Plato
In the fourth century BC, the ancient Greek philosopher Plato declared that there is a world consisting entirely of ideas – he called them forms – which shape everything in our world, albeit imperfectly. Plato likened the relationship between the forms and that which we see around us to the relationship between objects which are located at the entrance to a cave and the shadows that these objects throw onto the wall of the cave that is opposite to the entrance. He maintained that forms are real, and their manifestations in this world resemble them imperfectly, just like the shadows on the cave wall resemble the objects in the opening of the cave. For Plato, forms were pure, eternal and perfect, like nothing on earth. At the basis of Plato’s thinking lies the one to many principle: Where there are a number of objects of the same kind, or sharing a single property, it seems that there must be a single something which is this kind or property. This something exists in an abstract, non-material sense, independently of the objects which share the property. So it was that in his world of forms, there was a perfect chair, of which all the chairs in this world are vague copies. Any properties that these chairs have in common derive from the fact that the perfect chair has these properties. The mere fact that we have no way of knowing for sure what this perfect chair is like does not diminish its power to shape the chairs which we see around us. It is the blueprint, the design which all chairs follow. The concept somehow influences all its instantiations, wherever they are. All behaviour that chairs have in common is simply an expression of that blueprint.
The example of the chair – a human construction, which suggests that there is nothing eternal about it – illustrates a cardinal difficulty of Plato’s approach: Should each property that is shared amongst multiple objects in our world be regarded as being a form, or just some of them? For if it is just some of them, how do you tell which are and which are not? And if it is all of them, then our ability to invent new concepts – for example, an unemployment benefit application – seems to contradict Plato’s assertion that forms are eternal. What is the difference, in principle, between such an application and a chair, or between a chair and concepts such as an electron, of which we believe that all its instantiations are identical? Since Plato, the question as to which meaning we can attach to an observation that a single property is shared amongst multiple objects has remained high on the agenda of philosophers. So much so, in fact, that it has been remarked that all Western philosophy can be regarded as a series of footnotes to Plato.
Occam’s razor
In this paper we shall discuss whether Plato’s assertion that the universe is shaped by Platonic forms is credible, given what modern science can tell us about how the universe works. We shall attempt to establish the credibility by demonstrating that the assertion can be deduced from modern science using Occam’s razor, a heuristic which enables us to choose between two alternative explanations for the same phenomena. This approach enables us to avoid having to itemize all possible explanations, detail the arguments for and against each of them, assess the strengths of each of these arguments and then reach a balanced decision. Any explanation which can be deduced from known facts using Occam’s razor is credible, even though there may be better explanations. Stated briefly, Occam’s razor - a maxim attributed to William of Occam, a 14th century logician and Franciscan friar - asserts that to explain anything, one must not use more entities than necessary. If two factors are sufficient to explain a particular phenomenon, then it would be wrong to use three. The simpler the explanation, the more likely it is to be true. Isaac Newton applied this principle when he formulated his universal law of gravitation: one explanation which accounts for both planetary motions and falling bodies on earth is preferable to separate explanations for these phenomena. Einstein restated the razor as follows: “Everything should be as simple as it is, but not simpler”.
As originally formulated, the razor is somewhat vague. It implies that it’s just a matter of counting entities, and that the nature of an entity doesn’t matter. But of course it does. The more complicated an entity, the less it fits in with the spirit, if not the letter of the razor. For example, to explain that the universe is the way it is because an infinite entity (i.e. God) that also happens to be infinitely complicated created it that way, using powers that we can neither perceive nor comprehend, is to present an explanation that is orders of magnitude more complicated than the phenomena it explains. Information scientists have developed a sharper formulation of the razor, in which each entity is assigned a value according to the amount of information needed to describe it. With this sharper formulation, the God hypothesis fails to qualify for serious consideration.
The example of the God hypothesis reveals something else we should take into account when applying the razor – that to posit something we can neither perceive nor comprehend as all or part of an explanation must not be permitted as a way of making a ‘simpler’ solution, even if it can be described using few words. The Occam playing field is level only if the entities in each explanation have equal claim to being considered real. If an explanation includes things we can neither perceive nor comprehend, the explanation must be expanded to include explanations for these things, until we arrive at an explanation that has the same level of credibility as the competing explanations. To apply the razor, we need to have a workable definition of what we mean when we say that something is real. This is the subject of the next section of this article.
