Chapter 2
Changeless Laws, Permanent Energy
Intuitions of a timeless reality
In the context of the new cosmology, all physical reality is evolutionary. But the old idea of eternity lives on in the conception of eternal laws that transcend the physical universe.
If we question this assumption we find that it is very deeply held. But is there any persuasive reason, other than the power of tradition, to accept the idea of eternal physical laws? In an evolutionary universe, how can we rule out the possibility that the laws of nature evolve, or that the regularities of nature are habitual?
Even to entertain such notions involves a radical break with tradition. It means contemplating the possibility of a new understanding of the nature of nature. It would involve carrying forward towards completion the change of paradigm that has already gone so far; namely, the change from the idea of physical eternity to an evolutionary conception of the cosmos.
But the power of tradition is strong, often stronger than we are aware of, because so much of its influence is unconscious. If we are to question the assumption of a theoretical eternity, we should be aware of the long traditions that lie behind it. In this chapter we examine its historical development.
The idea of an eternity of matter in motion governed by eternal laws has come down to us through mechanistic science, but it is rooted in far older traditions, with origins more mystical than scientific.
The intuition of a timeless state of being, a reality where nothing alters, has been described, insofar as it can be described, by mystics throughout the centuries. For many who have experienced it, this vision of a changeless reality has been so powerful and so self-evidently true that they have concluded that the changing world of everyday experience is somehow less real. The impermanence of things in this world is an appearance, a reflection or an illusion. Underlying everything is the true reality, which neither comes into being nor passes away.
The Pythagoreans
One of the main currents of scientific thought can be traced back to the Greek religious community founded by Pythagoras in the sixth century before Christ. The Pythagoreans were influenced by ideas from the ancient civilizations of Egypt, Persia and Babylon. They worshipped the god Apollo and followed a variety of mystical practices.
In common with other Greek seekers, they looked beyond the changing world of experience for the divine, which they thought was without beginning or end. They found this principle in numbers. Numbers were divine and were the changeless principles underlying the changing world of experience. They were at the same time the symbols of ordering, the designators of position, the determiners of spatial extent and also, through ratio and proportion, the principles of natural law.1
Pythagoras himself is said to have made the seminal discovery that musical tones could be understood in terms of mathematical ratios. The properties of stretched strings are such that if the ratio of lengths is 1:2, the tones are an octave apart; the ratio of 3:2 gives the fifth, and 4:3 the fourth. He found that such relationships are not confined to stretched strings, but apply equally to pieces of metal and to flutes. Here were harmonic proportions that could be expressed exactly, understood by reason, and at the same time be heard. This discovery provided an astonishing synthesis of quality and quantity – tone and number – which was complemented by the synthesis of arithmetic and geometry, where numerical ratios and proportions could be seen and comprehended in geometrical figures. Thus ratio and proportion could be directly experienced through the senses and at the same time be understood as timeless, fundamental principles. The cosmos itself was understood to be a vast harmonic system of ratios. Pythagoras is said to have claimed that he actually heard this cosmic music, the harmony of the spheres, although ‘not with normal hearing’.2
Pythagorean mystical experience was not in conflict with reason, but in harmony with it: reason itself was considered above all to be the ability to experience proportions and ratios. Indeed this insight helped to shape the Greek understanding of the rational – in other words that which is concerned with ratio. Reason came to be regarded as the highest aspect of the soul, that which is not only closest to the divine, but actually participates in the divine nature.
According to Pythagorean cosmology, there were two primordial first principles, peras and apeirion, which can be roughly translated as ‘Limit’ and ‘the Unlimited’. These primary opposites produced ‘the One’ through the imposition of limits on the Unlimited. But some of the Unlimited remained outside the cosmos as a void, which the One breathed in to fill up the space between things.3 From the One, which is both odd and even, proceed numbers. These are the substance of the cosmos, both cause and substrate, modifications and states in the things that exist.
Although the Pythagoreans are often regarded as prototypic natural scientists, they were in fact steeped in a mystical and prescientific experience of the world. In non-literate cultures, numbers are not mere abstract concepts, but mysterious beings with a life of their own. ‘Each number has its own peculiar character, a kind of mystic atmosphere and “field of action” peculiar to itself.’4 Pythagoreanism took to an extreme such number mysticism, which is found in one form or another in traditional cultures all over the world.
The Pythagorean vision continues to exert its fascination, neither just because of the rational methods of mathematics nor just because of the successes of mathematical physics: ‘More important is the feeling that there is a kind of knowing which penetrates to the very core of the universe, which offers truth as something at once beatific and comforting, and presents the human being as cradled in a universal harmony.’5
This vision has been caught again and again by mathematicians and scientists over the centuries, and has motivated and inspired most leading physicists, among them Albert Einstein.6
Platonism, Aristotelianism and the rise of Western science
The insights of the Pythagoreans had a major influence on Plato and on the Platonic tradition that followed him. Impressed by the certainty of mathematics, Plato assumed that knowledge must be real, unitary and unchanging. Yet the world is full of a multitude of changing things. Hence these must be in some sense reflections of eternal Forms, Ideas or essences, which exist outside space and time, independently of any particular manifestations of them in the world of sense experience. The eternal Forms cannot be perceived with the senses, but grasped only by intellectual intuition. This intuition is not reached by mere thinking, but by mystical insight.
