by     Reginald O. Kapp



WE want to ask physicists a question. And the formulation of a question is one of the most difficult things in science and philosophy. When we once tried to put ours to an eminent physicist he found a formulation which an engineer could hardly have thought of and which impressed us by its neatness and clarity. "What you mean to ask me", he said, "is: What are the boundary conditions of a differential equation which defines the whole Material Universe?"

If the words "differential equation" are meant metaphorically this formulation probably covers exactly the question we want to ask. It may do so even if the words are meant literally, but we are not sure. In either case this formulation has the advantage that it occurs naturally to a physicist. Yet we cannot use it for the simple reason that we should probably not be able to understand the answer. We must sacrifice the best formulation for some other which may elicit facts comprehensible to us and to all those other laymen who like to be told things by physicists. A form of question which meets this requirement makes use of the word "specification". "What", we ask, "are the clauses in the Cosmic Specification?"

Perhaps we ought to add a few words to what we have said in previous chapters explaining what we mean by Cosmic Specification. This differs from the specifications for machines or living organisms discussed hitherto in one important particular. The latter do not contain clauses which define the nature of Matter any more than they contain clauses which demand conformity to the laws of physics and chemistry. Such clauses would be unnecessary, for if nothing in an engine or a sparrow is specified, carbon will have the properties of carbon, oxygen those of oxygen. But by Cosmic Specification we mean a definition of the restrictions imposed on the nature of Matter itself. We mean the sum of all those statements which declare that the nature of Matter is always thus and never otherwise. In a transcription of the Cosmic Specification we should, for instance, find those clauses (if any) which may be necessary to ensure that carbon and oxygen shall have the properties which they do have.

The distinction between the Cosmic Specification and others can be defined in this way: Specifications for machines and living organisms demand a choice between alternatives all of which are physically possible. The Cosmic Specification, like the Cosmic Statute Book, demands a choice between alternatives all of which are logically possible. Where any of these alternatives is permitted without preference the specification contains no clause. Things are allowed to be anyhow. The Cosmic Specification, if it contains any clauses at all, might be described metaphorically as the fetters placed during the Creation on the monkey of chance.

This makes it quite clear that the Cosmic Specification is not a description of the Material Universe. If the monkey of chance was completely unfettered a description of the results of his activities would be possible, but there would be no specification for those results.

"What are these fetters?" we ask of the physicist. "There are, among others, those which ensure the existence of carbon with its properties", says Jeans in effect on page 9 of The Mysterious Universe. Only he uses the word "limitations" instead of "fetters". "And in doing this these limitations are sufficient to constitute all the other limitations to which Matter in the organic world is subjected," is the gist of the context. Biologist-philosophers will be only too ready to agree. This is what they have always been saying.

Jeans's view seems to be, not exactly that the Material Universe is a skilled manufacturer, but rather that it is itself a skilfully manufactured machine capable of turning out living organisms as an automatic cutting tool may turn out screws. On page 9 of The Mysterious Universe, he says: "Although the problem is still far from solution, it is becoming increasingly likely that what specially distinguishes the matter of living bodies is the presence not of a 'vital force', but of the quite commonplace element carbon, always in conjunction with other atoms with which it forms exceptionally large molecules."

But is Jeans right even in the minor assumption that there would probably be no carbon if there had been no limitations? This is a part of the question which we want to put to physicists. But it is only a part. There are, perhaps, other things which the unfettered monkey of chance could not have given us. Some will say that, in the absence of any limitations, there would be no sun, no moon, no inhabitable earth. By suggesting that the laws of chemical combination are unique or ultimate laws, as mentioned in the last chapter, Broad implies that, in the absence of any limitations, oxygen and hydrogen would not combine and there would be no water. Yet Jeans would not agree that there is a specific limitation to ensure the existence of the sun and one to ensure the existence of the moon. He would say that heavenly bodies are allowed to have any size, and any temperature and that the specific properties of our sun, our moon, are automatically safeguarded by other more general limitations. He would say much the same of the reactivity of hydrogen and oxygen. Opinions differ evidently as to what clauses the Cosmic Specification does and does not contain and it has become necessary for someone to review its contents who does not keep one eye on the bishops and another on the biologists.