What is reality? – a pragmatic view
The question: “What is reality?” has been the subject of philosophical discussion for as long as there have been philosophers. How can we know whether what we see and think is real, and not just an illusion? How can we know we are not merely dreaming it all? After all, when we are dreaming, we have an illusion of reality. How can we know that that the things that we experience are really “out there”, and not, as in the film “The Matrix” just computer-generated sensory input to our brains? And while we are at it, how can we even know that we exist, and are not simply the subject of someone else’s dreams, or bit patterns in some computer? Unfortunately, it is logically impossible to prove that we are not just patterns of bits in some immensely complicated computer. There is no compelling reason why such a pattern of bits could not experience the illusion of thinking, given a sufficiently sophisticated program. No matter how cleverly we devise a test that will enable us to distinguish between reality and illusion, we can never rule out the existence of an illusion-generating mechanism that would be capable of passing the test and fooling us into calling its illusions real.
That we can’t tell the difference between reality and illusion is actually not such bad news. For if we can’t tell the difference, it doesn’t make a difference. Whether there is actually a universe “out there” or we create our own reality in our minds, whether we are bit patterns in a computer, thoughts in the mind of God or even just dreams in the leaves of a giant plant on the exoplanet Xglttal, makes no difference as to how we should act. Whatever the real situation is makes no difference to either our experience of pain when things go wrong or to our pleasure when things go right. Of course, some day it might lead to bad news, if the nature of reality is such that the future will be radically different from the past. Maybe somebody will turn off the computer, or God will shift his attention to other thoughts, or autumn will set in on Xglttal. Perhaps the day will come when something like this happens, but there is no way in which can meaningfully anticipate such an event. However, we can anticipate that the future will develop from the present, and as far as we can tell, it is extremely likely that this will be the case. That we cannot prove this to be so is entirely irrelevant, given that we cannot even prove that we exist. Whether we like it or not, “extremely likely” – or “utterly credible” - is about the best we can do. That is, unless we appeal to some authority, such as the clarity of our personal intuition or the certainty of some divine revelation, but these authorities carry no weight in scientific discourse.
All this paves the way for a pragmatic concept of reality. Reality, as Philip K. Dick said, consists of those things that don’t go away when you stop believing in them. Those of us who have stubbed their toes on stones which they hadn’t seen until after the event are inclined to expand this definition a little, to include the things that come into existence before you start believing in them. Reality consists of those things that have the capacity to produce an affirmative result when we conduct a test in order to determine whether they are there, even if we don’t believe that they are there when we conduct the test.
How can we know what is real?
This conception of reality makes it possible, at least in principle, to test whether something may safely be considered to be real. Firstly, we must ask ourselves what will change if we stop believing in some phenomenon. If we have no particular reason to believe that the phenomenon will cease to exist when we stop believing in it, then that phenomenon could possibly be real. But we may be deluded. Therefore we must go one step further. We must consider what it is that characterises things that actually do go away when you stop believing in them. What is it that makes for something to be an illusion, or perhaps a delusion? Any phenomenon with those characteristics we must suspect of being “not real”, even if other aspects of it lead us to believe that it will not be affected by our suspension of belief in its existence. We must consider why we have ever reached false conclusions as to the reality of things, and demonstrate that the same causes are not applicable to whatever it is that we claim is real. One source of error lies in our psyches. Once we have convinced ourselves that something exists, it can take inordinately much countervailing evidence to convince us otherwise. Therefore the universality of the belief in the existence of a phenomenon matters, for we know by experience that if we can see something, but nobody else can, then it is quite possible that its existence is dependent on our belief, particularly if there is no compelling reason why others should not be able to see it.
Another source of error lies in our senses. Our senses allow us to perceive and measure. However, our senses often deceive us. Books on psychology are full of examples: lines of the same length which our senses tell us are different, or the other way round; areas of the same colour which our senses tell us are different; even gorillas moving between the players on a basketball court without our senses registering them. We know by logical deduction that if different ways of measuring the same phenomenon produce contradictory results, then, somewhere along the way, our belief systems have led us to interpret at least some of the results incorrectly, and what we mean to see is at least in part an illusion. Conversely, the greater the number of observers, measurements, times and places involved, the greater the diversity between individual instances of these, and the greater the agreement between them, the less reason we have to doubt that the phenomenon is real. That applies even in cases where our senses delude us, because even when one of our senses delude us so consistently that we could be fooled, our other senses don’t join in; delusions do not manifest themselves consistently across all senses. Or maybe they do, but then the maxim applies that if we can’t tell the difference, it doesn’t make a difference. Therefore we may regard the things we collectively and consistently see, hear, taste, smell and feel as real, once we have corrected for such delusions.