Particular things, for example a horse, were said to imitate, participate in, or be made by their Form, in this case the Horse-Idea. This is the essence of what it means to be a horse; it is, in other words, the eternal ‘horseness’. This conception of eternal Ideas remained the central tenet of the Platonic and neo-Platonic tradition; and in Christian neo-Platonism, which developed within the Roman Empire in the first few centuries of the Christian era, the Platonic Forms were taken to be Ideas in the mind of God.
The other great philosophical tradition inherited by Christendom from the classical world was Aristotelian. Aristotle, a student of Plato, denied the existence of the transcendent Forms; he saw instead the forms of particular kinds of things as inherent in the things themselves. The form of the horse species, for example, exists in particular animals known as horses, but not in a transcendent Horse-Idea.
Aristotle’s philosophy was animistic. He believed that nature was animate and that all living beings had psyches, or souls. These souls were not transcendent, like Plato’s Ideas, but immanent in actual living beings. For example, the soul of a beech tree draws the developing seedling towards the mature form of its species, and towards flowering, fruiting and the setting of seed. The soul of the beech gives the matter of the tree its form and guides its progressive development. Souls contain within themselves the goals of the development and behaviour of living organisms; they give them their forms and purposes, and are the source of their purposive activity.7
In the Aristotelian system, natural processes of change were drawn towards ends or goals that were immanent in nature; nature was alive and permeated by natural purposes. Even stones had a purpose in falling: they were going home to Earth, their proper place.
However, the forms and purposes of things – the ends in which their souls were actualized, to use the Aristotelian terminology – were changeless. Souls did not evolve. Their natures were fixed.
In medieval Europe, there was a great synthesis of Aristotelian philosophy and Christian theology, a synthesis systematically expounded by Thomas Aquinas in the thirteenth century and developed in the medieval Schools. According to this scholastic philosophy nature was alive, and all the many kinds of living beings had souls. These souls were created in the first place by God, and had remained the same ever after. Their nature was changeless. By contrast, in the human realm there had been a process of progressive development, revealed in the divinely guided history of the Jews, and above all by the incarnation of God in human form in Jesus Christ. The journey of humanity after the Fall and expulsion from the Garden of Eden towards a new knowledge and experience of God was proclaimed by the prophets of Israel, made evident by God’s revealing of himself in human history, and drawn onwards by faith in God’s purposes. But only human beings could develop in this way; the souls of plants, animals and other living beings could not. They remained as they were when God first created them, and so they would remain until the end of this world.
This Christianized animistic philosophy became the dominant orthodoxy of the medieval universities and continued to be taught in the universities of Europe into the seventeenth century and beyond; indeed, it was still taught in a modernized form in many Roman Catholic seminaries in the twentieth century.
At the time of the Renaissance there was a great revival of the Pythagorean and Platonic traditions. The founders of modern science drew their inspiration from these intertwined philosophies, carrying over from them assumptions about eternal Ideas that were built into the foundations of the science they created. They rejected the Aristotelian philosophy.
From Nicholas of Cusa to Galileo
The fifteenth-century mathematician Nicholas of Cusa, a cardinal in the Roman Catholic Church, formed a Pythagorean conception of the world which had an enduring influence on sixteenth- and seventeenth-century natural philosophy. He saw in the world an infinite harmony in which all things had their mathematical proportions. He considered that ‘knowledge is always measurement’ and that cognition consists in the determination of ratios and therefore cannot be attained without the aid of numbers. He thought that ‘number is the first model of things in the mind of the creator’,8 and that all certain knowledge that is possible for man must be mathematical knowledge.9
Nicolaus Copernicus (1473–1543), a Roman Catholic priest from Poland, shared these opinions and became convinced that the whole universe is made of number. Hence what is mathematically true is also ‘really or astronomically true’.10 He made a detailed study of the ancient writings of astronomers of the Pythagorean school and adopted an old idea that had been taught in their tradition: the Earth is not at the centre of the cosmos, but rather circles around the Sun. According to the theory then orthodox, the Earth was a sphere around which the Moon, the Sun, the planets and the stars moved in a concentric series of spheres. Copernicus’s reasons for preferring everything to move around the Sun came from the strong intellectual appeal of this idea, and also from his reverence for the Sun:
Who, in our most beautiful temple, could set this light in another or better place, than that from which it can at once illuminate the world? Not to speak of the fact that not unfittingly do some call it the light of the world, others the soul, still others the governor.11
On this assumption he calculated the orbits of the Earth and planets, and found that a ‘more rational’ and harmonious geometry of the heavens could be constructed. The intellectual appeal of this theory drew the interest and support of mathematicians, but over 60 years elapsed before Copernicus’s theory was supported in a more empirical manner.
