The Reciprocal System
As explained in Chapter 2, modern physical theory has abandoned the traditional methods and practices of science, and has reverted to the use of what the present-day theorists call invention, or ad hoc assumptions, but which are simply the demons of earlier days equipped with new names. The results of such a policy could easily be predicted, but since the activities of the front line theorists are behind the scenes, so far as the general public or ordinary scientists are concerned, it will be advisable, before we begin a description of the major features of the Reciprocal System of theory, to point out that the results of this policy have been right in line with expectations. Those who turned to demons to solve their problems are now calling for something new to get them out of the morass into which they have been led by the demons.
To most laymen, and to the rank and file of the scientific profession as well, it will probably come as quite a surprise to find that the world picture painted by so-called “modern physics” is far from being either complete or accurate, and makes no pretense of being reasonable or rational. Spectacular practical achievements in the application of physical knowledge, much of it gained only very recently and still quite mysterious to the man-in-the-street, have raised the present-day physicist to a pinnacle of prestige and have surrounded him with an aura of omniscience that makes any questioning of his pronouncements practically a case of lese majeste. It must be conceded, of course, that the physicists have indeed achieved a great deal (mainly by the use of the traditional scientific methods and principles that have been discarded by the modern theorists) and they are entitled to view their record with pride and self-satisfaction. In recent years, however, serious theoretical difficulties have been encountered in one major physical field after another, and the theorists, finding their most strenuous efforts frustrated, have abandoned the search for a truly scientific basic theory, branding it as unattainable, and have reverted to the methods of the non-scientific disciplines, as discussed in the preceding chapter. But even the help of a multitude of demons has not solved the problems and, as W. F. G. Swann points out, “theoretical physics is at present in a rather messy state.”44 Warren Weaver describes the situation in this manner:
With the extremely small or the extremely large, with inconceivably brief or extended phenomena, science has a difficult time. It is by no means clear that our present concepts or even our existing language is suitable for these ranges.38
The principal theories of “modern” physical science, the nuclear theory of the atom, relativity, and the quantum theories, in the words of E. N. da C. Andrade, “admittedly are makeshifts.”45 Dirac is merely saying the same thing in milder language when he calls them “steppingstones to the better theories of the future.”46 In order to maintain some semblance of legitimacy for these theories, so that they can continue to be presented to the rank and file as the equivalent of established facts, extraordinary measures have to be taken. Toulmin and Goodfield express this caution against attributing any permanence to current ideas:
As an emergency measure, physicists have resorted to mathematical fudges of an arbitrary kind ... to accept them with any complacency, and call off the search for a more satisfactory physical explanation would be going against the principles of strategy on which the whole scientific tradition has been built up.47
Almost all of the qualified observers who have studied this situation in detail—even some of those who have played an important part in the construction of the theories that will be superseded by the new, more satisfactory, developments—agree with this assessment of the problem and concede that major changes must and will take place. Here are some typical statements:
Let us hope that in a decade or two, or, at least, just before the beginning of the twenty-first century, the present meager years of theoretical physics will come to an end in a burst of entirely new revolutionary ideas similar to those which heralded the beginning of the twentieth century.48 (George Gamow)
We await a big theoretical advance which will clarify our understanding of the many puzzling features which have been revealed in recent years.49 (Sir Harrie Massey)
What we badly need is a greater synthesis.50 (Abraham Pais)
There will have to be some new development that is quite unexpected, that we cannot even make a guess about.46 (P.A.M. Dirac)
We hope that the present fluctuations of thinking are only indications of an upheaval of old beliefs which in the end will lead to something better than the mess of formulas which today surrounds our subject.51 (Erwin Schrodinger)
For the last ten years it has been clear to most physicists that a basic conceptual innovation will be needed in order to come to grips with the properties of elementary particles.52 (Freeman J. Dyson)