A third source of error lies in the way our brains make sense of our observations. When we observe something, we make a model of it in our brains. When you stub your toe on a rock, your brain will probably record the event as a combination of the ideas “toe”, “Pain” and “hard object, possibly a rock”. It is hardly possible to do this without pre-existing conceptions of these ideas. Much of the mental development we go through in our childhood years, starting in the womb, is concerned with developing such conceptions. That process is essentially concerned with developing a model of ourselves and our environment. Our observations cannot be any more correct than the mental models with which we represent them. But these models are the product of our own development, which is different for each of us. For some, this has led to the conclusion that we cannot know what somebody else means when he says that he has stubbed his toe on a rock, because we cannot access his brain. Whether or not this is true is not relevant to our conception of reality, because we may, by a process of asking him to tell us what he means, come as close as we wish to the assurance that he means the same things. We may therefore conclude that shared mental models embody conceptions of reality.
Of course, even shared conceptions can be false. A mental model is a human construction. It comes into existence when somebody invents them and stops when the last person to think them dies. They may correspond to something real, in the way that the word – or, to use Plato’s terminology, the form – ‘rose’ corresponds to a flower having the particular characteristics which we associate with roses. Or they may not, for example the form ‘unicorn’. If any reality lies behind such forms, it does not come into existence when we start thinking them or go away when we stop. Whether we believe in unicorns or not has no effect on the number of unicorns on our planet. But is there then any essential difference between roses and unicorns? The answer, fortunately, is “Yes”. The form “rose” has predictive powers. For example, it tells us that if we have a plant which produces a rose, then all other flowers on the same plant will also have the characteristics which we ascribe to roses. Because these predictions are successfully confirmed, not only by ourselves but also by other agents at other times and places, we may be confident that there is something which we call a rose. The same does not apply to the unicorn; we have no record of this form ever having led to any confirmed prediction. Some models cannot even be used to make predictions: conspiracy theories, in which any stray fact is taken as proof of the conspiracy, and any normal fact as proof of the lengths to which the conspirators go in order to prevent us from discerning their conspiracy, are a case in point.
That predictions are confirmed is never a proof of the mental model. For example, the motions of stars and planets were successfully predicted by the Ptolemaic system for more than a thousand years. In the Ptolemaic system, the sun, stars and planets all revolve around the earth, and a system which employed circular epicycles to modify the planetary orbits and varying planetary speeds along the epicycles predicted the observed motions well enough. It predicted them better, in fact, than the heliocentric model of Copernicus; it was only when Kepler introduced elliptical orbits that the heliocentric view of the solar system improved on the accuracy of the Ptolemaic system. That a model works does not prove it to be true, but is a strong indication that there is an underlying order in the phenomena of which it is a model. No order and regularity can be sustained across all places and times without some underlying cause. The Ptolemaic system is an example of a contrived model: it was good at explaining the observations on which it was based, but never successfully predicted the results of new methods of observation. In order to fit the results of more accurate measurements, the Ptolemaic model always needed to be elaborated. We must be ware of such models, because they tell us more about our ability to contrive models than of the reality which they purport to represent. We must also be careful about confirmed predictions. Sometimes we see what we expect to see, even if that which we are observing is different. For example, there is a notorious experiment in which American whites were shown a film in which a dark-skinned man was attacked by a white man and were then asked who started the fighting. The vast majority said that the dark-skinned man started it.
Some such mental models never spread further than a small group, because different people expect to see different things. But history is strewn with models which have built on shared expectations in such a way as to have fooled all of the people some of the time. Although shared conceptions are more likely to be free of individual delusions, they can create delusions of their own. Given that the world's religions differ so much that at most one of them can be right, all of them, except perhaps one, produce collective delusions. These delusions can persist because the religions include collective taboos on asking those questions which, if properly addressed, would initiate a process in which the religion would be unmasked. Only a belief system which has no taboos can claim to be free of delusions.
Science aims to be such a belief system. It is a systematic approach to understanding the universe by means of testable explanations and predictions. It is carried out by a worldwide community of scientists, within which there is such a diversity of cultures and thought systems that biases to which an individual scientist may be prone are likely to be challenged by others. Test results that cannot be reproduced are rejected.
However, as the history of science demonstrates, even scientists are subject to collective delusions, which get in the way of them seeing things as they really are. Fortunately, there is one class of models for which we need have little concern that the expectations of scientists affect what they see: the models that make seemingly absurd predictions. Nobody expects absurd results, so it is extremely unlikely that observations that confirm them are in any way influenced by our expectations. Such models are, arguably, the closest we can get to the truth.