Johannes Kepler (1571–1630) was one of those who enthusiastically adopted this mathematical vision. He also had a strong sense of the centrality of the Sun, ‘whose essence is nothing else than the purest light’, and regarded it as the first principle and prime mover of the universe. The Sun ‘alone appears, by virtue of his dignity and power, suited for this motive duty and worthy to become the home of God Himself’.12 He found to his delight that the orbits of the planets bore a rough resemblance to the hypothetical spheres which could be inscribed within and circumscribed around the five regular Platonic solids (tetrahedron, octahedron, cube, icosahedron and dodecahedron – Fig. 2.1).
Figure 2.1 Kepler’s version of the solar system as one Platonic solid within another, the radii of the intervening concentric spheres corresponding to the orbits of the planets.
His third law (that the squares of the periodic times of the planets are proportional to the cube of their mean distance from the Sun), published in his Harmonices Mundi (1619), was embedded in a lengthy attempt to determine the music of the spheres according to precise laws and to express it in musical notation. But he went further than discovering such mathematical relationships: he believed that the mathematical harmony discovered in the observed facts was the cause of these facts, the reason why they are as they are. God created the world in accordance with the principle of perfect numbers; hence the mathematical harmonies in the mind of the creator provide the cause ‘why the number, the size and the motives of the orbits are as they are and not otherwise’.13
Kepler believed that the knowledge of things we have through the senses is obscure, confused and untrustworthy and that the only features of the world that can give certain knowledge are its quantitative characteristics: the real world is the mathematical harmony discoverable in things. The changeable qualities that we actually experience are at a lower level of reality; they do not so truly exist. God created the world in accordance with numerical harmonies and that is why he made the human mind in such a way that it could truly know only by means of quantity.
Likewise, to Galileo (1564–1642) nature appeared as a simple, orderly system in which everything happened with inexorable necessity: she ‘acts only through immutable laws which she never transgresses’. This necessity followed from her essentially mathematical character:
Philosophy is written in that great book which ever lies before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.14
This mathematical order is due to God, who thinks into the world its rigorous mathematical necessity and who also permits by the mathematical method an absolute certainty of scientific knowledge.
In accordance with these assumptions, Galileo made a clear distinction between that which is absolute, objective, immutable and mathematical and that which is relative, subjective and fluctuating. The former is the realm of knowledge, human and divine; the latter the realm of opinion and illusion. The objects we know by means of our senses are not real or mathematical objects; nevertheless they have certain qualities which, handled by mathematical rules, lead to a true knowledge. These are real or primary qualities, such as number, magnitude, position and motion. All other qualities, which are so prominent to the senses, are secondary, subordinate effects of the primary qualities; moreover, they are subjective. ‘These tastes, odours, colours, etc., on the side of the object in which they seem to exist, are nothing else than mere names, but hold their residence solely in the sensitive body; so that if the animal were removed, every such quality would be abolished and annihilated.’15
This distinction was of great importance in the subsequent development of science and was a major step towards banishing direct human experience from the realm of nature. Until the time of Galileo it had been taken for granted that humanity and nature were parts of a larger whole. But for Galileo and his successors, aspects of experience that could not be reduced to mathematical principles were excluded from the objective, external world. Practically the only thing left in common between human beings and the mathematical universe was the ability of human beings to comprehend mathematical order.
Descartes and the mechanical philosophy
Descartes took this mathematical theory of reality to an extreme that has dominated Western science ever since. On the one hand there was the material universe, extended in mathematical space and entirely governed by mathematical laws. On the other hand there were rational human minds which, like the mind of God, were non-material in nature. They were spiritual substances that were not extended in space.
All plants and animals became inanimate machines, and so did human bodies. Only rational minds were non-mechanical – they were spiritual – and human minds had the Godlike capacity to comprehend the mathematical order of the world. Mathematical knowledge was certain and true.
Descartes had already developed a deep interest in mathematics in his youth, but his faith was established in a visionary experience that was a turning point in his life. When he was living in Neuberg on the Danube, on 10 November, 1619, the eve of St Martin’s Day the Angel of Truth appeared to him in a dream and revealed to him that mathematics was the sole key needed to unlock the secrets of nature. He ‘was filled with enthusiasm, and discovered the foundations of a marvellous science’.16
In this mathematical science, geometry was the science of resting bodies, and physics the science of moving bodies in mathematical space. The geometric properties of bodies, their form and size, could not account for the fact that they moved; and so Descartes accounted for motion by supposing that God had set the material universe in motion in the beginning, and maintained the same quantity of motion by his ‘general concourse’. Since the creation, the world had therefore been nothing but a vast machine, with no freedom or spontaneity at any point. Everything continued to move mechanically in accordance with the eternal mathematical principles of extended space and the eternal mathematical laws of motion.