Physics is due for a breakthrough. The conditions are there: a large number of well-ordered facts, with no present way of explaining them, and a large body of frustrated scientists. (Science News, Feb. 17, 1968)
The development of the Reciprocal System of theory has now fulfilled these predictions (even though the scientific community is still only dimly beginning to recognize that fact). It has produced the “basic conceptual innovation” that Dyson saw was needed, and this innovation, a totally new concept of the nature of space and time, a modification of existing thought that, as Dirac predicted, was “quite unexpected,” has brought unity and coherence to physical science. This new system of theory is just the kind of product that the theorists tried for centuries to construct, until they finally lost heart and gave up the effort. It is not a model; it is a complete and comprehensive theory applicable to the entire universe: the “greater synthesis” that Pais asked for. It is not work-in-progress; the details can be developed much farther, of course, but those portions of the theory that have already been developed, including the basic phenomena and relations of the major fields of physical science, have been verified by the standard scientific methods and are now part of the permanent store of scientific knowledge. As expressed on page one of New Light on Space and Time:
In all essential respects this new theory is just the kind of a product that the scientific world would like to have. It is a unified theory; all of the principles governing all sub-divisions of physical activity are deduced from the same premises: two fundamental postulates as to the nature of space and time. It is a self-consistent theory; there are no internal contradictions or inconsistencies. It is an accurate theory; all of the deductions from the postulates are in full agreement with the results of observation and measurement, within the margin of accuracy of the latter or, at least, are not inconsistent with any of these results. It is an unequivocal theory; the consequences of the postulates are specific and definite and at no point is there any recourse to a “postulate of impotence” or other evasive device to avoid admitting a discrepancy. It is a rational theory; it provides definite and specific explanations for everything that happens, without calling upon ad hoc forces or transcendental agencies. It is a complete theory; the logical and unavoidable consequences of the postulates describe, both qualitatively and quantitatively, a complete theoretical universe, and it is not necessary to utilize any supplementary or auxiliary assumptions, nor is it necessary to introduce the results of observation as a foundation for the theoretical structure, because the theoretical deductions from the postulates provide for the existence of the various physical phenomena—matter, radiation, electrical and magnetic phenomena, gravitation, etc.—as well as establishing the relations between these entities.53
Development of this new theoretical structure was carried out strictly in accordance with the standard scientific procedure described in Chapter 2. It began with a careful, critical, and systematic reexamination of basic physical relations, a project extending over a long period of years (Step 1). Although originally undertaken with a much more limited objective in mind, this study ultimately culminated in the formulation of a general theory of the universe, expressed in the form of two postulates as to the nature and properties of space and time—45 words in all (Step 2). Another long period of years was then spent in developing the consequences of the postulates in great detail (Step 3), and finally verifying the theory by comparing these consequences with the corresponding results of observation and measurement (Step 4).
In order to formulate this complete and correct theoretical system, it was, of course, necessary to identify the basic error in previous thought and to make the required correction. The careful and critical reexamination of basic physical theory which constituted the initial phase of the present investigation located this basic error in the prevailing concept of the fundamental nature of the universe. To our earliest ancestors, the world in which they lived was a world of spirits. As they saw the situation, the ultimate realities were the spirits that inhabited and controlled the various physical objects, and the observable events and phenomena were merely the outward manifestations of the actions and emotions of these spirits. This view is not entirely dead even yet—the more primitive people of the earth still hold to it as tenaciously as ever—but over the last three thousand years or so, it has gradually been replaced by the concept of a universe of matter: one in which the basic entities are elementary units of matter existing in a framework provided by space and time. Prior to the development of the Reciprocal System, all modern physical theory was based on the “matter” concept.