Only a physicist can do this. Yet most physicists are less interested than many laymen. So we must encourage the physicists to help by making our question as plain as we can. To do this we will turn it into a questionnaire in which we hst things which certainly do not figure in the Cosmic Specification and things which, for all we know, may do so.

Our questionnaire must have such a form that it makes due allowance for the interest others take in this theme and particularly for the attitude of philosophers and theologians. We can do this if we cast our questionnaire in the dialogue form adopted, if not invented, by Plato two thousand years ago when he wished to give proper weight to a variety of points of view. So we will invent a number of spokesmen and an occasion for their meeting.

To get the dialogue going let us indulge in a daring fantasy. Its absurdity need not matter if only it enables us to convey the meaning of the concept "Cosmic Specification" without ambiguity.

A great degradation has spread over the whole of our earth and, as space travel is perfected, it extends to every inhabitable planet in the Material Universe. Saddened by the prevalent corruption a group of men and women appeal to the archangels. These are sympathetic and helpful. They offer a second Material Universe and promise to arrange for suspended animation of the prospective emigrants for such millions of years as may be required for completion of the work.

A committee is appointed to prepare a suitable specification for the New Universe. Several scientists are members of the committee of whom the most important is a Physicist. Among other members are a Mathematician, a Philosopher, a Theologian and a Future Citizen. This member serves as a representative of the emigrants and is there to watch their interests. The committee also has a Chairman and a competent Secretary.

At the beginning of the first committee meeting the Chairman explains the terms of reference. He says that a close resemblance to our own Universe is required. If the New Universe does not copy ours point for point, it must, at least, copy it in all essentials. It must contain stars and nebulae and, in some comer, an inhabitable planet like our Earth. All known substances must be present and these must possess all the properties with which we are familiar. Things must happen in the way things happen here. "Our specification must be so stringent", the Chairman says, "that the New Universe will be as much like ours as one stretch of sand and shingle resembles another on a featureless seashore, where nothing but an idle comparison of the exact size and position of individual pebbles would reveal a difference."

Here the Future Citizen interrupts. "We must make sure that the New Universe is as good as this one," he says. "We want to move into it without inconvenience."

"That is to be borne in mind," replies the Chairman. "When you land on one of the inhabitable planets you must feel at home there. The Cosmic Specification must be drafted accordingly. Your text-books on geography and your charts of the sky may prove useless, but you must be able to take all your text-books on physics and chemistry with you, in the certainty that they will be as serviceable there as here."

At this point the Secretary asks a question about stationery. "Our Universe is an elaborate affair," he says. "How much paper shall I need for all the clauses in the Cosmic Specification?"

The Philosopher says that he has heard a rumour emanating from an adjoining room where the Cosmic Statute Book is being prepared, that this document is very meagre. In fact someone has told him that it may contain nothing but empty pages. He asks whether the Cosmic Specification is likely to be an equally blank document.

"That is not certain," says the Physicist. "We know that the Cosmic Specification will not contain much. But we cannot say with certainty that it will contain nothing."

"Will half a sheet of notepaper be enough?" asks the Secretary with some surprise.

"Provide yourself with a few sheets and a blue pencil," the Physicist tells him. "You will have to put in some clauses which you may be able to strike out later."

"In the preparation of the Cosmic Statute Book," remarks the Philosopher, "I understand that the same thing has happened. Many laws were first included only to be struck out after a discussion which, showed that a distinction should be made between reducible and irreducible laws. I shall not be surprised if in the wider document we are preparing we shall have to distinguish between reducible and irreducible facts."

"We will now set to work", says the Chairman. "The first item in the agenda is 'Structure'. I suggest that we begin with the general layout and the main architectural features. In an architect's specification these are partly shown on drawings and partly described in the text. How shall we deal with them here?"