This new philosophy of nature was called the mechanical philosophy. Here, in a youthful form, was the mechanistic worldview.17
Descartes’ mechanical philosophy involved a conscious rejection of the old scholastic orthodoxy still taught in universities. In this Aristotelian tradition, the world was alive; nature was animate and contained within herself her own principle of life and her own ends; all living beings had souls. Descartes expelled all souls and purposes from nature; only human beings had conscious minds and conscious purposes, because their rational minds, like God’s, were spiritual and therefore not part of the material world. The human spirit was supposed by Descartes to interact with the human brain in the pineal gland, in a manner that remained unexplained by him or anyone else. The pineal gland has now been replaced by the cerebral cortex as the supposed seat of consciousness, but the problem of ‘the ghost in the machine’ is still with us today.18
Everything in nature worked entirely mechanically; in other words, everything was inanimate – except for human minds. Thus Descartes eliminated from the world all such disturbances as life, will and intentions. Nothing had its own principle of life or its own source of movement: these came from God. And the mathematical laws of nature were God-given metaphysical truths: ‘The metaphysical truths styled eternal have been established by God, and, like the rest of his creation, depend entirely on him.’19
The orthodox Christian conception of nature was very different from Descartes’. The world was alive, and the living God had created living beings with souls; he had not created inanimate machines. For Descartes, however, God became the sole living principle of everything, including rational human minds. Descartes was proposing a far more extreme form of monotheism than the orthodox doctrine of the Church. He thought his was a more elevated conception of God, and he had a low opinion of conventional ideas. As he said himself: ‘The majority of men do not think of God as an infinite and incomprehensible being, and as the sole author from whom all things flow; they go no further than the letters of his name … The vulgar almost imagine him as a finite thing.’20
In the twenty-first century, it is easy for us to forget that the mechanistic worldview started off with an elevated intellectual conception of God; it involved a new kind of theology as well as a new kind of science. God the all-powerful designer, maker and motive force of an inanimate world machine is not the God of traditional theology; nor is this idea of God taken seriously by most twenty-first century scientists. But the modern conception of eternal physical laws is rooted in this kind of theology, a theology taken further by Newton in his new interpretation of the world machine and its corresponding God.
Atomism and materialism
So far we have confined our attention to the influence of the Pythagorean-Platonic tradition on the development of science. But seventeenth-century science was heir to another ancient Greek tradition: the philosophy of atomism. The marriage of these two traditions in Newtonian physics was extremely fruitful, and continued harmoniously for over two centuries; today it survives in a modernized form in which the invisible atoms have been replaced by elusive ‘fundamental particles’.
The philosophy of atomism was first propounded in the fifth century before Christ by Leucippus and Democritus. The atomists, like other Greek philosophers, were seeking a changeless reality that underlay the changing world. Their starting point was the philosophy of Parmenides, who had tried to form an intellectual conception of ultimate changeless being. He concluded that being must be a changeless, undifferentiated sphere. There could only be one changeless thing, not many different things that change. But in fact the world we experience contains many different things that change. Parmenides could only regard this as the result of illusion.
This conclusion was unacceptable to philosophers who followed him, for obvious reasons. They looked for more plausible theories of Absolute Being; the Pythagoreans found it in numbers, and Plato in eternal Ideas. But the atomists found another answer: Absolute Being is not a vast, undifferentiated, changeless sphere, but rather consists of many tiny, undifferentiated, changeless things – material atoms moving in the void. These atoms are permanent: the very word atom means ‘that which cannot be split up’. Changes are due to the movement, combination and rearrangement of these real but invisible particles. Thus the permanent atoms are the changeless basis of the changing phenomena of the world: matter is Absolute Being.21
This is the essence of the philosophy of materialism, which remains so influential in the modern world. For materialists, unlike Platonists, there is no such thing as a universal mind, spirit or God. Human thoughts are merely an aspect of material changes in the body, and there is no reality other than matter in motion in which they can participate or to which they can refer.
This ancient philosophy was revived in the seventeenth century, and in his great synthesis Isaac Newton brought atomism together with the concept of eternal mathematical laws, producing a dual vision of changelessness – permanent matter in motion governed by permanent non-material laws. A cosmic dualism of physical reality and mathematical laws has been implicit within the scientific worldview ever since.