It is obvious, however, that recent discoveries have completely demolished this concept. The finding that matter could be converted to radiation is enough, in itself, to show that matter cannot be the basic constituent of the universe. The demonstrated interconvertibility clearly indicates that there must be some common denominator underlying both matter and non-matter. Some of the leading scientific investigators have recognized this point and have tried to identify the true basic entity. Werner Heisenberg, for instance, suggested that it might be energy. “One might say that the elementary particles are simply different forms which energy can assume in order to become matter.”54 But he conceded that he was unable to explain how energy could take these different forms. The truth is that since energy is a scalar quantity it is totally incapable of assuming the variety of forms that are required; the basic entity must be something that has the property of direction. What the development of the Reciprocal System has accomplished is to demonstrate that the common denominator of matter and non-matter is motion. The universe in which we live is a universe of motion.
This “motion” concept itself is by no means new. It has been clear for hundreds of years that motion would have some very definite advantages over matter as the basis of a physical theory, and a great many scientists and philosophers, including such prominent men as Eddington, Descartes, and Hobbes, have tried to construct a theory on this basis. All of these attempts ended in failure, and so the matter stood until the present studies revealed the nature of the obstacle that blocked the path. The reason for the failure of the previous investigators to reach their goal, we now find, was a lack of recognition of the fact that switching from the concept of a universe of matter to that of a universe of motion requires a redefinition of space and time.
For more than three thousand years, ever since man first began to speculate systematically about the nature of the entities that surround him, space has been regarded as a kind of setting in which the action of the universe takes place: a container for the material objects that participate in this action. Many differences of opinion have arisen with respect to the details—whether or not space is absolute and immovable, whether such a thing as empty space is possible, whether or not space and time are interconnected, and so on—but throughout all of the development of thought, the basic concept of space as a setting or container has remained intact. J. D. North summarizes the “setting” or “container” concept of space in this manner:
Most people would accept the following: Space is that in which material objects are situated and through which they move. It is a background for objects of which it is independent. Any measure of the distances between objects within it may be regarded as a measure of the distances between its corresponding parts.55
Here matters stood until the beginning of the great expansion of scientific knowledge in the eighteenth and nineteenth centuries. In this era, many new discoveries were made that were incompatible with the existing structure of theory, and it therefore became necessary to modify the ideas inherited from the Greek thinkers. The proposal that won general approval at the time was to postulate that the container space of the Greek atomists was filled with a substance having the properties of a connecting medium, through which the various influences originating at one spatial location could be transmitted to distant locations. But in 1887, an experiment by Michelson and Morley produced seemingly conclusive proof that this hypothetical substance, the “ether,” was non-existent, and the scientific world was thrown into confusion.
Some twenty years later, Einstein offered a way out of this awkward situation by proposing a theory in which the assumed properties of the ether were assigned to space itself, thus investing space with the ability to act as a transmitting medium. Einstein’s hypothesis, the basis of his relativity theory, involves a drastic change in the idea of the nature of space, one which gives space a far more active role in physical phenomena than had ever been attributed to it before. But his space is still a container, a much more flexible container than the space of the Greeks, to be sure, but definitely a container, nevertheless.
Nor was the container concept disturbed by the further development of the relativity theories which led to the conclusion that space is one component of a combination space-time structure, in which time plays a similar role. Time has always been more elusive than space, and the theorists have encountered great difficulty in formulating any clear-cut concept of its essential nature. It has been taken for granted, however, that time, as well as space, is a part of the setting in which the action of the universe takes place; that is, physical phenomena exist in space and in time. But just wherein time differs from space has been difficult to specify. In fact, the distinction between the two has become increasingly blurred and indefinite during the last half century, and as matters now stand, time is generally regarded as a sort of quasi-space, the boundary between space and time being indefinite and dependent upon the circumstances under which it is observed. The modern physicist has thus added another dimension to the spatial setting, and instead of visualizing physical phenomena as being located in a three-dimensional spatial container, he places them in a four-dimensional space-time container.
