The ‘universe’ being described here is not all of existence, but rather of that we directly observe: the universe of phenomena. The doctrine draws both on the association of physis with motion (Heracleitus), and on the idea of the mind as the active interpreter of an indefinite and ever-changing reality (Protagoras):

Thus, an act of perception of, say, a white thing, involves two types of motion, one fast and one slow. When the eyes and the thing come within range of one another, vision from the eyes and whiteness from the thing pass quickly in the space between. Vision from the eyes denotes a kind of light-physis which streams from the eye. As Plato explicates in his Timaeus, particles streaming from the thing meet and adjust themselves to vision-particles streaming from the eyes to create sensation. Sight is created in the eye while whiteness ‘saturates’ the object seen.

The eye perceives whiteness and the object whitens, both relatively slowly; the process never fully completes. And this is true of all sense perception.

The perceived world, the world of phenomena, is one of Becoming in two senses. Firstly everything we perceive is always changing position and qualities, or growing and dying. Secondly, and less obviously, perception itself is a continuing, always incomplete, process. We can now interpret the latter sense of Becoming to be the nervous system impressing its interpretations on a continually changing flux of input data.

This is an example of the prescience of great minds. Of course, we cannot be surprised that physical details of Plato’s description of vision are wrong (as did Plato who presented it merely as a likely story,--like his other likely story in the Timaeus,--and even avoided claiming its invention), but this is not important. What is important and amazing is that in critical respects, it is so close to scientific truth.

The processes he imagined taking place in the space between the eye and what it observes, actually take place instead along the visual tract between the eye and the cortex. Instead of streaming particles in space, there are streaming electrochemical signals moving in both directions along neurons. In an interaction mediated by the neuronal circuitry, they create the signals which constitute the basic elements of sense perception. The essential and essentially correct points are: (i) the active role played by the observer, (ii) the fact that this role must manifest itself through physical interactions somewhere along the path to the seat of perception, (iii) the understanding that there are short and long time components involved, (iv) the fact that properties we perceive pre-exists within the mind.

Plato’s perception of perception forms the basis upon which his vision of existence rests. He provides a poetic form of this vision in his parable of the Cave. He will lead out--e-duco in latin–literally, educate, the reader out of mental darkness, to light; out of the world of Becoming to that of Being. Behold! Open your mind, our guide urges us.

The prisoners (of their bodies and naivete) see flickering shadows. The walls of the cave are like the screen we often imagine is in our brain upon which an image of reality is being projected. Not only do the images flicker because of the light source, but they also vary because the shadows move along an irregular rock wall. The prisoners cannot even see each other directly: they see only their own shadows, or the shadows of one another.

In Plato’s theory, perceptions are creations of interacting vision streams emanating from our eyes and of light streaming from the universe really… motion and nothing else; so also in his parable, shadows on cave walls are creations of light streaming from the fire interacting with both objects and the cave wall. Shadows may be said to exist, but clearly, they possess only a secondary sort of reality; so also our direct, sensual perceptions. And because of the flickering, neither type of images–shadows or sensual perceptions--are every quite definite.

Thus, sensual perception is the lowest level of cognition, and constitute what the uneducated take to be reality. Even more so since the objects whose shadows are being seen are themselves of inferior reality.

Artificial means made by man, and art, but not by nature. Artificial things are real but, in the sense of art meant here, also of an imitative, and hence reduced level of reality. (There is another sense in which great art provides us with a heightened form of reality.)

Thus people mentally operating at the level of taking shadows of these objects as natural, are doubly misled. They are like watchers of television who get so involved in the images on the screen that they forget they are merely watching images. And even when they remember, they forget the artificiality of the scripts. Typically, both they and actors, confuse the emotions and characters portrayed with those of real people.

Next, the first effects of education:

The prisoner, still in the land of Becoming, sees the more-real objects whose shadows he and his fellows had mistaken for reality. Not only can he not even name what he now sees, he doubts their reality. Thus do we find that even first insights--that the earth rotates on its axis and travels around the sun, that disease may be due to invisible organisms, that we should therefore wash before delivering babies, that we are largely driven by unconscious needs, that our motivations are quite often not what we think they are, that color is created within us and not a primary attribute of objects,…, perceptions obtained not directly by the senses but indirectly by looking into things, beyond surface appearances–are regularly ridiculed as unreal by the ‘hard-headed realists’ amongst us who believe only what is in front of their eyes.