The tradition we have inherited is both materialist and Platonic. Some scientists (especially biologists) have emphasized its materialist aspect; others (especially physicists) have emphasized its Platonic aspect; and mechanistic science does indeed have both these aspects. It was born of a marriage between the eternal laws and the mathematical time and space of the Heavenly Father, and the ever-changing physical reality of Mother Nature. The great Mother became the forces of nature and matter in motion;22 and indeed the word matter still carries a dim memory of her, for mother and matter come from a common Indo-European root. In Latin, these words are mater and materia, from which the English words material and materialism are derived.
The Newtonian synthesis
The world machine of Descartes was not made up of atoms in a void; there was no void in his theoretical universe. Seemingly empty space was full of vortices of subtle matter. Each star was at the centre of a huge vortical system, and planets such as the Earth were lesser vortical systems swept along by the greater vortex of the solar system. Indeed the entire universe was a vast system of whirlpools of varying size and velocity.
By contrast, Newton’s universe was made up of permanent atomic matter moving in the void. Massive bodies such as the Earth did not move around the Sun because of vortices of subtle matter, but rather because of immaterial forces. The Earth and the Sun were linked by the attractive force of gravitation, which acted across empty space.
Gravitation was like a magic in that it involved unseen connections that acted at a distance. Newton spent many years in alchemical research and in the study of ancient doctrines of cosmic intelligences, angelic powers and the soul of the world. What influence these interests had on his scientific theories is a matter of debate.23 Nevertheless, his law of universal gravitation involves what would now be called a holistic vision: every particle of matter attracts every other particle; everything is interconnected. But in Newton’s opinion, such a force could not arise from the particles of matter themselves; they had no such attractive power. Rather, gravitational force depended on the being of God; it was an expression of his will. Likewise, the absolute mathematical space and time in which all matter existed was none other than an aspect of God, ‘containing in himself all things as their principle and place’.
He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity: he governs all things, and knows all things that are or can be done … He endures forever and is everywhere present; and by existing always and everywhere, he constitutes duration and space … He is all similar, all eye, all ear, all brain, all arm, all power to perceive, to understand, and to act; but in a manner not at all human, in a manner not at all corporeal, in a manner utterly unknown to us.24
This aspect of Newton’s thought was soon forgotten. The hidden forces permeating the space of the universe were soon attributed to matter itself – they arose from material reality rather than from God. And when God was finally dissolved away from Newton’s vision, what was left was a world machine in absolute mathematical space and time, containing inanimate forces and matter governed by eternal mathematical laws.
This mechanistic paradigm, supported and enlarged through the experimental methods of science, enabled many physical phenomena to be understood in terms of mathematical models; it enabled predictions to be made; and above all it proved to be extremely useful in the control and exploitation of the material world. The growing understanding of nature in mechanistic terms stimulated the development of new technologies, through which material reality could be manipulated ever more effectively for human ends. We see evidence of the power of this paradigm all around us today in the technologies that surround and sustain our lives.
The theory of relativity
James Clerk Maxwell’s unified theory of electromagnetism, developed in the 1860s, enabled electricity, magnetism and light to be brought within a broad mathematical framework. Physics was expanded, but it was also radically changed, for Maxwell’s theory placed in the heart of physics the concept of fields. What exactly are fields? Maxwell thought of them as modifications of a subtle medium, the aether. But the failure of experimental attempts to detect the aether led Einstein in his special theory of relativity (1905) to account for electromagnetic phenomena in terms of non-material fields.
Einstein revolutionized the Newtonian world view by abandoning the idea that mass, space and time are absolute quantities; rather, he took the speed of light as absolute. He unified the previously separate conceptions of mass and energy, and showed that both are aspects of the same reality, related through his famous equation E=mc2, where E is energy, m mass and c the velocity of light. Light itself is non-material; it consists of energetic vibrations moving in the electromagnetic field.
In his general theory of relativity, Einstein extended the field concept to gravitation, treating gravity as a property of a space-time continuum curved in the vicinity of matter. His equations are based on a four-dimensional geometry that treats time as if it were a spatial dimension: time is therefore essentially spatialized or geometricized.