The Astronomer rises and explains that nothing need be included in the Cosmic Specification under the sub-heading "General Layout". Matter, he tells the committee, is scattered unevenly and at random throughout space. There are large and small nebulae and large and small stars. All these are spaced at great and short distances. Stars are indiscriminately grouped in large and small clusters without plan or system. In the absence of drawings, the Astronomer points out, heavenly bodies in the New Universe will not occur just where they do in our Universe. But the general distribution will be the same. The differences will be no greater than those which would occur if we kicked the pebbles about which lie on the beach.

"Would any such differences make the New Universe less inhabitable than our own?" asks the Future Citizen.

"Certainly not," replies the Astronomer.

The Theologian looks surprised. "Do you mean to say", he asks, "that the great sweeping lines which span the world are not architected?"

The Astronomer tells him that there is no evidence of a plan. "If that seems irreligious", he continues, "I would point out that neither is there any need of one. Can you suggest any rearrangement of stars and nebulae which would provide a world in any way better or worse than the one we live in?"

The Chairman turns to the next sub-heading to the item "Structure". This is the structure of terrestrial features. He explains that the New Universe must contain at least one planet like the Earth with oceans and continents, mountains, lakes and rivers.

The Geologist tells the committee that they may pass over this sub-heading. If the Cosmic Specification places no restrictions on temperature in the New Universe, every temperature will occur from the region of the absolute zero to many millions of degrees. Somewhere is bound to be a planet at a moderate temperature. This will shrink as our Earth has shrunk, leaving an uneven surface, thereby ensuring the separation of land and water, the occurrence of mountains and plains. If the specification does not demand immobility the planet will move around its sun and on its axis. This will ensure the pageant of the seasons, the alternation of days and nights. Clouds, thunderstorms, rain, fog, and bright sunshine will occur whether called for or not. The vagrant winds will blow, and they will conform to no specification.

"I can believe that," says the Theologian. "For did not the Evangelist say: 'The wind bloweth where it listeth'?"

After a little discussion it is agreed that the visible features of the Earth's surface are no more architected than is the structure of whole galaxies. The Secretary has written nothing as yet and the Future Citizen is satisfied that the new climate he is to face will be no better and no worse than the terrestrial climate to which he has become accustomed.

The Secretary is using a typical architect's specification as a guide to his work. He refers to a clause in this which defines the purity of the substances to be used and another which states the proportions in which cement, sand and aggregate shall be mixed in the concrete. He asks what corresponding clauses the Cosmic Specification shall contain.

The Chemist interposes at once that substances may be mixed anyhow and that no degree of purity need be called for. He points out that pure substances hardly ever occur in Nature, though they can be obtained by a meticulous laboratory technique. In air nitrogen, oxygen, carbon dioxide and water are mixed together with traces of many other substances. The sea contains water, oxygen, nitrogen and many salts. Rocks and earth consist of an even more varied mixture of substances.

The Future Citizen looks alarmed. "If substances are allowed to be mixed anyhow", he complains, "the planet we go to may have too much oxygen in the atmosphere or perhaps too little. We must be able to breathe when we arrive there."

He is told that there will be many planets. Some will have more oxygen in their atmosphere, others less. He must choose a suitable one.

"But suppose the New Universe does not contain a suitable one?"

"Conditions on planets change," he is told. "If you wait long enough one out of the many must become suitable. Our own Earth only became fit to support Life quite recently. There is, of course, a risk that no planet in the New Universe will ever become so similar to our Earth that mankind could exist comfortably there at first. But it is almost certain that there will be planets able to accommodate Life in some form. A certain amount of biological adaptation may be necessary."

"The architect's specification I am using as a model", says the Secretary, "contains references to the way the bricklayer's work is to be done. All Matter is composed of small particles called atoms. These, I presume, correspond to the bricks used in a building. What shall I enter in the Cosmic Specification about the way atoms are to be assembled?"

"You can put 'anyhow'," the Chemist tells him. "In our Universe any grouping of atoms occurs and lasts for a longer or shorter time depending on its stability. Sometimes the association is a close one and the group is called a molecule. Molecules may contain any number of atoms, placed anyhow and of any kind. The arrangements found in Nature are those which chance brings together and equilibrium maintains. The New Universe will contain the same substances as those found here even if the Cosmic Specification says nothing about the way atoms shall be grouped."