In all of this ebb and flow of scientific thought, the basic concept has remained unchanged: space and time, it is assumed, are the containers, or the container, in which physical entities exist, the setting in which the drama of the universe unfolds—“a vast world-room, a perfection of emptiness, within which all the world-show plays itself away forever.”56 This is the way in which scientists, and laymen as well, now think, and this is the way in which they have always thought. It is probably correct to say that this is the only way in which many of them can think.
Whatever changes are proposed from time to time in the theories of space and time, they are expressed in, and considered in, “container” terms. Thus, Einstein’s “space” is not regarded as something new that replaces Democritus’ “space,” the container in which physical activity occurs, but rather as a modification of the earlier concept in which space is assigned the properties that were formerly attributed to the hypothetical “ether.” When an explanation of Einstein’s theory of gravitation refers to space as being “warped” or “distorted” in the vicinity of a massive aggregate of matter, it is the container that is visualized as being distorted.
Similarly, Minkowski’s concept of a four-dimensional space-time continuum, which Einstein accepted and utilized in his general theory, is simple three-dimensional container space joined to an additional space-like dimension. Thus the entire Einstein-Minkowski development can easily be fitted into the previously existing conceptual framework without difficulty. Some individuals may—and indeed do—refuse to accept the idea that space is curved or subject to distortion, or the idea that time is a dimension of a combination space-time structure, but it is not difficult for them to understand what is meant by these ideas. In fact, it is understanding that leads to their rejection of the theories. Detailed development of the consequences of the Einstein theories has led to mathematical and conceptual complications that are nearly, if not totally, incomprehensible, and the arguments that are used to justify these theories are admittedly difficult to follow, but the meaning of the basic concepts upon which they have been erected can easily be understood in terms of existing patterns of thought with no more than a few minor adjustments.
In the Reciprocal System, for the first time in scientific history, a totally new concept of the nature of space and time makes its appearance, one in which space is not a setting or a container, or anything resembling a container. The change of viewpoint here was not an arbitrary one. On the contrary, the significant conceptual advance that overcame the obstacle which blocked all previous attempts to construct a theory of a universe of motion was a recognition of the fact that space and time cannot be defined arbitrarily in such a universe because a specific definition of space and time is implicit in the concept of a universe composed entirely of motion.
Motion is defined as a relation between space and time, and is measured as speed or velocity. In its simplest form, the equation of motion, the mathematical representation of the phenomenon, is v = sit. As this equation shows, in motion, space and time are the two reciprocal aspects of that motion, and nothing else. In a universe of matter, the fact that space and time have only this limited significance in motion would not preclude them from having some other significance elsewhere, but in a universe composed entirely of motion, where everything that exists is a manifestation of motion, space and time cannot have any significance anywhere that they do not have in motion. The basic concept underlying the new theoretical system, the only concept of the nature of space and time that is consistent with a universe of motion, and hence replaces all of the hypotheses that have heretofore been proposed, all of the numerous variations of the “setting” or “container” concept, can be expressed as follows:
Space and time are simply the two reciprocal aspects of motion. They have no other significance.
Space is not the Euclidean setting for physical phenomena that is most commonly visualized by the layman; neither is it the modified type of container subject to distortion by various forces and highly dependent on the location and movement of the observer, as seen by the present-day physicist. In fact, it is not even a physical entity in its own right at all; it is simply and solely an aspect of motion. Time is not an order of succession, or a dimension of a quasi-space; neither is it a physical entity in its own right. It, too, is simply and solely an aspect of motion, similar in all respects to space, except that it is the reciprocal aspect.
The simplest way of defining the status of space and time is to say that space is the numerator in the expression sit, which is the speed or velocity, the measure of motion, and time is the denominator. If there is no fraction, there is no numerator or denominator; where there is no motion there is no space or time. Space does not exist alone, nor does time exist alone; neither exists except in association with the other as motion. A very rough analogy would compare motion to a box, and space and time to the inside and outside of the box. We cannot have either an inside or an outside unless we have a box, but if the box exists then we have both an inside and an outside, never just one alone. Similarly, we do not have either space or time unless there is motion, but if there is motion then both space and time exist in association with each other to constitute the motion.