Far from undermining the mathematical vision of classical physics, this theory can be regarded as its culmination. In it the timeless mathematical principles are primary, and enable all relative movements to be seen within the framework of a universal geometry. In a manner reminiscent of Kepler, Einstein spoke of gravitation as having a ‘geometrical cause’. Also like Kepler, he was strongly imbued with a sense of the mathematical rationality of the universe:
The individual feels the futility of human desires and aims and the sublimity and marvellous order which reveal themselves both in nature and in the world of thought. Individual existence impresses him as a kind of prison and he wants to experience the universe as a single magnificent whole … What a deep conviction of the rationality of the universe and what a yearning to understand, were it but a feeble reflection of the mind revealed in this world, Kepler and Newton must have had to enable them to spend years of solitary labour in disentangling the principles of celestial mechanics! Those whose acquaintance with scientific research is derived chiefly from its practical results easily develop a completely false notion of the mentality of the men who, surrounded by a sceptical world, have shown the way to kindred spirits scattered wide through the world and the centuries. Only one who has devoted his life to similar ends can have a vivid realization of what has inspired these men and given them the strength to remain true to their purpose in spite of countless failures.25
One of the first physicists to grasp Einstein’s theory of relativity fully was Arthur Eddington, who led the expedition to photograph the solar eclipse of 1919 that provided the first evidence for the theory. He wrote widely about the implications of Einstein’s theory, and concluded that it pointed to the idea that ‘the stuff of the world is mind stuff’. But ‘the mind stuff is not spread out in space and time; these are part of the cyclic scheme ultimately derived out of it’.26
James Jeans, Eddington’s contemporary, concluded in a similarly Platonic vein that ‘the universe can be best pictured, although still very imperfectly and inadequately, as consisting of pure thought, the thought of what, for want of a wider word, we must describe as a mathematical thinker’.27
Quantum theory
Quantum mechanics represents a far more radical break with classical physics than the theory of relativity. One of its most important consequences was the abandonment of strict determinism: its equations permit predictions only in terms of probabilities. However, in spite of its radical features, it remains a major development of the Pythagorean-Platonic tradition, for it enables the properties of atoms to be understood in terms of numbers and, moreover, harmonic series of numbers: it represents a further step towards the traditional goal of science, which was ‘to succeed in penetrating further into the realm of natural harmonies, to come to have a glimpse of a reflection of the order which rules in the universe, some portions of the deep and hidden realities which constitute it’, in the words of Louis de Broglie, one of the founders of quantum mechanics.28 Quantum theory extends the Platonic approach into the very heart of matter, which Democritus and succeeding atomists had regarded as solid and homogeneous. As Werner Heisenberg, another founder of quantum mechanics, put it:
On this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures, or – in Plato’s sense – ideas, which can be unambiguously spoken of only in the language of mathematics.29
Nevertheless, quantum physicists have still proceeded in the spirit of atomism to try to find the ultimate particles of matter. As they have penetrated further into the atom, into its nucleus and into nuclear particles, one of the surprises has been that there are so many kinds of quantum entities – over 200 have been identified so far. Attempts are still being made to fit them into numerical schemes, such as eight- and ten-membered families, which are thought to reflect different permutations and combinations of yet more fundamental components such as quarks (Fig. 2.2). In superstring and M-theories, which dominated theoretical physics in the late twentieth and early twenty-first centuries, with ten and eleven dimensions respectively, the ultimate elements are vibrating strings that follow the laws of ‘quantum geometry’.30 This is the area in which the Pythagorean quest is being pursued at present with most vigour: the attempt to find behind the changing world of experience an eternal mathematical reality, a reality that does not evolve in time and is unaffected by anything that actually happens.
Figure 2.2 Two ‘family groups’ of baryons. (After Pagels, 1983) Baryons are elementary particles which have a half-integral spin and take part in strong interactions. Each one contains three quarks, which come in three ‘flavours’: up, down and strange. The different kinds of baryons contain characteristic combinations of quarks; for example the proton has two up and one down, and the neutron has one up and two down. The octet of baryons is often called the ‘eightfold way’. The decuplet of baryons is arranged in the same way as the tetrachtys, the ancient symbol which lay at the heart of the Pythagorean number wisdom.
Eternal energy
As well as eternal laws, both Newtonian and modern physics presuppose other theoretical eternities in the form of physical quantities that are conserved in the same total amounts forever.
In Newtonian physics, the atoms of matter were regarded as indestructible; hence the total number of atoms in the universe always remained the same. This concept was expressed in a general form in the law of conservation of matter: matter is neither created nor destroyed.
Historically, the law of conservation of energy was introduced as an expression of the constancy of motion in the universe. The universe keeps going on its own; it does not need to be rewound like a mechanical clock. This law was therefore complementary to the law of conservation of matter: both the substance of the universe and its activity are eternal.
At first, the concept of mass was linked with matter, and both were conserved together: the mass of every atom is constant, and all atoms are conserved. This straightforward view was thrown into turmoil in the twentieth century when it was found that atoms can be split into particles, and some particles can split or fuse; the total number of particles is not conserved. Moreover, the mass of a particle can vary. But order was restored again when it was realized that the mass of a particle or system is simply another manifestation of its energy, or motion. The formula E=mc2 expresses the conversion between these two alternative ways of measuring the same thing. Thus the law of conservation of mass has now been subsumed within an expanded version of the law of conservation of energy.