"I can confirm that," says the Geologist. "Under the influence of the sun's warmth, for instance, water vapour will rise from the surface of the oceans. Salts will not evaporate. These will be left behind. Thus the seas will contain salt water. The vapour will condense on the hilltops and fill the rivers with fresh water. Some seas will occasionally dry up and leave deposits of limestone. You will find rocks formed of this substance. Other processes, of which I could tell you, will lead to the formation of clay and others to that of igneous rocks. The building of substances out of atoms in the New Universe need reveal no trace of the bricklayer's art. Uncoordinated physical processes will produce them inevitably."

"It appears", remarks the Chairman, "that chaos prevails in the structure of our Universe from astronomical down to molecular dimensions. But can we be sure that in its still finer structure Matter shows no evidence of architecting? The bricks of which you have spoken and which physicists call atoms are themselves elaborate configurations formed of atomic nuclei and electrons. May we not have to embody a clause to say how atoms shall be constructed?"

At this the Theologian looks up in astonishment and says: "I find such a theory hard to believe. If it were true, the Creator of the World would be like an architect who was particular about the bricks but quite indifferent to the way they were used."

"Yet there are scientists and philosophers who tell us that the atom is an organized structure," the Secretary points out. "I have often met this assertion."

Here the discussion deals with the structure of atoms and molecules and goes on to a comparison between the views of those who believe that Matter tends to become ever more highly organized and Eddington's statement that it becomes ever more disorganized. Nothing is said with which the reader has not already been made familiar in these pages, so we need not report this part of the proceedings.

After it has been decided that there need be no clause to determine the structure of atoms, the Chairman says: "So far we have confined our attention to the first item on the agenda. This is 'Structure'. Have we omitted to consider any aspect of Structure?" After a short discussion in which radiation and quantum mechanics are mentioned it is agreed that the Cosmic Specification need not contain any clauses to say how particles great or small are to be arranged.

At this point the Theologian has a question to ask of the Physicist. He says: "Do you then deny order, structure, organization? Would you assert that these things have no meaning? Do you refuse to see the order, the symmetry, the perfect organization of a flower, a bird, a beautiful building? Does your science prove that no purpose is ever served by the arrangement of things?"

"My science certainly does not prove that," is the reply. "It is my job to study how Matter behaves when it is left to itself. I find that it then behaves chaotically. My science merely proves that Matter unaided can never create the things you speak of. It can only shake down into stable structures. Flowers and birds and beautiful buildings are not the result of laws which cause Matter to settle down into a condition of maximum stability. Being a Theologian, you are not a Materialist. I think that you will readily accept what I say."

The Philosopher adds a word of explanation. "The less power we attribute to Matter," he says, "the more must be attributed to non-material influences. The blank pages on the Secretary's desk are the strongest refutation of Materialism which I have met. Had we found evidence of architecting in remote regions of space far from the activities of man or any living thing, we should have concluded that it is natural for Matter to be ordered, perhaps even organized. But science proves that it is natural for Matter to be chaotic. Consequently, for the origin of order and organization we must look to influences separate from the Material Universe." At this stage in the proceedings the Chairman adjourns the meeting for a short time.

When the committee has reassembled the Chairman announces the next item in the agenda: the properties of Matter.

"The architect's specification which I am using as a model", remarks the Secretary, "contains some clauses which state the qualities of the materials to be used in the work. We must now devise corresponding clauses for the Cosmic Specification."

"There are many substances," the Future Citizen points out, "and each has many properties. I fear that this part of our work will be laborious. However we must face it, for it is essential that Matter in the New Universe shall have precisely the same properties as here."

At this the Physicist says: "The work will not be laborious at all. We shall not need any clauses. Even Galileo could have told us that, three centuries ago. He realized that everything objectively true about properties is deducible from structure. Though we do not specify any properties you will find in the New Universe that the colour, taste, smell, sound, feel of things are all familiar."

The Chairman asks the Physicist to explain his meaning with the help of a simple example which they may all be able to understand.