Quantum mechanics
The theory of Quantum Mechanics fits the bill of making absurd predictions. It was developed early in the twentieth century in order to explain how matter and energy behave at the level of the very small. In particular, it describes how matter and energy can behave both as waves and as particles. Photons, electrons, atoms, even complicated molecules all behave exactly as Quantum Mechanics predicts. It is valid not only for single particles, but also for combinations of particles – physicists call them quantum systems - which interact with each other. All its predictions – even the seemingly absurd – have turned out to be valid. There is no scientifically documented evidence that appears to contradict the theory. It is the most accurate and reliable theory ever devised by science. In other words, of all scientific theories it is the one for which we have the least cause to doubt the reality of the picture it paints of our universe.
The wave behaviour of matter is intimately related to the particle behaviour. One way of summing up this relationship is to state: Waves let us see all the states in which the corresponding particles can possibly be, in the measure that they can be in each of these states. The mathematical representation of the wave behaviour of a quantum system is known as its wave function. The wave function describes, firstly, how the particles will affect the environment of the quantum system if it remains unmeasured and secondly, how great the probability is that a property of one of its particles will take on a particular value when measured. It is the first of these two aspects which plays the greatest role in shaping our world. For example, the hydrogen atoms in a water molecule are positioned at an angle of 108 degrees from each other, as seen from the oxygen nucleus, due to some very particular properties of the wave functions which define the hydrogen-oxygen bonds. That results in water having some very peculiar properties, including the property that its solid form – ice – is less dense than the liquid form and therefore floats on it. Even the mere stability of water molecules is due to the wave function of the electrons which the hydrogen atoms share with the oxygen atom: in this wave function the electrons are as much as near the oxygen atom as the hydrogen atom.
The wave function as such is merely a description, and will cease to exist when no one believes in it. But the phenomenon that the wave function represents satisfies our test of being real: it doesn’t go away when we stop believing in it. In the case of a water molecule, the hydrogen-oxygen bonds, as described by their wave functions, exist regardless of us. Water is still water, with all the peculiar properties that the angle of 108 degrees entails, whether we look at it or not. The wave which the wave function represents is real, regardless of whether the wave function is.
This discussion about the reality of waves does not fit well with traditional interpretations of Quantum Mechanics, for it violates Bohr’s taboo. Niels Bohr, one of the founders of Quantum Mechanics, forbade his students to even think about the reality of the objects which were described by wave functions. The mathematics always yielded correct results, whereas thinking in terms of something being “really there” invariably led to confusion. Bohr is quoted as saying that if you weren’t confused by Quantum Mechanics, then you hadn’t understood it. In the context of Bohr’s conception of reality – something is real if it exists in space-time – he was right. A particle which is governed by a wave is not “there” anywhere; all we can say is the value of the wave at any particular point in space-time is a number of the form a + bi, where i is the square root of minus 1, also known as the imaginary number. At points where a is zero, the particle is not present at all, but it is still capable of influencing particles in its environment. That makes it real according to our concept of reality. Phenomena are real for us if we can, in principle, set up an experiment which will have one result if the phenomenon has no existence and another if it does, regardless of the expectations of the experimenter. The imaginary components of the complex numbers involved with waves can and do affect the predicted outcomes of experiments. And the fact that the mathematics of wave functions works leads us to conclude that there is an underlying reality to them.
Why does quantum mechanics work?
The simplest explanation of the fact that the model works is that this behaviour is entirely attributable to the phenomena it describes, just as an image in a mirror is entirely attributable to that which it reflects. Because there is some sort of order and predictability intrinsically present in these phenomena, it is possible to make a model of them that works. But making or changing the model will not change the phenomena. This explanation assumes that all behaviour of real phenomena is intrinsic to those phenomena, that there is nothing external to them which is pulling the strings. In other words, everything that exists knows how to behave, all by itself, and needs nothing outside of itself to tell it what to do in particular circumstances, just like a ball ‘knows’ how to roll downhill and needs nothing external to it to tell it how to do so. The ‘intrinsic behaviour’- assumption indicates, for example, that whenever an electron comes into existence, it is created with inbuilt knowledge as to how it should respond to electromagnetic fields and to gravitation. It also has inbuilt knowledge as to how much energy should be released, should it ever revert to energy.
Plato would have disagreed with this ‘intrinsic behaviour assumption’. The Platonic viewpoint is that concepts exist in the world of forms and influence all concretisations of themselves in our universe. For example, the concept “electron” is more than just a model, but something which exists of itself and is somehow capable of influencing the behaviour of electrons.
Before we accept or reject the “intrinsic behaviour assumption”, it is important to understand how the choice matters. Suppose it turns out that there is no particular reason to assume the intrinsic behaviour assumption, but also no particular reason to reject it: what then? The application of Occam’s razor to this question leads us to conclude that if we have no particular reason to reject the intrinsic behaviour assumption, we should accept it, because to include something additional to the basic building blocks in our explanation of how the world works would be to add an entity unnecessarily. The Platonic explanation is more complicated than this assumption. If we do have reasons to prefer not to accept the assumption – such as an intuition that it can’t be right – we should at least accept it as a possibility that we can’t rule out.