Plato now addresses himself to those for whom there is a world beyond the cave within which the body’s senses confine us, a world beyond the material and its uncertain appearances. With further education, our bedazzled and suffering student ascends further:

He has been dragged—as students often must be--up and out of the cave of the senses within which we are physically bound. He accustoms himself to the brilliantly sunlit world by first making out simple shadows and reflections. These are the images studied by mathematics. They are images or shadows of more real forms to be discussed.

The objects of mathematical thought known to Plato, were perfect lines and exact quantity (in Geometry), and exact numbers (in Arithmetic). These are well-defined: a mathematical line is, whereas a physical line is not. It is merely becoming. When inspected, its indefinite nature, its state of becoming, becomes apparent. If we try to measure its length, the quest for precision is a never ending, its length is always becoming more precise. Even staring hard at it to more precisely determine a reading, its image shifts about; it always seems to be becoming something slightly different. We must impose definiteness upon it in order to think about it: we must take it from the land of Becoming to that of Being.

A physical measurement of a continuous quantity always does impose a definite numerical value on that quantity. A piece of wood may be measured to be 7 9/16 inches long, a certain rational number of inches, but it is really no such thing for a whole host of reasons: our eye can compare it with the ruler only with a certain precision, the ruler is constructed with limited precision, thermal motion of atoms means that sizes of all objects composed of them are in a constant flux, and finally, the size physics attributes to elementary particles is partly defined by convention.

The mathematical line is definite, but in what sense does it exist? Mathematical thought fits the sensible world into a rigid form, an axiomatic structure, and then reasons by deduction from axioms to theorems. The Pythagorean theorem, for example, fits indefinite images, projected as it were onto the rough cave walls of sensation, to definite right triangles and the constructions and axioms of geometry. Only after thus fixing the indefinite to the definite can logical thought be used.

Having accustomed his eyes by first contemplating mathematical forms, the former prisoner is better able to see the forms of which they are shadows and reflections. Mathematical forms, according to this analogy, do not represent the fullness of real forms; they are mere outlines, simplified shells of reality, like shadows of three-dimensional objects. This is a narrow vision of mathematics albeit fully justified by its relatively primitive state during Plato’s era and by the concept of physical experiment was yet unborn. To have gotten beyond this formidable limitation would have required a Pythagorean level of mysticism

Plato then completes his analogy as follows:

The Sun outside of the cave is to the fire within the cave as the Sun of the Intelligible world is to the (actual) Sun of the Visible world. The Sun of the Intelligible world is that principle which binds everything together in its light, which makes everything ultimately intelligible.

In the context of ordering one’s life and that of the state, which is the subject of the Republic, the sovereign in the intelligible world is the Good. It is the principle of Morality. In the context of mathematics, the sun stands for the One, the source of all number. The sovereign is a single form appearing differently in different contexts.

What the essential Form of Goodness actually is, Plato does not reveal. Indeed, he tells us that, like the sun itself, it is to be perceived and only with great difficulty, which suggests that a verbal description may not even be possible, that the Good is beyond mere words, that it is something to be experienced only through contemplation.

The person who has achieved a sense of The Good,

Here Plato evaluates imagination and belief, the types of thinking relevant to the visible world. They lead to visible worldly success. Thus, for example, having the best memory for the order in which good and services followed or accompanied one another so that he could make a good guess as to which was going to come next, thus knowing how their prices will rise and fall, normally leads to success in business. Knowing how opinions rise and fall does the same for politics.

Would our released prisoner be likely to covet those prizes or to envy the men exalted to honour and power in the Cave? Would he not feel like Homer’s Achilles, that he would far sooner ‘be on earth as a hired servant in the house of a landless man’ or endure anything rather than go back to his old beliefs and live in the old way?

Thus the philosopher’s vision of a higher calling in life, of a nobility of purpose. But this is not how most people judge things.

Plato’s Line, shown in Fig.1, is his attempt to construct an outline of the same basic structure of existence as that discovered by the prisoner as he was freed by education from the Cave. It outlines how Becoming relates to Being, and what modes of cognition are applicable to each. Thus we see a world of higher reality, that of ‘Intelligible Being’, and one of lesser reality, that of ‘Visible Becoming’. Its parts comprise the left column of Fig. 1, and the types of cognition required to apprehend them, labeled , A,B,C,D, are to the right.

Optical illusions illustrate the indefinite nature of Becoming.