We can, of course, focus our attention on the space aspect and deal with it as if the time aspect, the denominator of the fraction, remains constant. This is the familiar process known as abstraction, one of the useful tools of scientific inquiry. But any results obtained in this manner are valid only where the time aspect does, in fact, remain constant, or where the proper adjustment is made for whatever changes in this factor do take place.
One of the very important consequences that follows directly from the new space-time concept is that the reciprocal relation between space and time expressed by the equation of motion is a general relation; that is, space and time are reciprocally related everywhere in the physical universe. This is the kind of a thing that is totally incomprehensible on the basis of previous thinking. As long as space is looked upon as a container, the idea of the reciprocal of space is an absurdity, too ridiculous to be given any serious consideration. We might as well talk about the reciprocal of an apple or the reciprocal of a load of hay. But the new theory does not suggest anything of this nature. On the contrary, it says specifically that space is not a container, or anything resembling a container. In fact, it is not a physical entity at all; it has no existence other than as the numerator in the expression sit, which is the magnitude of the motion. The gist of the reciprocal statement is therefore an assertion that the denominator of a particular fractional expression stands in a reciprocal relation to the numerator: an assertion which is not only logical and rational, but is obviously correct.
In setting up any theory or theoretical system, it is necessary to begin with certain assumptions or postulates. The details of the theory are then derived by developing the consequences of the postulates. The new space-time concept is expressed in the Reciprocal System by postulating the general reciprocal relation between space and time. This is the only innovation that the new system of theory introduces into scientific thought. A few other assumptions must be made to complete the foundations of the theoretical structure, but these are familiar items. None of them is at all new, and they are all obtained by extrapolation of empirical findings, one of the standard inductive methods.
Even the one real innovation in the new system, the reciprocal postulate, can be obtained by a simple extrapolation of observed facts. The only relation between space and time of which we have any direct knowledge is motion, and in motion, space and time are already known to be reciprocally related from the scalar standpoint; that is, more time has exactly the same effect on the speed, the scalar measure of the motion, as less space, and vice versa. It makes no difference whether we go twice as far in the same time or cover the same distance in half the time; the speed doubles in either case. All that the reciprocal postulate does is to generalize this observed relation and to say that it is universally valid. Combining the reciprocal relation with the other assumptions derived by extrapolation, we arrive at the following basic postulates:
FIRST FUNDAMENTAL POSTULATE: The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.
SECOND FUNDAMENTAL POSTULATE: The physical universe conforms to the relations of ordinary commutative mathematics, its magnitudes are absolute and its geometry is Euclidean.
Most of the assumptions included in these postulates have been generally accepted throughout scientific history, and are still regarded as valid by almost all laymen and by the rank-and-file scientists as well, although their validity is denied by present-day physical theorists, who have found it necessary to resort to some bizarre substitutes to accommodate aspects of their theories that could not be fitted into the traditional framework. Included are Euclidean geometry, three-dimensional space, absolute magnitudes, and ordinary commutative mathematics. In all probability, these assumptions would never have been questioned by anyone if the difficulties encountered by the theorists had not become so serious that they were practically desperate for some way of escape.
Extension of three-dimensionality to time as well as space may cause some lifting of eyebrows, but this extension is obviously required by the reciprocal postulate, which implies that all properties of either space or time are properties of both space and time. It should also be noted that there is no actual evidence to support the prevailing belief that time is one-dimensional. To be sure, we have a vague impression that we are traveling along a path that leads unidirectionally from the past to the present and on into the future, but this is not the kind of a thing on which we can base scientific reasoning. The physicists do not draw their conclusions from this, but from the behavior of time in the mathematical equations that represent physical processes.