"I will choose the differences between the properties of solids, hquids and gases," says the Physicist. "These are due to nothing but differences in the arrangement of molecules. In a solid the molecules are packed in such a way that they cannot easily slide over each other. Force is, therefore, needed to distort a solid structure. In a liquid the molecules do not interlock, while in a gas they move so fast that their momentum overcomes the forces of mutual attraction. They then fly as far apart as the available space will allow until, colliding with the walls of the container or other molecules, they rebound. The result is a uniform distribution of particles in rapid, motion. The gas pressure is due to the sum of the impacts."

"Other examples would have illustrated the point equally well. The hardness, softness, ductility, tensile strength, and other mechanical properties of substances are all due to the shapes and relative positions of the constituent molecules."

"There are properties of Matter which we should not call mechanical properties," interposes the Secretary. "How do you account for colour, transparency, magnetism, electrical conductivity?"

"Properties of this type are due to the position and movement of the electrons associated with atomic nuclei," is the reply. "In good conductors of electricity, for instance, some of the electrons are held so loosely that a small voltage suffices to dislodge them. They move readily from place to place in the direction determined by the voltage difference and their movement constitutes an electric current. In a bad conductor all the electrons are held in position more firmly."

After the Physicist has provided further examples to illustrate how properties are related to structure, it is agreed that none of the physical properties of Matter need be included in the Cosmic Specification. The Chairman asks whether chemical properties may be left out as well.

"It is most necessary that two atoms of hydrogen shall combine readily with one of oxygen in the New Universe," says the Future Citizen. "If this combination is not ensured there will be no water for us."

The Chairman is not sure whether to call upon the Physicist or the Chemist to deal with this point. They are both prepared to do so. Eventually the Chemist rises. "To understand why this combination occurs," he says, "we must first appreciate some of the ways in which the text-book model of the atom differs from a solar system. Planets are kept in the vicinity of the sun by gravity. They are prevented from falling into the sun by centrifugal force. Electrons are kept in the vicinity of the atomic nucleus by electrostatic attraction. They are not prevented from falling into it by centrifugal force only. Their mutual electrostatic repulsion keeps them at a distance from each other and, therefore, also from any one single spot such as the nucleus. A compromise is reached between the pulls towards the nucleus and the pushes between the electrons when the system settles down to a condition in which the electrons are not very crowded. In the oxygen atom stability exists when two of the eight electrons describe orbits comparatively near the nucleus in what is called an inner shell, or K-ring, and the remaining six describe orbits in an outer shell, or L-ring. These six are not very crowded.

The electrons are said to shield the nucleus. This means that at a little distance from the atom the negative charges on the electrons completely cancel the positive charges on the nucleus. The atom behaves as if it carried no charges. It is electrically neutral and can neither attract nor repel other particles. But the wide spacing of the electrons in the oxygen atom causes the shielding to be imperfect at very short distances. Some of the electrical field of the nucleus gets through the mesh as it were, so that there are regions where a positive electrostatic field occurs. There are other regions very close to the atom where the negative field of the electrons preponderates. Consequently the atom can both attract and repel particles which come sufficiently close. It has some electrostatic activity.

The hydrogen atom consists of a nucleus carrying a single unit positive charge called a proton, and one negatively charged electron. Each sometimes comes into a region where it is attracted. The hydrogen atom is then captured. The proton allies itself with the oxygen nucleus and the electron which was associated with this proton in the hydrogen atom enters the outer shell. As I have said already, the six electrons in the outer shell of the oxygen atom are not very crowded. As many as eight can be accommodated in this shell before their mutual electrostatic repulsions become pronounced. But more than eight are not possible. If a ninth tried to enter, it would be too strongly repelled, even though the requisite attractive force existed at the nucleus. The ninth would have to stay outside in a third shell. Hence we say that the second shell is complete when it contains eight electrons. This number is provided when one atom of oxygen has combined with two of hydrogen. Then a molecule of water is formed.

This consists of three nuclei, one of oxygen and two of hydrogen. Together they carry ten unit positive charges and are neutralized by ten electrons. These then form a more perfect shield so that the water molecule is electrically less active than an atom of hydrogen."