Thus the total amount of energy in the universe is assumed to be constant. Neither the coming into being of our galaxy nor the advent of life on Earth has made any difference to the universal energy, which neither increases nor diminishes in its total amount: it is unaffected by anything that actually happens.31
The conservation laws mean that physical changes in isolated systems can be represented by means of equations. In spite of all the changes, the total amount of energy, electric charge and so on is the same before and afterwards. In the words of Richard Feynman:
A conservation law means that there is a number which you can calculate at one moment, then as nature undergoes its multitude of changes, if you calculate this quantity again at a later time it will be the same as it was before, the number does not change … It comes out the same answer always, no matter what happens.32
The equivalence of ‘before’ and ‘after’ in such equations means that changes can occur in either direction: they are, in principle, reversible. Things could go either way; in the world they describe there is no real and irreversible change, in other words no becoming. The fundamental realities of physics do not evolve; nor are they affected by anything that does in fact develop in time, for example the birth of a star or a new species of insect, or the extinction of either. As Ilya Prigogine expressed it:
Everything is given in classical physics: change is nothing but a denial of becoming and time is only a parameter, unaffected by the transformation that it describes. The image of a stable world, a world that escapes the process of becoming, has remained until now the very ideal of theoretical physics … Today we know that Newtonian dynamics describes only part of our physical experience … As the scales of very small objects (atoms, ‘elementary’ particles) or of hyperdense objects (such as neutron stars or black holes) are approached, new phenomena occur. To deal with such phenomena, Newtonian dynamics is replaced by quantum mechanics and by relativistic dynamics. However, these new forms of dynamics – by themselves quite revolutionary – have inherited the idea of Newtonian physics: a static universe, a universe of being without becoming.33
The only major physical principle that deals with irreversible change is the second law of thermodynamics, which used to be interpreted to mean that the universe is running down. However, thermodynamics does not challenge the eternity of energy: on the contrary, it affirms it. The first law of thermodynamics is in fact a statement of the law of conservation of energy.
The survival of eternal laws
The laws of nature in the form found in scientific textbooks are, of course, man-made. They are continually modified and updated as science progresses. Nevertheless, as this brief history of theoretical physics shows, scientists have generally assumed that they somehow point towards, or reflect, eternal mathematical principles of order. This is, of course, a metaphysical assumption, and has been the subject of debate among philosophers ever since David Hume challenged it in the eighteenth century. However, the continuing prevalence of this assumption has been little affected by such philosophical discussions. It is an integral part of the mechanistic paradigm, and the power of this paradigm has been sustained by the spectacular successes of physics and of the new technologies that have grown out of them.34
Over and above the successes of science and technology, the assumption of eternal mathematical realities is sustained by the enduring fascination of the realm of mathematics itself. Mathematical relationships seem to express strangely timeless truths, valid everywhere and forever. These truths are objective, and yet clearly part of the world of thought rather than the world of things. They do indeed appear to be like ideas in a universal mind.
Mathematicians and physicists are naturally far more aware of this mysterious, even mystical, aspect of mathematics than those who have never penetrated into these subjects. Heinrich Hertz, the nineteenth-century physicist who gave his name to our unit of frequency, put it as follows:
One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we, wiser even than their discoverers, that we get more out of them than was originally put into them.35
In the twentieth century, the prevailing influence of empiricism and positivism in academic philosophy made Platonism unfashionable and favoured instead a philosophy of mathematics called formalism, according to which much, if not all, of mathematics is merely an intellectual game, without any ultimate meaning. However, the allegiance of mathematicians themselves to formalism is less than wholehearted:
The majority of writers on the subject seem to agree that most mathematicians, when doing mathematics, are convinced that they are dealing with an objective reality, but then if challenged to give a philosophical account of this reality find it easiest to pretend that they do not believe in it after all … The typical mathematician is both a Platonist and a formalist – a secret Platonist with a formalist mask that he puts on when the occasion calls for it.36
Even though energy, fields and matter are currently thought to have arisen in time as the universe was born and grew, the mathematical laws of nature are still generally assumed to be eternal and to have existed in some sense before the cosmos began. Even those who postulate that our universe is just one of a vast, and perhaps infinite, number of universes assume that the laws and constants of each universe, including ours, were fixed from the outset.37 However, they do not explain how each universe in the multiverse ‘remembers’ its laws and constants.
Few scientists make this assumption explicit, but the idea of universal changeless laws is implicit in the very method of science as we know it, and is present in the background of all conventional scientific thinking. This assumption underlies the ideal of scientific repeatability.