Fig. 1 requires the brain to consciously decide on the interpretation of the three-dimensional orientation of the cube. In the perception of a real cube, this decision is made unconsciously by the visual system on the basis of other clues presented to it. But this artificial figure has no other clues, and is therefore ambiguous. We force a three dimensional interpretation on it that is unstable; one perception of the figure can switch at any time to its alternate! This is an extreme example of a perception always in a state of Becoming.

The scale dependence of perception illustrates another uncertainty of Becoming.

Fig.2 symbolizes another property of perception: people commonly say that all real lines are imperfect. By real lines, they generally mean features of physical objects (like edges) perceived as lines. But an apparently smooth lines on magnification always becomes irregular. Further magnification reveals that a physical line has no continuity at all because (1) it is an assemblage of discrete particles (e.g.atoms), (2) the data input to the eye comes in discrete packets of light quanta, (3) the data is received and transmitted discretely in time by discrete retinal photocells. Any continuity and regularity we perceive is therefore unconsciously impressed upon the actual data by the visual system.

We perceive a straight line segment only when our visual system unconsciously ‘fits’ data to a preconceived template: an ideal form already with us. Until the fit is achieved, we are uncertain as to what is being perceived. In fact, as we magnify a physical line perceived to be straight or smooth, and see something else, we are not seeing something ‘more real’, but only fitting the incoming visual data with another template!

One cannot be certain of or have certain knowledge of anything in the world of Becoming: anything that is itself uncertain, that is changeable, always becoming something else. The world of Becoming is larger than it may at first seem for observation can be made with multiple views: afar, close in, microscopically, sub-atomically, over a second, a day, a lifetime, and over an aeon.

For example, a civilization’s life, viewed over billions of seconds and meters, appears like a bloom of algae; over billionths of seconds and meters it appears as a loosely correlated motion of molecules. At both extremes the concept of a civilization loses the properties normally attributed to it. What then is a civilization, really? Is it what is observed? But that is no one thing. Similarly, are humans really just complexes of elementary particles, just machines; is consciousness real; is the animate really different from the inanimate; is there a reality, or is it just what we, individually or socially, make of it?

Plato points out, in effect, that these concepts themselves–humans, civilization, life,…,reality–are (or can be made) definite whereas the observations leading to them are always changeable and hence indefinite. Concepts, ideas, …., forms, are (or can be), whereas observations are always becoming.

Forms inhabit the world of Being, and, as the Line indicates, they are concepts that are or can be objects of clear thought. We may be unclear about a Form, but not by necessity (as with direct perceptions), for we can always clarify their meaning. The process of clarification, one of the meanings given to the term ‘dialetic’, involves explanation in terms of more basic Forms. In this way, dialectic can leads to ever more basic Forms.

A number of words are often used in place of Form--idea, concept, kind,…and so on--each for its own emphasis. But for general use, Form has the advantage of not being associated with the aura of unreality that our materialist world confers upon mental constructs. For most people, a ‘real’ chair, directly perceived by the senses, is ‘more real’ than the concept of chair–all direct sense perceptions are judged to be more real than concepts–whereas for Plato, just the reverse is true. It is especially when we want to keep this in mind, that the word Form should be used.

Serendiptitiously perhaps, forms and templates are similar material objects and as a result, the relationship between perception and reduction that is being developed here, allows them to be partially identified with one another! Thus, a chair is perceived only after a single coherent neurological signal, the code for chair, has been created by excitation of the appropriate template-circuit. That circuit generates its single output from the many signals input to it if they closely enough fit the form of a chair. A confirmed materialist may identify a Platonic Form with the form of the chair or the form of the neurological template-circuit that creates the perception of chair. Plato would not do so; for him, the Form exists independently of any material representation of it.

The concept of ‘chair’ is a popular though mundane example of a low-level form; below it in reality, instances of the form, are chairs directly perceived; above it are more general forms uncovered through the exercise of dialectic. The dialectician asks: chair is an example of what more general kind of thing? Of what collection is chair a member? Suppose we answer furniture, and from thence go on to manufactures, structures, and then materials, in increasing generality. Eventually, the most general will have to be reached, possibly the Form ‘Existent’; the genus consisting of all things which exist. We say, everything that exists shares in the quality of the form/concept of Existent; or Chair partakes in the concept of Existence, and so on.