In the velocity equation, v = sit, for example, the quantities v and s are vectorial, that is, they have direction as well as magnitude. But the quantity t is scalar; it has magnitude only. From this it has been concluded that time is one-dimensional. But the investigations carried out during the development of the Reciprocal System of theory have disclosed that this conclusion does not follow from the observed facts. What has been overlooked is that “direction” in the context of the velocity equation means “direction in space,” and time has no spatial direction. The time term in a space-velocity equation is scalar not because it is one-dimensional but because it has no spatial dimensions at all. Whatever dimensions it may have are dimensions of time, not dimensions of space. Thus the status of the time terms in the various physical equations tells us nothing at all about the dimensions of time. There is no physical evidence to contradict the assertion of the Reciprocal System that time is three-dimensional.
Because of the nature of the scientific enterprise, the scientist must necessarily accept certain assumptions of a philosophical nature in order that his activities may be meaningful. If what is learned today is inapplicable tomorrow, attempts to accumulate a store of scientific knowledge are futile; if the course of physical events, and the results thereof, are haphazard, there is nothing to be gained by attempts to formulate laws and principles governing those events; and so on. As a condition of becoming a scientist, it is therefore necessary to assume that the universe is logical, orderly, and rational. Since acceptance of these premises is a prerequisite for scientific activity, they are not ordinarily mentioned in scientific discourse. In effect, they constitute the starting point from which scientific work begins. But when we undertake an exploration of a hitherto unknown area, as we are now intending to do, we must recognize that, in addition to the two postulates that are set forth in the published accounts of the Reciprocal System of theory and were reproduced earlier in this chapter, there is an implied third postulate incorporating the assumption that the universe is logical, orderly, and rational.
All of the conclusions of the Reciprocal System, from broad general principles down to the most minute detail, have been derived entirely by developing the consequences of the fundamental postulates, without making any supplementary or subsidiary assumptions and without introducing anything from observation or from any other source outside the postulates. The mere existence of space and time with the postulated properties gives rise to certain primary consequences. Interaction of these consequences with each other and with the postulates then results in a large number and variety of secondary consequences, which, in turn, involve further consequences, and so on until a whole theoretical universe has been defined. Because of the nature of this process by which the theoretical universe of the Reciprocal System has been derived, it is possible to prove that the theoretical structure is an accurate representation of the actual physical universe.
Two general methods of verifying a theory are available. Both involve making a large number of comparisons between the assertions of the theory and the corresponding observed facts, so that the probability of the existence of any error can be reduced to the negligible level that is required in order that the theory may qualify as scientific knowledge, but the procedures and the results of the two methods are quite different. In the first method of verification, the only one that is usually available, and hence the one with which scientists are most familiar, verification of the whole is merely a summation of verification of the individual items. Here an individual agreement is a step toward proof, an inconclusive result means nothing at all, and a disagreement invalidates the theory in its existing form. This disagreement is not necessarily fatal, however, as the theory can usually be modified to secure agreement in the recalcitrant case. The verification process can then be resumed on the new basis until adequate verification is secured or until a new disagreement arises, in which case further modifications of the theory may be made. Long series of modifications of this kind are not at all exceptional. The quantum theories, for instance, have experienced an almost continuous series of modifications ever since Niels Bohr formulated the first crude form of this kind of theory in 1913.
The second method of verification is applicable only where no modifications of the theory are possible; that is, where all theoretical conclusions are derived from the same basic premises, without the use of supplementary assumptions, and the entire structure is therefore one unit which must stand or fall as a whole. An analogy that was used in the original presentation of the Reciprocal System compares the construction of a physical theory to the preparation of a map, the usual process of theory construction being compared to the traditional method of map making, and the development of a fully integrated system being compared to the production of a map by aerial photography. In testing a product of either the traditional map making or the usual theory construction process, we must employ the first of the methods of verification discussed in the preceding paragraph, verifying each and every feature of the map or theory individually, as there is little or no connection between the individual features, and with relatively few exceptions, verification of any one feature does not guarantee the accuracy of any other. But in testing an aerial map or an analogous theoretical product such as the Reciprocal System, where the entire map or theory is produced in one operation by a single process, every test that is made by comparing the product with the observed facts is a test of the process itself, verification of the individual features selected for the test being merely incidental.