Repeatable experiments
An essential aspect of the scientific method is that observations should be reproducible. Science deals with the regularities of nature, with those aspects of the world that are objective and repetitive. Under the same conditions, the same experiments should always give the same results for any competent experimenter, anywhere in the world, and at any time. Why? Because the laws of nature are the same everywhere and always. Whether we are aware of it or not, this metaphysical assumption underlies the ideal of reproducibility on which the traditional method of science is founded. In the words of Heinz Pagels:
The universality of physical laws is perhaps their deepest feature – all events, not just some, are subject to the same universal grammar of material creation. This fact is rather surprising, for nothing is less evident in the variety of nature than the existence of universal laws. Only with the development of the experimental method and its interpretive system of thought could the remarkable idea that the variety of nature was a consequence of universal laws be in fact verified.38
Karl Popper, the philosopher of science, argued that the metaphysical assumption of universal laws is actually necessary for science: ‘Only if we require that explanations shall use universal laws of nature (supplemented by initial conditions) can we make progress to realizing the idea of independent, or non-ad hoc, explanations.’39 Without this requirement, there would be no basis for the principle of objective reproducibility that is so essential for the scientific method. Popper is here simply making explicit what most scientists take for granted.
Then what are these universal laws of nature? Popper proposed that they state ‘structural properties of the world’. In doing so, he fully recognized an inherent ambiguity: for on the one hand the structures explain the laws, and on the other the laws explain the structures. But he conceived that ‘at some level, structure and law may become indistinguishable – that the laws impose a certain kind of structure on the world, and that they may be interpreted alternatively, as descriptions of that structure. This seems to be aimed at, if not yet actually achieved, by the field theories of matter.’40
However, the fundamental field theories of matter are now in a state of flux, and in contemporary theoretical physics evolutionary conceptions of fields are coming into being. In an evolutionary universe, the ‘structural properties of the world’ evolve. How can we any longer take it for granted that these structural properties are entirely governed by pre-existing laws? What if they are more like universal habits that have grown up within the growing universe?
To consider the possibility that nature is habitual involves more than just challenging the assumption that everything is governed by transcendent laws that are unaffected by anything that happens: it seems to challenge the basis of the scientific method itself. For if the structural properties of the world change, then how could experiments be reproducible? And how could the idea of repeatability have been so impressively verified by the successes of the scientific method?
A moment’s reflection shows that in physics it would probably make little difference in practice if nature were habitual. Entities such as electrons, atoms, stars, fundamental fields and indeed most of the things studied by physicists have been around for billions of years. Their nature may be so deeply habitual that they can be modelled by timeless mathematical laws. The idea that their nature is fixed eternally is an idealization that for most purposes works well. Experiments on them would in general be reproducible. The same is true of repeatable experiments on most of the systems studied by chemists, geologists, crystallographers, biologists and other scientists: systems that have existed countless times over thousands or millions of years. If nature is habitual, well-established phenomena will indeed appear to behave as if they are governed by transcendent, changeless laws.
The difference between the two approaches becomes apparent in the case of new phenomena that are not yet well established. An essential feature of the evolutionary process is that new organized systems come into being, with patterns of organization that have never existed before: for example the appearance of a new kind of molecule, or crystal, or plant, or instinct, or piece of music. Insofar as these things are truly new, they cannot be explained in terms of a simple repetition of what has gone before. They cannot already be habitual, although through repetition they will become so. But from the conventional point of view, everything new is determined by pre-existing laws that have always been in existence. These laws are not altered by anything that happens, and remain the same whether or not the phenomena they govern actually occur in the world.
Thus, from the orthodox standpoint, new kinds of molecules, crystals, organisms, instincts and ideas are governed by the same unalterable laws on the first occasion, the thousandth or the trillionth.
By contrast, if memory is inherent in the nature of things, the phenomena will not arise in exactly the same way on the first, thousandth or trillionth occasion. They will be affected by the very fact that they have existed before. They will be influenced by a cumulative memory of these previous occurrences and become increasingly habitual. Other things being equal, they will tend to arise everywhere more readily the more often they are repeated.
For example, the crystals of a newly synthesized kind of molecule should tend to form more readily all over the world the more frequently the substance is crystallized. Or when animals such as rats are trained to learn a new trick in one laboratory, other rats of the same breed everywhere else should subsequently tend to learn the same trick more quickly.
There is already evidence that such effects actually occur, and we will return to it in Chapter 7 and subsequent chapters. For the purpose of the present discussion, we need consider only the possibility that nature is habitual. This possibility means that we can no longer take for granted the conventional assumption that all scientific experiments should in principle be exactly repeatable. New phenomena will tend to become more probable through repetition, and experimental observations of them will therefore give quantitatively different results as time goes on. It should be possible to detect the growth of habits by measuring the rate or frequency with which they appear under standardized conditions. If a phenomenon is becoming more habitual, it should tend to arise more easily and with a higher probability as it is repeated again and again.
But how could the idea that nature is habitual ever be established scientifically if it undermines the scientific ideal of exact repeatability? At first sight, this appears to involve a paradox: for if nature is habitual, it will not be possible to study the growth of any particular habit over and over again. However, the growth of habits could be studied again and again with fresh kinds of molecule, crystal, behavioural pattern and so on. The same kinds of experiments could be repeated. And through such repeated experimentation, it could be established whether or not there is a general tendency for new natural phenomena to become more habitual the more often they arise.