Are waves and particles two manifestations of the same thing?
Modern physics is built on the assumption that waves and particles are just two sides of the same coin. A particle, or anything else for that matter, is also a wave, and vice-versa. Much of the intellectual effort which led to Quantum Mechanics was focussed on understanding how the particle and the wave can be two aspects of the same thing. Centuries of scientific controversy raged over questions such as: “Does light consist of waves or of particles?”, before Quantum Mechanics enabled us to appreciate that is both the one and the other. Whenever a wave changes, the corresponding particle changes with it, and whenever a property of a particle takes on a particular value – for example, as the result of a measurement – the wave changes accordingly.
For the purposes of this article, we shall ask the reverse question: how can waves and particles exist differently? Why is there not a one to one relationship between elementary waves and elementary particles? For there are elementary waves which correspond to multiple elementary particles, in such a way that whenever the wave changes, all of the particles do, wherever they may be at the time – even if that is on the other side of the universe. This insight may be attributed, in a backhand way, to Einstein. Einstein set out to demolish Quantum Mechanics, not to improve our understanding of it. He opposed the theory, because he thought that it amounted to saying, as he put it, that God played dice.
In order to demonstrate that Quantum Mechanics must be wrong, Einstein, together with fellow scientists Podolsky and Rosen, postulated a thought experiment. In this experiment, two elementary particles arise from the same event and then go their separate ways. Because of this common origin, they are, as the quantum physics pioneer Erwin Schrödinger put it, entangled: any measurement of the first particle also tells us something about the second particle. When particles are entangled, it no longer makes sense to talk about separate wave functions for each particle. Rather, there is a single wave function which describes how they both behave. For example, under the law of conservation of momentum, whatever the speed and direction of the first particle, the second particle must have the same speed and exactly the opposite direction. Suppose now that the speed and direction of the second particle is measured; then the first particle is effectively measured too. Whatever the measurement, the first particle instantaneously takes on the measured speed and the opposite of the measured direction, wherever it happens to be at the time, even if that is the other end of the universe. Einstein concluded that this amounted to instantaneous action at a distance, faster than the speed of light, and was therefore absurd.
In the last thirty years or so scientists have carried out ingenious experiments in order to test whether entanglement actually occurs. In each of them, it was demonstrated that Einstein was wrong. In 2015 scientists at the university of Delft conducted an experiment which is now accepted as the definitive proof that entanglement occurs. The instantaneous – Einstein called it spooky! – action at a distance that he predicted to be a consequence of Quantum Mechanics really occurs! In fact, it has been demonstrated to be effective over distances of four hundred kilometres, and there is no particular reason to think that it is in any way limited by distance. It is a consequence of Quantum Mechanics that whenever particles are entangled in this way, there is just one wave, even though there are two particles. We know that when the measurement causes a particle to change, the wave changes with it. So what is happening can best be understood as follows: the first particle changes, which is reflected in the wave, and the change in the wave causes the change in the second particle. Any other explanation, for example that the first particle somehow interacts with the second particle, would involve the introduction of a new mechanism in addition to those that we know. Therefore, by applying the razor we may conclude that somehow the wave reaches out to the unmeasured particle and dictates its behaviour, however far this particle happens to be from the measured one. In other words, the unmeasured particle exhibits behaviour which is not intrinsic to it; the wave is pulling, so to speak, on the strings.
Note that modern science has no explanation as to how this pulling on strings occurs. It predicts that it occurs, because that is a consequence of the theory of Quantum Mechanics. And the behaviour has been experimentally verified. But there is no explanation as to how instantaneous information exchange between the wave and the particle is carried out. Indeed, not even string theory [no pun intended] purports to explain this. That we cannot explain observed phenomena, makes them more credible, not less, because they are less likely to be a product of shared illusions.
Consequences
The fact that entanglement exists should make us cautious in deciding that something is purely a description, and therefore unreal. The relationship between waves and particles appears to be something like the relationship between the computer system which is used to automatically control and direct train movements on a model railway and the model railway itself: changes in the positions of the actual trains are reflected in the system, and commands issued by the system affect the behaviour of the trains, wherever they are. The computer system is more than a model which merely describes the reality of the model railway, it is part of that reality, and the behaviour of the model railway cannot be understood without considering the behaviour of the computer system. Once we admit that it is possible for a wave to affect a particle, wherever it is, where do we stop? To start off with, Occam’s razor dictates that we should apply this insight to all wave-particle duality. For if we were to declare that this action-at-a-distance behaviour was limited to only entangled quantum systems, we would be obliged to find reasons why waves act so differently in those systems than in non-entangled ones. Such an explanation would require more entities. It is just simpler to conclude that waves and particles are distinct entities, and that waves have the ability to influence the behaviour of particles, wherever the particles happen to be, and whether or not these particles are entangled. And conversely, of course: a particle influences any wave of which it is a part. Entanglement is a two way street.