"Suppose we started with an atom consisting of a single nucleus carrying ten unit positive charges and ten electrons. Would the perfect shielding you have spoken of render this atom electrically inactive?" someone asks.

"It would," is the reply. "You refer to an atom of neon. This is one of the six inert gases which form no chemical compounds."

"And if the nucleus carried eleven charges?"

"The electrons would then be grouped: two in the K-ring, eight in the L-ring, and the eleventh in a still more distant shell called the M-ring. The atom would be very active. It would be an atom of potassium."

"Is it then possible to predict all the chemical properties of an elementary substance from a knowledge of its atomic structure?"

"Certainly. This was done in the case of the element Hafnium. Substances had been discovered of which the atomic nuclei carried nearly all the numbers of positive unit charge from l to 92. These corresponded to all the known chemical elements. But there were a few gaps. For instance, no nucleus had been found with 72 charges. Physicists knew that such nuclei must exist and that they would represent an undiscovered element. Though no one had ever met it, its properties were predicted. Eventually nuclei carrying 72 charges were found. They belonged to the atoms of a new element which has received the name Hafnium. This exhibits the predicted properties."

"We have just heard of a striking instance where the establishment of a few basic facts facilitates the Physicist's task of predicting results," comments the Philosopher. "Because they had learnt how to cut all mention of properties out of the Cosmic Specification, physicists were able to predict the properties of an undiscovered substance. The unification of physics is not only of philosophical interest; it has a practical use as well. It enables physicists to replace induction by deduction."

"It would seem", comments the Chairman, "that recent scientific discoveries are full of philosophical implications."

"Not so very full by any means," is the Philosopher's rejoinder. "We have been told that the deducible nature of properties was known to Galileo three centuries ago. The notion was not even unfamiliar to the ancient Greeks. At most, modern science has provided brilliant confirmation of old surmise."

"We must proceed with our work," remarks the Chairman, heading off a discussion which threatens to deflect attention from the agenda. "A number of attributes of the Material Universe have still to be considered which cannot quite easily be classed either with laws, structure or properties. The first on my list is the geometry of space-time. Can the Mathematician tell us what this means?"

The Mathematician rises and says: "The geometry of space-time is considered in the restricted and general theories of relativity. It would take me too long to give you an adequate account of what this means. I must refer those who are not specialists to the many brilliant popular expositions of relativity which have appeared. It will suffice here for me to recall that the Euclidean relation of lines and angles is not the only possible one. Euclid's propositions do not hold, for instance, on the surface of a sphere. If Euclid's propositions did hold between any lines and angles in space-time we should have to conclude that of all possible geometries to which space-time might conform, the Euclidean one had been singled out. Then the Cosmic Specification would have to say that the geometry of space-time was to be Euclidean and no other. The specification would restrict the choice between many alternatives. Physicists would call such a restriction arbitrary.

"But we know now that many geometries are permitted. There are regions in empty space where the geometry approaches indefinitely closely to the Euclidean type, but Einstein has shown that in the vicinity of tangible substance there is a wide departure from the neat smoothness of that type. In these places the non-mathematical mind, trying to visualize everything presented to it, can only picture the geometry of the world as a chaos of bent corkscrews and tangled skeins. Einstein replaced the limited geometry of Euclid by the more general geometry of Riemann."

The Secretary asks whether he shall insert a clause to say that Riemann's geometry is to be adopted.

"Even that would restrict the New Universe too much," answers the Mathematician. "When he first propounded the general theory of relativity, Einstein took account of gravitational fields only. It has since been shown by Weyl that in electrical fields yet other geometries occur. Eddington has propounded a geometry even less restrictive than that of Weyl."

"But is the geometry of Eddington completely unrestricted?" asks the Philosopher. "Are there no further alternatives? Does every geometry occur somewhere which logic and mathematics show to be possible? We have already decided that the Cosmic Specification may allow any structure. Need we qualify this permission? Does the clause read: 'Any structure compatible with specified geometrical requirement', or does it read: 'Any structure compatible with any geometry'?"