The prosaic nature of this example helps reveal the essence of the dialectic process but conceals its import; what insight into chairs have we gained from dialectic? By imbedding chair in a classificatory scheme we have gained a clearer definition of what the concept is and what it is not. As a trivial example, a large rock on which someone could sit could be called a chair, but this classification scheme (reflecting how we have decided to use the word chair) will not allow it. That is not much, but only because there is not much in the chair concept in the first place.

A much richer subject of dialectic is the concept of Justice, the underlying topic of Plato’s Republic, and the Dialog in which the parable of the Cave and his Line both appear. At the very start, Polemarchus, quoting the poet Simonides, proposes included in Justice is the principle that we must render everyone his due. The passage goes as follows:

Socrates’ questioning quickly entangles Polemarchus in a web of unintended meanings and inferences. By this kind of questioning, which is the heart of Dialectic, Socrates attempts to refine the meaning of Justice. This is done with an overall structure in mind, which is just that introduced in the discussion of the Chair. The structure of the world of Forms can be understood with the help of the diagram shown in the figure which illustrates possible relations between forms.

Existence (area of vertical stripes) is a form shared by all Forms. All Forms (here using words and ideas current in Plato’s time) share either in the concept of Motion (area of diagonal stripes) or Rest (horizontal stripes). Motion includes all forms of change including growth. Animals (area of dots) partake in Motion and Existence. Bipeds (area of horizontal dashes) partake in the concept/form of Animal and therefore, Motion and Existence. Justice is a fixed concept, at rest in that it is unchanging and unchangeable.

It is important to note that Animal, being a form, being in the world of Being and not of Becoming, is unchanging. It is a fixed, unchanging form. At the same time, it partakes of Motion. Animals grow and move, though the concept of animals does not!

Note also that not only is Justice clear and fixed as a concept (by virtue of being a concept/form in the land of Being) but also each of the rules that make up a system of (true) Justice are fixed by virtue of partaking in the concept of Rest–at least according to the system of thought indicated in this figure! Thus, assuming that those engaged in the dialectic leading to the figure have at one point agreed that Justice partakes in Rest, none can later assert that such-and-such principle of justice evolves in time, or will depend on the culture under discussion. Conversely, had Justice been classed as a living, growing, concept–i.e. partaking in Motion–all its principles would be thereby assumed to be relative to time and place, even though the concept of Justice itself would not be.

Plato never finished explicating his theory of Forms. It is assumed that this was to have been accomplished in a Dialog called the Philosopher which never got to be written. Thus the theory has loose ends and hints lying about.

One hint, of special interest here, is the requirement that higher forms be collections of lower ones that designate the origins of the latter; that lower forms evolve from–are special forms of--the higher, and that in this sense, higher forms are richer and more pregnant than the lower. Thus Bipeds are special evolutionary forms of animals which in turn are special forms of living, evolving/moving, beings, which, finally, are special forms of existents. Similarly, Justice is one kind of fixed concept that has evolved from the more general class of fixed human concepts.

Behind all this, however, is the idea of the Milesian philosophers goal to explain all phenomena on the basis of a single form of physis. Out of this form–physis–all other forms are born. In the world of morals, the role of physis is taken by the Good: the principle shared by all morals just as physis is shared by all forms of phenomena. In the world of mathematics, this role is taken by the One: the principle shared by all number created from unity by sequential addition.

It is related that upon his retirement from leadership of the Academy which he founded, Plato gave a valedictory lecture. Everyone was invited, included his neighbors, the honest townsfolk who had probably been wondering over all those years about what was being discussed within the wall of the school. At the conclusion of his lecture, Plato proposed that the One and the Good were the same. It is reported that of those in the audience who were still awake, none could understand him. Neither, apparently, could Aristotle, who was one of his students. This proposal, however, was already buried deep within the dictum of Pythagoras, and has re-emerged as one of the proposals of modern science.

Plato characterized cognition in the world of Becoming as believing of which the lowest form is imagining. The Greek word doxa, translated here as belief, has a range of meanings

Knowledge requires thought. We know what a thing is by virtue of its connections with other things–connections which are realized in the physical connections between the neurological circuits which trigger perceptions. The characteristics of mother feed into the circuit which recognizes mother; their connections to that circuit constitute our knowledge of mother. These characteristics–definite shapes and forms–are objects of thought that we are barely aware of. If asked, we can recapitulate them verbally: state what are mother’s characteristics.