In this case, if anything that can definitely be seen on the map conflicts with anything that is positively known from direct observation of the terrain, then the map-making process itself is not accurate, and the map is not reliable. Likewise, if any of the consequences of a completely integrated theory conflict with facts that are definitely known, then the theory as a whole is invalid. Here no modifications to fit the recalcitrant facts—ad hoc modifications, in the jargon of science—are possible. The basic postulates of the theory can be changed, of course, but a major change of this kind can hardly be considered a modification; it leaves us with an entirely new theory. The original theory must be verified or disproved as a unit.
Since each check against the observed facts is a test of the theory as a whole, every additional test that is made without finding a discrepancy reduces the mathematical probability that any discrepancy exists anywhere. By making a sufficiently large number of such correlations in many different areas, this probability can be reduced to any specified level. The theoretical conclusions of the Reciprocal System have been checked against the results of observation and measurement in thousands of different applications throughout an extremely wide range of physical phenomena, and no contradiction or inconsistency has been found. This means, then, that the mathematical probability of any error in the basic structure of the system has been reduced to the point where it is negligible. The validity of this system of theory is thus a physical certainty. The Reciprocal System provides a true and accurate representation of the physical facts.
An important point in this connection is that proof of the validity of the theoretical structure as a whole carries with it a proof of the validity of every pan of that structure. Many of the individual conclusions of the theory cannot be confirmed by direct observation, as matters now stand, but the status of the unconfirmed conclusions is identical with that of the conclusions that can be tested against experience. If we confirm the accuracy of our aerial map in the areas where we are able to check it against direct observation and measurement, then we know that it is also accurate in the areas that are not accessible to direct observation. In total, the conclusions derived from the basic postulates of the Reciprocal System constitute a theoretical universe, and our proof of the validity of the system as a whole proves that each and every feature of the physical universe exists exactly as portrayed by the theoretical development.
A recognition of this point is particularly important as we move outward from the well-known phenomena of our everyday environment into the less familiar fields. Most of the theoretical conclusions pertaining to the local environment can be verified individually by direct observation. As we proceed outward, we encounter areas where many of the intermediate steps are unobservable and only the ultimate results are available for check. Finally we reach the outlying regions where nothing is observable except an isolated fact here and there. But the status of the theoretical conclusions is the same everywhere. Whether it can be individually verified or not, each of these conclusions participates in the proof of the validity of the system as a whole.
This is the factor that has made the present investigation of the metaphysical region possible. No longer are we limited to exploring the regions that are clearly visible, and leaving all else to speculation and fantasy. By extending the development of a theoretical system whose validity we have already verified as a whole, we are able to explore not only the regions that are dimly visible but also regions that are totally invisible. The demonstrated identity of the theoretical and actual physical universes has enabled us to make our inquiries in the clear light of the theoretical system, and then, when the appropriate answers have been obtained, to apply these to the actual universe with full confidence in their validity. By this means, we have arrived at a comprehensive and accurate knowledge of the physical universe.
Now we propose to utilize these findings of the Reciprocal System with respect to the physical universe as a base, and to extend the same procedure and the same investigative policies to a region hitherto beyond the reach of scientific methods, one in which demons have thus far held full sway. In so doing, we are following the great tradition of science, focusing the light of factual inquiry on whatever we can bring within its reach without regard to conventional lines of demarcation between disciplines. Margenau appropriately defines the policy governing this untrammeled course of inquiry in his “creed for scientists”:
I recognize no subjects and no facts which are alleged to be forever closed to inquiry or understanding: a mystery is but a challenge.57