"Physicists have hardly yet formulated their conceptions in such a way as to make it clear whether a mathematician could devise further geometries of which an example occurs nowhere," is the reply. "I move that the Secretary inserts a provisional clause defining the geometry on which physicists are now agreed. There is still some uncertainty. So he cannot make the clause complete. And he may be able to strike it out altogether after a few years."

The Secretary copies out a formula handed him by the Mathematician. This is the first entry he has made. While he is writing the Chairman refers to his notes.

"There are a few more items to be considered," he announces. "I will first take a group of facts which are all classed together here under the heading Cosmic Constants."

"Will you read them out?" requests the Secretary.

"Here are some of them," says the Chairman. "The velocity of light in empty space. The masses of the electron and the proton. The value of unit electric charge. The value of the unit of action, called a quantum. We must ask the Physicist to explain what these constants mean. But before doing so I will read out the last on the list. The meaning of this is quite plain. This item is worded: The total quantity of substance in the Universe."

"That is a most important figure to specify," says the Future Citizen. "It would be disastrous if the specification were so carelessly worded that a dishonest builder could fulfil his contract by providing only a speck or two."

"Is that what might have happened if our Universe had been built by the Devil and not by God?" asks the Theologian.

"So far as I can tell, yes," replies the Physicist. "But, frankly, I do not know. The question belongs to your domain and in no sense to mine. The reason why the Universe contains just so much, not more and not less, could only be given if we knew why there is a Universe at all. It is not for physicists to seek that reason. Our task is to investigate what is, not why it is. We study the nature of the Material Universe, not its origin. Our concern is with the created, not with the Creator. If I may adopt an expression used by the committee considering the Cosmic Statute Book, I would say that the total quantity of Matter in the Universe is, for physicists, a kurma fact. Perhaps the Philosopher can add something to what I have said?"

The Philosopher shakes his head.

It is generally agreed that the Secretary must specify the total contents of toe New Universe. He makes his second entry after having received an estimate from the Physicist. ("For what it may be worth," as the latter mutters to himself.)

The Chairman then asks what shall be done with the other Cosmic Constants. "We will consider the velocity of light next," he suggests.

The Physicist says: "Clark Maxwell proved that the velocity of light results from the properties of the electro-magnetic field. So we need not specify both these properties and the velocity. Mention of the one would ensure the other. According to Weyl's geometry of space-time the properties of the electro-magnetic field, in turn, result from the geometry of space-time. It is, therefore, possible that the velocity of light is due to this geometry."

"The velocity of light is 186,000 miles per second in empty space," says the Philosopher. "Is this not the maximum. velocity at which any particle can travel?"

"Yes. At this velocity the mass of a particle would become infinite. No force would suffice to accelerate it to a higher velocity. That follows from Riemann's geometry. But we have to consider now why light should travel at exactly that speed at which the mass of a particle is infinite."

"May this not be the inevitable result of Weyl's or Eddington's geometry?" the Philosopher asks.

"Perhaps. But I require notice of that question. Physicists are not in the habit of thinking in terms of the Cosmic Specification and have not always formulated their conclusions so that I could say with certainty whether the velocity of light needs to be included or not. I think the Secretary ought to enter this as though it were a kurma fact for the present. We may later be able to replace his entry by a cross-reference to the section headed 'Geometry.' "

"What is your opinion of the remaining constants?" asks the Chairman. "Does a kurma fact or two lurk among these? I have a note here staling that the mass at rest of all electrons is always exactly the same and that the mass of all protons is always some two thousand, times greater. Another note says that the electric charge on each electron or proton is always exactly 0.159 x 10-18 coulomb. Another note says that the quantum of action is always exactly 0.655 x 10-26 erg-seconds."

"It is certainly puzzling that these quantities are always exactly constant," interposes the Philosopher. "Nothing equivalent occurs on a larger scale. Heavenly bodies, as the Astronomer has told us, are sometimes large and sometimes small, sometimes hot and sometimes cold. Their substance is sometimes so dense that a pinch of it weighs a ton, sometimes more tenuous than the highest vacuum obtainable in an X-ray tube. Why should electrons not sometimes be large and sometimes small? Why should they not sometimes carry a large and sometimes a small charge of electricity?"