We fit data with a series of templates that work over a series of time scales. Most rapidly, early in data processing, visual fitting decides upon local boundaries and local shapes. Later, moving along the sensory system towards the brain, it more slowly identifies objects such as hands and faces. Later still, within the brain, it decides on qualities like beauty, fear, and even reality.

Thus there is a series stretching from (what seems to us to be) raw sensations, a first rapidly flickering of perception, to more slowly attained and stable realization. At its extreme upper end we find the One/Good, Plato’s development of Pythagoras’ ONE, Parmenides’ THAT WHICH IS, and Socrates’ GOOD, that which Nietzsche called the lap of Being, the intransitory (the opposite extreme to the transitory world of Becoming), and that which, in the context of religious monotheism, is the hidden God. These represent the most real, most certain of our concepts, within various traditions.

The degree to which God is hidden is a marker of religious belief. In the highest flowering of paganism as personified by Plato, the analogy is to the Sun; we can look at and attempt to see it, but only at great danger to ourselves and ultimate failure (think of the Indian holy men who stare at the sun and become blind). Only with great sacrifice and study can we glimpse the One of paganism; but a glimpse is nonetheless possible.

In Judaism and Islam, no such possibility exists; God is completely hidden. We see the emanations from the source of Existence (the light from the Sun) but not the source itself. Just as light travels in one direction from the Sun, these emanations are the modes of one-way communication between humans and God.

Christianity, as a marriage between Judaism and Greek paganism, especially as the later took the form of Platonism, has a viewpoint the flickers uncertainly between the two extremes. Christ is considered as supernatural by different sects with varying degrees; at one extreme he is God or a form of God, in which case humans can be said to be able to perceive God. Or, he is ‘Son’ of God, which may be interpreted as an Emanation, a Platonic Form (e.g. Love) made visible. Or, he may be just a human, albeit inspired, in which case God remains hidden.

However we may wish to interpret this range of beliefs existing today, there is no doubt that the completely hidden God of the Jews was too austere for the Gentiles to accept, and that Jesus represented an attempt to bring God closer to them, to give it, as it were, a ‘more human face’. Similarly, people today demand of science that it presents itself to us with a more human face, and also believe that it will allow us to glimpse the Ultimate Reality which was traditionally known as God.

Moving towards the upper end of the Line, from the land of Becoming one crosses over into that of Being. In the Line shown in the figure, and in Plato’s mind when he first conceived it, this is a sharp transition. On one side, in the land of Becoming, there are no clearly defined things, only appearances continually struggling to become individuated, to be something definite ( e.g. rough or smooth). In the land of Being are things that are: they have existence allowing us to have definite knowledge of them. They have become definite objects of knowledge (also ideas and ideals) that Plato called Forms.

In writings subsequent to the Republic, Plato stressed that the transition from Becoming to Being is not sharply defined. From a modern scientific viewpoint, this insight corresponds to the fact that the sequence of biological processes connecting image perception to idea creation has no sharp break, but is rather one of degrees of data reduction performed by successive neuronal connections (and one in which feedback at every stage blurs sharp distinctions between stages!). The transition between Being and Becoming also corresponds to that between conscious and unconscious data processing. Perceptions of attributes such as solidity, shape and color are products of lower level, unconscious, data processing by the sensory system. Ideas are products of higher level, conscious, data processing.

The Line can be viewed in a variety of parallel ways. (a) It is Plato’s outline of the structure of all existence. (b) It is an image of the nervous system that extend from sense receptors to brain modules responsible for the highest levels of cognition. (c) It is the view of an axis along which successive degrees of data reduction are achieved. (d) It is as the progression of realms of focus of the developing human, from womb, to self, to the environment–ever outward, ever increasing in individuation, often imagined as proceeding from Mother Earth to the (Male) Sky God. (e) It is a sequence of visions of reality as achieved in Plato’s parable of the Cave (to be discussed).

The lower level of mathematical thinking originates primarily in the distinction between deduction and dialectic. The mathematician deduces theorems from unquestioned axioms, the dialectician moves in the opposite direction, towards axioms, by continually testing and refining propositions. Dialectic involves both the making of hypotheses based on experience–information gathered in dialogue,–making deductions from these hypotheses, and then testing them again through dialogue. This is altogether the more difficult task.