But there is no particular reason to stop there. It is the mark of a churlish mind to limit the impact of new ideas to only those phenomena that absolutely require these ideas in order to be accounted for, and ignore all the phenomena for which we already can account for by other means. For many of the phenomena for which we already have an explanation could possibly be accounted for more simply if the new ideas are also applied to them. One phenomenon which allows for a different explanation is the fact that each and every electron is identical to every other electron in its behaviour, however and wherever it was formed. This could be explained by the hypothesis that the form “electron” exists independently of any actual electrons, and manifests itself in these electrons in the same way that a wave manifests itself in the particles to which it is tied. For if waves can pull the strings of particles wherever these particles happen to be, why can there not be a Platonic form “electron” which pulls at the strings of matter whenever an electron is created and whenever an electron is destroyed? In the current state of physics, Occam’s razor dictates that we accept the hypothesis, because it requires less entities to explain the same set of observations than the assumption that concepts such as “electron” are merely descriptions, with other factors dictating that the many processes by means of which electrons are created happen to have identical outcomes.
That need not always be so: if we knew the mechanism by means of which waves affect particles instantaneously regardless of distance, and there were reasons to expect that this mechanism was not applicable to interactions between Platonic forms and their manifestations, we would be justified in dismissing the hypothesis. But for the present, that option is not on the table. Occam’s razor does not demand that we understand how the entities that we invoke work, but only that we understand that they work. Newton did not understand how gravity works when he formulated his law of universal gravitation. In fact, he had profound reservations about it, which he expressed as follows: "That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it". Fortunately, he nevertheless applied the razor and published the law.
Before we explore the hypothesis that the Platonic form “electron” dictates the behaviour of electrons further, we must address the question as to whether this is a valid application of Occam’s razor. For if we invoke the razor in this way, what is to prevent us from taking two entirely separate phenomena and invoke the razor to suggest that they are actually the same phenomenon? We could, for example, hypothesize that Albert Einstein and Niels Bohr were actually one and the same person, and thereby arrive at an account of twentieth century physics that requires one less entity than the hypothesis that they were distinct persons. Is there any reason why Occam’s razor should not be applied to this hypothesis, whilst it should be applied to the hypothesis that waves and Platonic forms are basically the same type of phenomenon? Of course there is! The hypothesis that Albert Einstein and Niels Bohr were really one and the same person fails the test within Occam’s razor that determines which hypotheses may be compared with each other: it does not account for all the facts. The hypothesis cannot account for the occasions in which they were seen together, whereas the idea that they were distinct persons can. No hypothesis which is known not to be able to account for the facts can be preferred on the basis of the razor. For the present, we have no particular reason to believe that our hypothesis that waves and forms such as “electron” are basically the same type of phenomenon cannot account for the facts. We shall have to examine this idea in more detail, and see whether we encounter such difficulties. The hypothesis may come across as a big leap in the dark, but we won’t know whether it is we were justified in making the leap until we land somewhere. While we are at it, we shall expand the hypothesis to include natural laws. The observation that all electrons are alike is in principle no different to the observation that E = mc2 or to any other natural law which manifests itself, so there is no particular reason to affirm the one and deny the other. To do so would be to ignore the razor.
Limits to intuition
The sheer difficulty of imagining how a Platonic form can manifest itself has led linguistic philosophers such as Wittgenstein to reject the notion, and affirm instead that the relation between concepts and manifestations is an illusion that we invent in our own heads. Although this viewpoint is counter-intuitive, it must be admitted that past generations for the most part were wrong about many of the relations which they believed to exist between concepts and their manifestations, and there is no particular reason to believe that we are much better. Certainly, some connections we make between concepts and their manifestations are illusions. However, some such ‘illusions’ are so persistent, consistent, pervasive and complex that it is even more difficult to believe that we have created them than that they exist of themselves. Surely we are not that clever. And in any event, there is a difference between the concepts which exist in our minds and Platonic forms which exist of themselves, and it is with the latter which we are concerned here. It is even more difficult to believe that we have created an illusion as complicated and improbable as Quantum Mechanics. The same intuitive problems we have with Platonic forms which manifest themselves apply equally well to Quantum Mechanics. It is hardly consistent to reject the one and accept the other. We must accept that our intuitions as to how the universe could reasonably be ordered are prejudices, and be prepared to set them aside.
