is that the existence of irreversible processes is why a reverse movie of most real dynamical situations would look odd. Billiard balls, for instance, do not just keep bouncing around for ever – if they did, a reverse movie would look fine – but gradually come to a halt because of irreversible processes like loss of energy, to heat, through friction.

27. For a detailed discussion see I Prigogine and I Stengers, op cit.

28. Ibid, pp127ff.

29. This is the subject of Stephen Hawking's A Brief History of Time – which must now rank as the biggest selling scientific book in history. For an excellent discussion see Duncan Blackie's 'Revolution in Science' in International Socialism 42. Other useful, and not overly technical, discussions of these problems can be found in Paul Davies's Superforce: The Search for a Grand Unified Theory of Nature (London, 1987), P Davies and J Brown eds Superstrings: A Theory of Everything? (Cambridge University Press, 1988). More technical, but comprehensive, is the collection The New Physics, op cit.

30. Marx and Engels, The Communist Manifesto, in Karl Marx and Frederick Engels Selected Works Volume One (Moscow, 1977), p111.

31. Ibid, p113.

32. Which is why the would be 'radical science' school who talk of modern science as 'bourgeois ideology' and look forward to a distinctive 'proletarian science' are profoundly misguided.

33. See Carnot's introduction to Reflexions on the Motive Power of Fire by S Carnot translated and edited, with excellent and fascinating notes, by R Fox (Manchester University Press, 1986).

34. I Prigogine and I Stengers, op cit, p103.

35. It is no exaggeration to say that many successful scientists have only the most cursory knowledge of other areas of their own science beyond their immediate speciality, let alone any of other major branches of science. The best scientists bemoan the pressures which foster this situation, while doing their best to overcome it. Many, however, do not even see it as a problem.

36. See Ian Stewart op cit, James Gleick op cit, Jospeh Ford 'What is chaos that we should be mindful of it?' in The New Physics, (Cambridge University Press, 1989), or the series in New Scientist – op cit – and references in all of these for more detailed discussion of the developments underlying this section.

37. This hasn't yet been done for the weather, I use the example to make the point more easily, but the point has been shown for some simpler examples.

38. See for a brilliant selection B Mandelbrot's The Fractal Geometry of Nature (New York, 1977) or H O Peitgen and Peter Richter, The Beauty of Fractals, (Berlin, 1986). The name fractals derives from the fact that these curves and shapes, which can represent an underlying order in chaotic behaviour, generally have a fractional dimension. That is, for instance, they are something between a one dimensional line and a two dimensional surface. This sounds a little weird, but can be made mathematically precise. The name strange attractor derives from the fact that the motion is 'attracted' to this curve – in a suitable mathematical representation – in the way that for instance a ball in a dish is eventually 'attracted' to the point at the bottom. The label strange is largely due to the fact that until recent decades this type of chaotic behaviour was not known of or understood.

39. V I Lenin, Materialism and Empirio-Criticism (Peking, 1972), p311. None of the arguments in the text should be taken as suggesting chaos theory solves all, or even many, of the problems in science, far from it. And it also gives new problems. For instance, it seems chaotic behaviour does not exist in quantum mechanics – the whole area of 'quantum chaos' is currently undergoing furious development and examination at the moment.

40. See, for instance, I Prigogine and I Stengers, op cit; Paul Davies, The Cosmic Blueprint (Heinemann, 1988); Gregoire Nicolis' 'Physics of Far From Equilibrium Systems and Self Organisation' in The New Physics, op cit, and references in these for details.

41. That this is the case is nothing startling. Lenin wrote, 'Sensation, thought, consciousness are the supreme product of matter organised in a particular way. Such are the views of materialism in general and of Marx and Engels in particular.' Materialism and Empirio-Criticism, op cit, p51. The Enlightenment philosopher Diderot argued 200 years ago that 'sensation is a general property of matter, or a product of its organisation', quoted (approvingly) in Lenin, ibid, p28. What is exciting is the possibility of making such notions and the transition from one level or order in nature to another scientifically exact.

42. See, for example, The New Physics, op cit; P Davies Superforce ..., op cit.

43. Economic and Philosophical Manuscripts of 1844 (Lawrence and Wishart, 1961), p 105, quoted in D Caute ed, Essential writings of Karl Marx (London, 1967), p36.

44. Quoted in Trotsky and the Dialectic of History by John Rees in International Socialism 2:43.

45. Trotsky, Notebooks 1933-35: Writings on Lenin, Dialectics and Evolutionism translated by P Pomper (New York, 1986), p77. Quoted in J Rees, op cit.

46. The German Ideology (Lawrence and Wishart, 1963), p197, quoted in Came, op cit, p43.

47. Quoted in Lenin, Materialism..., op cit, p155.

48. Ibid, p154.

49. I Prigogine and I Stengers, op cit, p252.

50. Ibid. The judgement is correct. Marx wrote, 'Natural science will in time subsume itself under the science of man, just as the science of man will subsume itself under natural science: there will be one science.' Economic and Philosophical Manuscripts of 1844 (Lawrence and Wishart, 1961), p111, quoted in D Caute, op cit, p36.

51. I Prigogine and I Stengers, op cit, p313.

52. P Davies, God and the New Physics (Penguin, 1983), ix.

53. P Davies, Other Worlds (London, 1982), p12.

54. S Hawking, A Brief History of Time (Bantam, 1989), p175. To the best of my knowledge Hawking, Davies and Prigogine are not religious, rather either atheist or at least agnostic, but they still fall into talking in this fashion.

55. See note 2.


Last updated 3.12.01