Plato, and most everyone since him who has thought about this, felt that the less difficult form of thinking is the best possible way to train for the more difficult. Mathematical reasoning is the proper introduction to all reasoning. It is the arena in which to grow accustomed to before seeing things in that upper world, it which it is first easiest to make out shadows… in preparation to later seeing the things themselves. This is the source of the adage that everyone should study some mathematics to learn how to think logically.

This book will suggest, similarly, that everyone should study some physics to learn how to think at the higher level which Socrates initiated through his dialectic. The verbal testing and refining process characteristic of dialectic has its close counterpart in physical experiment and theory. But whereas dialectic itself, in its traditional sense, deals with the most difficult of problems, those like ethics not reducible (at least for the foreseeable future) to a science, physics analyzes the simplest systems found in nature.

The concept of Energy, of Mass, of the constancy of the velocity of light, and of the equation E=Mc² relating them, are all Platonic forms created by a generalization of the dialectic process from less refined Forms. Mass, for example, had to be refined out of the concept of volume, weight, and density, all mixed up in crude popular concepts of massiveness. The refining process employed in physics is a dialectic in which experiment and mathematical analysis takes the place of verbal dialogue.

Modern science, as Plato certainly would have noted had it then existed, is therefore the natural arena for learning how to think about all the systems of the Cosmos, including biological, social, and cultural, the latter being far more complex than those studied by science. That science does serve as such a natural arena can be seen from the fact that concepts generally useful in analyses system such as feedback, invariants, collective variables, and chaos, have all been discovered first in physics and then extended elsewhere. In fact, the science of systems analysis itself grew out of applied physics.

Plato was an acute enough observer to note that our most basic forms are (as we would say today) pre-wired. No one teaches the infant that Space is three dimensional or that Love is a good thing. The infant comes already prepared to realize such ideas (forms): prepared to fit observation to these templates.

How is this done? What is the mechanism for outfitting the infant’s mind in this fashion? This was a question for natural philosophy, and the only reasonable answer was that our shared sense of reality–our knowledge of the forms that constituted reality--had to come from a shared source. Today, some of us identify that source as our shared human evolution, but in Plato’s day, the only possibility was to identify it with Mind, (Nous). And indeed, most people today also call basic ideas, especially in the moral sphere, God given.

In a famous passage, Socrates (as represented by Plato) demonstrates how even the Pythagorean Theorem already lies within each of us from birth by virtue of our share of the universal mind. He does this by drawing out the theorem from an untutored slave boy using his method of dialectic. This is the Platonic model of how knowledge is to be obtained. Not from looking outward towards the uncertain world of Becoming, but by looking inward, and drawing out (to the conscious mind) the true knowledge already within us. This is another sense in which to educate means to lead out.

From Chapter XXVII of the Republic we have:

The general structure of scientific reality, the metaphysical house within which science has grown, was set up by Plato as outlined here. The 17^th century creators of modern science, were directly inspired by this vision. What it lacked, what they had to supply, and how they supplied it, major topics to be discussed, will be briefly sketched here.

A three dimensional object casts different two dimensional shadows depending on its orientation and on the screen onto which it is being projected; a shadow cast on to different sections of (a very irregular cave) wall can change its shape. Thus, much of the apparent variety and complexity of the shadow world can really be reduced to much simpler causes acting in combination. And in reverse, appearances can be predicted from knowing the true shape of an object and the way it is being projected.

Relative positions of object, screen, and lighting, screen textures, lighting colors, and so on, are not properties of the object being seen; they depend on its circumstances and are highly variable. Each, in combination with the object itself, creates a different shadow/appearance.

And further, the objects themselves can be touched as well as seen, thus explaining correlations between otherwise disconnected sensations; the shadow of the object misleads us dramatically as to what we touch. When we discover the real object behind its show/appearance, multiple types of sensations are understandable in terms of one object: reduced to one cause.

And yet further, shadows can and do rapidly move and flicker while the object itself remains invariant.

All these contribute to the sense in which the three dimensional object is called ‘more real’ than its shadow–even though the shadow is also real, and even though we may be prisoners, forced to directly experience only the shadows. We reach the knowledge of the real forms behind appearances through thought.

Similar reasons lead physicists to ascribe greater reality to their theoretical constructs than to the data gathered concerning their projections– the shadows that phenomena involving them cast upon our senses. In this sense we say that an electron is more real than any observed effect electrons have; that is we are more certain of the electron than of any measurement we make of it. Note, by the way, that we are so convinced of their reality that we say ‘electron’ and not ‘concept of electron’, even though concept is what it is.