"There appear to be four constants in this group," remarks the Secretary, "namely, unit electric charge, the mass of the electron, the mass of the proton, and the quantum of action. By the way, what is the quantum of action?"

"Action is energy multiplied by time," explains the Physicist. "The quantum is the smallest indivisible amount of this product which can occur. Just as we never meet anything less than unit electric charge, so we never meet anything less than the unit quantum of action. If in a small change called a quantum change, the energy is small, the time taken is long, and vice versa. In space-time there is no more difference between any two quanta of action than there is in space between any two electrons."

"Shall I call for all these four constants in the Cosmic Specification?" asks the Secretary.

"The safest thing would be to do so provisionally," is the Physicist's reply, "though we have little doubt that they are all related to one another so that mention of any one of them will inevitably ensure the others."

"Then I will mark three provisional and the fourth per- manent. Which should I select as a probable kurma constant?"

"It is not very material," replies the Physicist. "But I think the quantum of action, also known as Planck's constant, most deserves that position, because it involves the time dimensions in addition to the spatial ones more patently than the others do."

The Philosopher interposes an objection. ' If you cut out all the Cosmic Constants but one", he says, "the Specification will not be complete. You must then add mention of the principle by which all those constants are related to each other."

"That principle is not yet established," replies the Physicist, "though Born has pointed out that the number 137 plays an important part in it."

"A mystical Cosmic Number," suggests the Philosopher.

"Too mystical to be quite plausible. And the significance of Born's number has been questioned by other physicists. But, in any case, a single number would not suffice to make up a principle. I am afraid that this part of the Cosmic Specification must remain incomplete at present."

"May I make a few remarks to summarize the position?" says the Philosopher. "We have found that in nearly every aspect the Material Universe is completely unrestricted. There is the Creation, which must always be treated by physics as a kurma fact, and there is a very small number of facts and figures. Apart from these the New Universe will be like our own even if built to no specification. I find it hard to believe that even these few restrictions are real. The entries our Secretary has made seem to be so trivial and meaningless. Is it not possible that even these are not kurma facts at all, but statements which are true by definition? I mean that they are statements which arise from the methodology of physics, not facts imposed on the Material Universe from without. Students of Kant or, in modern times, of Wittgenstein, will wish to stress this possibility."

"That theory is conceivable," says the Physicist, "but at present it is pure speculation. We cannot prove it." "However, you tend to believe it?"

"I think we do."

At this stage the Future Citizen rises and says: "Something very important for the New Universe has not yet been mentioned. This is Life. On the planet to which we intend to emigrate we must find green woods and birds. There must be fish and game, and fields in which we may graze our cattle. Will the very meagre Cosmic Specification we have now prepared make these things inevitable?"

The Chairman turns to the Physicist: "You have proved to us that the ellipsoidal shape of stars is inevitable in a world built to no specification. You have proved the same for crystals and other inanimate regular shapes. Can you also convince us that in the absence of all restrictions, the shape of a blade of grass or a butterfly would be ensured?"

"I have never concerned myself with living things."

"Would you expect to be able to prove it?"

"That I would certainly not."

"Can the Biologist show that with the great degree of freedom which we have found Matter to possess it must inevitably settle down to the various detailed patterns exhibited by living organisms?"

"I cannot prove it," replies the Biologist, "and I do not consider it my job to attempt to do so. I am content to study the anatomy of living things and the laws which govern their behaviour. To me these are all kurma facts. So far as I can tell, every discovery in the domain of biology will have to be specified in a carefully worded clause. To specify every restriction imposed on Matter in the organic world, you will have to prepare an enormous document."

"It appears that if Matter is left to itself, it does not produce organic forms," comments the Chairman.

"How then shall we ensure that these forms will occur in the New Universe?" asks the Future Citizen anxiously.

"Put your trust in God," the Theologian tells him. "He will see to it that, in the New Universe, Matter is not left to itself. The Physicist has proved to you how useless it is to put your trust in Matter."

As this book does not deal with theology, we are not in a position to discuss the Theologian's comment. We must be content to note that it is at least more to the point than anything which a materialist could contribute.

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