Non-spatiality
Platonic forms are not confined to space and time, but exist independently of them and are expressed in them. For example, the Platonic form “E = mc2” is, as far as we can tell, capable of manifesting itself in all places and at all times. However, we are inclined to think of waves as entities existing in, and confined to space and time. If our inclination is correct, our application of the razor to hypothesize that waves and Platonic forms are basically the same type of phenomenon would be invalid. We must therefore consider how waves relate to space and time. The question: “Does a wave have a location?” sounds silly, because waves are always concerned with the behaviour of particles in space and time. But this question is different to the question as to whether waves affect things in space and time. Given that the wave of two entangled particles cannot be co-located with both of the particles at the same time, it is just simpler to assume that a wave itself has no location in space, but interacts with it. In other words, a wave is expressed in space, but is itself not located anywhere in space. That which we perceive as change is the result of the juxtaposition of distinct parts of the wave, which are expressed in different times.
Note that non-spatiality and atemporality are in principle independent characteristics. One can affirm the one and deny the other. Plato may not be right about the eternity of forms. Quantum waves express themselves across the entire universe, but unless the universe has always existed they have a beginning in time, and they will possibly cease to affect the universe at some time in the future.
Strictly speaking, we could draw the line between those concepts which are waves and those which are only our own mental constructions more or less as discussed above: elementary particles and natural laws are also waves, and all other concepts are not. But that would be a pity, for then concepts like beauty, love and you and I have no real existence either. What does the razor have to say about the status of such concepts? In order to discuss this question, we first examine what Quantum Mechanics can tell us about which waves exist and which don’t.
Resonance
Plato, as we have noted, could not tell us why some forms existed and others did not. Why should there be a Platonic form for the concept “beauty” but not for the concept “unemployment benefit application”? In this respect, we can take Plato a step further, using Quantum Mechanics. For one of the key consequences of Quantum Mechanics is that not all waves which are conceivable actually exist: only those waves that resonate do. It is exactly the same as the waves on a plucked string on a violin or a guitar: only those waves exist on the string for which the length of the string is a whole multiple of the length of the wave. Niels Bohr used this fact to calculate which electron waves can exist around atomic nuclei. His approach predicts perfectly why atoms and molecules are as they are. If, as we have hypothesized, Platonic forms are of the same nature as waves, then Occam’s razor leads to the further hypothesis that all Platonic forms resonate. The thoughts that we conceive are not subject to this constraint, and we should therefore not expect them to exhibit the same behaviour as Platonic forms. In this matter, both Wittgenstein – who maintained that concepts are human constructions and should not be treated as having any reality of their own – and Plato, who maintained that forms were the ultimate reality, are both right, but they were talking about different things.
The concept of resonance gives us some clues as to whether ideas such as beauty, truth, you the reader and myself, the author, exist as Platonic forms. The question to ask is: do these ideas exist as an identifiable set of elementary waves, which interact together in such a way that they resonate together, so that the whole is qualitatively more than the sum of the elementary waves? I am inclined to answer this question in the affirmative. You may make your own choice. Note that whether they are or they aren’t makes no difference to the argument line of this article.
The calculus of Platonic forms
The hypothesis that Platonic forms and quantum mechanical waves are the same type of phenomenon has profound consequences. To start off with, the mere fact that a Platonic form resonates does not mean that its negation resonates, any more than the negation of a wave resonates. In other words, the negation of a Platonic form is not necessarily a Platonic form too. If there is a ‘horse’ form, which includes in it all the similarities of physical form and genetic codes that characterise horses, it does not follow that ‘not horse’ is also a form. By extension, rules of logic which are valid for Platonic forms are not necessarily valid for their negations. We need to examine all our logical arguments in order to decide whether they depend on the actual existence of negations, and revise those that do so.
One example of where this thinking could lead us is concerned with Russell’s paradox, in which mathematical reasoning appears to break down. This breakdown can be illustrated with the example of Jacques, a barber living in a French mountain village. Jacques shaves each man in the village if and only if he does not shave himself. Now the question is: Does Jacques shave himself? Think about it - if he does, he doesn’t, and if he doesn’t, he does. We must conclude that the statement “Jacques shaves each man in the village if and only if he does not shave himself” contains contradictions. For mathematicians this is very disturbing, for how can we be sure that other lines of mathematical reasoning do not somehow contain contradictions as well? Yet, despite their best efforts, they have found no simple way to categorically exclude them. By applying the notion that the rules of logic are consistent and sound only when applied to concept that exist of themselves, we may conclude that the statement about Jacques implies the actual existence of a negation and is therefore unsound. It is therefore no surprise that it involves a contradiction.