Just as an object gives rise to many shadows depending on circumstances, so also do electrons contribute to, and correlate, the data from many phenomena. Just as shadows flicker, so also do data which all exhibit statistical fluctuations and experimental bias.

Plato understood, as many later philosophers did not, that we are born endowed with a great deal of intellectual as well as physical structure. These intellectual structures manifest themselves in propensities to use forms such as continuity, self, good and evil. No one teaches these to the infant just as no teaches it to grow a hand. It is born with all its potentials and only needs environment to stimulate their expression.

But how does the infant acquire them? The only possibility evident to the ancients was through the medium a God-connected physis. It required the modern understanding of evolution and genetics to give us a alternative mechanism, one that was not supernatural.

Less general structures, developed well after infancy, are still often attributed to the supernatural. The word ‘inspired’ literally means to be invested in a spirit, and each genius is helped by a genie. When discussing works of genius, people even today find themselves hard put to come up with alternative explanations.

The real point, however, is not to suggest that inspiration is supernatural but that it works in deeply hidden ways; one does not deduce new Forms or physical theories, but guesses and hypothesizes them.

Moral forms are tested by the process of Dialectic. It is an human experiment that is done at a completely verbal level. Is Justice the same as rendering to each their due? We test it by taking particular cases. The test is that of common understanding and can be done through question and answer. The experimental data are exact.

It took two millennia before the method of Dialectic was systematically adapted to the natural world in the form of physical experiment–before the question being put to nature could be made clear and the answer clearly received. Why this was so hard will be discussed. But because it was so hard, it was generally taken to be not merely hard but impossible in principle. Nature was taken to be, at its most basic level, chaotic and therefore unable of giving a straight answer. And even today, despite all the success of science, that belief persists in many quarters.

Plato had no problem in placing the indirectly perceived One/Good at the apex of the world Being, which was predicated and structured on the basis of the reality of forms/concepts indirectly perceived (not imagined or imposed on a real chaos). When reality depends on degree of reduction, and nothing can be reduced beyond One, then the One is the most real. By this means Plato comprehended Parmenides within his grand scheme (who had concluded that the only thing that was completely real was the One which he visualized in analogy to the Sun as did Plato in his parable), and reached towards both the Unity of Monotheism and of Science.

Whereas Parmenides One, however, was completely sterile, Plato’s was completely (maximally) fertile. Everything real evolved from the Form/concept/principle of the Pythagorean/Platonic One, just as all the variety of Existence is supposed to evolve from a Theory of Everything if such exists.

Everything also evolved from the Poetic/Sophistic idea of Chaos. It was maximally fertile but in a sense antithetical to that of Pythagorean/Platonic One. Whereas the order of Cosmos is imposed upon Chaos by forces of nature (much as the rule of law is imposed on unruly primitive society), no force or imposition is applied to the One; the latter is a natural evolution; order is the natural order of things, built into the universe (an echo of the forms that are built into the infant). In one case order is natural, in the other, it is disorder.

These two antagonistic intuitions/beliefs have had the most profound effects on human history. In Science in particular, without the Platonic belief that the One stood at the apex of the Real, modern science would have never developed. As we shall discuss, when Galileo fitted his uncertain and fluctuating data on falling objects with a law in which an integer (the 2 in the quadratic) was used to describe the relation between distance and time–an integer rather than any one of an infinite variety of real numbers–it was done with an inspiration that came to him from Pythagoras through Plato. He hypothesized that it was that form that was really there (in the Platonic world of Being) and represented The Truth rather that A Truth. He did not believe that he was imposing the simplicity of the integer on an uncertain, chaotic world.

Science is housed within Platonic reality. At each stage in its growth, the house of Science has a topmost level which represents our current best concept of the most real. At the top are housed the fundamental laws of physics. Succeeding levels, each one housing one or more sciences, accommodate images of the level above, and spread in area as they approach ground. At ground are phenomena.

Basic changes of physics occur when the room at the top needs to be topped. When it was extended upward with the addition of Quantum Mechanics, for examples, it was understood that the Newtonian theory previously at the top, was but an image, or shadow of Quantum Theory, which in turn is possibly the image of something yet higher, something more real. If so, we will build upon Quantum Theory. And the higher room will provide a new form of reality. But it will not alter the content of the lower levels. It cannot change data already been observed and their reduction to formula.