Applying this line of thinking further leads us to the conclusion that the difference between two Platonic forms is not necessarily a Platonic form, just as the difference between two waves is necessarily a wave. However, the joining of two Platonic forms automatically is a Platonic form, because it corresponds to the quantum system in which the quantum systems pertaining to the original Platonic forms are combined. Although the difference between two Platonic forms has no meaning, it is possible for a single Platonic forms to be split up into many, in other words to differentiate. Let us examine, by way of example, the relationship between the concept of electron and the natural law E = mc2. One possibility for this relationship is that it is indirect, that is to say that both Platonic forms operate directly on the world of particles and affect each other only indirectly. Another possibility is that E = mc2 operates on the Platonic forms corresponding to the electron and other particles in order to affect their behaviour, and these Platonic forms in their turn operate on the corresponding particles in the universe. If it is at all possible for waves to affect each other, the razor leads us to prefer the second possibility, because it involves fewer interactions.
It is important to note that addition and differentiation do not destroy the original Platonic forms, but create new Platonic forms in addition to them. For example, let us consider an Einstein-Podolsky-Rosen experiment in which two particles – let’s call them A and B – each go their separate ways, and then particle A spontaneously splits up into two new particles, A1 and A2. Then these A1 and A2 are themselves governed by a new wave, which exists alongside the A-and-B wave but does not replace it. Any change to the A1-and-A2 wave – for example, by means of a measurement of one of the particles it governs - will result in a change to the A-and-B wave, and any change to the A-and-B wave will affect the A1-and-A2 wave. It has been observed in experiments that entanglement works just as well in this second hand way as when particles are directly entangled.
The ultimate wave
In Quantum Mechanics, waves join together to produce a whole which more often than not is different to the sum of the parts. Whenever two quantum systems interact, the resulting wave contains, in addition to the possibilities of the original waves it, possibilities that arise from the combination (and sometimes, when the wave function collapses, less possibilities as well). In consequence, the new wave will not revert to two simpler quantum systems unless the natural progression of the wave towards lower energies leads to this result. That happens sometimes, but mostly the result of the joining is that the two systems are so tangled that they never separate. It’s like throwing two ropes together: mostly they will end up tangled together, because there are many more states of the ropes which are possible only in the combination than there are states which can exist without the ropes being put together. The rules which govern the joining and separation of waves make it far easier for waves to come together than to separate. That implies that even if at some stage in the journey from ultimate causes to ultimate effects all waves were separate, there will be a stage in this journey in which they will have all joined together. In other words, all waves will have joined together in one great super wave, which is composed of all waves and is greater than any of them.
Aggregation or differentiation
That the ultimate wave would have arisen if all Platonic forms were initially separate and then joined together does not mean that this is the only way things could have happened. It is also possible that the ultimate wave was originally a unity and came to consist of conjoined Platonic forms by means of a process of differentiation. Applying Occam’s razor to the choice between these two options leads us to prefer the differentiation hypothesis, because this requires only a few entities – one for the original Platonic form, and one for each differentiation mechanism - whereas the aggregation hypothesis requires an entity for each original Platonic form, and those are very diverse and very many. Given that aggregation and differentiation both occur in the ultimate wave, then the ultimate wave encompasses changes back and forth. Perhaps this involves a process in which these changes resonate in order to produce a stable ultimate wave. Looked at this way, not just the individual Platonic forms resonate, but also their combination, although the resonance of the whole is of an entirely different order. If that is so, then no Platonic forms can exist which do not harmonize with all the others.
Conclusions
We have shown that the simplest account for everything in the universe and all the concepts and natural laws that govern the behaviour of these things, is the QO explanation: This all originated from a single quantum wave by means of established quantum mechanical processes. At the level in which we have discussed it, this explanation requires only the adoption of something already observed to domains in which we hadn't looked for it. In contrast, the big bang theory requires a giant step of faith, namely that there somehow, sometime arose, out of nothing, something denser than anything ever observed, containing all the mass-energy of the universe. That doesn’t make QO true, but does mean that, of all the theories and explanations available to us, including those of mainstream science, it is the explanation to which we should be devoting the most investigative attention. It may well be that, during the course of this investigation, we encounter phenomena that categorically cannot be accounted for in QO terms, but we won’t know that until we try. In any event, there is a long road to go before we encounter steps of faith as daunting as those that the big bang theory confronts us with.